module symdata1;  %  Data for symmetry package, part 1.

% Author: Karin Gatermann <Gatermann@sc.ZIB-Berlin.de>.

set!*elems!*group('z2,'(id sz2))$
set!*generators('z2,'(sz2))$
set!*relations('z2,'(((sz2 sz2) (id))))$
set!*grouptable('z2,'((grouptable id sz2) (id id sz2) (sz2 sz2 id)))$
set!*inverse('z2,'((id sz2) (id sz2)))$
set!*elemasgen('z2,'(((sz2) (sz2))))$
set!*group('z2,'((id) (sz2)))$
set!*representation('z2,'((id (((1 . 1)))) (sz2 (((1 . 1))))),'complex)$
set!*representation('z2,
  '((id (((1 . 1)))) (sz2 (((-1 . 1))))),'complex)$
set!*representation('z2,
  '(realtype (id (((1 . 1)))) (sz2 (((1 . 1))))),'real)$
set!*representation('z2,
  '(realtype (id (((1 . 1)))) (sz2 (((-1 . 1))))),'real)$
set!*available 'z2$

set!*elems!*group('k4,'(id s1k4 s2k4 rk4))$
set!*generators('k4,'(s1k4 s2k4))$
set!*relations('k4,
               '(((s1k4 s1k4) (id))
                 ((s2k4 s2k4) (id))
                 ((s1k4 s2k4) (s2k4 s1k4))))$
set!*grouptable('k4,
                '((grouptable id s1k4 s2k4 rk4)
                  (id id s1k4 s2k4 rk4)
                  (s1k4 s1k4 id rk4 s2k4)
                  (s2k4 s2k4 rk4 id s1k4)
                  (rk4 rk4 s2k4 s1k4 id)))$
set!*inverse('k4,'((id s1k4 s2k4 rk4) (id s1k4 s2k4 rk4)))$
set!*elemasgen('k4,
  '(((s1k4) (s1k4)) ((s2k4) (s2k4)) ((rk4) (s1k4 s2k4))))$
set!*group('k4,'((id) (s1k4) (s2k4) (rk4)))$
set!*representation('k4,
                    '((id (((1 . 1))))
                      (s1k4 (((1 . 1))))
                      (s2k4 (((1 . 1))))
                      (rk4 (((1 . 1))))),'complex)$
set!*representation('k4,
                    '((id (((1 . 1))))
                      (s1k4 (((-1 . 1))))
                      (s2k4 (((1 . 1))))
                      (rk4 (((-1 . 1))))),'complex)$
set!*representation('k4,
                    '((id (((1 . 1))))
                      (s1k4 (((1 . 1))))
                      (s2k4 (((-1 . 1))))
                      (rk4 (((-1 . 1))))),'complex)$
set!*representation('k4,
                    '((id (((1 . 1))))
                      (s1k4 (((-1 . 1))))
                      (s2k4 (((-1 . 1))))
                      (rk4 (((1 . 1))))),'complex)$
set!*representation('k4,
                    '(realtype
                      (id (((1 . 1))))
                      (s1k4 (((1 . 1))))
                      (s2k4 (((1 . 1))))
                      (rk4 (((1 . 1))))),'real)$
set!*representation('k4,
                    '(realtype
                      (id (((1 . 1))))
                      (s1k4 (((-1 . 1))))
                      (s2k4 (((1 . 1))))
                      (rk4 (((-1 . 1))))),'real)$
set!*representation('k4,
                    '(realtype
                      (id (((1 . 1))))
                      (s1k4 (((1 . 1))))
                      (s2k4 (((-1 . 1))))
                      (rk4 (((-1 . 1))))),'real)$
set!*representation('k4,
                    '(realtype
                      (id (((1 . 1))))
                      (s1k4 (((-1 . 1))))
                      (s2k4 (((-1 . 1))))
                      (rk4 (((1 . 1))))),'real)$
set!*available 'k4$

set!*elems!*group('d3,'(id rd3 rot2d3 sd3 srd3 sr2d3))$
set!*generators('d3,'(rd3 sd3))$
set!*relations('d3,
               '(((sd3 sd3) (id))
                 ((rd3 rd3 rd3) (id))
                 ((sd3 rd3 sd3) (rd3 rd3))))$
set!*grouptable('d3,
                '((grouptable id rd3 rot2d3 sd3 srd3 sr2d3)
                  (id id rd3 rot2d3 sd3 srd3 sr2d3)
                  (rd3 rd3 rot2d3 id sr2d3 sd3 srd3)
                  (rot2d3 rot2d3 id rd3 srd3 sr2d3 sd3)
                  (sd3 sd3 srd3 sr2d3 id rd3 rot2d3)
                  (srd3 srd3 sr2d3 sd3 rot2d3 id rd3)
                  (sr2d3 sr2d3 sd3 srd3 rd3 rot2d3 id)))$
set!*inverse('d3,
   '((id rd3 rot2d3 sd3 srd3 sr2d3) (id rot2d3 rd3 sd3 srd3 sr2d3)))$
set!*elemasgen('d3,
               '(((rd3) (rd3))
                 ((rot2d3) (rd3 rd3))
                 ((sd3) (sd3))
                 ((srd3) (sd3 rd3))
                 ((sr2d3) (sd3 rd3 rd3))))$
set!*group('d3,'((id) (rd3 rot2d3) (sr2d3 sd3 srd3)))$
set!*representation('d3,
                    '((id (((1 . 1))))
                      (rd3 (((1 . 1))))
                      (rot2d3 (((1 . 1))))
                      (sd3 (((1 . 1))))
                      (srd3 (((1 . 1))))
                      (sr2d3 (((1 . 1))))),'complex)$
set!*representation('d3,
                    '((id (((1 . 1))))
                      (rd3 (((1 . 1))))
                      (rot2d3 (((1 . 1))))
                      (sd3 (((-1 . 1))))
                      (srd3 (((-1 . 1))))
                      (sr2d3 (((-1 . 1))))),'complex)$
set!*representation('d3,
                    '((id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (rd3
              (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
              ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
                         (-1 . 2))))
                      (rot2d3
              (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
              ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
                      (sd3 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
                      (srd3
              (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
              ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
                      (sr2d3
              (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
                        ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
                         (1 . 2))))),'complex)$
set!*representation('d3,
                    '(realtype
                      (id (((1 . 1))))
                      (rd3 (((1 . 1))))
                      (rot2d3 (((1 . 1))))
                      (sd3 (((1 . 1))))
                      (srd3 (((1 . 1))))
                      (sr2d3 (((1 . 1))))),'real)$
set!*representation('d3,
                    '(realtype
                      (id (((1 . 1))))
                      (rd3 (((1 . 1))))
                      (rot2d3 (((1 . 1))))
                      (sd3 (((-1 . 1))))
                      (srd3 (((-1 . 1))))
                      (sr2d3 (((-1 . 1))))),'real)$
set!*representation('d3,
                    '(realtype
                      (id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (rd3
             (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
                        ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
                         (-1 . 2))))
                      (rot2d3
             (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
             ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
                      (sd3 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
                      (srd3
             (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
             ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
                      (sr2d3
             (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
                        ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
                         (1 . 2))))),'real)$
set!*available 'd3$

set!*elems!*group('d4,'(id rd4 rot2d4 rot3d4 sd4 srd4 sr2d4 sr3d4))$
set!*generators('d4,'(rd4 sd4))$
set!*relations('d4,
               '(((sd4 sd4) (id))
                 ((rd4 rd4 rd4 rd4) (id))
                 ((sd4 rd4 sd4) (rd4 rd4 rd4))))$
set!*grouptable('d4,
                '((grouptable id rd4 rot2d4 rot3d4 sd4 srd4 sr2d4 sr3d4)
                  (id id rd4 rot2d4 rot3d4 sd4 srd4 sr2d4 sr3d4)
                  (rd4 rd4 rot2d4 rot3d4 id sr3d4 sd4 srd4 sr2d4)
                  (rot2d4 rot2d4 rot3d4 id rd4 sr2d4 sr3d4 sd4 srd4)
                  (rot3d4 rot3d4 id rd4 rot2d4 srd4 sr2d4 sr3d4 sd4)
                  (sd4 sd4 srd4 sr2d4 sr3d4 id rd4 rot2d4 rot3d4)
                  (srd4 srd4 sr2d4 sr3d4 sd4 rot3d4 id rd4 rot2d4)
                  (sr2d4 sr2d4 sr3d4 sd4 srd4 rot2d4 rot3d4 id rd4)
                  (sr3d4 sr3d4 sd4 srd4 sr2d4 rd4 rot2d4 rot3d4 id)))$
set!*inverse('d4,
             '((id rd4 rot2d4 rot3d4 sd4 srd4 sr2d4 sr3d4)
               (id rot3d4 rot2d4 rd4 sd4 srd4 sr2d4 sr3d4)))$
set!*elemasgen('d4,
               '(((rd4) (rd4))
                 ((rot2d4) (rd4 rd4))
                 ((rot3d4) (rd4 rd4 rd4))
                 ((sd4) (sd4))
                 ((srd4) (sd4 rd4))
                 ((sr2d4) (sd4 rd4 rd4))
                 ((sr3d4) (sd4 rd4 rd4 rd4))))$
set!*group('d4,'((id) (rd4 rot3d4) (rot2d4) (sd4 sr2d4) (sr3d4 srd4)))$
set!*representation('d4,
                    '((id (((1 . 1))))
                      (rd4 (((1 . 1))))
                      (rot2d4 (((1 . 1))))
                      (rot3d4 (((1 . 1))))
                      (sd4 (((1 . 1))))
                      (srd4 (((1 . 1))))
                      (sr2d4 (((1 . 1))))
                      (sr3d4 (((1 . 1))))),'complex)$
set!*representation('d4,
                    '((id (((1 . 1))))
                      (rd4 (((1 . 1))))
                      (rot2d4 (((1 . 1))))
                      (rot3d4 (((1 . 1))))
                      (sd4 (((-1 . 1))))
                      (srd4 (((-1 . 1))))
                      (sr2d4 (((-1 . 1))))
                      (sr3d4 (((-1 . 1))))),'complex)$
set!*representation('d4,
                    '((id (((1 . 1))))
                      (rd4 (((-1 . 1))))
                      (rot2d4 (((1 . 1))))
                      (rot3d4 (((-1 . 1))))
                      (sd4 (((1 . 1))))
                      (srd4 (((-1 . 1))))
                      (sr2d4 (((1 . 1))))
                      (sr3d4 (((-1 . 1))))),'complex)$
set!*representation('d4,
                    '((id (((1 . 1))))
                      (rd4 (((-1 . 1))))
