Errata:

Section 2. Lemma 2.1. replace "the order of $\Delta$ is odd" 
by "the exponent $M$ is odd"

Section 3. Step 1. The product runs over k = j modulo \delta

Section 3. Step 2. The product runs over k = j modulo dp^a

Section 3. page 926, line 10:   The polynomial F(t) is incorrect. 
The one listed is the minimum polynomial of N(eta)         
rather than  N(eta)^{X^2-1}. The correct polynomial is

t^6 - 1306394247628*t^5 + 359348182378798*t^4 - 5041499042385662*t^3 +
2462693434453*t^2 - 299638410*t + 1

(or its reciprocal; this depends on choices of primitive roots ...etc)
This time the polynomial G_1(t) DOES divide  F(t^2)

Section 4. Four lines before Table 4.3:  
       the annihilator is *also* principal for l = 4297.
Indeed, as we read a little further, the annihilator is generated by
T + 2\zeta and by 4 in the ring  W/8W[T]/(T^2 + 2T). Since we have
(T + 2\zeta)*(T + 2 - 2\zeta) = 4 modulo  (T^2 + 2T, 8),
the annihilator is actually generated by T + 2\zeta. Therefore  
B_{\phi} is isomorphic to its dual.

Main Table: the entry for l = 4049 is wrong. It is true that
q = 23, but the degree is 22 rather than 11.

Main Table: in the rightmost columns (both on page 935 and on
page 936) the header should read "deg" rather than "h_l^+".