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lfunc_lfunctions • Show schema
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{'Lhash': '1059554584295494563966348226523', 'a10': 0, 'a2': 0, 'a3': -5, 'a4': 0, 'a5': 9, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 46.257497444500665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '784.1', 'coefficient_field': '1.1.1.1', 'conductor': 784, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[1], [1, 5, 27], [1, -9, 125], [1], [1, -57, 1331], [1, -70, 2197], [1, 51, 4913], [1, -5, 6859], [1, 69, 12167], [1, -114, 24389], [1, -23, 29791], [1, 253, 50653], [1, -42, 68921], [1, -124, 79507], [1, -201, 103823], [1, 393, 148877], [1, -219, 205379], [1, -709, 226981], [1, 419, 300763], [1, -96, 357911], [1, -313, 389017], [1, 461, 493039], [1, 588, 571787], [1, -1017, 704969], [1, -1834, 912673], [1, -285, 1030301], [1, 499, 1092727], [1, -1107, 1225043], [1, -923, 1295029], [1, -1542, 1442897]], 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'rational': True, 'root_analytic_conductor': 6.801286455112788, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 1997144719626712650, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.835841188498416700760494647301', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.90832021112420557370008271482', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52964449604414804826757508467', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 46.257497444500665, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 784, 'conductor_radical': 14, 'degree': 2, 'dirichlet_coefficients': [1, 0, -5, 0, 9, 0, 0, 0, -2, 0, 57, 0, 70, 0, -45, 0, -51, 0, 5, 0, 0, 0, -69, 0, -44, 0, 145, 0, 114, 0, 23, 0, -285, 0, 0, 0, -253, 0, -350, 0, 42, 0, 124, 0, -18, 0, 201, 0, 0, 0, 255, 0, -393, 0, 513, 0, -25, 0, 219, 0, 709, 0, 0, 0, 630, 0, -419, 0, 345, 0, 96, 0, 313, 0, 220, 0, 0, 0, -461, 0, -671, 0, -588, 0, -459, 0, -570, 0, 1017, 0, 0, 0, -115, 0, 45, 0, 1834, 0, -114, 0], 'euler11': [1, -57, 1331], 'euler13': [1, -70, 2197], 'euler17': [1, 51, 4913], 'euler19': [1, -5, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 69, 12167], 'euler29': [1, -114, 24389], 'euler3': [1, 5, 27], 'euler31': [1, -23, 29791], 'euler37': [1, 253, 50653], 'euler41': [1, -42, 68921], 'euler43': [1, -124, 79507], 'euler47': [1, -201, 103823], 'euler5': [1, -9, 125], 'euler53': [1, 393, 148877], 'euler59': [1, -219, 205379], 'euler61': [1, -709, 226981], 'euler67': [1, 419, 300763], 'euler7': [1, 0, 0], 'euler71': [1, -96, 357911], 'euler73': [1, -313, 389017], 'euler79': [1, 461, 493039], 'euler83': [1, 588, 571787], 'euler89': [1, -1017, 704969], 'euler97': [1, -1834, 912673], 'euler_factors': [[1, 0, 0], [1, 5, 27], [1, -9, 125], [1, 0, 0], [1, -57, 1331], [1, -70, 2197], [1, 51, 4913], [1, -5, 6859], [1, 69, 12167], [1, -114, 24389], [1, -23, 29791], [1, 253, 50653], [1, -42, 68921], [1, -124, 79507], [1, -201, 103823], [1, 393, 148877], [1, -219, 205379], [1, -709, 226981], [1, 419, 300763], [1, -96, 357911], [1, -313, 389017], [1, 461, 493039], [1, 588, 571787], [1, -1017, 704969], [1, -1834, 912673]], 'index': 16, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/784/4/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/784/4/a/c'], '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': '2-28e2-1.1-c3-0-16', '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': '2-28e2-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.801286455112788, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1997144719626712650, 'z1': {'__RealLiteral__': 0, 'data': '0.835841188498416700760494647301', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20456446
{'Lhash': '1059554584295494563966348226523', 'Lhash_array': ['1059554584295494563966348226523'], 'label': '2-28e2-1.1-c3-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/784/4/a/c'}
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id: 24571967
{'Lhash': '1059554584295494563966348226523', 'Lhash_array': ['1059554584295494563966348226523'], 'label': '2-28e2-1.1-c3-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/784/4/a/c/1/1'}