SetDirectory[NotebookDirectory[]];
<<MaTeX`
texStyle={};
SetOptions[MaTeX,"BasePreamble"->{"\\usepackage{amsmath}","\\usepackage{xcolor}","\\usepackage{fourier}","\\usepackage{ebgaramond}"},FontSize->11];

frame[legend_]:=Framed[legend,FrameStyle->Thin,RoundingRadius->10,FrameMargins->0];

αλ[λ_,μ_]:=μ/(λ+2μ);
λα[α_,μ_]:=μ(1/α-2);
CWeyl[d_,λ_, μ_]:=((λ+2 μ)^(-d/2)+(d-1) μ^(-d/2)) /(4  Pi)^(d/2)/Gamma[1+d/2];
BDirLiu[d_,λ_, μ_]:=-((d-1)/μ^((d-1)/2)+1/(λ+2μ)^((d-1)/2))/4/(4 Pi)^((d-1)/2)/Gamma[1+(d-1)/2];
BDir[d_,α_, μ_]:=-μ^((1-d)/2)/(2^(d+1)Pi^((d-1)/2)Gamma[(1+d)/2]) (4(d-1)/Pi NIntegrate[τ^(d-2)ArcTan[Sqrt[(1-α τ^(-2))(τ^(-2)-1)]],{τ,Sqrt[α],1}]+α^((d-1)/2)+d-1);
BDirSaVa2[α_, μ_]:=1/(4Pi Sqrt[μ])(-1-Sqrt[α]-4/Pi NIntegrate[ArcTan[Sqrt[(1-α/ζ^2)(1/ζ^2-1)]],{ζ, Sqrt[α],1}]);
BDirSaVa3[λ_, μ_]:=-1/(16Pi)(3λ^2+13λ μ +16μ^2)/(λ^2 μ+5λ μ^2 +6μ^3);
γR[α_]:=Sqrt[Min[x/.Solve[(x^3)-8 (x^2)+16 (-1+α)+8(3-2 α) x ==0,x, Reals]]];
Bfree[d_,α_, μ_]:= μ^((1-d)/2)/(2^(d+1)Pi^((d-1)/2)Gamma[(1+d)/2]) (4(d-1)/Pi NIntegrate[τ^(d-2)ArcTan[(τ^(-2)-2)^2/(4Sqrt[(1-α τ^(-2))(τ^(-2)-1)])],{τ,Sqrt[α],1}]+α^((d-1)/2)+d-5+4γR[α]^(1-d));
BfreeSaVa2[α_, μ_]:=1/(4Pi Sqrt[μ])(4/γR[α]-3+Sqrt[α]+4/Pi NIntegrate[ArcTan[(2-1/ζ^2)^2/(4Sqrt[(1-α/ζ^2)(1/ζ^2-1)])],{ζ, Sqrt[α],1}]);
BfreeSaVa3[λ_, μ_]:=1/(16Pi) (3(λ+2μ)^2-3(λ+2μ)μ+2μ^2)/((λ+2μ)μ(λ+μ));

MyNlambdaSimple[evs_,Λ_]:=Sum[UnitStep[Λ-evs[[j]]],{j,1,Length[evs]}];

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503.4210141 503.455139 510.8214267 553.7466664 553.794035
600.5058649 618.0615865 621.2654701 630.0083253 638.7159763
651.6430951 651.6470775 693.6846911 704.2878463 720.3127763
720.3496146 767.6188354 767.7616412 773.4941525 773.6527388
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2854.387654 2868.392399 2870.494226 2871.398503 2872.266356
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evsSquareβ05=Flatten@ToExpression@StringSplit[str1];
evsSquareβ4=Flatten@ToExpression@StringSplit[str2];
evsSquareβ101=Flatten@ToExpression@StringSplit[str3];
bthis1=BDir[2,2/3, 1];
bthis2=BDir[2,1/5, 1];
bthis3=BDir[2,1/102, 1];

xtsq1 = Table[{x, MaTeX[x]}, {x,{800,1600}}];
xtsq2 = Table[{x, MaTeX[x]}, {x,{1200,2400}}];
xtsq3 = Table[{x, MaTeX[x]}, {x,{1400,2800}}];
ytsq = Table[{y, MaTeX[y]}, {y,-40,-10,10}];

