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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 1, 'A9': 0, 'Lhash': '1267118137239616630', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1354.6620702910225, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [5, [1]], [13, [1, -1]], [29, [1, 1]]], 'bad_primes': [2, 3, 5, 13, 29], 'central_character': '169650.1', 'coefficient_field': '1.1.1.1', 'conductor': 169650, 'conductor_radical': 11310, 'degree': 2, 'euler_factors': [[1, -1], [1], [1], [1, 1, 7], [1, -4, 11], [1, -1], [1, -3, 17], [1, 1, 19], [1, 0, 23], [1, 1], [1, -10, 31], [1, -2, 37], [1, -4, 41], [1, 6, 43], [1, 0, 47], [1, 1, 53], [1, -5, 59], [1, -1, 61], [1, -10, 67], [1, 8, 71], [1, -5, 73], [1, -8, 79], [1, 1, 83], [1, -14, 89], [1, 13, 97]], 'gamma_factors': [[], [0]], 'index': 56, 'label': '2-169650-1.1-c1-0-56', 'leading_term': '5.52064933307', 'load_key': 'Cremona', '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': 'EllipticCurve/Q/169650/dy', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [5.520649333073612, 4.40599677772141, 1.667478607090404, -0.9524376663861155, -1.505179373327627, 0.262954380709908, 2.161264293682417, 1.684533613464653, -0.8917485500754565, -2.533272724615446, -1.244357430657058, 1.178190056479526, 1.594386079881397, -0.009984653732818939, -0.7453218436341783, 0.434388551561135, 1.085010705489309, -0.3361961846350023, -1.462826924085342, -0.05976953302491343, 1.614227701842075, 0.3448913487318703, -2.215601827366863, -2.10251146017198, 0.05814493995596691, 0.4511732440787214, -0.598404424354286, 0.4245080973033365, 2.324494666934284, 0.4536150415193889, -3.651272449000067, -3.3894663567344, 0.7612606851694333, 1.063848612796826, -3.217248467642783, -3.702410050502581, 1.52981632026181, 3.863544329054352, 0.1238718317565137, -1.942277183480744, 0.7216849118601608, 0.8386510040520251, -3.831862499857801, -5.460256516297486, -1.566861838740572, 0.5579091153185765, -1.437840037617025, -1.832484254190865, 0.07827621424049643, -0.4359589947439431, -2.031117919606256, -0.3951775592294463, 1.505543043982057, -0.1932207356702846, -1.554739844128933, 0.2632432518397778, 0.7861760018250084, -1.183131182260125, -0.9580337810000396, 0.5758361766548981, -1.059656549668554, -2.541483063179018, 0.2045688478434202, 1.733080933331752, -1.18121446310145, -1.891307090920479, 0.8833746223124335, 0.1008763087635115, -2.31643850781909, 0.6631897532970213, 3.180689971387732, -1.52524495855334, -3.47843822820408, 4.253299292142117, 9.175304866572075, 3.995274686659102, -0.2133966340042861, 1.10814128348109, -0.2274014813475099, -3.222341462862917, -1.08049559044689, 1.073380712192062, -1.849656213356151, -2.872085430819428, 0.1798898906009241, 0.217955213104322, -1.577450389881779, 0.4105428957588469, 2.018730690137704, -0.05153965541550638, -0.5397752875521578, 0.608000709548715, -0.904933992780232, -1.577811929913744, 0.4260542528901282, -0.9262598854995733, -3.9600573750745, -1.647977899919009, 1.492456303672499, 0.1648491829952774, 0.1401344109880783, 1.7300305699107, -1.159791914197751, -3.053112908229972, 0.6924939236847258, 0.2232395334823428, -4.817462004101273, -1.77307265483254, 4.447652678358922, 0.907517945591937, -3.757683736274422, -0.479629149059473, 0.1547853017593612, -4.110955231558227, -2.497222090538938, 0.7658043926831704, -2.575092525526559, -3.986699552387816, 