-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3540330362542681007076362023351', 'a10': [0.0573271651579813, -1.5078900924488992], 'a2': [0.10919077767152784, 0.07933174364434314], 'a3': [0.9270509831248422, 2.853169548885461], 'a4': [-2.466506854620718, -7.5911275407961005], 'a5': [-6.223265800604651, -9.288216339805214], 'a6': [-0.12512149743747158, 0.385084372810022], 'a7': [-17.309896766054226, 0.0], 'a8': [0.6665549089496833, -2.05144506989779], 'a9': [-7.281152949374527, 5.2900672706322585], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.425143250430549, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.9270509831248422, -2.853169548885461]]], [5, [[1.0, 0], [6.223265800604651, 9.288216339805214]]]], 'bad_primes': [3, 5], 'central_character': '75.16', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '671381236936012785153938834276', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.10919077767152784, -0.07933174364434314], [2.4721359549995796, 7.608452130361228]], [[1.0, 0], [-0.9270509831248422, -2.853169548885461]], [[1.0, 0], [6.223265800604651, 9.288216339805214]], [[1.0, 0], [17.309896766054226, 0], [343.0, 0]], [[1.0, 0], [34.10365700916714, 24.777757177668036], [411.301619513055, 1265.8562231888493]], [[1.0, 0], [-68.3813227264269, 49.68193908200864], [678.9103366417595, -2089.4711663004523]], [[1.0, 0], [13.937412853541227, -42.894946090158605], [-3974.7004933641165, -2887.7889445129204]], [[1.0, 0], [-25.853417796341727, 79.56863833151465], [-5549.047564417764, -4031.619045474073]], [[1.0, 0], [16.933269499579726, 12.302740429620725], [3759.8097705599853, 11571.504633763134]], [[1.0, 0], [-68.0039463533895, -209.29462615477598], [-19731.11547581059, 14335.494518161127]], [[1.0, 0], [-49.51056323667106, 152.37784538977684], [-24101.42527942406, -17510.710451045066]], [[1.0, 0], [-212.95532311919763, 154.72109881122032], [15652.637816074212, -48173.865719898415]], [[1.0, 0], [331.81179079354104, -241.07537730512524], [21297.76026931575, -65547.76615957828]], [[1.0, 0], [-290.6991116039312, 0], [79507.0, 0]], [[1.0, 0], [142.4559807366401, 438.4344266853123], [-83994.57140699017, 61025.62824876144]], [[1.0, 0], [44.01716239078649, 135.4708960432933], [-120444.02307155904, 87507.70500554652]], [[1.0, 0], [-382.24021675107093, 277.71377338364016], [63465.60128773233, -195327.03626018236]], [[1.0, 0], [43.71799165630829, 31.762980177291503], [70140.98640021995, 215871.75912519026]], [[1.0, 0], [-139.04561189764112, 427.93839065382963], [-243322.37827919231, -176784.0558352411]], [[1.0, 0], [193.4624976352962, 595.4163440329575], [-289556.0814737318, 210374.80743325135]], [[1.0, 0], [39.432712005302655, 28.649542266439934], [120212.86410075892, 369977.1527995918]], [[1.0, 0], [200.11045119034202, 615.8766412452277], [-398876.9298896297, 289801.05300502863]], [[1.0, 0], [-206.9953555813237, 637.0661981443776], [-462585.4001626681, -336087.96605255635]], [[1.0, 0], [-700.6379167747742, -509.04324326995413], [217847.40150751232, 670465.3612360781]], [[1.0, 0], [54.71067049297949, 168.38212988406286], [-738367.9673071664, 536455.7295655283]], [[1.0, 0], [-810.6373771154292, 0], [1030301.0, 0]], [[1.0, 0], [-421.6013220324252, -1297.5554480705173], [-884034.7132123532, 642288.8153817973]], [[1.0, 0], [1109.5317078738572, 0], [1225043.0, 0]], [[1.0, 0], [1022.5634422288185, -742.9358283627896], [400185.96920839377, -1231645.7692411963]], [[1.0, 0], [-925.943513831083, 