Function: znchartokronecker
Section: number_theoretical
C-Name: znchartokronecker
Prototype: GGD0,L,
Help: znchartokronecker(G, chi, {flag=0}): let G be znstar(N,1), let chi
be a Dirichlet character mod N, return the discriminant D if chi is
real equal to the Kronecker symbol (D/.) and 0 otherwise. If flag
is set, return the fundamental discriminant attached to the corresponding
primitive character.
Doc: Let $G$ be attached to $(\Z/N\Z)^*$ (as per \kbd{G = znstar(N,1)})
and let \kbd{chi} be a Dirichlet character on $(\Z/N\Z)^*$, 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}.
If $\fl = 0$, return the discriminant $D$ if \kbd{chi} is real equal to the
Kronecker symbol $(D/.)$ and $0$ otherwise. The discriminant $D$ is
fundamental if and only if \kbd{chi} is primitive.
If $\fl = 1$, return the fundamental discriminant attached to the
corresponding primitive character.
\bprog
? G = znstar(8,1); CHARS = [1,3,5,7]; \\ Conrey labels
? apply(t->znchartokronecker(G,t), CHARS)
%2 = [4, -8, 8, -4]
? apply(t->znchartokronecker(G,t,1), CHARS)
%3 = [1, -8, 8, -4]
@eprog