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I am trying to produce a diagram like this:

enter image description here

However, when I try to do it in Wolfram with this code:

f = -(34.91307692307692`/Ω) + 
  0.5` √(4875.6917609467455`/Ω^2 + 
      0.001183431952662722` (-2.10024854401`*^11 - 15210.` Ω^2) + 
      0.0003944773175542406` (2.10024854401`*^11 + 
         15210.` Ω^2) + (0.002485051380463261` \
(-6.502457060608313`*^26 + 2.2360373408246284`*^31 Ω^2 - 
           1.6195076985488275`*^24 Ω^4 + 
           1.172847478703472`*^17 Ω^6))/(Ω \
(1.6453401488537164`*^57 Ω - 
            3.7717531641688455`*^61 Ω^3 + 
            4.098352224227726`*^54 Ω^5 + 
            2.967698194998834`*^47 Ω^7 - 
            1.4328046927166397`*^40 Ω^9 + \
√(3.498499802426748`*^109 - 9.020035930925002`*^113 Ω^2 - 
               6.4952975227022`*^114 Ω^4 - 
               1.1355258747416519`*^115 Ω^6 - 
               5.03883785494275`*^112 Ω^8 - 
               5.03640596299178`*^109 Ω^10 + 
               7.296556060973307`*^102 Ω^12 - 
               2.6421768873633545`*^95 Ω^14))^(1/3)) + 
      1/Ω 4.94066697104591`*^-13 (1.6453401488537164`*^57 \
Ω - 3.7717531641688455`*^61 Ω^3 + 
          4.098352224227726`*^54 Ω^5 + 
          2.967698194998834`*^47 Ω^7 - 
          1.4328046927166397`*^40 Ω^9 + \
√(3.498499802426748`*^109 - 9.020035930925002`*^113 Ω^2 - 
             6.4952975227022`*^114 Ω^4 - 
             1.1355258747416519`*^115 Ω^6 - 
             5.03883785494275`*^112 Ω^8 - 
             5.03640596299178`*^109 Ω^10 + 
             7.296556060973307`*^102 Ω^12 - 
             2.6421768873633545`*^95 Ω^14))^(1/3)) - 
  0.5` √(9751.383521893491`/Ω^2 + 
      0.0015779092702169625` (-2.10024854401`*^11 - 
         15210.` Ω^2) - (0.002485051380463261` \
(-6.502457060608313`*^26 + 2.2360373408246284`*^31 Ω^2 - 
           1.6195076985488275`*^24 Ω^4 + 
           1.172847478703472`*^17 Ω^6))/(Ω \
(1.6453401488537164`*^57 Ω - 
            3.7717531641688455`*^61 Ω^3 + 
            4.098352224227726`*^54 Ω^5 + 
            2.967698194998834`*^47 Ω^7 - 
            1.4328046927166397`*^40 Ω^9 + \
√(3.498499802426748`*^109 - 9.020035930925002`*^113 Ω^2 - 
               6.4952975227022`*^114 Ω^4 - 
               1.1355258747416519`*^115 Ω^6 - 
               5.03883785494275`*^112 Ω^8 - 
               5.03640596299178`*^109 Ω^10 + 
               7.296556060973307`*^102 Ω^12 - 
               2.6421768873633545`*^95 Ω^14))^(1/3)) - 
      1/Ω 4.94066697104591`*^-13 (1.6453401488537164`*^57 \
Ω - 3.7717531641688455`*^61 Ω^3 + 
          4.098352224227726`*^54 Ω^5 + 
          2.967698194998834`*^47 Ω^7 - 
          1.4328046927166397`*^40 Ω^9 + \
√(3.498499802426748`*^109 - 9.020035930925002`*^113 Ω^2 - 
             6.4952975227022`*^114 Ω^4 - 
             1.1355258747416519`*^115 Ω^6 - 
             5.03883785494275`*^112 Ω^8 - 
             5.03640596299178`*^109 Ω^10 + 
             7.296556060973307`*^102 Ω^12 - 
             2.6421768873633545`*^95 Ω^14))^(1/
          3) + (0.25` (-(2.7236064240503376`*^6/Ω^3) + \
(0.6610760127446518` (2.10024854401`*^11 + 
                15210.` Ω^2))/Ω - \
(6.311998221783861`*^-8 (2.173675466865639`*^18 + 
                3.10312759398801`*^14 \
Ω^2))/Ω))/(√(4875.6917609467455`/Ω^\
2 + 0.001183431952662722` (-2.10024854401`*^11 - 15210.` Ω^2) + 
           0.0003944773175542406` (2.10024854401`*^11 + 
              15210.` Ω^2) + (0.002485051380463261` \
(-6.502457060608313`*^26 + 2.2360373408246284`*^31 Ω^2 - 
                1.6195076985488275`*^24 Ω^4 + 
                1.172847478703472`*^17 Ω^6))/(Ω \
(1.6453401488537164`*^57 Ω - 
                 3.7717531641688455`*^61 Ω^3 + 
                 4.098352224227726`*^54 Ω^5 + 
                 2.967698194998834`*^47 Ω^7 - 
                 1.4328046927166397`*^40 Ω^9 + \
√(3.498499802426748`*^109 - 9.020035930925002`*^113 Ω^2 - 
                    6.4952975227022`*^114 Ω^4 - 
                    1.1355258747416519`*^115 Ω^6 - 
                    5.03883785494275`*^112 Ω^8 - 
                    5.03640596299178`*^109 Ω^10 + 
                    7.296556060973307`*^102 Ω^12 - 
                    2.6421768873633545`*^95 Ω^14))^(1/3)) + 
           1/Ω 4.94066697104591`*^-13 (1.6453401488537164`*^57 \
Ω - 3.7717531641688455`*^61 Ω^3 + 
               4.098352224227726`*^54 Ω^5 + 
               2.967698194998834`*^47 Ω^7 - 

