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