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artin_reps • Show schema
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{'BadPrimes': [5, 691], 'Baselabel': '2.3455.13t2.a', 'CharacterField': 13, 'Conductor': 3455, 'Container': '13t2', 'Dets': ['1.3455.2t1.a.a', '1.3455.2t1.a.a', '1.3455.2t1.a.a', '1.3455.2t1.a.a', '1.3455.2t1.a.a', '1.3455.2t1.a.a'], 'Dim': 2, 'GalConjSigns': [1, 1, 1, 1, 1, 1], 'Galn': 13, 'GaloisConjugates': [{'Sign': 1, 'Character': [[2], [0], [0, 0, 0, 0, 0, 0, 1, 1], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 1, 'HardFactors': [8, 9, 2, 2, 2, 2, 1, 9], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1]], [[1], [0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [0], [0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [8, 9, 2, 2, 2, 2, 1, 9], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1]], [[1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 1], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [8, 9, 2, 2, 2, 2, 1, 9], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1]], [[1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 1]], 'GalOrbIndex': 4, 'HardFactors': [8, 9, 2, 2, 2, 2, 1, 9], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]], 'GalOrbIndex': 5, 'HardFactors': [8, 9, 2, 2, 2, 2, 1, 9], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [0], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1]], 'GalOrbIndex': 6, 'HardFactors': [8, 9, 2, 2, 2, 2, 1, 9], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [-1]]]}], 'GaloisConjugatesSigns': [1, 1, 1, 1, 1, 1], 'GaloisLabel': '13T2', 'Galt': 2, 'HardPrimes': [3, 5, 7, 11, 31, 37, 53, 691], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [25, -80, 275, 1271, 1948, 1595, 532, -110, -157, -70, 7, 10, -2, 1], 'NumBadPrimes': 2, 'Proj_GAP': [26, 1], 'Proj_Polynomial': [25, -80, 275, 1271, 1948, 1595, 532, -110, -157, -70, 7, 10, -2, 1], 'Proj_nTj': [13, 2]}
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artin_field_data • Show schema
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{'ArtinReps': [{'GalConj': 1, 'Baselabel': '1.1.1t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.3455.2t1.a', 'Character': [[1], [-1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 2, 'Baselabel': '2.3455.13t2.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0]], 'CharacterField': 13}, {'GalConj': 6, 'Baselabel': '2.3455.13t2.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0]], 'CharacterField': 13}, {'GalConj': 4, 'Baselabel': '2.3455.13t2.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0]], 'CharacterField': 13}, {'GalConj': 1, 'Baselabel': '2.3455.13t2.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0]], 'CharacterField': 13}, {'GalConj': 3, 'Baselabel': '2.3455.13t2.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1]], 'CharacterField': 13}, {'GalConj': 5, 'Baselabel': '2.3455.13t2.