Formats: - HTML - YAML - JSON - 2026-01-30T07:49:43.451622
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '4970853515714909351402944637137', 'a10': 0, 'a2': 0, 'a3': -3, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7026835377872678, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [11, [1, 1]]], 'bad_primes': [2, 11], 'central_character': '88.1', 'coefficient_field': '1.1.1.1', 'conductor': 88, 'conductor_radical': 22, 'degree': 2, 'euler_factors': [[1], [1, 3, 3], [1, 3, 5], [1, 2, 7], [1, 1], [1, 0, 13], [1, 6, 17], [1, -4, 19], [1, -1, 23], [1, 8, 29], [1, 7, 31], [1, 1, 37], [1, -4, 41], [1, -6, 43], [1, 8, 47], [1, -2, 53], [1, 1, 59], [1, -4, 61], [1, 5, 67], [1, -3, 71], [1, -16, 73], [1, -2, 79], [1, 2, 83], [1, -15, 89], [1, 7, 97], [1, 10, 101], [1, 16, 103], [1, -2, 107], [1, 14, 109], [1, 7, 113]], 'euler_factors_factorization': [[1], [[[1, 3, 3], 1]], [[[1, 3, 5], 1]], [[[1, 2, 7], 1]], [[[1, 1], 1]], [[[1, 0, 13], 1]], [[[1, 6, 17], 1]], [[[1, -4, 19], 1]], [[[1, -1, 23], 1]], [[[1, 8, 29], 1]], [[[1, 7, 31], 1]], [[[1, 1, 37], 1]], [[[1, -4, 41], 1]], [[[1, -6, 43], 1]], [[[1, 8, 47], 1]], [[[1, -2, 53], 1]], [[[1, 1, 59], 1]], [[[1, -4, 61], 1]], [[[1, 5, 67], 1]], [[[1, -3, 71], 1]], [[[1, -16, 73], 1]], [[[1, -2, 79], 1]], [[[1, 2, 83], 1]], [[[1, -15, 89], 1]], [[[1, 7, 97], 1]], [[[1, 10, 101], 1]], [[[1, 16, 103], 1]], [[[1, -2, 107], 1]], [[[1, 14, 109], 1]], [[[1, 7, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 9595662, 'index': 2, 'label': '2-88-1.1-c1-0-2', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/88/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-1.3604957842730674e-120, 0.08634665758929015, 0.177037393011778, 0.27613206211523816, 0.3871783783842185, 0.5130625489726683, 0.655922251888276, 0.8170884592371374, 0.9970280171355987, 1.1952742189839376, 1.4103468423228354, 1.639672241160773, 1.8795185394446714, 2.1249623758281957, 2.36990324858646, 2.6071399102802557, 2.828520637373884, 3.025175528747839, 3.1878342195978053, 3.307226553030852, 3.3745569696821507, 3.3820359374507354, 3.3234440778025434, 3.1946973170334365, 2.9943750752109293, 2.7241689445944957, 2.3892072556345982, 1.9982120738515032, 1.5634500654934465, 1.1004476391172322, 0.6274538341176112, 0.16465123370341028, -0.2668650389354698, -0.6462986210886715, -0.9544901372041892, -1.1752989540494663, -1.2969288693261818, -1.3130879040219867, -1.2238700483722693, -1.0362539479575712, -0.7641310145434665, -0.42780336505514693, -0.05292938871021307, 0.3310604090527808, 0.6930054269705614, 1.0023934423593428, 1.2319089301874944, 1.359948764328271, 1.3728811552057156, 1.2668202888882456, 1.0487069196518484, 0.7365252743228289, 0.35854806988705606, -0.048419097462723534, -0.4417309191073363, -0.7763735713497075, -1.0089625738304828, -1.101938687462403, -1.027580304682743, -0.7714305678866901, -0.33475586795863427, 0.2642880915494113, 0.9910075067660207, 1.7961315797549946, 2.6193212210145616, 3.393999727167213, 4.053124906696049, 4.535393382674872, 4.791281946621755, 4.788301524575888, 4.51487518346049, 3.9823547044918417, 3.2248550822446003, 2.2967996630486325, 1.268310353469781, 0.21882199367629093, -0.7704805342146651, -1.6246373154176028, -2.2824455524901, -2.7026974743408094, -2.8683763904708286, -2.788262255817063, -2.4956751615589137, -2.0444120153020675, -1.5022715005742335, -0.9428737911225559, -0.4367233481720466, -0.042600037130785695, 0.19962886089111315, 0.2738150888807652, 0.18925705528564532, -0.02097935187334796, -0.30504136544806365, -0.6000215131867049, -0.8414947234590014, -0.9736210040922265, -0.9584321152271021, -0.7829581346922043, -0.46307361070675057, -0.043334493226372006, 0.4074069536325166, 0.8042450851440782, 1.0573960510559317, 1.084913293232847, 0.825251824778402, 