L = 1; lfunan(L, 100) lfun(L, 2) lfunzeros(L,30) \pb 32 ploth(t = 0, 100, lfunhardy(L,t)) L = lfuninit(L, [100]); ploth(t = 0, 100, lfunhardy(L,t)) \pb 64 x0 = 1e-10; lfun(1, 1e-10, 4) derivnum(x = x0, zeta(x), 4) \pb 640 \\\\\\\\\\\\\\\\\\\\\\\ L = lfuncreate('x^3-2); lfun(L, 2) lfunzeros(L,30) \pb 32 L = lfuninit(L, [30]); ploth(t = 0, 30, lfunhardy(L,t)) \\\\\\\\\\\\\\\\\\\\\\\ E = ellinit([0,0,1,-7,6]); L = lfuncreate(E); lfun(L, 1) lfun(E, 1) lfun(E, 1, 1) lfun(E, 1, 2) lfun(E, 1, 3) ellanalyticrank(E) lfunzeros(E,10) \pb 32 Lbad = lfuninit(E, [1/2, 0, 30]); ploth(t = 0, 30, lfunhardy(Lbad,t)) L = lfuninit(E, [1, 0, 30]); L = lfuninit(L, [30]); ploth(t = 0, 30, lfunhardy(L,t)) \\\\\\\\\\\\\\\\\\\\\\\ L=lfungenus2([x^2+x, x^3+x^2+1]); lfunan(L,30) L = lfuninit(L, [10]); lfun(L,1) lfunzeros(L,9) ploth(t = 0, 10, lfunhardy(L,t)) \\\\\\\\\\\\\\\\\\\\\\\ lfun(-23, 1) K = bnfinit(x^2+23); (2*Pi) * K.no / sqrt(abs(K.disc)) / K.tu[1] G = idealstar(, 100); G.cyc chi = [2, 0]; znconreyconductor(G,[2,0]) L = lfuncreate([G, chi]); lfun(L, 1) L = lfuninit(L, [30]); ploth(t = 0, 30, lfunhardy(L,t)) \\\\\\\\\\\\\\\\\\\\\\\ K = bnfinit(x^3-7); G = bnrinit(K, [11, [1]]); G.cyc chi = [2] bnrconductor(G, [2]) L = lfuncreate([G, chi]); lfun(L, 0) L = lfuninit(L, [1/2,30]); lfun(L, 0) lfun(L, 1) lfunzeros(L,29) ploth(t = 0, 30, lfunhardy(L,t)) \\\\\\\\\\\\\\\\\\\\\\\ P = quadhilbert(-47); N = nfinit(nfsplitting(P)); G = galoisinit(N); G.gen G.orders L1 = lfunartin(N,G, [[a,0;0,a^-1],[0,1;1,0]], 5); L2 = lfunartin(N,G, [[a^2,0;0,a^-2],[0,1;1,0]], 5); s = 1 + x + O(x^10); lfun(1,s)*lfun(-47,s)*lfun(L1,s)^2*lfun(L2,s)^2 - lfun(N,s)