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artin_reps • Show schema
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{'BadPrimes': [2, 3], 'Baselabel': '2.768.8t11.c', 'CharacterField': 4, 'Conductor': 768, 'Container': '8t11', 'Dets': ['1.3.2t1.a.a', '1.3.2t1.a.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 8, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [0], [0, -2], [0, 2], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [11, 12, 6], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, 2], [-1]], [[1], [0, -2], [-1]], [[1], [0], [1]], [[1], [0], [1]], [[1], [0], [1]], [[1]], [[1], [0, 1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [0], [0, 2], [0, -2], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [11, 12, 6], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, -2], [-1]], [[1], [0, 2], [-1]], [[1], [0], [1]], [[1], [0], [1]], [[1], [0], [1]], [[1]], [[1], [0, -1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '8T11', 'Galt': 11, 'HardPrimes': [2, 3, 11], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [9, 0, -12, 0, 8, 0, -4, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [4, 2], 'Proj_Polynomial': [1, 0, 4, 0, 1], 'Proj_nTj': [4, 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], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.24.2t1.a', 'Character': [[1], [1], [1], [-1], [1], [-1], [-1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.8.2t1.b', 'Character': [[1], [1], [-1], [1], [-1], [1], [1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.4.2t1.a', 'Character': [[1], [1], [1], [1], [-1], [-1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.12.2t1.a', 'Character': [[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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.24.2t1.b', 'Character': [[1], [1], [1], [-1], [-1], [1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.8.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [-1], [-1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.768.8t11.c', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 0], [0, -2], [0, 2], [0, 0], [0, 0], [0, 0]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '2.768.8t11.c', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 0], [0, 2], [0, -2], [0, 0], [0, 0], [0, 0]], 'CharacterField': 4}], 'ComplexConjugation': 5, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [8, 7, 6, 5, 4, 3, 2, 1]}, {'Size': '2', 'Order': 2, 'Representative': [2, 1, 4, 3, 6, 5, 8, 7]}, {'Size': '2', 'Order': 2, 'Representative': [1, 7, 3, 5, 4, 6, 2, 8]}, {'Size': '2', 'Order': 2, 'Representative': [5, 3, 2, 8, 1, 7, 6, 4]}, {'Size': '1', 'Order': 4, 'Representative': [6, 5, 1, 2, 7, 8, 4, 3]}, {'Size': '1', 'Order': 4, 'Representative': [3, 4, 8, 7, 2, 1, 5, 6]}, {'Size': '2', 'Order': 4, 'Representative': [7, 1, 5, 3, 6, 4, 8, 2]}, {'Size': '2', 'Order': 4, 'Representative': [5, 6, 2, 1, 8, 7, 3, 4]}, {'Size': '2', 'Order': 4, 'Representative': [6, 4, 1, 7, 2, 8, 5, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['-24', '1'], 'ConjugacyClass': 2}, {'RootOf': ['864', '0', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-1728', '0', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['16', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-16', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-192', '0', '1'], 'ConjugacyClass': 8}, {'RootOf': ['96', '0', '1'], 'ConjugacyClass': 9}, {'RootOf': ['32', '0', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [4, 4]}], 'Frobs': [4, 10, 3, 9, 6, 8, 4, 10, 5, 3, 9, 8, 4, 10, 5, 3, 7, 8, 10, 5, 1, 9, 7, 4, 1, 3, 9, 7, 8, 4, 9, 6, 4, 10, 3, 9, 8, 10, 5, 3, 6, 8, 5, 2, 3, 9, 10, 9, 7, 8, 4, 5, 2, 6, 4, 5, 3, 9, 8, 4, 10, 3, 10, 5, 1, 3, 10, 2, 6, 8, 4, 5, 9, 8, 10, 5, 3, 8, 4, 2, 7, 8, 5, 1, 9, 6, 4, 2, 3, 9, 7, 5, 9, 7, 10, 5, 3, 4, 10, 8, 10, 3, 7, 4, 10, 2, 7, 4, 5, 1, 9, 8, 4, 10, 9, 4, 10, 5, 3, 6, 8, 1, 3, 6, 10, 3, 8, 5, 9, 8, 10, 5, 9, 8, 4, 2, 3, 10, 3, 4, 10, 3, 9, 7, 8, 5, 8, 4, 10, 5, 8, 4, 10, 5, 10, 5, 9, 4, 2, 3, 6, 4, 9, 6, 4, 5, 9, 8], 'G-Gens': [[8, 7, 6, 5, 4, 3, 2, 1], [1, 7, 3, 5, 4, 6, 2, 8], [2, 1, 4, 3, 6, 5, 8, 7], [6, 5, 1, 2, 7, 8, 4, 3]], 'G-Name': 'D8:C2', 'Polynomial': [9, 0, -12, 0, 8, 0, -4, 0, 1], 'QpRts': [['730945656'], ['-436994410'], ['-69530294'], ['-995134067'], ['995134067'], ['69530294'], ['436994410'], ['-730945656']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 73, 'QpRts-prec': 5, 'Size': 16, 'TransitiveDegree': 8}