Database - hmf_fields (Information on base fields for Hilbert modular forms)

Formats: - HTML - YAML - JSON - 2026-03-15T15:48:10.998768

Query: /api/hmf_fields/?_offset=0

Column	Type
degree	smallint
discriminant	bigint
ideals	jsonb
label	text
narrow_class_no	smallint
primes	jsonb

{'degree': 3, 'discriminant': 788, 'id': 20, 'ideals': ['[1, 1, 1]', '[2, 2, -w - 1]', '[3, 3, w]', '[4, 2, w^2 - 2*w - 5]', '[5, 5, -w^2 + 2*w + 4]', '[6, 6, w^2 - w - 6]', '[8, 2, 2]', '[9, 3, w^2 - w - 7]', '[9, 9, w^2 - 2*w - 6]', '[10, 10, w - 1]', '[11, 11, -w^2 + 2*w + 2]', '[12, 6, -w^2 + 2*w + 3]', '[13, 13, w - 2]', '[15, 15, w^2 - 3*w - 3]', '[16, 4, -2*w - 2]', '[17, 17, w^2 - 2*w - 8]', '[18, 6, -w^2 + w + 4]', '[18, 18, w + 3]', '[20, 10, -w^2 + 1]', '[22, 22, -2*w^2 + 3*w + 11]', '[24, 6, 2*w]', '[25, 5, -w^2 + 2]', '[25, 25, -2*w^2 + 3*w + 14]', '[26, 26, -w^2 + w + 2]', '[27, 3, 3]', '[27, 27, -w^2 + w + 3]', '[30, 30, w^2 - w]', '[31, 31, 3*w^2 - 5*w - 19]', '[32, 4, 2*w^2 - 4*w - 10]', '[33, 33, -w^2 + w + 9]', '[34, 34, -w^2 + 3*w + 4]', '[36, 6, -w^2 + 4*w + 1]', '[36, 18, w^2 - 4*w - 3]', '[39, 39, w^2 - 2*w]', '[40, 10, -2*w^2 + 4*w + 8]', '[44, 22, w^2 - 5]', '[45, 15, 2*w^2 - 5*w - 2]', '[45, 45, 2*w^2 - 2*w - 15]', '[48, 12, 2*w^2 - 2*w - 12]', '[50, 10, -3*w^2 + 5*w + 16]', '[50, 50, w^2 - 3*w - 8]', '[51, 51, w^2 - 4*w]', '[52, 26, -3*w^2 + 4*w + 17]', '[53, 53, 2*w^2 - 3*w - 10]', '[53, 53, w^2 - 3*w - 5]', '[53, 53, 2*w - 1]', '[54, 6, -3*w - 3]', '[54, 54, w^2 + 3*w]', '[55, 55, w + 4]', '[59, 59, 2*w^2 - 4*w - 11]', '[59, 59, 2*w^2 - 6*w - 5]', '[59, 59, 2*w + 5]', '[60, 30, -w^2 + 2*w + 9]', '[62, 62, -w^2 + 3*w + 10]', '[64, 4, 4]', '[65, 65, 2*w^2 - 4*w - 13]', '[66, 66, w^2 - 3*w - 6]', '[67, 67, w^2 - 3*w - 7]', '[68, 34, -w^2 - 1]', '[71, 71, 2*w^2 - 2*w - 13]', '[72, 6, 2*w^2 - 2*w - 14]', '[72, 18, 2*w^2 - 4*w - 12]', '[73, 73, 2*w^2 - 4*w - 7]', '[75, 15, -3*w^2 + 5*w + 21]', '[75, 75, w^2 - 6]', '[78, 78, -2*w^2 + 3*w + 15]', '[79, 79, -w^2 + 10]', '[80, 20, 2*w - 2]', '[81, 9, 3*w]', '[81, 9, w^2 - 4*w - 4]', '[81, 81, -4*w - 3]', '[85, 85, 4*w^2 - 6*w - 23]', '[88, 22, -2*w^2 + 4*w + 4]', '[89, 89, 2*w^2 - w - 10]', '[90, 30, -w^2 + w + 10]', '[90, 90, -2*w^2 + 3*w + 9]', '[93, 93, -2*w^2 + 2*w + 9]', '[96, 12, -2*w^2 + 4*w + 6]', '[97, 97, -3*w^2 + 3*w + 23]', '[97, 97, -w^2 + w - 1]', '[97, 97, -w^2 - 2*w + 2]', '[99, 33, 2*w^2 - 5*w - 8]', '[99, 99, 2*w - 3]', '[100, 10, w^2 - 7]', '[100, 50, w^2 - 2*w + 1]', '[102, 102, 2*w^2 - 3*w - 3]', '[103, 103, 2*w^2 - 4*w - 5]', '[104, 26, 2*w - 4]', '[106, 106, -w^2 - w + 4]', '[106, 106, w^2 + w + 2]', '[106, 106, -2*w^2 - w + 1]', '[108, 6, 3*w^2 - 6*w - 15]', '[108, 54, w^2 - 9]', '[110, 110, 2*w^2 - 7*w - 5]', '[113, 113, w^2 - 8]', '[117, 39, -2*w^2 + 2*w + 17]', '[117, 117, -3*w^2 + 5*w + 15]', '[118, 118, w + 5]', '[118, 118, 4*w^2 - 7*w - 23]', '[118, 118, -5*w^2 + 7*w + 34]', '[120, 30, 2*w^2 - 6*w - 6]', '[121, 11, -4*w^2 + 9*w + 14]', '[121, 121, 4*w^2 - 7*w - 26]', '[124, 62, w^2 - 4*w - 5]', '[125, 5, 5]', '[125, 125, -w^2 + 5*w + 1]', '[127, 127, 2*w^2 - 3*w - 8]', '[127, 127, -3*w^2 + 4*w + 22]', '[127, 127, -4*w^2 + 5*w + 26]', '[128, 8, -4*w - 4]', '[130, 130, w^2 - 3*w + 2]', '[131, 131, w^2 - 2*w - 10]', '[132, 66, w^2 + 2*w + 3]', '[134, 134, w^2 + 3*w + 4]', '[135, 15, -3*w^2 + 6*w + 12]', '[135, 135, -w + 6]', '[136, 34, 2*w^2 - 4*w - 16]', '[139, 139, -w^2 - 3*w + 1]', '[142, 142, -2*w^2 + w + 7]', '[143, 143, -4*w - 5]', '[144, 12, -2*w^2 + 2*w + 8]', '[144, 36, 2*w + 6]', '[146, 146, -3*w + 1]', '[149, 149, -6*w^2 + 10*w + 35]', '[150, 30, 2*w^2 - 5*w - 9]', '[150, 150, -3*w^2 + 7*w + 6]', '[151, 151, -5*w^2 + 8*w + 28]', '[153, 51, 2*w^2 + w - 2]', '[153, 153, -3*w^2 + 7*w + 3]', '[155, 155, -2*w^2 + 3*w + 4]', '[156, 78, w^2 - 4*w - 9]', '[158, 158, 2*w^2 - 3*w - 7]', '[159, 159, -2*w^2 + 2*w + 3]', '[159, 159, -w^2 + 4*w + 6]', '[159, 159, 2*w^2 - w]', '[160, 20, -2*w^2 + 2]', '[162, 18, 3*w^2 - 3*w - 18]', '[162, 18, 4*w^2 - 7*w - 25]', '[162, 162, 3*w^2 - 7*w - 12]', '[163, 163, -5*w^2 + 10*w + 22]', '[163, 163, -3*w^2 + 7*w + 7]', '[163, 163, w^2 + 2]', '[165, 165, w^2 + 4*w]', '[167, 167, 2*w^2 - 3*w - 16]', '[169, 13, w^2 + w - 5]', '[169, 169, -w^2 + 3*w + 11]', '[170, 170, -2*w^2 + w + 11]', '[173, 173, 3*w^2 - 6*w - 16]', '[173, 173, 4*w^2 - 8*w - 17]', '[173, 173, -4*w^2 + 7*w + 20]', '[176, 44, -4*w^2 + 6*w + 22]', '[177, 177, 2*w^2 - w - 18]', '[177, 177, -2*w^2 + 3*w + 6]', '[177, 177, -8*w^2 + 11*w + 48]', '[178, 178, -3*w^2 - 3*w + 4]', '[179, 179, w^2 - w - 11]', '[180, 30, w^2 - 4*w - 7]', '[180, 90, w^2 + 2*w - 3]', '[181, 181, -2*w^2 + w + 20]', '[181, 181, 5*w + 4]', '[181, 181, w^2 - 4*w - 8]', '[186, 186, 2*w^2 + 3*w - 3]', '[187, 187, 2*w^2 - 2*w - 7]', '[192, 12, 4*w]', '[193, 193, -w^2 + 2*w - 