Reciprocal of 61

Theorem
The decimal expansion of the reciprocal of $61$ has the maximum period, that is: $60$:
 * $\dfrac 1 {61} = 0 \cdotp \dot 01639 \, 34426 \, 22950 \, 81967 \, 21311 \, 47540 \, 98360 \, 65573 \, 77049 \, 18032 \, 78688 \, 5245 \dot 9$

It also contains an equal number ($6$) of each of the digits from $0$ to $9$.

Proof
Performing the calculation using long division:

0.01639344262295081967213114754098360655737704918032786885245901... 61)1.00000000000000000000000000000000000000000000000000000000000000000    61     --     390     366     ---      240      183      ---       570       549       ---        210        183        ---         270         244         ---          260          244           --           160           122           ---            380            366            ---             140             122             ---              180              122              ---               580               549               ---                310                305                ---                  500                  488                  ---                   120                    61                   ---                    590                    549                    ---                     410                     366                     ---                      440                      427                      ---                       130                       122                       ---                         80                         61                         --                         190                         183                         ---                           70                           61                           --                            90                            61                            --                            290                            244                            ---                             460                             427                             ---                              330                              305                              ---                               250                               244                               ---                                 600                                 549                                 ---                                  510                                  488                                  ---                                   220                                   183                                   ---                                    370                                    366                                    ---                                      400                                      366                                      ---                                       340                                       305                                       ---                                        350                                        305                                        ---                                         450                                         427                                         ---                                          230                                          183                                          ---                                           470                                           427                                           ---                                            430                                            427                                            ---                                              300                                              244                                              ---                                               560                                               549                                               ---                                                110                                                 61                                                ---                                                 490                                                 488                                                 ---                                                   200                                                   183                                                   ---                                                    170                                                    122                                                    ---                                                     480                                                     427                                                     ---                                                      530                                                      488                                                      ---                                                       420                                                       366                                                       ---                                                        540                                                        488                                                        ---                                                         520                                                         488                                                         ---                                                          320                                                          305                                                          ---                                                           150                                                           122                                                           ---                                                            280                                                            244                                                            ---                                                             360                                                             305                                                             ---                                                              550                                                              549                                                              ---                                                                100                                                                 61                                                                ---                                                                ....