# Stored data for newform 150.6.a.e, downloaded from the LMFDB on 23 April 2024.
{"label": "150.6.a.e", "space_label": "150.6.a", "level": 150, "weight": 6, "hecke_orbit": 5, "hecke_orbit_code": 18014398610145430, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 504008679513086435, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[7, [1, 1]]], "qexp_display": "q-4q^{2}+9q^{3}+2^{4}q^{4}-6^{2}q^{6}-q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 5400, "fricke_eigenval": 1, "atkin_lehner_string": "+--", "analytic_conductor": 24.057572971947096, "hecke_ring_index": 1, "level_radical": 30, "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": 0, "analytic_rank_proved": true, "char_values": [150, 1, [101, 127], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 5], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.003", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.045", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.226", "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], [5, -1]], "trace_display": [-4, 9, 0, -1], "traces": [0, 1, -4, 9, 16, 0, -36, -1, -64, 81, 0, -210, 144, -667, 4, 0, 256, 114, -324, 581, 0, -9, 840, -4350, -576, 0, 2668, 729, -16, -126, 0, 7583, -1024, -1890, -456, 0, 1296, -3742, -2324, -6003, 0, -2856, 36, -18241, -3360, 0, 17400, -23370, 2304, -16806, 0, 1026, -10672, -21684, -2916, 0, 64, 5229, 504, -32310, 0, -7165, -30332, -81, 4096, 0, 7560, 59579, 1824, -39150, 0, -43080, -5184, -28942, 14968, 0, 9296, 210, 24012, 27608, 0, 6561, 11424, -1782, -144, 0, 72964, -1134, 13440, 50208, 0, 667, -69600, 68247, 93480, 0, -9216, 142793, 67224, -17010, 0, -164052, -4104, -107236, 42688, 0, 86736, 21012, 11664, 237545, 0, -33678, -256, 233388, -20916, 0, -2016, -54027, 129240, -114, 0, -116951, 28660, -25704, 121328, 0, 324, 138800, -16384, -164169, 0, -161340, -30240, -581, -238316, 0, -7296, 69054, 156600, 224396, 0, -210330, 172320, 140070, 20736, 0, 115768, -151254, -59872, -407646, 0, 216053, -37184, 9234, -840, 0, -96048, -188617, -110432, -195156, 0, 4350, -26244, -422251, -45696, 0, 7128, 41700, 576, 73596, 0, 47061, -291856, 266142, 4536, 0, -53760, -290790, -200832, -51846, 0, 499349, -2668, -64485, 278400, 0, -272988, -23940, -373920, -729, 0, 705906, 36864, -519973, -571172, 0, -268896, -200394, 68040, 553673, 0, 536211, 656208, 126, 16416, 0, 428944, -352350, -170752, -122010, 0, 777365, -346944, -387720, -84048, 0, -46656, -7583, -950180, -260478, 0, -76038, 134712, -776185, 1024, 0, -933552, 919992, 83664, -1132195, 0, 1890, 8064, 823128, 216108, 0, -516960, 248472, 456, 1328364, 0, 94937, 467804, 59049, -114640, 0, 102816, -387527, -485312, -16038, 0, -128124, -1296, 913500, -555200, 0, 65536, -1722852, 656676, 3742, 0, -10206, 645360, 692160, 120960, 0, 2324, 451872, 953264, 690894, 0, -1046896, 29184, 6003, -276216, 0, -626400, -1071367, -897584, 614223, 0, -1404162, 841320, 1682033, -689280, 0, -560280, 2856, -82944, -1406861, 0, 1285137, -463072, 1762926, 605016, 0, 239488, -153090, 1630584, 2901450, 0, 18241, -864212, -1476468, 148736, 0, -36936, 471905, 3360, -965124, 0, -1644390, 384192, 2379083, 754468, 0, 441728, 1326792, 780624, 26460, 0, 189108, -17400, 66234, 104976, 0, 1689004, 2137905, 182784, 23370, 0, 661172, -28512, -303102, -166800, 0, -2304, -1536751, -294384, 2100492, 0, -1592430, -188244, 33613, 1167424, 0, -1064568, 3865758, -18144, -4233910, 0, -486243, 