**********************************************************************
* The data in this directory are
* Copyright (C) 2010 Hatice Boylan <hatice.boylan@uni-siegen.de>
*                    Nils-Peter Skoruppa <nils.skoruppa@uni-siegen.de>
*
* Distributed under the terms of the GNU General Public License (GPL)
* http://www.gnu.org/licenses/
**********************************************************************

This directory  contains, for the first quadratic to septic fields $K$ with ring of integers $O$ in the range of the Bordeaux number field tables, extended information concerning the abelianized
group of $SL(2,O)$ and the indices for Jacobi forms over $K$.

These tables were built using the Bordeaux number field tables of the
PARI group which can be found under

http://pari.math.u-bordeaux.fr/pub/pari/packages/nftables.tgz

More precisely, the file Fnr.txt contains data for all fields
which are of degree n, possess r
real embeddings and whose discriminant is below the following bounds:

  F20: |disc| <   10^6,  303968 fields
  F22: |disc| <   10^6,  303957 fields

  F31: |disc| <   10^6,  182417 fields
  F33: |disc| < 2*10^6,  112444 fields

  F40: |disc| <   10^6,   81322 fields
  F42: |disc| <   10^6,   90671 fields
  F44: |disc| <   10^6,   13073 fields

  F51: |disc| <=  10^6,   28993 fields
  F53: |disc| <   10^6,   10800 fields
  F55: |disc| < 2*10^7,   22740 fields

  F60: |disc| < 2*10^5,     442 fields
  F62: |disc| < 4*10^5,    1179 fields
  F64: |disc| <   10^6,     405 fields
  F66: |disc| <   10^7,     398 fields

  F71: |disc| < 6*10^5,     121 fields
  F73: |disc| <18*10^5,     162 fields
  F75: |disc| <12*10^6,     201 fields
  F77: |disc| <15*10^7,     154 fields

Each line of a file F*.txt corresponds to one field and
contains the following information:

	 [disc., [coeff of gen. polyn. in *INCREASING* order],
	  class #, [elem. div. of class group],
    	  [# of primes of degree 1 over 2,
     	   # of primes of degree 1 over 3,
     	   _is_in_principle_genus( diff),
     	   number of f*diff^-1 in the principle genus,
	   where f is a (possibly empty) product of primes over 3 of degree 1,
     	   cardinality of the kernel of squaring map in the narrow class group
     	  ]]


This directory contains the following files:

Contents.txt   This file

F20.txt	       The data files
F22.txt
F31.txt
F33.txt
F40.txt
F42.txt
F44.txt
F51.txt
F53.txt
F55.txt
F60.txt
F62.txt
F64.txt
F66.txt
F71.txt
F73.txt
F75.txt
F77.txt



nftables.sage		Sage scripts for producing the F**.txt
lattice_index.sage	from the Bordeaux nftables using
			"Sage Version 4.5.3, Release Date: 2010-09-04"