{'Lhash': '2393345395356538328306752453422', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.5996764100727928, 1.038670010346586], 'a4': [0.0, 0.0], 'a5': [1.5615528128088303, 0.0], 'a6': [0.0, 0.0], 'a7': [1.536102794997064, -2.6606080865834745], 'a8': [0.0, 0.0], 'a9': [0.7807764064044151, -1.3523444052434932], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3217767240852654, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-3.342329219213245, -1.3523444052434932]]]], 'bad_primes': [2, 13], 'central_character': '416.289', 'coefficient_field': 'CDF', 'conductor': 416, 'conductor_radical': 26, 'conjugate': '1747496147729631685924476456198', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.5996764100727928, -1.038670010346586], [-1.5, 2.598076211353316]], [[1.0, 0], [-1.5615528128088303, 0], [5.0, 0]], [[1.0, 0], [-1.536102794997064, 2.6606080865834745], [-3.5, -6.06217782649107]], [[1.0, 0], [2.7354556151426497, 4.7379481072766465], [-5.5, 9.526279441628825]], [[1.0, 0], [-3.342329219213245, -1.3523444052434932]], [[1.0, 0], [-1.0615528128088303, 1.8386634067025478], [-8.5, -14.722431864335457]], [[1.0, 0], [3.6718820000669212, -6.359886183513535], [-9.5, -16.454482671904334]], [[1.0, 0], [-1.7990292302183786, -3.1160100310397585], [-11.5, 19.91858428704209]], [[1.0, 0], [-2.5, -4.330127018922194], [-14.5, 25.11473670974872]], [[1.0, 0], [6.670264050430886, 0], [31.0, 0]], [[1.0, 0], [-3.0615528128088303, -5.302765021840302], [-18.5, 32.04293994002423]], [[1.0, 0], [2.0615528128088303, 3.570714214271425], [-20.5, 35.50704155516198]], [[1.0, 0], [-0.3367499748514784, 0.5832680658903022], [-21.5, -37.239092362730865]], [[1.0, 0], [-0.525852870442629, 0], [47.0, 0]], [[1.0, 0], [-1.5615528128088303, 0], [53.0, 0]], [[1.0, 0], [5.134161255433821, -8.892628148662991], [-29.5, -51.09549882328188]], [[1.0, 0], [2.6231056256176606, -4.543352217189534], [-30.5, -52.827549630850754]], [[1.0, 0], [2.4725291799213354, 4.2825461628203625], [-33.5, 58.023702053557386]], [[1.0, 0], [-3.6718820000669212, 6.359886183513535], [-35.5, -61.48780366869514]], [[1.0, 0], [16.684658438426492, 0], [73.0, 0]], [[1.0, 0], [-15.739233741152942, 0], [79.0, 0]], [[1.0, 0], [-8.543116820279428, 0], [83.0, 0]], [[1.0, 0], [-0.8423292192132454, -1.4589570043771636], [-44.5, 77.07626093681505]], [[1.0, 0], [5.403882032022076, -9.359798237570782], [-48.5, -84.00446416709055]], [[1.0, 0], [4.06155281280883, 7.03481582940918], [-50.5, 87.4685657822283]], [[1.0, 0], [10.41596959012797, 0], [103.0, 0]], [[1.0, 0], [-2.4725291799213354, -4.2825461628203625], [-53.5, 92.66471820493493]], [[1.0, 0], [7.123105625617661, 0], [109.0, 0]], [[1.0, 0], [-4.18465843842649, 7.24804102767652], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 10285493, 'index': 9, 'label': '2-416-13.3-c1-0-9', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/416/2/i/g/289/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.8064182574958814, 1.837254400095543, 1.8675841033832399, 1.893448972101272, 1.9081744809327192, 1.903496572891096, 1.870792150244911, 1.8022664132879453, 1.692040066424964, 1.537118669193347, 1.3382201541699796, 1.1004103554345606, 0.8334715395425295, 0.5519168541799706, 0.27456882861748855, 0.023643434792197854, -0.17667845941072416, -0.30215605662516853, -0.33077016031908163, -0.24521502643913276, -0.03537342731401725, 0.2994982437107696, 0.7491699007291865, 1.291707382987489, 1.8938481402148284, 2.5126316897997842, 3.0983100622406425, 3.598413456220893, 3.9626847332849517, 4.148442719823607, 4.125810789570624, 3.882176110955896, 3.4252452227196435, 2.784145497220548, 2.0081920098243575, 1.1631858167917464, 0.32541038913749604, -0.4261859377866227, -1.018834570415117, -1.3948002846813896, -1.5191056849955984, -1.3850120583776606, -1.016326091011006, -0.46594034739746953, 0.18952156336166903, 0.8585497759854248, 1.446143121272679, 1.8663608978104045, 2.0543441588471865, 1.9760484036600099, 1.6341179582922345, 1.068778943804617, 0.3532899104406325, -0.4157155895675515, -1.1318456904288443, -1.694673065877032, -2.0252422859844246, -2.0789068428251314, -1.853297031108374, -1.3898585827963748, -0.7683509517363979, -0.0948205042198141, 0.515309059271717, 0.9564528040006718, 1.1512486039156091, 1.0649093849745472, 0.7128363242983068, 0.15979018240983645, -0.48970330936788653, -1.10850254575095, -1.568914857101213, -1.7659870929489603, -1.6378782430758292, -1.179442844093903, -0.44615678465184544, 0.4528821070956594, 1.3722033430695484, 2.154843013853649, 2.660654164872031, 