\input amstex
\documentstyle{amsppt}
\define\ep{{\epsilon}}
\define\epb{{\sqrt{i}\sqrt{\epsilon_1}}}
\define\epc{{\sqrt{-1}\sqrt{\epsilon_1}}}

\mag=\magstep1
\vcorrection{-.35in}

\topmatter
\title
Correction to the previous version of tables
\endtitle
\endtopmatter

\document

\head Correction to tables of real fields \endhead

On page 2 line -6, $h_{i+}=16h/Q_+$ should read $h_+=16h/Q_+$.

On Page 7. For $d=831744$ with $(d_1,d_2,d_3)=(24,76,456)$,
the correct value of $h$ is $2$ (not $1$).

On Page 8, there are $5$ errors for generatos of the totally positive units.
For $d=3600$, $\ep_1\sqrt{\ep_2\ep_3}$ should read $\ep_1^2$;
For $d=14400$, $\ep_1$ should read $\ep_1^2$;
For $d=24336$, $\ep_2$ should read $\ep_2\sqrt{\ep_3}$;
For $d=48841$, $\ep_1$ should read $\ep_1^2$;
For $d=69696$ with $(d_1,d_2,d_3)=(8,33,264)$, $\ep_1$ should read $\ep_1^2$.

On Page 10, there are $4$ errors for generatos of the totally positive units,
and $1$ for $Q_+$ and $h_+$.
For $d=370881$, $\ep_2$ should read $\ep_2^2$
and the correct values of $Q_+$ and $h_+$ are $4$ and $4$;
For $d=416025$, $\ep_2\sqrt{\ep_3}$ should read $\ep_2$;
For $d=435600$ with $(d_1,d_2,d_3)=(12,165,220)$,
$\ep_1$ should read $\ep_1\sqrt{\ep_2\ep_3}$;
For $d=435600$ with $(d_1,d_2,d_3)=(33,60,220)$,
$\ep_2$ should read $\ep_1\sqrt{\ep_1\ep_3}$.

On Page 11, there are $5$ errors for generatos of the totally positive units.
For $d=497025$, $\ep_2\sqrt{\ep_3}$ should read $\ep_2$;
For $d=648025$, $\ep_2\sqrt{\ep_3}$ should read $\ep_2$;
For $d=705600$ with $(d_1,d_2,d_3)=(21,120,280)$,
$\ep_1$ should read $\ep_1\sqrt{\ep_2\ep_3}$;
For $d=705600$ with $(d_1,d_2,d_3)=(24,105,280)$,
$\ep_1$ should read $\ep_1\sqrt{\ep_2\ep_3}$;
For $d=705600$ with $(d_1,d_2,d_3)=(56,105,120)$,
$\ep_1$ should read $\ep_1\sqrt{\ep_2\ep_3}$.

On Page 12, there are $1$ error for generatos of the totally positive units,
and $1$ for $Q_+$ and $3$ for $h_+$.
For $d=774400$ with $(d_1,d_2,d_3)=(8,220,440)$,
and the correct value of $h_+$ is $4$;
For $d=831744$ with $(d_1,d_2,d_3)=(24,76,456)$,
and the correct value of $h_+$ is $4$;
For $d=938961$, $\ep_2$ should read $\sqrt{\ep_2\ep_3}$
and the correct values of $Q_+$ and $h_+$ are $4$ and $4$.

\head Correction to tables of imaginary fields \endhead

There are $10$ errors for relative class numbers $h^-$.

On Page 5.
For $d=28224$ with $(d_1,d_2,d_3)=(21,-24,-56)$,
and the correct value of $h^-$ is $4$.

On Page 6.
For $d=67600$ with $(d_1,d_2,d_3)=(5,-52,-260)$,
and the correct value of $h^-$ is $8$.

On Page 7.
For $d=107584$, the correct value of $h^-$ is $2$.
For $d=118336$ with $(d_1,d_2,d_3)=(8,-43,-344)$,
and the correct value of $h^-$ is $10$.

On Page 8.
For $d=137641$, the correct value of $h^-$ is $4$.

On Page 14.
For $d=379456$ with $(d_1,d_2,d_3)=(616,-7,-88)$,
and the correct value of $h^-$ is $2$.

On Page 16.
For $d=511225$ with $(d_1,d_2,d_3)=(13,-55,-715)$,
and the correct value of $h^-$ is $8$.

On Page 17.
For $d=603729$ with $(d_1,d_2,d_3)=(777,-7,-111)$,
and the correct value of $h^-$ is $8$.

On Page 20.
For $d=795664$, the correct value of $h^-$ is $7$.

On Page 22.
For $d=898704$ with $(d_1,d_2,d_3)=(237,-4,-948)$,
and the correct value of $h^-$ is $6$.

For fundamental unit $\ep$.
On Page 12.
For $d=308025$ with $(d_1,d_2,d_3)=(37,-15,-555)$,
$\sqrt{i}\sqrt{\ep_1}$ should read $\ep_1$.

For some discriminants, some pair of fields are ordered incorrectly.
The correct order is reverse.

On Page 7.
For $d=74529$, fields with $d_1=273$.

On Page 14.
For $d=416025$, fields with $d_1=645$.

On Page 21.
For $d=846400$, fields with $d_1=40$.

On Page 23.
For $d=968256$, fields with $d_1=984$.
For $d=976144$, fields with $d_1=988$.

There are $8$ errors in Table 2.

On Page 24.
For $d=1089$, $\epc=2\sqrt{-3}+\sqrt{-11}$.
For $d=19881$, $\epc=4\sqrt{-3}+\sqrt{-47}$.
For $d=48400$, $\epc=3\sqrt{-5}+2\sqrt{-11}$.

On Page 25.
For $d=154449$, $\epc=2782\sqrt{-3}+421\sqrt{-131}$.
For $d=184041$, $\epc=(7\sqrt{-3}+\sqrt{-143})/2$.

On Page 26.
For $d=226576$, $\epb=(11+\sqrt{119}+11\sqrt{-1}+\sqrt{-119})/2$.
For $d=242064$, $\epb=(11+\sqrt{123}+11\sqrt{-1}+\sqrt{-123})/2$.
For $d=313600$, $\epc=5\sqrt{-5}+3\sqrt{-14}$.

\enddocument
