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hmf_forms • Show schema
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{'deg': 4, 'dimension': 1, 'disc': 16448, 'field_bad_primes': [2, 257], 'field_label': '4.4.16448.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.16448.1-22.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2, 11], 'level_ideal': '[22, 22, -w + 2]', 'level_label': '22.1', 'level_norm': 22, 'parallel_weight': 2, 'short_label': '22.1-b', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[2, 2, w]', 1], ['[11, 11, w^3 - 2*w^2 - 5*w - 1]', 1]], 'hecke_eigenvalues': [-1, -1, 1, -1, 6, 2, -6, -6, 0, -7, 9, -4, 5, -4, 10, 2, 9, -1, -15, -2, 7, -14, -9, -10, 0, 17, -13, -18, 10, 15, 0, 24, 16, 14, 10, 20, -23, 8, -10, -8, -1, 28, 7, 12, -2, 20, 12, 18, 27, 4, 4, 20, 0, 12, -32, -2, -12, -18, 3, 4, 24, -23, 26, 6, -3, 32, 32, 0, 26, 4, 0, 15, 14, 5, 2, -12, -15, 5, 2, 22, 8, 7, -34, 10, 0, 4, -26, -30, -35, 8, -12, 13, -4, 39, 42, 3, 15, 13, -23, 2, -9, -4, -3, -12, 33, 22, 36, -37, -34, 40, 5, 2, -42, 32, 23, 4, 38, -33, -15, -10, -14, -44, -24, 16, 2, 14, 39, -16, -26, -1, -21, 23, -40, -20, -52, 18, 27, -23, 38, 40, 21, -38, -8, -5, -45, 37, 18, -35, 40, 22, 47, 43, -27, -8, -13, -8, 28, 43, -12, -30, -15, -42, 3, 8, -12, 54, 14, 2], 'hecke_polynomial': 'x', 'label': '4.4.16448.1-22.1-b'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 16448, 'ideals': ['[1, 1, 1]', '[2, 2, w]', '[4, 2, w^3 - 3*w^2 - 4*w + 4]', '[5, 5, -w^3 + 3*w^2 + 2*w - 1]', '[5, 5, w - 1]', '[8, 2, -w^3 + 2*w^2 + 6*w]', '[10, 10, w^3 - 3*w^2 - 3*w + 4]', '[10, 10, -w^3 + 3*w^2 + 3*w]', '[11, 11, w^3 - 2*w^2 - 5*w - 1]', '[13, 13, -w^3 + 3*w^2 + 3*w - 1]', '[16, 2, 2]', '[17, 17, 2*w^3 - 5*w^2 - 9*w + 5]', '[20, 10, -w^3 + 3*w^2 + 4*w - 2]', '[20, 10, -w^2 + 2*w + 4]', '[22, 22, -w + 2]', '[23, 23, -w^3 + 3*w^2 + 4*w - 5]', '[25, 5, -w^3 + 2*w^2 + 5*w - 1]', '[25, 5, -w^2 + 3*w + 1]', '[25, 25, -w^3 + 4*w^2 - 3]', '[25, 25, w^2 - 2*w - 3]', '[26, 26, 2*w^3 - 6*w^2 - 7*w + 8]', '[29, 29, -2*w^3 + 6*w^2 + 5*w - 1]', '[31, 31, -w^2 + 2*w + 1]', '[32, 4, 2*w]', '[34, 34, -w^2 + 3*w + 4]', '[40, 10, w^3 - 4*w^2 + 4]', '[40, 10, w^3 - 2*w^2 - 6*w + 2]', '[43, 43, -w^3 + 3*w^2 + 2*w - 3]', '[43, 43, -w^3 + 2*w^2 + 6*w - 3]', '[44, 22, -w^2 + 2*w]', '[46, 46, w^3 - 2*w^2 - 5*w + 2]', '[50, 10, -w^3 + 3*w^2 + w]', '[50, 10, -w^3 + 2*w^2 + 5*w + 4]', '[50, 50, -w^2 + 3*w]', '[50, 50, 2*w^3 - 5*w^2 - 9*w + 2]', '[52, 26, -2*w^3 + 5*w^2 + 8*w - 4]', '[55, 55, -w^3 + 3*w^2 + 4*w - 1]', '[55, 55, w^3 - 3*w^2 - 3*w - 1]', '[58, 58, w^3 - w^2 - 7*w - 6]', '[59, 59, 2*w^3 - 6*w^2 - 7*w + 7]', '[62, 62, w^3 - 3*w^2 - 3*w + 6]', '[64, 4, 2*w^3 - 6*w^2 - 8*w + 8]', '[65, 65, w^2 - 3*w - 5]', '[65, 65, -2*w^3 + 5*w^2 + 10*w - 3]', '[68, 34, w^2 - 4*w]', '[73, 73, 3*w^3 - 6*w^2 - 16*w - 5]', '[79, 79, -5*w^3 + 14*w^2 + 20*w - 17]', '[80, 10, -2*w^3 + 6*w^2 + 4*w - 2]', '[80, 10, 2*w - 2]', '[81, 3, -3]', '[83, 83, -w - 3]', '[83, 83, w^2 - 3*w - 7]', '[85, 85, -2*w^3 + 6*w^2 + 5*w - 5]', '[85, 85, 2*w^3 - 5*w^2 - 8*w + 1]', '[86, 86, -3*w + 2]', '[86, 86, w^3 - 4*w^2 - 3*w + 2]', '[88, 22, 3*w^3 - 8*w^2 - 12*w + 10]', '[89, 89, w^2 - 2*w - 7]', '[92, 46, w^3 - 3*w^2 - 2*w - 2]', '[100, 10, -2*w^3 + 5*w^2 + 10*w - 4]', '[100, 10, -w^2 + 4*w + 2]', '[100, 50, -w^3 + 3*w^2 + 2*w - 4]', '[100, 50, -w^3 + 3*w^2 + 2*w - 6]', '[101, 101, -2*w^3 + 5*w^2 + 8*w - 3]', '[101, 101, 5*w^3 - 14*w^2 - 19*w + 17]', '[103, 103, -w^3 + w^2 + 8*w + 3]', '[103, 103, 2*w^3 - 5*w^2 - 7*w - 1]', '[104, 26, w^3 - 4*w^2 + 6]', '[109, 109, 3*w^3 - 7*w^2 - 14*w + 1]', '[109, 109, -w^2 + 4*w + 1]', '[110, 110, 2*w^3 - 4*w^2 - 11*w]', '[110, 110, -w^2 + 3*w - 2]', '[115, 115, 2*w^2 - 5*w - 7]', '[115, 115, 2*w^3 - 6*w^2 - 6*w + 3]', '[116, 58, -2*w^3 + 5*w^2 + 8*w - 2]', '[118, 118, -2*w^3 + 5*w^2 + 7*w - 4]', '[121, 121, 2*w^2 - 5*w - 9]', '[124, 62, -w^3 + 3*w^2 + 6*w - 2]', '[125, 5, -3*w^3 + 7*w^2 + 14*w - 3]', '[125, 5, w^3 - w^2 - 7*w - 7]', '[125, 25, w^3 - 3*w^2 - w + 3]', '[125, 25, -2*w^3 + 4*w^2 + 10*w + 3]', '[125, 125, w^2 - w - 5]', '[125, 125, 3*w^3 - 6*w^2 - 17*w - 1]', '[127, 127, -3*w^3 + 8*w^2 + 11*w - 7]', '[127, 127, -w^3 + 2*w^2 + 7*w + 1]', '[128, 4, -2*w^3 + 4*w^2 + 12*w]', '[130, 130, -w^3 + 2*w^2 + 7*w - 2]', '[130, 130, -w^3 + w^2 + 7*w + 8]', '[136, 