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{'Lhash': 'dirichlet_L_1157.1052', 'a10': [-0.9594929736144974, -0.28173255684142967], 'a2': [0.6548607339452851, 0.7557495743542583], 'a3': [0.14231483827328514, 0.9898214418809327], 'a4': [-0.14231483827328514, 0.9898214418809327], 'a5': [-0.8412535328311812, 0.5406408174555976], 'a6': [-0.6548607339452851, 0.7557495743542583], 'a7': [0.8412535328311812, -0.5406408174555976], 'a8': [-0.8412535328311812, 0.5406408174555976], 'a9': [-0.9594929736144974, 0.28173255684142967], 'algebraic': True, 'analytic_conductor': 5.373085411076043, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]], [89, [1]]], 'bad_primes': [13, 89], 'central_character': '1157.1052', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 1157, 'conductor_radical': 1157, 'conjugate': 'dirichlet_L_1157.584', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^3', 'a^5', 'a^6', 'a^9', 'a^8', 'a^20', 'a^9', 'a^10', 'a^12', 'a^13', 'a^11', 0, 'a^1', 'a^14', 'a^12', 'a^8', 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'1-1157-1157.1052-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.373085411076043, 'root_angle': -0.3563690505327139, 'root_number': '0.436072696851013568962282216889-0.899911441788070622470723728790*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.178184525266', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(22)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.615816362870713206151079569452+0.754377220151416089602173778852*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.31717022671', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.35750105645', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.01478568034', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.373085411076043, 'bad_primes': [13, 89], 'central_character': '1157.1052', 'conductor': 1157, 'conductor_radical': 1157, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1157/1052'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-1157-1157.1052-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1157-1157.1052-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.373085411076043, 'root_angle': -0.17818452526635695, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.31717022671', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1157.1052', 'Lhash_array': ['dirichlet_L_1157.1052'], 'label': '1-1157-1157.1052-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1157/1052'}