  The fast rotating magnetized white dwarf, AE Aquarii, was observed with
Suzaku, in October 2005 and October 2006 with exposures of 53.1 and 42.4 ks,
respectively. In addition to clear spin modulation in the 0.5--10 keV band of
the XIS data at the barycentric period of 33.0769 \pm 0.0001 s, the 10--30 keV
HXD data in the second half of the 2005 observation also showed statistically
significant periodic signals at a consistent period. On that occasion, the
spin-folded HXD light curve exhibited two sharp spikes separated by about 0.2
cycles in phase, in contrast to approximately sinusoidal profiles observed in
energies below about 4 keV. The folded 4--10 keV XIS light curves are
understood as a superposition of those two types of pulse profiles. The phase
averaged 1.5--10 keV spectra can be reproduced by two thermal components with
temperatures of $2.90_{-0.16}^{+0.20}$ keV and $0.53_{-0.13}^{+0.14}$ keV, but
the 12-25 keV HXD data show a significant excess above the extrapolated model.
This excess can be explained by either a power-law model with photon index of
$1.12_{-0.62}^{+0.63}$ or a third thermal component with a temperature of
$54_{-47}^{+26}$ keV. At a distance of 102 pc, the 4--30 keV luminosities of
the thermal and the additional components become $1.7_{-0.6}^{+1.3}$ and
$5.3_{-0.3}^{+15.3} \times 10^{29}$ erg s$^{-1}$, respectively. The latter
corresponds to 0.09% of the spin down energy of the object. Possible emission
mechanisms of the hard pulsations are discussed, including in particular
non-thermal ones.
