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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.62', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.5299192642332049, -0.848048096156426], 'a3': [0.8290375725550417, -0.5591929034707468], 'a4': [-0.4383711467890774, -0.898794046299167], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.03489949670250097, -0.9993908270190958], 'a7': [-0.9945218953682733, 0.10452846326765347], 'a8': [-0.9945218953682733, -0.10452846326765347], 'a9': [0.374606593415912, -0.9271838545667874], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.62', 'coeff_info': ['x^180 - 1', '0.999390827019096 + 0.0348994967025010*I', '\\\\zeta_{180}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.118', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^151', 'a^163', 'a^122', 0, 'a^134', 'a^87', 'a^93', 'a^146', 0, 0, 'a^105', 'a^161', 'a^58', 0, 'a^64', 'a^79', 'a^117', 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'-0.742753290907561785944590493448+0.669565193872849766428363456250*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.383240235767', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(180)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.806085907540532516135072223563-0.974048023496277815763913822249*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.36808757645', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.77217289534', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.45988924133', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.62', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/62'], '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': '1-1045-1045.62-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': '1-1045-1045.62-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.38324023576719085, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.36808757645', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.62', 'Lhash_array': ['dirichlet_L_1045.62'], 'factors': ['1-1045-1045.62-r0-0-0'], 'label': '1-1045-1045.62-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/62'}
Lfunction data - 1-1045-1045.62-r0-0-0