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lfunc_lfunctions • Show schema
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{'Lhash': '1183630261422668953781797381454', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 5, 'a6': 0, 'a7': -4, '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, 4, 343], [1, -72, 1331], [1, 6, 2197], [1, 38, 4913], [1, 52, 6859], [1, -152, 12167], [1, -78, 24389], [1, 120, 29791], [1, 150, 50653], [1, 362, 68921], [1, -484, 79507], [1, -280, 103823], [1, -670, 148877], [1, -696, 205379], [1, -222, 226981], [1, -4, 300763], [1, -96, 357911], [1, -178, 389017], [1, -632, 493039], [1, 612, 571787], [1, 994, 704969], [1, -1634, 912673], [1, 890, 1030301], [1, -524, 1092727], [1, -932, 1225043], [1, -446, 1295029], [1, -786, 1442897]], 'euler_factors_factorization': [[1], [1], [[[1, -5], 1]], [[[1, 4, 343], 1]], [[[1, -72, 1331], 1]], [[[1, 6, 2197], 1]], [[[1, 38, 4913], 1]], [[[1, 52, 6859], 1]], [[[1, -152, 12167], 1]], [[[1, -78, 24389], 1]], [[[1, 120, 29791], 1]], [[[1, 150, 50653], 1]], [[[1, 362, 68921], 1]], [[[1, -484, 79507], 1]], [[[1, -280, 103823], 1]], [[[1, -670, 148877], 1]], [[[1, -696, 205379], 1]], [[[1, -222, 226981], 1]], [[[1, -4, 300763], 1]], [[[1, -96, 357911], 1]], [[[1, -178, 389017], 1]], [[[1, -632, 493039], 1]], [[[1, 612, 571787], 1]], [[[1, 994, 704969], 1]], [[[1, -1634, 912673], 1]], [[[1, 890, 1030301], 1]], [[[1, -524, 1092727], 1]], [[[1, -932, 1225043], 1]], [[[1, -446, 1295029], 1]], [[[1, -786, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-720-1.1-c3-0-11', 'leading_term': '2.42408619016359249451136882699360000000000000000000000000000000000000000000000000000000000', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/720/4/a/v', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.4240861901635924, 2.412178683255783, 2.3765649023112223, 2.317571790260475, 2.2357465805415404, 2.1318600014124462, 2.0069101973002277, 1.8621268307440417, 1.6989747141714724, 1.5191562333156345, 1.3246117671608266, 1.1175172853971809, 0.900278314846917, 0.6755195114985102, 0.44606915395856633, 0.2149379857145015, -0.014708024799239007, -0.23958126883642897, -0.4563124975436497, -0.6614970982026623, -0.8517472827584216, -1.0237495923176527, -1.1743268863795442, -1.3005037547138676, -1.3995740698570212, -1.4691691962674645, -1.5073251955442892, -1.5125472230405395, -1.48386920677439, -1.4209068414144728, -1.3239019242818724, -1.1937561118338418, -1.0320522878413438, -0.8410619108562154, -0.6237369492961717, 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True, 'rational': True, 'root_analytic_conductor': 6.517773792034613, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 1508175901826734290, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.933719639472869479412692177614', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.13660290910793640930210806454', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51235449494208983025107828017', '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, -4, 0, 0, 0, 72, 0, -6, 0, 0, 0, -38, 0, -52, 0, 0, 0, 152, 0, 25, 0, 0, 0, 78, 0, -120, 0, 0, 0, -20, 0, -150, 0, 0, 0, -362, 0, 484, 0, 0, 0, 280, 0, -327, 0, 0, 0, 670, 0, 360, 0, 0, 0, 696, 0, 222, 0, 0, 0, -30, 0, 4, 0, 0, 0, 96, 0, 178, 0, 0, 0, -288, 0, 632, 0, 0, 0, -612, 0, -190, 0, 0, 0, -994, 0, 24, 0, 0, 0, -260, 0, 1634, 0, 0, 0], 'euler11': [1, -72, 1331], 'euler13': [1, 6, 2197], 'euler17': [1, 38, 4913], 'euler19': [1, 52, 6859], 'euler2': [1, 0, 0], 'euler23': [1, -152, 12167], 'euler29': [1, -78, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 120, 29791], 'euler37': [1, 150, 50653], 'euler41': [1, 362, 68921], 'euler43': [1, -484, 79507], 'euler47': [1, -280, 103823], 'euler5': [1, -5, 0], 'euler53': [1, -670, 148877], 'euler59': [1, -696, 205379], 'euler61': [1, -222, 226981], 'euler67': [1, -4, 300763], 'euler7': [1, 4, 343], 'euler71': [1, -96, 357911], 'euler73': [1, -178, 389017], 'euler79': [1, -632, 493039], 'euler83': [1, 612, 571787], 'euler89': [1, 994, 704969], 'euler97': [1, -1634, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -5, 0], [1, 4, 343], [1, -72, 1331], [1, 6, 2197], [1, 38, 4913], [1, 52, 6859], [1, -152, 12167], [1, -78, 24389], [1, 120, 29791], [1, 150, 50653], [1, 362, 68921], [1, -484, 79507], [1, -280, 103823], [1, -670, 148877], [1, -696, 205379], [1, -222, 226981], [1, -4, 300763], [1, -96, 357911], [1, -178, 389017], [1, -632, 493039], [1, 612, 571787], [1, 994, 704969], [1, -1634, 912673]], 'index': 11, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/4/a/v/1/1', 'ModularForm/GL2/Q/holomorphic/720/4/a/v'], '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-c3-0-11', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-720-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.517773792034613, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1508175901826734290, 'z1': {'__RealLiteral__': 0, 'data': '0.933719639472869479412692177614', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20472457
{'Lhash': '1183630261422668953781797381454', 'Lhash_array': ['1183630261422668953781797381454'], 'label': '2-720-1.1-c3-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/v'}
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id: 24569829
{'Lhash': '1183630261422668953781797381454', 'Lhash_array': ['1183630261422668953781797381454'], 'label': '2-720-1.1-c3-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/v/1/1'}