(*

In "S-unit equations, binary forms and curves of genus 2"
(Proc. London Math. Soc. (3) 75 (1997), no. 2, 271--307), N. P. Smart
lists all genus 2 curves with good reduction away from 2. He organizes
them into putative isogeny classes. This file contains a proof that
these isogeny classes are in fact correct. (Note that the isogenies in
this file are sometimes different than the ones in the published form
of the paper - both sets of isogenies are correct)

This file can be read by Mathematica 3.0

This file contains:

1) SmartCurves: A list containing all the curves given by Smart (the
  entry is a polynomial f(x), such that the curves is given by y^2 =
  f(x)). Each entry in the list is a list containing the curves in a
  given isogeny class.

2) The following arrays:
  s1, s2, alpha and nx.

  alpha[n,i,j] is the complex representation of an isogeny between the
  curves given by SmartCurves[[n,i]] and SmartCurves[[n,j]].  Let
  (x1,y1)+(x2,y2) represent the image of (x,y)+Q0 under this isogeny
  (where Q0 is a fixed Weierstrass point on the first curve). Then
  s1[n,i,j] is x1+x2 as a rational function of x. s2[n,i,j] is x1*x2.

  In some cases some of the curves in an isogeny class as listed by
  Smart are in fact isomorphic (over Q). If this is the case nx[n,i,j]
  gives the image of x under such an isomorphism.

3) The function CheckIsogeny.

Let alpha be the complex representation of an isogeny between two
genus 2 curves given by y^2 = pol1 and y^2 = pol2.  As above let s1 be
x1+x2 as a rational function of x. Let s2 = x1*x2. Then
CheckIsogeny[s1,s2,alpha,pol1,pol2] will return {t1,t2} where t1 = y1+y2
and t2 = x1*y1+x2*y2, if s1,s2,alpha is correct, and will return False
otherwise. 

4) The function CheckIsomorphism.

Let nx be the image of (x,y) on y^2 = pol1 under some isomorphism from
this curve to y^2 = pol2. Then CheckIsomorphism[nx,pol1,pol2] will give the new y if nx does give an isomorphism and False otherwise.

*)

CheckIsogeny[n_Integer,i_Integer,j_Integer] := CheckIsogeny[s1[n,i,j],s2[n,i,j],alpha[n,i,j],SmartCurves[[n,i]],SmartCurves[[n,j]]];

CheckIsogeny[xpx_,xmx_,alpha_,pol1_,pol2_] := Module[{sd,s1,s2,as,g2,g,q22,q32,ans},
  sd = PolynomialLCM[Denominator[xpx],Denominator[xmx],Extension -> Automatic];
  s1 = Simplify[xpx*sd];
  s2 = Simplify[xmx*sd];
  as = Join[CoefficientList[pol2,x],{0}];
  g2 = Expand[
  sd^6*as[[1]]^2 + s1*(sd^5*as[[1]]*as[[2]] + 
      s1*(sd^4*as[[1]]*as[[3]] + 
         s1*(sd^3*as[[1]]*as[[4]] + 
            s1*(sd^2*as[[1]]*as[[5]] + 
               s1*(sd*as[[1]]*as[[6]] + s1*as[[1]]*as[[7]] + 
                  s2*as[[2]]*as[[7]]) + 
               s2*(s2*as[[3]]*as[[7]] + 
                  sd*(as[[2]]*as[[6]] - 6*as[[1]]*as[[7]]))) + 
            s2*(sd^2*(as[[2]]*as[[5]] - 5*as[[1]]*as[[6]]) + 
               s2*(s2*as[[4]]*as[[7]] + 
                  sd*(as[[3]]*as[[6]] - 5*as[[2]]*as[[7]])))) + 
         s2*(sd^3*(as[[2]]*as[[4]] - 4*as[[1]]*as[[5]]) + 
            s2*(sd^2*(as[[3]]*as[[5]] - 4*as[[2]]*as[[6]] + 
                  9*as[[1]]*as[[7]]) + 
               s2*(s2*as[[5]]*as[[7]] + 
                  sd*(as[[4]]*as[[6]] - 4*as[[3]]*as[[7]]))))) + 
      s2*(sd^4*(as[[2]]*as[[3]] - 3*as[[1]]*as[[4]]) + 
         s2*(sd^3*(as[[3]]*as[[4]] - 3*as[[2]]*as[[5]] + 
               5*as[[1]]*as[[6]]) + 
            s2*(sd^2*(as[[4]]*as[[5]] - 3*as[[3]]*as[[6]] + 
                  5*as[[2]]*as[[7]]) + 
               s2*(s2*as[[6]]*as[[7]] + 
                  sd*(as[[5]]*as[[6]] - 3*as[[4]]*as[[7]])))))) + 
   s2*(sd^5*(as[[2]]^2 - 2*as[[1]]*as[[3]]) + 
      s2*(sd^4*(as[[3]]^2 - 2*as[[2]]*as[[4]] + 2*as[[1]]*as[[5]]) + 
         s2*(sd^3*(as[[4]]^2 - 2*as[[3]]*as[[5]] + 2*as[[2]]*as[[6]] - 
               2*as[[1]]*as[[7]]) + 
            s2*(sd^2*(as[[5]]^2 - 2*as[[4]]*as[[6]] + 2*as[[3]]*as[[7]]) + 
               s2*(s2*as[[7]]^2 + sd*(as[[6]]^2 - 2*as[[5]]*as[[7]]))))))];
  g = NFPolynomialSqrt[g2];
  If[g === False,
    Print["Could not find big square root!"],
  q22 = Expand[  s1^6*as[[7]] + sd*(s1^5*as[[6]] - 6*s1^4*s2*as[[7]] + 
      sd*(s1^4*as[[5]] + s2*(-5*s1^3*as[[6]] + 9*s1^2*s2*as[[7]]) + 
         sd*(s1^3*as[[4]] + sd*
             (s1^2*as[[3]] + sd*(2*sd*as[[1]] + s1*as[[2]] - 2*s2*as[[3]]) + 
               s2*(-3*s1*as[[4]] + 2*s2*as[[5]])) + 
            s2*(-4*s1^2*as[[5]] + s2*(5*s1*as[[6]] - 2*s2*as[[7]])))))];
  q32 = Expand[  s1^8*as[[7]] + sd*(s1^6*(s1*as[[6]] - 8*s2*as[[7]]) + 
      sd*(s1^4*(s1*(s1*as[[5]] - 7*s2*as[[6]]) + 20*s2^2*as[[7]]) + 
         sd*(s1^2*(s1*(s1*(s1*as[[4]] - 6*s2*as[[5]]) + 14*s2^2*as[[6]]) - 
               16*s2^3*as[[7]]) + 
            sd*(sd*(sd*(-2*s2*sd*as[[1]] + s1*(s1*as[[1]] - 3*s2*as[[2]]) + 
                     2*s2^2*as[[3]]) + 
                  s1*(s1*(s1*as[[2]] - 4*s2*as[[3]]) + 5*s2^2*as[[4]]) - 
                  2*s2^3*as[[5]]) + 
               s1*(s1*(s1*(s1*as[[3]] - 5*s2*as[[4]]) + 9*s2^2*as[[5]]) - 
                  7*s2^3*as[[6]]) + 2*s2^4*as[[7]]))))];
  ans = Join[CheckIs2[pol1,s1,s2,sd,g,q22,q32,alpha],CheckIs2[pol1,s1,s2,sd,-g,q22,q32,alpha]];
  If[Length[ans] === 0,False,
    If[Length[ans] === 1,ans[[1]],
      If[Length[ans] === 2,
        If[Simplify[ans[[1]]-ans[[2]]] === {0,0},ans[[1]],
          Print["Huh?"];ans]]]]]]
  
  
CheckIs2[pol1_,s1_,s2_,sd_,q1_,q22_,q32_,alpha_] := Module[{q2,q3},
  q2 = NFPolynomialSqrt[Cancel[(q22+2*q1*sd^3)/pol1]];
  If[q2 === False,{},
    q3 = NFPolynomialSqrt[Cancel[(q32+2*s2*q1*sd^4)/pol1]];
    If[q3 === False,{},
      Join[CheckIs3[pol1,s1,s2,sd,q1,q2,q3,alpha],CheckIs3[pol1,s1,s2,sd,q1,q2,-q3,alpha]]]]]

CheckIs3[pol1_,s1_,s2_,sd_,q1_,q2_,q3_,alpha_] := Module[{dum,dum2},
  dum = Cancel[pol1*((sd*D[s1,x]-s1*D[sd,x])*(s1^2*q2 - 2*sd*s2*q2 - s1*q3) + 
          sd*(sd*D[s2,x]-s2*D[sd,x])*(2*q3 - s1*q2))/((s1^2-4*s2*sd)*q1*sd^2)];
  dum = Cancel[dum/(alpha[[1]].{1,x})];
  If[Not[MemberQ[{-1,1},dum]],{},
    dum2 = Cancel[pol1*((sd*D[s1,x]-s1*D[sd,x])*(s1^3*q2 - 3*sd*s1*s2*q2 - s1^2*q3 + 2*sd*s2*q3) + sd*(sd*D[s2,x]-s2*D[sd,x])*(-s1^2*q2 + 2*sd*s2*q2 + s1*q3))/((s1^2-4*sd*s2)*q1*sd^3)];
    If[dum*Cancel[dum2/(alpha[[2]].{1,x})] =!= 1,{},
      {{y*dum*Cancel[q2/sd^3],y*dum*Cancel[q3/sd^4]}}]]];

NFPolynomialSqrt[pol_] := Module[{dum},
  If[NumberQ[N[pol]],Sqrt[pol],
  If[Not[PolynomialQ[pol,Variables[pol][[1]]]],False,
  dum = FactorSquareFree[pol,Extension -> Automatic];
  If[Head[dum] === Times,
    dum = Map[FactorSqrt,dum,1];
    If[Expand[dum^2 - pol] === 0,dum,False],
    dum = FactorSqrt[dum];
    If[Expand[dum^2 - pol] === 0,dum,False]]]]];

FactorSqrt[pol_] := 
  If[NumberQ[N[pol]],Sqrt[pol],
    If[Head[pol] === Power,
      If[Mod[pol[[2]],2] === 0,
        MapAt[#/2&,pol,{2}],
        False],
      False]]

CheckIsomorphism[n_Integer,i_Integer,j_Integer] := CheckIsomorphism[nx[n,i,j],SmartCurves[[n,i]],SmartCurves[[n,j]]];

CheckIsomorphism[nx_,pol1_,pol2_] := Module[{dum,dum2,dum3},
  dum = Cancel[(pol2 /. x -> nx)/pol1];
  dum2 = NFPolynomialSqrt[Numerator[dum]];
  If[dum2 === False,False,
    dum3 = NFPolynomialSqrt[Denominator[dum]];
    If[dum3 === False,False,
      y*Simplify[dum2/dum3]]]]

