Artin representation data - 6.226505550528.18t51.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, 3, 107], 'Baselabel': '6.226505550528.18t51.b', 'CharacterField': 1, 'Conductor': 226505550528, 'Container': '18t51', 'Dets': ['1.3.2t1.a.a'], 'Dim': 6, 'GalConjSigns': [1], 'Galn': 9, 'GaloisConjugates': [{'Sign': 1, 'Character': [[6], [0], [-2], [0], [-3], [0], [0], [0], [0], [1], [0]], 'GalOrbIndex': 1, 'HardFactors': [12, 13, 14, 2], 'LocalFactors': [[[1], [-6], [15], [-20], [15], [-6], [1]], [[1], [0], [-3], [0], [3], [0], [-1]], [[1], [2], [-1], [-4], [-1], [2], [1]], [[1], [0], [-3], [0], [3], [0], [-1]], [[1], [3], [6], [7], [6], [3], [1]], [[1], [0], [0], [-2], [0], [0], [1]], [[1], [0], [0], [-2], [0], [0], [1]], [[1], [0], [0], [-2], [0], [0], [1]], [[1], [0], [0], [0], [0], [0], [-1]], [[1], [-1], [2], [-1], [2], [-1], [1]], [[1], [0], [0], [0], [0], [0], [-1]], [[1]], [[1], [0], [0], [-1]], [[1], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T18', 'Galt': 18, 'HardPrimes': [2, 3, 107, 7183121441], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-1, 4, -6, 15, -24, 28, -21, 12, -4, 1], 'NumBadPrimes': 3, 'Proj_GAP': [108, 17], 'Proj_Polynomial': [-1, 4, -6, 15, -24, 28, -21, 12, -4, 1], 'Proj_nTj': [9, 18]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.3.2t1.a', 'Character': [[1], [-1], [1], [-1], [1], [1], [1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.107.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [1], [1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.321.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [1], [1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.963.6t3.b', 'Character': [[2], [-2], [0], [0], [2], [-1], [2], [-1], [1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.321.6t3.b', 'Character': [[2], [0], [0], [-2], [2], [2], [-1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.321.3t2.a', 'Character': [[2], [0], [0], [2], [2], [2], [-1], [-1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.107.3t2.a', 'Character': [[2], [2], [0], [0], [2], [-1], [2], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.103041.6t9.a', 'Character': [[4], [0], [0], [0], [4], [-2], [-2], [1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.226505550528.18t51.b', 'Character': [[6], [0], [-2], [0], [-3], [0], [0], [0], [0], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.19783872.9t18.b', 'Character': [[6], [0], [2], [0], [-3], [0], [0], [0], [0], [-1], [0]], 'CharacterField': 1}], 'ComplexConjugation': 4, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '9', 'Order': 2, 'Representative': [3, 5, 1, 4, 2, 8, 7, 6, 9]}, {'Size': '9', 'Order': 2, 'Representative': [1, 6, 3, 8, 9, 2, 7, 4, 5]}, {'Size': '9', 'Order': 2, 'Representative': [9, 2, 8, 5, 4, 7, 6, 3, 1]}, {'Size': '2', 'Order': 3, 'Representative': [7, 5, 1, 2, 4, 9, 3, 6, 8]}, {'Size': '6', 'Order': 3, 'Representative': [5, 8, 2, 9, 6, 1, 4, 3, 7]}, {'Size': '6', 'Order': 3, 'Representative': [7, 2, 1, 4, 5, 8, 3, 9, 6]}, {'Size': '12', 'Order': 3, 'Representative': [6, 1, 8, 3, 7, 2, 9, 4, 5]}, {'Size': '18', 'Order': 6, 'Representative': [8, 1, 6, 7, 3, 2, 9, 5, 4]}, {'Size': '18', 'Order': 6, 'Representative': [7, 9, 1, 6, 8, 5, 3, 2, 4]}, {'Size': '18', 'Order': 6, 'Representative': [8, 2, 6, 5, 4, 1, 9, 7, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-48522753', '-62089551', '-21486924', '-1435140', '707994', '200118', '24692', '1692', '63', '1'], 'ConjugacyClass': 2}, {'RootOf': ['42868224', '9363456', '5245824', '4121344', '1386304', '248400', '26424', '1700', '62', '1'], 'ConjugacyClass': 3}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 3, 3]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 2, 2]}, {'Data': 0, 'Classes': 11, 'Algorithm': 'CYC', 'CycleType': [1, 2, 6]}, {'Data': {'Powers': [1, 2], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['4', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-1307', '-121', '11', '1'], 'ConjugacyClass': 6}, {'RootOf': ['221569', '11702', '20255', '1908', '351', '22', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': {'Powers': [1, 5], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['40801', '-427967', '973676', '-469332', '-236442', '-33114', '-84', '364', '33', '1'], 'ConjugacyClass': 9}, {'RootOf': ['-275254784', '2269696', '11249536', '1492608', '-173824', '-39632', '-1736', '292', '34', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [3, 6]}], 'Frobs': [11, 9, 11, 10, 9, 8, 11, 8, 9, 2, 10, 8, 9, 10, 2, 9, 4, 8, 10, 11, 10, 6, 2, 9, 10, 9, 10, 2, 3, 11, 10, 11, 2, 3, 9, 8, 3, 6, 11, 11, 11, 10, 11, 6, 9, 8, 10, 8, 9, 10, 9, 9, 7, 2, 4, 9, 11, 7, 10, 4, 7, 9, 10, 11, 7, 4, 7, 8, 11, 10, 4, 11, 10, 7, 3, 9, 4, 5, 4, 10, 11, 8, 2, 3, 6, 4, 11, 8, 9, 6, 9, 11, 10, 11, 3, 9, 2, 11, 3, 10, 7, 11, 11, 9, 8, 8, 9, 11, 9, 3, 10, 10, 11, 10, 3, 11, 8, 4, 2, 4, 5, 10, 2, 2, 8, 11, 3, 11, 8, 10, 10, 9, 3, 10, 9, 3, 4, 10, 9, 11, 6, 11, 10, 11, 10, 2, 3, 9, 8, 11, 3, 9, 8, 11, 10, 4, 10, 11, 8, 2, 4, 4, 7, 11, 9, 11, 3, 7], 'G-Gens': [[6, 1, 8, 3, 7, 2, 9, 4, 5], [1, 4, 3, 5, 2, 9, 7, 6, 8], [7, 5, 1, 2, 4, 9, 3, 6, 8], [1, 2, 7, 5, 4, 8, 3, 6, 9], [1, 6, 3, 8, 9, 2, 7, 4, 5]], 'G-Name': 'He3:C2^2', 'Polynomial': [-1, 4, -6, 15, -24, 28, -21, 12, -4, 1], 'QpRts': [['-46324867885955978475', '3563132628683208887', '13398573158411631705'], ['55114854711365499852', '-50552207344511723876', '-19694532618674912012'], ['37620516827891160105', '-1254837822814476776', '-15123866275739905147'], ['-28121876503082956158', '47577193382484522330', '55164668433555746725'], ['13414848486977660692', '36690967634913796737', '51063437682543015140'], ['-5666744950518134483', '-51140326011167731217', '43892165359990014699'], ['42893649066172787262', '28712277894435300260', '27367266623409250110'], ['9866243319806886977', '-35436129812099319961', '-35939571406803109993'], ['33658783879300467361', '21839929450076423616', '-7672734004734338098']], 'QpRts-minpoly': [11, 2, 0, 1], 'QpRts-p': 13, 'QpRts-prec': 18, 'Size': 108, 'TransitiveDegree': 9}