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hmf_forms • Show schema
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{'deg': 4, 'dimension': 1, 'disc': 16448, 'field_bad_primes': [2, 257], 'field_label': '4.4.16448.2', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '4.4.16448.2-4.2-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [2], 'level_ideal': '[4, 2, w^2 - w - 4]', 'level_label': '4.2', 'level_norm': 4, 'parallel_weight': 2, 'short_label': '4.2-a', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[2, 2, w^3 - 3*w^2 - 3*w + 10]', -1], ['[2, 2, w^3 - 6*w - 5]', -1]], 'hecke_eigenvalues': [1, 1, 2, 2, 8, -10, -10, 8, 6, 6, -6, -6, -4, 0, 0, -4, -4, -4, -4, 10, 2, 2, 8, 8, -10, -10, -4, -4, -6, -6, -6, -6, -10, -10, -12, -12, 2, 2, -6, -6, -10, -22, -22, -10, 18, 18, 24, 24, 24, 24, 6, -30, 6, 12, 12, 32, 32, -24, -24, 32, 32, -12, -12, -10, -10, -28, -28, -24, -24, 0, 0, -10, -10, 24, 24, 6, 6, 6, 6, -10, -10, 0, 0, 14, 2, 2, 14, 8, 8, -18, -18, 8, 8, -40, -40, -18, -18, 44, 38, 30, 30, 14, 14, 0, 18, 18, 0, 24, 24, 38, 38, -40, -40, 42, 42, 32, -16, -16, -16, -16, 30, 30, -48, -48, 26, 26, 42, 42, 18, 18, 48, 12, 12, 48, 26, 26, -6, -6, 36, 36, 24, -48, -48, 24, -4, -4, 20, 20, 54, 54, 44, 8, 8, 44, 42, 42, -24, -24, 32, 32], 'hecke_polynomial': 'x', 'label': '4.4.16448.2-4.2-a'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 16448, 'ideals': ['[1, 1, 1]', '[2, 2, w^3 - 3*w^2 - 3*w + 10]', '[2, 2, w^3 - 6*w - 5]', '[4, 2, -w^2 + 4]', '[4, 2, w^2 - w - 4]', '[4, 2, w^2 - 2*w - 3]', '[7, 7, -w^3 + 3*w^2 + 2*w - 7]', '[7, 7, -w^3 + 5*w + 3]', '[8, 2, -w^3 + 3*w^2 + 4*w - 12]', '[8, 2, -w^3 + 7*w + 6]', '[8, 4, w^2 - 2*w - 2]', '[8, 4, w^2 - 3]', '[14, 14, w]', '[14, 14, -w^3 + w^2 + 5*w + 2]', '[14, 14, w^3 - 2*w^2 - 4*w + 7]', '[14, 14, w - 1]', '[16, 2, 2]', '[16, 4, -w^3 + w^2 + 4*w - 2]', '[16, 4, -w^2 + 2]', '[16, 4, -w^2 + 2*w + 1]', '[16, 4, -w^3 + 2*w^2 + 3*w - 2]', '[28, 14, -w^3 + 4*w^2 + 2*w - 14]', '[28, 14, w^2 - 3*w]', '[28, 14, w^3 + w^2 - 5*w - 7]', '[28, 14, w^3 - 4*w^2 + 10]', '[28, 14, -w^2 - w + 2]', '[28, 14, w^3 + w^2 - 7*w - 9]', '[31, 31, -w^3 + 2*w^2 + 3*w - 5]', '[31, 31, -w^2 - w + 1]', '[31, 31, -w^2 + 3*w - 1]', '[31, 31, -w^3 + w^2 + 4*w + 1]', '[32, 4, 2*w^3 - 6*w^2 - 6*w + 20]', '[32, 4, -w^3 + 3*w^2 + 2*w - 6]', '[32, 4, w^3 - 5*w - 2]', '[32, 4, 2*w^3 - 12*w - 10]', '[32, 8, -w^2 + 6]', '[32, 8, w^2 - 2*w - 5]', '[41, 41, -w^3 + 3*w^2 + 2*w - 9]', '[41, 41, w^3 + w^2 - 8*w - 11]', '[47, 47, w^3 - w^2 - 4*w + 1]', '[47, 47, w^3 - 2*w^2 - 3*w + 3]', '[49, 7, 2*w^2 - 2*w - 7]', '[49, 7, 2*w^2 - 2*w - 9]', '[49, 49, w^3 - 2*w^2 - 3*w + 7]', '[49, 49, w^3 - w^2 - 4*w - 3]', '[56, 14, w^3 - w^2 - 4*w]', '[56, 14, -w^3 + 4*w^2 + 3*w - 14]', '[56, 14, w^3 + w^2 - 8*w - 8]', '[56, 14, w^3 - 2*w^2 - 3*w + 4]', '[56, 28, -w^3 + 4*w]', '[56, 28, w^2 - 2*w - 6]', '[56, 28, -w^2 + 7]', '[56, 28, w^3 - 3*w^2 - w + 3]', '[62, 62, -w - 3]', '[62, 62, -w^3 + 2*w^2 + 4*w - 3]', '[62, 62, 2*w^2 - 3*w - 9]', '[62, 62, 2*w^3 - 6*w^2 - 3*w + 11]', '[62, 62, 2*w^3 - 9*w - 4]', '[62, 62, -2*w^2 + w + 10]', '[62, 62, w^3 - w^2 - 5*w + 2]', '[62, 62, w - 4]', '[64, 4, -2*w^2 + 8]', '[64, 4, 2*w^2 - 2*w - 8]', '[64, 4, 2*w^2 - 4*w - 6]', '[64, 8, 2*w^3 + w^2 - 8*w - 6]', '[64, 8, -w^3 - w^2 + 6*w + 6]', '[64, 8, 2*w^3 - 7*w^2 + 11]', '[64, 8, w^3 - 4*w^2 - w + 10]', '[71, 71, 5*w^3 - 16*w^2 - 17*w + 61]', '[71, 71, -2*w^3 - 2*w^2 + 10*w + 13]', '[73, 73, 3*w^3 + w^2 - 18*w - 17]', '[73, 73, w^3 - 5*w - 1]', '[73, 73, w^3 - 7*w - 3]', '[73, 73, -3*w^3 + 10*w^2 + 7*w - 31]', '[81, 3, -3]', '[82, 82, -4*w^3 + 12*w^2 + 15*w - 48]', '[82, 82, w^3 - 3*w^2 - 3*w + 8]', '[82, 82, -w^3 + 6*w + 3]', '[82, 82, w^3 - 2*w^2 - 2*w - 1]', '[94, 94, 2*w^3 - 6*w^2 - 7*w + 24]', '[94, 94, w^3 - 3*w^2 - 5*w + 16]', '[94, 94, -w^3 + 8*w + 9]', '[94, 94, -2*w^3 + 13*w + 13]', '[97, 97, w^3 - w^2 - 6*w - 3]', '[97, 97, -w^3 + 2*w^2 + 5*w - 9]', '[98, 14, -w^3 + 3*w^2 + 5*w - 14]', '[98, 14, -3*w^3 + 9*w^2 + 11*w - 34]', '[98, 14, -w^3 + 8*w + 7]', '[98, 14, -3*w^3 + 20*w + 17]', '[98, 98, w^3 - 5*w^2 + w + 14]', '[98, 98, -w^3 + 5*w^2 - 3*w - 8]', '[98, 98, w^3 + 2*w^2 - 4*w - 7]', '[98, 98, -w^3 - 2*w^2 + 6*w + 11]', '[103, 103, -3*w^2 + w + 11]', '[103, 103, -3*w^2 + 5*w + 9]', '[112, 14, -2*w^3 + 6*w^2 + 4*w - 14]', '[112, 14, -2*w^3 + 10*w + 6]', '[112, 28, w^3 - 3*w^2 - 4*w + 14]', '[112, 28, -w^3 - w^2 + 7*w + 7]', '[112, 28, w^3 - 2*w^2 - 2*w]', '[112, 28, w^3 - 