Formats: - HTML - YAML - JSON - 2026-04-30T11:25:34.585339
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '3598654010009238231654156216433', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -1.7320508075688772], 'a4': [0.0, 0.0], 'a5': [0.5, 0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.10979430277926053, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.5, -0.8660254037844386]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 11], 'central_character': '220.109', 'coefficient_field': 'CDF', 'conductor': 220, 'conductor_radical': 110, 'conjugate': '2415028830739970026269758276970', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-1.0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, -1.7320508075688772], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, -1.7320508075688772], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 19439615, 'index': 1, 'label': '2-220-55.54-c0-0-1', 'leading_term': '0.72229495748589560053897221466412', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/220/1/e/a/109/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.07421875', 'prec': 34}, 'plot_values': [0.7222949574858956, 0.7471344865515256, 0.7884392710212828, 0.8458328277846823, 0.918214132421424, 1.0040894282670927, 1.1018288612729867, 1.2098039053538223, 1.326427853765456, 1.4501399977470626, 1.5793663698433005, 1.712476852386416, 1.847748499972762, 1.9833391330183232, 2.1172723889760006, 2.2474341762928622, 2.371580019665616, 2.4873526536934403, 2.5923091905568256, 2.6839571557658184, 2.75979861591442, 2.8173815044253048, 2.8543570894446684, 2.8685423323047927, 2.8579856679569393, 2.8210345143687707, 2.7564026005166555, 2.6632350068970134, 2.541168652908305, 2.3903858560191775, 2.2116585414743293, 2.006380710210069, 1.7765868866375907, 1.5249544746157389, 1.2547882539764663, 0.9699856526553279, 0.674981928195845, 0.3746749802597385, 0.07433018139728705, -0.22053365927322507, -0.5042753161570522, -0.7712764824904141, -1.0160979789239646, -1.2336426632859319, -1.4193202158779512, -1.5692084319171273, -1.6802052544862924, -1.7501655592377088, -1.7780166841340785, -1.7638469064676257, -1.708961521184016, -1.6159018767312523, -1.4884236752163607, -1.3314320299265234, -1.1508721713345769, -0.9535762671659758, -0.747068526370415, -0.5393325339652362, -0.33854654776920096, -0.1527942060645775, 0.010240330290304758, 0.14358242590854783, 0.2412707817449747, 0.2986429013126844, 0.3125898591438938, 0.28176825706325365, 0.20675801013740625, 0.09015589183798339, -0.06340342134806518, -0.24730476411841065, -0.4530915781756495, -0.6706868243489479, -0.888692509074106, -1.0947611626054319, -1.276029162372912, -1.4195985197466234, -1.5130507994518447, -1.5449743736833101, -1.5054843742240356, -1.3867136254839383, -1.1832526249619841, -0.8925173595123298, -0.5150254428141225, -0.054563726159289234, 0.4817658798589395, 1.0836312286201792, 1.7376891773668122, 2.427937439377402, 3.136191398978366, 3.8426723771414424, 4.5266882250701475, 5.167382042373223, 5.744520536066177, 6.2392903076757245, 6.635068395263806, 6.918132875328164, 7.078280357531882, 7.109319825803125, 7.009416459862415, 6.781264700097487, 6.432076705733408, 5.973380237068139, 5.420628537189007, 4.792633614097651, 4.110843010882824, 3.3984882624384953, 2.679640339348146, 1.978213067027091, 1.3169594249531913, 0.7165074923028846, 0.19448241888858678, -0.2352419231656928, -0.5631229807711735, -0.7843298099821442, -0.8989012308716795, -0.9116700135590776, -0.831952814950176, -0.6730175762110776, -0.451351901518811, -0.1857669312721018, 0.1036192270040239, 0.39646691559674807, 0.6733125777042286, 0.9166199000534128, 