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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_75.71', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.8090169943749475, 0.5877852522924731], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, 0.0], 'a8': [-0.30901699437494745, 0.9510565162951535], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 8.059869359596876, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '75.71', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 75, 'conductor_radical': 15, 'conjugate': 'dirichlet_L_75.56', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 0, 'a^2', 0, 0, 'a^0', 'a^3', 0, 0, 'a^1', 0, 'a^4', 'a^1', 0, 'a^4', 'a^3', 0, 'a^8', 0, 0, 'a^2', 'a^1', 0, 0, 'a^5', 0, 'a^2', 'a^7', 0, 'a^8', 'a^5', 0, 'a^4', 0, 0, 'a^4', 'a^9', 0, 0, 'a^9', 0, 'a^0', 'a^3', 0, 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'192.06284920668881557495388639424', '192.87964862740831060695169646480', '193.27330095287377017692121775282', '194.7244134397678989518160541439', '194.88448433706183370878287911109', '195.90313309849182744215585931511', '196.38257187349882313296336369573', '197.57267505935948472681743767870', '198.11961696651092776631491701295', '198.77497181570212594198446601405', '199.69806191184913416485216753750'], 'prelabel': '1-75-75.71-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.059869359596876, 'root_angle': 0.24000000000000002, 'root_number': '0.0627905195293133760761782245655+0.998026728428271561952336806863*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.24', 'prec': 14}, 'spectral_label': 'r1-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.59949858147666384279431930585+0.850963512057227759066853108707*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.10377499585', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.06403665724', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.09561414301', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 8.059869359596876, 'bad_primes': [3, 5], 'central_character': '75.71', 'conductor': 75, 'conductor_radical': 15, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/75/71'], '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': '1-75-75.71-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': '1-75-75.71-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.059869359596876, 'root_angle': 0.24000000000000002, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.10377499585', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_75.71', 'Lhash_array': ['dirichlet_L_75.71'], 'factors': ['1-75-75.71-r1-0-0'], 'label': '1-75-75.71-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/75/71'}
Lfunction data - 1-75-75.71-r1-0-0