Question: Double integration and summation. How to speed up?

Hello.

Regarding to my previous question I'd like to speed up calculations of the expression. 

restart;
tt := -0.689609e-3; T_c := .242731; mu := .365908; k := 1;
R1 := a*tanh((a^2-mu)/(2*T_c))*ln((2*a^2+2*a*q+q^2-2*mu-(I*2)*Pi*N)/(2*a^2-2*a*q+q^2-2*mu-(I*2)*Pi*N))/q-2;
R2 := Int(R1, a = 0 .. 10000);
R3 := q*ln((-q^2-k^2+mu+I*(2*N*Pi*T_c-(2*m+1)*Pi*T_c)+k*q)/(-q^2-k^2+mu+I*(2*N*Pi*T_c-(2*m+1)*Pi*T_c)-k*q))/(k*(tt+R2));
R4 := Sum(R3, N = -100 .. 100);
m := 1;
R5 := Int(R4, q = 0.1e-2 .. 10000);
R6 := evalf(R5);

Here I have integration procedure inside the expression R3, then the summation over the integer parameter N and then finally the integration again.

Is it possible to speed up calculations of this cumbersome expression? Or actually was I correct to write this simple code?

Thank you in a advance.