Quelle  crystcat.grp

#############################################################################
##
#A  crystcat.grp                GAP group library              Volkmar Felsch
##
#Y  Copyright (C)  1994,  Lehrstuhl D fuer Mathematik,  RWTH Aachen,  Germany
##
##  This file contains functions  that allow to access most of the data which
##  are listed  in the tables  of the book  "Crystallographic groups of four-
##  dimensional space"  by Harold Brown, Rolf Buelow, Joachim Neubueser, Hans
##  Wondratschek, and Hans Zassenhaus (Wiley, New York, 1978).
##
##
##  For each  of the dimensions  2,  3,  and  4,  the tables  of the book are
##  arranged in the following hierarchical format:
##        dimension,
##          crystal family,
##            crystal system,
##              Q-class (geometric crystal class),
##                Z-class (arithmetic crystal class),
##                  space-group type.
##
##  The following conventions for  local variables are used throughout in all
##  functions of this library.
##
##  dim = dimension,
##  sys = crystal system number with respect to a given dimension,
##  qcl = Q-class number  with respect to given dimension and crystal system,
##  zcl = Z-class number with respect to given dimension, crystal system, and
##        Q-class,
##  sgt = space-group type  with respect to given dimension,  crystal system,
##        Q-class, and Z-class,
##  q   = Q-class number  with respect to the  list of all  Q-classes  of the
##        current dimension,
##  z   = Z-class number  with respect to the  list of all  Z-classes  of the
##        current dimension,
##  t   = space-group type  with respect to the list of all space-group types
##        of the current dimension,
##  CR  = catalogue   record   CrystGroupsCatalogue[dim]   for  the   current
##        dimension dim.
##
##  For most of the  functions in this library  there are two versions given,
##  a public version and an internal version  which are distinguished  by the
##  prefix  "CR_"  in the  name  of the  internal version  and  by  different
##  parameter lists.  The reason  for that distinction is  that in the public
##  functions  the  arguments  are  checked  for being  in range  whereas  no
##  argument checking is done in the internal functions.
##


#############################################################################
##
##  GLZ2  . . . . . . . . . . . . . . . . . . .  general linear group GL(2,Z)
##
GLZ2 := Group(
  [ [0,1], [1,0] ],
  [ [1,0], [1,1], ],
  [ [-1,0], [0,1], ] );
# GLZ2.operations := GLZOps;
SetName( GLZ2, "GLZ2" );
SetSize( GLZ2, "infinity" );


#############################################################################
##
##  GLZ3  . . . . . . . . . . . . . . . . . . .  general linear group GL(3,Z)
##
GLZ3 := Group(
  [ [0,1,0], [0,0,1], [1,0,0] ],
  [ [1,0,0], [1,1,0], [0,0,1] ],
  [ [-1,0,0], [0,1,0], [0,0,1] ] );
# GLZ3.operations := GLZOps;
SetName( GLZ3, "GLZ3" );
SetSize( GLZ3, "infinity" );


#############################################################################
##
##  GLZ4  . . . . . . . . . . . . . . . . . . .  general linear group GL(4,Z)
##
GLZ4 := Group(
  [ [0,1,0,0], [0,0,1,0], [0,0,0,1], [1,0,0,0] ],
  [ [1,0,0,0], [1,1,0,0], [0,0,1,0], [0,0,0,1] ],
  [ [-1,0,0,0], [0,1,0,0], [0,0,1,0], [0,0,0,1] ] );
# GLZ4.operations := GLZOps;
SetName( GLZ4, "GLZ4" );
SetSize( GLZ4, "infinity" );


#############################################################################
##
#F  CrystalGroupsCatalogue  . . . . . . . . . . . . . . . . . . . . . . . . .
##
##  The data  listed  in this  catalogue  are essentially  the same  as those
##  listed  in the  tables of  the book  "Crystallographic  groups  of  four-
##  dimensional space"  by Harold Brown, Rolf Buelow, Joachim Neubueser, Hans
##  Wondratschek, and  Hans Zassenhaus (Wiley, New York, 1978).
##
##  For each of the  dimensions 2, 3, and 4  the catalogue  contains a record
##  'CR', say, which consists of the folowing components.
##
##  'CR.bZClass'  is a Boolean list containing the numbers of those Z-classes
##      which are Bravais Z-classes.
##
##  'CR.codedConjugatorDadeGroup'  is a list  of matrices  used to  conjugate
##      Z-class representative groups  into subgroups  of Dade groups.  Each
##      entry is  of the form  p1 + 140 * p2 + 140^2 * p3 + ... + 140^(dim-1)
##      * p_dim,  where  dim  is  the  given  dimension,  and  the  pi's  are
##      pointers  to the  list 'CR.rowConjugatorDadeGroup'.  (It is addressed
##      by   pointers   which  are   contained   in  entries   of  the   list
##      'CR.codedDadeGroupsZClass'.)
##
##  'CR.codedDadeGroupsZClass'  is a list  which for each Z-class contains in
##      form of a  sublist  of consecutive entries  representatives  of those
##      conjugacy classes  of subgroups  of Dade groups  which contain groups
##      from that Z-class. Each entry is of the form d  or  p * 10 + d, where
##      d  is the  number  of a Dade group  and  p  is a pointer  to the list
##      'CR.codedConjugatorDadeGroup'.         (See         also         list
##      'CR.nullDadeGroupsZClass'.)
##
##  'CR.codedDecompositionQClass'  is a list  which for each Q-class contains
##      an entry of the form t1  or of the form  10 * t2 + t1,  where t1 is a
##      pointer to the text string list 'CR_TextStrings.QClass'  and  t2 is a
##      pointer to the text string list 'CR_TextStrings.QConstituents'.
##
##  'CR.codedGeneratorsSpaceGroup'  is a list which for each space-group type
##      that is not the  representative of its Z-Class  contains an  entry of
##      the form p1 + m * p2 + m^2 * p3 + ... + m^(n-1) * pn,  where m equals
##      'CR.modulSp',  and  n  is the  number  of the  given  non-translation
##      generators of the space group,  and the pi's are pointers to the list
##      'CR.columnGeneratorSpaceGroup'.
##
##  'CR.codedGeneratorZClass' is a list which for each Z-class representative
##      matrix group  contains  its  generators  in  form  of  a  sublist  of
##      consecutive entries. Each entry is of the form p1 + m * p2 + m^2 * p3
##      + ... + m^(dim-1) * p_dim,  where m equals 'CR.modulZ',  and  dim  is
##      the  given  dimension,   and  the  pi's  are  pointers  to  the  list
##      'CR.rowGeneratorZClass'.  (See also  list 'CR.nullGeneratorsZClass'.)
##
##  'CR.codedIsomorphismTypeQClass' provides for each Q-class an entry of the
##      form  100 * t + p,  where  t  is the  isomorphism type number  of the
##      respective representative group  (with respect  to all  groups of the
##      same order),  and  p  is either zero  or a pointer to the text string
##      list 'CR_TextStrings.isomorphismType'.
##
##  'CR.codedNormalizerZClass' provides for each Z-class an entry of the form
##      1000 * n2 + n1,  where each of  n1 and n2 is either zero or a pointer
##      to the list  'CR.GeneratorsZClass'.  Let us  abbreviate  that list by
##      "gens". Then the normalizer of the representative matrix group of the
##      given Z-class can be computed  from n1 and n2 as follows.  If n1 = 0,
##      then  the  normalizer  is  one  of  the  Z-class represenative matrix
##      groups,  and n2 is a pointer to its generators.  If n2 = 0,  then the
##      normalizer  is infinite  and will be  generated  by the  given  group
##      together with  the list  of generators  to which n1 points.  If both,
##      n1 and n2,  are non-zero,  then  n1  point to the  generators of some
##      Z-class representative  which  has  to  be  conjugated  by the  first
##      matrix in the lisin pointed to by nin in order to get the normalizer.
##
##  'CR.codedPresentationQClass'  provides  for each Q-class  an entry of the
##      form  10 * p + n,  where  n  is  the  number  of  generators  of  the
##      representative group of the given Q-class,  and p is a pointer to the
##      corresponding list of relators in 'CR.relatorNumbersQClass'.
##
##  'CR.codedPropertiesFamily'  provides for each crystal family  an entry of
##      the form  1000 * f + 100 * b + 10 * q + r,  where  f is the number of
##      free parameters,  b  is the number of Bravais systems  in the family,
##      and  q  and  r  are pointers to appropriate text strings  in the list
##      'CR_TextStrings.family'  which  describe the  rational  and the  real
##      decomposition pattern, respectively.
##
##  'CR.codedPropertiesZClass' provides for each Z-class an entry of the form
##      100 * c + 10 * b + d,   where  c  is  the  order  of  the  associated
##      cohomology group,  b  is the Bravais type  of the given Z-class,  and
##      d  is a pointer to a text string  in the list 'CR_TextStrings.ZClass'
##      which describes the decomposition pattern.
##
##  'CR.columnGeneratorSpaceGroup'  is a list of all different columns  which
##      occur  as last column  in at least one of the  space group generators
##      listed in the catalogue.  Note that each column in the list  has been
##      multiplied by the common denominator of its entries.
##
##  'CR.crystalSystemQClass'  provides  for each  Q-class  the  number of the
##      crystal system to which it belongs.
##
##  'CR.dimension' is the given dimension, i.e. 2, 3, or 4.
##
##  'CR.familyCrystalSystem'  provides for each crystal system  the family to
##      which it belongs.
##
##  'CR.fixedPointFreeSpaceGroup'   is  a   Boolean  list   containing  those
##      space-group  types  for which  the  corresponding  space  groups  are
##      fixed-point-free.
##
##  'CR.GLZ is the group GL(dim,Z), where dim is the given dimension.
##
##  'CR.HermannMauguinSymbol'  is a list of the Hermann-Mauguin associated to
##      the  given dimension  in the order  in which  they are listed  in the
##      International Tables. (Only for dimensions 2 or 3.)
##
##  'CR.hQClass'  is a Boolean list containing the numbers of those Q-classes
##      which are holohedries.
##
##  'CR.internatTableSpaceGroupType'  provides for each space-group  type its
##      number in the International Tables. If a space-group type splits into
##      an  enantiomorphic pair,  then the  corresponding entry  of the  list
##      contains  both  numbers  in  the  form  1000 * it1 + it2.  (Only  for
##      dimension 3.)
##
##  'CR.modulSp'  is an integer  used to pack and unpack  the entries of list
##      CR.codedGeneratorsSpaceGroup.
##
##  'CR.modulZ  is an integer  used to  pack and unpack  the entries  of list
##      CR.codedGeneratorZClass.
##
##  'CR.nameCrystalFamily'  provides for each crystal family its family name.
##
##  'CR.nullDadeGroupsZClass'  contains  for each Z-class  a pointer p to the
##      list 'CR.codedDadeGroupsZClass'  such that,  for some n,  the entries
##      p + 1  to  p + n  of  that  list  provide  representatives  of  those
##      conjugacy classes  of subgroups  of Dade groups  which contain groups
##      from the  respective Z-class.  The last entry points just to the last
##      generator in the list.
##
##  'CR.nullGeneratorsZClass'  contains  for each Z-class  a pointer p to the
##      list  'CR.codedGeneratorZClass'  such that,  for some n,  the entries
##      p + 1  to   p + n   of  that  list  provide  the  generators  of  the
##      representative  matrix group  of the  respective Z-class.  Additional
##      entries point  to sublists  which  represent  generators of  infinite
##      normalizers or conjugating elements which are used to compute certain
##      finite normalizers.  The last entry points just to the last generator
##      in the list.
##
##  'CR.nullQClass'  provides for each crystal system the number of Q-classes
##      in the  preceding  crystal systems.  An  additional  entry  gives the
##      number of all Q-classes.
##
##  'CR.nullSpaceGroup'  provides for each Z-class  the number of space-group
##      types  in the  preceding Z-classes.  An  additional entry  gives  the
##      number of all space-group types.
##
##  'CR.nullZClass'  provides for each Q-class the number of Z-classes in the
##      preceding  Q-classes.  An additional entry  gives  the number  of all
##      Z-classes.
##
##  'CR.orbitLengthSpaceGroup'  provides for each space-group type  which is
##      not the Z-class representative  the orbit length associated with that
##      space-group type.
##
##  'CR.orderQClass'  provides for each Q-class  the order  of the  groups in
##      that Q-class.
##
##  'CR.parametersDadeGroup' is a list which for each Dade group of the given
##      dimension contains its parameter list [ dim, sys, qcl, zcl ].
##
##  'CR.QClassZClass'  provides for each Z-class the number of the Q-class to
##      which it belongs.
##
##  'CR.relatorNumbersQClass'  is a list  of  lists  of  relators,  where the
##      relators  in the  lists  are  represented  by  pointers  to the  list
##      'CR.relatorWordsQClass'.
##
##  'CR.rowConjugatorDadeGroup'  is a list of all different rows  which occur
##      in the matrices  which are used  to conjugate  Z-class representative
##      groups  into subgroups  of Dade groups.  (It is addressed by pointers
##      which     are     contained     in     entries     of    the     list
##      'CR.codedConjugatorDadeGroup'.)
##
##  'CR.rowGeneratorZClass'  is a list of  all different rows  which occur in
##      the matrices  which are used to  generate the  Z-class representative
##      groups.  (It is addressed by pointers  which are contained in entries
##      of the lists 'CR.nullGeneratorsZClass' and 'CR.codedGeneratorZClass'.
##
##  'CR.spaceGroupIdentity'  is the  identity matrix  of the associated space
##      groups.
##
##  'CR.spaceGroupTypeInternatTable'   provides for each  International Table
##      number  the corresponding  "global parameters"  z und t (cf. function
##      'CR_Parameters') in the form 100 * t + z.  (Only for dimensions 2 and
##      3.)
##
##  'CR.splittingQClass'  is a Boolean list  containing the  numbers of those
##      Q-classes which split into enantiomorphic pairs.  (Only for dimension
##      4.)
##
##  'CR.splittingSpaceGroupType'   is  a   Boolean  list   containing   those
##      space-group types  which split into  enantiomorphic pairs.  (Only for
##      dimensions 3 and 4.)
##
##  'CR.splittingZClass'  is a Boolean list  containing the numbers  of those
##      Z-classes which split into enantiomorphic pairs.  (Only for dimension
##      4.)
##
##  'CR_TextStrings.roman' is a list of the 23 smallest non-negative integers
##      expressed by Roman numerals.
##

CR_TextStrings := rec( );
CR_2 := rec( );
CR_3 := rec( );
CR_4 := rec( );

CrystGroupsCatalogue := [ CR_TextStrings, CR_2, CR_3, CR_4 ];

CR_TextStrings.crystalSystem :=
  ["#I  Crystal system "," Q-class"," Q-classes","; holohedry (",",",": ",
  ")"];

CR_TextStrings.family :=
  ["irreducible","decomposition pattern ","1+1","1+1+1","1+1+1+1",
  "1+1+2","1+2","1+3","2+2","Q-","R-","#I Family ",": ","; ","s",
  " free parameter"," crystal system"," Bravais flock",";\n#I  "];

CR_TextStrings.isomorphismType :=
  ["C1","C2","C3","C2xC2","C4","C5","C6","D6","C2xC2xC2","C4xC2",
  "C8","D8","Q8","C3xC3","C10","D10","C6xC2","C12","D12","Q12",
  "A4","C2xC2xC2xC2","C4xC2xC2","C4xC4","D8xC2","<2,2,2>2","(4,4/2,2)",
  "<2,2/4;2>","<2,2/2>","D16","<-2,4/2>","C6xC3","D6xC3","D(C3xC3)",
  "D10xC2","C6xC2xC2","C12xC2","D8xC3","Q8xC3","D12xC2","D6xC4",
  "Q12xC2","<-2,2,3>","A4xC2","(4,6/2,2)","D24","<2,3,3>","S4",
  "D8xC2xC2","D8xC4","C4^S2","(C2xC2)^S2","D(C4xC4)","C6xC6","D6xC6",
  "Q12xC3","D(C3xC3)xC2","D6xD6","(3,4,4;3)","D8xC6","D12xC2xC2",
  "D12xC4","A4xC2xC2","(4,6/2,2)xC2","D24xC2","S4xC2","D8xD6","A5",
  "D8xD8","D12xC6","D(C6xC6)","(4,6/2,2)xC3","<2,3,3>xC3","D12xD6",
  "(3,4,4;3)xC2","D6^S2","S4xC2xC2","D12xD8","S5","A5xC2","(D6^S2)xC2",
  "D12xD12","S5xC2","D12^S2","C2^S4","[3,4,3]"];

CR_TextStrings.QClass :=
  ["Q-constituents ","Q-irreducible; ","R-irreducible; ","C-irreducible; ",
  "; cc; ","; ncc; ","#I   Q-class ","#I  *Q-class ","): size ",
  "; isomorphism type "," Z-class"," Z-classes"," space group",
  " space grps",",","(",".","H ","; "," = ",";\n#I    "];

CR_TextStrings.QConstituents :=
  ["(2,1,1)+(2,1,2)","(4,1,1)+(4,1,2)+(4,3,1)","(4,1,1)+(4,1,2)+(4,3,2)",
  "(4,1,1)+(4,1,2)+(4,4,1)","(4,1,1)+(4,1,2)+(4,4,2)",
  "(4,1,1)+(4,1,2)+(4,4,3)","(4,1,1)+(4,1,2)+(4,4,4)","(3,1,1)+2*(3,1,2)",
  "(4,1,1)+3*(4,1,2)","(3,1,1)+(3,3,1)","(3,1,1)+(3,3,2)","(3,1,1)+(3,4,1)",
  "(3,1,1)+(3,4,2)","(3,1,1)+(3,4,3)","(3,1,1)+(3,4,4)","(4,1,1)+(4,7,1)",
  "(4,1,1)+(4,7,2)","(4,1,1)+(4,7,3)","(4,1,1)+(4,7,4)","(4,1,1)+(4,7,5)",
  "(3,1,2)+(3,3,1)","(3,1,2)+(3,3,2)","(3,1,2)+(3,4,1)","(3,1,2)+(3,4,2)",
  "(3,1,2)+(3,4,3)","(3,1,2)+(3,4,4)","(4,1,2)+(4,7,1)","(4,1,2)+(4,7,2)",
  "(4,1,2)+(4,7,3)","(4,1,2)+(4,7,4)","(4,1,2)+(4,7,5)","2*(2,1,1)",
  "2*(3,1,1)+(3,1,2)","2*(4,1,1)+2*(4,1,2)","2*(4,1,1)+(4,3,1)",
  "2*(4,1,1)+(4,3,2)","2*(4,1,1)+(4,4,1)","2*(4,1,1)+(4,4,2)",
  "2*(4,1,1)+(4,4,3)","2*(4,1,1)+(4,4,4)","2*(2,1,2)","2*(4,1,2)+(4,3,1)",
  "2*(4,1,2)+(4,3,2)","2*(4,1,2)+(4,4,1)","2*(4,1,2)+(4,4,2)",
  "2*(4,1,2)+(4,4,3)","2*(4,1,2)+(4,4,4)","2*(4,3,1)","2*(4,3,2)",
  "2*(4,4,1)","2*(4,4,2)","2*(4,4,3)","2*(4,4,4)","3*(3,1,1)",
  "3*(4,1,1)+(4,1,2)","3*(3,1,2)","(4,3,1)+(4,3,2)","(4,3,1)+(4,4,1)",
  "(4,3,1)+(4,4,2)","(4,3,1)+(4,4,3)","(4,3,1)+(4,4,4)","(4,3,2)+(4,4,1)",
  "(4,3,2)+(4,4,2)","(4,3,2)+(4,4,3)","(4,3,2)+(4,4,4)","4*(4,1,1)",
  "4*(4,1,2)","(4,4,1)+(4,4,2)","(4,4,1)+(4,4,3)","(4,4,1)+(4,4,4)",
  "(4,4,2)+(4,4,3)","(4,4,2)+(4,4,4)","(4,4,3)+(4,4,4)"];

