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lfunc_lfunctions • Show schema
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{'Lhash': '1064028175026990830527300345031', 'a10': [0.7071067811865476, 0.7071067811865476], 'a2': [0.0, 1.0], 'a3': [0.0, 0.0], 'a4': [-1.0, 0.0], 'a5': [0.7071067811865476, -0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, -1.0], 'a9': [0.0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8165966459841287, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [7, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 5, 7, 13], 'central_character': '3640.3037', 'coefficient_field': 'CDF', 'conductor': 3640, 'conductor_radical': 910, 'conjugate': '1836638447649381179685600870507', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], 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'6.96482988920740425703211835217987', '7.936522663462771561098275446536670', '8.823787920532041927444989212746832'], 'prelabel': '2-3640-3640.3037-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.347811799170837, 'root_angle': -0.582624670269284, 'root_number': '-0.25666793515702424673625248004236 - 0.96649964876466954496044216126001*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.291312335134642', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.839370229332453173968129738486', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.18719344386117848685370072742', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.68516667309838955539178839105', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8165966459841287, 'bad_primes': [2, 5, 7, 13], 'central_character': '3640.3037', 'conductor': 3640, 'conductor_radical': 910, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3640/1/cm/f/3037/2'], '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': '2-3640-3640.3037-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3640-3640.3037-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.347811799170837, 'root_angle': -0.291312335134642, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.839370229332453173968129738486', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1064028175026990830527300345031', 'Lhash_array': ['1064028175026990830527300345031'], 'label': '2-3640-3640.3037-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3640/1/cm/f/3037/2'}