Artin representation data - 2.1368.12t18.b

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• artin_reps •

  Column	Type
  BadPrimes	jsonb
  Baselabel	text
  CharacterField	smallint
  Conductor	numeric
  Container	text
  Dets	text[]
  Dim	smallint
  GalConjSigns	jsonb
  Galn	smallint
  GaloisConjugates	jsonb
  GaloisConjugatesSigns	integer[]
  GaloisLabel	text
  Galt	integer
  HardPrimes	jsonb
  Hide	smallint
  Indicator	smallint
  Is_Even	boolean
  NFGal	jsonb
  NumBadPrimes	smallint
  Proj_GAP	integer[]
  Proj_Polynomial	numeric[]
  Proj_nTj	integer[]

  
  {'BadPrimes': [2, 3, 19], 'Baselabel': '2.1368.12t18.b', 'CharacterField': 3, 'Conductor': 1368, 'Container': '12t18', 'Dets': ['1.152.6t1.c.b', '1.152.6t1.c.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 12, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1], [0, -2], [2, 2], [0, 1], [-1, -1], [1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [19, 20, 15, 16, 21, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, -2], [-1, -1]], [[1], [2, 2], [0, 1]], [[1], [0, 1], [-1, -1]], [[1], [-1, -1], [0, 1]], [[1], [1], [1]], [[1], [0, 2], [-1, -1]], [[1], [-2, -2], [0, 1]], [[1], [0, -1], [-1, -1]], [[1], [1, 1], [0, 1]], [[1], [-1], [1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [-1, -1]], [[1]], [[1], [0, -1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1], [2, 2], [0, -2], [-1, -1], [0, 1], [1], [0], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [19, 20, 15, 16, 21, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [2, 2], [0, 1]], [[1], [0, -2], [-1, -1]], [[1], [-1, -1], [0, 1]], [[1], [0, 1], [-1, -1]], [[1], [1], [1]], [[1], [-2, -2], [0, 1]], [[1], [0, 2], [-1, -1]], [[1], [1, 1], [0, 1]], [[1], [0, -1], [-1, -1]], [[1], [-1], [1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0, 1]], [[1]], [[1], [1, 1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T18', 'Galt': 18, 'HardPrimes': [2, 3, 5, 13, 19, 691], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [9, -12, 16, -12, 5, 2, 2, -2, 5, -6, 3, -2, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [7, 13, -1, 1], 'Proj_nTj': [3, 2]}
• artin_field_data •

  Column	Type
  ArtinReps	jsonb
  ComplexConjugation	smallint
  ConjClasses	jsonb
  FrobResolvents	jsonb
  Frobs	jsonb
  G-Gens	jsonb
  G-Name	text
  Polynomial	jsonb
  QpRts	jsonb
  QpRts-minpoly	jsonb
  QpRts-p	integer
  QpRts-prec	integer
  Size	numeric
  TransitiveDegree	smallint

