# Stored data for newform 112.6.a.f, downloaded from the LMFDB on 10 June 2026.
{"Nk2": 4032, "analytic_conductor": 17.96298781905383, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [7, 1]], "atkin_lehner_string": "++", "char_conductor": 1, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [112, 1, [15, 85, 17], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[3, [-6, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22517998237515888, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "112.6.a.f", "level": 112, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 7], "level_radical": 14, "minimal_twist": "56.6.a.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+6q^{3}+4q^{5}-7^{2}q^{7}-207q^{9}+240q^{11}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "5.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "112.6.a", "trace_display": [0, 6, 4, -49], "trace_hash": 516785333937251491, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.022", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.116", "prec": 17}], "trace_zratio": 0, "traces": [0, 1, 0, 6, 0, 4, 0, -49, 0, -207, 0, 240, 0, -744, 0, 24, 0, -1042, 0, 986, 0, -294, 0, -184, 0, -3109, 0, -2700, 0, -734, 0, -5140, 0, 1440, 0, -196, 0, -6054, 0, -4464, 0, 7598, 0, -13016, 0, -828, 0, -14668, 0, 2401, 0, -6252, 0, -14522, 0, 960, 0, 5916, 0, 13362, 0, 9676, 0, 10143, 0, -2976, 0, 62124, 0, -1104, 0, 2112, 0, -28910, 0, -18654, 0, -11760, 0, 101768, 0, 34101, 0, 23922, 0, -4168, 0, -4404, 0, 141674, 0, 36456, 0, -30840, 0, 3944, 0, 99982, 0, -49680, 0, -108684, 0, -87396, 0, -1176, 0, -71892, 0, -118166, 0, -36324, 0, 252774, 0, -736, 0, 154008, 0, 51058, 0, -103451, 0, 45588, 0, -24936, 0, 3592, 0, -78096, 0, -364534, 0, -48314, 0, -10800, 0, -77246, 0, 122742, 0, -88008, 0, -178560, 0, -2936, 0, 14406, 0, -469234, 0, 411584, 0, 215694, 0, -20560, 0, -574632, 0, -87132, 0, 9016, 0, 264704, 0, 5760, 0, -343356, 0, 182243, 0, -204102, 0, -303296, 0, 152341, 0, 80172, 0, 362756, 0, -146560, 0, 58056, 0, -24216, 0, -250080, 0, 132300, 0, -552536, 0, 305358, 0, -17856, 0, 743838, 0, -286220, 0, 372744, 0, 35966, 0, 30392, 0, 38088, 0, 236640, 0, 895372, 0, 12672, 0, -52064, 0, 251860, 0, -173460, 0, 775248, 0, 1188120, 0, 643563, 0, -808822, 0, -344344, 0, -70560, 0, -334022, 0, -58672, 0, 610608, 0, 954272, 0, -272882, 0, 860706, 0, 9604, 0, -733584, 0, 143532, 0, -43754, 0, -44160, 0, -25008, 0, -1732014, 0, 296646, 0, 151938, 0, -613248, 0, -58088, 0, 850044, 0, -2013600, 0, 1221376, 0, 218736, 0, -746160, 0, 2118214, 0, 1063980, 0, -1645158, 0, -1663934, 0, 23664, 0, -372302, 0, -334093, 0, 599892, 0, -1157316, 0, 53448, 0, -648000, 0, 136896, 0, 637784, 0, -652104, 0, 38704, 0, -344998, 0, -524376, 0, -3287976, 0, -2210626, 0, 40572, 0, 1196310, 0, -176160, 0, -431352, 0, -1027412, 0, 2313096, 0, -708996, 0, 718732, 0, -2128280, 0, 1253178, 0, 248496, 0, 1898414, 0, 1516644, 0, -1233600, 0, -117649, 0, -4416, 0, -2175480, 0, 2129504, 0, 2008800, 0, -2541438, 0, 8448, 0, 306348, 0, 479280, 0, -1503903, 0, -620706, 0, -115640, 0, -1893896, 0, -1572786, 0, 711578, 0, 1566830, 0, -149616, 0, 546096, 0, 57360, 0, 21552, 0, 4412388, 0, -47040, 0, 2694312, 0, -872470, 0, 191728, 0, -2187204, 0, 407072, 0, 3631696, 0, -289884, 0, -3584226, 0, 3824160, 0, 136404, 0, -1452960, 0, 2183094, 0, -463476, 0, -654738, 0, 95688, 0, 736452, 0, 4911374, 0, 693766, 0, 3036276, 0, 3239578, 0, -474124, 0, -1071360, 0, 1250352, 0, 157750, 0, -17616, 0, -181424, 0, -263736, 0, -497007, 0, 1504100, 0, 566696, 0, -2815404, 0, 2111282, 0, 1823520, 0, 2469504, 0, 145824, 0, 3999382, 0, 2813400, 0, -2240904, 0, 1473040, 0, -123360, 0, -8504718, 0, -3044076, 0, -3447792, 0, -3123840, 0, -3065474, 0, 3006054, 0, 6569836, 0, 4504176, 0, 54096, 0, 399928, 0, -7710376, 0, 1588224, 0, -8721468, 0, 764828, 0, -198720, 0, -103488, 0, 7874300, 0, -2060136, 0, -8687264, 0, -434736, 0, 1093458, 0, -1341312, 0, 1416590, 0, -2662200, 0, -349584, 0, -3520320, 0, -1819776, 0, 6001854, 0, -11910854, 0, 914046, 0, 5355880, 0, -6402487, 0, -2765934, 0, -5652912, 0, -287568, 0, 2176536, 0, 576240, 0, -7207034, 0, -879360, 0, -472664, 0, -1651720, 0, -2002932, 0, -723724, 0, -4986632, 0, -145296, 0, -7581706, 0, 9683904, 0, -1500480, 0, 12656806, 0, 1011096, 0, -1670949, 0, 4574454, 0, 5778016, 0, -3315216, 0, 572056, 0, 5465202, 0, 1832148, 0, -1172178, 0, -3485280, 0, 616032, 0, -9893858, 0, -5068040, 0, 4463028, 0, 6126858, 0, 204232, 0, -1717320, 0, -299432, 0, -4981334, 0, -12859668, 0, -413804, 0, 11069408, 0, 215796, 0, 10912992, 0, -13782902, 0, 182352, 0, 11145030, 0, 3007218, 0, 496800, 0, -6942026, 0, 9615881, 0, 1419840, 0, 6308268, 0, 570304, 0, 5372232, 0, 14368, 0, -1786344, 0, -437184, 0, 13735934, 0, -2586922, 0, -312384, 0, -6524460, 0, 3206880, 0, 1511160, 0, 3757930, 0, -1458136, 0, 5984370, 0, 6974360, 0, 11705948, 0, 4651488, 0, -193256, 0, 135056, 0, 7128720, 0, 2322240, 0, -18282518, 0, 8394300, 0, 2056608, 0, -4899118, 0, -4852932, 0, -12491340, 0, -308984, 0, -2066064, 