# Stored data for newform 147.6.a.a, downloaded from the LMFDB on 25 April 2024. {"label": "147.6.a.a", "space_label": "147.6.a", "level": 147, "weight": 6, "hecke_orbit": 1, "hecke_orbit_code": 100663443, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 935951528234973643, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [6, 1]], [5, [6, 1]]], "qexp_display": "q-6q^{2}-9q^{3}+4q^{4}-6q^{5}+54q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 5292, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 23.57642151250815, "hecke_ring_index": 1, "level_radical": 21, "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": [147, 1, [50, 52], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [3, 7], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.027", "prec": 17}, {"__RealLiteral__": 0, "data": "0.988", "prec": 17}, {"__RealLiteral__": 0, "data": "0.029", "prec": 17}, {"__RealLiteral__": 0, "data": "1.953", "prec": 17}, {"__RealLiteral__": 0, "data": "0.014", "prec": 17}, {"__RealLiteral__": 0, "data": "4.823", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [7, -1]], "trace_display": [-6, -9, -6, 0], "traces": [0, 1, -6, -9, 4, -6, 54, 0, 168, 81, 36, -564, -36, -638, 0, 54, -1136, -882, -486, 556, -24, 0, 3384, -840, -1512, -3089, 3828, -729, 0, 4638, -324, -4400, 1440, 5076, 5292, 0, 324, -2410, -3336, 5742, -1008, 6870, 0, 9644, -2256, -486, 5040, 18672, 10224, 0, 18534, 7938, -2552, 33750, 4374, 3384, 0, -5004, -27828, 18084, 216, -39758, 26400, 0, 27712, 3828, -30456, -23068, -3528, 7560, 0, -4248, 13608, 41110, 14460, 27801, 2224, 0, -34452, 21920, 6816, 6561, -41220, -82452, 0, 5292, -57864, -41742, -94752, 94086, 2916, 0, -3360, 39600, -112032, -3336, -12960, -49442, 0, -45684, -12356, 143034, -47628, -53144, -107184, 0, -202500, 90828, -2916, -61666, -20304, 21690, 0, 10482, 30024, 5040, 18552, -51678, -108504, 0, 9072, 157045, 238548, -61830, -17600, 37284, 0, -171088, -212352, -86796, -22968, -258468, 20304, 0, 138408, 4374, -148176, 300234, -45360, 350164, 0, -168048, 25488, 359832, -92016, -27828, -246660, 0, -9640, -105258, -166806, 396392, 93408, -71442, 0, 26400, 22968, 137746, -131520, -303750, -8640, 0, -39366, 352676, 27480, -30456, 494712, 217560, 0, 35751, -31752, 45036, 38576, 163698, 250452, 0, 640704, -162756, -564516, 358740, -1944, 507130, 0, 357822, -141120, 14460, -237600, 497448, 74688, 0, 20016, -648384, -249408, -27838, 296652, -34452, 0, 611046, 274104, -879032, -518952, 207612, -858204, 0, 31752, -41220, 318864, -68040, 724768, -313584, 0, 48500, 135000, 38232, -544968, -57864, -122472, 0, 369996, -369990, 13536, 562716, -130140, 999472, 0, -250209, -62892, -606180, -20016, -1359926, -30240, 0, 779184, -392886, 310068, -112032, 72336, -197280, 0, -1325136, -61344, 990094, -942270, -59049, -159032, 0, 370980, -354728, -739200, 742068, -223704, -147132, 0, 473760, 1026528, -47628, 387328, 483582, 520776, 0, 15312, 375678, 1550808, 813576, 852768, -202500, 0, -846774, -92272, 461106, -26244, -1675136, 1001952, 0, -1801404, 1742196, 30240, 401126, -2100984, -356400, 0, -2309766, 1008288, 1128772, -16992, 30024, -2158992, 0, 116640, -641933, 166968, 444978, 164440, 938874, 0, -108504, -404880, 411156, 631548, 535920, 111204, 0, -2378352, -1287306, -631616, 238548, 428652, -692948, 0, 478296, -158400, -2943096, 964656, -885146, -826476, 0, 87680, 2508798, 1822500, -2615832, -166272, -817452, 0, -490392, 26244, 1970782, -2116056, 554994, 1154160, 0, 182736, -216148, -329808, -195210, -1305360, 138408, 0, 3252626, -214506, -94338, 21168, 2481600, -270216, 0, 1620192, -45360, -982188, -2932068, -166968, -905198, 0, 465102, -812160, -1917858, 