{'Lhash': '615591202228370425989774887471,1062340948094630491019741559119', 'a10': 4, 'a2': -1, 'a3': 0, 'a4': 0, 'a5': -4, 'a6': 0, 'a7': 0, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 446.40997850821833, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1, 1]], [3, [1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '2646.1', 'coefficient_field': '1.1.1.1', 'conductor': 7001316, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1, 1, 1], [1], [1, 4, 14, 20, 25], [1], [1, 2, 23, 22, 121], [1, -6, 23, -78, 169], [1, 5, 8, 85, 289], [1, -7, 30, -133, 361], [1, 8, 62, 184, 529], [1, 4, -13, 116, 841], [1, -6, 5, -186, 961], [1, 2, -33, 74, 1369], [1, -3, -32, -123, 1681], [1, -1, -42, -43, 1849], [1, 0, -47, 0, 2209], [1, -12, 91, -636, 2809], [1, 7, -10, 413, 3481], [1, -12, 83, -732, 3721], [1, 13, 102, 871, 4489], [1, -16, 206, -1136, 5041], [1, 1, -72, 73, 5329], [1, -6, -43, -474, 6241], [1, -16, 173, -1328, 6889], [1, 6, -53, 534, 7921], [1, -5, -72, -485, 9409], [1, -8, 218, -808, 10201], [1, -28, 402, -2884, 10609], [1, -3, -98, -321, 11449], [1, -2, -105, -218, 11881], [1, 10, -13, 1130, 12769]], 'euler_factors_factorization': [[[[1, 1, 1], 1]], [1], [[[1, 2, 5], 2]], [1], [[[1, 1, 11], 2]], [[[1, -6, 23, -78, 169], 1]], [[[1, 5, 8, 85, 289], 1]], [[[1, -8, 19], 1], [[1, 1, 19], 1]], [[[1, 4, 23], 2]], [[[1, 4, -13, 116, 841], 1]], [[[1, -6, 5, -186, 961], 1]], [[[1, 2, -33, 74, 1369], 1]], [[[1, -3, -32, -123, 1681], 1]], [[[1, -1, -42, -43, 1849], 1]], [[[1, 0, -47, 0, 2209], 1]], [[[1, -12, 91, -636, 2809], 1]], [[[1, 7, -10, 413, 3481], 1]], [[[1, -12, 83, -732, 3721], 1]], [[[1, 13, 102, 871, 4489], 1]], [[[1, -8, 71], 2]], [[[1, 1, -72, 73, 5329], 1]], [[[1, -6, -43, -474, 6241], 1]], [[[1, -16, 173, -1328, 6889], 1]], [[[1, 6, -53, 534, 7921], 1]], [[[1, -19, 97], 1], [[1, 14, 97], 1]], [[[1, -4, 101], 2]], [[[1, -14, 103], 2]], [[[1, -3, -98, -321, 11449], 1]], [[[1, -19, 109], 1], [[1, 17, 109], 1]], [[[1, 10, -13, 1130, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'id': 23579106, 'index': 8, 'label': '4-2646e2-1.1-c1e2-0-8', 'leading_term': '0.867324832382919736773300726681809461848622915859220645170846035672470483128642092785737047', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2646/2/h/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 37}, 'plot_values': [0.8673248323829197, 0.8622073249329841, 0.851153340544429, 0.8310791735572121, 0.8027613122877391, 0.7671119497724992, 0.7242620010342908, 0.6745108319611918, 0.6184221866335314, 0.5566349792219087, 0.48986991834300225, 0.41897471515083046, 0.3449275857431022, 0.2688317957852987, 0.19192391255960278, 0.11556512405499501, 0.041243447315580294, -0.029441774899076362, -0.0947912072067814, -0.1530225353548625, -0.20230021429898817, -0.24075430952364743, -0.26652596738198886, -0.27779253752206357, -0.2728223940547477, -0.2500079224976256, -0.20792634313232156, -0.14537524860138765, -0.06143918094139789, 0.044480959784090536, 0.17259811130603897, 0.32272206884072013, 0.49419450044411606, 0.6858873391106033, 0.896152808919188, 1.1228405868295759, 1.363270741829715, 1.614274064385923, 1.8721941652783463, 2.1329519434676674, 2.392083830962097, 2.6448266107874923, 2.8861955379507873, 3.111086216087614, 3.3143860535840473, 3.4910932575928832, 3.6364473635029295, 3.7460596265064923, 3.8160546150671695, 3.843186315646754, 3.8249973578773564, 3.759881868201953, 3.6472663192173136, 3.487594620902436, 3.282506413114568, 3.034756757811988, 2.7483344770695046, 2.4283532697367556, 2.0810593228947405, 1.7137112763015607, 1.3344714005461054, 0.9522544846585814, 0.5765424014829182, 0.21716908780208025, -0.11589641979585893, -0.41282645524207096, -0.6641692117708147, -0.8611399158741012, -0.9958774060777329, -1.0616903754194407, -1.0533240589225998, -0.96712546273871, -0.8012774995577595, -0.5558730451218363, -0.23306422530114498, 0.16295750915966098, 0.6259364318524007, 1.1476664402169567, 1.7181144104448451, 2.325614579172827, 2.9571524003779888, 3.5986116423875623, 4.235208201737045, 4.851760748842174, 5.433233823747227, 5.96500080702703, 6.433444996586186, 6.826159031347573, 7.132573866964536, 7.34400559202332, 7.454299482847238, 