Table lfunc_lfunctions
L-functions
{'Lhash': '1709436867630604014509273034557', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.45756184077814416, -0.3964795919777455], 'a4': [0.0, 0.0], 'a5': [-3.7929367074613642, 0.5453419690297061], 'a6': [0.0, 0.0], 'a7': [-0.4809565354985796, 1.0531479108155932], 'a8': [0.0, 0.0], 'a9': [-0.3747777435384112, 2.6066364617701887], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.876989588766239, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [0.6248277524306246, 4.754954287876225]]]], 'bad_primes': [2, 23], 'central_character': '736.561', 'coefficient_field': 'CDF', 'conductor': 736, 'conductor_radical': 46, 'conjugate': '756146589970138342002327017237', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.45756184077814416, 0.3964795919777455], [0.4269445148198554, -2.9694643256427984]], [[1.0, 0], [3.7929367074613642, -0.5453419690297061], [4.7974648680724865, -1.4086627842071484]], [[1.0, 0], [0.4809565354985796, -1.0531479108155932], [-4.584025137616996, -5.290247020479808]], [[1.0, 0], [-1.3587048462985623, 4.6273237564559935], [-9.253788861142993, -5.947048992011573]], [[1.0, 0], [-5.637198535689118, 2.574422310293549], [8.513189541288705, -9.824744466605358]], [[1.0, 0], [0.7617712976770555, 0.48956068654392415], [7.062055221032069, 15.463743921026813]], [[1.0, 0], [2.2165662577004324, 3.449044420694383], [-7.892885247035842, 17.28300791173585]], [[1.0, 0], [0.6248277524306246, 4.754954287876225]], [[1.0, 0], [-2.7032875303507145, 4.206397504111482], [-12.047035377054707, -26.379327865281034]], [[1.0, 0], [-4.49872463106412, 5.191804988185161], [-4.411759986471839, -30.684464698308915]], [[1.0, 0], [5.930878265093468, 0.8527315588470059], [35.5012400237364, 10.424104603132898]], [[1.0, 0], [0.1663858394850116, 1.1572389326780346], [-39.339211918194394, 11.551034830498617]], [[1.0, 0], [-2.418500662617263, 2.0956427535165245], [6.119538045751261, -42.56232200088011]], [[1.0, 0], [5.809237021610626, 0], [47.0, 0]], [[1.0, 0], [-0.9594735298365809, -0.4381768791198768], [34.70761889910011, 40.054727440775686]], [[1.0, 0], [10.827300342405778, -4.944662385982643], [38.63678330277182, -44.58922488690124]], [[1.0, 0], [-2.0333483766301303, -1.7619063979284375], [8.681205134670394, 60.379107954736895]], [[1.0, 0], [0.7167601058957108, 2.4410607459939295], [-56.363986699689136, 36.22293476952504]], [[1.0, 0], [-12.421652906923251, 3.6473263795575424], [59.72900083101386, -38.385498039347425]], [[1.0, 0], [-6.670143546741623, 4.286640969602009], [30.325295949137708, -66.40313566087984]], [[1.0, 0], [-1.7123273098113283, -3.7494738003526127], [-51.73399798167752, 59.704216373986405]], [[1.0, 0], [-2.181501815572129, -0.31365260938989764], [79.63791681000329, 23.383802217838664]], [[1.0, 0], [2.2207199361095427, 2.562847426144547], [-12.666020606322377, 88.094108327403]], [[1.0, 0], [0.5612313315471147, 3.903449651216032], [-93.07081844060625, 27.32805801361868]], [[1.0, 0], [5.632147113265818, 0.809780503474073], [96.90879033506424, 28.4549882409844]], [[1.0, 0], [-2.217517920965756, -0.6511220101611532], [86.64911388161165, 55.68600419792655]], [[1.0, 0], [9.583545489358164, 8.30418943777967], [15.22768769524151, 105.9108942812598]], [[1.0, 0], [2.443798065028348, -3.8026240146027233], [-45.28023641720562, -99.1498874936425]], [[1.0, 0], [-16.267019223625024, 4.776427805194008], [95.06164920992347, -61.09241237248253]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 13490689, 'index': 14, 'label': '2-736-184.101-c1-0-14', '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/736/2/x/a/561/14', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.0476146755812863, 1.1839244763563235, 1.2975750970551705, 1.3845429055977347, 1.436648907633634, 1.4425243143183593, 1.3891260965791898, 1.2635527738102508, 1.0549775573081497, 0.7565607436480032, 0.3672046147324568, -0.10701068966774901, -0.6518968343976043, -1.2449240214610406, -1.8558497184327722, -2.4483116518910353, -2.982390460833394, -3.418024008433343, -3.719018722356593, -3.857271594610562, -3.816710948648094, -3.5964067405474016, -3.212311261063679, -2.6971814605679323, -2.0984075468418686, -1.473719140982854, -0.8850364415707741, -0.39104304686845043, -0.03933343683310443, 0.14081785200068547, 0.14395203608149454, -0.008832133182478318, -0.27064244228693546, -0.5733892018801682, -0.8359981399257945, -0.9754388572204672, -0.9192251904499427, -0.6176418494049427, -0.05377762867507159, 0.7504386972858176, 1.7335767851958699, 2.8000861778293293, 3.831483180643507, 4.7021308883735315, 5.297516900301812, 5.532306432249803, 5.365218627001687, 4.80802786278425, 3.926739816087256, 2.834155069708261, 1.674446686568573, 0.6018125524389906, -0.24354121021338743, -0.7581162906320703, -0.8925160014354682, -0.6601756122687732, -0.1354400438200197, 0.5591731105813702, 1.2746930503063267, 1.862774265279884, 2.203286971997724, 