-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1639386146411863098357174796524', 'a10': [-111.97355166097061, 0.0], 'a2': [-4.478942066438824, 0.0], 'a3': [-9.0, 0.0], 'a4': [-11.939077965484714, 0.0], 'a5': [25.0, 0.0], 'a6': [40.31047859794942, 0.0], 'a7': [-168.81802593450115, 0.0], 'a8': [196.80058466014472, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.46333026914181, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [9.0, 0]]], [5, [[1.0, 0], [-25.0, 0]]], [11, [[1.0, 0], [-121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '165.1', 'coefficient_field': 'CDF', 'conductor': 165, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [4.478942066438824, 0], [32.0, 0]], [[1.0, 0], [9.0, 0]], [[1.0, 0], [-25.0, 0]], [[1.0, 0], [168.81802593450115, 0], [16807.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [-290.25941084744903, 0], [371293.0, 0]], [[1.0, 0], [-623.9641893822434, 0], [1419857.0, 0]], [[1.0, 0], [398.45571321641125, 0], [2476099.0, 0]], [[1.0, 0], [-3788.063444170974, 0], [6436343.0, 0]], [[1.0, 0], [-4220.42538063297, 0], [20511149.0, 0]], [[1.0, 0], [5594.574776162555, 0], [28629151.0, 0]], [[1.0, 0], [-301.2658916536699, 0], [69343957.0, 0]], [[1.0, 0], [14636.166641170495, 0], [115856201.0, 0]], [[1.0, 0], [-151.41838341766444, 0], [147008443.0, 0]], [[1.0, 0], [13534.97601783425, 0], [229345007.0, 0]], [[1.0, 0], [18116.096608659092, 0], [418195493.0, 0]], [[1.0, 0], [50582.3972885431, 0], [714924299.0, 0]], [[1.0, 0], [-5984.346686513841, 0], [844596301.0, 0]], [[1.0, 0], [-22450.694040773385, 0], [1350125107.0, 0]], [[1.0, 0], [-10017.645608714425, 0], [1804229351.0, 0]], [[1.0, 0], [476.1477662418681, 0], [2073071593.0, 0]], [[1.0, 0], [85024.73888446235, 0], [3077056399.0, 0]], [[1.0, 0], [25643.4237469531, 0], [3939040643.0, 0]], [[1.0, 0], [-1807.9098495586309, 0], [5584059449.0, 0]], [[1.0, 0], [-11688.495981208065, 0], [8587340257.0, 0]], [[1.0, 0], [135572.97862455965, 0], [10510100501.0, 0]], [[1.0, 0], [88490.49910992662, 0], [11592740743.0, 0]], [[1.0, 0], [-218742.42489422212, 0], [14025517307.0, 0]], [[1.0, 0], [-238399.13702288692, 0], [15386239549.0, 0]], [[1.0, 0], [-187224.82627809973, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-165-1.1-c5-0-16', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/165/6/a/c/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [-5.7003792291345224e-61, 0.12320048282520933, 0.24373051632108123, 0.35894767227486907, 0.4662657187691996, 0.563183085442593, 0.6473117193453967, 0.7164063800810292, 0.7683943564655034, 0.801405508033937, 0.81380244600927, 0.8042105728582843, 0.7715476006552855, 0.7150520697747139, 0.634310294742719, 0.5292810772978318, 0.4003174517620283, 0.24818466855250257, 0.07407358175162952, -0.12039141048621328, -0.3331507152276671, -0.5617149892042279, -0.803178416372442, -1.0542404573584465, -1.3112365781228978, -1.5701783018812767, -1.8268027344835003, -2.0766314914791972, -2.3150387084483306, -2.537327549455867, -2.738814347398254, -2.914919221318875, -3.061261727232314, -3.1737598192228975, -3.248730135868016, -3.2829873931501385, -3.2739404689480898, -3.219682615842977, -3.1190731478331166, -2.971807921357386, -2.7784759793742526, -2.5405998552192646, -2.2606572447721107, -1.9420820530846856, -1.5892432044990454, -1.2074000700746534, -0.8026339065285588, -0.3817553074728881, 0.047811671969474855, 0.47816735753938017, 0.9010941869926096, 1.3082315338454455, 1.691264132778262, 2.0421199681997826, 2.3531729117698292, 2.617444915390913, 2.8288022069046224, 2.98213971818212, 3.0735479183740924, 3.1004563439303885, 3.0617484221280753, 2.9578426813430743, 2.790736128143384, 2.5640064408289187, 2.2827706667134056, 1.9535992946284428, 1.5843858763550736, 1.1841737560518466, 0.7629428946359831, 0.3313612011558506, -0.09949384331440043, -0.5184362125537652, -0.9144868382552314, -1.2771944994113085, -1.5969523412626658, -1.8652998886552572, -2.0752003613852765, -2.2212833862391737, -2.300043844275463, -2.3099885925110937, -2.2517241434511788, -2.1279800470539216, -1.943564657319702, -1.7052521262094806, -1.4216017855384466, -1.1027134770782492, -0.7599247885011865, -0.40545845884142473, -0.05203034046230387, 0.2875698450026296, 0.6009112268067752, 0.876353193504684, 1.1034601426494046, 1.2733842129860067, 1.3792012057177692, 1.416186052711475, 1.3820159126541056, 1.276891233405816, 1.1035678487021814, 0.8672962959456453, 0.5756679445921914, 