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In future we present the files giving
\roster
\item"" the relative class numbers of the imaginary abelian number fields
of non prime power conductors $<10000$.
\endroster
Files are divided into two types:
\roster
\item"" The file ``nb\_a\_b'' presents
for each non prime power conductor $f$ with $a\leqq f<b$,
absolute norms of
$-\frac{\,1\,}{\,2\,}\,B_{1,\,\chi}$
and their factorization (not necessarily complete)
for odd Dirichlet characters $\chi$ of
non prime power conductors $f<10000$.
Regrettably, different from the prime power conductor case,
values are not uniquely determined by conductor and degree of $\chi$.
Therefore, for specification of values,
we need additional information.
\item"" The file ``rcnf\_a\_b'' presents
the relative class numbers of the imaginary abelian number fields
of non prime power conductors $f<10000$ with $a\leqq f<b$.
\endroster

We use the following notations.
$\chi_4$ denotes the unique primitive Dirichlet character of conductor $4$.
For odd prime numbers $p$, $\chi_p$ denotes
a primitive Dirichlet character of conductor $p$ and order $p-1$.
For prime powers $q=p^m$ ($\ne 4$), $\psi_q$ denotes
an even primitive Dirichlet character of conductor $q$ and
order $p^{m-1}$ or $2^{m-2}$ according as $p$ is odd or $p=2$.

We tried to factor $N(-\frac{\,1\,}{\,2\,}\,B_{1,\,\chi})$ as possible.
p(n) means the number is a prime with n (decimal) digits and
c(n) means the number is a composite with n digits.
c means the factor is a composite.
For large probable primes,
we certified the primality by `Titanix' and `Primo'.

In the File ``rcnf\_a\_b'',
for each non prime power conductor $f$ with $a\leqq f<b$.
the relative class numbers of the imaginary abelian number fields
of non prime power conductors $f<10000$ are given.
For each $f$,
data are ordered by conductor and degree.
Regrettably, different from the prime power conductor case,
fields are not uniquely determined by its conductor and degree.
Therefore, for specification of fields,
we need additional information.
We do not give information on factorization.

The computation was done on a PC.
We used the vector manipulation method.
(See \cite{2}.)

I will appreciate any information on further factorizations.

Acknowledgement.
I am indebted for factorization and primality proving to the following:
\NoBlackBoxes
\roster
\item"" factorize.c (included in GMP) due to GNU;
\item"" GMP-ECM due to P. Zimmermann et al.;
%\item"" FACTOR.EXE due to Shamus Software Ltd.;
\item"" PPMPQS.EXE due to S. Tomabechi
(available at\newline
http://www.asahi-net.or.jp/\~{}KC2H-MSM/mathland/matha1/index.htm);
\item"" msieve.EXE due to J. S. Papadopoulos
(available at\newline
http://www.boo.net/\~{}jasonp/qs.html);
\item"" Titanix and Primo due to M. Martin
(available
\footnote{Now, the use is forbidden in Canada, Japan and USA
because of Patent Office Policy.}
at http://www.ellipsa.net/).
\endroster
I appreciate the programmers and contributors.
\newpage

\Refs

\ref \no 1 \by H. Hasse
\book \"Uber die Klassenzahl abelscher Zahlk\"orper
\publ Akademie-Verlag \publaddr Berlin \yr 1952
\moreref MR {\bf 14}, 141
\moreref Nachdruck der ersten Aufgabe.
Mit einer Einleitung von J. Martinet 
\publ Springer-Verlag \publaddr New York and Berlin \yr 1985
\moreref MR 87j:11122a
\endref

\ref \no 2 \by R. Spira
\paper Calculation of the first factor of the cyclotomic class number
\inbook Computers in number theory
\bookinfo (Proc. Sci. Res. Council Atlas Sympos. No. 2, Oxford, 1969)
\ed A. O. L. Atkin and B. J. Birch
\publ Academic Press \publaddr London and New York
\yr 1971 \pages 149--151
\endref

\endRefs

\enddocument