976536, 25488, 376344, 0, -2152440, -2436984, -81648, -2166963, -3042780, -1413405, 0, -246660, -2146932, 984064, 954240, 556470, -86760, 0, 158400, 1703654, -2984688, -335556, 3136896, -2959044, 0, 2756540, -13344, 1539792, 3890304, -456576, 1911168, 0, 167028, 781164, -197768, -2006394, 206712, 740880, 0, 2326212, -3666276, -131520, -182736, 5770402, 5274192, 0, 3509104, 3006258, -1245672, 2807200, 572136, -39366, 0, 1359240, 1333584, -1533626, 247320, -2702106, -212576, 0, 408240, 494712, -918720, -3151476, 1881504, 3873756, 0, -1333066, -291000, 1512432, 5670000, 2724498, -229392, 0, 363312, -3238488, 347184, 6451920, 828144, 4165774, 0, 250452, -246664, -467040, 2219940, -792680, 568512, 0, -3376296, -1399812, 86760, -564516, -5996832, 947322, 0, 2992482, 1501254, -3874680, 41928, -3567528, 3637080, 0, -840672, 6299690, 8159556, 642978, 20160, -3403182, 0, -2230336, -5268768, -237600, 2357316, 6514092, -206712, 0, 672192, -1239714, 3038112, -5439216, 1183680, -1717484, 0, 2733750, 7950816, -2392320, 77760, 1537580, -5940564, 0, 628180, 296652, 354294, -6130888, -6679344, -3174084, 0, -1235892, -247320, -4090716, 2128368, 274104, 4998400, 0, -4452408, -9854956, 149136, -1958040, 882792, -1167768, 0, -858204, -2842560, -321759, -684352, -1049406, 285768, 0, 4471296, -405324, -2901492, 318864, -347184, -10531008, 0, -1473282, 643104, 9614070, -2254068, -6961484, -1033872, 0, -4881456, 3880800, -5766336, -5730743, 1215000, 1464804, 0, -4383060, 5080644, -544968, -3875424, -3228660, -2766636, 0, 17496, -712690, 10050816, -4564170, -1270080, 369996, 0, -3626140, 1200936, -3220398, -10453176, 2578728, 1270080, 0, -2406756, -130140, 1400656, 4848462, 2138400, -6152872, 0, -4477032, 13858596, -8504052, -672192, -62892, -6772632, 0, -713664, 362874, -180144, 4110236, 1439328, 5835456, 0, 2594760, 2244672, 7876798, 3851598, 250542, -111312, 0, -2669868, -19035000, 6906480, 310068, -5633244, -603948, 0, -2446400, 651024, -5499414, 2737760, 5390766, -2466936, 0, -421032, 7911288, -3215520, 4279992, 4670568, -1024826, 0, -1868508, 1585568, -942270, 7723836, -12434192, 800640, 0, -1431288, -11912736, -285768, 4215062, 4157688, 370980, 0, -4406646, -2869776, -4801676, 105600, 612360, 17658576, 0, -6522912, 9429421, 5310876, 2822256, 550984, 2125620, 0, 8307272, 3682560, -436500, -15052788, 1026528, -1215000, 0, 15694992, -344088, 1274112, 17695650, 4904712, 12839356, 0, 520776, 2942352, 20846808, 1102248, -10199376, -11824692, 0, 1410704, 12963246, -3329964, 1550808, -7804320, 3329910, 0, -5668620, -121824, 3114298, 1296888, -5064444, -13851936, 0, 1171260, -3895920, 870240, -8995248, -830448, 22423512, 0, 105890, -19515756, 2251881, 143004, 16091034, 566028, 0, 889056, 5455620, -14889600, 16077996, 180144, -1801404, 0, 12239334, -10955584, -21532500, 272160, 165964, 654792, 0, 17592408, -2100984, -7012656, -6059340, 5431188, 3535974, 0, 17724798, -2790612, -1339960, -15629568, 1008288, 11507148, 0, -651024, -10602346, -152928, 1775520, 15806448, 3696000, 0, -2158992, 1434960, 11926224, 14621904, -9032112, 552096, 0, 13001778, -8910846, 2028520, -14326782, 8480430, -18757544, 0, 531441, 1479960, -8506008, 1431288, 11777266, -5904384, 0, -1209600, 13010352, -3338820, 5889476, 57840, 3192552, 0, -10047576, 6652800, 631548, -10221924, -6678612, 1989792, 0, 2013336, 4815296, -21211392, 1324188, 17754264, -2378352, 0, 3129734, -16539240, -4263840, -560448, 11777286, -9238752, 0, -2593536, 428652, 2739456, -11537592, -3485952, 1493758, 0, -4352238, -111352, 22512474, -4686984, 13591600, -8306256, 0, 12038364, 3819720, -137808, 2395872, -4445280, -3381102, 0, -826476, -13957272, -11954708, 