{'Lhash': '1611306520971534587019003578006', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0662554376171682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]]], 'bad_primes': [2, 3], 'central_character': '384.1', 'coefficient_field': '1.1.1.1', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 0, 5], [1, -2, 7], [1, 4, 11], [1, -6, 13], [1, -6, 17], [1, 0, 19], [1, -4, 23], [1, -4, 29], [1, -10, 31], [1, -2, 37], [1, 2, 41], [1, -8, 43], [1, 12, 47], [1, 12, 53], [1, 4, 59], [1, -2, 61], [1, -4, 67], [1, 4, 71], [1, 10, 73], [1, 6, 79], [1, -12, 83], [1, -2, 89], [1, 6, 97], [1, -4, 101], [1, 10, 103], [1, 12, 107], [1, 2, 109], [1, 14, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, 0, 5], 1]], [[[1, -2, 7], 1]], [[[1, 4, 11], 1]], [[[1, -6, 13], 1]], [[[1, -6, 17], 1]], [[[1, 0, 19], 1]], [[[1, -4, 23], 1]], [[[1, -4, 29], 1]], [[[1, -10, 31], 1]], [[[1, -2, 37], 1]], [[[1, 2, 41], 1]], [[[1, -8, 43], 1]], [[[1, 12, 47], 1]], [[[1, 12, 53], 1]], [[[1, 4, 59], 1]], [[[1, -2, 61], 1]], [[[1, -4, 67], 1]], [[[1, 4, 71], 1]], [[[1, 10, 73], 1]], [[[1, 6, 79], 1]], [[[1, -12, 83], 1]], [[[1, -2, 89], 1]], [[[1, 6, 97], 1]], [[[1, -4, 101], 1]], [[[1, 10, 103], 1]], [[[1, 12, 107], 1]], [[[1, 2, 109], 1]], [[[1, 14, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 10137048, 'index': 1, 'label': '2-384-1.1-c1-0-1', '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/384/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2654142526979342, 1.2615885332249523, 1.2484838397919873, 1.2214982147925961, 1.1738098016107053, 1.0974048853036018, 0.9841867839341808, 0.8270520936307495, 0.6208922065875925, 0.36350486262163995, 0.05639025962821925, -0.2946189617651861, -0.6789673175655414, -1.0813102999972757, -1.4818530082438877, -1.8571541162038399, -2.181420434329293, -2.4282690780259513, -2.572876836702835, -2.5943752354880862, -2.4782920384204297, -2.2187936895659672, -1.8204568556416574, -1.2992984786374029, -0.682828224711646, -0.008957335624149652, 0.6762982456739989, 1.3222518670564387, 1.8779030000924848, 2.296858399601368, 2.542335620225225, 2.591684402397689, 2.4398380658884107, 2.101156056176681, 1.609245575730231, 1.0145501150848355, 0.3797497720206737, -0.2266942556076938, -0.7382362319412472, -1.0983319357233496, -1.267911601596196, -1.2312055777831776, -0.9989975153853383, -0.6086327000878204, -0.12048788869922292, 0.3889256712376112, 0.8365604827560477, 1.1440145484731703, 1.2488415236384787, 1.1143765681409366, 0.7365324891437337, 0.14632844177950297, -0.5925591157065009, -1.3912444255082115, -2.14734072121536, -2.75947229472105, -3.1425769113602833, -3.2416950549699814, -3.0419929051559547, -2.5731822082269566, -1.9072494521368037, -1.1493970149851787, -0.4231883189274211, 0.1480953542703831, 0.46111401763125065, 0.4500090840137572, 0.09882483999495086, -0.5535362853033022, -1.4170736236644088, -2.363021634946507, -3.243151749846718, -3.9131527805233874, -4.25633336837601, -4.203625882754811, -3.746299697617306, -2.9388839055328186, -1.8914026861808315, -0.7518826466493667, 0.31812333764272444, 1.1708707686574362, 1.6977972719738053, 1.8482790509971818, 1.6381539692345357, 1.1461663359508942, 0.49869377340459137, -0.15464386719263526, -0.6700515739709864, -0.9377967074798464, -0.904077043394167, -0.5820355628562348, -0.04943227877159101, 0.566935196194285, 1.1172919045405736, 1.4604187783970166, 1.494334658800593, 1.1797256235302171, 0.5509619474335642, -0.28808578878518715, -1.1831558568277354, -1.9602040283701367, -2.4615087466223198, -2.57984034299757, -2.2833424488171676, -1.6254243829117676, -0.7369102964480201, 0.1986334474831591, 0.9818225671799782, 1.4392294414037532, 1.4612466431054147, 1.027756248972164, 