-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1053401436784738256042260981655', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-3.3513343074907076, 0.0], 'a4': [0.0, 0.0], 'a5': [0.5646185748039909, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [8.23144164056422, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.569463560681836, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 7, 23], 'central_character': '2576.1', 'coefficient_field': 'CDF', 'conductor': 2576, 'conductor_radical': 322, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.3513343074907076, 0], [3.0, 0]], [[1.0, 0], [-0.5646185748039909, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.021462749995105, 0], [11.0, 0]], [[1.0, 0], [-5.9159528822946985, 0], [13.0, 0]], [[1.0, 0], [-2.564618574803991, 0], [17.0, 0]], [[1.0, 0], [-6.336951508264627, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [5.23144164056422, 0], [29.0, 0]], [[1.0, 0], [-4.222097157882725, 0], [31.0, 0]], [[1.0, 0], [5.172162649598191, 0], [37.0, 0]], [[1.0, 0], [-0.6607839598229029, 0], [41.0, 0]], [[1.0, 0], [-4.913688350382228, 0], [43.0, 0]], [[1.0, 0], [10.011077422481913, 0], [47.0, 0]], [[1.0, 0], [-6.0, 0], [53.0, 0]], [[1.0, 0], [-12.221056313051028, 0], [59.0, 0]], [[1.0, 0], [-5.478306925186219, 0], [61.0, 0]], [[1.0, 0], [-8.340948979977515, 0], [67.0, 0]], [[1.0, 0], [11.080741740961134, 0], [71.0, 0]], [[1.0, 0], [-6.209978890569115, 0], [73.0, 0]], [[1.0, 0], [4.340948979977515, 0], [79.0, 0]], [[1.0, 0], [6.996694623255832, 0], [83.0, 0]], [[1.0, 0], [-13.927030304776611, 0], [89.0, 0]], [[1.0, 0], [16.30690731303145, 0], [97.0, 0]], [[1.0, 0], [-9.72013389326363, 0], [101.0, 0]], [[1.0, 0], [-5.31948622998241, 0], [103.0, 0]], [[1.0, 0], [0.6597431149912052, 0], [107.0, 0]], [[1.0, 0], [17.376571631510668, 0], [109.0, 0]], [[1.0, 0], [14.50580878111865, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-2576-1.1-c1-0-18', 'leading_term': '1.152009987770847263575026694346', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2576/2/a/be/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.1520099877708472, 1.146114447626002, 1.128381042700679, 1.0986806137968645, 1.0568342631291516, 1.0026647287884403, 0.9360624092957125, 0.857061074903528, 0.7659179547322496, 0.6631929860824123, 0.5498224164370901, 0.4271825159635358, 0.29713977502622096, 0.16208455954709122, 0.024945753515801947, -0.11081555845689452, -0.24123479834314318, -0.361895879263531, -0.468006761338777, -0.5544982107786798, -0.6161446589609546, -0.6477052568325681, -0.6440823701581596, -0.6004938899340677, -0.5126548739143602, -0.37696322912375185, -0.1906834341083956, 0.04787827277127823, 0.3392142038027506, 0.6824781662616857, 1.0753780912914765, 1.5141050322613914, 1.9933045536213163, 2.506095563514557, 3.044140378937469, 3.5977682719502724, 4.156152964552068, 4.707542567756388, 5.2395383600332215, 5.739416646532746, 6.194485818150062, 6.592468730320635, 6.9218987407922885, 7.172516278397503, 7.335651751127012, 7.4045800222532785, 7.374831654537411, 7.244446692952123, 7.014157951817223, 6.687492593146645, 6.270783201808862, 5.773082523137261, 5.2059794441637575, 4.583317557370111, 3.920821607790281, 3.2356411322306147, 2.545824480585601, 1.86973998347249, 1.225464117852945, 0.6301589521116789, 0.09946277123345292, -0.35308153515577534, -0.7165360857724641, -0.9829928110043538, -1.1478931428408046, -1.2102258279432634, -1.172590573632746, -1.0411204913110994, -0.8252621393886554, -0.5374181487522298, -0.19246366709409637, 0.1928461073845373, 0.6005545158504338, 1.0122406575945264, 1.4097841128971653, 1.7761237239092054, 2.0959761543424595, 2.3564807192034793, 2.5477393911062856, 2.6632249104323913, 2.700035429704558, 2.6589809026324187, 2.5444942034754443, 2.364368384453262, 2.129330147837652, 1.8524680912451998, 1.5485421329851974, 1.2332073029541815, 0.922190391667269, 0.6304614415774455, 0.3714434764956782, 0.1563030307098443, -0.00663909383000061, -0.11234277735870689, -0.15930257441836093, -0.14960320589905224, -0.08876942889927297, 0.01458563627512745, 0.14929824519445017, 0.30235138862364397, 0.4596954163208676, 0.6071473207152337, 0.7313180255695974, 0.8205136122257771, 0.8655559521731087, 0.8604708575797811, 0.8029975994748266, 0.6948822870826664, 0.541928786012445, 0.3537940483152615, 