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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3784.971', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.8427209586540392, -0.5383506160906824], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9714900382928674, 0.2370803777154975], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.10452846326765347, -0.9945218953682733], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.4203572283095655, 0.9073586945678649], 'algebraic': True, 'analytic_conductor': 406.64727542286107, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [11, [1]], [43, [1]]], 'bad_primes': [2, 11, 43], 'central_character': '3784.971', 'coeff_info': ['x^210 - 1', '0.999552432283503 + 0.0299154661693985*I', '\\\\zeta_{210}'], 'conductor': 3784, 'conductor_radical': 946, 'conjugate': 'dirichlet_L_3784.2611', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^124', 0, 'a^307', 0, 'a^161', 0, 'a^38', 0, 0, 0, 'a^293', 0, 'a^221', 0, 'a^92', 0, 'a^4', 0, 'a^285', 0, 'a^115', 0, 'a^194', 0, 'a^162', 0, 'a^191', 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'198.631263180541648566324552759143', '199.231436604326145911736133093104', '199.85288319895449506453994249362'], 'prelabel': '1-3784-3784.971-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 406.64727542286107, 'root_angle': -0.6721661526416347, 'root_number': '-0.514887078801304516417727897022-0.857258010218311831940302970986*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(210)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.578199507997546774397289783296-0.101723438869081848462745414312*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.15014985908', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '0.966648503013', 'prec': 47}, 'z3': {'__RealLiteral__': 0, 'data': '1.93248061751', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 406.64727542286107, 'bad_primes': [2, 11, 43], 'central_character': '3784.971', 'conductor': 3784, 'conductor_radical': 946, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3784/971'], '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': '1-3784-3784.971-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-3784-3784.971-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 406.64727542286107, 'root_angle': -0.33608307632081735, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.15014985908', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3784.971', 'Lhash_array': ['dirichlet_L_3784.971'], 'label': '1-3784-3784.971-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3784/971'}
Lfunction data - 1-3784-3784.971-r1-0-0