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hmf_forms • Show schema
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{'deg': 4, 'dimension': 2, 'disc': 19429, 'field_bad_primes': [19429], 'field_label': '4.4.19429.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.19429.1-9.1-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [3], 'level_ideal': '[9, 9, -w^3 + 2*w^2 + 4*w - 2]', 'level_label': '9.1', 'level_norm': 9, 'parallel_weight': 2, 'short_label': '9.1-c', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[3, 3, -w^3 + 2*w^2 + 5*w - 3]', -1]], 'hecke_eigenvalues': [0, 'e', -4, '-e - 1', 'e - 1', '2*e - 1', 'e - 3', '-2*e + 2', '-2*e + 4', '-2*e + 2', -4, 'e + 6', -10, -6, '-e - 6', 'e - 6', 6, '-2*e', -10, '-2*e + 8', '-e - 12', '-6*e + 2', 8, '-2*e', '-3*e + 8', '-4*e + 2', '-3*e + 5', '-e', '4*e - 4', '2*e - 4', '4*e + 6', '-e - 10', '-e - 7', '3*e + 11', '-3*e - 6', '-3*e + 15', 20, '2*e - 10', -4, '-6*e + 6', '-e - 16', '-2*e + 18', -6, 'e + 8', '5*e + 5', 12, '6*e - 6', '2*e - 16', '2*e - 4', '5*e - 1', '3*e + 6', '-8*e + 6', '-3*e + 3', 'e + 21', '4*e - 6', 0, '3*e + 14', '-3*e - 16', '3*e - 18', '-3*e - 22', 8, '-8*e', '10*e', '-4*e - 10', '-4*e - 10', '4*e - 10', '2*e + 8', '5*e + 5', '-e - 13', -22, '2*e - 24', '-3*e + 5', '-9*e + 2', '3*e + 6', '-e - 4', '-2*e - 30', -12, '8*e - 12', '-4*e + 24', '4*e - 10', '8*e + 6', '-3*e + 3', '2*e - 12', '4*e + 12', '8*e - 12', '-2*e + 18', '6*e', '-8*e + 2', '3*e + 24', '-3*e + 9', '-7*e - 3', '-8*e + 6', '-5*e - 7', '-9*e', '5*e - 21', '2*e + 36', '-8*e + 6', '-9*e - 3', '4*e + 6', '8*e - 4', '10*e - 22', '-11*e + 11', '5*e - 4', '-5*e - 30', '11*e - 4', '8*e + 14', '-7*e + 11', '-3*e + 3', '-11*e + 12', 'e - 24', '9*e + 15', '8*e - 16', '6*e + 12', '-2*e - 42', '3*e + 21', '-7*e + 2', '-7*e + 5', '-e - 10', '3*e + 29', '3*e - 15', -6, '-4*e', '8*e - 28', '13*e - 3', '-e - 1', '-9*e + 17', '4*e + 26', '-7*e - 4', '6*e - 4', '10*e - 22', '5*e + 26', 14, '-8*e - 10', '8*e', '-6*e - 6', '-6*e + 18', '6*e + 18', 'e - 34', '5*e + 14', '13*e - 18', '8*e - 22', '7*e - 18', '4*e - 30', '15*e - 18', '3*e + 15', '-2*e - 18', '-e - 16', '-5*e + 17', '9*e + 23', 14, -18, '10*e + 8', '-2*e - 18', '-12*e - 6', '-3*e + 39', '3*e - 9', '-12*e + 14', '-12*e + 20', -42, '10*e - 12', '8*e + 6', '6*e + 32', '-3*e - 27', '5*e - 28', '-9*e - 15', 18, -36, '-5*e - 6', '5*e - 10', '-10*e - 24', -6, '4*e + 2', '-4*e - 34', '-9*e - 16', '-9*e + 11', -42, '8*e + 6', '-12*e + 26', '3*e - 40', '-7*e + 35', '8*e + 14', '-12*e + 8', 18, '8*e + 8', 'e - 40', '-5*e - 1', '11*e + 21', '-13*e - 3', '6*e', 18, '-15*e - 6', '5*e - 1', '4*e + 14', '-2*e', '-7*e + 14', '-e - 16', '5*e + 32', '7*e + 26', '-6*e', 60, '-4*e + 2', '7*e - 45', '-11*e - 3', 'e + 17', '-3*e + 35', '-9*e + 26', '3*e - 39', '4*e - 18', '-5*e + 21', '-3*e + 30', '9*e + 3', '-6*e - 28', '16*e - 10', '-7*e + 41', '9*e - 40', '-7*e - 25', '-5*e + 38', '7*e + 5', '6*e - 36', '-7*e - 24', 'e - 27', '-10*e + 14', '-7*e + 11', '-2*e + 8', '9*e - 19', '5*e - 46', '-6*e - 24', '-3*e - 58', '-11*e - 22', '-8*e + 6', '15*e + 8', '4*e - 46', '4*e - 12', '-7*e + 17', '9*e - 21', 44, '-4*e - 40', '18*e + 6', '10*e - 34', 66, '-3*e + 9', '6*e - 24', '5*e - 22', '2*e + 30', '-12*e + 18', '14*e - 30', '2*e + 50', '-2*e + 26', '-3*e - 43', '11*e - 3', '18*e - 28', '-6*e + 26', -16, '6*e + 18', '-3*e - 19', '-4*e - 30', 44, '-e - 25', '-5*e + 14', '8*e + 24', '6*e + 36', '8*e + 6', '13*e - 12', '7*e + 21', '9*e', '-7*e + 36', '-11*e + 36', '8*e - 28', '15*e + 3', '17*e + 5', '-2*e + 2', '-6*e + 14', '-e + 35', '18*e - 4', '20*e + 2', '18*e - 16', '-10*e + 2', '4*e - 46', '2*e - 24', '-2*e - 6', '6*e + 54', '20*e - 10', '-4*e - 12', '-6*e - 18', '-13*e - 4', '2*e + 12', '8*e - 36', '17*e - 19', '-15*e + 21', '7*e - 51', '6*e + 2', '-4*e + 6', '-12*e', '12*e', '16*e - 4', '-8*e + 56', '-12*e + 14', '9*e - 31'], 'hecke_polynomial': 'x^2 - x - 9', 'label': '4.4.19429.1-9.1-c'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 19429, 'ideals': ['[1, 1, 1]', '[3, 3, -w^3 + 2*w^2 + 5*w - 3]', '[5, 5, w]', '[7, 7, -w^3 + 2*w^2 + 4*w - 3]', '[9, 9, -w^3 + 2*w^2 + 4*w - 2]', '[13, 13, -w^2 + w + 4]', '[13, 13, -w^3 + 2*w^2 + 5*w - 2]', '[15, 15, w^2 - 2*w - 5]', '[16, 2, 2]', '[17, 17, -w + 2]', '[19, 19, -w^3 + 2*w^2 + 3*w - 2]', '[21, 21, w^2 - w - 6]', '[25, 25, -2*w^3 + 5*w^2 + 6*w - 5]', '[27, 3, w^3 - 3*w^2 - 4*w + 7]', '[27, 27, w^3 - w^2 - 5*w - 1]', '[31, 31, w^3 - 3*w^2 - 3*w + 7]', '[31, 31, -w^3 + w^2 + 6*w + 1]', '[35, 35, w^3 - 2*w^2 - 3*w]', '[39, 39, -w^3 + 2*w^2 + 3*w - 4]', '[39, 39, -w^2 + 2*w + 2]', '[41, 41, w^2 - w - 1]', '[43, 43, 2*w^3 - 5*w^2 - 6*w + 4]', '[45, 45, w^3 - 3*w^2 - 3*w + 5]', '[47, 47, -w^3 + 2*w^2 + 5*w - 1]', '[48, 6, -2*w^3 + 4*w^2 + 10*w - 6]', '[49, 49, -w^3 + 3*w^2 + 2*w - 6]', '[51, 51, w^2 - 4]', '[53, 53, -w - 3]', '[53, 53, -w^3 + 3*w^2 + 3*w - 6]', '[57, 57, w^3 - 3*w^2 - 4*w + 6]', '[59, 59, 2*w^2 - 3*w - 6]', '[59, 59, w^3 - w^2 - 7*w - 3]', '[63, 63, -2*w - 1]', '[65, 65, -2*w^3 + 5*w^2 + 8*w - 10]', '[65, 65, w^3 - 2*w^2 - 3*w + 5]', '[75, 75, w^3 - 2*w^2 - 5*w]', '[79, 79, 2*w^3 - 4*w^2 - 8*w + 3]', '[79, 79, w^2 - 2*w - 1]', '[80, 10, 2*w]', '[81, 3, 3]', '[81, 81, w^2 - 3*w - 4]', '[85, 85, -w^2 + 2*w]', '[91, 91, -w^3 + 2*w^2 + 6*w - 2]', '[91, 91, 2*w^2 - 3*w - 9]', '[93, 93, 2*w^2 - 2*w - 9]', '[93, 93, 2*w^3 - 6*w^2 - 7*w + 17]', '[95, 95, w^3 - 2*w^2 - 6*w]', '[101, 101, 2*w^3 - 4*w^2 - 9*w + 4]', '[103, 103, -w^3 + 3*w^2 + 4*w - 2]', '[103, 103, w^2 - 3*w - 2]', '[105, 105, w^3 - w^2 - 6*w]', '[107, 107, -w^3 + w^2 + 5*w - 1]', '[109, 109, -w^3 + 2*w^2 + 4*w - 6]', '[112, 14, -2*w^3 + 4*w^2 + 8*w - 6]', '[117, 117, -w^3 + w^2 + 7*w + 2]', '[117, 117, w^3 - 3*w^2 - 4*w + 9]', '[119, 119, -w^3 + 2*w^2 + 2*w - 4]', '[121, 11, -w^3 + 2*w^2 + 6*w - 3]', '[121, 