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lfunc_lfunctions • Show schema
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{'Lhash': '1016778083721111759756324595655', 'a10': -4, 'a2': 2, 'a3': 0, 'a4': 4, 'a5': -2, 'a6': 0, 'a7': -7, 'a8': 8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 81.77664726795653, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2]], [3, [1]], [7, [1, 7]], [11, [1, 11]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '1386.1', 'coefficient_field': '1.1.1.1', 'conductor': 1386, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[1, -2], [1], [1, 2, 125], [1, 7], [1, 11], [1, -26, 2197], [1, -46, 4913], [1, 48, 6859], [1, -128, 12167], [1, -146, 24389], [1, 128, 29791], [1, 26, 50653], [1, 10, 68921], [1, -52, 79507], [1, -544, 103823], [1, 318, 148877], [1, -48, 205379], [1, -466, 226981], [1, -516, 300763], [1, -392, 357911], [1, -754, 389017], [1, 0, 493039], [1, 624, 571787], [1, -1590, 704969], [1, -1018, 912673], [1, 474, 1030301], [1, 984, 1092727], [1, 92, 1225043], [1, -1246, 1295029], [1, 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'2-1386-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.043044137233686, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 2013556899349442254, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.802096479533121950393797408254', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.17971905077352842321075225407', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24467506311083167341188943444', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 81.77664726795653, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 1386, 'conductor_radical': 462, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, 4, -2, 0, -7, 8, 0, -4, -11, 0, 26, -14, 0, 16, 46, 0, -48, -8, 0, -22, 128, 0, -121, 52, 0, -28, 146, 0, -128, 32, 0, 92, 14, 0, -26, -96, 0, -16, -10, 0, 52, -44, 0, 256, 544, 0, 49, -242, 0, 104, -318, 0, 22, -56, 0, 292, 48, 0, 466, -256, 0, 64, -52, 0, 516, 184, 0, 28, 392, 0, 754, -52, 0, -192, 77, 0, 0, -32, 0, -20, -624, 0, -92, 104, 0, -88, 1590, 0, -182, 512, 0, 1088, 96, 0, 1018, 98, 0, -484], 'euler11': [1, 11, 0], 'euler13': [1, -26, 2197], 'euler17': [1, -46, 4913], 'euler19': [1, 48, 6859], 'euler2': [1, -2, 0], 'euler23': [1, -128, 12167], 'euler29': [1, -146, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 128, 29791], 'euler37': [1, 26, 50653], 'euler41': [1, 10, 68921], 'euler43': [1, -52, 79507], 'euler47': [1, -544, 103823], 'euler5': [1, 2, 125], 'euler53': [1, 318, 148877], 'euler59': [1, -48, 205379], 'euler61': [1, -466, 226981], 'euler67': [1, -516, 300763], 'euler7': [1, 7, 0], 'euler71': [1, -392, 357911], 'euler73': [1, -754, 389017], 'euler79': [1, 0, 493039], 'euler83': [1, 624, 571787], 'euler89': [1, -1590, 704969], 'euler97': [1, -1018, 912673], 'euler_factors': [[1, -2, 0], [1, 0, 0], [1, 2, 125], [1, 7, 0], [1, 11, 0], [1, -26, 2197], [1, -46, 4913], [1, 48, 6859], [1, -128, 12167], [1, -146, 24389], [1, 128, 29791], [1, 26, 50653], [1, 10, 68921], [1, -52, 79507], [1, -544, 103823], [1, 318, 148877], [1, -48, 205379], [1, -466, 226981], [1, -516, 300763], [1, -392, 357911], [1, -754, 389017], [1, 0, 493039], [1, 624, 571787], [1, -1590, 704969], [1, -1018, 912673]], 'index': 24, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1386/4/a/j/1/1', 'ModularForm/GL2/Q/holomorphic/1386/4/a/j'], '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': '2-1386-1.1-c3-0-24', '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': '2-1386-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.043044137233686, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 2013556899349442254, 'z1': {'__RealLiteral__': 0, 'data': '0.802096479533121950393797408254', 'prec': 107}}
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lfunc_instances • Show schema
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id: 21272740
{'Lhash': '1016778083721111759756324595655', 'Lhash_array': ['1016778083721111759756324595655'], 'label': '2-1386-1.1-c3-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1386/4/a/j'}
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id: 24591208
{'Lhash': '1016778083721111759756324595655', 'Lhash_array': ['1016778083721111759756324595655'], 'label': '2-1386-1.1-c3-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1386/4/a/j/1/1'}