On the Linking matrix of Cohort Sequences Solving general linear recurrence \
    equations of order up to the fifth, in the footsteps of Peter Larcombe



                              By Shalosh B. Ekhad





                           -------------------------



                             For order two we have





      We are interested in solutions of the GENERAL recurrence of order, 2



                         w[n + 2] = p w[n + 1] + q w[n]



                                    For n>=0



                        with generic initial conditions



                               w[0] = a, w[1] = b



                   Let H be the square matrix of dimension, 2



                                      [p    q]
                                  H = [      ]
                                      [1    0]



Following Peter Larcombe, Palestinian J. Mathematics,  11(3) (2022), 659-663\

    , we are interested in a square matrix of dimension, 2,

    let's call it B such that



Property 1:  B times the transpose of, [b, a],  equals the transpose of,

    [v1, v0]



                               Property 2: HB=BH



                                      Let



Alpha = a^2*q+a*b*p-b^2


           Solving we get the following square matrix of dimension, 2



                              [b[1, 1]    b[1, 2]]
                              [                  ]
                              [b[2, 1]    b[2, 2]]



                                     where



                                        beta[i, j]
                              b[i, j] = ----------
                                          Alpha



                       and the beta[i,j] are as follows





beta[1,1] = a*p*v1+a*q*v0-b*v1




beta[1,2] = q*(a*v1-b*v0)




beta[2,1] = a*v1-b*v0




beta[2,2] = a*q*v0+b*p*v0-b*v1




                    ----------------------------------------





                           -------------------------



                            For order three we have





      We are interested in solutions of the GENERAL recurrence of order, 3



                  w[n + 3] = p w[n + 2] + q w[n + 1] + r w[n]



                                    For n>=0



                        with generic initial conditions



                          w[0] = a, w[1] = b, w[2] = c



                   Let H be the square matrix of dimension, 3



                                   [p    q    r]
                                   [           ]
                               H = [1    0    0]
                                   [           ]
                                   [0    1    0]



Following Peter Larcombe, Palestinian J. Mathematics,  11(3) (2022), 659-663\

    , we are interested in a square matrix of dimension, 3,

    let's call it B such that



Property 1:  B times the transpose of, [c, b, a],  equals the transpose of,

    [v2, v1, v0]



                               Property 2: HB=BH



                                      Let



Alpha = a^3*r^2+2*a^2*b*q*r+a^2*c*p*r+a*b^2*p*r+a*b^2*q^2+a*b*c*p*q+b^3*p*q+b^2
*c*p^2-3*a*b*c*r-a*c^2*q+b^3*r-b^2*c*q-2*b*c^2*p+c^3


           Solving we get the following square matrix of dimension, 3



                        [b[1, 1]    b[1, 2]    b[1, 3]]
                        [                             ]
                        [b[2, 1]    b[2, 2]    b[2, 3]]
                        [                             ]
                        [b[3, 1]    b[3, 2]    b[3, 3]]



                                     where



                                        beta[i, j]
                              b[i, j] = ----------
                                          Alpha



                       and the beta[i,j] are as follows





beta[1,1] = a^2*p*r*v2+a^2*q*r*v1+a^2*r^2*v0+a*b*p*q*v2+a*b*q^2*v1+a*b*q*r*v0+b
^2*p^2*v2+b^2*p*q*v1+b^2*p*r*v0-a*b*r*v2-a*c*q*v2-a*c*r*v1+b^2*r*v1-2*b*c*p*v2-
b*c*q*v1-b*c*r*v0+c^2*v2




beta[1,2] = a^2*q*r*v2+a^2*r^2*v1+a*b*q^2*v2-a*b*r^2*v0+a*c*p*r*v1-a*c*q^2*v1-a
*c*q*r*v0+b^2*p*q*v2-b*c*p*q*v1-b*c*p*r*v0-a*c*r*v2+b^2*r*v2-b*c*q*v2-b*c*r*v1+
c^2*q*v1+c^2*r*v0




beta[1,3] = r*(a^2*r*v2+a*b*q*v2-a*b*r*v1-a*c*q*v1-a*c*r*v0+b^2*p*v2+b^2*r*v0-b
*c*p*v1-b*c*v2+c^2*v1)




beta[2,1] = a^2*r*v2+a*b*q*v2-a*b*r*v1-a*c*q*v1-a*c*r*v0+b^2*p*v2+b^2*r*v0-b*c*
p*v1-b*c*v2+c^2*v1




beta[2,2] = a^2*q*r*v1+a^2*r^2*v0+a*b*p*r*v1+a*b*q^2*v1+a*b*q*r*v0+a*c*p*q*v1+a
*c*p*r*v0+b^2*p*q*v1+b*c*p^2*v1-a*b*r*v2-a*c*q*v2-a*c*r*v1+b^2*r*v1-b*c*p*v2-b*
c*q*v1-b*c*r*v0-c^2*p*v1+c^2*v2




beta[2,3] = r*(a^2*r*v1+a*b*q*v1-a*b*r*v0+a*c*p*v1-b^2*q*v0-b*c*p*v0-a*c*v2+b^2
*v2-b*c*v1+c^2*v0)




beta[3,1] = a^2*r*v1+a*b*q*v1-a*b*r*v0+a*c*p*v1-b^2*q*v0-b*c*p*v0-a*c*v2+b^2*v2
-b*c*v1+c^2*v0




beta[3,2] = -a^2*p*r*v1-a*b*p*q*v1+a*b*p*r*v0-a*c*p^2*v1+b^2*p*q*v0+b*c*p^2*v0+
a^2*r*v2+a*b*q*v2-a*b*r*v1+a*c*p*v2-a*c*q*v1-a*c*r*v0+b^2*r*v0-c^2*p*v0-b*c*v2+
c^2*v1




beta[3,3] = a^2*r^2*v0+a*b*p*r*v1+2*a*b*q*r*v0+a*c*p*r*v0+b^2*p*q*v1+b^2*q^2*v0
+b*c*p^2*v1+b*c*p*q*v0-a*b*r*v2-a*c*r*v1-b^2*q*v2+b^2*r*v1-b*c*p*v2-b*c*r*v0-c^
2*p*v1-c^2*q*v0+c^2*v2




                    ----------------------------------------





                           -------------------------



                            For order four we have





      We are interested in solutions of the GENERAL recurrence of order, 4



            w[n + 4] = p w[n + 3] + q w[n + 2] + r w[n + 1] + s w[n]



                                    For n>=0



                        with generic initial conditions



                     w[0] = a, w[1] = b, w[2] = c, w[3] = d



                   Let H be the square matrix of dimension, 4



                                 [p    q    r    s]
                                 [                ]
                                 [1    0    0    0]
                             H = [                ]
                                 [0    1    0    0]
                                 [                ]
                                 [0    0    1    0]



Following Peter Larcombe, Palestinian J. Mathematics,  11(3) (2022), 659-663\

    , we are interested in a square matrix of dimension, 4,

    let's call it B such that



Property 1:  B times the transpose of, [d, c, b, a],  equals the transpose of,

    [v3, v2, v1, v0]



                               Property 2: HB=BH



                                      Let



Alpha = a^4*s^3+3*a^3*b*r*s^2+2*a^3*c*q*s^2+a^3*d*p*s^2+a^2*b^2*q*s^2+3*a^2*b^2
*r^2*s+3*a^2*b*c*p*s^2+4*a^2*b*c*q*r*s+2*a^2*b*d*p*r*s+a^2*c^2*p*r*s+a^2*c^2*q^
2*s+a^2*c*d*p*q*s-a*b^3*p*s^2+2*a*b^3*q*r*s+a*b^3*r^3+4*a*b^2*c*p*r*s+2*a*b^2*c
*q^2*s+2*a*b^2*c*q*r^2+a*b^2*d*p*q*s+a*b^2*d*p*r^2+5*a*b*c^2*p*q*s+a*b*c^2*p*r^
2+a*b*c^2*q^2*r+3*a*b*c*d*p^2*s+a*b*c*d*p*q*r+a*c^3*p^2*s+a*c^3*p*q*r+a*c^2*d*p
^2*r-b^4*p*r*s+b^4*q*r^2-b^3*c*p*q*s+b^3*c*p*r^2+2*b^3*c*q^2*r-b^3*d*p^2*s+b^3*
d*p*q*r+3*b^2*c^2*p*q*r+b^2*c^2*q^3+b^2*c*d*p^2*r+b^2*c*d*p*q^2+b*c^3*p^2*r+2*b
*c^3*p*q^2+2*b*c^2*d*p^2*q+c^4*p^2*q+c^3*d*p^3-4*a^2*b*d*s^2-2*a^2*c^2*s^2-3*a^
2*c*d*r*s-a^2*d^2*q*s+4*a*b^2*c*s^2-5*a*b^2*d*r*s+a*b*c^2*r*s-4*a*b*c*d*q*s-3*a
*b*c*d*r^2-3*a*b*d^2*p*s-a*b*d^2*q*r-2*a*c^3*q*s+a*c^3*r^2-5*a*c^2*d*p*s-a*c^2*
d*q*r-2*a*c*d^2*p*r-b^4*s^2+b^3*c*r*s-2*b^3*d*q*s-b^3*d*r^2+3*b^2*c^2*q*s+b^2*c
*d*p*s-5*b^2*c*d*q*r-b^2*d^2*p*r-b^2*d^2*q^2+b*c^3*p*s+b*c^3*q*r-4*b*c^2*d*p*r-\
2*b*c^2*d*q^2-4*b*c*d^2*p*q+c^4*p*r-2*c^3*d*p*q-3*c^2*d^2*p^2+4*a*c*d^2*s+a*d^3
*r+2*b^2*d^2*s-4*b*c^2*d*s+3*b*c*d^2*r+2*b*d^3*q+c^4*s-c^3*d*r+c^2*d^2*q+3*c*d^
3*p-d^4


           Solving we get the following square matrix of dimension, 4



                   [b[1, 1]    b[1, 2]    b[1, 3]    b[1, 4]]
                   [                                        ]
                   [b[2, 1]    b[2, 2]    b[2, 3]    b[2, 4]]
                   [                                        ]
                   [b[3, 1]    b[3, 2]    b[3, 3]    b[3, 4]]
                   [                                        ]
                   [b[4, 1]    b[4, 2]    b[4, 3]    b[4, 4]]



                                     where



                                        beta[i, j]
                              b[i, j] = ----------
                                          Alpha



                       and the beta[i,j] are as follows





beta[1,1] = a^3*p*s^2*v3+a^3*q*s^2*v2+a^3*r*s^2*v1+a^3*s^3*v0+2*a^2*b*p*r*s*v3+
2*a^2*b*q*r*s*v2+2*a^2*b*r^2*s*v1+2*a^2*b*r*s^2*v0+a^2*c*p*q*s*v3+a^2*c*q^2*s*
v2+a^2*c*q*r*s*v1+a^2*c*q*s^2*v0+a*b^2*p*q*s*v3+a*b^2*p*r^2*v3+a*b^2*q^2*s*v2+a
*b^2*q*r^2*v2+a*b^2*q*r*s*v1+a*b^2*q*s^2*v0+a*b^2*r^3*v1+a*b^2*r^2*s*v0+3*a*b*c
*p^2*s*v3+a*b*c*p*q*r*v3+3*a*b*c*p*q*s*v2+3*a*b*c*p*r*s*v1+3*a*b*c*p*s^2*v0+a*b
*c*q^2*r*v2+a*b*c*q*r^2*v1+a*b*c*q*r*s*v0+a*c^2*p^2*r*v3+a*c^2*p*q*r*v2+a*c^2*p
*r^2*v1+a*c^2*p*r*s*v0-b^3*p^2*s*v3+b^3*p*q*r*v3-b^3*p*q*s*v2-b^3*p*r*s*v1-b^3*
p*s^2*v0+b^3*q^2*r*v2+b^3*q*r^2*v1+b^3*q*r*s*v0+b^2*c*p^2*r*v3+b^2*c*p*q^2*v3+b
^2*c*p*q*r*v2+b^2*c*p*r^2*v1+b^2*c*p*r*s*v0+b^2*c*q^3*v2+b^2*c*q^2*r*v1+b^2*c*q
^2*s*v0+2*b*c^2*p^2*q*v3+2*b*c^2*p*q^2*v2+2*b*c^2*p*q*r*v1+2*b*c^2*p*q*s*v0+c^3
*p^3*v3+c^3*p^2*q*v2+c^3*p^2*r*v1+c^3*p^2*s*v0-a^2*b*s^2*v3-a^2*c*r*s*v3-a^2*c*
s^2*v2-a^2*d*q*s*v3-a^2*d*r*s*v2-a^2*d*s^2*v1-a*b^2*r*s*v3+a*b^2*s^2*v2-a*b*c*r
^2*v3+a*b*c*r*s*v2+2*a*b*c*s^2*v1-3*a*b*d*p*s*v3-a*b*d*q*r*v3-2*a*b*d*q*s*v2-a*
b*d*r^2*v2-3*a*b*d*r*s*v1-2*a*b*d*s^2*v0-2*a*c^2*p*s*v3-2*a*c^2*q*s*v2+a*c^2*r^
2*v2-a*c^2*s^2*v0-2*a*c*d*p*r*v3-a*c*d*p*s*v2-a*c*d*q*r*v2-a*c*d*r^2*v1-a*c*d*r
*s*v0-b^3*q*s*v3-b^3*s^2*v1+b^2*c*p*s*v3-b^2*c*q*r*v3+2*b^2*c*q*s*v2+b^2*c*r*s*
v1+b^2*c*s^2*v0-b^2*d*p*r*v3+b^2*d*p*s*v2-b^2*d*q^2*v3-2*b^2*d*q*r*v2-b^2*d*q*s
*v1-b^2*d*r^2*v1-b^2*d*r*s*v0-b*c^2*p*r*v3+b*c^2*q*r*v2+b*c^2*q*s*v1-4*b*c*d*p*
q*v3-b*c*d*p*r*v2-b*c*d*p*s*v1-2*b*c*d*q^2*v2-2*b*c*d*q*r*v1-2*b*c*d*q*s*v0+c^3
*p*r*v2+c^3*p*s*v1-3*c^2*d*p^2*v3-2*c^2*d*p*q*v2-2*c^2*d*p*r*v1-2*c^2*d*p*s*v0+
2*a*c*d*s*v3+a*d^2*r*v3+a*d^2*s*v2+b^2*d*s*v3-b*c^2*s*v3+b*c*d*r*v3-2*b*c*d*s*
v2+2*b*d^2*q*v3+b*d^2*r*v2+b*d^2*s*v1+c^3*s*v2-c^2*d*r*v2-c^2*d*s*v1+3*c*d^2*p*
v3+c*d^2*q*v2+c*d^2*r*v1+c*d^2*s*v0-d^3*v3




