Phis:=[ rec( AutGenerators := [ [ [ 1 ] ] ], Gram := [ [ -2 ] ], disc := rec( discf := [ [ 3/2 ] ], discg := [ 2 ], proj := [ [ 2 ] ], reps := [ [ 1/2 ] ] ), discAutGenerators := [ [ [ 1 ] ] ], overlattices := [ rec( Gram := [ [ -2 ] ], IsADE := [ "A1" ], StabGenerators := [ [ [ 1 ] ] ], embRRbar := [ [ 1 ] ], isotropicspace := [ [ 2 ] ], torsion := [ ] ) ], type := [ "A1" ] ), rec( AutGenerators := [ [ [ 0, 1 ], [ 1, 0 ] ] ], Gram := [ [ -2, 0 ], [ 0, -2 ] ], disc := rec( discf := [ [ 3/2, 0 ], [ 0, 3/2 ] ], discg := [ 2, 2 ], proj := [ [ 2, 0 ], [ 0, 2 ] ], reps := [ [ 1/2, 0 ], [ 0, 1/2 ] ] ), discAutGenerators := [ [ [ 0, 1 ], [ 1, 0 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0 ], [ 0, -2 ] ], IsADE := [ "A1", "A1" ], StabGenerators := [ [ [ 0, 1 ], [ 1, 0 ] ] ], embRRbar := [ [ 1, 0 ], [ 0, 1 ] ], isotropicspace := [ [ 2, 0 ], [ 0, 2 ] ], torsion := [ ] ) ], type := [ "A1", "A1" ] ), rec( AutGenerators := [ [ [ 0, 1 ], [ 1, 0 ] ] ], Gram := [ [ -2, 1 ], [ 1, -2 ] ], disc := rec( discf := [ [ 4/3 ] ], discg := [ 3 ], proj := [ [ 3 ], [ 0 ] ], reps := [ [ 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 2 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1 ], [ 1, -2 ] ], IsADE := [ "A2" ], StabGenerators := [ [ [ 0, 1 ], [ 1, 0 ] ] ], embRRbar := [ [ 1, 0 ], [ 0, 1 ] ], isotropicspace := [ [ 3 ] ], torsion := [ ] ) ], type := [ "A2" ] ), rec( AutGenerators := [ [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 0, 1, 0 ], [ 0, 0, 1 ], [ 1, 0, 0 ] ] ], Gram := [ [ -2, 0, 0 ], [ 0, -2, 0 ], [ 0, 0, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 3/2, 0 ], [ 0, 0, 3/2 ] ], discg := [ 2, 2, 2 ], proj := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 2 ] ], reps := [ [ 1/2, 0, 0 ], [ 0, 1/2, 0 ], [ 0, 0, 1/2 ] ] ), discAutGenerators := [ [ [ 0, 1, 0 ], [ 0, 0, 1 ], [ 1, 0, 0 ] ], [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0 ], [ 0, -2, 0 ], [ 0, 0, -2 ] ], IsADE := [ "A1", "A1", "A1" ], StabGenerators := [ [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 0, 1, 0 ], [ 0, 0, 1 ], [ 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 2 ] ], torsion := [ ] ) ], type := [ "A1", "A1", "A1" ] ), rec( AutGenerators := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 0, 1 ], [ 0, 1, 0 ] ] ], Gram := [ [ -2, 0, 0 ], [ 0, -2, 1 ], [ 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0 ], [ 0, 4/3 ] ], discg := [ 2, 3 ], proj := [ [ 2, 0 ], [ 0, 3 ], [ 0, 0 ] ], reps := [ [ 1/2, 0, 0 ], [ 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 1, 0 ], [ 0, 2 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0 ], [ 0, -2, 1 ], [ 0, 1, -2 ] ], IsADE := [ "A1", "A2" ], StabGenerators := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 0, 1 ], [ 0, 1, 0 ] ] ], embRRbar := [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], isotropicspace := [ [ 2, 0 ], [ 0, 3 ] ], torsion := [ ] ) ], type := [ "A1", "A2" ] ), rec( AutGenerators := [ [ [ 0, 0, 1 ], [ 0, 1, 0 ], [ 1, 0, 0 ] ] ], Gram := [ [ -2, 1, 0 ], [ 1, -2, 1 ], [ 0, 1, -2 ] ], disc := rec( discf := [ [ 5/4 ] ], discg := [ 4 ], proj := [ [ 4 ], [ 0 ], [ 0 ] ], reps := [ [ 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 3 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0 ], [ 1, -2, 1 ], [ 0, 1, -2 ] ], IsADE := [ "A3" ], StabGenerators := [ [ [ 0, 0, 1 ], [ 0, 1, 0 ], [ 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], isotropicspace := [ [ 4 ] ], torsion := [ ] ) ], type := [ "A3" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0 ], [ 0, -2, 0, 0 ], [ 0, 0, -2, 0 ], [ 0, 0, 0, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 3/2, 0, 0 ], [ 0, 0, 3/2, 0 ], [ 0, 0, 0, 3/2 ] ], discg := [ 2, 2, 2, 2 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], reps := [ [ 1/2, 0, 0, 0 ], [ 0, 1/2, 0, 0 ], [ 0, 0, 1/2, 0 ], [ 0, 0, 0, 1/2 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 0, 0, 0 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0 ], [ 0, -2, 0, 0 ], [ 0, 0, -2, 0 ], [ 0, 0, 0, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1" ], StabGenerators := [ [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 1, 0 ], [ 0, -2, 1, 0 ], [ 1, 1, -2, 1 ], [ 0, 0, 1, -2 ] ], IsADE := [ "D4" ], StabGenerators := [ [ [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 0, 0, 0 ] ], [ [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ] ] ], embRRbar := [ [ 0, 0, 1, 0 ], [ 1, 1, 1, 0 ], [ 1, 0, 1, 1 ], [ 0, 1, 1, 1 ] ], isotropicspace := [ [ 1, 1, 1, 1 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A1" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ] ] ], Gram := [ [ -2, 0, 0, 0 ], [ 0, -2, 0, 0 ], [ 0, 0, -2, 1 ], [ 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 3/2, 0 ], [ 0, 0, 4/3 ] ], discg := [ 2, 2, 3 ], proj := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 3 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0 ], [ 0, 1/2, 0, 0 ], [ 0, 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 2 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0 ], [ 0, -2, 0, 0 ], [ 0, 0, -2, 1 ], [ 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A2" ], StabGenerators := [ [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 3 ] ], torsion := [ ] ) ], type := [ "A1", "A1", "A2" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0 ], [ 0, -2, 1, 0 ], [ 0, 1, -2, 1 ], [ 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0 ], [ 0, 5/4 ] ], discg := [ 2, 4 ], proj := [ [ 2, 0 ], [ 0, 4 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0 ], [ 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 1, 0 ], [ 0, 3 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0 ], [ 0, -2, 1, 0 ], [ 0, 1, -2, 1 ], [ 0, 0, 1, -2 ] ], IsADE := [ "A1", "A3" ], StabGenerators := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0 ], [ 0, 4 ] ], torsion := [ ] ) ], type := [ "A1", "A3" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0 ], [ 1, -2, 0, 0 ], [ 0, 0, -2, 1 ], [ 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0 ], [ 0, 4/3 ] ], discg := [ 3, 3 ], proj := [ [ 3, 0 ], [ 0, 0 ], [ 0, 3 ], [ 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0 ], [ 0, 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 0, 1 ], [ 1, 0 ] ], [ [ 2, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0 ], [ 1, -2, 0, 0 ], [ 0, 0, -2, 1 ], [ 0, 0, 1, -2 ] ], IsADE := [ "A2", "A2" ], StabGenerators := [ [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0 ], [ 0, 3 ] ], torsion := [ ] ) ], type := [ "A2", "A2" ] ), rec( AutGenerators := [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0 ], [ 1, -2, 1, 0 ], [ 0, 1, -2, 1 ], [ 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 6/5 ] ], discg := [ 5 ], proj := [ [ 5 ], [ 0 ], [ 0 ], [ 0 ] ], reps := [ [ 1/5, 2/5, 3/5, 4/5 ] ] ), discAutGenerators := [ [ [ 4 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0 ], [ 1, -2, 1, 0 ], [ 0, 1, -2, 1 ], [ 0, 0, 1, -2 ] ], IsADE := [ "A4" ], StabGenerators := [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], isotropicspace := [ [ 5 ] ], torsion := [ ] ) ], type := [ "A4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 1 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 1, 0 ], [ 0, -2, 1, 0 ], [ 1, 1, -2, 1 ], [ 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 1, 1/2 ], [ 1/2, 1 ] ], discg := [ 2, 2 ], proj := [ [ 0, 2 ], [ 0, 0 ], [ 0, 0 ], [ 2, 0 ] ], reps := [ [ 1, 1/2, 1, 1/2 ], [ 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 0, 1 ], [ 1, 0 ] ], [ [ 1, 1 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 1, 0 ], [ 0, -2, 1, 0 ], [ 1, 1, -2, 1 ], [ 0, 0, 1, -2 ] ], IsADE := [ "D4" ], StabGenerators := [ [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 1 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0 ], [ 0, 2 ] ], torsion := [ ] ) ], type := [ "D4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0 ], [ 0, 0, -2, 0, 0 ], [ 0, 0, 0, -2, 0 ], [ 0, 0, 0, 0, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 3/2, 0 ], [ 0, 0, 0, 0, 3/2 ] ], discg := [ 2, 2, 2, 2, 2 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], reps := [ [ 1/2, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0 ], [ 0, 0, 0, 1/2, 0 ], [ 0, 0, 0, 0, 1/2 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0 ], [ 0, 0, -2, 0, 0 ], [ 0, 0, 0, -2, 0 ], [ 0, 0, 0, 0, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A1" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0 ], [ 0, 0, -2, 1, 0 ], [ 0, 1, 1, -2, 1 ], [ 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 1, 1, 1, 0 ], [ 0, 1, 0, 1, 1 ], [ 0, 0, 1, 1, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 1 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A1" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0 ], [ 0, 0, -2, 0, 0 ], [ 0, 0, 0, -2, 1 ], [ 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 3/2, 0, 0 ], [ 0, 0, 3/2, 0 ], [ 0, 0, 0, 4/3 ] ], discg := [ 2, 2, 2, 3 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 3 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0 ], [ 0, 0, 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 2 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0 ], [ 0, 0, -2, 0, 0 ], [ 0, 0, 0, -2, 1 ], [ 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A2" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 3 ] ], torsion := [ ] ) ], type := [ "A1", "A1", "A1", "A2" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0 ], [ 0, 0, -2, 1, 0 ], [ 0, 0, 1, -2, 1 ], [ 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 3/2, 0 ], [ 0, 0, 5/4 ] ], discg := [ 2, 2, 4 ], proj := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 4 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0 ], [ 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 3 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0 ], [ 0, 0, -2, 1, 0 ], [ 0, 0, 1, -2, 1 ], [ 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A3" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 1, 0, 0 ], [ 0, -2, 1, 0, 0 ], [ 1, 1, -2, 1, 0 ], [ 0, 0, 1, -2, 1 ], [ 0, 0, 0, 1, -2 ] ], IsADE := [ "D5" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0 ], [ 1, 1, 1, 0, 0 ], [ 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 1 ], [ 1, 0, 1, 1, 0 ] ], isotropicspace := [ [ 1, 1, 2 ], [ 0, 2, 0 ], [ 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A3" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0 ], [ 0, 1, -2, 0, 0 ], [ 0, 0, 0, -2, 1 ], [ 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 4/3, 0 ], [ 0, 0, 4/3 ] ], discg := [ 2, 3, 3 ], proj := [ [ 2, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 0 ], [ 0, 0, 3 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0 ], [ 0, 1/3, 2/3, 0, 0 ], [ 0, 0, 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 0, 1 ], [ 0, 1, 0 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0 ], [ 0, 1, -2, 0, 0 ], [ 0, 0, 0, -2, 1 ], [ 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "A2" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 3 ] ], torsion := [ ] ) ], type := [ "A1", "A2", "A2" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0 ], [ 0, 1, -2, 1, 0 ], [ 0, 0, 1, -2, 1 ], [ 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0 ], [ 0, 6/5 ] ], discg := [ 2, 5 ], proj := [ [ 2, 0 ], [ 0, 5 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0 ], [ 0, 1/5, 2/5, 3/5, 4/5 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 1, 0 ], [ 0, 4 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0 ], [ 0, 1, -2, 1, 0 ], [ 0, 0, 1, -2, 1 ], [ 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0 ], [ 0, 5 ] ], torsion := [ ] ) ], type := [ "A1", "A4" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0 ], [ 0, 0, -2, 1, 0 ], [ 0, 1, 1, -2, 1 ], [ 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 1, 1/2 ], [ 0, 1/2, 1 ] ], discg := [ 2, 2, 2 ], proj := [ [ 2, 0, 0 ], [ 0, 0, 2 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 2, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0 ], [ 0, 1, 1/2, 1, 1/2 ], [ 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 0, 1 ], [ 0, 1, 0 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 1 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0 ], [ 0, 0, -2, 1, 0 ], [ 0, 1, 1, -2, 1 ], [ 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 2 ] ], torsion := [ ] ) ], type := [ "A1", "D4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0 ], [ 1, -2, 0, 0, 0 ], [ 0, 0, -2, 1, 0 ], [ 0, 0, 1, -2, 1 ], [ 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0 ], [ 0, 5/4 ] ], discg := [ 3, 4 ], proj := [ [ 3, 0 ], [ 0, 0 ], [ 0, 4 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0 ], [ 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 3 ] ], [ [ 2, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0 ], [ 1, -2, 0, 0, 0 ], [ 0, 0, -2, 1, 0 ], [ 0, 0, 1, -2, 1 ], [ 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A3" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0 ], [ 0, 4 ] ], torsion := [ ] ) ], type := [ "A2", "A3" ] ), rec( AutGenerators := [ [ [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0 ], [ 1, -2, 1, 0, 0 ], [ 0, 1, -2, 1, 0 ], [ 0, 0, 1, -2, 1 ], [ 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 7/6 ] ], discg := [ 6 ], proj := [ [ 6 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ] ], reps := [ [ 1/6, 1/3, 1/2, 2/3, 5/6 ] ] ), discAutGenerators := [ [ [ 5 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0 ], [ 1, -2, 1, 0, 0 ], [ 0, 1, -2, 1, 0 ], [ 0, 0, 1, -2, 1 ], [ 0, 0, 0, 1, -2 ] ], IsADE := [ "A5" ], StabGenerators := [ [ [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 6 ] ], torsion := [ ] ) ], type := [ "A5" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 1, 0, 0 ], [ 0, -2, 1, 0, 0 ], [ 1, 1, -2, 1, 0 ], [ 0, 0, 1, -2, 1 ], [ 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/4 ] ], discg := [ 4 ], proj := [ [ 0 ], [ 4 ], [ -4 ], [ 4 ], [ 0 ] ], reps := [ [ 5/4, 3/4, 3/2, 1, 1/2 ] ] ), discAutGenerators := [ [ [ 3 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 1, 0, 0 ], [ 0, -2, 1, 0, 0 ], [ 1, 1, -2, 1, 0 ], [ 0, 0, 1, -2, 1 ], [ 0, 0, 0, 1, -2 ] ], IsADE := [ "D5" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 4 ] ], torsion := [ ] ) ], type := [ "D5" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0 ], [ 0, 0, 0, 0, -2, 0 ], [ 0, 0, 0, 0, 0, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0, 0 ], [ 0, 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 0, 3/2, 0 ], [ 0, 0, 0, 0, 0, 3/2 ] ], discg := [ 2, 2, 2, 2, 2, 2 ], proj := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 2 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0 ], [ 0, 0, 0, 0, 1/2, 0 ], [ 0, 0, 0, 0, 0, 1/2 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0 ], [ 0, 0, 0, 0, -2, 0 ], [ 0, 0, 0, 0, 0, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A1", "A1" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, -2, 1, 0 ], [ 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "D4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 1, 1, 1, 0 ], [ 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 1, 1, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 1 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0 ], [ 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 0 ], [ 1, 1, 1, 1, 1, 0 ], [ 1, 1, 2, 1, 0, 0 ], [ 1, 0, 1, 1, 1, 1 ], [ 0, 1, 1, 1, 1, 1 ] ], isotropicspace := [ [ 1, 0, 0, 1, 1, 1 ], [ 0, 1, 1, 0, 1, 1 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A1", "A1" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0 ], [ 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 3/2, 0 ], [ 0, 0, 0, 0, 4/3 ] ], discg := [ 2, 2, 2, 2, 3 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 3 ], [ 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0 ], [ 0, 0, 0, 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 2 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0 ], [ 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A2" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 3 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, -2, 1, 0 ], [ 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "D4" ], StabGenerators := [ [ [ 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 1, 1, 1, 0 ], [ 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 1, 1, 1 ], [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 1, 1, 1, 1, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 3 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A2" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 3/2, 0, 0 ], [ 0, 0, 3/2, 0 ], [ 0, 0, 0, 5/4 ] ], discg := [ 2, 2, 2, 4 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 4 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0 ], [ 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 3 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A3" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0 ], [ 0, 0, -2, 1, 0, 0 ], [ 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D5" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 1, 1, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 1, 0, 1, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 1, 1, 2 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A3" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0 ], [ 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 3/2, 0, 0 ], [ 0, 0, 4/3, 0 ], [ 0, 0, 0, 4/3 ] ], discg := [ 2, 2, 3, 3 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 3 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 1/3, 2/3, 0, 0 ], [ 0, 0, 0, 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0 ], [ 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A2", "A2" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 3 ] ], torsion := [ ] ) ], type := [ "A1", "A1", "A2", "A2" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0 ], [ 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 3/2, 0 ], [ 0, 0, 6/5 ] ], discg := [ 2, 2, 5 ], proj := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 5 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 1/5, 2/5, 3/5, 4/5 ] ] ), discAutGenerators := [ [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 4 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0 ], [ 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 5 ] ], torsion := [ ] ) ], type := [ "A1", "A1", "A4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, -2, 1, 0 ], [ 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 3/2, 0, 0 ], [ 0, 0, 1, 1/2 ], [ 0, 0, 1/2, 1 ] ], discg := [ 2, 2, 2, 2 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 0, 2 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 2, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, -2, 1, 0 ], [ 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "D4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0 ], [ 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0 ], [ 1, 1, 1, 0, 0, 0 ], [ 1, 0, 1, 1, 0, 0 ], [ 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 1, 1, 0, 1 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "D4" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 4/3, 0 ], [ 0, 0, 5/4 ] ], discg := [ 2, 3, 4 ], proj := [ [ 2, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 0 ], [ 0, 0, 4 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0 ], [ 0, 1/3, 2/3, 0, 0, 0 ], [ 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 3 ] ], [ [ 1, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "A3" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 4 ] ], torsion := [ ] ) ], type := [ "A1", "A2", "A3" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0 ], [ 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0 ], [ 0, 7/6 ] ], discg := [ 2, 6 ], proj := [ [ 2, 0 ], [ 0, 6 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0 ], [ 0, 1/6, 1/3, 1/2, 2/3, 5/6 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 1, 0 ], [ 0, 5 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0 ], [ 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A5" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0 ], [ 0, 6 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0 ], [ 0, -2, 1, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0 ], [ 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 1, 1, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 0, 0 ] ], isotropicspace := [ [ 1, 3 ], [ 0, 6 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A5" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0 ], [ 0, 0, -2, 1, 0, 0 ], [ 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0 ], [ 0, 3/4 ] ], discg := [ 2, 4 ], proj := [ [ 2, 0 ], [ 0, 0 ], [ 0, 4 ], [ 0, -4 ], [ 0, 4 ], [ 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0 ], [ 0, 5/4, 3/4, 3/2, 1, 1/2 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 1, 0 ], [ 0, 3 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0 ], [ 0, 0, -2, 1, 0, 0 ], [ 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D5" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0 ], [ 0, 4 ] ], torsion := [ ] ) ], type := [ "A1", "D5" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0 ], [ 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0, 0 ], [ 0, 4/3, 0 ], [ 0, 0, 4/3 ] ], discg := [ 3, 3, 3 ], proj := [ [ 3, 0, 0 ], [ 0, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 0 ], [ 0, 0, 3 ], [ 0, 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0 ], [ 0, 0, 1/3, 2/3, 0, 0 ], [ 0, 0, 0, 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 0, 1, 0 ], [ 0, 0, 1 ], [ 1, 0, 0 ] ], [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 2, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0 ], [ 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A2", "A2" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 3 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0 ], [ 0, -2, 1, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0 ], [ 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E6" ], StabGenerators := [ [ [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 1, 0, 0 ], [ 1, 0, 1, 1, 1, 0 ], [ 0, 1, 1, 1, 1, 0 ], [ 1, 0, 0, 1, 1, 1 ], [ 0, 0, 1, 1, 1, 1 ], [ 1, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 1, 1, 1 ], [ 0, 3, 0 ], [ 0, 0, 3 ] ], torsion := [ 3 ] ) ], type := [ "A2", "A2", "A2" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0 ], [ 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0 ], [ 0, 6/5 ] ], discg := [ 3, 5 ], proj := [ [ 3, 0 ], [ 0, 0 ], [ 0, 5 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0 ], [ 0, 0, 1/5, 2/5, 3/5, 4/5 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 4 ] ], [ [ 2, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0 ], [ 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0 ], [ 0, 5 ] ], torsion := [ ] ) ], type := [ "A2", "A4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, -2, 1, 0 ], [ 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0, 0 ], [ 0, 1, 1/2 ], [ 0, 1/2, 1 ] ], discg := [ 3, 2, 2 ], proj := [ [ 3, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 2 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 2, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0 ], [ 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 0, 1 ], [ 0, 1, 0 ] ], [ [ 1, 0, 0 ], [ 0, 1, 1 ], [ 0, 0, 1 ] ], [ [ 2, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, -2, 1, 0 ], [ 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "D4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 2 ] ], torsion := [ ] ) ], type := [ "A2", "D4" ] ), rec( AutGenerators := [ [ [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 5/4, 0 ], [ 0, 5/4 ] ], discg := [ 4, 4 ], proj := [ [ 4, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 4 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/4, 1/2, 3/4, 0, 0, 0 ], [ 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 0, 1 ], [ 1, 0 ] ], [ [ 3, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A3", "A3" ], StabGenerators := [ [ [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 4, 0 ], [ 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0 ], [ 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D6" ], StabGenerators := [ [ [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 0 ], [ 1, 1, 1, 0, 0, 0 ], [ 1, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1 ], [ 0, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 2, 2 ], [ 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A3", "A3" ] ), rec( AutGenerators := [ [ [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0 ], [ 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 8/7 ] ], discg := [ 7 ], proj := [ [ 7 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ] ], reps := [ [ 1/7, 2/7, 3/7, 4/7, 5/7, 6/7 ] ] ), discAutGenerators := [ [ [ 6 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0 ], [ 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A6" ], StabGenerators := [ [ [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 7 ] ], torsion := [ ] ) ], type := [ "A6" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 1, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0 ], [ 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 1/2, 1/2 ], [ 1/2, 1 ] ], discg := [ 2, 2 ], proj := [ [ 0, 2 ], [ 0, 0 ], [ 0, 0 ], [ 0, -2 ], [ 0, 2 ], [ 2, 0 ] ], reps := [ [ 3/2, 1, 2, 3/2, 1, 1/2 ], [ 1/2, 1/2, 1, 1, 1, 1 ] ] ), discAutGenerators := [ [ [ 1, 1 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 1, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0 ], [ 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0 ], [ 0, 2 ] ], torsion := [ ] ) ], type := [ "D6" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 1, 0, 0 ], [ 0, -2, 1, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0 ], [ 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 2/3 ] ], discg := [ 3 ], proj := [ [ 3 ], [ 3 ], [ -3 ], [ 0 ], [ 0 ], [ 0 ] ], reps := [ [ 1, 2/3, 4/3, 2, 5/3, 4/3 ] ] ), discAutGenerators := [ [ [ 2 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 1, 0, 0 ], [ 0, -2, 1, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0 ], [ 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3 ] ], torsion := [ ] ) ], type := [ "E6" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0 ], [ 0, 0, 0, 0, 0, 0, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0, 0, 0 ], [ 0, 0, 0, 3/2, 0, 0, 0 ], [ 0, 0, 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 0, 0, 3/2, 0 ], [ 0, 0, 0, 0, 0, 0, 3/2 ] ], discg := [ 2, 2, 2, 2, 2, 2, 2 ], proj := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 2 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0, 0 ], [ 0, 0, 0, 0, 1/2, 0, 0 ], [ 0, 0, 0, 0, 0, 1/2, 0 ], [ 0, 0, 0, 0, 0, 0, 1/2 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0 ], [ 0, 0, 0, 0, 0, 0, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A1", "A1", "A1" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "D4" ], StabGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 1, 1, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 1 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0 ], [ 0, 1, 1, 1, 1, 1, 0 ], [ 0, 1, 1, 2, 1, 0, 0 ], [ 0, 1, 0, 1, 1, 1, 1 ], [ 0, 0, 1, 1, 1, 1, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 1, 1, 1 ], [ 0, 0, 1, 1, 0, 1, 1 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E7" ], StabGenerators := [ [ [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 2, 1, 0, 0 ], [ 1, 1, 1, 2, 1, 1, 0 ], [ 1, 1, 2, 2, 1, 1, 1 ], [ 1, 1, 1, 2, 2, 1, 1 ], [ 1, 0, 1, 2, 2, 2, 1 ], [ 1, 1, 2, 2, 2, 1, 0 ] ], isotropicspace := [ [ 1, 0, 0, 0, 1, 1, 1 ], [ 0, 1, 0, 1, 0, 1, 1 ], [ 0, 0, 1, 1, 1, 0, 1 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2, 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A1", "A1", "A1" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0, 0 ], [ 0, 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 0, 3/2, 0 ], [ 0, 0, 0, 0, 0, 4/3 ] ], discg := [ 2, 2, 2, 2, 2, 3 ], proj := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 3 ], [ 0, 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0, 0 ], [ 0, 0, 0, 0, 1/2, 0, 0 ], [ 0, 0, 0, 0, 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 2 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A1", "A2" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 3 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "D4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 1, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 3 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A1", "A2" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 3/2, 0 ], [ 0, 0, 0, 0, 5/4 ] ], discg := [ 2, 2, 2, 2, 4 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 4 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0, 0 ], [ 0, 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 3 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A3" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "D5" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 1, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 1, 1, 2 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 4 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D7" ], StabGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0 ], [ 1, 1, 1, 1, 1, 0, 0 ], [ 1, 1, 2, 1, 0, 0, 0 ], [ 1, 0, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 1, 1, 1, 1, 0 ] ], isotropicspace := [ [ 1, 0, 0, 1, 2 ], [ 0, 1, 1, 0, 2 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 4 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A3", "D4" ], StabGenerators := [ [ [ 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 1, 1, 1, 1, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A3" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 4/3, 0 ], [ 0, 0, 0, 0, 4/3 ] ], discg := [ 2, 2, 2, 3, 3 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 3 ], [ 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 0, 1/3, 2/3, 0, 0 ], [ 0, 0, 0, 0, 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A2", "A2" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 3 ] ], torsion := [ ] ) ], type := [ "A1", "A1", "A1", "A2", "A2" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 3/2, 0, 0 ], [ 0, 0, 3/2, 0 ], [ 0, 0, 0, 6/5 ] ], discg := [ 2, 2, 2, 5 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 5 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 0, 1/5, 2/5, 3/5, 4/5 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 4 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 5 ] ], torsion := [ ] ) ], type := [ "A1", "A1", "A1", "A4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 1, 1/2 ], [ 0, 0, 0, 1/2, 1 ] ], discg := [ 2, 2, 2, 2, 2 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 1 ], [ 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "D4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 1, 1, 1, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 1, 1, 0, 1 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E7" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0 ], [ 1, 0, 0, 1, 1, 1, 1 ], [ 1, 0, 1, 2, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 1 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 1, 1, 0 ] ], isotropicspace := [ [ 1, 0, 1, 0, 1 ], [ 0, 1, 1, 1, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2 ] ) ], type := [ "A1", "A1", "A1", "D4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 3/2, 0, 0 ], [ 0, 0, 4/3, 0 ], [ 0, 0, 0, 5/4 ] ], discg := [ 2, 2, 3, 4 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 4 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 1/3, 2/3, 0, 0, 0 ], [ 0, 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 3 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A2", "A3" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "D5" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 1, 1, 0 ] ], isotropicspace := [ [ 1, 1, 0, 2 ], [ 0, 2, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A2", "A3" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 3/2, 0 ], [ 0, 0, 7/6 ] ], discg := [ 2, 2, 6 ], proj := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 6 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 1/6, 1/3, 1/2, 2/3, 5/6 ] ] ), discAutGenerators := [ [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 5 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A5" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 6 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 1, 3 ], [ 0, 0, 6 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A5" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 3/2, 0 ], [ 0, 0, 3/4 ] ], discg := [ 2, 2, 4 ], proj := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 0 ], [ 0, 0, 4 ], [ 0, 0, -4 ], [ 0, 0, 4 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 