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lfunc_lfunctions • Show schema
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{'Lhash': '1096655425467971507632290358980', 'a10': [-1.5615528128088303, 0.0], 'a2': [-1.5615528128088303, 0.0], 'a3': [0.0, 0.0], 'a4': [0.4384471871911697, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.56155281280883, 0.0], 'a8': [2.4384471871911697, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.1', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '1096655425467971507632290358980', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5615528128088303, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.56155281280883, 0], [7.0, 0]], [[1.0, 0], [-2.5615528128088303, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.5615528128088303, 0], [17.0, 0]], 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'8.350910787573878956863667662518787', '9.207299800836712096569848841156237', '9.653358587885398934409783415697513', '10.28573085179408317441480696403819'], 'prelabel': '2-585-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.865108591650197847522266697336', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.61435092927216633180023278223', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.89653316860569168523808732707', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/a/l/1/1'], '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': '2-585-1.1-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': '2-585-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.865108591650197847522266697336', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1096655425467971507632290358980', 'Lhash_array': ['1096655425467971507632290358980'], 'label': '2-585-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/a/l/1/1'}