-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1920519928044810928627276337645', 'a10': [0, 0], 'a2': [0, 0], 'a3': [200.2690669750293, 137.62739848210177], 'a4': [0, 0], 'a5': [0, -3630.4734623746162], 'a6': [0, 0], 'a7': [23226.529616651584, 0], 'a8': [0, 0], 'a9': [21166.398374097538, 55125.021368422174], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.49714812833877, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-200.2690669750293, -137.62739848210177]]]], 'bad_primes': [2, 3], 'central_character': '48.17', 'coefficient_field': 'CDF', 'conductor': 48, 'conductor_radical': 6, 'conjugate': '1209177963814796958577811094415', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-200.2690669750293, -137.62739848210177]], [[1.0, 0], [0, 3630.4734623746162], [-9765625.0, 0]], [[1.0, 0], [-23226.529616651584, 0], [282475249.0, 0]], [[1.0, 0], [0, 62442.66823691063], [-25937424601.0, 0]], [[1.0, 0], [170160.59233303164, 0], [137858491849.0, 0]], [[1.0, 0], [0, 2666261.019614036], [-2015993900449.0, 0]], [[1.0, 0], [766825.3728152035, 0], [6131066257801.0, 0]], [[1.0, 0], [0, 1403266.6525606064], [-41426511213649.0, 0]], [[1.0, 0], [0, -4832453.7337882845], [-420707233300201.0, 0]], [[1.0, 0], [-41829734.68270407, 0], [819628286980801.0, 0]], [[1.0, 0], [-50161900.34104759, 0], [4808584372417849.0, 0]], [[1.0, 0], [0, 149238758.38435915], [-13422659310152400, 0]], [[1.0, 0], [-198719042.38974768, 0], [21611482313284250, 0]], [[1.0, 0], [0, -155058581.64761353], [-52599132235830050, 0]], [[1.0, 0], [0, -42154060.07082022], [-174887470365513060, 0]], [[1.0, 0], [0, 292025856.7050006], [-511116753300641400, 0]], [[1.0, 0], [530726601.7895037, 0], [713342911662882600, 0]], [[1.0, 0], [522093290.87439704, 0], [1822837804551761400, 0]], [[1.0, 0], [0, 571364379.4879681], [-3255243551009881000, 0]], [[1.0, 0], [-2185876083.0001025, 0], [4297625829703557600, 0]], [[1.0, 0], [1965922696.9150977, 0], [9468276082626847000, 0]], [[1.0, 0], [0, -2185577339.1891484], [-15516041187205853000, 0]], [[1.0, 0], [0, 238742018.9409632], [-31181719929966182000, 0]], [[1.0, 0], [8841121837.894337, 0], [73742412689492830000, 0]], [[1.0, 0], [0, -16792828203.739288], [-110462212541120450000, 0]], [[1.0, 0], [8368649157.993578, 0], [134391637934412190000, 0]], [[1.0, 0], [0, -14355522534.676405], [-196715135728956540000, 0]], [[1.0, 0], [4725641389.807047, 0], [236736367459211740000, 0]], [[1.0, 0], [0, 13215836256.746756], [-339456738992222300000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-48-3.2-c10-0-15', 'load_key': 'CMFs-workshop', 'motivic_weight': 10, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [10], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/48/11/e/d/17/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [3.0674963270110553, 3.1955083158475324, 3.2288043632823316, 3.167226460389563, 3.014616465307459, 2.778663761871321, 2.470597690835851, 2.104732788782786, 1.69787986835645, 1.2686410018875751, 0.8366114164643883, 0.42151601516421217, 0.042312504841343426, -0.28370330600150667, -0.5417518468121038, -0.7203441816821108, -0.811937018035249, -0.8134307947646295, -0.7264772067592492, -0.557568507074054, -0.3178890168855998, -0.02291934525799201, 0.3082043947605623, 0.6535610185907127, 0.9895152288177129, 1.2919462411347615, 1.537578358014477, 1.7053467075802706, 1.7777230426160964, 1.7419218118603192, 1.5909064549755654, 1.324120622497928, 0.9478791031229916, 0.47536863946705066, -0.07377086743184838, -0.6742898340534267, -1.296574897390071, -1.9082463726363994, -2.4760283794177322, -2.9677874434218956, -3.3546149434125425, -3.612815267608789, -3.7256567469360125, -3.684747660057049, -3.4909155376177394, -3.1544945400379722, -2.6949618896786527, -2.1399083553965914, -1.5233769157993187, -0.8836545405403142, -0.26065057785780366, 0.3069626726468595, 0.7846400938399839, 1.1446601589054517, 1.3684028682235836, 1.4480027955286847, 1.3872079501393608, 1.201329612313805, 0.9162369056402897, 0.5664278813853787, 0.19229023301842108, -0.16325753451000832, -0.45848689692017996, -0.6566356668767876, -0.7294086405178818, -0.6598746292197759, -0.4444656267495904, -0.09384715182013728, 0.36748181731099194, 0.9028918168362536, 1.4665413506190605, 2.0073033111285223, 2.4733832593478913, 2.8172278398145956, 3.0002691550621146, 2.9970393427567656, 2.7982231091334024, 2.4122945592002067, 1.865503703607267, 1.2001283587966107, 0.4710756721414186, -0.2589118407075292, -0.9250355650871466, -1.466672469698692, -1.833451243783728, -1.9905486218615316, -1.9226297001722263, -1.6359675885868787, -1.1584448850999682, -0.5373477165341101, 0.1649075589063787, 0.8767481734793232, 1.5245534525714857, 2.0401844602040953, 2.368144339750541, 2.4715855013628243, 2.336473968660032, 1.9733972180210153, 1.416744243815338, 0.721271232471438, -0.04363741079594654, -0.8014286411487418, -1.476757899776117, -2.0038456411885437, -2.333844310775635, -2.4403293332360714, -2.3222194057609062, -2.0037147670791673, -1.5311873764504271, -0.9673250488556808, -0.3831784993058998, 