CR_TextStrings.spaceGroup :=
  ["#I     Space-group type ","#I    *Space-group type ","; IT(",
  "; fp-free","orbit size ","(",",",") = ",", IT(","; ",";\n#I      ",
  ")","#I  Non-translation generators of ","\n\n"];

CR_TextStrings.ZClass :=
  ["; Z-irreducible","; Z-reducible","; Z-decomposable",
  "; fully Z-reducible","#I    Z-class ","#I   *Z-class ",
  ": Bravais type "," space group"," space groups",
  "; cohomology group size "," = Z(",")",",","(","B ","/",";\n#I     "];

CR_TextStrings.roman :=
  ["I","II","III","IV","V","VI","VII","VIII","IX","X","XI","XII","XIII",
  "XIV","XV","XVI","XVII","XVIII","XIX","XX","XXI","XXII","XXIII"];

CR_2.bZClass := BlistList( [1..13], [2,5,6,8,13] );

CR_2.codedConjugatorDadeGroup := [142,421,563];

CR_2.codedDadeGroupsZClass := [2,1,2,1,21,12,32,21,1,12,1,1,1,2,2,2,2,2];

CR_2.codedDecompositionQClass := [325,415,16,416,3,4,3,4,3,4];

CR_2.codedGeneratorsSpaceGroup := [2,1,3,3];

CR_2.codedGeneratorZClass :=
  [16,6,10,26,10,6,26,6,25,6,10,25,6,19,1,19,26,19,6,19,26,6,19,10,2,17];

CR_2.codedIsomorphismTypeQClass := [101,102,102,104,205,412,103,208,107,319];

CR_2.codedNormalizerZClass := [14000,14000,5,6,8,8,8,8,13,13,13,13,13];

CR_2.codedPresentationQClass := [11,21,21,202,212,243,401,462,452,433];

CR_2.codedPropertiesFamily := [3133,2233,1101,1101];

CR_2.codedPropertiesZClass :=
  [114,114,214,122,414,122,111,211,111,111,111,111,111];

CR_2.columnGeneratorSpaceGroup := [[0,0,1],[0,1,2],[1,0,2],[1,1,2]];

CR_2.crystalSystemQClass := [1,1,2,2,3,3,4,4,4,4];

CR_2.dimension := 2;

CR_2.familyCrystalSystem := [1..4];

CR_2.fixedPointFreeSpaceGroup := BlistList( [1..17], [1,4] );

CR_2.GLZ := GLZ2;

CR_2.HermannMauguinSymbol :=
  ["p1","p2","pm","pg","cm","p2mm","p2mg","p2gg","c2mm","p4","p4mm",
  "p4gm","p3","p3m1","p31m","p6","p6mm"];

CR_2.hQClass := BlistList( [1..10], [2,4,6,10] );

CR_2.modulSp := 4;

CR_2.modulZ := 6;

CR_2.nameCrystalFamily := ["oblique","rectangular","square","hexagonal"];

CR_2.nullDadeGroupsZClass := [0,2,4,5,8,9,11,12,13,14,15,16,17,18];

CR_2.nullGeneratorsZClass := [0,1,2,3,4,6,8,10,13,14,16,18,20,23,26];

CR_2.nullQClass := [0,2,4,6,10];

CR_2.nullSpaceGroup := [0,1,2,4,5,8,9,10,12,13,14,15,16,17];

CR_2.nullZClass := [0,1,2,4,6,7,8,9,11,12,13];

CR_2.orbitLengthSpaceGroup := [1,2,1,1];

CR_2.orderQClass := [1,2,2,4,4,8,3,6,6,12];

CR_2.parametersDadeGroup := [[2,3,2,1,0],[2,4,4,1,0]];

CR_2.QClassZClass := [1,2,3,3,4,4,5,6,7,8,8,9,10];

CR_2.relatorNumbersQClass :=
  [[1], [2], [2,10,22,28,40,61,92,129,163,198],
  [2,10,22,31,34,40,61,92,116,129,166,186,199,228,247],
  [2,10,22,31,40,61,92,129,174,202], [2,10,22,40,61,129],
  [2,10,24,28,34,40,62,92,116,142,168,186,201,227,249],
  [2,10,24,28,40,62,92,142,163,198], [2,10,24,28,40,62,92,142,168,201],
  [2,10,24,28,40,62,92,142,168,214],
  [2,10,24,30,40,78,80,100,106,108,109,130,153,175,176,177,179,210,217,219,
  220],
  [2,10,24,33,40,78,80,100,107,108,110,111,112,113,114,115,130,153,175,176,
  178,180,181,182,183,184,185,211,218,219,221,222,223,224,225,226],
  [2,10,24,40,62,142], [2,10,26,28,40,62,104,142,163,209],
  [2,10,26,28,40,78,92,130,168,209], [2,10,26,28,40,78,92,130,168,216],
  [2,10,26,28,40,78,93,130,164,216], [2,10,26,40,62,142],
  [2,10,26,40,78,130], [2,10,40], [2,11,40],
  [2,11,22,28,40,61,92,142,163,198], [2,11,22,40,61,129],
  [2,11,22,40,61,142],
  [2,17,22,28,35,38,40,61,105,117,125,147,172,189,195,198,230,237,244,250,
  256],
  [2,17,22,28,36,37,40,61,105,120,124,147,172,190,194,198,231,236,241,251,
  259],
  [2,17,22,28,36,40,61,105,118,147,172,191,198,233,243],
  [2,17,22,32,34,40,79,99,116,129,172,192,205,228,248],
  [2,17,22,32,35,37,39,40,79,96,122,123,128,147,167,186,196,197,205,234,239,
  240,245,252,255,260,261,262],
  [2,17,22,32,35,37,40,79,96,122,123,147,167,186,196,205,234,239,245,252,
  260],
  [2,17,22,32,35,40,79,98,121,147,165,188,212,232,246],
  [2,17,22,32,40,79,95,129,172,199], [2,17,25,28,40,79,92,133,168,215],
  [2,17,25,40,79,133], [2,17,26,28,40,61,92,147,163,216],
  [2,19,26,28,40,61,92,136,173,216], [2,19,26,28,40,61,92,148,173,216],
  [2,19,26,40,61,136], [2,19,26,40,61,148], [3],
  [3,10,22,28,40,73,92,129,163,198], [3,10,22,40,61,129],
  [3,10,22,40,73,129], [3,10,22,41,61,129], [3,10,40], [3,10,41],
  [3,16,22,40,73,146], [3,16,25,28,40,66,101,143,169,215],
  [3,16,25,40,79,131], [3,16,40], [3,19,22,41,61,148], [3,19,22,41,73,137],
  [3,19,25,28,40,79,101,137,168,207], [3,19,25,28,40,79,105,137,173,215],
  [3,19,25,40,79,137], [3,19,41], [3,21,22,41,61,149], [3,21,22,41,73,136],
  [3,21,41], [4],
  [4,10,22,28,35,37,40,74,102,119,126,129,169,187,193,198,229,238,242,253,
  257],
  [4,10,22,28,35,37,40,74,102,119,127,129,169,187,193,198,229,235,242,254,
  258],
  [4,10,22,28,35,40,74,102,119,129,169,187,198,229,242],
  [4,10,22,28,40,63,102,129,163,200], [4,10,22,28,40,74,92,129,163,198],
  [4,10,22,28,40,74,102,129,169,198], [4,10,22,40,61,129],
  [4,10,22,40,63,129], [4,10,22,40,74,129], [4,10,22,40,74,143],
  [4,10,22,40,78,129], [4,10,22,42,61,129], [4,10,40], [4,10,42],
  [4,12,24,28,42,63,102,130,170,202], [4,12,24,28,42,78,102,132,168,214],
  [4,12,24,29,42,63,92,130,168,203], [4,12,24,42,63,130],
  [4,12,24,42,78,132], [4,12,27,28,42,62,102,144,170,208],
  [4,12,27,42,63,132], [4,12,42], [4,17,22,28,40,79,102,147,172,213],
  [4,17,22,40,67,129], [4,17,22,40,74,147], [4,17,22,42,74,147],
  [4,17,25,28,40,62,102,132,163,206], [4,17,25,40,67,144], [4,17,40],
  [4,17,42], [4,18,26,48,50,52,54,71,82,84,87,89,139,150,154,157,160],
  [4,18,26,48,50,52,54,72,81,85,86,90,140,151,156,159,161],
  [4,20,26,49,51,53,55,56,57,58,59,60,70,83,84,88,91,141,152,155,158,162],
  [5], [5,10,43], [5,17,42], [6], [6,10,22,28,44,61,92,129,163,198],
  [6,10,22,40,61,129], [6,10,22,40,62,132], [6,10,22,40,64,129],
  [6,10,22,40,75,129], [6,10,22,40,75,144], [6,10,22,44,61,129],
  [6,10,22,44,75,145], [6,10,40], [6,10,44], [6,13,44], [6,16,22,40,75,146],
  [6,16,40], [6,17,22,44,75,134], [6,17,44], [6,19,22,40,75,148],
  [6,19,22,44,61,148], [6,19,22,44,75,137], [6,19,22,44,75,148],
  [6,19,25,28,40,69,92,138,173,215], [6,19,25,40,68,135], [6,19,40],
  [6,19,44], [7], [7,10,22,28,44,64,97,129,163,212],
  [7,10,22,28,44,76,94,129,163,212], [7,10,22,44,64,129],
  [7,10,22,44,65,145], [7,10,22,44,76,129], [7,10,42], [7,10,44], [7,10,45],
  [8], [8,10,46], [8,17,42], [9], [9,10,22,40,76,129], [9,10,22,40,77,129],
  [9,10,22,44,61,129], [9,10,22,44,76,129], [9,10,22,44,77,145],
  [9,10,23,47,76,144], [9,10,40], [9,10,44], [9,10,45], [9,10,47],
  [9,14,24,28,45,65,103,132,171,204], [9,14,24,45,65,132], [9,14,45],
  [9,15,44]];

CR_2.rowConjugatorDadeGroup := [[0,-1],[1,-1],[1,0],[1,1]];

CR_2.rowGeneratorZClass := [[-1,0],[0,-1],[0,1],[1,-1],[1,0],[1,1]];

CR_2.spaceGroupIdentity :=
  [[1,0,0],[0,1,0],[0,0,1]];

CR_2.spaceGroupTypeInternatTable :=
  [101,202,303,403,504,605,705,805,906,1007,1108,1208,1309,1410,
  1511,1612,1713];

CR_3.bZClass :=
  BlistList( [1..73], [2,7,8,18,19,20,21,36,37,48,58,71,72,73] );

CR_3.codedConjugatorDadeGroup :=
  [79395,118877,176683,176831,177111,177382,177535,178513,178786,
  178792,196429,196575,217297,217709,256914,294149,296253,296396,
  334898];

CR_3.codedDadeGroupsZClass :=
  [1,2,3,4,1,2,3,4,141,142,191,51,142,123,23,144,134,141,42,
  31,81,42,93,13,174,74,141,142,191,81,142,93,123,174,134,2,
  61,2,3,184,13,4,2,61,2,51,61,142,143,184,104,113,13,144,
  2,61,2,3,184,13,4,2,13,144,2,13,144,2,13,144,142,13,144,
  2,13,144,142,2,13,144,13,144,142,13,144,42,163,154,1,42,
  163,154,1,42,163,154,1,1,42,163,154,1,1,42,163,154,1,1,1,
  1,1,1,1,1,1,1,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4];

CR_3.codedDecompositionQClass :=
  [545,565,85,335,565,566,86,566,106,216,216,226,116,226,226,
  126,256,246,136,266,146,236,256,266,156,246,266,4,4,4,4,4];

CR_3.codedGeneratorsSpaceGroup :=
  [4,1,1,14,56,70,14,84,88,102,14,112,56,1,57,62,63,14,70,
  71,76,1,14,112,1,113,18,112,8,14,798,1666,1176,1190,1568,
  1582,1232,1246,1624,1638,112,126,1428,1442,14,196,1568,1582,
  1764,252,112,1568,1092,17,1,104,14,1624,1638,994,238,14,1656,
  1922,1670,994,14,1,15,1658,1672,1659,1673,8,994,1002,14,1656,
  1670,1,1658,1659,8,994,14,196,210,23212,23226,23408,23422,
  23184,23198,23380,23394,112,126,308,322,112,20090,20062,2,28,
  28,113,1,1,1582,14,14,28,1,29,14,392,14,406,1,14,15,1,14,
  14,196,210,1092,1092,23324,15288,3528,15288,30156,23436,23436,
  20194,23325,3536,20194,1582,326550,326648,126,49504,49406,282716];

CR_3.codedGeneratorZClass :=
  [3092,2624,2719,2570,2997,3164,2624,2719,2624,2570,2719,2985,
  2570,2985,5062,276,4433,2783,2997,2985,3164,2985,2931,2570,
  1071,276,1643,2783,2624,2719,2985,2624,2570,2985,2624,5062,276,
  2624,4433,2783,3159,2985,1625,2783,2575,2985,4451,2783,2624,
  3159,2985,2624,1625,2783,2719,3159,2985,4433,1625,2783,2997,
  3159,2985,1643,1625,2783,2719,2575,2985,2997,2575,2985,1643,
  4451,2783,4433,4451,2783,2624,2719,3159,2985,2624,4433,1625,
  2783,3884,3121,2624,3884,2624,3121,2570,3884,2570,3121,2803,
  3121,3164,3884,2931,3121,3164,3121,2624,2570,3884,2624,2570,
  3121,2624,2803,3121,2985,3121,2731,3121,2624,2985,3121,2803,
  2985,3121,2931,2985,3121,2931,2731,3121,2803,2731,3121,2624,
  2803,2985,3121,3884,2719,2985,3884,5062,276,3884,4433,2783,
  2624,3884,2719,2985,2624,3884,5062,276,2624,3884,4433,2783,
  2803,3884,2719,2985,6595,3884,5062,276,3005,3884,4433,2783,
  2931,3884,2719,2985,204,3884,5062,276,2711,3884,4433,2783,2624,
  2803,3884,2719,2985,2624,6595,3884,5062,276,2624,3005,3884,
  4433,2783,979,3080,3884,3095,5252,3093,920,824,2636,3884,3095,
  5980,3112,424,458,3093,824,2636,3093,5157,2985,2719,3112,458,
  2783,3112,6052,3005,2570];

CR_3.codedIsomorphismTypeQClass :=
  [101,102,102,102,104,104,104,109,205,205,210,412,412,412,625,
  103,107,208,208,319,107,107,117,319,319,319,640,521,1044,
  1548,1548,3666];

CR_3.codedNormalizerZClass :=
  [75000,77000,76000,78000,80000,82000,79000,81000,71,36,72,73,36,
  36,19,74037,37,71,36,72,73,36,37,36,37,36,37,36,37,36,37,36,36,
  37,37,36,37,48,58,48,58,48,58,58,48,58,58,48,58,58,58,58,58,58,
  58,58,58,58,71,72,73,71,72,73,71,72,73,71,72,73,71,72,73];

CR_3.codedPresentationQClass :=
  [11,21,21,21,202,202,202,63,212,212,233,243,243,243,224,401,
  452,462,462,443,452,452,423,433,433,433,414,133,84,94,94,75];

CR_3.codedPropertiesFamily := [6144,4244,3444,2277,2277,1301];

CR_3.codedPropertiesZClass :=
  [114,114,214,123,414,223,814,223,814,223,132,242,1614,423,423,
  232,442,6414,823,232,842,414,222,114,122,414,222,814,222,814,
  422,414,414,222,222,1614,422,112,324,112,124,112,324,324,212,
  224,224,212,224,224,624,124,224,624,424,224,224,424,211,121,
  231,411,221,231,411,221,231,211,221,231,411,421,231];

CR_3.columnGeneratorSpaceGroup :=
  [[0,0,0,1],[0,0,1,2],[0,0,1,3],[0,0,1,4],[0,1,0,2],[0,1,1,2],
  [1,0,0,2],[1,0,1,2],[1,1,0,2],[1,1,1,2],[1,1,2,4],[2,0,1,4],
  [3,1,0,4],[3,2,3,4]];

CR_3.crystalSystemQClass :=
  [1,1,2,2,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,6,7,7,7,7,7];

CR_3.dimension := 3;

CR_3.familyCrystalSystem := [1,2,3,4,5,5,6];

CR_3.fixedPointFreeSpaceGroup :=
  BlistList( [1..219], [1,4,7,9,19,33,34,76,142,165] );

CR_3.GLZ := GLZ3;

CR_3.HermannMauguinSymbol :=
  ["P1","P-1","P2","P21","C2","Pm","Pc","Cm","Cc","P2/m","P21/m",
  "C2/m","P2/c","P21/c","C2/c","P222","P2221","P21212","P212121",
  "C2221","C222","F222","I222","I212121","Pmm2","Pmc21","Pcc2",
  "Pma2","Pca21","Pnc2","Pmn21","Pba2","Pna21","Pnn2","Cmm2","Cmc21",
  "Ccc2","Amm2","Abm2","Ama2","Aba2","Fmm2","Fdd2","Imm2","Iba2",
  "Ima2","Pmmm","Pnnn","Pccm","Pban","Pmma","Pnna","Pmna","Pcca",
  "Pbam","Pccn","Pbcm","Pnnm","Pmmn","Pbcn","Pbca","Pnma","Cmcm",
  "Cmca","Cmmm","Cccm","Cmma","Ccca","Fmmm","Fddd","Immm","Ibam",
  "Ibca","Imma","P4","P41","P42","P43","I4","I41","P-4","I-4",
  "P4/m","P42/m","P4/n","P42/n","I4/m","I41/a","P422","P4212",
  "P4122","P41212","P4222","P42212","P4322","P43212","I422","I4122",
  "P4mm","P4bm","P42cm","P42nm","P4cc","P4nc","P42mc","P42bc","I4mm",
  "I4cm","I41md","I41cd","P-42m","P-42c","P-421m","P-421c","P-4m2",
  "P-4c2","P-4b2","P-4n2","I-4m2","I-4c2","I-42m","I-42d","P4/mmm",
  "P4/mcc","P4/nbm","P4/nnc","P4/mbm","P4/mnc","P4/nmm","P4/ncc",
  "P42/mmc","P42/mcm","P42/nbc","P42/nnm","P42/mbc","P42/mnm",
  "P42/nmc","P42/ncm","I4/mmm","I4/mcm","I41/amd","I41/acd","P3",
  "P31","P32","R3","P-3","R-3","P312","P321","P3112","P3121",
  "P3212","P3221","R32","P3m1","P31m","P3c1","P31c","R3m","R3c",
  "P-31m","P-31c","P-3m1","P-3c1","R-3m","R-3c","P6","P61","P65",
  "P62","P64","P63","P-6","P6/m","P63/m","P622","P6122","P6522",
  "P6222","P6422","P6322","P6mm","P6cc","P63cm","P63mc","P-6m2",
  "P-6c2","P-62m","P-62c","P6/mmm","P6/mcc","P63/mcm","P63/mmc","P23",
  "F23","I23","P213","I213","Pm-3","Pn-3","Fm-3","Fd-3","Im-3",
  "Pa-3","Ia-3","P432","P4232","F432","F4132","I432","P4332","P4132",
  "I4132","P-43m","F-43m","I-43m","P-43n","F-43c","I-43d","Pm-3m",
  "Pn-3n","Pm-3n","Pn-3m","Fm-3m","Fm-3c","Fd-3m","Fd-3c","Im-3m",
  "Ia-3d"];

CR_3.hQClass := BlistList( [1..32], [2,5,8,15,20,27,32] );

