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hmf_forms • Show schema
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{'deg': 4, 'dimension': 3, 'disc': 17989, 'field_bad_primes': [17989], 'field_label': '4.4.17989.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.17989.1-5.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [5], 'level_ideal': '[5, 5, w^3 - 2*w^2 - 6*w + 2]', 'level_label': '5.1', 'level_norm': 5, 'parallel_weight': 2, 'short_label': '5.1-a', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[5, 5, w^3 - 2*w^2 - 6*w + 2]', -1]], 'hecke_eigenvalues': ['e', 1, '-2*e + 1', 'e^2 - e - 5', '-e^2 + 1', '-e^2 + e', '-e^2 + 5', 'e^2 - e - 7', '2*e - 6', '3*e + 2', '-3*e^2 + 2*e + 7', '-e^2 + 2*e - 2', 'e^2 - 2*e - 6', 'e - 4', 'e^2 - 4*e - 2', 'e^2 - 5*e - 4', '-3*e^2 + e + 6', '4*e^2 - 6*e - 6', '4*e^2 + e - 11', '2*e^2 - e - 1', '5*e^2 - 4*e - 11', '-3*e - 1', '4*e^2 - e - 15', '-3*e^2 - e + 4', 'e^2 - 4*e - 10', '-e^2 + 7*e - 6', '-2*e^2 + 7*e', '-4*e^2 + 6*e + 10', '-e^2 + 2*e + 6', '5*e^2 - 8*e - 8', '-e^2 - e + 3', '-6*e^2 + 12*e + 16', '-6*e^2 + 3*e + 12', '-9*e^2 + 9*e + 21', '-e^2 - 6*e + 13', '7*e^2 - 5*e - 11', '-9*e^2 + 7*e + 19', '-2*e^2 + 3*e + 17', '6*e^2 - e - 18', '-2*e^2 + 14*e + 2', '2*e^2 + e - 24', '5*e^2 + e - 19', '2*e^2 - 7*e - 12', '-6*e^2 + 9*e + 27', '-6*e^2 + 6*e + 7', '5*e^2 - 9*e', '2*e^2 - 5', '3*e^2 - 9*e + 2', '-5*e^2 + 11*e + 6', '2*e^2 + 11*e - 20', '-3*e^2 + e - 16', '11*e^2 - 7*e - 25', '2*e^2 - 7*e - 2', '9*e^2 - 14*e - 27', '5*e^2 - 3*e - 15', '5*e^2 - 2*e - 23', '-2*e^2 + 9*e', '6*e^2 + 6*e - 25', '5*e^2 + 3*e - 21', '7*e^2 - 3*e - 31', '5*e^2 + 7*e - 24', '-4*e^2 + 3*e + 29', '11*e^2 - 11*e - 29', '-6*e^2 + 10*e + 16', '-6*e^2 + 5*e + 35', '3*e^2 + 3*e + 3', '7*e^2 - 17*e - 18', '-7*e^2 + 13*e + 20', '-6*e^2 + 16*e + 16', '-6*e^2 - 2*e + 17', '-9*e^2 + e + 29', '10*e^2 - 9*e - 34', '-5*e^2 + e + 23', '4*e^2 - 6*e - 13', '-12*e^2 + 12*e + 32', 'e^2 - 15*e + 1', '2*e^2 + 2*e + 19', '-2*e^2 + 8*e + 2', '3*e^2 - 2*e - 23', '2*e^2 + 7*e - 8', '2*e^2 - 5*e - 16', '2*e^2 - 10*e + 16', '12*e - 2', '8*e^2 - 13*e - 7', '-e^2 - 17*e + 10', '-9*e^2 + e + 17', '13*e^2 - 6*e - 39', '-3*e^2 + 2*e - 20', '5*e^2 - 16*e - 5', '3*e^2 - e - 26', '-4*e^2 + 6*e - 3', '2*e + 26', '-2*e^2 - 5*e + 22', '-13*e^2 + 4*e + 46', '-7*e^2 + 17*e + 8', '12*e^2 - 9*e - 30', '-3*e^2 - 7*e + 6', '13*e^2 - 2*e - 42', '-8*e^2 + 15*e + 27', '3*e^2 - 2*e - 7', '-5*e^2 - 16*e + 30', '12*e^2 - e - 39', '-2*e^2 + 2*e - 2', '16*e^2 - 22*e - 44', '-12*e^2 + e + 40', '-e^2 + 13*e - 12', '-14*e^2 + 13*e + 20', '-7*e^2 + 14*e + 22', '-5*e^2 + 9*e + 36', '-3*e^2 + 17*e + 1', '8*e^2 - 4*e - 39', '-17*e^2 + 13*e + 38', '5*e^2 - 13*e - 16', '-15*e^2 + 10*e + 39', '6*e^2 - 17*e - 29', '2*e^2 - 9*e - 38', '-2*e^2 + 20*e - 6', '2*e^2 + 8*e + 11', '-e^2 - 4*e - 31', '-5*e^2 - 11*e + 21', 'e^2 - 2*e - 11', '11*e^2 + 2*e - 21', '-3*e^2 - 14*e + 24', '-9*e^2 + 24', '-10*e^2 - 3*e + 24', '15*e^2 - 21*e - 30', '14*e^2 - 31*e - 42', '-6*e^2 - 4*e + 17', '-13*e^2 + 8*e + 9', '2*e^2 + 6*e + 1', '-5*e^2 - 18*e + 36', '4*e^2 + e - 4', '18*e^2 - 23*e - 44', '-17*e^2 + 9*e + 38', 'e^2 - 10*e - 30', '-17*e^2 + 50', '-5*e^2 + 4*e + 34', '-6*e^2 + 10*e + 20', '10*e^2 + 17*e - 53', '9*e^2 - 26*e - 38', '5*e^2 - 23*e - 15', '-9*e^2 + 20*e + 49', 'e^2 + 8*e - 18', '-5*e - 31', '-9*e^2 + 2*e + 48', '6*e^2 - e - 13', '-14*e^2 + 13*e + 35', '11*e^2 - 22*e - 13', '-5*e^2 - 11*e + 23', '-7*e^2 + 16*e + 16', '4*e^2 - 7*e + 15', '-e^2 + 4*e + 39', '-2*e^2 - 5*e + 12', '-4*e^2 + 5*e + 51', '6*e^2 - 19*e + 3', '11*e^2 - 9*e - 39', '-2*e^2 - e + 18', '-10*e^2 + 4*e + 37', '2*e^2 - 18*e - 6', '-e^2 + 2*e - 39', '-9*e^2 + 3*e + 55', '-6*e^2 + 11*e - 7', '-7*e^2 + 20*e + 30', '-7*e^2 + 25*e + 3', '6*e^2 + 11*e - 23', 'e^2 - 11*e', '5*e^2 + 2*e - 32', '-8*e^2 - 9*e + 46'], 'hecke_polynomial': 'x^3 - x^2 - 4*x + 1', 'label': '4.4.17989.1-5.1-a'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 17989, 'ideals': ['[1, 1, 1]', '[3, 3, -w^3 + 2*w^2 + 4*w + 1]', '[5, 5, w^3 - 2*w^2 - 6*w + 2]', '[9, 9, w - 1]', '[11, 11, w^3 - 2*w^2 - 4*w]', '[13, 13, w^2 - 3*w - 2]', '[15, 15, -w^3 + 2*w^2 + 5*w]', '[16, 2, 2]', '[17, 17, -w^3 + 3*w^2 + 2*w - 2]', '[17, 17, -w^2 + 2*w + 3]', '[23, 23, -w^3 + w^2 + 6*w + 1]', '[25, 25, w - 2]', '[27, 3, -2*w^3 + 3*w^2 + 11*w - 1]', '[27, 27, -2*w^3 + 4*w^2 + 11*w - 4]', '[29, 29, w^3 - 2*w^2 - 5*w + 4]', '[31, 31, -w^3 + 2*w^2 + 6*w - 3]', '[31, 31, -w^3 + 2*w^2 + 5*w + 1]', '[31, 31, w^3 - 2*w^2 - 6*w]', '[31, 31, -w^2 + 2*w + 1]', '[33, 33, 2*w^3 - 3*w^2 - 12*w + 1]', '[37, 37, w^3 - w^2 - 7*w - 1]', '[39, 39, w^3 - 2*w^2 - 4*w + 2]', '[43, 43, w^2 - w - 4]', '[45, 45, w^3 - 2*w^2 - 7*w - 1]', '[48, 6, -2*w^3 + 4*w^2 + 8*w + 2]', '[51, 51, w^3 - w^2 - 6*w]', '[51, 51, -w^2 + w + 3]', '[55, 55, -w - 3]', '[65, 65, w^3 - w^2 - 7*w]', '[69, 69, -w^2 + 3*w + 4]', '[71, 71, w^3 - 2*w^2 - 6*w - 1]', '[71, 71, 5*w^3 - 8*w^2 - 29*w + 3]', '[75, 75, -w^2 + 4]', '[80, 10, 2*w^3 - 4*w^2 - 12*w + 4]', '[81, 3, 3]', '[81, 81, w^3 - w^2 - 8*w - 1]', '[85, 85, w^3 - w^2 - 8*w - 3]', '[85, 85, w^3 - 2*w^2 - 4*w + 3]', '[87, 87, -2*w^3 + 3*w^2 + 11*w + 3]', '[89, 89, -2*w^3 + 4*w^2 + 10*w - 7]', '[93, 93, 2*w^3 - 4*w^2 - 9*w - 1]', '[93, 93, -2*w^3 + 3*w^2 + 13*w + 1]', '[93, 93, w^3 - 2*w^2 - 3*w - 2]', '[93, 93, -2*w^3 + 3*w^2 + 11*w]', '[97, 97, -w^3 + 2*w^2 + 4*w - 4]', '[99, 99, -w^3 + 3*w^2 + 2*w - 4]', '[103, 103, w^3 - w^2 - 8*w - 2]', '[103, 103, -2*w^3 + 4*w^2 + 10*w - 1]', '[109, 109, 2*w^3 - 3*w^2 - 13*w]', '[111, 111, -w^3 + 4*w^2 - w - 5]', '[113, 113, 2*w^3 - 3*w^2 - 12*w - 3]', '[115, 115, w^3 - 9*w - 5]', '[117, 117, w^3 - 4*w^2 + w + 2]', '[121, 121, -2*w^3 + 4*w^2 + 9*w + 3]', '[125, 5, 2*w^3 - 3*w^2 - 10*w + 4]', '[125, 125, 2*w^3 - 3*w^2 - 13*w - 3]', '[129, 129, w^3 - 10*w - 6]', '[131, 131, 5*w^3 - 8*w^2 - 28*w + 5]', '[131, 131, 5*w^3 - 9*w^2 - 27*w + 9]', '[135, 15, 2*w^3 - 3*w^2 - 11*w - 2]', '[135, 135, w^3 - 3*w^2 - 3*w + 