between the input values of the data set and the 1$\sigma$-confidence interval for the obtained solution.

  parameter                                   values
  ------------------------------------------ --------
  mass $M$ \[$M_\odot$\]                       1.63
  metallicity $Z$                             0.016
  initial hydrogen abundance $X_i$             0.71
  mixing length parameter $\alpha_{MLT}$       1.8
  step core overshooting $\alpha_{ov}$         0.18
  mixing coefficient $D$ \[$cm^2 s^{-1}$\]     0.8
  $T_{\rm eff}$ \[K\]                          7047
  $\log g$ \[dex\]                             4.34
  $[M/H]$ \[dex\]                             0.094
  $v_{\rm eq}$ \[km$\rm s^{-1}$\]             69.38
  $f_{\rm rot}$ \[$\rm d^{-1}$\]              0.674
  $\Delta\Pi_{l=1}$ \[$s$\]                   3186.5
  central hydrogen abundance $X_c$            0.357

  : \[tab:synth\] The parameter values of the simulated period spacing pattern. *Top:* the input parameters of the MESA evolution track. *Bottom:* the parameters of the model for which the pulsation periods were computed.

![\[fig:synth\_obsfit\] *Top:* the input period spacing pattern (black dots and grey triangles) with the best-fitting pattern (white squares) as obtained from the $\chi^2$-minimisation in Fig.\[fig:synth\_chi2\_2d\] assuming ($l$,$m$) = (1,1). The black part of the input patterns was used to determine $f_{rot}$ and $\Delta\Pi_{l}$, while the grey section was excluded. *Bottom:* the residuals of the fit.](synth_obsfit2.pdf){width="88mm"}

![\[fig:synth\_chi2\] The best $\chi^2$-values for the synthetic data shown in Fig.\[tab:synth\] for each ($l,m$)-combination, as a function of the asymptotic spacing $\Delta\Pi_l$. The black and light grey lines correspond to $l=1$ and $l=2$ respectively, while 