# Stored data for newform 261.6.a.a, downloaded from the LMFDB on 18 April 2024.
{"label": "261.6.a.a", "space_label": "261.6.a", "level": 261, "weight": 6, "hecke_orbit": 1, "hecke_orbit_code": 100663557, "dim": 4, "is_polredabs": true, "nf_label": "4.4.3257317.1", "trace_hash": 99736073224850759, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [196, -168, -69, 0, 1]]], "qexp_display": "q+\\beta _{2}q^{2}+(2-3\\beta _{1}+5\\beta _{2}-\\beta _{3})q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 9396, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 41.86017697118795, "hecke_ring_index": 4, "level_radical": 87, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [261, 1, [146, 118], [1, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 1, "level_primes": [3, 29], "conrey_indexes": [1], "field_disc": 3257317, "field_disc_factorization": [[7, 1], [465331, 1]], "field_poly": [10, -27, -34, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.718", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "39.650", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "652.917", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [29, -1]], "trace_display": [0, 0, 68, -208], "traces": [0, 4, 0, 0, 10, 68, 0, -208, 504, 0, -788, 124, 0, -460, -768, 0, -414, -184, 0, -2392, -2822, 0, 5538, 1192, 0, 1824, -4724, 0, 44, 3364, 0, -19212, -6552, 0, -7612, 22944, 0, -10928, 456, 0, -20, 1120, 0, -21420, 1932, 0, -7588, -23772, 0, 10452, -43240, 0, -29062, -8860, 0, -52652, -34304, 0, 0, 10840, 0, 49448, -18518, 0, -20734, -97836, 0, -7840, -20724, 0, -77496, 48744, 0, -74992, 35920, 0, -140792, -128656, 0, -106076, -58638, 0, -234132, -62888, 0, 23848, 216014, 0, -39426, -107568, 0, -268896, 26268, 0, 30542, -147352, 0, -49520, -242304, 0, 11840, -112912, 0, 9352, 19612, 0, 194012, -24336, 0, 197772, 228234, 0, -122724, -305928, 0, -289336, 8410, 0, 169340, 22448, 0, -188888, 275236, 0, -389816, 489708, 0, -140488, -598920, 0, 687288, 539608, 0, -379760, 378744, 0, 28636, -72832, 0, -879592, 184940, 0, 316252, 216476, 0, 57188, -118768, 0, 533024, 419020, 0, -660912, -743528, 0, 286156, 264636, 0, 368912, -844378, 0, 601852, -839856, 0, 122236, -1304384, 0, -52036, 515080, 0, 378080, 62476, 0, 729556, -520312, 0, 1520032, 873756, 0, 987028, 1161496, 0, 1051860, 1889096, 0, 712292, -928592, 0, -331992, -963696, 0, 2250200, 950200, 0, 2423344, 1337812, 0, -438238, 1370648, 0, -1742384, 495784, 0, -2072624, -174928, 0, 114176, 297012, 0, 7602, 1442896, 0, -2548228, 2036674, 0, 2156864, -3241284, 0, 1880528, 1286036, 0, -1128824, 462456, 0, 1165976, 1604320, 0, -2615432, -630296, 0, -476416, 702404, 0, 423864, -2607756, 0, 645756, 2522436, 0, 477336, -1286856, 0, -652028, -965880, 0, 3744876, -1104428, 0, 2451912, -3990218, 0, -1043588, -2445620, 0, 263880, -1902768, 0, -1169854, 2004988, 0, -278624, 1794418, 0, 2507392, -1277460, 0, -1339228, 3870064, 0, 4392176, 784216, 0, -1411876, -712644, 0, 474072, -4323856, 0, -3025512, 5570668, 0, 4548696, 2680612, 0, -103464, 3260112, 0, -3700950, -2723440, 0, -5194628, -662708, 0, -2539496, -2115592, 0, -3059624, 852944, 0, -1048348, 4620984, 0, -4324880, -1022920, 0, 3964104, 1632680, 0, -4993196, -880680, 0, 4671002, -3695656, 0, -7901372, -2396020, 0, -3251856, -2863032, 0, 104284, 2769458, 0, 3553832, -189744, 0, -5431840, -8687114, 0, -265980, 2472928, 0, 224220, -3774436, 0, -3146676, -3281856, 0, -1350632, -5211944, 0, 1688580, -262940, 0, -1832864, -1225646, 