2. I changed the Magma reference to:
\bibitem{magma}
W.~Bosma, J.~Cannon, and C.~Playoust, \emph{The {M}agma algebra system {I}:
{T}he user language}, J. Symb. Comp. \textbf{24} (1997), no.~3-4, 235--265,
\\\protect{\sf http://www.maths.usyd.edu.au:8000/u/magma/}.
because David Kohel told me that this is the canonical reference.
3. \footnote{But I checked using magma and it [$\alp - 1$] doesn't!
So something is wrong here, I think.}
> I don't know what I did wrong here. I just re-created the character
> in Magma and got $2\alp + 1$ instead of $\alp - 1$. Here's the Magma
> code:
> > k:=F(25);
> > MinimalPolynomial(a);
> $.1^2 + 4*$.1 + 2
> > (a-1)^3;
> a^3
> > Order(a-1);
> 24
> > Order(a);
> > Order(a);
> 24
> > G:=DirichletGroup(1376,k);
> > e:=G.3;
> > e;
> $.3
> > e^3;
> $.3^3
> > Order(e);
> 6
> > e43:=e^2;
> > e43;
> $.3^2
> > Order(e43);
> 3
> > CRT([1,3],[2^5,43]);
> 1121
> > 1121 mod 2^5;
> 1
> > 1121 mod 43;
> 3
> > Evaluate(e43,1121);
> a^8
> > R:=PolynomialRing(F(5));
> > kk:=quo;
> > #kk;
> 25
> > x^8;
> x^8
> > kk:=quo;
> > aa;
> aa
> > aa^8;
> 2*aa + 1
> > Order(2*a+1);
> 3
> I recreated all of the computations and using the above choice of
> alpha appears to give exactly the same tables as in our paper.
4.