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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_143.103', 'a10': [1.0, 0.0], 'a2': [-0.30901699437494745, -0.9510565162951535], 'a3': [-0.8090169943749475, -0.5877852522924731], 'a4': [-0.8090169943749475, 0.5877852522924731], 'a5': [-0.30901699437494745, 0.9510565162951535], 'a6': [-0.30901699437494745, 0.9510565162951535], 'a7': [0.8090169943749475, -0.5877852522924731], 'a8': [0.8090169943749475, 0.5877852522924731], 'a9': [0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.103', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.25', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 'a^6', 'a^4', 'a^3', 'a^3', 'a^9', 'a^1', 'a^2', 'a^0', 0, 'a^0', 0, 'a^6', 'a^9', 'a^8', 'a^8', 'a^9', 'a^1', 'a^7', 'a^5', 0, 'a^0', 'a^7', 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{'__RealLiteral__': 0, 'data': '4.09491453266', 'prec': 44}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.103', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/103'], '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': '1-143-143.103-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': '1-143-143.103-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': -0.19621626289782826, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.0707314353', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_143.103', 'Lhash_array': ['dirichlet_L_143.103'], 'factors': ['1-143-143.103-r0-0-0'], 'label': '1-143-143.103-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/103'}