-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '880570478284798827136822269174', 'a10': [921.9915173073556, 0.0], 'a2': [-3.6622807227741943, 0.0], 'a3': [42.344927282040146, 0.0], 'a4': [-114.58769990759653, 0.0], 'a5': [-251.7533709455628, 0.0], 'a6': [-155.07901089229068, 0.0], 'a7': [-343.0, 0.0], 'a8': [888.424256953722, 0.0], 'a9': [-393.907133478732, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.427037319055092, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [343.0, 0]]], [13, [[1.0, 0], [2197.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '91.1', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'euler_factors': [[[1.0, 0], [3.6622807227741943, 0], [128.0, 0]], [[1.0, 0], [-42.344927282040146, 0], [2187.0, 0]], [[1.0, 0], [251.7533709455628, 0], [78125.0, 0]], [[1.0, 0], [343.0, 0]], [[1.0, 0], [2926.603995068195, 0], [19487171.0, 0]], [[1.0, 0], [2197.0, 0]], [[1.0, 0], [-27794.842100176902, 0], [410338673.0, 0]], [[1.0, 0], [-34316.14851766567, 0], [893871739.0, 0]], [[1.0, 0], [21674.191429458388, 0], [3404825447.0, 0]], [[1.0, 0], [-115034.68752406159, 0], [17249876309.0, 0]], [[1.0, 0], [-13017.077557820146, 0], [27512614111.0, 0]], [[1.0, 0], [-481168.681436537, 0], [94931877133.0, 0]], [[1.0, 0], [-316117.5165198454, 0], [194754273881.0, 0]], [[1.0, 0], [-75163.90943801022, 0], [271818611107.0, 0]], [[1.0, 0], [-500395.1751354393, 0], [506623120463.0, 0]], [[1.0, 0], [466960.28267717717, 0], [1174711139837.0, 0]], [[1.0, 0], [-1347665.584184978, 0], [2488651484819.0, 0]], [[1.0, 0], [-2226180.4624331137, 0], [3142742836021.0, 0]], [[1.0, 0], [2367448.566632028, 0], [6060711605323.0, 0]], [[1.0, 0], [-619229.0709519918, 0], [9095120158391.0, 0]], [[1.0, 0], [-4506146.671242907, 0], [11047398519097.0, 0]], [[1.0, 0], [188250.4117658077, 0], [19203908986159.0, 0]], [[1.0, 0], [5109016.542708009, 0], [27136050989627.0, 0]], [[1.0, 0], [-1609699.9842498798, 0], [44231334895529.0, 0]], [[1.0, 0], [811101.0830769781, 0], [80798284478113.0, 0]], [[1.0, 0], [2553473.8450187645, 0], [107213535210701.0, 0]], [[1.0, 0], [-12026967.863851253, 0], [122987386542487.0, 0]], [[1.0, 0], [-4991524.09693546, 0], [160578147647843.0, 0]], [[1.0, 0], [16392720.203381522, 0], [182803912081669.0, 0]], [[1.0, 0], [6669181.450806807, 0], [235260548044817.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-91-1.1-c7-0-8', 'leading_term': '1.18405082629868943001086528987', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/91/8/a/d/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.07421875', 'prec': 34}, 'plot_values': [1.1840508262986895, 1.1690098553933206, 1.124104776671509, 1.0499867216630703, 0.9477330065902628, 0.8188352737511538, 0.6651828850142854, 0.4890415717386212, 0.2930273588383257, 0.08007580266678106, -0.14659338583321077, -0.3835162187674187, -0.6270286420459295, -0.8733148465837999, -1.1184593714214937, -1.3585026044648574, -1.589499192281095, -1.8075787695739376, -2.009008314022004, -2.190255325977325, -2.3480509283716215, -2.4794518836975006, -2.5819004360205398, -2.653280810714011, -2.6919711471403733, -2.6968896039356527, -2.6675333668111976, -2.6040093084843283, -2.5070551026382946, -2.378049681240241, -2.2190120489100957, -2.0325876302399384, -1.8220215259011687, -1.591118289805153, -1.3441881100430413, -1.085979577083072, -0.8215995487009706, -0.5564209660133872, -0.2959798311795748, -0.04586291608492916, 0.1884118771332288, 0.401520249080756, 0.5884587701207793, 0.7446718573783706, 0.8661754249045125, 0.9496740200693382, 0.9926681820470613, 0.9935487629268297, 0.9516750459151734, 0.8674336836592753, 0.7422757659053741, 0.5787297097842988, 0.3803881452600536, 0.1518675367565414, -0.10126006956384181, -0.372563067558175, -0.6548732092216176, -0.9404337464925526, -1.2210703130331586, -1.4883812640319316, -1.733943432112355, -1.9495285621866945, -2.1273250841537013, -2.2601593955607058, -2.341710480920397, -2.3667115118377624, -2.3311320704064826, -2.2323348308902413, -2.069200929548457, -1.8422188515220075, -1.5535324621961193, -1.2069447965576154, -0.8078753746660972, -0.3632701081984619, 0.11853573098241986, 0.6279995334208043, 1.1545949178398978, 1.6870719143086133, 2.2137474359402214, 2.7228184342886763, 3.202689036345988, 3.642302091367983, 4.031464957829936, 4.3611590721164, 4.623822890000482, 4.813598198231743, 4.926530563604366, 4.9607158149068145, 4.916385919873783, 4.795929391688219, 4.603843391332478, 4.346616924219717, 4.032546891938265, 3.6714911732690383, 3.274565286751268, 2.8537914399280133, 2.421710807290225, 1.9909716119872818, 1.573906934190126, 