R=N[1/12(({{-6+8I, 11I}, {4I, -6-8I}}))];

G=N[1/12(({{2-2I, -1-5I}, {4-4I, -2-10I}}))];

(Subscript[N, c])=4;

Lc=3;

(Subscript[k, 0])=100;

(Subscript[M, q_])[n_,s_]:=

(Subscript[F, q_])[n_,s_,l_]:=N[(D[((((G[[1,1]]z+R[[1,1]]z t+G[[1,2]]+t R[[1,2]]))^n)/(((G[[2,1]]z+R[[2,1]]z t+G[[2,2]]+t R[[2,2]]))^(n+q))),{z,s},{t,l}]/.{z->0,t->0})/(s! l!)]

(Subscript[F, q_])[n_,s_,l_]:=N[(D[(D[(((((G[[1,1]]/t+R[[1,1]])z+G[[1,2]]/t+R[[1,2]]))^n)/((((G[[2,1]]/t+R[[2,1]])z+G[[2,2]]/t+R[[2,2]]))^(n+q))),{z,s}]/.z->0),{t,l}]/.t->0)/(s! l!)]

(Subscript[F, q_])[n_,s_,l_]:=If[l==0&&s==0,N[((R[[1,2]])^n)/((R[[2,2]])^(n+q))],N[(D[((((G[[1,1]]z+R[[1,1]]z t+G[[1,2]]+t R[[1,2]]))^n)/(((G[[2,1]]z+R[[2,1]]z t+G[[2,2]]+t R[[2,2]]))^(n+q))),{z,s},{t,l}]/.{z->0,t->0})/s!/l!]]

(Subscript[La, q_])[k_,m_,n_,r_,s_]:=N[(∑_(l=0)^Lc)(k^(-(l+2q)))(∑_(lp=0)^l)(Subscript[F, q])[m,r,l-lp]\[Conjugate](Subscript[F, q])[n,s,lp]]

(Subscript[L, q_])[k0_,m_,n_,r_,s_]:=N[2 Re[(∑_(k=1)^(k0-1))(Subscript[La, q])[k,m,n,r,s]]]

Lm[q_,k0_,Nc_]:=Table[(Subscript[L, q])[k0,m,n,r,s],{m,Nc},{n,Nc},{r,Nc},{s,Nc}]

nextStep[c_,q_,Nc_,k0_,P_]:=(∑_(m=1)^Nc)((∑_(n=1)^Nc)(c[[m,n]]Table[P[[m,n,r,s]],{r,Nc},{s,Nc}]))

Φ00=Table[If[m==n&&m==1,1.,0.],{m,4},{n,4}]

Φ2[[1,1]]/Φ[[1,1]]

P=Lm[1.3,10,15];

Φ2/Φ//MatrixForm

Φ2=nextStep[Φ,1.3,4,10,P]

λ[q_]:=Block[{Nc=6,iter=10,k=100,Φ=Φ00,previous=Φ00},
For[i=0,i<iter,i++,
previous=Φ;
Φ=nextStep[Φ,q,Nc,k];
];
Φ[[1,1]]/previous[[1,1]]
]

λ[1.3]

secant[x0_,y0_,x1_,y1_]:=x0-(y0-1)(((x1-x0)/(y1-y0)))

secant[1.28,0.965962,1.31,0.949541]