{'Lhash': '4289691133008511265587457743789', 'a10': [-3.3190778623577253, 5.748811491880681], 'a2': [-0.9396926207859084, -1.6275953626987474], 'a3': [-0.32635182233306964, 0.565257937423568], 'a4': [-0.766044443118978, 1.3268278963378768], 'a5': [-1.7660444431189781, -3.058878703906754], 'a6': [1.2266815969056775, -2.7023779555739693e-62], 'a7': [0.41874808778511735, -2.6124031157109555], 'a8': [-0.8793852415718167, 0.0], 'a9': [1.286988976119769, 2.2291302954204886], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6148480955638592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-0.41874808778511735, 2.6124031157109555]]], [11, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [7, 11], 'central_character': '77.67', 'coefficient_field': 'CDF', 'conductor': 77, 'conductor_radical': 77, 'conjugate': '1432721495722430047218762740688', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9396926207859084, 1.6275953626987474], [-1.0, 1.7320508075688772]], [[1.0, 0], [0.32635182233306964, -0.565257937423568], [-1.5, -2.598076211353316]], [[1.0, 0], [1.7660444431189781, 3.058878703906754], [-2.5, 4.330127018922194]], [[1.0, 0], [-0.41874808778511735, 2.6124031157109555]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-4.411474127809773, 0], [13.0, 0]], [[1.0, 0], [-2.6244851516900036, 4.545741626437199], [-8.5, -14.722431864335457]], [[1.0, 0], [0.9076037345479523, 1.5720157813763098], [-9.5, 16.454482671904334]], [[1.0, 0], [-3.166374217691586, -5.484321020817983], [-11.5, 19.91858428704209]], [[1.0, 0], [-1.921274307573399, 0], [29.0, 0]], [[1.0, 0], [0.733955556881022, -1.2712483150154392], [-15.5, -26.846787517317598]], [[1.0, 0], [2.2266815969056775, 3.856725658119236], [-18.5, 32.04293994002423]], [[1.0, 0], [-0.28311858285794855, 0], [41.0, 0]], [[1.0, 0], [3.4114741278097727, 0], [43.0, 0]], [[1.0, 0], [-2.277188796356143, -3.9442066937154574], [-23.5, 40.703193977868615]], [[1.0, 0], [-3.6172111917146594, 6.265193565756556], [-26.5, -45.89934640057525]], [[1.0, 0], [4.769914836380798, -8.261734844388132], [-29.5, -51.09549882328188]], [[1.0, 0], [-0.5739779522395382, -0.9941589757032225], [-30.5, 52.827549630850754]], [[1.0, 0], [-0.3472963553338607, 0.6015349327217412], [-33.5, -58.023702053557386]], [[1.0, 0], [-9.461103980334997, 0], [71.0, 0]], [[1.0, 0], [1.1736481776669303, -2.032818273929748], [-36.5, -63.21985447626402]], [[1.0, 0], [-6.209607457166707, -10.755355610871318], [-39.5, 68.41600689897065]], [[1.0, 0], [11.332748435383172, 0], [83.0, 0]], [[1.0, 0], [-1.7339555568810219, -3.0032991225843166], [-44.5, 77.07626093681505]], [[1.0, 0], [-15.34729635533386, 0], [97.0, 0]], [[1.0, 0], [3.351166748595681, -5.804391073203118], [-50.5, -87.4685657822283]], [[1.0, 0], [1.1244851516900038, 1.9476654150838826], [-51.5, 89.20061658979718]], [[1.0, 0], [-5.766044443118978, -9.987081934182264], [-53.5, 92.66471820493493]], [[1.0, 0], [-5.992726040024656, 10.379705977163745], [-54.5, -94.39676901250381]], [[1.0, 0], [-5.007740786523641, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 9593485, 'index': 4, 'label': '2-77-7.4-c1-0-4', '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/77/2/e/a/67/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5925897907394545, 0.6585749241058999, 0.736507720928315, 0.8285076503842507, 0.9359243155951704, 1.0593328906917627, 1.1985535477302567, 1.3526573319881476, 1.5199434193162527, 1.6978919613534116, 1.8831069582881892, 2.0712666391336447, 2.2570981751688373, 2.434391550949513, 2.5960650355852257, 2.7342920875684085, 2.8406965288832007, 2.9066192393738612, 2.9234553301047037, 2.88305575323025, 2.778181721736122, 2.602994395090856, 2.3535563992743653, 2.0283163502960417, 1.6285431673066386, 1.1586741571072008, 0.6265401779405184, 0.04343313478517602, -0.576014013453881, -1.2141564587191995, -1.8508864743673354, -2.4643985956840435, -3.032151447960828, -3.531989309887923, -3.943369244338454, -4.248623888632358, -4.434177363827399, -4.491623834371288, -4.4185764775956455, -4.219200149761937, -3.9043545302508025, -3.491296034186667, -3.002915617023346, -2.4665242682668804, -1.9122362372025978, -1.3710388909164035, -0.8726741010388963, -0.44348546747746187, -0.10440487488830504, 0.13074233645984254, 0.25644424000166777, 0.27607864142040195, 0.2017594028301663, 0.05341074007602605, -0.14290472611582553, -0.3573056096431124, -0.5588894700260456, -0.7187769945130468, -0.8131255336217702, -0.8258124201985835, -0.7504941168699891, -0.5917835633226606, -0.365354818604386, -0.09687758671915377, 0.18020249397095475, 0.4278987920763928, 0.6076741207599825, 0.6848220038741519, 0.632798167440184, 0.4370261948660014, 