How do you build your intution in algebraic number theory ?

Generally my intuition in elementary number theory came from just numerically fiddling with python (and also elementary number theory is pretty easy so you can build intuition without much effort anyway).

But for ANT I don't know any software package to help me fiddle with algebraic number theory -- and on top that ANT is hard, so for example how does people even find results like Dirichlet's unit theorem (for an easier example, say $\mathbb{Z}[\zeta_{23}]$ is not an UFD) to be ``intuive" ?