  Universal values of dimensional effective coupling constants $g_{2k}$ that
determine nonlinear susceptibilities $\chi_{2k}$ and enter the scaling equation
of state are calculated for $n$-vector field theory within the
pseudo-$\epsilon$ expansion approach. Pseudo-$\epsilon$ expansions for $g_6$
and $g_8$ at criticality are derived for arbitrary $n$. Analogous series for
ratios $R_6 = g_6/g_4^2$ and $R_8 = g_8/g_4^3$ figuring in the equation of
state are also found and the pseudo-$\epsilon$ expansion for Wilson fixed point
location $g_{4}^*$ descending from the six-loop RG expansion for
$\beta$-function is reported. Numerical results are presented for $0 \le n \le
64$ with main attention paid to physically important cases $n = 0, 1, 2, 3$.
Pseudo-$\epsilon$ expansions for quartic and sextic couplings have rapidly
diminishing coefficients, so Pad\'e resummation turns out to be sufficient to
yield high-precision numerical estimates. Moreover, direct summation of these
series with optimal truncation gives the values of $g_4^*$ and $R_6^*$ almost
as accurate as those provided by Pad\'e technique. Pseudo-$\epsilon$ expansion
estimates for $g_8^*$ and $R_8^*$ are found to be much worse than that for the
lower-order couplings independently on the resummation method employed.
Numerical effectiveness of the pseudo-$\epsilon$ expansion approach in two
dimensions is also studied. Pseudo-$\epsilon$ expansion for $g_4^*$ originating
from the five-loop RG series for $\beta$-function of 2D $\lambda\phi^4$ field
theory is used to get numerical estimates for $n$ ranging from 0 to 64. The
approach discussed gives accurate enough values of $g_{4}^*$ down to $n = 2$
and leads to fair estimates for Ising and polymer ($n = 0$) models.
