Formats: - HTML - YAML - JSON - 2026-08-26T01:37:08.140633
  • lfunc_lfunctions • Show schema
    {'Lhash': '466746950236146113939388391888', 'a10': [0.0, 0.0], 'a2': [0.09662435104963618, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.9906637347842366, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5084440901037562, 0.0], 'a8': [-0.38559529363084427, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.47545968271595, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 37], 'central_character': '8325.1', 'coefficient_field': 'CDF', 'conductor': 8325, 'conductor_radical': 555, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.09662435104963618, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5084440901037562, 0], [7.0, 0]], [[1.0, 0], [2.0290293915424287, 0], [11.0, 0]], [[1.0, 0], [3.212941828425938, 0], [13.0, 0]], [[1.0, 0], [2.7536258185734797, 0], [17.0, 0]], [[1.0, 0], [3.7705139987809924, 0], [19.0, 0]], [[1.0, 0], [0.27140617389299926, 0], [23.0, 0]], [[1.0, 0], [2.049128080251298, 0], [29.0, 0]], [[1.0, 0], [0.07815747179372692, 0], [31.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.508444090103756, 0], [41.0, 0]], [[1.0, 0], [3.013567369612259, 0], [43.0, 0]], [[1.0, 0], [-6.782655210115909, 0], [47.0, 0]], [[1.0, 0], [-3.9475511091534483, 0], [53.0, 0]], [[1.0, 0], [13.436646080344982, 0], [59.0, 0]], [[1.0, 0], [-5.042596761154688, 0], [61.0, 0]], [[1.0, 0], [3.022227046347326, 0], [67.0, 0]], [[1.0, 0], [13.0035545159158, 0], [71.0, 0]], [[1.0, 0], [6.010356861110902, 0], [73.0, 0]], [[1.0, 0], [1.1495441792012666, 0], [79.0, 0]], [[1.0, 0], [-6.9253970441220725, 0], [83.0, 0]], [[1.0, 0], [3.687017660847452, 0], [89.0, 0]], [[1.0, 0], [-3.056626884838484, 0], [97.0, 0]], [[1.0, 0], [-8.431222522991689, 0], [101.0, 0]], [[1.0, 0], [-0.7926680638123682, 0], [103.0, 0]], [[1.0, 0], [-13.50725163714696, 0], [107.0, 0]], [[1.0, 0], [-4.830357132089864, 0], [109.0, 0]], [[1.0, 0], [-16.70124990904288, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-8325-1.1-c1-0-13', 'leading_term': '0.60765633349459842756154031428715', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/8325/2/a/ck/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 17}, 'plot_values': [0.6076563334945985, 0.5976587725962372, 0.5676847802829084, 0.5177963990363934, 0.4481165119559085, 0.3588566104606595, 0.2503528997175696, 0.12310825895932603, -0.022162776512120706, -0.1844890003541091, -0.3626004536552321, -0.5548920737285764, -0.7593955893756045, -0.9737618214457252, -1.1952551422697726, -1.420761415231792, -1.6468102896521735, -1.8696122736308454, -2.0851105521497124, -2.2890470616181524, -2.4770418774735288, -2.6446845222294737, -2.7876353634986746, -2.901734853403837, -2.9831179730601303, -3.028330900884702, -3.0344466349564336, -2.9991760815528488, -2.9209709880451578, -2.7991150611379214, -2.633799681720936, -2.4261808134893106, -2.1784140088793587, -1.8936648438756885, -1.576092659767005, -1.230806147354357, -0.8637900651875192, -0.48180322124773556, -0.09224874582830327, 0.2969813830961707, 0.6776846606780078, 1.0415454056541438, 1.3803464666483458, 1.6861898448595047, 1.9517201527969696, 2.1703443439368573, 2.336440847662437, 2.445551151364796, 2.4945470051960417, 2.4817667959798877, 2.4071152487550744, 2.272121462460486, 2.0799513565577823, 1.8353718750560144, 1.5446657317073735, 1.2154970450115248, 0.8567298566095783, 0.4782031980304014, 0.09046801038577337, -0.2955072313428239, -0.6686539446814284, -1.0181344923685052, -1.3336765263376542, -1.6058996948581625, -1.8266235491333978, -1.9891456363733326, -2.0884793193075675, -2.1215418189167683, -2.087284324184574, -1.9867577205624025, -1.8231095127327503, -1.6015097975869022, -1.3290066072917701, -1.01431350594252, -0.6675348941299918, -0.29983695603466554, 0.07692552608262596, 0.45061426219598444, 0.8092305973531643, 1.141341689608175, 1.436494066656314, 1.6855988413170968, 1.881273406865194, 2.018125584421988, 2.0929679379836803, 2.1049522651802817, 2.05561704621249, 1.9488437994627386, 1.7907217396186388, 1.5893237356547543, 1.3544001822851086, 1.0970008830389206, 0.8290382481431934, 0.5628078929804312, 0.31048495119403025, 0.08361597591731057, -0.10737289861492223, -0.25363088847592813, -0.34828081987434617, -0.38674268819625646, -0.3669670366321934, -0.28956596295993864, -0.15783347960774535, 0.02234864479672, 0.24271871324526492, 0.49295089897653427, 0.7610685412576065, 1.0339399718194915, 1.2978378990447643, 1.5390400483846909, 