Inverse of Exp[-ZetaZero[z]/Im[ZetaZero[z]]*Pi*2]

z = Range[15];
x = N[Exp[-ZetaZero[z]/Im[ZetaZero[z]]*Pi*2], 20];
-Log[Sum[(-1)^k*x^(Log[k]*Im[ZetaZero[z]]/Pi), {k, 1, Infinity}]]*
 Re[ZetaZero[z]]/Pi*I
Arg[%]

z = Range[15];
x = N[Exp[-ZetaZero[z]/Im[ZetaZero[z]]*Pi*2], 20];
-Log[Sum[(-1)^k*x^(Log[k]*Im[ZetaZero[z]]/Pi), {k, 1, Infinity}]]*
 Im[ZetaZero[z]]/Pi
Arg[%]