5]', '[137, 137, -2*w^3 + 3*w^2 + 11*w + 1]', '[137, 137, w^3 - 3*w^2 - 6*w + 4]', '[143, 143, w^3 - 2*w^2 - 8*w - 1]', '[144, 18, 2*w - 2]', '[145, 145, -w^2 + 4*w + 1]', '[153, 153, -2*w^2 + 6*w + 5]', '[153, 153, -w^3 + 3*w^2 + w - 3]', '[155, 155, -w^3 + 2*w^2 + 3*w + 4]', '[155, 155, -w^3 + 2*w^2 + 5*w - 5]', '[155, 155, -w^3 + 3*w^2 + 4*w - 7]', '[155, 155, -2*w^3 + 4*w^2 + 9*w + 2]', '[157, 157, -3*w^3 + 4*w^2 + 18*w + 6]', '[157, 157, 3*w^3 - 6*w^2 - 16*w + 6]', '[163, 163, 4*w^3 - 8*w^2 - 23*w + 8]', '[163, 163, w^3 - 2*w^2 - 3*w - 3]', '[165, 165, 2*w^3 - 3*w^2 - 10*w - 4]', '[167, 167, w^2 - 3*w - 5]', '[167, 167, 2*w^3 - 2*w^2 - 13*w - 4]', '[169, 169, -w^3 + 2*w^2 + 7*w - 3]', '[176, 22, 2*w^3 - 4*w^2 - 8*w]', '[179, 179, -w^3 + 3*w^2 + 3*w - 4]', '[181, 181, 5*w^3 - 9*w^2 - 29*w + 5]', '[185, 185, 4*w^3 - 7*w^2 - 24*w + 4]', '[187, 187, -w^3 + 4*w^2 - 2*w - 3]', '[187, 187, -3*w^3 + 4*w^2 + 18*w + 3]', '[191, 191, -3*w^3 + 5*w^2 + 18*w]', '[191, 191, 4*w^3 - 8*w^2 - 23*w + 7]', '[193, 193, 3*w^3 - 4*w^2 - 20*w - 5]', '[193, 193, -w^3 + w^2 + 8*w - 3]', '[195, 195, -2*w^3 + 6*w^2 + 3*w - 4]', '[197, 197, -3*w^3 + 4*w^2 + 18*w + 9]', '[207, 207, w^3 - 2*w^2 - 8*w]', '[208, 26, 2*w^2 - 6*w - 4]', '[211, 211, w^3 - 7*w - 8]', '[213, 213, 2*w^3 - 4*w^2 - 7*w - 3]', '[213, 213, -w^3 + 3*w^2 + 3*w - 8]', '[215, 215, -3*w^3 + 5*w^2 + 15*w - 6]', '[221, 221, -w - 4]', '[221, 221, -2*w^3 + 4*w^2 + 12*w - 1]', '[225, 225, -2*w^3 + 3*w^2 + 12*w + 5]', '[233, 233, 2*w^3 - 2*w^2 - 15*w - 7]', '[233, 233, 4*w^3 - 7*w^2 - 24*w + 2]', '[239, 239, w^2 - 5]', '[240, 30, -2*w^3 + 4*w^2 + 10*w]', '[243, 9, -3*w^3 + 6*w^2 + 12*w + 3]', '[243, 243, -2*w^3 + 3*w^2 + 14*w + 3]', '[253, 253, -w^3 + 2*w^2 + 3*w - 3]', '[255, 255, 2*w^3 - 3*w^2 - 9*w + 4]', '[255, 255, -2*w^2 + 5*w + 3]', '[256, 4, 4]', '[261, 261, -2*w^3 + 4*w^2 + 12*w - 5]', '[263, 263, w^2 - 3*w - 6]', '[267, 267, 3*w^3 - 4*w^2 - 18*w - 5]', '[269, 269, w^3 - 2*w^2 - 4*w + 6]', '[271, 271, 4*w^3 - 6*w^2 - 23*w + 2]', '[272, 34, -2*w^3 + 6*w^2 + 4*w - 4]', '[272, 34, -2*w^2 + 4*w + 6]', '[275, 275, -2*w^3 + 3*w^2 + 11*w + 7]', '[277, 277, -w^3 + 3*w^2 + 2*w - 5]', '[277, 277, 3*w^3 - 4*w^2 - 17*w - 1]', '[277, 277, -3*w^3 + 5*w^2 + 17*w + 1]', '[277, 277, -2*w^3 + w^2 + 17*w + 6]', '[279, 279, -2*w^3 + 3*w^2 + 13*w + 4]', '[279, 279, -w^3 + 2*w^2 + 4*w + 4]', '[279, 279, -2*w^2 + 4*w + 7]', '[279, 279, -w^3 + 3*w^2 + 4*w - 6]', '[281, 281, 2*w - 3]', '[283, 283, -3*w^3 + 5*w^2 + 16*w + 1]', '[283, 283, -3*w^2 + 7*w + 9]', '[283, 283, 4*w^3 - 6*w^2 - 22*w - 11]', '[283, 283, 3*w^3 - 4*w^2 - 18*w - 4]', '[289, 17, 4*w^3 - 6*w^2 - 24*w + 1]', '[289, 17, 3*w^3 - 6*w^2 - 13*w]', '[289, 289, -w^3 + 3*w^2 + 7*w - 4]', '[289, 289, 2*w^3 - 3*w^2 - 10*w]', '[291, 291, w^3 - 9*w - 4]', '[293, 293, -w^3 + 3*w^2 + 5*w - 5]', '[293, 293, 3*w^3 - 4*w^2 - 18*w - 1]', '[297, 33, -2*w^3 + 3*w^2 + 11*w - 4]', '[297, 297, -w^2 + 3*w + 7]', '[299, 299, w^3 - w^2 - 5*w - 5]', '[307, 307, 2*w^3 - 3*w^2 - 10*w - 3]', '[309, 309, -w^3 + 5*w^2 - 3*w - 7]', '[309, 309, -3*w^3 + 8*w^2 + 6*w + 1]', '[311, 311, -3*w^3 + 6*w^2 + 15*w - 8]', '[311, 311, -w^2 + 4*w + 5]', '[319, 319, 3*w^3 - 5*w^2 - 16*w + 1]', '[325, 325, -w^3 + 2*w^2 + 3*w - 6]', '[327, 327, -w^3 + 4*w^2 - 6]', '[333, 333, -w^3 + w^2 + 9*w]', '[339, 339, 3*w^3 - 5*w^2 - 14*w - 8]', '[341, 341, 2*w^3 - 2*w^2 - 14*w - 3]', '[341, 341, -w^3 - w^2 + 12*w + 7]', '[341, 341, -3*w^3 + 6*w^2 + 13*w + 3]', '[341, 341, -w^3 + w^2 + 7*w + 7]', '[345, 345, w^3 - 3*w^2 - 5*w + 4]', '[347, 347, -w^3 + 3*w^2 + 4*w - 4]', '[349, 349, 6*w^3 - 11*w^2 - 36*w + 6]', '[349, 349, -w^3 + 4*w^2 - 5]', '[351, 39, -w^3 + 3*w^2 + 4*w - 5]', '[351, 351, -3*w^3 + 5*w^2 + 16*w]', '[355, 355, -4*w^3 + 5*w^2 + 26*w + 5]', '[355, 355, 3*w^3 - 4*w^2 - 15*w + 2]', '[363, 363, -2*w^3 + 2*w^2 + 15*w + 6]', '[368, 46, -2*w^3 + 2*w^2 + 12*w + 2]', '[375, 15, -2*w^3 + 3*w^2 + 10*w + 1]', '[375, 375, 2*w^3 - 2*w^2 - 12*w - 9]', '[377, 377, 2*w^3 - 2*w^2 - 15*w - 4]', '[383, 383, -2*w^3 + 3*w^2 + 10*w + 2]', '[383, 383, 2*w^3 - 2*w^2 - 13*w - 3]', '[387, 387, w^3 - 2*w^2 - 3*w + 4]', '[389, 389, w^3 - 2*w^2 - 5*w - 4]', '[391, 391, -2*w^3 + 3*w^2 + 13*w + 5]', '[391, 391, 2*w^3 - 4*w^2 - 10*w - 1]', '[393, 393, -2*w^3 + 4*w^2 + 9*w - 5]', '[393, 393, -3*w^3 + 4*w^2 + 19*w + 1]', '[397, 397, -w^3 + w^2 + 5*w - 3]', '[400, 50, 2*w - 4]', '[401, 401, w^3 - 11*w - 7]', '[403, 403, w^3 - 3*w^2 - w + 4]', '[403, 403, -w^3 + 10*w + 2]', '[403, 403, 4*w^3 - 6*w^2 - 23*w]', '[403, 403, 3*w^3 - 5*w^2 - 19*w + 1]', '[405, 15, 3*w^3 - 6*w^2 - 18*w + 6]', '[405, 405, 2*w^2 - 2*w - 9]', '[407, 407, 2*w^3 - 5*w^2 - 6*w + 4]', '[411, 411, -2*w^3 + 4*w^2 + 8*w + 5]', '[411, 411, -w^3 + w^2 + 9*w + 3]', '[419, 419, 2*w^2 - 2*w - 11]', '[419, 419, -2*w^3 + 5*w^2 + 12*w - 5]', '[421, 421, w^3 - 10*w - 11]', '[421, 421, -2*w^3 + 2*w^2 + 15*w + 5]', '[421, 421, -4*w^3 + 6*w^2 + 21*w - 6]', '[421, 421, w^2 + w - 4]', '[425, 425, -w^3 + 4*w^2 - w - 6]', '[425, 425, 3*w^3 - 4*w^2 - 17*w + 1]', '[429, 429, -2*w + 5]', '[431, 431, -2*w^2 + 5*w + 2]', '[432, 6, -4*w^3 + 6*w^2 + 22*w - 2]', '[432, 54, -4*w^3 + 8*w^2 + 22*w - 8]', '[433, 433, -2*w^3 + 4*w^2 + 11*w]', '[435, 435, -4*w^3 + 7*w^2 + 23*w - 2]', '[443, 443, -w^3 + 2*w^2 + 3*w - 5]', '[443, 443, -3*w^3 + 7*w^2 + 18*w - 8]', '[445, 445, -w^3 + 8*w + 12]', '[459, 51, 2*w^3 - 3*w^2 - 14*w + 1]', '[459, 51, -2*w^3 + 3*w^2 + 14*w + 2]', '[459, 459, -3*w^3 + 4*w^2 + 19*w + 7]', '[459, 459, -w^3 + 2*w^2 + 5*w - 6]', '[461, 461, -2*w^3 + 4*w^2 + 9*w - 7]', '[461, 461, w^2 - 6]', '[464, 58, 2*w^3 - 4*w^2 - 10*w + 8]', '[465, 465, w^3 - 7*w - 9]', '[465, 465, 3*w^3 - 5*w^2 - 15*w - 4]', '[465, 465, -3*w^3 + 4*w^2 + 20*w + 3]', '[465, 465, -w^3 + 3*w^2 + 2*w + 2]', '[467, 467, w^3 - w^2 - 5*w - 6]', '[471, 471, -w^3 + 11*w + 2]', '[471, 471, -5*w^3 + 8*w^2 + 25*w + 14]', '[473, 473, -w^3 + w^2 + 9*w + 2]', '[479, 479, -4*w^3 + 6*w^2 + 23*w + 4]', '[479, 479, 3*w^3 - 4*w^2 - 