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artin_reps • Show schema
{'BadPrimes': [73, 709], 'Baselabel': '9.19222708129279278029545878649.20t145.a', 'CharacterField': 1, 'Conductor': 19222708129279278029545878649, 'Container': '20t145', 'Dets': ['1.1.1t1.a.a'], 'Dim': 9, 'GalConjSigns': [1], 'Galn': 6, 'GaloisConjugates': [{'Sign': 1, 'Character': [[9], [-3], [-3], [1], [0], [0], [1], [1], [-1], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [12, 13], 'LocalFactors': [[[1], [-9], [36], [-84], [126], [-126], [84], [-36], [9], [-1]], [[1], [3], [0], [-8], [-6], [6], [8], [0], [-3], [-1]], [[1], [3], [0], [-8], [-6], [6], [8], [0], [-3], [-1]], [[1], [-1], [-4], [4], [6], [-6], [-4], [4], [1], [-1]], [[1], [0], [0], [-3], [0], [0], [3], [0], [0], [-1]], [[1], [0], [0], [-3], [0], [0], [3], [0], [0], [-1]], [[1], [-1], [0], [0], [-2], [2], [0], [0], [1], [-1]], [[1], [-1], [0], [0], [-2], [2], [0], [0], [1], [-1]], [[1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1]], [[1], [0], [0], [1], [0], [0], [-1], [0], [0], [-1]], [[1], [0], [0], [1], [0], [0], [-1], [0], [0], [-1]], [[1], [1], [-1], [-1]], [[1], [-1], [1], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '6T16', 'Galt': 16, 'HardPrimes': [73, 709], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [1, 1, -2, -2, 0, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [720, 763], 'Proj_Polynomial': [1, 1, -2, -2, 0, 0, 1], 'Proj_nTj': [6, 16]} -
artin_field_data • Show schema
{'ArtinReps': [{'GalConj': 1, 'Baselabel': '1.1.1t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.51757.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.51757.6t16.a', 'Character': [[5], [-1], [3], [1], [-1], [2], [-1], [1], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.2678787049.12t183.a', 'Character': [[5], [-3], [1], [1], [2], [-1], [-1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.7175900053890128401.12t183.a', 'Character': [[5], [1], [-3], [1], [-1], [2], [-1], [-1], [0], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.138645981295093.6t16.a', 'Character': [[5], [3], [-1], [1], [2], [-1], [-1], [1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '9.138645981295093.10t32.a', 'Character': [[9], [3], [3], [1], [0], [0], [1], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '9.19222708129279278029545878649.20t145.a', 'Character': [[9], [-3], [-3], [1], [0], [0], [1], [1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '10.19222708129279278029545878649.30t164.a', 'Character': [[10], [2], [-2], [-2], [1], [1], [0], [0], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '10.7175900053890128401.30t164.a', 'Character': [[10], [-2], [2], [-2], [1], [1], [0], [0], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '16.51493541583420347689617739076266816801.36t1252.a', 'Character': [[16], [0], [0], [0], [-2], [-2], [0], [0], [1], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 4, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6]}, {'Size': '15', 'Order': 2, 'Representative': [2, 1, 4, 3, 6, 5]}, {'Size': '15', 'Order': 2, 'Representative': [2, 1, 3, 4, 5, 6]}, {'Size': '45', 'Order': 2, 'Representative': [2, 1, 4, 3, 5, 6]}, {'Size': '40', 'Order': 3, 'Representative': [2, 3, 1, 5, 6, 4]}, {'Size': '40', 'Order': 3, 'Representative': [2, 3, 1, 4, 5, 6]}, {'Size': '90', 'Order': 4, 'Representative': [2, 3, 4, 1, 6, 5]}, {'Size': '90', 'Order': 4, 'Representative': [2, 3, 4, 1, 5, 6]}, {'Size': '144', 'Order': 5, 'Representative': [2, 3, 4, 5, 1, 6]}, {'Size': '120', 'Order': 6, 'Representative': [2, 3, 4, 5, 6, 1]}, {'Size': '120', 'Order': 6, 'Representative': [2, 3, 1, 5, 4, 6]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 2]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 3]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [1, 1, 4]}, {'Data': 0, 'Classes': 11, 'Algorithm': 'CYC', 'CycleType': [1, 2, 3]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [1, 5]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [2, 4]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [3, 3]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [6]}], 'Frobs': [10, 7, 10, 11, 10, 9, 9, 5, 10, 11, 9, 11, 10, 11, 11, 6, 8, 10, 9, 8, 4, 10, 7, 11, 11, 9, 10, 6, 11, 2, 7, 4, 8, 9, 7, 8, 10, 11, 4, 10, 10, 9, 10, 10, 9, 8, 9, 11, 5, 9, 7, 7, 7, 9, 6, 8, 10, 11, 10, 4, 7, 9, 9, 11, 10, 8, 9, 6, 8, 11, 8, 8, 10, 4, 6, 10, 5, 9, 9, 8, 10, 9, 10, 7, 8, 9, 7, 7, 7, 7, 4, 9, 5, 11, 10, 10, 8, 11, 5, 5, 8, 10, 8, 11, 8, 10, 9, 5, 9, 8, 9, 9, 9, 11, 10, 10, 4, 11, 8, 11, 6, 6, 6, 11, 9, 7, 8, 4, 8, 11, 10, 11, 7, 9, 7, 11, 10, 4, 8, 7, 7, 9, 9, 11, 9, 6, 7, 11, 5, 6, 11, 10, 4, 3, 9, 9, 9, 10, 7, 10, 9, 11, 3, 8, 11, 10, 9, 8], 'G-Gens': [[2, 1, 3, 4, 5, 6], [2, 3, 4, 5, 6, 1]], 'G-Name': 'S6', 'Polynomial': [1, 1, -2, -2, 0, 0, 1], 'QpRts': [['-1325132727', '4731149224'], ['3646563994', '1287852260'], ['-6339342869', '-2632596921'], ['2543948285', '-1287852260'], ['-138057733', '-4731149224'], ['1612021050', '2632596921']], 'QpRts-minpoly': [3, 101, 1], 'QpRts-p': 113, 'QpRts-prec': 5, 'Size': 720, 'TransitiveDegree': 6}
Artin representation data - 9.19222708129279278029545878649.20t145.a