Artin representation data - 4.6383.8t44.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': [13, 491], 'Baselabel': '4.6383.8t44.a', 'CharacterField': 1, 'Conductor': 6383, 'Container': '8t44', 'Dets': ['1.6383.2t1.a.a'], 'Dim': 4, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[4], [-4], [2], [-2], [0], [0], [2], [-2], [0], [1], [0], [2], [-2], [0], [0], [0], [1], [-1], [-1], [0]], 'GalOrbIndex': 1, 'HardFactors': [21, 5, 22], 'LocalFactors': [[[1], [-4], [6], [-4], [1]], [[1], [4], [6], [4], [1]], [[1], [-2], [0], [2], [-1]], [[1], [2], [0], [-2], [-1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [-2], [0], [2], [-1]], [[1], [2], [0], [-2], [-1]], [[1], [0], [-2], [0], [1]], [[1], [-1], [0], [-1], [1]], [[1], [0], [2], [0], [1]], [[1], [-2], [2], [-2], [1]], [[1], [2], [2], [2], [1]], [[1], [0], [0], [0], [-1]], [[1], [0], [0], [0], [-1]], [[1], [0], [0], [0], [-1]], [[1], [-1], [0], [1], [-1]], [[1], [1], [0], [-1], [-1]], [[1], [1], [0], [1], [1]], [[1], [0], [0], [0], [1]], [[1], [0], [0], [1]], [[1], [1], [-1], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T44', 'Galt': 44, 'HardPrimes': [13, 47, 491], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [1, -1, 1, -2, 3, -2, 1, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [192, 955], 'Proj_Polynomial': [9, 28, 16, -10, 3, 8, -3, -1, 1], 'Proj_nTj': [8, 41]}
• 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], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.491.2t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [1], [1], [-1], [-1], [1], [-1], [-1], [1], [1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.6383.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [1], [-1], [-1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.13.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [1], [1], [1], [-1], [1], [1], [-1], [-1], [-1], [1], [1], [-1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.491.3t2.a', 'Character': [[2], [2], [2], [2], [2], [2], [0], [0], [0], [-1], [2], [0], [0], [2], [0], [0], [-1], [-1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.82979.6t3.a', 'Character': [[2], [2], [-2], [-2], [2], [2], [0], [0], [0], [-1], [2], [0], [0], [-2], [0], [0], [1], [1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.491.4t5.b', 'Character': [[3], [3], [3], [3], [3], [-1], [1], [1], [1], [0], [-1], [1], [1], [-1], [1], [-1], [0], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.241081.6t8.d', 'Character': [[3], [3], [3], [3], [3], [-1], [-1], [-1], [-1], [0], [-1], [-1], [-1], [-1], [-1], [1], [0], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.529654957.6t11.b', 'Character': [[3], [3], [-3], [-3], [3], [-1], [-1], [-1], [1], [0], [-1], [1], [1], [1], [-1], [1], [0], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.1078727.6t11.b', 'Character': [[3], [3], [-3], [-3], [3], [-1], [1], [1], [-1], [0], [-1], [-1], [-1], [1], [1], [-1], [0], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.6383.8t44.a', 'Character': [[4], [-4], [2], [-2], [0], [0], [2], [-2], [0], [1], [0], [2], [-2], [0], [0], [0], [1], [-1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.1078727.8t44.a', 'Character': [[4], [-4], [-2], [2], [0], [0], [2], [-2], [0], [1], [0], [-2], [2], [0], [0], [0], [-1], [1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.1538820023.8t44.a', 