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hmf_forms • Show schema
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{'deg': 4, 'dimension': 1, 'disc': 4752, 'field_bad_primes': [2, 3, 11], 'field_label': '4.4.4752.1', 'is_CM': 'yes', 'is_base_change': 'yes', 'label': '4.4.4752.1-9.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [3], 'level_ideal': '[9, 3, -w^2 + w + 2]', 'level_label': '9.1', 'level_norm': 9, 'parallel_weight': 2, 'short_label': '9.1-b', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[3, 3, -w - 1]', -1]], 'hecke_eigenvalues': [0, -4, 0, -4, -4, 0, 0, 0, 0, 0, 0, -10, -10, 0, 0, -16, -16, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 20, 20, -22, -22, -22, -22, -22, -10, 0, 0, 0, 0, 14, 14, 0, 0, 0, 0, -4, -4, -4, -4, 8, 8, 0, 0, -28, -28, -16, -16, 0, 0, 32, 32, 0, 0, 0, 0, -10, -10, 0, 0, 0, 0, 14, 14, 0, 0, -40, -40, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, -46, 20, 20, 2, 2, 2, 2, 0, 0, 0, 0, -10, -10, -34, -34, 14, 0, 0, 50, 50, 50, 50, -46, -46, 0, 0, 44, 44, 44, 44, 0, 0, -4, -4, 0, 0, 0, 0, 50, 50, 0, 0, 0, 0, 20, 20, 20, 20, 0, 0, -40, -40, -46, -46, 0, 0, -58, -58, 0, 0, 0, 0, 0, 0, 38, 38, 0, 0, 62, 62, 0, 0, 0, 0, 62, 62], 'hecke_polynomial': 'x', 'label': '4.4.4752.1-9.1-b'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 4752, 'ideals': ['[1, 1, 1]', '[3, 3, -w - 1]', '[4, 2, -w^3 + w^2 + 3*w]', '[9, 3, -w^2 + w + 2]', '[11, 11, -w^2 + 3]', '[12, 6, w^3 - w^2 - 3*w + 2]', '[13, 13, w^3 - 2*w^2 - w + 1]', '[13, 13, w^3 - w^2 - 2*w + 1]', '[16, 2, 2]', '[23, 23, -w^3 + w^2 + 4*w - 2]', '[23, 23, w^3 - 2*w^2 - 3*w + 2]', '[27, 3, w^3 - 3*w - 2]', '[33, 33, 2*w - 1]', '[36, 6, -w^3 + w^2 + 5*w]', '[39, 39, w^2 - 2*w - 3]', '[39, 39, w^2 - 4]', '[44, 22, -w^3 + w^2 + w - 2]', '[47, 47, -w^3 + 2*w^2 + 3*w - 1]', '[47, 47, -w^3 + w^2 + 4*w - 3]', '[48, 6, -2*w - 2]', '[52, 26, -w^3 + w^2 + 5*w - 2]', '[52, 26, -w^3 + 2*w^2 + 4*w - 3]', '[59, 59, w^2 - 5]', '[59, 59, w^2 - 2*w - 4]', '[61, 61, -w^3 + 2*w^2 + 4*w - 4]', '[61, 61, w^3 - w^2 - 5*w + 1]', '[64, 4, -2*w^3 + 2*w^2 + 6*w]', '[69, 69, -2*w^2 + w + 3]', '[69, 69, 2*w^2 - 3*w - 2]', '[71, 71, w^3 - w^2 - 2*w - 2]', '[71, 71, -w^3 + 2*w^2 + w - 4]', '[73, 73, 2*w^2 - w - 5]', '[73, 73, w^3 - 2*w^2 - 2*w + 6]', '[81, 3, 3]', '[83, 83, -2*w^3 + 3*w^2 + 6*w - 6]', '[83, 83, -2*w^3 + 4*w^2 + 5*w - 5]', '[83, 83, -2*w^3 + 2*w^2 + 7*w - 2]', '[83, 83, 2*w^3 - 3*w^2 - 6*w + 1]', '[92, 46, w^3 - 3*w^2 - w + 2]', '[92, 46, -w^3 + 4*w - 1]', '[97, 97, -w - 3]', '[97, 97, 2*w^2 - 3*w - 3]', '[97, 97, 2*w^2 - w - 4]', '[97, 97, w - 4]', '[99, 33, w^3 - 2*w^2 - w + 5]', '[107, 107, -w^3 + 3*w^2 - 5]', '[107, 107, -2*w^3 + w^2 + 6*w - 1]', '[107, 107, 2*w^3 - 5*w^2 - 2*w + 4]', '[107, 107, w^3 - 3*w - 3]', '[108, 6, w^3 - 3*w^2 - 3*w + 4]', '[109, 109, 2*w^3 - 3*w^2 - 5*w + 4]', '[109, 109, -2*w^3 + 3*w^2 + 5*w - 2]', '[117, 39, w^2 - 4*w + 1]', '[117, 39, -w^2 - 2*w + 2]', '[121, 11, -2*w^2 + 2*w + 5]', '[121, 11, 2*w^2 - 2*w - 3]', '[132, 66, 2*w^3 - 3*w^2 - 5*w + 3]', '[141, 141, 2*w^3 - 4*w^2 - 3*w + 3]', '[141, 141, 2*w^3 - 2*w^2 - 5*w + 2]', '[143, 143, w^3 - 5*w + 1]', '[143, 143, w^3 - 3*w^2 - 2*w + 3]', '[144, 6, -2*w^2 + 2*w + 4]', '[156, 78, -w^3 + w^2 + w + 2]', '[156, 78, w^3 - 2*w^2 + 3]', '[157, 157, 2*w^3 - 2*w^2 - 9*w + 3]', '[157, 157, -w^3 + 2*w^2 + 3*w - 7]', '[157, 157, -w^3 + w^2 + 4*w + 3]', '[157, 157, -2*w^3 + 4*w^2 + 7*w - 6]', '[169, 13, 2*w^3 - 2*w^2 - 9*w]', '[169, 13, -w^2 + w + 6]', '[169, 169, 2*w^3 - 4*w^2 - 3*w + 4]', '[169, 169, 2*w^3 - 2*w^2 - 5*w + 1]', '[176, 22, -2*w^2 + 6]', '[177, 177, -w^3 - w^2 + 5*w + 5]', '[177, 177, -w^3 + w^2 + 6*w + 4]', '[179, 179, w^3 + 2]', '[179, 179, -2*w^3 + w^2 + 10*w - 1]', '[183, 183, -2*w^3 + 3*w^2 + 8*w]', '[183, 183, w^3 - 3*w^2 - 4*w + 3]', '[188, 94, -w^2 - w + 5]', '[188, 94, -w^2 + 3*w + 3]', '[191, 191, -2*w^3 + 5*w^2 + 4*w - 7]', '[191, 191, 2*w^3 - w^2 - 8*w]', '[192, 12, 2*w^3 - 2*w^2 - 6*w + 4]', '[193, 193, 3*w^2 - 2*w - 9]', '[193, 193, 3*w^2 - 4*w - 8]', '[207, 69, -2*w^3 + 4*w^2 + 5*w - 4]', '[207, 69, 2*w^3 - 2*w^2 - 7*w + 3]', '[208, 26, 2*w^3 - 4*w^2 - 2*w + 2]', '[208, 26, 2*w^3 - 2*w^2 - 4*w + 2]', '[213, 213, -2*w^3 + 8*w + 3]', '[213, 213, w^3 - w + 3]', '[219, 