2444184, -7322184, 789120, 0, -7674912, 25365604, -34622412, 1822500, -3516128, -540798, 0, -16468704, -4448160, 7620966, -18037548, -23186040, 830448, 0, -16843200, -4149954, 24029712, -6142230, 236196, 31673428, 0, 15076224, -8155440, -2116056, -9017568, 5362064, 9201756, 0, -164880, 26617494, 16212636, 36281672, -8928192, -15679764, 0, 1090332, -272160, 10301650, -2968272, -3610134, -17680256, 0, 18908856, -1305360, -1254336, 3207600, -23242536, 19613400, 0, 999895, 7998396, 20787894, 194000, -214506, -9074592, 0, -38340000, -10158948, -16346988, 2024400, 152928, -32756486, 0, -270216, 15259104, 25795302, 19430928, 19854820, -231456, 0, -38711520, -673056, -1049760, -982188, -24994644, 5777397, 0, -12362880, -1502712, 14717384, -10359888, -4004802, 2802240, 0, -1479960, 5321150, 4756080, -8449866, -3844224, -27889074, 0, -28378636, 2250864, 976536, 8398872, -42267768, 3643920, 0, 3387096, -3700404, 3997888, 10381632, -5683932, -2152440, 0, -4823280, -17954892, -20407200, -1000836, -29767500, 23248080, 0, 1760976, -3042780, 21405168, 31952588, -2424720, 11585754, 0, -11642928, 5684544, 46502928, -37798140, -2146932, -5439704, 0, -3857868, 1398440, 846720, 6236532, 20419092, 2710224, 0, 7444490, 13382016, -4304664, 6678720, 16679166, 1425600, 0, -1571544, 26487864, -39084552, -2984688, -8681904, 24795574, 0, 7966314, -448128, -27957390, 7438284, -5770800, -20543424, 0, 32635296, 7649364, -789120, -26228180, 10304904, -22579182, 0, -46217862, -16402500, 3890304, -5300544, 23542488, 14353920, 0, 1496448, -9269151, -9225480, 7357068, 3960376, 167028, 0, 20855672, 26383560, 4413528, -1779912, 45815220, -236196, 0, 36785328, -17737038, 45165088, -1095438, 19044504, -53064504, 0, -4994946, 7415352, -52581720, -10387440, -3666276, 24544296, 0, -1418912, -8100960, -1644624, -49038928, -6336000, 1945332, 0, 5274192, 2968272, -3054614, 59129736, 1756890, 6263712, 0, 11748240, -15950088, -588528, -1245672, 7006608, 18765000, 0, 49496690, 5149224, -29273634, 1895040, -7459062, 1930554, 0, -28742784, 849042, 6296436, -43687716, -190512, 26022322, 0, -22334400, -39222272, -21221430, 2431944, -13984960, 1934328, 0, -1913184, -49542456, -14581728, -1720534, 63186048, 408240, 0, 35066556, 8839692, -53993888, -4348608, 26388612, -57684420, 0, 1502712, 1881504, 41768904, 8146782, -43422624, -57889914, 0, 10874300, 3254304, -4185918, -23284800, -291000, 7309440, 0, 34384458, 17260722, -810000, 21252006, -8788824, 51822376, 0, -229392, 26298360, 27885288, -3387096, 60108610, 3269808, 0, 26205248, -11177580, 19371960, -29790316, 1844424, 21932856, 0, 52604376, 734832, -15684480, 4276140, 19502667, -6700544, 0, 27385020, -71831920, -24441984, 12720645, -2219976, 37790844, 0, 13671062, 21756840, 2219940, 50439312, -42401898, 19322388, 0, 6968784, -8856576, -15472368, 23190864, -8588160, -3376296, 0, -5008230, 1604504, 38003370, 780840, -80671176, 58827552, 0, -29090772, -5996832, -1425600, 19108622, 36917232, -15332886, 0, 10054704, 26862192, -21170948, -9239064, 3020004, 51024312, 0, -28232064, 36795338, 377352, 26631396, 4515088, 29973216, 0, 3637080, 4825728, -24808860, -2177244, 20345976, 120096, 0, -24661416, -13858128, 60451776, 8159556, -35012736, 10604000, 0, 4109184, -15568560, 11327616, -17200512, -17413634, -47260788, 0, -2567732, -60026868, -1503252, -22105448, -4675104, -7030476, 0, 1988652, 1779912, 2357316, 114210000, 18057546, -46700960, 0, -1860408, 69748148, 3755496, -6667920, 3623688, -57677808, 0, -51226992, 14678400, -20935908, -434016, 18026754, 32996484, 0, -3470400, 1183680, -32344596, -15610428, 1644624, 31863060, 0, -51933618, -17683344, 92146998, -47467728, 