Artin representation data - 1.31.10t1.a

Formats: - HTML - YAML - JSON - 2026-04-16T15:01:18.987055

• 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': [31], 'Baselabel': '1.31.10t1.a', 'CharacterField': 5, 'Conductor': 31, 'Container': '10t1', 'Dets': ['31.29', '31.27', '31.23', '31.15'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 10, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1], [0, 1], [1, 1, 1, 1], [0, 0, -1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [6, 1, 5, 9, 11, 1, 7, 10], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1], [0, 0, 1], [0, 0, 0, -1], [1, 1, 1, 1], [0, -1], [0, 0, -1]], 'GalOrbIndex': 2, 'HardFactors': [6, 1, 5, 9, 11, 1, 7, 10], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 1]], [[1], [0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [-1, -1, -1, -1], [0, 1], [0, 0, 0, 1], [0, 0, -1], [0, -1], [1, 1, 1, 1], [0, 0, 0, -1]], 'GalOrbIndex': 3, 'HardFactors': [6, 1, 5, 9, 11, 1, 7, 10], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [-1, -1, -1, -1], [0, -1], [0, 0, 0, -1], [0, 0, -1], [1, 1, 1, 1]], 'GalOrbIndex': 4, 'HardFactors': [6, 1, 5, 9, 11, 1, 7, 10], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '10T1', 'Galt': 1, 'HardPrimes': [2, 5, 7, 17, 31, 67, 199, 229], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [25, -20, 63, -6, 43, 11, -9, 16, 2, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.31.2t1.a', 'Character': [[1], [-1], [1], [1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.31.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 1, 0], [0, 0, 0, 1], [0, 1, 0, 0]], 'CharacterField': 5}, {'GalConj': 1, 'Baselabel': '1.31.10t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 1, 1, 1], [0, 0, -1, 0], [0, 0, 0, -1], [0, -1, 0, 0]], 'CharacterField': 5}, {'GalConj': 2, 'Baselabel': '1.31.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 1, 0]], 'CharacterField': 5}, {'GalConj': 2, 'Baselabel': '1.31.10t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 1, 0], [0, 0, 0, -1], [1, 1, 1, 1], [0, -1, 0, 0], [0, 0, -1, 0]], 'CharacterField': 5}, {'GalConj': 3, 'Baselabel': '1.31.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1]], 'CharacterField': 5}, {'GalConj': 3, 'Baselabel': '1.31.10t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, -1, 0], [0, -1, 0, 0], [1, 1, 1, 1], [0, 0, 0, -1]], 'CharacterField': 5}, {'GalConj': 4, 'Baselabel': '1.31.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [-1, -1, -1, -1]], 'CharacterField': 5}, {'GalConj': 4, 'Baselabel': '1.31.10t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1], [0, -1, 0, 0], [0, 0, 0, -1], [0, 0, -1, 0], [1, 1, 1, 1]], 'CharacterField': 5}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]}, {'Size': '1', 'Order': 2, 'Representative': [9, 3, 2, 8, 10, 7, 6, 4, 1, 5]}, {'Size': '1', 'Order': 5, 'Representative': [7, 1, 9, 10, 3, 8, 4, 5, 6, 2]}, {'Size': '1', 'Order': 5, 'Representative': [4, 7, 6, 2, 9, 5, 10, 3, 8, 1]}, {'Size': '1', 'Order': 5, 'Representative': [10, 4, 8, 1, 6, 3, 2, 9, 5, 7]}, {'Size': '1', 'Order': 5, 'Representative': [2, 10, 5, 7, 8, 9, 1, 6, 3, 4]}, {'Size': '1', 'Order': 10, 'Representative': [6, 9, 1, 5, 2, 4, 8, 10, 7, 3]}, {'Size': '1', 'Order': 10, 'Representative': [5, 8, 4, 9, 7, 2, 3, 1, 10, 6]}, {'Size': '1', 'Order': 10, 'Representative': [8, 6, 7, 3, 1, 10, 5, 2, 4, 9]}, {'Size': '1', 'Order': 10, 'Representative': [3, 5, 10, 6, 4, 1, 9, 7, 2, 8]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [2, 5, -2, -7, 1]}, 'Classes': [{'RootOf': ['-22', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-239', '1'], 'ConjugacyClass': 4}, {'RootOf': ['412', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-53', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [5, 5]}, {'Data': {'Powers': [1], 'Resolvent': [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['-9794', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-21543', '1'], 'ConjugacyClass': 8}, {'RootOf': ['-2044', '1'], 'ConjugacyClass': 9}, {'RootOf': ['21051', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [10]}], 'Frobs': [6, 7, 1, 5, 8, 7, 9, 6, 9, 10, 1, 2, 6, 10, 3, 9, 3, 2, 1, 4, 8, 9, 10, 8, 5, 4, 6, 4, 3, 5, 7, 5, 7, 7, 1, 8, 6, 4, 10, 3, 8, 2, 1, 5, 8, 7, 1, 2, 6, 10, 3, 9, 8, 7, 4, 7, 10, 9, 10, 6, 5, 4, 3, 1, 7, 5, 10, 8, 2, 4, 10, 3, 2, 1, 5, 8, 9, 1, 10, 2, 3, 3, 3, 2, 1, 4, 7, 9, 8, 10, 6, 4, 9, 2, 7, 5, 7, 1, 8, 4, 5, 2, 1, 8, 7, 6, 10, 5, 6, 10, 3, 8, 3, 2, 8, 10, 9, 8, 6, 4, 6, 9, 2, 1, 4, 6, 8, 2, 4, 5, 2, 2, 5, 7, 9, 1, 10, 10, 9, 7, 1, 7, 9, 10, 9, 6, 3, 5, 9, 2, 4, 7, 7, 6, 4, 10, 5, 2, 5, 8, 9, 9, 2, 6, 3, 9, 2, 1], 'G-Gens': [[7, 1, 9, 10, 3, 8, 4, 5, 6, 2], [9, 3, 2, 8, 10, 7, 6, 4, 1, 5]], 'G-Name': 'C10', 'Polynomial': [25, -20, 63, -6, 43, 11, -9, 16, 2, -1, 1], 'QpRts': [['396044606', '-259613172', '-51165377', '-14580314', '-371494403'], ['9787834', '234242663', '-79678001', '124818557', '425813143'], ['142164868', '319404912', '-434164961', '-119349071', '14417315'], ['-398065037', '-83892527', '-330032374', '410767567', '-346553879'], ['150579168', '302197862', '431190947', '141073163', '16520890'], ['-134085573', '152167369', '-100353439', '-213707043', '-278113230'], ['-227706349', '5204453', '356731857', '-303797790', '-303964207'], ['28375281', '112990166', '-436190340', '60108930', '209437853'], ['235444296', '7111430', '-354353946', '131874021', '37737172'], ['-202539093', '104058583', '104143895', '-217208020', '-297672393']], 'QpRts-minpoly': [17, 5, 0, 0, 0, 1], 'QpRts-p': 19, 'QpRts-prec': 7, 'Size': 10, 'TransitiveDegree': 10}