-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '989362864337854914546453027089', 'a10': -1, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': 1, 'a6': 0, 'a7': 1, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.091725982022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1, -1]], [7, [1, -1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1890.1', 'coefficient_field': '1.1.1.1', 'conductor': 1890, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, -1], [1, -1], [1, 6, 11], [1, 4, 13], [1, 6, 17], [1, -2, 19], [1, -6, 23], [1, -9, 29], [1, -5, 31], [1, -11, 37], [1, -9, 41], [1, -8, 43], [1, 3, 47], [1, 6, 53], [1, -3, 59], [1, 1, 61], [1, -14, 67], [1, 9, 71], [1, -11, 73], [1, -8, 79], [1, 0, 83], [1, -6, 89], [1, 10, 97], [1, -12, 101], [1, 4, 103], [1, 3, 107], [1, 16, 109], [1, 9, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [1], [[[1, -1], 1]], [[[1, -1], 1]], [[[1, 6, 11], 1]], [[[1, 4, 13], 1]], [[[1, 6, 17], 1]], [[[1, -2, 19], 1]], [[[1, -6, 23], 1]], [[[1, -9, 29], 1]], [[[1, -5, 31], 1]], [[[1, -11, 37], 1]], [[[1, -9, 41], 1]], [[[1, -8, 43], 1]], [[[1, 3, 47], 1]], [[[1, 6, 53], 1]], [[[1, -3, 59], 1]], [[[1, 1, 61], 1]], [[[1, -14, 67], 1]], [[[1, 9, 71], 1]], [[[1, -11, 73], 1]], [[[1, -8, 79], 1]], [[[1, 0, 83], 1]], [[[1, -6, 89], 1]], [[[1, 10, 97], 1]], [[[1, -12, 101], 1]], [[[1, 4, 103], 1]], [[[1, 3, 107], 1]], [[[1, 16, 109], 1]], [[[1, 9, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-1890-1.1-c1-0-2', 'leading_term': '1.140493554187610724911429440590000000000000000000000000000000000000000000000000000000000000', '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/1890/2/a/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.1404935541876107, 1.1347310067075635, 1.1173539838623454, 1.0881037784323164, 1.0465799027892997, 0.9922835964736341, 0.92467406167748, 0.8432335380901816, 0.7475371093690222, 0.6373232731868221, 0.5125616815271657, 0.373514940299978, 0.2207918478209653, 0.05538989189798968, -0.121274803563043, -0.3073515790537845, -0.5005546034555746, -0.6981784385829735, -0.8971304344496385, -1.093980229878583, -1.2850262168069932, -1.4663783467341884, -1.6340561196798837, -1.7841000124019226, -1.9126939920478325, -2.016296147159398, -2.0917738767818084, -2.1365395394133224, -2.1486820068125807, -2.1270892232221157, -2.0715566668367074, -1.9828765729628506, -1.8629029286826835, -1.7145876028004245, -1.541983541452968, -1.350211740136114, -1.1453896893506816, -0.9345201664941408, -0.7253405841839682, -0.5261345684598034, -0.3455089837600346, -0.19214119160969942, -0.07450286636685655, -0.0005681292029279912, 0.022484966627052835, -0.011430472644994964, -0.10702932655956504, -0.26739904329586306, -0.4937808450330741, -0.7853982859099522, -1.1393429782657079, -1.5505259255616295, -2.0117010763143552, -2.5135654789974313, -3.0449378303460892, -3.593014346036328, -4.143697838955336, -4.681992777747662, -5.192456040836852, -5.659690210399655, -6.068863701229072, -6.406239922425146, -6.6596961475776935, -6.8192119283200645, -6.877306812143935, -6.829407876453005, -6.674129193479476, -6.413447785883353, -6.05276387376847, -5.600837165066701, -5.069595479756637, -4.473816966426859, -3.8306923794214187, -3.159279124755583, -2.479863826153578, -1.8132547757837207, -1.1800295886438406, -0.5997664613671775, -0.09028945795945907, 0.33304094414560376, 0.65796131886565, 0.8758339085785581, 0.982044761554187, 0.9762502673417421, 