  The energy spectra and wavefunctions of up to 14 interacting quasielectrons
(QE's) in the Laughlin nu=1/3 fractional quantum Hall (FQH) state are
investigated using exact numerical diagonalization. It is shown that at
sufficiently high density the QE's form pairs or larger clusters. This
behavior, opposite to Laughlin correlations, invalidates the (sometimes
invoked) reapplication of the composite fermion picture to the individual QE's.
The series of finite-size incompressible ground states are identified at the QE
filling factors nu_QE=1/2, 1/3, 2/3, corresponding to the electron fillings
nu=3/8, 4/11, 5/13. The equivalent quasihole (QH) states occur at nu_QH=1/4,
1/5, 2/7, corresponding to nu=3/10, 4/13, 5/17. All these six novel FQH states
were recently discovered experimentally. Detailed analysis indicates that QE or
QH correlations in these states are different from those of well-known FQH
electron states (e.g., Laughlin or Moore-Read states), leaving the origin of
their incompressibility uncertain. Halperin's idea of Laughlin states of QP
pairs is also explored, but is does not seem adequate.