7.459647987514687, 7.359208915172882, 7.154685585777312, 6.850827822198661, 6.454837087794825, 5.9766541492180485, 5.4282619880043015, 4.823733197012196, 4.178464749419665, 3.5090407163211204, 2.832414413861144, 2.165673537111569, 1.5252225077936807, 0.9265123457058481, 0.38332122634582216, -0.09250617797788402, -0.4915836307579725, -0.8071785174892615, -1.035485709077094, -1.1756946159035198, -1.2299932743467203, -1.203467576940007, -1.1038462520093466, -0.9412210732437873, -0.7275906805928143, -0.4764027581592902, -0.20200394725547147, 0.08096934672967904, 0.35812811201438705, 0.6159922370159864, 0.8424653682670264, 1.0273814949753959, 1.1629019212406637, 1.2438077064533402, 1.2677578731391546, 1.2353072051057403, 1.1498975910205278, 1.0176835529731072, 0.847167742683073, 0.6488996701539653, 0.4348113088135768, 0.21778713656369056, 0.010881793547065654, -0.17324635304502886, -0.3230437310339122, -0.42868101923719365, -0.48257990421968305, -0.47992188768401695, -0.41894492185576826, -0.30118532544590254, -0.13151310700933436, 0.08198289501077598, 0.3282269199477808, 0.5936535542371633, 0.8626548282458717, 1.118431328091035, 1.3435488521828556, 1.5210481241552551, 1.6349803381991062, 1.6716251377203326, 1.6198566429494665, 1.4723121166891937, 1.2254266667333862, 0.8804180500454256, 0.4428696481044747, -0.07659524948523097, -0.6631989886421178, -1.2977538666615445, -1.9579387829306605, -2.6184813175466894, -3.2527142552430472, -3.8330837897457393, -4.332849568086881, -4.726741912243102, -4.992586652390367, -5.111966854121257, -5.071478090953207, -4.863276094972603, -4.485734540843571, -3.943708069000334, -3.2485331099812793, -2.4178244879397077, -1.4748719607631775, -0.44793078894983773, 0.6309265278080625, 1.7268798814995465, 2.803927648139727, 3.8261586850673157, 4.759370659973059, 5.572524502707485, 6.238888199205852, 6.7376392840867165, 7.054185221559908, 7.1816179074206, 7.12027963453116, 6.878534729775256, 6.471900903662797, 5.922803860574271, 5.259433106341301, 4.5146258794592535, 3.7243927279987155, 2.9263999245715953, 2.158169526528806, 1.4555768903774626, 0.8510202807215004, 0.3721439893456764, 0.04040806151840599, -0.12979702340876056, -0.1318827903325241, 0.03264198526713664, 0.3542333695765622, 0.8157216755835311, 1.3931388416076909, 2.056793056740238, 2.772669120743542, 3.504076126316468, 4.213203495885399, 4.863234158818436, 5.419586604298538, 5.852193582307931, 6.13623359200206, 6.253953444256145, 6.195018271353794, 5.957275339130342, 5.546803137704638, 4.977485411794377, 4.270553140735121, 3.4533793712034444, 2.5582345449493973, 1.6208304479955644, 0.6784047017565177, -0.23174213798766843, -1.0742958147391202, -1.8173215736555954, -2.4338748285561915, -2.903124186153344, -3.2112555287229276, -3.351984764852083, -3.326743639052687, -3.1443661897482813, -2.8206118999768988, -2.3770742188918943, -1.8401766812449982, -1.2395002645907522, -0.6065578542938936, 0.027229933678951886, 0.6315809738817375, 1.1794351577839883, 1.6475123958015239, 2.018088060225924, 2.2789214079077498, 2.424422668572823, 2.4549060208554563, 2.3770591677551223, 2.2025537471243597, 1.947912566250118, 1.6326712116362023, 1.2788076687977517, 0.9088052506216003, 0.5448534144340014, 0.20718546966894302, -0.08668230409528267, -0.32306679917287684, -0.49257995315624303, -0.5905550702428182, -0.6170529626397246, -0.5765990344111371, -0.4776930967120356, -0.33204290205196735, -0.15362579044670086, 0.042267986189695614, 0.24023825538289478, 0.42565724011750494, 0.585769490134789, 0.7103798845661954, 0.7924647828484972, 0.8285751251186033, 0.8188051157215748, 0.7667566936981114, 0.6790127648973168, 0.5645555125715545, 0.4340009027914977, 0.29861534708260556, 0.16949094010680305, 0.05651852015026389, -0.03234351994781688, -0.09179756356020245, -0.11963620382466565, -0.11699793026080137, -0.08831159808767594, -0.041039465411813095, 0.014881751077194232, 0.06775305410179505, 0.10503387042979287, 0.11430226489643615, 0.08433518623239925, 