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lfunc_lfunctions • Show schema
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{'Lhash': '2304575852815849308922777665372', 'a10': [1.0, 1.0], 'a2': [1.0, 1.0], 'a3': [0.0, 0.0], 'a4': [0.0, 1.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, -1.0], 'a8': [0.0, 0.0], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0006253503291698, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.0, 0]]], [401, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 401], 'central_character': '2005.1202', 'coefficient_field': 'CDF', 'conductor': 2005, 'conductor_radical': 2005, 'conjugate': '1638509520491969451869060550038', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, -1.0], [0, 1.0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 1.0], [0, 1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, -2.0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 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'2.49167989300290052548453385175979', '3.16664143017195651785313608553531', '4.36086444443641520119793377362856', '5.22585919524142474087844407206266', '5.82117491680344010526795957342479', '6.51510200986283288967670550135779', '7.78353551958036844312843160141365', '8.667637977783349476637630414116942', '9.643087538873229781352202371049191'], 'prelabel': '2-2005-2005.1202-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0003126262969841, 'root_angle': -0.1762081911747834, 'root_number': '0.85065080835203993218154049706283 - 0.52573111211913360602566908484825*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.08810409558739168', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.81798979340279615411955186206', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49167989300290052548453385176', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.16664143017195651785313608554', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0006253503291698, 'bad_primes': [5, 401], 'central_character': '2005.1202', 'conductor': 2005, 'conductor_radical': 2005, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2005/1/g/a/1202/1'], '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': '2-2005-2005.1202-c0-0-3', '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': '2-2005-2005.1202-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0003126262969841, 'root_angle': -0.0881040955873917, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.81798979340279615411955186206', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2304575852815849308922777665372', 'Lhash_array': ['2304575852815849308922777665372'], 'label': '2-2005-2005.1202-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2005/1/g/a/1202/1'}