figsq1=Plot[{MyNlambdaSimple[evsSquareβ05,Λ]-CWeyl[2,-0.5, 1]Λ,4bthis1 Sqrt[Λ], 4BDirLiu[2,-0.5,1]Sqrt[Λ]},{Λ,0,1696},PlotStyle->{Black, Blue, Red}, Ticks->{xtsq1,ytsq}, AxesLabel->{MaTeX["\\Lambda"],None},Epilog->Inset[Framed[MaTeX["\\lambda=-0.5"], RoundingRadius->2, ContentPadding->False,FrameMargins->Tiny],Scaled[{0.1,0}],Scaled[{0,0}]]];
figsq2=Plot[{MyNlambdaSimple[evsSquareβ4,Λ]-CWeyl[2,3, 1]Λ,4bthis2 Sqrt[Λ], 4BDirLiu[2,3,1]Sqrt[Λ]},{Λ,0,2400},PlotStyle->{Black, Blue, Red},Ticks->{xtsq2,ytsq}, AxesLabel->{MaTeX["\\Lambda"],None},Epilog->Inset[Framed[MaTeX["\\lambda=3"], RoundingRadius->2, ContentPadding->False,FrameMargins->Tiny],Scaled[{0.1,0}],Scaled[{0,0}]]]; 
figsq3=Plot[{MyNlambdaSimple[evsSquareβ101,Λ]-CWeyl[2,100, 1]Λ,4bthis3 Sqrt[Λ], 4BDirLiu[2,100,1]Sqrt[Λ]},{Λ,0,2925},PlotStyle->{Black, Blue, Red},Ticks->{xtsq3,ytsq}, AxesLabel->{MaTeX["\\Lambda"],None},Epilog->Inset[Framed[MaTeX["\\lambda=100"], RoundingRadius->2, ContentPadding->False,FrameMargins->Tiny],Scaled[{0.1,0}],Scaled[{0,0}]]] ;
legendsq=LineLegend[{Black, Blue, Red},MaTeX[{"\\text{computed }\\mathcal{N}_{\\mathrm{Dir}}(\\Lambda)-a\\Lambda\\qquad\\qquad","4b_{\\mathrm{Dir}}\\sqrt{\\Lambda}\\qquad\\qquad","4b_{\\mathrm{Dir}}^{\\mathrm{Liu}}\\sqrt{\\Lambda}"}],LegendFunction->None,LegendLayout->{"Row",1}];
figsq=GraphicsColumn[{GraphicsRow[{figsq1,figsq2,figsq3},ImageSize->Full,Spacings->{Scaled[0.05],Automatic}],
legendsq},ImageSize->Full,Spacings->{0,Automatic}]

Export["figsq.pdf",figsq]

