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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_968.171', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.30901699437494745, 0.9510565162951535], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.08557500847883974, -0.9963317308626913], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9934817353485502, -0.11399140989054063], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.8090169943749475, 0.5877852522924731], 'algebraic': True, 'analytic_conductor': 4.495373101055843, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [11, [1]]], 'bad_primes': [2, 11], 'central_character': '968.171', 'coeff_info': ['x^110 - 1', '0.998369103926136 + 0.0570888108627680*I', '\\\\zeta_{110}'], 'conductor': 968, 'conductor_radical': 22, 'conjugate': 'dirichlet_L_968.651', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^22', 0, 'a^81', 0, 'a^108', 0, 'a^44', 0, 0, 0, 'a^144', 0, 'a^103', 0, 'a^41', 0, 'a^47', 0, 'a^130', 0, 'a^145', 0, 'a^52', 0, 'a^66', 0, 'a^58', 0, 'a^109', 0, 0, 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'1.00685066150209113246408702766+0.381041905492598983787623934162*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.50039154602', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.33977650228', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.99402163545', 'prec': 44}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 4.495373101055843, 'bad_primes': [2, 11], 'central_character': '968.171', 'conductor': 968, 'conductor_radical': 22, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/968/171'], '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': '1-968-968.171-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': '1-968-968.171-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.495373101055843, 'root_angle': 0.321900826446281, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.50039154602', 'prec': 44}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_968.171', 'Lhash_array': ['dirichlet_L_968.171'], 'factors': ['1-968-968.171-r0-0-0'], 'label': '1-968-968.171-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/968/171'}