One way of introducing the $p$-adic Riemmann zeta function is to first define a $p$-adic pseudomeasure $\zeta_p$ via interpolation. Namely, $\zeta_p$ is uniquely defined by the property that
$$\int_{\mathbb{Z}_p^{\times}} x^k \cdot \zeta_p=\left(1-p^k\right)\zeta(-k),$$
where $\zeta(-)$ is the usual zeta function. If I am not mistaken, such a pseudomeasure can be viewed as an element in $\mathbb{Q}_p[[\mathbb{Z}_p]]:=\varprojlim \mathbb{Q}_p [ \mathbb{Z}/p^n\mathbb{Z}]$.
Elements of $ \mathbb{Q}_p [ \mathbb{Z}/p^n\mathbb{Z}]$ can be described explicitely for a given $n$, i.e, one only needs to list the coefficients $c_x$ in the sum expansion $\sum_{x\in \mathbb{Z}/p^n\mathbb{Z}}c_x [x]$.
Is there some online source where I can find these coefficients (for small values of $n$)? If not, is there some easy way I could compute them myself?
These would be nice to have, because then I could do concrete computations with $\zeta_p$, and get good numerical data for conjectures. Thanks in advance!