1.182117060293969, 0.8260715642234085, 0.5147461339854873, 0.2553084017712333, 0.05286570431419033, -0.08971418529071992, -0.1719007063513602, -0.19551072389728663, -0.16462867061777314, -0.08543740018504242, 0.034035933179054956, 0.18425114518352267, 0.35455227571598663, 0.5336166281417393, 0.7099388113220448, 0.8723309946054678, 1.0104192648773918, 1.1151154268751478, 1.1790438724205603, 1.1969042878985758, 1.1657529640508533, 1.0851882731031826, 0.9574294037740612, 0.7872815779281138, 0.5819855645571077, 0.3509541810849536, 0.1054034313348334, -0.14210923699160333, -0.37822258053451663, -0.5893642003523987, -0.7623740710699874, -0.8851325910758129, -0.9471655851481587, -0.9401986551619904, -0.8586344565896563, -0.6999288791227201, -0.4648456748425934, -0.15757369773940816, 0.21430356811459111, 0.6399903180495958, 1.1058100720899167, 1.5956773765965038, 2.0916936577924057, 2.574845158938744, 3.0257754916122908, 3.425600971974105, 3.7567338383813205, 4.003676851264207, 4.153752793297365, 4.19773408117104, 4.130341057304535, 3.950582459280929, 3.6619178970827653, 3.2722296602375383, 2.7935995203868624, 2.241895027954685, 1.6361787247436395, 0.9979622872279738, 0.35033545692405177, -0.28299369702310845, -0.878705463470749, -1.4148770454580506, -1.8719465926539813, -2.2335871746935214, -2.4874482269182847, -2.6257272000977467, -2.6455412961531497, -2.549077986788182, -2.3435131123280626, -2.040696287442023, -1.6566145845702132, -1.210656476671224, -0.7247082427852174, -0.22212393783053436, 0.2733828844220352, 0.7388726402423766, 1.1532829891303296, 1.4984469174071913, 1.7599738178627815, 1.9279476348243771, 1.9974045080297702, 1.9685628335355585, 1.8467907844444078, 1.642309516618693, 1.3696438692050248, 1.046845659492929, 0.6945269629154258, 0.3347513893137534, -0.010160288858042784, -0.3188482343460777, -0.5720910283952483, -0.7538791410287502, -0.8523253312355799, -0.8603605181010546, -0.7761741960983883, -0.6033714431782963, -0.35083335113786907, -0.03228353933274548, 0.3344205388502108, 0.7282373921764201, 1.1260844029939536, 1.5041142965492516, 1.8390570494655, 2.109554114863988, 2.297410762464759, 2.388695336593782, 2.3746212591265445, 2.252158357270546, 2.024334069958919, 1.7002015787963987, 1.2944700562517846, 0.8268110445830312, 0.32087342872921, -0.19694350684354464, -0.6988948425094883, -1.157397218408134, -1.5465558036239448, -1.843625656780172, -2.0303241690857305, -2.0939181467547057, -2.0280204623905407, -1.833046531273095, -1.516299352320183, -1.0916724954180603, -0.5789820672256418, -0.002960110093551593, 0.6080381692701252, 1.223543678807533, 1.812616041400628, 2.3455274184528356, 2.795391776625815, 3.139645685987127, 3.3612941549327027, 3.44984764024502, 3.4018935673579045, 3.221266516088676, 2.9188044921030856, 2.5117030625899153, 2.0225031393130593, 1.4777703872924837, 0.9065432460564951, 0.3386411614095106, -0.1970661285197694, -0.6743241868668027, -1.0709933875320403, -1.3702907208371218, -1.5616973899287685, -1.6414757380538905, -1.612762860083435, -1.4852344101036064, -1.2743590220712622, -1.0002897344937598, -0.6864621993331402, -0.357988735886327, -0.03995116745526991, 0.24429712581421645, 0.47470898197804634, 0.6358967128656451], 'positive_zeros': ['0.69464762461064572171608488658672', '2.90862220437325154832540882805827', '3.97886541521018069206200973170629', '5.47437468325190947382748799713161', '7.66859782573741137923503826714349', '8.070774301789460284001701249687357', '9.308793133193854476623161794553359', '10.12667583731171861481096510044544', '11.69301434076027506584294673141500', '12.79855601663954017464238655390435'], 'prelabel': '2-91-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.331701165580746, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.69464762461064572171608488659', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.90862220437325154832540882806', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97886541521018069206200973171', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 28.427037319055092, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/8/a/d/1/5'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-91-1.1-c7-0-8', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-91-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.331701165580746, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.69464762461064572171608488659', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '880570478284798827136822269174', 'Lhash_array': ['880570478284798827136822269174'], 'label': '2-91-1.1-c7-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/8/a/d/1/5'}