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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1309.13', 'a10': [2.9010907910729803e-30, -1.0], 'a2': [-0.8090169943749475, -0.5877852522924731], 'a3': [-0.9510565162951535, -0.30901699437494745], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [0.5877852522924731, 0.8090169943749475], 'a6': [0.5877852522924731, 0.8090169943749475], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [0.8090169943749475, 0.5877852522924731], 'algebraic': True, 'analytic_conductor': 6.078970443473242, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]], [17, [1]]], 'bad_primes': [7, 11, 17], 'central_character': '1309.13', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 1309, 'conductor_radical': 1309, 'conjugate': 'dirichlet_L_1309.1007', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^12', 'a^11', 'a^4', 'a^3', 'a^3', 0, 'a^16', 'a^2', 'a^15', 0, 'a^15', 'a^12', 0, 'a^14', 'a^8', 0, 'a^14', 'a^6', 'a^7', 0, 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6.078970443473242, 'root_angle': 0.29099564976612086, 'root_number': '-0.254744294221701223455346426846+0.967008451132402110536043969164*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.290995649766', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.522492082082103463547994648697+0.0243875600130785789725459957912*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.1859932967', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.15141533166', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.94907899541', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 6.078970443473242, 'bad_primes': [7, 11, 17], 'central_character': '1309.13', 'conductor': 1309, 'conductor_radical': 1309, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1309/13'], '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': '1-1309-1309.13-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': '1-1309-1309.13-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.078970443473242, 'root_angle': 0.29099564976612086, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.1859932967', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1309.13', 'Lhash_array': ['dirichlet_L_1309.13'], 'factors': ['1-1309-1309.13-r0-0-0'], 'label': '1-1309-1309.13-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1309/13'}
Lfunction data - 1-1309-1309.13-r0-0-0