Formats: - HTML - YAML - JSON - 2026-08-27T03:45:51.489920
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '5529231308959443969539426230047', 'a10': [0.0, 0.0], 'a2': [-0.5, 0.8660254037844386], 'a3': [-1.5, -0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [1.5, -0.8660254037844386], 'a7': [-1.0, 1.7320508075688772], 'a8': [1.0, 0.0], 'a9': [1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.14373072363830475, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [1.5, 0.8660254037844386]]]], 'bad_primes': [2, 3], 'central_character': '18.7', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '6999306331500799189943033973487', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [1.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-2.5, 4.330127018922194]], [[1.0, 0], [1.0, -1.7320508075688772], [-3.5, -6.06217782649107]], [[1.0, 0], [-1.5, 2.598076211353316], [-5.5, -9.526279441628825]], [[1.0, 0], [1.0, 1.7320508075688772], [-6.5, 11.258330249197702]], [[1.0, 0], [3.0, 0], [17.0, 0]], [[1.0, 0], [1.0, 0], [19.0, 0]], [[1.0, 0], [-3.0, -5.196152422706632], [-11.5, 19.91858428704209]], [[1.0, 0], [3.0, -5.196152422706632], [-14.5, -25.11473670974872]], [[1.0, 0], [-2.0, -3.4641016151377544], [-15.5, 26.846787517317598]], [[1.0, 0], [4.0, 0], [37.0, 0]], [[1.0, 0], [4.5, 7.794228634059948], [-20.5, 35.50704155516198]], [[1.0, 0], [-0.5, 0.8660254037844386], [-21.5, -37.239092362730865]], [[1.0, 0], [-3.0, 5.196152422706632], [-23.5, -40.703193977868615]], [[1.0, 0], [-12.0, 0], [53.0, 0]], [[1.0, 0], [1.5, 2.598076211353316], [-29.5, 51.09549882328188]], [[1.0, 0], [4.0, -6.928203230275509], [-30.5, -52.827549630850754]], [[1.0, 0], [2.5, 4.330127018922194], [-33.5, 58.023702053557386]], [[1.0, 0], [12.0, 0], [71.0, 0]], [[1.0, 0], [-11.0, 0], [73.0, 0]], [[1.0, 0], [-2.0, 3.4641016151377544], [-39.5, -68.41600689897065]], [[1.0, 0], [6.0, -10.392304845413264], [-41.5, -71.88010851410841]], [[1.0, 0], [-6.0, 0], [89.0, 0]], [[1.0, 0], [2.5, -4.330127018922194], [-48.5, -84.00446416709055]], [[1.0, 0], [0, 0], [-50.5, -87.4685657822283]], [[1.0, 0], [7.0, 12.12435565298214], [-51.5, 89.20061658979718]], [[1.0, 0], [-3.0, 0], [107.0, 0]], [[1.0, 0], [16.0, 0], [109.0, 0]], [[1.0, 0], [3.0, 5.196152422706632], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 9589468, 'index': 0, 'label': '2-18-9.7-c1-0-0', '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/18/2/c/a/7/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 27}, 'plot_values': [0.41667430063456856, 0.4207823491959876, 0.4409022384524177, 0.475884677194713, 0.5244714068943845, 0.5854656798299991, 0.6577371288835387, 0.7401047575243558, 0.831168820054775, 0.9291390790909178, 1.0316825074595155, 1.1358014022413945, 1.237749769424597, 1.332996599029133, 1.416246156132184, 1.481526166609822, 1.5223540987266944, 1.5319893029170002, 1.5037744114405143, 1.4315630934609247, 1.3102231506233981, 1.1361943726902761, 0.908070146603718, 0.6271613819866821, 0.29799198743406446, -0.07133178998931144, -0.46893895307298755, -0.8792569634264242, -1.2833707828891228, -1.6597123162406036, -1.9850918499782844, -2.2360534076991874, -2.3905011413316752, -2.4295065246019183, -2.3391697357777055, -2.1123774950059055, -1.7502784598929875, -1.2632907170974632, -0.6714679050274935, -0.004083696529430243, 0.7016505945805551, 1.4027455357041958, 2.0533903158608626, 2.6085291269072335, 3.0277846601497047, 3.2793759414798695, 3.3436246923663258, 3.215630084514397, 2.9067248751916073, 2.4444106631713516, 1.8706045794196933, 1.2382053676563232, 0.606187690059975, 0.03363757398259807, -0.426677116913039, -0.7344770965824517, -0.8671046945931606, -0.8228819697841104, -0.6221005044369486, -0.30529232026286085, 0.07124675823663888, 0.44234312775393775, 0.7425366971204086, 0.9153608525181127, 0.9220879811164863, 0.7486611707291552, 0.4096547689023875, -0.051588092125345514, -0.5670263857205959, -1.0520083720846631, -1.4165685009927032, -1.5785657362712262, -1.4768790750942766, -1.08268789421273, -0.4069604502359258, 0.4973291339705152, 1.539065819663217, 2.598886319538806, 3.5441031264755565, 4.246788258764769, 4.602486295823629, 4.5467142030286505, 4.066526224733261, 3.204997890007627, 2.0574608617256147, 0.7595725029595164, -0.5313570641462654, -1.6591532621329388, -2.4922028203968223, -2.943719338668753, -2.9853617036614377, -2.6516552111281726, -2.03411051146523, -1.265669055172897, -0.49783393905391904, 