Excitation Bq

For[j01=0,j01<5,j01++,l=2;
(*A loop to go through m=-L,...,L*)
m=-l+j01;

s=-2;
Δ=(10^(-7));
k1=(1/2)Abs[m-s];
k2=(1/2)Abs[m+s];


Nmax=300;
ϵϵϵ=(10^(-8));

rows=1000;



nu=2.3168097107558374+0.4151910472915969I;

tempωql2n0=0.7473433688360838` -0.1779246313778714` I;(*0-overtone*)
tempωql2n1=0.6934219937583269` -0.5478297505824696` I;(*1-overtone*)
tempωql2n2=0.6021069092247324` -0.9565539664461437` I;(*2-overtone*)
tempωql2n3=0.5030099243712871` -1.4102964048667352` I;(*3-overtone*)
tempωql2n4=0.41503197365943806` -1.8936938488646722` I;(*4-overtone*)
tempωql2n5=0.33850670625899` -2.391220657858395` I;(*5-overtone*)
tempωql2n6=0.2665046886` -2.895821264` I;(*6-overtone*)
tempωql2n7=0.18564479582` -3.407682654` I;(*7-overtone*)


nul2n3=Table[0,{i,rows},{j,1}];
step=0.0005;


Ninversionθ=l-Max[Abs[m],Abs[s]];


(*for different overtones, change two parameters below*)
Ninversionr=0;
tempωq=tempωql2n0;
(*===========================================*)


tempθ=0;
ithstop=0;

Gravl2n3=Table[0,{i,rows},{j,9}];


For[ith=ithstop,ith<1000,ith++,a=ith step;b=(Sqrt[1-4(a^2)]);



(*Alm=(l(l+1)-s(s+1)+θ)*)

αθ[n_,ω_]:=-2(n+1)(n+2k1+1);
βθ[n_,ω_,θ_]:=n(n-1)+2n(k1+k2+1-2a ω)-(2a ω(2k1+s+1)-(k1+k2)(k1+k2+1))-((a^2)(ω^2)+s(s+1)+(l(l+1)-s(s+1)+θ));
γθ[n_,ω_]:=2a ω(n+k1+k2+s);


αr[n_,ω_]:=(n^2)+((1-s-I ω-((2I)/b)((ω/2)-a m))+1)n+(1-s-I ω-((2I)/b)((ω/2)-a m));
βr[n_,ω_,θ_]:=-2(n^2)+((-4+2I ω(2+b)+((4I)/b)((ω/2)-a m))+2)n+((ω^2)(4+2b-(a^2))-2a m ω-s-1+(2+b)I ω-(l(l+1)-s(s+1)+θ)+((4ω+2I)/b)((ω/2)-a m));
γr[n_,ω_]:=(n^2)+((s+3-3I ω-((2I)/b)((ω/2)-a m))-3)n+(s+1-2(ω^2)-(2s+3)I ω-((4ω+2I)/b)((ω/2)-a m))-(s+3-3I ω-((2I)/b)((ω/2)-a m))+2;





TnInfiniteθ=Module[{Tn},For[{n=Nmax-1;Tn=βθ[n+1,ω,θ];},n>=Ninversionθ,{Tn=βθ[n,ω,θ]-((αθ[n,ω]γθ[n+1,ω])/Tn);n--}];Tn];

Tnfiniteθ=βθ[Ninversionθ,ω,θ]-Module[{Tn},For[{n=0;Tn=βθ[0,ω,θ];},n<Ninversionθ,{Tn=βθ[n+1,ω,θ]-((αθ[n,ω]γθ[n+1,ω])/Tn);n++}];Tn];

TnInfiniter=Module[{Tn},For[{n=Nmax-1;Tn=βr[n+1,ω,θ];},n>=Ninversionr,{Tn=βr[n,ω,θ]-((αr[n,ω]γr[n+1,ω])/Tn);n--}];Tn];