beta[1,2] = a^3*q*s^2*v3+a^3*r*s^2*v2+a^3*s^3*v1+2*a^2*b*q*r*s*v3-a^2*b*q*s^2*
v2+2*a^2*b*r^2*s*v2+a^2*b*r*s^2*v1-a^2*b*s^3*v0+a^2*c*p*s^2*v2+a^2*c*q^2*s*v3+a
^2*c*q*s^2*v1-a^2*c*r^2*s*v1-a^2*c*r*s^2*v0+a^2*d*p*r*s*v2+a^2*d*p*s^2*v1-a^2*d
*q^2*s*v2-a^2*d*q*r*s*v1-a^2*d*q*s^2*v0-a*b^2*p*s^2*v2+a*b^2*q^2*s*v3+a*b^2*q*r
^2*v3+a*b^2*q*s^2*v1+a*b^2*r^3*v2-a*b^2*r*s^2*v0+3*a*b*c*p*q*s*v3+2*a*b*c*p*r*s
*v2+a*b*c*p*s^2*v1+a*b*c*q^2*r*v3+a*b*c*q*r*s*v1-a*b*c*r^3*v1-a*b*c*r^2*s*v0-a*
b*d*p*q*s*v2+a*b*d*p*r^2*v2-a*b*d*p*s^2*v0-a*b*d*q^2*r*v2-a*b*d*q*r^2*v1-a*b*d*
q*r*s*v0+a*c^2*p*q*r*v3-a*c^2*p*r*s*v1-a*c^2*p*s^2*v0+a*c*d*p^2*s*v2-a*c*d*p*q*
r*v2-a*c*d*p*r^2*v1-a*c*d*p*r*s*v0-b^3*p*q*s*v3-b^3*p*r*s*v2+b^3*q^2*r*v3-b^3*q
^2*s*v2+b^3*q*r^2*v2-b^3*q*s^2*v0+b^2*c*p*q*r*v3-b^2*c*p*q*s*v2+b^2*c*p*r^2*v2+
b^2*c*p*r*s*v1+b^2*c*q^3*v3+b^2*c*q^2*s*v1-b^2*c*q*r^2*v1-b^2*c*q*r*s*v0-b^2*d*
p^2*s*v2+b^2*d*p*q*r*v2+b^2*d*p*q*s*v1-b^2*d*q^3*v2-b^2*d*q^2*r*v1-b^2*d*q^2*s*
v0+2*b*c^2*p*q^2*v3+b*c^2*p*q*s*v1-b*c^2*p*r^2*v1-b*c^2*p*r*s*v0+b*c*d*p^2*r*v2
+b*c*d*p^2*s*v1-2*b*c*d*p*q^2*v2-2*b*c*d*p*q*r*v1-2*b*c*d*p*q*s*v0+c^3*p^2*q*v3
-c^2*d*p^2*q*v2-c^2*d*p^2*r*v1-c^2*d*p^2*s*v0-a^2*c*s^2*v3-a^2*d*r*s*v3-a^2*d*s
^2*v2+a*b^2*s^2*v3+a*b*c*r*s*v3+2*a*b*c*s^2*v2-2*a*b*d*q*s*v3-a*b*d*r^2*v3-3*a*
b*d*r*s*v2-2*a*b*d*s^2*v1-2*a*c^2*q*s*v3+a*c^2*r^2*v3-a*c^2*s^2*v1-a*c*d*p*s*v3
-a*c*d*q*r*v3+2*a*c*d*q*s*v2-a*c*d*r^2*v2+a*c*d*r*s*v1+2*a*c*d*s^2*v0-a*d^2*p*s
*v2+a*d^2*q*r*v2+a*d^2*r^2*v1+a*d^2*r*s*v0-b^3*s^2*v2+2*b^2*c*q*s*v3+b^2*c*r*s*
v2+b^2*c*s^2*v1+b^2*d*p*s*v3-2*b^2*d*q*r*v3-b^2*d*r^2*v2+b^2*d*s^2*v0+b*c^2*q*r
*v3-b*c^2*r*s*v1-b*c^2*s^2*v0-b*c*d*p*r*v3+b*c*d*p*s*v2-2*b*c*d*q^2*v3-b*c*d*q*
r*v2-2*b*c*d*q*s*v1+b*c*d*r^2*v1+b*c*d*r*s*v0-b*d^2*p*r*v2-b*d^2*p*s*v1+2*b*d^2
*q^2*v2+2*b*d^2*q*r*v1+2*b*d^2*q*s*v0+c^3*p*r*v3-2*c^2*d*p*q*v3-c^2*d*p*r*v2-c^
2*d*p*s*v1+2*c*d^2*p*q*v2+2*c*d^2*p*r*v1+2*c*d^2*p*s*v0+a*d^2*s*v3-2*b*c*d*s*v3
+b*d^2*r*v3+b*d^2*s*v2+c^3*s*v3-c^2*d*r*v3-c^2*d*s*v2+c*d^2*q*v3+c*d^2*r*v2+c*d
^2*s*v1-d^3*q*v2-d^3*r*v1-d^3*s*v0




beta[1,3] = a^3*r*s^2*v3+a^3*s^3*v2+2*a^2*b*r^2*s*v3+a^2*b*r*s^2*v2-a^2*b*s^3*
v1+a^2*c*q*r*s*v3+a^2*c*q*s^2*v2-a^2*c*r^2*s*v2-2*a^2*c*r*s^2*v1-a^2*c*s^3*v0+a
^2*d*p*s^2*v2-a^2*d*q*r*s*v2-a^2*d*r^2*s*v1-a^2*d*r*s^2*v0+a*b^2*q*r*s*v3+a*b^2
*q*s^2*v2+a*b^2*r^3*v3+a*b^2*s^3*v0+3*a*b*c*p*r*s*v3+a*b*c*p*s^2*v2+a*b*c*q*r^2
*v3+a*b*c*q*r*s*v2-2*a*b*c*q*s^2*v1-a*b*c*r^3*v2+a*b*c*r*s^2*v0-a*b*d*p*s^2*v1-
a*b*d*q*r^2*v2-a*b*d*r^3*v1-a*b*d*r^2*s*v0+a*c^2*p*r^2*v3-a*c^2*p*r*s*v2-a*c^2*
p*s^2*v1-2*a*c^2*q*r*s*v1-a*c^2*q*s^2*v0+a*c^2*r^3*v1+a*c^2*r^2*s*v0-a*c*d*p*r^
2*v2-2*a*c*d*p*r*s*v1-a*c*d*p*s^2*v0-b^3*p*r*s*v3+b^3*q*r^2*v3+b^2*c*p*r^2*v3+b
^2*c*p*r*s*v2+b^2*c*q^2*r*v3+b^2*c*q^2*s*v2-b^2*c*q*r^2*v2+b^2*c*q*s^2*v0+b^2*d
*p*q*s*v2+b^2*d*p*r*s*v1+b^2*d*p*s^2*v0-b^2*d*q^2*r*v2-b^2*d*q*r^2*v1-b^2*d*q*r
*s*v0+2*b*c^2*p*q*r*v3+b*c^2*p*q*s*v2-b*c^2*p*r^2*v2-b*c^2*p*r*s*v1-b*c^2*q^2*s
*v1+b*c^2*q*r^2*v1+b*c^2*q*r*s*v0+b*c*d*p^2*s*v2-2*b*c*d*p*q*r*v2-b*c*d*p*q*s*
v1-b*c*d*p*r^2*v1-b*c*d*p*r*s*v0+c^3*p^2*r*v3-c^3*p*q*s*v1+c^3*p*r^2*v1+c^3*p*r
*s*v0-c^2*d*p^2*r*v2-c^2*d*p^2*s*v1-a^2*d*s^2*v3+2*a*b*c*s^2*v3-3*a*b*d*r*s*v3-\
2*a*b*d*s^2*v2-a*c^2*s^2*v2-a*c*d*r^2*v3+a*c*d*r*s*v2+2*a*c*d*s^2*v1+a*d^2*r^2*
v2+2*a*d^2*r*s*v1+a*d^2*s^2*v0-b^3*s^2*v3+b^2*c*r*s*v3+b^2*c*s^2*v2-b^2*d*q*s*
v3-b^2*d*r^2*v3+b^2*d*s^2*v1+b*c^2*q*s*v3-b*c^2*r*s*v2-b*c^2*s^2*v1-b*c*d*p*s*
v3-2*b*c*d*q*r*v3-2*b*c*d*q*s*v2+b*c*d*r^2*v2-b*c*d*r*s*v1-2*b*c*d*s^2*v0-b*d^2
*p*s*v2+2*b*d^2*q*r*v2+b*d^2*q*s*v1+b*d^2*r^2*v1+b*d^2*r*s*v0+c^3*p*s*v3+c^3*r*
s*v1+c^3*s^2*v0-2*c^2*d*p*r*v3-c^2*d*p*s*v2+c^2*d*q*s*v1-c^2*d*r^2*v1-c^2*d*r*s
*v0+2*c*d^2*p*r*v2+2*c*d^2*p*s*v1+b*d^2*s*v3-c^2*d*s*v3+c*d^2*r*v3+c*d^2*s*v2-d
^3*r*v2-d^3*s*v1




beta[1,4] = s*(a^3*s^2*v3+2*a^2*b*r*s*v3-a^2*b*s^2*v2+a^2*c*q*s*v3-a^2*c*r*s*v2
-a^2*c*s^2*v1-a^2*d*q*s*v2-a^2*d*r*s*v1-a^2*d*s^2*v0+a*b^2*q*s*v3+a*b^2*r^2*v3-
a*b^2*r*s*v2+a*b^2*s^2*v1+3*a*b*c*p*s*v3+a*b*c*q*r*v3-a*b*c*r^2*v2+a*b*c*r*s*v1
+2*a*b*c*s^2*v0-a*b*d*p*s*v2-a*b*d*q*r*v2-a*b*d*r^2*v1-a*b*d*r*s*v0+a*c^2*p*r*
v3-a*c^2*p*s*v2-a*c^2*q*s*v1+a*c^2*r^2*v1+a*c^2*r*s*v0-a*c*d*p*r*v2-a*c*d*p*s*
v1-b^3*p*s*v3+b^3*q*r*v3-b^3*q*s*v2-b^3*s^2*v0+b^2*c*p*r*v3+b^2*c*q^2*v3-b^2*c*
q*r*v2+b^2*c*q*s*v1+b^2*d*p*s*v1-b^2*d*q^2*v2-b^2*d*q*r*v1-b^2*d*q*s*v0+2*b*c^2
*p*q*v3-b*c^2*p*r*v2+b*c^2*q*r*v1+b*c^2*q*s*v0-2*b*c*d*p*q*v2-b*c*d*p*r*v1-b*c*
d*p*s*v0+c^3*p^2*v3+c^3*p*r*v1+c^3*p*s*v0-c^2*d*p^2*v2-2*a*b*d*s*v3-a*c^2*s*v3-
a*c*d*r*v3+2*a*c*d*s*v2+a*d^2*r*v2+a*d^2*s*v1+b^2*c*s*v3-b^2*d*r*v3+b^2*d*s*v2-
b*c^2*s*v2-2*b*c*d*q*v3+b*c*d*r*v2-2*b*c*d*s*v1+2*b*d^2*q*v2+b*d^2*r*v1+b*d^2*s
*v0+c^3*s*v1-2*c^2*d*p*v3-c^2*d*r*v1-c^2*d*s*v0+2*c*d^2*p*v2+c*d^2*v3-d^3*v2)




