# Stored data for newform 198.6.a.i, downloaded from the LMFDB on 19 April 2024.
{"label": "198.6.a.i", "space_label": "198.6.a", "level": 198, "weight": 6, "hecke_orbit": 9, "hecke_orbit_code": 36028797119627462, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2227710880471094002, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-51, 1]], [7, [166, 1]]], "qexp_display": "q+4q^{2}+2^{4}q^{4}+51q^{5}-166q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 7128, "fricke_eigenval": -1, "atkin_lehner_string": "---", "analytic_conductor": 31.755996322970166, "hecke_ring_index": 1, "level_radical": 66, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [198, 1, [155, 145], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 11], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.029", "prec": 17}, {"__RealLiteral__": 0, "data": "0.982", "prec": 17}, {"__RealLiteral__": 0, "data": "0.051", "prec": 17}, {"__RealLiteral__": 0, "data": "1.976", "prec": 17}, {"__RealLiteral__": 0, "data": "0.147", "prec": 17}, {"__RealLiteral__": 0, "data": "4.965", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, -1], [11, -1]], "trace_display": [4, 0, 51, -166], "traces": [0, 1, 4, 0, 16, 51, 0, -166, 64, 0, 204, 121, 0, 692, -664, 0, 256, 738, 0, 1424, 816, 0, 484, 1779, 0, -524, 2768, 0, -2656, 2064, 0, 6245, 1024, 0, 2952, -8466, 0, -14785, 5696, 0, 3264, -5304, 0, 17798, 1936, 0, 7116, 17184, 0, 10749, -2096, 0, 11072, 30726, 0, 6171, -10624, 0, 8256, 34989, 0, -45940, 24980, 0, 4096, 35292, 0, 25343, 11808, 0, -33864, -13311, 0, -53260, -59140, 0, 22784, -20086, 0, 77234, 13056, 0, -21216, -55014, 0, 37638, 71192, 0, 7744, -125415, 0, -114872, 28464, 0, 68736, 72624, 0, -88807, 42996, 0, -8384, -1482, 0, -117496, 44288, 0, 122904, 79362, 0, 87842, 24684, 0, -42496, 47247, 0, 90729, 33024, 0, 139956, -122508, 0, 14641, -183760, 0, 99920, -186099, 0, -239416, 16384, 0, 141168, 98142, 0, -236384, 101372, 0, 47232, -400137, 0, 205766, -135456, 0, -53244, 83732, 0, 105264, -213040, 0, -236560, -87726, 0, -432778, 91136, 0, -80344, 318495, 0, -34075, 308936, 0, 52224, -295314, 0, 45020, -84864, 0, -220056, -482556, 0, 107571, 150552, 0, 284768, 766254, 0, 86984, 30976, 0, -501660, -303399, 0, -285181, -459488, 0, 113856, -754035, 0, 89298, 274944, 0, 290496, -767067, 0, 411668, -355228, 0, 171984, 759258, 0, -46600, -33536, 0, -5928, -342624, 0, -270504, -469984, 0, 177152, 172304, 0, -932428, 491616, 0, 317448, 907698, 0, -1036670, 351368, 0, 98736, 510696, 0, 169745, -169984, 0, 188988, -198078, 0, -849997, 362916, 0, 132096, 401832, 0, 876384, 559824, 0, -490032, -855174, 0, 1125464, 58564, 0, -735040, 548199, 0, 985408, 399680, 0, -744396, 1197513, 0, 215259, -957664, 0, 65536, -37758, 0, 2454310, 564672, 0, 392568, 631254, 0, 1567026, -945536, 0, 405488, 1080342, 0, -816100, 188928, 0, -1600548, -63404, 0, 1688198, 823064, 0, -541824, 879042, 0, 1540268, -212976, 0, 334928, 880464, 0, -875213, 421056, 0, -852160, -720840, 0, 1784439, -946240, 0, -350904, 1231068, 0, -2954468, -1731112, 0, 364544, -2342940, 0, -1039048, -321376, 0, 1273980, 1251348, 0, -1443361, -136300, 0, 1235744, 2012079, 0, 249744, 208896, 0, -1181256, 