N = nfinit(x^6+108);
G = galoisinit(N);

[T,o] = galoischartable(G);
T~

L = lfunartin(N,G,T[,3],o);
lfuncheckfeq(L)
L[2..5]
z = lfun(L,0,1)
p = algdep(exp(z),3)

bnr = bnrinit(bnfinit(a^2+a+1),6);
lfunan([bnr,[1]],100)==lfunan(L,100)

default(parisize,"16M");
E=ellinit([0,-1,1,-10,-20]);
  \\ or ellinit("11a1") if elldata is available
P=elldivpol(E,3)
Q=polresultant(P,y^2-elldivpol(E,2));
R=nfsplitting(Q)

N=nfinit(R); G=galoisinit(N);
[T,o]=galoischartable(G); T~
o

minpoly(Mod(y^5+y^3-y, polcyclo(24,y)))

L = lfunartin(N,G,T[,3],o);
L[2..5]
lfuncheckfeq(L)

dT = galoischardet(G,T[,3],o)
dL = lfunartin(N,G,dT,o);
dL[2..5]

S = lfunan(L,1000); SE = lfunan(E,1000);
Smod3 = round(real(S))-round(imag(S)/sqrt(2));
[(Smod3[i]-SE[i])%3|i<-[1..#Smod3],gcd(i,33)==1]

bnf6=bnfinit(a^6-3*a^5+6*a^4+4*a^3+6*a^2-3*a+1);
bnr6=bnrinit(bnf6,1);
bnf4=bnfinit(a^4-a^3+3*a^2+a-1);
pr4 = idealprimedec(bnf4,3)[1];
bnr4=bnrinit(bnf4,[pr4,[0,1]]);
L1=lfuncreate([bnr6,[5]]);
L1[2..5]
L2=lfuncreate([bnr4,[1]]);
L2[2..5]

LL = lfundiv(L1,L2);
round(lfunan(L,1000)-lfunan(LL,1000),&e)
e