Tnfiniter=βr[Ninversionr,ω,θ]-Module[{Tn},For[{n=0;Tn=βr[0,ω,θ];},n<Ninversionr,{Tn=βr[n+1,ω,θ]-((αr[n,ω]γr[n+1,ω])/Tn);n++}];Tn];




freq=FindRoot[{Tnfiniteθ==TnInfiniteθ,TnInfiniter==Tnfiniter},{{ω,tempωq},{θ,tempθ}}];


ωq=ω/.freq;
θ0=θ/.freq;

ωq0=ωq;
Alm0=l(l+1)-s(s+1)+θ0;

tempωq=ωq0;
tempθ=θ0;

Gravl2n3[[ith+1]][[1]]=2a;
Gravl2n3[[ith+1]][[2]]=Re[ωq0];
Gravl2n3[[ith+1]][[3]]=Im[ωq0];
Gravl2n3[[ith+1]][[4]]=Re[Alm0];
Gravl2n3[[ith+1]][[5]]=Im[Alm0];


ϵ=ωq;

λ=Alm0+(((a ωq))^2)-2a m ωq;
λ0=Alm0+(((a ωq))^2)-2a m ωq;
q=2a;(*   a=J/M   q=a/M=J/(M^2)  *)
κ=(Sqrt[1-(q^2)]);
τ=((ϵ-m q)/κ);
ϵplus=((ϵ+τ)/2);




αMST[n_,mu_]:=((I ϵ κ(n+mu+1+s+I ϵ)(n+mu+1+s-I ϵ)(n+mu+1+I τ))/((n+mu+1)(2n+2mu+3)));
αprimeMST[n_,mu_]:=-I(((n+mu+1-s+I ϵ)(n+mu+1-s-I ϵ))/((n+mu+1+s+I ϵ)(n+mu+1+s-I ϵ)))αMST[n,mu];
βMST[n_,mu_]:=-λ-s(1+s)+(n+mu)(n+mu+1)+(ϵ^2)+ϵ(ϵ-m q)+((ϵ(ϵ-m q)((s^2)+(ϵ^2)))/((n+mu)(n+mu+1)));
γMST[n_,mu_]:=-((I ϵ κ(n+mu-s+I ϵ)(n+mu-s-I ϵ)(n+mu-I τ))/((n+mu)(2n+2mu-1)));
γprimeMST[n_,mu_]:=I(((mu+n+s+I ϵ)(mu+n+s-I ϵ))/((mu+n-s+I ϵ)(mu+n-s-I ϵ)))γMST[n,mu];

NmaxMST=100;
NMST=0; 

MSTplus=Module[{Tn},For[{n=NmaxMST-1;Tn=βMST[n+1,ν];},n>=NMST,{Tn=βMST[n,ν]-((αprimeMST[n,ν]γprimeMST[n+1,ν])/Tn);n--}];Tn];

MSTminus=βMST[NMST,ν]-Module[{Tn},For[{n=NmaxMST-1;Tn=βMST[-n-1,ν];},n≥-NMST,{Tn=βMST[-n,ν]-((αprimeMST[-n-1,ν]γprimeMST[-n,ν])/Tn);n--}];Tn];
nu=ν/.FindRoot[MSTplus==MSTminus,{ν,nu}];


nul2n3[[ith+1]][[1]]=nu;
(*Gravl2m2[[ith+1]][[4]]=nu;*)

aMSTNcut=200;
aMST[0]=1;
(*
aMSTNcut is to control how many terms for aMST[n] I want;
NmaxMST is to control for each term of aMST[n]; from which (lowest,staying at most bottom level of the continued fraction)term of βMST[n,nu], it start the recurrence, going from most bottom to the most up. See the example below.
*)
(*================================================================================================================================*)
(*================================= Next Build All Positive aMST[L] Terms =================================*)


For[i=1,i<aMSTNcut+1,i++,aMST[i]=(1/(αMST[i-1,nu]))(-βMST[i-1,nu]+Module[{Tn},For[{n=NmaxMST-1;Tn=βMST[n+1,nu];},n≥(i-1),{Tn=βMST[n,nu]-((αMST[n,nu]γMST[n+1,nu])/Tn);n--}];Tn])aMST[i-1]];


