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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_43.38', 'a10': [0.9555728057861407, -0.2947551744109042], 'a2': [-0.9009688679024191, -0.4338837391175581], 'a3': [0.8262387743159949, 0.5633200580636221], 'a4': [0.6234898018587335, 0.7818314824680298], 'a5': [-0.7330518718298263, 0.6801727377709194], 'a6': [-0.5, -0.8660254037844386], 'a7': [-0.5, 0.8660254037844386], 'a8': [-0.2225209339563144, -0.9749279121818236], 'a9': [0.36534102436639504, 0.9308737486442042], 'algebraic': True, 'analytic_conductor': 0.1996911604807864, 'analytic_normalization': 0, 'bad_lfactors': [[43, [1]]], 'bad_primes': [43], 'central_character': '43.38', 'coeff_info': ['x^21 - 1', '0.955572805786141 + 0.294755174410904*I', '\\\\zeta_{21}'], 'conductor': 43, 'conductor_radical': 43, 'conjugate': 'dirichlet_L_43.17', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^12', 'a^2', 'a^3', 'a^8', 'a^14', 'a^7', 'a^15', 'a^4', 'a^20', 'a^18', 'a^5', 'a^1', 'a^19', 'a^10', 'a^6', 'a^13', 'a^16', 'a^17', 'a^11', 'a^9', 'a^9', 'a^11', 'a^17', 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'198.895750442490333343476869538572', '199.65620730358843616594320031773'], 'prelabel': '1-43-43.38-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1996911604807864, 'root_angle': 0.23529652719867167, 'root_number': '0.739003817438230548234772597854+0.673701237798864679408901016093*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.117648263599', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(21)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.765587642488180835279300267880+0.152473896457911767735650636468*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.62523286656', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.75816814826', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.71548433182', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.1996911604807864, 'bad_primes': [43], 'central_character': '43.38', 'conductor': 43, 'conductor_radical': 43, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/43/38'], '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': '1-43-43.38-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': '1-43-43.38-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1996911604807864, 'root_angle': 0.11764826359933583, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.62523286656', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_43.38', 'Lhash_array': ['dirichlet_L_43.38'], 'label': '1-43-43.38-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/43/38'}
Lfunction data - 1-43-43.38-r0-0-0