Artin representation data - 3.5239.6t6.a

Formats: - HTML - YAML - JSON - 2024-06-06T01:37:55.943890

• 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': [13, 31], 'Baselabel': '3.5239.6t6.a', 'CharacterField': 1, 'Conductor': 5239, 'Container': '6t6', 'Dets': ['1.31.2t1.a.a'], 'Dim': 3, 'GalConjSigns': [1], 'Galn': 6, 'GaloisConjugates': [{'Sign': 1, 'Character': [[3], [-3], [1], [-1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [5, 9, 10], 'LocalFactors': [[[1], [-3], [3], [-1]], [[1], [3], [3], [1]], [[1], [-1], [-1], [1]], [[1], [1], [-1], [-1]], [[1], [0], [0], [-1]], [[1], [0], [0], [-1]], [[1], [0], [0], [1]], [[1], [0], [0], [1]], [[1], [1]], [[1], [2], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '6T6', 'Galt': 6, 'HardPrimes': [2, 13, 31], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [1, -3, -1, 7, -3, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [12, 3], 'Proj_Polynomial': [18, 7, -6, -1, 1], 'Proj_nTj': [4, 4]}
• 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': '1.31.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.13.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.403.6t1.e', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [-1, -1], [0, 1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.403.6t1.e', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [-1, -1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.13.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '3.162409.4t4.a', 'Character': [[3], [3], [-1], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.5239.6t6.a', 'Character': [[3], [-3], [1], [-1], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6]}, {'Size': '1', 'Order': 2, 'Representative': [6, 3, 2, 5, 4, 1]}, {'Size': '3', 'Order': 2, 'Representative': [6, 2, 3, 4, 5, 1]}, {'Size': '3', 'Order': 2, 'Representative': [6, 3, 2, 4, 5, 1]}, {'Size': '4', 'Order': 3, 'Representative': [4, 1, 6, 2, 3, 5]}, {'Size': '4', 'Order': 3, 'Representative': [2, 4, 5, 1, 6, 3]}, {'Size': '4', 'Order': 6, 'Representative': [5, 1, 6, 2, 3, 4]}, {'Size': '4', 'Order': 6, 'Representative': [2, 4, 5, 6, 1, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 2]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['2675', '205', '91', '4', '1'], 'ConjugacyClass': 5}, {'RootOf': ['1973', '-1069', '221', '-22', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['2613', '143', '91', '4', '1'], 'ConjugacyClass': 7}, {'RootOf': ['2314', '-1131', '221', '-22', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [6]}], 'Frobs': [6, 8, 4, 5, 8, 2, 7, 5, 8, 8, 4, 8, 6, 7, 4, 2, 5, 7, 6, 5, 3, 3, 3, 8, 5, 6, 4, 6, 4, 5, 8, 4, 7, 7, 5, 3, 1, 5, 8, 5, 8, 3, 5, 6, 8, 7, 6, 8, 5, 3, 4, 3, 7, 7, 6, 8, 7, 8, 7, 1, 6, 5, 1, 4, 2, 4, 7, 3, 7, 6, 8, 4, 8, 5, 6, 7, 3, 5, 8, 7, 6, 4, 6, 7, 6, 4, 7, 8, 7, 2, 4, 6, 7, 8, 3, 5, 8, 4, 8, 1, 4, 8, 5, 8, 2, 4, 8, 4, 4, 8, 5, 8, 5, 3, 7, 7, 7, 8, 6, 5, 6, 8, 3, 5, 6, 4, 7, 7, 4, 4, 8, 8, 6, 8, 7, 6, 7, 7, 7, 8, 4, 8, 7, 3, 8, 5, 4, 1, 3, 2, 5, 8, 2, 6, 6, 3, 5, 7, 4, 3, 8, 7, 3, 5, 6, 3, 8, 5], 'G-Gens': [[6, 2, 3, 4, 5, 1], [1, 2, 3, 5, 4, 6], [1, 3, 2, 4, 5, 6], [4, 1, 6, 2, 3, 5]], 'G-Name': 'C2*A4', 'Polynomial': [1, -3, -1, 7, -3, -1, 1], 'QpRts': [['-592980486', '0'], ['-2748048602', '-387956011'], ['3930756564', '387956011'], ['-937797867', '-5088536345'], ['1682815749', '5088536345'], ['-1334745357', '0']], 'QpRts-minpoly': [5, 45, 1], 'QpRts-p': 47, 'QpRts-prec': 6, 'Size': 24, 'TransitiveDegree': 6}