-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '631774986332867316037834441589,804103854848423201574215010476,2266143888543667060157826809864,2302217843903602629097507239794', 'a10': 0, 'a2': 0, 'a3': 4, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 10, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24077.246635059513, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -4, 6, -4, 1]], [5, [1, 0, 2, 0, 1]], [13, [1, -4, 30, -52, 169]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.1', 'coefficient_field': '1.1.1.1', 'conductor': 5922408960000, 'conductor_radical': 390, 'degree': 8, 'euler_factors': [[1], [1, -4, 6, -4, 1], [1, 0, 2, 0, 1], [1, 0, -4, 0, 102, 0, -196, 0, 2401], [1, 0, -44, 0, 726, 0, -5324, 0, 14641], [1, -4, 30, -52, 169], [1, 16, 140, 880, 4198, 14960, 40460, 78608, 83521], [1, 0, -20, 0, 54, 0, -7220, 0, 130321], [1, 24, 284, 2232, 12582, 51336, 150236, 292008, 279841], [1, 0, 92, 0, 3798, 0, 77372, 0, 707281], [1, 0, -116, 0, 5286, 0, -111476, 0, 923521], [1, 0, -20, 0, 2838, 0, -27380, 0, 1874161], [1, 0, -156, 0, 9446, 0, -262236, 0, 2825761], [1, 0, 76, 0, 5142, 0, 140524, 0, 3418801], [1, 0, -156, 0, 10502, 0, -344604, 0, 4879681], [1, -8, 236, -1304, 19414, -69112, 662924, -1191016, 7890481], [1, 0, -12, 0, -5290, 0, -41772, 0, 12117361], [1, 8, 172, 1112, 15478, 67832, 640012, 1815848, 13845841], [1, 0, -260, 0, 25878, 0, -1167140, 0, 20151121], [1, 0, -156, 0, 13094, 0, -786396, 0, 25411681], [1, 0, -68, 0, 10086, 0, -362372, 0, 28398241], [1, -16, 316, -3280, 38470, -259120, 1972156, -7888624, 38950081], [1, 0, -236, 0, 27702, 0, -1625804, 0, 47458321], [1, 0, -188, 0, 17766, 0, -1489148, 0, 62742241], [1, 0, -164, 0, 20742, 0, -1543076, 0, 88529281], [1, -16, 284, -3376, 45430, -340976, 2897084, -16484816, 104060401], [1, 0, 412, 0, 63654, 0, 4370908, 0, 112550881], [1, -32, 812, -12320, 154966, -1318240, 9296588, -39201376, 131079601], [1, 0, -340, 0, 50934, 0, -4039540, 0, 141158161], [1, -48, 1292, -22608, 283878, -2554704, 16497548, -69259056, 163047361]], 'euler_factors_factorization': [[1], [[[1, -1], 4]], [[[1, 0, 1], 2]], [[[1, -4, 7], 2], [[1, 4, 7], 2]], [[[1, 0, -11], 4]], [[[1, -2, 13], 2]], [[[1, 8, 38, 136, 289], 2]], [[[1, 0, -20, 0, 54, 0, -7220, 0, 130321], 1]], [[[1, 12, 70, 276, 529], 2]], [[[1, 0, 46, 0, 841], 2]], [[[1, 0, -58, 0, 961], 2]], [[[1, 0, -10, 0, 1369], 2]], [[[1, 0, -78, 0, 1681], 2]], [[[1, 0, 38, 0, 1849], 2]], [[[1, 0, -78, 0, 2209], 2]], [[[1, -2, 53], 4]], [[[1, 0, -12, 0, -5290, 0, -41772, 0, 12117361], 1]], [[[1, 4, 78, 244, 3721], 2]], [[[1, 0, -130, 0, 4489], 2]], [[[1, 0, -156, 0, 13094, 0, -786396, 0, 25411681], 1]], [[[1, 0, -68, 0, 10086, 0, -362372, 0, 28398241], 1]], [[[1, -8, 126, -632, 6241], 2]], [[[1, 0, -118, 0, 6889], 2]], [[[1, 0, -188, 0, 17766, 0, -1489148, 0, 62742241], 1]], [[[1, 0, -164, 0, 20742, 0, -1543076, 0, 88529281], 1]], [[[1, -8, 110, -808, 10201], 2]], [[[1, 0, 103], 4]], [[[1, -8, 107], 4]], [[[1, 0, -340, 0, 50934, 0, -4039540, 0, 141158161], 1]], [[[1, -24, 358, -2712, 12769], 2]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 4, 'label': '8-1560e4-1.1-c1e4-0-4', 'leading_term': '6.8908374599405422958647645811087330062746456428515306320577534355022538742142697279076921', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1560/2/g/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0146484375', 'prec': 40}, 'plot_values': [6.890837459940542, 6.878047371674588, 6.84969802709393, 6.80435118169936, 6.7406440702288455, 6.657616889980244, 6.555635191879072, 6.435447296623536, 6.297869332898429, 6.14369441785691, 5.973441694745789, 5.787631911555292, 5.5868784499353445, 5.371907427003705, 5.143610549624664, 4.902991420530486, 4.651148057724653, 4.389268153509504, 