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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -3, 'Lhash': '1961458173262380813', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'algebraic': True, 'analytic_conductor': 1871.8211840220472, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]], [13, [1, -1]], [23, [1, 1]]], 'bad_primes': [2, 7, 13, 23], 'central_character': '234416.1', 'coefficient_field': '1.1.1.1', 'conductor': 234416, 'conductor_radical': 4186, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1, 0, 5], [1], [1, 4, 11], [1, -1], [1, 6, 17], [1, 6, 19], [1, 1], [1, -10, 29], [1, 2, 31], [1, -10, 37], [1, 8, 41], [1, 12, 43], [1, -10, 47], [1, -2, 53], [1, 8, 59], [1, 8, 61], [1, 4, 67], [1, -8, 71], [1, 16, 73], [1, -8, 79], [1, -6, 83], [1, 2, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 19, 'label': '2-234416-1.1-c1-0-19', 'leading_term': '4.04240315117', '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': 1, 'origin': 'EllipticCurve/Q/234416/y', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.7510075996993303, 0.1476845465280331, -2.085544482232094, -4.415160505499675, -4.515434283516192, -1.888559079902976, 0.996245743612057, 1.342780320289452, -0.3654383357387552, -1.045923236683013, 0.2895468610238694, 0.7852376040857442, -1.617571298338938, -4.080706971396195, -2.701547642218295, 1.034948520950179, 2.157490925212856, 0.2051832756297734, -0.1746299953119823, 2.414806871464857, 3.47258956173419, 0.8461775830925937, -1.099443441870899, 0.4721673265936129, 1.658127182628054, -0.1786183423659364, -0.6566846347450438, 2.951490701015767, 5.141536117776804, 1.738709468780653, -2.11442516995566, -1.410058236313974, 0.2126045142910234, -0.7086475283577358, -0.4091568895555562, 2.522624926603973, 2.281499036384778, -2.112610580363459, -3.108395557855072, 0.9954029724707482, 2.679905779872308, 0.1726452261219889, -0.4398580335789644, 0.7500540684416672, -1.359983194651481, -3.897025668950449, -1.679874971736217, 0.5183480228739722, -2.096972985637131, -3.274965525010828, 0.9345740037734135, 3.319815178220158, 0.823168334178718, -0.331532587320994, -0.06619770522078967, -3.556598376163053, -6.447682580909106, -2.76233741878908, 1.133079451606002, -0.4314204225553738, -1.394472716987874, 0.4883798685868746, -0.9652412976482644, -3.68188800913385, -0.957486012076679, 2.079872223639951, -0.5218892098926403, -2.012106161671497, 0.9647327194332814, 1.03819637870312, -1.652541758539594, -0.5749134046667512, 0.4622030867711831, -2.48110417599086, -1.839400792076256, 3.467786285303711, 3.715635907377232, 0.04422835224013852, 0.7097207820612734, 2.01117098375677, -0.07662935280422735, 0.7966297324662365, 3.601996106121845, 0.5056724887635305, -3.43609621686822, -1.31664479902072, 0.4189321224060383, 0.01301122520125514, 4.575875556039855, 9.018694040849676, 4.928030447597344, -0.1129641276672183, 0.1286119300642167, -0.04046204014250335, 0.2184019386315078, 3.927064960370135, 2.585012473651639, -4.514726789949836, -4.947385642780748, 0.03677134443153604, 0.3227330092775809, -0.1633115278940477, 2.106789440266282, 0.4991004582227236, -2.088814991672508, 0.5109766123847208, 1.245703940975544, -1.388995129608683, 1.036880221654961, 3.300380169216671, -1.842418327615463, -4.330226334009601, -0.1972533703280555, 0.8487481987300188, -0.2944191405546832, 0.8420646863409899, -0.7088712385044619, -1.405345342614629, 5.096966979792096, 7.969552133447369], 'positive_zeros': ['0.5230780119192186', '1.646969011448375', '2.199302653148780', '2.705030041083820', '3.112981223989513', '3.926142364507142', '4.527619318241575', '4.775778049551362', '5.568920129667845', '5.949528423316029', '6.480188204610440', '6.815821602580326', '7.588970231844389', '8.177935150526146', '8.363757701026971', '8.791641345323358', '9.385359583862075', '9.944268857081947', '10.51819059889277', '10.82510688925310', '11.14324221814391', '11.87902858838293', '12.09017452748538', '12.70311568609746', '13.33734180317843', '13.61003145110550', '13.73524123132977', '14.63691120541452', '14.96023677960717', '15.42424088446508', '15.67148578683032', '16.30186029560291', '16.71553130419602', '17.17444177230452', '17.58722110935539', '18.05897149194749', '18.30682324927440', '18.83930903387776', '19.50538330918469', '19.66989980630218'], 'prelabel': '2-234416-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.26454881334194, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1961458173262380813, 'z1': {'__RealLiteral__': 0, 'data': '0.5230780119192186', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.646969011448375', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.199302653148780', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1871.8211840220472, 'bad_primes': [2, 7, 13, 23], 'central_character': '1.1', 'conductor': 234416, 'conductor_radical': 4186, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -3, 0, -4, 0, 1, 0, 0, 0, -6, 0, -6, 0, 0, 0, -1, 0, -5, 0, 0, 0, 10, 0, -2, 0, 0, 0, 0, 0, 10, 0, 0, 0, -8, 0, -12, 0, 0, 0, 10, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, -4, 0, 0, 0, 8, 0, -16, 0, 0, 0, 0, 0, 8, 0, 9, 0, 6, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -10, 0, 12, 0], 'euler11': [1, 4, 11], 'euler13': [1, -1, 0], 'euler17': [1, 6, 17], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, -10, 29], 'euler3': [1, 0, 3], 'euler31': [1, 2, 31], 'euler37': [1, -10, 37], 'euler41': [1, 8, 41], 'euler43': [1, 12, 43], 'euler47': [1, -10, 47], 'euler5': [1, 0, 5], 'euler53': [1, -2, 53], 'euler59': [1, 8, 59], 'euler61': [1, 8, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 0], 'euler71': [1, -8, 71], 'euler73': [1, 16, 73], 'euler79': [1, -8, 79], 'euler83': [1, -6, 83], 'euler89': [1, 2, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, 0, 5], [1, 0, 0], [1, 4, 11], [1, -1, 0], [1, 6, 17], [1, 6, 19], [1, 1, 0], [1, -10, 29], [1, 2, 31], [1, -10, 37], [1, 8, 41], [1, 12, 43], [1, -10, 47], [1, -2, 53], [1, 8, 59], [1, 8, 61], [1, 4, 67], [1, -8, 71], [1, 16, 73], [1, -8, 79], [1, -6, 83], [1, 2, 89], [1, 10, 97]], 'index': 19, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/234416/y'], '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': '2-234416-1.1-c1-0-19', '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': '2-234416-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.26454881334194, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1961458173262380813, 'z1': {'__RealLiteral__': 0, 'data': '0.5230780119192186', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1961458173262380813', 'Lhash_array': ['1961458173262380813'], 'label': '2-234416-1.1-c1-0-19', 'type': 'ECQ', 'url': 'EllipticCurve/Q/234416/y'}