  The spin-quantum Hall (or class C) transition represents one of the few
localization-delocalization transitions for which some of the critical
exponents are known exactly. Not known, however, is the multifractal spectrum,
$\tau_q$, which describes the system-size scaling of inverse participation
ratios $P_q$, i.e., the $q$-moments of critical wavefunction amplitudes. We
here report simulations based on the class C Chalker-Coddington network and
demonstrate that $\tau_q$ is (essentially) a quartic polynomial in $q$.
Analytical results fix all prefactors except the quartic curvature that we
obtain as $\gamma=(2.22\pm{0.15})\cdot10^{-3}$. In order to achieve the
necessary accuracy in the presence of sizable corrections to scaling, we have
analyzed the evolution with system size of the entire $P_q$-distribution
function. As it turns out, in a sizable window of $q$-values this distribution
function exhibits a (single-parameter) scaling collapse already in the
pre-asymptotic regime, where finite-size corrections are {\em not} negligible.
This observation motivates us to propose a novel approach for extracting
$\tau_q$ based on concepts borrowed from the Kolmogorov-Smirnov test of
mathematical statistics. We believe that our work provides the conceptual means
for high-precision investigations of multifractal spectra also near other
localization-delocalization transitions of current interest, especially the
integer (class A) quantum Hall effect.
