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hmf_forms • Show schema
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{'deg': 4, 'dimension': 1, 'disc': 9248, 'field_bad_primes': [2, 17], 'field_label': '4.4.9248.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.9248.1-16.2-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [2], 'level_ideal': '[16, 4, -w^3 - w^2 + 4*w + 2]', 'level_label': '16.2', 'level_norm': 16, 'parallel_weight': 2, 'short_label': '16.2-c', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[2,2,w]', -1], ['[2,2,w+1]', -1]], 'hecke_eigenvalues': [0, 1, -2, 6, 4, -4, -4, 4, 2, 2, 6, -2, -4, 4, -4, -4, 10, 12, -4, -6, 2, 2, 10, 6, -10, -8, -16, -8, 8, 16, 8, -16, -8, -2, -10, -8, 8, 16, 8, 14, -10, -6, -4, -4, 30, -10, -12, 12, 8, 24, -16, 24, -22, 22, 6, 28, 12, 12, 4, -2, -2, 10, -10, -26, 0, 0, -32, 32, 6, 6, 6, -26, 2, 34, 2, 2, 4, -36, -22, 10, -22, -22, -18, 30, -40, 16, 40, 0, -12, 28, -28, 20, 6, -2, 4, -12, -14, -30, 14, -18, 4, -36, -14, -6, -38, -30, 4, -28, -14, -30, 34, 18, -16, -24, 40, -8, -26, 30, 26, -36, 12, 22, -26, -18, 30, -26, -2, -44, -20, 6, -42, 14, 6, 38, -18, 30, -50, 20, 4, -48, -40, -16, -24, -20, -36, 26, -46, -30, -6, 2, 2, -12, -12, 58, 18, 50, -54], 'hecke_polynomial': 'x', 'label': '4.4.9248.1-16.2-c'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 9248, 'ideals': ['[1, 1, 1]', '[2, 2, w]', '[2, 2, w + 1]', '[4, 2, -w^2 + 4]', '[4, 2, w^2 - w - 2]', '[4, 2, -w^2 + 1]', '[8, 2, w^3 - w^2 - 4*w + 4]', '[8, 2, -w^3 + 5*w]', '[8, 4, -w^3 + 4*w]', '[8, 4, -w^2 - 2*w + 1]', '[13, 13, -w^2 + w + 3]', '[13, 13, w^2 + w - 3]', '[16, 2, 2]', '[16, 4, -w^3 - w^2 + 4*w + 2]', '[16, 4, -w^2 + 3]', '[16, 4, -w^2 + 2]', '[16, 4, -w^3 + 5*w + 2]', '[19, 19, -w^3 + 3*w + 1]', '[19, 19, -w^3 + 3*w - 1]', '[26, 26, -w^3 + w^2 + 3*w]', '[26, 26, -w^3 + 4*w - 3]', '[26, 26, -w^3 + 4*w + 3]', '[26, 26, w^3 + w^2 - 3*w]', '[32, 4, 2*w]', '[32, 4, w^3 - w^2 - 6*w + 2]', '[32, 4, -w^3 + 3*w]', '[32, 4, 2*w + 2]', '[32, 8, -w^3 + 2*w]', '[32, 8, -w^3 - w^2 + 3*w + 3]', '[38, 38, -w - 3]', '[38, 38, w^3 + w^2 - 5*w - 2]', '[38, 38, w^3 - w^2 - 5*w + 2]', '[38, 38, w - 3]', '[43, 43, -w^2 + w - 1]', '[43, 43, w^2 + w + 1]', '[49, 7, w^3 + w^2 - 6*w - 3]', '[49, 7, w^3 - w^2 - 6*w + 3]', '[52, 26, 2*w^3 + w^2 - 8*w - 3]', '[52, 26, w^3 - 6*w - 2]', '[52, 26, w^2 + w - 4]', '[52, 26, -2*w^3 + w^2 + 8*w - 3]', '[52, 26, -w^2 + w + 4]', '[52, 26, -w^3 + 6*w - 2]', '[53, 53, 2*w^3 - w^2 - 9*w + 3]', '[53, 53, 2*w^3 + w^2 - 9*w - 3]', '[59, 59, w^3 - w^2 - 4*w + 1]', '[59, 59, -w^3 - w^2 + 4*w + 1]', '[64, 4, -2*w^2 + 8]', '[64, 4, 2*w^2 - 2*w - 4]', '[64, 4, -2*w^2 + 2]', '[64, 8, w^2 + 1]', '[64, 8, -w^2 + 6]', '[64, 8, w^3 - w^2 - 2*w - 2]', '[64, 8, -w^3 + 3*w - 4]', '[67, 67, 3*w^3 - 13*w + 1]', '[67, 67, -w^3 + w^2 + 6*w - 5]', '[76, 38, -2*w^3 - w^2 + 10*w + 4]', '[76, 38, w^2 + 2*w - 3]', '[76, 38, -w^2 - 3*w]', '[76, 38, -2*w^3 + w^2 + 10*w - 4]', '[76, 38, w^2 - 3*w]', '[76, 38, w^2 - 2*w - 3]', '[81, 3, -3]', '[83, 83, -2*w^3 - w^2 + 9*w + 7]', '[83, 83, 4*w^3 - 18*w - 1]', '[86, 86, 3*w^3 - w^2 - 13*w + 4]', '[86, 86, 2*w^3 - 7*w - 3]', '[86, 86, -2*w^3 + 7*w - 3]', '[86, 86, -3*w^3 - w^2 + 13*w + 4]', '[89, 89, -2*w^3 + 10*w + 1]', '[89, 89, -w^2 + w + 5]', '[89, 89, w^2 + w - 5]', '[89, 89, 2*w^3 - 10*w + 1]', '[98, 14, -2*w^3 + 9*w + 2]', '[98, 14, -2*w^3 + 9*w - 2]', '[98, 14, -w^3 - 2*w^2 + 4*w + 7]', '[98, 14, w^3 - 2*w^2 - 4*w + 7]', '[101, 101, -2*w^3 + 8*w + 1]', '[101, 101, 2*w^3 - 8*w + 1]', '[103, 103, w^3 + 2*w^2 - 5*w - 7]', '[103, 103, w^3 + w^2 - 6*w - 7]', '[103, 103, -w^2 - 3*w + 1]', '[103, 103, -w^3 + 2*w^2 + 5*w - 7]', '[104, 26, w^3 + 2*w^2 - 3*w - 4]', '[104, 26, w^3 + w^2 - 4*w]', '[104, 26, -w^3 + w^2 + 4*w]', '[104, 26, w^3 - 2*w^2 - 3*w + 4]', '[104, 52, -w^2 - 2*w - 2]', '[104, 52, -w^3 - w^2 + 5*w + 1]', '[104, 52, w^3 - w^2 - 5*w + 1]', '[104, 52, w^2 - 2*w + 2]', '[106, 106, w^3 - 6*w - 1]', '[106, 106, w^3 + w^2 - 3*w - 4]', '[106, 106, -w^3 + w^2 + 3*w - 4]', '[106, 106, 3*w^3 + 2*w^2 - 12*w - 7]', '[118, 118, -w^3 + w^2 + w - 2]', '[118, 118, -2*w^3 - 2*w^2 + 5*w + 3]', '[118, 118, -3*w - 1]', '[118, 118, -w^3 - w^2 + w + 2]', '[127, 127, -w^3 + 2*w^2 + 5*w - 5]', '[127, 127, w^3 + 3*w^2 - 4*w - 13]', '[127, 127, -w^3 + 3*w^2 + 4*w - 13]', '[127, 127, w^3 + 2*w^2 - 5*w - 5]', '[128, 4, 2*w^3 - 2*w^2 - 8*w + 8]', '[128, 4, -2*w^3 + 10*w]', '[128, 8, -3*w^3 + 13*w]', '[128, 8, -2*w^3 + 8*w]', '[128, 8, -w^3 - w^2 + 6*w + 6]', '[128, 8, -2*w^2 - 4*w + 2]', '[128, 16, -w^3 + 6*w]', '[128, 16, 2*w^3 + w^2 - 6*w + 1]', '[134, 134, w^3 - w^2 - 5*w - 2]', '[134, 134, 2*w^2 + w - 3]', '[134, 134, 2*w^3 - 11*w - 7]', '[134, 134, w^3 + w^2 - 5*w + 2]', '[149, 149, -2*w^3 - w^2 + 7*w - 1]', '[149, 149, 2*w^3 - w^2 - 7*w - 1]', '[151, 151, -w^3 + w^2 + 2*w - 3]', '[151, 151, 2*w^3 - 10*w + 3]', '[151, 151, -2*w^3 + 10*w + 3]', '[151, 151, w^3 + w^2 - 2*w - 3]', '[152, 38, -w^3 - w^2 + 6*w]', '[152, 38, -w^3 - 2*w^2 + 5*w + 6]', '[152, 38, -w^3 + w^2 + 6*w]', '[152, 38, w^3 - 2*w^2 - 5*w + 6]', '[152, 76, -2*w^3 + w^2 + 8*w - 1]', '[152, 76, w^3 - 4*w + 4]', '[152, 76, -w^3 + 4*w + 4]', '[152, 76, -2*w^3 - w^2 + 8*w + 1]', '[157, 157, w^3 + 2*w^2 - 3*w - 1]', '[157, 157, -w^3 + 2*w^2 + 3*w - 1]', '[162, 6, -3*w]', '[162, 6, -3*w - 3]', '[166, 166, -3*w^3 - 2*w^2 + 16*w + 11]', '[166, 166, 2*w^2 - w - 8]', '[166, 166, -w^3 - w^2 + 7*w + 4]', '[166, 166, 4*w^3 + 2*w^2 - 19*w - 9]', '[169, 13, 2*w^2 - 7]', '[169, 13, 2*w^2 - 3]', '[169, 169, w^3 - w^2 - 4*w + 7]', '[169, 169, -w^3 - w^2 + 4*w + 7]', '[172, 86, -w^3 + w^2 + 5*w - 7]', '[172, 86, -w^3 + 2*w^2 + 4*w - 6]', '[172, 86, 2*w^3 + w^2 - 9*w - 2]', '[172, 86, -w^3 - w^2 + 5*w + 7]', '[172, 86, -2*w^3 + w^2 + 9*w - 2]', '[172, 86, -w^3 - 2*w^2 + 4*w + 6]', '[178, 178, w + 4]', '[178, 178, -w^3 + w^2 + 5*w]', '[178, 178, w^3 + 2*w^2 - 4*w - 5]', '[178, 178, 2*w^3 - 11*w + 5]', '[178, 178, -2*w^3 + 9*w - 3]', '[178, 178, -w^3 + 6*w + 5]', '[178, 178, w^3 + w^2 - 5*w]', '[178, 178, w - 4]', '[179, 179, 2*w^3 + w^2 - 7*w - 3]', '[179, 179, -2*w^3 + w^2 + 7*w - 3]', '[196, 14, -w^3 - w^2 + 3*w + 5]', '[196, 14, w^3 - w^2 - 3*w + 5]', '[196, 14, -2*w^3 + w^2 + 7*w - 2]', '[196, 14, -w^2 + 2*w + 4]', '[196, 14, -w^2 - 2*w + 4]', '[196, 14, -2*w^3 - w^2 + 7*w + 2]', '[202, 202, -2*w^3 - 2*w^2 + 9*w + 5]', '[202, 202, 2*w^2 + w - 4]', '[202, 202, -2*w^2 + w + 4]', '[202, 202, 2*w^3 + 2*w^2 - 7*w - 3]', '[206, 206, 2*w^3 - 7*w - 2]', '[206, 206, 2*w^3 - 13*w - 9]', '[206, 206, w^3 + w^2 - 7*w + 2]', '[206, 206, w^3 + 2*w^2 - 2*w - 5]', '[206, 206, 3*w^3 + 2*w^2 - 12*w - 9]', '[206, 206, w^3 - w^2 - 7*w - 2]', '[206, 206, 2*w^2 - w - 5]', '[206, 206, 2*w^3 - 7*w + 2]', '[208, 26, -2*w^2 + 2*w + 6]', '[208, 26, 2*w^2 + 2*w - 6]', '[208, 52, -3*w^3 - w^2 + 12*w + 6]', '[208, 52, -w^3 + w + 2]', '[208, 52, -w^3 - w^2 + 3*w + 7]', '[208, 52, -w^3 + 2*w + 4]', '[208, 52, -w^3 + w^2 + 3*w - 7]', '[208, 52, -w^3 + 2*w - 4]', '[208, 52, -w^3 + w - 2]', '[208, 52, 3*w^3 - w^2 - 12*w + 6]', '[212, 106, -w^2 - w - 2]', '[212, 106, w^3 - 2*w^2 - 4*w + 2]', '[212, 106, w^3 + w^2 - 5*w + 1]', '[212, 106, w^3 + 2*w^2 - 4*w - 2]', '[212, 106, 2*w^3 + 3*w^2 - 7*w - 6]', '[212, 106, w^3 - w^2 - 5*w - 1]', '[229, 229, -w^3 + 2*w^2 + 3*w - 7]', '[229, 229, w^3 + 2*w^2 - 3*w - 7]', '[236, 118, 3*w^2 - 2*w - 1]', '[236, 118, 3*w^3 - 14*w + 2]', '[236, 118, -3*w^2 + 5*w + 2]', '[236, 118, 3*w^2 + 2*w - 1]', '[236, 118, 2*w^3 - w^2 - 7*w - 2]', '[236, 118, -3*w^3 + 14*w + 2]', '[247, 247, w^3 - w^2 - 6*w - 1]', '[247, 247, 2*w^3 - 2*w^2 - 6*w + 1]', '[247, 247, -2*w^3 - 2*w^2 + 6*w + 1]', '[247, 247, -w^3 - w^2 + 6*w - 1]', '[251, 251, -2*w^3 + 2*w^2 + 8*w - 9]', '[251, 251, -2*w^3 - 2*w^2 + 8*w + 9]', '[254, 254, w^3 + 2*w^2 - 3]', '[254, 254, -2*w^3 + 2*w^2 + 9*w - 11]', '[254, 254, 3*w^3 - w^2 - 13*w + 2]', '[254, 254, 2*w^3 - 5*w - 2]', '[254, 254, 2*w^3 - 5*w + 2]', '[254, 254, 3*w^3 + w^2 - 13*w - 2]', '[254, 254, -4*w^3 + 4*w^2 + 17*w - 15]', '[254, 254, 3*w^3 + 2*w^2 - 10*w - 7]', '[256, 4, 4]', '[256, 8, -2*w^3 - 2*w^2 + 8*w + 4]', '[256, 8, -2*w^2 + 6]', '[256, 8, -2*w^2 + 4]', '[256, 8, -2*w^3 + 10*w + 4]', '[256, 16, w^2 + 2]', '[256, 16, -w^3 + w^2 + 6*w + 2]', '[256, 16, -w^2 + 7]', '[256, 16, -3*w^3 - 2*w^2 + 13*w + 6]', '[263, 263, 2*w^3 - w^2 - 3*w + 1]', '[263, 263, -2*w^3 + 2*w^2 + 10*w - 5]', '[263, 263, -2*w^3 - 2*w^2 + 10*w + 5]', '[263, 263, -2*w^3 - w^2 + 3*w + 1]', '[268, 134, 5*w^3 + 4*w^2 - 22*w - 18]', '[268, 134, -4*w^3 - w^2 + 15*w + 10]', '[268, 134, 2*w^3 + w^2 - 4*w - 3]', '[268, 134, 2*w^3 - 3*w^2 - 5*w + 6]', '[268, 134, -5*w^3 + 4*w^2 + 22*w - 18]', '[268, 134, -2*w^3 + w^2 + 4*w - 3]', '[289, 17, 2*w^2 - 5]', '[293, 293, 4*w^3 - w^2 - 19*w + 7]', '[293, 293, -4*w^3 - w^2 + 19*w + 7]', '[298, 298, -3*w^3 - 4*w^2 + 6*w + 3]', '[298, 298, w^3 - 3*w^2 + w + 4]', '[298, 298, -w^3 - 3*w^2 - w + 4]', '[298, 298, -w^3 - 2*w^2 + 8*w + 5]', '[302, 302, -2*w^2 - w - 1]', '[302, 302, 2*w^3 - 7*w - 1]', '[302, 302, 3*w + 4]', '[302, 302, w^3 + 3*w^2 - 3*w - 2]', '[302, 302, w^3 - 3*w^2 - 3*w + 2]', '[302, 302, 3*w - 4]', '[302, 302, -2*w^3 + 13*w + 7]', '[302, 302, 2*w^3 + 4*w^2 - 5*w - 5]', '[304, 38, -2*w^3 + 6*w + 2]', '[304, 38, -2*w^3 + 6*w - 2]', '[304, 76, w^3 - 2*w^2 - w + 4]', '[304, 76, -w^3 + 2*w^2 + 6*w - 8]', '[304, 76, -w^3 - w^2 + 7*w + 3]', '[304, 76, w^3 + w^2 + 2]', '[304, 76, -w^3 + w^2 + 2]', '[304, 76, w^3 + 2*w^2 - 6*w - 8]', '[304, 76, -w^3 + w^2 + 7*w - 3]', '[304, 76, -w^3 - 2*w^2 + w + 4]', '[307, 307, -w^3 + 3*w - 5]', '[307, 307, w^3 - 3*w - 5]', '[314, 314, 2*w^2 - w - 10]', '[314, 314, 2*w^2 + 3*w - 5]', '[314, 314, 2*w^3 + 2*w^2 - 3*w + 3]', '[314, 314, -2*w^2 - w + 10]', '[324, 6, 3*w^2 - 12]', '[324, 6, -3*w^2 + 3*w + 6]', '[324, 6, 3*w^2 - 3]', '[331, 331, 4*w^3 - 2*w^2 - 18*w + 7]', '[331, 331, 5*w^3 - 3*w^2 - 22*w + 11]', '[332, 166, -w^3 + 2*w^2 + 4*w + 2]', '[332, 166, -w^3 - 3*w^2 + 5*w + 5]', '[332, 166, -2*w^3 + w^2 + 11*w + 6]', '[332, 166, 2*w^3 - w^2 - 8*w]', '[332, 166, 2*w^3 + w^2 - 9*w - 8]', '[332, 166, 2*w^3 + w^2 - 10*w - 1]', '[338, 26, 2*w^3 - 7*w]', '[338, 26, 4*w^3 - 19*w]', '[338, 26, 2*w^3 + 2*w^2 - 7*w - 7]', '[338, 26, -w^3 + 2*w^2 + 8*w - 3]', '[338, 338, -w^3 + w^2 + 7*w - 2]', '[338, 338, -3*w + 5]', '[338, 338, 3*w + 5]', '[338, 338, -w^3 - w^2 + 7*w + 2]', '[344, 86, w^3 + w^2 - 2*w - 4]', '[344, 86, w^3 - 7*w + 2]', '[344, 86, w^3 - w^2 - 2*w + 4]', '[344, 86, -w^3 + 7*w + 2]', '[344, 172, 2*w^3 - w^2 - 6*w + 2]', '[344, 172, -w^2 - 2*w + 5]', '[344, 172, w^2 - 2*w - 5]', '[344, 172, -2*w^3 - w^2 + 6*w + 2]', '[349, 349, -3*w^3 + 13*w + 3]', '[349, 349, -3*w^3 + 13*w - 3]', '[356, 178, -2*w^3 - w^2 + 6*w + 1]', '[356, 178, w^2 + 4*w]', '[356, 178, w^2 + 5*w + 4]', '[356, 178, -w^3 - w^2 + w + 3]', '[356, 178, w^3 + 2]', '[356, 178, w^2 + 5*w + 2]', '[356, 178, -w^3 + w^2 + w - 3]', '[356, 178, 2*w^3 + w^2 - 5*w - 2]', '[356, 178, w^3 - 2]', '[356, 178, 2*w^3 - w^2 - 6*w + 1]', '[356, 178, w^2 - 3*w - 4]', '[356, 178, w^2 - 4*w]', '[358, 358, w^3 + 3*w^2 - 3*w - 4]', '[358, 358, -w^3 - 2*w^2 + 4*w + 1]', '[358, 358, 3*w^3 + 4*w^2 - 10*w - 7]', '[358, 358, w^3 - 3*w^2 - 3*w + 4]', '[361, 19, 2*w^2 - 11]', '[361, 19, 2*w^2 + 1]', '[361, 361, 2*w^3 - w^2 - 9*w + 1]', '[361, 361, 2*w^3 + w^2 - 9*w - 1]', '[373, 373, w^3 + 2*w^2 + w - 3]', '[373, 373, -w^3 + 2*w^2 - w - 3]', '[383, 383, -w^3 + 5*w + 5]', '[383, 383, -3*w^3 + 2*w^2 + 11*w - 5]', '[383, 383, 3*w^3 + 2*w^2 - 11*w - 5]', '[383, 383, w^3 - 5*w + 5]', '[389, 389, w^3 - 4*w^2 + w + 7]', '[389, 389, -2*w^3 - w^2 + 7*w + 7]', '[392, 14, w^3 - 3*w^2 - 2*w + 4]', '[392, 14, -w^3 - 3*w^2 + 2*w + 4]', '[392, 14, -w^3 - 2*w^2 + 5*w + 2]', '[392, 14, -w^3 + 2*w^2 + 5*w - 2]', '[392, 28, -w^3 - 2*w^2 + 4*w]', '[392, 28, -w^3 + 2*w^2 + 4*w]', '[392, 28, w^2 + 2*w + 3]', '[392, 28, w^2 - 2*w + 3]', '[404, 202, 2*w^3 + 3*w^2 - 13*w - 6]', '[404, 202, -6*w^3 - w^2 + 28*w + 4]', '[404, 202, -w^2 + 4*w + 1]', '[404, 202, 6*w^3 - w^2 - 28*w + 4]', '[404, 202, -2*w^3 - w^2 + 11*w + 2]', '[404, 202, -w^2 - 4*w + 1]', '[412, 206, 4*w^3 + 5*w^2 - 18*w - 24]', '[412, 206, -4*w^3 - w^2 + 15*w + 12]', '[412, 206, w^3 - w^2 - 3*w - 3]', '[412, 206, -4*w^3 - 3*w^2 + 17*w + 14]', '[412, 206, 5*w^3 + 6*w^2 - 22*w - 26]', '[412, 206, 2*w^3 + 3*w^2 - 4*w - 5]', '[412, 206, -5*w^3 + 6*w^2 + 22*w - 26]', '[412, 206, 2*w^3 - 5*w^2 - 3*w + 10]', '[412, 206, -2*w^3 + 3*w^2 + 4*w - 5]', '[412, 206, -4*w^3 + 5*w^2 + 18*w - 24]', '[412, 206, -w^3 - w^2 + 3*w - 3]', '[412, 206, -w^2 - w + 8]', '[416, 52, -2*w^3 + 2*w^2 + 6*w]', '[416, 52, -2*w^3 + 8*w - 6]', '[416, 52, -w^3 - 2*w^2 + 7*w + 2]', '[416, 52, 3*w^3 - w^2 - 14*w + 2]', '[416, 52, w^3 - 2*w^2 - 7*w + 2]', '[416, 52, -3*w^3 - w^2 + 14*w + 2]', '[416, 52, -2*w^3 + 8*w + 6]', '[416, 52, 2*w^3 + 2*w^2 - 6*w]', '[416, 104, 2*w^3 + 3*w^2 - 8*w - 10]', '[416, 104, -2*w^3 + 3*w^2 + 10*w - 9]', '[416, 104, -2*w^3 - 3*w^2 + 10*w + 9]', '[416, 104, 2*w^3 - 3*w^2 - 8*w + 10]', '[421, 421, -w^3 - w^2 - 2*w + 1]', '[421, 421, w^3 - w^2 + 2*w + 1]', '[424, 106, -w^3 + w^2 + 4]', '[424, 106, w^3 + w - 2]', '[424, 106, -w^3 - w - 2]', '[424, 106, -w^3 - 3*w^2 + 8*w + 8]', '[424, 212, 3*w^3 - w^2 - 11*w + 9]', '[424, 212, 2*w^3 + 3*w^2 - 10*w - 14]', '[424, 212, -2*w^3 + 3*w^2 + 10*w - 14]', '[424, 212, -w^3 - 3*w^2 + w + 7]', '[433, 433, 4*w^3 - 2*w^2 - 16*w + 5]', '[433, 433, -4*w + 1]', '[433, 433, 4*w + 1]', '[433, 433, -5*w^3 + 3*w^2 + 24*w - 13]', '[443, 443, -w^3 + w^2 + 3]', '[443, 443, -4*w^2 + 6*w + 7]', '[457, 457, 3*w^3 + w^2 - 12*w - 3]', '[457, 457, -2*w^3 + 6*w - 1]', '[457, 457, 2*w^3 - 6*w - 1]', '[457, 457, 3*w^3 - 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3]', '[916, 458, -2*w^3 - 3*w^2 + 11*w + 12]', '[916, 458, 2*w^3 + 5*w^2 - 10*w - 24]', '[922, 922, -3*w^3 + 3*w^2 + 7*w - 2]', '[922, 922, 4*w^3 + 6*w^2 - 9*w - 9]', '[922, 922, -2*w^3 + 5*w + 5]', '[922, 922, 3*w^3 + 3*w^2 - 7*w - 2]', '[926, 926, w^3 + 2*w^2 - 2*w - 7]', '[926, 926, -w^3 + 3*w^2 + 5*w - 16]', '[926, 926, -2*w^3 - 2*w^2 + 3*w - 5]', '[926, 926, -3*w^3 - w^2 + 11*w + 4]', '[926, 926, 3*w^3 - w^2 - 11*w + 4]', '[926, 926, 2*w^3 - 7*w + 7]', '[926, 926, -w^3 - 3*w^2 + 5*w + 16]', '[926, 926, -5*w^3 - 4*w^2 + 20*w + 15]', '[931, 133, -4*w^3 + 18*w + 3]', '[931, 133, 3*w^2 + w - 5]', '[931, 133, -4*w^3 + 18*w - 3]', '[931, 133, 3*w^2 - w - 5]', '[934, 934, w^3 - 2*w^2 - 6*w - 1]', '[934, 934, 2*w^2 + w + 2]', '[934, 934, -2*w^2 + w - 2]', '[934, 934, -w^3 + 2*w^2 + 8*w + 3]', '[944, 118, 2*w^3 - 2*w^2 - 8*w + 2]', '[944, 118, -2*w^3 - 2*w^2 + 8*w + 2]', '[944, 236, w^3 + 3*w^2 - 4*w - 6]', '[944, 236, -3*w^3 - 4*w^2 + 11*w + 10]', '[944, 236, 2*w^3 + w^2 - 10*w + 1]', '[944, 236, w^3 + 2*w^2 - 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5]', '[1862, 266, -2*w^3 - 2*w^2 + 13*w + 3]', '[1862, 266, -2*w^2 - 3*w + 8]', '[1862, 266, 4*w^3 - 2*w^2 - 15*w + 12]', '[1862, 266, -2*w^2 + 3*w + 8]', '[1862, 266, -4*w^3 - 2*w^2 + 15*w + 12]', '[1862, 266, -4*w^3 - 2*w^2 + 15*w + 5]', '[1862, 266, -2*w^3 + 2*w^2 + 13*w - 3]', '[1868, 934, 6*w^3 - w^2 - 26*w + 4]', '[1868, 934, 3*w^3 - w^2 - 5*w + 1]', '[1868, 934, -4*w^3 + 3*w^2 + 11*w]', '[1868, 934, -6*w^3 - w^2 + 26*w + 4]', '[1868, 934, 4*w^3 - w^2 - 13*w - 4]', '[1868, 934, -3*w^3 - w^2 + 5*w + 1]', '[1871, 1871, 4*w^3 + w^2 - 15*w - 13]', '[1871, 1871, w^3 - 9*w - 3]', '[1871, 1871, -w^3 + 9*w - 3]', '[1871, 1871, w^3 - w - 9]', '[1879, 1879, 7*w^2 - 9*w - 11]', '[1879, 1879, -2*w^3 + 6*w^2 + 10*w - 27]', '[1879, 1879, 2*w^3 + 6*w^2 - 10*w - 27]', '[1879, 1879, -w^3 + 4*w^2 + w - 7]', '[1888, 236, -2*w^3 + 2*w^2 + 2*w - 4]', '[1888, 236, -4*w^3 - 4*w^2 + 10*w + 6]', '[1888, 236, w^3 + w - 4]', '[1888, 236, 3*w^3 - w^2 - 10*w + 10]', '[1888, 236, w^3 + w + 4]', '[1888, 236, w^3 + 5*w^2 + 2*w - 10]', '[1888, 236, -6*w - 2]', '[1888, 236, -2*w^3 - 2*w^2 + 2*w + 4]', '[1888, 472, 2*w^3 - w^2 - 2]', '[1888, 472, -w^3 + w^2 + 11*w + 5]', '[1888, 472, 3*w^3 + w^2 - 9*w - 3]', '[1888, 472, 2*w^3 + w^2 + 2]', '[1889, 1889, 4*w^3 - 20*w - 1]', '[1889, 1889, 5*w^2 + 5*w - 13]', '[1889, 1889, 3*w^3 - 2*w^2 - 11*w + 13]', '[1889, 1889, 4*w^3 - 20*w + 1]', '[1906, 1906, -2*w^3 + 2*w^2 + 11*w + 5]', '[1906, 1906, 2*w^3 + 2*w^2 - 9*w - 1]', '[1906, 1906, -2*w^3 - 4*w^2 + 7*w + 8]', '[1906, 1906, -w^3 - 3*w^2 + 3*w - 2]', '[1906, 1906, -w^3 + 3*w^2 + 3*w + 2]', '[1906, 1906, w^3 - w^2 - 7*w - 6]', '[1906, 1906, -2*w^3 + 2*w^2 + 9*w - 1]', '[1906, 1906, -4*w^2 - 5*w + 1]', '[1919, 1919, w^3 - 5*w + 7]', '[1919, 1919, -3*w^3 + 11*w + 9]', '[1919, 1919, -3*w^3 + 11*w - 9]', '[1919, 1919, w^3 - 5*w - 7]', '[1922, 62, -6*w^3 + 4*w^2 + 27*w - 14]', '[1922, 62, 5*w^3 - 3*w^2 - 21*w + 8]', '[1922, 62, w^3 + 2*w^2 - 4*w - 13]', '[1922, 62, w^3 - 2*w^2 - 4*w + 13]', '[1937, 1937, 2*w^3 - 6*w^2 - 18*w + 9]', '[1937, 1937, -4*w^3 + 16*w - 1]', '[1937, 1937, 4*w^3 - 16*w - 1]', '[1937, 1937, -2*w^3 - 6*w^2 + 18*w + 9]', '[1942, 1942, -w^3 - 2*w^2 + 2*w + 9]', '[1942, 1942, 4*w^3 + 2*w^2 - 15*w - 6]', '[1942, 1942, -3*w^3 - w^2 + 17*w + 8]', '[1942, 1942, -w^3 + 2*w^2 + 2*w - 9]', '[1951, 1951, -w^3 + 2*w^2 + 5*w - 13]', '[1951, 1951, -3*w^3 + 2*w^2 + 7*w - 1]', '[1951, 1951, 3*w^3 + 2*w^2 - 7*w - 1]', '[1951, 1951, -w^3 - 2*w^2 + 5*w + 13]', '[1954, 1954, -w^3 + 12*w + 7]', '[1954, 1954, 5*w + 6]', '[1954, 1954, 3*w^3 - 10*w - 1]', '[1954, 1954, w^3 + w^2 + 3*w - 4]', '[1954, 1954, w^3 - w^2 + 3*w + 4]', '[1954, 1954, -3*w^3 + 10*w - 1]', '[1954, 1954, w^3 + w^2 - 9*w - 8]', '[1954, 1954, 3*w^3 + 2*w^2 - 6*w - 1]', '[1957, 1957, 4*w^3 - 3*w^2 - 13*w + 1]', '[1957, 1957, 4*w^3 + 4*w^2 - 22*w - 13]', '[1957, 1957, 6*w^3 - 5*w^2 - 25*w + 15]', '[1957, 1957, 2*w^3 - 12*w + 1]', '[1957, 1957, 2*w^3 - 12*w - 1]', '[1957, 1957, 6*w^3 + 5*w^2 - 25*w - 15]', '[1957, 1957, 4*w^3 - 4*w^2 - 22*w + 13]', '[1957, 1957, 4*w^3 + 3*w^2 - 13*w - 1]', '[1963, 1963, w^3 + 4*w^2 - 7*w - 9]', '[1963, 1963, -6*w^3 - 3*w^2 + 29*w + 