Formats: - HTML - YAML - JSON - 2026-10-16T01:54:41.918814
  • lfunc_lfunctions • Show schema
    {'Lhash': '1117899129996966443451282474601', 'a10': [-3.4632070631977605, -1.5440621253203706], 'a2': [-1.406542487658318, 0.14709938957028543], 'a3': [0.8660254037844386, 0.5], 'a4': [1.9567235391760989, -0.4138030826784186], 'a5': [2.3220086409264056, 1.3406123138994974], 'a6': [-1.2916512205994064, -0.5758794355801081], 'a7': [-0.9504902300086696, 1.646297370472844], 'a8': [-2.6913446135880403, 0.8698644554817961], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.090715699489701, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [1.406542487658318, -0.14709938957028543]]], [3, [[1.0, 0], [-0.8660254037844386, -0.5]]], [37, [[1.0, 0], [1.319018106840004, 5.938029238209274]]]], 'bad_primes': [2, 3, 37], 'central_character': '888.877', 'coefficient_field': 'CDF', 'conductor': 888, 'conductor_radical': 222, 'conjugate': '2035610814751039931723663599930', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.406542487658318, -0.14709938957028543]], [[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [-2.3220086409264056, -1.3406123138994974], [2.5, 4.330127018922194]], [[1.0, 0], [0.9504902300086696, -1.646297370472844], [-3.5, -6.06217782649107]], [[1.0, 0], [0, 2.6873401570748574], [-11.0, 0]], [[1.0, 0], [0.5966555426909322, 0.34447923818609194], [6.5, 11.258330249197702]], [[1.0, 0], [-3.3328447773955245, -5.772656488189633], [-8.5, 14.722431864335457]], [[1.0, 0], [-2.711090918801254, -1.5652490717674539], [9.5, 16.454482671904334]], [[1.0, 0], [5.584349223160361, 0], [23.0, 0]], [[1.0, 0], [0, -9.646590870230877], [-29.0, 0]], [[1.0, 0], [-9.33663235511183, 0], [31.0, 0]], [[1.0, 0], [1.319018106840004, 5.938029238209274]], [[1.0, 0], [1.9505815866031144, -3.3785064123049064], [-20.5, -35.50704155516198]], [[1.0, 0], [0, 8.0935433564341], [-43.0, 0]], [[1.0, 0], [6.225654200997701, 0], [47.0, 0]], [[1.0, 0], [-1.1012138379782899, 0.6357861057921066], [26.5, -45.89934640057525]], [[1.0, 0], [-9.298263888503977, 5.368355159023947], [29.5, -51.09549882328188]], [[1.0, 0], [-2.7401869851380902, -1.5820476934993855], [30.5, 52.827549630850754]], [[1.0, 0], [3.41298018511919, 1.9704850286174231], [33.5, 58.023702053557386]], [[1.0, 0], [7.209414108989048, -12.487071529572939], [-35.5, -61.48780366869514]], [[1.0, 0], [10.692474909468093, 0], [73.0, 0]], [[1.0, 0], [1.6177837396897914, -2.8020836328015015], [-39.5, -68.41600689897065]], [[1.0, 0], [-7.473777781184577, 4.314987613830359], [41.5, -71.88010851410841]], [[1.0, 0], [-0.2923715407809201, -0.5064023633197495], [-44.5, 77.07626093681505]], [[1.0, 0], [-3.3320355267630455, 0], [97.0, 0]], [[1.0, 0], [0, -12.461997581231536], [-101.0, 0]], [[1.0, 0], [5.557227935625447, 0], [103.0, 0]], [[1.0, 0], [4.016294193007621, 2.3188085334776805], [53.5, 92.66471820493493]], [[1.0, 0], [-2.0690679173010005, 1.194576919025351], [54.5, -94.39676901250381]], [[1.0, 0], [8.658595651055965, 14.997127589823853], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 24, 'label': '2-888-296.285-c1-0-24', '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/888/2/bh/a/877/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.3672259251331147, 1.2274671228277116, 1.0733345672713177, 0.9012407159909348, 0.7080571199134627, 0.4929848488986616, 0.25898515729369775, 0.013589460511796499, -0.23097553815073502, -0.4583624491681709, -0.6493698024879809, -0.7838588342254319, -0.8432175257435794, -0.813184378295192, -0.6867505467845286, -0.4667748547606966, -0.1678921828004715, 0.1827094042887628, 0.5460091639089051, 0.8736094241512073, 1.1119679424385835, 1.2081995638985243, 1.1169661318909174, 0.8077128033673309, 0.2713056575877441, -0.4749751883436168, -1.3850929923758322, -2.3853657102869232, -3.379469161455235, -4.257269173929416, -4.906839336930756, -5.228440542802696, -5.148752775597096, -4.63335434800561, -3.695419157584373, -2.3988960868819205, -0.8550471932155416, 0.7879013127679744, 2.3612076075733626, 3.696336710264423, 4.647264226749824, 5.11114242719513, 5.044056777463713, 4.469087468669875, 3.474893944260392, 2.204442546789525, 0.835093286674036, -0.4472125811656873, -1.475747346714109, -2.1282778830191145, -2.3455125249593505, -2.139356653269624, -1.5892565141287343, -0.8269668181036731, -0.012194943991509596, 0.6966480346746453, 1.1712896240769362, 1.3366265841841143, 1.183482025391344, 0.7684948813638832, 0.20101900886734594, -0.380486017358676, -0.8378830640496927, -1.062589429140666, -0.9984822319315925, -0.6535322302441787, -0.09752062386806655, 0.5538366354016553, 1.1650133182598046, 1.6113064722258033, 1.8070415143264587, 1.7247503991791562, 1.4006072649769241, 0.9244813145608951, 0.4165806384634789, -0.004011635707194399, -0.2513788165331276, -0.2973353878846542, -0.18187726112156213, -0.006019612922091747, 0.0922664412071988, -0.02600761840593133, -0.4614191948526365, -1.2431013557783737, -2.311120891490838, -3.520086249589723, -4.664904480285267, -5.524104751057208, -5.911377402947509, -5.723194500991699, -4.970427936264494, -3.7849611742672455, -2.397846873186191, -1.0923738367344538, -0.14184546985982427, 