Database - lat_lattices (Integral lattices)

Formats: - HTML - YAML - JSON - 2026-03-01T15:10:29.221602 - next page

Query: /api/lat_lattices/?_offset=0

Column	Type
aut	numeric
base_label	text
class_number	smallint
comments	text
density	numeric
det	bigint
dim	smallint
genus_reps	jsonb
gram	jsonb
hermite	numeric
index	smallint
kissing	bigint
label	text
level	bigint
minimum	integer
name	jsonb
shortest	jsonb
theta_series	jsonb

0. label: 1.2.4.1.1
   {'aut': 2, 'base_label': '1.2.4.1', 'class_number': 1, 'comments': 'This is a root lattice', 'density': {'__RealLiteral__': 0, 'data': '1.00000000000000000000000000000', 'prec': 103}, 'det': 2, 'dim': 1, 'genus_reps': [[[2]]], 'gram': [[2]], 'hermite': {'__RealLiteral__': 0, 'data': '1.00000000000000000000000000000', 'prec': 103}, 'index': 1, 'kissing': 2, 'label': '1.2.4.1.1', 'level': 4, 'minimum': 2, 'name': ['A1'], 'shortest': [[1]], 'theta_series': [1, 0, 2, 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, 0, 0, 0, 0, 2, 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, 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, 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, 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, 0, 0, 0, 0, 0, 0]}
1. label: 2.1.2.1.1
   {'aut': 8, 'base_label': '2.1.2.1', 'class_number': 1, 'comments': 'This is the square lattice Z2', 'density': {'__RealLiteral__': 0, 'data': '0.785398163397448309615660845820', 'prec': 107}, 'det': 1, 'dim': 2, 'genus_reps': [[[1, 0], [0, 1]]], 'gram': [[1, 0], [0, 1]], 'hermite': {'__RealLiteral__': 0, 'data': '1.00000000000000000000000000000', 'prec': 103}, 'index': 1, 'kissing': 4, 'label': '2.1.2.1.1', 'level': 2, 'minimum': 1, 'name': ['Z2', 'I2'], 'shortest': [[1, 0], [0, 1]], 'theta_series': [1, 4, 4, 0, 4, 8, 0, 0, 4, 4, 8, 0, 0, 8, 0, 0, 4, 8, 4, 0, 8, 0, 0, 0, 0, 12, 8, 0, 0, 8, 0, 0, 4, 0, 8, 0, 4, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 4, 12, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 4, 16, 0, 0, 8, 0, 0, 0, 4, 8, 8, 0, 0, 0, 0, 0, 8, 4, 8, 0, 0, 16, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 4, 0, 12, 8, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 0, 4, 8, 0, 0, 16, 0, 0, 4, 0, 16, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 4, 16, 8, 0, 8, 8, 0]}
2. label: 2.2.4.1.1
   {'aut': 4, 'base_label': '2.2.4.1', 'class_number': 1, 'comments': '', 'density': {'__RealLiteral__': 0, 'data': '0.555360367269795780876985123758', 'prec': 107}, 'det': 2, 'dim': 2, 'genus_reps': [[[1, 0], [0, 2]]], 'gram': [[1, 0], [0, 2]], 'hermite': {'__RealLiteral__': 0, 'data': '0.707106781186547524400844362105', 'prec': 107}, 'index': 1, 'kissing': 2, 'label': '2.2.4.1.1', 'level': 4, 'minimum': 1, 'name': '', 'shortest': [[1, 0]], 'theta_series': [1, 2, 2, 4, 2, 0, 4, 0, 2, 6, 0, 4, 4, 0, 0, 0, 2, 4, 6, 4, 0, 0, 4, 0, 4, 2, 0, 8, 0, 0, 0, 0, 2, 8, 4, 0, 6, 0, 4, 0, 0, 4, 0, 4, 4, 0, 0, 0, 4, 2, 2, 8, 0, 0, 8, 0, 0, 8, 0, 4, 0, 0, 0, 0, 2, 0, 8, 4, 4, 0, 0, 0, 6, 4, 0, 4, 4, 0, 0, 0, 0, 10, 4, 4, 0, 0, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 2, 12, 2, 0, 8, 0, 0, 0, 0, 4, 8, 0, 0, 0, 0, 4, 8, 0, 0, 0, 4, 0, 0, 6, 0, 8, 0, 0, 0, 0, 2, 8, 0, 4, 8, 0, 4, 0, 4, 4, 0, 4, 0, 0, 0, 0, 6, 0, 4, 4, 0, 0, 4]}
3. label: 2.3.3.1.1
   {'aut': 12, 'base_label': '2.3.3.1', 'class_number': 1, 'comments': 'This is a root lattice', 'density': {'__RealLiteral__': 0, 'data': '0.906899682117108925297039128820', 'prec': 107}, 'det': 3, 'dim': 2, 'genus_reps': [[[2, 1], [1, 2]]], 'gram': [[2, -1], [-1, 2]], 'hermite': {'__RealLiteral__': 0, 'data': '1.15470053837925152901829756100', 'prec': 103}, 'index': 1, 'kissing': 6, 'label': '2.3.3.1.1', 'level': 3, 'minimum': 2, 'name': ['A2'], 'shortest': [[1, 0], [1, 1], [0, 1]], 'theta_series': [1, 0, 6, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, 12, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, 12, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 12, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 12, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 12, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 18, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 12, 0, 6, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 6]}
