# Stored data for newform 245.6.a.e, downloaded from the LMFDB on 16 April 2024.
{"label": "245.6.a.e", "space_label": "245.6.a", "level": 245, "weight": 6, "hecke_orbit": 5, "hecke_orbit_code": 18014398610145525, "dim": 4, "is_polredabs": true, "trace_hash": 1801346536642159014, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [964, 250, -64, -7, 1]], [3, [-1584, -11976, -775, 14, 1]]], "qexp_display": "q+(2-\\beta _{1})q^{2}+(-4+\\beta _{1}-\\beta _{3})q^{3}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 8820, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 39.29403585418026, "hecke_ring_index": 1, "level_radical": 35, "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": [245, 1, [197, 101], [1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [5, 7], "conrey_indexes": [1], "field_disc": 240305320, "field_disc_factorization": [[2, 3], [5, 1], [1483, 1], [4051, 1]], "field_poly": [1168, 58, -82, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.098", "prec": 17}, {"__RealLiteral__": 0, "data": "3.928", "prec": 17}, {"__RealLiteral__": 0, "data": "0.758", "prec": 17}, {"__RealLiteral__": 0, "data": "43.328", "prec": 20}, {"__RealLiteral__": 0, "data": "12.371", "prec": 20}, {"__RealLiteral__": 0, "data": "721.975", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[5, 1], [7, -1]], "trace_display": [7, -14, -100, 0], "traces": [0, 4, 7, -14, 49, -100, -136, 0, 489, 774, -175, 770, -840, -58, 0, 350, -615, -2006, -1409, -564, -1225, 0, -1736, -6340, 6244, 2500, 8730, 7438, 0, 8066, 3400, 5856, -3495, 8130, -3402, 0, -28759, 29544, 36860, 57466, -12225, -13156, 0, -5692, 44952, -19350, 30928, -39926, 57156, 0, 4375, 9830, 23398, 20300, -77292, -19250, 0, -50876, -22234, -8432, 21000, -30540, 137568, 0, 37121, 1450, 166756, 32792, 72554, 36540, 0, -83920, -71795, 75424, 168762, -8750, 125092, 0, -89204, 129486, 15375, 146308, -247230, 187520, 0, 50150, 36156, 238670, 475556, 30324, 35225, 0, 124464, 8256, -245756, 14100, -172340, -180270, 0, -420668, 30625, -79168, 422132, -142286, 310954, 0, 145842, -272876, -211396, -95762, 43400, 228012, 0, -114104, -266376, 158500, -189382, 30752, -591476, 0, -156100, 774598, -73386, -199040, 231552, -62500, 0, -89848, -128423, 448300, -218250, 20756, -59956, 0, -723828, -185950, 449126, -514708, 102232, 441932, 0, 942706, -79240, 164330, -607395, -201650, 139658, 0, 567702, 35728, -85000, -47586, -294676, -1676624, 0, -146400, -490748, -649872, 341404, 584224, 87375, 0, 816559, 172644, -1295090, -203250, 1076660, 569634, 0, 1455446, 85050, -609968, -950972, -95926, -591836, 0, 804420, 996136, -209566, -1046080, 718975, -883020, 0, -455712, -198568, -738600, -2201952, 1958902, -1164500, 0, -921500, 1531826, -1077108, -620516, -919850, -1436650, 0, -448188, -3540996, 612040, 305625, -29216, 1182870, 0, 910460, 328900, 326028, -2450696, 3212394, -1352284, 0, -187410, -88802, 974576, -1590884, 142300, 2941040, 0, -1946354, 1525092, -1123800, 147318, -2630160, -1292622, 0, 483750, -3477122, 2090954, 1098632, -1330140, -773200, 0, 1369830, -1620764, -4597178, 998150, -3292460, -192682, 0, -474586, -1428900, 2030768, 3021543, 1721720, -23334, 0, 848440, 974788, -793920, 969368, -109375, -560588, 0, -610596, 1093120, -245750, -2093695, 2608536, -3975416, 0, -584950, 4410096, -1376484, 944572, -4709192, -507500, 0, 502360, -3833612, 1368272, 1932300, 390688, 2082342, 0, -157842, 481250, 1985768, 262640, -736652, 3444768, 0, 2462458, 2457332, -986378, 2131688, 1271900, 12102092, 0, -4088027, -5114, 555850, -2485234, 165030, -3595646, 0, 210800, 4465446, 6807430, 7317338, 4013420, -525000, 0, -2171020, -827348, 1776300, 763500, -4844278, 2243478, 0, -3137398, -3439200, 766324, 4143936, 2684046, 6030638, 0, 337076, 1378008, -4170728, 818590, -928025, 9792316, 0, -517828, 810889, -36250, 7402564, -3612182, -6083786, 0, -4168900, 7722528, 5862284, 7362420, -186740, -819800, 0, 4537272, -4511787, 7674244, -1813850, -8019648, 2692276, 0, -5308868, -913500, -1159262, -4830660, -5657556, -4395528, 0, 6723966, 2494988, 4210098, 319712, 