34, w^3 - 4*w^2 - 2*w + 8]', '[137, 137, -2*w^3 + 5*w^2 + 9*w - 1]', '[139, 139, -w^3 + 3*w^2 + 2*w - 5]', '[143, 143, w^3 - 2*w^2 - 4*w - 3]', '[145, 145, -2*w^3 + 4*w^2 + 12*w + 1]', '[145, 145, w^3 - 3*w^2 - 5*w + 5]', '[146, 146, 2*w^2 - 5*w - 6]', '[149, 149, w^3 - 3*w^2 - w - 1]', '[149, 149, -2*w^3 + 4*w^2 + 10*w + 1]', '[155, 155, w^3 - 4*w^2 - w + 7]', '[155, 155, 4*w^3 - 10*w^2 - 18*w + 9]', '[158, 158, 4*w^3 - 9*w^2 - 21*w + 4]', '[160, 20, 2*w^3 - 6*w^2 - 6*w + 8]', '[160, 20, -2*w^3 + 6*w^2 + 6*w]', '[162, 6, -3*w]', '[163, 163, w^3 - 4*w^2 - w + 11]', '[163, 163, 2*w^3 - 4*w^2 - 10*w + 1]', '[166, 166, w^3 - 3*w^2 - 7*w]', '[166, 166, -w^2 - 3*w]', '[169, 169, 2*w^2 - 4*w - 9]', '[170, 170, -w^3 + 4*w^2 + w - 4]', '[170, 170, w^3 - 5*w^2 + 3*w + 4]', '[172, 86, -3*w^3 + 9*w^2 + 12*w - 10]', '[172, 86, -7*w^3 + 19*w^2 + 30*w - 20]', '[173, 173, -4*w^3 + 11*w^2 + 15*w - 13]', '[176, 22, 2*w^3 - 4*w^2 - 10*w - 2]', '[178, 178, w^3 - 2*w^2 - 7*w]', '[179, 179, 2*w^2 - 6*w - 3]', '[179, 179, -w^3 + 2*w^2 + 7*w - 1]', '[181, 181, w^3 - 10*w - 9]', '[181, 181, -3*w^3 + 8*w^2 + 14*w - 7]', '[184, 46, -w^3 + 4*w^2 - 2*w - 2]', '[187, 187, 2*w^3 - 6*w^2 - 6*w + 9]', '[199, 199, w^3 - 8*w - 9]', '[200, 10, w^3 - 4*w^2 - 2*w + 10]', '[200, 10, w^3 - 2*w^2 - 4*w + 4]', '[200, 50, 3*w^3 - 8*w^2 - 10*w]', '[200, 50, 3*w^3 - 6*w^2 - 16*w - 4]', '[202, 202, w^3 - 4*w^2 - 3*w + 4]', '[202, 202, 3*w^3 - 5*w^2 - 19*w - 6]', '[206, 206, -w^3 + 2*w^2 + 3*w + 2]', '[206, 206, -w^3 + 5*w^2 - w - 4]', '[208, 26, -2*w^3 + 6*w^2 + 6*w - 2]', '[211, 211, 2*w - 3]', '[215, 215, -2*w^3 + 8*w^2 - 3]', '[215, 215, w^3 - 2*w^2 - 9*w + 5]', '[215, 215, 4*w^3 - 13*w^2 - 6*w + 7]', '[215, 215, 2*w^3 - 7*w^2 - 5*w + 5]', '[218, 218, -w^3 + 4*w^2 + w - 6]', '[218, 218, -w^3 + 4*w^2 + w]', '[220, 110, 3*w^3 - 5*w^2 - 20*w - 8]', '[220, 110, w^2 - 4]', '[221, 221, -3*w^3 + 9*w^2 + 10*w - 9]', '[223, 223, -w^3 + 4*w^2 + w - 5]', '[227, 227, w^3 - 2*w^2 - 5*w - 5]', '[227, 227, -3*w^3 + 7*w^2 + 14*w - 5]', '[227, 227, -4*w^3 + 10*w^2 + 19*w - 7]', '[227, 227, w^2 - 4*w - 5]', '[230, 230, 2*w^3 - 5*w^2 - 7*w]', '[230, 230, w^3 - 4*w^2 - 3*w + 8]', '[232, 58, w^3 - 4*w^2 - 2*w + 4]', '[236, 118, w^3 - 5*w^2 - 4*w + 4]', '[239, 239, -2*w^3 + 5*w^2 + 7*w - 3]', '[242, 242, 2*w^3 - 5*w^2 - 9*w]', '[248, 62, -w^3 + 2*w^2 + 4*w + 4]', '[250, 10, w^3 - 4*w^2 - 3*w + 6]', '[250, 10, w^3 - w^2 - 7*w - 2]', '[250, 50, -4*w^3 + 10*w^2 + 17*w - 8]', '[250, 50, w^3 - 3*w^2 - w - 2]', '[250, 250, w^2 - w - 6]', '[250, 250, -3*w^3 + 8*w^2 + 11*w - 6]', '[251, 251, -w^3 + 4*w^2 + 2*w - 11]', '[251, 251, 2*w^3 - 6*w^2 - 6*w + 1]', '[253, 253, -3*w^3 + 7*w^2 + 15*w - 1]', '[254, 254, 2*w^3 - 7*w^2 - 7*w + 6]', '[254, 254, w^2 + w + 2]', '[256, 4, 4]', '[257, 257, -3*w^3 + 6*w^2 + 16*w + 3]', '[260, 130, w^2 - 2*w + 2]', '[260, 130, -w^3 + w^2 + 8*w + 2]', '[263, 263, -w^3 + 3*w^2 + 3*w - 7]', '[263, 263, w^3 - 4*w^2 + 7]', '[269, 269, -2*w^3 + 6*w^2 + 6*w - 11]', '[269, 269, -w^3 + 4*w^2 - w - 5]', '[271, 271, -3*w^3 + 9*w^2 + 11*w - 11]', '[271, 271, w^2 - 5*w - 3]', '[272, 34, 4*w^3 - 10*w^2 - 18*w + 10]', '[274, 274, w^3 - 3*w^2 - w + 4]', '[275, 55, 2*w^2 - 6*w - 7]', '[275, 55, 2*w^3 - 6*w^2 - 7*w + 11]', '[275, 275, 3*w^3 - 7*w^2 - 14*w - 1]', '[275, 275, -2*w^2 + 7*w + 5]', '[277, 277, w^3 - 4*w^2 - 2*w + 7]', '[277, 277, -2*w^3 + 7*w^2 + 8*w - 9]', '[278, 278, w^3 - 4*w^2 - 5*w + 2]', '[281, 281, 2*w^2 - 4*w - 5]', '[281, 281, 2*w^3 - 4*w^2 - 11*w + 1]', '[283, 283, -3*w^3 + 8*w^2 + 14*w - 11]', '[286, 286, -3*w^3 + 9*w^2 + 7*w - 4]', '[289, 289, -2*w^3 + 7*w^2 + w - 5]', '[290, 290, w + 4]', '[290, 290, 2*w^3 - 5*w^2 - 9*w - 2]', '[292, 146, 2*w^3 - 5*w^2 - 6*w]', '[293, 293, w^3 - 2*w^2 - 6*w + 5]', '[295, 295, -4*w^3 + 11*w^2 + 14*w - 11]', '[295, 295, -w^2 + 5*w - 1]', '[298, 298, -w^3 + 5*w^2 - w - 2]', '[298, 298, -2*w^2 + w + 4]', '[299, 299, 3*w^3 - 8*w^2 - 11*w + 5]', '[307, 307, -2*w^3 + 5*w^2 + 7*w - 1]', '[310, 310, -2*w^3 + 5*w^2 + 7*w - 2]', '[310, 310, -w^3 + 11*w + 10]', '[313, 313, 2*w^3 - 4*w^2 - 9*w + 3]', '[313, 313, -2*w^3 + 5*w^2 + 6*w - 3]', '[316, 158, -w^3 + 3*w^2 + 4*w - 8]', '[317, 317, -2*w^3 + 5*w^2 + 9*w + 1]', '[319, 319, 2*w^3 - 6*w^2 - 4*w + 5]', '[320, 20, -2*w^3 + 6*w^2 + 8*w - 4]', '[320, 20, -2*w^2 + 4*w + 8]', '[324, 6, -3*w^3 + 9*w^2 + 12*w - 12]', '[325, 65, 3*w^3 - 11*w^2 - 2*w + 7]', '[325, 65, w^3 - 4*w^2 - 2*w + 5]', '[325, 325, 2*w^2 - 5*w - 3]', '[325, 325, -3*w^3 + 6*w^2 + 17*w + 5]', '[326, 326, -2*w^3 + 5*w^2 + 11*w - 2]', '[326, 326, 2*w^2 + w - 4]', '[332, 166, -2*w^3 + 7*w^2 + 8*w - 10]', '[332, 166, -4*w^3 + 13*w^2 + 14*w - 20]', '[338, 338, -3*w^3 + 7*w^2 + 15*w - 6]', '[340, 170, -w^2 + 2*w + 8]', '[340, 170, 5*w^3 - 13*w^2 - 22*w + 10]', '[341, 341, -w^3 + 3*w^2 + 2*w + 3]', '[344, 86, 3*w^3 - 8*w^2 - 12*w + 4]', '[344, 86, 3*w^3 - 8*w^2 - 14*w + 12]', '[346, 346, 4*w^3 - 10*w^2 - 17*w + 4]', '[347, 347, 4*w^3 - 9*w^2 - 21*w + 3]', '[347, 347, 4*w^3 - 10*w^2 - 18*w + 5]', '[349, 349, -2*w^3 + 6*w^2 + 7*w - 3]', '[352, 44, -2*w + 4]', '[353, 353, -w^3 + 12*w + 5]', '[353, 353, w^2 - w - 7]', '[356, 178, -w^2 - 2]', '[358, 358, 2*w^3 - 6*w^2 - 3*w]', '[358, 358, w^2 - w + 2]', '[359, 359, -2*w^3 + 5*w^2 + 6*w - 7]', '[359, 359, -w^3 + 4*w^2 - 11]', '[362, 362, -w^2 + w + 8]', '[362, 362, 2*w^3 - 4*w^2 - 9*w - 2]', '[365, 365, 4*w^3 - 11*w^2 - 12*w - 3]', '[365, 365, -3*w^3 + 8*w^2 + 11*w - 1]', '[368, 46, -2*w^3 + 6*w^2 + 8*w - 10]', '[373, 373, -w^3 + 2*w^2 + 6*w + 5]', '[374, 374, -2*w^3 + 6*w^2 + 9*w - 4]', '[377, 377, 3*w^3 - 8*w^2 - 12*w + 11]', '[379, 379, -3*w^3 + 8*w^2 + 14*w - 5]', '[391, 391, 3*w^3 - 9*w^2 - 8*w + 1]', '[395, 395, -w^3 + 5*w^2 - w - 13]', '[395, 395, 4*w^3 - 11*w^2 - 16*w + 9]', '[397, 397, 6*w^3 - 14*w^2 - 30*w + 7]', '[398, 398, 2*w^3 - 2*w^2 - 9*w - 2]', '[400, 10, -2*w^3 + 4*w^2 + 10*w - 2]', '[400, 10, -2*w^2 + 6*w + 2]', '[400, 50, -2*w^3 + 8*w^2 - 6]', '[400, 50, 2*w^2 - 4*w - 6]', '[401, 401, 3*w^3 - 5*w^2 - 20*w - 7]', '[403, 403, 2*w^3 - 7*w^2 - 4*w + 13]', '[404, 202, -7*w^3 + 19*w^2 + 30*w - 18]', '[404, 202, w^3 - w^2 - 6*w - 6]', '[405, 15, 3*w^3 - 9*w^2 - 6*w + 3]', '[405, 15, -3*w + 3]', '[409, 409, 3*w^3 - 7*w^2 - 12*w - 3]', '[409, 409, 2*w^2 - 4*w - 7]', '[412, 206, -3*w^3 + 7*w^2 + 16*w - 2]', '[412, 206, 2*w^3 - 5*w^2 - 10*w]', '[415, 415, w^3 - 4*w^2 - 4*w + 7]', '[415, 415, 2*w^3 - 4*w^2 - 9*w - 1]', '[415, 415, -w^2 - 2*w + 3]', '[415, 415, 2*w^3 - 5*w^2 - 5*w + 1]', '[416, 52, 4*w^3 - 12*w^2 - 14*w + 16]', '[421, 421, w^3 - 11*w - 11]', '[421, 421, -w^3 + 3*w^2 + w - 7]', '[422, 422, 2*w^2 - 3*w]', '[425, 85, w^3 - 3*w^2 - w + 5]', '[425, 85, 3*w^3 - 10*w^2 - 4*w + 1]', '[425, 425, -3*w^3 + 8*w^2 + 13*w - 5]', '[425, 425, -3*w^3 + 9*w^2 + 9*w - 5]', '[430, 430, 3*w^3 - 11*w^2 - 3*w + 6]', '[430, 430, -2*w^3 + 5*w^2 + 9*w - 8]', '[430, 430, -7*w^3 + 19*w^2 + 27*w - 18]', '[430, 430, -2*w^3 + 7*w^2 - w - 4]', '[431, 431, 2*w^3 - 3*w^2 - 14*w - 3]', '[431, 431, -4*w^3 + 11*w^2 + 15*w - 15]', '[433, 433, 2*w^3 - 5*w^2 - 6*w + 1]', '[436, 218, 2*w^3 - 5*w^2 - 6*w + 2]', '[436, 218, -3*w^3 + 7*w^2 + 14*w - 6]', '[439, 439, -4*w^3 + 11*w^2 + 13*w - 9]', '[439, 439, -2*w^3 + 6*w^2 + 8*w - 11]', '[440, 110, w^3 - 4*w^2 + 8]', '[440, 110, -3*w^3 + 8*w^2 + 10*w - 6]', '[442, 442, -2*w^2 + 7*w + 4]', '[443, 443, 2*w - 5]', '[443, 443, -6*w^3 + 17*w^2 + 24*w - 21]', '[445, 445, w^3 - 3*w^2 - 5*w + 7]', '[445, 445, 3*w^3 - 8*w^2 - 10*w + 1]', '[446, 446, 2*w^3 - 5*w^2 - 5*w + 2]', '[449, 449, w^3 - 2*w^2 - 8*w + 3]', '[449, 449, 4*w^3 - 12*w^2 - 15*w + 17]', '[454, 454, 2*w^3 - 5*w^2 - 7*w + 8]', '[454, 454, w^3 - 4*w^2 - 5*w]', '[454, 454, w^2 - 5*w - 2]', '[454, 454, -w^3 + w^2 + 7*w + 10]', '[457, 457, -2*w^3 + 4*w^2 + 9*w + 5]', '[460, 230, -2*w^3 + 7*w^2 + 4*w - 14]', '[460, 230, -3*w^3 + 5*w^2 + 20*w + 6]', '[461, 461, -3*w^3 + 6*w^2 + 15*w - 1]', '[461, 461, -3*w^3 + 7*w^2 + 17*w + 1]', '[463, 463, -4*w^3 + 10*w^2 + 17*w - 7]', '[463, 463, -3*w^3 + 10*w^2 + 9*w - 17]', '[464, 58, -4*w^3 + 12*w^2 + 10*w - 2]', '[467, 467, 4*w^3 - 8*w^2 - 21*w - 7]', '[467, 467, w^3 - 6*w^2 + 3*w + 19]', '[472, 118, -7*w^3 + 20*w^2 + 30*w - 20]', '[473, 473, -2*w^3 + 6*w^2 + 5*w - 7]', '[473, 473, -w^3 + w^2 + 7*w + 1]', '[478, 478, w^3 - 5*w^2 - 3*w + 4]', '[479, 479, -w^3 + w^2 + 8*w + 1]', '[484, 242, -w^3 + 3*w^2 - 4]', '[487, 487, -4*w^3 + 11*w^2 + 14*w - 15]', '[487, 487, 3*w^3 - 6*w^2 - 15*w - 5]', '[491, 491, w^2 - 5]', '[493, 493, -w^3 + 2*w^2 + 3*w + 3]', '[496, 62, -2*w^2 + 4*w + 2]', '[500, 10, -3*w^3 + 7*w^2 + 14*w + 2]', '[500, 10, 2*w^3 - 7*w^2 - 4*w + 6]', '[500, 50, 2*w^3 - 3*w^2 - 14*w - 