2]', '[193, 193, -4*w^2 + 9*w + 16]', '[193, 193, 2*w^2 - 6*w - 7]', '[194, 194, w^2 + 7*w + 4]', '[194, 194, 3*w^2 - 5*w - 14]', '[194, 194, -3*w^2 + 3*w + 22]', '[195, 195, -2*w^2 + w + 6]', '[197, 197, 2*w^2 - 5*w - 10]', '[197, 197, -5*w^2 + 9*w + 25]', '[198, 66, w^2 - w + 2]', '[198, 198, -2*w^2 + w + 3]', '[199, 199, w^2 - 5*w - 5]', '[200, 10, -2*w^2 + 4]', '[200, 50, -4*w^2 + 6*w + 28]', '[201, 201, -2*w^2 + 3]', '[204, 102, 3*w^2 - 4*w - 15]', '[206, 206, -5*w - 1]', '[208, 52, -2*w^2 + 2*w + 4]', '[211, 211, 3*w - 2]', '[212, 106, 3*w^2 - 6*w - 5]', '[212, 106, -w^2 + 13]', '[212, 106, -3*w^2 + 6*w + 11]', '[213, 213, w + 6]', '[216, 6, 6]', '[216, 54, -2*w^2 + 2*w + 6]', '[219, 219, -2*w^2 + 7*w + 6]', '[220, 110, 3*w^2 - 6*w - 17]', '[221, 221, -3*w^2 + 3*w + 19]', '[225, 15, 2*w^2 - 5*w - 14]', '[225, 45, -w^2 + 5*w - 3]', '[225, 75, -2*w^2 + 2*w + 5]', '[225, 225, w^2 + w + 3]', '[226, 226, -2*w^2 + w + 5]', '[227, 227, -w^2 + 5*w - 1]', '[229, 229, -2*w^2 + w + 4]', '[234, 78, 2*w^2 - 5*w - 11]', '[234, 234, w^2 + w - 6]', '[236, 118, -5*w^2 + 6*w + 37]', '[236, 118, -w^2 + 2*w + 11]', '[236, 118, 3*w^2 - 6*w - 19]', '[237, 237, -w^2 + 3*w - 3]', '[240, 60, 2*w^2 - 2*w]', '[241, 241, -w^2 - w + 13]', '[242, 22, -w^2 + 5*w - 2]', '[242, 242, -w + 7]', '[243, 9, 3*w^2 - 3*w - 21]', '[243, 27, 3*w^2 - 6*w - 18]', '[243, 243, 2*w^2 - w - 12]', '[248, 62, 6*w^2 - 10*w - 38]', '[250, 10, -5*w - 5]', '[250, 250, 3*w^2 - 3*w - 20]', '[254, 254, -w^2 - 3*w + 2]', '[254, 254, 2*w^2 - 5*w - 13]', '[254, 254, 3*w^2 - 3*w - 14]', '[255, 255, -2*w^2 + 5*w + 12]', '[256, 8, 4*w^2 - 8*w - 20]', '[260, 130, w^2 - 6*w - 5]', '[262, 262, 5*w + 7]', '[263, 263, 3*w^2 - 7*w - 13]', '[264, 66, -2*w^2 + 2*w + 18]', '[265, 265, -3*w^2 + 11*w + 7]', '[265, 265, 3*w^2 - 8*w - 10]', '[265, 265, 3*w - 8]', '[267, 267, w^2 + 4*w + 6]', '[268, 134, -3*w^2 + 4*w + 23]', '[269, 269, -2*w - 7]', '[270, 30, 3*w - 3]', '[270, 270, w^2 - 5*w - 6]', '[271, 271, w^2 + 2*w + 4]', '[272, 68, -2*w^2 + 6*w + 8]', '[275, 55, 6*w^2 - 10*w - 37]', '[275, 275, -3*w^2 + 5*w + 13]', '[277, 277, 3*w^2 - 6*w - 10]', '[278, 278, -2*w^2 + w + 17]', '[279, 93, w^2 + 2*w - 4]', '[279, 279, -5*w - 6]', '[281, 281, -3*w - 8]', '[283, 283, -w^2 + 5*w - 7]', '[284, 142, -9*w^2 + 14*w + 53]', '[286, 286, 5*w^2 - 9*w - 28]', '[288, 12, -2*w^2 + 8*w + 2]', '[288, 36, 2*w^2 - 8*w - 6]', '[289, 17, w^2 + 