Artin representation data - 2.178215.27t8.a

Formats: - HTML - YAML - JSON - 2024-05-16T00:47:31.012554

• 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': [3, 5, 109], 'Baselabel': '2.178215.27t8.a', 'CharacterField': 27, 'Conductor': 178215, 'Container': '27t8', 'Dets': ['1.15.2t1.a.a', '1.15.2t1.a.a', '1.15.2t1.a.a', '1.15.2t1.a.a', '1.15.2t1.a.a', '1.15.2t1.a.a', '1.15.2t1.a.a', '1.15.2t1.a.a', '1.15.2t1.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, 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': 1, 'HardFactors': [7, 16, 16, 2, 2, 2, 12, 2, 17, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 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, -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': 2, 'HardFactors': [7, 16, 16, 2, 2, 2, 12, 2, 17, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 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, 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': 3, 'HardFactors': [7, 16, 16, 2, 2, 2, 12, 2, 17, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 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': 4, 'HardFactors': [7, 16, 16, 2, 2, 2, 12, 2, 17, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 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, -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': 5, 'HardFactors': [7, 16, 16, 2, 2, 2, 12, 2, 17, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 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, 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': 6, 'HardFactors': [7, 16, 16, 2, 2, 2, 12, 2, 17, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 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, 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': 7, 'HardFactors': [7, 16, 16, 2, 2, 2, 12, 2, 17, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 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': 8, 'HardFactors': [7, 16, 16, 2, 2, 2, 12, 2, 17, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 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]]]}, {'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': 9, 'HardFactors': [7, 16, 16, 2, 2, 2, 12, 2, 17, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 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]]]}], 'GaloisConjugatesSigns': [1, 1, 1, 1, 1, 1, 1, 1, 1], 'GaloisLabel': '27T8', 'Galt': 8, 'HardPrimes': [2, 3, 5, 7, 11, 13, 19, 103, 109, 523, 641, 859, 6701, 19141, 37013, 92077, 178691, 452537, 744761, 154463821, 1146457331, 1945745419, 5875802213, 22829132917, 56817654911, 98588120129, 175234798573], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-403417708534024695, 192614433481703520, -5285509387016283, -148935808330194339, -19653142689957861, 19164121771855527, 2512960932249207, -324170737967403, 94418097588513, -54542846745063, -16686030795034, 1542463152066, 277314343372, 78412982262, -4368885822, -1907648811, -667433366, 116115168, 1046198, 4807612, -87714, 4376, -14130, 1116, -366, 77, -3, 1], 'NumBadPrimes': 3, 'Proj_GAP': [54, 1], 'Proj_Polynomial': [-403417708534024695, 192614433481703520, -5285509387016283, -148935808330194339, -19653142689957861, 19164121771855527, 2512960932249207, -324170737967403, 94418097588513, -54542846745063, -16686030795034, 1542463152066, 277314343372, 78412982262, -4368885822, -1907648811, -667433366, 116115168, 1046198, 4807612, -87714, 4376, -14130, 1116, -366, 77, -3, 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': '1.15.2t1.a', 'Character': [[1], [-1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.178215.3t2.a', 'Character': [[2], [0], [2], [2], [2], [2], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 2, 'Baselabel': '2.178215.9t3.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': 1, 'Baselabel': '2.178215.9t3.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': '2.178215.9t3.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': 3, 'Baselabel': '2.178215.27t8.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': 2, 'Baselabel': '2.178215.27t8.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': 5, 'Baselabel': '2.178215.27t8.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': 9, 'Baselabel': '2.178215.27t8.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': 6, 'Baselabel': '2.178215.27t8.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': 1, 'Baselabel': '2.178215.27t8.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, 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