0, 2723224, -1508776, 0, 694380, -6013168, 0, -1666866, 4271032, 0, -3272200, 4044720, 0, 490620, -8702532, 0, 1678292, 1445092, 0, 4755820, 4638800, 0, 6610872, -2026932, 0, -156080, 1488032, 0, 835252, -540700, 0, -8303598, -386860, 0, -4969256, 1000376, 0, -238008, -1356576, 0, -6139888, -1900396, 0, 295832, 3043712, 0, 1194016, 5829976, 0, -2889808, -3204644, 0, -5831420, 6929976, 0, -7649664, 1452468, 0, -2179036, -1071264, 0, -645888, -1200496, 0, -4463560, 10363468, 0, -948616, -4143600, 0, 471576, -4260884, 0, -12061304, 4261096, 0, 3350328, -1068906, 0, 4233292, 2079616, 0, 6459696, 11966132, 0, 9841382, -9894328, 0, -1981856, 3136444, 0, 6562894, 506576, 0, 3396328, -12374570, 0, 1808716, 1885032, 0, 1148592, 6910444, 0, 3015004, -1690728, 0, -1897568, -11868700, 0, -4729124, -2840592, 0, 5707848, -10951988, 0, 3123236, -2583336, 0, 10399000, -348174, 0, 18162120, 6066444, 0, 956512, 9801102, 0, 11034948, 12635020, 0, -17356032, 3118792, 0, -2905228, -9890396, 0, 4872240, 15750784, 0, 112004, -19118576, 0, 9300832, 14143452, 0, 5532348, 8679684, 0, -154744, -6567272, 0, 8105640, -6796288, 0, -583800, 14380238, 0, 9223166, 4720676, 0, 6172592, -3233628, 0, -2792304, 19127460, 0, 14734784, 11783688, 0, 4190216, 11161656, 0, 6075420, -36896, 0, -13398224, -15867324, 0, -18632320, 7348760, 0, 17550998, 63592, 0, -9597084, -12342280, 0, 9442096, 27322256, 0, 549504, 11854216, 0, -3165116, -5698900, 0, 3195088, 9238518, 0, 690460, -14769860, 0, -2596384, -11158112, 0, 17257328, -2011672, 0, -5620032, 1278512, 0, 28336396, -28289016, 0, 17408948, -18838692, 0, -6710216, 23069620, 0, -1931976, -13457788, 0, 16154308, -10405384, 0, -13694496, -3020040, 0, 33137928, -10645248, 0, 12482280, 1405424, 0, -2373302, 882288, 0, -4223300, -22276592, 0, -2322416, 22451448, 0, 22888032, -12589164, 0, -7963680, 30814964, 0, 4557424, 889494, 0, -19054076, 15365052, 0, -9523120, 13579860, 0, -299652, 17632248, 0, 6080860, 6945304, 0, -46644948, -9122316, 0, 26783948, -35611690, 0, -20503356, 8586176, 0, -36041092, 11560052, 0, -1269688, 23464208, 0, 4048444, -9357680, 0, -43377592, 991360, 0, -15937560, -6178950, 0, 25633948, 39568856, 0, 40866692, 4657458, 0, -12885236, 11215176, 0, -32316288, 6804456, 0, 10325664, -36170440, 0, -3149112, 40656216, 0, -42080028, 3590944, 0, 25768184, -4156128, 0, 4662484, -13458964, 0, 27577336, -2290106, 0, -22840668, -40971952, 0, 1002472, 7767688, 0, -26570280, -17177064, 0, 39084180, -11758708, 0, -11928592, -13540744, 0, -39880592, 7109492, 0, -31114332, 18870544, 0, 10966880, 47769856, 0, 17363460, -12242076, 0, -16248832, -22744636, 0, -36782508, -55799368, 0, 13619216, -4484300, 0, 1317824, 7354972, 0, -14144320, -35548404, 0, 3283064, 19405344, 0, 11196756, -21735428, 0, -20003844, -30288088, 0, 32290948, 16718184, 0, -32966606, -45438904, 0, 26988608, -17977792, 0, 3133522, 1533984, 0, 12951624, -53570312, 0, 13570016, -7897288, 0, 21878784, -28601104, 0, -24374812, -9121648, 0, -31097740, 8229696, 0, -28229464, -17282840, 0, -17574100, -53986148, 0, -5091988, 30522448, 0, -15103224, 32006640, 0, -3972884, 3476224, 0, 11480168, 42218352, 0, -38019480, 36138056, 0, -42831776, -37956808, 0, -49385264, 13133000, 0, -19323432, 49321980, 0, -10910600, -18344720, 0, -615792, -14378308, 0, 16013776, 43714784, 0, 3029736, -4562848, 0, -29250918, -21443888, 0, -5070360, -19379844, 0, 48769638, -2194144, 0, -62136008, -8708532, 0, -10296636, 59729048, 0, -6347608, 21459688, 