11, w^2 - 3*w - 3]', '[123, 123, -w^3 + 3*w^2 + 5*w - 7]', '[125, 5, -w^3 + w^2 + 7*w + 1]', '[125, 125, 2*w^3 - 3*w^2 - 10*w]', '[127, 127, 2*w^3 - 5*w^2 - 5*w + 7]', '[127, 127, 2*w^3 - 5*w^2 - 7*w + 6]', '[129, 129, -w^3 + 3*w^2 + 2*w - 7]', '[133, 133, w^2 - w + 1]', '[135, 15, -2*w^3 + 3*w^2 + 8*w - 5]', '[135, 135, w^3 - 8*w - 5]', '[141, 141, 2*w^3 - 5*w^2 - 7*w + 13]', '[144, 18, -2*w^3 + 4*w^2 + 8*w - 4]', '[147, 147, -w^2 + 3*w + 7]', '[153, 153, -w^3 + 3*w^2 + w - 6]', '[155, 155, 2*w^2 - w - 5]', '[155, 155, -w^2 + 5]', '[159, 159, 2*w^3 - 4*w^2 - 11*w + 4]', '[159, 159, 4*w^3 - 8*w^2 - 18*w + 13]', '[167, 167, -2*w^3 + 5*w^2 + 7*w - 11]', '[169, 13, -w^2 - 1]', '[169, 13, -w^2 + w + 8]', '[169, 169, -2*w^3 + 4*w^2 + 7*w - 2]', '[169, 169, -2*w + 3]', '[171, 171, -w^3 + 3*w^2 + 2*w - 1]', '[175, 175, -w^3 + 4*w^2 + w - 5]', '[177, 177, w^3 - 6*w - 7]', '[177, 177, -w^3 + 4*w^2 + w - 16]', '[181, 181, -2*w^3 + 5*w^2 + 8*w - 7]', '[189, 21, -4*w^3 + 9*w^2 + 19*w - 16]', '[189, 189, -w^3 + 2*w^2 + 3*w - 7]', '[193, 193, -w^3 + 3*w^2 + 3*w - 1]', '[195, 195, w^3 - 3*w^2 - w]', '[195, 195, -w^3 + 2*w^2 + 2*w]', '[197, 197, 2*w^3 - 4*w^2 - 7*w + 8]', '[197, 197, 3*w^3 - 7*w^2 - 10*w + 9]', '[199, 199, w^3 - 2*w^2 - 3*w - 3]', '[205, 205, w^3 - w^2 - w]', '[208, 26, -2*w^2 + 2*w + 8]', '[208, 26, -2*w^3 + 4*w^2 + 10*w - 4]', '[211, 211, -w^3 + w^2 + 7*w - 2]', '[211, 211, w^3 - w^2 - 6*w + 1]', '[215, 215, -2*w^3 + 2*w^2 + 11*w + 5]', '[217, 217, -w - 4]', '[217, 217, 2*w^3 - 5*w^2 - 7*w + 12]', '[221, 221, w^3 - 3*w^2 - 2*w + 8]', '[221, 221, -3*w^3 + 6*w^2 + 13*w - 9]', '[225, 225, -w^3 + 3*w^2 + 2*w - 10]', '[227, 227, 2*w^3 - 3*w^2 - 9*w + 3]', '[229, 229, 3*w^3 - 6*w^2 - 13*w + 8]', '[235, 235, w^3 - 2*w^2 - 2*w + 5]', '[237, 237, -3*w^3 + 8*w^2 + 11*w - 19]', '[237, 237, -2*w^3 + 5*w^2 + 9*w - 12]', '[239, 239, 2*w^3 - 4*w^2 - 9*w + 3]', '[239, 239, 2*w^3 - 4*w^2 - 6*w + 1]', '[240, 30, 2*w^2 - 4*w - 10]', '[241, 241, 3*w^3 - 7*w^2 - 9*w + 6]', '[241, 241, -2*w^3 + 4*w^2 + 6*w - 3]', '[243, 9, -3*w^3 + 6*w^2 + 15*w - 9]', '[243, 243, w^2 - 2*w - 8]', '[245, 245, 2*w^3 - 5*w^2 - 7*w + 5]', '[247, 247, -w^3 + 2*w^2 + 5*w - 7]', '[247, 247, -w^2 - w + 4]', '[251, 251, -4*w^3 + 10*w^2 + 15*w - 16]', '[251, 251, -w^3 + 3*w^2 - 3]', '[255, 255, -w^3 + 4*w^2 + w - 10]', '[256, 4, 4]', '[265, 265, 2*w^3 - 4*w^2 - 7*w + 5]', '[265, 265, -w^2 - 3*w]', '[271, 271, -w^3 + 4*w^2 + 4*w - 11]', '[271, 271, -3*w^3 + 9*w^2 + 6*w - 13]', '[272, 34, -2*w + 4]', '[273, 273, -2*w^3 + 4*w^2 + 7*w - 3]', '[273, 273, 2*w^3 - 5*w^2 - 6*w + 9]', '[277, 277, -w^3 + 3*w^2 + 2*w - 9]', '[279, 279, w^3 - 4*w^2 - w + 13]', '[279, 279, w^3 - w^2 - 6*w - 6]', '[281, 281, -w^3 + 4*w^2 + w - 8]', '[285, 285, 2*w^2 - 3*w - 5]', '[287, 287, -2*w^3 + 4*w^2 + 6*w - 7]', '[289, 289, -w^3 + 3*w^2 - 4]', '[293, 293, 3*w^3 - 7*w^2 - 11*w + 13]', '[293, 293, w^2 - 6]', '[293, 293, -4*w^3 + 11*w^2 + 9*w - 14]', '[293, 293, 3*w^3 - 5*w^2 - 15*w + 6]', '[295, 295, -2*w - 5]', '[295, 295, 2*w^3 - 3*w^2 - 6*w]', '[301, 301, -2*w^3 + 2*w^2 + 13*w + 4]', '[303, 303, -5*w^3 + 12*w^2 + 20*w - 27]', '[304, 38, -2*w^3 + 4*w^2 + 6*w - 4]', '[309, 309, w^3 - 2*w^2 - 2*w + 6]', '[309, 309, -2*w^3 + 5*w^2 + 8*w - 14]', '[311, 311, -2*w^3 + 4*w^2 + 7*w - 4]', '[313, 313, -w^3 + 4*w^2 + 3*w - 13]', '[313, 313, -w^3 + w^2 + 6*w - 2]', '[315, 315, -w^3 + 2*w^2 + 7*w - 5]', '[317, 317, w^3 - 4*w^2 - w + 9]', '[321, 321, 3*w^3 - 8*w^2 - 13*w + 18]', '[323, 323, -w^3 + 4*w^2 + 2*w - 12]', '[325, 325, -2*w^2 + 4*w + 5]', '[325, 325, -w + 5]', '[327, 327, 6*w^3 - 13*w^2 - 28*w + 23]', '[329, 329, w^3 - 3*w^2 - 5*w + 8]', '[336, 42, 2*w^2 - 2*w - 12]', '[337, 337, 3*w^3 - 7*w^2 - 8*w + 7]', '[343, 7, -2*w^3 + 3*w^2 + 9*w + 1]', '[343, 343, w^3 - w^2 - 7*w + 3]', '[351, 39, w^3 - 3*w^2 - w + 13]', '[351, 39, -5*w^3 + 9*w^2 + 23*w - 14]', '[351, 351, w^3 - w^2 - 6*w + 3]', '[351, 351, 2*w^3 - 6*w^2 - 4*w + 11]', '[357, 357, -w^3 + 9*w + 7]', '[359, 359, -w^3 + 2*w^2 + 4*w - 7]', '[359, 359, 2*w^3 - 3*w^2 - 10*w + 4]', '[361, 361, w^3 - 6*w - 3]', '[363, 33, 5*w^3 - 11*w^2 - 21*w + 24]', '[363, 33, -w^3 + 3*w^2 + 3*w - 11]', '[367, 367, 2*w^3 - 4*w^2 - 5*w + 2]', '[367, 367, 2*w^3 - 3*w^2 - 11*w - 2]', '[367, 367, 2*w - 7]', '[367, 367, w^3 - 7*w - 4]', '[369, 369, -2*w^3 + 5*w^2 + 5*w - 8]', '[371, 371, 2*w^3 - 4*w^2 - 11*w + 8]', '[371, 371, 2*w^3 - 3*w^2 - 8*w + 4]', '[373, 373, -w^3 + 4*w^2 + w - 14]', '[373, 373, -2*w^3 + 4*w^2 + 10*w - 11]', '[375, 15, 3*w^3 - 8*w^2 - 11*w + 22]', '[375, 375, -3*w^3 + 7*w^2 + 12*w - 10]', '[379, 379, w^3 - 2*w^2 - 2*w - 1]', '[381, 381, -3*w^3 + 7*w^2 + 13*w - 11]', '[381, 381, -4*w^3 + 9*w^2 + 16*w - 18]', '[383, 383, w^3 - 8*w - 4]', '[387, 387, 4*w^3 - 8*w^2 - 19*w + 11]', '[395, 395, -2*w^3 + 6*w^2 + 5*w - 10]', '[395, 395, w^3 - 2*w^2 - w]', '[397, 397, 4*w^3 - 10*w^2 - 12*w + 7]', '[397, 397, -2*w^3 + 3*w^2 + 9*w - 2]', '[399, 399, 2*w^3 - 4*w^2 - 9*w + 2]', '[400, 50, -4*w^3 + 10*w^2 + 12*w - 10]', '[401, 401, -w^3 + 6*w + 8]', '[403, 403, w^3 - 5*w^2 - w + 18]', '[403, 403, -3*w^3 + 3*w^2 + 19*w + 9]', '[403, 403, w^3 + w^2 - 7*w - 11]', '[403, 403, 2*w^3 - w^2 - 16*w - 13]', '[405, 15, 3*w^2 - 3*w - 15]', '[405, 405, -w^2 + 4*w]', '[409, 409, 2*w^3 - 3*w^2 - 11*w + 4]', '[413, 413, -w^3 + 4*w^2 + 3*w - 11]', '[413, 413, -w^3 + 3*w^2 - 7]', '[419, 419, 3*w^3 - 6*w^2 - 15*w + 7]', '[419, 419, -w^2 + 4*w + 8]', '[423, 423, -w^2 + 7]', '[425, 425, 2*w^3 - 4*w^2 - 11*w + 5]', '[431, 431, 5*w^3 - 15*w^2 - 10*w + 18]', '[431, 431, 3*w^3 - 4*w^2 - 16*w - 2]', '[432, 6, 2*w^3 - 6*w^2 - 8*w + 14]', '[432, 54, 2*w^3 - 2*w^2 - 10*w - 2]', '[439, 439, w^3 - w^2 - 4*w - 4]', '[441, 441, -w^3 + 4*w^2 + 4*w - 7]', '[443, 443, -4*w^3 + 9*w^2 + 15*w - 16]', '[455, 455, 2*w^3 - 3*w^2 - 9*w]', '[455, 455, -3*w^3 + 6*w^2 + 13*w - 5]', '[459, 