Note that eπ√58=3964−104.00000017…
The terms have been factored to show some interesting connections to Pell equations. If we define the fundamental unit U29=5+√292, then
(U29)3=70+13√29,thus702−29⋅132=−1
(U29)6=9801+1820√29,thus98012−29⋅18202=1
26((U29)6+(U29)−6)2=3964
A similar situation happens with a pi formula using, of all things, the golden ratio. The fact that these are so has to do with the Dedekind eta function, but that's another story.
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