-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1541285636162432408059868687659', 'a10': -1, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': 1, 'a6': 0, 'a7': -1, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 55.336328600747336, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1, -1]], [7, [1, 1]], [11, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '6930.1', 'coefficient_field': '1.1.1.1', 'conductor': 6930, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, -1], [1, 1], [1, -1], [1, 6, 13], [1, 0, 17], [1, -6, 19], [1, 4, 23], [1, -2, 29], [1, -4, 31], [1, 12, 37], [1, -2, 41], [1, -6, 43], [1, 6, 47], [1, -6, 53], [1, 4, 59], [1, -8, 61], [1, -10, 67], [1, 10, 71], [1, 10, 73], [1, -8, 79], [1, 0, 83], [1, -6, 89], [1, -2, 97], [1, 6, 101], [1, 8, 103], [1, 12, 107], [1, 6, 109], [1, 10, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [1], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, -1], 1]], [[[1, 6, 13], 1]], [[[1, 0, 17], 1]], [[[1, -6, 19], 1]], [[[1, 4, 23], 1]], [[[1, -2, 29], 1]], [[[1, -4, 31], 1]], [[[1, 12, 37], 1]], [[[1, -2, 41], 1]], [[[1, -6, 43], 1]], [[[1, 6, 47], 1]], [[[1, -6, 53], 1]], [[[1, 4, 59], 1]], [[[1, -8, 61], 1]], [[[1, -10, 67], 1]], [[[1, 10, 71], 1]], [[[1, 10, 73], 1]], [[[1, -8, 79], 1]], [[[1, 0, 83], 1]], [[[1, -6, 89], 1]], [[[1, -2, 97], 1]], [[[1, 6, 101], 1]], [[[1, 8, 103], 1]], [[[1, 12, 107], 1]], [[[1, 6, 109], 1]], [[[1, 10, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 68, 'label': '2-6930-1.1-c1-0-68', '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/6930/2/a/k', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-3.986619162379794e-61, 0.14428940238392912, 0.28743079918845565, 0.42824766319899993, 0.5655090075812182, 0.69790842603848, 0.8240501506245702, 0.9424436875727746, 1.0515080396280392, 1.1495859505588923, 1.2349680579311522, 1.305926345514682, 1.3607558647670508, 1.3978233514860372, 1.4156210960520355, 1.4128242260328352, 1.3883494193345132, 1.3414129767595966, 1.2715861395097834, 1.178845537489924, 1.0636166984731925, 0.9268086383781854, 0.7698376921438662, 0.5946389360582485, 0.40366379820027476, 0.19986275471877474, -0.013347635162570322, -0.23213369676022044, -0.4523095011860448, -0.6694170250114186, -0.8788205020843931, -1.0758133389224214, -1.2557354469699678, -1.4140983481483111, -1.5467149527048032, -1.64983050905997, -1.7202509026640238, -1.7554642524562178, -1.7537516354193523, -1.7142827756488566, -1.6371926749685919, -1.5236354443597047, -1.3758120219501628, -1.196969031874508, -0.9913667416500177, -0.7642149011938258, -0.5215761762582289, -0.27023789977627344, -0.017553928526583957, 0.22874052235634307, 0.4607371235134512, 0.670580791421031, 0.8507082730592171, 0.9940922644970347, 1.094483739625317, 1.1466447324934061, 1.1465636137048143, 1.0916449516158142, 0.9808663688998142, 0.8148954022097515, 0.5961602456726667, 0.32886939629128653, 0.01897659922738872, -0.3259109186092501, -0.6966811790395085, -1.0829215223082291, -1.4731744543066836, -1.8552397776700664, -2.216515654536034, -2.5443695339440873, -2.826528375445491, -3.0514763787705994, -3.2088475476025184, -3.2897999251640417, -3.287358280766636, -3.1967124265899183, -3.0154592143588617, -2.7437775971838505, -2.3845279200327063, -1.9432687828032869, -1.428187345202782, -0.8499417389839108, -0.22141723270506017, 0.44259914242348386, 1.1258177578755024, 