-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1107263907644896208282269933698', 'a10': [14.597409824171056, 0.0], 'a2': [-3.735489498215868, 0.0], 'a3': [0.0, 0.0], 'a4': [5.953881791281038, 0.0], 'a5': [-3.907763582562077, 0.0], 'a6': [0.0, 0.0], 'a7': [-36.41293698929521, 0.0], 'a8': [7.643253080777945, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.74190511873151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [3.735489498215868, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.907763582562077, 0], [125.0, 0]], [[1.0, 0], [36.41293698929521, 0], [343.0, 0]], [[1.0, 0], [-19.194269744117967, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-83.88391598572694, 0], [4913.0, 0]], [[1.0, 0], [46.849171671201404, 0], [6859.0, 0]], [[1.0, 0], [103.90460961265947, 0], [12167.0, 0]], [[1.0, 0], [108.34084429456567, 0], [24389.0, 0]], [[1.0, 0], [-147.53196006878105, 0], [29791.0, 0]], [[1.0, 0], [-160.01218607023074, 0], [50653.0, 0]], [[1.0, 0], [-231.49002291069183, 0], [68921.0, 0]], [[1.0, 0], [340.31384272782793, 0], [79507.0, 0]], [[1.0, 0], [-119.65339766985326, 0], [103823.0, 0]], [[1.0, 0], [-732.8794473026862, 0], [148877.0, 0]], [[1.0, 0], [229.78209756373673, 0], [205379.0, 0]], [[1.0, 0], [-108.94305780131177, 0], [226981.0, 0]], [[1.0, 0], [10.395542787707544, 0], [300763.0, 0]], [[1.0, 0], [869.2012476829918, 0], [357911.0, 0]], [[1.0, 0], [-1099.070898076436, 0], [389017.0, 0]], [[1.0, 0], [-140.41033292361675, 0], [493039.0, 0]], [[1.0, 0], [159.47413296633434, 0], [571787.0, 0]], [[1.0, 0], [-1067.9332355314718, 0], [704969.0, 0]], [[1.0, 0], [858.8809769205142, 0], [912673.0, 0]], [[1.0, 0], [-1574.1632986773682, 0], [1030301.0, 0]], [[1.0, 0], [129.72386601250815, 0], [1092727.0, 0]], [[1.0, 0], [-1957.4335358063825, 0], [1225043.0, 0]], [[1.0, 0], [1228.7725408441836, 0], [1295029.0, 0]], [[1.0, 0], [1629.497525393192, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 80, 'label': '2-39e2-1.1-c3-0-80', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1521/4/a/u/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.81980379778083e-61, 0.08424986055030163, 0.16641355389264748, 0.24443014705226643, 0.316289275627676, 0.3800566600047391, 0.43389984933168985, 0.4761141872873482, 0.5051489281102632, 0.5196333549541655, 0.5184026687593327, 0.5005233282092665, 0.46531743393585845, 0.4123856669960545, 0.34162821678375666, 0.2532630708174484, 0.147840991840832, 0.026256479603936955, -0.11024599168937145, -0.26007115175494905, -0.4212781768574616, -0.5915925755907643, -0.7684252004289578, -0.9488987451483623, -1.1298819407299998, -1.3080314919558211, -1.4798416064748474, -1.6417007612907186, -1.7899551328215515, -1.9209778910268134, -2.031243331340273, -2.1174045965882478, -2.1763735314213726, -2.2054010210308297, -2.202156001144265, -2.1648011945035894, -2.0920635369237846, -1.9832972098124815, -1.8385372011475092, -1.6585413778485942, -1.4448191725347244, -1.1996451687282648, -0.9260561109665038, -0.6278301685902477, -0.30944764092415195, 0.023967298051136326, 0.3667237627449751, 0.7126596839709745, 1.055254644780083, 1.3877584405809693, 1.7033332555010836, 1.9952068392376383, 2.256833593433641, 2.482060049891468, 2.6652908605700616, 2.8016511365362033, 2.8871407839440177, 2.9187764021197053, 2.8947163421679507, 2.8143646817608716, 2.678450157376954, 2.4890765101933443, 2.249741243278871, 1.9653204488761373, 1.6420181345081306, 1.2872793404606429, 0.909667280058012, 0.5187057256690407, 0.12468888201647331, -0.26153799398389105, -0.6288229809268184, -0.9659717175095807, -1.2620254617831372, -1.506546274769819, -1.6899020621283039, -1.8035438292253343, -1.840267326163739, -1.794451297016918, -1.6622648130703885, -1.4418366682273596, -1.1333805439090034, -0.7392706014685112, -0.26406331557328805, 0.2855373019551302, 0.9007724529075238, 1.570979045904769, 2.28379603416305, 3.025423013387702, 3.7809258390787273, 4.534582449163528, 5.270260640245838, 5.971818295046863, 6.623515542571183, 7.210427593729845, 7.718846569299168, 8.136660551468784, 8.453698362352313, 8.66202920936247, 8.756207333330531, 8.733453133685318, 8.59376389685786, 8.339949178654603, 7.97758803713452, 7.514907618450294, 6.96258499515977, 6.33347656974775, 5.642281706977161, 