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<a>:=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<x>:=PolynomialRing(F(5));
>   > kk:=quo<R|x^2+4*x+2>;
>   > #kk;
>   25
>   > x^8;
>   x^8
>   > kk<aa>:=quo<R|x^2+4*x+2>;
>   > 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.