3*w + 5]', '[289, 289, w^2 - 7*w - 5]', '[291, 291, 2*w - 9]', '[291, 291, -8*w - 3]', '[291, 291, -5*w^2 + 9*w + 33]', '[292, 146, -w^2 - 2*w + 17]', '[295, 295, 3*w^2 - 2*w - 26]', '[295, 295, w^2 + w - 7]', '[295, 295, -3*w^2 + 4*w + 14]', '[297, 33, -3*w^2 + 6*w + 6]', '[297, 297, 2*w^2 - 3*w]', '[298, 298, 2*w^2 - 3*w - 17]', '[300, 30, w^2 + 3]', '[300, 150, -5*w^2 + 8*w + 27]', '[302, 302, -4*w^2 - w + 1]', '[306, 102, 4*w^2 - 7*w - 19]', '[306, 306, w^2 - w - 12]', '[307, 307, 4*w - 1]', '[309, 309, -2*w^2 + 9*w + 6]', '[310, 310, -5*w^2 + 7*w + 28]', '[312, 78, 2*w^2 - 4*w]', '[316, 158, -w^2 - 4*w + 1]', '[317, 317, 3*w - 4]', '[318, 318, -4*w^2 + 5*w + 21]', '[318, 318, -2*w^2 - 3*w - 3]', '[318, 318, -w^2 + 3*w + 12]', '[320, 20, -4*w^2 + 8*w + 16]', '[324, 18, w^2 - 4*w + 5]', '[324, 18, -3*w^2 + 6*w + 9]', '[324, 162, w^2 - 2*w + 3]', '[325, 65, w^2 - 5*w - 7]', '[325, 325, 5*w^2 - 6*w - 34]', '[326, 326, -w^2 - w + 16]', '[326, 326, 3*w - 7]', '[326, 326, -w^2 + 7*w + 2]', '[330, 330, w^2 + w - 12]', '[334, 334, -w^2 + 5*w + 10]', '[335, 335, 2*w^2 - w - 16]', '[337, 337, 6*w + 5]', '[338, 26, -3*w^2 - 3*w + 2]', '[338, 338, 2*w^2 - 7*w - 7]', '[339, 339, w^2 - w + 3]', '[340, 170, 3*w^2 - 6*w - 7]', '[341, 341, 2*w^2 - w - 14]', '[343, 7, -7]', '[346, 346, w + 7]', '[346, 346, w^2 + w - 8]', '[346, 346, -3*w + 5]', '[347, 347, w^2 + 7*w + 5]', '[347, 347, -7*w^2 + 9*w + 47]', '[347, 347, 3*w^2 - 6*w - 8]', '[349, 349, 6*w^2 - 11*w - 32]', '[351, 39, 3*w - 6]', '[351, 351, 2*w^2 - 6*w - 9]', '[352, 44, 2*w^2 - 10]', '[354, 354, -3*w^2 + 5*w + 12]', '[354, 354, -9*w^2 + 13*w + 54]', '[354, 354, 2*w^2 - w - 15]', '[355, 355, 7*w^2 - 12*w - 40]', '[356, 178, -7*w^2 + 10*w + 41]', '[358, 358, -w^2 + 5*w + 8]', '[359, 359, -5*w^2 + 6*w + 32]', '[360, 30, 4*w^2 - 10*w - 4]', '[360, 90, 4*w^2 - 4*w - 30]', '[362, 362, -4*w^2 + 9*w + 17]', '[362, 362, 2*w^2 + 5*w + 5]', '[362, 362, 3*w^2 - 7*w - 14]', '[363, 33, 5*w^2 - 14*w - 12]', '[363, 363, -4*w^2 + 9*w + 12]', '[365, 365, -w^2 + 6*w - 10]', '[367, 367, -2*w^2 - 3*w + 4]', '[372, 186, 5*w^2 - 6*w - 33]', '[373, 373, 3*w^2 - 3*w - 13]', '[374, 374, 3*w^2 - 11*w - 4]', '[375, 15, 5*w]', '[375, 375, 4*w^2 - 8*w - 21]', '[379, 379, -4*w^2 + 6*w + 29]', '[379, 379, w^2 + w - 11]', '[379, 379, 6*w^2 - 9*w - 34]', '[381, 381, w^2 + w - 9]', '[381, 381, -w^2 + 6*w + 6]', '[381, 381, w^2 - 2*w - 12]', '[383, 