L = lfuncreate(1); \\ '1' = Riemann zeta function
lfun(L, 2)
lfunzeros(L,30)
\pb 32
L = lfuninit(L, [1/2, 0, 30]);
ploth(t = 0, 30, lfunhardy(L,t))

\\\\\\\\\\\\\\\\\

L = lfuncreate('x^3-2); \\ Q(2^(1/3))
lfun(L, 2)
lfunzeros(L,30)
\ pb 32
L = lfuninit(L, [1/2, 0, 30]);
ploth(t = 0, 30, lfunhardy(L,t))

\\\\\\\\\\\\\\\\\

E = ellinit([0,0,1,-7,6]);
L = lfuncreate(E); \\ L(E,s)

lfun(L, 1)
lfun(E, 1)
lfun(L, 1, 1)\\  L' 
lfun(L, 1, 2)\\  2nd derivative
lfun(L, 1, 3)\\  3rd derivative
ellanalyticrank(E)
lfunzeros(L,30)
\ pb 32
Lbad = lfuninit(L, [1/2, 0, 30]); \\ BUG !!!   
ploth(t = 0, 30, lfunhardy(Lbad,t))
L = lfuninit(L, [1, 0, 30]); \\ Better    
ploth(t = 0, 30, lfunhardy(L,t))

\\\\\\\\\\\\\\\\\

G = idealstar(, 100); 
G.cyc 
chi = [2,0]; \\ in terms of SNF gens. 
m = znconreyexp(G, chi) 
c = znconreylog(G, m)
s = ideallog(, m, G)
znconreylog(G, chi)
znconreychar(G, m)
znconreychar(G, c) \\ Bad input ! 
znconreychar(G, s) \\ OK

\\\\\\\\\\\\\\\\\

N = 100; G = idealstar(, N); \\ (Z/100Z)^* 
G.cyc 
chi = [2, 0]
L = lfuncreate([G, chi]);

znconreyconductor(G, chi) \\ not primitive !
lfun(L, 1)
lfunlambda(L, 1)
lfuntheta(L, 1)
N = znconreyconductor(G, chi, \&chi0)
G0 = idealstar(,N);

\\\\\\\\\\\\\\\\\

K = bnfinit(x^3-7);
G = bnrinit(K, [11, [1]]);
G.cyc
chi = [1]
L = lfuncreate([G, chi]);

lfun(L, 0)
L = lfuninit(L, [1/2,1/2,30]);
lfun(L, 0)
lfun(L, 1)
lfunzeros(L,30)
ploth(t = 0, 30, lfunhardy(L,t))