  By performing time-of-flight neutron scattering measurements on a large
amount of single crystals of Sr$_2$RuO$_4$, we studied detailed structure of
the imaginary part of the dynamic spin susceptibility over a wide range of
phase space. In the normal state at T=5 K, strong incommensurate (IC) peaks
were clearly observed at around $\mathbf{Q}_\text{c}=(0.3,0.3)$ up to at least
$\hbar\omega=80$ meV. In addition, our data also show strong magnetic
fluctuations that exist on the ridges connecting the IC peaks around the
$(\pi,\pi)$ point rather than around the $\Gamma$ point. Our results are
consistent with the semi-mean-field random phase approximation calculation for
a two dimensional Fermi liquid with a characteristic energy of 5.0 meV.
Furthermore, the IC fluctuations were observed even at room temperature.