0.14352926296207386, -0.07311666967613327, -0.2786000319771751, -0.45464660656898254, -0.5834208485039187, -0.6487345061368871, -0.6372238790355746, -0.539423402273442, -0.35066592262113655, -0.07174691919036091, 0.2906991914043123, 0.7241480932956275, 1.2104800907729756, 1.7266209851022696, 2.2455099963404415, 2.737355448470895, 3.1711203716996663, 3.5161641711189424, 3.7439541204418947, 3.829752548847178, 3.7541828545503564, 3.504580278015966, 3.0760417643117797, 2.4721029702116244, 1.7049889301186376, 0.7954071813344332, -0.2281229060194589, -1.3303846209638452, -2.4709762455840054, -3.6061510150839933, -4.690893522801497, -5.681125051946328, -6.535919734047323, -7.219609426231146, -7.703658214174151, -7.968197522588146, -8.003129560278845, -7.808729433299443, -7.395703535654305, -6.784692258564274, -6.005236894165188, -5.094261958314895, -4.094153107174519, -3.0505355562675143, -2.009876824231774, -1.0170494317497358, -0.11299301467955307, 0.6673892380338493, 1.2969777180306856, 1.7577254238695665, 2.041414107628936, 2.1498345863882498, 2.094383073855909, 1.8951010443888447, 1.5792204004369819, 1.179306376776727, 0.7311156730987114, 0.27130507922202857, -0.16486489287048373, -0.5456868306572331, -0.8448884643297486, -1.043122834589313, -1.1289753521091295, -1.0994284792516507, -0.9597607641373221, -0.7228946265501276, -0.40824411945343153, -0.040147373254080326, 0.35400373354848713, 0.7458038983670072, 1.1079007613991432, 1.41594211101822, 1.6502675739513226, 1.7972268724782556, 1.8500335560654604, 1.8090965254251303, 1.6818093664934053, 1.4818168636988795, 1.227816269777805, 0.9419852130232086, 0.6481559960851974, 0.3698753772435858, 0.12849819988468014, -0.058538373932559326, -0.17912580950835205, -0.2274688253534644, -0.2045635791576606, -0.11812715718996489, 0.018022246855168907, 0.18509269464410344, 0.3608716753760008, 0.5215888611039771, 0.6439459057281414, 0.7071547793822348, 0.6948219470500206, 0.5965238968300167, 0.408939778728086, 0.1364379943640638, -0.20894659960093456, -0.6081624406851621, -1.036387127577881, -1.4647911454154245, -1.8626983753034034, -2.1999874971238746, -2.449554455458033, -2.5896452384248723, -2.605871538825117, -2.49273960708491, -2.254553863634737, -1.905599665050064, -1.4695611332594207, -0.9781865390629073, -0.46927126876915026, 0.01591741006521099, 0.43560291314651506, 0.7506429811643098, 0.9276270386310228, 0.9416950972522958, 0.7788583685993941, 0.4376308321942076, -0.07017484147816537, -0.7195772353996497, -1.4735074583964236, -2.284798633079862, -3.0989730834017015, -3.857655496009468, -4.5023900054124235, -4.978603713056328, -5.239441582178538, -5.2491996808773385, -4.98610568210874, -4.444236201945404, -3.634417375168893, -2.5840241805981576, -1.3356705924463539, 0.055138847890410715, 1.5232507193239642, 2.9977869817766467, 4.406490083766572, 5.68019445231799, 6.757118133611369, 7.5866786942713995, 8.13256943729411, 8.374883396922472, 8.311139824496836, 7.956146096537451, 7.340711418855961], 'positive_zeros': ['0.830987210983123064216723576889210', '1.57124578382546931865264560519073', '3.52762732653632995166956248324856', '4.13142839498812836924461091218840', '5.38777038398113381282228304521168', '5.67641891466900595308130377036998', '6.48403730597141432055741998293835', '6.98534528909665767706945809508703', '7.956145325354831615322861623556189', '9.148516417488195888191976712903331'], 'prelabel': '2-2576-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.535357048864161, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.830987210983123064216723576889', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.57124578382546931865264560519', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52762732653632995166956248325', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 20.569463560681836, 'bad_primes': [2, 7, 23], 'central_character': '1.1', 'conductor': 2576, 'conductor_radical': 322, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2576/2/a/be/1/1'], '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': '2-2576-1.1-c1-0-18', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2576-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.535357048864161, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.830987210983123064216723576889', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1053401436784738256042260981655', 'Lhash_array': ['1053401436784738256042260981655'], 'label': '2-2576-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2576/2/a/be/1/1'}