I am trying to determine values of a lowpass filter by using Chebyshev polynomials. Here is a transfer function of the fifth order lowpass filter. $$H(s)=\dfrac{0.0626}{(s^2+0.1098s+0.936)(s^2+0.2873s+0.377)(s+0.1775)}$$ In the second step, I find $|\rho(j\omega)|^2$ of the filter as $|\rho(s)|^2=1-|H(s)|^2$. As a third step, I use $\rho(j\omega)$ to find $Z_{in}$ which equals to
$$Z_{in}(s)=R_1\dfrac{1-\rho(s)}{1+\rho(s)}$$ or $$Z_{in}(s)=R_1\dfrac{1+\rho(s)}{1-\rho(s)}$$
To realize second step, $s=j\omega$ then found $|\rho(s)|^2$ as shown below. $$|\rho(j\omega)|^2=\dfrac{-\omega^{10}-2.4998^8-2.187\omega^6-0.781\omega^4-0.09769\omega^2-0.996}{-\omega^{10}-2.4998^8-2.187\omega^6-0.781\omega^4-0.09769\omega^2+0.003918}$$ But I could not find the $\rho(s)$. Are my calculations true in the second step and how can I find $\rho(s)$ hence $Z_{in}(s)$?