219, -2*w^3 - w^2 + 6*w + 5]', '[219, 219, -w^3 + w^2 - 5]', '[227, 227, -w^3 + 3*w^2 + 3*w - 3]', '[227, 227, w^3 - 3*w - 4]', '[227, 227, -w^3 + 3*w^2 - 6]', '[227, 227, w^3 - 6*w + 2]', '[229, 229, w^3 + w^2 - 6*w - 4]', '[229, 229, w^3 + w^2 - 5*w - 3]', '[229, 229, 2*w^3 - 9*w - 3]', '[229, 229, -w^3 + 4*w^2 + w - 8]', '[236, 118, 3*w^3 - 4*w^2 - 10*w + 1]', '[236, 118, 4*w^3 - 3*w^2 - 15*w - 1]', '[241, 241, 2*w^3 - 3*w^2 - 4*w + 2]', '[241, 241, -2*w^3 + 3*w^2 + 4*w - 3]', '[243, 9, -3*w - 3]', '[244, 122, -w^3 - w^2 + 5*w + 4]', '[244, 122, 3*w^3 - w^2 - 13*w - 4]', '[249, 249, 3*w^3 - 3*w^2 - 8*w + 4]', '[249, 249, 2*w^3 - 3*w^2 - 8*w + 3]', '[249, 249, 4*w^3 - 3*w^2 - 13*w]', '[249, 249, -3*w^3 + 3*w^2 + 13*w + 1]', '[251, 251, -2*w^3 + 4*w^2 + 4*w - 1]', '[251, 251, -2*w^3 + 2*w^2 + 6*w - 5]', '[253, 253, 2*w^3 - 2*w^2 - 9*w + 2]', '[253, 253, -2*w^3 + 4*w^2 + 7*w - 7]', '[256, 4, 4]', '[276, 138, -w^3 + 2*w^2 + 2*w - 7]', '[276, 138, -w^3 + w^2 + 3*w + 4]', '[277, 277, w^3 - w^2 - 6*w + 1]', '[277, 277, -w^3 + 2*w^2 + 5*w - 5]', '[284, 142, 3*w^3 - 4*w^2 - 10*w - 1]', '[284, 142, 2*w^3 - w^2 - 7*w + 1]', '[289, 17, w^3 - w^2 - 6*w + 3]', '[289, 17, -w^3 + 2*w^2 + 5*w - 3]', '[291, 291, -2*w^3 + w^2 + 6*w + 3]', '[291, 291, w^2 + 4*w + 3]', '[291, 291, -w^2 + 3*w + 4]', '[291, 291, -2*w^3 - w^2 + 5*w + 4]', '[292, 146, 2*w^3 - 3*w^2 - 9*w + 1]', '[292, 146, -3*w^3 + 3*w^2 + 9*w - 2]', '[297, 33, -2*w^3 + 3*w^2 + 3*w - 2]', '[299, 299, -w^3 + 2*w^2 - 4]', '[299, 299, -2*w^2 + 5*w + 3]', '[299, 299, 2*w^2 + w - 6]', '[299, 299, -w^3 + w^2 + w + 3]', '[311, 311, 2*w^3 - 3*w^2 - 3*w + 6]', '[311, 311, -3*w^3 + 7*w^2 + 8*w - 12]', '[321, 321, w + 4]', '[321, 321, 5*w^3 - w^2 - 13*w - 1]', '[321, 321, -w^3 + w^2 + 6*w - 2]', '[321, 321, -3*w^3 + 10*w + 4]', '[324, 6, -3*w^3 + 3*w^2 + 9*w]', '[327, 327, 3*w^3 - 2*w^2 - 9*w + 2]', '[327, 327, 3*w^3 - 2*w^2 - 11*w]', '[332, 166, -w^2 + 3*w + 5]', '[332, 166, -2*w^3 + w^2 + 7*w + 5]', '[332, 166, -3*w^3 + 2*w^2 + 14*w + 5]', '[332, 166, 5*w^3 - 4*w^2 - 18*w - 5]', '[337, 337, -w^3 + w^2 + 4*w - 6]', '[337, 337, -2*w^3 + 3*w^2 + 8*w - 5]', '[347, 347, 2*w^3 - 6*w^2 - 5*w + 10]', '[347, 347, 4*w^3 - 5*w^2 - 13*w + 6]', '[347, 347, -4*w^3 + 7*w^2 + 11*w - 8]', '[347, 347, -2*w^3 + 11*w + 1]', '[349, 349, 3*w^2 - w - 6]', '[349, 349, -2*w^3 + 3*w^2 + 10*w + 3]', '[351, 39, -w^3 + 3*w^2 - 7]', '[351, 39, w^3 - 3*w - 5]', '[359, 359, 2*w^3 - 2*w^2 - 7*w + 4]', '[359, 359, -3*w^3 + 4*w^2 + 11*w - 7]', '[359, 359, w^3 - 2*w^2 + w - 4]', '[359, 359, 2*w^3 - 4*w^2 - 5*w + 3]', '[363, 33, -2*w^3 + w^2 + 6*w - 3]', '[363, 33, -2*w^3 + 5*w + 3]', '[368, 46, -2*w^3 + 2*w^2 + 8*w - 4]', '[368, 46, 2*w^3 - 4*w^2 - 6*w + 4]', '[373, 373, -3*w^3 + 3*w^2 + 9*w - 1]', '[373, 373, w^3 + 2*w^2 - 7*w - 9]', '[383, 383, 2*w^2 - 7]', '[383, 383, 2*w^2 - 4*w - 5]', '[388, 194, 4*w^3 - 3*w^2 - 13*w - 1]', '[388, 194, 2*w^3 - w^2 - 11*w - 1]', '[388, 194, w^3 - 2*w^2 - 6*w + 1]', '[388, 194, 3*w^3 - 4*w^2 - 8*w + 1]', '[396, 66, w^3 + w^2 - w - 4]', '[409, 409, -w^3 + 5*w^2 - 3*w - 7]', '[409, 409, -w^3 - 2*w^2 + 4*w + 6]', '[419, 419, w^3 - 3*w - 6]', '[419, 419, -w^3 + 3*w^2 - 8]', '[423, 141, -2*w^3 + w^2 + 8*w - 1]', '[423, 141, -2*w^3 + 5*w^2 + 4*w - 6]', '[428, 214, 2*w^3 - w^2 - 9*w + 1]', '[428, 214, -w^3 + 2*w^2 + 8*w + 3]', '[428, 214, 2*w^3 - 3*w^2 - 3*w - 3]', '[428, 214, 3*w^3 - 4*w^2 - 12*w - 1]', '[429, 429, 3*w^2 - 2*w - 8]', '[429, 429, 3*w^2 - 4*w - 7]', '[432, 6, 2*w^3 - 6*w - 4]', '[436, 218, -w^3 + w^2 + 5*w + 4]', '[436, 218, -3*w^3 + 3*w^2 + 11*w + 4]', '[443, 443, -3*w^3 + 5*w^2 + 10*w - 12]', '[443, 443, -3*w^3 + 7*w^2 + 7*w - 11]', '[457, 457, -w^3 + 2*w^2 + 3*w - 8]', '[457, 457, w^3 - w^2 - 4*w - 4]', '[467, 467, w^2 + 2*w - 6]', '[467, 467, w^2 - 4*w - 3]', '[468, 78, -3*w^3 + 5*w^2 + 7*w - 4]', '[468, 78, -3*w^3 + 4*w^2 + 8*w - 5]', '[471, 471, w^3 - 2*w^2 + 6]', '[471, 471, 2*w^3 - 5*w^2 - 9*w + 4]', '[471, 471, -4*w^3 + 5*w^2 + 14*w - 1]', '[471, 471, w^3 - w^2 - w - 5]', '[484, 22, -w^2 + w - 3]', '[484, 22, w^3 - w^2 - 7*w]', '[491, 491, 3*w^3 - 2*w^2 - 10*w - 4]', '[491, 491, -2*w^3 + 2*w^2 + 7*w - 5]', '[491, 491, -2*w^3 + 4*w^2 + 5*w - 2]', '[491, 491, -3*w^3 + 7*w^2 + 5*w - 13]', '[507, 39, -4*w^3 + 5*w^2 + 17*w + 2]', '[507, 39, -w^3 + 4*w^2 + 3*w - 5]', '[507, 507, -2*w^3 + w^2 + 7*w - 2]', '[507, 507, -2*w^3 + 5*w^2 + 3*w - 4]', '[517, 517, -3*w^3 + 3*w^2 + 8*w - 3]', '[517, 517, -3*w^3 + 6*w^2 + 5*w - 5]', '[528, 66, 4*w - 2]', '[529, 23, 3*w^2 - 3*w - 8]', '[529, 23, 3*w^2 - 3*w - 4]', '[529, 529, -w^2 + 8]', '[529, 529, -w^2 + 2*w + 7]', '[531, 177, -w^3 + 4*w^2 - w - 9]', '[531, 177, w^3 + w^2 - 4*w - 7]', '[537, 537, 3*w^2 - 2*w - 5]', '[537, 537, 5*w^3 - 5*w^2 - 17*w - 1]', '[541, 541, 2*w^3 - 2*w^2 - 5*w + 7]', '[541, 541, -4*w^3 + 7*w^2 + 10*w - 12]', '[549, 183, -3*w^3 + 5*w^2 + 7*w - 7]', '[549, 183, 3*w^3 - 4*w^2 - 8*w + 2]', '[564, 282, w^3 + 2*w^2 - 4*w - 5]', '[564, 282, -w^3 + 5*w^2 - 3*w - 6]', '[572, 286, -3*w^3 + 5*w^2 + 9*w - 4]', '[572, 286, -3*w^3 + 4*w^2 + 10*w - 7]', '[573, 573, -5*w^3 + 3*w^2 + 16*w + 2]', '[573, 573, w^3 - 3*w^2 - 5*w + 5]', '[576, 12, -2*w^3 + 2*w^2 + 10*w]', '[577, 577, 3*w^2 - 2*w - 7]', '[577, 577, -3*w^3 + 6*w^2 + 10*w - 10]', '[577, 577, -2*w^3 - w^2 + 7*w + 4]', '[577, 577, 3*w^2 - 4*w - 6]', '[579, 579, -3*w^3 - w^2 + 11*w + 9]', '[579, 579, -3*w^3 + w^2 + 12*w + 8]', '[587, 587, 2*w^3 - w^2 - 6*w - 4]', '[587, 587, 2*w^3 - w^2 - 11*w - 4]', '[599, 599, -4*w^3 + 3*w^2 + 14*w + 5]', '[599, 599, -w^3 + 7*w + 5]', '[601, 601, 3*w^3 - 4*w^2 - 8*w + 4]', '[601, 601, -3*w^3 + 5*w^2 + 7*w - 5]', '[611, 611, -3*w^3 + 5*w^2 + 8*w - 2]', '[611, 611, -2*w^3 + 4*w^2 + 7*w - 3]', '[611, 611, -2*w^3 + 2*w^2 + 9*w - 6]', '[611, 611, -3*w^3 + 4*w^2 + 9*w - 8]', '[613, 613, 3*w^2 - 2*w - 6]', '[613, 613, 3*w^2 - 4*w - 5]', '[621, 69, w^3 - 3*w + 4]', '[621, 69, w^3 - 3*w^2 - 2]', '[624, 78, 2*w^2 - 4*w - 6]', '[624, 78, 2*w^2 - 8]', '[625, 5, -5]', '[628, 314, 4*w^3 - w^2 - 19*w - 7]', '[628, 314, 3*w^3 - 4*w^2 - 8*w + 3]', '[628, 314, -3*w^3 + 5*w^2 + 7*w - 6]', '[628, 314, -3*w^3 + 12*w + 7]', '[639, 213, 2*w^2 - 5*w - 4]', '[639, 213, 2*w^2 + w - 7]', '[647, 647, 3*w^3 - 3*w^2 - 12*w + 4]', '[647, 647, -3*w^3 + 6*w^2 + 9*w - 8]', '[649, 649, -2*w^3 + 5*w^2 + 4*w - 14]', '[649, 649, 4*w^2 - 2*w - 11]', '[657, 219, -w^3 + 2*w^2 + w - 8]', '[657, 219, w^3 - 5*w^2 - w + 11]', '[661, 661, w^3 + 2*w^2 - 5*w - 7]', '[661, 661, -w^2 - 3]', '[661, 661, -w^2 + 2*w - 4]', '[661, 661, -w^3 + 5*w^2 - 2*w - 9]', '[671, 671, 3*w^3 - 3*w^2 - 10*w + 4]', '[671, 671, -4*w^3 + 6*w^2 + 11*w - 12]', '[673, 673, 3*w^3 - 3*w^2 - 8*w + 2]', '[673, 673, -3*w^3 + 6*w^2 + 5*w - 6]', '[676, 26, 3*w^2 - 3*w - 5]', '[676, 26, 7*w^3 - 4*w^2 - 28*w - 7]', '[676, 338, w^3 - 2*w^2 - 2*w - 3]', '[676, 338, -w^3 + w^2 + 3*w - 6]', '[681, 681, -3*w^2 - 4*w + 2]', '[681, 681, -3*w^3 + 11*w + 5]', '[681, 681, 2*w + 5]', '[681, 681, -3*w^3 + 3*w^2 + 8*w - 1]', '[683, 683, -w^3 + 3*w^2 - 2*w - 4]', '[683, 683, w^3 - w - 4]', '[687, 687, -4*w^3 + 2*w^2 + 14*w + 5]', '[687, 687, -w^3 - w^2 + 2*w + 5]', '[687, 687, -3*w^2 - w + 8]', '[687, 687, -w^3 - 2*w^2 + 3*w + 7]', '[704, 44, -2*w^3 + 2*w^2 + 2*w - 4]', '[708, 354, -3*w^3 + 6*w^2 + 10*w - 11]', '[708, 354, -4*w^3 + 5*w^2 + 11*w - 7]', '[709, 709, 4*w^3 - 7*w^2 - 10*w + 8]', '[709, 709, w^3 - w^2 - 3*w - 5]', '[709, 709, -w^3 + 2*w^2 + 2*w - 8]', '[709, 709, -w^3 + 5*w^2 + w - 9]', '[716, 358, -3*w^3 + 2*w^2 + 8*w - 5]', '[716, 358, -5*w^3 + 2*w^2 + 24*w + 7]', '[719, 719, 2*w^3 - w^2 - 8*w + 2]', '[719, 719, -2*w^3 + 5*w^2 + 4*w - 5]', '[723, 723, -3*w^3 + w^2 + 10*w]', '[723, 723, 3*w^3 - w^2 - 9*w + 1]', '[729, 9, -3*w^2 + 3*w + 6]', '[732, 366, -w^3 - w^2 + 3*w + 6]', '[732, 366, -w^3 + 5*w^2 + 3*w - 12]', '[733, 733, -w^3 + 5*w^2 - w - 11]', '[733, 733, 3*w^3 - 5*w^2 - 6*w + 7]', '[743, 743, w^2 - 4*w - 4]', '[743, 743, -3*w^3 + 7*w^2 + 6*w - 9]', '[743, 743, 3*w^3 - 2*w^2 - 11*w + 1]', '[743, 743, w^2 + 2*w - 7]', '[747, 249, -3*w^3 + 7*w^2 + 8*w - 11]', '[747, 249, -3*w^3 + 4*w^2 + 11*w - 8]', '[747, 249, -3*w^3 + 5*w^2 + 10*w - 4]', '[747, 249, 3*w^3 - 2*w^2 - 13*w + 1]', '[752, 94, -2*w^3 + 4*w^2 + 6*w - 2]', '[752, 94, -2*w^3 + 2*w^2 + 8*w - 6]', '[753, 753, 4*w^3 - 2*w^2 - 9*w + 3]', '[753, 753, 2*w^3 - 2*w^2 - 11*w - 1]', '[759, 759, -w^3 + w^2 + 4]', '[759, 759, -w^3 + 2*w^2 - w - 4]', '[764, 382, -w^3 + 2*w + 5]', '[764, 382, 4*w^3 - 3*w^2 - 19*w - 5]', '[767, 767, -3*w^3 + 7*w^2 + 4*w - 5]', '[767, 767, -2*w^3 + 5*w^2 + 5*w - 6]', '[767, 767, -2*w^3 + w^2 + 9*w - 2]', '[767, 767, -3*w^3 + 2*w^2 + 9*w - 3]', '[768, 12, -4*w - 4]', '[769, 769, -2*w^2 - 3*w + 4]', '[769, 769, 4*w^3 - 4*w^2 - 14*w - 5]', '[772, 386, 5*w^3 - 6*w^2 - 20*w + 1]', '[772, 386, 6*w^3 - 5*w^2 - 25*w - 1]', '[781, 781, -w - 5]', '[781, 781, -w^3 + 6*w^2 + 2*w - 12]', '[793, 793, -w^3 - 2*w^2 + 5*w + 4]', '[793, 793, -4*w^2 + 7*w + 4]', '[793, 793, 4*w^2 - w - 7]', '[793, 793, -w^3 + 5*w^2 - 2*w - 6]', '[803, 803, 2*w^3 - 8*w^2 - 5*w + 18]', '[803, 803, -3*w^3 + 5*w^2 + 5*w - 13]', '[827, 827, -w^2 + 4*w + 7]', '[827, 827, -2*w^3 + w^2 + 7*w - 4]', '[827, 827, -2*w^3 + 5*w^2 + 3*w - 2]', '[827, 827, -2*w^3 + w^2 + 11*w + 6]', '[828, 138, w^3 + w^2 - 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3*w^2 + 3*w + 4]', '[1413, 471, 5*w^3 - 8*w^2 - 13*w + 6]', '[1413, 471, -2*w^3 + 7*w^2 + 2*w - 13]', '[1413, 471, -2*w^3 - w^2 + 10*w + 6]', '[1413, 471, -5*w^3 + 7*w^2 + 14*w - 10]', '[1417, 1417, -2*w^3 + w^2 + 4*w - 6]', '[1417, 1417, -w^2 + 2*w - 5]', '[1417, 1417, -w^2 - 4]', '[1417, 1417, 2*w^3 - 5*w^2 - 3]', '[1429, 1429, w^3 - 3*w^2 - 3]', '[1429, 1429, -w^3 + 3*w - 5]', '[1436, 718, w^3 - 8*w - 5]', '[1436, 718, -3*w^3 + 16*w + 9]', '[1436, 718, 4*w^3 - 7*w^2 - 9*w + 1]', '[1436, 718, 4*w^3 - 3*w^2 - 13*w - 5]', '[1439, 1439, 4*w^3 - 4*w^2 - 15*w + 4]', '[1439, 1439, -4*w^3 + 8*w^2 + 11*w - 11]', '[1451, 1451, -2*w^3 + 4*w^2 + 2*w - 9]', '[1451, 1451, 2*w^3 - w^2 - 10*w + 4]', '[1451, 1451, -2*w^3 + 5*w^2 + 6*w - 5]', '[1451, 1451, 2*w^3 - 2*w^2 - 4*w - 5]', '[1452, 66, 3*w^3 - 7*w^2 - 9*w + 10]', '[1452, 66, -w^3 + 5*w^2 + 3*w - 6]', '[1453, 1453, 3*w^3 - 4*w^2 - 5*w + 3]', '[1453, 1453, -w^3 + w^2 + 3*w - 7]', '[1453, 1453, w^3 - 2*w^2 - 2*w - 4]', '[1453, 1453, -3*w^3 + 5*w^2 + 4*w - 3]', '[1472, 92, 2*w^3 - 6*w^2 - 2*w + 4]', '[1472, 92, -2*w^3 + 8*w - 2]', '[1473, 1473, -7*w^3 + 3*w^2 + 26*w + 7]', '[1473, 1473, 4*w^3 - 3*w^2 - 10*w + 3]', '[1473, 1473, 2*w^3 - 3*w^2 - 11*w]', '[1473, 1473, 2*w^3 - 3*w^2 - 4*w + 10]', '[1487, 1487, -2*w^3 + 6*w^2 + 5*w - 8]', '[1487, 1487, w^3 + 2*w^2 - 3*w - 8]', '[1487, 1487, -w^3 + 5*w^2 - 4*w - 8]', '[1487, 1487, 2*w^3 - 11*w + 1]', '[1492, 746, w^3 - 2*w^2 - 2*w + 9]', '[1492, 746, 9*w^3 - 8*w^2 - 36*w - 3]', '[1499, 1499, -w^3 + 2*w^2 - 2*w - 4]', '[1499, 1499, w^3 - w^2 + w - 5]', '[1511, 1511, 4*w^3 - 8*w^2 - 9*w + 8]', '[1511, 1511, -4*w^3 + 4*w^2 + 13*w - 5]', '[1521, 39, -4*w^2 + 4*w + 11]', '[1521, 39, 5*w^3 - 5*w^2 - 16*w]', '[1521, 507, w^3 - w^2 - 8*w + 6]', '[1521, 507, w^3 - 2*w^2 - 7*w + 2]', '[1523, 1523, -3*w^3 + 4*w^2 + 11*w - 10]', '[1523, 1523, 3*w^3 - 5*w^2 - 10*w + 2]', '[1532, 766, 3*w^3 - 5*w^2 - 11*w + 2]', '[1532, 766, 5*w^3 - 3*w^2 - 21*w - 2]', '[1549, 1549, -w^2 - w - 4]', '[1549, 1549, -w^3 + 2*w^2 + w - 9]', '[1549, 1549, w^3 - w^2 - 2*w - 7]', '[1549, 1549, -w^2 + 3*w - 6]', '[1551, 1551, 3*w^3 - 7*w^2 - 7*w + 9]', '[1551, 1551, 3*w^3 - 2*w^2 - 12*w + 2]', '[1552, 194, -2*w - 6]', '[1552, 194, 4*w^2 - 6*w - 6]', '[1552, 194, 4*w^2 - 2*w - 8]', '[1552, 194, 2*w - 8]', '[1559, 1559, 3*w^2 - 10]', '[1559, 1559, -2*w^3 + 5*w^2 + 5*w - 4]', '[1559, 1559, 2*w^3 - w^2 - 9*w + 4]', '[1559, 1559, 3*w^2 - 6*w - 7]', '[1571, 1571, 2*w^2 - 5*w - 6]', '[1571, 1571, 2*w^2 + w - 9]', '[1573, 143, w^3 - 9*w + 3]', '[1573, 143, w^3 - 4*w^2 + 7*w - 1]', '[1573, 143, w^3 + w^2 + 2*w - 3]', '[1573, 143, w^3 - 3*w^2 - 6*w + 5]', '[1583, 1583, w^3 + w^2 - 9*w - 5]', '[1583, 1583, -3*w^3 + 6*w^2 + 7*w - 4]', '[1583, 1583, -3*w^3 + 3*w^2 + 10*w - 6]', '[1583, 1583, -w^3 + 4*w^2 + 4*w - 12]', '[1584, 66, 2*w^3 - 4*w^2 - 2*w + 10]', '[1587, 69, 3*w^3 - 7*w^2 - 4*w + 3]', '[1587, 69, -3*w^3 + 7*w + 4]', '[1587, 1587, -2*w^3 + 6*w^2 + 4*w - 7]', '[1587, 1587, -2*w^3 + 10*w - 1]', '[1593, 177, -w^3 + 6*w + 8]', '[1593, 177, -4*w^3 + 15*w + 8]', '[1597, 1597, -w - 6]', '[1597, 1597, w - 7]', '[1607, 1607, w^3 + 2*w^2 - 5*w - 14]', '[1607, 1607, 2*w^3 - w^2 - 12*w + 7]', '[1609, 1609, -3*w^3 + 6*w^2 + 11*w - 9]', '[1609, 1609, 3*w^3 - 3*w^2 - 14*w - 6]', '[1609, 1609, -w^3 - 3*w^2 + 5*w + 9]', '[1609, 1609, -3*w^3 + 3*w^2 + 14*w - 5]', '[1611, 537, -3*w^3 - w^2 + 7*w + 5]', '[1611, 537, -5*w^3 + 8*w^2 + 13*w - 3]', '[1619, 1619, -3*w^3 + 8*w^2 + 5*w - 10]', '[1619, 1619, 5*w^3 - 4*w^2 - 17*w - 6]', '[1619, 1619, -6*w^3 + 11*w^2 + 18*w - 16]', '[1619, 1619, -3*w^3 + w^2 + 12*w]', '[1621, 1621, -w^3 + 3*w^2 + 2*w - 12]', '[1621, 1621, 4*w^2 - 3*w - 6]', '[1621, 1621, 4*w^2 - 5*w - 5]', '[1621, 1621, w^3 - 5*w - 8]', '[1623, 1623, -4*w^3 + w^2 + 6*w - 5]', '[1623, 1623, 5*w^3 + w^2 - 12*w - 5]', '[1633, 1633, 4*w^3 - 7*w^2 - 9*w + 10]', '[1633, 1633, -2*w^3 + 5*w^2 + 8*w - 9]', '[1633, 1633, 2*w^3 - w^2 - 12*w + 2]', '[1633, 1633, -4*w^3 + 5*w^2 + 11*w - 2]', '[1636, 818, 3*w^3 - w^2 - 17*w]', '[1636, 818, -3*w^3 + 5*w^2 + 15*w]', '[1647, 183, 4*w^3 - 3*w^2 - 12*w + 4]', '[1647, 183, -5*w^3 + 3*w^2 + 18*w + 1]', '[1657, 1657, -w^3 - 3*w^2 + 10*w + 5]', '[1657, 1657, 5*w^3 - 6*w^2 - 15*w + 6]', '[1669, 1669, 2*w^3 - 3*w^2 - 10*w + 2]', '[1669, 1669, -2*w^3 + 3*w^2 + 10*w - 9]', '[1676, 838, 6*w^3 - 7*w^2 - 21*w - 1]', '[1676, 838, 5*w^3 - 4*w^2 - 18*w + 1]', '[1679, 1679, 4*w^3 - 9*w^2 - 12*w + 14]', '[1679, 1679, -5*w^3 + 6*w^2 + 15*w - 9]', '[1679, 1679, -5*w^3 + 8*w^2 + 15*w - 15]', '[1679, 1679, 4*w^3 - 8*w^2 - 12*w + 11]', '[1681, 41, -2*w^3 + 5*w^2 + 8*w - 10]', '[1681, 41, 2*w^3 - w^2 - 12*w + 1]', '[1692, 282, 2*w^3 - 5*w^2 - w + 9]', '[1692, 282, -2*w^3 + w^2 + 5*w + 5]', '[1693, 1693, -w^3 + 9*w - 2]', '[1693, 1693, -w^3 + 3*w^2 + 6*w - 6]', '[1712, 214, -2*w^3 + 6*w^2 - 10]', '[1712, 214, -4*w^3 + 2*w^2 + 12*w - 2]', '[1712, 214, 4*w^3 - 10*w^2 - 4*w + 8]', '[1712, 214, 2*w^3 - 6*w - 6]', '[1716, 858, w^3 - 2*w + 5]', '[1716, 858, -w^3 + 3*w^2 - w + 4]', '[1719, 573, -3*w^3 + 4*w^2 + 11*w - 11]', '[1719, 573, 3*w^3 - 5*w^2 - 10*w + 1]', '[1727, 1727, 3*w^3 - 8*w^2 - 2*w + 4]', '[1727, 1727, 5*w^3 - 7*w^2 - 17*w + 11]', '[1727, 1727, -7*w^3 + 10*w^2 + 19*w - 18]', '[1727, 1727, -3*w^3 + 9*w^2 + 8*w - 21]', '[1728, 12, 2*w^3 - 6*w^2 - 6*w + 8]', '[1731, 1731, 3*w^3 + w^2 - 9*w - 7]', '[1731, 1731, 3*w^3 - 7*w^2 - 12*w + 7]', '[1731, 1731, -w^3 + 3*w^2 - 2*w - 6]', '[1731, 1731, -3*w^3 + w^2 + 10*w + 6]', '[1737, 579, -w^3 + 4*w^2 - w - 15]', '[1737, 579, w^3 + w^2 - 4*w - 13]', '[1744, 218, -4*w^3 + 6*w^2 + 10*w - 8]', '[1744, 218, -4*w^3 + 6*w^2 + 10*w - 4]', '[1761, 1761, w^3 - 6*w^2 - w + 12]', '[1761, 1761, w^3 - w^2 - w + 7]', '[1772, 886, 8*w^3 - 9*w^2 - 29*w + 1]', '[1772, 886, -w^3 - w^2 + 3*w + 8]', '[1777, 1777, 2*w^3 - w^2 - 13*w + 6]', '[1777, 1777, 2*w^3 - 5*w^2 - 9*w + 6]', '[1787, 1787, 3*w^3 - 2*w^2 - 8*w - 4]', '[1787, 1787, 4*w^3 - 7*w^2 - 12*w + 7]', '[1789, 1789, -2*w^3 + 4*w^2 + 9*w - 5]', '[1789, 1789, -2*w^3 + 2*w^2 + 11*w - 6]', '[1797, 1797, 4*w^2 - 3*w - 10]', '[1797, 1797, 4*w^2 - 5*w - 9]', '[1801, 1801, -w^3 + w^2 + 2*w - 7]', '[1801, 1801, w^3 - 2*w^2 - w - 5]', '[1803, 1803, -5*w^3 + 3*w^2 + 16*w - 1]', '[1803, 1803, 4*w^3 - 3*w^2 - 14*w + 2]', '[1828, 914, 4*w^3 - 5*w^2 - 11*w + 3]', '[1828, 914, 7*w^3 - 6*w^2 - 24*w - 3]', '[1833, 1833, 3*w^3 - 3*w^2 - 14*w + 1]', '[1833, 1833, 4*w^3 - 7*w^2 - 9*w + 8]', '[1833, 1833, 4*w^3 - 5*w^2 - 11*w + 4]', '[1833, 1833, 3*w^3 - 6*w^2 - 11*w + 13]', '[1839, 1839, -3*w^3 + w^2 + 9*w + 5]', '[1839, 1839, -3*w^3 - w^2 + 8*w + 6]', '[1847, 1847, -3*w^3 + 3*w^2 + 13*w - 7]', '[1847, 1847, -2*w^3 + 4*w^2 + w - 7]', '[1847, 1847, 2*w^3 - 2*w^2 - 3*w - 4]', '[1847, 1847, -3*w^3 + 6*w^2 + 10*w - 6]', '[1859, 143, 5*w^3 - 4*w^2 - 17*w + 2]', '[1859, 143, 4*w^3 - 10*w^2 - 5*w + 10]', '[1859, 1859, 3*w^3 - w^2 - 14*w]', '[1859, 1859, 3*w^3 - 8*w^2 - 7*w + 12]', '[1861, 1861, 4*w^3 - 8*w^2 - 7*w + 10]', '[1861, 1861, 4*w^3 - 4*w^2 - 11*w + 1]', '[1863, 69, -3*w^3 + 3*w^2 + 12*w - 6]', '[1863, 69, 3*w^3 - 6*w^2 - 9*w + 6]', '[1868, 934, 2*w^3 - 5*w^2 - 5*w + 3]', '[1868, 934, 5*w^3 - 2*w^2 - 20*w - 3]', '[1871, 1871, w^3 + 2*w^2 - 5*w - 13]', '[1871, 1871, -4*w^3 + 10*w^2 + 9*w - 16]', '[1872, 78, 2*w^2 - 8*w + 2]', '[1872, 78, -2*w^2 - 4*w + 4]', '[1873, 1873, -w^3 + w^2 + 4*w - 8]', '[1873, 1873, 4*w^3 - 3*w^2 - 8*w + 4]', '[1873, 1873, -w^3 + 3*w^2 + 10*w + 1]', '[1873, 1873, w^3 - 2*w^2 - 3*w - 4]', '[1875, 15, 5*w + 5]', '[1884, 942, -5*w^3 + 8*w^2 + 14*w - 17]', '[1884, 942, -w^3 + 8*w^2 + 2*w - 19]', '[1884, 942, -3*w^2 + w + 13]', '[1884, 942, 5*w^3 - 7*w^2 - 15*w]', '[1907, 1907, -5*w^3 + 9*w^2 + 13*w - 9]', '[1907, 1907, -2*w^3 + 7*w^2 - 3*w - 8]', '[1909, 1909, -w^3 + 4*w^2 + w - 15]', '[1909, 1909, 2*w^3 + 2*w^2 - 13*w - 9]', '[1909, 1909, 2*w^3 + 2*w^2 - 10*w - 11]', '[1909, 1909, 3*w^3 - 7*w^2 - 7*w + 19]', '[1909, 1909, -3*w^3 + 2*w^2 + 12*w + 8]', '[1909, 1909, 2*w^3 - 8*w^2 + 17]', '[1909, 1909, -2*w^3 + 8*w^2 + 3*w - 18]', '[1909, 1909, -w^3 - w^2 + 6*w + 11]', '[1917, 213, -2*w^3 + 3*w^2 + 9*w + 4]', '[1917, 213, -2*w^3 - 3*w^2 + 6*w + 7]', '[1933, 1933, -4*w^3 + 8*w^2 + 7*w - 9]', '[1933, 1933, 4*w^3 - 4*w^2 - 11*w + 2]', '[1936, 22, -4*w^2 + 4*w + 10]', '[1936, 22, 4*w^2 - 4*w - 6]', '[1941, 1941, -6*w^3 + 6*w^2 + 20*w - 1]', '[1941, 1941, 3*w^3 - 6*w^2 - 13*w + 5]', '[1947, 1947, 2*w^3 - w^2 - 10*w + 5]', '[1947, 1947, 2*w^3 - 5*w^2 - 6*w + 4]', '[1964, 982, 9*w^3 - 9*w^2 - 35*w - 6]', '[1964, 982, -w^2 + 5*w + 5]', '[1964, 982, -5*w^3 + 4*w^2 + 16*w + 5]', '[1964, 982, 3*w^3 - 3*w^2 - 11*w + 6]', '[1969, 1969, -4*w^3 + 5*w^2 + 16*w - 6]', '[1969, 1969, -w^3 - 3*w + 3]', '[1971, 219, w^3 + 3*w + 7]', '[1971, 219, 2*w^3 + 3*w^2 - 6*w - 10]', '[1979, 1979, -3*w^3 + 3*w^2 + 10*w - 7]', '[1979, 1979, -6*w^3 + 10*w^2 + 17*w - 10]', '[1979, 1979, -6*w^3 + 8*w^2 + 19*w - 11]', '[1979, 1979, -3*w^3 + 6*w^2 + 7*w - 3]', '[1983, 1983, w^3 - w^2 + 2*w + 4]', '[1983, 1983, -5*w^3 + 16*w + 8]', '[1983, 1983, -2*w^3 + 7*w + 8]', '[1983, 1983, w^3 + w^2 + 3*w + 3]', '[1993, 1993, -w^3 + 2*w^2 + 7*w - 6]', '[1993, 1993, w^3 - w^2 - 8*w + 2]', '[2003, 2003, w^3 + w^2 - 2*w - 7]', '[2003, 2003, -w^3 + 4*w^2 - 3*w - 7]', '[2013, 2013, w^3 - 3*w^2 - w - 3]', '[2013, 2013, w^3 - 4*w + 6]', '[2017, 2017, 4*w^3 - 6*w^2 - 10*w + 7]', '[2017, 2017, 4*w^3 - 7*w^2 - 8*w + 10]', '[2017, 2017, 4*w^3 - 5*w^2 - 10*w + 1]', '[2017, 2017, -4*w^3 + 6*w^2 + 10*w - 5]', '[2019, 2019, -6*w^3 + 2*w^2 + 18*w + 1]', '[2019, 2019, 3*w^3 - 2*w^2 - 11*w + 3]', '[2027, 2027, 3*w^3 - 9*w^2 - 8*w + 15]', '[2027, 2027, 3*w^3 - 17*w - 1]', '[2028, 78, -3*w^3 + 10*w + 7]', '[2028, 78, 5*w^3 - 8*w^2 - 14*w + 5]', '[2028, 1014, 3*w^3 - 6*w^2 - 4*w + 11]', '[2028, 1014, -3*w^3 + 3*w^2 + 7*w + 4]', '[2039, 2039, -4*w^3 + 6*w^2 + 13*w + 1]', '[2039, 2039, -3*w^3 + w^2 + 11*w - 1]', '[2041, 2041, w^3 - 8*w^2 + 10*w + 8]', '[2041, 2041, -4*w^3 + 9*w^2 + 4*w - 8]', '[2041, 2041, w^3 - 6*w^2 + 3*w + 12]', '[2041, 2041, 4*w^2 - 3*w - 9]', '[2041, 2041, -4*w^2 + 5*w + 8]', '[2041, 2041, -4*w^3 + 6*w^2 + 8*w - 9]', '[2041, 2041, -2*w^3 + 2*w^2 + 5*w + 8]', '[2041, 2041, w^3 + 5*w^2 - 3*w - 11]', '[2043, 681, -3*w^3 + 2*w^2 + 10*w - 4]', '[2043, 681, 2*w^2 - 5*w - 7]', '[2043, 681, 2*w^2 + w - 10]', '[2043, 681, 3*w^3 - 7*w^2 - 5*w + 5]', '[2049, 2049, 2*w^2 + 2*w + 3]', '[2049, 2049, -3*w^3 - 2*w^2 + 9*w + 5]', '[2053, 2053, -3*w^3 + 5*w^2 + 12*w - 6]', '[2053, 2053, 3*w^3 - 4*w^2 - 13*w + 8]', '[2061, 687, 2*w^3 - 2*w^2 - 7*w - 6]', '[2061, 687, w^3 - 2*w^2 - 4*w - 4]', '[2061, 687, 3*w^3 - 4*w^2 - 11*w - 4]', '[2061, 687, -2*w^3 + 4*w^2 + 5*w - 13]', '[2068, 1034, w^3 - 6*w^2 + 4*w + 9]', '[2068, 1034, -w^3 - 3*w^2 + 5*w + 8]', '[2089, 2089, 4*w^2 - 3*w - 8]', '[2089, 2089, 4*w^2 - 5*w - 7]', '[2099, 2099, 4*w^3 - 4*w^2 - 11*w + 10]', '[2099, 2099, 4*w^3 - 8*w^2 - 7*w + 1]', '[2101, 2101, -6*w^3 + 11*w^2 + 14*w - 20]', '[2101, 2101, 2*w^3 - 4*w^2 - 10*w + 3]', '[2111, 2111, -w^3 + 5*w^2 - 3*w - 11]', '[2111, 2111, -2*w^3 + w^2 + 12*w + 7]', '[2111, 2111, -2*w^3 + 5*w^2 + 8*w - 18]', '[2111, 2111, w^3 + 2*w^2 - 4*w - 10]', '[2112, 132, 4*w^3 - 6*w^2 - 10*w + 6]', '[2116, 46, w^2 - 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12]', '[2517, 2517, -6*w^3 + 3*w^2 + 17*w + 2]', '[2517, 2517, -2*w^3 + 2*w^2 + 11*w + 7]', '[2519, 2519, 2*w^2 - 5*w - 9]', '[2519, 2519, 6*w^2 - 7]', '[2519, 2519, 5*w^2 - 4]', '[2519, 2519, -5*w^3 + 10*w^2 + 10*w - 22]', '[2521, 2521, 5*w^3 - 9*w^2 - 12*w + 12]', '[2521, 2521, -w^3 + 6*w^2 - w - 9]', '[2523, 87, -4*w^3 - w^2 + 15*w + 12]', '[2523, 87, 3*w^3 - 3*w^2 - 11*w + 7]', '[2531, 2531, w^3 + 2*w^2 - 3*w - 9]', '[2531, 2531, -w^3 + 5*w^2 - 4*w - 9]', '[2543, 2543, -4*w^3 + 9*w^2 + 10*w - 13]', '[2543, 2543, -2*w^3 + 5*w^2 - 8]', '[2543, 2543, 2*w^3 - w^2 - 4*w - 5]', '[2543, 2543, -4*w^3 + 3*w^2 + 16*w - 2]', '[2556, 426, 5*w^3 - 2*w^2 - 22*w - 3]', '[2556, 426, 2*w^3 - 5*w^2 - 7*w + 3]', '[2559, 2559, 4*w^3 - 7*w^2 - 16*w + 4]', '[2559, 2559, 5*w^3 - 7*w^2 - 18*w + 3]', '[2579, 2579, 3*w^3 - 3*w^2 - 5*w - 3]', '[2579, 2579, -3*w^3 + 6*w^2 + 2*w - 8]', '[2588, 1294, 5*w^3 - 2*w^2 - 24*w - 9]', '[2588, 1294, -4*w^3 + w^2 + 15*w + 9]', '[2589, 2589, 6*w^3 - 8*w^2 - 14*w + 15]', '[2589, 2589, -6*w^3 + 5*w^2 + 14*w - 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6*w - 8]', '[5641, 5641, -w^3 + 7*w^2 - 5*w - 9]', '[5641, 5641, -w^3 - 5*w^2 + 5*w + 13]', '[5652, 942, 8*w^3 - 7*w^2 - 29*w - 11]', '[5652, 942, 3*w^3 - 4*w^2 - 14*w + 5]', '[5652, 942, -3*w^3 + 5*w^2 + 13*w - 10]', '[5652, 942, -3*w^3 + 2*w^2 + 16*w + 11]', '[5653, 5653, 7*w^3 - 8*w^2 - 21*w + 8]', '[5653, 5653, -7*w^3 + 8*w^2 + 29*w]', '[5668, 2834, w^3 - 8*w^2 + 19]', '[5668, 2834, w^3 - 7*w^2 + 3*w + 16]', '[5668, 2834, -w^3 - 4*w^2 + 8*w + 13]', '[5668, 2834, -w^3 - 5*w^2 + 13*w + 12]', '[5687, 517, 3*w^3 - 13*w + 1]', '[5687, 517, -5*w^3 + 4*w^2 + 19*w - 3]', '[5687, 517, -5*w^3 + 11*w^2 + 12*w - 15]', '[5687, 517, 3*w^3 - 9*w^2 - 4*w + 9]', '[5689, 5689, -w^3 - 6*w^2 + 9*w + 22]', '[5689, 5689, -w^3 + 9*w^2 - 6*w - 24]', '[5711, 5711, w^3 + 3*w^2 - 11*w - 11]', '[5711, 5711, w^3 + 3*w^2 - 4*w - 13]', '[5711, 5711, -w^3 + 6*w^2 - 5*w - 13]', '[5711, 5711, -w^3 + 6*w^2 + 2*w - 18]', '[5716, 2858, 6*w^3 - 7*w^2 - 15*w - 1]', '[5716, 2858, 5*w^3 - 4*w^2 - 12*w + 1]', '[5721, 5721, 6*w^3 - 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1]', '[4, 2, -w^3 + w^2 + 3*w]', '[11, 11, -w^2 + 3]', '[13, 13, w^3 - 2*w^2 - w + 1]', '[13, 13, w^3 - w^2 - 2*w + 1]', '[23, 23, -w^3 + w^2 + 4*w - 2]', '[23, 23, w^3 - 2*w^2 - 3*w + 2]', '[47, 47, -w^3 + 2*w^2 + 3*w - 1]', '[47, 47, -w^3 + w^2 + 4*w - 3]', '[59, 59, w^2 - 5]', '[59, 59, w^2 - 2*w - 4]', '[61, 61, -w^3 + 2*w^2 + 4*w - 4]', '[61, 61, w^3 - w^2 - 5*w + 1]', '[71, 71, w^3 - w^2 - 2*w - 2]', '[71, 71, -w^3 + 2*w^2 + w - 4]', '[73, 73, 2*w^2 - w - 5]', '[73, 73, w^3 - 2*w^2 - 2*w + 6]', '[83, 83, -2*w^3 + 3*w^2 + 6*w - 6]', '[83, 83, -2*w^3 + 4*w^2 + 5*w - 5]', '[83, 83, -2*w^3 + 2*w^2 + 7*w - 2]', '[83, 83, 2*w^3 - 3*w^2 - 6*w + 1]', '[97, 97, -w - 3]', '[97, 97, 2*w^2 - 3*w - 3]', '[97, 97, 2*w^2 - w - 4]', '[97, 97, w - 4]', '[107, 107, -w^3 + 3*w^2 - 5]', '[107, 107, -2*w^3 + w^2 + 6*w - 1]', '[107, 107, 2*w^3 - 5*w^2 - 2*w + 4]', '[107, 107, w^3 - 3*w - 3]', '[109, 109, 2*w^3 - 3*w^2 - 5*w + 4]', '[109, 109, -2*w^3 + 3*w^2 + 5*w - 2]', '[121, 11, 2*w^2 - 2*w - 3]', '[157, 157, 2*w^3 - 2*w^2 - 9*w + 3]', '[157, 157, -w^3 + 2*w^2 + 3*w - 7]', '[157, 157, -w^3 + w^2 + 4*w + 3]', '[157, 157, -2*w^3 + 4*w^2 + 7*w - 6]', '[169, 13, 2*w^3 - 2*w^2 - 9*w]', '[179, 179, w^3 + 2]', '[179, 179, -2*w^3 + w^2 + 10*w - 1]', '[191, 191, -2*w^3 + 5*w^2 + 4*w - 7]', '[191, 191, 2*w^3 - w^2 - 8*w]', '[193, 193, 3*w^2 - 2*w - 9]', '[193, 193, 3*w^2 - 4*w - 8]', '[227, 227, -w^3 + 3*w^2 + 3*w - 3]', '[227, 227, w^3 - 3*w - 4]', '[227, 227, -w^3 + 3*w^2 - 6]', '[227, 227, w^3 - 6*w + 2]', '[229, 229, w^3 + w^2 - 6*w - 4]', '[229, 229, w^3 + w^2 - 5*w - 3]', '[229, 229, 2*w^3 - 9*w - 3]', '[229, 229, -w^3 + 4*w^2 + w - 8]', '[241, 241, 2*w^3 - 3*w^2 - 4*w + 2]', '[241, 241, -2*w^3 + 3*w^2 + 4*w - 3]', '[251, 251, -2*w^3 + 4*w^2 + 4*w - 1]', '[251, 251, -2*w^3 + 2*w^2 + 6*w - 5]', '[277, 277, w^3 - w^2 - 6*w + 1]', '[277, 277, -w^3 + 2*w^2 + 5*w - 5]', '[289, 17, w^3 - w^2 - 6*w + 3]', '[289, 17, -w^3 + 2*w^2 + 5*w - 3]', '[311, 311, 2*w^3 - 3*w^2 - 3*w + 6]', '[311, 311, -3*w^3 + 7*w^2 + 8*w - 12]', '[337, 337, -w^3 + w^2 + 4*w - 6]', '[337, 337, -2*w^3 + 3*w^2 + 8*w - 5]', '[347, 347, 2*w^3 - 6*w^2 - 5*w + 10]', '[347, 347, 4*w^3 - 5*w^2 - 13*w + 6]', '[347, 347, -4*w^3 + 7*w^2 + 11*w - 8]', '[347, 347, -2*w^3 + 11*w + 1]', '[349, 349, 3*w^2 - w - 6]', '[349, 349, -2*w^3 + 3*w^2 + 10*w + 3]', '[359, 359, 2*w^3 - 2*w^2 - 7*w + 4]', '[359, 359, -3*w^3 + 4*w^2 + 11*w - 7]', '[359, 359, w^3 - 2*w^2 + w - 4]', '[359, 359, 2*w^3 - 4*w^2 - 5*w + 3]', '[373, 373, -3*w^3 + 3*w^2 + 9*w - 1]', '[373, 373, w^3 + 2*w^2 - 7*w - 9]', '[383, 383, 2*w^2 - 7]', '[383, 383, 2*w^2 - 4*w - 5]', '[409, 409, -w^3 + 5*w^2 - 3*w - 7]', '[409, 409, -w^3 - 2*w^2 + 4*w + 6]', '[419, 419, w^3 - 3*w - 6]', '[419, 419, -w^3 + 3*w^2 - 8]', '[443, 443, -3*w^3 + 5*w^2 + 10*w - 12]', '[443, 443, -3*w^3 + 7*w^2 + 