3*w^2 + 2]', '[112, 28, w^3 - 3*w]', '[112, 28, w^3 - 4*w^2 - 2*w + 12]', '[112, 28, w^3 - w^2 - 3*w + 3]', '[112, 28, -w^3 + 7*w + 8]', '[121, 11, w^2 + w - 3]', '[121, 11, -w^2 + 3*w + 1]', '[124, 62, w^3 - 2*w^2 - 4*w + 2]', '[124, 62, -w^3 + 5*w^2 - w - 13]', '[124, 62, -w^2 - w + 6]', '[124, 62, -w^3 - w^2 + 9*w + 11]', '[124, 62, -2*w^3 - w^2 + 11*w + 10]', '[124, 62, -w^3 + 2*w^2 + 2*w + 2]', '[124, 62, w^3 - w^2 - 3*w + 5]', '[124, 62, 2*w^3 - 7*w^2 - 3*w + 18]', '[124, 62, -w^3 + 4*w^2 + 4*w - 18]', '[124, 62, -w^3 + w^2 + 5*w - 3]', '[124, 62, w^2 - 3*w - 4]', '[124, 62, w^3 + 2*w^2 - 6*w - 10]', '[127, 127, w^3 - 5*w^2 + 17]', '[127, 127, -w^3 - 2*w^2 + 7*w + 13]', '[128, 4, -2*w^3 + 6*w^2 + 8*w - 24]', '[128, 4, -2*w^3 + 14*w + 12]', '[128, 8, 2*w^2 - 4*w - 4]', '[128, 8, -w^3 + 3*w^2 + 2*w - 10]', '[128, 8, -w^3 + 5*w + 6]', '[128, 8, 2*w^2 - 6]', '[128, 16, -3*w^2 + 4*w + 10]', '[128, 16, -3*w^2 + 2*w + 11]', '[137, 137, w^3 - 5*w^2 + 2*w + 13]', '[137, 137, 2*w^3 - 5*w^2 - 7*w + 15]', '[137, 137, 2*w^3 - w^2 - 11*w - 5]', '[137, 137, -w^3 - 2*w^2 + 5*w + 11]', '[142, 142, 3*w^3 - 5*w^2 - 11*w + 16]', '[142, 142, -w^3 + w^2 + 5*w + 4]', '[142, 142, -w^3 + 2*w^2 + 4*w - 9]', '[142, 142, 2*w^2 - w - 11]', '[146, 146, w^3 - 2*w^2 - 4*w + 1]', '[146, 146, w^3 - 5*w^2 + 3*w + 10]', '[146, 146, 3*w^3 - 11*w^2 - 7*w + 40]', '[146, 146, -w^3 + 4*w^2 - 11]', '[146, 146, w^3 + w^2 - 5*w - 8]', '[146, 146, w^3 - 2*w^2 - 6*w + 11]', '[146, 146, -6*w^3 - 2*w^2 + 41*w + 43]', '[146, 146, w^3 - w^2 - 5*w + 4]', '[151, 151, -4*w^3 - w^2 + 25*w + 25]', '[151, 151, 4*w^3 - 13*w^2 - 11*w + 45]', '[162, 6, -3*w^3 + 9*w^2 + 9*w - 30]', '[162, 6, -3*w^3 + 18*w + 15]', '[164, 82, -2*w^3 + 7*w^2 + 2*w - 15]', '[164, 82, -w^3 + 6*w^2 + 2*w - 22]', '[164, 82, -w^2 - w + 8]', '[164, 82, 4*w^3 - 13*w^2 - 14*w + 52]', '[164, 82, -2*w^3 - w^2 + 13*w + 16]', '[164, 82, -3*w^2 + 2*w + 13]', '[167, 167, -2*w^3 - w^2 + 15*w + 17]', '[167, 167, -2*w^3 + 7*w^2 + 7*w - 29]', '[169, 13, -w^3 - w^2 + 6*w + 5]', '[169, 13, w^3 - 4*w^2 - w + 9]', '[188, 94, -3*w^2 + 4*w + 11]', '[188, 94, -w^3 - 4*w^2 + 6*w + 18]', '[188, 94, w^2 + w - 4]', '[188, 94, -w^2 + 3*w + 2]', '[188, 94, w^3 - 7*w^2 + 5*w + 19]', '[188, 94, -3*w^2 + 2*w + 12]', '[191, 191, w^3 - 2*w^2 - 3*w + 9]', '[191, 191, w^3 - w^2 - 4*w - 5]', '[193, 193, -4*w^2 + 2*w + 17]', '[193, 193, w^2 + w - 5]', '[193, 193, w^2 - 3*w - 3]', '[193, 193, -4*w^2 + 6*w + 15]', '[194, 194, -2*w^2 + w + 12]', '[194, 194, -9*w^3 + 29*w^2 + 27*w - 104]', '[194, 194, -9*w^3 - 2*w^2 + 58*w + 57]', '[194, 194, 2*w^2 - 3*w - 11]', '[196, 14, -2*w^3 + w^2 + 8*w]', '[196, 14, w^2 - w]', '[196, 14, -2*w^3 + 3*w^2 + 8*w - 8]', '[196, 14, -w^2 + w + 8]', '[196, 14, -2*w^3 + 5*w^2 + 4*w - 7]', '[196, 14, -2*w^3 + 3*w^2 + 8*w - 1]', '[196, 98, w^2]', '[196, 98, 3*w^2 - w - 14]', '[196, 98, w^3 - 3*w^2 - 3*w + 7]', '[196, 98, -w^3 + 6*w + 2]', '[196, 98, -3*w^2 + 5*w + 12]', '[196, 98, w^2 - 2*w + 1]', '[206, 206, 2*w^3 - 6*w^2 - 3*w + 12]', '[206, 206, 3*w^3 + w^2 - 19*w - 18]', '[206, 206, -3*w^3 + 10*w^2 + 8*w - 33]', '[206, 206, 2*w^3 - 9*w - 5]', '[217, 217, w^3 - 4*w^2 - 3*w + 13]', '[217, 217, -2*w^3 + 6*w^2 + 4*w - 15]', '[217, 217, -3*w^3 - w^2 + 20*w + 19]', '[217, 217, w^3 - 3*w^2 - 2*w + 11]', '[217, 217, w^3 - 5*w - 7]', '[217, 217, 3*w^3 - 10*w^2 - 9*w + 35]', '[217, 217, -2*w^3 + 10*w + 7]', '[217, 217, -w^3 - w^2 + 8*w + 7]', '[224, 28, 2*w]', '[224, 28, -w^3 - 3*w^2 + 6*w + 14]', '[224, 28, -w^3 + 4*w^2 + w - 14]', '[224, 28, -2*w^3 + 2*w^2 + 10*w + 4]', '[224, 28, 2*w^3 - 4*w^2 - 8*w + 14]', '[224, 28, -w^3 - w^2 + 6*w + 10]', '[224, 28, w^3 - 6*w^2 + 3*w + 16]', '[224, 28, 2*w - 2]', '[224, 56, -2*w^3 - w^2 + 12*w + 14]', '[224, 56, 3*w^2 - 10]', '[224, 56, 3*w^2 - 6*w - 7]', '[224, 56, -2*w^3 + 7*w^2 + 4*w - 23]', '[233, 233, -3*w^3 + 10*w^2 + 11*w - 41]', '[233, 233, -3*w^3 - w^2 + 22*w + 23]', '[239, 239, 2*w^2 - 4*w - 3]', '[239, 239, w^3 + 2*w^2 - 7*w - 11]', '[239, 239, -w^3 + 5*w^2 - 15]', '[239, 239, 2*w^2 - 5]', '[242, 22, -4*w^2 + 7*w + 12]', '[242, 22, -2*w^3 + 9*w + 6]', '[242, 22, -2*w^3 + 6*w^2 + 3*w - 13]', '[242, 22, -4*w^2 + w + 15]', '[248, 62, w^3 + 3*w^2 - 4*w - 12]', '[248, 62, -w^3 - 2*w^2 + 7*w + 12]', '[248, 62, w^3 - 7*w - 2]', '[248, 62, -w^3 + 3*w^2 + 2*w - 12]', '[248, 62, -w^3 + 5*w + 8]', '[248, 62, -w^3 + 3*w^2 + 4*w - 8]', '[248, 62, w^3 - 5*w^2 + 16]', '[248, 62, w^3 - 6*w^2 + 5*w + 12]', '[248, 124, -w^3 - w^2 + 9*w + 9]', '[248, 