-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1854275776324149347481098276966', 'a10': 0, 'a2': -4, 'a3': 14, 'a4': 16, 'a5': 0, 'a6': -56, 'a7': 158, 'a8': -64, 'a9': -47, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.019190990649033, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 4]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '50.1', 'coefficient_field': '1.1.1.1', 'conductor': 50, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[1, 4], [1, -14, 243], [1], [1, -158, 16807], [1, 148, 161051], [1, -684, 371293], [1, -2048, 1419857], [1, -2220, 2476099], [1, 1246, 6436343], [1, 270, 20511149], [1, 2048, 28629151], [1, 4372, 69343957], [1, 2398, 115856201], [1, -2294, 147008443], [1, 10682, 229345007], [1, -2964, 418195493], [1, 39740, 714924299], [1, 42298, 844596301], [1, -32098, 1350125107], [1, 4248, 1804229351], [1, -30104, 2073071593], [1, -35280, 3077056399], [1, 27826, 3939040643], [1, 85210, 5584059449], [1, 97232, 8587340257], [1, 4298, 10510100501], [1, -124114, 11592740743], [1, 42342, 14025517307], [1, 35990, 15386239549], [1, 228816, 18424351793]], 'euler_factors_factorization': [[[[1, 4], 1]], [[[1, -14, 243], 1]], [1], [[[1, -158, 16807], 1]], [[[1, 148, 161051], 1]], [[[1, -684, 371293], 1]], [[[1, -2048, 1419857], 1]], [[[1, -2220, 2476099], 1]], [[[1, 1246, 6436343], 1]], [[[1, 270, 20511149], 1]], [[[1, 2048, 28629151], 1]], [[[1, 4372, 69343957], 1]], [[[1, 2398, 115856201], 1]], [[[1, -2294, 147008443], 1]], [[[1, 10682, 229345007], 1]], [[[1, -2964, 418195493], 1]], [[[1, 39740, 714924299], 1]], [[[1, 42298, 844596301], 1]], [[[1, -32098, 1350125107], 1]], [[[1, 4248, 1804229351], 1]], [[[1, -30104, 2073071593], 1]], [[[1, -35280, 3077056399], 1]], [[[1, 27826, 3939040643], 1]], [[[1, 85210, 5584059449], 1]], [[[1, 97232, 8587340257], 1]], [[[1, 4298, 10510100501], 1]], [[[1, -124114, 11592740743], 1]], [[[1, 42342, 14025517307], 1]], [[[1, 35990, 15386239549], 1]], [[[1, 228816, 18424351793], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-50-1.1-c5-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/50/6/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.8059859359999693, 1.7906552598786392, 1.7448151262331228, 1.6689312636138927, 1.563812616823852, 1.4306578392601943, 1.2711152616636259, 1.0873514164435054, 0.8821220720669123, 0.6588388138578922, 0.4216235408491376, 0.17534288051453756, -0.07438549512613168, -0.32122228484789495, -0.5581785009556283, -0.7777354011692511, -0.9720160102067347, -1.1330094367729833, -1.2528462885182663, -1.3241201414577404, -1.3402463430732579, -1.2958455814273646, -1.187135847313609, -1.0123129088992437, -0.7718964999092216, -0.46901740495694244, -0.10961982138187691, 0.29744592581674656, 0.7404628040425811, 1.2050367872495436, 1.6744487548403513, 2.1301723480124655, 2.552551833954736, 2.921623113068373, 3.218049472836374, 3.4241322709658863, 3.5248462665563647, 3.50884073106938, 3.3693416922226382, 3.1048885627094047, 2.719840706405246, 2.2245966927655783, 1.635481271488861, 0.9742722738013188, 0.2673611009990734, -0.45543485706715453, -1.1623630935290727, -1.8214590065599088, -2.4024057433366113, -2.8784157291185886, -3.22800547187323, -3.4365303970170213, -3.49735151225604, -3.412521422606623, -3.192903589758619, -2.8576748110767114, -2.4332047661547263, -1.95135530090787, -1.447292257688564, -0.9569499204579224, -0.5143280861063939, -0.14883009224157742, 0.11713691872427187, 0.27008340500474864, 0.3066891264992894, 0.23423775500622837, 0.07014815154690039, -0.1594095976341627, -0.42174342930828784, -0.6805614688842414, -0.899359572875724, -1.0449866592293104, -1.09106253367837, -1.020913312965873, -0.8297115690807881, -0.5255626916507425, -0.12936321490082883, 0.3266347690140701, 