215040, -2414586, 1163160, 0, 803328, -1026, 207384, 2948016, 0, -2138538, -1997396, -1052559, 10672, 0, 257940, 679793, -1113600, -231336, 0, 21684, 1091952, -3608881, 95760, 0, 1495680, 84042, 2916, -386809, 0, 1249200, -2823624, -645060, -147456, 0, 2079892, -1477521, 2284688, -812976, 0, -495900, 1075584, -1452060, 801576, 0, -272160, -988813, -2214692, -5229, 0, 2145804, -2144844, -5057861, -2624832, 0, -504, 785820, -65664, -5776579, 0, 621486, -1715776, 32310, 1409400, 0, 683008, 2019564, 488040, -5073180, 0, -3012970, -3109460, -1892970, 1387776, 0, 1550880, 7165, 336192, 1260630, 0, 5594490, 186624, 5634539, 30332, 0, 3800720, -2527350, 1041912, 860663, 0, -1361286, 304152, -2753352, -538848, 0, 3104740, -3668814, -4096, -2831676, 0, 599760, 3734208, 1944477, -3679968, 0, -334656, -4662346, 4528780, 83106, 0, -5271540, -7560, -7169536, -32256, 0, -3292512, 4304406, -864432, -59579, 0, -1697553, 2067840, 3830610, -993888, 0, -1824, -1756404, -5313456, 190506, 0, 2495914, -379748, 39150, -1871216, 0, -236196, -128887, 458560, -3800259, 0, -304296, -411264, -14364, 1550108, 0, 1941248, 43080, 64152, 6419741, 0, 375300, 512496, -1555344, 5184, 0, -3654000, 662364, 2220800, -541506, 0, 28942, -262144, 423549, 6891408, 0, -2626704, 4907700, -14968, 2395278, 0, -888762, 40824, 7699505, -2581440, 0, -2768640, 864462, -483840, 12486157, 0, -2617110, -9296, 1904952, -1807488, 0, -3813056, -466614, -2763576, 3529260, 0, -3018775, 4187584, 4494141, -116736, 0, -24012, 7234808, 1104864, -580365, 0, -73206, 2505600, -27608, 4285468, 0, 3590336, -9887118, -2456892, 12166747, 0, -215460, 5616648, 946362, -3365280, 0, -6728132, -6561, 2757120, -4515522, 0, 7578245, 2241120, 6353154, -11424, 0, 331776, 11168843, 5627444, -4679757, 0, 1782, -5140548, 4553640, 1852288, 0, -7051704, 1010532, -2420064, 4405723, 0, -1803546, -957952, 11367360, 612360, 0, -6522336, 4983057, -11605800, 2567316, 0, 15983723, -72964, 4825899, 3456848, 0, 5905872, -10162576, -594944, 1134, 0, 15587790, 147744, 5830418, -1887620, 0, -13440, -15102900, 3860496, -5385151, 0, -3171150, 6577560, -50208, -1536768, 0, -9516332, -1098090, -3017872, -426588, 0, -5593453, -1766912, 6996285, -5307168, 0, -3122496, 11209602, -105840, -3489480, 0, -10007220, -756432, -9950356, 69600, 0, -264936, -9169044, -419904, 6785100, 0, -68247, -6756016, -17712678, -8551620, 0, -731136, -2344302, -93480, -20794872, 0, -1517446, -2644688, -684342, 114048, 0, 1212408, 548100, 667200, -6985665, 0, 1504650, 9216, -2904826, 6147004, 0, 1177536, -7060494, -8401968, -142793, 0, 8279928, 6369720, 3814152, 752976, 0, -134452, -10189755, -4669696, 14463228, 0, -8951656, 4258272, 17010, -15463032, 0, 72576, -325584, 16935640, 7408152, 0, 8452974, 1944972, -2174102, -860160, 0, 9658344, 164052, -4652640, -11803267, 0, 2236248, -3213312, -32986050, 4104, 0, -829536, 11955276, -11792064, -26808870, 0, 107236, 8554152, 854433, 7989584, 0, 4210236, -2006377, -42688, 531441, 0, -2079474, -1031760, -9165538, -2719172, 0, 4454400, -12511590, 925344, 15589748, 0, -3487743, -86736, -3783036, -4367808, 0, 14435524, -144342, -383040, -21012, 0, 12472640, -5982720, -1153116, -336168, 0, -11664, 1871213, 1547236, 8221500, 0, 25363788, -4996800, -237545, 11294496, 0, 2580240, 21550770, 589824, -14372893, 0, -15505668, -8319568, -16418472, 5910084, 0, -9138752, 33678, 3251904, -1659336, 0, 9046800, 1983600, -91854, -4302336, 0, 