0.21562076707549843, -0.8142870621463378, -1.8484432397945105, -2.6642691739288753, -3.0769259427910622, -2.979258032866208, -2.366013917710149, -1.3366560438654542, -0.0756335653092102, 1.1860450107199667, 2.2198403478771005, 2.8486442329295563, 2.984775060217559, 2.64834408416712, 1.9616044882943173, 1.1202880893352467, 0.3482315118527938, -0.15444039322967013, -0.2576381931980566, 0.06870793116099613, 0.7481816613077286, 1.6166601183481677, 2.4620868792377637, 3.0758927466064225, 3.3037656312646897, 3.0834324270527893, 2.460081813439491, 1.575385464556703, 0.6325223901587284, -0.15438399592024235, -0.6139474105360809, -0.6608064541468538, -0.3173300802233228, 0.2922367581392352, 0.9742908679607092, 1.5173057616209493, 1.7493527739978663, 1.5869121797991705, 1.0619411612914036, 0.3193349039629589, -0.41571285345732195, -0.8931875104550313, -0.9031458835266685, -0.3336752160849772, 0.7932484718039122, 2.318046228914912, 3.9741294146794264, 5.446269177422358, 6.442923009727028, 6.764747323625597, 6.35203423002247, 5.298779318861624, 3.8293490142055377, 2.243208285539953, 0.8414470839598014, -0.14628721935297864, -0.6157387274722071, -0.6089498521822624, -0.29672356504642394, 0.07269267668131293, 0.24506658597185407, 0.03269576194528212, -0.631525956261935, -1.6731710293948678, -2.8943037268303624, -4.025765401375236, -4.799630656676569, -5.022097633908257, -4.626778324859533, -3.6935789594966497, -2.4277526538410874, -1.1047275531565182, 0.004082494333678033, 0.7038051749806501, 0.926566434059613, 0.7455125419343833, 0.3482491079257481, -0.022885123865239224, -0.14664592367930793, 0.10717587613334825, 0.7343744605331699, 1.5928616027734086, 2.441101572147622, 3.0082182358398732, 3.0759821636631703, 2.548825422132904, 1.4908037773426572, 0.1174173080989736, -1.2570242811434877, -2.302850092575986, -2.76627295868401, -2.542443231158998, -1.7088007764324886, -0.50804229692485, 0.7157758009957301, 1.6109379657213792, 1.9155823715045248, 1.5314172764346716, 0.5523582613079269, -0.7606014263931823, -2.0516575659311864, -2.9693453936749865, -3.2643977708296292, -2.858318037146586, -1.8630220685259762, -0.5460651352800079, 0.7481652275706827, 1.6980146754482508, 2.095543381496731, 1.9022101363240596, 1.2531576009640915, 0.40946679149910864, -0.3265521130126321, -0.7067921264402839, -0.6140535879292108, -0.09636963562950439, 0.651582883386259, 1.3540644430734072, 1.746177118763221, 1.6629898350700238, 1.0973714856364916, 0.20757490220718844, -0.7287191726608006, -1.4002328169037193, -1.5611994951938326, -1.112399261953287, -0.1378540243198038, 1.1155663856325562, 2.3105255996488854, 3.121862254034711, 3.3376601134309545, 2.926683453514794, 2.0500544765683495, 1.0122416667501737, 0.16558270943648012, -0.20235345993804293, 0.03686292773140959, 0.8068642312463395, 1.845223309332167, 2.782203522009854, 3.2560184036085826, 3.029021333016197, 2.0681896538920395, 0.5637874080820534, -1.1209341332597031, -2.554580989221719, -3.3652489682055933], 'positive_zeros': ['1.27109672072212401682622254955146', '3.12662782741322079682173901719503', '4.57667813854686016923499181308418', '5.52928834758807112839354938677360', '6.40139715881748782453956361829362', '7.83756825226352882885863464518527', '8.272861522300808832842531458006846', '9.710853337608498914769336043467873', '10.59394573181229341824784268537678', '11.26026602445558485918915487569685'], 'prelabel': '2-384-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.7510726534376488, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 251377476746839428, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27109672072212401682622254955', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.12662782741322079682173901720', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.57667813854686016923499181308', 'prec': 103}}