-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '171826184190344544077180077611', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-3.180978896799668, 0.6761379370486376], 'a4': [0.0, 0.0], 'a5': [-0.4120375699915872, 2.6015028316374074], 'a6': [0.0, 0.0], 'a7': [-3.924869011569097, 2.5488397384185797], 'a8': [0.0, 0.0], 'a9': [6.920827859040644, -3.0813510889273568], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.56744299561724, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [2.4625783735051487, -2.2216452809448985]]], [13, [[1.0, 0], [0.5847277110043128, -3.557821454764651]]]], 'bad_primes': [2, 11, 13], 'central_character': '572.249', 'coefficient_field': 'CDF', 'conductor': 572, 'conductor_radical': 286, 'conjugate': '3191566753118480794488341346786', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.180978896799668, -0.6761379370486376], [2.7406363729278027, -1.2202099292274007]], [[1.0, 0], [0.4120375699915872, -2.6015028316374074], [-4.755282581475768, -1.545084971874737]], [[1.0, 0], [3.924869011569097, -2.5488397384185797], [2.8471565015306015, -6.394818203498207]], [[1.0, 0], [2.4625783735051487, -2.2216452809448985]], [[1.0, 0], [0.5847277110043128, -3.557821454764651]], [[1.0, 0], [-0.18934528764319003, -1.801500074326918], [-16.628509212474697, 3.5344987439019087]], [[1.0, 0], [-0.15482433890257435, 2.9542243731871776], [-18.895916011997194, -1.986040802085416]], [[1.0, 0], [-1.3623527183084234, 0.7865547086465866], [11.5, -19.91858428704209]], [[1.0, 0], [4.2984627157465365, 3.870353213521658], [3.0313254347619507, 28.841134965679927]], [[1.0, 0], [-7.062306604373624, 1.1185594789339928], [29.48275200514976, -9.57952682562337]], [[1.0, 0], [7.3727399986444055, -0.3863889305602055], [36.797310128626115, -3.8675531409031785]], [[1.0, 0], [1.2812734546378663, 0.8320687104042366], [16.67620236610781, 37.45536376334664]], [[1.0, 0], [-2.4646694380303265, 4.268932690530758], [-21.5, -37.239092362730865]], [[1.0, 0], [0.7337543329381683, -0.37386650630880497], [27.625906857746237, -38.02379873562253]], [[1.0, 0], [0.2949801217606169, 0.21431560337528774], [16.377900701872214, 50.405995363643136]], [[1.0, 0], [-8.309746876289973, -12.795888072966601], [-23.997461941472213, 53.899182000913456]], [[1.0, 0], [8.125588691784992, -0.8540337855334902], [59.66700364476215, -12.682613139883319]], [[1.0, 0], [-2.6516183365140633, -0.7104989919045003], [58.023702053557386, 33.5]], [[1.0, 0], [1.481364674401038, 1.1995854606690812], [14.761730048060913, 69.4484796521002]], [[1.0, 0], [-5.789053812761928, -2.9496702460949584], [42.90832341735054, 59.05824058937116]], [[1.0, 0], [3.4864719667827964, -4.798716981309415], [-24.412342555620846, -75.13346478731714]], [[1.0, 0], [-10.139801395071382, -1.605986768960333], [78.93769085249775, 25.648410533120636]], [[1.0, 0], [-0.1361586530837393, 0.5081510111986599], [-77.07626093681505, -44.5]], [[1.0, 0], [-4.653729328604823, 12.12337938399325], [-72.08504807130724, -64.90566881680925]], [[1.0, 0], [0.9631536665166325, -9.163795008660001], [-98.79290767411437, -20.999080772593693]], [[1.0, 0], [14.628722344852463, -4.753160020564991], [83.32875042061958, -60.54188098612473]], [[1.0, 0], [0.6496982147130146, 3.0565897830132465], [-97.7493639677583, 43.520820809110624]], [[1.0, 0], [-4.293122308706384, -4.293122308706384], [0, 109.0]], [[1.0, 0], [-7.037201928759249, -7.815604531460156], [-11.811716349244842, 