(*================================= Next Build All Negative a[-L] Terms =================================*)
(*================================= Next Build All Negative a[-L] Terms =================================*)

For[i=1,i<aMSTNcut+1,i++,aMST[-i]=-αMST[-i,nu](((Module[{Tn},For[{n=-NmaxMST+1;Tn=βMST[n-1,nu];},n<-i+1,{Tn=βMST[n,nu]-((γMST[n,nu]αMST[n-1,nu])/Tn);n++}];Tn]))^(-1))aMST[-i+1]];
(*=============================================================*)

For[n=-aMSTNcut,n<aMSTNcut+1,n++,aMSTmνm1[n]=aMST[-n]];

int=1;KK[ν_,ϵ_]:=(((E^(I ϵ κ))(((2ϵ κ))^(s-ν-int))(2^(-s))(I^int)Gamma[1-s-2I ϵplus]Gamma[int+2ν+2])/(Gamma[int+ν+1-s+I ϵ]Gamma[int+ν+1+I τ]Gamma[int+ν+1+s+I ϵ]))Sum[(((-1))^n)((Gamma[n+int+2ν+1])/((n-int)!))((Gamma[n+ν+1+s+I ϵ])/(Gamma[n+ν+1-s-I ϵ]))((Gamma[n+ν+1+I τ])/(Gamma[n+ν+1-I τ]))aMST[n],{n,int,60}](((Sum[((((-1))^n)/((int-n)!))((Gamma[int+2ν+2])/(Gamma[n+int+2ν+2]))((Gamma[n+ν+1+s-I ϵ])/(Gamma[ν+1+s-I ϵ]))((Gamma[ν+1-s+I ϵ])/(Gamma[n+ν+1-s+I ϵ]))aMST[n],{n,-60,int}]))^(-1));

KKmνm1[ν_,ϵ_]:=(((E^(I ϵ κ))(((2ϵ κ))^(s-ν-int))(2^(-s))(I^int)Gamma[1-s-2I ϵplus]Gamma[int+2ν+2])/(Gamma[int+ν+1-s+I ϵ]Gamma[int+ν+1+I τ]Gamma[int+ν+1+s+I ϵ]))Sum[(((-1))^n)((Gamma[n+int+2ν+1])/((n-int)!))((Gamma[n+ν+1+s+I ϵ])/(Gamma[n+ν+1-s-I ϵ]))((Gamma[n+ν+1+I τ])/(Gamma[n+ν+1-I τ]))aMSTmνm1[n],{n,int,60}](((Sum[((((-1))^n)/((int-n)!))((Gamma[int+2ν+2])/(Gamma[n+int+2ν+2]))((Gamma[n+ν+1+s-I ϵ])/(Gamma[ν+1+s-I ϵ]))((Gamma[ν+1-s+I ϵ])/(Gamma[n+ν+1-s+I ϵ]))aMSTmνm1[n],{n,-60,int}]))^(-1));

(*KK2[ν_,ϵ_]:=(((((ϵ))^(-m-ν-int))(2^(-ν-int))(((-I))^int)Gamma[1+m-2I ϵ])/(Gamma[int+ν+1+I ϵ]Gamma[int+ν+1+m-I ϵ]Gamma[int+ν+1+m+I ϵ]))Sum[((Gamma[n+ν+1+I ϵ])/((n-int)!))((Gamma[n+int+2ν+1])/(Gamma[n+ν+1-I ϵ]))aMST[n],{n,int,60}](((Sum[((((-I))^n)/((int-n)!))((bMST[n])/(Gamma[n+int+2ν+2])),{n,-60,int}]))^(-1))*)


