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lfunc_lfunctions • Show schema
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{'Lhash': '429358897074645822409814419465', 'a10': [7.443628445876343, 1.1586864336743943], 'a2': [-1.1798661260659409, -1.6149043081749919], 'a3': [-3.4196122051613402, -3.4196122051613402], 'a4': [-1.2158318491242983, 3.8107417801072523], 'a5': [-2.6634131929687643, 2.6634131929687643], 'a6': [-1.4876618772513124, 9.557031087554352], 'a7': [-1.3590712832103564, -1.3590712832103564], 'a8': [7.588502131811515, -2.532713050365575], 'a9': [0.0, 14.387495267376806], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.7057315953000383, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.1798661260659409, 1.6149043081749919]]], [17, [[1.0, 0], [-12.574649755963359, -11.440200326692302]]]], 'bad_primes': [2, 17], 'central_character': '136.115', 'coefficient_field': 'CDF', 'conductor': 136, 'conductor_radical': 34, 'conjugate': '1773228513183614042520606685085', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1798661260659409, 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'root_analytic_conductor': 1.9250276868918115, 'root_angle': -0.15655283195938616, 'root_number': '0.8814723903868161 - 0.4722355609076391*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0782764159797', 'prec': 54}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.33870444821100034103273149945', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.12861742906176870256806945686', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.23581814149348774733774642626', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.7057315953000383, 'bad_primes': [2, 17], 'central_character': '136.115', 'conductor': 136, 'conductor_radical': 34, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/136/3/j/b/115/10'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-136-136.115-c2-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-136-136.115-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9250276868918115, 'root_angle': -0.07827641597969308, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.33870444821100034103273149945', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '429358897074645822409814419465', 'Lhash_array': ['429358897074645822409814419465'], 'label': '2-136-136.115-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/136/3/j/b/115/10'}