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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_675.103', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.6946583704589973, 0.7193398003386512], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.03489949670250097, 0.9993908270190958], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.3420201433256687, 0.9396926207859084], 'a8': [-0.7431448254773942, 0.6691306063588582], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 72.5388242363719, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '675.103', 'coeff_info': ['x^180 - 1', '0.999390827019096 + 0.0348994967025010*I', '\\\\zeta_{180}'], 'conductor': 675, 'conductor_radical': 15, 'conjugate': 'dirichlet_L_675.367', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^23', 0, 'a^46', 0, 0, 'a^35', 'a^69', 0, 0, 'a^128', 0, 'a^157', 'a^58', 0, 'a^92', 'a^39', 0, 'a^114', 0, 0, 'a^151', 'a^73', 0, 0, 'a^0', 0, 'a^81', 'a^86', 0, 'a^64', 'a^115', 0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 72.5388242363719, 'bad_primes': [3, 5], 'central_character': '675.103', 'conductor': 675, 'conductor_radical': 15, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/675/103'], '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': '1-675-675.103-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': '1-675-675.103-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 72.5388242363719, 'root_angle': -0.2951851851851852, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84641219274', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_675.103', 'Lhash_array': ['dirichlet_L_675.103'], 'label': '1-675-675.103-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/675/103'}