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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_431.174', 'a10': [-0.7349421204029338, -0.6781298398224631], 'a2': [-0.3228804047714462, -0.9464397731576093], 'a3': [0.9054482374931466, 0.4244566988758151], 'a4': [-0.7914964884292541, 0.6111737140978493], 'a5': [0.8791074610922622, -0.47662361654865226], 'a6': [0.10937120837787438, -0.9940009752399459], 'a7': [-0.06570689230570283, -0.9978389671202096], 'a8': [0.8339978178898779, 0.5517677407704459], 'a9': [0.6396730215588913, 0.768647139778532], 'algebraic': True, 'analytic_conductor': 2.0015555852841613, 'analytic_normalization': 0, 'bad_lfactors': [[431, [1]]], 'bad_primes': [431], 'central_character': '431.174', 'coeff_info': ['x^215 - 1', '0.999573005862893 + 0.0292199580804198*I', '\\\\zeta_{215}'], 'conductor': 431, 'conductor_radical': 431, 'conjugate': 'dirichlet_L_431.270', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^150', 'a^15', 'a^85', 'a^198', 'a^165', 'a^159', 'a^20', 'a^30', 'a^133', 'a^27', 'a^100', 'a^108', 'a^94', 'a^213', 'a^170', 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'1-431-431.174-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0015555852841613, 'root_angle': -0.36992539756112636, 'root_number': '0.397362974311790651002120581084-0.917661520739584679687017748498*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.184962698781', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(215)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.22322848857361620481117451465-0.530735659411538559547185031806*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.19544147112', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.19951735192', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.25700706311', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.0015555852841613, 'bad_primes': [431], 'central_character': '431.174', 'conductor': 431, 'conductor_radical': 431, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/431/174'], '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': '1-431-431.174-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': '1-431-431.174-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0015555852841613, 'root_angle': -0.18496269878056318, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19544147112', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_431.174', 'Lhash_array': ['dirichlet_L_431.174'], 'label': '1-431-431.174-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/431/174'}
Lfunction data - 1-431-431.174-r0-0-0