sqrt(exp)

[Kouznetsov]

..

I doubt about "isolated". There should be a branchpoint.

So thats something left to find out

I work with slog. I have rotated the cutlines, and I found out the \( 2\pi \mathrm{i} \) periodicity and set of logarithmic singularities (with set of cutlines, of course) at the left hand side from the cutline
   
I do not copypast here desctiption from the previous figure; the only changes: I have rorated the cutline for 90 degrees, and I add levels \( \Re(\sqrt{\exp}(z))=-3,-4,..-9 \)