Artin representation data - 8.316113500535561.36t555.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': [3, 29], 'Baselabel': '8.316113500535561.36t555.b', 'CharacterField': 5, 'Conductor': 316113500535561, 'Container': '36t555', 'Dets': ['1.1.1t1.a.a', '1.1.1t1.a.a'], 'Dim': 8, 'GalConjSigns': [1, 1], 'Galn': 6, 'GaloisConjugates': [{'Sign': 1, 'Character': [[8], [0], [-1], [-1], [0], [1, 0, 1, 1], [0, 0, -1, -1]], 'GalOrbIndex': 1, 'HardFactors': [6, 8, 5, 9], 'LocalFactors': [[[1], [-8], [28], [-56], [70], [-56], [28], [-8], [1]], [[1], [0], [-4], [0], [6], [0], [-4], [0], [1]], [[1], [1], [1], [-2], [-2], [-2], [1], [1], [1]], [[1], [1], [1], [-2], [-2], [-2], [1], [1], [1]], [[1], [0], [0], [0], [-2], [0], [0], [0], [1]], [[1], [-1, 0, -1, -1], [1, 0, 1, 1], [-1], [0], [-1], [1, 0, 1, 1], [-1, 0, -1, -1], [1]], [[1], [0, 0, 1, 1], [0, 0, -1, -1], [-1], [0], [-1], [0, 0, -1, -1], [0, 0, 1, 1], [1]], [[1]], [[1], [0], [-1]]]}, {'Sign': 1, 'Character': [[8], [0], [-1], [-1], [0], [0, 0, -1, -1], [1, 0, 1, 1]], 'GalOrbIndex': 2, 'HardFactors': [6, 8, 5, 9], 'LocalFactors': [[[1], [-8], [28], [-56], [70], [-56], [28], [-8], [1]], [[1], [0], [-4], [0], [6], [0], [-4], [0], [1]], [[1], [1], [1], [-2], [-2], [-2], [1], [1], [1]], [[1], [1], [1], [-2], [-2], [-2], [1], [1], [1]], [[1], [0], [0], [0], [-2], [0], [0], [0], [1]], [[1], [0, 0, 1, 1], [0, 0, -1, -1], [-1], [0], [-1], [0, 0, -1, -1], [0, 0, 1, 1], [1]], [[1], [-1, 0, -1, -1], [1, 0, 1, 1], [-1], [0], [-1], [1, 0, 1, 1], [-1, 0, -1, -1], [1]], [[1]], [[1], [0], [-1]]]}], 'GaloisConjugatesSigns': [1, 1], 'GaloisLabel': '6T15', 'Galt': 15, 'HardPrimes': [2, 3, 7, 29], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [4, -3, 0, -3, 0, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [360, 118], 'Proj_Polynomial': [4, -3, 0, -3, 0, 0, 1], 'Proj_nTj': [6, 15]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.515607849.6t15.b', 'Character': [[5], [1], [2], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.613089.6t15.b', 'Character': [[5], [1], [-1], [2], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.316113500535561.36t555.b', 'Character': [[8, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [1, 0, 1, 1], [0, 0, -1, -1]], 'CharacterField': 5}, {'GalConj': 2, 'Baselabel': '8.316113500535561.36t555.b', 'Character': [[8, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, -1], [1, 0, 1, 1]], 'CharacterField': 5}, {'GalConj': 1, 'Baselabel': '9.316113500535561.10t26.b', 'Character': [[9], [1], [0], [0], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '10.2845021504820049.30t88.b', 'Character': [[10], [-2], [1], [1], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6]}, {'Size': '45', 'Order': 2, 'Representative': [2, 1, 4, 3, 5, 6]}, {'Size': '40', 'Order': 3, 'Representative': [2, 3, 1, 5, 6, 4]}, {'Size': '40', 'Order': 3, 'Representative': [2, 3, 1, 4, 5, 6]}, {'Size': '90', 'Order': 4, 'Representative': [2, 3, 4, 1, 6, 5]}, {'Size': '72', 'Order': 5, 'Representative': [2, 3, 4, 5, 1, 6]}, {'Size': '72', 'Order': 5, 'Representative': [3, 1, 4, 5, 2, 6]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 3]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2]}, {'Data': [1, 3, 4, 5, 6, 2], 'Classes': [{'RootOf': ['5481', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-5481', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'ALT', 'CycleType': [1, 5]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [2, 4]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [3, 3]}], 'Frobs': [6, 5, 5, 5, 7, 6, 7, 2, 6, 2, 5, 3, 5, 7, 5, 5, 6, 7, 5, 3, 3, 7, 7, 5, 3, 6, 7, 4, 7, 6, 6, 7, 2, 3, 6, 5, 2, 6, 3, 4, 5, 5, 6, 6, 5, 3, 7, 5, 3, 2, 7, 7, 6, 7, 4, 5, 2, 6, 5, 2, 5, 7, 6, 7, 6, 2, 7, 7, 2, 5, 5, 7, 2, 5, 3, 2, 5, 6, 6, 4, 2, 5, 7, 6, 5, 4, 2, 2, 5, 4, 4, 4, 4, 5, 4, 5, 5, 3, 7, 6, 6, 3, 5, 6, 7, 6, 7, 5, 6, 6, 3, 2, 4, 7, 6, 7, 2, 6, 6, 6, 6, 6, 5, 5, 2, 4, 5, 3, 7, 7, 5, 4, 7, 3, 3, 5, 5, 5, 7, 6, 7, 5, 7, 7, 6, 3, 2, 3, 3, 6, 6, 5, 3, 4, 5, 6, 5, 3, 5, 7, 3, 6, 3, 6, 3, 6, 6, 5], 'G-Gens': [[2, 3, 1, 4, 5, 6], [2, 1, 4, 5, 6, 3]], 'G-Name': 'A6', 'Polynomial': [4, -3, 0, -3, 0, 0, 1], 'QpRts': [['-1131049', '0'], ['345472', '764271'], ['-1114501', '1209163'], ['1049434', '0'], ['-594544', '-1209163'], ['-1030911', '-764271']], 'QpRts-minpoly': [2, 18, 1], 'QpRts-p': 19, 'QpRts-prec': 5, 'Size': 360, 'TransitiveDegree': 6}