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A new computational strategy is proposed to approximate, with a simple but accurate expression, theMaierSaupefree energy for nematic order. Instead of the traditional approach of expanding the free energy with a truncatedTaylor series, we employ a least-squares fitting to obtain the coefficients of a polynomial expression. Both methodsare compared, and the fitting with at most five polynomial terms is shown to provide a satisfactory fitting, and togive much more accurate results than the traditional Taylor expansion. We perform the analysis in terms of thetensor order parameter, so the results are valid in uniaxial and biaxial states.