Dirichlet L series principal characters

["ra.dwars@quicknet.nl" <ra.dwars@quicknet.nl>]

Dear developers,

 

I’d like to generate Dirichlet L-functions and used for instance:

 

default(realprecision,30)

p = 2; q = 3;

L =lfuncreate(Mod(p,q));

print(lfun(L,2));

 

This method works well for all non-principal characters, however seems to fail for the principal ones with q > 1:

 

default(realprecision,30)

p = 1; q = 3;

L =lfuncreate(Mod(p,q));

print(lfun(L,2));

 

1.64493406684822643647241516665 = (pi^2)/6

which should be:

1.46216361497620127686436903702 = (4*pi^2)/27

 

It always seems to default to the zeta-function even when the modulus is greater than 1.

 

Maybe I do something wrong here and is the Mod(p,q) not allowed for principal characters. Keen to learn how to obtain the right outcome.

 

Thanks,

Rudolph