Artin representation data - 4.91375.8t44.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': [5, 17, 43], 'Baselabel': '4.91375.8t44.d', 'CharacterField': 1, 'Conductor': 91375, 'Container': '8t44', 'Dets': ['1.3655.2t1.a.a'], 'Dim': 4, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[4], [-4], [-2], [2], [0], [0], [2], [-2], [0], [1], [0], [-2], [2], [0], [0], [0], [-1], [1], [-1], [0]], 'GalOrbIndex': 1, 'HardFactors': [21, 22, 22], 'LocalFactors': [[[1], [-4], [6], [-4], [1]], [[1], [4], [6], [4], [1]], [[1], [2], [0], [-2], [-1]], [[1], [-2], [0], [2], [-1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [-2], [0], [2], [-1]], [[1], [2], [0], [-2], [-1]], [[1], [0], [-2], [0], [1]], [[1], [-1], [0], [-1], [1]], [[1], [0], [2], [0], [1]], [[1], [2], [2], [2], [1]], [[1], [-2], [2], [-2], [1]], [[1], [0], [0], [0], [-1]], [[1], [0], [0], [0], [-1]], [[1], [0], [0], [0], [-1]], [[1], [1], [0], [-1], [-1]], [[1], [-1], [0], [1], [-1]], [[1], [1], [0], [1], [1]], [[1], [0], [0], [0], [1]], [[1], [1]], [[1], [-1], [1], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T44', 'Galt': 44, 'HardPrimes': [5, 17, 43], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [1, 0, 0, -1, 1, -1, 0, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [192, 955], 'Proj_Polynomial': [1, -8, 14, -8, -3, 8, -3, -1, 1], 'Proj_nTj': [8, 41]}
• 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], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.731.2t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [1], [1], [-1], [-1], [1], [-1], [-1], [1], [1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.3655.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [1], [-1], [-1], [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], [-1], [-1], [1], [1], [-1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.731.3t2.a', 'Character': [[2], [2], [2], [2], [2], [2], [0], [0], [0], [-1], [2], [0], [0], [2], [0], [0], [-1], [-1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.18275.6t3.b', 'Character': [[2], [2], [-2], [-2], [2], [2], [0], [0], [0], [-1], [2], [0], [0], [-2], [0], [0], [1], [1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.731.4t5.a', 'Character': [[3], [3], [3], [3], [3], [-1], [1], [1], [1], [0], [-1], [1], [1], [-1], [1], [-1], [0], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.534361.6t8.c', 'Character': [[3], [3], [3], [3], [3], [-1], [-1], [-1], [-1], [0], [-1], [-1], [-1], [-1], [-1], [1], [0], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.91375.6t11.b', 'Character': [[3], [3], [-3], [-3], [3], [-1], [-1], [-1], [1], [0], [-1], [1], [1], [1], [-1], [1], [0], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.66795125.6t11.b', 'Character': [[3], [3], [-3], [-3], [3], [-1], [1], [1], [-1], [0], [-1], [-1], [-1], [1], [1], [-1], [0], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.3655.8t44.d', 'Character': [[4], [-4], [2], [-2], [0], [0], [2], [-2], [0], [1], [0], [2], [-2], [0], [0], [0], [1], [-1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.91375.8t44.d', 'Character': [[4], [-4], [-2], [2], [0], [0], [2], [-2], [0], [1], [0], [-2], [2], [0], [0], [0], [-1], [1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.1953089455.8t44.d', 