4. label: 2.3.6.1.1
   {'aut': 4, 'base_label': '2.3.6.1', 'class_number': 1, 'comments': '', 'density': {'__RealLiteral__': 0, 'data': '0.453449841058554462648519564411', 'prec': 107}, 'det': 3, 'dim': 2, 'genus_reps': [[[1, 0], [0, 3]]], 'gram': [[1, 0], [0, 3]], 'hermite': {'__RealLiteral__': 0, 'data': '0.577350269189625764509148780502', 'prec': 107}, 'index': 1, 'kissing': 2, 'label': '2.3.6.1.1', 'level': 6, 'minimum': 1, 'name': '', 'shortest': [[1, 0]], 'theta_series': [1, 2, 0, 2, 6, 0, 0, 4, 0, 2, 0, 0, 6, 4, 0, 0, 6, 0, 0, 4, 0, 4, 0, 0, 0, 2, 0, 2, 12, 0, 0, 4, 0, 0, 0, 0, 6, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 6, 6, 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 6, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 2, 12, 0, 0, 4, 0, 2, 0, 0, 12, 0, 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, 6, 4, 0, 4, 12, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 12, 0, 0, 4, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 6, 12, 0, 0]}
5. label: 2.4.8.1.1
   {'aut': 4, 'base_label': '2.4.8.1', 'class_number': 1, 'comments': '', 'density': {'__RealLiteral__': 0, 'data': '0.392699081698724154807830422910', 'prec': 107}, 'det': 4, 'dim': 2, 'genus_reps': [[[1, 0], [0, 4]]], 'gram': [[1, 0], [0, 4]], 'hermite': {'__RealLiteral__': 0, 'data': '0.500000000000000000000000000000', 'prec': 107}, 'index': 1, 'kissing': 2, 'label': '2.4.8.1.1', 'level': 8, 'minimum': 1, 'name': '', 'shortest': [[1, 0]], 'theta_series': [1, 2, 0, 0, 4, 4, 0, 0, 4, 2, 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 8, 0, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 8, 4, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 8, 0, 0, 8, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 8, 2, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 12, 4, 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 8, 4, 0, 0, 0, 2, 0, 0, 0, 8, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 4, 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 8, 4, 0]}
6. label: 2.5.10.1.1
   {'aut': 4, 'base_label': '2.5.10.1', 'class_number': 1, 'comments': '', 'density': {'__RealLiteral__': 0, 'data': '0.351240736552036319657818732160', 'prec': 107}, 'det': 5, 'dim': 2, 'genus_reps': [[[1, 0], [0, 5]]], 'gram': [[1, 0], [0, 5]], 'hermite': {'__RealLiteral__': 0, 'data': '0.447213595499957939281834733746', 'prec': 107}, 'index': 1, 'kissing': 2, 'label': '2.5.10.1.1', 'level': 10, 'minimum': 1, 'name': '', 'shortest': [[1, 0]], 'theta_series': [1, 2, 0, 0, 2, 2, 4, 0, 0, 6, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 8, 0, 0, 4, 2, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 4, 0, 0, 0, 6, 4, 0, 0, 6, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 10, 0, 0, 8, 0, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 2, 4, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 0, 2, 12, 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 8, 0, 0, 6, 4, 0, 0, 0, 4, 4]}
7. label: 2.5.10.1.2
   {'aut': 4, 'base_label': '2.5.10.1', 'class_number': 1, 'comments': '', 'density': {'__RealLiteral__': 0, 'data': '0.702481473104072639315637464320', 'prec': 107}, 'det': 5, 'dim': 2, 'genus_reps': [[[2, 1], [1, 3]]], 'gram': [[2, 1], [1, 3]], 'hermite': {'__RealLiteral__': 0, 'data': '0.894427190999915878563669467492', 'prec': 107}, 'index': 2, 'kissing': 2, 'label': '2.5.10.1.2', 'level': 10, 'minimum': 2, 'name': '', 'shortest': [[1, 0]], 'theta_series': [1, 0, 2, 4, 0, 0, 0, 4, 2, 0, 2, 0, 4, 0, 0, 4, 0, 0, 6, 0, 0, 0, 0, 4, 0, 0, 0, 8, 4, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 2, 0, 8, 4, 0, 0, 0, 4, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 8, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 4, 0, 0, 0, 4, 8, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 4, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0]}
8. label: 2.6.12.1.1
