It is clear that the found values for $\Delta\Pi_l$ are far too large for $l=2$. We can therefore safely identify the simulated data as (1,1)-modes, and obtain $f_{\rm
  rot} = 0.664\pm0.013\,d^{-1}$ and $\Delta\Pi_{l=1} = 3020\pm190\,s$.

It is important to exclude any significant dips in the period spacing structure from this analysis. In our technique, we do not take the influence of chemical gradients in the stellar interior into account. As shown by @Miglio2008a, these result in non-uniform deviations from the asymptotic spacing series. Because we can only observe a small part of a period spacing pattern, any non-uniform variations in the pattern will change the measured mean spacing and/or the measured slope of the pattern. This, in turn, will influence our analysis. By ignoring significant non-uniform variations in the period spacing structure, we limit their influence on the analysis, so that we obtain results which are correct within or on the order of $1\sigma$. For our simulated data set this is illustrated with the 2-dimensional $\chi^2$-distribution shown in Fig.\[fig:synth\_chi2\_2d\]. While we ignored the large dip in the period spacing structure (as seen in Fig.\[fig:synth\_obsfit\]), the remaining non-uniform variations still impacted the analysis. As a result, there is a small offset 