CR_3.internatTableSpaceGroupType :=
  [1,2,3,4,5,6,7,8,9,10,13,11,14,12,15,16,17,18,19,21,20,
  22,23,24,25,28,27,30,32,34,26,31,29,33,35,37,36,38,39,40,
  41,42,43,44,46,45,47,49,50,48,51,54,53,52,57,60,59,56,55,
  58,62,61,65,66,63,67,68,64,69,70,71,72,74,73,75,78076,77,
  79,80,81,82,83,84,85,86,87,88,89,95091,93,90,96092,94,97,
  98,99,105,103,101,100,106,104,102,107,108,109,110,111,112,
  113,114,115,116,117,118,119,120,121,122,123,124,131,132,125,
  126,133,134,129,130,137,138,127,128,135,136,139,140,141,142,
  146,143,145144,148,147,155,149,153151,150,154152,160,161,156,
  158,157,159,166,167,162,163,164,165,168,171172,173,170169,174,
  175,176,177,180181,182,179178,183,184,186,185,187,188,189,190,
  191,192,194,193,195,198,196,197,199,200,201,205,202,203,204,
  206,207,213212,208,209,210,211,214,215,218,216,219,217,220,
  221,223,222,224,225,226,228,227,229,230];

CR_3.modulSp := 14;

CR_3.modulZ := 19;

CR_3.nameCrystalFamily :=
  ["triclinic","monoclinic","orthorhombic","tetragonal","hexagonal",
  "cubic"];

CR_3.nullDadeGroupsZClass :=
  [0,4,8,10,17,19,26,28,35,36,38,40,42,43,45,48,51,54,55,
  57,59,61,62,64,65,67,68,70,71,73,74,76,77,78,80,82,83,85,
  88,89,92,93,96,97,98,101,102,103,106,107,108,109,110,111,
  112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,
  127,128,129,130,131];

CR_3.nullGeneratorsZClass :=
  [0,1,2,3,4,5,6,8,10,12,14,16,18,20,22,24,26,28,31,34,37,
  40,42,44,46,48,51,54,57,60,63,66,69,72,75,78,82,86,87,88,
  90,92,94,96,98,100,102,104,107,110,113,115,117,120,123,126,
  129,132,136,139,142,145,149,153,157,161,165,169,173,177,181,
  186,191,196,197,200,204,207,211,214,218,221,225];

CR_3.nullQClass := [0,2,5,8,15,20,27,32];

CR_3.nullSpaceGroup :=
  [0,1,2,4,5,7,9,13,15,19,21,22,24,34,37,41,43,46,62,68,
  70,74,77,79,80,81,85,87,93,95,103,107,111,115,117,119,135,
  139,140,142,143,144,145,147,149,151,153,155,157,159,161,165,
  166,168,172,176,178,180,184,186,187,189,192,194,196,199,201,
  203,205,207,209,213,217,219];

CR_3.nullZClass :=
  [0,1,2,4,6,8,12,17,21,23,25,27,29,31,35,37,39,41,44,47,
  50,51,52,53,54,55,57,58,61,64,67,70,73];

CR_3.orbitLengthSpaceGroup :=
  [1,3,1,3,1,3,1,3,3,1,1,1,2,1,2,1,1,2,2,2,2,1,2,1,1,
  1,1,2,1,3,3,1,6,6,6,6,6,6,3,3,3,3,6,2,1,2,1,1,2,1,
  3,3,1,2,1,1,1,1,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,2,2,2,1,1,1,1,1,1,2,1,2,1,2,1,2,1,1,1,1,1,1,1,
  1,1,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1];

CR_3.orderQClass :=
  [1,2,2,2,4,4,4,8,4,4,8,8,8,8,16,3,6,6,6,12,6,6,12,12,12,
  12,24,12,24,24,24,48];

CR_3.parametersDadeGroup :=
  [[3,6,7,1,0],[3,7,5,1,0],[3,7,5,2,0],[3,7,5,3,0]];

CR_3.QClassZClass :=
  [1,2,3,3,4,4,5,5,6,6,6,6,7,7,7,7,7,8,8,8,8,9,9,10,
  10,11,11,12,12,13,13,14,14,14,14,15,15,16,16,17,17,18,18,
  18,19,19,19,20,20,20,21,22,23,24,25,26,26,27,28,28,28,29,
  29,29,30,30,30,31,31,31,32,32,32];

CR_3.relatorNumbersQClass := CR_2.relatorNumbersQClass;

CR_3.rowConjugatorDadeGroup :=
  [[-1,-1,-1],[-1,-1,0],[-1,0,0],[-1,0,1],[-1,1,0],
  [0,-1,-1],[0,-1,0],[0,-1,1],[0,0,1],[0,1,-1],
  [0,1,0],[0,1,1],[1,-1,0],[1,0,-1],[1,0,0],
  [1,0,1],[1,1,1],[1,1,2]];

CR_3.rowGeneratorZClass :=
  [[-1,-1,-1],[-1,-1,1],[-1,0,0],[-1,0,1],[-1,1,0],[0,-1,0],
  [0,-1,1],[0,0,-1],[0,0,1],[0,1,-1],[0,1,0],[0,1,1],[1,-1,0],
  [1,0,-1],[1,0,0],[1,0,1],[1,1,-1],[1,1,0],[1,1,1]];

CR_3.spaceGroupIdentity :=
  [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]];

CR_3.spaceGroupTypeInternatTable :=
  [101,202,303,403,504,605,705,806,906,1007,1207,1408,1107,1307,
  1508,1609,1709,1809,1909,2110,2010,2211,2312,2412,2513,3113,
  2713,2613,3313,2813,3213,2913,3413,3013,3514,3714,3614,3815,
  3915,4015,4115,4216,4316,4417,4617,4517,4718,5018,4818,4918,
  5118,5418,5318,5218,5918,5818,5518,6018,5718,5618,6218,6118,
  6519,6819,6319,6419,6619,6719,6920,7020,7121,7221,7421,7321,
  7522,7622,7722,7622,7823,7923,8024,8125,8226,8326,8426,8526,
  8627,8727,8828,9128,8928,9228,9028,9328,8928,9228,9429,9529,
  9630,10030,9930,10330,9830,10230,9730,10130,10431,10531,10631,
  10731,10832,10932,11032,11132,11233,11333,11433,11533,11634,
  11734,11835,11935,12036,12136,12436,12536,13236,13336,12836,
  12936,12236,12336,12636,12736,13436,13536,13036,13136,13637,
  13737,13837,13937,14139,14239,14239,14038,14441,14340,14643,
  14844,14743,14944,14743,14944,14542,15246,15447,15346,15547,
  15045,15145,15849,15949,16050,16150,15648,15748,16251,16551,
  16551,16351,16351,16451,16652,16753,16853,16954,17254,17254,
  17054,17054,17154,17355,17455,17655,17555,17756,17856,17957,
  18057,18158,18258,18458,18358,18559,18760,18861,18659,18961,
  19062,19162,19363,19463,19564,19262,19664,19765,19965,20066,
  20166,20267,19865,19865,20367,20468,20669,20870,20568,20769,
  20970,21071,21271,21171,21371,21472,21572,21772,21672,21873,21973];

CR_3.splittingSpaceGroupType :=
  BlistList( [ 1 .. 219 ], [76,89,92,142,147,149,163,165,170,172,198] );

CR_4.bZClass :=
  BlistList( [1..710],
  [2,7,8,12,13,14,34,35,36,37,38,39,53,86,87,88,89,90,91,
  92,93,108,109,120,130,131,133,173,242,243,244,245,246,295,
  296,329,330,331,332,333,337,338,359,378,379,419,428,464,482,
  507,563,564,565,566,567,569,574,576,604,621,636,637,691,710] );

CR_4.codedConjugatorDadeGroup :=
  [4273681,6400667,8480660,9279532,11195122,12279467,12298451,12357446,
  15623922,16613802,19260299,19325973,19338622,21004202,22465651,
  25279713,26836042,28656840,31486984,33244423,33246395,36157062,
  36697684,38833653,41968382,44304724,44306282,44363772,45130978,
  45337662,45343783,45784833,46572214,47083975,47317495,47397622,
  48109758,48237718,49885273,50081235,51253736,52059902,52533832,
  55437104,55553703,55555115,55574723,55789055,56101272,56102655,
  56162732,57492995,57493012,57494114,58023035,58431983,60708505,
  60747994,60822328,60823741,60825332,60933786,61155935,61158054,
  61216434,61217245,61274523,61389605,61588992,63349460,63376504,
  63493248,63508795,63508934,63546728,63548155,63549675,63604695,
  63605108,63605942,63663387,63664324,63804066,63804487,63804624,
  63804626,63807003,63811766,63862367,63921812,63980875,64018544,
  64021624,64137261,64137683,64137684,64137687,64137703,64140233,
  64235684,64236099,64354121,64371353,64373855,64470184,64470461,
  64470884,64604452,64604453,65725012,66724894,69053908,69054764,
  69056855,69066244,69163383,69508195,69527678,69565344,69626658,
  69722984,69800681,69843532,71449321,72153765,74193323,77232724,
  77585524,78052841,78052983,78052987,78053401,78053406,78053680,
  78053683,78053684,78873935,80453739,82383716,83069624,85693922,
  88404015,88424440,89811601,90220655,91360562,93731575,93749676,
  93990720,93991022,94000098,94049515,94144560,94145297,94167383,
  94318062,94402300,94435083,94525188,96497283,96594861,96595283,
  96595284,96646684,96709223,96715422,96849822,96889263,96944864,
  97003944,97009124,97084602,97087783,97123763,97123802,97124043,
  97160044,97165504,97199664,97204424,97223164,97261260,97261266,
  97261401,97261683,97261687,97261824,97261826,97264204,97277358,
  97283267,97303124,97318514,97398601,97398883,97426038,98124517,
  99809001,101220593,102435678,104963063,105118346,105177144,105179776,
  105179923,105391650,105491164,105501275,105515550,105531615,
  107883357,108140112,110197006,110610142,110668942,110785343,
  110950612,112021303,112270943,112962124,112972335,113058164,
  113061524,113137486,113193264,113196183,113196222,113369253,
  113375115,113376112,113529243,113686904,113726523,113736472,
  113884749,113956684,114747111,115518080,116058522,117390613,
  118450126,118684357,118686726,118745508,118778275,118783303,
  118798855,118823915,118898424,118898523,118900903,118901264,
  118901615,118902315,118918123,119074923,119074962,119075763,
  119117465,119117591,119195194,119214521,120488549,121194121,
  121542872,121544700,121546903,121646337,121662343,121664503,
  121664542,121671914,121758723,121761702,121780558,121781453,
  121957692,121958521,122114674,124330002,124488183,126679743,
  126681704,126682123,126682124,126916222,126918720,126975403,
  127074103,127074142,127095115,127152503,127152542,127187664,
  127249422,127251923,127251924,127427176,127444143,127446519,
  127486992,127487272,127487552,128465703,129424592,129716346,
  129719250,129815762,129818103,129835323,129835362,129837703,
  129838442,129874523,129874562,129876942,129879322,129995649,
  130346222,131229342,132461757,132579328,132902595,133805883,
  133931728,134659472,134896493,135145544,135160113,135482363,
  135579684,139346101,140793123,140793722,142416874,143007661,
  143007801,143008083,143088733,143245818,143301783,143478468,
  143478502,143497783,143534066,143536563,143536602,143556902,
  143595783,143596242,143598324,143615702,143623386,143691569,
  143694068,143729623,143735822,143804284,143811261,143811401,
  143811683,143811684,143889365,143906045,143908987,143909266,
  143909401,143909407,143909687,143909824,143912169,143951124,
  143984729,144043244,144043526,144046460,144046883,144047024,
  144047026,144058224,144063553,144871043,145634912,145990618,
  146009419,146120862,146136109,146454023,146459944,146460222,
  146469882,146548284,146674135,146695115,146799706,147614890,
  149198344,149610766,151966145,154716260,155552903,156808724,
  156865704,156905324,156921385,157157744,157355695,157371664,
  157433401,157433683,157628564,157629260,157629266,157629401,
  157629683,157629684,157631644,158747155,160011634,164016851,
  165317789,165958163,166020021,167790612,168410783,170524795,
  170682584,170682861,170682866,170683006,170683284,170816844,
  170820061,170820066,170820206,170823013,170876764,170918475,
  170918492,170935564,170937655,170938232,170977292,170995346,
  170996875,171035252,171035655,171035795,171035812,171039457,
  171055692,171151980,171152020,171152983,171152984,171153261,
  171153401,171153406,171153407,171153543,171153683,171153684,
  171153826,171154684,171165583,171251266,171251687,171251824,
  171255463,171388052,171389733,171389855,171391552,171485003,
  171508026,172169252,172341709,172739034,172742693,173328575,
  173628193,174092146,174096229,174136122,174190160,174195053,
  175429162,176069896,176075689,176289703,176405792,176425795,
  176425812,176525064,176662103,176683562,176835995,176836134,
  176837248,176838533,176838672,176839093,176854112,176859549,
  176860522,176977282,176978682,177049063,179054884,179267833,
  181427494,182286904,182286927,182288714,182326550,182484449,
  184815843,184893683,185030926,185090286,187628482,189698662,
  190557687,190600682,190811390,192160007,193127686,193323518,
  193442795,196026785,198446904,200706302,201673422,203352398,
  203411195,204027793,204106189,204359435,204437275,207260107,
  209678062,209685034,209708584,210904042,212461485,212461611,
  214156126,214894765,214907506,215828706,216925333,220802872,
  223509220,227338635,229114262,229133722,233222658,234926586,
  236132345,236891767,237759067,237812967,241385693,243228437,244256273];

CR_4.codedDadeGroupsZClass :=
  [1,2,3,4,5,6,7,8,9,1,2,3,4,5,6,7,8,9,1321,2032,233,
  2978,1341,2181,3091,4702,4732,2173,4513,3524,3165,3205,1166,
  3537,3058,3509,2219,1321,2032,233,1698,1011,3251,3221,4182,
  1372,3233,4073,3184,3215,2115,2026,1977,2128,899,3249,1321,
  2032,233,1698,1341,2181,3091,4702,4732,2173,4513,3524,3165,
  2155,1166,3537,3058,3509,2219,1,1321,5,2208,771,1021,3752,
  3022,4822,692,623,1233,603,4803,678,4469,4261,4721,2384,1424,
  5424,4944,1565,495,1535,4525,1036,4196,1567,47,458,3649,1,5,
  3488,1021,3022,692,1233,603,988,4469,4261,5434,2404,1735,1725,
  4645,746,3907,4958,3649,4091,1678,1291,2181,4635,4388,521,4931,
  3742,3802,443,3723,4328,3012,4243,4913,4429,541,481,164,5015,
  5025,3925,3906,3897,4958,3719,3032,5522,513,919,1361,2418,3091,
  2181,1291,2155,2145,2878,521,4921,3742,3802,1273,3723,4328,531,
  4931,1772,1782,263,1923,478,2342,4763,4393,4913,889,5501,5491,
  5611,21,5644,5515,5475,5625,5605,1386,5657,5598,4029,19,2602,
  152,5462,4203,1269,4101,1678,1311,3041,3655,3438,1101,4491,
  1792,1802,713,1893,878,2342,4763,4393,4429,5501,5481,174,5585,
  105,145,136,127,118,1489,2592,5452,4053,669,1321,2418,1291,
  2181,3165,4388,521,4921,3742,3802,1273,3723,4328,3012,4243,
  4913,4429,1571,1551,5434,1655,1045,3915,5016,5007,3948,3719,
  3032,5522,513,4659,5634,2764,2374,305,325,5326,706,277,5247,
  288,1698,961,2438,1841,1601,908,4172,4043,4172,1283,4043,3999,
  4331,4571,1,4345,4155,3488,4112,1193,5122,2322,1703,1179,4239,
  4509,1404,315,5076,5337,288,8,951,4498,4172,1283,4539,1,5,
  2998,4112,3283,1179,4509,1698,1951,3601,4438,3621,2788,4172,
  3283,4172,1283,1213,3999,3591,3361,2551,4355,4165,3488,4112,
  3283,5122,2322,1703,1179,4239,4509,1698,1951,3601,4438,4301,
  2338,4172,4403,4043,4172,1713,789,1941,3601,2481,955,4145,3488,
  4112,2322,1703,4112,3283,4759,3429,639,8,3611,2968,4172,3283,
  4539,3601,5,2998,4112,3283,1179,4509,1351,4488,612,5033,99,
  1301,4488,432,5033,4879,1351,4488,612,5033,99,1321,4488,1321,
  4488,612,5033,99,612,723,99,1331,4488,4992,5033,4879,1351,
  4488,4992,723,4879,1321,4488,612,723,99,2792,333,5254,2366,
  417,5118,5299,5579,1,4595,2882,3823,5384,1516,3267,3878,5409,
  1599,1,2715,3192,423,1964,2196,297,5228,5299,189,1,4595,1,
  4635,3192,423,1964,2196,297,5228,5299,189,1,4615,1,4595,3072,
  3963,5394,1526,3837,3298,5409,2089,1,2715,1,2905,1,3685,1,
  2935,1,3695,1,3675,1,3675,1,2715,1,2905,1,3695,4475,2318,
  3009,2664,3155,3359,2664,4345,2249,5564,3404,1505,1645,3576,
  2356,4717,1087,468,3458,1071,4271,2628,1132,4083,3512,1003,
  1549,4699,5444,3905,3585,1666,747,468,928,4311,2648,1132,1003,
  5109,3989,5554,3854,1665,4785,5006,2636,3907,1097,468,3458,
  3458,1061,4311,2628,1051,4291,2628,1132,4033,1132,4033,3512,
  2943,3512,3313,1549,1549,4699,4699,5554,3854,4975,4785,5006,
  2636,3907,1097,468,3458,3458,1061,4291,2628,1051,4291,2628,
  1132,933,1132,4033,3512,3313,3512,3313,1549,1549,4699,4699,
  5414,3575,4795,4986,737,468,928,928,4281,2648,1071,2648,1132,
  3313,1132,3313,5109,5109,3989,3989,3458,1071,4271,2628,1132,
  4083,3512,1003,1939,3939,3458,1611,3371,2828,1132,4083,3512,
  1003,1419,3979,4458,4561,961,1688,2032,2223,2032,2073,1439,
  3979,4458,941,4541,1688,4062,2233,4062,4373,1479,5099,928,3371,
  2858,1132,1003,1419,3979,3458,1061,4311,2628,1132,4033,3512,
  2943,4969,5099,3458,3458,1631,3361,2828,3371,1621,2858,1132,
  4033,1132,4033,3512,2943,3512,3313,589,1419,3979,769,3458,1051,
  4291,2628,1132,4033,3512,2943,1939,3939,3498,4551,1688,2032,
  2073,1439,3979,928,3381,2858,1132,2833,1419,3979,2392,2583,
  2658,4854,1126,5357,2759,5369,1,3081,1835,4665,3332,1753,3448,
  5194,646,77,259,4819,2911,3081,835,3795,2052,3413,2678,2052,
  3413,2678,5154,3066,5267,5169,59,574,3066,377,5169,59,2911,
  2911,3081,4345,4135,3081,3705,3785,2392,2563,2678,5284,796,87,
  1499,2069,2911,3081,2505,2545,3302,1743,2298,364,806,387,1499,
  819,2911,3081,3125,3135,2392,2583,2658,4224,796,5347,2759,5379,
  1,1,3081,1835,4685,3081,1865,4675,2392,2583,2658,3734,596,
  5347,2759,5379,1,1,3081,1875,4685,3081,1865,4665,3332,1753,
  3448,344,656,197,259,4219,2911,2911,3081,835,3795,3081,845,
  3795,2012,2573,3448,5134,1186,197,259,4219,2911,2911,3081,845,
  3765,3081,855,3775,2802,1763,2678,5174,756,67,1499,3849,2911,
  2911,3081,2465,2535,3081,3145,3175,2911,1,1885,4665,1,1,3145,
  1,1,2895,1,1,1825,4155,1,1,1,3115,1,3105,2911,1,1835,4125,
  1,1,1,2515,1,2465,1,1,3665,2911,1,3695,5235,1,1,1,2705,1,
  2925,1,1,865,1,1,975,3485,2868,568,2619,1115,4258,4779,2694,
  2455,2284,2455,5544,2524,2305,1445,1459,2494,1855,4744,2725,
  225,2169,3885,3398,2268,2049,4975,4785,3398,4448,2268,2009,
  2049,3865,4368,2268,3478,2258,2009,2009,2049,3565,3398,2268,
  2268,2049,1589,505,3398,2268,4448,2268,2009,2009,1589,2848,
  2109,2268,3959,2268,3329,3478,3478,2109,559,2268,3959,2268,
  2009,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,204,34,995,4625,
  4014,4905,4585,214,4004,995,3884,4004,995,4625,4625,1394,5085,
  4605,5154,1209,5,3814,5539,5,4864,3279,1209,4585,4585,2094,
  5279,1209,4585,4585,5144,1209,684,1209,5,5,4585,354,2139,5539,
  5,4585,394,5539,5,5,1904,1209,5,4585,5,1914,5209,1209,4585,
  4585,5,5,5184,1209,5,5,5,404,5539,5,5,5,5,5,5,5,5,5,5,
  5,5,5,5,5,5,5,5,5046,4837,4888,8,2,3559,3,1259,5046,4837,
  4898,8,2,1159,3,1249,5066,4847,4888,8,2,3559,3,1259,5066,
  4847,4888,8,2,3559,3,1259,5056,5067,4898,8,2,1159,3,1249,8,
  2,3559,3,1259,8,2,3349,3,1259,8,2,3559,3,1259,8,2,3559,3,
  1259,8,2,1159,3,1249,8,2,1159,3,1249,8,2,3559,3,1259,8,2,
  3559,3,1259,8,2,3349,3,1259,8,2,3349,3,1259,8,2,1159,3,
  1249,4348,2989,2478,2989,826,1227,3546,2447,826,3637,826,1987,
  3546,1817,2735,5219,1145,5219,4,2424,4585,4,4585,4,4,4,2685,
  5,4,4,2685,5,4,5,4,5,5,4,4,5,2685,4,4,5,2685,4,5,5,
  4585,2685,2685,4605,4585,4585,2685,4585,4585,5,5,5,5,5,5,
  2816,2816,2777,2777,2956,7,6,7,6,7,6,7,6,7,6,7,3468,9,
  3478,2749,3478,2749,2278,9,4418,9,1469,3478,2749,3468,9,3478,
  2749,3468,8,2278,5319,5319,8,9,4418,1999,249,3468,9,3468,
  3468,9,9,2278,8,1999,9,2278,5319,8,9,9,3468,9,8,1999,9,8,
  9,9,8,9,9,8,1999,9,2749,5309,9,5309,9,9,2749,2749,9,9,
  2749,2749,9,9,9,9,9];

