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lfunc_lfunctions • Show schema
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{'Lhash': '1432094264709029999646224573534', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.8660254037844386, -0.5], 'a4': [0.0, 0.0], 'a5': [0.1552798239510387, 0.26895254447354966], 'a6': [0.0, 0.0], 'a7': [-2.585807265625089, 0.5600007009285793], 'a8': [0.0, 0.0], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.365947015830044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.8660254037844386, 0.5]]], [7, [[1.0, 0], [2.585807265625089, -0.5600007009285793]]]], 'bad_primes': [2, 3, 7], 'central_character': '672.367', 'coefficient_field': 'CDF', 'conductor': 672, 'conductor_radical': 42, 'conjugate': '1141440158508976423350320586693', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [-0.1552798239510387, -0.26895254447354966], [-2.5, 4.330127018922194]], [[1.0, 0], [2.585807265625089, 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'10.57470810394636020709192386946250'], 'prelabel': '2-672-56.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3164513843010055, 'root_angle': 0.1573618667283241, 'root_number': '0.8802692833710617 + 0.4744744342463538*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0786809333642', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12972317802018470615619503389', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.09135533588140122629043211155', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.96403119945134201733705850344', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.365947015830044, 'bad_primes': [2, 3, 7], 'central_character': '56.3', 'conductor': 672, 'conductor_radical': 42, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/672/2/bb/a/367/5'], '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': '2-672-56.3-c1-0-8', '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': '2-672-56.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3164513843010055, 'root_angle': 0.07868093336416206, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12972317802018470615619503389', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1432094264709029999646224573534', 'Lhash_array': ['1432094264709029999646224573534'], 'label': '2-672-56.3-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/672/2/bb/a/367/5'}