handful of modes could be resolved using ground-based data, the space missions have provided us with near-continuous high S/N observations of thousands of stars on a long time base, resulting in the accurate determination of dozens to hundreds of pulsation frequencies for many targets. In particular, this has proven to be invaluable for $\gamma$Dor stars, as their gravity and/or gravito-inertial mode frequencies form a very dense spectrum in the range of 0.3 to 3$\rm
d^{-1}$. Period spacing patterns have now been detected for dozens of $\gamma$Dor stars [e.g. @Chapellier2012; @Kurtz2014; @Bedding2015; @Saio2015; @Keen2015; @VanReeth2015; @Murphy2016].

In this study we focus on the period spacing patterns detected by @VanReeth2015 in a sample of 68 $\gamma$Dor stars with spectroscopic characterisation and aim to derive the stars’ internal rotation rate and the asymptotic period spacing value of the series. This serves as a first step for future detailed analyses of differential rotation, similar to the studies which have previously been carried out in slow rotators among g-mode pulsators interpreted recently in terms of angular momentum transport by internal gravity waves [e.g., @Triana2015; @Rogers2015]. In this paper we present a grid of theoretical models, which we use as a starting point (Section \[sec:grid\]), and 