CR_4.codedDecompositionQClass :=
  [665,675,555,95,675,345,675,345,95,675,675,96,676,96,676,676,
  425,355,425,435,435,365,435,375,465,385,455,475,395,445,465,
  405,475,455,475,485,505,525,26,426,36,436,436,26,426,436,36,
  426,36,436,436,436,436,66,46,56,466,476,76,476,56,456,476,
  66,446,466,76,456,76,456,466,476,476,476,476,495,515,535,
  486,576,496,496,496,576,486,576,496,496,496,586,606,596,596,
  606,646,636,626,616,646,656,636,656,616,616,656,636,646,656,
  656,656,656,696,526,726,536,506,526,686,716,516,736,536,516,
  726,536,536,696,526,736,706,726,716,736,536,536,726,536,166,
  286,196,296,316,176,276,186,306,286,316,206,316,306,296,316,
  2,2,2,2,2,2,2,2,3,3,4,4,4,4,4,4,4,3,3,3,3,3,4,3,4,
  4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,4,4,3,4,4,4,4,4,
  4,4,4,4,4,4,4,4,3,3,3,4,3,3,3,4,4,3,4,4,4,4,4,4];

CR_4.codedGeneratorsSpaceGroup :=
  [4,42,1,1,4,6,15,1,15,1,19,4,23,1,15,19,401,415,419,1515,
  1519,1542,1546,2319,2346,1500,1515,1542,1500,1,1501,15,1515,
  19,1519,4200,4201,4215,4219,1500,1515,42,1542,1554,442,1500,
  1542,401,15,419,1515,4,1,6,100,104,101,106,1500,1504,1501,
  1506,1900,1904,1901,1906,4,1500,1504,1500,1,1501,100,1900,101,
  1901,100,1500,1900,4200,4600,4,1500,1504,4200,4204,1500,1500,
  104,15,1,19,401,419,15,1500,100,1900,15,400,15,1,401,4,6,
  404,406,15,19,415,419,23,27,423,427,104,106,606,115,119,615,
  619,123,127,623,627,1515,1519,2319,1523,1527,2323,2327,1542,
  1546,2346,1549,1550,2349,2350,1923,1927,2727,1949,1950,2750,4,
  15,23,1515,1523,1542,1549,1,15,19,42,46,100,101,115,119,142,
  146,1500,1501,1515,1519,1542,1546,1900,1901,1915,1919,1942,
  1946,400,42,442,15,415,1542,2342,1515,2315,1554,2354,4242,
  4942,1500,1542,15,104,123,1515,15,1,19,54,58,119,154,454,
  458,4,1,6,101,106,5400,1,5401,401,6101,5400,1,5401,100,54,
  154,4954,5054,400,4200,4942,5400,1,100,442,642,5400,400,49,1,
  19,115,119,419,619,6,27,123,623,154,458,654,658,63,1923,
  2346,2358,1,5400,58,101,158,6,63,106,104,163,5804,606,663,1,
  4900,58,158,49,50,150,2349,2350,2342,2300,4215,2349,4923,5400,
  6300,1,4204,1506,5400,400,2715,23,42,1,46,49,50,142,101,146,
  104,149,106,150,1542,1546,1504,1549,1506,1550,1942,1946,1949,
  1906,1950,4242,4246,4249,4250,4646,4649,4650,5449,5450,5850,
  10100,10142,10146,10149,10150,11542,11546,11504,11549,11506,
  11550,11942,11946,11904,11949,11950,14242,14246,14249,14250,
  14642,14649,14650,15449,15450,15849,41500,41542,41501,41546,
  41549,41550,41900,41942,41901,41946,41950,44242,44201,44246,
  44642,44601,44646,44650,45400,45442,45401,45446,45450,45800,
  45842,45801,45846,45850,61900,61942,61946,61949,64642,64646,
  65400,65442,65446,65800,65842,65846,235442,235446,235846,275842,
  40000,40001,540000,610000,540001,610001,400,40400,401,40401,
  540400,610400,540401,610401,545400,615400,615401,6100,46100,6101,
  46101,546100,616100,546101,616101,10400,60400,10401,580400,630400,
  580401,630401,586100,636100,586101,40000,1,40001,40100,101,40101,
  40400,40401,40601,540000,610000,540001,610001,610100,540101,
  610101,610400,610401,610601,10000,60000,10001,60001,10100,60100,
  60101,60400,60401,60600,580000,630000,580001,630001,580100,630100,
  630101,630400,630401,630600,490000,1,490001,490100,101,490101,
  494900,494901,495001,540100,540101,230101,544900,544901,545001,
  10100,500100,505000,585000,540000,540049,100,540100,149,540149,
  5400,545400,5449,545449,5800,545800,5849,545849,490100,230100,
  490149,230149,495400,235400,495449,495800,235800,495849,235849,
  10100,580100,580149,15800,585800,15849,585849,505800,275800,
  505849,54,42,540000,540042,540015,540400,540454,540415,420000,
  420054,420400,420454,420415,150442,424200,540000,54,600,540600,
  654,10000,1,10100,150404,190404,150406,190604,540000,10000,
  580000,10100,580100,44204,614204,64204,634204,64604,634604,54,
  540000,400,454,540400,540000,40000,610000,40400,610400,190004,
  194649,10404,42,100,142,146,49,149,50,1549,1949,40000,40042,
  40100,40142,40001,40046,40146,40004,40049,40104,40149,40006,
  40050,40150,41542,41942,41546,41549,41949,41550,230000,230042,
  230100,230142,230001,230046,230101,230146,230004,230049,230104,
  230149,230106,230150,231500,231542,231900,231942,231901,231946,
  610000,610042,610100,610142,610001,610046,610004,610104,611542,
  611942,100,540000,540100,104,540104,40000,40100,610000,610100,
  40004,40104,610004,610104,60000,60100,630000,630100,60004,630004,
  100,40000,40100,1,40001,540000,540100,610000,610100,540001,
  610001,400,600,40400,40600,401,40401,540400,540600,610400,610600,
  540401,610401,100,230000,230100,230049,230149,540000,540100,
  490000,490100,540049,540149,10000,10100,270000,270100,270049,
  270149,580000,580100,500000,500100,580049,580149,4900,100,5000,
  230000,234900,230100,235000,230101,235001,400,150000,150042,40000,
  40400,230000,230400,230042,230442,60000,54,60054,100,10000,10100,
  490404,490604,500404,500604,100,540000,540100,400,40000,40400,
  540000,40000,610000,464242,15,42,54,115,142,154,420015,420100,
  420115,420154,46,58,158,420119,23,61,123,161,420123,420161,63,
  442,454,642,654,420415,420600,420615,401,419,446,458,619,646,
  658,420401,420419,420446,420458,420619,449,461,623,649,661,
  420449,420461,420623,420661,406,427,450,463,650,663,420406,
  420427,420450,420463,420650,420663,2342,2354,2742,2754,422700,
  2346,2358,2746,422301,2349,2749,2306,2350,422306,424200,424215,
  424615,424201,424219,424619,424223,424623,424227,424901,424919,
  425019,425023,424906,424927,426106,10415,10442,10454,10600,10615,
  10642,10654,460415,460454,460600,460615,460654,10446,10458,460401,
  460419,460619,10449,10461,10604,10623,10649,10661,460461,460604,
  460623,460649,460661,10406,10427,10450,10463,10663,460406,460427,
  460450,460463,460663,12342,12700,12715,12742,12754,462300,462342,
  462700,462715,462742,12304,12349,12704,12749,462304,462349,462704,
  12706,12750,462706,14654,464600,464615,14223,14261,14623,464261,
  464623,464661,464663,15042,15054,464915,465000,465015,14923,14961,
  15004,15023,15049,15061,464923,464961,465004,465023,465061,14927,
  14950,14963,15063,464906,464927,464963,465027,16100,16300,16315,
  16342,466100,466300,466315,466354,16104,16149,16304,466104,466304,
  466349,466306,62342,62700,62742,62754,502342,502700,502742,502754,
  62346,62358,62349,505000,505015,65400,65800,505800,66300,506300,
  636300,1,400,401,10400,10401,6,100,600,601,10100,10101,10600,
  10601,104,10104,10106,5400,5401,6100,6101,15400,16100,16101,
  5404,5406,15404,5800,6300,6301,15800,15801,16300,16301,5804,
  15804,15806,40100,40101,40600,60101,60600,60601,60606,45400,
  45401,46100,46101,65400,65401,66100,46104,46106,66104,45800,
  45801,46300,65800,65801,66300,66301,46304,66304,66306,545400,
  545401,546100,546101,586100,586101,545406,545800,546300,546301,
  585800,585801,586300,586301,545804,585804,585806,615800,615801,
  616300,635801,636300,636301,636306,1,544900,58,4900,4901,540000,
  4958,27,540049,4927,100,545000,158,5000,5001,540100,149,150,
  545049,540149,5027,5400,5401,545400,2358,542349,5427,2350,5800,
  545800,542749,10100,585000,10158,15000,15001,580100,580149,15027,
  15400,15401,585400,12358,582349,15427,12350,15800,585800,582749,
  495400,232358,235401,492349,235427,495800,232749,492749,505800,
  502749,15,42,54,6142,23,5442,454,442,5404,5423,5449,2354,
  45400,45442,40454,40442,44254,41554,60000,545400,635400,65400,
  636300,1,54,58,100,154,44204,41506,44261,41563,44604,44661,
  10100,10154,64604,64661,40000,4,40004,540000,540004,400,40400,
  540400,10042,10149,17,15,17,15,4,100,1500,1900,100,1500,15,
  404,423,400,1500,2300,1500,1542,100,1500,4400,4200,404,5204,
  4904,1700,1500,404,4200,404,4904,15,4215,1515,423,4923,2323,
  4200,406,15,4215,427,54,4254,463,6,15,27,40000,40006,40015,
  40027,150015,150027,150000,150006,150054,150063,230015,230027,
  230000,230006,230054,230063,15,54,10004,610049,610004,150015,
  150000,150042,43,16,15,15,15,4300,1600,1600,15,15,15,18,16,
  15,15,1500,15,1515,4215,1800,1600,1500,15,15,15,1500,1515,
  1542,17,15,42,3,1,42,4,42,100,1500,2300,5400,6100,100,4200,
  4600,100,400,600,600,400,100,4200,54,1500,42,1542,404,2304,
  449,2349,15,1515,54,1554,423,2323,461,2361,1500,100,1900,42,
  1542,142,1942,15,1515,115,1915,54,1554,154,1954,5400,401,6101,
  1500,2301,100,54,154,4200,4600,100,454,654,1,101,458,658,100,
  5400,5800,1,101,5401,5801,100,2354,2754,400,600,1554,1954,100,
  5400,5800,1515,1915,4215,4615,650,606,42,406,100,42,15,54,
  4600,100,4200,5400,2304,1500,404,6104,1700,1500,404,2904,2304,
  42,1742,1542,449,2949,2349,1700,1500,100,2200,1900,42,1742,
  1542,142,2242,1942,100,4200,4600,401,1500,2301,300,100,1554,
  3454,1954,300,100,1515,3415,1915,1,1515,1519,1,1500,1501,15,
  100,115,800,600,100,2346,1500,446,54,15,40001,40019,150015,
  150000,230019,230001,420015,490001,490019,540015,540000,610019,
  610001,40023,6,27,230023,150027,150006,490023,420027,610023,
  540027,540006,54,40058,150054,230058,490058,540054,610058,63,
  150063,540063,6,15,27,40000,10000,40015,40027,150015,150027,
  150000,150006,230015,230027,230000,190000,420015,420027,490015,
  490027,540015,540027,540000,540006,610015,610027,610000,580000,54,
  63,40054,40063,150054,150063,230054,230063,540054,540063,610054,
  610063,60000,54,60054,10000,40000,10054,40054,420000,500000,
  460000,490000,540000,40004,40061,6,63,150000,230004,150006,1,
  10001,10000,49,50,10050,10049,40054,150001,190001,60054,40023,
  150050,190050,60023,1,490000,50,10001,10000,10050,500000,40015,
  150019,420015,150063,190019,60015,190063,460015,15,150000,630063,
  54,630027,40006,610027,40050,15,54,630054,630042,630000,10000,
  420000,540000,610061,610004,10046,50,150000,150050,150027,1700,
  1500,42,1742,1542,6,1706,1506,50,1750,1550,15,1715,1515,54,
  1754,1554,27,1727,1527,63,1763,1563,5600,5400,6,5606,5406,300,
  100,1,301,101,1554,3454,1954,1558,3458,1958,100,49,149,400,
  600,449,649,117,15,42,184,54,406,4900,4206,100,1500,1900,42,
  142,1542,1942,100,100,2300,2700,1,400,401,600,100,400,1500,
  2300,42,442,1542,2342,401,100,1515,1915,100,1554,1954,15,401,
  4400,4200,1500,6700,5400,400,5200,4900,2300,7100,6100,15,4415,
  4215,1515,6715,5415,415,5215,4915,2315,7115,6115,5600,5400,401,
  6501,6101,100,1,101,400,600,401,601,300,100,49,349,149,400,
  1200,600,449,1249,649,2200,1500,15,2215,1515,4250,4949,401,15,
  40000,40015,150015,150000,230015,230000,420015,490000,490015,
  540015,540000,610015,610000,6,27,40027,150027,150006,230027,
  420027,490027,540027,540006,610027,54,40054,150054,230054,490054,
  540054,610054,63,150063,540063,54,40000,40054,6,63,1,10001,
  10000,150000,610001,630001,190000,49,50,10050,10049,150049,
  610050,630050,190049,15,630000,150000,54,630042,490006,420006,
  150000,42,150042,600,150600,642,150642,420000,540000,420042,
  540042,420600,540600,420642,540642,6,150006,50,150050,606,150606,
  650,150650,420006,540006,420050,540050,420606,540606,420650,
  540650,15,150015,54,150054,615,150615,654,150654,420015,540015,
  420054,540054,420615,540615,420654,540654,27,150027,63,150063,
  627,150627,663,150663,420027,540027,420063,540063,420627,540627,
  420663,540663,1500,151500,1542,151542,2700,152700,2742,152742,
  421500,541500,421542,541542,422700,542700,422742,542742,1506,
  151506,1550,151550,2706,152706,2750,152750,421506,541506,421550,
  541550,422706,542706,422750,542750,1515,151515,1554,151554,2715,
  152715,2754,152754,421515,541515,421554,541554,422715,542715,
  422754,542754,1527,151527,1563,151563,2727,152727,2763,152763,
  421527,541527,421563,541563,422727,542727,422763,542763,54,600,
  654,540000,540054,540600,540654,6,63,606,663,540006,540063,
  540606,540663,10000,490000,500000,1,10001,490001,500001,41554,
  61554,421554,461554,41558,61558,421558,461558,100,10100,490100,
  500100,101,10101,490101,500101,41954,61954,421954,461954,41958,
  61958,421958,461958,10100,100,10000,49,10149,149,10049,152300,
  192700,152700,192300,152349,192749,152749,192349,4900,15000,5000,
  14900,4949,15049,5049,14949,155400,195800,155800,195400,155449,
  195849,155849,195449,421500,1500,420000,42,421542,1542,420042,
  4200,425400,5400,424200,4242,425442,5442,424242,540000,40106,
  610106,494900,234900,425006,155006,40100,150000,230100,420000,
  490100,540000,610100,42,40142,150042,230142,420042,490142,540042,
  610142,40400,600,230400,150600,490400,420600,610400,540600,40442,
  642,230442,150642,490442,420642,610442,540642,1500,41900,151500,
  231900,421500,491900,541500,611900,1542,41942,151542,231942,
  421542,491942,541542,611942,42300,2700,232300,152700,492300,
  422700,612300,542700,42342,2742,232342,152742,492342,422742,
  612342,542742,40000,150000,230000,600,40600,150600,230600,4200,
  44200,154200,234200,5000,45000,155000,235000,42,40042,150042,
  230042,642,40642,150642,230642,4242,44242,154242,234242,5042,
  45042,155042,235042,1500,41500,151500,231500,2700,42700,152700,
  232700,5400,45400,155400,235400,6300,46300,156300,236300,1542,
  41542,151542,231542,2742,42742,152742,232742,5442,45442,155442,
  235442,6342,46342,156342,236342,40400,5400,46100,40100,600,45800,
  6300,40000,600,40600,5400,45400,6300,46300,10000,235400,275400,
  45454,65454,150054,190054,100,10100,235800,275800,45854,65854,
  150154,190154,10000,230000,270000,4900,14900,234900,274900,100,
  10100,230100,270100,5000,15000,235000,275000,100,1,101,152300,
  152700,152301,152701,4900,5000,4901,5001,155400,155800,155401,
  155801,100,4900,5000,1,101,4901,5001,151500,151900,156100,
  156300,151501,151901,156101,156301,15,420000,420015,4200,4215,
  424200,424215,15,420000,420015,1500,1515,421500,421515,5400,
  40400,46100,460006,10000,420006,170000,150000,420000,840000,
  540000,600,170600,150600,420600,840600,540600,6,170006,150006,
  420006,840006,540006,606,170606,150606,420606,840606,540606,15,
  170015,150015,420015,840015,540015,615,170615,150615,420615,
  840615,540615,27,170027,150027,420027,840027,540027,627,170627,
  150627,420627,840627,540627,4200,174200,154200,424200,844200,
  544200,5000,175000,155000,425000,845000,545000,4206,174206,154206,
  424206,844206,544206,5006,175006,155006,425006,845006,545006,4215,
  174215,154215,424215,844215,544215,5015,175015,155015,425015,
  845015,545015,4227,174227,154227,424227,844227,544227,5027,175027,
  155027,425027,845027,545027,560000,540000,6,560006,540006,40100,
  650100,610100,40106,650106,610106,30000,10000,4900,34900,14900,1,
  30001,10001,4901,34901,14901,41554,121554,61554,46154,126154,
  66154,41558,121558,61558,46158,126158,66158,10000,49,10049,100,
  10100,149,10149,45400,65400,45449,65449,45800,65800,45849,65849,
  440000,420000,42,440042,420042,1500,441500,421500,1542,441542,
  421542,10006,460000,420006,60000,42,60042,10000,10042,40042,
  150000,150006,150042,150050,230006,230000,230050,230042,420042,
  420050,490050,490042,540042,540050,540000,540006,610050,610042,
  610006,54,60054,10054,150054,150063,230063,230054,540054,540063,
  610063,40004,540000,610004,6,540006,540000,10000,10049,150015,
  420015,630061,630015,1,540001,10001,10050,150019,420019,630063,
  630019,42,150000,150042,54,150054,40001,150050,15,600,615,1500,
  1515,2700,2715,1000000,1000015,4000000,4000015,1001500,1001515,
  4001500,4001515,15000000,15000015,15000600,15000615,15001500,
  15001515,15002700,15002715,19000000,19000015,23000000,23000015,
  19001500,19001515,23001500,23001515,42000015,42000615,42001500,
  42001515,42002700,42002715,46000000,46000015,49000000,49000015,
  46001500,46001515,49001500,49001515,54000000,54000015,54000600,
  54000615,54001500,54001515,54002700,54002715,58000000,58000015,
  61000000,61000015,58001500,58001515,61001500,61001515,6,27,606,
  627,1506,1527,2706,2727,1000027,4000027,1001506,1001527,4001506,
  4001527,15000006,15000027,15000606,15000627,15001506,15001527,
  15002706,15002727,19000027,23000027,19001506,19001527,23001506,
  23001527,42000027,42000627,42001506,42001527,42002706,42002727,
  46000027,49000027,46001506,46001527,49001506,49001527,54000006,
  54000027,54000606,54000627,54001506,54001527,54002706,54002727,
  58000027,61000027,58001506,58001527,61001506,61001527,54,654,1542,
  1554,2742,2754,1000054,4000054,1001542,1001554,4001542,4001554,
  15000054,15000654,15001542,15001554,15002742,15002754,19000054,
  23000054,19001542,19001554,23001542,23001554,42001542,42001554,
  42002742,42002754,46000054,49000054,46001542,46001554,49001542,
  49001554,54000054,54000654,54001542,54001554,54002742,54002754,
  58000054,61000054,58001542,58001554,61001542,61001554,63,663,1550,
  1563,2750,2763,1001550,1001563,4001550,4001563,15000063,15000663,
  15001550,15001563,15002750,15002763,19001550,19001563,23001550,
  23001563,42001550,42001563,42002750,42002763,46001550,46001563,
  49001550,49001563,54000063,54000663,54001550,54001563,54002750,
  54002763,58001550,58001563,61001550,61001563,5400,5415,6300,6315,
  1005400,1005415,4005400,4005415,15005400,15005415,15006300,15006315,
  19005400,19005415,23005400,23005415,42005415,42006315,46005400,
  46005415,49005400,49005415,54005400,54005415,54006300,54006315,
  58005400,58005415,61005400,61005415,5406,5427,6306,6327,1005427,
  4005427,15005406,15005427,15006306,15006327,19005427,23005427,
  42005427,42006327,46005427,49005427,54005406,54005427,54006306,
  54006327,58005427,61005427,5454,6354,1005454,4005454,15005454,
  15006354,19005454,23005454,46005454,49005454,54005454,54006354,
