kerr_bound_quasinormal_modes.nb

(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 12.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[    232054,       5006]
NotebookOptionsPosition[    229626,       4958]
NotebookOutlinePosition[    229960,       4973]
CellTagsIndexPosition[    229917,       4970]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell[TextData[{
 "Massive scalar field in Kerr background\n",
 StyleBox["(Computes the frequency spectra for quasinormal and bound states \
using the continued fraction method)", "Subtitle"]
}], "Title",
 CellChangeTimes->{{3.800802755801477*^9, 3.800802902093563*^9}, {
  3.800802971353327*^9, 3.80080299521341*^9}, {3.807458638931636*^9, 
  3.8074587037103977`*^9}, {3.807458741414425*^9, 3.807458761179991*^9}, {
  3.807458969445446*^9, 3.807458971733262*^9}, {3.807471273189993*^9, 
  3.807471303321804*^9}},ExpressionUUID->"303eacf5-055b-4a2f-9851-\
660338238a2f"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"ClearAll", "[", "\"\<Global`*\>\"", "]"}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"$MinPrecision", "=", 
    RowBox[{"10", " ", "$MachinePrecision"}]}], ";"}], "\[IndentingNewLine]", 
  
  RowBox[{"(*", 
   RowBox[{
   "Function", " ", "to", " ", "determine", " ", "the", " ", "angular", " ", 
    "frequency"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"findfreq", "[", 
   RowBox[{
   "a_", ",", "\[Mu]_", ",", "l_", ",", "m_", ",", "N_", ",", "state_", ",", 
    "islzero_"}], "]"}], ":=", 
  RowBox[{"(", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"b", "=", 
     RowBox[{"Sqrt", "[", 
      RowBox[{"1", "-", 
       SuperscriptBox["a", "2"]}], "]"}]}], ";", "\[IndentingNewLine]", 
    RowBox[{"If", "[", 
     RowBox[{
      RowBox[{"StringMatchQ", "[", 
       RowBox[{"state", ",", "\"\<*bound*\>\""}], "]"}], ",", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"q", "=", 
         RowBox[{"-", 
          SqrtBox[
           RowBox[{
            SuperscriptBox["\[Mu]", "2"], "-", 
            SuperscriptBox["\[Omega]", "2"]}]]}]}], ",", 
        RowBox[{"\[Omega]0", "=", 
         RowBox[{"\[Mu]", "*", 
          RowBox[{"(", 
           RowBox[{"1", "-", 
            FractionBox[
             SuperscriptBox["\[Mu]", "2"], 
             RowBox[{"2", 
              RowBox[{"(", 
               RowBox[{
                RowBox[{"2", "l"}], "+", "1"}], ")"}]}]]}], ")"}]}]}]}], 
       "}"}], ",", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"q", "=", 
         SqrtBox[
          RowBox[{
           SuperscriptBox["\[Mu]", "2"], "-", 
           SuperscriptBox["\[Omega]", "2"]}]]}], ",", 
        RowBox[{"\[Omega]0", "=", 
         RowBox[{"0.5", "+", 
          RowBox[{"0", "\[ImaginaryI]"}]}]}]}], "}"}]}], "]"}], ";", " ", 
    RowBox[{"(*", 
     RowBox[{
      RowBox[{"While", " ", "passing", " ", "state"}], ",", " ", 
      RowBox[{"\"\<*bound*\>\"", "\[Rule]", 
       RowBox[{"bound", " ", "state"}]}], ",", " ", 
      RowBox[{
      "anything", " ", "else", " ", "will", " ", "simply", " ", "be", " ", 
       "evaluated", " ", "as", " ", "quasinormal", " ", "mode"}]}], "*)"}], 
    " ", "\[IndentingNewLine]", 
    RowBox[{"If", "[", 
     RowBox[{
      RowBox[{"StringMatchQ", "[", 
       RowBox[{"islzero", ",", "\"\<yes\>\""}], "]"}], ",", 
      RowBox[{"\[Omega]0", "=", 
       RowBox[{"\[Mu]", "*", "0.99"}]}]}], "]"}], ";", "\[IndentingNewLine]", 
    
