The data and code used to process the files and generate this and the preceeding graphs in this section  is attached to the figure.  Click on the </> Code button to view and then run the Jupyter notebook containing the Python code.

Padé fit to \(c_i\left(B\right)\)

To narrow down our choice of P and Q in Eq.\ref{eq:Pade_zero_index}  and , in addition, to determine initial values for \(\gamma_{i,p}\) and \(\kappa_{i,q}\)coefficients in Eq.\ref{eq:Pade_zero_index} , let's generate Pade approximants  (also known as rational polynomials) for functions resembling the variation of  \(y_i\left(B\right)\) with respect to magnetic field \(B\), then use those functional forms as our  first attempts at modeling \(y_i\left(B\right)\)
Padé approximants to a function can be generated from a power series expansion of that function; the 2D array of rational Padé approximants generated for various choices of P and Q is known as a Padé table.  For an example, see the sample Padé table for the exponential function \(e^z\)  posted on Wikipedia
Although Pade approximants can be calculated analytically, we will instead use the mpmath Python module to generate both the power series expansion and the corresponding Padé series. 

mpmath package

Here is an example of how to use the mpmath package to generate a series expansion  for \(e^z\) for \(z\ <1\)