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lfunc_lfunctions • Show schema
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{'Lhash': '3568284197516516224941451897654', 'a10': 0, 'a2': 1, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': -3, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.393642085904418, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [17, [1, 1]]], 'bad_primes': [5, 17], 'central_character': '425.1', 'coefficient_field': '1.1.1.1', 'conductor': 425, 'conductor_radical': 85, 'degree': 2, 'euler_factors': [[1, -1, 2], [1, 0, 3], [1], [1, 4, 7], [1, 0, 11], [1, -2, 13], [1, 1], [1, 4, 19], [1, 4, 23], [1, -6, 29], [1, -4, 31], [1, -2, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, 6, 53], [1, 12, 59], [1, 10, 61], [1, 4, 67], [1, 4, 71], [1, -6, 73], [1, -12, 79], [1, -4, 83], [1, -10, 89], [1, 2, 97], [1, 10, 101], [1, 8, 103], [1, 8, 107], [1, -6, 109], [1, -14, 113]], 'euler_factors_factorization': [[[[1, -1, 2], 1]], [[[1, 0, 3], 1]], [1], [[[1, 4, 7], 1]], [[[1, 0, 11], 1]], [[[1, -2, 13], 1]], [[[1, 1], 1]], 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-1.132253515728792, -0.29465592905687676, 0.4758913221545283, 0.9484932877771439, 1.0160522573548596, 0.7233496642551411, 0.24005482816446802, -0.21046705611824496, -0.4402067890056214], 'positive_zeros': ['2.81487990213871067436976361734811', '3.65018359123648798290459605256286', '4.80649914207535836447968757694087', '6.17758072304443788931561074861214', '6.35152667842976526245521811088875', '8.168398023537064973431856329279317', '8.937056862978491777438433539079148', '9.761797486220196322650120602678853', '10.72578212794540769377358721235265'], 'prelabel': '2-425-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.8421840532108669, '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': 1070917116953349603, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.81487990213871067436976361735', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.65018359123648798290459605256', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.80649914207535836447968757694', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.393642085904418, 'bad_primes': [5, 17], 'central_character': '1.1', 'conductor': 425, 'conductor_radical': 85, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, -1, 0, 0, -4, -3, -3, 0, 0, 0, 2, -4, 0, -1, -1, -3, -4, 0, 0, 0, -4, 0, 0, 2, 0, 4, 6, 0, 4, 5, 0, -1, 0, 3, 2, -4, 0, 0, -6, 0, -4, 0, 0, -4, 0, 0, 9, 0, 0, -2, -6, 0, 0, 12, 0, 6, -12, 0, -10, 4, 12, 7, 0, 0, -4, 1, 0, 0, -4, 9, 6, 2, 0, 4, 0, 0, 12, 0, 9, -6, 4, 0, 0, -4, 0, 0, 10, 0, -8, 4, 0, 0, 0, 0, -2, 9, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -2, 13], 'euler17': [1, 1, 0], 'euler19': [1, 4, 19], 'euler2': [1, -1, 2], 'euler23': [1, 4, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 3], 'euler31': [1, -4, 31], 'euler37': [1, -2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, 12, 59], 'euler61': [1, 10, 61], 'euler67': [1, 4, 67], 'euler7': [1, 4, 7], 'euler71': [1, 4, 71], 'euler73': [1, -6, 73], 'euler79': [1, -12, 79], 'euler83': [1, -4, 83], 'euler89': [1, -10, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, -1, 2], [1, 0, 3], [1, 0, 0], [1, 4, 7], [1, 0, 11], [1, -2, 13], [1, 1, 0], [1, 4, 19], [1, 4, 23], [1, -6, 29], [1, -4, 31], [1, -2, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, 6, 53], [1, 12, 59], [1, 10, 61], [1, 4, 67], [1, 4, 71], [1, -6, 73], [1, -12, 79], [1, -4, 83], [1, -10, 89], [1, 2, 97]], 'index': 24, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/425/d', 'ModularForm/GL2/Q/holomorphic/425/2/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/425/2/a/d'], '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': '2-425-1.1-c1-0-24', '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': '2-425-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.8421840532108669, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1070917116953349603, 'z1': {'__RealLiteral__': 0, 'data': '2.81487990213871067436976361735', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10695351
{'Lhash': '3568284197516516224941451897654', 'Lhash_array': ['3568284197516516224941451897654'], 'label': '2-425-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/425/2/a/d'}
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id: 24549302
{'Lhash': '3568284197516516224941451897654', 'Lhash_array': ['3568284197516516224941451897654'], 'label': '2-425-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/425/2/a/d/1/1'}
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id: 23748
{'Lhash': '1070917116953349603', 'Lhash_array': ['1070917116953349603'], 'label': '2-425-1.1-c1-0-24', 'type': 'ECQ', 'url': 'EllipticCurve/Q/425/d'}