beta[2,1] = a^3*s^2*v3+2*a^2*b*r*s*v3-a^2*b*s^2*v2+a^2*c*q*s*v3-a^2*c*r*s*v2-a^
2*c*s^2*v1-a^2*d*q*s*v2-a^2*d*r*s*v1-a^2*d*s^2*v0+a*b^2*q*s*v3+a*b^2*r^2*v3-a*b
^2*r*s*v2+a*b^2*s^2*v1+3*a*b*c*p*s*v3+a*b*c*q*r*v3-a*b*c*r^2*v2+a*b*c*r*s*v1+2*
a*b*c*s^2*v0-a*b*d*p*s*v2-a*b*d*q*r*v2-a*b*d*r^2*v1-a*b*d*r*s*v0+a*c^2*p*r*v3-a
*c^2*p*s*v2-a*c^2*q*s*v1+a*c^2*r^2*v1+a*c^2*r*s*v0-a*c*d*p*r*v2-a*c*d*p*s*v1-b^
3*p*s*v3+b^3*q*r*v3-b^3*q*s*v2-b^3*s^2*v0+b^2*c*p*r*v3+b^2*c*q^2*v3-b^2*c*q*r*
v2+b^2*c*q*s*v1+b^2*d*p*s*v1-b^2*d*q^2*v2-b^2*d*q*r*v1-b^2*d*q*s*v0+2*b*c^2*p*q
*v3-b*c^2*p*r*v2+b*c^2*q*r*v1+b*c^2*q*s*v0-2*b*c*d*p*q*v2-b*c*d*p*r*v1-b*c*d*p*
s*v0+c^3*p^2*v3+c^3*p*r*v1+c^3*p*s*v0-c^2*d*p^2*v2-2*a*b*d*s*v3-a*c^2*s*v3-a*c*
d*r*v3+2*a*c*d*s*v2+a*d^2*r*v2+a*d^2*s*v1+b^2*c*s*v3-b^2*d*r*v3+b^2*d*s*v2-b*c^
2*s*v2-2*b*c*d*q*v3+b*c*d*r*v2-2*b*c*d*s*v1+2*b*d^2*q*v2+b*d^2*r*v1+b*d^2*s*v0+
c^3*s*v1-2*c^2*d*p*v3-c^2*d*r*v1-c^2*d*s*v0+2*c*d^2*p*v2+c*d^2*v3-d^3*v2




beta[2,2] = a^3*q*s^2*v2+a^3*r*s^2*v1+a^3*s^3*v0+a^2*b*p*s^2*v2+2*a^2*b*q*r*s*
v2+2*a^2*b*r^2*s*v1+2*a^2*b*r*s^2*v0+a^2*c*p*r*s*v2+a^2*c*p*s^2*v1+a^2*c*q^2*s*
v2+a^2*c*q*r*s*v1+a^2*c*q*s^2*v0+a^2*d*p*q*s*v2+a^2*d*p*r*s*v1+a^2*d*p*s^2*v0+a
*b^2*p*r*s*v2-a*b^2*p*s^2*v1+a*b^2*q^2*s*v2+a*b^2*q*r^2*v2+a*b^2*q*r*s*v1+a*b^2
*q*s^2*v0+a*b^2*r^3*v1+a*b^2*r^2*s*v0+3*a*b*c*p*q*s*v2+a*b*c*p*r^2*v2+2*a*b*c*p
*r*s*v1+a*b*c*p*s^2*v0+a*b*c*q^2*r*v2+a*b*c*q*r^2*v1+a*b*c*q*r*s*v0+a*b*d*p^2*s
*v2+a*b*d*p*q*r*v2+a*b*d*p*r^2*v1+a*b*d*p*r*s*v0+a*c^2*p^2*s*v2+a*c^2*p*q*r*v2+
a*c^2*p*q*s*v1+a*c*d*p^2*r*v2+a*c*d*p^2*s*v1-b^3*p*r*s*v1+b^3*q^2*r*v2+b^3*q*r^
2*v1+b^3*q*r*s*v0+2*b^2*c*p*q*r*v2-b^2*c*p*q*s*v1+b^2*c*p*r^2*v1+b^2*c*p*r*s*v0
+b^2*c*q^3*v2+b^2*c*q^2*r*v1+b^2*c*q^2*s*v0-b^2*d*p^2*s*v1+b^2*d*p*q^2*v2+b^2*d
*p*q*r*v1+b^2*d*p*q*s*v0+b*c^2*p^2*r*v2+2*b*c^2*p*q^2*v2+b*c^2*p*q*r*v1+b*c^2*p
*q*s*v0+2*b*c*d*p^2*q*v2+b*c*d*p^2*r*v1+b*c*d*p^2*s*v0+c^3*p^2*q*v2+c^2*d*p^3*
v2-a^2*b*s^2*v3-a^2*c*r*s*v3-a^2*c*s^2*v2-a^2*d*q*s*v3-a^2*d*r*s*v2-a^2*d*s^2*
v1-a*b^2*r*s*v3+a*b^2*s^2*v2-a*b*c*r^2*v3+a*b*c*r*s*v2+2*a*b*c*s^2*v1-a*b*d*p*s
*v3-a*b*d*q*r*v3-2*a*b*d*q*s*v2-a*b*d*r^2*v2-3*a*b*d*r*s*v1-2*a*b*d*s^2*v0-a*c^
2*p*s*v3-2*a*c^2*q*s*v2+a*c^2*r^2*v2-a*c^2*s^2*v0-a*c*d*p*r*v3-3*a*c*d*p*s*v2-a
*c*d*q*r*v2-a*c*d*r^2*v1-a*c*d*r*s*v0-a*d^2*p*r*v2-a*d^2*p*s*v1-b^3*q*s*v3-b^3*
s^2*v1-b^2*c*q*r*v3+2*b^2*c*q*s*v2+b^2*c*r*s*v1+b^2*c*s^2*v0-b^2*d*q^2*v3-2*b^2
*d*q*r*v2-b^2*d*q*s*v1-b^2*d*r^2*v1-b^2*d*r*s*v0-b*c^2*p*r*v3+b*c^2*p*s*v2+b*c^
2*q*r*v2+b*c^2*q*s*v1-2*b*c*d*p*q*v3-2*b*c*d*p*r*v2+b*c*d*p*s*v1-2*b*c*d*q^2*v2
-2*b*c*d*q*r*v1-2*b*c*d*q*s*v0-2*b*d^2*p*q*v2-b*d^2*p*r*v1-b*d^2*p*s*v0+c^3*p*r
*v2-c^2*d*p^2*v3-2*c^2*d*p*q*v2-c^2*d*p*r*v1-c^2*d*p*s*v0-2*c*d^2*p^2*v2+2*a*c*
d*s*v3+a*d^2*r*v3+a*d^2*s*v2+b^2*d*s*v3-b*c^2*s*v3+b*c*d*r*v3-2*b*c*d*s*v2+2*b*
d^2*q*v3+b*d^2*r*v2+b*d^2*s*v1+c^3*s*v2-c^2*d*r*v2-c^2*d*s*v1+2*c*d^2*p*v3+c*d^
2*q*v2+c*d^2*r*v1+c*d^2*s*v0+d^3*p*v2-d^3*v3




beta[2,3] = a^3*r*s^2*v2+a^3*s^3*v1+2*a^2*b*r^2*s*v2+a^2*b*r*s^2*v1-a^2*b*s^3*
v0+a^2*c*p*s^2*v2+a^2*c*q*r*s*v2+2*a^2*c*q*s^2*v1-a^2*c*r^2*s*v1-a^2*c*r*s^2*v0
+a^2*d*p*r*s*v2+a^2*d*p*s^2*v1-a*b^2*p*s^2*v2+a*b^2*q*r*s*v2+a*b^2*r^3*v2-a*b^2
*r*s^2*v0+2*a*b*c*p*r*s*v2+a*b*c*p*s^2*v1+a*b*c*q*r^2*v2-2*a*b*c*q*s^2*v0-a*b*c
*r^3*v1-a*b*c*r^2*s*v0+a*b*d*p*r^2*v2-a*b*d*p*s^2*v0+a*c^2*p*q*s*v2-a*c^2*p*r*s
*v1-a*c^2*p*s^2*v0+a*c^2*q^2*s*v1-a*c^2*q*r^2*v1-a*c^2*q*r*s*v0+a*c*d*p^2*s*v2+
a*c*d*p*q*s*v1-a*c*d*p*r^2*v1-a*c*d*p*r*s*v0-b^3*p*r*s*v2+b^3*q*r^2*v2-b^2*c*p*
q*s*v2+b^2*c*p*r^2*v2+b^2*c*p*r*s*v1+b^2*c*q^2*r*v2-b^2*c*q*r^2*v1-b^2*c*q*r*s*
v0-b^2*d*p^2*s*v2+b^2*d*p*q*r*v2+b*c^2*p*q*r*v2+b*c^2*p*q*s*v1-b*c^2*p*r^2*v1-b
*c^2*p*r*s*v0-b*c^2*q^2*r*v1-b*c^2*q^2*s*v0+b*c*d*p^2*r*v2+b*c*d*p^2*s*v1-b*c*d
*p*q*r*v1-b*c*d*p*q*s*v0-c^3*p*q*r*v1-c^3*p*q*s*v0-c^2*d*p^2*r*v1-c^2*d*p^2*s*
v0-a^2*c*s^2*v3-a^2*d*r*s*v3-a^2*d*s^2*v2+a*b^2*s^2*v3+a*b*c*r*s*v3+2*a*b*c*s^2
*v2-a*b*d*r^2*v3-3*a*b*d*r*s*v2-2*a*b*d*s^2*v1-a*c^2*q*s*v3+a*c^2*r^2*v3-a*c^2*
s^2*v1-a*c*d*p*s*v3-a*c*d*r^2*v2+a*c*d*r*s*v1+2*a*c*d*s^2*v0-a*d^2*p*s*v2-a*d^2
*q*s*v1+a*d^2*r^2*v1+a*d^2*r*s*v0-b^3*s^2*v2+b^2*c*q*s*v3+b^2*c*r*s*v2+b^2*c*s^
2*v1+b^2*d*p*s*v3-b^2*d*q*r*v3-b^2*d*q*s*v2-b^2*d*r^2*v2+b^2*d*s^2*v0+b*c^2*q*r
*v3+b*c^2*q*s*v2-b*c^2*r*s*v1-b*c^2*s^2*v0-b*c*d*p*r*v3+b*c*d*p*s*v2-2*b*c*d*q*
r*v2+b*c*d*r^2*v1+b*c*d*r*s*v0-b*d^2*p*r*v2-b*d^2*p*s*v1+b*d^2*q*r*v1+b*d^2*q*s
*v0+c^3*p*r*v3-c^3*q*s*v1-c^2*d*p*r*v2-c^2*d*p*s*v1+c^2*d*q*r*v1+c^2*d*q*s*v0+2
*c*d^2*p*r*v1+2*c*d^2*p*s*v0+a*d^2*s*v3-2*b*c*d*s*v3+b*d^2*r*v3+b*d^2*s*v2+c^3*
s*v3-c^2*d*r*v3-c^2*d*s*v2+c*d^2*r*v2+c*d^2*s*v1-d^3*r*v1-d^3*s*v0




beta[2,4] = s*(a^3*s^2*v2+2*a^2*b*r*s*v2-a^2*b*s^2*v1+a^2*c*q*s*v2-a^2*c*r*s*v1
-a^2*c*s^2*v0+a^2*d*p*s*v2+a*b^2*q*s*v2+a*b^2*r^2*v2-a*b^2*r*s*v1+a*b^2*s^2*v0+
a*b*c*p*s*v2+a*b*c*q*r*v2-2*a*b*c*q*s*v1-a*b*c*r^2*v1-a*b*c*r*s*v0+a*b*d*p*r*v2
-a*b*d*p*s*v1-a*c^2*p*s*v1-a*c^2*q*r*v1-a*c^2*q*s*v0-a*c*d*p*r*v1-a*c*d*p*s*v0+
b^3*q*r*v2+b^3*r*s*v0+b^2*c*p*r*v2+b^2*c*q^2*v2-b^2*c*q*r*v1+b^2*c*q*s*v0+b^2*d
*p*q*v2+b^2*d*p*s*v0+b*c^2*p*q*v2-b*c^2*p*r*v1-b*c^2*q^2*v1+b*c*d*p^2*v2-b*c*d*
p*q*v1-c^3*p*q*v1-c^2*d*p^2*v1-a^2*d*s*v3+2*a*b*c*s*v3-a*b*d*r*v3-2*a*b*d*s*v2+
a*c^2*r*v3-a*c^2*s*v2-a*c*d*r*v2+2*a*c*d*s*v1+a*d^2*r*v1+a*d^2*s*v0-b^3*s*v3+b^
2*c*s*v2-b^2*d*q*v3-b^2*d*r*v2+b^2*d*s*v1+b*c^2*q*v3-b*c^2*s*v1-b*c*d*p*v3-2*b*
c*d*q*v2+b*c*d*r*v1-2*b*c*d*s*v0-b*d^2*p*v2+b*d^2*q*v1+c^3*p*v3+c^3*s*v0-c^2*d*
p*v2+c^2*d*q*v1+2*c*d^2*p*v1+b*d^2*v3-c^2*d*v3+c*d^2*v2-d^3*v1)