7950816, 2143680, 0, -25679952, 34779624, -31581936, -30128014, 6148956, -27056322, 0, -5940564, 11211048, 3746736, 66593856, -25264800, 5653620, 0, -5149224, 34753262, 74605152, 354294, 15407872, -60129858, 0, -28350000, 954192, -12233160, 71476416, -50163336, -12002256, 0, -25290372, 13802634, -2771792, -48561618, -2225880, 32625472, 0, 24318954, 26439876, 2128368, 1913184, 41342554, 28810056, 0, 4435200, -36259020, -3674160, -5911848, -11772384, -4452408, 0, 44728872, 8268480, -61587554, -56576526, 28363284, -3540584, 0, -16933536, 882792, 23141328, -34863804, -12753720, -6298092, 0, 31543996, -49843632, 11997594, -24901120, -2842560, 2619000, 0, 10035192, -13611888, -6159168, -30228000, -51030000, -12825808, 0, -24520482, -10463328, -98944830, 2064528, 48283216, -2323968, 0, -106173900, 11715396, -3269808, -2901492, -77036136, 29146392, 0, 5052522, -3124656, 29748916, -1961568, -58067280, -125080848, 0, -7453296, 12074834, 61196256, -37491966, 7883128, -119285142, 0, -64417720, 59249568, -2254068, -77779476, -32076732, 2219976, 0, -9304848, 4203360, 9892800, -91255692, -19979460, -4881456, 0, 7134120, 34011720, 93700344, -5116608, 34509622, -18685788, 0, -864592, -104253750, 30386664, 33634304, 93665472, 12598308, 0, 2259384, -780840, -42433600, 23375520, 5080644, 36550080, 0, 53971488, 33905872, 553632, -8525898, -134541072, -19333440, 0, -2766636, -635340, -26932338, 13010504, -2361888, -13511286, 0, 6006168, 34872120, -96546204, 10050816, -377352, -15190560, 0, 32107752, -6011712, 34781262, -32733720, 86600736, 9926400, 0, -96467976, -4722984, 7566048, -63535857, 10808424, -56697210, 0, 36786174, -73436004, -21028176, 13887360, -5786802, 129195000, 0, -181440, 46001654, -995784, 30628638, 27501264, -2406756, 0, 22857160, -11728272, 20073024, 12605904, -57948264, 47418912, 0, 36356040, 2138400, -3620792, 96493632, -21215844, -73107368, 0, -58626828, -106348788, 33396720, 1860408, 13858596, 8039760, 0, 119766528, -24428190, -6049728, 72722664, -7671432, 11157426, 0, -6772632, -27343008, 39342908, 63614076, 48952944, 101952, 0, -10653120, 111809792, -106881696, 15457356, -22176000, 105501612, 0, -25304890, 12953952, -24603750, 60268320, -44788026, -71557344, 0, -9747936, 21530880, 54192672, -92056896, -699840, 145775952, 0, -13838220, -8667852, 3851598, 53465076, 95545192, 85197840, 0, 85960692, 73170444, -5653620, 91088990, 112545264, -2669868, 0, -82156800, -3188646, 84181516, -986640, 55177992, 51036048, 0, 60114096, -5633244, -70663596, 28566756, 3936256, -6687516, 0, 113842736, -23278080, 11123028, -78062112, -55861476, 2225880, 0, -35336856, 36816444, 2429280, 85847658, -19155312, -130499852, 0, -2466936, 60285456, 34589328, -44985600, -82761938, -3789288, 0, 6814616, 90650646, 40071672, -3215520, 83571264, 88694604, 0, 106650204, -1342224, 12187520, -28891776, 17622360, 26887680, 0, -7945128, -169331976, -11836176, 10509912, 14270112, 59684472, 0, -82983852, -18778404, 7723836, 11026160, -16556700, 25583040, 0, 3789696, 2895831, -70663716, 14184372, 6159168, 122812462, 0, 9444654, -108928512, -197492496, -2571912, -57860444, -1826304, 0, 69225552, 4157688, -40241664, 156532500, -8962548, 3647916, 0, 19377120, 26113428, 74811304, -4676784, -2869776, -135074844, 0, 3124656, -118096738, -81549600, 94779072, 56166112, 55365294, 0, 17658576, -8025576, 13259538, -22918320, 172675464, -5787936, 0, -14375232, -86526630, 2963520, 5310876, 20286612, -129246896, 0, 62653356, 4958856, 35563260, 9304848, -100194710, 71728248, 0, 102655728, -45843312, 43933104, -99815284, -526080, -34927200, 0, -15241104, 51897024, -15052788, -152193624, 51576687, 23081608, 