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artin_reps • Show schema
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{'BadPrimes': [2, 263], 'Baselabel': '2.16832.26t3.a', 'CharacterField': 13, 'Conductor': 16832, 'Container': '26t3', 'Dets': ['1.263.2t1.a.a', '1.263.2t1.a.a', '1.263.2t1.a.a', '1.263.2t1.a.a', '1.263.2t1.a.a', '1.263.2t1.a.a'], 'Dim': 2, 'GalConjSigns': [1, 1, 1, 1, 1, 1], 'Galn': 26, 'GaloisConjugates': [{'Sign': 1, 'Character': [[2], [-2], [0], [0], [0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, -1, -1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, -1, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [17, 12, 3, 3, 13, 3, 3, 3, 18, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1]], [[1], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, 1, 1], [1]], [[1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 1, 0, 0, 1], [1]], [[1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [-2], [0], [0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, -1, 0, 0, -1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, -1, -1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1]], 'GalOrbIndex': 2, 'HardFactors': [17, 12, 3, 3, 13, 3, 3, 3, 18, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, 1, 0, 0, 1], [1]], [[1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [1]], [[1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 1, 1], [1]], [[1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [1]], [[1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [-2], [0], [0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 0, -1, -1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1]], 'GalOrbIndex': 3, 'HardFactors': [17, 12, 3, 3, 13, 3, 3, 3, 18, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1]], [[1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [1]], [[1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 1, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 1, 1], [1]], [[1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [-2], [0], [0], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, -1, 0, 0, -1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, -1, -1]], 'GalOrbIndex': 4, 'HardFactors': [17, 12, 3, 3, 13, 3, 3, 3, 18, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 1, 0, 0, 1], [1]], [[1], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, 1, 1], [1]], [[1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [-2], [0], [0], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, -1, -1], [0, 0, 0, 0, 0, -1, 0, 0, -1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], 'GalOrbIndex': 5, 'HardFactors': [17, 12, 3, 3, 13, 3, 3, 3, 18, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, 1, 1], [1]], [[1], [0, 0, 0, 0, 0, 1, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [1]], [[1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [-2], [0], [0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 1], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, -1, -1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, -1, 0, 0, -1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1]], 'GalOrbIndex': 6, 'HardFactors': [17, 12, 3, 3, 13, 3, 3, 3, 18, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, -1, 0, 0, -1], [1]], [[1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [1]], [[1], [0, 0, 0, 0, 0, 0, -1, -1], [1]], [[1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1]], [[1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 0, 0, 1, 1], [1]], [[1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [1]], [[1], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [1]], [[1], [0, 0, 0, 0, 0, 1, 0, 0, 1], [1]], [[1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1]], [[1]], [[1], [-1]]]}], 'GaloisConjugatesSigns': [1, 1, 1, 1, 1, 1], 'GaloisLabel': '26T3', 'Galt': 3, 'HardPrimes': [2, 3, 5, 7, 11, 19, 41, 211, 263, 1061], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-8192, 0, 131072, 0, 204800, 0, 46080, 0, -19456, 0, 30208, 0, -3328, 0, -1408, 0, 1312, 0, -272, 0, -24, 0, 44, 0, -12, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [26, 1], 'Proj_Polynomial': [-1, 8, -16, 27, -38, 36, -22, 12, -13, 19, -21, 15, -6, 1], 'Proj_nTj': [13, 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.2104.2t1.b', 'Character': [[1], [-1], [1], [-1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.263.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.8.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 2, 'Baselabel': '2.16832.26t3.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0]], 'CharacterField': 13}, {'GalConj': 5, 'Baselabel': '2.263.13t2.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1]], 'CharacterField': 13}, {'GalConj': 2, 'Baselabel': '2.263.13t2.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0]], 'CharacterField': 13}, {'GalConj': 1, 'Baselabel': '2.16832.26t3.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 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'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [-1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1]], 'CharacterField': 13}, {'GalConj': 4, 'Baselabel': '2.263.13t2.a', 'Character': [[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [-1, 0, 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