20*w - 7]', '[481, 481, -2*w^3 + 4*w^2 + 7*w + 5]', '[485, 485, -6*w^3 + 12*w^2 + 35*w - 10]', '[487, 487, -w^3 + 3*w^2 + 5*w - 8]', '[487, 487, -6*w^3 + 10*w^2 + 33*w - 6]', '[489, 489, -3*w^3 + 5*w^2 + 18*w + 1]', '[489, 489, 7*w^3 - 17*w^2 - 21*w - 2]', '[493, 493, -2*w^2 + 3*w + 9]', '[493, 493, -w^3 + w^2 + 4*w + 4]', '[495, 495, 3*w^3 - 3*w^2 - 20*w - 7]', '[496, 62, -2*w^3 + 4*w^2 + 12*w - 6]', '[496, 62, -2*w^3 + 4*w^2 + 10*w + 2]', '[496, 62, 2*w^3 - 4*w^2 - 12*w]', '[496, 62, -2*w^2 + 4*w + 2]', '[499, 499, -2*w^3 + 4*w^2 + 9*w - 6]', '[501, 501, 4*w^2 - 10*w - 9]', '[501, 501, w^3 + w^2 - 12*w - 11]', '[503, 503, w^3 - 2*w^2 - 3*w - 6]', '[507, 507, 3*w^3 - 7*w^2 - 11*w]', '[509, 509, w^3 - 11*w - 9]', '[515, 515, -7*w^3 + 12*w^2 + 38*w - 8]', '[515, 515, 4*w^3 - 6*w^2 - 23*w + 3]', '[521, 521, w^3 - 9*w - 3]', '[527, 527, w^3 - 8*w - 3]', '[527, 527, -4*w^3 + 8*w^2 + 22*w - 7]', '[527, 527, -2*w^3 + w^2 + 17*w + 9]', '[527, 527, -4*w^3 + 7*w^2 + 22*w - 8]', '[527, 527, -2*w^2 + 5*w + 1]', '[527, 527, 2*w^3 - 5*w^2 - 11*w + 7]', '[527, 527, -w^3 + 3*w^2 + 2*w - 6]', '[527, 527, -3*w^2 + 7*w + 6]', '[528, 66, 4*w^3 - 6*w^2 - 24*w + 2]', '[529, 529, 3*w^3 - 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w - 10]', '[1567, 1567, -6*w^3 + 8*w^2 + 36*w + 5]', '[1567, 1567, -w^3 + 4*w^2 + 3*w - 11]', '[1573, 1573, 4*w^3 - 5*w^2 - 24*w - 7]', '[1579, 1579, 4*w^3 - 7*w^2 - 22*w - 1]', '[1581, 1581, -5*w^3 + 9*w^2 + 31*w - 5]', '[1581, 1581, -2*w^3 + 4*w^2 + 8*w - 7]', '[1581, 1581, -2*w^3 + 2*w^2 + 16*w + 5]', '[1581, 1581, -4*w^3 + 5*w^2 + 24*w + 8]', '[1581, 1581, 5*w^3 - 7*w^2 - 29*w - 2]', '[1581, 1581, w^3 - 12*w - 1]', '[1581, 1581, 4*w^3 - 7*w^2 - 20*w - 1]', '[1581, 1581, -6*w^3 + 10*w^2 + 33*w - 4]', '[1583, 1583, -w^3 + 5*w^2 - w - 14]', '[1584, 198, -2*w^3 + 6*w^2 + 4*w - 8]', '[1587, 1587, 4*w^3 - 5*w^2 - 26*w - 3]', '[1591, 1591, -4*w^3 + 6*w^2 + 25*w + 5]', '[1595, 1595, -5*w^3 + 10*w^2 + 21*w + 3]', '[1601, 1601, -7*w^3 + 11*w^2 + 43*w]', '[1611, 1611, 3*w^3 - 7*w^2 - 10*w + 5]', '[1613, 1613, -3*w^3 + 5*w^2 + 14*w]', '[1613, 1613, 5*w^3 - 6*w^2 - 34*w - 11]', '[1619, 1619, 2*w^3 - 5*w^2 - 14*w]', '[1621, 1621, -w^3 + 4*w^2 - 10]', '[1625, 65, 2*w^3 - 3*w^2 - 15*w - 1]', '[1625, 1625, -w^3 - w^2 + 12*w + 13]', '[1629, 1629, 5*w^3 - 11*w^2 - 19*w - 2]', '[1633, 1633, -6*w^3 + 10*w^2 + 33*w]', '[1633, 1633, 3*w^2 + w - 6]', '[1635, 1635, -4*w^3 + 8*w^2 + 19*w - 8]', '[1637, 1637, 10*w^3 - 18*w^2 - 59*w + 11]', '[1637, 1637, -4*w^3 + 7*w^2 + 23*w]', '[1648, 206, 2*w^3 - 2*w^2 - 16*w - 4]', '[1648, 206, -4*w^3 + 8*w^2 + 20*w - 2]', '[1649, 1649, w^3 - 6*w - 9]', '[1649, 1649, -3*w + 5]', '[1657, 1657, w^3 + 3*w^2 - 18*w - 12]', '[1657, 1657, 3*w^3 - 5*w^2 - 17*w - 6]', '[1665, 1665, w^3 - 4*w^2 - 5*w + 8]', '[1677, 1677, -w^3 + 3*w^2 + 7*w - 6]', '[1681, 41, -7*w^3 + 10*w^2 + 42*w + 4]', '[1681, 41, 4*w^2 - 9*w - 12]', '[1683, 1683, 6*w^3 - 10*w^2 - 33*w + 10]', '[1683, 1683, 4*w^3 - 7*w^2 - 24*w]', '[1693, 1693, -w^3 + 4*w^2 + 2*w - 10]', '[1695, 1695, w - 7]', '[1697, 1697, 4*w^3 - 7*w^2 - 27*w - 2]', '[1697, 1697, -3*w^3 + 8*w^2 + 9*w - 9]', '[1699, 1699, 3*w^3 - 3*w^2 - 20*w - 5]', '[1699, 1699, w^3 - w^2 - 7*w - 9]', '[1703, 1703, 3*w^3 - 6*w^2 - 18*w + 8]', '[1703, 1703, 6*w^3 - 10*w^2 - 35*w + 1]', '[1705, 1705, 7*w^3 - 12*w^2 - 42*w + 6]', '[1705, 1705, -4*w^3 + 7*w^2 + 20*w - 1]', '[1705, 1705, 2*w^3 - 5*w^2 - 12*w + 8]', '[1705, 1705, -3*w^3 + 4*w^2 + 21*w + 1]', '[1719, 1719, 2*w^3 - 7*w^2 - 2*w + 7]', '[1719, 1719, 5*w^3 - 8*w^2 - 27*w + 3]', '[1721, 1721, 3*w^3 - 6*w^2 - 21*w - 2]', '[1723, 1723, 2*w^3 - w^2 - 17*w - 4]', '[1723, 1723, 4*w^3 - 5*w^2 - 25*w - 3]', '[1725, 1725, -w^3 + 5*w^2 - 2*w - 8]', '[1727, 1727, 2*w^2 - 5*w - 11]', '[1727, 1727, 2*w^3 - 4*w^2 - 7*w - 8]', '[1731, 1731, 3*w^3 - 8*w^2 - 6*w - 4]', '[1733, 1733, 3*w^3 - 4*w^2 - 16*w - 5]', '[1733, 1733, 3*w^3 - 6*w^2 - 15*w - 1]', '[1735, 1735, -6*w^3 + 10*w^2 + 31*w - 9]', '[1737, 1737, -4*w^3 + 5*w^2 + 24*w + 2]', '[1737, 1737, w^3 - 14*w + 4]', '[1744, 218, 4*w^3 - 6*w^2 - 26*w]', '[1745, 1745, -3*w^3 + 6*w^2 + 13*w - 6]', '[1745, 1745, -4*w^3 + 6*w^2 + 26*w + 1]', '[1751, 1751, 4*w^3 - 6*w^2 - 21*w - 8]', '[1751, 1751, -3*w^3 + 11*w^2 - 2*w - 2]', '[1751, 1751, -5*w^3 + 11*w^2 + 18*w + 1]', '[1751, 1751, -3*w^2 + 8*w + 3]', '[1753, 1753, -4*w^3 + 7*w^2 + 20*w]', '[1755, 195, w^3 - 6*w^2 + 5*w + 11]', '[1755, 1755, w^3 - 3*w^2 - 2*w + 13]', '[1761, 1761, -11*w^3 + 25*w^2 + 36*w + 10]', '[1773, 1773, 4*w^3 - 7*w^2 - 18*w - 6]', '[1775, 1775, -3*w^3 + 5*w^2 + 14*w + 1]', '[1775, 1775, -13*w^3 + 22*w^2 + 76*w - 11]', '[1776, 222, -2*w^3 + 8*w^2 - 2*w - 10]', '[1777, 1777, -2*w^3 + 5*w^2 + 11*w - 10]', '[1777, 1777, 2*w^3 - 4*w^2 - 9*w + 10]', '[1777, 1777, 3*w^3 - 4*w^2 - 21*w - 4]', '[1777, 1777, 2*w^3 - 3*w^2 - 12*w + 6]', '[1779, 1779, 5*w^3 - 7*w^2 - 30*w - 10]', '[1779, 1779, -w^3 + 4*w^2 - w - 8]', '[1781, 1781, 3*w^3 - 4*w^2 - 16*w - 3]', '[1781, 1781, -w^3 + 5*w^2 - 2*w - 9]', '[1783, 1783, -2*w^2 + 8*w + 1]', '[1793, 1793, 7*w^3 - 13*w^2 - 41*w + 7]', '[1793, 1793, -6*w^3 + 15*w^2 + 18*w - 1]', '[1801, 1801, 4*w^3 - 3*w^2 - 31*w - 11]', '[1808, 226, 4*w^3 - 6*w^2 - 24*w - 6]', '[1811, 1811, 4*w^3 - 4*w^2 - 30*w - 5]', '[1811, 1811, -w^3 - 2*w^2 + 14*w + 9]', '[1815, 1815, -5*w^3 + 7*w^2 + 29*w - 1]', '[1837, 1837, -3*w^2 + 7*w + 4]', '[1837, 1837, w^3 - 3*w^2 - w + 7]', '[1839, 1839, -w^3 + 7*w^2 - 10*w - 11]', '[1839, 1839, -6*w^3 + 7*w^2 + 37*w + 19]', '[1840, 230, 2*w^3 - 18*w - 10]', '[1847, 1847, 2*w^2 - 6*w - 9]', '[1847, 1847, w^2 + 2*w - 5]', '[1849, 1849, -w^3 + 11*w + 15]', '[1853, 1853, 4*w^3 - 6*w^2 - 22*w - 5]', '[1853, 1853, -5*w^3 + 10*w^2 + 22*w - 1]', '[1857, 1857, 12*w^3 - 22*w^2 - 53*w - 24]', '[1857, 1857, 6*w^3 - 9*w^2 - 35*w - 4]', '[1857, 1857, -2*w^3 + 3*w^2 + 11*w + 9]', '[1857, 1857, 3*w^3 - 4*w^2 - 16*w - 4]', '[1859, 1859, -w^3 + 2*w^2 + 6*w + 6]', '[1861, 1861, 4*w^3 - 9*w^2 - 24*w + 10]', '[1861, 1861, -2*w^3 + 