Artin representation data - 3.727207.6t11.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': [13, 331], 'Baselabel': '3.727207.6t11.b', 'CharacterField': 1, 'Conductor': 727207, 'Container': '6t11', 'Dets': ['1.4303.2t1.a.a'], 'Dim': 3, 'GalConjSigns': [1], 'Galn': 6, 'GaloisConjugates': [{'Sign': 1, 'Character': [[3], [-3], [1], [-1], [1], [-1], [0], [1], [-1], [0]], 'GalOrbIndex': 1, 'HardFactors': [9, 11, 3, 3, 12], 'LocalFactors': [[[1], [-3], [3], [-1]], [[1], [3], [3], [1]], [[1], [-1], [-1], [1]], [[1], [1], [-1], [-1]], [[1], [-1], [-1], [1]], [[1], [1], [-1], [-1]], [[1], [0], [0], [-1]], [[1], [-1], [1], [-1]], [[1], [1], [1], [1]], [[1], [0], [0], [1]], [[1]], [[1], [2], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '6T11', 'Galt': 11, 'HardPrimes': [3, 13, 89, 107, 331], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-182, 13, 51, 42, -15, -2, 1], 'NumBadPrimes': 2, 'Proj_GAP': [24, 12], 'Proj_Polynomial': [-1, 1, 1, -1, 1], 'Proj_nTj': [4, 5]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.4303.2t1.a', 'Character': [[1], [-1], [-1], [1], [-1], [1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.331.2t1.a', 'Character': [[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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.55939.6t3.a', 'Character': [[2], [-2], [-2], [2], [0], [0], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.331.3t2.a', 'Character': [[2], [2], [2], [2], [0], [0], [-1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.331.4t5.a', 'Character': [[3], [3], [-1], [-1], [1], [1], [0], [-1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.727207.6t11.b', 'Character': [[3], [-3], [1], [-1], [1], [-1], [0], [1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.240705517.6t11.b', 'Character': [[3], [-3], [1], [-1], [-1], [1], [0], [-1], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.109561.6t8.c', 'Character': [[3], [3], [-1], [-1], [-1], [-1], [0], [1], [1], [0]], 'CharacterField': 1}], 'ComplexConjugation': 5, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6]}, {'Size': '1', 'Order': 2, 'Representative': [6, 4, 5, 2, 3, 1]}, {'Size': '3', 'Order': 2, 'Representative': [1, 2, 5, 4, 3, 6]}, {'Size': '3', 'Order': 2, 'Representative': [1, 4, 5, 2, 3, 6]}, {'Size': '6', 'Order': 2, 'Representative': [2, 1, 3, 6, 5, 4]}, {'Size': '6', 'Order': 2, 'Representative': [2, 1, 5, 6, 3, 4]}, {'Size': '8', 'Order': 3, 'Representative': [3, 1, 2, 6, 4, 5]}, {'Size': '6', 'Order': 4, 'Representative': [1, 3, 4, 5, 2, 6]}, {'Size': '6', 'Order': 4, 'Representative': [4, 1, 5, 6, 3, 2]}, {'Size': '8', 'Order': 6, 'Representative': [3, 1, 4, 6, 2, 5]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['247424', '688', '6', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-33090579367', '1827261556', '-33142864', '545207', '985', '-29', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [1, 1, 2, 2]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [1, 1, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-11', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-6546229', '2339860', '-562888', '38597', '673', '-107', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [2, 4]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [3, 3]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [6]}], 'Frobs': [8, 9, 10, 8, 8, 5, 7, 10, 5, 9, 10, 8, 8, 7, 6, 7, 6, 9, 10, 10, 6, 7, 3, 3, 8, 5, 4, 5, 10, 1, 7, 7, 8, 4, 10, 6, 7, 10, 10, 4, 7, 9, 7, 3, 10, 9, 5, 10, 6, 8, 7, 3, 10, 9, 5, 9, 7, 10, 5, 10, 7, 3, 6, 5, 7, 8, 6, 7, 4, 6, 10, 6, 4, 9, 6, 8, 4, 6, 10, 8, 7, 8, 3, 7, 9, 5, 10, 10, 10, 3, 5, 6, 10, 9, 6, 4, 8, 9, 9, 6, 7, 6, 7, 7, 9, 8, 3, 8, 7, 7, 7, 6, 6, 6, 8, 5, 6, 7, 5, 7, 8, 9, 5, 2, 6, 7, 6, 5, 9, 3, 10, 10, 4, 1, 6, 6, 10, 3, 5, 5, 10, 6, 7, 10, 7, 3, 10, 7, 7, 8, 3, 7, 9, 7, 1, 9, 5, 6, 9, 10, 8, 4, 6, 5, 8, 10, 7, 7], 'G-Gens': [[1, 3, 2, 5, 4, 6], [3, 1, 2, 6, 4, 5], [1, 2, 5, 4, 3, 6]], 'G-Name': 'C2*S4', 'Polynomial': [-182, 13, 51, 42, -15, -2, 1], 'QpRts': [['229021954608349720', '0'], ['99882287984873621', '56537621814321614'], ['-236772679969489731', '-215263850899556859'], ['251477293429465244', '215263850899556859'], ['-79335046242945507', '-56537621814321614'], ['239762552126214038', '0']], 'QpRts-minpoly': [5, 21, 1], 'QpRts-p': 23, 'QpRts-prec': 13, 'Size': 48, 'TransitiveDegree': 6}