-
artin_reps • Show schema
{'BadPrimes': [7, 167], 'Baselabel': '12.219708209445758929.18t206.a', 'CharacterField': 1, 'Conductor': 219708209445758929, 'Container': '18t206', 'Dets': ['1.1.1t1.a.a'], 'Dim': 12, 'GalConjSigns': [1], 'Galn': 9, 'GaloisConjugates': [{'Sign': 1, 'Character': [[12], [4], [0], [0], [0], [3], [-3], [0], [0], [-2], [-2], [1], [0], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [18, 5, 19, 6], 'LocalFactors': [[[1], [-12], [66], [-220], [495], [-792], [924], [-792], [495], [-220], [66], [-12], [1]], [[1], [-4], [2], [12], [-17], [-8], [28], [-8], [-17], [12], [2], [-4], [1]], [[1], [0], [-6], [0], [15], [0], [-20], [0], [15], [0], [-6], [0], [1]], [[1], [0], [-6], [0], [15], [0], [-20], [0], [15], [0], [-6], [0], [1]], [[1], [0], [0], [-4], [0], [0], [6], [0], [0], [-4], [0], [0], [1]], [[1], [-3], [3], [-4], [9], [-9], [6], [-9], [9], [-4], [3], [-3], [1]], [[1], [3], [6], [5], [0], [-9], [-12], [-9], [0], [5], [6], [3], [1]], [[1], [0], [0], [-4], [0], [0], [6], [0], [0], [-4], [0], [0], [1]], [[1], [0], [0], [-4], [0], [0], [6], [0], [0], [-4], [0], [0], [1]], [[1], [2], [2], [0], [-2], [-2], [-2], [-2], [-2], [0], [2], [2], [1]], [[1], [2], [2], [0], [-2], [-2], [-2], [-2], [-2], [0], [2], [2], [1]], [[1], [-1], [2], [-3], [4], [-5], [4], [-5], [4], [-3], [2], [-1], [1]], [[1], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [0], [1]], [[1], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [0], [1]], [[1], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [0], [1]], [[1], [0], [0], [-1], [0], [0], [0], [0], [0], [-1], [0], [0], [1]], [[1], [0], [0], [-1], [0], [0], [0], [0], [0], [-1], [0], [0], [1]], [[1], [1], [1]], [[1], [-2], [-2], [6], [0], [-6], [2], [2], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T28', 'Galt': 28, 'HardPrimes': [7, 11, 167, 433], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-1, 4, -4, 0, 0, 0, 0, 2, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [648, 705], 'Proj_Polynomial': [-1, 4, -4, 0, 0, 0, 0, 2, -1, 1], 'Proj_nTj': [9, 28]} -
artin_field_data • Show schema
{'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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.167.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [1], [-1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.1169.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, 0], [-1, 0], [-1, 0], [1, 0], [1, 1], [0, -1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.7.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.7.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1]], 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{'GalConj': 1, 'Baselabel': '12.219708209445758929.18t206.a', 'Character': [[12], [4], [0], [0], [0], [3], [-3], [0], [0], [-2], [-2], [1], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.170888237000408744029100209.36t1101.a', 'Character': [[12], [-4], [0], [0], [0], [3], [-3], [0], [0], [2], [2], [-1], [0], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '9', 'Order': 2, 'Representative': [2, 1, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '27', 'Order': 2, 'Representative': [2, 1, 4, 3, 8, 6, 7, 5, 9]}, {'Size': '27', 'Order': 2, 'Representative': [2, 1, 3, 4, 5, 6, 7, 9, 8]}, {'Size': '6', 'Order': 3, 'Representative': [1, 2, 4, 6, 5, 3, 7, 8, 9]}, {'Size': '8', 'Order': 3, 'Representative': [2, 7, 4, 6, 8, 3, 1, 9, 5]}, {'Size': '12', 'Order': 3, 'Representative': [1, 2, 4, 6, 8, 3, 7, 9, 5]}, {'Size': '36', 'Order': 3, 'Representative': [5, 8, 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Artin representation data - 12.219708209445758929.18t206.a