An approximation of first zeta zero

In case this means something:

 2*pi*e^sqrt(2) / (2*sqrt(2) - 1)  is approximately
    14.13472486539888320737873054362765411254519...

 The first non-trivial zeta zero is approximately   
    14.13472514173469379045725198356247027078425...

 The difference is approximately
    -.000000276335810583078521439934816158239053...
  or around -1/3618785.4114...

Here are some other calculations,
where z1 = first zeta zero, g = gamma:
 z1/pi            = 4.4992227511047348484865414231801574...
 sqrt(z1/2*pi)    = 1.4998704529233074482191259501034442...
 g - g^pi         = 3.9929698161176810954018841193514217...
 z1/pi - (g-g^pi) = 4.0999257694929667389463530112450152...

Gerald