  Fractional quantum Hall states (FQHS) with the filling factor nu = p/q of q <
21 are examined and their energies are calculated. The classical Coulomb energy
is evaluated among many electrons; that energy is linearly dependent on 1/nu.
The residual binding energies are also evaluated. The electron pair in nearest
Landau-orbitals is more affected via Coulomb transition than an electron pair
in non-nearest orbitals. Each nearest electron pair can transfer to some empty
orbital pair, but it cannot transfer to the other empty orbital pair because of
conservation of momentum. Counting the numbers of the allowed and forbidden
transitions, the binding energies are evaluated for filling factors of 126
fraction numbers. Gathering the classical Coulomb energy and the pair
transition energy, we obtain the spectrum of energy versus nu. This energy
spectrum elucidates the precise confinement of Hall resistance at specific
fractional filling factors.