    RowBox[{"\[CapitalLambda]", " ", "=", " ", 
     RowBox[{
      RowBox[{"SpheroidalEigenvalue", "[", 
       RowBox[{"l", ",", "m", ",", 
        RowBox[{"\[ImaginaryI]", "*", "a", 
         SqrtBox[
          RowBox[{
           SuperscriptBox["\[Omega]", "2"], "-", 
           SuperscriptBox["\[Mu]", "2"]}]]}]}], "]"}], "-", 
      RowBox[{
       SuperscriptBox["a", "2"], 
       RowBox[{"(", 
        RowBox[{
         SuperscriptBox["\[Omega]", "2"], "-", 
         SuperscriptBox["\[Mu]", "2"]}], ")"}]}]}]}], ";", 
    RowBox[{"(*", 
     RowBox[{
     "Since", " ", "the", " ", "angular", " ", "equation", " ", "varies", " ",
       "by", " ", "a", " ", "factor", " ", "of", " ", "the", " ", 
      "spheroidicity"}], "*)"}], "\[IndentingNewLine]", 
    RowBox[{"c0", " ", "=", " ", 
     RowBox[{"1", "-", 
      RowBox[{"2", "\[ImaginaryI]", "*", "\[Omega]"}], "-", 
      RowBox[{
       FractionBox[
        RowBox[{"2", "\[ImaginaryI]"}], "b"], 
       RowBox[{"(", 
        RowBox[{"\[Omega]", "-", 
         FractionBox[
          RowBox[{"a", "*", "m"}], "2"]}], ")"}]}]}]}], ";", 
    "\[IndentingNewLine]", 
    RowBox[{"c1", " ", "=", " ", 
     RowBox[{
      RowBox[{"-", "4"}], "+", 
      RowBox[{"4", "\[ImaginaryI]", 
       RowBox[{"(", 
        RowBox[{"\[Omega]", "-", 
         RowBox[{"\[ImaginaryI]", "*", "q", 
          RowBox[{"(", 
           RowBox[{"1", "+", "b"}], ")"}]}]}], ")"}]}], "+", 
      RowBox[{
       FractionBox[
        RowBox[{"4", "\[ImaginaryI]"}], "b"], 
       RowBox[{"(", 
        RowBox[{"\[Omega]", "-", 
         FractionBox[
          RowBox[{"a", "*", "m"}], "2"]}], ")"}]}], "-", 
      FractionBox[
       RowBox[{"2", 
        RowBox[{"(", 
         RowBox[{
          SuperscriptBox["\[Omega]", "2"], "+", 
          SuperscriptBox["q", "2"]}], ")"}]}], "q"]}]}], ";", 
    "\[IndentingNewLine]", 
    RowBox[{"c2", " ", "=", " ", 
     RowBox[{"3", "-", 
      RowBox[{"2", "\[ImaginaryI]", "*", "\[Omega]"}], "-", 
      FractionBox[
       RowBox[{"2", 
        RowBox[{"(", 
         RowBox[{
          SuperscriptBox["q", "2"], "-", 
          SuperscriptBox["\[Omega]", "2"]}], ")"}]}], "q"], "-", 
      RowBox[{
       FractionBox[
        RowBox[{"2", "\[ImaginaryI]"}], "b"], 
       RowBox[{"(", 
        RowBox[{"\[Omega]", "-", 
         FractionBox[
          RowBox[{"a", "*", "m"}], "2"]}], ")"}]}]}]}], ";", 
    "\[IndentingNewLine]", 
    RowBox[{"c3", " ", "=", " ", 
     RowBox[{
      FractionBox[
       RowBox[{"2", "\[ImaginaryI]", 
        SuperscriptBox[
         RowBox[{"(", 
          RowBox[{"\[Omega]", "-", 
           RowBox[{"\[ImaginaryI]", "*", "q"}]}], ")"}], "3"]}], "q"], "+", 
      RowBox[{"2", 
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{"\[Omega]", "-", 
          RowBox[{"\[ImaginaryI]", "*", "q"}]}], ")"}], "2"], "b"}], " ", "+", 
      RowBox[{
       SuperscriptBox["q", "2"], "*", 
       SuperscriptBox["a", "2"]}], "+", 
      RowBox[{"2", "\[ImaginaryI]", "*", "q", "*", "a", "*", "m"}], "-", 
      "\[CapitalLambda]", "-", "1", "-", 
      FractionBox[
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{"\[Omega]", "-", 
          RowBox[{"\[ImaginaryI]", "*", "q"}]}], ")"}], "2"], "q"], "+", 
      RowBox[{"2", "q", "*", "b"}], "+", 
      RowBox[{
       FractionBox[
        RowBox[{"2", "\[ImaginaryI]"}], "b"], 
       RowBox[{"(", 
        RowBox[{
         FractionBox[
          SuperscriptBox[
           RowBox[{"(", 
            RowBox[{"\[Omega]", "-", 
             RowBox[{"\[ImaginaryI]", "*", "q"}]}], ")"}], "2"], "q"], "+", 
         "1"}], ")"}], 
       RowBox[{"(", 
        RowBox[{"\[Omega]", "-", 
         FractionBox[
          RowBox[{"a", "*", "m"}], "2"]}], ")"}]}]}]}], ";", 
    "\[IndentingNewLine]", 
    RowBox[{"c4", " ", "=", 
     RowBox[{
      FractionBox[
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{"\[Omega]", "-", 
          RowBox[{"\[ImaginaryI]", "*", "q"}]}], ")"}], "4"], 
       SuperscriptBox["q", "2"]], "+", 
      FractionBox[
       RowBox[{"2", "\[ImaginaryI]", "*", "\[Omega]", 
        SuperscriptBox[
         RowBox[{"(", 
          RowBox[{"\[Omega]", "-", 
           RowBox[{"\[ImaginaryI]", "*", "q"}]}], ")"}], "2"]}], "q"], "-", 
      RowBox[{
       FractionBox[
        RowBox[{"2", "\[ImaginaryI]"}], "b"], 
       FractionBox[
        SuperscriptBox[
         RowBox[{"(", 
          RowBox[{"\[Omega]", "-", 
           RowBox[{"\[ImaginaryI]", "*", "q"}]}], ")"}], "2"], "q"], 
       RowBox[{"(", 
        RowBox[{"\[Omega]", "-", 
         FractionBox[
          RowBox[{"a", "*", "m"}], "2"]}], ")"}]}]}]}], ";", 
    "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"\[Alpha]", "[", "n_", "]"}], ":=", " ", 
     RowBox[{
      SuperscriptBox["n", "2"], "+", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"c0", "+", "1"}], ")"}], "n"}], "+", "c0"}]}], ";", 
    "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"\[Beta]", "[", "n_", "]"}], ":=", " ", 
     RowBox[{
      RowBox[{
       RowBox[{"-", "2"}], 
       SuperscriptBox["n", "2"]}], "+", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"c1", "+", "2"}], ")"}], "n"}], "+", "c3"}]}], ";", 
    "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"\[Gamma]", "[", "n_", "]"}], ":=", 
     RowBox[{
      SuperscriptBox["n", "2"], "+", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"c2", "-", "3"}], ")"}], "n"}], "+", "c4"}]}], ";", 
    "\[IndentingNewLine]", 
    RowBox[{"temp", "=", "1"}], ";", "\[IndentingNewLine]", 
    RowBox[{"For", "[", 
     RowBox[{
      RowBox[{"n", "=", "N"}], ",", 
      RowBox[{"n", ">", "0"}], ",", 
      RowBox[{"n", "--"}], ",", 
      RowBox[{"temp", "=", 
       FractionBox[
        RowBox[{"\[Gamma]", "[", "n", "]"}], 
        RowBox[{
         RowBox[{"\[Beta]", "[", "n", "]"}], "-", 
         RowBox[{
          RowBox[{"\[Alpha]", "[", "n", "]"}], "*", "temp"}]}]]}]}], "]"}], 
    ";", "\[IndentingNewLine]", 
    RowBox[{"recur", " ", "=", " ", 
     RowBox[{
      FractionBox[
       RowBox[{"\[Beta]", "[", "0", "]"}], 
       RowBox[{"\[Alpha]", "[", "0", "]"}]], "-", "temp"}]}], ";", 
    "\[IndentingNewLine]", 
    RowBox[{"sol", " ", "=", " ", 
     RowBox[{"FindRoot", "[", 
      RowBox[{
       RowBox[{"recur", "\[Equal]", "0"}], ",", 
       RowBox[{"{", 
        RowBox[{"\[Omega]", ",", "\[Omega]0"}], "}"}], ",", 
       RowBox[{"MaxIterations", "\[Rule]", "500"}]}], "]"}]}]}], 
   "\[IndentingNewLine]", ")"}]}]}], "Input",
 CellChangeTimes->{{3.805900059298888*^9, 3.8059001559074574`*^9}, {
   3.805900258655409*^9, 3.805900360780531*^9}, {3.805906783951248*^9, 
   3.805906833462723*^9}, {3.805906912614555*^9, 3.805907386347287*^9}, {
   3.805907419521076*^9, 3.8059075561078444`*^9}, {3.805907595263134*^9, 
   3.805907654858523*^9}, {3.805907713818461*^9, 3.805907809091701*^9}, {
   3.8059078419058437`*^9, 3.805907882895102*^9}, {3.805907916212482*^9, 
   3.8059079299489*^9}, {3.805907963215931*^9, 3.80590796690841*^9}, {
   3.8059080096757097`*^9, 3.8059081128350077`*^9}, {3.8059081823106728`*^9, 
   3.805908193546445*^9}, {3.805909441322275*^9, 3.805909660801087*^9}, {
   3.805909719321475*^9, 3.805909729256063*^9}, {3.805909779414567*^9, 
   3.805909817001157*^9}, {3.805909851747795*^9, 3.805909853122303*^9}, 
   3.805909935099144*^9, {3.805909977371159*^9, 3.805910010921391*^9}, {
   3.8059100701435833`*^9, 3.805910107650588*^9}, {3.805910285116736*^9, 
   3.805910441654604*^9}, {3.805910474834399*^9, 3.80591056945452*^9}, {
   3.8059106457747507`*^9, 3.805910645959928*^9}, {3.80591068291051*^9, 
   3.805910703699691*^9}, {3.8059107465155487`*^9, 3.805910815571587*^9}, {
   3.805910870204514*^9, 3.805910924032343*^9}, {3.805911005372319*^9, 
   3.805911182051648*^9}, {3.805911215520053*^9, 3.805911223949286*^9}, {
   3.805911321095128*^9, 3.805911445711543*^9}, {3.8059115401025133`*^9, 
   3.805911562874977*^9}, {3.805911714821*^9, 3.8059117257848673`*^9}, {
   3.805911785853059*^9, 3.8059118428316*^9}, {3.805911880011401*^9, 
   3.805911895438814*^9}, {3.805912261485903*^9, 3.8059122634452*^9}, 
   3.8059123350358877`*^9, {3.805913384570897*^9, 3.805913391513608*^9}, {
   3.8059135190364122`*^9, 3.8059135493286943`*^9}, {3.805913586604623*^9, 
   3.805913599526478*^9}, {3.805914750419435*^9, 3.805914751059073*^9}, {
   3.805914894031591*^9, 3.8059148944648647`*^9}, {3.80592617017092*^9, 
   3.805926170713068*^9}, {3.805983458727265*^9, 3.80598346234023*^9}, {
   3.8059841524714413`*^9, 3.8059841676106787`*^9}, {3.805984217560062*^9, 
   3.805984242094308*^9}, {3.805984339488752*^9, 3.805984341905311*^9}, {
   3.80598537938941*^9, 3.80598538266078*^9}, {3.805985942763674*^9, 
   3.805985952179035*^9}, {3.805986178145959*^9, 3.805986262316373*^9}, {
   3.80598716645243*^9, 3.8059871678949337`*^9}, {3.805987861409052*^9, 
   3.8059878724632807`*^9}, {3.805988130089933*^9, 3.8059881325620937`*^9}, {
   3.805988168248722*^9, 3.805988188681293*^9}, {3.805988287296574*^9, 
   3.805988289744109*^9}, {3.805988379796647*^9, 3.805988383866461*^9}, {
   3.805988420147842*^9, 3.805988444031516*^9}, {3.8059886609703493`*^9, 
   3.805988681676919*^9}, 3.805989349013332*^9, 3.8059922418877993`*^9, {
   3.805992952029746*^9, 3.805992953035905*^9}, 3.805993065155972*^9, {
   3.805993161455186*^9, 3.805993163790373*^9}, {3.806066005355773*^9, 
   3.806066263569633*^9}, {3.8060688070385857`*^9, 3.806068857546406*^9}, {
   3.8060690228381357`*^9, 3.806069048736617*^9}, 3.806069415825446*^9, {
   3.806071060696178*^9, 3.806071079196434*^9}, {3.8060749167717133`*^9, 
   3.8060749305129833`*^9}, {3.8060750890481377`*^9, 
   3.8060751131778517`*^9}, {3.806075273105019*^9, 3.806075273631317*^9}, {
   3.80607582703852*^9, 3.806075912077928*^9}, {3.806077314940445*^9, 
   3.8060773170223618`*^9}, {3.806078392502452*^9, 3.806078398115529*^9}, {
   3.806080131383812*^9, 3.806080154672099*^9}, 3.806080297010788*^9, {
   3.806080347679583*^9, 3.806080365480091*^9}, {3.806157806616324*^9, 
   3.8061578129765587`*^9}, {3.806158080551692*^9, 3.8061580877733917`*^9}, {
   3.806158127671382*^9, 3.806158190807547*^9}, {3.806158224824869*^9, 
   3.806158265205119*^9}, {3.806158308443284*^9, 3.806158326176991*^9}, {
   3.8061584523998747`*^9, 3.806158518446899*^9}, {3.8061585534805527`*^9, 
   3.806158601307417*^9}, {3.8061586489657288`*^9, 3.8061586506270647`*^9}, {
   3.806158681312426*^9, 3.8061586816107483`*^9}, {3.806158713147992*^9, 
   3.806158714483045*^9}, {3.806158767598744*^9, 3.806158768575305*^9}, 
   3.806159069988624*^9, {3.806159665592596*^9, 3.806159674078319*^9}, {
   3.806159908778006*^9, 3.806159910251503*^9}, {3.806160640983161*^9, 
   3.806160656325716*^9}, {3.806160699362442*^9, 3.806160709451145*^9}, {
   3.8061612201716003`*^9, 3.806161222288913*^9}, {3.806161753382678*^9, 
   3.8061617894531193`*^9}, {3.806161828669245*^9, 3.806161854551347*^9}, {
   3.806161908127927*^9, 3.806161971799494*^9}, {3.80745880802255*^9, 
   3.8074588086932707`*^9}, 3.807458983584454*^9},
 CellLabel->"In[2]:=",ExpressionUUID->"fb5faef1-8bcc-48f9-b703-e83317d1e09e"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", 
   RowBox[{
   "Plotting", " ", "the", " ", "quasinormal", " ", "frequencies", " ", "for",
     " ", "a", " ", "bunch", " ", "of", " ", "spins"}], "*)"}], 
  "\[IndentingNewLine]", 
  RowBox[{"\[Omega]", "/.", 
   RowBox[{"findfreq", "[", 
    RowBox[{"0.95", ",", "0", ",", "1", ",", 
     RowBox[{"-", "1"}], ",", "200", ",", "\"\<quasinormal\>\"", ",", 
     "\"\<no\>\""}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.805900059298888*^9, 3.8059001559074574`*^9}, {
   3.805900258655409*^9, 3.805900360780531*^9}, {3.805906783951248*^9, 
   3.805906833462723*^9}, {3.805906912614555*^9, 3.805907386347287*^9}, {
   3.805907419521076*^9, 3.8059075561078444`*^9}, {3.805907595263134*^9, 
   3.805907654858523*^9}, {3.805907713818461*^9, 3.805907809091701*^9}, {
   3.8059078419058437`*^9, 3.805907882895102*^9}, {3.805907916212482*^9, 
   3.8059079299489*^9}, {3.805907963215931*^9, 3.80590796690841*^9}, {
   3.8059080096757097`*^9, 3.8059081128350077`*^9}, {3.8059081823106728`*^9, 
   3.805908193546445*^9}, {3.805909441322275*^9, 3.805909660801087*^9}, {
   3.805909719321475*^9, 3.805909729256063*^9}, {3.805909779414567*^9, 
   3.805909817001157*^9}, {3.805909851747795*^9, 3.805909853122303*^9}, 
   3.805909935099144*^9, {3.805909977371159*^9, 3.805910010921391*^9}, {
   3.8059100701435833`*^9, 3.805910107650588*^9}, {3.805910285116736*^9, 
   3.805910441654604*^9}, {3.805910474834399*^9, 3.80591056945452*^9}, {
   3.8059106457747507`*^9, 3.805910645959928*^9}, {3.80591068291051*^9, 
   3.805910703699691*^9}, {3.8059107465155487`*^9, 3.805910815571587*^9}, {
   3.805910870204514*^9, 3.805910924032343*^9}, {3.805911005372319*^9, 
   3.805911182051648*^9}, {3.805911215520053*^9, 3.805911223949286*^9}, {
   3.805911321095128*^9, 3.805911445711543*^9}, {3.8059115401025133`*^9, 
   3.805911562874977*^9}, {3.805911714821*^9, 3.805911732571947*^9}, {
   3.805912266403262*^9, 3.8059123440167503`*^9}, {3.805913399101294*^9, 
   3.8059134140962963`*^9}, {3.805913452894232*^9, 3.80591345507253*^9}, {
   3.805913489494843*^9, 3.805913512063972*^9}, {3.805913604888558*^9, 
   3.805913605162548*^9}, 3.805914502636875*^9, {3.805914724895647*^9, 
   3.8059147314243298`*^9}, {3.805914785083248*^9, 3.805914963057639*^9}, {
   3.805915003058117*^9, 3.805915052943758*^9}, {3.805915141810622*^9, 
   3.805915155274927*^9}, {3.80592452333957*^9, 3.805924537986411*^9}, {
   3.805930812700094*^9, 3.8059308460799713`*^9}, {3.805930919718371*^9, 
   3.805930928042488*^9}, 3.80593096227921*^9, {3.805931398048492*^9, 
   3.805931410575218*^9}, {3.805982905068416*^9, 3.805982960017633*^9}, {
   3.805984175547433*^9, 3.805984200157148*^9}, {3.8059876111653757`*^9, 
   3.805987611447248*^9}, {3.805987958477262*^9, 3.8059879860702763`*^9}, {
   3.80598850881124*^9, 3.805988510826281*^9}, 3.805988669926757*^9, 
   3.806066251355298*^9, {3.806157844475954*^9, 3.80615784473768*^9}, {
   3.80615804979523*^9, 3.806158054363716*^9}, {3.806158617555435*^9, 
   3.806158804029684*^9}, {3.8062490347537203`*^9, 3.806249037178308*^9}, {
   3.8074589068405848`*^9, 3.807458958973847*^9}},
 CellLabel->"In[8]:=",ExpressionUUID->"f600187f-5a1a-4bed-916a-d2eb3cd7affb"],