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	1116.914903	1117.279252	1170.638311	1208.239511	1208.262277
	1210.093342	1214.82406	1216.441919	1227.530101	1230.000138
	1230.015133	1246.948671	1254.524688	1260.514132	1263.819317
	1265.282938	1276.075234	1298.375032	1298.824612	1308.479636
	1308.495565	1329.210918	1339.328362	1360.521866	1360.527707
	1393.179386	1402.213687	1402.251765	1426.550159	1426.562679
	1427.928487	1427.957756	1436.092631	1436.181578	1458.626322
	1458.685707	1465.376718	1466.689331	1492.245802	1499.720758
	1499.74774	1559.649411	1559.681888	1572.318134	1573.314615
	1586.022346	1590.441919	1592.991324	1594.357622	1599.936849
	1603.680973	1616.766894	1618.562996	1623.794137	1679.868408
	1680.394782	1680.836384	1680.968119	1682.452064	1726.195459
	1726.299748	1753.289263	1758.115495	1758.161036	1781.560785
	1783.448377	1783.466476	1785.761484	1785.786065	1795.623861
	1795.707809	1806.862034	1824.116008	1836.657732	1836.706819
	1848.220714	1848.261285	1864.26118	1920.24606	1923.551687
	1939.057009	1939.167011	1952.970552	1953.181616	1964.648057
	1975.868612	1977.80985	1978.404693	1981.395933	1985.139356
	1990.273182	1990.478345	1993.825405	1993.877979	2003.093103
	2013.532876	2055.190326	2090.338192	2108.497001	2114.250469
	2114.309844	2119.182448	2138.502284	2138.547958	2175.313967
	2179.34797	2179.383998	2180.49281	2180.51758	2187.441924
	2187.563311	2192.002008	2192.035234	2237.880134	2239.136395
	2239.161116	2240.832152	2276.01088	2276.192338	2282.873238";
strfr3="0	  0	  0	15.77472163	19.7392192
	23.1190593	23.11906806	36.67811371	42.14207716	42.14212471
	62.79639989	69.47293846	78.95732576	84.64519802	84.64548229
	87.25646389	118.8252651	118.8257258	122.9598543	142.9947082
	142.9959902	153.7326011	167.3297603	168.9587306	177.65898
	197.6369549	200.8332164	200.8343716	232.5379	232.5384164
	241.2496976	243.5595895	243.5608996	281.1232304	288.5814086
	304.0251602	304.0283511	306.065346	315.8582776	316.2454051
	316.252388	356.0170616	379.8867687	379.9028164	389.4593553
	389.465887	398.9098697	398.9201258	402.3218612	442.812214
	442.8283538	459.1195053	463.6705827	483.2037523	489.3743431
	493.601254	496.3183023	506.9665669	524.5004247	533.5068394
	555.8532603	555.8732436	585.3820967	585.413541	596.5894156
	596.6138994	609.6574518	609.6894488	609.9724499	653.3413886
	653.4309884	673.5925014	699.8421478	703.111737	710.934934
	711.1892528	712.3675864	714.7088193	722.9859913	723.0580321
	736.7238024	777.0580727	818.7355944	826.4857469	830.7487811
	830.7517077	835.264451	835.3255212	839.9551045	839.9929162
	845.7006224	868.2538048	868.285788	913.6851676	913.7765665
	925.5363839	968.0210321	969.4642975	970.7557419	972.2806178
	972.8176581	992.0359219	995.6418939	1005.219678	1005.650874
	1033.905694	1057.969007	1073.007889	1073.960601	1074.309456
	1112.975085	1113.143267	1118.797909	1118.900251	1127.667024
	1127.686265	1138.667307	1169.192273	1169.424683	1212.094942
	1215.129525	1228.68681	1256.931606	1257.041552	1264.981973
	1270.52156	1270.947497	1277.755253	1282.630421	1289.20724
	1289.300608	1300.807871	1301.027352	1346.632463	1364.598557
	1371.722915	1430.38453	1430.55596	1438.100893	1439.197533
	1442.734664	1443.268783	1447.703906	1448.364404	1455.788051
	1482.141873	1482.590711	1486.68772	1495.693135	1521.466288
	1521.734291	1564.878892	1585.752362	1586.01102	1602.153523
	1609.4264	1612.451356	1623.665601	1629.368955	1637.752806
	1669.134077	1673.791353	1686.580087	1691.931144	1697.348844
	1710.215714	1727.111308	1727.484063	1760.298465	1761.11658
	1788.172512	1788.404972	1803.956162	1804.98358	1809.930864
	1823.78967	1828.80486	1829.581067	1837.021072	1854.660103
	1855.649574	1935.121515	1935.874245	1952.808776	1952.927515
	1955.490348	1979.764982	1987.778708	1989.727161	1995.04969
	1998.708381	2007.608495	2010.838773	2022.915334	2023.809711
	2024.712487	2029.883776	2051.333891	2056.874594	2077.286448
	2087.636428	2087.844281	2146.903208	2177.924753	2185.953341
	2186.525251	2194.875851	2203.73406	2205.078399	2232.313303
	2233.789239	2239.63656	2241.14649	2245.257004	2250.750583
	2252.41489	2283.000484	2284.19441	2319.047085	2319.723838
	2349.341449	2349.982103	2359.362313	2368.31407	2378.16499
	2398.313715	2407.091317	2410.56839	2434.321861	2443.044002
	2460.701273	2473.611355	2474.735925	2475.181206	2507.227532
	2531.625372	2539.718552	2548.08828	2553.272881	2593.318105
	2600.897702	2602.308568	2602.560716	2602.989274	2608.061746
	2624.952997	2625.549818	2647.122508	2649.555144	2670.756855";

evsFreeSquareβ05=Flatten@ToExpression@StringSplit[strfr1];
evsFreeSquareβ4=Flatten@ToExpression@StringSplit[strfr2];
evsFreeSquareβ101=Flatten@ToExpression@StringSplit[strfr3];
bthisf1=Bfree[2,2/3, 1];
bthisf2=Bfree[2,1/5, 1];
bthisf3=Bfree[2,1/102, 1];

bLiuthisf1=-BDirLiu[2,-0.5,1];
bLiuthisf2=-BDirLiu[2,3,1];
bLiuthisf3=-BDirLiu[2,100,1];

xtsqf1 = Table[{x, MaTeX[x]}, {x,{750,1500}}];
xtsqf2 = Table[{x, MaTeX[x]}, {x,{1000,2000}}];
xtsqf3 = Table[{x, MaTeX[x]}, {x,{1300,2600}}];
ytsqf= Table[{y, MaTeX["\\ "<>ToString[y]]}, {y,10,40,10}];