Aplus[ν_,ϵ_]:=(E^(-(π/2)ϵ))(E^((π/2)I(ν+1-s)))(2^(-1+s-I ϵ))((Gamma[ν+1-s+I ϵ])/(Gamma[ν+1+s-I ϵ]))Sum[aMST[n],{n,-70,70}];
Amins[ν_,ϵ_]:=(E^(-(π/2)ϵ))(E^(-(π/2)I(ν+1+s)))(2^(-1-s+I ϵ))Sum[(((-1))^n)((Gamma[n+ν+1+s-I ϵ])/(Gamma[ν+1+s-I ϵ]))((Gamma[ν+1-s+I ϵ])/(Gamma[n+ν+1-s+I ϵ]))aMST[n],{n,-70,70}];

Binc[ν_,ϵ_]:=(1/ϵ)(KK[ν,ϵ]-I (E^(-I π ν))((Sin[π(ν-s+I ϵ)])/(Sin[π(ν+s-I ϵ)]))KKmνm1[-ν-1,ϵ])Aplus[ν,ϵ](E^(-I(ϵ Log[ϵ])));
Bref[ν_,ϵ_]:=(ϵ^(-1-2s))(KK[ν,ϵ]+I (E^(I π ν))KKmνm1[-ν-1,ϵ])Amins[ν,ϵ](E^(I(ϵ Log[ϵ])));
(*Btrn[ν_,ϵ_]:=(κ^(2s)) (E^(I κ ϵplus(1+((2Log[κ])/(1+κ)))))Sum[aMST[n],{n,-70,70}];*)
(*Binc1[ν_,ϵ_]:=(E^(-(π/2)ϵ))(E^((π/2)I(ν+1+m)))(2^(-1-m-I ϵ))(KK[ν,ϵ]-I (E^(-I π ν))((Sin[π(ν+m+I ϵ)])/(Sin[π(ν-m-I ϵ)]))KK[-ν-1,ϵ])Sum[(I^n)((Gamma[n+ν+1+m+I ϵ])/(Gamma[n+ν+1-m-I ϵ]))bMST[n],{n,-40,40}]
Binc2[ν_,ϵ_]:=(E^(-(π/2)ϵ))(E^((π/2)I(ν+1+m)))(2^(-1-m-I ϵ))(KK2[ν,ϵ]-I (E^(-I π ν))((Sin[π(ν+m+I ϵ)])/(Sin[π(ν-m-I ϵ)]))KK2[-ν-1,ϵ])Sum[(I^n)((Gamma[n+ν+1+m+I ϵ])/(Gamma[n+ν+1-m-I ϵ]))bMST[n],{n,-40,40}]*)

(*TeukBinNorm[ν_,ϵ_]:=((Binc[ν,ϵ])/(Btrn[ν,ϵ]));
TeukBoutNorm[ν_,ϵ_]:=((Bref[ν,ϵ])/(Btrn[ν,ϵ]));*)

TeukBinNorm[ν_,ϵ_]:=Binc[ν,ϵ];
TeukBoutNorm[ν_,ϵ_]:=Bref[ν,ϵ];

TeukBinNorm0=TeukBinNorm[nu,ϵ];

TeukBout=TeukBoutNorm[nu,ϵ];


(*
rplus=(1/2)+(Sqrt[(1/4)-(a^2)]);

c0=-6I ϵ+λ(λ+2)-12a ϵ(a ϵ-m);

Atrn[ν_,ϵ_]:=Btrn[ν,ϵ](Sqrt[rplus])((8-12I ϵ-4(ϵ^2))(rplus^2)+(12I a m-8+8a m ϵ+6I ϵ)rplus+(-4(a^2)(m^2)-6I a m+2));

Aref[ν_,ϵ_]:=-(c0/(4(ϵ^2)))Bref[ν,ϵ];
Ainc[ν_,ϵ_]:=-4(ϵ^2)Binc[ν,ϵ];

LeaverAin[ν_,ϵ_]:=((Ainc[ν,ϵ])/(Atrn[ν,ϵ]));
LeaverAout[ν_,ϵ_]:=((Aref[ν,ϵ])/(Atrn[ν,ϵ]));
AoutL=LeaverAout[nu,ϵ];