1050912, 0, -362608, 180080, 0, -339456, -2852544, 0, 2017337, -880224, 0, -1930224, 1292493, 0, 264122, 430284, 0, 602208, 755645, 0, 1005628, 1139072, 0, 3065016, 1710492, 0, 218822, 347936, 0, 123904, -3681915, 0, -678861, -2006640, 0, -1213596, -1885284, 0, -448323, -1140724, 0, -1837952, -2716260, 0, -3116659, 455424, 0, -3016140, -5100516, 0, 1394414, 357192, 0, 1099776, 1428288, 0, -4260355, 1161984, 0, -3068268, -201765, 0, -1024386, 1646672, 0, -1420912, -1948821, 0, 1312902, 687936, 0, 3037032, 3938934, 0, -1468258, -186400, 0, -134144, -2246178, 0, 4321540, -23712, 0, -1370496, -1788985, 0, -3614878, -1082016, 0, -1879936, -5808174, 0, -2805714, 708608, 0, 689216, 3812388, 0, 1973462, -3729712, 0, 1966464, -386712, 0, 7626040, 1269792, 0, 3630792, 2083590, 0, -72691, -4146680, 0, 1405472, 2533296, 0, 594392, 394944, 0, 2042784, -4566507, 0, -6396165, 678980, 0, -679936, 5443821, 0, -641784, 755952, 0, -792312, -5858472, 0, 6703124, -3399988, 0, 1451664, 1259940, 0, -5023081, 528384, 0, 1607328, 2356605, 0, -4206938, 3505536, 0, 2239296, 2153558, 0, -746176, -1960128, 0, -3420696, 6722580, 0, -10231220, 4501856, 0, 234256, -4529157, 0, 1960013, -2940160, 0, 2192796, 579624, 0, 1523232, 3941632, 0, 1598720, 2209626, 0, 1369052, -2977584, 0, 4790052, -1833426, 0, -75582, 861036, 0, -3830656, 1712661, 0, 8841160, 262144, 0, -151032, -5992296, 0, 2079264, 9817240, 0, 2258688, 789435, 0, 627392, 1570272, 0, 2525016, 4608810, 0, -3271502, 6268104, 0, -3782144, -3670368, 0, 4047462, 1621952, 0, 4321368, 1300629, 0, 3208952, -3264400, 0, 755712, 4479942, 0, 3426584, -6402192, 0, -253616, 2939136, 0, -12820844, 6752792, 0, 3292256, -10519830, 0, 12316216, -2167296, 0, 3516168, -5472876, 0, 2409597, 6161072, 0, -851904, 11778672, 0, -8356276, 1339712, 0, 3521856, -932196, 0, -13775839, -3500852, 0, 1684224, 9132324, 0, 3717846, -3408640, 0, -2883360, 12709308, 0, 8892880, 7137756, 0, -3784960, -1008252, 0, -6247908, -1403616, 0, 4924272, -10510032, 0, -199390, -11817872, 0, -6924448, 746691, 0, 16190, 1458176, 0, -9371760, 11891328, 0, -11525344, -4156192, 0, -1285504, -16997394, 0, -18487471, 5095920, 0, 5005392, 20818890, 0, -7853549, -5773444, 0, -545200, -10911330, 0, -4542811, 4942976, 0, 8048316, -12210216, 0, 7438308, 998976, 0, 835584, -18428631, 0, 9666035, -4725024, 0, 4203648, 4514301, 0, 4233669, -1450432, 0, 720320, 5372349, 0, 5005242, -1357824, 0, -11410176, -9879558, 0, 10805201, 8069348, 0, -3520896, -12055584, 0, 3671856, -7720896, 0, 5169972, -5558740, 0, 11327486, 1056488, 0, 1721136, 12059490, 0, 14741962, 2408832, 0, 3022580, 5141664, 0, -20406987, 4022512, 0, 4556288, 21262392, 0, 13124255, 12260064, 0, 6841968, 10494066, 0, -3914352, 875288, 0, 1391744, -3659562, 0, -21053840, 495616, 0, -14727660, 246012, 0, 10225211, -2715444, 0, -8026560, 11109855, 0, 4270332, -4854384, 0, -7541136, -24168285, 0, 19504336, -1793292, 0, -4562896, -1081536, 0, 16824641, -7351808, 0, -10865040, 13134924, 0, -5041684, -12466636, 0, 1821696, 3066503, 0, -6263746, -12064560, 0, -20402064, -3639756, 0, -4474026, 5577656, 0, 1428768, -13174092, 0, -18736957, 4399104, 0, 5713152, -22071678, 0, 489242, -17041420, 0, 