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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_177.137', 'a10': [-0.8568571761675893, -0.5155538571770217], 'a2': [0.5611870653623824, 0.8276889981568906], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.37013815533991434, 0.9289767198167914], 'a5': [-0.907575419670957, 0.4198891015602646], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.2675283385292208, -0.9635499925192229], 'a8': [-0.9766205557100867, 0.21497044021102407], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 19.021291688648628, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [59, [1]]], 'bad_primes': [3, 59], 'central_character': '177.137', 'coeff_info': ['x^58 - 1', '0.994137957154360 + 0.108119018423942*I', '\\\\zeta_{58}'], 'conductor': 177, 'conductor_radical': 177, 'conjugate': 'dirichlet_L_177.146', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 0, 'a^18', 'a^25', 0, 'a^46', 'a^27', 0, 'a^34', 'a^51', 0, 'a^28', 'a^55', 0, 'a^36', 'a^41', 0, 'a^52', 'a^43', 0, 'a^2', 'a^19', 0, 'a^50', 'a^37', 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.021291688648628, 'bad_primes': [3, 59], 'central_character': '177.137', 'conductor': 177, 'conductor_radical': 177, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/177/137'], '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': '1-177-177.137-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': '1-177-177.137-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.021291688648628, 'root_angle': -0.09020988292801177, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.411312908053', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_177.137', 'Lhash_array': ['dirichlet_L_177.137'], 'label': '1-177-177.137-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/177/137'}