  We prove new bounds for weighted mean values of sums involving Fourier
coefficients of cusp forms that are automorphic with respect to a Hecke
congruence subgroup \Gamma =\Gamma_0(q) of the group SL(2,Z[i]), and correspond
to exceptional eigenvalues of the Laplace operator on the space
L^2(\Gamma\SL(2,C)/SU(2)). These results are, for certain applications, an
effective substitute for the generalised Selberg eigenvalue conjecture. We give
a proof of one such application, which is an upper bound for a sum of
generalised Kloosterman sums (of significance in the study of certain mean
values of Hecke zeta-functions with groessencharakters).
  Our proofs make extensive use of Lokvenec-Guleska's generalisation of the
Bruggeman-Motohashi summation formulae for PSL(2,Z[i])\PSL(2,C). We also employ
a bound of Kim and Shahidi for the first eigenvalues of the relevant Laplace
operators, and an `unweighted' spectral large sieve inequality (our proof of
which is to appear separately).