  58005454,61005454,5463,6363,15005463,15006363,54005463,54006363,
  54005400,600,54006300,5400,54000000,6300,54000600,4000000,61005400,
  4000600,61006300,4005400,61000000,4006300,61000600,6,54005406,606,
  54006306,5406,54000006,6306,54000606,1,100,101,4900,4901,5000,
  5001,1000000,1000001,1000100,1000101,1004900,1004901,1005000,
  1005001,49,50,149,150,4949,4950,5049,5050,1000049,1000050,
  1000149,1000150,1004949,1004950,1005049,1005050,42001500,61006101,
  42001900,61006301,42006100,61001501,42006300,61001901,46001500,
  63006101,46001900,63006301,46006100,63001501,46006300,63001901,
  42001549,61006150,42001949,61006350,42006149,61001550,42006349,
  61001950,46001549,63006150,46001949,63006350,46006149,63001550,
  46006349,63001950,50005000,1500,50006300,42000000,6005000,42001500,
  6006300,50005042,1542,50006342,6005042,42001542,6006342,6002700,
  42005400,50002700,5400,6002742,50002742,5400,49000606,49006306,
  42000006,42005406,45,43,42,43,18,16,15,43,15,18,16,15,43,
  4300,2301,9201,42,2800,1600,42,1642,4300,15,4315,5500,8300,42,
  27,63,42,15,54,400,42,442,42,15,54,4200,404,4904,42,4242,
  449,4949,54,1500,15,1515,42,1542,54,1554,1500,15,1515,42,
  1542,54,1554,54,54,4500,4300,4200,1500,7300,9000,5400,1643,
  1800,1600,1500,42,1842,1642,1542,1800,1600,1500,42,1842,1642,
  1542,1643,1643,2304,42,2349,404,1500,449,1542,54,1500,15,1515,
  42,1542,54,1554,1500,15,1515,42,1542,54,1554,54,54,42,100,
  142,1800,1600,1500,42,1842,1642,1542,1800,1600,1500,42,1842,
  1642,1542,3243,3243,4200,10001,14201,42,4242,10046,14246,2700,
  6300,12701,16301,2742,6342,12746,16346,54,4200,15,4215,42,4242,
  54,4254,1500,5400,1515,5415,1542,5442,1554,5454,4200,15,4215,
  42,4242,54,4254,1500,5400,1515,5415,1542,5442,1554,5454,54,54,
  1800,1600,1500,15,1815,1615,1515,42,1842,1642,1542,54,1854,
  1654,1554,4300,54,4354,1500,1542,1500,1542,1800,1600,1500,4200,
  9400,9500,5400,42,1842,1642,1542,4242,9442,9542,5442,5700,5500,
  5400,42,54,1500,1542,150000,15,150015,42,150042,54,150054,1500,
  151500,1515,151515,1542,151542,1554,151554,4200,154200,4215,
  154215,4242,154242,4254,154254,5400,155400,5415,155415,5442,
  155442,5454,155454,54,5400,5454,150000,540000,1500,151500,421500,
  541500,5400,155400,545400,420000,420015,1500,421500,1515,421515,
  5400,425400,425415,5400,5400,150000,540000,15,150015,420015,
  540015,54,150054,420054,54,180000,160000,150000,42,180042,160042,
  150042,1500,181500,161500,151500,1542,181542,161542,151542,4200,
  184200,164200,154200,4242,184242,164242,154242,5400,185400,165400,
  155400,5442,185442,165442,155442,160043,5400,165443,150000,150042,
  1500,151500,1542,151542,5400,155400,155442,420000,420015,1500,
  421500,1515,421515,5400,425400,425415,5400,5400,42,54,1500,1542,
  1515,1554,5400,5442,5415,5400,15000000,54000000,15,15000015,
  42000015,54000015,54,15000054,42000054,150000,15150000,42150000,
  54150000,150015,15150015,42150015,54150015,150042,15150042,42150042,
  54150042,150054,15150054,42150054,54150054,540000,15540000,54540000,
  540015,15540015,42540015,54540015,540054,15540054,42540054,540000,
  54,540054,404,4200,4901,4200,4206,600,442,54,6,40004,540054,
  540063,610061,6,10004,150015,150027,230023,420042,150050,460049,
  54,63,40061,630006,610004,27,54,270000,60015,60063,54,54,60054,
  540000,40000,610000,6,63,10000,190000,6,230006,150006,63,40000,
  60050,60000,60000,54,270000,150027,64215,40600,490600,40000,
  490000,45400,6300,540000,150000,580004,190004,150600,5400,490600,
  500000,10600,60042,420042,14200,505000,425042,54000000,5454,600,
  54000600,606,6,54006306,54005406,663,63,54005463,5400,6000000,
  5406,1000400,1006100,5454,54,5463,6000054,1006154,1000454,1000100,
  1005800,600,6300,6000600,6306,1005854,1000154,6354,654,6363,
  6000654,6000000,54,6000054,6005400,5454,6005454,42001500,42001506,
  42001554,42001563,1000454,1006154,46002300,46002306,46002354,
  46002363,1000154,1005854,46001900,46001906,654,663,6363,46000400,
  42000600,61000450,54,63000650,5400,6006300,6000600,42000600,
  42001500,2700,5454,2727,2750,50,5427,6006350,6006327,6000627,
  6004254,6004200,600,1500,2700,5000,600,2700,615,40400,150000,
  230400,5400,46100,155400,236100,40100,600,230100,150600,45800,
  6300,235800,156300,501506,420000,61506,60000,5400,65400,404,
  60404,6104,66104,424215,504215,421515,501515,424923,504923,422323,
  502323,541500,600,542700,1500,540000,2700,540600,40104,611904,
  40404,612304,41904,610104,42304,610404,606,64200,65006,54,150650,
  150627,40600,40000,600,45015,44215,5015,45042,5042,40654,150042,
  61500,271542,54000000,6060000,63060000,54005400,6065400,63065400,
  6000000,63000000,60000,54060000,6005400,63005400,65400,54065400,
  15000000,27060000,15005400,27065400,50000000,27000000,42060000,
  15060000,50005400,27005400,15065400,58040001,61010001,61015401,
  61040001,58010001,61045401,58015401,23040001,19010001,23045401,
  540000,50060600,50630600,42420015,6500615,54,54,4200,4215,4200,
  54,4242,54,54,4215,4200,54,4200,425400,425400,54,5442,421500,
  421500,5442,5415,42,420000,5400,425400,150015,5400,155415,150000,
  5400,155400,5400,150042,155442,150000,5400,155400,420042,420015,
  54,54,420054,420000,5400,150015,155415,54,5400,5454,5400,150015,
  155415,420000,5400,425400,5400,4200,1500,1542,1515,54,5400,
  421500,424200,54,5454,421554,424254,8000,8300,8700,1005,743,
  6600,205,6805,6600,78316,110000,118300,8300,667655,1111,71616,
  830000,870202,110202,900,900,90000,1005,90000,96216,43,62300,
  62343,43,61900,61943,43,585000,585043,43,43,190600,62300,61923,
  582300,40100,61900,42,1904,42,1949,23191901,42,23191946,42,
  23500004,27001915,42,27001954,42,27,59853210,27232517,2315,4300,
  27239717,9215,4300,23190015,23194315,69623300,23500004,88983304,
  4300,15011500,15019000,42006115,4300,42009915,42,6190000,1501,
  6191501,42,6190042,1546,6191546,19230004,42,19230049,58230054,42,
  1150600,270404,1060104,42,1150642,270449,1060149,42420100,421515,
  42001915,42,42420142,45,43,42,230600,230645,230643,230642,192300,
  192345,192343,192342,45,43,42,62300,62345,62343,62342,45,43,42,
  235800,235845,45,43,42,41500,41545,41543,41542,202416,196100,
  419616,231900,15,231915,192300,585000,61915,39312100,19231900,42,
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CR_4.codedGeneratorZClass :=
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  140268822,134238885,82620289,77132230,69768323,139744251,77148730,
  107683172,107548895,78837817,78792061,107885304,82620313,140097899,
  140067395,109451423,107683183,78837807,138175775,107885303,82620303,
  78837795,76931296,134238885,82620289,113376395,113620427,69768323,
  113371807,96201407,77133431,107683172,107548895,138362305,96124154,
  107885304,82620313,96197230,140050903,107683183,107548891,111496722,
  113620427,82620303,134238899,138362323,140067384,134238885,82620289,
  96197230,140095295,69768323,113371807,96197230,77133431,107683172,
  107548895,98015402,138408061,82620313,107885304,109807427,113112938,
  107683183,107548891,140097899,78962842,82620303,107885303,98015394,
  113387972,82620289,107885303,140097899,77043322,113371807,69768323,
  113376395,95953206,109451414,107683172,113620303,107548891,109451423,
  77132311,82620303,134238899,140268890,82620289,134238885,77132311,
  113371807,139744251,113620291,109451414,107683172,113112814,
  107548891,107683183,140067314,134238899,82620303,96124079,134238885,
  107885303,140067314,139744251,113371807,95953331,107548895,107683172,
  77040799,77147687,109451423,107683183,138362395,113620427,107885303,
  82620303,138362391,140067384,134238885,82620289,96197311,140095295,
  69768323,113371807,96197303,77133431,107683172,107548895,109807346,
  140050903,107548891,109451423,78837726,113620427,107885303,82620303,
  78837728,140067384,134238885,82620289,113376314,140095295,69768323,
  113371807,113376319,77133431,107683172,107548895,113112814,109451423,
  109455434,107544718,140067314,82620303,82899222,107544718,78791972,
  82620289,109314322,107544718,109804494,113371807,77455870,107544718,
  95953331,109451414,109455442,107544718,77179102,140051938,109451423,
  107548891,98015318,111252690,107885303,82620303,107671705,140268822,
  82620289,134238885,109807346,107395546,113371807,139744251,113376319,
  95953206,109451414,107683172,109807427,113113019,107548891,109451423,
  109807427,138408151,82620303,107885303,140097888,77132306,82620289,
  134238885,69554795,96520207,139744251,69768323,96201407,77148806,
  109451414,107548895,139959434,77148803,107548891,107683183,109466842,
  138408151,82620303,107885303,111496725,77132306,82620289,134238885,
  107392198,96520207,139744251,69768323,96197230,77148806,109451414,
  107548895,109807427,113112814,107548891,109451423,107671775,78791970,
  82620303,107885303,109807427,111454198,134238885,107885303,69554795,
  109804494,139744251,69768323,96201407,113620343,107683172,107548895,
  77040718,113112814,107683183,109451423,109466842,78791970,107885303,
  82620303,77040726,96124079,134238885,107885303,147583822,109804494,
  69768323,139744251,113372218,113620343,107548895,107683172,96201403,
  140052019,107683183,109589726,107544718,109807427,140268895,82620303,
  109314322,107544718,109807427,140268890,82620289,109314322,107544718,
  109807427,147585887,113371807,147431302,107544718,96201407,140052011,
  107683172,109589722,107544718,27576557,96204109,27576557,158869959,
  182585867,108225274,158869959,108913343,111702976,182259101,
  182585867,181755521,113369397,181755521,47934243,111455580,44981181,
  138667762,158871959,96125708,155826758,98117181,159716768,98117181,
  77548170,159720646,96117135,33044800,111448420,138667762,113369397,
  47934243,111455580,109472131,27053511,96125708,98011667,140650523,
  111447007,107884306,155073341,111455580,109315317,155073341,
  111455580,159717639,111454395,96125708,140651645,111454395,96117135,
  137670403,79424159,113394487,109472131,44074618,98117181,112759425,
  98117181,32804382,182258855,98117181,111454395,140651523,113385549,
  96124523,33322950,27464439,138667762,32804382,109807427,95553448,
  111455580,44977972,113376395,182258855,96125708,111454395,109470891,
  27315024,96125708,111454395,107392198,77127802,138667762,32804382,
  27466552,26959129,138667762,155073341,111496350,159717506,96125708,
  111454395,113372222,77548542,96125708,111454395,107667795,107393259,
  113394487,155073341,159717763,159716893,98117181,111454395,76487218,
  76487226,98126119,111454395,44074867,98117181,96202643,159717885,
  139544319,159717885,109466787,140651399,98117181,159717763,107548891,
  98117181,44073872,96117135,140651399,96202643,159717885,140651520,
  98116015,107544718,159717763,44982048,111447007,109472131,77547424,
  96117135,109472131,139544451,113384383,107544718,182258855,98119230,
  109596615,113376395,44073997,98117181,111454395,109470891,27053757,
  113385549,96124523,113376395,182258855,98123403,109596615,182585006,
  180336730,26926245,180336730,1129611,113625044,106992518,113625044,
  140071823,182585867,108684957,27560102,180336730,140067395,140651399,
  182259101,112502653,110145677,110138347,108689421,138729274,
  158885580,140651645,181136653,113951609,181138391,182416742,76905711,
  182524859,210345466,181136407,107399674,29236895,140067395,140651399,
  182259101,95553518,109811855,113379101,140651399,159706391,113154150,
  76486480,210345466,27560102,27314770,27315149,139405819,73912854,
  12062103,107548891,76486481,73225567,3861162,109448144,181751447,
  179843991,3861162,182259101,109589726,96209441,106999650,73225567,
  12062103,108899105,139405819,96209441,114137949,73912854,12062103,
  108731107,143225515,12062103,113372303,107548891,181751447,205138627,
  73225567,3861162,113379101,107548891,27822178,185854767,73225567,
  3861162,76487218,107548891,27822178,106999650,73225567,3861162,
  109448177,27315149,96194032,113117692,139405819,107683183,77732807,
  96209441,107548891,199402399,72509660,109807335,24008150,143225515,
  109807335,27314032,107687194,109455434,140651266,106999650,185854767,
  73225567,12062103,113376314,140067395,27315149,96209441,179843991,
  114137949,73912854,12062103,180004943,108731107,22927425,143225515,
  109455434,109458221,109589726,76487596,185854767,205138627,73225567,
  3861162,109596605,109451423,109589726,27822178,109589807,113379101,
  109589726,140650529,109807427,185854767,73225567,3861162,79083823,
  107392292,73225567,3861162,107551597,107689948,181751692,113369024,
  107544799,139405943,96219452,109589726,109466843,185839514,199417652,
  108433328,144126578,23095197,185564992,73225567,181751438,109596572,
  113363692,199402399,110324711,144659217,182043605,27314032,113379101,
  107548891,96209441,114137949,106999650,185854767,73225567,12062103,
  144666519,11487648,144126672,73225567,12062103,109586528,139405943,
  96212606,109586561,109807427,3861152,179996524,78794035,109811846,
  109589726,113379101,181751692,76487218,109463711,110138719,23657354,
  72509660,199066843,140830695,143913050,199066843,143225515,199961357,
  108901934,27606937,96194032,76487218,109455434,139405819,79083823,
  114137949,106999650,185854767,73225567,12062103,109596605,24003722,
  143913050,12351902,108735549,199763058,27604936,27607028,77732683,
  27822556,109451423,27821441,205138627,114137949,106999650,185854767,
  73225567,12062103,205138627,199424831,11487648,144126672,143913050,
  199417652,77179183,140050822,109589726,96204109,76487351,27822556,
  109807427,107663072,106999650,185854767,72509660,199066843,109314415,
  111454554,143913050,23657354,72509660,23095174,73912854,139420588,
  138939322,139420588,180826528,73912854,12062103,73912854,179843991,
  139420588,110685804,73912854,12062103,205138627,180826528,73912854,
  12062103,182786209,73912854,139420588,96782940,23095174,12062103,
  73225567,205138627,113123150,73912854,12062103,29515599,180826528,
  73912854,12062103,179843991,182786209,73912854,139420588,205138627,
  3912460,23095174,12062103,73225567,114137949,138139576,106999650,
  12062103,73225567,199740636,114137949,106999650,185854767,12062103,
  73225567,180826569,22934718,12351902,143913050,199763058,73072955,
  205138627,207368000,5756963,106999650,12062103,73225567,109807427,
  205138627,207368000,5756963,106999650,12062103,73225567,109593804,
  76856198,28365006,140097940,219263013,160405546,179629517,132440821,
  82765556,138362323,153690461,181703188,181873564,200523788,50162752,
  174171184,44448336,107689948,143613617,41658462,79670051,39631319,
  210471581,70783101,182259101,182045573,26743634,182258731,140651399,
  181797699,153692231,31588701,115178093,87498568,86161352,51024595,
  110148670,234995099,73225567,113356927,110944135,109807427,98015771,
  107671899,96202643,83119279,111362264,58517558,109593818,109597867,
  109593918,109417392,109416331,109420671,113369024,113372303,
  113367963,107679904,107678843,107683183,96212606,107679904,107683183,
  107678843,107695280,107694219,107698559,107695280,107694219,
  107698559,120860334,88208556,109594026,107549262,209084286,113625101,
  109593909,109593818,76487351,78440103,82191847,113361019,113379101,
  76487351,78440103,84098471,115267643,107698569,140651399,142601998,
  109589726,109586065,109593917,109455805,109586065,109593917,96201818,
  109586065,109593917,113371807,110145677,109597867,107687194,
  110145677,109597867,109451423,109427469,109428650,109424682,
  109427469,109428650,109424682,101982779,109458221,109459402,
  109455434,109458221,109459402,109455434,113361019,96204109,96205290,
  96201322,107689981,107687194,107691162,107689981,107691162,107687194,
  96216779,109596605,109586593,109596572,113379101,115178093,107689981,
  109596605,109586593,109596572,113379101,115178093,107689981,
  140651399,182259101,109596605,109586593,109586561,107705357,
  107706538,107702570,107705357,107706538,107702570,120864507,17686571,
  174188104,109594513,53210107,107548891,109589726,109594513,53210107,
  107548891,140651399,138145270,174785400,32821756,138145270,174785400,
  82620291,32821756,109589311,109593917,109586065,109589683,115179274,
  107683183,109593915,113379101,109624650,107544718,115168734,
  113368651,109589683,115179274,107683183,109593915,113379101,90066506,
  115168734,113368651,139959515,35516804,47444107,109594397,107548891,
  140650529,109599231,109593909,107702570,120858726,109599231,
  109593909,107698558,120869842,109599231,109593909,109420671,
  109589116,109430715,109599975,109599231,109593909,109420671,
  101988104,109599479,109593909,109455434,109599479,109593909,
  107683183,109599479,109593909,109451426,109599603,109593909,
  107687191,96212605,109599603,109593909,107683184,96216782,109599603,
  109593909,109451426,109599603,109593909,109451426,113361020,
  107687276,109609275,121033638,109599355,109593909,107683184,
  230601192,55191886,107687276,109609275,121033638,109599355,109593909,
  107683184,107687194,109589725,128752393,103766397,105888288,
  119117005,130397624,122786500,101988148,109593905,110193563,
  109594519,109855291,109417392,109416331,109420671,109589726,
  109593905,110193563,109594519,109855291,107705357,107706538,
  107702570,107548891,109593915,109599479,109455434,113379101,
  109593915,109599479,109451302,109455434,109593915,109599479,
  109451302,113379101,109593918,109597867,96201322,109593918,109597867,
  113372303];