5/4, 3/4, 3/2, 1, 1/2 ] ] ), discAutGenerators := [ [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 3 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "D5" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0, 0 ], [ 1, 1, 1, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 0, 0, 0 ], [ 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 1, 1, 2 ], [ 0, 2, 0 ], [ 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "D5" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 4/3, 0, 0 ], [ 0, 0, 4/3, 0 ], [ 0, 0, 0, 4/3 ] ], discg := [ 2, 3, 3, 3 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 3 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 1/3, 2/3, 0, 0, 0, 0 ], [ 0, 0, 0, 1/3, 2/3, 0, 0 ], [ 0, 0, 0, 0, 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "A2", "A2" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 3 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 1, 0, 1, 1, 1, 0 ], [ 0, 0, 1, 1, 1, 1, 0 ], [ 0, 1, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 1, 1, 1, 1 ], [ 0, 1, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 1, 1, 1 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 3 ] ], torsion := [ 3 ] ) ], type := [ "A1", "A2", "A2", "A2" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 4/3, 0 ], [ 0, 0, 6/5 ] ], discg := [ 2, 3, 5 ], proj := [ [ 2, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 0 ], [ 0, 0, 5 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 1/3, 2/3, 0, 0, 0, 0 ], [ 0, 0, 0, 1/5, 2/5, 3/5, 4/5 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 4 ] ], [ [ 1, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "A4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 5 ] ], torsion := [ ] ) ], type := [ "A1", "A2", "A4" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 4/3, 0, 0 ], [ 0, 0, 1, 1/2 ], [ 0, 0, 1/2, 1 ] ], discg := [ 2, 3, 2, 2 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 2 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 2, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 1/3, 2/3, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "D4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ ] ) ], type := [ "A1", "A2", "D4" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 5/4, 0 ], [ 0, 0, 5/4 ] ], discg := [ 2, 4, 4 ], proj := [ [ 2, 0, 0 ], [ 0, 4, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 4 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 1/4, 1/2, 3/4, 0, 0, 0 ], [ 0, 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 0, 1 ], [ 0, 1, 0 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A3", "A3" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 4, 0 ], [ 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 0 ], [ 0, 1, 1, 1, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1 ], [ 0, 0, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 2, 2 ], [ 0, 0, 4 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 1, 2, 1, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0 ], [ 1, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 1 ], [ 1, 0, 0, 1, 1, 1, 1 ], [ 0, 1, 1, 1, 1, 0, 0 ], [ 1, 0, 1, 1, 1, 1, 0 ] ], isotropicspace := [ [ 1, 1, 1 ], [ 0, 2, 2 ], [ 0, 0, 4 ] ], torsion := [ 4 ] ) ], type := [ "A1", "A3", "A3" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0 ], [ 0, 8/7 ] ], discg := [ 2, 7 ], proj := [ [ 2, 0 ], [ 0, 7 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 1/7, 2/7, 3/7, 4/7, 5/7, 6/7 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 1, 0 ], [ 0, 6 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0 ], [ 0, 7 ] ], torsion := [ ] ) ], type := [ "A1", "A6" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 1/2, 1/2 ], [ 0, 1/2, 1 ] ], discg := [ 2, 2, 2 ], proj := [ [ 2, 0, 0 ], [ 0, 0, 2 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, -2 ], [ 0, 0, 2 ], [ 0, 2, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 3/2, 1, 2, 3/2, 1, 1/2 ], [ 0, 1/2, 1/2, 1, 1, 1, 1 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 1 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 1, 1, 1, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 0, 0, 0 ] ], isotropicspace := [ [ 1, 1, 0 ], [ 0, 2, 0 ], [ 0, 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "A1", "D6" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0 ], [ 0, 2/3 ] ], discg := [ 2, 3 ], proj := [ [ 2, 0 ], [ 0, 3 ], [ 0, 3 ], [ 0, -3 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 2/3, 4/3, 2, 5/3, 4/3 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 1, 0 ], [ 0, 2 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0 ], [ 0, 3 ] ], torsion := [ ] ) ], type := [ "A1", "E6" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0, 0 ], [ 0, 4/3, 0 ], [ 0, 0, 5/4 ] ], discg := [ 3, 3, 4 ], proj := [ [ 3, 0, 0 ], [ 0, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 0 ], [ 0, 0, 4 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0, 0 ], [ 0, 0, 1/3, 2/3, 0, 0, 0 ], [ 0, 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 3 ] ], [ [ 2, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A2", "A3" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 4 ] ], torsion := [ ] ) ], type := [ "A2", "A2", "A3" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0 ], [ 0, 7/6 ] ], discg := [ 3, 6 ], proj := [ [ 3, 0 ], [ 0, 0 ], [ 0, 6 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0, 0 ], [ 0, 0, 1/6, 1/3, 1/2, 2/3, 5/6 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 5 ] ], [ [ 2, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A5" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0 ], [ 0, 6 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E7" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 1, 1, 1, 0, 0 ], [ 0, 1, 1, 1, 1, 0, 0 ], [ 1, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 1, 1, 1, 0 ], [ 1, 1, 1, 1, 0, 0, 0 ] ], isotropicspace := [ [ 1, 2 ], [ 0, 6 ] ], torsion := [ 3 ] ) ], type := [ "A2", "A5" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0 ], [ 0, 3/4 ] ], discg := [ 3, 4 ], proj := [ [ 3, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 4 ], [ 0, -4 ], [ 0, 4 ], [ 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0, 0 ], [ 0, 0, 5/4, 3/4, 3/2, 1, 1/2 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 3 ] ], [ [ 2, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "D5" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0 ], [ 0, 4 ] ], torsion := [ ] ) ], type := [ "A2", "D5" ] ), rec( AutGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 5/4, 0 ], [ 0, 6/5 ] ], discg := [ 4, 5 ], proj := [ [ 4, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 5 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/4, 1/2, 3/4, 0, 0, 0, 0 ], [ 0, 0, 0, 1/5, 2/5, 3/5, 4/5 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 4 ] ], [ [ 3, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A3", "A4" ], StabGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 4, 0 ], [ 0, 5 ] ], torsion := [ ] ) ], type := [ "A3", "A4" ] ), rec( AutGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 5/4, 0, 0 ], [ 0, 1, 1/2 ], [ 0, 1/2, 1 ] ], discg := [ 4, 2, 2 ], proj := [ [ 4, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 2 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 2, 0 ] ], reps := [ [ 1/4, 1/2, 3/4, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 0, 1 ], [ 0, 1, 0 ] ], [ [ 1, 0, 0 ], [ 0, 1, 1 ], [ 0, 0, 1 ] ], [ [ 3, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A3", "D4" ], StabGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 4, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 0, 0 ], [ 1, 1, 1, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 0, 0, 0 ], [ 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 1 ], [ 0, 2, 0 ], [ 0, 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "A3", "D4" ] ), rec( AutGenerators := [ [ [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 9/8 ] ], discg := [ 8 ], proj := [ [ 8 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ] ], reps := [ [ 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8 ] ] ), discAutGenerators := [ [ [ 7 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A7" ], StabGenerators := [ [ [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 8 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E7" ], StabGenerators := [ [ [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 0 ], [ 1, 0, 1, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1 ], [ 1, 0, 0, 1, 1, 0, 0 ] ], isotropicspace := [ [ 4 ] ], torsion := [ 2 ] ) ], type := [ "A7" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 1/4 ] ], discg := [ 4 ], proj := [ [ 0 ], [ 4 ], [ -4 ], [ 4 ], [ -4 ], [ 4 ], [ 0 ] ], reps := [ [ 7/4, 5/4, 5/2, 2, 3/2, 1, 1/2 ] ] ), discAutGenerators := [ [ [ 3 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D7" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 4 ] ], torsion := [ ] ) ], type := [ "D7" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 1, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 1/2 ] ], discg := [ 2 ], proj := [ [ 0 ], [ 2 ], [ 0 ], [ 0 ], [ -2 ], [ 2 ], [ 0 ] ], reps := [ [ 3/2, 1, 2, 3, 5/2, 2, 3/2 ] ] ), discAutGenerators := [ [ [ 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2 ] ], torsion := [ ] ) ], type := [ "E7" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 3/2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 3/2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 3/2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 3/2 ] ], discg := [ 2, 2, 2, 2, 2, 2, 2, 2 ], proj := [ [ 2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1/2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1/2 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A1", "A1", "A1", "A1" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "D4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 1, 1, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 1 ], [ 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -4, -1, -1, -1, -1, -1, -1, -1 ], [ -1, -2, 0, 0, 0, 0, 0, 0 ], [ -1, 0, -2, 0, 0, 0, 0, 0 ], [ -1, 0, 0, -2, 0, 0, 0, 0 ], [ -1, 0, 0, 0, -2, 0, 0, 0 ], [ -1, 0, 0, 0, 0, -2, 0, 0 ], [ -1, 0, 0, 0, 0, 0, -2, 0 ], [ -1, 0, 0, 0, 0, 0, 0, -2 ] ], IsADE := false, StabGenerators := [ [ [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ -2, 1, 1, 1, 1, 1, 1, 1 ], [ 0, -1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, -1 ] ], isotropicspace := [ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ 0, 2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "D6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 1, 1, 1, 1, 1, 0 ], [ 0, 0, 1, 1, 2, 1, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 1, 1 ], [ 0, 0, 0, 1, 1, 1, 1, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 1, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D4", "D4" ], StabGenerators := [ [ [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 1, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 1, 1, 1 ] ], isotropicspace := [ [ 1, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 1, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 2, 1, 0, 0 ], [ 0, 1, 1, 1, 2, 1, 1, 0 ], [ 0, 1, 1, 2, 2, 1, 1, 1 ], [ 0, 1, 1, 1, 2, 2, 1, 1 ], [ 0, 1, 0, 1, 2, 2, 2, 1 ], [ 0, 1, 1, 2, 2, 2, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 1, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 1, 1, 1, 0, 1 ], [ 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2, 2 ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D8" ], StabGenerators := [ [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 1, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 0 ], [ 1, 1, 2, 1, 1, 1, 0, 0 ], [ 1, 1, 2, 2, 1, 0, 0, 0 ], [ 0, 1, 1, 1, 1, 1, 1, 1 ], [ 1, 0, 1, 1, 1, 1, 1, 1 ] ], isotropicspace := [ [ 1, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 1, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 1, 1, 0, 0, 1, 1 ], [ 0, 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2, 2 ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E8" ], StabGenerators := [ [ [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 2, 2, 1, 0, 0, 0 ], [ 1, 1, 2, 2, 2, 2, 1, 0 ], [ 1, 1, 2, 3, 2, 2, 1, 1 ], [ 1, 1, 2, 3, 3, 2, 2, 1 ], [ 2, 1, 2, 3, 2, 2, 2, 1 ], [ 2, 1, 2, 3, 3, 2, 1, 1 ], [ 2, 1, 2, 4, 3, 2, 1, 0 ] ], isotropicspace := [ [ 1, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 1, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 1, 0, 1, 1, 0, 1 ], [ 0, 0, 0, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2, 2, 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A1", "A1", "A1", "A1" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0, 0, 0 ], [ 0, 0, 0, 3/2, 0, 0, 0 ], [ 0, 0, 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 0, 0, 3/2, 0 ], [ 0, 0, 0, 0, 0, 0, 4/3 ] ], discg := [ 2, 2, 2, 2, 2, 2, 3 ], proj := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 3 ], [ 0, 0, 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 2 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A1", "A1", "A2" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 3 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A2", "D4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 3 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "D6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 1, 1, 1, 1, 1, 0 ], [ 0, 0, 1, 1, 2, 1, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 1, 1 ], [ 0, 0, 0, 1, 1, 1, 1, 1 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 1, 0, 0, 1, 1, 1, 0 ], [ 0, 1, 1, 0, 1, 1, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 3 ] ], torsion := [ 2, 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A1", "A1", "A2" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0, 0 ], [ 0, 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 0, 3/2, 0 ], [ 0, 0, 0, 0, 0, 5/4 ] ], discg := [ 2, 2, 2, 2, 2, 4 ], proj := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 4 ], [ 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 3 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A1", "A3" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "D5" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 1, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 2 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 4 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 1, 1, 1, 1, 1, 0, 0 ], [ 0, 1, 1, 2, 1, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 1, 1, 1, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 1, 2 ], [ 0, 0, 1, 1, 0, 2 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 4 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A3", "D4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 1, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A1", "A3" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0, 0 ], [ 0, 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 0, 4/3, 0 ], [ 0, 0, 0, 0, 0, 4/3 ] ], discg := [ 2, 2, 2, 2, 3, 3 ], proj := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 3 ], [ 0, 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/3, 2/3, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A2", "A2" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 3 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A2", "D4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 1, 1, 1, 1, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 3 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A2", "A2" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 3/2, 0 ], [ 0, 0, 0, 0, 6/5 ] ], discg := [ 2, 2, 2, 2, 5 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 5 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/5, 2/5, 3/5, 4/5 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 4 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 5 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A4", "D4" ], StabGenerators := [ [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 1, 1, 1, 1, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 5 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0, 0 ], [ 0, 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 0, 1, 1/2 ], [ 0, 0, 0, 0, 1/2, 1 ] ], discg := [ 2, 2, 2, 2, 2, 2 ], proj := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2 ], [ 