Solution
= Solution
The shift <matrix> obeys $A^4=I$ and $B=aI+bA+cA^2+dA^3$. Evaluating $g(t)=a+bt+ct^2+dt^3$ at $1,i,-1,-i$ gives
$$
\boxed{a+b+c+d,quad a-c+i(b-d),quad a-b+c-d,quad a-c-i(b-d).}
$$
= Solution
The shift <matrix> obeys $A^4=I$ and $B=aI+bA+cA^2+dA^3$. Evaluating $g(t)=a+bt+ct^2+dt^3$ at $1,i,-1,-i$ gives
$$
\boxed{a+b+c+d,quad a-c+i(b-d),quad a-b+c-d,quad a-c-i(b-d).}
$$