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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_507.128', 'a10': [-0.9485364419471455, 0.3166679938014725], 'a2': [-0.9605181116313724, -0.27821746391645263], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.8451900855437947, 0.5344658261278011], 'a5': [0.8229838658936564, -0.5680647467311558], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.3166679938014725, -0.9485364419471455], 'a8': [-0.6631226582407952, -0.7485107481711011], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.3544981014827604, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '507.128', 'coeff_info': ['x^156 - 1', '0.999188998171570 + 0.0402659401094151*I', '\\\\zeta_{156}'], 'conductor': 507, 'conductor_radical': 39, 'conjugate': 'dirichlet_L_507.305', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^85', 0, 'a^14', 'a^141', 0, 'a^125', 'a^99', 0, 'a^70', 'a^19', 0, 0, 'a^54', 0, 'a^28', 'a^8', 0, 'a^143', 'a^155', 0, 'a^104', 'a^52', 0, 'a^126', 0, 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'0.688242199052449843983744434833-0.725480995921635432522032340226*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.129191321499', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(156)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.899338824502771963682556103890-0.233392871643162426620987120937*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.10611895932', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.72793410644', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.20151914081', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.3544981014827604, 'bad_primes': [3, 13], 'central_character': '507.128', 'conductor': 507, 'conductor_radical': 39, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/507/128'], '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': '1-507-507.128-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': '1-507-507.128-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3544981014827604, 'root_angle': -0.1291913214990138, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10611895932', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_507.128', 'Lhash_array': ['dirichlet_L_507.128'], 'label': '1-507-507.128-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/507/128'}
Lfunction data - 1-507-507.128-r0-0-0