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We present an ultra-high-precision numerical study of the spectrum ofmultifractal exponents $\Delta_q$ characterizing anomalous scaling of wavefunction moments $<|\psi|^{2q}>$ at the quantum Hall transition. The resultreads $\Delta_q = 2q(1-q)[b_0 + b_1(q-1/2)^2 + ...]$, with $b_0 = 0.1291\pm0.0002$ and $b_1 = 0.0029\pm 0.0003$. The central finding is that the spectrumis not exactly parabolic, $b_1\ne 0$. This rules out a class of theories ofWess-Zumino-Witten type proposed recently as possible conformal field theoriesof the quantum Hall critical point.

Multifractality at the quantum Hall transition: Beyond the parabolic paradigm