function Lambda_spectrum(fig1)
jmax = 50;
dx = 2*pi/jmax;
k = 1;
a = 1.0;
alpha = 3.0;
k_dx = [0:jmax]*dx;
Zer_o = zeros(size(k_dx,2),1)';
fig1 = 0;
lab1(1,:) = {'   \sigma = 1 Contour                                            '};
lab1(2,:) = lab1(1,:);
lab1(3,:) = lab1(1,:);
lab1(4,:) = lab1(1,:);
lab1(5,:) = lab1(1,:);
lab1(6,:) = lab1(1,:);
lab1(7,:) = lab1(1,:);
lab1(8,:) = lab1(1,:);
sym(1,:) = 'rx-';
sym(2,:) = 'ko-';
sym(3,:) = 'bs-';
sym(4,:) = 'g*-';
sym(5,:) = 'c+-';
sym(6,:) = 'yd-';
is = 0;
menu0 = 0;
cfl = 1;  cfl = Enter('Cfl #',cfl);

while menu0 >= 0 

  menu0 = menu('Choose','Differencing Method','Change Cfl','return');
  
  if menu0 == 1
    is = is + 1; if is > 6 return; end
    menu1 = menu('Plot lambda spectrum',...
	'2nd O Central',...
	'1st O backward',...
	'2nd O backward',...
	'3rd O Opt Pade');

    if menu1 == 1
      ks_c =sin(k_dx);
      ks_d = Zer_o;
      ll = {[' O(\Delta x^2)  Central: CFL =' num2str(cfl)]};
      lab1(is+1,1:size(ll)) = ll;
    elseif menu1 == 2
      ks_c =sin(k_dx);
% thp       ks_d = exp(-(1-cos(k_dx)));
      ks_d = (1-cos(k_dx));
      ll = {[' O(\Delta x  ) Backward: CFL =' num2str(cfl)]};
      lab1(is+1,1:size(ll)) = ll;
    elseif menu1 == 3
      ks_c =(4*sin(k_dx)-sin(2*k_dx))*0.5;
% thp       ks_d = exp(-(3-4*cos(k_dx)+cos(2*k_dx))*0.5);
      ks_d = (3-4*cos(k_dx)+cos(2*k_dx))*0.5;
      ll = {[' O(\Delta x^2) Backward: CFL =' num2str(cfl)]};
      lab1(is+1,1:size(ll)) = ll;
    elseif menu1 == 4
      kss = (2-2*cos(k_dx) + 3*i*sin(k_dx))./(2 + cos(k_dx) - i*sin(k_dx));
      ks_c = imag(kss);
% thp       ks_d = exp(-real(kss));
      ks_d = real(kss);
      ll = {[' O(\Delta x^6) Opt Pade: CFL =' num2str(cfl)]};
      lab1(is+1,1:size(ll)) = ll;
    end 
    ks = ks_d + i*ks_c;
    ks = -ks*cfl;
    ks_d = -cfl*ks_d; ks_c = -cfl*ks_c;
    
    plot(ks_d,ks_c,sym(is,:),'Markersize',8,'Linewidth',2);
    legend(lab1(1:is+1,:));
  end

  if menu0 == 2
    cfl = Enter('CFL #',cfl);
  end
  if menu0 == 3 break; end

end