   {'aut': 4, 'base_label': '2.6.12.1', 'class_number': 1, 'comments': '', 'density': {'__RealLiteral__': 0, 'data': '0.320637457540466023886009089918', 'prec': 107}, 'det': 6, 'dim': 2, 'genus_reps': [[[1, 0], [0, 6]]], 'gram': [[1, 0], [0, 6]], 'hermite': {'__RealLiteral__': 0, 'data': '0.408248290463863016366214012451', 'prec': 107}, 'index': 1, 'kissing': 2, 'label': '2.6.12.1.1', 'level': 12, 'minimum': 1, 'name': '', 'shortest': [[1, 0]], 'theta_series': [1, 2, 0, 0, 2, 0, 2, 4, 0, 2, 4, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 4, 0, 2, 6, 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 2, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 2, 8, 0, 0, 4, 0, 4, 0, 0, 4, 2, 0, 0, 0, 0, 0, 8, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 0, 0, 0, 2, 4, 0, 0, 6, 0, 0, 4, 0, 8, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 6, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 8, 0, 0, 0, 0, 6]}
9. label: 2.6.12.1.2
   {'aut': 4, 'base_label': '2.6.12.1', 'class_number': 1, 'comments': '', 'density': {'__RealLiteral__': 0, 'data': '0.641274915080932047772018179835', 'prec': 107}, 'det': 6, 'dim': 2, 'genus_reps': [[[2, 0], [0, 3]]], 'gram': [[2, 0], [0, 3]], 'hermite': {'__RealLiteral__': 0, 'data': '0.816496580927726032732428024902', 'prec': 107}, 'index': 2, 'kissing': 2, 'label': '2.6.12.1.2', 'level': 12, 'minimum': 2, 'name': '', 'shortest': [[1, 0]], 'theta_series': [1, 0, 2, 2, 0, 4, 0, 0, 2, 0, 0, 4, 2, 0, 4, 0, 0, 0, 2, 0, 4, 4, 0, 0, 0, 0, 0, 2, 0, 4, 4, 0, 2, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 2, 0, 6, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 6, 0, 8, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 6, 4, 0, 4, 0, 0, 0, 0, 0, 4, 2, 0, 8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 8, 4, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 4, 6, 0, 4, 0]}
10. label: 2.7.7.1.1
    {'aut': 4, 'base_label': '2.7.7.1', 'class_number': 1, 'comments': '', 'density': {'__RealLiteral__': 0, 'data': '0.593705205861862974392312648974', 'prec': 107}, 'det': 7, 'dim': 2, 'genus_reps': [[[2, 1], [1, 4]]], 'gram': [[2, 1], [1, 4]], 'hermite': {'__RealLiteral__': 0, 'data': '0.755928946018454454429033072468', 'prec': 107}, 'index': 1, 'kissing': 2, 'label': '2.7.7.1.1', 'level': 7, 'minimum': 2, 'name': '', 'shortest': [[1, 0]], 'theta_series': [1, 0, 2, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 8, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 10, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 12, 0, 0, 0, 8, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 14, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 8, 0, 0, 0, 8, 0, 0]}
11. label: 2.7.14.1.1
    {'aut': 4, 'base_label': '2.7.14.1', 'class_number': 1, 'comments': '', 'density': {'__RealLiteral__': 0, 'data': '0.296852602930931487196156324487', 'prec': 107}, 'det': 7, 'dim': 2, 'genus_reps': [[[1, 0], [0, 7]]], 'gram': [[1, 0], [0, 7]], 'hermite': {'__RealLiteral__': 0, 'data': '0.377964473009227227214516536234', 'prec': 107}, 'index': 1, 'kissing': 2, 'label': '2.7.14.1.1', 'level': 14, 'minimum': 1, 'name': '', 'shortest': [[1, 0]], 'theta_series': [1, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 4, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 2, 4, 0, 0, 8, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 10, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 6, 4, 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 4, 12, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 4, 4, 0]}
12. label: 2.8.16.1.1
    {'aut': 4, 'base_label': '2.8.16.1', 'class_number': 1, 'comments': '', 'density': {'__RealLiteral__': 0, 'data': '0.277680183634897890438492561879', 'prec': 107}, 'det': 8, 'dim': 2, 'genus_reps': [[[1, 0], [0, 8]]], 'gram': [[1, 0], [0, 8]], 'hermite': {'__RealLiteral__': 0, 'data': '0.353553390593273762200422181053', 'prec': 107}, 'index': 1, 'kissing': 2, 'label': '2.8.16.1.1', 'level': 16, 'minimum': 1, 'name': '', 'shortest': [[1, 0]], 'theta_series': [1, 2, 0, 0, 2, 0, 0, 0, 2, 6, 0, 0, 4, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 2, 8, 0, 0, 6, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 6, 4, 0, 0, 4, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 2, 8, 0, 0, 8, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0]}