Cell[BoxData[
 RowBox[{"0.24137210469028325`", "\[VeryThinSpace]", "-", 
  RowBox[{"0.09412411427561686`", " ", "\[ImaginaryI]"}]}]], "Output",
 CellChangeTimes->{3.8074588268176813`*^9, 3.807458988381401*^9},
 CellLabel->"Out[8]=",ExpressionUUID->"d5f33b79-1e40-48b3-a78d-e6a0344964c1"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", 
   RowBox[{
    RowBox[{
    "Plotting", " ", "quasinormal", " ", "mode", " ", "frequencies", " ", 
     "for", " ", "l"}], "=", "1"}], "*)"}], "\[IndentingNewLine]", 
  RowBox[{"ListPlot", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Re", "[", 
           RowBox[{"\[Omega]", "/.", 
            RowBox[{"findfreq", "[", 
             RowBox[{
             "a", ",", "0", ",", "1", ",", "1", ",", "100", ",", 
              "\"\<quasinormal\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], ",", 
          RowBox[{"-", 
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "a", ",", "0", ",", "1", ",", "1", ",", "100", ",", 
               "\"\<quasinormal\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}]}]}],
          "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"a", ",", 
          RowBox[{"{", 
           RowBox[{
           "0", ",", "0.1", ",", "0.2", ",", "0.3", ",", "0.4", ",", "0.5", 
            ",", "0.6", ",", "0.7", ",", "0.8", ",", "0.9", ",", "0.92", ",", 
            "0.94", ",", "0.95", ",", "0.96", ",", "0.98", ",", "0.99", ",", 
            "0.995"}], "}"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Re", "[", 
           RowBox[{"\[Omega]", "/.", 
            RowBox[{"findfreq", "[", 
             RowBox[{
             "a", ",", "0.1", ",", "1", ",", "1", ",", "100", ",", 
              "\"\<quasinormal\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], ",", 
          RowBox[{"-", 
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "a", ",", "0.1", ",", "1", ",", "1", ",", "100", ",", 
               "\"\<quasinormal\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}]}]}],
          "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"a", ",", 
          RowBox[{"{", 
           RowBox[{
           "0", ",", "0.1", ",", "0.2", ",", "0.3", ",", "0.4", ",", "0.5", 
            ",", "0.6", ",", "0.7", ",", "0.8", ",", "0.9", ",", "0.92", ",", 
            "0.94", ",", "0.95", ",", "0.96", ",", "0.98", ",", "0.99", ",", 
            "0.995"}], "}"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Re", "[", 
           RowBox[{"\[Omega]", "/.", 
            RowBox[{"findfreq", "[", 
             RowBox[{
             "a", ",", "0.2", ",", "1", ",", "1", ",", "100", ",", 
              "\"\<quasinormal\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], ",", 
          RowBox[{"-", 
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "a", ",", "0.2", ",", "1", ",", "1", ",", "100", ",", 
               "\"\<quasinormal\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}]}]}],
          "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"a", ",", 
          RowBox[{"{", 
           RowBox[{
           "0", ",", "0.1", ",", "0.2", ",", "0.3", ",", "0.4", ",", "0.5", 
            ",", "0.6", ",", "0.7", ",", "0.8", ",", "0.9", ",", "0.92", ",", 
            "0.94", ",", "0.95", ",", "0.96", ",", "0.98", ",", "0.99", ",", 
            "0.995"}], "}"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Re", "[", 
           RowBox[{"\[Omega]", "/.", 
            RowBox[{"findfreq", "[", 
             RowBox[{
             "a", ",", "0.3", ",", "1", ",", "1", ",", "100", ",", 
              "\"\<quasinormal\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], ",", 
          RowBox[{"-", 
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "a", ",", "0.3", ",", "1", ",", "1", ",", "100", ",", 
               "\"\<quasinormal\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}]}]}],
          "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"a", ",", 
          RowBox[{"{", 
           RowBox[{
           "0", ",", "0.1", ",", "0.2", ",", "0.3", ",", "0.4", ",", "0.5", 
            ",", "0.6", ",", "0.7", ",", "0.8", ",", "0.9", ",", "0.92", ",", 
            "0.94", ",", "0.95", ",", "0.96", ",", "0.98", ",", "0.99", ",", 
            "0.995"}], "}"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Re", "[", 
           RowBox[{"\[Omega]", "/.", 
            RowBox[{"findfreq", "[", 
             RowBox[{
             "a", ",", "0", ",", "1", ",", "0", ",", "100", ",", 
              "\"\<quasinormal\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], ",", 
          RowBox[{"-", 
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "a", ",", "0", ",", "1", ",", "0", ",", "100", ",", 
               "\"\<quasinormal\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}]}]}],
          "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"a", ",", 
          RowBox[{"{", 
           RowBox[{
           "0", ",", "0.1", ",", "0.2", ",", "0.3", ",", "0.4", ",", "0.5", 
            ",", "0.6", ",", "0.7", ",", "0.8", ",", "0.9", ",", "0.92", ",", 
            "0.94", ",", "0.95", ",", "0.96", ",", "0.98", ",", "0.99", ",", 
            "0.995"}], "}"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Re", "[", 
           RowBox[{"\[Omega]", "/.", 
            RowBox[{"findfreq", "[", 
             RowBox[{
             "a", ",", "0.1", ",", "1", ",", "0", ",", "100", ",", 
              "\"\<quasinormal\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], ",", 
          RowBox[{"-", 
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "a", ",", "0.1", ",", "1", ",", "0", ",", "100", ",", 
               "\"\<quasinormal\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}]}]}],
          "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"a", ",", 
          RowBox[{"{", 
           RowBox[{
           "0", ",", "0.1", ",", "0.2", ",", "0.3", ",", "0.4", ",", "0.5", 
            ",", "0.6", ",", "0.7", ",", "0.8", ",", "0.9", ",", "0.92", ",", 
            "0.94", ",", "0.95", ",", "0.96", ",", "0.98", ",", "0.99", ",", 
            "0.995"}], "}"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Re", "[", 
           RowBox[{"\[Omega]", "/.", 
            RowBox[{"findfreq", "[", 
             RowBox[{
             "a", ",", "0.2", ",", "1", ",", "0", ",", "100", ",", 
              "\"\<quasinormal\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], ",", 
          RowBox[{"-", 
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "a", ",", "0.2", ",", "1", ",", "0", ",", "100", ",", 
               "\"\<quasinormal\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}]}]}],
          "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"a", ",", 
          RowBox[{"{", 
           RowBox[{
           "0", ",", "0.1", ",", "0.2", ",", "0.3", ",", "0.4", ",", "0.5", 
            ",", "0.6", ",", "0.7", ",", "0.8", ",", "0.9", ",", "0.92", ",", 
            "0.94", ",", "0.95", ",", "0.96", ",", "0.98", ",", "0.99", ",", 
            "0.995"}], "}"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Re", "[", 
           RowBox[{"\[Omega]", "/.", 
            RowBox[{"findfreq", "[", 
             RowBox[{
             "a", ",", "0.3", ",", "1", ",", "0", ",", "100", ",", 
              "\"\<quasinormal\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], ",", 
          RowBox[{"-", 
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "a", ",", "0.3", ",", "1", ",", "0", ",", "100", ",", 
               "\"\<quasinormal\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}]}]}],
          "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"a", ",", 
          RowBox[{"{", 
           RowBox[{
           "0", ",", "0.1", ",", "0.2", ",", "0.3", ",", "0.4", ",", "0.5", 
            ",", "0.6", ",", "0.7", ",", "0.8", ",", "0.9", ",", "0.92", ",", 
            "0.94", ",", "0.95", ",", "0.96", ",", "0.98", ",", "0.99", ",", 
            "0.995"}], "}"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Re", "[", 
           RowBox[{"\[Omega]", "/.", 
            RowBox[{"findfreq", "[", 
             RowBox[{"a", ",", "0", ",", "1", ",", 
              RowBox[{"-", "1"}], ",", "100", ",", "\"\<quasinormal\>\"", 
              ",", "\"\<no\>\""}], "]"}]}], "]"}], ",", 
          RowBox[{"-", 
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{"a", ",", "0", ",", "1", ",", 
               RowBox[{"-", "1"}], ",", "100", ",", "\"\<quasinormal\>\"", 
               ",", "\"\<no\>\""}], "]"}]}], "]"}]}]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"a", ",", 
          RowBox[{"{", 
           RowBox[{
           "0", ",", "0.1", ",", "0.2", ",", "0.3", ",", "0.4", ",", "0.5", 
            ",", "0.6", ",", "0.7", ",", "0.8", ",", "0.9", ",", "0.92", ",", 
            "0.94", ",", "0.95", ",", "0.96", ",", "0.98", ",", "0.99", ",", 
            "0.995"}], "}"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Re", "[", 
           RowBox[{"\[Omega]", "/.", 
            RowBox[{"findfreq", "[", 
             RowBox[{"a", ",", "0.1", ",", "1", ",", 
              RowBox[{"-", "1"}], ",", "100", ",", "\"\<quasinormal\>\"", 
              ",", "\"\<no\>\""}], "]"}]}], "]"}], ",", 
          RowBox[{"-", 
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{"a", ",", "0.1", ",", "1", ",", 
               RowBox[{"-", "1"}], ",", "100", ",", "\"\<quasinormal\>\"", 
               ",", "\"\<no\>\""}], "]"}]}], "]"}]}]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"a", ",", 
          RowBox[{"{", 
           RowBox[{
           "0", ",", "0.1", ",", "0.2", ",", "0.3", ",", "0.4", ",", "0.5", 
            ",", "0.6", ",", "0.7", ",", "0.8", ",", "0.9", ",", "0.92", ",", 
            "0.94", ",", "0.95", ",", "0.96", ",", "0.98", ",", "0.99", ",", 
            "0.995"}], "}"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Re", "[", 
           RowBox[{"\[Omega]", "/.", 
            RowBox[{"findfreq", "[", 
             RowBox[{"a", ",", "0.2", ",", "1", ",", 
              RowBox[{"-", "1"}], ",", "100", ",", "\"\<quasinormal\>\"", 
              ",", "\"\<no\>\""}], "]"}]}], "]"}], ",", 
          RowBox[{"-", 
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{"a", ",", "0.2", ",", "1", ",", 
               RowBox[{"-", "1"}], ",", "100", ",", "\"\<quasinormal\>\"", 
               ",", "\"\<no\>\""}], "]"}]}], "]"}]}]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"a", ",", 
          RowBox[{"{", 
           RowBox[{
           "0", ",", "0.1", ",", "0.2", ",", "0.3", ",", "0.4", ",", "0.5", 
            ",", "0.6", ",", "0.7", ",", "0.8", ",", "0.9", ",", "0.92", ",", 
            "0.94", ",", "0.95", ",", "0.96", ",", "0.98", ",", "0.99", ",", 
            "0.995"}], "}"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Re", "[", 
           RowBox[{"\[Omega]", "/.", 
            RowBox[{"findfreq", "[", 
             RowBox[{"a", ",", "0.3", ",", "1", ",", 
              RowBox[{"-", "1"}], ",", "100", ",", "\"\<quasinormal\>\"", 
              ",", "\"\<no\>\""}], "]"}]}], "]"}], ",", 
          RowBox[{"-", 
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{"a", ",", "0.3", ",", "1", ",", 
               RowBox[{"-", "1"}], ",", "100", ",", "\"\<quasinormal\>\"", 
               ",", "\"\<no\>\""}], "]"}]}], "]"}]}]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"a", ",", 
          RowBox[{"{", 
           RowBox[{
           "0", ",", "0.1", ",", "0.2", ",", "0.3", ",", "0.4", ",", "0.5", 
            ",", "0.6", ",", "0.7", ",", "0.8", ",", "0.9", ",", "0.92", ",", 
            "0.94", ",", "0.95", ",", "0.96", ",", "0.98", ",", " ", "0.99", 
            ",", "0.995"}], "}"}]}], "}"}]}], "]"}]}], "}"}], ",", 
    RowBox[{"PlotStyle", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
      "Red", ",", "Red", ",", "Red", ",", "Red", ",", "Green", ",", "Green", 
       ",", "Green", ",", "Green", ",", "Blue", ",", "Blue", ",", "Blue", ",",
        "Blue"}], "}"}]}], ",", 
    RowBox[{"Joined", "\[Rule]", "False"}], ",", 
    RowBox[{"Mesh", "\[Rule]", "True"}], ",", 
    RowBox[{"AxesLabel", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{"\"\<Re(\[Omega])\>\"", ",", "\"\<-Im(\[Omega])\>\""}], "}"}]}],
     ",", 
    RowBox[{"ImageSize", "\[Rule]", "Large"}], ",", 
    RowBox[{"PlotRange", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"0.2", ",", "0.55"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"0.02", ",", "0.11"}], "}"}]}], "}"}]}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.805911751687701*^9, 3.805911775946032*^9}, 
   3.805912347950191*^9, {3.80591525677773*^9, 3.805915264454012*^9}, {
   3.805923103021019*^9, 3.80592325317212*^9}, {3.805923380210314*^9, 
   3.805923452879683*^9}, {3.8059235322728767`*^9, 3.8059235367028*^9}, {
   3.8059236037925663`*^9, 3.805923616713677*^9}, {3.805923736284194*^9, 
   3.805923739502713*^9}, {3.805923774132803*^9, 3.8059238221402693`*^9}, {
   3.80592385381525*^9, 3.805923855306294*^9}, {3.8059243661975193`*^9, 
   3.805924374518959*^9}, {3.805924592769023*^9, 3.805924782642645*^9}, {
   3.8059252751130238`*^9, 3.805925298300166*^9}, {3.805925396483963*^9, 
   3.805925478568001*^9}, 3.805925549482914*^9, {3.80592612705729*^9, 
   3.805926128989101*^9}, {3.80592633941502*^9, 3.80592640848639*^9}, {
   3.805926463377355*^9, 3.8059264667141533`*^9}, {3.8059265203749723`*^9, 
   3.8059265434674807`*^9}, {3.805930990369968*^9, 3.805931000650567*^9}, {
   3.805931415802086*^9, 3.805931464183941*^9}, {3.805977812391182*^9, 
   3.805977816206505*^9}, {3.805987561217162*^9, 3.805987645540373*^9}, {
   3.806075332238759*^9, 3.806075370310554*^9}, {3.806158835927485*^9, 
   3.806158993840207*^9}, {3.8061591869275227`*^9, 3.806159187045313*^9}, {
   3.8061620064470873`*^9, 3.8061620692031527`*^9}, {3.8074590266127*^9, 
   3.807459078984704*^9}, {3.807459377119862*^9, 3.8074594125494537`*^9}, {
   3.80746036150629*^9, 3.807460401840148*^9}, {3.8074605163780603`*^9, 
   3.8074605732424*^9}},
 CellLabel->"In[13]:=",ExpressionUUID->"72391553-852b-47ee-8d2c-da44eddf6ab9"],

Cell[BoxData[
 TemplateBox[{
  "FindRoot","lstol",
   "\"The line search decreased the step size to within tolerance specified \
by AccuracyGoal and PrecisionGoal but was unable to find a sufficient \
decrease in the merit function. You may need more than \
\\!\\(\\*RowBox[{\\\"MachinePrecision\\\"}]\\) digits of working precision to \
meet these tolerances.\"",2,13,17,19812611925877513508,"Local"},
  "MessageTemplate"]], "Message", "MSG",
 CellChangeTimes->{3.807459113929449*^9, 3.807460765393455*^9},
 CellLabel->
  "During evaluation of \
In[13]:=",ExpressionUUID->"ece68250-6f23-4538-b627-0997d5cd2ad6"],

Cell[BoxData[
 TemplateBox[{
  "FindRoot","lstol",
   "\"The line search decreased the step size to within tolerance specified \
by AccuracyGoal and PrecisionGoal but was unable to find a sufficient \
decrease in the merit function. You may need more than \
\\!\\(\\*RowBox[{\\\"MachinePrecision\\\"}]\\) digits of working precision to \
meet these tolerances.\"",2,13,18,19812611925877513508,"Local"},
  "MessageTemplate"]], "Message", "MSG",
 CellChangeTimes->{3.807459113929449*^9, 3.8074607695858927`*^9},
 CellLabel->
  "During evaluation of \
In[13]:=",ExpressionUUID->"8fd6aef4-8fba-48cf-bfeb-f41194a50123"],