2098000, 2593582, 0, -2318980, 2540336, 1794875, -543524, -4965170, -17718316, 0, -1885600, 2730024, -11618006, 6862680, 4555772, -4219050, 0, -1513728, 5176244, 10714804, 218750, -921528, 7384222, 0, 11767440, -3127300, 8880552, -46028, 4332488, 3161180, 0, 4193206, 12675632, -8350582, -1052106, 2230100, 5614804, 0, -17480276, -9779086, -3237150, -12447388, -9811350, -9336264, 0, -384375, 2353558, -759728, 11222016, 9225466, -3657700, 0, 1434636, -14954496, -4596920, 6180750, 4585480, 10228580, 0, -3896472, -4688000, -5263070, -13803564, 11834616, 7358904, 0, 5104046, -10130616, -4014660, 1624006, -1253750, 13063936, 0, -15889724, 4085378, -903900, -2189030, 4877904, 954672, 0, -5966750, -3138638, 9440312, -5502976, -3697044, -11888900, 0, 17193344, 861588, -9201264, -758100, -10985500, -7762620, 0, 2570722, -880625, -8635072, -13325294, 15132982, -3686296, 0, 4184480, 533612, -11310658, 887394, -3111600, -3867516, 0, 9938576, 3471078, -206400, -10735074, -809522, -25038102, 0, 6143900, -368084, -4867404, -23186356, -11316996, -352500, 0, 12907340, -16872788, -5675748, 4308500, 21861636, 8801778, 0, 25675841, 4506750, -1188164, 10837444, -4214958, -19602148, 0, 2846902, 660712, -9078622, -2488624, 10516700, 8626176, 0, -8522912, 1127402, -765625, -28287718, 4175444, -6780674, 0, 1979200, 31526360, -2322944, -14012544, -8448400, -10553300, 0, -16697463, -27512788, -2511790, 3557150, -8095880, 1623266, 0, 2273742, -7773850, 15687896, -13649878, 10719120, -15719420, 0, 18669504, -17415168, -5865384, -2682644, -3646050, 21864312, 0, -27304152, 12456936, 6821900, -7938332, -8461720, 6080798, 0, 5284900, -11393966, 13679824, 10862864, 10503278, 2394050, 0, 349224, 10973314, -11840460, -1085000, -12650676, -8788784, 0, -25432646, -5700300, -2709108, -6949716, 5435904, 20478636, 0, -40426466, -2741622, 1597696, -2074788, 2852600, -13354856, 0, 14456232, -4348216, 6659400, -3530448, 30452900, -22497558, 0, -3962500, 22192141, -25401962, 11272553, 5977384, 4734550, 0, -4103484, -9767200, 14473990, -768800, 17978794, -15760392, 0, 28953600, 14786900, 8572216, 18026118, -29419194, 4067068, 0, 37698294, 38032376, -2842936, -13862118, 3902500, 12933736, 0, 35819576, -20140004, -19364950, 13205632, 8506942, 7231004, 0, 1834650, 17823722, 3115878, 25204816, -3112848, 4976000, 0, -37715232, 37041284, 25717460, -5788800, -24853580, 14211552, 0, -28348128, 1562500, 3705190, 41648980, 34735042, -22558308, 0, 13602906, 6123208, 14803470, -3875134, 2246200, -13351064, 0, 835556, -55342944, 3210575, 31038728, -14089720, 6650546, 0, -11207500, -6409616, -19471376, 22932417, -9484696, 5456250, 0, 34975388, 1871792, 32217212, -518900, -37412778, 26768228, 0, -7774902, 1498900, -1176092, 2651364, -50805578, 41167596, 0, -31147734, -18382460, -3587164, 46835770, 18095700, -449760, 0, 1926252, 16274078, 4648750, 9471427, -68596330, 26786576, 0, -11228150, -19603894, 38618016, 3117912, -96980, 12867700, 0, -19803488, 5915004, 34086696, -2555800, 28504352, 7068030, 0, -8222692, -11048300, 34550624, -10576200, -12778082, 47009792, 0, -30832262, 22013564, 17253384, -17403060, -23567650, -3823466, 0, -21059616, 25584594, 1981000, 45950948, 28690790, 18843264, 0, -4108250, -43790140, -21385362, 24330488, 14003212, 15184875, 0, -12974165, 24161524, -55001278, 5041250, -859204, 30974256, 0, -16388460, -3491450, -43706412, 14043192, -20589362, 8689924, 0, 11615816, -13318816, 53872954, -13262894, -14192550, -49528092, 0, 16659168, 67846080, -893200, 27189218, 16323288, 37331164, 0, 2125000, -30965058, 20642280, -50077284, -17182992, 1189650, 0, 476412, 41833972, 5196940, 7366900, 50170496, -69712688, 0, -12610308, 41915600, -25979072, -8317000, -30964036, -36476248, 0, -9233780, 12083770, -1024458, 22936324, 3660000, -70434698, 0, 60712550, -40265360, 12268700, 58773616, 29499448, 74811866, 0, 16246800, -30548792, -9957254, -33510530, -85602916, -8535100, 0, 3084188, -23093928, -74488894, -14605600, -8646904, 16017530, 0, 25785910, -2184375, -32256596, 59564810, 11609604, -25122128, 0, -54836832, -66867124, 25990906, 