The subject of this paper is to study the critical N-vector model in 4-ε{lunate} dimensions in one-loop order. We analyse the spectrum of anomalous dimensions of composite operators with an arbitrary number of fields and gradients. For composite operators with three elementary fields and gradients we work out the complete spectrum of anomalous dimensions, thus extending the old solution of Wilson and Kogut for two fields and gradients. In the general case we prove some properties of the spectrum, in particular a lower limit 0 + O(ε{lunate}²). Thus one-loop contributions generally improve the stability of the nontrivial fixed point in contrast to some 2 + ε{lunate} expansions. Furthermore we explicitly find conformal invariance at the nontrivial fixed point.