                      (rot2d4 (((1 . 1))))
                      (rot3d4 (((-1 . 1))))
                      (sd4 (((-1 . 1))))
                      (srd4 (((1 . 1))))
                      (sr2d4 (((-1 . 1))))
                      (sr3d4 (((1 . 1))))),'complex)$
set!*representation('d4,
                    '((id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (rd4 (((nil . 1) (1 . 1)) ((-1 . 1) (nil . 1))))
                 (rot2d4 (((-1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
                 (rot3d4 (((nil . 1) (-1 . 1)) ((1 . 1) (nil . 1))))
                      (sd4 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
                      (srd4 (((nil . 1) (1 . 1)) ((1 . 1) (nil . 1))))
                      (sr2d4 (((-1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                 (sr3d4 (((nil . 1) (-1 . 1)) ((-1 . 1) (nil . 1))))),
                    'complex)$
set!*representation('d4,
                    '(realtype
                      (id (((1 . 1))))
                      (rd4 (((1 . 1))))
                      (rot2d4 (((1 . 1))))
                      (rot3d4 (((1 . 1))))
                      (sd4 (((1 . 1))))
                      (srd4 (((1 . 1))))
                      (sr2d4 (((1 . 1))))
                      (sr3d4 (((1 . 1))))),'real)$
set!*representation('d4,
                    '(realtype
                      (id (((1 . 1))))
                      (rd4 (((1 . 1))))
                      (rot2d4 (((1 . 1))))
                      (rot3d4 (((1 . 1))))
                      (sd4 (((-1 . 1))))
                      (srd4 (((-1 . 1))))
                      (sr2d4 (((-1 . 1))))
                      (sr3d4 (((-1 . 1))))),'real)$
set!*representation('d4,
                    '(realtype
                      (id (((1 . 1))))
                      (rd4 (((-1 . 1))))
                      (rot2d4 (((1 . 1))))
                      (rot3d4 (((-1 . 1))))
                      (sd4 (((1 . 1))))
                      (srd4 (((-1 . 1))))
                      (sr2d4 (((1 . 1))))
                      (sr3d4 (((-1 . 1))))),'real)$
set!*representation('d4,
                    '(realtype
                      (id (((1 . 1))))
                      (rd4 (((-1 . 1))))
                      (rot2d4 (((1 . 1))))
                      (rot3d4 (((-1 . 1))))
                      (sd4 (((-1 . 1))))
                      (srd4 (((1 . 1))))
                      (sr2d4 (((-1 . 1))))
                      (sr3d4 (((1 . 1))))),'real)$
set!*representation('d4,
                    '(realtype
                      (id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (rd4 (((nil . 1) (1 . 1)) ((-1 . 1) (nil . 1))))
                  (rot2d4 (((-1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
                  (rot3d4 (((nil . 1) (-1 . 1)) ((1 . 1) (nil . 1))))
                      (sd4 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
                      (srd4 (((nil . 1) (1 . 1)) ((1 . 1) (nil . 1))))
                  (sr2d4 (((-1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                  (sr3d4 (((nil . 1) (-1 . 1)) ((-1 . 1) (nil . 1))))),
                    'real)$
set!*available 'd4$

set!*elems!*group('d5,
   '(id rd5 r2d5 r3d5 r4d5 sd5 srd5 sr2d5 sr3d5 sr4d5))$
set!*generators('d5,'(rd5 sd5))$
set!*relations('d5,
               '(((sd5 sd5) (id))
                 ((rd5 rd5 rd5 rd5 rd5) (id))
                 ((sd5 rd5 sd5) (rd5 rd5 rd5 rd5))))$
set!*grouptable('d5,
      '((grouptable id rd5 r2d5 r3d5 r4d5 sd5 srd5 sr2d5 sr3d5 sr4d5)
               (id id rd5 r2d5 r3d5 r4d5 sd5 srd5 sr2d5 sr3d5 sr4d5)
               (rd5 rd5 r2d5 r3d5 r4d5 id sr4d5 sd5 srd5 sr2d5 sr3d5)
               (r2d5 r2d5 r3d5 r4d5 id rd5 sr3d5 sr4d5 sd5 srd5 sr2d5)
               (r3d5 r3d5 r4d5 id rd5 r2d5 sr2d5 sr3d5 sr4d5 sd5 srd5)
               (r4d5 r4d5 id rd5 r2d5 r3d5 srd5 sr2d5 sr3d5 sr4d5 sd5)
               (sd5 sd5 srd5 sr2d5 sr3d5 sr4d5 id rd5 r2d5 r3d5 r4d5)
               (srd5 srd5 sr2d5 sr3d5 sr4d5 sd5 r4d5 id rd5 r2d5 r3d5)
               (sr2d5 sr2d5 sr3d5 sr4d5 sd5 srd5 r3d5 r4d5 id rd5 r2d5)
               (sr3d5 sr3d5 sr4d5 sd5 srd5 sr2d5 r2d5 r3d5 r4d5 id rd5)
        (sr4d5 sr4d5 sd5 srd5 sr2d5 sr3d5 rd5 r2d5 r3d5 r4d5 id)))$
set!*inverse('d5,
             '((id rd5 r2d5 r3d5 r4d5 sd5 srd5 sr2d5 sr3d5 sr4d5)
               (id r4d5 r3d5 r2d5 rd5 sd5 srd5 sr2d5 sr3d5 sr4d5)))$
set!*elemasgen('d5,
               '(((rd5) (rd5))
                 ((r2d5) (rd5 rd5))
                 ((r3d5) (rd5 rd5 rd5))
                 ((r4d5) (rd5 rd5 rd5 rd5))
                 ((sd5) (sd5))
                 ((srd5) (sd5 rd5))
                 ((sr2d5) (sd5 rd5 rd5))
                 ((sr3d5) (sd5 rd5 rd5 rd5))
                 ((sr4d5) (sd5 rd5 rd5 rd5 rd5))))$
set!*group('d5,
 '((id) (rd5 r4d5) (r2d5 r3d5) (srd5 sr2d5 sd5 sr4d5 sr3d5)))$
set!*representation('d5,
                    '((id (((1 . 1))))
                      (rd5 (((1 . 1))))
                      (r2d5 (((1 . 1))))
                      (r3d5 (((1 . 1))))
                      (r4d5 (((1 . 1))))
                      (sd5 (((1 . 1))))
                      (srd5 (((1 . 1))))
                      (sr2d5 (((1 . 1))))
                      (sr3d5 (((1 . 1))))
                      (sr4d5 (((1 . 1))))),'complex)$
set!*representation('d5,
                    '((id (((1 . 1))))
                      (rd5 (((1 . 1))))
                      (r2d5 (((1 . 1))))
                      (r3d5 (((1 . 1))))
                      (r4d5 (((1 . 1))))
                      (sd5 (((-1 . 1))))
                      (srd5 (((-1 . 1))))
                      (sr2d5 (((-1 . 1))))
                      (sr3d5 (((-1 . 1))))
                      (sr4d5 (((-1 . 1))))),'complex)$
set!*representation('d5,
                    '((id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (rd5
                  (((((((cos (quotient (times 2 pi) 5)) . 1) . 1)) . 1)
                  (((((sin (quotient (times 2 pi) 5)) . 1) . -1)) . 1))
                  ((((((sin (quotient (times 2 pi) 5)) . 1) . 1)) . 1)
                  (((((cos (quotient (times 2 pi) 5)) . 1) . 1)) . 1))))
                      (r2d5
                       (((((((sin (quotient (times 2 pi) 5)) . 2) . -1)
                           (((cos (quotient (times 2 pi) 5)) . 2) . 1))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 1)
                    (((cos (quotient (times 2 pi) 5)) . 1) . -2)))
                          . 1))
                        ((((((sin (quotient (times 2 pi) 5)) . 1)
                    (((cos (quotient (times 2 pi) 5)) . 1) . 2)))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 2) . -1)
                           (((cos (quotient (times 2 pi) 5)) . 2) . 1))
                          . 1))))
                      (r3d5
                       (((((((sin (quotient (times 2 pi) 5)) . 2)
                      (((cos (quotient (times 2 pi) 5)) . 1) . -3))
                           (((cos (quotient (times 2 pi) 5)) . 3) . 1))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 3) . 1)
                           (((sin (quotient (times 2 pi) 5)) . 1)
                     (((cos (quotient (times 2 pi) 5)) . 2) . -3)))
                          . 1))
                        ((((((sin (quotient (times 2 pi) 5)) . 3) . -1)
                           (((sin (quotient (times 2 pi) 5)) . 1)
                     (((cos (quotient (times 2 pi) 5)) . 2) . 3)))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 2)
                        (((cos (quotient (times 2 pi) 5)) . 1) . -3))
                     (((cos (quotient (times 2 pi) 5)) . 3) . 1))
                          . 1))))
                      (r4d5
                       (((((((sin (quotient (times 2 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 2 pi) 5)) . 2)
                         (((cos (quotient (times 2 pi) 5)) . 2) . -6))
                        (((cos (quotient (times 2 pi) 5)) . 4) . 1))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 3)
                            (((cos (quotient (times 2 pi) 5)) . 1) . 4))
                           (((sin (quotient (times 2 pi) 5)) . 1)
                          (((cos (quotient (times 2 pi) 5)) . 3) . -4)))
                          . 1))
                        ((((((sin (quotient (times 2 pi) 5)) . 3)
                          (((cos (quotient (times 2 pi) 5)) . 1) . -4))
                           (((sin (quotient (times 2 pi) 5)) . 1)
                          (((cos (quotient (times 2 pi) 5)) . 3) . 4)))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 2 pi) 5)) . 2)
                          (((cos (quotient (times 2 pi) 5)) . 2) . -6))
                           (((cos (quotient (times 2 pi) 5)) . 4) . 1))
                          . 1))))
                      (sd5 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
                      (srd5
                  (((((((cos (quotient (times 2 pi) 5)) . 1) . 1)) . 1)
                  (((((sin (quotient (times 2 pi) 5)) . 1) . -1)) . 1))
                  ((((((sin (quotient (times 2 pi) 5)) . 1) . -1)) . 1)
               (((((cos (quotient (times 2 pi) 5)) . 1) . -1)) . 1))))
                      (sr2d5
                       (((((((sin (quotient (times 2 pi) 5)) . 2) . -1)
                           (((cos (quotient (times 2 pi) 5)) . 2) . 1))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 1)
                         (((cos (quotient (times 2 pi) 5)) . 1) . -2)))
                          . 1))
                        ((((((sin (quotient (times 2 pi) 5)) . 1)
                        (((cos (quotient (times 2 pi) 5)) . 1) . -2)))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 2) . 1)