54015478, -20413975, 36252868, 0, -36034880, 74646384, -4316100, -59710176, 11578744, -572278, 0, 32377250, -29494042, 65748952, -4891472, 31943600, 5081250, 0, 22642732, 8664344, -74031228, -26916500, 43255188, -61896430, 0, -14105192, -14240850, 56715208, -50815680, 30235748, -578844, 0, -15206554, -31078090, -3930514, -18290328, -36386150, -38705192, 0, 23517222, -41946410, -2126250, -10406808, 27215616, 41991008, 0, 15249200, -43670820, 53861136, -141536204, 131130240, 23774300, 0, 114194900, -12022504, -42506680, 2398150, 78527090, -37564392, 0, -14647898, 14795900, -59635920, -10016922, 22946816, -44317488, 0, -37828448, -6380720, 63171792, -63936842, -20110500, -34625828, 0, 83662352, 61422928, -24903400, 1538508, -33899248, 102593496, 0, 5239150, -17311918, -70068980, -47040156, -12107008, 26152000, 0, -148140484, 115777106, 18117120, -17974375, -39897672, -177464776, 0, 18311106, 22075500, -27640548, -73681820, 21325640, -106551412, 0, 60554400, -9562848, 58448728, -120394962, 11392800, -86588558, 0, 80000836, -57279978, 4964200, -18054330, 34798694, 33179824, 0, 18465000, -54411200, -170854532, -47983410, -35685540, 55048800, 0, -21632206, 13677812, -95318272, -48972550, 52952618, 1249506, 0, 56717642, 29112500, 59933316, 32899968, -54968704, -37696908, 0, -13530232, 5165728, -37224620, 69293596, 23037500, -182647988, 0, -56493524, -24905078, -38295650, -35543580, 9831846, 91144088, 0, 26927700, 47355524, 15434844, 84732816, 29206846, 15512900, 0, -9430972, 81308453, 131050332, 22996250, -55637664, -28738620, 0, -25072816, 35916250, -13847886, -60353408, -29756952, 91958360, 0, -57933960, -97366240, -106466962, -24995352, 11204700, 30852912, 0, 111382512, 9208808, 88524900, 80236736, -27472512, 3246552, 0, -15301000, -41611872, -25252094, -8663648, 58966932, -7640625, 0, -34040028, -38649080, 58249260, 730400, 46384980, 15401200, 0, -68763410, -29571750, -138183020, 54015400, 90083272, 63398908, 0, -77478544, 30611436, -99069554, 68028280, -22761500, -62582744, 0, 237408192, -94995919, -8222500, 36062776, 17466974, 40850590, 0, -8150700, -42116078, 141579648, -69255552, 37715764, 61267400, 0, 30599496, 53644564, 161873412, -80309850, -56422268, 120605498, 0, -115192346, 33807100, 36097708, -78792844, -182642372, -76312652, 0, 57730682, 77325344, 200328182, -23531424, 4685250, -44970080, 0, -102254001, -55333426, 2220050, -8746394, 16843372, 22269976, 0, -24364400, -99747260, -147306914, 1149176, 913444, 39772100, 0, -107822172, 105082284, -68081120, -3557500, 43809362, -58397968, 0, 120562792, -73526000, 38798972, 181820102, 734482, 115233232, 0, -62448696, 32130888, -68956418, -23194838, 48658850, -40885264, 0, 67204888, -71873044, -38127300, 58386634, -17164024, 33561534, 0, 28095000, 32342866, 34437712, 47997256, -140048688, -3682950, 0, 10683024, -90758154, -23511984, 65754000, 82079756, -43153324, 0, 27429274, 32315550, -100804224, 2912740, -246341312, 64424456, 0, -133723536, -165872500, -6704350, 94862582, -12093750, -143608172, 0, -60385112, 15864582, 86928050, 196792286, 56545912, 167406394, 0, -52273850, 98188968, -40443448, -38128394, -81476592, -27465800, 0, 92576084, 206684848, -12787776, 33253500, -111681020, 189891648, 0, -2425272, 19330000, 101993712, 258420277, -25473008, -9383330, 0, -62884017, 2280928, -14065672, 6681360, -34245750, 6826788, 0, -2069580, 40288876, 40519100, 71457560, 20385826, 50980518, 0, 114929450, -10018314, 12552886, 13997188, -27037220, -24953750, 0, -158332708, 40380480, 150613760, 82311500, 135432460, 95390952, 0, -68343546, 4817050, -105862898, 148589328, 9599188, -17316392, 0, 197004142, 59760790, 117769686, 131610320, 11864650, 138494840, 0, -199038164, 83858522, 35722500, -90290958, -141068470, -2073462, 0, -50769200, 100489564, 187978448, -6987952, 13538496, -75538575, 0, 73235008, -54901636, -175849028, -43043000, -47957956, -151640022, 0, -318400, 583350, 209118156, -95111004, 70403122, -12914138, 0, -33400214, 175766172, 126475296, -3731704, -21211000, 135335476, 0, -301438060, -4411850, -24369700, 126248972, -7299784, 97593092, 