Artin representation data - 2.71.7t2.a

Formats: - HTML - YAML - JSON - 2025-12-06T16:24:13.365161

• 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': [71], 'Baselabel': '2.71.7t2.a', 'CharacterField': 7, 'Conductor': 71, 'Container': '7t2', 'Dets': ['1.71.2t1.a.a', '1.71.2t1.a.a', '1.71.2t1.a.a'], 'Dim': 2, 'GalConjSigns': [1, 1, 1], 'Galn': 7, 'GaloisConjugates': [{'Sign': 1, 'Character': [[2], [0], [-1, 0, -1, -1, -1, -1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 1]], 'GalOrbIndex': 1, 'HardFactors': [4, 3, 5, 6], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1, 0, 1, 1, 1, 1], [1]], [[1], [0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, 0, -1, -1], [1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [0], [0, 0, 0, 1, 1], [-1, 0, -1, -1, -1, -1], [0, 0, 1, 0, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [4, 3, 5, 6], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [0, 0, 0, -1, -1], [1]], [[1], [1, 0, 1, 1, 1, 1], [1]], [[1], [0, 0, -1, 0, 0, -1], [1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [0], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 1], [-1, 0, -1, -1, -1, -1]], 'GalOrbIndex': 3, 'HardFactors': [4, 3, 5, 6], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, 0, -1, -1], [1]], [[1], [1, 0, 1, 1, 1, 1], [1]], [[1], [-1]]]}], 'GaloisConjugatesSigns': [1, 1, 1], 'GaloisLabel': '7T2', 'Galt': 2, 'HardPrimes': [2, 3, 5, 71], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [1, 2, -1, -1, 1, -1, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [14, 1], 'Proj_Polynomial': [1, 2, -1, -1, 1, -1, -1, 1], 'Proj_nTj': [7, 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': '1.71.2t1.a', 'Character': [[1], [-1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.71.7t2.a', 'Character': [[2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-1, 0, -1, -1, -1, -1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 1, 0]], 'CharacterField': 7}, {'GalConj': 2, 'Baselabel': '2.71.7t2.a', 'Character': [[2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0], [-1, 0, -1, -1, -1, -1], [0, 0, 1, 0, 0, 1]], 'CharacterField': 7}, {'GalConj': 3, 'Baselabel': '2.71.7t2.a', 'Character': [[2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 1, 0], [-1, 0, -1, -1, -1, -1]], 'CharacterField': 7}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7]}, {'Size': '7', 'Order': 2, 'Representative': [2, 1, 6, 7, 5, 3, 4]}, {'Size': '2', 'Order': 7, 'Representative': [3, 7, 5, 1, 6, 2, 4]}, {'Size': '2', 'Order': 7, 'Representative': [5, 4, 6, 3, 2, 7, 1]}, {'Size': '2', 'Order': 7, 'Representative': [6, 1, 2, 5, 7, 4, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 2]}, {'Data': {'Powers': [1, 6], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['6', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-6', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-14', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [7]}], 'Frobs': [4, 3, 5, 2, 2, 2, 2, 4, 2, 3, 2, 4, 2, 5, 2, 2, 2, 2, 2, 1, 5, 5, 4, 3, 2, 4, 3, 1, 3, 2, 2, 5, 2, 2, 2, 3, 3, 2, 5, 2, 5, 2, 3, 2, 2, 4, 2, 4, 2, 5, 4, 2, 2, 4, 2, 5, 2, 3, 4, 2, 2, 1, 2, 4, 4, 2, 2, 2, 2, 2, 2, 5, 5, 5, 3, 2, 2, 2, 2, 3, 3, 2, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 3, 3, 1, 5, 2, 2, 4, 3, 2, 5, 4, 5, 3, 3, 2, 2, 2, 3, 5, 2, 2, 4, 1, 1, 2, 3, 2, 2, 3, 2, 2, 2, 2, 4, 2, 2, 1, 2, 2, 2, 2, 2, 2, 3, 4, 2, 5, 4, 2, 2, 4, 4, 3, 3, 2, 2, 5, 5, 2, 2, 2, 2, 2, 4, 2, 4, 5, 5, 2, 1, 3, 4, 2, 5], 'G-Gens': [[2, 1, 6, 7, 5, 3, 4], [7, 3, 2, 4, 6, 5, 1]], 'G-Name': 'D14', 'Polynomial': [1, 2, -1, -1, 1, -1, -1, 1], 'QpRts': [['22012', '33430'], ['68266', '-58174'], ['46567', '-60846'], ['-50947', '-33430'], ['-7669', '58174'], ['-67564', '0'], ['-10664', '60846']], 'QpRts-minpoly': [2, 7, 1], 'QpRts-p': 11, 'QpRts-prec': 5, 'Size': 14, 'TransitiveDegree': 7}