Isn't it just 413?

First note that $f(1)+1$ is one more than the sum of coefficients of $f$ . Since $f(f(1)+1)_{f(1)+1}$ has the coefficients of $f$ as it's digits in the same order, we only need to know the value of $f(f(1)+1)=f\left(612^{1025}+1\right)$ , and that's only $\fbox{1}$ additional value.