I have the function
$$ F(\omega)=\frac{\cos \left(a \sqrt{\omega }\right)+\cosh \left(a \sqrt{\omega }\right)}{\cos \left(\sqrt{\omega }\right) \cosh \left(\sqrt{\omega }\right)-1} \,. $$
where a is a constant value $$0<a<1$$ It should be noted that the function is even, namely,$$F(\omega )=F(-\omega )$$ How can I find the analytical form of inverse Fourier transform?