5808240, -14631991, -3206304, 6229440, 0, -233388, 1088640, 4779055, 3955252, 0, 8858768, 26179620, 20916, -2664180, 0, 4066848, -8583216, 6077820, 8579376, 0, 20231444, 6218046, 10499328, 29905116, 0, -31287259, 2016, -9422064, -3143280, 0, 262656, -10598021, 23106316, 54027, 0, -32429082, -2485944, 19170035, 6863104, 0, -129240, -98052, -5637600, 5774258, 0, -9642303, -2732032, -1915884, -8078256, 0, -1952160, 5528007, 20292720, -16935426, 0, -20495273, 12051880, -12637458, 12437840, 0, 7571880, 116951, -5551104, 15138297, 0, 16277700, -6203520, 5043911, -28660, 0, -1344768, 12882948, -5042520, -35952184, 0, 25704, -22377960, 22034496, -746496, 0, -22538156, -12661749, -121328, -5797680, 0, -39739193, -15202880, 11566233, 10109400, 0, -4167648, 13453103, -3442652, 15866334, 0, 23633136, 5445144, 34958759, -1216608, 0, 11013408, 31116810, 2155392, -138800, 0, -1377810, -12418960, -13577970, 14675256, 0, 16384, 26113050, 11326704, -955458, 0, -2471976, -2399040, 164169, -14936832, 0, -7777908, -19731964, 14719872, -13288212, 0, -44071998, 1338624, 374220, 18649384, 0, -18115120, 161340, -332424, -43362091, 0, 4247145, 21086160, 28734360, 30240, 0, 28678144, -8686116, 129024, 16523454, 0, -9764286, 13170048, -14799510, -17217624, 0, 3457728, 20354639, 238316, 21411747, 0, -51240642, 6790212, 12423600, -8271360, 0, -15322440, 27973554, 3975552, 19304314, 0, 11941128, 7296, 26833704, 7025616, 0, 21253824, 238140, -762024, -69054, 0, 28872738, -9983656, 1701972, 1518992, 0, -156600, -52483096, 7484864, 596106, 0, 50102934, 944784, -224396, 515548, 0, -1834240, -45018078, 15201036, -10543680, 0, 19241145, 1217184, -32690676, 1645056, 0, 57456, 210330, -6200432, 79348350, 0, 6246059, -7764992, 5950548, -172320, 0, -256608, 28501034, -25678964, -2727918, 0, -140070, -1501200, -3683340, -2049984, 0, 6221376, -12598404, -20736, 3206237, 0, -13830759, 14616000, -43559286, -2649456, 0, -8883200, 18904428, 2166024, -30016722, 0, -37318081, -115768, -14331870, 1048576, 0, -1694196, -18414536, -27565632, 302517, 0, 54295434, 10506816, 1002005, -19630800, 0, 59872, -816810, -9581112, 14165441, 0, 34791822, 3555048, 407646, -163296, 0, -30798020, -38105190, 10325760, 29545728, 0, 22029293, 11074560, -4376187, -3457848, 0, 1935360, -216053, -49944628, -21731274, 0, 10705302, 10468440, -37086937, 37184, 0, -7619808, -29986530, 7229952, -37464001, 0, -9234, 15252224, 471492, 1866456, 0, 11054304, 26532144, -14117040, 1188594, 0, 101659500, 12075100, -19246842, -16750336, 0, -17976564, 16563227, 466944, -9473031, 0, -70380312, 96048, -58259515, -28939232, 0, -4419456, -73516326, 2321460, 188617, 0, 6118137, 292824, 74272590, -10022400, 0, 110432, -2082024, -17141872, -24574146, 0, 34450920, -14361344, 195156, 39548472, 0, 9827568, -3561667, -48666988, -32479929, 0, -18772110, 861840, -41979883, -22466592, 0, -3785448, 73106100, 13461120, 1345781, 0, 756378, 26912528, 22519560, 26244, 0, -11028480, -3481281, 18062088, 6792006, 0, 422251, -30312980, 11242800, -8964480, 0, -25412616, -28375586, 45696, -5805540, 0, 51942246, -1327104, 40623377, -44675372, 0, -22509776, -33488736, 18719028, -4162865, 0, -13297689, -7128, -28507872, 20562192, 0, -18214560, -7316784, -7409152, -41700, 0, 6760427, 28206816, -4463100, -4042128, 0, 9680256, -4412520, -17622892, -13068540, 0, -53307090, 7214184, -73596, 3831808, 0, -45469440, -18469434, -2449440, 359856, 0, -8899317, 26089344, 