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artin_reps • Show schema
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{'BadPrimes': [334727], 'Baselabel': '6.334727.7t7.a', 'CharacterField': 1, 'Conductor': 334727, 'Container': '7t7', 'Dets': ['1.334727.2t1.a.a'], 'Dim': 6, 'GalConjSigns': [1], 'Galn': 7, 'GaloisConjugates': [{'Sign': 1, 'Character': [[6], [4], [0], [2], [3], [0], [2], [0], [1], [-1], [1], [0], [-1], [-1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [16], 'LocalFactors': [[[1], [-6], [15], [-20], [15], [-6], [1]], [[1], [-4], [5], [0], [-5], [4], [-1]], [[1], [0], [-3], [0], [3], [0], [-1]], [[1], [-2], [-1], [4], [-1], [-2], [1]], [[1], [-3], [3], [-2], [3], [-3], [1]], [[1], [0], [0], [-2], [0], [0], [1]], [[1], [-2], [1], [0], [-1], [2], [-1]], [[1], [0], [-1], [0], [-1], [0], [1]], [[1], [-1], [0], [0], [0], [-1], [1]], [[1], [1], [-1], [-2], [-1], [1], [1]], [[1], [-1], [-1], [0], [1], [1], [-1]], [[1], [0], [0], [0], [0], [0], [-1]], [[1], [1], [1], [1], [1], [1], [1]], [[1], [1], [0], [0], [0], [-1], [-1]], [[1], [1], [1], [0], [-1], [-1], [-1]], [[1], [-1], [0], [0], [-1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '7T7', 'Galt': 7, 'HardPrimes': [334727], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [1, 1, 2, -1, -2, -1, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [1, 1, 2, -1, -2, -1, 0, 1], 'Proj_nTj': [7, 7]}
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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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.334727.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [-1], [1], [1], [1], [-1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.4201977530904444663185562407.14t46.a', 'Character': [[6], [-4], [0], [2], [3], [0], [-2], [0], [1], [-1], [-1], [0], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.334727.7t7.a', 'Character': [[6], [4], [0], [2], [3], [0], [2], [0], [1], [-1], [1], [0], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.12553446632343505791841.21t38.a', 'Character': [[14], [6], [2], [2], [2], [-1], [0], [0], [-1], [2], [0], [-1], [0], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.17656615170225813204486323058018274846363601088891633649.42t413.a', 'Character': [[14], [-6], [-2], [2], [2], [-1], [0], [0], [-1], [2], [0], [1], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.52749300684515480389948594102113886380135456921287.30t565.a', 'Character': [[14], [-4], [0], [2], [-1], [2], [2], [0], [-1], [-1], [-1], [0], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.4201977530904444663185562407.30t565.a', 'Character': [[14], [4], [0], [2], [-1], [2], [-2], [0], [-1], [-1], [1], [0], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '15.4201977530904444663185562407.42t412.a', 'Character': [[15], [5], [-3], [-1], [3], [0], [1], [-1], [0], [-1], [-1], [0], [1], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '15.17656615170225813204486323058018274846363601088891633649.42t411.a', 'Character': [[15], [-5], [3], [-1], [3], [0], [-1], [-1], [0], [-1], [1], [0], [1], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '20.17656615170225813204486323058018274846363601088891633649.70.a', 'Character': [[20], [0], [0], [-4], [2], [2], [0], [0], [0], [2], [0], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.17656615170225813204486323058018274846363601088891633649.84.a', 'Character': [[21], [1], [-3], [1], [-3], [0], [-1], [-1], [1], [1], [1], [0], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.5910145826084175776498093458241283084498749101681429856428823.42t418.a', 'Character': [[21], [-1], [3], [1], [-3], [0], [1], [-1], [1], [1], [-1], [0], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.311756059269448322603890039130772905531122835827885265690089115159043234229536816867090967782542630788029055201.126.a', 'Character': [[35], [-5], [-1], [-1], [-1], [-1], [1], [1], [0], [-1], [1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.74192700217115423471860801950206076411859387331892352890877718624431817789070633143.70.a', 'Character': [[35], [5], [1], [-1], [-1], [-1], [-1], [1], [0], [-1], [-1], [1], [0], [0], [-1]], 'CharacterField': 1}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7]}, {'Size': '21', 'Order': 2, 'Representative': [2, 1, 3, 4, 5, 6, 7]}, {'Size': '105', 'Order': 2, 'Representative': [2, 1, 4, 3, 6, 5, 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': '210', 'Order': 4, 'Representative': [2, 3, 4, 1, 5, 6, 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': '420', 'Order': 6, 'Representative': [2, 3, 1, 5, 4, 6, 7]}, {'Size': '840', 'Order': 6, 'Representative': [2, 3, 4, 5, 6, 1, 7]}, {'Size': '720', 'Order': 7, 'Representative': [2, 3, 4, 5, 6, 7, 1]}, {'Size': '504', 'Order': 10, 'Representative': [2, 3, 4, 5, 1, 7, 6]}, {'Size': '420', 'Order': 12, 'Representative': [2, 3, 4, 1, 6, 7, 5]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 3]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 4]}, {'Data': 0, 'Classes': 11, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 3]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [1, 1, 5]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 2]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [1, 2, 4]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [1, 3, 3]}, {'Data': 0, 'Classes': 12, 'Algorithm': 'CYC', 'CycleType': [1, 6]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [2, 2, 3]}, {'Data': 0, 'Classes': 14, 'Algorithm': 'CYC', 'CycleType': [2, 5]}, {'Data': 0, 'Classes': 15, 'Algorithm': 'CYC', 'CycleType': [3, 4]}, {'Data': 0, 'Classes': 13, 'Algorithm': 'CYC', 'CycleType': [7]}], 'Frobs': [13, 10, 15, 15, 13, 6, 12, 15, 15, 13, 3, 13, 12, 11, 8, 12, 7, 10, 12, 8, 12, 11, 8, 6, 15, 9, 8, 9, 9, 7, 15, 8, 13, 13, 13, 13, 9, 12, 6, 14, 13, 12, 9, 13, 13, 12, 11, 14, 12, 13, 12, 3, 14, 15, 8, 4, 15, 6, 12, 9, 9, 13, 12, 12, 11, 13, 13, 8, 12, 6, 13, 13, 15, 15, 11, 7, 8, 9, 3, 15, 12, 11, 9, 8, 12, 13, 8, 9, 6, 7, 13, 12, 8, 9, 15, 9, 9, 13, 12, 11, 12, 14, 13, 15, 11, 12, 12, 14, 8, 10, 14, 10, 9, 8, 12, 10, 15, 9, 12, 9, 13, 12, 10, 12, 14, 14, 14, 12, 6, 11, 15, 3, 8, 6, 9, 11, 11, 7, 13, 10, 13, 8, 6, 15, 11, 12, 15, 12, 12, 11, 8, 12, 6, 13, 8, 12, 11, 13, 11, 14, 11, 5, 14, 12, 11, 11, 7, 12], 'G-Gens': [[2, 3, 4, 5, 6, 7, 1], [2, 1, 3, 4, 5, 6, 7]], 'G-Name': 'S7', 'Polynomial': [1, 1, 2, -1, -2, -1, 0, 1], 'QpRts': [['-4762273', '-9850434'], ['-11983860', '0'], ['-693656', '-151253'], ['3692681', '151253'], ['13028992', '-5684663'], ['6109313', '5684663'], ['-5391197', '9850434']], 'QpRts-minpoly': [3, 29, 1], 'QpRts-p': 31, 'QpRts-prec': 5, 'Size': 5040, 'TransitiveDegree': 7}