                         (((cos (quotient (times 2 pi) 5)) . 2) . -1))
                          . 1))))
                      (sr3d5
                       (((((((sin (quotient (times 2 pi) 5)) . 2)
                          (((cos (quotient (times 2 pi) 5)) . 1) . -3))
                           (((cos (quotient (times 2 pi) 5)) . 3) . 1))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 3) . 1)
                           (((sin (quotient (times 2 pi) 5)) . 1)
                          (((cos (quotient (times 2 pi) 5)) . 2) . -3)))
                          . 1))
                        ((((((sin (quotient (times 2 pi) 5)) . 3) . 1)
                           (((sin (quotient (times 2 pi) 5)) . 1)
                          (((cos (quotient (times 2 pi) 5)) . 2) . -3)))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 2)
                            (((cos (quotient (times 2 pi) 5)) . 1) . 3))
                           (((cos (quotient (times 2 pi) 5)) . 3) . -1))
                          . 1))))
                      (sr4d5
                       (((((((sin (quotient (times 2 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 2 pi) 5)) . 2)
                          (((cos (quotient (times 2 pi) 5)) . 2) . -6))
                           (((cos (quotient (times 2 pi) 5)) . 4) . 1))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 3)
                            (((cos (quotient (times 2 pi) 5)) . 1) . 4))
                           (((sin (quotient (times 2 pi) 5)) . 1)
                          (((cos (quotient (times 2 pi) 5)) . 3) . -4)))
                          . 1))
                        ((((((sin (quotient (times 2 pi) 5)) . 3)
                            (((cos (quotient (times 2 pi) 5)) . 1) . 4))
                           (((sin (quotient (times 2 pi) 5)) . 1)
                          (((cos (quotient (times 2 pi) 5)) . 3) . -4)))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 4) . -1)
                           (((sin (quotient (times 2 pi) 5)) . 2)
                            (((cos (quotient (times 2 pi) 5)) . 2) . 6))
                           (((cos (quotient (times 2 pi) 5)) . 4) . -1))
                          . 1))))),'complex)$
set!*representation('d5,
                    '((id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (rd5
                   (((((((cos (quotient (times 4 pi) 5)) . 1) . 1)) . 1)
                   (((((sin (quotient (times 4 pi) 5)) . 1) . -1)) . 1))
                   ((((((sin (quotient (times 4 pi) 5)) . 1) . 1)) . 1)
                (((((cos (quotient (times 4 pi) 5)) . 1) . 1)) . 1))))
                      (r2d5
                       (((((((sin (quotient (times 4 pi) 5)) . 2) . -1)
                           (((cos (quotient (times 4 pi) 5)) . 2) . 1))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 1)
                         (((cos (quotient (times 4 pi) 5)) . 1) . -2)))
                          . 1))
                        ((((((sin (quotient (times 4 pi) 5)) . 1)
                          (((cos (quotient (times 4 pi) 5)) . 1) . 2)))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 2) . -1)
                           (((cos (quotient (times 4 pi) 5)) . 2) . 1))
                          . 1))))
                      (r3d5
                       (((((((sin (quotient (times 4 pi) 5)) . 2)
                         (((cos (quotient (times 4 pi) 5)) . 1) . -3))
                           (((cos (quotient (times 4 pi) 5)) . 3) . 1))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 3) . 1)
                           (((sin (quotient (times 4 pi) 5)) . 1)
                         (((cos (quotient (times 4 pi) 5)) . 2) . -3)))
                          . 1))
                        ((((((sin (quotient (times 4 pi) 5)) . 3) . -1)
                           (((sin (quotient (times 4 pi) 5)) . 1)
                         (((cos (quotient (times 4 pi) 5)) . 2) . 3)))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 2)
                         (((cos (quotient (times 4 pi) 5)) . 1) . -3))
                           (((cos (quotient (times 4 pi) 5)) . 3) . 1))
                          . 1))))
                      (r4d5
                       (((((((sin (quotient (times 4 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 4 pi) 5)) . 2)
                          (((cos (quotient (times 4 pi) 5)) . 2) . -6))
                           (((cos (quotient (times 4 pi) 5)) . 4) . 1))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 3)
                            (((cos (quotient (times 4 pi) 5)) . 1) . 4))
                           (((sin (quotient (times 4 pi) 5)) . 1)
                         (((cos (quotient (times 4 pi) 5)) . 3) . -4)))
                          . 1))
                        ((((((sin (quotient (times 4 pi) 5)) . 3)
                         (((cos (quotient (times 4 pi) 5)) . 1) . -4))
                           (((sin (quotient (times 4 pi) 5)) . 1)
                         (((cos (quotient (times 4 pi) 5)) . 3) . 4)))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 4 pi) 5)) . 2)
                         (((cos (quotient (times 4 pi) 5)) . 2) . -6))
                           (((cos (quotient (times 4 pi) 5)) . 4) . 1))
                          . 1))))
                      (sd5 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
                      (srd5
                 (((((((cos (quotient (times 4 pi) 5)) . 1) . 1)) . 1)
                 (((((sin (quotient (times 4 pi) 5)) . 1) . -1)) . 1))
                 ((((((sin (quotient (times 4 pi) 5)) . 1) . -1)) . 1)
                 (((((cos (quotient (times 4 pi) 5)) . 1) . -1)) . 1))))
                      (sr2d5
                       (((((((sin (quotient (times 4 pi) 5)) . 2) . -1)
                           (((cos (quotient (times 4 pi) 5)) . 2) . 1))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 1)
                         (((cos (quotient (times 4 pi) 5)) . 1) . -2)))
                          . 1))
                        ((((((sin (quotient (times 4 pi) 5)) . 1)
                         (((cos (quotient (times 4 pi) 5)) . 1) . -2)))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 2) . 1)
                        (((cos (quotient (times 4 pi) 5)) . 2) . -1))
                          . 1))))
                      (sr3d5
                       (((((((sin (quotient (times 4 pi) 5)) . 2)
                         (((cos (quotient (times 4 pi) 5)) . 1) . -3))
                           (((cos (quotient (times 4 pi) 5)) . 3) . 1))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 3) . 1)
                           (((sin (quotient (times 4 pi) 5)) . 1)
                         (((cos (quotient (times 4 pi) 5)) . 2) . -3)))
                       . 1))
                        ((((((sin (quotient (times 4 pi) 5)) . 3) . 1)
                           (((sin (quotient (times 4 pi) 5)) . 1)
                         (((cos (quotient (times 4 pi) 5)) . 2) . -3)))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 2)
                            (((cos (quotient (times 4 pi) 5)) . 1) . 3))
                           (((cos (quotient (times 4 pi) 5)) . 3) . -1))
                          . 1))))
                      (sr4d5
                       (((((((sin (quotient (times 4 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 4 pi) 5)) . 2)
                         (((cos (quotient (times 4 pi) 5)) . 2) . -6))
                           (((cos (quotient (times 4 pi) 5)) . 4) . 1))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 3)
                            (((cos (quotient (times 4 pi) 5)) . 1) . 4))
                           (((sin (quotient (times 4 pi) 5)) . 1)
                        (((cos (quotient (times 4 pi) 5)) . 3) . -4)))
                          . 1))
                        ((((((sin (quotient (times 4 pi) 5)) . 3)
                            (((cos (quotient (times 4 pi) 5)) . 1) . 4))
                           (((sin (quotient (times 4 pi) 5)) . 1)
                         (((cos (quotient (times 4 pi) 5)) . 3) . -4)))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 4) . -1)
                           (((sin (quotient (times 4 pi) 5)) . 2)
                            (((cos (quotient (times 4 pi) 5)) . 2) . 6))
                           (((cos (quotient (times 4 pi) 5)) . 4) . -1))
                          . 1))))),'complex)$
set!*representation('d5,
                    '(realtype
                      (id (((1 . 1))))
                      (rd5 (((1 . 1))))
                      (r2d5 (((1 . 1))))
                      (r3d5 (((1 . 1))))
                      (r4d5 (((1 . 1))))
                      (sd5 (((1 . 1))))
                      (srd5 (((1 . 1))))
                      (sr2d5 (((1 . 1))))
                      (sr3d5 (((1 . 1))))
                      (sr4d5 (((1 . 1))))),'real)$
set!*representation('d5,
                    '(realtype
                      (id (((1 . 1))))
                      (rd5 (((1 . 1))))
                      (r2d5 (((1 . 1))))
                      (r3d5 (((1 . 1))))
                      (r4d5 (((1 . 1))))
                      (sd5 (((-1 . 1))))
                      (srd5 (((-1 . 1))))
                      (sr2d5 (((-1 . 1))))
                      (sr3d5 (((-1 . 1))))
                      (sr4d5 (((-1 . 1))))),'real)$
set!*representation('d5,
                    '(realtype
                      (id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (rd5
                 (((((((cos (quotient (times 2 pi) 5)) . 1) . 1)) . 1)
                  (((((sin (quotient (times 2 pi) 5)) . 1) . -1)) . 1))
                   ((((((sin (quotient (times 2 pi) 5)) . 1) . 1)) . 1)