2.792961417065555, 2.5184923880460266, 1.8765026962577211, 0.9748344216795963, -0.026988612191799186, -0.9450465898120514, -1.6039910300155402, -1.8696754109326603, -1.6752172971592583, -1.0352575298941131, -0.045259344190459835, 1.1345092974529938, 2.3076680819492386, 3.2778480127106886, 3.885347337433227, 4.037094825872769, 3.7238287716194614, 3.0208249074259714, 2.07177580906386, 1.0588905357302278, 0.16522421149154437, -0.46298264908740755, -0.7460018954965139, -0.6859244902073512, -0.3641095738248019, 0.07888121820423138, 0.4766652816531122, 0.6764844454653586, 0.5759222100823979, 0.14847842191514746, -0.5481251763859873, -1.3832764027419777, -2.182373164421747, -2.7670973344836045, -2.998007183089659, -2.809517056756281, -2.2287283749100046, -1.373019237194006, -0.4260794915814177, 0.402863602473925, 0.9277203150738407, 1.0309551274854258, 0.6948662977873934, 0.010707478990986981, -0.8374935851387499, -1.611735571500058, -2.0733384658555853, -2.038863057509604, -1.4256981803459332, -0.2762971541141047, 1.2453336567325517, 2.884987869716334, 4.351008828506125, 5.376777551248002, 5.778690103398804, 5.496117790382842, 4.603840722719076, 3.293821993090413, 1.8304581735676098, 0.48984763269814163, -0.5024337197096639, -1.0201015174749353, -1.0597528304839159, -0.7337334512685717, -0.23438763350231764, 0.2209886858641988, 0.4502276171264139, 0.35577810407805477, -0.04937474834717418, -0.6462861149998473, -1.244089249879564, -1.6346271844967117, -1.6531645164558846, -1.228748203604683, -0.41020091363815947, 0.640049607149, 1.6836300240592796, 2.4661723365604438, 2.7840686507683454, 2.5402403321353746, 1.7735585613567073, 0.6531983480407673, -0.5615935431153133, -1.5864944969587573, -2.1850855526401793, -2.2304221637087633, -1.7383808718358478, -0.8631886736105284, 0.14442098929196281, 1.0057883485707921, 1.4914428987966715, 1.4857722781021387, 1.0211663235957804, 0.27151294417065597, -0.4941205268997767, -0.9857680187474066, -0.9749196853331974, -0.36231895783866136, 0.7879798187866851, 2.25862254659296, 3.7314317070117706, 4.868973165691364, 5.403512104280499, 5.20917609494676, 4.337329920846642, 3.004988434640879, 1.538909473210294, 0.2902767111194634, -0.4568567092481472, -0.5583291138176923, -0.04395037402474483, 0.8961945273505072, 1.968891922999853, 2.8618252497943732, 3.330371059648215, 3.262439608140637, 2.703175428213723, 1.8331808968779217, 0.907646539549183, 0.1753314352084383, -0.1977179480718822, -0.17632794563909504, 0.13855027939617037, 0.5490955552822464, 0.8321239398021694, 0.8202863536337163, 0.46685891710730953, -0.12749424016574076, -0.7362873676824854, -1.0725440999639602, -0.8793848474123489, -0.018658680231414277, 1.4702135416222581, 3.3611014422082506, 5.2873363065476084, 6.83224687798488, 7.6393042413962995, 7.510331175638828, 6.4627354999009095, 4.728029748763177, 2.690815340479634, 0.7849627065232105, -0.6233812924510354, -1.3320769971779138, -1.3505316817217305, -0.8848022854338762, -0.2651795917098285, 0.1615506045690445, 0.142315956864769, -0.40312635738712876, -1.3581753222304151, -2.447521522082229, -3.3252914950621895, -3.6855760243900133, -3.36077976694348, -2.3770586463513244, -0.9495725397128394, 0.5808027799886282, 1.8492279040989799, 2.574933051936252, 2.6414544249212444, 2.123977660921353, 1.2557388097721112, 0.34511086579383676, -0.3290283100332416, -0.6090060016379574, -0.5067588623068667, -0.1928332451102545, 0.0703724924039036, 0.02870647855715719, -0.46429445352917953, -1.383042799415002, -2.523960565177556, -3.5621538391922116, -4.153862437694011, -4.051880289453234, -3.195675994425995, -1.7450596544604005], 'positive_zeros': ['1.88801661508749921013684767836452', '2.51573433466867128932413780596820', '4.55165130598770223806425384933694', '5.46490284142844472566588320409326', '6.55747016909679500672543117618245', '7.64307195770352831188042693497816', '8.406585032564876468205785615368713', '9.313721966537304198844016705439262', '10.37159971198266096263764138228747', '11.13005317468900341295673218473969'], 'prelabel': '2-416-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.822574202628048, 'root_angle': 0.018504012351454654, 'root_number': '0.9932489348975145 + 0.11600238499683055*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0185040123515', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.88801661508749921013684767836', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51573433466867128932413780597', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.55165130598770223806425384934', 'prec': 103}}