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lfunc_lfunctions • Show schema
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{'Lhash': '2263700073111293601578283634152', 'a10': [0.0, 6.928203230275509], 'a2': [0.0, 1.7320508075688772], 'a3': [0.0, 1.7320508075688772], 'a4': [1.0, 0.0], 'a5': [4.0, 0.0], 'a6': [-3.0, 0.0], 'a7': [-10.0, 0.0], 'a8': [0.0, 8.660254037844387], 'a9': [-3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5531375068536926, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, -1.7320508075688772]]], [19, [[1.0, 0], [-19.0, 0]]]], 'bad_primes': [3, 19], 'central_character': '57.37', 'coefficient_field': 'CDF', 'conductor': 57, 'conductor_radical': 57, 'conjugate': '3999091051818464053273368001597', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.7320508075688772], [-4.0, 0]], [[1.0, 0], [0, -1.7320508075688772]], [[1.0, 0], [-4.0, 0], [25.0, 0]], [[1.0, 0], [10.0, 0], [49.0, 0]], [[1.0, 0], [-10.0, 0], [121.0, 0]], [[1.0, 0], [0, 24.24871130596428], [-169.0, 0]], [[1.0, 0], [-10.0, 0], [289.0, 0]], [[1.0, 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'12.27637028248028792295121542288441', '13.39349028415373568368380864032963', '14.26780274337332871431694253017537'], 'prelabel': '2-57-19.18-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.246249375868928, 'root_angle': -0.5, 'root_number': '6.123233995736766e-17 - 1.0*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78574448882344567633074320409', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.51234070508552345571568617431', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.21793170496981181423693146114', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5531375068536926, 'bad_primes': [3, 19], 'central_character': '19.18', 'conductor': 57, 'conductor_radical': 57, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/57/3/c/a/37/2'], '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': '2-57-19.18-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-57-19.18-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.246249375868928, 'root_angle': -0.25, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.78574448882344567633074320409', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2263700073111293601578283634152', 'Lhash_array': ['2263700073111293601578283634152'], 'label': '2-57-19.18-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/57/3/c/a/37/2'}