                 (((((cos (quotient (times 2 pi) 5)) . 1) . 1)) . 1))))
                      (r2d5
                       (((((((sin (quotient (times 2 pi) 5)) . 2) . -1)
                           (((cos (quotient (times 2 pi) 5)) . 2) . 1))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 1)
                        (((cos (quotient (times 2 pi) 5)) . 1) . -2)))
                          . 1))
                        ((((((sin (quotient (times 2 pi) 5)) . 1)
                          (((cos (quotient (times 2 pi) 5)) . 1) . 2)))
                        . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 2) . -1)
                           (((cos (quotient (times 2 pi) 5)) . 2) . 1))
                          . 1))))
                      (r3d5
                       (((((((sin (quotient (times 2 pi) 5)) . 2)
                          (((cos (quotient (times 2 pi) 5)) . 1) . -3))
                           (((cos (quotient (times 2 pi) 5)) . 3) . 1))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 3) . 1)
                           (((sin (quotient (times 2 pi) 5)) . 1)
                         (((cos (quotient (times 2 pi) 5)) . 2) . -3)))
                          . 1))
                        ((((((sin (quotient (times 2 pi) 5)) . 3) . -1)
                           (((sin (quotient (times 2 pi) 5)) . 1)
                          (((cos (quotient (times 2 pi) 5)) . 2) . 3)))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 2)
                         (((cos (quotient (times 2 pi) 5)) . 1) . -3))
                         (((cos (quotient (times 2 pi) 5)) . 3) . 1))
                          . 1))))
                      (r4d5
                       (((((((sin (quotient (times 2 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 2 pi) 5)) . 2)
                          (((cos (quotient (times 2 pi) 5)) . 2) . -6))
                           (((cos (quotient (times 2 pi) 5)) . 4) . 1))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 3)
                          (((cos (quotient (times 2 pi) 5)) . 1) . 4))
                          (((sin (quotient (times 2 pi) 5)) . 1)
                         (((cos (quotient (times 2 pi) 5)) . 3) . -4)))
                          . 1))
                        ((((((sin (quotient (times 2 pi) 5)) . 3)
                           (((cos (quotient (times 2 pi) 5)) . 1) . -4))
                          (((sin (quotient (times 2 pi) 5)) . 1)
                          (((cos (quotient (times 2 pi) 5)) . 3) . 4)))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 2 pi) 5)) . 2)
                          (((cos (quotient (times 2 pi) 5)) . 2) . -6))
                           (((cos (quotient (times 2 pi) 5)) . 4) . 1))
                          . 1))))
                      (sd5 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
                      (srd5
                 (((((((cos (quotient (times 2 pi) 5)) . 1) . 1)) . 1)
                 (((((sin (quotient (times 2 pi) 5)) . 1) . -1)) . 1))
                 ((((((sin (quotient (times 2 pi) 5)) . 1) . -1)) . 1)
                (((((cos (quotient (times 2 pi) 5)) . 1) . -1)) . 1))))
                      (sr2d5
                       (((((((sin (quotient (times 2 pi) 5)) . 2) . -1)
                           (((cos (quotient (times 2 pi) 5)) . 2) . 1))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 1)
                        (((cos (quotient (times 2 pi) 5)) . 1) . -2)))
                          . 1))
                        ((((((sin (quotient (times 2 pi) 5)) . 1)
                       (((cos (quotient (times 2 pi) 5)) . 1) . -2)))
                        . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 2) . 1)
                           (((cos (quotient (times 2 pi) 5)) . 2) . -1))
                          . 1))))
                      (sr3d5
                       (((((((sin (quotient (times 2 pi) 5)) . 2)
                         (((cos (quotient (times 2 pi) 5)) . 1) . -3))
                           (((cos (quotient (times 2 pi) 5)) . 3) . 1))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 3) . 1)
                           (((sin (quotient (times 2 pi) 5)) . 1)
                         (((cos (quotient (times 2 pi) 5)) . 2) . -3)))
                          . 1))
                        ((((((sin (quotient (times 2 pi) 5)) . 3) . 1)
                           (((sin (quotient (times 2 pi) 5)) . 1)
                         (((cos (quotient (times 2 pi) 5)) . 2) . -3)))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 2)
                            (((cos (quotient (times 2 pi) 5)) . 1) . 3))
                           (((cos (quotient (times 2 pi) 5)) . 3) . -1))
                          . 1))))
                      (sr4d5
                       (((((((sin (quotient (times 2 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 2 pi) 5)) . 2)
                         (((cos (quotient (times 2 pi) 5)) . 2) . -6))
                           (((cos (quotient (times 2 pi) 5)) . 4) . 1))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 3)
                            (((cos (quotient (times 2 pi) 5)) . 1) . 4))
                           (((sin (quotient (times 2 pi) 5)) . 1)
                         (((cos (quotient (times 2 pi) 5)) . 3) . -4)))
                          . 1))
                        ((((((sin (quotient (times 2 pi) 5)) . 3)
                            (((cos (quotient (times 2 pi) 5)) . 1) . 4))
                           (((sin (quotient (times 2 pi) 5)) . 1)
                         (((cos (quotient (times 2 pi) 5)) . 3) . -4)))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 4) . -1)
                           (((sin (quotient (times 2 pi) 5)) . 2)
                            (((cos (quotient (times 2 pi) 5)) . 2) . 6))
                           (((cos (quotient (times 2 pi) 5)) . 4) . -1))
                          . 1))))),'real)$
set!*representation('d5,
                    '(realtype
                      (id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (rd5
                  (((((((cos (quotient (times 4 pi) 5)) . 1) . 1)) . 1)
                   (((((sin (quotient (times 4 pi) 5)) . 1) . -1)) . 1))
                   ((((((sin (quotient (times 4 pi) 5)) . 1) . 1)) . 1)
                  (((((cos (quotient (times 4 pi) 5)) . 1) . 1)) . 1))))
                   (r2d5
                       (((((((sin (quotient (times 4 pi) 5)) . 2) . -1)
                           (((cos (quotient (times 4 pi) 5)) . 2) . 1))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 1)
                        (((cos (quotient (times 4 pi) 5)) . 1) . -2)))
                        . 1))
                        ((((((sin (quotient (times 4 pi) 5)) . 1)
                        (((cos (quotient (times 4 pi) 5)) . 1) . 2)))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 2) . -1)
                           (((cos (quotient (times 4 pi) 5)) . 2) . 1))
                          . 1))))
                      (r3d5
                       (((((((sin (quotient (times 4 pi) 5)) . 2)
                        (((cos (quotient (times 4 pi) 5)) . 1) . -3))
                         (((cos (quotient (times 4 pi) 5)) . 3) . 1))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 3) . 1)
                           (((sin (quotient (times 4 pi) 5)) . 1)
                        (((cos (quotient (times 4 pi) 5)) . 2) . -3)))
                          . 1))
                        ((((((sin (quotient (times 4 pi) 5)) . 3) . -1)
                           (((sin (quotient (times 4 pi) 5)) . 1)
                         (((cos (quotient (times 4 pi) 5)) . 2) . 3)))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 2)
                          (((cos (quotient (times 4 pi) 5)) . 1) . -3))
                           (((cos (quotient (times 4 pi) 5)) . 3) . 1))
                          . 1))))
                      (r4d5
                       (((((((sin (quotient (times 4 pi) 5)) . 4) . 1)
                         (((sin (quotient (times 4 pi) 5)) . 2)
                          (((cos (quotient (times 4 pi) 5)) . 2) . -6))
                           (((cos (quotient (times 4 pi) 5)) . 4) . 1))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 3)
                           (((cos (quotient (times 4 pi) 5)) . 1) . 4))
                           (((sin (quotient (times 4 pi) 5)) . 1)
                         (((cos (quotient (times 4 pi) 5)) . 3) . -4)))
                          . 1))
                        ((((((sin (quotient (times 4 pi) 5)) . 3)
                           (((cos (quotient (times 4 pi) 5)) . 1) . -4))
                           (((sin (quotient (times 4 pi) 5)) . 1)
                          (((cos (quotient (times 4 pi) 5)) . 3) . 4)))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 4 pi) 5)) . 2)
                          (((cos (quotient (times 4 pi) 5)) . 2) . -6))
                           (((cos (quotient (times 4 pi) 5)) . 4) . 1))
                          . 1))))
                      (sd5 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
                      (srd5
                  (((((((cos (quotient (times 4 pi) 5)) . 1) . 1)) . 1)
                   (((((sin (quotient (times 4 pi) 5)) . 1) . -1)) . 1))
                   ((((((sin (quotient (times 4 pi) 5)) . 1) . -1)) . 1)
               (((((cos (quotient (times 4 pi) 5)) . 1) . -1)) . 1))))
                      (sr2d5
                       (((((((sin (quotient (times 4 pi) 5)) . 2) . -1)
                           (((cos (quotient (times 4 pi) 5)) . 2) . 1))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 1)
                        (((cos (quotient (times 4 pi) 5)) . 1) . -2)))
                       . 1))
