Could cull out the ones in the first quadrant, then select the smallest.

rts = pmn /. {{pmn -> -73252.56817861203 - 
       36.62627493273828 I}, {pmn -> -72839.37694161737 - 
       36.41967936634442 I}, {pmn -> -371.2553758930693 - 
       0.18562764153961991 I}, {pmn -> 
      371.2553758930693 + 0.18562764153961991 I}, {pmn -> 
      72839.3769416172 + 36.41967936589304 I}, {pmn -> 
      73252.56817861232 + 36.626274932707695 I}};
rtsPos = Select[rts, Re[#] > 0 && Im[#] >= 0 &];
SelectFirst[rtsPos, Abs[#] == Min[Abs[rtsPos]] &]

(* Out[1645]= 371.255375893 + 0.18562764154 I *)

There are of course other methods (and really the post should indicate what has already been tried).