nm = 100;
Reap[For[v2 = -10., v2 < -9, v2 = v2 + 1/10.,
   v[x_] := I*x^3 + I*v2*x^2;
   c[m_, n_] := 1./Sqrt[2^(m + n)*Factorial[m]*Factorial[n]*Pi];
   x1[m_, 
     n_] := (1/Sqrt[2.])*(Sqrt[n + 1]*KroneckerDelta[m, n + 1] + 
       Sqrt[n]*KroneckerDelta[m, n - 1]);
   g[m_, n_] := 
    c[m, n]*Integrate[
      Exp[-x^2]*HermiteH[m, x]*x^3*HermiteH[n, x], {x, -Infinity, 
       Infinity}];
   p2[m_, 
     n_] := .5*(2*n + 1)*KroneckerDelta[m, n] - .5*Sqrt[n*(n - 1)]*
      KroneckerDelta[m, n - 2] - .5*Sqrt[(n + 1)*(n + 2)]*
      KroneckerDelta[m, n + 2];
   x3[m_, 
     n_] := (1/
       Sqrt[8.])*(Sqrt[(n + 1.)*(n + 2)*(n + 3)]*
        KroneckerDelta[m, n + 3.] + 
       Sqrt[n*(n - 1)*(n - 2)]*
        KroneckerDelta[m, n - 3] + (3*(n + 1)*Sqrt[n + 1])*
        KroneckerDelta[m, n + 1] + 
       3*n*Sqrt[n]*KroneckerDelta[m, n - 1]);
   h[m_, n_] := p2[m, n] + I*x3[m, n] + I*v2*x[m, n];
   mat = Table[h[m, n], {m, 0, nm}, {n, 0, nm}];
   Eigenvalues[mat];
   a = Sort[Re[Select[Eigenvalues[mat], Abs[Im[#]] < 10^-5 &]]];
   j = Length[a];
   b = a[[1 ;; 7]];
   Sow[Join[{v2, Part[b, 1]}]]]][[2, 1]]