0, 19848000, -59500540, 192351976, 98102180, 12503072, -24234200, 0, 102331396, -129302328, 227245504, 2734375, 129212896, -3476134, 0, 25917544, 14014700, 45875042, -156419456, 57009540, -91579116, 0, -167267266, -126783572, 4101530, -25150488, 15264900, 147045756, 0, 7324654, 152554678, -27328000, -168969792, 161425512, -166022240, 0, 6143750, -4505844, -162717694, -188819080, -42423380, 52342375, 0, -49960306, -65027104, -90563496, -65213400, -88190216, 66830124, 0, 168869760, 99385400, 52869368, 10018128, 9087666, -59121640, 0, 155216241, 173999412, -263961632, 98827876, 14623750, 226873312, 0, 66659744, -19067756, -110252400, -120748734, 51726794, 60959028, 0, 34412100, 61579480, -10918298, 63788052, -126834678, -23614300, 0, -229106484, 1241600, -94262636, 117729800, -269709276, 41392206, 0, 160509468, 12687500, -130764372, 33800428, 132989484, -257070468, 0, 105260574, -383006298, 210004224, 57293912, -12559000, -136043312, 0, 22465860, -93715134, 95840300, -246032332, -37104600, -142756094, 0, -34206800, 12580022, -333110106, 97351954, -8930592, -48307500, 0, 291344455, -82443376, -132067598, -9767200, -90550800, -140293072, 0, 194144404, -52058550, 27104732, 62540692, 55052126, 165828864, 0, 49867908, 118106004, -357719796, 143675132, 3946050, 122880040, 0, 90357568, -29868600, -12031250, -128080244, -182760326, -120419708, 0, -49644200, 244982304, 247064164, -170065136, 79413530, -6566000, 0, -34865672, -53260700, 277111056, 18416300, 259541372, 75634752, 0, -176678116, -86119200, -94869838, -380123544, 209194856, -136017164, 0, 221946846, 10279286, 36277440, -199703564, -61561450, 252536040, 0, -476988260, 65273614, -61433300, -40018216, -161437366, -449184836, 0, 24659450, 60070096, -294859702, 180844478, 370984028, -53292200, 0, 19010360, 13633684, 47114502, -31797500, -190717248, 1756890, 0, -91317000, -302552300, 84375216, -406707420, 170459314, 233318956, 0, 112995560, 212333836, -12833944, 211873722, 102200675, -389109556, 0, 352605852, -30826259, 127850, -159877664, 28197298, -295367942, 0, -13896250, -213635920, 62630756, 112099156, 345888616, 62130850, 0, -160673088, -354247309, 89970388, -4125750, 41434404, -62757376, 0, -121076616, 89891150, -146236358, -177582784, 57172780, 23179628, 0, -64346320, -191181240, -205562106, -544762288, -5270000, 358432374, 0, 479360, -289070846, -111636150, 104813446, 416763752, -117451542, 0, -170185750, -87603640, -13982686, 79416576, -271987724, -182933450, 0, 142701902, -118410644, -282911980, -100335500, -28911744, 174482490, 0, -39750682, 13125000, 15517420, 15664124, 183767804, -52353456, 0, 152972072, 263397128, -164568448, -343129978, 54275500, 38386732, 0, 143153792, -74779950, 20683700, 100890572, -327047160, -416520360, 0, -44407500, 151131398, 245197114, 17821272, -143991952, -19087500, 0, 314074956, -75189592, -63142476, 121106950, 90374408, -40333632, 0, -261867384, -56086950, -41956932, 161935192, -100879406, 53488428, 0, -294799552, 87822000, -250020966, -31369374, 78434950, -229804462, 0, -32406084, 191573112, 85980000, -323224470, -234174282, -6240346, 0, -19158100, 271454938, -160900232, -195394888, 405329900, -103598400, 0, 452384000, -392505844, -5752952, -67101150, -192112428, 184756208, 0, 110712056, -150765950, 186556, 93943288, -463233648, 449665272, 0, -11026570, 101403984, -137018440, -66616018, -8426900, 352502592, 0, -146760612, 124312476, -34450200, 27742764, -39749398, -378559586, 0, 104268200, 194028504, 431819576, 368141272, -330094606, -20464750, 0, -159789232, 214533660, 124453616, 23200625, -282946592, -219921782, 0, 82922454, -244807900, 152573824, -166704384, 100782576, -55839380, 0, 181540200, 225457152, 132517184, -22300352, 12945700, 197247642, 0, -225335214, 66180602, -20272225, 241439592, -28322076, -236573826, 0, 906250, 127435616, 63721584, 549420240, 307475684, -185064100, 0, 146415096, 241713952, -195764512, 90304550, 23546502, 125451606, 0, 77893860, 152094650, -109252304, -99143146, 265147584, 167447944, 0, 490265912, -137687088, 98007888, -126098942, 104222500, 435408392, 