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lfunc_lfunctions • Show schema
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{'Lhash': '1170859487183350599506891611272', 'a10': [0.0, 0.0], 'a2': [-0.17364817766693036, -0.984807753012208], 'a3': [0.766044443118978, -0.6427876096865394], 'a4': [-0.9396926207859084, 0.3420201433256687], 'a5': [0.0, 0.0], 'a6': [-0.766044443118978, -0.6427876096865394], 'a7': [0.0, 0.0], 'a8': [0.5, 0.8660254037844386], 'a9': [2.609659603860185e-80, -3.570757855729511e-80], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.441299756484111, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.17364817766693036, 0.984807753012208]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 19], 'central_character': '2888.2555', 'coefficient_field': 'CDF', 'conductor': 2888, 'conductor_radical': 38, 'conjugate': '1915812288989815196522852004103', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.17364817766693036, 0.984807753012208]], [[1.0, 0], [-0.766044443118978, 0.6427876096865394], [0.17364817766693036, -0.984807753012208]], 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'8.414299334865891283984789439086762', '8.915282386766325044860552216062651'], 'prelabel': '2-2888-152.123-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.200541443051472, 'root_angle': 0.2468254491536717, 'root_number': '0.71412357776524019915514888281056 + 0.70001965378107273099273844971307*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.12341272457683584', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.923645274946067624005142048956', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.82641898652551433707878187510', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50341200695774901342190382091', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.441299756484111, 'bad_primes': [2, 19], 'central_character': '152.123', 'conductor': 2888, 'conductor_radical': 38, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2888/1/u/d/2555/1'], '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': '2-2888-152.123-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': '2-2888-152.123-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.200541443051472, 'root_angle': 0.12341272457683584, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.923645274946067624005142048956', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1170859487183350599506891611272', 'Lhash_array': ['1170859487183350599506891611272'], 'label': '2-2888-152.123-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2888/1/u/d/2555/1'}