{'Lhash': '3024762687972326146812520943304', 'a10': [2.7125426658552, 3.035336644066789], 'a2': [-0.9749279121818236, 0.2225209339563144], 'a3': [-0.8752234219087537, -0.4837188871052398], 'a4': [0.9009688679024191, -0.4338837391175581], 'a5': [-1.969107613016761, -3.5628319445714673], 'a6': [0.9609173219450995, 0.2768355114248494], 'a7': [-1.674783964260727, -2.100112665336463], 'a8': [-0.7818314824680298, 0.6234898018587335], 'a9': [0.5320320765153366, 0.8467241992282841], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.413857257042813, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9749279121818236, -0.2225209339563144]]], [3, [[1.0, 0], [0.8752234219087537, 0.4837188871052398]]], [113, [[1.0, 0], [-0.3391420378396173, -10.62473447565491]]]], 'bad_primes': [2, 3, 113], 'central_character': '678.667', 'coefficient_field': 'CDF', 'conductor': 678, 'conductor_radical': 678, 'conjugate': '259276898084089989882090529019', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9749279121818236, -0.2225209339563144]], [[1.0, 0], [0.8752234219087537, 0.4837188871052398]], [[1.0, 0], [1.969107613016761, 3.5628319445714673], [-2.6601603825766826, 4.233620996141421]], [[1.0, 0], [1.674783964260727, 2.100112665336463], [-1.5576465376942008, 6.8244953852727654]], [[1.0, 0], [1.9243746791745224, -0.6733678236275156], [8.600146307148329, -6.858387820446069]], [[1.0, 0], [-0.7579672491234858, 6.727145397958491], [-12.674062858363706, -2.8927721414320873]], [[1.0, 0], [4.808655311205452, -3.411922895918352], [5.614744053237841, -16.046016615242248]], [[1.0, 0], [-3.3885068820648137, 0.9762120155813249], [16.0877597853374, -10.108609453791395]], [[1.0, 0], [-1.4530606571523077, 5.043685140349553], [-19.474656582250535, -12.23673775985274]], [[1.0, 0], [-5.360405365372486, -7.554784359649095], [-9.578092796699845, 27.372616578942658]], [[1.0, 0], [-7.165175266598134, -0.8073213621871738], [30.222765277636533, 6.898148952645746]], [[1.0, 0], [7.224473879719119, -6.456184580185023], [4.142685615822391, -36.76735176604998]], [[1.0, 0], [4.324028797145655, 1.513043115743789], [32.05509078118922, 25.563081876208074]], [[1.0, 0], [-0.8254398057339145, 4.8581907343461594], [-40.586983203259805, -14.201999664072185]], [[1.0, 0], [2.911083533508648, -0.16348294458191387], [46.704473864982404, -5.262330376855469]], [[1.0, 0], [-1.1672477695764643, -2.4238149686268646], [-33.044959498512874, 41.43706857080558]], [[1.0, 0], [0.2892753112250559, 1.0040968224651858], [-49.956727754468766, 31.389892514404856]], [[1.0, 0], [-0.037436967333501506, -0.10698870583624094], [-47.69172043054982, 38.03287791338275]], [[1.0, 0], [0.39780030040183567, -7.0834906178506065], [-66.57871806284726, -7.501619898921627]], [[1.0, 0], [6.42504108824006, 15.511421334033543], [-50.204581464244875, 50.204581464244875]], [[1.0, 0], [-1.5397907643767983, -0.6378022178217047], [51.61879502661797, 51.61879502661797]], [[1.0, 0], [10.219297003529078, -11.435398625014509], [-8.84519361216132, -78.50326458156617]], [[1.0, 0], [1.7504418173935465, 7.669186696665044], [-74.78041603590079, 36.01235034675732]], [[1.0, 0], [8.435163821826697, -1.433191977663152], [84.00561639744471, -29.39483651400987]], [[1.0, 0], [-2.446324376592981, 3.0675937413050383], [-21.584530593762498, -94.56800748163688]], [[1.0, 0], [-8.407561093513063, -0.4721585033539774], [100.3649331992175, 