Artin representation data - 2.3040.12t18.b

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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, 19], 'Baselabel': '2.3040.12t18.b', 'CharacterField': 3, 'Conductor': 3040, 'Container': '12t18', 'Dets': ['1.760.6t1.b.b', '1.760.6t1.b.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 12, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1], [2, 2], [0, -2], [0, 1], [-1, -1], [1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [19, 16, 20, 14, 16, 21, 3, 11, 10, 13, 11, 15, 15], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, -2], [-1, -1]], [[1], [2, 2], [0, 1]], [[1], [-1, -1], [0, 1]], [[1], [0, 1], [-1, -1]], [[1], [1], [1]], [[1], [-2, -2], [0, 1]], [[1], [0, 2], [-1, -1]], [[1], [0, -1], [-1, -1]], [[1], [1, 1], [0, 1]], [[1], [-1], [1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1]], [[1], [1, 1]], [[1], [-1, -1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [-2, -2], [0, 2], [0, -1], [1, 1], [-1], [0, -2], [2, 2], [-1, -1], [0, 1], [1], [0], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [19, 16, 20, 14, 16, 21, 3, 11, 10, 13, 11, 15, 15], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [2, 2], [0, 1]], [[1], [0, -2], [-1, -1]], [[1], [0, 1], [-1, -1]], [[1], [-1, -1], [0, 1]], [[1], [1], [1]], [[1], [0, 2], [-1, -1]], [[1], [-2, -2], [0, 1]], [[1], [1, 1], [0, 1]], [[1], [0, -1], [-1, -1]], [[1], [-1], [1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1]], [[1], [0, -1]], [[1], [0, 1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T18', 'Galt': 18, 'HardPrimes': [2, 3, 5, 11, 17, 19, 31, 47, 59, 131, 251, 3467, 14107], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, -8, 0, 46, 0, 42, 0, 17, 0, -10, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [26, -6, -1, 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], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.40.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.40.2t1.b', 'Character': [[1], [1], [-1], [-1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.4.2t1.a', 'Character': [[1], [-1], [1], [-1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.76.6t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [0, -1], [1, 1], [1, 1], [0, -1], [-1, 0], [-1, -1], [0, 1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.760.6t1.a', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [0, -1], [1, 1], [1, 1], [0, -1], [-1, 0], [1, 1], [0, -1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.760.6t1.a', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [1, 1], [0, -1], [0, -1], [1, 1], [-1, 0], [0, -1], [1, 1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.760.6t1.b', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.19.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.76.6t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [1, 1], [0, -1], [0, -1], [1, 1], [-1, 0], [0, 1], [-1, -1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.19.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.760.6t1.b', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.14440.3t2.a', 'Character': [[2], [2], [0], [0], [2], [2], [-1], [-1], [-1], [2], [2], [-1], [-1], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.57760.6t3.c', 'Character': [[2], [-2], [0], [0], [2], [2], [-1], [-1], [-1], [-2], [-2], [1], [1], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.3040.12t18.b', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1, 0], [2, 2], [0, -2], [0, 1], [-1, -1], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.760.6t5.a', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1, 0], [-2, -2], [0, 2], [0, -1], [1, 1], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.3040.12t18.b', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [0, -1], [1, 1], [-1, 0], [0, -2], [2, 2], [-1, -1], [0, 1], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.760.6t5.a', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [0, -1], [1, 1], [-1, 0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}], 'ComplexConjugation': 4, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]}, {'Size': '1', 'Order': 2, 'Representative': [7, 8, 10, 9, 11, 12, 1, 2, 4, 3, 5, 6]}, {'Size': '3', 'Order': 2, 'Representative': [3, 6, 1, 11, 9, 2, 10, 12, 5, 7, 4, 8]}, {'Size': '3', 'Order': 2, 'Representative': [10, 12, 7, 5, 4, 8, 3, 6, 11, 1, 9, 2]}, {'Size': '1', 'Order': 3, 'Representative': [9, 10, 5, 6, 8, 7, 4, 3, 12, 11, 2, 1]}, {'Size': '1', 'Order': 3, 'Representative': [12, 