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lfunc_lfunctions • Show schema
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{'Lhash': '456598313263099593160770018398', 'a10': [-3.9675513719280566, -4.255569368280518], 'a2': [-1.0343910986704326, 0.9643832510943849], 'a3': [0.5044863843382582, -1.6569530735712799], 'a4': [0.13992989001724876, -1.995098901277769], 'a5': [0.0, 4.114081582633945], 'a6': [1.0761015666415796, 2.200455729677727], 'a7': [0.0, 2.356170846470195], 'a8': [1.7792977319973156, 2.1986585867089983], 'a9': [-2.4909869760346224, -1.6718205302082778], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5453578497448506, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0343910986704326, -0.9643832510943849]]], [3, [[1.0, 0], [-0.5044863843382582, 1.6569530735712799]]], [37, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 37], 'central_character': '444.371', 'coefficient_field': 'CDF', 'conductor': 444, 'conductor_radical': 222, 'conjugate': '2905760955459017189754235651227', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21913314818386888498847005296', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84147164095032347582823344573', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5453578497448506, 'bad_primes': [2, 3, 37], 'central_character': '12.11', 'conductor': 444, 'conductor_radical': 222, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/444/2/c/c/371/6'], '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': '2-444-12.11-c1-0-2', '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': '2-444-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8829120663867578, 'root_angle': -0.4418175010042971, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.36019255872311586572816449662', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '456598313263099593160770018398', 'Lhash_array': ['456598313263099593160770018398'], 'label': '2-444-12.11-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/444/2/c/c/371/6'}