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]], 'CharacterField': 13}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]}, {'Size': '13', 'Order': 2, 'Representative': [12, 9, 3, 5, 4, 10, 13, 11, 2, 6, 8, 1, 7]}, {'Size': '2', 'Order': 13, 'Representative': [9, 12, 7, 8, 13, 1, 4, 6, 2, 11, 5, 10, 3]}, {'Size': '2', 'Order': 13, 'Representative': [2, 10, 4, 6, 3, 9, 8, 1, 12, 5, 13, 11, 7]}, {'Size': '2', 'Order': 13, 'Representative': [12, 11, 8, 1, 7, 2, 6, 9, 10, 13, 3, 5, 4]}, {'Size': '2', 'Order': 13, 'Representative': [10, 5, 6, 9, 4, 12, 1, 2, 11, 3, 7, 13, 8]}, {'Size': '2', 'Order': 13, 'Representative': [11, 13, 1, 2, 8, 10, 9, 12, 5, 7, 4, 3, 6]}, {'Size': '2', 'Order': 13, 'Representative': [5, 3, 9, 12, 6, 11, 2, 10, 13, 4, 8, 7, 1]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1, 12], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-49', '1'], 'ConjugacyClass': 3}, {'RootOf': ['22', '1'], 'ConjugacyClass': 4}, {'RootOf': ['106', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-2', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-84', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-34', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [13]}], 'Frobs': [3, 8, 1, 2, 2, 4, 6, 2, 5, 8, 2, 2, 2, 2, 2, 1, 5, 5, 4, 6, 7, 3, 6, 7, 2, 6, 2, 7, 2, 2, 2, 2, 3, 8, 7, 7, 7, 1, 2, 2, 8, 4, 2, 2, 2, 2, 2, 2, 3, 7, 2, 2, 5, 2, 8, 2, 2, 4, 5, 2, 2, 7, 6, 4, 5, 2, 8, 8, 2, 2, 2, 5, 6, 2, 7, 2, 4, 8, 3, 2, 4, 2, 7, 3, 2, 4, 6, 5, 2, 7, 2, 4, 3, 6, 6, 4, 2, 2, 3, 2, 7, 8, 2, 8, 2, 2, 1, 2, 3, 3, 2, 2, 2, 3, 5, 5, 2, 2, 6, 7, 2, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 7, 2, 3, 2, 2, 2, 2, 2, 2, 3, 5, 2, 2, 2, 3, 3, 2, 7, 2, 6, 7, 3, 2, 2, 2, 5, 5, 4, 2, 2, 2, 2, 2, 5, 5, 2, 2], 'G-Gens': [[10, 2, 7, 13, 8, 11, 3, 5, 12, 1, 6, 9, 4], [12, 9, 3, 5, 4, 10, 13, 11, 2, 6, 8, 1, 7]], 'G-Name': 'D26', 'Polynomial': [25, -80, 275, 1271, 1948, 1595, 532, -110, -157, -70, 7, 10, -2, 1], 'QpRts': [['-128336', '-530085', '583561', '211165', '-559173', '677766', '-558588', '176711', '427242', '-78242', '93919', '32187', '385136'], ['-559575', '-596884', '-672015', '189700', '-437091', '630060', '634127', '-566777', '-528613', '129674', '-465566', '-239181', '440760'], ['-462561', '363640', '347104', '455048', '-36364', '155459', '-164275', '-325972', '596983', '597479', '152602', '216631', '400438'], ['339777', '636819', '623813', '-85062', '-119161', '-439305', '-77588', '-538404', '266169', '511531', '-422954', '134710', '-346201'], ['542542', '638257', '267438', '123877', '-7517', '-656293', '-45700', '95897', '-688236', '-263709', '-301844', '508103', '575574'], ['-695279', '584520', '-509541', '-150621', '-292936', '218092', '-478692', '-602868', '388109', '-466839', '591934', '-279500', '83883'], ['-486331', '161260', '-612176', '-563231', '-707343', '20236', '-150390', '344146', '-557147', '169574', '-386766', '159685', '-626731'], ['-491861', '-111702', '347635', '140569', '319427', '-446163', '655004', '666766', '522073', '442756', '94627', '-420902', '240560'], ['-404277', '635676', '-385219', '108380', '284501', '-502983', '136455', '80803', '518603', '433963', '657233', '-561007', '120676'], ['-576379', '701636', '260431', '61082', '130114', '-287467', '-624945', '632786', '505238', '81723', '-487520', '618651', '407994'], ['-116585', '175382', '-162783', '190992', '502452', '-252696', '-166686', '394590', '90445', '-481291', '91361', '380707', '78349'], ['400193', '289142', '576795', '447244', '-52750', '-550214', '164727', '561869', '210799', '-1372', '222245', '194445', '-373390'], ['-201040', '-107947', '-665043', '290714', '-444016', '13651', '676551', '500310', '-331808', '344610', '160729', '675328', '32809']], 'QpRts-minpoly': [14, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'QpRts-p': 17, 'QpRts-prec': 5, 'Size': 26, 'TransitiveDegree': 13}