  For a fixed SL(3, Z) Maass form g, we consider the family of L-functions L(g
\times u_j, s) where u_j runs over the family of Hecke-Maass cusp forms on
SL(2,Z). We obtain an estimate for the second moment of this family of
L-functions at the special points \half + it_j consistent with the Lindel\"{o}f
Hypothesis. We also obtain a similar upper bound on the sixth moment of the
family of Hecke-Maass cusp forms at these special points; this is apparently
the first occurrence of a Lindel\"{o}f-consistent estimate for a sixth power
moment of a family of GL(2) L-functions.