0, 10804368, 0, -176630, 0, 2434320, 0, 490968, 0, -7917116, 0, -2004132, 0, 4031114, 0, -5969244, 0, -352032, 0, 5325516, 0, 14183914, 0, -21065976, 0, 945760, 0, -714240, 0, 5725632, 0, 24627180, 0, 4282404, 0, -1637292, 0, 2282006, 0, 13048156, 0, -3122307, 0, 13562672, 0, -20886980, 0, 57624, 0, 14909760, 0, 14761472, 0, -4401504, 0, 4445696, 0, -1876936, 0, -4951854, 0, 3522708, 0, -11909360, 0, -262524, 0, 1646336, 0, -25503542, 0, -264960, 0, -14692506, 0, 5790134, 0, 862776, 0, -9941328, 0, -19277930, 0, -10392084, 0, -8565844, 0, 15980260, 0, 1779876, 0, 7491628, 0, 506880, 0, 1981800, 0, -2298528, 0, -18902686, 0, -3679488, 0, -12385926, 0, -7198944, 0, -348528, 0, -17125920, 0, 15284056, 0, -29326518, 0, -6938400, 0, 36064, 0, -12081600, 0, 28451142, 0, -6556038, 0, 7328256, 0, 1058816, 0, -12833776, 0, -7546392, 0, -3143562, 0, -16219112, 0, -4476960, 0, 4747068, 0, 34733276, 0, 12709284, 0, -2501842, 0, -1373424, 0, 13878000, 0, 6105516, 0, -19972393, 0, -9870948, 0, 728972, 0, 5069099, 0, -9983604, 0, 1113936, 0, 27561304, 0, -816408, 0, -18209994, 0, -33592042, 0, -2233812, 0, -32608360, 0, -1213184, 0, -2004558, 0, 24424320, 0, -46220256, 0, -20696274, 0, 1221864, 0, 13335170, 0, -6943896, 0, 14319434, 0, -4015564, 0, 320688, 0, 42904908, 0, -176008, 0, 8184240, 0, -14462648, 0, 1451024, 0, 821376, 0, 3772760, 0, 15131924, 0, 3826704, 0, -586240, 0, 30470620, 0, 22497588, 0, 27574840, 0, 5741280, 0, 232224, 0, 17862166, 0, -33334600, 0, -2069988, 0, -1571328, 0, 18821886, 0, 18090972, 0, 20862446, 0, 2367386, 0, -19727856, 0, -1000320, 0, -16661838, 0, -13263756, 0, -33620196, 0, -1398032, 0, 529200, 0, 42533512, 0, 21509040, 0, 7177860, 0, 32061290, 0, -2210144, 0, -1056960, 0, 3785054, 0, -2209551, 0, 14881644, 0, 1221432, 0, 56511528, 0, -6164472, 0, -44157998, 0, -6014358, 0, 13878576, 0, -26905302, 0, 34001760, 0, 24460362, 0, -8686884, 0, 2975352, 0, 4312392, 0, 2394944, 0, 15490896, 0, -12769680, 0, -1144880, 0, -4475876, 0, 16345800, 0, 8749440, 0, -13923204, 0, 1490976, 0, -14318692, 0, 24612222, 0, 11390484, 0, -25872952, 0, 143864, 0, -52324218, 0, 60295924, 0, 15080520, 0, -7401600, 0, -23622182, 0, -75715392, 0, -705894, 0, 41829888, 0, 12277690, 0, 152352, 0, -10082392, 0, -48611940, 0, -13052880, 0, 22992466, 0, 946560, 0, 12777024, 0, 33032386, 0, 2054284, 0, -25371144, 0, 3581488, 0, -20167616, 0, -15248628, 0, 16533930, 0, -14754880, 0, 50688, 0, 23995680, 0, 59868412, 0, -10569006, 0, 4443636, 0, 40466744, 0, 2875680, 0, -17797968, 0, 2698912, 0, -9023418, 0, 1007440, 0, -42792352, 0, 21414357, 0, -47058490, 0, 11895154, 0, -693840, 0, 35246426, 0, 28156968, 0, -11363376, 0, -47583720, 0, 3100992, 0, -20514600, 0, -64084416, 0, -26084160, 0, 4269468, 0, 4752480, 0, -16398466, 0, 9400980, 0, 13174932, 0, -52009910, 0, 5161752, 0, -441784, 0, 9946530, 0, 3276576, 0, -20975040, 0, -3235288, 0, 344160, 0, -64733208, 0, -12970496, 0, -743544, 0, -1377376, 0, 31117560, 0, 26474328, 0, -47960508, 0, 27976946, 0, -282240, 0, -105405456, 0, 9540536, 0, 35143200, 0, -33710556, 0, -1336088, 0, -5234820, 0, 16824444, 0, 13629268, 0, 1150368, 0, 45602812, 0, -17254080, 0, 75458538, 0, -7324584, 0, -8929907, 0, 2442432, 0, -42503372, 0, -5576932, 0, 21790176, 0, -61983390, 0, 3817088, 0, 10000998, 0, -28359840, 0, -68003186, 0, -21505356, 0, -1091528, 0, -2200704, 0, 22944960, 0, 14861504, 0, 2736098, 0, 3442824, 0, -15105286, 0, 2672048, 0, -8717760, 0, 38649832, 0, -7464709, 0, 13098564, 0, -59927618, 0, 46871700, 0, 15989922, 0, -2934336, 0, -42582580, 0, -3928428, 0, 30124220, 0, 60665760, 0, 574128, 0, 9553744, 0, 54590458, 0, -25407594, 0, -17775044, 0, -175016, 0, 29468244, 0, -71833686, 0, -74386608, 0, 4162596, 0, -176640, 0, 7181440, 0, 39603600, 0, -39053720, 0, 61254264, 0, 19437468, 0, -13329588, 0, 66623620, 0, -2844744, 0, 39160512, 0, -6928056, 0, 36961920, 0, 49735582, 0, -33058738, 0, 7502112, 0, 1186584, 0, -6012498, 0, 946500, 0, -76877484, 0, 82677440, 0, 607752, 0, 67619202, 0, 12253920, 0, -1088544, 0, 80860896, 0, -2452992, 0, -1582416, 0, 27484424, 0, -11187882, 0, -6482700, 0, 45148898, 0, 29435664, 0, 9024600, 0, -63480480, 0, 66902240, 0, 3400176, 0, 27074264, 0, 65022624, 0, 97131438, 0, -106042256, 0, -8054400, 0, 12667692, 0, 2082432, 0, -14962542, 0, 10941120, 0, 4885504, 0, -2458608, 0, -85197888, 0, 97753750, 0, 10766312, 0, 874944, 0, -10019304, 0, -32693041, 0, 23996292, 0, -65860006, 0, -5984640, 0, -35533242, 0, -36448062, 0, 49617858, 0, -13445424, 0, 8472856, 0, -28505260, 0, 8838240, 0, 53487648, 0, 14024780, 0, 4255920, 0, 862080, 0, 130045784, 0, -51028308, 0, -1780384, 0, -6580632, 0, -18264456, 0, 59086930, 0, -24926724, 0, 118948824, 0, -6655736, 0, 87915504, 0, -18743040, 0, -1762334, 0, -135760992, 0, -18392844, 0, -29068262, 0, -49387246, 0, 39209400, 0, -61150950, 0, -1489208, 0, 39419016, 0, -143796256, 0, -87488160, 0, 27025056, 0, -1336372, 0, 67785632, 0, -1866312, 0, 3263328, 0, -3939446, 0, 2399568, 0, 75393520, 0, 30230638, 0, -46262256, 