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "D4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "D6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 0, 1 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 1, 0, 0, 1, 1, 1, 1 ], [ 0, 1, 0, 1, 2, 1, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 1, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 0, 1 ], [ 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E8" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 2, 1, 0, 0, 0 ], [ 1, 1, 1, 2, 1, 1, 0, 0 ], [ 1, 1, 2, 2, 2, 1, 0, 0 ], [ 1, 1, 1, 2, 2, 1, 1, 0 ], [ 1, 0, 1, 2, 2, 2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 1, 2, 2, 1, 1, 1, 0 ] ], isotropicspace := [ [ 1, 0, 0, 1, 0, 1 ], [ 0, 1, 0, 1, 1, 0 ], [ 0, 0, 1, 1, 1, 1 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2, 2 ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D8" ], StabGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0 ], [ 1, 1, 1, 1, 1, 0, 0, 0 ], [ 1, 1, 2, 1, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 1, 1, 0, 0 ], [ 1, 0, 1, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 1, 0, 0, 1, 0, 1 ], [ 0, 1, 1, 0, 0, 1 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D4", "D4" ], StabGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 1, 1, 1, 1, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "D4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 4/3, 0 ], [ 0, 0, 0, 0, 5/4 ] ], discg := [ 2, 2, 2, 3, 4 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 4 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/3, 2/3, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 3 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A2", "A3" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "D5" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 1, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 1, 1, 0, 2 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A2", "A3" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 3/2, 0, 0 ], [ 0, 0, 3/2, 0 ], [ 0, 0, 0, 7/6 ] ], discg := [ 2, 2, 2, 6 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 6 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/6, 1/3, 1/2, 2/3, 5/6 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 5 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A5" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 6 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "E6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 1, 3 ], [ 0, 0, 0, 6 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A5" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 3/2, 0, 0 ], [ 0, 0, 3/2, 0 ], [ 0, 0, 0, 3/4 ] ], discg := [ 2, 2, 2, 4 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 4 ], [ 0, 0, 0, -4 ], [ 0, 0, 0, 4 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 5/4, 3/4, 3/2, 1, 1/2 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 3 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "D5" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 1, 1, 2 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "D5" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0 ], [ 0, 0, 4/3, 0, 0 ], [ 0, 0, 0, 4/3, 0 ], [ 0, 0, 0, 0, 4/3 ] ], discg := [ 2, 2, 3, 3, 3 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 3, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 3 ], [ 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/3, 2/3, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/3, 2/3, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A2", "A2", "A2" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 3, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 3 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "E6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 0 ], [ 0, 0, 1, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 0, 1, 1, 1, 1 ], [ 0, 0, 1, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 1, 1, 1 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 3 ] ], torsion := [ 3 ] ) ], type := [ "A1", "A1", "A2", "A2", "A2" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 3/2, 0, 0 ], [ 0, 0, 4/3, 0 ], [ 0, 0, 0, 6/5 ] ], discg := [ 2, 2, 3, 5 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 5 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/3, 2/3, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/5, 2/5, 3/5, 4/5 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 4 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A2", "A4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 5 ] ], torsion := [ ] ) ], type := [ "A1", "A1", "A2", "A4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0 ], [ 0, 0, 4/3, 0, 0 ], [ 0, 0, 0, 1, 1/2 ], [ 0, 0, 0, 1/2, 1 ] ], discg := [ 2, 2, 3, 2, 2 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 3, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/3, 2/3, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 1 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A2", "D4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 3, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "D6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 1, 1, 0, 0, 1 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 3, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A2", "D4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 3/2, 0, 0 ], [ 0, 0, 5/4, 0 ], [ 0, 0, 0, 5/4 ] ], discg := [ 2, 2, 4, 4 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 4, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 4 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/4, 1/2, 3/4, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A3", "A3" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 4, 0 ], [ 0, 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "D6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1 ], [ 0, 0, 0, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 2 ], [ 0, 0, 0, 4 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 1, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 1 ], [ 0, 1, 0, 0, 1, 1, 1, 1 ], [ 0, 0, 1, 1, 1, 1, 0, 0 ], [ 0, 1, 0, 1, 1, 1, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 1, 1, 1 ], [ 0, 0, 2, 2 ], [ 0, 0, 0, 4 ] ], torsion := [ 4 ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E8" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 1, 2, 1, 0, 0, 0 ], [ 1, 0, 1, 2, 2, 2, 1, 0 ], [ 1, 1, 1, 2, 1, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 1, 1 ], [ 1, 1, 1, 2, 2, 1, 1, 0 ], [ 1, 1, 2, 2, 1, 1, 1, 0 ], [ 1, 0, 0, 1, 1, 1, 1, 1 ], [ 1, 1, 2, 2, 2, 1, 0, 0 ] ], isotropicspace := [ [ 1, 0, 1, 1 ], [ 0, 1, 1, 3 ], [ 0, 0, 2, 2 ], [ 0, 0, 0, 4 ] ], torsion := [ 4, 2 ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 1, 2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 0 ], [ 1, 1, 1, 1, 1, 0, 0, 0 ], [ 0, 1, 1, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1 ], [ 1, 0, 1, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 1, 1, 0, 2 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 2 ], [ 0, 0, 0, 4 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A3", "D5" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 1, 1, 0 ] ], isotropicspace := [ [ 1, 1, 0, 2 ], [ 0, 2, 0, 0 ], [ 0, 0, 4, 0 ], [ 0, 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A3", "A3" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 3/2, 0 ], [ 0, 0, 8/7 ] ], discg := [ 2, 2, 7 ], proj := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 7 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/7, 2/7, 3/7, 4/7, 5/7, 6/7 ] ] ), discAutGenerators := [ [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 6 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 7 ] ], torsion := [ ] ) ], type := [ "A1", "A1", "A6" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 3/2, 0, 0 ], [ 0, 0, 1/2, 1/2 ], [ 0, 0, 1/2, 1 ] ], discg := [ 2, 2, 2, 2 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 0, 2 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, -2 ], [ 0, 0, 0, 2 ], [ 0, 0, 2, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 3/2, 1, 2, 3/2, 1, 1/2 ], [ 0, 0, 1/2, 1/2, 1, 1, 1, 1 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "D6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E8" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0 ], [ 1, 0, 1, 2, 1, 0, 0, 0 ], [ 1, 0, 1, 1, 1, 1, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 1, 1, 1, 1, 0 ] ], isotropicspace := [ [ 1, 0, 1, 0 ], [ 0, 1, 1, 1 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 1, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 1, 1, 0, 1 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "D6" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 3/2, 0 ], [ 0, 0, 2/3 ] ], discg := [ 2, 2, 3 ], proj := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 3 ], [ 0, 0, 3 ], [ 0, 0, -3 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 2/3, 4/3, 2, 5/3, 4/3 ] ] ), discAutGenerators := [ [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 2 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "E6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 3 ] ], torsion := [ ] ) ], type := [ "A1", "A1", "E6" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 4/3, 0, 0 ], [ 0, 0, 4/3, 0 ], [ 0, 0, 0, 5/4 ] ], discg := [ 2, 3, 3, 4 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 4 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/3, 2/3, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/3, 2/3, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 3 ] ], [ [ 1, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "A2", "A3" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 4 ] ], torsion := [ ] ) ], type := [ "A1", "A2", "A2", "A3" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 4/3, 0 ], [ 0, 0, 7/6 ] ], discg := [ 2, 3, 6 ], proj := [ [ 2, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 0 ], [ 0, 0, 6 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/3, 2/3, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/6, 1/3, 1/2, 2/3, 5/6 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 5 ] ], [ [ 1, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "A5" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 6 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 0, 0 ], [ 0, 1, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 1, 1, 1, 0 ], [ 0, 1, 1, 1, 1, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 1, 2 ], [ 0, 0, 6 ] ], torsion := [ 3 ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0 ], [ 1, 0, 1, 1, 1, 1, 1, 0 ], [ 0, 0, 1, 1, 1, 1, 1, 1 ], [ 1, 1, 1, 1, 1, 1, 0, 0 ], [ 1, 0, 1, 2, 1, 0, 0, 0 ], [ 0, 1, 1, 1, 1, 1, 1, 0 ], [ 1, 0, 0, 1, 1, 1, 1, 1 ] ], isotropicspace := [ [ 1, 0, 3 ], [ 0, 1, 2 ], [ 0, 0, 6 ] ], torsion := [ 6 ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "E6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 0, 0 ] ], isotropicspace := [ [ 1, 0, 3 ], [ 0, 3, 0 ], [ 0, 0, 6 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A2", "A5" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 4/3, 0 ], [ 0, 0, 3/4 ] ], discg := [ 2, 3, 4 ], proj := [ [ 2, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 4 ], [ 0, 0, -4 ], [ 0, 0, 4 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/3, 2/3, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 5/4, 3/4, 3/2, 1, 1/2 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 3 ] ], [ [ 1, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "D5" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 4 ] ], torsion := [ ] ) ], type := [ "A1", "A2", "D5" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 5/4, 0 ], [ 0, 0, 6/5 ] ], discg := [ 2, 4, 5 ], proj := [ [ 2, 0, 0 ], [ 0, 4, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 5 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/4, 1/2, 3/4, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/5, 2/5, 3/5, 4/5 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 4 ] ], [ [ 1, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A3", "A4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 4, 0 ], [ 0, 0, 5 ] ], torsion := [ ] ) ], type := [ "A1", "A3", "A4" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 5/4, 0, 0 ], [ 0, 0, 1, 1/2 ], [ 0, 0, 1/2, 1 ] ], discg := [ 2, 4, 2, 2 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 4, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 2 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 2, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/4, 1/2, 3/4, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A3", "D4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 4, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 0, 0 ], [ 0, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 1 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A3", "D4" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0 ], [ 0, 9/8 ] ], discg := [ 2, 8 ], proj := [ [ 2, 0 ], [ 0, 8 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 1, 0 ], [ 0, 7 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0 ], [ 0, 8 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 0 ], [ 0, 1, 0, 1, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1 ], [ 0, 1, 0, 0, 1, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0 ], [ 0, 4 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 1, 2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 1, 1, 1, 1, 0 ], [ 0, 1, 1, 1, 1, 0, 0, 0 ], [ 1, 0, 1, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 1, 2 ], [ 0, 4 ] ], torsion := [ 4 ] ) ], type := [ "A1", "A7" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0 ], [ 0, 1/4 ] ], discg := [ 2, 4 ], proj := [ [ 2, 0 ], [ 0, 0 ], [ 0, 4 ], [ 0, -4 ], [ 0, 4 ], [ 0, -4 ], [ 0, 4 ], [ 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 7/4, 5/4, 5/2, 2, 3/2, 1, 1/2 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 1, 0 ], [ 0, 3 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0 ], [ 0, 4 ] ], torsion := [ ] ) ], type := [ "A1", "D7" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0 ], [ 0, 1/2 ] ], discg := [ 2, 2 ], proj := [ [ 2, 0 ], [ 0, 0 ], [ 0, 2 ], [ 0, 0 ], [ 0, 0 ], [ 0, -2 ], [ 0, 2 ], [ 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 3/2, 1, 2, 3, 5/2, 2, 3/2 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0 ], [ 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 0, 0, 0, 0 ] ], isotropicspace := [ [ 1, 1 ], [ 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "A1", "E7" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0, 0, 0 ], [ 0, 4/3, 0, 0 ], [ 0, 0, 4/3, 0 ], [ 0, 0, 0, 4/3 ] ], discg := [ 3, 3, 3, 3 ], proj := [ [ 3, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 3 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/3, 2/3, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/3, 2/3, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 0, 0, 0 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 2, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A2", "A2", "A2" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 3 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "E6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 0 ], [ 0, 0, 1, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 0, 1, 1, 1, 1 ], [ 0, 0, 1, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 3, 0, 0, 0 ], [ 0, 1, 1, 1 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 3 ] ], torsion := [ 3 ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E8" ], StabGenerators := [ [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ] ], [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 2, 3, 2, 1, 0, 0 ], [ 1, 0, 1, 2, 1, 1, 1, 0 ], [ 1, 1, 1, 2, 2, 1, 1, 1 ], [ 1, 1, 2, 2, 2, 1, 1, 0 ], [ 1, 0, 1, 2, 2, 2, 1, 1 ], [ 1, 1, 2, 2, 1, 1, 1, 1 ], [ 1, 1, 1, 2, 2, 2, 1, 0 ] ], isotropicspace := [ [ 1, 0, 1, 1 ], [ 0, 1, 1, 2 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 3 ] ], torsion := [ 3, 3 ] ) ], type := [ "A2", "A2", "A2", "A2" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0, 0 ], [ 0, 4/3, 0 ], [ 0, 0, 6/5 ] ], discg := [ 3, 3, 5 ], proj := [ [ 3, 0, 0 ], [ 0, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 0 ], [ 0, 0, 5 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/3, 2/3, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/5, 2/5, 3/5, 4/5 ] ] ), discAutGenerators := [ [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 4 ] ], [ [ 2, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A2", "A4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 5 ] ], torsion := [ ] ) ], type := [ "A2", "A2", "A4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0, 0, 0 ], [ 0, 4/3, 0, 0 ], [ 0, 0, 1, 1/2 ], [ 0, 0, 1/2, 1 ] ], discg := [ 3, 3, 2, 2 ], proj := [ [ 3, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 2 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 2, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/3, 2/3, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ], [ [ 2, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A2", "D4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ ] ) ], type := [ "A2", "A2", "D4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0, 0 ], [ 0, 5/4, 0 ], [ 0, 0, 5/4 ] ], discg := [ 3, 4, 4 ], proj := [ [ 3, 0, 0 ], [ 0, 0, 0 ], [ 0, 4, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 4 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/4, 1/2, 3/4, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 0, 1 ], [ 0, 1, 0 ] ], [ [ 1, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 1 ] ], [ [ 2, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A3", "A3" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0, 0 ], [ 0, 4, 0 ], [ 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "D6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1 ], [ 0, 0, 0, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 3, 0, 0 ], [ 0, 2, 2 ], [ 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A2", "A3", "A3" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0 ], [ 0, 8/7 ] ], discg := [ 3, 7 ], proj := [ [ 3, 0 ], [ 0, 0 ], [ 0, 7 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/7, 2/7, 3/7, 4/7, 5/7, 6/7 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 6 ] ], [ [ 2, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0 ], [ 0, 7 ] ], torsion := [ ] ) ], type := [ "A2", "A6" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0, 0 ], [ 0, 1/2, 1/2 ], [ 0, 1/2, 1 ] ], discg := [ 3, 2, 2 ], proj := [ [ 3, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 2 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, -2 ], [ 0, 0, 2 ], [ 0, 2, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 3/2, 1, 2, 3/2, 1, 1/2 ], [ 0, 0, 1/2, 1/2, 1, 1, 1, 1 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 1, 1 ], [ 0, 0, 1 ] ], [ [ 2, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "D6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 2 ] ], torsion := [ ] ) ], type := [ "A2", "D6" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0 ], [ 0, 2/3 ] ], discg := [ 3, 3 ], proj := [ [ 3, 0 ], [ 0, 0 ], [ 0, 3 ], [ 0, 3 ], [ 0, -3 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 2/3, 4/3, 2, 5/3, 4/3 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 2 ] ], [ [ 2, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "E6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0 ], [ 0, 3 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E8" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 1, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 1, 1, 1, 1, 0, 0, 0 ] ], isotropicspace := [ [ 1, 1 ], [ 0, 3 ] ], torsion := [ 3 ] ) ], type := [ "A2", "E6" ] ), rec( AutGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 5/4, 0 ], [ 0, 7/6 ] ], discg := [ 4, 6 ], proj := [ [ 4, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 6 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/4, 1/2, 3/4, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/6, 1/3, 1/2, 2/3, 5/6 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 5 ] ], [ [ 3, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A3", "A5" ], StabGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 4, 0 ], [ 0, 6 ] ], torsion := [ ] ) ], type := [ "A3", "A5" ] ), rec( AutGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 5/4, 0 ], [ 0, 3/4 ] ], discg := [ 4, 4 ], proj := [ [ 4, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 4 ], [ 0, -4 ], [ 0, 4 ], [ 0, 0 ] ], reps := [ [ 1/4, 1/2, 3/4, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 5/4, 3/4, 3/2, 1, 1/2 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 3 ] ], [ [ 3, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A3", "D5" ], StabGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 4, 0 ], [ 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E8" ], StabGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 1, 1, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 1, 0 ], [ 1, 0, 0, 1, 1, 1, 1, 0 ], [ 1, 0, 1, 1, 1, 1, 0, 0 ], [ 0, 1, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1 ], [ 1, 0, 1, 2, 1, 0, 0, 0 ] ], isotropicspace := [ [ 1, 1 ], [ 0, 4 ] ], torsion := [ 4 ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 0, 0, 0 ], [ 1, 1, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 2 ], [ 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A3", "D5" ] ), rec( AutGenerators := [ [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 6/5, 0 ], [ 0, 6/5 ] ], discg := [ 5, 5 ], proj := [ [ 5, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 5 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/5, 2/5, 3/5, 4/5, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/5, 2/5, 3/5, 4/5 ] ] ), discAutGenerators := [ [ [ 0, 1 ], [ 1, 0 ] ], [ [ 4, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A4", "A4" ], StabGenerators := [ [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 5, 0 ], [ 0, 5 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E8" ], StabGenerators := [ [ [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 1, 2, 1, 1, 0, 0 ], [ 0, 1, 1, 1, 1, 1, 1, 0 ], [ 1, 0, 0, 1, 1, 1, 1, 1 ], [ 1, 0, 1, 1, 1, 1, 1, 0 ], [ 1, 1, 1, 2, 1, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 1, 1 ], [ 1, 1, 1, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 1, 2 ], [ 0, 5 ] ], torsion := [ 5 ] ) ], type := [ "A4", "A4" ] ), rec( AutGenerators := [ [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 6/5, 0, 0 ], [ 0, 1, 1/2 ], [ 0, 1/2, 1 ] ], discg := [ 5, 2, 2 ], proj := [ [ 5, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 2 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 2, 0 ] ], reps := [ [ 1/5, 2/5, 3/5, 4/5, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 0, 1 ], [ 0, 1, 0 ] ], [ [ 1, 0, 0 ], [ 0, 1, 1 ], [ 0, 0, 1 ] ], [ [ 4, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A4", "D4" ], StabGenerators := [ [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 5, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 2 ] ], torsion := [ ] ) ], type := [ "A4", "D4" ] ), rec( AutGenerators := [ [ [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 10/9 ] ], discg := [ 9 ], proj := [ [ 9 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ] ], reps := [ [ 1/9, 2/9, 1/3, 4/9, 5/9, 2/3, 7/9, 8/9 ] ] ), discAutGenerators := [ [ [ 8 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A8" ], StabGenerators := [ [ [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 9 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E8" ], StabGenerators := [ [ [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 0 ], [ 0, 1, 1, 1, 1, 0, 0, 0 ], [ 1, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1 ], [ 0, 0, 1, 1, 1, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 0, 0, 0 ] ], isotropicspace := [ [ 3 ] ], torsion := [ 3 ] ) ], type := [ "A8" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 1, 1/2, 0, 0 ], [ 1/2, 1, 0, 0 ], [ 0, 0, 1, 1/2 ], [ 0, 0, 1/2, 1 ] ], discg := [ 2, 2, 2, 2 ], proj := [ [ 0, 2, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 2, 0, 0, 0 ], [ 0, 0, 0, 2 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 2, 0 ] ], reps := [ [ 1, 1/2, 1, 1/2, 0, 0, 0, 0 ], [ 1/2, 1/2, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 1, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D4", "D4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D8" ], StabGenerators := [ [ [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 1, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 0 ], [ 0, 1, 1, 1, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 1, 0, 1 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E8" ], StabGenerators := [ [ [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0 ], [ 1, 1, 1, 2, 1, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 1, 1 ], [ 1, 0, 0, 1, 1, 1, 1, 1 ], [ 1, 0, 1, 2, 1, 1, 1, 0 ], [ 0, 1, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 2, 2, 1, 0, 0 ] ], isotropicspace := [ [ 1, 0, 0, 1 ], [ 0, 1, 1, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ 2, 2 ] ) ], type := [ "D4", "D4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 0, 1/2 ], [ 1/2, 1 ] ], discg := [ 2, 2 ], proj := [ [ 0, 2 ], [ 0, 0 ], [ 0, 0 ], [ 0, -2 ], [ 0, 2 ], [ 0, -2 ], [ 0, 2 ], [ 2, 0 ] ], reps := [ [ 2, 3/2, 3, 5/2, 2, 3/2, 1, 1/2 ], [ 1/2, 1/2, 1, 1, 1, 1, 1, 1 ] ] ), discAutGenerators := [ [ [ 1, 1 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D8" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0 ], [ 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0 ], [ 1, 0, 1, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 1, 1, 0, 0, 0 ] ], isotropicspace := [ [ 1, 0 ], [ 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "D8" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ ] ], discg := [ ], proj := [ [ ] ], reps := [ ] ), discAutGenerators := [ ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0 ], [ 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ ], torsion := [ ] ) ], type := [ "E8" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, -2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 3/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 3/2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 3/2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 3/2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 3/2 ] ], discg := [ 2, 2, 2, 2, 2, 2, 2, 2, 2 ], proj := [ [ 2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 2 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1/2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1/2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1/2 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, -2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A1", "A1", "A1", "A1", "A1" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A1", "D4" ], StabGenerators := [ [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 1 ], [ 0, 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -4, -1, -1, -1, -1, -1, -1, -1 ], [ 0, -1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, -1, 0, -2, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, -2, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, -2, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0, -2, 0, 0 ], [ 0, -1, 0, 0, 0, 0, 0, -2, 0 ], [ 0, -1, 0, 0, 0, 0, 0, 0, -2 ] ], IsADE := false, StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ -1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 1, 1, 1, 1, 1, 1 ], [ 0, 0, -1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, -1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 0, 0, 2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "D6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 1, 1, 2, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 1, 1, 1, 1 ], [ 0, 0, 0, 0, 1, 1, 1, 1, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 0, 1, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D4", "D4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 1, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "E7" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 2, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 2, 1, 1, 0 ], [ 0, 0, 1, 1, 2, 2, 1, 1, 1 ], [ 0, 0, 1, 1, 1, 2, 2, 1, 1 ], [ 0, 0, 1, 0, 1, 2, 2, 2, 1 ], [ 0, 0, 1, 1, 2, 2, 2, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 1, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 1 ], [ 0, 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2, 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 1, 0 ], [ 0, 1, 1, 1, 1, 1, 1, 1, 0 ], [ 0, 1, 1, 2, 1, 1, 1, 0, 0 ], [ 0, 1, 1, 2, 2, 1, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 1, 1, 1 ], [ 0, 1, 0, 1, 1, 1, 1, 1, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 1, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 1, 1, 0, 0, 1, 1 ], [ 0, 0, 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2, 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 2, 2, 1, 0, 0, 0 ], [ 0, 1, 1, 2, 2, 2, 2, 1, 0 ], [ 0, 1, 1, 2, 3, 2, 2, 1, 1 ], [ 0, 1, 1, 2, 3, 3, 2, 2, 1 ], [ 0, 2, 1, 2, 3, 2, 2, 2, 1 ], [ 0, 2, 1, 2, 3, 3, 2, 1, 1 ], [ 0, 2, 1, 2, 4, 3, 2, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 1, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 1, 0, 1, 1, 0, 1 ], [ 0, 0, 0, 0, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2, 2, 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A1", "A1", "A1", "A1", "A1" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 3/2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 3/2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 3/2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 4/3 ] ], discg := [ 2, 2, 2, 2, 2, 2, 2, 3 ], proj := [ [ 2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 3 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1/2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A1", "A1", "A1", "A2" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 3 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A2", "D4" ], StabGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 3 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "D6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 1, 1, 2, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 1, 1, 1, 1 ], [ 0, 0, 0, 0, 1, 1, 1, 1, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 1, 1, 0, 1, 1, 0 ], [ 0, 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 3 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "E7" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 2, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 2, 1, 1, 0 ], [ 0, 0, 1, 1, 2, 2, 1, 1, 1 ], [ 0, 0, 1, 1, 1, 2, 2, 1, 1 ], [ 0, 0, 1, 0, 1, 2, 2, 2, 1 ], [ 0, 0, 1, 1, 2, 2, 2, 1, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 1, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 1, 0, 1, 0, 1, 1, 0 ], [ 0, 0, 1, 1, 1, 0, 1, 0 ], [ 0, 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 3 ] ], torsion := [ 2, 2, 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A1", "A1", "A1", "A2" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0, 0, 0 ], [ 0, 0, 0, 3/2, 0, 0, 0 ], [ 0, 0, 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 0, 0, 3/2, 0 ], [ 0, 0, 0, 0, 0, 0, 5/4 ] ], discg := [ 2, 2, 2, 2, 2, 2, 4 ], proj := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 4 ], [ 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 3 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A1", "A1", "A3" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "D5" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 1, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 2 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 4 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "D7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 1, 0, 0 ], [ 0, 0, 1, 1, 2, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 1, 1, 1, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 1, 2 ], [ 0, 0, 0, 1, 1, 0, 2 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 4 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D9" ], StabGenerators := [ [ [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 1, 0, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 0, 0 ], [ 1, 1, 2, 1, 1, 1, 0, 0, 0 ], [ 1, 1, 2, 2, 1, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 1, 1, 1, 1, 1, 1, 0 ] ], isotropicspace := [ [ 1, 0, 0, 0, 0, 1, 2 ], [ 0, 1, 0, 0, 1, 0, 2 ], [ 0, 0, 1, 1, 0, 0, 2 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 4 ] ], torsion := [ 2, 2, 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A3", "D4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 4 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A3", "D6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 1, 1, 2, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 1, 1, 1, 1 ], [ 0, 0, 0, 0, 1, 1, 1, 1, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 1, 0, 0, 1, 1, 1, 0 ], [ 0, 1, 1, 0, 1, 1, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 4 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D4", "D5" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 1, 1, 0 ] ], isotropicspace := [ [ 1, 0, 0, 0, 0, 1, 2 ], [ 0, 1, 1, 1, 1, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 4 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -6, -1, -1, -1, -1, -1, -2, -4, -6 ], [ -1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ -1, 0, -2, 0, 0, 0, 0, 0, 0 ], [ -1, 0, 0, -2, 0, 0, 0, 0, 0 ], [ -1, 0, 0, 0, -2, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, -2, 0, 0, 0 ], [ -2, 0, 0, 0, 0, 0, -2, -3, -4 ], [ -4, 0, 0, 0, 0, 0, -3, -6, -8 ], [ -6, 0, 0, 0, 0, 0, -4, -8, -12 ] ], IsADE := false, StabGenerators := [ [ [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ -2, 1, 1, 1, 1, 1, 0, 0, 1 ], [ 0, -1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -1 ] ], isotropicspace := [ [ 1, 1, 1, 1, 1, 1, 2 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A1", "A1", "A3" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0, 0, 0 ], [ 0, 0, 0, 3/2, 0, 0, 0 ], [ 0, 0, 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 0, 0, 4/3, 0 ], [ 0, 0, 0, 0, 0, 0, 4/3 ] ], discg := [ 2, 2, 2, 2, 2, 3, 3 ], proj := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 3 ], [ 0, 0, 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/3, 2/3, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A1", "A2", "A2" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 0, 3 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "A2", "D4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 1, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 0, 3 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A1", "A2", "A2" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0, 0 ], [ 0, 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 0, 3/2, 0 ], [ 0, 0, 0, 0, 0, 6/5 ] ], discg := [ 2, 2, 2, 2, 2, 5 ], proj := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 5 ], [ 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/5, 2/5, 3/5, 4/5 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 4 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A1", "A4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 5 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A4", "D4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 1, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 5 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A1", "A4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0, 0, 0 ], [ 0, 0, 0, 3/2, 0, 0, 0 ], [ 0, 0, 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1/2 ], [ 0, 0, 0, 0, 0, 1/2, 1 ] ], discg := [ 2, 2, 2, 2, 2, 2, 2 ], proj := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2 ], [ 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 0, 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A1", "D4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "D6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 0, 1 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "E7" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 1, 0, 0, 1, 1, 1, 1 ], [ 0, 0, 1, 0, 1, 2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 1, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 1, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 0, 1 ], [ 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 2, 1, 0, 0, 0 ], [ 0, 1, 1, 1, 2, 1, 1, 0, 0 ], [ 0, 1, 1, 2, 2, 2, 1, 0, 0 ], [ 0, 1, 1, 1, 2, 2, 1, 1, 0 ], [ 0, 1, 0, 1, 2, 2, 2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 1, 2, 2, 1, 1, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 1, 0, 1 ], [ 0, 0, 1, 0, 1, 1, 0 ], [ 0, 0, 0, 1, 1, 1, 1 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2, 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 1, 1, 1, 1, 1, 0, 0, 0 ], [ 0, 1, 1, 2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 1, 0, 0 ], [ 0, 1, 0, 1, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 1, 0, 1 ], [ 0, 0, 1, 1, 0, 0, 1 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D4", "D4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 1, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A1", "D4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0, 0 ], [ 0, 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 0, 4/3, 0 ], [ 0, 0, 0, 0, 0, 5/4 ] ], discg := [ 2, 2, 2, 2, 3, 4 ], proj := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 4 ], [ 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/3, 2/3, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 3 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A2", "A3" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A2", "D5" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 1, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 0, 2 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 4 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "D7" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 1, 0, 0 ], [ 0, 0, 1, 1, 2, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 1, 1, 1, 1, 0 ] ], isotropicspace := [ [ 1, 0, 0, 1, 0, 2 ], [ 0, 1, 1, 0, 0, 2 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 4 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A3", "D4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 1, 1, 1, 1, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A2", "A3" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 3/2, 0 ], [ 0, 0, 0, 0, 7/6 ] ], discg := [ 2, 2, 2, 2, 6 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 6 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/6, 1/3, 1/2, 2/3, 5/6 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 5 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "A5" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 6 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "E6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 1, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 1, 3 ], [ 0, 0, 0, 0, 6 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A5", "D4" ], StabGenerators := [ [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ], [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 1, 1, 1, 1, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 6 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "A5" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 3/2, 0 ], [ 0, 0, 0, 0, 3/4 ] ], discg := [ 2, 2, 2, 2, 4 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 4 ], [ 0, 0, 0, 0, -4 ], [ 0, 0, 0, 0, 4 ], [ 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 5/4, 3/4, 3/2, 1, 1/2 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 3 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A1", "D5" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "D7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 1, 1, 2 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 4 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D9" ], StabGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0, 0 ], [ 1, 1, 1, 1, 1, 0, 0, 0, 0 ], [ 1, 1, 2, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 1, 1, 0, 0, 0 ], [ 0, 1, 1, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 1, 0, 0, 1, 2 ], [ 0, 1, 1, 0, 2 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 4 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D4", "D5" ], StabGenerators := [ [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 1, 1, 1, 1, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A1", "D5" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0, 0 ], [ 0, 0, 0, 4/3, 0, 0 ], [ 0, 0, 0, 0, 4/3, 0 ], [ 0, 0, 0, 0, 0, 4/3 ] ], discg := [ 2, 2, 2, 3, 3, 3 ], proj := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 3, 0, 0 ], [ 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 3 ], [ 0, 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/3, 2/3, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/3, 2/3, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A2", "A2", "A2" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 3, 0, 0 ], [ 0, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 3 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "E6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 1, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 1 ], [ 0, 0, 0, 1, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 3 ] ], torsion := [ 3 ] ) ], type := [ "A1", "A1", "A1", "A2", "A2", "A2" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 4/3, 0 ], [ 0, 0, 0, 0, 6/5 ] ], discg := [ 2, 2, 2, 3, 5 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 5 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/3, 2/3, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/5, 2/5, 3/5, 4/5 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 4 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A2", "A4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 5 ] ], torsion := [ ] ) ], type := [ "A1", "A1", "A1", "A2", "A4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0, 0 ], [ 0, 0, 0, 4/3, 0, 0 ], [ 0, 0, 0, 0, 1, 1/2 ], [ 0, 0, 0, 0, 1/2, 1 ] ], discg := [ 2, 2, 2, 3, 2, 2 ], proj := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 3, 0, 0 ], [ 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2 ], [ 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/3, 2/3, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 0, 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A2", "D4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 3, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "D6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 0, 0, 1 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 3, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "E7" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 1, 0, 0, 1, 1, 1, 1 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 1, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 1, 1, 0 ] ], isotropicspace := [ [ 1, 0, 1, 0, 0, 1 ], [ 0, 1, 1, 0, 1, 0 ], [ 0, 0, 2, 0, 0, 0 ], [ 0, 0, 0, 3, 0, 0 ], [ 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2 ] ) ], type := [ "A1", "A1", "A1", "A2", "D4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 5/4, 0 ], [ 0, 0, 0, 0, 5/4 ] ], discg := [ 2, 2, 2, 4, 4 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 4, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 4 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/4, 1/2, 3/4, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A3", "A3" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 4, 0 ], [ 0, 0, 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "D6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 1 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 2 ], [ 0, 0, 0, 0, 4 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "E7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 1, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 1, 1 ], [ 0, 0, 1, 0, 0, 1, 1, 1, 1 ], [ 0, 0, 0, 1, 1, 1, 1, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 1, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 1, 1, 1 ], [ 0, 0, 0, 2, 2 ], [ 0, 0, 0, 0, 4 ] ], torsion := [ 4 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 2, 1, 0, 0, 0 ], [ 0, 1, 0, 1, 2, 2, 2, 1, 0 ], [ 0, 1, 1, 1, 2, 1, 1, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 1, 1 ], [ 0, 1, 1, 1, 2, 2, 1, 1, 0 ], [ 0, 1, 1, 2, 2, 1, 1, 1, 0 ], [ 0, 1, 0, 0, 1, 1, 1, 1, 1 ], [ 0, 1, 1, 2, 2, 2, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 1 ], [ 0, 0, 1, 1, 3 ], [ 0, 0, 0, 2, 2 ], [ 0, 0, 0, 0, 4 ] ], torsion := [ 4, 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 1, 2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 0 ], [ 0, 1, 1, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 1 ], [ 0, 1, 0, 1, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 1, 1, 0, 2 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 2 ], [ 0, 0, 0, 0, 4 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A3", "D5" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 1, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 1, 1, 0, 2 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 4, 0 ], [ 0, 0, 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "A3", "A3" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 3/2, 0, 0 ], [ 0, 0, 3/2, 0 ], [ 0, 0, 0, 8/7 ] ], discg := [ 2, 2, 2, 7 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 7 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/7, 2/7, 3/7, 4/7, 5/7, 6/7 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 6 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "A6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 7 ] ], torsion := [ ] ) ], type := [ "A1", "A1", "A1", "A6" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0 ], [ 0, 0, 3/2, 0, 0 ], [ 0, 0, 0, 1/2, 1/2 ], [ 0, 0, 0, 1/2, 1 ] ], discg := [ 2, 2, 2, 2, 2 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 2 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2 ], [ 0, 0, 0, 0, 2 ], [ 0, 0, 0, 2, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 3/2, 1, 2, 3/2, 1, 1/2 ], [ 0, 0, 0, 1/2, 1/2, 1, 1, 1, 1 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 1 ], [ 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "D6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "E7" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 1, 1, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 1, 0, 1, 2, 1, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 1, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 1, 1, 1, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 0 ], [ 0, 0, 1, 1, 1 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 1, 1, 0, 1 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A1", "D6" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 3/2, 0, 0 ], [ 0, 0, 3/2, 0 ], [ 0, 0, 0, 2/3 ] ], discg := [ 2, 2, 2, 3 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 3 ], [ 0, 0, 0, 3 ], [ 0, 0, 0, -3 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 2/3, 4/3, 2, 5/3, 4/3 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 2 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A1", "E6" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 3 ] ], torsion := [ ] ) ], type := [ "A1", "A1", "A1", "E6" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0 ], [ 0, 0, 4/3, 0, 0 ], [ 0, 0, 0, 4/3, 0 ], [ 0, 0, 0, 0, 5/4 ] ], discg := [ 2, 2, 3, 3, 4 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 3, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 4 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/3, 2/3, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/3, 2/3, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 3 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A2", "A2", "A3" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 3, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A2", "D5" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 1, 1, 0 ] ], isotropicspace := [ [ 1, 1, 0, 0, 2 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 3, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A2", "A2", "A3" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 3/2, 0, 0 ], [ 0, 0, 4/3, 0 ], [ 0, 0, 0, 7/6 ] ], discg := [ 2, 2, 3, 6 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 6 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/3, 2/3, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/6, 1/3, 1/2, 2/3, 5/6 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 5 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A2", "A5" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 6 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "E7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 1, 1, 1, 0 ], [ 0, 0, 1, 1, 1, 1, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 1, 2 ], [ 0, 0, 0, 6 ] ], torsion := [ 3 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 1, 0, 1, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 1, 1 ], [ 0, 1, 1, 1, 1, 1, 1, 0, 0 ], [ 0, 1, 0, 1, 2, 1, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 1, 1, 0 ], [ 0, 1, 0, 0, 1, 1, 1, 1, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 