4.118617366828511, 3.8405577754286235, 3.5565523368234233, 3.268167160952571, 2.977080851800993, 2.685071065096885, 2.3940068810998874, 2.1058479661944456, 1.8226501913667903, 1.5465464004424245, 1.2797343045275429, 1.0244720161846181, 0.7830793065124722, 0.557908878292412, 0.35132848311700465, 0.1657106385020401, 0.0034243029981047036, -0.13319794028442544, -0.24188141659758708, -0.32042593193126134, -0.36672590487455525, -0.3788021940946891, -0.35482432851859363, -0.29313202264577265, -0.1922663349703852, -0.05099432349931048, 0.13167224423380935, 0.35645397890204045, 0.6237662116538876, 0.9337074437244194, 1.2860490033055931, 1.6802162142982047, 2.1152522861689294, 2.589824330249711, 3.102225901523211, 3.6503687454791773, 4.231758593415789, 4.843520230531282, 5.482415790881278, 6.144853101981352, 6.826883980482536, 7.524245474546521, 8.232393733287289, 8.946532684793194, 9.661643057637075, 10.37253173996497, 11.073876952748748, 11.760277072540498, 12.426313719973447, 13.066596236432838, 13.675809586908054, 14.248778309791783, 14.780560453964823, 15.266470885016938, 15.702120045738136, 16.08348351854509, 16.407016883702894, 16.66964137463187, 16.868760649162976, 17.002323751129406, 17.068945996205393, 17.06784440392108, 16.998821972245125, 16.86231217586724, 16.659489487688482, 16.392150096153234, 16.0626590390988, 15.673968316581412, 15.229703560845193, 14.73399661036237, 14.191399353577442, 13.60687450587832, 12.985851896415957, 12.33403107240763, 11.65727482197439, 10.961579930831588, 10.253105769614274, 9.537974019185226, 8.822161863799106, 8.111467031468388, 7.411519965020933, 6.727610879621639, 6.064604898657117, 5.426918745900748, 4.818532661898382, 4.242870434584778, 3.702754702843042, 3.2004100736889627, 2.737489908454988, 2.315022976235895, 1.933417077544973, 1.592495155052241, 1.2915448713655813, 1.029328927389224, 0.8041315651086874, 0.6138226249797326, 0.45592662981428433, 0.32767741675513024, 0.22608918442212628, 0.14803234489284828, 0.09030775207211367, 0.04971556756684277, 0.023124975133579945, 0.007539481662255941, 0.00015572631013099984, -0.0015844435225969601, 4.9677904165446424e-05, 0.0031119358374771824, 0.006004242573503062, 0.007490652688179562, 0.0067004914326239794, 0.003121441782459213, -0.003417098999877868, -0.012771643791267951, -0.024520207972837393, -0.038005025224109076, -0.052382445919520584, -0.0666772076021512, -0.07983873331746105, -0.09079934755161642, -0.09853429531090692, -0.10211527658051427, -0.10076008289695859, -0.0938783478443313, -0.08111194784248452, -0.06236027280688977, -0.037798096768378815, -0.007884900350623862, 0.02663799815152261, 0.06476489026370531, 0.10525056421662508, 0.1466458840740809, 0.18734948061804158, 0.22566093480139907, 0.2598385944528299, 0.2881670900746948, 0.3090398228944505, 0.32102050151395867, 0.3229055589947237, 0.31379252139896174, 0.2931566155142417, 0.260884123372682, 0.2173041805747399, 0.16322138142662349, 0.09994609208359874, 0.029271418944715147, -0.04655096176713631, -0.12483873080127848, -0.20251952285699237, -0.27621419677834735, -0.3423179279490425, -0.3970870532914209, -0.4367439365906102, -0.4575937295438394, -0.45613423010667375, -0.42916961149393107, -0.3739386479432458, -0.2882160207345693, -0.17040283419530292, -0.01961509234402678, 0.1642266461448914, 0.3803611652266206, 0.6271626288519618, 0.9021275126983683, 1.2018805541256672, 1.522228601613179, 1.8582254546838408, 2.204257490020431, 2.554169317023495, 2.90138955288179, 3.239066105043021, 3.560231169361632, 3.858021110448862, 4.125814206128123, 4.3573795753008815, 4.547062430844584, 4.690027966534835, 4.782331580882126, 4.821008121688299, 4.804201403253526, 4.731344408768242, 4.603099238622061, 4.421330541634334, 4.189121002931143, 3.9108220832932346, 3.591851614189888, 