  We calculate various CFT data for the $O(N)$ vector model with the long-range
interaction, working at the next-to-leading order in the $1/N$ expansion. Our
results provide additional evidence for the existence of conformal symmetry at
the long-range fixed point, as well as the continuity of the CFT data at the
long-range to short-range crossover point $s_\star$ of the exponent parameter
$s$. We also develop the $N>1$ generalization of the recently proposed IR
duality between the long-range and the deformed short-range models, providing
further evidence for its non-perturbative validity in the entire region
$d/2<s<s_\star$.
