Artin representation data - 8.792930743933500747267165271434973708881265625.21t14.a

Formats: - HTML - YAML - JSON - 2024-05-11T18:10:57.621755

• 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': [3, 5, 47, 3942493], 'Baselabel': '8.792930743933500747267165271434973708881265625.21t14.a', 'CharacterField': 1, 'Conductor': 792930743933500747267165271434973708881265625, 'Container': '21t14', 'Dets': ['1.1.1t1.a.a'], 'Dim': 8, 'GalConjSigns': [1], 'Galn': 7, 'GaloisConjugates': [{'Sign': 1, 'Character': [[8], [0], [-1], [0], [1], [1]], 'GalOrbIndex': 1, 'HardFactors': [3, 7, 8, 9, 9], 'LocalFactors': [[[1], [-8], [28], [-56], [70], [-56], [28], [-8], [1]], [[1], [0], [-4], [0], [6], [0], [-4], [0], [1]], [[1], [1], [1], [-2], [-2], [-2], [1], [1], [1]], [[1], [0], [0], [0], [-2], [0], [0], [0], [1]], [[1], [-1], [0], [0], [0], [0], [0], [-1], [1]], [[1], [-1], [0], [0], [0], [0], [0], [-1], [1]], [[1], [-1]], [[1], [0], [-1]], [[1], [0], [-2], [0], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '7T5', 'Galt': 5, 'HardPrimes': [2, 3, 5, 47, 3942493], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [7200, -88200, 0, -210, -735, 0, -1, 1], 'NumBadPrimes': 4, 'Proj_GAP': [168, 42], 'Proj_Polynomial': [7200, -88200, 0, -210, -735, 0, -1, 1], 'Proj_nTj': [7, 5]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.625756132806494067225.42t37.a', 'Character': [[3, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0], [-1, -1, -1, 0, -1, 0]], 'CharacterField': 7}, {'GalConj': 2, 'Baselabel': '3.625756132806494067225.42t37.a', 'Character': [[3, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [-1, -1, -1, 0, -1, 0], [0, 1, 1, 0, 1, 0]], 'CharacterField': 7}, {'GalConj': 1, 'Baselabel': '6.1267156168933150486130625.7t5.a', 'Character': [[6], [2], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '7.391570737744938640625760627869122819200625.8t37.a', 'Character': [[7], [-1], [1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.792930743933500747267165271434973708881265625.21t14.a', 'Character': [[8], [0], [-1], [0], [1], [1]], 'CharacterField': 1}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7]}, {'Size': '21', 'Order': 2, 'Representative': [1, 2, 4, 3, 5, 7, 6]}, {'Size': '56', 'Order': 3, 'Representative': [1, 6, 4, 5, 3, 7, 2]}, {'Size': '42', 'Order': 4, 'Representative': [5, 2, 6, 7, 1, 4, 3]}, {'Size': '24', 'Order': 7, 'Representative': [5, 3, 6, 1, 7, 4, 2]}, {'Size': '24', 'Order': 7, 'Representative': [2, 4, 1, 7, 3, 5, 6]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 2, 4]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 3, 3]}, {'Data': [2, 3, 4, 5, 6, 7, 1], 'Classes': [{'RootOf': ['-177254124936139800000', '1'], 'ConjugacyClass': 5}, {'RootOf': ['177254124936139800000', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'ALT', 'CycleType': [7]}], 'Frobs': [3, 1, 2, 3, 6, 6, 3, 4, 4, 3, 4, 3, 5, 3, 2, 4, 5, 2, 3, 3, 4, 5, 4, 5, 6, 3, 3, 4, 4, 3, 4, 5, 3, 3, 5, 3, 2, 5, 2, 5, 6, 4, 5, 4, 4, 3, 3, 2, 4, 3, 6, 3, 2, 4, 6, 4, 4, 4, 6, 5, 2, 3, 5, 4, 4, 3, 6, 4, 4, 2, 4, 6, 6, 5, 6, 4, 3, 3, 5, 4, 6, 3, 3, 3, 5, 5, 3, 5, 4, 3, 4, 6, 6, 5, 3, 6, 3, 3, 5, 2, 2, 4, 5, 3, 3, 5, 2, 4, 3, 5, 4, 5, 6, 6, 6, 4, 6, 4, 3, 2, 6, 6, 3, 3, 4, 2, 3, 3, 5, 3, 3, 2, 3, 2, 2, 5, 6, 4, 5, 6, 2, 5, 2, 4, 5, 3, 3, 3, 3, 3, 6, 3, 2, 3, 4, 3, 6, 5, 2, 4, 3, 4, 2, 6, 3, 3, 6, 4], 'G-Gens': [[5, 2, 6, 7, 1, 4, 3], [7, 3, 2, 4, 5, 6, 1]], 'G-Name': 'PSL(2,7)', 'Polynomial': [7200, -88200, 0, -210, -735, 0, -1, 1], 'QpRts': [['5913804854098477574589', '0', '0'], ['6905197694293842812620', '2922119051416246841667', '4888914947578091247010'], ['2121603938138666152067', '2976106485286565707937', '4745066539379188751685'], ['1910961555292836979153', '-5898225536702812549604', '4429102965110444992314'], ['4968765822267298835780', '-3508580887961818019084', '1815848302245135021875'], ['3245634686988383418160', '-3323568977591564886231', '-768848400673238104555'], ['3060200353055944209650', '6832149865553382905315', '-1046999901571896917320']], 'QpRts-minpoly': [14, 1, 0, 1], 'QpRts-p': 17, 'QpRts-prec': 18, 'Size': 168, 'TransitiveDegree': 7}