3.2385427063230336, 2.858035046724912, 2.458185757665694, 2.0472771082412287, 1.6337903304013588, 1.2262209331534486, 0.8329044857625114, 0.4617350383231124, 0.11995428901921888, -0.18602040600808972, -0.45075694429503205, -0.6699733968860015, -0.8406420335027327, -0.9610598465268602, -1.0308999040299875, -1.0511990730848035, -1.0243079214562678, -0.9538154970625649, -0.8444456999387024, -0.7018862904257975, -0.5326088899950808, -0.34367412001043707, -0.14250487697347913, 0.06334897365597124, 0.266431567807842, 0.4596076100085745, 0.6363150067944777, 0.790736492683154, 0.9179491471392404, 1.0140748799783668, 1.0764441403539262, 1.103605585482475, 1.095325308028658, 1.0525895457505954, 0.9776075390489618, 0.8736431987306962, 0.7448623428897726, 0.5961925182330048, 0.43317702469335984, 0.2617070328928705, 0.08779702539374191, -0.08261580533880981, -0.24387366895137194, -0.39083099006499455, -0.5190289525096735, -0.6248391738630475, -0.7055981175974331, -0.7596859426177217, -0.7865542077135196, -0.786726192453337, -0.7617796275778888, -0.7142359619163487, -0.6474263478466473, -0.5653456543839247, -0.47249163900095226, -0.37363618994312, -0.273609758736389, -0.17709629104756014, -0.08842918615947118, -0.01138580562391384, 0.05097710674707295, 0.09645796798107262, 0.12382243622841417, 0.13285633734022695, 0.12437236663986875, 0.10018074536506896, 0.06302460262191195, 0.016443268148276766, -0.03539122675036667, -0.08786077894564032, -0.1361146766369664, -0.17531202101035442, -0.2008575622271856, -0.20863255451680227, -0.19522066928227297, -0.15809758650525296, -0.09578500125883103, -0.007968480275283437, 0.10443235527538092, 0.23925994798927439, 0.39315978709787086, 0.5616770103653504, 0.7394324461053142, 0.9203163236813618, 1.0977136276330852, 1.264783789125822, 1.414821533635543, 1.5415128909418203, 1.6391995843370362, 1.703178592849366, 1.7300514575144887, 1.7178315673534807, 1.6660474943318884, 1.575859076184318, 1.4501768779653028, 1.293471185544427, 1.1115920499760414, 0.911595078756618, 0.7015406616385124, 0.49003787783340325, 0.28584156310338765, 0.09747441334077468, -0.067165467220982, -0.20129041765392225, -0.29960670691602365, -0.3586337746575803, -0.3769841436010264, -0.3555583570978795, -0.29761199828318496, -0.20872338304587737, -0.09665910694147489, 0.02892552507298746, 0.1568917564340922, 0.27512205494348235, 0.37114641360430567, 0.4328528920362016, 0.44923230001909725, 0.41116782465134905, 0.31228180692332114, 0.14966951217457322, -0.07542816047831882, -0.35700823146475835, -0.6837763586344323, -1.0389019243670894, -1.3999110124185905, -1.7387438351878732, -2.022059837819734, -2.2118181200562628, -2.2660165929630804, -2.1396507385058063, -1.7859907457338837, -1.15789926950005, -0.2092579387849963, 1.1034408382089105, 2.8193048833945853, 4.971524929114472, 7.58585763499163, 10.679134923111654, 14.257932533605981, 18.317580067547517, 22.8413153714959, 27.799779864295633, 33.15121508415252, 38.84147823378621, 44.80436753626562, 50.96267442267504, 57.23053014580783, 63.51428276291016, 69.71388346277949, 75.72538774832564, 81.44522747538755, 86.77111983614735, 91.60375114176654, 95.84990328657024, 99.42758006434966, 102.26577677737261, 104.30537738699192, 105.50172200301596, 105.82911716243605, 105.27856591633844, 103.85703987315192, 101.58853199671098, 98.51677216035398, 94.70085075886598, 90.21277016405618, 85.13676540825958, 79.56990946208438, 73.61657262278797, 67.38503296958244, 60.98572004422559, 54.53038711479587, 48.12700012747342, 41.87671750109597, 35.872242960540945, 30.196834214278958, 24.921124696572257, 20.101652810861115, 15.780395841624692, 11.984759494953982, 8.727004918160542, 6.0047576753064265, 3.8020915802012842, 2.090890687248897, 