-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1375575002865161919217042540894', 'a10': [0.0, 0.0], 'a2': [0.5, -0.8660254037844386], 'a3': [-1.517718726778325, 2.628765946378806], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [1.517718726778325, 2.628765946378806], 'a7': [-4.93155075966216, 0.0], 'a8': [-1.0, 0.0], 'a9': [-3.1069402672272397, -5.381378398919204], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.58578819202164, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-3.1246589940055647, 3.03916208372968]]]], 'bad_primes': [2, 5, 19], 'central_character': '950.201', 'coefficient_field': 'CDF', 'conductor': 950, 'conductor_radical': 190, 'conjugate': '511985986535993598830505180633', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [1.517718726778325, -2.628765946378806], [-1.5, -2.598076211353316]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.93155075966216, 0], [7.0, 0]], [[1.0, 0], [-1.2823297747923195, 0], [11.0, 0]], [[1.0, 0], [-1.9834941066094052, -3.4355125691609287], [-6.5, 11.258330249197702]], [[1.0, 0], [-1.1069402672272397, 1.9172767837814495], [-8.5, -14.722431864335457]], [[1.0, 0], [-3.1246589940055647, 3.03916208372968]], [[1.0, 0], [3.842329219213245, 6.655109427083795], [-11.5, 19.91858428704209]], [[1.0, 0], [-2.1411648873961595, -3.7086063723526426], [-14.5, 25.11473670974872]], [[1.0, 0], [4.14543129411664, 0], [31.0, 0]], [[1.0, 0], [-9.38864213546227, 0], [37.0, 0]], [[1.0, 0], [-2.3000485015706444, 3.9838008645930207], [-20.5, -35.50704155516198]], [[1.0, 0], [-3.3246104924349202, 5.758394288273867], [-21.5, -37.239092362730865]], [[1.0, 0], [3.46577537983108, 6.002899045488754], [-23.5, 40.703193977868615]], [[1.0, 0], [-3.46577537983108, -6.002899045488754], [-26.5, 45.89934640057525]], [[1.0, 0], [-3.1588836141744845, 5.47134691494701], [-29.5, -51.09549882328188]], [[1.0, 0], [5.64237772078389, 9.772884887892378], [-30.5, 52.827549630850754]], [[1.0, 0], [-0.9657753798310801, -1.6727720265665615], [-33.5, 58.023702053557386]], [[1.0, 0], [4.160096447562215, -7.205498411564552], [-35.5, -61.48780366869514]], [[1.0, 0], [-3.4138320328838354, 5.912930529460949], [-36.5, -63.21985447626402]], [[1.0, 0], [1.7696135721549255, -3.0650606167357846], [-39.5, -68.41600689897065]], [[1.0, 0], [3.2847554415677793, 0], [83.0, 0]], [[1.0, 0], [4.46698821321881, 7.737050542106297], [-44.5, 77.07626093681505]], [[1.0, 0], [-1.0715028136705897, 1.8558973137304693], [-48.5, -84.00446416709055]], [[1.0, 0], [5.2726671454876755, 9.132527387383815], [-50.5, 87.4685657822283]], [[1.0, 0], [3.6431138382043406, 0], [103.0, 0]], [[1.0, 0], [-5.07455638700334, 0], [107.0, 0]], [[1.0, 0], [2.371551315241234, -4.107647370754613], [-54.5, -94.39676901250381]], [[1.0, 0], [12.441447597080861, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-950-19.11-c1-0-14', '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/950/2/e/m/201/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7224372935465767, 0.8554032867123474, 0.9488257154119427, 0.9983939534542137, 0.9958892261767492, 0.9306319709885233, 0.7915666746347286, 0.5696410309898183, 0.2602011612505233, -0.1348298477799327, -0.6052174674894076, -1.1313651650963168, -1.6841868599631586, -2.2261049075212807, -2.7132930444795647, -3.0991545552198048, -3.3388607113893976, -3.39459191539489, -3.240949548568262, -2.8698702547849355, -2.2943067334784533, -1.5499660880781203, -0.6945345810376115, 0.19593227289171827, 1.0334298055193039, 1.7268051425075803, 2.1920986887996277, 2.363233415025423, 2.2016323401163036, 1.703301415786646, 0.902092792672189, -0.13173181648698287, -1.297918249036127, -2.4771742480536623, -3.5454735663462014, -4.389880615676581, -4.923650368475718, -5.098268246383912, -4.910386750795633, -4.402283792312907, -3.6554366931443423, -2.7779351828914582, -1.8875586149131711, -1.0932118348948363, -0.4778654540259553, -0.0860535134123137, 0.08169011074735369, 0.06625075797399821, -0.06050192066234691, -0.212162019804918, -0.30711001740904265, -0.28681289257764486, -0.12919060888667266, 0.14606049673241314, 0.4817729752055997, 0.7968383799363545, 1.0064870848937324, 1.0451305921350786, 0.8866356982779771, 0.5570090836910965, 0.13571451035391474, -0.2559382060580165, -0.4780980246074124, -0.40332988564899974, 0.05100631571828564, 0.8961995515762641, 2.058186226848593, 3.3807529721778957, 4.647248295862907, 5.618125583208151, 6.077853468177343, 5.88201035691951, 4.994442115513579, 3.505583212518309, 1.6263436006035872, -0.3432126944686232, -2.065780711631299, -3.2299104626532924, -3.6118063370357634, -3.122820880458856, -1.8319423418695229, 0.042610354035072996, 2.1721842217423646, 4.1797762263135265, 5.712973018753804, 6.512545415394016, 6.462041297439957, 5.607596392111064, 4.143621152552185, 2.3676119559129734, 0.6143288342126054, -0.8156941275170331, -1.7170729756565675, -2.0162761034359216, -1.7763202853902023, -1.1694640046516542, -0.4257043736157432, 0.22925509756937254, 