Sovle this transcendtal eqaution

Hello, I try to solve this transcendtal eqaution k=+-i*r/sinh(r) when k=diffrent number(0.25,0.5,1,2,3,5,10 ....). This is an equation in DFB to solve discrect value for threshold gain. r should be a complex value. And sketch a plot about a-b plane. a and b satisfy a-i*b=r*coth(r) so, a and b are real number. for +- sign, the plot has 2 lobs, it's symmetric. So only need to consider one of both.

   *function a=pair(k)
   f=@(x)k-1i*x/sinh(x);
   r=fsolve(f,1)
   a=r*coth(r);
  end*
 t=[.25 .5 1 2 3 4 5 10];
a=zeros(1,8);
for i=1:8
    a(i)=pair(t(i));
end
 plot(imag(a),real(a),'m-o','MarkerSize',5)
axis([0 14 0 5])
    % code
  end

And in textbook, its picture should include other modes not only mode 1. I tried several initial guess far away from 1, like fsove(f,2), fsolve(f,5). all got the same value. so how can I find mode 2, 3 sketch? anyone help me?