

gap> K:=ContractibleGcomplex("SL(3,Z)a");;
gap> V:=DualComplex(K);;
gap> R:=FreeGResolution(V,1);; #first two terms of a free SL(3,Z)-resolution
gap> G:=HAPCongruenceSubgroupGamma0(3,701);;
gap> S:=ResolutionFiniteSubgroup(R,G);; #first two terms of a free G-resolution
gap> C:=TensorWithIntegersSparse(S);;
gap> for r in [1..200] do   #careful step-by-step reduction of the complex C
> C:=ContractedComplexViaChild(C,r);;
> od;

Homology(C,0);
[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
  2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6, 18, 18, 18, 18, 
  14574272748332562519126602132425986851137745473252230639812547826590, 
  14574272748332562519126602132425986851137745473252230639812547826590, 0, 0, 
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

gap> Factors(14574272748332562519126602132425986851137745473252230639812547826590);
[ 2, 3, 3, 3, 5, 7, 13, 113, 541, 23867527870278363301, 
  406535606513108747882997061430663240539 ]
