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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1037.112', 'a10': [0.7253743710122876, -0.688354575693754], 'a2': [-0.9986295347545738, -0.052335956242943835], 'a3': [-0.996917333733128, 0.07845909572784494], 'a4': [0.9945218953682733, 0.10452846326765347], 'a5': [-0.688354575693754, 0.7253743710122876], 'a6': [0.9996573249755573, -0.026176948307873153], 'a7': [-0.5664062369248328, 0.8241261886220157], 'a8': [-0.9876883405951378, -0.15643446504023087], 'a9': [0.9876883405951378, -0.15643446504023087], 'algebraic': True, 'analytic_conductor': 4.81580775392036, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]], [61, [1]]], 'bad_primes': [17, 61], 'central_character': '1037.112', 'coeff_info': ['x^240 - 1', '0.999657324975557 + 0.0261769483078731*I', '\\\\zeta_{240}'], 'conductor': 1037, 'conductor_radical': 1037, 'conjugate': 'dirichlet_L_1037.250', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^122', 'a^117', 'a^4', 'a^89', 'a^239', 'a^83', 'a^126', 'a^234', 'a^211', 'a^135', 'a^121', 'a^20', 'a^205', 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[1, 'a^62'], [1, 'a^72'], [1, 'a^193'], [1, 'a^140']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1037-1037.112-r0-0-0', 'leading_term': '0.247000453063356285046185646130-0.0670608327692953016326806490302*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/1037/112', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.2559421401512743, -0.046514121946075015, -0.7394160509215613, -1.637097461406358, -2.062437421774041, -1.3823723398750516, 0.3130916386237683, 2.0006216885872563, 2.3513342253504894, 0.8728186202212768, -1.3877228226820337, -2.401532856033924, -0.7833473508454027, 2.8211842590050704, 5.9606167205888205, 6.285345743433608, 3.5732914937961904, -0.02580612140313812, -1.8905408343875165, -1.248212148436376, 0.33164380856803544, 0.7538585125259762, 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False, 'root_analytic_conductor': 4.81580775392036, 'root_angle': -0.1687743804767626, 'root_number': '0.862695653365661522560799546266-0.505723451763900681083524646381*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0843871902384', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(240)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.368752279875425778853312469274+0.0660707013098237295012120144670*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.280717667632', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.82387965407', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.93169913897', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.81580775392036, 'bad_primes': [17, 61], 'central_character': '1037.112', 'conductor': 1037, 'conductor_radical': 1037, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1037/112'], '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': '1-1037-1037.112-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': '1-1037-1037.112-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.81580775392036, 'root_angle': -0.0843871902383813, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.280717667632', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1037.112', 'Lhash_array': ['dirichlet_L_1037.112'], 'label': '1-1037-1037.112-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1037/112'}
Lfunction data - 1-1037-1037.112-r0-0-0