python-control: stability_margins doesn't find gain=1 crossover frequency correctly for DT systems

stability_margins doesn’t find gain=1 crossover frequency correctly for DT systems, but it seems to mostly do so for CT systems. I think the probelm may be in how margins.poly_z_mag1_crossing is finding roots, but there were a few steps in that function I couldn’t follow, e.g. why H(z)*H(1/z)=1 implies |H(z)| = 1.

Example:

import control as ct
omegan = 2*np.pi
zeta = 0.2
plant = 1.1*ct.tf(omegan**2, [1, 2*zeta*omegan, omegan**2])
Ts = .05
plantdisc = ct.c2d(plant,Ts,'zoh')
#_ = ct.bode_plot(plant, margins=True) # gives correct gain=1 crossover freq
_ = ct.bode_plot(plantdisc, margins=True) # no gain=1/no phase margin given

As an example of what it should look like, here is Matlab:

omegan = 2*pi;
zeta = 0.2;
plant = 1.1*tf(omegan^2, [1, 2*zeta*omegan, omegan^2])
Ts = .05;
plantdisc = c2d(plant,Ts,'zoh')
margin(plantdisc)