Formats: - HTML - YAML - JSON - 2026-08-14T22:53:31.142245
  • lfunc_lfunctions • Show schema
    {'Lhash': '1693941707906220828163736429927', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [28.416615162732697, 0.0], 'a6': [0.0, 0.0], 'a7': [-49.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 161.6668903714845, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [49.0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1008.1', 'coefficient_field': 'CDF', 'conductor': 1008, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-28.416615162732697, 0], [3125.0, 0]], [[1.0, 0], [49.0, 0]], [[1.0, 0], [-424.08307581366347, 0], [161051.0, 0]], [[1.0, 0], [-508.49969097639615, 0], [371293.0, 0]], [[1.0, 0], [-539.9156880919212, 0], [1419857.0, 0]], [[1.0, 0], [2602.998145858377, 0], [2476099.0, 0]], [[1.0, 0], [-261.2510815826134, 0], [6436343.0, 0]], [[1.0, 0], [6879.66151627327, 0], [20511149.0, 0]], [[1.0, 0], [5686.998145858377, 0], [28629151.0, 0]], [[1.0, 0], [-4909.501545118019, 0], [69343957.0, 0]], [[1.0, 0], [-5723.417233209941, 0], [115856201.0, 0]], [[1.0, 0], [-1733.9938195279235, 0], [147008443.0, 0]], [[1.0, 0], [10147.836320561504, 0], [229345007.0, 0]], [[1.0, 0], [-31181.494128551527, 0], [418195493.0, 0]], [[1.0, 0], [38845.49536464594, 0], [714924299.0, 0]], [[1.0, 0], [-13650.984548819808, 0], [844596301.0, 0]], [[1.0, 0], [-30741.505253401265, 0], [1350125107.0, 0]], [[1.0, 0], [45627.90703543102, 0], [1804229351.0, 0]], [[1.0, 0], [-21753.50648949568, 0], [2073071593.0, 0]], [[1.0, 0], [32295.46199009673, 0], [3077056399.0, 0]], [[1.0, 0], [46637.32921301862, 0], [3939040643.0, 0]], [[1.0, 0], [-63757.35172020593, 0], [5584059449.0, 0]], [[1.0, 0], [-115122.49351050433, 0], [8587340257.0, 0]], [[1.0, 0], [136802.6784610357, 0], [10510100501.0, 0]], [[1.0, 0], [-30425.993819527925, 0], [11592740743.0, 0]], [[1.0, 0], [134611.85017508792, 0], [14025517307.0, 0]], [[1.0, 0], [-7722.00247218883, 0], [15386239549.0, 0]], [[1.0, 0], [214596.2074577187, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 61, 'label': '2-1008-1.1-c5-0-61', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1008/6/a/bf/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [-1.7903323250565355e-60, 0.3269557823969183, 0.6473601679851202, 0.9547937598002798, 1.2430990477400983, 1.5065060785120588, 1.7397518227374194, 1.9381911843172155, 2.097897644048655, 2.2157515968017134, 2.2895145343209733, 2.3178873491286214, 2.3005511941538193, 2.2381895321606513, 2.1324902524414218, 1.986127021953727, 1.8027193748586245, 1.5867714271031979, 1.343589527984906, 1.0791796229470159, 0.8001255932367493, 0.5134503482355737, 0.22646196277238387, -0.05341233987958748, -0.3188010744029479, -0.5625685215185742, -0.7779957865780504, -0.9589584713508248, -1.100096330231812, -1.1969701813731504, -1.2462013672634205, -1.2455892192682028, -1.1942022843663802, -1.0924395234219122, -0.942058287828377, -0.7461666191907629, -0.5091782834576501, -0.2367299297308133, 0.06443916735565275, 0.38664319155136134, 0.7214389430603341, 1.0598441614840433, 1.3925799905652503, 1.7103315314382104, 2.004019525063677, 2.2650754622978813, 2.4857118786543846, 2.659179283173171, 2.7800011241300746, 2.8441784286556104, 2.849356280247777, 2.794945119612182, 2.6821909617472084, 2.5141899962520275, 2.295844647918507, 2.033759979418488, 1.736081265888104, 1.4122756021261573, 1.0728624493884222, 0.7291000175772104, 0.39263623438276596, 0.07513469990406246, -0.2121126094624829, -0.4585731076234526, -0.6548484462352517, -0.7930228975169642, -0.8669720568068005, -0.8726194803041759, -0.808130202861311, -0.6740318861398887, -0.4732565867194888, -0.21109874512178078, 0.10491209981318278, 0.46522226746158124, 0.8585437736652964, 1.2722151093542453, 1.6926220243888117, 2.105664671800778, 2.497255163562411, 2.853827802468144, 3.1628430827571936, 3.4132660721143275, 3.596000052937577, 3.7042573367962603, 3.733850967940474, 3.68339356271989, 3.5543927227508942, 3.351236210441919, 3.0810642572554006, 2.753530834379151, 2.3804602793730236, 1.9754101548493177, 1.5531554245950088, 1.1291127792701963, 0.7187270490663968, 0.3368439446222773, -0.0029052627931134656, -0.2886811739436275, -0.510950613505289, -0.6629145662389547, -0.7408292911806273, -0.7442041229571986, -0.6758642408714582, -0.5418721396539172, -0.3513074581821592, -0.11591097108130446, 0.15039534081093806, 0.43209442516068464, 0.7127435645468209, 0.9756997425593618, 1.2048703474509435, 1.3854565397611813, 