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artin_reps • Show schema
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{'BadPrimes': [3, 11], 'Baselabel': '2.297.12t18.b', 'CharacterField': 3, 'Conductor': 297, 'Container': '12t18', 'Dets': ['1.99.6t1.a.b', '1.99.6t1.a.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 12, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 2], [-2, -2], [-1], [0, -1], [1, 1], [0, -2], [2, 2], [1], [0, 1], [-1, -1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [15, 19, 13, 20], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-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, 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], [0], [0, -1]], [[1], [0], [1, 1]], [[1]], [[1], [-1, -1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [-2, -2], [0, 2], [-1], [1, 1], [0, -1], [2, 2], [0, -2], [1], [-1, -1], [0, 1], [0], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [15, 19, 13, 20], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-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], [-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]], [[1], [0], [0, -1]], [[1]], [[1], [0, 1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T18', 'Galt': 18, 'HardPrimes': [2, 3, 5, 11], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, -1, -2, -7, 12, 4, 9, -3, -2, -4, 1, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-1, 6, 0, 1], 'Proj_nTj': [3, 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], [1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.33.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.11.2t1.a', 'Character': [[1], [1], [-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], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.99.6t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.9.6t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [1, 1], [0, -1], [-1, 0], [1, 1], [0, -1], [0, 1], [-1, -1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.99.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [1, 1], [0, -1], [-1, 0], [1, 1], [0, -1], [0, -1], [1, 1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.99.6t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.99.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, -1], [1, 1], [-1, 0], [0, -1], [1, 1], [1, 1], [0, -1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.9.6t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, -1], [1, 1], [-1, 0], [0, -1], [1, 1], [-1, -1], [0, 1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.891.3t2.b', 'Character': [[2], [2], [0], [0], [2], [2], [-1], [-1], [-1], [2], [2], [-1], [-1], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.891.6t3.b', 'Character': [[2], [-2], [0], [0], [2], [2], [-1], [-1], [-1], [-2], [-2], [1], [1], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.99.6t5.a', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [-1, 0], [0, -1], [1, 1], [0, 2], [-2, -2], [-1, 0], [0, -1], [1, 1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.99.6t5.a', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [-1, 0], [1, 1], [0, -1], [-2, -2], [0, 2], [-1, 0], [1, 1], [0, -1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.297.12t18.b', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [-1, 0], [0, -1], [1, 1], [0, -2], [2, 2], [1, 0], [0, 1], [-1, -1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.297.12t18.b', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [-1, 0], [1, 1], [0, -1], [2, 2], [0, -2], [1, 0], [-1, -1], [0, 1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}], 'ComplexConjugation': 4, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]}, {'Size': '1', 'Order': 2, 'Representative': [10, 5, 6, 7, 2, 3, 4, 11, 12, 1, 8, 9]}, {'Size': '3', 'Order': 2, 'Representative': [5, 10, 8, 9, 1, 11, 12, 3, 4, 2, 6, 7]}, {'Size': '3', 'Order': 2, 'Representative': [3, 12, 1, 11, 9, 10, 8, 7, 5, 6, 4, 2]}, {'Size': '1', 'Order': 3, 'Representative': [11, 3, 4, 2, 