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lfunc_lfunctions • Show schema
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{'Lhash': '1342771137321051917628597610458', 'a10': [-4.361271153136939, 4.204780469308229], 'a2': [2.346301287119591, 1.3546376797184614], 'a3': [-0.8660254037844386, 0.5], 'a4': [2.6700864866260337, 4.624725455439368], 'a5': [-0.6180919820208903, 2.148944462232909], 'a6': [-2.7092753594369228, -3.9929843789365235e-61], 'a7': [0.0, 0.0], 'a8': [0.0, 9.049448332688991], 'a9': [0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.869004548564111, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8660254037844386, -0.5]]], [5, [[1.0, 0], [0.6180919820208903, -2.148944462232909]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '735.79', 'coefficient_field': 'CDF', 'conductor': 735, 'conductor_radical': 105, 'conjugate': '3552867525935517317436624106212', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.346301287119591, -1.3546376797184614], [1.0, 1.7320508075688772]], 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'8.208388323071605512057507227220356', '9.625176841336398959893988180604135', '10.29821574240674863512080136039205'], 'prelabel': '2-735-35.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.422602845817719, 'root_angle': -0.870506297432557, 'root_number': '-0.9183851600921008 - 0.3956876264461734*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.435253148716', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05925965489173256460656674755', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22980091733756435314805183149', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60949240775900384470358886802', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.869004548564111, 'bad_primes': [3, 5, 7], 'central_character': '35.9', 'conductor': 735, 'conductor_radical': 105, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/735/2/q/e/79/6'], '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': '2-735-35.9-c1-0-14', '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': '2-735-35.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.422602845817719, 'root_angle': -0.4352531487162785, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05925965489173256460656674755', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1342771137321051917628597610458', 'Lhash_array': ['1342771137321051917628597610458'], 'label': '2-735-35.9-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/735/2/q/e/79/6'}