0, -11595360, 0, -4629264, 0, -54793728, 0, -188063856, 0, 12511088, 0, -52328808, 0, -41542458, 0, -43873228, 0, 4588968, 0, -38858278, 0, 34415402, 0, -2592000, 0, 68769648, 0, -99865810, 0, -620928, 0, 14095230, 0, 547584, 0, 47245800, 0, 121166788, 0, 100343248, 0, 71074692, 0, 2551136, 0, -18539040, 0, -52123584, 0, -133633584, 0, -147624308, 0, -2608416, 0, -45998292, 0, -12341140, 0, -37724301, 0, -64736104, 0, -30082684, 0, -8047872, 0, 29458080, 0, 91472602, 0, 8499540, 0, -1379992, 0, 10659148, 0, 33623586, 0, -11430816, 0, 34594816, 0, -2097504, 0, -37987152, 0, -24429026, 0, -21121920, 0, -105766806, 0, -13151904, 0, 62782272, 0, 26032852, 0, -58217880, 0, 36011124, 0, -8842504, 0, -63406672, 0, -71465124, 0, 3146138, 0, 76967544, 0, -31534587, 0, 23587092, 0, -88226616, 0, 32135280, 0, 46669376, 0, 4785240, 0, -38414922, 0, 39632278, 0, 78798864, 0, -36077400, 0, -704640, 0, 7649510, 0, -33917472, 0, 71908882, 0, 16872856, 0, -1725408, 0, -64871072, 0, -90701526, 0, -75090492, 0, -7919908, 0, -4109648, 0, 3457440, 0, -35002956, 0, 150558626, 0, -43242204, 0, 18552384, 0, 141624766, 0, 30337920, 0, 16367078, 0, -388608, 0, -2835984, 0, 61928868, 0, -112616160, 0, -9910320, 0, 74643080, 0, 2874928, 0, -26125200, 0, -104181244, 0, -2672448, 0, -4342344, 0, -8513120, 0, -16541178, 0, -29919792, 0, 98780160, 0, 31322608, 0, 5012712, 0, -137268048, 0, 67037220, 0, -45490236, 0, -46759328, 0, -193143516, 0, 58103424, 0, 5319440, 0, -58126597, 0, 51766560, 0, 7593656, 0, 13371218, 0, 75940836, 0, 139690564, 0, 48869116, 0, 6066576, 0, 47788782, 0, -88168130, 0, -42174594, 0, 271213296, 0, -4934400, 0, 27446724, 0, 186549686, 0, -9807708, 0, 34668096, 0, -470596, 0, 113248728, 0, 114374952, 0, -50078614, 0, -8202564, 0, 3432336, 0, -137911680, 0, 35945616, 0, 32791212, 0, -60451422, 0, -8701920, 0, -63209106, 0, 88800072, 0, 96759520, 0, -7033068, 0, 8518016, 0, 13660952, 0, -20911680, 0, 91066632, 0, 151726610, 0, 8035200, 0, 2143946, 0, 94577592, 0, -59363148, 0, -98895568, 0, -10165752, 0, -30408240, 0, -7102184, 0, 2163840, 0, -153974466, 0, -6566208, 0, 208946418, 0, 36761148, 0, 57471024, 0, -107143712, 0, 1225392, 0, 106221752, 0, -152939930, 0, 59247540, 0, 63528960, 0, 1917120, 0, -1796592, 0, 84868686, 0, -227391586, 0, -29888004, 0, -6015612, 0, -91320048, 0, -167734800, 0, 218386914, 0, -14535654, 0, -2482824, 0, -18725312, 0, 74911464, 0, 66416448, 0, 179436120, 0, 89881190, 0, -7444962, 0, -68680680, 0, 99570712, 0, 65477952, 0, -7575584, 0, -82405440, 0, -82697412, 0, 30049152, 0, 98582252, 0, -6291144, 0, 48715548, 0, 22407813, 0, 66870180, 0, 123128972, 0, 2846312, 0, 18043308, 0, 43738320, 0, 184925388, 0, -6274584, 0, 6267320, 0, -185929238, 0, -41652156, 0, 93510168, 0, -32348670, 0, 57695286, 0, -160675138, 0, 21625980, 0, -48984480, 0, 98666400, 0, 2184384, 0, 37849608, 0, -231449022, 0, -49734640, 0, 3421824, 0, 229440, 0, -59847424, 0, -185342004, 0, -74229042, 0, -72791040, 0, 86208, 0, -250185278, 0, -4401648, 0, -10718064, 0, -28530026, 0, 17649552, 0, -5702400, 0, -107162424, 0, -263390508, 0, 82415604, 0, 36561840, 0, -111447464, 0, -15521532, 0, -287477414, 0, 195755630, 0, 10777248, 0, 349110096, 0, -103792486, 0, -39146760, 0, -45599016, 0, -3489880, 0, 19241280, 0, -295788784, 0, -200191824, 0, -52135020, 0, 766912, 0, -86172456, 0, 22547580, 0, 87916188, 0, -306218496, 0, -8748816, 0, 80612742, 0, 87061440, 0, 78057000, 0, 88403104, 0, -316396712, 0, 41846160, 0, 72149766, 0, 81532766, 0, 70235688, 0, 14526784, 0, 62563702, 0, -160476336, 0, -35174400, 0, -9925738, 0, -1159536, 0, 89233242, 0, 136719360, 0, 810336, 0, 333838512, 0, -14336904, 0, -245940840, 0, 18242798, 0, -44915160, 0, 13933440, 0, 15296640, 0, 184928330, 0, -109695108, 0, 190918688, 0, 16370557, 0, -106020009, 0, -217956456, 0, -250672748, 0, 12339648, 0, -70885512, 0, -5811840, 0, -29394708, 0, -172070312, 0, 427526208, 0, 167426154, 0, 8732376, 0, -26068016, 0, -74948040, 0, 56708484, 0, -336142762, 0, -1853904, 0, 107795942, 0, -1550208, 0, 71279208, 0, 2554280, 0, -2618952, 0, 64826208, 0, -117103046, 0, -116511676, 0, -1059780, 0, -74373498, 0, -319317360, 0, 31752000, 0, 110592986, 0, -189477856, 0, 2945808, 0, 139859312, 0, -129530006, 0, -47502696, 0, -6707904, 0, 19645496, 0, 69142554, 0, 198401926, 0, -132608640, 0, 24186684, 0, 2775064, 0, -31251416, 0, -35815464, 0, 328580032, 0, 319280698, 0, 12145104, 0, 21219940, 0, -196939776, 0, 31953096, 0, 73285920, 0, 25983312, 0, 85103484, 0, 111500610, 0, 345733438, 0, -274773600, 0, -1896496, 0, -86549566, 0, 5674560, 0, 10598796, 0, 177906392, 0, -4285440, 0, 249235164, 0, 16904902, 0, -197534304, 0, 195365302, 0, 5001408, 0, 147763080, 0, -3742864, 0, -310853770, 0, 25694424, 0, 631000, 0, 178521120, 0, 56486574, 0, 255456864, 0, -110338156, 0, 13692036, 0, 161110824, 0, -293802376, 0, 78288936, 0, -80893548, 0, -725696, 0, -227885400, 0, -68692800, 0, 108320674, 0, 81376032, 0, -1054944, 0, 140653200, 0, -125321880, 0, -10855680, 0, 426398186, 0, -1988028, 