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lfunc_lfunctions • Show schema
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{'Lhash': '2579483341453165882061693546313', 'a10': [-2.7491175477465215, 2.163331110119617], 'a2': [-0.16745199268671332, 1.4042648717906636], 'a3': [-0.7071067811865476, 0.7071067811865476], 'a4': [-1.9439196602904978, -0.47029390208259725], 'a5': [1.7491175477465217, 1.7491175477465217], 'a6': [-0.8745587738732609, -1.111371652977211], 'a7': [0.0, -2.5576472913278487], 'a8': [0.9859304268504719, -2.6510264414770455], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.38328192970214603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.16745199268671332, -1.4042648717906636]]], [3, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 3], 'central_character': '48.37', 'coefficient_field': 'CDF', 'conductor': 48, 'conductor_radical': 6, 'conjugate': '5290704610155753977248473436237', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.16745199268671332, -1.4042648717906636]], [[1.0, 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.236942860055', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.03485356374126472316235332668', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.70926013905730747314928032047', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.20256932774519786608727753118', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.38328192970214603, 'bad_primes': [2, 3], 'central_character': '16.5', 'conductor': 48, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/48/2/j/a/37/2'], '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': '2-48-16.5-c1-0-0', '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': '2-48-16.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6190976737980414, 'root_angle': -0.23694286005510581, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.03485356374126472316235332668', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2579483341453165882061693546313', 'Lhash_array': ['2579483341453165882061693546313'], 'label': '2-48-16.5-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/48/2/j/a/37/2'}