EOSS | Apache Shiro , RBAC , 权限管理 , Spring Boot | Security Framework library

I have to find the zero of the following equation:

This is an equation of state, and it doesn't matter a whole lot if you don't know exactly what an EoS is. With the root of the above equation I compute (among other things) the compressibility factors of a gaseous substance, Z, for different pressures and temperatures. With those solutions I can plot families of curves having pressures as abscissas, Zs as ordinates and temperatures as parameters. Beta, delta, eta and phi are constants, as well as pr and Tr.

After banging my head unsuccessfully against the Newton-Raphson method (which works fine with several other EoSs) I decided to try Scipy's root() function. To my discontent, I obtained this chart:

As one can easily perceive, this saw-toothed chart is totally flawed. I should've gotten smooth curves instead. Also, Z typically ranges between 0.25 and 2.0. Thus, Zs equal to, say, 3 or above are completely off the mark. Yet the curves with Z < 2 look OK, although highly compressed because of the scale.

Then I tried Octave's fzero() solver, and got this:

Which is exactly what I should've gotten, as those are curves with the correct/expected shape!

Here comes my question. Apparently Scipy's root() and Octave's fzero() are based on the same algorithm hybrid from MINPACK. Still, the results clearly aren't the same. Do any of you know why?

I plotted a curve of the Zs obtained by Octave (abscissas) against the ones obtained with Scipy and got this:

The points at the bottom hinting a straight line represent y = x, i.e., the points for which Octave and Scipy agreed in the solutions they presented. The other points are in total disagreement and, unfortunately, they're too many to be simply ignored.

I might always use Octave from now on since it works, but I want to keep using Python.

What's your take on this? Any suggestion?

PS: Here's the original Python code. It produces the first chart shown here.