10]', '[500, 50, -w^3 + 5*w^2 - 2*w - 2]', '[500, 250, 2*w^3 - 5*w^2 - 8*w - 4]', '[500, 250, w^3 - w^2 - 6*w]', '[502, 502, 2*w^3 - 4*w^2 - 11*w + 2]', '[502, 502, -2*w^3 + 6*w^2 + w - 4]', '[503, 503, 2*w^3 - 5*w^2 - 11*w + 3]', '[505, 505, -w^3 + 4*w^2 + 1]', '[505, 505, -3*w^3 + 7*w^2 + 15*w - 7]', '[505, 505, 3*w^3 - 9*w^2 - 11*w + 7]', '[505, 505, -2*w^2 + 4*w + 13]', '[506, 506, w^3 - 3*w^2 - w + 6]', '[508, 254, -12*w^3 + 33*w^2 + 50*w - 34]', '[508, 254, -4*w^3 + 9*w^2 + 18*w - 6]', '[512, 8, 4*w]', '[514, 514, -2*w^2 + 3*w + 6]', '[515, 515, -3*w^3 + 10*w^2 + 6*w - 3]', '[515, 515, 6*w^3 - 20*w^2 - 9*w + 5]', '[515, 515, w^2 - 5*w - 1]', '[515, 515, 2*w^3 - 8*w^2 + 2*w + 7]', '[520, 130, 5*w^3 - 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8]', '[1780, 890, 5*w^3 - 13*w^2 - 22*w + 8]', '[1781, 1781, -w^3 + 3*w^2 + 2*w + 5]', '[1782, 66, 3*w - 6]', '[1784, 446, 5*w^3 - 12*w^2 - 22*w + 2]', '[1789, 1789, -4*w^3 + 11*w^2 + 15*w - 5]', '[1789, 1789, 3*w^3 - 5*w^2 - 17*w - 13]', '[1790, 1790, -5*w^3 + 21*w^2 - 5*w - 16]', '[1790, 1790, 2*w^3 - 8*w^2 + 3*w + 8]', '[1790, 1790, 5*w^3 - 13*w^2 - 19*w + 4]', '[1790, 1790, -6*w^3 + 16*w^2 + 25*w - 12]', '[1793, 1793, -w^3 + 13*w + 15]', '[1793, 1793, -11*w^3 + 30*w^2 + 48*w - 29]', '[1795, 1795, w^3 - 6*w + 1]', '[1795, 1795, 3*w^3 - 10*w^2 - 11*w + 13]', '[1795, 1795, w^3 - 2*w^2 - 7*w - 7]', '[1795, 1795, 2*w^3 - 3*w^2 - 12*w - 1]', '[1796, 898, 9*w^3 - 23*w^2 - 38*w + 24]', '[1796, 898, -w^2 + 2*w + 10]', '[1798, 1798, -4*w^3 + 10*w^2 + 17*w]', '[1807, 1807, w^3 - 2*w^2 - 9*w + 1]', '[1810, 1810, -5*w^3 + 15*w^2 + 13*w - 4]', '[1810, 1810, -2*w^3 + 7*w^2 + 7*w - 2]', '[1810, 1810, -w^3 + 2*w^2 + 7*w - 8]', '[1810, 1810, 3*w^3 - 10*w^2 - 7*w]', '[1814, 1814, -3*w^3 + 8*w^2 + 13*w - 2]', '[1814, 1814, -w^3 + 4*w^2 - w - 10]', '[1814, 1814, -3*w^3 + 8*w^2 + 9*w - 10]', '[1814, 1814, 3*w^3 - 7*w^2 - 7*w + 4]', '[1816, 454, 5*w^3 - 8*w^2 - 34*w - 10]', '[1816, 454, -w^3 + 4*w^2 + 2*w + 2]', '[1816, 454, 11*w^3 - 32*w^2 - 46*w + 36]', '[1816, 454, 5*w^3 - 10*w^2 - 28*w - 8]', '[1817, 1817, -w^3 + 3*w^2 + 9]', '[1822, 1822, 2*w^3 - 9*w^2 - 5*w + 6]', '[1825, 365, 2*w^3 - 21*w - 21]', '[1825, 365, -w^3 + 5*w^2 - 7]', '[1825, 1825, -7*w^3 + 9*w^2 + 52*w + 27]', '[1825, 1825, -8*w^2 + 24*w + 19]', '[1826, 1826, w^2 + w - 6]', '[1826, 1826, -w^3 + 5*w^2 + w - 14]', '[1828, 914, -w^2 + 4*w + 10]', '[1829, 1829, -3*w^3 + 9*w^2 + 11*w - 5]', '[1831, 1831, w^3 - 4*w^2 - 4*w + 9]', '[1838, 1838, 5*w^3 - 15*w^2 - 19*w + 18]', '[1838, 1838, -w^3 + 2*w^2 + 3*w + 8]', '[1840, 230, 4*w^2 - 10*w - 14]', '[1840, 230, 4*w^3 - 12*w^2 - 12*w + 6]', '[1844, 922, -10*w^3 + 27*w^2 + 46*w - 22]', '[1844, 922, -10*w^3 + 23*w^2 + 44*w - 16]', '[1849, 43, -6*w^3 + 10*w^2 + 39*w + 11]', '[1849, 43, -12*w^3 + 32*w^2 + 52*w - 31]', '[1849, 1849, -4*w^3 + 13*w^2 + 14*w - 19]', '[1849, 1849, 2*w^3 - 5*w^2 - 5*w - 3]', '[1852, 926, -16*w^3 + 43*w^2 + 68*w - 42]', '[1852, 926, 3*w^2 - 8*w - 14]', '[1853, 1853, -2*w^3 + 7*w^2 + 4*w - 17]', '[1853, 1853, -3*w^3 + 8*w^2 + 15*w - 13]', '[1856, 116, -4*w^3 + 10*w^2 + 16*w - 4]', '[1859, 1859, 4*w^3 - 11*w^2 - 11*w + 1]', '[1861, 1861, w^3 - 2*w^2 - 3*w - 7]', '[1863, 69, 3*w^3 - 9*w^2 - 12*w + 15]', '[1865, 1865, w^3 - 2*w^2 - w - 3]', '[1865, 1865, -4*w^3 + 11*w^2 + 10*w - 1]', '[1867, 1867, -3*w^3 + 6*w^2 + 15*w + 11]', '[1868, 934, 3*w^3 - 7*w^2 - 8*w]', '[1868, 934, w^3 - 5*w^2 - 2*w + 8]', '[1870, 1870, -w^3 + w^2 + 11*w + 4]', '[1870, 1870, -w^3 + 2*w^2 - w + 2]', '[1871, 1871, -3*w^3 + 9*w^2 + 8*w - 11]', '[1873, 1873, 4*w^3 - 8*w^2 - 23*w + 1]', '[1873, 1873, w^3 - 9*w - 3]', '[1877, 1877, -5*w^3 + 15*w^2 + 18*w - 15]', '[1877, 1877, w^3 - 2*w^2 - 6*w - 7]', '[1879, 1879, 5*w^3 - 14*w^2 - 15*w + 3]', '[1879, 1879, 7*w^3 - 17*w^2 - 32*w + 13]', '[1885, 1885, -4*w^3 + 11*w^2 + 12*w - 7]', '[1885, 1885, w^3 - 5*w^2 + 3*w + 11]', '[1888, 236, -4*w^3 + 10*w^2 + 14*w - 8]', '[1892, 946, 3*w^2 - 8*w + 4]', '[1892, 946, 4*w^3 - 11*w^2 - 8*w + 6]', '[1894, 1894, 8*w^3 - 20*w^2 - 35*w + 18]', '[1894, 1894, 3*w^3 - 7*w^2 - 17*w + 2]', '[1894, 1894, w^3 - 9*w + 4]', '[1894, 1894, 4*w^2 - 7*w - 6]', '[1895, 1895, -w^2 - 2*w + 5]', '[1895, 1895, 5*w^3 - 12*w^2 - 19*w + 11]', '[1898, 1898, -w^3 + 7*w^2 - 9*w - 8]', '[1903, 1903, 4*w^3 - 13*w^2 - 10*w + 7]', '[1906, 1906, -3*w^3 + 9*w^2 + 13*w - 6]', '[1906, 1906, 5*w^3 - 13*w^2 - 23*w + 8]', '[1909, 1909, 4*w^3 - 14*w^2 - 11*w + 27]', '[1909, 1909, 2*w^3 - 7*w^2 - 7*w + 13]', '[1912, 478, 3*w^3 - 10*w^2 - 8*w + 14]', '[1916, 958, -5*w^3 + 13*w^2 + 24*w - 10]', '[1922, 1922, -2*w^3 + 3*w^2 + 11*w]', '[1933, 1933, -3*w^3 + 8*w^2 + 9*w - 11]', '[1934, 1934, -3*w^3 + 10*w^2 + 7*w - 18]', '[1936, 242, 4*w^2 - 10*w - 18]', '[1937, 1937, -w^3 + w^2 + 5*w + 7]', '[1937, 1937, 6*w^3 - 19*w^2 - 10*w + 7]', '[1948, 974, -w^3 + 5*w^2 - 10]', '[1948, 974, 4*w^3 - 9*w^2 - 22*w - 2]', '[1949, 1949, 7*w^3 - 20*w^2 - 25*w + 27]', '[1949, 1949, 3*w^3 - 9*w^2 - 5*w - 1]', '[1951, 1951, -w^3 + 5*w^2 - 4*w - 9]', '[1951, 1951, -w^3 - 2*w^2 + 15*w + 17]', '[1955, 1955, 3*w^3 - 6*w^2 - 19*w - 3]', '[1955, 1955, -w^3 + 4*w^2 + 6*w - 7]', '[1958, 1958, -w^3 - w^2 + 11*w + 12]', '[1964, 982, -5*w^3 + 13*w^2 + 18*w - 18]', '[1969, 1969, -w^3 - 2*w^2 + 17*w + 15]', '[1969, 1969, 3*w^2 - 6*w - 11]', '[1972, 986, 2*w^3 - 5*w^2 - 6*w + 10]', '[1975, 395, 9*w^3 - 23*w^2 - 41*w + 21]', '[1975, 395, w^3 - 13*w - 3]', '[1975, 1975, 4*w^3 - 12*w^2 - 12*w + 15]', '[1975, 1975, 5*w^3 - 15*w^2 - 16*w + 23]', '[1978, 1978, -4*w^3 + 10*w^2 + 13*w - 8]', '[1978, 1978, -5*w^3 + 12*w^2 + 23*w - 16]', '[1979, 1979, 5*w^3 - 16*w^2 - 15*w + 25]', '[1979, 1979, -2*w^3 + 8*w^2 + w - 9]', '[1984, 124, -2*w^3 + 6*w^2 + 12*w - 4]', '[1985, 1985, -8*w^3 + 20*w^2 + 37*w - 19]', '[1985, 1985, -3*w^3 + 11*w^2 + 4*w - 15]', '[1987, 1987, -3*w^3 + 10*w^2 + 9*w - 15]', '[1987, 1987, 9*w^3 - 23*w^2 - 41*w + 19]', '[1990, 1990, 5*w^3 - 7*w^2 - 29*w - 14]', '[1990, 1990, -w^3 + 7*w^2 - 3*w - 22]', '[1991, 1991, 4*w^3 - 9*w^2 - 17*w + 5]', '[1991, 1991, -w^3 + 5*w^2 - w + 1]', '[1999, 1999, 2*w^3 - 6*w^2 - 4*w + 9]', '[2000, 10, -6*w^3 + 14*w^2 + 28*w - 6]', '[2000, 10, 2*w^3 - 2*w^2 - 14*w - 14]', '[2000, 50, 2*w^3 - 6*w^2 - 2*w + 6]', '[2000, 50, -4*w^3 + 8*w^2 + 20*w + 6]', '[2000, 250, 2*w^2 - 2*w - 10]', '[2000, 250, 6*w^3 - 12*w^2 - 34*w - 2]', '[2003, 2003, -2*w^3 + 5*w^2 + 12*w - 11]', '[2003, 2003, 8*w^3 - 20*w^2 - 35*w + 15]', '[2005, 2005, -2*w^3 + 3*w^2 + 13*w + 1]', '[2005, 2005, 4*w^2 - 10*w - 11]', '[2006, 2006, -12*w^3 + 32*w^2 + 47*w - 34]', '[2008, 502, 9*w^3 - 24*w^2 - 40*w + 22]', '[2008, 502, -w^3 + 6*w^2 - 6*w - 12]', '[2012, 1006, 10*w^3 - 25*w^2 - 42*w + 24]', '[2015, 2015, -w^3 + 12*w + 1]', '[2015, 2015, -5*w^3 + 15*w^2 + 17*w - 17]', '[2017, 2017, -2*w^3 + 7*w^2 + 3*w - 15]', '[2017, 2017, -5*w^3 + 12*w^2 + 23*w - 11]', '[2018, 2018, w^3 - 3*w^2 + 5*w + 6]', '[2018, 2018, -2*w^3 + 8*w^2 + 7*w - 12]', '[2020, 1010, 3*w^3 - 9*w^2 - 14*w + 12]', '[2020, 1010, 8*w^3 - 17*w^2 - 42*w - 2]', '[2020, 1010, -4*w^3 + 9*w^2 + 22*w - 2]', '[2020, 1010, w^2 + 4]', '[2024, 506, w^3 - 6*w^2 + 4*w + 8]', '[2025, 15, 3*w^3 - 6*w^2 - 15*w + 3]', '[2025, 15, 3*w^2 - 9*w - 3]', '[2025, 75, 3*w^3 - 12*w^2 + 9]', '[2025, 75, -3*w^2 + 6*w + 9]', '[2026, 2026, 3*w^2 - 7*w - 4]', '[2029, 2029, 2*w^3 - 8*w^2 - 5*w + 17]', '[2029, 2029, -8*w^3 + 21*w^2 + 35*w - 17]', '[2032, 254, -6*w^3 + 16*w^2 + 22*w - 14]', '[2032, 254, -2*w^3 + 4*w^2 + 14*w + 2]', '[2039, 2039, 5*w^2 - 10*w - 27]', '[2039, 2039, 3*w^3 - 8*w^2 - 8*w - 3]', '[2039, 2039, 7*w^3 - 18*w^2 - 33*w + 13]', '[2039, 2039, -3*w^3 + 7*w^2 + 11*w - 3]', '[2045, 2045, 8*w^3 - 26*w^2 - 14*w + 5]', '[2045, 2045, 2*w^3 - 6*w^2 - 3*w + 7]', '[2045, 2045, -w^3 + 5*w^2 - 6*w - 5]', '[2045, 2045, -4*w^3 + 13*w^2 + 9*w - 3]', '[2047, 2047, -2*w^3 + 7*w^2 + 3*w + 1]', '[2048, 8, -4*w^3 + 8*w^2 + 24*w]', '[2053, 2053, 2*w^3 - 8*w^2 - 2*w + 7]', '[2053, 2053, -w^2 + 8*w - 3]', '[2054, 2054, -4*w^3 + 14*w^2 + 7*w - 20]', '[2056, 514, w^3 - 6*w^2 + 8*w + 10]', '[2057, 2057, -4*w^3 + 13*w^2 + 9*w - 5]', '[2060, 1030, 3*w^3 - 3*w^2 - 26*w - 14]', '[2060, 1030, 2*w^3 - 5*w^2 - 4*w - 2]', '[2060, 1030, -6*w^3 + 11*w^2 + 36*w + 14]', '[2060, 1030, w^3 - 5*w^2 + 8]', '[2063, 2063, -3*w^3 + 6*w^2 + 19*w - 3]', '[2063, 2063, 2*w^3 - 8*w^2 - 4*w + 19]', '[2075, 415, 3*w^3 - 5*w^2 - 14*w + 1]', '[2075, 415, w^3 - 10*w - 3]', '[2075, 415, 4*w^3 - 7*w^2 - 24*w - 5]', '[2075, 415, 6*w^3 - 12*w^2 - 30*w + 1]', '[2075, 2075, w^3 - 6*w^2 + 3*w + 7]', '[2075, 2075, -w^3 - w^2 + 11*w + 11]', '[2075, 2075, -w^3 - w^2 + 9*w + 9]', '[2075, 2075, -3*w^3 + 2*w^2 + 23*w + 19]', '[2080, 260, -2*w^3 + 4*w^2 + 14*w - 4]', '[2080, 260, -2*w^3 + 2*w^2 + 14*w + 16]', '[2081, 2081, 3*w^3 - 2*w^2 - 27*w - 21]', '[2083, 2083, -3*w^3 + 9*w^2 + 10*w - 3]', '[2083, 2083, -6*w^3 + 16*w^2 + 22*w - 19]', '[2092, 1046, -3*w^3 + 7*w^2 + 6*w - 2]', '[2098, 2098, -4*w^3 + 9*w^2 + 21*w + 2]', '[2104, 526, 7*w^3 - 16*w^2 - 36*w + 6]', '[2104, 526, -5*w^3 + 12*w^2 + 20*w - 10]', '[2105, 2105, 2*w^3 - 8*w^2 - 8*w + 9]', '[2105, 2105, w^3 + w^2 - 13*w - 7]', '[2105, 2105, w^3 - 5*w^2 + 9]', '[2105, 2105, w^3 - 7*w - 1]', '[2106, 78, -6*w^3 + 18*w^2 + 21*w - 24]', '[2108, 1054, -3*w^2 + 8*w + 16]', '[2110, 2110, 5*w^3 - 15*w^2 - 9*w + 4]', '[2110, 2110, -5*w^3 + 15*w^2 + 17*w - 16]', '[2113, 2113, 3*w^3 - 8*w^2 - 12*w + 13]', '[2116, 1058, 3*w^2 - 6*w - 10]', '[2117, 2117, 2*w^3 - 6*w^2 - 6*w - 3]', '[2119, 2119, -5*w^3 + 12*w^2 + 24*w - 3]', '[2119, 2119, -w^3 + 5*w^2 + w - 9]', '[2125, 85, -7*w^3 + 17*w^2 + 34*w - 11]', '[2125, 85, -3*w^3 + 7*w^2 + 14*w + 7]', '[2125, 425, -2*w^3 + 2*w^2 + 18*w + 7]', '[2125, 425, -2*w^3 + 7*w^2 + 3*w - 13]', '[2125, 2125, -w^3 + 3*w^2 - w + 3]', '[2125, 2125, -8*w^3 + 21*w^2 + 36*w - 19]', '[2126, 2126, 4*w^3 - 9*w^2 - 17*w - 4]', '[2137, 2137, -w^3 + 2*w^2 + 4*w + 9]', '[2141, 2141, -4*w^3 + 12*w^2 + 14*w - 21]', '[2141, 2141, 3*w - 7]', '[2143, 2143, -2*w^3 + 9*w^2 - 2*w - 17]', '[2143, 2143, 2*w^3 - 6*w^2 - 4*w + 11]', '[2150, 430, -w^3 + 13*w - 2]', '[2150, 430, 3*w^3 - 11*w^2 + 3*w + 2]', '[2150, 430, -4*w^3 + 15*w^2 + 5*w - 8]', '[2150, 430, -2*w^3 + 8*w^2 - w - 10]', '[2150, 2150, 5*w^3 - 15*w^2 - 11*w + 8]', '[2150, 2150, 3*w^2 - 11*w + 6]', '[2150, 2150, -3*w^3 + 7*w^2 + 17*w - 6]', '[2150, 2150, -8*w^3 + 23*w^2 + 29*w - 24]', '[2152, 538, w^3 - 8*w - 2]', '[2152, 538, 5*w^3 - 12*w^2 - 22*w - 2]', '[2155, 2155, 4*w^3 - 10*w^2 - 15*w + 7]', '[2155, 2155, -3*w^3 + 12*w^2 - 2*w - 11]', '[2155, 2155, 3*w^2 - 8*w - 15]', '[2155, 2155, -w^3 + w^2 + 11*w - 1]', '[2158, 2158, -7*w^3 + 23*w^2 + 21*w - 40]', '[2158, 2158, -4*w^3 + 13*w^2 + 13*w - 20]', '[2159, 2159, -20*w^3 + 54*w^2 + 80*w - 57]', '[2159, 2159, -4*w^3 + 12*w^2 + 16*w - 17]', '[2161, 2161, -4*w^3 + 13*w^2 + 10*w - 11]', '[2161, 2161, 3*w^3 - 7*w^2 - 17*w - 3]', '[2165, 2165, -3*w^3 + 11*w^2 + 7*w - 5]', '[2165, 2165, 5*w^3 - 18*w^2 - 6*w + 5]', '[2168, 542, 11*w^3 - 28*w^2 - 48*w + 22]', '[2168, 542, 3*w^3 - 6*w^2 - 16*w - 10]', '[2176, 68, 2*w^3 - 8*w^2 - 4*w + 16]', '[2179, 2179, w^3 - 3*w^2 - 6*w + 9]', '[2180, 1090, -3*w^3 + 9*w^2 + 12*w - 16]', '[2180, 1090, -4*w^3 + 9*w^2 + 18*w + 2]', '[2180, 1090, -w^3 + 7*w^2 - 8*w - 8]', '[2180, 1090, 3*w^3 - 9*w^2 - 6*w + 8]', '[2182, 2182, 5*w^2 - w]', '[2182, 2182, -w^3 + 5*w^2 + w - 8]', '[2188, 1094, 5*w^3 - 13*w^2 - 26*w + 6]', '[2188, 1094, 2*w^3 - 3*w^2 - 4*w - 2]', '[2189, 2189, -8*w^3 + 14*w^2 + 53*w + 23]', '[2192, 274, -4*w^3 + 10*w^2 + 18*w - 2]', '[2194, 2194, -2*w^2 + 5*w + 14]', '[2194, 2194, w^3 + w^2 - 5*w]', '[2195, 2195, -4*w^3 + 16*w^2 - w - 3]', '[2195, 2195, 4*w^3 - 10*w^2 - 19*w + 15]', '[2195, 2195, 5*w^3 - 15*w^2 - 14*w + 7]', '[2195, 2195, 7*w^3 - 22*w^2 - 22*w + 17]', '[2197, 13, -4*w^3 + 10*w^2 + 19*w - 3]', '[2197, 2197, 3*w^3 - 5*w^2 - 19*w - 3]', '[2200, 110, -5*w^3 + 12*w^2 + 24*w - 12]', '[2200, 110, w^3 - 6*w^2 + 6*w + 4]', '[2200, 550, -3*w^3 + 10*w^2 + 10*w - 14]', '[2200, 550, -3*w^3 + 10*w^2 + 8*w - 10]', '[2203, 2203, 2*w^3 - w^2 - 16*w - 23]', '[2203, 2203, -2*w^3 + 7*w^2 - 7]', '[2210, 2210, 3*w^3 - 10*w^2 - 11*w + 12]', '[2210, 2210, -2*w^3 + 9*w^2 - 3*w - 4]', '[2215, 2215, 2*w^2 - 7*w + 5]', '[2215, 2215, -w^3 + 6*w^2 - 3*w - 17]', '[2215, 2215, 7*w^3 - 23*w^2 - 12*w + 9]', '[2215, 2215, 5*w^3 - 14*w^2 - 20*w + 11]', '[2216, 554, -7*w^3 + 16*w^2 + 34*w - 4]', '[2216, 554, w^3 - 6*w^2 - 6*w + 2]', '[2218, 2218, -w^3 + 7*w^2 + 7*w - 4]', '[2222, 2222, -5*w^3 + 14*w^2 + 19*w - 10]', '[2222, 2222, -3*w^3 + 10*w^2 + 11*w - 16]', '[2224, 278, -2*w^3 + 6*w^2 + 4*w - 10]', '[2225, 445, 2*w^3 - 6*w^2 - 12*w + 5]', '[2225, 445, 6*w^3 - 13*w^2 - 31*w + 3]', '[2225, 2225, w^3 - 7*w^2 + 8*w + 13]', '[2225, 2225, -2*w^3 + 20*w + 19]', '[2228, 1114, -14*w^3 + 39*w^2 + 56*w - 44]', '[2228, 1114, -3*w^3 + 5*w^2 + 12*w - 6]', '[2230, 2230, -2*w^3 + 10*w^2 - 5*w - 8]', '[2230, 2230, -2*w^3 + 6*w^2 + 9*w - 12]', '[2234, 2234, 4*w^2 - 5*w + 2]', '[2236, 1118, 4*w^3 - 9*w^2 - 