  Discussed are $\pm m$ modes and $\pm m$ resonances of Dirac operators with
vector potentials $H_{\!A}= \alpha \cdot (D - A(x)) + m \beta$. Asymptotic
limits of $\pm m$ modes at infinity are derived when $|A(x)| \le C<x>^{-\rho}$,
$\rho > 1$, provided that $H_A$ has $\pm m$ modes. In wider classes of vector
potentials, sparseness of the vector potentials which give rise to the $\pm m$
modes of $H_A$ are established. It is proved that no $H_A$ has $\pm m$
resonances if $|A(x)|\le C<x>^{-\rho}$, $\rho >3/2$.