30198654, -19932228, 0, 46423200, -47061, -10269264, -49884450, 0, 87838550, -63934892, 19312236, 291856, 0, -19303596, -4911120, -13827392, -45520749, 0, -266142, -23623488, 42462086, 40650304, 0, 2379776, 25481610, -4536, 94325400, 0, 7072380, -62351160, 87970074, -590976, 0, -23321672, -51989211, 7550480, 11675328, 0, 32472428, 53760, 5593374, 60411600, 0, -15441984, 86980922, 21540604, 290790, 0, -3299388, 12684600, -49011480, -26310240, 0, 200832, 2298366, 6147072, 89428874, 0, 18176076, 38065328, 51846, 4392360, 0, 12071488, -45658620, 1706352, -27159900, 0, -95242931, 22373812, -27116730, 7067648, 0, -27985140, -499349, 21228672, -17036730, 0, -21657048, 12489984, 34615399, -44838408, 0, 423360, 2980770, 13957920, 25098305, 0, 64485, 40028880, 44391942, 3025728, 0, 39801424, 11345670, -278400, 109600140, 0, -88193413, 1059744, 50350410, 36676176, 0, 1679616, -17699533, -27140400, 50710851, 0, -49713438, 272988, -29039989, 27024064, 0, 70850712, 109321500, 34206480, 23940, 0, -22746150, 2924544, 109422684, 9377208, 0, 373920, 7745967, 83179488, -47701578, 0, 10388966, 6069784, -12251574, 10578752, 0, 2737368, 59280215, -456192, -24780168, 0, 58380420, -4849632, -138321503, -2192400, 0, -2668800, -705906, 27942660, 71526412, 0, -33019326, -6018600, 3147312, -36864, 0, 11619304, -25485084, -24588016, -25029480, 0, 519973, -4710144, 5397840, 28241976, 0, 33607872, 140548500, 571172, 17500293, 0, -85946646, -33119712, 2944620, -25478880, 0, -15256608, 55465416, -3011904, -55341393, 0, -41961114, 537808, -28187106, 40759020, 0, 18678784, 747954, -57852912, 200394, 0, -44856655, 35806624, -47443860, -17033088, 0, -68040, -16815302, 61852128, -64525824, 0, -14015004, -290304, -553673, 1302336, 0, -67742560, -29148000, -29632608, 111477965, 0, 38739654, -33811896, 31167750, -7779888, 0, 8696408, -536211, 3440640, -40674750, 0, -203148, -38633376, -15277977, -656208, 0, 18610560, -158442515, 47213068, 34475490, 0, 2117556, -8944992, -27923848, 12853248, 0, 131944200, 75246888, -16416, -105233233, 0, -15807636, 3318144, -106591446, -47821104, 0, 47168256, 1714554, 107235480, 115918830, 0, 33881400, -428944, 22463226, -34216608, 0, -3417732, -1071895, -31958336, 352350, 0, -67854282, -16840944, 22139633, 8025508, 0, 170752, -177214710, -2125764, -58843420, 0, -1159983, 8317896, 122010, 4127040, 0, 36662152, -34202331, 10876688, -155669796, 0, -126060331, -17817600, -2738664, 50046360, 0, -3701376, -777365, -62358992, -129276, 0, 124693878, 13950972, 24669428, 346944, 0, 15132144, 50719464, 17471232, -6536350, 0, 387720, -57742096, -54647916, 577368, 0, 1532160, 57777669, 84048, -44239842, 0, 16040248, -49890560, 3377700, 23930880, 0, 4612464, -14501340, 1344672, -13998096, 0, 122614932, 46656, 5723712, -7484852, 0, -6188944, 10687152, -32886000, -127439898, 0, 5961276, -101455152, -170943186, 19987200, 0, 950180, -4873554, -45177984, -47123160, 0, 152101595, -10320960, 260478, -86203080, 0, -2359296, 2732184, 57491572, 3811941, 0, -259168650, 62022672, -80706823, 33278272, 0, 65673888, 76038, -23640336, -159821557, 0, 44169300, 36555008, 74477094, -134712, 0, -13007616, 21557502, 6637344, 37506402, 0, 776185, -36187200, -7998858, -7934400, 0, 367416, 24250037, 17209344, 69295545, 0, 54578334, -23232960, 78006317, 58527964, 0, 12825216, -1035342, -24917760, 48525107, 0, 7780158, 933552, -80719206, -4354560, 0, -19116220, 112375413, -15821008, -919992, 0, 