0.8323982442833032, -0.020836451498005434, -0.5228482793193907, -0.7320586585286121, -0.7089581066115155, -0.5139214001516933, -0.2051627661919453, 0.16320820773233574, 0.5427944842245558, 0.892153637990912, 1.1777709624818957, 1.3748028699547328, 1.4671550215516451, 1.4472664860133426, 1.3156738134554873, 1.0803323681007555, 0.7553721866394427, 0.3598098346379974, -0.08379990594315999, -0.5508479794944842, -1.0162477844303663, -1.4558180774538234, -1.8475646145677864, -2.17293613683003, -2.4176521069100376, -2.5722608071826643, -2.6325315420806987, -2.599709675232678, -2.480115622637499, -2.2845932334515093, -2.027860187261273, -1.727736588567634, -1.4039002609325564, -1.076715123033479, -0.7661170884377664, -0.49051601097119946, -0.2656396404998213, -0.10363198602511935, -0.01235448844173685, 0.005126969255267524, -0.04920308644440611, -0.16833990063453816, -0.3405346768784071, -0.549835120138997, -0.776865650171649, -0.9997675761447117, -1.1952952055654362, -1.3400875884125432, -1.4118673532515444, -1.390611213623077, -1.2596995505551878, -1.0070108567329188, -0.625631132543334, -0.11440403499739618, 0.5217106351908735, 1.2715902994253003, 2.118263980063255, 3.0393947614491967, 4.008038188831863, 4.993858883506806, 5.964227067420296, 6.885401896544395, 7.723968962661905, 8.448701684809542, 9.031573045454193, 9.44878168234816, 9.681951683083698, 9.719581035308394, 9.557083075888935, 9.196866591482134, 8.64852620808814, 7.9290870630724894, 7.061812258280908, 6.0751774551360676, 5.001958187518085, 3.8782798574460675, 2.7417677057726717, 1.630013791419296, 0.5792138417039232, -0.3771797511642296, -1.209917862931563, -1.8950407279852401, -2.4147409048146886, -2.7580720073349037, -2.921208389101327, -2.907427263496558, -2.726876594906163, -2.396080724204532, -1.936981373379125, -1.3759057641193644, -0.7424019651151149, -0.06781849754512351, 0.6160911498417302, 1.2784492598286337, 1.8905619296744467, 2.4273668734434453, 2.868227360717153, 3.197562535468941, 3.4054485299983512, 3.4882206974036034, 3.4480862220144055, 3.292695009558353, 3.034715918162724, 2.6913533179795968, 2.2830363288703936, 1.83227604136148, 1.3626303106751931, 0.897663513552667, 0.4595912002793802, 0.06824765628538984, -0.2597445498065871, -0.5116930772090882, -0.6793812051324166, -0.7592943652182776, -0.7526325379856292, -0.6651332540996758, -0.5065768963126708, -0.29013099092029426, -0.031569187800122765, 0.25166591180328474, 0.5414780680338653, 0.8200898770032334, 1.071003282885084, 1.2799883109106696, 1.4357723957492667, 1.5305686185007852, 1.560494098261736, 1.5258874034598104, 1.431136641654105, 1.2843766056250912, 1.097079436261237, 0.8835158364212405, 0.6598709704574621, 0.4433634684072635, 0.2513569509443954, 0.10044935524112268, 0.005549821863924303, -0.020912997055163078, 0.030340044994830687, 0.16493311421099446, 0.3845203377269239, 0.6866383708104798, 1.0647702201400293, 1.5087305980613548, 2.0050746625165807, 2.5376209298880315, 3.088204265230176, 3.6378022318854373, 4.167178717302285, 4.657582353577482, 5.091654513192844, 5.454656628811139, 5.7346553179003275, 5.922788645547329, 6.0137371790851155, 6.006421065023743, 5.903375549611861, 5.7103392744482155, 5.436085228920057, 5.092416519897557, 4.692986388992976, 4.252493246680137, 3.7861708250712756, 3.309432402404909, 2.836780658394113, 2.3811706412501814, 1.9536741507657336, 1.5632968003911405, 1.216512817182245, 0.9171803369816413, 0.6666785214354791, 0.4641522951362473, 0.3067161043566006, 0.18984901323839717, 0.10786772465323026, 0.054411247540705865, 0.022897829754330006, 0.0069778016281418, 0.0009304772027432277, -2.0595598064120666e-05, 0.0005138283245710717, 0.0002090054545569878, -0.0019593662045271007, -0.005801704620836823, -0.01009122095165923, -0.012815066569650913, -0.01147987226508438, -0.0034396809655309396, 