Artin representation data - 4.5080.8t44.c

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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, 5, 127], 'Baselabel': '4.5080.8t44.c', 'CharacterField': 1, 'Conductor': 5080, 'Container': '8t44', 'Dets': ['1.5080.2t1.b.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, 22, 23, 4], '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], [1], [1], [1]], [[1], [0], [0], [1]], [[1], [-1], [-1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T44', 'Galt': 44, 'HardPrimes': [2, 5, 127, 1433], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [1, 1, 0, 0, -1, 0, 0, -1, 1], 'NumBadPrimes': 3, 'Proj_GAP': [192, 955], 'Proj_Polynomial': [1, -2, -8, 7, -6, 6, 0, -3, 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': '1.1016.2t1.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': '1.5080.2t1.b', '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': '1.5.2t1.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': '2.1016.3t2.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': '2.25400.6t3.b', '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': '3.1016.4t5.a', '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': '3.1032256.6t8.a', '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': '3.129032000.6t11.a', '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': '3.127000.6t11.a', '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': '4.5080.8t44.c', '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': '4.127000.8t44.c', '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': '4.5243860480.8t44.c', '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': '4.131096512000.8t44.c', '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': '6.129032000.8t41.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': '6.133194056192000.12t108.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': '6.131096512000.8t41.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': '6.131096512000.12t108.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': '8.16649257024000000.24t708.c', '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': '8.26638811238400.24t708.c', 'Character': [[8], [-8], [4], [-4], [0], [0], [0], [0], [0], [-1], [0], [0], [0], [0], [0], [0], [-1], [1], [1], [0]], 'CharacterField': 1}], 'ComplexConjugation': 6, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [6, 5, 4, 3, 2, 1, 8, 7]}, {'Size': '4', 'Order': 2, 'Representative': [1, 2, 4, 3, 5, 6, 7, 8]}, {'Size': '4', 'Order': 2, 'Representative': [1, 5, 4, 3, 2, 6, 8, 7]}, {'Size': '6', 'Order': 2, 'Representative': [6, 2, 4, 3, 5, 1, 7, 8]}, {'Size': '12', 'Order': 2, 'Representative': [3, 7, 1, 6, 8, 4, 2, 5]}, {'Size': '12', 'Order': 2, 'Representative': [2, 1, 3, 4, 6, 5, 7, 8]}, {'Size': '12', 'Order': 2, 'Representative': [7, 5, 4, 3, 2, 8, 1, 6]}, {'Size': '24', 'Order': 2, 'Representative': [2, 1, 4, 3, 6, 5, 7, 8]}, {'Size': '32', 'Order': 3, 'Representative': [3, 2, 7, 8, 5, 4, 1, 6]}, {'Size': '12', 'Order': 4, 'Representative': [3, 7, 6, 1, 8, 4, 5, 2]}, {'Size': '12', 'Order': 4, 'Representative': [2, 6, 3, 4, 1, 5, 7, 8]}, {'Size': '12', 'Order': 4, 'Representative': [6, 5, 8, 7, 2, 1, 3, 4]}, {'Size': '24', 'Order': 4, 'Representative': [3, 7, 6, 1, 8, 4, 2, 5]}, {'Size': '24', 'Order': 4, 'Representative': [2, 6, 4, 3, 1, 5, 7, 8]}, {'Size': '48', 'Order': 4, 'Representative': [2, 3, 7, 8, 4, 5, 1, 6]}, {'Size': '32', 'Order': 6, 'Representative': [1, 7, 