0.8624566236519584, 0.648923372312007, 0.34788944041044173, -0.024872184481356824, -0.45065726431971065, -0.9085692702395904, -1.3763663588655368, -1.83138244039775, -2.2514839447955364, -2.6160210167252522, -2.9067307939661227, -3.1085512771221144, -3.210307122619779, -3.205233433668765, -3.091310136207007, -2.871387565978814, -2.553093129482895, -2.14851893215499, -1.6737006311095926, -1.147907969739869, -0.5927769771854852, -0.03132216942798074, 0.5131261883654405, 1.0180100013419358, 1.462604324768606, 1.8289994502231894, 2.102954921057666, 2.2745816309449, 2.3388158544885114, 2.295658797951579, 2.150166601846339, 1.9121881356461008, 1.595860782713417, 1.2188870593969614, 0.8016266728755896, 0.36604884843802493, -0.06540214063249027, -0.47096982304376844, -0.8307158447865012, -1.1275575442930381, -1.3481565480984117, -1.4836092443228435, -1.529899915614307, -1.48808959598942, -1.364227742214801, -1.168988848323926, -0.9170513704732223, -0.6262509212151952, -0.3165528006294407, -0.00889977856816219, 0.2760010451570592, 0.5188840225669525, 0.7030544493823104, 0.8153761178271518, 0.8470584079935671, 0.7941950496594197, 0.6580203367942703, 0.4448645011961932, 0.16580727306212698, -0.1639536095848762, -0.5259850709437094, -0.8997032197241418, -1.2635975557136425, -1.596523298426302, -1.87898497634541, -2.094333631107819, -2.229803881107264, -2.277325533533099, -2.234057032286989, -2.1026041159244917, -1.8909057364615014, -1.6117894734844593, -1.2822191616221748, -0.9222769731804867, -0.5539395252561207, -0.19972157686405145, 0.11872941315036807, 0.38199990101849435, 0.5741508181625165, 0.6837511169758441, 0.7046348885713849, 0.6363288693998457, 0.48411716124572696, 0.25873259894001477, -0.024311963224428364, -0.3457156064563264, -0.6836459243731783, -1.0151830643339157, -1.3178600656685622, -1.5711998782894683, -1.7581472615265459, -1.8662981642038985, -1.888840074423774, -1.8251336775707379, -1.6808880452307622, -1.4679072102503976, -1.2034137933910125, -0.9089835730505423, -0.6091516875077767, -0.32977472182856843, -0.09625160835932642, 0.06828131945132004, 0.1446606449885307, 0.11919378422544928, -0.015162677867334525, -0.25803337625300893, -0.6013279293037908, -1.0294531918069898, -1.5200363483664177, -2.045127282776236, -2.5728158126468648, -3.069169819249354, -3.5003760978630147, -3.8349486781609556, -4.0458607702817115, -4.112457207867697, -4.022014514904771, -3.7708351177097783, -3.3647897318874693, -2.8192559771322414, -2.1584397266257094, -1.4141061399319932, -0.6237871111884185, 0.1714316920096264, 0.9294104518614298, 1.6095852481568966, 2.1755596115087137, 2.597486905009213, 2.854082431698095, 2.9341247268528887, 2.8373359463809575, 2.5745698110499053, 2.1672798215373845, 1.6462875835163993, 1.0499179704542518, 0.42161133755448665, -0.19283993108823114, -0.7482552603065518, -1.2030379923909063, -1.5219593742227613, -1.6785668710732136, -1.6570508940646778, -1.453437264817607, -1.0760155536844458, -0.5449630961902154, 0.10882223313055074, 0.8456140936404106, 1.6193584834154628, 2.380624504570162, 3.079813768934229, 3.67041708862216, 4.11210115943551, 4.373416744926846, 4.433943032357527, 4.285718981415194, 3.9338593181729578, 3.396307253517112, 2.7027343602947695, 1.8926563276141353, 1.0128874688206317, 0.11450306576162943, -0.7504864359834336, -1.5325242825979852, -2.1877286167336023, -2.680725765865893, -2.986901253100497, -3.093913865668849, -3.0023689268591407, -2.725605339811146, -2.2886129209371338, -1.726157633873404, -1.0802482040496821, -0.39712420260092823], 