4647936, -14696940, 0, -14581772, -12273072, 0, -807060, 24212388, 0, 24207236, -4097544, 0, 6586688, -13526010, 0, -3272380, -5683648, 0, -7795284, -7552896, 0, -1610631, 5251608, 0, 2751744, -1737825, 0, 14209424, 12148128, 0, 15755736, -7843002, 0, -31790480, -5873032, 0, -745600, 7933335, 0, 12681792, -536576, 0, -8984712, -6444460, 0, -15061014, 17286160, 0, -94848, 10468512, 0, 11914742, -5481984, 0, -7155940, 2296020, 0, 25344352, -14459512, 0, -4328064, 1861122, 0, 23015285, -7519744, 0, -23232696, 16835148, 0, -23529859, -11222856, 0, 2834432, 7932762, 0, -24610356, 2756864, 0, 15249552, -29154921, 0, -16251053, 7893848, 0, -14918848, 5486121, 0, -2430406, 7865856, 0, -1546848, -26302515, 0, -9490522, 30504160, 0, 5079168, 1815528, 0, -10781209, 14523168, 0, 8334360, 28335456, 0, 39078954, -290764, 0, -16586720, 9345314, 0, 17537356, 5621888, 0, 10133184, 30892434, 0, -26891884, 2377568, 0, 1579776, 19213227, 0, 11593100, 8171136, 0, -18266028, -13185678, 0, 39743056, -25584660, 0, 2715920, 24470016, 0, -15473349, -2719744, 0, 21775284, 12889680, 0, 22675788, -2567136, 0, 3023808, -14544231, 0, 2981948, -3169248, 0, -23433888, -29657868, 0, -6656694, 26812496, 0, -13599952, -16291572, 0, 31805678, 5806656, 0, 5039760, -9211212, 0, 7747340, -20092324, 0, 2113536, 23344446, 0, 15306576, 6429312, 0, 9426420, 4554198, 0, 20737208, -16827752, 0, 14022144, -26919282, 0, -9435816, 8957184, 0, 8614232, -10189563, 0, -36855920, -2984704, 0, -7840512, -10392354, 0, -39120417, -13682784, 0, 26890320, 66422742, 0, 10370874, -40924880, 0, 18007424, 20995068, 0, -8188768, 937024, 0, -18116628, 17327439, 0, -34157156, 7840052, 0, -11760640, 438963, 0, -15175215, 8771184, 0, 2318496, 27912387, 0, 38722158, 6092928, 0, 15766528, 31662642, 0, -42684640, 6394880, 0, 8838504, -2376600, 0, -22104418, 5476208, 0, -11910336, -13899512, 0, 25821882, 19160208, 0, -7333704, 43753824, 0, 46840214, -302328, 0, 3444144, -4000323, 0, -17473824, -15322624, 0, 6850644, 24429414, 0, 20516822, 35364640, 0, 1048576, 2779296, 0, 53445928, -604128, 0, -23969184, -41730240, 0, -17447872, 8317056, 0, 39268960, -33903720, 0, -6909769, 9034752, 0, 3157740, 14562516, 0, 8787504, 2509568, 0, 6281088, 30162111, 0, 3561854, 10100064, 0, 18435240, -47553828, 0, 71841148, -13086008, 0, 25072416, -14762943, 0, -27333484, -15128576, 0, -14681472, -10745647, 0, -56891380, 16189848, 0, 6487808, -30516240, 0, -9326152, 17285472, 0, 5202516, -38069688, 0, 30570336, 12835808, 0, -13057600, -52870170, 0, -71744368, 3022848, 0, 17919768, -27058938, 0, 11792537, 13706336, 0, -25608768, 3886650, 0, 5656450, -1014464, 0, 11756544, -65021223, 0, 26045496, -51283376, 0, 27011168, 41519262, 0, -179322, 13169024, 0, -42079320, 8656995, 0, -3887872, 49264864, 0, -8669184, 49824336, 0, -12266968, 14064672, 0, -21891504, 19122471, 0, -58252654, 9638388, 0, 24644288, -14217016, 0, -10101978, -3407616, 0, 47114688, 18703134, 0, -7473320, -33425104, 0, 5358848, -43349847, 0, -92332325, 14087424, 0, -3728784, -38482758, 0, -16395127, -55103356, 0, -14003408, -86787180, 0, -65418560, 6736896, 0, 36529296, -52163934, 0, 20493432, 14871384, 0, -13634560, 80104296, 0, -42674893, -11533440, 