Artin representation data - 6.371131.7t7.a

Formats: - HTML - YAML - JSON - 2024-05-02T16:52:35.529315

• 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': [371131], 'Baselabel': '6.371131.7t7.a', 'CharacterField': 1, 'Conductor': 371131, 'Container': '7t7', 'Dets': ['1.371131.2t1.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': [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], [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], [-1], [0], [0], [-1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '7T7', 'Galt': 7, 'HardPrimes': [2, 371131], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-1, -1, -2, 0, -1, 0, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [-1, -1, -2, 0, -1, 0, 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': '1.371131.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [-1], [1], [1], [1], [-1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.7041029421575111979242944651.14t46.a', 'Character': [[6], [-4], [0], [2], [3], [0], [-2], [0], [1], [-1], [-1], [0], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.371131.7t7.a', 'Character': [[6], [4], [0], [2], [3], [0], [2], [0], [1], [-1], [1], [0], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.18971817017643667543921.21t38.a', 'Character': [[14], [6], [2], [2], [2], [-1], [0], [0], [-1], [2], [0], [-1], [0], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.49576095315486355973768982977399891341107170761449511801.42t413.a', 'Character': [[14], [-6], [-2], [2], [2], [-1], [0], [0], [-1], [2], [0], [1], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.133581121801968458505942599721930777383476914516571.30t565.a', 'Character': [[14], [-4], [0], [2], [-1], [2], [2], [0], [-1], [-1], [-1], [0], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.7041029421575111979242944651.30t565.a', 'Character': [[14], [4], [0], [2], [-1], [2], [-2], [0], [-1], [-1], [1], [0], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '15.7041029421575111979242944651.42t412.a', 'Character': [[15], [5], [-3], [-1], [3], [0], [1], [-1], [0], [-1], [-1], [0], [1], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '15.49576095315486355973768982977399891341107170761449511801.42t411.a', 'Character': [[15], [-5], [3], [-1], [3], [0], [-1], [-1], [0], [-1], [1], [0], [1], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '20.49576095315486355973768982977399891341107170761449511801.70.a', 'Character': [[20], [0], [0], [-4], [2], [2], [0], [0], [0], [2], [0], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.49576095315486355973768982977399891341107170761449511801.84.a', 'Character': [[21], [1], [-3], [1], [-3], [0], [-1], [-1], [1], [1], [1], [0], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.18399225830531766778900856421385399073316445391867518764216931.42t418.a', 'Character': [[21], [-1], [3], [1], [-3], [0], [1], [-1], [1], [1], [-1], [0], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.2457789226730188209450418021889599783652723407745331956876192623415766771185894781481904098446785361981238263601.126.a', 'Character': [[35], [-5], [-1], [-1], [-1], [-1], [1], [1], [0], [-1], [1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.349066745723151515635412748107057132551197570553075451713939066415694720077614326451.70.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': [14, 15, 13, 13, 13, 15, 8, 12, 14, 7, 10, 8, 8, 12, 13, 9, 15, 12, 8, 8, 13, 8, 7, 8, 6, 11, 8, 10, 14, 12, 11, 8, 9, 12, 13, 12, 13, 11, 15, 15, 15, 10, 14, 8, 14, 13, 12, 4, 7, 13, 9, 6, 13, 12, 9, 6, 8, 4, 6, 9, 13, 8, 7, 12, 13, 14, 12, 13, 5, 13, 13, 10, 12, 6, 13, 7, 6, 13, 8, 12, 14, 8, 11, 13, 11, 8, 15, 13, 8, 11, 13, 12, 8, 10, 9, 9, 13, 7, 7, 8, 9, 9, 13, 15, 12, 12, 15, 12, 4, 8, 9, 11, 9, 13, 13, 6, 9, 14, 14, 13, 12, 15, 13, 15, 15, 15, 5, 8, 14, 14, 11, 13, 9, 14, 12, 15, 6, 8, 11, 13, 6, 9, 13, 8, 12, 15, 10, 4, 14, 14, 6, 12, 13, 12, 6, 13, 9, 8, 7, 3, 8, 15, 12, 8, 12, 13, 13, 8], 'G-Gens': [[2, 3, 4, 5, 6, 7, 1], [2, 1, 3, 4, 5, 6, 7]], 'G-Name': 'S7', 'Polynomial': [-1, -1, -2, 0, -1, 0, 0, 1], 'QpRts': [['220476555918', '-241342224088'], ['-150445158136', '81891150644'], ['-262180475294', '0'], ['-49777898141', '-81891150644'], ['64219577095', '241342224088'], ['-214642419225', '0'], ['-159123259560', '0']], 'QpRts-minpoly': [3, 221, 1], 'QpRts-p': 223, 'QpRts-prec': 5, 'Size': 5040, 'TransitiveDegree': 7}