Please write legibly and show all work and steps.

Definition Call a number field L super-constructible if there is a tower of field extensions, Q =Ko CK, C . .. CK = L, where [Kit1 : Ki] = 1, 2, or 3.3) Use techniques from the text to describe the field automorphisms in Auto(Q(S7)) = 10, 02, 0', 04, 05, 00 = e' explicitly by their action on (7. Use this to write an isomorphism: Auto(Q(57)) ~ Zy ~ 76. You may not use the result of Exercise 162.5