'Character': [[4], [-4], [2], [-2], [0], [0], [-2], [2], [0], [1], [0], [-2], [2], [0], [0], [0], [1], [-1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.48827236375.8t44.d', 'Character': [[4], [-4], [-2], [2], [0], [0], [-2], [2], [0], [1], [0], [2], [-2], [0], [0], [0], [-1], [1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.66795125.8t41.b', 'Character': [[6], [6], [0], [0], [-2], [2], [2], [2], [0], [0], [-2], [0], [0], [0], [-2], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.35692709790125.12t108.b', 'Character': [[6], [6], [0], [0], [-2], [2], [-2], [-2], [0], [0], [-2], [0], [0], [0], [2], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.48827236375.8t41.b', 'Character': [[6], [6], [0], [0], [-2], [-2], [0], [0], [2], [0], [2], [-2], [-2], [0], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.48827236375.12t108.b', 'Character': [[6], [6], [0], [0], [-2], [-2], [0], [0], [-2], [0], [2], [2], [2], [0], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.4461588723765625.24t708.d', 'Character': [[8], [-8], [-4], [4], [0], [0], [0], [0], [0], [-1], [0], [0], [0], [0], [0], [0], [1], [-1], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.7138541958025.24t708.d', 'Character': [[8], [-8], [4], [-4], [0], [0], [0], [0], [0], [-1], [0], [0], [0], [0], [0], [0], [-1], [1], [1], [0]], 'CharacterField': 1}], 'ComplexConjugation': 8, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [8, 7, 6, 5, 4, 3, 2, 1]}, {'Size': '4', 'Order': 2, 'Representative': [1, 2, 6, 4, 5, 3, 7, 8]}, {'Size': '4', 'Order': 2, 'Representative': [1, 7, 6, 5, 4, 3, 2, 8]}, {'Size': '6', 'Order': 2, 'Representative': [8, 2, 6, 4, 5, 3, 7, 1]}, {'Size': '12', 'Order': 2, 'Representative': [3, 4, 1, 2, 7, 8, 5, 6]}, {'Size': '12', 'Order': 2, 'Representative': [2, 1, 3, 4, 5, 6, 8, 7]}, {'Size': '12', 'Order': 2, 'Representative': [4, 7, 6, 1, 8, 3, 2, 5]}, {'Size': '24', 'Order': 2, 'Representative': [2, 1, 6, 4, 5, 3, 8, 7]}, {'Size': '32', 'Order': 3, 'Representative': [3, 2, 4, 1, 8, 5, 7, 6]}, {'Size': '12', 'Order': 4, 'Representative': [3, 4, 8, 7, 2, 1, 5, 6]}, {'Size': '12', 'Order': 4, 'Representative': [2, 8, 3, 4, 5, 6, 1, 7]}, {'Size': '12', 'Order': 4, 'Representative': [8, 7, 5, 3, 6, 4, 2, 1]}, {'Size': '24', 'Order': 4, 'Representative': [3, 4, 8, 2, 7, 1, 5, 6]}, {'Size': '24', 'Order': 4, 'Representative': [2, 8, 6, 4, 5, 3, 1, 7]}, {'Size': '48', 'Order': 4, 'Representative': [2, 3, 4, 1, 8, 5, 6, 7]}, {'Size': '32', 'Order': 6, 'Representative': [1, 4, 7, 3, 6, 2, 5, 8]}, {'Size': '32', 'Order': 6, 'Representative': [3, 7, 4, 1, 8, 5, 2, 6]}, {'Size': '32', 'Order': 6, 'Representative': [3, 7, 5, 1, 8, 4, 2, 6]}, {'Size': '48', 'Order': 8, 'Representative': [4, 1, 7, 3, 6, 2, 8, 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, 1, 1, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-43', '144', '-210', '81', '9', '-9', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-164303', '9826', '113955', '22211', '-47330', '-4487', '8798', '765', '-1346', '143', '59', '-15', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 12, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['15', '23', '-9', '-3', '1'], 'ConjugacyClass': 