               1.4328046927166397`*^40 Ω^9 + \
√(3.498499802426748`*^109 - 9.020035930925002`*^113 Ω^2 - 
                  6.4952975227022`*^114 Ω^4 - 
                  1.1355258747416519`*^115 Ω^6 - 
                  5.03883785494275`*^112 Ω^8 - 
                  5.03640596299178`*^109 Ω^10 + 
                  7.296556060973307`*^102 Ω^12 - 
                  2.6421768873633545`*^95 Ω^14))^(1/3))))

ParametricPlot[{Re[f],Im[f/(2*Pi)]},{Ω,Pi,20Pi}] 

I get only this:

enter image description here

I already checked the evaluation of the function comparing its values versus Matlab (where the figure comes from) and it is correct. My question is: How can I correct the commands of the ParametricPlot in order to obtain the desired figure?.

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  • 1
    $\begingroup$ Maybe add AspectRatio->1 or AspectRatio->1/GoldenRatio? $\endgroup$ – Carl Woll Apr 23 at 15:56
  • $\begingroup$ @CarlWoll: I already tried what your recommend, unfortunately it did not work. $\endgroup$ – Alfredo Apr 23 at 16:14
  • $\begingroup$ It seems like your function pretty rapidly oscillates between +1763 and -1763 (or thereabouts). The imaginary part does not seem to evaluate to a positive number at 1.1 Pi or 1.2 Pi as well as many other values of Omega. $\endgroup$ – MassDefect Apr 23 at 17:53
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One branch can be displayed in the following way

ParametricPlot[{Re[f], Abs[Im[f]/(2*Pi)]}, {\[CapitalOmega], Pi, 
  20 Pi}, PlotRange -> {{-5, 10}, {1780, 1810}}, PlotPoints -> 400, 
 AspectRatio -> 1/2]

fig1

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  • $\begingroup$ Your approach works acceptably. This ParametricPlot is very sensible to the PlotPoints. In this case the value PlotPoints->350 results better for me. $\endgroup$ – Alfredo Apr 24 at 8:44

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