6, 7, 5, 9, 10, 8, 12, 1]}, {'Size': '1', 'Order': 3, 'Representative': [12, 4, 2, 3, 7, 5, 6, 10, 8, 9, 1, 11]}, {'Size': '2', 'Order': 3, 'Representative': [12, 3, 4, 2, 6, 7, 5, 10, 8, 9, 1, 11]}, {'Size': '2', 'Order': 3, 'Representative': [1, 4, 2, 3, 7, 5, 6, 8, 9, 10, 11, 12]}, {'Size': '2', 'Order': 3, 'Representative': [1, 3, 4, 2, 6, 7, 5, 8, 9, 10, 11, 12]}, {'Size': '1', 'Order': 6, 'Representative': [8, 6, 7, 5, 3, 4, 2, 12, 1, 11, 9, 10]}, {'Size': '1', 'Order': 6, 'Representative': [9, 7, 5, 6, 4, 2, 3, 1, 11, 12, 10, 8]}, {'Size': '2', 'Order': 6, 'Representative': [8, 7, 5, 6, 4, 2, 3, 12, 1, 11, 9, 10]}, {'Size': '2', 'Order': 6, 'Representative': [10, 7, 5, 6, 4, 2, 3, 11, 12, 1, 8, 9]}, {'Size': '2', 'Order': 6, 'Representative': [10, 6, 7, 5, 3, 4, 2, 11, 12, 1, 8, 9]}, {'Size': '3', 'Order': 6, 'Representative': [7, 9, 10, 8, 12, 1, 11, 2, 3, 4, 5, 6]}, {'Size': '3', 'Order': 6, 'Representative': [6, 8, 9, 10, 11, 12, 1, 4, 2, 3, 7, 5]}, {'Size': '3', 'Order': 6, 'Representative': [2, 11, 12, 1, 8, 9, 10, 6, 7, 5, 3, 4]}, {'Size': '3', 'Order': 6, 'Representative': [4, 1, 11, 12, 10, 8, 9, 5, 6, 7, 2, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['60', '-8', '1'], 'ConjugacyClass': 8}, {'RootOf': ['48', '-4', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['6', '1'], 'ConjugacyClass': 2}, {'RootOf': ['8', '24', '0', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-1', '6', '0', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['15', '4', '1'], 'ConjugacyClass': 13}, {'RootOf': ['12', '2', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['8', '1'], 'ConjugacyClass': 5}, {'RootOf': ['4', '1'], 'ConjugacyClass': 6}, {'RootOf': ['212', '12', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-4', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-2', '1'], 'ConjugacyClass': 11}, {'RootOf': ['53', '-6', '1'], 'ConjugacyClass': 12}, {'RootOf': ['368', '-12', '0', '1'], 'ConjugacyClass': 15}, {'RootOf': ['-136', '-48', '0', '1'], 'ConjugacyClass': 16}, {'RootOf': ['-46', '-3', '0', '1'], 'ConjugacyClass': 17}, {'RootOf': ['17', '-12', '0', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [6, 6]}], 'Frobs': [17, 10, 13, 15, 11, 16, 4, 3, 10, 17, 8, 7, 18, 15, 14, 12, 13, 15, 8, 12, 3, 15, 17, 2, 9, 17, 8, 4, 3, 13, 3, 18, 14, 16, 18, 15, 8, 7, 18, 17, 12, 7, 14, 16, 4, 7, 16, 6, 17, 5, 4, 18, 15, 2, 10, 17, 12, 3, 15, 17, 16, 18, 3, 13, 6, 11, 9, 16, 18, 15, 11, 4, 9, 16, 1, 13, 14, 7, 13, 16, 13, 9, 4, 1, 15, 14, 12, 15, 17, 5, 12, 17, 7, 18, 8, 4, 10, 12, 3, 3, 15, 4, 18, 17, 16, 7, 14, 4, 10, 15, 16, 3, 13, 9, 7, 11, 5, 2, 13, 17, 8, 15, 17, 12, 9, 4, 9, 12, 9, 16, 3, 18, 8, 7, 18, 16, 2, 16, 13, 4, 3, 17, 5, 4, 7, 11, 15, 17, 8, 2, 16, 12, 7, 18, 6, 14, 3, 14, 3, 18, 14, 4, 16, 2, 10, 14, 1, 15], 'G-Gens': [[8, 7, 5, 6, 4, 2, 3, 12, 1, 11, 9, 10], [1, 4, 2, 3, 7, 5, 6, 8, 9, 10, 11, 12], [10, 5, 6, 7, 2, 3, 4, 11, 12, 1, 8, 9], [7, 9, 10, 8, 12, 1, 11, 2, 3, 4, 5, 6]], 'G-Name': 'C6*S3', 'Polynomial': [1, -1, -2, -7, 12, 4, 9, -3, -2, -4, 1, 0, 1], 'QpRts': [['376591', '-613022', '-204676', '1826583', '-595335', '-830008'], ['854125', '237516', '1805321', '-1318055', '-2281430', '-1311947'], ['1401170', '1550204', '104373', '-862936', '2128412', '-903662'], ['-2255295', '-1787720', '-1909694', '2180991', '153018', '2215609'], ['-44424', '-347745', '-1673366', '708662', '-2325360', '1556659'], ['-655682', '-2358650', '837461', '1478749', '-1854190', '1307314'], ['700106', '-2120414', '835905', '-2187411', '-647259', '1962836'], ['-2363755', '-1110952', '88938', '2366131', '-393740', '960515'], ['1427211', '80167', '-112224', '-2401458', '1214274', '2249366'], ['936544', '1030785', '23286', '35327', '-820534', '1616928'], ['934987', '-2191651', '1446980', '305243', '1344888', '-1140408'], ['-1311578', '-2022136', '-1242304', '-2131826', '-749553', '1970416']], 'QpRts-minpoly': [2, 11, 11, 10, 0, 0, 1], 'QpRts-p': 13, 'QpRts-prec': 6, 'Size': 36, 'TransitiveDegree': 12}