Artin representation data - 2.1759.27t8.a

Formats: - HTML - YAML - JSON - 2024-10-07T04:13:00.369464

• 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': [1759], 'Baselabel': '2.1759.27t8.a', 'CharacterField': 27, 'Conductor': 1759, 'Container': '27t8', 'Dets': ['1.1759.2t1.a.a', '1.1759.2t1.a.a', '1.1759.2t1.a.a', '1.1759.2t1.a.a', '1.1759.2t1.a.a', '1.1759.2t1.a.a', '1.1759.2t1.a.a', '1.1759.2t1.a.a', '1.1759.2t1.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, -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': 1, 'HardFactors': [4, 2, 15, 2, 8, 10, 2, 2, 11, 2, 7, 2, 2, 2, 2, 2, 2, 2, 16], '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]]]}, {'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': 2, 'HardFactors': [4, 2, 15, 2, 8, 10, 2, 2, 11, 2, 7, 2, 2, 2, 2, 2, 2, 2, 16], '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]]]}, {'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': 3, 'HardFactors': [4, 2, 15, 2, 8, 10, 2, 2, 11, 2, 7, 2, 2, 2, 2, 2, 2, 2, 16], '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]]]}, {'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': 4, 'HardFactors': [4, 2, 15, 2, 8, 10, 2, 2, 11, 2, 7, 2, 2, 2, 2, 2, 2, 2, 16], '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]]]}, {'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': 5, 'HardFactors': [4, 2, 15, 2, 8, 10, 2, 2, 11, 2, 7, 2, 2, 2, 2, 2, 2, 2, 16], '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]]]}, {'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': 6, 'HardFactors': [4, 2, 15, 2, 8, 10, 2, 2, 11, 2, 7, 2, 2, 2, 2, 2, 2, 2, 16], '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]]]}, {'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': 7, 'HardFactors': [4, 2, 15, 2, 8, 10, 2, 2, 11, 2, 7, 2, 2, 2, 2, 2, 2, 2, 16], '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]]]}, {'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': 8, 'HardFactors': [4, 2, 15, 2, 8, 10, 2, 2, 11, 2, 7, 2, 2, 2, 2, 2, 2, 2, 16], '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]]]}, {'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': 9, 'HardFactors': [4, 2, 15, 2, 8, 10, 2, 2, 11, 2, 7, 2, 2, 2, 2, 2, 2, 2, 16], '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]]]}], 'GaloisConjugatesSigns': [1, 1, 1, 1, 1, 1, 1, 1, 1], 'GaloisLabel': '27T8', 'Galt': 8, 'HardPrimes': [2, 3, 5, 7, 13, 17, 29, 37, 41, 67, 71, 73, 97, 103, 151, 283, 859, 1039, 1759], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-1, 179, -1350, 5393, -14664, 31122, -54357, 81027, -105567, 121785, -125268, 115269, -94575, 68751, -43548, 23103, -9345, 1935, 966, -1350, 807, -243, -51, 117, -80, 31, -6, 1], 'NumBadPrimes': 1, 'Proj_GAP': [54, 1], 'Proj_Polynomial': [-1, 179, -1350, 5393, -14664, 31122, -54357, 81027, -105567, 121785, -125268, 115269, -94575, 68751, -43548, 23103, -9345, 1935, 966, -1350, 807, -243, -51, 117, -80, 31, -6, 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': '1.1759.2t1.a', 'Character': [[1], [-1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.1759.3t2.a', 'Character': [[2], [0], [2], [2], [2], [2], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.1759.9t3.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': '2.1759.9t3.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': '2.1759.9t3.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': 8, 'Baselabel': '2.1759.27t8.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': 5, 'Baselabel': '2.1759.27t8.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': 4, 'Baselabel': '2.1759.27t8.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': 7, 'Baselabel': '2.1759.27t8.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': 1, 'Baselabel': '2.1759.27t8.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': 2, 'Baselabel': '2.1759.27t8.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, 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