0, 70735992, 0, -14194783, 0, 89458560, 0, 60814338, 0, 6016400, 0, 88568832, 0, -58619190, 0, -17275290, 0, 151851888, 0, -440464466, 0, 379844428, 0, 26674176, 0, -18396688, 0, 8631840, 0, -11261616, 0, 3135114, 0, 317435396, 0, -64589400, 0, -420810914, 0, 8445128, 0, 21136248, 0, 225652224, 0, -249355268, 0, -71456160, 0, 7294080, 0, -58578504, 0, 9057078, 0, 50343188, 0, 148597400, 0, 9878016, 0, 12783722, 0, 40779658, 0, -153021252, 0, 10125506, 0, -113341704, 0, 9141120, 0, 189018352, 0, 239384906, 0, -88155036, 0, 15997528, 0, 106096292, 0, 34740804, 0, -74697712, 0, 319858302, 0, 11253600, 0, 38387814, 0, -102002686, 0, -59647968, 0, -35217868, 0, -8963616, 0, -115667580, 0, -178522080, 0, 40990864, 0, 358526898, 0, 5892160, 0, 104285720, 0, -51395064, 0, 214889280, 0, 19997856, 0, 95881560, 0, -269890464, 0, 80490332, 0, -61405722, 0, 378595066, 0, -34018872, 0, 44949768, 0, 206693208, 0, -376960832, 0, 3041280, 0, -12176304, 0, -326804656, 0, -25030134, 0, -363538856, 0, 109040640, 0, -13791168, 0, -398559812, 0, -93022286, 0, -113416116, 0, -127897164, 0, -12495360, 0, 126942336, 0, 16080864, 0, 506462902, 0, -74315556, 0, -24586896, 0, 113227834, 0, -43193664, 0, 163868190, 0, 270170964, 0, 12024216, 0, 60446400, 0, -307136610, 0, -102755520, 0, 256061970, 0, 26279344, 0, 91704336, 0, -333070068, 0, 5764801, 0, -382519800, 0, 18016704, 0, -17558748, 0, -41630400, 0, -315061438, 0, 3541712, 0, 216384, 0, 61835058, 0, 101524476, 0, 416815200, 0, 280553784, 0, -310844038, 0, 170706852, 0, 106598520, 0, 186059520, 0, -39336228, 0, -30841504, 0, -124370242, 0, -252824832, 0, -440289102, 0, -104345696, 0, 6352896, 0, -10459224, 0, -523087520, 0, -77002656, 0, 285148800, 0, -34885872, 0, -98431200, 0, -348070452, 0, 13228128, 0, -18861372, 0, 3059312, 0, 328026906, 0, -97314672, 0, 124530462, 0, -381166282, 0, 154455120, 0, -387501888, 0, -376098696, 0, 28482408, 0, 411086784, 0, -413952, 0, 208399656, 0, -359430524, 0, 213008696, 0, -438470298, 0, 31497200, 0, -194117280, 0, -15011052, 0, 73518248, 0, -602191560, 0, -8240544, 0, 21742544, 0, -227186352, 0, -175279140, 0, -23484720, 0, -34749056, 0, 36633096, 0, -82642560, 0, -451776506, 0, -119834358, 0, 337898556, 0, 73691247, 0, 340547706, 0, -278469820, 0, 488941828, 0, 4373832, 0, -173919792, 0, -189768314, 0, 30414594, 0, 512942976, 0, -5365248, 0, 344434338, 0, 266177342, 0, 255156680, 0, 6683616, 0, 5666360, 0, -45787674, 0, 165367824, 0, -553415472, 0, -80165280, 0, -10648800, 0, -428870528, 0, 92800904, 0, -109259964, 0, -122959080, 0, 271714164, 0, -201552252, 0, 11477482, 0, -103988716, 0, 77066514, 0, -14081280, 0, 212947680, 0, -195650160, 0, 4285680, 0, 263540954, 0, -7279104, 0, -34867322, 0, -46510416, 0, 69157251, 0, -76164556, 0, 24007416, 0, 146545920, 0, 104707054, 0, -76774670, 0, -277321536, 0, -47643416, 0, 361551766, 0, -269951400, 0, 364824512, 0, -125942816, 0, 7331184, 0, -12786048, 0, 229025280, 0, 80011020, 0, -338404346, 0, 21423520, 0, 239564412, 0, -26758704, 0, 121023612, 0, 85916604, 0, -25609948, 0, -401792872, 0, -24093384, 0, -65491680, 0, -2810640, 0, -11063736, 0, -679842414, 0, 92358934, 0, 257429448, 0, 169421304, 0, -22611648, 0, -1056048, 0, 598766544, 0, 450436840, 0, 206569440, 0, 223512228, 0, -192054268, 0, -86775888, 0, -216207012, 0, 515181796, 0, 8706144, 0, -672027836, 0, 705624830, 0, -28337472, 0, 581393588, 0, 2304960, 0, 22636560, 0, -488476164, 0, 175021140, 0, 90791544, 0, -28828136, 0, 454766718, 0, -132021288, 0, 153879472, 0, 369662546, 0, -3517440, 0, -176060160, 0, 399592796, 0, 182823720, 0, 42751030, 0, 367378094, 0, 293446800, 0, 46407086, 0, -381613252, 0, 165449040, 0, -6606880, 0, -9394672, 0, 34447680, 0, 491790090, 0, -666156768, 0, -8011728, 0, 472018152, 0, 671637420, 0, 107172996, 0, -542243054, 0, -2894896, 0, -200007600, 0, -728204360, 0, -10500960, 0, 71414586, 0, -19946528, 0, 262230384, 0, -9427968, 0, -275821568, 0, -195993816, 0, 112931316, 0, 35123382, 0, -177953104, 0, 235969200, 0, 19034984, 0, -30326824, 0, 125174676, 0, 317501704, 0, -272512964, 0, 14204316, 0, 38735616, 0, -322884466, 0, 680611032, 0, -97624930, 0, 110515326, 0, -6001920, 0, 175627074, 0, -207307009, 0, -99971028, 0, -73386788, 0, 50627224, 0, 457599582, 0, -407193882, 0, -187383840, 0, -201721176, 0, -785874366, 0, -415683360, 0, -8388192, 0, -462664724, 0, 693412410, 0, -6683796, 0, -374082270, 0, 357776952, 0, 255201072, 0, 757868576, 0, 18297816, 0, 129054240, 0, 71195040, 0, 852113996, 0, -247636170, 0, 23112064, 0, 230192778, 0, 192367740, 0, 310693656, 0, -106971606, 0, -13260864, 0, -141927568, 0, 405821824, 0, 36465120, 0, -189897206, 0, 4588224, 0, 22710324, 0, 73422472, 0, -808605984, 0, -13257306, 0, 21860808, 0, 750711356, 0, 194108400, 0, 32082162, 0, -147179520, 0, 7328592, 0, -777700338, 0, -883961280, 0, 339069168, 0, 242640640, 0, -4688712, 0, 212674284, 0, -810554022, 0, 16046976, 0, -264947988, 0, -13941120, 0, -683438260, 0, -36086148, 0, -660928, 0, -616103472, 0, -478810872, 0, -239518656, 