13. label: 2.8.16.1.2
    {'aut': 4, 'base_label': '2.8.16.1', 'class_number': 1, 'comments': '', 'density': {'__RealLiteral__': 0, 'data': '0.833040550904693671315477685636', 'prec': 107}, 'det': 8, 'dim': 2, 'genus_reps': [[[3, 1], [1, 3]]], 'gram': [[3, -1], [-1, 3]], 'hermite': {'__RealLiteral__': 0, 'data': '1.06066017177982128660126654316', 'prec': 103}, 'index': 2, 'kissing': 4, 'label': '2.8.16.1.2', 'level': 16, 'minimum': 3, 'name': '', 'shortest': [[1, 0], [0, 1]], 'theta_series': [1, 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 4, 4, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 8, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 4, 4, 0, 0, 0, 6, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 12, 2, 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 2, 0, 0, 4, 8, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0]}
14. label: 2.9.18.1.1
    {'aut': 4, 'base_label': '2.9.18.1', 'class_number': 1, 'comments': '', 'density': {'__RealLiteral__': 0, 'data': '0.261799387799149436538553615273', 'prec': 107}, 'det': 9, 'dim': 2, 'genus_reps': [[[1, 0], [0, 9]]], 'gram': [[1, 0], [0, 9]], 'hermite': {'__RealLiteral__': 0, 'data': '0.333333333333333333333333333333', 'prec': 107}, 'index': 1, 'kissing': 2, 'label': '2.9.18.1.1', 'level': 18, 'minimum': 1, 'name': '', 'shortest': [[1, 0]], 'theta_series': [1, 2, 0, 0, 2, 0, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 4, 0, 0, 6, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 4, 0, 0]}
15. label: 2.9.18.1.2
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16. label: 2.10.20.1.1
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17. label: 2.10.20.1.2
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18. label: 2.11.11.1.1
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19. label: 2.12.24.1.1
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20. label: 2.12.24.1.2
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21. label: 2.13.26.1.1
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22. label: 2.13.26.1.2
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23. label: 2.14.28.1.1
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24. label: 2.15.15.1.1
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25. label: 2.15.15.1.2
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26. label: 2.15.30.1.1
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27. label: 2.15.30.1.2
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28. label: 2.16.32.1.1
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29. label: 2.16.32.1.2
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30. label: 2.17.34.1.1
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31. label: 2.18.36.1.1
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32. label: 2.18.36.1.2
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33. label: 2.19.19.1.1
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34. label: 2.20.40.1.1
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35. label: 2.21.42.1.1
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36. label: 2.21.42.1.2
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37. label: 2.21.42.1.3
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38. label: 2.21.42.1.4
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39. label: 2.22.44.1.1
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40. label: 2.22.44.1.2
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41. label: 2.24.48.1.1
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42. label: 2.24.48.1.2
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43. label: 2.24.48.1.3
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44. label: 2.24.48.1.4
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45. label: 2.25.50.1.1
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46. label: 2.25.50.1.2