SmartCurves = 
  {{(-1 + x)*x*(1 + x)*(1 + x^2)}, 
   {(-2 + x)*(-1 + x)*x*(-2 + x^2), x*(1 - 8*x + 18*x^2 + 8*x^3 + x^4), 
    x*(16 - 64*x + 72*x^2 + 16*x^3 + x^4), 
    (-2 + x^2)*(2 + x^2)*(6 - 8*x + 3*x^2)}, 
   {(-2 + x)*x*(2 + x)*(-2 + x^2), x*(4 + x^2)*(8 + x^2), 
    x*(1 + 20*x + 102*x^2 + 148*x^3 + x^4), 
    x*(1 - 20*x + 102*x^2 - 148*x^3 + x^4)}, 
   {(-4 + x)*x*(4 + x)*(-8 + x^2), x*(1 + x^2)*(2 + x^2), 
    x*(16 + 160*x + 408*x^2 + 296*x^3 + x^4), 
    x*(16 - 160*x + 408*x^2 - 296*x^3 + x^4)}, 
   {x*(2 - 2*x + x^2)*(2 + 2*x + x^2)}, 
   {x*(8 + x^2)*(8 - 4*x + x^2), x*(2 + x^2)*(2 - 2*x + x^2), 
    x*(4 + 16*x + 12*x^2 + 8*x^3 + x^4), 
    (3 + 2*x + x^2)*(23 + 20*x + 30*x^2 + 12*x^3 + 7*x^4), 
    2*(3 + 2*x + x^2)*(23 + 20*x + 30*x^2 + 12*x^3 + 7*x^4)}, 
   {x*(2 + x^2)*(2 + 2*x + x^2), x*(8 + x^2)*(8 + 4*x + x^2), 
    x*(4 - 16*x + 12*x^2 - 8*x^3 + x^4), 
    -2*(3 + 2*x + x^2)*(23 + 20*x + 30*x^2 + 12*x^3 + 7*x^4), 
    -((3 + 2*x + x^2)*(23 + 20*x + 30*x^2 + 12*x^3 + 7*x^4))}, 
   {x*(-2 + x^2)*(2 - 2*x + x^2), x*(-8 + x^2)*(8 + 4*x + x^2), 
    x*(16 - 96*x + 136*x^2 - 40*x^3 + x^4), 
    x*(1 + 12*x + 34*x^2 + 20*x^3 + x^4), 
    2*(-2 + x^2)*(2 - 4*x + x^2)*(6 - 4*x + x^2)}, 
   {x*(-8 + x^2)*(8 - 4*x + x^2), x*(-2 + x^2)*(2 + 2*x + x^2), 
    x*(1 - 12*x + 34*x^2 - 20*x^3 + x^4), 
    x*(16 + 96*x + 136*x^2 + 40*x^3 + x^4), 
    (-2 + x^2)*(2 - 4*x + x^2)*(6 - 4*x + x^2)}, 
   {x*(8 - 8*x + x^2)*(8 - 4*x + x^2), x*(2 - 4*x + x^2)*(2 - 2*x + x^2), 
    -2*(-1 + 2*x^2)*(17 - 24*x - 12*x^2 + 16*x^3 + 4*x^4), 
    -((-1 + 2*x^2)*(17 - 24*x - 12*x^2 + 16*x^3 + 4*x^4)), 
    -2*(1 + x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4), 
    -((1 + x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4))}, 
   {x*(2 + 2*x + x^2)*(2 + 4*x + x^2), x*(8 + 4*x + x^2)*(8 + 8*x + x^2), 
    (-1 + 2*x^2)*(17 - 24*x - 12*x^2 + 16*x^3 + 4*x^4), 
    2*(-1 + 2*x^2)*(17 - 24*x - 12*x^2 + 16*x^3 + 4*x^4), 
    (1 + x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4), 
    2*(1 + x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4)}, 
   {x*(4 + x^2)*(-4 - 4*x + x^2)}, {x*(1 + x^2)*(-1 - 2*x + x^2)}, 
   {x*(1 + x^2)*(-1 + 2*x + x^2)}, {x*(4 + x^2)*(-4 + 4*x + x^2)}, 
   {x*(-2 + x^2)*(2 + x^2), (2 + x^2)*(2 + 4*x + x^2)*(6 + 8*x + 3*x^2), 
    2*(2 + x^2)*(2 + 4*x + x^2)*(6 + 8*x + 3*x^2)}, 
   {x*(8 + x^2)*(8 - 8*x + x^2), x*(64 + 256*x + 240*x^2 + 32*x^3 + x^4), 
    x*(4 + 32*x + 60*x^2 + 16*x^3 + x^4), 
    (3 - 2*x + x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4), 
    2*(3 - 2*x + x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4)}, 
   {x*(2 + x^2)*(2 + 4*x + x^2), x*(4 - 32*x + 60*x^2 - 16*x^3 + x^4), 
    x*(64 - 256*x + 240*x^2 - 32*x^3 + x^4), 
    -2*(3 - 2*x + x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4), 
    -((3 - 2*x + x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4))}, 
   {x*(-4 - 4*x + x^2)*(-4 + 4*x + x^2), x*(1 + 6*x^2 + x^4), 
    (-1 + 2*x + x^2)*(5 - 8*x - 6*x^2 + 8*x^3 + 5*x^4)}, 
   {x*(-1 - 2*x + x^2)*(-1 + 2*x + x^2), x*(16 + 24*x^2 + x^4), 
    2*(-1 + 2*x + x^2)*(5 - 8*x - 6*x^2 + 8*x^3 + 5*x^4)}, 
   {x*(-8 + x^2)*(8 - 8*x + x^2), x*(-2 + x^2)*(2 + 4*x + x^2), 
    x*(16 + 96*x + 40*x^2 + 8*x^3 + x^4), 
    x*(1 - 12*x + 10*x^2 - 4*x^3 + x^4), 
    2*(-2 + x^2)*(2 + x^2)*(2 - 2*x + x^2)}, 
   {x*(-2 + x^2)*(2 - 4*x + x^2), x*(-8 + x^2)*(8 + 8*x + x^2), 
    x*(1 + 12*x + 10*x^2 + 4*x^3 + x^4), 
    x*(16 - 96*x + 40*x^2 - 8*x^3 + x^4), 
    (-2 + x^2)*(2 + x^2)*(2 - 2*x + x^2)}, 
   {x*(2 - 4*x + x^2)*(2 + 4*x + x^2), x*(4 + 12*x^2 + x^4)}, 
   {x*(128 + 128*x + 48*x^2 + 8*x^3 + x^4), 
    x*(1 + 4*x - 2*x^2 - 12*x^3 + x^4), x*(1 + 4*x^2 + 4*x^3 + x^4), 
    -2*(2 + 2*x + x^2)*(2 + x^4)}, 
   {x*(8 + 16*x + 12*x^2 + 4*x^3 + x^4), 
    x*(16 + 32*x - 8*x^2 - 24*x^3 + x^4), x*(16 + 16*x^2 + 8*x^3 + x^4), 
    -((2 + 2*x + x^2)*(2 + x^4))}, 
   {x*(8 - 16*x + 12*x^2 - 4*x^3 + x^4), 
    x*(16 - 32*x - 8*x^2 + 24*x^3 + x^4), x*(16 + 16*x^2 - 8*x^3 + x^4), 
    (2 + 2*x + x^2)*(2 + x^4)}, 
   {x*(128 - 128*x + 48*x^2 - 8*x^3 + x^4), 
    x*(1 - 4*x - 2*x^2 + 12*x^3 + x^4), x*(1 + 4*x^2 - 4*x^3 + x^4), 
    2*(2 + 2*x + x^2)*(2 + x^4)}, 
   {x*(1 + x^4), x*(16 + x^4), 
    -((-2 + x^2)*(14 - 8*x + x^2)*(6 - 4*x + x^2)), 
    (-2 + x^2)*(14 - 8*x + x^2)*(6 - 4*x + x^2)}, 
   {x*(-16 + 32*x + 24*x^2 + 8*x^3 + x^4), x*(-2 + 4*x^2 + 4*x^3 + x^4)}, 
   {x*(-1 + 4*x + 6*x^2 + 4*x^3 + x^4), x*(-32 + 16*x^2 + 8*x^3 + x^4)}, 
   {x*(-1 - 4*x + 6*x^2 - 4*x^3 + x^4), x*(-32 + 16*x^2 - 8*x^3 + x^4)}, 
   {x*(-16 - 32*x + 24*x^2 - 8*x^3 + x^4), x*(-2 + 4*x^2 - 4*x^3 + x^4)}, 
   {x*(-2 + x^4), x*(-32 + x^4)}, 
   {x*(32 + 64*x + 48*x^2 + 16*x^3 + x^4), x*(-2 + 8*x - 8*x^2 + x^4)}, 
   {x*(2 + 8*x + 12*x^2 + 8*x^3 + x^4), x*(-32 + 64*x - 32*x^2 + x^4)}, 
   {x*(2 - 8*x + 12*x^2 - 8*x^3 + x^4), x*(-32 - 64*x - 32*x^2 + x^4)}, 
   {x*(32 - 64*x + 48*x^2 - 16*x^3 + x^4), x*(-2 - 8*x - 8*x^2 + x^4)}, 
   {x*(1 - 12*x + 6*x^2 - 12*x^3 + x^4), -2*(2 + x^2)*(-2 + x^4)}, 
   {x*(16 - 96*x + 24*x^2 - 24*x^3 + x^4), -((2 + x^2)*(-2 + x^4))}, 
   {x*(16 + 96*x + 24*x^2 + 24*x^3 + x^4), (2 + x^2)*(-2 + x^4)}, 
   {x*(1 + 12*x + 6*x^2 + 12*x^3 + x^4), 2*(2 + x^2)*(-2 + x^4)}, 
   {x*(2 + x^4), x*(32 + x^4)}, 
   {x*(1 + 4*x + 10*x^2 - 4*x^3 + x^4), 
    x*(16 + 32*x - 24*x^2 - 8*x^3 + x^4)}, 
   {x*(16 + 32*x + 40*x^2 - 8*x^3 + x^4), x*(1 - 4*x - 6*x^2 + 4*x^3 + x^4)}, 
   {x*(4 - 16*x + 28*x^2 - 8*x^3 + x^4), 
    (3 + 2*x + x^2)*(5 + 8*x + 6*x^2 + x^4), 
    2*(3 + 2*x + x^2)*(5 + 8*x + 6*x^2 + x^4)}, 
   {x*(4 + 16*x + 28*x^2 + 8*x^3 + x^4), 
    -2*(3 + 2*x + x^2)*(5 + 8*x + 6*x^2 + x^4), 
    -((3 + 2*x + x^2)*(5 + 8*x + 6*x^2 + x^4))}, 
   {x*(2 - 4*x^2 + x^4), x*(32 + 16*x^2 + x^4)}, 
   {x*(32 - 16*x^2 + x^4), x*(2 + 4*x^2 + x^4)}, 
   {x*(-16 + 32*x + 8*x^2 - 8*x^3 + x^4), 
    x*(8 - 16*x + 16*x^2 - 8*x^3 + x^4)}, 
   {x*(-1 + 4*x + 2*x^2 - 4*x^3 + x^4), 
    x*(128 - 128*x + 64*x^2 - 16*x^3 + x^4)}, 
   {x*(-1 - 4*x + 2*x^2 + 4*x^3 + x^4), 
    x*(128 + 128*x + 64*x^2 + 16*x^3 + x^4)}, 
   {x*(-16 - 32*x + 8*x^2 + 8*x^3 + x^4), 
    x*(8 + 16*x + 16*x^2 + 8*x^3 + x^4)}, 
   {x*(1 + 4*x - 26*x^2 + 4*x^3 + x^4), (1 + x^2)*(2 + 4*x^2 + x^4)}, 
   {x*(16 + 32*x - 104*x^2 + 8*x^3 + x^4), 2*(1 + x^2)*(2 + 4*x^2 + x^4)}, 
   {x*(16 - 32*x - 104*x^2 - 8*x^3 + x^4), -2*(1 + x^2)*(2 + 4*x^2 + x^4)}, 
   {x*(1 - 4*x - 26*x^2 - 4*x^3 + x^4), -((1 + x^2)*(2 + 4*x^2 + x^4))}, 
   {x*(32 + 128*x + 80*x^2 + 16*x^3 + x^4), 
    x*(2 + 16*x + 20*x^2 + 8*x^3 + x^4)}, 
   {x*(2 - 16*x + 20*x^2 - 8*x^3 + x^4), 
    x*(32 - 128*x + 80*x^2 - 16*x^3 + x^4)}, 
   {x*(-128 - 256*x - 128*x^2 - 16*x^3 + x^4)}, 
   {x*(-8 - 32*x - 32*x^2 - 8*x^3 + x^4)}, 
   {x*(-8 + 32*x - 32*x^2 + 8*x^3 + x^4)}, 
   {x*(-128 + 256*x - 128*x^2 + 16*x^3 + x^4)}, 
   {x*(16 + 224*x + 280*x^2 + 56*x^3 + x^4), 
    2*(-1 + 2*x^2)*(2 - 4*x^2 + x^4), -((4 + x^2)*(2 + 4*x^2 + x^4)), 
    2*(1 + 2*x^2)*(2 + 4*x^2 + x^4)}, 
   {x*(1 + 28*x + 70*x^2 + 28*x^3 + x^4), (-1 + 2*x^2)*(2 - 4*x^2 + x^4), 
    -2*(4 + x^2)*(2 + 4*x^2 + x^4), (1 + 2*x^2)*(2 + 4*x^2 + x^4)}, 
   {x*(1 - 28*x + 70*x^2 - 28*x^3 + x^4), -((-1 + 2*x^2)*(2 - 4*x^2 + x^4)), 
    2*(4 + x^2)*(2 + 4*x^2 + x^4), -((1 + 2*x^2)*(2 + 4*x^2 + x^4))}, 
   {x*(16 - 224*x + 280*x^2 - 56*x^3 + x^4), 
    -2*(-1 + 2*x^2)*(2 - 4*x^2 + x^4), (4 + x^2)*(2 + 4*x^2 + x^4), 
    -2*(1 + 2*x^2)*(2 + 4*x^2 + x^4)}, 
   {x*(-64 + 1152*x + 336*x^2 + 32*x^3 + x^4)}, 
   {x*(-4 + 144*x + 84*x^2 + 16*x^3 + x^4)}, 
   {x*(-4 - 144*x + 84*x^2 - 16*x^3 + x^4)}, 
   {x*(-64 - 1152*x + 336*x^2 - 32*x^3 + x^4)}, 
   {x*(-4 + 12*x^2 - 8*x^3 + x^4), -2*(2 + 2*x + x^2)*(-4 + 4*x^2 + x^4)}, 
   {x*(-64 + 48*x^2 - 16*x^3 + x^4), -((2 + 2*x + x^2)*(-4 + 4*x^2 + x^4))}, 
   {x*(-64 + 48*x^2 + 16*x^3 + x^4), (2 + 2*x + x^2)*(-4 + 4*x^2 + x^4)}, 
   {x*(-4 + 12*x^2 + 8*x^3 + x^4), 2*(2 + 2*x + x^2)*(-4 + 4*x^2 + x^4)}, 
   {x*(64 - 80*x^2 - 32*x^3 + x^4), -2*(6 - 4*x + x^2)*(4 + 12*x^2 + x^4), 
    2*(-2 + x^2)*(12 - 16*x - 12*x^2 + 8*x^3 + 11*x^4), 
    -2*(6 + 4*x + x^2)*(4 - 8*x + 4*x^2 + 4*x^3 + x^4)}, 
   {x*(4 - 20*x^2 - 16*x^3 + x^4), -((6 - 4*x + x^2)*(4 + 12*x^2 + x^4)), 
    (-2 + x^2)*(12 - 16*x - 12*x^2 + 8*x^3 + 11*x^4), 
    -((6 + 4*x + x^2)*(4 - 8*x + 4*x^2 + 4*x^3 + x^4))}, 
   {x*(4 - 20*x^2 + 16*x^3 + x^4), (6 - 4*x + x^2)*(4 + 12*x^2 + x^4), 
    -((-2 + x^2)*(12 - 16*x - 12*x^2 + 8*x^3 + 11*x^4)), 
    (6 + 4*x + x^2)*(4 - 8*x + 4*x^2 + 4*x^3 + x^4)}, 
   {x*(64 - 80*x^2 + 32*x^3 + x^4), 2*(6 - 4*x + x^2)*(4 + 12*x^2 + x^4), 
    -2*(-2 + x^2)*(12 - 16*x - 12*x^2 + 8*x^3 + 11*x^4), 
    2*(6 + 4*x + x^2)*(4 - 8*x + 4*x^2 + 4*x^3 + x^4)}, 
   {x*(4 + 16*x + 4*x^2 - 8*x^3 + x^4), 
    2*(-2 + x^2)*(4 - 8*x + 4*x^2 + 4*x^3 + x^4)}, 
   {x*(4 - 16*x + 4*x^2 + 8*x^3 + x^4), 
    (-2 + x^2)*(4 - 8*x + 4*x^2 + 4*x^3 + x^4)}, 
   {x*(-1 - 2*x^2 + x^4), x*(-16 - 8*x^2 + x^4)}, 
   {x*(1 - 4*x - 2*x^2 - 4*x^3 + x^4), 2*(1 + x^2)*(-1 - 2*x^2 + x^4), 
    (2 + x^2)*(-4 + 4*x^2 + x^4), 2*(-2 + x^2)*(-4 + 4*x^2 + x^4)}, 
   {x*(16 - 32*x - 8*x^2 - 8*x^3 + x^4), (1 + x^2)*(-1 - 2*x^2 + x^4), 
    2*(2 + x^2)*(-4 + 4*x^2 + x^4), (-2 + x^2)*(-4 + 4*x^2 + x^4)}, 
   {x*(16 + 32*x - 8*x^2 + 8*x^3 + x^4), -((1 + x^2)*(-1 - 2*x^2 + x^4)), 
    -2*(2 + x^2)*(-4 + 4*x^2 + x^4), -((-2 + x^2)*(-4 + 4*x^2 + x^4))}, 
   {x*(1 + 4*x - 2*x^2 + 4*x^3 + x^4), -2*(1 + x^2)*(-1 - 2*x^2 + x^4), 
