Artin representation data - 3.184900.18t24.d

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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, 43], 'Baselabel': '3.184900.18t24.d', 'CharacterField': 3, 'Conductor': 184900, 'Container': '18t24', 'Dets': ['1.1.1t1.a.a', '1.1.1t1.a.a'], 'Dim': 3, 'GalConjSigns': [0, 0], 'Galn': 9, 'GaloisConjugates': [{'Sign': 0, 'Character': [[3], [-1], [-3, -3], [0, 3], [0], [0], [0], [0], [1, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [11, 12, 9, 5, 13, 10], 'LocalFactors': [[[1], [-3], [3], [-1]], [[1], [1], [-1], [-1]], [[1], [3, 3], [0, 3], [-1]], [[1], [0, -3], [-3, -3], [-1]], [[1], [0], [0], [-1]], [[1], [0], [0], [-1]], [[1], [0], [0], [-1]], [[1], [0], [0], [-1]], [[1], [-1, -1], [0, -1], [-1]], [[1], [0, 1], [1, 1], [-1]], [[1], [0, 1]], [[1], [1]], [[1], [0, -1]]]}, {'Sign': 0, 'Character': [[3], [-1], [0, 3], [-3, -3], [0], [0], [0], [0], [0, -1], [1, 1]], 'GalOrbIndex': 2, 'HardFactors': [11, 12, 9, 5, 13, 10], 'LocalFactors': [[[1], [-3], [3], [-1]], [[1], [1], [-1], [-1]], [[1], [0, -3], [-3, -3], [-1]], [[1], [3, 3], [0, 3], [-1]], [[1], [0], [0], [-1]], [[1], [0], [0], [-1]], [[1], [0], [0], [-1]], [[1], [0], [0], [-1]], [[1], [0, 1], [1, 1], [-1]], [[1], [-1, -1], [0, -1], [-1]], [[1], [-1, -1]], [[1], [1]], [[1], [1, 1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '9T12', 'Galt': 12, 'HardPrimes': [2, 5, 7, 31, 43, 712843], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [1, -2, -5, 5, 11, -2, -4, 3, -3, 1], 'NumBadPrimes': 3, 'Proj_GAP': [18, 4], 'Proj_Polynomial': [-27, -56, -4, 139, -58, 0, -11, 4, -2, 1], 'Proj_nTj': [9, 5]}
• 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': '1.43.2t1.a', 'Character': [[1], [-1], [1], [1], [1], [1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.172.3t2.a', 'Character': [[2], [0], [2], [2], [-1], [-1], [2], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.1075.3t2.a', 'Character': [[2], [0], [2], [2], [2], [-1], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.4300.3t2.a', 'Character': [[2], [0], [2], [2], [-1], [-1], [-1], [2], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.4300.3t2.b', 'Character': [[2], [0], [2], [2], [-1], [2], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.4300.9t12.d', 'Character': [[3, 0], [1, 0], [0, 3], [-3, -3], [0, 0], [0, 0], [0, 0], [0, 0], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '3.4300.9t12.d', 'Character': [[3, 0], [1, 0], [-3, -3], [0, 3], [0, 0], [0, 0], [0, 0], [0, 0], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '3.184900.18t24.d', 'Character': [[3, 0], [-1, 0], [-3, -3], [0, 3], [0, 0], [0, 0], [0, 0], [0, 0], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '3.184900.18t24.d', 'Character': [[3, 0], [-1, 0], [0, 3], [-3, -3], [0, 0], [0, 0], [0, 0], [0, 0], [0, -1], [1, 1]], 