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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_324.155', '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': [-0.39607976603915684, 0.918216106880274], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.05814482891047583, 0.9983081582712682], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 1.5046496743203441, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '324.155', 'coeff_info': ['x^54 - 1', '0.993238357741943 + 0.116092914125230*I', '\\\\zeta_{54}'], 'conductor': 324, 'conductor_radical': 6, 'conjugate': 'dirichlet_L_324.23', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^17', 0, 'a^67', 0, 0, 0, 'a^46', 0, 'a^20', 0, 0, 0, 'a^15', 0, 'a^39', 0, 0, 0, 'a^68', 0, 'a^34', 0, 0, 0, 'a^25', 0, 'a^77', 0, 0, 0, 'a^30', 0, 'a^24', 0, 0, 0, 'a^11', 0, 'a^55', 0, 0, 0, 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'1-18e2-324.155-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5046496743203441, 'root_angle': 0.33024691358024694, 'root_number': '-0.483112599296638483215346463171+0.875558231302090850106792563259*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.33024691358', 'prec': 37}, 'spectral_label': 'r0-0', 'st_group': 'mu(54)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.829879177187660314285031690563+0.353077401538849034785472089791*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.88214327813', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '3.01796362571', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.07059986646', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 1.5046496743203441, 'bad_primes': [2, 3], 'central_character': '324.155', 'conductor': 324, 'conductor_radical': 6, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/324/155'], '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': '1-18e2-324.155-r0-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-18e2-324.155-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5046496743203441, 'root_angle': 0.33024691358024694, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.88214327813', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_324.155', 'Lhash_array': ['dirichlet_L_324.155'], 'factors': ['1-18e2-324.155-r0-0-0'], 'label': '1-18e2-324.155-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/324/155'}