0, -345059092, 466324732, -193063200, -184740184, 74431414, -4619722, 0, -146557100, -126706810, 172969504, -101571652, 53131794, -184060500, 0, -7755404, -3492280, 320957988, 4668500, 61429424, 256719520, 0, -94344480, 20495000, 84101116, 114303884, 384992176, -82678152, 0, 39201700, -325481659, 420288852, -219619510, -113431800, 296869268, 0, 165670716, -88974440, 112794675, -98138464, 111137672, -180978226, 0, -191856100, -138103370, -8298128, 521626796, -328414044, 45346250, 0, 82562208, -792223092, -457751008, 200491200, -136270234, 878267892, 0, -11456330, -67306900, 247132904, 150832860, 125959528, -235173958, 0, -8198820, 286567116, 178126988, 603081436, 132721700, 109628544, 0, -504392056, 375027228, 22837500, -226113216, 130356236, -19368536, 0, 28981550, -20411102, 480489598, -81724272, -459561700, 120766500, 0, -195723036, -120445764, -255215748, 141438900, -326148148, -239341928, 0, -262745562, 109888200, 562380410, 214635128, 58418416, 339325424, 0, 512068830, 273252728, 29199298, 330217314, -168099150, 229398864, 0, -163730236, -439970232, -62374700, 54679808, 242945610, 9418320, 0, -105252450, 507417804, -626052480, -238984012, -162309336, -7992800, 0, -242500620, -17936036, -162903096, -52450000, 272019672, -90798664, 0, 573112754, -64839550, 175471104, 517973368, 83032410, -91878952, 0, -446886712, 64642352, 219230752, 168961312, 57974500, 13075264, 0, -87540548, 391705912, -63508400, 488726190, -37363486, -57188640, 0, -44871875, 226453590, 56347100, 242954268, -899466136, 13588100, 0, -605225932, -23886750, 350756928, 124129250, -279160452, -230057356, 0, -402475652, 442957900, 313486212, -206274956, -251571818, -189923324, 0, 264572566, 200440432, 17481138, 336081200, 47140000, 625032800, 0, -422676926, -279373440, -68250600, 190815758, -603799798, -355332590, 0, 290450150, 295662284, -257461430, 127879684, -164662988, -171567000, 0, 429819948, -19238132, 57493354, -113894300, 466619664, 470750896, 0, 45219644, 105476250, -290951764, 62908128, 231215542, -233530768, 0, 25899358, -129973828, 115997562, 838643552, 37843200, 179516472, 0, -31078756, 211211594, -129406100, -276331000, -142295030, -471110448, 0, -267870100, -44079718, 232001418, 436073088, 628553374, -5468750, 0, -106214192, -204393348, 374625760, 23038200, -709521544, -119272346, 0, 342825248, -184605550, -107995312, -18887004, -219353484, 243055724, 0, -152632512, -475849672, -328809502, -531309236, -294186000, 434400376, 0, -10842068, -148680708, 78182500, -372801482, 45937776, 299915934, 0, -222013800, -107233090, -347447874, -374712570, -25160624, 1150700, 0, -51476152, -131362884, -68983300, -108312200, 245007592, 69498704, 0, 277191016, -79029500, 127005556, -127261273, -294522268, 420198468, 0, -83324060, 186984848, 350731678, -387353934, -104830150, -230774280, 0, 163774160, 11797296, -316890800, -400914699, 282001756, 189501208, 0, 208764550, -699570528, 22001724, 246619216, 105240692, 26302650, 0, -248775576, -402234096, 39672828, -55752500, 15426380, 115365090, 0, -97059954, -140370100, 281643448, 132333908, 245622504, -594113564, 0, 470162472, 197925034, 417361246, -440181168, 437006900, -234253036, 0, 163755432, -1003105880, 244477150, 445127612, 247431328, 381168038, 0, 80928750, 630838408, -261977318, -503183824, 228892176, 311184700, 0, 313180576, -290851648, -111022848, 245283750, 199980768, 75582514, 0, -229595732, 233406600, -804785456, 360624176, -363363542, 198878890, 0, -650963664, -748726048, -450928488, -259338798, 9609375, -553827468, 0, 523683176, 94859884, -58838950, -68696136, 212902444, -38395100, 0, 18993200, -175557850, -268029124, -171280752, 85068728, -280550400, 0, -162876192, 603870554, 40551832, -230636650, 154016780, -170564208, 0, -342907696, 91442500, 162665686, -624890684, -330870908, 382287316, 0, 116313018, 209102832, -296330088, -364289906, -35865900, -930366174, 0, 404056004, 832719456, 373862400, 479793460, -106796418, 194851860, 0, 114923000, 170324256, -24802480, -16552615, 171061008, -154518750, 0, 295500360, 618296404, -89057876, -114637000, 