  For Bloch electrons in a magnetic field, explicit solutions are obtained at
the center of the spectrum for the Bethe ansatz equations recently proposed by
Wiegmann and Zabrodin. When the magnetic flux per plaquette is $1/Q$ where $Q$
is an odd integer, distribution of the roots is uniform on the unit circle in
the complex plane. For the semi-classical limit, $ Q\rightarrow\infty$, the
wavefunction obeys the power low and is given by $|\psi(x)|^2=(2/ \sin \pi x)$
which is critical and unnormalizable. For the golden mean flux, the
distribution of roots has the exact self-similarity and the distribution
function is nowhere differentiable. The corresponding wavefunction also shows a
clear self-similar structure.