1.8109086944913446, 2.4800138892297214, 3.115293529939222, 3.6994892779592288, 4.216485622379399, 4.651850018919249, 4.993332493298612, 5.231306122923331, 5.359131255238365, 5.373428452558936, 5.27424792034123, 5.0651265005323864, 4.753027090541075, 4.348159455948357, 3.863685697488716, 3.3153179528145196, 2.720820096113645, 2.0994290773032205, 1.471214955947326, 0.8564014838011297, 0.2746711429694846, -0.2555202523671604, -0.7175940103972461, -1.097439390621356, -1.3839217999242528, -1.569287964072339, -1.649451166299746, -1.6241438842069198, -1.4969300057349775, -1.275074088298005, -0.9692706422601607, -0.593241954499172, -0.16321829557490092, 0.3026807479722011, 0.7851408187550584, 1.2643967921501509, 1.720997395729838, 2.1365603025876037, 2.4944874648921123, 2.7806116044182105, 2.983747152353875, 3.096122461778175, 3.1136746819615606, 3.036194115467233, 2.867310966449255, 2.614323887036625, 2.2878763693574347, 1.9014935313455013, 1.47099792141148, 1.013828347934938, 0.5482901754777805, 0.09276880706372376, -0.3350599769203778, -0.7189886407561232, -1.0449722731716622, -1.3017279786067253, -1.481212388314937, -1.5789555072584458, -1.5942352687768615, -1.5300841167206864, -1.3931263755691154, -1.1932527752148743, -0.9431459258926904, -0.6576774479644829, -0.35320352512835906, -0.04679057416967453, 0.24459373790559874, 0.5048869360359441, 0.7196981770241545, 0.8769986940121746, 0.9677034189767246, 0.9861157027528915, 0.9302131815680857, 0.8017600865230149, 0.6062393339376643, 0.35260620165984347, 0.05287389323846474, -0.2784505871138266, -0.6250544760015136, -0.9695992233701073, -1.2945556534819496, -1.5830545238771432, -1.8197115289689045, -1.991386604166522, -2.0878401601406824, -2.1022535108869094, -2.031587055949522, -1.8767574531202926, -1.6426237161234047, -1.3377814778226598, -0.9741741209282285, -0.5665386264459951, -0.13171236357980715, 0.3121657878244737, 0.7465210084776392, 1.1532321381724637, 1.515501048588234, 1.81865816901175, 2.050863395543635, 2.203666575113752, 2.2723986038444703, 2.2563725927189267, 2.1588841234465788, 1.9870098680254422, 1.7512142569844324, 1.4647839159441625, 1.1431187199317172, 0.8029160492096404, 0.4612907424687771, 0.13487699389595004, -0.16104020207987324, -0.4133176008197715, -0.6116274245580167, -0.7489753802544512, -0.8220341263594338, -0.8312730107171479, -0.7808757460216441, -0.6784491417678583, -0.5345374669726985, -0.36196785825310884, -0.17506181591665623, 0.011244297486576517, 0.18232118651067528, 0.3247593217032528, 0.4272204454257002, 0.4811784734641612, 0.481505705798425, 0.42686812172260225, 0.31990355419206146, 0.16716820992342502, -0.021150282244432335, -0.23174203048575903, -0.44888224891761436, -0.6553011646087914, -0.8331708455807153, -0.9651557053969677, -1.035468605940209, -1.0308727714406727, -0.9415713109620208, -0.7619310123754499, -0.49099502539095674, -0.13274972570730206, 0.30387608168163804, 0.8052870673785281, 1.3537646785883748, 1.928255024747525, 2.505364338526943, 3.0605125188553264, 3.569185228630948, 4.008218054009655, 4.357042796843803, 4.5988263438338315, 4.721436806571098, 4.718179612637127, 4.588257594102409, 4.336923313636821, 3.9753081661925656, 3.5199303369935, 2.991901535213851, 2.4158695687566896, 1.818749305530948, 1.2283074771819653, 0.671676341363023, 