0.013770160915995212, 0.0421129239112528, 0.08277711810043684, 0.13600509079189227, 0.20096193281544997, 0.2756784362492137, 0.357111789168014, 0.44138656536488197, 0.5239758873018074, 0.5999470510528333, 0.6643208676707308, 0.7125863128952035, 0.7409420394727911, 0.7465562474090369, 0.7278829548143307, 0.6850316176949274, 0.6197054949154926, 0.5351430845969867, 0.4360693312690498, 0.3286103948708923, 0.21982945539728405, 0.11731287070745508, 0.028777029258844698, -0.038362869934894746, -0.07755493805754247, -0.08354992835700381, -0.052763761803097865, 0.016404510720017352, 0.12337039671148169, 0.26530963606530367, 0.43722294919911114, 0.6321309376714601, 0.8414096874372137, 1.0552164081876283, 1.263013510794726, 1.4542254008628885, 1.6187973375646192, 1.7477456517543268, 1.8337334448410052, 1.8716886607799623, 1.8590147849459477, 1.7957434126104503, 1.6846528449638336, 1.5313268993148168, 1.343699798583954, 1.1315990813797199, 0.9062712769211394, 0.6798360108980654, 0.46443309547519646, 0.27149342598579934, 0.111083225811591, -0.008718130011051003, -0.08239571501626326, -0.10736451375110569, -0.08417167619706944, -0.016527704602088463, 0.08888713766688147, 0.2227919434802979, 0.3738401332431049, 0.5293652657513129, 0.6761792623245888, 0.8013998170380278, 0.8933398795402829, 0.9424916639179415, 0.9421763158983252, 0.8890823316967822, 0.7837309314565137, 0.6308428391848628, 0.43913028205044435, 0.22096488765588185, -0.008080045797323585, -0.22989091334096387, -0.42488074650928814, -0.5730466398247808, -0.655066179728074, -0.6535000808318586, -0.5539259885686197, -0.34589110845994286, -0.023732025876871926, 0.4127568547436372, 0.958069242071735, 1.6009784773901985, 2.3247950232072148, 3.10801601469675, 3.925193466883935, 4.747956060429683, 5.54630343183491, 6.290346293209223, 6.951519785001558, 7.503804858979322, 7.925129130579341, 8.199062045912292, 8.315153457615022, 8.26925428673376, 8.063943807767096, 7.70904573233057, 7.220471883725273, 6.619225905276012, 5.930561764032762, 5.183159104650635, 4.407065886735502, 3.632081051973003, 2.8864387764238804, 2.195622079334855, 1.58080352658274, 1.0578828816029282, 0.6369292668176891, 0.32190906404301933, 0.11067218122791637, -0.004593834725928683, -0.03658732831120332, -0.0018366031865909686, 0.08059956105668728, 0.19053753242175733, 0.3081302925771825, 0.41537171497813685, 0.4973520687807981, 0.5432754612897199, 0.5472551797162313, 0.5088526605635257, 0.4329872403717058, 0.32953386581895555, 0.21263001486760388, 0.09964848231796627, 0.00972000192275858, -0.03781723347501146, -0.025037084945746097, 0.06291072963463444, 0.2362733070157067, 0.4994337675128637, 0.8499456754586026, 1.2780199162132664, 1.7664857457546168, 2.2911659687325727, 2.821776305319097, 3.3235999601819697, 3.7591792676244036, 4.090256525106408, 4.280146616900435, 4.296734663336128, 4.114404321377274, 3.715899701036126, 3.0942735543612576, 2.2548970234572048, 1.2155551852247144, 0.006314885069479756, -1.330837521516221, -2.742852388445492, -4.168123819043369, -5.539058871978998, -6.784888552003018, -7.8350420819301245, -8.622795947931749, -9.088616407630052, -9.183402049338058, -8.871718627926157, -8.133903632471428, -6.967602856469965, -5.388720170852146, -3.431459385045963, -1.147249702157072, 1.3968564367115404, 4.120727244347055, 6.935287005516811, 9.745701860667301, 12.454895115126208, 14.968123110880594, 17.199251578299297, 19.072815941288283, 20.52645341642623, 21.51442155501124, 22.012442916583353, 22.015733740887907, 21.53798141676495, 20.611563552753733, 19.28865402008419, 17.63513511897419, 15.72642780951673, 13.64488681852796, 11.477926117388037, 9.310888297005267, 7.2226213542007045, 5.282862569679376, 3.5504380614827413, 2.069058941730081, 