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lfunc_lfunctions • Show schema
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{'Lhash': '2335631922910239531800242040851', 'a10': 3, 'a2': 1, 'a3': -1, 'a4': 1, 'a5': 3, 'a6': -1, 'a7': -1, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.060140372149035, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 1]], [43, [1, 1]]], 'bad_primes': [2, 3, 43], 'central_character': '258.1', 'coefficient_field': '1.1.1.1', 'conductor': 258, 'conductor_radical': 258, 'degree': 2, 'euler_factors': [[1, -1], [1, 1], [1, -3, 5], [1, 1, 7], [1, 1, 11], [1, -1, 13], [1, -4, 17], [1, -1, 19], [1, 4, 23], [1, 9, 29], [1, -2, 31], [1, -2, 37], [1, 8, 41], [1, 1], [1, 11, 47], [1, -4, 53], [1, 12, 59], [1, 0, 61], [1, -2, 67], [1, -12, 71], [1, -4, 73], [1, -14, 79], [1, -3, 83], [1, 10, 89], [1, -17, 97], [1, 6, 101], [1, 6, 103], [1, -17, 107], [1, -5, 109], [1, 3, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, 1], 1]], [[[1, -3, 5], 1]], [[[1, 1, 7], 1]], [[[1, 1, 11], 1]], [[[1, -1, 13], 1]], [[[1, -4, 17], 1]], [[[1, -1, 19], 1]], [[[1, 4, 23], 1]], [[[1, 9, 29], 1]], [[[1, -2, 31], 1]], [[[1, -2, 37], 1]], [[[1, 8, 41], 1]], [[[1, 1], 1]], [[[1, 11, 47], 1]], [[[1, -4, 53], 1]], [[[1, 12, 59], 1]], [[[1, 0, 61], 1]], [[[1, -2, 67], 1]], [[[1, -12, 71], 1]], [[[1, -4, 73], 1]], [[[1, -14, 79], 1]], [[[1, -3, 83], 1]], [[[1, 10, 89], 1]], [[[1, -17, 97], 1]], [[[1, 6, 101], 1]], [[[1, 6, 103], 1]], [[[1, -17, 107], 1]], [[[1, -5, 109], 1]], [[[1, 3, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-258-1.1-c1-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/258/2/a/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.8534601936141426, 1.85871266916048, 1.8728718294986493, 1.891377706179281, 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2.8116683538677, 3.8765315241937555, 4.334082322025197, 4.115544348257214, 3.3203656709650486, 2.1854450843640705, 1.0164187245478855, 0.10115564660818913], 'positive_zeros': ['1.84248871297006401888237448811880', '3.44011472926701267604846728864479', '5.05944331396204869879222544336168', '5.83597222229059038041503973728524', '6.57965006759949692624968813084978', '7.898097193807439752541133446540871', '9.525196116906290475153981211782820', '10.10423741400409243353873564384451', '11.12723047030870688222744658684721', '12.15247372662594913756253828027368'], 'prelabel': '2-258-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.4353189095629706, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 530923847701543212, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84248871297006401888237448812', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.44011472926701267604846728864', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.05944331396204869879222544336', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.060140372149035, 'bad_primes': [2, 3, 43], 'central_character': '1.1', 'conductor': 258, 'conductor_radical': 258, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, 3, -1, -1, 1, 1, 3, -1, -1, 1, -1, -3, 1, 4, 1, 1, 3, 1, -1, -4, -1, 4, 1, -1, -1, -9, -3, 2, 1, 1, 4, -3, 1, 2, 1, -1, 3, -8, 1, -1, -1, 3, -4, -11, -1, -6, 4, -4, 1, 4, -1, -3, -1, -1, -9, -12, -3, 0, 2, -1, 1, 3, 1, 2, 4, 4, -3, 12, 1, 4, 2, -4, 1, 1, -1, 14, 3, 1, -8, 3, 1, 12, -1, 9, -1, -10, 3, -1, -4, -2, -11, 3, -1, 17, -6, -1, 4], 'euler11': [1, 1, 11], 'euler13': [1, -1, 13], 'euler17': [1, -4, 17], 'euler19': [1, -1, 19], 'euler2': [1, -1, 0], 'euler23': [1, 4, 23], 'euler29': [1, 9, 29], 'euler3': [1, 1, 0], 'euler31': [1, -2, 31], 'euler37': [1, -2, 37], 'euler41': [1, 8, 41], 'euler43': [1, 1, 0], 'euler47': [1, 11, 47], 'euler5': [1, -3, 5], 'euler53': [1, -4, 53], 'euler59': [1, 12, 59], 'euler61': [1, 0, 61], 'euler67': [1, -2, 67], 'euler7': [1, 1, 7], 'euler71': [1, -12, 71], 'euler73': [1, -4, 73], 'euler79': [1, -14, 79], 'euler83': [1, -3, 83], 'euler89': [1, 10, 89], 'euler97': [1, -17, 97], 'euler_factors': [[1, -1, 0], [1, 1, 0], [1, -3, 5], [1, 1, 7], [1, 1, 11], [1, -1, 13], [1, -4, 17], [1, -1, 19], [1, 4, 23], [1, 9, 29], [1, -2, 31], [1, -2, 37], [1, 8, 41], [1, 1, 0], [1, 11, 47], [1, -4, 53], [1, 12, 59], [1, 0, 61], [1, -2, 67], [1, -12, 71], [1, -4, 73], [1, -14, 79], [1, -3, 83], [1, 10, 89], [1, -17, 97]], 'index': 2, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/258/e', 'ModularForm/GL2/Q/holomorphic/258/2/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/258/2/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': '2-258-1.1-c1-0-2', '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': '2-258-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.4353189095629706, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 530923847701543212, 'z1': {'__RealLiteral__': 0, 'data': '1.84248871297006401888237448812', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10119175
{'Lhash': '2335631922910239531800242040851', 'Lhash_array': ['2335631922910239531800242040851'], 'factors': ['2-258-1.1-c1-0-2'], 'label': '2-258-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/258/2/a/e'}
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id: 24548819
{'Lhash': '2335631922910239531800242040851', 'Lhash_array': ['2335631922910239531800242040851'], 'factors': ['2-258-1.1-c1-0-2'], 'label': '2-258-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/258/2/a/e/1/1'}
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id: 38336
{'Lhash': '530923847701543212', 'Lhash_array': ['530923847701543212'], 'factors': ['2-258-1.1-c1-0-2'], 'label': '2-258-1.1-c1-0-2', 'type': 'ECQ', 'url': 'EllipticCurve/Q/258/e'}