# Stored data for newform 529.4.a.m, downloaded from the LMFDB on 10 July 2025.
{"Nk2": 8464, "analytic_conductor": 31.212010393036785, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[23, -1]], "atkin_lehner_string": "-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [529, 1, [5], [1]], "cm_discs": [], "conrey_index": 1, "dim": 25, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [1319713792, 7891914240, -29406208, -35213483264, -5878703744, 59756429184, 5293957904, -47394157576, -1916623624, 20295504904, 348372797, -5190810205, -33020432, 842567424, 1441101, -89674158, -704, 6324581, -2457, -292209, 88, 8482, -1, -140, 0, 1]], [3, [-628808799728627, 1704514776651617, 165221149291086, -2703901812890425, 488956616614515, 1546957487396346, -323670697366198, -439286145944155, 80510726228652, 71562133974810, -10147914797472, -7128213167241, 717077642910, 446025201147, -30043672038, -17823903582, 767144709, 457939854, -11931475, -7491671, 108861, 75139, -525, -420, 1, 1]], [5, [3604035492131596572071, 12576603616498631664885, 13416658755675053916842, 3325930984881758383795, -1976187170069932807484, -874780002702226032735, 99150492337304814875, 73608157290364944779, -1405131291447329374, -3194092084574016262, -55585028886028360, 81311154878873012, 2946069135023958, -1275463290763620, -62062526482241, 12469962096213, 738386008817, -74274857764, -5284991864, 247272378, 22481232, -329303, -52254, -307, 51, 1]]], "hecke_orbit": 13, "hecke_orbit_code": 54043195595555345, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "529.4.a.m", "level": 529, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": true, "level_is_square": true, "level_is_squarefree": false, "level_primes": [23], "level_radical": 23, "minimal_twist": "23.4.c.a", "prim_orbit_index": 1, "related_objects": [], "relative_dim": 25, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "529.4.a", "trace_display": [0, -1, -51, -73], "traces": [25, 0, -1, 80, -51, 86, -73, 3, 166, -139, -221, -191, -27, -372, -310, 152, -365, -538, -405, -578, -352, -155, 0, 803, 90, -850, 368, -459, 175, -893, 287, 164, -1020, -335, 462, -1092, -471, -810, -822, -1405, -73, -556, -901, -2073, -1384, 0, 1452, -4028, -1092, 364, -2214, 1287, -2071, 2052, 1006, -4879, -418, 2796, -2713, -2805, -1225, -2852, -4003, 217, -2030, -2933, -767, -4175, 0, 4851, -1683, -5265, 2203, -3089, 2333, -5252, 2760, -692, -5425, -4689, 1929, -2725, -5425, -4317, -912, -4359, -4404, -2610, -4933, -2695, -3619, 0, 6375, -5117, -1338, 20, -2085, 5951, -7317, 5433, 3683, -930, -3903, 1231, -1312, -6015, -5401, -3659, -4373, 1413, -9936, -681, -3673, -4082, 0, 796, 67, -853, 2974, -1751, -458, -6239, -6496, -3674, -10110, 925, -2859, -1775, -7793, 6951, -1179, 6949, -3228, -4761, -7066, -276, -1686, 0, 1274, -3598, -1914, -7885, -11046, 759, 2882, 10888, -2474, 16957, -9191, 5564, 1857, 6774, 2337, -901, -8168, 5961, 7013, 11808, -3682, 18889, 0, -5751, 4201, 8679, 7912, 22567, -15135, 28091, -14914, 1223, -899, 26391, -6575, 2455, 9651, 2267, 7480, 27341, -891, 28889, 5183, 12571, -3099, 0, -10113, 7723, 1538, -10920, -3350, 3822, -13727, -5192, 3823, 8029, 6990, 2928, 7883, 35777, -11611, 8321, 4464, 18772, -5532, 23905, 