-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1125639156288189117603165741470', 'a10': [-290565860.11234784, 0], 'a2': [-237.84415922346454, 0], 'a3': [-14184.621280873474, 0], 'a4': [-74502.15592328325, 0], 'a5': [1221664.89629602, 0], 'a6': [3373729.322452614, 0], 'a7': [10556377.646355093, 0], 'a8': [48894612.273646705, 0], 'a9': [72063317.88180864, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.134405329922345, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '8.5', 'prec': 10}, 'bad_lfactors': [[29, [[1.0, 0], [-500246412961.0, 0]]]], 'bad_primes': [29], 'central_character': '29.1', 'coefficient_field': 'CDF', 'conductor': 29, 'conductor_radical': 29, 'degree': 2, 'euler_factors': [[[1.0, 0], [237.84415922346454, 0], [131072.0, 0]], [[1.0, 0], [14184.621280873474, 0], [129140163.0, 0]], [[1.0, 0], [-1221664.89629602, 0], [762939453125.0, 0]], [[1.0, 0], [-10556377.646355093, 0], [232630513987207.0, 0]], [[1.0, 0], [-982200267.1991818, 0], [505447028499293760, 0]], [[1.0, 0], [-5209422923.928067, 0], [8650415919381338000, 0]], [[1.0, 0], [24840478211.85431, 0], [827240261886336800000, 0]], [[1.0, 0], [-73513937552.30995, 0], [5480386857784803000000, 0]], [[1.0, 0], [463391286314.37305, 0], [141050039560662970000000, 0]], [[1.0, 0], [-500246412961.0, 0]], [[1.0, 0], [-4008080273996.885, 0], [22550116774162744000000000, 0]], [[1.0, 0], [-9746123730323.625, 0], [456487940826035130000000000, 0]], [[1.0, 0], [-57965602518850.98, 0], [2614120267500775300000000000, 0]], [[1.0, 0], [87467903071371.62, 0], [5874403106360420000000000000, 0]], [[1.0, 0], [-89491675591141.78, 0], [26647936506962194000000000000, 0]], [[1.0, 0], [-603302739412625.1, 0], [205442259656281400000000000000, 0]], [[1.0, 0], [-908899201611035.2, 0], [1271991467017507700000000000000, 0]], [[1.0, 0], [2235416736561572.8, 0], [2241853325254885400000000000000, 0]], [[1.0, 0], [-1042683622608649.8, 0], [11047694236668359000000000000000, 0]], [[1.0, 0], [-2030349680856253.8, 0], [29606831241262270000000000000000, 0]], [[1.0, 0], [3655307620372388.0, 0], [47477585226700100000000000000000, 0]], [[1.0, 0], [-6952745024928186.0, 0], [181827912146592060000000000000000, 0]], [[1.0, 0], [10515557772487876, 0], [421044084813170700000000000000000, 0]], [[1.0, 0], [36327309739356320, 0], [1379209096840925500000000000000000, 0]], [[1.0, 0], [-137558768371273700, 0], [5958260438588052000000000000000000, 0]], [[1.0, 0], [204385613985961920, 0], [11843044313729356000000000000000000, 0]], [[1.0, 0], [11817959321904384, 0], [16528476322717512000000000000000000, 0]], [[1.0, 0], [247034449184561380, 0], [31588152109649857000000000000000000, 0]], [[1.0, 0], [5514122887980961.0, 0], [43276334103547420000000000000000000, 0]], [[1.0, 0], [-25147466429870884, 0], [79860778452816620000000000000000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-29-1.1-c17-0-14', 'leading_term': '1.405775071378568585533804468057615046632188244239541307', 'load_key': 'CMFs-workshop', 'motivic_weight': 17, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [17], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/29/18/a/b/1/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.08203125', 'prec': 34}, 'plot_values': [1.4057750713785686, 1.3883805504082585, 1.336816659008588, 1.2529251072463397, 1.139718169701855, 1.001294349663135, 0.8427233272337339, 0.66990312462953, 0.4893931406303901, 0.30822733874150343, 0.1337124047215987, -0.026783894481819837, -0.1660486274664852, -0.2772382105377534, -0.3540858164515308, -0.3910961030564067, -0.383721946977348, -0.32851826463116884, -0.22326852781344048, -0.06708022322925618, 0.13955374889670866, 0.39472990886184633, 0.6951465340791136, 1.0361538183254695, 1.4118411983607828, 1.815160215209443, 2.2380803221618755, 2.6717741428538098, 3.1068278445171122, 3.53347154653358, 3.9418240540086167, 4.3221457092664295, 4.665092807260049, 4.9619668369444145, 5.204951799031585, 5.3873330165000075, 5.5036911986452735, 5.550066038629247, 5.524084310013343, 5.425048266588387, 5.253981124349993, 5.013627492867495, 4.708407799842522, 4.344326988287359, 3.928839028694917, 3.470670045068945, 2.9796040688430745, 2.4662365734191525, 1.9417019699143896, 1.4173821290711308, 0.9046037052348471, 0.4143325496386754, -0.043126209625104585, -0.45841379071243993, -0.8233806483118106, -1.1313186398376538, -1.3771551671203075, -1.5576029187571359, -1.6712599796593557, -1.7186564053434696, -1.7022448462510416, -1.6263344128096613, -1.496968650841659, -1.3217502009607436, -1.1096163936473147, -0.8705716312941614, -0.6153838774318502, -0.35525386123053304, -0.10146666545605397, 0.13496384321244717, 0.3436467959532616, 0.5151512140336328, 0.6413171013348341, 0.7155303724597941, 0.732952146396138, 0.6906941632465728, 0.5879336139465389, 0.42596247094615486, 0.2081684218666458, -0.06005332079875988, -0.3714557994526365, -0.7171598668555296, -1.0869314824485494, -1.4695086291359787, -1.852967855871466, -2.225118860114988, -2.5739142807571547, -2.887861031833203, -3.156419113835047, -3.3703739223214866, -3.5221686468518834, -3.60618441421457, -3.618957358160944, -3.5593237554779034, -3.42848670030968, -3.230000424462164, -2.9696712263597833, -2.6553769493163917, -2.2968099463709573, -1.9051513747768014, -1.49268736794126, -1.0723800288785277, -0.6574081769996168, -0.2606942706219039, 