'CharacterField': 3}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '9', 'Order': 2, 'Representative': [1, 2, 5, 8, 3, 7, 6, 4, 9]}, {'Size': '1', 'Order': 3, 'Representative': [2, 9, 4, 6, 8, 3, 5, 7, 1]}, {'Size': '1', 'Order': 3, 'Representative': [9, 1, 6, 3, 7, 4, 8, 5, 2]}, {'Size': '6', 'Order': 3, 'Representative': [7, 5, 2, 9, 3, 1, 6, 4, 8]}, {'Size': '6', 'Order': 3, 'Representative': [8, 7, 2, 9, 4, 1, 3, 6, 5]}, {'Size': '6', 'Order': 3, 'Representative': [1, 2, 4, 6, 7, 3, 8, 5, 9]}, {'Size': '6', 'Order': 3, 'Representative': [6, 3, 8, 7, 1, 5, 9, 2, 4]}, {'Size': '9', 'Order': 6, 'Representative': [2, 9, 8, 7, 4, 5, 3, 6, 1]}, {'Size': '9', 'Order': 6, 'Representative': [9, 1, 7, 5, 6, 8, 4, 3, 2]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-6', '1'], 'ConjugacyClass': 3}, {'RootOf': ['15', '1'], 'ConjugacyClass': 4}, {'RootOf': ['1752976', '-323056', '6940', '3380', '-235', '-6', '1'], 'ConjugacyClass': 5}, {'RootOf': ['77841', '7254', '-1505', '480', '35', '-6', '1'], 'ConjugacyClass': 6}, {'RootOf': ['435991', '79914', '9315', '960', '-75', '-6', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-8205056', '3885184', '-1198296', '353849', '-92476', '16231', '-2184', '271', '-24', '1'], 'ConjugacyClass': 9}, {'RootOf': ['507112475', '408450825', '143858300', '27055576', '2719514', '130210', '3800', '460', '39', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [3, 6]}], 'Frobs': [10, 9, 2, 9, 8, 8, 5, 9, 6, 9, 6, 10, 6, 10, 7, 6, 7, 9, 5, 10, 10, 7, 8, 2, 6, 8, 5, 7, 6, 2, 8, 9, 9, 6, 9, 9, 2, 2, 5, 7, 10, 7, 10, 6, 3, 2, 2, 9, 9, 8, 2, 7, 10, 6, 2, 9, 5, 5, 2, 5, 6, 7, 8, 5, 2, 5, 2, 8, 2, 9, 8, 5, 7, 9, 5, 2, 10, 1, 5, 10, 2, 9, 8, 9, 8, 3, 9, 10, 7, 10, 9, 5, 4, 2, 9, 10, 5, 2, 9, 5, 6, 6, 6, 8, 10, 10, 10, 9, 6, 2, 10, 7, 8, 7, 2, 9, 7, 2, 2, 6, 6, 10, 10, 5, 9, 7, 8, 7, 9, 2, 2, 2, 9, 10, 10, 7, 9, 4, 1, 7, 9, 5, 8, 7, 2, 9, 5, 7, 10, 10, 5, 8, 8, 9, 8, 10, 5, 9, 10, 8, 8, 2, 6, 5, 7, 10, 2, 9], 'G-Gens': [[1, 2, 5, 8, 3, 7, 6, 4, 9], [2, 9, 4, 6, 8, 3, 5, 7, 1], [1, 2, 4, 6, 7, 3, 8, 5, 9], [7, 5, 2, 9, 3, 1, 6, 4, 8]], 'G-Name': 'He3:C2', 'Polynomial': [1, -2, -5, 5, 11, -2, -4, 3, -3, 1], 'QpRts': [['5694295574816509984', '0', '0'], ['50559424545883330323', '0', '0'], ['-4502154811126457256', '44756748044536726608', '36687667839730402884'], ['-55298192003425742840', '38306273198396699316', '11289649243580760092'], ['51358310508404607568', '24320226034481759406', '-22675382488311289847'], ['-57640641548261010735', '33128461866015152317', '-47977317083311162976'], ['-15845272877364088364', '23804858069002453953', '-56277174181195637813'], ['22231222606143886100', '-48125084103484213359', '-37238926439441650581'], ['3443008004928965223', '0', '0']], 'QpRts-minpoly': [42, 3, 0, 1], 'QpRts-p': 47, 'QpRts-prec': 12, 'Size': 54, 'TransitiveDegree': 9}