                        ((((((sin (quotient (times 4 pi) 5)) . 1)
                        (((cos (quotient (times 4 pi) 5)) . 1) . -2)))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 2) . 1)
                         (((cos (quotient (times 4 pi) 5)) . 2) . -1))
                         . 1))))
                      (sr3d5
                       (((((((sin (quotient (times 4 pi) 5)) . 2)
                         (((cos (quotient (times 4 pi) 5)) . 1) . -3))
                           (((cos (quotient (times 4 pi) 5)) . 3) . 1))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 3) . 1)
                           (((sin (quotient (times 4 pi) 5)) . 1)
                         (((cos (quotient (times 4 pi) 5)) . 2) . -3)))
                          . 1))
                        ((((((sin (quotient (times 4 pi) 5)) . 3) . 1)
                           (((sin (quotient (times 4 pi) 5)) . 1)
                         (((cos (quotient (times 4 pi) 5)) . 2) . -3)))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 2)
                            (((cos (quotient (times 4 pi) 5)) . 1) . 3))
                           (((cos (quotient (times 4 pi) 5)) . 3) . -1))
                          . 1))))
                      (sr4d5
                       (((((((sin (quotient (times 4 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 4 pi) 5)) . 2)
                          (((cos (quotient (times 4 pi) 5)) . 2) . -6))
                           (((cos (quotient (times 4 pi) 5)) . 4) . 1))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 3)
                           (((cos (quotient (times 4 pi) 5)) . 1) . 4))
                           (((sin (quotient (times 4 pi) 5)) . 1)
                          (((cos (quotient (times 4 pi) 5)) . 3) . -4)))
                          . 1))
                        ((((((sin (quotient (times 4 pi) 5)) . 3)
                            (((cos (quotient (times 4 pi) 5)) . 1) . 4))
                           (((sin (quotient (times 4 pi) 5)) . 1)
                         (((cos (quotient (times 4 pi) 5)) . 3) . -4)))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 4) . -1)
                           (((sin (quotient (times 4 pi) 5)) . 2)
                            (((cos (quotient (times 4 pi) 5)) . 2) . 6))
                           (((cos (quotient (times 4 pi) 5)) . 4) . -1))
                          . 1))))),'real)$
set!*available 'd5$

set!*elems!*group('d6,
                  '(id
                    rd6
                    r2d6
                    r3d6
                    r4d6
                    r5d6
                    sd6
                    srd6
                    sr2d6
                    sr3d6
                    sr4d6
                    sr5d6))$
set!*generators('d6,'(rd6 sd6))$
set!*relations('d6,
               '(((sd6 sd6) (id))
                 ((rd6 rd6 rd6 rd6 rd6 rd6) (id))
                 ((sd6 rd6 sd6) (rd6 rd6 rd6 rd6 rd6))))$
set!*grouptable('d6,
                '((grouptable
                   id
                   rd6
                   r2d6
                   r3d6
                   r4d6
                   r5d6
                   sd6
                   srd6
                   sr2d6
                   sr3d6
                   sr4d6
                   sr5d6)
                  (id
                   id
                   rd6
                   r2d6
                   r3d6
                   r4d6
                   r5d6
                   sd6
                   srd6
                   sr2d6
                   sr3d6
                   sr4d6
                   sr5d6)
                  (rd6
                   rd6
                   r2d6
                   r3d6
                   r4d6
                   r5d6
                   id
                   sr5d6
                   sd6
                   srd6
                   sr2d6
                   sr3d6
                   sr4d6)
                  (r2d6
                   r2d6
                   r3d6
                   r4d6
                   r5d6
                   id
                   rd6
                   sr4d6
                   sr5d6
                   sd6
                   srd6
                   sr2d6
                   sr3d6)
                  (r3d6
                   r3d6
                   r4d6
                   r5d6
                   id
                   rd6
                   r2d6
                   sr3d6
                   sr4d6
                   sr5d6
                   sd6
                   srd6
                   sr2d6)
                  (r4d6
                   r4d6
                   r5d6
                   id
                   rd6
                   r2d6
                   r3d6
                   sr2d6
                   sr3d6
                   sr4d6
                   sr5d6
                   sd6
                   srd6)
                  (r5d6
                   r5d6
                   id
                   rd6
                   r2d6
                   r3d6
                   r4d6
                   srd6
                   sr2d6
                   sr3d6
                   sr4d6
                   sr5d6
                   sd6)
                  (sd6
                   sd6
                   srd6
                   sr2d6
                   sr3d6
                   sr4d6
                   sr5d6
                   id
                   rd6
                   r2d6
                   r3d6
                   r4d6
                   r5d6)
                  (srd6
                   srd6
                   sr2d6
                   sr3d6
                   sr4d6
                   sr5d6
                   sd6
                   r5d6
                   id
                   rd6
                   r2d6
                   r3d6
                   r4d6)
                  (sr2d6
                   sr2d6
                   sr3d6
                   sr4d6
                   sr5d6
                   sd6
                   srd6
                   r4d6
                   r5d6
                   id
                   rd6
                   r2d6
                   r3d6)
                  (sr3d6
                   sr3d6
                   sr4d6
                   sr5d6
                   sd6
                   srd6
                   sr2d6
                   r3d6
                   r4d6
                   r5d6
                   id
                   rd6
                   r2d6)
                  (sr4d6
                   sr4d6
                   sr5d6
                   sd6
                   srd6
                   sr2d6
                   sr3d6
                   r2d6
                   r3d6
                   r4d6
                   r5d6
                   id
                   rd6)
                  (sr5d6
                   sr5d6
                   sd6
                   srd6
                   sr2d6
                   sr3d6
                   sr4d6
                   rd6
                   r2d6
                   r3d6
                   r4d6
                   r5d6
                   id)))$
set!*inverse('d6,
       '((id rd6 r2d6 r3d6 r4d6 r5d6 sd6 srd6 sr2d6 sr3d6 sr4d6 sr5d6)
       (id r5d6 r4d6 r3d6 r2d6 rd6 sd6 srd6 sr2d6 sr3d6 sr4d6 sr5d6)))$
set!*elemasgen('d6,
               '(((rd6) (rd6))
                 ((r2d6) (rd6 rd6))
                 ((r3d6) (rd6 rd6 rd6))
                 ((r4d6) (rd6 rd6 rd6 rd6))
                 ((r5d6) (rd6 rd6 rd6 rd6 rd6))
                 ((sd6) (sd6))
                 ((srd6) (sd6 rd6))
                 ((sr2d6) (sd6 rd6 rd6))
                 ((sr3d6) (sd6 rd6 rd6 rd6))
                 ((sr4d6) (sd6 rd6 rd6 rd6 rd6))
                 ((sr5d6) (sd6 rd6 rd6 rd6 rd6 rd6))))$
set!*group('d6,
           '((id)
             (rd6 r5d6)
             (r2d6 r4d6)
             (r3d6)
             (sr2d6 sd6 sr4d6)
             (srd6 sr5d6 sr3d6)))$
set!*representation('d6,
                    '((id (((1 . 1))))
                      (rd6 (((1 . 1))))
                      (r2d6 (((1 . 1))))
                      (r3d6 (((1 . 1))))
                      (r4d6 (((1 . 1))))
                      (r5d6 (((1 . 1))))
                      (sd6 (((1 . 1))))
                      (srd6 (((1 . 1))))
                      (sr2d6 (((1 . 1))))
                      (sr3d6 (((1 . 1))))
                      (sr4d6 (((1 . 1))))
                      (sr5d6 (((1 . 1))))),'complex)$
set!*representation('d6,
                    '((id (((1 . 1))))
                      (rd6 (((1 . 1))))
                      (r2d6 (((1 . 1))))
                      (r3d6 (((1 . 1))))
                      (r4d6 (((1 . 1))))
                      (r5d6 (((1 . 1))))
                      (sd6 (((-1 . 1))))
                      (srd6 (((-1 . 1))))
                      (sr2d6 (((-1 . 1))))
                      (sr3d6 (((-1 . 1))))
                      (sr4d6 (((-1 . 1))))
                      (sr5d6 (((-1 . 1))))),'complex)$
set!*representation('d6,
                    '((id (((1 . 1))))
                      (rd6 (((-1 . 1))))
                      (r2d6 (((1 . 1))))
                      (r3d6 (((-1 . 1))))
                      (r4d6 (((1 . 1))))
                      (r5d6 (((-1 . 1))))
                      (sd6 (((1 . 1))))
                      (srd6 (((-1 . 1))))
                      (sr2d6 (((1 . 1))))
                      (sr3d6 (((-1 . 1))))
                      (sr4d6 (((1 . 1))))
                      (sr5d6 (((-1 . 1))))),'complex)$
set!*representation('d6,
                    '((id (((1 . 1))))
                      (rd6 (((-1 . 1))))
                      (r2d6 (((1 . 1))))
                      (r3d6 (((-1 . 1))))
                      (r4d6 (((1 . 1))))
                      (r5d6 (((-1 . 1))))
                      (sd6 (((-1 . 1))))
