  The partition function of ABJ(M) theories on the three-sphere can be regarded
as the canonical partition function of an ideal Fermi gas with a non-trivial
Hamiltonian. We propose an exact expression for the spectral determinant of
this Hamiltonian, which generalizes recent results obtained in the maximally
supersymmetric case. As a consequence, we find an exact WKB quantization
condition determining the spectrum which is in agreement with numerical
results. In addition, we investigate the factorization properties and
functional equations for our conjectured spectral determinants. These
functional equations relate the spectral determinants of ABJ theories with
consecutive ranks of gauge groups but the same Chern-Simons coupling.
