Artin representation data - 2.3400.12t11.b

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• 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, 5, 17], 'Baselabel': '2.3400.12t11.b', 'CharacterField': 4, 'Conductor': 3400, 'Container': '12t11', 'Dets': ['1.136.2t1.b.a', '1.136.2t1.b.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 12, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [-1], [0, -2], [0, 2], [0], [0], [1], [0, -1], [0, 1]], 'GalOrbIndex': 1, 'HardFactors': [13, 14, 13, 1, 3], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, 2], [-1]], [[1], [0, -2], [-1]], [[1], [0], [1]], [[1], [0], [1]], [[1], [-1], [1]], [[1], [0, 1], [-1]], [[1], [0, -1], [-1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [-1], [0, 2], [0, -2], [0], [0], [1], [0, 1], [0, -1]], 'GalOrbIndex': 2, 'HardFactors': [13, 14, 13, 1, 3], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, -2], [-1]], [[1], [0, 2], [-1]], [[1], [0], [1]], [[1], [0], [1]], [[1], [-1], [1]], [[1], [0, -1], [-1]], [[1], [0, 1], [-1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T11', 'Galt': 11, 'HardPrimes': [2, 5, 17, 181, 211], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [25, -75, 290, -240, -54, 163, -23, -60, 21, 15, -7, -1, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [10, -6, -1, 1], 'Proj_nTj': [3, 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], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.680.2t1.b', 'Character': [[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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.136.2t1.b', 'Character': [[1], [1], [-1], [-1], [1], [-1], [-1], [1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.5.4t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [1, 0], [0, 1], [0, -1], [0, -1], [0, 1], [-1, 0], [0, -1], [0, 1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '1.680.4t1.g', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [1, 0], [0, 1], [0, -1], [0, 1], [0, -1], [-1, 0], [0, -1], [0, 1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '1.5.4t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [1, 0], [0, -1], [0, 1], [0, 1], [0, -1], [-1, 0], [0, 1], [0, -1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '1.680.4t1.g', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [1, 0], [0, -1], [0, 1], [0, -1], [0, 1], [-1, 0], [0, 1], [0, -1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '2.680.3t2.a', 'Character': [[2], [2], [0], [0], [-1], [2], [2], [0], [0], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.680.6t3.b', 'Character': [[2], [2], [0], [0], [-1], [-2], [-2], [0], [0], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.3400.12t11.b', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [-1, 0], [0, -2], [0, 2], [0, 0], [0, 0], [1, 0], [0, -1], [0, 1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '2.3400.12t11.b', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [-1, 0], [0, 2], [0, -2], [0, 0], [0, 0], [1, 0], [0, 1], [0, -1]], 'CharacterField': 4}], 'ComplexConjugation': 4, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]}, {'Size': '1', 'Order': 2, 'Representative': [11, 7, 8, 5, 4, 10, 2, 3, 12, 6, 1, 9]}, {'Size': '3', 'Order': 2, 'Representative': [1, 2, 10, 9, 12, 8, 7, 6, 4, 3, 11, 5]}, {'Size': '3', 'Order': 2, 'Representative': [9, 8, 7, 5, 4, 10, 3, 2, 1, 6, 12, 11]}, {'Size': '2', 'Order': 3, 'Representative': [5, 10, 2, 9, 12, 8, 6, 7, 11, 3, 4, 1]}, {'Size': '1', 'Order': 4, 'Representative': [2, 11, 9, 6, 10, 5, 1, 12, 8, 4, 7, 3]}, {'Size': '1', 'Order': 4, 'Representative': [7, 1, 12, 10, 6, 4, 11, 9, 3, 5, 2, 8]}, {'Size': '3', 'Order': 4, 'Representative': [6, 5, 12, 2, 7, 11, 4, 9, 3, 1, 10, 8]}, {'Size': '3', 'Order': 4, 'Representative': [10, 4, 9, 7, 2, 1, 5, 12, 8, 11, 6, 3]}, {'Size': '2', 'Order': 6, 'Representative': [9, 8, 6, 1, 11, 2, 3, 10, 5, 7, 12, 4]}, {'Size': '2', 'Order': 12, 'Representative': [6, 5, 1, 3, 8, 9, 4, 11, 2, 12, 10, 7]}, {'Size': '2', 'Order': 12, 'Representative': [10, 4, 11, 8, 3, 12, 5, 1, 7, 9, 6, 2]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-7', '1'], 'ConjugacyClass': 2}, {'RootOf': ['432', '72', '-15', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-3', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-28', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-592', '92', '0', '1'], 'ConjugacyClass': 8}, {'RootOf': ['-652', '72', '-15', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [4, 4, 4]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [6, 6]}, {'Data': {'Powers': [1, 5], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['28', '1'], 'ConjugacyClass': 11}, {'RootOf': ['-12', '1'], 'ConjugacyClass': 12}], 'Algorithm': 'RES', 'CycleType': [12]}], 'Frobs': [6, 11, 1, 9, 3, 11, 6, 10, 8, 10, 5, 9, 3, 8, 12, 11, 10, 5, 9, 5, 11, 2, 8, 10, 12, 3, 7, 6, 10, 11, 12, 3, 9, 4, 4, 3, 6, 7, 9, 8, 2, 1, 3, 7, 9, 10, 3, 11, 12, 4, 11, 4, 3, 1, 9, 11, 10, 3, 9, 5, 11, 11, 9, 1, 7, 9, 5, 12, 12, 4, 8, 4, 9, 7, 4, 11, 4, 9, 3, 10, 4, 3, 1, 8, 2, 8, 4, 9, 3, 11, 9, 10, 9, 5, 4, 8, 4, 3, 8, 1, 12, 12, 8, 10, 3, 9, 9, 8, 4, 3, 9, 11, 12, 4, 3, 3, 7, 12, 8, 10, 3, 11, 9, 11, 3, 3, 10, 10, 12, 7, 10, 8, 5, 12, 1, 10, 7, 12, 6, 4, 3, 5, 8, 6, 4, 10, 8, 12, 10, 7, 9, 3, 8, 9, 12, 1, 4, 4, 9, 5, 12, 8, 6, 5, 9, 8, 5, 9], 'G-Gens': [[1, 2, 10, 9, 12, 8, 7, 6, 4, 3, 11, 5], [5, 10, 2, 9, 12, 8, 6, 7, 11, 3, 4, 1], [9, 8, 6, 1, 11, 2, 3, 10, 5, 7, 12, 4], [6, 5, 1, 3, 8, 9, 4, 11, 2, 12, 10, 7]], 'G-Name': 'C4*S3', 'Polynomial': [25, -75, 290, -240, -54, 163, -23, -60, 21, 15, -7, -1, 1], 'QpRts': [['-27441319', '31654542', '-59399897', '30681578'], ['-40673077', '4480638', '-54244413', '-25329187'], ['-17335196', '-23840817', '-20031242', '2680330'], ['9260663', '60713011', '27343832', '-34202715'], ['-31871828', '62947783', '-53982748', '-64888205'], ['-36218499', '-26095146', '-71189751', '-43967905'], ['73673337', '-60141616', '36562392', '-13877884'], ['-61985781', '48215912', '46670158', '-51625299'], ['50211423', '-42831951', '-59020628', '23147293'], ['-11828024', '14255842', '42905378', '-41280702'], ['-27415891', '24006436', '-70953971', '8525493'], ['-26411696', '54671255', '-60730888', '62101314']], 'QpRts-minpoly': [5, 19, 3, 0, 1], 'QpRts-p': 23, 'QpRts-prec': 6, 'Size': 24, 'TransitiveDegree': 12}