Artin representation data - 2.57600.8t5.b

Formats: - HTML - YAML - JSON - 2023-12-04T17:27:25.329415

• 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, 3, 5], 'Baselabel': '2.57600.8t5.b', 'CharacterField': 1, 'Conductor': 57600, 'Container': '8t5', 'Dets': ['1.1.1t1.a.a'], 'Dim': 2, 'GalConjSigns': [-1], 'Galn': 8, 'GaloisConjugates': [{'Sign': -1, 'Character': [[2], [-2], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [6, 6, 6, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [1]], [[1], [0], [1]], [[1], [0], [1]], [[1]]]}], 'GaloisConjugatesSigns': [-1], 'GaloisLabel': '8T5', 'Galt': 5, 'HardPrimes': [2, 3, 5, 19], 'Hide': 0, 'Indicator': -1, 'Is_Even': True, 'NFGal': [900, 0, 1800, 0, 810, 0, 60, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [4, 2], 'Proj_Polynomial': [19, 14, -13, -2, 1], 'Proj_nTj': [4, 2]}
• 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': '1.120.2t1.a', 'Character': [[1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.5.2t1.a', 'Character': [[1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.24.2t1.a', 'Character': [[1], [1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.57600.8t5.b', 'Character': [[2], [-2], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [8, 7, 6, 5, 4, 3, 2, 1]}, {'Size': '2', 'Order': 4, 'Representative': [6, 5, 1, 2, 7, 8, 4, 3]}, {'Size': '2', 'Order': 4, 'Representative': [4, 6, 2, 8, 1, 7, 3, 5]}, {'Size': '2', 'Order': 4, 'Representative': [7, 1, 4, 6, 3, 5, 8, 2]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['-1448296200000', '0', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-10563706800000', '0', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-481213440000', '0', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [4, 4]}], 'Frobs': [4, 4, 1, 4, 3, 4, 4, 1, 5, 2, 3, 4, 3, 5, 5, 5, 3, 3, 5, 1, 5, 3, 4, 3, 5, 2, 4, 4, 3, 4, 4, 3, 4, 1, 1, 3, 4, 5, 5, 5, 3, 3, 2, 5, 5, 3, 2, 4, 4, 3, 4, 1, 2, 3, 4, 5, 2, 3, 4, 3, 5, 5, 5, 2, 5, 5, 1, 5, 4, 3, 4, 1, 4, 4, 2, 5, 2, 4, 3, 1, 3, 3, 2, 5, 3, 4, 3, 5, 2, 4, 4, 2, 4, 3, 2, 5, 1, 3, 5, 3, 5, 5, 4, 3, 1, 5, 4, 4, 1, 1, 4, 4, 4, 1, 3, 3, 5, 5, 5, 3, 3, 5, 5, 4, 2, 2, 3, 1, 4, 4, 2, 5, 3, 4, 3, 1, 5, 5, 5, 3, 1, 1, 4, 4, 3, 1, 4, 4, 2, 5, 4, 3, 5, 5, 5, 1, 3, 3, 5, 1, 4, 4, 4, 3, 4, 5, 3, 4], 'G-Gens': [[8, 7, 6, 5, 4, 3, 2, 1], [4, 6, 2, 8, 1, 7, 3, 5], [6, 5, 1, 2, 7, 8, 4, 3]], 'G-Name': 'Q8', 'Polynomial': [900, 0, 1800, 0, 810, 0, 60, 0, 1], 'QpRts': [['15137790872300442375'], ['-82222622667074630354'], ['-72639616434004491888'], ['-23728754679891853401'], ['23728754679891853401'], ['72639616434004491888'], ['82222622667074630354'], ['-15137790872300442375']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 71, 'QpRts-prec': 11, 'Size': 8, 'TransitiveDegree': 8}