672.7373413290019], [445879.6941326285, -1372276.5941927282]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-75-25.16-c3-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/75/4/g/b/16/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8532904145633031, 1.0326057800890789, 1.2034772907180349, 1.3654240494660332, 1.5175103022178849, 1.658280015679774, 1.785732640131694, 1.8973427871747055, 1.9901249468923952, 2.0607429687700263, 2.1056627102365266, 2.12134482709582, 2.1044729672237956, 2.0522105318143744, 1.9624766890794325, 1.834229572151682, 1.6677417682477957, 1.4648505848276536, 1.2291634837460168, 0.966197851726385, 0.6834342647949042, 0.39026390966859975, 0.0978140822249912, -0.1813591741902112, -0.43371520059889157, -0.6453047862526393, -0.8024632045486924, -0.892594304169391, -0.9050086698647585, -0.8317685680891245, -0.6684838562753304, -0.4149972988818155, -0.07589579572964099, 0.3392132544395544, 0.8157132496497715, 1.3343166275179328, 1.8717504967666856, 2.4017866066884377, 2.896585699259331, 3.328297728277295, 3.6708314218209144, 3.9016817387211713, 4.003684594131344, 3.9665573764173367, 3.7880834613916137, 3.47481073097651, 3.0421587107375596, 2.5138659397654393, 1.9207569233816189, 1.298863569995726, 0.6869952778199802, 0.12390976924651897, -0.3547122552391673, -0.7192472782014017, -0.9488022143786572, -1.033320766416816, -0.9748892771740937, -0.7880598355413786, -0.4990826443398436, -0.14403208921357544, 0.23408559388768505, 0.5890498261659656, 0.8756783926610241, 1.0542479896584114, 1.0946672424203574, 0.979976224076169, 0.7087782867261587, 0.296285152674858, -0.2262288807103494, -0.8136213802592179, -1.4106173426551605, -1.956810187208236, -2.392499327112433, -2.66481542921013, -2.733513705737035, -2.57580629112869, -2.189663357524899, -1.5951384035282574, -0.8334576379022259, 0.03615944386529272, 0.9417337369116797, 1.8053589315477516, 2.5509709574628094, 3.11224807786372, 3.4397735873025117, 3.5066279011441908, 3.311711079642728, 2.880321631396934, 2.2618121807010576, 1.524476473050753, 0.7481572556723, 0.01535981748861442, -0.598127653854565, -1.0320002435868263, -1.2485080182101258, -1.236914125648045, -1.0147060997092714, -0.6253083337733942, -0.13247678443299865, 0.38801095923266626, 0.8583824307512764, 1.2093613136759525, 1.3897567428011635, 1.3738465470075558, 1.1654886759472642, 0.7982885120010863, 0.33165362582405666, -0.15688059058712672, -0.5821439486870414, -0.8633044217492145, -0.9357175519412516, -0.7609933875005022, -0.3337951393985941, 0.3157264632198724, 1.124395922991272, 2.003239463762067, 2.848662059611824, 3.5561647052610432, 4.034767243340629, 4.220120448176876, 4.084390905801365, 3.6413832697893413, 2.945985234465842, 2.08780206581094, 1.1796828325071016, 0.34260905658449364, -0.3109984783907816, -0.69319291620658, -0.7533037502838651, -0.4856763254333932, 0.06891935526777894, 0.8285783830609477, 1.6816290865625798, 2.502530088837376, 3.1700207659323816, 3.5848464742964863, 3.6843745280825546, 3.4518253044292444, 2.918616933237615, 2.1593540613756272, 1.2801281028582463, 0.40186208280587793, -0.35874435580494307, -0.9076750214881728, -1.1884956026882312, -1.1912307553119443, -0.9536804943598153, -0.5548344837810407, -0.10133178149184353, 0.2909153220954553, 0.5169590928280757, 0.5015541571183293, 0.21319540812819884, -0.32904121768459277, -1.0572079036757487, -1.8646882540981624, -2.623395193715381, -3.205228843739227, -3.5042508317924486, -3.4558016357878842, -3.049196126829209, -2.3316312255910905, -1.4023766482696969, -0.39796174840315296, 0.529359016487982, 1.2363573801601482, 