Artin representation data - 6.289831.7t7.a

Formats: - HTML - YAML - JSON - 2024-05-02T22:47:34.009774

• 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': [109, 2659], 'Baselabel': '6.289831.7t7.a', 'CharacterField': 1, 'Conductor': 289831, 'Container': '7t7', 'Dets': ['1.289831.2t1.a.a'], 'Dim': 6, 'GalConjSigns': [1], 'Galn': 7, 'GaloisConjugates': [{'Sign': 1, 'Character': [[6], [4], [0], [2], [3], [0], [2], [0], [1], [-1], [1], [0], [-1], [-1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [16, 17], '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], [0], [0], [-2], [0], [0], [1]], [[1], [-2], [1], [0], [-1], [2], [-1]], [[1], [0], [-1], [0], [-1], [0], [1]], [[1], [-1], [0], [0], [0], [-1], [1]], [[1], [1], [-1], [-2], [-1], [1], [1]], [[1], [-1], [-1], [0], [1], [1], [-1]], [[1], [0], [0], [0], [0], [0], [-1]], [[1], [1], [1], [1], [1], [1], [1]], [[1], [1], [0], [0], [0], [-1], [-1]], [[1], [1], [1], [0], [-1], [-1], [-1]], [[1], [0], [0], [0], [0], [-1]], [[1], [-1], [0], [0], [-1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '7T7', 'Galt': 7, 'HardPrimes': [109, 2659], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-1, 1, -1, 1, -1, 1, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [-1, 1, -1, 1, -1, 1, 0, 1], 'Proj_nTj': [7, 7]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.289831.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [-1], [1], [1], [1], [-1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.2045145337234126302686958151.14t46.a', 'Character': [[6], [-4], [0], [2], [3], [0], [-2], [0], [1], [-1], [-1], [0], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.289831.7t7.a', 'Character': [[6], [4], [0], [2], [3], [0], [2], [0], [1], [-1], [1], [0], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.7056337442282317290721.21t38.a', 'Character': [[14], [6], [2], [2], [2], [-1], [0], [0], [-1], [2], [0], [-1], [0], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.4182619450410488201473381192073448921516686705225338801.42t413.a', 'Character': [[14], [-6], [-2], [2], [2], [-1], [0], [0], [-1], [2], [0], [1], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.14431235618034262040545632427426496549771027616871.30t565.a', 'Character': [[14], [-4], [0], [2], [-1], [2], [2], [0], [-1], [-1], [-1], [0], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.2045145337234126302686958151.30t565.a', 'Character': [[14], [4], [0], [2], [-1], [2], [-2], [0], [-1], [-1], [1], [0], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '15.2045145337234126302686958151.42t412.a', 'Character': [[15], [5], [-3], [-1], [3], [0], [1], [-1], [0], [-1], [-1], [0], [1], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '15.4182619450410488201473381192073448921516686705225338801.42t411.a', 'Character': [[15], [-5], [3], [-1], [3], [0], [-1], [-1], [0], [-1], [1], [0], [1], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '20.4182619450410488201473381192073448921516686705225338801.70.a', 'Character': [[20], [0], [0], [-4], [2], [2], [0], [0], [0], [2], [0], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.4182619450410488201473381192073448921516686705225338801.84.a', 'Character': [[21], [1], [-3], [1], [-3], [0], [-1], [-1], [1], [1], [1], [0], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.1212252777931922205921231544279839774372102824462165170032631.42t418.a', 