[newbie] problem with determining modulus of complex quantity

I defined the following function:
calpgon(m,s):=product(1/(s+4*(cos((k*%pi)/(2*m+1)))^2),k,1,m);

simplified it for the case m=3 like this:
trigrat(calpgon(3,s));
                                        1
(%o2)                         -------------------
                                3      2
                               s  + 5 s  + 6 s + 1


substituted s by i*omega like this

s : %i*omega;

tried to calculate the modulus of calpgon(3,i*omega) like this
abs(trigrat(calpgon(3,s)));

and got this:
                     !         3                     2    !
                     !%i (omega  - 6 omega) - 5 omega  + 1!
(%o4)               --------------------------------------
                            6           4           2
                       omega  + 13 omega  + 26 omega  + 1

however I hoped to get this "neater" form:
                                      1
                      --------------------------------
                      sqrt(omega^6+13 omega^4 +26 omega^2+1)

Can anyone here tell me how to make maxima go for the last expression?

thanks in advance
hugo