0.17387681654666431, -0.24356706511006793, -0.5638438450838891, -0.7758296817084197, -0.8747638429496204, -0.8625811685224409, -0.7478762109497719, -0.5454937610336491, -0.2757611844188523], 'positive_zeros': ['1.21585998214723947752686109049177', '2.25328386941589949833792874144675', '2.90894721432896775965863908181483', '3.85960543735152724934769853802464', '4.94549316134359719566249050259055', '5.50111194514034854736292346912211', '6.38485001647481648603295929389985', '7.03855046615157838557552728009068', '7.55460407730694378021877194786090'], 'prelabel': '2-6930-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.438839197129303, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 189600520810620853, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21585998214723947752686109049', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.25328386941589949833792874145', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.90894721432896775965863908181', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 55.336328600747336, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 6930, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 1, 0, -1, -1, 0, -1, 1, 0, -6, 1, 0, 1, 0, 0, 6, 1, 0, -1, -4, 0, 1, 6, 0, -1, 2, 0, 4, -1, 0, 0, -1, 0, -12, -6, 0, -1, 2, 0, 6, 1, 0, 4, -6, 0, 1, -1, 0, -6, 6, 0, 1, 1, 0, -2, -4, 0, 8, -4, 0, 1, -6, 0, 10, 0, 0, 1, -10, 0, -10, 12, 0, 6, -1, 0, 8, 1, 0, -2, 0, 0, 0, -6, 0, -1, 6, 0, 6, -4, 0, 6, 6, 0, 2, -1, 0, 1], 'euler11': [1, -1, 0], 'euler13': [1, 6, 13], 'euler17': [1, 0, 17], 'euler19': [1, -6, 19], 'euler2': [1, 1, 0], 'euler23': [1, 4, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, 12, 37], 'euler41': [1, -2, 41], 'euler43': [1, -6, 43], 'euler47': [1, 6, 47], 'euler5': [1, -1, 0], 'euler53': [1, -6, 53], 'euler59': [1, 4, 59], 'euler61': [1, -8, 61], 'euler67': [1, -10, 67], 'euler7': [1, 1, 0], 'euler71': [1, 10, 71], 'euler73': [1, 10, 73], 'euler79': [1, -8, 79], 'euler83': [1, 0, 83], 'euler89': [1, -6, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, -1, 0], [1, 1, 0], [1, -1, 0], [1, 6, 13], [1, 0, 17], [1, -6, 19], [1, 4, 23], [1, -2, 29], [1, -4, 31], [1, 12, 37], [1, -2, 41], [1, -6, 43], [1, 6, 47], [1, -6, 53], [1, 4, 59], [1, -8, 61], [1, -10, 67], [1, 10, 71], [1, 10, 73], [1, -8, 79], [1, 0, 83], [1, -6, 89], [1, -2, 97]], 'index': 68, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6930/k', 'ModularForm/GL2/Q/holomorphic/6930/2/a/k/1/1', 'ModularForm/GL2/Q/holomorphic/6930/2/a/k'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-6930-1.1-c1-0-68', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-6930-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.438839197129303, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 189600520810620853, 'z1': {'__RealLiteral__': 0, 'data': '1.21585998214723947752686109049', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 21628259
{'Lhash': '1541285636162432408059868687659', 'Lhash_array': ['1541285636162432408059868687659'], 'label': '2-6930-1.1-c1-0-68', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6930/2/a/k'}
-
id: 24577300
{'Lhash': '1541285636162432408059868687659', 'Lhash_array': ['1541285636162432408059868687659'], 'label': '2-6930-1.1-c1-0-68', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6930/2/a/k/1/1'}
-
id: 42624
{'Lhash': '189600520810620853', 'Lhash_array': ['189600520810620853'], 'label': '2-6930-1.1-c1-0-68', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6930/k'}