  
  {'ArtinReps': [{'GalConj': 1, 'Baselabel': '1.1.1t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.3.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.8.2t1.b', 'Character': [[1], [1], [-1], [-1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.24.2t1.a', 'Character': [[1], [-1], [1], [-1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.152.6t1.c', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.19.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.19.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.456.6t1.b', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [-1, 0], [-1, -1], [0, 1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.57.6t1.a', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [-1, 0], [1, 1], [0, -1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.152.6t1.c', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.57.6t1.a', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [-1, 0], [0, -1], [1, 1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.456.6t1.b', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [-1, 0], [0, 1], [-1, -1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.2888.3t2.b', 'Character': [[2], [2], [0], [0], [2], [2], [-1], [-1], [-1], [2], [2], [-1], [-1], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.25992.6t3.b', 'Character': [[2], [-2], [0], [0], [2], [2], [-1], [-1], [-1], [-2], [-2], [1], [1], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.152.6t5.a', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1, 0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.1368.12t18.b', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1, 0], [0, -2], [2, 2], [0, 1], [-1, -1], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.152.6t5.a', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1, 0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.1368.12t18.b', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1, 0], [2, 2], [0, -2], [-1, -1], [0, 1], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]}, {'Size': '1', 'Order': 2, 'Representative': [10, 11, 12, 7, 8, 9, 4, 5, 6, 1, 2, 3]}, {'Size': '3', 'Order': 2, 'Representative': [5, 6, 4, 3, 1, 2, 12, 10, 11, 8, 9, 7]}, {'Size': '3', 'Order': 2, 'Representative': [8, 9, 7, 12, 10, 11, 3, 1, 2, 5, 6, 4]}, {'Size': '1', 'Order': 3, 'Representative': [2, 3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10]}, {'Size': '1', 'Order': 3, 'Representative': [3, 1, 2, 6, 4, 5, 9, 7, 8, 12, 10, 11]}, {'Size': '2', 'Order': 3, 'Representative': [1, 2, 3, 6, 4, 5, 9, 7, 8, 10, 11, 12]}, {'Size': '2', 'Order': 3, 'Representative': [1, 2, 3, 5, 6, 4, 8, 9, 7, 10, 11, 12]}, {'Size': '2', 'Order': 3, 'Representative': [2, 3, 1, 6, 4, 5, 9, 7, 8, 11, 12, 10]}, {'Size': '1', 'Order': 6, 'Representative': [11, 12, 10, 8, 9, 7, 5, 6, 4, 2, 3, 1]}, {'Size': '1', 'Order': 6, 'Representative': [12, 10, 11, 9, 7, 8, 6, 4, 5, 3, 1, 2]}, {'Size': '2', 'Order': 6, 'Representative': [10, 11, 12, 9, 7, 8, 6, 4, 5, 1, 2, 3]}, {'Size': '2', 'Order': 6, 'Representative': [10, 11, 12, 8, 9, 7, 5, 6, 4, 1, 2, 3]}, {'Size': '2', 'Order': 6, 'Representative': [12, 10, 11, 8, 9, 7, 5, 6, 4, 3, 1, 2]}, {'Size': '3', 'Order': 6, 'Representative': [4, 5, 6, 2, 3, 1, 11, 12, 10, 7, 8, 9]}, {'Size': '3', 'Order': 6, 'Representative': [6, 4, 5, 1, 2, 3, 10, 11, 12, 9, 7, 8]}, {'Size': '3', 'Order': 6, 'Representative': [7, 8, 9, 11, 12, 10, 2, 3, 1, 4, 5, 6]}, {'Size': '3', 'Order': 6, 'Representative': [9, 7, 8, 10, 11, 12, 1, 2, 3, 6, 4, 5]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['108', '-12', '1'], 'ConjugacyClass': 7}, {'RootOf': ['24', '8', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['4', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-172', '33', '-2', '1'], 'ConjugacyClass': 3}, {'RootOf': ['1376', '132', '4', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['27', '6', '1'], 'ConjugacyClass': 12}, {'RootOf': ['6', '-4', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['16', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-4', '1'], 'ConjugacyClass': 6}, {'RootOf': ['164', '12', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-8', '1'], 'ConjugacyClass': 10}, {'RootOf': ['2', '1'], 'ConjugacyClass': 11}, {'RootOf': ['41', '-6', '1'], 'ConjugacyClass': 14}, {'RootOf': ['-20', '14', '-2', '1'], 'ConjugacyClass': 15}, {'RootOf': ['56', '-5', '-2', '1'], 'ConjugacyClass': 16}, {'RootOf': ['160', '56', '4', '1'], 'ConjugacyClass': 17}, {'RootOf': ['-448', '-20', '4', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [6, 6]}], 'Frobs': [11, 8, 15, 4, 14, 18, 11, 8, 16, 16, 4, 4, 13, 6, 16, 16, 13, 18, 7, 15, 8, 17, 14, 10, 8, 16, 4, 2, 17, 14, 18, 13, 12, 7, 15, 4, 17, 9, 16, 15, 14, 18, 3, 6, 3, 18, 6, 17, 14, 4, 13, 3, 7, 12, 12, 15, 15, 17, 4, 12, 8, 3, 8, 3, 7, 16, 9, 8, 13, 4, 14, 15, 18, 4, 1, 15, 16, 17, 13, 7, 2, 17, 16, 5, 17, 12, 14, 9, 15, 4, 14, 16, 4, 11, 8, 16, 16, 14, 5, 18, 5, 16, 14, 2, 9, 9, 11, 12, 16, 9, 4, 17, 12, 1, 18, 13, 8, 3, 3, 10, 18, 1, 3, 2, 1, 15, 18, 15, 17, 4, 8, 15, 18, 17, 14, 5, 16, 9, 3, 14, 5, 16, 18, 12, 4, 15, 17, 13, 7, 3, 17, 14, 7, 16, 8, 3, 4, 13, 7, 16, 11, 13, 17, 13, 14, 15, 17, 18], 'G-Gens': [[4, 5, 6, 2, 3, 1, 11, 12, 10, 7, 8, 9], [10, 11, 12, 7, 8, 9, 4, 5, 6, 1, 2, 3], [1, 2, 3, 6, 4, 5, 9, 7, 8, 10, 11, 12], [11, 12, 10, 8, 9, 7, 5, 6, 4, 2, 3, 1]], 'G-Name': 'C6*S3', 'Polynomial': [9, -12, 16, -12, 5, 2, 2, -2, 5, -6, 3, -2, 1], 'QpRts': [['240363', '-576193', '-671669', '-1592310', '2073947', '2359928'], ['-1214359', '-29053', '1068477', '187703', '689625', '1547931'], ['1937443', '605246', '-396808', '1404607', '2063237', '918950'], ['-1793181', '-1751664', '2344109', '-1103763', '-2081741', '2106860'], ['-1614344', '1807917', '627865', '-2390505', '2211185', '-1659234'], ['-2382730', '-56253', '1854835', '-1332541', '-129444', '-447626'], ['-2277210', '2170998', '1949795', '2377537', '289812', '-1110064'], ['-258972', '-854612', '-988326', '-912262', '1750079', '-1141272'], ['-1327180', '-1316386', '-961469', '-1465275', '-2039891', '2251336'], ['-1195868', '114181', '1680840', '1588100', '1625994', '-1999175'], ['301963', '360300', '2248829', '-666247', '-2051716', '-647809'], ['-69541', '-474481', '897140', '-921853', '425722', '-2179825']], 'QpRts-minpoly': [2, 11, 11, 10, 0, 0, 1], 'QpRts-p': 13, 'QpRts-prec': 6, 'Size': 36, 'TransitiveDegree': 12}