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artin_reps • Show schema
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{'BadPrimes': [5, 19], 'Baselabel': '1.95.12t1.a', 'CharacterField': 12, 'Conductor': 95, 'Container': '12t1', 'Dets': ['95.68', '95.87', '95.83', '95.7'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 12, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [-1, 0, 1], [0, 0, -1], [0, 0, 0, 1], [0, 0, 0, -1], [0, 0, 1], [1, 0, -1], [0, 1], [0, -1, 0, 1], [0, -1], [0, 1, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [12, 13, 6, 1, 10, 13, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [-1, 0, 1]], [[1], [0, -1]], [[1], [0, 1, 0, -1]], [[1], [0, 1]], [[1], [0, -1, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, 0, 1], [0, 0, -1], [0, 0, 0, -1], [0, 0, 0, 1], [0, 0, 1], [1, 0, -1], [0, -1], [0, 1, 0, -1], [0, 1], [0, -1, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [12, 13, 6, 1, 10, 13, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [-1, 0, 1]], [[1], [0, 1]], [[1], [0, -1, 0, 1]], [[1], [0, -1]], [[1], [0, 1, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [-1, 0, 1], [0, 0, 0, 1], [0, 0, 0, -1], [1, 0, -1], [0, 0, 1], [0, -1, 0, 1], [0, 1], [0, 1, 0, -1], [0, -1]], 'GalOrbIndex': 3, 'HardFactors': [12, 13, 6, 1, 10, 13, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [1, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [-1, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 1, 0, -1]], [[1], [0, -1]], [[1], [0, -1, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [-1, 0, 1], [0, 0, 0, -1], [0, 0, 0, 1], [1, 0, -1], [0, 0, 1], [0, 1, 0, -1], [0, -1], [0, -1, 0, 1], [0, 1]], 'GalOrbIndex': 4, 'HardFactors': [12, 13, 6, 1, 10, 13, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [1, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [-1, 0, 1]], [[1], [0, 0, -1]], [[1], [0, -1, 0, 1]], [[1], [0, 1]], [[1], [0, 1, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '12T1', 'Galt': 1, 'HardPrimes': [3, 5, 7, 11, 17, 19, 31, 151], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [2401, -2058, 2107, -1757, 1513, -351, 266, -62, 41, -6, 7, -1, 1], 'NumBadPrimes': 2, '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], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.5.4t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [1, 0], [0, 1], [0, -1], [-1, 0], [-1, 0], [0, -1], [0, -1], [0, 1], [0, 1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '1.5.2t1.a', 'Character': [[1], [1], [1], [1], [-1], [-1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 2, 'Baselabel': '1.5.4t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [1, 0], [0, -1], [0, 1], [-1, 0], [-1, 0], [0, 1], [0, 1], [0, -1], [0, -1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '1.19.3t1.a', 'Character': [[1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.95.12t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [0, 0, 0, 1], [0, 0, 0, -1], [0, 0, 1, 0], [1, 0, -1, 0], [0, 1, 0, 0], [0, -1, 0, 1], [0, -1, 0, 0], [0, 1, 0, -1]], 'CharacterField': 12}, {'GalConj': 1, 'Baselabel': '1.95.6t1.a', 'Character': [[1, 0], [1, 0], [0, 1], [-1, -1], [-1, 0], [-1, 0], [-1, -1], [0, 1], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.95.12t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [0, 0, 0, -1], [0, 0, 0, 1], [0, 0, 1, 0], [1, 0, -1, 0], [0, -1, 0, 0], [0, 1, 0, -1], [0, 1, 0, 0], [0, -1, 0, 1]], 'CharacterField': 12}, {'GalConj': 2, 'Baselabel': '1.19.3t1.a', 'Character': [[1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 3, 'Baselabel': '1.95.12t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [0, 0, 0, 1], [0, 0, 0, -1], [1, 0, -1, 0], [0, 0, 1, 