0, 50837232, -9004416, 0, 9602802, 35571520, 0, 28551024, 36398226, 0, -17856786, -15139840, 0, -4033008, 59098068, 0, -10947456, -24991632, 0, -5614464, -6177099, 0, -43613874, 19697088, 0, -42040128, 10628882, 0, -46748350, -797560, 0, -47271488, 57398664, 0, -9823518, -27697792, 0, 2986764, -127198164, 0, 28561019, 64760, 0, 5832704, 1819578, 0, 54661554, -37487040, 0, 47565312, -95883210, 0, -5632476, -46101376, 0, -16624768, -86519820, 0, 20445818, -5142016, 0, -67989576, 50255808, 0, 19571858, -73949884, 0, 20383680, -39305880, 0, 5716887, 20021568, 0, 83275560, 36735072, 0, -50258488, -31414196, 0, -23093776, 50364234, 0, 61073163, -2180800, 0, -43645320, -94130505, 0, -61454444, -18171244, 0, 19771904, 10978209, 0, 47340046, 32193264, 0, -48840864, -33123480, 0, 36088432, 29753232, 0, 3995904, 50363523, 0, 57234683, 3342336, 0, -73714524, -21525636, 0, -1925658, 38664140, 0, -18900096, 74632656, 0, 50284088, 16814592, 0, 18057204, 125169810, 0, 73451360, 16934676, 0, -5801728, -24779055, 0, -7490947, 2881280, 0, 21489396, 103208844, 0, -14823468, 20020968, 0, -5431296, -1025544, 0, 32193954, -45640704, 0, -39518232, -73816518, 0, -110776657, 43220804, 0, 32277392, -16100424, 0, 36047420, -14083584, 0, -48222336, 1771561, 0, 111148510, 14687424, 0, -30883584, 127333122, 0, -81307232, 20679888, 0, -22234960, 56998692, 0, 55097442, 45309944, 0, 4225952, -18954864, 0, -68336888, 6884544, 0, 48237960, -41621100, 0, 62245431, 58967848, 0, 9635328, 60922164, 0, 35467776, 12090320, 0, 20566656, -1905264, 0, 149252268, -81627948, 0, 16090048, -43631067, 0, -22517979, 18225152, 0, 85049568, -126036828, 0, 28361708, 52497020, 0, 49040256, 86098098, 0, -75842240, 27367872, 0, 41976264, 54918504, 0, 7735600, -15657408, 0, 3501152, -28969336, 0, -115668316, 5566976, 0, -14638248, -81727260, 0, 44831142, -84215360, 0, 1982464, -90489225, 0, -40600332, -58910640, 0, 984048, 78553668, 0, 60786664, 40900844, 0, -10861776, 22185936, 0, 74295335, -32106240, 0, 44439420, 110184756, 0, -33801790, 17081328, 0, -19417536, 102809514, 0, 44903664, -30164544, 0, -96673140, -39099816, 0, 11875182, 78017344, 0, -7173168, -44635863, 0, -57888508, -18251584, 0, -4326144, 109220340, 0, -115614235, 67298564, 0, -29407232, 107314080, 0, 101330372, -43460160, 0, 52539696, -28602464, 0, -36762840, -20166736, 0, -49866544, 32694924, 0, -47134270, 7286784, 0, 12266012, -18334236, 0, 154783048, -25054984, 0, -48258240, -118483824, 0, -147515737, -81608256, 0, -14559024, 79509954, 0, -31402855, -17896104, 0, 22310624, 60066468, 0, 62784468, 5715072, 0, -52696368, 134217447, 0, 109981216, -74947828, 0, 17596416, -150677868, 0, -48416577, 22852608, 0, -88286712, -94187007, 0, -92556270, 1956968, 0, -68165680, 78419640, 0, 67127505, 18591744, 0, -58787760, 91196463, 0, 24072560, -58327088, 0, -49092288, 24897686, 0, 126560432, -3228240, 0, 96849552, -52991448, 0, 63418464, 96828944, 0, -16390176, 45085197, 0, 145126700, 26346752, 0, -54104040, -84775536, 0, 67153637, -13089520, 0, -22734592, -61738680, 0, 63818748, -31181136, 0, -30211584, 101243460, 0, -28177670, -6442524, 0, 21006432, -73611411, 0, 43954220, 11006976, 0, -6951300, 178737972, 