0.8658276718444319, -0.048643668030190504, -0.6793412652328411, -1.0463604902150563, -1.1826418560687009, -1.1308542537767365, -0.939974204551135, -0.6619002695801952, -0.3476869259399772, -0.043947021536215276, 0.2102940417235014, 0.38609594476028875, 0.4664232240686435, 0.44709812814117356, 0.33683015912189385, 0.1562694113810178, -0.06380252733698573, -0.28506696238016505, -0.464819543868946, -0.5595816643759138, -0.5289785460218331, -0.3395693214462989, 0.031989967255485786, 0.5959351580737563, 1.3468982392105933, 2.2625281715263372, 3.304216590053297, 4.417340238711537, 5.532411579535842, 6.568015888451413, 7.436611813395391, 8.047458879695622, 8.310357068752257, 8.141144950174079, 7.469656448357546, 6.241812208419451, 4.4223221548225204, 1.9986264241461298, -1.0139813624379752, -4.574520022088153, -8.617749227971235, -13.054898280289356, -17.774523643892007, -22.649020988514824, -27.53993590546122, -32.30281394182922, -36.79278868787453, -40.871678405820035, -44.41355085371956, -47.30984129072978, -49.47500713292584, -50.84941821901979, -51.40104387425153, -51.12680508735519, -50.053957191264374, -48.23683178370161, -45.75340755910198, -42.701953777617724, -39.19750472287578, -35.36501745095924, -31.33351143782666, -27.230812320896764, -23.178409719873777, -19.286093948471077, -15.64805488525727, -12.33982471685006, -9.415739424046105, -6.908613008596124, -4.830324351543862, -3.172924919613804, -1.9102933664237562, -1.0022547292960737, -0.3984346170917573, -0.04191532974017772, 0.12703319810901295, 0.16627745211450876, 0.1283515599671856, 0.05778264824905568, -0.011079805937141581, -0.05558528308372384, -0.06503668068776979, -0.04013601251122906, 0.008206351637490065, 0.061021357684328405, 0.09393563616382922, 0.08005393416413986, -0.007023393487863953, -0.19009477221732002, -0.48566482784872494, -0.9017505099070187, -1.4363044701841727, -2.0763449171315664, -2.79788514314369, -3.566689301661748, -4.340005478007874, -5.068669567206873, -5.699706378451003, -6.179478407866618, -6.457426601523701, -6.488947208685003, -6.238195235654288, -5.680813864042352, -4.8063625036211395, -3.619069567205064, -2.1382223055768184, -0.3979858820308455, 1.5538615051210616, 3.658105340009129, 5.846477134265878, 8.044710899051145, 10.176873284351196, 12.168424759820523, 13.949207257187172, 15.456929868284696, 16.641544062106416, 17.466177475161413, 17.90804225847939, 17.95970472961401, 17.630716831484218, 16.94515956691297, 15.939640741225155, 14.661740700617807, 13.16856829997447, 11.522471968783616, 9.787755054798442, 8.028028654024236, 6.303760271364673, 4.669093843710581, 3.1697998642745553, 1.8418775277433623, 0.7105034462801287, -0.21023157164978953, -0.916918454870586, -1.4160676277079784, -1.7230625242440338, -1.8601450675243947, -1.8544634833697564, -1.736202022068082, -1.53670268632632, -1.286355472547884, -1.0130255920035558, -0.7408354666830762, -0.48918023686073253, -0.27218785055191363, -0.09866439441539294, 0.027672911000053667, 0.1077409867567828, 0.1461651509692326, 0.1502685702507728, 0.12906011049614785, 0.09222556878639601, 0.049073104040652536, 0.007727713802310898, -0.025457811075858688, -0.046296458838986934, -0.052910180729417104, -0.0456177561405124, -0.02663533905670799, 0.00038753655570280177, 0.030961729066198453, 0.06037650471046735, 0.0843068807615146, 0.09938949330851533, 0.1036325968575747, 0.09666928613971003, 0.07986134533732939, 0.05624163300835079, 0.03022069748297097, 0.007177796924915329, -0.007039037945206901, -0.006686047932560457, 0.013285343283971305, 0.05669498628051424, 0.12568794862717525, 0.22043745136023035, 0.33899814210573814, 0.47731087916425485, 0.6294069849490529, 0.78789511674823, 0.9443976194469863, 1.0900731072853598, 1.2162963130460402, 1.315548358177198, 