-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2422728759653019357257089636012', 'a10': [1.6309863136978342, -1.0897902135516373], 'a2': [0.9238795325112867, 0.3826834323650898], 'a3': [0.0, 0.0], 'a4': [0.7071067811865476, 0.7071067811865476], 'a5': [1.0897902135516373, -1.6309863136978342], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.3826834323650898, 0.9238795325112867], 'a9': [0.9238795325112867, -0.3826834323650898], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9238795325112867, -0.3826834323650898]]], [7, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [0.3826834323650898, -0.9238795325112867]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.1371', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '1732610209907514782599944362720', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9238795325112867, -0.3826834323650898]], [[1.0, 0], [0, 0], [-0.9238795325112867, 0.3826834323650898]], [[1.0, 0], [-1.0897902135516373, 1.6309863136978342], [-0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.9238795325112867, -0.3826834323650898]], [[1.0, 0], [1.0, 1.0], [0, 1.0]], [[1.0, 0], [0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [0.9238795325112867, 0.3826834323650898]], [[1.0, 0], [1.0897902135516373, -1.6309863136978342], [-0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [0, 0], [0.9238795325112867, -0.3826834323650898]], [[1.0, 0], [0.07612046748871325, 0.3826834323650898], [-0.9238795325112867, 0.3826834323650898]], [[1.0, 0], [-0.6173165676349103, -0.9238795325112867], [-0.3826834323650898, 0.9238795325112867]], [[1.0, 0], [0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0.7071067811865476, 0.2928932188134525], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [1.3826834323650898, -0.9238795325112867], [0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.9238795325112867, -0.3826834323650898]], [[1.0, 0], [-0.21677275132473922, 0.32442334882145774], [-0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [0, 0], [-0.9238795325112867, -0.3826834323650898]], [[1.0, 0], [0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [-0.32442334882145774, -0.21677275132473922], [0.3826834323650898, 0.9238795325112867]], [[1.0, 0], [-2.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [0.9238795325112867, -0.6173165676349103], [0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [-1.6309863136978342, -0.32442334882145774], [0.9238795325112867, 0.3826834323650898]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-3332-476.419-c0-0-3', 'leading_term': '2.7323404662863760382755638828654', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3332/1/bn/b/1371/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.732340466286376, 2.778776558053128, 2.851336151123777, 2.947715851558176, 3.0637159286516362, 3.193821165382184, 3.331784248262784, 3.4711048414410994, 3.6053730463059384, 3.7284955398086317, 3.8348406028784447, 3.919336099827952, 3.977544658654347, 4.005730078694588, 4.000921070576415, 3.960973138170864, 3.8846262237163094, 3.7715540277139397, 3.622400191453368, 3.438796462275818, 3.2233583457316897, 2.979654461263337, 2.712146781584317, 2.426100096028275, 2.1274603489724444, 1.822702920750107, 1.5186533914219296, 1.2222848033558273, 0.9404968576416171, 0.6798837789732634, 0.4464986990759873, 0.24562327634493755, 0.08155182953822507, -0.04260053593465783, -0.12505653054428173, -0.1654933610728616, -0.16510990345465862, -0.12663827645573317, -0.05429561685580125, 0.046325904447328, 0.16843027375013772, 0.30424678872375915, 0.44531116737105, 0.5827898928478565, 0.7078365490472949, 0.8119666949728438, 0.8874360693491862, 0.9276057310062675, 0.9272772280502836, 0.8829811280166225, 0.7932032798330622, 0.6585350285691851, 0.48173623825549183, 0.267703327746618, 0.023338479469698466, -0.24267940852535125, -0.5202167747995113, -0.7980904576470773, -1.0645412075922658, -1.3077569332155026, -1.516423461042004, -1.6802779602881688, -1.7906386199090571, -1.8408838207827032, -1.8268550197743365, -1.7471598929089824, -1.6033559415954124, -1.3999996465234368, -1.144552184478008, -0.8471394622078832, -0.5201714674888189, -0.17783334203296652, 0.16453223651153787, 0.491125209269268, 0.7864391083678403, 1.0360269216732136, 1.2272433846308557, 1.349924593830984, 1.396967243048119, 1.3647732771047465, 1.2535312717078324, 1.0673131920168648, 0.8139740595001963, 0.5048520623328381, 0.15427728840212906, -0.22109201404169024, -0.6030765284794971, -0.9728880917166305, -1.3121014005062865, -1.6036343286541435, -1.832683353840371, -1.9875608579357333, -2.060384356596388, -2.047574002863244, -1.9501237893101235, -1.7736233639958274, -1.5280207351860335, -1.22713068713095, -0.8879086753495021, -0.5295244592728646, -0.172282887309798, 0.16354976976168037, 