>>881

S(a) = a + a^3 + a^4 + a^5 + a^9,

S(a~) = S(a)~
  = a^10 + a^8 + a^7 + a^6 + a^2,

S(a) + S(a)~ +1 = Σ[k=0,10] a^k = 0,

{2S(a) +1}{2S(a)~ +1} = -11,

 S(a) = {-1±(√11)i}/2,