    -((2 + x^2)*(-4 + 4*x^2 + x^4)), -2*(-2 + x^2)*(-4 + 4*x^2 + x^4)}, 
   {x*(-64 - 128*x - 80*x^2 - 16*x^3 + x^4), 
    x*(-4 - 16*x - 20*x^2 - 8*x^3 + x^4), 
    x*(-4 + 16*x - 20*x^2 + 8*x^3 + x^4), 
    x*(-64 + 128*x - 80*x^2 + 16*x^3 + x^4)}, 
   {x*(1 + 20*x - 26*x^2 + 20*x^3 + x^4), -((4 + x^2)*(-4 + 4*x^2 + x^4)), 
    (2 + x^2)*(8 + 4*x^2 + x^4), -((-2 + x^2)*(2 - 2*x^2 + x^4))}, 
   {x*(16 + 160*x - 104*x^2 + 40*x^3 + x^4), 
    -2*(4 + x^2)*(-4 + 4*x^2 + x^4), 2*(2 + x^2)*(8 + 4*x^2 + x^4), 
    -2*(-2 + x^2)*(2 - 2*x^2 + x^4)}, 
   {x*(16 - 160*x - 104*x^2 - 40*x^3 + x^4), 2*(4 + x^2)*(-4 + 4*x^2 + x^4), 
    -2*(2 + x^2)*(8 + 4*x^2 + x^4), 2*(-2 + x^2)*(2 - 2*x^2 + x^4)}, 
   {x*(1 - 20*x - 26*x^2 - 20*x^3 + x^4), (4 + x^2)*(-4 + 4*x^2 + x^4), 
    -((2 + x^2)*(8 + 4*x^2 + x^4)), (-2 + x^2)*(2 - 2*x^2 + x^4)}, 
   {x*(-4 + 4*x^2 + x^4)}, {x*(-64 + 16*x^2 + x^4)}, 
   {x*(32 - 64*x + 40*x^2 - 8*x^3 + x^4), 
    x*(2 - 8*x + 10*x^2 - 4*x^3 + x^4), x*(2 + 8*x + 10*x^2 + 4*x^3 + x^4), 
    x*(32 + 64*x + 40*x^2 + 8*x^3 + x^4)}, 
   {x*(1 - 4*x + 22*x^2 - 4*x^3 + x^4), 2*(1 + 2*x^2)*(-1 - 2*x^2 + x^4), 
    2*(-2 + x^2)*(-1 - 2*x^2 + x^4), 2*(4 + x^2)*(8 + 4*x^2 + x^4)}, 
   {x*(16 - 32*x + 88*x^2 - 8*x^3 + x^4), (1 + 2*x^2)*(-1 - 2*x^2 + x^4), 
    (-2 + x^2)*(-1 - 2*x^2 + x^4), (4 + x^2)*(8 + 4*x^2 + x^4)}, 
   {x*(16 + 32*x + 88*x^2 + 8*x^3 + x^4), -((1 + 2*x^2)*(-1 - 2*x^2 + x^4)), 
    -((-2 + x^2)*(-1 - 2*x^2 + x^4)), -((4 + x^2)*(8 + 4*x^2 + x^4))}, 
   {x*(1 + 4*x + 22*x^2 + 4*x^3 + x^4), -2*(1 + 2*x^2)*(-1 - 2*x^2 + x^4), 
    -2*(-2 + x^2)*(-1 - 2*x^2 + x^4), -2*(4 + x^2)*(8 + 4*x^2 + x^4)}, 
   {x*(2 - 2*x^2 + x^4), x*(128 + 16*x^2 + x^4)}, 
   {x*(32 - 8*x^2 + x^4), x*(8 + 4*x^2 + x^4)}, 
   {x*(4 + 8*x + 12*x^2 + 4*x^3 + x^4), 
    -2*(3 + 2*x + x^2)*(11 + 12*x + 14*x^2 + 4*x^3 + 3*x^4), 
    -((3 + 2*x + x^2)*(11 + 12*x + 14*x^2 + 4*x^3 + 3*x^4))}, 
   {x*(4 - 8*x + 12*x^2 - 4*x^3 + x^4), 
    (3 + 2*x + x^2)*(11 + 12*x + 14*x^2 + 4*x^3 + 3*x^4), 
    2*(3 + 2*x + x^2)*(11 + 12*x + 14*x^2 + 4*x^3 + 3*x^4)}, 
   {x*(4 - 8*x + 4*x^2 + 4*x^3 + x^4), 
    2*(-2 + x^2)*(4 + 16*x + 4*x^2 - 8*x^3 + x^4)}, 
   {x*(4 + 8*x + 4*x^2 - 4*x^3 + x^4), 
    (-2 + x^2)*(4 + 16*x + 4*x^2 - 8*x^3 + x^4)}, 
   {-((2 + x^2)*(2 - 2*x + x^2)*(2 + 2*x + x^2)), 
    -((2 + x^2)*(4 + 12*x^2 + x^4))}, 
   {(2 + x^2)*(2 - 2*x + x^2)*(2 + 2*x + x^2), (2 + x^2)*(4 + 12*x^2 + x^4)}, 
   {-2*(1 + x^2)*(-1 + 2*x + x^2)*(5 + 4*x + x^2), 
    (1 + x^2)*(-1 + 2*x + x^2)*(5 + 4*x + x^2), 
    -2*(-2 + x^2)*(14 - 8*x + x^2)*(2 - 4*x + x^2), 
    (-2 + x^2)*(14 - 8*x + x^2)*(2 - 4*x + x^2)}, 
   {-((1 + x^2)*(-1 + 2*x + x^2)*(5 + 4*x + x^2)), 
    2*(1 + x^2)*(-1 + 2*x + x^2)*(5 + 4*x + x^2), 
    -((-2 + x^2)*(14 - 8*x + x^2)*(2 - 4*x + x^2)), 
    2*(-2 + x^2)*(14 - 8*x + x^2)*(2 - 4*x + x^2)}, 
   {-2*(2 + x^2)*(2 - 2*x + x^2)*(6 - 8*x + 3*x^2), 
    -((2 + x^2)*(2 - 2*x + x^2)*(6 - 8*x + 3*x^2))}, 
   {(2 + x^2)*(2 - 2*x + x^2)*(6 - 8*x + 3*x^2), 
    2*(2 + x^2)*(2 - 2*x + x^2)*(6 - 8*x + 3*x^2)}, 
   {-((2 + x^2)*(2 + 2*x + x^2)*(2 + 4*x + x^2)), 
    -2*(1 + x^2)*(23 + 20*x + 30*x^2 + 12*x^3 + 7*x^4), 
    -((1 + x^2)*(23 + 20*x + 30*x^2 + 12*x^3 + 7*x^4)), 
    -2*(-1 + 2*x + x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4), 
    -((-1 + 2*x + x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4))}, 
   {(2 + x^2)*(2 + 2*x + x^2)*(2 + 4*x + x^2), 
    (1 + x^2)*(23 + 20*x + 30*x^2 + 12*x^3 + 7*x^4), 
    2*(1 + x^2)*(23 + 20*x + 30*x^2 + 12*x^3 + 7*x^4), 
    (-1 + 2*x + x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4), 
    2*(-1 + 2*x + x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4)}, 
   {(-2 + x^2)*(2 - 4*x + x^2)*(2 - 2*x + x^2), 
    (-2 + x^2)*(4 + 12*x^2 + x^4)}, 
   {2*(-2 + x^2)*(2 - 4*x + x^2)*(2 - 2*x + x^2), 
    2*(-2 + x^2)*(4 + 12*x^2 + x^4)}, {-2*(1 + x^2)*(1 + x^4)}, 
   {-((1 + x^2)*(1 + x^4))}, {(1 + x^2)*(1 + x^4)}, {2*(1 + x^2)*(1 + x^4)}, 
   {-2*(1 + x^2)*(-2 + x^4), (-2 + x^2)*(-2 + x^4)}, 
   {-((1 + x^2)*(-2 + x^4)), 2*(-2 + x^2)*(-2 + x^4)}, 
   {(1 + x^2)*(-2 + x^4), -2*(-2 + x^2)*(-2 + x^4)}, 
   {2*(1 + x^2)*(-2 + x^4), -((-2 + x^2)*(-2 + x^4))}, 
   {-2*(2 + 2*x + x^2)*(4 + 4*x^2 + 8*x^3 + 3*x^4)}, 
   {-((2 + 2*x + x^2)*(4 + 4*x^2 + 8*x^3 + 3*x^4))}, 
   {(2 + 2*x + x^2)*(4 + 4*x^2 + 8*x^3 + 3*x^4)}, 
   {2*(2 + 2*x + x^2)*(4 + 4*x^2 + 8*x^3 + 3*x^4)}, 
   {-2*(1 + x^2)*(11 + 12*x + 14*x^2 + 4*x^3 + 3*x^4), 
    -((1 + x^2)*(11 + 12*x + 14*x^2 + 4*x^3 + 3*x^4)), 
    -2*(-1 - 2*x + x^2)*(5 + 8*x + 6*x^2 + x^4), 
    -((-1 - 2*x + x^2)*(5 + 8*x + 6*x^2 + x^4))}, 
   {(1 + x^2)*(11 + 12*x + 14*x^2 + 4*x^3 + 3*x^4), 
    2*(1 + x^2)*(11 + 12*x + 14*x^2 + 4*x^3 + 3*x^4), 
    (-1 - 2*x + x^2)*(5 + 8*x + 6*x^2 + x^4), 
    2*(-1 - 2*x + x^2)*(5 + 8*x + 6*x^2 + x^4)}, 
   {-2*(2 - 4*x + 3*x^2)*(12 - 16*x - 12*x^2 + 8*x^3 + 11*x^4), 
    -((2 - 4*x + 3*x^2)*(12 - 16*x - 12*x^2 + 8*x^3 + 11*x^4))}, 
   {(2 - 4*x + 3*x^2)*(12 - 16*x - 12*x^2 + 8*x^3 + 11*x^4), 
    2*(2 - 4*x + 3*x^2)*(12 - 16*x - 12*x^2 + 8*x^3 + 11*x^4)}, 
   {2*(-2 + x^2)*(4 + 4*x^2 + 8*x^3 + 3*x^4), 
    2*(-1 - 2*x + x^2)*(1 - 4*x - 6*x^2 + 4*x^3 + x^4)}, 
   {(-2 + x^2)*(4 + 4*x^2 + 8*x^3 + 3*x^4), 
    (-1 - 2*x + x^2)*(1 - 4*x - 6*x^2 + 4*x^3 + x^4)}, 
   {-((-1 + 2*x^2)*(9 - 16*x + 4*x^2 + 4*x^4)), 
    -2*(1 + x^2)*(5 + 8*x + 6*x^2 + x^4), 
    -((1 + x^2)*(5 + 8*x + 6*x^2 + x^4))}, 
   {(-1 + 2*x^2)*(9 - 16*x + 4*x^2 + 4*x^4), 
    (1 + x^2)*(5 + 8*x + 6*x^2 + x^4), 2*(1 + x^2)*(5 + 8*x + 6*x^2 + x^4)}, 
   {(1 - 4*x + 2*x^2)*(9 - 16*x + 4*x^2 + 4*x^4), 
    -((-1 + 2*x + x^2)*(11 + 12*x + 14*x^2 + 4*x^3 + 3*x^4)), 
    2*(-1 + 2*x + x^2)*(11 + 12*x + 14*x^2 + 4*x^3 + 3*x^4)}, 
   {-((1 - 4*x + 2*x^2)*(9 - 16*x + 4*x^2 + 4*x^4)), 
    -2*(-1 + 2*x + x^2)*(11 + 12*x + 14*x^2 + 4*x^3 + 3*x^4), 
    (-1 + 2*x + x^2)*(11 + 12*x + 14*x^2 + 4*x^3 + 3*x^4)}, 
   {-2*(1 + x^2)*(1 - 4*x - 6*x^2 + 4*x^3 + x^4), 
    (1 + x^2)*(1 - 4*x - 6*x^2 + 4*x^3 + x^4)}, 
   {-((1 + x^2)*(1 - 4*x - 6*x^2 + 4*x^3 + x^4)), 
    2*(1 + x^2)*(1 - 4*x - 6*x^2 + 4*x^3 + x^4)}, 
   {-((2 + x^2)*(4 + 16*x + 4*x^2 - 8*x^3 + x^4))}, 
   {(2 + x^2)*(4 + 16*x + 4*x^2 - 8*x^3 + x^4)}, 
   {-2*(-2 + x^2)*(2 - 4*x^2 + x^4), -2*(2 + x^2)*(2 + 4*x^2 + x^4)}, 
   {-((-2 + x^2)*(2 - 4*x^2 + x^4)), -((2 + x^2)*(2 + 4*x^2 + x^4))}, 
   {(-2 + x^2)*(2 - 4*x^2 + x^4), (2 + x^2)*(2 + 4*x^2 + x^4)}, 
   {2*(-2 + x^2)*(2 - 4*x^2 + x^4), 2*(2 + x^2)*(2 + 4*x^2 + x^4)}, 
   {-2*(1 - 4*x + 2*x^2)*(17 - 24*x - 12*x^2 + 16*x^3 + 4*x^4), 
    (1 - 4*x + 2*x^2)*(17 - 24*x - 12*x^2 + 16*x^3 + 4*x^4), 
    -((-1 + 2*x + x^2)*(23 + 20*x + 30*x^2 + 12*x^3 + 7*x^4)), 
    2*(-1 + 2*x + x^2)*(23 + 20*x + 30*x^2 + 12*x^3 + 7*x^4)}, 
   {-((1 - 4*x + 2*x^2)*(17 - 24*x - 12*x^2 + 16*x^3 + 4*x^4)), 
    2*(1 - 4*x + 2*x^2)*(17 - 24*x - 12*x^2 + 16*x^3 + 4*x^4), 
    -2*(-1 + 2*x + x^2)*(23 + 20*x + 30*x^2 + 12*x^3 + 7*x^4), 
    (-1 + 2*x + x^2)*(23 + 20*x + 30*x^2 + 12*x^3 + 7*x^4)}, 
   {-2*(1 + 4*x + 2*x^2)*(17 - 24*x - 12*x^2 + 16*x^3 + 4*x^4), 
    -((7 - 20*x + 14*x^2)*(17 - 24*x - 12*x^2 + 16*x^3 + 4*x^4))}, 
   {-((1 + 4*x + 2*x^2)*(17 - 24*x - 12*x^2 + 16*x^3 + 4*x^4)), 
    -2*(7 - 20*x + 14*x^2)*(17 - 24*x - 12*x^2 + 16*x^3 + 4*x^4)}, 
   {(1 + 4*x + 2*x^2)*(17 - 24*x - 12*x^2 + 16*x^3 + 4*x^4), 
    2*(7 - 20*x + 14*x^2)*(17 - 24*x - 12*x^2 + 16*x^3 + 4*x^4)}, 
   {2*(1 + 4*x + 2*x^2)*(17 - 24*x - 12*x^2 + 16*x^3 + 4*x^4), 
    (7 - 20*x + 14*x^2)*(17 - 24*x - 12*x^2 + 16*x^3 + 4*x^4)}, 
   {-2*(2 + 4*x + x^2)*(4 + 16*x + 4*x^2 - 8*x^3 + x^4), 
    (1 - 2*x + 3*x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4)}, 
   {-((2 + 4*x + x^2)*(4 + 16*x + 4*x^2 - 8*x^3 + x^4)), 
    2*(1 - 2*x + 3*x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4)}, 
   {(2 + 4*x + x^2)*(4 + 16*x + 4*x^2 - 8*x^3 + x^4), 
    -2*(1 - 2*x + 3*x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4)}, 
   {2*(2 + 4*x + x^2)*(4 + 16*x + 4*x^2 - 8*x^3 + x^4), 
    -((1 - 2*x + 3*x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4))}, 
   {-2*(-1 - 2*x + x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4), 
    (-1 - 2*x + x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4), 
    -2*(-1 + 2*x + x^2)*(5 + 8*x + 6*x^2 + x^4), 
    (-1 + 2*x + x^2)*(5 + 8*x + 6*x^2 + x^4)}, 
   {-((-1 - 2*x + x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4)), 
    2*(-1 - 2*x + x^2)*(-7 + 12*x - 6*x^2 + 4*x^3 + x^4), 
    -((-1 + 2*x + x^2)*(5 + 8*x + 6*x^2 + x^4)), 
    2*(-1 + 2*x + x^2)*(5 + 8*x + 6*x^2 + x^4)}, 
   {-2*(1 + x^2)*(5 - 8*x - 6*x^2 + 8*x^3 + 5*x^4)}, 
   {-((1 + x^2)*(5 - 8*x - 6*x^2 + 8*x^3 + 5*x^4))}, 
   {(1 + x^2)*(5 - 8*x - 6*x^2 + 8*x^3 + 5*x^4)}, 
   {2*(1 + x^2)*(5 - 8*x - 6*x^2 + 8*x^3 + 5*x^4)}, 
   {-2*(3 - 2*x + x^2)*(5 + 8*x + 6*x^2 + x^4), 
    -((1 + 2*x + 3*x^2)*(5 + 8*x + 6*x^2 + x^4)), 
    -((2 + 4*x + x^2)*(4 - 8*x + 4*x^2 + 4*x^3 + x^4))}, 
   {-((3 - 2*x + x^2)*(5 + 8*x + 6*x^2 + x^4)), 
    -2*(1 + 2*x + 3*x^2)*(5 + 8*x + 6*x^2 + x^4), 
    -2*(2 + 4*x + x^2)*(4 - 8*x + 4*x^2 + 4*x^3 + x^4)}, 
   {(3 - 2*x + x^2)*(5 + 8*x + 6*x^2 + x^4), 
    2*(1 + 2*x + 3*x^2)*(5 + 8*x + 6*x^2 + x^4), 
    2*(2 + 4*x + x^2)*(4 - 8*x + 4*x^2 + 4*x^3 + x^4)}, 
   {2*(3 - 2*x + x^2)*(5 + 8*x + 6*x^2 + x^4), 
    (1 + 2*x + 3*x^2)*(5 + 8*x + 6*x^2 + x^4), 
    (2 + 4*x + x^2)*(4 - 8*x + 4*x^2 + 4*x^3 + x^4)}, 
   {-((2 + x^2)*(4 - 8*x + 4*x^2 + 4*x^3 + x^4))}, 
   {(2 + x^2)*(4 - 8*x + 4*x^2 + 4*x^3 + x^4)}}