CR_4.codedIsomorphismTypeQClass :=
  [101,102,102,102,104,102,104,104,104,104,109,104,109,109,109,
  122,205,205,210,412,412,412,625,103,107,208,208,319,107,107,
  117,319,319,319,640,205,103,107,205,210,412,412,625,210,210,
  412,412,223,625,625,625,625,849,107,107,208,117,319,319,319,
  319,319,640,117,117,117,319,319,640,640,136,640,640,640,1561,
  412,208,319,210,927,927,625,3352,1028,324,1450,3600,3453,
  15469,218,218,420,741,237,438,1246,438,741,438,1246,1145,1145,
  842,1662,3867,3867,660,2565,3867,2464,678,107,117,319,640,114,
  132,333,333,434,555,957,1358,1358,1358,3174,132,154,555,555,
  957,555,1170,1771,3174,3174,682,521,1044,1548,1548,3666,1044,
  1044,1548,1548,2263,3666,3666,3666,3666,3666,577,311,1230,106,
  115,216,335,218,1246,333,555,1358,1459,3174,3475,4776,4776,
  481,420,741,438,1145,656,3867,2572,4300,3300,200,300,500,284,
  500,1000,1368,179,179,280,183,513,1129,1331,826,1447,4400,
  4700,3151,4600,4200,4900,26100,25000,25900,25200,100,100,100,
  200,300,185,539,943,1447,4700,3500,4900,2873,200,300,400,100,
  400,100,100,200,186];

CR_4.codedNormalizerZClass :=
  [767000,767000,774000,812000,775000,811000,774000,812000,783000,
  810000,794000,784000,809000,795000,782000,787000,803000,799000,
  815000,806000,778000,776000,804000,803000,800000,814000,807000,
  762000,765000,802000,798000,813000,805000,779000,777000,804000,
  801000,815000,808000,748507,738563,739242,243,740564,747244,
  718565,243,722566,752244,757246,745245,719567,733685,691,378,
  740564,734693,680,723566,758379,727692,738563,243,735242,740564,
  747244,718565,243,723566,752244,757246,744245,719567,738563,243,
  739242,747244,740564,729565,243,752244,723566,715245,743246,
  756567,691,378,740564,734693,680,723566,758379,727692,785000,
  793000,785000,793000,785000,793000,763000,761000,771000,772000,
  763000,771000,781000,773000,761000,771000,759000,785000,759000,
  785000,816000,776000,786000,817000,760000,764000,816000,776000,
  780000,785000,785000,785000,776000,760000,776000,780000,776000,
  768000,769000,769000,173,242,243,244,244,245,246,359,378,378,
  244,728379,750379,173,242,242,243,243,244,244,244,244,245,245,
  246,246,173,242,242,243,243,244,244,244,244,245,245,246,246,
  359,378,378,378,378,244,244,728379,728379,750379,750379,242,
  243,244,244,245,246,242,243,244,244,245,246,242,243,244,244,
  245,246,242,243,244,244,245,246,378,378,244,728379,724379,242,
  243,244,244,245,246,242,242,243,243,244,244,244,244,245,245,
  246,246,242,243,244,244,245,246,378,378,244,730379,724379,378,
  378,244,728379,724379,295,296,329,330,295,296,329,330,295,295,
  296,296,329,329,330,330,295,296,329,330,295,296,329,330,295,
  296,329,329,330,330,295,296,329,329,330,330,295,296,329,329,
  330,330,295,296,329,329,330,330,295,296,329,329,330,330,329,
  330,419,419,419,419,329,330,419,419,419,419,329,330,419,419,
  419,419,419,419,329,330,419,419,419,419,419,419,419,419,
  770000,797000,766000,770000,770000,789000,770000,790000,751671,
  680,714681,359,378,378,379,379,751671,680,378,680,713681,379,
  714681,751671,680,680,714681,713681,751671,680,378,680,713681,
  379,713681,378,379,680,737681,378,379,378,378,379,379,680,
  737681,680,713681,419,419,419,419,419,419,419,419,419,419,419,
  419,419,419,419,419,419,419,419,419,419,419,419,419,419,419,
  419,419,419,419,419,419,419,419,419,419,419,419,419,419,428,
  477,731613,617,428,428,429,755429,732613,753613,741604,621,
  717604,621,464,482,482,464,482,482,742604,721604,621,621,482,
  464,482,482,726604,621,621,746604,621,482,621,464,482,482,482,
  482,716604,621,482,621,725604,621,621,482,482,621,482,482,482,
  482,482,482,482,621,482,482,482,482,621,507,563,564,565,566,
  567,507,563,564,565,566,567,507,563,564,565,566,567,507,563,
  564,565,566,567,507,563,564,565,566,567,563,564,565,566,567,
  563,564,565,566,567,563,564,565,566,567,563,564,565,566,567,
  563,564,565,566,567,563,564,565,566,567,563,564,565,566,567,
  563,564,565,566,567,563,564,565,566,567,563,564,565,566,567,
  563,564,565,566,567,796000,796000,792000,792000,791000,792000,
  791000,788000,788000,591,591,592,591,617,604,604,591,606,605,
  604,604,606,605,604,621,604,621,621,604,604,605,606,604,604,
  605,606,604,621,621,617,613,613,754613,617,617,613,617,617,
  621,621,621,621,621,621,720626,720626,711627,711627,626,627,
  636,637,636,637,636,637,636,637,636,637,688,709,665,666,649,
  650,665,752705,662,749704,749704,665,666,680,681,665,666,671,
  736680,680,712681,712681,691,710,662,663,664,680,681,680,680,
  681,681,680,691,692,693,680,712681,691,710,710,680,681,691,692,
  693,691,710,710,691,693,712692,691,692,693,704,697,709,697,
  752705,702,704,709,752705,752705,704,705,710,710,710,710,710];

CR_4.codedPresentationQClass :=
  [11,21,21,21,202,21,202,202,202,202,63,202,63,63,63,34,601,
  601,732,742,742,742,693,401,971,462,462,1072,971,971,1062,
  1072,1072,1072,1043,601,401,971,601,732,742,742,693,732,732,
  742,742,673,723,723,723,693,654,971,971,462,1062,1072,1072,
  1072,1072,1072,1023,1062,1062,1062,1072,1072,1043,1043,993,
  1023,1043,1023,984,742,462,1072,732,683,713,693,644,902,892,
  843,863,853,834,1331,1331,1082,1412,1402,1422,1432,1422,1412,
  1422,1432,1013,1003,1122,1363,1373,1373,1343,1353,1373,1113,
  354,971,1062,1072,1053,502,1102,562,562,473,1202,1093,513,513,
  513,1143,1102,1192,1202,1202,1093,1202,393,1133,1163,1153,374,
  133,183,104,94,174,193,183,94,94,54,174,164,154,154,144,45,
  1211,1292,941,1301,952,1312,1331,1432,562,1202,523,493,1163,
  553,484,484,544,1082,1412,1422,1033,592,1383,383,573,583,364,
  1183,534,1174,962,1322,114,923,913,124,933,822,1282,1272,703,
  793,1263,1243,1253,343,664,764,1234,1224,334,883,635,874,275,
  626,616,266,1462,1472,783,1393,813,754,1453,324,804,774,1444,
  285,315,256,306,297];

CR_4.codedPropertiesFamily :=
  [10155,7255,6355,5655,4955,4266,4266,4199,4199,3666,3466,3399,
  3299,2399,2199,2399,2688,2119,2119,2119,1201,1201,1201];

CR_4.codedPropertiesZClass :=
  [114,114,814,423,214,123,1614,423,414,223,132,1614,423,132,
  6414,1623,1633,1643,452,863,3214,823,833,833,843,252,463,1614,
  423,433,443,152,263,25614,3223,3233,3243,452,863,112,3224,833,
  833,843,843,852,263,473,473,282,282,492,112,25624,3233,3243,
  3252,463,873,482,892,51224,6433,6433,6443,6443,6452,863,1673,
  1673,882,882,892,25624,3233,3233,3243,3243,3252,463,873,873,
  482,482,492,409624,25633,25643,25652,1663,3273,1682,892,114,
  122,1614,822,814,422,814,814,422,422,3214,822,3214,1622,6414,
  1622,313,924,113,124,413,424,424,313,924,924,413,424,424,
  3624,124,424,1624,3624,424,424,1624,114,114,114,112,424,233,
  443,243,252,262,112,824,433,443,452,462,212,1624,1624,833,
  833,843,843,843,843,852,452,462,862,112,1624,1624,433,433,
  843,843,443,443,452,452,262,462,212,6424,6424,1633,1633,1643,
  1643,1652,852,462,1662,3224,833,1643,843,852,462,824,233,443,
  443,252,262,824,233,443,443,252,262,3224,833,843,1643,852,
  462,6424,833,1643,852,462,12824,1633,3243,3243,1652,862,6424,
  6424,833,833,1643,1643,1643,1643,852,852,462,462,12824,1633,
  3243,1643,1652,462,6424,833,1643,852,462,51224,3233,6443,3252,
  862,613,322,634,343,213,122,634,343,613,213,322,122,634,634,
  343,343,413,122,434,143,413,122,434,143,813,222,834,834,243,
  243,1213,322,1234,1234,343,343,813,222,834,834,243,243,413,
  122,1234,1234,343,343,1613,222,1634,1634,243,243,2434,643,434,
  143,434,143,2434,643,434,434,143,143,3234,443,1634,1634,243,
  243,1634,243,4834,643,1634,1634,243,243,1634,243,6434,443,414,
  424,132,114,114,124,114,124,112,424,432,212,824,1624,432,832,
  212,424,824,1624,432,232,832,212,1624,1624,232,1632,412,1624,
  3224,6424,832,432,3232,424,232,424,232,1624,432,1624,1624,432,
  432,1624,432,6424,832,114,114,114,114,214,214,214,214,214,
  214,214,214,214,214,214,214,214,214,214,214,214,214,214,214,
  214,214,414,414,414,414,414,414,414,414,414,414,414,414,414,
  814,112,134,112,134,112,112,134,134,112,134,322,934,122,134,
  122,134,334,322,934,334,322,122,134,934,334,122,134,134,122,
  134,134,122,134,134,134,122,134,134,334,334,322,934,334,134,
  122,134,134,134,334,134,334,134,134,334,134,334,134,134,134,
  334,134,134,134,312,624,634,642,354,362,112,424,234,242,254,
  262,212,424,434,442,454,462,312,1224,634,642,654,662,212,824,
  434,442,854,862,2424,1234,1242,1254,662,424,234,242,254,162,
  824,434,442,454,262,624,634,342,654,362,1624,434,442,854,262,
  824,434,242,854,262,1624,834,442,1654,462,2424,1234,642,2454,
  662,824,434,242,854,262,1624,434,442,854,262,3224,834,442,
  3254,462,111,211,111,111,111,111,111,111,111,111,311,321,111,
  121,111,311,111,121,321,311,111,121,321,111,121,111,121,121,
  111,111,121,121,111,311,321,121,111,121,121,121,121,121,121,
  121,121,121,121,121,121,121,121,121,121,121,111,111,121,121,
  111,121,311,321,111,121,311,321,111,121,111,121,111,421,211,
  221,211,221,211,1621,111,121,121,411,421,411,421,211,421,211,
  411,411,821,821,411,6421,211,121,121,411,821,411,811,821,421,
  411,811,1621,3221,411,421,111,421,121,811,821,211,121,221,
  211,421,421,211,221,121,411,221,221,121,121,421,121,421,221,
  121,421,221,221,121,221,121,121,121,121,121];

CR_4.columnGeneratorSpaceGroup :=
  [[0,0,0,0,1],[0,0,0,1,2],[0,0,0,1,3],[0,0,0,1,4],[0,0,1,0,2],
  [0,0,1,0,3],[0,0,1,1,2],[0,0,1,1,3],[0,0,1,1,4],[0,0,1,2,3],
  [0,0,2,0,3],[0,0,2,1,3],[0,0,2,1,4],[0,0,2,2,3],[0,0,3,1,4],
  [0,1,0,0,2],[0,1,0,0,3],[0,1,0,0,4],[0,1,0,0,6],[0,1,0,1,2],
  [0,1,0,1,3],[0,1,0,1,4],[0,1,0,2,4],[0,1,1,0,2],[0,1,1,0,3],
  [0,1,1,0,4],[0,1,1,0,6],[0,1,1,1,2],[0,1,1,1,3],[0,1,2,0,4],
  [0,1,2,3,4],[0,1,3,2,4],[0,2,0,0,3],[0,2,0,1,3],[0,2,0,1,4],
  [0,2,1,0,3],[0,2,1,2,3],[0,3,0,1,4],[0,3,1,0,6],[0,3,2,1,4],
  [0,3,3,2,4],[0,5,0,5,6],[1,0,0,0,2],[1,0,0,0,3],[1,0,0,0,4],
  [1,0,0,0,6],[1,0,0,1,2],[1,0,0,2,3],[1,0,0,3,6],[1,0,1,0,2],
  [1,0,1,1,2],[1,0,2,0,3],[1,0,2,0,4],[1,0,3,0,6],[1,1,0,0,2],
  [1,1,0,0,3],[1,1,0,0,4],[1,1,0,0,6],[1,1,0,1,2],[1,1,0,1,3],
  [1,1,0,2,3],[1,1,1,0,2],[1,1,1,0,3],[1,1,1,1,2],[1,1,2,0,3],
  [1,1,2,0,4],[1,2,0,0,3],[1,2,0,0,4],[1,2,0,1,3],[1,2,1,1,3],
  [1,2,1,2,3],[1,2,2,0,4],[1,2,2,1,3],[1,3,0,0,6],[1,3,0,3,6],
  [1,3,3,0,6],[2,0,0,0,3],[2,0,0,1,3],[2,0,0,3,6],[2,0,1,0,3],
  [2,0,1,1,3],[2,0,2,2,3],[2,0,3,0,6],[2,1,0,0,3],[2,1,0,0,4],
  [2,1,1,2,3],[2,1,2,0,3],[2,1,2,1,3],[2,1,5,2,6],[2,2,1,1,3],
  [2,3,0,0,6],[2,3,0,3,6],[2,3,3,0,6],[3,0,1,5,6],[3,1,0,0,6],
  [3,2,0,0,6],[3,5,5,0,6],[4,3,3,0,12],[5,2,5,3,6],[5,3,3,0,6]];

CR_4.crystalSystemQClass :=
  [1,1,2,2,2,3,3,4,4,4,4,5,5,6,6,6,7,7,7,7,7,7,7,8,8,
  8,8,8,9,9,9,9,9,9,9,10,11,11,12,12,12,12,12,13,13,13,
  13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,15,15,
  15,15,15,15,15,15,15,15,15,15,16,17,17,18,18,18,18,18,19,
  19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,
  20,20,20,20,20,20,20,20,21,21,21,21,22,22,22,22,22,22,22,
  22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,
  24,25,25,25,25,25,25,25,25,25,25,25,26,26,27,27,27,27,28,
  28,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,30,30,30,
  30,30,30,30,31,31,31,31,31,31,31,32,32,32,32,32,32,32,32,
  32,32,32,32,32,32,32,32,32,32,32,32,32,33,33,33,33,33,33,
  33,33,33,33,33,33,33,33,33,33];

CR_4.dimension := 4;

CR_4.familyCrystalSystem :=
  [1,2,3,4,5,5,6,7,7,8,9,10,10,11,11,12,13,14,14,15,16,
  16,16,17,17,18,19,20,21,21,22,23,23];

CR_4.fixedPointFreeSpaceGroup :=
  BlistList( [ 1 .. 4783 ],
  [1,4,6,8,17,19,33,34,37,38,40,44,48,55,56,61,70,79,82,83,
  87,95,122,242,243,244,245,251,257,267,271,279,389,393,397,
  411,412,414,429,430,431,440,669,692,1239,1242,1325,1327,1349,
  1378,1381,1383,1388,1451,1494,1533,1741,1744,1771,1851,1857,
  1860,1886,3047,3053,3062,3070,3079,3083,3286,3314,4030,4038,4139] );

CR_4.GLZ := GLZ4;

CR_4.hQClass :=
  BlistList( [1..227],
  [2,5,7,11,13,16,23,28,35,36,38,43,53,63,75,76,78,83,89,
  111,115,126,137,142,153,155,159,161,170,183,190,211,227] );

CR_4.modulSp := 100;

CR_4.modulZ := 124;

CR_4.nameCrystalFamily :=
  ["hexaclinic","triclinic","diclinic","monoclinic","orthogonal",
  "tetragonal monoclinic","hexagonal monoclinic","ditetragonal diclinic",
  "dihexagonal diclinic","tetragonal orthogonal","hexagonal orthogonal",
  "ditetragonal monoclinic","dihexagonal monoclinic",
  "ditetragonal orthogonal","hexagonal tetragonal","dihexagonal orthogonal",
  "cubic orthogonal","octagonal","decagonal","dodecagonal",
  "di-isohexagonal orthogonal","icosahedral","hypercubic"];