0.8014952616377403, 1.2493203457379687, 1.6237174407894512, 1.8826089656679683, 1.992917266006476, 1.934636437880157, 1.703830372492152, 1.314174147914552, 0.7967797410228031, 0.19820755301762497, -0.42325172066909905, -1.0027526176557175, -1.4750830208561159, -1.7812825425696457, -1.8750240951557027, -1.7280728140351225, -1.3341908038363306, -0.710982967707546, 0.10063030100418856, 1.0393901626803992, 2.028941225022234, 2.984895774139781, 3.823053405787651, 4.467945575225436, 4.860794568572087, 4.96599447528691, 4.775342054776958, 4.30946039097024, 3.616148710052632, 2.7657282856373717, 1.8438001622235416, 0.9421452140497358, 0.14874173087699896, -0.461982764896479, -0.8375329586835657, -0.9533463917801882, -0.8156445999164174, -0.4607147697047508, 0.0493835078809283, 0.6342593498771004, 1.2049549310795789, 1.6748969508207754, 1.9707167604943778, 2.0415963869609937, 1.8659415445641594, 1.4544837737903327, 0.8493402243159283, 0.11906160146297508, -0.6497855843419615, -1.3634938324740347, -1.9331913951014323, -2.2863856615075204, -2.3765545442636364, -2.189486060975902, -1.745465653006667, -1.0969435154292286, -0.3219129487823446, 0.4861838498508883, 1.2307149255022554, 1.8246491819210637, 2.2021356948387036, 2.3272589557182615, 2.1987166877039286, 1.8497128068805295, 1.3430193755986186, 0.7618474425592108, 0.19777972345894787, -0.262532951175496, -0.5499954493219332, -0.623156606428758, -0.47424103138027907, -0.13017304369075844, 0.35163110176400714, 0.8921442089648598, 1.403002435813579, 1.8003436906824808, 2.0180935265383773, 2.0186100110853644, 1.7989502611588237, 1.3916540382476454, 0.8597672202246728, 0.28672942304920024, -0.23741191147167615, -0.6313577050199948, -0.8370455183917849, -0.8308687233122178, -0.6296448826448966, -0.2901045470816351, 0.09834595331197031, 0.4267672721300151, 0.5839286249276202, 0.4750957623242322, 0.03943718555977177, -0.7368086757294078, -1.813735843754084, -3.099153327546136, -4.458173393169758, -5.729957003151208, -6.7494024666153685, -7.370695803223577, -7.489221253372939, -7.05844217363776, -6.099009126718524, -4.698450848421612, -3.0011970071483107, -1.1901583946503391, 0.5375812845939077, 1.9974432227848486, 3.042445454743854, 3.5829287358588013, 3.597910721154741, 3.136326489519249, 2.3079734503294005, 1.265588899854661, 0.18088871162021042, -0.781645791059549, -1.4890924995886046, -1.8587031154900833, -1.8679324946437366, -1.5544315757791844, -1.006221096619926, -0.34389744978358244, 0.30195534621553927, 0.8141908798681745, 1.1093023187476536, 1.150939392678208, 0.9544815505116906, 0.5820098219387014, 0.12874071862843045, -0.296478857720791, -0.5929428254577036, -0.6880366880072699, -0.5516108961586391, -0.20204281675575486, 0.2972073277740541, 0.8499602802392536, 1.3463175064192539, 1.6847155110135288, 1.7928057036935834, 1.6430683994802706, 1.2599848431773064, 0.7171312659718049, 0.12444994874900603, -0.3921533242328426, -0.7151961935619127, -0.7594182987128787, -0.4903786543161184, 0.06592420409658425, 0.8246028674098781, 1.654744493971779, 2.4015826940831895, 2.9141367236135203, 3.0733083593046486, 2.8151701021399083, 2.144911522843765, 1.1385260487882471, -0.06846065151424537, -1.3035000957802025, -2.386881465098155, -3.1635633064263575, -3.531081131474512, -3.4582246776783876, -2.9907919113148824, -2.24308545769387, -1.3764909467514423, -0.5689625781609718, 0.01894254629584459, 0.2750595436744936, 0.15765140874345288, -0.2959098449645679, -0.9757346209454284, -1.7202938843222055, -2.347818292650788, -2.6923380939416535, -2.637460323744195, -2.141272150280116, -1.247340686667437, -0.07937168757775435, 1.1797902735888315], 