LeaverAin0=LeaverAin[nu,ϵ];
*)


ωq=ωq0+Δ;

αθ[n_,ω_]:=-2(n+1)(n+2k1+1);
βθ[n_,ω_,θ_]:=n(n-1)+2n(k1+k2+1-2a ω)-(2a ω(2k1+s+1)-(k1+k2)(k1+k2+1))-((a^2)(ω^2)+s(s+1)+(l(l+1)-s(s+1)+θ));
γθ[n_,ω_]:=2a ω(n+k1+k2+s);


tryTnInfiniteθ=Module[{Tn},For[{n=Nmax-1;Tn=βθ[n+1,ωq,θ];},n>=Ninversionθ,{Tn=βθ[n,ωq,θ]-((αθ[n,ωq]γθ[n+1,ωq])/Tn);n--}];Tn];

tryTnfiniteθ=βθ[Ninversionθ,ωq,θ]-Module[{Tn},For[{n=0;Tn=βθ[0,ωq,θ];},n<Ninversionθ,{Tn=βθ[n+1,ωq,θ]-((αθ[n,ωq]γθ[n+1,ωq])/Tn);n++}];Tn];



θtry=FindRoot[tryTnfiniteθ==tryTnInfiniteθ,{θ,tempθ}];
θnew=θ/.θtry;

Almnew=l(l+1)-s(s+1)+θnew;

ϵ=ωq;


λ=Almnew+(((a ωq))^2)-2a m ωq;


τ=((ϵ-m q)/κ);
ϵplus=((ϵ+τ)/2);


αMST[n_,mu_]:=((I ϵ κ(n+mu+1+s+I ϵ)(n+mu+1+s-I ϵ)(n+mu+1+I τ))/((n+mu+1)(2n+2mu+3)));
αprimeMST[n_,mu_]:=-I(((n+mu+1-s+I ϵ)(n+mu+1-s-I ϵ))/((n+mu+1+s+I ϵ)(n+mu+1+s-I ϵ)))αMST[n,mu];
βMST[n_,mu_]:=-λ-s(1+s)+(n+mu)(n+mu+1)+(ϵ^2)+ϵ(ϵ-m q)+((ϵ(ϵ-m q)((s^2)+(ϵ^2)))/((n+mu)(n+mu+1)));
γMST[n_,mu_]:=-((I ϵ κ(n+mu-s+I ϵ)(n+mu-s-I ϵ)(n+mu-I τ))/((n+mu)(2n+2mu-1)));
γprimeMST[n_,mu_]:=I(((mu+n+s+I ϵ)(mu+n+s-I ϵ))/((mu+n-s+I ϵ)(mu+n-s-I ϵ)))γMST[n,mu];


NMST=0; 

MSTplus=Module[{Tn},For[{n=NmaxMST-1;Tn=βMST[n+1,ν];},n>=NMST,{Tn=βMST[n,ν]-((αprimeMST[n,ν]γprimeMST[n+1,ν])/Tn);n--}];Tn];

MSTminus=βMST[NMST,ν]-Module[{Tn},For[{n=NmaxMST-1;Tn=βMST[-n-1,ν];},n≥-NMST,{Tn=βMST[-n,ν]-((αprimeMST[-n-1,ν]γprimeMST[-n,ν])/Tn);n--}];Tn];
nu=ν/.FindRoot[MSTplus==MSTminus,{ν,nu}];


aMST[0]=1;
(*
aMSTNcut is to control how many terms for aMST[n] I want;
NmaxMST is to control for each term of aMST[n]; from which (lowest,staying at most bottom level of the continued fraction)term of βMST[n,nu], it start the recurrence, going from most bottom to the most up. See the example below.
*)
(*================================================================================================================================*)
(*================================= Next Build All Positive aMST[L] Terms =================================*)


