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lfunc_lfunctions • Show schema
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{'Lhash': '2058758197244821825606446377867', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.04108607387354, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '3136.1', 'coefficient_field': '1.1.1.1', 'conductor': 3136, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1, -2, 5], [1], [1, 4, 11], [1, -2, 13], [1, -6, 17], [1, 8, 19], [1, 0, 23], [1, 6, 29], [1, -8, 31], [1, -2, 37], [1, 2, 41], [1, 4, 43], [1, 8, 47], [1, 6, 53], [1, 0, 59], [1, 6, 61], [1, 4, 67], [1, -8, 71], [1, 10, 73], [1, 16, 79], [1, 8, 83], [1, -6, 89], [1, -6, 97], [1, -2, 101], [1, 16, 103], [1, 12, 107], [1, -10, 109], [1, -2, 113]], 'euler_factors_factorization': [[1], [[[1, 0, 3], 1]], [[[1, -2, 5], 1]], [1], [[[1, 4, 11], 1]], [[[1, -2, 13], 1]], [[[1, -6, 17], 1]], [[[1, 8, 19], 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-0.38974598666019844, -0.768444082127792, -1.0499573666370587, -1.2245037041515507, -1.2887544007788752, -1.245939209456949, -1.1055702014231095], 'positive_zeros': ['1.62407385510972851799092712087460', '2.58182243115007516792385368987785', '3.32773603072291404011890923635258', '4.53211800578457486655010876487427', '5.47493819124631815597461836959172', '5.91740132798549001211232285062661', '6.59264336057149769206055975153916', '7.84054312303988042972335609462336', '8.227785865636410870393529644581278'], 'prelabel': '2-56e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.004106920707584, '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': 293581156173131875, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.62407385510972851799092712087', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.58182243115007516792385368988', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.32773603072291404011890923635', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.04108607387354, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 3136, 'conductor_radical': 14, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 0, 0, -3, 0, -4, 0, 2, 0, 0, 0, 6, 0, -8, 0, 0, 0, 0, 0, -1, 0, 0, 0, -6, 0, 8, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, -4, 0, -6, 0, -8, 0, 0, 0, 0, 0, -6, 0, -8, 0, 0, 0, 0, 0, -6, 0, 0, 0, 4, 0, -4, 0, 0, 0, 8, 0, -10, 0, 0, 0, 0, 0, -16, 0, 9, 0, -8, 0, 12, 0, 0, 0, 6, 0, 0, 0, 0, 0, -16, 0, 6, 0, 12, 0], 'euler11': [1, 4, 11], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 3], 'euler31': [1, -8, 31], 'euler37': [1, -2, 37], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, -2, 5], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, 6, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 0], 'euler71': [1, -8, 71], 'euler73': [1, 10, 73], 'euler79': [1, 16, 79], 'euler83': [1, 8, 83], 'euler89': [1, -6, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, -2, 5], [1, 0, 0], [1, 4, 11], [1, -2, 13], [1, -6, 17], [1, 8, 19], [1, 0, 23], [1, 6, 29], [1, -8, 31], [1, -2, 37], [1, 2, 41], [1, 4, 43], [1, 8, 47], [1, 6, 53], [1, 0, 59], [1, 6, 61], [1, 4, 67], [1, -8, 71], [1, 10, 73], [1, 16, 79], [1, 8, 83], [1, -6, 89], [1, -6, 97]], 'index': 62, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3136/p', 'ModularForm/GL2/Q/holomorphic/3136/2/a/p/1/1', 'ModularForm/GL2/Q/holomorphic/3136/2/a/p'], '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': '2-56e2-1.1-c1-0-62', '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': '2-56e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.004106920707584, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 293581156173131875, 'z1': {'__RealLiteral__': 0, 'data': '1.62407385510972851799092712087', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20278428
{'Lhash': '2058758197244821825606446377867', 'Lhash_array': ['2058758197244821825606446377867'], 'label': '2-56e2-1.1-c1-0-62', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3136/2/a/p'}
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id: 24560213
{'Lhash': '2058758197244821825606446377867', 'Lhash_array': ['2058758197244821825606446377867'], 'label': '2-56e2-1.1-c1-0-62', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3136/2/a/p/1/1'}
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id: 25319
{'Lhash': '293581156173131875', 'Lhash_array': ['293581156173131875'], 'label': '2-56e2-1.1-c1-0-62', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3136/p'}