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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_125.44', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.18738131458572463, -0.9822872507286887], 'a3': [-0.9685831611286311, 0.2486898871648548], 'a4': [-0.9297764858882515, -0.368124552684678], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.06279051952931337, 0.9980267284282716], 'a7': [-0.30901699437494745, 0.9510565162951535], 'a8': [-0.5358267949789967, 0.8443279255020151], 'a9': [0.8763066800438636, -0.48175367410171527], 'algebraic': True, 'analytic_conductor': 0.5804975595371697, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]]], 'bad_primes': [5], 'central_character': '125.44', 'coeff_info': ['x^50 - 1', '0.992114701314478 + 0.125333233564304*I', '\\\\zeta_{50}'], 'conductor': 125, 'conductor_radical': 5, 'conjugate': 'dirichlet_L_125.54', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^39', 'a^23', 'a^28', 0, 'a^12', 'a^15', 'a^17', 'a^46', 0, 'a^14', 'a^1', 'a^21', 'a^4', 0, 'a^6', 'a^47', 'a^35', 'a^2', 0, 'a^38', 'a^3', 'a^9', 'a^40', 0, 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'195.25979244800193200186805482698', '195.86230639898139350497197197052', '196.11635925044031445815608370287', '197.721622674237636075334706724541', '198.64929660498835205249997812532', '199.23207390124139851127217322178', '199.89297850036151742287258958665'], 'prelabel': '1-5e3-125.44-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5804975595371697, 'root_angle': 0.092, 'root_number': '0.837528040042141711038762730372+0.546394346734269086087862225261*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.092', 'prec': 17}, 'spectral_label': 'r0-0', 'st_group': 'mu(50)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.696429893756262063201369462836-0.0808100151395609646207665205793*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.71527401902', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.3270577674', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.90377666656', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.5804975595371697, 'bad_primes': [5], 'central_character': '125.44', 'conductor': 125, 'conductor_radical': 5, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/125/44'], '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': '1-5e3-125.44-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': '1-5e3-125.44-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5804975595371697, 'root_angle': 0.092, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.71527401902', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_125.44', 'Lhash_array': ['dirichlet_L_125.44'], 'factors': ['1-5e3-125.44-r0-0-0'], 'label': '1-5e3-125.44-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/125/44'}
Lfunction data - 1-5e3-125.44-r0-0-0