                      (srd6 (((1 . 1))))
                      (sr2d6 (((-1 . 1))))
                      (sr3d6 (((1 . 1))))
                      (sr4d6 (((-1 . 1))))
                      (sr5d6 (((1 . 1))))),'complex)$
set!*representation('d6,
                    '((id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (rd6
                  (((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
                ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2) (1 . 2))))
                      (r2d6
              (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
                        ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
                         (-1 . 2))))
                  (r3d6 (((-1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
                      (r4d6
              (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
             ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
                      (r5d6
               (((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
               ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
                      (sd6 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
                      (srd6
                (((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
             ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
                      (sr2d6
              (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
              ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
                   (sr3d6 (((-1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (sr4d6
             (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
             ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2) (1 . 2))))
                      (sr5d6
              (((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
                   ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
                         (-1 . 2))))),'complex)$
set!*representation('d6,
                    '((id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (rd6
              (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
                        ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
                         (-1 . 2))))
                      (r2d6
               (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
              ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
                      (r3d6 (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (r4d6
                 (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
                 ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
                         (-1 . 2))))
                      (r5d6
               (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
               ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
                      (sd6 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
                      (srd6
                (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
                ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
                      (sr2d6
                (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
                ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2) (1 . 2))))
                      (sr3d6 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
                      (sr4d6
                (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
                ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
                      (sr5d6
                (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
                ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
                (1 . 2))))),'complex)$
set!*representation('d6,
                    '(realtype
                      (id (((1 . 1))))
                      (rd6 (((1 . 1))))
                      (r2d6 (((1 . 1))))
                      (r3d6 (((1 . 1))))
                      (r4d6 (((1 . 1))))
                      (r5d6 (((1 . 1))))
                      (sd6 (((1 . 1))))
                      (srd6 (((1 . 1))))
                      (sr2d6 (((1 . 1))))
                      (sr3d6 (((1 . 1))))
                      (sr4d6 (((1 . 1))))
                      (sr5d6 (((1 . 1))))),'real)$
set!*representation('d6,
                    '(realtype
                      (id (((1 . 1))))
                      (rd6 (((1 . 1))))
                      (r2d6 (((1 . 1))))
                      (r3d6 (((1 . 1))))
                      (r4d6 (((1 . 1))))
                      (r5d6 (((1 . 1))))
                      (sd6 (((-1 . 1))))
                      (srd6 (((-1 . 1))))
                      (sr2d6 (((-1 . 1))))
                      (sr3d6 (((-1 . 1))))
                      (sr4d6 (((-1 . 1))))
                      (sr5d6 (((-1 . 1))))),'real)$
set!*representation('d6,
                    '(realtype
                      (id (((1 . 1))))
                      (rd6 (((-1 . 1))))
                      (r2d6 (((1 . 1))))
                      (r3d6 (((-1 . 1))))
                      (r4d6 (((1 . 1))))
                      (r5d6 (((-1 . 1))))
                      (sd6 (((1 . 1))))
                      (srd6 (((-1 . 1))))
                      (sr2d6 (((1 . 1))))
                      (sr3d6 (((-1 . 1))))
                      (sr4d6 (((1 . 1))))
                      (sr5d6 (((-1 . 1))))),'real)$
set!*representation('d6,
                    '(realtype
                      (id (((1 . 1))))
                      (rd6 (((-1 . 1))))
                      (r2d6 (((1 . 1))))
                      (r3d6 (((-1 . 1))))
                      (r4d6 (((1 . 1))))
                      (r5d6 (((-1 . 1))))
                      (sd6 (((-1 . 1))))
                      (srd6 (((1 . 1))))
                      (sr2d6 (((-1 . 1))))
                      (sr3d6 (((1 . 1))))
                      (sr4d6 (((-1 . 1))))
                      (sr5d6 (((1 . 1))))),'real)$
set!*representation('d6,
                    '(realtype
                      (id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (rd6
                (((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
                ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2) (1 . 2))))
                      (r2d6
               (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
                        ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
                         (-1 . 2))))
                      (r3d6 (((-1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
                      (r4d6
                (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
               ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
                      (r5d6
               (((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
               ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
                      (sd6 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
                      (srd6
                (((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
              ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
                      (sr2d6
               (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
               ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
                    (sr3d6 (((-1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (sr4d6
              (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
              ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2) (1 . 2))))
                      (sr5d6
               (((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
                        ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
                         (-1 . 2))))),'real)$
set!*representation('d6,
                    '(realtype
                      (id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (rd6
               (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
                        ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
                         (-1 . 2))))
                      (r2d6
             (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
             ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
                     (r3d6 (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (r4d6
              (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
                        ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
                         (-1 . 2))))
                      (r5d6
             (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
            ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
                    (sd6 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
                      (srd6
              (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
              ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
                      (sr2d6
             (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
             ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2) (1 . 2))))
                   (sr3d6 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
                      (sr4d6
               (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
               ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
                      (sr5d6
              (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
                        ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
                         (1 . 2))))),'real)$
set!*available 'd6$

set!*elems!*group('c3,'(id rc3 r2c3))$
set!*generators('c3,'(rc3))$
