Artin representation data - 2.448.8t17.b

Formats: - HTML - YAML - JSON - 2024-04-25T06:46:35.745901

• 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, 7], 'Baselabel': '2.448.8t17.b', 'CharacterField': 4, 'Conductor': 448, 'Container': '8t17', 'Dets': ['1.112.4t1.b.a', '1.112.4t1.b.b'], '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, 14, 16, 11, 8], '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]], [[1], [0, -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, 14, 16, 11, 8], '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]], [[1], [0, 1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '8T17', 'Galt': 17, 'HardPrimes': [2, 3, 7, 41, 709], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [2, 0, 2, 0, 3, 0, 3, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [8, 3], 'Proj_Polynomial': [-14, 0, -4, 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': '1.8.2t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.56.2t1.b', 'Character': [[1], [1], [1], [-1], [1], [1], [-1], [-1], [-1], [-1], [1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.7.2t1.a', 'Character': [[1], [1], [1], [-1], [1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.112.4t1.b', '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': '1.112.4t1.b', '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': '1.16.4t1.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': '1.16.4t1.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': '2.1792.4t3.e', 'Character': [[2], [2], [-2], [0], [2], [2], [0], [0], [0], [0], [-2], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.56.4t3.c', 'Character': [[2], [2], [2], [0], [-2], [-2], [0], [0], [0], [0], [-2], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.448.8t17.b', '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': '2.896.8t17.d', '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': '2.448.8t17.b', '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': '2.896.8t17.d', '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': [8, 7, 6, 5, 4, 3, 2, 1]}, {'Size': '2', 'Order': 2, 'Representative': [8, 2, 3, 5, 4, 6, 7, 1]}, {'Size': '4', 'Order': 2, 'Representative': [7, 8, 5, 6, 3, 4, 1, 2]}, {'Size': '1', 'Order': 4, 'Representative': [5, 6, 2, 1, 8, 7, 3, 4]}, {'Size': '1', 'Order': 4, 'Representative': [4, 3, 7, 8, 1, 2, 6, 5]}, {'Size': '2', 'Order': 4, 'Representative': [4, 2, 3, 8, 1, 6, 7, 5]}, {'Size': '2', 'Order': 4, 'Representative': [5, 2, 3, 1, 8, 6, 7, 4]}, {'Size': '2', 'Order': 4, 'Representative': [5, 7, 6, 1, 8, 3, 2, 4]}, {'Size': '2', 'Order': 4, 'Representative': [4, 7, 6, 8, 1, 3, 2, 5]}, {'Size': '2', 'Order': 4, 'Representative': [4, 6, 2, 8, 1, 7, 3, 5]}, {'Size': '4', 'Order': 4, 'Representative': [6, 5, 1, 2, 7, 8, 4, 3]}, {'Size': '4', 'Order': 8, 'Representative': [3, 8, 5, 7, 2, 4, 1, 6]}, {'Size': '4', 'Order': 8, 'Representative': [2, 4, 8, 3, 6, 1, 5, 7]}], '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': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['1656', '66', '1'], 'ConjugacyClass': 7}, {'RootOf': ['1576', '54', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 4]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['18', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-290304', '0', '-576', '0', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['1656', '-66', '1'], 'ConjugacyClass': 9}, {'RootOf': ['1576', '-54', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [2, 2, 4]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['-6', '1'], 'ConjugacyClass': 5}, {'RootOf': ['6', '1'], 'ConjugacyClass': 6}, {'RootOf': ['28', '0', '1'], 'ConjugacyClass': 11}, {'RootOf': ['-3584', '0', '-64', '0', '1'], 'ConjugacyClass': 12}], 'Algorithm': 'RES', 'CycleType': [4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['4608', '0', '-64', '0', '1'], 'ConjugacyClass': 13}, {'RootOf': ['1492992', '0', '-1152', '0', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [8]}], 'Frobs': [8, 14, 13, 12, 8, 14, 4, 14, 3, 9, 4, 10, 12, 10, 4, 8, 13, 14, 9, 5, 12, 11, 14, 12, 4, 13, 12, 10, 7, 11, 1, 14, 3, 13, 8, 3, 14, 7, 12, 14, 7, 13, 11, 11, 10, 12, 9, 4, 14, 13, 3, 2, 4, 13, 4, 6, 14, 4, 10, 3, 13, 13, 14, 12, 12, 9, 8, 11, 10, 14, 4, 3, 4, 10, 8, 4, 10, 14, 11, 12, 14, 8, 1, 4, 12, 8, 2, 5, 14, 11, 14, 4, 3, 10, 7, 12, 14, 12, 13, 7, 7, 7, 14, 6, 10, 4, 13, 4, 5, 12, 4, 8, 5, 13, 6, 11, 14, 12, 7, 9, 13, 2, 13, 10, 14, 7, 8, 4, 12, 14, 7, 3, 2, 8, 12, 4, 13, 14, 14, 5, 13, 10, 5, 8, 14, 12, 13, 12, 13, 11, 9, 4, 9, 12, 8, 2, 6, 4, 12, 14, 9, 3, 3, 13, 1, 12, 11, 13], 'G-Gens': [[4, 2, 3, 8, 1, 6, 7, 5], [8, 7, 6, 5, 4, 3, 2, 1], [8, 2, 3, 5, 4, 6, 7, 1], [5, 6, 2, 1, 8, 7, 3, 4], [3, 8, 5, 7, 2, 4, 1, 6]], 'G-Name': 'C4wrC2', 'Polynomial': [2, 0, 2, 0, 3, 0, 3, 0, 1], 'QpRts': [['111421037337198'], ['-147961694416094'], ['-23593436750641'], ['-182471905520991'], ['182471905520991'], ['23593436750641'], ['147961694416094'], ['-111421037337198']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 127, 'QpRts-prec': 7, 'Size': 32, 'TransitiveDegree': 8}