1.111726701792591, 1.247634021404241, 1.3175911477661433, 1.3194404523799883, 1.2556983544611242, 1.1333629816049855, 0.9634543409998082, 0.7603082627719396, 0.5406601426308836, 0.3225677199942203, 0.12423295554818667, -0.03720920435560654, -0.14686334408011428, -0.1931355610589866, -0.16861734171217663, -0.07073214573040111, 0.09790228335273264, 0.3294274145653599, 0.611026860287236, 0.9255329760105123, 1.25233158538564, 1.5685202956556357, 1.8502588401364586, 2.0742359262792585, 2.219167148794468, 2.2672334116772306, 2.205369494554175, 2.0263180980976307, 1.729375781596787, 1.3207731984263287, 0.8136521553244933, 0.2276251949112907, -0.41207167949627765, -1.075797320815726, -1.7310350522473104, -2.3441527018920683, -2.8822952610130126, -3.3153008673051843, -3.617525646144651, -3.7694646599194863, -3.7590649581940316, -3.582642191838397, -3.245333718306429, -2.7610474422773605, -2.151895315718124, -1.4471317065633598, -0.6816478136625592, 0.10589801129847244, 0.875209666412527, 1.5866194113599539, 2.20335625160648, 2.693678904954995, 3.032741020119122, 3.204070189634343, 3.2005640281186323, 3.0249349821380336, 2.6895689382919477, 2.2157990626504165, 1.632633343964498, 0.975009621895109, 0.2816831038672557, -0.40712363932022166, -1.052161250171283, -1.617530155937527, -2.072840969429787, -2.3950190589850604, -2.5696355971089746, -2.591677545289297, -2.465705483924646, -2.205388600242484, -1.8324478251749883, -1.375078233186982, -0.8659575993518241, -0.33997689505658196, 0.16815163077617074, 0.6262438394871697, 1.006787720182571, 1.2887327606070644, 1.4587996568018744, 1.512218771806421, 1.4528461176746212, 1.2926501675195117, 1.050608372743678, 0.7510955877194271, 0.4218845014421292, 0.09190777762221612, -0.2110494135450774, -0.4625510268584205, -0.6434366878483047, -0.7413228566467274, -0.7515588729199392, -0.6775582696717404, -0.5304726316732643, -0.3282255481263994, -0.09397415371819705, 0.1458884170307298, 0.36403819209168037, 0.5346542959991851, 0.6357885573775108, 0.6514779795179985, 0.5734224469750367, 0.40207935144996504, 0.14706839218628134, -0.17316921213362935, -0.5324561212710688, -0.8986495934638479, -1.2359827953493323, -1.507813727587555, -1.6795816635104184, -1.721748154179464, -1.612493260652929, -1.3399487001794996, -0.903777695926129, -0.31595483808497243, 0.3993446939315321, 1.206772567220149, 2.061708890412625, 2.912928196183737, 3.705859185260703, 4.386217990747586, 4.903760428563974, 5.215882739972666, 5.290804382941253, 5.110090669648189, 4.670316106615037, 3.9837283176575196, 3.0778432664197704, 1.9939799870821187, 0.784821393396527, -0.4888390090868923, -1.7619422398956675, -2.9693318718588775, -4.049949046364155], 'positive_zeros': ['2.83883745991311174958759578064985', '4.44806780003700737466445685372104', '5.01816571985453217309847345593320', '6.16819194162180967358625418537919', '8.195590797707479658159659135352582', '8.880042955447999587174155591468505', '10.00039946931955901204771160350788', '10.35125654164405097163988718077621', '11.53086444641975556756976949227357', '12.68141026790170625600555325741021'], 'prelabel': '2-220-55.54-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3313522337019332, 'root_angle': 0.16666666666666666, 'root_number': '0.50000000000000000000000000000000 + 0.86602540378443864676372317075312*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.16666666666666666', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.83883745991311174958759578065', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.44806780003700737466445685372', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.01816571985453217309847345593', 'prec': 103}}