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artin_reps • Show schema
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{'BadPrimes': [17, 11863], 'Baselabel': '14.1654145878304378602081.21t38.a', 'CharacterField': 1, 'Conductor': 1654145878304378602081, 'Container': '21t38', 'Dets': ['1.1.1t1.a.a'], 'Dim': 14, 'GalConjSigns': [1], 'Galn': 7, 'GaloisConjugates': [{'Sign': 1, 'Character': [[14], [6], [2], [2], [2], [-1], [0], [0], [-1], [2], [0], [-1], [0], [1], [0]], 'GalOrbIndex': 1, 'HardFactors': [16, 17], 'LocalFactors': [[[1], [-14], [91], [-364], [1001], [-2002], [3003], [-3432], [3003], [-2002], [1001], [-364], [91], [-14], [1]], [[1], [-6], [11], [4], [-39], [38], [27], [-72], [27], [38], [-39], [4], [11], [-6], [1]], [[1], [-2], [-5], [12], [9], [-30], [-5], [40], [-5], [-30], [9], [12], [-5], [-2], [1]], [[1], [-2], [-5], [12], [9], [-30], [-5], [40], [-5], [-30], [9], [12], [-5], [-2], [1]], [[1], [-2], [1], [-4], [8], [-4], [6], [-12], [6], [-4], [8], [-4], [1], [-2], [1]], [[1], [1], [1], [-4], [-4], [-4], [6], [6], [6], [-4], [-4], [-4], [1], [1], [1]], [[1], [0], [-1], [0], [-3], [0], [3], [0], [3], [0], [-3], [0], [-1], [0], [1]], [[1], [0], [-1], [0], [-3], [0], [3], [0], [3], [0], [-3], [0], [-1], [0], [1]], [[1], [1], [1], [1], [1], [-2], [-2], [-2], [-2], [-2], [1], [1], [1], [1], [1]], [[1], [-2], [1], [0], [0], [0], [-2], [4], [-2], [0], [0], [0], [1], [-2], [1]], [[1], [0], [-1], [-2], [0], [2], [0], [0], [0], [2], [0], [-2], [-1], [0], [1]], [[1], [1], [1], [0], [0], [0], [-2], [-2], [-2], [0], [0], [0], [1], [1], [1]], [[1], [0], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [0], [0], [1]], [[1], [-1], [1], [-1], [1], [-2], [2], [-2], [2], [-2], [1], [-1], [1], [-1], [1]], [[1], [0], [-1], [0], [0], [0], [0], [0], [0], [0], [0], [0], [-1], [0], [1]], [[1], [-2], [-3], [8], [2], [-12], [2], [8], [-3], [-2], [1]], [[1], [0], [-1], [0], [-2], [0], [2], [0], [1], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '7T7', 'Galt': 7, 'HardPrimes': [17, 11863], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-1, 2, -2, 2, -2, 2, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [-1, 2, -2, 2, -2, 2, -1, 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': '1.201671.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [-1], [1], [1], [1], [-1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.333593253423522337060277351.14t46.a', 'Character': [[6], [-4], [0], [2], [3], [0], [-2], [0], [1], [-1], [-1], [0], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.201671.7t7.a', 'Character': [[6], [4], [0], [2], [3], [0], [2], [0], [1], [-1], [1], [0], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.1654145878304378602081.21t38.a', 'Character': [[14], [6], [2], [2], [2], [-1], [0], [0], [-1], [2], [0], [-1], [0], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.111284458729690397455571927193624784131011933043577201.42t413.a', 'Character': [[14], [-6], [-2], [2], [2], [-1], [0], [0], [-1], [2], [0], [1], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.551811905180667510229888914090894497131525767431.30t565.a', 'Character': [[14], [-4], [0], [2], [-1], [2], [2], [0], [-1], [-1], [-1], [0], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.333593253423522337060277351.30t565.a', 'Character': [[14], [4], [0], [2], [-1], [2], [-2], [0], [-1], [-1], [1], [0], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '15.333593253423522337060277351.42t412.a', 'Character': [[15], [5], [-3], [-1], [3], [0], [1], [-1], [0], [-1], [-1], [0], [1], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '15.111284458729690397455571927193624784131011933043577201.42t411.a', 'Character': [[15], [-5], [3], [-1], [3], [0], [-1], [-1], [0], [-1], [1], [0], [1], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '20.111284458729690397455571927193624784131011933043577201.70.a', 'Character': [[20], [0], [0], [-4], [2], [2], [0], [0], [0], [2], [0], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.111284458729690397455571927193624784131011933043577201.84.a', 'Character': [[21], [1], [-3], [1], [-3], [0], [-1], [-1], [1], [1], [1], [0], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.22442848076475392145262646129065503840485307548831257702871.42t418.a', 'Character': [[21], [-1], [3], [1], [-3], [0], [1], [-1], [1], [1], [-1], [0], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.12384230754760165309743878134386520354261437970681714338033458818773445356806976861713923677378038446994401.126.a', 'Character': [[35], [-5], [-1], [-1], [-1], [-1], [1], [1], [0], [-1], [1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.37123744643113121409753622964537691085083884963308363371092428280694938240274551.70.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, 13, 15, 13, 12, 4, 12, 8, 10, 12, 9, 9, 14, 9, 13, 7, 8, 12, 9, 15, 8, 15, 15, 6, 11, 12, 12, 6, 11, 14, 14, 8, 11, 15, 14, 12, 12, 6, 13, 14, 6, 10, 8, 14, 8, 8, 8, 8, 8, 8, 5, 14, 11, 12, 6, 13, 9, 3, 11, 15, 9, 8, 6, 13, 9, 9, 13, 15, 9, 7, 15, 14, 13, 9, 15, 8, 15, 8, 13, 8, 6, 11, 11, 13, 12, 13, 4, 12, 15, 11, 12, 14, 14, 6, 9, 8, 10, 8, 8, 12, 11, 7, 6, 9, 8, 9, 15, 6, 12, 13, 12, 9, 11, 14, 3, 13, 3, 11, 12, 12, 6, 15, 14, 13, 10, 10, 11, 7, 12, 12, 12, 8, 9, 12, 8, 6, 11, 12, 13, 13, 14, 11, 12, 13, 12, 8, 14, 4, 12, 3, 12, 7, 8, 12, 8, 13, 13, 13, 10, 13, 12, 3, 12, 8, 13, 12, 12], 'G-Gens': [[2, 3, 4, 5, 6, 7, 1], [2, 1, 3, 4, 5, 6, 7]], 'G-Name': 'S7', 'Polynomial': [-1, 2, -2, 2, -2, 2, -1, 1], 'QpRts': [['513566149707', '762715551533'], ['-637809765580', '374411763055'], ['442143432366', '338248744367'], ['-486672257759', '-374411763055'], ['811363306906', '0'], ['271012249761', '-762715551533'], ['717189909757', '-338248744367']], 'QpRts-minpoly': [5, 274, 1], 'QpRts-p': 277, 'QpRts-prec': 5, 'Size': 5040, 'TransitiveDegree': 7}