Blue and Red - Pade Approximant (eps-1 calculated along the imaginary axis)
Other curves - Calculation directly on the real axis

In the plot: G= 1 1 1, G' = 1 1 1, q = 0
I calculated eps^-1 and simply did 1/(Re inveps + j * Im inveps) in Octave
(brutal but quick).

The comparison with HL86 is very good, and the Pade continuation regularizes
the curves significantly -> Excellent