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artin_reps • Show schema
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{'BadPrimes': [2, 3, 7], 'Baselabel': '10.14117306610774528.70.a', 'CharacterField': 7, 'Conductor': 14117306610774528, 'Container': '70', 'Dets': ['1.1.1t1.a.a', '1.1.1t1.a.a'], 'Dim': 10, 'GalConjSigns': [0, 0], 'Galn': 7, 'GaloisConjugates': [{'Sign': 0, 'Character': [[10], [-2], [1], [1], [0], [0], [1], [-1, -1, -1, 0, -1], [0, 1, 1, 0, 1]], 'GalOrbIndex': 1, 'HardFactors': [10, 11, 12], 'LocalFactors': [[[1], [-10], [45], [-120], [210], [-252], [210], [-120], [45], [-10], [1]], [[1], [2], [-3], [-8], [2], [12], [2], [-8], [-3], [2], [1]], [[1], [-1], [0], [-3], [3], [0], [3], [-3], [0], [-1], [1]], [[1], [-1], [0], [-3], [3], [0], [3], [-3], [0], [-1], [1]], [[1], [0], [1], [0], [-2], [0], [-2], [0], [1], [0], [1]], [[1], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [1]], [[1], [-1], [0], [1], [-1], [0], [-1], [1], [0], [-1], [1]], [[1], [1, 1, 1, 0, 1], [0, 1, 1, 0, 1], [-1], [0], [0], [0], [-1], [-1, -1, -1, 0, -1], [0, -1, -1, 0, -1], [1]], [[1], [0, -1, -1, 0, -1], [-1, -1, -1, 0, -1], [-1], [0], [0], [0], [-1], [0, 1, 1, 0, 1], [1, 1, 1, 0, 1], [1]], [[1], [-1]], [[1]], [[1], [0], [1]]]}, {'Sign': 0, 'Character': [[10], [-2], [1], [1], [0], [0], [1], [0, 1, 1, 0, 1], [-1, -1, -1, 0, -1]], 'GalOrbIndex': 2, 'HardFactors': [10, 11, 12], 'LocalFactors': [[[1], [-10], [45], [-120], [210], [-252], [210], [-120], [45], [-10], [1]], [[1], [2], [-3], [-8], [2], [12], [2], [-8], [-3], [2], [1]], [[1], [-1], [0], [-3], [3], [0], [3], [-3], [0], [-1], [1]], [[1], [-1], [0], [-3], [3], [0], [3], [-3], [0], [-1], [1]], [[1], [0], [1], [0], [-2], [0], [-2], [0], [1], [0], [1]], [[1], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [1]], [[1], [-1], [0], [1], [-1], [0], [-1], [1], [0], [-1], [1]], [[1], [0, -1, -1, 0, -1], [-1, -1, -1, 0, -1], [-1], [0], [0], [0], [-1], [0, 1, 1, 0, 1], [1, 1, 1, 0, 1], [1]], [[1], [1, 1, 1, 0, 1], [0, 1, 1, 0, 1], [-1], [0], [0], [0], [-1], [-1, -1, -1, 0, -1], [0, -1, -1, 0, -1], [1]], [[1], [-1]], [[1]], [[1], [0], [1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '7T6', 'Galt': 6, 'HardPrimes': [2, 3, 7], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-3, 1, 3, -9, 3, 3, -3, 1], 'NumBadPrimes': 3, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [-3, 1, 3, -9, 3, 3, -3, 1], 'Proj_nTj': [7, 6]}
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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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.112021056.7t6.a', 'Character': [[6], [2], [3], [0], [0], [1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '10.14117306610774528.70.a', 'Character': [[10, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [-1, -1, -1, 0, -1, 0], [0, 1, 1, 0, 1, 0]], 'CharacterField': 7}, {'GalConj': 2, 'Baselabel': '10.14117306610774528.70.a', 