0.630494475983034, 0.7104720059991084, 0.5068234360754305, 0.14027754041718082, -0.23026862403129922, -0.4621972934335012, -0.47714751617097867, -0.2882670367552395, 0.0017358381202025519, 0.23188705166172852, 0.23511882324649336, -0.10363137064133408, -0.8007703851066498, -1.7537364870082006, -2.7550108418506407, -3.5388942568712287, -3.849904109982886, -3.5147576430208805, -2.4978134068889983, -0.923371236446279, 0.9433546913145779, 2.7536423249574087, 4.157291579184366, 4.888122491931099, 4.830041167056114, 4.045398549593406, 2.7572820169733583, 1.2899399438395571, -0.016759075742465237, -0.8954667596470056, -1.2177672227746856, -1.0205152917970264, -0.48511230583688664, 0.1237344278144262, 0.5414376295422797, 0.5842937622431081, 0.20352962366959873, -0.5034161002300391, -1.327477428202657, -2.0174601296618473, -2.36262071022338, -2.262200395901737, -1.7595770456558388, -1.0295865091166445, -0.3223294405913762, 0.1191273199880955, 0.14081771925289524, -0.26736485355376705, -0.9633071605809735, -1.695312923636767, -2.183736145255192, -2.216167850592355, -1.7249438473107672, -0.8198570899102468, 0.23784117527553814, 1.1155650850040044, 1.5209356623320123, 1.3101559723681622, 0.5571774245725395, -0.4423552698639756, -1.2394103064573252, -1.3567361148076291, -0.4365334354805338, 1.6330888262347545, 4.6529316945170995, 8.13266457612112, 11.395507791802999, 13.741987179579063, 14.628622084539922, 13.811542198619836, 11.41392844499471, 7.897478123476383, 3.94556379500747, 0.29113558843223897, -2.4620087746951556, -3.9749427940975894, -4.230466765332737, -3.4994936342722878, -2.232448896046443, -0.9126562491920013, 0.0820150485068404, 0.568449884907643, 0.5758257330678549, 0.2931287299402963, -0.0289912690362623, -0.18427638836243035, -0.08708032642752327, 0.20605812347959668, 0.5332990087612756, 0.7051616036089138, 0.5909106046732187, 0.17936859606751868, -0.40965006503120094, -0.9678225781053028, -1.2783732808181512, -1.2026256874117285, -0.7389625039053058, -0.030104059762641106, 0.6859042792333008, 1.1637994556288385, 1.2451974954708196, 0.9218267052521077, 0.34136760525765697, -0.2495527846776327, -0.6063478651741232, -0.594106876981791, -0.25927107748072864, 0.1665566616574303, 0.33894321935161936, -0.07115279578439689, -1.2366055910499543, -3.072845216189504, -5.2182926784969625, -7.112688115986553, -8.155656450450044, -7.89790983822843, -6.2023765911046915, -3.318488930381467, 0.16110674073502723, 3.4541578956765036, 5.808211060043377, 6.717709123257394, 6.069388184426684, 4.168690996176124, 1.6383911802970947, -0.7774317578414724, -2.4398683455509405, -2.9985152582528922, -2.47368618096491, -1.2147173824465867, 0.2459165065912366, 1.388076990548189, 1.8793419057930076, 1.6704111909820416, 0.981492047494938, 0.1910548205682088, -0.32644460862110286, -0.35012507390709235, 0.10725563880859305, 0.8173242977749297, 1.4422196788650126, 1.6845773953682037, 1.42023213159999, 0.7594414125172061, 0.010599695389928285, -0.44097970079767457, -0.29247869087386924, 0.5419120589155977, 1.8763866889550944, 3.303992313606687, 4.336915685621118, 4.585790146523347, 3.9104437792571116, 2.483399896484971, 0.7391462194034444, -0.7749961481519335, -1.592858180138136, -1.4966548592046145, -0.594708544598849], 'positive_zeros': ['1.08513734195960753942756619998510', '2.84730480058810184550735860943566', '3.86017231633254803269085929043394', '5.67075155095553773009518818478131', '5.94828922139835310944776846775853', '6.56405254957959445849696453653367', '7.54017274934103360782905931485762', '7.990020188325863699582310659708028', '9.352687085585181953294972860264176', '10.12241506741515927455642635861567'], 'prelabel': '2-950-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7542309619967678, 'root_angle': 0.35332829693135986, 'root_number': '0.4446493513704504 + 0.8957047249656762*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.176664148466', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08513734195960753942756619999', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.84730480058810184550735860944', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86017231633254803269085929043', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.58578819202164, 'bad_primes': [2, 5, 19], 'central_character': '19.11', 'conductor': 950, 'conductor_radical': 190, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/950/2/e/m/201/1'], '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': '2-950-19.11-c1-0-14', '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': '2-950-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7542309619967678, 'root_angle': 0.17666414846567993, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08513734195960753942756619999', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1375575002865161919217042540894', 'Lhash_array': ['1375575002865161919217042540894'], 'label': '2-950-19.11-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/950/2/e/m/201/1'}