0, -68825312, -4685264, 0, 18499664, 51662970, 0, 18050160, 12564000, 0, 26677152, 37004, 0, -3319520, 31662212, 0, 35031344, -48043032, 0, 45407368, 25372604, 0, 1629208, -19949556, 0, -12901528, -27268300, 0, -7109416, 41930084, 0, 46083442, 19277096, 0, 26198904, -31684712, 0, 26928380, 2833060, 0, 2829124, -4906868, 0, 45772, -17438688, 0, 61661216, -22077222, 0, -1034672, 25825984, 0, 53761992, -92902568, 0, -1215808, 55908332, 0, 35782764, -14580872, 0, -24945172, -27553592, 0, -55583800, -12777280, 0, 14399648, -20698932, 0, -15989472, 40318356, 0, -27017472, -2233216, 0, 2236476, -5957124, 0, 70717032, -19601336, 0, -20272816, 2857444, 0, 84115656, 10772428, 0, 105574000, -24971244, 0, 23133872, 64168192, 0, 8925288, -2635584, 0, -95248928, -16157292, 0, -5514568, -55447752, 0, -31307176, 23473572, 0, -45705864, -86699376, 0, 8771216, -58157596, 0, 22853048, 92313896, 0, -54794088, 32062096, 0, 12892888, -33818980, 0, -29015392, 3382184, 0, -8790848, 72794356, 0, -5510232, 46300184, 0, 65672, 116178082, 0, -57916622, -13216344, 0, 29211704, -53267376, 0, -5302028, 33889204, 0, 53594608, -40046892, 0, -53578984, -57424212, 0, -47401776, 123471776, 0, 879272, 27910372, 0, 15543704, 73258028, 0, 73402346, 17710048, 0, 41020776, -21311024, 0, 117122922, 127009296, 0, 372700, -22022856, 0, 90706372, -2031016, 0, 8967984, 22687016, 0, -56652132, 53926908, 0, 6002688, 56715474, 0, -95451898, 16865924, 0, 134331288, -6401692, 0, 51438968, 48064280, 0, -118498712, 83316262, 0, -28703320, -28200864, 0, 76014464, -137168972, 0, 134819020, 45634912, 0, 824288, 78156628, 0, 90621034, -80210264, 0, 61687444, -20888496, 0, 20195044, -95899872, 0, 19295904, -29464848, 0, 116911252, -79248656, 0, -8106452, -12044704, 0, -12402046, -24384960, 0, 125001524, -9109162, 0, -33459964, -26363080, 0, -10918600, -56895692, 0, -30014400, -12876896, 0, -61836328, 70537194, 0, 1748584, -88562976, 0, 172799840, 32770056, 0, 22739488, 110002136, 0, 84266112, 112637280, 0, 54684588, -65341404, 0, 71593744, -48786864, 0, -16591206, 28720168, 0, 47685604, -53039088, 0, -11495348, 121343840, 0, -78244008, -99916616, 0, -54677520, -9190448, 0, -160100720, -84134084, 0, -28594790, 11720648, 0, -80316888, 95525696, 0, 64385048, -149266256, 0, 34232436, 50894940, 0, -15543464, -71789356, 0, 19742120, 34753000, 0, -75241496, 62520076, 0, -173239984, -16677128, 0, 383496, -44786384, 0, -32644968, 133943396, 0, -129397156, 3835388, 0, -136305696, -64824812, 0, 1546160, -962584, 0, 128600136, -141984058, 0, -44209800, -97840336, 0, -68798120, 15364378, 0, -13302910, 133340808, 0, -13178456, 134692528, 0, -36291580, -4948888, 0, -101742248, -36647472, 0, 75362176, -8316160, 0, -27764000, -81233528, 0, 62140150, 166984224, 0, -35389776, 148320416, 0, 56573712, 145411712, 0, 37917428, -19466876, 0, -5393562, -142363104, 0, -227972720, -16820, 0, 54479976, 88389964, 0, -136742700, 60575282, 0, 51313080, 20186144, 0, -76301628, -153547420, 0, 133821924, -40460752, 0, 12054608, 73422168, 0, -8061172, -90694960, 0, -117990624, -51852592, 0, -2283832, -56619176, 0, 941920, -47456184, 0, 98877044, 12190984, 0, 84415640, -81822908, 0, -18423902, 75645100, 0, 75768000, -52801668, 0, -62015256, -12770044, 0, -8624656, -71094808, 0, -60697600, -122108736, 0, -176396872, -29996554, 0, -19325560, -198270612, 0, 19277240, -75855644, 0, 69493870, -52037888, 0, -18951648, 114317420, 0, -82911052, -17604784, 0, -129348760, 76484184, 0, -1157256, 