-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2080054818487031313798883710063', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [2.8284271247461903, 0.0], 'a6': [0.0, 0.0], 'a7': [2.8284271247461903, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.1325108752343365, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3], 'central_character': '768.1', 'coefficient_field': 'CDF', 'conductor': 768, 'conductor_radical': 6, 'conjugate': '2080054818487031313798883710063', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [5.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [7.0, 0]], [[1.0, 0], [-4.0, 0], [11.0, 0]], [[1.0, 0], [5.656854249492381, 0], [13.0, 0]], [[1.0, 0], [2.0, 0], [17.0, 0]], [[1.0, 0], [-4.0, 0], [19.0, 0]], [[1.0, 0], [5.656854249492381, 0], [23.0, 0]], [[1.0, 0], [2.8284271247461903, 0], [29.0, 0]], [[1.0, 0], [8.48528137423857, 0], [31.0, 0]], [[1.0, 0], [0, 0], [37.0, 0]], [[1.0, 0], [10.0, 0], [41.0, 0]], [[1.0, 0], [-12.0, 0], [43.0, 0]], [[1.0, 0], [-5.656854249492381, 0], [47.0, 0]], [[1.0, 0], [2.8284271247461903, 0], [53.0, 0]], [[1.0, 0], [4.0, 0], [59.0, 0]], [[1.0, 0], [-11.313708498984761, 0], [61.0, 0]], [[1.0, 0], [-4.0, 0], [67.0, 0]], [[1.0, 0], [-5.656854249492381, 0], [71.0, 0]], [[1.0, 0], [-2.0, 0], [73.0, 0]], [[1.0, 0], [8.48528137423857, 0], [79.0, 0]], [[1.0, 0], [4.0, 0], [83.0, 0]], [[1.0, 0], [6.0, 0], [89.0, 0]], [[1.0, 0], [-14.0, 0], [97.0, 0]], [[1.0, 0], [14.142135623730951, 0], [101.0, 0]], [[1.0, 0], [2.8284271247461903, 0], [103.0, 0]], [[1.0, 0], [-12.0, 0], [107.0, 0]], [[1.0, 0], [-5.656854249492381, 0], [109.0, 0]], [[1.0, 0], [-2.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-768-1.1-c1-0-9', '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/768/2/a/l/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.5180452226690133, 2.5145534607917983, 2.501545941011252, 2.4719947428162836, 2.4158999928872187, 2.3223425439972396, 2.1816352105186074, 1.9872839680314751, 1.7376066120578852, 1.436916876350775, 1.0961830331134468, 0.7330555124318741, 0.3711615732598379, 0.03860169227423937, -0.23434636062620234, -0.41821075176923633, -0.4877768415591755, -0.4256742427767119, -0.22567495622083153, 0.10477445544138467, 0.5432582344409725, 1.0527303773485226, 1.583733756435046, 2.078529804916513, 2.4769056991509304, 2.7231465383182103, 2.773405046744996, 2.6025155312694035, 2.2092245733202036, 1.6188805317332127, 0.88285210821519, 0.07432415602806253, -0.719388799892609, -1.40732505408918, -1.9069490094219783, -2.1562074262614166, -2.1237588784688533, -1.8156290693642874, -1.276899473687556, -0.5876657117862724, 0.14666367630265928, 0.809732684609856, 1.2914042342658418, 1.5052107414071587, 1.4032738222342518, 0.9860305864713952, 0.3047335732711574, -0.5442591277851525, -1.4330589246309047, -2.221945273142185, -2.782227267973388, -3.018509400941831, -2.8864147181177295, -2.4023364220940864, -1.6429831788273614, -0.7341916702810644, 0.16957601773341408, 0.9118046705202393, 1.361973914660877, 1.4399220064968319, 1.1317578011426783, 0.49390325863115725, -0.35603704493420485, -1.2603704331747108, -2.050733231371093, -2.580338470254356, -2.752715867993462, -2.5410100019143647, -1.9935600030550595, -1.2241318610259333, -0.3883180837410048, 0.34937940751267127, 0.8510639007421644, 1.0359609793848872, 0.8990721084923605, 0.5133759532682878, 0.014409358179686253, -0.43006462691486497, -0.6591034397352276, -0.5578530399602892, -0.08804020592675812, 0.6977924520547513, 1.6624753183538508, 2.610525751552014, 3.329631812797619, 3.6385688517040666, 3.430838063127388, 2.7037187682382617, 1.5652521906650607, 0.21640196038803144, -1.088738559981192, -2.0965774087100404, -2.6097768128808942, -2.5323933973474637, -1.8936134760190906, -0.8438745847620158, 0.37658381176507394, 1.4902059658444162, 2.243934489276848, 2.466103627985151, 2.1049738366965762, 1.2395695413261483, 0.05997866717282365, -1.1783582092716824, -2.2154063204152328, -2.8475235324898915, -2.973632637036521, -2.6151130392161233, -1.9045210230951861, -1.0462146134352228, -0.2592892933876199, 0.2820120389891617, 0.49439825578758617, 0.4055187462006936, 0.1420965867299283, -0.1109212379180343, -0.16923401839905639, 0.09022812096150948, 