0.24790959801119206, -0.6394613425158325, -1.7886805051150143, -3.114013552575389, -4.500393127336769, -5.816043071824064, -6.928002748857179, -7.718566971948691, -8.100434557506071, -8.028440869269119, -7.50614087884391, -6.58616773705643, -5.364134203794556, -3.966755185262482, -2.5357174174081405, -1.2094780883070735, -0.10553155170409745, 0.6943239836852294, 1.1535735130613607, 1.2839999749566913, 1.141657996615319, 0.8163939155917501, 0.4164936884662408, 0.050815588882020785, -0.18880873846593058, -0.2421228998637741, -0.08960641571381481, 0.24525931711937665, 0.701030136902202, 1.1898611531833942, 1.6137129481584855, 1.882506699335377, 1.9311420799782981, 1.7324071358917517, 1.3034302275673537, 0.7043648062756227, 0.02929790330026766, -0.6092785383898277, -1.0999266361828752, -1.352365574368835, -1.3146915403764565, -0.9845493885849188, -0.4120183414016315, 0.306669644479724, 1.0438925390553326, 1.661680607269773, 2.0356415151780634, 2.0777177056640665, 1.7537519483760964, 1.092567692215718, 0.18460763481781697, -0.8300925016327536, -1.7829758239888878, -2.5038312710257418, -2.8490801073100904, -2.726704637981194, -2.1134612845397047, -1.0612156690633263, 0.30897604024278363, 1.8243348852562897, 3.2866575060834258, 4.503139922699959, 5.316557044649856, 5.629660111285724, 5.419599059301105, 4.739885461646297, 3.7095913560466514, 2.4917428539847215, 1.264802284407401, 0.19237674623199533, -0.6033979019076785, -1.0600437468771968, -1.1813315283677475, -1.0313021488966232, -0.7171380337143338, -0.36443951147966086, -0.08992537273083338, 0.022926983964927664, -0.05962786243349145, -0.31633874986993465, -0.6780072352698057, -1.0454108746399027, -1.3143738862892098, -1.4026796912041153, -1.2729875437458051, -0.9465690724872892, -0.5044249958787705, -0.07485914478568681, 0.19060940843501595, 0.14858580156942, -0.30374946784560847, -1.201764151292324, -2.4979651172971566, -4.0619227499004795, -5.6964986038184415, -7.168130824243196, -8.246034326150506, -8.743187975254068, -8.551340499955838, -7.663145180799876, -6.176804012179883, -4.281853198786251, -2.228331085855137, -0.28482413491079506, 1.3068740726747947, 2.3720032006263088, 2.8304034912104283, 2.706266457242166, 2.118401427498067, 1.253184182427445, 0.325769682569697, -0.4625538722938963, -0.9622994254818346, -1.1014986755467284, -0.8943114813602263, -0.43126103684520545, 0.14629162427742737, 0.6815073914849412, 1.0393009106686621, 1.137168944685033, 0.9628285480612389, 0.57485934550582, 0.08637760020820597, -0.36438084312941504, -0.6496799527165664, -0.6857260085077546, -0.4559435612789072, -0.018311948314890872, 0.5054291820702361, 0.9567301142124899, 1.177539554612184, 1.0495723994514186, 0.52638208426031, -0.34960126663043156, -1.4497534252974316, -2.5820144522173827, -3.5295107935914016, -4.097051996915654, -4.155405681638993, -3.673347194523064, -2.7298241979884614, -1.5027168137838083, -0.23573827944875853, 0.8100969742082669, 1.4104087901339548, 1.425279788530936, 0.8304930733646044, -0.2749352886354261, -1.6870266748597906, -3.1374282638120827, -4.347918620101395, -5.087289228078524], 'positive_zeros': ['3.92131200412791242288608029353793', '5.26718062023912132586056594916564', '6.61017530637467554226176574175775', '7.57356519540538183281509096087310', '9.401670233685537405973889044671104', '10.89204680724752420498113582025195', '11.36466946676257259431485654443013', '12.38704213422326524860027303075672', '13.16442893918528910310079055859128'], 'prelabel': '2-88-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.8382622130260123, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1435130181846567800, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.92131200412791242288608029354', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.26718062023912132586056594917', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.61017530637467554226176574176', 'prec': 103}}