107673640, 0, 270551552, 6967006, 0, 43999046, -6299104, 0, -68199784, -135600008, 0, -141339784, -18014220, 0, 44068416, -107993080, 0, -3054454, -63137344, 0, -163138188, -52684764, 0, -8022944, -1886152, 0, 129788544, 198354916, 0, -50236656, 2272616, 0, -35324800, 77267900, 0, -132866544, 15243600, 0, -176941376, -86159908, 0, 1624812, -12393508, 0, -191768524, 149615890, 0, -65017060, -116783336, 0, 3586892, -131347488, 0, -177613160, 28691636, 0, 40034252, 48192000, 0, -137144596, -3898016, 0, 149878624, 68675884, 0, 37607888, 105284856, 0, -82840436, -1295542, 0, -17566308, -87039252, 0, -11059664, -210113040, 0, 13296228, 95984752, 0, -99078204, 22076528, 0, -87496570, 59600248, 0, 27790244, 137504320, 0, -91008652, 39151520, 0, -75474816, 95431692, 0, 143792464, -143705220, 0, -14722340, -6381508, 0, 139457684, -120799312, 0, -171828856, -30557440, 0, 255688388, 63344744, 0, 32884472, 105473896, 0, 17462292, -126657664, 0, 60127344, 129459784, 0, 118046568, -285174508, 0, 126727872, 144521464, 0, -35954220, -131516800, 0, -19992252, -117695182, 0, -18117288, 178634336, 0, -121365076, 79554776, 0, 127590472, 50958728, 0, -164345812, -114687998, 0, -26229352, 166879328, 0, 209844488, 135419488, 0, -161783944, 126301848, 0, 101003872, -98482208, 0, 81447092, -274965632, 0, 103870448, 58847912, 0, 122629798, -207257040, 0, -118187168, 264245296, 0, 198809780, -39153984, 0, 60268964, -104740544, 0, -3205650, -206594232, 0, -8296608, 152826764, 0, 57409888, 12907608, 0, 71810652, -51153604, 0, -60602536, 8790132, 0, -150865772, 60485712, 0, 61228220, -52442448, 0, 94109224, -154785446, 0, 202123396, -52912304, 0, 42329328, -106773176, 0, 9343692, -292267416, 0, 59205536, -135502408, 0, 65384994, -98994628, 0, -87554020, 98610964, 0, -36364840, -123760768, 0, 45319040, 230671144, 0, 198641244, 304038540, 0, -254016192, 25948728, 0, -7201220, 211275328, 0, -110984904, 196261544, 0, -73950176, 291900856, 0, 258728, 114964908, 0, 134018656, -11814080, 0, 83826496, -184149062, 0, -44365424, 25690976, 0, -7829848, -158170788, 0, -73738376, 26330712, 0, -100115672, 8388248, 0, -8090878, 259698336, 0, -25361512, -39951844, 0, -324415744, 8440624, 0, 134378624, 258062208, 0, 172725282, -256561712, 0, 87777712, -24441142, 0, 48620192, 279408492, 0, -63061616, -288921772, 0, 242214376, -79589408, 0, -215337852, 356328120, 0, -74579112, 59593300, 0, 263776448, 7926072, 0, -35996168, 131203240, 0, 97060488, -332292988, 0, -161852588, 61208220, 0, -7451260, 210164268, 0, 37912864, 82459008, 0, 62577512, 191561372, 0, 375368764, -120123568, 0, 89344336, 199398272, 0, 218547672, 198067352, 0, 154248760, 234411760, 0, 208538640, 192208152, 0, -59670624, 132285912, 0, -43040288, 39182996, 0, -161583720, -143329016, 0, 459620444, -454698136, 0, -176733160, 118576572, 0, 31131488, 242744080, 0, -53399240, 267459236, 0, 348869712, 39391820, 0, -139906040, 53655404, 0, -65859750, -360732608, 0, 211277168, -390252248, 0, -126474116, -44280332, 0, 45837288, 90972788, 0, 228953536, 94276596, 0, 351805488, -272121262, 0, -98189032, 174644100, 0, -171282352, -22713704, 0, 346197412, 398487344, 0, -123224784, -315211872, 0, 359456248, -213847552, 0, 17798080, -88552536, 0, -28849664, -55993636, 0, 19661668, 162496112, 0, 203254862, 160205712, 0, 132984880, -533517384, 0, -255845148, 278669464, 0, 23883012, 67012, 0, 337698892, -157231068, 0, -340728576, 301256000, 0, 75173976, -67072400, 0, -366433256, -137210728, 0, -403219414, 