Artin representation data - 6.37606811.9t28.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': [11, 43], 'Baselabel': '6.37606811.9t28.a', 'CharacterField': 1, 'Conductor': 37606811, 'Container': '9t28', 'Dets': ['1.11.2t1.a.a'], 'Dim': 6, 'GalConjSigns': [1], 'Galn': 9, 'GaloisConjugates': [{'Sign': 1, 'Character': [[6], [4], [0], [2], [3], [-3], [0], [0], [0], [1], [1], [-2], [-1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [12, 16, 16, 14, 18, 19, 14, 16, 16, 16, 14, 16], 'LocalFactors': [[[1], [-6], [15], [-20], [15], [-6], [1]], [[1], [-4], [5], [0], [-5], [4], [-1]], [[1], [0], [-3], [0], [3], [0], [-1]], [[1], [-2], [-1], [4], [-1], [-2], [1]], [[1], [-3], [3], [-2], [3], [-3], [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], [-1], [-1], [0], [1], [1], [-1]], [[1], [-1], [-1], [0], [1], [1], [-1]], [[1], [2], [2], [0], [-2], [-2], [-1]], [[1], [1], [-1], [-2], [-1], [1], [1]], [[1], [0], [0], [0], [0], [0], [-1]], [[1], [0], [0], [0], [0], [0], [-1]], [[1], [0], [0], [1], [0], [0], [1]], [[1], [0], [0], [1], [0], [0], [1]], [[1], [0], [-1], [-1], [0], [1]], [[1], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T28', 'Galt': 28, 'HardPrimes': [2, 3, 5, 7, 11, 43, 277, 509, 751, 2377, 3121, 4663003], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [4, 9, -4, -10, 8, 3, -4, -3, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [648, 705], 'Proj_Polynomial': [4, 9, -4, -10, 8, 3, -4, -3, 0, 1], 'Proj_nTj': [9, 28]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.11.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [1], [-1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.473.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, 0], [-1, 0], [-1, 0], [1, 0], [1, 1], [0, -1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.43.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.43.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.473.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [-1, 0], [-1, 0], [-1, 0], [1, 0], [0, -1], [1, 1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '3.20339.6t6.a', 'Character': [[3], [1], [-3], [-1], [3], [3], [3], [0], [0], [1], [1], [1], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.223729.4t4.a', 'Character': [[3], [-1], [3], [-1], [3], [3], [3], [0], [0], [-1], [-1], [-1], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.4550424131.18t197.a', 'Character': [[6], [0], [0], [-2], [3], [-3], [0], [0], [0], [-3], [3], [0], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.37606811.9t28.a', 'Character': [[6], [4], [0], [2], [3], [-3], [0], [0], [0], [1], [1], [-2], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.550601319851.18t202.a', 'Character': [[6], [-4], [0], [2], [3], [-3], [0], [0], [0], [-1], [-1], [2], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.4550424131.18t197.b', 'Character': [[6], [0], [0], [-2], [3], [-3], [0], [0], [0], [3], [-3], [0], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.50054665441.12t176.a', 'Character': [[8], [0], [0], [0], [-4], [-1], [2], [2], [2], [0], [0], [0], [0], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.92551076400409.24t1539.a', 'Character': [[8, 0], [0, 0], [0, 0], [0, 0], [-4, 0], [-1, 0], [2, 0], [0, 2], [-2, -2], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '8.92551076400409.24t1539.a', 'Character': [[8, 0], [0, 0], [0, 0], [0, 0], [-4, 0], [-1, 0], [2, 0], [-2, -2], [0, 2], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '12.171126940264356241.18t206.a', 'Character': [[12], [4], [0], [0], [0], [3], [-3], [0], [0], [-2], [-2], [1], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.2505469532410439724481.36t1101.a', 'Character': [[12], [-4], [0], [0], [0], [3], [-3], [0], [0], [2], [2], [-1], [0], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '9', 'Order': 2, 'Representative': [6, 2, 3, 4, 5, 1, 7, 8, 9]}, {'Size': '27', 'Order': 2, 'Representative': [6, 5, 4, 3, 2, 1, 7, 8, 9]}, {'Size': '27', 'Order': 2, 'Representative': [6, 2, 3, 4, 7, 1, 5, 8, 9]}, {'Size': '6', 'Order': 3, 'Representative': [1, 2, 4, 9, 5, 6, 7, 8, 3]}, {'Size': '8', 'Order': 3, 'Representative': [6, 5, 4, 9, 7, 8, 2, 1, 3]}, {'Size': '12', 'Order': 3, 'Representative': [1, 5, 4, 9, 7, 6, 2, 8, 3]}, {'Size': '36', 'Order': 3, 'Representative': [2, 3, 1, 6, 4, 5, 9, 7, 8]}, {'Size': '36', 'Order': 3, 'Representative': [3, 1, 2, 5, 6, 4, 8, 9, 7]}, {'Size': '18', 'Order': 6, 'Representative': [6, 2, 4, 9, 5, 1, 7, 8, 3]}, {'Size': '18', 'Order': 6, 'Representative': [6, 5, 3, 4, 7, 1, 2, 8, 9]}, {'Size': '36', 'Order': 6, 'Representative': [6, 5, 4, 9, 7, 1, 2, 8, 3]}, {'Size': '54', 'Order': 6, 'Representative': [6, 2, 4, 9, 7, 1, 5, 8, 3]}, {'Size': '108', 'Order': 6, 'Representative': [5, 3, 1, 6, 4, 2, 9, 7, 8]}, {'Size': '108', 'Order': 6, 'Representative': [3, 6, 2, 5, 1, 4, 8, 9, 7]}, {'Size': '72', 'Order': 9, 'Representative': [2, 3, 6, 8, 4, 5, 9, 7, 1]}, {'Size': '72', 'Order': 9, 'Representative': [3, 6, 5, 7, 8, 4, 1, 9, 2]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 3]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 2, 2]}, {'Data': {'Powers': [1, 5], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['358949902712', '-124199140008', '13564568974', '-42595927', '-59592944', '1323039', '81358', '-2145', '-36', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-301707871672', '-116344278408', '-16489601798', '-907940311', '5580952', '2326143', '39562', '-2145', '-36', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 2, 3]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 3, 3]}, {'Data': 0, 'Classes': 13, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2, 3]}, {'Data': 0, 'Classes': 12, 'Algorithm': 'CYC', 'CycleType': [1, 2, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['2513620080', '631714128', '106772012', '10835928', '850233', '44712', '1914', '48', '1'], 'ConjugacyClass': 6}, {'RootOf': 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'13285291726391680586285821296', '-5042171425103914852431611064', '1722157689694113985905127467', '-398590114185367436370411738', '58962095739432902024676945', '-8097258154339342934756848', '137448787879608071653575', '549254741353082836883568', '-131915875302746487317125', '-13151284430049563113800', '9734874769812849730035', '-297146016513771089900', '-270994566574341861300', '62809509501602890626', '5180468439673625970', '-1104010680954663702', '155644180274533347', '38771473308291472', '-1914799625312076', '158916271139892', '96367567909509', '-2019130379406', '80125810569', '96677553310', '-1164893148', '20102910', '46607457', '-330030', '2016', '10902', '-36', '0', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['2570425919896417436960066169275374364484872606608937085358600036803619959412825183228264448', 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