-
artin_reps • Show schema
Hide schema
{'BadPrimes': [2, 13], 'Baselabel': '2.1352.6t5.a', 'CharacterField': 3, 'Conductor': 1352, 'Container': '6t5', 'Dets': ['1.104.6t1.b.a', '1.104.6t1.b.b'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [0], [0, 2], [-2, -2], [-1], [0, -1], [1, 1], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [10, 7, 6, 8, 11], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [0, -2], [-1, -1]], [[1], [2, 2], [0, 1]], [[1], [1], [1]], [[1], [0, 1], [-1, -1]], [[1], [-1, -1], [0, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[2], [0], [-2, -2], [0, 2], [-1], [1, 1], [0, -1], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [10, 7, 6, 8, 11], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [2, 2], [0, 1]], [[1], [0, -2], [-1, -1]], [[1], [1], [1]], [[1], [-1, -1], [0, 1]], [[1], [0, 1], [-1, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T5', 'Galt': 5, 'HardPrimes': [2, 3, 7, 11, 13], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [27, 60, 44, 6, -7, -2, 1], 'NumBadPrimes': 2, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-2, -1, 0, 1], 'Proj_nTj': [3, 2]}
-
artin_field_data • Show schema
Hide schema
{'ArtinReps': [{'GalConj': 1, 'Baselabel': '1.1.1t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.104.2t1.b', 'Character': [[1], [-1], [1], [1], [1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.104.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.104.6t1.b', 'Character': [[1, 0], [-1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.13.3t1.a', 'Character': [[1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.13.3t1.a', 'Character': [[1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.104.3t2.b', 'Character': [[2], [0], [2], [2], [-1], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.1352.6t5.a', 'Character': [[2, 0], [0, 0], [0, 2], [-2, -2], [-1, 0], [0, -1], [1, 1], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.1352.6t5.a', 'Character': [[2, 0], [0, 0], [-2, -2], [0, 2], [-1, 0], [1, 1], [0, -1], [0, 0], [0, 0]], 'CharacterField': 3}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6]}, {'Size': '3', 'Order': 2, 'Representative': [4, 3, 2, 1, 6, 5]}, {'Size': '1', 'Order': 3, 'Representative': [3, 5, 6, 2, 4, 1]}, {'Size': '1', 'Order': 3, 'Representative': [6, 4, 1, 5, 2, 3]}, {'Size': '2', 'Order': 3, 'Representative': [3, 4, 6, 5, 2, 1]}, {'Size': '2', 'Order': 3, 'Representative': [1, 4, 3, 5, 2, 6]}, {'Size': '2', 'Order': 3, 'Representative': [1, 5, 3, 2, 4, 6]}, {'Size': '3', 'Order': 6, 'Representative': [5, 1, 4, 6, 3, 2]}, {'Size': '3', 'Order': 6, 'Representative': [2, 6, 5, 3, 1, 4]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['2467', '-38', '1'], 'ConjugacyClass': 6}, {'RootOf': ['1310', '-12', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 3]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['20', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-6', '1'], 'ConjugacyClass': 4}, {'RootOf': ['153', '14', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['14188', '-490', '-18', '1'], 'ConjugacyClass': 8}, {'RootOf': ['9196', '-165', '-18', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [6]}], 'Frobs': [4, 7, 5, 6, 8, 1, 6, 9, 8, 8, 1, 7, 8, 6, 5, 2, 9, 9, 8, 6, 2, 2, 2, 8, 9, 8, 2, 4, 5, 3, 8, 5, 9, 6, 3, 5, 2, 9, 4, 9, 7, 2, 9, 8, 7, 9, 7, 7, 9, 5, 5, 5, 9, 3, 7, 8, 9, 7, 9, 2, 4, 6, 2, 2, 5, 1, 9, 5, 6, 7, 8, 1, 8, 9, 8, 6, 2, 3, 8, 9, 7, 5, 7, 6, 8, 5, 9, 8, 6, 1, 1, 7, 3, 7, 2, 9, 4, 5, 4, 5, 5, 7, 6, 7, 5, 2, 8, 2, 2, 7, 9, 4, 9, 2, 6, 3, 9, 8, 8, 3, 4, 7, 2, 9, 8, 2, 3, 9, 2, 5, 8, 7, 8, 8, 9, 8, 6, 9, 9, 7, 2, 7, 9, 2, 8, 3, 5, 1, 1, 5, 6, 7, 5, 8, 7, 2, 9, 9, 1, 5, 8, 6, 5, 6, 8, 5, 8, 9], 'G-Gens': [[5, 1, 4, 6, 3, 2], [3, 4, 6, 5, 2, 1], [1, 4, 3, 5, 2, 6]], 'G-Name': 'C3*S3', 'Polynomial': [27, 60, 44, 6, -7, -2, 1], 'QpRts': [['-639490683', '-4709330530'], ['8202857088', '-2122721325'], ['-754905684', '2586609205'], ['5487410045', '-2586609205'], ['8474093997', '4709330530'], ['1394396368', '2122721325']], 'QpRts-minpoly': [2, 49, 1], 'QpRts-p': 53, 'QpRts-prec': 6, 'Size': 18, 'TransitiveDegree': 6}