Cell[BoxData[
 TemplateBox[{
  "FindRoot","lstol",
   "\"The line search decreased the step size to within tolerance specified \
by AccuracyGoal and PrecisionGoal but was unable to find a sufficient \
decrease in the merit function. You may need more than \
\\!\\(\\*RowBox[{\\\"MachinePrecision\\\"}]\\) digits of working precision to \
meet these tolerances.\"",2,13,19,19812611925877513508,"Local"},
  "MessageTemplate"]], "Message", "MSG",
 CellChangeTimes->{3.807459113929449*^9, 3.807460780948105*^9},
 CellLabel->
  "During evaluation of \
In[13]:=",ExpressionUUID->"276ab943-4509-4d01-905e-7a7897190d2b"],

Cell[BoxData[
 TemplateBox[{
  "General","stop",
   "\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"FindRoot\\\", \
\\\"::\\\", \\\"lstol\\\"}], \\\"MessageName\\\"]\\) will be suppressed \
during this calculation.\"",2,13,20,19812611925877513508,"Local"},
  "MessageTemplate"]], "Message", "MSG",
 CellChangeTimes->{3.807459113929449*^9, 3.8074607809523573`*^9},
 CellLabel->
  "During evaluation of \
In[13]:=",ExpressionUUID->"25b21a15-701b-4df5-97c9-1e7eea55e7bb"],

Cell[BoxData[
 GraphicsBox[{{}, GraphicsComplexBox[CompressedData["
1:eJztl3k0Vfvfx4+4IrMMEbeURCFSKOqNhNyKDA2SdIsGhQxxNZDSRElIGRpQ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    "], {{
      {RGBColor[1, 0, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6], PointBox[{83, 84, 100, 101, 117, 118, 134, 135, 150, 151, 152, 
        167, 168, 169, 184, 185, 186}]}, 
      {RGBColor[1, 0, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6], PointBox[{202, 203, 219, 220, 221, 222, 223, 224, 225, 226, 227, 
        228, 229, 230, 231, 232, 233}]}, 
      {RGBColor[1, 0, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6], PointBox[{234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 
        245, 246, 247, 248, 249, 250}]}, 
      {RGBColor[1, 0, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6], PointBox[{251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 
        262, 263, 264, 265, 266, 267}]}, 
      {RGBColor[0, 1, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6], PointBox[{268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 
        279, 280, 281, 282, 283, 284}]}, 
      {RGBColor[0, 1, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6], PointBox[{285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 
        296, 297, 298, 299, 300, 301}]}, 
      {RGBColor[0, 1, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6], PointBox[{302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 
        313, 314, 315, 316, 317, 318}]}, 
      {RGBColor[0, 1, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6], PointBox[{319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 
        330, 331, 332, 333, 334, 335}]}, 
      {RGBColor[0, 0, 1], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6], PointBox[{336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 
        347, 348, 349, 350, 351, 352}]}, 
      {RGBColor[0, 0, 1], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6], PointBox[{353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 
        364, 365, 366, 367, 368, 369}]}, 
      {RGBColor[0, 0, 1], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6], PointBox[{370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 
        381, 382, 383, 384, 385, 386}]}, 
      {RGBColor[0, 0, 1], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6], PointBox[{387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 
        398, 399, 400, 401, 402, 403}]}}, {
      {RGBColor[1, 0, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[1, 0, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[1, 0, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[1, 0, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[0, 1, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[0, 1, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[0, 1, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[0, 1, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[0, 0, 1], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[0, 0, 1], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[0, 0, 1], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[0, 0, 1], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}}, {
      {RGBColor[1, 0, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[1, 0, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[1, 0, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[1, 0, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[0, 1, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[0, 1, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[0, 1, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[0, 1, 0], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[0, 0, 1], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[0, 0, 1], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[0, 0, 1], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, 
      {RGBColor[0, 0, 1], PointSize[0.009166666666666668], AbsoluteThickness[
       1.6]}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}}}], {{}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{
    FormBox["\"Re(\[Omega])\"", TraditionalForm], 
    FormBox["\"-Im(\[Omega])\"", TraditionalForm]},
  AxesOrigin->{0.2, 0.02},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImageSize->Large,
  Method->{
   "OptimizePlotMarkers" -> True, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0.2, 0.55}, {0.02, 0.11}},
  PlotRangeClipping->True,
  PlotRangePadding->{{0, 0}, {0, 0}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.8074591928182287`*^9, 3.807460844743587*^9},
 CellLabel->"Out[13]=",ExpressionUUID->"884ded2d-496c-4e34-935c-abf08c5e8c30"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", 
   RowBox[{
    RowBox[{
    "Plotting", " ", "bound", " ", "state", " ", "frequency", " ", "spectra", 
     " ", 
     RowBox[{"(", "Re", ")"}], " ", "for", " ", "a"}], "=", 
    RowBox[{
     RowBox[{"0.99", " ", "and", " ", "l"}], "=", "1"}]}], "*)"}], 
  "\[IndentingNewLine]", 
  RowBox[{"ListPlot", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Re", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.99", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.05", ",", "1.6", ",", "0.05"}], "}"}]}], 
       "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Re", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.99", ",", "\[Mu]", ",", "1", ",", "0", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.05", ",", "1.6", ",", "0.05"}], "}"}]}], 
       "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Re", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{"0.99", ",", "\[Mu]", ",", "1", ",", 
               RowBox[{"-", "1"}], ",", "200", ",", "\"\<bound\>\"", ",", 
               "\"\<no\>\""}], "]"}]}], "]"}], "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.05", ",", "1.6", ",", "0.05"}], "}"}]}], 
       "]"}]}], "}"}], ",", 
    RowBox[{"ImageSize", "\[Rule]", "Large"}], ",", 
    RowBox[{"PlotRange", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"0", ",", "1.6"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"0.86", ",", "1.04"}], "}"}]}], "}"}]}], ",", 
    RowBox[{"Joined", "\[Rule]", "True"}], ",", 
    RowBox[{"Mesh", "\[Rule]", "True"}], ",", 
    RowBox[{"MeshStyle", "\[Rule]", 
     RowBox[{"PointSize", "[", "Medium", "]"}]}], ",", 
    RowBox[{"AxesLabel", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
      "\"\<M\[Mu]\>\"", ",", 
       "\"\<Re(\!\(\*FractionBox[\(\[Omega]\), \(\[Mu]\)]\))\>\""}], "}"}]}], 
    ",", 
    RowBox[{"PlotStyle", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{"Red", ",", "Green", ",", "Blue"}], "}"}]}], ",", 
    RowBox[{"PlotLegends", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
      "\"\<l=1,m=1\>\"", ",", "\"\<l=1,m=0\>\"", ",", "\"\<l=1,m=-1\>\""}], 
      "}"}]}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.807459101768965*^9, 3.807459134922922*^9}},
 CellLabel->"In[10]:=",ExpressionUUID->"b129db9b-bb08-405f-8b64-7aceec2602eb"],

Cell[BoxData[
 TemplateBox[{GraphicsBox[{{}, 
     GraphicsComplexBox[CompressedData["
1:eJzt1I9PE2cYB/CyieCWTuIPsuFEJnWZE3/MihZFHoUUAVFB07oIQgcWcY1g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      "], {{{}, {}, {
         Hue[0.67, 0.6, 0.6], 
         Directive[
          PointSize[0.011000000000000001`], 
          AbsoluteThickness[1.6], 
          RGBColor[1, 0, 0]], 
         LineBox[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 
          18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32}]}, {
         Hue[0.9060679774997897, 0.6, 0.6], 
         Directive[
          PointSize[0.011000000000000001`], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 0]], 
         LineBox[{33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 
          48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 
          64}]}, {
         Hue[0.1421359549995791, 0.6, 0.6], 
         Directive[
          PointSize[0.011000000000000001`], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 0, 1]], 
         LineBox[{65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 
          80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 
          96}]}}, {{
         Directive[
          PointSize[0.011000000000000001`], 
          AbsoluteThickness[1.6], 
          RGBColor[1, 0, 0]]}, {
         Directive[
          PointSize[0.011000000000000001`], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 0]]}, {
         Directive[
          PointSize[0.011000000000000001`], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 0, 1]]}}, {{
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[1, 0, 0], 
          PointSize[Medium]], 
         PointBox[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 
          18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32}]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 0], 
          PointSize[Medium]], 
         PointBox[{33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47,
           48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 
          64}]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 0, 1], 
          PointSize[Medium]], 
         PointBox[{65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79,
           80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 
          96}]}, {}, {}, {}, {}, {}, {}, {}}, {{
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[1, 0, 0], 
          PointSize[Medium]]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 0], 
          PointSize[Medium]]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 0, 1], 
          PointSize[Medium]]}, {}, {}, {}, {}, {}, {}, {}}}], {{}, {}}}, {
    DisplayFunction -> Identity, DisplayFunction -> Identity, AspectRatio -> 
     NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True}, 
     AxesLabel -> {
       FormBox["\"M\[Mu]\"", TraditionalForm], 
       FormBox[
       "\"Re(\\!\\(\\*FractionBox[\\(\[Omega]\\), \\(\[Mu]\\)]\\))\"", 
        TraditionalForm]}, AxesOrigin -> {0, 0.86}, DisplayFunction :> 
     Identity, Frame -> {{False, False}, {False, False}}, 
     FrameLabel -> {{None, None}, {None, None}}, 
     FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}}, 
     GridLines -> {None, None}, GridLinesStyle -> Directive[
       GrayLevel[0.5, 0.4]], ImageSize -> Large, 
     Method -> {
      "OptimizePlotMarkers" -> True, 
       "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
           (Identity[#]& )[
            Part[#, 1]], 
           (Identity[#]& )[
            Part[#, 2]]}& ), "CopiedValueFunction" -> ({
           (Identity[#]& )[
            Part[#, 1]], 
           (Identity[#]& )[
            Part[#, 2]]}& )}}, PlotRange -> {{0, 1.6}, {0.86, 1.04}}, 
     PlotRangeClipping -> True, PlotRangePadding -> {{0, 0}, {0, 0}}, 
     Ticks -> {Automatic, Automatic}}],FormBox[
    FormBox[
     TemplateBox[{"\"l=1,m=1\"", "\"l=1,m=0\"", "\"l=1,m=-1\""}, 
      "PointLegend", DisplayFunction -> (FormBox[
        StyleBox[
         StyleBox[
          PaneBox[
           TagBox[
            GridBox[{{
               TagBox[
                GridBox[{{
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0, 0]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0, 0]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 1, 0]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 1, 0]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 0, 1]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 0, 1]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}}, 
                 GridBoxAlignment -> {
                  "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, 
                 AutoDelete -> False, 
                 GridBoxDividers -> {
                  "Columns" -> {{False}}, "Rows" -> {{False}}}, 
                 GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
                  GridBoxSpacings -> {
                  "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}}, 
             GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, 
             AutoDelete -> False, 
             GridBoxItemSize -> {
              "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, 
             GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], 
            "Grid"], Alignment -> Left, AppearanceElements -> None, 
           ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> 
           "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
         FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> 
         False], TraditionalForm]& ), 
      InterpretationFunction :> (RowBox[{"PointLegend", "[", 
         RowBox[{
           RowBox[{"{", 
             RowBox[{
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.011000000000000001`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[1, 0, 0], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0.6666666666666666, 0., 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"1", ",", "0", ",", "0"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[1, 0, 0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[1, 0, 0], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.011000000000000001`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[0, 1, 0], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0., 0.6666666666666666, 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"0", ",", "1", ",", "0"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[0, 1, 0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[0, 1, 0], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.011000000000000001`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[0, 0, 1], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0., 0., 0.6666666666666666], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"0", ",", "0", ",", "1"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[0, 0, 1]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[0, 0, 1], Editable -> False, Selectable -> 
                    False]}], "]"}]}], "}"}], ",", 
           RowBox[{"{", 
             RowBox[{#, ",", #2, ",", #3}], "}"}], ",", 
           RowBox[{"LegendMarkers", "\[Rule]", 
             RowBox[{"{", 
               RowBox[{
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}]}], "}"}]}], ",", 
           RowBox[{"Joined", "\[Rule]", 
             RowBox[{"{", 
               RowBox[{"True", ",", "True", ",", "True"}], "}"}]}], ",", 
           RowBox[{"LabelStyle", "\[Rule]", 
             RowBox[{"{", "}"}]}], ",", 
           RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), 
      Editable -> True], TraditionalForm], TraditionalForm]},
  "Legended",
  DisplayFunction->(GridBox[{{
      TagBox[
       ItemBox[
        PaneBox[
         TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, 
         BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], 
       "SkipImageSizeLevel"], 
      ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, 
    GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, 
    AutoDelete -> False, GridBoxItemSize -> Automatic, 
    BaselinePosition -> {1, 1}]& ),
  Editable->True,
  InterpretationFunction->(RowBox[{"Legended", "[", 
     RowBox[{#, ",", 
       RowBox[{"Placed", "[", 
         RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output",
 CellChangeTimes->{3.807459210105422*^9},
 CellLabel->"Out[10]=",ExpressionUUID->"b128dbaf-0363-45f3-805a-85fc81ef2698"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", 
   RowBox[{
    RowBox[{
    "Plotting", " ", "bound", " ", "state", " ", "frequency", " ", "spectra", 
     " ", 
     RowBox[{"(", "Im", ")"}], " ", "for", " ", "a"}], "=", 
    RowBox[{
     RowBox[{"0.99", " ", "and", " ", "l"}], "=", "1"}]}], "*)"}], 
  "\[IndentingNewLine]", 
  RowBox[{"ListPlot", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.99", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.05", ",", "1.6", ",", "0.05"}], "}"}]}], 
       "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.99", ",", "\[Mu]", ",", "1", ",", "0", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.05", ",", "1.6", ",", "0.05"}], "}"}]}], 
       "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{"0.99", ",", "\[Mu]", ",", "1", ",", 
               RowBox[{"-", "1"}], ",", "200", ",", "\"\<bound\>\"", ",", 
               "\"\<no\>\""}], "]"}]}], "]"}], "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.05", ",", "1.6", ",", "0.05"}], "}"}]}], 
       "]"}]}], "}"}], ",", 
    RowBox[{"ImageSize", "\[Rule]", "Large"}], ",", 
    RowBox[{"PlotRange", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"0", ",", "1.6"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"-", "0.35"}], ",", "0.05"}], "}"}]}], "}"}]}], ",", 
    RowBox[{"Joined", "\[Rule]", "True"}], ",", 
    RowBox[{"Mesh", "\[Rule]", "True"}], ",", 
    RowBox[{"MeshStyle", "\[Rule]", 
     RowBox[{"PointSize", "[", "Medium", "]"}]}], ",", 
    RowBox[{"AxesLabel", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
      "\"\<M\[Mu]\>\"", ",", 
       "\"\<Im(\!\(\*FractionBox[\(\[Omega]\), \(\[Mu]\)]\))\>\""}], "}"}]}], 
    ",", 
    RowBox[{"PlotStyle", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{"Red", ",", "Green", ",", "Blue"}], "}"}]}], ",", 
    RowBox[{"PlotLegends", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
      "\"\<l=1,m=1\>\"", ",", "\"\<l=1,m=0\>\"", ",", "\"\<l=1,m=-1\>\""}], 
      "}"}]}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.807459154351493*^9, 3.807459170402874*^9}},
 CellLabel->"In[11]:=",ExpressionUUID->"2be7ae3f-b52b-4b8c-9e9d-82299d14a643"],

