{'Lhash': '1666173898215897411385711715702', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.0, -2.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 5.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.388032161702434, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '800.143', 'coefficient_field': 'CDF', 'conductor': 800, 'conductor_radical': 10, 'conjugate': '926724231546753200329925523140', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.0, 2.0], [0, 3.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0, 7.0]], [[1.0, 0], [-6.0, 0], [11.0, 0]], [[1.0, 0], [0, 0], [0, -13.0]], [[1.0, 0], [-4.0, 4.0], [0, -17.0]], [[1.0, 0], [0, 2.0], [-19.0, 0]], [[1.0, 0], [0, 0], [0, -23.0]], [[1.0, 0], [0, 0], [29.0, 0]], [[1.0, 0], [0, 0], [-31.0, 0]], [[1.0, 0], [0, 0], [0, 37.0]], [[1.0, 0], [6.0, 0], [41.0, 0]], [[1.0, 0], [6.0, 6.0], [0, 43.0]], [[1.0, 0], [0, 0], [0, 47.0]], [[1.0, 0], [0, 0], [0, -53.0]], [[1.0, 0], [0, 6.0], [-59.0, 0]], [[1.0, 0], [0, 0], [-61.0, 0]], [[1.0, 0], [-6.0, 6.0], [0, -67.0]], [[1.0, 0], [0, 0], [-71.0, 0]], [[1.0, 0], [-12.0, -12.0], [0, 73.0]], [[1.0, 0], [0, 0], [79.0, 0]], [[1.0, 0], [2.0, 2.0], [0, 83.0]], [[1.0, 0], [0, 18.0], [-89.0, 0]], [[1.0, 0], [-12.0, 12.0], [0, -97.0]], [[1.0, 0], [0, 0], [-101.0, 0]], [[1.0, 0], [0, 0], [0, -103.0]], [[1.0, 0], [14.0, -14.0], [0, -107.0]], [[1.0, 0], [0, 0], [109.0, 0]], [[1.0, 0], [8.0, 8.0], [0, 113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 14613778, 'index': 8, 'label': '2-800-40.3-c1-0-8', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/800/2/o/a/143/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.0653764295998929, 1.1948881407931726, 1.3077665891675094, 1.3977455381359447, 1.4544004213707675, 1.4638214484087368, 1.4099474035620643, 1.2763437401897868, 1.0482516396963117, 0.7147639728379934, 0.27097366221576175, -0.2800972281667609, -0.9260185120911638, -1.6441734343133463, -2.401916655624232, -3.157848270232148, -3.864284317523677, -4.470867966392047, -4.929104771547266, -5.197439303629211, -5.246343265126859, -5.062783518941304, -4.653407477624561, -4.045842378444177, -3.2876630868698564, -2.4428350849689857, -1.585763787148152, -0.7934408014000965, -0.13652177380486705, 0.32955835475356327, 0.5721842729769339, 0.5866552796245321, 0.39778418702312224, 0.05742325736395182, -0.3620951110269845, -0.7779733740096457, -1.1091678669016256, -1.2890667022887794, -1.2766192029522512, -1.063955916153008, -0.6789266600657861, -0.18169122396401213, 0.34456106362594907, 0.8076495841900406, 1.123128101933302, 1.2309348047871258, 1.1089350213181648, 0.7805812568452926, 0.31471140136713227, -0.18324358545701622, -0.58784942320122, -0.7757267575372976, -0.649489875420705, -0.15926693668576622, 0.6824639473803973, 1.7961383168999854, 3.0422969778073914, 4.240443637366306, 5.197071608930778, 5.738407422509687, 5.742154999867963, 5.16226381567173, 4.041628421894872, 2.5095761929150435, 0.7637123476643365, -0.9613191968671511, -2.4329173857923747, -3.4603974172247254, -3.9281021429734104, -3.8151910779613023, -3.1979268229463056, -2.233634156258355, -1.1291897944327522, -0.10014939342024387, 0.6712839037246571, 1.070808780284885, 1.0718541236306194, 0.736467663409436, 0.19709059417802313, -0.3767445461797545, -0.8193194768506606, -1.007921639909229, -0.8912435823955541, -0.5002693672475134, 0.06106031071797409, 0.6433227726368536, 1.0906895422538547, 1.2820323374790796, 1.163681365785546, 0.7651859008910356, 0.19338843304468914, -0.3945495249180223, -0.8330976352249229, -0.995028029864038, -0.8307487829265024, -0.38941185208386075, 0.18506390344982834, 0.6838779032993014, 0.8833330438452106, 0.6035388406228304, -0.23857835101473807, -1.595921011437205, -3.287458599078299, -5.027196113676951, -6.481004028377888, -7.3391906541653364, -7.38809036552029, -6.563289645863237, -4.970788423111158, -2.8696763034171515, -0.6191088562669577, 