68257822, -35435072, -23553990, -104718480, 0, -83664, -182274058, 10656720, 17144568, 0, 178493346, -16267392, 1132195, 34332864, 0, -24311280, -32316732, -34317504, -127419619, 0, -4199526, -80925776, -162829446, -24872184, 0, -41997312, 31763340, -119620464, 52487052, 0, -17479039, 125149036, -27168975, -8064, 0, 37688256, 108813308, 12573120, 40447269, 0, -823128, -1050624, 187398000, 42392084, 0, -92425264, 30420588, -216108, 85605660, 0, 65113272, 129716328, -164429772, 9943776, 0, -76680140, -5223285, -27452416, 16278402, 0, -92579600, 516960, -658854, 392208, 0, 22550400, 33180158, -23097032, -248472, 0, -45371130, 38569212, 59179715, 10928128, 0, 7663536, -24605478, 32313024, -1987498, 0, -88984062, 7808640, -1328364, -22112028, 0, -81170880, 109500723, 67741704, 125897700, 0, -107699465, 81981092, -1939140, -48207520, 0, 50549832, -94937, -49751360, 8517258, 0, 29170848, -30287520, -36545881, -467804, 0, 22204416, -201768582, -60553188, 56987384, 0, -59049, -65110800, 107613780, 24814080, 0, -20175644, -40639698, 114640, 187264290, 0, 4071060, 5379072, 68204205, -51531792, 0, 20170080, -18701928, 143808736, 57178386, 0, 155190312, -102816, 174721076, 89511840, 0, -88137984, 39609570, 2985984, 387527, 0, 100519587, 90152624, 103789026, 50646996, 0, 485312, -42117813, 23190720, 87450540, 0, -121450129, 158956772, 16038, 60811520, 0, -46264932, -110056120, -40437600, 40982760, 0, -12224904, 16670592, 120459866, -53812412, 0, 13770608, 128124, -63465336, -154816885, 0, 9094788, -94532544, 52096296, -21780576, 0, -139835036, 39651507, 4866432, 902790, 0, -913500, -44053632, -16231914, -124467240, 0, -8621568, 76932329, 555200, 102306240, 0, -46059018, 5511240, 27380507, 49675840, 0, 54311880, 70153266, -58701024, -28717657, 0, 44847513, -65536, 88672710, -104452200, 0, -45306816, 23105844, 3821832, 1722852, 0, 104810183, 9887904, 143853507, 9596160, 0, -656676, -149672132, 59747328, 43433091, 0, 215098560, 31111632, 62888052, 78927856, 0, -58879488, -120094800, 53152848, 2395368, 0, -91463184, 176287992, -74081232, -5354496, 0, -1496880, 10206, -74597536, -245006730, 0, -102585520, 72460480, 140290110, -645360, 0, 1329696, -8757000, 173448364, 52473762, 0, -692160, -16988580, 82962733, -84344640, 0, -114937440, 89974782, -120960, 185725638, 0, -135926100, -114712576, 27080130, 34744464, 0, -516096, -48466359, -66093816, -15455160, 0, 921155, 39057144, -28540350, -52680192, 0, 59198040, -48683071, 68870496, -451872, 0, 69411654, -13830912, 211495601, -81418556, 0, -953264, -3798192, -85646988, 104013248, 0, -9882810, 204962568, -690894, -27160848, 0, -49694400, -3839292, 33085440, -101979984, 0, -54332195, 61289760, -50341077, -111894216, 0, -15902208, 1046896, -77217256, 62966565, 0, -225855750, -47764512, -55889820, -29184, 0, -107334816, -131171460, -28102464, 7751700, 0, 100886418, -85015296, -71234484, -952560, 0, 3048096, -31405320, 276216, -95314212, 0, 26606232, -115490952, -90064980, 39934624, 0, -6807888, 66744720, -6075968, -89553204, 0, 69360120, 626400, -71334781, 209932384, 0, -29939456, 271899882, -2384424, 1071367, 0, -82521396, -200411736, -7506954, -3779136, 0, 897584, 61065900, -2062192, 79245408, 0, 135100151, 7336960, -614223, 180072312, 0, -60804144, -62304116, 42174720, -159414102, 0, 81141528, -76964580, -144107351, -4868736, 0, 130762704, 1404162, -6580224, 10887660, 0, -21098718, -229824, -88877832, -841320, 0, 