Artin representation data - 2.3240.12t18.b

Formats: - HTML - YAML - JSON - 2024-12-14T22:10:02.158923

• 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, 3, 5], 'Baselabel': '2.3240.12t18.b', 'CharacterField': 3, 'Conductor': 3240, 'Container': '12t18', 'Dets': ['1.360.6t1.b.b', '1.360.6t1.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, 20, 21, 16, 7, 7, 3, 3, 1, 8], '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], [0, -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, 20, 21, 16, 7, 7, 3, 3, 1, 8], '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], [0, 1]], [[1]], [[1], [1, 1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T18', 'Galt': 18, 'HardPrimes': [2, 3, 5, 7, 11, 29, 53, 107, 179, 419], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [151, 510, 693, 210, -33, 90, 62, -30, -9, 0, -6, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-6, 3, 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], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.24.2t1.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': '1.120.2t1.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': '1.5.2t1.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': '1.45.6t1.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': '1.72.6t1.c', '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': '1.72.6t1.c', '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': '1.360.6t1.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': '1.9.3t1.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': '1.45.6t1.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': '1.9.3t1.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': '1.360.6t1.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': '2.1080.3t2.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': '2.1080.6t3.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': '2.3240.12t18.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': '2.3240.6t5.c', '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': '2.3240.12t18.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': '2.3240.6t5.c', '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': 3, '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, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6]}, {'Size': '3', 'Order': 2, 'Representative': [4, 9, 8, 1, 12, 11, 10, 3, 2, 7, 6, 5]}, {'Size': '3', 'Order': 2, 'Representative': [10, 3, 2, 7, 6, 5, 4, 9, 8, 1, 12, 11]}, {'Size': '1', 'Order': 3, 'Representative': [6, 7, 4, 11, 9, 8, 12, 1, 10, 5, 3, 2]}, {'Size': '1', 'Order': 3, 'Representative': [8, 12, 11, 3, 10, 1, 2, 6, 5, 9, 4, 7]}, {'Size': '2', 'Order': 3, 'Representative': [1, 2, 4, 11, 9, 6, 7, 8, 10, 5, 3, 12]}, {'Size': '2', 'Order': 3, 'Representative': [1, 2, 11, 3, 10, 6, 7, 8, 5, 9, 4, 12]}, {'Size': '2', 'Order': 3, 'Representative': [8, 12, 4, 11, 9, 1, 2, 6, 10, 5, 3, 7]}, {'Size': '1', 'Order': 6, 'Representative': [2, 6, 5, 9, 4, 7, 8, 12, 11, 3, 10, 1]}, {'Size': '1', 'Order': 6, 'Representative': [12, 1, 10, 5, 3, 2, 6, 7, 4, 11, 9, 8]}, {'Size': '2', 'Order': 6, 'Representative': [2, 6, 9, 10, 11, 7, 8, 12, 3, 4, 5, 1]}, {'Size': '2', 'Order': 6, 'Representative': [12, 1, 9, 10, 11, 2, 6, 7, 3, 4, 5, 8]}, {'Size': '2', 'Order': 6, 'Representative': [12, 1, 5, 9, 4, 2, 6, 7, 11, 3, 10, 8]}, {'Size': '3', 'Order': 6, 'Representative': [11, 10, 1, 6, 2, 3, 5, 4, 7, 12, 8, 9]}, {'Size': '3', 'Order': 6, 