{'Lhash': '531129453483976224401027020399', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.3068080087857066, 1.7046609181139074], 'a4': [0, 0], 'a5': [0, 2.23606797749979], 'a6': [0, 0], 'a7': [2.6457513110645907, 0], 'a8': [0, 0], 'a9': [-2.8117376914898995, 1.0460072438826846], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.414867539575111, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.3068080087857066, -1.7046609181139074]]], [5, [[1.0, 0], [0, -2.23606797749979]]], [7, [[1.0, 0], [-2.6457513110645907, 0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1680.209', 'coefficient_field': 'CDF', 'conductor': 1680, 'conductor_radical': 210, 'conjugate': '2769473782432164070121241232973', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.3068080087857066, -1.7046609181139074]], [[1.0, 0], [0, -2.23606797749979]], [[1.0, 0], [-2.6457513110645907, 0]], [[1.0, 0], [0, -5.556116102903124], [-11.0, 0]], [[1.0, 0], [7.132350674843421, 0], [13.0, 0]], [[1.0, 0], [0, 5.755829553683865], [-17.0, 0]], [[1.0, 0], [0, 0], [-19.0, 0]], [[1.0, 0], [0, 0], [23.0, 0]], [[1.0, 0], [0, -4.8361887425101395], [-29.0, 0]], [[1.0, 0], [0, 0], [-31.0, 0]], [[1.0, 0], [0, 0], [-37.0, 0]], [[1.0, 0], [0, 0], [41.0, 0]], [[1.0, 0], [0, 0], [-43.0, 0]], [[1.0, 0], [0, 1.2836935986842857], [-47.0, 0]], [[1.0, 0], [0, 0], [53.0, 0]], [[1.0, 0], [0, 0], [59.0, 0]], [[1.0, 0], [0, 0], [-61.0, 0]], [[1.0, 0], [0, 0], [-67.0, 0]], [[1.0, 0], [0, -11.832159566199232], [-71.0, 0]], [[1.0, 0], [-10.583005244258363, 0], [73.0, 0]], [[1.0, 0], [-14.870426148939398, 0], [79.0, 0]], [[1.0, 0], [0, -8.94427190999916], [-83.0, 0]], [[1.0, 0], [0, 0], [89.0, 0]], [[1.0, 0], [3.4506545694149415, 0], [97.0, 0]], [[1.0, 0], [0, 0], [101.0, 0]], [[1.0, 0], [16.10554940240108, 0], [103.0, 0]], [[1.0, 0], [0, 0], [107.0, 0]], [[1.0, 0], [20.870426148939398, 0], [109.0, 0]], [[1.0, 0], [0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23358833, 'index': 12, 'label': '2-1680-105.104-c1-0-12', 'leading_term': '1.194522136304926879279951971751592304697247965820985268', '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/1680/2/k/d/209/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.194522136304927, 1.038650702651369, 0.8858488486190105, 0.7360230062300335, 0.5891207497539255, 0.4451652851599222, 0.3042848389992398, 0.16673568932304336, 0.03291800249254423, -0.09661594175114412, -0.22116118147062655, -0.3398669024441975, -0.45175018648050314, -0.5557160482606524, -0.6505830397282205, -0.7351136501508896, -0.8080487018529584, -0.8681449222522389, -0.9142148527463808, -0.9451682292282273, -0.9600539364786863, -0.9581016012276664, -0.9387618500981657, -0.9017442238972235, -0.8470517141960849, -0.7750108772208252, -0.6862964887291831, -0.581949736106999, -0.4633890038802675, -0.33241239875530354, -0.1911912816728182, -0.04225422758081381, 0.11153898207630301, 0.26703351574989215, 0.42082573929421707, 0.5693192358260165, 0.7087900019946786, 0.8354599378496979, 0.9455774583452231, 1.035503771290704, 1.101803098021244, 1.1413348683675955, 1.1513457099153512, 1.1295588821542575, 1.074258687568648, 0.9843673318729301, 0.8595117112282188, 0.7000776807671997, 0.5072495097948234, 0.2830324563602597, 0.030256697070896697, -0.2474387757492446, -0.5456432334223977, -0.8592327065978562, -1.1824497831760592, -1.509004003315657, -1.8321915327972214, -2.1450321765569593, -2.440421186907567, -2.7112927449019963, -2.9507914680216207, -3.1524478423262696, -3.3103531110899738, -3.4193288920591827, -3.47508665703615, -3.474372203015993, -3.415090382769873, -3.2964056498733485, -3.11881440970257, -2.8841857501599386, -2.5957678452533655, -2.25815816759242, -1.8772365939759825, -1.460061518537291, -1.0147301732479195, -0.5502054653014399, -0.07611274159550636, 0.3974890530101192, 0.8603563807367469, 1.30232397585077, 1.7135745554520025, 2.084907832100299, 2.4080009622166845, 2.675652471643374, 2.8820018520995476, 3.022717427656313, 3.095145748937784, 3.0984166762463614, 3.033499444249042, 2.903206334689781, 2.7121420860353567, 2.46659879872146, 2.1743978039268734, 1.844681699530281, 1.487661462399454, 1.1143251628514308, 0.7361162765075565, 0.3645908544942828, 