0, 10131572, 56837696, 0, 48592512, -78339936, 0, -147785266, 63022944, 0, -31372008, -37833750, 0, 102616029, -127161920, 0, -23492128, 32880948, 0, -263143430, -2982400, 0, 31733340, 12736944, 0, -56628640, 50727168, 0, -2146304, 15439806, 0, 141099502, -35938848, 0, -25777840, -31400931, 0, 15247094, -60244056, 0, 69144640, -151084482, 0, 53596512, -379392, 0, 41874048, -41073876, 0, -150717994, 47658968, 0, -21927936, -128780508, 0, 105485234, -28623760, 0, 9184080, -66704112, 0, -23680269, 101377408, 0, -57838048, -88531677, 0, -10614846, -17312256, 0, 7444488, 191883870, 0, -145479744, 92061140, 0, -30078976, -65539566, 0, -165675872, -92930784, 0, 67340592, 102884187, 0, -77171506, -94119436, 0, -44891424, -52366138, 0, 83178716, 11337728, 0, 31731048, -60193680, 0, 2129498, -98441424, 0, 11027456, 141958884, 0, -13279732, 60998208, 0, -116619684, -94749540, 0, -87723785, -65004212, 0, 31575392, 13470222, 0, -186827024, -59675392, 0, 21944484, -178590960, 0, -197062414, -9721624, 0, 31463424, 156568938, 0, 188167928, -6187392, 0, -105210060, 67914264, 0, 38537895, -37962088, 0, 122016640, 93028617, 0, 72217296, 20316672, 0, 7262112, 51287028, 0, -1093716, -43124836, 0, 58092672, 28170723, 0, 155817854, 33337440, 0, 113341824, -4123075, 0, -163577728, 156315816, 0, -1163056, -35681538, 0, 87235092, -66346880, 0, 37381256, -254065440, 0, -56194651, 70149424, 0, 22487552, 11159922, 0, -181878127, 40532736, 0, 123569736, -86712048, 0, 56592770, -107567536, 0, 9510272, -198787158, 0, 169997912, 6319104, 0, 76852908, -94400592, 0, -187777665, 46372400, 0, 32684544, -94820160, 0, -35732994, -73064112, 0, -52742712, 6974964, 0, 216231848, 158972224, 0, -102338640, -276894804, 0, 191561681, 10863680, 0, 97880064, 55829823, 0, -210858430, -61893396, 0, -10878976, 5447420, 0, -96149484, 87101136, 0, 51558720, 6267828, 0, 237811412, 90703152, 0, -10268544, -22864473, 0, 142390072, 12095232, 0, -58176924, -115463652, 0, -158923965, 11927792, 0, -12676992, 137399286, 0, 58569156, -93735552, 0, -118631472, 278598696, 0, 27908240, -26626776, 0, 107249984, 218506305, 0, -58940137, -54399808, 0, -65166288, -158949609, 0, -58389276, 127222712, 0, 23226624, -104788164, 0, -126461168, 20159040, 0, -36844848, 74955756, 0, 169760361, 30989360, 0, -80369296, 64827396, 0, -260126316, 8454144, 0, 93377784, 13016091, 0, -236591770, 61226304, 0, 25717248, 71115114, 0, 283064084, 37705680, 0, 18216792, -113251671, 0, 172704314, 82948832, 0, -67311008, 128554566, 0, -17739481, 56088576, 0, -107677128, -179336772, 0, 72842688, -37743264, 0, 35828736, 127223658, 0, -286895300, 34456928, 0, -40758252, -217278105, 0, 135472600, -147423680, 0, -11938816, 163172415, 0, 92716734, -31362048, 0, -41569416, 86875308, 0, -97869906, -156481668, 0, -54731136, 128385924, 0, -10290015, 107561280, 0, 265690968, -2110368, 0, 34868286, 41483496, 0, -163699520, 10525064, 0, -91143936, 72029696, 0, 83980272, -124309506, 0, 65554574, -32755072, 0, 3748096, -60706392, 0, -280240868, -72466512, 0, 69309756, 52307952, 0, -99389871, -136628624, 0, 31360208, 251506536, 0, 222790451, -47042560, 0, 1755852, 66958002, 0, -167314304, -60700860, 0, 35084736, -454283910, 