'Character': [[4], [-4], [2], [-2], [0], [0], [-2], [2], [0], [1], [0], [-2], [2], [0], [0], [0], [1], [-1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.260060583887.8t44.a', 'Character': [[4], [-4], [-2], [2], [0], [0], [-2], [2], [0], [1], [0], [2], [-2], [0], [0], [0], [-1], [1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.529654957.8t41.a', 'Character': [[6], [6], [0], [0], [-2], [2], [2], [2], [0], [0], [-2], [0], [0], [0], [-2], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.127689746688517.12t108.a', 'Character': [[6], [6], [0], [0], [-2], [2], [-2], [-2], [0], [0], [-2], [0], [0], [0], [2], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.260060583887.8t41.a', 'Character': [[6], [6], [0], [0], [-2], [-2], [0], [0], [2], [0], [2], [-2], [-2], [0], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.260060583887.12t108.a', 'Character': [[6], [6], [0], [0], [-2], [-2], [0], [0], [-2], [0], [2], [2], [2], [0], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.280534373474671849.24t708.a', 'Character': [[8], [-8], [-4], [4], [0], [0], [0], [0], [0], [-1], [0], [0], [0], [0], [0], [0], [1], [-1], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.9822288206809.24t708.a', 'Character': [[8], [-8], [4], [-4], [0], [0], [0], [0], [0], [-1], [0], [0], [0], [0], [0], [0], [-1], [1], [1], [0]], 'CharacterField': 1}], 'ComplexConjugation': 8, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [8, 7, 6, 5, 4, 3, 2, 1]}, {'Size': '4', 'Order': 2, 'Representative': [8, 2, 3, 4, 5, 6, 7, 1]}, {'Size': '4', 'Order': 2, 'Representative': [8, 7, 3, 5, 4, 6, 2, 1]}, {'Size': '6', 'Order': 2, 'Representative': [8, 2, 6, 4, 5, 3, 7, 1]}, {'Size': '12', 'Order': 2, 'Representative': [3, 4, 1, 2, 7, 8, 5, 6]}, {'Size': '12', 'Order': 2, 'Representative': [1, 2, 4, 3, 6, 5, 7, 8]}, {'Size': '12', 'Order': 2, 'Representative': [8, 3, 2, 5, 4, 7, 6, 1]}, {'Size': '24', 'Order': 2, 'Representative': [8, 2, 4, 3, 6, 5, 7, 1]}, {'Size': '32', 'Order': 3, 'Representative': [2, 3, 1, 4, 5, 8, 6, 7]}, {'Size': '12', 'Order': 4, 'Representative': [6, 5, 1, 2, 7, 8, 4, 3]}, {'Size': '12', 'Order': 4, 'Representative': [1, 2, 4, 6, 3, 5, 7, 8]}, {'Size': '12', 'Order': 4, 'Representative': [7, 1, 6, 5, 4, 3, 8, 2]}, {'Size': '24', 'Order': 4, 'Representative': [6, 4, 1, 2, 7, 8, 5, 3]}, {'Size': '24', 'Order': 4, 'Representative': [8, 2, 4, 6, 3, 5, 7, 1]}, {'Size': '48', 'Order': 4, 'Representative': [2, 3, 4, 1, 8, 5, 6, 7]}, {'Size': '32', 'Order': 6, 'Representative': [5, 1, 3, 2, 7, 6, 8, 4]}, {'Size': '32', 'Order': 6, 'Representative': [2, 3, 1, 5, 4, 8, 6, 7]}, {'Size': '32', 'Order': 6, 'Representative': [7, 3, 1, 5, 4, 8, 6, 2]}, {'Size': '48', 'Order': 8, 'Representative': [5, 1, 2, 3, 6, 7, 8, 4]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-709', '1170', '-584', '15', '61', '-15', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-26055', '-60903', '-11037', '64405', '-4378', '-19339', '2132', '4351', '-1522', '-39', '101', '-18', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 12, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['1', '42', '2', '-7', '1'], 'ConjugacyClass': 