'positive_zeros': ['0.78046968475361332650244099665934', '2.52020627086300638853200938474041', '2.62517870902814040020602194777881', '4.58180937392774756013376694888461', '5.09402137740493503058047757718002', '6.15564272677636715602065280661095', '7.02221071530441165788923442646588', '7.79471102810866322798440026886365', '8.350703020696169487107416840172808', '9.352131274056106694400154928291092'], 'prelabel': '2-1890-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.884807071402903, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 602721957517942256, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78046968475361332650244099666', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52020627086300638853200938474', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.62517870902814040020602194778', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 15.091725982022, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 1890, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 1, 0, 1, -1, 0, -1, -6, 0, -4, -1, 0, 1, -6, 0, 2, 1, 0, 6, 6, 0, 1, 4, 0, 1, 9, 0, 5, -1, 0, 6, 1, 0, 11, -2, 0, -1, 9, 0, 8, -6, 0, -6, -3, 0, 1, -1, 0, -4, -6, 0, -6, -1, 0, -9, 3, 0, -1, -5, 0, 1, -4, 0, 14, -6, 0, -1, -9, 0, 11, -11, 0, 2, -6, 0, 8, 1, 0, -9, 0, 0, -6, -8, 0, 6, 6, 0, -4, 6, 0, 3, 2, 0, -10, -1, 0, 1], 'euler11': [1, 6, 11], 'euler13': [1, 4, 13], 'euler17': [1, 6, 17], 'euler19': [1, -2, 19], 'euler2': [1, 1, 0], 'euler23': [1, -6, 23], 'euler29': [1, -9, 29], 'euler3': [1, 0, 0], 'euler31': [1, -5, 31], 'euler37': [1, -11, 37], 'euler41': [1, -9, 41], 'euler43': [1, -8, 43], 'euler47': [1, 3, 47], 'euler5': [1, -1, 0], 'euler53': [1, 6, 53], 'euler59': [1, -3, 59], 'euler61': [1, 1, 61], 'euler67': [1, -14, 67], 'euler7': [1, -1, 0], 'euler71': [1, 9, 71], 'euler73': [1, -11, 73], 'euler79': [1, -8, 79], 'euler83': [1, 0, 83], 'euler89': [1, -6, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, -1, 0], [1, -1, 0], [1, 6, 11], [1, 4, 13], [1, 6, 17], [1, -2, 19], [1, -6, 23], [1, -9, 29], [1, -5, 31], [1, -11, 37], [1, -9, 41], [1, -8, 43], [1, 3, 47], [1, 6, 53], [1, -3, 59], [1, 1, 61], [1, -14, 67], [1, 9, 71], [1, -11, 73], [1, -8, 79], [1, 0, 83], [1, -6, 89], [1, 10, 97]], 'index': 2, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1890/i', 'ModularForm/GL2/Q/holomorphic/1890/2/a/i/1/1', 'ModularForm/GL2/Q/holomorphic/1890/2/a/i'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-1890-1.1-c1-0-2', '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': '2-1890-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.884807071402903, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 602721957517942256, 'z1': {'__RealLiteral__': 0, 'data': '0.78046968475361332650244099666', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20710773
{'Lhash': '989362864337854914546453027089', 'Lhash_array': ['989362864337854914546453027089'], 'label': '2-1890-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1890/2/a/i'}
-
id: 24554959
{'Lhash': '989362864337854914546453027089', 'Lhash_array': ['989362864337854914546453027089'], 'label': '2-1890-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1890/2/a/i/1/1'}
-
id: 93989
{'Lhash': '602721957517942256', 'Lhash_array': ['602721957517942256'], 'label': '2-1890-1.1-c1-0-2', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1890/i'}