Cell[BoxData[
 TemplateBox[{GraphicsBox[{{}, 
     GraphicsComplexBox[CompressedData["
1:eJzt1ItPU1ccB/DaAukWhExXx0gUUaoyZI2ADEV7aMYzYFPAuaGZC0Ne0wGN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      "], {{{}, {}, {
         Hue[0.67, 0.6, 0.6], 
         Directive[
          PointSize[0.011000000000000001`], 
          AbsoluteThickness[1.6], 
          RGBColor[1, 0, 0]], 
         LineBox[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 
          18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32}]}, {
         Hue[0.9060679774997897, 0.6, 0.6], 
         Directive[
          PointSize[0.011000000000000001`], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 0]], 
         LineBox[{33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 
          48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 
          64}]}, {
         Hue[0.1421359549995791, 0.6, 0.6], 
         Directive[
          PointSize[0.011000000000000001`], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 0, 1]], 
         LineBox[{65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 
          80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 
          96}]}}, {{
         Directive[
          PointSize[0.011000000000000001`], 
          AbsoluteThickness[1.6], 
          RGBColor[1, 0, 0]]}, {
         Directive[
          PointSize[0.011000000000000001`], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 0]]}, {
         Directive[
          PointSize[0.011000000000000001`], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 0, 1]]}}, {{
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[1, 0, 0], 
          PointSize[Medium]], 
         PointBox[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 
          18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32}]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 0], 
          PointSize[Medium]], 
         PointBox[{33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47,
           48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 
          64}]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 0, 1], 
          PointSize[Medium]], 
         PointBox[{65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79,
           80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 
          96}]}, {}, {}, {}, {}, {}, {}, {}}, {{
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[1, 0, 0], 
          PointSize[Medium]]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 0], 
          PointSize[Medium]]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 0, 1], 
          PointSize[Medium]]}, {}, {}, {}, {}, {}, {}, {}}}], {{}, {}}}, {
    DisplayFunction -> Identity, DisplayFunction -> Identity, AspectRatio -> 
     NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True}, 
     AxesLabel -> {
       FormBox["\"M\[Mu]\"", TraditionalForm], 
       FormBox[
       "\"Im(\\!\\(\\*FractionBox[\\(\[Omega]\\), \\(\[Mu]\\)]\\))\"", 
        TraditionalForm]}, AxesOrigin -> {0, 0}, DisplayFunction :> Identity, 
     Frame -> {{False, False}, {False, False}}, 
     FrameLabel -> {{None, None}, {None, None}}, 
     FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}}, 
     GridLines -> {None, None}, GridLinesStyle -> Directive[
       GrayLevel[0.5, 0.4]], ImageSize -> Large, 
     Method -> {
      "OptimizePlotMarkers" -> True, 
       "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
           (Identity[#]& )[
            Part[#, 1]], 
           (Identity[#]& )[
            Part[#, 2]]}& ), "CopiedValueFunction" -> ({
           (Identity[#]& )[
            Part[#, 1]], 
           (Identity[#]& )[
            Part[#, 2]]}& )}}, PlotRange -> {{0, 1.6}, {-0.35, 0.05}}, 
     PlotRangeClipping -> True, PlotRangePadding -> {{0, 0}, {0, 0}}, 
     Ticks -> {Automatic, Automatic}}],FormBox[
    FormBox[
     TemplateBox[{"\"l=1,m=1\"", "\"l=1,m=0\"", "\"l=1,m=-1\""}, 
      "PointLegend", DisplayFunction -> (FormBox[
        StyleBox[
         StyleBox[
          PaneBox[
           TagBox[
            GridBox[{{
               TagBox[
                GridBox[{{
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0, 0]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0, 0]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 1, 0]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 1, 0]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 0, 1]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 0, 1]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}}, 
                 GridBoxAlignment -> {
                  "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, 
                 AutoDelete -> False, 
                 GridBoxDividers -> {
                  "Columns" -> {{False}}, "Rows" -> {{False}}}, 
                 GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
                  GridBoxSpacings -> {
                  "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}}, 
             GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, 
             AutoDelete -> False, 
             GridBoxItemSize -> {
              "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, 
             GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], 
            "Grid"], Alignment -> Left, AppearanceElements -> None, 
           ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> 
           "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
         FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> 
         False], TraditionalForm]& ), 
      InterpretationFunction :> (RowBox[{"PointLegend", "[", 
         RowBox[{
           RowBox[{"{", 
             RowBox[{
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.011000000000000001`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[1, 0, 0], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0.6666666666666666, 0., 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"1", ",", "0", ",", "0"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[1, 0, 0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[1, 0, 0], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.011000000000000001`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[0, 1, 0], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0., 0.6666666666666666, 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"0", ",", "1", ",", "0"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[0, 1, 0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[0, 1, 0], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.011000000000000001`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[0, 0, 1], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0., 0., 0.6666666666666666], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"0", ",", "0", ",", "1"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[0, 0, 1]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[0, 0, 1], Editable -> False, Selectable -> 
                    False]}], "]"}]}], "}"}], ",", 
           RowBox[{"{", 
             RowBox[{#, ",", #2, ",", #3}], "}"}], ",", 
           RowBox[{"LegendMarkers", "\[Rule]", 
             RowBox[{"{", 
               RowBox[{
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}]}], "}"}]}], ",", 
           RowBox[{"Joined", "\[Rule]", 
             RowBox[{"{", 
               RowBox[{"True", ",", "True", ",", "True"}], "}"}]}], ",", 
           RowBox[{"LabelStyle", "\[Rule]", 
             RowBox[{"{", "}"}]}], ",", 
           RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), 
      Editable -> True], TraditionalForm], TraditionalForm]},
  "Legended",
  DisplayFunction->(GridBox[{{
      TagBox[
       ItemBox[
        PaneBox[
         TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, 
         BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], 
       "SkipImageSizeLevel"], 
      ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, 
    GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, 
    AutoDelete -> False, GridBoxItemSize -> Automatic, 
    BaselinePosition -> {1, 1}]& ),
  Editable->True,
  InterpretationFunction->(RowBox[{"Legended", "[", 
     RowBox[{#, ",", 
       RowBox[{"Placed", "[", 
         RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output",
 CellChangeTimes->{3.807459227585554*^9},
 CellLabel->"Out[11]=",ExpressionUUID->"0f041a97-eba7-4670-abc1-117eb8aa7544"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", 
   RowBox[{
    RowBox[{
     RowBox[{
     "Plotting", " ", "bound", " ", "state", " ", "frequency", " ", "spectra",
       " ", 
      RowBox[{"(", "Re", ")"}], " ", "for", " ", "l"}], "=", "1"}], ",", 
    RowBox[{"m", "=", 
     RowBox[{"1", " ", "and", " ", "different", " ", "spins"}]}]}], "*)"}], 
  "\[IndentingNewLine]", 
  RowBox[{"ListPlot", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Re", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.05", ",", "1.6", ",", "0.05"}], "}"}]}], 
       "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Re", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.3", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.05", ",", "1.6", ",", "0.05"}], "}"}]}], 
       "]"}], ",", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Re", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.5", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.05", ",", "1.6", ",", "0.05"}], "}"}]}], 
       "]"}], ",", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Re", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.7", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.05", ",", "1.6", ",", "0.05"}], "}"}]}], 
       "]"}], ",", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Re", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.9", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.05", ",", "1.6", ",", "0.05"}], "}"}]}], 
       "]"}], ",", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Re", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.99", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.05", ",", "1.6", ",", "0.05"}], "}"}]}], 
       "]"}]}], "}"}], ",", 
    RowBox[{"ImageSize", "\[Rule]", "Large"}], ",", 
    RowBox[{"PlotRange", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"0", ",", "1.6"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"0.86", ",", "1.04"}], "}"}]}], "}"}]}], ",", 
    RowBox[{"Joined", "\[Rule]", "True"}], ",", 
    RowBox[{"Mesh", "\[Rule]", "True"}], ",", 
    RowBox[{"MeshStyle", "\[Rule]", 
     RowBox[{"PointSize", "[", "Medium", "]"}]}], ",", 
    RowBox[{"AxesLabel", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{"\"\<M\[Mu]\>\"", ",", "\"\<Re(\[Omega])/\[Mu]\>\""}], "}"}]}], 
    ",", 
    RowBox[{"PlotStyle", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
      "Red", ",", "Green", ",", "Blue", ",", "Pink", ",", "Cyan", ",", 
       "Yellow", ",", "Black"}], "}"}]}], ",", 
    RowBox[{"PlotLegends", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
      "\"\<a=0\>\"", ",", "\"\<a=0.3\>\"", ",", "\"\<a=0.5\>\"", ",", 
       "\"\<a=0.7\>\"", ",", "\"\<a=0.9\>\"", ",", "\"\<a=0.99\>\""}], 
      "}"}]}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.8059911603945637`*^9, 3.805991160408408*^9}, {
   3.806061097159216*^9, 3.8060611003866262`*^9}, {3.806061706076289*^9, 
   3.8060617416660852`*^9}, {3.806061811675908*^9, 3.8060620399659433`*^9}, {
   3.806062080008512*^9, 3.806062170592326*^9}, 3.806062230088418*^9, {
   3.806062876108879*^9, 3.806062950065875*^9}, {3.8060631151034317`*^9, 
   3.8060631189311*^9}, {3.806063879574164*^9, 3.80606390614716*^9}, {
   3.806065701467957*^9, 3.806065702460783*^9}, {3.8060756245551558`*^9, 
   3.806075683614085*^9}, {3.806076229428146*^9, 3.806076244319463*^9}, {
   3.806076583356333*^9, 3.806076588981694*^9}, {3.806160006753014*^9, 
   3.806160016303845*^9}, {3.8061622292528954`*^9, 3.806162243145228*^9}, 
   3.8061630968296137`*^9, 3.8062526996999187`*^9, {3.8062536517110233`*^9, 
   3.806253653217575*^9}, {3.807460900992155*^9, 3.807460915851013*^9}, {
   3.807470328807232*^9, 3.807470348838266*^9}},
 CellLabel->"In[5]:=",ExpressionUUID->"75f01040-97cb-403a-959a-b0da7bcffe56"],