2.227201892910988, 1.9301751556329692, 1.3738095151633432, 0.673842848203032, -0.022913103763747895, -0.568693519561369, -0.8461090056710769, -0.7942684458146798, -0.42401630790005884, 0.18142988563853055, 0.8812880662968273, 1.5050890904673837, 1.8883330664407445, 1.908678790274898, 1.5149088901543601, 0.7420514767418489, -0.2913151199174454, -1.403880086011347, -2.386902129543122, -3.0469964676986443, -3.2474143821812484, -2.938726165888693, -2.171750544199463, -1.0892136778923294, 0.10276385823752732, 1.1776652720897407, 1.9368690281605219, 2.252487661664041, 2.0948674901944306, 1.5380581368182882, 0.7414584957072015, -0.0886270358687858, -0.7489138256748226, -1.088909669139977, -1.0485384186177025, -0.6741332599367176, -0.10823640668284512, 0.44512308801176886, 0.7719152568082654, 0.7041664421416888, 0.16678422689231737, -0.7969132296234459, -2.028216310001494, -3.2850272162082135, -4.2960778769725385, -4.824792659283051, -4.72735160157337, -3.9904087158766, -2.7385160265206396, -1.2085728855251845, 0.3031921761800907, 1.5091564841280476, 2.196556229443406, 2.275550817683623, 1.7969345042821596, 0.9349245280148863, -0.060592684697030205, -0.929982692311144, -1.4706880295071436, -1.5872975645034306, -1.3115275363030814, -0.7867928436392023, -0.22166897747554515, 0.17480704331104052, 0.257780577051378, -0.007377370727075196, -0.5313184517713037, -1.1240978157252453, -1.550031861042054, -1.5991333052045433, -1.1548907836718763, -0.23839606976851757, 0.9852246725752253, 2.24191532473928, 3.217448840786964, 3.6419979372106313, 3.36737909170286, 2.414896102762012, 0.979079729629646, -0.6155618741424059, -1.9946013529465896, -2.829740807670066, -2.9249356282914833, -2.2687518869824217, -1.0379844096994297, 0.44911692938288555, 1.8175909501759318, 2.73525088392095, 2.9993287614639947, 2.5861796432073176, 1.650405274189866, 0.47425993054593124, -0.6174346601918305, -1.3516446143841634, -1.5829251073956048, -1.3285045772630524, -0.7528278850739536, -0.10711825041360758, 0.35668210352319996, 0.4702579136818582, 0.2046179083084381, -0.32099046865139824, -0.8804434469091748, -1.219840414237803, -1.1493585579606214, -0.6180335648400569, 0.25387814348282056, 1.1976232773906583, 1.8693073581655246, 1.9531211794339425, 1.2633527423344666, -0.18679749740985382, -2.1724668898624424, -4.306744661858318, -6.139900339326693, -7.279858902471014, -7.498358914970711, -6.790925411960189, -5.372468412517245, -3.609890209340161, -1.9124948881427146, -0.6141027938347318, 0.11668091783336093, 0.3105831554593237, 0.16651976094466361, -0.03341442801383888, -0.03391927406123981, 0.2957191425576378, 0.9093074273462949, 1.5952870891021331, 2.0493027432682505, 1.9842795366493649, 1.2412203786467155, -0.1373667505622982, -1.8981181844134392, -3.6376553822224875, -4.916542809894035, -5.391136163692515, -4.921123420208042, -3.6173480210052364, -1.8131119798959188, 0.03332178259763062, 1.4748745851254446, 2.207411008844556, 2.1551745117441548, 1.4828712630684353, 0.5313100954238047, -0.30141282169695943, -0.693348859362123, -0.5023516334764516, 0.19409715629120966, 1.1350847741056591, 1.974693108047125, 2.4076040246274175, 2.277656251744676, 1.6312828738482839, 0.697238509520702, -0.19984971396069404, -0.7608998501830806, -0.8247129736520774, -0.4298877053512461, 0.197465698821624, 0.7275183445704427, 0.8531998473701621, 0.4140891611063075, -0.528184451264597, -1.6930830640758383, -2.6657355378966003, -3.036701364347614, -2.549865279078718, -1.206554615911129, 0.712719449408281, 2.720190690035197, 4.265645323465355, 4.907584121940521, 4.453994170602133, 3.0251795767081964, 1.0168650058633646, -1.0246006697653025, -2.5732719651106906, -3.2835820681509933, -3.0861573188882963, -2.188956327754572, -0.9863278672260657, 0.08948527506592993, 0.7204435589380822, 0.8044390407497949, 0.47202201958333384, 0.015136296422349748, -0.24271903485183183, -0.08417603347308834, 0.50955141867382, 1.3470378127143554, 2.100503445528885, 2.4369735228016194, 2.156101668289855], 'positive_zeros': ['1.34850791481724921693482811237072', '3.51924026194414728121590365749236', '3.86986028051491852908979073166376', '4.75959796420059630357203335412331', '6.45921304504051323579722975414387', '7.02604461083925127299932559967332', '8.120573591291224035073977932263998', '8.715868211742303840078117387107918', '9.591701151270298330117911160194506', '10.61407139054352034985208342422059'], 'prelabel': '2-736-184.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.424250314791408, 'root_angle': 0.19892970185657866, 'root_number': '0.3154057011348288 + 0.9489569240443146*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.198929701857', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.34850791481724921693482811237', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.51924026194414728121590365749', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.86986028051491852908979073166', 'prec': 100}}