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lfunc_lfunctions • Show schema
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{'Lhash': '2396815820869459025704102646193', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.137261107234623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -1]], [19, [1, -1]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.1', 'coefficient_field': '1.1.1.1', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1, -1], [1, 0, 7], [1, -4, 11], [1, 6, 13], [1, 6, 17], [1, -1], [1, 8, 23], [1, 2, 29], [1, 0, 31], [1, -2, 37], [1, -2, 41], [1, 4, 43], [1, -8, 47], [1, 6, 53], [1, -4, 59], [1, 2, 61], [1, 8, 67], [1, 8, 71], [1, -2, 73], [1, -8, 79], [1, 4, 83], [1, 14, 89], [1, -14, 97], [1, 10, 101], [1, 4, 103], [1, -8, 107], [1, 10, 109], [1, -14, 113]], 'euler_factors_factorization': [[1], [[[1, 0, 3], 1]], [[[1, -1], 1]], [[[1, 0, 7], 1]], [[[1, -4, 11], 1]], [[[1, 6, 13], 1]], 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0.5880082881363937, 0.37164754099697433, 0.05556939075515146, -0.3411749717003315, -0.7921503176700793, -1.2652784505505301, -1.725020877714811, -2.1348556440108446], 'positive_zeros': ['1.89075429809912392568711002350678', '2.73770469087314233186868460582456', '4.01896931255446458307976642593425', '4.87366194948920245730018828426091', '5.88666763008921616620555990760225', '6.53479363753959069873167494535300', '7.42607731770411783498514204493753', '8.367215276624493802870113616305882', '9.205033424604682780071294890562864'], 'prelabel': '2-1520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 2061144263689062572, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89075429809912392568711002351', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.73770469087314233186868460582', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.01896931255446458307976642593', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.137261107234623, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, 0, 0, -3, 0, 4, 0, -6, 0, 0, 0, -6, 0, 1, 0, 0, 0, -8, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, -4, 0, -3, 0, 8, 0, -7, 0, 0, 0, -6, 0, 4, 0, 0, 0, 4, 0, -2, 0, 0, 0, -6, 0, -8, 0, 0, 0, -8, 0, 2, 0, 0, 0, 0, 0, 8, 0, 9, 0, -4, 0, -6, 0, 0, 0, -14, 0, 0, 0, 0, 0, 1, 0, 14, 0, -12, 0], 'euler11': [1, -4, 11], 'euler13': [1, 6, 13], 'euler17': [1, 6, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, 2, 29], 'euler3': [1, 0, 3], 'euler31': [1, 0, 31], 'euler37': [1, -2, 37], 'euler41': [1, -2, 41], 'euler43': [1, 4, 43], 'euler47': [1, -8, 47], 'euler5': [1, -1, 0], 'euler53': [1, 6, 53], 'euler59': [1, -4, 59], 'euler61': [1, 2, 61], 'euler67': [1, 8, 67], 'euler7': [1, 0, 7], 'euler71': [1, 8, 71], 'euler73': [1, -2, 73], 'euler79': [1, -8, 79], 'euler83': [1, 4, 83], 'euler89': [1, 14, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, -1, 0], [1, 0, 7], [1, -4, 11], [1, 6, 13], [1, 6, 17], [1, -1, 0], [1, 8, 23], [1, 2, 29], [1, 0, 31], [1, -2, 37], [1, -2, 41], [1, 4, 43], [1, -8, 47], [1, 6, 53], [1, -4, 59], [1, 2, 61], [1, 8, 67], [1, 8, 71], [1, -2, 73], [1, -8, 79], [1, 4, 83], [1, 14, 89], [1, -14, 97]], 'index': 31, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1520/f', 'ModularForm/GL2/Q/holomorphic/1520/2/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/1520/2/a/f'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-1520-1.1-c1-0-31', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2061144263689062572, 'z1': {'__RealLiteral__': 0, 'data': '1.89075429809912392568711002351', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20676480
{'Lhash': '2396815820869459025704102646193', 'Lhash_array': ['2396815820869459025704102646193'], 'label': '2-1520-1.1-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/a/f'}
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id: 24553460
{'Lhash': '2396815820869459025704102646193', 'Lhash_array': ['2396815820869459025704102646193'], 'label': '2-1520-1.1-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/a/f/1/1'}
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id: 100496
{'Lhash': '2061144263689062572', 'Lhash_array': ['2061144263689062572'], 'label': '2-1520-1.1-c1-0-31', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1520/f'}