0.09771453999289785, -0.3687122781540711, -0.9298493529391384, -1.5393362344003572, -2.140605441932044, -2.672090741185152, -3.0734438759144105, -3.2921546529853245, -3.2898701358838855, -3.0476809929709985, -2.5696968368891318, -1.8843691056352212, -1.0432313818324799, -0.11699501839876422, 0.8107639812826853, 1.6517953342281584, 2.322452959380164, 2.753086685522974, 2.8964867615431023, 2.734353963354162, 2.2809256613445155, 1.5831608886198154, 0.7172509906117385, -0.21836065515224523, -1.112843221212321, -1.8547429099974595, -2.344380340116271, -2.5054679740143015, -2.2945527720603693, -1.7070794983321405, -0.7792193418071655, 0.41491776520491663, 1.7705234126891265, 3.163068418511378, 4.461815704326985, 5.5443094408399345, 6.310108278819625, 6.692072082577462, 6.663772665073319, 6.242054968996749, 5.48437372500592, 4.481197600569849, 3.344420989134755, 2.193264083267008, 1.1394967530042044, 0.2739354532662427, -0.34398915750348247, -0.6922005085228023, -0.7866949234492284, -0.6769568421480691, -0.4367695048698845, -0.15178651561024814, 0.09429077839979384, 0.23286867392728203, 0.22097417682013099, 0.04753545378908021, -0.2655271551264263, -0.6675639600560825, -1.0881431611367232, -1.4492663366419518, -1.6788960719947903, -1.7235982744422704, -1.5582069604999, -1.1908656700422389, -0.6625265981487828, -0.04088756680025502, 0.5903230068951119, 1.1449942152468215, 1.548946406517817, 1.7524571041769414, 1.7387686283458899, 1.526959346717176, 1.1684762601683973, 0.737704306834603, 0.31801125037419187, -0.014426550843156671, -0.2062018250162858, -0.2387943622851085, -0.1348150398832038, 0.04314271316924244, 0.20134941032228726, 0.23044965082623792, 0.025359245054724512, -0.4936522482566332, -1.36232425386655, -2.559673680805581, -4.003853679111915, -5.558002413863755, -7.045878156365289, -8.27541017755045, -9.06684523709579, -9.281195558827301, -8.844387209605907, -7.762954879100327, -6.1282929022328885, -4.108191405797519, -1.9263965836291628, 0.16709068542649963, 1.9306578278462303, 3.1653941663158784, 3.74369303681876, 3.6275374698380327, 2.873427472664417, 1.623014985107239, 0.08082314372703252, -1.5174483022904852, -2.940956547128831, -3.9982731657538237, -4.564885365778558, -4.59924631785746, -4.144923109413623, -3.3187623326671556, -2.2873815149962837, -1.23627849585936, -0.3370756789529249, 0.2813409359340093, 0.5528145190391887, 0.4817450100982112, 0.13771691536344952, -0.36167420987343746, -0.8762446069428018, -1.2718704603663982, -1.4468234378821616, -1.3507972128050514, -0.9931219820010796, -0.4388221894166493, 0.20642241761821037, 0.8191702395474009, 1.2841945598892786, 1.5182015650064795, 1.486453259763954, 1.2089450982226746, 0.7549606620158266, 0.22724729267257826, -0.26076730246861984, -0.6098191893353094, -0.7563512624557055, -0.6860576688044857, -0.43640519129704386, -0.08745674840470426, 0.2571344515128082, 0.4948907698430863, 0.5495880071931315, 0.3909608814950551, 0.04434566894136014, -0.41237677963139463, -0.8644637314774237, -1.185735439448105, -1.268551454464327, -1.0518616173505724, -0.5409127731327468, 0.18635613746513652, 0.9885975127936035, 1.685135346302988, 2.09072517486779, 2.054343318468703, 1.4940958275682061, 0.42068122719141027, -1.0562069064135848, -2.740924506768915, -4.382869951444665, -5.72016384766227, -6.527904016765375, -6.661578471693029, -6.0867933640279315, -4.888883094218576, -3.2597880306657947, -1.4640745818272898, 0.20977008495895508, 1.5034959204880454, 2.238086218976201, 2.347764457295628, 1.8919948003807605, 1.0427667626198065, 0.04940570467947371, -0.8122621826173818, -1.296294295342171, -1.2372218620516582, -0.5845674120320802, 0.5857977219958795, 2.085859813942495, 3.6524192991260143, 4.999314241507309, 5.874286450821669, 6.108921002121984, 5.651549598098406, 4.576572341470548], 'positive_zeros': ['3.38396963030364195163891180328485', '6.04866766317231801552341841295837', '6.66134489220317241257638117196064', '7.918299842298887121279945495677225', '8.778969099977385008748664845826829', '10.39053295457640230907969598485787', '11.59589249101043568080119867579074', '12.58401896920947302311404055950929', '14.42402216600869875738822759549583', '15.19721065691897039893042004406216'], 'prelabel': '2-77-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7841225003555625, 'root_angle': 0.3687159358349428, 'root_number': '-0.6786435618665664 + 0.7344677773306736*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.368715935835', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.38396963030364195163891180328', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.04866766317231801552341841296', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.66134489220317241257638117196', 'prec': 103}}