s1[2, 1, 2] = (-2*(8 + 8*x - 24*x^2 - 16*x^3 + 36*x^4 - 14*x^5 + x^6))/
   ((-2 + x)^3*x*(-2 + x^2))
 
s2[2, 1, 2] = x^2/(-2 + x)^2
 
alpha[2, 1, 2] = {{0, -1}, {-2, 1}}

s1[2, 1, 3] = 8/((-2 + x)*x)
 
s2[2, 1, 3] = 4/(-1 + x)^2
 
alpha[2, 1, 3] = {{1/2, -1/2}, {1, 0}}

s1[2, 1, 4] = 0
 
s2[2, 1, 4] = (-2*(-3*x + 2*x^2))/(-4 + 3*x)
 
alpha[2, 1, 4] = {{1/2, 0}, {0, 1/2}}

s1[3, 1, 2] = 0
 
s2[3, 1, 2] = 16/x^2
 
alpha[3, 1, 2] = {{0, -1/2}, {2, 0}}

s1[3, 1, 3] = (-2*(-64 + 224*x - 48*x^2 - 100*x^3 + 6*x^4 + 10*x^5 + x^6))/
   (x^3*(4 - 2*x - 2*x^2 + x^3))
 
s2[3, 1, 3] = -((-16 - 8*x - x^2)/x^2)
 
alpha[3, 1, 3] = {{2, 1/2}, {0, -1/2}}

s1[3, 1, 4] = (2*(-64 - 224*x - 48*x^2 + 100*x^3 + 6*x^4 - 10*x^5 + x^6))/
   (x^3*(-4 - 2*x + 2*x^2 + x^3))
 
s2[3, 1, 4] = -((-16 + 8*x - x^2)/x^2)
 
alpha[3, 1, 4] = {{-2, 1/2}, {0, 1/2}}

s1[4, 1, 2] = 0
 
s2[4, 1, 2] = 16/x^2
 
alpha[4, 1, 2] = {{0, -2}, {8, 0}}

s1[4, 1, 3] = (-4*(-4096 + 7168*x - 768*x^2 - 800*x^3 + 24*x^4 + 20*x^5 + 
       x^6))/(x^3*(32 - 8*x - 4*x^2 + x^3))
 
s2[4, 1, 3] = (4*(64 + 16*x + x^2))/x^2
 
alpha[4, 1, 3] = {{-2, -1/4}, {0, 1/2}}

s1[4, 1, 4] = (4*(-4096 - 7168*x - 768*x^2 + 800*x^3 + 24*x^4 - 20*x^5 + 
       x^6))/(x^3*(-32 - 8*x + 4*x^2 + x^3))
 
s2[4, 1, 4] = (4*(64 - 16*x + x^2))/x^2
 
alpha[4, 1, 4] = {{-2, 1/4}, {0, 1/2}}

nx[6, 1, 2] = 4/x

s1[6, 1, 3] = (-4*x^2)/(8 + x^2)
 
s2[6, 1, 3] = x^2/4
 
alpha[6, 1, 3] = {{4, 0}, {0, -2}}

s1[6, 1, 4] = (-2*(-256 + 448*x - 256*x^2 + 128*x^3 - 28*x^4 + 5*x^5))/
   (-256 + 576*x - 320*x^2 + 160*x^3 - 36*x^4 + 7*x^5)
 
s2[6, 1, 4] = -((256 - 1216*x + 768*x^2 - 416*x^3 + 100*x^4 - 21*x^5 + x^6)/
     (-256 + 576*x - 320*x^2 + 160*x^3 - 36*x^4 + 7*x^5))
 
alpha[6, 1, 4] = {{2, 0}, {-2, 1}}

nx[6, 4, 5] = (1 - x)/(1 + x)

nx[7, 1, 2] = 4/x

s1[7, 1, 3] = 8/(2 + x^2)
 
s2[7, 1, 3] = 4/x^2
 
alpha[7, 1, 3] = {{0, -1}, {2, 0}}

s1[7, 2, 5] = (-2*(256 + 448*x + 256*x^2 + 128*x^3 + 28*x^4 + 5*x^5))/
   (256 + 576*x + 320*x^2 + 160*x^3 + 36*x^4 + 7*x^5)
 
s2[7, 2, 5] = -((-256 - 1216*x - 768*x^2 - 416*x^3 - 100*x^4 - 21*x^5 - x^6)/
     (256 + 576*x + 320*x^2 + 160*x^3 + 36*x^4 + 7*x^5))
 
alpha[7, 2, 5] = {{2, 0}, {-2, -1}}

nx[7, 4, 5] = (1 - x)/(1 + x)

nx[8, 1, 2] = -4/x

s1[8, 1, 5] = 4
 
s2[8, 1, 5] = (-2*(4 - 3*x + x^2))/(-2 + x)
 
alpha[8, 1, 5] = {{-1/2, 0}, {-1, 1/2}}

s1[8, 3, 5] = 2
 
s2[8, 3, 5] = -((-4 + 8*x - x^2)/((-2 + x)*x))
 
alpha[8, 3, 5] = {{0, 1}, {2, 1}}

s1[8, 4, 5] = (4*(1 + 3*x))/(1 + 4*x + x^2)
 
s2[8, 4, 5] = (4*(1 + 3*x))/(1 + 4*x + x^2)
 
alpha[8, 4, 5] = {{-1/2, -1/2}, {-1, 0}}

nx[9, 1, 2] = -4/x

s1[9, 1, 5] = 4
 
s2[9, 1, 5] = -((16 - 6*x + x^2)/(-4 + x))
 
alpha[9, 1, 5] = {{-2, 0}, {-4, 1}}

s1[9, 3, 5] = 2
 
s2[9, 3, 5] = -((-1 + 4*x - x^2)/((-1 + x)*x))
 
alpha[9, 3, 5] = {{0, 1}, {1, 1}}

s1[9, 4, 5] = (8*(2 + 3*x))/(4 + 8*x + x^2)
 
s2[9, 4, 5] = (8*(2 + 3*x))/(4 + 8*x + x^2)
 
alpha[9, 4, 5] = {{-2, -1}, {-4, 0}}

nx[10, 1, 2] = 4/x

s1[10, 1, 3] = (-2*(8 - 4*x + x^2))/(-8 + x^2)
 
s2[10, 1, 3] = -(-128 + 144*x - 72*x^2 + 14*x^3 - x^4)/
   (4*(32 - 8*x - 4*x^2 + x^3))
 
alpha[10, 1, 3] = {{2, 0}, {2, -1/2}}

s1[10, 1, 5] = (-2*(8 - 8*x + x^2))/(-8 + x^2)
 
s2[10, 1, 5] = -(-32 + 48*x - 36*x^2 + 10*x^3 - x^4)/
   (2*(16 - 8*x - 2*x^2 + x^3))
 
alpha[10, 1, 5] = {{2, 0}, {2, -1}}

nx[10, 3, 4] = (1/2 - x)/(1 - x)

nx[10, 5, 6] = (-1 - x)/(1 - x)

nx[11, 1, 2] = 4/x

s1[11, 1, 3] = (-2*(2 + 2*x + x^2))/(-2 + x^2)
 
s2[11, 1, 3] = -(8 + 18*x + 18*x^2 + 7*x^3 + x^4)/(2*(-4 - 2*x + 2*x^2 + x^3))
 
alpha[11, 1, 3] = {{1, 0}, {1, 1/2}}

s1[11, 2, 6] = (-2*(8 + 8*x + x^2))/(-8 + x^2)
 
s2[11, 2, 6] = -(32 + 48*x + 36*x^2 + 10*x^3 + x^4)/
   (2*(-16 - 8*x + 2*x^2 + x^3))
 
alpha[11, 2, 6] = {{2, 0}, {2, 1}}

nx[11, 3, 4] = (1/2 - x)/(1 - x)

nx[11, 5, 6] = (-1 - x)/(1 - x)

s1[16, 1, 2] = (-4*(2 + 4*x + 3*x^2 + 2*x^3))/(2 + 4*x + 5*x^2 + 4*x^3)
 
s2[16, 1, 2] = (2*(2 + 8*x + 5*x^2 + 2*x^3))/(2 + 4*x + 5*x^2 + 4*x^3)
 
alpha[16, 1, 2] = {{1/2, -1/2}, {0, 1/2}}

nx[16, 2, 3] = 2/x

s1[17, 1, 2] = -128/(8 + x^2)
 
s2[17, 1, 2] = 64/x^2
 
alpha[17, 1, 2] = {{0, -1/2}, {4, 0}}

s1[17, 1, 5] = (-4*(64 - 64*x + 48*x^2 - 24*x^3 + 5*x^4))/
   (-128 + 192*x - 160*x^2 + 64*x^3 - 18*x^4 + x^5)
 
s2[17, 1, 5] = -(256 - 384*x + 640*x^2 - 320*x^3 + 84*x^4 - 10*x^5 + x^6)/
   (2*(-128 + 192*x - 160*x^2 + 64*x^3 - 18*x^4 + x^5))
 
alpha[17, 1, 5] = {{-2, 0}, {-2, 1}}

nx[17, 2, 3] = 4/x

nx[17, 4, 5] = (-1 - x)/(1 - x)

s1[18, 1, 2] = 16/(2 + x^2)
 
s2[18, 1, 2] = 4/x^2
 
alpha[18, 1, 2] = {{0, -1}, {2, 0}}

s1[18, 1, 5] = (2*(4 + 8*x + 12*x^2 + 12*x^3 + 5*x^4))/
   (4 + 12*x + 20*x^2 + 16*x^3 + 9*x^4 + x^5)
 
s2[18, 1, 5] = -((-4 - 12*x - 40*x^2 - 40*x^3 - 21*x^4 - 5*x^5 - x^6)/
     (4 + 12*x + 20*x^2 + 16*x^3 + 9*x^4 + x^5))
 
alpha[18, 1, 5] = {{-1, 0}, {-1, -1}}

nx[18, 2, 3] = 4/x

nx[18, 4, 5] = (-1 - x)/(1 - x)

s1[19, 1, 2] = 0
 
s2[19, 1, 2] = 4/x^2
 
alpha[19, 1, 2] = {{0, -2}, {4, 0}}

s1[19, 1, 3] = (2*(16 + 8*x^2 + x^4))/(-16 + 16*x - 12*x^3 + x^4)
 
s2[19, 1, 3] = -((16 + 48*x - 4*x^3 - x^4)/(-16 + 16*x - 12*x^3 + x^4))
 
alpha[19, 1, 3] = {{-2, 1}, {2, 1}}

s1[20, 1, 2] = 0
 
s2[20, 1, 2] = 4/x^2
 
alpha[20, 1, 2] = {{0, -1/2}, {1, 0}}

s1[20, 1, 3] = (-2*(1 + 2*x^2 + x^4))/(-1 + 6*x - 2*x^3 + x^4)
 
s2[20, 1, 3] = -((1 + 2*x - 6*x^3 - x^4)/(-1 + 6*x - 2*x^3 + x^4))
 
alpha[20, 1, 3] = {{-1/2, 1/2}, {-1/2, -1/2}}

nx[21, 1, 2] = -4/x

s1[21, 1, 4] = 2
 
s2[21, 1, 4] = 1 - x + x^2/4
 
alpha[21, 1, 4] = {{-4, 0}, {-4, 2}}

s1[21, 1, 5] = 0
 
s2[21, 1, 5] = -(-4*x + x^2)/(2*(-2 + x))
 
alpha[21, 1, 5] = {{2, 0}, {0, 1}}

s1[21, 2, 3] = -4
 
s2[21, 2, 3] = 4*(1 + 2*x + x^2)
 
alpha[21, 2, 3] = {{1/2, 0}, {-1, -1}}

nx[22, 1, 2] = -4/x

s1[22, 1, 4] = 4
 
s2[22, 1, 4] = 4*(1 - 2*x + x^2)
 
alpha[22, 1, 4] = {{1/2, 0}, {1, -1}}

s1[22, 1, 5] = 0
 
s2[22, 1, 5] = -((-2*x + x^2)/(-1 + x))
 
