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lfunc_lfunctions • Show schema
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{'Lhash': '1731530922708426808312047106906', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, -0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [-1.3732841234978586, 2.3785978751259838], 'a6': [0.0, 0.0], 'a7': [-2.6451026912004223, 0.05858116595188849], '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], [0.5, 0.8660254037844386]]], [7, [[1.0, 0], [2.6451026912004223, -0.05858116595188849]]]], 'bad_primes': [2, 3, 7], 'central_character': '672.289', 'coefficient_field': 'CDF', 'conductor': 672, 'conductor_radical': 42, 'conjugate': '643511450478228035488262072911', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [1.3732841234978586, -2.3785978751259838], [-2.5, -4.330127018922194]], [[1.0, 0], [2.6451026912004223, 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'2-672-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3164513843010055, 'root_angle': 0.47277858092485103, 'root_number': '0.0854144091975565 + 0.9963455117083794*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.236389290462', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36593705110594339848532864332', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.56365676583528729550983293537', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.98123892043118129213566176476', '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': '7.2', 'conductor': 672, 'conductor_radical': 42, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/672/2/q/k/289/1'], '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': '2-672-7.2-c1-0-9', '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': '2-672-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3164513843010055, 'root_angle': 0.23638929046242552, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36593705110594339848532864332', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1731530922708426808312047106906', 'Lhash_array': ['1731530922708426808312047106906'], 'label': '2-672-7.2-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/672/2/q/k/289/1'}