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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_6025.4837', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.4539904997395468, 0.8910065241883679], 'a3': [-0.4539904997395468, 0.8910065241883679], 'a4': [-0.5877852522924731, -0.8090169943749475], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.5877852522924731, -0.8090169943749475], 'a7': [-0.23344536385590542, -0.9723699203976766], 'a8': [0.9876883405951378, -0.15643446504023087], 'a9': [-0.5877852522924731, -0.8090169943749475], 'algebraic': True, 'analytic_conductor': 27.979982369691584, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [241, [1]]], 'bad_primes': [5, 241], 'central_character': '6025.4837', 'coeff_info': ['x^80 - 1', '0.996917333733128 + 0.0784590957278449*I', '\\\\zeta_{80}'], 'conductor': 6025, 'conductor_radical': 1205, 'conjugate': 'dirichlet_L_6025.3048', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^26', 'a^26', 'a^52', 0, 'a^52', 'a^57', 'a^78', 'a^52', 0, 'a^61', 'a^78', 'a^23', 'a^3', 0, 'a^24', 'a^15', 'a^78', 'a^33', 0, 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False, 'root_analytic_conductor': 27.979982369691584, 'root_angle': -0.3258697825447816, 'root_number': '-0.458853051040626397323803091988-0.888512170738650212144204390907*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(80)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.480884260694420054285727440195+0.317024183380537173735645197290*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.974683779918', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.86796395627', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.50024993323', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 27.979982369691584, 'bad_primes': [5, 241], 'central_character': '6025.4837', 'conductor': 6025, 'conductor_radical': 1205, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6025/4837'], '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': '1-6025-6025.4837-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': '1-6025-6025.4837-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.979982369691584, 'root_angle': -0.3258697825447816, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.974683779918', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_6025.4837', 'Lhash_array': ['dirichlet_L_6025.4837'], 'factors': ['1-6025-6025.4837-r0-0-0'], 'label': '1-6025-6025.4837-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6025/4837'}
Lfunction data - 1-6025-6025.4837-r0-0-0