{'Lhash': '1735350315403681810924872574466,2013662148258534736479250283761', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.1594021675740025, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '800.1', 'coefficient_field': '1.1.1.1', 'conductor': 640000, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1], [1, 0, 0, 0, 1], [1], [1, 0, 0, 0, 1], [1, 0, 2, 0, 1], [1, -2, 2, -2, 1], [1, -2, 2, -2, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 2, 2, 2, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [1, 2, 2, 2, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 0, 2, 0, 1], [1, 2, 2, 2, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 2, 2, 2, 1], [1, 4, 6, 4, 1], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [1, 0, 2, 0, 1], [1, -2, 2, -2, 1]], 'euler_factors_factorization': [[1], [[[1, 0, 0, 0, 1], 1]], [1], [[[1, 0, 0, 0, 1], 1]], [[[1, 0, 1], 2]], [[[1, -1], 2], [[1, 0, 1], 1]], [[[1, -1], 2], [[1, 0, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 0, 0, 0, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 0, 1], 2]], [[[1, 1], 2], [[1, 0, 1], 1]], [[[1, 0, 1], 2]], [[[1, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 1], 1]], [[[1, 1], 2], [[1, 0, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 0, 1], 2]], [[[1, 0, 0, 0, 1], 1]], [[[1, 0, 1], 2]], [[[1, 1], 2], [[1, 0, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 0, 0, 0, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 1], 2], [[1, 0, 1], 1]], [[[1, 1], 4]], [[[1, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 1], 1]], [[[1, 0, 1], 2]], [[[1, -1], 2], [[1, 0, 1], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'id': 19446200, 'index': 3, 'label': '4-800e2-1.1-c0e2-0-3', 'leading_term': '1.03625716613014687145467568837032543989417155543015357570584576000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/800/1/p/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 24}, 'plot_values': [1.0362571661301467, 1.04057861177344, 1.048800385387114, 1.0640112941534396, 1.0857645115654806, 1.112924103460382, 1.1451604424809934, 1.18227019734121, 1.223700718594729, 1.268786474131257, 1.3168503306606756, 1.3671638126651593, 1.4189151518963277, 1.4712273722104428, 1.5231825987642595, 1.573814519115679, 1.6221296015231441, 1.667103395204208, 1.7077109591397028, 1.7429223047022786, 1.7717364503273385, 1.793178442521284, 1.8063376826932214, 1.8103652418258278, 1.8045158605560807, 1.7881441800038178, 1.7607500134101712, 1.7219714996625652, 1.6716326383638076, 1.6097312887349398, 1.5364873557972107, 1.4523236554951615, 1.3579124884290836, 1.254147737903184, 1.1421870327140693, 1.0234140011917567, 0.8994728965731033, 0.7722206831133114, 0.6437509683774938, 0.5163365103615808, 0.39243963727391457, 0.2746467820898838, 0.1656633106548792, 0.06824273377266891, -0.014834990552586535, -0.08083594689495459, -0.12710991437642816, -0.1511601554589127, -0.15069467629104735, -0.12368843917976907, -0.06844398335633352, 0.016358861461973878, 0.1315990899662053, 0.27768175686816154, 0.45447850691554476, 0.6613151608480743, 0.8969254379734146, 1.1594606630293354, 1.4464658647520463, 1.7549112220851155, 2.0811992708087885, 2.4212151656539116, 2.7703723216704543, 3.1236758402791205, 3.4758115489824735, 3.821214289288989, 4.154202104340324, 4.469038822801122, 4.760111302875079, 5.021974190666321, 5.249563995121018, 5.438213351961205, 5.583891699809959, 5.683177078713688, 5.733509776468002, 5.733111767563645, 5.681237374274679, 5.578033902192136, 5.4247725277387016, 5.223648341584973, 4.977975626926102, 4.69193104212837, 4.3707003092612515, 4.020174154051112, 3.647038079352355, 3.2584363128958302, 2.8620024537317703, 2.4655113704307507, 2.0768555074506527, 1.703707753740157, 1.353455318222045, 1.0328974753232725, 0.7481552854541201, 0.504426431646888, 0.30589377658352906, 0.15555511094385363, 0.055155808488432316, 0.00510441052316893, 0.004453891699513025, 0.05090514625552253, 0.14085736594735035, 0.26949153137166965, 0.4309032931799194, 0.618248614374508, 0.8239629386107095, 1.0399424214697162, 1.257842079925019, 1.469259824186586, 1.6660950500275091, 1.8406999892723257, 1.9862703504703645, 2.0969300502169297, 2.1681185344341727, 2.196580952365719, 2.1807139806589757, 2.120443597777259, 2.0174934299073484, 1.8751455188978683, 1.6984026467469977, 1.4936423731042288, 1.2686569918381478, 1.0322257649331543, 0.7940319083034022, 0.5641903220365675, 0.3530584425219802, 0.17076492668765633, 