Artin representation data - 16.129746337890625000000000000.36t1252.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': [2, 3, 5], 'Baselabel': '16.129746337890625000000000000.36t1252.a', 'CharacterField': 1, 'Conductor': 129746337890625000000000000, 'Container': '36t1252', 'Dets': ['1.1.1t1.a.a'], 'Dim': 16, 'GalConjSigns': [1], 'Galn': 6, 'GaloisConjugates': [{'Sign': 1, 'Character': [[16], [0], [0], [0], [-2], [-2], [0], [0], [1], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [12, 13, 14], 'LocalFactors': [[[1], [-16], [120], [-560], [1820], [-4368], [8008], [-11440], [12870], [-11440], [8008], [-4368], [1820], [-560], [120], [-16], [1]], [[1], [0], [-8], [0], [28], [0], [-56], [0], [70], [0], [-56], [0], [28], [0], [-8], [0], [1]], [[1], [0], [-8], [0], [28], [0], [-56], [0], [70], [0], [-56], [0], [28], [0], [-8], [0], [1]], [[1], [0], [-8], [0], [28], [0], [-56], [0], [70], [0], [-56], [0], [28], [0], [-8], [0], [1]], [[1], [2], [3], [-2], [-7], [-12], [-2], [8], [18], [8], [-2], [-12], [-7], [-2], [3], [2], [1]], [[1], [2], [3], [-2], [-7], [-12], [-2], [8], [18], [8], [-2], [-12], [-7], [-2], [3], [2], [1]], [[1], [0], [0], [0], [-4], [0], [0], [0], [6], [0], [0], [0], [-4], [0], [0], [0], [1]], [[1], [0], [0], [0], [-4], [0], [0], [0], [6], [0], [0], [0], [-4], [0], [0], [0], [1]], [[1], [-1], [0], [0], [0], [-3], [3], [0], [0], [0], [3], [-3], [0], [0], [0], [-1], [1]], [[1], [0], [1], [0], [1], [0], [-2], [0], [-2], [0], [-2], [0], [1], [0], [1], [0], [1]], [[1], [0], [1], [0], [1], [0], [-2], [0], [-2], [0], [-2], [0], [1], [0], [1], [0], [1]], [[1], [0], [1], [0], [1]], [[1], [0], [0], [0], [-1]], [[1], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '6T16', 'Galt': 16, 'HardPrimes': [2, 3, 5], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [4, 12, 0, 5, 0, -3, 1], 'NumBadPrimes': 3, 'Proj_GAP': [720, 763], 'Proj_Polynomial': [4, 12, 0, 5, 0, -3, 1], 'Proj_nTj': [6, 16]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.5.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.25312500.6t16.a', 'Character': [[5], [-1], [3], [1], [-1], [2], [-1], [1], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.506250000.12t183.a', 'Character': [[5], [-3], [1], [1], [2], [-1], [-1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.126562500.12t183.a', 'Character': [[5], [1], [-3], [1], [-1], [2], [-1], [-1], [0], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.101250000.6t16.a', 'Character': [[5], [3], [-1], [1], [2], [-1], [-1], [1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '9.12814453125000000.10t32.a', 'Character': [[9], [3], [3], [1], [0], [0], [1], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '9.2562890625000000.20t145.a', 'Character': [[9], [-3], [-3], [1], [0], [0], [1], [1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '10.64072265625000000.30t164.a', 'Character': [[10], [2], [-2], [-2], [1], [1], [0], [0], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '10.64072265625000000.30t164.b', 'Character': [[10], [-2], [2], [-2], [1], [1], [0], [0], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '16.129746337890625000000000000.36t1252.a', 'Character': [[16], [0], [0], [0], [-2], [-2], [0], [0], [1], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 4, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6]}, {'Size': '15', 'Order': 2, 'Representative': [2, 1, 4, 3, 6, 5]}, {'Size': '15', 'Order': 2, 'Representative': [2, 1, 3, 4, 5, 6]}, {'Size': '45', 'Order': 2, 'Representative': [2, 1, 4, 3, 5, 6]}, {'Size': '40', 'Order': 3, 'Representative': [2, 3, 1, 5, 6, 4]}, {'Size': '40', 'Order': 3, 'Representative': [2, 3, 1, 4, 5, 6]}, {'Size': '90', 'Order': 4, 'Representative': [2, 3, 4, 1, 6, 5]}, {'Size': '90', 'Order': 4, 'Representative': [2, 3, 4, 1, 5, 6]}, {'Size': '144', 'Order': 5, 'Representative': [2, 3, 4, 5, 1, 6]}, {'Size': '120', 'Order': 6, 'Representative': [2, 3, 4, 5, 6, 1]}, {'Size': '120', 'Order': 6, 'Representative': [2, 3, 1, 5, 4, 6]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 2]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 3]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [1, 1, 4]}, {'Data': 0, 'Classes': 11, 'Algorithm': 'CYC', 'CycleType': [1, 2, 3]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [1, 5]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [2, 4]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [3, 3]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [6]}], 'Frobs': [11, 8, 1, 11, 7, 10, 2, 9, 11, 5, 7, 11, 9, 10, 10, 11, 9, 7, 10, 6, 8, 7, 11, 7, 11, 9, 10, 10, 7, 10, 10, 5, 10, 9, 9, 4, 8, 10, 10, 8, 7, 6, 9, 10, 10, 4, 9, 11, 3, 7, 8, 9, 5, 7, 11, 11, 9, 9, 11, 7, 3, 11, 8, 4, 11, 10, 5, 10, 10, 6, 3, 5, 8, 11, 9, 10, 7, 11, 4, 9, 9, 9, 7, 8, 9, 11, 7, 10, 9, 11, 11, 6, 11, 7, 5, 8, 9, 9, 11, 4, 10, 11, 10, 5, 7, 11, 11, 10, 6, 9, 8, 11, 11, 9, 9, 7, 8, 8, 10, 7, 6, 10, 11, 8, 4, 9, 9, 9, 2, 11, 4, 10, 5, 10, 7, 7, 8, 8, 10, 9, 9, 6, 11, 10, 9, 9, 8, 11, 9, 8, 10, 6, 10, 10, 8, 9, 7, 6, 11, 7, 11, 8, 10, 7, 10, 11, 9, 10], 'G-Gens': [[2, 1, 3, 4, 5, 6], [2, 3, 4, 5, 6, 1]], 'G-Name': 'S6', 'Polynomial': [4, 12, 0, 5, 0, -3, 1], 'QpRts': [['-386536', '671120'], ['-21642', '283966'], ['-194275', '123241'], ['234400', '-671120'], ['-305527', '-283966'], ['673583', '-123241']], 'QpRts-minpoly': [3, 16, 1], 'QpRts-p': 17, 'QpRts-prec': 5, 'Size': 720, 'TransitiveDegree': 6}