Cell[BoxData[
 TemplateBox[{GraphicsBox[{{}, 
     GraphicsComplexBox[CompressedData["
1:eJzt1v83VGkcB/CxdSqn1PTFCUl0iFQoRUjPpk5ZqqNE39BUozCroXyJKV9b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      "], {{{}, {}, {
         Hue[0.67, 0.6, 0.6], 
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[1, 0, 0]], 
         LineBox[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 
          18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32}]}, {
         Hue[0.9060679774997897, 0.6, 0.6], 
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 0]], 
         LineBox[{33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 
          48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 
          64}]}, {
         Hue[0.1421359549995791, 0.6, 0.6], 
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 0, 1]], 
         LineBox[{65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 
          80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 
          96}]}, {
         Hue[0.37820393249936934`, 0.6, 0.6], 
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[1, 0.5, 0.5]], 
         LineBox[{97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 
          109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 
          122, 123, 124, 125, 126, 127, 128}]}, {
         Hue[0.6142719099991583, 0.6, 0.6], 
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 1]], 
         LineBox[{129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 
          141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 
          154, 155, 156, 157, 158, 159, 160}]}, {
         Hue[0.8503398874989481, 0.6, 0.6], 
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[1, 1, 0]], 
         LineBox[{161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 
          173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 
          186, 187, 188, 189, 190, 191, 192}]}}, {{
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[1, 0, 0]]}, {
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 0]]}, {
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 0, 1]]}, {
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[1, 0.5, 0.5]]}, {
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 1]]}, {
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[1, 1, 0]]}}, {{
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[1, 0, 0], 
          PointSize[Medium]], 
         PointBox[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 
          18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32}]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 0], 
          PointSize[Medium]], 
         PointBox[{33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47,
           48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 
          64}]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 0, 1], 
          PointSize[Medium]], 
         PointBox[{65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79,
           80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 
          96}]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[1, 0.5, 0.5], 
          PointSize[Medium]], 
         PointBox[{97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 
          109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 
          122, 123, 124, 125, 126, 127, 128}]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 1], 
          PointSize[Medium]], 
         PointBox[{129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140,
           141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 
          154, 155, 156, 157, 158, 159, 160}]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[1, 1, 0], 
          PointSize[Medium]], 
         PointBox[{161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172,
           173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 
          186, 187, 188, 189, 190, 191, 
          192}]}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}}, {{
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[1, 0, 0], 
          PointSize[Medium]]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 0], 
          PointSize[Medium]]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 0, 1], 
          PointSize[Medium]]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[1, 0.5, 0.5], 
          PointSize[Medium]]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 1], 
          PointSize[Medium]]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[1, 1, 0], 
          PointSize[
          Medium]]}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}}}], {{}, \
{}}}, {DisplayFunction -> Identity, DisplayFunction -> Identity, AspectRatio -> 
     NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True}, 
     AxesLabel -> {
       FormBox["\"M\[Mu]\"", TraditionalForm], 
       FormBox["\"Re(\[Omega])/\[Mu]\"", TraditionalForm]}, 
     AxesOrigin -> {0, 0.86}, DisplayFunction :> Identity, 
     Frame -> {{False, False}, {False, False}}, 
     FrameLabel -> {{None, None}, {None, None}}, 
     FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}}, 
     GridLines -> {None, None}, GridLinesStyle -> Directive[
       GrayLevel[0.5, 0.4]], ImageSize -> Large, 
     Method -> {
      "OptimizePlotMarkers" -> True, 
       "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
           (Identity[#]& )[
            Part[#, 1]], 
           (Identity[#]& )[
            Part[#, 2]]}& ), "CopiedValueFunction" -> ({
           (Identity[#]& )[
            Part[#, 1]], 
           (Identity[#]& )[
            Part[#, 2]]}& )}}, PlotRange -> {{0, 1.6}, {0.86, 1.04}}, 
     PlotRangeClipping -> True, PlotRangePadding -> {{0, 0}, {0, 0}}, 
     Ticks -> {Automatic, Automatic}}],FormBox[
    FormBox[
     TemplateBox[{
      "\"a=0\"", "\"a=0.3\"", "\"a=0.5\"", "\"a=0.7\"", "\"a=0.9\"", 
       "\"a=0.99\""}, "PointLegend", DisplayFunction -> (FormBox[
        StyleBox[
         StyleBox[
          PaneBox[
           TagBox[
            GridBox[{{
               TagBox[
                GridBox[{{
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0, 0]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0, 0]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 1, 0]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 1, 0]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 0, 1]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 0, 1]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0.5, 0.5]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0.5, 0.5]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 1, 1]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 1, 1]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #5}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 1, 0]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 1, 0]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #6}}, 
                 GridBoxAlignment -> {
                  "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, 
                 AutoDelete -> False, 
                 GridBoxDividers -> {
                  "Columns" -> {{False}}, "Rows" -> {{False}}}, 
                 GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
                  GridBoxSpacings -> {
                  "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}}, 
             GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, 
             AutoDelete -> False, 
             GridBoxItemSize -> {
              "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, 
             GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], 
            "Grid"], Alignment -> Left, AppearanceElements -> None, 
           ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> 
           "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
         FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> 
         False], TraditionalForm]& ), 
      InterpretationFunction :> (RowBox[{"PointLegend", "[", 
         RowBox[{
           RowBox[{"{", 
             RowBox[{
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[1, 0, 0], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0.6666666666666666, 0., 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"1", ",", "0", ",", "0"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[1, 0, 0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[1, 0, 0], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[0, 1, 0], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0., 0.6666666666666666, 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"0", ",", "1", ",", "0"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[0, 1, 0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[0, 1, 0], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[0, 0, 1], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0., 0., 0.6666666666666666], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"0", ",", "0", ",", "1"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[0, 0, 1]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[0, 0, 1], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[1, 0.5, 0.5], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> 
                    RGBColor[
                    0.6666666666666666, 0.33333333333333337`, 
                    0.33333333333333337`], FrameTicks -> None, 
                    PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"1", ",", "0.5`", ",", "0.5`"}], "]"}], 
                    NumberMarks -> False]], Appearance -> None, 
                    BaseStyle -> {}, BaselinePosition -> Baseline, 
                    DefaultBaseStyle -> {}, ButtonFunction :> 
                    With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[1, 0.5, 0.5]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[1, 0.5, 0.5], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[0, 1, 1], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> 
                    RGBColor[0., 0.6666666666666666, 0.6666666666666666], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"0", ",", "1", ",", "1"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[0, 1, 1]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[0, 1, 1], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[1, 1, 0], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> 
                    RGBColor[0.6666666666666666, 0.6666666666666666, 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"1", ",", "1", ",", "0"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[1, 1, 0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[1, 1, 0], Editable -> False, Selectable -> 
                    False]}], "]"}]}], "}"}], ",", 
           RowBox[{"{", 
             RowBox[{#, ",", #2, ",", #3, ",", #4, ",", #5, ",", #6}], "}"}], 
           ",", 
           RowBox[{"LegendMarkers", "\[Rule]", 
             RowBox[{"{", 
               RowBox[{
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}]}], "}"}]}], ",", 
           RowBox[{"Joined", "\[Rule]", 
             RowBox[{"{", 
               
               RowBox[{
                "True", ",", "True", ",", "True", ",", "True", ",", "True", 
                 ",", "True"}], "}"}]}], ",", 
           RowBox[{"LabelStyle", "\[Rule]", 
             RowBox[{"{", "}"}]}], ",", 
           RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), 
      Editable -> True], TraditionalForm], TraditionalForm]},
  "Legended",
  DisplayFunction->(GridBox[{{
      TagBox[
       ItemBox[
        PaneBox[
         TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, 
         BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], 
       "SkipImageSizeLevel"], 
      ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, 
    GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, 
    AutoDelete -> False, GridBoxItemSize -> Automatic, 
    BaselinePosition -> {1, 1}]& ),
  Editable->True,
  InterpretationFunction->(RowBox[{"Legended", "[", 
     RowBox[{#, ",", 
       RowBox[{"Placed", "[", 
         RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output",
 CellChangeTimes->{3.8074703540435543`*^9, 3.8074704903034573`*^9},
 CellLabel->"Out[5]=",ExpressionUUID->"3f724869-cab8-4f86-b30e-099119394e95"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", 
   RowBox[{
    RowBox[{
     RowBox[{
     "Plotting", " ", "bound", " ", "state", " ", "frequency", " ", "spectra",
       " ", 
      RowBox[{"(", "Im", ")"}], " ", "for", " ", "l"}], "=", "1"}], ",", 
    RowBox[{"m", "=", 
     RowBox[{"1", " ", "and", " ", "different", " ", "spins"}]}]}], "*)"}], 
  "\[IndentingNewLine]", 
  RowBox[{"ListPlot", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.05", ",", "1.6", ",", "0.05"}], "}"}]}], 
       "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.3", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.05", ",", "1.6", ",", "0.05"}], "}"}]}], 
       "]"}], ",", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.5", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.05", ",", "1.6", ",", "0.05"}], "}"}]}], 
       "]"}], ",", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.7", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.05", ",", "1.6", ",", "0.05"}], "}"}]}], 
       "]"}], ",", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.9", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.05", ",", "1.6", ",", "0.05"}], "}"}]}], 
       "]"}], ",", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.99", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.05", ",", "1.6", ",", "0.05"}], "}"}]}], 
       "]"}]}], "}"}], ",", 
    RowBox[{"ImageSize", "\[Rule]", "Large"}], ",", 
    RowBox[{"PlotRange", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"0", ",", "1.6"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"-", "0.35"}], ",", "0.05"}], "}"}]}], "}"}]}], ",", 
    RowBox[{"Joined", "\[Rule]", "True"}], ",", 
    RowBox[{"Mesh", "\[Rule]", "True"}], ",", 
    RowBox[{"MeshStyle", "\[Rule]", 
     RowBox[{"PointSize", "[", "Medium", "]"}]}], ",", 
    RowBox[{"AxesLabel", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{"\"\<M\[Mu]\>\"", ",", "\"\<Im(\[Omega])/\[Mu]\>\""}], "}"}]}], 
    ",", 
    RowBox[{"PlotStyle", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
      "Red", ",", "Green", ",", "Blue", ",", "Pink", ",", "Cyan", ",", 
       "Yellow", ",", "Black"}], "}"}]}], ",", 
    RowBox[{"PlotLegends", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
      "\"\<a=0\>\"", ",", "\"\<a=0.3\>\"", ",", "\"\<a=0.5\>\"", ",", 
       "\"\<a=0.7\>\"", ",", "\"\<a=0.9\>\"", ",", "\"\<a=0.99\>\""}], 
      "}"}]}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.8059911603945637`*^9, 3.805991160408408*^9}, {
   3.806061097159216*^9, 3.8060611003866262`*^9}, {3.806061706076289*^9, 
   3.8060617416660852`*^9}, {3.806061811675908*^9, 3.8060620399659433`*^9}, {
   3.806062080008512*^9, 3.806062170592326*^9}, 3.806062230088418*^9, {
   3.806062876108879*^9, 3.806062950065875*^9}, {3.8060631151034317`*^9, 
   3.8060631189311*^9}, {3.806063879574164*^9, 3.80606390614716*^9}, {
   3.806065701467957*^9, 3.806065702460783*^9}, {3.8060756245551558`*^9, 
   3.8060756614116383`*^9}, {3.8060756985485687`*^9, 3.806075711736063*^9}, {
   3.806160028069126*^9, 3.806160040716209*^9}, {3.806162260718256*^9, 
   3.806162274430664*^9}, 3.806252696986923*^9, {3.8062536730795097`*^9, 
   3.806253674070643*^9}, {3.8074703986567287`*^9, 3.8074704306004143`*^9}},
 CellLabel->"In[6]:=",ExpressionUUID->"723a5692-1906-4e99-aadc-23c1e2735068"],

