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artin_reps • Show schema
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{'BadPrimes': [29, 43, 241], 'Baselabel': '6.300527.7t7.a', 'CharacterField': 1, 'Conductor': 300527, 'Container': '7t7', 'Dets': ['1.300527.2t1.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, 17, 17], '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], [-3], [2], [2], [-3], [1]], [[1], [-1], [0], [0], [-1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '7T7', 'Galt': 7, 'HardPrimes': [29, 43, 241], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [1, -3, 4, -2, 0, 2, -2, 1], 'NumBadPrimes': 3, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [1, -3, 4, -2, 0, 2, -2, 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': '1.300527.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [-1], [1], [1], [1], [-1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.2451418618672605445461951407.14t46.a', 'Character': [[6], [-4], [0], [2], [3], [0], [-2], [0], [1], [-1], [-1], [0], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.300527.7t7.a', 'Character': [[6], [4], [0], [2], [3], [0], [2], [0], [1], [-1], [1], [0], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.8157066149372952997441.21t38.a', 'Character': [[14], [6], [2], [2], [2], [-1], [0], [0], [-1], [2], [0], [-1], [0], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.6009453243974704947599620664727261140560621332429279649.42t413.a', 'Character': [[14], [-6], [-2], [2], [2], [-1], [0], [0], [-1], [2], [0], [1], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.19996383832316913114627373463040795471157737349487.30t565.a', 'Character': [[14], [-4], [0], [2], [-1], [2], [2], [0], [-1], [-1], [-1], [0], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.2451418618672605445461951407.30t565.a', 'Character': [[14], [4], [0], [2], [-1], [2], [-2], [0], [-1], [-1], [1], [0], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '15.2451418618672605445461951407.42t412.a', 'Character': [[15], [5], [-3], [-1], [3], [0], [1], [-1], [0], [-1], [-1], [0], [1], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '15.6009453243974704947599620664727261140560621332429279649.42t411.a', 'Character': [[15], [-5], [3], [-1], [3], [0], [-1], [-1], [0], [-1], [1], [0], [1], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '20.6009453243974704947599620664727261140560621332429279649.70.a', 'Character': [[20], [0], [0], [-4], [2], [2], [0], [0], [0], [2], [0], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.6009453243974704947599620664727261140560621332429279649.84.a', 'Character': [[21], [1], [-3], [1], [-3], [0], [-1], [-1], [1], [1], [1], [0], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.1806002955051986153787271199508489608789261847170974125075023.42t418.a', 'Character': [[21], [-1], [3], [1], [-3], [0], [1], [-1], [1], [1], [-1], [0], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.36113528291518104666591420673305289609125534029022793754436627174830601817326103924195860601430025953045563201.126.a', 'Character': [[35], [-5], [-1], [-1], [-1], [-1], [1], [1], [0], [-1], [1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.14731685570322079005748799878628717614101803413780121115800597444655009266852016143.70.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, 13, 12, 13, 10, 15, 13, 12, 12, 2, 8, 11, 12, 7, 14, 13, 6, 8, 9, 13, 12, 15, 9, 15, 14, 13, 12, 9, 14, 9, 8, 12, 15, 12, 13, 15, 12, 15, 12, 12, 6, 13, 13, 3, 15, 9, 9, 11, 9, 3, 15, 8, 7, 11, 12, 7, 6, 12, 14, 6, 11, 4, 8, 9, 12, 8, 4, 14, 14, 15, 12, 12, 13, 13, 8, 9, 11, 12, 5, 12, 8, 8, 3, 9, 15, 13, 14, 12, 10, 13, 5, 14, 9, 13, 13, 15, 13, 13, 12, 12, 14, 8, 11, 12, 8, 14, 13, 9, 13, 13, 13, 7, 14, 13, 9, 13, 10, 5, 12, 11, 14, 12, 3, 8, 15, 15, 12, 13, 9, 8, 8, 8, 7, 12, 8, 8, 8, 8, 8, 13, 8, 13, 11, 13, 6, 8, 13, 9, 14, 4, 13, 14, 6, 8, 9, 9, 8, 8, 12, 14, 8, 9, 15, 9, 12, 12, 11, 12], 'G-Gens': [[2, 3, 4, 5, 6, 7, 1], [2, 1, 3, 4, 5, 6, 7]], 'G-Name': 'S7', 'Polynomial': [1, -3, 4, -2, 0, 2, -2, 1], 'QpRts': [['-39485456783', '1414556890'], ['-43295195470', '-1414556890'], ['48120516104', '121524720426'], ['-47497399317', '0'], ['12685219103', '-121524720426'], ['-901201902', '-32449656024'], ['70373518267', '32449656024']], 'QpRts-minpoly': [5, 192, 1], 'QpRts-p': 193, 'QpRts-prec': 5, 'Size': 5040, 'TransitiveDegree': 7}