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47. label: 2.27.27.1.1
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48. label: 2.28.56.1.1
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49. label: 2.28.56.1.2
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50. label: 2.30.60.1.1
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51. label: 2.30.60.1.2
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52. label: 2.30.60.1.3
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53. label: 2.30.60.1.4
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54. label: 2.32.64.1.1
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55. label: 2.33.66.1.1
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56. label: 2.33.66.1.2
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57. label: 2.33.66.1.3
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58. label: 2.33.66.1.4
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59. label: 2.34.68.1.1
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60. label: 2.35.35.1.1
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61. label: 2.35.35.1.2
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62. label: 2.36.72.1.1
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63. label: 2.37.74.1.1
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64. label: 2.37.74.1.2
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65. label: 2.39.39.1.1
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66. label: 2.39.78.1.1
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67. label: 2.40.80.1.1
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68. label: 2.40.80.1.2
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69. label: 2.40.80.1.3
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70. label: 2.40.80.1.4
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71. label: 2.42.84.1.1
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72. label: 2.42.84.1.2
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73. label: 2.42.84.1.3
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74. label: 2.42.84.1.4
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75. label: 2.43.43.1.1
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76. label: 2.45.90.1.1
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77. label: 2.45.90.1.2
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78. label: 2.45.90.1.3
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79. label: 2.45.90.1.4
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80. label: 2.46.92.1.1
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81. label: 2.48.96.1.1
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82. label: 2.48.96.1.2
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83. label: 2.48.96.1.3
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84. label: 2.48.96.1.4
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85. label: 2.49.98.1.1
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86. label: 2.51.51.1.1
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87. label: 2.51.51.1.2
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88. label: 2.52.104.1.1
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89. label: 2.55.55.1.1
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90. label: 2.55.110.1.1
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91. label: 2.56.112.1.1
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92. label: 2.56.112.1.2
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93. label: 2.57.114.1.1
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94. label: 2.57.114.1.2
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95. label: 2.57.114.1.3
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96. label: 2.57.114.1.4
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97. label: 2.58.116.1.1
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98. label: 2.58.116.1.2
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99. label: 2.60.120.1.1
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