Artin representation data - 1.127.7t1.a

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• 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': [127], 'Baselabel': '1.127.7t1.a', 'CharacterField': 7, 'Conductor': 127, 'Container': '7t1', 'Dets': ['127.64', '127.32', '127.16', '127.8', '127.4', '127.2'], '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': [7, 4, 3, 3, 2, 3, 1, 1, 8], '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': [7, 4, 3, 3, 2, 3, 1, 1, 8], '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': [7, 4, 3, 3, 2, 3, 1, 1, 8], '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': [7, 4, 3, 3, 2, 3, 1, 1, 8], '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': [7, 4, 3, 3, 2, 3, 1, 1, 8], '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': [7, 4, 3, 3, 2, 3, 1, 1, 8], '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, 13, 19, 37, 127], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1121, -1713, 32, 558, 31, -54, -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': '1.127.7t1.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': '1.127.7t1.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': '1.127.7t1.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': '1.127.7t1.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': '1.127.7t1.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': '1.127.7t1.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, 3, 5, 7, 4, 1, 6]}, {'Size': '1', 'Order': 7, 'Representative': [3, 5, 4, 6, 7, 2, 1]}, {'Size': '1', 'Order': 7, 'Representative': [5, 4, 7, 1, 6, 3, 2]}, {'Size': '1', 'Order': 7, 'Representative': [4, 7, 6, 2, 1, 5, 3]}, {'Size': '1', 'Order': 7, 'Representative': [7, 6, 1, 3, 2, 4, 5]}, {'Size': '1', 'Order': 7, 'Representative': [6, 1, 2, 5, 3, 7, 4]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['3350', '1'], 'ConjugacyClass': 2}, {'RootOf': ['1572', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-79', '1'], 'ConjugacyClass': 4}, {'RootOf': ['1953', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-968', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-714', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [7]}], 'Frobs': [7, 4, 3, 3, 2, 3, 3, 1, 7, 4, 6, 1, 3, 4, 6, 7, 1, 4, 4, 7, 2, 7, 7, 7, 5, 2, 1, 1, 6, 2, 1, 6, 2, 2, 1, 1, 5, 5, 7, 6, 1, 2, 2, 4, 4, 4, 4, 6, 3, 5, 6, 6, 3, 4, 4, 7, 6, 3, 7, 3, 4, 6, 7, 4, 1, 2, 4, 7, 2, 3, 1, 1, 2, 5, 7, 7, 5, 4, 1, 1, 7, 7, 4, 1, 3, 5, 1, 6, 6, 2, 3, 4, 6, 3, 7, 3, 1, 3, 6, 5, 6, 5, 4, 4, 2, 3, 7, 5, 5, 2, 1, 1, 6, 4, 6, 3, 5, 2, 6, 1, 2, 7, 5, 7, 7, 4, 7, 4, 5, 4, 7, 1, 2, 3, 1, 3, 2, 5, 5, 6, 5, 1, 4, 5, 4, 4, 5, 3, 5, 2, 2, 5, 3, 7, 6, 1, 5, 7, 7, 1, 3, 2, 5, 2, 6, 5, 5, 1], 'G-Gens': [[2, 3, 5, 7, 4, 1, 6]], 'G-Name': 'C7', 'Polynomial': [-1121, -1713, 32, 558, 31, -54, -1, 1], 'QpRts': [['7334401', '8956385', '-7864728', '965762', '-5903402', '-984661', '7010993'], ['190781', '7710457', '4544805', '-9741630', '3861960', '-3842581', '8175299'], ['-8565626', '1099540', '-1932106', '-2195773', '-8426637', '6092809', '-4934204'], ['-867018', '-1328797', '-8600716', '-5042621', '8641330', '862386', '3806947'], ['7885521', '1200255', '5772603', '-2057049', '6782937', '181352', '-5819711'], ['5646178', '-8502440', '-5062818', '-1869914', '2214953', '-2831814', '8954491'], ['7862935', '-9135400', '-6344211', '454054', '-7171141', '522509', '2293356']], 'QpRts-minpoly': [9, 4, 0, 0, 0, 0, 0, 1], 'QpRts-p': 11, 'QpRts-prec': 7, 'Size': 7, 'TransitiveDegree': 7}