set!*relations('c3,'(((rc3 rc3 rc3) (id))))$
set!*grouptable('c3,
                '((grouptable id rc3 r2c3)
                  (id id rc3 r2c3)
                  (rc3 rc3 r2c3 id)
                  (r2c3 r2c3 id rc3)))$
set!*inverse('c3,'((id rc3 r2c3) (id r2c3 rc3)))$
set!*elemasgen('c3,'(((rc3) (rc3)) ((r2c3) (rc3 rc3))))$
set!*group('c3,'((id) (rc3) (r2c3)))$
set!*representation('c3,
             '((id (((1 . 1)))) (rc3 (((1 . 1)))) (r2c3 (((1 . 1))))),
                    'complex)$
set!*representation('c3,
                    '((id (((1 . 1))))
                      (rc3
               (((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1)) . -1)
                          . 2))))
                      (r2c3
              (((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . -1)) . -1)
                          . 2))))),'complex)$
set!*representation('c3,
                    '((id (((1 . 1))))
                      (rc3
              (((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . -1)) . -1)
                          . 2))))
                      (r2c3
               (((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1)) . -1)
                          . 2))))),'complex)$
set!*representation('c3,
                    '(realtype
                      (id (((1 . 1))))
                      (rc3 (((1 . 1))))
                      (r2c3 (((1 . 1))))),'real)$
set!*representation('c3,
                    '(complextype
                      (id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (rc3
              (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
              ((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
                      (r2c3
               (((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
                        ((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
                         (-1 . 2))))),'real)$
set!*available 'c3$

set!*elems!*group('c4,'(id rc4 r2c4 r3c4))$
set!*generators('c4,'(rc4))$
set!*relations('c4,'(((rc4 rc4 rc4 rc4) (id))))$
set!*grouptable('c4,
                '((grouptable id rc4 r2c4 r3c4)
                  (id id rc4 r2c4 r3c4)
                  (rc4 rc4 r2c4 r3c4 id)
                  (r2c4 r2c4 r3c4 id rc4)
                  (r3c4 r3c4 id rc4 r2c4)))$
set!*inverse('c4,'((id rc4 r2c4 r3c4) (id r3c4 r2c4 rc4)))$
set!*elemasgen('c4,
    '(((rc4) (rc4)) ((r2c4) (rc4 rc4)) ((r3c4) (rc4 rc4 rc4))))$
set!*group('c4,'((id) (rc4) (r2c4) (r3c4)))$
set!*representation('c4,
                    '((id (((1 . 1))))
                      (rc4 (((1 . 1))))
                      (r2c4 (((1 . 1))))
                      (r3c4 (((1 . 1))))),'complex)$
set!*representation('c4,
                    '((id (((1 . 1))))
                      (rc4 (((-1 . 1))))
                      (r2c4 (((1 . 1))))
                      (r3c4 (((-1 . 1))))),'complex)$
set!*representation('c4,
                    '((id (((1 . 1))))
                      (rc4 ((((((i . 1) . 1)) . 1))))
                      (r2c4 (((-1 . 1))))
                      (r3c4 ((((((i . 1) . -1)) . 1))))),'complex)$
set!*representation('c4,
                    '((id (((1 . 1))))
                      (rc4 ((((((i . 1) . -1)) . 1))))
                      (r2c4 (((-1 . 1))))
                      (r3c4 ((((((i . 1) . 1)) . 1))))),'complex)$
set!*representation('c4,
                    '(realtype
                      (id (((1 . 1))))
                      (rc4 (((1 . 1))))
                      (r2c4 (((1 . 1))))
                      (r3c4 (((1 . 1))))),'real)$
set!*representation('c4,
                    '(realtype
                      (id (((1 . 1))))
                      (rc4 (((-1 . 1))))
                      (r2c4 (((1 . 1))))
                      (r3c4 (((-1 . 1))))),'real)$
set!*representation('c4,
                    '(complextype
                      (id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (rc4 (((nil . 1) (-1 . 1)) ((1 . 1) (nil . 1))))
                      (r2c4 (((-1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
             (r3c4 (((nil . 1) (1 . 1)) ((-1 . 1) (nil . 1))))),'real)$
set!*available 'c4$

set!*elems!*group('c5,'(id rc5 r2c5 r3c5 r4c5))$
set!*generators('c5,'(rc5))$
set!*relations('c5,'(((rc5 rc5 rc5 rc5 rc5) (id))))$
set!*grouptable('c5,
                '((grouptable id rc5 r2c5 r3c5 r4c5)
                  (id id rc5 r2c5 r3c5 r4c5)
                  (rc5 rc5 r2c5 r3c5 r4c5 id)
                  (r2c5 r2c5 r3c5 r4c5 id rc5)
                  (r3c5 r3c5 r4c5 id rc5 r2c5)
                  (r4c5 r4c5 id rc5 r2c5 r3c5)))$
set!*inverse('c5,'((id rc5 r2c5 r3c5 r4c5) (id r4c5 r3c5 r2c5 rc5)))$
set!*elemasgen('c5,
               '(((rc5) (rc5))
                 ((r2c5) (rc5 rc5))
                 ((r3c5) (rc5 rc5 rc5))
                 ((r4c5) (rc5 rc5 rc5 rc5))))$
set!*group('c5,'((id) (rc5) (r2c5) (r3c5) (r4c5)))$
set!*representation('c5,
                    '((id (((1 . 1))))
                      (rc5 (((1 . 1))))
                      (r2c5 (((1 . 1))))
                      (r3c5 (((1 . 1))))
                      (r4c5 (((1 . 1))))),'complex)$
set!*representation('c5,
                    '((id (((1 . 1))))
                      (rc5
              (((((((sin (quotient (times 2 pi) 5)) . 1) ((i . 1) . 1))
                           (((cos (quotient (times 2 pi) 5)) . 1) . 1))
                          . 1))))
                      (r2c5
                       (((((((sin (quotient (times 2 pi) 5)) . 2) . -1)
                           (((sin (quotient (times 2 pi) 5)) . 1)
                            (((cos (quotient (times 2 pi) 5)) . 1)
                             ((i . 1) . 2)))
                           (((cos (quotient (times 2 pi) 5)) . 2) . 1))
                          . 1))))
                      (r3c5
                       (((((((sin (quotient (times 2 pi) 5)) . 3)
                            ((i . 1) . -1))
                           (((sin (quotient (times 2 pi) 5)) . 2)
                         (((cos (quotient (times 2 pi) 5)) . 1) . -3))
                           (((sin (quotient (times 2 pi) 5)) . 1)
                            (((cos (quotient (times 2 pi) 5)) . 2)
                             ((i . 1) . 3)))
                         (((cos (quotient (times 2 pi) 5)) . 3) . 1))
                          . 1))))
                      (r4c5
                       (((((((sin (quotient (times 2 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 2 pi) 5)) . 3)
                            (((cos (quotient (times 2 pi) 5)) . 1)
                             ((i . 1) . -4)))
                           (((sin (quotient (times 2 pi) 5)) . 2)
                          (((cos (quotient (times 2 pi) 5)) . 2) . -6))
                           (((sin (quotient (times 2 pi) 5)) . 1)
                            (((cos (quotient (times 2 pi) 5)) . 3)
                             ((i . 1) . 4)))
                           (((cos (quotient (times 2 pi) 5)) . 4) . 1))
                          . 1))))),'complex)$
set!*representation('c5,
                    '((id (((1 . 1))))
                      (rc5
             (((((((sin (quotient (times 4 pi) 5)) . 1) ((i . 1) . 1))
                           (((cos (quotient (times 4 pi) 5)) . 1) . 1))
                          . 1))))
                      (r2c5
                       (((((((sin (quotient (times 4 pi) 5)) . 2) . -1)
                           (((sin (quotient (times 4 pi) 5)) . 1)
                            (((cos (quotient (times 4 pi) 5)) . 1)
                             ((i . 1) . 2)))
                           (((cos (quotient (times 4 pi) 5)) . 2) . 1))
                          . 1))))
                      (r3c5
                       (((((((sin (quotient (times 4 pi) 5)) . 3)
                            ((i . 1) . -1))
                           (((sin (quotient (times 4 pi) 5)) . 2)
                          (((cos (quotient (times 4 pi) 5)) . 1) . -3))
                           (((sin (quotient (times 4 pi) 5)) . 1)
                            (((cos (quotient (times 4 pi) 5)) . 2)
                             ((i . 1) . 3)))
                           (((cos (quotient (times 4 pi) 5)) . 3) . 1))
                          . 1))))
                      (r4c5
                       (((((((sin (quotient (times 4 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 4 pi) 5)) . 3)
                            (((cos (quotient (times 4 pi) 5)) . 1)
                             ((i . 1) . -4)))
                           (((sin (quotient (times 4 pi) 5)) . 2)
                          (((cos (quotient (times 4 pi) 5)) . 2) . -6))
                           (((sin (quotient (times 4 pi) 5)) . 1)
                            (((cos (quotient (times 4 pi) 5)) . 3)
                             ((i . 1) . 4)))
                           (((cos (quotient (times 4 pi) 5)) . 4) . 1))
                          . 1))))),'complex)$
set!*representation('c5,
                    '((id (((1 . 1))))
                      (rc5
                       (((((((sin (quotient (times 4 pi) 5)) . 1)
                            ((i . 1) . -1))
                           (((cos (quotient (times 4 pi) 5)) . 1) . 1))
                          . 1))))
                      (r2c5
                       (((((((sin (quotient (times 4 pi) 5)) . 2) . -1)
                           (((sin (quotient (times 4 pi) 5)) . 1)
                            (((cos (quotient (times 4 pi) 5)) . 1)
                             ((i . 1) . -2)))
                           (((cos (quotient (times 4 pi) 5)) . 2) . 1))
                          . 1))))
                      (r3c5
               (((((((sin (quotient (times 4 pi) 5)) . 3) ((i . 1) . 1))
