---------------------------------------

       The Generalized Capsules for the coefficient of q^(m*n+m-1) mod m

      for the unique formal power series satisying thefunctional equation

                                               m
                                          q f(q )
                          f(q) = 1 + -----------------
                                                2
                                     (1 - q) (-q  + 1)

       for m from 3 to 20, except those that are 2 mod 4 are as follows

                                    m is, 3

                         1 + 2 q
                    [---------------, [0, 1, 1], [1, 1, 2]]
                      3    2
                     q  - q  - q + 1

                                    m is, 4

                      2
                [------------, [0, 1, 3, 3, 1], [2, 2, 0, 2, 0]]
                  2
                 q  - 2 q + 1

                                    m is, 5

             2 + 3 q
        [---------------, [0, 1, 1, 3, 3, 1, 1], [2, 2, 4, 1, 3, 2, 1]]
          3    2
         q  - q  - q + 1

                                    m is, 7

     3 + 4 q
[---------------, [0, 1, 1, 3, 3, 6, 6, 3, 3, 1, 1],
  3    2
 q  - q  - q + 1

    [3, 3, 6, 2, 5, 4, 0, 2, 1, 6, 1]]

                                    m is, 8

      4
[------------, [0, 1, 3, 7, 5, 6, 2, 2, 6, 5, 7, 3, 1],
  2
 q  - 2 q + 1

    [4, 4, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4]]

                                    m is, 9

     4 + 5 q
[---------------, [0, 1, 1, 3, 3, 6, 6, 1, 1, 6, 6, 3, 3, 1, 1],
  3    2
 q  - q  - q + 1

    [4, 4, 8, 3, 7, 6, 1, 4, 8, 6, 5, 7, 1, 7, 5]]

                                    m is, 11

     5 + 6 q
[---------------, [0, 1, 1, 3, 3, 6, 6, 10, 10, 4, 4, 10, 10, 6, 6, 3, 3, 1, 1],
  3    2
 q  - q  - q + 1

    [5, 5, 10, 4, 9, 8, 2, 6, 0, 9, 3, 6, 5, 2, 6, 8, 6, 2, 5]]

                                    m is, 12

      6
[------------,
  2
 q  - 2 q + 1

    [0, 1, 3, 7, 1, 10, 10, 2, 10, 11, 5, 5, 11, 10, 2, 10, 10, 1, 7, 3, 1],

    [6, 6, 0, 6, 0, 0, 6, 0, 6, 6, 0, 6, 0, 6, 0, 6, 0, 6, 0, 6, 0]]

                                    m is, 13

     6 + 7 q
[---------------,
  3    2
 q  - q  - q + 1

    [0, 1, 1, 3, 3, 6, 6, 10, 10, 2, 2, 8, 8, 2, 2, 10, 10, 6, 6, 3, 3, 1, 1],

    [6, 6, 12, 5, 11, 10, 3, 8, 1, 12, 5, 9, 2, 12, 11, 1, 6, 2, 0, 2, 6, 1, 11

    ]]

                                    m is, 15

     7 + 8 q
[---------------, [0, 1, 1, 3, 3, 6, 6, 10, 10, 0, 0, 6, 6, 13, 13, 6, 6, 0, 0,
  3    2
 q  - q  - q + 1

    10, 10, 6, 6, 3, 3, 1, 1], [7, 7, 14, 6, 13, 12, 4, 10, 2, 0, 7, 12, 4, 1,

    8, 12, 11, 7, 13, 1, 14, 9, 14, 1, 13, 7, 11]]

                                    m is, 16

      8
[------------, [0, 1, 3, 7, 13, 6, 2, 2, 6, 15, 13, 1, 11, 12, 4, 4, 12, 11, 1,
  2
 q  - 2 q + 1

    13, 15, 6, 2, 2, 6, 13, 7, 3, 1], [8, 8, 0, 8, 0, 0, 8, 0, 8, 8, 0, 8, 0, 0,

    8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8]]

                                    m is, 17

     8 + 9 q
[---------------, [0, 1, 1, 3, 3, 6, 6, 10, 10, 15, 15, 4, 4, 11, 11, 2, 2, 11,
  3    2
 q  - q  - q + 1

    11, 4, 4, 15, 15, 10, 10, 6, 6, 3, 3, 1, 1], [8, 8, 16, 7, 15, 14, 5, 12, 3,

    1, 9, 15, 6, 3, 11, 16, 7, 3, 2, 6, 13, 8, 6, 9, 15, 9, 6, 8, 13, 6, 2]]

                                    m is, 19

    9 + 10 q
[---------------, [0, 1, 1, 3, 3, 6, 6, 10, 10, 15, 15, 2, 2, 9, 9, 17, 17, 7,
  3    2
 q  - q  - q + 1

    7, 17, 17, 9, 9, 2, 2, 15, 15, 10, 10, 6, 6, 3, 3, 1, 1], [9, 9, 18, 8, 17,

    16, 6, 14, 4, 2, 11, 18, 8, 5, 14, 1, 10, 6, 15, 1, 0, 14, 3, 7, 5, 18, 6,

    9, 6, 18, 5, 7, 3, 14, 0]]

                                    m is, 20

      10
[------------, [0, 1, 3, 7, 13, 2, 14, 10, 10, 15, 5, 1, 3, 12, 8, 12, 4, 5, 15,
  2
 q  - 2 q + 1

    15, 5, 4, 12, 8, 12, 3, 1, 5, 15, 10, 10, 14, 2, 13, 7, 3, 1], [10, 10, 0,

    10, 0, 0, 10, 0, 10, 10, 0, 10, 0, 0, 10, 0, 10, 10, 0, 10, 0, 10, 0, 10, 0,

    10, 0, 10, 0, 10, 0, 10, 0, 10, 0, 10, 0]]

                          This took, 0.368, seconds.