norm of fundamental unit

[Max Alekseyev <maxale@gmail.com>]

I apologize if my question is not directly related to PARI.
It is about quadratic fields Q(sqrt(d)) where d is a positive
non-square integer. I wonder how to classify such d that there exists
an element of norm -1, while the norm of fundamental unit (computed by
PARI) is 1?

An example is given by d=34:

? bnfinit(x^2-34).fu[1]
%1 = Mod(6*x + 35, x^2 - 34)
? norm(%)
%2 = 1
? norm(Mod(1/5*x-3/5,x^2 - 34))
%3 = -1

Thanks,
Max