Artin representation data - 2.16775.10t3.b

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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': [5, 11, 61], 'Baselabel': '2.16775.10t3.b', 'CharacterField': 5, 'Conductor': 16775, 'Container': '10t3', 'Dets': ['1.671.2t1.a.a', '1.671.2t1.a.a'], 'Dim': 2, 'GalConjSigns': [1, 1], 'Galn': 10, 'GaloisConjugates': [{'Sign': 1, 'Character': [[2], [-2], [0], [0], [-1, 0, -1, -1], [0, 0, 1, 1], [1, 0, 1, 1], [0, 0, -1, -1]], 'GalOrbIndex': 1, 'HardFactors': [7, 8, 9, 2, 10, 3, 10, 3, 3], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [1, 0, 1, 1], [1]], [[1], [0, 0, -1, -1], [1]], [[1], [-1, 0, -1, -1], [1]], [[1], [0, 0, 1, 1], [1]], [[1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [-2], [0], [0], [0, 0, 1, 1], [-1, 0, -1, -1], [0, 0, -1, -1], [1, 0, 1, 1]], 'GalOrbIndex': 2, 'HardFactors': [7, 8, 9, 2, 10, 3, 10, 3, 3], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, 0, -1, -1], [1]], [[1], [1, 0, 1, 1], [1]], [[1], [0, 0, 1, 1], [1]], [[1], [-1, 0, -1, -1], [1]], [[1]], [[1], [-1]]]}], 'GaloisConjugatesSigns': [1, 1], 'GaloisLabel': '10T3', 'Galt': 3, 'HardPrimes': [2, 3, 5, 7, 11, 13, 61, 67, 2657], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [11, 165, -202, 190, 2, 3, 49, 2, -11, -1, 1], 'NumBadPrimes': 3, 'Proj_GAP': [10, 1], 'Proj_Polynomial': [7, -9, 7, 2, -1, 1], 'Proj_nTj': [5, 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], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.671.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.3355.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.5.2t1.a', 'Character': [[1], [-1], [1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 2, 'Baselabel': '2.16775.10t3.b', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 1], [-1, 0, -1, -1], [0, 0, -1, -1], [1, 0, 1, 1]], 'CharacterField': 5}, {'GalConj': 1, 'Baselabel': '2.671.5t2.a', 'Character': [[2, 0, 0, 0], [2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 1], [-1, 0, -1, -1], [0, 0, 1, 1], [-1, 0, -1, -1]], 'CharacterField': 5}, {'GalConj': 2, 'Baselabel': '2.671.5t2.a', 'Character': [[2, 0, 0, 0], [2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-1, 0, -1, -1], [0, 0, 1, 1], [-1, 0, -1, -1], [0, 0, 1, 1]], 'CharacterField': 5}, {'GalConj': 1, 'Baselabel': '2.16775.10t3.b', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-1, 0, -1, -1], [0, 0, 1, 1], [1, 0, 1, 1], [0, 0, -1, -1]], 'CharacterField': 5}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]}, {'Size': '1', 'Order': 2, 'Representative': [2, 1, 4, 3, 6, 5, 8, 7, 10, 9]}, {'Size': '5', 'Order': 2, 'Representative': [10, 9, 8, 7, 5, 6, 4, 3, 2, 1]}, {'Size': '5', 'Order': 2, 'Representative': [9, 10, 7, 8, 6, 5, 3, 4, 1, 2]}, {'Size': '2', 'Order': 5, 'Representative': [7, 8, 9, 10, 4, 3, 5, 6, 2, 1]}, {'Size': '2', 'Order': 5, 'Representative': [5, 6, 2, 1, 10, 9, 4, 3, 8, 7]}, {'Size': '2', 'Order': 10, 'Representative': [8, 7, 10, 9, 3, 4, 6, 5, 1, 2]}, {'Size': '2', 'Order': 10, 'Representative': [3, 4, 7, 8, 2, 1, 9, 10, 5, 6]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-23', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-59591', '6193', '-10330', '718', '1', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2]}, {'Data': {'Powers': [1, 4], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['26', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-22', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [5, 5]}, {'Data': {'Powers': [1, 9], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['36', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-12', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [10]}], 'Frobs': [7, 8, 6, 2, 1, 4, 7, 3, 4, 5, 3, 4, 3, 7, 8, 4, 3, 1, 4, 3, 4, 6, 4, 3, 7, 1, 7, 4, 3, 7, 4, 3, 8, 5, 3, 6, 4, 8, 4, 8, 1, 3, 3, 8, 4, 6, 5, 4, 8, 6, 8, 3, 3, 3, 8, 4, 5, 3, 7, 1, 4, 4, 8, 3, 4, 7, 3, 7, 4, 5, 2, 5, 7, 7, 6, 4, 3, 4, 3, 5, 3, 3, 3, 4, 3, 7, 6, 2, 3, 8, 4, 3, 8, 3, 3, 4, 3, 3, 8, 6, 8, 8, 4, 3, 3, 4, 4, 2, 3, 3, 4, 4, 4, 5, 3, 3, 4, 4, 4, 3, 3, 8, 8, 7, 5, 6, 3, 5, 2, 4, 6, 8, 5, 8, 5, 6, 7, 7, 7, 3, 6, 5, 4, 4, 6, 1, 4, 4, 5, 2, 2, 1, 4, 8, 4, 6, 3, 6, 4, 6, 4, 7, 4, 5, 7, 4, 6, 8], 'G-Gens': [[1, 2, 6, 5, 4, 3, 10, 9, 8, 7], [10, 9, 8, 7, 5, 6, 4, 3, 2, 1], [2, 1, 4, 3, 6, 5, 8, 7, 10, 9]], 'G-Name': 'D20', 'Polynomial': [11, 165, -202, 190, 2, 3, 49, 2, -11, -1, 1], 'QpRts': [['204447262003233', '37865443462795', '102477144866358', '80741306939738', '176105909838939'], ['51870978603393', '37865443462795', '102477144866358', '80741306939738', '176105909838939'], ['-48369833936582', '-192852735348997', '192090503341656', '169671716253654', '-40955775927801'], ['104206449463258', '-192852735348997', '192090503341656', '169671716253654', '-40955775927801'], ['166511069407234', '-25246622318724', '-53869503573640', '-61981394649514', '-14995517617811'], ['13934786007394', '-25246622318724', '-53869503573640', '-61981394649514', '-14995517617811'], ['-150787884328045', '-26197282675247', '47561657112951', '193573042516761', '98209137750940'], ['117343065572316', '-26197282675247', '47561657112951', '193573042516761', '98209137750940'], ['114841145204181', '206431196880173', '132447431552876', '38702562239562', '202343479255934'], ['-153289804696180', '206431196880173', '132447431552876', '38702562239562', '202343479255934']], 'QpRts-minpoly': [27, 3, 0, 0, 0, 1], 'QpRts-p': 29, 'QpRts-prec': 10, 'Size': 20, 'TransitiveDegree': 10}