alpha[22, 1, 5] = {{-1, 0}, {0, -1}}

s1[22, 2, 3] = -2
 
s2[22, 2, 3] = (4 + 4*x + x^2)/4
 
alpha[22, 2, 3] = {{4, 0}, {-4, -2}}

s1[23, 1, 2] = 0
 
s2[23, 1, 2] = 4/x^2
 
alpha[23, 1, 2] = {{0, -1}, {2, 0}}

s1[24, 1, 2] = -8/(2 + x)^2
 
s2[24, 1, 2] = 4/(2 + x)^2
 
alpha[24, 1, 2] = {{-4, -2}, {4, 0}}

s1[24, 1, 3] = -2
 
s2[24, 1, 3] = -((-16 - 8*x - x^2)/x^2)
 
alpha[24, 1, 3] = {{0, -2}, {8, 2}}

s1[24, 1, 4] = 0
 
s2[24, 1, 4] = (8*(2 + x))/(x*(4 + x))
 
alpha[24, 1, 4] = {{0, 1}, {4, 0}}

s1[25, 1, 2] = -4/(1 + x)^2
 
s2[25, 1, 2] = 4/(1 + x)^2
 
alpha[25, 1, 2] = {{-1/2, -1/2}, {1, 0}}

s1[25, 1, 3] = -4
 
s2[25, 1, 3] = (4*(4 + 4*x + x^2))/x^2
 
alpha[25, 1, 3] = {{0, -1/2}, {2, 1}}

s1[25, 1, 4] = 0
 
s2[25, 1, 4] = (4*(1 + x))/(x*(2 + x))
 
alpha[25, 1, 4] = {{0, 1}, {2, 0}}

s1[26, 1, 2] = 4/(-1 + x)^2
 
s2[26, 1, 2] = 4/(-1 + x)^2
 
alpha[26, 1, 2] = {{1/2, -1/2}, {1, 0}}

s1[26, 1, 3] = 4
 
s2[26, 1, 3] = (4*(4 - 4*x + x^2))/x^2
 
alpha[26, 1, 3] = {{0, 1/2}, {-2, 1}}

s1[26, 1, 4] = 0
 
s2[26, 1, 4] = (-4*(-1 + x))/((-2 + x)*x)
 
alpha[26, 1, 4] = {{0, 1}, {-2, 0}}

s1[27, 1, 2] = 8/(-2 + x)^2
 
s2[27, 1, 2] = 4/(-2 + x)^2
 
alpha[27, 1, 2] = {{4, -2}, {4, 0}}

s1[27, 1, 3] = 2
 
s2[27, 1, 3] = -((-16 + 8*x - x^2)/x^2)
 
alpha[27, 1, 3] = {{0, 2}, {-8, 2}}

s1[27, 1, 4] = 0
 
s2[27, 1, 4] = (-8*(-2 + x))/((-4 + x)*x)
 
alpha[27, 1, 4] = {{0, 1}, {-4, 0}}

s1[28, 1, 2] = 0
 
s2[28, 1, 2] = 4/x^2
 
alpha[28, 1, 2] = {{0, -1/2}, {1, 0}}

s1[28, 1, 3] = (4*(6 + 9*x + 10*x^2 + 8*x^3 + 4*x^4 + 18*x^5 + 12*x^6 + 
       8*x^7 - 2*x^8 - 7*x^9 + 2*x^10))/
   (4 + x + 4*x^2 + 8*x^3 + 8*x^4 + 18*x^5 + 8*x^6 + 8*x^7 + 4*x^8 + x^9 + 
     4*x^10)
 
s2[28, 1, 3] = (2*(18 + 39*x + 50*x^2 + 24*x^3 - 12*x^4 - 2*x^5 + 20*x^6 + 
       24*x^7 + 2*x^8 - 25*x^9 + 2*x^10))/
   (4 + x + 4*x^2 + 8*x^3 + 8*x^4 + 18*x^5 + 8*x^6 + 8*x^7 + 4*x^8 + x^9 + 
     4*x^10)
 
alpha[28, 1, 3] = {{-1/2, 1/2}, {-3/2, 1/2}}

s1[28, 3, 4] = (4*(6 - 6*x + x^2))/(2 - 4*x + x^2)
 
s2[28, 3, 4] = (2*(18 - 12*x + x^2))/(2 - 4*x + x^2)
 
alpha[28, 3, 4] = {{-2, 1}, {-6, 2}}

s1[29, 1, 2] = -2
 
s2[29, 1, 2] = (4 + 4*x + x^2)/4
 
alpha[29, 1, 2] = {{4, 0}, {-4, -2}}

s1[30, 1, 2] = -4
 
s2[30, 1, 2] = 4*(1 + 2*x + x^2)
 
alpha[30, 1, 2] = {{1/2, 0}, {-1, -1}}

s1[31, 1, 2] = 4
 
s2[31, 1, 2] = 4*(1 - 2*x + x^2)
 
alpha[31, 1, 2] = {{1/2, 0}, {1, -1}}

s1[32, 1, 2] = 2
 
s2[32, 1, 2] = 1 - x + x^2/4
 
alpha[32, 1, 2] = {{4, 0}, {4, -2}}

s1[33, 1, 2] = 0
 
s2[33, 1, 2] = 4*x^2
 
alpha[33, 1, 2] = {{1/2, 0}, {0, -1}}

s1[34, 1, 2] = (2*x^2)/(2 + x)^2
 
s2[34, 1, 2] = x^2/(2 + x)^2
 
alpha[34, 1, 2] = {{4, 2}, {0, 2}}

s1[35, 1, 2] = (4*x^2)/(1 + x)^2
 
s2[35, 1, 2] = (4*x^2)/(1 + x)^2
 
alpha[35, 1, 2] = {{1/2, 1/2}, {0, 1}}

s1[36, 1, 2] = (-4*x^2)/(-1 + x)^2
 
s2[36, 1, 2] = (4*x^2)/(-1 + x)^2
 
alpha[36, 1, 2] = {{-1/2, 1/2}, {0, -1}}

s1[37, 1, 2] = (-2*x^2)/(-2 + x)^2
 
s2[37, 1, 2] = x^2/(-2 + x)^2
 
alpha[37, 1, 2] = {{-4, 2}, {0, -2}}

s1[38, 1, 2] = (-4*(-1 + 12*x - 5*x^2 + 5*x^4 - 12*x^5 + x^6))/
   (1 + 30*x - 49*x^2 + 100*x^3 - 49*x^4 + 30*x^5 + x^6)
 
s2[38, 1, 2] = (4*(1 - 8*x + 157*x^2 - 256*x^3 + 482*x^4 - 240*x^5 + 
       482*x^6 - 256*x^7 + 157*x^8 - 8*x^9 + x^10))/
   (1 + 34*x + 45*x^2 - 872*x^3 + 1746*x^4 - 2932*x^5 + 1746*x^6 - 872*x^7 + 
     45*x^8 + 34*x^9 + x^10)
 
alpha[38, 1, 2] = {{-1, -1}, {-2, 2}}

s1[39, 1, 2] = (4*(-64 + 384*x - 80*x^2 + 20*x^4 - 24*x^5 + x^6))/
   (64 + 960*x - 784*x^2 + 800*x^3 - 196*x^4 + 60*x^5 + x^6)
 
s2[39, 1, 2] = (4*(1024 - 4096*x + 40192*x^2 - 32768*x^3 + 30848*x^4 - 
       7680*x^5 + 7712*x^6 - 2048*x^7 + 628*x^8 - 16*x^9 + x^10))/
   (1024 + 17408*x + 11520*x^2 - 111616*x^3 + 111744*x^4 - 93824*x^5 + 
     27936*x^6 - 6976*x^7 + 180*x^8 + 68*x^9 + x^10)
 
alpha[39, 1, 2] = {{4, 2}, {-8, 4}}

s1[40, 1, 2] = (-4*(-64 - 384*x - 80*x^2 + 20*x^4 + 24*x^5 + x^6))/
   (64 - 960*x - 784*x^2 - 800*x^3 - 196*x^4 - 60*x^5 + x^6)
 
s2[40, 1, 2] = (4*(1024 + 4096*x + 40192*x^2 + 32768*x^3 + 30848*x^4 + 
       7680*x^5 + 7712*x^6 + 2048*x^7 + 628*x^8 + 16*x^9 + x^10))/
   (1024 - 17408*x + 11520*x^2 + 111616*x^3 + 111744*x^4 + 93824*x^5 + 
     27936*x^6 + 6976*x^7 + 180*x^8 - 68*x^9 + x^10)
 
alpha[40, 1, 2] = {{-4, 2}, {-8, -4}}

s1[41, 1, 2] = (4*(-1 - 12*x - 5*x^2 + 5*x^4 + 12*x^5 + x^6))/
   (1 - 30*x - 49*x^2 - 100*x^3 - 49*x^4 - 30*x^5 + x^6)
 
s2[41, 1, 2] = (4*(1 + 8*x + 157*x^2 + 256*x^3 + 482*x^4 + 240*x^5 + 
       482*x^6 + 256*x^7 + 157*x^8 + 8*x^9 + x^10))/
   (1 - 34*x + 45*x^2 + 872*x^3 + 1746*x^4 + 2932*x^5 + 1746*x^6 + 872*x^7 + 
     45*x^8 - 34*x^9 + x^10)
 
alpha[41, 1, 2] = {{-1, 1}, {2, 2}}

s1[42, 1, 2] = 0
 
s2[42, 1, 2] = 4*x^2
 
alpha[42, 1, 2] = {{1/2, 0}, {0, -1}}

s1[43, 1, 2] = (4*(-1 - 8*x + 7*x^2 + 32*x^3 - 7*x^4 - 8*x^5 + x^6))/
   ((1 + x)^2*(1 + 4*x + 10*x^2 - 4*x^3 + x^4))
 
s2[43, 1, 2] = (4*(1 - 2*x + x^2))/(1 + x)^2
 
alpha[43, 1, 2] = {{-1/2, 1/2}, {1, 1}}

s1[44, 1, 2] = (2*(-64 - 256*x + 112*x^2 + 256*x^3 - 28*x^4 - 16*x^5 + x^6))/
   ((-2 + x)^2*(16 + 32*x + 40*x^2 - 8*x^3 + x^4))
 
s2[44, 1, 2] = -((-4 - 4*x - x^2)/(-2 + x)^2)
 
alpha[44, 1, 2] = {{4, 2}, {-4, 2}}

s1[45, 1, 3] = (-2*(-4 + 20*x - 28*x^2 + 4*x^3 - x^4 + x^5))/
   (-4 + 24*x - 44*x^2 + 32*x^3 - 9*x^4 + 2*x^5)
 
s2[45, 1, 3] = -((4 - 32*x + 48*x^2 - 40*x^3 + 37*x^4 - 12*x^5 + x^6)/
     (-4 + 24*x - 44*x^2 + 32*x^3 - 9*x^4 + 2*x^5))
 
alpha[45, 1, 3] = {{1, 0}, {-1, 1}}

nx[45, 2, 3] = (1 - x)/(1 + x)

s1[46, 1, 2] = (-2*(4 + 20*x + 28*x^2 + 4*x^3 + x^4 + x^5))/
   (4 + 24*x + 44*x^2 + 32*x^3 + 9*x^4 + 2*x^5)
 
s2[46, 1, 2] = -((-4 - 32*x - 48*x^2 - 40*x^3 - 37*x^4 - 12*x^5 - x^6)/
     (4 + 24*x + 44*x^2 + 32*x^3 + 9*x^4 + 2*x^5))
 
alpha[46, 1, 2] = {{1, 0}, {-1, -1}}

nx[46, 2, 3] = (1 - x)/(1 + x)

s1[47, 1, 2] = 0
 
s2[47, 1, 2] = 4*x^2
 
alpha[47, 1, 2] = {{1/2, 0}, {0, -1}}

s1[48, 1, 2] = 0
 
s2[48, 1, 2] = x^2/4
 
alpha[48, 1, 2] = {{4, 0}, {0, -2}}

s1[49, 1, 2] = 16/(-2 + x)^2
 
s2[49, 1, 2] = 16/(-2 + x)^2
 
alpha[49, 1, 2] = {{2, -1}, {4, 0}}

s1[50, 1, 2] = 8/(-1 + x)^2
 
s2[50, 1, 2] = 16/(-1 + x)^2
 
alpha[50, 1, 2] = {{1/4, -1/4}, {1, 0}}

s1[51, 1, 2] = -8/(1 + x)^2
 
s2[51, 1, 2] = 16/(1 + x)^2
 
alpha[51, 1, 2] = {{-1/4, -1/4}, {1, 0}}

s1[52, 1, 2] = -16/(2 + x)^2
 
s2[52, 1, 2] = 16/(2 + x)^2
 
alpha[52, 1, 2] = {{-2, -1}, {4, 0}}

s1[53, 1, 2] = (-2*(-1 - 4*x + 27*x^2 - 27*x^4 + 4*x^5 + x^6))/
   (1 - 22*x - x^2 - 84*x^3 - x^4 - 22*x^5 + x^6)
 
s2[53, 1, 2] = -((-1 + 26*x + 17*x^2 - 20*x^3 + 17*x^4 + 26*x^5 - x^6)/
     (1 - 22*x - x^2 - 84*x^3 - x^4 - 22*x^5 + x^6))
 
alpha[53, 1, 2] = {{-2, 2}, {-2, -2}}

s1[54, 1, 2] = (-2*(-64 - 128*x + 432*x^2 - 108*x^4 + 8*x^5 + x^6))/
   (64 - 704*x - 16*x^2 - 672*x^3 - 4*x^4 - 44*x^5 + x^6)
 
s2[54, 1, 2] = -((-64 + 832*x + 272*x^2 - 160*x^3 + 68*x^4 + 52*x^5 - x^6)/
     (64 - 704*x - 16*x^2 - 672*x^3 - 4*x^4 - 44*x^5 + x^6))
 
alpha[54, 1, 2] = {{-4, 2}, {-4, -2}}

s1[55, 1, 2] = (2*(-64 + 128*x + 432*x^2 - 108*x^4 - 8*x^5 + x^6))/
   (64 + 704*x - 16*x^2 + 672*x^3 - 4*x^4 + 44*x^5 + x^6)
 
s2[55, 1, 2] = -((-64 - 832*x + 272*x^2 + 160*x^3 + 68*x^4 - 52*x^5 - x^6)/
     (64 + 704*x - 16*x^2 + 672*x^3 - 4*x^4 + 44*x^5 + x^6))
 
alpha[55, 1, 2] = {{4, 2}, {-4, 2}}

s1[56, 1, 2] = (-2*(-1 + 4*x + 27*x^2 - 27*x^4 - 4*x^5 + x^6))/
   (1 + 22*x - x^2 + 84*x^3 - x^4 + 22*x^5 + x^6)
 
