?? trying to actually see, for example, where 4th roots of integers live in "jugendtraum" picture of elliptic function on lemniscate ... ???..... ?? or are we not guaranteed that they'll actually show up as specific values of the function, as opposed to as just some sort of weird algebraic combinations (?? "gauss sums" ???) of such values ???? .....

hmmm ... octagonal / "dihedral" orbit ... ????.....