52285604, 0, 105934708, -354366796, 0, 15577508, -131319408, 0, -120436680, 344103676, 0, -3173068, 225439804, 0, -85966408, -264360900, 0, 145653864, 463038928, 0, 70740160, 88801032, 0, -138847082, -269133664, 0, 214800332, 0, 0, 45257364, 239887576, 0, 278149936, -250942806, 0, 102812856, -88926496, 0, -254958024, -167180176, 0, -129845156, -174084312, 0, -46743932, 40384176, 0, 16291040, -549369416, 0, 357414884, 37082352, 0, -308852984, 56078384, 0, 9116440, 40143684, 0, -234984464, -126887296, 0, 149717536, 174069818, 0, -469045062, 3782664, 0, -285635144, 26548468, 0, 73486228, 345467456, 0, 101101328, 528403024, 0, -175799776, 69058580, 0, 403108808, 391109748, 0, -302659580, -200702576, 0, -461531332, -103427368, 0, 31736118, -91040532, 0, 29198744, 29704864, 0, -261072216, -47448080, 0, -54471420, 405405780, 0, -6830868, -14601504, 0, -288328136, 51989446, 0, 62397120, -131001888, 0, 265796536, -219028656, 0, 67598356, 41585768, 0, 4837008, 345246304, 0, -546331314, -32955616, 0, 182290528, -327094240, 0, -149908504, -137616576, 0, 321267428, 103453556, 0, 54636648, -385517416, 0, 139869620, -319262996, 0, 358788700, -194650788, 0, 25138948, -405192796, 0, -15573638, -194919024, 0, 19425136, -82987780, 0, -300122196, 491298708, 0, -25127064, -107924268, 0, -221617120, 168032248, 0, 149947152, 403976696, 0, -229573020, 268509288, 0, -128285680, -244099172, 0, 41873018, -279683096, 0, 111331328, -232353788, 0, 53543620, -433970360, 0, 116958296, -219532156, 0, -544167488, 217110296, 0, -268028600, -624132668, 0, 44092596, 116211664, 0, 459197888, -217390036, 0, -251969860, 150881264, 0, 176821480, 72385280, 0, 459544788, -55295912, 0, 99695984, -17437294, 0, -69715344, -102617632, 0, -1987512, 88714664, 0, -126781040, 9661284, 0, -286348776, -322774100, 0, 133446124, 128432136, 0, 20082280, -290827600, 0, -315849888, -195377536, 0, -303291312, -26397454, 0, 377045628, -147134576, 0, -82280076, -342221176, 0, -321422844, 575616028, 0, -474075112, 269354654, 0, -421182062, -763931272, 0, -455348144, 398173280, 0, 127656928, 431421836, 0, 458058392, -4823064, 0, -478153264, 527652392, 0, -140572480, 216430392, 0, 98474412, 4036300, 0, -24440912, 241528120, 0, 15643792, -329037440, 0, 174682576, 291759392, 0, -212342592, -392597056, 0, -14495760, 63775544, 0, -668062524, 160776572, 0, -51683512, 547811874, 0, -158491980, 383145324, 0, 409156576, -186079536, 0, -89335512, -6593440, 0, -492553504, -152627448, 0, -209319172, -556842148, 0, -21213476, -187204452, 0, -396481000, -24773344, 0, -35073120, 100270808, 0, -49917188, 346470384, 0, -38444000, -360546348, 0, 77484774, -105916976, 0, -28453224, -512082376, 0, -17428884, 37271604, 0, -87170576, 562099240, 0, -89387780, 326808512, 0, -57127568, 161755164, 0, 33037208, -272088620, 0, -263771080, -205193856, 0, 459347536, 94318132, 0, -299808248, 163645016, 0, -541940028, 301972808, 0, 113426776, -581218698, 0, -113258884, -188100708, 0, 523543700, -148728272, 0, -43189246, 711310368, 0, -449907880, 176630504, 0, -267319432, 367103164, 0, 422054660, -407602920, 0, 542161984, -44183260, 0, 259674576, 181509788, 0, -60371640, 60406164, 0, -425622876, -65174136, 0, -239215248, -417006864, 0, -55423824, 154716882, 0, 236047512, -712713472, 0, 804550240, -565167644, 0, 63181392, 644543256, 0, -419159760, 16446360, 0, 442525568, -343690176, 0, 185575236, 21928774, 0, 138645328, 47597440, 0, 40993704, -155614832, 0, 549987812, 677793736, 0, 312902288, 