1.3817871446324392, 1.4108085606532719, 1.4006636047943826, 1.3521154690898078, 1.2682801333220142, 1.1543042082431831, 1.017091370705579, 0.8650006053909493, 0.7069076881638017, 0.5514896490884936, 0.40666702916859304, 0.2791103314899139, 0.17359019375031864, 0.092680760968249, 0.03670060200622498, 0.0038149800629113874, -0.009704756002718685, -0.008971488995549183, 0.00016461973393141845, 0.01184073067079042, 0.020965274839141564, 0.023965431537114557, 0.01942761962987724, 0.008580160554844778, -0.004433303798435895, -0.01253746786778496, -0.00597974242879178, 0.027137030452376365, 0.10008521219252936, 0.2265354660122169, 0.4194289116636273, 0.6898120968527085, 1.0456789033152114, 1.4908742911330903, 2.024218270517678, 2.6391347008003043, 3.3233055223087384, 4.058629263594414, 4.821765165319086, 5.585653053856244, 6.320342003012975, 6.994163895404887, 7.575607339196802, 8.036205285630352, 8.35142927322841, 8.501853407721972, 8.474878717285952, 8.267068432929234, 7.883488105100187, 7.337365522226958, 6.65013997005757, 5.851648791482869, 4.977493756293183, 4.067004491303779, 3.161590280358579, 2.303076320116814, 1.530601166811892, 0.8784011048446232, 0.3741235968960171, 0.0373490896256243, -0.12182874549367897, -0.10332080906692409, 0.08303312239435394, 0.41807385326969976, 0.8745064589577138, 1.4185037663540156, 2.0116187558664995, 2.612991695760053, 3.1818016103996887, 3.6796366829502682, 4.073114856055577, 4.337074335665183, 4.4545771241581305, 4.417101379838556, 4.2241521064836975, 3.8820793202362402, 3.4066958363582702, 2.823165014341475, 2.165590512618705, 1.4747843883210803, 0.786508611285785], 'positive_zeros': ['0.49838258761453807251792423687948', '0.63432609482743220931541321750758', '1.78767231927762088122458355030154', '1.81612965235776202488247120732639', '1.89746195740558517590128789611128', '2.12753298020841327654925831594529', '2.39344231282427532720249758587195', '2.59447098850014418079709855461669', '3.11099499953696935587985133525710', '3.32069045162436061317637858151960', '3.58169674682013576088143160722047', '3.85495911682734687008970311210331', '3.97447528938125082979015326789485', '4.11736279741253384691915458507866', '4.47614689340581573276596584720344', '4.61095698782783472847953192096952', '4.74160069557908469244641392038980', '4.92452454666002789685259393181072', '5.68314064924324496929208136518094', '5.76515490979629974613050217027324', '5.92993244478442683364607437410755', '6.22969186819600376702190917173083', '6.24310100219035096770994133083495', '6.44816651119498056662420047686010', '6.82018985966045975947085867574324', '7.00340259689958347511092861736531', '7.26843365630984372423652199830457', '7.39914055472024530727153478205608', '7.66250431150642275047763409920924', '7.68455356368695309521367541618362', '8.285375528831897005108027513248388', '8.291929336983584580267783342468824', '8.322618540975914885189061888732472', '8.411946289841632801856100824822976', '8.750761329335907931682316402257455', '8.815521784643619010102925405523064', '9.168637980183300997450898738239779', '9.231168139653664886686091084058272', '9.447725496130645979788598178120326', '9.566336893098136936573843252553383'], 'prelabel': '8-1560e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.5293997670028463, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 1985119381990947344, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49838258761453807251792423688', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.63432609482743220931541321751', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.78767231927762088122458355030', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 24077.246635059513, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 5922408960000, 'conductor_radical': 390, 'degree': 