0, -10935000, -23242040, -147677376, -13183236, 3244788, 15694992, 0, 57531950, 98812224, 39447540, -85602368, 31162878, -45725796, 0, 12025032, 4904712, 139116240, -142521240, 34878816, -119708906, 0, 29057940, 11228800, -4936206, 24899724, 2942352, -162486624, 0, 36853380, 186726708, -157464, -104967898, -190040568, 6414210, 0, -23787192, -90457344, -69230012, 5436960, 41077530, 12696336, 0, 11430720, 3568320, -32172384, -3329964, -6134504, 79981434, 0, 59365512, -6924960, 32635260, -159704964, -148500000, -10808424, 0, -217690032, 28983582, 60371584, 43607844, 94078584, 109154144, 0, -23208552, -6541992, 1296888, -11430720, -56389466, -61809900, 0, 1978848, -223565088, 21660804, 55266224, 135480576, 1171260, 0, 309540, -12605904, -79229078, 7832160, -43636158, -52682112, 0, -19245600, 71257052, 15495024, 55375848, -117680400, -34532400, 0, -68659301, -5999370, 40293288, -5332264, -19515756, -124727364, 0, 8148000, 76536468, 1287036, 52311816, 6049728, 122450578, 0, 566028, 48600000, 43663998, 60953688, 10529788, 10897992, 0, -12146400, 164902584, 6422976, -14889600, 196538916, -3265866, 0, -220464306, 1621296, 83873592, -103180608, -36992124, -154771812, 0, -12953952, -126155988, -119128920, -52519104, -9721152, 18010662, 0, -213343300, 25807680, -23352840, 4038336, -77688744, -20202048, 0, 5893128, -70891182, 16663096, 16030662, -34664382, 17592408, 0, -2254878, 74177280, -44999520, 1001808, -90633374, -88304304, 0, 70052576, 5431188, 24028812, 151165748, -1868160, 171315000, 0, 46873008, -62158320, 129727174, -31926900, -2790612, -3170720, 0, 50699196, 114719408, 4872960, 5435532, 167334444, 66254280, 0, 11507148, 170271816, 22017600, 94536288, -184397604, -5859216, 0, -5599248, 49494726, 253606608, 13122072, -24639840, -230809778, 0, -48516894, -2258064, -191549292, 22202424, 60719704, 167911296, 0, -62289792, 27279996, 3789288, 79508750, 12914640, -71201592, 0, -198909264, 28939680, 14621904, 11969928, -38519928, 122443200, 0, -42035112, -86532694, 178605000, 9223434, -15498720, 13001778, 0, -223404632, -11907552, 16816572, 18256680, -47012340, -14270112, 0, -191715528, 8480430, -101838240, -18412800, -69514524, -80110296, 0, 111907728, 69857568, 182562240, -7205760, -126988790, -279017568, 0, 25198760, -79569600, 12881592, 197520344, -228467568, 107214624, 0, -5904384, 2571912, -122703840, -8390640, -37935558, -5725440, 0, -37419192, -27489752, -13612728, -3338820, -16261344, 202462440, 0, -54001707, -44666940, 39659814, -8921344, 54389412, 25827984, 0, 128528256, 43215084, -100074996, -20163564, -950400, 197520394, 0, -5511240, -66004848, -10221924, -158927184, 255313972, 26056368, 0, 17908128, -23428080, 58706208, -37932334, -148773444, -84864789, 0, 270558294, -47797884, 99573592, -18821376, -25400304, 167744340, 0, -4958856, 17754264, 34624800, -19130580, 26040960, -115838370, 0, 174935200, -21756864, -74765448, -45896184, -16539240, -33143040, 0, 157369080, 3928500, -6869936, 149650446, 135475092, -92325672, 0, -9238752, 277307172, 205185132, 10935000, 69259680, -23341824, 0, -222622848, -68666214, -141254928, 2739456, -9569280, 3096792, 0, 79526904, -11467008, -9245124, 55614906, -159260850, 6150320, 0, -44142408, 128276640, 166335792, -115554204, -1002168, 139877076, 0, 306839966, -125134032, -4686984, -178403120, 67154604, -26481168, 0, 1186608, -187621272, -274891320, -106989384, -9920232, 12038364, 0, 91794384, -24523552, -122823870, 106422228, 180455728, -57251520, 0, 6572628, -4445280, -12696336, -29548064, 318387024, -116669214, 0, -81337500, 29969676, -252898096, -4943568, -13957272, 315490320, 0, 70238880, -202329360, 21997656, -29969190, -16362864, -261676758, 