51, 4*w^3 - 9*w^2 - 16*w + 19]', '[459, 459, 2*w^3 - 4*w^2 - 10*w + 3]', '[461, 461, 2*w^3 - 2*w^2 - 13*w - 1]', '[465, 465, -3*w^3 + 22*w + 20]', '[465, 465, 4*w^3 - 3*w^2 - 25*w - 15]', '[467, 467, 2*w^3 - 6*w^2 - 2*w + 7]', '[467, 467, 3*w^3 - 3*w^2 - 19*w - 6]', '[475, 475, w^3 - 9*w - 5]', '[477, 477, 2*w^3 - 3*w^2 - 9*w + 1]', '[477, 477, w^3 - w^2 - 8*w + 2]', '[479, 479, w^2 - 8]', '[479, 479, -3*w^3 + 7*w^2 + 14*w - 11]', '[491, 491, 3*w^3 - 5*w^2 - 16*w + 2]', '[496, 62, 2*w^3 - 6*w^2 - 6*w + 14]', '[496, 62, -2*w^3 + 2*w^2 + 12*w + 2]', '[499, 499, -w^2 + w - 2]', '[501, 501, 9*w^3 - 19*w^2 - 41*w + 33]', '[505, 505, -2*w^3 + 5*w^2 + 6*w - 10]', '[507, 39, -w^3 + 2*w^2 + 7*w - 8]', '[507, 39, -2*w^3 + 3*w^2 + 11*w + 3]', '[507, 507, w^3 - 4*w^2 - 2*w + 11]', '[507, 507, 3*w^3 - 5*w^2 - 14*w + 1]', '[509, 509, -w^3 + 5*w^2 - w - 11]', '[509, 509, w^3 - 5*w - 1]', '[513, 57, -w^3 + 3*w^2 + 7*w - 4]', '[513, 513, -2*w^3 + 4*w^2 + 11*w - 7]', '[515, 515, w^3 - 3*w^2 - 2*w]', '[515, 515, 2*w^3 - 3*w^2 - 3*w + 5]', '[521, 521, -w^3 + 4*w^2 + 3*w - 7]', '[521, 521, -w^3 + 2*w^2 + 7*w - 4]', '[525, 525, w^2 + w - 5]', '[527, 527, 2*w^3 - 4*w^2 - 9*w + 1]', '[527, 527, -2*w^3 + 3*w^2 + 12*w - 3]', '[531, 531, -w^3 + 5*w^2 - 3*w - 13]', '[531, 531, 3*w^2 - 4*w - 14]', '[533, 533, -w^3 + 4*w^2 + 4*w - 8]', '[533, 533, w^3 - 3*w^2 - 6*w + 1]', '[535, 535, -2*w^2 - 2*w + 5]', '[541, 541, -2*w^3 + 4*w^2 + 11*w - 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9]', '[1623, 1623, 9*w^3 - 20*w^2 - 38*w + 43]', '[1625, 65, -4*w^3 + 4*w^2 + 23*w + 9]', '[1625, 65, 2*w^3 - 7*w^2 - 4*w + 23]', '[1625, 1625, -2*w^3 + 4*w^2 + 5*w]', '[1625, 1625, -w^2 + 5*w]', '[1627, 1627, 4*w^3 - 9*w^2 - 16*w + 11]', '[1629, 1629, w^3 - 2*w^2 - 8*w + 9]', '[1635, 1635, w^3 - 4*w^2 + 15]', '[1643, 1643, -w^3 + w^2 + 10*w - 6]', '[1643, 1643, 4*w^3 - 7*w^2 - 20*w + 4]', '[1643, 1643, -w^3 + 5*w^2 + w - 16]', '[1643, 1643, w^3 - 10*w - 7]', '[1645, 1645, 3*w^3 - 5*w^2 - 12*w]', '[1648, 206, -2*w^3 + 6*w^2 + 8*w - 4]', '[1648, 206, 2*w^2 - 6*w - 4]', '[1651, 1651, -w^3 + 2*w^2 + 8*w - 4]', '[1651, 1651, -2*w^3 + 4*w^2 + 9*w - 12]', '[1651, 1651, -w^3 + w^2 + 2*w + 3]', '[1651, 1651, w^3 - 7*w - 1]', '[1657, 1657, 2*w^3 - 8*w^2 - w + 12]', '[1657, 1657, -4*w^3 + 11*w^2 + 15*w - 17]', '[1659, 1659, -6*w^3 + 9*w^2 + 31*w + 2]', '[1659, 1659, -2*w^3 + 2*w^2 + 14*w + 1]', '[1667, 1667, -w^3 + 5*w^2 - 6]', '[1667, 1667, -3*w^3 + 6*w^2 + 10*w - 6]', '[1671, 1671, 2*w^3 - 6*w^2 - 5*w + 21]', '[1671, 1671, 4*w^3 - 7*w^2 - 20*w + 11]', '[1673, 1673, -w^3 - 3*w^2 + 11*w + 21]', '[1673, 1673, -2*w^3 + 5*w^2 + 10*w - 14]', '[1677, 1677, 3*w^3 - 5*w^2 - 17*w + 4]', '[1677, 1677, w^3 + w^2 - 7*w - 13]', '[1680, 210, 2*w^3 - 2*w^2 - 12*w]', '[1681, 1681, 8*w^3 - 21*w^2 - 21*w + 21]', '[1685, 1685, -2*w^3 + 4*w^2 + 11*w]', '[1687, 1687, -3*w^3 + 3*w^2 + 17*w + 3]', '[1687, 1687, -4*w^3 + 5*w^2 + 23*w + 1]', '[1689, 1689, -5*w^3 + 14*w^2 + 17*w - 38]', '[1689, 1689, -w^3 + 6*w^2 + w - 21]', '[1697, 1697, w^3 + w^2 - 9*w - 7]', '[1697, 1697, 3*w^3 - 6*w^2 - 13*w + 2]', '[1697, 1697, w^3 - 6*w + 1]', '[1697, 1697, -5*w^3 + 11*w^2 + 22*w - 17]', '[1701, 63, 3*w^3 - 3*w^2 - 12*w + 3]', '[1701, 1701, 4*w^3 - 7*w^2 - 18*w + 9]', '[1707, 1707, -w^3 + 4*w^2 + 4*w - 13]', '[1707, 1707, -2*w^3 + 5*w^2 + 5*w - 11]', '[1709, 1709, w^3 - w^2 - 8*w - 9]', '[1709, 1709, -w^3 + 3*w^2 - 13]', '[1712, 214, -2*w^3 + 2*w^2 + 10*w - 2]', '[1713, 1713, 5*w^3 - 9*w^2 - 25*w + 8]', '[1713, 1713, -8*w^3 + 17*w^2 + 33*w - 33]', '[1715, 35, w^3 - 5*w^2 - w + 10]', '[1715, 1715, 4*w - 5]', '[1717, 1717, 6*w^3 - 13*w^2 - 24*w + 18]', '[1723, 1723, 2*w^3 - 3*w^2 - 7*w - 3]', '[1729, 1729, w^3 - 5*w^2 - 4*w + 9]', '[1729, 1729, 2*w^2 - 6*w - 7]', '[1731, 1731, -2*w^3 + 5*w^2 + 9*w - 3]', '[1731, 1731, -w^3 + w^2 + 9*w - 3]', '[1733, 1733, -w^3 + 4*w^2 + 3*w - 19]', '[1737, 1737, 5*w^3 - 11*w^2 - 20*w + 26]', '[1741, 1741, -w^3 + 5*w^2 - 14]', '[1744, 218, -2*w^3 + 4*w^2 + 8*w - 12]', '[1747, 1747, -4*w^3 + 6*w^2 + 22*w + 1]', '[1747, 1747, 2*w^3 - 5*w^2 - 9*w + 2]', '[1751, 1751, -4*w^3 + 9*w^2 + 11*w - 9]', '[1751, 1751, -w^3 + 5*w^2 - 4*w - 4]', '[1753, 1753, -2*w^3 + 5*w^2 + 3*w - 1]', '[1755, 195, -11*w^3 + 24*w^2 + 47*w - 50]', '[1755, 195, 4*w^3 - 12*w^2 - 19*w + 25]', '[1755, 1755, -4*w^3 + 10*w^2 + 13*w - 10]', '[1755, 1755, 3*w^3 - 10*w^2 - 5*w + 15]', '[1757, 1757, -4*w^3 + 11*w^2 + 13*w - 16]', '[1757, 1757, 7*w^3 - 15*w^2 - 36*w + 33]', '[1759, 1759, -w^3 + 2*w^2 + 4*w - 9]', '[1763, 1763, 3*w^3 - 4*w^2 - 17*w - 7]', '[1767, 1767, -4*w^3 + 8*w^2 + 20*w - 9]', '[1767, 1767, w^3 - 2*w^2 - 9*w - 2]', '[1773, 1773, 2*w^3 - 6*w^2 - w + 8]', '[1773, 1773, -3*w^3 + 5*w^2 + 15*w - 11]', '[1779, 1779, -w^2 - w + 8]', '[1783, 1783, -3*w^3 + 8*w^2 + 5*w - 12]', '[1783, 1783, -2*w^3 + 6*w^2 + 3*w - 12]', '[1783, 1783, 2*w^3 - 7*w^2 - 4*w + 17]', '[1783, 1783, 2*w^3 - 6*w^2 - w + 7]', '[1785, 1785, 2*w^3 - 3*w^2 - 13*w + 5]', '[1787, 1787, -5*w^3 + 8*w^2 + 25*w - 3]', '[1791, 1791, 6*w^3 - 13*w^2 - 22*w + 11]', '[1792, 28, -4*w^3 + 8*w^2 + 16*w - 12]', '[1795, 1795, w^3 - 3*w^2 - 8*w + 5]', '[1795, 1795, -w^3 + 4*w^2 + 6*w - 10]', '[1803, 1803, 9*w^3 - 18*w^2 - 41*w + 32]', '[1805, 1805, -3*w^3 + 5*w^2 + 15*w - 10]', '[1815, 165, -4*w^3 + 5*w^2 + 22*w + 10]', '[1815, 165, 3*w^3 - 5*w^2 - 16*w]', '[1819, 1819, -2*w^3 + 4*w^2 + 12*w - 7]', '[1823, 1823, w^3 - 8*w - 1]', '[1823, 1823, -3*w^3 + 5*w^2 + 14*w + 6]', '[1829, 1829, -w^3 + 2*w^2 - 9]', '[1829, 1829, w^2 - 5*w - 4]', '[1829, 1829, w^3 - 2*w^2 - 8*w + 2]', '[1829, 1829, -3*w^3 + 8*w^2 + 7*w - 13]', '[1831, 1831, -3*w^3 + 8*w^2 + 14*w - 18]', '[1833, 1833, w^3 - 3*w^2 - 8*w + 4]', '[1833, 1833, w^3 - 5*w^2 + 13]', '[1835, 1835, -w^3 + 3*w^2 - 10]', '[1835, 1835, 2*w^2 - 7*w]', '[1835, 1835, w^3 - 3*w - 5]', '[1835, 