18*w + 10]', '[2236, 1118, 10*w^3 - 27*w^2 - 38*w + 28]', '[2245, 2245, -6*w^3 + 21*w^2 + 8*w - 11]', '[2245, 2245, -4*w^3 + 11*w^2 + 17*w - 7]', '[2245, 2245, -w^3 + 11*w - 5]', '[2245, 2245, -w^3 - 2*w^2 + 14*w + 19]', '[2246, 2246, 5*w^3 - 13*w^2 - 19*w + 10]', '[2248, 562, 5*w^3 - 10*w^2 - 26*w - 8]', '[2248, 562, -w^3 + 6*w^2 - 2*w - 22]', '[2249, 2249, 5*w^3 - 13*w^2 - 24*w + 13]', '[2251, 2251, -2*w^3 + 2*w^2 + 14*w + 15]', '[2252, 1126, -15*w^3 + 41*w^2 + 64*w - 42]', '[2258, 2258, 3*w^3 - 6*w^2 - 13*w]', '[2258, 2258, 2*w^3 - 10*w^2 - w + 6]', '[2263, 2263, w^3 + 3*w^2 - 20*w - 17]', '[2264, 566, 13*w^3 - 36*w^2 - 56*w + 38]', '[2266, 2266, 5*w^3 - 15*w^2 - 13*w + 2]', '[2266, 2266, -w^3 + 13*w + 4]', '[2267, 2267, 5*w^3 - 13*w^2 - 17*w + 11]', '[2269, 2269, 4*w^2 - 10*w - 13]', '[2270, 2270, w^2 - 3*w - 10]', '[2270, 2270, -3*w^3 + 7*w^2 + 9*w - 4]', '[2270, 2270, 3*w - 8]', '[2270, 2270, 6*w^3 - 16*w^2 - 21*w - 4]', '[2270, 2270, 3*w^2 - 13*w - 10]', '[2270, 2270, -6*w^3 + 17*w^2 + 17*w - 2]', '[2270, 2270, -3*w^3 + 10*w^2 + 15*w - 12]', '[2270, 2270, -2*w^3 + 8*w^2 + w - 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37]', '[9988, 4994, 4*w^3 - 9*w^2 - 10*w + 2]', '[9988, 4994, 5*w^3 - 15*w^2 - 22*w + 20]', '[9988, 4994, 2*w^3 + w^2 - 22*w - 20]', '[9988, 4994, -w^3 + 7*w^2 - 8*w - 4]', '[9992, 2498, -w^3 - 4*w^2 + 20*w + 24]', '[9995, 9995, 4*w^3 - 14*w^2 - 13*w + 13]', '[9995, 9995, -w^3 + 7*w^2 - 6*w - 3]', '[9997, 9997, -6*w^3 + 20*w^2 + 13*w - 9]', '[10000, 10, 10]', '[10000, 50, -2*w^3 + 10*w^2 - 10*w - 14]', '[10000, 50, -16*w^3 + 44*w^2 + 62*w - 50]', '[10000, 50, 6*w^3 - 16*w^2 - 22*w - 2]', '[10000, 50, 8*w^3 - 22*w^2 - 34*w + 18]', '[10000, 250, 4*w^3 - 12*w^2 - 14*w + 2]', '[10000, 250, -6*w^3 + 14*w^2 + 32*w - 10]', '[10000, 1250, 2*w^3 - 4*w^2 - 8*w + 10]', '[10000, 1250, -2*w^3 + 10*w^2 - 6*w - 18]'], 'label': '4.4.16448.1', 'narrow_class_no': 2, 'primes': ['[2, 2, w]', '[5, 5, -w^3 + 3*w^2 + 2*w - 1]', '[5, 5, w - 1]', '[11, 11, w^3 - 2*w^2 - 5*w - 1]', '[13, 13, -w^3 + 3*w^2 + 3*w - 1]', '[17, 17, 2*w^3 - 5*w^2 - 9*w + 5]', '[23, 23, -w^3 + 3*w^2 + 4*w - 5]', '[25, 5, -w^2 + 3*w + 1]', '[29, 29, -2*w^3 + 6*w^2 + 5*w - 1]', '[31, 31, -w^2 + 2*w + 1]', '[43, 43, -w^3 + 3*w^2 + 2*w - 3]', '[43, 43, -w^3 + 2*w^2 + 6*w - 3]', '[59, 59, 2*w^3 - 6*w^2 - 7*w + 7]', '[73, 73, 3*w^3 - 6*w^2 - 16*w - 5]', '[79, 79, -5*w^3 + 14*w^2 + 20*w - 17]', '[81, 3, -3]', '[83, 83, -w - 3]', '[83, 83, w^2 - 3*w - 7]', '[89, 89, w^2 - 2*w - 7]', '[101, 101, -2*w^3 + 5*w^2 + 8*w - 3]', '[101, 101, 5*w^3 - 14*w^2 - 19*w + 17]', '[103, 103, -w^3 + w^2 + 8*w + 3]', '[103, 103, 2*w^3 - 5*w^2 - 7*w - 1]', '[109, 109, 3*w^3 - 7*w^2 - 14*w + 1]', '[109, 109, -w^2 + 4*w + 1]', '[127, 127, -3*w^3 + 8*w^2 + 11*w - 7]', '[127, 127, -w^3 + 2*w^2 + 7*w + 1]', '[137, 137, -2*w^3 + 5*w^2 + 9*w - 1]', '[139, 139, -w^3 + 3*w^2 + 2*w - 5]', '[149, 149, w^3 - 3*w^2 - w - 1]', '[149, 149, -2*w^3 + 4*w^2 + 10*w + 1]', '[163, 163, w^3 - 4*w^2 - w + 11]', '[163, 163, 2*w^3 - 4*w^2 - 10*w + 1]', '[173, 173, -4*w^3 + 11*w^2 + 15*w - 13]', '[179, 179, 2*w^2 - 6*w - 3]', '[179, 179, -w^3 + 2*w^2 + 7*w - 1]', '[181, 181, w^3 - 10*w - 9]', '[181, 181, -3*w^3 + 8*w^2 + 14*w - 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9*w^2 - 21*w + 3]', '[347, 347, 4*w^3 - 10*w^2 - 18*w + 5]', '[349, 349, -2*w^3 + 6*w^2 + 7*w - 3]', '[353, 353, -w^3 + 12*w + 5]', '[353, 353, w^2 - w - 7]', '[359, 359, -2*w^3 + 5*w^2 + 6*w - 7]', '[359, 359, -w^3 + 4*w^2 - 11]', '[373, 373, -w^3 + 2*w^2 + 6*w + 5]', '[379, 379, -3*w^3 + 8*w^2 + 14*w - 5]', '[397, 397, 6*w^3 - 14*w^2 - 30*w + 7]', '[401, 401, 3*w^3 - 5*w^2 - 20*w - 7]', '[409, 409, 3*w^3 - 7*w^2 - 12*w - 3]', '[409, 409, 2*w^2 - 4*w - 7]', '[421, 421, w^3 - 11*w - 11]', '[421, 421, -w^3 + 3*w^2 + w - 7]', '[431, 431, 2*w^3 - 3*w^2 - 14*w - 3]', '[431, 431, -4*w^3 + 11*w^2 + 15*w - 15]', '[433, 433, 2*w^3 - 5*w^2 - 6*w + 1]', '[439, 439, -4*w^3 + 11*w^2 + 13*w - 9]', '[439, 439, -2*w^3 + 6*w^2 + 8*w - 11]', '[443, 443, 2*w - 5]', '[443, 443, -6*w^3 + 17*w^2 + 24*w - 21]', '[449, 449, w^3 - 2*w^2 - 8*w + 3]', '[449, 449, 4*w^3 - 12*w^2 - 15*w + 17]', '[457, 457, -2*w^3 + 4*w^2 + 9*w + 5]', '[461, 461, -3*w^3 + 6*w^2 + 15*w - 1]', '[461, 461, -3*w^3 + 7*w^2 + 17*w + 1]', '[463, 463, -4*w^3 + 10*w^2 + 17*w - 