Artin representation data - 1.23.11t1.a

Formats: - HTML - YAML - JSON - 2025-05-13T13:12:09.186049

• 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': [23], 'Baselabel': '1.23.11t1.a', 'CharacterField': 11, 'Conductor': 23, 'Container': '11t1', 'Dets': ['23.3', '23.9', '23.4', '23.12', '23.13', '23.16', '23.2', '23.6', '23.18', '23.8'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'Galn': 11, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [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, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]], 'GalOrbIndex': 1, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [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]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 4, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 5, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 6, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1]], 'GalOrbIndex': 7, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1]], 'GalOrbIndex': 8, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 1]], 'GalOrbIndex': 9, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [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, -1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 1], [0, 1]], 'GalOrbIndex': 10, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [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, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'GaloisLabel': '11T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 7, 11, 19, 23, 61, 163, 167, 241], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [1, -6, -15, 35, 35, -56, -28, 36, 9, -10, -1, 1], 'NumBadPrimes': 1, '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], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.23.11t1.a', 'Character': [[1, 0, 0, 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, 0], [0, 0, 0, 1, 0, 0, 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, 0, 0, 0, 0, 1, 0, 0, 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, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]], 'CharacterField': 11}, {'GalConj': 2, 'Baselabel': '1.23.11t1.a', 'Character': [[1, 0, 0, 0, 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, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 1, 0, 0, 0, 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, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]], 'CharacterField': 11}, {'GalConj': 3, 'Baselabel': '1.23.11t1.a', 'Character': [[1, 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, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 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, 1, 0, 0], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 1, 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, 1, 0]], 'CharacterField': 11}, {'GalConj': 4, 'Baselabel': '1.23.11t1.a', 'Character': [[1, 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, 1, 0], [0, 1, 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, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0]], 'CharacterField': 11}, {'GalConj': 5, 'Baselabel': '1.23.11t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0]], 'CharacterField': 11}, {'GalConj': 6, 'Baselabel': '1.23.11t1.a', 'Character': [[1, 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, 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, 0, 1, 0], [0, 0, 0, 1, 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, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0]], 'CharacterField': 11}, {'GalConj': 7, 'Baselabel': '1.23.11t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 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, 1], [0, 0, 0, 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, 1, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0]], 'CharacterField': 11}, {'GalConj': 8, 'Baselabel': '1.23.11t1.a', 'Character': [[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, 1, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 1, 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, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0]], 'CharacterField': 11}, {'GalConj': 