# Zeta function universality: How to compute the shift parameter for simple functions?

I've come across Zeta function universality. For a nice function $f$ in a nice subset $U$ of the complex strip between real $0$ and $1$, one can find a real $t$, such the zeta function $\zeta$ shifted by $it$ approximates $f$:

I've plugged in $|\zeta(s+it)-f(s)|$ to an computer algebra system and varied $t$. For the $t$ I've tried (some smaller values), that absolute never got small at all $s$ in some interval I tried at once. Analytically, I doN't quite know how to find the $t$, even for simple $f$ like $\frac{1}{1-s}$ or polyomials in $s$, because sums over running $n^{-it}$ are rather mystical to me.

How to compute $t$ for $\frac{1}{1-s}$ or $2+s-3s^2$? Any finite $U$ you choose.