figsqfree1=Plot[{MyNlambdaSimple[evsFreeSquareβ05,Λ]-CWeyl[2,-0.5, 1]Λ,4bthisf1 Sqrt[Λ]},{Λ,0,1566},PlotStyle->{Black, Blue}, Ticks->{xtsqf1,ytsqf}, AxesLabel->{MaTeX["\\Lambda"],None},Epilog->Inset[Framed[MaTeX["\\lambda=-0.5"], RoundingRadius->2, ContentPadding->False,FrameMargins->Tiny],Scaled[{0.1,1}],Scaled[{0,1}]]];
figsqfree2=Plot[{MyNlambdaSimple[evsFreeSquareβ4,Λ]-CWeyl[2,3, 1]Λ,4bthisf2 Sqrt[Λ]},{Λ,0,2283},PlotStyle->{Black, Blue},Ticks->{xtsqf2,ytsqf}, AxesLabel->{MaTeX["\\Lambda"],None},Epilog->Inset[Framed[MaTeX["\\lambda=3"], RoundingRadius->2, ContentPadding->False,FrameMargins->Tiny],Scaled[{0.1,1}],Scaled[{0,1}]]]; 
figsqfree3=Plot[{MyNlambdaSimple[evsFreeSquareβ101,Λ]-CWeyl[2,100, 1]Λ,4bthisf3 Sqrt[Λ]},{Λ,0,2671},PlotStyle->{Black, Blue},Ticks->{xtsqf3,ytsqf}, AxesLabel->{MaTeX["\\Lambda"],None},Epilog->Inset[Framed[MaTeX["\\lambda=100"], RoundingRadius->2, ContentPadding->False,FrameMargins->Tiny],Scaled[{0.1,1}],Scaled[{0,1}]]] ;
legendsq=LineLegend[{Black, Blue, Red},MaTeX[{"\\text{computed }\\mathcal{N}_{\\mathrm{free}}(\\Lambda)-a\\Lambda\\qquad\\qquad","4b_{\\mathrm{free}}\\sqrt{\\Lambda}\\qquad\\qquad"}],LegendFunction->None,LegendLayout->{"Row",1}];
figsqfree=GraphicsColumn[{GraphicsRow[{figsqfree1,figsqfree2,figsqfree3},ImageSize->Full, Spacings->{Scaled[0.05],Automatic}],
legendsq},ImageSize->Full, Spacings->{0,Automatic}]

Export["figsqfree.pdf",figsqfree]

figsqfree1new=Plot[{MyNlambdaSimple[evsFreeSquareβ05,Λ]-CWeyl[2,-0.5, 1]Λ,4bthisf1 Sqrt[Λ], 4bLiuthisf1 Sqrt[Λ]},{Λ,0,1566},PlotStyle->{Black, Blue,Red}, Exclusions->None,Ticks->{xtsqf1,ytsqf}, AxesLabel->{MaTeX["\\Lambda"],None},Epilog->Inset[Framed[MaTeX["\\lambda=-0.5"], RoundingRadius->2, ContentPadding->False,FrameMargins->Tiny],Scaled[{0.1,1}],Scaled[{0,1}]]];
figsqfree2new=Plot[{MyNlambdaSimple[evsFreeSquareβ4,Λ]-CWeyl[2,3, 1]Λ,4bthisf2 Sqrt[Λ], 4bLiuthisf2 Sqrt[Λ]},{Λ,0,2283},PlotStyle->{Black, Blue,Red},Exclusions->None,Ticks->{xtsqf2,ytsqf}, AxesLabel->{MaTeX["\\Lambda"],None},Epilog->Inset[Framed[MaTeX["\\lambda=3"], RoundingRadius->2, ContentPadding->False,FrameMargins->Tiny],Scaled[{0.1,1}],Scaled[{0,1}]]]; 
figsqfree3new=Plot[{MyNlambdaSimple[evsFreeSquareβ101,Λ]-CWeyl[2,100, 1]Λ,4bthisf3 Sqrt[Λ], 4bLiuthisf3 Sqrt[Λ]},{Λ,0,2671},PlotStyle->{Black, Blue,Red},Exclusions->None,Ticks->{xtsqf3,ytsqf}, AxesLabel->{MaTeX["\\Lambda"],None},Epilog->Inset[Framed[MaTeX["\\lambda=100"], RoundingRadius->2, ContentPadding->False,FrameMargins->Tiny],Scaled[{0.1,1}],Scaled[{0,1}]]] ;
legendsqnew=LineLegend[{Black, Blue, Red},MaTeX[{"\\text{computed }\\mathcal{N}_{\\mathrm{free}}(\\Lambda)-a\\Lambda\\qquad\\qquad","4b_{\\mathrm{free}}\\sqrt{\\Lambda}\\qquad\\qquad","4b_{\\mathrm{free}}^{\\mathrm{Liu}}\\sqrt{\\Lambda}\\qquad\\qquad"}],LegendFunction->None,LegendLayout->{"Row",1}];
figsqfreenew=GraphicsColumn[{GraphicsRow[{figsqfree1new,figsqfree2new,figsqfree3new},ImageSize->Full, Spacings->{Scaled[0.05],Automatic}],
legendsqnew},ImageSize->Full, Spacings->{0,Automatic}]

Export["figsqfreenew.pdf",figsqfreenew]