8433, 7411, 0, -22167, 13192, 16117, 13277, 17641, -16550, 34216, -8676, -7195, 12846, 5274, -17928, 13086, -2528, 43160, 14945, -2298, -3829, 25491, -14657, 35494, 2296, 0, -3813, 22000, 11359, -19903, 2724, -7524, 15202, -3294, 14697, 54326, -4621, -2490, 16315, 19035, -4089, 10997, 1994, -12178, 4424, 30122, -22095, 44870, 0, -45028, 23885, 10352, -12179, 51977, 2158, 18118, -26531, -33931, -19353, 13749, -21438, 12548, 18619, 11413, 1321, 59515, 445, -519, 21075, 24984, -18338, 0, 16168, -4591, -3971, -10613, -21527, 9642, -3799, 12891, 4931, 39961, -33510, -8386, -1782, -2054, 4082, -1362, -25801, 16320, -9008, -13847, 7362, 30442, 0, -2440, 32192, 23650, 42800, -4908, -25546, 20761, -10429, 15397, -9776, 46132, -13311, 5701, 2391, -21699, 19910, 15763, -30021, 24254, -20038, -29507, -3015, 0, -4331, -4216, -3221, -46954, -23088, 16524, -25618, 6230, 1973, -14648, 14990, 32038, 19142, 4793, 13785, -4745, -33608, 32144, -34184, 24586, -7448, -26441, 0, -18895, -38071, 1673, 16247, 18558, -8614, 9135, -8207, -37489, -19342, -42007, -12208, -34034, -59025, 12277, -32574, -5340, 15225, 14096, -12404, 26355, -31866, 0, 28526, -49708, -17753, -3446, -10035, -9419, -29774, 8136, 47196, 4519, -4363, 44870, -47614, 22695, -54125, -41008, 11625, -18971, -16615, -6068, -42717, 14563, 0, 48014, -130, -44150, 35886, -11079, 6671, -24268, 11470, -12538, -45929, 21067, 6390, -32577, -19354, 6878, 39022, 26088, -3549, -3915, -49356, 6835, -34831, 0, 40219, -50376, -34058, 21542, -73479, 55592, -18675, 98806, -7886, -31292, -53803, 63668, 31410, -51219, -667, -60854, -107679, 33692, -19961, -21513, -3593, -6347, 0, 28559, 2361, 26703, 11501, 25874, -3977, -71236, -8052, 36660, -61970, 27571, 33159, -21294, -54906, -23331, -47160, 11487, -56392, -24880, -11707, -69337, -71401, 0, 50926, -7496, -35313, -39917, -2797, 48588, -52529, 13616, -1242, -38637, -60224, -15534, -1418, -44185, -24083, 52646, -38841, -9017, -126331, -4382, -19866, -25328, 0, 1629, -31893, -62972, 10611, -58543, 22582, -40911, 10949, -27749, 1197, -50446, -58289, -55486, -74246, -9422, -4275, -112175, -10650, -37437, -89635, -4081, -13725, 0, 37660, -40512, 26399, 35298, -77692, 4424, 15309, 6080, 37420, -105022, -22508, -28210, -53294, 38499, -107413, -45299, -53437, -113291, 46619, -43338, -109162, 26697, 0, 62919, -23145, -91102, -18208, -27455, 14766, -71594, -42208, 2565, -56693, -17595, 5241, 23359, 8209, -23350, 14174, -4804, 11851, -5048, 9021, 25127, -125367, 0, -4495, -50364, -56588, 27438, 21825, 89928, -47306, 34494, -24481, 16102, -36807, 26466, -47252, -65930, 8381, -65445, -8261, 36360, 8383, -59479, 119196, 28993, 0, -4262, 47697, 107867, 67800, 28623, -62612, 25426, 25050, 82731, 94260, -17838, 10369, 14510, 69640, 34359, 20558, 97809, -15203, -116, 50237, -114009, 162707, 0, -76328, 84444, 21387, -98707, 93819, -32291, 82727, -10663, -87847, 25426, 148872, -5826, 86284, 40534, 134323, 114025, 21728, 61024, 50513, 125354, 88741, -38044, 0, 26336, -111938, 1237, -9877, -97618, -24469, 107852, -4222, 14400, -5965, 21741, 17034, 31064, -28512, 3615, -42071, -9269, 60621, 97635, 27053, 25914, 39752, 0, -23695, 144436, -10209, 97336, 97978, -126546, 27118, -86216, 159527, 