383, 5*w^2 - 9*w - 29]', '[384, 24, 4*w^2 - 4*w - 24]', '[386, 386, 7*w + 5]', '[386, 386, -w^2 + 3*w - 4]', '[386, 386, 2*w^2 - w + 1]', '[388, 194, -w^2 - 2*w + 5]', '[388, 194, -3*w^2 + 8*w + 11]', '[388, 194, 3*w^2 - 4*w - 13]', '[389, 389, w - 8]', '[390, 390, -2*w^2 + 9*w + 3]', '[393, 393, -w^2 - 3*w + 3]', '[394, 394, w^2 + w + 4]', '[394, 394, w^2 + w - 10]', '[395, 395, -2*w^2 - w - 2]', '[396, 66, -5*w^2 + 8*w + 35]', '[396, 198, -5*w^2 + 6*w + 27]', '[397, 397, -w^2 + 14]', '[398, 398, 3*w^2 + 3*w + 2]', '[400, 20, -6*w^2 + 10*w + 32]', '[400, 100, 2*w^2 - 6*w - 16]', '[402, 402, -6*w^2 + 7*w + 33]', '[403, 403, -8*w^2 + 12*w + 47]', '[405, 45, 3*w^2 - 9*w - 9]', '[405, 45, 2*w^2 + w - 8]', '[405, 405, -w^2 + 6*w]', '[408, 102, 2*w^2 - 8*w]', '[412, 206, w^2 - 6*w + 7]', '[416, 52, -6*w^2 + 8*w + 34]', '[417, 417, -4*w^2 + 8*w + 27]', '[421, 421, -4*w^2 + 3*w + 34]', '[422, 422, -3*w^2 - w + 2]', '[424, 106, 4*w^2 - 6*w - 20]', '[424, 106, 2*w^2 - 6*w - 10]', '[424, 106, 4*w - 2]', '[425, 85, 3*w^2 - 5*w - 11]', '[425, 425, -3*w^2 + 10*w + 8]', '[426, 426, -11*w^2 + 17*w + 72]', '[429, 429, 2*w^2 - 21]', '[432, 12, -6*w - 6]', '[432, 108, 2*w^2 + 6*w]', '[438, 438, -5*w^2 + 9*w + 30]', '[439, 439, 4*w^2 - 9*w - 8]', '[440, 110, 2*w + 8]', '[442, 442, 4*w^2 - 9*w - 11]', '[445, 445, 5*w^2 - 9*w - 31]', '[447, 447, 4*w^2 - 7*w - 18]', '[450, 30, 2*w^2 - 5*w + 1]', '[450, 90, -3*w^2 + 5*w + 6]', '[450, 150, -8*w^2 + 11*w + 47]', '[450, 450, -2*w^2 + w + 21]', '[452, 226, -7*w^2 + 12*w + 37]', '[453, 453, 5*w^2 - 5*w - 3]', '[454, 454, -3*w^2 + 3*w + 4]', '[458, 458, -6*w^2 + 11*w + 29]', '[459, 51, 3*w^2 - 6*w - 24]', '[459, 459, 4*w^2 - 8*w - 15]', '[461, 461, 2*w^2 - 7*w - 8]', '[463, 463, 2*w^2 - 2*w - 19]', '[465, 465, -3*w^2 + 4*w + 24]', '[467, 467, 2*w^2 - 8*w - 7]', '[468, 78, w^2 + 2*w + 5]', '[468, 234, -5*w^2 + 12*w + 9]', '[472, 118, 4*w^2 - 8*w - 22]', '[472, 118, 4*w^2 - 12*w - 10]', '[472, 118, 4*w + 10]', '[474, 474, -w^2 + 7*w + 6]', '[477, 159, -2*w^2 + 2*w - 1]', '[477, 159, -5*w^2 + 8*w + 26]', '[477, 159, -w^2 + w + 13]', '[477, 477, -2*w^2 + 3*w + 18]', '[477, 477, -3*w^2 + 4*w + 12]', '[477, 477, 3*w^2 - w - 3]', '[479, 479, 4*w^2 - 5*w - 20]', '[479, 479, 6*w + 7]', '[479, 479, 2*w^2 - 11]', '[480, 60, -2*w^2 + 4*w + 18]', '[482, 482, 3*w^2 - 5*w - 10]', '[484, 22, w^2 + 6*w - 31]', '[484, 242, w^2 - 6*w - 7]', '[485, 485, -w^2 - 4]', '[485, 485, -2*w^2 + 6*w + 11]', '[485, 485, 4*w^2 - 9*w - 10]', '[486, 18, -3*w^2 + 3*w + 12]', '[486, 54, 3*w + 9]', '[486, 486, -4*w^2 + 9*w + 9]', '[489, 489, 4*w^2 - 14*w - 9]', '[489, 489, 5*w^2 - 13*w - 15]', '[489, 489, -5*w^2 + 7*w + 27]', '[495, 165, 4*w^2 - 4*w - 25]', '[495, 495, 3*w^2 - 7*w - 21]', '[496, 124, -2*w^2 + 6*w + 20]', '[499, 499, -w^2 - 4*w + 2]', '[499, 499, -w^2 + 2*w - 4]', '[499, 499, 4*w^2 - 4*w - 29]', '[500, 10, 5*w^2 - 10*w - 25]', '[500, 250, -3*w^2 + 2*w + 11]', '[501, 501, -w^2 - 2*w + 6]', '[507, 39, 2*w^2 + 2*w + 3]', '[507, 507, -3*w^2 + 11*w + 3]', '[508, 254, -3*w^2 + 2*w + 25]', '[508, 254, w^2 + 4*w + 7]', '[508, 254, -3*w^2 - 4*w + 5]', '[509, 509, 3*w^2 - 5*w - 7]', '[510, 510, -w^2 - 3*w - 6]', '[512, 8, 8]', '[515, 515, -3*w^2 + 10*w - 2]', '[519, 519, -3*w^2 + 5*w + 9]', '[519, 519, 3*w^2 - 8*w - 12]', '[519, 519, -4*w^2 + 11*w + 12]', '[520, 130, 4*w^2 - 8*w - 26]', '[523, 523, -w - 8]', '[524, 262, -7*w^2 + 12*w + 41]', '[526, 526, w^2 - w + 4]', '[527, 527, -2*w^2 - 7*w - 8]', '[528, 132, 2*w^2 - 6*w - 12]', '[530, 530, 2*w^2 - 3*w + 1]', '[530, 530, -3*w^2 + 7*w + 16]', '[530, 530, -3*w^2 + 5*w + 8]', '[531, 177, -11*w^2 + 17*w + 65]', '[531, 177, -5*w^2 + 11*w + 17]', '[531, 177, 5*w^2 - 5*w - 29]', '[531, 531, w^2 - 4*w + 6]', '[531, 531, -7*w^2 + 10*w + 48]', '[531, 531, 4*w^2 - 9*w - 18]', '[534, 534, -8*w^2 + 15*w + 57]', '[536, 134, 2*w^2 - 6*w - 14]', '[537, 537, -4*w + 3]', '[538, 538, 2*w^2 + 9*w + 7]', '[540, 30, -3*w^2 + 3]', '[540, 270, 7*w^2 - 12*w - 45]', '[541, 541, 4*w^2 - 8*w - 23]', '[542, 542, -3*w^2 + 3*w + 26]', '[543, 543, -w^2 + 6*w - 6]', '[543, 543, -3*w^2 - w + 3]', '[543, 543, -3*w^2 + 2*w + 18]', '[544, 68, -2*w^2 - 2]', '[547, 547, 2*w^2 - 6*w - 13]', '[550, 110, -2*w^2 + 5*w + 19]', '[550, 550, w^2 + 3*w - 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8]', '[1854, 1854, 4*w^2 - 3*w - 9]', '[1857, 1857, -w^2 + 11*w + 9]', '[1857, 1857, -10*w^2 + 14*w + 57]', '[1857, 1857, 4*w^2 - 12*w - 15]', '[1858, 1858, 6*w^2 - 13*w - 17]', '[1859, 143, 2*w^2 - 11*w - 10]', '[1859, 1859, -4*w^2 + 3*w + 10]', '[1860, 930, 3*w^2 + 8*w + 9]', '[1865, 1865, 4*w^2 - 5*w - 34]', '[1867, 1867, -4*w^2 + 2*w + 35]', '[1868, 934, 3*w^2 - 10*w + 5]', '[1870, 1870, -2*w^2 + 9*w + 13]', '[1871, 1871, -8*w^2 + 15*w + 44]', '[1872, 156, 4*w^2 - 10*w - 22]', '[1872, 468, 2*w^2 + 2*w - 