Artin representation data - 5.27971.6t16.a

Formats: - HTML - YAML - JSON - 2024-05-03T00:38:44.254076

• 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': [83, 337], 'Baselabel': '5.27971.6t16.a', 'CharacterField': 1, 'Conductor': 27971, 'Container': '6t16', 'Dets': ['1.27971.2t1.a.a'], 'Dim': 5, 'GalConjSigns': [1], 'Galn': 6, 'GaloisConjugates': [{'Sign': 1, 'Character': [[5], [-1], [3], [1], [-1], [2], [-1], [1], [0], [-1], [0]], 'GalOrbIndex': 1, 'HardFactors': [12, 13], 'LocalFactors': [[[1], [-5], [10], [-10], [5], [-1]], [[1], [1], [-2], [-2], [1], [1]], [[1], [-3], [2], [2], [-3], [1]], [[1], [-1], [-2], [2], [1], [-1]], [[1], [1], [1], [-1], [-1], [-1]], [[1], [-2], [1], [-1], [2], [-1]], [[1], [1], [0], [0], [-1], [-1]], [[1], [-1], [0], [0], [-1], [1]], [[1], [0], [0], [0], [0], [-1]], [[1], [1], [1], [1], [1], [1]], [[1], [0], [-1], [-1], [0], [1]], [[1], [-1], [0], [-1], [1]], [[1], [0], [0], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '6T16', 'Galt': 16, 'HardPrimes': [83, 337], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [1, -2, 3, -2, 1, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [720, 763], 'Proj_Polynomial': [1, -2, 3, -2, 1, -1, 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': '1.27971.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.27971.6t16.a', 'Character': [[5], [-1], [3], [1], [-1], [2], [-1], [1], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.782376841.12t183.a', 'Character': [[5], [-3], [1], [1], [2], [-1], [-1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.612113521333139281.12t183.a', 'Character': [[5], [1], [-3], [1], [-1], [2], [-1], [-1], [0], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.21883862619611.6t16.a', 'Character': [[5], [3], [-1], [1], [2], [-1], [-1], [1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '9.21883862619611.10t32.a', 'Character': [[9], [3], [3], [1], [0], [0], [1], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '9.478903443154007619281791321.20t145.a', 'Character': [[9], [-3], [-3], [1], [0], [0], [1], [1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '10.478903443154007619281791321.30t164.a', 'Character': [[10], [2], [-2], [-2], [1], [1], [0], [0], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '10.612113521333139281.30t164.a', 'Character': [[10], [-2], [2], [-2], [1], [1], [0], [0], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '16.374682962998855557663618582545196961.36t1252.a', 'Character': [[16], [0], [0], [0], [-2], [-2], [0], [0], [1], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 2, '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': [10, 7, 9, 9, 11, 10, 10, 5, 8, 11, 11, 9, 9, 10, 10, 7, 8, 11, 9, 9, 6, 10, 6, 9, 5, 5, 8, 3, 10, 9, 11, 4, 11, 9, 8, 10, 9, 9, 7, 9, 10, 10, 8, 5, 10, 11, 10, 7, 9, 7, 11, 10, 9, 8, 9, 8, 9, 7, 8, 10, 10, 10, 4, 8, 7, 8, 10, 8, 9, 9, 5, 10, 9, 4, 10, 3, 10, 8, 9, 6, 4, 11, 5, 10, 6, 8, 11, 5, 4, 9, 7, 11, 3, 5, 6, 6, 4, 11, 10, 9, 8, 9, 7, 7, 10, 9, 7, 7, 10, 9, 8, 7, 8, 7, 10, 9, 5, 10, 11, 11, 8, 9, 10, 10, 10, 5, 9, 9, 8, 11, 8, 7, 11, 11, 9, 11, 11, 7, 10, 9, 5, 8, 10, 9, 2, 9, 9, 8, 8, 9, 9, 10, 11, 4, 4, 9, 7, 9, 10, 10, 11, 10, 4, 9, 11, 7, 2, 9], 'G-Gens': [[2, 1, 3, 4, 5, 6], [2, 3, 4, 5, 6, 1]], 'G-Name': 'S6', 'Polynomial': [1, -2, 3, -2, 1, -1, 1], 'QpRts': [['6544907831', '4656572955'], ['-1680647352', '0'], ['-1400201170', '0'], ['3593315519', '0'], ['3182660576', '0'], ['3785481904', '-4656572955']], 'QpRts-minpoly': [2, 103, 1], 'QpRts-p': 107, 'QpRts-prec': 5, 'Size': 720, 'TransitiveDegree': 6}