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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_111.89', 'a10': [-0.5, -0.8660254037844386], 'a2': [0.6427876096865394, -0.766044443118978], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.17364817766693036, -0.984807753012208], 'a5': [0.3420201433256687, -0.9396926207859084], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9396926207859084, -0.3420201433256687], 'a8': [-0.8660254037844386, -0.5], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.5154818328690067, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [37, [1]]], 'bad_primes': [3, 37], 'central_character': '111.89', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 111, 'conductor_radical': 111, 'conjugate': 'dirichlet_L_111.5', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^31', 0, 'a^26', 'a^29', 0, 'a^20', 'a^21', 0, 'a^24', 'a^12', 0, 'a^35', 'a^15', 0, 'a^16', 'a^1', 0, 'a^23', 'a^19', 0, 'a^7', 'a^33', 0, 'a^22', 'a^30', 0, 'a^10', 'a^3', 0, 'a^9', 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0.5154818328690067, 'root_angle': -0.653821725854481, 'root_number': '-0.464655218301390630503789214850-0.885491687202814466754129293715*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.326910862927', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.01969060392963581075407218786-0.816087942840008723392126838564*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.17151015876', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.86869010281', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.28345031345', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.5154818328690067, 'bad_primes': [3, 37], 'central_character': '111.89', 'conductor': 111, 'conductor_radical': 111, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/111/89'], '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': '1-111-111.89-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': '1-111-111.89-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5154818328690067, 'root_angle': -0.3269108629272405, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17151015876', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_111.89', 'Lhash_array': ['dirichlet_L_111.89'], 'label': '1-111-111.89-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/111/89'}
Lfunction data - 1-111-111.89-r0-0-0