Can someone please help me in drawing this RegionPlot with high precision?

Question

Can someone who has access to Mathematica, please, help me in drawing this RegionPlot with high precision. (I used the basic plan of WolframCloud which I could not increase the precision). I do not want to use the result, I just want to know their shape, so, only a less quality image of the results can help me.
I want to know the following RegionPlot for different values of $a={0,frac12,frac13,frac5 {13},8.13, 20.353}$
a:=0;

RegionPlot[      (2 Sin[b x] Sin[b x-2 π x] Sin[a π-π x] Sin[a π+π x])>0     ,   {x,1000,1010}  ,{b,0,π}    ,  PlotPoints->100    ]

```

cvgmt · Accepted Answer

Here we also use ContourPlot and set Contours->{0},ContourShading->{None,Blue} instead of RegionPlot.

a=0

fig1 = With[{a = 0}, 
  ContourPlot[
   2 Sin[b x] Sin[b x - 2 π x] Sin[a π - π x] Sin[
     a π + π x], {x, 100, 110}, {b, 0, π}, 
   Contours -> {0}, ContourShading -> {None, Blue}, 
   ContourStyle -> None, BoundaryStyle -> Automatic, PlotPoints -> 50,
    MaxRecursion -> 2]]

a=5/13

Can someone please help me in drawing this RegionPlot with high precision?

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