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lfunc_lfunctions • Show schema
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{'Lhash': '1836301687597751859796976029136', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -5, 'a6': 0, 'a7': -14, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.481375204133265, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 5]]], 'bad_primes': [2, 3, 5], 'central_character': '720.1', 'coefficient_field': '1.1.1.1', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1, 5], [1, 14, 343], [1, 6, 1331], [1, -68, 2197], [1, -78, 4913], [1, 44, 6859], [1, 120, 12167], [1, -126, 24389], [1, -244, 29791], [1, 304, 50653], [1, 480, 68921], [1, 104, 79507], [1, 600, 103823], [1, 258, 148877], [1, 534, 205379], [1, -362, 226981], [1, -268, 300763], [1, -972, 357911], [1, -470, 389017], [1, 1244, 493039], [1, 396, 571787], [1, 972, 704969], [1, 46, 912673], [1, 1506, 1030301], [1, -1474, 1092727], [1, 924, 1225043], [1, -698, 1295029], [1, 222, 1442897]], 'euler_factors_factorization': [[1], [1], [[[1, 5], 1]], [[[1, 14, 343], 1]], [[[1, 6, 1331], 1]], [[[1, -68, 2197], 1]], [[[1, -78, 4913], 1]], [[[1, 44, 6859], 1]], [[[1, 120, 12167], 1]], [[[1, -126, 24389], 1]], [[[1, -244, 29791], 1]], [[[1, 304, 50653], 1]], [[[1, 480, 68921], 1]], [[[1, 104, 79507], 1]], [[[1, 600, 103823], 1]], [[[1, 258, 148877], 1]], [[[1, 534, 205379], 1]], [[[1, -362, 226981], 1]], [[[1, -268, 300763], 1]], [[[1, -972, 357911], 1]], [[[1, -470, 389017], 1]], [[[1, 1244, 493039], 1]], [[[1, 396, 571787], 1]], [[[1, 972, 704969], 1]], [[[1, 46, 912673], 1]], [[[1, 1506, 1030301], 1]], [[[1, -1474, 1092727], 1]], [[[1, 924, 1225043], 1]], [[[1, -698, 1295029], 1]], [[[1, 222, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-720-1.1-c3-0-17', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/720/4/a/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-1.161953633913135e-60, 0.20299369298124678, 0.40345163121046446, 0.598849719687219, 0.786687846257206, 0.9645034966368645, 1.1298872218264708, 1.2805004195519851, 1.4140957656982585, 1.528540483926412, 1.6218424772714528, 1.692179170408127, 1.7379287315871068, 1.7577031651283692, 1.7503825948140994, 1.715149901278003, 1.6515247379105915, 1.5593958348391845, 1.4390504136779676, 1.29119948094754, 1.116997748744187, 0.918056950182154, 0.6964513764202271, 0.45471456300266927, 0.1958261961771031, -0.07681150583192452, -0.3594084576653496, -0.6478326782406288, -0.9376675361447669, -1.2242799165362803, -1.5028986172455356, -1.7687019301443612, -2.0169130097990036, -2.2429012852832417, -2.442287843969391, -2.6110524198229594, -2.745639365098995, -2.8430597851119996, -2.9009868820993128, -2.9178414962974566, -2.8928648589407824, 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{'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 1085657990168060965, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.44858661153723415934145873834', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.10608834109513979569047647138', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.78791583437946911555016635701', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.481375204133265, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -5, 0, -14, 0, 0, 0, -6, 0, 68, 0, 0, 0, 78, 0, -44, 0, 0, 0, -120, 0, 25, 0, 0, 0, 126, 0, 244, 0, 0, 0, 70, 0, -304, 0, 0, 0, -480, 0, -104, 0, 0, 0, -600, 0, -147, 0, 0, 0, -258, 0, 30, 0, 0, 0, -534, 0, 362, 0, 0, 0, -340, 0, 268, 0, 0, 0, 972, 0, 470, 0, 0, 0, 84, 0, -1244, 0, 0, 0, -396, 0, -390, 0, 0, 0, -972, 0, -952, 0, 0, 0, 220, 0, -46, 0, 0, 0], 'euler11': [1, 6, 1331], 'euler13': [1, -68, 2197], 'euler17': [1, -78, 4913], 'euler19': [1, 44, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 120, 12167], 'euler29': [1, -126, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -244, 29791], 'euler37': [1, 304, 50653], 'euler41': [1, 480, 68921], 'euler43': [1, 104, 79507], 'euler47': [1, 600, 103823], 'euler5': [1, 5, 0], 'euler53': [1, 258, 148877], 'euler59': [1, 534, 205379], 'euler61': [1, -362, 226981], 'euler67': [1, -268, 300763], 'euler7': [1, 14, 343], 'euler71': [1, -972, 357911], 'euler73': [1, -470, 389017], 'euler79': [1, 1244, 493039], 'euler83': [1, 396, 571787], 'euler89': [1, 972, 704969], 'euler97': [1, 46, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 5, 0], [1, 14, 343], [1, 6, 1331], [1, -68, 2197], [1, -78, 4913], [1, 44, 6859], [1, 120, 12167], [1, -126, 24389], [1, -244, 29791], [1, 304, 50653], [1, 480, 68921], [1, 104, 79507], [1, 600, 103823], [1, 258, 148877], [1, 534, 205379], [1, -362, 226981], [1, -268, 300763], [1, -972, 357911], [1, -470, 389017], [1, 1244, 493039], [1, 396, 571787], [1, 972, 704969], [1, 46, 912673]], 'index': 17, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/4/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/720/4/a/e'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-720-1.1-c3-0-17', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-720-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.517773792034613, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1085657990168060965, 'z1': {'__RealLiteral__': 0, 'data': '1.44858661153723415934145873834', 'prec': 103}}
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lfunc_instances • Show schema
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id: 19979645
{'Lhash': '1836301687597751859796976029136', 'Lhash_array': ['1836301687597751859796976029136'], 'label': '2-720-1.1-c3-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/e'}
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id: 24569812
{'Lhash': '1836301687597751859796976029136', 'Lhash_array': ['1836301687597751859796976029136'], 'label': '2-720-1.1-c3-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/e/1/1'}