1835, -w^3 + w^2 + 9*w + 10]', '[1839, 1839, -11*w^3 + 26*w^2 + 48*w - 54]', '[1839, 1839, 6*w^3 - 13*w^2 - 25*w + 29]', '[1845, 1845, 3*w^3 - 9*w^2 - 10*w + 10]', '[1847, 1847, w^3 - 3*w^2 - w + 14]', '[1847, 1847, -2*w^3 + 2*w^2 + 11*w + 11]', '[1849, 1849, 3*w^3 - 5*w^2 - 13*w + 2]', '[1851, 1851, -w^3 + 2*w^2 + 8*w - 3]', '[1851, 1851, -2*w - 7]', '[1853, 1853, -3*w^3 + 7*w^2 + 15*w - 17]', '[1855, 1855, 3*w^3 - 9*w^2 - 5*w + 15]', '[1855, 1855, -2*w^3 + 2*w^2 + 8*w + 5]', '[1861, 1861, 2*w^2 - w - 12]', '[1865, 1865, 2*w^3 - 4*w^2 - 13*w + 10]', '[1865, 1865, 3*w^3 - 6*w^2 - 15*w + 5]', '[1871, 1871, 4*w^3 - 8*w^2 - 19*w + 9]', '[1871, 1871, -w^3 + 5*w^2 - w - 7]', '[1872, 234, -2*w^3 + 2*w^2 + 14*w + 4]', '[1872, 234, 2*w^3 - 6*w^2 - 8*w + 18]', '[1873, 1873, -3*w^3 + 5*w^2 + 13*w - 4]', '[1875, 15, 5*w^3 - 5*w^2 - 30*w - 15]', '[1875, 1875, 4*w^3 - 9*w^2 - 13*w + 15]', '[1877, 1877, -4*w^3 + 8*w^2 + 16*w - 7]', '[1877, 1877, 3*w^3 - 5*w^2 - 15*w - 2]', '[1879, 1879, -w^3 + 4*w^2 - w - 12]', '[1895, 1895, -w^3 + 5*w^2 - 5]', '[1897, 1897, 6*w^3 - 14*w^2 - 29*w + 23]', '[1897, 1897, w^3 - 6*w^2 + 27]', '[1899, 1899, 5*w^3 - 13*w^2 - 16*w + 24]', '[1899, 1899, -3*w^3 + 8*w^2 + 9*w - 17]', '[1904, 238, -2*w^3 + 4*w^2 + 4*w - 8]', '[1905, 1905, 2*w^3 - 5*w^2 - 6*w]', '[1905, 1905, -2*w^2 + 6*w + 5]', '[1907, 1907, w^3 - w^2 - 10*w - 6]', '[1911, 1911, w^2 - 2*w + 4]', '[1911, 1911, w^3 - w - 3]', '[1915, 1915, w^3 - w^2 - 3*w - 5]', '[1919, 1919, w^3 - 2*w^2 - w - 3]', '[1923, 1923, -14*w^3 + 31*w^2 + 60*w - 62]', '[1923, 1923, 13*w^3 - 29*w^2 - 55*w + 56]', '[1927, 1927, -6*w^3 + 13*w^2 + 24*w - 21]', '[1929, 1929, 9*w^3 - 19*w^2 - 39*w + 34]', '[1931, 1931, -w^3 + 5*w^2 - w - 19]', '[1931, 1931, -6*w^3 + 17*w^2 + 12*w - 22]', '[1935, 1935, -2*w^3 + w^2 + 13*w + 15]', '[1936, 22, -2*w^3 + 4*w^2 + 12*w - 6]', '[1936, 22, 2*w^2 - 6*w - 6]', '[1939, 1939, 4*w^3 - 7*w^2 - 19*w + 12]', '[1941, 1941, 5*w^3 - 9*w^2 - 23*w + 12]', '[1941, 1941, 7*w^3 - 14*w^2 - 32*w + 27]', '[1951, 1951, 4*w^3 - 10*w^2 - 14*w + 21]', '[1951, 1951, -2*w^3 + 4*w^2 + 13*w - 13]', '[1953, 1953, -w^3 - 3*w^2 + 7*w + 12]', '[1953, 1953, w^3 + w^2 - 6*w - 11]', '[1957, 1957, -4*w^3 + 7*w^2 + 8*w - 6]', '[1957, 1957, -4*w^3 + 12*w^2 + 9*w - 16]', '[1959, 1959, 9*w^3 - 19*w^2 - 42*w + 34]', '[1967, 1967, w^2 - 5*w - 1]', '[1968, 246, -2*w^3 + 6*w^2 + 10*w - 14]', '[1975, 1975, 8*w^3 - 21*w^2 - 18*w + 15]', '[1975, 1975, -9*w^3 + 25*w^2 + 21*w - 30]', '[1983, 1983, -15*w^3 + 29*w^2 + 71*w - 43]', '[1983, 1983, 7*w^3 - 15*w^2 - 34*w + 24]', '[1985, 1985, w^3 - 5*w^2 - 4*w + 10]', '[1985, 1985, -4*w^3 + 3*w^2 + 23*w + 15]', '[1989, 1989, w^3 - w^2 - 9*w - 3]', '[1989, 1989, -2*w^3 + 2*w^2 + 13*w - 1]', '[1993, 1993, 2*w^3 - 2*w^2 - 11*w + 1]', '[1993, 1993, -w^3 + 6*w + 14]', '[1995, 1995, -2*w^3 + 5*w^2 + 4*w - 10]', '[2000, 10, -2*w^3 + 2*w^2 + 14*w + 2]', '[2000, 250, 4*w^3 - 6*w^2 - 20*w]', '[2005, 2005, -w^3 - w^2 + 7*w + 5]', '[2009, 2009, -4*w^3 + 9*w^2 + 12*w - 9]', '[2015, 2015, 2*w^3 - 10*w - 5]', '[2015, 2015, -2*w^3 + 3*w^2 + 13*w]', '[2015, 2015, -4*w^3 + 6*w^2 + 19*w - 5]', '[2015, 2015, 7*w^3 - 14*w^2 - 33*w + 20]', '[2019, 2019, 5*w^3 - 9*w^2 - 26*w + 12]', '[2019, 2019, -3*w^3 + 5*w^2 + 11*w - 7]', '[2021, 2021, -5*w^3 + 8*w^2 + 24*w - 8]', '[2023, 2023, -3*w^3 + 9*w^2 + 9*w - 13]', '[2025, 75, 3*w^3 - 3*w^2 - 15*w]', '[2025, 2025, 4*w^3 - 6*w^2 - 21*w + 5]', '[2031, 2031, 5*w^3 - 9*w^2 - 22*w + 14]', '[2032, 254, 4*w^3 - 10*w^2 - 10*w + 14]', '[2032, 254, 4*w^3 - 10*w^2 - 14*w + 12]', '[2033, 2033, 2*w^3 - 3*w^2 - 4*w + 7]', '[2039, 2039, 3*w^3 - 6*w^2 - 14*w + 4]', '[2039, 2039, -4*w^3 + 11*w^2 + 12*w - 23]', '[2043, 2043, -2*w^3 + 5*w^2 + 7*w - 16]', '[2045, 2045, -w^3 + 3*w^2 + 6*w - 10]', '[2049, 2049, -8*w^3 + 21*w^2 + 31*w - 53]', '[2049, 2049, -3*w^3 + 4*w^2 + 18*w - 4]', '[2051, 2051, -7*w^3 + 14*w^2 + 33*w - 29]', '[2051, 2051, 2*w^3 - 6*w^2 - 7*w + 21]', '[2051, 2051, 4*w^3 - 9*w^2 - 18*w + 13]', '[2051, 2051, -8*w^3 + 18*w^2 + 33*w - 38]', '[2057, 187, -3*w^3 + 5*w^2 + 16*w - 11]', '[2057, 187, -w^3 + 5*w^2 - 3*w - 6]', '[2061, 2061, -3*w^3 + 7*w^2 + 14*w - 21]', '[2063, 2063, -5*w^3 + 13*w^2 + 10*w - 11]', '[2064, 258, -2*w^3 + 6*w^2 + 4*w - 14]', '[2065, 2065, 3*w^3 - 12*w^2 + 3*w + 25]', '[2065, 2065, -2*w^3 - w^2 + 16*w + 15]', '[2067, 2067, 2*w^3 - 2*w^2 - 4*w + 7]', '[2067, 2067, w^3 + w^2 - 8*w - 6]', '[2067, 2067, w^3 - 3*w^2 - 7*w + 9]', '[2067, 2067, 4*w^3 - 9*w^2 - 15*w + 8]', '[2071, 2071, 3*w^3 - 5*w^2 - 10*w + 7]', '[2073, 2073, -3*w^3 + 7*w^2 + 12*w - 19]', '[2081, 2081, w^2 - 5*w - 3]', '[2083, 2083, 5*w^3 - 10*w^2 - 19*w + 17]', '[2089, 2089, -3*w^3 + 5*w^2 + 12*w - 6]', '[2091, 2091, 2*w^2 + 5*w - 1]', '[2095, 2095, -3*w^3 + 6*w^2 + 10*w - 15]', '[2095, 2095, -w^3 + 4*w^2 + 8*w]', '[2103, 2103, -2*w^3 + 7*w^2 + 5*w - 19]', '[2107, 2107, 3*w^3 - 9*w^2 - 10*w + 23]', '[2111, 2111, -2*w^3 + 7*w^2 + 5*w - 11]', '[2111, 2111, 5*w^3 - 10*w^2 - 20*w + 17]', '[2115, 2115, -w^3 + 7*w]', '[2121, 2121, -7*w^3 + 11*w^2 + 36*w - 4]', '[2125, 85, -2*w^3 + 2*w^2 + 14*w - 3]', '[2125, 2125, -3*w^2 + 7*w + 15]', '[2127, 2127, -14*w^3 + 27*w^2 + 67*w - 41]', '[2127, 2127, 2*w^3 - 3*w^2 - 10*w - 7]', '[2127, 2127, w^3 - 4*w^2 + 3*w + 3]', '[2127, 2127, -6*w^3 + 14*w^2 + 25*w - 33]', '[2128, 266, 2*w^2 - 2*w + 2]', '[2133, 237, w^3 - 3*w^2 + 2*w - 2]', '[2133, 237, -4*w^3 + 9*w^2 + 19*w - 13]', '[2133, 2133, -w^3 - w^2 + 9*w + 17]', '[2133, 2133, w^3 - 3*w^2 + 11]', '[2137, 2137, w^2 + w - 9]', '[2141, 2141, -5*w^3 + 9*w^2 + 22*w - 3]', '[2141, 2141, -2*w^3 + 4*w^2 + 10*w - 13]', '[2143, 2143, -6*w^3 + 19*w^2 + 10*w - 24]', '[2151, 2151, -2*w^3 + 7*w^2 + 7*w - 21]', '[2151, 2151, w^2 + w - 11]', '[2155, 2155, -w^3 + 5*w^2 + w - 15]', '[2155, 2155, 3*w^2 - 8*w - 15]', '[2159, 2159, 7*w^3 - 19*w^2 - 19*w + 24]', '[2159, 