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Abstract We extend the Fermi gas approach to a class of ABJM-like necklace quiver theories without parity invariance. The resulting partition function on S 3 retains the form of an Airy function, but now includes a phase that scales as Nk in the large-N limit where k is an overall Chern-Simons level. We demonstrate the presence of this phase both analytically and numerically in the case of a three node quiver.