7]', '[463, 463, -3*w^3 + 10*w^2 + 9*w - 17]', '[467, 467, 4*w^3 - 8*w^2 - 21*w - 7]', '[467, 467, w^3 - 6*w^2 + 3*w + 19]', '[479, 479, -w^3 + w^2 + 8*w + 1]', '[487, 487, -4*w^3 + 11*w^2 + 14*w - 15]', '[487, 487, 3*w^3 - 6*w^2 - 15*w - 5]', '[491, 491, w^2 - 5]', '[503, 503, 2*w^3 - 5*w^2 - 11*w + 3]', '[523, 523, -3*w^3 + 7*w^2 + 13*w + 1]', '[547, 547, 2*w^3 - 3*w^2 - 12*w - 3]', '[547, 547, 2*w^3 - 3*w^2 - 12*w - 9]', '[557, 557, -3*w^3 + 9*w^2 + 9*w - 11]', '[557, 557, -6*w^3 + 15*w^2 + 27*w - 13]', '[563, 563, -3*w^3 + 7*w^2 + 14*w - 7]', '[571, 571, -5*w^3 + 11*w^2 + 26*w - 3]', '[593, 593, -6*w^3 + 15*w^2 + 26*w - 7]', '[599, 599, 7*w^3 - 18*w^2 - 29*w + 17]', '[599, 599, -2*w^3 + 6*w^2 + 8*w - 3]', '[601, 601, -7*w^3 + 20*w^2 + 28*w - 23]', '[601, 601, 3*w^3 - 7*w^2 - 12*w + 5]', '[607, 607, 5*w^3 - 12*w^2 - 24*w + 9]', '[607, 607, w^3 - 5*w^2 + 15]', '[613, 613, -w^3 + 5*w^2 - 2*w - 9]', '[617, 617, w^3 + w^2 - 13*w - 15]', '[617, 617, 2*w^3 - 4*w^2 - 8*w - 1]', '[619, 619, 5*w^3 - 10*w^2 - 27*w - 7]', '[619, 619, 2*w^3 - 4*w^2 - 10*w + 3]', '[643, 643, w^3 - 5*w^2 + 5*w + 5]', '[643, 643, 4*w^3 - 9*w^2 - 20*w - 1]', '[643, 643, 3*w^3 - 7*w^2 - 14*w - 3]', '[643, 643, -3*w^3 + 7*w^2 + 13*w - 3]', '[647, 647, -3*w^3 + 8*w^2 + 12*w - 3]', '[653, 653, -w^3 + 9*w + 13]', '[653, 653, -w^3 + 4*w^2 + 3*w - 9]', '[653, 653, -2*w^3 + 7*w^2 + 4*w - 7]', '[653, 653, w^2 - 4*w - 9]', '[673, 673, -w^3 + 5*w^2 + w - 13]', '[683, 683, w^3 - 3*w^2 - 3*w - 3]', '[701, 701, 5*w^3 - 13*w^2 - 23*w + 9]', '[709, 709, 2*w^3 - w^2 - 19*w - 15]', '[719, 719, -5*w^3 + 15*w^2 + 20*w - 19]', '[727, 727, -w - 5]', '[751, 751, -4*w^3 + 10*w^2 + 15*w - 9]', '[751, 751, 6*w^3 - 17*w^2 - 22*w + 21]', '[757, 757, 3*w^3 - 6*w^2 - 18*w - 1]', '[757, 757, -w^3 + 4*w^2 + 2*w + 1]', '[769, 769, w^2 - 2*w + 3]', '[773, 773, 5*w^3 - 12*w^2 - 23*w + 9]', '[787, 787, 2*w^3 - 4*w^2 - 5*w + 1]', '[797, 797, -3*w^3 + 8*w^2 + 10*w - 3]', '[809, 809, 2*w^2 - 5*w - 1]', '[809, 809, 4*w^3 - 6*w^2 - 28*w - 11]', '[827, 827, 4*w^3 - 8*w^2 - 22*w - 1]', '[827, 827, 2*w^2 - 6*w - 9]', '[829, 829, -w^3 + w^2 + 10*w + 1]', '[839, 839, -2*w^3 + 2*w^2 + 16*w + 7]', '[877, 877, 6*w^3 - 16*w^2 - 25*w + 13]', '[877, 877, w^3 - w^2 - 7*w + 1]', '[881, 881, 2*w^3 - 2*w^2 - 15*w - 7]', '[881, 881, -4*w^3 + 7*w^2 + 26*w + 9]', '[887, 887, 2*w^3 - 4*w^2 - 13*w - 1]', '[907, 907, 5*w^3 - 11*w^2 - 26*w - 1]', '[907, 907, 5*w^3 - 13*w^2 - 22*w + 9]', '[907, 907, w^3 - 5*w^2 + 2*w + 13]', '[907, 907, -2*w^3 + 7*w^2 + 5*w - 7]', '[911, 911, -3*w^3 + 8*w^2 + 9*w - 5]', '[919, 919, -2*w^3 + 7*w^2 + 6*w - 3]', '[919, 919, -3*w^3 + 8*w^2 + 15*w - 7]', '[947, 947, -2*w^3 + 5*w^2 + 12*w - 9]', '[947, 947, -w^2 + w - 3]', '[947, 947, 3*w^3 - 6*w^2 - 14*w - 7]', '[947, 947, -w^3 + 5*w^2 - w - 17]', '[953, 953, 3*w^3 - 9*w^2 - 9*w + 13]', '[953, 953, -4*w^3 + 13*w^2 + 11*w - 23]', '[967, 967, 8*w^3 - 20*w^2 - 33*w + 19]']}
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nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [2, 0, -6, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 16448, 'disc_rad': 514, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 1]]], [5, [[2, 1], [1, 2]]], [7, [[4, 1]]], [11, [[3, 1], [1, 1]]], [13, [[3, 1], [1, 1]]], [17, [[3, 1], [1, 1]]], [19, [[4, 1]]], [23, [[3, 1], [1, 1]]], [29, [[3, 1], [1, 1]]], [31, [[3, 1], [1, 1]]], [37, [[4, 1]]], [41, [[4, 1]]], [43, [[2, 1], [1, 2]]], [47, [[4, 1]]], [53, [[4, 1]]], [59, [[3, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [36, 12], 'galois_label': '4T5', 'galt': 5, 'grd': 45.34313619501854, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.16448.1', 'local_algs': ['2.4.6.7', 'm257.1.2.0', 'm257.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 257], 'rd': 11.3247408948, 'regulator': {'__RealLiteral__': 0, 'data': '10.4571501982', 'prec': 44}, 'res': {'gal': ['1,0,-258,0,4785,0,-32862,0,107902,0,-191968,0,197815,0,-121522,0,44272,0,-9178,0,1000,0,-52,0,1'], 'sib': ['-1,0,7,0,-6,0,1', '-257,0,208,0,-33,0,1', '1,-12,-102,-124,182,302,-100,-224,21,62,-6,-6,1', '1,0,-55,0,201,0,-249,0,123,0,-23,0,1', '34,-880,-1690,-342,385,82,-32,-4,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 1 \\)', '\\( a^{3} - 3 a^{2} - 4 a + 3 \\)', '\\( a^{2} - 2 a - 5 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}