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\define\ord{{\operatorname{ord}}}
\define\ds{\displaystyle}

\mag=\magstep1

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These files present 
\roster
\item"" absolute norms of $\frac{\,1\,}{\,4\,}\,B_{2,\,\chi}$
for even nontrinial Dirichlet characters $\chi$ of
prime conductors $<500$ and
the cuspidal class numbers of the modular curve $X_1(p)$ of prime level $p<500$.
\endroster
Files are divided into two types:
\roster
\item"" The file ``B2chi\_a\_b'' presents
for each prime number $p$ with $a\leqq p<b$,
(normalizations of) absolute norms of
$\frac{\,1\,}{\,4\,}\,B_{2,\,\chi}$
and their factorization (not necessarily complete)
for even nontrinial Dirichlet characters $\chi$ of
of prime conductors $p$ with $a\leqq p<b$.
\item"" The file ``ccn\_a\_b'' presents
the square root of cuspidal class numbers
of the modular curve $X_1(p)$ of level $p$
for each prime number $p$ with $a\leqq p<b$.
\endroster

We use the following notations.
For odd prime numbers $p$, $\chi_p$ denotes
a primitive Dirichlet character of conductor $p$ and order $p-1$.
For a prime $p$, we denote by $h_1(p)$
the cuspidal class number of the modular curve $X_1(p)$ of level $p$.
Then we have
$$
h_1(p)=\ds\left( p\prod_{\chi\text{ even}\ne 1}
\,\frac{\,1\,}{\,4\,}\,B_{2,\,\chi}\right)^2
=(h_1^0(p))^2,
$$
where $h_1^0(p)$ is the order of the subgroup of the cuspidal divisor group
generated by the cusps of the first type.

I will appreciate any information on further factorizations.

Acknowledgement.
I am indebted for factorization and primality proving to the following:
\roster
\item"" factorize.c (included in GMP) due to GNU;
\item"" GMP-ECM due to P. Zimmermann et al.;
\item"" PPMPQS.EXE due to S. Tomabechi;
\item"" msieve.EXE due to J. S. Papadopoulos;
\item"" ggnfs due to C. Monico.
\item"" Titanix due to M. Martin.
\endroster
I appreciate the programmers and contributors.

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