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artin_reps • Show schema
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{'BadPrimes': [2, 3], 'Baselabel': '14.682326912718312833024.30t565.a', 'CharacterField': 1, 'Conductor': 682326912718312833024, 'Container': '30t565', 'Dets': ['1.4.2t1.a.a'], 'Dim': 14, 'GalConjSigns': [1], 'Galn': 7, 'GaloisConjugates': [{'Sign': 1, 'Character': [[14], [4], [0], [2], [-1], [2], [-2], [0], [-1], [-1], [1], [0], [0], [-1], [1]], 'GalOrbIndex': 1, 'HardFactors': [16, 16], 'LocalFactors': [[[1], [-14], [91], [-364], [1001], [-2002], [3003], [-3432], [3003], [-2002], [1001], [-364], [91], [-14], [1]], [[1], [-4], [1], [16], [-19], [-20], [45], [0], [-45], [20], [19], [-16], [-1], [4], [-1]], [[1], [0], [-7], [0], [21], [0], [-35], [0], [35], [0], [-21], [0], [7], [0], [-1]], [[1], [-2], [-5], [12], [9], [-30], [-5], [40], [-5], [-30], [9], [12], [-5], [-2], [1]], [[1], [1], [1], [-4], [-4], [-4], [6], [6], [6], [-4], [-4], [-4], [1], [1], [1]], [[1], [-2], [1], [-4], [8], [-4], [6], [-12], [6], [-4], [8], [-4], [1], [-2], [1]], [[1], [2], [1], [0], [-3], [-6], [-3], [0], [3], [6], [3], [0], [-1], [-2], [-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], [1], [1], [0], [0], [0], [-2], [-2], [-2], [0], [0], [0], [1], [1], [1]], [[1], [-1], [1], [-2], [2], [-2], [0], [0], [0], [2], [-2], [2], [-1], [1], [-1]], [[1], [0], [-1], [0], [0], [0], [-2], [0], [2], [0], [0], [0], [1], [0], [-1]], [[1], [0], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [0], [0], [1]], [[1], [1], [1], [1], [1], [0], [0], [0], [0], [0], [-1], [-1], [-1], [-1], [-1]], [[1], [-1], [1], [0], [0], [0], [0], [0], [0], [0], [0], [0], [-1], [1], [-1]], [[1], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '7T7', 'Galt': 7, 'HardPrimes': [2, 3], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [6, 19, 12, 3, -2, -3, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [6, 19, 12, 3, -2, -3, 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': '1.4.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [-1], [1], [1], [1], [-1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.967458816.14t46.a', 'Character': [[6], [-4], [0], [2], [3], [0], [-2], [0], [1], [-1], [-1], [0], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.60466176.7t7.b', 'Character': [[6], [4], [0], [2], [3], [0], [2], [0], [1], [-1], [1], [0], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.6140942214464815497216.21t38.a', 'Character': [[14], [6], [2], [2], [2], [-1], [0], [0], [-1], [2], [0], [-1], [0], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.393020301725748191821824.42t413.a', 'Character': [[14], [-6], [-2], [2], [2], [-1], [0], [0], [-1], [2], [0], [1], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.10917230603493005328384.30t565.a', 'Character': [[14], [-4], [0], [2], [-1], [2], [2], [0], [-1], [-1], [-1], [0], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.682326912718312833024.30t565.a', 'Character': [[14], [4], [0], [2], [-1], [2], [-2], [0], [-1], [-1], [1], [0], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '15.3537182715531733726396416.42t412.a', 'Character': [[15], [5], [-3], [-1], [3], [0], [1], [-1], [0], [-1], [-1], [0], [1], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '15.56594923448507739622342656.42t411.a', 'Character': [[15], [-5], [3], [-1], [3], [0], [-1], [-1], [0], [-1], [1], [0], [1], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '20.13688314407775983685466978280013824.70.a', 'Character': [[20], [0], [0], [-4], [2], [2], [0], [0], [0], [2], [0], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.277188366757463669630706310170279936.84.a', 'Character': [[21], [1], [-3], [1], [-3], [0], [-1], [-1], [1], [1], [1], [0], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.277188366757463669630706310170279936.42t418.a', 'Character': [[21], [-1], [3], [1], [-3], [0], [1], [-1], [1], [1], [-1], [0], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.15687454397455543882046198280554209995350191319756531633750016.126.a', 'Character': [[35], [-5], [-1], [-1], [-1], [-1], [1], [1], [0], [-1], [1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.245116474960242873156971848133659531177346739371195806777344.70.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': [4, 3, 13, 15, 12, 9, 13, 15, 15, 9, 14, 8, 13, 7, 12, 6, 12, 10, 12, 12, 13, 14, 14, 6, 8, 9, 14, 14, 13, 13, 12, 12, 8, 12, 13, 11, 8, 12, 12, 13, 11, 8, 14, 9, 9, 7, 12, 14, 12, 13, 13, 7, 13, 11, 8, 11, 13, 12, 13, 5, 11, 13, 14, 14, 4, 13, 12, 4, 14, 8, 8, 11, 7, 9, 12, 12, 8, 13, 13, 9, 12, 10, 12, 13, 12, 7, 10, 9, 13, 15, 11, 12, 15, 14, 14, 7, 9, 8, 11, 8, 11, 9, 15, 13, 12, 9, 12, 13, 15, 9, 11, 8, 13, 14, 14, 8, 15, 12, 8, 12, 13, 13, 9, 11, 12, 13, 13, 2, 12, 8, 15, 14, 14, 13, 10, 13, 10, 11, 13, 8, 14, 8, 12, 7, 10, 12, 13, 8, 11, 15, 13, 8, 12, 15, 15, 12, 12, 5, 8, 8, 12, 6, 12, 12, 9, 11, 11, 9], 'G-Gens': [[2, 3, 4, 5, 6, 7, 1], [2, 1, 3, 4, 5, 6, 7]], 'G-Name': 'S7', 'Polynomial': [6, 19, 12, 3, -2, -3, 0, 1], 'QpRts': [['-328061809968', '0'], ['801313530074', '-694526001075'], ['1149655093703', '0'], ['808310404709', '-1300864942087'], ['-194463057772', '694526001075'], ['-752877385370', '0'], ['-1483876775376', '1300864942087']], 'QpRts-minpoly': [10, 310, 1], 'QpRts-p': 313, 'QpRts-prec': 5, 'Size': 5040, 'TransitiveDegree': 7}