112.38097417661488]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-572-143.106-c1-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/572/2/bv/a/249/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.1487938782821697, 0.010514885897504234, -0.10256696679656271, -0.18900228398730756, -0.24419439535852203, -0.2605452124672408, -0.22814180599027686, -0.13584899187866342, 0.027312149208299996, 0.2705969980847899, 0.599876869419868, 1.0160017491214124, 1.513334447076597, 2.0786324820179987, 2.6904671477074538, 3.3193590658096017, 3.9287712115131677, 4.477032589064531, 4.920171174835956, 5.215520609461224, 5.325842995395852, 5.22359538684403, 4.894877845681121, 4.34255421150173, 3.5880484823448766, 2.671400047751485, 1.649311989590756, 0.5911401741912674, -0.42697216306854646, -1.329338471722987, -2.048627266351505, -2.5335049937852987, -2.7550286369208448, -2.710837720482528, -2.4263826011475875, -1.9527492919507958, -1.3610713980399007, -0.7340062444131642, -0.1552273557719806, 0.30172684159732194, 0.5836808289143547, 0.6655491735961372, 0.5542229665518887, 0.28775170140205814, -0.07037648660736263, -0.4412836818448961, -0.7437516817601514, -0.9083307020360223, -0.8902168535056917, -0.6786129314143321, -0.30068502894431504, 0.181007333776555, 0.6776917495826003, 1.089101569370931, 1.3215784128509482, 1.3066000296499247, 1.0164227419675027, 0.4737386402553688, -0.2469586545861515, -1.0273159179564946, -1.7217880527120673, -2.1808088653983138, -2.276859352991296, -1.9289857761868743, -1.1212261392887546, 0.08885585242326961, 1.5738215284286121, 3.152427187769778, 4.616086206712582, 5.761645748124699, 6.424970260217685, 6.509336182361825, 6.003260163676401, 4.984064533105802, 3.6059725972736456, 2.0743867295935345, 0.6106928728060736, -0.5860882583696857, -1.373655978261003, -1.6901948719166728, -1.562845578575743, -1.0990867945384177, -0.462614737971636, 0.1615226442005498, 0.6054904349084637, 0.7529978030029133, 0.5622257321920752, 0.0724969161560934, -0.6067400733138071, -1.3222087257152229, -1.912575402752299, -2.245679989052392, -2.248754152242717, -1.9246133611931333, -1.3499273388700754, -0.6557992725963281, 0.004902913578002981, 0.49570680064581346, 0.7308442609451998, 0.6969674279705346, 0.45628548338922525, 0.12949170273348343, -0.13816253590587013, -0.21984984023321782, -0.04863089600516483, 0.3535080783297508, 0.8676123956421996, 1.2946673295300248, 1.3955175141297984, 0.946032578189456, -0.20457186084929857, -2.0860297565267896, -4.582173800379072, -7.436603967303352, -10.289862998580006, -12.74181528503204, -14.426744429007163, -15.085153686995232, -14.616341599702261, -13.099663322111837, -10.779197480505562, -8.014782035807613, -5.210115399408065, -2.733955291876458, -0.852035120400765, 0.3153046650157968, 0.8010271959383455, 0.7644927981415968, 0.43781770838642275, 0.05995041598408938, -0.1844177133498774, -0.20573855911893343, -0.020647664350947764, 0.26826458739488834, 0.5168355897565097, 0.5941877125581039, 0.43159612028573835, 0.05070780662273723, -0.4375857287386693, -0.8637926509801978, -1.0514077890261893, -0.874382441118846, -0.3031067529293004, 0.5757988452139421, 1.5735252244575173, 2.444990341686548, 2.955184693590706, 2.9478659100540927, 2.3967762765868366, 1.4234370401880247, 0.2742412205421432, -0.7392219015285995, -1.3219978155590062, -1.2780609559275584, -0.5700864230605266, 0.661151985911727, 2.1252027871293984, 3.452648444686615, 4.29058609167327, 4.397762176164349, 3.7133622592968063, 2.37978379657466, 0.7117345760926718, -0.88148235555139, -2.0006132886162638, -2.3603138012041165, -1.8642044533919246, -0.6305795137052812, 