We are given a prime field of size $p$ (~ $2^{256}$) with generator $3$.
Define $\omega := 3^{\left(p-1\right)/T}$ where $T$ is a power of two. (so a generator of a subgroup of size $T$)
We are also given a field element $z$.
Q: Is there a way to optimally (sublinear number of operations) evaluate $\prod_{i=0}^N\left(z-\omega^i\right)$ (the value at $z$ of the polynomial that is $0$ at exactly $\omega^0, \omega^1, \ldots, \omega^N$)
We can assume that $N < T << p$.
(e.g. $x^N$ can be calculated sublinearly by repeated squaring in $\mathrm{log}N$)