Artin representation data - 4.12960000.8t23.c

Formats: - HTML - YAML - JSON - 2025-09-02T23:24:36.344276

• 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': '4.12960000.8t23.c', 'CharacterField': 1, 'Conductor': 12960000, 'Container': '8t23', 'Dets': ['1.1.1t1.a.a'], 'Dim': 4, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[4], [-4], [0], [1], [0], [-1], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [9, 9, 9, 3], 'LocalFactors': [[[1], [-4], [6], [-4], [1]], [[1], [4], [6], [4], [1]], [[1], [0], [-2], [0], [1]], [[1], [-1], [0], [-1], [1]], [[1], [0], [2], [0], [1]], [[1], [1], [0], [1], [1]], [[1], [0], [0], [0], [1]], [[1], [0], [0], [0], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T23', 'Galt': 23, 'HardPrimes': [2, 3, 5, 1049], 'Hide': 1, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-5, -10, 10, -40, 40, -10, 4, -4, 1], 'NumBadPrimes': 3, 'Proj_GAP': [24, 12], 'Proj_Polynomial': [4, -8, 0, -2, 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], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.3.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.300.3t2.a', 'Character': [[2], [2], [0], [-1], [2], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.3600.24t22.d', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, -1, 0, -1], [0, 1, 0, 1]], 'CharacterField': 8}, {'GalConj': 2, 'Baselabel': '2.3600.24t22.d', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 1], [0, -1, 0, -1]], 'CharacterField': 8}, {'GalConj': 1, 'Baselabel': '3.3600.6t8.b', 'Character': [[3], [3], [-1], [0], [-1], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.10800.4t5.d', 'Character': [[3], [3], [1], [0], [-1], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.12960000.8t23.c', 'Character': [[4], [-4], [0], [1], [0], [-1], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [4, 3, 2, 1, 7, 8, 5, 6]}, {'Size': '12', 'Order': 2, 'Representative': [5, 2, 3, 7, 1, 8, 4, 6]}, {'Size': '8', 'Order': 3, 'Representative': [8, 4, 1, 6, 5, 2, 7, 3]}, {'Size': '6', 'Order': 4, 'Representative': [5, 8, 6, 7, 4, 2, 1, 3]}, {'Size': '8', 'Order': 6, 'Representative': [2, 8, 6, 3, 7, 1, 5, 4]}, {'Size': '6', 'Order': 8, 'Representative': [3, 5, 7, 2, 6, 1, 8, 4]}, {'Size': '6', 'Order': 8, 'Representative': [2, 7, 5, 3, 8, 4, 6, 1]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 3, 3]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [2, 6]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [4, 4]}, {'Data': {'Powers': [1, 3], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['-6480', '1080', '-60', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-6480', '1440', '-60', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [8]}], 'Frobs': [3, 3, 3, 4, 7, 4, 8, 4, 8, 8, 4, 5, 3, 6, 8, 3, 8, 6, 4, 3, 5, 5, 7, 3, 4, 3, 2, 3, 4, 3, 5, 3, 7, 5, 7, 6, 4, 6, 3, 8, 8, 4, 8, 4, 7, 6, 6, 4, 3, 6, 3, 3, 4, 3, 3, 3, 7, 5, 6, 8, 4, 7, 6, 8, 6, 3, 5, 4, 7, 5, 8, 3, 4, 4, 4, 3, 3, 4, 3, 6, 3, 5, 8, 6, 4, 3, 3, 1, 3, 5, 7, 7, 6, 3, 6, 3, 8, 8, 6, 6, 1, 8, 8, 7, 4, 6, 3, 3, 3, 6, 5, 5, 3, 6, 4, 3, 5, 3, 8, 3, 5, 5, 7, 3, 2, 7, 4, 7, 4, 5, 5, 3, 5, 6, 3, 6, 3, 4, 3, 3, 6, 8, 6, 3, 2, 8, 6, 3, 2, 3, 4, 3, 4, 8, 5, 7, 6, 8, 4, 8, 8, 3, 5, 8, 8, 3, 6, 5], 'G-Gens': [[6, 2, 3, 8, 4, 7, 1, 5], [4, 3, 2, 1, 7, 8, 5, 6], [5, 8, 6, 7, 4, 2, 1, 3], [5, 2, 3, 7, 1, 8, 4, 6], [6, 5, 7, 8, 3, 4, 2, 1]], 'G-Name': 'GL2(F3)', 'Polynomial': [-5, -10, 10, -40, 40, -10, 4, -4, 1], 'QpRts': [['34490425520812', '74590134966823'], ['91404202782059', '76646118929436'], ['125289093009140', '-76646118929436'], ['124827541274032', '67721495817144'], ['70449156916746', '0'], ['146502706327187', '-74590134966823'], ['-108665432416298', '0'], ['-156915759019713', '-67721495817144']], 'QpRts-minpoly': [6, 38, 1], 'QpRts-p': 41, 'QpRts-prec': 9, 'Size': 48, 'TransitiveDegree': 8}