(* The tentative proper Zolotarev-polynomial S13αβ[x]=a0+a1*x+a2*x^2+a3*x^3+a4*x^4+a5*x^5+a6*x^6+a7*x^7+a8*x^8+a9*x^9+a10*x^10+a11*x^11+a12*x^12+a13*x^13 *)

(* we write down the single coefficients *)

Coefficient[%1,x,13]

(* above is coefficient a13 *)

Coefficient[%1,x,12]//Simplify

(* above is coefficient a12 = -n*s = -13*s ; division by (-13) would yield s=s13(α,β)*)

Coefficient[%1,x,11]//Simplify

(* above is coefficient a11 *)

Coefficient[%1,x,10]//Simplify

(* above is coefficient a10 *)

Coefficient[%1,x,9]//Simplify

(* above is coefficient a9 *)

Coefficient[%1,x,8]//Simplify

(* above is coefficient a8 *)

Coefficient[%1,x,7]//Simplify

(* above is coefficient a7 *)

Coefficient[%1,x,6]//Simplify

(* above is coefficient a6 *)

Coefficient[%1,x,5]//Simplify

(* above is coefficient a5 *)

Coefficient[%1,x,4]//Simplify

(* above is coefficient a4 *)

Coefficient[%1,x,3]//Simplify

(* above is coefficient a3 *)

Coefficient[%1,x,2]//Simplify

(* above is coefficient a2 *)

Coefficient[%1,x,1]//Simplify

(* above is coefficient a1 *)

Coefficient[%1,x,0]//Simplify

(* above is coefficient a0 *)