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lfunc_lfunctions • Show schema
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{'Lhash': '2433121599789786133711116309713', 'a10': 2, 'a2': -1, 'a3': 2, 'a4': -1, 'a5': -2, 'a6': -2, 'a7': 1, 'a8': 3, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.763329051202452, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1, -1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.1', 'coefficient_field': '1.1.1.1', 'conductor': 847, 'conductor_radical': 77, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, -2, 3], [1, 2, 5], [1, -1], [1], [1, 4, 13], [1, 4, 17], [1, 0, 19], [1, 4, 23], [1, -6, 29], [1, -10, 31], [1, 6, 37], [1, 4, 41], [1, 12, 43], [1, 10, 47], [1, 6, 53], [1, -2, 59], [1, 0, 61], [1, -8, 67], [1, 12, 71], [1, -8, 73], [1, 8, 79], [1, 0, 83], [1, 6, 89], [1, 10, 97], [1, -4, 101], [1, -14, 103], [1, 12, 107], [1, -14, 109], [1, -18, 113]], 'euler_factors_factorization': [[[[1, 1, 2], 1]], [[[1, -2, 3], 1]], [[[1, 2, 5], 1]], [[[1, -1], 1]], [1], [[[1, 4, 13], 1]], [[[1, 4, 17], 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-0.9183693775715505, -0.7923958582942507, -0.3249381068543008, 0.1969586479892337, 0.47630268212187743, 0.3517277497551442, -0.11447955306305453, -0.6450215235140397], 'positive_zeros': ['1.91939450772296709675161614005593', '3.17103530919462504679231815836915', '4.28286203006294711588571475852676', '4.94559945005359926667122742610478', '6.70583207072298392541889211635109', '7.67378178112872223010860918103407', '8.339912824949481407935374648788439', '8.572504027942197515704035369997552', '9.742618950410792459548371471550565'], 'prelabel': '2-847-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.6006401233547196, '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': 1199446253023546385, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91939450772296709675161614006', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.17103530919462504679231815837', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.28286203006294711588571475853', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.763329051202452, 'bad_primes': [7, 11], 'central_character': '1.1', 'conductor': 847, 'conductor_radical': 77, 'degree': 2, 'dirichlet_coefficients': [1, -1, 2, -1, -2, -2, 1, 3, 1, 2, 0, -2, -4, -1, -4, -1, -4, -1, 0, 2, 2, 0, -4, 6, -1, 4, -4, -1, 6, 4, 10, -5, 0, 4, -2, -1, -6, 0, -8, -6, -4, -2, -12, 0, -2, 4, -10, -2, 1, 1, -8, 4, -6, 4, 0, 3, 0, -6, 2, 4, 0, -10, 1, 7, 8, 0, 8, 4, -8, 2, -12, 3, 8, 6, -2, 0, 0, 8, -8, 2, -11, 4, 0, -2, 8, 12, 12, 0, -6, 2, -4, 4, 20, 10, 0, -10, -10, -1, 0, 1], 'euler11': [1, 0, 0], 'euler13': [1, 4, 13], 'euler17': [1, 4, 17], 'euler19': [1, 0, 19], 'euler2': [1, 1, 2], 'euler23': [1, 4, 23], 'euler29': [1, -6, 29], 'euler3': [1, -2, 3], 'euler31': [1, -10, 31], 'euler37': [1, 6, 37], 'euler41': [1, 4, 41], 'euler43': [1, 12, 43], 'euler47': [1, 10, 47], 'euler5': [1, 2, 5], 'euler53': [1, 6, 53], 'euler59': [1, -2, 59], 'euler61': [1, 0, 61], 'euler67': [1, -8, 67], 'euler7': [1, -1, 0], 'euler71': [1, 12, 71], 'euler73': [1, -8, 73], 'euler79': [1, 8, 79], 'euler83': [1, 0, 83], 'euler89': [1, 6, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 1, 2], [1, -2, 3], [1, 2, 5], [1, -1, 0], [1, 0, 0], [1, 4, 13], [1, 4, 17], [1, 0, 19], [1, 4, 23], [1, -6, 29], [1, -10, 31], [1, 6, 37], [1, 4, 41], [1, 12, 43], [1, 10, 47], [1, 6, 53], [1, -2, 59], [1, 0, 61], [1, -8, 67], [1, 12, 71], [1, -8, 73], [1, 8, 79], [1, 0, 83], [1, 6, 89], [1, 10, 97]], 'index': 37, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/847/a', 'ModularForm/GL2/Q/holomorphic/847/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/847/2/a/a'], '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': '2-847-1.1-c1-0-37', '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': '2-847-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.6006401233547196, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1199446253023546385, 'z1': {'__RealLiteral__': 0, 'data': '1.91939450772296709675161614006', 'prec': 103}}
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lfunc_instances • Show schema
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id: 15922338
{'Lhash': '2433121599789786133711116309713', 'Lhash_array': ['2433121599789786133711116309713'], 'label': '2-847-1.1-c1-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/847/2/a/a'}
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id: 24550754
{'Lhash': '2433121599789786133711116309713', 'Lhash_array': ['2433121599789786133711116309713'], 'label': '2-847-1.1-c1-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/847/2/a/a/1/1'}
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id: 98759
{'Lhash': '1199446253023546385', 'Lhash_array': ['1199446253023546385'], 'label': '2-847-1.1-c1-0-37', 'type': 'ECQ', 'url': 'EllipticCurve/Q/847/a'}