5, 2, 8, 6, 3, 4]}, {'Size': '32', 'Order': 6, 'Representative': [3, 5, 7, 8, 2, 4, 1, 6]}, {'Size': '32', 'Order': 6, 'Representative': [3, 5, 8, 7, 2, 4, 1, 6]}, {'Size': '48', 'Order': 8, 'Representative': [7, 1, 5, 2, 6, 8, 3, 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': ['-9', '0', '-25', '0', '1', '0', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-2767', '33095', '-115809', '98664', '-21925', '-1935', '5191', '-3536', '1151', '-317', '66', '-7', '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': ['8', '4', '2', '2', '1'], 'ConjugacyClass': 4}, {'RootOf': ['24881688592', '-29590333600', '21562818020', '-2793093112', '5371040061', '-4603747390', '3544280761', '-872877046', '834115434', '-515636126', '315227715', '-102466246', '63240661', '-25429912', '12926462', '-3520280', '1670034', '-248712', '122262', '-9404', '5055', '-190', '111', '-2', '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': ['1', '-4', '-65', '34', '926', '1232', '75', '-38', '14', '-52', '7', '-2', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-8951', '-64751', '-147773', '-116994', '-40185', '-14195', '5407', '1760', '1533', '219', '76', '5', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-4156', '-3809', '3567', '240', '128', '5', '1'], 'ConjugacyClass': 13}, {'RootOf': ['-247916', '-357818', '173589', '-146580', '73081', '-17948', '8598', '-1672', '418', '-170', '5', '-4', '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': ['4', '-24', '32', '16', '-11', '-2', '1'], 'ConjugacyClass': 11}, {'RootOf': ['615424', '14357504', '113378048', '401362432', '683227456', '475705472', '-90645600', '-324366464', '-142930320', '20682208', '26048840', '3715376', '2315076', '-228848', '-894108', '251468', '-903', '-26316', '12964', '-5460', '1794', '-404', '64', '-8', '1'], 'ConjugacyClass': 16}], 'Algorithm': 'RES', 'CycleType': [4, 4]}, {'Data': 0, 'Classes': 20, 'Algorithm': 'CYC', 'CycleType': [8]}], 'Frobs': [14, 20, 17, 18, 19, 20, 18, 19, 17, 11, 16, 20, 19, 20, 12, 18, 15, 15, 9, 15, 14, 15, 12, 16, 9, 10, 20, 14, 6, 18, 3, 19, 20, 16, 15, 19, 20, 18, 18, 3, 10, 19, 16, 20, 20, 16, 11, 18, 18, 2, 20, 19, 16, 19, 12, 20, 16, 16, 17, 16, 20, 18, 20, 10, 13, 17, 15, 9, 13, 10, 14, 10, 9, 17, 16, 20, 15, 13, 7, 16, 10, 11, 16, 18, 10, 17, 10, 17, 10, 20, 20, 16, 14, 7, 16, 9, 16, 11, 4, 10, 9, 20, 13, 10, 16, 17, 3, 20, 19, 8, 20, 18, 12, 7, 11, 16, 17, 18, 20, 7, 7, 4, 20, 20, 16, 10, 15, 15, 14, 12, 11, 18, 6, 20, 8, 16, 9, 18, 20, 19, 19, 19, 12, 20, 19, 19, 17, 20, 16, 4, 9, 16, 17, 18, 17, 8, 16, 16, 20, 16, 20, 17, 14, 6, 14, 9, 6, 14], 'G-Gens': [[6, 2, 3, 4, 5, 1, 7, 8], [2, 1, 3, 4, 6, 5, 7, 8], [2, 3, 7, 8, 4, 5, 1, 6]], 'G-Name': 'C2wrS4', 'Polynomial': [1, 1, 0, 0, -1, 0, 0, -1, 1], 'QpRts': [['55197151226350655151777976903160030147', '-8346606058448857383391559755864059179'], ['72318322944410979262299917583066264073', '0'], ['25353689159820257191314613190268428670', '90863357344437094501115437168929712337'], ['-86836937093691549838607572886522741377', '8346606058448857383391559755864059179'], ['58781421658192486390332518212636723208', '0'], ['89171183147058544869508463093390216381', '-90863357344437094501115437168929712337'], ['-68684284733707418359293331417494036367', '43620592723555673283877055728531505517'], ['77322877025672785380685353457867948533', '-43620592723555673283877055728531505517']], 'QpRts-minpoly': [2, 63, 1], 'QpRts-p': 67, 'QpRts-prec': 21, 'Size': 384, 'TransitiveDegree': 8}