0, -67710880, -59594304, 51017580, 48605760, 127558980, 1096416, 0, 294233568, -28028682, -121932800, -34622412, -11671992, -308998724, 0, 45579996, -31645152, -286021320, 124667424, 144842518, 18327684, 0, -39419824, -90943506, -10541340, -60780832, -42354624, 35063280, 0, 173637492, -7832160, -18037548, 95700528, 80957232, -24718176, 0, 7474032, -45145252, -4671072, -201811608, -112590000, -16843200, 0, -242938078, -296980140, -953010, -3432816, 180072768, 175641804, 0, 79591680, -20266929, 44754372, -227970132, -1287036, 229654306, 0, -144819306, 194355968, 50500368, -5094252, -8155440, -4197624, 0, 262126296, 233645784, -8001504, -87881948, -156133932, -49100580, 0, 9201756, 134006400, -79032240, 92252160, -144701964, 127328580, 0, -1621296, 102241334, 83909760, 16212636, 81241776, -138513690, 0, -19702224, 1275456, -110154006, 297254736, 283153776, 98600256, 0, 10323204, 193792500, -42124032, 264205494, -2449440, -34286296, 0, -1493676, -210399336, 254694228, -5893128, 101499200, 323963328, 0, 5512320, -76236990, -158331672, -143341084, 38456280, 18908856, 0, 387341928, 63113904, -138723914, -11289024, 54534060, -27845936, 0, -48880692, -23242536, 293619648, -31823766, 347339484, 136500972, 0, 365688576, -65245800, -159523182, 136680768, 7998396, 25115508, 0, 15523200, 12059640, 1746000, -60145248, 140666112, -119673410, 0, -9074592, -22922972, 190668180, -103564332, -225007288, -34020000, 0, -127512036, 15700632, 5859216, -32884488, -310934256, 95421114, 0, -270004782, 1376352, 5125900, -17532240, -15979680, -167311728, 0, -142258032, 125237690, -360651660, -33264000, -2179872, -170604126, 0, -183542416, -33217920, 19430928, 67065480, 5827992, -12914640, 0, 178741896, -107336016, 77465808, 292633194, -131597136, -38711520, 0, 81289008, -315626256, 150899616, -4968864, -331066226, 94106880, 0, -2850760, -24994644, -117016002, -344629944, -281422848, 80197614, 0, -138803280, -18256680, 231862500, 430991520, 128941038, 187294464, 0, -76323870, -54997180, 1479984, 168817896, -226745064, -43582440, 0, 2802240, -82026372, -4782969, -14504560, 495774048, -13319640, 0, -341065824, 76554072, 254411388, 4756080, -12881592, 214075796, 0, -105995394, 292688928, 18691200, 53139456, -357835676, 10314912, 0, -139145184, 367718304, 10886400, 119298577, 20257776, -117093168, 0, -33165018, 30049380, 8398872, 67389168, -53005284, -228020220, 0, -520560, 232260062, 484027056, -28732968, -397786304, -290631654, 0, 227968776, 19393848, 90428184, 35980992, 41531280, -59875200, 0, -114651732, -5683932, -24611488, -97188258, 91997316, 85360720, 0, 60107508, -60328224, -229873188, -17908128, -17954892, 127025688, 0, -388040688, -104439324, -18120024, -450344212, -34016208, -43337664, 0, 23248080, 190902528, 95816780, -220772028, -11917692, -251568, 0, -159788376, -180884000, 189633696, 21405168, -179839296, -148803804, 0, -43028818, -21822480, -28167606, -6117120, -151618722, 148853160, 0, 1451496, 38374560, -122075856, 325485000, 5044032, 13440502, 0, -105995574, 16440944, -37798140, 83148768, 132896608, -408769152, 0, -48957336, 101664960, 23341824, -380684506, -63624000, -3857868, 0, -103149510, -24655104, 87317020, 10379040, 103838328, -67965696, 0, 31373568, 20419092, 104481804, -13443822, 31507192, 222919194, 0, 230563832, -107844744, 39170142, 360161208, 13382016, 1002168, 0, 132632688, -202612266, 31612608, -27354000, 42182856, -120148560, 0, -122324400, -11931912, -228876120, 74756304, -264806388, -14143896, 0, -76140000, -207430818, -108345276, -39084552, 59198400, -34377480, 0, -46385820, 1240272, -172737398, -418488888, -21562848, 157730832, 0, 40007520, 242263436, -2415792, 30429918, 