norml2() with variables in vector?

[hermann@stamm-wilbrandt.de]

There is no constant term in "v[1]^2+v[2]^2+v[3]^2" below.
How can it be that "norml2(v)" reports 417 ?

$ gp -q
? G=[-102, -107, 93; 22, 23, -20; 1, 1, -1];
? v=G^-1*[a,b,c]~
[3*a + (14*b - c), -2*a + (-9*b - 6*c), a + (5*b - 8*c)]~
? v[1]^2+v[2]^2+v[3]^2
14*a^2 + (130*b + 2*c)*a + (302*b^2 + 101*c^2)
? norml2(v)
417
?

Regards,

Hermann.