-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '265489441207447803033785433647', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.7960930657056438, 0.6051742151937651], 'a4': [-0.16178199655276473, 0.9868265225415261], 'a5': [-0.46840844069979015, 0.8835120444460229], 'a6': [0.0, 0.0], 'a7': [0.9941379571543596, -0.10811901842394177], 'a8': [0.0, 0.0], 'a9': [-1.994788450526988e-80, 2.9138367777778325e-80], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7372453089754814, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[59, [[1.0, 0], [0, 0]]]], 'bad_primes': [59], 'central_character': '3481.1311', 'coefficient_field': 'CDF', 'conductor': 3481, 'conductor_radical': 59, 'conjugate': '2665858864519534202877452642879', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.16178199655276473, -0.9868265225415261]], [[1.0, 0], [0.7960930657056438, -0.6051742151937651], [0.2675283385292208, -0.9635499925192229]], [[1.0, 0], [0.46840844069979015, -0.8835120444460229], [-0.5611870653623824, -0.8276889981568906]], [[1.0, 0], [-0.9941379571543596, 0.10811901842394177], [0.9766205557100867, -0.21497044021102407]], [[1.0, 0], [0, 0], [-0.7960930657056438, 0.6051742151937651]], [[1.0, 0], [0, 0], [0.8568571761675893, -0.5155538571770217]], [[1.0, 0], [1.9882759143087192, 0.21623803684788354], [0.9766205557100867, 0.21497044021102407]], [[1.0, 0], [0.054138908585417526, 0.9985334138511238], [-0.9941379571543596, 0.10811901842394177]], [[1.0, 0], [0, 0], [-0.6473862847818277, -0.7621620551276365]], [[1.0, 0], [0.6473862847818277, -0.7621620551276365], [-0.16178199655276473, -0.9868265225415261]], [[1.0, 0], [0, 0], [0.9941379571543596, 0.10811901842394177]], [[1.0, 0], [0, 0], [-0.46840844069979015, -0.8835120444460229]], [[1.0, 0], [0.907575419670957, -0.4198891015602646], [0.6473862847818277, -0.7621620551276365]], [[1.0, 0], [0, 0], [-0.7960930657056438, -0.6051742151937651]], [[1.0, 0], [0, 0], [0.5611870653623824, -0.8276889981568906]], [[1.0, 0], [0.9766205557100867, 0.21497044021102407], [0.907575419670957, 0.4198891015602646]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.16178199655276473, -0.9868265225415261]], [[1.0, 0], [0, 0], [-0.46840844069979015, 0.8835120444460229]], [[1.0, 0], [-0.9368168813995803, -1.7670240888920459], [-0.5611870653623824, 0.8276889981568906]], [[1.0, 0], [0, 0], [-0.054138908585417526, -0.9985334138511238]], [[1.0, 0], [0.7960930657056438, 0.6051742151937651], [0.2675283385292208, 0.9635499925192229]], [[1.0, 0], [0, 0], [0.7259954919231308, 0.6876994588534233]], [[1.0, 0], [0, 0], [0.16178199655276473, 0.9868265225415261]], [[1.0, 0], [0, 0], [-0.054138908585417526, 0.9985334138511238]], [[1.0, 0], [0, 0], [-0.9766205557100867, -0.21497044021102407]], [[1.0, 0], [0, 0], [0.9476531711828025, -0.31930153013597995]], [[1.0, 0], [-0.9476531711828025, 0.31930153013597995], [0.7960930657056438, -0.6051742151937651]], [[1.0, 0], [0, 0], [0.8568571761675893, 0.5155538571770217]], [[1.0, 0], [0, 0], [0.5611870653623824, 0.8276889981568906]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-59e2-59.13-c0-0-0', 'leading_term': '0.32246968650616473299829412565124', '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/3481/1/d/a/1311/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.32246968650616475, 0.2397069578978592, 0.16110599427559402, 0.0848182498819146, 0.00937036261065795, -0.06624180444503124, -0.1425148679824015, -0.2194468144887652, -0.2965787045156958, -0.37305519437837786, -0.4476935083832739, -0.5190546880636857, -0.585514258063518, -0.6453315142093113, -0.6967176450778615, -0.7379031849197473, -0.7672051659965292, -0.7830940045145912, -0.784259747033089, -0.7696768973681105, -0.7386666771078036, -0.6909552664298599, -0.6267263367907426, -0.5466660293286651, -0.4519984562727691, -0.344509809720108, -0.22655925413815078, -0.1010749558936293, 0.02846613657355416, 0.15807580811868044, 0.2833100196437124, 0.3993424297468499, 0.5010556112288472, 0.5831490009686668, 0.6402620181692357, 0.6671101744714197, 0.6586313999063123, 0.6101392424765787, 0.5174790885142407, 0.3771831181612499, 0.18661937701116427, -0.05586986870108965, -0.35084540215259635, -0.6976687841139516, -1.0944251335680415, -1.5378751480195225, -2.023439974816827, -2.5452218055147933, -3.0960621743916197, -3.66763891777977, -4.25060161717961, -4.834744136358289, -5.409211606197342, -5.962737950715311, -6.483908826493541, -6.961443710646512, -7.3844898648985415, -7.742920069424054, -8.027625401078188, -8.230793962954564, -8.346166385866422, -8.36925913929793, -8.29754722206472, -8.130598653150972, -7.870154341251946, -7.520148355790217, -7.086665318958885, -6.577833542510082, -6.00365458878043, -5.375772077860078, -4.707184719580729, -4.011910642806938, -3.3046120456782497, -2.600190919840702, -1.9133680338657297, -1.2582584273624837, -0.6479573090738728, -0.09415042369816234, 0.3932373770630801, 0.8063424664434066, 1.139600134581522, 1.389909928157499, 1.5567211901904094, 1.6420339857162223, 1.6503135168592478, 1.5883192338674303, 1.4648530253261762, 1.2904340008026385, 1.0769103383157526, 0.8370213337529506, 0.5839250420042663, 