For[i=1,i<aMSTNcut+1,i++,aMST[i]=(1/(αMST[i-1,nu]))(-βMST[i-1,nu]+Module[{Tn},For[{n=NmaxMST-1;Tn=βMST[n+1,nu];},n≥(i-1),{Tn=βMST[n,nu]-((αMST[n,nu]γMST[n+1,nu])/Tn);n--}];Tn])aMST[i-1]];


(*================================= Next Build All Negative a[-L] Terms =================================*)
(*================================= Next Build All Negative a[-L] Terms =================================*)

For[i=1,i<aMSTNcut+1,i++,aMST[-i]=-αMST[-i,nu](((Module[{Tn},For[{n=-NmaxMST+1;Tn=βMST[n-1,nu];},n<-i+1,{Tn=βMST[n,nu]-((γMST[n,nu]αMST[n-1,nu])/Tn);n++}];Tn]))^(-1))aMST[-i+1]];
(*=============================================================*)

For[n=-aMSTNcut,n<aMSTNcut+1,n++,aMSTmνm1[n]=aMST[-n]];

int=1;

KK[ν_,ϵ_]:=(((E^(I ϵ κ))(((2ϵ κ))^(s-ν-int))(2^(-s))(I^int)Gamma[1-s-2I ϵplus]Gamma[int+2ν+2])/(Gamma[int+ν+1-s+I ϵ]Gamma[int+ν+1+I τ]Gamma[int+ν+1+s+I ϵ]))Sum[(((-1))^n)((Gamma[n+int+2ν+1])/((n-int)!))((Gamma[n+ν+1+s+I ϵ])/(Gamma[n+ν+1-s-I ϵ]))((Gamma[n+ν+1+I τ])/(Gamma[n+ν+1-I τ]))aMST[n],{n,int,60}](((Sum[((((-1))^n)/((int-n)!))((Gamma[int+2ν+2])/(Gamma[n+int+2ν+2]))((Gamma[n+ν+1+s-I ϵ])/(Gamma[ν+1+s-I ϵ]))((Gamma[ν+1-s+I ϵ])/(Gamma[n+ν+1-s+I ϵ]))aMST[n],{n,-60,int}]))^(-1));

KKmνm1[ν_,ϵ_]:=(((E^(I ϵ κ))(((2ϵ κ))^(s-ν-int))(2^(-s))(I^int)Gamma[1-s-2I ϵplus]Gamma[int+2ν+2])/(Gamma[int+ν+1-s+I ϵ]Gamma[int+ν+1+I τ]Gamma[int+ν+1+s+I ϵ]))Sum[(((-1))^n)((Gamma[n+int+2ν+1])/((n-int)!))((Gamma[n+ν+1+s+I ϵ])/(Gamma[n+ν+1-s-I ϵ]))((Gamma[n+ν+1+I τ])/(Gamma[n+ν+1-I τ]))aMSTmνm1[n],{n,int,60}](((Sum[((((-1))^n)/((int-n)!))((Gamma[int+2ν+2])/(Gamma[n+int+2ν+2]))((Gamma[n+ν+1+s-I ϵ])/(Gamma[ν+1+s-I ϵ]))((Gamma[ν+1-s+I ϵ])/(Gamma[n+ν+1-s+I ϵ]))aMSTmνm1[n],{n,-60,int}]))^(-1));




Aplus[ν_,ϵ_]:=(E^(-(π/2)ϵ))(E^((π/2)I(ν+1-s)))(2^(-1+s-I ϵ))((Gamma[ν+1-s+I ϵ])/(Gamma[ν+1+s-I ϵ]))Sum[aMST[n],{n,-70,70}];
Amins[ν_,ϵ_]:=(E^(-(π/2)ϵ))(E^(-(π/2)I(ν+1+s)))(2^(-1-s+I ϵ))Sum[(((-1))^n)((Gamma[n+ν+1+s-I ϵ])/(Gamma[ν+1+s-I ϵ]))((Gamma[ν+1-s+I ϵ])/(Gamma[n+ν+1-s+I ϵ]))aMST[n],{n,-70,70}];