0.026948051661196633, -0.0696667857601651, -0.11155363917074516, -0.09271605912832977, -0.00894265001680602, 0.14198812267583694, 0.36014085398852763, 0.6433598898606283, 0.9872417951377912, 1.3852094803023642, 1.828661216115464, 2.3071566456747594, 2.808758966582127, 3.3202876670685724, 3.8278462222179965, 4.31708172433681, 4.773865482338618, 5.184492603018142, 5.536460835798632, 5.818545326019867, 6.0216053713015265, 6.138481492392277, 6.164753244454069, 6.098426482685045, 5.940569613794724, 5.694786095500746, 5.367671608367509, 4.968096854373372, 4.5074524967004255, 3.9987959039753056, 3.4568812057962224, 2.8972463214333786, 2.336057783018549, 1.7892272970950234, 1.2721301735287183, 0.798841116043274, 0.3818063932698054, 0.03127560353308033, -0.24498269739758458, -0.4420017615297642, -0.5577721889049322, -0.5932981496674884, -0.55255705004875, -0.442312925956115, -0.2718433023276732, -0.052568785570796306, 0.20245224073953003, 0.4789889576799986, 0.7623357331371741, 1.0377663460770816, 1.2913497414789146, 1.5102860034774996, 1.6837426720285738, 1.802981369439723, 1.8621092948839382, 1.8579368091991197, 1.7905487350658522, 1.6628755385149605, 1.4810162249367305, 1.2535524897507624, 0.9915956249347241, 0.7079164821602275, 0.4167366206091551, 0.13277958017169242, -0.12912642379965586, -0.35495471165992226, -0.5319605704476412, -0.6494285284553499, -0.6991088621087834, -0.6757149642382845, -0.5771882729260457, -0.40489743561131497, -0.16362588846004092, 0.13852227671241585, 0.49047604377723414, 0.8785252014925183, 1.2870238943545316, 1.6988456042369895, 2.096385055793359, 2.4620044493442186, 2.779228246646177, 3.0330382525523123, 3.211117792234041, 3.303872502488159, 3.305566104589132, 3.213986560372784, 3.0313288848363533, 2.76348608302662, 2.420574255060675, 2.015894400834692, 1.5660555430688015, 1.0897151673055836, 0.6073271992052542, 0.13981389150636897, -0.2919652824174339, -0.6684382796727402, -0.971980096350934, -1.1878734765740357, -1.304917359944729, -1.3160048597723173, -1.2185037504317666, -1.0143985070995973, -0.710301668066338, -0.3171851080485481, 0.150055800551287, 0.6731794117008036, 1.2314791370525124, 1.802505639732268, 2.3633098891594613, 2.891113650850322, 3.3647616465832124, 3.7651461492454636, 4.076673606745413, 4.2872883239660595, 4.389752717116376, 4.381184996132259, 4.263984277886451, 4.044885741945467, 3.7354272009011757, 3.3506161152424903, 2.9089212197562038, 2.4307216077455243, 1.9378992411567688, 1.452285808960301, 0.9950113294462336, 0.5851697177369614, 0.2391290143336186, -0.030400854234258232, -0.21488041257442866, -0.31036140851497046, -0.3176390190644131, -0.24214939969632124, -0.09365021405766147, 0.11431457831577359, 0.36522153450579026, 0.6403585698863584, 0.9200330771662524, 1.1843879891191171, 1.4148384943546557, 1.5946747544491904, 1.7105014305153634, 1.752428394126889, 1.7152801354189164, 1.598256980693405, 1.4057234937813599, 1.1463296171124184, 0.8332714869735468, 0.4829731367611724, 0.11482363637915202, -0.2503875301063783, -0.5911387022832216, -0.8867401148814958, -1.1181949770672692, -1.2695135945102485, -1.3285014757035394, -1.2876249816675909, -1.1444613298526363, -0.9020124176603597, -0.5686083368605546, -0.15768658910993952, 0.31295621771726573, 0.8217816165228257, 1.3448853632975997, 1.8567778112090896, 2.332234480004229, 2.746958341289923, 3.079649889635231, 3.3122817634860446, 3.432081793894161, 3.431221365912793, 3.308416218013973, 3.067947218029565, 2.7206574462350144, 2.282363995919962, 1.7741522397396203, 1.2203703809434687, 0.648267933348989, 0.08586188667089699, -0.43889449795929936, -0.9000463273544915, -1.2746501315433474, -1.5442119660736284, -1.695553164841925, -1.7215496108621238, -1.6215506541389109, -1.4013586186478701, -1.0729971353704035, -0.6540283271740068, -0.16660920363178425, 0.36361468666077973, 0.9090676062417264, 1.4414417980082337, 1.9336336268050702, 2.360679053457, 2.7017413625345945, 2.9404835393538074, 3.066763899895635, 3.0762658948427095, 2.971617917737113, 2.7612634748449105, 2.4598471300345537, 2.0864765477742093, 1.6643809509147809, 1.2188535754945318, 0.776355590887565, 0.3625014191170336, 0.0009117013940288446, -0.2884033652964869, -0.4900746337101899, -0.5943260806652373, -0.5975409907712059, -0.5024342043525867, -0.3179060156749993, -0.05850002137085045, 0.2565435149299592, 0.6043098473464257, 0.9598617742989363, 1.2973896804936589, 1.5923089218584332, 1.8221474171529692, 1.968721107183223, 2.0184210450312334, 1.964076738815237, 1.8044371707803122, 