1, 0, 3 ], [ 0, 0, 1, 2 ], [ 0, 0, 0, 6 ] ], torsion := [ 6 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "E6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 1, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 1, 0, 3 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 6 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A2", "A5" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 3/2, 0, 0 ], [ 0, 0, 4/3, 0 ], [ 0, 0, 0, 3/4 ] ], discg := [ 2, 2, 3, 4 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 4 ], [ 0, 0, 0, -4 ], [ 0, 0, 0, 4 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/3, 2/3, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 5/4, 3/4, 3/2, 1, 1/2 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 3 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A2", "D5" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "D7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 1, 1, 0, 2 ], [ 0, 2, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A2", "D5" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 3/2, 0, 0 ], [ 0, 0, 5/4, 0 ], [ 0, 0, 0, 6/5 ] ], discg := [ 2, 2, 4, 5 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 4, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 5 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/4, 1/2, 3/4, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/5, 2/5, 3/5, 4/5 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 4 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A3", "A4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 4, 0 ], [ 0, 0, 0, 5 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A4", "D5" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 1, 1, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 1, 1, 2, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 4, 0 ], [ 0, 0, 0, 5 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A3", "A4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 3/2, 0, 0, 0 ], [ 0, 0, 5/4, 0, 0 ], [ 0, 0, 0, 1, 1/2 ], [ 0, 0, 0, 1/2, 1 ] ], discg := [ 2, 2, 4, 2, 2 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 4, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/4, 1/2, 3/4, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 0, 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 1 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 3, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A3", "D4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 4, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "D7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 1 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D9" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 1, 2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 0, 0 ], [ 1, 1, 1, 1, 1, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 1, 1, 0, 0, 0 ], [ 0, 1, 1, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 1, 1, 0, 0, 1 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 1 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2 ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A3", "D6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 1, 1, 0, 0, 1 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 4, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D4", "D5" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 1, 1, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 1, 1, 2, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 4, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "A3", "D4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 3/2, 0 ], [ 0, 0, 9/8 ] ], discg := [ 2, 2, 8 ], proj := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 8 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8 ] ] ), discAutGenerators := [ [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 7 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "A7" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 8 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "E7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 0 ], [ 0, 0, 1, 0, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 1 ], [ 0, 0, 1, 0, 0, 1, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 4 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 1, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 1, 1, 1, 1, 0 ], [ 0, 0, 1, 1, 1, 1, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 1, 2 ], [ 0, 0, 4 ] ], torsion := [ 4 ] ) ], type := [ "A1", "A1", "A7" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 3/2, 0 ], [ 0, 0, 1/4 ] ], discg := [ 2, 2, 4 ], proj := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 0 ], [ 0, 0, 4 ], [ 0, 0, -4 ], [ 0, 0, 4 ], [ 0, 0, -4 ], [ 0, 0, 4 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 7/4, 5/4, 5/2, 2, 3/2, 1, 1/2 ] ] ), discAutGenerators := [ [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 3 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "D7" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D9" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 1, 1, 2 ], [ 0, 2, 0 ], [ 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "D7" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 3/2, 0 ], [ 0, 0, 1/2 ] ], discg := [ 2, 2, 2 ], proj := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 0 ], [ 0, 0, 2 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, -2 ], [ 0, 0, 2 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 3/2, 1, 2, 3, 5/2, 2, 3/2 ] ] ), discAutGenerators := [ [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A1", "E7" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 0, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 1, 1 ], [ 0, 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A1", "E7" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 4/3, 0, 0, 0 ], [ 0, 0, 4/3, 0, 0 ], [ 0, 0, 0, 4/3, 0 ], [ 0, 0, 0, 0, 4/3 ] ], discg := [ 2, 3, 3, 3, 3 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 3, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 3, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 3 ], [ 0, 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/3, 2/3, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/3, 2/3, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/3, 2/3, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1/3, 2/3 ] ] ), discAutGenerators := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "A2", "A2", "A2" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 3, 0, 0, 0 ], [ 0, 0, 3, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 3 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "E6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 1, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 1 ], [ 0, 0, 0, 1, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 3, 0, 0, 0 ], [ 0, 0, 1, 1, 1 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 3 ] ], torsion := [ 3 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 2, 3, 2, 1, 0, 0 ], [ 0, 1, 0, 1, 2, 1, 1, 1, 0 ], [ 0, 1, 1, 1, 2, 2, 1, 1, 1 ], [ 0, 1, 1, 2, 2, 2, 1, 1, 0 ], [ 0, 1, 0, 1, 2, 2, 2, 1, 1 ], [ 0, 1, 1, 2, 2, 1, 1, 1, 1 ], [ 0, 1, 1, 1, 2, 2, 2, 1, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 1 ], [ 0, 0, 1, 1, 2 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 3 ] ], torsion := [ 3, 3 ] ) ], type := [ "A1", "A2", "A2", "A2", "A2" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 4/3, 0, 0 ], [ 0, 0, 4/3, 0 ], [ 0, 0, 0, 6/5 ] ], discg := [ 2, 3, 3, 5 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 5 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/3, 2/3, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/3, 2/3, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/5, 2/5, 3/5, 4/5 ] ] ), discAutGenerators := [ [ [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 4 ] ], [ [ 1, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "A2", "A4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 5 ] ], torsion := [ ] ) ], type := [ "A1", "A2", "A2", "A4" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 4/3, 0, 0, 0 ], [ 0, 0, 4/3, 0, 0 ], [ 0, 0, 0, 1, 1/2 ], [ 0, 0, 0, 1/2, 1 ] ], discg := [ 2, 3, 3, 2, 2 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 3, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 3, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/3, 2/3, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/3, 2/3, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 0, 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 1 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "A2", "D4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 3, 0, 0, 0 ], [ 0, 0, 3, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ ] ) ], type := [ "A1", "A2", "A2", "D4" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 4/3, 0, 0 ], [ 0, 0, 5/4, 0 ], [ 0, 0, 0, 5/4 ] ], discg := [ 2, 3, 4, 4 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 4, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 4 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/3, 2/3, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/4, 1/2, 3/4, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "A3", "A3" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 4, 0 ], [ 0, 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "D6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 1 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 2, 2 ], [ 0, 0, 0, 4 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "E7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 1, 2, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 1, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 1, 1 ], [ 0, 0, 1, 0, 0, 1, 1, 1, 1 ], [ 0, 0, 0, 1, 1, 1, 1, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 1, 1, 0 ] ], isotropicspace := [ [ 1, 0, 1, 1 ], [ 0, 3, 0, 0 ], [ 0, 0, 2, 2 ], [ 0, 0, 0, 4 ] ], torsion := [ 4 ] ) ], type := [ "A1", "A2", "A3", "A3" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 4/3, 0 ], [ 0, 0, 8/7 ] ], discg := [ 2, 3, 7 ], proj := [ [ 2, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 0 ], [ 0, 0, 7 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/3, 2/3, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/7, 2/7, 3/7, 4/7, 5/7, 6/7 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 6 ] ], [ [ 1, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "A6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 7 ] ], torsion := [ ] ) ], type := [ "A1", "A2", "A6" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 4/3, 0, 0 ], [ 0, 0, 1/2, 1/2 ], [ 0, 0, 1/2, 1 ] ], discg := [ 2, 3, 2, 2 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 2 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, -2 ], [ 0, 0, 0, 2 ], [ 0, 0, 2, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/3, 2/3, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 3/2, 1, 2, 3/2, 1, 1/2 ], [ 0, 0, 0, 1/2, 1/2, 1, 1, 1, 1 ] ] ), discAutGenerators := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 2, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "D6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "E7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 0, 0, 0 ] ], isotropicspace := [ [ 1, 0, 1, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A2", "D6" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 4/3, 0 ], [ 0, 0, 2/3 ] ], discg := [ 2, 3, 3 ], proj := [ [ 2, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 0 ], [ 0, 0, 3 ], [ 0, 0, 3 ], [ 0, 0, -3 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/3, 2/3, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 2/3, 4/3, 2, 5/3, 4/3 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 2 ] ], [ [ 1, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A2", "E6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 3 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 1, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 1, 1 ], [ 0, 0, 3 ] ], torsion := [ 3 ] ) ], type := [ "A1", "A2", "E6" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 5/4, 0 ], [ 0, 0, 7/6 ] ], discg := [ 2, 4, 6 ], proj := [ [ 2, 0, 0 ], [ 0, 4, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 6 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/4, 1/2, 3/4, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/6, 1/3, 1/2, 2/3, 5/6 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 5 ] ], [ [ 1, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A3", "A5" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 4, 0 ], [ 0, 0, 6 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A3", "E6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 1, 1, 0, 0 ] ], isotropicspace := [ [ 1, 0, 3 ], [ 0, 4, 0 ], [ 0, 0, 6 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A3", "A5" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 5/4, 0 ], [ 0, 0, 3/4 ] ], discg := [ 2, 4, 4 ], proj := [ [ 2, 0, 0 ], [ 0, 4, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 4 ], [ 0, 0, -4 ], [ 0, 0, 4 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/4, 1/2, 3/4, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 5/4, 3/4, 3/2, 1, 1/2 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 3 ] ], [ [ 1, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A3", "D5" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 4, 0 ], [ 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 1, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 1, 0 ], [ 0, 1, 0, 0, 1, 1, 1, 1, 0 ], [ 0, 1, 0, 1, 1, 1, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 1, 0, 1, 2, 1, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 1, 1 ], [ 0, 0, 4 ] ], torsion := [ 4 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 0, 0, 0 ], [ 0, 1, 1, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 2, 2 ], [ 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A1", "A3", "D5" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 6/5, 0 ], [ 0, 0, 6/5 ] ], discg := [ 2, 5, 5 ], proj := [ [ 2, 0, 0 ], [ 0, 5, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 5 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/5, 2/5, 3/5, 4/5, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/5, 2/5, 3/5, 4/5 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 0, 1 ], [ 0, 1, 0 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 4, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A4", "A4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 5, 0 ], [ 0, 0, 5 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 1, 2, 1, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 1, 1, 1, 0 ], [ 0, 1, 0, 0, 1, 1, 1, 1, 1 ], [ 0, 1, 0, 1, 1, 1, 1, 1, 0 ], [ 0, 1, 1, 1, 2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 1, 1 ], [ 0, 1, 1, 1, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 1, 2 ], [ 0, 0, 5 ] ], torsion := [ 5 ] ) ], type := [ "A1", "A4", "A4" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0 ], [ 0, 6/5, 0, 0 ], [ 0, 0, 1, 1/2 ], [ 0, 0, 1/2, 1 ] ], discg := [ 2, 5, 2, 2 ], proj := [ [ 2, 0, 0, 0 ], [ 0, 5, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 2 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 2, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/5, 2/5, 3/5, 4/5, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 0, 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 4, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A4", "D4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0 ], [ 0, 5, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ ] ) ], type := [ "A1", "A4", "D4" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0 ], [ 0, 10/9 ] ], discg := [ 2, 9 ], proj := [ [ 2, 0 ], [ 0, 9 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/9, 2/9, 1/3, 4/9, 5/9, 2/3, 7/9, 8/9 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 1, 0 ], [ 0, 8 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "A8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0 ], [ 0, 9 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 0 ], [ 0, 0, 1, 1, 1, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 1 ], [ 0, 0, 0, 1, 1, 1, 1, 0, 0 ], [ 0, 1, 1, 1, 1, 0, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0 ], [ 0, 3 ] ], torsion := [ 3 ] ) ], type := [ "A1", "A8" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0, 0, 0 ], [ 0, 1, 1/2, 0, 0 ], [ 0, 1/2, 1, 