0, -299482376, 9273984, 0, 111649548, -145920972, 0, -36711279, 154888632, 0, 24371712, 44406309, 0, -40470616, 63066112, 0, 126650568, 109609470, 0, -255684488, -170738560, 0, 25579520, -74881158, 0, 218416982, 35354016, 0, -9506400, -34506901, 0, 279244574, -88417672, 0, 21904832, 30061368, 0, -94991164, -47641344, 0, -55598048, 148772436, 0, -114555078, 103287528, 0, 76640832, -57012696, 0, 101502413, -29334816, 0, 175015296, 220398540, 0, 118137791, 187360856, 0, -1209312, 305840832, 0, 145285358, 13776576, 0, -16001292, 245996535, 0, 104649569, -69895296, 0, -61290496, 113011488, 0, -91238235, 27402576, 0, 97717656, 170653380, 0, -23579900, 82067288, 0, 141458560, -184358778, 0, -223113285, 4194304, 0, 11117184, 119659440, 0, 155780372, 213783712, 0, -2416512, 10805058, 0, -27473904, -95876736, 0, -166920960, -48674616, 0, -296216874, -69791488, 0, 33268224, -204216678, 0, 125087008, 157075840, 0, -135614880, 28827336, 0, 158267035, -27639076, 0, 36139008, -303450270, 0, 42282863, 12630960, 0, 58250064, 248734512, 0, 91897526, 35150016, 0, 10038272, -204357288, 0, 194431788, 25124352, 0, 120648444, 73205859, 0, -92815107, 14247416, 0, 40400256, 100646562, 0, 191310702, 73740960, 0, -190215312, 141780642, 0, -295695094, 287364592, 0, -52344032, -109928640, 0, 31153840, 100289664, 0, -59051772, 49811828, 0, -137341062, -109333936, 0, -60514304, 175915212, 0, 10270580, -58725888, 0, -42982588, 388928040, 0, 9619793, -227565520, 0, 64759392, -191900430, 0, 373726991, 25951232, 0, -122064960, 67279728, 0, 172481968, -37304608, 0, 69141888, -211694838, 0, 106263090, 20810064, 0, -152278752, -176689008, 0, 34548563, 122281344, 0, 51343232, -3707241, 0, 91870218, -52230400, 0, -211480680, -333928752, 0, -162970704, -286977472, 0, 12091392, -207723768, 0, 91896077, 71679072, 0, -108235752, -517312365, 0, 129198096, 47170148, 0, 54825344, -5638600, 0, 239597926, -102435072, 0, 15546600, 30313992, 0, -182495624, 22625800, 0, -4057856, -83127195, 0, 178143737, 47026176, 0, -260084892, 370075872, 0, 65944849, 104181984, 0, -205133504, -205863156, 0, -232891857, 108044672, 0, 166077048, -334005114, 0, 34975166, -717288, 0, 52676096, 65717460, 0, 72428796, -168317280, 0, 34627980, -157987653, 0, -41457504, -15551488, 0, 197059456, 165672690, 0, -399285202, -34676736, 0, 199297344, 461136936, 0, 277634871, -49067872, 0, 56258688, 530247768, 0, -66358528, -87566016, 0, 76489884, -32730984, 0, 679222900, -233010616, 0, 38553552, -174451392, 0, -332608700, 98577152, 0, -56868064, 64202517, 0, -311897707, -40407912, 0, -13630464, 457268028, 0, 60192928, 188458752, 0, 74812536, 546861348, 0, -123114817, -29893280, 0, -133700416, 341859324, 0, 245596034, 21435392, 0, -173399388, 159410976, 0, -268428199, -369329300, 0, 56349696, -127213287, 0, 20848784, -14915136, 0, -153931032, 184710816, 0, 64256940, -65580508, 0, -220413424, -388431804, 0, 182902577, -56013632, 0, -347148720, -256177131, 0, -334877942, -261674240, 0, 26947584, -112823788, 0, -2636478, 146117184, 0, -208655736, -209952108, 0, -295301106, 81973728, 0, 59485536, -48206751, 0, 120186855, -54538240, 0, 320417184, 28498986, 0, -487573657, -170699572, 0, -46133760, -214553838, 