Table lfunc_lfunctions
L-functions
{'Lhash': '1096541207285835004899510687493', 'a10': [-17.301341439377175, 0.0], 'a2': [-3.460268287875435, 0.0], 'a3': [0.0, 0.0], 'a4': [3.9734566240763964, 0.0], 'a5': [5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [17.675436876636724, 0.0], 'a8': [13.932920353463343, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 61.06697685594156, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-5.0, 0]]], [23, [[1.0, 0], [-23.0, 0]]]], 'bad_primes': [3, 5, 23], 'central_character': '1035.1', 'coefficient_field': 'CDF', 'conductor': 1035, 'conductor_radical': 345, 'degree': 2, 'euler_factors': [[[1.0, 0], [3.460268287875435, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [-17.675436876636724, 0], [343.0, 0]], [[1.0, 0], [37.939710082808084, 0], [1331.0, 0]], [[1.0, 0], [-69.03044763794955, 0], [2197.0, 0]], [[1.0, 0], [-126.30421853019051, 0], [4913.0, 0]], [[1.0, 0], [-11.196779581427535, 0], [6859.0, 0]], [[1.0, 0], [-23.0, 0]], [[1.0, 0], [109.66151753092205, 0], [24389.0, 0]], [[1.0, 0], [-210.3217374930509, 0], [29791.0, 0]], [[1.0, 0], [-436.9534238061689, 0], [50653.0, 0]], [[1.0, 0], [-132.62645859466662, 0], [68921.0, 0]], [[1.0, 0], [-110.00638187063018, 0], [79507.0, 0]], [[1.0, 0], [280.8653138808195, 0], [103823.0, 0]], [[1.0, 0], [-247.61053421679085, 0], [148877.0, 0]], [[1.0, 0], [306.380768489526, 0], [205379.0, 0]], [[1.0, 0], [619.0050224002675, 0], [226981.0, 0]], [[1.0, 0], [89.37178215251824, 0], [300763.0, 0]], [[1.0, 0], [944.9848998209787, 0], [357911.0, 0]], [[1.0, 0], [-1032.3432088342513, 0], [389017.0, 0]], [[1.0, 0], [-347.71986000322545, 0], [493039.0, 0]], [[1.0, 0], [1084.6570425579043, 0], [571787.0, 0]], [[1.0, 0], [1283.127936627795, 0], [704969.0, 0]], [[1.0, 0], [135.04284453044977, 0], [912673.0, 0]], [[1.0, 0], [-780.37679779628, 0], [1030301.0, 0]], [[1.0, 0], [-70.93145768310116, 0], [1092727.0, 0]], [[1.0, 0], [161.16545312043783, 0], [1225043.0, 0]], [[1.0, 0], [-1391.3507155389273, 0], [1295029.0, 0]], [[1.0, 0], [370.6733365660945, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 20085741, 'index': 36, 'label': '2-1035-1.1-c3-0-36', 'leading_term': '1.481717913531167903534979086255', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1035/4/a/v/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [1.481717913531168, 1.4722704304409033, 1.4440800923188633, 1.3976027520567706, 1.3335964702970298, 1.2531186562684908, 1.157521447816814, 1.0484447561280033, 0.9278062951757439, 0.7977878507207533, 0.6608170238652481, 0.519543712926742, 0.3768106759936184, 0.23561764427829154, 0.09907863076242862, -0.02962770461955736, -0.14731451871402046, -0.2508496806500358, -0.3372243985453005, -0.4036265622008868, -0.4475174711696702, -0.466710312633786, -0.4594484707245561, -0.42448150020656267, -0.3611363947240723, -0.26938163459546344, -0.1498814222164776, -0.004037514123692857, 0.1659838542716029, 0.35724227629828953, 0.5660327644161318, 0.7879163028169983, 1.0177725766762586, 1.2498755393454632, 1.4779918469566848, 1.6955014925982403, 1.8955392262422142, 2.0711545722111473, 2.2154874764946295, 2.3219558575570693, 2.3844506241980366, 2.397533091396478, 2.356629198885264, 2.258214545545057, 2.0999840216214496, 1.8809997731015746, 1.6018113868203592, 1.2645425540156041, 0.8729390606445763, 0.4323737639952254, -0.05019476185767238, -0.5663120116500613, -1.1061664792238102, -1.6587769254181712, -2.2122255632876513, -2.7539330838247627, -3.270969800207517, -3.7503956137664987, -4.179620061602742, -4.5467724554670195, -4.8410711233412895, -5.053180073733978, -5.175541065512079, -5.202669121153093, -5.131399994897838, -4.961079012046006, -4.693682028959405, -4.333861006317537, -3.8889088050841765, -3.368640253074856, -2.785189221657045, -2.1527243142796952, -1.487088706355576, -0.8053725853419589, -0.12542941067374067, 0.5346502663962193, 1.1570915224569565, 1.7249967223108176, 2.222897376341852, 2.63727693446801, 2.957045422710826, 3.1739477093707222, 3.2828887882889304, 3.282161763544786, 3.173567161016315, 2.9624156967182302, 2.65741059186933, 2.270409808158684, 1.8160730314287623, 1.3114026907007015, 