Result1CN1:= [
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Result1CN2:=
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];

function ReadEntry(S)
  K:= NumberField(Polynomial(S[1]));
  L:= [];
  for s in S[3] do
    if Type(K) eq FldRat then
      E:= QuaternionAlgebra(Integers() ! s[1]);
    else
      E:= QuaternionAlgebra( Integers(K) * (K ! s[1]), InfinitePlaces(K) );
    end if;
    Append(~L, E);
  end for;
  return L;
end function;

function Lattices(M)
  K:= BaseField(Algebra(M));
  N, h:= NarrowClassGroup(K);
  S:= {@ n: n in N @};
  U, g:= UnitGroup(K);
  if Type(K) eq FldRat then 
    T:= sub< U | >;
  else
    P:= Subsets({u @ g : u in Generators(U)});
    x:= [ u : p in P | IsTotallyPositive(u) where u:= &*p ];
    T:= sub< U | 2*U, [u @@ g : u in x] >;
  end if;

  L:= LeftIdealClasses(M);
  C:= [ {* Integers() | *}^^#S ];
  for j in [1..#L] do
    I:= L[j];
    i:= #S eq 1 select 1 else Index(S, Norm(I) @@ h);
    assert i gt 0;
    UO, hO:= UnitGroup(RightOrder(I));
    idx:= #T eq 1 select 1 else #quo< T | 2*U, [ Norm(u @ hO) @@ g  : u in Generators(UO) ] >;
    Include(~C[i], j^^idx);
  end for;
  assert forall{c: c in C | not IsEmpty(c) };
  CN:= Sort(Setseq({ #c: c in C }));
  return &cat [ [ < L[Rep(c)], i > : c in C | #c eq i ] : i in CN ];
end function;