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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -4, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 1, 'Lhash': '1897023473951404908', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-1.7888543819998317, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 788.4109293973144, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [11, [1]], [17, [1, -1]]], 'bad_primes': [2, 3, 11, 17], 'central_character': '98736.1', 'coefficient_field': '1.1.1.1', 'conductor': 98736, 'conductor_radical': 1122, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 4, 5], [1, 2, 7], [1], [1, -6, 13], [1, -1], [1, -4, 19], [1, 6, 23], [1, -4, 29], [1, -6, 31], [1, 4, 37], [1, -10, 41], [1, 4, 43], [1, 4, 47], [1, 2, 53], [1, 12, 59], [1, -4, 61], [1, -12, 67], [1, -6, 71], [1, 2, 73], [1, -10, 79], [1, 12, 83], [1, 2, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 54, 'label': '2-98736-1.1-c1-0-54', 'leading_term': '6.03564752938', '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/98736/ci', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.336048267591434, 1.718447305340557, 0.7343734169753114, -0.8426242286914044, -1.229977015761309, 0.7787886574927876, 4.130868491751242, 5.967343420369706, 4.444641503481819, 0.9567077075040246, -1.256949567042504, -0.8393577259515943, 0.3640318266823406, 0.2823892274477463, -0.3837804095802764, 0.2094925171955158, 1.283575443353856, 0.1069830321996481, -3.004158103172705, -3.547721691289599, 0.9344917936107652, 6.042970164003637, 5.718301012042243, 0.858500132813565, -1.952374676779593, -0.2058988026627435, 1.473917786729254, -0.455606467364003, -2.892867705791104, -2.092455386475799, -0.009764715473882562, 0.04192761503536715, -0.5026217087432145, 0.7208598788806792, 1.302929764590321, -1.336038210405336, -3.602580891844366, -1.433671586943449, 1.428217114847313, -0.6562073679128482, -4.640783794445566, -3.744043989735343, 0.3227114040526701, 0.7283385970296447, -1.863479802994995, -1.485969193483138, 1.15209274251566, 0.8281067325642569, -1.046896839862711, 0.3233111383220437, 2.349604774532304, -0.01227046851892692, -3.190625027670359, -1.433255455187355, 1.632426441136048, 0.4180172842822758, -1.180399758826188, 1.84336361570205, 4.783326342511893, 2.493224197291456, -0.7451405240139881, -0.5370352737472645, 0.0983081070938138, -0.4976632497769773, 0.1364046671625613, -0.6658899316733888, -6.771294153135097, -10.81447616418491, -4.080907409228193, 5.503810473707977, 5.086423309528494, -1.218061454380405, -2.054408111766548, 0.7253020471044158, 0.06982386695155073, -1.426390628145129, -0.1259335895432343, 0.3197322263593861, -1.080295624225699, -0.5832723828775838, 0.08181355988394841, -1.970798609890941, -1.877971240848186, 1.948194495117265, 1.322775333098462, -4.17092046383751, -3.328658227126631, 4.173739880551284, 6.093878082043019, 1.371429132431336, -0.5543375450490771, 0.1305508301722959, -1.459413107903976, -1.579113028370851, 1.394829377717992, 1.029725836741848, -1.688861051138231, 0.213218821361831, 2.474085447176295, -1.543536304311198, -4.649961107924347, -0.7816302290726482, 2.263892908461373, 0.4983463235619908, 0.09464203668843157, 0.7724196699050294, -1.720786381906153, -2.661762265496808, 0.5328369398482913, 0.9137600616314339, -1.66524254983524, -0.7599269331775022, 0.2463017974376094, -2.026007775371373, 0.8915428877775563, 8.98743196866389, 8.515541452697857, 0.3423351715542437, -0.9120698252457347, 3.457194192208949], 'positive_zeros': ['0.8629180104758154', '1.431284686172814', '2.577727093436737', '3.156842818361416', '3.588324257042554', '3.955837399977172', '4.509907908640712', '5.210453698802950', '6.046143880651219', '6.518772267215581', '6.962387094425090', '7.751913148668748', '8.012092909630713', '8.388334581817235', '8.900796340880643', '9.596205282817385', '9.960079976139262', '10.72526145747921', '11.07300848871911', '11.63127489712683', '12.09170433838300', '12.47059651771800', '12.99924987027682', '13.59362827629289', '14.03809288831977', '14.38721534675606', '15.16712007756949', '15.62735885702066', '15.80263482676909', '16.21690103968817', '16.43978158214012', '17.34215885748587', '17.94356851354109', '18.41888248284533', '18.75791559394057', '19.26908646526629', '19.56198666263479'], 'prelabel': '2-98736-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.078656118078626, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1897023473951404908, 'z1': {'__RealLiteral__': 0, 'data': '0.8629180104758154', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.431284686172814', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.577727093436737', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 788.4109293973144, 'bad_primes': [2, 3, 11, 17], 'central_character': '1.1', 'conductor': 98736, 'conductor_radical': 1122, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -4, 0, -2, 0, 1, 0, 0, 0, 6, 0, -4, 0, 1, 0, 4, 0, -2, 0, -6, 0, 11, 0, 1, 0, 4, 0, 6, 0, 0, 0, 8, 0, -4, 0, 6, 0, 10, 0, -4, 0, -4, 0, -4, 0, -3, 0, 1, 0, -2, 0, 0, 0, 4, 0, -12, 0, 4, 0, -2, 0, -24, 0, 12, 0, -6, 0, 6, 0, -2, 0, 11, 0, 0, 0, 10, 0, 1, 0, -12, 0, -4, 0, 4, 0, -2, 0, -12, 0, 6, 0, -16, 0, 6, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, -6, 13], 'euler17': [1, -1, 0], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, -4, 29], 'euler3': [1, -1, 0], 'euler31': [1, -6, 31], 'euler37': [1, 4, 37], 'euler41': [1, -10, 41], 'euler43': [1, 4, 43], 'euler47': [1, 4, 47], 'euler5': [1, 4, 5], 'euler53': [1, 2, 53], 'euler59': [1, 12, 59], 'euler61': [1, -4, 61], 'euler67': [1, -12, 67], 'euler7': [1, 2, 7], 'euler71': [1, -6, 71], 'euler73': [1, 2, 73], 'euler79': [1, -10, 79], 'euler83': [1, 12, 83], 'euler89': [1, 2, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 4, 5], [1, 2, 7], [1, 0, 0], [1, -6, 13], [1, -1, 0], [1, -4, 19], [1, 6, 23], [1, -4, 29], [1, -6, 31], [1, 4, 37], [1, -10, 41], [1, 4, 43], [1, 4, 47], [1, 2, 53], [1, 12, 59], [1, -4, 61], [1, -12, 67], [1, -6, 71], [1, 2, 73], [1, -10, 79], [1, 12, 83], [1, 2, 89], [1, -6, 97]], 'index': 54, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/98736/ci'], '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': '2-98736-1.1-c1-0-54', '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': '2-98736-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.078656118078626, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1897023473951404908, 'z1': {'__RealLiteral__': 0, 'data': '0.8629180104758154', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1897023473951404908', 'Lhash_array': ['1897023473951404908'], 'label': '2-98736-1.1-c1-0-54', 'type': 'ECQ', 'url': 'EllipticCurve/Q/98736/ci'}