56295, 78024, 33545, 19921, 145026, -114327, 16244, 140593, -58228, 58848, 89368, 28751, -55643, 0, -103779, 113060, 27943, -110088, 103673, 61703, 58099, 38528, -136076, 347, 70184, 1520, 23686, 156399, 79671, 95741, 35322, 94742, -48122, -39608, 178223, 86565, 0, -100096, -25203, 117481, 54011, -4592, -142432, 108668, -105462, -179167, 127939, -29591, -95811, 20070, -907, 177392, 53778, -9114, 78389, 227455, -692, -51527, 86030, 0, -57738, -6249, 91244, -124662, 106049, 15343, 86329, -4828, 97100, 230804, 36709, 34025, -13384, 23631, 43799, -63992, 46327, -24324, -26068, 253263, -107298, 68111, 0, -32217, 21371, 41929, -73070, 97566, -31986, -65553, -65459, 24526, -14927, -47216, -103413, 23322, 10773, 29675, 53171, 345828, 51380, -129288, -77238, 85563, -7349, 0, -29734, 85425, 21087, 92480, -142417, 54212, 24692, 61435, 19197, 125943, -77447, -11680, 134761, 124795, -51815, 93527, -176957, 3100, -23268, -23604, 95964, 216879, 0, -184609, 169317, 97966, 20020, -19221, -76880, 177656, -219903, -86254, 68545, 270512, -153992, 153186, -144202, -77127, -77472, 81386, -230922, 183391, -97500, -62012, -35528, 0, -50813, 27552, 9504, -124251, -13929, -29515, -59306, -41892, -9078, -82572, 9842, -30436, 50375, 33297, 816, -70851, -13376, 82073, -126100, 222766, 94312, -116018, 0, 118140, -39401, -63850, 19323, 186289, 4921, 121992, 90304, -23961, 21397, -221407, -79058, -122122, -80930, 206702, 61425, 134005, 42391, -34591, 112595, 235618, -7124, 0, 311, -29161, 113351, -59596, 91205, -51733, 11640, 25939, -1106, 198304, -46366, 31903, 42083, 223008, -145774, 58613, 19447, 5284, 114233, -65674, -109232, 263626, 0, -225527, 154701, 62681, 92486, -7922, 157354, -34019, -68207, -131815, -47162, 283548, 67427, -27143, 178733, 238604, 73725, 13906, 116202, 82594, -22295, -103949, -143079, 0, -37780, -119092, -79062, -176278, -188186, 92836, 10196, 84842, -28765, 84329, -197416, 99124, 51744, -239819, 24648, -134276, -238697, 90795, -28610, 34909, 64754, -57964, 0, 220201, 135906, 32692, 92533, 230249, -148421, -103363, 40379, 212655, -167282, -13233, 103948, -124238, -38094, -135550, 146853, 10273, -107702, -11436, -53807, -62605, -100527, 0, 103374, -25025, -143229, -64257, 72421, 3664, -123030, 90772, 117919, -26627, 100967, 111676, 72012, 133813, -57487, 30130, 23027, -56864, -128714, 15435, -67721, -29351, 0, -50328, -132079, 60046, 234736, -192455, -167785, 179036, 6124, -193937, -126207, 10071, -149282, 25446, 18877, 19799, 35863, -154589, -27211, 90850, -350136, 25596, -36616, 0, 120874, -132915, -133073, 28560, -171813, 130726, -96151, 27797, 279150, -176134, -55258, 228574, -239819, 63666, -210356, -243454, -100341, 123414, 188113, 191009, -135194, -120893, 0, -102210, -163306, -111943, -73105, 81159, 9892, -148923, -146875, -26743, -339293, 62360, -41354, -18577, -321324, 13549, -294632, 160588, -122395, -225231, 6966, 256879, -130039, 0, 350757, 22312, -162190, 54991, -207204, 169818, -225841, 260192, -26673, 145524, -222601, 8736, -209886, -200543, -218035, 154749, -295271, -109053, -108956, -336050, -289004, 181685, 0, 127047, -256576, -93829, 238370, -6365, 2850, 178068, -57255, -77850, -78416, 99607, -156833, -151397, -201434, 78302, 