CR_4.nullDadeGroupsZClass :=
  [0,9,18,22,37,41,56,60,75,79,91,107,110,117,127,129,133,
  140,144,154,158,160,166,173,180,185,199,204,206,210,217,221,
  231,235,237,241,248,252,262,266,276,277,279,282,284,287,288,
  294,296,299,300,301,302,307,308,310,312,313,316,318,319,320,
  321,324,326,328,331,332,338,340,343,344,345,346,347,350,352,
  355,357,358,364,367,369,370,371,372,373,375,377,378,381,383,
  384,385,387,390,392,395,397,400,402,404,407,410,412,415,417,
  420,422,425,433,435,443,445,453,455,457,465,467,469,477,479,
  481,483,485,487,489,491,493,495,497,500,503,506,515,516,519,
  521,523,524,525,531,532,534,536,537,538,547,548,549,552,555,
  557,559,561,563,564,565,566,567,576,577,578,581,584,586,588,
  590,592,593,594,595,596,602,603,604,606,608,610,612,613,614,
  615,616,617,620,622,624,625,626,627,630,632,634,635,636,637,
  640,642,644,645,646,647,650,652,654,655,656,657,659,661,662,
  663,664,667,669,671,672,673,674,675,678,681,683,685,687,689,
  690,691,692,693,694,697,699,701,702,703,704,706,708,709,710,
  711,713,715,716,717,720,725,726,729,732,737,738,741,744,747,
  752,757,758,759,762,765,768,773,774,777,780,785,786,789,792,
  797,798,799,802,805,808,813,814,815,818,821,824,829,830,831,
  834,837,840,845,846,847,850,853,856,861,862,863,866,869,870,
  873,874,876,877,879,880,883,884,885,887,889,890,893,894,895,
  897,899,900,902,903,906,907,908,910,912,913,915,916,918,920,
  922,925,927,929,934,936,940,942,943,944,947,948,949,950,951,
  953,954,955,956,957,958,959,961,962,963,964,965,967,968,969,
  970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,
  985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,
  1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,
  1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,
  1024,1025,1026,1027,1030,1031,1033,1034,1037,1040,1041,1042,
  1044,1045,1047,1048,1050,1051,1054,1055,1056,1059,1060,1061,
  1063,1065,1066,1067,1068,1071,1072,1073,1075,1076,1077,1079,
  1080,1081,1082,1085,1086,1087,1088,1089,1091,1092,1093,1094,
  1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,
  1108,1109,1110,1111,1112,1113,1114,1117,1118,1119,1120,1121,
  1122,1125,1126,1127,1128,1129,1130,1133,1134,1135,1136,1137,
  1138,1141,1142,1143,1144,1145,1146,1149,1150,1151,1152,1153,
  1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,
  1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,
  1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,
  1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,
  1202,1203,1204,1205,1206,1207,1208,1209,1211,1213,1215,1217,
  1219,1221,1223,1225,1227,1228,1229,1230,1231,1232,1233,1234,
  1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,
  1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,
  1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,
  1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,
  1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,
  1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,
  1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,
  1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,
  1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,
  1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,
  1355,1356,1357,1358,1359,1360,1361];

CR_4.nullGeneratorsZClass :=
  [0,1,2,3,4,5,6,8,10,11,12,13,15,17,19,21,23,25,27,29,31,
  33,35,37,39,41,43,45,47,49,51,53,55,57,60,63,66,69,72,75,
  77,79,81,83,85,87,89,91,93,95,97,99,101,104,107,110,113,
  116,119,122,125,128,131,134,137,140,143,146,149,152,155,158,
  161,164,167,170,173,176,179,182,185,188,191,194,197,200,204,
  208,212,216,220,224,228,232,233,234,235,236,238,240,242,244,
  246,248,250,252,254,256,259,262,263,264,265,266,268,270,272,
  274,276,278,280,282,284,285,286,288,290,292,294,296,299,300,
  301,302,303,304,305,306,307,308,309,311,313,315,317,319,321,
  323,325,327,329,331,333,335,337,339,341,343,345,347,349,351,
  353,355,357,359,361,363,365,367,369,371,373,376,379,382,385,
  388,391,394,397,400,403,406,408,410,412,414,416,418,420,422,
  424,426,428,430,432,434,436,438,440,442,444,446,448,450,452,
  454,457,460,463,466,469,472,475,478,481,484,487,490,493,496,
  499,502,505,508,511,514,517,520,523,526,529,532,535,538,541,
  544,547,550,553,556,560,564,568,572,576,577,578,579,580,581,
  582,583,584,586,588,590,592,594,596,598,600,602,604,606,608,
  610,612,614,616,618,620,622,624,626,628,630,632,634,636,638,
  640,642,644,646,648,650,652,654,656,658,660,662,664,667,670,
  673,676,679,682,684,686,688,690,692,694,696,698,700,702,704,
  706,709,712,715,718,721,724,727,730,733,736,739,742,745,748,
  751,754,758,762,764,766,768,770,772,774,776,778,780,782,784,
  787,790,793,796,799,802,805,808,811,814,817,820,823,826,829,
  832,835,839,843,847,851,855,859,863,865,867,869,871,874,877,
  880,883,886,889,892,895,899,903,904,905,907,909,911,913,915,
  917,919,921,923,925,927,929,931,933,935,938,941,944,947,950,
  953,956,959,961,964,967,970,973,976,979,982,985,988,991,994,
  997,1000,1004,1005,1006,1008,1010,1012,1014,1016,1018,1021,
  1024,1026,1028,1030,1032,1034,1036,1038,1040,1042,1044,1047,
  1050,1053,1056,1059,1061,1063,1065,1068,1071,1074,1077,1080,
  1083,1086,1089,1092,1095,1098,1101,1104,1107,1110,1113,1116,
  1119,1122,1125,1127,1129,1131,1133,1136,1139,1141,1143,1146,
  1149,1152,1155,1158,1161,1165,1168,1171,1174,1177,1180,1183,
  1186,1189,1192,1195,1198,1201,1205,1209,1213,1217,1221,1225,
  1229,1233,1237,1241,1245,1249,1253,1257,1261,1265,1269,1273,
  1276,1279,1282,1285,1288,1291,1294,1297,1300,1303,1307,1311,
  1315,1319,1323,1327,1331,1335,1339,1343,1347,1351,1355,1359,
  1363,1367,1371,1375,1379,1383,1387,1391,1395,1399,1403,1407,
  1411,1415,1419,1423,1427,1431,1435,1439,1443,1447,1451,1455,
  1459,1463,1468,1473,1478,1483,1488,1489,1491,1492,1493,1495,
  1497,1499,1500,1502,1504,1506,1508,1510,1512,1515,1518,1521,
  1524,1527,1530,1533,1536,1539,1542,1545,1548,1551,1554,1558,
  1562,1566,1570,1574,1578,1582,1586,1590,1594,1598,1600,1602,
  1604,1607,1610,1612,1615,1618,1621,1624,1628,1631,1635,1639,
  1643,1645,1647,1649,1651,1653,1655,1659,1663,1666,1669,1672,
  1675,1679,1683,1686,1689,1691,1693,1695,1697,1699,1701,1704,
  1707,1710,1713,1716,1719,1722,1725,1728,1731,1734,1737,1740,
  1743,1746,1749,1753,1757,1761,1765,1769,1773,1777,1781,1785,
  1789,1793,1797,1801,1805,1809,1812,1815,1820,1825,1830,1834,
  1838,1843,1848,1853,1859,1865,1871,1877,1883,1889,1895,1901,
  1907,1909,1911,1914,1917,1920,1924,1927,1931,1935,1939,1943,
  1948,1953,1959,1965,1971,1978,1979,1980,1981,1982,1983,1984,
  1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,
  1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,
  2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,
  2021,2022,2023,2024,2025,2026,2029,2032,2035,2039,2042,2045,
  2049,2053,2056,2061,2066,2069,2072,2075,2078,2081,2084,2087,
  2091,2094,2098,2101,2104,2108,2114,2122,2125,2128,2132,2134,
  2138,2142,2145,2149,2152,2161,2169,2171,2175,2179,2183,2189,
  2193,2196,2199,2202,2206,2210,2213,2217,2225,2240,2248,2256,
  2260,2264,2268,2271,2274];

CR_4.nullQClass :=
  [0,2,5,7,11,13,16,23,28,35,36,38,43,53,63,75,76,78,83,89,
  111,115,126,137,142,153,155,159,161,170,183,190,211,227];

CR_4.nullSpaceGroup :=
  [0,1,2,4,6,8,9,13,15,17,19,20,23,26,27,40,44,56,63,66,
  71,87,91,99,105,111,113,116,122,124,128,131,132,134,180,188,
  212,226,229,234,235,245,251,257,261,267,271,273,275,279,281,
  283,285,286,305,319,329,335,338,342,345,348,452,488,528,548,
  584,600,606,614,626,632,638,642,702,722,746,770,780,790,794,
  802,806,810,814,816,1034,1122,1182,1201,1207,1223,1232,1235,
  1236,1237,1240,1244,1248,1251,1255,1259,1262,1265,1271,1275,
  1285,1294,1314,1323,1325,1327,1328,1329,1331,1333,1335,1337,
  1339,1341,1343,1345,1347,1351,1352,1354,1359,1363,1365,1367,
  1372,1373,1374,1375,1376,1379,1381,1384,1386,1388,1390,1391,
  1397,1401,1405,1408,1411,1413,1429,1445,1451,1457,1465,1473,
  1481,1489,1495,1499,1503,1509,1510,1522,1534,1538,1542,1548,
  1554,1558,1562,1566,1569,1571,1575,1577,1613,1653,1665,1674,
  1690,1706,1715,1721,1724,1733,1757,1763,1775,1783,1789,1793,
  1801,1803,1807,1811,1813,1815,1823,1825,1829,1833,1835,1837,
  1861,1867,1875,1887,1893,1897,1933,1939,1955,1961,1964,2092,
  2108,2140,2172,2188,2196,2260,2324,2332,2340,2356,2372,2388,
  2404,2412,2420,2424,2428,2524,2536,2560,2576,2588,2592,2628,
  2634,2650,2656,2659,2931,2955,3019,3039,3045,3049,3051,3055,
  3057,3059,3060,3064,3066,3070,3072,3074,3075,3079,3083,3085,
  3087,3091,3092,3096,3097,3101,3102,3106,3107,3115,3117,3125,
  3133,3135,3137,3145,3147,3155,3163,3165,3167,3175,3177,3185,
  3193,3195,3197,3201,3202,3210,3218,3220,3222,3238,3240,3256,
  3272,3274,3276,3292,3296,3299,3300,3303,3304,3320,3324,3327,
  3330,3331,3332,3364,3368,3378,3388,3390,3392,3402,3404,3436,
  3440,3450,3460,3462,3464,3474,3476,3512,3516,3518,3521,3522,
  3523,3524,3525,3526,3527,3528,3531,3534,3536,3542,3554,3557,
  3563,3565,3568,3574,3581,3584,3586,3591,3593,3600,3606,3608,
  3617,3620,3630,3654,3678,3684,3688,3702,3706,3708,3711,3713,
  3729,3733,3749,3765,3769,3773,3783,3787,3823,3829,3830,3831,
  3832,3833,3835,3837,3839,3841,3843,3845,3847,3849,3851,3853,
  3855,3857,3859,3861,3863,3865,3867,3869,3871,3873,3875,3877,
  3881,3885,3889,3893,3897,3901,3905,3909,3913,3917,3921,3925,
  3929,3937,3938,3939,3940,3941,3942,3943,3944,3945,3946,3947,
  3949,3952,3953,3954,3955,3956,3958,3960,3964,3966,3968,3969,
  3970,3973,3975,3976,3977,3978,3979,3980,3981,3982,3983,3984,
  3985,3986,3987,3988,3990,3992,3994,3997,3999,4000,4001,4002,
  4003,4004,4006,4007,4009,4010,4011,4013,4014,4016,4017,4018,
  4019,4021,4022,4023,4024,4026,4030,4034,4038,4040,4042,4043,
  4046,4048,4050,4052,4054,4056,4060,4064,4067,4071,4074,4076,
  4082,4086,4090,4094,4098,4100,4108,4112,4115,4123,4129,4141,
  4149,4155,4163,4167,4171,4173,4175,4177,4178,4184,4188,4191,
  4195,4197,4201,4205,4207,4211,4213,4225,4229,4232,4240,4242,
  4250,4254,4256,4264,4266,4282,4290,4294,4310,4314,4330,4338,
  4342,4358,4362,4370,4374,4376,4384,4386,4398,4402,4405,4413,
  4415,4447,4455,4459,4491,4495,4496,4498,4499,4500,4501,4502,
  4503,4504,4505,4506,4508,4510,4511,4512,4513,4515,4516,4517,
  4519,4521,4522,4523,4525,4526,4527,4528,4529,4530,4531,4532,
  4533,4534,4535,4537,4539,4540,4541,4542,4543,4544,4545,4546,
  4547,4548,4549,4550,4551,4552,4553,4554,4555,4556,4557,4558,
  4559,4560,4561,4562,4563,4564,4566,4568,4569,4570,4572,4574,
  4575,4576,4577,4578,4579,4581,4583,4585,4587,4589,4591,4597,
  4598,4599,4600,4603,4607,4610,4614,4616,4620,4622,4625,4628,
  4634,4640,4642,4649,4651,4652,4653,4657,4663,4667,4673,4679,
  4683,4687,4691,4696,4706,4710,4714,4715,4717,4718,4726,4734,
  4736,4737,4739,4741,4743,4745,4747,4749,4750,4754,4756,4758,
  4759,4760,4762,4763,4766,4768,4769,4771,4773,4775,4776,4778,
  4779,4780,4781,4782,4783];

CR_4.nullZClass :=
  [0,1,2,4,6,8,11,14,20,27,33,39,52,61,73,85,93,95,97,99,
  103,105,107,109,111,113,116,119,122,123,124,125,126,127,129,
  130,131,132,133,140,146,159,172,183,189,195,201,207,212,218,
  230,236,241,246,250,254,262,266,270,276,282,288,294,300,302,
  304,306,308,312,314,318,320,322,326,328,330,333,336,338,341,
  346,353,358,365,367,369,371,375,377,379,380,381,383,385,386,
  387,389,390,392,394,396,400,404,405,406,408,410,411,412,416,
  418,419,421,423,427,429,431,433,436,439,444,447,450,454,459,
  463,467,468,469,470,471,473,475,476,477,479,481,482,488,494,
  500,506,512,517,522,527,532,537,542,547,552,557,562,567,568,
  569,570,571,573,574,575,576,579,581,586,590,592,595,599,603,
  606,607,608,609,611,612,613,614,615,616,617,618,620,621,625,
  627,629,631,633,635,637,639,641,643,645,648,650,652,654,659,
  661,664,666,670,674,676,679,681,684,687,690,693,694,695,696,
  697,698,699,700,701,702,703,704,705,706,708,709,710];