                           (((sin (quotient (times 4 pi) 5)) . 2)
                         (((cos (quotient (times 4 pi) 5)) . 1) . -3))
                           (((sin (quotient (times 4 pi) 5)) . 1)
                            (((cos (quotient (times 4 pi) 5)) . 2)
                             ((i . 1) . -3)))
                           (((cos (quotient (times 4 pi) 5)) . 3) . 1))
                          . 1))))
                      (r4c5
                       (((((((sin (quotient (times 4 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 4 pi) 5)) . 3)
                            (((cos (quotient (times 4 pi) 5)) . 1)
                             ((i . 1) . 4)))
                           (((sin (quotient (times 4 pi) 5)) . 2)
                         (((cos (quotient (times 4 pi) 5)) . 2) . -6))
                           (((sin (quotient (times 4 pi) 5)) . 1)
                            (((cos (quotient (times 4 pi) 5)) . 3)
                             ((i . 1) . -4)))
                           (((cos (quotient (times 4 pi) 5)) . 4) . 1))
                          . 1))))),'complex)$
set!*representation('c5,
                    '((id (((1 . 1))))
                      (rc5
                       (((((((sin (quotient (times 2 pi) 5)) . 1)
                            ((i . 1) . -1))
                           (((cos (quotient (times 2 pi) 5)) . 1) . 1))
                          . 1))))
                      (r2c5
                       (((((((sin (quotient (times 2 pi) 5)) . 2) . -1)
                           (((sin (quotient (times 2 pi) 5)) . 1)
                            (((cos (quotient (times 2 pi) 5)) . 1)
                             ((i . 1) . -2)))
                           (((cos (quotient (times 2 pi) 5)) . 2) . 1))
                          . 1))))
                      (r3c5
             (((((((sin (quotient (times 2 pi) 5)) . 3) ((i . 1) . 1))
                           (((sin (quotient (times 2 pi) 5)) . 2)
                         (((cos (quotient (times 2 pi) 5)) . 1) . -3))
                           (((sin (quotient (times 2 pi) 5)) . 1)
                            (((cos (quotient (times 2 pi) 5)) . 2)
                             ((i . 1) . -3)))
                           (((cos (quotient (times 2 pi) 5)) . 3) . 1))
                          . 1))))
                      (r4c5
                       (((((((sin (quotient (times 2 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 2 pi) 5)) . 3)
                            (((cos (quotient (times 2 pi) 5)) . 1)
                             ((i . 1) . 4)))
                           (((sin (quotient (times 2 pi) 5)) . 2)
                         (((cos (quotient (times 2 pi) 5)) . 2) . -6))
                           (((sin (quotient (times 2 pi) 5)) . 1)
                            (((cos (quotient (times 2 pi) 5)) . 3)
                             ((i . 1) . -4)))
                        (((cos (quotient (times 2 pi) 5)) . 4) . 1))
                          . 1))))),'complex)$
set!*representation('c5,
                    '(realtype
                      (id (((1 . 1))))
                      (rc5 (((1 . 1))))
                      (r2c5 (((1 . 1))))
                      (r3c5 (((1 . 1))))
                      (r4c5 (((1 . 1))))),'real)$
set!*representation('c5,
                    '(complextype
                      (id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (rc5
                 (((((((cos (quotient (times 2 pi) 5)) . 1) . 1)) . 1)
                 (((((sin (quotient (times 2 pi) 5)) . 1) . -1)) . 1))
                  ((((((sin (quotient (times 2 pi) 5)) . 1) . 1)) . 1)
                (((((cos (quotient (times 2 pi) 5)) . 1) . 1)) . 1))))
                      (r2c5
                       (((((((sin (quotient (times 2 pi) 5)) . 2) . -1)
                           (((cos (quotient (times 2 pi) 5)) . 2) . 1))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 1)
                         (((cos (quotient (times 2 pi) 5)) . 1) . -2)))
                          . 1))
                        ((((((sin (quotient (times 2 pi) 5)) . 1)
                          (((cos (quotient (times 2 pi) 5)) . 1) . 2)))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 2) . -1)
                           (((cos (quotient (times 2 pi) 5)) . 2) . 1))
                          . 1))))
                      (r3c5
                       (((((((sin (quotient (times 2 pi) 5)) . 2)
                         (((cos (quotient (times 2 pi) 5)) . 1) . -3))
                           (((cos (quotient (times 2 pi) 5)) . 3) . 1))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 3) . 1)
                           (((sin (quotient (times 2 pi) 5)) . 1)
                         (((cos (quotient (times 2 pi) 5)) . 2) . -3)))
                          . 1))
                        ((((((sin (quotient (times 2 pi) 5)) . 3) . -1)
                           (((sin (quotient (times 2 pi) 5)) . 1)
                          (((cos (quotient (times 2 pi) 5)) . 2) . 3)))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 2)
                          (((cos (quotient (times 2 pi) 5)) . 1) . -3))
                           (((cos (quotient (times 2 pi) 5)) . 3) . 1))
                          . 1))))
                      (r4c5
                       (((((((sin (quotient (times 2 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 2 pi) 5)) . 2)
                          (((cos (quotient (times 2 pi) 5)) . 2) . -6))
                           (((cos (quotient (times 2 pi) 5)) . 4) . 1))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 3)
                            (((cos (quotient (times 2 pi) 5)) . 1) . 4))
                           (((sin (quotient (times 2 pi) 5)) . 1)
                          (((cos (quotient (times 2 pi) 5)) . 3) . -4)))
                          . 1))
                        ((((((sin (quotient (times 2 pi) 5)) . 3)
                         (((cos (quotient (times 2 pi) 5)) . 1) . -4))
                           (((sin (quotient (times 2 pi) 5)) . 1)
                         (((cos (quotient (times 2 pi) 5)) . 3) . 4)))
                          . 1)
                         (((((sin (quotient (times 2 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 2 pi) 5)) . 2)
                         (((cos (quotient (times 2 pi) 5)) . 2) . -6))
                           (((cos (quotient (times 2 pi) 5)) . 4) . 1))
                          . 1))))),'real)$
set!*representation('c5,
                    '(complextype
                      (id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
                      (rc5
                  (((((((cos (quotient (times 4 pi) 5)) . 1) . 1)) . 1)
                  (((((sin (quotient (times 4 pi) 5)) . 1) . -1)) . 1))
                   ((((((sin (quotient (times 4 pi) 5)) . 1) . 1)) . 1)
                 (((((cos (quotient (times 4 pi) 5)) . 1) . 1)) . 1))))
                      (r2c5
                       (((((((sin (quotient (times 4 pi) 5)) . 2) . -1)
                           (((cos (quotient (times 4 pi) 5)) . 2) . 1))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 1)
                          (((cos (quotient (times 4 pi) 5)) . 1) . -2)))
                          . 1))
                        ((((((sin (quotient (times 4 pi) 5)) . 1)
                          (((cos (quotient (times 4 pi) 5)) . 1) . 2)))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 2) . -1)
                           (((cos (quotient (times 4 pi) 5)) . 2) . 1))
                          . 1))))
                      (r3c5
                       (((((((sin (quotient (times 4 pi) 5)) . 2)
                          (((cos (quotient (times 4 pi) 5)) . 1) . -3))
                           (((cos (quotient (times 4 pi) 5)) . 3) . 1))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 3) . 1)
                           (((sin (quotient (times 4 pi) 5)) . 1)
                         (((cos (quotient (times 4 pi) 5)) . 2) . -3)))
                          . 1))
                        ((((((sin (quotient (times 4 pi) 5)) . 3) . -1)
                           (((sin (quotient (times 4 pi) 5)) . 1)
                         (((cos (quotient (times 4 pi) 5)) . 2) . 3)))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 2)
                         (((cos (quotient (times 4 pi) 5)) . 1) . -3))
                           (((cos (quotient (times 4 pi) 5)) . 3) . 1))
                          . 1))))
                      (r4c5
                       (((((((sin (quotient (times 4 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 4 pi) 5)) . 2)
                          (((cos (quotient (times 4 pi) 5)) . 2) . -6))
                           (((cos (quotient (times 4 pi) 5)) . 4) . 1))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 3)
                            (((cos (quotient (times 4 pi) 5)) . 1) . 4))
                           (((sin (quotient (times 4 pi) 5)) . 1)
                        (((cos (quotient (times 4 pi) 5)) . 3) . -4)))
                          . 1))
                        ((((((sin (quotient (times 4 pi) 5)) . 3)
                          (((cos (quotient (times 4 pi) 5)) . 1) . -4))
                           (((sin (quotient (times 4 pi) 5)) . 1)
                          (((cos (quotient (times 4 pi) 5)) . 3) . 4)))
                          . 1)
                         (((((sin (quotient (times 4 pi) 5)) . 4) . 1)
                           (((sin (quotient (times 4 pi) 5)) . 2)
                          (((cos (quotient (times 4 pi) 5)) . 2) . -6))
                           (((cos (quotient (times 4 pi) 5)) . 4) . 1))
                          . 1))))),'real)$
set!*available 'c5$

endmodule;

end;
