bnf = bnfinit(a^2+23); bnr = bnrinit(bnf, 1); bnr.clgp Hecke = lfuncreate([bnr,[1]]); Hecke[2..5] z=lfun(Hecke,0,1) algdep(exp(z),3) N = nfinit(x^6+108); G = galoisinit(N); [T,o] = galoischartable(G); T~ galoisconjclasses(G) L = lfunartin(N,G,T[,3],o); lfuncheckfeq(L) L[2..5] z = lfun(L,0,1) algdep(exp(z),3) bnr = bnrinit(bnfinit(a^2+a+1),6); lfunan([bnr,[1]],100)==lfunan(L,100) E=ellinit([0,-1,0,-4,4]); 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^3+y, polcyclo(o,y))) L = lfunartin(N,G,T[,4],o); L[2..5] lfuncheckfeq(L) dT = galoischardet(G,T[,3],o) dL = lfunartin(N,G,dT,o); dL[2..5] mf=mfinit([1944,1,-3],0); M=mfeigenbasis(mf); C=mfcoefs(M[1],100); subst(lift(C,y,sqrt(-2))[^1]==lfunan(L,100) 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] E = ellinit([0,-1,1,-10,-20]); G = znstar(5,1); L=lfuntwist(E,[G, [1]]); lfunan(E,10) lfunan([G, [1]],10) lfunan(L,10) nf=nfinit(polcyclo(5,'a)); E2=ellinit(E[1..5],nf); localbitprec(64); lfun(E2,2) L2=lfuntwist(E,Mod(4,5)); lfun(E,2)*lfun(L2,2)*norm(lfun(L,2)) L=lfungenus2([x^2+x,x^3+1]); L[2..5] lfun(L,1) lfunan(L,10) E = ellinit([0,0,1,-7,6]);\\ 5077a1 L = lfunsympow(E,2); L[2..5] lfun(L,2) ellmoddegree(E)