Table 1: Results for a constant mass-energy density model ($\mu =\mu _0$) with $\bar{p}_{\rm c}=1$, $r_{\rm p}/r_{\rm e}=0.7$. Here, $\bar{p}_{\rm c}=p_{\rm c}/\mu_0$, $\bar{\Omega}=\Omega/\mu_0^{1/2}$, $\bar{M}=M \mu_0^{1/2}$, $\bar{R}_{\rm circ}={R}_{\rm circ}~\mu_0^{1/2}$ and $\bar{J}=J\mu_0$ are normalized values of the physical quantities, see Eqs.  (56, 57). Apart from the virial identities GRV2 and GRV3 in the $m{\rm th}$ order approximation, the Cols. 3-11 display the relative deviation of the specific quantity in the $m{\rm th}$ order approximation with respect to the numerical result obtained for m=24. The quantities $M_{\rm in},J_{\rm in}$ and $M_{\rm out},J_{\rm out}$ refer to the corresponding numerical values resulting from (56, 57) and (19) respectively.
  m=6 m=8 m=10 m=12 m=14 m=16 m=18 m=20 m=22
$\bar{p}_{\rm c}$ 1                  
$r_{\rm p}/r_{\rm e}$ 0.7                  
$\bar{\Omega}$ 1.41170848318 1.9e-04 1.3e-05 7.8e-07 2.9e-08 8.5e-10 4.6e-11 3.0e-12 1.3e-13 8.0e-15
$\bar{M}$ 0.135798178809 1.8e-04 3.5e-06 5.9e-08 3.4e-09 3.8e-10 2.6e-11 8.5e-13 3.3e-14 6.8e-15
$\bar{R}_{\rm circ}$ 0.345476187602 2.0e-08 1.5e-06 1.7e-08 1.8e-09 4.2e-11 1.8e-11 1.6e-12 1.1e-13 1.3e-14
$\protect\bar{J}$ 0.0140585992949 8.7e-04 6.8e-05 3.7e-06 1.2e-08 1.2e-08 6.8e-10 8.4e-12 3.5e-12 2.0e-13
$Z_{\rm p}$ 1.70735395213 3.2e-05 6.5e-06 2.4e-07 3.6e-09 4.6e-10 9.1e-12 7.1e-13 1.7e-13 1.6e-14
GRV2   7.5e-05 3.9e-06 3.9e-07 2.2e-08 8.9e-10 4.2e-11 3.1e-12 3.0e-13 7.7e-14
GRV3   1.2e-05 7.5e-06 1.2e-07 2.9e-08 1.4e-09 3.5e-11 1.3e-12 1.8e-13 6.5e-14
$\vert 1-M_{\rm in}/M_{\rm out}\vert$   2.8e-04 4.9e-06 1.9e-07 1.1e-08 4.1e-10 3.4e-12 1.5e-12 4.2e-13 2.3e-13
$\vert 1-J_{\rm in}/J_{\rm out}\vert$   1.2e-03 7.0e-05 4.1e-06 5.0e-08 1.1e-08 7.1e-10 4.6e-12 2.9e-12 1.1e-13


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