8, 'dirichlet_coefficients': [1, 0, 4, 0, 0, 0, 0, 0, 10, 0, 0, 0, 4, 0, 0, 0, -16, 0, 0, 0, 0, 0, -24, 0, -2, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -64, 0, 8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, -8, 0, 0, 0, 16, 0, 35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -44, 0, 726, 0, -5324, 0, 14641], 'euler13': [1, -4, 30, -52, 169, 0, 0, 0, 0], 'euler17': [1, 16, 140, 880, 4198, 14960, 40460, 78608, 83521], 'euler19': [1, 0, -20, 0, 54, 0, -7220, 0, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 24, 284, 2232, 12582, 51336, 150236, 292008, 279841], 'euler29': [1, 0, 92, 0, 3798, 0, 77372, 0, 707281], 'euler3': [1, -4, 6, -4, 1, 0, 0, 0, 0], 'euler31': [1, 0, -116, 0, 5286, 0, -111476, 0, 923521], 'euler37': [1, 0, -20, 0, 2838, 0, -27380, 0, 1874161], 'euler41': [1, 0, -156, 0, 9446, 0, -262236, 0, 2825761], 'euler43': [1, 0, 76, 0, 5142, 0, 140524, 0, 3418801], 'euler47': [1, 0, -156, 0, 10502, 0, -344604, 0, 4879681], 'euler5': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler53': [1, -8, 236, -1304, 19414, -69112, 662924, -1191016, 7890481], 'euler59': [1, 0, -12, 0, -5290, 0, -41772, 0, 12117361], 'euler61': [1, 8, 172, 1112, 15478, 67832, 640012, 1815848, 13845841], 'euler67': [1, 0, -260, 0, 25878, 0, -1167140, 0, 20151121], 'euler7': [1, 0, -4, 0, 102, 0, -196, 0, 2401], 'euler71': [1, 0, -156, 0, 13094, 0, -786396, 0, 25411681], 'euler73': [1, 0, -68, 0, 10086, 0, -362372, 0, 28398241], 'euler79': [1, -16, 316, -3280, 38470, -259120, 1972156, -7888624, 38950081], 'euler83': [1, 0, -236, 0, 27702, 0, -1625804, 0, 47458321], 'euler89': [1, 0, -188, 0, 17766, 0, -1489148, 0, 62742241], 'euler97': [1, 0, -164, 0, 20742, 0, -1543076, 0, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -4, 6, -4, 1, 0, 0, 0, 0], [1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 0, -4, 0, 102, 0, -196, 0, 2401], [1, 0, -44, 0, 726, 0, -5324, 0, 14641], [1, -4, 30, -52, 169, 0, 0, 0, 0], [1, 16, 140, 880, 4198, 14960, 40460, 78608, 83521], [1, 0, -20, 0, 54, 0, -7220, 0, 130321], [1, 24, 284, 2232, 12582, 51336, 150236, 292008, 279841], [1, 0, 92, 0, 3798, 0, 77372, 0, 707281], [1, 0, -116, 0, 5286, 0, -111476, 0, 923521], [1, 0, -20, 0, 2838, 0, -27380, 0, 1874161], [1, 0, -156, 0, 9446, 0, -262236, 0, 2825761], [1, 0, 76, 0, 5142, 0, 140524, 0, 3418801], [1, 0, -156, 0, 10502, 0, -344604, 0, 4879681], [1, -8, 236, -1304, 19414, -69112, 662924, -1191016, 7890481], [1, 0, -12, 0, -5290, 0, -41772, 0, 12117361], [1, 8, 172, 1112, 15478, 67832, 640012, 1815848, 13845841], [1, 0, -260, 0, 25878, 0, -1167140, 0, 20151121], [1, 0, -156, 0, 13094, 0, -786396, 0, 25411681], [1, 0, -68, 0, 10086, 0, -362372, 0, 28398241], [1, -16, 316, -3280, 38470, -259120, 1972156, -7888624, 38950081], [1, 0, -236, 0, 27702, 0, -1625804, 0, 47458321], [1, 0, -188, 0, 17766, 0, -1489148, 0, 62742241], [1, 0, -164, 0, 20742, 0, -1543076, 0, 88529281]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1560/2/g/g'], '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': '8-1560e4-1.1-c1e4-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-1560e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.5293997670028463, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1985119381990947344, 'z1': {'__RealLiteral__': 0, 'data': '0.49838258761453807251792423688', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '631774986332867316037834441589,804103854848423201574215010476,2266143888543667060157826809864,2302217843903602629097507239794', 'Lhash_array': ['631774986332867316037834441589', '804103854848423201574215010476', '2266143888543667060157826809864', '2302217843903602629097507239794'], 'label': '8-1560e4-1.1-c1e4-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1560/2/g/g'}