Artin representation data - 4.2433600.8t22.k

Formats: - HTML - YAML - JSON - 2024-05-11T15:41:18.297459

• 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, 5, 13], 'Baselabel': '4.2433600.8t22.k', 'CharacterField': 1, 'Conductor': 2433600, 'Container': '8t22', 'Dets': ['1.1.1t1.a.a'], 'Dim': 4, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[4], [-4], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [18, 19, 18, 3, 19, 12, 3, 3, 3, 12, 12], 'LocalFactors': [[[1], [-4], [6], [-4], [1]], [[1], [4], [6], [4], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [2], [0], [1]], [[1], [0], [2], [0], [1]], [[1], [0], [2], [0], [1]], [[1], [0], [2], [0], [1]], [[1], [0], [2], [0], [1]], [[1], [0], [2], [0], [1]], [[1], [0], [-1]], [[1], [0], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T22', 'Galt': 22, 'HardPrimes': [2, 3, 5, 11, 13, 19, 23, 31, 83, 653, 883], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-16, 4, 49, 4, -17, -8, -1, 0, 1], 'NumBadPrimes': 4, 'Proj_GAP': [16, 14], 'Proj_Polynomial': [1, -68, 4684, 3616, 19433, -21740, 45816, -22604, 19562, -4648, 4842, -1000, 539, -64, 34, -4, 1], 'Proj_nTj': [16, 3]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.5.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [-1], [1], [1], [-1], [1], [1], [-1], [1], [-1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.104.2t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [1], [-1], [1], [-1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.520.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [-1], [-1], [-1], [1], [-1], [1], [1], [1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.120.2t1.b', 'Character': [[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.b', 'Character': [[1], [1], [1], [-1], [-1], [1], [1], [-1], [-1], [1], [1], [1], [-1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.39.2t1.a', 'Character': [[1], [1], [1], [-1], [-1], [1], [-1], [1], [1], [-1], [1], [-1], [-1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.195.2t1.a', 'Character': [[1], [1], [-1], [1], [-1], [-1], [-1], [1], [-1], [-1], [1], [1], [-1], [-1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.1560.2t1.b', 'Character': [[1], [1], [1], [1], [-1], [-1], [1], [-1], [-1], [-1], [-1], [1], [1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.312.2t1.b', 'Character': [[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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.15.2t1.a', 'Character': [[1], [1], [1], [1], [-1], [-1], [-1], [1], [1], [1], [-1], [-1], [1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.65.2t1.a', 'Character': [[1], [1], [1], [-1], [1], [-1], [1], [1], [1], [-1], [-1], [1], [-1], [-1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.13.2t1.a', 'Character': [[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.a', 'Character': [[1], [1], [-1], [1], [1], [1], [-1], [-1], [1], [1], [-1], [1], [-1], [-1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.40.2t1.a', 'Character': [[1], [1], [1], [-1], [1], [-1], [-1], [-1], [-1], [1], [-1], [-1], [-1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.2433600.8t22.k', 'Character': [[4], [-4], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 5, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [4, 8, 5, 1, 3, 7, 6, 2]}, {'Size': '2', 'Order': 2, 'Representative': [6, 3, 2, 7, 8, 1, 4, 5]}, {'Size': '2', 'Order': 2, 'Representative': [8, 4, 6, 2, 7, 3, 5, 1]}, {'Size': '2', 'Order': 2, 'Representative': [4, 8, 3, 1, 5, 6, 7, 2]}, {'Size': '2', 'Order': 2, 'Representative': [2, 1, 6, 8, 7, 3, 5, 4]}, {'Size': '2', 'Order': 2, 'Representative': [4, 2, 5, 1, 3, 6, 7, 8]}, {'Size': '2', 'Order': 2, 'Representative': [1, 8, 5, 4, 3, 6, 7, 2]}, {'Size': '2', 'Order': 2, 'Representative': [7, 3, 2, 6, 8, 4, 1, 5]}, {'Size': '2', 'Order': 2, 'Representative': [5, 6, 4, 3, 1, 2, 8, 7]}, {'Size': '2', 'Order': 2, 'Representative': [3, 6, 1, 5, 4, 2, 8, 7]}, {'Size': '2', 'Order': 4, 'Representative': [6, 5, 2, 7, 8, 4, 1, 3]}, {'Size': '2', 'Order': 4, 'Representative': [3, 6, 4, 5, 1, 8, 2, 7]}, {'Size': '2', 'Order': 4, 'Representative': [2, 4, 7, 8, 6, 3, 5, 1]}, {'Size': '2', 'Order': 4, 'Representative': [8, 1, 7, 2, 6, 3, 5, 4]}, {'Size': '2', 'Order': 4, 'Representative': [5, 6, 1, 3, 4, 8, 2, 7]}, {'Size': '2', 'Order': 4, 'Representative': [7, 5, 2, 6, 8, 1, 4, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['51', '-16', '1'], 'ConjugacyClass': 5}, {'RootOf': ['19', '-16', '1'], 'ConjugacyClass': 7}, {'RootOf': ['64', '-16', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['56', '1'], 'ConjugacyClass': 2}, {'RootOf': ['712', '-38', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-686', '-12', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-1238', '-12', '1'], 'ConjugacyClass': 6}, {'RootOf': ['1576', '-38', '1'], 'ConjugacyClass': 9}, {'RootOf': ['786', '12', '1'], 'ConjugacyClass': 10}, {'RootOf': ['42', '12', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['259', '16', '1'], 'ConjugacyClass': 12}, {'RootOf': ['402', '36', '1'], 'ConjugacyClass': 13}, {'RootOf': ['314', '-36', '1'], 'ConjugacyClass': 14}, {'RootOf': ['194', '-36', '1'], 'ConjugacyClass': 15}, {'RootOf': ['714', '36', '1'], 'ConjugacyClass': 16}, {'RootOf': ['67', '16', '1'], 'ConjugacyClass': 17}], 'Algorithm': 'RES', 'CycleType': [4, 4]}], 'Frobs': [9, 15, 11, 12, 11, 17, 4, 13, 4, 7, 10, 17, 16, 14, 9, 15, 11, 8, 17, 16, 12, 1, 3, 16, 12, 7, 6, 15, 13, 4, 6, 7, 9, 8, 11, 10, 14, 17, 9, 15, 7, 8, 5, 12, 3, 2, 8, 12, 3, 13, 4, 16, 10, 7, 4, 4, 7, 10, 14, 16, 14, 3, 17, 5, 6, 3, 13, 6, 15, 13, 9, 16, 6, 14, 13, 9, 7, 17, 16, 10, 7, 13, 16, 6, 2, 15, 16, 12, 11, 12, 15, 16, 12, 7, 13, 4, 11, 5, 14, 13, 14, 3, 15, 5, 8, 12, 3, 9, 5, 1, 6, 17, 9, 13, 10, 5, 17, 4, 15, 7, 13, 6, 15, 3, 13, 7, 13, 5, 6, 17, 13, 9, 2, 14, 16, 10, 3, 17, 15, 5, 13, 11, 6, 3, 8, 16, 17, 4, 8, 9, 17, 5, 14, 4, 14, 5, 2, 16, 6, 11, 3, 4, 12, 7, 9, 9, 2, 14], 'G-Gens': [[4, 2, 5, 1, 3, 6, 7, 8], [6, 3, 2, 7, 8, 1, 4, 5], [8, 4, 6, 2, 7, 3, 5, 1], [4, 8, 3, 1, 5, 6, 7, 2], [2, 1, 6, 8, 7, 3, 5, 4], [4, 2, 3, 1, 5, 7, 6, 8], [7, 3, 2, 6, 8, 4, 1, 5]], 'G-Name': 'D8:C2^2', 'Polynomial': [-16, 4, 49, 4, -17, -8, -1, 0, 1], 'QpRts': [['883493586'], ['237182032'], ['760672696'], ['-1167619027'], ['-1131996568'], ['-133723323'], ['417848764'], ['134141840']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 79, 'QpRts-prec': 5, 'Size': 32, 'TransitiveDegree': 8}