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artin_reps • Show schema
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{'BadPrimes': [3, 13, 109], 'Baselabel': '4.54213003.8t29.a', 'CharacterField': 1, 'Conductor': 54213003, 'Container': '8t29', 'Dets': ['1.3.2t1.a.a'], 'Dim': 4, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[4], [-4], [0], [0], [0], [0], [-2], [2], [0], [0], [0], [0], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [14, 17, 14, 3, 18, 3, 18, 3, 3, 3], 'LocalFactors': [[[1], [-4], [6], [-4], [1]], [[1], [4], [6], [4], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [2], [0], [-2], [-1]], [[1], [-2], [0], [2], [-1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [0], [2], [0], [1]], [[1], [0], [2], [0], [1]], [[1], [0], [2], [0], [1]], [[1], [0], [0], [0], [-1]], [[1], [0], [0], [0], [-1]], [[1], [0], [0], [0], [-1]], [[1], [-1]], [[1], [0], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T29', 'Galt': 29, 'HardPrimes': [2, 3, 5, 7, 13, 67, 109, 6073, 89599, 498271], 'Hide': 1, 'Indicator': 1, 'Is_Even': False, 'NFGal': [321, 63, 313, -89, 100, -35, 17, -3, 1], 'NumBadPrimes': 3, 'Proj_GAP': [32, 27], 'Proj_Polynomial': [49, -35, -37, 9, 32, 3, -7, -2, 1], 'Proj_nTj': [8, 18]}
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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], [1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.4251.2t1.a', 'Character': [[1], [1], [1], [1], [1], [-1], [-1], [-1], [1], [-1], [1], [-1], [-1], [1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.39.2t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [1], [-1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.109.2t1.a', 'Character': [[1], [1], [1], [1], [1], [-1], [1], [1], [-1], [1], [-1], [-1], [1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.13.2t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.327.2t1.a', 'Character': [[1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [1], [-1], [-1], [1], [1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.3.2t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [-1], [-1], [1], [1], [1], [1], [1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.1417.2t1.a', 'Character': [[1], [1], [1], [1], [1], [-1], [1], [1], [1], [-1], [1], [-1], [-1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.55263.4t3.b', 'Character': [[2], [2], [-2], [-2], [2], [0], [0], [0], [0], [-2], [0], [0], [2], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.327.4t3.c', 'Character': [[2], [2], [-2], [-2], [2], [0], [0], [0], [0], [2], [0], [0], [-2], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.4251.4t3.c', 'Character': [[2], [2], [-2], [2], [-2], [0], [0], [0], [-2], [0], [2], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.463359.4t3.a', 'Character': [[2], [2], [2], [-2], [-2], [-2], [0], [0], [0], [0], [0], [2], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.4251.4t3.d', 'Character': [[2], [2], [-2], [2], [-2], [0], [0], [0], [2], [0], [-2], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.39.4t3.b', 'Character': [[2], [2], [2], [-2], [-2], [2], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.54213003.8t29.a', 'Character': [[4], [-4], [0], [0], [0], [0], [-2], [2], [0], [0], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.6023667.8t29.a', 'Character': [[4], [-4], [0], [0], [0], [0], [2], [-2], [0], [0], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 7, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [2, 