Artin representation data - 4.350464.8t40.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, 37], 'Baselabel': '4.350464.8t40.b', 'CharacterField': 1, 'Conductor': 350464, 'Container': '8t40', 'Dets': ['1.1.1t1.a.a'], 'Dim': 4, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[4], [-4], [0], [0], [0], [1], [0], [0], [-2], [2], [-1], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [14, 6, 15, 2], 'LocalFactors': [[[1], [-4], [6], [-4], [1]], [[1], [4], [6], [4], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [-1], [0], [-1], [1]], [[1], [0], [2], [0], [1]], [[1], [0], [2], [0], [1]], [[1], [2], [2], [2], [1]], [[1], [-2], [2], [-2], [1]], [[1], [1], [0], [1], [1]], [[1], [0], [0], [0], [1]], [[1], [0], [0], [0], [1]], [[1]], [[1], [0], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T40', 'Galt': 40, 'HardPrimes': [2, 3, 37, 8963], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [3, -4, 12, -10, 12, -8, 2, -2, 1], 'NumBadPrimes': 2, 'Proj_GAP': [96, 227], 'Proj_Polynomial': [81, 108, -202, 52, -18, 32, -6, -4, 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': '1.37.2t1.a', 'Character': [[1], [1], [1], [1], [-1], [1], [1], [1], [-1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.148.3t2.a', 'Character': [[2], [2], [2], [2], [0], [-1], [2], [2], [0], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.21904.6t8.c', 'Character': [[3], [3], [3], [-1], [-1], [0], [-1], [-1], [-1], [-1], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.810448.4t5.a', 'Character': [[3], [3], [-1], [-1], [1], [0], [-1], [3], [-1], [-1], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.5476.6t8.a', 'Character': [[3], [3], [-1], [-1], [-1], [0], [3], [-1], [1], [1], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.202612.4t5.a', 'Character': [[3], [3], [-1], [-1], [1], [0], [3], [-1], [-1], [-1], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.592.4t5.a', 'Character': [[3], [3], [3], [-1], [1], [0], [-1], [-1], [1], [1], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.21904.6t8.a', 'Character': [[3], [3], [-1], [-1], [-1], [0], [-1], [3], [1], [1], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.350464.8t40.b', 'Character': [[4], [-4], [0], [0], [0], [1], [0], [0], [-2], [2], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.479785216.8t40.b', 'Character': [[4], [-4], [0], [0], [0], [1], [0], [0], [2], [-2], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.17752052992.8t34.a', 'Character': [[6], [6], [-2], [2], [0], [0], [-2], [-2], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.168147445940224.24t332.b', 'Character': [[8], [-8], [0], [0], [0], [-1], [0], [0], [0], [0], [1], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 4, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [4, 5, 8, 1, 2, 7, 6, 3]}, {'Size': '6', 'Order': 2, 'Representative': [1, 2, 8, 4, 5, 7, 6, 3]}, {'Size': '12', 'Order': 2, 'Representative': [8, 6, 4, 3, 7, 2, 5, 1]}, {'Size': '24', 'Order': 2, 'Representative': [7, 5, 3, 6, 2, 4, 1, 8]}, {'Size': '32', 'Order': 3, 'Representative': [1, 6, 5, 4, 7, 8, 3, 2]}, {'Size': '6', 'Order': 4, 'Representative': [6, 8, 2, 7, 3, 4, 1, 5]}, {'Size': '6', 'Order': 4, 'Representative': [5, 1, 7, 2, 4, 3, 8, 6]}, {'Size': '12', 'Order': 4, 'Representative': [6, 5, 8, 7, 2, 4, 1, 3]}, {'Size': '12', 'Order': 4, 'Representative': [8, 2, 1, 3, 5, 6, 7, 4]}, {'Size': '32', 'Order': 6, 'Representative': [4, 3, 6, 1, 8, 5, 2, 