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

                                      for

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

                      for m from 2 to 10, are as follows

                                  [1, [1, 0]]

                                 [1, [1, 2, 0]]

                               [1, [1, 2, 3, 0]]

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

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

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

                         [1, [1, 2, 3, 4, 5, 6, 7, 0]]

                        [1, [1, 2, 3, 4, 5, 6, 7, 8, 0]]

                      [1, [1, 2, 3, 4, 5, 6, 7, 8, 9, 0]]

                          This took, 0.051, seconds.