Artin representation data - 4.7537.8t39.a

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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': [7537], 'Baselabel': '4.7537.8t39.a', 'CharacterField': 1, 'Conductor': 7537, 'Container': '8t39', 'Dets': ['1.7537.2t1.a.a'], 'Dim': 4, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[4], [-4], [0], [0], [0], [2], [-2], [1], [0], [0], [0], [0], [-1]], 'GalOrbIndex': 1, 'HardFactors': [14], '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], [-2], [0], [2], [-1]], [[1], [2], [0], [-2], [-1]], [[1], [-1], [0], [-1], [1]], [[1], [0], [2], [0], [1]], [[1], [0], [0], [0], [-1]], [[1], [0], [0], [0], [-1]], [[1], [0], [0], [0], [-1]], [[1], [1], [0], [1], [1]], [[1], [-1], [-1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T39', 'Galt': 39, 'HardPrimes': [7537], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [1, -1, -1, 1, -1, 1, -1, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [96, 227], 'Proj_Polynomial': [13368, -3211, -3042, 338, 416, -26, -26, 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': '1.7537.2t1.a', 'Character': [[1], [1], [1], [1], [1], [-1], [-1], [1], [1], [-1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.7537.3t2.a', 'Character': [[2], [2], [2], [2], [2], [0], [0], [-1], [2], [0], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.7537.4t5.b', 'Character': [[3], [3], [3], [-1], [-1], [1], [1], [0], [-1], [1], [-1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.56806369.6t8.c', 'Character': [[3], [3], [-1], [3], [-1], [-1], [-1], [0], [-1], [1], [-1], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.7537.4t5.a', 'Character': [[3], [3], [-1], [-1], [3], [1], [1], [0], [-1], [-1], [-1], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.56806369.6t8.a', 'Character': [[3], [3], [-1], [-1], [3], [-1], [-1], [0], [-1], [1], [1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.7537.4t5.c', 'Character': [[3], [3], [-1], [3], [-1], [1], [1], [0], [-1], [-1], [1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.56806369.6t8.b', 'Character': [[3], [3], [3], [-1], [-1], [-1], [-1], [0], [-1], [-1], [1], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.7537.8t39.a', 'Character': [[4], [-4], [0], [0], [0], [2], [-2], [1], [0], [0], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.428149603153.8t39.a', 'Character': [[4], [-4], [0], [0], [0], [-2], [2], [1], [0], [0], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.428149603153.8t34.a', 'Character': [[6], [6], [-2], [-2], [-2], [0], [0], [0], [2], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.3226963558964161.24t333.a', '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': [8, 7, 6, 5, 4, 3, 2, 1]}, {'Size': '6', 'Order': 2, 'Representative': [4, 3, 2, 1, 8, 7, 6, 5]}, {'Size': '6', 'Order': 2, 'Representative': [5, 3, 2, 8, 1, 7, 6, 4]}, {'Size': '6', 'Order': 2, 'Representative': [8, 7, 3, 4, 5, 6, 2, 1]}, {'Size': '12', 'Order': 2, 'Representative': [3, 2, 1, 4, 5, 8, 7, 6]}, {'Size': '12', 'Order': 2, 'Representative': [8, 7, 4, 3, 6, 5, 2, 1]}, {'Size': '32', 'Order': 3, 'Representative': [1, 3, 4, 2, 7, 5, 6, 8]}, {'Size': '12', 'Order': 4, 'Representative': [4, 6, 2, 8, 1, 7, 3, 5]}, {'Size': '24', 'Order': 4, 'Representative': [3, 1, 4, 2, 7, 5, 8, 6]}, {'Size': '24', 'Order': 4, 'Representative': [6, 8, 4, 2, 7, 5, 1, 3]}, {'Size': '24', 'Order': 4, 'Representative': [3, 7, 8, 4, 5, 1, 2, 6]}, {'Size': '32', 'Order': 6, 'Representative': [4, 8, 6, 2, 7, 3, 1, 5]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-1', '-24', '-32', '36', '1', '-6', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-46664', '-139952', '-8266', '168961', '-25631', '-28908', '31310', '-12303', '685', '545', '-67', '-7', '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': [0, 0, 1]}, 'Classes': [{'RootOf': ['-1', '1'], 'ConjugacyClass': 2}, {'RootOf': ['49', '203', '121', '47', '-1', '-1', '1'], 'ConjugacyClass': 3}, {'RootOf': ['19', '71', '41', '5', '-11', '-1', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-1728', '16272', '-40152', '22795', '13302', '-424', '-1605', '-1267', '217', '149', '-16', '-7', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': 0, 'Classes': 13, 'Algorithm': 'CYC', 'CycleType': [2, 6]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['1225', '1680', '646', '-22', '-47', '-2', '1'], 'ConjugacyClass': 9}, {'RootOf': ['1990519', '-10047', '227397', '-87216', '86970', '-11437', '5608', '1215', '-129', '65', '26', '-4', '1'], 'ConjugacyClass': 10}, {'RootOf': ['13675', '-15245', '14251', '-6644', '-1016', '-475', '2126', '-905', '-35', '101', '-14', '-4', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [4, 4]}], 'Frobs': [13, 13, 11, 10, 10, 9, 11, 7, 8, 11, 13, 9, 10, 10, 8, 13, 12, 13, 8, 10, 13, 5, 12, 12, 12, 11, 8, 8, 9, 12, 8, 6, 9, 8, 10, 4, 8, 4, 8, 12, 9, 9, 11, 12, 8, 12, 12, 13, 12, 13, 3, 13, 11, 13, 9, 5, 13, 13, 7, 13, 13, 8, 4, 3, 13, 10, 6, 13, 13, 10, 11, 12, 11, 12, 13, 3, 10, 6, 4, 12, 7, 11, 7, 8, 10, 11, 11, 8, 6, 10, 10, 13, 13, 8, 11, 11, 10, 11, 10, 10, 11, 13, 9, 8, 12, 5, 8, 10, 12, 8, 10, 13, 13, 8, 13, 7, 13, 10, 13, 11, 10, 12, 8, 11, 6, 13, 13, 11, 4, 12, 12, 10, 10, 8, 10, 8, 13, 12, 6, 8, 9, 8, 10, 3, 10, 6, 8, 10, 7, 12, 12, 13, 8, 13, 5, 6, 11, 8, 11, 13, 8, 7, 7, 8, 2, 8, 7, 6], 'G-Gens': [[3, 2, 1, 4, 5, 8, 7, 6], [3, 1, 4, 2, 7, 5, 8, 6], [6, 8, 4, 2, 7, 5, 1, 3], [6, 2, 8, 4, 5, 1, 7, 3]], 'G-Name': 'C2^3:S4', 'Polynomial': [1, -1, -1, 1, -1, 1, -1, -1, 1], 'QpRts': [['379533157600101231782', '-2155929035995132239737', '1056919870255377415281'], ['186531323101084622493', '0', '0'], ['740867070973582698736', '2127655191590739949973', '371833854812459486766'], ['2549655866882209869353', '-283209447340145058670', '1151359298296709231219'], ['2419025536172863969721', '-521297511623706353306', '-2969005108048828546716'], ['114341382977481582048', '2439138483335277298407', '-2208279168552086646500'], ['2167282891449211194142', '0', '0'], ['-2424626813475536519313', '-1606357679967033596667', '2597171253236369059950']], 'QpRts-minpoly': [18, 2, 0, 1], 'QpRts-p': 23, 'QpRts-prec': 16, 'Size': 192, 'TransitiveDegree': 8}