  We estimated the ratios of $^{63}$Cu hyperfine coupling constants in the
double-layer high-$T_\mathrm{c}$ superconductor HgBa$_2$CaCu$_2$O$_{6+\delta}$
from the anisotropies in Cu nuclear spin-lattice relaxation rates and spin
Knight shifts to study the nature of the ultraslow fluctuations causing the
$T_2$ anomaly in the Cu nuclear spin-echo decay. The ultraslow fluctuations may
come from uniform magnetic fluctuations spread around the wave vector $q$ = 0,
otherwise the electric origins.