1.0384632785809267, 2.7362125088093876, 4.057269007514384, 4.701272013730313, 4.546256937471217, 3.6721995526174025, 2.329513073491225, 0.8628765793088451, -0.3867444011265014, -1.1733123058144368, -1.404311788298703, -1.1511751782392625, -0.6107686149599599, -0.031939617213432685, 0.3686029499395523, 0.47417323497827346, 0.2986570173131829, -0.028956311487212286, -0.31961250839840577, -0.3993283045028406, -0.17822865711286953, 0.31086368830175926, 0.9186655123830533, 1.4298610305983346, 1.641818818420812, 1.4452037308011962, 0.8780087307159221, 0.13189450271846537, -0.4954700959493545, -0.6906324207626113, -0.23068952874583168, 0.9279966958132643, 2.6091934001195414, 4.441538496716142, 5.946327635285765, 6.666113113296053, 6.297845753761702, 4.790834515688579, 2.3784588004663823, -0.46886758661434036, -3.1589082449404247, -5.12981476067595, -5.996437811456372, -5.648818060375072, -4.274564198561641, -2.2991199817533907, -0.262137936192243, 1.3331144553869818, 2.152969038659421, 2.1109924210387025, 1.3695875303687322, 0.26881655929056664, -0.7921325991047474, -1.4817758366900586, -1.6314941207584306, -1.2709561828171374, -0.5963221911706017, 0.11387955679596454, 0.6035940990546688, 0.7276153976275777, 0.4935730467989317, 0.04503150179266897, -0.4053520485691737, -0.6657261235633505, -0.6430066678574491, -0.378550786936372, -0.027033176049509704, 0.21449059918352015, 0.20088054623935026, -0.08018479456990968, -0.4745070497643094, -0.6930149322439392, -0.4036237692868756, 0.6447069275853655, 2.5079789678947977, 4.985554386048947, 7.638363659088305, 9.88884805481422, 11.176788287740289, 11.124575237902944, 9.659451102567736, 7.051491872666405, 3.8515264970040457, 0.7447793616447198, -1.6365786679712089, -2.8848194816297674, -2.9192488832444323, -1.9889210782027633, -0.5763516538382357], 'positive_zeros': ['0.13554695920106750448745292542529', '0.982611716085993855086470454125142', '3.44636695974824593071241086387679', '4.78812817178051855088060397420127', '5.47664260290006389387994477854768', '6.32979239486696183358605088208592', '7.20942320189598865820033075057457', '8.116861634959211416785011210230228', '9.559225557736422540072537688604008', '10.34033043654460899998431939282216'], 'prelabel': '2-572-143.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1371576908635546, 'root_angle': 0.5818843200703161, 'root_number': '-0.25441928194310914 + 0.9670940124804582*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.290942160035', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.13554695920106750448745292543', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.982611716085993855086470454125', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '3.44636695974824593071241086388', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.56744299561724, 'bad_primes': [2, 11, 13], 'central_character': '143.106', 'conductor': 572, 'conductor_radical': 286, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/572/2/bv/a/249/1'], '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': '2-572-143.106-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-572-143.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1371576908635546, 'root_angle': 0.29094216003515805, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.13554695920106750448745292543', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '171826184190344544077180077611', 'Lhash_array': ['171826184190344544077180077611'], 'label': '2-572-143.106-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/572/2/bv/a/249/1'}