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lfunc_lfunctions • Show schema
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{'Lhash': '1143252825901699863817602094599', 'a10': -24, 'a2': -2, 'a3': 0, 'a4': 4, 'a5': 12, 'a6': 0, 'a7': 7, 'a8': -8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 96.64512858940317, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2]], [3, [1]], [7, [1, -7]], [13, [1, 13]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '1638.1', 'coefficient_field': '1.1.1.1', 'conductor': 1638, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[1, 2], [1], [1, -12, 125], [1, -7], [1, -50, 1331], [1, 13], [1, -58, 4913], [1, 40, 6859], [1, -64, 12167], [1, -110, 24389], [1, -124, 29791], [1, 50, 50653], [1, 84, 68921], [1, 12, 79507], [1, -82, 103823], [1, -442, 148877], [1, -618, 205379], [1, 278, 226981], [1, -20, 300763], [1, -390, 357911], [1, 2, 389017], [1, 680, 493039], [1, 322, 571787], [1, 968, 704969], [1, -1022, 912673], [1, 54, 1030301], [1, -1416, 1092727], [1, 1252, 1225043], [1, -930, 1295029], 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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/1638/4/a/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.461188473640436, 2.449988024008602, 2.4165259869127906, 2.361219557808514, 2.2847615542340156, 2.188116509721523, 2.0725149260900833, 1.9394454240306505, 1.7906444839855287, 1.6280834397384398, 1.4539523783915667, 1.2706406142283195, 1.080713441204559, 0.8868849294606751, 0.6919866144229914, 0.4989320310593623, 0.31067716819440416, 0.1301770553002158, -0.03966115693038748, -0.1960281049613268, -0.33626443418302604, -0.45791450295003117, -0.5587805901892342, -0.6369764936641138, -0.6909792904521661, -0.7196779395289064, -0.7224173434331461, -0.6990364562587357, -0.6498990325395511, -0.5759156591008545, -0.4785558019035277, -0.35984873356348634, -0.22237238471265208, -0.06922938257204245, 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True, 'rational': True, 'root_analytic_conductor': 9.830825427674075, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 1880242844503768540, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.901867459137294766704125628510', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.69744418920316327205172004387', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.68218841865384642607123064299', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 96.64512858940317, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 1638, 'conductor_radical': 546, 'degree': 2, 'dirichlet_coefficients': [1, -2, 0, 4, 12, 0, 7, -8, 0, -24, 50, 0, -13, -14, 0, 16, 58, 0, -40, 48, 0, -100, 64, 0, 19, 26, 0, 28, 110, 0, 124, -32, 0, -116, 84, 0, -50, 80, 0, -96, -84, 0, -12, 200, 0, -128, 82, 0, 49, -38, 0, -52, 442, 0, 600, -56, 0, -220, 618, 0, -278, -248, 0, 64, -156, 0, 20, 232, 0, -168, 390, 0, -2, 100, 0, -160, 350, 0, -680, 192, 0, 168, -322, 0, 696, 24, 0, -400, -968, 0, -91, 256, 0, -164, -480, 0, 1022, -98, 0, 76], 'euler11': [1, -50, 1331], 'euler13': [1, 13, 0], 'euler17': [1, -58, 4913], 'euler19': [1, 40, 6859], 'euler2': [1, 2, 0], 'euler23': [1, -64, 12167], 'euler29': [1, -110, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -124, 29791], 'euler37': [1, 50, 50653], 'euler41': [1, 84, 68921], 'euler43': [1, 12, 79507], 'euler47': [1, -82, 103823], 'euler5': [1, -12, 125], 'euler53': [1, -442, 148877], 'euler59': [1, -618, 205379], 'euler61': [1, 278, 226981], 'euler67': [1, -20, 300763], 'euler7': [1, -7, 0], 'euler71': [1, -390, 357911], 'euler73': [1, 2, 389017], 'euler79': [1, 680, 493039], 'euler83': [1, 322, 571787], 'euler89': [1, 968, 704969], 'euler97': [1, -1022, 912673], 'euler_factors': [[1, 2, 0], [1, 0, 0], [1, -12, 125], [1, -7, 0], [1, -50, 1331], [1, 13, 0], [1, -58, 4913], [1, 40, 6859], [1, -64, 12167], [1, -110, 24389], [1, -124, 29791], [1, 50, 50653], [1, 84, 68921], [1, 12, 79507], [1, -82, 103823], [1, -442, 148877], [1, -618, 205379], [1, 278, 226981], [1, -20, 300763], [1, -390, 357911], [1, 2, 389017], [1, 680, 493039], [1, 322, 571787], [1, 968, 704969], [1, -1022, 912673]], 'index': 36, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1638/4/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/1638/4/a/g'], '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': '2-1638-1.1-c3-0-36', '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': '2-1638-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.830825427674075, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1880242844503768540, 'z1': {'__RealLiteral__': 0, 'data': '0.901867459137294766704125628510', 'prec': 107}}
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lfunc_instances • Show schema
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id: 21264259
{'Lhash': '1143252825901699863817602094599', 'Lhash_array': ['1143252825901699863817602094599'], 'factors': ['2-1638-1.1-c3-0-36'], 'label': '2-1638-1.1-c3-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1638/4/a/g'}
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id: 24591857
{'Lhash': '1143252825901699863817602094599', 'Lhash_array': ['1143252825901699863817602094599'], 'factors': ['2-1638-1.1-c3-0-36'], 'label': '2-1638-1.1-c3-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1638/4/a/g/1/1'}