  We study solutions to the Dirac equation in Minkowski space
$\mathbb{R}^{1,d+1}$ that transform as $d$-dimensional conformal primary
spinors under the Lorentz group $SO(1,d+1)$. Such solutions are parameterized
by a point in $\mathbb{R}^d$ and a conformal dimension $\Delta$. The set of
wavefunctions that belong to the principal continuous series, $\Delta
=\frac{d}2 + i\nu$, with $\nu\geq 0$ and $\nu \in \mathbb{R}$ in the massive
and massless cases, respectively, form a complete basis of delta-function
normalizable solutions of the Dirac equation. In the massless case, the
conformal primary wavefunctions are related to the wavefunctions in momentum
space by a Mellin transform.
