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

                                      for

                       infinity
                       --------'
                      '  |  |                1
                         |  |    -------------------------
                         |  |    /       i \ /         i \
                         |  |    |     (m )| |     (2 m )|
                        i = 0    \1 - q    / \1 - q      /

                    for m odd from 3 to 23, are as follows

                                    m is, 3



                                 [2, [1, 1, 0]]

                                    m is, 5



                            [3, [1, 1, 3, 3, 1, 1]]

                                    m is, 7



                      [4, [1, 1, 3, 3, 6, 6, 3, 3, 1, 1]]

                                    m is, 9



                [5, [1, 1, 3, 3, 6, 6, 1, 1, 6, 6, 3, 3, 1, 1]]

                                    m is, 11



        [6, [1, 1, 3, 3, 6, 6, 10, 10, 4, 4, 10, 10, 6, 6, 3, 3, 1, 1]]

                                    m is, 13



  [7, [1, 1, 3, 3, 6, 6, 10, 10, 2, 2, 8, 8, 2, 2, 10, 10, 6, 6, 3, 3, 1, 1]]

                                    m is, 15



[8, [1, 1, 3, 3, 6, 6, 10, 10, 0, 0, 6, 6, 13, 13, 6, 6, 0, 0, 10, 10, 6, 6, 3,

    3, 1, 1]]

                                    m is, 17



[9, [1, 1, 3, 3, 6, 6, 10, 10, 15, 15, 4, 4, 11, 11, 2, 2, 11, 11, 4, 4, 15, 15,

    10, 10, 6, 6, 3, 3, 1, 1]]

                                    m is, 19



[10, [1, 1, 3, 3, 6, 6, 10, 10, 15, 15, 2, 2, 9, 9, 17, 17, 7, 7, 17, 17, 9, 9,

    2, 2, 15, 15, 10, 10, 6, 6, 3, 3, 1, 1]]

                                    m is, 21



[11, [1, 1, 3, 3, 6, 6, 10, 10, 15, 15, 0, 0, 7, 7, 15, 15, 3, 3, 13, 13, 3, 3,

    15, 15, 7, 7, 0, 0, 15, 15, 10, 10, 6, 6, 3, 3, 1, 1]]

                                    m is, 23



[12, [1, 1, 3, 3, 6, 6, 10, 10, 15, 15, 21, 21, 5, 5, 13, 13, 22, 22, 9, 9, 20,

    20, 9, 9, 22, 22, 13, 13, 5, 5, 21, 21, 15, 15, 10, 10, 6, 6, 3, 3, 1, 1]]



             And for m divisible by 4 from 4 to 40 are as follows

                                    m is, 4



                               [2, [1, 3, 3, 1]]

                                    m is, 8



                   [4, [1, 3, 7, 5, 6, 2, 2, 6, 5, 7, 3, 1]]

                                    m is, 12



   [6, [1, 3, 7, 1, 10, 10, 2, 10, 11, 5, 5, 11, 10, 2, 10, 10, 1, 7, 3, 1]]

                                    m is, 16



[8, [1, 3, 7, 13, 6, 2, 2, 6, 15, 13, 1, 11, 12, 4, 4, 12, 11, 1, 13, 15, 6, 2,

    2, 6, 13, 7, 3, 1]]

                                    m is, 20



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

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

                                    m is, 24



[12, [1, 3, 7, 13, 22, 10, 2, 22, 23, 5, 17, 11, 12, 20, 12, 12, 21, 15, 19, 9,

    10, 22, 22, 10, 9, 19, 15, 21, 12, 12, 20, 12, 11, 17, 5, 23, 22, 2, 10, 22,

    13, 7, 3, 1]]

                                    m is, 28



[14, [1, 3, 7, 13, 22, 6, 22, 14, 11, 13, 21, 7, 0, 0, 8, 24, 21, 27, 15, 13,

    22, 14, 18, 6, 7, 21, 21, 7, 6, 18, 14, 22, 13, 15, 27, 21, 24, 8, 0, 0, 7,

    21, 13, 11, 14, 22, 6, 22, 13, 7, 3, 1]]

                                    m is, 32



[16, [1, 3, 7, 13, 22, 2, 18, 6, 31, 29, 1, 11, 28, 20, 20, 28, 13, 7, 11, 25,

    18, 22, 6, 2, 11, 1, 5, 23, 24, 8, 8, 24, 23, 5, 1, 11, 2, 6, 22, 18, 25,

    11, 7, 13, 28, 20, 20, 28, 11, 1, 29, 31, 6, 18, 2, 22, 13, 7, 3, 1]]

                                    m is, 36



[18, [1, 3, 7, 13, 22, 34, 14, 34, 23, 17, 17, 23, 0, 20, 12, 12, 21, 3, 31, 33,

    10, 34, 34, 10, 35, 1, 17, 11, 20, 8, 12, 32, 33, 15, 15, 33, 32, 12, 8, 20,

    11, 17, 1, 35, 10, 34, 34, 10, 33, 31, 3, 21, 12, 12, 20, 0, 23, 17, 17, 23,

    34, 14, 34, 22, 13, 7, 3, 1]]

                                    m is, 40



[20, [1, 3, 7, 13, 22, 34, 10, 30, 15, 5, 1, 3, 12, 28, 12, 4, 5, 15, 35, 25,

    26, 38, 22, 18, 27, 9, 5, 15, 0, 0, 16, 8, 17, 3, 7, 29, 30, 10, 10, 30, 29,

    7, 3, 17, 8, 16, 0, 0, 15, 5, 9, 27, 18, 22, 38, 26, 25, 35, 15, 5, 4, 12,

    28, 12, 3, 1, 5, 15, 30, 10, 34, 22, 13, 7, 3, 1]]

                          This took, 0.202, seconds.