0, 79774056, 0, -161431812, 0, -240657326, 0, -39575432, 0, 204010560, 0, 686174862, 0, 316034432, 0, 319048200, 0, -20272160, 0, -33994534, 0, -52121304, 0, 601763568, 0, 842198574, 0, 17852112, 0, -237940236, 0, -483264000, 0, -148777524, 0, -315952136, 0, 24507432, 0, 14369664, 0, -450891894, 0, 215895022, 0, 92945376, 0, -158739322, 0, 256191936, 0, 440553960, 0, 293130240, 0, -566587152, 0, -6869280, 0, 64148664, 0, 23232076, 0, -26855256, 0, -219658180, 0, -1197728, 0, -206447454, 0, 435005620, 0], "weight": 6, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, 0, 6, 0, 4, 0, -49, 0, -207, 0, 240, 0, -744, 0, 24, 0, -1042, 0, 986, 0, -294, 0, -184, 0, -3109, 0, -2700, 0, -734, 0, -5140, 0, 1440, 0, -196, 0, -6054, 0, -4464, 0, 7598, 0, -13016, 0, -828, 0, -14668, 0, 2401, 0, -6252, 0, -14522, 0, 960, 0, 5916, 0, 13362, 0, 9676, 0, 10143, 0, -2976, 0, 62124, 0, -1104, 0, 2112, 0, -28910, 0, -18654, 0, -11760, 0, 101768, 0, 34101, 0, 23922, 0, -4168, 0, -4404, 0, 141674, 0, 36456, 0, -30840, 0, 3944, 0, 99982, 0, -49680, 0, -108684, 0, -87396, 0, -1176, 0, -71892, 0, -118166, 0, -36324, 0, 252774, 0, -736, 0, 154008, 0, 51058, 0, -103451, 0, 45588, 0, -24936, 0, 3592, 0, -78096, 0, -364534, 0, -48314, 0, -10800, 0, -77246, 0, 122742, 0, -88008, 0, -178560, 0, -2936, 0, 14406, 0, -469234, 0, 411584, 0, 215694, 0, -20560, 0, -574632, 0, -87132, 0, 9016, 0, 264704, 0, 5760, 0, -343356, 0, 182243, 0, -204102, 0, -303296, 0, 152341, 0, 80172, 0, 362756, 0, -146560, 0, 58056, 0, -24216, 0, -250080, 0, 132300, 0, -552536, 0, 305358, 0, -17856, 0, 743838, 0, -286220, 0, 372744, 0, 35966, 0, 30392, 0, 38088, 0, 236640, 0, 895372, 0, 12672, 0, -52064, 0, 251860, 0, -173460, 0, 775248, 0, 1188120, 0, 643563, 0, -808822, 0, -344344, 0, -70560, 0, -334022, 0, -58672, 0, 610608, 0, 954272, 0, -272882, 0, 860706, 0, 9604, 0, -733584, 0, 143532, 0, -43754, 0, -44160, 0, -25008, 0, -1732014, 0, 296646, 0, 151938, 0, -613248, 0, -58088, 0, 850044, 0, -2013600, 0, 1221376, 0, 218736, 0, -746160, 0, 2118214, 0, 1063980, 0, -1645158, 0, -1663934, 0, 23664, 0, -372302, 0, -334093, 0, 599892, 0, -1157316, 0, 53448, 0, -648000, 0, 136896, 0, 637784, 0, -652104, 0, 38704, 0, -344998, 0, -524376, 0, -3287976, 0, -2210626, 0, 40572, 0, 1196310, 0, -176160, 0, -431352, 0, -1027412, 0, 2313096, 0, -708996, 0, 718732, 0, -2128280, 0, 1253178, 0, 248496, 0, 1898414, 0, 1516644, 0, -1233600, 0, -117649, 0, -4416, 0, -2175480, 0, 2129504, 0, 2008800, 0, -2541438, 0, 8448, 0, 306348, 0, 479280, 0, -1503903, 0, -620706, 0, -115640, 0, -1893896, 0, -1572786, 0, 711578, 0, 1566830, 0, -149616, 0, 546096, 0, 57360, 0, 21552, 0, 4412388, 0, -47040, 0, 2694312, 0, -872470, 0, 191728, 0, -2187204, 0, 407072, 0, 3631696, 0, -289884, 0, -3584226, 0, 3824160, 0, 136404, 0, -1452960, 0, 2183094, 0, -463476, 0, -654738, 0, 95688, 0, 736452, 0, 4911374, 0, 693766, 0, 3036276, 0, 3239578, 0, -474124, 0, -1071360, 0, 1250352, 0, 157750, 0, -17616, 0, -181424, 0, -263736, 0, -497007, 0, 1504100, 0, 566696, 0, -2815404, 0, 2111282, 0, 1823520, 0, 2469504, 0, 145824, 0, 3999382, 0, 2813400, 0, -2240904, 0, 1473040, 0, -123360, 0, -8504718, 0, -3044076, 0, -3447792, 0, -3123840, 0, -3065474, 0, 3006054, 0, 6569836, 0, 4504176, 0, 54096, 0, 399928, 0, -7710376, 0, 1588224, 0, -8721468, 0, 764828, 0, -198720, 0, -103488, 0, 7874300, 0, -2060136, 0, -8687264, 0, -434736, 0, 1093458, 0, -1341312, 0, 1416590, 0, -2662200, 0, -349584, 0, -3520320, 0, -1819776, 0, 6001854, 0, -11910854, 0, 914046, 0, 5355880, 0, -6402487, 0, -2765934, 0, -5652912, 0, -287568, 0, 2176536, 0, 576240, 0, -7207034, 0, -879360, 0, -472664, 0, -1651720, 0, -2002932, 0, -723724, 0, -4986632, 0, -145296, 0, -7581706, 0, 9683904, 0, -1500480, 0, 12656806, 0, 1011096, 0, -1670949, 0, 4574454, 0, 5778016, 0, -3315216, 0, 572056, 0, 5465202, 0, 1832148, 0, -1172178, 0, -3485280, 0, 616032, 0, -9893858, 0, -5068040, 0, 4463028, 0, 6126858, 0, 204232, 0, -1717320, 0, -299432, 0, -4981334, 0, -12859668, 0, -413804, 0, 11069408, 0, 215796, 0, 10912992, 0, -13782902, 0, 182352, 0, 11145030, 0, 3007218, 0, 496800, 0, -6942026, 0, 9615881, 0, 1419840, 0, 6308268, 0, 570304, 0, 5372232, 0, 14368, 0, -1786344, 0, -437184, 0, 13735934, 0, -2586922, 0, -312384, 0, -6524460, 0, 3206880, 0, 1511160, 0, 3757930, 0, -1458136, 0, 5984370, 0, 6974360, 0, 11705948, 0, 4651488, 0, -193256, 0, 135056, 0, 7128720, 0, 2322240, 0, -18282518, 0, 8394300, 0, 2056608, 0, -4899118, 0, -4852932, 0, -12491340, 0, -308984, 0, -2066064, 0, 10804368, 0, -176630, 0, 2434320, 0, 490968, 0, -7917116, 0, -2004132, 0, 4031114, 0, -5969244, 0, -352032, 0, 5325516, 0, 14183914, 0, -21065976, 0, 945760, 0, -714240, 0, 5725632, 0, 24627180, 0, 4282404, 0, -1637292, 0, 2282006, 0, 13048156, 0, -3122307, 0, 13562672, 0, -20886980, 0, 57624, 0, 14909760, 0, 14761472, 0, -4401504, 0, 4445696, 0, -1876936, 0, -4951854, 0, 3522708, 0, -11909360, 0, -262524, 0, 1646336, 0, -25503542, 0, -264960, 0, -14692506, 0, 5790134, 0, 862776, 0, -9941328, 