Artin representation data - 2.961.15t4.a

Formats: - HTML - YAML - JSON - 2025-01-24T12:42:41.982155

• 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': [31], 'Baselabel': '2.961.15t4.a', 'CharacterField': 5, 'Conductor': 961, 'Container': '15t4', 'Dets': ['1.31.10t1.a.d', '1.31.10t1.a.c', '1.31.10t1.a.b', '1.31.10t1.a.a'], 'Dim': 2, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 15, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [0], [-1], [-2, -2, -2, -2], [0, 0, 0, 2], [0, 0, 2], [0, 2], [0], [0], [0], [0], [1, 1, 1, 1], [0, 0, 0, -1], [0, -1], [0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [15, 10, 12, 16, 1, 8, 1, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [2, 2, 2, 2], [0, 0, 0, 1]], [[1], [0, 0, 0, -2], [0, 1]], [[1], [0, 0, -2], [-1, -1, -1, -1]], [[1], [0, -2], [0, 0, 1]], [[1], [0], [0, 0, 0, -1]], [[1], [0], [1, 1, 1, 1]], [[1], [0], [0, -1]], [[1], [0], [0, 0, -1]], [[1], [-1, -1, -1, -1], [0, 0, 0, 1]], [[1], [0, 0, 0, 1], [0, 1]], [[1], [0, 1], [0, 0, 1]], [[1], [0, 0, 1], [-1, -1, -1, -1]], [[1]]]}, {'Sign': 0, 'Character': [[2], [0], [-1], [0, 0, 2], [-2, -2, -2, -2], [0, 2], [0, 0, 0, 2], [0], [0], [0], [0], [0, 0, -1], [1, 1, 1, 1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 2, 'HardFactors': [15, 10, 12, 16, 1, 8, 1, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, 0, -2], [-1, -1, -1, -1]], [[1], [2, 2, 2, 2], [0, 0, 0, 1]], [[1], [0, -2], [0, 0, 1]], [[1], [0, 0, 0, -2], [0, 1]], [[1], [0], [1, 1, 1, 1]], [[1], [0], [0, 0, -1]], [[1], [0], [0, 0, 0, -1]], [[1], [0], [0, -1]], [[1], [0, 0, 1], [-1, -1, -1, -1]], [[1], [-1, -1, -1, -1], [0, 0, 0, 1]], [[1], [0, 0, 0, 1], [0, 1]], [[1], [0, 1], [0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[2], [0], [-1], [0, 0, 0, 2], [0, 2], [-2, -2, -2, -2], [0, 0, 2], [0], [0], [0], [0], [0, 0, 0, -1], [0, -1], [0, 0, -1], [1, 1, 1, 1]], 'GalOrbIndex': 3, 'HardFactors': [15, 10, 12, 16, 1, 8, 1, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, 0, 0, -2], [0, 1]], [[1], [0, -2], [0, 0, 1]], [[1], [2, 2, 2, 2], [0, 0, 0, 1]], [[1], [0, 0, -2], [-1, -1, -1, -1]], [[1], [0], [0, -1]], [[1], [0], [0, 0, 0, -1]], [[1], [0], [0, 0, -1]], [[1], [0], [1, 1, 1, 1]], [[1], [0, 0, 0, 1], [0, 1]], [[1], [0, 1], [0, 0, 1]], [[1], [0, 0, 1], [-1, -1, -1, -1]], [[1], [-1, -1, -1, -1], [0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[2], [0], [-1], [0, 2], [0, 0, 2], [0, 0, 0, 2], [-2, -2, -2, -2], [0], [0], [0], [0], [0, -1], [0, 0, -1], [1, 1, 1, 1], [0, 0, 0, -1]], 'GalOrbIndex': 4, 'HardFactors': [15, 10, 12, 16, 1, 8, 1, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [0, -2], [0, 0, 1]], [[1], [0, 0, -2], [-1, -1, -1, -1]], [[1], [0, 0, 0, -2], [0, 1]], [[1], [2, 2, 2, 2], [0, 0, 0, 1]], [[1], [0], [0, 0, -1]], [[1], [0], [0, -1]], [[1], [0], [1, 1, 1, 1]], [[1], [0], [0, 0, 0, -1]], [[1], [0, 1], [0, 0, 1]], [[1], [0, 0, 1], [-1, -1, -1, -1]], [[1], [-1, -1, -1, -1], [0, 0, 0, 1]], [[1], [0, 0, 0, 1], [0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '15T4', 'Galt': 4, 'HardPrimes': [2, 3, 7, 31, 67, 151, 14347, 36151], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [-1, -18, -22, 50, 62, -17, -69, -100, 172, -7, -87, 51, -17, 7, -4, 1], 'NumBadPrimes': 1, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-1, 1, 0, 1], 'Proj_nTj': [3, 2]}