0, 414395573, 203348928, 0, -36017664, -210646464, 0, -197345252, 38411208, 0, 142286080, 243365661, 0, -43844252, 114204096, 0, 145592904, 151855308, 0, 109831458, -71427144, 0, -60559360, -209025384, 0, 317805020, -16132032, 0, 236392272, -265004976, 0, -66566437, -43789824, 0, -99966528, -274941822, 0, 147489188, -22457856, 0, -24708396, -125437070, 0, 93211766, -174455496, 0, 78788352, 61180794, 0, 342851580, -168160512, 0, 42515528, -528163887, 0, -347592691, -186993400, 0, -3190240, -521792220, 0, -113548896, -189085952, 0, 229594656, -13765554, 0, -340928384, -39294072, 0, -110791168, 41479062, 0, -185581656, 11947056, 0, -508792656, -194490123, 0, 46534868, 114244076, 0, 259040, -283941672, 0, 61794216, 23330816, 0, 7278312, 99960663, 0, 218356070, 218646216, 0, -149948160, 50613366, 0, -36324452, 190261248, 0, -383532840, -428661873, 0, 482326330, -22529904, 0, -184405504, 20539145, 0, 29560824, -66499072, 0, -346079280, 490554174, 0, 141184998, 81783272, 0, -20568064, 77684832, 0, -244349323, -271958304, 0, 201023232, 611197890, 0, -218873011, 78287432, 0, -295799536, -82632768, 0, -374696255, 81534720, 0, -157223520, -530810364, 0, 112690926, 22867548, 0, 80086272, 139754208, 0, 527995584, 333102240, 0, 146940288, 69821652, 0, -23967438, -201033952, 0, -125656784, 243665760, 0, -245849974, -92375104, 0, 201456936, 156270918, 0, 284874256, 244292652, 0, -8723200, 312957144, 0, -93504726, -174581280, 0, -376522020, -102849637, 0, -560740696, -245817776, 0, -72684976, 776568, 0, 74421618, 79087616, 0, 43912836, -196314135, 0, -64741788, 189360184, 0, 128773056, 622734222, 0, 207530336, -195363456, 0, -132493920, -101087382, 0, 87345711, 144353728, 0, 119012928, -248003484, 0, -6535414, 15983616, 0, 201454092, 450899160, 0, -69862471, 228938732, 0, 13369344, 525406536, 0, 48621672, -294858096, 0, -86102544, -319390164, 0, 517365394, -7702632, 0, 154656560, -343562430, 0, 61567904, -75600384, 0, 298530624, 194268660, 0, -258856560, 201136352, 0, 67258368, 106042464, 0, -32247200, 72228816, 0, 500679240, 268713342, 0, -167048818, 293805440, 0, 67738704, 330273774, 0, 84052413, -23206912, 0, -99116220, -569795088, 0, 40261185, -29963788, 0, 11525120, -316466514, 0, -231472724, 85957584, 0, 412835376, 31996992, 0, 284704898, -59293872, 0, 80083872, -59509878, 0, -817640120, -21725184, 0, -4102176, 196803135, 0, -103476054, 128775816, 0, -182562816, 517196481, 0, 235049310, -158072928, 0, -295266072, -237095808, 0, 293010784, -443106628, 0, 172883216, -166846602, 0, 17947154, 129109568, 0, -64401696, 136181144, 0, 707218930, 144189680, 0, -56334336, -166800822, 0, -17925112, -192889344, 0, 7086244, 580326795, 0, -187188768, 444594040, 0, 58749696, -25147350, 0, 696606800, -123534336, 0, 509332488, -41585688, 0, 183687965, -325228928, 0, 82719552, 33492990, 0, -398912560, -88939840, 0, 227994768, -270847245, 0, 148496189, 220389768, 0, 181239776, 26160861, 0, 66332079, 16903808, 0, -75819456, -358507647, 0, 787449100, -273347552, 0, 27538176, 163656552, 0, -456789127, 192951840, 0, -166484400, 743353851, 0, 647422136, 248981724, 0, 235871392, 119234368, 0, -595897666, 38541312, 0, 243688656, 323504286, 0, -46029208, 