4*w^2 + 7*w - 5]', '[1863, 69, -3*w^3 + 3*w^2 + 18*w + 3]', '[1863, 1863, -w^3 + 3*w^2 + 6*w - 8]', '[1867, 1867, -3*w^3 + 2*w^2 + 25*w + 7]', '[1871, 1871, 6*w^3 - 9*w^2 - 36*w + 2]', '[1871, 1871, 3*w^3 - 5*w^2 - 13*w + 5]', '[1872, 234, 2*w^3 - 8*w^2 + 2*w + 4]', '[1873, 1873, -w^3 + 4*w^2 + 2*w - 6]', '[1875, 15, -5*w^3 + 10*w^2 + 30*w - 5]', '[1875, 1875, -w^3 + 2*w^2 + 4*w - 8]', '[1885, 1885, 7*w^3 - 11*w^2 - 41*w + 5]', '[1887, 1887, 3*w^3 - 5*w^2 - 18*w - 4]', '[1887, 1887, 2*w^3 - 3*w^2 - 11*w + 6]', '[1893, 1893, -w^3 + 4*w^2 - 2*w - 7]', '[1893, 1893, -6*w^3 + 9*w^2 + 31*w + 17]', '[1899, 1899, 2*w + 7]', '[1913, 1913, 5*w^3 - 10*w^2 - 32*w + 6]', '[1913, 1913, -3*w^3 + 6*w^2 + 16*w]', '[1915, 1915, 6*w^3 - 11*w^2 - 37*w + 5]', '[1915, 1915, -4*w^3 + 8*w^2 + 24*w - 3]', '[1917, 213, -2*w^3 + 6*w^2 + 14*w - 7]', '[1917, 213, -w^3 - 3*w^2 + 13*w + 25]', '[1917, 1917, 3*w^3 - 7*w^2 - 14*w + 9]', '[1917, 1917, -5*w^3 + 7*w^2 + 28*w - 3]', '[1921, 1921, -4*w^2 + 11*w + 6]', '[1921, 1921, 3*w^3 - w^2 - 25*w - 14]', '[1923, 1923, 5*w^3 - 7*w^2 - 28*w - 12]', '[1923, 1923, -w^3 + 7*w - 3]', '[1931, 1931, -2*w^2 - w + 7]', '[1933, 1933, -w^3 + 4*w^2 + 3*w - 5]', '[1935, 1935, -4*w^3 + 3*w^2 + 22*w + 6]', '[1936, 242, -4*w^3 + 8*w^2 + 18*w + 6]', '[1945, 1945, -w^3 + 3*w^2 + 8*w - 5]', '[1949, 1949, w^3 + 5*w^2 - 22*w - 21]', '[1949, 1949, 5*w^3 - 8*w^2 - 29*w - 3]', '[1951, 1951, 2*w^3 - 17*w - 10]', '[1951, 1951, 3*w^3 - 4*w^2 - 21*w - 3]', '[1955, 1955, 4*w^3 - 9*w^2 - 20*w + 14]', '[1955, 1955, -4*w^3 + 5*w^2 + 21*w]', '[1959, 1959, 2*w^3 - 3*w^2 - 10*w - 10]', '[1959, 1959, w^3 - 2*w^2 - 5*w - 6]', '[1965, 1965, -12*w^3 + 21*w^2 + 70*w - 13]', '[1965, 1965, -10*w^3 + 19*w^2 + 57*w - 15]', '[1969, 1969, w^3 - 5*w^2 + 6*w + 2]', '[1983, 1983, -w^3 + 6*w^2 - 8*w - 9]', '[1985, 1985, -6*w^3 + 13*w^2 + 38*w - 10]', '[1987, 1987, w^3 - w^2 - 4*w - 7]', '[1989, 1989, 3*w^3 - 7*w^2 - 15*w + 10]', '[1989, 1989, 4*w^3 - 4*w^2 - 27*w - 9]', '[1991, 1991, 6*w^3 - 11*w^2 - 36*w + 10]', '[1993, 1993, -3*w^3 + 7*w^2 + 13*w - 13]', '[1997, 1997, -5*w^3 + 9*w^2 + 22*w + 8]', '[1999, 1999, -w^3 + 4*w^2 + 2*w - 9]', '[1999, 1999, 7*w^3 - 11*w^2 - 40*w + 7]', '[2000, 10, 4*w^3 - 6*w^2 - 20*w + 8]', '[2000, 250, 4*w^3 - 6*w^2 - 26*w - 6]', '[2001, 2001, -2*w^2 + 5*w + 12]', '[2003, 2003, 5*w^3 - 7*w^2 - 28*w - 17]', '[2005, 2005, 2*w^3 - w^2 - 12*w - 3]', '[2011, 2011, -w^2 + 7*w + 4]', '[2011, 2011, w^3 - 12*w - 6]', '[2015, 2015, -2*w^2 + 5*w + 13]', '[2015, 2015, -2*w^3 + 6*w^2 + 6*w - 5]', '[2015, 2015, 6*w^3 - 9*w^2 - 35*w - 2]', '[2015, 2015, -2*w^3 + w^2 + 18*w + 6]', '[2017, 2017, w^2 + w - 7]', '[2019, 2019, -8*w^3 + 20*w^2 + 22*w - 1]', '[2019, 2019, -9*w^3 + 21*w^2 + 28*w + 8]', '[2019, 2019, 4*w^3 - 9*w^2 - 12*w - 4]', '[2019, 2019, 4*w^3 - 4*w^2 - 29*w - 10]', '[2025, 75, 3*w - 6]', '[2025, 2025, 3*w^3 - 5*w^2 - 13*w - 3]', '[2027, 2027, -3*w^3 + 5*w^2 + 19*w + 4]', '[2027, 2027, -2*w^3 + 5*w^2 + 7*w - 9]', '[2029, 2029, -5*w^3 + 10*w^2 + 24*w - 9]', '[2029, 2029, w^3 - w^2 - 3*w - 5]', '[2035, 2035, -3*w^3 + 3*w^2 + 19*w + 4]', '[2039, 2039, 3*w^2 - 5*w - 8]', '[2039, 2039, -5*w^3 + 9*w^2 + 24*w + 4]', '[2041, 2041, 5*w^3 - 9*w^2 - 25*w]', '[2041, 2041, w^3 + 5*w^2 - 21*w - 22]', '[2047, 2047, 2*w^3 - 6*w^2 - 5*w + 11]', '[2049, 2049, -2*w^3 + 2*w^2 + 11*w + 10]', '[2053, 2053, w^3 + w^2 - 8*w - 14]', '[2055, 2055, -4*w^3 + 5*w^2 + 22*w - 2]', '[2055, 2055, w^3 - 2*w^2 - 8*w + 6]', '[2057, 2057, -w^3 + 2*w^2 + 5*w - 8]', '[2057, 2057, -6*w^3 + 11*w^2 + 34*w - 5]', '[2059, 2059, w^2 - w - 11]', '[2059, 2059, 4*w^3 - 7*w^2 - 25*w - 1]', '[2063, 2063, -3*w^3 + 6*w^2 + 19*w]', '[2063, 2063, w^3 - 12*w - 2]', '[2064, 258, 2*w^3 - 20*w - 12]', '[2069, 2069, -w^3 + 3*w^2 - 6]', '[2081, 2081, -5*w^3 + 6*w^2 + 31*w + 6]', '[2083, 2083, -w^3 - 2*w^2 + 11*w + 18]', '[2087, 2087, -2*w^3 + w^2 + 18*w + 9]', '[2087, 2087, w^3 + 2*w^2 - 11*w - 8]', '[2089, 2089, 4*w^3 - 8*w^2 - 18*w - 3]', '[2089, 2089, 3*w^2 - 8]', '[2095, 2095, -9*w^3 + 16*w^2 + 48*w - 18]', '[2095, 2095, w^3 - 4*w^2 - 2*w + 7]', '[2096, 262, 10*w^3 - 16*w^2 - 56*w + 10]', '[2096, 262, 10*w^3 - 18*w^2 - 54*w + 18]', '[2097, 2097, 5*w^3 - 9*w^2 - 24*w - 8]', '[2097, 2097, -2*w^3 + w^2 + 14*w + 5]', '[2101, 2101, -2*w^3 + 4*w^2 + 13*w - 7]', '[2101, 2101, 6*w^3 - 11*w^2 - 37*w + 7]', '[2103, 2103, -4*w^3 + 2*w^2 + 33*w + 20]', '[2105, 2105, w^3 - w^2 - 7*w + 5]', '[2105, 2105, -5*w^3 + 7*w^2 + 25*w - 8]', '[2105, 2105, -3*w^3 + 8*w^2 + 17*w - 12]', '[2105, 2105, -6*w^3 + 9*w^2 + 35*w - 3]', '[2119, 2119, 4*w^3 - 15*w^2 + 2*w + 10]', '[2119, 2119, 5*w^3 - 7*w^2 - 30*w]', '[2123, 2123, -7*w^3 + 16*w^2 + 25*w - 5]', '[2123, 2123, w^3 - 4*w^2 - 3*w + 10]', '[2125, 85, -3*w^3 + 7*w^2 + 15*w - 6]', '[2125, 85, w^3 - 4*w^2 - 5*w + 7]', '[2125, 2125, -3*w^3 + 7*w^2 + 14*w - 7]', '[2125, 2125, -2*w^3 + w^2 + 16*w + 5]', '[2127, 2127, -2*w^3 + 3*w^2 + 8*w + 6]', '[2127, 2127, 4*w^3 - 7*w^2 - 18*w - 12]', '[2129, 2129, 3*w^3 - 3*w^2 - 21*w - 4]', '[2129, 2129, 5*w^3 - 6*w^2 - 31*w - 11]', '[2137, 2137, -3*w^3 + 4*w^2 + 17*w + 13]', '[2137, 2137, -3*w^3 + 7*w^2 + 14*w - 8]', '[2139, 2139, 5*w^3 - 10*w^2 - 22*w - 3]', '[2139, 2139, -w^3 + 4*w^2 + 2*w - 8]', '[2139, 2139, -w^3 + 6*w^2 - 7*w - 4]', '[2139, 2139, w^3 - w^2 - 11*w - 4]', '[2141, 2141, w^3 - w^2 - w - 3]', '[2143, 2143, 9*w^3 - 16*w^2 - 50*w + 16]', '[2143, 2143, -3*w^3 + 26*w + 21]', '[2145, 2145, -5*w^3 + 7*w^2 + 32*w + 8]', '[2151, 2151, w^3 - w^2 - 5*w + 5]', '[2153, 2153, 4*w^3 - 7*w^2 - 21*w - 4]', '[2155, 2155, -3*w^3 + 5*w^2 + 21*w - 3]', '[2160, 30, 4*w^3 - 6*w^2 - 22*w - 4]', '[2160, 270, 2*w^3 - 6*w^2 - 6*w + 10]', '[2161, 2161, -5*w^2 + 14*w + 11]', '[2161, 2161, -w^3 + 4*w^2 + 4*w - 9]', '[2165, 2165, -7*w^3 + 11*w^2 + 37*w - 7]', '[2167, 2167, 6*w^3 - 9*w^2 - 38*w - 3]', '[2171, 2171, -5*w^3 + 9*w^2 + 24*w + 9]', '[2171, 2171, -3*w^3 + 3*w^2 + 18*w + 14]', '[2175, 2175, -w^3 - w^2 + 14*w + 9]', '[2179, 2179, -w^2 + w - 4]', '[2187, 