NIntegrate numerical accuracy and errors

I have the following 3x3 matrix

M = {{-I*ω + Γ/2, I*g1, 0}, {I*g1, -I*ω + κ1/2, I*g2}, {0, I*g2, -I*ω + κ2/2}}; 

Finding the eigenvalues and eigenvectors

vals = Eigenvalues[M, Cubics -> True]; vecs = Simplify[ Eigenvectors[M /. Complex[0, -1] -> mi, Cubics -> True] /. mi -> -I]; 

All of this is to diagonalize the initial M matrix

P = Transpose[{vecs[[1]], vecs[[2]], vecs[[3]]}]; Dmat = DiagonalMatrix[{Sqrt[Γ], Sqrt[κ1], Sqrt[κ2]}]; Diag = DiagonalMatrix[vals]; 

Check if the diagonalization works. This should give the zero matrix

Inverse[P].M.P - Diag // Simplify 

Define the new matrix Modemat taking certain fixed values for the parameters

Modemat = Inverse[Diag].Inverse[P].Dmat /. {Γ -> 0.01, κ1 -> 1, κ2 -> 20, g2 -> 10}; 

Recall that now, the matrix elements of Modemat are dependent on ω and g1. Defining the following functions from the matrix elements of Modemat

M11[ω11_, g11_] := Modemat[[1, 1]] /. {ω -> ω11, g1 -> g11}; M12[ω12_, g12_] := Modemat[[1, 2]] /. {ω -> ω12, g1 -> g12}; M13[ω13_, g13_] := Modemat[[1, 3]] /. {ω -> ω13, g1 -> g13}; fsbb[ω_, g1_] := 300*Abs[M11[ω, g1]]^2 + 0.1*Abs[M12[ω, g1]]^2 + 0.1*Abs[M13[ω, g1]]^2; 

Now I'm interested in finding the area under the curve of fsbb against ω

poptab = Table[{cc1, 1/(2 π)* NIntegrate[ Evaluate[(fsbb[ω, g1]) /. {g1 -> Sqrt[cc1*1*0.01]/ 2}], {ω, -40, 40}]}, {cc1, 0.001, 10^5, 10}] 

Here's where the problem lies, upon computing poptab, I was returned with warnings that says Numerical Integration converging too slowly; suspect one of the following: singularity, value of the integration is 0....

And also "NIntegrate failed to converge to prescribed accuracy after 7 \ recursive bisections in ω near {ω} = {0.60181878}. \ NIntegrate obtained 8.5216538.*^-6 and 7.08893718.*^-6 for the \ integral and "

I've Googled with dealing precision issues and tried something like

poptab = Table[{cc1, 1/(2 π)* NIntegrate[ Evaluate[(fsbb[ω, g1]) /. {g1 -> Sqrt[cc1*1*0.01]/ 2}], {ω, -40, 40}, MaxRecursion -> 7, WorkingPrecision -> 8]}, {cc1, 0.001, 10^5, 10}] 

But it didn't help and the warnings remain. I know it's just a warning and not an error but it directly affects the NIntegrate function since it spits out different integration values if I tweak around with the MaxRecursion option for the same parameters. I could really use some help troubleshooting this.

Thank you in advance.