11.308412086434094]], [[1.0, 0], [-1.9076394295772934, -2.134649506955155], [-11.532341038640709, 102.35235761900398]], [[1.0, 0], [-6.319018765063259, -1.820477944958362], [90.5994893174264, 56.927432187141015]], [[1.0, 0], [-13.351301299617088, 6.429647833947561], [67.96038840260195, -85.21963158901525]], [[1.0, 0], [-0.3391420378396173, -10.62473447565491]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 12640361, 'index': 18, 'label': '2-678-113.102-c1-0-18', '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/678/2/r/b/667/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.24862819952436513, 0.42780513965424244, 0.6297105440570172, 0.8555352278981269, 1.1043273719101294, 1.3718661980604696, 1.6500257622692844, 1.9266503079934325, 2.1859277517337583, 2.4092490508999087, 2.576538954646511, 2.668018414212393, 2.6663099818784604, 2.558733850889263, 2.339576308291878, 2.012057635571789, 1.5896958196675497, 1.0967671627968558, 0.5676132483858306, 0.04463916811406413, -0.42501252930983296, -0.7939544874116242, -1.0198672892592195, -1.071106000110841, -0.9319321713153252, -0.6066279172310832, -0.12176563477542408, 0.47396820945409274, 1.1127618586326562, 1.7135159550960324, 2.1901735482577505, 2.461779135527581, 2.463143141968467, 2.154737895792864, 1.530367822508776, 0.6212800666678637, -0.504275130830121, -1.7464832333998994, -2.98416894743659, -4.088794217379795, -4.940603329632344, -5.444767110955018, -5.545158552890079, -5.233525006113649, -4.552328333799027, -3.590363727118033, -2.4713372560455342, -1.3367259197077384, -0.32527452856638167, 0.4477881777749241, 0.9084633290016205, 1.035558185397425, 0.8638952277759511, 0.47821875006611125, -0.0015771529153279639, -0.4417107731504317, -0.7187927064934504, -0.7429079439005831, -0.47526471198293074, 0.06306084981824278, 0.7932901366903067, 1.5920848515002661, 2.313659859268103, 2.817041523820217, 2.9934604550922264, 2.7885897932897383, 2.215088036673048, 1.352597517875066, 0.33470605994043373, -0.6750366250045647, -1.5136597707550596, -2.049964379213607, -2.2100871146460097, -1.9920660548012012, -1.4661197398584795, -0.7602237151371091, -0.03366116712020833, 0.5561206650897877, 0.8864015941604764, 0.8947162321357117, 0.5913076470997263, 0.05553023954148006, -0.5832530065295268, -1.1761833758047668, -1.5899679227543073, -1.7383291744783533, -1.6022347756714197, -1.23367738490905, -0.7415233104934095, -0.26225492602806205, 0.07770120793716151, 0.19890116602909563, 0.09552663537742069, -0.15585444389821648, -0.4090623443064172, -0.4811408211788405, -0.19864130677110642, 0.5531462697996719, 1.7901178885277127, 3.4092868550477937, 5.195572642943114, 6.8563235320533416, 8.077818934573367, 8.592278577177263, 8.240550621234238, 7.015629729763653, 5.075687016942438, 2.721740068133286, 0.3430649758464543, -1.6588881673583507, -2.9518364486526867, -3.341155562044375, -2.809776427183497, -1.5199369160202685, 0.22408950774805508, 2.0440432500924173, 3.570903614599236, 4.523953641024606, 4.7672565159895495, 4.3305472412733135, 3.3902382911912508, 2.2160724251099624, 1.0974606554896438, 0.2685313812174887, -0.14894080438849466, -0.1703591844995685, 0.06493379798355577, 0.34067481095409335, 0.4312036376131905, 0.17074607935492778, -0.4947371377286956, -1.487568116471655, -2.615934229865474, -3.6243647316297785, -4.263261098482774, -4.358223132453162, -3.8598067003945618, -2.8596593205082628, -1.568293301710184, -0.2605028699698349, 