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artin_reps • Show schema
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{'BadPrimes': [2, 691], 'Baselabel': '8.933839279558656.21t14.a', 'CharacterField': 1, 'Conductor': 933839279558656, 'Container': '21t14', 'Dets': ['1.1.1t1.a.a'], 'Dim': 8, 'GalConjSigns': [1], 'Galn': 7, 'GaloisConjugates': [{'Sign': 1, 'Character': [[8], [0], [-1], [0], [1], [1]], 'GalOrbIndex': 1, 'HardFactors': [7, 8], 'LocalFactors': [[[1], [-8], [28], [-56], [70], [-56], [28], [-8], [1]], [[1], [0], [-4], [0], [6], [0], [-4], [0], [1]], [[1], [1], [1], [-2], [-2], [-2], [1], [1], [1]], [[1], [0], [0], [0], [-2], [0], [0], [0], [1]], [[1], [-1], [0], [0], [0], [0], [0], [-1], [1]], [[1], [-1], [0], [0], [0], [0], [0], [-1], [1]], [[1], [1], [1]], [[1], [0], [-2], [0], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '7T5', 'Galt': 5, 'HardPrimes': [2, 691], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [1, -2, -1, 3, -5, 4, -3, 1], 'NumBadPrimes': 2, 'Proj_GAP': [168, 42], 'Proj_Polynomial': [1, -2, -1, 3, -5, 4, -3, 1], 'Proj_nTj': [7, 5]}
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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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.30558784.42t37.a', 'Character': [[3, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0], [-1, -1, -1, 0, -1, 0]], 'CharacterField': 7}, {'GalConj': 2, 'Baselabel': '3.30558784.42t37.a', 'Character': [[3, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [-1, -1, -1, 0, -1, 0], [0, 1, 1, 0, 1, 0]], 'CharacterField': 7}, {'GalConj': 1, 'Baselabel': '6.30558784.7t5.a', 'Character': [[6], [2], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '7.933839279558656.8t37.a', 'Character': [[7], [-1], [1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.933839279558656.21t14.a', 'Character': [[8], [0], [-1], [0], [1], [1]], 'CharacterField': 1}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7]}, {'Size': '21', 'Order': 2, 'Representative': [1, 4, 3, 2, 6, 5, 7]}, {'Size': '56', 'Order': 3, 'Representative': [5, 7, 3, 2, 6, 1, 4]}, {'Size': '42', 'Order': 4, 'Representative': [4, 3, 2, 5, 7, 6, 1]}, {'Size': '24', 'Order': 7, 'Representative': [4, 5, 2, 3, 6, 7, 1]}, {'Size': '24', 'Order': 7, 'Representative': [2, 7, 6, 5, 1, 4, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 2, 4]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 3, 3]}, {'Data': [2, 3, 4, 5, 6, 7, 1], 'Classes': [{'RootOf': ['5528', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-5528', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'ALT', 'CycleType': [7]}], 'Frobs': [3, 5, 5, 4, 6, 3, 5, 4, 3, 2, 4, 6, 3, 5, 4, 5, 3, 4, 2, 3, 3, 3, 4, 3, 3, 6, 4, 5, 5, 2, 4, 4, 3, 5, 3, 3, 6, 3, 6, 6, 3, 5, 5, 4, 6, 5, 3, 6, 6, 3, 3, 4, 3, 2, 3, 5, 3, 5, 4, 4, 3, 3, 6, 3, 3, 2, 6, 5, 5, 6, 4, 3, 4, 5, 5, 4, 4, 5, 2, 5, 4, 3, 6, 4, 3, 3, 5, 2, 2, 3, 3, 5, 3, 4, 3, 4, 4, 2, 3, 4, 2, 3, 2, 6, 4, 4, 2, 2, 4, 2, 5, 1, 4, 2, 3, 2, 6, 5, 3, 2, 3, 5, 3, 5, 2, 3, 3, 4, 5, 2, 3, 6, 6, 2, 3, 4, 6, 4, 4, 4, 3, 5, 3, 3, 5, 5, 3, 6, 3, 5, 2, 5, 3, 5, 5, 3, 3, 4, 4, 4, 6, 6, 3, 4, 3, 3, 4, 4], 'G-Gens': [[4, 3, 2, 5, 7, 6, 1], [1, 4, 3, 2, 6, 5, 7]], 'G-Name': 'PSL(2,7)', 'Polynomial': [1, -2, -1, 3, -5, 4, -3, 1], 'QpRts': [['-15724', '-152143', '33912'], ['10794', '4745', '131853'], ['-111506', '-184723', '40128'], ['-23025', '179978', '-171981'], ['156802', '-107026', '-22340'], ['47395', '-112124', '-11572'], ['-64733', '0', '0']], 'QpRts-minpoly': [11, 2, 0, 1], 'QpRts-p': 13, 'QpRts-prec': 5, 'Size': 168, 'TransitiveDegree': 7}