0.12574333000005597, 0.4946384164088927, 0.5513914212613675, 0.30183598706284714, -0.1861687980656705, -0.795713043193454, -1.3834142509846326, -1.8075701043103602, -1.9566104956225452, -1.7722936312750326, -1.2628924560892103, -0.5034058935098513, 0.37769605650007565, 1.2229844504645495, 1.8772451766132883, 2.2191553151276837, 2.1869354603132827, 1.7924264038530975, 1.1202291119121182, 0.3115592037099606, -0.46429416826604086, -1.045232872692981, -1.3109680458684263, -1.2094417960853154, -0.7689662450087403, -0.09287531881745252, 0.662772754437677, 1.3240851287765156, 1.739415406986145, 1.8156991156294866, 1.542515457020826, 0.9977238871753177, 0.3324428905628914, -0.26220778446341847, -0.5998192689294681, -0.5450357080288034, -0.05076285205505969, 0.8230126726573918, 1.9143009626578615, 2.9883462646517187, 3.7856871068592537, 4.079039270390059, 3.72642367684197, 2.708187514623829, 1.1386916727481837, -0.7511299271545119, -2.65756630305156, -4.265311179419279, -5.3127258438624505, -5.646518471539261, -5.253235906671725, -4.260079091596033, -2.9045964603107266, -1.4801357138059903, -0.2697648842363771, 0.5157658873810976, 0.7813470835379478, 0.5619687475646566, 0.005276649752085108, -0.6728572882551368, -1.2480372819844183, -1.546738909787369, -1.4899428365343905, -1.109721652404401, -0.5346959234601082, 0.05133694604827447, 0.4659447613021424, 0.5838130559758244, 0.37574672377029084, -0.08061353973708274, -0.6221245564189688, -1.0482236907840312, -1.182588355196284, -0.9307721091522372, -0.31662325853367446, 0.5143797807056105, 1.3277823570263048, 1.86148646476474, 1.8998208983721967, 1.339887795205511, 0.23080110375223428, -1.2269285825678413, -2.7240215916102124, -3.917507695424116, -4.519111826883263, -4.373176059272983, -3.5022118713037793, -2.1062906108242108, -0.5148067059640191, 0.897639201922344, 1.809110585001635, 2.0353445214897237, 1.5781786399835795, 0.6233705774534347, -0.5122703272009739, -1.4701984750814772, -1.951067051207704, -1.7987609765441248, -1.043454300363554, 0.1088823984777842, 1.3377386738835157, 2.3024908207912476, 2.742516728104825, 2.553573670950578, 1.8177504361172658, 0.7778846369156945, -0.23617382938258674, -0.9075702306450365, -1.0287349998035498, -0.5648247076628834, 0.3351065010772651, 1.3828768551113606, 2.238501651256458, 2.6135449576697756, 2.358866197492987, 1.509765185837791, 0.274602679562977, -1.0294860508512922, -2.073611473020985, -2.6163832124972033, -2.574161049603617, -2.0402928715087882, -1.2476941137682271, -0.487451267221339, -0.010502895115859006, 0.05489409228857054, -0.2577170935003954, -0.7705744292480201, -1.2302119889306087, -1.4036336699263026, -1.1688196990765163, -0.5672524918627492, 0.20175780193799986, 0.8456977270426, 1.0826521944208083, 0.7498583466802834, -0.12097420799390618, -1.2903327213409295, -2.3688328150089384, -2.9320441129236356, -2.6577996609913703, -1.4420176251613972, 0.5463488228848913, 2.8927860854257528, 5.042949694793978, 6.45704893776474, 6.766531363776497, 5.884426679250696, 4.0340828429795845, 1.6861028159487774, -0.5778616765973187, -2.2325459720813337, -2.9558613250695602, -2.70991957904656, -1.732577715599355, -0.44484088709530667, 0.6934476332676814, 1.3311057362568508, 1.328042586961629, 0.7808191222724512, -0.03351090892477355, -0.7720027876857363], 'positive_zeros': ['4.36179441556210697223984606647442', '6.85650392855044452343093046473175', '9.327762105443371388541282310587141', '10.51435608625116348572044517929889', '11.75914826730233688681995342362333', '13.09153056920829555057476441676887', '15.04331307163907501027393190909017', '16.65829432309937211505679158925827', '17.34259594350077650929836362353579', '18.73425098025001598515848722622874'], 'prelabel': '2-18-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.379118350437307, 'root_angle': -0.05555555555555555, 'root_number': '0.9396926207859084 - 0.3420201433256687*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0555555555556', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.36179441556210697223984606647', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '6.85650392855044452343093046473', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '9.327762105443371388541282310587', 'prec': 103}}