4.905149467613252, 4.139239305091293, 3.3622482823225694, 2.5919187017440968, 1.8455409614220564, 1.1394669092371577, 0.4886489359059315, -0.09378048826758889, -0.5968751655047162, -1.0121752626743523, -1.3339309560491468, -1.559241790733394, -1.688106583630627, -1.7233815989997414, -1.67064776411745, -1.5379907663266097, -1.3357008743578573, -1.0759021481537807, -0.7721232376811844, -0.43882412484962197, -0.09089484727239702, 0.2568566134430018, 0.5902095466534605, 0.8960111767922265, 1.1626158391536678, 1.3802670722652426, 1.5414089634361423, 1.6409155453911424, 1.676229951666157, 1.6474082963748193, 1.5570667339811466, 1.4102337490048815, 1.2141132891920596, 0.9777677515955612, 0.7117329254802583, 0.42757966386711926, 0.13743918554464005, -0.1464895911941849, -0.4124314828568948, -0.6495059879702417, -0.8481591961750188, -1.0005395560564798, -1.1008025448140721, -1.145332052774905, -1.132869587669674, -1.0645460923852184, -0.943815111502921, -0.7762900787614925, -0.5694924647894537, -0.3325212565712274, -0.07565757797417308, 0.1900789417495529, 0.4534033136462806, 0.7032477477186608, 0.9292329980034354, 1.1221082164642793, 1.2741402609796086, 1.379435461624363, 1.434179669635226, 1.4367858855826587, 1.3879427473257073, 1.290561488895856, 1.1496234743538267, 0.9719348705132995, 0.76579925098847, 0.5406227288843681, 0.30646941870901706, 0.07358747465398757, -0.14807248249143296, -0.34932414188878974, -0.5221754949742948, -0.6602014934540177, -0.7588412331908204, -0.8156048172744111, -0.8301790948732961, -0.8044260958552579, -0.7422729835629406, -0.6494975059125991, -0.5334180015923926, -0.4025017746193272, -0.2659098564815525, -0.1329996196226904, -0.012809208004951785, 0.08645083209904994, 0.15787310024949952, 0.19627143259659469, 0.1985190918795278, 0.16378794361890264, 0.09367384640211134, -0.007801342455798516, -0.1343149615977429, -0.2774936221084552, -0.4272796444724667, -0.5723993580073503, -0.7009133070824284, -0.8008237469620447, -0.8607111948121898, -0.8703694342461857, -0.8214074076139417, -0.7077869598287775, -0.5262674432371588, -0.2767317055448093, 0.03762715886991595, 0.410272899009828, 0.8314547225549904, 1.288497595525431, 1.7662465976185384, 2.2476500181455377, 2.714458664078452, 3.1480124723133605, 3.530080305772702, 3.8437150553462938, 4.074084094609829, 4.209234896355796, 4.240757290925086, 4.164307408814283, 3.9799636956525246, 3.692392319171815, 3.3108075257953287, 2.8487216980518095, 2.323489605412426, 1.7556611834372589, 1.1681666535051494, 0.5853664449470904, 0.032005765372888864, -0.4678806073475577, -0.8920639900856894, -1.221167065551427, -1.4396087371286566, -1.5364017627053954, -1.505761887074323, -1.3474948282955914, -1.067136918743129, -0.6758360590441369, -0.1899714364075724, 0.36947734677604954, 0.9777890616237866, 1.6075536042715666, 2.2298747751212264, 2.8156709811603013, 3.3370158346597876, 3.768457287376946, 4.088253418165844, 4.279465379590754, 4.330853264556683, 4.237528597225294, 4.0013274701520904, 3.6308806065308703, 3.1413702838874324, 2.5539784946882462], 'positive_zeros': ['0.873477208503307636792463945465459', '2.28156326127550384971913573599125', '3.46933826248398265101768088613964', '4.18927408566201933598434553611377', '5.78042120064467830866333698017851', '6.46240351099753395076800363429360', '7.28602911265057059055142842482529', '7.987193047777157911475014431801499', '8.852408024740362329321133654473331'], 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.873477208503307636792463945465', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.28156326127550384971913573599', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.46933826248398265101768088614', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 89.74190511873151, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 80, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/u/1/1'], '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': '2-39e2-1.1-c3-0-80', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.873477208503307636792463945465', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1107263907644896208282269933698', 'Lhash_array': ['1107263907644896208282269933698'], 'label': '2-39e2-1.1-c3-0-80', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/u/1/1'}