Artin representation data - 3.340736.42t37.a

Formats: - HTML - YAML - JSON - 2024-04-30T13:20:00.901704

• 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, 11], 'Baselabel': '3.340736.42t37.a', 'CharacterField': 7, 'Conductor': 340736, 'Container': '42t37', 'Dets': ['1.1.1t1.a.a', '1.1.1t1.a.a'], 'Dim': 3, 'GalConjSigns': [0, 0], 'Galn': 7, 'GaloisConjugates': [{'Sign': 0, 'Character': [[3], [-1], [0], [1], [0, 1, 1, 0, 1], [-1, -1, -1, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [7, 7, 4], 'LocalFactors': [[[1], [-3], [3], [-1]], [[1], [1], [-1], [-1]], [[1], [0], [0], [-1]], [[1], [-1], [1], [-1]], [[1], [0, -1, -1, 0, -1], [-1, -1, -1, 0, -1], [-1]], [[1], [1, 1, 1, 0, 1], [0, 1, 1, 0, 1], [-1]], [[1]]]}, {'Sign': 0, 'Character': [[3], [-1], [0], [1], [-1, -1, -1, 0, -1], [0, 1, 1, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [7, 7, 4], 'LocalFactors': [[[1], [-3], [3], [-1]], [[1], [1], [-1], [-1]], [[1], [0], [0], [-1]], [[1], [-1], [1], [-1]], [[1], [1, 1, 1, 0, 1], [0, 1, 1, 0, 1], [-1]], [[1], [0, -1, -1, 0, -1], [-1, -1, -1, 0, -1], [-1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '7T5', 'Galt': 5, 'HardPrimes': [2, 11, 193], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-2, 10, 10, -14, -12, 2, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [168, 42], 'Proj_Polynomial': [-2, 10, 10, -14, -12, 2, -1, 1], 'Proj_nTj': [7, 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.340736.42t37.a', 'Character': [[3, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0], [-1, -1, -1, 0, -1, 0]], 'CharacterField': 7}, {'GalConj': 2, 'Baselabel': '3.340736.42t37.a', 'Character': [[3, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [-1, -1, -1, 0, -1, 0], [0, 1, 1, 0, 1, 0]], 'CharacterField': 7}, {'GalConj': 1, 'Baselabel': '6.1814078464.7t5.a', 'Character': [[6], [2], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '7.116101021696.8t37.a', 'Character': [[7], [-1], [1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.464404086784.21t14.a', 'Character': [[8], [0], [-1], [0], [1], [1]], 'CharacterField': 1}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7]}, {'Size': '21', 'Order': 2, 'Representative': [1, 6, 4, 3, 5, 2, 7]}, {'Size': '56', 'Order': 3, 'Representative': [4, 7, 2, 5, 1, 6, 3]}, {'Size': '42', 'Order': 4, 'Representative': [7, 1, 3, 2, 6, 5, 4]}, {'Size': '24', 'Order': 7, 'Representative': [7, 1, 4, 6, 2, 5, 3]}, {'Size': '24', 'Order': 7, 'Representative': [4, 3, 5, 2, 7, 1, 6]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 2, 4]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 3, 3]}, {'Data': [2, 3, 4, 5, 6, 7, 1], 'Classes': [{'RootOf': ['8220256', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-8220256', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'ALT', 'CycleType': [7]}], 'Frobs': [4, 4, 6, 6, 3, 6, 2, 3, 3, 3, 6, 3, 3, 6, 3, 3, 2, 4, 4, 6, 3, 5, 6, 4, 3, 4, 4, 3, 3, 5, 3, 3, 4, 5, 6, 4, 4, 3, 2, 6, 4, 4, 5, 4, 3, 5, 4, 3, 5, 3, 6, 3, 3, 3, 6, 5, 2, 4, 4, 3, 4, 6, 4, 3, 3, 5, 6, 6, 3, 4, 2, 3, 6, 4, 5, 3, 2, 5, 4, 3, 3, 3, 3, 3, 3, 4, 4, 3, 4, 6, 3, 4, 6, 3, 5, 3, 3, 3, 3, 5, 3, 3, 5, 6, 5, 4, 2, 4, 4, 3, 2, 3, 6, 3, 2, 3, 4, 2, 5, 5, 3, 4, 4, 4, 3, 4, 6, 4, 6, 2, 4, 4, 5, 3, 4, 4, 4, 2, 3, 3, 2, 4, 6, 6, 4, 2, 5, 3, 2, 5, 3, 6, 6, 3, 6, 4, 4, 5, 2, 3, 6, 3, 4, 2, 4, 3, 4, 4], 'G-Gens': [[7, 1, 3, 2, 6, 5, 4], [1, 6, 4, 3, 5, 2, 7]], 'G-Name': 'PSL(2,7)', 'Polynomial': [-2, 10, 10, -14, -12, 2, -1, 1], 'QpRts': [['442892015', '-52149453', '258062547'], ['248457184', '-195327249', '-333862364'], ['-147025242', '-90096700', '-258700339'], ['1169085', '0', '0'], ['209128544', '-175713873', '58667278'], ['399898588', '227863326', '-316729825'], ['-260648434', '285423949', '-301309036']], 'QpRts-minpoly': [17, 4, 0, 1], 'QpRts-p': 19, 'QpRts-prec': 7, 'Size': 168, 'TransitiveDegree': 7}