/usr/share/labplot2/themes/Solarized is in labplot-data 2.4.0-1ubuntu4.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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ThemeName=Solarized
ThemePaletteColor1=220,50,47
ThemePaletteColor2=133,153,0
ThemePaletteColor3=181,137,0
ThemePaletteColor4=38,139,210
ThemePaletteColor5=211,54,130
[Axis]
LabelsFontColor=131,148,150
LabelsOpacity=1
LineColor=131,148,150
LineOpacity=1
LineStyle=1
LineWidth=3.52778
MajorGridColor=131,148,150
MajorGridOpacity=0.3
MajorGridStyle=1
MajorGridWidth=1.76389
MajorTicksColor=131,148,150
MajorTicksLineStyle=1
MajorTicksOpacity=1
MajorTicksType=0
MajorTicksWidth=3.52778
MinorGridColor=131,148,150
MinorGridOpacity=0.3
MinorGridStyle=2
MinorGridWidth=1.76389
MinorTicksColor=0,0,0
MinorTicksLineStyle=0
MinorTicksOpacity=1
MinorTicksType=0
MinorTicksWidth=0.283465
[CartesianPlot]
BackgroundBrushStyle=1
BackgroundColorStyle=0
BackgroundFirstColor=0,43,54
BackgroundImageStyle=1
BackgroundOpacity=1
BackgroundSecondColor=7,54,66
BackgroundType=0
BorderColor=0,0,0
BorderCornerRadius=0
BorderOpacity=1
BorderStyle=0
BorderWidth=3.52778
[Label]
TeXFontColor=109,109,109
[XYCurve]
DropLineOpacity=1
DropLineStyle=1
DropLineWidth=3.52778
ErrorBarsOpacity=1
ErrorBarsStyle=1
ErrorBarsWidth=3.52778
FillingBrushStyle=1
FillingColorStyle=0
FillingOpacity=0.4
FillingPosition=0
FillingSecondColor=0,43,54
FillingType=0
LineOpacity=1
LineStyle=1
LineWidth=3.52778
SymbolOpacity=1
ValuesColor=0,0,0
ValuesFont=Droid Sans,8,-1,5,50,0,0,0,0,0
ValuesOpacity=1
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