0.10556515251308529, 0.43034787988412654, 0.704216001031857, 0.9196712150296372, 1.0714409097450017, 1.1566827460897826, 1.1750983144518516, 1.1289497153007488, 1.0229765391450012, 0.864214552416789, 0.6617212919284597, 0.42621757951278244, 0.16965753603599373, -0.09525715055467805, -0.3556003060221168, -0.5987613178411009, -0.81298054548218, -0.9878581023081484, -1.1148145154219073, -1.187483160375546, -1.2020166262919287, -1.157292231356051, -1.055005680692159, -0.8996462069940794, -0.6983512983885006, -0.4606441136790983, -0.19806171122219438, 0.0763129360266735, 0.3483977111208061, 0.603715618705237, 0.8280321706276186, 1.0079993696756315, 1.1317786850023563, 1.189615474996485, 1.1743385604531662, 1.0817610713496788, 0.9109622214847357, 0.6644341931868447, 0.3480836779282393, -0.028916385987389027, -0.454422949889142, -0.9137584224423948, -1.3902708663649563, -1.8659981025489287, -2.3224097968466832, -2.7411973727127115, -3.105078552954981, -3.398581662068848, -3.6087746382927155, -3.725905070555992, -3.7439204813251523, -3.6608424437137543, -3.478973802974442, -3.204925056714704, -2.8494535653841675, -2.4271173978872196, -1.9557539150921914, -1.455801285354397, -0.9494886364969357, -0.45992711752508775, -0.010139441451220484, 0.3779307735404468, 0.6843865726806997, 0.8922787913751434, 0.9883993032248023, 0.9639288104530719, 0.8149072764328896, 0.542502386838956, 0.15306002657548995, -0.34206969147535543, -0.9269272341581034, -1.581545537109049, -2.2827354849311616, -3.0050226355683747, -3.72169530557286, -4.405918307726959, -5.03186283781739, -5.575801473336562, -6.017118100204391, -6.3391858381824555, -6.530071588499984, -6.5830334599842315, -6.496786716363777, -6.275524606124427, -5.928691989372432, -5.470521511636535, -4.919353612654755, -4.296772319829967, -3.626598012075145, -2.9337856598156433, -2.243282045973219, -1.578897854321561, -0.9622501059046144, -0.4118272004526122, 0.05777710849404538, 0.43642285271430703, 0.7187485867763522, 0.9042461982841924, 0.9970832118081002, 1.0056832480142233, 0.9420881416518778, 0.8211369784208236, 0.6595073360194458, 0.47467174116125554, 0.28382732444124137, 0.1028585487091887, -0.054608457218743786, -0.17800599873389597, -0.26043300089443655, -0.29903522739634075, -0.2951339507686958, -0.25409348996482595, -0.18493281534703165, -0.09970118498932486, -0.012651696145792311, 0.060741086114215165, 0.10486335106062727, 0.10508111370478501, 0.04882964605282359, -0.07339298772086376, -0.2671905159140489, -0.533645691503506, -0.8689536856499662, -1.2643413671930603, -1.7062863439576517, -2.1770325846991914, -2.655382119116563, -3.1177257121646886, -3.539260498377707, -3.895330242491565, -4.162814941096313, -4.321491501297096, -4.355286619790508, -4.25334689239357, -4.010859506793014, -3.6295692494364697, -3.1179533862484647, -2.4910344352789315, -1.769830941835345, -0.9804669756187454, -0.1529810170917936, 0.6801069844033013, 1.4853964113760896, 2.2302893645391033, 2.8846646942488046, 3.422449208263792, 3.8229964130101255, 4.072192232924492, 4.163221097587324, 4.096943890114465, 3.881860551369556, 3.5336534594639852, 3.074331730889214], 'positive_zeros': ['0.887972723781716850296972329588515', '1.58748124921774700233115227452869', '4.25758292376878231104200351477167', '5.61238385387607476718305731073913', '6.46327816078076640464976113180190', '8.506739263630567185202379251385854', '9.568205081757098329171617332079027', '10.72339259313876738591249202581103', '11.72456431746384482802319028891159', '13.45509737135551415277588915454105'], 'prelabel': '2-29-1.1-c17-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.289335040312137, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c17-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.887972723781716850296972329589', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.58748124921774700233115227453', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.25758292376878231104200351477', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 53.134405329922345, 'bad_primes': [29], 'central_character': '1.1', 'conductor': 29, 'conductor_radical': 29, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/29/18/a/b/1/8'], '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': '2-29-1.1-c17-0-14', 'motivic_weight': 17, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [17], 'order_of_vanishing': 0, 'prelabel': '2-29-1.1-c17-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.289335040312137, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c17-0', 'z1': {'__RealLiteral__': 0, 'data': '0.887972723781716850296972329589', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1125639156288189117603165741470', 'Lhash_array': ['1125639156288189117603165741470'], 'label': '2-29-1.1-c17-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/29/18/a/b/1/8'}