Let $I^a_b : \mathbb{C} \to \mathbb{C}$ be defined as circle inversion mapping of a circle at the point $a \in \mathbb{C}$ of radius $b = \frac{1}{r}$
What happens to the zero's of the zeta function if you apply the following composition of functions?
$$I^0_2(\zeta(I^0_2(z))$$
In other words, do the various individual zero's of the zeta function get mapped to the same point in the complex plane under this composition, or do they get swapped with their complex conjugate?