0.011063822904601344, -0.3137446091464473, -0.6000510841648197, -0.8393284220298693, -1.0245911647727106, -1.1506371333742849, -1.214235929940253, -1.2142568102031908, -1.1517301564874722, -1.0298388495293636, -0.8538381066893773, -0.6309047519875932, -0.36991933011495587, -0.08118688699443807, 0.22389547385643002, 0.5332140735998101, 0.8343452100358568, 1.1149793950416889, 1.3633489109260433, 1.5686438210453881, 1.7214015917059726, 1.8138560413968141, 1.840232427971201, 1.7969770926015407, 1.6829121591069833, 1.4993082771345303, 1.2498712183525194, 0.9406411914404629, 0.579806926860443, 0.17743977992531298, -0.2548438104323868, -0.7042803107107288, -1.157403820609777, -1.6005217716346996, -2.0202043171825044, -2.4037692460512954, -2.7397440389800285, -3.0182871807704856, -3.231552040814739, -3.3739785165636467, -3.4425001437809453, -3.436657433648394, -3.358611694646625, -3.2130574101172473, -3.0070352271028122, -2.749651613370236, -2.4517150965783494, -2.125302552072275, -1.7832721006876393, -1.4387416758856424, -1.1045541011643707, -0.7927504902903149, -0.5140738811906267, -0.27752421020723655, -0.0899840342617587, 0.044068140735882305, 0.12274338428409226, 0.14681714640195417, 0.11968824394843934, 0.04722173127787449, -0.06251970204040229, -0.19964629215077356, -0.3528996112637987, -0.5101806032843408, -0.6591255749864728, -0.7877058634468359, -0.8848252630197618, -0.9408887284985881, -0.9483164309593687, -0.9019789380321134, -0.7995320811637123, -0.6416338703811063, -0.43203048731219384, -0.17750375292599563, 0.11232168492623096, 0.4253071076553853, 0.7472540130630482, 1.0624677250828891, 1.3544088636887095, 1.6064067453077242, 1.8024053218712102, 1.9277099899910246, 1.9697026444736172, 1.918492792149817, 1.7674744031526894, 1.513761415601653, 1.1584793223345016, 0.7068958916970053, 0.1683805914104893, -0.44381056763627497, -1.1129205703999865, -1.819235630497572, -2.540769255410161, -3.2540607549676412, -3.9350572263933272, -4.560043692692717, -5.106583159301078, -5.554427051240018, -5.88635689616313, -6.088920249982874, -6.153027666451656, -6.07438285855959, -5.853724883591652, -5.496868935527379, -5.0145408238822515, -4.422009091613217, -3.7385275854270152, -2.986609740713947, -2.191163491414673, -1.3785222016809024, -0.5754120260433657, 0.19210061600687356, 0.8996363961554315, 1.5254608456787073, 2.051330763950044, 2.4631920624647603, 2.751698149524599, 2.9125257489759404, 2.9464739759365273, 2.8593421666880947, 2.6615919404554953, 2.3678087973248734, 1.9959877682564395, 1.5666757906055644, 1.1020101891326695, 0.6246975640598584, 0.15698026996659448, -0.2803616486889369, -0.6689267758420209, -0.993484391052363, -1.2426056173196929, -1.4091046109866954, -1.4902698295242813, -1.4878755074381003, -1.4079741050546153, -1.2604811562466318, -1.0585741074214567, -0.8179359065794322, -0.5558818055666934, -0.29041368442056403, -0.039249884425541295, 0.1811201595787605, 0.35630835689117496, 0.47478292904696057, 0.5284672361395956, 0.5131516608031056, 0.4286972478376908, 0.2790204577934768, 0.07185968406906901, -0.18166446546051393, -0.4676722916556846, -0.7702989575892611, -1.0725785558110117, -1.3573914745952471, -1.608424536260476, -1.8110922790873232, -1.9533693556432978, -2.0264882775945146, -2.0254634642724616], 'positive_zeros': ['0.41898726146491076680131555003575', '1.58828859841099929987369309903652', '2.54481033531360542667717350449870', '3.86750407790646016181016830856532', '4.97821292762474697443090738125681', '5.65041799292954383898282761262400', '6.47040662309942752855425836465629', '7.75039075221181891359993985069505', '7.996393159919406152295235061573949', '8.715293866222593212817107402332734'], 'prelabel': '2-1680-105.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6626312317205936, 'root_angle': 0.47165842809286174, 'root_number': '-0.98418643995009905472367605505834840733030827121157844731 + 0.17713568646196075688662281770548501811144987517221710585*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4716584280928618', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41898726146491076680131555004', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.58828859841099929987369309904', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.54481033531360542667717350450', 'prec': 103}}