0, -19277930, 0, -10392084, 0, -8565844, 0, 15980260, 0, 1779876, 0, 7491628, 0, 506880, 0, 1981800, 0, -2298528, 0, -18902686, 0, -3679488, 0, -12385926, 0, -7198944, 0, -348528, 0, -17125920, 0, 15284056, 0, -29326518, 0, -6938400, 0, 36064, 0, -12081600, 0, 28451142, 0, -6556038, 0, 7328256, 0, 1058816, 0, -12833776, 0, -7546392, 0, -3143562, 0, -16219112, 0, -4476960, 0, 4747068, 0, 34733276, 0, 12709284, 0, -2501842, 0, -1373424, 0, 13878000, 0, 6105516, 0, -19972393, 0, -9870948, 0, 728972, 0, 5069099, 0, -9983604, 0, 1113936, 0, 27561304, 0, -816408, 0, -18209994, 0, -33592042, 0, -2233812, 0, -32608360, 0, -1213184, 0, -2004558, 0, 24424320, 0, -46220256, 0, -20696274, 0, 1221864, 0, 13335170, 0, -6943896, 0, 14319434, 0, -4015564, 0, 320688, 0, 42904908, 0, -176008, 0, 8184240, 0, -14462648, 0, 1451024, 0, 821376, 0, 3772760, 0, 15131924, 0, 3826704, 0, -586240, 0, 30470620, 0, 22497588, 0, 27574840, 0, 5741280, 0, 232224, 0, 17862166, 0, -33334600, 0, -2069988, 0, -1571328, 0, 18821886, 0, 18090972, 0, 20862446, 0, 2367386, 0, -19727856, 0, -1000320, 0, -16661838, 0, -13263756, 0, -33620196, 0, -1398032, 0, 529200, 0, 42533512, 0, 21509040, 0, 7177860, 0, 32061290, 0, -2210144, 0, -1056960, 0, 3785054, 0, -2209551, 0, 14881644, 0, 1221432, 0, 56511528, 0, -6164472, 0, -44157998, 0, -6014358, 0, 13878576, 0, -26905302, 0, 34001760, 0, 24460362, 0, -8686884, 0, 2975352, 0, 4312392, 0, 2394944, 0, 15490896, 0, -12769680, 0, -1144880, 0, -4475876, 0, 16345800, 0, 8749440, 0, -13923204, 0, 1490976, 0, -14318692, 0, 24612222, 0, 11390484, 0, -25872952, 0, 143864, 0, -52324218, 0, 60295924, 0, 15080520, 0, -7401600, 0, -23622182, 0, -75715392, 0, -705894, 0, 41829888, 0, 12277690, 0, 152352, 0, -10082392, 0, -48611940, 0, -13052880, 0, 22992466, 0, 946560, 0, 12777024, 0, 33032386, 0, 2054284, 0, -25371144, 0, 3581488, 0, -20167616, 0, -15248628, 0, 16533930, 0, -14754880, 0, 50688, 0, 23995680, 0, 59868412, 0, -10569006, 0, 4443636, 0, 40466744, 0, 2875680, 0, -17797968, 0, 2698912, 0, -9023418, 0, 1007440, 0, -42792352, 0, 21414357, 0, -47058490, 0, 11895154, 0, -693840, 0, 35246426, 0, 28156968, 0, -11363376, 0, -47583720, 0, 3100992, 0, -20514600, 0, -64084416, 0, -26084160, 0, 4269468, 0, 4752480, 0, -16398466, 0, 9400980, 0, 13174932, 0, -52009910, 0, 5161752, 0, -441784, 0, 9946530, 0, 3276576, 0, -20975040, 0, -3235288, 0, 344160, 0, -64733208, 0, -12970496, 0, -743544, 0, -1377376, 0, 31117560, 0, 26474328, 0, -47960508, 0, 27976946, 0, -282240, 0, -105405456, 0, 9540536, 0, 35143200, 0, -33710556, 0, -1336088, 0, -5234820, 0, 16824444, 0, 13629268, 0, 1150368, 0, 45602812, 0, -17254080, 0, 75458538, 0, -7324584, 0, -8929907, 0, 2442432, 0, -42503372, 0, -5576932, 0, 21790176, 0, -61983390, 0, 3817088, 0, 10000998, 0, -28359840, 0, -68003186, 0, -21505356, 0, -1091528, 0, -2200704, 0, 22944960, 0, 14861504, 0, 2736098, 0, 3442824, 0, -15105286, 0, 2672048, 0, -8717760, 0, 38649832, 0, -7464709, 0, 13098564, 0, -59927618, 0, 46871700, 0, 15989922, 0, -2934336, 0, -42582580, 0, -3928428, 0, 30124220, 0, 60665760, 0, 574128, 0, 9553744, 0, 54590458, 0, -25407594, 0, -17775044, 0, -175016, 0, 29468244, 0, -71833686, 0, -74386608, 0, 4162596, 0, -176640, 0, 7181440, 0, 39603600, 0, -39053720, 0, 61254264, 0, 19437468, 0, -13329588, 0, 66623620, 0, -2844744, 0, 39160512, 0, -6928056, 0, 36961920, 0, 49735582, 0, -33058738, 0, 7502112, 0, 1186584, 0, -6012498, 0, 946500, 0, -76877484, 0, 82677440, 0, 607752, 0, 67619202, 0, 12253920, 0, -1088544, 0, 80860896, 0, -2452992, 0, -1582416, 0, 27484424, 0, -11187882, 0, -6482700, 0, 45148898, 0, 29435664, 0, 9024600, 0, -63480480, 0, 66902240, 0, 3400176, 0, 27074264, 0, 65022624, 0, 97131438, 0, -106042256, 0, -8054400, 0, 12667692, 0, 2082432, 0, -14962542, 0, 10941120, 0, 4885504, 0, -2458608, 0, -85197888, 0, 97753750, 0, 10766312, 0, 874944, 0, -10019304, 0, -32693041, 0, 23996292, 0, -65860006, 0, -5984640, 0, -35533242, 0, -36448062, 0, 49617858, 0, -13445424, 0, 8472856, 0, -28505260, 0, 8838240, 0, 53487648, 0, 14024780, 0, 4255920, 0, 862080, 0, 130045784, 0, -51028308, 0, -1780384, 0, -6580632, 0, -18264456, 0, 59086930, 0, -24926724, 0, 118948824, 0, -6655736, 0, 87915504, 0, -18743040, 0, -1762334, 0, -135760992, 0, -18392844, 0, -29068262, 0, -49387246, 0, 39209400, 0, -61150950, 0, -1489208, 0, 39419016, 0, -143796256, 0, -87488160, 0, 27025056, 0, -1336372, 0, 67785632, 0, -1866312, 0, 3263328, 0, -3939446, 0, 2399568, 0, 75393520, 0, 30230638, 0, -46262256, 0, -11595360, 0, -4629264, 0, -54793728, 0, -188063856, 0, 12511088, 0, -52328808, 0, -41542458, 0, -43873228, 0, 4588968, 0, -38858278, 0, 34415402, 0, -2592000, 0, 68769648, 0, -99865810, 0, -620928, 0, 14095230, 0, 547584, 0, 47245800, 0, 121166788, 0, 100343248, 0, 71074692, 0, 2551136, 0, -18539040, 0, -52123584, 0, -133633584, 0, -147624308, 0, -2608416, 0, -45998292, 0, -12341140, 0, -37724301, 0, -64736104, 0, -30082684, 0, -8047872, 0, 29458080, 0, 91472602, 0, 8499540, 0, -1379992, 0, 10659148, 