Binc[ν_,ϵ_]:=(1/ϵ)(KK[ν,ϵ]-I (E^(-I π ν))((Sin[π(ν-s+I ϵ)])/(Sin[π(ν+s-I ϵ)]))KKmνm1[-ν-1,ϵ])Aplus[ν,ϵ](E^(-I(ϵ Log[ϵ])));
Bref[ν_,ϵ_]:=(ϵ^(-1-2s))(KK[ν,ϵ]+I (E^(I π ν))KKmνm1[-ν-1,ϵ])Amins[ν,ϵ](E^(I(ϵ Log[ϵ])));
(*Btrn[ν_,ϵ_]:=(κ^(2s)) (E^(I κ ϵplus(1+((2Log[κ])/(1+κ)))))Sum[aMST[n],{n,-70,70}];*)

(*TeukBinNorm[ν_,ϵ_]:=((Binc[ν,ϵ])/(Btrn[ν,ϵ]));*)

TeukBinNorm[ν_,ϵ_]:=Binc[ν,ϵ];
TeukBinNorm1=TeukBinNorm[nu,ϵ];



(*c0=-6I ϵ+λ(λ+2)-12a ϵ(a ϵ-m);

Atrn[ν_,ϵ_]:=Btrn[ν,ϵ](Sqrt[rplus])((8-12I ϵ-4(ϵ^2))(rplus^2)+(12I a m-8+8a m ϵ+6I ϵ)rplus+(-4(a^2)(m^2)-6I a m+2));

Aref[ν_,ϵ_]:=-(c0/(4(ϵ^2)))Bref[ν,ϵ];
Ainc[ν_,ϵ_]:=-4(ϵ^2)Binc[ν,ϵ];

LeaverAin[ν_,ϵ_]:=((Ainc[ν,ϵ])/(Atrn[ν,ϵ]));

LeaverAin1=LeaverAin[nu,ϵ];

αq=((LeaverAin1-LeaverAin0)/Δ)I;
ExcitationBq=(AoutL/(2(-I ωq0) αq ));
*)




Teukαq=((TeukBinNorm1-TeukBinNorm0)/Δ)I;
TeukExcitationBq=(TeukBout/(2(-I ωq0) Teukαq ));

RWBqGrav=(((λ0(λ0+2)-6I ωq0-12a ωq0(a ωq0-m)))/(16((ωq0)^4)))TeukExcitationBq;

If[Abs[TeukBinNorm0]<ϵϵϵ,Print[2a,"    ",Abs[TeukBinNorm0],"    ",TeukExcitationBq,"    ",RWBqGrav];
Gravl2n3[[ith+1]][[6]]=Re[TeukExcitationBq];
Gravl2n3[[ith+1]][[7]]=Im[TeukExcitationBq];
Gravl2n3[[ith+1]][[8]]=Re[RWBqGrav];
Gravl2n3[[ith+1]][[9]]=Im[RWBqGrav];
If[Element[ith/30,Integers],Export["tempBql2n3.dat",Grid[N[Round[Gravl2n3,10^-10],8]]]],(*nul2n3[[ith+1]][[1]]=-777;*)Print[2a,"    ",Abs[TeukBinNorm0],"    ",nul2n3[[ith+1]][[1]],"    ",Nmax];
If[ith<999,Nmax=Nmax+200;ith=ith-1,ϵϵϵ=(10^(-7));Nmax=Nmax+700;ith=ith-1]]];

If[m==2,Print[Gravl2n3];Export["Bql2m2n3.dat",Grid[N[Round[Gravl2n3,(10^(-10))],8]]],
If[m==1,Print[Gravl2n3];Export["Bql2m1n3.dat",Grid[N[Round[Gravl2n3,(10^(-10))],8]]],
If[m==-1,Print[Gravl2n3];Export["Bql2mm1n3.dat",Grid[N[Round[Gravl2n3,(10^(-10))],8]]],
Print[Gravl2n3];Export["Bql2mm2n3.dat",Grid[N[Round[Gravl2n3,(10^(-10))],8]]]]]]
]