342715528, 0, -291281322, -809872736, 0, -63877000, -152441760, 0, -258059536, -224369088, 0, -446622928, -816579300, 0, -52568096, -508937256, 0, 75191416, 136746202, 0, 279250520, 713510768, 0, -200000356, -632965160, 0, 306291208, -722021776, 0, 753694296, 203399448, 0, -499493112, 290330872, 0, 374919200, -133463800, 0, 11154186, 401406296, 0, 65251556, 263836196, 0, 516303454, 700321928, 0, -57474828, -11958320, 0, -336857942, -63068272, 0, 615932892, 3241712, 0, -317116644, -121136912, 0, 101634168, 195210342, 0, 408905520, -879277832, 0, -18745100, 174787112, 0, -442965056, 649054768, 0, 929245844, -515655912, 0, -419583500, 315327976, 0, 375040476, -344530616, 0, 30208720, 424496464, 0, 412831248, 804583824, 0, -198652644, -193941372, 0, -98298584, -22373348, 0, 89994276, 69132144, 0, 11084832, 102758020, 0, 131077520, -207603552, 0, -228288984, 160926314, 0, 285721628, -47084952, 0, -616124368, -96466626, 0, 132917372, 530120432, 0, -427128488, -297629066, 0, 136993426, 520863744, 0, 66776432, -194060048, 0, 265926580, 386687376, 0, 858921040, 383535072, 0, 604985128, 898426952, 0, 998318812, 1109520712, 0, -675301936, -650060152, 0, -570970912, -118406072, 0, -788151408, -112510804, 0, -128288728, 70188452, 0, 467367152, -435940028, 0, -185046968, -1073132320, 0, 678212060, 132243920, 0, 197313312, 12452768, 0, 202454844, 129053632, 0, -231363408, 216108740, 0, -286555892, 244764880, 0, -108199696, -470286844, 0, -331247736, 481938268, 0, -196927232, 468864988, 0, -462015968, -535764712, 0, 1129003288, 324592416, 0, 498624480, 569256008, 0, -112334772, -230127892, 0, -453130516, 253750864, 0, 313307520, 997856156, 0, 750142484, -185772576, 0, 901313616, 110778908, 0, 178839216, -112289488, 0, 1137651416, 1296951420, 0, -427984412, -1430576088, 0, -206350496, 349231980, 0, -201373968, 349104724, 0, -121590280, 803542788, 0, -498339904, -34847224, 0, 386165872, -548011656, 0, -169016644, -89209916, 0, -71716152, -337810816, 0, -507161672, 826073128, 0, -352815120, -6933552, 0, 496551008, -672749132, 0, 435303640, -533308976, 0, -19282004, 485426504, 0, 399852048, -642979048, 0, 346286228, -397678056, 0, -50531296, -59464672, 0, -49314558, -134949380, 0, 378871968, 193630440, 0, 354577406, -110243240, 0, -94061376, -180144316, 0, 540251800, 121672968, 0, 282751524, 591417808, 0, -229378488, 136819292, 0, -381254952, -495382114, 0, -735807776, 318789600, 0, -217594296, -57933340, 0, 437620832, 106744316, 0, -331030876, 527441748, 0, 729314088, -65141544, 0, 748256016, -196863156, 0, 1093399616, -215092352, 0, 992600476, 722074640, 0, 82856800, -571593424, 0, -74653544, 1031538322, 0, -220023232, -1333583432, 0, -408481304, -196905012, 0, -132661864, -667612040, 0, 303123896, -215223522, 0, -274771736, 654699584, 0, -9600504, -962556868, 0, 712796348, 635105064, 0, -449564756, -106930288, 0, 180237598, -549662884, 0, 36549844, -741303512, 0, -1241758696, 429205840, 0, -52888808, -851885412, 0, -910581076, 1222851024, 0, -613128832, -254155320, 0, -139967124, -223617384, 0, -363349232, 254928436, 0, 845916560, -808370776, 0, -1330947200, 616692712, 0, -228465608, 913523584, 0, 214429240, 902296920, 0, -208548536, 56797840, 0, -266737804, 266187796, 0, 474966324, -80818644, 0, -106132000, 744741892, 0, -417679248, -273352756, 0, 272345884, 299853496, 0, 859154990, 305895752, 0, 614619660, -309102006, 0, -191774620, 366202376, 0, -572599952, -22643740, 0, 112548708, 20056168, 0, 157192468, 627101696, 