7]}, {'Size': '24', 'Order': 8, 'Representative': [5, 7, 4, 2, 6, 3, 8, 1]}, {'Size': '24', 'Order': 8, 'Representative': [8, 7, 2, 3, 6, 4, 1, 5]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 4]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['4', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-1693908992', '-2523529216', '-909262848', '36634624', '71028736', '13033472', '53760', '-368128', '-63424', '-3264', '224', '32', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [2, 2, 4]}, {'Data': 0, 'Classes': 11, 'Algorithm': 'CYC', 'CycleType': [2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['222976', '126208', '11008', '2560', '224', '16', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-4352', '12544', '-832', '192', '224', '16', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['5905421985211356282880', '5479456968336971137024', '2903408010750716805120', '1094592241544927903744', '329283106606694793216', '83035420643102294016', '18187928162447392768', '3554105663160320000', '633085594089488384', '104424227493380096', '16130166787538944', '2341215356452864', '318939393933312', '40439182655488', '4734565015552', '506184818688', '48966174464', '4239031296', '325427712', '21816832', '1258016', '60608', '2336', '64', '1'], 'ConjugacyClass': 12}, {'RootOf': ['758539942686818828288', '706492119382856040448', '418146566296764940288', '168314841954768650240', '65457264448164069376', '21716270280721039360', '5861616989650288640', '1289940583835500544', '229320977959288832', '32687221775532032', '3510055064436736', '220849549475840', '-7991827316736', '-4398111850496', '-637125304320', '-48781631488', '102096640', '647173120', '111777280', '12155392', '959648', '55872', '2336', '64', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'RES', 'CycleType': [8]}], 'Frobs': [5, 6, 12, 11, 11, 12, 13, 13, 10, 9, 5, 10, 6, 12, 6, 11, 5, 5, 8, 11, 11, 13, 11, 13, 5, 6, 12, 4, 13, 9, 11, 13, 4, 3, 11, 4, 11, 12, 13, 6, 9, 11, 5, 12, 11, 10, 11, 11, 5, 6, 4, 9, 9, 12, 5, 6, 7, 6, 5, 5, 5, 3, 11, 13, 12, 4, 10, 6, 9, 4, 13, 6, 4, 6, 6, 5, 5, 6, 12, 5, 6, 13, 12, 11, 5, 11, 13, 12, 12, 9, 10, 9, 13, 4, 5, 13, 11, 11, 12, 5, 5, 10, 12, 5, 11, 13, 13, 6, 6, 8, 13, 6, 6, 6, 13, 6, 10, 13, 5, 6, 13, 11, 6, 12, 4, 5, 13, 11, 13, 11, 6, 11, 11, 10, 11, 9, 11, 6, 5, 9, 6, 11, 3, 9, 5, 8, 10, 13, 13, 4, 4, 4, 5, 6, 5, 12, 12, 8, 11, 4, 13, 6, 10, 8, 5, 6, 12, 10], 'G-Gens': [[8, 6, 4, 3, 7, 2, 5, 1], [1, 6, 2, 4, 7, 3, 8, 5], [5, 7, 4, 2, 6, 3, 8, 1], [1, 7, 5, 4, 6, 3, 8, 2], [4, 3, 6, 1, 8, 5, 2, 7], [1, 2, 8, 4, 5, 7, 6, 3]], 'G-Name': 'Q8:S4', 'Polynomial': [3, -4, 12, -10, 12, -8, 2, -2, 1], 'QpRts': [['6975983606935417327999427190787069481454798', '7784029644215533974316330043191371054909008'], ['-6307013357468350068978776732015085515592509', '5930201757641455988158434454709402620365513'], ['6867959295315859884787257065979283235700825', '0'], ['4447622729779705288148183348842224753132573', '1035406033914844634303684598410241401294280'], ['-663986798131593927335675304026733867849676', '-5930201757641455988158434454709402620365513'], ['-5618223038188292169288903324289457944895182', '-7784029644215533974316330043191371054909008'], ['-7817264500656891126834899943598673120567276', '-1035406033914844634303684598410241401294280'], ['2114922062414144791503387698321372978616449', '0']], 'QpRts-minpoly': [3, 29, 1], 'QpRts-p': 31, 'QpRts-prec': 29, 'Size': 192, 'TransitiveDegree': 8}