12]', '[1874, 1874, -5*w^2 + 3*w + 44]', '[1875, 75, -6*w^2 + 10*w + 27]', '[1875, 75, 5*w^2 - 15*w - 15]', '[1875, 1875, -5*w^2 - 3*w + 3]', '[1879, 1879, 6*w^2 - 12*w - 35]', '[1882, 1882, -2*w^2 + 9*w + 19]', '[1888, 236, -10*w^2 + 12*w + 74]', '[1888, 236, -2*w^2 + 4*w + 22]', '[1888, 236, 6*w^2 - 12*w - 38]', '[1889, 1889, 2*w^2 - 10*w - 11]', '[1889, 1889, -15*w^2 + 27*w + 77]', '[1889, 1889, -4*w^2 - 9*w + 2]', '[1894, 1894, 3*w^2 + 7*w + 8]', '[1895, 1895, 10*w^2 - 21*w - 44]', '[1895, 1895, 2*w^2 + 12*w + 11]', '[1895, 1895, 5*w^2 + 11*w - 1]', '[1896, 474, -2*w^2 + 6*w - 6]', '[1898, 1898, -3*w^2 + 7*w - 2]', '[1899, 633, -2*w^2 + 2*w + 23]', '[1899, 1899, -5*w^2 + 7*w + 21]', '[1901, 1901, 7*w^2 - 16*w - 20]', '[1902, 1902, -4*w^2 + 7*w + 33]', '[1903, 1903, -2*w^2 + 10*w - 5]', '[1903, 1903, 3*w^2 - 11*w + 7]', '[1903, 1903, -7*w^2 + 22*w + 2]', '[1905, 1905, 10*w^2 - 11*w - 54]', '[1905, 1905, 2*w^2 - 10*w + 3]', '[1905, 1905, 7*w^2 - 14*w - 48]', '[1906, 1906, -4*w^2 - 7*w + 5]', '[1908, 318, -5*w^2 + 14*w + 17]', '[1908, 318, -7*w^2 + 16*w + 13]', '[1908, 318, 7*w^2 - 16*w - 7]', '[1908, 954, 5*w^2 - 10*w - 3]', '[1908, 954, -7*w^2 + 12*w + 9]', '[1908, 954, w^2 - 8*w + 3]', '[1913, 1913, -9*w^2 + 15*w + 47]', '[1915, 1915, -5*w^2 - 4*w + 4]', '[1916, 958, -11*w^2 + 14*w + 73]', '[1916, 958, w^2 - 2*w - 17]', '[1916, 958, -9*w^2 + 14*w + 49]', '[1917, 213, 6*w^2 - 6*w - 39]', '[1917, 1917, 5*w^2 - 11*w - 33]', '[1920, 120, 4*w^2 - 4*w]', '[1921, 1921, -10*w^2 + 12*w + 61]', '[1922, 62, 5*w^2 - 11*w - 28]', '[1922, 1922, 3*w^2 - 3*w + 2]', '[1923, 1923, -2*w^2 + 8*w - 9]', '[1928, 482, -2*w^2 - 2*w + 26]', '[1929, 1929, -w^2 + 9*w + 15]', '[1930, 1930, -6*w^2 + 13*w + 13]', '[1930, 1930, 2*w^2 - 11*w - 1]', '[1930, 1930, 9*w^2 - 21*w - 28]', '[1933, 1933, w^2 + 4*w - 8]', '[1933, 1933, 3*w^2 - 4*w - 28]', '[1933, 1933, 6*w - 5]', '[1934, 1934, -w + 13]', '[1936, 44, -2*w^2 + 10*w - 4]', '[1936, 484, -2*w + 14]', '[1937, 1937, 16*w^2 - 27*w - 88]', '[1940, 970, -5*w^2 + 12*w + 23]', '[1940, 970, 3*w^2 - 2*w - 31]', '[1940, 970, 7*w^2 + 4*w - 1]', '[1941, 1941, 5*w^2 - 5*w - 21]', '[1942, 1942, -w^2 - 7*w + 2]', '[1944, 18, 6*w^2 - 6*w - 42]', '[1944, 54, 6*w^2 - 12*w - 36]', '[1944, 486, 4*w^2 - 2*w - 24]', '[1945, 1945, 9*w^2 - 19*w - 35]', '[1947, 1947, 15*w^2 - 25*w - 87]', '[1947, 1947, 4*w^2 - 10*w - 27]', '[1947, 1947, -5*w^2 + 9*w + 39]', '[1949, 