1, 5, 6, 3, 4, 8, 7]}, {'Size': '2', 'Order': 2, 'Representative': [2, 1, 3, 4, 5, 6, 8, 7]}, {'Size': '2', 'Order': 2, 'Representative': [8, 7, 6, 5, 4, 3, 2, 1]}, {'Size': '2', 'Order': 2, 'Representative': [8, 7, 4, 3, 6, 5, 2, 1]}, {'Size': '4', 'Order': 2, 'Representative': [2, 1, 3, 6, 5, 4, 7, 8]}, {'Size': '4', 'Order': 2, 'Representative': [8, 7, 5, 6, 3, 4, 2, 1]}, {'Size': '4', 'Order': 2, 'Representative': [8, 7, 3, 4, 5, 6, 2, 1]}, {'Size': '4', 'Order': 2, 'Representative': [4, 6, 7, 1, 8, 2, 3, 5]}, {'Size': '4', 'Order': 2, 'Representative': [4, 6, 8, 1, 7, 2, 5, 3]}, {'Size': '4', 'Order': 4, 'Representative': [4, 6, 8, 2, 7, 1, 3, 5]}, {'Size': '4', 'Order': 4, 'Representative': [7, 8, 4, 5, 6, 3, 2, 1]}, {'Size': '4', 'Order': 4, 'Representative': [4, 6, 7, 2, 8, 1, 5, 3]}, {'Size': '8', 'Order': 4, 'Representative': [7, 8, 5, 4, 3, 6, 2, 1]}, {'Size': '8', 'Order': 4, 'Representative': [5, 3, 7, 1, 8, 2, 6, 4]}, {'Size': '8', 'Order': 4, 'Representative': [5, 3, 7, 2, 8, 1, 4, 6]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-117', '13', '1'], 'ConjugacyClass': 3}, {'RootOf': ['386659', '7631', '756', '26', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-104628', '-16664', '-549', '21', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 14, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-8', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-244', '-21', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-571', '-21', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-59856', '9340', '-19', '-37', '1'], 'ConjugacyClass': 7}, {'RootOf': ['439588', '-42604', '759', '83', '1'], 'ConjugacyClass': 9}, {'RootOf': ['139075', '26720', '2394', '83', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['532012', '-49738', '483', '83', '1'], 'ConjugacyClass': 11}, {'RootOf': ['81009', '-1197', '498', '-42', '1'], 'ConjugacyClass': 12}, {'RootOf': ['281203', '43784', '2772', '83', '1'], 'ConjugacyClass': 13}, {'RootOf': ['338172716608', '-57504594704', '2586227320', '32348056', '-5598242', '34315', '8368', '166', '1'], 'ConjugacyClass': 15}, {'RootOf': ['29916183625', '13046815165', '2363901328', '232503448', '13868722', '522853', '12292', '166', '1'], 'ConjugacyClass': 16}], 'Algorithm': 'RES', 'CycleType': [4, 4]}], 'Frobs': [15, 8, 16, 10, 15, 12, 14, 9, 14, 8, 13, 11, 15, 3, 15, 14, 15, 5, 9, 16, 13, 12, 16, 16, 13, 14, 6, 14, 13, 8, 12, 8, 16, 6, 15, 9, 3, 11, 15, 7, 14, 6, 7, 10, 16, 12, 5, 13, 16, 9, 8, 16, 11, 14, 14, 8, 14, 11, 6, 16, 12, 16, 10, 7, 12, 15, 10, 12, 8, 10, 16, 15, 6, 4, 11, 15, 14, 9, 16, 13, 14, 10, 16, 5, 3, 7, 15, 10, 16, 13, 7, 16, 9, 14, 13, 14, 16, 14, 2, 13, 6, 16, 14, 14, 4, 9, 15, 16, 14, 12, 6, 9, 15, 10, 11, 14, 9, 8, 8, 8, 13, 6, 14, 16, 11, 14, 9, 14, 5, 11, 11, 16, 2, 12, 15, 11, 15, 11, 7, 8, 10, 15, 1, 16, 5, 15, 9, 7, 12, 16, 13, 8, 12, 7, 5, 14, 12, 15, 12, 15, 16, 8, 9, 14, 16, 15, 6, 3], 'G-Gens': [[1, 2, 3, 6, 5, 4, 8, 7], [2, 1, 3, 6, 5, 4, 7, 8], [8, 7, 5, 6, 3, 4, 2, 1], [4, 6, 8, 2, 7, 1, 3, 5], [1, 2, 5, 6, 3, 4, 7, 8]], 'G-Name': 'C2wrC2^2', 'Polynomial': [321, 63, 313, -89, 100, -35, 17, -3, 1], 'QpRts': [['-25321615287428273972133'], ['-58332857118322908160298'], ['44465572132139279911632'], ['-7599352748045235755228'], ['-82958863076581520521313'], ['-102804243008966946652588'], ['41704086813387279287930'], ['-19626837676192494864080']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 823, 'QpRts-prec': 8, 'Size': 64, 'TransitiveDegree': 8}