  The Coulomb and Higgs indices of the 3d $\mathcal{N}=4$ $U(N)$ ADHM theories
can be decorated by line defect operators as the line defect correlators. We
obtain exact closed-form expressions and various non-trivial algebraic
relations for the correlators of the Wilson lines in the fundamental and
(anti)symmetric representations by means of the Hall-Littlewood expansion, the
Fermi-gas method and the residue calculation. From the large $N$ limit of the
correlators we obtain the single particle gravity indices which are expected to
encode the spectra of fluctuation modes on the gravity duals of line operators
in M2-brane SCFTs.