0.1509579426618695, 0.5747226998838386, 0.8457633729126998, 0.9456515770917545, 0.8828080722417526, 0.6919589022336782, 0.4300685914550243, 0.1691475406012625, -0.013249144124457431, -0.04468084600370178, 0.1317109637202147, 0.5483087803321282, 1.2069343684895897, 2.076494212689194, 3.0948265270888777, 4.1746899874769765, 5.213287932769664, 6.104232152205932, 6.750485418443047, 7.076636070024289, 7.038884040457179, 6.631361448750989, 5.887848527143702, 4.878525993797767, 3.70205480744035, 2.4739075426169665, 1.3124048591007424, 0.3242588047665036, -0.4084629862871549, -0.8381860312468536, -0.9571213179642286, -0.7972306996733778, -0.42481831352769844, 0.06954921206051065, 0.5844206875703912, 1.0222710958978047, 1.3036421844430093, 1.378569566535807, 1.2336106114701302, 0.8934002630575242, 0.41644806208941565, -0.11426155654206123, -0.6045161765193057, -0.9640133454194126, -1.1211042417296921, -1.034864690440907, -0.7025680766822923, -0.1612913905531601, 0.5167439852308404, 1.2345371533371123, 1.884917310514832, 2.367233350065707, 2.6035681176415633, 2.5519160212464556, 2.2141557079600513, 1.6373941566556625, 0.908250700530675, 0.1407423906622, -0.5405423566329056, -1.0195004415870346, -1.2068896101581301, -1.0551260639230169, -0.5670797054520446, 0.20268702687518167, 1.1546474141373362, 2.1581732753303444, 3.070551899564991, 3.758310499533276, 4.117564651543848, 4.090182497197534, 3.673146934694534, 2.919523058454564, 1.9307439501975519, 0.8413102978897836, -0.20176473323117852, -1.0615499428097661, -1.6322358787557127, -1.8552273562648156, -1.7276578052093272, -1.3019033087912315, -0.676139144321352, 0.022536080641254074, 0.6596319788107744, 1.1158714104948173, 1.3070728426980351, 1.1979400559098563, 0.8073959899289699, 0.20452445746583398, -0.5042061898483158, -1.1942439420939532, -1.745422092110856, -2.0636435269127142, -2.097914650061986, -1.8496335374246253, -1.3723702486079656, -0.7620508067412173, -0.13918127424209106, 0.37378132608161496, 0.6758578066528893, 0.7074819474753129, 0.4631772561479331, -0.00556623758039806, -0.5980402653323463, -1.1816027099983542, -1.615637538290357, -1.7780250443330503, -1.5893690640668192, -1.0304835983326772, -0.1497191123750531, 0.9415629344565136, 2.0849747253698583, 3.1000812861358926, 3.814225711852699, 4.092071787837688, 3.8596551347884738, 3.1185905915944097, 1.9477436516925788, 0.491853700883136, -1.0610892621517238, -2.5098842241346935, -3.672378067900235, -4.414304046389324, -4.669638317599661, -4.4489218185514945, -3.834168820641321, -2.961428566221949, -1.994330335014924, -1.0935991613589033, -0.38826046983305773, 0.04609170271751158, 0.19795350470808973, 0.11762580983893518, -0.09737688552086514, -0.3261822797850054, -0.4528119375712942, -0.3930700331294781, -0.11454612471350134, 0.35445837785173934, 0.929084940311263, 1.4845372492831457, 1.8820024646869997, 1.9987483462259936, 1.7562930931367806, 1.140770799506289, 0.21102772270743633, -0.9076702871229179], 'positive_zeros': ['1.51502308893242200633719031819025', '2.63401499170346589744028010826700', '4.23399236582004066704141522008759', '6.30541573102605911872587130057108', '7.56583269676154654047569938387408', '8.402714793225725746142988820001313', '10.07998021395726622268800802634034', '11.22127531117165443829325885169999', '12.49295676385987939876530595553031', '13.83753787493901251892927287901750'], 'prelabel': '2-48-3.2-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.522422306229284, 'root_angle': 0.19165185774227864, 'root_number': '0.8241525389918901 + 0.5663678949880732*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.09582592887113932', 'prec': 64}, 'spectral_label': 'c10-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51502308893242200633719031819025', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.63401499170346589744028010826700', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.23399236582004066704141522008759', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 30.49714812833877, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 48, 'conductor_radical': 6, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/48/11/e/d/17/4'], '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': '2-48-3.2-c10-0-15', 'motivic_weight': 10, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [10], 'order_of_vanishing': 0, 'prelabel': '2-48-3.2-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.522422306229284, 'root_angle': 0.09582592887113932, 'self_dual': False, 'spectral_label': 'c10-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51502308893242200633719031819025', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1920519928044810928627276337645', 'Lhash_array': ['1920519928044810928627276337645'], 'label': '2-48-3.2-c10-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/48/11/e/d/17/4'}