1949, -6*w^2 + 12*w + 37]', '[1950, 390, -7*w^2 + 15*w + 24]', '[1950, 1950, w^2 - 9*w - 12]', '[1954, 1954, -w^2 - 13*w - 4]', '[1956, 978, 9*w^2 - 26*w - 9]', '[1956, 978, -7*w^2 + 10*w + 51]', '[1956, 978, -5*w^2 + 8*w + 9]', '[1958, 1958, 15*w^2 - 25*w - 98]', '[1963, 1963, 7*w^2 - 17*w - 7]', '[1965, 1965, -4*w^2 + 11*w + 18]', '[1966, 1966, 3*w + 13]', '[1969, 1969, 6*w^2 - 13*w - 16]', '[1970, 1970, -5*w^2 + 9*w + 16]', '[1970, 1970, 9*w^2 - 19*w - 40]', '[1971, 219, 6*w^2 - 12*w - 21]', '[1971, 1971, -w^2 + 3*w - 9]', '[1973, 1973, -10*w^2 + 21*w + 40]', '[1975, 395, -4*w^2 + 10*w + 23]', '[1975, 1975, 5*w^2 - 9*w - 11]', '[1977, 1977, -8*w^2 + 9*w + 42]', '[1980, 330, -w^2 + 10*w + 1]', '[1980, 990, w^2 - 12*w - 9]', '[1984, 124, 12*w^2 - 20*w - 76]', '[1985, 1985, 2*w^2 + 11*w + 2]', '[1987, 1987, 5*w^2 - 4*w - 20]', '[1989, 663, -w^2 + 10*w + 10]', '[1989, 1989, -2*w^2 - 9*w]', '[1990, 1990, -5*w^2 + 7*w + 8]', '[1991, 1991, 7*w^2 - 11*w - 35]', '[1991, 1991, -6*w^2 + 8*w + 29]', '[1991, 1991, 8*w - 1]', '[1994, 1994, 2*w^2 - w + 5]', '[1996, 998, 5*w^2 - 8*w - 19]', '[1996, 998, -7*w^2 + 16*w + 29]', '[1996, 998, 3*w^2 + 6*w - 5]', '[1997, 1997, 2*w^2 - 9*w - 14]', '[1999, 1999, -14*w^2 + 24*w + 79]', '[1999, 1999, -4*w^2 + 3*w + 38]', '[1999, 1999, -w^2 + 4*w - 10]', '[2000, 20, -10*w - 10]', '[2000, 500, 6*w^2 - 6*w - 40]', '[2004, 1002, 7*w^2 - 12*w - 33]', '[2006, 2006, -2*w^2 - 3*w - 7]', '[2006, 2006, w^2 + w - 20]', '[2006, 2006, -w^2 + 9*w + 14]', '[2010, 2010, -11*w - 9]', '[2011, 2011, 6*w^2 - 6*w - 41]', '[2011, 2011, 6*w^2 - 13*w - 14]', '[2011, 2011, -w^2 + 9*w + 13]', '[2015, 2015, -w^2 - 11*w - 13]', '[2019, 2019, -w^2 + 13*w + 9]', '[2022, 2022, 6*w^2 - 13*w - 15]', '[2025, 45, -9*w^2 + 15*w + 63]', '[2025, 45, 2*w^2 + 10*w + 1]', '[2025, 225, 3*w^2 - 18]', '[2025, 225, 5*w^2 - 11*w - 29]', '[2025, 405, -8*w^2 + 15*w + 36]', '[2025, 2025, 2*w^2 - 9*w - 18]', '[2027, 2027, -2*w^2 + 4*w - 5]', '[2028, 78, 3*w^2 - 10*w - 15]', '[2028, 1014, -5*w^2 + 6*w + 21]', '[2031, 2031, -w^2 - 16*w - 6]', '[2032, 508, -2*w^2 - 6*w + 4]', '[2032, 508, 4*w^2 - 10*w - 26]', '[2032, 508, 6*w^2 - 6*w - 28]', '[2034, 678, 5*w^2 - 11*w - 32]', '[2034, 2034, 4*w^2 - w - 21]', '[2036, 1018, w^2 - 8*w + 11]', '[2039, 2039, 11*w^2 - 14*w - 70]', '[2040, 510, -4*w^2 + 10*w + 24]', '[2043, 681, -w^2 - 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