13]', '[1963, 1963, w^3 + 2*w^2 + w + 5]', '[1963, 1963, 6*w^3 - 3*w^2 - 23*w + 5]', '[1963, 1963, 6*w^3 + 3*w^2 - 23*w - 5]', '[1963, 1963, w^3 - 2*w^2 + w - 5]', '[1963, 1963, -6*w^3 + 3*w^2 + 29*w - 13]', '[1963, 1963, w^3 - 4*w^2 - 7*w + 9]', '[1964, 982, 2*w^3 - w^2 - 2*w - 3]', '[1964, 982, -4*w^3 + w^2 + 11*w + 10]', '[1964, 982, 2*w^3 + 5*w^2 - 8*w - 24]', '[1964, 982, -3*w^2 + 3*w + 10]', '[1964, 982, -2*w^3 - w^2 + 2*w - 3]', '[1964, 982, -2*w^3 + 5*w^2 + 8*w - 24]', '[1973, 1973, -w^3 + 2*w^2 + 7*w - 11]', '[1973, 1973, -w^3 - 2*w^2 + 7*w + 11]', '[1976, 494, w^3 + 2*w^2 - 7*w - 12]', '[1976, 494, 3*w^3 - w^2 - 16*w + 4]', '[1976, 494, 5*w^3 + w^2 - 20*w - 8]', '[1976, 494, -3*w^3 - 2*w^2 + 7*w + 2]', '[1976, 494, 3*w^3 - 2*w^2 - 7*w + 2]', '[1976, 494, -5*w^3 + w^2 + 20*w - 8]', '[1976, 494, -3*w^3 - w^2 + 16*w + 4]', '[1976, 494, w^3 - 2*w^2 - 7*w + 12]', '[1976, 988, 2*w^3 + 3*w^2 - 6*w - 10]', '[1976, 988, 2*w^3 - w^2 - 4*w + 5]', '[1976, 988, w^3 + 8]', '[1976, 988, -5*w^3 - w^2 + 21*w + 5]', '[1976, 988, 5*w^3 - w^2 - 21*w + 5]', '[1976, 988, w^3 - 8]', '[1976, 988, 2*w^3 + w^2 - 4*w - 5]', '[1976, 988, 2*w^3 - 3*w^2 - 6*w + 10]', '[1987, 1987, -3*w^3 + 9*w - 11]', '[1987, 1987, 2*w^3 - w^2 - 7*w + 11]', '[1993, 1993, w^3 - w^2 + 4*w - 1]', '[1993, 1993, -w^3 + 2*w^2 + w - 7]', '[1993, 1993, w^3 + 2*w^2 - w - 7]', '[1993, 1993, -w^3 - w^2 - 4*w - 1]', '[1997, 1997, -7*w^3 + 3*w^2 + 30*w - 15]', '[1997, 1997, 4*w^3 - 22*w + 7]', '[2008, 502, -w^3 - 3*w^2 + 10*w]', '[2008, 502, w^3 + 4*w^2 - 5*w]', '[2008, 502, 5*w^3 - w^2 - 18*w - 8]', '[2008, 502, -w^3 + 4*w^2 + 5*w]', '[2008, 1004, -4*w^3 + 5*w^2 + 22*w - 13]', '[2008, 1004, -7*w^3 - 2*w^2 + 32*w + 12]', '[2008, 1004, 7*w^3 - 2*w^2 - 32*w + 12]', '[2008, 1004, 4*w^3 + 3*w^2 - 14*w - 3]', '[2014, 2014, w^3 + 3*w^2 - 7*w - 2]', '[2014, 2014, 3*w^3 - w^2 - 13*w - 6]', '[2014, 2014, 4*w^2 + 3*w - 7]', '[2014, 2014, -2*w^2 - 5*w - 5]', '[2014, 2014, -2*w^2 + 5*w - 5]', '[2014, 2014, 4*w^2 - 3*w - 7]', '[2014, 2014, 3*w^3 + w^2 - 13*w + 6]', '[2014, 2014, w^3 - 3*w^2 - 7*w + 2]', '[2027, 2027, -3*w^3 - w^2 + 14*w - 7]', '[2027, 2027, 3*w^3 - w^2 - 14*w - 7]', '[2032, 254, -2*w^3 + 4*w^2 + 10*w - 10]', '[2032, 254, 2*w^3 + 6*w^2 - 8*w - 26]', '[2032, 254, -2*w^3 + 6*w^2 + 8*w - 26]', '[2032, 254, 2*w^3 + 4*w^2 - 10*w - 10]', '[2032, 508, 3*w^3 + 2*w^2 - 11*w]', '[2032, 508, -3*w^3 - 2*w^2 + 11*w + 12]', '[2032, 508, -2*w^3 - w^2 + 8*w - 6]', '[2032, 508, -3*w^3 + w^2 + 13*w - 11]', '[2032, 508, w^3 + 4*w^2 - 6*w - 20]', '[2032, 508, 2*w^3 + 3*w^2 - 2*w - 5]', '[2032, 508, -3*w^3 + 3*w^2 + 4*w + 6]', '[2032, 508, 5*w^3 + w^2 - 24*w - 14]', '[2032, 508, w^3 - 3*w^2 - 8*w + 2]', '[2032, 508, -w^3 - 3*w^2 + 8*w + 10]', '[2032, 508, -w^3 + 4*w^2 + 6*w - 20]', '[2032, 508, -2*w^3 + 3*w^2 + 2*w - 5]', '[2032, 508, 2*w^3 - w^2 - 8*w - 6]', '[2032, 508, 3*w^3 + w^2 - 13*w - 11]', '[2032, 508, w^3 - 6*w^2 + 3*w + 12]', '[2032, 508, 7*w^3 + 6*w^2 - 31*w - 20]', '[2036, 1018, 3*w^3 + 8*w^2 - 14*w - 38]', '[2036, 1018, -4*w^3 - 3*w^2 + 17*w + 18]', '[2036, 1018, -w^2 - 2*w - 5]', '[2036, 1018, -2*w^3 - w^2 + 5*w + 14]', '[2036, 1018, -3*w^3 + 8*w^2 + 14*w - 38]', '[2036, 1018, -w^2 + 2*w - 5]', '[2038, 2038, 3*w^3 - w^2 - 9*w]', '[2038, 2038, 3*w^3 + 4*w^2 - 8*w - 9]', '[2038, 2038, 3*w^3 + 2*w^2 - 10*w - 9]', '[2038, 2038, 3*w^3 + w^2 - 9*w]', '[2039, 2039, -3*w^3 + 3*w^2 + 16*w - 17]', '[2039, 2039, w^3 - 3*w^2 - 6*w + 1]', '[2039, 2039, w^3 + 3*w^2 - 6*w - 1]', '[2039, 2039, -4*w^3 + 4*w^2 + 20*w - 19]', '[2041, 2041, 2*w^3 + 3*w^2 - 11*w - 15]', '[2041, 2041, 4*w^3 - 5*w^2 - 15*w + 17]', '[2041, 2041, -4*w^3 - 5*w^2 + 15*w + 17]', '[2041, 2041, -2*w^3 + 3*w^2 + 11*w - 15]', '[2042, 2042, -2*w^3 + 2*w^2 + 9*w + 3]', '[2042, 2042, -w^3 - 3*w^2 + w - 2]', '[2042, 2042, -w^3 + 3*w^2 + w + 2]', '[2042, 2042, -4*w^2 - 7*w - 1]', '[2048, 8, 4*w^3 - 4*w^2 - 16*w + 16]', '[2048, 8, -4*w^3 + 20*w]', '[2048, 16, -6*w^3 + 26*w]', '[2048, 16, -4*w^3 + 16*w]', '[2048, 16, -2*w^3 - 2*w^2 + 12*w + 12]', '[2048, 16, -4*w^2 - 8*w + 4]', '[2048, 32, -2*w^3 + 12*w]', '[2048, 32, -3*w^3 - 3*w^2 + 10*w + 10]', '[2048, 32, -5*w^3 + 2*w^2 + 19*w - 14]', '[2048, 32, 4*w^3 + 2*w^2 - 12*w + 2]', '[2048, 64, -3*w^3 + 10*w]', '[2048, 64, 2*w^3 - 3*w^2 - 14*w + 5]', '[2053, 2053, 4*w^3 + 6*w^2 - 18*w - 25]', '[2053, 2053, 4*w^2 - 2*w + 1]', '[2066, 2066, 4*w^3 + 4*w^2 - 17*w - 10]', '[2066, 2066, 6*w^3 + 2*w^2 - 27*w - 15]', '[2066, 2066, -2*w^3 + 7*w - 8]', '[2066, 2066, -w^3 + 4*w - 7]', '[2066, 2066, w^3 - 4*w - 7]', '[2066, 2066, 2*w^3 - 7*w - 8]', '[2066, 2066, 2*w^3 - 2*w^2 - 13*w - 1]', '[2066, 2066, 3*w^3 + 3*w^2 - 11*w - 4]', '[2078, 2078, -2*w^2 - w - 3]', '[2078, 2078, -3*w^3 - 4*w^2 + 12*w + 17]', '[2078, 2078, -8*w^3 + 4*w^2 + 39*w - 22]', '[2078, 2078, 2*w^3 + 4*w^2 - 7*w - 4]', '[2078, 2078, 2*w^3 - 4*w^2 - 7*w + 4]', '[2078, 2078, -5*w^3 + w^2 + 21*w - 4]', '[2078, 2078, 3*w^3 - 4*w^2 - 12*w + 17]', '[2078, 2078, 4*w^3 + 6*w^2 - 13*w - 11]', '[2083, 2083, -6*w^3 - 3*w^2 + 25*w + 13]', '[2083, 2083, -6*w^3 + 3*w^2 + 25*w - 13]', '[2087, 2087, 2*w^2 - 4*w - 7]', '[2087, 2087, -3*w^3 + w^2 + 14*w + 1]', '[2087, 2087, 3*w^3 + w^2 - 14*w + 1]', '[2087, 2087, 2*w^2 + 4*w - 7]', '[2092, 1046, -2*w^3 - 3*w^2 - w - 2]', '[2092, 1046, 3*w^3 + w^2 - 7*w + 1]', '[2092, 1046, -w^3 - 2*w^2 - 4*w + 2]', '[2092, 1046, 3*w^3 - w^2 - 7*w - 1]', '[2092, 1046, w^2 - 7*w - 6]', '[2092, 1046, -w^3 + 2*w^2 - 4*w - 2]', '[2099, 2099, 4*w^3 - 3*w^2 - 13*w + 5]', '[2099, 2099, -4*w^3 - 3*w^2 + 13*w + 5]', '[2104, 526, -w^3 + 4*w^2 + 3*w - 6]', '[2104, 526, w^3 - 3*w^2 - 6*w]', '[2104, 526, -3*w^3 - 4*w^2 - w + 4]', '[2104, 526, w^3 - w^2 + 2*w - 4]', '[2104, 526, -w^3 + 9*w^2 - 10*w - 12]', '[2104, 526, 3*w^3 - 4*w^2 + w + 4]', '[2104, 526, -w^3 + 3*w^2 + 10*w + 4]', '[2104, 526, -w^3 - 4*w^2 + 3*w + 6]', '[2104, 1052, -3*w^2 + 2*w - 2]', '[2104, 1052, -6*w^3 - 3*w^2 + 16*w - 9]', '[2104, 1052, -3*w^3 - 4*w^2 + 16*w + 16]', '[2104, 1052, -4*w^3 - 