1.5046559582494257, 1.552292268003676, 1.5213413831294678, 1.4083279727751619, 1.2135709630201064, 0.9412629913473579, 0.5993759073707522, 0.19939214392289864, -0.24413023233884526, -0.7141431060366714, -1.1918214558513305, -1.657374430330961, -2.090919369976086, -2.4733799052706122, -2.7873670895116907, -3.018002227887489, -3.153641716578648, -3.1864677926155376, -3.112914507412193, -2.9339052722870718, -2.654886694530365, -2.285652763922441, -1.8399633379571474, -1.33497084370026, -0.7904786795492178, -0.228063478975989, 0.32989926380712403, 0.8612611122908457, 1.345129535204113, 1.7628498561932788, 2.0988917037180927, 2.3415950303744575, 2.483736773931841, 2.52288733136034, 2.4615358619558942, 2.3069745762721374, 2.0709440735616367, 1.76905387578645, 1.420003957734746, 1.0446436808367994, 0.6649135289261763, 0.3027219101542139, -0.021186381297344025, -0.28831194878972516, -0.4833762062480332, -0.5951382643985205, -0.6170084174129312, -0.5474231540765515, -0.3899584757518657, -0.1531716481982489, 0.14982432429700507, 0.5020349685296867, 0.8834752497524297, 1.2722328548060065, 1.6456495359484806, 1.9815588427224302, 2.2595143700268023, 2.461941914178136, 2.5751517795630576, 2.59015384879332, 2.503227657288106, 2.3162121517403036, 2.0364944476096634, 1.6766929831269934, 1.2540471462368388, 0.7895418211486455, 0.30681045092330195, -0.16912672583513227, -0.6132224063363978, -1.0017863611697395, -1.313817662626927, -1.5322101298401933, -1.644761768711304, -1.6449286256178164, -1.5322766521350515, -1.3126012305161083, -0.997702094302134, -0.6048205171206337, -0.15576477368862404, 0.3242320866778784, 0.807862222578769, 1.2672280141677121, 1.675380484712451, 2.0078250958703188, 2.243909306178313, 2.368011617001798, 2.3704618699148687, 2.2481368206701062, 2.0046927578320615, 1.650417199761101, 1.2017033643597208, 0.680172927753192, 0.11149330028038199, -0.4760459822904935, -1.0531182494466393, -1.591016066945362, -2.0632835955095246, -2.4472296747953703, -2.725232116485281, -2.885754815289324, -2.924015227378034, -2.8422596602072163, -2.64962654943089, -2.361602158348464, -1.9990974955347458, -1.5871982447185229, -1.1536597284503896, -0.7272351142233223, -0.33593616906516166, -0.005331115537250378, 0.24301688065757557, 0.3928743983214325, 0.43434274127846506, 0.3644789004642196, 0.18749096757474878, -0.08550786759171534, -0.4371755933109294, -0.845010068464282, -1.2827475137759243, -1.722006945178861, -2.1340803536428474, -2.491758095506129, -2.7710753610481587, -2.9528690741659815, -3.0240450427142727, -2.9784720874761867, -2.8174422729673076, -2.549662927190487, -2.190775264529034, -1.76242431906341, -1.2909336760465966, -0.8056643144985394, -0.3371580553174122, 0.08481877694499983, 0.43320788754496514, 0.6854439242157089, 0.8249756286823142, 0.8424223021982516, 0.7362865649612279, 0.5131716875545171, 0.1874827989393874, -0.21937590517003905, -0.6802633024175313, -1.1639480485841898, -1.6370393094713924], 'positive_zeros': ['1.33628438909052813276167543332365', '2.21441376989172694708514872591882', '3.58887889145828041099398340385215', '4.20027496028757755077374614581216', '5.62445925909879558583495406493347', '6.17849038766310963069514310134831', '6.99958280704156735019284454359509', '8.051104124478749091926629119294199', '9.019304493183041706347359607186040'], 'prelabel': '2-1008-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.714829545514345, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33628438909052813276167543332', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.21441376989172694708514872592', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.58887889145828041099398340385', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 161.6668903714845, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1008, 'conductor_radical': 42, 'degree': 2, 'index': 61, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1008/6/a/bf/1/2'], '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': '2-1008-1.1-c5-0-61', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-1008-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.714829545514345, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33628438909052813276167543332', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1693941707906220828163736429927', 'Lhash_array': ['1693941707906220828163736429927'], 'factors': ['2-1008-1.1-c5-0-61'], 'label': '2-1008-1.1-c5-0-61', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1008/6/a/bf/1/2'}