7*w - 11]', '[457, 457, -w^3 + 2*w^2 + 3*w - 8]', '[457, 457, w^3 - w^2 - 4*w - 4]', '[467, 467, w^2 + 2*w - 6]', '[467, 467, w^2 - 4*w - 3]', '[491, 491, 3*w^3 - 2*w^2 - 10*w - 4]', '[491, 491, -2*w^3 + 2*w^2 + 7*w - 5]', '[491, 491, -2*w^3 + 4*w^2 + 5*w - 2]', '[491, 491, -3*w^3 + 7*w^2 + 5*w - 13]', '[529, 23, 3*w^2 - 3*w - 4]', '[541, 541, 2*w^3 - 2*w^2 - 5*w + 7]', '[541, 541, -4*w^3 + 7*w^2 + 10*w - 12]', '[577, 577, 3*w^2 - 2*w - 7]', '[577, 577, -3*w^3 + 6*w^2 + 10*w - 10]', '[577, 577, -2*w^3 - w^2 + 7*w + 4]', '[577, 577, 3*w^2 - 4*w - 6]', '[587, 587, 2*w^3 - w^2 - 6*w - 4]', '[587, 587, 2*w^3 - w^2 - 11*w - 4]', '[599, 599, -4*w^3 + 3*w^2 + 14*w + 5]', '[599, 599, -w^3 + 7*w + 5]', '[601, 601, 3*w^3 - 4*w^2 - 8*w + 4]', '[601, 601, -3*w^3 + 5*w^2 + 7*w - 5]', '[613, 613, 3*w^2 - 2*w - 6]', '[613, 613, 3*w^2 - 4*w - 5]', '[625, 5, -5]', '[647, 647, 3*w^3 - 3*w^2 - 12*w + 4]', '[647, 647, -3*w^3 + 6*w^2 + 9*w - 8]', '[661, 661, w^3 + 2*w^2 - 5*w - 7]', '[661, 661, -w^2 - 3]', '[661, 661, -w^2 + 2*w - 4]', '[661, 661, -w^3 + 5*w^2 - 2*w - 9]', '[673, 673, 3*w^3 - 3*w^2 - 8*w + 2]', '[673, 673, -3*w^3 + 6*w^2 + 5*w - 6]', '[683, 683, -w^3 + 3*w^2 - 2*w - 4]', '[683, 683, w^3 - w - 4]', '[709, 709, 4*w^3 - 7*w^2 - 10*w + 8]', '[709, 709, w^3 - w^2 - 3*w - 5]', '[709, 709, -w^3 + 2*w^2 + 2*w - 8]', '[709, 709, -w^3 + 5*w^2 + w - 9]', '[719, 719, 2*w^3 - w^2 - 8*w + 2]', '[719, 719, -2*w^3 + 5*w^2 + 4*w - 5]', '[733, 733, -w^3 + 5*w^2 - w - 11]', '[733, 733, 3*w^3 - 5*w^2 - 6*w + 7]', '[743, 743, w^2 - 4*w - 4]', '[743, 743, -3*w^3 + 7*w^2 + 6*w - 9]', '[743, 743, 3*w^3 - 2*w^2 - 11*w + 1]', '[743, 743, w^2 + 2*w - 7]', '[769, 769, -2*w^2 - 3*w + 4]', '[769, 769, 4*w^3 - 4*w^2 - 14*w - 5]', '[827, 827, -w^2 + 4*w + 7]', '[827, 827, -2*w^3 + w^2 + 7*w - 4]', '[827, 827, -2*w^3 + 5*w^2 + 3*w - 2]', '[827, 827, -2*w^3 + w^2 + 11*w + 6]', '[829, 829, -2*w^3 + 4*w^2 + 8*w - 9]', '[829, 829, -3*w^3 + 5*w^2 + 6*w - 3]', '[829, 829, 3*w^3 - 4*w^2 - 7*w + 5]', '[829, 829, 2*w^3 - 2*w^2 - 10*w + 1]', '[839, 839, 2*w^3 - 9*w]', '[839, 839, 2*w^2 - 4*w - 7]', '[841, 29, -4*w^3 + 9*w^2 + 6*w - 11]', '[841, 29, 4*w^2 - 3*w - 12]', '[853, 853, -3*w^3 + 5*w^2 + 11*w - 7]', '[853, 853, -3*w^3 + 4*w^2 + 12*w - 6]', '[863, 863, -3*w^3 + 2*w^2 + 10*w - 2]', '[863, 863, 4*w^3 - 6*w^2 - 11*w + 13]', '[877, 877, -w^3 - w^2 + 10*w]', '[877, 877, w^3 - 3*w^2 - 8*w]', '[887, 887, -3*w^3 + 4*w^2 + 10*w - 8]', '[887, 887, w^3 - 5*w^2 - 4*w + 12]', '[887, 887, w^3 + 2*w^2 - 11*w - 4]', '[887, 887, 3*w^3 - 5*w^2 - 9*w + 3]', '[911, 911, 4*w^3 - 3*w^2 - 14*w + 1]', '[911, 911, 5*w^3 - 6*w^2 - 17*w - 1]', '[937, 937, w^3 + 2*w^2 - 7*w - 7]', '[937, 937, w^3 - 5*w^2 + 11]', '[947, 947, 2*w^3 - w^2 - 10*w + 3]', '[947, 947, -2*w^3 + 5*w^2 + 6*w - 6]', '[961, 31, -4*w^3 + 8*w^2 + 13*w - 13]', '[961, 31, 2*w^3 + w^2 - 8*w - 5]', '[971, 971, -5*w^3 + 7*w^2 + 15*w - 11]', '[971, 971, -2*w^3 + 6*w + 5]', '[983, 983, 2*w^3 - 4*w^2 - 7*w + 1]', '[983, 983, 4*w^2 + 3*w - 3]', '[997, 997, 3*w^3 - 5*w^2 - 6*w + 4]', '[997, 997, -3*w^3 + 4*w^2 + 7*w - 4]']}
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nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 4, -3, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 4752, 'disc_rad': 66, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[4, 1]]], [7, [[4, 1]]], [11, [0]], [13, [[2, 1], [1, 2]]], [17, [[2, 2]]], [19, [[4, 1]]], [23, [[2, 1], [1, 2]]], [29, [[2, 2]]], [31, [[2, 2]]], [37, [[2, 2]]], [41, [[2, 2]]], [43, [[4, 1]]], [47, [[2, 1], [1, 2]]], [53, [[4, 1]]], [59, [[2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [8, 6, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 15.120539229772588, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.4752.1', 'local_algs': ['2.4.4.1', '3.4.3.2', '11.2.0.1', '11.2.1.2'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 3, 11], 'rd': 8.30269545139, 'regulator': {'__RealLiteral__': 0, 'data': '3.7053371595', 'prec': 40}, 'res': {'gal': ['1,0,-11,0,24,0,-11,0,1'], 'sib': ['1,-1,-6,-1,1', '1,0,-11,0,24,0,-11,0,1']}, 'subfield_mults': [1], 'subfields': ['-3.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 1 \\)', '\\( a \\)', '\\( a^{2} - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}