Artin representation data - 1.19.9t1.a

Formats: - HTML - YAML - JSON - 2023-01-28T20:57:38.446260

• 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': [19], 'Baselabel': '1.19.9t1.a', 'CharacterField': 9, 'Conductor': 19, 'Container': '9t1', 'Dets': ['19.9', '19.5', '19.6', '19.16', '19.4', '19.17'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0], 'Galn': 9, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [-1, 0, 0, -1], [0, 1], [0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1], [0, 0, -1, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [6, 4, 5, 10, 9, 8], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 1, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, 0, 0, -1], [0, 0, 0, 1], [0, 0, 1], [0, 0, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, 1], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1]], 'GalOrbIndex': 2, 'HardFactors': [6, 4, 5, 10, 9, 8], 'LocalFactors': [[[1], [-1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [-1, 0, 0, -1], [0, 0, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [6, 4, 5, 10, 9, 8], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, 0, 0, -1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 1], [0, -1, 0, 0, -1], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1]], 'GalOrbIndex': 4, 'HardFactors': [6, 4, 5, 10, 9, 8], 'LocalFactors': [[[1], [-1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [-1, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1], [0, 0, 1]], 'GalOrbIndex': 5, 'HardFactors': [6, 4, 5, 10, 9, 8], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, 0, 0, -1], [0, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 1], [0, 1]], 'GalOrbIndex': 6, 'HardFactors': [6, 4, 5, 10, 9, 8], 'LocalFactors': [[[1], [-1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0], 'GaloisLabel': '9T1', 'Galt': 1, 'HardPrimes': [2, 5, 13, 19, 23, 79], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1, 5, 10, -20, -15, 21, 7, -8, -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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.19.9t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1, 0], [0, 0, -1, 0, 0, -1]], 'CharacterField': 9}, {'GalConj': 2, 'Baselabel': '1.19.9t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1, 0]], 'CharacterField': 9}, {'GalConj': 1, 'Baselabel': '1.19.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 3, 'Baselabel': '1.19.9t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1]], 'CharacterField': 9}, {'GalConj': 4, 'Baselabel': '1.19.9t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, -1, 0, 0, -1, 0], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1, 0]], 'CharacterField': 9}, {'GalConj': 2, 'Baselabel': '1.19.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 5, 'Baselabel': '1.19.9t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]], 'CharacterField': 9}, {'GalConj': 6, 'Baselabel': '1.19.9t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]], 'CharacterField': 9}], 'ComplexConjugation': 1, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '1', 'Order': 3, 'Representative': [6, 3, 5, 1, 2, 4, 8, 9, 7]}, {'Size': '1', 'Order': 3, 'Representative': [4, 5, 2, 6, 3, 1, 9, 7, 8]}, {'Size': '1', 'Order': 9, 'Representative': [2, 8, 9, 5, 7, 3, 1, 6, 4]}, {'Size': '1', 'Order': 9, 'Representative': [8, 6, 4, 7, 1, 9, 2, 3, 5]}, {'Size': '1', 'Order': 9, 'Representative': [3, 9, 7, 2, 8, 5, 6, 4, 1]}, {'Size': '1', 'Order': 9, 'Representative': [9, 4, 1, 8, 6, 7, 3, 5, 2]}, {'Size': '1', 'Order': 9, 'Representative': [5, 7, 8, 3, 9, 2, 4, 1, 6]}, {'Size': '1', 'Order': 9, 'Representative': [7, 1, 6, 9, 4, 8, 5, 2, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['-98', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-155', '1'], 'ConjugacyClass': 3}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['-459', '1'], 'ConjugacyClass': 4}, {'RootOf': ['92', '1'], 'ConjugacyClass': 5}, {'RootOf': ['2315', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-117', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-1409', '1'], 'ConjugacyClass': 8}, {'RootOf': ['852', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [9]}], 'Frobs': [6, 8, 4, 3, 2, 5, 6, 1, 9, 7, 3, 1, 8, 4, 7, 9, 6, 9, 7, 4, 8, 8, 3, 5, 6, 5, 2, 3, 4, 1, 5, 6, 9, 5, 8, 1, 4, 2, 9, 6, 2, 7, 1, 8, 3, 7, 6, 4, 1, 1, 4, 2, 5, 9, 7, 8, 8, 4, 2, 9, 6, 2, 8, 3, 7, 5, 2, 4, 4, 3, 2, 6, 5, 3, 1, 8, 7, 6, 6, 7, 1, 8, 5, 9, 6, 5, 3, 1, 4, 3, 2, 9, 3, 8, 4, 7, 9, 2, 7, 7, 9, 5, 3, 1, 1, 3, 6, 9, 7, 3, 1, 4, 7, 2, 9, 4, 8, 1, 3, 5, 9, 2, 3, 1, 3, 6, 5, 8, 4, 2, 6, 6, 7, 8, 1, 7, 5, 2, 1, 2, 5, 9, 5, 7, 3, 8, 6, 6, 9, 2, 8, 3, 7, 5, 4, 1, 3, 6, 5, 7, 8, 8, 6, 6, 2, 4, 8, 7], 'G-Gens': [[2, 8, 9, 5, 7, 3, 1, 6, 4], [4, 5, 2, 6, 3, 1, 9, 7, 8]], 'G-Name': 'C9', 'Polynomial': [-1, 5, 10, -20, -15, 21, 7, -8, -1, 1], 'QpRts': [['-651684', '-346958', '-422760'], ['-186475', '-773507', '-207005'], ['-528673', '-579285', '422127'], ['-710966', '-347363', '418559'], ['-787818', '-418769', '-215122'], ['-672923', '694321', '4201'], ['17864', '510103', '-871237'], ['140261', '313972', '-336549'], ['-162707', '-824075', '-563775']], 'QpRts-minpoly': [9, 2, 0, 1], 'QpRts-p': 11, 'QpRts-prec': 6, 'Size': 9, 'TransitiveDegree': 9}