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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_605.218', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.8844329309978143, 0.4666673232256737], 'a3': [0.9510565162951535, 0.30901699437494745], 'a4': [0.5644432188667692, 0.825471896962774], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.6969375686552934, 0.7171318047589635], 'a7': [0.9671468547019572, 0.25421833419348694], 'a8': [0.11399140989054063, 0.9934817353485502], 'a9': [0.8090169943749475, 0.5877852522924731], 'algebraic': True, 'analytic_conductor': 65.01627950074814, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]]], 'bad_primes': [5, 11], 'central_character': '605.218', 'coeff_info': ['x^220 - 1', '0.999592192828189 + 0.0285560507936963*I', '\\\\zeta_{220}'], 'conductor': 605, 'conductor_radical': 55, 'conjugate': 'dirichlet_L_605.247', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^17', 'a^11', 'a^34', 0, 'a^28', 'a^9', 'a^51', 'a^22', 0, 0, 'a^45', 'a^67', 'a^26', 0, 'a^68', 'a^173', 'a^39', 'a^146', 0, 'a^20', 0, 'a^35', 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'197.69133418361364952946039941745', '198.31638092709386985272865685544', '198.64925183652397541634454658675', '199.35329335230910805896634603323'], 'prelabel': '1-605-605.218-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 65.01627950074814, 'root_angle': 0.6138744534533159, 'root_number': '-0.350164902573586159805737675423+0.936688070280406054877215644138*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.306937226727', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(220)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.32076247843194219348425037473+1.49373170031799483049331140944*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.67637690948', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.60340367326', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.56604365292', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 65.01627950074814, 'bad_primes': [5, 11], 'central_character': '605.218', 'conductor': 605, 'conductor_radical': 55, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/605/218'], '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': '1-605-605.218-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-605-605.218-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 65.01627950074814, 'root_angle': 0.30693722672665796, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.67637690948', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_605.218', 'Lhash_array': ['dirichlet_L_605.218'], 'label': '1-605-605.218-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/605/218'}
Lfunction data - 1-605-605.218-r1-0-0