  The unknown parameters of the recently-proposed (Int J. Geom. Meth. Mod.
Phys. 1, 751 [2004]) Castro-Mahecha model of the imaginary parts (lambda_{j})
of the nontrivial Riemann zeros are the phases (alpha_{k}) and the frequency
parameter (gamma) of the Weierstrass function of fractal dimension D=3/2 and
the turning points (x_{j}) of the supersymmetric potential-squared Phi^2(x) --
which incorporates the smooth Wu-Sprung potential (Phys. Rev. E 48, 2595
[1993]), giving the average level density of the Riemann zeros. We conduct
numerical investigations to estimate/determine these parameters -- as well as a
parameter (sigma) we introduce to scale the fractal contribution. Our primary
analyses involve two sets of coupled equations: one set being of the form
Phi^{2}(x_{j}) = lambda_{j}, and the other set corresponding to the fractal
extension -- according to an ansatz of Castro and Mahecha -- of the
Comtet-Bandrauk-Campbell (CBC) quasi-classical quantization conditions for good
supersymmetry. Our analyses suggest the possibility strongly that gamma
converges to its theoretical lower bound of 1, and the possibility that all the
phases (alpha_{k}) should be set to zero. We also uncover interesting formulas
for certain fractal turning points.