0.3307086335146346, 0.08989971451289702, -0.12700269571855452, -0.309959117057237, -0.45076509949968907, -0.5433556157566427, -0.5840251601289747, -0.5715534149126276, -0.5072299148524132, -0.3947750939611839, -0.2401592874526379, -0.05132551834431468, 0.16217395279085012, 0.38961347455260276, 0.6195850070938961, 0.840524262201593, 1.0412499510836284, 1.2114929774167187, 1.342392241353041, 1.4269345513670468, 1.4603179753272726, 1.4402207562431306, 1.3669615839625797, 1.2435414218217788, 1.0755620689190384, 0.8710219941335928, 0.6399954824594974, 0.39420654737319105, 0.14651413917203748, -0.08967032153076791, -0.3010083569967529, -0.47487536106684647, -0.5999880631205368, -0.6669892633055575, -0.6689616145637907, -0.6018445891561159, -0.4647323908684228, -0.26003533706975174, 0.006507041719349222, 0.32596648330430716, 0.6865184435097075, 1.073877836409626, 1.4718624916751823, 1.8630623555600347, 2.229586873031543, 2.553858499428097, 2.8194171484137747, 3.0116987820169996, 3.1187514155088, 3.131853597790872, 3.046003910146351, 2.8602550945941703, 2.5778728903716095, 2.206307262741635, 1.7569721285030373, 1.2448385433013403, 0.6878552092588911, 0.10621866435119535, -0.47847679128720527, -1.044172885934719, -1.5693233978108885, -2.033867818113204, -2.42015700399719, -2.713786261938798, -2.904294559593041, -2.985693894002233, -2.956800048125994, -2.8213447506742257, -2.587859234187104, -2.2693299108953946, -1.8826378525147163, -1.4478044392408522, -0.9870754038064627, -0.5238840324437981, -0.08174104083813256, 0.31689676020282836, 0.6517247408466603, 0.9056018601466441, 1.065424510557993, 1.1228177870063376, 1.074607201191292, 0.9230439015183795, 0.675768053140994, 0.3455076383227864, -0.050477053112322375, -0.49118020381533634, -0.9528335980012326, -1.410040802576819, -1.8370087914024213, -2.2088176211107693, -2.5026658608600894, -2.6990296572843917, -2.782676634596898, -2.7434821830146747, -2.577004812407607, -2.2847887294317664, -1.874375091460417, -1.3590178496713052, -0.7571149926887173, -0.09138057915083862, 0.6122035584711627, 1.3256058652504539, 2.020073047868565, 2.667501885879523, 3.241785825233712, 3.7200679212907066, 4.083835886250933, 4.319802593675894, 4.420526050525226, 4.38473604531326, 4.217349754864265, 3.9291747648055537, 3.5363143810173487, 3.059305903557619, 2.522036843195842, 1.950496092144054, 1.3714261343411407, 0.8109479665558655, 0.29323215178000844, -0.16071280204744623, -0.5340696783095705, -0.8150040913213225, -0.9971758855666485, -1.0799432632804964, -1.0682494442861703, -0.9721992952210358, -0.8063507187909899, -0.5887616907395434, -0.3398477521212665, -0.08111569564854547, 0.16615352722287277, 0.38219646474041213, 0.5499583198420946, 0.6561139963839289, 0.6918589536489556, 0.6534228699125483, 0.542275051061771, 0.36500842151216195, 0.13290778885803556, -0.13877320353003378, -0.43178452443288845, -0.726044460171327, -1.0009273936217677, -1.2365973765645344, -1.4153065977533503, -1.522578991624057, -1.548205140253435, -1.4869850184538844, -1.339169473170006, -1.110568825101658, -0.8123166431885513, -0.4602974354394437, -0.0742675049893455, 0.32328269041905167, 0.7084598309486208, 1.0574149454729171, 1.3478203726443059, 1.560286911485278, 1.6796335457038138, 1.6959293902565167, 1.605239754615777, 1.4100248013141636, 1.1191592840537994, 0.7475641368275368, 0.31546395447720865, -0.15269272813079734], 'positive_zeros': ['0.20943424091752786736050272788044', '1.41077548446022280969860339567045', '2.07124994796079228364226414875274', '3.91942254964707014733297486553435', '4.69211157296652603576319705693790', '5.19234888162753563989825319742521', '6.07399124276222268137595971188765', '6.54965790627511418612335932938016', '7.52481402352806569200480018617467', '8.388798842870355551607475026011439'], 'prelabel': '2-59e2-59.13-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.318046019293515, 'root_angle': 0.694115980042675, 'root_number': '-0.57273084702150189844009606993549 + 0.81974348235898343736953321592042*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.34705799002133747', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.20943424091752786736050272788', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.41077548446022280969860339567', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.07124994796079228364226414875', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.7372453089754814, 'bad_primes': [59], 'central_character': '59.13', 'conductor': 3481, 'conductor_radical': 59, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3481/1/d/a/1311/1'], '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': '2-59e2-59.13-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-59e2-59.13-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.318046019293515, 'root_angle': 0.3470579900213375, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.20943424091752786736050272788', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '265489441207447803033785433647', 'Lhash_array': ['265489441207447803033785433647'], 'label': '2-59e2-59.13-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3481/1/d/a/1311/1'}