-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '127694243011501020027124719607', 'a10': [0, 0], 'a2': [0, -1.4142135623730951], 'a3': [-2.4655591216568045, 1.7090986564897086], 'a4': [-2.0, 0], 'a5': [0, 0], 'a6': [2.4170304994413816, 3.486827148679749], 'a7': [-2.6457513110645907, 0], 'a8': [0, 2.8284271247461903], 'a9': [3.1579635647701463, -8.427767564639181], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.61042775783118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.4142135623730951]]], [3, [[1.0, 0], [2.4655591216568045, -1.7090986564897086]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.6457513110645907, 0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.701', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '1556913994116403742158907708628', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.4142135623730951]], [[1.0, 0], [2.4655591216568045, -1.7090986564897086]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.6457513110645907, 0]], [[1.0, 0], [0, 2.6662050339081715], [-121.0, 0]], [[1.0, 0], [-5.562417554522112, 0], [169.0, 0]], [[1.0, 0], [0, -18.552518066678353], [-289.0, 0]], [[1.0, 0], [0.6349991467756898, 0], [361.0, 0]], [[1.0, 0], [0, 15.614351516319736], [-529.0, 0]], [[1.0, 0], [0, 43.351738358247914], [-841.0, 0]], [[1.0, 0], [-13.541144403717938, 0], [961.0, 0]], [[1.0, 0], [35.001397795397565, 0], [1369.0, 0]], [[1.0, 0], [0, 15.611550283146691], [-1681.0, 0]], [[1.0, 0], [-64.46987639522592, 0], [1849.0, 0]], [[1.0, 0], [0, -52.55763825683677], [-2209.0, 0]], [[1.0, 0], [0, -51.60562596250986], [-2809.0, 0]], [[1.0, 0], [0, -32.93835384228581], [-3481.0, 0]], [[1.0, 0], [104.19739681514383, 0], [3721.0, 0]], [[1.0, 0], [113.58817859718648, 0], [4489.0, 0]], [[1.0, 0], [0, -36.874624483029], [-5041.0, 0]], [[1.0, 0], [144.9262289851437, 0], [5329.0, 0]], [[1.0, 0], [57.94870677368941, 0], [6241.0, 0]], [[1.0, 0], [0, -45.093552397935575], [-6889.0, 0]], [[1.0, 0], [0, 80.97331401497803], [-7921.0, 0]], [[1.0, 0], [96.22552099654342, 0], [9409.0, 0]], [[1.0, 0], [0, -91.96956709636278], [-10201.0, 0]], [[1.0, 0], [-30.604290567567922, 0], [10609.0, 0]], [[1.0, 0], [0, -190.64494377512221], [-11449.0, 0]], [[1.0, 0], [73.99648215696054, 0], [11881.0, 0]], [[1.0, 0], [0, -128.8613913859324], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-1050-3.2-c2-0-5', 'leading_term': '0.25672899659709651939168341331945196954277542011571594', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1050/3/e/e/701/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.2567289965970965, 0.10903496639638402, -0.043061725606749174, -0.19789298092982868, -0.3537112744833235, -0.5086750225125194, -0.6608366160450752, -0.8081346324038516, -0.9483915815845722, -1.0793183325905396, -1.198526110125918, -1.3035466673354024, -1.3918609372861246, -1.460936154449313, -1.5082711253032715, -1.531449020272677, -1.5281967621867079, -1.4964498032930724, -1.4344208176055178, -1.3406705924580529, -1.214179187825115, -1.0544152503382913, -0.861401227848415, -0.6357721372257836, -0.3788255003923914, -0.09256008858024474, 0.22029879102141756, 0.5562895635253055, 0.9112220604275939, 1.2802041249222558, 1.6576882704901206, 2.0375390376860554, 2.4131211503483403, 2.777407972498355, 3.1231091244459828, 3.4428154475153754, 3.729158830514299, 3.9749837490385413, 4.173526744126204, 4.318599503922287, 4.4047707354364185, 4.4275416471410916, 4.383509629495291, 4.270514639403984, 4.087762882551251, 3.835922656437342, 3.5171876734487904, 3.13530382796186, 2.6955561982226817, 2.204714069405537, 1.6709329084563322, 1.1036134866154208, 0.5132196977167859, -0.08894198068916816, -0.6909770358195964, -1.280685776986016, -1.8458675462159801, -2.3746382217473605, -2.855752048989379, -3.278918174872134, -3.6351018899304663, -3.9168005311137164, -4.118284290757976, -4.235792825772222, -4.267679565693382, -4.214496965179851, -4.079017608088868, -3.866188004955135, -3.583014078602792, -3.2383796368579096, -2.8428015097005033, -2.408127395625342, -1.9471847283661181, -1.4733909486388932, -1.000337356206223, -0.5413601410328895, -0.10911317374870169, 0.28484238663365274, 0.6304166809073867, 0.9193235925252289, 1.1453539278167106, 1.304577999093728, 1.395468574471206, 1.4189379050034538, 1.378285645775599, 1.279057843932083, 1.1288206480184766, 0.9368558623123167, 0.7137887831790969, 0.47116176718728536, 0.22096955336843974, -0.02482563305862228, -0.25477984069305104, -0.45843409679894326, -0.6267423945246312, -0.7524424010558673, -0.830352259175901, -0.8575795725072449, -0.8336320803545861, -0.7604235203536676, -0.642172593323507, -0.4851976058344219, -0.2976140735984161, -0.08894711303599745, 0.13032538287363227, 0.3492791998913981, 0.557077483811777, 