Zeta = lfuncreate(1) lfun(Zeta,2) lfun(Zeta,0,1) lfun(Zeta,1) lfun(Zeta,1+x+O(x^10)) lfunzeros(Zeta,20) lfunlambda(Zeta,2) G=znstar(4,1); G.clgp Dir=lfuncreate([G,[1]]); Dir[2..5] lfunan(Dir,30) lfun(Dir,2) Catalan G=znstar(1001,1); G.clgp chi = [1,0,1]; Dir1001=lfuncreate([G,chi]); Dir1001[2..5] lfunan(Dir1001,10) abs(%) L = lfuninit(Dir1001,[1/2,0,50]); ploth(x=0,50,lfunhardy(L,x)); Dedek = lfuncreate(x^2+1); Dedek[2..5] lfun(Dedek,2) zeta(2)*Catalan L=lfunmul(Zeta,Dir); lfun(L,2) L2=lfundiv(Dedek,1); lfun(L2,2) K = bnfinit(x^3-21*x+35); K.pol K.sign K.disc K.no K.reg L = lfuncreate(K); L[2..5] lfun(L,1+x+O(x^2)) {2^K.r1*(2*Pi)^K.r2*K.no*K.reg/ (K.tu[1]*sqrt(abs(K.disc)))} lfun(L,0,2)/2! -K.no*K.reg/2 bestappr(lfun(L,-5)) lfun(L,-11) bestappr(lfun(L,-11)) \p100 realprecision = 115 significant digits (100 digits displayed) bestappr(lfun(L,-11))