Cell[BoxData[
 TemplateBox[{GraphicsBox[{{}, 
     GraphicsComplexBox[CompressedData["
1:eJzt1vs3lHkcB/BxSZtcupjqaJXZBqHBLrnUmi+FVZt7csmKlHWJLsQOkg2D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      "], {{{}, {}, {
         Hue[0.67, 0.6, 0.6], 
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[1, 0, 0]], 
         LineBox[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 
          18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32}]}, {
         Hue[0.9060679774997897, 0.6, 0.6], 
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 0]], 
         LineBox[{33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 
          48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 
          64}]}, {
         Hue[0.1421359549995791, 0.6, 0.6], 
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 0, 1]], 
         LineBox[{65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 
          80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 
          96}]}, {
         Hue[0.37820393249936934`, 0.6, 0.6], 
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[1, 0.5, 0.5]], 
         LineBox[{97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 
          109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 
          122, 123, 124, 125, 126, 127, 128}]}, {
         Hue[0.6142719099991583, 0.6, 0.6], 
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 1]], 
         LineBox[{129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 
          141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 
          154, 155, 156, 157, 158, 159, 160}]}, {
         Hue[0.8503398874989481, 0.6, 0.6], 
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[1, 1, 0]], 
         LineBox[{161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 
          173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 
          186, 187, 188, 189, 190, 191, 192}]}}, {{
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[1, 0, 0]]}, {
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 0]]}, {
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 0, 1]]}, {
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[1, 0.5, 0.5]]}, {
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 1]]}, {
         Directive[
          PointSize[0.009166666666666668], 
          AbsoluteThickness[1.6], 
          RGBColor[1, 1, 0]]}}, {{
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[1, 0, 0], 
          PointSize[Medium]], 
         PointBox[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 
          18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32}]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 0], 
          PointSize[Medium]], 
         PointBox[{33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47,
           48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 
          64}]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 0, 1], 
          PointSize[Medium]], 
         PointBox[{65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79,
           80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 
          96}]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[1, 0.5, 0.5], 
          PointSize[Medium]], 
         PointBox[{97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 
          109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 
          122, 123, 124, 125, 126, 127, 128}]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 1], 
          PointSize[Medium]], 
         PointBox[{129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140,
           141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 
          154, 155, 156, 157, 158, 159, 160}]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[1, 1, 0], 
          PointSize[Medium]], 
         PointBox[{161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172,
           173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 
          186, 187, 188, 189, 190, 191, 
          192}]}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}}, {{
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[1, 0, 0], 
          PointSize[Medium]]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 0], 
          PointSize[Medium]]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 0, 1], 
          PointSize[Medium]]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[1, 0.5, 0.5], 
          PointSize[Medium]]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[0, 1, 1], 
          PointSize[Medium]]}, {
         Directive[
          AbsoluteThickness[1.6], 
          RGBColor[1, 1, 0], 
          PointSize[
          Medium]]}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}}}], {{}, \
{}}}, {DisplayFunction -> Identity, DisplayFunction -> Identity, AspectRatio -> 
     NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True}, 
     AxesLabel -> {
       FormBox["\"M\[Mu]\"", TraditionalForm], 
       FormBox["\"Im(\[Omega])/\[Mu]\"", TraditionalForm]}, 
     AxesOrigin -> {0, 0}, DisplayFunction :> Identity, 
     Frame -> {{False, False}, {False, False}}, 
     FrameLabel -> {{None, None}, {None, None}}, 
     FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}}, 
     GridLines -> {None, None}, GridLinesStyle -> Directive[
       GrayLevel[0.5, 0.4]], ImageSize -> Large, 
     Method -> {
      "OptimizePlotMarkers" -> True, 
       "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
           (Identity[#]& )[
            Part[#, 1]], 
           (Identity[#]& )[
            Part[#, 2]]}& ), "CopiedValueFunction" -> ({
           (Identity[#]& )[
            Part[#, 1]], 
           (Identity[#]& )[
            Part[#, 2]]}& )}}, PlotRange -> {{0, 1.6}, {-0.35, 0.05}}, 
     PlotRangeClipping -> True, PlotRangePadding -> {{0, 0}, {0, 0}}, 
     Ticks -> {Automatic, Automatic}}],FormBox[
    FormBox[
     TemplateBox[{
      "\"a=0\"", "\"a=0.3\"", "\"a=0.5\"", "\"a=0.7\"", "\"a=0.9\"", 
       "\"a=0.99\""}, "PointLegend", DisplayFunction -> (FormBox[
        StyleBox[
         StyleBox[
          PaneBox[
           TagBox[
            GridBox[{{
               TagBox[
                GridBox[{{
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0, 0]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0, 0]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 1, 0]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 1, 0]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 0, 1]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 0, 1]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0.5, 0.5]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0.5, 0.5]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 1, 1]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 1, 1]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #5}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 1, 0]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 1, 0]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #6}}, 
                 GridBoxAlignment -> {
                  "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, 
                 AutoDelete -> False, 
                 GridBoxDividers -> {
                  "Columns" -> {{False}}, "Rows" -> {{False}}}, 
                 GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
                  GridBoxSpacings -> {
                  "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}}, 
             GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, 
             AutoDelete -> False, 
             GridBoxItemSize -> {
              "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, 
             GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], 
            "Grid"], Alignment -> Left, AppearanceElements -> None, 
           ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> 
           "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
         FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> 
         False], TraditionalForm]& ), 
      InterpretationFunction :> (RowBox[{"PointLegend", "[", 
         RowBox[{
           RowBox[{"{", 
             RowBox[{
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[1, 0, 0], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0.6666666666666666, 0., 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"1", ",", "0", ",", "0"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[1, 0, 0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[1, 0, 0], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[0, 1, 0], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0., 0.6666666666666666, 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"0", ",", "1", ",", "0"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[0, 1, 0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[0, 1, 0], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[0, 0, 1], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0., 0., 0.6666666666666666], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"0", ",", "0", ",", "1"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[0, 0, 1]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[0, 0, 1], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[1, 0.5, 0.5], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> 
                    RGBColor[
                    0.6666666666666666, 0.33333333333333337`, 
                    0.33333333333333337`], FrameTicks -> None, 
                    PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"1", ",", "0.5`", ",", "0.5`"}], "]"}], 
                    NumberMarks -> False]], Appearance -> None, 
                    BaseStyle -> {}, BaselinePosition -> Baseline, 
                    DefaultBaseStyle -> {}, ButtonFunction :> 
                    With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[1, 0.5, 0.5]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[1, 0.5, 0.5], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[0, 1, 1], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> 
                    RGBColor[0., 0.6666666666666666, 0.6666666666666666], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"0", ",", "1", ",", "1"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[0, 1, 1]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[0, 1, 1], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[1, 1, 0], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> 
                    RGBColor[0.6666666666666666, 0.6666666666666666, 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"1", ",", "1", ",", "0"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[1, 1, 0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[1, 1, 0], Editable -> False, Selectable -> 
                    False]}], "]"}]}], "}"}], ",", 
           RowBox[{"{", 
             RowBox[{#, ",", #2, ",", #3, ",", #4, ",", #5, ",", #6}], "}"}], 
           ",", 
           RowBox[{"LegendMarkers", "\[Rule]", 
             RowBox[{"{", 
               RowBox[{
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}]}], "}"}]}], ",", 
           RowBox[{"Joined", "\[Rule]", 
             RowBox[{"{", 
               
               RowBox[{
                "True", ",", "True", ",", "True", ",", "True", ",", "True", 
                 ",", "True"}], "}"}]}], ",", 
           RowBox[{"LabelStyle", "\[Rule]", 
             RowBox[{"{", "}"}]}], ",", 
           RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), 
      Editable -> True], TraditionalForm], TraditionalForm]},
  "Legended",
  DisplayFunction->(GridBox[{{
      TagBox[
       ItemBox[
        PaneBox[
         TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, 
         BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], 
       "SkipImageSizeLevel"], 
      ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, 
    GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, 
    AutoDelete -> False, GridBoxItemSize -> Automatic, 
    BaselinePosition -> {1, 1}]& ),
  Editable->True,
  InterpretationFunction->(RowBox[{"Legended", "[", 
     RowBox[{#, ",", 
       RowBox[{"Placed", "[", 
         RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output",
 CellChangeTimes->{3.8074706060387793`*^9},
 CellLabel->"Out[6]=",ExpressionUUID->"e255b41a-b744-4317-bd7f-fc28bce537ff"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", 
   RowBox[{
    RowBox[{
     RowBox[{
     "Plotting", " ", "gdecay", " ", "width", " ", "as", " ", "a", " ", 
      "function", " ", "of", " ", "gravtational", " ", "coupling", " ", "for",
       " ", "l"}], "=", "1"}], ",", 
    RowBox[{"m", "=", 
     RowBox[{"1", " ", "mode"}]}]}], "*)"}], "\[IndentingNewLine]", 
  RowBox[{"ListLogPlot", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.5", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.06", ",", "0.2", ",", "0.002"}], "}"}]}], 
       "]"}], ",", "\[IndentingNewLine]", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.6", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.06", ",", "0.2", ",", "0.002"}], "}"}]}], 
       "]"}], ",", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.7", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.06", ",", "0.25", ",", "0.002"}], "}"}]}], 
       "]"}], ",", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.8", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.06", ",", "0.3", ",", "0.002"}], "}"}]}], 
       "]"}], ",", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.9", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.06", ",", "0.35", ",", "0.002"}], "}"}]}], 
       "]"}], ",", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.95", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.06", ",", "0.4", ",", "0.002"}], "}"}]}], 
       "]"}], ",", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.99", ",", "\[Mu]", ",", "1", ",", "1", ",", "200", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.06", ",", "0.5", ",", "0.002"}], "}"}]}], 
       "]"}], ",", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", 
          FractionBox[
           RowBox[{"Im", "[", 
            RowBox[{"\[Omega]", "/.", 
             RowBox[{"findfreq", "[", 
              RowBox[{
              "0.999", ",", "\[Mu]", ",", "1", ",", "1", ",", "600", ",", 
               "\"\<bound\>\"", ",", "\"\<no\>\""}], "]"}]}], "]"}], 
           "\[Mu]"]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Mu]", ",", "0.06", ",", "0.55", ",", "0.002"}], "}"}]}], 
       "]"}]}], "}"}], ",", 
    RowBox[{"ImageSize", "\[Rule]", "Large"}], ",", 
    RowBox[{"PlotRange", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"0", ",", "0.55"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{
         SuperscriptBox["10", 
          RowBox[{"-", "11"}]], ",", 
         SuperscriptBox["10", 
          RowBox[{"-", "6"}]]}], "}"}]}], "}"}]}], ",", 
    RowBox[{"Joined", "\[Rule]", "True"}], ",", 
    RowBox[{"AxesLabel", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{"\"\<M\[Mu]\>\"", ",", "\"\<Im(\[Omega])/\[Mu]\>\""}], "}"}]}], 
    ",", 
    RowBox[{"PlotStyle", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
      "Red", ",", "Green", ",", "Blue", ",", "Yellow", ",", "Cyan", ",", 
       "Pink", ",", "Black", ",", "Orange"}], "}"}]}], ",", 
    RowBox[{"PlotLegends", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
      "\"\<a=0.5\>\"", ",", "\"\<a=0.6\>\"", ",", "\"\<a=0.7\>\"", ",", 
       "\"\<a=0.8\>\"", ",", "\"\<a=0.9\>\"", ",", "\"\<a=0.95\>\"", ",", 
       "\"\<a=0.99\>\"", ",", "\"\<a=0.999\>\""}], "}"}]}]}], 
   "]"}]}]], "Input",
 CellChangeTimes->{{3.806064989949621*^9, 3.806065014400963*^9}, {
  3.806065058217016*^9, 3.806065070621179*^9}, {3.806065396295286*^9, 
  3.80606554393055*^9}, {3.806065577129279*^9, 3.80606569145827*^9}, {
  3.8060766149774103`*^9, 3.806076659337247*^9}, {3.806077232001862*^9, 
  3.80607723238483*^9}, {3.8060775378373203`*^9, 3.806077537948827*^9}, {
  3.8061600491682034`*^9, 3.806160061203895*^9}, {3.80616080388128*^9, 
  3.806160804344483*^9}, {3.80616086644025*^9, 3.8061608672043257`*^9}, {
  3.806160918668853*^9, 3.8061610076282787`*^9}, {3.806161090966454*^9, 
  3.806161134940289*^9}, {3.80616228513605*^9, 3.806162300331859*^9}, {
  3.8062525604866047`*^9, 3.806252576850071*^9}, {3.807470481112235*^9, 
  3.807470493993806*^9}, {3.807470575680517*^9, 3.807470593983716*^9}},
 CellLabel->"In[7]:=",ExpressionUUID->"cced2108-da9a-404a-aaab-c4f099341565"],