beta[3,1] = a^3*s^2*v2+2*a^2*b*r*s*v2-a^2*b*s^2*v1+a^2*c*q*s*v2-a^2*c*r*s*v1-a^
2*c*s^2*v0+a^2*d*p*s*v2+a*b^2*q*s*v2+a*b^2*r^2*v2-a*b^2*r*s*v1+a*b^2*s^2*v0+a*b
*c*p*s*v2+a*b*c*q*r*v2-2*a*b*c*q*s*v1-a*b*c*r^2*v1-a*b*c*r*s*v0+a*b*d*p*r*v2-a*
b*d*p*s*v1-a*c^2*p*s*v1-a*c^2*q*r*v1-a*c^2*q*s*v0-a*c*d*p*r*v1-a*c*d*p*s*v0+b^3
*q*r*v2+b^3*r*s*v0+b^2*c*p*r*v2+b^2*c*q^2*v2-b^2*c*q*r*v1+b^2*c*q*s*v0+b^2*d*p*
q*v2+b^2*d*p*s*v0+b*c^2*p*q*v2-b*c^2*p*r*v1-b*c^2*q^2*v1+b*c*d*p^2*v2-b*c*d*p*q
*v1-c^3*p*q*v1-c^2*d*p^2*v1-a^2*d*s*v3+2*a*b*c*s*v3-a*b*d*r*v3-2*a*b*d*s*v2+a*c
^2*r*v3-a*c^2*s*v2-a*c*d*r*v2+2*a*c*d*s*v1+a*d^2*r*v1+a*d^2*s*v0-b^3*s*v3+b^2*c
*s*v2-b^2*d*q*v3-b^2*d*r*v2+b^2*d*s*v1+b*c^2*q*v3-b*c^2*s*v1-b*c*d*p*v3-2*b*c*d
*q*v2+b*c*d*r*v1-2*b*c*d*s*v0-b*d^2*p*v2+b*d^2*q*v1+c^3*p*v3+c^3*s*v0-c^2*d*p*
v2+c^2*d*q*v1+2*c*d^2*p*v1+b*d^2*v3-c^2*d*v3+c*d^2*v2-d^3*v1




beta[3,2] = -a^3*p*s^2*v2-2*a^2*b*p*r*s*v2+a^2*b*p*s^2*v1-a^2*c*p*q*s*v2+a^2*c*
p*r*s*v1+a^2*c*p*s^2*v0-a^2*d*p^2*s*v2-a*b^2*p*q*s*v2-a*b^2*p*r^2*v2+a*b^2*p*r*
s*v1-a*b^2*p*s^2*v0-a*b*c*p^2*s*v2-a*b*c*p*q*r*v2+2*a*b*c*p*q*s*v1+a*b*c*p*r^2*
v1+a*b*c*p*r*s*v0-a*b*d*p^2*r*v2+a*b*d*p^2*s*v1+a*c^2*p^2*s*v1+a*c^2*p*q*r*v1+a
*c^2*p*q*s*v0+a*c*d*p^2*r*v1+a*c*d*p^2*s*v0-b^3*p*q*r*v2-b^3*p*r*s*v0-b^2*c*p^2
*r*v2-b^2*c*p*q^2*v2+b^2*c*p*q*r*v1-b^2*c*p*q*s*v0-b^2*d*p^2*q*v2-b^2*d*p^2*s*
v0-b*c^2*p^2*q*v2+b*c^2*p^2*r*v1+b*c^2*p*q^2*v1-b*c*d*p^3*v2+b*c*d*p^2*q*v1+c^3
*p^2*q*v1+c^2*d*p^3*v1+a^3*s^2*v3+2*a^2*b*r*s*v3-a^2*b*s^2*v2+a^2*c*q*s*v3-a^2*
c*r*s*v2-a^2*c*s^2*v1+a^2*d*p*s*v3-a^2*d*q*s*v2-a^2*d*r*s*v1-a^2*d*s^2*v0+a*b^2
*q*s*v3+a*b^2*r^2*v3-a*b^2*r*s*v2+a*b^2*s^2*v1+a*b*c*p*s*v3+a*b*c*q*r*v3-a*b*c*
r^2*v2+a*b*c*r*s*v1+2*a*b*c*s^2*v0+a*b*d*p*r*v3+a*b*d*p*s*v2-a*b*d*q*r*v2-a*b*d
*r^2*v1-a*b*d*r*s*v0-a*c^2*q*s*v1+a*c^2*r^2*v1+a*c^2*r*s*v0-3*a*c*d*p*s*v1-a*d^
2*p*r*v1-a*d^2*p*s*v0+b^3*q*r*v3-b^3*q*s*v2-b^3*s^2*v0+b^2*c*p*r*v3-b^2*c*p*s*
v2+b^2*c*q^2*v3-b^2*c*q*r*v2+b^2*c*q*s*v1+b^2*d*p*q*v3+b^2*d*p*r*v2-b^2*d*q^2*
v2-b^2*d*q*r*v1-b^2*d*q*s*v0+b*c^2*p*q*v3-b*c^2*p*r*v2+b*c^2*p*s*v1+b*c^2*q*r*
v1+b*c^2*q*s*v0+b*c*d*p^2*v3-2*b*c*d*p*r*v1+b*c*d*p*s*v0+b*d^2*p^2*v2-b*d^2*p*q
*v1+c^3*p*r*v1-c^2*d*p*q*v1-2*c*d^2*p^2*v1-2*a*b*d*s*v3-a*c^2*s*v3-a*c*d*r*v3+2
*a*c*d*s*v2+a*d^2*r*v2+a*d^2*s*v1+b^2*c*s*v3-b^2*d*r*v3+b^2*d*s*v2-b*c^2*s*v2-2
*b*c*d*q*v3+b*c*d*r*v2-2*b*c*d*s*v1-b*d^2*p*v3+2*b*d^2*q*v2+b*d^2*r*v1+b*d^2*s*
v0+c^3*s*v1-c^2*d*p*v3-c^2*d*r*v1-c^2*d*s*v0+c*d^2*p*v2+d^3*p*v1+c*d^2*v3-d^3*
v2




beta[3,3] = a^3*r*s^2*v1+a^3*s^3*v0+a^2*b*p*s^2*v2+a^2*b*q*s^2*v1+2*a^2*b*r^2*s
*v1+2*a^2*b*r*s^2*v0+a^2*c*p*r*s*v2+a^2*c*p*s^2*v1+2*a^2*c*q*r*s*v1+2*a^2*c*q*s
^2*v0+a^2*d*p*r*s*v1+a^2*d*p*s^2*v0+a*b^2*p*r*s*v2-a*b^2*p*s^2*v1+2*a*b^2*q*r*s
*v1+a*b^2*r^3*v1+a*b^2*r^2*s*v0+2*a*b*c*p*q*s*v2+a*b*c*p*r^2*v2+2*a*b*c*p*r*s*
v1+a*b*c*p*s^2*v0+2*a*b*c*q^2*s*v1+2*a*b*c*q*r^2*v1+2*a*b*c*q*r*s*v0+a*b*d*p^2*
s*v2+a*b*d*p*q*s*v1+a*b*d*p*r^2*v1+a*b*d*p*r*s*v0+a*c^2*p^2*s*v2+a*c^2*p*q*r*v2
+2*a*c^2*p*q*s*v1+a*c^2*q^2*r*v1+a*c^2*q^2*s*v0+a*c*d*p^2*r*v2+a*c*d*p^2*s*v1+a
*c*d*p*q*r*v1+a*c*d*p*q*s*v0-b^3*p*r*s*v1+b^3*q*r^2*v1+b^2*c*p*q*r*v2-b^2*c*p*q
*s*v1+b^2*c*p*r^2*v1+b^2*c*p*r*s*v0+2*b^2*c*q^2*r*v1-b^2*d*p^2*s*v1+b^2*d*p*q*r
*v1+b*c^2*p^2*r*v2+b*c^2*p*q^2*v2+2*b*c^2*p*q*r*v1+b*c^2*p*q*s*v0+b*c^2*q^3*v1+
b*c*d*p^2*q*v2+b*c*d*p^2*r*v1+b*c*d*p^2*s*v0+b*c*d*p*q^2*v1+c^3*p^2*q*v2+c^3*p*
q^2*v1+c^2*d*p^3*v2+c^2*d*p^2*q*v1-a^2*b*s^2*v3-a^2*c*r*s*v3-a^2*c*s^2*v2-a^2*d
*r*s*v2-a^2*d*s^2*v1-a*b^2*r*s*v3+a*b^2*s^2*v2-2*a*b*c*q*s*v3-a*b*c*r^2*v3+a*b*
c*r*s*v2+2*a*b*c*s^2*v1-a*b*d*p*s*v3-a*b*d*r^2*v2-3*a*b*d*r*s*v1-2*a*b*d*s^2*v0
-a*c^2*p*s*v3-a*c^2*q*r*v3-a*c^2*q*s*v2+a*c^2*r^2*v2-a*c^2*s^2*v0-a*c*d*p*r*v3-\
3*a*c*d*p*s*v2-2*a*c*d*q*s*v1-a*c*d*r^2*v1-a*c*d*r*s*v0-a*d^2*p*r*v2-a*d^2*p*s*
v1-a*d^2*q*r*v1-a*d^2*q*s*v0-b^3*s^2*v1-b^2*c*q*r*v3+b^2*c*q*s*v2+b^2*c*r*s*v1+
b^2*c*s^2*v0-b^2*d*q*r*v2-2*b^2*d*q*s*v1-b^2*d*r^2*v1-b^2*d*r*s*v0-b*c^2*p*r*v3
+b*c^2*p*s*v2-b*c^2*q^2*v3+b*c^2*q*r*v2+2*b*c^2*q*s*v1-b*c*d*p*q*v3-2*b*c*d*p*r
*v2+b*c*d*p*s*v1-3*b*c*d*q*r*v1-b*d^2*p*q*v2-b*d^2*p*r*v1-b*d^2*p*s*v0-b*d^2*q^
2*v1-c^3*p*q*v3+c^3*p*r*v2-c^3*q*s*v0-c^2*d*p^2*v3-c^2*d*p*q*v2-c^2*d*p*r*v1-c^
2*d*p*s*v0-c^2*d*q^2*v1-2*c*d^2*p^2*v2-2*c*d^2*p*q*v1+2*a*c*d*s*v3+a*d^2*r*v3+a
*d^2*s*v2+b^2*d*s*v3-b*c^2*s*v3+b*c*d*r*v3-2*b*c*d*s*v2+b*d^2*q*v3+b*d^2*r*v2+b
*d^2*s*v1+c^3*s*v2+c^2*d*q*v3-c^2*d*r*v2-c^2*d*s*v1+2*c*d^2*p*v3+c*d^2*r*v1+c*d
^2*s*v0+d^3*p*v2+d^3*q*v1-d^3*v3




beta[3,4] = s*(a^3*s^2*v1+2*a^2*b*r*s*v1-a^2*b*s^2*v0+a^2*c*p*s*v2+2*a^2*c*q*s*
v1+a^2*d*p*s*v1-a*b^2*p*s*v2+a*b^2*r^2*v1-2*a*b^2*r*s*v0+a*b*c*p*r*v2+a*b*c*p*s
*v1+2*a*b*c*q*r*v1-2*a*b*c*q*s*v0+a*b*d*p*r*v1-a*b*d*p*s*v0+a*c^2*p*q*v2-a*c^2*
p*s*v0+a*c^2*q^2*v1+a*c*d*p^2*v2+a*c*d*p*q*v1-b^3*p*r*v2-b^3*r^2*v0-b^2*c*p*q*
v2+b^2*c*p*r*v1-2*b^2*c*q*r*v0-b^2*d*p^2*v2-b^2*d*p*r*v0+b*c^2*p*q*v1-b*c^2*p*r
*v0-b*c^2*q^2*v0+b*c*d*p^2*v1-b*c*d*p*q*v0-c^3*p*q*v0-c^2*d*p^2*v0-a^2*c*s*v3-a
^2*d*s*v2+a*b^2*s*v3-a*b*c*r*v3+2*a*b*c*s*v2-a*b*d*r*v2-2*a*b*d*s*v1-a*c^2*q*v3
+a*c^2*r*v2-a*c^2*s*v1-a*c*d*p*v3-a*c*d*r*v1+2*a*c*d*s*v0-a*d^2*p*v2-a*d^2*q*v1
+b^3*r*v3-b^3*s*v2+b^2*c*q*v3+b^2*c*s*v1+b^2*d*p*v3-b^2*d*q*v2-b^2*d*r*v1+b^2*d
*s*v0+b*c^2*q*v2-b*c^2*s*v0+b*c*d*p*v2+3*b*c*d*r*v0-b*d^2*p*v1+b*d^2*q*v0-c^3*q
*v1-c^3*r*v0-c^2*d*p*v1+c^2*d*q*v0+2*c*d^2*p*v0+a*d^2*v3-2*b*c*d*v3+b*d^2*v2+c^
3*v3-c^2*d*v2+c*d^2*v1-d^3*v0)




beta[4,1] = a^3*s^2*v1+2*a^2*b*r*s*v1-a^2*b*s^2*v0+a^2*c*p*s*v2+2*a^2*c*q*s*v1+
a^2*d*p*s*v1-a*b^2*p*s*v2+a*b^2*r^2*v1-2*a*b^2*r*s*v0+a*b*c*p*r*v2+a*b*c*p*s*v1
+2*a*b*c*q*r*v1-2*a*b*c*q*s*v0+a*b*d*p*r*v1-a*b*d*p*s*v0+a*c^2*p*q*v2-a*c^2*p*s
*v0+a*c^2*q^2*v1+a*c*d*p^2*v2+a*c*d*p*q*v1-b^3*p*r*v2-b^3*r^2*v0-b^2*c*p*q*v2+b
^2*c*p*r*v1-2*b^2*c*q*r*v0-b^2*d*p^2*v2-b^2*d*p*r*v0+b*c^2*p*q*v1-b*c^2*p*r*v0-
b*c^2*q^2*v0+b*c*d*p^2*v1-b*c*d*p*q*v0-c^3*p*q*v0-c^2*d*p^2*v0-a^2*c*s*v3-a^2*d
*s*v2+a*b^2*s*v3-a*b*c*r*v3+2*a*b*c*s*v2-a*b*d*r*v2-2*a*b*d*s*v1-a*c^2*q*v3+a*c
^2*r*v2-a*c^2*s*v1-a*c*d*p*v3-a*c*d*r*v1+2*a*c*d*s*v0-a*d^2*p*v2-a*d^2*q*v1+b^3
*r*v3-b^3*s*v2+b^2*c*q*v3+b^2*c*s*v1+b^2*d*p*v3-b^2*d*q*v2-b^2*d*r*v1+b^2*d*s*
v0+b*c^2*q*v2-b*c^2*s*v0+b*c*d*p*v2+3*b*c*d*r*v0-b*d^2*p*v1+b*d^2*q*v0-c^3*q*v1
-c^3*r*v0-c^2*d*p*v1+c^2*d*q*v0+2*c*d^2*p*v0+a*d^2*v3-2*b*c*d*v3+b*d^2*v2+c^3*
v3-c^2*d*v2+c*d^2*v1-d^3*v0




