  We investigate resonances of spin 1 bosons in a three-dimensional magnetic
quadrupole field. Complementary to the well-known positive energy resonances it
is shown that there exist short-lived, i.e. broad, negative energy resonances.
The latter are characterized by an atomic spin that is aligned antiparallel to
the local magnetic field direction. In contrast to the positive energy
resonances the lifetimes of the negative energy resonances decreases with
increasing total magnetic quantum number. We derive a mapping of the two
branches of the spectrum.
