Artin representation data - 1.85.8t1.b

Formats: - HTML - YAML - JSON - 2026-06-22T00:17:04.998434

• 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': [5, 17], 'Baselabel': '1.85.8t1.b', 'CharacterField': 8, 'Conductor': 85, 'Container': '8t1', 'Dets': ['85.32', '85.43', '85.2', '85.8'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 8, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [0, 0, -1], [0, 1], [0, 0, 0, 1], [0, -1], [0, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [2, 5, 9, 9, 1, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [0, 0, 1], [0, 0, 0, 1], [0, 1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 2, 'HardFactors': [2, 5, 9, 9, 1, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [0, 0, -1], [0, -1], [0, 0, 0, -1], [0, 1], [0, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [2, 5, 9, 9, 1, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [0, 0, 1], [0, 0, 0, -1], [0, -1], [0, 0, 0, 1], [0, 1]], 'GalOrbIndex': 4, 'HardFactors': [2, 5, 9, 9, 1, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '8T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 17, 53, 101, 733], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [596, -846, 245, 41, 134, -79, 10, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.85.8t1.b', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 1, 0], [0, 0, -1, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, -1, 0, 0], [0, 0, 0, -1]], 'CharacterField': 8}, {'GalConj': 1, 'Baselabel': '1.85.4t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [0, -1], [0, 1], [0, -1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '1.85.8t1.b', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, -1, 0], [0, 0, 1, 0], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 0, -1], [0, -1, 0, 0]], 'CharacterField': 8}, {'GalConj': 1, 'Baselabel': '1.17.2t1.a', 'Character': [[1], [1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 3, 'Baselabel': '1.85.8t1.b', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 1, 0], [0, 0, -1, 0], [0, -1, 0, 0], [0, 0, 0, -1], [0, 1, 0, 0], [0, 0, 0, 1]], 'CharacterField': 8}, {'GalConj': 2, 'Baselabel': '1.85.4t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, -1], [0, 1], [0, -1], [0, 1]], 'CharacterField': 4}, {'GalConj': 4, 'Baselabel': '1.85.8t1.b', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, -1, 0], [0, 0, 1, 0], [0, 0, 0, -1], [0, -1, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0]], 'CharacterField': 8}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [3, 8, 1, 7, 6, 5, 4, 2]}, {'Size': '1', 'Order': 4, 'Representative': [8, 1, 2, 5, 7, 4, 6, 3]}, {'Size': '1', 'Order': 4, 'Representative': [2, 3, 8, 6, 4, 7, 5, 1]}, {'Size': '1', 'Order': 8, 'Representative': [7, 5, 4, 2, 1, 3, 8, 6]}, {'Size': '1', 'Order': 8, 'Representative': [6, 7, 5, 1, 8, 2, 3, 4]}, {'Size': '1', 'Order': 8, 'Representative': [4, 6, 7, 8, 3, 1, 2, 5]}, {'Size': '1', 'Order': 8, 'Representative': [5, 4, 6, 3, 2, 8, 1, 7]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [2, 5, -2, -7, 1]}, 'Classes': [{'RootOf': ['1950', '1'], 'ConjugacyClass': 3}, {'RootOf': ['930', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['-957', '1'], 'ConjugacyClass': 5}, {'RootOf': ['743', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-787', '1'], 'ConjugacyClass': 7}, {'RootOf': ['63', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [8]}], 'Frobs': [2, 5, 7, 6, 7, 3, 1, 4, 6, 6, 6, 7, 5, 2, 4, 1, 3, 5, 3, 6, 7, 5, 1, 1, 5, 1, 4, 5, 7, 6, 1, 8, 3, 8, 1, 3, 4, 8, 7, 5, 3, 7, 2, 6, 6, 6, 5, 1, 8, 3, 7, 2, 6, 2, 2, 2, 8, 1, 5, 4, 6, 3, 3, 8, 8, 8, 4, 7, 6, 3, 3, 4, 6, 4, 6, 2, 4, 8, 5, 2, 5, 2, 7, 2, 8, 4, 7, 2, 3, 3, 1, 8, 8, 3, 5, 8, 2, 7, 3, 6, 7, 4, 1, 3, 5, 3, 1, 1, 1, 7, 5, 4, 5, 7, 3, 8, 5, 3, 8, 1, 3, 8, 7, 5, 7, 2, 6, 6, 4, 1, 3, 7, 6, 1, 2, 1, 2, 5, 2, 7, 8, 8, 8, 8, 1, 5, 5, 6, 3, 3, 6, 6, 4, 7, 8, 5, 2, 5, 2, 7, 5, 4, 2, 3, 1, 5, 8, 8], 'G-Gens': [[3, 8, 1, 7, 6, 5, 4, 2], [8, 1, 2, 5, 7, 4, 6, 3], [7, 5, 4, 2, 1, 3, 8, 6]], 'G-Name': 'C8', 'Polynomial': [596, -846, 245, 41, 134, -79, 10, -1, 1], 'QpRts': [['-499717927'], ['1022712403'], ['-1403870198'], ['-78759903'], ['1716190795'], ['686460018'], ['1186965147'], ['1309060309']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 83, 'QpRts-prec': 5, 'Size': 8, 'TransitiveDegree': 8}