0.6843464597573549, 1.5081001982916575, 2.354066461106618, 2.963478656692892, 3.096165255873805, 2.600794026817788, 1.4658456176125125, -0.16387443907146088, -2.0115886780057335, -3.7292302997591062, -4.979777385144194, -5.5200636615060485, -5.26198893217767, -4.295208882618024, -2.864382874692275, -1.3062776351435332, 0.036878906063975515, 0.9045718482756694, 1.1819682161086542, 0.9230751603486901, 0.32669461084041795, -0.32797731854447154, -0.7677184441546968, -0.8087427115507222, -0.41294175512906167, 0.29979958600595535, 1.0873040490444248, 1.6588520401794433, 1.7656000469778326, 1.2809362323140896, 0.2464808239616278, -1.130867242143437, -2.5311898057154103, -3.608800337620907, -4.089450419450222, -3.848981294127827, -2.9498904678939795, -1.6244124396951263, -0.2084914528098524, 0.9542378320929936, 1.610136005231974, 1.6658118583304693, 1.209902564526991, 0.479926932319743, -0.21549685159036552, -0.5950042033268481, -0.4928649557038948, 0.09018775024875891, 0.9896153860362704, 1.932330785656762, 2.626883043242669, 2.8594877412005797, 2.5645337887331374, 1.8459802297544263, 0.941652146952682, 0.14102990686523645, -0.3172253725584314, -0.3342127404125477, 0.004354120673418312, 0.44458703666950283, 0.6399100659101185, 0.2638755774061132, -0.8745827208863197, -2.7507503383347096, -5.10634857660153, -7.5033394227023305, -9.43597530864134, -10.46895621249525, -10.360400891805442, -9.132001415069885, -7.064343673874998, -4.618204678051985, -2.305517303158908, -0.5493082137117027, 0.4248267821566239, 0.6334057655172882, 0.30415754892353103, -0.2179711804612505, -0.5953713226048328, -0.6111191938057573, -0.23395238869710194, 0.38535743080972173, 0.9828625981595306, 1.289829375436394, 1.1414948759572368, 0.547065706766599, -0.30454237535427003, -1.106099527544334, -1.5395942215926504, -1.3920894507742216, -0.6383273916753979, 0.5406365737173874, 1.8115233316484936, 2.7987916355937177, 3.2132998456583093, 2.9547472005137854, 2.1508604135607357, 1.1174672347897774, 0.2509878277305841, -0.1109752905811107, 0.1870653701673063, 1.0551614923294381, 2.1788039085952406, 3.1195251972263356, 3.462829137931043, 2.963658426746128, 1.6391139696412698, -0.22488565091685656, -2.157391265359818, -3.650003706364304, -4.319224057563175, -4.028807596445307, -2.930515593482421, -1.4093961716698034, 0.047480076742456516, 1.0134907821327956, 1.2601062203142757, 0.8225922296628991, -0.027835091815349045, -0.8938612781361149, -1.403365446618933, -1.3470803804602471, -0.7528385029033818, 0.1301034373707671, 0.9302360927206899, 1.299360757571394, 1.0502171108584024, 0.2344937107917801, -0.8687397761866852, -1.8511435707372372, -2.3244969866567473, -2.066549242588016, -1.109031370558331, 0.26581805945591314, 1.6204575159376022, 2.515288956703195, 2.664387984150844, 2.036639718088065, 0.8648599070487386], 'positive_zeros': ['1.64087392702100692375591053738948', '2.33996003394886694012888149437593', '3.88639137135655259937820080149096', '4.97470018237362601528702752031236', '5.79682295214575974826715623297469', '6.97543633674586192712503611083579', '7.69998266941098431523815804069490', '8.812090365385096052225426965659451', '9.503604753036850784671055094741526', '10.01654175763543856388739183934722'], 'prelabel': '2-768-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4763906951921655, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64087392702100692375591053739', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33996003394886694012888149438', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.88639137135655259937820080149', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.1325108752343365, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/768/2/a/l/1/2'], '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': '2-768-1.1-c1-0-9', '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': '2-768-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4763906951921655, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64087392702100692375591053739', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2080054818487031313798883710063', 'Lhash_array': ['2080054818487031313798883710063'], 'label': '2-768-1.1-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/2/a/l/1/2'}