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lfunc_lfunctions • Show schema
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{'Lhash': '2552889684399529837166029632747', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, -1.8660254037844386], 'a4': [0.0, 0.0], 'a5': [2.0, -1.0], 'a6': [0.0, 0.0], 'a7': [1.8660254037844386, 3.232050807568877], 'a8': [0.0, 0.0], 'a9': [-0.6339745962155614, 0.36602540378443865], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.076110452553291, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.0, 1.0]]], [13, [[1.0, 0], [-2.0, 3.0]]]], 'bad_primes': [2, 5, 13], 'central_character': '260.137', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '1752222352714588661225088433422', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5, 1.8660254037844386], [-2.598076211353316, 1.5]], [[1.0, 0], [-2.0, 1.0]], [[1.0, 0], [-1.8660254037844386, -3.232050807568877], [-3.5, 6.06217782649107]], [[1.0, 0], [0.5980762113533159, 2.232050807568877], 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'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.35516599680618277, 'root_number': '0.43947079375096676 + 0.8982568794280928*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.177582998403', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.01387486736479624708741480889', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.10798740537627876937749113685', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.60535029183819381395175427330', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.076110452553291, 'bad_primes': [2, 5, 13], 'central_character': '65.7', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/bf/a/137/1'], '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': '2-260-65.7-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': '2-260-65.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.17758299840309139, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.01387486736479624708741480889', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2552889684399529837166029632747', 'Lhash_array': ['2552889684399529837166029632747'], 'label': '2-260-65.7-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/bf/a/137/1'}