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lfunc_lfunctions • Show schema
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{'Lhash': '2138467118012446066859977283699', 'a10': 6, 'a2': 2, 'a3': 0, 'a4': 2, 'a5': 3, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1, 1]], [13, [1, 1]]], 'bad_primes': [3, 7, 13], 'central_character': '819.1', 'coefficient_field': '1.1.1.1', 'conductor': 819, 'conductor_radical': 273, 'degree': 2, 'euler_factors': [[1, -2, 2], [1], [1, -3, 5], [1, 1], [1, -6, 11], [1, 1], [1, 4, 17], [1, -5, 19], [1, 3, 23], [1, -5, 29], [1, 3, 31], [1, 4, 37], [1, -6, 41], [1, 1, 43], [1, 7, 47], [1, -9, 53], [1, 8, 59], [1, 10, 61], [1, 6, 67], [1, -8, 71], [1, 13, 73], [1, -3, 79], [1, 15, 83], [1, 3, 89], [1, -7, 97], [1, -14, 101], [1, 4, 103], [1, -4, 107], [1, 2, 109], [1, -3, 113]], 'euler_factors_factorization': [[[[1, -2, 2], 1]], [1], [[[1, -3, 5], 1]], [[[1, 1], 1]], [[[1, -6, 11], 1]], [[[1, 1], 1]], [[[1, 4, 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'2.87743708330085578837178550046', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.93866594968967426469354468549', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'bad_primes': [3, 7, 13], 'central_character': '1.1', 'conductor': 819, 'conductor_radical': 273, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, 2, 3, 0, -1, 0, 0, 6, 6, 0, -1, -2, 0, -4, -4, 0, 5, 6, 0, 12, -3, 0, 4, -2, 0, -2, 5, 0, -3, -8, 0, -8, -3, 0, -4, 10, 0, 0, 6, 0, -1, 12, 0, -6, -7, 0, 1, 8, 0, -2, 9, 0, 18, 0, 0, 10, -8, 0, -10, -6, 0, -8, -3, 0, -6, -8, 0, -6, 8, 0, -13, -8, 0, 10, -6, 0, 3, -12, 0, 12, -15, 0, -12, -2, 0, 0, -3, 0, 1, -6, 0, -14, 15, 0, 7, 2, 0, 8], 'euler11': [1, -6, 11], 'euler13': [1, 1, 0], 'euler17': [1, 4, 17], 'euler19': [1, -5, 19], 'euler2': [1, -2, 2], 'euler23': [1, 3, 23], 'euler29': [1, -5, 29], 'euler3': [1, 0, 0], 'euler31': [1, 3, 31], 'euler37': [1, 4, 37], 'euler41': [1, -6, 41], 'euler43': [1, 1, 43], 'euler47': [1, 7, 47], 'euler5': [1, -3, 5], 'euler53': [1, -9, 53], 'euler59': [1, 8, 59], 'euler61': [1, 10, 61], 'euler67': [1, 6, 67], 'euler7': [1, 1, 0], 'euler71': [1, -8, 71], 'euler73': [1, 13, 73], 'euler79': [1, -3, 79], 'euler83': [1, 15, 83], 'euler89': [1, 3, 89], 'euler97': [1, -7, 97], 'euler_factors': [[1, -2, 2], [1, 0, 0], [1, -3, 5], [1, 1, 0], [1, -6, 11], [1, 1, 0], [1, 4, 17], [1, -5, 19], [1, 3, 23], [1, -5, 29], [1, 3, 31], [1, 4, 37], [1, -6, 41], [1, 1, 43], [1, 7, 47], [1, -9, 53], [1, 8, 59], [1, 10, 61], [1, 6, 67], [1, -8, 71], [1, 13, 73], [1, -3, 79], [1, 15, 83], [1, 3, 89], [1, -7, 97]], 'index': 18, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/819/f', 'ModularForm/GL2/Q/holomorphic/819/2/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/819/2/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': '2-819-1.1-c1-0-18', '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': '2-819-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 657121555018845936, 'z1': {'__RealLiteral__': 0, 'data': '1.68695310650066648413239890440', 'prec': 103}}
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lfunc_instances • Show schema
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id: 15349429
{'Lhash': '2138467118012446066859977283699', 'Lhash_array': ['2138467118012446066859977283699'], 'label': '2-819-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/a/f'}
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id: 24550670
{'Lhash': '2138467118012446066859977283699', 'Lhash_array': ['2138467118012446066859977283699'], 'label': '2-819-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/a/f/1/1'}
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id: 98722
{'Lhash': '657121555018845936', 'Lhash_array': ['657121555018845936'], 'label': '2-819-1.1-c1-0-18', 'type': 'ECQ', 'url': 'EllipticCurve/Q/819/f'}