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lfunc_lfunctions • Show schema
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{'Lhash': '3556200962682382943117110060270', 'a10': -1, 'a2': 1, 'a3': 0, 'a4': -1, 'a5': -1, 'a6': 0, 'a7': -3, 'a8': -3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.233941281861857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, 1]]], 'bad_primes': [3, 5], 'central_character': '405.1', 'coefficient_field': '1.1.1.1', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[1, -1, 2], [1], [1, 1], [1, 3, 7], [1, 2, 11], [1, 2, 13], [1, -4, 17], [1, 8, 19], [1, -3, 23], [1, 1, 29], [1, 0, 31], [1, 4, 37], [1, -5, 41], [1, 8, 43], [1, -7, 47], [1, 2, 53], [1, 14, 59], [1, -7, 61], [1, 3, 67], [1, -2, 71], [1, -4, 73], [1, 6, 79], [1, -9, 83], [1, 15, 89], [1, -2, 97], [1, 18, 101], [1, -8, 103], [1, -3, 107], [1, -5, 109], [1, 8, 113]], 'euler_factors_factorization': [[[[1, -1, 2], 1]], [1], [[[1, 1], 1]], [[[1, 3, 7], 1]], [[[1, 2, 11], 1]], [[[1, 2, 13], 1]], [[[1, -4, 17], 1]], 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-1.9886402852616463, -1.318124752851124, -0.6092871128352526, -0.08814301540826956, 0.12019687269651923, 0.029138527717417956, -0.22383785075380633, -0.43783947557166814], 'positive_zeros': ['2.80534791056945823123328757931120', '3.77402379572268668385012510927258', '4.82687436247101660115281422977376', '5.86971236166707955375003452448657', '6.84595624283791199980948871072071', '8.053933674867411547003077582597014', '9.019286204430249539319170001575054', '9.898527011341948118823413441918769', '10.77469071826085469350446623926754'], 'prelabel': '2-405-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.7983162352216746, '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': 724084082576346916, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.80534791056945823123328757931', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.77402379572268668385012510927', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.82687436247101660115281422977', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.233941281861857, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, -1, -1, 0, -3, -3, 0, -1, -2, 0, -2, -3, 0, -1, 4, 0, -8, 1, 0, -2, 3, 0, 1, -2, 0, 3, -1, 0, 0, 5, 0, 4, 3, 0, -4, -8, 0, 3, 5, 0, -8, 2, 0, 3, 7, 0, 2, 1, 0, 2, -2, 0, 2, 9, 0, -1, -14, 0, 7, 0, 0, 7, 2, 0, -3, -4, 0, 3, 2, 0, 4, -4, 0, 8, 6, 0, -6, 1, 0, 5, 9, 0, -4, -8, 0, 6, -15, 0, 6, -3, 0, 7, 8, 0, 2, 2, 0, -1], 'euler11': [1, 2, 11], 'euler13': [1, 2, 13], 'euler17': [1, -4, 17], 'euler19': [1, 8, 19], 'euler2': [1, -1, 2], 'euler23': [1, -3, 23], 'euler29': [1, 1, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, 4, 37], 'euler41': [1, -5, 41], 'euler43': [1, 8, 43], 'euler47': [1, -7, 47], 'euler5': [1, 1, 0], 'euler53': [1, 2, 53], 'euler59': [1, 14, 59], 'euler61': [1, -7, 61], 'euler67': [1, 3, 67], 'euler7': [1, 3, 7], 'euler71': [1, -2, 71], 'euler73': [1, -4, 73], 'euler79': [1, 6, 79], 'euler83': [1, -9, 83], 'euler89': [1, 15, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, -1, 2], [1, 0, 0], [1, 1, 0], [1, 3, 7], [1, 2, 11], [1, 2, 13], [1, -4, 17], [1, 8, 19], [1, -3, 23], [1, 1, 29], [1, 0, 31], [1, 4, 37], [1, -5, 41], [1, 8, 43], [1, -7, 47], [1, 2, 53], [1, 14, 59], [1, -7, 61], [1, 3, 67], [1, -2, 71], [1, -4, 73], [1, 6, 79], [1, -9, 83], [1, 15, 89], [1, -2, 97]], 'index': 15, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/405/e', 'ModularForm/GL2/Q/holomorphic/405/2/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/405/2/a/e'], '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': '2-405-1.1-c1-0-15', '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': '2-405-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.7983162352216746, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 724084082576346916, 'z1': {'__RealLiteral__': 0, 'data': '2.80534791056945823123328757931', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10599280
{'Lhash': '3556200962682382943117110060270', 'Lhash_array': ['3556200962682382943117110060270'], 'label': '2-405-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/2/a/e'}
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id: 24549246
{'Lhash': '3556200962682382943117110060270', 'Lhash_array': ['3556200962682382943117110060270'], 'label': '2-405-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/2/a/e/1/1'}
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id: 100803
{'Lhash': '724084082576346916', 'Lhash_array': ['724084082576346916'], 'label': '2-405-1.1-c1-0-15', 'type': 'ECQ', 'url': 'EllipticCurve/Q/405/e'}