40470, -52369, -78483, -51112, 15067, -275988, 32718, 0, 142549, -268529, -127386, -131222, -313339, 188355, -223815, 26941, -30706, -350191, -154881, -25911, 50886, -114367, -77739, -197071, -216287, -50434, -178217, 106756, -271988, -211578, 0, 154401, 2834, -90770, 237245, -41765, 95457, -192276, 187010, 218953, -211952, -37428, 164935, -185781, 30753, -210990, -149485, -158424, -79340, 154249, -389087, 126235, -262020, 0, -7691, 138427, 46323, -7548, -271503, 26527, -122454, 120810, 67314, 177364, -165012, 107422, 46768, 39058, -232453, 66991, -68128, -84908, -509101, -276124, -41631, 224791, 0, -736, 74346, 156581, -83890, 8047, -145113, -88966, -132781, -76086, -180791, -188829, -83895, 132231, -210835, 45852, 158889, -195680, -83344, -37314, -20488, -85161, -382236, 0, 186904, -233776, -334149, -66800, 228352, 181933, -363640, -81911, -74541, -36167, -54304, 135582, -3921, -313841, 209083, -180770, -56121, 89804, -128693, 146321, -310315, -32321, 0, 229945, -220419, -227616, 23773, -17513, 93796, -80770, 100706, 240556, -179450, -103022, -72288, -187152, -266655, -181178, 163398, 417505, 39097, -219076, -103598, -40301, -30061, 0, -54068, 304866, -36878, 72541, -154301, -198223, -39979, 214400, -79580, 81547, -35930, -81273, -188341, 329682, 57111, -39247, -186139, -102491, -5605, -138635, 321223, 123175, 0, -52765, -67795, 410218, -194824, -148838, 308539, 175277, 206772, -193736, -247407, 272484, 95528, -105834, -100129, 5254, -151272, -234149, 80349, 128954, 106897, 74488, -94895, 0, 134851, -34140, 166982, -125206, 65299, -31406, 40330, -85820, -80246, 21935, -117372, 327885, 334224, 8151, 178778, -96802, -141350, 35563, 144531, 278892, 84263, -330377, 0, -4608, -53543, -128421, 136182, 424780, 1889, -86964, 56757, -60141, 445422, 4600, 40875, 14713, -118596, 226747, 42248, 375724, 178119, -8031, 80677, 135648, 469275, 0, -147531, -110524, -96506, 195544, 8740, -137050, 226871, -186021, 139771, 120169, -75258, -232703, 271809, 216559, -143962, 247601, 558676, -35374, 157720, -104424, 271538, 214637, 0, -302749, 361801, -116831, 165627, 120720, 146489, 1599, -8607, -72462, 171965, 133598, 72597, 167536, 263772, 23708, -356387, -310988, 45072, 495758, 40825, -44639, -166570, 0, -124550, -194915, 160990, -156879, -331211, 34230, 103882, -145291, 127267, -101343, 513756, -107266, -322907, -244771, -346173, -393925, 133143, 127008, 21457, 112521, -31142, -73633, 0, -93986, 253037, 180028, -326851, -59984, -278343, 143059, -154171, -123731, -30051, -354332, 294437, -21116, 529195, 84654, 125227, 148003, 192452, -372549, 587029, -13440, -194492, 0, -66756, 15885, 246026, -129535, 422563, -40987, 127869, 175768, -243875, 222353, 166614, -362526, -27357, 37764, 531357, 440676, 39967, 165249, 130489, 241175, 251582, 237361, 0, -129556, -347598, -145699, 89081, -292708, -504894, 308961, -93080, -111842, 258452, 175632, -82919, 363781, 436672, -73740, 475602, 74774, -251756, 252885, -496713, -167977, 816047, 0, -211275, 267325, 353957, 150751, 510689, -195554, 259709, -265570, 336426, 13587, 473400, -48836, -54938, 262414, 471386, 148014, 226791, 69569, 231771, -17568, 138667, -298402, 0, -131455, 175182, 19037, -388037, 10564, 243956, -12722, -291863, -45675, 