0.7751925859438146, 0.22740163399843646, -0.31152634532866924, -0.8213731518045977, -1.2828614787142292, -1.6783484104063064, -1.9924706593044976, -2.2127161562266826, -2.329898757859651, -2.338515990562512, -2.236973819025305, -2.027667277581165, -1.716911258017213, -1.3147216040887997, -0.834452687337774, -0.29230358220567004, 0.2932894347309777, 0.902351317281313, 1.514130673065671, 2.1078960706607, 2.66373415745176, 3.1633168729636125, 3.590605792372781, 3.932463785579999, 4.179147674449364, 4.324660297592605, 4.366946171469278, 4.307921537604085, 4.153336732012788, 3.9124761938975787, 3.59770871483893, 3.2239073795546997, 2.8077647370419934, 2.3670337644937707, 1.9197288848083973, 1.4833234659007906, 1.0739807274783906, 0.705853745632331, 0.3904872964538566, 0.136349719518916, -0.05148300543407436, -0.17147593075250847, -0.22560952348778854, -0.21918118814141746, -0.16044388793416847, -0.060099988936262984, 0.06932416184088736, 0.21419119433135322, 0.3605167681262188, 0.49474534816340815, 0.6044973700805545, 0.6792485623437671, 0.7109053432155512, 0.6942452939240733, 0.6271985028144369, 0.5109537608332606, 0.34988276638787785, 0.15128520384959204, -0.0750327098266643, -0.3173243816913237, -0.562583643787008, -0.7973033821419044, -1.0082702947280544, -1.1833513839625567, -1.3122274836233943, -1.3870312818500405, -1.4028518760943536, -1.3580746930467509, -1.254534308873378, -1.0974678796063746, -0.8952680102198978, -0.6590453568246182, -0.4020224344712494, -0.1387903542881327, 0.11553106919083715, 0.34618275702511503, 0.5396541403807524, 0.6845167605491989, 0.7721528760910459, 0.7973329391878899, 0.7586033001633778, 0.6584554732769525, 0.5032602557504089, 0.30296331217989275, 0.07055279470694138, -0.1786766198766645, -0.4280260363346686, -0.6604126230073084, -0.8594508119247571, -1.0105316979174166, -1.1018357227241946, -1.1252152545562972, -1.0768889640404047, -0.9578987839429897, -0.7742923376598104, -0.537008444593031, -0.26145989950515036, 0.03317471857835464, 0.3249209102666873, 0.5901939907155292, 0.8051404266176174, 0.9470629937024745, 0.995850194579044, 0.9353269231475202, 0.7544445941250197, 0.4482349758558849, 0.018462597893097128, -0.5260745966821901, -1.1696284278056337, -1.889978776975573, -2.659296110575052, -3.445354966107428, -4.213043889650434, -4.926098446754774, -5.548968620471693, -6.048721165733201, -6.396872083492027, -6.571044800136007, -6.55635605342402, -6.346443717184343, -5.944068320009729, -5.361241979562955, -4.618863749366307, -3.745867596387161, -2.7779168775542264, -1.755705673307834, -0.722951099242065, 0.2758197001175757, 1.197570017875753, 2.0030158964680562, 2.6587239251716204, 3.138924656225583, 3.426935304215656, 3.516105349337357, 3.4102240357770417, 3.12335818805974, 2.679120634511191, 2.109402019009275, 1.4526300116942947, 0.7516480395667395, 0.05132893562478498, -0.6039441134834505, -1.1727873772180153, -1.6191737600029965, -1.914500869354211, -2.0392484934639943, -1.9841263499077706, -1.7506414462839388, -1.3510474164614845, -0.8076738674328438, -0.15167000421054946, 0.5787685623478757, 1.3405899722297034, 2.088368031477764, 2.7769325150543627, 3.3639946913637373, 3.812614165692243, 4.093361607181471, 4.186049180658243, 4.08092559249127, 3.779264128135102, 3.293308048207851, 2.6455760602545237, 1.8675689659840529, 0.9979546438507622, 0.08034003036973865, -0.8392362610766566], 'positive_zeros': ['0.865018489391644947576306318407176', '1.58352225995218499647825430730998', '2.92379543322230420286904726480403', '4.34688947879824989638240852916019', '5.35651003597376439022555275406789', '6.18201189549397271531044842879728', '7.59885311235206324120066146946642', '7.938635338928957048481784903231279', '8.653054204123174077433989533127866', '9.582281336055592187881628986573322'], 'prelabel': '2-1035-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.81453625341527, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.865018489391644947576306318407', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.58352225995218499647825430731', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.92379543322230420286904726480', 'prec': 100}}