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lfunc_lfunctions • Show schema
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{'Lhash': '2009677773988538109761646476557', 'a10': [-0.05229432628661498, -6.412142103891861e-82], 'a2': [0.374606593415912, -0.6488376526466565], 'a3': [0.6691306063588582, -0.7431448254773942], 'a4': [0.21933980033865114, 0.379907678308557], 'a5': [-0.03489949670250097, -0.06044770144731418], 'a6': [-0.2315196071408462, -0.7125440834306647], 'a7': [0.0, 0.0], 'a8': [1.0778777284533778, 3.6052134978195074e-81], 'a9': [-0.10452846326765347, -0.9945218953682733], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0734888421735882, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.6691306063588582, 0.7431448254773942]]], [239, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [3, 239], 'central_character': '2151.1672', 'coefficient_field': 'CDF', 'conductor': 2151, 'conductor_radical': 717, 'conjugate': '1857672578855594341744302589848', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.374606593415912, 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'rational': False, 'root_analytic_conductor': 1.036093066366911, 'root_angle': 0.35555555555555557, 'root_number': '0.43837114678907741745273454065864 + 0.89879404629916699278229567669567*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17777777777777778', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.58535622799114614601859237730', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.93625116568905334398190775322', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65528061960915712996399414038', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0734888421735882, 'bad_primes': [3, 239], 'central_character': '2151.1672', 'conductor': 2151, 'conductor_radical': 717, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2151/1/f/b/1672/8'], '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': '2-2151-2151.1672-c0-0-10', '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': '2-2151-2151.1672-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.036093066366911, 'root_angle': 0.17777777777777778, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.58535622799114614601859237730', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2009677773988538109761646476557', 'Lhash_array': ['2009677773988538109761646476557'], 'label': '2-2151-2151.1672-c0-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2151/1/f/b/1672/8'}