  We obtain the clustering properties and part of the structure of zeroes of
the Jain states at filling $\frac{k}{2k+1}$: they are a direct product of a
Vandermonde determinant (which has to exist for any fermionic state) and a
bosonic polynomial at filling $\frac{k}{k+1}$ which vanishes when $k+1$
particles cluster together. We show that all Jain states satisfy a "squeezing
rule" (they are "squeezed polynomials") which severely reduces the dimension of
the Hilbert space necessary to generate them. The squeezing rule also proves
the clustering conditions that these states satisfy. We compute the topological
entanglement spectrum of the Jain $\nu={2/5}$ state and compare it to both the
Coulomb ground-state and the non-unitary Gaffnian state. All three states have
very similar "low energy" structure. However, the Jain state entanglement
"edge" state counting matches both the Coulomb counting as well as two
decoupled U(1) free bosons, whereas the Gaffnian edge counting misses some of
the "edge" states of the Coulomb spectrum. The spectral decomposition as well
as the edge structure is evidence that the Jain state is universally equivalent
to the ground state of the Coulomb Hamiltonian at $\nu={2/5}$. The evidence is
much stronger than usual overlap studies which cannot meaningfully
differentiate between the Jain and Gaffnian states. We compute the entanglement
gap and present evidence that it remains constant in the thermodynamic limit.
We also analyze the dependence of the entanglement gap and overlap as we drive
the composite fermion system through a phase transition.