536230286, -39764544, 0, -244217072, -255714500, 344009188, 338869260, 351251648, 30832128, 0, 560446806, 351595088, -615524868, -124932502, 97411800, -340855932, 0, 766289736, -59321100, 117200000, 51337052, -385318272, -25287656, 0, 131576750, 234972320, 181234104, 600433940, 925457462, 345089100, 0, 4421244, 714172166, -97850732, -295865400, 43898512, -169386028, 0, 102437808, -183972600, -1068027780, -522398972, -130675838, -11702180, 0, -328773990, 382906648, -483334746, -292390264, -127601150, -354113142, 0, 235213824, -963545064, 253265400, -189449574, 239371648, 12292186, 0, 100366500, -266635927, 447526004, -696630780, -175386244, -40600150, 0, 629474278, -161784280, 189952436, 31343750, -12344600, -694661426, 0, -282349762, -326598400, -15123180, -1070532292, 170503138, -1068433020, 0, -367108984, -508254244, -568626906, -312759936, 397243100, -306583216, 0, -593307296, -217746044, -102134450, -276811356, -832244136, 178958880, 0, 22597500, -274611884, -96960654, -535799792, -190484096, 54725750, 0, 7995804, 597260472, -717680264, -121947600, -673801028, -71385032, 0, 774190938, -23866800, 174331112, 239725112, 326973264, 548418692, 0, -1128413614, -105139016, -286721112, -24129888, 149168750, -886329474, 0, 280675331, 582056278, 78465950, -533666944, 173047284, -246319968, 0, -236007800, -175304518, 19513970, -466944524, 1174285624, 137574400, 0, 522486186, 76478260, -41981478, 92426100, 391089810, -456200810, 0, 108447202, 297222500, -476867328, 536385332, -157587184, 322007600, 0, 73617072, -826083816, 448415680, -37956106, -429833600, -133099264, 0, -345776644, -184752400, -21539700, 208955702, 1269099234, 435839910, 0, 230031600, -748341128, 1087580672, -1328789080, -787261356, 18952500, 0, -685160460, 450083894, 511320304, 274637500, -66377468, -787378560, 0, -967122278, 194065500, -630771904, -1003496292, -253911032, 662762900, 0, 376185512, -379447120, 1034897222, -53126556, -64268050, -749732168, 0, 937166642, -2338354, 22015625, -432234432, -186710036, 566637958, 0, 215876800, -778519416, -415550376, -39787470, -849974896, 333132350, 0, -574013092, 322261056, 343257468, -378324550, 796678084, -81042766, 0, 243824526, 92157400, 327367152, 287508264, 421098416, -990614400, 0, -292326726, 194930152, -466775128, 524932176, -104612000, -185340168, 0, 297948852, 108182956, -13340300, 239068752, 58969482, 1173792864, 0, 282766450, 377895546, -299477908, 780125832, 649203264, -22184850, 0, 95017932, 192610000, 444582704, 77790000, 780444616, 8568480, 0, 273412797, 96687900, -278615486, 508474092, -149360606, -790828592, 0, 166205970, -914061581, 140707588, 774708692, -248464400, 162045672, 0, -205157784, 17243194, -86776950, 726857502, -168445528, 580174952, 0, 5160000, -136572100, -496696040, 8563552, 981799584, 268376850, 0, 210741992, 413347424, -193562484, 20238050, -299582714, 288149472, 0, 290255936, 625952550, 438275944, -79084072, -1277941584, -1036466334, 0, -864224440, 648223872, -188582236, 969127058, -153597500, 24025612, 0, 42332456, -14222456, 9202100, 620797440, -1342706870, 2057581732, 0, 121685100, 83928122, -360856282, -456067508, -65392264, 579658900, 0, -186341288, -146712330, 509584588, 282924900, 188841680, -824202382, 0, 1104807772, 8812500, -85973352, 615491460, 269340, -524600784, 0, 548781014, 551714196, 344560746, 626371254, -322683500, 366499494, 0, -546994768, 975524198, 421819700, 308550110, 528453888, 234189880, 0, 141893700, -524269180, -1362559858, -1018128452, -68443364, -107712500, 0, -974671806, 420097304, -141010746, -546540900, -1009089652, 473574904, 0, 241103396, -220044450, 146441292, 373493412, 271862096, 846652272, 0, 211575408, -130093848, 1455404448, 823879472, -641896025, -30165444, 0, -594968276, -612039672, -112668750, 712685898, 722990138, -194521196, 0, 29704100, -754708090, -17109892, 530522060, -608976666, -270936100, 0, 743725788, -176637040, -981167904, 105373950, -4711068, 434563512, 0, -762813332, 490053700, -783436372, 119442904, 466991430, 550827840, 0, -1366482696, -3179066, -262415254, 297173360, -71172550, 1060857636, 0, 