data {#subsec:synthdata}
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To illustrate our method we first analyse a simulated period spacing pattern. The simulated data were computed using the MESA and GYRE codes with the input values provided in Table \[tab:synth\], further taking ($l$,$m$) = (1,1). For the computation of the evolution track itself the influence of rotation was not taken into account. The rotation was only included in the GYRE computations using the traditional approximation module. The computed pattern is shown in Fig.\[fig:synth\_obsfit\] and the values of the pulsation periods are listed in the appendix in Table \[tab:synthP\].

The results of our analysis are shown in Figs.\[fig:synth\_obsfit\] to \[fig:synth\_chi2\_2d\]. As we can see in Fig.\[fig:synth\_obsfit\] we fitted the simulated data nicely when we excluded the dips in the pattern from the analysis and assumed ($l$,$m$) = (1,1). However, similar good results were obtained when we treated the pulsations as (2,1)-modes or (2,2)-modes during our analysis, as illustrated in Fig.\[fig:synth\_chi2\]. In other words, we cannot obtain a clear mode identification if we base ourselves solely on the obtained $\chi^2$-values. This problem is solved when we look back to the expected values of the asymptotic spacing $\Delta\Pi_l$ for different values of $l$, which we previously showed in Fig.\[fig:Spacing\_dist\]. 