'Character': [[10, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [1, 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, 1, 0, 1, 0], [-1, -1, -1, 0, -1, 0]], 'CharacterField': 7}, {'GalConj': 1, 'Baselabel': '14.21964383255760327839744.15t47.a', 'Character': [[14], [2], [-1], [2], [0], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.21964383255760327839744.21t33.a', 'Character': [[14], [2], [2], [-1], [0], [-1], [2], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '15.197679449301842950557696.42t294.a', 'Character': [[15], [-1], [3], [0], [-1], [0], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.1793685113483563715477940482605056.42t299.a', 'Character': [[21], [1], [-3], [0], [-1], [1], [1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.354574685454344552857366707698313319755263283342109310976.70.a', 'Character': [[35], [-1], [-1], [-1], [1], [0], [-1], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7]}, {'Size': '105', 'Order': 2, 'Representative': [2, 1, 4, 3, 5, 6, 7]}, {'Size': '70', 'Order': 3, 'Representative': [2, 3, 1, 4, 5, 6, 7]}, {'Size': '280', 'Order': 3, 'Representative': [2, 3, 1, 5, 6, 4, 7]}, {'Size': '630', 'Order': 4, 'Representative': [2, 3, 4, 1, 6, 5, 7]}, {'Size': '504', 'Order': 5, 'Representative': [2, 3, 4, 5, 1, 6, 7]}, {'Size': '210', 'Order': 6, 'Representative': [2, 3, 1, 5, 4, 7, 6]}, {'Size': '360', 'Order': 7, 'Representative': [2, 3, 4, 5, 6, 7, 1]}, {'Size': '360', 'Order': 7, 'Representative': [3, 1, 4, 5, 6, 7, 2]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 3]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [1, 1, 5]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [1, 2, 4]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 3, 3]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [2, 2, 3]}, {'Data': [2, 3, 4, 5, 6, 7, 1], 'Classes': [{'RootOf': ['-84672', '1'], 'ConjugacyClass': 8}, {'RootOf': ['84672', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'ALT', 'CycleType': [7]}], 'Frobs': [4, 5, 7, 5, 8, 9, 6, 5, 8, 5, 5, 8, 8, 5, 8, 4, 9, 8, 6, 5, 9, 5, 5, 9, 5, 9, 8, 6, 5, 5, 9, 9, 9, 9, 6, 6, 7, 7, 5, 6, 6, 6, 9, 8, 8, 4, 5, 8, 6, 6, 6, 6, 3, 4, 8, 7, 6, 6, 8, 9, 6, 6, 9, 4, 6, 5, 5, 5, 6, 8, 5, 8, 5, 6, 4, 6, 8, 7, 5, 6, 6, 4, 8, 8, 5, 5, 8, 6, 8, 4, 7, 9, 7, 6, 5, 8, 7, 6, 5, 6, 9, 4, 8, 8, 7, 8, 5, 9, 9, 6, 5, 8, 6, 6, 7, 5, 7, 4, 5, 2, 5, 8, 5, 5, 8, 4, 6, 2, 5, 9, 5, 3, 7, 6, 4, 9, 2, 4, 7, 5, 5, 3, 7, 6, 4, 5, 7, 5, 4, 8, 5, 7, 6, 4, 8, 9, 9, 4, 5, 5, 8, 8, 5, 6, 7, 8, 4, 6], 'G-Gens': [[1, 2, 4, 5, 6, 7, 3], [2, 3, 1, 4, 5, 6, 7]], 'G-Name': 'A7', 'Polynomial': [-3, 1, 3, -9, 3, 3, -3, 1], 'QpRts': [['-33607789329806', '-32820984033063'], ['-32702723633905', '0'], ['-58689137160182', '0'], ['-37581961136268', '32820984033063'], ['60819929144853', '-15696239361142'], ['26003223887046', '15696239361142'], ['-48528933179034', '0']], 'QpRts-minpoly': [2, 655, 1], 'QpRts-p': 659, 'QpRts-prec': 5, 'Size': 2520, 'TransitiveDegree': 7}