124, 2*w^3 - 5*w^2 - 6*w + 15]', '[248, 124, w^3 - 5*w^2 - w + 17]', '[248, 124, -2*w^3 - w^2 + 10*w + 11]', '[248, 124, -2*w^3 + 7*w^2 + 2*w - 18]', '[248, 124, -w^3 - 2*w^2 + 8*w + 12]', '[248, 124, 2*w^3 - w^2 - 10*w - 6]', '[248, 124, -w^3 + 4*w^2 + 4*w - 16]', '[254, 254, 6*w^3 - 18*w^2 - 23*w + 72]', '[254, 254, 3*w^3 - 9*w^2 - 11*w + 32]', '[254, 254, 3*w^3 - 20*w - 15]', '[254, 254, 6*w^3 - 41*w - 37]', '[256, 4, 4]', '[256, 8, -2*w^3 + 2*w^2 + 8*w - 4]', '[256, 8, -2*w^2 + 4]', '[256, 8, -2*w^2 + 4*w + 2]', '[256, 8, -2*w^3 + 4*w^2 + 6*w - 4]', '[256, 16, w^2 - 4*w + 2]', '[256, 16, 3*w^3 + 3*w^2 - 14*w - 18]', '[256, 16, -w^2 - 2*w + 1]', '[256, 16, 3*w^3 - 12*w^2 + w + 26]', '[257, 257, -5*w^3 - 2*w^2 + 35*w + 37]', '[257, 257, 2*w - 1]', '[257, 257, -2*w^3 + 5*w^2 + 5*w - 9]', '[263, 263, 2*w^2 - 11]', '[263, 263, 2*w^2 - 4*w - 9]', '[271, 271, -w^3 + w^2 + 4*w - 5]', '[271, 271, w^3 - 2*w^2 - 3*w - 1]', '[274, 274, w^3 + w^2 - 9*w - 12]', '[274, 274, w^3 + 2*w^2 - 8*w - 13]', '[274, 274, 2*w^2 - 5*w - 3]', '[274, 274, -w^3 + 3*w^2 + w - 2]', '[274, 274, -w^3 + 4*w - 1]', '[274, 274, -2*w^2 - w + 6]', '[274, 274, -w^3 + 5*w^2 + w - 18]', '[274, 274, -w^3 + 4*w^2 + 4*w - 19]', '[281, 281, 2*w^3 + 2*w^2 - 12*w - 15]', '[281, 281, 2*w^3 - 8*w^2 - 2*w + 23]', '[284, 142, 2*w^3 - 7*w^2 - 4*w + 20]', '[284, 142, -8*w^3 + 25*w^2 + 25*w - 90]', '[284, 142, -2*w^3 + w^2 + 10*w + 3]', '[284, 142, 2*w^3 - 5*w^2 - 6*w + 12]', '[284, 142, -2*w^3 - w^2 + 7*w + 4]', '[284, 142, 2*w^3 + w^2 - 12*w - 11]', '[287, 287, -3*w^3 + 9*w^2 + 10*w - 35]', '[287, 287, 2*w^2 - 8*w + 7]', '[287, 287, -w^2 - w + 9]', '[287, 287, 2*w^3 - w^2 - 9*w + 1]', '[289, 17, 3*w^2 - 3*w - 11]', '[289, 17, 3*w^2 - 3*w - 13]', '[292, 146, -2*w^3 + 7*w^2 + 6*w - 24]', '[292, 146, 2*w^3 + 3*w^2 - 8*w - 13]', '[292, 146, -2*w^3 + w^2 + 15*w + 12]', '[292, 146, -2*w^3 + w^2 + 8*w + 4]', '[292, 146, -3*w^2 + w + 10]', '[292, 146, w^3 - w^2 - 3*w - 3]', '[292, 146, -3*w^3 + 3*w^2 + 13*w + 9]', '[292, 146, -3*w^2 + 2*w + 16]', '[292, 146, -2*w^3 + 3*w^2 + 9*w - 2]', '[292, 146, -2*w^3 - w^2 + 14*w + 13]', '[292, 146, -2*w^3 + 5*w^2 + 11*w - 26]', '[292, 146, -2*w^3 + 9*w^2 - 4*w - 16]', '[302, 302, -4*w^2 + 7*w + 15]', '[302, 302, -w^3 + 4*w^2 + 2*w - 11]', '[302, 302, -w^3 - w^2 + 7*w + 6]', '[302, 302, -4*w^2 + w + 18]', '[311, 311, 5*w^2 - w - 19]', '[311, 311, -w^3 + 2*w^2 + 5*w - 11]', '[313, 313, 2*w^3 - 5*w^2 - 11*w + 25]', '[313, 313, -2*w^3 + 8*w^2 + 4*w - 29]', '[324, 6, 3*w^2 - 12]', '[324, 6, -3*w^2 + 3*w + 12]', '[324, 6, -3*w^2 + 6*w + 9]', '[328, 82, w^3 - 2*w^2 - 5*w + 2]', '[328, 82, 7*w^3 - 23*w^2 - 20*w + 80]', '[328, 82, -w^3 + w^2 + 6*w - 4]', '[328, 82, w^3 - 6*w^2 + 3*w + 18]', '[328, 164, -3*w^3 + 10*w^2 + 4*w - 24]', '[328, 164, 2*w^3 - 5*w^2 - 6*w + 18]', '[328, 164, -3*w^2 + 13]', '[328, 164, w^2 - 4*w + 5]', '[329, 329, -2*w^3 - w^2 + 7*w + 3]', '[329, 329, 2*w - 7]', '[329, 329, -2*w - 5]', '[329, 329, 2*w^3 - 7*w^2 + w + 7]', '[334, 334, -w^3 + 3*w^2 + 3*w - 6]', '[334, 334, -2*w^3 + 2*w^2 + 7*w - 6]', '[334, 334, -2*w^3 + 4*w^2 + 5*w - 1]', '[334, 334, w^3 - 6*w - 1]', '[337, 337, -2*w^3 + 5*w^2 + 5*w - 13]', '[337, 337, 2*w^3 - w^2 - 9*w - 5]', '[338, 26, -2*w^3 + 6*w^2 + 5*w - 20]', '[338, 26, w^3 - 3*w^2 - 7*w + 20]', '[338, 26, w^3 - 10*w - 11]', '[338, 26, -2*w^3 + 11*w + 11]', '[343, 7, w^3 - w^2 - 8*w + 7]', '[343, 7, w^3 - 2*w^2 - 7*w + 1]', '[343, 49, -w^3 + 5*w^2 - 4*w - 7]', '[343, 49, -w^3 - 2*w^2 + 3*w + 7]', '[343, 343, 2*w^3 - w^2 - 13*w - 9]', '[343, 343, -2*w^3 + 5*w^2 + 9*w - 21]', '[353, 353, -2*w^3 + 8*w^2 + 4*w - 27]', '[353, 353, -3*w^3 + 2*w^2 + 13*w - 3]', '[359, 359, 4*w^3 + w^2 - 25*w - 23]', '[359, 359, 4*w^3 - 13*w^2 - 11*w + 43]', '[367, 367, 6*w^3 - 18*w^2 - 22*w + 71]', '[367, 367, -2*w^3 + 5*w^2 + 3*w - 3]', '[376, 94, 3*w^3 + 2*w^2 - 19*w - 22]', '[376, 94, -3*w^3 + 11*w^2 + 8*w - 40]', '[376, 94, 3*w^3 + 2*w^2 - 21*w - 24]', '[376, 94, -3*w^3 + 11*w^2 + 6*w - 36]', '[376, 188, w^3 - 4*w^2 + 12]', '[376, 188, 2*w^3 - 9*w^2 + 2*w + 22]', '[376, 188, 2*w^3 + 3*w^2 - 10*w - 17]', '[376, 188, w^3 + w^2 - 5*w - 9]', '[382, 382, -w^3 + w^2 + 3*w + 6]', '[382, 382, -3*w^3 - w^2 + 21*w + 24]', '[382, 382, -3*w^3 + 10*w^2 + 10*w - 41]', '[382, 382, w^3 - 2*w^2 - 2*w + 9]', '[383, 383, w^3 - 9*w - 11]', '[383, 383, 3*w^3 - 17*w - 13]', '[386, 386, -4*w^3 + 14*w^2 + 11*w - 51]', '[386, 386, -4*w^3 + 14*w^2 + 11*w - 50]', '[386, 386, 2*w^3 - 8*w^2 - 3*w + 26]', '[386, 