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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_5041.18', 'a10': [-0.927525502407365, 0.3737598726240755], 'a2': [-0.8826836684021234, 0.4699675962618808], 'a3': [0.025913657990824294, -0.9996641847788359], 'a4': [0.5582609169276597, -0.82966544379713], 'a5': [0.994366641917739, 0.10599519536865329], 'a6': [0.44693621129254335, 0.8945658293471013], 'a7': [0.22621690178970905, -0.9740769545290892], 'a8': [-0.10285191975635598, 0.9946966786927722], 'a9': [-0.9986569646590692, -0.05180991158006987], 'algebraic': True, 'analytic_conductor': 23.41030558101498, 'analytic_normalization': 0, 'bad_lfactors': [[71, [1]]], 'bad_primes': [71], 'central_character': '5041.18', 'coeff_info': ['x^2485 - 1', '0.999996803485171 + 0.00252844209755057*I', '\\\\zeta_{2485}'], 'conductor': 5041, 'conductor_radical': 71, 'conjugate': 'dirichlet_L_5041.4761', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1049', 'a^1874', 'a^2098', 'a^42', 'a^438', 'a^1954', 'a^662', 'a^1263', 'a^1091', 'a^1704', 'a^1487', 'a^2146', 'a^518', 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'1-71e2-5041.18-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 23.41030558101498, 'root_angle': -0.308294839459291, 'root_number': '-0.358142139435027635191260472057-0.933667075547221608906086823416*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(2485)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.847102874586038392115846506037-0.363312300562615911582909048130*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.655307267153', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.06827072941', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.05375059427', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.41030558101498, 'bad_primes': [71], 'central_character': '5041.18', 'conductor': 5041, 'conductor_radical': 71, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5041/18'], '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': '1-71e2-5041.18-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': '1-71e2-5041.18-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 23.41030558101498, 'root_angle': -0.308294839459291, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.655307267153', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_5041.18', 'Lhash_array': ['dirichlet_L_5041.18'], 'factors': ['1-71e2-5041.18-r0-0-0'], 'label': '1-71e2-5041.18-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/5041/18'}