0.4537314965501036, 1.554261415506984, -0.3489629918833085], 'positive_zeros': ['0.6442434122838454', '1.221711714282925', '1.919955127161359', '2.620076680327035', '3.248504049764479', '3.676963993128287', '4.205534737616093', '4.756638119362646', '5.281641628379971', '5.991905802775225', '6.348157066159785', '6.698977095541945', '7.277256315093645', '7.950163239439730', '8.321950569478621', '8.933205475999166', '9.507037814950760', '9.941326570560678', '10.30688674980187', '11.10979302513560', '11.34854823164315', '11.98547771694963', '12.18706923809562', '12.78473328130168', '13.23152491757729', '13.71989335037788', '14.10591555899700', '14.62278424754249', '14.89570394651311', '15.48564398493628', '15.91354682986945', '16.41434798680640', '16.75807783645154', '17.21517740135252', '17.68756216209810', '18.13532549001211', '18.95517104490704', '19.09121391268185', '19.48389120486576'], 'prelabel': '2-169650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 36.80573420393923, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1267118137239616630, 'z1': {'__RealLiteral__': 0, 'data': '0.6442434122838454', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.221711714282925', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.919955127161359', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1354.6620702910225, 'bad_primes': [2, 3, 5, 13, 29], 'central_character': '1.1', 'conductor': 169650, 'conductor_radical': 11310, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, -1, 1, 0, 0, 4, 0, 1, -1, 0, 1, 3, 0, -1, 0, 0, 4, 0, 0, 0, 1, 0, -1, -1, 0, 10, 1, 0, 3, 0, 0, 2, -1, 0, 0, 4, 0, -6, 4, 0, 0, 0, 0, -6, 0, 0, 1, -1, 0, 0, -1, 0, -1, 5, 0, 1, 10, 0, 1, 0, 0, 10, 3, 0, 0, -8, 0, 5, 2, 0, -1, -4, 0, 8, 0, 0, 4, -1, 0, 0, -6, 0, 4, 14, 0, -1, 0, 0, 0, 0, 0, -13, -6, 0, 0], 'euler11': [1, -4, 11], 'euler13': [1, -1, 0], 'euler17': [1, -3, 17], 'euler19': [1, 1, 19], 'euler2': [1, -1, 0], 'euler23': [1, 0, 23], 'euler29': [1, 1, 0], 'euler3': [1, 0, 0], 'euler31': [1, -10, 31], 'euler37': [1, -2, 37], 'euler41': [1, -4, 41], 'euler43': [1, 6, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 1, 53], 'euler59': [1, -5, 59], 'euler61': [1, -1, 61], 'euler67': [1, -10, 67], 'euler7': [1, 1, 7], 'euler71': [1, 8, 71], 'euler73': [1, -5, 73], 'euler79': [1, -8, 79], 'euler83': [1, 1, 83], 'euler89': [1, -14, 89], 'euler97': [1, 13, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 0, 0], [1, 1, 7], [1, -4, 11], [1, -1, 0], [1, -3, 17], [1, 1, 19], [1, 0, 23], [1, 1, 0], [1, -10, 31], [1, -2, 37], [1, -4, 41], [1, 6, 43], [1, 0, 47], [1, 1, 53], [1, -5, 59], [1, -1, 61], [1, -10, 67], [1, 8, 71], [1, -5, 73], [1, -8, 79], [1, 1, 83], [1, -14, 89], [1, 13, 97]], 'index': 56, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/169650/dy'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, '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': '2-169650-1.1-c1-0-56', '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': '2-169650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 36.80573420393923, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1267118137239616630, 'z1': {'__RealLiteral__': 0, 'data': '0.6442434122838454', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1267118137239616630', 'Lhash_array': ['1267118137239616630'], 'label': '2-169650-1.1-c1-0-56', 'type': 'ECQ', 'url': 'EllipticCurve/Q/169650/dy'}