346066848, 269936880, 0, -323548940, 307361952, 7438284, -9785600, 178675434, 125615448, 0, -18228672, 107592372, -108160524, -308844648, -21997656, 32635296, 0, 65899656, -66785920, 44640960, -7102080, -102373316, 21563064, 0, 93662568, 20729904, 69074208, -87903574, -191178360, -228290436, 0, -129846450, 311601708, -181384448, 119573088, -16402500, -552881988, 0, 31645152, -324524026, -47704896, 4867182, 90034560, -166337082, 0, 14353920, 17119968, 148218336, -208677744, 40462176, 40033440, 0, 180768084, -68588694, -4099304, -9225480, 162337932, -382412376, 0, 208674360, 35643384, -7927884, -7474032, -95124928, -22480416, 0, -450301312, 162967506, 151588800, 124237080, -3769080, 37349586, 0, -533659848, -216267408, 152726338, -208519572, 55280070, -49736768, 0, -2125764, -317371824, -118067712, -285060852, 360779148, 36785328, 0, 493988342, 170100000, -135686016, 40076064, 130611606, 73398960, 0, -47650944, 19044504, 300980016, 212591376, 81158112, -96448000, 0, -48258576, 16860248, -563702208, -82815804, 7415352, -116415264, 0, 291369708, 292446876, 1483920, -76295520, -195752832, -239557446, 0, 24544296, -145913724, 500848252, -17626584, -326535048, -12770208, 0, 80353728, 168525770, -248055324, 141117876, -19206704, -129290862, 0, 55593880, -29990400, -9812988, 217554120, 413668992, 2449440, 0, 35471088, -92714850, -494440128, -143708208, 26714448, 630180000, 0, 32491206, -268373232, 59129736, 159122304, 341885520, 369525324, 0, 37717684, -273137460, -170179704, 376276952, -148704528, 11748240, 0, 51799440, 11289024, 17760644, -5296752, -28868400, -156479456, 0, 209182824, 7006608, 8502480, -176520600, 37788552, 766998264, 0, 168523706, -189263976, -8999055, 33229088, -441832026, -71985564, 0, 31564800, -187091046, 17055360, -164812956, -1746000, 92837556, 0, 1930554, 421478064, 174402096, 81671328, -131024684, 4106112, 0, 181368000, -377527440, 345060000, 6296436, 76954848, 91430532, 0, 518700054, 147122892, -29566664, -439459776, -18219600, 593668980, 0, -1376352, 47949230, -289699296, 294808374, -26827776, -389847348, 0, 221587704, 70782600, 2431944, -70292376, -349617744, -137331936, 0, 17408952, -232157718, 51357424, 362788800, -174878352, 164161816, 0, -178693380, -30315132, -474015444, 2083104, 436370868, -178493496, 0, -82385856, 63186048, 348403680, 560822416, 83387232, 6057504, 0, 200281248, 9447840, 162225502, -72449004, 8839692, -40797504, 0, 224951796, -8804880, 331091376, -51996573, 715710852, 166930104, 0, -57684420, 386506320, 111265920, -400639936, 45734958, 13524408, 0, 51852984, -132456456, 192460392, 41768904, 93238992, 622446502, 0, 36043218, 6203232, -542826462, -25220160, -383426152, 190381440, 0, 547534152, 10237680, 13319640, 747376704, 29288736, -47890350, 0, -617247606, -42804720, -23284800, -22674480, 76048794, -562202064, 0, 34598016, 194691184, -207057732, 251001666, 12457192, 34384458, 0, -518449624, -36312864, 255407724, 625522500, -558413016, -20257776, 0, -201805824, -8788824, -118730880, -46887198, -75589848, -33978788, 0, 380409912, -13556304, 337130136, -32795280, 26298360, 254601600, 0, -15583680, -121491972, -30483864, 73937984, -247148160, 33303636, 0, -280567692, -35980992, -90828998, -203435232, -93434688, 23252544, 0, 51155388, -383888356, 89694048, 19371960, 116000640, 96009312, 0, -472298494, 16599816, 43409520, 423560, 658386618, 161594028, 0, 546441168, 183664800, 14171328, 501163308, 9007524, -99075100, 0, 267907500, -40613136, 4276140, -209232720, 266418220, 64364136, 0, -60304896, -48893352, -15848784, -399817414, 91143360, 27385020, 0, 200066592, -192646512, -731781200, 7620480, -287573292, -208687572, 0, 21822480, 