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lfunc_lfunctions • Show schema
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{'Lhash': '1727927499782498284933463742493', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 3, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.129426657363098, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [19, [1, -1]]], 'bad_primes': [2, 3, 19], 'central_character': '3648.1', 'coefficient_field': '1.1.1.1', 'conductor': 3648, 'conductor_radical': 114, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1, 5], [1, -3, 7], [1, 5, 11], [1, -2, 13], [1, 1, 17], [1, -1], [1, 4, 23], [1, -6, 29], [1, -10, 31], [1, 0, 37], [1, 0, 41], [1, 11, 43], [1, 9, 47], [1, 10, 53], [1, -4, 59], [1, -5, 61], [1, 4, 67], [1, 8, 71], [1, -13, 73], [1, 4, 79], [1, 4, 83], [1, 6, 89], [1, -2, 97], [1, -6, 101], [1, 10, 103], [1, -18, 107], [1, -8, 109], [1, -6, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, 1, 5], 1]], [[[1, -3, 7], 1]], [[[1, 5, 11], 1]], [[[1, -2, 13], 1]], 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-2.845212001965653, -2.665567338222388, -2.364694306188736, -1.9552098432883878, -1.456011923200212, -0.8913261903545762, -0.2894185461009327, 0.31895652008808245, 0.902284934218757], 'positive_zeros': ['1.36309445163470127656106423644838', '2.43726074335480144289137857493346', '3.52150549884707699550976993427004', '4.68719487779910370709247985619746', '4.90222652055451670072407703452164', '5.90641506250154868855227026944946', '6.60850791131037206491890289679578', '7.65627920571478032514336271694251', '8.137259653188121390855447482026543'], 'prelabel': '2-3648-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.397168392533542, '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': 1411483842001532545, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36309445163470127656106423645', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.129426657363098, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 3648, 'conductor_radical': 114, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 3, 0, 1, 0, -5, 0, 2, 0, 1, 0, -1, 0, 1, 0, -3, 0, -4, 0, -4, 0, -1, 0, 6, 0, 10, 0, 5, 0, -3, 0, 0, 0, -2, 0, 0, 0, -11, 0, -1, 0, -9, 0, 2, 0, 1, 0, -10, 0, 5, 0, -1, 0, 4, 0, 5, 0, 3, 0, -2, 0, -4, 0, 4, 0, -8, 0, 13, 0, 4, 0, -15, 0, -4, 0, 1, 0, -4, 0, 1, 0, -6, 0, -6, 0, 6, 0, -10, 0, -1, 0, 2, 0, -5, 0], 'euler11': [1, 5, 11], 'euler13': [1, -2, 13], 'euler17': [1, 1, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -10, 31], 'euler37': [1, 0, 37], 'euler41': [1, 0, 41], 'euler43': [1, 11, 43], 'euler47': [1, 9, 47], 'euler5': [1, 1, 5], 'euler53': [1, 10, 53], 'euler59': [1, -4, 59], 'euler61': [1, -5, 61], 'euler67': [1, 4, 67], 'euler7': [1, -3, 7], 'euler71': [1, 8, 71], 'euler73': [1, -13, 73], 'euler79': [1, 4, 79], 'euler83': [1, 4, 83], 'euler89': [1, 6, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 5], [1, -3, 7], [1, 5, 11], [1, -2, 13], [1, 1, 17], [1, -1, 0], [1, 4, 23], [1, -6, 29], [1, -10, 31], [1, 0, 37], [1, 0, 41], [1, 11, 43], [1, 9, 47], [1, 10, 53], [1, -4, 59], [1, -5, 61], [1, 4, 67], [1, 8, 71], [1, -13, 73], [1, 4, 79], [1, 4, 83], [1, 6, 89], [1, -2, 97]], 'index': 51, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3648/g', 'ModularForm/GL2/Q/holomorphic/3648/2/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/3648/2/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': 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': '2-3648-1.1-c1-0-51', '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': '2-3648-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.397168392533542, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1411483842001532545, 'z1': {'__RealLiteral__': 0, 'data': '1.36309445163470127656106423645', 'prec': 103}}
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lfunc_instances • Show schema
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id: 19994809
{'Lhash': '1727927499782498284933463742493', 'Lhash_array': ['1727927499782498284933463742493'], 'label': '2-3648-1.1-c1-0-51', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3648/2/a/g'}
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id: 24562423
{'Lhash': '1727927499782498284933463742493', 'Lhash_array': ['1727927499782498284933463742493'], 'label': '2-3648-1.1-c1-0-51', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3648/2/a/g/1/1'}
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id: 22553
{'Lhash': '1411483842001532545', 'Lhash_array': ['1411483842001532545'], 'label': '2-3648-1.1-c1-0-51', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3648/g'}