A derivative nonlinear Schrodinger model is shown to support localized N-body bound states for several ranges (called bands) of the coupling constant eta. The ranges of eta within each band can be completely determined using number theoretic concepts such as Farey sequences and continued fractions. For N greater than or equal to 3, the N-body bound states can have both positive and negative momenta. For eta > 0, bound states with positive momentum have positive binding energy, while states with negative momentum have negative binding energy.