'positive_zeros': ['1.46276566744046286466573347456228', '3.28499825800365520275696337730622', '5.54626952739052738478306820478826', '7.68859691366184980347896374583278', '8.291327428170497872094901139815477', '9.536697094708796313829082460503655', '10.91476061918097024736032333102529', '11.98569556409143960566713686926097', '13.77684563564674653682899144954580', '14.48894733048733978744819970322037'], 'prelabel': '2-50-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.8318176125324586, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 2169163589709273263, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46276566744046286466573347456', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.28499825800365520275696337731', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.54626952739052738478306820479', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 8.019190990649033, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 50, 'conductor_radical': 10, 'degree': 2, 'dirichlet_coefficients': [1, -4, 14, 16, 0, -56, 158, -64, -47, 0, -148, 224, 684, -632, 0, 256, 2048, 188, 2220, 0, 2212, 592, -1246, -896, 0, -2736, -4060, 2528, -270, 0, -2048, -1024, -2072, -8192, 0, -752, -4372, -8880, 9576, 0, -2398, -8848, 2294, -2368, 0, 4984, -10682, 3584, 8157, 0, 28672, 10944, 2964, 16240, 0, -10112, 31080, 1080, -39740, 0, -42298, 8192, -7426, 4096, 0, 8288, 32098, 32768, -17444, 0, -4248, 3008, 30104, 17488, 0, 35520, -23384, -38304, 35280, 0, -45419, 9592, -27826, 35392, 0, -9176, -3780, 9472, -85210, 0, 108072, -19936, -28672, 42728, 0, -14336, -97232, -32628, 6956, 0], 'euler11': [1, 148, 161051], 'euler13': [1, -684, 371293], 'euler17': [1, -2048, 1419857], 'euler19': [1, -2220, 2476099], 'euler2': [1, 4, 0], 'euler23': [1, 1246, 6436343], 'euler29': [1, 270, 20511149], 'euler3': [1, -14, 243], 'euler31': [1, 2048, 28629151], 'euler37': [1, 4372, 69343957], 'euler41': [1, 2398, 115856201], 'euler43': [1, -2294, 147008443], 'euler47': [1, 10682, 229345007], 'euler5': [1, 0, 0], 'euler53': [1, -2964, 418195493], 'euler59': [1, 39740, 714924299], 'euler61': [1, 42298, 844596301], 'euler67': [1, -32098, 1350125107], 'euler7': [1, -158, 16807], 'euler71': [1, 4248, 1804229351], 'euler73': [1, -30104, 2073071593], 'euler79': [1, -35280, 3077056399], 'euler83': [1, 27826, 3939040643], 'euler89': [1, 85210, 5584059449], 'euler97': [1, 97232, 8587340257], 'euler_factors': [[1, 4, 0], [1, -14, 243], [1, 0, 0], [1, -158, 16807], [1, 148, 161051], [1, -684, 371293], [1, -2048, 1419857], [1, -2220, 2476099], [1, 1246, 6436343], [1, 270, 20511149], [1, 2048, 28629151], [1, 4372, 69343957], [1, 2398, 115856201], [1, -2294, 147008443], [1, 10682, 229345007], [1, -2964, 418195493], [1, 39740, 714924299], [1, 42298, 844596301], [1, -32098, 1350125107], [1, 4248, 1804229351], [1, -30104, 2073071593], [1, -35280, 3077056399], [1, 27826, 3939040643], [1, 85210, 5584059449], [1, 97232, 8587340257]], 'index': 2, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/50/6/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/50/6/a/c'], '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': '2-50-1.1-c5-0-2', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-50-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.8318176125324586, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 2169163589709273263, 'z1': {'__RealLiteral__': 0, 'data': '1.46276566744046286466573347456', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 10837870
{'Lhash': '1854275776324149347481098276966', 'Lhash_array': ['1854275776324149347481098276966'], 'label': '2-50-1.1-c5-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/50/6/a/c'}
-
id: 24551377
{'Lhash': '1854275776324149347481098276966', 'Lhash_array': ['1854275776324149347481098276966'], 'label': '2-50-1.1-c5-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/50/6/a/c/1/1'}