1.3987605834006582, 2.8619777223117513, 3.578244074058129, 3.5237697743720755, 2.8420061727375465, 1.8026621871856499, 0.7313973500190933, -0.07195850982041362, -0.4058908517997503, -0.21209846361834586, 0.41818666495992624, 1.2771987965082185, 2.1032228333479255, 2.655169668553301, 2.7784878271421154, 2.4443941683636132, 1.7520705009452788, 0.8940661707605746, 0.09569882728949806, -0.45326530396604636, -0.6541534905976002, -0.5254435132438994, -0.19142918406484527, 0.16309551303371236, 0.3582011173761764, 0.28375300068384685, -0.057055445940636364, -0.5405818615639857, -0.956229215637901, -1.0721741121546067, -0.714350420972966, 0.16557650180059497, 1.4556150973317803, 2.8957433758549267, 4.1371164880332225, 4.833934364983065, 4.742932795758384, 3.8015922929124146, 2.160717250033479, 0.15907421889075968, -1.7559425804411173, -3.1417774273491137, -3.677729215614507, -3.2527128551141233, -1.9982301156596858, -0.25595314846389633, 1.512236628301733, 2.8473151842858733, 3.4150405750485597, 3.092511009755166, 1.9951550627776538, 0.4371477454888493, -1.1624266268756005, -2.3996467291008727, -2.996715662146856, -2.8717503578626395, -2.1482518187629442, -1.1036974471784473, -0.07522239249159558, 0.6469286373261913, 0.9045469793649482, 0.7092701230160738, 0.2229747565919994, -0.31044669041136486, -0.6573396435397832, -0.678455115111455, -0.37613866411226415, 0.11140279948245416, 0.5662936652932926, 0.7774740349837099, 0.6263361516651401, 0.1400174283812878, -0.5085090594608104, -1.0561326881743895, -1.243830240562475, -0.9175340755211828, -0.09962050981557864, 0.9967897911834547, 2.0202339245778744, 2.586962830330315, 2.408282338321154, 1.397468298352444, -0.28117035396774037, -2.2413938251338426, -3.977825765653856, -5.013454071447242, -5.046791509252888, -4.051711121850799, -2.2963312445281656, -0.27211468961630375, 1.4472179862130174, 2.374501877652134, 2.2535493107430296, 1.1340444847724198, -0.6465849640034105, -2.568391158905619, -4.087637931420336, -4.798649038418541, -4.5479904751416536, -3.4663656224785138, -1.910914869678331, -0.339924055920481, 0.836566436127078, 1.380251119687949, 1.2826387388902114, 0.7418883778360323, 0.07107921439001486, -0.4260463965286564, -0.5657335048766275, -0.3416999845867693, 0.08940385512464422, 0.48620004919203, 0.6323003942177539, 0.43375966559515367, -0.03464240720808589, -0.5535378415660588, -0.845523816925611, -0.6914290577992308, -0.030823717804274453, 0.9943803437268524, 2.074105797958832, 2.8338033611992377, 2.9721140677479334, 2.3818668917930093, 1.2070932402070012, -0.18996858830507918, -1.3457627079168761, -1.8585267857337082, -1.5406767592331558, -0.5041681170089899, 0.8562392517679605, 1.9819381835135017, 2.3352146326225807, 1.588282288188977, -0.24900036241608733, -2.809370791069005, -5.467009438868705, -7.524967988167331, -8.430101216135176, -7.9441447239554295, -6.213996236337851, -3.718530023934605, -1.1114247953052687, 0.9853593404183864, 2.1670814881393166, 2.3494619863194193], 'positive_zeros': ['1.31437944960221481870748300332702', '3.53134546627626128718760516225785', '4.14300174892925885753815429607148', '5.16783668080927167766382205172536', '6.07799681313080001687520879052288', '6.65291589380958311300919344950497', '8.054130074138071708319466951204520', '9.138740062090640023502522260446141', '9.791874234471254702659467099494970', '10.48722080064354338540539401990415'], 'prelabel': '2-800-40.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.527455669582047, 'root_angle': 0.2868959044126083, 'root_number': '-0.22975292054736113 + 0.9732489894677302*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.286895904413', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.31437944960221481870748300333', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.53134546627626128718760516226', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.14300174892925885753815429607', 'prec': 100}}