Artin representation data - 1.71.7t1.a

Formats: - HTML - YAML - JSON - 2024-04-28T19:48:53.957463

• 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': '1.71.7t1.a', 'CharacterField': 7, 'Conductor': 71, 'Container': '7t1', 'Dets': ['71.20', '71.45', '71.48', '71.37', '71.30', '71.32'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0], 'Galn': 7, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1]], 'GalOrbIndex': 1, 'HardFactors': [4, 7, 1, 5, 6, 1, 7, 4, 8, 7, 5, 5], 'LocalFactors': [[[1], [-1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 1], [0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1], [0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [4, 7, 1, 5, 6, 1, 7, 4, 8, 7, 5, 5], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [-1, -1, -1, -1, -1, -1], [0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [4, 7, 1, 5, 6, 1, 7, 4, 8, 7, 5, 5], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 1], [-1, -1, -1, -1, -1, -1], [0, 0, 0, 1]], 'GalOrbIndex': 4, 'HardFactors': [4, 7, 1, 5, 6, 1, 7, 4, 8, 7, 5, 5], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 1], [0, 0, 1]], 'GalOrbIndex': 5, 'HardFactors': [4, 7, 1, 5, 6, 1, 7, 4, 8, 7, 5, 5], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 1], [0, 1]], 'GalOrbIndex': 6, 'HardFactors': [4, 7, 1, 5, 6, 1, 7, 4, 8, 7, 5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0], 'GaloisLabel': '7T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 7, 11, 17, 29, 37, 71, 157, 1103, 1109], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-137, -245, 246, 254, -3, -30, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.71.7t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1]], 'CharacterField': 7}, {'GalConj': 2, 'Baselabel': '1.71.7t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [-1, -1, -1, -1, -1, -1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]], 'CharacterField': 7}, {'GalConj': 3, 'Baselabel': '1.71.7t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, -1, -1, -1, -1, -1], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]], 'CharacterField': 7}, {'GalConj': 4, 'Baselabel': '1.71.7t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [-1, -1, -1, -1, -1, -1], [0, 0, 0, 1, 0, 0]], 'CharacterField': 7}, {'GalConj': 5, 'Baselabel': '1.71.7t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [-1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]], 'CharacterField': 7}, {'GalConj': 6, 'Baselabel': '1.71.7t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [-1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]], 'CharacterField': 7}], 'ComplexConjugation': 1, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7]}, {'Size': '1', 'Order': 7, 'Representative': [2, 7, 4, 6, 3, 1, 5]}, {'Size': '1', 'Order': 7, 'Representative': [7, 5, 6, 1, 4, 2, 3]}, {'Size': '1', 'Order': 7, 'Representative': [5, 3, 1, 2, 6, 7, 4]}, {'Size': '1', 'Order': 7, 'Representative': [3, 4, 2, 7, 1, 5, 6]}, {'Size': '1', 'Order': 7, 'Representative': [4, 6, 7, 5, 2, 3, 1]}, {'Size': '1', 'Order': 7, 'Representative': [6, 1, 5, 3, 7, 4, 2]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['41741', '1'], 'ConjugacyClass': 2}, {'RootOf': ['32014', '1'], 'ConjugacyClass': 3}, {'RootOf': ['24133', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-54180', '1'], 'ConjugacyClass': 5}, {'RootOf': ['24559', '1'], 'ConjugacyClass': 6}, {'RootOf': ['9720', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [7]}], 'Frobs': [4, 7, 1, 5, 6, 3, 1, 2, 5, 7, 3, 4, 3, 4, 2, 2, 6, 4, 7, 1, 4, 3, 6, 2, 6, 3, 2, 5, 5, 7, 7, 6, 1, 7, 5, 6, 7, 4, 1, 3, 4, 2, 2, 7, 6, 1, 4, 4, 1, 6, 7, 6, 4, 5, 5, 4, 7, 3, 5, 7, 1, 6, 5, 5, 7, 5, 2, 2, 3, 3, 4, 7, 6, 2, 2, 4, 4, 7, 1, 1, 5, 1, 1, 5, 3, 1, 5, 3, 5, 4, 3, 2, 4, 3, 4, 3, 6, 2, 6, 5, 4, 6, 1, 1, 7, 6, 2, 1, 3, 5, 2, 6, 2, 7, 3, 4, 7, 3, 1, 7, 2, 4, 5, 5, 2, 6, 1, 6, 1, 5, 7, 5, 3, 2, 7, 6, 3, 3, 6, 4, 3, 3, 7, 1, 5, 3, 1, 1, 5, 6, 1, 7, 3, 5, 6, 6, 7, 3, 1, 2, 2, 3, 5, 5, 1, 6, 7, 7], 'G-Gens': [[2, 7, 4, 6, 3, 1, 5]], 'G-Name': 'C7', 'Polynomial': [-137, -245, 246, 254, -3, -30, -1, 1], 'QpRts': [['66923194', '-41405600', '37443355', '-45378741', '43710667', '-103608646', '46314125'], ['12347902', '-35641696', '-94290291', '34527157', '-71237786', '-90898893', '-76783109'], ['51430748', '-71613139', '-40350490', '102198418', '-58522376', '-98557378', '59658735'], ['-25721195', '74422812', '63908278', '73008605', '-57257801', '-33874161', '46087705'], ['-21801533', '-101022451', '71417033', '71984927', '-11384022', '-38662557', '100820660'], ['70896099', '46023883', '-93578953', '-102114432', '-92073260', '-55319592', '56404509'], ['60283667', '-85122690', '55451068', '80132947', '32405697', '-7796535', '-18143744']], 'QpRts-minpoly': [9, 4, 0, 0, 0, 0, 0, 1], 'QpRts-p': 11, 'QpRts-prec': 8, 'Size': 7, 'TransitiveDegree': 7}