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lfunc_lfunctions • Show schema
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{'Lhash': '2128840527404317607071287440422', '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, -4, 11], [1, 2, 13], [1, 6, 17], [1, 4, 19], [1, 0, 23], [1, 2, 29], [1, 0, 31], [1, 6, 37], [1, 2, 41], [1, -4, 43], [1, 0, 47], [1, 6, 53], [1, 12, 59], [1, -2, 61], [1, 4, 67], [1, 0, 71], [1, 6, 73], [1, 16, 79], [1, 12, 83], [1, -14, 89], [1, -18, 97], [1, 14, 101], [1, -8, 103], [1, 4, 107], [1, 18, 109], [1, -14, 113]], 'euler_factors_factorization': [[[[1, -1, 2], 1]], [[[1, -1], 1]], [1], [1], [[[1, -4, 11], 1]], [[[1, 2, 13], 1]], [[[1, 6, 17], 1]], 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-1.1966294336664616, -1.2955641626271652, -1.3104025518997464, -1.2439525708341304, -1.1042849703618132, -0.9040710085866781, -0.6596414522267425, -0.38982998310918066], 'positive_zeros': ['1.67935906551934617681697486496257', '2.69870051831794005458111315936241', '3.64262157144388694664848575283265', '4.32385123346365347175721472715188', '4.81505610216268765778329020979326', '5.94933200323688252851139603476833', '6.57215946307210072487478723379300', '7.31923002930315464027308864727469', '8.383266094837325727408472045987304'], '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': 980299494559147339, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67935906551934617681697486496', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.69870051831794005458111315936', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64262157144388694664848575283', '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, 4, -1, -2, 0, 0, -1, -6, 1, -4, 0, 0, 4, 0, -3, 0, -2, 1, 0, -2, 0, 0, 5, 4, -6, 0, -1, -6, -4, -2, 0, -2, 0, 4, -4, 0, 0, 0, -1, 0, 0, -6, 2, -6, 1, 0, 0, -4, -2, -12, 0, 2, 0, 0, 7, 0, 4, -4, 6, 0, 0, 0, -3, -6, -6, 0, 4, 0, -2, -16, 0, 1, -2, -12, 0, 0, 4, -2, -12, 14, 0, 0, 0, 0, 0, 0, 5, 18, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, 2, 13], 'euler17': [1, 6, 17], 'euler19': [1, 4, 19], 'euler2': [1, -1, 2], 'euler23': [1, 0, 23], 'euler29': [1, 2, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 6, 37], 'euler41': [1, 2, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, 12, 59], 'euler61': [1, -2, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, 6, 73], 'euler79': [1, 16, 79], 'euler83': [1, 12, 83], 'euler89': [1, -14, 89], 'euler97': [1, -18, 97], 'euler_factors': [[1, -1, 2], [1, -1, 0], [1, 0, 0], [1, 0, 0], [1, -4, 11], [1, 2, 13], [1, 6, 17], [1, 4, 19], [1, 0, 23], [1, 2, 29], [1, 0, 31], [1, 6, 37], [1, 2, 41], [1, -4, 43], [1, 0, 47], [1, 6, 53], [1, 12, 59], [1, -2, 61], [1, 4, 67], [1, 0, 71], [1, 6, 73], [1, 16, 79], [1, 12, 83], [1, -14, 89], [1, -18, 97]], 'index': 118, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3675/n', 'ModularForm/GL2/Q/holomorphic/3675/2/a/n/1/1', 'ModularForm/GL2/Q/holomorphic/3675/2/a/n'], '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-c1-0-118', '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': 980299494559147339, 'z1': {'__RealLiteral__': 0, 'data': '1.67935906551934617681697486496', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20291775
{'Lhash': '2128840527404317607071287440422', 'Lhash_array': ['2128840527404317607071287440422'], 'label': '2-3675-1.1-c1-0-118', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3675/2/a/n'}
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id: 24562598
{'Lhash': '2128840527404317607071287440422', 'Lhash_array': ['2128840527404317607071287440422'], 'label': '2-3675-1.1-c1-0-118', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3675/2/a/n/1/1'}
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id: 94351
{'Lhash': '980299494559147339', 'Lhash_array': ['980299494559147339'], 'label': '2-3675-1.1-c1-0-118', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3675/n'}