0, 0 ], [ 0, 0, 0, 1, 1/2 ], [ 0, 0, 0, 1/2, 1 ] ], discg := [ 2, 2, 2, 2, 2 ], proj := [ [ 2, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 0, 0, 2 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 1/2, 1, 1/2, 0, 0, 0, 0 ], [ 0, 1/2, 1/2, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 0, 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 1, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D4", "D4" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 1 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 1, 0, 1 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 1, 1, 1, 2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 1, 1 ], [ 0, 1, 0, 0, 1, 1, 1, 1, 1 ], [ 0, 1, 0, 1, 2, 1, 1, 1, 0 ], [ 0, 0, 1, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 2, 2, 1, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 1 ], [ 0, 0, 1, 1, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 2 ] ], torsion := [ 2, 2 ] ) ], type := [ "A1", "D4", "D4" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2, 0, 0 ], [ 0, 0, 1/2 ], [ 0, 1/2, 1 ] ], discg := [ 2, 2, 2 ], proj := [ [ 2, 0, 0 ], [ 0, 0, 2 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, -2 ], [ 0, 0, 2 ], [ 0, 0, -2 ], [ 0, 0, 2 ], [ 0, 2, 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 2, 3/2, 3, 5/2, 2, 3/2, 1, 1/2 ], [ 0, 1/2, 1/2, 1, 1, 1, 1, 1, 1 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 1 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "D8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 0, 1, 0, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 1, 0, 0, 1, 1, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "A1", "D8" ] ), rec( AutGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 3/2 ] ], discg := [ 2 ], proj := [ [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ] ], reps := [ [ 1/2, 0, 0, 0, 0, 0, 0, 0, 0 ] ] ), discAutGenerators := [ [ [ 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A1", "E8" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2 ] ], torsion := [ ] ) ], type := [ "A1", "E8" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0, 0, 0 ], [ 0, 4/3, 0, 0 ], [ 0, 0, 4/3, 0 ], [ 0, 0, 0, 5/4 ] ], discg := [ 3, 3, 3, 4 ], proj := [ [ 3, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 4 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/3, 2/3, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/3, 2/3, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 3 ] ], [ [ 2, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A2", "A2", "A3" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A3", "E6" ], StabGenerators := [ [ [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 1, 0 ], [ 0, 0, 0, 1, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 1 ], [ 0, 0, 0, 1, 1, 1, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ] ], isotropicspace := [ [ 1, 1, 1, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 3, 0 ], [ 0, 0, 0, 4 ] ], torsion := [ 3 ] ) ], type := [ "A2", "A2", "A2", "A3" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0, 0 ], [ 0, 4/3, 0 ], [ 0, 0, 7/6 ] ], discg := [ 3, 3, 6 ], proj := [ [ 3, 0, 0 ], [ 0, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 0 ], [ 0, 0, 6 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/3, 2/3, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/6, 1/3, 1/2, 2/3, 5/6 ] ] ), discAutGenerators := [ [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 5 ] ], [ [ 2, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A2", "A5" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 6 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "E7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 1, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 1, 1, 1, 0 ], [ 0, 0, 1, 1, 1, 1, 0, 0, 0 ] ], isotropicspace := [ [ 3, 0, 0 ], [ 0, 1, 2 ], [ 0, 0, 6 ] ], torsion := [ 3 ] ) ], type := [ "A2", "A2", "A5" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0, 0 ], [ 0, 4/3, 0 ], [ 0, 0, 3/4 ] ], discg := [ 3, 3, 4 ], proj := [ [ 3, 0, 0 ], [ 0, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 4 ], [ 0, 0, -4 ], [ 0, 0, 4 ], [ 0, 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/3, 2/3, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 5/4, 3/4, 3/2, 1, 1/2 ] ] ), discAutGenerators := [ [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 3 ] ], [ [ 2, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A2", "D5" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 4 ] ], torsion := [ ] ) ], type := [ "A2", "A2", "D5" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0, 0 ], [ 0, 5/4, 0 ], [ 0, 0, 6/5 ] ], discg := [ 3, 4, 5 ], proj := [ [ 3, 0, 0 ], [ 0, 0, 0 ], [ 0, 4, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 5 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/4, 1/2, 3/4, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1/5, 2/5, 3/5, 4/5 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 4 ] ], [ [ 1, 0, 0 ], [ 0, 3, 0 ], [ 0, 0, 1 ] ], [ [ 2, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A3", "A4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0, 0 ], [ 0, 4, 0 ], [ 0, 0, 5 ] ], torsion := [ ] ) ], type := [ "A2", "A3", "A4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0, 0, 0 ], [ 0, 5/4, 0, 0 ], [ 0, 0, 1, 1/2 ], [ 0, 0, 1/2, 1 ] ], discg := [ 3, 4, 2, 2 ], proj := [ [ 3, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 4, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 2 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 2, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/4, 1/2, 3/4, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 0, 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ] ], [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0 ], [ 0, 3, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 2, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A3", "D4" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0, 0, 0 ], [ 0, 4, 0, 0 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "D7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0, 0, 0 ], [ 0, 2, 0, 1 ], [ 0, 0, 2, 0 ], [ 0, 0, 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "A2", "A3", "D4" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0 ], [ 0, 9/8 ] ], discg := [ 3, 8 ], proj := [ [ 3, 0 ], [ 0, 0 ], [ 0, 8 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 7 ] ], [ [ 2, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "A7" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0 ], [ 0, 8 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "E7" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 0 ], [ 0, 0, 1, 0, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 1 ], [ 0, 0, 1, 0, 0, 1, 1, 0, 0 ] ], isotropicspace := [ [ 3, 0 ], [ 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "A2", "A7" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0 ], [ 0, 1/4 ] ], discg := [ 3, 4 ], proj := [ [ 3, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 4 ], [ 0, -4 ], [ 0, 4 ], [ 0, -4 ], [ 0, 4 ], [ 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 7/4, 5/4, 5/2, 2, 3/2, 1, 1/2 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 3 ] ], [ [ 2, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "D7" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0 ], [ 0, 4 ] ], torsion := [ ] ) ], type := [ "A2", "D7" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 4/3, 0 ], [ 0, 1/2 ] ], discg := [ 3, 2 ], proj := [ [ 3, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 2 ], [ 0, 0 ], [ 0, 0 ], [ 0, -2 ], [ 0, 2 ], [ 0, 0 ] ], reps := [ [ 1/3, 2/3, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 3/2, 1, 2, 3, 5/2, 2, 3/2 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 2, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, -2, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A2", "E7" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 3, 0 ], [ 0, 2 ] ], torsion := [ ] ) ], type := [ "A2", "E7" ] ), rec( AutGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 5/4, 0, 0 ], [ 0, 5/4, 0 ], [ 0, 0, 5/4 ] ], discg := [ 4, 4, 4 ], proj := [ [ 4, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 4, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 4 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], reps := [ [ 1/4, 1/2, 3/4, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/4, 1/2, 3/4, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1/4, 1/2, 3/4 ] ] ), discAutGenerators := [ [ [ 0, 1, 0 ], [ 0, 0, 1 ], [ 1, 0, 0 ] ], [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 3, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A3", "A3", "A3" ], StabGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 4, 0, 0 ], [ 0, 4, 0 ], [ 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A3", "D6" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 0 ], [ 0, 0, 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 1 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ] ], isotropicspace := [ [ 4, 0, 0 ], [ 0, 2, 2 ], [ 0, 0, 4 ] ], torsion := [ 2 ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D9" ], StabGenerators := [ [ [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 1, 0, 0 ], [ 1, 1, 2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 1, 0 ], [ 1, 1, 1, 1, 1, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 1, 1, 1, 1, 1, 0, 0, 0 ] ], isotropicspace := [ [ 2, 0, 2 ], [ 0, 2, 2 ], [ 0, 0, 4 ] ], torsion := [ 2, 2 ] ) ], type := [ "A3", "A3", "A3" ] ), rec( AutGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 5/4, 0 ], [ 0, 8/7 ] ], discg := [ 4, 7 ], proj := [ [ 4, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 7 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/4, 1/2, 3/4, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1/7, 2/7, 3/7, 4/7, 5/7, 6/7 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 6 ] ], [ [ 3, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A3", "A6" ], StabGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 4, 0 ], [ 0, 7 ] ], torsion := [ ] ) ], type := [ "A3", "A6" ] ), rec( AutGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 5/4, 0, 0 ], [ 0, 1/2, 1/2 ], [ 0, 1/2, 1 ] ], discg := [ 4, 2, 2 ], proj := [ [ 4, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 2 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, -2 ], [ 0, 0, 2 ], [ 0, 2, 0 ] ], reps := [ [ 1/4, 1/2, 3/4, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 3/2, 1, 2, 3/2, 1, 1/2 ], [ 0, 0, 0, 1/2, 1/2, 1, 1, 1, 1 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 1, 1 ], [ 0, 0, 1 ] ], [ [ 3, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A3", "D6" ], StabGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 4, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 2 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D9" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 0, 0, 0, 0 ], [ 1, 1, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 1 ], [ 0, 2, 0 ], [ 0, 0, 2 ] ], torsion := [ 2 ] ) ], type := [ "A3", "D6" ] ), rec( AutGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 5/4, 0 ], [ 0, 2/3 ] ], discg := [ 4, 3 ], proj := [ [ 4, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 3 ], [ 0, 3 ], [ 0, -3 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/4, 1/2, 3/4, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 2/3, 4/3, 2, 5/3, 4/3 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 2 ] ], [ [ 3, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -2, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A3", "E6" ], StabGenerators := [ [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 4, 0 ], [ 0, 3 ] ], torsion := [ ] ) ], type := [ "A3", "E6" ] ), rec( AutGenerators := [ [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 6/5, 0 ], [ 0, 7/6 ] ], discg := [ 5, 6 ], proj := [ [ 5, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 6 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ] ], reps := [ [ 1/5, 2/5, 3/5, 4/5, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1/6, 1/3, 1/2, 2/3, 5/6 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 5 ] ], [ [ 4, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A4", "A5" ], StabGenerators := [ [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 5, 0 ], [ 0, 6 ] ], torsion := [ ] ) ], type := [ "A4", "A5" ] ), rec( AutGenerators := [ [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 6/5, 0 ], [ 0, 3/4 ] ], discg := [ 5, 4 ], proj := [ [ 5, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 4 ], [ 0, -4 ], [ 0, 4 ], [ 0, 0 ] ], reps := [ [ 1/5, 2/5, 3/5, 4/5, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 5/4, 3/4, 3/2, 1, 1/2 ] ] ), discAutGenerators := [ [ [ 1, 0 ], [ 0, 3 ] ], [ [ 4, 0 ], [ 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A4", "D5" ], StabGenerators := [ [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 5, 0 ], [ 0, 4 ] ], torsion := [ ] ) ], type := [ "A4", "D5" ] ), rec( AutGenerators := [ [ [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 7/6, 0, 0 ], [ 0, 1, 1/2 ], [ 0, 1/2, 1 ] ], discg := [ 6, 2, 2 ], proj := [ [ 6, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 2 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 2, 0 ] ], reps := [ [ 1/6, 1/3, 1/2, 2/3, 5/6, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1/2, 1, 1/2 ], [ 0, 0, 0, 0, 0, 1/2, 1/2, 1, 1 ] ] ), discAutGenerators := [ [ [ 1, 0, 0 ], [ 0, 0, 1 ], [ 0, 1, 0 ] ], [ [ 1, 0, 0 ], [ 0, 1, 1 ], [ 0, 0, 1 ] ], [ [ 5, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A5", "D4" ], StabGenerators := [ [ [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 6, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 2 ] ], torsion := [ ] ) ], type := [ "A5", "D4" ] ), rec( AutGenerators := [ [ [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ] ] ], Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 11/10 ] ], discg := [ 10 ], proj := [ [ 10 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ] ], reps := [ [ 1/10, 1/5, 3/10, 2/5, 1/2, 3/5, 7/10, 4/5, 9/10 ] ] ), discAutGenerators := [ [ [ 9 ] ] ], overlattices := [ rec( Gram := [ [ -2, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "A9" ], StabGenerators := [ [ [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 10 ] ], torsion := [ ] ) ], type := [ "A9" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 1, 1/2, 0 ], [ 1/2, 1, 0 ], [ 0, 0, 3/4 ] ], discg := [ 2, 2, 4 ], proj := [ [ 0, 2, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ], [ 2, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 4 ], [ 0, 0, -4 ], [ 0, 0, 4 ], [ 0, 0, 0 ] ], reps := [ [ 1, 1/2, 1, 1/2, 0, 0, 0, 0, 0 ], [ 1/2, 1/2, 1, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 5/4, 3/4, 3/2, 1, 1/2 ] ] ), discAutGenerators := [ [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 3 ] ], [ [ 1, 1, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -2, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D4", "D5" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 4 ] ], torsion := [ ] ), rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D9" ], StabGenerators := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 0, 0 ], [ 0, 1, 1, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 2, 0, 0 ], [ 0, 1, 2 ], [ 0, 0, 4 ] ], torsion := [ 2 ] ) ], type := [ "D4", "D5" ] ), rec( AutGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], disc := rec( discf := [ [ 7/4 ] ], discg := [ 4 ], proj := [ [ 0 ], [ 4 ], [ -4 ], [ 4 ], [ -4 ], [ 4 ], [ -4 ], [ 4 ], [ 0 ] ], reps := [ [ 9/4, 7/4, 7/2, 3, 5/2, 2, 3/2, 1, 1/2 ] ] ), discAutGenerators := [ [ [ 3 ] ] ], overlattices := [ rec( Gram := [ [ -2, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, -2, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 1, -2, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -2, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, -2, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -2, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, -2, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, -2, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 1, -2 ] ], IsADE := [ "D9" ], StabGenerators := [ [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ], embRRbar := [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], isotropicspace := [ [ 4 ] ], torsion := [ ] ) ], type := [ "D9" ] ) ];