2159, 7*w^3 - 17*w^2 - 22*w + 22]', '[2160, 30, -4*w^3 + 6*w^2 + 16*w - 10]', '[2160, 270, 2*w^3 - 16*w - 10]', '[2161, 2161, 3*w^3 - 7*w^2 - 10*w + 18]', '[2163, 2163, 3*w^3 - 4*w^2 - 14*w - 3]', '[2163, 2163, -3*w^3 + 2*w^2 + 21*w + 7]', '[2169, 2169, 9*w^3 - 18*w^2 - 41*w + 29]', '[2169, 2169, 6*w^3 - 11*w^2 - 27*w + 17]', '[2171, 2171, -w^3 + 5*w^2 + 2*w - 19]', '[2171, 2171, 7*w^3 - 14*w^2 - 34*w + 22]', '[2173, 2173, -w^3 + 6*w^2 - 22]', '[2173, 2173, 2*w^3 - 8*w^2 - w + 17]', '[2177, 2177, w^3 - w^2 - 6*w + 7]', '[2179, 2179, -3*w^3 + 11*w^2 + 3*w - 18]', '[2181, 2181, -5*w^3 + 13*w^2 + 13*w - 18]', '[2181, 2181, -5*w^3 + 12*w^2 + 18*w - 31]', '[2187, 9, -3*w^3 + 9*w^2 + 12*w - 21]', '[2187, 81, 3*w^3 - 3*w^2 - 15*w - 3]', '[2187, 2187, 4*w^3 - 6*w^2 - 20*w + 1]', '[2191, 2191, 7*w^3 - 15*w^2 - 33*w + 24]', '[2191, 2191, 5*w^3 - 11*w^2 - 19*w + 21]', '[2193, 2193, -4*w^3 + 11*w^2 + 12*w - 19]', '[2195, 2195, 3*w^2 - 3*w - 5]', '[2197, 13, -4*w^3 + 11*w^2 + 12*w - 17]', '[2197, 13, 4*w^3 - 10*w^2 - 13*w + 9]', '[2197, 169, -5*w^3 + 10*w^2 + 21*w - 16]', '[2197, 169, w^2 - 12]', '[2197, 2197, -w^3 + 5*w + 9]', '[2197, 2197, 2*w^3 - 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4]', '[2251, 2251, 8*w^3 - 21*w^2 - 21*w + 17]', '[2256, 282, 4*w^3 - 10*w^2 - 14*w + 26]', '[2259, 2259, -5*w^3 + 14*w^2 + 13*w - 19]', '[2259, 2259, 3*w^3 - 5*w^2 - 21*w + 17]', '[2261, 2261, 5*w^3 - 10*w^2 - 25*w + 16]', '[2267, 2267, -2*w^3 + 7*w^2 + 4*w - 16]', '[2269, 2269, 3*w^3 - 6*w^2 - 17*w + 13]', '[2271, 2271, -8*w^3 + 17*w^2 + 37*w - 28]', '[2271, 2271, 3*w^3 - 8*w^2 - 10*w + 24]', '[2275, 2275, -w^3 + 5*w^2 + 2*w - 10]', '[2275, 2275, 3*w^3 - 8*w^2 - 8*w + 15]', '[2279, 2279, -4*w^3 + 11*w^2 + 10*w - 18]', '[2279, 2279, 5*w^3 - 11*w^2 - 17*w + 16]', '[2283, 2283, w^3 - 3*w^2 + 2*w + 6]', '[2287, 2287, -2*w^3 + 6*w^2 + w - 12]', '[2289, 2289, 3*w^3 - 9*w^2 - 11*w + 26]', '[2293, 2293, -w^3 + 6*w^2 - 4*w - 12]', '[2295, 255, -5*w^3 + 12*w^2 + 23*w - 20]', '[2295, 2295, -2*w^3 + 4*w^2 + 5*w - 10]', '[2297, 2297, 2*w^3 - w^2 - 11*w - 3]', '[2299, 209, 2*w^3 - 7*w^2 - 7*w + 11]', '[2299, 209, -3*w^3 + 10*w^2 + 6*w - 14]', '[2301, 2301, -3*w^3 + 4*w^2 + 9*w - 1]', '[2301, 2301, 5*w^3 - 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28]', '[5087, 5087, 3*w^2 - 2*w - 17]', '[5089, 5089, -3*w^3 + 9*w^2 + 14*w - 21]', '[5089, 5089, -w^3 + 11*w + 1]', '[5091, 5091, -w^3 + 6*w^2 + w - 24]', '[5091, 5091, -3*w^3 + 9*w^2 + 8*w - 26]', '[5091, 5091, 18*w^3 - 40*w^2 - 77*w + 81]', '[5091, 5091, -5*w^3 + 13*w^2 + 23*w - 28]', '[5095, 5095, 4*w^3 - 5*w^2 - 9*w + 5]', '[5099, 5099, -5*w^3 + 6*w^2 + 27*w + 1]', '[5099, 5099, -5*w^3 + 13*w^2 + 14*w - 21]', '[5101, 5101, -2*w^3 + 2*w^2 + 9*w + 11]', '[5101, 5101, -6*w^3 + 17*w^2 + 13*w - 14]', '[5103, 63, -2*w^3 + 3*w^2 + 8*w - 11]', '[5103, 189, -6*w^3 + 18*w^2 + 27*w - 39]', '[5103, 5103, 2*w^2 - 7*w - 4]', '[5105, 5105, -2*w^3 + 2*w^2 + 16*w + 15]', '[5105, 5105, 4*w^3 - 8*w^2 - 18*w + 5]', '[5107, 5107, -2*w^3 + 8*w^2 - w - 9]', '[5113, 5113, -3*w^3 + 10*w^2 + 6*w - 21]', '[5113, 5113, -w^3 + 2*w^2 + 3*w - 11]', '[5117, 5117, -4*w^3 + 5*w^2 + 24*w - 2]', '[5119, 5119, -5*w^3 + 14*w^2 + 14*w - 28]', '[5121, 5121, -3*w^3 + 9*w^2 + 5*w - 17]', '[5121, 5121, 7*w^3 - 15*w^2 - 33*w + 23]', '[5123, 5123, -w^3 + 5*w^2 + 2*w - 26]', '[5125, 205, w^3 - w^2 - 2*w - 6]', '[5125, 5125, 2*w^3 - 6*w^2 - 3*w + 15]', '[5127, 5127, 4*w^3 - 6*w^2 - 25*w - 3]', '[5127, 5127, 8*w^3 - 16*w^2 - 41*w + 19]', '[5131, 5131, -2*w^3 + 2*w^2 + 12*w - 7]', '[5131, 5131, 8*w^3 - 17*w^2 - 32*w + 33]', '[5135, 5135, 4*w^3 - 7*w^2 - 15*w + 10]', '[5135, 5135, -7*w^3 + 16*w^2 + 29*w - 25]', '[5135, 5135, 3*w^3 - 4*w^2 - 17*w + 5]', '[5135, 5135, -6*w^3 + 11*w^2 + 32*w - 20]', '[5136, 642, 6*w^3 - 16*w^2 - 26*w + 36]', '[5139, 5139, -w^2 + 8*w - 7]', '[5139, 5139, w^3 + 2*w^2 - 13*w - 8]', '[5145, 105, 4*w^3 + w^2 - 32*w - 30]', '[5145, 5145, -5*w^3 + 9*w^2 + 22*w - 5]', '[5149, 5149, 6*w^3 - 9*w^2 - 35*w + 12]', '[5149, 5149, 2*w^3 - 7*w^2 - 13*w + 7]', '[5151, 5151, -5*w^3 + 8*w^2 + 24*w - 6]', '[5153, 5153, 4*w^3 - 8*w^2 - 13*w + 7]', '[5161, 5161, -3*w^3 + 4*w^2 + 21*w + 7]', '[5161, 5161, -4*w^3 + 8*w^2 + 13*w + 2]', '[5161, 5161, 2*w^3 - 8*w^2 - 7*w + 24]', '[5161, 5161, 3*w^3 - 6*w^2 - 13*w - 4]', '[5165, 5165, 3*w^3 - 8*w^2 - 15*w + 10]', '[5165, 5165, -3*w^3 + 10*w^2 + 7*w - 15]', '[5168, 646, -2*w^3 + 8*w^2 + 4*w - 24]', '[5169, 5169, 3*w^3 - 3*w^2 - 17*w - 1]', '[5171, 5171, -3*w^3 + 4*w^2 + 18*w - 6]', '[5171, 5171, -2*w^3 + 5*w^2 - 8]', '[5173, 5173, 5*w^3 - 10*w^2 - 23*w + 24]', '[5177, 5177, 6*w^3 - 15*w^2 - 18*w + 23]', '[5177, 5177, 3*w^3 - 2*w^2 - 19*w - 7]', '[5187, 5187, 3*w^3 - w^2 - 20*w - 12]', '[5187, 5187, -w^3 + 4*w^2 + w - 19]', '[5189, 5189, 2*w^2 - 7*w - 6]', '[5193, 5193, 3*w^3 - 7*w^2 - 9*w + 19]', '[5193, 5193, 9*w^3 - 20*w^2 - 39*w + 44]', '[5197, 5197, w^3 - 6*w^2 + 7*w + 8]', '[5197, 5197, w^3 - 6*w^2 + 7*w + 17]', '[5199, 5199, 16*w^3 - 31*w^2 - 77*w + 47]', '[5200, 650, -4*w^2 + 8*w + 10]', '[5200, 650, -2*w + 10]', '[5201, 5201, -2*w^3 + 7*w^2 + 7*w - 23]', '[5201, 5201, w^3 - 2*w^2 - 9*w + 11]', '[5201, 5201, -w^3 + w^2 + 4*w - 8]', '[5201, 5201, 5*w^3 - 9*w^2 - 23*w + 22]', '[5203, 473, 3*w^3 - 4*w^2 - 14*w + 13]', '[5203, 473, 8*w^3 - 24*w^2 - 13*w + 33]', '[5207, 5207, 4*w^3 - 8*w^2 - 20*w + 7]', '[5207, 5207, -2*w^3 + 5*w^2 + 4*w - 14]', '[5211, 579, -w^3 + 6*w^2 + 4*w - 13]', '[5211, 5211, 3*w^3 - 9*w^2 - 10*w + 19]', '[5213, 5213, 7*w^3 - 11*w^2 - 37*w + 3]', '[5213, 5213, -5*w^3 + 5*w^2 + 28*w + 9]', '[5223, 5223, 7*w^3 - 12*w^2 - 34*w + 12]', '[5227, 5227, w^3 + 2*w^2 - 7*w - 16]', '[5231, 5231, -5*w^3 + 11*w^2 + 18*w - 1]', '[5232, 654, 12*w^3 - 26*w^2 - 56*w + 46]', '[5237, 5237, 4*w^3 - 6*w^2 - 21*w + 7]', '[5237, 5237, -4*w^3 + 7*w^2 + 16*w - 