Are there closed forms for $\Psi(z)=\sum_{n=1}^\infty \frac{1}{3^{n^z}} $ for $z \in \Bbb N/\{1,2\} $

Question

Are there closed forms for $$ \Psi(z)=\sum_{n=1}^\infty \frac{1}{3^{n^z}} $$

for $\Psi(z)=\sum_{n=1}^\infty \frac{1}{3^{n^z}} $ for $z \in \Bbb N/\{1,2\}? $

I found closed forms for $\Psi(1)$ and $\Psi(2).$ I haven't been able to proceed for $\Psi(3)$ or larger integral values.