  We prove, in respect of an arbitrary Hecke congruence subgroup \Gamma
=\Gamma_0(q_0) of the group SL(2,Z[i]), some new upper bounds (or `spectral
large sieve inequalities') for sums involving Fourier coefficients of \Gamma
-automorphic cusp forms on SL(2,C). The Fourier coefficients in question may
arise from the Fourier expansion at any given cusp c of \Gamma : our results
are not limited to the case in which c is the cusp at infinity. For this
reason, our proof is reliant upon an extension, to arbitrary cusps, of the
spectral-Kloosterman sum formula for \Gamma\SL(2,C) obtained by Hristina
Lokvenec-Guleska in her doctoral thesis (generalising the sum formulae of
Roelof Bruggeman and Yoichi Motohashi for PSL(2,Z[i])\PSL(2,C) in several
respects, though not as regards the choice of cusps). A proof of the required
extension of the sum formula is given in an appendix.