'Representative': [3, 5, 6, 8, 7, 4, 9, 11, 12, 2, 1, 10]}, {'Size': '3', 'Order': 6, 'Representative': [5, 4, 7, 12, 8, 9, 11, 10, 1, 6, 2, 3]}, {'Size': '3', 'Order': 6, 'Representative': [9, 11, 12, 2, 1, 10, 3, 5, 6, 8, 7, 4]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['1080', '0', '1'], 'ConjugacyClass': 7}, {'RootOf': ['270', '0', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-6', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-864', '-162', '0', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-1350', '405', '0', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['9', '6', '1'], 'ConjugacyClass': 12}, {'RootOf': ['36', '-12', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [2, 5, -2, -7, 1]}, 'Classes': [{'RootOf': ['-408', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-138', '1'], 'ConjugacyClass': 6}, {'RootOf': ['75609', '-546', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['12', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-6', '1'], 'ConjugacyClass': 11}, {'RootOf': ['9', '6', '1'], 'ConjugacyClass': 14}, {'RootOf': ['-864', '-162', '0', '1'], 'ConjugacyClass': 15}, {'RootOf': ['6912', '-648', '0', '1'], 'ConjugacyClass': 16}, {'RootOf': ['-1350', '405', '0', '1'], 'ConjugacyClass': 17}, {'RootOf': ['10800', '1620', '0', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [6, 6]}], 'Frobs': [10, 14, 17, 18, 7, 12, 14, 3, 12, 7, 8, 2, 15, 13, 13, 4, 5, 16, 11, 3, 4, 7, 18, 3, 18, 7, 17, 4, 3, 12, 4, 8, 10, 15, 8, 7, 12, 14, 11, 18, 1, 3, 16, 17, 4, 9, 15, 18, 18, 15, 2, 15, 7, 9, 12, 10, 9, 1, 10, 16, 11, 17, 14, 15, 18, 18, 16, 17, 17, 16, 13, 3, 18, 12, 3, 12, 7, 14, 15, 8, 8, 16, 3, 4, 6, 18, 3, 18, 6, 17, 4, 16, 4, 5, 15, 14, 8, 3, 14, 3, 13, 4, 17, 16, 15, 4, 18, 14, 15, 7, 17, 14, 12, 16, 1, 16, 12, 2, 17, 6, 15, 18, 18, 4, 16, 9, 16, 3, 18, 11, 3, 12, 8, 14, 15, 8, 4, 12, 17, 3, 3, 6, 17, 4, 3, 16, 13, 10, 15, 14, 12, 3, 2, 12, 13, 16, 9, 16, 4, 8, 18, 14, 17, 9, 12, 13, 9, 13], 'G-Gens': [[2, 6, 5, 9, 4, 7, 8, 12, 11, 3, 10, 1], [1, 2, 4, 11, 9, 6, 7, 8, 10, 5, 3, 12], [11, 10, 1, 6, 2, 3, 5, 4, 7, 12, 8, 9], [7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6]], 'G-Name': 'C6*S3', 'Polynomial': [151, 510, 693, 210, -33, 90, 62, -30, -9, 0, -6, 0, 1], 'QpRts': [['2484233091', '-1753991720', '-224202132', '1851909786', '-130505680', '1796943085'], ['3159510504', '-590021474', '-1552507405', '-930667334', '-665863696', '308012418'], ['1728352592', '2247188862', '-1472499007', '3023486732', '2077524459', '372359228'], ['3433098888', '-249149284', '-3477151293', '-3456339534', '619086693', '-3205692843'], ['-2982811191', '1895664801', '3114683644', '-1741632969', '-788309935', '588122072'], ['2823765218', '1202349112', '-254674622', '-1233833539', '1343135347', '-272784599'], ['-2089184878', '1412527204', '-3363446496', '-1201816901', '-1596884537', '-1182572834'], ['1667759132', '551642608', '478876754', '-618076247', '-1212629667', '-1524158486'], ['1830354140', '-3370495552', '3169631075', '2641607592', '-1681655524', '2079286999'], ['1152457051', '1474830751', '691442722', '-899974623', '2469965459', '-2667409071'], ['1814305961', '-1998039578', '-2026107141', '432852802', '-2696611152', '2833333615'], ['-1070325626', '-822505730', '-2059803540', '2132484235', '2262748233', '874560416']], 'QpRts-minpoly': [3, 3, 10, 0, 2, 0, 1], 'QpRts-p': 17, 'QpRts-prec': 8, 'Size': 36, 'TransitiveDegree': 12}