4}, {'RootOf': ['138885808', '-361466792', '871802556', '-1067557742', '-639235353', '2945767748', '-2403420788', '-440544086', '1827540003', '-849446672', '-304075029', '415141822', '-88222166', '-52451460', '28252830', '50264', '-2785028', '424644', '116894', '-32836', '-1368', '1024', '-41', '-12', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 15, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 4]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [1, 1, 3, 3]}, {'Data': 0, 'Classes': 17, 'Algorithm': 'CYC', 'CycleType': [1, 1, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['0', '1'], 'ConjugacyClass': 2}, {'RootOf': ['1', '-12', '60', '30', '-178', '2', '319', '134', '-133', '-100', '-9', '6', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-731', '-2336', '2215', '2153', '-4638', '-4445', '236', '1191', '142', '-151', '-37', '3', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-5851', '840', '784', '-111', '-53', '3', '1'], 'ConjugacyClass': 13}, {'RootOf': ['749', '1812', '-230', '-3032', '1400', '6194', '3019', '-1144', '-1277', '-290', '15', '12', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [2, 2, 4]}, {'Data': 0, 'Classes': 18, 'Algorithm': 'CYC', 'CycleType': [2, 3, 3]}, {'Data': 0, 'Classes': 19, 'Algorithm': 'CYC', 'CycleType': [2, 6]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['1', '6', '15', '20', '15', '6', '1'], 'ConjugacyClass': 11}, {'RootOf': ['679681', '-8225128', '26766812', '32764352', '-193013876', '-273128476', '201939702', '515700208', '82574098', '-355005916', '-204009218', '80521732', '99836759', '9874228', '-18188154', '-6265424', '885587', '814080', '89484', '-31556', '-8785', '-220', '174', '24', '1'], 'ConjugacyClass': 16}], 'Algorithm': 'RES', 'CycleType': [4, 4]}, {'Data': 0, 'Classes': 20, 'Algorithm': 'CYC', 'CycleType': [8]}], 'Frobs': [20, 18, 17, 14, 16, 18, 14, 16, 20, 11, 15, 18, 15, 14, 17, 17, 10, 19, 17, 10, 17, 16, 17, 16, 20, 11, 17, 13, 16, 18, 18, 19, 20, 16, 15, 16, 20, 17, 9, 20, 16, 8, 15, 9, 20, 19, 19, 9, 3, 10, 3, 11, 6, 19, 20, 9, 15, 19, 17, 19, 20, 14, 14, 16, 17, 9, 16, 13, 17, 16, 18, 19, 20, 9, 8, 9, 8, 20, 16, 7, 6, 16, 7, 13, 16, 18, 10, 12, 10, 20, 20, 7, 9, 16, 19, 17, 10, 6, 9, 16, 20, 18, 14, 19, 5, 12, 9, 13, 19, 10, 18, 14, 20, 7, 16, 10, 20, 13, 14, 5, 19, 18, 14, 13, 5, 19, 16, 16, 20, 20, 15, 17, 10, 20, 7, 19, 9, 12, 18, 16, 6, 16, 20, 20, 16, 19, 20, 9, 16, 13, 20, 16, 17, 14, 9, 19, 10, 11, 20, 16, 13, 20, 3, 10, 14, 18, 10, 3], 'G-Gens': [[2, 3, 4, 1, 8, 5, 6, 7], [2, 1, 3, 4, 5, 6, 8, 7], [8, 2, 3, 4, 5, 6, 7, 1]], 'G-Name': 'C2wrS4', 'Polynomial': [1, 0, 0, -1, 1, -1, 0, 0, 1], 'QpRts': [['-10418234667662113103151407822942504700', '-2298903977141407070763639520774627779'], ['-22953860778495054628583224122497649952', '0'], ['29374327339152398281103098504555568170', '-13830250543742220555612510224248370402'], ['-9589012674383116837495785248156711713', '13726863911503973458689070684714075638'], ['4482642508335280749999865429497882252', '2298903977141407070763639520774627779'], ['2653758413678537853231510154182167276', '13830250543742220555612510224248370402'], ['-27843357343265693994770823559548371338', '0'], ['-26825793302272934969268714534448350722', '-13726863911503973458689070684714075638']], 'QpRts-minpoly': [5, 166, 1], 'QpRts-p': 167, 'QpRts-prec': 17, 'Size': 384, 'TransitiveDegree': 8}