Artin representation data - 2.68.8t17.a

Formats: - HTML - YAML - JSON - 2024-04-23T20:46:53.134157

• 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, 17], 'Baselabel': '2.68.8t17.a', 'CharacterField': 4, 'Conductor': 68, 'Container': '8t17', 'Dets': ['1.68.4t1.a.b', '1.68.4t1.a.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 8, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, -2], [0, 2], [1, -1], [1, 1], [-1, -1], [-1, 1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [15, 16], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, 2], [-1]], [[1], [0, -2], [-1]], [[1], [-1, 1], [0, -1]], [[1], [-1, -1], [0, 1]], [[1], [1, 1], [0, 1]], [[1], [1, -1], [0, -1]], [[1], [0], [1]], [[1], [0], [1]], [[1], [0], [0, -1]], [[1], [0], [0, 1]], [[1], [0, -1]], [[1], [1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 2], [0, -2], [1, 1], [1, -1], [-1, 1], [-1, -1], [0], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [15, 16], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, -2], [-1]], [[1], [0, 2], [-1]], [[1], [-1, -1], [0, 1]], [[1], [-1, 1], [0, -1]], [[1], [1, -1], [0, -1]], [[1], [1, 1], [0, 1]], [[1], [0], [1]], [[1], [0], [1]], [[1], [0], [0, 1]], [[1], [0], [0, -1]], [[1], [0, 1]], [[1], [1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '8T17', 'Galt': 17, 'HardPrimes': [2, 17], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, -2, 3, 0, -4, 4, 0, -2, 1], 'NumBadPrimes': 2, 'Proj_GAP': [8, 3], 'Proj_Polynomial': [-17, 0, 0, 0, 1], 'Proj_nTj': [4, 3]}
• 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], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.17.2t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.68.2t1.a', 'Character': [[1], [1], [1], [-1], [1], [1], [-1], [-1], [-1], [-1], [1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.4.2t1.a', 'Character': [[1], [1], [1], [-1], [1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.68.4t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [0, 1], [0, -1], [0, -1], [0, 1], [1, 0], [1, 0], [0, 1], [0, -1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '1.68.4t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [0, -1], [0, 1], [0, 1], [0, -1], [1, 0], [1, 0], [0, -1], [0, 1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '1.17.4t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [1, 0], [-1, 0], [-1, 0], [0, -1], [0, 1], [0, 1], [0, -1], [1, 0], [-1, 0], [0, 1], [0, -1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '1.17.4t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [0, -1], [0, -1], [0, 1], [1, 0], [-1, 0], [0, -1], [0, 1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '2.1156.4t3.c', 'Character': [[2], [2], [-2], [0], [2], [2], [0], [0], [0], [0], [-2], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.68.4t3.a', 'Character': [[2], [2], [2], [0], [-2], [-2], [0], [0], [0], [0], [-2], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.68.8t17.a', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, -2], [0, 2], [1, -1], [1, 1], [-1, -1], [-1, 1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '2.1156.8t17.a', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, -2], [0, 2], [-1, 1], [-1, -1], [1, 1], [1, -1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '2.68.8t17.a', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [0, -2], [1, 1], [1, -1], [-1, 1], [-1, -1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '2.1156.8t17.a', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [0, -2], [-1, -1], [-1, 1], [1, -1], [1, 1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 4}], 'ComplexConjugation': 4, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [4, 3, 2, 1, 6, 5, 8, 7]}, {'Size': '2', 'Order': 2, 'Representative': [1, 3, 2, 4, 5, 6, 8, 7]}, {'Size': '4', 'Order': 2, 'Representative': [2, 1, 4, 3, 7, 8, 5, 6]}, {'Size': '1', 'Order': 4, 'Representative': [5, 7, 8, 6, 4, 1, 3, 2]}, {'Size': '1', 'Order': 4, 'Representative': [6, 8, 7, 5, 1, 4, 2, 3]}, {'Size': '2', 'Order': 4, 'Representative': [1, 7, 8, 4, 5, 6, 3, 2]}, {'Size': '2', 'Order': 4, 'Representative': [1, 8, 7, 4, 5, 6, 2, 3]}, {'Size': '2', 'Order': 4, 'Representative': [5, 3, 2, 6, 4, 1, 8, 7]}, {'Size': '2', 'Order': 4, 'Representative': [6, 3, 2, 5, 1, 4, 8, 7]}, {'Size': '2', 'Order': 4, 'Representative': [5, 8, 7, 6, 4, 1, 2, 3]}, {'Size': '4', 'Order': 4, 'Representative': [8, 6, 5, 7, 2, 3, 1, 4]}, {'Size': '4', 'Order': 8, 'Representative': [2, 6, 5, 3, 7, 8, 1, 4]}, {'Size': '4', 'Order': 8, 'Representative': [8, 4, 1, 7, 2, 3, 6, 5]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['1', '0', '1'], 'ConjugacyClass': 7}, {'RootOf': ['25', '6', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-6', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-16', '-4', '6', '-4', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['41', '-10', '1'], 'ConjugacyClass': 9}, {'RootOf': ['5', '-4', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [2, 2, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-4', '1'], 'ConjugacyClass': 5}, {'RootOf': ['2', '1'], 'ConjugacyClass': 6}, {'RootOf': ['26', '-2', '1'], 'ConjugacyClass': 11}, {'RootOf': ['-16', '-4', '6', '-4', '1'], 'ConjugacyClass': 12}], 'Algorithm': 'RES', 'CycleType': [4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['1', '-4', '6', '-4', '1'], 'ConjugacyClass': 13}, {'RootOf': ['69', '-4', '6', '-4', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [8]}], 'Frobs': [6, 13, 9, 14, 14, 11, 3, 12, 14, 8, 13, 9, 7, 12, 4, 3, 12, 10, 4, 13, 8, 14, 12, 11, 9, 11, 4, 13, 10, 10, 12, 13, 11, 13, 1, 12, 1, 14, 13, 8, 12, 10, 4, 7, 7, 13, 14, 12, 14, 5, 9, 4, 8, 4, 6, 12, 9, 4, 8, 3, 14, 2, 4, 13, 7, 7, 12, 8, 14, 3, 2, 12, 14, 11, 13, 12, 5, 10, 7, 2, 14, 11, 14, 6, 13, 4, 10, 6, 3, 4, 12, 13, 14, 12, 14, 14, 2, 7, 4, 9, 13, 11, 12, 3, 14, 11, 12, 3, 4, 7, 13, 1, 9, 14, 12, 9, 13, 4, 7, 4, 3, 10, 8, 13, 14, 11, 8, 13, 4, 3, 12, 13, 13, 5, 11, 11, 6, 13, 3, 10, 13, 8, 14, 14, 1, 14, 9, 7, 12, 4, 10, 8, 4, 13, 14, 14, 4, 7, 3, 7, 13, 11, 12, 12, 3, 13, 13, 7], 'G-Gens': [[8, 6, 5, 7, 2, 3, 1, 4], [1, 3, 2, 4, 5, 6, 8, 7], [4, 3, 2, 1, 6, 5, 8, 7], [5, 7, 8, 6, 4, 1, 3, 2], [1, 7, 8, 4, 5, 6, 3, 2]], 'G-Name': 'C4wrC2', 'Polynomial': [1, -2, 3, 0, -4, 4, 0, -2, 1], 'QpRts': [['-22403714477'], ['-18958294612'], ['35271373802'], ['714519764'], ['-34761006454'], ['-23584871797'], ['18214672153'], ['-27932454126']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 149, 'QpRts-prec': 5, 'Size': 32, 'TransitiveDegree': 8}