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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_529.162', 'a10': [0.6825531432186541, -0.7308359642781241], 'a2': [-0.5766803221148672, 0.816969893010442], 'a3': [-0.5766803221148672, 0.816969893010442], 'a4': [-0.33487961217098616, -0.9422609221188205], 'a5': [-0.9906859460363308, -0.1361666490962466], 'a6': [-0.33487961217098616, -0.9422609221188205], 'a7': [-0.33487961217098616, 0.9422609221188205], 'a8': [0.9629172873477992, 0.2697967711570243], 'a9': [-0.33487961217098616, -0.9422609221188205], 'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '529.162', 'coeff_info': ['x^23 - 1', '0.962917287347799 + 0.269796771157024*I', '\\\\zeta_{23}'], 'conductor': 529, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_529.369', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 'a^8', 'a^16', 'a^12', 'a^16', 'a^7', 'a^1', 'a^16', 'a^20', 'a^6', 'a^1', 'a^3', 'a^15', 'a^20', 'a^9', 'a^3', 'a^1', 'a^8', 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False, 'root_analytic_conductor': 2.4566656719613023, 'root_angle': -0.6427221172022685, 'root_number': '-0.433501513057719791235714534802-0.901152838411258402520884127266*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.321361058601', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(23)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.301164194885895208837130218075+0.389024187813341267112920771836*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.58603588192', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.52887494469', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.47032306293', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'bad_primes': [23], 'central_character': '529.162', 'conductor': 529, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/529/162'], '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': '1-23e2-529.162-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': '1-23e2-529.162-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4566656719613023, 'root_angle': -0.32136105860113423, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.58603588192', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_529.162', 'Lhash_array': ['dirichlet_L_529.162'], 'label': '1-23e2-529.162-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/529/162'}