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lfunc_lfunctions • Show schema
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{'Lhash': '3982169618411754947695011455785', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': -4, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.44716225131917037, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -1]]], 'bad_primes': [2, 7], 'central_character': '56.1', 'coefficient_field': '1.1.1.1', 'conductor': 56, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[1], [1, -2, 3], [1, 4, 5], [1, -1], [1, 0, 11], [1, 0, 13], [1, 2, 17], [1, 2, 19], [1, -8, 23], [1, -2, 29], [1, -4, 31], [1, 6, 37], [1, 2, 41], [1, -8, 43], [1, 4, 47], [1, 10, 53], [1, -6, 59], [1, -4, 61], [1, 12, 67], [1, 0, 71], [1, 14, 73], [1, 8, 79], [1, -6, 83], [1, -10, 89], [1, 2, 97], [1, -12, 101], [1, 12, 103], [1, 12, 107], [1, -10, 109], [1, -6, 113]], 'euler_factors_factorization': [[1], [[[1, -2, 3], 1]], [[[1, 4, 5], 1]], [[[1, -1], 1]], [[[1, 0, 11], 1]], [[[1, 0, 13], 1]], [[[1, 2, 17], 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-0.26724165139055545, -0.5450870760901558, -0.7280870444991303, -0.7140465537167916, -0.44525000419111355, 0.07277020743911193], 'positive_zeros': ['3.14137792992390816749783057890505', '4.50185552371175935345657331178732', '7.14438434722230698367292292955154', '8.188057214509100026281306554310771', '8.928329697232844766585907221766651', '10.85093898417625194511634818884263', '11.85083361056233693149695469962806', '13.10747313979957160372604181413690', '14.47141648264651804115718476827873', '15.16780114648984000281229819869216'], 'prelabel': '2-56-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.6687019151454333, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 537829933984420021, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.14137792992390816749783057891', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.50185552371175935345657331179', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.14438434722230698367292292955', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.44716225131917037, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 56, 'conductor_radical': 14, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, -4, 0, 1, 0, 1, 0, 0, 0, 0, 0, -8, 0, -2, 0, -2, 0, 2, 0, 8, 0, 11, 0, -4, 0, 2, 0, 4, 0, 0, 0, -4, 0, -6, 0, 0, 0, -2, 0, 8, 0, -4, 0, -4, 0, 1, 0, -4, 0, -10, 0, 0, 0, -4, 0, 6, 0, 4, 0, 1, 0, 0, 0, -12, 0, 16, 0, 0, 0, -14, 0, 22, 0, 0, 0, -8, 0, -11, 0, 6, 0, 8, 0, 4, 0, 10, 0, 0, 0, 8, 0, 8, 0, -2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 0, 13], 'euler17': [1, 2, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, -2, 29], 'euler3': [1, -2, 3], 'euler31': [1, -4, 31], 'euler37': [1, 6, 37], 'euler41': [1, 2, 41], 'euler43': [1, -8, 43], 'euler47': [1, 4, 47], 'euler5': [1, 4, 5], 'euler53': [1, 10, 53], 'euler59': [1, -6, 59], 'euler61': [1, -4, 61], 'euler67': [1, 12, 67], 'euler7': [1, -1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 14, 73], 'euler79': [1, 8, 79], 'euler83': [1, -6, 83], 'euler89': [1, -10, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, -2, 3], [1, 4, 5], [1, -1, 0], [1, 0, 11], [1, 0, 13], [1, 2, 17], [1, 2, 19], [1, -8, 23], [1, -2, 29], [1, -4, 31], [1, 6, 37], [1, 2, 41], [1, -8, 43], [1, 4, 47], [1, 10, 53], [1, -6, 59], [1, -4, 61], [1, 12, 67], [1, 0, 71], [1, 14, 73], [1, 8, 79], [1, -6, 83], [1, -10, 89], [1, 2, 97]], 'index': 1, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/56/b', 'ModularForm/GL2/Q/holomorphic/56/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/56/2/a/b'], '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': '2-56-1.1-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-56-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.6687019151454333, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 537829933984420021, 'z1': {'__RealLiteral__': 0, 'data': '3.14137792992390816749783057891', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9956926
{'Lhash': '3982169618411754947695011455785', 'Lhash_array': ['3982169618411754947695011455785'], 'label': '2-56-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/56/2/a/b'}
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id: 24546196
{'Lhash': '3982169618411754947695011455785', 'Lhash_array': ['3982169618411754947695011455785'], 'label': '2-56-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/56/2/a/b/1/1'}
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id: 21996
{'Lhash': '537829933984420021', 'Lhash_array': ['537829933984420021'], 'label': '2-56-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/56/b'}