Artin representation data - 2.14884.10t3.a

Formats: - HTML - YAML - JSON - 2024-06-12T12:54:22.879234

• 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, 61], 'Baselabel': '2.14884.10t3.a', 'CharacterField': 5, 'Conductor': 14884, 'Container': '10t3', 'Dets': ['1.4.2t1.a.a', '1.4.2t1.a.a'], 'Dim': 2, 'GalConjSigns': [1, 1], 'Galn': 10, 'GaloisConjugates': [{'Sign': 1, 'Character': [[2], [-2], [0], [0], [0, 0, 1, 1], [-1, 0, -1, -1], [1, 0, 1, 1], [0, 0, -1, -1]], 'GalOrbIndex': 1, 'HardFactors': [9, 3, 3, 3, 10, 1, 3, 3, 2, 3, 2], '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], [-1, 0, -1, -1], [1]], [[1], [0, 0, 1, 1], [1]], [[1], [1]], [[1]]]}, {'Sign': 1, 'Character': [[2], [-2], [0], [0], [-1, 0, -1, -1], [0, 0, 1, 1], [0, 0, -1, -1], [1, 0, 1, 1]], 'GalOrbIndex': 2, 'HardFactors': [9, 3, 3, 3, 10, 1, 3, 3, 2, 3, 2], '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], [0, 0, 1, 1], [1]], [[1], [-1, 0, -1, -1], [1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1, 1], 'GaloisLabel': '10T3', 'Galt': 3, 'HardPrimes': [2, 3, 7, 11, 61, 73, 107, 211, 233, 359, 16481], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [2061, -225, 11345, 2792, -1890, -622, 222, 56, -27, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [10, 1], 'Proj_Polynomial': [-72, -15, 14, 26, -2, 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': '1.4.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.61.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.244.2t1.a', 'Character': [[1], [-1], [1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 2, 'Baselabel': '2.14884.10t3.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], [0, 0, -1, -1], [1, 0, 1, 1]], 'CharacterField': 5}, {'GalConj': 2, 'Baselabel': '2.14884.5t2.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], [0, 0, 1, 1], [-1, 0, -1, -1]], 'CharacterField': 5}, {'GalConj': 1, 'Baselabel': '2.14884.5t2.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], [-1, 0, -1, -1], [0, 0, 1, 1]], 'CharacterField': 5}, {'GalConj': 1, 'Baselabel': '2.14884.10t3.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], [1, 0, 1, 1], [0, 0, -1, -1]], 'CharacterField': 5}], 'ComplexConjugation': 4, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]}, {'Size': '1', 'Order': 2, 'Representative': [4, 9, 6, 1, 7, 3, 5, 10, 2, 8]}, {'Size': '5', 'Order': 2, 'Representative': [6, 9, 4, 3, 8, 1, 10, 5, 2, 7]}, {'Size': '5', 'Order': 2, 'Representative': [3, 2, 1, 6, 10, 4, 8, 7, 9, 5]}, {'Size': '2', 'Order': 5, 'Representative': [3, 10, 5, 6, 2, 7, 9, 4, 8, 1]}, {'Size': '2', 'Order': 5, 'Representative': [2, 3, 10, 9, 1, 8, 4, 7, 6, 5]}, {'Size': '2', 'Order': 10, 'Representative': [9, 6, 8, 2, 4, 10, 1, 5, 3, 7]}, {'Size': '2', 'Order': 10, 'Representative': [8, 7, 4, 10, 6, 1, 3, 2, 5, 9]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['147', '1'], 'ConjugacyClass': 2}, {'RootOf': ['11028049408', '-43692992', '1619884', '8324', '3', '1'], 'ConjugacyClass': 3}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2]}, {'Data': {'Powers': [1, 4], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-194', '1'], 'ConjugacyClass': 5}, {'RootOf': ['50', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [5, 5]}, {'Data': {'Powers': [1, 9], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['1810', '1'], 'ConjugacyClass': 7}, {'RootOf': ['590', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [10]}], 'Frobs': [2, 4, 5, 3, 3, 5, 7, 4, 3, 7, 3, 2, 5, 3, 4, 8, 3, 1, 3, 3, 1, 3, 4, 7, 5, 2, 4, 4, 6, 6, 4, 4, 6, 3, 6, 3, 8, 4, 4, 7, 4, 7, 3, 7, 5, 4, 3, 3, 3, 1, 2, 4, 6, 3, 6, 4, 6, 4, 8, 8, 4, 6, 3, 3, 7, 5, 3, 8, 4, 7, 6, 3, 4, 8, 4, 3, 8, 7, 8, 8, 3, 8, 4, 7, 4, 4, 5, 2, 1, 4, 3, 4, 4, 4, 3, 4, 8, 7, 3, 7, 3, 8, 4, 6, 4, 7, 3, 8, 3, 6, 4, 6, 8, 4, 3, 8, 3, 3, 8, 4, 2, 7, 7, 4, 4, 7, 8, 4, 4, 6, 3, 3, 4, 5, 7, 8, 5, 3, 6, 5, 3, 8, 3, 4, 5, 4, 6, 1, 4, 4, 7, 5, 3, 3, 3, 4, 4, 1, 6, 8, 3, 7, 4, 4, 1, 3, 4, 8], 'G-Gens': [[6, 9, 4, 3, 8, 1, 10, 5, 2, 7], [4, 9, 6, 1, 7, 3, 5, 10, 2, 8], [10, 3, 2, 8, 5, 9, 7, 4, 6, 1]], 'G-Name': 'D20', 'Polynomial': [2061, -225, 11345, 2792, -1890, -622, 222, 56, -27, -1, 1], 'QpRts': [['-11529257763056262', '23911666131857770', '-6301110725876900', '6966769082740416', '17766029042299382'], ['16533263551069032', '-8834861501492120', '16254989704771494', '6819206756728219', '-18252089434365876'], ['21418392161914103', '-6574280699277081', '-18705345583731106', '4462601835829790', '-13526368430096119'], ['-13843279385194517', '-12353455105755775', '5842909616478700', '16653647499618197', '-102000394082372'], ['-20504104701897634', '6456540019528165', '-14175637412530301', '-22732270760251747', '2164916120388764'], ['-24906961479747165', '22186103567739278', '-14181085848417293', '-13907013106540785', '22033545458415304'], ['8085737885142998', '-7969613604347652', '-24368171538039441', '-2580786475226975', '22746409069801463'], ['16519734096846045', '-8519991525258283', '8904164060274729', '-15822449526204351', '2988204692293959'], ['-2253728723611237', '6656956667622432', '23802183709703305', '15656601608353914', '3519734187662403'], ['10480204358534638', '-14959063950616734', '22927104017366813', '4483693084953322', '11847512701773849']], 'QpRts-minpoly': [11, 4, 0, 0, 0, 1], 'QpRts-p': 13, 'QpRts-prec': 15, 'Size': 20, 'TransitiveDegree': 10}