5*w^2 + 14*w + 9]', '[2104, 1052, 2*w^3 + 3*w^2 - 8*w - 3]', '[2104, 1052, 3*w^3 - 4*w^2 - 16*w + 16]', '[2104, 1052, 2*w^3 + 3*w^2 - 4*w - 7]', '[2104, 1052, 3*w^2 + 2*w + 2]', '[2106, 78, 3*w^3 - 3*w^2 - 9*w]', '[2106, 78, 3*w^3 - 12*w + 9]', '[2106, 78, 3*w^3 - 12*w - 9]', '[2106, 78, -3*w^3 - 3*w^2 + 9*w]', '[2107, 301, -w^3 + 3*w^2 + 2*w - 11]', '[2107, 301, -3*w^3 + 3*w^2 + 16*w - 15]', '[2107, 301, -w^3 - 3*w^2 + 2*w + 11]', '[2107, 301, -3*w^3 - 3*w^2 + 16*w + 15]', '[2116, 46, 2*w^3 - w^2 - 15*w - 6]', '[2116, 46, -w^3 - 6]', '[2116, 46, -w^3 + 6]', '[2116, 46, -4*w^3 - w^2 + 15*w + 6]', '[2116, 46, w^3 + 3*w^2 - w - 9]', '[2116, 46, w^3 - 3*w^2 - w + 9]', '[2138, 2138, 2*w^3 - 4*w^2 - 13*w + 7]', '[2138, 2138, 6*w^3 + 2*w^2 - 27*w - 6]', '[2138, 2138, -6*w^3 + 2*w^2 + 27*w - 6]', '[2138, 2138, -4*w^3 - 4*w^2 + 11*w + 1]', '[2141, 2141, 8*w^3 + w^2 - 37*w - 7]', '[2141, 2141, -8*w^3 + w^2 + 37*w - 7]', '[2143, 2143, -6*w^3 + 4*w^2 + 26*w - 13]', '[2143, 2143, 5*w^3 - 21*w + 1]', '[2143, 2143, 5*w^3 - 21*w - 1]', '[2143, 2143, 5*w^3 - 3*w^2 - 22*w + 9]', '[2144, 268, 2*w^3 - 2*w^2 - 10*w - 4]', '[2144, 268, 4*w^2 + 2*w - 6]', '[2144, 268, -3*w^3 + w^2 + 18*w + 6]', '[2144, 268, 3*w^3 + 4*w^2 - 13*w - 8]', '[2144, 268, -9*w^3 + 3*w^2 + 38*w - 22]', '[2144, 268, 3*w^3 - 4*w^2 - 13*w + 8]', '[2144, 268, 4*w^3 - 22*w - 14]', '[2144, 268, 2*w^3 + 2*w^2 - 10*w + 4]', '[2144, 536, 2*w^3 + 5*w^2 - 8*w - 6]', '[2144, 536, -w^3 - w^2 + 3*w - 5]', '[2144, 536, 7*w^3 + 7*w^2 - 29*w - 21]', '[2144, 536, 2*w^3 - 5*w^2 - 8*w + 6]', '[2158, 2158, -w^3 - 6*w^2 + 8*w + 7]', '[2158, 2158, -6*w^3 + 23*w + 12]', '[2158, 2158, 4*w^2 - 3*w - 9]', '[2158, 2158, 3*w^3 + 3*w^2 - 11*w - 20]', '[2158, 2158, 4*w^3 + 4*w^2 - 15*w - 8]', '[2158, 2158, w^3 - 4*w^2 - 6*w - 1]', '[2158, 2158, w^3 - 5*w^2 - 5*w + 20]', '[2158, 2158, -w + 7]', '[2161, 2161, w^3 - w^2 - 4*w - 5]', '[2161, 2161, -2*w^3 - 3*w^2 + 7*w - 1]', '[2161, 2161, -2*w^3 + 3*w^2 + 7*w + 1]', '[2161, 2161, -w^3 - w^2 + 4*w - 5]', '[2174, 2174, -2*w^3 + 3*w - 4]', '[2174, 2174, 5*w^3 + 2*w^2 - 22*w - 5]', '[2174, 2174, -5*w^3 + 3*w^2 + 25*w - 20]', '[2174, 2174, -4*w^3 - 2*w^2 + 13*w + 7]', '[2174, 2174, -2*w^2 - 7*w - 1]', '[2174, 2174, -2*w^3 + 4*w^2 + 9*w - 14]', '[2174, 2174, 5*w^3 - 2*w^2 - 22*w + 5]', '[2174, 2174, -2*w^3 + 3*w + 4]', '[2194, 2194, 3*w^3 - 16*w - 1]', '[2194, 2194, 4*w^3 + 4*w^2 - 13*w - 11]', '[2194, 2194, -3*w^3 + w^2 + 9*w - 2]', '[2194, 2194, 3*w^3 + 3*w^2 - 11*w - 12]', '[2194, 2194, -3*w^3 + 3*w^2 + 11*w - 12]', '[2194, 2194, 3*w^3 + w^2 - 9*w - 2]', '[2194, 2194, -2*w^3 - 2*w^2 + 5*w + 7]', '[2194, 2194, 9*w^3 + 6*w^2 - 38*w - 23]', '[2197, 13, -7*w^3 - 3*w^2 + 30*w + 11]', '[2197, 13, 7*w^3 - 3*w^2 - 30*w + 11]', '[2197, 169, -w^3 + w^2 + 10*w + 3]', '[2197, 169, w^3 + w^2 - 10*w + 3]', '[2197, 2197, w^3 + 4*w^2 - 3*w - 17]', '[2197, 2197, w^3 - 4*w^2 - 3*w + 17]', '[2206, 2206, w^3 + 2*w^2 - 8*w - 9]', '[2206, 2206, -2*w^3 - 4*w^2 + 7*w + 11]', '[2206, 2206, -3*w^3 + w^2 + 13*w + 2]', '[2206, 2206, w^3 - w^2 - 9*w]', '[2206, 2206, w^3 + w^2 - 9*w]', '[2206, 2206, -4*w^3 + 23*w + 12]', '[2206, 2206, 2*w^3 - 4*w^2 - 7*w + 11]', '[2206, 2206, w^3 - 10*w - 9]', '[2209, 47, 2*w^2 - 13]', '[2209, 47, -2*w^2 - 3]', '[2218, 2218, -2*w^3 - 6*w^2 + 7*w + 6]', '[2218, 2218, w^3 + 4*w^2 - 2*w + 1]', '[2218, 2218, -5*w^3 - 8*w^2 + 16*w + 13]', '[2218, 2218, -2*w^3 + 6*w^2 + 7*w - 6]', '[2228, 1114, -w^3 + w^2 + w - 7]', '[2228, 1114, 4*w^3 + 3*w^2 - 13*w - 6]', '[2228, 1114, w^3 + 2*w^2 - 6]', '[2228, 1114, -2*w^3 - w^2 + 13*w + 6]', '[2228, 1114, -w^3 - w^2 + w + 7]', '[2228, 1114, w^3 - 2*w^2 + 6]', '[2236, 1118, -3*w^3 - w^2 + 9*w + 1]', '[2236, 1118, w^2 + 6*w]', '[2236, 1118, -w^2 - 5*w + 6]', '[2236, 1118, w^3 - w^2 - 9*w + 3]', '[2236, 1118, 2*w^3 + 3*w^2 - 3*w - 6]', '[2236, 1118, 3*w^3 - 8*w + 2]', '[2236, 1118, -2*w^3 + 3*w^2 + 3*w - 6]', '[2236, 1118, w^3 + w^2 - 9*w - 3]', '[2236, 1118, 3*w^3 - 8*w - 2]', '[2236, 1118, -3*w^3 + w^2 + 9*w - 1]', '[2236, 1118, -w^2 + 5*w + 6]', '[2236, 1118, -w^2 + 6*w]', '[2242, 2242, -2*w^3 + 2*w^2 + 11*w - 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22]', '[5296, 1324, w^3 + 4*w^2 - 5*w - 22]', '[5296, 1324, 3*w^3 + w^2 - 9*w + 9]', '[5296, 1324, 6*w^3 + w^2 - 28*w - 10]', '[5296, 1324, -w^3 + 5*w^2 + 4*w - 18]', '[5308, 2654, -4*w^3 - 5*w^2 + 12*w + 5]', '[5308, 2654, -5*w^2 - 3*w + 8]', '[5308, 2654, -3*w^3 + 8*w^2 + 20*w - 22]', '[5308, 2654, 5*w^3 + 5*w^2 - 13*w - 7]', '[5308, 2654, 2*w^3 + 3*w^2 - w - 6]', '[5308, 2654, -7*w^2 - 8*w + 16]', '[5308, 2654, 2*w^3 - 3*w^2 - w + 6]', '[5308, 2654, -w^3 - w^2 + 11*w + 5]', '[5308, 2654, -3*w^3 + 2*w^2 + 10*w - 14]', '[5308, 2654, -5*w^2 + 3*w + 8]', '[5308, 2654, -4*w^3 - 5*w^2 + 18*w + 11]', '[5308, 2654, 5*w^2 + 2*w - 16]', '[5312, 332, -2*w^3 + 4*w^2 + 8*w + 4]', '[5312, 332, -2*w^3 - 6*w^2 + 10*w + 10]', '[5312, 332, -4*w^3 + 2*w^2 + 22*w + 12]', '[5312, 332, 4*w^3 - 2*w^2 - 16*w]', '[5312, 332, 4*w^3 + 2*w^2 - 18*w - 16]', '[5312, 332, 4*w^3 + 2*w^2 - 20*w - 2]', '[5312, 664, -7*w^3 - 8*w^2 + 29*w + 20]', '[5312, 664, -w^3 - 8*w^2 + 6*w + 8]', '[5312, 664, -3*w^3 + w^2 + 13*w + 9]', '[5312, 664, -9*w^3 + 3*w^2 + 42*w - 10]', '[5312, 664, w^3 - w^2 - 10*w - 10]', '[5312, 664, 2*w^3 + 3*w^2 - 12*w - 2]', '[5312, 664, 6*w^3 - w^2 - 26*w - 1]', '[5312, 664, 5*w^3 + 6*w^2 - 23*w - 22]', '[5323, 5323, 5*w^3 + 2*w^2 - 19*w - 7]', '[5323, 5323, -5*w^3 + 2*w^2 + 19*w - 7]', '[5329, 73, -w^3 - 6*w^2 + 5*w + 3]', '[5329, 73, w^3 - 6*w^2 - 5*w + 3]', '[5342, 5342, -2*w^3 + 4*w^2 + 9*w - 22]', '[5342, 5342, -w^3 + 7*w^2 + 3*w - 30]', '[5342, 5342, w^3 + 8*w^2 + 6*w - 15]', '[5342, 5342, -4*w^3 + 2*w^2 + 11*w + 9]', '[5342, 5342, -2*w^3 + 2*w^2 + 3*w + 7]', '[5342, 5342, 3*w^3 - 2*w^2 - 10*w + 13]', '[5342, 5342, -w^3 - 7*w^2 + 3*w + 30]', '[5342, 5342, 2*w^3 + 4*w^2 - 9*w - 22]', '[5347, 5347, -2*w^3 - 4*w^2 + 8*w - 1]', '[5347, 5347, 2*w^3 - 4*w^2 - 8*w - 1]', '[5353, 5353, -2*w^3 + 2*w^2 + 14*w - 