Build and analyze a quotient ring as follows:
(a) Use P.<z>=Integers(7)[] to construct a ring P of polynomials in z with coefficients from Z7.
(b) Use \texttt{K = P.ideal(z\^2+z+3)} to build a principal ideal K generated by the polynomial z2+z+3.
(c) Use H = P.quotient(K) to build H, the quotient ring of P by K.
(d) Use Sage to verify that H is a field.
(e) As in the previous exercise, obtain a generator and examine the proper collection of powers of that generator.