9]', '[5239, 403, -3*w^3 + 2*w^2 + 10*w + 2]', '[5239, 403, 3*w^2 - 3*w + 2]', '[5239, 403, -w^3 + 7*w^2 + 2*w - 22]', '[5239, 403, 2*w^3 - w^2 - 11*w - 1]', '[5239, 5239, 3*w^3 - 7*w^2 - 13*w + 4]', '[5239, 5239, 4*w^3 - 6*w^2 - 21*w - 11]', '[5239, 5239, -3*w^3 + 5*w^2 + 18*w - 7]', '[5239, 5239, -5*w^2 + 10*w + 23]', '[5241, 5241, -2*w^3 + 5*w^2 + 4*w - 16]', '[5241, 5241, 6*w^3 - 12*w^2 - 25*w + 19]', '[5243, 5243, 4*w^3 - 7*w^2 - 17*w + 6]', '[5253, 5253, 3*w^3 - w^2 - 9*w - 2]', '[5253, 5253, -2*w^3 + w^2 + 13*w + 3]', '[5255, 5255, -4*w^3 + 11*w^2 + 16*w - 15]', '[5259, 5259, -5*w^3 + 9*w^2 + 25*w - 17]', '[5261, 5261, -4*w^3 + 13*w^2 + 3*w - 19]', '[5261, 5261, 5*w^3 - 10*w^2 - 20*w + 14]', '[5261, 5261, -2*w^3 + 8*w^2 + 7*w - 21]', '[5261, 5261, w - 9]', '[5263, 5263, w^3 + w^2 - 7*w - 2]', '[5264, 658, 2*w^3 - 6*w^2 - 10*w + 16]', '[5265, 195, -6*w^3 + 15*w^2 + 24*w - 30]', '[5265, 195, 3*w^3 - 6*w^2 - 9*w + 15]', '[5265, 5265, 5*w^3 - 12*w^2 - 18*w + 25]', '[5265, 5265, -4*w^3 + 7*w^2 + 17*w - 5]', '[5271, 5271, 11*w^3 - 25*w^2 - 44*w + 46]', '[5271, 5271, -w^3 - w^2 + 11*w + 3]', '[5275, 5275, -6*w^3 + 17*w^2 + 15*w - 25]', '[5275, 5275, 11*w^3 - 30*w^2 - 28*w + 40]', '[5277, 5277, 9*w^3 - 19*w^2 - 43*w + 32]', '[5281, 5281, 5*w^3 - 9*w^2 - 25*w + 6]', '[5281, 5281, -5*w^2 + 2*w + 17]', '[5281, 5281, 4*w^3 - 11*w^2 - 14*w + 22]', '[5281, 5281, -w^3 + 7*w^2 - 4*w - 22]', '[5287, 5287, -6*w^3 + 15*w^2 + 20*w - 18]', '[5289, 5289, 5*w^2 - 9*w - 29]', '[5297, 5297, 7*w^3 - 13*w^2 - 32*w + 12]', '[5299, 5299, -5*w^3 + 9*w^2 + 24*w - 18]', '[5299, 5299, 3*w^3 - 9*w^2 - 11*w + 19]', '[5301, 5301, 4*w^3 - 7*w^2 - 14*w + 2]', '[5301, 5301, -w^3 - w^2 + 10*w + 4]', '[5303, 5303, 5*w^3 - 11*w^2 - 14*w + 12]', '[5305, 5305, 2*w^3 - 5*w^2 - 13*w]', '[5309, 5309, -2*w^3 + 9*w^2 + w - 13]', '[5315, 5315, -2*w^2 + 7*w + 5]', '[5317, 5317, 4*w^3 - 12*w^2 - 11*w + 17]', '[5317, 5317, -6*w^3 + 15*w^2 + 22*w - 21]', '[5319, 591, -w^3 + 6*w^2 + w - 19]', '[5319, 591, -5*w^3 + 9*w^2 + 23*w - 2]', '[5319, 5319, w^3 - 2*w^2 - 4*w + 11]', '[5319, 5319, 4*w^3 - 4*w^2 - 16*w + 7]', '[5321, 5321, -5*w^3 + 12*w^2 + 20*w - 31]', '[5321, 5321, -2*w^3 + 3*w^2 + 15*w - 9]', '[5327, 5327, 3*w^2 - 8*w - 17]', '[5333, 5333, -w^3 + 5*w^2 + w - 1]', '[5333, 5333, 6*w^3 - 15*w^2 - 24*w + 23]', '[5337, 5337, -8*w^3 + 15*w^2 + 38*w - 24]', '[5339, 5339, -4*w^3 + 11*w^2 + 5*w - 14]', '[5341, 5341, 4*w^3 - 10*w^2 - 13*w + 21]', '[5345, 5345, 4*w^3 - 6*w^2 - 10*w + 5]', '[5345, 5345, 7*w^3 - 16*w^2 - 23*w + 25]', '[5349, 5349, 5*w^3 - 10*w^2 - 24*w + 11]', '[5349, 5349, 3*w^3 - 7*w^2 - 14*w + 6]', '[5349, 5349, -10*w^3 + 19*w^2 + 47*w - 26]', '[5349, 5349, 2*w^3 - 4*w^2 - 9*w + 14]', '[5353, 5353, 4*w^3 - 7*w^2 - 21*w + 2]', '[5353, 5353, -8*w^3 + 21*w^2 + 15*w - 23]', '[5355, 5355, -3*w^3 + 5*w^2 + 19*w]', '[5361, 5361, 10*w^3 - 27*w^2 - 37*w + 69]', '[5369, 5369, 3*w^3 - w^2 - 15*w - 13]', '[5369, 5369, -9*w^3 + 5*w^2 + 59*w + 42]', '[5369, 5369, 3*w^2 - 8*w - 24]', '[5369, 5369, -8*w^3 + 7*w^2 + 49*w + 34]', '[5373, 597, -4*w^3 + 12*w^2 + 13*w - 31]', '[5373, 5373, -5*w^3 + 6*w^2 + 27*w + 8]', '[5375, 215, -w^3 + w^2 + 7*w - 9]', '[5375, 5375, -4*w^3 + 11*w^2 + 14*w - 20]', '[5376, 84, 4*w^2 - 4*w - 24]', '[5381, 5381, -6*w^3 + 20*w^2 + 7*w - 28]', '[5381, 5381, -w^3 - w^2 + 9*w + 4]', '[5383, 5383, -3*w^3 + 5*w^2 + 18*w - 4]', '[5385, 5385, w^3 - 5*w^2 + 2*w + 20]', '[5385, 5385, -5*w^3 + 6*w^2 + 27*w + 5]', '[5387, 5387, -3*w^3 + 9*w^2 + 10*w - 18]', '[5389, 5389, 5*w^3 - 14*w^2 - 12*w + 23]', '[5392, 674, 6*w^3 - 14*w^2 - 16*w + 14]', '[5393, 5393, -3*w^3 + 4*w^2 + 12*w + 6]', '[5399, 5399, -5*w^3 + 7*w^2 + 27*w + 6]', '[5399, 5399, -2*w^3 + 7*w^2 + 3*w - 22]', '[5409, 5409, 6*w^3 - 13*w^2 - 26*w + 18]', '[5411, 5411, -10*w^3 + 24*w^2 + 39*w - 49]', '[5413, 5413, -3*w^3 + 7*w^2 + 13*w - 3]', '[5413, 5413, w^3 - 7*w^2 + 6*w + 23]', '[5415, 5415, -2*w^3 + 9*w^2 + 2*w - 30]', '[5417, 5417, 6*w^3 - 10*w^2 - 28*w + 1]', '[5417, 5417, 3*w^2 - 6*w - 4]', '[5425, 5425, 2*w^3 - 4*w^2 - 9*w - 5]', '[5425, 5425, 2*w^3 - 6*w^2 + 2*w + 15]', '[5431, 5431, 5*w^3 - 10*w^2 - 15*w + 6]', '[5437, 5437, -2*w^3 + 5*w^2 + 11*w - 16]', '[5443, 5443, 6*w^3 - 15*w^2 - 16*w + 8]', '[5443, 5443, 6*w^3 - 14*w^2 - 20*w + 9]', '[5445, 495, 5*w^3 - 11*w^2 - 16*w + 10]', '[5445, 495, -5*w^3 + 10*w^2 + 19*w - 15]', '[5447, 5447, -3*w^3 + 4*w^2 + 22*w + 9]', '[5447, 5447, 6*w^3 - 7*w^2 - 32*w - 2]', '[5447, 5447, -7*w^3 + 17*w^2 + 26*w - 44]', '[5447, 5447, -4*w^3 - w^2 + 25*w + 27]', '[5449, 5449, -3*w^3 + 10*w^2 + 6*w - 17]', '[5449, 5449, 4*w^3 - 10*w^2 - 15*w + 11]', '[5453, 5453, -w^3 + 8*w^2 + w - 6]', '[5457, 5457, 2*w^3 - 6*w^2 - 15*w + 4]', '[5459, 5459, -w^3 + 7*w^2 - 3*w - 17]', '[5459, 5459, -w^3 + 6*w^2 - w - 8]', '[5459, 5459, w^3 - 11*w - 6]', '[5459, 5459, -3*w^3 + 7*w^2 + 8*w - 14]', '[5461, 5461, -7*w^3 + 14*w^2 + 30*w - 23]', '[5461, 5461, -3*w^3 + 4*w^2 + 13*w + 9]', '[5469, 5469, -3*w^3 + 2*w^2 + 22*w + 12]', '[5469, 5469, -5*w^3 + 13*w^2 + 21*w - 32]', '[5471, 5471, -3*w^3 + 9*w^2 + 11*w - 18]', '[5477, 5477, -2*w^3 + 8*w^2 + w - 8]', '[5477, 5477, -4*w^3 + 11*w^2 + 11*w - 22]', '[5479, 5479, -4*w^3 + 11*w^2 + 16*w - 31]', '[5483, 5483, -3*w^3 + 10*w^2 + 2*w - 19]', '[5483, 5483, -3*w^3 + 3*w^2 + 15*w + 13]', '[5485, 5485, -6*w^3 + 13*w^2 + 15*w - 15]', '[5485, 5485, 4*w^3 - 7*w^2 - 14*w + 10]', '[5487, 5487, -6*w^3 + 13*w^2 + 24*w - 31]', '[5487, 5487, 6*w^3 - 13*w^2 - 27*w + 19]', '[5487, 5487, 5*w^3 - 11*w^2 - 27*w + 12]', '[5487, 5487, -2*w^3 + 5*w^2 + 6*w - 18]', '[5488, 14, -4*w^3 + 6*w^2 + 18*w + 2]', '[5488, 686, 2*w^3 - 2*w^2 - 14*w + 6]', '[5491, 5491, -3*w^3 + 5*w^2 + 17*w + 4]', '[5493, 5493, 18*w^3 - 37*w^2 - 80*w + 69]', '[5499, 5499, -4*w^2 + 8*w + 23]', '[5499, 5499, -6*w^3 + 10*w^2 + 29*w - 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7*w^2 - 10*w + 9]', '[199, 199, w^3 - 2*w^2 - 3*w - 3]', '[211, 211, -w^3 + w^2 + 7*w - 2]', '[211, 211, w^3 - w^2 - 6*w + 1]', '[227, 227, 2*w^3 - 3*w^2 - 9*w + 3]', '[229, 229, 3*w^3 - 6*w^2 - 13*w + 8]', '[239, 239, 2*w^3 - 4*w^2 - 9*w + 3]', '[239, 239, 2*w^3 - 4*w^2 - 6*w + 1]', '[241, 241, 3*w^3 - 7*w^2 - 9*w + 6]', '[241, 241, -2*w^3 + 4*w^2 + 6*w - 3]', '[251, 251, -4*w^3 + 10*w^2 + 15*w - 16]', '[251, 251, -w^3 + 3*w^2 - 3]', '[271, 271, -w^3 + 4*w^2 + 4*w - 11]', '[271, 271, -3*w^3 + 9*w^2 + 6*w - 13]', '[277, 277, -w^3 + 3*w^2 + 2*w - 9]', '[281, 281, -w^3 + 4*w^2 + w - 8]', '[293, 293, 3*w^3 - 7*w^2 - 11*w + 13]', '[293, 293, w^2 - 6]', '[293, 293, -4*w^3 + 11*w^2 + 9*w - 14]', '[293, 293, 3*w^3 - 5*w^2 - 15*w + 6]', '[311, 311, -2*w^3 + 4*w^2 + 7*w - 4]', '[313, 313, -w^3 + 4*w^2 + 3*w - 13]', '[313, 313, -w^3 + w^2 + 6*w - 2]', '[317, 317, w^3 - 4*w^2 - w + 9]', '[337, 337, 3*w^3 - 7*w^2 - 8*w + 7]', '[343, 7, -2*w^3 + 3*w^2 + 9*w + 1]', '[359, 359, -w^3 + 2*w^2 + 4*w - 7]', '[359, 359, 2*w^3 - 3*w^2 - 10*w + 4]', '[367, 367, 2*w^3 - 4*w^2 - 5*w + 2]', '[367, 367, 2*w^3 - 3*w^2 - 11*w - 2]', '[367, 367, 2*w - 7]', '[367, 367, w^3 - 7*w - 4]', '[373, 373, -w^3 + 4*w^2 + w - 14]', '[373, 373, -2*w^3 + 4*w^2 + 10*w - 11]', '[379, 379, w^3 - 2*w^2 - 2*w - 1]', '[383, 383, w^3 - 8*w - 4]', '[397, 397, 4*w^3 - 10*w^2 - 12*w + 7]', '[397, 397, -2*w^3 + 3*w^2 + 9*w - 2]', '[401, 401, -w^3 + 6*w + 8]', '[409, 409, 2*w^3 - 3*w^2 - 11*w + 4]', '[419, 419, 3*w^3 - 6*w^2 - 15*w + 7]', '[419, 419, -w^2 + 4*w + 8]', '[431, 431, 5*w^3 - 15*w^2 - 10*w + 18]', '[431, 431, 3*w^3 - 4*w^2 - 16*w - 2]', '[439, 439, w^3 - w^2 - 4*w - 4]', '[443, 443, -4*w^3 + 9*w^2 + 15*w - 16]', '[461, 461, 2*w^3 - 2*w^2 - 13*w - 1]', '[467, 467, 2*w^3 - 6*w^2 - 2*w + 7]', '[467, 467, 3*w^3 - 3*w^2 - 19*w - 6]', '[479, 479, w^2 - 8]', '[479, 479, -3*w^3 + 7*w^2 + 14*w - 11]', '[491, 491, 3*w^3 - 5*w^2 - 16*w + 2]', '[499, 499, -w^2 + w - 2]', '[509, 509, -w^3 + 5*w^2 - w - 11]', '[509, 509, w^3 - 5*w - 1]', '[521, 521, -w^3 + 4*w^2 + 3*w - 7]', '[521, 521, -w^3 + 2*w^2 + 7*w - 4]', '[541, 541, -2*w^3 + 4*w^2 + 11*w - 6]', '[557, 557, -w^3 + w^2 + 8*w + 3]', '[557, 557, w^3 - 2*w^2 - 2*w - 2]', '[563, 563, 2*w^3 - 2*w^2 - 10*w - 3]', '[563, 563, 3*w^3 - 5*w^2 - 15*w + 1]', '[569, 569, 2*w^2 - 3*w - 4]', '[569, 569, 3*w^3 - 8*w^2 - 9*w + 7]', '[571, 571, -w^3 + 4*w^2 - 11]', '[571, 571, 3*w^3 - 8*w^2 - 11*w + 11]', '[577, 577, 3*w^3 - 8*w^2 - 5*w + 11]', '[577, 577, -4*w^3 + 11*w^2 + 9*w - 9]', '[593, 593, 2*w^3 - 7*w^2 - 2*w + 9]', '[601, 601, -w^3 + 3*w^2 + 5*w - 9]', '[613, 613, 3*w^3 - 5*w^2 - 14*w + 8]', '[613, 613, -w^3 + 2*w^2 + 7*w - 3]', '[617, 617, -2*w^3 + 6*w^2 + 5*w - 4]', '[617, 617, -w^3 + 3*w^2 - w - 6]', '[641, 641, 4*w^3 - 9*w^2 - 17*w + 14]', '[641, 641, -5*w^3 + 12*w^2 + 18*w - 17]', '[643, 643, -3*w^3 + 8*w^2 + 10*w - 13]', '[647, 647, 3*w - 4]', '[647, 647, -w^3 + 4*w^2 + 2*w - 9]', '[653, 653, -w^3 + 2*w^2 + 5*w - 8]', '[661, 661, 2*w^3 - 7*w^2 - 5*w + 21]', '[661, 661, -w^3 + 2*w^2 + 3*w - 8]', '[673, 673, 2*w^3 - 7*w^2 - 5*w + 9]', '[673, 673, w^3 - 2*w^2 - 3*w - 4]', '[677, 677, -w^3 + 4*w^2 + 3*w - 8]', '[683, 683, -3*w^3 + 4*w^2 + 17*w - 1]', '[683, 683, -3*w^3 + 7*w^2 + 8*w - 2]', '[691, 691, w^2 - 4*w - 2]', '[701, 701, 3*w^3 - 6*w^2 - 11*w + 3]', '[709, 709, -w^3 + 4*w^2 + 3*w - 17]', '[709, 709, w^3 + w^2 - 10*w - 8]', '[709, 709, -3*w^3 + 10*w^2 + 2*w - 16]', '[709, 709, w^3 - w^2 - 8*w + 1]', '[727, 727, -w^3 + 5*w^2 - w - 13]', '[727, 727, 2*w^3 - 4*w^2 - 11*w + 2]', '[733, 733, -2*w^3 + 3*w^2 + 10*w - 6]', '[733, 733, 2*w^3 - 5*w^2 - 5*w + 9]', '[739, 739, -3*w^3 + 6*w^2 + 12*w - 8]', '[743, 743, 3*w^3 - 4*w^2 - 17*w - 4]', '[743, 743, 2*w^3 - 3*w^2 - 8*w + 1]', '[743, 743, -3*w^3 + 7*w^2 + 11*w - 7]', '[743, 743, -3*w^3 + 6*w^2 + 11*w - 9]', '[757, 757, 2*w^3 - 5*w^2 - 6*w + 11]', '[757, 757, -w^3 + w^2 + 8*w + 2]', '[761, 761, -5*w^3 + 14*w^2 + 13*w - 12]', '[769, 769, -3*w^2 + 4*w + 13]', '[773, 773, 3*w^3 - 4*w^2 - 18*w + 3]', '[797, 797, 4*w^3 - 7*w^2 - 21*w + 8]', '[797, 797, -3*w^3 + 7*w^2 + 11*w - 16]', '[809, 809, -2*w^2 + 5*w + 11]', '[827, 827, w - 6]', '[829, 829, -w^3 - w^2 + 11*w + 8]', '[841, 29, -3*w^3 + 6*w^2 + 14*w - 6]', '[841, 29, -2*w^3 + 5*w^2 + 8*w - 4]', '[853, 853, 3*w^3 - 6*w^2 - 9*w + 8]', '[857, 857, 2*w^2 - 3*w - 3]', '[859, 859, -w^3 + w^2 + 4*w + 7]', '[863, 863, 2*w^3 - 3*w^2 - 7*w - 2]', '[863, 863, -3*w^3 + 6*w^2 + 10*w - 11]', '[881, 881, -3*w^2 + 4*w + 12]', '[881, 881, w^2 - 2*w + 3]', '[883, 883, 4*w^3 - 13*w^2 - 6*w + 17]', '[883, 883, -2*w^3 + 4*w^2 + 12*w - 3]', '[887, 887, -3*w^3 + 5*w^2 + 16*w - 8]', '[887, 887, 3*w^3 - 5*w^2 - 14*w + 3]', '[911, 911, -w^3 + 10*w + 1]', '[919, 919, 5*w^3 - 13*w^2 - 14*w + 11]', '[929, 929, 2*w^3 - 3*w^2 - 12*w - 4]', '[937, 937, -3*w - 7]', '[941, 941, -w^3 + 3*w^2 + 3*w - 12]', '[947, 947, 2*w^3 - 6*w^2 - 9*w + 8]', '[947, 947, -4*w^3 + 7*w^2 + 19*w - 6]', '[953, 953, 3*w^2 - w - 9]', '[961, 31, 4*w^3 - 12*w^2 - 5*w + 17]', '[971, 971, 3*w^3 - 6*w^2 - 16*w + 12]', '[983, 983, w^3 + w^2 - 7*w - 12]', '[991, 991, -2*w^3 + 7*w^2 + 3*w - 12]', '[991, 991, -2*w^3 + 4*w^2 + 12*w - 9]', '[997, 997, 3*w^3 - 5*w^2 - 14*w + 9]', '[997, 997, -2*w^3 + 3*w^2 + 11*w - 7]', '[1013, 1013, -2*w^3 + 6*w^2 + 3*w - 11]', '[1019, 1019, -w^3 + 5*w^2 + 2*w - 8]', '[1021, 1021, -w^3 + 5*w^2 - w - 17]', '[1021, 1021, 3*w^3 - 6*w^2 - 8*w + 3]', '[1033, 1033, -2*w^3 + 5*w^2 + 6*w - 13]', '[1033, 1033, 3*w^3 - 6*w^2 - 11*w + 4]', '[1051, 1051, 3*w^3 - 7*w^2 - 10*w + 13]', '[1061, 1061, 2*w^2 - 5*w - 13]', '[1063, 1063, -w^3 + w^2 + 5*w + 8]', '[1069, 1069, -5*w^3 + 12*w^2 + 19*w - 18]', '[1069, 1069, w^3 - 5*w^2 - w + 9]', '[1097, 1097, -3*w^3 + 9*w^2 + 8*w - 12]', '[1097, 1097, -2*w^3 + 6*w^2 + 7*w - 12]', '[1103, 1103, -3*w^3 + 