0.2537115128977555, 0.016546694427321956, -0.7868314007144498, -1.9574242245464462, -3.2079622833201773, -4.230109034678757, -4.768963873551974, -4.686601522154286, -3.998315377911623, -2.871420451529292, -1.5855515854182505, -0.46317198596150855, 0.21300823910489383, 0.27497184111772327, -0.2828830700692516, -1.29653196572408, -2.468924993455512, -3.442453345384904, -3.88973354186523, -3.599801523170275, -2.5372640180123223, -0.8583188619123876, 1.1216524602737483, 3.0017189721846664, 4.392131173730815, 5.009621390898109, 4.7467119287257304, 3.6969611883601035, 2.129488721728277, 0.4194602876076875, -1.0471051744490592, -1.9690325605021763, -2.201001151032041, -1.7815320925349778, -0.9114982933742491, 0.10966728775893278, 0.971325897256994, 1.4375879736300194, 1.4078052400067234, 0.9353037608048184, 0.20045431237537495, -0.5524186959526174, -1.094310631631817, -1.282567164401329, -1.102164412543962, -0.665144778397066, -0.16918268052944466, 0.1710071914088192, 0.19722720255944795, -0.13742694265346583, -0.750394954966497, -1.4542843697316126, -2.016774225717973, -2.2367516005717087, -2.01207544954712, -1.3766369410861605, -0.4939390474634708, 0.391667979637536, 1.0310901747103292, 1.2496219833825075, 1.003224112301161, 0.39297124051916804, -0.36792694420611016, -1.0244818808495042, -1.3648063283819691, -1.291071930965373, -0.8518677764297767, -0.22354887855285005, 0.3548169130964375, 0.672027220471619, 0.6299833265631994, 0.2927234149664517, -0.12105914417133123, -0.30414983088581643, 0.03240179701988077, 1.0453111819615208, 2.6766773096920358, 4.634680248906214, 6.450544521837968, 7.600939432024799, 7.662754131985045, 6.454085902375918, 4.116114061823682, 1.105850334157658, -1.9045297286526042, -4.1975894561452884, -5.203204347785372, -4.658270295679175, -2.685779139322851, 0.23185110512756915, 3.3793825962946245, 5.999717317437138, 7.494269190516835, 7.575025166074695, 6.325376350457895, 4.1546494522157955, 1.6634517067141248, -0.5366562316140066, -1.9932860234331518, -2.5226764612912773, -2.229137401222705, -1.43487819815176, -0.5491157853931926, 0.0766678450632215, 0.25864540502102806, 0.021573003669900618, -0.437994783571639, -0.8475344893593997, -0.9749249615402323, -0.7213039230234084, -0.15670602402423306, 0.5129716405916971, 1.0331791358935807, 1.2074025549497747, 0.9815197131419305, 0.47253971090264424, -0.07052403655417949, -0.3601017142889102, -0.18327985165706553, 0.508121511933576, 1.5658871147050826, 2.6864179898709883, 3.51182459898102, 3.755709455270458, 3.3080645086054794, 2.2802066052062044, 0.9718090744614947, -0.22966564813425377, -0.9818006767022771, -1.1045496912500903, -0.6392946703699481, 0.17215821320305913, 0.9810402320124493, 1.462930849179356, 1.4378742212573328, 0.9340724377440117, 0.17092155954743915, -0.5322607561149437, -0.8867225821196235, -0.7530170636354664, -0.20048071729985886, 0.5180392201545885, 1.0689910264544231, 1.1801173771582396, 0.7658839647327161, -0.01581504830419452, -0.8036322594715216, -1.1609677627514592, -0.7487356739112193, 0.5213784822717535, 2.4142929453560815, 4.414241225659653, 5.876414961409932, 6.24005973744011, 5.229882917719062, 2.972661307553651, -0.017208457134874382, -2.9845734740732377, -5.166996909306997, -6.036770197014572, -5.468246144152995, -3.771841775830711], 'positive_zeros': ['0.881866919635188500824440219440509', '2.06139047623065891295651798080898', '3.04932188607589122783032572388168', '4.56520164577187403793167473916213', '5.82932440272878926742311997203951', '6.75194001379345078883178049896814', '7.54200697275212600454464397028497', '8.269270857950454484028189448056228', '9.373547117744651824615752790523394', '9.879703272088484412368884714389838'], 'prelabel': '2-888-296.285-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6628397810401023, 'root_angle': -0.22779646756860042, 'root_number': '0.13905681141613174 - 0.9902844052083111*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.227796467569', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.881866919635188500824440219441', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.06139047623065891295651798081', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.04932188607589122783032572388', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 7.090715699489701, 'bad_primes': [2, 3, 37], 'central_character': '296.285', 'conductor': 888, 'conductor_radical': 222, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/888/2/bh/a/877/6'], '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': '2-888-296.285-c1-0-24', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-888-296.285-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6628397810401023, 'root_angle': -0.22779646756860042, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.881866919635188500824440219441', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1117899129996966443451282474601', 'Lhash_array': ['1117899129996966443451282474601'], 'factors': ['2-888-296.285-c1-0-24'], 'label': '2-888-296.285-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/888/2/bh/a/877/6'}