• 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': '1.31.2t1.a', 'Character': [[1], [-1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.31.10t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [1, 0, 0, 0], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, -1, 0], [0, -1, 0, 0], [1, 1, 1, 1], [0, 0, 0, -1], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 1, 0, 0]], 'CharacterField': 5}, {'GalConj': 1, 'Baselabel': '1.31.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 0, 0, 1]], 'CharacterField': 5}, {'GalConj': 2, 'Baselabel': '1.31.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 1, 0], [0, 0, 0, 1], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 1, 0]], 'CharacterField': 5}, {'GalConj': 2, 'Baselabel': '1.31.10t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1], [0, -1, 0, 0], [0, 0, 0, -1], [0, 0, -1, 0], [1, 1, 1, 1], [0, 1, 0, 0], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 0, 0, 1]], 'CharacterField': 5}, {'GalConj': 3, 'Baselabel': '1.31.10t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [1, 0, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 1, 1, 1], [0, 0, -1, 0], [0, 0, 0, -1], [0, -1, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 1, 0]], 'CharacterField': 5}, {'GalConj': 3, 'Baselabel': '1.31.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 1, 0, 0]], 'CharacterField': 5}, {'GalConj': 4, 'Baselabel': '1.31.5t1.a', 'Character': [[1, 0, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 1, 0], [-1, -1, -1, -1]], 'CharacterField': 5}, {'GalConj': 4, 'Baselabel': '1.31.10t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 1, 0], [0, 0, 0, -1], [1, 1, 1, 1], [0, -1, 0, 0], [0, 0, -1, 0], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 1, 0], [-1, -1, -1, -1]], 'CharacterField': 5}, {'GalConj': 1, 'Baselabel': '2.31.3t2.b', 'Character': [[2], [0], [-1], [2], [2], [2], [2], [0], [0], [0], [0], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.961.15t4.a', 'Character': [[2, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [-2, -2, -2, -2], [0, 0, 0, 2], [0, 0, 2, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1, 1, 1, 1], [0, 0, 0, -1], [0, -1, 0, 0], [0, 0, -1, 0]], 'CharacterField': 5}, {'GalConj': 2, 'Baselabel': '2.961.15t4.a', 'Character': [[2, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 2, 0], [-2, -2, -2, -2], [0, 2, 0, 0], [0, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [1, 1, 1, 1], [0, 0, 0, -1], [0, -1, 0, 0]], 'CharacterField': 5}, {'GalConj': 3, 'Baselabel': '2.961.15t4.a', 'Character': [[2, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 2], [0, 2, 0, 0], [-2, -2, -2, -2], [0, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -1], [0, -1, 0, 0], [0, 0, -1, 0], [1, 1, 1, 1]], 'CharacterField': 5}, {'GalConj': 4, 'Baselabel': '2.961.15t4.a', 'Character': [[2, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 2, 0, 0], [0, 0, 2, 0], [0, 0, 0, 2], [-2, -2, -2, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1, 0, 0], [0, 0, -1, 0], [1, 1, 1, 1], [0, 0, 0, -1]], 'CharacterField': 5}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]}, {'Size': '3', 'Order': 2, 'Representative': [2, 1, 3, 9, 5, 6, 15, 8, 4, 13, 14, 12, 10, 11, 7]}, {'Size': '2', 'Order': 3, 'Representative': [6, 1, 14, 8, 10, 2, 12, 9, 4, 13, 3, 15, 5, 11, 7]}, {'Size': '1', 'Order': 5, 'Representative': [11, 14, 12, 1, 8, 3, 13, 6, 2, 9, 7, 5, 4, 15, 10]}, {'Size': '1', 'Order': 5, 'Representative': [7, 15, 5, 11, 6, 12, 4, 3, 14, 2, 13, 8, 1, 10, 9]}, {'Size': '1', 'Order': 5, 'Representative': [13, 10, 8, 7, 3, 5, 1, 12, 15, 14, 4, 6, 11, 9, 2]}, {'Size': '1', 'Order': 5, 'Representative': [4, 9, 6, 13, 12, 8, 11, 5, 10, 15, 1, 3, 7, 2, 14]}, {'Size': '3', 'Order': 10, 'Representative': [14, 11, 12, 2, 8, 3, 10, 6, 1, 4, 15, 5, 9, 7, 13]}, {'Size': '3', 'Order': 10, 'Representative': [10, 13, 8, 15, 3, 5, 2, 12, 7, 11, 9, 6, 14, 4, 1]}, {'Size': '3', 'Order': 10, 'Representative': [15, 7, 5, 14, 6, 12, 9, 3, 11, 1, 10, 8, 2, 13, 4]}, {'Size': '3', 'Order': 10, 'Representative': [9, 