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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3025.804', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.4666673232256737, -0.8844329309978143], 'a3': [-0.30901699437494745, -0.9510565162951535], 'a4': [-0.5644432188667692, -0.825471896962774], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.985353835847693, -0.17052219263262378], 'a7': [-0.8412535328311812, -0.5406408174555976], 'a8': [-0.9934817353485502, 0.11399140989054063], 'a9': [-0.8090169943749475, 0.5877852522924731], 'algebraic': True, 'analytic_conductor': 14.048040940799508, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]]], 'bad_primes': [5, 11], 'central_character': '3025.804', 'coeff_info': ['x^110 - 1', '0.998369103926136 + 0.0570888108627680*I', '\\\\zeta_{110}'], 'conductor': 3025, 'conductor_radical': 55, 'conjugate': 'dirichlet_L_3025.2344', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^91', 'a^77', 'a^72', 0, 'a^58', 'a^65', 'a^53', 'a^44', 0, 0, 'a^39', 'a^39', 'a^46', 0, 'a^34', 'a^103', 'a^25', 'a^18', 0, 'a^32', 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'198.14653961810312297793028520742', '199.08744790133982942957324591672', '199.73805704971370913554902544891'], 'prelabel': '1-55e2-3025.804-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.048040940799508, 'root_angle': -0.34677685950413223, 'root_number': '-0.571281963371870086752322802381-0.820753871953085144006373389463*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(110)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.674083899646255945706345018478-0.686662444801378834434441058195*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.61880676259', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.47645793444', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.29431414005', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 14.048040940799508, 'bad_primes': [5, 11], 'central_character': '3025.804', 'conductor': 3025, 'conductor_radical': 55, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3025/804'], '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': '1-55e2-3025.804-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': '1-55e2-3025.804-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.048040940799508, 'root_angle': -0.34677685950413223, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61880676259', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3025.804', 'Lhash_array': ['dirichlet_L_3025.804'], 'factors': ['1-55e2-3025.804-r0-0-0'], 'label': '1-55e2-3025.804-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3025/804'}
Lfunction data - 1-55e2-3025.804-r0-0-0