5]', '[5353, 5353, -w^3 - 3*w^2 + 12*w + 1]', '[5353, 5353, w^3 - 3*w^2 - 12*w + 1]', '[5353, 5353, 2*w^3 + 2*w^2 - 14*w - 5]', '[5354, 5354, -w^3 + 5*w^2 + 5*w - 18]', '[5354, 5354, w^3 - 8*w^2 + 6*w + 11]', '[5354, 5354, w^3 - 6*w^2 + 2*w + 9]', '[5354, 5354, w^3 + 5*w^2 - 5*w - 18]', '[5356, 2678, 7*w^3 + w^2 - 35*w + 1]', '[5356, 2678, 7*w^3 - 2*w^2 - 28*w + 2]', '[5356, 2678, 6*w^3 + 5*w^2 - 25*w - 26]', '[5356, 2678, -13*w^3 - 7*w^2 + 61*w + 33]', '[5356, 2678, -2*w^3 - 5*w^2 + 11*w + 22]', '[5356, 2678, -11*w^3 - 6*w^2 + 48*w + 26]', '[5356, 2678, 16*w^3 - 11*w^2 - 68*w + 39]', '[5356, 2678, 10*w^3 - 3*w^2 - 52*w + 28]', '[5356, 2678, -4*w^3 + 7*w^2 + 15*w - 24]', '[5356, 2678, -8*w^3 + w^2 + 36*w - 1]', '[5356, 2678, 6*w^3 - 5*w^2 - 29*w + 28]', '[5356, 2678, -6*w^3 - w^2 + 28*w]', '[5356, 2678, 6*w^3 + 5*w^2 - 29*w - 28]', '[5356, 2678, 8*w^3 + w^2 - 36*w - 1]', '[5356, 2678, 6*w^3 - w^2 - 28*w]', '[5356, 2678, -16*w^3 - 11*w^2 + 68*w + 39]', '[5356, 2678, -4*w^3 - 7*w^2 + 15*w + 24]', '[5356, 2678, -10*w^3 - 3*w^2 + 52*w + 28]', '[5356, 2678, -2*w^3 + 5*w^2 + 11*w - 22]', '[5356, 2678, 13*w^3 - 7*w^2 - 61*w + 33]', '[5356, 2678, 11*w^3 - 6*w^2 - 48*w + 26]', '[5356, 2678, -7*w^3 + w^2 + 35*w + 1]', '[5356, 2678, 6*w^3 - 5*w^2 - 25*w + 26]', '[5356, 2678, -7*w^3 - 2*w^2 + 28*w + 2]', '[5374, 5374, 3*w^3 + 4*w^2 - 10*w - 3]', '[5374, 5374, 3*w^3 + 3*w^2 - 17*w - 18]', '[5374, 5374, -6*w^3 + 25*w + 1]', '[5374, 5374, -w^3 - 5*w^2 + 5*w + 8]', '[5374, 5374, -w^3 + 5*w^2 + 5*w - 8]', '[5374, 5374, 6*w^3 - 25*w + 1]', '[5374, 5374, -4*w^3 - 4*w^2 + 21*w + 20]', '[5374, 5374, -5*w^3 - 6*w^2 + 20*w + 13]', '[5381, 5381, -3*w^2 + 3*w + 13]', '[5381, 5381, 3*w^2 + 3*w - 13]', '[5387, 5387, 4*w^3 + 4*w^2 - 18*w - 9]', '[5387, 5387, -4*w^3 + 4*w^2 + 18*w - 9]', '[5393, 5393, 7*w^3 + 3*w^2 - 34*w - 13]', '[5393, 5393, -2*w^3 - 5*w^2 + 13*w + 17]', '[5393, 5393, 2*w^3 - 5*w^2 - 13*w + 17]', '[5393, 5393, 7*w^3 - 3*w^2 - 34*w + 13]', '[5398, 5398, w^3 - 5*w^2 + 3*w + 10]', '[5398, 5398, w^3 + 6*w^2 - 6*w - 27]', '[5398, 5398, -w^3 + 6*w^2 + 6*w - 27]', '[5398, 5398, -4*w^3 + 2*w^2 + 9*w + 8]', '[5408, 52, 3*w^3 - 17*w]', '[5408, 52, 11*w^3 - 49*w]', '[5408, 52, 4*w^3 - 14*w]', '[5408, 52, w^3 + w^2 - 10*w - 10]', '[5408, 52, 8*w^3 - 38*w]', '[5408, 52, -7*w^3 + 7*w^2 + 30*w - 30]', '[5408, 52, 4*w^3 + 4*w^2 - 14*w - 14]', '[5408, 52, -2*w^3 + 4*w^2 + 16*w - 6]', '[5408, 104, 7*w^3 - 30*w]', '[5408, 104, w^3 - 10*w]', '[5408, 104, -6*w^3 - w^2 + 22*w - 5]', '[5408, 104, 3*w^3 + 3*w^2 - 17*w - 17]', '[5408, 676, -2*w^3 + 2*w^2 + 14*w - 4]', '[5408, 676, -6*w + 10]', '[5408, 676, -3*w^3 - 5*w^2 + 6*w + 10]', '[5408, 676, -5*w^3 + 19*w - 4]', '[5408, 676, 3*w^3 - 5*w^2 - 6*w + 10]', '[5408, 676, -5*w^3 + 19*w + 4]', '[5408, 676, 6*w + 10]', '[5408, 676, -2*w^3 - 2*w^2 + 14*w + 4]', '[5408, 1352, -4*w^3 - w^2 + 12*w - 2]', '[5408, 1352, 3*w^3 - 5*w^2 - 9*w + 15]', '[5408, 1352, -3*w^3 - 5*w^2 + 9*w + 15]', '[5408, 1352, -4*w^3 + w^2 + 12*w + 2]', '[5414, 5414, -w^3 - w^2 - 3*w - 6]', '[5414, 5414, 4*w^3 - 13*w - 3]', '[5414, 5414, 2*w^3 - 2*w^2 - 19*w - 9]', '[5414, 5414, w^3 - w^2 + 3*w - 6]', '[5419, 5419, 9*w^3 - 4*w^2 - 39*w + 17]', '[5419, 5419, -8*w^3 + 3*w^2 + 39*w - 17]', '[5422, 5422, -4*w^3 + 4*w^2 + 15*w - 16]', '[5422, 5422, w^3 - 5*w^2 - w + 8]', '[5422, 5422, 5*w^3 + 6*w^2 - 16*w - 9]', '[5422, 5422, 5*w^3 + 10*w^2 - 4*w - 9]', '[5422, 5422, 4*w^3 - 21*w - 1]', '[5422, 5422, -3*w^3 - 4*w^2 + 14*w + 7]', '[5422, 5422, w^3 + 5*w^2 - w - 8]', '[5422, 5422, 5*w^3 + 5*w^2 - 9*w]', '[5427, 201, 3*w^3 + 3*w^2 - 18*w - 15]', '[5427, 201, -3*w^3 + 3*w^2 + 18*w - 15]', '[5431, 5431, 3*w^3 - 4*w^2 - 15*w + 23]', '[5431, 5431, 4*w^2 - 4*w - 13]', '[5431, 5431, -4*w^2 - 4*w + 13]', '[5431, 5431, 3*w^3 + 4*w^2 - 15*w - 23]', '[5444, 2722, -w^3 + 7*w^2 - 5*w - 3]', '[5444, 2722, -9*w^2 + 15*w + 8]', '[5444, 2722, 8*w^3 + w^2 - 38*w]', '[5444, 2722, 3*w^3 + 7*w^2 - 7*w - 5]', '[5444, 2722, 9*w^3 + 4*w^2 - 40*w - 14]', '[5444, 2722, -4*w^3 - 5*w^2 + 21*w + 12]', '[5444, 2722, 3*w^3 - 7*w^2 - 7*w + 5]', '[5444, 2722, -6*w^3 + 7*w^2 + 15*w - 4]', '[5444, 2722, 9*w^3 - 4*w^2 - 40*w + 14]', '[5444, 2722, 4*w^3 - w^2 - 17*w - 4]', '[5444, 2722, w^3 + 7*w^2 + 5*w - 3]', '[5444, 2722, -8*w^3 + w^2 + 38*w]', '[5459, 5459, 10*w^3 + 3*w^2 - 47*w - 13]', '[5459, 5459, w^3 - 3*w - 9]', '[5459, 5459, 9*w^3 - 43*w + 3]', '[5459, 5459, -3*w^3 - 7*w^2 + 6*w + 3]', '[5459, 5459, 3*w^3 - 7*w^2 - 6*w + 3]', '[5459, 5459, 9*w^3 - 43*w - 3]', '[5459, 5459, -w^3 + 3*w - 9]', '[5459, 5459, 10*w^3 - 3*w^2 - 47*w + 13]', '[5461, 5461, 5*w^3 - 6*w^2 - 19*w + 21]', '[5461, 5461, w^3 - 7*w^2 + 2*w + 7]', '[5461, 5461, w^3 + 4*w^2 - 7*w - 17]', '[5461, 5461, 3*w^3 + 7*w^2 - 12*w - 11]', '[5461, 5461, 3*w^3 - 7*w^2 - 12*w + 11]', '[5461, 5461, w^3 - 4*w^2 - 7*w + 17]', '[5461, 5461, w^3 + 7*w^2 + 2*w - 7]', '[5461, 5461, 5*w^3 + 6*w^2 - 19*w - 21]', '[5473, 5473, 4*w^3 + 2*w^2 - 20*w - 17]', '[5473, 5473, 4*w + 11]', '[5473, 5473, -4*w + 11]', '[5473, 5473, -4*w^3 + 2*w^2 + 20*w - 17]', '[5482, 5482, 2*w^3 + 6*w^2 - 3*w - 8]', '[5482, 5482, -2*w^3 - 4*w^2 + 11*w + 5]', '[5482, 5482, 6*w^3 + 8*w^2 - 17*w - 11]', '[5482, 5482, 2*w^3 - 6*w^2 - 3*w + 8]', '[5483, 5483, -2*w^3 + 7*w^2 + 9*w - 29]', '[5483, 5483, -6*w^3 + 24*w - 11]', '[5491, 323, w^3 + 2*w^2 - 11*w - 5]', '[5491, 323, w^3 - 2*w^2 - 11*w + 5]', '[5492, 2746, 3*w^3 + 3*w^2 - 3*w - 5]', '[5492, 2746, 3*w^3 + 6*w^2 - 12*w - 26]', '[5492, 2746, -4*w^3 - w^2 + 13*w + 12]', '[5492, 2746, -3*w^3 + 3*w^2 + 3*w - 5]', '[5492, 2746, 2*w^3 - 7*w^2 + w + 12]', '[5492, 2746, -3*w^3 + 6*w^2 + 12*w - 26]', '[5504, 172, 2*w^3 + 2*w^2 - 4*w - 8]', '[5504, 172, 2*w^3 - 14*w + 4]', '[5504, 172, 2*w^3 - 2*w^2 - 4*w + 8]', '[5504, 172, -2*w^3 + 14*w + 4]', '[5504, 344, 4*w^3 - 2*w^2 - 12*w + 4]', '[5504, 344, -w^3 + w^2 - 2*w - 6]', '[5504, 344, 5*w^3 - 2*w^2 - 19*w + 6]', '[5504, 344, -2*w^2 - 4*w + 10]', '[5504, 344, 2*w^2 - 4*w - 10]', '[5504, 344, -w^3 - w^2 - 