Table B.1: Exact eigenfrequencies $\omega$ for the first five g-modes of degree $\ell = 1$ , corresponding to an horizontal wavenumber $k_x = 2\pi /L_x =\pi$ (here L_x=2), in the complete case, in the anelastic approximation, and the corresponding relative errors.
Order n $\omega$ $\omega_{\hbox{\scriptsize anel}}$ rel. error

0 0.572 054 0.567 455 0.804%

1 0.363 084 0.362 606 0.132%

2 0.257 381 0.257 295 0.033%

3 0.197 644 0.197 621 0.012%

4 0.159 920 0.159 912 0.005%

**Table B.1:** Exact eigenfrequencies $\omega$ for the first five g-modes of degree $\ell = 1$ , corresponding to an horizontal wavenumber $k_x = 2\pi /L_x =\pi$ (here L_x=2), in the complete case, in the anelastic approximation, and the corresponding relative errors.
Order n	$\omega$	$\omega_{\hbox{\scriptsize anel}}$	rel. error
0	0.572 054	0.567 455	0.804%
1	0.363 084	0.362 606	0.132%
2	0.257 381	0.257 295	0.033%
3	0.197 644	0.197 621	0.012%
4	0.159 920	0.159 912	0.005%

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