s2[56, 1, 2] = -((-1 - 26*x + 17*x^2 + 20*x^3 + 17*x^4 - 26*x^5 - x^6)/
     (1 + 22*x - x^2 + 84*x^3 - x^4 + 22*x^5 + x^6))
 
alpha[56, 1, 2] = {{-2, -2}, {-2, 2}}

s1[57, 1, 2] = -4
 
s2[57, 1, 2] = (16 + 8*x + x^2)/4
 
alpha[57, 1, 2] = {{4, 0}, {-8, -2}}

s1[58, 1, 2] = 8
 
s2[58, 1, 2] = 4*(4 - 4*x + x^2)
 
alpha[58, 1, 2] = {{1/2, 0}, {2, -1}}

s1[63, 1, 2] = (-2*(-4 + x^2))/(4 + 12*x + x^2)
 
s2[63, 1, 2] = -((-4 + 4*x - x^2)/(4 + 12*x + x^2))
 
alpha[63, 1, 2] = {{-4, -2}, {-4, 2}}

s1[63, 2, 3] = (-4*(4 - 24*x^2 + 48*x^4 - 36*x^6 + 7*x^8))/
   (x*(-12 + 48*x^2 - 60*x^4 + 24*x^6 + x^8))
 
s2[63, 2, 3] = (2*(-4 + 24*x^2 - 60*x^4 + 72*x^6 - 33*x^8 + 6*x^10))/
   (x^2*(-12 + 48*x^2 - 60*x^4 + 24*x^6 + x^8))
 
alpha[63, 2, 3] = {{0, 2}, {4, 0}}

s1[63, 3, 4] = (-2*x)/(2 + x^2)
 
s2[63, 3, 4] = 2/(2 + x^2)
 
alpha[63, 3, 4] = {{0, -1}, {2, 0}}

s1[64, 1, 2] = (2*(-1 + x^2))/(1 + 6*x + x^2)
 
s2[64, 1, 2] = -((-1 + 2*x - x^2)/(1 + 6*x + x^2))
 
alpha[64, 1, 2] = {{2, 2}, {-2, 2}}

s1[64, 2, 3] = (-4*(4 - 24*x^2 + 48*x^4 - 36*x^6 + 7*x^8))/
   (x*(-12 + 48*x^2 - 60*x^4 + 24*x^6 + x^8))
 
s2[64, 2, 3] = (2*(-4 + 24*x^2 - 60*x^4 + 72*x^6 - 33*x^8 + 6*x^10))/
   (x^2*(-12 + 48*x^2 - 60*x^4 + 24*x^6 + x^8))
 
alpha[64, 2, 3] = {{0, 1}, {2, 0}}

s1[64, 3, 4] = (-2*x)/(2 + x^2)
 
s2[64, 3, 4] = 2/(2 + x^2)
 
alpha[64, 3, 4] = {{0, -2}, {4, 0}}

s1[65, 1, 2] = (2*(-1 + x^2))/(1 - 6*x + x^2)
 
s2[65, 1, 2] = -((-1 - 2*x - x^2)/(1 - 6*x + x^2))
 
alpha[65, 1, 2] = {{-2, 2}, {2, 2}}

s1[65, 1, 4] = -((-1 + 24*x + 165*x^2 - 3696*x^3 + 8598*x^4 - 8598*x^6 + 
       3696*x^7 - 165*x^8 - 24*x^9 + x^10)/
     (1 + 44*x - 195*x^2 + 1584*x^3 - 7614*x^4 + 13896*x^5 - 7614*x^6 + 
       1584*x^7 - 195*x^8 + 44*x^9 + x^10))
 
s2[65, 1, 4] = -(-1 - 202*x + 2259*x^2 - 7032*x^3 - 2514*x^4 + 13956*x^5 - 
      2514*x^6 - 7032*x^7 + 2259*x^8 - 202*x^9 - x^10)/
   (4*(1 + 44*x - 195*x^2 + 1584*x^3 - 7614*x^4 + 13896*x^5 - 7614*x^6 + 
       1584*x^7 - 195*x^8 + 44*x^9 + x^10))
 
alpha[65, 1, 4] = {{4, -4}, {2, 2}}

s1[65, 3, 4] = (2*x)/(2 + x^2)
 
s2[65, 3, 4] = 2/(2 + x^2)
 
alpha[65, 3, 4] = {{0, 2}, {4, 0}}

s1[66, 1, 2] = (-2*(-4 + x^2))/(4 - 12*x + x^2)
 
s2[66, 1, 2] = -((-4 - 4*x - x^2)/(4 - 12*x + x^2))
 
alpha[66, 1, 2] = {{-4, 2}, {-4, -2}}

s1[66, 2, 3] = (-4*(4 - 24*x^2 + 48*x^4 - 36*x^6 + 7*x^8))/
   (x*(-12 + 48*x^2 - 60*x^4 + 24*x^6 + x^8))
 
s2[66, 2, 3] = (2*(-4 + 24*x^2 - 60*x^4 + 72*x^6 - 33*x^8 + 6*x^10))/
   (x^2*(-12 + 48*x^2 - 60*x^4 + 24*x^6 + x^8))
 
alpha[66, 2, 3] = {{0, 2}, {4, 0}}

s1[66, 3, 4] = (-2*x)/(2 + x^2)
 
s2[66, 3, 4] = 2/(2 + x^2)
 
alpha[66, 3, 4] = {{0, -1}, {2, 0}}

s1[71, 1, 2] = 0
 
s2[71, 1, 2] = (-4*(-1 + x))/((-2 + x)*x)
 
alpha[71, 1, 2] = {{0, 1/2}, {-1, 0}}

s1[72, 1, 2] = 0
 
s2[72, 1, 2] = (-8*(-2 + x))/((-4 + x)*x)
 
alpha[72, 1, 2] = {{0, 1}, {-4, 0}}

s1[73, 1, 2] = 0
 
s2[73, 1, 2] = (8*(2 + x))/(x*(4 + x))
 
alpha[73, 1, 2] = {{0, 1}, {4, 0}}

s1[74, 1, 2] = 0
 
s2[74, 1, 2] = (4*(1 + x))/(x*(2 + x))
 
alpha[74, 1, 2] = {{0, 1/2}, {1, 0}}

s1[75, 1, 2] = 0
 
s2[75, 1, 2] = (4*(4 + 3*x))/(x*(2 + x))
 
alpha[75, 1, 2] = {{0, -1/2}, {2, 0}}

s1[75, 2, 3] = (8*x)/(6 - 4*x + 3*x^2)
 
s2[75, 2, 3] = (-2*(2 - 4*x + x^2))/(6 - 4*x + 3*x^2)
 
alpha[75, 2, 3] = {{0, 1}, {2, 0}}

s1[75, 2, 4] = (-4*(-2 + x^2))/(-2 - 4*x + x^2)
 
s2[75, 2, 4] = -2
 
alpha[75, 2, 4] = {{-2, 0}, {4, -2}}

s1[76, 1, 2] = 0
 
s2[76, 1, 2] = (2*(2 + 3*x))/(x*(1 + x))
 
alpha[76, 1, 2] = {{0, -1/2}, {1, 0}}

s1[76, 2, 3] = (8*x)/(6 - 4*x + 3*x^2)
 
s2[76, 2, 3] = (-2*(2 - 4*x + x^2))/(6 - 4*x + 3*x^2)
 
alpha[76, 2, 3] = {{0, 1}, {2, 0}}

s1[76, 2, 4] = (-4*(-2 + x^2))/(-2 - 4*x + x^2)
 
s2[76, 2, 4] = -2
 
alpha[76, 2, 4] = {{-2, 0}, {4, -2}}

s1[77, 1, 2] = 0
 
s2[77, 1, 2] = (-2*(-2 + 3*x))/((-1 + x)*x)
 
alpha[77, 1, 2] = {{0, 1/2}, {1, 0}}

s1[77, 2, 3] = (8*x)/(6 - 4*x + 3*x^2)
 
s2[77, 2, 3] = (-2*(2 - 4*x + x^2))/(6 - 4*x + 3*x^2)
 
alpha[77, 2, 3] = {{0, -1}, {-2, 0}}

s1[77, 2, 4] = (-4*(-2 + x^2))/(-2 - 4*x + x^2)
 
s2[77, 2, 4] = -2
 
alpha[77, 2, 4] = {{-2, 0}, {4, -2}}

s1[78, 1, 2] = 0
 
s2[78, 1, 2] = (-4*(-4 + 3*x))/((-2 + x)*x)
 
alpha[78, 1, 2] = {{0, 1/2}, {2, 0}}

s1[78, 2, 3] = (8*x)/(6 - 4*x + 3*x^2)
 
s2[78, 2, 3] = (-2*(2 - 4*x + x^2))/(6 - 4*x + 3*x^2)
 
alpha[78, 2, 3] = {{0, -1}, {-2, 0}}

s1[78, 2, 4] = (-4*(-2 + x^2))/(-2 - 4*x + x^2)
 
s2[78, 2, 4] = -2
 
alpha[78, 2, 4] = {{-2, 0}, {4, -2}}

s1[79, 1, 2] = (-2*(4*x + 16*x^2 + 4*x^3 - 8*x^4 + x^5))/
   (-4 - 8*x + 12*x^2 + 16*x^3 - 9*x^4 + 2*x^5)
 
s2[79, 1, 2] = -((16*x + 36*x^2 + 32*x^3 - 12*x^4 - 4*x^5 + x^6)/
     (-4 - 8*x + 12*x^2 + 16*x^3 - 9*x^4 + 2*x^5))
 
alpha[79, 1, 2] = {{-1, 0}, {0, 1}}

s1[80, 1, 2] = (4*(4 - 16*x + 4*x^2 + 8*x^3 + x^4))/
   (-16 + 36*x - 32*x^2 - 12*x^3 + 4*x^4 + x^5)
 
s2[80, 1, 2] = (4*(4 - 8*x - 12*x^2 + 16*x^3 + 9*x^4 + 2*x^5))/
   (x*(-16 + 36*x - 32*x^2 - 12*x^3 + 4*x^4 + x^5))
 
alpha[80, 1, 2] = {{0, -1}, {2, 0}}

s1[81, 1, 2] = 0
 
s2[81, 1, 2] = 4/x^2
 
alpha[81, 1, 2] = {{0, 1/2}, {1, 0}}

s1[82, 1, 2] = (-2*(-1 + 4*x + 3*x^2 - 3*x^4 - 4*x^5 + x^6))/
   (1 - 2*x + 23*x^2 - 12*x^3 + 23*x^4 - 2*x^5 + x^6)
 
s2[82, 1, 2] = -((-1 - 2*x - 7*x^2 + 20*x^3 - 7*x^4 - 2*x^5 - x^6)/
     (1 - 2*x + 23*x^2 - 12*x^3 + 23*x^4 - 2*x^5 + x^6))
 
alpha[82, 1, 2] = {{-1, -1}, {-1, 1}}

s1[82, 2, 4] = (-8*(x - 6*x^5 + x^9))/
   (1 + 15*x^2 + 6*x^4 - 6*x^6 - 3*x^8 + 3*x^10)
 
s2[82, 2, 4] = (-2*(-3 - 3*x^2 + 6*x^4 + 6*x^6 - 15*x^8 + x^10))/
   (1 + 15*x^2 + 6*x^4 - 6*x^6 - 3*x^8 + 3*x^10)
 
alpha[82, 2, 4] = {{1, 0}, {0, -2}}

s1[82, 3, 4] = (4*(-4*x + 4*x^3 + x^5))/(-16 - 4*x^2 + x^6)
 
s2[82, 3, 4] = (4*(4 + 4*x^2 + 3*x^4))/(-16 - 4*x^2 + x^6)
 
alpha[82, 3, 4] = {{0, -1}, {2, 0}}

s1[83, 1, 2] = (2*(-64 + 128*x + 48*x^2 - 12*x^4 - 8*x^5 + x^6))/
   (64 - 64*x + 368*x^2 - 96*x^3 + 92*x^4 - 4*x^5 + x^6)
 
s2[83, 1, 2] = -((-64 - 64*x - 112*x^2 + 160*x^3 - 28*x^4 - 4*x^5 - x^6)/
     (64 - 64*x + 368*x^2 - 96*x^3 + 92*x^4 - 4*x^5 + x^6))
 
alpha[83, 1, 2] = {{4, 2}, {-4, 2}}

s1[83, 2, 4] = (-8*(x - 6*x^5 + x^9))/
   (1 + 15*x^2 + 6*x^4 - 6*x^6 - 3*x^8 + 3*x^10)
 
s2[83, 2, 4] = (-2*(-3 - 3*x^2 + 6*x^4 + 6*x^6 - 15*x^8 + x^10))/
   (1 + 15*x^2 + 6*x^4 - 6*x^6 - 3*x^8 + 3*x^10)
 
alpha[83, 2, 4] = {{-1, 0}, {0, 2}}

s1[83, 3, 4] = (4*(-4*x + 4*x^3 + x^5))/(-16 - 4*x^2 + x^6)
 
s2[83, 3, 4] = (4*(4 + 4*x^2 + 3*x^4))/(-16 - 4*x^2 + x^6)
 
alpha[83, 3, 4] = {{0, 2}, {-4, 0}}

s1[84, 1, 2] = (2*(-64 - 128*x + 48*x^2 - 12*x^4 + 8*x^5 + x^6))/
   (64 + 64*x + 368*x^2 + 96*x^3 + 92*x^4 + 4*x^5 + x^6)
 
s2[84, 1, 2] = -((-64 + 64*x - 112*x^2 - 160*x^3 - 28*x^4 + 4*x^5 - x^6)/
     (64 + 64*x + 368*x^2 + 96*x^3 + 92*x^4 + 4*x^5 + x^6))
 
alpha[84, 1, 2] = {{-4, 2}, {4, 2}}

s1[84, 2, 3] = (8*(x - 6*x^5 + x^9))/
   (-3 - 19*x^2 - 42*x^4 - 10*x^6 + x^8 + x^10)
 
s2[84, 2, 3] = (-2*(-1 + 5*x^2 + 26*x^4 + 30*x^6 + 3*x^8 + x^10))/
   (-3 - 19*x^2 - 42*x^4 - 10*x^6 + x^8 + x^10)
 
alpha[84, 2, 3] = {{0, 1}, {-1, 0}}

s1[84, 3, 4] = (4*(-4*x + 4*x^3 + x^5))/(-16 - 4*x^2 + x^6)
 
s2[84, 3, 4] = (4*(4 + 4*x^2 + 3*x^4))/(-16 - 4*x^2 + x^6)
 
alpha[84, 3, 4] = {{0, -2}, {4, 0}}

s1[85, 1, 2] = (2*(-1 - 4*x + 3*x^2 - 3*x^4 + 4*x^5 + x^6))/
   (1 + 2*x + 23*x^2 + 12*x^3 + 23*x^4 + 2*x^5 + x^6)
 
s2[85, 1, 2] = -((-1 + 2*x - 7*x^2 - 20*x^3 - 7*x^4 + 2*x^5 - x^6)/
     (1 + 2*x + 23*x^2 + 12*x^3 + 23*x^4 + 2*x^5 + x^6))
 