386, w^3 + 2*w^2 - 6*w - 13]', '[386, 386, w^3 - 5*w^2 + w + 16]', '[386, 386, 2*w^3 + 2*w^2 - 13*w - 17]', '[386, 386, -4*w^3 - 2*w^2 + 27*w + 29]', '[386, 386, 4*w^3 + 2*w^2 - 27*w - 30]', '[388, 194, w^3 - 2*w + 2]', '[388, 194, -2*w^3 - w^2 + 13*w + 12]', '[388, 194, -2*w^3 - 3*w^2 + 18*w + 23]', '[388, 194, -2*w^3 + 9*w^2 + 6*w - 36]', '[388, 194, 2*w^3 - 7*w^2 - 5*w + 22]', '[388, 194, w^3 - 3*w^2 + w - 1]', '[392, 14, 3*w^3 - 9*w^2 - 8*w + 28]', '[392, 14, 3*w^3 - 17*w - 14]', '[392, 14, 5*w^3 - 31*w - 26]', '[392, 14, 5*w^3 - 15*w^2 - 16*w + 52]', '[392, 28, -2*w^3 + 5*w^2 + 6*w - 10]', '[392, 28, -2*w^3 + 7*w^2 + 2*w - 14]', '[392, 28, 2*w^3 + w^2 - 10*w - 7]', '[392, 28, 2*w^3 - w^2 - 10*w - 1]', '[392, 98, w^3 - 3*w^2]', '[392, 98, 3*w^3 + 2*w^2 - 15*w - 14]', '[392, 98, -3*w^3 + 11*w^2 + 2*w - 24]', '[392, 98, -w^3 + 3*w - 2]', '[392, 196, 2*w^3 - 5*w^2 - 6*w + 14]', '[392, 196, -w^2 - 2*w + 10]', '[392, 196, w^2 - 4*w - 7]', '[392, 196, 2*w^3 - w^2 - 10*w - 5]', '[401, 401, 5*w^3 + w^2 - 30*w - 29]', '[401, 401, -5*w^3 - 2*w^2 + 35*w + 39]', '[401, 401, -5*w^3 + 17*w^2 + 16*w - 67]', '[401, 401, -5*w^3 + 16*w^2 + 13*w - 53]', '[409, 409, w^3 + w^2 - 6*w - 11]', '[409, 409, -w^3 + 4*w^2 + w - 15]', '[412, 206, w^3 - 3*w^2 - w + 9]', '[412, 206, -w^3 + 2*w + 2]', '[412, 206, -2*w^3 + w^2 + 9*w - 2]', '[412, 206, w^3 - 4*w - 6]', '[412, 206, 2*w^3 - 5*w^2 - 5*w + 6]', '[412, 206, -w^3 + 3*w^2 - w - 3]', '[431, 431, w^3 - 6*w^2 + w + 17]', '[431, 431, w^3 + 3*w^2 - 8*w - 13]', '[433, 433, -8*w^3 + 25*w^2 + 25*w - 89]', '[433, 433, w^3 - 5*w^2 + 19]', '[433, 433, w^3 + 2*w^2 - 7*w - 15]', '[433, 433, 8*w^3 + w^2 - 51*w - 47]', '[434, 434, -w^3 + 2*w - 1]', '[434, 434, w^3 - 6*w - 9]', '[434, 434, -w^3 + w^2 + 3*w + 4]', '[434, 434, 2*w^3 - 10*w^2 + 3*w + 26]', '[434, 434, 2*w^2 - 5*w]', '[434, 434, 2*w^3 - 13*w - 14]', '[434, 434, 2*w^3 - 4*w^2 - 7*w + 7]', '[434, 434, 3*w^3 - 14*w - 7]', '[434, 434, 3*w^3 - 9*w^2 - 5*w + 18]', '[434, 434, 2*w^3 - 2*w^2 - 9*w + 2]', '[434, 434, -2*w^3 + 6*w^2 + 7*w - 25]', '[434, 434, 2*w^2 + w - 3]', '[434, 434, -2*w^3 - 4*w^2 + 11*w + 21]', '[434, 434, -w^3 + 2*w^2 + 2*w - 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2*w^2 - 17*w - 11]', '[1918, 1918, -3*w^3 + 2*w^2 + 16*w + 13]', '[1918, 1918, -w^3 + w^2 + w + 6]', '[1918, 1918, w^3 + 2*w^2 - 12*w - 7]', '[1918, 1918, w^3 - 5*w^2 - 5*w + 16]', '[1918, 1918, w^3 - 2*w^2 + 7]', '[1918, 1918, -3*w^3 + 7*w^2 + 11*w - 28]', '[1918, 1918, 2*w^3 - 4*w^2 - 15*w + 28]', '[1918, 1918, w^3 - 7*w^2 + 5*w + 22]', '[1918, 1918, -3*w^3 + w^2 + 15*w + 8]', '[1918, 1918, -4*w^3 + 14*w^2 + 3*w - 27]', '[1918, 1918, -w^3 + 7*w^2 - w - 28]', '[1922, 62, -3*w^3 + 9*w^2 + 13*w - 38]', '[1922, 62, 2*w^3 - 6*w^2 - 3*w + 6]', '[1922, 62, -w^3 + 3*w^2 + 5*w - 4]', '[1922, 62, -3*w^3 + 7*w^2 + 9*w - 24]', '[1922, 62, 4*w^3 - 12*w^2 - 9*w + 34]', '[1922, 62, 2*w^2 - 5*w - 12]', '[1922, 62, -3*w^3 + 2*w^2 + 14*w + 11]', '[1922, 62, 4*w^3 - 21*w - 17]', '[1922, 62, -3*w^3 + 22*w + 19]', '[1922, 62, -2*w^2 - w + 15]', '[1922, 62, w^3 - 8*w + 3]', '[1922, 62, -2*w^3 + 9*w - 1]', '[1922, 1922, -3*w^3 + 10*w^2 + 8*w - 31]', '[1922, 1922, 4*w^3 - 27*w - 27]', '[1922, 1922, 2*w^3 - 15*w - 17]', '[1922, 1922, 3*w^3 - 2*w^2 - 12*w + 1]', '[1922, 1922, 3*w^3 - 7*w^2 - 7*w + 10]', '[1922, 1922, -2*w^3 + 6*w^2 + 9*w - 30]', '[1922, 1922, -4*w^3 + 12*w^2 + 15*w - 50]', '[1922, 1922, 3*w^3 + w^2 - 19*w - 16]', '[1927, 1927, -6*w^3 - 3*w^2 + 37*w + 41]', '[1927, 1927, 4*w^3 - 13*w^2 - 13*w + 45]', '[1927, 1927, -3*w^3 + 4*w^2 + 11*w - 15]', '[1927, 1927, -6*w^3 + 21*w^2 + 13*w - 69]', '[1934, 1934, -3*w^3 + 13*w^2 - 3*w - 30]', '[1934, 1934, 5*w^3 + 3*w^2 - 33*w - 36]', '[1934, 1934, -3*w^3 + 11*w^2 + w - 26]', '[1934, 1934, 3*w^3 + 3*w^2 - 19*w - 24]', '[1934, 1934, 3*w^3 - 12*w^2 - 4*w + 37]', '[1934, 1934, 3*w^3 + 2*w^2 - 14*w - 17]', '[1934, 1934, 5*w^3 - 18*w^2 - 12*w + 61]', '[1934, 1934, 3*w^3 + 4*w^2 - 14*w - 23]', '[1936, 22, 2*w^2 + 2*w - 6]', '[1936, 22, -2*w^2 + 6*w + 2]', '[1936, 44, -w^3 + 4*w^2 - 2*w - 12]', '[1936, 44, -5*w^3 + w^2 + 32*w + 26]', '[1936, 44, -w^3 - w^2 + 3*w + 11]', '[1936, 44, w^3 - 7*w^2 + 26]', '[1936, 44, -5*w^3 + 16*w^2 + 14*w - 52]', '[1936, 44, 5*w^3 + w^2 - 31*w - 27]', '[1936, 44, -w^3 - 4*w^2 + 11*w + 20]', '[1936, 44, 5*w^3 - 14*w^2 - 19*w + 54]', '[1948, 974, w^3 - 4*w^2 - 4*w + 10]', '[1948, 974, -w^3 + 7*w^2 - w - 23]', '[1948, 974, 2*w^3 - w^2 - 9*w - 10]', '[1948, 974, -2*w^3 + 5*w^2 + 5*w - 18]', '[1948, 974, -w^3 - 4*w^2 + 10*w + 18]', '[1948, 974, w^3 + w^2 - 9*w - 3]', '[1951, 1951, -2*w^3 + 8*w^2 + 6*w - 27]', '[1951, 1951, -2*w^3 - 2*w^2 + 16*w + 15]', '[1954, 1954, 9*w^3 - 27*w^2 - 29*w + 92]', '[1954, 1954, -12*w^3 + 36*w^2 + 41*w - 132]', '[1954, 1954, 12*w^3 - 77*w - 67]', '[1954, 1954, -9*w^3 + 56*w + 45]', '[1966, 1966, 2*w^3 + 4*w^2 - 17*w - 29]', '[1966, 1966, -13*w^3 - 4*w^2 + 84*w + 85]', '[1966, 1966, -13*w^3 + 43*w^2 + 37*w - 152]', '[1966, 1966, 2*w^3 - 10*w^2 - 3*w + 40]', '[1967, 1967, 8*w^2 - 2*w - 35]', '[1967, 1967, w^3 - 5*w^2 + 7]', '[1967, 1967, w^3 + 2*w^2 - 7*w - 3]', '[1967, 1967, 8*w^2 - 14*w - 29]', '[1982, 1982, -2*w^3 + 6*w^2 + 9*w - 24]', '[1982, 1982, -5*w^3 + 15*w^2 + 21*w - 64]', '[1982, 1982, -5*w^3 + 36*w + 33]', '[1982, 1982, -2*w^3 + 15*w + 11]', '[1984, 124, 2*w^3 - 4*w^2 - 8*w + 4]', '[1984, 124, -2*w^3 + 10*w^2 - 2*w - 26]', '[1984, 124, -2*w^2 - 2*w + 12]', '[1984, 124, -2*w^3 - 2*w^2 + 18*w + 22]', '[1984, 124, -4*w^3 - 2*w^2 + 22*w + 20]', '[1984, 124, -2*w^3 + 4*w^2 + 4*w + 4]', '[1984, 124, 2*w^3 - 2*w^2 - 6*w + 10]', '[1984, 124, 4*w^3 - 14*w^2 - 6*w + 36]', '[1984, 124, -2*w^3 + 8*w^2 + 8*w - 36]', '[1984, 124, -2*w^3 + 2*w^2 + 10*w - 6]', '[1984, 124, 2*w^2 - 6*w - 8]', '[1984, 124, 2*w^3 + 4*w^2 - 12*w - 20]', '[1984, 248, 5*w^3 - 16*w^2 - 13*w + 54]', '[1984, 248, -w^3 + 2*w^2 + 6*w + 4]', '[1984, 248, -w^3 - w^2 + 11*w + 15]', '[1984, 248, w^3 + 4*w^2 - 9*w - 22]', '[1984, 248, -3*w^3 + 2*w^2 + 15*w + 4]', '[1984, 248, 3*w^3 - 6*w^2 - 10*w + 4]', '[1984, 248, 2*w^3 + w^2 - 16*w - 13]', '[1984, 248, w^3 - 6*w^2 + 3*w + 20]', '[1984, 248, w^3 + 3*w^2 - 6*w - 18]', '[1984, 248, -3*w^3 + 3*w^2 + 13*w - 9]', '[1984, 248, 2*w^3 - 7*w^2 - 8*w + 26]', '[1984, 248, -3*w^3 + 7*w^2 + 10*w - 18]', '[1984, 248, -w^3 + 7*w^2 - 2*w - 26]', '[1984, 248, w^3 - w^2 - 7*w + 11]', '[1984, 248, -w^3 + 4*w^2 + 6*w - 24]', '[1984, 248, 5*w^3 + w^2 - 30*w - 30]', '[1988, 994, 5*w^2 - 2*w - 24]', '[1988, 994, w^3 - 5*w^2 - 5*w + 23]', '[1988, 994, 2*w^3 - 5*w^2 - 7*w + 10]', '[1988, 994, -8*w^3 + 21*w^2 + 28*w - 77]', '[1988, 994, w^3 + 10*w^2 - 8*w - 42]', '[1988, 994, -3*w^2 - w + 14]', '[1988, 994, -3*w^2 + 7*w + 10]', '[1988, 994, 2*w^3 - 3*w^2 - 10*w + 11]', '[1988, 994, -w^3 - 4*w^2 + 8*w + 18]', '[1988, 994, 2*w^3 - w^2 - 11*w]', '[1988, 994, -3*w^3 + 4*w^2 + 10*w - 14]', '[1988, 994, 5*w^2 - 8*w - 21]', '[1993, 1993, 4*w^3 - 15*w^2 - 7*w + 47]', '[1993, 1993, -6*w^3 - 2*w^2 + 42*w + 47]', '[1999, 1999, 4*w^3 - 14*w^2 - 8*w + 41]', '[1999, 1999, 2*w^3 + w^2 - 11*w - 15]', '[1999, 1999, 2*w^3 - 7*w^2 - 3*w + 23]', '[1999, 1999, 4*w^3 + 2*w^2 - 24*w - 23]', '[2009, 287, -w^3 + w^2 + 7]', '[2009, 287, w^3 - 5*w^2 - 4*w + 25]', '[2009, 287, -3*w^3 - w^2 + 18*w + 21]', '[2009, 287, -3*w^3 + w^2 + 12*w + 9]', '[2009, 2009, -2*w^3 - 4*w^2 + 12*w + 21]', '[2009, 2009, -4*w^3 + 9*w^2 + 15*w - 35]', '[2009, 2009, -w^3 + 5*w^2 + 4*w - 15]', '[2009, 2009, 2*w^3 - 10*w^2 + 2*w + 27]', '[2017, 2017, -9*w^3 - 3*w^2 + 56*w + 57]', '[2017, 2017, -9*w^3 + 30*w^2 + 23*w - 101]', '[2018, 2018, -3*w^3 + 10*w^2 + 4*w - 27]', '[2018, 2018, 2*w^3 - 2*w^2 - 7*w + 9]', '[2018, 2018, 2*w^3 - 4*w^2 - 5*w - 2]', '[2018, 2018, -2*w^3 - 2*w^2 + 17*w + 24]', '[2023, 119, w^3 - 11*w + 7]', '[2023, 119, -w^3 + 6*w^2 - 7*w - 7]', '[2023, 119, -w^3 - 3*w^2 + 2*w + 9]', '[2023, 119, w^3 - 3*w^2 - 8*w + 3]', '[2032, 254, 2*w^3 - 10*w^2 + 34]', '[2032, 254, -2*w^3 - 4*w^2 + 14*w + 26]', '[2032, 508, -3*w^3 + 9*w^2 + 12*w - 34]', '[2032, 508, -6*w^3 + 21*w^2 + 8*w - 53]', '[2032, 508, w^3 + 2*w^2 - 10*w - 8]', '[2032, 508, w^3 + 7*w^2 - 4*w - 26]', '[2032, 508, w^3 - 10*w^2 + 13*w + 22]', '[2032, 508, 6*w^3 + 3*w^2 - 32*w - 30]', '[2032, 508, -w^3 + 5*w^2 + 3*w - 15]', '[2032, 508, -3*w^3 + 21*w + 16]', '[2039, 2039, 8*w^3 - 27*w^2 - 23*w + 95]', '[2039, 2039, w^3 + 6*w^2 - 15*w - 29]', '[2039, 2039, -w^3 + 9*w^2 - 37]', '[2039, 2039, 8*w^3 + 3*w^2 - 53*w - 53]', '[2044, 1022, 4*w^3 - w^2 - 22*w - 16]', '[2044, 1022, -w^3 + 5*w^2 - 3*w - 15]', '[2044, 1022, 2*w^3 + w^2 - 11*w - 6]', '[2044, 1022, -2*w^3 + w^2 + 14*w + 7]', '[2044, 1022, -2*w^3 + 3*w^2 + 3*w + 14]', '[2044, 1022, -5*w^3 + 14*w^2 + 16*w - 42]', '[2044, 1022, 7*w^2 - 13*w - 22]', '[2044, 1022, 3*w^3 - 11*w^2 - 3*w + 25]', '[2044, 1022, 5*w^2 - 6*w - 20]', '[2044, 1022, 5*w^3 - 17*w^2 - 5*w + 35]', '[2044, 1022, w^2 + 3*w - 14]', '[2044, 1022, -3*w^3 + 10*w^2 + 2*w - 14]', '[2044, 1022, -8*w^3 + w^2 + 