CR_4.orbitLengthSpaceGroup :=
  [7,3,1,1,7,7,3,3,1,6,9,2,1,2,6,6,1,6,6,3,6,6,12,3,6,
  6,3,6,2,1,2,1,2,1,2,1,1,1,1,4,2,2,4,2,1,2,1,2,2,2,
  1,1,1,1,1,1,1,1,3,3,3,3,3,3,3,3,1,3,3,1,1,1,1,1,1,
  1,1,2,2,1,1,1,2,2,1,1,1,1,2,3,2,6,1,3,3,1,1,1,2,1,
  1,2,1,2,2,2,2,6,6,6,6,6,6,6,6,1,2,1,6,6,6,6,6,6,6,
  6,3,6,3,6,6,6,6,6,12,6,12,12,12,12,3,6,3,6,12,6,1,6,
  6,3,3,6,6,1,2,2,1,1,1,1,2,2,1,1,1,1,2,2,1,1,1,1,2,
  2,1,1,1,2,2,4,4,4,4,2,2,2,2,1,1,2,1,2,2,2,1,3,3,6,
  3,3,3,6,1,3,1,2,2,1,1,1,2,2,1,1,1,3,3,1,2,2,1,1,3,
  3,1,1,3,1,1,1,1,1,3,12,12,24,12,24,4,6,12,24,12,24,24,
  12,12,3,8,6,24,4,1,4,2,2,2,2,4,2,4,2,1,1,3,3,6,3,3,
  3,6,1,3,12,3,12,3,1,2,1,3,1,3,1,2,4,3,6,3,6,3,3,6,
  3,6,6,6,6,6,6,6,3,6,6,6,6,6,6,3,6,3,6,6,6,3,6,6,3,
  6,3,1,6,6,3,3,6,6,6,6,3,6,6,6,3,6,6,6,3,6,6,3,6,6,
  6,3,3,6,6,6,6,2,6,6,6,6,6,6,3,6,3,6,6,6,6,3,6,6,6,
  6,3,6,6,6,6,6,6,6,2,3,3,3,6,6,3,6,6,1,3,3,1,2,1,2,
  2,2,2,2,2,2,2,2,2,2,2,1,2,1,2,2,2,2,2,2,2,2,2,1,1,
  2,2,2,2,2,1,1,2,2,2,2,1,2,1,2,1,1,2,2,2,2,1,2,1,2,
  1,2,2,1,2,1,2,2,2,1,1,2,2,1,2,1,2,2,2,1,1,3,3,3,6,
  3,6,3,6,3,3,6,3,1,3,3,1,3,3,1,2,1,2,2,2,2,2,2,2,2,
  2,2,2,2,2,2,2,2,2,1,1,2,2,2,2,1,2,1,2,2,2,2,2,1,1,
  6,3,3,6,6,6,3,3,3,6,6,3,6,2,1,1,2,1,1,2,3,3,1,1,3,
  3,1,1,2,2,1,1,1,1,2,2,1,1,2,1,1,2,1,1,2,2,1,1,3,3,
  1,3,3,6,3,3,6,3,1,3,3,6,3,6,6,6,6,3,6,3,6,6,6,6,3,
  3,6,3,3,6,6,6,6,6,6,6,6,6,3,3,6,6,3,3,3,3,6,6,3,3,
  3,3,3,6,6,3,1,3,1,3,2,1,2,1,1,2,2,2,2,2,2,2,2,2,1,
  2,1,1,1,2,1,2,1,1,1,2,1,2,1,1,1,2,1,2,1,1,1,2,1,2,
  1,1,1,2,2,1,1,2,2,1,1,1,1,1,1,2,2,1,1,2,2,1,1,1,1,
  1,3,3,3,3,6,6,3,3,3,3,1,3,3,6,6,3,3,1,1,1,1,1,1,1,
  1,1,1,3,1,3,1,1,1,1,1,1,3,12,12,24,12,24,24,24,12,24,
  4,6,12,24,12,6,12,24,24,12,12,6,24,24,24,24,24,12,24,24,
  24,24,24,8,24,24,24,24,24,24,24,24,24,12,24,24,12,24,24,
  12,12,24,24,24,24,24,12,24,24,24,24,24,24,12,24,24,12,24,
  12,24,24,12,24,4,12,12,4,24,12,12,24,24,12,24,12,24,24,
  8,12,12,24,4,24,24,24,12,24,24,24,24,12,24,24,12,24,24,
  24,24,6,8,24,24,24,24,24,24,24,24,24,24,12,24,24,24,24,
  24,24,24,24,24,24,24,12,24,12,12,24,24,24,24,24,24,12,12,
  24,24,24,12,12,24,24,6,12,12,12,24,24,6,12,3,24,24,24,
  24,24,24,24,24,24,12,24,24,24,24,24,24,24,12,24,12,24,24,
  12,24,12,12,24,24,24,24,12,4,24,12,24,24,12,12,12,24,12,
  24,24,24,12,24,12,8,24,6,4,12,3,12,12,6,12,1,2,4,4,2,
  2,1,4,4,4,2,2,4,4,4,2,2,2,2,4,4,4,4,4,2,2,4,4,4,4,
  2,2,4,4,4,2,2,2,2,4,4,1,2,1,4,4,2,2,4,4,4,2,2,4,4,
  4,4,4,4,2,2,4,2,2,1,2,4,4,2,2,1,4,4,4,2,2,4,4,4,2,
  2,2,2,4,4,1,2,1,3,6,6,3,3,3,6,3,3,3,3,6,6,6,6,3,6,
  6,6,6,6,3,6,3,6,6,6,6,3,3,6,1,6,6,3,3,3,3,3,3,6,3,
  6,6,6,6,3,3,6,3,6,3,1,3,6,3,3,3,1,12,12,12,24,6,24,
  12,24,24,12,8,4,12,24,12,24,6,3,4,2,4,4,1,3,1,3,3,3,
  1,3,1,3,3,3,1,1,1,1,2,2,4,1,2,1,2,1,4,3,12,3,4,1,2,
  1,3,3,2,1,3,1,3,1,3,3,2,1,2,1,12,3,1,12,3,4,1,2,3,
  1,3,3,6,3,3,6,3,1,2,2,2,4,1,1,2,1,3,3,1,1,3,3,3,3,
  3,3,6,6,3,3,3,3,6,6,2,1,2,4,2,1,2,1,2,8,3,3,3,2,8,
  8,3,3,3,24,8,3,3,3,3,3,6,24,8,3,3,3,3,3,3,6,2,1,1,
  2,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,2,2,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,
  1,2,2,1,1,2,1,1,2,1,1,2,1,1,2,1,2,1,1,2,1,1,2,1,1,
  2,1,1,1,1,1,1,1,2,1,1,2,1,2,1,1,2,1,1,1,1,1,1,1,1,
  1,1,2,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,
  2,2,2,2,2,2,2,2,1,1,2,2,2,2,1,2,1,2,1,1,2,2,1,1,2,
  2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,2,2,1,1,1,1,1,1,
  2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,2,2,1,1,2,
  4,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,2,1,2,1,1,4,2,2,2,1,1,2,1,2,1,1,2,2,
  4,2,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,
  1,2,1,2,1,1,2,1,2,1,1,2,1,1,2,1,1,2,1,1,1,1,1,1,1,
  1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,2,1,1,2,1,1,
  2,1,1,2,1,1,2,1,1,2,1,1,2,1,2,1,1,2,1,1,1,1,1,1,1,
  1,2,1,1,2,1,1,2,1,1,2,1,2,1,1,2,1,1,1,1,2,2,2,2,2,
  2,2,2,2,2,2,1,2,2,1,2,2,2,2,2,2,2,2,1,2,1,2,2,2,2,
  1,2,1,2,1,1,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  2,2,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,
  1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,
  1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,
  2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,2,1,
  1,2,1,1,2,1,1,2,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,
  1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,
  2,1,1,2,1,1,2,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,
  2,2,2,2,2,2,1,1,2,2,2,1,1,2,2,2,2,2,1,1,2,2,1,2,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,1,2,1,2,1,
  2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
  2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,1,2,2,2,2,
  2,2,2,2,2,2,2,2,2,1,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,
  2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,
  2,1,2,2,2,2,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,2,
  2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,2,
  2,2,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
  2,2,2,2,2,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,1,2,1,
  2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,1,2,2,2,
  2,2,1,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,1,2,2,2,1,
  1,2,2,2,2,2,2,2,2,1,1,2,2,1,1,2,2,1,1,1,1,1,1,1,1,
  1,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,2,2,2,1,2,2,2,1,2,2,1,2,2,2,1,2,1,1,1,1,
  2,2,1,1,2,2,1,2,2,2,1,2,1,2,2,1,2,2,1,2,1,2,2,1,2,
  2,1,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,2,2,1,2,2,
  2,1,1,2,2,1,2,2,1,1,2,2,1,2,2,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,2,2,1,2,
  2,1,1,2,2,1,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,2,1,2,2,
  1,2,1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,2,2,1,2,1,2,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,1,2,1,2,1,2,2,2,2,1,
  2,1,1,1,2,1,2,2,2,2,2,1,1,1,2,2,1,1,2,2,1,1,2,2,1,
  1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,1,2,2,1,2,1,2,2,1,
  2,2,2,2,1,2,1,2,1,2,2,2,2,1,2,1,1,1,2,1,2,2,2,2,2,
  1,1,1,2,1,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,
  2,2,2,1,2,1,2,2,2,2,2,1,1,1,1,1,3,2,1,2,1,1,2,1,1,
  2,1,1,2,1,2,1,1,2,1,1,2,1,1,2,1,2,2,1,1,2,1,1,2,1,
  1,2,2,1,1,4,2,2,2,4,1,2,1,1,4,1,1,1,1,2,1,4,4,2,2,
  2,4,1,4,4,1,2,1,2,1,1,4,2,2,2,1,2,1,2,2,2,2,1,2,1,
  1,1,1,2,2,1,1,1,1,2,2,2,2,1,1,1,1,2,2,1,1,1,1,2,2,
  2,1,2,2,4,4,4,4,4,4,4,4,2,2,4,4,2,2,1,2,1,2,1,2,1,
  1,1,1,1,2,4,4,1,2,2,4,4,1,2,1,2,2,1,1,1,1,2,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,2,2,2,2,1,2,2,1,1,1,1,1,2,2,2,2,1,2,2,2,2,2,
  2,2,2,2,2,2,2,2,2,2,1,2,1,2,2,1,2,1,2,2,2,2,2,1,1,
  1,1,1,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,4,
  4,2,2,2,2,4,2,2,4,4,2,2,2,2,4,4,2,2,2,2,2,2,2,2,1,
  2,2,1,2,2,1,2,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1,1,2,1,
  1,1,1,2,2,2,1,2,4,2,2,1,2,2,1,2,2,1,2,1,2,2,1,1,1,
  1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,2,2,1,1,2,2,1,
  1,2,2,1,2,4,4,2,2,2,1,1,2,2,1,2,2,1,2,4,2,2,1,1,2,
  2,1,2,1,2,1,1,1,1,1,1,2,1,1,2,1,1,1,1,2,1,1,1,1,1,
  2,1,2,2,1,2,2,2,1,2,2,1,1,1,1,1,1,1,2,2,2,2,1,1,1,
  1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,
  1,2,2,1,1,2,2,1,1,2,2,1,2,2,1,1,2,2,1,2,2,1,2,2,1,
  1,2,2,1,1,2,2,1,1,2,2,1,2,2,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,2,1,1,2,1,1,2,1,1,2,1,1,1,1,2,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,1,1,1,
  1,1,6,1,3,3,2,2,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,2,2,
  1,1,2,2,1,1,2,1,2,1,1,3,9,9,18,3,18,6,1,1,1,1,2,1,
  2,1,1,1,1,1,2,1,1,2,1,1,1,1,2,2,1,1,1,1,1,1,3,3,1,
  3,3,6,3,3,6,3,3,6,3,3,3,1,1,1,1,1,1,1,3,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,1,1,1,3,3,1,1,1,1,1,1,1,3,1,2,1,
  3,1,1,1];

CR_4.orderQClass :=
  [1,2,2,2,4,2,4,4,4,4,8,4,8,8,8,16,4,4,8,8,8,8,16,3,
  6,6,6,12,6,6,12,12,12,12,24,4,3,6,4,8,8,8,16,8,8,
  8,8,16,16,16,16,16,32,6,6,6,12,12,12,12,12,12,24,12,
  12,12,12,12,24,24,24,24,24,24,48,8,6,12,8,16,16,16,
  32,16,16,32,32,32,64,12,12,12,24,24,24,24,24,24,24,24,
  24,24,24,48,48,48,48,48,48,48,96,6,12,12,24,9,18,18,
  18,18,36,36,36,36,36,72,18,36,36,36,36,36,72,72,72,72,
  144,12,24,24,24,48,24,24,24,24,48,48,48,48,48,48,96,8,
  16,5,10,10,20,12,24,18,36,36,36,72,72,72,72,144,12,24,
  24,24,36,48,72,72,72,144,144,144,288,20,40,60,120,120,
  120,240,8,16,16,16,24,32,32,32,32,32,48,64,64,64,64,
  96,128,192,192,192,384,24,24,24,48,48,48,72,96,96,96,
  144,192,288,576,576,1152];

CR_4.parametersDadeGroup :=
  [[4,20,22,1,0],[4,25,11,2,0],[4,25,11,4,0],[4,29,9,1,0],[4,30,13,1,0],
  [4,31,7,1,0],[4,31,7,2,0],[4,32,21,1,0],[4,33,16,1,0]];

CR_4.QClassZClass :=
  [1,2,3,3,4,4,5,5,6,6,6,7,7,7,8,8,8,8,8,8,9,9,9,9,9,
  9,9,10,10,10,10,10,10,11,11,11,11,11,11,12,12,12,12,12,
  12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,14,14,
  14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,
  15,15,15,16,16,16,16,16,16,16,16,17,17,18,18,19,19,20,20,
  20,20,21,21,22,22,23,23,24,24,25,25,26,26,26,27,27,27,28,
  28,28,29,30,31,32,33,34,34,35,36,37,38,39,39,39,39,39,39,
  39,40,40,40,40,40,40,41,41,41,41,41,41,41,41,41,41,41,41,
  41,42,42,42,42,42,42,42,42,42,42,42,42,42,43,43,43,43,43,
  43,43,43,43,43,43,44,44,44,44,44,44,45,45,45,45,45,45,46,
  46,46,46,46,46,47,47,47,47,47,47,48,48,48,48,48,49,49,49,
  49,49,49,50,50,50,50,50,50,50,50,50,50,50,50,51,51,51,51,
  51,51,52,52,52,52,52,53,53,53,53,53,54,54,54,54,55,55,55,
  55,56,56,56,56,56,56,56,56,57,57,57,57,58,58,58,58,59,59,
  59,59,59,59,60,60,60,60,60,60,61,61,61,61,61,61,62,62,62,
  62,62,62,63,63,63,63,63,63,64,64,65,65,66,66,67,67,68,68,
  68,68,69,69,70,70,70,70,71,71,72,72,73,73,73,73,74,74,75,
  75,76,76,76,77,77,77,78,78,79,79,79,80,80,80,80,80,81,81,
  81,81,81,81,81,82,82,82,82,82,83,83,83,83,83,83,83,84,84,
  85,85,86,86,87,87,87,87,88,88,89,89,90,91,92,92,93,93,94,
  95,96,96,97,98,98,99,99,100,100,101,101,101,101,102,102,
  102,102,103,104,105,105,106,106,107,108,109,109,109,109,110,
  110,111,112,112,113,113,114,114,114,114,115,115,116,116,117,
  117,118,118,118,119,119,119,120,120,120,120,120,121,121,121,
  122,122,122,123,123,123,123,124,124,124,124,124,125,125,125,
  125,126,126,126,126,127,128,129,130,131,131,132,132,133,134,
  135,135,136,136,137,138,138,138,138,138,138,139,139,139,139,
  139,139,140,140,140,140,140,140,141,141,141,141,141,141,142,
  142,142,142,142,142,143,143,143,143,143,144,144,144,144,144,
  145,145,145,145,145,146,146,146,146,146,147,147,147,147,147,
  148,148,148,148,148,149,149,149,149,149,150,150,150,150,150,
  151,151,151,151,151,152,152,152,152,152,153,153,153,153,153,
  154,155,156,157,158,158,159,160,161,162,162,162,163,163,164,
  164,164,164,164,165,165,165,165,166,166,167,167,167,168,168,
  168,168,169,169,169,169,170,170,170,171,172,173,174,174,175,
  176,177,178,179,180,181,182,182,183,184,184,184,184,185,185,
  186,186,187,187,188,188,189,189,190,190,191,191,192,192,193,
  193,194,194,195,195,195,196,196,197,197,198,198,199,199,199,
  199,199,200,200,201,201,201,202,202,203,203,203,203,204,204,
  204,204,205,205,206,206,206,207,207,208,208,208,209,209,209,
  210,210,210,211,211,211,212,213,214,215,216,217,218,219,220,
  221,222,223,224,225,225,226,227];

CR_4.relatorNumbersQClass := CR_2.relatorNumbersQClass;

CR_4.rowConjugatorDadeGroup :=
  [[-5,3,-3,1],[-3,2,-2,1],[-2,-2,-1,-1],[-2,-1,1,-1],
  [-2,1,-1,-1],[-2,1,-1,0],[-2,1,-1,1],[-2,2,-1,-1],
  [-2,2,-1,1],[-1,-3,1,-1],[-1,-2,1,-1],[-1,-1,-1,-1],
  [-1,-1,-1,0],[-1,-1,-1,1],[-1,-1,0,-1],[-1,-1,0,0],
  [-1,-1,1,-1],[-1,-1,1,0],[-1,0,-1,-1],[-1,0,-1,0],
  [-1,0,-1,1],[-1,0,0,-1],[-1,0,0,0],[-1,0,0,1],
  [-1,0,1,0],[-1,1,-1,0],[-1,1,0,-1],[-1,1,0,0],
  [-1,1,0,1],[0,-2,0,-1],[0,-1,-1,-1],[0,-1,-1,0],
  [0,-1,-1,1],[0,-1,0,-1],[0,-1,0,0],[0,-1,0,1],
  [0,-1,1,-1],[0,-1,1,0],[0,-1,1,1],[0,0,-1,-1],
  [0,0,-1,0],[0,0,-1,1],[0,0,0,-1],[0,0,0,1],
  [0,0,1,-1],[0,0,1,0],[0,0,1,1],[0,1,-1,-1],
  [0,1,-1,0],[0,1,-1,1],[0,1,0,-1],[0,1,0,0],
  [0,1,0,1],[0,1,1,0],[0,1,1,1],[0,2,0,1],
  [1,-1,0,0],[1,-1,1,-1],[1,-1,1,0],[1,0,-1,0],
  [1,0,0,-1],[1,0,0,0],[1,0,0,1],[1,0,1,0],
  [1,0,1,1],[1,1,-1,0],[1,1,-1,1],[1,1,0,-1],
  [1,1,0,0],[1,1,0,1],[1,1,1,-2],[1,1,1,-1],
  [1,1,1,1],[1,2,-1,1],[1,2,0,1],[2,-2,1,-1],
  [2,-2,1,1],[2,-1,1,-1],[2,-1,1,0],[2,0,1,1],
  [2,1,-1,1],[2,2,1,-1],[2,2,1,1],[2,3,-1,1],
  [3,-2,1,-1],[3,-2,2,-1],[4,2,2,1],[5,-3,2,-2],
  [10,-6,5,-3],[-6,4,-3,2],[-4,2,-2,1],[-3,1,-1,-1],
  [-3,2,-1,1],[-2,-3,1,-1],[-2,-1,-1,0],[-2,0,-1,0],
  [-2,1,0,-1],[-2,1,0,1],[-1,-2,0,-1],[-1,-2,1,0],
  [-1,-1,-2,-1],[-1,-1,0,1],[-1,-1,1,1],[-1,0,1,1],
  [-1,0,1,2],[-1,0,2,1],[-1,1,-2,-1],[-1,1,-1,-1],
  [-1,1,-1,1],[-1,1,1,-1],[0,-3,1,-1],[0,-2,-1,0],
  [0,-2,2,1],[0,0,-2,-1],[0,0,2,1],[0,1,-2,-1],
  [0,1,1,-1],[0,2,2,1],[1,-2,1,0],[1,-1,0,-1],
  [1,-1,0,1],[1,-1,1,1],[1,0,-1,-1],[1,0,1,-1],
  [1,1,-2,-1],[1,1,-1,-1],[1,1,1,0],[1,2,-1,0],
  [1,3,-1,1],[2,-1,0,1],[2,-1,1,1],[2,0,0,-1],
  [2,0,1,0],[2,1,1,1],[2,1,2,1],[3,3,-1,1],
  [5,-3,2,-1],[5,6,-2,2],[7,9,-3,3]];

CR_4.rowGeneratorZClass :=
  [[-1,-1,-1,-1],[-1,-1,-1,0],[-1,-1,-1,1],[-1,-1,-1,2],[-1,-1,0,-1],
  [-1,-1,0,0],[-1,-1,0,1],[-1,-1,1,-1],[-1,-1,1,0],[-1,-2,2,0],
  [-1,0,-1,-1],[-1,0,-1,0],[-1,0,-1,1],[-1,0,0,-1],[-1,0,0,0],
  [-1,0,0,1],[-1,0,1,-1],[-1,0,1,0],[-1,0,1,1],[-1,1,-1,-1],
  [-1,1,-1,0],[-1,1,-1,1],[-1,1,0,-1],[-1,1,0,0],[-1,1,0,1],
  [-1,1,1,-1],[-1,1,1,0],[-2,-1,0,1],[-2,-2,0,-1],[-2,0,-1,0],
  [-2,0,-1,1],[-2,0,0,-1],[-2,0,0,1],[-2,0,1,-2],[-2,1,0,-2],
  [-4,3,0,2],[0,-1,-1,-1],[0,-1,-1,0],[0,-1,-1,1],[0,-1,0,-1],
  [0,-1,0,0],[0,-1,0,1],[0,-1,1,-1],[0,-1,1,0],[0,-1,1,1],
  [0,-2,-1,-1],[0,-2,-1,0],[0,-2,0,-1],[0,0,-1,-1],[0,0,-1,-2],
  [0,0,-1,0],[0,0,-1,1],[0,0,-1,2],[0,0,-2,-1],[0,0,-2,3],
  [0,0,-4,3],[0,0,0,-1],[0,0,0,1],[0,0,1,-1],[0,0,1,0],
  [0,0,1,1],[0,0,1,2],[0,0,2,-1],[0,0,2,1],[0,0,2,3],
  [0,0,3,-1],[0,0,3,-2],[0,0,4,-1],[0,0,4,3],[0,1,-1,-1],
  [0,1,-1,0],[0,1,-1,1],[0,1,0,-1],[0,1,0,0],[0,1,0,1],
  [0,1,1,-1],[0,1,1,0],[0,1,1,1],[0,1,2,1],[0,2,-2,-1],
  [1,-1,-1,0],[1,-1,-1,1],[1,-1,0,-1],[1,-1,0,0],[1,-1,0,1],
  [1,-1,1,-1],[1,-1,1,0],[1,-1,1,1],[1,0,-1,-1],[1,0,-1,-2],
  [1,0,-1,0],[1,0,-1,1],[1,0,-2,-1],[1,0,-2,1],[1,0,0,-1],
  [1,0,0,0],[1,0,0,1],[1,0,1,-1],[1,0,1,0],[1,0,1,1],
  [1,0,2,-1],[1,0,2,1],[1,1,-1,0],[1,1,-1,1],[1,1,0,-1],
  [1,1,0,0],[1,1,0,1],[1,1,1,-1],[1,1,1,-2],[1,1,1,0],
  [1,1,1,1],[1,2,0,1],[1,2,1,0],[1,2,1,1],[1,3,-1,1],
  [2,0,1,1],[2,1,0,-1],[2,1,0,1],[2,1,1,0],[2,1,1,1],
  [2,2,0,1],[4,-1,0,-2],[4,1,0,-2],[4,1,1,1]];

CR_4.spaceGroupIdentity :=
  [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]];

CR_4.splittingQClass :=
  BlistList( [1..227],
  [36,37,38,76,77,78,112,113,114,115,154,155,160,161,162,163,
  171,172,173,174,175,176,177,178,191,192,193,194,195,196,198,
  201,212,213,214,215,216,217,218,219,220,221,222,223] );

CR_4.splittingSpaceGroupType :=
  BlistList( [ 1 .. 4783 ],
  [1373,1374,1375,3517,3518,3519,3520,3521,3522,3523,3524,
  3525,3526,3527,3606,3615,3938,3939,3940,3941,3942,3943,3944,
  3945,3946,3947,4496,4497,4498,4504,4505,4506,4507,4508,4509,
  4510,4511,4512,4516,4544,4545,4546,4547,4548,4549,4550,4551,
  4552,4579,4580,4581,4582,4583,4584,4585,4586,4587,4588,4589,
  4590,4591,4592,4593,4594,4595,4596,4597,4598,4599,4600,4601,
  4602,4603,4604,4605,4606,4607,4615,4616,4617,4618,4619,4620,
  4646,4649,4650,4651,4652,4653,4659,4661,4759,4760,4761,4762,
  4763,4764,4765,4766,4767,4768,4769,4770,4771,4772,4773,4774,
  4775,4776,4777,4778] );

CR_4.splittingZClass :=
  BlistList( [1..710],
  [131,132,133,331,332,333,334,335,336,337,338,420,421,422,423,
  424,425,426,427,428,429,568,569,575,576,577,578,579,580,581,
  584,607,608,609,610,611,612,613,614,615,638,639,640,641,642,
  643,644,645,646,647,648,649,650,653,654,662,663,664,694,695,
  696,697,698,699,700,701,702,703,704,705] );