190486274, -519604416, -104271786, 416908800, 298528854, 0, 100898540, 64311984, 104786352, 28337904, 21756840, -51160896, 0, 381215142, -418526352, -7205616, -10211466, 340183260, -30943000, 0, 19322388, -220717044, -158477160, 48957336, -107946062, 126169056, 0, 267254528, 441127458, 34720812, -15472368, -86130000, -12585960, 0, -413978400, -7620480, 82982448, -276009924, -56128788, 663856, 0, -183771828, 198794240, -185960928, -24392016, 14440536, -311060232, 0, 337664448, -137142960, -67000410, -492587424, -68360730, -120438144, 0, -8403936, 38741976, 347689584, -131917800, -60108480, -29090772, 0, -150112494, -24237360, 494515386, -12830400, 407324680, -152073264, 0, -578961792, 36917232, 14143896, -36976738, 438644208, -238390776, 0, -591194094, 351760968, 563301964, 70899192, 26862192, -200380320, 0, 78137136, 720867007, -83151576, -223160166, -5359840, -229311996, 0, 51024312, -218452992, -71696826, 146569140, -505846596, 4033152, 0, -436335984, 251616510, -322200144, -32378898, -66944556, -272740248, 0, 51937200, 40635792, -58523448, 184890816, -538537298, -236057448, 0, -42409384, 285479958, -293717664, -191887920, 4281984, -68844276, 0, 415979100, 7102080, -2177244, -670858752, 236053620, 135483840, 0, -92744136, -649736284, 14784000, 203212638, -633009672, -24661416, 0, 472130378, 151829340, 415960758, -8635968, 525587346, 147622500, 0, -407528640, -35012736, 268728156, -742361376, 47704896, 220393952, 0, -211882392, -409413312, -31532382, -129185280, -31318560, -36128448, 0, 552341376, -53948736, -13468032, -222467792, -874655712, 83422359, 0, -47260788, 83029320, 275496232, -364049784, -66213612, -23109588, 0, -35643384, -458856864, -573271152, -1503252, -576099680, -702402930, 0, -637663136, -57307128, -187701048, -439022664, -152983608, -237452040, 0, -546533940, -39721752, -75030176, 615081342, 16019208, -29183760, 0, -412336980, 492940800, 114210000, 2125764, -85776086, -505089096, 0, -41438880, 143713920, -331067952, -52827200, -34024032, 159633342, 0, 608583216, -406485792, 663391692, 33799464, 9858942, 47109064, 0, -171400536, 3623688, 165322752, 477580536, 40125096, 212865924, 0, -144381636, -683056416, 44954514, 178375680, 14678400, -66738168, 0, 52041408, 473235480, 335168856, 386742840, 93486960, -741865898, 0, 32996484, 23557904, 398119602, -220898664, -260063784, -16426560, 0, -515085948, 99758100, 12770208, -32344596, 782999112, 72908640, 0, -431811270, 14801616, -752966876, -40190304, 441350352, -207535968, 0, 57024000, 867632788, 496571628, -17507988, 2526192, 944776704, 0, 76586776, 286213872, -47467728, -543903876, -246481872, -26714448, 0, 19293120, 27491526, -565100928, 282425700, -532167624, -25679952, 0, -15812010, -639901224, 732623784, -56373408], "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": "3.6.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], [1], [-6], [-9], [4], [-6], [54], [0], [168], [81], [36], [-564], [-36], [-638], [0], [54], [-1136], [-882], [-486], [556], [-24], [0], [3384], [-840], [-1512], [-3089], [3828], [-729], [0], [4638], [-324], [-4400], [1440], [5076], [5292], [0], [324], [-2410], [-3336], [5742], [-1008], [6870], [0], [9644], [-2256], [-486], [5040], [18672], [10224], [0], [18534], [7938], [-2552], [33750], [4374], [3384], [0], [-5004], [-27828], [18084], [216], [-39758], [26400], [0], [27712], [3828], [-30456], [-23068], [-3528], [7560], [0], [-4248], [13608], [41110], [14460], [27801], [2224], [0], [-34452], [21920], [6816], [6561], [-41220], [-82452], [0], [5292], [-57864], [-41742], [-94752], [94086], [2916], [0], [-3360], [39600], [-112032], [-3336], [-12960], [-49442], [0], [-45684], [-12356]]}