0, 33623586, 0, -11430816, 0, 34594816, 0, -2097504, 0, -37987152, 0, -24429026, 0, -21121920, 0, -105766806, 0, -13151904, 0, 62782272, 0, 26032852, 0, -58217880, 0, 36011124, 0, -8842504, 0, -63406672, 0, -71465124, 0, 3146138, 0, 76967544, 0, -31534587, 0, 23587092, 0, -88226616, 0, 32135280, 0, 46669376, 0, 4785240, 0, -38414922, 0, 39632278, 0, 78798864, 0, -36077400, 0, -704640, 0, 7649510, 0, -33917472, 0, 71908882, 0, 16872856, 0, -1725408, 0, -64871072, 0, -90701526, 0, -75090492, 0, -7919908, 0, -4109648, 0, 3457440, 0, -35002956, 0, 150558626, 0, -43242204, 0, 18552384, 0, 141624766, 0, 30337920, 0, 16367078, 0, -388608, 0, -2835984, 0, 61928868, 0, -112616160, 0, -9910320, 0, 74643080, 0, 2874928, 0, -26125200, 0, -104181244, 0, -2672448, 0, -4342344, 0, -8513120, 0, -16541178, 0, -29919792, 0, 98780160, 0, 31322608, 0, 5012712, 0, -137268048, 0, 67037220, 0, -45490236, 0, -46759328, 0, -193143516, 0, 58103424, 0, 5319440, 0, -58126597, 0, 51766560, 0, 7593656, 0, 13371218, 0, 75940836, 0, 139690564, 0, 48869116, 0, 6066576, 0, 47788782, 0, -88168130, 0, -42174594, 0, 271213296, 0, -4934400, 0, 27446724, 0, 186549686, 0, -9807708, 0, 34668096, 0, -470596, 0, 113248728, 0, 114374952, 0, -50078614, 0, -8202564, 0, 3432336, 0, -137911680, 0, 35945616, 0, 32791212, 0, -60451422, 0, -8701920, 0, -63209106, 0, 88800072, 0, 96759520, 0, -7033068, 0, 8518016, 0, 13660952, 0, -20911680, 0, 91066632, 0, 151726610, 0, 8035200, 0, 2143946, 0, 94577592, 0, -59363148, 0, -98895568, 0, -10165752, 0, -30408240, 0, -7102184, 0, 2163840, 0, -153974466, 0, -6566208, 0, 208946418, 0, 36761148, 0, 57471024, 0, -107143712, 0, 1225392, 0, 106221752, 0, -152939930, 0, 59247540, 0, 63528960, 0, 1917120, 0, -1796592, 0, 84868686, 0, -227391586, 0, -29888004, 0, -6015612, 0, -91320048, 0, -167734800, 0, 218386914, 0, -14535654, 0, -2482824, 0, -18725312, 0, 74911464, 0, 66416448, 0, 179436120, 0, 89881190, 0, -7444962, 0, -68680680, 0, 99570712, 0, 65477952, 0, -7575584, 0, -82405440, 0, -82697412, 0, 30049152, 0, 98582252, 0, -6291144, 0, 48715548, 0, 22407813, 0, 66870180, 0, 123128972, 0, 2846312, 0, 18043308, 0, 43738320, 0, 184925388, 0, -6274584, 0, 6267320, 0, -185929238, 0, -41652156, 0, 93510168, 0, -32348670, 0, 57695286, 0, -160675138, 0, 21625980, 0, -48984480, 0, 98666400, 0, 2184384, 0, 37849608, 0, -231449022, 0, -49734640, 0, 3421824, 0, 229440, 0, -59847424, 0, -185342004, 0, -74229042, 0, -72791040, 0, 86208, 0, -250185278, 0, -4401648, 0, -10718064, 0, -28530026, 0, 17649552, 0, -5702400, 0, -107162424, 0, -263390508, 0, 82415604, 0, 36561840, 0, -111447464, 0, -15521532, 0, -287477414, 0, 195755630, 0, 10777248, 0, 349110096, 0, -103792486, 0, -39146760, 0, -45599016, 0, -3489880, 0, 19241280, 0, -295788784, 0, -200191824, 0, -52135020, 0, 766912, 0, -86172456, 0, 22547580, 0, 87916188, 0, -306218496, 0, -8748816, 0, 80612742, 0, 87061440, 0, 78057000, 0, 88403104, 0, -316396712, 0, 41846160, 0, 72149766, 0, 81532766, 0, 70235688, 0, 14526784, 0, 62563702, 0, -160476336, 0, -35174400, 0, -9925738, 0, -1159536, 0, 89233242, 0, 136719360, 0, 810336, 0, 333838512, 0, -14336904, 0, -245940840, 0, 18242798, 0, -44915160, 0, 13933440, 0, 15296640, 0, 184928330, 0, -109695108, 0, 190918688, 0, 16370557, 0, -106020009, 0, -217956456, 0, -250672748, 0, 12339648, 0, -70885512, 0, -5811840, 0, -29394708, 0, -172070312, 0, 427526208, 0, 167426154, 0, 8732376, 0, -26068016, 0, -74948040, 0, 56708484, 0, -336142762, 0, -1853904, 0, 107795942, 0, -1550208, 0, 71279208, 0, 2554280, 0, -2618952, 0, 64826208, 0, -117103046, 0, -116511676, 0, -1059780, 0, -74373498, 0, -319317360, 0, 31752000, 0, 110592986, 0, -189477856, 0, 2945808, 0, 139859312, 0, -129530006, 0, -47502696, 0, -6707904, 0, 19645496, 0, 69142554, 0, 198401926, 0, -132608640, 0, 24186684, 0, 2775064, 0, -31251416, 0, -35815464, 0, 328580032, 0, 319280698, 0, 12145104, 0, 21219940, 0, -196939776, 0, 31953096, 0, 73285920, 0, 25983312, 0, 85103484, 0, 111500610, 0, 345733438, 0, -274773600, 0, -1896496, 0, -86549566, 0, 5674560, 0, 10598796, 0, 177906392, 0, -4285440, 0, 249235164, 0, 16904902, 0, -197534304, 0, 195365302, 0, 5001408, 0, 147763080, 0, -3742864, 0, -310853770, 0, 25694424, 0, 631000, 0, 178521120, 0, 56486574, 0, 255456864, 0, -110338156, 0, 13692036, 0, 161110824, 0, -293802376, 0, 78288936, 0, -80893548, 0, -725696, 0, -227885400, 0, -68692800, 0, 108320674, 0, 81376032, 0, -1054944, 0, 140653200, 0, -125321880, 0, -10855680, 0, 426398186, 0, -1988028, 0, 70735992, 0, -14194783, 0, 89458560, 0, 60814338, 0, 6016400, 0, 88568832, 0, -58619190, 0, -17275290, 0, 151851888, 0, -440464466, 0, 379844428, 0, 26674176, 0, -18396688, 0, 8631840, 0, -11261616, 0, 3135114, 0, 317435396, 0, -64589400, 0, -420810914, 0, 8445128, 0, 21136248, 0, 225652224, 0, -249355268, 0, -71456160, 0, 7294080, 0, -58578504, 0, 9057078, 0, 50343188, 0, 148597400, 0, 9878016, 0, 12783722, 0, 40779658, 0, -153021252, 0, 10125506, 0, -113341704, 0, 9141120, 0, 189018352, 0, 239384906, 