407641906, 225616858, -16517800, 191641544, -200548872, 952331282, 0, 226965550, -883268090, 365601856, -307811782, -1293156384, 62215600, 0, -1464935832, -74861544, 490079766, -262917500, 1043612, -708185718, 0, -308263728, -215654400, -214537676, 301162676, -908659870, 481329496, 0, -613752944, 936967216, -69498664, 87824056, 213072800, -43615120, 0, 450403300, -317756256, -28185050, 1048381160, 952941946, 1072829762, 0, 19140625, 211444056, 1051161420, -1229144668, 492127150, 707192950, 0, -341104756, 210976024, 579743744, -104386100, 1333104096, 1030146882, 0, -625308624, 169516850, 944416668, 1023073700, -1519367420, -1229024032, 0, -61216274, -1273016336, 2176120688, -207555772, -49480000, -394525700, 0, -283980512, -625891256, -788159000, -335954742, -122072556, 425007044, 0, 58073600, -827073634, 456382160, 771347292, -751117384, 350313600, 0, -472100736, 515755400, 168216552, 211210000, -37149616, -1554444852, 0, 1090545338, 263832500, 434930764, 87652576, -746444568, 742738850, 0, 6338536, 1120818400, 668212024, -1563079924, 417436575, -439943072, 0, 838837312, 390441698, 687819700, 190799644, -412734334, 726635392, 0, 62794750, 684465172, -308981640, 846581376, -270000928, -88928750, 0, -102797192, 266404758, -198333704, 202397000, -604032, -13289044, 0, 947728952, -40581650, -852005164, 725344824, -399912984, -534169160, 0, -1834124766, -735277647, 380070934, 1044957590, -56843550, -1724209824, 0, 123708576, -490208200, 194346250, 1190138510, 1364401894, 68472352, 0, -392197400, 562221816, 958740734, 46592148, 40740400, 341246950, 0, 135423886, 1647480896, 437624448, -267978000, -1116059696, 904525486, 0, -841127846, 392985500, 62963776, 706242928, -291334608, 743944982, 0, 1029095188, -652797024, -1111624250, 656102142, -466737600, -1302870652, 0, 791472280, -283158696, 435379200, 248830096, -685539048, 631531152, 0, 146634600, -151195960, 29532562, -737000368, 633585794, 67066100, 0, 374732352, 1826078268, -191639816, 91151250, 230479124, 677023460, 0, -1089984616, -546607800, -182189268, -601672248, -957787416, 477212080, 0, 156470848, -365937196, -481844238, -602758530, 682603800, -1089208128, 0, 484443432, 1089980972, -311423400, 239518202, -1423615632, -200845728, 0, -170547500, -382759156, -6698154, 1892775812, 363855604, 198458300, 0, -391711014, -545102560, -294461256, 211543000, -328185964, -1131787418, 0, -1019737978, -152019950, -890605272, -282111878, 1946168034, -673536412, 0, -70086046, 602468160, -425056160, -96384722, -132122500, 1062504864, 0, -184408784, -560058249, 284849150, 684594400, 704161936, -835180530, 0, -341995600, -533610262, -469127864, -678248060, 22793536, -271571600, 0, 2595420612, -409723856, 755575944, -262581950, 1004841772, 193455114, 0, -290147268, -59851250, -124013236, -691343820, 965768640, 361121860, 0, -286770206, 577037148, -2551241392, -1281425248, -8730600, -1379855412, 0, 1056396521, 553282968, -274332850, -737906480, 875092312, -229740570, 0, 296011500, -89625550, 1286797200, 208902104, 611026076, 27125000, 0, 23629484, 123948004, 596117190, 316266900, -15817060, -517957618, 0, -627643200, 219719600, 450254652, -540848918, -1140008100, 812630460, 0, -329172120, 36027180, 192656538, -1926112144, 635816150, 70065028, 0, 899416840, 511586184, 142507500, -994202644, 212964210, 906352576, 0, 67727700, -782437698, -2490603648, -982922792, -1380502216, 173742900, 0, -1695360048, -991305692, -1968123924, -135897600, 1237801572, -1277698814, 0, 231365072, -511965900, -29834344, 1340190424, 580762144, 569279080, 0, 498853298, 245812508, 975138896, -509167830, 1010661650, -105914640, 0, 10082888, -960061964, 68540550, -1022660146, 1774224408, -512113542, 0, -39942400, -1324816388, 1035831800, -1996084278, 90817632, 51869700, 0, 657718536, -37055728, -973776458, -71315000, -861434834, 1450692332, 0, 629923808, 333871400, 1633547512, 197426256, 240607394, 795263880, 0, 916876066, 226384264, -464925320, -821132594, -361405800, -1454310200, 0, 59851692, -921606904, 108705400, 382467976, 1291064404, 196832630, 0, -166485000, 2197585136, 