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lfunc_lfunctions • Show schema
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{'Lhash': '3099538342878947189494750969587', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, -0.8660254037844386], 'a4': [0.5, -0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.5, -0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.48658838731717735, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5, 0.8660254037844386]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 13], 'central_character': '975.101', 'coefficient_field': 'CDF', 'conductor': 975, 'conductor_radical': 195, 'conjugate': '837429429326530778243932961932', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.5, 0.8660254037844386], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-1.0, 0]], 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'6.27159936783007483939384332111047', '6.87816176147505392195646336753746', '8.426514500827832571216009803274302', '8.791037834137066813027696600431649', '9.818694976065765683003596648741096', '10.51765468841867645645644145286065'], 'prelabel': '2-975-39.23-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6975588773122864, 'root_angle': 0.8374152361184667, 'root_number': '-0.87236585943566271307206279130642 + 0.48885356426140289006372607505883*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.41870761805923334', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.44510462293072115045458923242', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.50484480480085403486912670265', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.04866188662035645577902502127', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.48658838731717735, 'bad_primes': [3, 5, 13], 'central_character': '39.23', 'conductor': 975, 'conductor_radical': 195, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/975/1/x/a/101/1'], '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': '2-975-39.23-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-975-39.23-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6975588773122864, 'root_angle': 0.41870761805923334, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.44510462293072115045458923242', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3099538342878947189494750969587', 'Lhash_array': ['3099538342878947189494750969587'], 'label': '2-975-39.23-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/975/1/x/a/101/1'}