# Plotting results of a NSolve problem

I am calculating, numerically, the zeros of a determinant. a1 and a2 are constants, q is a parameter. I would like to vary q and find the roots w as a function of q and plot roots w vs. q. All roots w associated with a q should be plotted "above/below" that q in the plot. For this determinant, I have eight roots w corresponding to each value of q. Thus, my final plot should consist of 8 dots placed above and/or below the corresponding q-value. The q-value should be on the horizontal axis.

ClearAll["Global*"]
(*constants*)
a1 = 2; a2 = 3;
(*determinant*)
det[q_, w_] := (1 - q/w^2 (1 + Exp[-2 a1 q ] 1/(2 w^2 - 1))) (1 -
q/w^2 (1 + Exp[-2 q] 1/(2 w^2 - 1))) -
q^2/w^4 (Exp[-q Abs[a1 - a2]] +
Exp[-q (a1 + a2)] 1/(2 w^2 - 1)) (Exp[-q Abs[a2 - a1]] +
Exp[-q (a2 + a1)] 1/(2 w^2 - 1));
(*numerical solve*)
sol = NSolve[det[q, w] == 0, w];
(*build table for {q,{w1,w2,w3,w4,w5,w6,w7,w8}} pairs*)
MF = Table[{q, sol[[All, 1, 2]]}, {q, 0, 2, 0.5}] // MatrixForm;
(*this should be plotted on the horizontal axis*)
xvar = Table[MF[[1, ii]][], {ii, 1, 5}];
(*this should be plotted on the vertical axis*)
yvar = Table[MF[[1, ii]][], {ii, 1, 5}];
(*my listplot*)
Show[ListPlot[{xvar, #}] & /@ yvar]


the problem with the plot (below) is that xvar-s are also plotted against the vertical axis (blue dots) yvar-s (orange dots) are plotted at x=1, x=2 etc. instead of the corresponding q-values, which, in this case, are 0, 0.5, 1, 1.5 etc. (I have two questions: 1. How can I get the plot I want? 2. Is there a better way of doing this?)

ListPlot requires lists of point coordinates, but the code was providing it with lists of lists. This can be fixed by replacing the last two lines by
yvar = Transpose[Table[MF[[1, ii]][], {ii, 1, 5}]];
` 