beta[4,2] = -a^3*p*s^2*v1-2*a^2*b*p*r*s*v1+a^2*b*p*s^2*v0-a^2*c*p^2*s*v2-2*a^2*
c*p*q*s*v1-a^2*d*p^2*s*v1+a*b^2*p^2*s*v2-a*b^2*p*r^2*v1+2*a*b^2*p*r*s*v0-a*b*c*
p^2*r*v2-a*b*c*p^2*s*v1-2*a*b*c*p*q*r*v1+2*a*b*c*p*q*s*v0-a*b*d*p^2*r*v1+a*b*d*
p^2*s*v0-a*c^2*p^2*q*v2+a*c^2*p^2*s*v0-a*c^2*p*q^2*v1-a*c*d*p^3*v2-a*c*d*p^2*q*
v1+b^3*p^2*r*v2+b^3*p*r^2*v0+b^2*c*p^2*q*v2-b^2*c*p^2*r*v1+2*b^2*c*p*q*r*v0+b^2
*d*p^3*v2+b^2*d*p^2*r*v0-b*c^2*p^2*q*v1+b*c^2*p^2*r*v0+b*c^2*p*q^2*v0-b*c*d*p^3
*v1+b*c*d*p^2*q*v0+c^3*p^2*q*v0+c^2*d*p^3*v0+a^3*s^2*v2+2*a^2*b*r*s*v2-a^2*b*s^
2*v1+a^2*c*p*s*v3+a^2*c*q*s*v2-a^2*c*r*s*v1-a^2*c*s^2*v0+2*a^2*d*p*s*v2-a*b^2*p
*s*v3+a*b^2*q*s*v2+a*b^2*r^2*v2-a*b^2*r*s*v1+a*b^2*s^2*v0+a*b*c*p*r*v3-a*b*c*p*
s*v2+a*b*c*q*r*v2-2*a*b*c*q*s*v1-a*b*c*r^2*v1-a*b*c*r*s*v0+2*a*b*d*p*r*v2+a*b*d
*p*s*v1+a*c^2*p*q*v3-a*c^2*p*r*v2-a*c^2*q*r*v1-a*c^2*q*s*v0+a*c*d*p^2*v3-3*a*c*
d*p*s*v0+a*d^2*p^2*v2+a*d^2*p*q*v1-b^3*p*r*v3+b^3*p*s*v2+b^3*q*r*v2+b^3*r*s*v0-
b^2*c*p*q*v3+b^2*c*p*r*v2-b^2*c*p*s*v1+b^2*c*q^2*v2-b^2*c*q*r*v1+b^2*c*q*s*v0-b
^2*d*p^2*v3+2*b^2*d*p*q*v2+b^2*d*p*r*v1-b*c^2*p*r*v1+b*c^2*p*s*v0-b*c^2*q^2*v1-
b*c*d*p*q*v1-3*b*c*d*p*r*v0+b*d^2*p^2*v1-b*d^2*p*q*v0+c^3*p*r*v0-c^2*d*p*q*v0-2
*c*d^2*p^2*v0-a^2*d*s*v3+2*a*b*c*s*v3-a*b*d*r*v3-2*a*b*d*s*v2+a*c^2*r*v3-a*c^2*
s*v2-a*c*d*r*v2+2*a*c*d*s*v1-a*d^2*p*v3+a*d^2*r*v1+a*d^2*s*v0-b^3*s*v3+b^2*c*s*
v2-b^2*d*q*v3-b^2*d*r*v2+b^2*d*s*v1+b*c^2*q*v3-b*c^2*s*v1+b*c*d*p*v3-2*b*c*d*q*
v2+b*c*d*r*v1-2*b*c*d*s*v0-2*b*d^2*p*v2+b*d^2*q*v1+c^3*s*v0+c^2*d*q*v1+c*d^2*p*
v1+d^3*p*v0+b*d^2*v3-c^2*d*v3+c*d^2*v2-d^3*v1




beta[4,3] = -a^3*p*s^2*v2-a^3*q*s^2*v1-2*a^2*b*p*r*s*v2+a^2*b*p*s^2*v1-2*a^2*b*
q*r*s*v1+a^2*b*q*s^2*v0-2*a^2*c*p*q*s*v2+a^2*c*p*r*s*v1+a^2*c*p*s^2*v0-2*a^2*c*
q^2*s*v1-a^2*d*p^2*s*v2-a^2*d*p*q*s*v1-a*b^2*p*r^2*v2+a*b^2*p*r*s*v1-a*b^2*p*s^
2*v0-a*b^2*q*r^2*v1+2*a*b^2*q*r*s*v0-a*b*c*p^2*s*v2-2*a*b*c*p*q*r*v2+a*b*c*p*q*
s*v1+a*b*c*p*r^2*v1+a*b*c*p*r*s*v0-2*a*b*c*q^2*r*v1+2*a*b*c*q^2*s*v0-a*b*d*p^2*
r*v2+a*b*d*p^2*s*v1-a*b*d*p*q*r*v1+a*b*d*p*q*s*v0+a*c^2*p^2*s*v1-a*c^2*p*q^2*v2
+a*c^2*p*q*r*v1+2*a*c^2*p*q*s*v0-a*c^2*q^3*v1-a*c*d*p^2*q*v2+a*c*d*p^2*r*v1+a*c
*d*p^2*s*v0-a*c*d*p*q^2*v1-b^3*p*r*s*v0+b^3*q*r^2*v0-b^2*c*p^2*r*v2-b^2*c*p*q*s
*v0+2*b^2*c*q^2*r*v0-b^2*d*p^2*s*v0+b^2*d*p*q*r*v0-b*c^2*p^2*q*v2+b*c^2*p^2*r*
v1+b*c^2*p*q*r*v0+b*c^2*q^3*v0-b*c*d*p^3*v2+b*c*d*p*q^2*v0+c^3*p^2*q*v1+c^3*p*q
^2*v0+c^2*d*p^3*v1+c^2*d*p^2*q*v0+a^3*s^2*v3+2*a^2*b*r*s*v3-a^2*b*s^2*v2+2*a^2*
c*q*s*v3-a^2*c*r*s*v2-a^2*c*s^2*v1+a^2*d*p*s*v3-a^2*d*r*s*v1-a^2*d*s^2*v0+a*b^2
*r^2*v3-a*b^2*r*s*v2+a*b^2*s^2*v1+a*b*c*p*s*v3+2*a*b*c*q*r*v3-2*a*b*c*q*s*v2-a*
b*c*r^2*v2+a*b*c*r*s*v1+2*a*b*c*s^2*v0+a*b*d*p*r*v3+a*b*d*p*s*v2+2*a*b*d*q*s*v1
-a*b*d*r^2*v1-a*b*d*r*s*v0+a*c^2*q^2*v3-a*c^2*q*r*v2+a*c^2*r^2*v1+a*c^2*r*s*v0+
a*c*d*p*q*v3-3*a*c*d*p*s*v1+a*c*d*q*r*v1-2*a*c*d*q*s*v0+a*d^2*p*q*v2-a*d^2*p*r*
v1-a*d^2*p*s*v0+a*d^2*q^2*v1-b^3*s^2*v0+b^2*c*p*r*v3-b^2*c*p*s*v2-b^2*c*q*r*v2+
b^2*d*p*r*v2-2*b^2*d*q*s*v0+b*c^2*p*q*v3-b*c^2*p*r*v2+b*c^2*p*s*v1-b*c^2*q^2*v2
+b*c^2*q*r*v1+2*b*c^2*q*s*v0+b*c*d*p^2*v3-b*c*d*p*q*v2-2*b*c*d*p*r*v1+b*c*d*p*s
*v0-3*b*c*d*q*r*v0+b*d^2*p^2*v2-b*d^2*q^2*v0+c^3*p*r*v1+c^3*q^2*v1+c^3*q*r*v0-c
^2*d*q^2*v0-2*c*d^2*p^2*v1-2*c*d^2*p*q*v0-2*a*b*d*s*v3-a*c^2*s*v3-a*c*d*r*v3+2*
a*c*d*s*v2-a*d^2*q*v3+a*d^2*r*v2+a*d^2*s*v1+b^2*c*s*v3-b^2*d*r*v3+b^2*d*s*v2-b*
c^2*s*v2+b*c*d*r*v2-2*b*c*d*s*v1-b*d^2*p*v3+b*d^2*q*v2+b*d^2*r*v1+b*d^2*s*v0-c^
3*q*v3+c^3*s*v1-c^2*d*p*v3+c^2*d*q*v2-c^2*d*r*v1-c^2*d*s*v0+c*d^2*p*v2-c*d^2*q*
v1+d^3*p*v1+d^3*q*v0+c*d^2*v3-d^3*v2




beta[4,4] = a^3*s^3*v0+a^2*b*p*s^2*v2+a^2*b*q*s^2*v1+3*a^2*b*r*s^2*v0+a^2*c*p*s
^2*v1+2*a^2*c*q*s^2*v0+a^2*d*p*s^2*v0+2*a*b^2*p*r*s*v2-a*b^2*p*s^2*v1+2*a*b^2*q
*r*s*v1+3*a*b^2*r^2*s*v0+2*a*b*c*p*q*s*v2+a*b*c*p*r*s*v1+a*b*c*p*s^2*v0+2*a*b*c
*q^2*s*v1+4*a*b*c*q*r*s*v0+a*b*d*p^2*s*v2+a*b*d*p*q*s*v1+2*a*b*d*p*r*s*v0+a*c^2
*p^2*s*v2+2*a*c^2*p*q*s*v1+a*c^2*p*r*s*v0+a*c^2*q^2*s*v0+a*c*d*p^2*s*v1+a*c*d*p
*q*s*v0+b^3*p*r^2*v2-b^3*p*r*s*v1+b^3*q*r^2*v1+b^3*r^3*v0+2*b^2*c*p*q*r*v2-b^2*
c*p*q*s*v1+b^2*c*p*r*s*v0+2*b^2*c*q^2*r*v1+2*b^2*c*q*r^2*v0+b^2*d*p^2*r*v2-b^2*
d*p^2*s*v1+b^2*d*p*q*r*v1+b^2*d*p*r^2*v0+b*c^2*p^2*r*v2+b*c^2*p*q^2*v2+b*c^2*p*
q*r*v1+b*c^2*p*q*s*v0+b*c^2*p*r^2*v0+b*c^2*q^3*v1+b*c^2*q^2*r*v0+b*c*d*p^2*q*v2
+b*c*d*p^2*s*v0+b*c*d*p*q^2*v1+b*c*d*p*q*r*v0+c^3*p^2*q*v2+c^3*p*q^2*v1+c^3*p*q
*r*v0+c^2*d*p^3*v2+c^2*d*p^2*q*v1+c^2*d*p^2*r*v0-a^2*b*s^2*v3-a^2*c*s^2*v2-a^2*
d*s^2*v1-2*a*b^2*r*s*v3+a*b^2*s^2*v2-2*a*b*c*q*s*v3-a*b*c*r*s*v2+2*a*b*c*s^2*v1
-a*b*d*p*s*v3-a*b*d*r*s*v1-2*a*b*d*s^2*v0-a*c^2*p*s*v3-a*c^2*q*s*v2+a*c^2*r*s*
v1-a*c^2*s^2*v0-3*a*c*d*p*s*v2-2*a*c*d*q*s*v1-3*a*c*d*r*s*v0-a*d^2*p*s*v1-a*d^2
*q*s*v0-b^3*r^2*v3+b^3*r*s*v2-b^3*s^2*v1-2*b^2*c*q*r*v3+b^2*c*q*s*v2+b^2*c*s^2*
v0-b^2*d*p*r*v3-2*b^2*d*q*s*v1-2*b^2*d*r*s*v0-b*c^2*p*r*v3+b*c^2*p*s*v2-b*c^2*q
^2*v3+2*b*c^2*q*s*v1+b*c^2*r*s*v0-b*c*d*p*q*v3-3*b*c*d*p*r*v2+b*c*d*p*s*v1-3*b*
c*d*q*r*v1-3*b*c*d*r^2*v0-b*d^2*p*q*v2-b*d^2*p*s*v0-b*d^2*q^2*v1-b*d^2*q*r*v0-c
^3*p*q*v3+c^3*p*r*v2+c^3*q*r*v1-c^3*q*s*v0+c^3*r^2*v0-c^2*d*p^2*v3-c^2*d*p*q*v2
-c^2*d*p*s*v0-c^2*d*q^2*v1-c^2*d*q*r*v0-2*c*d^2*p^2*v2-2*c*d^2*p*q*v1-2*c*d^2*p
*r*v0+2*a*c*d*s*v3+a*d^2*s*v2+b^2*d*s*v3-b*c^2*s*v3+3*b*c*d*r*v3-2*b*c*d*s*v2+b
*d^2*q*v3+b*d^2*s*v1-c^3*r*v3+c^3*s*v2+c^2*d*q*v3-c^2*d*s*v1+2*c*d^2*p*v3+c*d^2
*s*v0+d^3*p*v2+d^3*q*v1+d^3*r*v0-d^3*v3




