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lfunc_lfunctions • Show schema
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{'Lhash': '3013909004172690625946819807249', 'a10': [-5.196152422706632, 3.0], 'a2': [0.36602540378443865, -1.3660254037844386], 'a3': [0.0, 0.0], 'a4': [-1.7320508075688772, -1.0], 'a5': [-3.0, -3.0], 'a6': [0.0, 0.0], 'a7': [0.7320508075688773, 2.732050807568877], 'a8': [-2.0, 2.0], 'a9': [4.5, -7.794228634059948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.209832935378037, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.36602540378443865, 1.3660254037844386]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 13], 'central_character': '338.89', 'coefficient_field': 'CDF', 'conductor': 338, 'conductor_radical': 26, 'conjugate': '280865999954802934427442120801', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.36602540378443865, 1.3660254037844386]], [[1.0, 0], [0, 0], [-4.5, 7.794228634059948]], [[1.0, 0], [3.0, 3.0], [0, 25.0]], [[1.0, 0], [-0.7320508075688773, -2.732050807568877], [-42.4352447854375, 24.5]], 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{'__RealLiteral__': 0, 'data': '-0.41975080906', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.37755498528542697382829607215', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.02332793436250553759373833282', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.79589425395880233235867020766', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.209832935378037, 'bad_primes': [2, 13], 'central_character': '13.11', 'conductor': 338, 'conductor_radical': 26, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/338/3/f/b/89/1'], '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': '2-338-13.11-c2-0-21', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-338-13.11-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.034770656141587, 'root_angle': -0.419750809060183, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.37755498528542697382829607215', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3013909004172690625946819807249', 'Lhash_array': ['3013909004172690625946819807249'], 'label': '2-338-13.11-c2-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/338/3/f/b/89/1'}