{'Lhash': '1586996894349256882092062592976', 'a10': [0.0, 0.0], 'a2': [-1.3646639987427946, 1.9489421696772455], 'a3': [1.6309568474739453, 0.5830778350082003], 'a4': [-1.2520274646302376, -3.4399171876085988], 'a5': [0.0, 0.0], 'a6': [-3.362093074102329, 2.382935247065249], 'a7': [2.1975782508527004, -1.0247475677674809], 'a8': [3.8164981702949015, 1.0226276026453762], 'a9': [2.3200404766442997, 1.9019495752338154], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.389902136436429, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.6309568474739453, -0.5830778350082003]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '675.68', 'coefficient_field': 'CDF', 'conductor': 675, 'conductor_radical': 15, 'conjugate': '1607337374570752515884565789817', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3646639987427946, -1.9489421696772455], [-0.6840402866513374, -1.8793852415718169]], [[1.0, 0], [-1.6309568474739453, -0.5830778350082003]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.1975782508527004, 1.0247475677674809], [4.499513267805775, -5.362311101832846]], [[1.0, 0], [-0.002750557507510475, -0.0032779867912125843], [-1.9101299543362338, 10.832885283134289]], [[1.0, 0], [-1.1320608251625106, 0.7926775234906942], [4.446261863233693, -12.216004070216808]], [[1.0, 0], [1.9036228256580106, -0.5100741988285158], [14.722431864335457, -8.5]], [[1.0, 0], [-6.691818935474218, 3.8635234637642744], [9.5, -16.454482671904334]], [[1.0, 0], [-3.124271167183858, 6.70002113957426], [-14.784115022790404, -17.619022191736494]], [[1.0, 0], [-1.741095500685764, -9.874243259257366], [-27.251086002791343, 9.918584156444393]], [[1.0, 0], [5.62931818482493, -2.048904258489723], [23.747377736688318, -19.92641590028272]], [[1.0, 0], [-0.4512722396825267, -1.68417092654059], [-32.04293994002423, 18.5]], [[1.0, 0], [2.9519105389463527, 0.520501472653908], [38.527397452222246, 14.022825876352417]], [[1.0, 0], [-7.18901229096235, -0.6289570774077371], [42.34673337952495, 7.466871639678005]], [[1.0, 0], [-0.8713666474136381, -1.8686518056797594], [-30.211017655267348, 36.00408882659197]], [[1.0, 0], [-1.2531546674528966, 1.2531546674528966], [0, -53.0]], [[1.0, 0], [0.7633113560666055, 0.6404942773489181], [10.24524248234889, 58.10365742772028]], [[1.0, 0], [6.397448596923413, 2.3284808645282022], [46.728711030257664, 39.2100441908789]], [[1.0, 0], [5.219638255702793, 7.454415970796831], [-22.915349602819806, 62.95940559265586]], [[1.0, 0], [-8.325642062508248, -4.806811685965608], [35.5, 61.48780366869514]], [[1.0, 0], [0.7442039499961823, -2.777406952579201], [-63.21985447626402, -36.5]], [[1.0, 0], [6.959963437720179, -1.2272293388145077], [74.23571704208676, -27.01959132272783]], [[1.0, 0], [8.346395041143738, 5.844208724684986], [28.387671896030504, 77.9944875252304]], [[1.0, 0], [3.037852105419156, 5.261714192466063], [-44.5, 77.07626093681505]], [[1.0, 0], [1.098238421472311, -12.552922598330573], [-95.52635204218419, -16.843873233692243]], [[1.0, 0], [1.6764477302393974, -4.6060022837286985], [-77.37048875501678, -64.92154857834048]], [[1.0, 0], [-1.010125874985494, -11.545791583456763], [-101.43519856025743, 17.885762299693827]], [[1.0, 0], [3.318442660438472, 3.318442660438472], [0, 107.0]], [[1.0, 0], [0, 11.253808612024516], [-109.0, 0]], [[1.0, 0], [1.8776429134305856, -0.16427246907496418], [111.28327609037952, -19.62224407636313]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 12592481, 'index': 26, 'label': '2-675-135.68-c1-0-26', '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/675/2/ba/b/68/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3951562648028606, 1.3220204673808624, 1.2374849076218915, 1.1389258422989745, 1.0229528206757503, 0.8869989683992234, 0.7306304033717732, 0.5564225308715035, 0.3703564395054273, 0.18173213883942602, 0.0026060155210785533, -0.1532291404001262, -0.2716748837039, -0.3400746608668149, -0.3491250527242376, -0.2947380433894026, -0.1795945624363835, -0.01410775656013733, 0.1834709603632347, 0.38801148212641917, 0.5696339204229129, 0.6969645052027897, 0.741301380724517, 0.6812901750193253, 0.5075445985410325, 0.22653116160172573, -0.13700138308610796, -0.5397047150706762, -0.9219067542017024, -1.2126759283000472, -1.337495613470308, -1.2279497230338936, -0.8324093713640874, -0.12637578452747855, 0.8790566250702287, 2.132144233333279, 3.540128969383783, 4.97436717284098, 6.281074465140368, 7.297001389816912, 7.8685299445226295, 7.871967686229822, 7.232344220577761, 5.937894654579759, 4.047713712068353, 1.6907900086253151, -0.9442806771268513, -3.6282840071884737, -6.117095629187608, -8.180941095810677, -9.633242458743068, -10.35485273911195, -10.309900547838845, -9.550532418977983, -8.20942529421081, -6.480818129191134, -4.592679438249249, -2.7741619161605064, -1.2234044558187878, -0.08082490985410734, 0.5877607840652075, 0.7954602830025115, 0.6254813966929166, 