                    ----------------------------------------





                           -------------------------



                            For order five we have





      We are interested in solutions of the GENERAL recurrence of order, 5



     w[n + 5] = p w[n + 4] + q w[n + 3] + r w[n + 2] + s w[n + 1] + t w[n]



                                    For n>=0



                        with generic initial conditions



                w[0] = a, w[1] = b, w[2] = c, w[3] = d, w[4] = e



                   Let H be the square matrix of dimension, 5



                              [p    q    r    s    t]
                              [                     ]
                              [1    0    0    0    0]
                              [                     ]
                          H = [0    1    0    0    0]
                              [                     ]
                              [0    0    1    0    0]
                              [                     ]
                              [0    0    0    1    0]



Following Peter Larcombe, Palestinian J. Mathematics,  11(3) (2022), 659-663\

    , we are interested in a square matrix of dimension, 5,

    let's call it B such that



Property 1:  B times the transpose of, [e, d, c, b, a],

     equals the transpose of, [v4, v3, v2, v1, v0]



                               Property 2: HB=BH



                                      Let



Alpha = a^5*t^4+4*a^4*b*s*t^3+3*a^4*c*r*t^3+2*a^4*d*q*t^3+a^4*e*p*t^3+a^3*b^2*r
*t^3+6*a^3*b^2*s^2*t^2+3*a^3*b*c*q*t^3+9*a^3*b*c*r*s*t^2+4*a^3*b*d*p*t^3+6*a^3*
b*d*q*s*t^2+3*a^3*b*e*p*s*t^2+2*a^3*c^2*p*t^3+a^3*c^2*q*s*t^2+3*a^3*c^2*r^2*t^2
+3*a^3*c*d*p*s*t^2+4*a^3*c*d*q*r*t^2+2*a^3*c*e*p*r*t^2+a^3*d^2*p*r*t^2+a^3*d^2*
q^2*t^2+a^3*d*e*p*q*t^2-a^2*b^3*q*t^3+3*a^2*b^3*r*s*t^2+4*a^2*b^3*s^3*t-4*a^2*b
^2*c*p*t^3+7*a^2*b^2*c*q*s*t^2+3*a^2*b^2*c*r^2*t^2+9*a^2*b^2*c*r*s^2*t+9*a^2*b^
2*d*p*s*t^2+2*a^2*b^2*d*q*r*t^2+6*a^2*b^2*d*q*s^2*t+a^2*b^2*e*p*r*t^2+3*a^2*b^2
*e*p*s^2*t+a^2*b*c^2*p*s*t^2+8*a^2*b*c^2*q*r*t^2+2*a^2*b*c^2*q*s^2*t+6*a^2*b*c^
2*r^2*s*t+8*a^2*b*c*d*p*r*t^2+6*a^2*b*c*d*p*s^2*t+6*a^2*b*c*d*q^2*t^2+8*a^2*b*c
*d*q*r*s*t+3*a^2*b*c*e*p*q*t^2+4*a^2*b*c*e*p*r*s*t+7*a^2*b*d^2*p*q*t^2+2*a^2*b*
d^2*p*r*s*t+2*a^2*b*d^2*q^2*s*t+4*a^2*b*d*e*p^2*t^2+2*a^2*b*d*e*p*q*s*t+4*a^2*c
^3*p*r*t^2-a^2*c^3*p*s^2*t+a^2*c^3*q^2*t^2+2*a^2*c^3*q*r*s*t+a^2*c^3*r^3*t+7*a^
2*c^2*d*p*q*t^2+4*a^2*c^2*d*p*r*s*t+2*a^2*c^2*d*q^2*s*t+2*a^2*c^2*d*q*r^2*t+2*a
^2*c^2*e*p^2*t^2+a^2*c^2*e*p*q*s*t+a^2*c^2*e*p*r^2*t+4*a^2*c*d^2*p^2*t^2+5*a^2*
c*d^2*p*q*s*t+a^2*c*d^2*p*r^2*t+a^2*c*d^2*q^2*r*t+3*a^2*c*d*e*p^2*s*t+a^2*c*d*e
*p*q*r*t+a^2*d^3*p^2*s*t+a^2*d^3*p*q*r*t+a^2*d^2*e*p^2*r*t+a*b^4*p*t^3-2*a*b^4*
q*s*t^2+3*a*b^4*r*s^2*t+a*b^4*s^4-5*a*b^3*c*p*s*t^2-2*a*b^3*c*q*r*t^2+5*a*b^3*c
*q*s^2*t+6*a*b^3*c*r^2*s*t+3*a*b^3*c*r*s^3+2*a*b^3*d*p*r*t^2+6*a*b^3*d*p*s^2*t-\
2*a*b^3*d*q^2*t^2+4*a*b^3*d*q*r*s*t+2*a*b^3*d*q*s^3-a*b^3*e*p*q*t^2+2*a*b^3*e*p
*r*s*t+a*b^3*e*p*s^3-7*a*b^2*c^2*p*r*t^2-a*b^2*c^2*p*s^2*t+12*a*b^2*c^2*q*r*s*t
+a*b^2*c^2*q*s^3+3*a*b^2*c^2*r^3*t+3*a*b^2*c^2*r^2*s^2-5*a*b^2*c*d*p*q*t^2+14*a
*b^2*c*d*p*r*s*t+3*a*b^2*c*d*p*s^3+8*a*b^2*c*d*q^2*s*t+4*a*b^2*c*d*q*r^2*t+4*a*
b^2*c*d*q*r*s^2-4*a*b^2*c*e*p^2*t^2+4*a*b^2*c*e*p*q*s*t+2*a*b^2*c*e*p*r^2*t+2*a
*b^2*c*e*p*r*s^2+2*a*b^2*d^2*p^2*t^2+9*a*b^2*d^2*p*q*s*t+a*b^2*d^2*p*r^2*t+a*b^
2*d^2*p*r*s^2+a*b^2*d^2*q^2*r*t+a*b^2*d^2*q^2*s^2+5*a*b^2*d*e*p^2*s*t+a*b^2*d*e
*p*q*r*t+a*b^2*d*e*p*q*s^2-a*b*c^3*p*q*t^2-a*b*c^3*p*s^3+2*a*b*c^3*q^2*s*t+7*a*
b*c^3*q*r^2*t+2*a*b*c^3*q*r*s^2+a*b*c^3*r^3*s-4*a*b*c^2*d*p^2*t^2+8*a*b*c^2*d*p
*q*s*t+6*a*b*c^2*d*p*r^2*t+4*a*b*c^2*d*p*r*s^2+10*a*b*c^2*d*q^2*r*t+2*a*b*c^2*d
*q^2*s^2+2*a*b*c^2*d*q*r^2*s-a*b*c^2*e*p^2*s*t+5*a*b*c^2*e*p*q*r*t+a*b*c^2*e*p*
q*s^2+a*b*c^2*e*p*r^2*s+7*a*b*c*d^2*p^2*s*t+11*a*b*c*d^2*p*q*r*t+5*a*b*c*d^2*p*
q*s^2+a*b*c*d^2*p*r^2*s+3*a*b*c*d^2*q^3*t+a*b*c*d^2*q^2*r*s+4*a*b*c*d*e*p^2*r*t
+3*a*b*c*d*e*p^2*s^2+3*a*b*c*d*e*p*q^2*t+a*b*c*d*e*p*q*r*s+2*a*b*d^3*p^2*r*t+a*
b*d^3*p^2*s^2+3*a*b*d^3*p*q^2*t+a*b*d^3*p*q*r*s+3*a*b*d^2*e*p^2*q*t+a*b*d^2*e*p
^2*r*s+a*c^4*p^2*t^2-a*c^4*p*q*s*t+2*a*c^4*p*r^2*t-a*c^4*p*r*s^2+2*a*c^4*q^2*r*
t+a*c^4*q*r^2*s-a*c^3*d*p^2*s*t+9*a*c^3*d*p*q*r*t-a*c^3*d*p*q*s^2+a*c^3*d*p*r^2
*s+2*a*c^3*d*q^3*t+2*a*c^3*d*q^2*r*s+2*a*c^3*e*p^2*r*t-a*c^3*e*p^2*s^2+a*c^3*e*
p*q^2*t+a*c^3*e*p*q*r*s+5*a*c^2*d^2*p^2*r*t+8*a*c^2*d^2*p*q^2*t+3*a*c^2*d^2*p*q
*r*s+a*c^2*d^2*q^3*s+5*a*c^2*d*e*p^2*q*t+a*c^2*d*e*p^2*r*s+a*c^2*d*e*p*q^2*s+7*
a*c*d^3*p^2*q*t+a*c*d^3*p^2*r*s+2*a*c*d^3*p*q^2*s+4*a*c*d^2*e*p^3*t+2*a*c*d^2*e
*p^2*q*s+a*d^4*p^3*t+a*d^4*p^2*q*s+a*d^3*e*p^3*s+b^5*p*s*t^2-b^5*q*s^2*t+b^5*r*
s^3+b^4*c*p*r*t^2-b^4*c*p*s^2*t-2*b^4*c*q*r*s*t+b^4*c*q*s^3+3*b^4*c*r^2*s^2+b^4
*d*p*q*t^2+2*b^4*d*p*r*s*t+b^4*d*p*s^3-2*b^4*d*q^2*s*t+2*b^4*d*q*r*s^2+b^4*e*p^
2*t^2-b^4*e*p*q*s*t+b^4*e*p*r*s^2-4*b^3*c^2*p*r*s*t-b^3*c^2*q*r^2*t+4*b^3*c^2*q
*r*s^2+3*b^3*c^2*r^3*s-2*b^3*c*d*p*q*s*t+2*b^3*c*d*p*r^2*t+6*b^3*c*d*p*r*s^2-2*
b^3*c*d*q^2*r*t+2*b^3*c*d*q^2*s^2+4*b^3*c*d*q*r^2*s-b^3*c*e*p^2*s*t-b^3*c*e*p*q
*r*t+b^3*c*e*p*q*s^2+2*b^3*c*e*p*r^2*s+2*b^3*d^2*p^2*s*t+2*b^3*d^2*p*q*r*t+2*b^
3*d^2*p*q*s^2+b^3*d^2*p*r^2*s-b^3*d^2*q^3*t+b^3*d^2*q^2*r*s+2*b^3*d*e*p^2*r*t+b
^3*d*e*p^2*s^2-b^3*d*e*p*q^2*t+b^3*d*e*p*q*r*s-b^2*c^3*p*q*s*t-3*b^2*c^3*p*r^2*
t-b^2*c^3*p*r*s^2+b^2*c^3*q^2*s^2+5*b^2*c^3*q*r^2*s+b^2*c^3*r^4-4*b^2*c^2*d*p^2
*s*t-4*b^2*c^2*d*p*q*r*t+4*b^2*c^2*d*p*q*s^2+7*b^2*c^2*d*p*r^2*s+6*b^2*c^2*d*q^
2*r*s+2*b^2*c^2*d*q*r^3-3*b^2*c^2*e*p^2*r*t+3*b^2*c^2*e*p*q*r*s+b^2*c^2*e*p*r^3
+2*b^2*c*d^2*p^2*r*t+3*b^2*c*d^2*p^2*s^2-b^2*c*d^2*p*q^2*t+10*b^2*c*d^2*p*q*r*s
+b^2*c*d^2*p*r^3+b^2*c*d^2*q^3*s+b^2*c*d^2*q^2*r^2-b^2*c*d*e*p^2*q*t+5*b^2*c*d*
e*p^2*r*s+b^2*c*d*e*p*q^2*s+b^2*c*d*e*p*q*r^2+2*b^2*d^3*p^2*q*t+2*b^2*d^3*p^2*r
*s+b^2*d^3*p*q^2*s+b^2*d^3*p*q*r^2+2*b^2*d^2*e*p^3*t+b^2*d^2*e*p^2*q*s+b^2*d^2*
e*p^2*r^2+b*c^4*p^2*s*t-b*c^4*p*q*r*t-b*c^4*p*q*s^2-b*c^4*p*r^2*s+2*b*c^4*q^2*r
*s+2*b*c^4*q*r^3-4*b*c^3*d*p^2*r*t-b*c^3*d*p^2*s^2-b*c^3*d*p*q^2*t+5*b*c^3*d*p*
q*r*s+2*b*c^3*d*p*r^3+2*b*c^3*d*q^3*s+4*b*c^3*d*q^2*r^2-b*c^3*e*p^2*q*t-b*c^3*e
*p^2*r*s+b*c^3*e*p*q^2*s+2*b*c^3*e*p*q*r^2-4*b*c^2*d^2*p^2*q*t+4*b*c^2*d^2*p^2*
r*s+7*b*c^2*d^2*p*q^2*s+6*b*c^2*d^2*p*q*r^2+2*b*c^2*d^2*q^3*r-4*b*c^2*d*e*p^3*t
