Finding complex roots of a complex equation

Dear all,

I want to find complex roots of a complex equation.

function = -S1*(F*(I-G*S)+conjugate(F)*(S-conjugate(G))

in which S, F, G, S1 are 2*2 complex matrix.

S and S1 are known and contain complex numbers.

F(a1,a2) and G(a1,a2) are unknown in the fractional form.

I used fsolve but it has problem finding a unique answer. changing the initial values changes the answers. for the real part of a1 and a2, it is approximately correct but the imaginary parts are not correct at all. I know tha answers are a1=10+30i and a2=20-100i but the fsolves return a1=9.9+.02i and a2=16+13i for exemple.

Is there any solution for this ?

Thanks

[Alan Stevens]

Upload the values of S, F, G and S1.

[Forgo_napar]

I modified my question and attached a txt file that contains all.