bnf = bnfinit(polcyclo(5),1);
gc = gcharinit(bnf,5);
gc.cyc

chi = [0,0,0,5,0.1*I]~;
gcharconductor(gc,chi)
gcharconductor(gc,4*chi)

pr11 = idealprimedec(bnf,11)[1];
gchareval(gc,chi,pr11)

gcharlocal(gc,chi,1)
gcharlocal(gc,chi,2)

pr5 = idealprimedec(bnf,5)[1];
loc = gcharlocal(gc,chi,pr5,&bid)
bid.cyc
charorder(bid,loc[1..-2])

L = lfuncreate([gc,chi[1..-2]]);
lfunparams(L)[1]
lfunparams(L)[3]*1.
lfuncheckfeq(L)
lfun(L,1)

gcharisalgebraic(gc,chi)
chi2 = [0,1,0,0,0]~;
gcharisalgebraic(gc,chi2,&typ)
typ
gcharlocal(gc,chi2,1)
gcharlocal(gc,chi2,2)

gcharalgebraic(gc)

gcharalgebraic(gc,[[1,2],[3,4]])
gcharalgebraic(gc,[[2,-2],[-1,1]])

pr31 = idealprimedec(bnf,31)[1];
gcharidentify(gc,[pr11,pr31],[0.261946,-0.497068])
localprec(6); chi3=gcharidentify(gc,[pr11,pr31],[0.261946,-0.497068])
gchareval(gc,chi3,pr11,0)
gchareval(gc,chi3,pr31,0)
chi4 = gcharidentify(gc,[1,2,pr11],[[-26,-0.1],[13,0.1],0.])
gcharlocal(gc,chi4,1)
gcharlocal(gc,chi4,2)
gchareval(gc,chi4,pr11)

C = [-2*x^4 - 2*x^3 + 2*x^2 + 3*x - 2, x^3];
L = lfungenus2(C);
lfunparams(L)
factor(lfunparams(L)[1])
E = bnfinit(y^4 - y^3 + 2*y^2 + 4*y + 3, 1);
poldegree(nfsubfieldscm(E)[1])
pr13 = idealprimedec(E,13)[1];
gc2 = gcharinit(E,pr13);
gc2.cyc
chiC = [1, -1, -1, 0, -1/2]~
gcharisalgebraic(gc2,chiC,&typ)
typ
L2 = lfuncreate([gc2,chiC]);
lfunparams(L2)
exponent(lfunan(L,1000)-lfunan(L2,1000))

gc3 = gcharinit(x^3-3*x+1,2^20);
chiapprox = gcharidentify(gc3,[1,2,3],[[0,Pi],[0,exp(1)],[0,-Pi-exp(1)]])
gcharlocal(gc3,chiapprox,1)
gcharlocal(gc3,chiapprox,2)

gc4 = gcharinit(x^4-5,1);
gc4.cyc
chipart = [1,0,0,0]~
gcharlocal(gc4,chipart,1)
gcharlocal(gc4,chipart,2)
gcharlocal(gc4,chipart,3)