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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1225.484', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.8584487936018661, 0.5128992774059061], 'a3': [0.9639628606958532, 0.2660368455666751], 'a4': [0.4738686624729987, -0.880595531856738], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.9639628606958532, 0.2660368455666751], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.044864830350514924, 0.9989930665413147], 'a9': [0.8584487936018661, 0.5128992774059061], 'algebraic': True, 'analytic_conductor': 5.6888760834642635, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]]], 'bad_primes': [5, 7], 'central_character': '1225.484', 'coeff_info': ['x^70 - 1', '0.995974293995239 + 0.0896393089034335*I', '\\\\zeta_{70}'], 'conductor': 1225, 'conductor_radical': 35, 'conjugate': 'dirichlet_L_1225.939', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^29', 'a^3', 'a^58', 0, 'a^32', 0, 'a^17', 'a^6', 0, 'a^64', 'a^61', 'a^1', 0, 0, 'a^46', 'a^47', 'a^35', 'a^42', 0, 0, 'a^23', 'a^9', 'a^20', 0, 'a^30', 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5.6888760834642635, 'root_angle': 0.09061224489795919, 'root_number': '0.959755291466548284273444559124+0.280837640821099603014943309489*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.045306122449', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(70)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.11439885593215762814832259182+0.208360327945903371608003638312*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.925523336374', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.95789691369', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.9518641901', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 5.6888760834642635, 'bad_primes': [5, 7], 'central_character': '1225.484', 'conductor': 1225, 'conductor_radical': 35, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1225/484'], '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': '1-35e2-1225.484-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': '1-35e2-1225.484-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.6888760834642635, 'root_angle': 0.045306122448979594, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.925523336374', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1225.484', 'Lhash_array': ['dirichlet_L_1225.484'], 'label': '1-35e2-1225.484-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1225/484'}
Lfunction data - 1-35e2-1225.484-r0-0-0