661951488, -1704956, 967368760, 88261200, 0, 242130232, 95743274, 1463143176, -761322500, -144830412, -413374000, 0, -896404380, 562438950, -419194130, 99459600, 278516132, -623990164, 0, 344179844, 149182632, 136212012, -708952872, 99062500, 57130200, 0, 2116581572, 1041071978, -554803525, 256969056, -4303918264, -2174103118, 0, 635049050, 279548328, -792250616, 21876405, 1292391508, -281813825, 0, -751046624, -750454340, -965030996, -149434600, -439407078, 332823536, 0, 971022226, -118363750, -399526268, -1908466652, 398351010, -253445700, 0, -464201782, -379900520, 2095569176, 957638238, 102587100, -499777664, 0, -584748648, -2189979744, 244180000, -1048261787, -339228832, -246369268, 0, -361849750, 319570992, -1434667000, 1267514004, -85449728, 19220000, 0, -520972140, -317067336, -770018660, -449469850, -823261732, -924726458, 0, 688354028, 394009800, -712240248, -1435667576, -250865100, -140536128, 0, 635703730, -1742691296, 18181870, -387922520, -723840000, 242416844, 0, -2147027536, 266791094, -369672500, -1097092718, 1535073566, 1869273742, 0, -214305400, 447587472, -324009750, 673312612, -29535956, -450652950, 0, -410735214, 72354832, 814775128, 735479850, 1686978576, -1526640184, 0, -187823208, -101676700, -652816384, 263401912, 1419168336, -988944300, 0, 4764288, -1653246152, -1670975686, 269218488, -942457350, 1062339008, 0, 1575274280, 1284216678, -950809400, -554088430, -1419317146, -2498069972, 0, 71073400, 858541750, -1163829792, -610552568, -2259560012, 346552950, 0, 2813996520, -2609819344, 497524384, -97562500], "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": "35.6.a.d", "char_is_minimal": true, "conrey_index": 1, "id": null, "nf_label": 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], [2, -1, 0, 0], [-4, 1, 0, -1], [15, -5, 3, 0], [-25, 0, 0, 0], [-29, 2, 11, 0], [0, 0, 0, 0], [133, -7, 21, -6], [165, 33, -40, -1], [-50, 25, 0, 0], [228, -7, 72, -9], [-192, -30, 16, 10], [-14, -41, 0, -39], [0, 0, 0, 0], [100, -25, 0, 25], [-117, -87, 51, -42], [-418, -55, 144, -9], [-427, 49, -165, 80], [-92, -226, -24, 18], [-375, 125, -75, 0], [0, 0, 0, 0], [-197, -510, 291, -144], [-1488, -274, 72, -30], [1358, 40, -370, -32], [625, 0, 0, 0], [2593, -304, 669, 0], [1736, 559, 128, -191], [0, 0, 0, 0], [1814, 333, -168, -141], [725, -50, -275, 0], [1368, -576, -456, -48], [-641, -283, 279, 90], [1632, -519, -1120, 119], [-577, -224, 579, -288], [0, 0, 0, 0], [-7361, 413, -317, 362], [7326, -528, -264, -240], [9522, -424, 378, 48], [13664, 1429, -680, -21], [-3325, 175, -525, 150], [-3842, 1474, -504, 270], [0, 0, 0, 0], [-2300, 370, -1464, -210], [12752, -2702, 1824, -294], [-4125, -825, 1000, 25], [8314, 300, 1386, -144], [-10304, 1149, 144, -429], [13764, 672, -924, 420], [0, 0, 0, 0], [1250, -625, 0, 0], [2560, -2245, -1528, 1221], [8002, -4200, 2250, -90], [4534, -158, -960, -402], [-18411, -1398, 1253, -256], [-5700, 175, -1800, 225], [0, 0, 0, 0], [-10840, -398, 3320, 478], [-4901, -1016, 639, 336], [-3884, 4128, -1344, -288], [4800, 750, -400, -250], [-7254, -186, 504, 330], [35856, -1968, 1488, 912], [0, 0, 0, 0], [8187, 2189, -1485, 786], [350, 1025, 0, 975], [40883, 766, -2349, 2240], [5956, 5404, -1968, 372], [18926, -1512, 1254, -870], [10680, -1458, 1208, 2306], [0, 0, 0, 0], [-18424, -1968, 4464, -672], [-21709, 9793, -1661, -1926], [18054, 604, -768, -1068], [46860, -9318, 4416, 528], [-2500, 625, 0, -625], [33116, -4456, 2124, -1332], [0, 0, 0, 0], [-22777, -7442, -5353, 1360], [31064, 295, -2424, -87], [2925, 2175, -1275, 1050], [34409, -1136, -3632, -2544], [-68942, 11126, -9210, 1008], [48476, -4704, 1536, -1392], [0, 0, 0, 0], [10450, 1375, -3600, 225], [7534, 6752, -1098, 2928], [53560, 9551, -5568, -3743], [125278, -11480, 6558, 960], [9934, -178, 4872, -510], [10675, -1225, 4125, -2000], [0, 0, 0, 0], [32336, -3524, 1584, -1812], [4344, 9984, 10872, -2640], [-62881, 11174, 2847, -288], [2300, 5650, 600, -450], [-39280, -8156, 2096, 2872], [-49042, 5437, -6480, 2499], [0, 0, 0, 0], [-106900, 15730, 6224, -3650], [9375, -3125, 1875, 0]]}