50*w + 41]', '[2044, 1022, -4*w^3 - 3*w^2 + 27*w + 36]', '[2044, 1022, 5*w^3 - 14*w^2 - 10*w + 26]', '[2044, 1022, 3*w^3 + 2*w^2 - 16*w - 14]', '[2044, 1022, 7*w^2 - w - 28]', '[2044, 1022, -5*w^2 + 4*w + 21]', '[2044, 1022, -3*w^2 - 2*w + 5]', '[2044, 1022, -4*w^3 + 15*w^2 - w - 24]', '[2044, 1022, -3*w^3 + 8*w^2 + 6*w - 18]', '[2044, 1022, -4*w^3 + 11*w^2 + 12*w - 35]', '[2044, 1022, 2*w^3 - 7*w^2 - 3*w + 14]', '[2044, 1022, w^3 + 2*w^2 - 4*w - 14]', '[2048, 8, -4*w^3 + 12*w^2 + 16*w - 48]', '[2048, 8, -4*w^3 + 28*w + 24]', '[2048, 16, 4*w^2 - 8*w - 8]', '[2048, 16, -2*w^3 + 6*w^2 + 4*w - 20]', '[2048, 16, -2*w^3 + 10*w + 12]', '[2048, 16, 4*w^2 - 12]', '[2048, 32, -6*w^2 + 8*w + 20]', '[2048, 32, 3*w^3 - 3*w^2 - 14*w + 2]', '[2048, 32, 3*w^3 - 6*w^2 - 11*w + 12]', '[2048, 32, -6*w^2 + 4*w + 22]', '[2048, 64, -3*w^3 + 2*w^2 + 18*w + 12]', '[2048, 64, 3*w^3 - 7*w^2 - 13*w + 29]', '[2056, 514, -w^3 + 14*w^2 - 17*w - 44]', '[2056, 514, w^3 + 3*w^2 - 12*w - 12]', '[2056, 514, 3*w^3 - 9*w^2 - 12*w + 40]', '[2056, 514, -3*w^3 + 21*w + 22]', '[2056, 514, -w^3 + 6*w^2 + 3*w - 20]', '[2056, 514, 3*w^3 - w^2 - 14*w - 8]', '[2056, 1028, -w^3 + 4*w^2 - 16]', '[2056, 1028, 2*w^3 - 5*w^2 - 2*w + 2]', '[2056, 1028, -3*w^3 - 2*w^2 + 12*w + 8]', '[2056, 1028, 3*w^3 - 11*w^2 + w + 15]', '[2056, 1028, 2*w^3 - w^2 - 6*w + 3]', '[2056, 1028, -w^3 - w^2 + 5*w + 13]', '[2062, 2062, -3*w^3 + 5*w^2 + 11*w - 4]', '[2062, 2062, 4*w^3 - 25*w - 18]', '[2062, 2062, 4*w^3 - 12*w^2 - 13*w + 39]', '[2062, 2062, 3*w^3 - 4*w^2 - 12*w + 9]', '[2063, 2063, 2*w^3 - 5*w^2 - 5*w + 19]', '[2063, 2063, 2*w^3 - w^2 - 9*w - 11]', '[2066, 2066, w^3 + 4*w^2 - 8*w - 19]', '[2066, 2066, -5*w^3 + 16*w^2 + 14*w - 57]', '[2066, 2066, -2*w^3 - 6*w^2 + 9*w + 26]', '[2066, 2066, w^3 - 7*w^2 + 3*w + 22]', '[2081, 2081, -2*w^3 + 3*w^2 + 7*w - 13]', '[2081, 2081, 7*w^3 + 2*w^2 - 45*w - 43]', '[2081, 2081, 7*w^3 - 23*w^2 - 20*w + 79]', '[2081, 2081, 2*w^3 - 3*w^2 - 7*w - 5]', '[2084, 1042, 2*w^3 - 9*w^2 - 2*w + 25]', '[2084, 1042, 3*w^2 - 7*w - 8]', '[2084, 1042, 5*w^2 - 4*w - 20]', '[2084, 1042, -2*w^3 - 9*w^2 + 12*w + 40]', '[2084, 1042, -5*w^2 + 6*w + 19]', '[2084, 1042, 3*w^2 + w - 12]', '[2087, 2087, 3*w^3 - 2*w^2 - 15*w - 5]', '[2087, 2087, 10*w^3 + w^2 - 63*w - 55]', '[2087, 2087, 10*w^3 - 31*w^2 - 31*w + 107]', '[2087, 2087, 3*w^3 - 7*w^2 - 10*w + 19]', '[2089, 2089, 2*w^3 - 7*w^2 - 9*w + 37]', '[2089, 2089, 2*w^3 + w^2 - 17*w - 23]', '[2098, 2098, 7*w^3 + 2*w^2 - 44*w - 45]', '[2098, 2098, 3*w^3 + 3*w^2 - 21*w - 26]', '[2098, 2098, -2*w^3 + 8*w^2 - w - 20]', '[2098, 2098, 2*w^3 + 2*w^2 - 17*w - 23]', '[2098, 2098, -2*w^3 + 8*w^2 + 7*w - 36]', '[2098, 2098, 2*w^3 + 2*w^2 - 9*w - 15]', '[2098, 2098, 3*w^3 - 12*w^2 - 6*w + 41]', '[2098, 2098, -7*w^3 + 23*w^2 + 19*w - 80]', '[2104, 526, 3*w^3 - 17*w - 10]', '[2104, 526, 9*w^3 - 27*w^2 - 32*w + 104]', '[2104, 526, 9*w^3 - 59*w - 54]', '[2104, 526, 3*w^3 - 9*w^2 - 8*w + 24]', '[2104, 1052, -w^2 + 6*w - 6]', '[2104, 1052, -4*w^3 + 9*w^2 + 10*w - 10]', '[2104, 1052, 4*w^3 - 3*w^2 - 16*w + 5]', '[2104, 1052, -w^2 - 4*w - 1]', '[2111, 2111, -3*w^3 + 6*w^2 + 7*w - 11]', '[2111, 2111, -3*w^3 + 3*w^2 + 10*w + 1]', '[2113, 2113, -3*w^3 + 14*w^2 - 7*w - 23]', '[2113, 2113, w^2 - 3*w + 5]', '[2113, 2113, -w^2 - w - 3]', '[2113, 2113, w^3 - 4*w^2 - 7*w + 25]', '[2114, 2114, -2*w^3 - 4*w^2 + 11*w + 23]', '[2114, 2114, -w^3 + 4*w^2 - 6*w + 7]', '[2114, 2114, -5*w^3 - 2*w^2 + 32*w + 31]', '[2114, 2114, -5*w^3 - 2*w^2 + 24*w + 21]', '[2114, 2114, 5*w^3 - 17*w^2 - 5*w + 38]', '[2114, 2114, -5*w^3 + 17*w^2 + 13*w - 56]', '[2114, 2114, w^3 + w^2 + w + 4]', '[2114, 2114, 2*w^3 - 10*w^2 + 3*w + 28]', '[2116, 46, w^3 - 7*w^2 + 7*w + 17]', '[2116, 46, -w^3 + 6*w^2 + 4*w - 22]', '[2116, 46, -5*w^2 + 5*w + 22]', '[2116, 46, w^3 + 4*w^2 - 4*w - 18]', '[2116, 46, -5*w^2 + 5*w + 18]', '[2116, 46, -w^3 - 3*w^2 + 13*w + 13]', '[2126, 2126, -3*w^3 - 4*w^2 + 20*w + 31]', '[2126, 2126, -2*w^3 + 8*w^2 - 3*w - 15]', '[2126, 2126, -w^3 + 6*w + 11]', '[2126, 2126, -4*w^2 - w + 11]', '[2126, 2126, 12*w^3 - 40*w^2 - 37*w + 148]', '[2126, 2126, 6*w^2 - 5*w - 20]', '[2126, 2126, -3*w^3 + 3*w^2 + 13*w - 4]', '[2126, 2126, 6*w^3 - 41*w - 36]', '[2143, 2143, 2*w^3 - 12*w - 5]', '[2143, 2143, -2*w^3 + 6*w^2 + 6*w - 15]', '[2153, 2153, -4*w^3 + 15*w^2 + 9*w - 53]', '[2153, 2153, -4*w^3 - 3*w^2 + 27*w + 33]', '[2161, 2161, 6*w^3 - 18*w^2 - 18*w + 61]', '[2161, 2161, 6*w^3 - 36*w - 31]', '[2168, 542, w^3 - 2*w^2 - 9*w - 2]', '[2168, 542, 