Artin representation data - 2.1676.27t8.a

Formats: - HTML - YAML - JSON - 2024-04-30T16:23:19.181041

• 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, 419], 'Baselabel': '2.1676.27t8.a', 'CharacterField': 27, 'Conductor': 1676, 'Container': '27t8', 'Dets': ['1.419.2t1.a.a', '1.419.2t1.a.a', '1.419.2t1.a.a', '1.419.2t1.a.a', '1.419.2t1.a.a', '1.419.2t1.a.a', '1.419.2t1.a.a', '1.419.2t1.a.a', '1.419.2t1.a.a'], 'Dim': 2, 'GalConjSigns': [1, 1, 1, 1, 1, 1, 1, 1, 1], 'Galn': 27, 'GaloisConjugates': [{'Sign': 1, 'Character': [[2], [0], [-1], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]], 'GalOrbIndex': 1, 'HardFactors': [16, 14, 2, 13, 2, 2, 2, 2, 2, 17, 2, 2, 2, 2, 2, 1, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1], [1]], [[1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [0], [-1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [16, 14, 2, 13, 2, 2, 2, 2, 2, 17, 2, 2, 2, 2, 2, 1, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [0], [-1], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [16, 14, 2, 13, 2, 2, 2, 2, 2, 17, 2, 2, 2, 2, 2, 1, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1], [1]], [[1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [0], [-1], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1]], 'GalOrbIndex': 4, 'HardFactors': [16, 14, 2, 13, 2, 2, 2, 2, 2, 17, 2, 2, 2, 2, 2, 1, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1], [1]], [[1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [0], [-1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1]], 'GalOrbIndex': 5, 'HardFactors': [16, 14, 2, 13, 2, 2, 2, 2, 2, 17, 2, 2, 2, 2, 2, 1, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1], [1]], [[1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1], [1]], [[1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [0], [-1], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1]], 'GalOrbIndex': 6, 'HardFactors': [16, 14, 2, 13, 2, 2, 2, 2, 2, 17, 2, 2, 2, 2, 2, 1, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [0], [-1], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1]], 'GalOrbIndex': 7, 'HardFactors': [16, 14, 2, 13, 2, 2, 2, 2, 2, 17, 2, 2, 2, 2, 2, 1, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [0], [-1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1]], 'GalOrbIndex': 8, 'HardFactors': [16, 14, 2, 13, 2, 2, 2, 2, 2, 17, 2, 2, 2, 2, 2, 1, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1], [1]], [[1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [0], [-1], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1]], 'GalOrbIndex': 9, 'HardFactors': [16, 14, 2, 13, 2, 2, 2, 2, 2, 17, 2, 2, 2, 2, 2, 1, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1]], [[1], [-1]]]}], 'GaloisConjugatesSigns': [1, 1, 1, 1, 1, 1, 1, 1, 1], 'GaloisLabel': '27T8', 'Galt': 8, 'HardPrimes': [2, 7, 11, 13, 19, 67, 71, 101, 233, 419, 613, 1009, 1973, 3917, 4241, 7433, 85531], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-16, 32, 48, -244, -368, 572, 1728, -28, -3848, 639, 2422, -1300, -2352, 4978, 94, -7109, 