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lfunc_lfunctions • Show schema
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{'Lhash': '1350102499281887956211156890654', 'a10': 0, 'a2': -1, 'a3': -1, 'a4': -1, 'a5': 0, 'a6': 1, 'a7': 0, 'a8': 3, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.345022742820554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [5, [1]], [7, [1]]], 'bad_primes': [3, 5, 7], 'central_character': '3675.1', 'coefficient_field': '1.1.1.1', 'conductor': 3675, 'conductor_radical': 105, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, 1], [1], [1], [1, 6, 11], [1, -2, 13], [1, 4, 17], [1, -6, 19], [1, 0, 23], [1, 2, 29], [1, -10, 31], [1, 4, 37], [1, 2, 41], [1, 4, 43], [1, 0, 47], [1, -6, 53], [1, -8, 59], [1, -2, 61], [1, 16, 67], [1, -10, 71], [1, -6, 73], [1, -4, 79], [1, 8, 83], [1, 6, 89], [1, -2, 97], [1, -6, 101], [1, 8, 103], [1, -4, 107], [1, -2, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, 1, 2], 1]], [[[1, 1], 1]], [1], [1], [[[1, 6, 11], 1]], [[[1, -2, 13], 1]], [[[1, 4, 17], 1]], 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-3.6697870983910037, -3.395049992318871, -3.0044733082048047, -2.5240572519697553, -1.9841723851320856, -1.41774917658296, -0.8583011920731877], 'positive_zeros': ['1.06504307972466057410251062188232', '2.33462003232101750035985685626819', '3.45367463617503835925378630299591', '4.56813311176270756452064483968730', '5.11647068828854224957302425430200', '5.80251515017269393523381865598034', '6.87365214021075367013688836972808', '7.55446969326170854719470118234254', '8.256055578461575445003684081516019'], 'prelabel': '2-3675-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.417104645732862, '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': 1844387834297686483, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06504307972466057410251062188', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33462003232101750035985685627', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.45367463617503835925378630300', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.345022742820554, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 3675, 'conductor_radical': 105, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, -1, 0, 1, 0, 3, 1, 0, -6, 1, 2, 0, 0, -1, -4, -1, 6, 0, 0, 6, 0, -3, 0, -2, -1, 0, -2, 0, 10, -5, 6, 4, 0, -1, -4, -6, -2, 0, -2, 0, -4, 6, 0, 0, 0, 1, 0, 0, 4, -2, 6, 1, 0, 0, -6, 2, 8, 0, 2, -10, 0, 7, 0, -6, -16, 4, 0, 0, 10, 3, 6, 4, 0, -6, 0, 2, 4, 0, 1, 2, -8, 0, 0, 4, 2, -18, -6, 0, 0, 0, -10, 0, 0, 5, 2, 0, -6, 0], 'euler11': [1, 6, 11], 'euler13': [1, -2, 13], 'euler17': [1, 4, 17], 'euler19': [1, -6, 19], 'euler2': [1, 1, 2], 'euler23': [1, 0, 23], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, -10, 31], 'euler37': [1, 4, 37], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, -8, 59], 'euler61': [1, -2, 61], 'euler67': [1, 16, 67], 'euler7': [1, 0, 0], 'euler71': [1, -10, 71], 'euler73': [1, -6, 73], 'euler79': [1, -4, 79], 'euler83': [1, 8, 83], 'euler89': [1, 6, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 1, 2], [1, 1, 0], [1, 0, 0], [1, 0, 0], [1, 6, 11], [1, -2, 13], [1, 4, 17], [1, -6, 19], [1, 0, 23], [1, 2, 29], [1, -10, 31], [1, 4, 37], [1, 2, 41], [1, 4, 43], [1, 0, 47], [1, -6, 53], [1, -8, 59], [1, -2, 61], [1, 16, 67], [1, -10, 71], [1, -6, 73], [1, -4, 79], [1, 8, 83], [1, 6, 89], [1, -2, 97]], 'index': 61, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3675/d', 'ModularForm/GL2/Q/holomorphic/3675/2/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/3675/2/a/d'], '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': '2-3675-1.1-c1-0-61', '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': '2-3675-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.417104645732862, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1844387834297686483, 'z1': {'__RealLiteral__': 0, 'data': '1.06504307972466057410251062188', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20291781
{'Lhash': '1350102499281887956211156890654', 'Lhash_array': ['1350102499281887956211156890654'], 'label': '2-3675-1.1-c1-0-61', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3675/2/a/d'}
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id: 24562588
{'Lhash': '1350102499281887956211156890654', 'Lhash_array': ['1350102499281887956211156890654'], 'label': '2-3675-1.1-c1-0-61', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3675/2/a/d/1/1'}
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id: 102688
{'Lhash': '1844387834297686483', 'Lhash_array': ['1844387834297686483'], 'label': '2-3675-1.1-c1-0-61', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3675/d'}