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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2793.2081', 'a10': [0.41128710313061156, -0.9115058523116731], 'a2': [0.9801724878485438, -0.19814614319939758], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9214762118704076, -0.38843479627469474], 'a5': [0.5837436722347898, -0.8119380057158565], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.8262387743159949, -0.5633200580636221], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 12.970637470298522, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [19, [1]]], 'bad_primes': [3, 7, 19], 'central_character': '2793.2081', 'coeff_info': ['x^126 - 1', '0.998756921218922 + 0.0498458856606972*I', '\\\\zeta_{126}'], 'conductor': 2793, 'conductor_radical': 399, 'conjugate': 'dirichlet_L_2793.914', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^122', 0, 'a^118', 'a^107', 0, 0, 'a^114', 0, 'a^103', 'a^3', 0, 'a^73', 0, 0, 'a^110', 'a^71', 0, 0, 'a^99', 0, 'a^125', 'a^97', 0, 'a^88', 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'-0.425830122924125764017196166243-0.904803131300076758015978729212*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.320008941122', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(126)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.85713417802988710835902835491-0.913338399590565724472769765222*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.654766875165', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.76974483283', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.34976566345', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 12.970637470298522, 'bad_primes': [3, 7, 19], 'central_character': '2793.2081', 'conductor': 2793, 'conductor_radical': 399, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2793/2081'], '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': '1-2793-2793.2081-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': '1-2793-2793.2081-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.970637470298522, 'root_angle': -0.3200089411219241, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.654766875165', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2793.2081', 'Lhash_array': ['dirichlet_L_2793.2081'], 'factors': ['1-2793-2793.2081-r0-0-0'], 'label': '1-2793-2793.2081-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2793/2081'}
Lfunction data - 1-2793-2793.2081-r0-0-0