0.7964146746446918, 1.4115452096245888, 1.5170338358520892, 1.179566926273192, 0.5738236637068844, -0.07387501856970106, -0.5547390670996604, -0.7387034642834223, -0.6091858380225081, -0.26087914126892664, 0.13868941599655576, 0.4118340019156884, 0.43776895976953506, 0.20226294071264997, -0.18713197972463824, -0.5270510150665624, -0.5794832169023223, -0.15065370551613927, 0.8364376907577995, 2.2993166635719895, 3.998807138800617, 5.589825017118558, 6.708198623766585, 7.069900155547899, 6.554052723966158, 5.244484973961994, 3.4157722992958215, 1.4655688572078314, -0.18902061620777016, -1.222081171831977, -1.4847017403924627, -1.0407018739308804, -0.1413642766534131, 0.8537295247363271, 1.5863895475342549, 1.8071406614337504, 1.447612567433018, 0.6357585825840907, -0.3509417857146338, -1.1798984787165199, -1.575894034347658, -1.4158567452717272, -0.7750289538298768, 0.09160824082700046, 0.8285366448516568, 1.0958892495828934, 0.6863828847571747, -0.3947420862484389, -1.9140948298969114, -3.466742555405649, -4.590454885289313, -4.904345326671752, -4.229891856030778, -2.6564246850356126, -0.5291996377587614, 1.6386115310808673, 3.3053956374875493, 4.051331772259119, 3.694925536830617, 2.341293356166181, 0.3482512275710366, -1.7788102171400926, -3.530824287036988, -4.534025245215402, -4.6427640631316764, -3.96022171729999, -2.784236411662108, -1.4989797692960296, -0.4495214540047032, 0.15976202229002048, 0.31152135163226724, 0.15471761277355325, -0.07194879070332276, -0.14268420346384336, 0.06440050817910303, 0.5203985260867796, 1.0587740360439057, 1.4426340716871004, 1.4605574276513331, 1.0150632917850235, 0.170356161446012, -0.8593810558783446, -1.7782940723695941, -2.31006176339732, -2.2957005121205447, -1.752031184516376, -0.868327887422909, 0.059348788806320774, 0.7338720245517708, 0.9652587319671037, 0.7417306858645055, 0.23630017248655263, -0.2557542103988285, -0.42797384525532817, -0.08320578433256709, 0.7807256577790287, 1.9535193987300536, 3.072989054298832, 3.7456368961266118, 3.6864452544444553, 2.828243191708576, 1.3596805193814856, -0.32533244053591415, -1.7528279009367378, -2.5273468368081646, -2.468821751387333, -1.6780754926004595, -0.5045659923385926, 0.5762745115392873, 1.1362415808025186, 0.9585259017112221, 0.13384283630174326, -0.9490600213358338, -1.720628155776609, -1.620015696890774, -0.29489816335863167, 2.256352400465758], 'positive_zeros': ['2.38611703211259008174048493026173', '3.27708929839258694399990738154070', '4.44630088642847483297732655961022', '6.04724680186877601019221614895909', '6.74959122692336270591026935020328', '7.36272081106828626598354472011676', '8.540313822414030382790678702418375', '9.506196673922443223192813481736409', '10.13626590561151797088666579951060', '11.21402438872195248579777247838567'], 'prelabel': '2-678-113.102-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.326769704341797, 'root_angle': -0.3731802356935992, 'root_number': '-0.6989757364595913 - 0.715145383709335*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.373180235694', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.38611703211259008174048493026', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.27708929839258694399990738154', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.44630088642847483297732655961', 'prec': 103}}
