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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1617.356', 'a10': [0.2225209339563144, 0.9749279121818236], 'a2': [0.6910626489868646, 0.7227948638273916], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.044864830350514924, 0.9989930665413147], 'a5': [0.8584487936018661, 0.5128992774059061], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.753071466003611, 0.6579387259397126], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 7.509316430172828, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [11, [1]]], 'bad_primes': [3, 7, 11], 'central_character': '1617.356', 'coeff_info': ['x^70 - 1', '0.995974293995239 + 0.0896393089034335*I', '\\\\zeta_{70}'], 'conductor': 1617, 'conductor_radical': 231, 'conjugate': 'dirichlet_L_1617.377', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 0, 'a^18', 'a^6', 0, 0, 'a^27', 0, 'a^15', 0, 0, 'a^9', 0, 0, 'a^36', 'a^66', 0, 'a^7', 'a^24', 0, 0, 'a^25', 0, 'a^12', 'a^18', 0, 0, 'a^3', 0, 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'198.32362235440564585666439052996', '198.83092150543070732816956102811', '199.797068509267574909900693647906'], 'prelabel': '1-1617-1617.356-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.509316430172828, 'root_angle': 0.3558245534287024, 'root_number': '-0.616992462327193535189093205477+0.786969060021692762761771923909*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.355824553429', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(70)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.41204124436877071867693567391+1.11714064974348908508448142004*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.44594336206', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.50660201767', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.43183798606', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 7.509316430172828, 'bad_primes': [3, 7, 11], 'central_character': '1617.356', 'conductor': 1617, 'conductor_radical': 231, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1617/356'], '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': '1-1617-1617.356-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': '1-1617-1617.356-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.509316430172828, 'root_angle': 0.3558245534287024, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.44594336206', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1617.356', 'Lhash_array': ['dirichlet_L_1617.356'], 'factors': ['1-1617-1617.356-r0-0-0'], 'label': '1-1617-1617.356-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1617/356'}
Lfunction data - 1-1617-1617.356-r0-0-0