1.744446276142244, 1.902185878941959, 2.0021884144586015, 2.0366920880285786, 2.0006656541374306, 1.892122790320599, 1.712311931663087, 1.4657694658598603, 1.1602297961400967, 0.8063918586458676, 0.4175479789543474, 0.009087196938603109, -0.4021089000358997, -0.7983544939047438, -1.1619042264930277, -1.4757231485580382, -1.724248755018072, -1.8941112947390304, -1.97477939716091, -1.9591004155760112, -1.8437086901086288, -1.6292800563795478, -1.320617177691431, -0.9265574102953039, -0.45970262504272175, 0.06402163004459119, 0.6259623899723272, 1.2054683405137558, 1.780722525387395, 2.3296441238859336, 2.8308207636391094, 3.264430525786519, 3.6131123050355067, 3.862744578286284, 4.003095899756439, 4.028315476335635, 3.937238796235519, 3.7334912185772637, 3.4253813431263755, 3.0255854737685253, 2.550634133640977, 2.0202209321584497, 1.4563626747317235, 0.8824470189650058, 0.3222098360090502, -0.20131158292206652, -0.6668014602853477, -1.055616961009735, -1.352623116417097, -1.546871086409522, -1.6320864570055909, -1.6069428452994878, -1.475105998932879, -1.2450443763605554, -0.9296133675195385, -0.5454313216902187, -0.11207584596798147, 0.3488620975809815, 0.8148214070885899, 1.2633612193834178, 1.673245444481225, 2.0254681788215785, 2.3041690990970625, 2.497392894843731, 2.597654127868844, 2.6022782817927794, 2.5135007463500503, 2.3383175385438477, 2.088094100316213, 1.777950897375975, 1.4259561385592205, 1.0521661298278968, 0.677562022137513, 0.32293754839804106, 0.007795428137820752, -0.2506897576158355, -0.4385873106829522, -0.5459556761258494, -0.5673765828367586, -0.5022481552314451, -0.3548195455983065, -0.133963197607878, 0.1473051856045893, 0.4725352660219253, 0.8227430216819448, 1.1774569497087828, 1.5158540043591455, 1.8179241701288407, 2.0656001980476484, 2.2437900575022995, 2.34125408198461, 2.3512764370944836, 2.272091056895526, 2.1070350616274505, 1.8644172290875907, 1.5571045816398148, 1.2018457426266833, 0.8183645594353394, 0.42827075873624265, 0.05384533504027978, -0.2832336682748182, -0.5631548406075385, -0.769155704087483, -0.8885559861752155, -0.9135812156144453, -0.8419264744909501, -0.6770235960511722, -0.4279908440533793, -0.10926131857032233, 0.26009591860198766, 0.6573306909057967, 1.057195304782038, 1.433296073936247, 1.7595414530988363, 2.011608723559627, 2.16834862981143, 2.213049242035378, 2.1344865913858757, 1.9277000267898636, 1.5944442702445876, 1.1432870871751055, 0.5893404478945374, -0.04636698532716907, -0.7378483491274458, -1.455401695713692, -2.1670749955143638, -2.8402771191744063, -3.443449734347367, -3.9477104795043227, -4.328378115371251, -4.566295659823148, -4.648877559661139, -4.570821246522151, -4.33444121997703, -3.9496041446043963, -3.4332652266144326, -2.8086281388000565, -2.1039717495547734, -1.3512056824088599, -0.5842321971869252, 0.16279687276516733, 0.8572330561234838, 1.4695979631153766, 1.9750721134904328, 2.3547238418015675, 2.5964106204926547, 2.695303456966152], 'positive_zeros': ['0.36819842167243277329656792302759', '1.79231973104743399111222132964991', '2.72966840509265850681224836076169', '3.55294751730822688386056552553654', '4.47244653567338606830802206974663', '4.82287542875936338614401694784990', '5.67290697906270622449184746454025', '6.32260669617492198692828473794812', '7.24708047136715632469764898729588', '7.79282046624070423252665199127885'], 'prelabel': '2-8325-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.15324841291592, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.36819842167243277329656792303', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.79231973104743399111222132965', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.72966840509265850681224836076', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 66.47545968271595, 'bad_primes': [3, 5, 37], 'central_character': '1.1', 'conductor': 8325, 'conductor_radical': 555, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8325/2/a/ck/1/3'], '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': '2-8325-1.1-c1-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-8325-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.15324841291592, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.36819842167243277329656792303', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '466746950236146113939388391888', 'Lhash_array': ['466746950236146113939388391888'], 'factors': ['2-8325-1.1-c1-0-13'], 'label': '2-8325-1.1-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8325/2/a/ck/1/3'}