4952, 1448, -3756, 1948, 40, -715, 458, -84, -52, 38, -10, 1], 'NumBadPrimes': 2, 'Proj_GAP': [54, 1], 'Proj_Polynomial': [-16, 32, 48, -244, -368, 572, 1728, -28, -3848, 639, 2422, -1300, -2352, 4978, 94, -7109, 4952, 1448, -3756, 1948, 40, -715, 458, -84, -52, 38, -10, 1], 'Proj_nTj': [27, 8]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.419.2t1.a', 'Character': [[1], [-1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.419.3t2.a', 'Character': [[2], [0], [2], [2], [2], [2], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.419.9t3.a', 'Character': [[2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, -1, 1, 0, -1, 0], [0, 0, 0, 0, 1, 1], [0, 1, -1, 0, 0, -1], [0, 1, -1, 0, 0, -1], [0, 0, 0, 0, 1, 1], [0, -1, 1, 0, -1, 0], [0, -1, 1, 0, -1, 0], [0, 0, 0, 0, 1, 1], [0, 1, -1, 0, 0, -1]], 'CharacterField': 9}, {'GalConj': 2, 'Baselabel': '2.419.9t3.a', 'Character': [[2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1], [0, 1, -1, 0, 0, -1], [0, -1, 1, 0, -1, 0], [0, -1, 1, 0, -1, 0], [0, 1, -1, 0, 0, -1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1], [0, 1, -1, 0, 0, -1], [0, -1, 1, 0, -1, 0]], 'CharacterField': 9}, {'GalConj': 3, 'Baselabel': '2.419.9t3.a', 'Character': [[2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 1, -1, 0, 0, -1], [0, -1, 1, 0, -1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1], [0, -1, 1, 0, -1, 0], [0, 1, -1, 0, 0, -1], [0, 1, -1, 0, 0, -1], [0, -1, 1, 0, -1, 0], [0, 0, 0, 0, 1, 1]], 'CharacterField': 9}, {'GalConj': 6, 'Baselabel': '2.1676.27t8.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0]], 'CharacterField': 27}, {'GalConj': 4, 'Baselabel': '2.1676.27t8.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0]], 'CharacterField': 27}, {'GalConj': 3, 'Baselabel': '2.1676.27t8.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]], 'CharacterField': 27}, {'GalConj': 1, 'Baselabel': '2.1676.27t8.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0]], 'CharacterField': 27}, {'GalConj': 2, 'Baselabel': '2.1676.27t8.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0]], 'CharacterField': 27}, {'GalConj': 5, 'Baselabel': '2.1676.27t8.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0]], 'CharacterField': 27}, {'GalConj': 9, 'Baselabel': '2.1676.27t8.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1]], 'CharacterField': 27}, {'GalConj': 8, 'Baselabel': '2.1676.27t8.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0]], 'CharacterField': 27}, {'GalConj': 7, 'Baselabel': '2.1676.27t8.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0]], 'CharacterField': 27}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]}, {'Size': '27', 'Order': 2, 'Representative': [1, 25, 7, 22, 14, 19, 3, 21, 10, 9, 20, 26, 15, 5, 13, 24, 23, 27, 6, 11, 8, 4, 17, 16, 2, 12, 18]}, {'Size': '2', 'Order': 3, 'Representative': [24, 3, 8, 23, 10, 5, 25, 2, 14, 6, 27, 17, 11, 19, 18, 1, 22, 20, 9, 15, 7, 12, 26, 16, 21, 4, 13]}, {'Size': '2', 'Order': 9, 'Representative': [14, 27, 13, 15, 1, 16, 23, 11, 5, 24, 12, 2, 22, 10, 7, 9, 3, 25, 6, 21, 