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lfunc_lfunctions • Show schema
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{'Lhash': '1805450235452908739661841249746', 'a10': [-0.5782385088587418, -1.2905968490868165], 'a2': [1.321466154524493, 0.5037134130100653], 'a3': [-0.7071067811865476, 0.7071067811865476], 'a4': [1.4925455951075026, 1.3312804537456375], 'a5': [-0.7071067811865476, -0.7071067811865476], 'a6': [-1.2905968490868165, 0.5782385088587418], 'a7': [0.0, 2.695289229287688], 'a8': [1.301764666989379, 2.511057297589609], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9164096485107303, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.321466154524493, -0.5037134130100653]]], [3, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 3, 5], 'central_character': '240.181', 'coefficient_field': 'CDF', 'conductor': 240, 'conductor_radical': 30, 'conjugate': '3184810528371672322233180738170', 'degree': 2, 'euler_factors': 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'root_angle': -0.41131710429438556, 'root_number': '0.2750152208353826 - 0.9614398724355391*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.205658552147', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.42424910707087048937052727043', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.42970319318287108872590293539', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.32746686241613772648610361423', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9164096485107303, 'bad_primes': [2, 3, 5], 'central_character': '16.5', 'conductor': 240, 'conductor_radical': 30, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/240/2/s/c/181/10'], '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': '2-240-16.5-c1-0-4', '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': '2-240-16.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.384344483324411, 'root_angle': -0.20565855214719278, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.42424910707087048937052727043', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1805450235452908739661841249746', 'Lhash_array': ['1805450235452908739661841249746'], 'label': '2-240-16.5-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/240/2/s/c/181/10'}