0, -1259188536, 527742528, 0, -718669952, -253573868, 0, 170999364, -233340592, 0, 777377344, 463080036, 0, 274794704, 151096504, 0, 468178560, -844731932, 0, -1161507592, -507949024, 0, -547623148, -620118656, 0, 181667774, 766732296, 0, 720455544, 317747724, 0, -11728730, -1372595728, 0, 22993928, -905772008, 0, -342652568, 454171768, 0, -1173652032, 208339446, 0, 755382792, 657666176, 0, -725719508, -191491680, 0, -421170240, -647300688, 0, -211977128, -1102468796, 0, 579849088, 953237888, 0, 1156233776, 7921866, 0, -267587076, 1260052212, 0, 108120520, -360937832, 0, -470118524, 615023832, 0, -162302584, 301093616, 0, 1999283200, 591873296, 0, -459522492, -602713376, 0, -465770414, -1184315032, 0, -1010749064, -33157266, 0, -42342868, -696958720, 0, -748859348, -685698514, 0, 579782940, -1271581576, 0, 117297820, -801383308, 0, 786977652, 87797776, 0, -311292752, -94062756, 0, -473444556, 806494136, 0, 381594592, 443558280, 0, -663381360, -502484120, 0, -90464688, -515345454, 0, 73917888, 985977484, 0, -414583808, -171119404, 0, 344380896, -628224268, 0, -457152104, 50001564, 0, 748232404, -95337612, 0, 490574032, -1064052568, 0, -26726336, 673930368, 0, -440672076, 935001886, 0, -327674892, -945723772, 0, -226798112, -445835800, 0, -567599470, -1042114496, 0, 462369588, 254164952, 0, -1053112872, -1029958576, 0, -316193592, 1420502336, 0, 715511504, 477653152, 0, -1177696600, -439245162, 0, 660021948, 695913244, 0, -219483064, -779277628, 0, -350736472, -226141536, 0, 2589200, 1104373128, 0, -3951124, -615926364, 0, 785820092, -338406726, 0, -458032328, -176285220, 0, -931620592, -5822088, 0, 422240676, 1212789912, 0, 51576080, -398975664, 0, -686672658, 102578912, 0, -902784144, -1319747684, 0, 22091388, 70190352, 0, 616351208, -756912024, 0, 483999344, 309024864, 0, -346223644, 611396036, 0, -46980888, -637936336, 0, -393636548, 877935212, 0, 335332612, -267625448, 0, -1061904936, 599758444, 0, 689259186, 1241729092, 0, -338553756, -102739596, 0, -687331568, -488122948, 0, -516439488, -1113305096, 0, -567145488, -675215856, 0, -452203732, 380714108, 0, 726829318, -216050052, 0, -1457202812, -23809664, 0, -122887248, -880653088, 0, 295977984, -63800140, 0, 679029408, -1123334976, 0, -742469568, 25685822, 0, -209765660, 477502512, 0, 367251432, -214836104, 0, -1068096768, 78022800, 0, -269924544, 178704896, 0, -239149456, -63313352, 0, 652362748, -609688704, 0, 80941960, -1165241920, 0, 214063816, 1374070254, 0, -880506988, -153306120, 0, -123923032, -653188038, 0, -1063015392, 763487856, 0, 38194828, 1085704452, 0, -215963448, -158241568, 0, -1128005992, 1090338036, 0, 1114924024, 474189864, 0, -1213409240, 716757152, 0, -225272180, -556745892, 0, -254298400, -252218636, 0, 232499640, -533585056, 0, -181307640, 10613968, 0, 399602424, -2055400820, 0, -620470920, 768082564, 0, 566885184, 1849025484, 0, 547839948, 185831880, 0, -1100514624, -1033023928, 0, -1208246044, 1718215022, 0, 695204576, 537871088, 0, -526954592, -733895228, 0, 245232192, -41646320, 0, 1688422540, -322485508, 0, -1080731608, 120829968, 0, 1902972928, 292334560, 0, 844613432, -27435328, 0, 509236892, 565993408, 0, 200925532, -96555784, 0, 158111224, -1258713544, 0, 765965450, -41788204, 0, 212469904, -340538140, 0, -203777664, -1571546432, 0, -681251048, 154759062, 0, 393128988, 246611616, 0, -157114840, 321054108, 0, -216103528, -164725728, 0, -53806016, 1266209664, 0, 568797476, -162083016, 0, 1527895456, -410780664, 