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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1984.75', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.3338068592337709, -0.9426414910921784], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.6087614290087207, -0.7933533402912352], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.7771459614569709, -0.6293203910498375], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.7771459614569709, -0.6293203910498375], 'algebraic': True, 'analytic_conductor': 9.213657264973959, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [31, [1]]], 'bad_primes': [2, 31], 'central_character': '1984.75', 'coeff_info': ['x^240 - 1', '0.999657324975557 + 0.0261769483078731*I', '\\\\zeta_{240}'], 'conductor': 1984, 'conductor_radical': 62, 'conjugate': 'dirichlet_L_1984.291', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^193', 0, 'a^155', 0, 'a^214', 0, 'a^386', 0, 'a^119', 0, 'a^173', 0, 'a^348', 0, 'a^316', 0, 'a^277', 0, 'a^167', 0, 'a^426', 0, 'a^310', 0, 'a^99', 0, 'a^177', 0, 0, 0, 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'194.506472001037257778937612703642', '194.87664167024690746733698407580', '195.50229991804476594023837741465', '196.08831206551531670172505626277', '196.33626929395269752150370299233', '197.17176099252607300319600747398', '197.39610599447357132375818547438', '198.38876490650929507560158067901', '198.90833711250128032968942402867', '199.284156140605757881925689927662'], 'prelabel': '1-1984-1984.75-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.213657264973959, 'root_angle': 0.33747583662907793, 'root_number': '-0.522369108360512926786294614861+0.852719481793774138170710443762*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.337475836629', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(240)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.696943225054329052241653311256-0.540500705350433267444120839067*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.207405011954', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.18129447466', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.03820474572', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 9.213657264973959, 'bad_primes': [2, 31], 'central_character': '1984.75', 'conductor': 1984, 'conductor_radical': 62, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1984/75'], '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': '1-1984-1984.75-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': '1-1984-1984.75-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.213657264973959, 'root_angle': 0.33747583662907793, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.207405011954', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1984.75', 'Lhash_array': ['dirichlet_L_1984.75'], 'factors': ['1-1984-1984.75-r0-0-0'], 'label': '1-1984-1984.75-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1984/75'}
Lfunction data - 1-1984-1984.75-r0-0-0