0.743507350649191, 0.899494290395503, 1.0175695262853697, 1.0922669566443464, 1.1204289184721499, 1.1014036949943997, 1.0371223134615417, 0.9320475638837739, 0.7929940891734648, 0.6288245915783488, 0.45003338366391993, 0.2682343864606856, 0.09557594629691049, -0.05589077509429533, -0.17485983524701595, -0.2514030624841432, -0.27755480099050955, -0.2478176841601368, -0.1595610114103277, -0.013287557975927254, 0.18724973115778903, 0.4350929438911233, 0.7202904539214591, 1.0302702349247834, 1.350362972663217, 1.6644547133354632, 1.955741475886903, 2.2075520284076933, 2.404200242239583, 2.531825393010281, 2.5791777016223945, 2.538307436530064, 2.4051190669149993, 2.179757192948376, 1.8667981042492523, 1.475229547116432, 1.018211237431038, 0.5126193830302053, -0.02161053794447447, -0.5623178069878186, -1.0860925288208825, -1.5693505013519107, -1.98945708470037, -2.3258459639413678, -2.561076992104135, -2.681778367927551, -2.679422296652614, -2.5508899067894686, -2.2987903108788585, -1.931509924560446, -1.4629809921953518, -0.9121721025485833, -0.3023176335022481, 0.3400831823925998, 0.9864542574212098, 1.6074636020138475, 2.1744147717795115, 2.6606409636417747, 3.0428318734986233, 3.3022249399492662, 3.4255976981930023, 3.4060064982819145, 3.2432284580561235, 2.943877703355184, 2.5211830230100647, 1.9944312378315832, 1.3880979720455173, 0.7307042045586924, 0.053452058281618926, -0.6112940895637496, -1.2316056648153617, -1.7775859664090103, -2.2228816349042493, -2.546029814067578, -2.7315685271348444, -2.770849047881298, -2.6625038213422956, -2.412541058185217, -2.034056596163993, -1.5465739700582928, -0.9750437620995556, -0.348552107216195, 0.3011953625839005, 0.9415347889791463, 1.5405623064568241, 2.0688167404708455, 2.5008351578190755, 2.8164955797632203, 3.002071963866172, 3.050941697187162, 2.9639045468924574, 2.749093290562891, 2.4214789358626176, 2.001996271305772, 1.516337165947968, 0.9934782955274191, 0.4640256697794654, -0.04153049219250232, -0.49455106319729253, -0.8698737533541757, -1.1472350856388414, -1.3124054506042115, -1.3579701356982772, -1.2837093897292968, -1.0965537433169072, -0.8101156403491085, -0.443823499053762, -0.02170813018751456, 0.4290874417404755, 0.8799865807645175, 1.3027458393159357, 1.6712035503307512, 1.9629039584050427, 2.1604972041680526, 2.252828155605936, 2.2356451925932115, 2.111882575043746, 1.891495653165536, 1.5908553907112055, 1.231735826563132, 0.8399535301032538, 0.44374022336471325, 0.07194713741938885, -0.24780880037426226, -0.49094198577775733, -0.637525596566126, -0.6736459457945793, -0.5923959605803301, -0.3944414589376947, -0.08811974630667696, 0.31094124327792805, 0.7806652360696792, 1.2937842685117658, 1.8194361769161924, 2.325007244688147, 2.778107909521165, 3.1485598759178735, 3.4102709737975814, 3.542879876330889, 3.5330660721035674, 3.375440527970315, 3.0729580865405555, 2.63682224996441, 2.0858847650199017, 1.4455743351216637, 0.7464187979236631, 0.022251273178497618, -0.6917886216812832, -1.3613337582303433, -1.9548182362010496], 'positive_zeros': ['0.10073299613356455525567657452258', '1.48267898968041601208883453583996', '3.09684167004689861298138966688634', '4.46873094901449364921569297728551', '5.32598333496649503715631540948218', '6.05910256735177285979191281415956', '7.00836489322940191149667930696849', '7.38722736374602377748253114056307', '8.493753896389366252124908626851460', '9.344194301402840365068768641066229'], 'prelabel': '2-1050-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': -0.6929404292770903, 'root_number': '-0.56969955216323619430734342204534370676149292216863213 - 0.82185304055226815376517730925841633920914494771043140*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3464702146385452', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.10073299613356455525567657452', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.48267898968041601208883453584', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.09684167004689861298138966689', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 28.61042775783118, 'bad_primes': [2, 3, 5, 7], 'central_character': '3.2', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/3/e/e/701/9'], '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': '2-1050-3.2-c2-0-5', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1050-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': -0.34647021463854516, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.10073299613356455525567657452', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '127694243011501020027124719607', 'Lhash_array': ['127694243011501020027124719607'], 'label': '2-1050-3.2-c2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/3/e/e/701/9'}