7*w^3 - 23*w^2 - 24*w + 88]', '[2168, 542, 3*w^3 + 4*w^2 - 15*w - 24]', '[2168, 542, 5*w^3 + 3*w^2 - 32*w - 36]', '[2168, 1084, -2*w^3 - 7*w^2 + 10*w + 29]', '[2168, 1084, w^3 - 3*w^2 - 5*w + 3]', '[2168, 1084, -w^3 + 8*w - 4]', '[2168, 1084, -4*w^3 + 15*w^2 + 10*w - 54]', '[2177, 2177, -4*w^3 + 8*w^2 + 12*w - 7]', '[2177, 2177, -8*w^3 - 3*w^2 + 45*w + 43]', '[2177, 2177, 8*w^3 - 27*w^2 - 15*w + 77]', '[2177, 2177, 4*w^3 - 4*w^2 - 16*w + 9]', '[2191, 2191, -2*w^3 - 7*w^2 + 25*w + 33]', '[2191, 2191, -4*w^3 - 4*w^2 + 32*w + 39]', '[2191, 2191, -3*w^3 + 6*w^2 + 9*w - 7]', '[2191, 2191, -w^3 + w^2 + 6*w + 7]', '[2192, 274, 2*w^3 - 10*w^2 + 4*w + 26]', '[2192, 274, 4*w^3 - 10*w^2 - 14*w + 30]', '[2192, 274, 4*w^3 - 2*w^2 - 22*w - 10]', '[2192, 274, -2*w^3 - 4*w^2 + 10*w + 22]', '[2192, 548, -w^3 - w^2 + 8*w + 2]', '[2192, 548, 3*w^3 - 4*w^2 - 10*w + 12]', '[2192, 548, -8*w^3 + 29*w^2 + 2*w - 57]', '[2192, 548, 13*w^3 + 2*w^2 - 83*w - 78]', '[2192, 548, 3*w^3 - 4*w^2 - 13*w + 12]', '[2192, 548, -w^3 - 3*w^2 + 4*w + 6]', '[2192, 548, 4*w^3 + w^2 - 22*w - 17]', '[2192, 548, -w^3 - 2*w^2 + 6*w + 16]', '[2192, 548, -4*w^3 + 13*w^2 + 8*w - 34]', '[2192, 548, -w^3 + 5*w^2 - w - 19]', '[2192, 548, -w^3 + 6*w^2 - 5*w - 6]', '[2192, 548, -3*w^3 + 5*w^2 + 12*w - 2]', '[2192, 548, 13*w^3 - 41*w^2 - 40*w + 146]', '[2192, 548, -3*w^3 + 5*w^2 + 9*w + 1]', '[2192, 548, 8*w^3 + 5*w^2 - 36*w - 34]', '[2192, 548, -w^3 + 4*w^2 + 3*w - 8]', '[2194, 2194, -w^3 - 4*w^2 + 4*w + 13]', '[2194, 2194, 4*w^3 - 12*w^2 - 17*w + 51]', '[2194, 2194, 4*w^3 - 29*w - 26]', '[2194, 2194, w^3 - 7*w^2 + 7*w + 12]', '[2201, 2201, -2*w^3 + 2*w^2 + 8*w - 9]', '[2201, 2201, 5*w^3 - 13*w^2 - 16*w + 47]', '[2201, 2201, -3*w^3 + 11*w^2 + 6*w - 39]', '[2201, 2201, -4*w^3 + 15*w^2 + 9*w - 51]', '[2201, 2201, -4*w^3 - 3*w^2 + 27*w + 31]', '[2201, 2201, -2*w^3 - 11*w^2 + 11*w + 47]', '[2201, 2201, 3*w^2 + w - 13]', '[2201, 2201, 3*w^3 - 12*w^2 - 9*w + 43]', '[2206, 2206, -w^3 + 6*w^2 + 4*w - 25]', '[2206, 2206, -2*w^3 + 2*w^2 + 11*w - 5]', '[2206, 2206, -2*w^3 + 4*w^2 + 9*w - 6]', '[2206, 2206, w^3 + 3*w^2 - 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34*w - 25]', '[3769, 3769, -w^3 + 5*w^2 + 2*w - 11]', '[3769, 3769, w^3 + 2*w^2 - 9*w - 5]', '[3778, 3778, -3*w^3 + 2*w^2 + 20*w + 13]', '[3778, 3778, -6*w^3 - 2*w^2 + 39*w + 37]', '[3778, 3778, -6*w^3 + 20*w^2 + 17*w - 68]', '[3778, 3778, -3*w^3 + 7*w^2 + 15*w - 32]', '[3793, 3793, -3*w^3 + 9*w^2 + 8*w - 23]', '[3793, 3793, 2*w^3 + 5*w^2 - 15*w - 23]', '[3793, 3793, -2*w^3 + 11*w^2 - w - 31]', '[3793, 3793, 3*w^3 - 17*w - 9]', '[3794, 3794, 6*w^2 - 5*w - 22]', '[3794, 3794, -4*w^2 - w + 19]', '[3794, 3794, -2*w^3 + 2*w^2 + 11*w - 7]', '[3794, 3794, -w^3 - 3*w^2 + 3*w + 14]', '[3794, 3794, -w^3 + 6*w^2 - 6*w - 13]', '[3794, 3794, 2*w^3 - 4*w^2 - 9*w + 4]', '[3794, 3794, 4*w^3 - 8*w^2 - 13*w + 28]', '[3794, 3794, -7*w^3 + 14*w^2 + 26*w - 49]', '[3807, 141, 3*w^3 - 3*w^2 - 12*w + 3]', '[3807, 141, 3*w^3 - 6*w^2 - 9*w + 9]', '[3812, 1906, 3*w^3 - 5*w^2 - 11*w + 11]', '[3812, 1906, -3*w^3 - 2*w^2 + 14*w + 18]', '[3812, 1906, -4*w^3 + 5*w^2 + 15*w - 18]', '[3812, 1906, -3*w^3 + 4*w^2 + 12*w - 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w^2 - 35*w - 25]', '[5329, 5329, -3*w^3 + 12*w^2 + 7*w - 39]', '[5329, 5329, 3*w^3 + 3*w^2 - 22*w - 23]', '[5329, 5329, -6*w^3 + 17*w^2 + 19*w - 55]', '[5342, 5342, -3*w^3 + 12*w^2 + 6*w - 37]', '[5342, 5342, -2*w^3 - 8*w^2 + 27*w + 41]', '[5342, 5342, 2*w^3 - 14*w^2 - 5*w + 58]', '[5342, 5342, -3*w^3 - 3*w^2 + 21*w + 22]', '[5344, 668, -2*w^3 + 6*w^2 + 6*w - 12]', '[5344, 668, 3*w^3 - 14*w^2 + w + 36]', '[5344, 668, -w^3 - 5*w^2 + 6*w + 26]', '[5344, 668, -4*w^3 + 4*w^2 + 14*w - 12]', '[5344, 668, -4*w^3 + 8*w^2 + 10*w - 2]', '[5344, 668, -w^3 + 8*w^2 - 7*w - 26]', '[5344, 668, -3*w^3 - 5*w^2 + 18*w + 26]', '[5344, 668, 2*w^3 - 12*w - 2]', '[5344, 1336, -3*w^2 + 2]', '[5344, 1336, 7*w^3 + 8*w^2 - 30*w - 40]', '[5344, 1336, 7*w^3 - 29*w^2 + 7*w + 55]', '[5344, 1336, -3*w^2 + 6*w - 1]', '[5348, 2674, -5*w^2 + 11*w + 8]', '[5348, 2674, 3*w^3 - 10*w^2 - 6*w + 34]', '[5348, 2674, 4*w^3 + 5*w^2 - 26*w - 39]', '[5348, 2674, -w^3 + 7*w^2 + 3*w - 23]', '[5348, 2674, -4*w^3 + w^2 + 27*w + 18]', '[5348, 2674, -3*w^3 - 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27]', '[353, 353, -3*w^3 + 2*w^2 + 13*w - 3]', '[359, 359, 4*w^3 + w^2 - 25*w - 23]', '[359, 359, 4*w^3 - 13*w^2 - 11*w + 43]', '[367, 367, 6*w^3 - 18*w^2 - 22*w + 71]', '[367, 367, -2*w^3 + 