0.2383710896737454, -0.13313624298422533, -0.5260265580698352, -0.9265627851403699, -1.3206015680081398, -1.6941214479934867, -2.0337558367095183, -2.3273098277613937, -2.5642398771982657, -2.7360762279661386, -2.8367696671249436, -2.8629467522020247, -2.814060953019569, -2.6924311192786066, -2.5031631598862334, -2.2539556358953474, -1.9547949301222547, -1.6175505523516756, -1.255485751702647, -0.8827027216812929, -0.5135450953471652, -0.16198295661169082, 0.15899291077649896, 0.43794046226899935, 0.6654732979970323, 0.8346808815228356, 0.9414411575539052, 0.9846089621894101, 0.9660688404964428, 0.8906468155133777, 0.76588204249391, 0.6016658519538698, 0.40976213347664403, 0.20322903023986905, -0.004232800403310843, -0.19897583283329462, -0.3681126836365675, -0.5002003825199465, -0.5858678226512063, -0.618353979831094, -0.593927792241311, -0.5121654310731559, -0.37606689205357335, -0.19200114923525013, 0.03052277967379829, 0.279252970741737, 0.5397454884956084, 0.7960464328335765, 1.031475195799477, 1.2294728694427373, 1.3744752050396238, 1.452766848828745, 1.4532729786972511, 1.368246052466254, 1.1938091579824532, 0.9303233233689191, 0.5825538869966367, 0.15962032086573316, -0.3252756647850178, -0.855337822168184, -1.4108617633921126, -1.9700922116127033, -2.5102135584114293, -3.008428044911664, -3.4430697983778953, -3.7946993121769923, -4.047122036283578, -4.188276698409379, -4.21094380853736, -4.113232367817754, -3.8988128129791924, -3.576876246452386, -3.161813474684438, -2.672621649149095, -2.132060655817384, -1.5655950775561236, -1.0001698159388779, -0.46287760794687305, 0.020415900336437955, 0.4264196429269017, 0.7356666288256789, 0.9335979037539166, 1.011420115601339, 0.9666859175234565, 0.8035595328380137, 0.5327452850405139, 0.17107401080111434, -0.2592398434292249, -0.7316399268781372, -1.2165213915320192, -1.6827143696751838, -2.099084260457883, -2.4361675471396413, -2.6677580000524586, -2.7723587296153562, -2.7344207281691344, -2.5452981194445345, -2.203863912841275, -1.716746996406255, -1.0981705534967001, -0.36939304684253865, 0.4422257377027095, 1.3044905260821498, 2.1819065736542043, 3.0374085469189565, 3.8341932741245595, 4.537560373627975, 5.11666294165508, 5.546074029169482, 5.807083467021666, 5.888653312656762, 5.787978106008472, 5.510617297161314, 5.070190497289719, 4.487650315349686, 3.790171110691251, 3.0097136556383477, 2.1813441863220664, 1.3414005105385447, 0.5256068550828811, -0.2327576227715638, -0.9045345289764611, -1.4661127432467531, -1.9005266061439632, -2.198165618213845, -2.357058116925088, -2.3827163722009908, -2.2875563900057347, -2.0899308893982633, -1.81283689319214, -1.4823787292080481, -1.1260817625277533, -0.7711609335021969, -0.4428505689357374, -0.16289775849301247, 0.051688955230744515, 0.18956013546988404, 0.24556092812210817, 0.2208517408931902, 0.12261100439595007, -0.03665620470330457, -0.24015441163260848, -0.46810717547668684, -0.6992501439854993, -0.9124060498228879, -1.0880344530951822, -1.2096505632309096, -1.2650160255550595, -1.2470196552569688, -1.1541868263208315, -0.9907812708575786, -0.7664908019689598, -0.49571711937641993, -0.19651747842528366, 0.11072927981614099, 0.40483974673467993], 'positive_zeros': ['1.29324763946524851849160716601656', '3.36720458660070725424361496679312', '4.90553161478220412891672427014745', '6.19802634034931418836389869134565', '7.14726641791697984368910402827574', '8.612606613157344566155336451451192', '9.490724777722922210731898760875956', '10.18622369971246515459419562954606', '11.13341914292434618718985364344953'], 'prelabel': '2-165-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.144252158394047, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29324763946524851849160716602', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.36720458660070725424361496679', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.90553161478220412891672427015', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 26.46333026914181, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 165, 'conductor_radical': 165, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/165/6/a/c/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': '2-165-1.1-c5-0-16', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-165-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.144252158394047, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29324763946524851849160716602', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1639386146411863098357174796524', 'Lhash_array': ['1639386146411863098357174796524'], 'label': '2-165-1.1-c5-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/165/6/a/c/1/1'}