Artin representation data - 3.257.4t5.a

Formats: - HTML - YAML - JSON - 2025-01-14T02:15:28.461248

• 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': [257], 'Baselabel': '3.257.4t5.a', 'CharacterField': 1, 'Conductor': 257, 'Container': '4t5', 'Dets': ['1.257.2t1.a.a'], 'Dim': 3, 'GalConjSigns': [1], 'Galn': 4, 'GaloisConjugates': [{'Sign': 1, 'Character': [[3], [-1], [1], [0], [-1]], 'GalOrbIndex': 1, 'HardFactors': [6], 'LocalFactors': [[[1], [-3], [3], [-1]], [[1], [1], [-1], [-1]], [[1], [-1], [-1], [1]], [[1], [0], [0], [-1]], [[1], [1], [1], [1]], [[1], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '4T5', 'Galt': 5, 'HardPrimes': [257], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [1, -1, 1, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [24, 12], 'Proj_Polynomial': [1, -1, 1, 0, 1], 'Proj_nTj': [4, 5]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.257.2t1.a', 'Character': [[1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.257.3t2.a', 'Character': [[2], [2], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.66049.6t8.a', 'Character': [[3], [-1], [-1], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.257.4t5.a', 'Character': [[3], [-1], [1], [0], [-1]], 'CharacterField': 1}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4]}, {'Size': '3', 'Order': 2, 'Representative': [2, 1, 4, 3]}, {'Size': '6', 'Order': 2, 'Representative': [2, 1, 3, 4]}, {'Size': '8', 'Order': 3, 'Representative': [2, 3, 1, 4]}, {'Size': '6', 'Order': 4, 'Representative': [2, 3, 4, 1]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 3]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [4]}], 'Frobs': [4, 5, 5, 5, 4, 4, 4, 3, 4, 4, 4, 5, 3, 5, 3, 5, 4, 2, 2, 3, 4, 4, 3, 4, 3, 5, 3, 3, 3, 2, 3, 5, 4, 4, 5, 5, 1, 5, 5, 4, 3, 5, 5, 2, 2, 4, 4, 4, 2, 5, 3, 4, 2, 5, 3, 3, 3, 5, 3, 5, 4, 4, 4, 3, 3, 4, 3, 3, 3, 4, 5, 3, 3, 4, 4, 3, 3, 4, 4, 5, 2, 3, 5, 4, 5, 3, 5, 4, 3, 5, 5, 4, 5, 4, 2, 4, 3, 5, 4, 3, 5, 5, 4, 5, 4, 3, 2, 4, 3, 5, 5, 4, 5, 3, 2, 3, 1, 4, 1, 5, 5, 4, 3, 4, 3, 4, 4, 4, 4, 5, 2, 5, 5, 5, 3, 4, 4, 4, 4, 3, 5, 1, 2, 5, 4, 4, 5, 5, 1, 2, 3, 3, 5, 4, 2, 4, 3, 2, 3, 3, 1, 3, 4, 2, 5, 3, 3, 2], 'G-Gens': [[2, 3, 4, 1], [2, 1, 3, 4]], 'G-Name': 'S4', 'Polynomial': [1, -1, 1, 0, 1], 'QpRts': [['-6462442719'], ['2002909206'], ['-20884558328'], ['25344091841']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 157, 'QpRts-prec': 5, 'Size': 24, 'TransitiveDegree': 4}