4, 6, 10, 12, 8, 14, 5, 13, 7, 2, 3, 15, 1, 11]}, {'Size': '2', 'Order': 15, 'Representative': [3, 11, 15, 6, 9, 14, 5, 2, 1, 4, 12, 10, 8, 7, 13]}, {'Size': '2', 'Order': 15, 'Representative': [15, 12, 13, 14, 1, 7, 9, 11, 3, 6, 10, 4, 2, 5, 8]}, {'Size': '2', 'Order': 15, 'Representative': [8, 4, 2, 5, 15, 9, 3, 10, 13, 7, 6, 14, 12, 1, 11]}, {'Size': '2', 'Order': 15, 'Representative': [5, 13, 9, 12, 14, 10, 6, 15, 7, 11, 8, 2, 3, 4, 1]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 2, 2, 2, 2, 2]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [3, 3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['-38', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-255', '1'], 'ConjugacyClass': 5}, {'RootOf': ['179', '1'], 'ConjugacyClass': 6}, {'RootOf': ['24', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [5, 5, 5]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['1971', '245', '-4', '1'], 'ConjugacyClass': 8}, {'RootOf': ['-5221', '431', '-35', '1'], 'ConjugacyClass': 9}, {'RootOf': ['-58696', '-1212', '-4', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-2803', '-375', '-4', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [5, 10]}, {'Data': {'Powers': [1, 11], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['-174', '1'], 'ConjugacyClass': 12}, {'RootOf': ['198', '1'], 'ConjugacyClass': 13}, {'RootOf': ['43', '1'], 'ConjugacyClass': 14}, {'RootOf': ['12', '1'], 'ConjugacyClass': 15}], 'Algorithm': 'RES', 'CycleType': [15]}], 'Frobs': [15, 10, 3, 12, 8, 10, 11, 15, 11, 9, 1, 2, 15, 9, 5, 11, 13, 2, 1, 14, 8, 11, 9, 8, 12, 14, 15, 14, 13, 12, 10, 4, 10, 10, 1, 8, 15, 14, 9, 5, 8, 2, 3, 12, 8, 10, 3, 2, 6, 9, 13, 11, 8, 10, 14, 10, 9, 11, 9, 15, 4, 7, 13, 3, 10, 12, 9, 8, 2, 7, 9, 13, 2, 3, 4, 8, 11, 3, 9, 2, 13, 13, 5, 2, 3, 14, 10, 11, 8, 9, 15, 14, 11, 2, 10, 12, 10, 1, 8, 14, 12, 2, 3, 8, 10, 6, 9, 12, 15, 9, 5, 8, 5, 2, 8, 9, 11, 8, 6, 14, 15, 11, 2, 3, 14, 15, 8, 2, 14, 12, 2, 2, 12, 10, 11, 3, 9, 9, 11, 10, 1, 10, 11, 9, 11, 6, 5, 4, 11, 2, 14, 10, 10, 15, 14, 9, 4, 2, 4, 8, 11, 11, 2, 6, 13, 11, 2, 3], 'G-Gens': [[1, 6, 14, 4, 10, 2, 7, 9, 8, 5, 11, 15, 13, 3, 12], [2, 1, 3, 9, 5, 6, 15, 8, 4, 13, 14, 12, 10, 11, 7], [11, 14, 12, 1, 8, 3, 13, 6, 2, 9, 7, 5, 4, 15, 10]], 'G-Name': 'C5*S3', 'Polynomial': [-1, -18, -22, 50, 62, -17, -69, -100, 172, -7, -87, 51, -17, 7, -4, 1], 'QpRts': [['210235830019', '112934912882', '-114617499708', '8219867485', '195336692715'], ['14979020994', '-168741911311', '70113186231', '-24768282371', '-139806225188'], ['-32418731728', '-17581907302', '55944178442', '-894047860', '-194502658769'], ['54398260220', '-3960733769', '212808790409', '133914814123', '127195510582'], ['-25655520326', '-178982390500', '191643760447', '-238757309255', '67262915715'], ['21156311642', '110866390159', '240225654937', '-71539488154', '125777705675'], ['-77967251574', '-199821002408', '230814801377', '-70073136525', '215050181071'], ['-218913549745', '128299182195', '-112295801082', '-32098096845', '-47653840943'], ['-157414414301', '-245950598731', '-8994534924', '-7166513444', '-228642239191'], ['-239349534106', '-109401933651', '164003953017', '-51001461336', '48906201400'], ['-36054384919', '77240536911', '2401929743', '-251414614660', '140785484274'], ['-141497774333', '-42601274552', '131105327719', '-163334178349', '49115878322'], ['119219925489', '13606286384', '175215098642', '179353069577', '-171744748179'], ['83041195224', '121925297835', '223452163384', '6915010302', '198583052831'], ['-80382503015', '-104453974605', '58048352755', '76021246849', '120959210148']], 'QpRts-minpoly': [42, 1, 0, 0, 0, 1], 'QpRts-p': 47, 'QpRts-prec': 7, 'Size': 30, 'TransitiveDegree': 15}