0.45894749733582907, 0.6972833076062329, 0.8653737135770593, 0.9543412913875302, 0.9602357207953458, 0.8843656633495497, 0.7333092523427508, 0.5185890723586364, 0.25601734062584425, -0.035262546467925295, -0.33399208018782317, -0.6182072695617992, -0.8667627750954899, -1.060880561743461, -1.1856271181357139, -1.2312228882806764, -1.194093030496769, -1.0775799124087257, -0.8922544664543179, -0.6557849097956308, -0.3923462935456575, -0.1315815328578564, 0.09284757725572533, 0.2450540104142485, 0.28897432698235753, 0.1905633274870567, -0.0799889146517874, -0.5461483770213168, -1.2231671920853078, -2.1165747353671684, -3.2211359395205363, -4.520360019402761, -5.9866137612036425, -7.581860056966649, -9.259006329286374, -10.963810999148802, -12.637261423529813, -14.218305964390366, -15.646798078120225, -16.866493265174213, -17.827931702988653, -18.491041190084797, -18.82730685456185, -18.8213755013743, -18.471992447123828, -17.792205603422133, -16.808813317348854, -15.56107658912769, -14.098760071477535, -12.479606967645955, -10.766387964610972, -9.023691340290611, -7.314638501979098, -5.69771517271019, -4.223902659412662, -2.934276276209262, -1.8582099790090618, -1.0122892289108476, -0.399990300175658, -0.012136429309401888, 0.17190757410149937, 0.18238718901175982, 0.05678270157701435, -0.16293426766529476, -0.4332300731482257, -0.7119312110921163, -0.9609483484905674, -1.148625980088404, -1.2515681141180823, -1.255827166399131, -1.1573877140692541, -0.9619259105867918, -0.6838758166138315, -0.3448821497084232, 0.028238394021187857, 0.4058710787578958, 0.7581332427980655, 1.0573713791004733, 1.2804394502601977, 1.4105896166441634, 1.4388357686741826, 1.3646897306783503, 1.1962169383181183, 0.9494094021501291, 0.64692513679075, 0.3162911694260449, -0.012291837130680178, -0.3083745064051221, -0.5437260749098496, -0.6946526744541597, -0.7439852615314942, -0.682579854366355, -0.5102088673119698, -0.23576801353152713, 0.12322488421415288, 0.5418086564202221, 0.9893522222853223, 1.431793232629108, 1.834175342195702, 2.1632928287485074, 2.39024102477201, 2.492676188620171, 2.4566087991357133, 2.2775884164600178, 1.9611837284164673, 1.5227147996735124, 0.9862517998712662, 0.38295119033108127, -0.2511479364156831, -0.8777020464166234, -1.4588204759344152, -1.9597914036892985, -2.351567352326835, -2.6128188697682333, -2.731398038797623, -2.7050992127259037, -2.5416593622543417, -2.2580003442811596, -1.8787755150800123, -1.4343385782968077, -0.9582988640215131, -0.4848605422725104, -0.046160750627726246, 0.3301783189089981, 0.6230858534089548, 0.8195037067303895, 0.9151564381195579, 0.9145714807241667, 0.8303535560185624, 0.6817802715879949, 0.4928434900740537, 0.2899086310174465, 0.09919742542573429, -0.05568422766301218, -0.15595436429392426, -0.18940167880425537, -0.15151246140647887, -0.04587255842828107, 0.11619767316685384, 0.316749600025357, 0.5329611686223817, 0.7393879700797182, 0.910510500792337, 1.0233466667490023, 1.0598873822993553, 1.009123113494829, 0.868460072428623, 0.6443743310865715, 0.35221656480199615, 0.015154238117325346, -0.3376843909500623, -0.6737257263025658, -0.9599224928069318, -1.1659295631180158, -1.2672036511439797], 'positive_zeros': ['1.91119600244485999334217766605916', '2.25995878626728419718030403788249', '3.16936810715799331158382917919683', '4.19042157806563526349719489177428', '4.94626846915300455026515513030260', '5.88875164885539569733987236704693', '6.49697655073959609450608583920591', '7.23962112203092582071172051827213', '7.48630868532192889407489944523917', '9.436159429142385511348501309755909'], 'prelabel': '2-3332-476.419-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': 0.07137058215724044, 'root_number': '0.97496843457065373237104635820461 + 0.22234331919544803822966687045697*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.03568529107862022', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91119600244485999334217766606', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.25995878626728419718030403788', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.16936810715799331158382917920', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '476.419', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/bn/b/1371/1'], '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': '2-3332-476.419-c0-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3332-476.419-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': 0.03568529107862022, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91119600244485999334217766606', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2422728759653019357257089636012', 'Lhash_array': ['2422728759653019357257089636012'], 'label': '2-3332-476.419-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/bn/b/1371/1'}