Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e))

[Gottfried]

A better view of the contours of the imaginary zeros of z=u^(1/u).
This is a plot of imag(z) for u in the right half complex (half-unit)-square.
The black lines are interpolations for the zeros of imag(z), where the sign of imag(z) changes (as far as the given computation accuracy allows).
x-axis is the real part of u, y-axis is the imaginary part of u, color is a scaling of imag(z).
The plot is a bit rough; the black lines shouldn't be dotted this way.

   

Gottfried