Artin representation data - 2.57600.8t5.d

Formats: - HTML - YAML - JSON - 2025-01-25T18:19:28.465297

• 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.d', '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], '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], 'Hide': 0, 'Indicator': -1, 'Is_Even': True, 'NFGal': [22500, 0, 9000, 0, 1170, 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': '1.5.2t1.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': '1.120.2t1.a', 'Character': [[1], [1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.57600.8t5.d', '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': [4, 3, 7, 8, 1, 2, 6, 5]}, {'Size': '2', 'Order': 4, 'Representative': [7, 1, 5, 3, 6, 4, 8, 2]}, {'Size': '2', 'Order': 4, 'Representative': [3, 5, 8, 2, 7, 1, 4, 6]}], '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': ['-822288240000', '0', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-956593800000', '0', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-414892800000', '0', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [4, 4]}], 'Frobs': [3, 5, 1, 5, 4, 5, 5, 2, 3, 1, 4, 5, 4, 3, 3, 3, 4, 4, 3, 1, 3, 4, 5, 4, 3, 1, 5, 5, 4, 5, 5, 4, 5, 2, 2, 4, 5, 3, 3, 3, 4, 4, 2, 3, 3, 4, 1, 5, 5, 4, 5, 1, 2, 4, 5, 3, 1, 4, 5, 4, 3, 3, 3, 2, 3, 3, 2, 3, 5, 4, 5, 1, 5, 5, 1, 3, 1, 5, 4, 1, 4, 4, 2, 3, 4, 5, 4, 3, 1, 5, 5, 2, 5, 4, 1, 3, 2, 4, 3, 4, 3, 3, 5, 4, 2, 3, 5, 5, 1, 1, 5, 5, 5, 2, 4, 4, 3, 3, 3, 4, 4, 3, 3, 5, 1, 1, 4, 1, 5, 5, 1, 3, 4, 5, 4, 1, 3, 3, 3, 4, 2, 2, 5, 5, 4, 1, 5, 5, 1, 3, 5, 4, 3, 3, 3, 1, 4, 4, 3, 2, 5, 5, 5, 4, 5, 3, 4, 5], 'G-Gens': [[8, 7, 6, 5, 4, 3, 2, 1], [7, 1, 5, 3, 6, 4, 8, 2], [4, 3, 7, 8, 1, 2, 6, 5]], 'G-Name': 'Q8', 'Polynomial': [22500, 0, 9000, 0, 1170, 0, 60, 0, 1], 'QpRts': [['5043745730136588583'], ['1524503414784184615'], ['-2546986480986345700'], ['646030353015333179'], ['-646030353015333179'], ['2546986480986345700'], ['-1524503414784184615'], ['-5043745730136588583']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 29, 'QpRts-prec': 13, 'Size': 8, 'TransitiveDegree': 8}