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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_179.147', 'a10': [-0.8252907256929773, 0.5647080821850868], 'a2': [-0.9844653278615834, -0.17557909396732074], 'a3': [0.9776556239997144, 0.2102129417084711], 'a4': [0.9383439635232295, 0.3457030606163563], 'a5': [0.7133191714243802, -0.700839325151233], 'a6': [-0.9255590665712211, -0.37860324125370337], 'a7': [-0.32908887327600994, 0.9442989534495557], 'a8': [-0.8630688675320841, -0.5050862598575473], 'a9': [0.9116210382765418, 0.41103172939762184], 'algebraic': True, 'analytic_conductor': 0.8312725052572271, 'analytic_normalization': 0, 'bad_lfactors': [[179, [1]]], 'bad_primes': [179], 'central_character': '179.147', 'coeff_info': ['x^89 - 1', '0.997509025150764 + 0.0705389590423110*I', '\\\\zeta_{89}'], 'conductor': 179, 'conductor_radical': 179, 'conjugate': 'dirichlet_L_179.151', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^47', 'a^3', 'a^5', 'a^78', 'a^50', 'a^27', 'a^52', 'a^6', 'a^36', 'a^82', 'a^8', 'a^18', 'a^74', 'a^81', 'a^10', 'a^59', 'a^53', 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'0.997376535660364124061762231636+0.0723881628039447536154528665890*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0115310194357', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(89)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.05922490257230722975795669464+0.00357713898679146222342024406766*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.62746993044', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.52786311164', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.01778324194', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.8312725052572271, 'bad_primes': [179], 'central_character': '179.147', 'conductor': 179, 'conductor_radical': 179, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/179/147'], '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': '1-179-179.147-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': '1-179-179.147-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8312725052572271, 'root_angle': 0.011531019435743016, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.62746993044', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_179.147', 'Lhash_array': ['dirichlet_L_179.147'], 'label': '1-179-179.147-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/179/147'}
Lfunction data - 1-179-179.147-r0-0-0