+4*b*c^2*d*e*p^2*q*s+2*b*c^2*d*e*p^2*r^2+2*b*c^2*d*e*p*q^2*r+6*b*c*d^3*p^2*q*s+
2*b*c*d^3*p^2*r^2+4*b*c*d^3*p*q^2*r+3*b*c*d^2*e*p^3*s+4*b*c*d^2*e*p^2*q*r+b*d^4
*p^3*s+2*b*d^4*p^2*q*r+2*b*d^3*e*p^3*r+c^5*p^2*r*t-c^5*p*q*r*s+c^5*q^2*r^2+c^4*
d*p^2*q*t-c^4*d*p^2*r*s-c^4*d*p*q^2*s+2*c^4*d*p*q*r^2+2*c^4*d*q^3*r+c^4*e*p^3*t
-c^4*e*p^2*q*s+c^4*e*p*q^2*r-c^3*d^2*p^2*q*s+c^3*d^2*p^2*r^2+5*c^3*d^2*p*q^2*r+
c^3*d^2*q^4-c^3*d*e*p^3*s+2*c^3*d*e*p^2*q*r+c^3*d*e*p*q^3+4*c^2*d^3*p^2*q*r+3*c
^2*d^3*p*q^3+c^2*d^2*e*p^3*r+3*c^2*d^2*e*p^2*q^2+c*d^4*p^3*r+3*c*d^4*p^2*q^2+3*
c*d^3*e*p^3*q+d^5*p^3*q+d^4*e*p^4-5*a^3*b*e*t^3-5*a^3*c*d*t^3-4*a^3*c*e*s*t^2-2
*a^3*d^2*s*t^2-3*a^3*d*e*r*t^2-a^3*e^2*q*t^2+5*a^2*b^2*d*t^3-11*a^2*b^2*e*s*t^2
+5*a^2*b*c^2*t^3-2*a^2*b*c*d*s*t^2-9*a^2*b*c*e*r*t^2-8*a^2*b*c*e*s^2*t+3*a^2*b*
d^2*r*t^2-4*a^2*b*d^2*s^2*t-6*a^2*b*d*e*q*t^2-6*a^2*b*d*e*r*s*t-4*a^2*b*e^2*p*t
^2-2*a^2*b*e^2*q*s*t+3*a^2*c^3*s*t^2-7*a^2*c^2*d*r*t^2+4*a^2*c^2*d*s^2*t-3*a^2*
c^2*e*q*t^2-5*a^2*c^2*e*r*s*t-8*a^2*c*d^2*q*t^2+a^2*c*d^2*r*s*t-13*a^2*c*d*e*p*
t^2-4*a^2*c*d*e*q*s*t-3*a^2*c*d*e*r^2*t-3*a^2*c*e^2*p*s*t-a^2*c*e^2*q*r*t-3*a^2
*d^3*p*t^2-2*a^2*d^3*q*s*t+a^2*d^3*r^2*t-5*a^2*d^2*e*p*s*t-a^2*d^2*e*q*r*t-2*a^
2*d*e^2*p*r*t-5*a*b^3*c*t^3+6*a*b^3*d*s*t^2-3*a*b^3*e*r*t^2-7*a*b^3*e*s^2*t-a*b
^2*c^2*s*t^2+a*b^2*c*d*r*t^2+3*a*b^2*c*d*s^2*t-6*a*b^2*c*e*q*t^2-16*a*b^2*c*e*r
*s*t-4*a*b^2*c*e*s^3+7*a*b^2*d^2*q*t^2+a*b^2*d^2*r*s*t-2*a*b^2*d^2*s^3-3*a*b^2*
d*e*p*t^2-8*a*b^2*d*e*q*s*t-3*a*b^2*d*e*r^2*t-3*a*b^2*d*e*r*s^2-5*a*b^2*e^2*p*s
*t-a*b^2*e^2*q*r*t-a*b^2*e^2*q*s^2+7*a*b*c^3*r*t^2-a*b*c^3*s^2*t+4*a*b*c^2*d*q*
t^2-4*a*b*c^2*d*r*s*t+4*a*b*c^2*d*s^3+7*a*b*c^2*e*p*t^2-14*a*b*c^2*e*q*s*t-6*a*
b*c^2*e*r^2*t-5*a*b*c^2*e*r*s^2+7*a*b*c*d^2*p*t^2-4*a*b*c*d^2*q*s*t+a*b*c*d^2*r
*s^2-18*a*b*c*d*e*p*s*t-17*a*b*c*d*e*q*r*t-4*a*b*c*d*e*q*s^2-3*a*b*c*d*e*r^2*s-\
4*a*b*c*e^2*p*r*t-3*a*b*c*e^2*p*s^2-3*a*b*c*e^2*q^2*t-a*b*c*e^2*q*r*s-4*a*b*d^3
*p*s*t+a*b*d^3*q*r*t-2*a*b*d^3*q*s^2+a*b*d^3*r^2*s-8*a*b*d^2*e*p*r*t-5*a*b*d^2*
e*p*s^2-3*a*b*d^2*e*q^2*t-a*b*d^2*e*q*r*s-6*a*b*d*e^2*p*q*t-2*a*b*d*e^2*p*r*s+2
*a*c^4*q*t^2+3*a*c^4*r*s*t-a*c^4*s^3-a*c^3*d*p*t^2+6*a*c^3*d*q*s*t-2*a*c^3*d*r^
2*t+a*c^3*d*r*s^2+2*a*c^3*e*p*s*t-5*a*c^3*e*q*r*t-2*a*c^3*e*q*s^2-a*c^3*e*r^2*s
+5*a*c^2*d^2*p*s*t-4*a*c^2*d^2*q*r*t+3*a*c^2*d^2*q*s^2-14*a*c^2*d*e*p*r*t+a*c^2
*d*e*p*s^2-6*a*c^2*d*e*q^2*t-5*a*c^2*d*e*q*r*s-5*a*c^2*e^2*p*q*t-a*c^2*e^2*p*r*
s-a*c^2*e^2*q^2*s+a*c*d^3*p*s^2-3*a*c*d^3*q^2*t+a*c*d^3*q*r*s-16*a*c*d^2*e*p*q*
t-4*a*c*d^2*e*p*r*s-2*a*c*d^2*e*q^2*s-8*a*c*d*e^2*p^2*t-4*a*c*d*e^2*p*q*s-3*a*d
^4*p*q*t+a*d^4*p*r*s-7*a*d^3*e*p^2*t-2*a*d^3*e*p*q*s-3*a*d^2*e^2*p^2*s+b^5*t^3-
b^4*c*s*t^2+3*b^4*d*r*t^2+b^4*d*s^2*t+2*b^4*e*q*t^2-3*b^4*e*r*s*t-b^4*e*s^3-4*b
^3*c^2*r*t^2-2*b^3*c*d*q*t^2+6*b^3*c*d*r*s*t-b^3*c*e*p*t^2-3*b^3*c*e*r^2*t-7*b^
3*c*e*r*s^2+2*b^3*d^2*p*t^2+4*b^3*d^2*q*s*t+3*b^3*d^2*r^2*t-2*b^3*d^2*r*s^2-4*b
^3*d*e*p*s*t+b^3*d*e*q*r*t-2*b^3*d*e*q*s^2-3*b^3*d*e*r^2*s-2*b^3*e^2*p*r*t-b^3*
e^2*p*s^2+b^3*e^2*q^2*t-b^3*e^2*q*r*s-b^2*c^3*q*t^2-b^2*c^3*r*s*t-4*b^2*c^2*d*p
*t^2-b^2*c^2*d*r^2*t+4*b^2*c^2*d*r*s^2+5*b^2*c^2*e*p*s*t-4*b^2*c^2*e*q*r*t-5*b^
2*c^2*e*q*s^2-8*b^2*c^2*e*r^2*s+8*b^2*c*d^2*p*s*t+6*b^2*c*d^2*q*r*t-2*b^2*c*d^2
*q*s^2+b^2*c*d^2*r^2*s-4*b^2*c*d*e*p*r*t-7*b^2*c*d*e*p*s^2-11*b^2*c*d*e*q*r*s-3
*b^2*c*d*e*r^3+b^2*c*e^2*p*q*t-5*b^2*c*e^2*p*r*s-b^2*c*e^2*q^2*s-b^2*c*e^2*q*r^
2+4*b^2*d^3*p*r*t-2*b^2*d^3*p*s^2+3*b^2*d^3*q^2*t-2*b^2*d^3*q*r*s+b^2*d^3*r^3+b
^2*d^2*e*p*q*t-9*b^2*d^2*e*p*r*s-b^2*d^2*e*q^2*s-b^2*d^2*e*q*r^2-4*b^2*d*e^2*p^
2*t-2*b^2*d*e^2*p*q*s-2*b^2*d*e^2*p*r^2+b*c^4*p*t^2+2*b*c^4*r^2*t-b*c^4*r*s^2-6
*b*c^3*d*p*s*t-b*c^3*d*q*r*t+4*b*c^3*d*q*s^2+b*c^3*d*r^2*s+6*b*c^3*e*p*r*t+b*c^
3*e*p*s^2-2*b*c^3*e*q^2*t-9*b*c^3*e*q*r*s-2*b*c^3*e*r^3+4*b*c^2*d^2*p*s^2-b*c^2
*d^2*q^2*t+4*b*c^2*d^2*q*r*s-4*b*c^2*d*e*p*q*t-8*b*c^2*d*e*p*r*s-6*b*c^2*d*e*q^
2*s-10*b*c^2*d*e*q*r^2+4*b*c^2*e^2*p^2*t-4*b*c^2*e^2*p*q*s-2*b*c^2*e^2*p*r^2-2*
b*c^2*e^2*q^2*r+6*b*c*d^3*p*q*t+2*b*c*d^3*p*r*s-2*b*c*d^3*q^2*s+2*b*c*d^3*q*r^2
+3*b*c*d^2*e*p^2*t-14*b*c*d^2*e*p*q*s-8*b*c*d^2*e*p*r^2-4*b*c*d^2*e*q^2*r-6*b*c
*d*e^2*p^2*s-8*b*c*d*e^2*p*q*r+b*d^4*p^2*t-2*b*d^4*p*q*s+2*b*d^4*p*r^2-6*b*d^3*
e*p^2*s-4*b*d^3*e*p*q*r-6*b*d^2*e^2*p^2*r+c^5*p*s*t+2*c^5*q*r*t-c^5*q*s^2-c^4*d
*p*s^2+2*c^4*d*q^2*t+c^4*d*q*r*s+3*c^4*e*p*q*t+c^4*e*p*r*s-2*c^4*e*q^2*s-2*c^4*
e*q*r^2-c^3*d^2*p*q*t+c^3*d^2*p*r*s+3*c^3*d^2*q^2*s-c^3*d*e*p^2*t-2*c^3*d*e*p*r
^2-7*c^3*d*e*q^2*r+c^3*e^2*p^2*s-2*c^3*e^2*p*q*r-c^3*e^2*q^3+4*c^2*d^3*p*q*s+c^
2*d^3*q^2*r+c^2*d^2*e*p^2*s-12*c^2*d^2*e*p*q*r-3*c^2*d^2*e*q^3-2*c^2*d*e^2*p^2*
r-6*c^2*d*e^2*p*q^2+c*d^4*p^2*s+2*c*d^4*p*q*r-5*c*d^3*e*p^2*r-6*c*d^3*e*p*q^2-9
*c*d^2*e^2*p^2*q+d^5*p^2*r-3*d^4*e*p^2*q-4*d^3*e^2*p^3+5*a^2*c*e^2*t^2+5*a^2*d^
2*e*t^2+4*a^2*d*e^2*s*t+a^2*e^3*r*t+5*a*b^2*e^2*t^2-5*a*b*c*d*e*t^2+13*a*b*c*e^
2*s*t-5*a*b*d^3*t^2+3*a*b*d^2*e*s*t+6*a*b*d*e^2*r*t+4*a*b*d*e^2*s^2+3*a*b*e^3*q
*t+a*b*e^3*r*s-5*a*c^3*e*t^2+5*a*c^2*d^2*t^2-7*a*c^2*d*e*s*t+3*a*c^2*e^2*r*t+2*
a*c^2*e^2*s^2+a*c*d^3*s*t+6*a*c*d^2*e*r*t-4*a*c*d^2*e*s^2+9*a*c*d*e^2*q*t+3*a*c
*d*e^2*r*s+4*a*c*e^3*p*t+2*a*c*e^3*q*s-2*a*d^4*r*t+a*d^4*s^2+3*a*d^3*e*q*t-a*d^
3*e*r*s+11*a*d^2*e^2*p*t+a*d^2*e^2*q*s+3*a*d*e^3*p*s-5*b^3*d*e*t^2+3*b^3*e^2*s*
t+5*b^2*c^2*e*t^2+5*b^2*c*d^2*t^2-7*b^2*c*d*e*s*t+8*b^2*c*e^2*r*t+4*b^2*c*e^2*s
^2-2*b^2*d^3*s*t-7*b^2*d^2*e*r*t+2*b^2*d^2*e*s^2-3*b^2*d*e^2*q*t+7*b^2*d*e^2*r*
s+2*b^2*e^3*p*t+b^2*e^3*q*s+b^2*e^3*r^2-5*b*c^3*d*t^2+b*c^3*e*s*t+4*b*c^2*d^2*s
*t-4*b*c^2*d*e*r*t-4*b*c^2*d*e*s^2+7*b*c^2*e^2*q*t+7*b*c^2*e^2*r*s+2*b*c*d^3*r*
t-b*c*d^2*e*q*t-5*b*c*d^2*e*r*s+2*b*c*d*e^2*p*t+8*b*c*d*e^2*q*s+6*b*c*d*e^2*r^2
+3*b*c*e^3*p*s+4*b*c*e^3*q*r-3*b*d^4*q*t+b*d^4*r*s-6*b*d^3*e*p*t+2*b*d^3*e*q*s-\
2*b*d^3*e*r^2+9*b*d^2*e^2*p*s+2*b*d^2*e^2*q*r+6*b*d*e^3*p*r+c^5*t^2-c^4*d*s*t-2
*c^4*e*r*t+c^4*e*s^2+c^3*d^2*r*t-7*c^3*d*e*q*t-c^3*d*e*r*s-3*c^3*e^2*p*t+4*c^3*
e^2*q*s+c^3*e^2*r^2+4*c^2*d^3*q*t+c^2*d^2*e*p*t-7*c^2*d^2*e*q*s+c^2*d*e^2*p*s+8
*c^2*d*e^2*q*r+c^2*e^3*p*r+3*c^2*e^3*q^2+c*d^4*p*t+c*d^4*q*s-5*c*d^3*e*p*s-2*c*
d^3*e*q*r+7*c*d^2*e^2*p*r+3*c*d^2*e^2*q^2+9*c*d*e^3*p*q+d^5*p*s-2*d^4*e*p*r+3*d
^3*e^2*p*q+6*d^2*e^3*p^2-5*a*d*e^3*t-a*e^4*s-5*b*c*e^3*t+5*b*d^2*e^2*t-4*b*d*e^
3*s-2*b*e^4*r+5*c^2*d*e^2*t-2*c^2*e^3*s-5*c*d^3*e*t+4*c*d^2*e^2*s-3*c*d*e^3*r-3
*c*e^4*q+d^5*t-d^4*e*s+d^3*e^2*r-d^2*e^3*q-4*d*e^4*p+e^5


