Artin representation data - 1.671.5t1.a

Formats: - HTML - YAML - JSON - 2025-10-21T19:57:47.342441

• 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': [11, 61], 'Baselabel': '1.671.5t1.a', 'CharacterField': 5, 'Conductor': 671, 'Container': '5t1', 'Dets': ['671.20', '671.400', '671.619', '671.302'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 5, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [-1, -1, -1, -1]], 'GalOrbIndex': 1, 'HardFactors': [1, 2, 6, 2, 5, 6, 1], 'LocalFactors': [[[1], [-1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 1], [-1, -1, -1, -1], [0, 1], [0, 0, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [1, 2, 6, 2, 5, 6, 1], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1], [0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [1, 2, 6, 2, 5, 6, 1], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1], [0, 1]], 'GalOrbIndex': 4, 'HardFactors': [1, 2, 6, 2, 5, 6, 1], 'LocalFactors': [[[1], [-1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '5T1', 'Galt': 1, 'HardPrimes': [2, 3, 11, 19, 23, 61, 107], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1024, 4128, -1020, -268, -1, 1], 'NumBadPrimes': 2, '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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.671.5t1.a', 'Character': [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1]], 'CharacterField': 5}, {'GalConj': 2, 'Baselabel': '1.671.5t1.a', 'Character': [[1, 0, 0, 0], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 0, 1]], 'CharacterField': 5}, {'GalConj': 3, 'Baselabel': '1.671.5t1.a', 'Character': [[1, 0, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 1, 0]], 'CharacterField': 5}, {'GalConj': 4, 'Baselabel': '1.671.5t1.a', 'Character': [[1, 0, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]], 'CharacterField': 5}], 'ComplexConjugation': 1, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5]}, {'Size': '1', 'Order': 5, 'Representative': [3, 4, 5, 1, 2]}, {'Size': '1', 'Order': 5, 'Representative': [5, 1, 2, 3, 4]}, {'Size': '1', 'Order': 5, 'Representative': [2, 3, 4, 5, 1]}, {'Size': '1', 'Order': 5, 'Representative': [4, 5, 1, 2, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [2, 5, -2, -7, 1]}, 'Classes': [{'RootOf': ['-288564', '1'], 'ConjugacyClass': 2}, {'RootOf': ['1010492', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-492548', '1'], 'ConjugacyClass': 4}, {'RootOf': ['452220', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [5]}], 'Frobs': [1, 2, 2, 5, 1, 4, 2, 2, 5, 2, 2, 5, 3, 2, 5, 5, 4, 1, 5, 4, 3, 5, 5, 3, 2, 4, 4, 1, 1, 4, 2, 5, 4, 1, 4, 5, 2, 2, 2, 1, 4, 5, 3, 4, 1, 4, 1, 5, 1, 5, 4, 4, 3, 2, 2, 3, 1, 3, 1, 1, 2, 3, 3, 4, 4, 5, 3, 2, 5, 4, 1, 5, 2, 4, 3, 3, 1, 4, 5, 5, 2, 4, 3, 1, 2, 3, 1, 1, 2, 4, 3, 2, 5, 4, 2, 1, 5, 4, 5, 5, 2, 3, 4, 3, 3, 5, 1, 5, 3, 1, 1, 2, 4, 4, 2, 3, 5, 2, 3, 2, 2, 1, 2, 2, 2, 3, 2, 2, 5, 2, 2, 3, 2, 2, 4, 4, 3, 2, 2, 1, 1, 4, 2, 5, 5, 1, 3, 3, 5, 2, 4, 2, 5, 4, 4, 3, 2, 3, 1, 5, 1, 1, 5, 4, 4, 5, 2, 2], 'G-Gens': [[3, 4, 5, 1, 2]], 'G-Name': 'C5', 'Polynomial': [-1024, 4128, -1020, -268, -1, 1], 'QpRts': [['-595371062553'], ['-517474505212'], ['-451887242650'], ['189172858801'], ['-301540159226']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 109, 'QpRts-prec': 6, 'Size': 5, 'TransitiveDegree': 5}