2*w + 6]', '[5504, 344, -5*w^3 - 2*w^2 + 19*w + 6]', '[5504, 344, -4*w^3 - 2*w^2 + 12*w + 4]', '[5504, 688, w^2 - 8*w + 2]', '[5504, 688, 2*w^3 - 3*w^2 - 6*w + 13]', '[5504, 688, 2*w^3 + 3*w^2 - 6*w - 13]', '[5504, 688, w^2 + 8*w + 2]', '[5507, 5507, w^3 + w^2 - 9]', '[5507, 5507, -w^3 + w^2 - 9]', '[5512, 1378, 3*w^3 - 5*w^2 - 14*w + 16]', '[5512, 1378, -5*w^3 - 2*w^2 + 21*w + 2]', '[5512, 1378, -w^3 + w^2 + 6*w - 12]', '[5512, 1378, 7*w^3 - 2*w^2 - 35*w + 18]', '[5512, 1378, -7*w^3 - 2*w^2 + 35*w + 18]', '[5512, 1378, -w^3 - w^2 + 6*w + 12]', '[5512, 1378, 3*w^3 + 5*w^2 - 14*w - 16]', '[5512, 1378, 5*w^3 - 2*w^2 - 21*w + 2]', '[5512, 2756, 4*w^3 - 3*w^2 - 18*w + 19]', '[5512, 2756, 7*w^3 - 6*w^2 - 28*w + 16]', '[5512, 2756, -2*w^3 - 5*w^2 + 8*w + 17]', '[5512, 2756, 3*w^3 + 2*w^2 - 16*w]', '[5512, 2756, -3*w^3 + 2*w^2 + 16*w]', '[5512, 2756, -2*w^3 + 5*w^2 + 8*w - 17]', '[5512, 2756, -7*w^3 - 6*w^2 + 28*w + 16]', '[5512, 2756, 4*w^3 + 3*w^2 - 18*w - 19]', '[5524, 2762, -3*w^3 - 3*w^2 + 11*w - 3]', '[5524, 2762, 4*w^3 + w^2 - 21*w + 4]', '[5524, 2762, -15*w^3 + 6*w^2 + 68*w - 30]', '[5524, 2762, -10*w^3 - w^2 + 39*w + 20]', '[5524, 2762, 3*w^3 - 3*w^2 - 11*w - 3]', '[5524, 2762, 15*w^3 + 6*w^2 - 68*w - 30]', '[5534, 5534, 4*w^2 + 11*w + 2]', '[5534, 5534, -w^3 + 4*w^2 + 8*w + 1]', '[5534, 5534, -4*w^2 - w - 2]', '[5534, 5534, w^3 - 4*w^2 + 2*w + 9]', '[5534, 5534, -w^3 - 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10*w - 3]', '[9886, 9886, -5*w^3 + 3*w^2 + 23*w - 6]', '[9886, 9886, -7*w^3 - 6*w^2 + 38*w + 27]', '[9896, 2474, 9*w^3 + 2*w^2 - 43*w - 8]', '[9896, 2474, -5*w^3 + 7*w^2 + 20*w - 28]', '[9896, 2474, -11*w^3 + 9*w^2 + 48*w - 40]', '[9896, 2474, 9*w^3 - 2*w^2 - 43*w + 8]', '[9896, 4948, 8*w^3 + w^2 - 34*w - 6]', '[9896, 4948, -2*w^3 + 7*w^2 + 20*w - 11]', '[9896, 4948, -2*w^3 + 3*w^2 + 16*w - 3]', '[9896, 4948, 8*w^3 - w^2 - 34*w + 6]', '[9898, 1414, -11*w^3 - 4*w^2 + 52*w + 19]', '[9898, 1414, -9*w^3 + 44*w - 5]', '[9898, 1414, 2*w^3 + 6*w^2 - 7*w - 26]', '[9898, 1414, -6*w^3 + 6*w^2 + 25*w - 30]', '[9898, 1414, 2*w^3 - 6*w^2 - 7*w + 26]', '[9898, 1414, -6*w^3 - 6*w^2 + 25*w + 30]', '[9898, 1414, 11*w^3 - 4*w^2 - 52*w + 19]', '[9898, 1414, 9*w^3 - 44*w - 5]', '[9902, 9902, 7*w^3 + w^2 - 35*w]', '[9902, 9902, 3*w^3 - 7*w^2 - 9*w + 6]', '[9902, 9902, 6*w^3 + 10*w^2 - 17*w - 15]', '[9902, 9902, -7*w^3 + 8*w^2 + 34*w - 35]', '[9902, 9902, -7*w^3 + 6*w^2 + 36*w - 35]', '[9902, 9902, -4*w^2 - w - 3]', '[9902, 9902, 3*w^3 + 7*w^2 - 9*w - 6]', '[9902, 9902, 7*w^3 - w^2 - 35*w]', '[9907, 9907, 6*w^3 + 2*w^2 - 28*w - 3]', '[9907, 9907, 6*w^3 - 2*w^2 - 28*w + 3]', '[9929, 9929, -3*w^3 + w^2 + 16*w - 15]', '[9929, 9929, 2*w^3 - 10*w - 11]', '[9929, 9929, -2*w^3 + 10*w - 11]', '[9929, 9929, 3*w^3 + w^2 - 16*w - 15]', '[9937, 9937, w^3 + 5*w^2 - 4*w - 11]', '[9937, 9937, 3*w^3 + 7*w^2 - 18*w - 17]', '[9937, 9937, -3*w^3 + 7*w^2 + 18*w - 17]', '[9937, 9937, -w^3 + 5*w^2 + 4*w - 11]', '[9941, 9941, -9*w^3 + w^2 + 38*w - 9]', '[9941, 9941, 9*w^3 + w^2 - 38*w - 9]', '[9946, 9946, 2*w^2 - 9*w]', '[9946, 9946, -2*w^2 - 11*w - 9]', '[9946, 9946, 2*w^2 - 7*w - 9]', '[9946, 9946, -2*w^2 - 9*w]', '[9949, 9949, 2*w^3 - 3*w^2 - 5*w + 13]', '[9949, 9949, -2*w^3 - 3*w^2 + 5*w + 13]', '[9958, 9958, 5*w^3 + 3*w^2 - 17*w + 6]', '[9958, 9958, 12*w^3 - 8*w^2 - 49*w + 31]', '[9958, 9958, -5*w^3 + 7*w^2 + 13*w - 6]', '[9958, 9958, -6*w^3 + 4*w^2 + 17*w + 1]', '[9958, 9958, 3*w^3 + 7*w^2 + 5*w + 6]', '[9958, 9958, -2*w^3 - 2*w^2 + 5*w - 7]', '[9958, 9958, 5*w^3 + 3*w^2 - 17*w - 14]', '[9958, 9958, -8*w^3 - 2*w^2 + 35*w + 23]', '[9958, 9958, -8*w^3 + 2*w^2 + 35*w - 23]', '[9958, 9958, -5*w^3 + 3*w^2 + 17*w - 14]', '[9958, 9958, -2*w^3 + 2*w^2 + 5*w + 7]', '[9958, 9958, -3*w^3 + 7*w^2 - 5*w + 6]', '[9958, 9958, -6*w^3 - 4*w^2 + 17*w - 1]', '[9958, 9958, 5*w^3 + 7*w^2 - 13*w - 6]', '[9958, 9958, 12*w^3 + 8*w^2 - 49*w - 31]', '[9958, 9958, -5*w^3 + 3*w^2 + 17*w + 6]', '[9971, 767, -5*w^3 - w^2 + 24*w - 3]', '[9971, 767, 2*w^3 + 7*w^2 - 3*w - 17]', '[9971, 767, 5*w^3 - w^2 - 24*w - 3]', '[9971, 767, -2*w^3 + 7*w^2 + 3*w - 17]', '[9971, 9971, 6*w^3 - 2*w^2 - 24*w - 1]', '[9971, 9971, -6*w^3 - 4*w^2 + 28*w + 11]', '[9971, 9971, 6*w^3 - 4*w^2 - 28*w + 11]', '[9971, 9971, -6*w^3 - 2*w^2 + 24*w - 1]', '[9983, 9983, -4*w^3 + 2*w^2 + 4*w + 3]', '[9983, 9983, -7*w^3 + 2*w^2 + 27*w - 13]', '[9983, 9983, 7*w^3 + 2*w^2 - 27*w - 13]', '[9983, 9983, 4*w^3 + 2*w^2 - 4*w + 3]', '[9994, 9994, 3*w^3 - 12*w^2 + 4*w + 11]', '[9994, 9994, 5*w^3 - w^2 - 17*w - 2]', '[9994, 9994, -w^3 + 4*w^2 + 8*w + 5]', '[9994, 9994, 7*w^3 - 3*w^2 - 27*w + 14]', '[9994, 9994, -4*w^2 + 5*w + 13]', '[9994, 9994, -2*w^3 - 6*w^2 + 7*w + 2]', '[9994, 9994, -4*w^3 - 6*w^2 + 11*w + 15]', '[9994, 9994, -6*w^3 - 6*w^2 + 17*w - 6]', '[9994, 9994, -6*w^3 + 6*w^2 + 17*w + 6]', '[9994, 9994, -4*w^3 + 6*w^2 + 11*w - 15]', '[9994, 9994, -2*w^3 + 6*w^2 + 7*w - 2]', '[9994, 9994, 4*w^2 + 5*w - 13]', '[9994, 9994, -7*w^3 - 3*w^2 + 27*w + 14]', '[9994, 9994, w^3 + 4*w^2 - 8*w + 5]', '[9994, 9994, -5*w^3 - w^2 + 17*w - 2]', '[9994, 9994, -3*w^3 - 12*w^2 - 4*w + 11]', '[10000, 10, 10]', '[10000, 20, 5*w^3 + 5*w^2 - 20*w - 10]', '[10000, 20, 5*w^2 - 15]', '[10000, 20, 5*w^2 - 10]', '[10000, 20, 5*w^3 - 25*w - 10]'], 'label': '4.4.9248.1', 'narrow_class_no': 2, 'primes': ['[2, 2, w]', '[2, 2, w + 1]', '[13, 13, -w^2 + w + 3]', '[13, 13, w^2 + w - 3]', '[19, 19, -w^3 + 3*w + 1]', '[19, 19, -w^3 + 3*w - 1]', '[43, 43, -w^2 + w - 1]', '[43, 43, w^2 + w + 1]', '[49, 7, w^3 + w^2 - 6*w - 3]', '[49, 7, w^3 - w^2 - 6*w + 3]', '[53, 53, 2*w^3 - w^2 - 9*w + 3]', '[53, 53, 2*w^3 + w^2 - 9*w - 3]', '[59, 59, w^3 - w^2 - 4*w + 1]', '[59, 59, -w^3 - w^2 + 4*w + 1]', '[67, 67, 3*w^3 - 13*w + 1]', '[67, 67, -w^3 + w^2 + 6*w - 5]', '[81, 3, -3]', '[83, 83, -2*w^3 - w^2 + 9*w + 7]', '[83, 83, 4*w^3 - 18*w - 1]', '[89, 89, -2*w^3 + 10*w + 1]', '[89, 89, -w^2 + w + 5]', '[89, 89, w^2 + w - 5]', '[89, 89, 2*w^3 - 10*w + 1]', '[101, 101, -2*w^3 + 8*w + 1]', '[101, 