4*w^2 + 15*w - 3]', '[1103, 1103, -w^3 + 3*w^2 + 5*w - 11]', '[1109, 1109, 5*w^3 - 11*w^2 - 16*w + 6]', '[1129, 1129, -w^2 + 3*w - 4]', '[1129, 1129, 2*w^3 - 2*w^2 - 10*w - 9]', '[1151, 1151, 4*w^3 - 10*w^2 - 14*w + 13]', '[1153, 1153, -2*w^3 + 5*w^2 + 11*w - 12]', '[1153, 1153, -2*w^3 + 8*w^2 - 13]', '[1153, 1153, -w^3 + 3*w^2 + 5*w - 12]', '[1153, 1153, 2*w^3 - w^2 - 11*w - 4]', '[1163, 1163, -w^3 + w^2 + 9*w - 4]', '[1163, 1163, 2*w^3 - 4*w^2 - 10*w - 1]', '[1171, 1171, 3*w^3 - 4*w^2 - 18*w - 1]', '[1193, 1193, w^3 - 4*w^2 + 2*w + 6]', '[1193, 1193, w^3 - 2*w^2 - 5*w - 4]', '[1201, 1201, 2*w^3 - 4*w^2 - 9*w - 3]', '[1201, 1201, 4*w^3 - 10*w^2 - 13*w + 11]', '[1213, 1213, -4*w^3 + 7*w^2 + 19*w - 11]', '[1217, 1217, -2*w^3 + 8*w^2 + 2*w - 13]', '[1229, 1229, -4*w^3 + 13*w^2 + 6*w - 19]', '[1229, 1229, -4*w^3 + 8*w^2 + 16*w - 13]', '[1229, 1229, -3*w^3 + 9*w^2 + 6*w - 16]', '[1229, 1229, 2*w^3 - 3*w^2 - 6*w - 1]', '[1231, 1231, -3*w^3 + 6*w^2 + 16*w - 8]', '[1231, 1231, -3*w^2 + w + 12]', '[1237, 1237, -2*w^3 + 5*w^2 + 4*w - 9]', '[1237, 1237, -w^2 - 3]', '[1237, 1237, -w^3 + 6*w - 3]', '[1237, 1237, -4*w - 1]', '[1249, 1249, -2*w^3 + 4*w^2 + 5*w - 8]', '[1283, 1283, 3*w - 8]', '[1289, 1289, 2*w^3 - w^2 - 14*w - 6]', '[1289, 1289, 4*w^3 - 9*w^2 - 13*w + 8]', '[1291, 1291, w^3 - w^2 - 3*w - 4]', '[1297, 1297, 4*w^3 - 9*w^2 - 15*w + 9]', '[1303, 1303, -w^3 + 4*w^2 - 13]', '[1321, 1321, 3*w^3 - 6*w^2 - 13*w + 3]', '[1321, 1321, -3*w^3 + 6*w^2 + 11*w - 7]', '[1367, 1367, -2*w^3 + 6*w^2 + 4*w - 13]', '[1369, 37, 2*w^2 - w - 11]', '[1369, 37, w^3 - 2*w^2 - w - 2]', '[1373, 1373, -w^3 + 3*w^2 + 8*w - 6]', '[1381, 1381, -w^3 + 3*w^2 - 9]', '[1381, 1381, 3*w^3 - 8*w^2 - 8*w + 14]', '[1427, 1427, 3*w^3 - 7*w^2 - 9*w + 12]', '[1429, 1429, 4*w^3 - 9*w^2 - 11*w + 8]', '[1433, 1433, -w^3 + 8*w + 12]', '[1447, 1447, -4*w^3 + 10*w^2 + 15*w - 14]', '[1447, 1447, 6*w^3 - 14*w^2 - 21*w + 19]', '[1451, 1451, w^3 - w^2 - 9*w - 4]', '[1459, 1459, 3*w^3 - 7*w^2 - 13*w + 9]', '[1481, 1481, -3*w^2 + 3*w + 19]', '[1481, 1481, -w^3 + 5*w^2 - 3*w - 14]', '[1487, 1487, -2*w^3 + 6*w^2 + w - 6]', '[1489, 1489, -3*w^3 + 3*w^2 + 19*w + 3]', '[1499, 1499, 3*w^2 - 4*w - 7]', '[1511, 1511, 4*w^3 - 6*w^2 - 20*w + 3]', '[1523, 1523, 8*w^3 - 23*w^2 - 17*w + 27]', '[1531, 1531, -w^3 + 2*w^2 + 3*w - 9]', '[1531, 1531, 3*w^3 - 9*w^2 - 8*w + 19]', '[1549, 1549, -5*w^3 + 11*w^2 + 17*w - 18]', '[1553, 1553, 2*w^2 - 9]', '[1567, 1567, 2*w^3 - 7*w^2 - 4*w + 22]', '[1579, 1579, -2*w^3 + 4*w^2 + 8*w + 3]', '[1579, 1579, -3*w^3 + 5*w^2 + 13*w - 1]', '[1607, 1607, w^3 - w^2 - 6*w - 8]', '[1609, 1609, -4*w^3 + 7*w^2 + 19*w - 2]', '[1619, 1619, -5*w^3 + 11*w^2 + 13*w - 9]', '[1627, 1627, 4*w^3 - 9*w^2 - 16*w + 11]', '[1657, 1657, 2*w^3 - 8*w^2 - w + 12]', '[1657, 1657, -4*w^3 + 11*w^2 + 15*w - 17]', '[1667, 1667, -w^3 + 5*w^2 - 6]', '[1667, 1667, -3*w^3 + 6*w^2 + 10*w - 6]', '[1697, 1697, w^3 + w^2 - 9*w - 7]', '[1697, 1697, 3*w^3 - 6*w^2 - 13*w + 2]', '[1697, 1697, w^3 - 6*w + 1]', '[1697, 1697, -5*w^3 + 11*w^2 + 22*w - 17]', '[1709, 1709, w^3 - w^2 - 8*w - 9]', '[1709, 1709, -w^3 + 3*w^2 - 13]', '[1723, 1723, 2*w^3 - 3*w^2 - 7*w - 3]', '[1733, 1733, -w^3 + 4*w^2 + 3*w - 19]', '[1741, 1741, -w^3 + 5*w^2 - 14]', '[1747, 1747, -4*w^3 + 6*w^2 + 22*w + 1]', '[1747, 1747, 2*w^3 - 5*w^2 - 9*w + 2]', '[1753, 1753, -2*w^3 + 5*w^2 + 3*w - 1]', '[1759, 1759, -w^3 + 2*w^2 + 4*w - 9]', '[1783, 1783, -3*w^3 + 8*w^2 + 5*w - 12]', '[1783, 1783, -2*w^3 + 6*w^2 + 3*w - 12]', '[1783, 1783, 2*w^3 - 7*w^2 - 4*w + 17]', '[1783, 1783, 2*w^3 - 6*w^2 - w + 7]', '[1787, 1787, -5*w^3 + 8*w^2 + 25*w - 3]', '[1823, 1823, w^3 - 8*w - 1]', '[1823, 1823, -3*w^3 + 5*w^2 + 14*w + 6]', '[1831, 1831, -3*w^3 + 8*w^2 + 14*w - 18]', '[1847, 1847, w^3 - 3*w^2 - w + 14]', '[1847, 1847, -2*w^3 + 2*w^2 + 11*w + 11]', '[1861, 1861, 2*w^2 - w - 12]', '[1871, 1871, 4*w^3 - 8*w^2 - 19*w + 9]', '[1871, 1871, -w^3 + 5*w^2 - w - 7]', '[1873, 1873, -3*w^3 + 5*w^2 + 13*w - 4]', '[1877, 1877, -4*w^3 + 8*w^2 + 16*w - 7]', '[1877, 1877, 3*w^3 - 5*w^2 - 15*w - 2]', '[1879, 1879, -w^3 + 4*w^2 - w - 12]', '[1907, 1907, w^3 - w^2 - 10*w - 6]', '[1931, 1931, -w^3 + 5*w^2 - w - 19]', '[1931, 1931, -6*w^3 + 17*w^2 + 12*w - 22]', '[1951, 1951, 4*w^3 - 10*w^2 - 14*w + 21]', '[1951, 1951, -2*w^3 + 4*w^2 + 13*w - 13]', '[1993, 1993, 2*w^3 - 2*w^2 - 11*w + 1]', '[1993, 1993, -w^3 + 6*w + 14]']}
-
nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [5, -1, -7, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 19429, 'disc_rad': 19429, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[3, 1], [1, 1]]], [5, [[3, 1], [1, 1]]], [7, [[3, 1], [1, 1]]], [11, [[2, 2]]], [13, [[2, 1], [1, 2]]], [17, [[3, 1], [1, 1]]], [19, [[3, 1], [1, 1]]], [23, [[4, 1]]], [29, [[2, 2]]], [31, [[2, 1], [1, 2]]], [37, [[2, 2]]], [41, [[3, 1], [1, 1]]], [43, [[3, 1], [1, 1]]], [47, [[3, 1], [1, 1]]], [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': [12], 'galois_label': '4T5', 'galt': 5, 'grd': 139.38794782907166, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.19429.1', 'local_algs': ['m19429.1.1.0', 'm19429.1.1.0', 'm19429.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [19429], 'rd': 11.8062673114, 'regulator': {'__RealLiteral__': 0, 'data': '8.44055652657', 'prec': 44}, 'res': {'gal': ['204304,0,-4851864,0,34846165,0,-105447032,0,146475922,0,-105480880,0,42433935,0,-9976510,0,1393578,0,-114002,0,5189,0,-118,0,1'], 'sib': ['-1369,105961,153456,-454863,72081,173723,-37098,-17134,3412,570,-103,-6,1', '-9526,28339,8025,-322,-180,-1,1', '1,-8,-6,27,-11,-3,1', '208,304,-2124,-132,4037,-617,-2281,299,496,-25,-41,0,1', '818805,-577343,-309175,13869,13952,57,-211,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 1 \\)', '\\( a^{2} - 2 a - 4 \\)', '\\( a^{3} - a^{2} - 6 a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}