  The t-invariant can be considered as the Turaev-Viro invariant of order 5
computed for integer colors only. We compute all values of the t-invariant for
Seifert manifolds with base sphere and three singular fibers. As a result we
show that the manifolds parameters modulo five define the value of the
t-invariant. Partially we show that there are 12 distinct values of the
t-invariant for these manifolds. Some examples show that the t-invariant for
these manifolds is not defined by the first homology group.
