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lfunc_lfunctions • Show schema
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{'Lhash': '1478127451542169499889098156472', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.0, 2.0], 'a4': [0.0, 0.0], 'a5': [-2.0, -1.0], 'a6': [0.0, 0.0], 'a7': [2.0, 2.0], 'a8': [0.0, 0.0], 'a9': [0.0, 5.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.110425729361947, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.0, 1.0]]]], 'bad_primes': [2, 5], 'central_character': '640.63', 'coefficient_field': 'CDF', 'conductor': 640, 'conductor_radical': 10, 'conjugate': '2353853039074501971560610780215', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, -2.0], [0, 3.0]], [[1.0, 0], [2.0, 1.0]], [[1.0, 0], [-2.0, -2.0], [0, 7.0]], [[1.0, 0], [-4.0, 0], [11.0, 0]], [[1.0, 0], [-3.0, 3.0], [0, -13.0]], [[1.0, 0], [3.0, -3.0], [0, -17.0]], [[1.0, 0], [0, 0], [-19.0, 0]], [[1.0, 0], [6.0, -6.0], [0, -23.0]], [[1.0, 0], [2.0, 0], [29.0, 0]], [[1.0, 0], [0, 4.0], [-31.0, 0]], 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0.9732489894677302*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.213104095587', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16603695945558309403988358106', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.37312902068764667396529395229', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.74578683485653843943465030451', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.110425729361947, 'bad_primes': [2, 5], 'central_character': '40.3', 'conductor': 640, 'conductor_radical': 10, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/640/2/o/g/63/1'], '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': '2-640-40.3-c1-0-6', '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': '2-640-40.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.260625074921082, 'root_angle': -0.21310409558739168, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16603695945558309403988358106', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1478127451542169499889098156472', 'Lhash_array': ['1478127451542169499889098156472'], 'label': '2-640-40.3-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/640/2/o/g/63/1'}