1. In Remark 6.2 and Theorem 7.1 the argument needs d < b(n), i.e. d <= ceil(b(n)) - 1, not d <= ceil(b(n)). Hence the bounds on d in Theorem 7.1 for n = 119, 133, 209, 247, 323, 361 drop from 10, 11, 27, 38, 65, 93 to 9, 10, 26, 37, 64, 92 (still with the condition that |<a>| does not divide d); the omitted cases d = ceil(b(n)) are not covered by the argument. Likewise, the bound 38 in the first improvement in Example 7.2 should be 37.

2. The estimate h_Delta <= (2/pi) sqrt(Delta) used in (A.1) is false (e.g. h_47 = 5 > 2 sqrt(47)/pi), so the proof of Proposition A.2 must be replaced. Proposition A.2 still holds: a new proof uses h_Delta <= (sqrt(Delta)/pi)(log Delta + 2) and a new finite class number computation, with degree 1 treated separately using X_0(163).

This does not affect the classification of torsion groups over quartic fields (Theorem 1.1).