24801728, -187153848, -317393400, -263645490, 0, -1682033, -24984236, -13657014, 31059968, 0, -23802192, 233414348, 689280, -6159078, 0, -104863290, 1026432, -194966650, -114004136, 0, 102715856, 228073428, 10911672, 61257635, 0, 4932900, 560280, -185868042, 6004800, 0, 14733360, -62870985, 8199936, 47997936, 0, 40256828, -24885504, 13541850, 50393616, 0, 82944, -119333179, -12824948, -26143434, 0, 426292170, 55323036, 1406861, -58464000, 0, 174237144, -195410508, 10597824, 135310529, 0, -63544446, 35532800, 12207972, -75617712, 0, -8664096, -1285137, 120066888, -54969132, 0, 125807539, 149272324, 74519352, 463072, 0, 57327480, -218404800, -4194304, 34327368, 0, -1762926, 6776784, -220435594, 73658144, 0, 110262528, -13332414, -1210068, 5428080, 0, -91707795, -217181736, -96417282, -42027264, 0, -4008020, 130169052, 78523200, -59241684, 0, 138013645, -239488, -80564904, 3267240, 0, 38324448, 451787557, -56661764, 153090, 0, 88686396, -139167288, -342955357, -14220192, 0, -1630584, -239471358, 653184, 2357081, 0, -2930256, 123192080, -2901450, 152420760, 0, -41303040, 66673368, -118182912, -367065282, 0, -148240260, -88117172, 76076766, -44298240, 0, 17504748, 306558246, 13831392, -19566918, 0, -266803596, -7741440, -147364495, 864212, 0, 199778512, 3646692, 86925096, 281641417, 0, 1476468, -42821208, 109194330, -41873760, 0, 148347748, -106229403, -148736, 149640750, 0, 132914624, 30479232, 20126232, 119946120, 0, -28919808, -240252157, 149856004, -296874450, 0, 14994516, 36936, -102803041, -61008896, 0, -1885968, 135598428, -7465824, -471905, 0, 107597484, -44217216, 88936866, -106128576, 0, 56468160, -241279830, -4754376, 15823200, 0, 7323482, -406638000, 965124, -48300400, 0, 76987368, 42082740, 67001344, 7689897, 0, -27813900, 71906256, 61929504, -66252908, 0, -1867776, 1644390, 37892124, -182880235, 0, -18057393, 281521248, 120904020, -384192, 0, 233038060, 4782969, 115756928, -116271330, 0, -2379083, 17677824, -18715266, 294065304, 0, -9285840, 198563899, -754468, -82489842, 0, -326675640, -24472548, 195497741, -1171296, 0, -297090360, -405334218, 40089600, 316811893, 0, -112604310, -441728, -422916984, 8328096, 0, 68567488, 140307732, 98296584, -1326792, 0, -159402703, -137803680, -31389687, 57445376, 0, -780624, -18392760, -158193888, -34047324, 0, -621149550, -39310272, -26460, 14246668, 0, 194667952, 261366774, 129919716, -386276413, 0, -1299078, 75088440, 158124450, -3447360, 0, 167919532, -189108, 89866368, -177516714, 0, -471828187, 15141792, 112253760, -292424400, 0, -53844480, 26811430, -5383124, -10378044, 0, -66234, -3025512, -219467186, -107650112, 0, -90078240, -114453156, -104976, 267803051, 0, 16840917, 44113920, 42050532, 13925124, 0, -72248352, 73993500, -27168024, 395537844, 0, 120002189, -1689004, 228274092, 121251920, 0, -44971200, 126908120, 35857920, -2137905, 0, -3478608, 101650464, -444250549, 113502344, 0, -182784, -135215928, 23222160, -67948531, 0, 193956930, -207768984, 392756220, 5308416, 0, -162493508, -129356037, 178701488, -61998918, 0, -13895695, 90039104, -139551012, 133954944, 0, -74876112, -661172, 16651460, -147766248, 0, -163246650, 53190756, 713626200, 28512, 0, 114031488, 34581282, -82248768, 7872156, 0, 303102, 72858240, 416227182, 29267136, 0, 29636608, -14934024, 166800, 407256594, 0, 110027393, -27041708, 81421200, -112827264, 0, 17852400, 232136669, 16168512, -826686, 0, -167393532, -38721024, -333065783, 