0.005994000291668082, -0.12679428692639197, -0.316481253101234, -0.5613697335001767, -0.8554527816260519, -1.1886514004096873, -1.5470163169167088, -1.9137746657941022, -2.2698719238000113, -2.5955545842702854, -2.871176717926606, -3.078918185575739, -3.203601461563395, -3.2341981980934196, -3.1643098559526375, -2.9931552103895402, -2.725490945761063, -2.371800705040635, -1.9476504383626527, -1.4729486167631984, -0.9708820378490861, -0.4663767079425075, 0.015138714369435886, 0.44973872345038185, 0.8160443860696129, 1.097299649204748, 1.281816764185938, 1.364715937327868, 1.3475115837806142, 1.2391295368485857, 1.0546175688101957, 0.8152156077167625, 0.546363442664248, 0.2768900649405239, 0.03662435451833358, -0.14497223666286996, -0.24115721000338794, -0.22938671528748394, -0.09313908471265692, 0.17696376251649948, 0.5822377715707587, 1.1155885518485358, 1.761668633507201, 2.4974931958002693, 3.2936586590427117, 4.115797654816011, 4.926608023525461, 5.687870936430031, 6.362655072293273, 6.917687354917873, 7.324859765763087, 7.563699140737793, 7.62156448116062, 7.4956773126816465, 7.192034961067473, 6.7262669991294395, 6.12174109692205, 5.408909496918439, 4.623001677072279, 3.8022399512145144, 2.985347421792922, 2.2094277111657985, 1.507623632804727, 0.9073514361215091, 0.4286601803866861, 0.083230295864829, -0.12612976739229462, -0.20544800884556422, -0.16891753607332358, -0.03773625581465694, 0.16146483006481735, 0.39862835145126235, 0.6423388580023647, 0.8621121407391301, 1.0304048069929848, 1.1246535653959118, 1.1285493986945847, 1.0334614857469753, 0.8385049545816385, 0.5510282043873095, 0.18553120644280785, -0.23705856436276146, -0.6911330296269205, -1.1482445864365254, -1.579011362516457, -1.955480146153171, -2.2528000015236134, -2.451304740148895, -2.5375881061666243, -2.505696220596402, -2.3572874630954574, -2.1016400151381274, -1.7548647920300589, -1.3386728521355857, -0.8789884714136446, -0.403703904344788, 0.058778414117762884, 0.48224390679732887, 0.8436944647699547, 1.1257942356082997, 1.3170480042041097, 1.413448515768264, 1.4175363452803746, 1.338996983376399, 1.1926658841618378, 0.9980804407630894, 0.7768924234250004, 0.5516313813134119, 0.3431976056508188, 0.1693745559426363, 0.043010285025721885, -0.02904320152027062, -0.04665785959616329, -0.016512660341364907, 0.04838770169952636, 0.12984184738822105, 0.20590442584264793, 0.25309601435795465, 0.24826263747915983, 0.17138901112500848, 0.007141367478984186, -0.25242061962847756, -0.6073123926037522, -1.047698715566027, -1.5548696078104296, -2.100562639566153, -2.6495111520959624, -3.16020758444548, -3.588514837662786, -3.889735018568467, -4.022404125063942, -3.9510414946295764, -3.6492932069181996, -3.1022922603416325, -2.3085388466947987, -1.280890789081606, -0.0466785135016618, 1.3531036202122082, 2.8656442205587602, 4.428912415526547, 5.974878273315449, 7.433754771573161, 8.737276427128572, 9.82407472553752, 10.641844371663655, 11.152444191797484, 11.33270294654215, 11.177347114077135, 10.698588713474896, 9.925889846208278, 8.904471970172917, 7.691936290654855, 6.354639974460565, 4.965583561379577, 3.598530113715504, 2.3176119745271153, 1.1828596593251726], 'positive_zeros': ['0.48561583303596323392159799102746', '0.838039241967278125687629409221192', '1.86448457309065429023780747651972', '2.18582867691027681027792759570418', '3.09940198233352821221106510789067', '3.44865069292980736599652054521161', '3.89810385030482013172080098629756', '4.14951385249271210161872419793898', '4.56624098498399379404468894281251', '5.10993824603754659375049173356323', '5.77643839851255798247956702337752', '5.85529277817401938098218486610827', '6.49628179168409664082774137112351', '6.91278515068091232076092668254517', '7.37361004215331648845711461190867', '7.64026422292377683334903142509873', '8.074185992594133302064861435516284', '8.254029065573014026360465971435951', '8.409856516810259143372194725756839', '9.051773431572888299287554977646146'], 'prelabel': '4-2646e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.596565715273829, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 995985428000831252, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48561583303596323392159799103', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.838039241967278125687629409221', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.86448457309065429023780747652', 'prec': 103}}