11, 8, 7, 3, 4, 6, 5, 1, 2, 10, 9]}, {'Size': '2', 'Order': 3, 'Representative': [1, 10, 5, 4, 8, 6, 7, 3, 9, 11, 2, 12]}, {'Size': '2', 'Order': 3, 'Representative': [1, 11, 8, 4, 3, 6, 7, 5, 9, 2, 10, 12]}, {'Size': '2', 'Order': 3, 'Representative': [12, 10, 5, 7, 8, 4, 6, 3, 1, 11, 2, 9]}, {'Size': '1', 'Order': 6, 'Representative': [6, 5, 2, 1, 10, 9, 12, 11, 7, 8, 3, 4]}, {'Size': '1', 'Order': 6, 'Representative': [4, 3, 11, 12, 2, 1, 9, 10, 6, 5, 8, 7]}, {'Size': '2', 'Order': 6, 'Representative': [6, 8, 10, 1, 11, 9, 12, 2, 7, 3, 5, 4]}, {'Size': '2', 'Order': 6, 'Representative': [4, 8, 10, 12, 11, 1, 9, 2, 6, 3, 5, 7]}, {'Size': '2', 'Order': 6, 'Representative': [4, 5, 2, 12, 10, 1, 9, 11, 6, 8, 3, 7]}, {'Size': '3', 'Order': 6, 'Representative': [5, 7, 9, 2, 12, 10, 11, 1, 8, 4, 6, 3]}, {'Size': '3', 'Order': 6, 'Representative': [8, 4, 12, 10, 1, 11, 2, 9, 3, 6, 7, 5]}, {'Size': '3', 'Order': 6, 'Representative': [11, 1, 4, 8, 6, 3, 5, 7, 2, 9, 12, 10]}, {'Size': '3', 'Order': 6, 'Representative': [2, 9, 6, 3, 7, 5, 8, 4, 10, 12, 1, 11]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['71084', '-476', '1'], 'ConjugacyClass': 7}, {'RootOf': ['59176', '-448', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['-60', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-86400', '4896', '-132', '1'], 'ConjugacyClass': 3}, {'RootOf': ['86400', '4896', '132', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['59176', '448', '1'], 'ConjugacyClass': 12}, {'RootOf': ['71084', '476', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['-124', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-96', '1'], 'ConjugacyClass': 6}, {'RootOf': ['12740', '-220', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['96', '1'], 'ConjugacyClass': 10}, {'RootOf': ['124', '1'], 'ConjugacyClass': 11}, {'RootOf': ['12740', '220', '1'], 'ConjugacyClass': 14}, {'RootOf': ['6581536', '122088', '628', '1'], 'ConjugacyClass': 15}, {'RootOf': ['6700096', '124140', '628', '1'], 'ConjugacyClass': 16}, {'RootOf': ['-6581536', '122088', '-628', '1'], 'ConjugacyClass': 17}, {'RootOf': ['-6700096', '124140', '-628', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [6, 6]}], 'Frobs': [16, 18, 6, 14, 14, 5, 16, 10, 12, 15, 4, 9, 7, 18, 11, 8, 10, 15, 17, 18, 16, 18, 4, 8, 16, 15, 14, 4, 16, 3, 12, 13, 15, 11, 16, 4, 7, 4, 12, 7, 14, 15, 4, 16, 9, 17, 13, 13, 4, 3, 16, 4, 5, 11, 15, 13, 16, 18, 1, 8, 18, 9, 18, 4, 15, 8, 14, 16, 18, 3, 3, 18, 11, 9, 2, 10, 15, 7, 6, 8, 14, 16, 17, 15, 18, 17, 9, 3, 16, 14, 4, 17, 14, 13, 13, 12, 15, 1, 17, 15, 17, 8, 4, 9, 2, 3, 18, 15, 17, 9, 14, 7, 15, 14, 17, 6, 18, 14, 9, 12, 15, 3, 9, 4, 14, 16, 15, 18, 10, 9, 13, 13, 17, 7, 9, 5, 8, 4, 9, 1, 12, 15, 12, 17, 3, 18, 6, 16, 12, 14, 7, 9, 17, 11, 18, 4, 4, 7, 15, 15, 18, 16, 10, 10, 3, 13, 18, 8], 'G-Gens': [[6, 5, 2, 1, 10, 9, 12, 11, 7, 8, 3, 4], [5, 7, 9, 2, 12, 10, 11, 1, 8, 4, 6, 3], [7, 8, 10, 9, 11, 12, 1, 2, 4, 3, 5, 6], [1, 10, 5, 4, 8, 6, 7, 3, 9, 11, 2, 12]], 'G-Name': 'C6*S3', 'Polynomial': [1, 0, -8, 0, 46, 0, 42, 0, 17, 0, -10, 0, 1], 'QpRts': [['8331086978039', '-1244097182282', '-2943149824350', '13517453376046', '-15572110607016', '8381858855055'], ['-9876113237909', '8402048634248', '-12898120881428', '14810378360364', '-10384326115428', '-6521626008970'], ['-4806876098449', '1660171800153', '8572854864510', '-11144083928368', '-1318316286876', '-16643596985815'], ['15985828592447', '-8812706186899', '15665258211144', '12482963834524', '3896398209040', '-9126571634781'], ['-15390604197169', '-15493375777242', '15058442848687', '-12993122338788', '-7947922717005', '2960547465736'], ['-6780234437209', '-14666643606720', '-16350885748502', '-3641198778365', '15921474603124', '10347006978727'], ['-8331086978039', '1244097182282', '2943149824350', '-13517453376046', '15572110607016', '-8381858855055'], ['9876113237909', '-8402048634248', '12898120881428', '-14810378360364', '10384326115428', '6521626008970'], ['-15985828592447', '8812706186899', '-15665258211144', '-12482963834524', '-3896398209040', '9126571634781'], ['4806876098449', '-1660171800153', '-8572854864510', '11144083928368', '1318316286876', '16643596985815'], ['15390604197169', '15493375777242', '-15058442848687', '12993122338788', '7947922717005', '-2960547465736'], ['6780234437209', '14666643606720', '16350885748502', '3641198778365', '-15921474603124', '-10347006978727']], 'QpRts-minpoly': [3, 3, 10, 0, 2, 0, 1], 'QpRts-p': 17, 'QpRts-prec': 11, 'Size': 36, 'TransitiveDegree': 12}