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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_100.47', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9510565162951535, 0.30901699437494745], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [2.9010907910729803e-30, -1.0], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.8090169943749475, -0.5877852522924731], 'algebraic': True, 'analytic_conductor': 0.4643980476297358, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '100.47', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 100, 'conductor_radical': 10, 'conjugate': 'dirichlet_L_100.83', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^29', 0, 0, 0, 'a^15', 0, 'a^18', 0, 'a^22', 0, 'a^3', 0, 0, 0, 'a^1', 0, 'a^16', 0, 'a^4', 0, 'a^17', 0, 0, 0, 'a^27', 0, 'a^14', 0, 'a^26', 0, 'a^11', 0, 0, 0, 'a^13', 0, 'a^12', 0, 'a^8', 0, 'a^25', 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'188.0490120012674211873957641790', '188.59322191867008377416777646792', '189.66987337694694454022006140273', '190.23986232452500846254013990140', '191.07823454056901255839761690000', '192.17655706042964703590214262688', '192.80132921695997636464854697376', '193.556507549643792044836370048725', '194.44756058628594124262294686007', '195.01801568333258364110870366158', '195.509925437835385293601091330518', '196.69605602799819064928841903775', '197.57845009063130629548147188534', '198.33654591505728374690786227219', '198.91002440887030110552999030044', '199.93457878770750330203227301852'], 'prelabel': '1-10e2-100.47-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.4643980476297358, 'root_angle': -0.02, 'root_number': '0.998026728428271561952336806863-0.0627905195293133760761782245655*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.01', 'prec': 17}, 'spectral_label': 'r0-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.863252940958366559257769804213+0.00241869751864508063235338977502*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.25220763079', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.77373672129', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.78825877237', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.4643980476297358, 'bad_primes': [2, 5], 'central_character': '100.47', 'conductor': 100, 'conductor_radical': 10, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/100/47'], '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': '1-10e2-100.47-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': '1-10e2-100.47-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.4643980476297358, 'root_angle': -0.01, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25220763079', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_100.47', 'Lhash_array': ['dirichlet_L_100.47'], 'label': '1-10e2-100.47-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/100/47'}
Lfunction data - 1-10e2-100.47-r0-0-0