Artin representation data - 8.1579300663853056.24t333.e

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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, 197], 'Baselabel': '8.1579300663853056.24t333.e', 'CharacterField': 1, 'Conductor': 1579300663853056, 'Container': '24t333', 'Dets': ['1.1.1t1.a.a'], 'Dim': 8, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[8], [-8], [0], [0], [0], [0], [0], [-1], [0], [0], [0], [0], [1]], 'GalOrbIndex': 1, 'HardFactors': [14, 10, 15], 'LocalFactors': [[[1], [-8], [28], [-56], [70], [-56], [28], [-8], [1]], [[1], [8], [28], [56], [70], [56], [28], [8], [1]], [[1], [0], [-4], [0], [6], [0], [-4], [0], [1]], [[1], [0], [-4], [0], [6], [0], [-4], [0], [1]], [[1], [0], [-4], [0], [6], [0], [-4], [0], [1]], [[1], [0], [-4], [0], [6], [0], [-4], [0], [1]], [[1], [0], [-4], [0], [6], [0], [-4], [0], [1]], [[1], [1], [1], [-2], [-2], [-2], [1], [1], [1]], [[1], [0], [4], [0], [6], [0], [4], [0], [1]], [[1], [0], [0], [0], [-2], [0], [0], [0], [1]], [[1], [0], [0], [0], [-2], [0], [0], [0], [1]], [[1], [0], [0], [0], [-2], [0], [0], [0], [1]], [[1], [-1], [1], [2], [-2], [2], [1], [-1], [1]], [[1]], [[1], [0], [-2], [0], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T39', 'Galt': 39, 'HardPrimes': [2, 3, 197], 'Hide': 1, 'Indicator': 1, 'Is_Even': True, 'NFGal': [4, 0, 0, 0, -20, 0, -8, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [96, 227], 'Proj_Polynomial': [127, -144, 88, -16, 40, -8, 4, 0, 1], 'Proj_nTj': [8, 34]}
• 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], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.197.2t1.a', 'Character': [[1], [1], [1], [1], [1], [-1], [-1], [1], [1], [-1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.788.3t2.a', 'Character': [[2], [2], [2], [2], [2], [0], [0], [-1], [2], [0], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.50432.4t5.b', 'Character': [[3], [3], [3], [-1], [-1], [1], [1], [0], [-1], [1], [-1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.155236.6t8.a', 'Character': [[3], [3], [-1], [3], [-1], [-1], [-1], [0], [-1], [1], [-1], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.50432.4t5.a', 'Character': [[3], [3], [-1], [-1], [3], [1], [1], [0], [-1], [-1], [-1], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.9935104.6t8.a', 'Character': [[3], [3], [-1], [-1], [3], [-1], [-1], [0], [-1], [1], [1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.788.4t5.a', 'Character': [[3], [3], [-1], [3], [-1], [1], [1], [0], [-1], [-1], [1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.9935104.6t8.b', 'Character': [[3], [3], [3], [-1], [-1], [-1], [-1], [0], [-1], [-1], [1], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.201728.8t39.e', 'Character': [[4], [-4], [0], [0], [0], [2], [-2], [1], [0], [0], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.7828861952.8t39.e', 'Character': [[4], [-4], [0], [0], [0], [-2], [2], [1], [0], [0], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.501047164928.8t34.a', 'Character': [[6], [6], [-2], [-2], [-2], [0], [0], [0], [2], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.1579300663853056.24t333.e', 'Character': [[8], [-8], [0], [0], [0], [0], [0], [-1], [0], [0], [0], [0], [1]], 'CharacterField': 1}], 'ComplexConjugation': 5, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [5, 6, 7, 8, 1, 2, 3, 4]}, {'Size': '6', 'Order': 2, 'Representative': [4, 3, 2, 1, 8, 7, 6, 5]}, {'Size': '6', 'Order': 2, 'Representative': [8, 3, 2, 5, 4, 7, 6, 1]}, {'Size': '6', 'Order': 2, 'Representative': [5, 2, 3, 8, 1, 6, 7, 4]}, {'Size': '12', 'Order': 2, 'Representative': [2, 1, 3, 4, 6, 5, 7, 8]}, {'Size': '12', 'Order': 2, 'Representative': [8, 6, 7, 5, 4, 2, 3, 1]}, {'Size': '32', 'Order': 3, 'Representative': [4, 5, 3, 6, 8, 1, 7, 2]}, {'Size': '12', 