141871104, 0, 48361280, 192700002, 0, -242716060, 82266624, 0, -7621056, 174755784, 0, -217941732, 597009072, 0, -326511792, 48998418, 0, -645240176, 64360192, 0, -174524268, -134419272, 0, -309247030, -90071916, 0, 72900608, -341444169, 0, 149895936, 340198272, 0, -504147312, -783216675, 0, 144899073, 113446832, 0, 209988080, -653863044, 0, 386814464, 196161024, 0, 344392392, 33224760, 0, 601250976, -303368960, 0, 109471488, 353784138, 0, 243730828, 167905056, 0, 219674016, 26046339, 0, -536511330, 30942400, 0, -62629632, 227824596, 0, -548586466, 14004608, 0, -115877344, 628127016, 0, -132981034, -462673264, 0, 22267904, 509200860, 0, 125255492, -58552992, 0, -326909040, 372865548, 0, 525891583, 179324568, 0, -336861440, -183297648, 0, -279116676, 7929856, 0, -361956900, 185884959, 0, -717375640, -162401328, 0, -235642560, -24757428, 0, -4568718, 3936192, 0, 314214672, -124921824, 0, -244673302, 243146656, 0, 163603376, -88962090, 0, -356126328, -43447104, 0, 88743744, -457572924, 0, 600712272, 297181340, 0, -128424960, 296971510, 0, 54144158, 177757680, 0, 440739024, -426170076, 0, 57922190, -135207160, 0, 68325312, 505240155, 0, 600069748, -77670144, 0, 411238056, -789432960, 0, -616275872, 179614656, 0, -120658176, 79387398, 0, -331070121, -386692560, 0, -156399264, -264008664, 0, 451054714, 47500728, 0, 312069376, -702567789, 0, -128626051, -28692672, 0, -178543452, 376096761, 0, 76381734, -231554032, 0, -73006336, 184923738, 0, 117463540, -17304576, 0, 436881360, 77067726, 0, 465748524, -462456940, 0, 269194256, -484650771, 0, 70601544, -117628928, 0, 429256320, 189610146, 0, -729847384, 405321488, 0, -173840640, -425921064, 0, -1141904690, 210158784, 0, -114409856, -433189968, 0, -3058848, -147051360, 0, -80666944, -632856408, 0, 648174708, -199466176, 0, 130779696, 411526446, 0, 565495452, -188537080, 0, 29147136, 453536880, 0, -327594692, 49064048, 0, -73336944, -137069976, 0, -116153206, 619132192, 0, -100219936, 884767713, 0, 130721382, -193032960, 0, -473935296, -880540809, 0, -51420852, -590062948, 0, -326433024, 253775610, 0, -375178147, -58236096, 0, 318039816, 64194192, 0, -588197924, -125611420, 0, -71584416, -98748100, 0, -48522800, 89242496, 0, 240265872, -242511744, 0, -493809060, 251137872, 0, 22860288, 282491040, 0, -536011632, -210785472, 0, 536869788, 427294992, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "22.6.a.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [4], [0], [16], [51], [0], [-166], [64], [0], [204], [121], [0], [692], [-664], [0], [256], [738], [0], [1424], [816], [0], [484], [1779], [0], [-524], [2768], [0], [-2656], [2064], [0], [6245], [1024], [0], [2952], [-8466], [0], [-14785], [5696], [0], [3264], [-5304], [0], [17798], [1936], [0], [7116], [17184], [0], [10749], [-2096], [0], [11072], [30726], [0], [6171], [-10624], [0], [8256], [34989], [0], [-45940], [24980], [0], [4096], [35292], [0], [25343], [11808], [0], [-33864], [-13311], [0], [-53260], [-59140], [0], [22784], [-20086], [0], [77234], [13056], [0], [-21216], [-55014], [0], [37638], [71192], [0], [7744], [-125415], [0], [-114872], [28464], [0], [68736], [72624], [0], [-88807], [42996], [0], [-8384]]}