9, 'Baselabel': '1.23.11t1.a', 'Character': [[1, 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, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0]], 'CharacterField': 11}, {'GalConj': 10, 'Baselabel': '1.23.11t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0]], 'CharacterField': 11}], 'ComplexConjugation': 1, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]}, {'Size': '1', 'Order': 11, 'Representative': [4, 5, 8, 6, 7, 2, 10, 9, 1, 11, 3]}, {'Size': '1', 'Order': 11, 'Representative': [6, 7, 9, 2, 10, 5, 11, 1, 4, 3, 8]}, {'Size': '1', 'Order': 11, 'Representative': [2, 10, 1, 5, 11, 7, 3, 4, 6, 8, 9]}, {'Size': '1', 'Order': 11, 'Representative': [5, 11, 4, 7, 3, 10, 8, 6, 2, 9, 1]}, {'Size': '1', 'Order': 11, 'Representative': [7, 3, 6, 10, 8, 11, 9, 2, 5, 1, 4]}, {'Size': '1', 'Order': 11, 'Representative': [10, 8, 2, 11, 9, 3, 1, 5, 7, 4, 6]}, {'Size': '1', 'Order': 11, 'Representative': [11, 9, 5, 3, 1, 8, 4, 7, 10, 6, 2]}, {'Size': '1', 'Order': 11, 'Representative': [3, 1, 7, 8, 4, 9, 6, 10, 11, 2, 5]}, {'Size': '1', 'Order': 11, 'Representative': [8, 4, 10, 9, 6, 1, 2, 11, 3, 5, 7]}, {'Size': '1', 'Order': 11, 'Representative': [9, 6, 11, 1, 2, 4, 5, 3, 8, 7, 10]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['1243', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-436', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-505', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-160', '1'], 'ConjugacyClass': 5}, {'RootOf': ['10811', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-459', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-7129', '1'], 'ConjugacyClass': 8}, {'RootOf': ['-2897', '1'], 'ConjugacyClass': 9}, {'RootOf': ['-965', '1'], 'ConjugacyClass': 10}, {'RootOf': ['5084', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [11]}], 'Frobs': [6, 8, 9, 10, 7, 3, 2, 11, 1, 2, 5, 4, 9, 8, 1, 10, 3, 5, 6, 6, 11, 3, 4, 8, 9, 4, 7, 5, 2, 6, 7, 10, 1, 1, 7, 3, 11, 6, 2, 7, 9, 8, 10, 4, 3, 5, 11, 10, 8, 1, 8, 4, 7, 6, 11, 3, 10, 9, 1, 9, 10, 2, 5, 7, 4, 9, 4, 5, 6, 11, 5, 4, 1, 9, 7, 5, 6, 2, 3, 9, 9, 10, 2, 11, 6, 2, 7, 8, 1, 8, 10, 11, 11, 5, 10, 8, 8, 5, 2, 7, 9, 9, 7, 2, 11, 6, 7, 9, 1, 8, 4, 5, 11, 6, 3, 8, 1, 8, 4, 5, 2, 2, 3, 10, 1, 7, 11, 2, 4, 8, 8, 10, 5, 6, 6, 3, 4, 9, 5, 11, 2, 10, 9, 1, 1, 7, 6, 2, 5, 7, 8, 10, 4, 3, 3, 4, 1, 4, 2, 6, 11, 3, 1, 9, 7, 2, 6, 5], 'G-Gens': [[4, 5, 8, 6, 7, 2, 10, 9, 1, 11, 3]], 'G-Name': 'C11', 'Polynomial': [1, -6, -15, 35, 35, -56, -28, 36, 9, -10, -1, 1], 'QpRts': [['-25071976', '10010490', '-15771523', '-9096703', '1734438', '-11205837', '-1464487', '-24474560', '5110455', '10113989', '-28017613'], ['26608211', '30058229', '-198585', '9940685', '-22369132', '22019945', '23582285', '20853816', '-30376943', '-27533052', '9756344'], ['-29845214', '-7752864', '12583123', '22784489', '-14901568', '-19113390', '-567425', '-11533218', '-4279641', '-12795704', '-485159'], ['2198740', '30244415', '-16747109', '-24570230', '30571065', '18472857', '-10971123', '-22619566', '29125890', '10676996', '-13835116'], ['-24470162', '-23233649', '3807249', '-31208757', '-12798485', '29776917', '15872025', '526732', '9429282', '31021782', '-11064010'], ['21517399', '14686954', '18150022', '595358', '-10754982', '-6778996', '-12734672', '4803152', '30158181', '27227752', '-476756'], ['7095199', '-19438210', '-26595983', '-25729214', '-6235490', '-15572760', '5306151', '-21978731', '13714969', '31169331', '-5764896'], ['-15421550', '2536033', '-31021845', '4874500', '21669922', '5563897', '12498994', '28477513', '8378930', '11514152', '-20295889'], ['-4635203', '-25596757', '-4422413', '-19409436', '-8522266', '22647832', '-1932537', '-23656079', '3743890', '6247823', '2483660'], ['-3816883', '-27703391', '4991791', '-22359441', '18443809', '27342387', '12434842', '23879861', '-13448928', '24325343', '23699883'], ['-16907077', '16188750', '-7523244', '-31318285', '3162689', '-10404335', '20724464', '25721080', '11192432', '13528622', '-18748965']], 'QpRts-minpoly': [11, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'QpRts-p': 13, 'QpRts-prec': 7, 'Size': 11, 'TransitiveDegree': 11}