  We show that the discrete set of pair amplitudes $A_m$ introduced by Haldane
are an angular-momentum resolved generalization of the Tan two-body contact,
which parametrizes universal short-range correlations in atomic quantum gases.
The pair amplitudes provide a complete description of translation-invariant and
rotation-invariant states in the lowest Landau level (LLL), both compressible
and incompressible. To leading nontrivial order beyond the non-interacting
high-temperature limit, they are determined analytically in terms of the
Haldane pseudopotential parameters $V_m$, which provides a qualitative
description of the crossover towards incompressible ground states for different
filling factors. Moreover, we show that for contact interactions $\sim g_2
\delta^{(2)}({\bf x})$, which are scale invariant at the classical level, the
non-commutativity of the guiding center coordinates gives rise to a quantum
anomaly in the commutator $i [\hat{H}_{\rm LLL}, \hat{D}_R] = (2 + \ell
\partial_\ell) \hat{H}_{\rm LLL}$ with the dilatation operator $\hat{D}_R$ in
the LLL, which replaces the trace anomaly in the absence of a magnetic field.
The interaction-induced breaking of scale invariance gives rise to a finite
frequency shift of the breathing mode in a harmonic trap, which describes
transitions between different Landau levels, the strength of which is estimated
in terms of the relevant dimensionless coupling constant $\tilde{g}_2$.
