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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_648.83', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.8936326403234123, -0.44879918020046217], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.28680323271109026, -0.9579895123154889], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.0092993486406883, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '648.83', 'coeff_info': ['x^54 - 1', '0.993238357741943 + 0.116092914125230*I', '\\\\zeta_{54}'], 'conductor': 648, 'conductor_radical': 6, 'conjugate': 'dirichlet_L_648.203', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^50', 0, 'a^43', 0, 0, 0, 'a^13', 0, 'a^35', 0, 0, 0, 'a^33', 0, 'a^48', 0, 0, 0, 'a^38', 0, 'a^46', 0, 0, 0, 'a^64', 0, 'a^47', 0, 0, 0, 'a^39', 0, 'a^69', 0, 0, 0, 'a^53', 0, 'a^22', 0, 0, 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'0.268172612760637362542102394984-0.963370878615880333081185945689*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.206790123457', 'prec': 40}, 'spectral_label': 'r0-0', 'st_group': 'mu(54)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.17501347289983457870463116364-0.339773173196021152056250110078*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.790258039251', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '1.98425193055', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.02111947033', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 3.0092993486406883, 'bad_primes': [2, 3], 'central_character': '648.83', 'conductor': 648, 'conductor_radical': 6, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/648/83'], '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': '1-648-648.83-r0-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-648-648.83-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0092993486406883, 'root_angle': -0.20679012345679013, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.790258039251', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_648.83', 'Lhash_array': ['dirichlet_L_648.83'], 'factors': ['1-648-648.83-r0-0-0'], 'label': '1-648-648.83-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/648/83'}