17650080, 0, 70491568, 24378588, 52274160, 1536751, 0, -131687919, 213228360, 25581144, -28856736, 0, 294384, 56064960, -15327232, 466476600, 0, 30908405, 181877760, -2100492, 73877736, 0, 9797760, 215875370, -1439424, 43011495, 0, -105489378, 35597268, 312359213, -104357376, 0, -120794616, 1592430, 79728912, -33072841, 0, 235616580, -185692800, 170143206, 188244, 0, 41077056, -23977620, 199537800, -105614088, 0, 282424829, -351354200, 36601632, 255739568, 0, -77248944, 224532, -1167424, 54700380, 0, -23465538, 77214384, 80642800, 19644480, 0, 55309568, 387534186, 182082996, 92277360, 0, 55962414, 1064568, 107184858, 94493952, 0, -169848344, 269146044, -162601216, -3865758, 0, 15967980, -9519104, -281585331, -101926440, 0, 18144, -63974305, -377301600, -84798576, 0, 559715622, -28289520, 4233910, 249404640, 0, -351880296, 392516910, 2363904, 209351464, 0, -95382189, 93286688, 162998850, 207956844, 0, -30201920, 486243, -46701312, 92340960, 0, -91402200, -129889712, -291861738, -215040, 0, -22373496, -439485532, -241646400, 172530315, 0, 2414586, 61767936, 347779187, -347923688, 0, -86162416, 2207160, -1163160, -222944618, 0, -882468, 13197552, -470839302, -50738400, 0, 196045920, 51968322, 105240960, -93738540, 0, 506755080, -803328, -86780727, -9193464, 0, -24588288, -193198320, -357715496, -17242956, 0, 20463240, -72704304, 59526812, -152261312, 0, -207384, -1033320750, -17569440, 346821991, 0, 49752063, -48285952, -2948016, 182634480, 0, -6825408, -152418834, 108639600, 237760950, 0, -136553929, 380971724, -184457457, -89495248, 0, 108466920, 2138538, -28270592, -113737122, 0, 16870116, 111940560, -46471644, 1997396, 0, -84914688, 589366710, 68146920, -491353141, 0, 1052559, 86628192, 289591278, -49959936, 0, -138461596, 136244673, 179353632, 208308732, 0, -17274160, -1693440, 146499300, -11923080, 0, -55831680, -324133483, -100393220, 45395199, 0, 133662798, -257940, -172856880, -160115520, 0, -177567768, 24630042, -12102912, -679793, 0, 115946532, -159205696, -13512906, -45382680, 0, 1113600, -323569656, -438400560, 58810464, 0, -6326208, 352773652, 231336, -4238976, 0, -201401640, -369299891, -146704704, 198310464, 0, -182464482, -6718464, -301580449, 70798132, 0, 108561600, 364421304, -202843404, -1015237800, 0, -113955741, 198853752, 40120374, -1091952, 0, 116159956, -52179120, -108096256, -197607228, 0, 3608881, -283402848, -357652737, -437286000, 0, -136825920, -202654891, -95760, 104096097, 0, 647339118, 90984600, 130696765, -11698176, 0, -437690736, 161205360, -37508832, -278956440, 0, 121077927, -1495680, -192649626, -30983868, 0, -332717952, 142797006, 190806312, -84042, 0, 130374076, -41555864, 212698224, -24279136, 0, 49006296, -263074912, -42315008, 314628831, 0, -19936770, -10949472, 386809, -237120860, 0, 1824768, 134975112, 99120672, -67681612, 0, 280051290, -233521680, -213000522, 19398528, 0, 553286012, -1249200, 8769600, -21502338, 0, 84721943, 10675200, -12400290, 2823624, 0, -111770640, -727012666, -286105648, -122201730, 0, 645060, 132077304, 430517468, 24074400, 0, -12589248, -279825546, 147456, -565794403, 0, 235017450, -46477216, 163825056, 101940336, 0, 98352064, -8599122, 100117920, -420705828, 0, 108300964, -2079892, -22247784, 18840576, 0, -21591360, 479697827, -112967904, 1477521, 0, 150918774, -134431488, -710531863, -562194000, 0, -2284688, 81380670, -70001172, 444214127, 0, -177587676, 343786584, 812976, 