Artin representation data - 4.1254400.8t22.f

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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, 5, 7], 'Baselabel': '4.1254400.8t22.f', 'CharacterField': 1, 'Conductor': 1254400, '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, 3, 19, 19, 3, 12, 3, 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]], [[1], [0], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T22', 'Galt': 22, 'HardPrimes': [2, 3, 5, 7, 17, 23, 83, 157], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [18, 24, -16, -28, 8, 16, -2, -4, 1], 'NumBadPrimes': 3, 'Proj_GAP': [16, 14], 'Proj_Polynomial': [256, 0, 0, 0, 112, 0, 0, 0, 753, 0, 0, 0, 7, 0, 0, 0, 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': '1.28.2t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [1], [-1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.140.2t1.a', 'Character': [[1], [1], [-1], [-1], [-1], [1], [1], [-1], [1], [-1], [-1], [1], [1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.5.2t1.a', 'Character': [[1], [1], [-1], [-1], [-1], [1], [1], [1], [-1], [1], [1], [-1], [1], [-1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.7.2t1.a', 'Character': [[1], [1], [1], [1], [-1], [1], [-1], [-1], [-1], [1], [1], [1], [-1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.4.2t1.a', 'Character': [[1], [1], [1], [1], [-1], [1], [-1], [1], [1], [-1], [-1], [-1], [-1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.35.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [1], [-1], [-1], [1], [1], [1], [-1], [-1], [1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.20.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [1], [-1], [1], [-1], [-1], [-1], [1], [-1], [-1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.56.2t1.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': '1.280.2t1.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': '1.56.2t1.b', 'Character': [[1], [1], [-1], [1], [1], [-1], [-1], [-1], [-1], [1], [-1], [1], [1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.8.2t1.b', 'Character': [[1], [1], [-1], [1], [1], [-1], [-1], [1], [1], [-1], [1], [-1], [1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.280.2t1.b', 'Character': [[1], [1], [1], [-1], [-1], [-1], [-1], [-1], [1], [1], [-1], [-1], [1], [-1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.40.2t1.b', 'Character': [[1], [1], [1], [-1], [-1], [-1], [-1], [1], [-1], [-1], [1], [1], [1], [1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.1254400.8t22.f', 'Character': [[4], [-4], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 7, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [3, 7, 1, 5, 4, 8, 2, 6]}, {'Size': '2', 'Order': 2, 'Representative': [2, 1, 7, 6, 8, 4, 3, 5]}, {'Size': '2', 'Order': 2, 'Representative': [3, 7, 1, 4, 5, 6, 2, 8]}, {'Size': '2', 'Order': 2, 'Representative': [6, 4, 8, 2, 7, 1, 5, 3]}, {'Size': '2', 'Order': 2, 'Representative': [7, 3, 2, 6, 8, 4, 1, 5]}, {'Size': '2', 'Order': 2, 'Representative': [4, 6, 5, 1, 3, 2, 8, 7]}, {'Size': '2', 'Order': 2, 'Representative': [3, 2, 1, 5, 4, 6, 7, 8]}, {'Size': '2', 'Order': 2, 'Representative': [1, 7, 3, 5, 4, 6, 2, 8]}, {'Size': '2', 'Order': 2, 'Representative': [5, 6, 4, 3, 1, 2, 8, 7]}, {'Size': '2', 'Order': 2, 'Representative': [6, 5, 8, 7, 2, 1, 4, 3]}, {'Size': '2', 'Order': 4, 'Representative': [4, 8, 5, 3, 1, 2, 6, 7]}, {'Size': '2', 'Order': 4, 'Representative': [8, 5, 6, 2, 7, 1, 4, 3]}, {'Size': '2', 'Order': 4, 'Representative': [7, 1, 2, 8, 6, 4, 3, 5]}, {'Size': '2', 'Order': 4, 'Representative': [8, 4, 6, 7, 2, 1, 5, 3]}, {'Size': '2', 'Order': 4, 'Representative': [2, 3, 7, 8, 6, 4, 1, 5]}, {'Size': '2', 'Order': 4, 'Representative': [5, 8, 4, 1, 3, 2, 6, 7]}], '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': ['200', '-28', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-452', '-28', '1'], 'ConjugacyClass': 8}, {'RootOf': ['228', '-28', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['12', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-216', '-12', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-244', '-12', '1'], 'ConjugacyClass': 5}, {'RootOf': ['64', '-12', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-444', '-28', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-304', '-28', '1'], 'ConjugacyClass': 10}, {'RootOf': ['176', '-12', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['376', '-28', '1'], 'ConjugacyClass': 12}, {'RootOf': ['36', '-12', '1'], 'ConjugacyClass': 13}, {'RootOf': ['-188', '-12', '1'], 'ConjugacyClass': 14}, {'RootOf': ['-104', '-12', '1'], 'ConjugacyClass': 15}, {'RootOf': ['92', '-12', '1'], 'ConjugacyClass': 16}, {'RootOf': ['236', '-28', '1'], 'ConjugacyClass': 17}], 'Algorithm': 'RES', 'CycleType': [4, 4]}], 'Frobs': [4, 5, 14, 17, 11, 14, 9, 13, 12, 6, 7, 3, 8, 15, 17, 3, 13, 16, 15, 10, 9, 10, 5, 8, 9, 16, 17, 15, 6, 4, 12, 13, 4, 13, 6, 10, 14, 15, 17, 14, 11, 16, 10, 4, 3, 7, 11, 17, 5, 16, 4, 10, 8, 13, 9, 12, 16, 7, 3, 2, 5, 14, 5, 7, 9, 3, 11, 4, 15, 16, 9, 10, 17, 3, 11, 17, 6, 14, 2, 8, 13, 6, 10, 9, 7, 15, 2, 4, 16, 12, 5, 7, 12, 11, 11, 17, 16, 8, 5, 6, 15, 3, 5, 1, 11, 9, 5, 9, 10, 8, 17, 3, 4, 13, 10, 1, 5, 17, 3, 11, 16, 4, 14, 15, 13, 6, 6, 7, 17, 14, 11, 12, 10, 3, 8, 8, 14, 5, 14, 2, 13, 6, 12, 15, 16, 7, 14, 9, 13, 12, 3, 8, 15, 17, 15, 10, 10, 8, 9, 16, 15, 4, 12, 13, 4, 17, 10, 14], 'G-Gens': [[3, 2, 1, 4, 5, 8, 7, 6], [2, 1, 7, 6, 8, 4, 3, 5], [3, 7, 1, 4, 5, 6, 2, 8], [6, 4, 8, 2, 7, 1, 5, 3], [8, 4, 6, 2, 7, 3, 5, 1], [7, 3, 2, 6, 8, 4, 1, 5], [3, 2, 1, 5, 4, 6, 7, 8]], 'G-Name': 'D8:C2^2', 'Polynomial': [18, 24, -16, -28, 8, 16, -2, -4, 1], 'QpRts': [['19318159260748'], ['-22304080374300'], ['10835533495109'], ['15467313391961'], ['2103841868296'], ['-9280360497064'], ['-7849612381555'], ['-8290794763191']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 569, 'QpRts-prec': 5, 'Size': 32, 'TransitiveDegree': 8}