  We explore the effects of the general non-minimally coupled $RF^2$-type
couplings on the holographic s-wave superconductors numerically in the
Schwarzschild-AdS background. We calculate the condensation and conductivity of
the model for the coupling parameters $a_1$ and $\beta$. We obtain that the
bigger deviations of the parameter $a_1$ from the minimal case lead to the
larger deviations of the gap frequency from the universal value $\omega_g/T_c
\approx 8$. Moreover the smaller $\beta $ and $a_1$ cause to gradually stronger
and narrower coherence peak.