'Order': 4, 'Representative': [4, 3, 6, 5, 8, 7, 2, 1]}, {'Size': '24', 'Order': 4, 'Representative': [3, 1, 4, 2, 7, 5, 8, 6]}, {'Size': '24', 'Order': 4, 'Representative': [3, 1, 8, 6, 7, 5, 4, 2]}, {'Size': '24', 'Order': 4, 'Representative': [4, 2, 7, 5, 8, 6, 3, 1]}, {'Size': '32', 'Order': 6, 'Representative': [2, 4, 7, 5, 6, 8, 3, 1]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['-61917364224', '0', '50429952', '0', '-12672', '0', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-25974383825859379200', '-4147056640492830720', '-202314244593549312', '-6535831854514176', '-226693229838336', '-5071490777088', '23887872', '3153199104', '106997760', '2350080', '34560', '288', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 12, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 4]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['-48', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-764411904', '0', '-2654208', '0', '1152', '0', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-764411904', '0', '3981312', '0', '4608', '0', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-25974383825859379200', '4147056640492830720', '-202314244593549312', '6535831854514176', '-226693229838336', '5071490777088', '23887872', '-3153199104', '106997760', '-2350080', '34560', '-288', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': 0, 'Classes': 13, 'Algorithm': 'CYC', 'CycleType': [2, 6]}, {'Data': {'Powers': [1, 3], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['0', '0', '0', '0', '0', '0', '1'], 'ConjugacyClass': 9}, {'RootOf': ['115112135118450327552', '0', '71011786681221120', '0', '-33462895509504', '0', '32105299968', '0', '13271040', '0', '4608', '0', '1'], 'ConjugacyClass': 10}, {'RootOf': ['115112135118450327552', '0', '468677792096059392', '0', '593526094036992', '0', '374561832960', '0', '119439360', '0', '18432', '0', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [4, 4]}], 'Frobs': [6, 10, 10, 13, 12, 12, 11, 8, 8, 13, 6, 13, 13, 8, 13, 5, 4, 8, 7, 10, 10, 10, 8, 12, 9, 8, 10, 13, 13, 12, 9, 7, 13, 10, 11, 12, 13, 9, 11, 9, 11, 4, 13, 4, 3, 11, 12, 8, 10, 10, 13, 13, 12, 13, 8, 11, 6, 11, 12, 11, 11, 13, 12, 8, 8, 10, 13, 7, 9, 11, 13, 10, 10, 10, 5, 11, 11, 11, 13, 13, 13, 12, 8, 13, 10, 8, 8, 13, 11, 11, 11, 3, 13, 13, 9, 13, 12, 13, 11, 7, 11, 13, 9, 9, 6, 12, 9, 10, 11, 13, 13, 8, 9, 3, 13, 12, 12, 6, 8, 11, 13, 12, 6, 8, 8, 6, 10, 10, 5, 9, 3, 12, 3, 6, 7, 13, 13, 5, 8, 10, 13, 8, 6, 3, 5, 13, 8, 11, 6, 7, 10, 8, 6, 6, 7, 7, 12, 10, 12, 6, 6, 12, 6, 12, 10, 11, 8, 7], 'G-Gens': [[3, 1, 4, 2, 7, 5, 8, 6], [2, 1, 3, 4, 6, 5, 7, 8], [6, 5, 3, 4, 2, 1, 7, 8], [3, 5, 4, 6, 7, 1, 8, 2]], 'G-Name': 'C2^3:S4', 'Polynomial': [4, 0, 0, 0, -20, 0, -8, 0, 1], 'QpRts': [['33089946715918321764392411897553038503742', '-5914796874839896414449143615386983167451', '-35874534939253038683395338408586283246649'], ['-12759940647366939350246138684961210847540', '31718028176088521013191761218270103864374', '9330594095180592872186907502127312434941'], ['-33142317349678001820477923726589878157172', '25803231301248624598742617602883120696923', '-26543940844072445811208430906458970811708'], ['4346718683777326188857736557647824323226', '0', '0'], ['-33089946715918321764392411897553038503742', '5914796874839896414449143615386983167451', '35874534939253038683395338408586283246649'], ['12759940647366939350246138684961210847540', '-31718028176088521013191761218270103864374', '-9330594095180592872186907502127312434941'], ['33142317349678001820477923726589878157172', '-25803231301248624598742617602883120696923', '26543940844072445811208430906458970811708'], ['-4346718683777326188857736557647824323226', '0', '0']], 'QpRts-minpoly': [17, 4, 0, 1], 'QpRts-p': 19, 'QpRts-prec': 32, 'Size': 192, 'TransitiveDegree': 8}