4, 8, 18, 19, 26, 20, 17]}, {'Size': '2', 'Order': 9, 'Representative': [10, 17, 22, 7, 14, 9, 18, 12, 1, 19, 2, 27, 8, 24, 23, 5, 13, 26, 16, 4, 15, 11, 25, 6, 20, 21, 3]}, {'Size': '2', 'Order': 9, 'Representative': [19, 13, 11, 18, 24, 1, 26, 27, 10, 16, 17, 3, 12, 6, 25, 14, 8, 21, 5, 7, 23, 2, 20, 9, 4, 15, 22]}, {'Size': '2', 'Order': 27, 'Representative': [13, 20, 15, 5, 3, 2, 14, 18, 17, 8, 25, 26, 7, 22, 1, 27, 4, 24, 12, 16, 9, 23, 10, 11, 19, 6, 21]}, {'Size': '2', 'Order': 27, 'Representative': [7, 16, 1, 3, 15, 20, 22, 24, 4, 18, 19, 6, 14, 23, 13, 21, 5, 11, 26, 27, 17, 10, 8, 25, 12, 2, 9]}, {'Size': '2', 'Order': 27, 'Representative': [22, 21, 7, 1, 13, 27, 10, 25, 3, 11, 26, 20, 23, 8, 14, 17, 15, 19, 2, 9, 5, 18, 24, 12, 6, 16, 4]}, {'Size': '2', 'Order': 27, 'Representative': [23, 9, 14, 13, 7, 21, 8, 19, 15, 25, 6, 16, 10, 18, 22, 4, 1, 12, 20, 17, 3, 24, 11, 26, 2, 27, 5]}, {'Size': '2', 'Order': 27, 'Representative': [8, 4, 23, 14, 22, 17, 24, 26, 13, 12, 20, 21, 18, 11, 10, 3, 7, 6, 27, 5, 1, 25, 19, 2, 16, 9, 15]}, {'Size': '2', 'Order': 27, 'Representative': [18, 5, 10, 22, 23, 4, 11, 6, 7, 26, 16, 9, 24, 25, 8, 15, 14, 2, 21, 3, 13, 19, 12, 20, 27, 17, 1]}, {'Size': '2', 'Order': 27, 'Representative': [11, 15, 18, 10, 8, 3, 19, 20, 22, 2, 21, 4, 25, 12, 24, 13, 23, 16, 17, 1, 14, 26, 6, 27, 9, 5, 7]}, {'Size': '2', 'Order': 27, 'Representative': [25, 1, 24, 8, 18, 15, 12, 16, 23, 20, 9, 5, 19, 26, 11, 7, 10, 27, 4, 13, 22, 6, 2, 21, 17, 3, 14]}, {'Size': '2', 'Order': 27, 'Representative': [12, 7, 25, 24, 11, 13, 6, 21, 8, 27, 4, 15, 26, 2, 19, 22, 18, 9, 3, 14, 10, 20, 16, 17, 5, 1, 23]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [3, 3, 3, 3, 3, 3, 3, 3, 3]}, {'Data': {'Powers': [1, 8], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-25', '1'], 'ConjugacyClass': 4}, {'RootOf': ['29', '1'], 'ConjugacyClass': 5}, {'RootOf': ['27', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [9, 9, 9]}, {'Data': {'Powers': [1, 26], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-11', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-28', '1'], 'ConjugacyClass': 8}, {'RootOf': ['-8', '1'], 'ConjugacyClass': 9}, {'RootOf': ['-16', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-26', '1'], 'ConjugacyClass': 11}, {'RootOf': ['-17', '1'], 'ConjugacyClass': 12}, {'RootOf': ['11', '1'], 'ConjugacyClass': 13}, {'RootOf': ['-14', '1'], 'ConjugacyClass': 14}, {'RootOf': ['-42', '1'], 'ConjugacyClass': 15}], 'Algorithm': 'RES', 'CycleType': [27]}], 'Frobs': [2, 15, 5, 14, 2, 13, 2, 2, 8, 12, 2, 9, 11, 4, 7, 2, 9, 2, 2, 2, 12, 10, 2, 2, 4, 2, 2, 3, 2, 2, 2, 11, 10, 8, 10, 6, 11, 2, 2, 15, 2, 2, 6, 2, 6, 5, 2, 2, 2, 2, 2, 2, 2, 14, 4, 2, 9, 2, 2, 4, 2, 7, 2, 2, 2, 2, 2, 5, 7, 4, 2, 2, 2, 7, 13, 2, 14, 2, 15, 9, 1, 2, 13, 2, 13, 2, 2, 8, 2, 2, 11, 10, 2, 2, 8, 12, 2, 12, 2, 14, 2, 2, 1, 2, 12, 2, 2, 2, 15, 2, 11, 2, 12, 2, 2, 2, 2, 2, 2, 4, 2, 15, 2, 8, 2, 2, 2, 4, 2, 2, 12, 1, 2, 2, 6, 2, 2, 10, 2, 2, 2, 13, 2, 6, 2, 15, 6, 2, 13, 11, 10, 7, 9, 9, 7, 5, 9, 14, 2, 2, 2, 10, 