alpha[85, 1, 2] = {{-1, 1}, {1, 1}}

s1[85, 2, 3] = (8*(x - 6*x^5 + x^9))/
   (-3 - 19*x^2 - 42*x^4 - 10*x^6 + x^8 + x^10)
 
s2[85, 2, 3] = (-2*(-1 + 5*x^2 + 26*x^4 + 30*x^6 + 3*x^8 + x^10))/
   (-3 - 19*x^2 - 42*x^4 - 10*x^6 + x^8 + x^10)
 
alpha[85, 2, 3] = {{0, -2}, {2, 0}}

s1[85, 3, 4] = (4*(-4*x + 4*x^3 + x^5))/(-16 - 4*x^2 + x^6)
 
s2[85, 3, 4] = (4*(4 + 4*x^2 + 3*x^4))/(-16 - 4*x^2 + x^6)
 
alpha[85, 3, 4] = {{0, -1}, {2, 0}}

s1[86, 1, 2] = (-2*x^2)/(2 + x)^2
 
s2[86, 1, 2] = x^2/(2 + x)^2
 
alpha[86, 1, 2] = {{-4, -2}, {0, 2}}

s1[86, 1, 4] = (-4*(64 + 192*x + 240*x^2 + 144*x^3 + 35*x^4 + x^5))/
   (x*(-8 - 4*x + x^2)^2)
 
s2[86, 1, 4] = (4*(-64 - 128*x - 80*x^2 - 16*x^3 + x^4))/(-8 - 4*x + x^2)^2
 
alpha[86, 1, 4] = {{-1, 1/2}, {-4, -1}}

s1[86, 3, 4] = (4*x^2)/(-1 + x)^2
 
s2[86, 3, 4] = (4*x^2)/(-1 + x)^2
 
alpha[86, 3, 4] = {{-1/2, 1/2}, {0, 1}}

s1[87, 1, 3] = (4*(-1 - 2*x + 2*x^3 + x^4))/(1 - 36*x + 54*x^2 - 36*x^3 + x^4)
 
s2[87, 1, 3] = (4*(1 - 20*x + 22*x^2 - 20*x^3 + x^4))/
   (1 - 36*x + 54*x^2 - 36*x^3 + x^4)
 
alpha[87, 1, 3] = {{-1, 1}, {2, 2}}

s1[87, 1, 4] = (2*(-1 + x))/(1 + x)
 
s2[87, 1, 4] = -((-1 + 6*x - x^2)/(1 + x)^2)
 
alpha[87, 1, 4] = {{2, 2}, {-2, 2}}

s1[87, 2, 4] = (-4*x)/(-4 + 2*x^2 + x^4)
 
s2[87, 2, 4] = (-2*(-2 + 3*x^2 + x^4))/(-4 + 2*x^2 + x^4)
 
alpha[87, 2, 4] = {{-4, 0}, {0, 2}}

s1[88, 1, 3] = (-4*(-16 - 16*x + 4*x^3 + x^4))/
   (16 - 288*x + 216*x^2 - 72*x^3 + x^4)
 
s2[88, 1, 3] = (4*(16 - 160*x + 88*x^2 - 40*x^3 + x^4))/
   (16 - 288*x + 216*x^2 - 72*x^3 + x^4)
 
alpha[88, 1, 3] = {{-2, 1}, {-4, -2}}

s1[88, 1, 4] = (2*(-2 + x))/(2 + x)
 
s2[88, 1, 4] = -((-4 + 12*x - x^2)/(2 + x)^2)
 
alpha[88, 1, 4] = {{4, 2}, {-4, 2}}

s1[88, 2, 4] = (-4*x)/(-4 + 2*x^2 + x^4)
 
s2[88, 2, 4] = (-2*(-2 + 3*x^2 + x^4))/(-4 + 2*x^2 + x^4)
 
alpha[88, 2, 4] = {{-4, 0}, {0, 2}}

s1[89, 1, 3] = (4*(-16 + 16*x - 4*x^3 + x^4))/
   (16 + 288*x + 216*x^2 + 72*x^3 + x^4)
 
s2[89, 1, 3] = (4*(16 + 160*x + 88*x^2 + 40*x^3 + x^4))/
   (16 + 288*x + 216*x^2 + 72*x^3 + x^4)
 
alpha[89, 1, 3] = {{2, 1}, {-4, 2}}

s1[89, 1, 4] = (2*(2 + x))/(-2 + x)
 
s2[89, 1, 4] = -((-4 - 12*x - x^2)/(-2 + x)^2)
 
alpha[89, 1, 4] = {{4, -2}, {-4, -2}}

s1[89, 2, 4] = (4*x)/(-4 + 2*x^2 + x^4)
 
s2[89, 2, 4] = (-2*(-2 + 3*x^2 + x^4))/(-4 + 2*x^2 + x^4)
 
alpha[89, 2, 4] = {{-4, 0}, {0, -2}}

s1[90, 1, 3] = (4*(-1 + 2*x - 2*x^3 + x^4))/(1 + 36*x + 54*x^2 + 36*x^3 + x^4)
 
s2[90, 1, 3] = (4*(1 + 20*x + 22*x^2 + 20*x^3 + x^4))/
   (1 + 36*x + 54*x^2 + 36*x^3 + x^4)
 
alpha[90, 1, 3] = {{1, 1}, {-2, 2}}

s1[90, 2, 3] = (4*x)/(2 + x^2)
 
s2[90, 2, 3] = 8/(2 + x^2)
 
alpha[90, 2, 3] = {{0, 1}, {4, 0}}

s1[90, 2, 4] = (-4*x)/(-4 + 2*x^2 + x^4)
 
s2[90, 2, 4] = (-2*(-2 + 3*x^2 + x^4))/(-4 + 2*x^2 + x^4)
 
alpha[90, 2, 4] = {{4, 0}, {0, -2}}

s1[93, 1, 2] = (2*x^2)/(-2 + x)^2
 
s2[93, 1, 2] = x^2/(-2 + x)^2
 
alpha[93, 1, 2] = {{-4, 2}, {0, 2}}

s1[93, 1, 4] = -((-32 + 128*x - 152*x^2 + 72*x^3 - 17*x^4 + 2*x^5)/
     ((-2 + x)^4*x))
 
s2[93, 1, 4] = -((-32 + 64*x - 40*x^2 + 8*x^3 - x^4)/(-2 + x)^4)
 
alpha[93, 1, 4] = {{1, -1}, {-4, 1}}

s1[93, 3, 4] = (-4*x^2)/(1 + x)^2
 
s2[93, 3, 4] = (4*x^2)/(1 + x)^2
 
alpha[93, 3, 4] = {{-1/2, -1/2}, {0, 1}}

s1[94, 1, 2] = (2*(-1 + 6*x - 6*x^3 + x^4))/(1 - 4*x + 54*x^2 - 4*x^3 + x^4)
 
s2[94, 1, 2] = -((-1 - 4*x - 6*x^2 - 4*x^3 - x^4)/
     (1 - 4*x + 54*x^2 - 4*x^3 + x^4))
 
alpha[94, 1, 2] = {{-1, 1}, {1, 1}}

s1[94, 1, 3] = (2*(-1 + x))/(1 + x)
 
s2[94, 1, 3] = -((-1 + 6*x - x^2)/(1 + x)^2)
 
alpha[94, 1, 3] = {{1, 1}, {-1, 1}}

s1[94, 3, 4] = (2*x)/(-1 - x^2 + x^4)
 
s2[94, 3, 4] = (2*(-1 - 3*x^2 + 2*x^4))/(-1 - x^2 + x^4)
 
alpha[94, 3, 4] = {{-1, 0}, {0, -1}}

s1[95, 1, 2] = (2*(-16 + 48*x - 12*x^3 + x^4))/
   (16 - 32*x + 216*x^2 - 8*x^3 + x^4)
 
s2[95, 1, 2] = -((-16 - 32*x - 24*x^2 - 8*x^3 - x^4)/
     (16 - 32*x + 216*x^2 - 8*x^3 + x^4))
 
alpha[95, 1, 2] = {{-4, 2}, {4, 2}}

s1[95, 1, 3] = (2*(-2 + x))/(2 + x)
 
s2[95, 1, 3] = -((-4 + 12*x - x^2)/(2 + x)^2)
 
alpha[95, 1, 3] = {{4, 2}, {-4, 2}}

s1[95, 3, 4] = (-2*x)/(-1 - x^2 + x^4)
 
s2[95, 3, 4] = (2*(-1 - 3*x^2 + 2*x^4))/(-1 - x^2 + x^4)
 
alpha[95, 3, 4] = {{1, 0}, {0, -1}}

s1[96, 1, 2] = (-2*(-16 - 48*x + 12*x^3 + x^4))/
   (16 + 32*x + 216*x^2 + 8*x^3 + x^4)
 
s2[96, 1, 2] = -((-16 + 32*x - 24*x^2 + 8*x^3 - x^4)/
     (16 + 32*x + 216*x^2 + 8*x^3 + x^4))
 
alpha[96, 1, 2] = {{4, 2}, {4, -2}}

s1[96, 1, 3] = (2*(2 + x))/(-2 + x)
 
s2[96, 1, 3] = -((-4 - 12*x - x^2)/(-2 + x)^2)
 
alpha[96, 1, 3] = {{4, -2}, {-4, -2}}

s1[96, 3, 4] = (2*x)/(-1 - x^2 + x^4)
 
s2[96, 3, 4] = (2*(-1 - 3*x^2 + 2*x^4))/(-1 - x^2 + x^4)
 
alpha[96, 3, 4] = {{-1, 0}, {0, -1}}

s1[97, 1, 3] = (-2*(1 + x))/(-1 + x)
 
s2[97, 1, 3] = -((-1 - 6*x - x^2)/(-1 + x)^2)
 
alpha[97, 1, 3] = {{-1, 1}, {-1, -1}}

s1[97, 2, 4] = 2/x
 
s2[97, 2, 4] = (2*(1 + x^2))/x^2
 
alpha[97, 2, 4] = {{0, -1}, {-1, 0}}

s1[97, 3, 4] = (2*x)/(-1 - x^2 + x^4)
 
s2[97, 3, 4] = (2*(-1 - 3*x^2 + 2*x^4))/(-1 - x^2 + x^4)
 
alpha[97, 3, 4] = {{-1, 0}, {0, -1}}

s1[98, 1, 2] = 0
 
s2[98, 1, 2] = 16/x^2
 
alpha[98, 1, 2] = {{0, -1/4}, {1, 0}}

s1[99, 1, 2] = 0
 
s2[99, 1, 2] = 16/x^2
 
alpha[99, 1, 2] = {{0, -1}, {4, 0}}

s1[100, 1, 3] = 
  (-2*(4 + 16*x + 20*x^2 + 12*x^3 + 5*x^4 + 2*x^5))/
   (4 + 20*x + 28*x^2 + 24*x^3 + 9*x^4 + 3*x^5)
 
s2[100, 1, 3] = 
  -((-4 - 36*x - 48*x^2 - 48*x^3 - 29*x^4 - 11*x^5 - x^6)/
     (4 + 20*x + 28*x^2 + 24*x^3 + 9*x^4 + 3*x^5))
 
alpha[100, 1, 3] = {{1, 0}, {-1, -1}}

nx[100, 2, 3] = (1 - x)/(1 + x)

s1[101, 1, 2] = 
  (-2*(-4 + 16*x - 20*x^2 + 12*x^3 - 5*x^4 + 2*x^5))/
   (-4 + 20*x - 28*x^2 + 24*x^3 - 9*x^4 + 3*x^5)
 
s2[101, 1, 2] = 
  -((4 - 36*x + 48*x^2 - 48*x^3 + 29*x^4 - 11*x^5 + x^6)/
     (-4 + 20*x - 28*x^2 + 24*x^3 - 9*x^4 + 3*x^5))
 
alpha[101, 1, 2] = {{1, 0}, {-1, 1}}

nx[101, 2, 3] = (1 - x)/(1 + x)

s1[102, 1, 2] = 
  (-4*(4 - 8*x + 4*x^2 + 4*x^3 + x^4))/
   (-8 + 36*x - 16*x^2 - 12*x^3 + 2*x^4 + x^5)
 
s2[102, 1, 2] = 
  (4*(4 - 4*x - 12*x^2 + 8*x^3 + 9*x^4 + x^5))/
   (x*(-8 + 36*x - 16*x^2 - 12*x^3 + 2*x^4 + x^5))
 
alpha[102, 1, 2] = {{0, 1/2}, {1, 0}}

s1[103, 1, 2] = 
  (2*(4*x + 8*x^2 + 4*x^3 - 4*x^4 + x^5))/
   (-4 - 4*x + 12*x^2 + 8*x^3 - 9*x^4 + x^5)
 
s2[103, 1, 2] = 
  -((8*x + 36*x^2 + 16*x^3 - 12*x^4 - 2*x^5 + x^6)/
     (-4 - 4*x + 12*x^2 + 8*x^3 - 9*x^4 + x^5))
 
alpha[103, 1, 2] = {{1, 0}, {0, 1}}

s1[104, 1, 2] = (-8*x)/(-2 + x^2)
 
s2[104, 1, 2] = -2
 
alpha[104, 1, 2] = {{-1, 0}, {0, -1}}

s1[105, 1, 2] = (8*x)/(-2 + x^2)
 
s2[105, 1, 2] = -2
 
alpha[105, 1, 2] = {{-1, 0}, {0, 1}}

nx[106, 1, 2] = (1 - x)/(1 + x)

s1[106, 1, 4] = (16*(2 + 3*x + x^2))/(3 + 8*x + 3*x^2)
 
s2[106, 1, 4] = (2*(33 + 32*x + 9*x^2))/(3 + 8*x + 3*x^2)
 
alpha[106, 1, 4] = {{-1, -1}, {-4, -2}}

nx[106, 3, 4] = (1 - x)/(1 - x/2)

nx[107, 1, 2] = (1 - x)/(1 + x)

s1[107, 2, 4] = (-16*(3 + x))/(-7 + x^2)
 
s2[107, 2, 4] = (-2*(37 + 24*x + 5*x^2))/(-7 + x^2)
 
alpha[107, 2, 4] = {{-1, 0}, {-3, -1}}

nx[107, 3, 4] = (1 - x)/(1 - x/2)

nx[108, 1, 2] = 2/x

nx[109, 1, 2] = 2/x

s1[110, 1, 2] = (-4*(2 + 6*x + 5*x^2 + x^3))/(8 + 12*x + 6*x^2 + 2*x^3 + x^4)
 
s2[110, 1, 2] = 
  -((-8 - 20*x - 26*x^2 - 14*x^3 - 3*x^4)/(8 + 12*x + 6*x^2 + 2*x^3 + x^4))
 
