Function: gcharconductor
Section: number_fields
C-Name: gchar_conductor
Prototype: GG
Help: gcharconductor(gc,chi): returns the conductor of chi, as a modulus over gc.bnf.
Doc: returns the conductor of \kbd{chi}, as a modulus over \kbd{gc.bnf}. This is
 the minimum modulus $\goth{m}$ such that
 $U(\goth{m})\subset\text{ker}(\var{chi})$
 indicating the exact ramification of \var{chi}.

 \item for a real place $v$, $v\mid \goth{m}$ iff $\chi_{v}(-1)=-1$.

 \item for a finite place~$\goth{p}$, the prime power~$\goth{p}^{e}$ divides
 exactly $\goth{m}$ if $e\ge 0$ is the smallest integer such that $\chi_{\goth{p}}
 (U_{e})=1$ where~$U_{0} = \Z_{\goth{p}}^{\times}$ and~$U_{i} =
 1+\goth{p}^{i}\Z_{\goth{p}}$ for~$i>0$.

 \bprog
 ? bnf = bnfinit(x^2-5,1);
 ? gc = gcharinit(bnf,[(13*19)^2,[1,1]]);
 ? gc.cyc
 % = [8892, 6, 2, 0, 0.E-57]
 ? chi = [0,0,1,1]~;
 ? gcharconductor(gc,chi)
 % = [[61009, 7267; 0, 169], [1, 0]]
 ? gcharconductor(gc,13*chi)
 % = [[4693, 559; 0, 13], [1, 0]]
 ? gcharconductor(gc,13*19*chi)
 % = [[247, 65; 0, 13], [1, 0]]
 ? gcharconductor(gc,13*19*168*chi)
 % = [[19, 5; 0, 1], [0, 0]]
 @eprog