0, -986277448, -1138743112, 0, -50778992, -1071042360, 0, -917369682, 390813024, 0, 755117784, -227482968, 0, 86385656, -163122780, 0, 783008368, 1317808872, 0, -241886096, 1590220264, 0, -171051544, 370987736, 0, 1002804260, 764698104, 0, 142859388, -1678524414, 0, 120303402, -605443648, 0, -595416232, 9957440, 0, 390005960, -1005154468, 0, -982952144, -1676863352, 0, 1116665528, 133973976, 0, -622689792, 813854872, 0, 192580072, -717797628, 0, 354554440, -128368880, 0, 558803648, -1096357392, 0, 459040848, -370524364, 0, -792056464, 72357988, 0, -94958992, 2178533640, 0, 631150120, 1741130016, 0, -1064616072, 966958160, 0, 456992368, -1381765100, 0, -175976912, -576912120, 0, 326792900, 749740080, 0, 760719248, 1193307768, 0, -331921040, 2223948872, 0, -630673828, 712853188, 0, -1040585932, -524623116, 0, 553339432, -214993920, 0, 979069752, -1024874072, 0, 142829444, 1311462852, 0, 58347864, -1441934608, 0, -495655240, 1152238496, 0, -353585184, 311292928, 0, -1019973136, 1531834948, 0, 113230526, 604889756, 0, 2599182656, 1202772828, 0, 1980928852, 7865032, 0, -602942328, 267606108, 0, 58597788, -163703296, 0, 1421700324, -1399291496, 0, -389572208, 1764879460, 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": "29.6.a.a", "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, 0, 0, 0], [1, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [2, -3, 5, -1], [15, 2, -6, -4], [0, 0, 0, 0], [-58, 0, -4, -12], [126, -14, 5, 0], [0, 0, 0, 0], [-184, 22, -17, 26], [41, 21, 29, 20], [0, 0, 0, 0], [-85, -10, -38, 60], [-160, 24, -66, 64], [0, 0, 0, 0], [-90, 81, 33, 27], [-44, -14, -50, 4], [0, 0, 0, 0], [-540, 168, -80, 116], [-698, -39, -169, 15], [0, 0, 0, 0], [1320, -107, 103, -129], [368, -146, -14, 140], [0, 0, 0, 0], [316, -140, -220, -280], [-1312, 54, -305, -262], [0, 0, 0, 0], [76, 134, -498, 130], [841, 0, 0, 0], [0, 0, 0, 0], [-4849, 485, -319, -92], [-1722, 322, -355, -168], [0, 0, 0, 0], [-1888, 146, -256, 30], [5626, -564, -304, -220], [0, 0, 0, 0], [-2712, -712, 544, 40], [-136, 124, -1560, -500], [0, 0, 0, 0], [-374, -212, -897, -738], [682, 366, -1950, 804], [0, 0, 0, 0], [-4969, -341, 1603, 772], [434, -852, 1357, -98], [0, 0, 0, 0], [-2240, -98, 596, -686], [-5979, 1675, -449, -72], [0, 0, 0, 0], [3133, -1152, -1424, 1040], [-10000, 940, -84, 1620], [0, 0, 0, 0], [-7418, 1497, -1521, -305], [-2529, -1898, 2258, -628], [0, 0, 0, 0], [-12305, 2181, 545, 1716], [-9676, 596, -834, -2200], [0, 0, 0, 0], [0, 0, 841, 0], [2780, -3098, 2466, 140], [0, 0, 0, 0], [11164, -3142, 3582, -2396], [-4240, 1049, -7807, 779], [0, 0, 0, 0], [-5018, -1359, -5351, 331], [-24043, 384, 4716, 832], [0, 0, 0, 0], [-2476, -4428, 4676, -1032], [-5192, 1186, -2036, -22], [0, 0, 0, 0], [-18672, 1132, 6018, 1404], [12234, -3250, 3598, 96], [0, 0, 0, 0], [-19500, 3784, -2200, -1504], [8608, -1672, 2104, -744], [0, 0, 0, 0], [-35024, -196, -5248, 348], [-31226, 1742, 1122, 1876], [0, 0, 0, 0], [-25087, -1457, -5901, 2864], [-12606, 4677, 1923, 4107], [0, 0, 0, 0], [-59568, 5046, -10970, -2070], [-15168, 5038, -2566, 1108], [0, 0, 0, 0], [5276, -1642, 1298, -1372], [51272, -5581, 3297, -5463], [0, 0, 0, 0], [-8226, -549, 6577, 3261], [-29082, 842, 7382, -4380], [0, 0, 0, 0], [-69790, 4708, 12448, -5132], [5744, 3570, 2168, -1646], [0, 0, 0, 0], [8040, 1419, -13177, 809], [-32932, 7528, 12232, 7812], [0, 0, 0, 0], [-8790, 3962, 7150, 7180], [-62464, 3232, -1571, -3776], [0, 0, 0, 0], [3432, 3112, -7820, 944]]}