70186, 67187, -192072, 76884, -3055, -338989, -181717, 166241, 84661, -74251, -32098, 481941, 199420, 0, -19084, 463286, 379979, 31519, 479870, -272048, 300417, -144849, -72290, 276166, -312882, 128408, 18282, 67659, 164838, 353617, 72392, -54490, 694670, -79586, -568466, -38979, 0, -271990, 408836, -136135, -305295, 153593, -111359, -39669, 10773, 138695, 643457, 105092, -57270, 261527, -202579, 372696, -14572, -34542, 3398, 416, 981623, -362857, 268958, 0, -654457, -354723, 269825, 25760, -403999, -27036, 717861, 5985, -536531, -316542, -84157, -281003, 375708, 254562, 184762, -98713, 290552, 311707, -306642, -200695, 550068, 216491, 0, 270143, 461860, 200991, 443932, 189284, 324630, -318687, 73816, 495725, 682253, -315558, -305477, 2166, 673801, -154141, 234504, -168310, -195769, -113663, 352539, 258159, 396967, 0, -139975, 446004, -285944, 250830, 108889, 40098, 152595, -309362, 53526, -182375, 1025174, -394728, 171886, -207955, -352908, 302190, 835130, -484755, -203360, -166913, 352950, 186304, 0, -52282, 250755, 169367, -582111, -303604, -337401, 60576, -42899, -286437, 232925, -178313, 185987, 523022, -54779, 183235, -30697, -286691, 65098, 211619, 135678, -335730, 182186, 0, 218466, -48719, -89627, 207373, 650311, -65127, 850311, 21292, -164583, 368248, -294535, -154420, -436945, -220801, 113127, -248228, 94918, 12212, 291772, 439204, 434087, -498163, 0, 180668, -256886, -186057, -161856, -7332, -244293, 27247, -187587, 328539, -148138, -100901, -184072, -162823, 570215, -517424, -297356, 442346, -224326, 95342, -404097, -156392, 219840, 0, -514752, 315940, -167516, 632354, 163150, -32460, -936506, -53740, 250760, -106858, 24407, -30302, -243086, 16869, 868791, 680664, -437430, 45527, 304724, -280059, 161633, -35365, 0, -25015, -179672, 301716, -158732, -699474, 896236, 325903, 151780, 29532, 17043, 62158, 643868, 468600, -252457, 94982, 33144, -643505, 224192, -129747, -507978, 204387, 244302, 0, -137933, 212310, 910888, -145368, 1016022, -473150, -729904, -545027, -90397, -291318, 241013, -65136, 197828, -295892, -484284, 278653, 244328, -30190, 11986, 390340, -306925, -250260, 0, 402111, -306910, -586476, -494066, 85535, -267636, 58299, 270068, -9794, 246570, -350389, -218886, -325576, -168824, 52030, -4610, -169112, 271509, -617320, 237951, -29140, -805162, 0, 62530, -277343, 78391, 157596, -532766, -382745, 1030515, 475956, 406777, -477276, -450731, -403631, -246916, -68909, -241280, -111971, 185699, 2387, 861888, -941399, -645789, 231771, 0, -131429, -93301, -240260, 24681, -292904, 495626, -67987, 449719, 13305, -430531, 186105, 776490, -416930, 1364822, -142632, -659739, -433993, 471641, 10029, 819495, -136493, 11930, 0, -219499, -306540, -327353, -152348, -450641, 561647, -547410, -121031, -1118395, -250049, 473423, -2852, 101983, -515059, 134576, -347978, 329883, -303224, -517549, -82684, 1154644, -608565, 0, 320999, -44550, -139230, 260262, -180811, -161681, -878131, -63818, 129724, 782430, -428078, 406534, 229509, -354861, -178154, 40779, -339852, -71395, -56003, 370389, -485343, 384304, 0, 98217, 130091, -119465, 337509, 350647, -109098, 98449, -277951, -51291, 154149, 976285, 320623, -125436, 1721, 199397, -52395, 