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

Topological Entanglement and Clustering of Jain Hierarchy States