101, 2*w^3 - 8*w + 1]', '[103, 103, w^3 + 2*w^2 - 5*w - 7]', '[103, 103, w^3 + w^2 - 6*w - 7]', '[103, 103, -w^2 - 3*w + 1]', '[103, 103, -w^3 + 2*w^2 + 5*w - 7]', '[127, 127, -w^3 + 2*w^2 + 5*w - 5]', '[127, 127, w^3 + 3*w^2 - 4*w - 13]', '[127, 127, -w^3 + 3*w^2 + 4*w - 13]', '[127, 127, w^3 + 2*w^2 - 5*w - 5]', '[149, 149, -2*w^3 - w^2 + 7*w - 1]', '[149, 149, 2*w^3 - w^2 - 7*w - 1]', '[151, 151, -w^3 + w^2 + 2*w - 3]', '[151, 151, 2*w^3 - 10*w + 3]', '[151, 151, -2*w^3 + 10*w + 3]', '[151, 151, w^3 + w^2 - 2*w - 3]', '[157, 157, w^3 + 2*w^2 - 3*w - 1]', '[157, 157, -w^3 + 2*w^2 + 3*w - 1]', '[169, 13, 2*w^2 - 3]', '[179, 179, 2*w^3 + w^2 - 7*w - 3]', '[179, 179, -2*w^3 + w^2 + 7*w - 3]', '[229, 229, -w^3 + 2*w^2 + 3*w - 7]', '[229, 229, w^3 + 2*w^2 - 3*w - 7]', '[251, 251, -2*w^3 + 2*w^2 + 8*w - 9]', '[251, 251, -2*w^3 - 2*w^2 + 8*w + 9]', '[263, 263, 2*w^3 - w^2 - 3*w + 1]', '[263, 263, -2*w^3 + 2*w^2 + 10*w - 5]', '[263, 263, -2*w^3 - 2*w^2 + 10*w + 5]', '[263, 263, -2*w^3 - w^2 + 3*w + 1]', '[289, 17, 2*w^2 - 5]', '[293, 293, 4*w^3 - w^2 - 19*w + 7]', '[293, 293, -4*w^3 - w^2 + 19*w + 7]', '[307, 307, -w^3 + 3*w - 5]', '[307, 307, w^3 - 3*w - 5]', '[331, 331, 4*w^3 - 2*w^2 - 18*w + 7]', '[331, 331, 5*w^3 - 3*w^2 - 22*w + 11]', '[349, 349, -3*w^3 + 13*w + 3]', '[349, 349, -3*w^3 + 13*w - 3]', '[361, 19, 2*w^2 - 11]', '[373, 373, w^3 + 2*w^2 + w - 3]', '[373, 373, -w^3 + 2*w^2 - w - 3]', '[383, 383, -w^3 + 5*w + 5]', '[383, 383, -3*w^3 + 2*w^2 + 11*w - 5]', '[383, 383, 3*w^3 + 2*w^2 - 11*w - 5]', '[383, 383, w^3 - 5*w + 5]', '[389, 389, w^3 - 4*w^2 + w + 7]', '[389, 389, -2*w^3 - w^2 + 7*w + 7]', '[421, 421, -w^3 - w^2 - 2*w + 1]', '[421, 421, w^3 - w^2 + 2*w + 1]', '[433, 433, 4*w^3 - 2*w^2 - 16*w + 5]', '[433, 433, -4*w + 1]', '[433, 433, 4*w + 1]', '[433, 433, -5*w^3 + 3*w^2 + 24*w - 13]', '[443, 443, -w^3 + w^2 + 3]', '[443, 443, -4*w^2 + 6*w + 7]', '[457, 457, 3*w^3 + w^2 - 12*w - 3]', '[457, 457, -2*w^3 + 6*w - 1]', '[457, 457, 2*w^3 - 6*w - 1]', '[457, 457, 3*w^3 - w^2 - 12*w + 3]', '[461, 461, w^3 - 3*w^2 - 2*w + 7]', '[461, 461, w^3 + 3*w^2 - 2*w - 7]', '[463, 463, -2*w^3 + 3*w^2 + 9*w - 11]', '[463, 463, 2*w^3 - w^2 - 5*w + 1]', '[463, 463, -2*w^3 - w^2 + 5*w + 1]', '[463, 463, -2*w^3 - 3*w^2 + 9*w + 11]', '[467, 467, w^3 - 7*w + 1]', '[467, 467, -w^3 + 7*w + 1]', '[491, 491, 2*w^2 - 2*w - 7]', '[491, 491, 2*w^2 + 2*w - 7]', '[509, 509, w^3 + 3*w^2 - 4*w - 11]', '[509, 509, -w^3 + 3*w^2 + 4*w - 11]', '[523, 523, 2*w^3 - w^2 - 11*w + 3]', '[523, 523, 2*w^3 + w^2 - 11*w - 3]', '[529, 23, 3*w^2 - w - 15]', '[529, 23, -3*w^2 - w + 15]', '[557, 557, 3*w^2 + w - 13]', '[557, 557, -3*w^2 + w + 13]', '[563, 563, -3*w^3 + 3*w^2 + 12*w - 7]', '[563, 563, 2*w^3 - 2*w^2 - 8*w + 3]', '[569, 569, w^3 + 3*w^2 - 6*w - 9]', '[569, 569, 4*w^3 - w^2 - 17*w + 1]', '[569, 569, -4*w^3 - w^2 + 17*w + 1]', '[569, 569, -w^3 + 3*w^2 + 6*w - 9]', '[587, 587, -w^3 + w^2 + 2*w - 5]', '[587, 587, w^3 + w^2 - 2*w - 5]', '[593, 593, 3*w^3 - 2*w^2 - 15*w + 5]', '[593, 593, -w^3 - 2*w^2 + 5*w + 1]', '[593, 593, w^3 - 2*w^2 - 5*w + 1]', '[593, 593, -3*w^3 - 2*w^2 + 15*w + 5]', '[599, 599, w^3 + w^2 - 3]', '[599, 599, -w^2 - w - 3]', '[599, 599, -w^2 + w - 3]', '[599, 599, -w^3 + w^2 - 3]', '[613, 613, -w^3 + w^2 + 6*w - 9]', '[613, 613, w^3 + w^2 - 6*w - 9]', '[625, 5, -5]', '[659, 659, -2*w^3 + 4*w^2 + 4*w - 1]', '[659, 659, 2*w^3 + 4*w^2 - 4*w - 1]', '[661, 661, w^3 + 3*w^2 - 6*w - 7]', '[661, 661, -2*w^3 + 6*w^2 - 7]', '[701, 701, -w^3 - 2*w^2 + 3*w + 9]', '[701, 701, -w^3 + 2*w^2 + 3*w - 9]', '[733, 733, w^3 + 2*w^2 - 7*w - 1]', '[733, 733, -4*w^3 + w^2 + 19*w - 11]', '[739, 739, -w^3 - w^2 + 2*w + 9]', '[739, 739, -w^3 + w^2 + 2*w - 9]', '[757, 757, 3*w^3 - w^2 - 10*w + 5]', '[757, 757, -3*w^3 - w^2 + 10*w + 5]', '[773, 773, -4*w^3 + 5*w^2 + 19*w - 23]', '[773, 773, -7*w^3 + 6*w^2 + 33*w - 29]', '[797, 797, 3*w^3 - 13*w + 5]', '[797, 797, 3*w^3 - 13*w - 5]', '[829, 829, -2*w^3 - w^2 + 9*w - 1]', '[829, 829, 2*w^3 - w^2 - 9*w - 1]', '[859, 859, 3*w^3 - w^2 - 14*w + 1]', '[859, 859, -3*w^3 - w^2 + 14*w + 1]', '[863, 863, -5*w^3 + 21*w + 3]', '[863, 863, -3*w^3 - w^2 + 12*w - 1]', '[863, 863, 3*w^3 - w^2 - 12*w - 1]', '[863, 863, -5*w^3 + 21*w - 3]', '[883, 883, -2*w^3 + 4*w^2 + 8*w - 17]', '[883, 883, 2*w^3 + 4*w^2 - 8*w - 17]', '[953, 953, -w^3 - w^2 + 8*w + 3]', '[953, 953, 4*w^3 - 2*w^2 - 16*w + 7]', '[953, 953, -3*w^3 + w^2 + 16*w - 7]', '[953, 953, w^3 - w^2 - 8*w + 3]', '[961, 31, -4*w^3 + 2*w^2 + 12*w + 3]', '[961, 31, 3*w^3 - w^2 - 10*w - 1]', '[971, 971, 3*w^3 - 4*w^2 - 13*w + 15]', '[971, 971, -4*w^3 + 3*w^2 + 19*w - 17]', '[977, 977, -2*w^3 + w^2 + 9*w + 3]', '[977, 977, -4*w^3 + w^2 + 19*w - 9]', '[977, 977, 3*w^3 - 15*w + 5]', '[977, 977, 2*w^3 + w^2 - 9*w + 3]']}
-
nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [2, 0, -5, 0, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 9248, 'disc_rad': 34, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 1]]], [5, [[4, 1]]], [7, [[2, 2]]], [11, [[4, 1]]], [13, [[2, 1], [1, 2]]], [17, [0]], [19, [[2, 1], [1, 2]]], [23, [[2, 2]]], [29, [[4, 1]]], [31, [[2, 2]]], [37, [[4, 1]]], [41, [[2, 2]]], [43, [[2, 1], [1, 2]]], [47, [[2, 2]]], [53, [[2, 1], [1, 2]]], [59, [[2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [16, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 16.492422502470642, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '4.4.9248.1', 'local_algs': ['2.2.3.3', '2.2.2.1', '17.4.2.1'], 'minimal_sibling': [2, -4, -6, 0, 1], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 17], 'rd': 9.80645309178, 'regulator': {'__RealLiteral__': 0, 'data': '9.93835336634', 'prec': 44}, 'res': {'gal': ['2,-4,-14,16,27,-12,-14,0,1'], 'sib': ['2,-4,-6,0,1', '2,-4,-14,16,27,-12,-14,0,1']}, 'subfield_mults': [1], 'subfields': ['-4.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{3} - a^{2} - 4 a + 3 \\)', '\\( a^{2} - a - 1 \\)', '\\( a^{2} + a - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}