  We present an ultra-high-precision numerical study of the spectrum of
multifractal exponents $\Delta_q$ characterizing anomalous scaling of wave
function moments $<|\psi|^{2q}>$ at the quantum Hall transition. The result
reads $\Delta_q = 2q(1-q)[b_0 + b_1(q-1/2)^2 + ...]$, with $b_0 = 0.1291\pm
0.0002$ and $b_1 = 0.0029\pm 0.0003$. The central finding is that the spectrum
is not exactly parabolic, $b_1\ne 0$. This rules out a class of theories of
Wess-Zumino-Witten type proposed recently as possible conformal field theories
of the quantum Hall critical point.