1.5454008572094349, 1.1986686611739337, 0.7821664296179714, 0.31803980046783237, -0.16771251725029224, -0.6475757799544832, -1.0934643512065823, -1.4789826971290878, -1.7805904601526163, -1.9793932717937948, -2.0621035415947757, -2.0220751849218894, -1.85967002742295, -1.582429675470165, -1.2045860218495767, -0.7464722418642975, -0.23311073595005244, 0.30684592733550065, 0.8433001265006924, 1.345824689104165, 1.7862854254683904, 2.1395742116627545, 2.3862227480587803, 2.5123953940081583, 2.512041507918193, 2.3859607526045155, 2.1431431060027597, 1.7989404077676647, 1.3754309675546286, 0.8989502633187928, 0.39954741678862515, -0.09170825079429665, -0.5438938369954577, -0.9286667074050692, -1.2216173534735837, -1.4040085467895977, -1.4638302423601053, -1.3965643430338999, -1.2055283533696708, -0.9016129089194335, -0.5026749527392806, -0.032439686902913926, 0.48105968218087186, 1.0070212561116325, 1.5141499894967647, 1.9721337878951568, 2.3542102683304513, 2.6380864905119754, 2.8082897773736084, 2.856170311654344, 2.7815717936732467, 2.5917790521363666, 2.3022054416316573, 1.934407289038436, 1.5157265966094078, 1.0767264142979778, 0.6499908151453351, 0.2674814475527591, -0.04108379573693532, -0.25043106845308055, -0.34123244887939147, -0.30145160460541504, -0.12719845887785194, 0.17697398533980527, 0.5982450818245557, 1.116201891013139, 1.7041847025139978, 2.330601321588726, 2.961301072715882, 3.561018340549715, 4.09638352601996, 4.536936683882676, 4.858229246535973, 5.041941522596172, 5.078510036532336, 4.966097278881431, 4.712302600409574, 4.332016570483528, 3.848008482537717, 3.287979675931424, 2.6841084488646274, 2.0698244235195196, 1.4786580601118966, 0.9413369408235965, 0.4844625785945151, 0.1284569007206504, -0.11337323374596817, -0.23571879333408857, -0.2413674371463677, -0.1408862271848682, 0.04833206999275149, 0.3033149976008994, 0.5974386545578172, 0.9020990485574016, 1.1892598521807758, 1.4329434051184615, 1.611857914096928, 1.710157999432721, 1.7195703874683277, 1.639074296812704, 1.4760626793136913, 1.244886316880141, 0.966837011236373, 0.6678087247453586, 0.37720620287571577, 0.1252189587564082, -0.05893993287077573, -0.14954218667947788, -0.1261668545973395, 0.024557539052311058, 0.3077260075078342, 0.719520276391952, 1.2471095200224243, 1.8691491135600975, 2.5570714711332605, 3.2764244662688293, 3.9894675669731505, 4.6567992412079136, 5.240839171690512, 5.70708222972446, 6.027814927648938, 6.182399533268779, 6.160506039685866, 5.961061067698128, 5.594396620401375, 5.0798368181159, 4.446443175577367, 3.729569531166947, 2.970249199159313, 2.211328840707801, 1.4958996238547957, 0.8637467506736181, 0.3494794846056489, -0.02003304474509761, -0.22709812731797382, -0.26435154284151924, -0.13514127479061003, 0.1467968956607615, 0.5583448080137351, 1.068483716371142, 1.6406516845985, 2.2347608183582426, 2.8105048914328155, 3.3291504831579304, 3.757137543866929, 4.066945230324263, 4.240249149385596, 4.267416955954487, 4.149616914567734, 3.8968570926396153, 3.528706540001678, 3.071239258292966, 2.5564877397939303, 2.0187685751377527, 1.4931173833614018, 1.0122537424052238, 0.6050579957115629, 0.2933887440074921, 0.09079420245877529, 0.0034416522179693807, 0.028006515958658613, 0.1495268972579865], 'positive_zeros': ['1.36895002068491677992741418240529', '1.58849934508451499306883648860043', '3.04004687598663522254644475154736', '3.05444402249148542367272708883178', '3.94475876647355079220750533822326', '4.06483515617659980911558398078529', '5.09689581356146083295485265420871', '5.35050401038494667986764952730944', '5.92165793282480784092446772764309', '6.20513009170500104962279076152946', '6.85352309348448355130523764018813', '7.17792146549312341326590544182491', '7.902183045738170981526358898506122', '8.077543216265555129976011944201211', '8.572212431423190890905315262017886', '8.917100478281945147692390632368891', '9.473674477475567967323353023604522', '9.822517529218652472810256623788522', '10.37508677141032781256638495774915', '10.59992151531658934819817186096703'], 'prelabel': '4-800e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.6318639173955116, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e2-0', 'trace_hash': 1662113613702498533, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36895002068491677992741418241', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.58849934508451499306883648860', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.04004687598663522254644475155', 'prec': 103}}
