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artin_reps • Show schema
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{'BadPrimes': [7], 'Baselabel': '1.49.7t1.a', 'CharacterField': 7, 'Conductor': 49, 'Container': '7t1', 'Dets': ['49.43', '49.36', '49.29', '49.22', '49.15', '49.8'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0], 'Galn': 7, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1]], 'GalOrbIndex': 1, 'HardFactors': [6, 2, 8, 5, 1, 1, 4, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 1], [0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1], [0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [6, 2, 8, 5, 1, 1, 4, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [-1, -1, -1, -1, -1, -1], [0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [6, 2, 8, 5, 1, 1, 4, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 1], [-1, -1, -1, -1, -1, -1], [0, 0, 0, 1]], 'GalOrbIndex': 4, 'HardFactors': [6, 2, 8, 5, 1, 1, 4, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 1], [0, 0, 1]], 'GalOrbIndex': 5, 'HardFactors': [6, 2, 8, 5, 1, 1, 4, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 1], [0, 1]], 'GalOrbIndex': 6, 'HardFactors': [6, 2, 8, 5, 1, 1, 4, 7], 'LocalFactors': [[[1], [-1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0], 'GaloisLabel': '7T1', 'Galt': 1, 'HardPrimes': [2, 5, 7, 17, 19, 31, 53, 239], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-97, -84, 112, 91, -21, -21, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
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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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.49.7t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1]], 'CharacterField': 7}, {'GalConj': 2, 'Baselabel': '1.49.7t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [-1, -1, -1, -1, -1, -1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]], 'CharacterField': 7}, {'GalConj': 3, 'Baselabel': '1.49.7t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, -1, -1, -1, -1, -1], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]], 'CharacterField': 7}, {'GalConj': 4, 'Baselabel': '1.49.7t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0], [-1, -1, -1, -1, -1, -1], [0, 0, 0, 1, 0, 0]], 'CharacterField': 7}, {'GalConj': 5, 'Baselabel': '1.49.7t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [-1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]], 'CharacterField': 7}, {'GalConj': 6, 'Baselabel': '1.49.7t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [-1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]], 'CharacterField': 7}], 'ComplexConjugation': 1, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7]}, {'Size': '1', 'Order': 7, 'Representative': [4, 1, 2, 7, 6, 3, 5]}, {'Size': '1', 'Order': 7, 'Representative': [7, 4, 1, 5, 3, 2, 6]}, {'Size': '1', 'Order': 7, 'Representative': [5, 7, 4, 6, 2, 1, 3]}, {'Size': '1', 'Order': 7, 'Representative': [6, 5, 7, 3, 1, 4, 2]}, {'Size': '1', 'Order': 7, 'Representative': [3, 6, 5, 2, 4, 7, 1]}, {'Size': '1', 'Order': 7, 'Representative': [2, 3, 6, 1, 7, 5, 4]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['24941', '1'], 'ConjugacyClass': 2}, {'RootOf': ['28665', '1'], 'ConjugacyClass': 3}, {'RootOf': ['36456', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-28518', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-13769', '1'], 'ConjugacyClass': 6}, {'RootOf': ['13230', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [7]}], 'Frobs': [6, 2, 2, 1, 6, 6, 5, 1, 4, 5, 1, 5, 2, 7, 6, 4, 7, 5, 1, 4, 3, 1, 3, 3, 1, 2, 2, 3, 6, 3, 5, 7, 7, 2, 6, 4, 7, 7, 5, 4, 5, 3, 2, 2, 1, 2, 3, 4, 1, 7, 5, 7, 4, 7, 5, 1, 3, 4, 5, 6, 6, 1, 6, 5, 1, 4, 5, 7, 4, 7, 7, 7, 3, 1, 6, 3, 2, 2, 3, 5, 4, 5, 7, 2, 6, 6, 2, 7, 5, 4, 4, 6, 2, 1, 3, 6, 1, 1, 7, 6, 2, 1, 3, 1, 5, 6, 1, 2, 6, 6, 1, 3, 5, 1, 7, 4, 7, 7, 7, 4, 3, 6, 3, 2, 2, 3, 4, 7, 2, 6, 4, 2, 7, 4, 4, 3, 6, 2, 6, 3, 4, 5, 7, 7, 4, 7, 5, 3, 4, 1, 2, 1, 1, 2, 3, 5, 5, 6, 7, 7, 7, 4, 6, 3, 2, 2, 6, 5], 'G-Gens': [[4, 1, 2, 7, 6, 3, 5]], 'G-Name': 'C7', 'Polynomial': [-97, -84, 112, 91, -21, -21, 0, 1], 'QpRts': [['3651114', '23090040', '35615859', '46420388', '40166502', '65468818', '-52524812'], ['-100117277', '81320725', '-49976098', '-55975179', '59127707', '9380055', '69046948'], ['63954312', '34201035', '88230162', '-2575685', '-3888394', '-19096569', '18653341'], ['-42525645', '-92110392', '80094880', '36829978', '-21583314', '-30358127', '14391547'], ['-69122188', '59672208', '-81942556', '-58759757', '-104291644', '53557143', '15565842'], ['72577436', '8130866', '87452010', '-10320985', '-33166943', '-94473922', '56894899'], ['71582248', '100054399', '54884624', '44381240', '63636086', '15522602', '92331116']], 'QpRts-minpoly': [9, 4, 0, 0, 0, 0, 0, 1], 'QpRts-p': 11, 'QpRts-prec': 8, 'Size': 7, 'TransitiveDegree': 7}