0, -88155036, 0, 15997528, 0, 106096292, 0, 34740804, 0, -74697712, 0, 319858302, 0, 11253600, 0, 38387814, 0, -102002686, 0, -59647968, 0, -35217868, 0, -8963616, 0, -115667580, 0, -178522080, 0, 40990864, 0, 358526898, 0, 5892160, 0, 104285720, 0, -51395064, 0, 214889280, 0, 19997856, 0, 95881560, 0, -269890464, 0, 80490332, 0, -61405722, 0, 378595066, 0, -34018872, 0, 44949768, 0, 206693208, 0, -376960832, 0, 3041280, 0, -12176304, 0, -326804656, 0, -25030134, 0, -363538856, 0, 109040640, 0, -13791168, 0, -398559812, 0, -93022286, 0, -113416116, 0, -127897164, 0, -12495360, 0, 126942336, 0, 16080864, 0, 506462902, 0, -74315556, 0, -24586896, 0, 113227834, 0, -43193664, 0, 163868190, 0, 270170964, 0, 12024216, 0, 60446400, 0, -307136610, 0, -102755520, 0, 256061970, 0, 26279344, 0, 91704336, 0, -333070068, 0, 5764801, 0, -382519800, 0, 18016704, 0, -17558748, 0, -41630400, 0, -315061438, 0, 3541712, 0, 216384, 0, 61835058, 0, 101524476, 0, 416815200, 0, 280553784, 0, -310844038, 0, 170706852, 0, 106598520, 0, 186059520, 0, -39336228, 0, -30841504, 0, -124370242, 0, -252824832, 0, -440289102, 0, -104345696, 0, 6352896, 0, -10459224, 0, -523087520, 0, -77002656, 0, 285148800, 0, -34885872, 0, -98431200, 0, -348070452, 0, 13228128, 0, -18861372, 0, 3059312, 0, 328026906, 0, -97314672, 0, 124530462, 0, -381166282, 0, 154455120, 0, -387501888, 0, -376098696, 0, 28482408, 0, 411086784, 0, -413952, 0, 208399656, 0, -359430524, 0, 213008696, 0, -438470298, 0, 31497200, 0, -194117280, 0, -15011052, 0, 73518248, 0, -602191560, 0, -8240544, 0, 21742544, 0, -227186352, 0, -175279140, 0, -23484720, 0, -34749056, 0, 36633096, 0, -82642560, 0, -451776506, 0, -119834358, 0, 337898556, 0, 73691247, 0, 340547706, 0, -278469820, 0, 488941828, 0, 4373832, 0, -173919792, 0, -189768314, 0, 30414594, 0, 512942976, 0, -5365248, 0, 344434338, 0, 266177342, 0, 255156680, 0, 6683616, 0, 5666360, 0, -45787674, 0, 165367824, 0, -553415472, 0, -80165280, 0, -10648800, 0, -428870528, 0, 92800904, 0, -109259964, 0, -122959080, 0, 271714164, 0, -201552252, 0, 11477482, 0, -103988716, 0, 77066514, 0, -14081280, 0, 212947680, 0, -195650160, 0, 4285680, 0, 263540954, 0, -7279104, 0, -34867322, 0, -46510416, 0, 69157251, 0, -76164556, 0, 24007416, 0, 146545920, 0, 104707054, 0, -76774670, 0, -277321536, 0, -47643416, 0, 361551766, 0, -269951400, 0, 364824512, 0, -125942816, 0, 7331184, 0, -12786048, 0, 229025280, 0, 80011020, 0, -338404346, 0, 21423520, 0, 239564412, 0, -26758704, 0, 121023612, 0, 85916604, 0, -25609948, 0, -401792872, 0, -24093384, 0, -65491680, 0, -2810640, 0, -11063736, 0, -679842414, 0, 92358934, 0, 257429448, 0, 169421304, 0, -22611648, 0, -1056048, 0, 598766544, 0, 450436840, 0, 206569440, 0, 223512228, 0, -192054268, 0, -86775888, 0, -216207012, 0, 515181796, 0, 8706144, 0, -672027836, 0, 705624830, 0, -28337472, 0, 581393588, 0, 2304960, 0, 22636560, 0, -488476164, 0, 175021140, 0, 90791544, 0, -28828136, 0, 454766718, 0, -132021288, 0, 153879472, 0, 369662546, 0, -3517440, 0, -176060160, 0, 399592796, 0, 182823720, 0, 42751030, 0, 367378094, 0, 293446800, 0, 46407086, 0, -381613252, 0, 165449040, 0, -6606880, 0, -9394672, 0, 34447680, 0, 491790090, 0, -666156768, 0, -8011728, 0, 472018152, 0, 671637420, 0, 107172996, 0, -542243054, 0, -2894896, 0, -200007600, 0, -728204360, 0, -10500960, 0, 71414586, 0, -19946528, 0, 262230384, 0, -9427968, 0, -275821568, 0, -195993816, 0, 112931316, 0, 35123382, 0, -177953104, 0, 235969200, 0, 19034984, 0, -30326824, 0, 125174676, 0, 317501704, 0, -272512964, 0, 14204316, 0, 38735616, 0, -322884466, 0, 680611032, 0, -97624930, 0, 110515326, 0, -6001920, 0, 175627074, 0, -207307009, 0, -99971028, 0, -73386788, 0, 50627224, 0, 457599582, 0, -407193882, 0, -187383840, 0, -201721176, 0, -785874366, 0, -415683360, 0, -8388192, 0, -462664724, 0, 693412410, 0, -6683796, 0, -374082270, 0, 357776952, 0, 255201072, 0, 757868576, 0, 18297816, 0, 129054240, 0, 71195040, 0, 852113996, 0, -247636170, 0, 23112064, 0, 230192778, 0, 192367740, 0, 310693656, 0, -106971606, 0, -13260864, 0, -141927568, 0, 405821824, 0, 36465120, 0, -189897206, 0, 4588224, 0, 22710324, 0, 73422472, 0, -808605984, 0, -13257306, 0, 21860808, 0, 750711356, 0, 194108400, 0, 32082162, 0, -147179520, 0, 7328592, 0, -777700338, 0, -883961280, 0, 339069168, 0, 242640640, 0, -4688712, 0, 212674284, 0, -810554022, 0, 16046976, 0, -264947988, 0, -13941120, 0, -683438260, 0, -36086148, 0, -660928, 0, -616103472, 0, -478810872, 0, -239518656, 0, 79774056, 0, -161431812, 0, -240657326, 0, -39575432, 0, 204010560, 0, 686174862, 0, 316034432, 0, 319048200, 0, -20272160, 0, -33994534, 0, -52121304, 0, 601763568, 0, 842198574, 0, 17852112, 0, -237940236, 0, -483264000, 0, -148777524, 0, -315952136, 0, 24507432, 0, 14369664, 0, -450891894, 0, 215895022, 0, 92945376, 0, -158739322, 0, 256191936, 0, 440553960, 0, 293130240, 0, -566587152, 0, -6869280, 0, 64148664, 0, 23232076, 0, -26855256, 0, -219658180, 0, -1197728, 0, -206447454, 0, 435005620, 0]}