On your 1st sheet, you have
\[ F(\zeta)=\sum_{r=1}^{q1}A_r\zeta^r\]
so there is no term with \(\zeta^0\) (or \(\zeta^q\) which is also 1).
On your 2nd sheet, you apply the idea to a polynomial which does have a term with \(\zeta^0\).
Is the book you are using a well known one? If one of has it, perhaps we can help you pinpoint where the misunderstanding arises.
