Artin representation data - 2.949.8t12.a

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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': [13, 73], 'Baselabel': '2.949.8t12.a', 'CharacterField': 3, 'Conductor': 949, 'Container': '8t12', 'Dets': ['1.949.3t1.b.a', '1.949.3t1.b.b'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 8, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [1, 1], [0, -1], [0], [0, 1], [-1, -1]], 'GalOrbIndex': 1, 'HardFactors': [5, 8, 8], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [-1, -1], [0, 1]], [[1], [0, 1], [-1, -1]], [[1], [0], [1]], [[1], [0, -1], [-1, -1]], [[1], [1, 1], [0, 1]], [[1], [1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0, -1], [1, 1], [0], [-1, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [5, 8, 8], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0, 1], [-1, -1]], [[1], [-1, -1], [0, 1]], [[1], [0], [1]], [[1], [1, 1], [0, 1]], [[1], [0, -1], [-1, -1]], [[1], [1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '8T12', 'Galt': 12, 'HardPrimes': [2, 13, 73], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [169, 0, 255, 0, 116, 0, 19, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [12, 3], 'Proj_Polynomial': [49, -8, -19, 0, 1], 'Proj_nTj': [4, 4]}
• 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': '1.949.3t1.b', 'Character': [[1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.949.3t1.b', 'Character': [[1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.900601.24t7.a', 'Character': [[2], [-2], [-1], [-1], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.949.8t12.a', 'Character': [[2, 0], [-2, 0], [1, 1], [0, -1], [0, 0], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.949.8t12.a', 'Character': [[2, 0], [-2, 0], [0, -1], [1, 1], [0, 0], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '3.900601.4t4.b', 'Character': [[3], [3], [0], [0], [-1], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [5, 6, 7, 8, 1, 2, 3, 4]}, {'Size': '4', 'Order': 3, 'Representative': [1, 4, 2, 3, 5, 8, 6, 7]}, {'Size': '4', 'Order': 3, 'Representative': [1, 3, 4, 2, 5, 7, 8, 6]}, {'Size': '6', 'Order': 4, 'Representative': [2, 5, 8, 3, 6, 1, 4, 7]}, {'Size': '4', 'Order': 6, 'Representative': [5, 7, 8, 6, 1, 3, 4, 2]}, {'Size': '4', 'Order': 6, 'Representative': [5, 8, 6, 7, 1, 4, 2, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['52416', '-71552', '-676', '186', '1'], 'ConjugacyClass': 3}, {'RootOf': ['16832192', '-337168', '-8996', '134', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [1, 1, 3, 3]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['16832192', '337168', '-8996', '-134', '1'], 'ConjugacyClass': 6}, {'RootOf': ['52416', '71552', '-676', '-186', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [2, 6]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [4, 4]}], 'Frobs': [5, 6, 4, 3, 7, 7, 7, 6, 3, 5, 7, 7, 7, 7, 4, 7, 4, 5, 5, 6, 7, 7, 5, 5, 3, 7, 5, 5, 6, 5, 5, 6, 3, 7, 7, 6, 6, 3, 4, 7, 7, 6, 2, 3, 6, 6, 4, 7, 3, 5, 3, 3, 3, 5, 3, 5, 5, 4, 5, 6, 4, 7, 6, 7, 5, 7, 4, 4, 6, 2, 3, 7, 5, 3, 5, 6, 5, 5, 7, 4, 5, 5, 4, 5, 6, 4, 2, 1, 5, 7, 3, 3, 3, 5, 4, 7, 5, 5, 7, 5, 4, 6, 7, 3, 3, 5, 6, 5, 4, 4, 5, 1, 5, 6, 5, 6, 6, 4, 7, 6, 3, 5, 3, 5, 5, 7, 3, 5, 2, 5, 6, 5, 6, 4, 6, 5, 3, 4, 4, 5, 2, 2, 4, 5, 3, 2, 4, 7, 5, 7, 7, 3, 5, 7, 5, 6, 3, 4, 6, 5, 5, 5, 3, 7, 7, 3, 1, 4], 'G-Gens': [[2, 5, 8, 3, 6, 1, 4, 7], [3, 5, 6, 4, 7, 1, 2, 8], [8, 3, 6, 1, 4, 7, 2, 5], [5, 6, 7, 8, 1, 2, 3, 4]], 'G-Name': 'SL2(F3)', 'Polynomial': [169, 0, 255, 0, 116, 0, 19, 0, 1], 'QpRts': [['450960270800246', '246480171028204123', '84598468676459848'], ['128562739828425733', '0', '0'], ['-176578781411367480', '-98556643324472498', '35323846436348418'], ['-10034373639138997', '158999547583790762', '-49274622240111430'], ['-450960270800246', '-246480171028204123', '-84598468676459848'], ['-128562739828425733', '0', '0'], ['176578781411367480', '98556643324472498', '-35323846436348418'], ['10034373639138997', '-158999547583790762', '49274622240111430']], 'QpRts-minpoly': [18, 2, 0, 1], 'QpRts-p': 23, 'QpRts-prec': 13, 'Size': 24, 'TransitiveDegree': 8}