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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_400.277', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.8090169943749475, 0.5877852522924731], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [2.9010907910729803e-30, -1.0], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 42.98596991785001, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '400.277', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 400, 'conductor_radical': 10, 'conjugate': 'dirichlet_L_400.13', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^22', 0, 0, 0, 'a^15', 0, 'a^24', 0, 'a^21', 0, 'a^34', 0, 0, 0, 'a^13', 0, 'a^33', 0, 'a^17', 0, 'a^21', 0, 0, 0, 'a^6', 0, 'a^17', 0, 'a^8', 0, 'a^3', 0, 0, 0, 'a^14', 0, 'a^16', 0, 'a^14', 0, 'a^0', 0, 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{'__RealLiteral__': 0, 'data': '3.35037712428', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.98596991785001, 'bad_primes': [2, 5], 'central_character': '400.277', 'conductor': 400, 'conductor_radical': 10, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/400/277'], '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': '1-20e2-400.277-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-20e2-400.277-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 42.98596991785001, 'root_angle': -0.14250000000000002, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62129384838', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_400.277', 'Lhash_array': ['dirichlet_L_400.277'], 'label': '1-20e2-400.277-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/400/277'}