9, -6*w^3 + 9*w^2 + 33*w - 3]', '[2187, 81, -6*w^3 + 12*w^2 + 33*w - 12]', '[2187, 2187, 3*w^3 - 3*w^2 - 17*w - 1]', '[2192, 274, -4*w^3 + 6*w^2 + 22*w + 2]', '[2192, 274, 2*w^3 - 6*w^2 - 12*w + 8]', '[2193, 2193, w^3 - w^2 - 10*w - 11]', '[2193, 2193, -3*w^3 + 6*w^2 + 20*w + 1]', '[2197, 13, 2*w^3 + 3*w^2 - 26*w - 19]', '[2197, 2197, -3*w^2 + 8*w + 2]', '[2199, 2199, -5*w^3 + 17*w^2 + 3*w - 12]', '[2199, 2199, 3*w^2 - 5*w - 13]', '[2201, 2201, w^3 - 3*w^2 - 5*w - 4]', '[2201, 2201, -4*w^3 + 9*w^2 + 21*w - 13]', '[2201, 2201, w^3 - 3*w + 4]', '[2201, 2201, 2*w^3 + w^2 - 20*w - 21]', '[2201, 2201, -4*w^3 + 6*w^2 + 21*w - 1]', '[2201, 2201, -3*w + 7]', '[2201, 2201, -w^3 + 5*w^2 + 2*w - 4]', '[2201, 2201, -10*w^3 + 14*w^2 + 63*w + 9]', '[2203, 2203, -4*w^3 + 9*w^2 + 20*w - 6]', '[2207, 2207, -5*w^3 + 9*w^2 + 25*w - 12]', '[2207, 2207, 7*w^3 - 10*w^2 - 41*w]', '[2213, 2213, -4*w^3 + 5*w^2 + 22*w + 2]', '[2215, 2215, -3*w^2 + 8*w + 11]', '[2215, 2215, -2*w^2 + w + 11]', '[2217, 2217, -w^3 - w^2 + 12*w + 14]', '[2217, 2217, -7*w^3 + 16*w^2 + 23*w + 7]', '[2221, 2221, -3*w^3 + 8*w^2 + 12*w - 16]', '[2225, 2225, 6*w^3 - 12*w^2 - 33*w + 16]', '[2227, 2227, 5*w^3 - 9*w^2 - 30*w + 2]', '[2227, 2227, -7*w^3 + 13*w^2 + 39*w - 7]', '[2227, 2227, 3*w^3 - 7*w^2 - 16*w + 13]', '[2227, 2227, -6*w^3 + 11*w^2 + 35*w - 12]', '[2229, 2229, -6*w^3 + 17*w^2 + 12*w - 8]', '[2231, 2231, 5*w^3 - 6*w^2 - 27*w - 1]', '[2237, 2237, -3*w^3 + 5*w^2 + 21*w + 6]', '[2237, 2237, 3*w^3 - 4*w^2 - 13*w - 5]', '[2239, 2239, -5*w^3 + 11*w^2 + 29*w - 13]', '[2251, 2251, -5*w^3 + 8*w^2 + 25*w + 15]', '[2269, 2269, 5*w^3 - 7*w^2 - 33*w - 9]', '[2271, 2271, -4*w^3 + 9*w^2 + 18*w - 8]', '[2271, 2271, -4*w^3 + 13*w^2 + 3*w - 9]', '[2277, 2277, 4*w^3 - 6*w^2 - 22*w - 3]', '[2281, 2281, -6*w^3 + 10*w^2 + 32*w - 5]', '[2283, 2283, -4*w^3 + 3*w^2 + 30*w + 13]', '[2283, 2283, w^3 + 2*w^2 - 16*w - 8]', '[2287, 2287, 7*w^3 - 9*w^2 - 41*w - 21]', '[2287, 2287, w^3 + 4*w^2 - 19*w - 15]', '[2288, 286, 2*w^3 - 4*w^2 - 16*w - 2]', '[2293, 2293, -4*w^3 + 7*w^2 + 23*w - 10]', '[2295, 255, w^3 - 6*w^2 + 8*w + 5]', '[2295, 255, 2*w^3 - 20*w - 11]', '[2295, 2295, -6*w^3 + 9*w^2 + 34*w - 1]', '[2295, 2295, -3*w^3 + 5*w^2 + 14*w + 11]', '[2304, 36, 4*w - 4]', '[2305, 2305, -6*w^3 + 10*w^2 + 32*w - 11]', '[2305, 2305, -3*w^2 + 7*w + 13]', '[2307, 2307, 4*w^2 - 9*w - 16]', '[2307, 2307, 2*w^3 - w^2 - 18*w - 7]', '[2320, 290, -2*w^2 + 8*w + 2]', '[2321, 2321, -3*w^3 + 5*w^2 + 18*w + 5]', '[2325, 2325, -w^3 + 6*w^2 - 5*w - 6]', '[2325, 2325, 5*w^3 - 7*w^2 - 31*w]', '[2325, 2325, 5*w^3 - 9*w^2 - 28*w + 2]', '[2325, 2325, -3*w^3 + 8*w^2 + 7*w + 3]', '[2327, 2327, -6*w^3 + 13*w^2 + 22*w + 3]', '[2329, 2329, 3*w + 8]', '[2329, 2329, 3*w^2 - 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6]', '[4497, 4497, -2*w^3 + 6*w^2 + 7*w - 8]', '[4507, 4507, -3*w^3 + 7*w^2 + 10*w - 7]', '[4509, 501, 5*w^3 - 6*w^2 - 29*w - 2]', '[4509, 501, -5*w^3 + 9*w^2 + 23*w - 16]', '[4509, 4509, 3*w^3 - 7*w^2 - 17*w + 12]', '[4509, 4509, -10*w^3 + 17*w^2 + 60*w - 4]', '[4511, 4511, -5*w^3 + 10*w^2 + 20*w + 3]', '[4513, 4513, w^3 - 8*w - 15]', '[4513, 4513, 3*w^3 - 3*w^2 - 24*w - 11]', '[4521, 4521, -8*w^3 + 15*w^2 + 42*w - 16]', '[4521, 4521, -2*w^3 + 7*w^2 + 4*w - 6]', '[4525, 4525, -14*w^3 + 24*w^2 + 78*w - 15]', '[4527, 4527, -2*w^3 + 6*w^2 + 5]', '[4528, 566, -6*w^3 + 10*w^2 + 32*w + 2]', '[4528, 566, -6*w^2 + 14*w + 18]', '[4528, 566, 8*w^3 - 12*w^2 - 44*w - 22]', '[4528, 566, 6*w^3 - 8*w^2 - 36*w - 8]', '[4531, 4531, -2*w^3 + w^2 + 16*w + 2]', '[4533, 4533, -8*w^3 + 19*w^2 + 25*w + 6]', '[4535, 4535, 8*w^3 - 13*w^2 - 44*w + 6]', '[4537, 4537, 5*w^3 - 10*w^2 - 28*w + 4]', '[4537, 4537, 4*w^3 - 7*w^2 - 21*w + 11]', '[4539, 4539, 5*w^3 - 3*w^2 - 40*w - 22]', '[4539, 4539, -w^3 - 3*w^2 + 19*w + 9]', '[4547, 4547, -6*w^3 + 13*w^2 + 31*w - 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125*w + 23]', '[5157, 5157, 3*w^3 - 3*w^2 - 20*w + 2]', '[5161, 5161, -2*w^2 + 9*w + 3]', '[5163, 5163, 2*w^3 - w^2 - 11*w - 11]', '[5165, 5165, 7*w^3 - 12*w^2 - 35*w + 17]', '[5165, 5165, 12*w^3 - 19*w^2 - 69*w + 8]', '[5167, 5167, -4*w^3 + 4*w^2 + 26*w + 21]', '[5169, 5169, -5*w^3 + 18*w^2 - 16]', '[5169, 5169, 4*w^2 - 10*w - 15]', '[5175, 5175, -3*w^3 + 3*w^2 + 19*w - 1]', '[5177, 5177, 2*w^3 - 6*w^2 - 8*w + 11]', '[5177, 5177, -2*w^3 + 3*w^2 + 17*w + 4]', '[5177, 5177, w^3 + 2*w^2 - 10*w - 13]', '[5177, 5177, w^3 + w^2 - 15*w - 9]', '[5177, 5177, w^3 - 2*w^2 - 7*w - 8]', '[5177, 5177, 4*w^3 - 7*w^2 - 16*w - 4]', '[5177, 5177, -7*w^3 + 11*w^2 + 44*w + 1]', '[5177, 5177, w^3 - 5*w^2 - 5*w + 11]', '[5179, 5179, 6*w^3 - 10*w^2 - 31*w - 12]', '[5179, 5179, -7*w^3 + 10*w^2 + 38*w + 18]', '[5181, 5181, -7*w^3 + 19*w^2 + 18*w - 9]', '[5181, 5181, -5*w^3 + 12*w^2 + 22*w - 23]', '[5189, 5189, -4*w^3 + 7*w^2 + 22*w - 11]', '[5189, 5189, w^3 - 2*w^2 - 2*w + 11]', '[5191, 5191, -5*w^3 + 11*w^2 + 25*w - 15]', '[5193, 5193, -7*w^3 + 14*w^2 + 35*w - 6]', '[5195, 5195, 6*w^3 - 10*w^2 - 36*w - 1]', '[5195, 5195, -7*w^3 + 12*w^2 + 41*w - 14]', '[5199, 5199, 6*w^3 - 12*w^2 - 25*w - 11]', '[5199, 5199, 7*w^3 - 17*w^2 - 19*w - 4]', '[5200, 650, -2*w^3 + 4*w^2 + 6*w - 12]', '[5203, 5203, 3*w^3 - 25*w - 16]', '[5205, 5205, 2*w^3 - w^2 - 16*w]', '[5209, 5209, -5*w^3 + 11*w^2 + 34*w - 6]', '[5209, 5209, 2*w^3 + w^2 - 24*w - 19]', '[5211, 579, 4*w^3 - 6*w^2 - 25*w - 10]', '[5211, 579, 14*w^3 - 24*w^2 - 77*w + 16]', '[5211, 5211, -3*w^2 + 8*w + 13]', '[5211, 5211, 18*w^3 - 33*w^2 - 100*w + 25]', '[5213, 5213, -8*w^3 + 15*w^2 + 36*w + 16]', '[5219, 5219, -w^3 - 3*w^2 + 19*w + 14]', '[5219, 5219, -4*w^3 + 14*w^2 - w - 8]', '[5227, 5227, -4*w^3 + 5*w^2 + 26*w - 2]', '[5231, 5231, 7*w^3 - 9*w^2 - 43*w - 11]', '[5232, 654, -2*w^3 + 8*w^2 - 12]', '[5233, 5233, 3*w^3 - 2*w^2 - 20*w - 7]', '[5235, 5235, -2*w^3 + 9*w^2 - 5*w - 5]', '[5235, 5235, -13*w^3 + 22*w^2 + 70*w - 19]', '[5237, 5237, 3*w^3 - 5*w^2 - 12*w - 8]', '[5239, 5239, -5*w^3 + 11*w^2 + 26*w - 15]', '[5239, 5239, w^3 - 