Manipulate function not working possibly because of Arg?

Question

I have the following function

eigen1 = 1/3*(p + sig - u2/(2^(8/3)*sig) - 3*I*ω);

Where

p = (Γ + κ1 + κ2)/2;
u1 = 36 g1^2 (-2 p + 3 κ2) + (36 g2^2 + (2 p - 3 κ1) (2 p - 3 κ2)) (4 p 
   - 3(κ1 + κ2));
u2 = (2^(2/3)*(12 g1^2 + 12 g2^2 - 4 p^2 + 6 p (κ1 + κ2) - 3 (κ1^2 + κ1 κ2 + 
   κ2^2)));
sig = ((u1 + Sqrt[u1^2 + u2^3])/16)^(1/3);

I am only interested in plotting the imaginary part of eigen1 as a function of g1 while varying the parameter g2 and letting the other parameters (κ1, κ2, Γ, ω) take on fixed values

testplot1 = ComplexExpand[Im[eigen1]] /. {Γ -> 1, κ1 -> 2, κ2 -> 3, ω -> 0};

This should leave testplot1 only dependent on g1 and g2. But doing

Manipulate[Plot[Evaluate@testplot1, {g1, 0, 5}, PlotRange -> All], {g2, 1, 10}]

returns a blank graph. I decided to print testplot1 to see if there are any missing variables that I have yet to define, but everything in testplot1 really is just a function of g1 and g2. Printing testplot1 gives

-((7 Sin[1/
    3 Arg[108 g1^2 - 108 g2^2 + 
      Sqrt[(108 g1^2 - 108 g2^2)^2 + 
       4 (-3 + 12 g1^2 + 12 g2^2)^3]]])/(3 2^(
  2/3) ((108 g1^2 - 
      108 g2^2 + (((108 g1^2 - 108 g2^2)^2 + 
          4 (-3 + 12 g1^2 + 12 g2^2)^3)^2)^(1/4)
        Cos[1/2 Arg[(108 g1^2 - 108 g2^2)^2 + 
           4 (-3 + 12 g1^2 + 12 g2^2)^3]])^2 + 
    Sqrt[((108 g1^2 - 108 g2^2)^2 + 
       4 (-3 + 12 g1^2 + 12 g2^2)^3)^2]
      Sin[1/2 Arg[(108 g1^2 - 108 g2^2)^2 + 
         4 (-3 + 12 g1^2 + 12 g2^2)^3]]^2)^(1/6))) + (2 2^(1/3)
 Sin[1/3 Arg[
   108 g1^2 - 108 g2^2 + 
    Sqrt[(108 g1^2 - 108 g2^2)^2 + 
     4 (-3 + 12 g1^2 + 12 g2^2)^3]]])/(3 ((108 g1^2 - 
    108 g2^2 + (((108 g1^2 - 108 g2^2)^2 + 
        4 (-3 + 12 g1^2 + 12 g2^2)^3)^2)^(1/4)
      Cos[1/2 Arg[(108 g1^2 - 108 g2^2)^2 + 
         4 (-3 + 12 g1^2 + 12 g2^2)^3]])^2 + 
  Sqrt[((108 g1^2 - 108 g2^2)^2 + 4 (-3 + 12 g1^2 + 12 g2^2)^3)^2]
    Sin[1/2 Arg[(108 g1^2 - 108 g2^2)^2 + 
       4 (-3 + 12 g1^2 + 12 g2^2)^3]]^2)^(1/6)) + (2 2^(1/3)
 g1^2 Sin[
 1/3 Arg[108 g1^2 - 108 g2^2 + 
    Sqrt[(108 g1^2 - 108 g2^2)^2 + 
     4 (-3 + 12 g1^2 + 12 g2^2)^3]]])/((108 g1^2 - 
  108 g2^2 + (((108 g1^2 - 108 g2^2)^2 + 
      4 (-3 + 12 g1^2 + 12 g2^2)^3)^2)^(1/4)
    Cos[1/2 Arg[(108 g1^2 - 108 g2^2)^2 + 
       4 (-3 + 12 g1^2 + 12 g2^2)^3]])^2 + 
Sqrt[((108 g1^2 - 108 g2^2)^2 + 4 (-3 + 12 g1^2 + 12 g2^2)^3)^2]
  Sin[1/2 Arg[(108 g1^2 - 108 g2^2)^2 + 
     4 (-3 + 12 g1^2 + 12 g2^2)^3]]^2)^(1/6) + (2 2^(1/3)
 g2^2 Sin[
 1/3 Arg[108 g1^2 - 108 g2^2 + 
    Sqrt[(108 g1^2 - 108 g2^2)^2 + 
     4 (-3 + 12 g1^2 + 12 g2^2)^3]]])/((108 g1^2 - 
  108 g2^2 + (((108 g1^2 - 108 g2^2)^2 + 
      4 (-3 + 12 g1^2 + 12 g2^2)^3)^2)^(1/4)
    Cos[1/2 Arg[(108 g1^2 - 108 g2^2)^2 + 
       4 (-3 + 12 g1^2 + 12 g2^2)^3]])^2 + 
Sqrt[((108 g1^2 - 108 g2^2)^2 + 4 (-3 + 12 g1^2 + 12 g2^2)^3)^2]
  Sin[1/2 Arg[(108 g1^2 - 108 g2^2)^2 + 
     4 (-3 + 12 g1^2 + 12 g2^2)^3]]^2)^(1/6) + (1/(6 2^(1/3)))((108 g1^2 - 
  108 g2^2 + (((108 g1^2 - 108 g2^2)^2 + 
      4 (-3 + 12 g1^2 + 12 g2^2)^3)^2)^(1/4)
    Cos[1/2 Arg[(108 g1^2 - 108 g2^2)^2 + 
       4 (-3 + 12 g1^2 + 12 g2^2)^3]])^2 + 
Sqrt[((108 g1^2 - 108 g2^2)^2 + 4 (-3 + 12 g1^2 + 12 g2^2)^3)^2]
  Sin[1/2 Arg[(108 g1^2 - 108 g2^2)^2 + 
     4 (-3 + 12 g1^2 + 12 g2^2)^3]]^2)^(1/6)Sin[1/3 Arg[
 108 g1^2 - 108 g2^2 + 
  Sqrt[(108 g1^2 - 108 g2^2)^2 + 4 (-3 + 12 g1^2 + 12 g2^2)^3]]]]]]

which seems long and nasty. The point is that the only variables in here are g1 and g2 so Manipulate should really work and I don't know what went wrong. My initial diagnosis would be that the Arg that appears in testplot1 throughout was interfering with Manipulate but I am not sure if that's the real issue. I intend to vary not just g2 but eventually all of the other parameters (κ1, κ2, Γ, ω) down the road but I cannot vary even one parameter at this point. Any thoughts?

Answer 1

As I said in my comment, your plot will always give you 0, since you're trying to take the Im part of a real number - before you print test1 for examination you should get rid of the ComplexExpand, it will be easier to interpret. Here is an MWE of the issue with Manipulate

test=y*x;
Manipulate[
Plot[test,{x,0,1}],
{y,0,1}
]

This gives a blank plot, one solution is:

test=y*x;
Manipulate[
Plot[test/.y->yy,{x,0,1}],
{yy,0,1}
]

Though I doubt this is the canonical way to handle this sort of thing.