15, 2, 13, 13, 2, 2], 'G-Gens': [[24, 3, 8, 23, 10, 5, 25, 2, 14, 6, 27, 17, 11, 19, 18, 1, 22, 20, 9, 15, 7, 12, 26, 16, 21, 4, 13], [14, 27, 13, 15, 1, 16, 23, 11, 5, 24, 12, 2, 22, 10, 7, 9, 3, 25, 6, 21, 4, 8, 18, 19, 26, 20, 17], [13, 20, 15, 5, 3, 2, 14, 18, 17, 8, 25, 26, 7, 22, 1, 27, 4, 24, 12, 16, 9, 23, 10, 11, 19, 6, 21], [1, 25, 7, 22, 14, 19, 3, 21, 10, 9, 20, 26, 15, 5, 13, 24, 23, 27, 6, 11, 8, 4, 17, 16, 2, 12, 18]], 'G-Name': 'D54', 'Polynomial': [-16, 32, 48, -244, -368, 572, 1728, -28, -3848, 639, 2422, -1300, -2352, 4978, 94, -7109, 4952, 1448, -3756, 1948, 40, -715, 458, -84, -52, 38, -10, 1], 'QpRts': [['-6341642', '-7191732', '-2957373', '-8433618', '-2166975', '9141214', '-9263717', '6684891', '1915536', '-9203504', '6915093', '-661900', '-455964', '-3083811', '-8465713', '-8785501', '-2610878', '-9348135', '-8725570', '-3910723', '-2749808', '927851', '2515828', '10014336', '-9420376', '-5771805', '-5007771'], ['9260849', '9460087', '5161529', '-9518817', '-1697347', '595552', '4049278', '7355004', '-3355049', '1735528', '150454', '-1478578', '8948298', '7770961', '-9153306', '-5370424', '4406020', '7938983', '7697748', '7208386', '6776206', '-8868402', '-5324586', '4036880', '5530673', '-8006969', '2517022'], ['-7528596', '-5848168', '3800284', '-10209101', '3255054', '-9726019', '-8853214', '1832278', '-152458', '1493237', '6852693', '-351266', '-5590606', '-8700205', '-3559456', '6119055', '9086714', '-420804', '-1197255', '5833035', '-7174981', '-4483524', '-3804877', '-389490', '3802189', '9656031', '-1507035'], ['5211723', '3055969', '1507536', '6432435', '-4107207', '8918246', '-3997148', '2589522', '-7581082', '8569897', '4920489', '-5299368', '1341512', '-1639883', '3231005', '-8811838', '-964085', '-3078112', '-1310906', '9495797', '-7761833', '-9055269', '6734612', '4897022', '9491713', '-5264046', '-4843401'], ['2267529', '-6706727', '-5294812', '-4498278', '4426816', '-2919933', '-574752', '6769573', '8729788', '-14686', '9039579', '-8187313', '5481438', '-4096921', '6488249', '-9750817', '-8404193', '758029', '10140563', '-6060776', '-4576099', '2059126', '-1145816', '2091756', '7828562', '-3549829', '6299193'], ['-8419888', '4805120', '-5365592', '-8049861', '-8271849', '-3775375', '-3548084', '-1880565', '2357647', '-10153271', '-6085222', '7214150', '-4231540', '-9468911', '-6138201', '-914960', '932393', '-1749432', '9194144', '524421', '-5785735', '-7587415', '4117563', '-4081800', '2502155', '-2002621', '5456296'], ['-4449903', '-10001463', '-9680430', '-6417427', '-1420089', '-4517821', '2128816', '-7812233', '-4670542', '5260182', '1093971', '-4799453', '-4883519', '7697167', '9966925', '-470381', '-1936754', '-8319494', '7622325', '9335957', '-3470586', '-9932951', '1648470', '4519783', '3307670', '9000873', '5634521'], ['-5363281', '-273867', '1341441', '7875310', '4872410', '-277830', '8910924', '-9648610', '-8163528', '2473781', '-5095382', '-9689645', '-10245163', '6359515', '-3220446', '-10245982', '-779775', '4065420', '-1662812', '10094885', '7389696', '-1877643', '2393205', '1783944', '7411174', '-8247192', '-47329'], ['-4890441', '-2037523', '8210849', '-9795630', '-5651804', '-3046927', '3344545', '-5484264', '3819851', '7820417', '1644417', '-7490878', '9498917', '-3936945', '1069394', '-5954842', '-4855279', '-1968137', '1369595', '-5475246', '2164036', '-5734088', '-3549651', '-8075640', '8400855', '-6310126', '-9022987'], ['5623428', '-4162380', '-3355601', '-4526847', '-4010455', '6643286', '4242631', '-9421720', '-2339488', '-1971606', '409083', '9703823', '5193471', '531451', '4646913', '3032819', '9951819', '-1043196', '-71944', '6162860', '-2403283', '6376575', '2953787', '5955340', '-4808534', '7590247', '7417494'], ['6853930', '-3421143', '-6723864', '4806747', '7780793', '-8328725', '781390', '-1762587', '7095251', '9021975', '-6784911', '-4109762', '4885062', '-1179200', '-8123897', '3445103', '7143204', '4519237', '-3521175', '-4296496', '4864347', '5179120', '-6038674', '-9419290', '7459292', '-1522235', '8695323'], ['9403274', '-5552640', '-10141382', '-9405013', '224684', '-2336160', '4398026', '-6907501', '-499117', '-2411947', '-2406907', '-1482724', '4841241', '7275677', '7387879', '4570445', '-2544204', '-7418243', '7380525', '5621509', '9954019', '-9608997', '-174831', '-738370', '-9639522', '-828255', '9764938'], ['-4329697', '-1770637', '3344627', '-5573541', '6581443', '-3194839', '6721942', '3157848', '-5859655', '-9551694', '-9365326', '10173025', '8762531', '-8992839', '-1792998', '-5960845', '8021076', '1221028', '431336', '-9464456', '-3084782', '-1276753', '9389246', '-8965004', '-3421465', '8239017', '7337131'], ['-9242919', '-6565985', '9324462', '-5504941', '-7629279', '9227234', '886510', '8583765', '5589869', '-4823135', '9175650', '-4455373', '-8062414', '-8334357', '7289770', '524451', '-4589189', '-9526738', '10170890', '-2116920', '2346137', '-9049807', '-980621', '-4892779', '-3434060', '3492319', '6968281'], ['-1342440', '-1588341', '-8267716', '-5892506', '8412503', '-1808252', '4611314', '8566639', '9639849', '5584050', '-1230497', '-5981812', '477325', '-5322509', '-9697725', '8110312', '-4074094', '-3609751', '5316240', '-8877599', '-7737102', '-7670723', '5248261', '-9518218', '9595203', '-575755', '183708'], ['8926274', '3226707', '4500291', '-3901641', '-4304528', '198915', '649200', '-4208797', '4690215', '5366866', '-1175590', '5529269', '4493064', '2785861', '-4992447', '-7346349', '3721702', '9296477', '4865516', '-5678540', '-393657', '-4518169', '10197982', '-1266879', '-5839267', '-10238390', '-1774873'], ['-9933289', '-5209142', '4291454', '7832198', '7725642', '-8685250', '3557246', '4904457', '5682820', '-6619459', '-9712236', '7162159', '6661435', '-6613681', '2033147', '-4345787', '-2836610', '8698500', '-5846427', '5792139', '4769486', '-6615617', '6857491', '8604189', '8048170', '-6832907', '7829139'], ['-1777774', '-579168', '1969492', '-7966696', '2278102', '-1603106', '-1110200', '-96027', '6300702', '6950103', '1726770', '-1779209', '1565323', '5813480', '5515509', '-2242278', '540