291536, -236568, -453587, 174161, -289324, -4303, 0, 290471, -646203, -93103, 12621, 34169, 236338, 97298, 447776, 146386, -986726, -247810, -15029, -414037, -578256, -132969, -334973, -427755, 241585, -118852, -362010, -220377, -134776, 0, 655804, 11700, -309606, 307007, -362690, -247240, 173362, -159672, 248172, -462366, -141112, 272140, -313089, -168595, -663195, -514582, -262369, 218642, 536494, -165688, -184480, -693564, 0, -36244, -89916, 265290, -1081585, -160466, 363562, -406014, 364253, 209399, -341414, -73154, 237494, 175076, -368853, 24497, 160094, -239371, 9931, -547285, -718817, 82816, 323343, 0, 421535, -375448, -59820, 260006, -315870, 65732, -261970, 285671, -737423, -334858, -1007669, 30486, 215819, -2678, 1275459, -280003, -438887, 28147, -405537, -729933, 427720, -358551, 0, 140598, -997920, 7653, -60881, -20190, 330210, -352178, 1093798, -152945, 493062, -260735, 207411, -404750, -1097782, -128123, -67088, 12125, -28684, -111051, 425882, -653203, 282249, 0, -365788, 13709, -213632, 24388, -21176, 259373, -499095, -308599, 597799, -622285, -550163, -380670, 148306, -707078, -524069, 336989, 1319122, -735298, -576324, -487996, -1449981, -466188, 0, 266019, 477312, -515581, 626556, -509551, 206373, -788368, 107260, 197334, -335656, 455923, -52028, -501832, 80, -534165, -14930, -448772, 29076, -644847, -399596, 159211, -232556, 0, 433548, 94904, -160989, 35854, -40932, 43201, 25264, -312866, 305153, -289738, 229829, 58702, -947626, -343202, -846768, -729999, -1129985, -540250, 193023, -94585, -152657, -58000, 0, 832015, -172372, 154910, 111942, -544479, -286770, -249368, -196221, 273275, 386845, -209605, -61436, 107933, 192525, -563672, 224580, -384687, -440217, -534635, 170228, 194065, -1560618, 0, 436978, 25181, -851432, -238575, 714354, -134165, -192843, 324570, -337933, -573060, -974986, 121638, 310388, 272228, 789102, 230277, -782100, 414649, -89722, 59299, 863783, 479686, 0, 439811, -1144495, 195626, 1348692, -799630, 514548, -5516, -330897, 313104, 63799, -856122, 35536, -39207, -412794, -349113, -10811, -66468, 204796, -396340, -552742, -22667, 1152651, 0, -277500, 521971, -450111, -139061, 82977, 797, -717624, -244770, -271951, -157200, 822887, 112764, 642201, 288111, -352732, -409956, 157735, -543936, 349779, -635296, -598704, -167706, 0, 57265, -95977, -312506, -567660, -386622, 654144, -595085, 548182, -282892, -586160, 92294, -289701, -454889, -1037144, -123444, 160207, 197233, 570759, -244368, -574873, -513034, -340056, 0, -94683, 235712, 258794, 369368, -186509, 151572, 483428, 100790, 831969, 48736, 157873, 135072, -483530, -225609, -408499, -73586, -669172, -1145535, 21354, 250254, -393767, -183686, 0, -286867, 27877, 262670, -561559, 521581, -105478, 213804, 103071, 453291, -397594, 5172, -512786, -351109, -3197, 250837, 113335, -108907, -85144, 595424, 1442448, -161590, -405146, 0, 379662, -505626, 32763, 295454, -954354, 301279, 453602, -171085, -427764, 162552, -112598, 24827, -1422, 227704, -300322, 951844, 797447, 622556, 524371, 243887, 580539, -80279, 0, -236203, 722281, 247362, 518804, 520927, -759269, 45893, 472225, 336390, -252361, -20368, 575229, 685135, 564310, 539847, 36953, -338996, 65836, 