'Character': [[21], [-1], [3], [1], [-3], [0], [1], [-1], [1], [1], [-1], [0], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.17494305466952134371124666226010037764501455393990266778064454092968185425697119128942383592245458985236117601.126.a', 'Character': [[35], [-5], [-1], [-1], [-1], [-1], [1], [1], [0], [-1], [1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.8554064666431773908607966583208734279175508510687037600015340801843124683083516951.70.a', 'Character': [[35], [5], [1], [-1], [-1], [-1], [-1], [1], [0], [-1], [-1], [1], [0], [0], [-1]], 'CharacterField': 1}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7]}, {'Size': '21', 'Order': 2, 'Representative': [2, 1, 3, 4, 5, 6, 7]}, {'Size': '105', 'Order': 2, 'Representative': [2, 1, 4, 3, 6, 5, 7]}, {'Size': '105', 'Order': 2, 'Representative': [2, 1, 4, 3, 5, 6, 7]}, {'Size': '70', 'Order': 3, 'Representative': [2, 3, 1, 4, 5, 6, 7]}, {'Size': '280', 'Order': 3, 'Representative': [2, 3, 1, 5, 6, 4, 7]}, {'Size': '210', 'Order': 4, 'Representative': [2, 3, 4, 1, 5, 6, 7]}, {'Size': '630', 'Order': 4, 'Representative': [2, 3, 4, 1, 6, 5, 7]}, {'Size': '504', 'Order': 5, 'Representative': [2, 3, 4, 5, 1, 6, 7]}, {'Size': '210', 'Order': 6, 'Representative': [2, 3, 1, 5, 4, 7, 6]}, {'Size': '420', 'Order': 6, 'Representative': [2, 3, 1, 5, 4, 6, 7]}, {'Size': '840', 'Order': 6, 'Representative': [2, 3, 4, 5, 6, 1, 7]}, {'Size': '720', 'Order': 7, 'Representative': [2, 3, 4, 5, 6, 7, 1]}, {'Size': '504', 'Order': 10, 'Representative': [2, 3, 4, 5, 1, 7, 6]}, {'Size': '420', 'Order': 12, 'Representative': [2, 3, 4, 1, 6, 7, 5]}], '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, 1, 1, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 3]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 4]}, {'Data': 0, 'Classes': 11, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 3]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [1, 1, 5]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 2]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [1, 2, 4]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [1, 3, 3]}, {'Data': 0, 'Classes': 12, 'Algorithm': 'CYC', 'CycleType': [1, 6]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [2, 2, 3]}, {'Data': 0, 'Classes': 14, 'Algorithm': 'CYC', 'CycleType': [2, 5]}, {'Data': 0, 'Classes': 15, 'Algorithm': 'CYC', 'CycleType': [3, 4]}, {'Data': 0, 'Classes': 13, 'Algorithm': 'CYC', 'CycleType': [7]}], 'Frobs': [13, 15, 13, 8, 12, 13, 13, 15, 11, 6, 8, 9, 6, 15, 6, 15, 6, 9, 15, 12, 15, 13, 3, 4, 11, 15, 11, 14, 9, 9, 12, 12, 10, 14, 8, 7, 8, 8, 9, 8, 8, 14, 9, 13, 14, 10, 13, 13, 9, 8, 11, 12, 14, 13, 11, 8, 9, 13, 6, 14, 8, 8, 13, 13, 14, 11, 9, 12, 13, 11, 8, 10, 12, 6, 6, 8, 7, 12, 11, 13, 13, 2, 13, 3, 15, 12, 14, 14, 13, 15, 12, 12, 11, 13, 8, 8, 15, 8, 12, 15, 7, 15, 11, 3, 6, 9, 9, 13, 9, 6, 12, 8, 9, 13, 14, 8, 12, 8, 8, 11, 10, 9, 15, 15, 8, 7, 12, 15, 10, 7, 6, 9, 14, 13, 11, 8, 8, 12, 8, 12, 14, 11, 14, 7, 12, 15, 7, 11, 7, 7, 13, 10, 8, 13, 9, 4, 7, 12, 15, 7, 12, 13, 12, 12, 6, 12, 12, 8], 'G-Gens': [[2, 3, 4, 5, 6, 7, 1], [2, 1, 3, 4, 5, 6, 7]], 'G-Name': 'S7', 'Polynomial': [-1, 1, -1, 1, -1, 1, 0, 1], 'QpRts': [['842366024', '-639127060'], ['-863493946', '666431487'], ['-991752279', '-600360802'], ['-1895784058', '639127060'], ['969345769', '600360802'], ['-364306878', '-666431487'], ['-1635415275', '0']], 'QpRts-minpoly': [2, 82, 1], 'QpRts-p': 83, 'QpRts-prec': 5, 'Size': 5040, 'TransitiveDegree': 7}