If $f$ is a polynomial of degree $k$, can we quickly compute $f(1),f(2),\dots,f(n).$ $f(x)=\left(\sum_{i=1}^k{a_ix^i}\right) \pmod P$
$P > n \gg k.$
Obviously calculating $f(1),f(2)..f(n)$ takes $O(nk)$.
So is there a faster way to speed up the process? $k$ is not very big. $k$ is only about $30.$

Thanks for your reply.In fact, both n and P are large, P>n, k is small.
I know how to use FFT to speed up multipoint evaluations of polynomials, it takes $O(nlog^2n)$.
Because k is small here, and x is 1,2,3...,n, so I guess there's a faster way to do it.