549331, -855102, 498939, 362026, 0, 170627, 300230, 41296, 2663, 685139, -441380, 519759, -281422, -604350, 384247, 755555, -339778, 441219, 111260, 226748, -363377, 657042, 746477, -208236, 13089, 257057, 395428, 0, -36303, -423092, -24620, -252186, 671926, -307621, 875072, -308217, -99989, 103654, -107477, -108720, -134803, 428322, 614896, 59620, -120394, -74498, 171928, 13756, -148574, 385994, 0, -347845, -208127, -377303, -329096, 449914, -217482, -319711, 438602, 297515, 478255, -83, 79816, -209347, -103699, 225469, -421469, 255065, 484803, -509075, 681102, -851077, 124543, 0, -190902, -35997, 380371, -439100, -1253901, -303995, 291810, -439035, -311937, -440458, 566745, 421478, -236248, 2042061, 190214, -319360, 488462, -321975, -269772, 641632, 723355, 341538, 0, -299905, 140775, 739084, 112741, -169688, 907002, -60191, -115343, -175851, 457046, 106853, 634115, 92071, -104449, 205099, 370348, -269416, -101995, 1404402, -174309, 652119, -52111, 0, -673312, 618008, -241178, -515373, 157936, -219097, -209611, -332770, -610843, 917240, 1395809, 220913, 526244, 167178, -372356, -861495, 451357, -213166, 53163, -89365, 436316, 26158, 0, -468358, 443951, 398732, 274758, 1018484, -925865, 198222, -431245, 674531, 36917, -346718, -242074, 495982, -69050, 97590, 814508, 396014, 55932, 239064, 422092, 250255, 670924, 0, -501190, -179602, -1039749, -518031, 976104, 596966, 773170, -683894, -282413, 1395292, -314666, -668544, 426380, -50585, -48266, 575840, 584648, 931539, 771697, 923834, 371679, 123164, 0, -175582, -818772, 304570, -80226, -367348, -991925, 876085, 734458, -354440, -159278, -70432, -878027, -416375, 940776, 888481, 9573, -96570, 72032, 835872, -58268, -936525, 593101, 0, 202665, 861863, 141576, 681299, 40266, -226988, 319546, -178718, -90300, 780925, -823528, 10219, 219494, 971910, 609954, 568541, -27744, 52361, 201345, 367817, -318179, -1053001, 0, -1143544, 146560, 1627648, -1131613, 163832, 553312, 808466, 518474, -635422, -19174, 464501, -36936, 1912, 163485, 885040, -356203, -1082891, 871767, -1773487, 475654, 1864793, 24906, 0, -466594, 1362973, 1662332, 215081, 956635, 218121, -228722, -1028825, -200339, 107134, 86072, -153113, 72435, -562996, 74606, 682604, 1346723, -505228, 123121, -182764, -861217, 215653, 0, -327727, 995181, -61494, -470553, 222210, -254420, -138930, -143017, 668166, 1060720, 550741, -240945, 474070, 398488, -686779, 469294, 961667, -507364, -919374, -137520, 560049, 795374, 0, 43047, 353618, -623835, -92591, 78904, -1228476, 31978, 44308, 479002, -456992, 566310, -854112, 342622, -261860, -396399, 660738, 347347, -69502, 1995548, -1082993, 125201, 117698, 0, -23877, -322795, -837224, 214778, 161937, 1001214, 264380, -911751, 92621, -80603, -866206, -213610, 668216, 723331, -1070277, -265822, -188740, -331561, 1177557, 1361968, 963165, -746238, 0, -322433, -30581, 671791, -10386, 1142872, -63903, 132374, 119242, -184881, 4795, 716387, -543210, 252225, -994367, 466089, -403796, -39834, -449073, 253914, -254365, 710416, 830150, 0, 510605, 24777, -441954, 627848, -1622696, -254121, -688308, -202068, 255302, 653050, 463844, 510517, 701819, 170901, 623016, 834032, -325558, 572993, -1592304, 824180, 142459, 