0.2108984234281428, -0.29318871889679227, -0.7398876849085512, -1.017467576558004, -1.0679872829911397, -0.8941776435998231, -0.5534942856323246, -0.14085901313813498, 0.23605318266569125, 0.48354374942124917, 0.544737711284425, 0.41344627505783066, 0.13587240268033404, -0.20033082413726824, -0.4872689916260209, -0.6234796189556991, -0.5398598530579551, -0.21861336245088658, 0.29959184402411554, 0.9224456170694684, 1.5257349035566323, 1.9817816341674268, 2.190059258814044, 2.102617954612046, 1.7378376662122632, 1.1785435223586547, 0.5541463630086546, 0.010394631275623999, -0.3264011620235989, -0.38203229685882495, -0.15556193253074033, 0.2770167160331142, 0.7786271389600319, 1.1836591382751462, 1.3400018113138734, 1.1504375505000526, 0.6027263897529703, -0.22017383158523304, -1.1538642402626524, -1.9885356423859135, -2.5197514729083004, -2.6021151116698564, -2.1922941593288767, -1.3695259559841624, -0.3265230910236388, 0.6693439519485912, 1.337188934624983, 1.452458280461835, 0.9086173355608095, -0.24543552211660344, -1.8034739680507288, -3.4387841570320696, -4.773560369630839, -5.466182828265854, -5.296303619177268, -4.226904234503504, -2.4268357499423203, -0.24602124013515814, 1.8534321022529596, 3.396125916844286, 4.000281705035033, 3.467814785108662, 1.8358071053418266, -0.623870594992059, -3.458021890593068, -6.127266965259767, -8.121316962817588, -9.067775049095568, -8.809243470571863, -7.43109513684097, -5.234209474790514, -2.660299042315104, -0.1887989763182796, 1.769226366777067, 2.954719400944321, 3.302817402013766, 2.9357346217139884, 2.1113107517552923, 1.143309484956053, 0.3160211042439448, -0.18407664817881111, -0.3028035000121977, -0.11241446661136383, 0.22945463864092064, 0.5412169291094238, 0.6793518333848159, 0.5822484649238783, 0.28366533600922766, -0.10642379204383537, -0.4455190126430278, -0.6112647758084834, -0.5451784587065837, -0.27292721206368364, 0.10529210296454042, 0.45060470925603135, 0.634996397054358, 0.5872626890344987, 0.3191313205950753, -0.07810064855557497, -0.46601283288445694, -0.7099211594319736, -0.7304765868016156, -0.5371160218910331, -0.2297759631860395, 0.03433772486711892, 0.09987388156593552, -0.12078370054486302, -0.598345123258442, -1.174258313284376, -1.5947110939178661, -1.585671388962497, -0.9490313657252811, 0.34960885004972947, 2.1318515347180673, 4.017574914981425, 5.50100086596574, 6.076766860585851, 5.3839647984587575, 3.327374933004627, 0.13805883333975255, -3.649937106285962, -7.307380340506734, -10.078375872278707, -11.366896666957778, -10.891062465104524, -8.761588172854028, -5.46039767455009, -1.7226218873828356, 1.6476638343678607, 3.9785273920471287, 4.893429149098436, 4.392398054947803, 2.830149842048839, 0.7995142123370647, -1.0446403912045263, -2.1694512786210574, -2.303503860493074, -1.4935747354310687, -0.06605851337126542, 1.4908976430411176, 2.685482223458174, 3.170953660683022, 2.8404427224914612, 1.841833200475352, 0.5127525038469282, -0.7392418227628149, -1.5700407993696097, -1.8023592472979255, -1.467384172031529, -0.7747205229243204, -0.02487413158806242, 0.5029030314866556, 0.6476853394930615, 0.4159589854309301, -0.032312441276529644, -0.4531208558449335, -0.6164689007333979, -0.3966861721487872, 0.17780729674689086, 0.9329452016477215, 1.6120412224670189, 1.9699897421072674, 1.8640105818841841, 1.3076433993079455, 0.4681000517191071, -0.392275180810198, -1.0092646785710955, -1.2108022179848332, -0.9773786545821825, -0.4466182451807202, 0.13975041732000015, 0.5270378330440059, 0.5430997551796674, 0.16257992660147036, -0.48433530983293277, -1.1622229675041214, -1.6210222811554806, -1.6925089223233514, -1.3553568228038781, -0.7428615307665419, -0.0891084971940643, 0.36652420509762934, 0.47931594012330325, 0.26284659500866037, -0.11213195916674304, -0.3878041232120429, -0.3350328994372398, 0.12902607144238812, 0.8701106634857115, 1.5478769081908812, 1.7153860193107298, 0.9800636154061938, -0.8274644445713947, -3.5393637919562697], 'positive_zeros': ['1.25191980665928921888755830875019', '2.13445994138232077638285501855876', '3.20534470481559922014589902894231', '4.14290134201411265888026504491166', '5.70605722235965038367395553962090', '7.38637757235446998977880549871033', '7.927770732453441640476077185559667', '8.793600272228715794112866312154242', '9.425943208531429301354094200895269', '10.05753707972975401070186674400535'], 'prelabel': '2-675-135.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.321616276742655, 'root_angle': -0.2667608113769158, 'root_number': '-0.10511673315006302 - 0.9944598897953896*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.266760811377', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25191980665928921888755830875', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.13445994138232077638285501856', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.20534470481559922014589902894', 'prec': 103}}