-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1545005801644643949555393097982', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.8793852415718169, 0.6840402866513374], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.9396926207859084, -0.3420201433256687], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.649', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1949993371601513762557110382271', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-1.8793852415718169, -0.6840402866513374]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.8682408883346517, -4.924038765061041]], [[1.0, 0], [-0.9396926207859084, 0.3420201433256687], [5.362311101832846, -4.499513267805775]], [[1.0, 0], [0, 0], [1.9101299543362338, 10.832885283134289]], [[1.0, 0], [-0.8682408883346517, -4.924038765061041], [-12.216004070216808, 4.446261863233693]], [[1.0, 0], [0, 0], [-8.5, 14.722431864335457]], [[1.0, 0], [-3.5, 6.06217782649107], [-9.5, -16.454482671904334]], [[1.0, 0], [0, 0], [17.619022191736494, 14.784115022790404]], [[1.0, 0], [0, 0], [-27.251086002791343, -9.918584156444393]], [[1.0, 0], [-3.7587704831436337, -1.3680805733026749], [23.747377736688318, 19.92641590028272]], [[1.0, 0], [5.5, 9.526279441628825], [-18.5, 32.04293994002423]], [[1.0, 0], [0, 0], [-38.527397452222246, 14.022825876352417]], [[1.0, 0], [-6.128355544951824, -5.142300877492315], [7.466871639678005, 42.34673337952495]], [[1.0, 0], [0, 0], [36.00408882659197, -30.211017655267348]], [[1.0, 0], [0, 0], [53.0, 0]], [[1.0, 0], [0, 0], [10.24524248234889, -58.10365742772028]], [[1.0, 0], [-0.9396926207859084, 0.3420201433256687], [46.728711030257664, -39.2100441908789]], [[1.0, 0], [-0.8682408883346517, -4.924038765061041], [-62.95940559265586, 22.915349602819806]], [[1.0, 0], [0, 0], [-35.5, 61.48780366869514]], [[1.0, 0], [-3.5, 6.06217782649107], [-36.5, -63.21985447626402]], [[1.0, 0], [-2.952019020337816, 16.741731801207536], [-74.23571704208676, -27.01959132272783]], [[1.0, 0], [0, 0], [-77.9944875252304, -28.387671896030504]], [[1.0, 0], [0, 0], [-44.5, -77.07626093681505]], [[1.0, 0], [14.554844419260583, 12.212964584044247], [16.843873233692243, 95.52635204218419]], [[1.0, 0], [0, 0], [77.37048875501678, -64.92154857834048]], [[1.0, 0], [9.958577760546714, -8.35623892592501], [17.885762299693827, -101.43519856025743]], [[1.0, 0], [0, 0], [107.0, 0]], [[1.0, 0], [-2.0, 0], [109.0, 0]], [[1.0, 0], [0, 0], [19.62224407636313, -111.28327609037952]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-3e6-27.25-c1-0-15', '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/729/2/e/f/649/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.0089474632616673, 1.9421488868312935, 1.859683594903601, 1.7547179101362784, 1.6185637042014187, 1.442725390548873, 1.2208820772111348, 0.9505679682247323, 0.6344361089497469, 0.2810373477327159, -0.0949558586542556, -0.47315978081333204, -0.8285898194779979, -1.1334921171780998, -1.3598430158669985, -1.4823677453823398, -1.4818270176473407, -1.3482261773193431, -1.0835337743316782, -0.7034718770208612, -0.23797306701102988, 0.2700030780317908, 0.7674384855574885, 1.1959376750736341, 1.4977996376600873, 1.6229082118345755, 1.5356552163137522, 1.2209742519096995, 0.6885394584807719, -0.025703034112274613, -0.8612459515018879, -1.7381633885949168, -2.565399705372213, -3.251416737883611, -3.7159564113573733, -3.9013497571992346, -3.7816784744409184, -3.368221621679269, -2.710012998760395, -1.8889662789742427, -1.009821817868831, -0.18601892353666605, 0.4766372441258339, 0.8961056654451818, 1.0274353313186433, 0.8709150998713293, 0.473335354893722, -0.07832808995688251, -0.6702538077005173, -1.1803192032277945, -1.4989709035615686, -1.5489032188225322, -1.2999685716799694, -0.776335406850466, -0.054103602625664715, 0.7507823252047539, 1.5026843541701649, 2.071212054632973, 2.356533986486858, 2.3102519926084613, 1.9475435159825436, 1.3476672560175758, 0.6419951328846903, -0.0088762618445517, -0.4451210595008071, -0.539307946363987, -0.2234897437874628, 0.4938919994925853, 1.5252436738611694, 2.7165377813178027, 3.8737900719168916, 4.798669749497179, 5.326492149918374, 5.358997526682786, 4.885016356500014, 3.9843117016626657, 2.8131968874571123, 1.5743072118800665, 0.4763657500794824, -0.307848349780294, -0.6764272223587426, -0.6184823796495508, -0.214816233078423, 0.38142701066066015, 0.9802225501569897, 1.3985742723599133, 1.5030439494347092, 1.241077037060538, 0.653581576305467, -0.13464901640087892, -0.9449702767903537, -1.5887570206186774, -1.9149323060399186, -1.8497050549611922, -1.4184960837432883, -0.7439526770037103, -0.019534845784941194, 0.5358763623449855, 0.7319880917201245, 