4}, {'RootOf': ['133459056', '-9881208', '244686384', '2456854244', '1547271589', '-2660448102', '-4613419936', '6237433181', '-1506373415', '-352481386', '-326665719', '259165425', '130337291', '-123767429', '11244287', '13309719', '-3641075', '-375889', '259657', '-15584', '-7115', '1087', '42', '-18', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 15, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 4]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [1, 1, 3, 3]}, {'Data': 0, 'Classes': 17, 'Algorithm': 'CYC', 'CycleType': [1, 1, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-1', '1'], 'ConjugacyClass': 2}, {'RootOf': ['8011', '63799', '162320', '203639', '140022', '47617', '-193', '-6941', '-2667', '-366', '22', '12', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-27', '171', '-198', '-145', '231', '133', '-194', '-158', '-160', '-112', '-33', '0', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-1325', '-475', '-183', '-141', '-38', '0', '1'], 'ConjugacyClass': 13}, {'RootOf': ['29124001', '82430848', '93752291', '56962644', '19771519', '3530036', '46063', '-117484', '-23120', '-1274', '144', '24', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [2, 2, 4]}, {'Data': 0, 'Classes': 18, 'Algorithm': 'CYC', 'CycleType': [2, 3, 3]}, {'Data': 0, 'Classes': 19, 'Algorithm': 'CYC', 'CycleType': [2, 6]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['2401', '392', '-572', '-146', '28', '12', '1'], 'ConjugacyClass': 11}, {'RootOf': ['397293586717', '811954568476', '3412055327140', '5640527136924', '1419842233850', '-4425399549164', '-4216288732309', '-520120142336', '1226047862558', '779586219476', '126487553812', '-56257298978', '-30522062775', '-3548268756', '1263888486', '487074584', '39210324', '-11858214', '-3369787', '-240734', '35486', '9614', '960', '48', '1'], 'ConjugacyClass': 16}], 'Algorithm': 'RES', 'CycleType': [4, 4]}, {'Data': 0, 'Classes': 20, 'Algorithm': 'CYC', 'CycleType': [8]}], 'Frobs': [20, 19, 14, 20, 17, 17, 19, 20, 16, 16, 17, 18, 18, 19, 9, 15, 20, 6, 20, 17, 20, 11, 18, 12, 17, 10, 16, 10, 13, 15, 11, 10, 9, 10, 13, 13, 16, 3, 12, 15, 11, 19, 16, 9, 17, 10, 16, 14, 14, 18, 11, 4, 18, 16, 19, 6, 6, 9, 19, 20, 16, 17, 9, 16, 16, 20, 18, 16, 7, 18, 9, 9, 15, 15, 17, 12, 10, 20, 18, 14, 10, 20, 20, 15, 7, 15, 20, 14, 17, 18, 19, 20, 13, 5, 20, 6, 20, 8, 15, 20, 10, 9, 16, 15, 10, 20, 20, 20, 19, 16, 15, 20, 14, 20, 20, 16, 18, 19, 15, 19, 13, 10, 16, 18, 13, 19, 3, 16, 7, 13, 9, 20, 19, 16, 20, 12, 14, 9, 15, 19, 17, 9, 19, 13, 16, 20, 20, 16, 7, 17, 17, 15, 16, 5, 8, 15, 10, 14, 7, 9, 17, 11, 20, 16, 9, 18, 19, 10], 'G-Gens': [[2, 3, 4, 1, 8, 5, 6, 7], [1, 2, 4, 3, 6, 5, 7, 8], [1, 2, 6, 4, 5, 3, 7, 8]], 'G-Name': 'C2wrS4', 'Polynomial': [1, -1, 1, -2, 3, -2, 1, -1, 1], 'QpRts': [['83023222424362334268173863547973766126', '-125446783887608082356632384173561137947'], ['101516324383190592040371641982896345077', '0'], ['-16748416274585774575469064273817006719', '125446783887608082356632384173561137947'], ['-36185812267128712987852949541032027822', '36114640508593076289596558572095856578'], ['62118438938576398447931979404267020306', '-36114640508593076289596558572095856578'], ['18904463573052825982132563368124207389', '-104259338330289654617128428406251349685'], ['-40057532618439904269914692850611564179', '0'], ['114673157523037831839231669143801358846', '104259338330289654617128428406251349685']], 'QpRts-minpoly': [5, 45, 1], 'QpRts-p': 47, 'QpRts-prec': 23, 'Size': 384, 'TransitiveDegree': 8}