5*w^2 + 14]', '[5239, 5239, -5*w^3 + 8*w^2 + 32*w + 5]', '[5239, 5239, -w + 9]', '[5245, 5245, 9*w^3 - 15*w^2 - 55*w + 3]', '[5245, 5245, -10*w^3 + 19*w^2 + 58*w - 17]', '[5249, 5249, -3*w^3 + 8*w^2 + 11*w - 8]', '[5253, 5253, w^3 - 3*w^2 - 8*w + 7]', '[5253, 5253, -2*w^3 + w^2 + 15*w + 1]', '[5253, 5253, 4*w^3 - 5*w^2 - 22*w - 7]', '[5253, 5253, -5*w^3 + 11*w^2 + 26*w - 8]', '[5255, 5255, -17*w^3 + 32*w^2 + 99*w - 25]', '[5255, 5255, 4*w^3 - 8*w^2 - 29*w - 2]', '[5259, 5259, -6*w^3 + 15*w^2 + 16*w + 5]', '[5265, 195, 3*w^3 - 3*w^2 - 21*w]', '[5265, 5265, -6*w^3 + 7*w^2 + 37*w + 16]', '[5269, 5269, -w^3 + 5*w + 10]', '[5269, 5269, w^3 - 3*w^2 + w - 9]', '[5273, 5273, -13*w^3 + 22*w^2 + 70*w - 18]', '[5275, 5275, -w^3 + 9*w + 15]', '[5279, 5279, -4*w^3 + 10*w^2 + 23*w - 15]', '[5279, 5279, 4*w^3 - 5*w^2 - 18*w - 10]', '[5281, 5281, 13*w^3 - 25*w^2 - 74*w + 22]', '[5281, 5281, -6*w^3 + 10*w^2 + 32*w + 1]', '[5283, 5283, 7*w^3 - 15*w^2 - 27*w - 1]', '[5287, 5287, 2*w^3 - 3*w^2 - 16*w + 10]', '[5287, 5287, 6*w^3 - 14*w^2 - 17*w - 4]', '[5287, 5287, 2*w^2 - w - 15]', '[5287, 5287, -5*w^3 + 7*w^2 + 25*w + 14]', '[5291, 5291, w^3 - 4*w^2 - 7*w + 9]', '[5297, 5297, 4*w^3 - 5*w^2 - 22*w - 6]', '[5303, 5303, 5*w^3 - 2*w^2 - 41*w - 24]', '[5303, 5303, 3*w^3 - 6*w^2 - 19*w + 9]', '[5315, 5315, -5*w^3 + 12*w^2 + 31*w - 10]', '[5319, 591, -2*w^3 + 14*w + 17]', '[5319, 5319, 5*w^3 - 5*w^2 - 34*w - 11]', '[5325, 5325, 4*w^3 - 10*w^2 - 17*w + 17]', '[5325, 5325, 4*w^3 - 3*w^2 - 20*w - 5]', '[5328, 666, -2*w^3 + 2*w^2 + 18*w]', '[5331, 5331, 5*w^3 - 8*w^2 - 28*w - 8]', '[5331, 5331, -5*w^3 + 7*w^2 + 28*w + 9]', '[5331, 5331, 5*w^2 - 11*w - 15]', '[5331, 5331, -6*w^3 + 13*w^2 + 22*w + 1]', '[5335, 5335, 2*w^3 - 3*w^2 - 5*w + 11]', '[5337, 5337, -4*w^3 + 17*w^2 - 7*w - 15]', '[5337, 5337, 9*w^3 - 15*w^2 - 43*w - 23]', '[5343, 5343, 4*w^3 - 8*w^2 - 17*w - 9]', '[5343, 5343, -4*w^3 + 5*w^2 + 25*w - 2]', '[5345, 5345, -11*w^3 + 20*w^2 + 66*w - 14]', '[5347, 5347, -2*w^3 + 6*w^2 + 10*w - 9]', '[5347, 5347, -8*w^3 + 15*w^2 + 47*w - 14]', '[5349, 5349, 11*w^3 - 32*w^2 - 20*w + 11]', '[5351, 5351, 6*w^3 - 7*w^2 - 36*w - 6]', '[5357, 5357, -5*w^3 + 9*w^2 + 28*w]', '[5357, 5357, -7*w^3 + 11*w^2 + 41*w - 11]', '[5359, 5359, 3*w^3 - 20*w - 20]', '[5359, 5359, -3*w^3 + 3*w^2 + 24*w + 2]', '[5365, 5365, w^3 - 3*w^2 + 2*w - 5]', '[5375, 215, -4*w^3 + w^2 + 35*w + 27]', '[5375, 5375, -7*w^3 + 7*w^2 + 44*w + 15]', '[5379, 5379, -w^3 + 2*w^2 + 9*w - 7]', '[5379, 5379, -4*w^3 + 5*w^2 + 29*w]', '[5381, 5381, -6*w^3 + 7*w^2 + 37*w + 12]', '[5381, 5381, -3*w^3 + 8*w^2 + 11*w - 9]', '[5381, 5381, 5*w^3 - 7*w^2 - 29*w + 8]', '[5381, 5381, 4*w^3 - w^2 - 36*w - 23]', '[5403, 5403, -2*w^3 + 16*w^2 - 22*w - 31]', '[5407, 5407, 11*w^3 - 21*w^2 - 65*w + 17]', '[5419, 5419, 2*w^2 - 7*w - 11]', '[5423, 5423, -w^3 - 3*w^2 + 17*w + 18]', '[5423, 5423, 2*w^3 - w^2 - 19*w - 5]', '[5424, 678, 6*w^3 - 10*w^2 - 28*w - 16]', '[5433, 5433, -5*w^3 + 20*w^2 - 4*w - 23]', '[5433, 5433, -2*w^3 + 6*w^2 + 9*w - 7]', '[5435, 5435, 15*w^3 - 28*w^2 - 85*w + 22]', '[5441, 5441, -w^3 - 2*w^2 + 9*w + 19]', '[5443, 5443, -3*w^3 + 7*w^2 + 19*w - 9]', '[5445, 5445, w^3 - 4*w^2 + w + 11]', '[5447, 5447, -6*w^3 + 5*w^2 + 43*w + 20]', '[5447, 5447, -4*w^3 + 6*w^2 + 20*w + 1]', '[5456, 682, 4*w^3 - 4*w^2 - 28*w - 6]', '[5456, 682, -2*w^3 - 2*w^2 + 24*w + 14]', '[5456, 682, -6*w^3 + 12*w^2 + 26*w + 6]', '[5456, 682, -2*w^3 + 2*w^2 + 14*w + 14]', '[5473, 5473, 5*w^3 - 8*w^2 - 25*w - 16]', '[5473, 5473, -7*w^3 + 8*w^2 + 46*w + 24]', '[5473, 5473, -3*w^3 + 5*w^2 + 22*w - 2]', '[5473, 5473, -w^3 - 2*w^2 + 13*w + 7]', '[5477, 5477, -2*w^3 + 5*w^2 + 6*w - 10]', '[5479, 5479, -7*w^3 + 9*w^2 + 43*w + 20]', '[5483, 5483, -3*w^3 + 6*w^2 + 22*w - 2]', '[5483, 5483, -5*w^3 + 8*w^2 + 26*w - 1]', '[5485, 5485, w^3 - w^2 - 3*w - 8]', '[5485, 5485, -7*w^3 + 13*w^2 + 36*w - 13]', '[5489, 5489, -3*w^3 + 3*w^2 + 21*w - 1]', '[5497, 5497, 4*w^3 - 7*w^2 - 29*w - 5]', '[5503, 5503, 5*w^3 - 7*w^2 - 24*w - 11]', '[5503, 5503, -5*w^3 + 7*w^2 + 27*w + 11]', '[5507, 5507, 7*w^3 - 12*w^2 - 35*w - 12]', '[5507, 5507, 8*w^3 - 13*w^2 - 43*w + 7]', '[5511, 5511, -6*w^3 + 9*w^2 + 34*w + 2]', '[5511, 5511, 5*w^3 - 10*w^2 - 25*w + 18]', '[5517, 5517, 2*w^3 - 5*w^2 - 3*w + 6]', '[5517, 5517, 2*w^2 - 11]', '[5519, 5519, 4*w^3 - 6*w^2 - 26*w - 9]', '[5519, 5519, 7*w^3 - 10*w^2 - 39*w + 5]', '[5520, 690, 2*w^3 - 6*w^2 - 10*w + 8]', '[5525, 5525, -w^2 - 2*w + 8]', '[5525, 5525, 6*w^3 - 10*w^2 - 31*w + 4]', '[5533, 5533, -9*w^3 + 21*w^2 + 30*w - 1]', '[5539, 5539, -4*w^3 + 8*w^2 + 21*w]', '[5539, 5539, -16*w^3 + 27*w^2 + 94*w - 10]', '[5541, 5541, -w^3 + 10*w^2 - 16*w - 17]', '[5541, 5541, 5*w^3 - 11*w^2 - 20*w - 4]', '[5545, 5545, 6*w^3 - 10*w^2 - 32*w + 1]', '[5547, 5547, -7*w^3 + 7*w^2 + 45*w + 24]', '[5549, 5549, -3*w^3 + 3*w^2 + 20*w]', '[5549, 5549, 5*w^3 - 12*w^2 - 18*w]', '[5549, 5549, 6*w^3 - 12*w^2 - 29*w + 12]', '[5549, 5549, 4*w^2 - 10*w - 5]', '[5552, 694, -2*w^3 + 6*w^2 + 8*w - 8]', '[5557, 5557, 5*w^3 - 11*w^2 - 27*w + 5]', '[5557, 5557, 11*w^3 - 18*w^2 - 66*w + 2]', '[5559, 5559, 5*w^3 - 7*w^2 - 28*w - 3]', '[5559, 5559, 5*w^3 - 10*w^2 - 30*w + 11]', '[5563, 5563, 2*w^3 - 5*w^2 - 18*w - 2]', '[5569, 5569, -3*w^3 + 2*w^2 + 17*w + 3]', '[5571, 5571, -7*w^3 + 13*w^2 + 32*w + 7]', '[5571, 5571, 4*w^3 - 8*w^2 - 24*w + 1]', '[5571, 5571, 5*w^3 - 8*w^2 - 24*w - 18]', '[5571, 5571, 5*w^3 - 10*w^2 - 21*w - 10]', '[5577, 5577, 2*w^3 - 5*w^2 - 6*w + 15]', '[5581, 5581, -3*w^3 + w^2 + 25*w + 12]', '[5583, 5583, -2*w^3 + 9*w^2 - 4*w - 6]', '[5583, 5583, -4*w^3 + 7*w^2 + 24*w + 3]', '[5584, 698, 12*w^3 - 22*w^2 - 72*w + 12]', '[5584, 698, -2*w^3 + 8*w^2 - 10]', '[5585, 5585, -3*w^3 + 4*w^2 + 15*w + 13]', '[5589, 207, -3*w^2 + 9*w + 12]', '[5589, 5589, 5*w^3 - 9*w^2 - 25*w - 7]', '[5597, 5597, 5*w^3 - 5*w^2 - 31*w - 22]', '[5597, 5597, -11*w^3 + 19*w^2 + 63*w - 18]', '[5599, 5599, -5*w^2 + 10*w + 9]', '[5601, 5601, 5*w^3 - 21*w^2 + 7*w + 24]', '[5603, 5603, 9*w^3 - 23*w^2 - 22*w - 2]', '[5611, 5611, 5*w^3 - 12*w^2 - 16*w + 7]', '[5611, 5611, 2*w^3 - 3*w^2 - 8*w - 10]', '[5611, 5611, -5*w^3 + 8*w^2 + 27*w - 10]', '[5611, 5611, -9*w^3 + 14*w^2 + 52*w - 1]', '[5613, 5613, -2*w^3 + 7*w^2 + 2*w - 13]', '[5613, 5613, w^3 - 6*w^2 + 5*w + 3]', '[5615, 5615, -7*w^3 + 16*w^2 + 43*w - 14]', '[5615, 5615, -7*w^3 + 12*w^2 + 39*w]', '[5616, 78, -2*w^3 + 6*w^2 + 8*w - 10]', '[5616, 702, -6*w^3 + 10*w^2 + 32*w]', '[5619, 5619, -3*w^3 + 12*w^2 - 5*w - 10]', '[5623, 5623, 8*w^3 - 12*w^2 - 44*w - 19]', '[5625, 45, -5*w + 5]', '[5625, 5625, 5*w^3 - 8*w^2 - 25*w - 8]', '[5629, 5629, -3*w^3 + 9*w^2 + 4*w - 8]', '[5633, 5633, 2*w^3 - w^2 - 19*w - 8]', '[5633, 5633, -w^3 + 5*w^2 + w - 7]', '[5639, 5639, -4*w^3 + 7*w^2 + 27*w - 1]', '[5645, 5645, -w^3 - 2*w^2 + 14*w + 18]', '[5647, 5647, 3*w^3 - 3*w^2 - 20*w + 1]', '[5651, 5651, 6*w^3 - 7*w^2 - 39*w - 9]', '[5651, 5651, 2*w^3 - 3*w^2 - 12*w + 8]', '[5653, 5653, 6*w^3 - 12*w^2 - 23*w - 6]', '[5655, 5655, -3*w^3 + 8*w^2 + 9*w - 11]', '[5659, 5659, -9*w^3 + 19*w^2 + 54*w - 15]', '[5661, 5661, 5*w^3 - 9*w^2 - 21*w - 11]', '[5661, 5661, -5*w^3 + 10*w^2 + 20*w + 2]', '[5665, 5665, -3*w^3 + 4*w^2 + 23*w + 7]', '[5665, 5665, 4*w^3 - 8*w^2 - 23*w + 1]', '[5669, 5669, -5*w^3 + 11*w^2 + 20*w + 3]', '[5679, 5679, -2*w^3 + 4*w^2 + 17*w - 1]', '[5679, 5679, 4*w^3 - 6*w^2 - 20*w - 5]', '[5680, 710, -8*w^3 + 10*w^2 + 52*w + 10]', '[5680, 710, 6*w^3 - 8*w^2 - 30*w + 4]', '[5683, 5683, 3*w^3 - 2*w^2 - 23*w - 7]', '[5683, 5683, -5*w^3 + 8*w^2 + 31*w - 11]', '[5689, 5689, w^3 + 5*w^2 - 21*w - 17]', '[5697, 633, 7*w^3 - 12*w^2 - 46*w - 4]', '[5697, 5697, 5*w^3 - 10*w^2 - 23*w + 19]', '[5701, 5701, 8*w^3 - 15*w^2 - 46*w + 16]', '[5713, 5713, -w^3 + 3*w^2 - w - 8]', '[5717, 5717, -4*w^3 + 2*w^2 + 34*w + 15]', '[5731, 5731, 4*w^3 - 11*w^2 - 8*w + 7]', '[5735, 5735, -9*w^3 + 14*w^2 + 54*w + 3]', '[5735, 5735, 2*w^3 + w^2 - 24*w - 7]', '[5735, 5735, -7*w^3 + 10*w^2 + 43*w]', '[5735, 5735, -2*w^3 + 8*w^2 - 11]', '[5737, 5737, -w^3 + 3*w^2 - 13]', '[5737, 5737, 3*w^2 - 7*w - 16]', '[5739, 5739, -3*w^3 + 8*w^2 + 13*w - 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9*w^2 - 34*w - 13]', '[5797, 5797, -2*w^3 + 9*w^2 - 3*w - 12]', '[5797, 5797, 4*w^3 - 7*w^2 - 27*w + 2]', '[5797, 5797, -w^3 - w^2 + 7*w + 14]', '[5797, 5797, -w^3 + 6*w^2 - 9*w - 9]', '[5797, 5797, w^3 - 3*w^2 + 10]', '[5797, 5797, -4*w^2 + 11*w + 3]', '[5797, 5797, 6*w^3 - 9*w^2 - 33*w + 1]', '[5799, 5799, -3*w^3 + 11*w^2 - 3*w - 8]', '[5801, 5801, -7*w^3 + 10*w^2 + 40*w - 3]', '[5805, 645, -5*w^3 + 6*w^2 + 35*w + 11]', '[5805, 5805, 2*w^2 - 3*w - 17]', '[5807, 5807, -3*w^3 - w^2 + 30*w + 26]', '[5808, 726, -4*w^3 + 4*w^2 + 30*w + 12]', '[5809, 5809, 5*w^3 - 10*w^2 - 24*w]', '[5809, 5809, 3*w^3 - 5*w^2 - 22*w - 2]', '[5819, 5819, -10*w^3 + 16*w^2 + 58*w - 9]', '[5825, 5825, -11*w^3 + 18*w^2 + 62*w - 8]', '[5825, 5825, -4*w^3 + 3*w^2 + 29*w + 12]', '[5827, 5827, -3*w^3 + 2*w^2 + 26*w]', '[5835, 5835, 4*w^3 - 9*w^2 - 17*w - 2]', '[5843, 5843, 5*w^3 - 8*w^2 - 26*w - 5]', '[5847, 5847, 2*w^3 - w^2 - 19*w - 6]', '[5847, 5847, 5*w^3 - 9*w^2 - 21*w - 14]', '[5849, 5849, w^3 - 2*w^2 - 5*w - 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17]', '[9959, 9959, 2*w^3 - 7*w^2 - 12*w + 9]', '[9965, 9965, -20*w^3 + 37*w^2 + 112*w - 32]', '[9969, 9969, 7*w^3 - 15*w^2 - 24*w - 10]', '[9973, 9973, -6*w^3 + 13*w^2 + 32*w - 10]', '[9973, 9973, w^2 - w - 14]', '[9977, 9977, -2*w^3 + 5*w^2 + 2*w + 6]', '[9979, 9979, -10*w^3 + 34*w^2 + 3*w - 16]', '[9979, 9979, -w^3 - 9*w^2 + 33*w + 26]', '[9981, 9981, -7*w^3 + 15*w^2 + 26*w + 2]', '[9984, 156, 4*w^3 - 8*w^2 - 16*w + 8]', '[9985, 9985, -4*w^3 + 8*w^2 + 21*w + 3]', '[9987, 9987, -4*w^3 + 11*w^2 + 10*w - 11]', '[9987, 9987, 6*w^3 - 10*w^2 - 30*w - 17]', '[9991, 9991, -6*w^3 + 10*w^2 + 37*w + 3]', '[9991, 9991, -7*w^3 + 12*w^2 + 44*w - 6]', '[9993, 9993, 8*w^3 - 16*w^2 - 34*w - 9]', '[9993, 9993, -3*w^3 + 11*w^2 - 14]', '[9995, 9995, -9*w^3 + 16*w^2 + 47*w - 16]', '[9995, 9995, -3*w^3 + 2*w^2 + 25*w + 1]', '[9997, 9997, -6*w^3 + 9*w^2 + 33*w + 7]', '[9997, 9997, -2*w^3 + w^2 + 12*w + 21]', '[10000, 10, 10]', '[10000, 1250, -2*w^3 + 6*w^2 - 8]'], 'label': '4.4.17989.1', 'narrow_class_no': 1, 'primes': ['[3, 3, -w^3 + 2*w^2 + 4*w + 1]', '[5, 5, w^3 - 2*w^2 - 6*w + 2]', '[11, 11, w^3 - 2*w^2 - 4*w]', '[13, 13, w^2 - 3*w - 2]', '[16, 2, 2]', '[17, 17, -w^3 + 3*w^2 + 2*w - 2]', '[17, 17, -w^2 + 2*w + 3]', '[23, 23, -w^3 + w^2 + 6*w + 1]', '[27, 3, -2*w^3 + 3*w^2 + 11*w - 1]', '[29, 29, w^3 - 2*w^2 - 5*w + 4]', '[31, 31, -w^3 + 2*w^2 + 6*w - 3]', '[31, 31, -w^3 + 2*w^2 + 5*w + 1]', '[31, 31, w^3 - 2*w^2 - 6*w]', '[31, 31, -w^2 + 2*w + 1]', '[37, 37, w^3 - w^2 - 7*w - 1]', '[43, 43, w^2 - w - 4]', '[71, 71, w^3 - 2*w^2 - 6*w - 1]', '[71, 71, 5*w^3 - 8*w^2 - 29*w + 3]', '[89, 89, -2*w^3 + 4*w^2 + 10*w - 7]', '[97, 97, -w^3 + 2*w^2 + 4*w - 4]', '[103, 103, w^3 - w^2 - 8*w - 2]', '[103, 103, -2*w^3 + 4*w^2 + 10*w - 1]', '[109, 109, 2*w^3 - 3*w^2 - 13*w]', '[113, 113, 2*w^3 - 3*w^2 - 12*w - 3]', '[125, 5, 2*w^3 - 3*w^2 - 10*w + 4]', '[131, 131, 5*w^3 - 8*w^2 - 28*w + 5]', '[131, 131, 5*w^3 - 9*w^2 - 27*w + 9]', '[137, 137, -2*w^3 + 3*w^2 + 11*w + 1]', '[137, 137, w^3 - 3*w^2 - 6*w + 4]', '[157, 157, -3*w^3 + 4*w^2 + 18*w + 6]', '[157, 157, 3*w^3 - 6*w^2 - 16*w + 6]', '[163, 163, 4*w^3 - 8*w^2 - 23*w + 8]', '[163, 163, w^3 - 2*w^2 - 3*w - 3]', '[167, 167, w^2 - 3*w - 5]', '[167, 167, 2*w^3 - 2*w^2 - 13*w - 4]', '[179, 179, -w^3 + 3*w^2 + 3*w - 4]', '[181, 181, 5*w^3 - 9*w^2 - 29*w + 5]', '[191, 191, -3*w^3 + 5*w^2 + 18*w]', '[191, 191, 4*w^3 - 8*w^2 - 23*w + 7]', '[193, 193, 3*w^3 - 4*w^2 - 20*w - 5]', '[193, 193, -w^3 + w^2 + 8*w - 3]', '[197, 197, -3*w^3 + 4*w^2 + 18*w + 9]', '[211, 211, w^3 - 7*w - 8]', '[233, 233, 2*w^3 - 2*w^2 - 15*w - 7]', '[233, 233, 4*w^3 - 7*w^2 - 24*w + 2]', '[239, 239, w^2 - 5]', '[263, 263, w^2 - 3*w - 6]', '[269, 269, w^3 - 2*w^2 - 4*w + 6]', '[271, 271, 4*w^3 - 6*w^2 - 23*w + 2]', '[277, 