Correlations in partially filled electron and composite fermion Landau levels are studied numerically. Insight into the nature of the correlations is obtained by using model pair pseudopotentials. Energy spectra of a model short-range three-body repulsion are calculated. Moore-Read ground state at the half-filling and its quasielectron, quasihole, magnetoroton, and pair-breaking excitations are all identified. The quasielectron/quasihole excitations are described by a composite fermion model for Laughlin-correlated electron pairs. Comparison of energy spectra and wavefunction overlaps obtained for different pseudopotentials suggests that finite-size effects can be important in numerical diagonalization studies on a sphere.
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