1.6126442163798436, 1.599442151441453, 1.1999856627779235, 0.47959025824228574, -0.4448132740729756, -1.4240469275478749, -2.301727393216307, -2.9406890995261445, -3.2461681146634307, -3.1816154227328193, -2.7742482438373313, -2.109236867225227, -1.313453337005115, -0.5316154482136387, 0.10090587190557765, 0.4836605619760457, 0.5703258582468137, 0.3778816944225035, -0.016120959068208752, -0.48789815479297405, -0.8909052136154291, -1.0842095961233316, -0.9605198827156052, -0.4685750363711463, 0.3744588482948193, 1.4831517535382608, 2.7167884935551037, 3.9030049900237986, 4.867864757121211, 5.466854540074106, 5.61099755630148, 5.283104188885366, 4.540971942747033, 3.5067867263748282, 2.344609624745375, 1.2301514270393459, 0.31858318840976646, -0.28341424930067705, -0.5359093521581147, -0.4706706583428864, -0.1817754604957111, 0.19632045773338688, 0.518915695460896, 0.6633446207413265, 0.5568135835690282, 0.19397369746387413, -0.3596207490037096, -0.9792259926317264, -1.5057756730235394, -1.7791363745850268, -1.6731375263397568, -1.1252063292240253, -0.15432563483839767, 1.136779043242934, 2.5762376131401203, 3.952064148262782, 5.050281499678765, 5.694831041134212, 5.781412259397601, 5.298428908753063, 4.3306530444648415, 3.0445898319242217, 1.6581659234176267, 0.4005337311915268, -0.5301743877604869, -1.0028322231240263, -0.9759488763938353, -0.5025192674454535, 0.2837214132665665, 1.1976605329243422, 2.0416106776852434, 2.6454497737295197, 2.89976299840665, 2.7751749222256166, 2.324034692114128, 1.6644200946888381, 0.9502492494546274, 0.3343060079589781, -0.0674672693028812, -0.2023336307332099, -0.09177272351686559, 0.17544388720417017, 0.46664626756628735, 0.639875581183175, 0.5817829741689617, 0.2399505233343071, -0.35819152365697154, -1.1048381928378552, -1.8306149759688528, -2.3392770767623654, -2.4511248842779993], 'positive_zeros': ['2.79282821457685224554808780955825', '4.02454250194091312590327069913118', '6.40502448446631637706003984093244', '7.42269353390679690128178304548397', '8.448442682194050707448730757062044', '9.869975518011324552515089915315795', '11.37780947548168439572934816442675', '12.28169404329182035475979971350954', '13.33414589476481676699368344868007', '14.06888842884162304659238952512110'], 'prelabel': '2-75-25.16-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.103602445908102, 'root_angle': 0.6641914440107717, 'root_number': '-0.4932506149322011 + 0.8698872518142828*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.332095722005', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.79282821457685224554808780956', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.02454250194091312590327069913', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.40502448446631637706003984093', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.425143250430549, 'bad_primes': [3, 5], 'central_character': '25.16', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/4/g/b/16/4'], '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': '2-75-25.16-c3-0-10', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-75-25.16-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.103602445908102, 'root_angle': 0.33209572200538584, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.79282821457685224554808780956', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3540330362542681007076362023351', 'Lhash_array': ['3540330362542681007076362023351'], 'label': '2-75-25.16-c3-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/4/g/b/16/4'}