0], [0, -1, 0, 1], [0, 1, 0, 0], [0, 1, 0, -1], [0, -1, 0, 0]], 'CharacterField': 12}, {'GalConj': 2, 'Baselabel': '1.95.6t1.a', 'Character': [[1, 0], [1, 0], [-1, -1], [0, 1], [-1, 0], [-1, 0], [0, 1], [-1, -1], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 4, 'Baselabel': '1.95.12t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [0, 0, 0, -1], [0, 0, 0, 1], [1, 0, -1, 0], [0, 0, 1, 0], [0, 1, 0, -1], [0, -1, 0, 0], [0, -1, 0, 1], [0, 1, 0, 0]], 'CharacterField': 12}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]}, {'Size': '1', 'Order': 2, 'Representative': [7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6]}, {'Size': '1', 'Order': 3, 'Representative': [11, 9, 10, 2, 12, 1, 5, 3, 4, 8, 6, 7]}, {'Size': '1', 'Order': 3, 'Representative': [6, 4, 8, 9, 7, 11, 12, 10, 2, 3, 1, 5]}, {'Size': '1', 'Order': 4, 'Representative': [4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3]}, {'Size': '1', 'Order': 4, 'Representative': [10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '1', 'Order': 6, 'Representative': [12, 10, 2, 3, 1, 5, 6, 4, 8, 9, 7, 11]}, {'Size': '1', 'Order': 6, 'Representative': [5, 3, 4, 8, 6, 7, 11, 9, 10, 2, 12, 1]}, {'Size': '1', 'Order': 12, 'Representative': [8, 6, 7, 11, 9, 10, 2, 12, 1, 5, 3, 4]}, {'Size': '1', 'Order': 12, 'Representative': [3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10, 2]}, {'Size': '1', 'Order': 12, 'Representative': [2, 12, 1, 5, 3, 4, 8, 6, 7, 11, 9, 10]}, {'Size': '1', 'Order': 12, 'Representative': [9, 7, 11, 12, 10, 2, 3, 1, 5, 6, 4, 8]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['2', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-17', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-8', '1'], 'ConjugacyClass': 5}, {'RootOf': ['2', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [4, 4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-17', '1'], 'ConjugacyClass': 7}, {'RootOf': ['2', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [6, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['2', '1'], 'ConjugacyClass': 9}, {'RootOf': ['-17', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-8', '1'], 'ConjugacyClass': 11}, {'RootOf': ['68', '1'], 'ConjugacyClass': 12}], 'Algorithm': 'RES', 'CycleType': [12]}], 'Frobs': [10, 12, 4, 6, 1, 11, 10, 2, 11, 8, 1, 6, 4, 12, 9, 11, 7, 3, 9, 4, 12, 7, 5, 8, 10, 3, 5, 6, 7, 5, 9, 4, 9, 8, 7, 1, 10, 5, 9, 12, 2, 3, 1, 12, 6, 8, 4, 12, 6, 2, 12, 2, 3, 3, 9, 12, 7, 4, 6, 3, 12, 5, 10, 1, 11, 9, 1, 10, 10, 2, 5, 7, 9, 5, 2, 12, 8, 10, 4, 8, 2, 4, 3, 11, 7, 11, 2, 6, 4, 5, 6, 8, 6, 4, 7, 11, 8, 1, 11, 3, 9, 9, 5, 2, 1, 6, 10, 11, 8, 1, 6, 12, 9, 2, 3, 4, 12, 6, 5, 8, 3, 5, 6, 5, 1, 4, 8, 7, 10, 5, 7, 12, 3, 10, 1, 8, 11, 6, 6, 2, 3, 3, 11, 9, 2, 7, 12, 10, 8, 5, 10, 1, 11, 9, 10, 1, 2, 7, 9, 3, 10, 12, 10, 4, 6, 12, 4, 9], 'G-Gens': [[8, 6, 7, 11, 9, 10, 2, 12, 1, 5, 3, 4]], 'G-Name': 'C12', 'Polynomial': [2401, -2058, 2107, -1757, 1513, -351, 266, -62, 41, -6, 7, -1, 1], 'QpRts': [['23289169', '14504049', '-29700377', '-26456304'], ['-30673302', '25638524', '-3878464', '-19949038'], ['3090443', '-34268764', '24004037', '-9060916'], ['9895326', '11833317', '-6775476', '-15611455'], ['10690099', '-11910347', '17910558', '-25135017'], ['-22763621', '20040696', '726932', '20349359'], ['-1264656', '-5657544', '-32822245', '-23447652'], ['28541125', '7249795', '-33645483', '-27107946'], ['-8829927', '-34139795', '-1351510', '13764976'], ['34144668', '-20679822', '-45859', '-3828546'], ['34085991', '-20977972', '19613389', '2848044'], ['-10861357', '-20976094', '-23379459', '-25053419']], 'QpRts-minpoly': [2, 24, 6, 0, 1], 'QpRts-p': 37, 'QpRts-prec': 5, 'Size': 12, 'TransitiveDegree': 12}