0.4567678577791345, -0.29070015316838554, -1.3930743194930884, -2.636283456848197, -3.755726769413369, -4.496881133621721, -4.676062186565763, -4.226479141019885, -3.217801018013364, -1.843597303656278, -0.3788042894634012, 0.8831079220918867, 1.6982568373596447, 1.9290417808600266, 1.5751889526828484, 0.7711210195461327, -0.24995561294638055, -1.2163245468219406, -1.8870586247354029, -2.1124556214817756, -1.8698158507093812, -1.265087924133171, -0.49988947722898436, 0.1872853501980557, 0.5897337386730043, 0.5921996749413762, 0.20478323814739724, -0.43881256544189906, -1.1188712933296021, -1.5932046402830624, -1.6691775450399902, -1.2638382764818967, -0.43451242502486, 0.6299711351666385, 1.6563981407545725, 2.3606637928841847, 2.527744369316578, 2.0756806334243225, 1.0848340469751163, -0.21714091702655341, -1.5119481755160067, -2.474391145788768, -2.8605404051141483, -2.5757289560498577, -1.702788680350989, -0.4816835514269586, 0.7547443661305472, 1.6716398157746841, 2.0244214375503438, 1.726446166650171, 0.872631067574239, -0.28802722635658234, -1.4234720016940632, -2.212921736951463, -2.437356991929717, -2.039928502782899, -1.1387350193682122, 0.01159655156178002, 1.0978896699887315, 1.8424290098483218, 2.084550754720208, 1.825007691777389, 1.219568551426834, 0.5238830207348489, 0.0068169197014376634, -0.1404600178845259, 0.1293956000018912, 0.7002651311698017, 1.3268287320258305, 1.7131292882647056, 1.611434962736016, 0.9101777992166799, -0.3177967676306582, -1.8237908658369348, -3.248315689222749, -4.224452480171294, -4.488595563623458, -3.964288887047076, -2.7921833626612242, -1.2951472088902494, 0.11254846369711967, 1.0454388152124956, 1.2602240281857795, 0.7274629270063546, -0.36084124403211565, -1.6505777802376094, -2.7337963285019966, -3.272507693717627, -3.0995977541626596, -2.2655448062784336, -1.0167535155437066, 0.28692788197477226, 1.288520767296903, 1.7462992094618806, 1.6059405278685108, 1.0094670906502639, 0.23892826871645872, -0.3855426517332182, -0.6184074334142287, -0.3735892715113428, 0.2477122203099483, 0.996169274717401, 1.5673817606541325, 1.716906403550374, 1.357041370399493, 0.6005108813431834, -0.2663134423002072, -0.8740806360551338, -0.8960852561262944, -0.16682786975293315, 1.247597835110507, 3.0534090087050823, 4.809099341552806, 6.05757402608845, 6.468279300309088, 5.9426517082699375, 4.647354332501326, 2.963124575718085, 1.3649634574046459, 0.2724705643241986, -0.08054385895238933, 0.28583549037424466, 1.1140891030510116, 2.0041436569485946, 2.5540300522828807, 2.4982074442660647, 1.7964172436844765, 0.6431324235066214, -0.6047559662699358, -1.555948574209017, -1.9230269750252815, -1.6221707471114453, -0.7992411434934131, 0.22657634265937165, 1.0808943136147946, 1.4711088153287741, 1.292403892543511, 0.6639295337689906, -0.1185069148810915, -0.6964423574768733, -0.7879055318022795, -0.30020377207490223, 0.6264280112276077, 1.6624912143402426, 2.406549683957568, 2.5349813442025897, 1.9297456148263978, 0.7361524300899186, -0.6732705105577996, -1.8192364646286128, -2.2800118095114077, -1.8420807511880706, -0.5829998744807527, 1.144774658644276, 2.8256454051165374, 3.9507030605285696, 4.186940246667058, 3.486732717823118], 'positive_zeros': ['1.21879467525710883604211949684313', '2.55910998280373179008796778096680', '3.62090610091713417808477378266932', '5.15651556945074164642761987560029', '5.85837831947177063687722787420148', '6.75858138093147949467261678962552', '7.87305415028100094866877835357590', '8.296594641017158319484057693854616', '9.818383213622276193531768044828432', '10.29771174607494653914169656128917'], 'prelabel': '2-3e6-27.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.14814814814814817, 'root_number': '0.8936326403234123 - 0.4487991802004622*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0740740740741', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21879467525710883604211949684', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.55910998280373179008796778097', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62090610091713417808477378267', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.25', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/f/649/1'], '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': '2-3e6-27.25-c1-0-15', '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': '2-3e6-27.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.07407407407407408, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21879467525710883604211949684', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1545005801644643949555393097982', 'Lhash_array': ['1545005801644643949555393097982'], 'label': '2-3e6-27.25-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/f/649/1'}