1791413, 0, -671813, 447893, 428217, 336524, -274010, -454719, 1126255, -290961, -806521, 325610, 59096, 288037, 677136, -546197, 1373175, -49906, 658096, -1032562, -907641, 725586, 223175, 821096, 0, 982544, 315377, 937094, -339996, 872059, 976772, 357846, 193537, 612736, 236594, -56987, -241186, -527183, -287678, -1312868, 69033, 480738, 840632, 688909, -343611, -933055, -440816, 0, -21385, 1136369, -735954, 585882, -242621, -789102, 409304, -767301, 549168, 1118099, -395711, -501821, -152438, 982194, -543387, -485610, 1114375, -38183, -742556, -419899, -174651, -737346, 0, -623871, 241204, 905678, -358187, -323298, -439322, 166996, 880932, 712471, 408536, -982219, 205797, -115531, 472381, -81818, 80481, -262426, 186696, 902730, -54730, -495767, -791117, 0, -603133, 165523, 432623, -284980, 497984, 498164, 489661, 317967, -866541, 22661, -168576, -257298, 43480, 544904, 569724, 384964, 302815, 504095, 973150, 669165, -336796, -337709, 0, -455375, -751387, 89444, -335274, 181999, 258335, -1274554, 613701, -1575022, 121686, -31246, 609466, -163878, -430607, 1329350, -620787, 929495, 279653, 69083, 164157, -392438, 394139, 0, 609879, -474402, -915700, 618259, 941792, -506194, -825584, -832393, 482692, -82463, 233736, -1238184, 210311, -263449, -122931, 164308, -30580, 307651, -501554, -707398, 1263666, 1309762, 0, -796243, -431020, -83100, -570485, -587221, -233291, 1001015, 421381, -81433, -242151, 799281, 691140, -759171, 670075, 425873, 472080, -1216756, 58050, -785375, -757801, -181940, 1206250, 0, -613436, -696601, 961438, -318324, -68745, 860024, 513284, -627286, -463711, -1947218, 613106, 894633, -86910, -821137, 565558, -759045, -751928, 84409, 412556, 578259, -470405, -1432721, 0, 1137368, -832236, -410710, -962527, -699392, -475064, 631029, 211927, 513678, 321140, -34908, 525479, -296257, -305245, -198107, -807361, 173008, -78848, 221414, -144360, 284766, 33054, 0, 111573, 41825, 286076, 741976, -294933, -1192125, 276328, -404630, -271497, -105889, -815451, 23468, -1062460, 157250, 240818, 114479, 296105, -264374, 965869, 633406, 537778, -1089484, 0, 465648, -377926, -524496, -112264, 311866, 201487, -244963, -258724, 719, 1544256, -26920, 278758, 44267, 800390, -676100, 158910, -429605, 96749, -820881, 142266, -389262, -614303, 0, -464959, -369554, -60059, 213643, 190490, -64967, -1001852, 840755, -841391, -375187, 2649192, 463968, 737315, -778113, -579348, -577775, -810364, 658737, 878997, -145482, -65915, 134921, 0, -41101, 87303, -1806833, -147865, -1228298, 541890, -1987044, -412992, 751930, 66616, 142133, 1121700, 861382, -749978, -551569, 144091, 466175, 449523, -1676053, 1117850, -1708506, -494584, 0, 453115, 223088, 94172, -345278, 777414, -650208, 736258, -105448, 285207, -1702061], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "field_poly_is_cyclotomic": null, "field_poly_is_real_cyclotomic": null, "field_poly_root_of_unity": null, "hecke_ring_generator_nbound": null, "hecke_ring_index": null, "hecke_ring_index_factorization": null, "hecke_ring_index_proved": null, "is_polredabs": null, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp_display": null, "trace_hash": null, "trace_moments": null, "trace_zratio": null}