Function: znconreyconductor
Section: number_theoretical
C-Name: znconreyconductor
Prototype: GGD&
Help: znconreyconductor(G,chi, {&chi0}): let G be znstar(q,1) and chi
 be a Dirichlet character on (Z/qZ)* given by its Conrey logarithm. Return
 the conductor of chi, and set chi0 to (the Conrey logarithm of) the
 attached primitive character. If chi0 != chi, return the conductor
 and its factorization.
Doc: Let \var{G} be attached to $(\Z/q\Z)^*$ (as per
 \kbd{G = znstar(q, 1)}) and \kbd{chi} be a Dirichlet character on
 $(\Z/q\Z)^*$, given by

 \item a \typ{VEC}: a standard character on \kbd{bid.gen},

 \item a \typ{INT} or a \typ{COL}: a Conrey index in $(\Z/q\Z)^*$ or its
 Conrey logarithm;
 see \secref{se:dirichletchar} or \kbd{??character}.

 Return the conductor of \kbd{chi}, as the \typ{INT} \kbd{bid.mod}
 if \kbd{chi} is primitive, and as a pair \kbd{[N, faN]} (with \kbd{faN} the
 factorization of $N$) otherwise.

 If \kbd{chi0} is present, set it to the Conrey logarithm of the attached
 primitive character.

 \bprog
 ? G = znstar(126000, 1);
 ? znconreyconductor(G,11)   \\ primitive
 %2 = 126000
 ? znconreyconductor(G,1)    \\ trivial character, not primitive!
 %3 = [1, matrix(0,2)]
 ? N0 = znconreyconductor(G,1009, &chi0) \\ character mod 5^3
 %4 = [125, Mat([5, 3])]
 ? chi0
 %5 = [14]~
 ? G0 = znstar(N0, 1);      \\ format [N,factor(N)] accepted
 ? znconreyexp(G0, chi0)
 %7 = 9
 ? znconreyconductor(G0, chi0) \\ now primitive, as expected
 %8 = 125
 @eprog\noindent The group \kbd{G0} is not computed as part of
 \kbd{znconreyconductor} because it needs to be computed only once per
 conductor, not once per character.