432', '-4077273', '-6441126', '5795534', '-6304915', '-4339972', '5696050', '-5004877', '-2808825', '9221876', '-3423931'], ['-23113', '5790396', '1608680', '1062004', '10073849', '-211922', '-8959736', '1530776', '-8805075', '-3422854', '5988580', '9127350', '6330084', '8033187', '-7935037', '3567178', '-648455', '-5053326', '-6700427', '3271804', '4692953', '8268072', '-3000226', '6756473', '3576406', '-5956682', '764888'], ['2594573', '3574486', '-680631', '-4604383', '4718769', '7512774', '-6997834', '-6593546', '-2419709', '-7126641', '4784988', '5273190', '6742945', '-8412546', '2999722', '6913245', '1986399', '2960956', '-2587329', '-3061331', '6530358', '-7211237', '10067819', '-9827437', '8257925', '9061951', '9794377'], ['5237615', '-5113598', '2223549', '3501100', '-1238165', '-4493039', '6524835', '-7382800', '-2124649', '-10105175', '7764145', '-6255777', '-1697307', '4187886', '708810', '8438171', '-6104596', '2412124', '-4765629', '431773', '-5977453', '-1190542', '7092753', '-4286957', '9458644', '-5131905', '4650171'], ['-5254223', '2302063', '9455349', '5225103', '-1875414', '-9006645', '2000696', '2965614', '10137684', '7635020', '-5840369', '-8336506', '804268', '-1236388', '-1653907', '6229018', '3849114', '-8588336', '-10072370', '423552', '-2389553', '5156975', '4718611', '9681078', '-4183905', '-306708', '7954827'], ['-6327682', '-6041110', '7778213', '-1571787', '-939341', '-10094674', '-7286376', '-5848319', '7117100', '-7971117', '9988221', '6275680', '-5522252', '7876697', '-9095369', '3529266', '-8893636', '-10178395', '-5846231', '-4733289', '-1042464', '425030', '1801972', '-5435421', '391932', '-8267383', '-259932'], ['-2086923', '-1035160', '-7654101', '-5599997', '9035132', '8492723', '-1277989', '8732103', '6623951', '-8181574', '9101427', '-3758412', '-1095082', '-5945484', '-5630128', '176208', '-9686732', '1259707', '-1761487', '8144755', '5217514', '1399951', '8439188', '9098630', '-1689146', '5677996', '-2956080'], ['7593687', '306202', '5021638', '1816318', '6337204', '-1708717', '-5566805', '-7252595', '-4266183', '20689', '-9086516', '-197677', '2360421', '9955772', '5258183', '7047521', '-9239503', '5625905', '9579038', '5608553', '769409', '5738032', '-4226983', '4516961', '7296900', '7093466', '-2369823'], ['7607704', '-6648330', '-4816869', '-1274276', '-8027665', '1316649', '8709014', '-3898366', '-981194', '4766715', '9825702', '9729046', '8811910', '-1841666', '-5501383', '-163196', '6765343', '3536261', '-6788094', '6861600', '-5943960', '-5923199', '-1393641', '-9310613', '8448984', '-669307', '-9455280'], ['6731235', '6203786', '-4601023', '-7851451', '-3871134', '3177492', '-4080512', '-5985689', '-7971385', '-5652946', '8423992', '4127961', '-4393100', '-9993457', '7853358', '8660408', '-8747382', '1575596', '-6469138', '4091114', '-9189099', '7880129', '1300515', '9256383', '-4029900', '-10062810', '-9576569']], 'QpRts-minpoly': [8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'QpRts-p': 29, 'QpRts-prec': 5, 'Size': 54, 'TransitiveDegree': 27}