132478848, 0, -11778480, -119593908, 101915520, -46422348, 0, -530117005, 61026432, -396647982, -221861664, 0, 12047616, 495900, 221365572, 3367980, 0, 4114236, 167844456, -518502455, -2151232, 0, 112748424, -170157624, -163036080, -325490806, 0, 1452060, -74715136, 118570500, -2991816, 0, 231411648, -390258819, -801576, 380727264, 0, 26906040, 179426620, 38224305, -143226496, 0, 189775440, -675158287, 68132352, 258609240, 0, -48136614, 272160, 755084700, 67261208, 0, -247408512, 182180316, 258103296, 988813, 0, -78175044, 56060016, 508736850, 1161216, 0, 2214692, 148711086, -5209344, 355360860, 0, 395323904, 270970240, -87878574, 116592000, 0, 118530432, -250447339, -445911860, -133195590, 0, 474323784, -154958616, -46700731, 135247584, 0, -124671000, -2145804, 31119552, 52000363, 0, 183191751, -34785632, -17991918, 2144844, 0, -13762560, 192705723, 162699000, 136747092, 0, 5057861, 812592, -461165778, 154533504, 0, 61111908, 361798920, 2624832, 111812400, 0, -236842326, -74442240, 754455503, 633770060, 0, -188852272, -53200596, -137901960, 4753800, 0, 251761986, -8470224, -550764810, 35779968, 0, 111695392, 173738826, -51412992, -785820, 0, -158304091, -527776800, 107470152, -300987552, 0, 65664, 31700693, 420932932, 241503336, 0, -106379556, 63230544, 5776579, -13272576, 0, 426365784, 167446050, 191284416, 125526793, 0, 2143260, -188673024, 8389944, -6858216, 0, -428941920, -621486, -463675320, -31188786, 0, -1086780539, -135525600, 259854642, 1715776, 0, -89852904, 370649033, 136866432, 15317748, 0, 543001860, 13670928, -145353600, 4287580, 0, 127833344, 571288152, -1409400, 517715395, 0, -472347864, 271417128, 96142524, 67363776, 0, -88558532, 5364954, -32102032, 666209592, 0, 123036480, -683008, 450926406, 708858840, 0, 8503056, 388945979, 235373680, -2019564, 0, -603780000, 4639932, -103309136, -33271584, 0, -488040, -401726022, -16508160, 20670552, 0, -405162702, -146648608, 5073180, 136809324, 0, -43506752, -94893120, 622679184, -446292282, 0, 30340188, 504241324, 173170305, 71270400, 0, 10954656, 3012970, -200185440, -294216084, 0, -613634664, 14805504, -165261922, 3109460, 0, 249435968, 144048768, 517104, -145087740, 0, 1892970, -498775512, -374187216, -55803888, 0, -98677712, 714135150, -1387776, -249226836, 0, 249667235, -60528576, 56214531, -202877856, 0, -69884928, 755174065, 26145400, 53554932, 0, 219848160, -1550880, -109586477, 230968384, 0, 218591664, 13511736, -2309472, 120414990, 0, 256509306, -6128640, 82658352, -231110676, 0, -336192, -24551262, 176959368, 936069366, 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": "150.6.a.e", "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], [9], [16], [0], [-36], [-1], [-64], [81], [0], [-210], [144], [-667], [4], [0], [256], [114], [-324], [581], [0], [-9], [840], [-4350], [-576], [0], [2668], [729], [-16], [-126], [0], [7583], [-1024], [-1890], [-456], [0], [1296], [-3742], [-2324], [-6003], [0], [-2856], [36], [-18241], [-3360], [0], [17400], [-23370], [2304], [-16806], [0], [1026], [-10672], [-21684], [-2916], [0], [64], [5229], [504], [-32310], [0], [-7165], [-30332], [-81], [4096], [0], [7560], [59579], [1824], [-39150], [0], [-43080], [-5184], [-28942], [14968], [0], [9296], [210], [24012], [27608], [0], [6561], [11424], [-1782], [-144], [0], [72964], [-1134], [13440], [50208], [0], [667], [-69600], [68247], [93480], [0], [-9216], [142793], [67224], [-17010], [0]]}