alpha[110, 1, 2] = {{-1, 0}, {1, 1}}

s1[110, 1, 5] = 
  (2*(-4 + 8*x + 20*x^2 + 12*x^3 + 3*x^4))/(4 + 8*x + 12*x^2 + 12*x^3 + 5*x^4)
 
s2[110, 1, 5] = 
  -((-28 - 56*x - 52*x^2 - 20*x^3 - 3*x^4)/
     (4 + 8*x + 12*x^2 + 12*x^3 + 5*x^4))
 
alpha[110, 1, 5] = {{0, -1}, {-2, -1}}

nx[110, 2, 3] = (1 - x)/(1 + x)

nx[110, 4, 5] = (-1 - x)/(1 - x)

s1[111, 1, 5] = 
  (-2*(-12 - 24*x - 20*x^2 - 4*x^3 + x^4))/(20 + 24*x + 12*x^2 + 4*x^3 + x^4)
 
s2[111, 1, 5] = 
  -((-12 - 40*x - 52*x^2 - 28*x^3 - 7*x^4)/(20 + 24*x + 12*x^2 + 4*x^3 + x^4))
 
alpha[111, 1, 5] = {{1, 0}, {1, 1}}

nx[111, 2, 3] = (1 - x)/(1 + x)

s1[111, 3, 4] = 
  (2*(-21 - 4*x - 9*x^2 + 24*x^3 + 13*x^4 + 12*x^5 + x^6))/
   (35 + 74*x + 121*x^2 + 108*x^3 + 81*x^4 + 34*x^5 + 11*x^6)
 
s2[111, 3, 4] = 
  -((-39 - 14*x - 37*x^2 - 20*x^3 - 13*x^4 - 6*x^5 + x^6)/
     (35 + 74*x + 121*x^2 + 108*x^3 + 81*x^4 + 34*x^5 + 11*x^6))
 
alpha[111, 3, 4] = {{2, 2}, {-2, 2}}

nx[111, 4, 5] = (-1 - x)/(1 - x)

s1[112, 1, 2] = (-4*(2 - 4*x + x^2))/(6 - 4*x + x^2)
 
s2[112, 1, 2] = (2*(2 - 4*x + 3*x^2))/(6 - 4*x + x^2)
 
alpha[112, 1, 2] = {{1, -1/2}, {-1, 1}}

s1[113, 1, 2] = (-4*(2 - 4*x + x^2))/(6 - 4*x + x^2)
 
s2[113, 1, 2] = (2*(2 - 4*x + 3*x^2))/(6 - 4*x + x^2)
 
alpha[113, 1, 2] = {{1, -1/2}, {-1, 1}}

s1[118, 1, 2] = (-4*(-2*x + x^5))/(4 + 2*x^2 - 2*x^4 + x^6)
 
s2[118, 1, 2] = 
  (2*(-4 + 4*x^2 + 12*x^4 + 4*x^6 - x^8 + x^10))/
   (8 + 20*x^2 + 8*x^4 - 4*x^6 + 2*x^8 + x^10)
 
alpha[118, 1, 2] = {{0, 2}, {4, 0}}

s1[119, 1, 2] = (-4*(-2*x + x^5))/(4 + 2*x^2 - 2*x^4 + x^6)
 
s2[119, 1, 2] = 
  (2*(-4 + 4*x^2 + 12*x^4 + 4*x^6 - x^8 + x^10))/
   (8 + 20*x^2 + 8*x^4 - 4*x^6 + 2*x^8 + x^10)
 
alpha[119, 1, 2] = {{0, 1}, {2, 0}}

s1[120, 1, 2] = (-4*(-2*x + x^5))/(4 + 2*x^2 - 2*x^4 + x^6)
 
s2[120, 1, 2] = 
  (2*(-4 + 4*x^2 + 12*x^4 + 4*x^6 - x^8 + x^10))/
   (8 + 20*x^2 + 8*x^4 - 4*x^6 + 2*x^8 + x^10)
 
alpha[120, 1, 2] = {{0, 1}, {2, 0}}

s1[121, 1, 2] = (-4*(-2*x + x^5))/(4 + 2*x^2 - 2*x^4 + x^6)
 
s2[121, 1, 2] = 
  (2*(-4 + 4*x^2 + 12*x^4 + 4*x^6 - x^8 + x^10))/
   (8 + 20*x^2 + 8*x^4 - 4*x^6 + 2*x^8 + x^10)
 
alpha[121, 1, 2] = {{0, 2}, {4, 0}}

nx[126, 1, 2] = (1 - x)/(1 + x)

s1[126, 1, 3] = 
  (-2*(5 + 19*x + 23*x^2 + 22*x^3 + 11*x^4 + 3*x^5 + x^6))/
   (-5 - 8*x + 4*x^3 + 7*x^4 + 4*x^5 + 2*x^6)
 
s2[126, 1, 3] = 
  -((-16 - 20*x - 25*x^2 - 12*x^3 - 10*x^4 - x^6)/
     (-5 - 8*x + 4*x^3 + 7*x^4 + 4*x^5 + 2*x^6))
 
alpha[126, 1, 3] = {{2, 0}, {0, 2}}

nx[126, 3, 4] = (1 - x)/(1 + x)

nx[127, 1, 2] = (1 - x)/(1 + x)

s1[127, 1, 3] = 
  (-2*(5 + 19*x + 23*x^2 + 22*x^3 + 11*x^4 + 3*x^5 + x^6))/
   (-5 - 8*x + 4*x^3 + 7*x^4 + 4*x^5 + 2*x^6)
 
s2[127, 1, 3] = 
  -((-16 - 20*x - 25*x^2 - 12*x^3 - 10*x^4 - x^6)/
     (-5 - 8*x + 4*x^3 + 7*x^4 + 4*x^5 + 2*x^6))
 
alpha[127, 1, 3] = {{-2, 0}, {0, -2}}

nx[127, 3, 4] = (1 - x)/(1 + x)

nx[128, 1, 2] = (1 - x)/(1 - (3*x)/2)

nx[129, 1, 2] = (1 - x)/(1 - (3*x)/2)

s1[130, 1, 2] = 
  (2*(-4 - 12*x - 8*x^2 + 12*x^3 + 17*x^4 + 7*x^5 + x^6))/
   (4 - 8*x + 32*x^3 + 31*x^4 + 10*x^5 + x^6)
 
s2[130, 1, 2] = 
  -((-4 - 16*x - 12*x^2 + 8*x^3 + 5*x^4 - 4*x^5 - 2*x^6)/
     (4 - 8*x + 32*x^3 + 31*x^4 + 10*x^5 + x^6))
 
alpha[130, 1, 2] = {{2, 2}, {2, 0}}

s1[131, 1, 2] = 
  (2*(-4 - 12*x - 8*x^2 + 12*x^3 + 17*x^4 + 7*x^5 + x^6))/
   (4 - 8*x + 32*x^3 + 31*x^4 + 10*x^5 + x^6)
 
s2[131, 1, 2] = 
  -((-4 - 16*x - 12*x^2 + 8*x^3 + 5*x^4 - 4*x^5 - 2*x^6)/
     (4 - 8*x + 32*x^3 + 31*x^4 + 10*x^5 + x^6))
 
alpha[131, 1, 2] = {{2, 2}, {2, 0}}

s1[132, 1, 2] = 
  (2*(-9 + 34*x - 36*x^2 + 8*x^3 - 4*x^4 + 8*x^5))/
   (19 - 76*x + 108*x^2 - 48*x^3 - 20*x^4 + 16*x^5)
 
s2[132, 1, 2] = 
  -((-19 + 40*x - 8*x^2 - 32*x^3 + 36*x^4 - 32*x^5 + 16*x^6)/
     (19 - 76*x + 108*x^2 - 48*x^3 - 20*x^4 + 16*x^5))
 
alpha[132, 1, 2] = {{-2, 2}, {0, -2}}

nx[132, 2, 3] = (1 - x)/(1 + x)

s1[133, 1, 2] = 
  (-2*(9*x - 16*x^2 + 4*x^3 + 4*x^5))/
   (5 - 7*x + 4*x^2 + 4*x^3 - 12*x^4 + 4*x^5)
 
s2[133, 1, 2] = 
  -((14 - 46*x + 47*x^2 - 8*x^3 - 12*x^4 + 8*x^5 - 4*x^6)/
     (-5 + 12*x - 11*x^2 + 16*x^4 - 16*x^5 + 4*x^6))
 
alpha[133, 1, 2] = {{2, 0}, {2, -4}}

nx[133, 2, 3] = (1 - x)/(1 + x)

s1[134, 1, 2] = (-2*(-1 + 2*x^2))/(3 - 4*x + 2*x^2)
 
s2[134, 1, 2] = -((-1 + 4*x - 6*x^2)/(3 - 4*x + 2*x^2))
 
alpha[134, 1, 2] = {{1, 0}, {1, -2}}

nx[134, 2, 3] = (1 - x)/(1 + x)

s1[135, 1, 2] = (-2*(-1 + 2*x^2))/(3 - 4*x + 2*x^2)
 
s2[135, 1, 2] = -((-1 + 4*x - 6*x^2)/(3 - 4*x + 2*x^2))
 
alpha[135, 1, 2] = {{-1, 1}, {0, -1}}

nx[135, 2, 3] = (1 - x)/(1 + x)

nx[136, 1, 2] = (-1 + x)/(1 + x)

nx[137, 1, 2] = (-1 + x)/(1 + x)

s1[140, 1, 2] = (2*(2*x - 4*x^3 + x^5))/(-2 - 4*x^2 + 3*x^4)
 
s2[140, 1, 2] = -((8 - 2*x^2 - x^6)/(-2 - 4*x^2 + 3*x^4))
 
alpha[140, 1, 2] = {{-2, 0}, {0, 2}}

s1[141, 1, 2] = (2*(2*x - 4*x^3 + x^5))/(-2 - 4*x^2 + 3*x^4)
 
s2[141, 1, 2] = -((8 - 2*x^2 - x^6)/(-2 - 4*x^2 + 3*x^4))
 
alpha[141, 1, 2] = {{-2, 0}, {0, 2}}

s1[142, 1, 2] = (-2*(2*x - 4*x^3 + x^5))/(-2 - 4*x^2 + 3*x^4)
 
s2[142, 1, 2] = -((8 - 2*x^2 - x^6)/(-2 - 4*x^2 + 3*x^4))
 
alpha[142, 1, 2] = {{-2, 0}, {0, -2}}

s1[143, 1, 2] = (2*(2*x - 4*x^3 + x^5))/(-2 - 4*x^2 + 3*x^4)
 
s2[143, 1, 2] = -((8 - 2*x^2 - x^6)/(-2 - 4*x^2 + 3*x^4))
 
alpha[143, 1, 2] = {{2, 0}, {0, -2}}

nx[144, 1, 2] = (1/2 - x)/(1 - x)

s1[144, 1, 3] = (-2*(-1 + 2*x^2))/(3 - 4*x + 2*x^2)
 
s2[144, 1, 3] = -((-1 + 4*x - 6*x^2)/(3 - 4*x + 2*x^2))
 
alpha[144, 1, 3] = {{-2, 2}, {0, -2}}

nx[144, 3, 4] = (1 - x)/(1 + x)

nx[145, 1, 2] = (1/2 - x)/(1 - x)

s1[145, 1, 3] = (-2*(-1 + 2*x^2))/(3 - 4*x + 2*x^2)
 
s2[145, 1, 3] = -((-1 + 4*x - 6*x^2)/(3 - 4*x + 2*x^2))
 
alpha[145, 1, 3] = {{-1, 1}, {0, -1}}

nx[145, 3, 4] = (1 - x)/(1 + x)

nx[146, 1, 2] = (1/2 - x)/(1 - x)

nx[147, 1, 2] = (1/2 - x)/(1 - x)

nx[148, 1, 2] = (1/2 - x)/(1 - x)

nx[149, 1, 2] = (1/2 - x)/(1 - x)

s1[150, 1, 2] = (-2*(-2 + x^2))/(-2 - 4*x + x^2)
 
s2[150, 1, 2] = -((-2 + 4*x + x^2)/(-2 - 4*x + x^2))
 
alpha[150, 1, 2] = {{2, 2}, {2, 0}}

s1[151, 1, 2] = (-2*(-2 + x^2))/(-2 - 4*x + x^2)
 
s2[151, 1, 2] = -((-2 + 4*x + x^2)/(-2 - 4*x + x^2))
 
alpha[151, 1, 2] = {{1, 1}, {1, 0}}

s1[152, 1, 2] = (-2*(-2 + x^2))/(-2 - 4*x + x^2)
 
s2[152, 1, 2] = -((-2 + 4*x + x^2)/(-2 - 4*x + x^2))
 
alpha[152, 1, 2] = {{1, 1}, {1, 0}}

s1[153, 1, 2] = (-2*(-2 + x^2))/(-2 - 4*x + x^2)
 
s2[153, 1, 2] = -((-2 + 4*x + x^2)/(-2 - 4*x + x^2))
 
alpha[153, 1, 2] = {{2, 2}, {2, 0}}

nx[154, 1, 2] = (-1 - x)/(1 - x)

s1[154, 1, 4] = (-2*(3 - 6*x + x^2))/(1 - 2*x + 3*x^2)
 
s2[154, 1, 4] = -((-11 + 6*x - x^2)/(1 - 2*x + 3*x^2))
 
alpha[154, 1, 4] = {{0, -2}, {-2, 0}}

nx[154, 3, 4] = (1 - x)/(1 + x)

nx[155, 1, 2] = (-1 - x)/(1 - x)

s1[155, 1, 3] = (2*(-5 + 2*x + x^2))/(3 + 2*x + x^2)
 
s2[155, 1, 3] = -((-9 + 10*x - 3*x^2)/(3 + 2*x + x^2))
 
alpha[155, 1, 3] = {{1, 1}, {-1, 1}}

nx[155, 3, 4] = (1 - x)/(1 + x)

nx[160, 1, 2] = (1 - x)/(1 + x)

s1[160, 1, 3] = (-4*(1 + x^2))/(-1 - 2*x + x^2)
 
s2[160, 1, 3] = -2
 
alpha[160, 1, 3] = {{-2, 0}, {2, -2}}

nx[161, 1, 2] = (1 - x)/(1 + x)

s1[161, 1, 3] = (-4*(1 + x^2))/(-1 - 2*x + x^2)
 
s2[161, 1, 3] = -2
 
alpha[161, 1, 3] = {{-1, 0}, {1, -1}}

nx[162, 1, 2] = (1 - x)/(1 + x)

s1[162, 1, 3] = (-4*(1 + x^2))/(-1 - 2*x + x^2)
 
s2[162, 1, 3] = -2
 
alpha[162, 1, 3] = {{-1, 0}, {1, -1}}

nx[163, 1, 2] = (1 - x)/(1 + x)

s1[163, 1, 3] = (-4*(1 + x^2))/(-1 - 2*x + x^2)
 
s2[163, 1, 3] = -2
 
alpha[163, 1, 3] = {{-2, 0}, {2, -2}}