Artin representation data - 4.1334025.8t22.e

Formats: - HTML - YAML - JSON - 2024-06-09T20:17:11.494955

• 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': [3, 5, 7, 11], 'Baselabel': '4.1334025.8t22.e', 'CharacterField': 1, 'Conductor': 1334025, 'Container': '8t22', 'Dets': ['1.1.1t1.a.a'], 'Dim': 4, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[4], [-4], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [12, 18, 18, 19, 19, 3, 3, 12], 'LocalFactors': [[[1], [-4], [6], [-4], [1]], [[1], [4], [6], [4], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [2], [0], [1]], [[1], [0], [2], [0], [1]], [[1], [0], [2], [0], [1]], [[1], [0], [2], [0], [1]], [[1], [0], [2], [0], [1]], [[1], [0], [2], [0], [1]], [[1], [0], [1]], [[1], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T22', 'Galt': 22, 'HardPrimes': [2, 3, 5, 7, 11, 13, 37, 113], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [7, 7, 22, 9, 19, -1, 6, -3, 1], 'NumBadPrimes': 4, 'Proj_GAP': [16, 14], 'Proj_Polynomial': [1936, 968, -2640, 10890, 1565, -15094, 4680, -7916, 11490, -736, -1374, -458, 272, 36, -18, -2, 1], 'Proj_nTj': [16, 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], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.77.2t1.a', 'Character': [[1], [1], [1], [1], [-1], [-1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.35.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [-1], [1], [-1], [1], [-1], [1], [1], [-1], [1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.55.2t1.a', 'Character': [[1], [1], [-1], [1], [-1], [1], [1], [-1], [1], [1], [-1], [-1], [1], [-1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.165.2t1.a', 'Character': [[1], [1], [-1], [-1], [-1], [1], [-1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.105.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [-1], [-1], [1], [1], [-1], [-1], [-1], [1], [1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.3.2t1.a', 'Character': [[1], [1], [1], [-1], [1], [1], [-1], [-1], [1], [1], [-1], [-1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.231.2t1.a', 'Character': [[1], [1], [1], [-1], [-1], [-1], [-1], [-1], [1], [-1], [1], [1], [1], [-1], [1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.15.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [-1], [1], [-1], [-1], [1], [-1], [1], [-1], [-1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.1155.2t1.a', 'Character': [[1], [1], [-1], [-1], [-1], [1], [1], [-1], [-1], [-1], [1], [-1], [1], [1], [1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.33.2t1.a', 'Character': [[1], [1], [1], [-1], [-1], [-1], [1], [1], [-1], [1], [1], [-1], [-1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.21.2t1.a', 'Character': [[1], [1], [1], [-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], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.11.2t1.a', 'Character': [[1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [1], [-1], [1], [1], [1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.385.2t1.a', 'Character': [[1], [1], [-1], [1], [-1], [1], [-1], [1], [-1], [-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], [-1], [1], [1], [-1], [1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.1334025.8t22.e', 'Character': [[4], [-4], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 8, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [3, 6, 1, 5, 4, 2, 8, 7]}, {'Size': '2', 'Order': 2, 'Representative': [3, 6, 1, 4, 5, 2, 7, 8]}, {'Size': '2', 'Order': 2, 'Representative': [5, 8, 4, 3, 1, 7, 6, 2]}, {'Size': '2', 'Order': 2, 'Representative': [1, 6, 3, 4, 5, 2, 8, 7]}, {'Size': '2', 'Order': 2, 'Representative': [3, 2, 1, 4, 5, 6, 8, 7]}, {'Size': '2', 'Order': 2, 'Representative': [6, 3, 2, 8, 7, 1, 5, 4]}, {'Size': '2', 'Order': 2, 'Representative': [2, 1, 6, 8, 7, 3, 5, 4]}, {'Size': '2', 'Order': 2, 'Representative': [8, 5, 7, 6, 2, 4, 3, 1]}, {'Size': '2', 'Order': 2, 'Representative': [7, 5, 8, 6, 2, 4, 1, 3]}, {'Size': '2', 'Order': 2, 'Representative': [5, 7, 4, 3, 1, 8, 2, 6]}, {'Size': '2', 'Order': 4, 'Representative': [6, 1, 2, 8, 7, 3, 4, 5]}, {'Size': '2', 'Order': 4, 'Representative': [2, 3, 6, 8, 7, 1, 4, 5]}, {'Size': '2', 'Order': 4, 'Representative': [8, 4, 7, 6, 2, 5, 1, 3]}, {'Size': '2', 'Order': 4, 'Representative': [7, 4, 8, 6, 2, 5, 3, 1]}, {'Size': '2', 'Order': 4, 'Representative': [5, 7, 4, 1, 3, 8, 6, 2]}, {'Size': '2', 'Order': 4, 'Representative': [5, 8, 4, 1, 3, 7, 2, 6]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-272', '16', '1'], 'ConjugacyClass': 3}, {'RootOf': ['512', '16', '1'], 'ConjugacyClass': 5}, {'RootOf': ['652', '16', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-8', '1'], 'ConjugacyClass': 2}, {'RootOf': ['51', '13', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-572', '-22', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-407', '-22', '1'], 'ConjugacyClass': 8}, {'RootOf': ['1', '2', '1'], 'ConjugacyClass': 9}, {'RootOf': ['-164', '2', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-169', '13', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['297', '-22', '1'], 'ConjugacyClass': 12}, {'RootOf': ['352', '-22', '1'], 'ConjugacyClass': 13}, {'RootOf': ['-384', '2', '1'], 'ConjugacyClass': 14}, {'RootOf': ['1', '2', '1'], 'ConjugacyClass': 15}, {'RootOf': ['-194', '13', '1'], 'ConjugacyClass': 16}, {'RootOf': ['136', '13', '1'], 'ConjugacyClass': 17}], 'Algorithm': 'RES', 'CycleType': [4, 4]}], 'Frobs': [16, 14, 13, 6, 4, 9, 7, 15, 17, 11, 10, 3, 8, 6, 12, 17, 13, 15, 3, 4, 9, 5, 7, 13, 14, 8, 14, 16, 5, 17, 6, 8, 17, 15, 11, 5, 14, 3, 7, 7, 4, 10, 4, 6, 16, 10, 5, 14, 7, 10, 16, 11, 15, 13, 12, 16, 13, 15, 6, 11, 9, 7, 9, 13, 14, 17, 1, 6, 16, 15, 12, 11, 14, 6, 1, 12, 4, 14, 4, 15, 13, 1, 11, 14, 15, 17, 4, 6, 8, 3, 12, 8, 3, 11, 1, 7, 13, 13, 9, 5, 6, 16, 7, 11, 5, 14, 12, 7, 4, 15, 9, 6, 17, 10, 2, 4, 14, 12, 17, 11, 10, 6, 7, 17, 10, 11, 1, 13, 14, 9, 5, 16, 2, 3, 8, 15, 12, 9, 12, 11, 15, 11, 3, 16, 10, 13, 9, 7, 10, 17, 6, 13, 3, 7, 3, 4, 5, 13, 9, 8, 17, 16, 6, 13, 17, 12, 2, 9], 'G-Gens': [[3, 6, 1, 4, 5, 2, 7, 8], [6, 1, 2, 8, 7, 3, 4, 5], [2, 3, 6, 8, 7, 1, 4, 5], [8, 4, 7, 6, 2, 5, 1, 3], [3, 2, 1, 4, 5, 6, 8, 7], [7, 4, 8, 6, 2, 5, 3, 1], [3, 2, 1, 5, 4, 6, 7, 8]], 'G-Name': 'D8:C2^2', 'Polynomial': [7, 7, 22, 9, 19, -1, 6, -3, 1], 'QpRts': [['22102979817'], ['1004884915829'], ['1961549723883'], ['-185187712047'], ['-1080381099555'], ['1582221037283'], ['-1046467909965'], ['1714473875409']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 331, 'QpRts-prec': 5, 'Size': 32, 'TransitiveDegree': 8}