Cell[BoxData[
 TemplateBox[{GraphicsBox[{{}, {{{}, {}, {
        Hue[0.67, 0.6, 0.6], 
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[1, 0, 0]], 
        LineBox[CompressedData["
1:eJxTTMoPSmViYGCQBGIQzVQssVyYdZv9vxDJJJEQywO7PHmYtNu32SvfrDmh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         "]]}, {
        Hue[0.9060679774997897, 0.6, 0.6], 
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[0, 1, 0]], 
        LineBox[CompressedData["
1:eJwdknsslXEYx4/oJulCwspQ2Ylksvf3vmed9mSlg6EpoZt0RsmxTrOmyFyn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         "]]}, {
        Hue[0.1421359549995791, 0.6, 0.6], 
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[0, 0, 1]], 
        LineBox[CompressedData["
1:eJwtkw9MlGUcx/HCTDKGeuGftIEidRLebj7ve+9B9NNb6CE4gW4KYZNOrlhS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         "]]}, {
        Hue[0.37820393249936934`, 0.6, 0.6], 
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[1, 1, 0]], 
        LineBox[CompressedData["
1:eJwtlHlQE2cYhylQpEotKkcESz1a1IrD8O1mk1DtWxAELChSalGUQbAjoyiW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         "]]}, {
        Hue[0.6142719099991583, 0.6, 0.6], 
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[0, 1, 1]], 
        LineBox[CompressedData["
1:eJwtlAtQFWUUxxFNxQyRiAQNUZF8JOy39+59mHFKERQlRNHATI3JIEklVFTw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         "]]}, {
        Hue[0.8503398874989481, 0.6, 0.6], 
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[1, 0.5, 0.5]], 
        LineBox[CompressedData["
1:eJwtlXtYTfkax2MSQ1OdQukiEiJZl33N7TUalMR0MROaOB0pl0nikGpKuSVy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         "]]}, {
        Hue[0.08640786499873876, 0.6, 0.6], 
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         GrayLevel[0]], 
        LineBox[CompressedData["
1:eJwtlXlYzfkXx8nyI2P50SBjUkSo73aXlhGnbCNGBiEmMQ1+VCpLNMlYEyNj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         "]]}, {
        Hue[0.3224758424985268, 0.6, 0.6], 
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[1, 0.5, 0]], 
        LineBox[CompressedData["
1:eJwtlQtUTWkbx1NqZpoYXTTUUPoqhvY+e5/TOaemeIyElNGFJr6Gxm1olEsu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         "]]}}, {{
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[1, 0, 0]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[0, 1, 0]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[0, 0, 1]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[1, 1, 0]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[0, 1, 1]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[1, 0.5, 0.5]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         GrayLevel[0]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[1, 0.5, 0]]}}, {{
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[1, 0, 0]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[0, 1, 0]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[0, 0, 1]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[1, 1, 0]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[0, 1, 1]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[1, 0.5, 0.5]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         GrayLevel[0]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[
         1, 0.5, 0]]}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}}, {{
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[1, 0, 0]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[0, 1, 0]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[0, 0, 1]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[1, 1, 0]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[0, 1, 1]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[1, 0.5, 0.5]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         GrayLevel[0]]}, {
        Directive[
         PointSize[0.0055000000000000005`], 
         AbsoluteThickness[1.6], 
         RGBColor[
         1, 0.5, 0]]}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, \
{}, {}, {}, {}, {}, {}}}, {{}, {}}}, {
    DisplayFunction -> Identity, GridLines -> {None, None}, DisplayFunction -> 
     Identity, DisplayFunction -> Identity, DisplayFunction -> Identity, 
     DisplayFunction -> Identity, AspectRatio -> 
     NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True}, 
     AxesLabel -> {
       FormBox["\"M\[Mu]\"", TraditionalForm], 
       FormBox["\"Im(\[Omega])/\[Mu]\"", TraditionalForm]}, 
     AxesOrigin -> {0, -25.328436022934504`}, DisplayFunction :> Identity, 
     Frame -> {{False, False}, {False, False}}, 
     FrameLabel -> {{None, None}, {None, None}}, FrameTicks -> {{
        Charting`ScaledTicks[{Log, Exp}], 
        Charting`ScaledFrameTicks[{Log, Exp}]}, {Automatic, Automatic}}, 
     GridLines -> {None, None}, GridLinesStyle -> Directive[
       GrayLevel[0.5, 0.4]], ImageSize -> Large, 
     Method -> {
      "OptimizePlotMarkers" -> True, 
       "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
           (Identity[#]& )[
            Part[#, 1]], 
           (Exp[#]& )[
            Part[#, 2]]}& ), "CopiedValueFunction" -> ({
           (Identity[#]& )[
            Part[#, 1]], 
           (Exp[#]& )[
            Part[#, 2]]}& )}}, PlotRange -> 
     NCache[{{0, 0.55}, {-Log[100000000000], -Log[1000000]}}, {{
        0, 0.55}, {-25.328436022934504`, -13.815510557964274`}}], 
     PlotRangeClipping -> True, PlotRangePadding -> {{0, 0}, {0, 0}}, 
     Ticks -> {Automatic, 
       Charting`ScaledTicks[{Log, Exp}]}}],FormBox[
    FormBox[
     TemplateBox[{
      "\"a=0.5\"", "\"a=0.6\"", "\"a=0.7\"", "\"a=0.8\"", "\"a=0.9\"", 
       "\"a=0.95\"", "\"a=0.99\"", "\"a=0.999\""}, "PointLegend", 
      DisplayFunction -> (FormBox[
        StyleBox[
         StyleBox[
          PaneBox[
           TagBox[
            GridBox[{{
               TagBox[
                GridBox[{{
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0, 0]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0, 0]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 1, 0]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 1, 0]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 0, 1]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 0, 1]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 1, 0]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 1, 0]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 1, 1]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 1, 1]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #5}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0.5, 0.5]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0.5, 0.5]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #6}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    GrayLevel[0]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    GrayLevel[0]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #7}, {
                   GraphicsBox[{{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0.5, 0]], {
                    LineBox[{{0, 10}, {20, 10}}]}}, {
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0.5, 0]], {}}}, AspectRatio -> Full, 
                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
                    ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #8}}, 
                 GridBoxAlignment -> {
                  "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, 
                 AutoDelete -> False, 
                 GridBoxDividers -> {
                  "Columns" -> {{False}}, "Rows" -> {{False}}}, 
                 GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
                  GridBoxSpacings -> {
                  "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}}, 
             GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, 
             AutoDelete -> False, 
             GridBoxItemSize -> {
              "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, 
             GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], 
            "Grid"], Alignment -> Left, AppearanceElements -> None, 
           ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> 
           "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
         FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> 
         False], TraditionalForm]& ), 
      InterpretationFunction :> (RowBox[{"PointLegend", "[", 
         RowBox[{
           RowBox[{"{", 
             RowBox[{
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.0055000000000000005`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[1, 0, 0], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0.6666666666666666, 0., 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"1", ",", "0", ",", "0"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[1, 0, 0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[1, 0, 0], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.0055000000000000005`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[0, 1, 0], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0., 0.6666666666666666, 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"0", ",", "1", ",", "0"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[0, 1, 0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[0, 1, 0], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.0055000000000000005`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[0, 0, 1], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0., 0., 0.6666666666666666], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"0", ",", "0", ",", "1"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[0, 0, 1]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[0, 0, 1], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.0055000000000000005`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[1, 1, 0], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> 
                    RGBColor[0.6666666666666666, 0.6666666666666666, 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"1", ",", "1", ",", "0"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[1, 1, 0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[1, 1, 0], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.0055000000000000005`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[0, 1, 1], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> 
                    RGBColor[0., 0.6666666666666666, 0.6666666666666666], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"0", ",", "1", ",", "1"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[0, 1, 1]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[0, 1, 1], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.0055000000000000005`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[1, 0.5, 0.5], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> 
                    RGBColor[
                    0.6666666666666666, 0.33333333333333337`, 
                    0.33333333333333337`], FrameTicks -> None, 
                    PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"1", ",", "0.5`", ",", "0.5`"}], "]"}], 
                    NumberMarks -> False]], Appearance -> None, 
                    BaseStyle -> {}, BaselinePosition -> Baseline, 
                    DefaultBaseStyle -> {}, ButtonFunction :> 
                    With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[1, 0.5, 0.5]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[1, 0.5, 0.5], Editable -> False, Selectable -> 
                    False]}], "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.0055000000000000005`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    GrayLevel[0], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> GrayLevel[0.], FrameTicks -> None, 
                    PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"GrayLevel", "[", "0", "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    GrayLevel[0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["GrayLevelColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    GrayLevel[0], Editable -> False, Selectable -> False]}], 
                 "]"}], ",", 
               RowBox[{"Directive", "[", 
                 RowBox[{
                   RowBox[{"PointSize", "[", "0.0055000000000000005`", "]"}], 
                   ",", 
                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
                   InterpretationBox[
                    ButtonBox[
                    TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[1, 0.5, 0], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> 
                    RGBColor[0.6666666666666666, 0.33333333333333337`, 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
                    AbsoluteCurrentValue[Magnification]}]], 
                    StyleBox[
                    RowBox[{"RGBColor", "[", 
                    RowBox[{"1", ",", "0.5`", ",", "0"}], "]"}], NumberMarks -> 
                    False]], Appearance -> None, BaseStyle -> {}, 
                    BaselinePosition -> Baseline, DefaultBaseStyle -> {}, 
                    ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[1, 0.5, 0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                    Automatic, Method -> "Preemptive"], 
                    RGBColor[1, 0.5, 0], Editable -> False, Selectable -> 
                    False]}], "]"}]}], "}"}], ",", 
           RowBox[{"{", 
             
             RowBox[{#, ",", #2, ",", #3, ",", #4, ",", #5, ",", #6, ",", #7, 
               ",", #8}], "}"}], ",", 
           RowBox[{"LegendMarkers", "\[Rule]", 
             RowBox[{"{", 
               RowBox[{
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
                 RowBox[{"{", 
                   RowBox[{"False", ",", "Automatic"}], "}"}]}], "}"}]}], ",", 
           RowBox[{"Joined", "\[Rule]", 
             RowBox[{"{", 
               
               RowBox[{
                "True", ",", "True", ",", "True", ",", "True", ",", "True", 
                 ",", "True", ",", "True", ",", "True"}], "}"}]}], ",", 
           RowBox[{"LabelStyle", "\[Rule]", 
             RowBox[{"{", "}"}]}], ",", 
           RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), 
      Editable -> True], TraditionalForm], TraditionalForm]},
  "Legended",
  DisplayFunction->(GridBox[{{
      TagBox[
       ItemBox[
        PaneBox[
         TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, 
         BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], 
       "SkipImageSizeLevel"], 
      ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, 
    GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, 
    AutoDelete -> False, GridBoxItemSize -> Automatic, 
    BaselinePosition -> {1, 1}]& ),
  Editable->True,
  InterpretationFunction->(RowBox[{"Legended", "[", 
     RowBox[{#, ",", 
       RowBox[{"Placed", "[", 
         RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output",
 CellChangeTimes->{3.8074708814038*^9},
 CellLabel->"Out[7]=",ExpressionUUID->"0f6ad396-68f9-4aed-abef-6e7a93f052e9"]
}, Open  ]]
}, Open  ]]
},
WindowSize->{1920, 1012},
WindowMargins->{{0, Automatic}, {1, Automatic}},
FrontEndVersion->"12.0 for Linux x86 (64-bit) (April 8, 2019)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 569, 10, 135, "Title",ExpressionUUID->"303eacf5-055b-4a2f-9851-660338238a2f"],
Cell[1152, 34, 13622, 327, 789, "Input",ExpressionUUID->"fb5faef1-8bcc-48f9-b703-e83317d1e09e"],
Cell[CellGroupData[{
Cell[14799, 365, 3205, 49, 55, "Input",ExpressionUUID->"f600187f-5a1a-4bed-916a-d2eb3cd7affb"],
Cell[18007, 416, 287, 4, 35, "Output",ExpressionUUID->"d5f33b79-1e40-48b3-a78d-e6a0344964c1"]
}, Open  ]],
Cell[CellGroupData[{
Cell[18331, 425, 15832, 360, 354, "Input",ExpressionUUID->"72391553-852b-47ee-8d2c-da44eddf6ab9"],
Cell[34166, 787, 612, 12, 23, "Message",ExpressionUUID->"ece68250-6f23-4538-b627-0997d5cd2ad6"],
Cell[34781, 801, 614, 12, 23, "Message",ExpressionUUID->"8fd6aef4-8fba-48cf-bfeb-f41194a50123"],
Cell[35398, 815, 612, 12, 23, "Message",ExpressionUUID->"276ab943-4509-4d01-905e-7a7897190d2b"],
Cell[36013, 829, 471, 10, 23, "Message",ExpressionUUID->"25b21a15-701b-4df5-97c9-1e7eea55e7bb"],
Cell[36487, 841, 11465, 206, 373, "Output",ExpressionUUID->"884ded2d-496c-4e34-935c-abf08c5e8c30"]
}, Open  ]],
Cell[CellGroupData[{
Cell[47989, 1052, 3218, 86, 207, "Input",ExpressionUUID->"b129db9b-bb08-405f-8b64-7aceec2602eb"],
Cell[51210, 1140, 18356, 385, 398, "Output",ExpressionUUID->"b128dbaf-0363-45f3-805a-85fc81ef2698"]
}, Open  ]],
Cell[CellGroupData[{
Cell[69603, 1530, 3243, 87, 207, "Input",ExpressionUUID->"2be7ae3f-b52b-4b8c-9e9d-82299d14a643"],
Cell[72849, 1619, 18439, 386, 383, "Output",ExpressionUUID->"0f041a97-eba7-4670-abc1-117eb8aa7544"]
}, Open  ]],
Cell[CellGroupData[{
Cell[91325, 2010, 5845, 146, 242, "Input",ExpressionUUID->"75f01040-97cb-403a-959a-b0da7bcffe56"],
Cell[97173, 2158, 32978, 688, 385, "Output",ExpressionUUID->"3f724869-cab8-4f86-b30e-099119394e95"]
}, Open  ]],
Cell[CellGroupData[{
Cell[130188, 2851, 5750, 145, 242, "Input",ExpressionUUID->"723a5692-1906-4e99-aadc-23c1e2735068"],
Cell[135941, 2998, 33180, 692, 370, "Output",ExpressionUUID->"e255b41a-b744-4317-bd7f-fc28bce537ff"]
}, Open  ]],
Cell[CellGroupData[{
Cell[169158, 3695, 6855, 175, 287, "Input",ExpressionUUID->"cced2108-da9a-404a-aaab-c4f099341565"],
Cell[176016, 3872, 53582, 1082, 367, "Output",ExpressionUUID->"0f6ad396-68f9-4aed-abef-6e7a93f052e9"]
}, Open  ]]
}, Open  ]]
}
]
*)