Table 1: A comparison between numerical polar eigenfrequencies (Num.), adiabatic ones ( $\omega ^0_n$ ) and a WKB approximation. The numerical values were obtained using a least square method on the eigenvalues corresponding to $E = E_{{\rm m}}= 10^{-4}$ and correspond to the intersection between the eigenbranches and the imaginary axis.
n Num. $\omega ^0_n$ WKB

0 3.8167 3.8171 6.3789

1 17.6147 17.5996 19.1367

2 30.6762 30.6363 31.8945

3 43.6358 43.5575 44.6524

4 56.5614 56.4305 57.4102

5 69.4727 69.2767 70.1680

6 82.3822 82.1057 82.9258

7 95.2896 94.9228 95.6836

**Table 1:** A comparison between numerical polar eigenfrequencies (Num.), adiabatic ones ( $\omega ^0_n$ ) and a WKB approximation. The numerical values were obtained using a least square method on the eigenvalues corresponding to $E = E_{{\rm m}}= 10^{-4}$ and correspond to the intersection between the eigenbranches and the imaginary axis.
n	Num.	$\omega ^0_n$	WKB
0	3.8167	3.8171	6.3789
1	17.6147	17.5996	19.1367
2	30.6762	30.6363	31.8945
3	43.6358	43.5575	44.6524
4	56.5614	56.4305	57.4102
5	69.4727	69.2767	70.1680
6	82.3822	82.1057	82.9258
7	95.2896	94.9228	95.6836

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