277, -w^3 + 3*w^2 + 2*w - 5]', '[277, 277, 3*w^3 - 4*w^2 - 17*w - 1]', '[277, 277, -3*w^3 + 5*w^2 + 17*w + 1]', '[277, 277, -2*w^3 + w^2 + 17*w + 6]', '[281, 281, 2*w - 3]', '[283, 283, -3*w^3 + 5*w^2 + 16*w + 1]', '[283, 283, -3*w^2 + 7*w + 9]', '[283, 283, 4*w^3 - 6*w^2 - 22*w - 11]', '[283, 283, 3*w^3 - 4*w^2 - 18*w - 4]', '[289, 17, 3*w^3 - 6*w^2 - 13*w]', '[293, 293, -w^3 + 3*w^2 + 5*w - 5]', '[293, 293, 3*w^3 - 4*w^2 - 18*w - 1]', '[307, 307, 2*w^3 - 3*w^2 - 10*w - 3]', '[311, 311, -3*w^3 + 6*w^2 + 15*w - 8]', '[311, 311, -w^2 + 4*w + 5]', '[347, 347, -w^3 + 3*w^2 + 4*w - 4]', '[349, 349, 6*w^3 - 11*w^2 - 36*w + 6]', '[349, 349, -w^3 + 4*w^2 - 5]', '[383, 383, -2*w^3 + 3*w^2 + 10*w + 2]', '[383, 383, 2*w^3 - 2*w^2 - 13*w - 3]', '[389, 389, w^3 - 2*w^2 - 5*w - 4]', '[397, 397, -w^3 + w^2 + 5*w - 3]', '[401, 401, w^3 - 11*w - 7]', '[419, 419, 2*w^2 - 2*w - 11]', '[419, 419, -2*w^3 + 5*w^2 + 12*w - 5]', '[421, 421, w^3 - 10*w - 11]', '[421, 421, -2*w^3 + 2*w^2 + 15*w + 5]', '[421, 421, -4*w^3 + 6*w^2 + 21*w - 6]', '[421, 421, w^2 + w - 4]', '[431, 431, -2*w^2 + 5*w + 2]', '[433, 433, -2*w^3 + 4*w^2 + 11*w]', '[443, 443, -w^3 + 2*w^2 + 3*w - 5]', '[443, 443, -3*w^3 + 7*w^2 + 18*w - 8]', '[461, 461, -2*w^3 + 4*w^2 + 9*w - 7]', '[461, 461, w^2 - 6]', '[467, 467, w^3 - w^2 - 5*w - 6]', '[479, 479, -4*w^3 + 6*w^2 + 23*w + 4]', '[479, 479, 3*w^3 - 4*w^2 - 20*w - 7]', '[487, 487, -w^3 + 3*w^2 + 5*w - 8]', '[487, 487, -6*w^3 + 10*w^2 + 33*w - 6]', '[499, 499, -2*w^3 + 4*w^2 + 9*w - 6]', '[503, 503, w^3 - 2*w^2 - 3*w - 6]', '[509, 509, w^3 - 11*w - 9]', '[521, 521, w^3 - 9*w - 3]', '[577, 577, 4*w^3 - 7*w^2 - 21*w + 2]', '[587, 587, -4*w^3 + 7*w^2 + 20*w + 5]', '[593, 593, -2*w^3 + 5*w^2 + 10*w - 11]', '[593, 593, 3*w^3 - 4*w^2 - 18*w]', '[613, 613, -w^3 + 9*w + 12]', '[613, 613, 2*w^2 - 3*w - 6]', '[619, 619, -2*w^3 + 3*w^2 + 9*w - 6]', '[619, 619, -7*w^3 + 13*w^2 + 38*w - 15]', '[619, 619, 5*w^3 - 7*w^2 - 29*w - 12]', '[619, 619, -3*w^3 + 4*w^2 + 17*w + 2]', '[631, 631, 2*w^3 - 2*w^2 - 12*w - 1]', '[631, 631, -3*w^3 + 4*w^2 + 19*w + 8]', '[641, 641, -3*w^3 + 7*w^2 + 11*w + 1]', '[641, 641, w^2 - 2*w - 9]', '[653, 653, 3*w^3 - 4*w^2 - 16*w]', '[653, 653, 4*w^3 - 6*w^2 - 23*w - 1]', '[661, 661, 2*w^2 - 2*w - 5]', '[673, 673, -w^2 + 3*w - 3]', '[673, 673, -4*w^3 + 7*w^2 + 20*w + 3]', '[673, 673, -3*w^3 + 7*w^2 + 15*w - 12]', '[673, 673, 2*w^3 - 4*w^2 - 11*w - 1]', '[683, 683, -3*w^3 + 5*w^2 + 19*w + 2]', '[701, 701, -w^3 - w^2 + 9*w + 12]', '[709, 709, -2*w^3 + 4*w^2 + 13*w + 1]', '[709, 709, 4*w^3 - 6*w^2 - 23*w - 3]', '[733, 733, w^3 - 11*w - 3]', '[733, 733, 5*w^3 - 8*w^2 - 31*w]', '[739, 739, -4*w^3 + 5*w^2 + 24*w + 3]', '[739, 739, -3*w^3 + 5*w^2 + 15*w + 3]', '[743, 743, 2*w^3 - 2*w^2 - 15*w + 1]', '[757, 757, 8*w^3 - 14*w^2 - 47*w + 9]', '[757, 757, w^3 - 9*w - 2]', '[761, 761, 2*w^3 - 5*w^2 - 8*w + 12]', '[761, 761, -2*w^3 + 5*w^2 + 9*w - 8]', '[769, 769, 5*w^3 - 7*w^2 - 31*w - 2]', '[769, 769, -2*w^3 + 5*w^2 + 10*w - 8]', '[797, 797, -4*w^3 + 7*w^2 + 25*w]', '[809, 809, -2*w^3 + 5*w^2 + 9*w + 2]', '[811, 811, -w^3 + 4*w^2 + w - 9]', '[811, 811, w - 6]', '[821, 821, -3*w^3 + 7*w^2 + 17*w - 10]', '[823, 823, 8*w^3 - 13*w^2 - 45*w + 9]', '[823, 823, -4*w^3 + 7*w^2 + 24*w - 1]', '[827, 827, 2*w^3 - 5*w^2 - 11*w + 9]', '[827, 827, w^2 - 4*w - 7]', '[829, 829, 2*w^2 - 2*w - 7]', '[829, 829, 6*w^3 - 9*w^2 - 35*w]', '[839, 839, 2*w^3 + w^2 - 20*w - 17]', '[857, 857, w^3 + w^2 - 13*w - 8]', '[863, 863, 5*w^3 - 7*w^2 - 32*w - 4]', '[877, 877, w^3 - 2*w^2 - 8*w + 4]', '[877, 877, -5*w^3 + 7*w^2 + 30*w + 9]', '[881, 881, w^3 - 11*w - 4]', '[883, 883, 3*w^3 - 4*w^2 - 19*w + 1]', '[887, 887, w^2 - 8]', '[907, 907, 3*w^3 - 5*w^2 - 17*w - 3]', '[919, 919, -3*w^3 + 6*w^2 + 15*w - 11]', '[919, 919, w^3 - 8*w - 1]', '[929, 929, -4*w^3 + 7*w^2 + 23*w - 1]', '[937, 937, -3*w^3 + 5*w^2 + 15*w + 2]', '[937, 937, w^3 - 2*w^2 - 3*w + 8]', '[937, 937, -5*w^2 + 13*w + 11]', '[937, 937, 5*w^3 - 8*w^2 - 30*w - 1]', '[941, 941, -2*w^3 + 5*w^2 + 9*w - 5]', '[947, 947, -3*w^3 + 5*w^2 + 20*w - 3]', '[947, 947, 3*w^3 - 5*w^2 - 20*w - 1]', '[967, 967, -8*w^3 + 13*w^2 + 46*w - 7]', '[971, 971, 4*w^3 - 4*w^2 - 25*w - 10]', '[971, 971, 3*w^3 - 3*w^2 - 18*w - 4]', '[977, 977, 7*w^3 - 14*w^2 - 41*w + 11]', '[977, 977, w^2 - 2*w + 3]', '[991, 991, w^3 - 2*w^2 - 2*w - 4]', '[991, 991, 4*w^3 - 8*w^2 - 20*w + 11]', '[997, 997, w^3 + 2*w^2 - 13*w - 12]', '[997, 997, w^3 - 6*w - 8]']}
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nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -3, -7, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 17989, 'disc_rad': 17989, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[3, 1], [1, 1]]], [5, [[3, 1], [1, 1]]], [7, [[4, 1]]], [11, [[3, 1], [1, 1]]], [13, [[3, 1], [1, 1]]], [17, [[2, 1], [1, 2]]], [19, [[4, 1]]], [23, [[3, 1], [1, 1]]], [29, [[3, 1], [1, 1]]], [31, [[1, 4]]], [37, [[3, 1], [1, 1]]], [41, [[2, 2]]], [43, [[3, 1], [1, 1]]], [47, [[4, 1]]], [53, [[4, 1]]], [59, [[2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12], 'galois_label': '4T5', 'galt': 5, 'grd': 134.12307780542466, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.17989.1', 'local_algs': ['m17989.1.1.0', 'm17989.1.1.0', 'm17989.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [17989], 'rd': 11.5811518341, 'regulator': {'__RealLiteral__': 0, 'data': '7.70130427442', 'prec': 44}, 'res': {'gal': ['961,-12555,-101273,290004,1857036,-1880657,-11363498,3652717,26103038,-3298571,-27483016,1531412,15257452,-254332,-4783258,-48789,860457,23561,-86676,-2924,4603,136,-115,-2,1'], 'sib': ['-1,144,-849,-1673,2040,2347,-1568,-927,442,105,-41,-3,1', '-10763,-10100,3411,561,-157,-1,1', '-31,-48,34,27,-11,-3,1', '-3307,31375,8676,-66453,717,34565,-4320,-5758,928,330,-55,-6,1', '992797,82799,-201367,-17646,11523,656,-232,-4,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a + 1 \\)', '\\( 3 a^{3} - 5 a^{2} - 17 a + 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}