5*w^2 + 3*w - 3]', '[383, 383, w^3 - 9*w - 11]', '[383, 383, 3*w^3 - 17*w - 13]', '[401, 401, 5*w^3 + w^2 - 30*w - 29]', '[401, 401, -5*w^3 - 2*w^2 + 35*w + 39]', '[401, 401, -5*w^3 + 17*w^2 + 16*w - 67]', '[401, 401, -5*w^3 + 16*w^2 + 13*w - 53]', '[409, 409, w^3 + w^2 - 6*w - 11]', '[409, 409, -w^3 + 4*w^2 + w - 15]', '[431, 431, w^3 - 6*w^2 + w + 17]', '[431, 431, w^3 + 3*w^2 - 8*w - 13]', '[433, 433, -8*w^3 + 25*w^2 + 25*w - 89]', '[433, 433, w^3 - 5*w^2 + 19]', '[433, 433, w^3 + 2*w^2 - 7*w - 15]', '[433, 433, 8*w^3 + w^2 - 51*w - 47]', '[439, 439, 4*w^2 - 2*w - 19]', '[439, 439, -4*w^2 + 6*w + 17]', '[449, 449, w^3 - 2*w^2 - 5*w + 1]', '[449, 449, -w^3 + w^2 + 6*w - 5]', '[463, 463, -4*w^3 - w^2 + 29*w + 31]', '[463, 463, 4*w^3 - 13*w^2 - 15*w + 55]', '[487, 487, -3*w^2 + 5*w + 13]', '[487, 487, -3*w^2 + w + 15]', '[521, 521, -2*w^3 + 4*w^2 + 6*w - 5]', '[521, 521, 2*w^3 - 2*w^2 - 8*w + 3]', '[529, 23, -w^2 + w - 1]', '[529, 23, w^2 - w - 9]', '[569, 569, 11*w^3 + 2*w^2 - 71*w - 67]', '[569, 569, w^3 + 4*w^2 - 9*w - 25]', '[577, 577, 5*w^3 + 2*w^2 - 33*w - 33]', '[577, 577, 5*w^3 - 17*w^2 - 14*w + 59]', '[593, 593, 2*w^3 - w^2 - 9*w - 3]', '[593, 593, -w^3 - w^2 + 10*w + 15]', '[593, 593, w^3 - 4*w^2 - 5*w + 23]', '[593, 593, -2*w^3 + 5*w^2 + 5*w - 11]', '[599, 599, -2*w^3 + 2*w^2 + 8*w + 5]', '[599, 599, -2*w^3 + 4*w^2 + 6*w - 13]', '[601, 601, 5*w^3 + w^2 - 32*w - 33]', '[601, 601, 4*w^2 - 8*w - 11]', '[607, 607, -2*w^3 + 3*w^2 + 9*w - 9]', '[607, 607, 2*w^3 - 3*w^2 - 9*w + 1]', '[617, 617, w^3 + w^2 - 6*w - 13]', '[617, 617, -w^3 + 4*w^2 + w - 17]', '[625, 5, -5]', '[631, 631, 3*w^3 - 5*w^2 - 12*w + 5]', '[631, 631, w^3 + 3*w^2 - 10*w - 17]', '[631, 631, -w^3 + 6*w^2 + w - 23]', '[631, 631, 8*w^3 + 3*w^2 - 55*w - 59]', '[641, 641, -2*w^3 + 14*w + 15]', '[641, 641, 2*w^3 - 6*w^2 - 8*w + 27]', '[743, 743, 4*w^3 - w^2 - 25*w - 19]', '[743, 743, 4*w^3 - 11*w^2 - 15*w + 41]', '[751, 751, 2*w^2 - 4*w - 11]', '[751, 751, 2*w^2 - 13]', '[761, 761, -2*w^3 + 2*w^2 + 8*w + 1]', '[761, 761, -2*w^3 + 4*w^2 + 6*w - 9]', '[809, 809, 5*w^3 + w^2 - 32*w - 29]', '[809, 809, 5*w^3 - 16*w^2 - 15*w + 55]', '[839, 839, -7*w^2 + 3*w + 31]', '[839, 839, -2*w^2 + 15]', '[839, 839, -2*w^2 + 4*w + 13]', '[839, 839, 7*w^2 - 11*w - 27]', '[841, 29, -5*w^3 - 2*w^2 + 31*w + 33]', '[841, 29, 3*w^3 - 17*w - 11]', '[857, 857, -5*w^2 + 7*w + 17]', '[857, 857, 3*w^3 - 4*w^2 - 13*w - 3]', '[881, 881, -w^3 + 4*w^2 + 3*w - 11]', '[881, 881, w^3 + w^2 - 8*w - 5]', '[887, 887, 6*w^3 - 20*w^2 - 16*w + 67]', '[887, 887, -2*w^3 + 5*w^2 + 9*w - 13]', '[887, 887, 2*w^3 - w^2 - 13*w - 1]', '[887, 887, 6*w^3 + 2*w^2 - 38*w - 37]', '[919, 919, 2*w^3 + 4*w^2 - 8*w - 15]', '[919, 919, -9*w^3 + 30*w^2 + 27*w - 109]', '[937, 937, -7*w^3 + 24*w^2 + 19*w - 87]', '[937, 937, -7*w^3 - 3*w^2 + 46*w + 51]', '[953, 953, -7*w^2 + 3*w + 29]', '[953, 953, -3*w^3 + 7*w^2 + 12*w - 25]', '[967, 967, w^3 + 4*w^2 - 7*w - 17]', '[967, 967, w^3 - 9*w^2 + 8*w + 25]', '[967, 967, w^3 + 6*w^2 - 7*w - 25]', '[967, 967, w^3 - 7*w^2 + 4*w + 19]', '[977, 977, -w^3 - 2*w^2 + 7*w + 19]', '[977, 977, -w^3 + 5*w^2 - 23]', '[983, 983, -w^3 + 2*w^2 + 7*w - 11]', '[983, 983, w^3 - w^2 - 8*w - 3]', '[991, 991, w^3 + 3*w^2 - 8*w - 15]', '[991, 991, -w^3 + 6*w^2 - w - 19]']}
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nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [14, 8, -7, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 16448, 'disc_rad': 514, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 1]]], [5, [[4, 1]]], [7, [[2, 1], [1, 2]]], [11, [[2, 2]]], [13, [[2, 2]]], [17, [[2, 2]]], [19, [[4, 1]]], [23, [[2, 2]]], [29, [[2, 2]]], [31, [[1, 4]]], [37, [[4, 1]]], [41, [[2, 1], [1, 2]]], [43, [[4, 1]]], [47, [[2, 1], [1, 2]]], [53, [[4, 1]]], [59, [[2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 45.34313619501854, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '4.4.16448.2', 'local_algs': ['2.2.3.1', '2.2.3.1', 'm257.1.1.0', 'm257.1.1.0', 'm257.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 257], 'rd': 11.3247408948, 'regulator': {'__RealLiteral__': 0, 'data': '15.0596746811', 'prec': 44}, 'res': {'gal': ['484,0,-1132,0,397,0,-42,0,1'], 'sib': ['8,0,-17,0,1', '484,0,-1132,0,397,0,-42,0,1']}, 'subfield_mults': [1], 'subfields': ['-2.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - a - 5 \\)', '\\( a^{3} - 2 a^{2} - 3 a + 1 \\)', '\\( 2 a^{3} + a^{2} - 11 a - 11 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}