           Solving we get the following square matrix of dimension, 5



             [b[1, 1]    b[1, 2]    b[1, 3]    b[1, 4]    b[1, 5]]
             [                                                   ]
             [b[2, 1]    b[2, 2]    b[2, 3]    b[2, 4]    b[2, 5]]
             [                                                   ]
             [b[3, 1]    b[3, 2]    b[3, 3]    b[3, 4]    b[3, 5]]
             [                                                   ]
             [b[4, 1]    b[4, 2]    b[4, 3]    b[4, 4]    b[4, 5]]
             [                                                   ]
             [b[5, 1]    b[5, 2]    b[5, 3]    b[5, 4]    b[5, 5]]



                                     where



                                        beta[i, j]
                              b[i, j] = ----------
                                          Alpha



                       and the beta[i,j] are as follows





beta[1,1] = a^4*p*t^3*v4+a^4*q*t^3*v3+a^4*r*t^3*v2+a^4*s*t^3*v1+a^4*t^4*v0+3*a^
3*b*p*s*t^2*v4+3*a^3*b*q*s*t^2*v3+3*a^3*b*r*s*t^2*v2+3*a^3*b*s^2*t^2*v1+3*a^3*b
*s*t^3*v0+2*a^3*c*p*r*t^2*v4+2*a^3*c*q*r*t^2*v3+2*a^3*c*r^2*t^2*v2+2*a^3*c*r*s*
t^2*v1+2*a^3*c*r*t^3*v0+a^3*d*p*q*t^2*v4+a^3*d*q^2*t^2*v3+a^3*d*q*r*t^2*v2+a^3*
d*q*s*t^2*v1+a^3*d*q*t^3*v0+a^2*b^2*p*r*t^2*v4+3*a^2*b^2*p*s^2*t*v4+a^2*b^2*q*r
*t^2*v3+3*a^2*b^2*q*s^2*t*v3+a^2*b^2*r^2*t^2*v2+3*a^2*b^2*r*s^2*t*v2+a^2*b^2*r*
s*t^2*v1+a^2*b^2*r*t^3*v0+3*a^2*b^2*s^3*t*v1+3*a^2*b^2*s^2*t^2*v0+3*a^2*b*c*p*q
*t^2*v4+4*a^2*b*c*p*r*s*t*v4+3*a^2*b*c*q^2*t^2*v3+4*a^2*b*c*q*r*s*t*v3+3*a^2*b*
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-3*a^2*b*e*q*t^2*v3-2*a^2*b*e*r*s*t*v3-3*a^2*b*e*r*t^2*v2-2*a^2*b*e*s^2*t*v2-5*
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s^2*v3-a*c^2*e*p*t^2*v1-a*c^2*e*q^2*s*v4-3*a*c^2*e*q^2*t*v3-2*a*c^2*e*q*r*s*v3-\
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3*b*c^2*e*q^2*s*v3-4*b*c^2*e*q*r^2*v3-5*b*c^2*e*q*r*s*v2-2*b*c^2*e*q*r*t*v1-3*b
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*d^2*p^2*s*v4-2*c^2*d^2*p*q*r*v4+2*c^2*d^2*p*q*s*v3+c^2*d^2*p*q*t*v2+c^2*d^2*p*
r*s*v2+c^2*d^2*p*s^2*v1+c^2*d^2*p*s*t*v0+c^2*d^2*q^2*r*v3+c^2*d^2*q^2*s*v2+c^2*
d^2*q^2*t*v1-2*c^2*d*e*p^2*r*v4+c^2*d*e*p^2*s*v3+c^2*d*e*p^2*t*v2-6*c^2*d*e*p*q
^2*v4-4*c^2*d*e*p*q*r*v3-2*c^2*d*e*p*q*s*v2-2*c^2*d*e*p*q*t*v1-2*c^2*d*e*p*r^2*
v2-2*c^2*d*e*p*r*s*v1-2*c^2*d*e*p*r*t*v0-3*c^2*d*e*q^3*v3-3*c^2*d*e*q^2*r*v2-3*
c^2*d*e*q^2*s*v1-3*c^2*d*e*q^2*t*v0-c*d^3*p^2*r*v4+2*c*d^3*p*q*r*v3+2*c*d^3*p*q
*s*v2+2*c*d^3*p*q*t*v1-9*c*d^2*e*p^2*q*v4-c*d^2*e*p^2*r*v3-c*d^2*e*p^2*s*v2-c*d
^2*e*p^2*t*v1-6*c*d^2*e*p*q^2*v3-6*c*d^2*e*p*q*r*v2-6*c*d^2*e*p*q*s*v1-6*c*d^2*
e*p*q*t*v0+d^4*p^2*r*v3+d^4*p^2*s*v2+d^4*p^2*t*v1-4*d^3*e*p^3*v4-3*d^3*e*p^2*q*
v3-3*d^3*e*p^2*r*v2-3*d^3*e*p^2*s*v1-3*d^3*e*p^2*t*v0+2*a^2*c*e*t^2*v4+a^2*d^2*
t^2*v4+2*a^2*d*e*s*t*v4+2*a^2*d*e*t^2*v3+a^2*e^2*r*t*v4+a^2*e^2*s*t*v3+a^2*e^2*
t^2*v2+2*a*b^2*e*t^2*v4-a*b*c*d*t^2*v4+5*a*b*c*e*s*t*v4-a*b*c*e*t^2*v3-3*a*b*d^
2*t^2*v3+2*a*b*d*e*r*t*v4+2*a*b*d*e*s^2*v4+a*b*d*e*s*t*v3-a*b*d*e*t^2*v2+3*a*b*
e^2*q*t*v4+a*b*e^2*r*s*v4+2*a*b*e^2*r*t*v3+a*b*e^2*s^2*v3+3*a*b*e^2*s*t*v2+2*a*
b*e^2*t^2*v1-a*c^3*t^2*v4-a*c^2*d*s*t*v4+2*a*c^2*d*t^2*v3+a*c^2*e*s^2*v4-2*a*c^
2*e*s*t*v3-3*a*c^2*e*t^2*v2+2*a*c*d^2*r*t*v4-a*c*d^2*s^2*v4+a*c*d^2*s*t*v3+2*a*
c*d^2*t^2*v2+3*a*c*d*e*q*t*v4+a*c*d*e*r*s*v4+2*a*c*d*e*r*t*v3-2*a*c*d*e*s^2*v3-\
3*a*c*d*e*s*t*v2-a*c*d*e*t^2*v1+4*a*c*e^2*p*t*v4+2*a*c*e^2*q*s*v4+3*a*c*e^2*q*t
*v3+a*c*e^2*r*s*v3+2*a*c*e^2*r*t*v2+a*c*e^2*s^2*v2+3*a*c*e^2*s*t*v1+2*a*c*e^2*t
^2*v0-2*a*d^3*r*t*v3+a*d^3*s^2*v3-a*d^3*t^2*v1+6*a*d^2*e*p*t*v4+3*a*d^2*e*q*t*
v3-a*d^2*e*r*s*v3+2*a*d^2*e*r*t*v2-a*d^2*e*s^2*v2+a*d^2*e*s*t*v1+2*a*d^2*e*t^2*
v0+3*a*d*e^2*p*s*v4+2*a*d*e^2*p*t*v3+a*d*e^2*q*s*v3+a*d*e^2*r*s*v2+a*d*e^2*s^2*
v1+a*d*e^2*s*t*v0-b^3*d*t^2*v4+b^3*e*s*t*v4-b^3*e*t^2*v3+b^2*c^2*t^2*v4-b^2*c*d
*s*t*v4+2*b^2*c*d*t^2*v3+4*b^2*c*e*r*t*v4+b^2*c*e*s^2*v4-b^2*c*e*s*t*v3+2*b^2*c
*e*t^2*v2-b^2*d^2*r*t*v4-b^2*d^2*s*t*v3+b^2*d^2*t^2*v2-3*b^2*d*e*q*t*v4+3*b^2*d
*e*r*s*v4-4*b^2*d*e*r*t*v3+b^2*d*e*s^2*v3-2*b^2*d*e*s*t*v2-3*b^2*d*e*t^2*v1+2*b
^2*e^2*p*t*v4+b^2*e^2*q*s*v4+b^2*e^2*r^2*v4+2*b^2*e^2*r*s*v3+2*b^2*e^2*r*t*v2+b
^2*e^2*s^2*v2+2*b^2*e^2*s*t*v1+b^2*e^2*t^2*v0-b*c^3*t^2*v3-2*b*c^2*d*r*t*v4+b*c
^2*d*s*t*v3-3*b*c^2*d*t^2*v2+4*b*c^2*e*q*t*v4+2*b*c^2*e*r*s*v4-b*c^2*e*s^2*v3+b
*c^2*e*s*t*v2+2*b*c^2*e*t^2*v1+b*c*d^2*q*t*v4-b*c*d^2*r*s*v4+2*b*c*d^2*r*t*v3+2
*b*c*d^2*s*t*v2+2*b*c*d^2*t^2*v1+2*b*c*d*e*q*s*v4-b*c*d*e*q*t*v3+2*b*c*d*e*r^2*
v4-3*b*c*d*e*r*s*v3-2*b*c*d*e*r*t*v2-2*b*c*d*e*s^2*v2-3*b*c*d*e*s*t*v1-b*c*d*e*
t^2*v0+3*b*c*e^2*p*s*v4-2*b*c*e^2*p*t*v3+4*b*c*e^2*q*r*v4+3*b*c*e^2*q*s*v3+b*c*
e^2*q*t*v2+2*b*c*e^2*r^2*v3+4*b*c*e^2*r*s*v2+2*b*c*e^2*r*t*v1+2*b*c*e^2*s^2*v1+
2*b*c*e^2*s*t*v0-2*b*d^3*p*t*v4-3*b*d^3*q*t*v3+b*d^3*r*s*v3-b*d^3*s*t*v1-b*d^3*
t^2*v0+4*b*d^2*e*p*s*v4-2*b*d^2*e*p*t*v3+2*b*d^2*e*q*s*v3+b*d^2*e*q*t*v2-2*b*d^
2*e*r^2*v3-b*d^2*e*r*s*v2-2*b*d^2*e*r*t*v1+b*d^2*e*s^2*v1+b*d^2*e*s*t*v0+6*b*d*
e^2*p*r*v4+2*b*d*e^2*p*s*v3+2*b*d*e^2*p*t*v2+2*b*d*e^2*q*r*v3+2*b*d*e^2*r^2*v2+
2*b*d*e^2*r*s*v1+2*b*d*e^2*r*t*v0+c^4*t^2*v2-2*c^3*d*q*t*v4-c^3*d*s*t*v2-c^3*d*
t^2*v1-2*c^3*e*p*t*v4+2*c^3*e*q*s*v4-2*c^3*e*q*t*v3-2*c^3*e*r*t*v2+c^3*e*s^2*v2
-c^3*e*t^2*v0+c^2*d^2*p*t*v4-c^2*d^2*q*s*v4+3*c^2*d^2*q*t*v3+c^2*d^2*r*t*v2+c^2
*d^2*s*t*v1+c^2*d^2*t^2*v0+2*c^2*d*e*p*t*v3+2*c^2*d*e*q*r*v4-4*c^2*d*e*q*s*v3-3
*c^2*d*e*q*t*v2-c^2*d*e*r*s*v2-c^2*d*e*s^2*v1-c^2*d*e*s*t*v0+c^2*e^2*p*r*v4-c^2
*e^2*p*s*v3-c^2*e^2*p*t*v2+3*c^2*e^2*q^2*v4+3*c^2*e^2*q*r*v3+2*c^2*e^2*q*s*v2+2
*c^2*e^2*q*t*v1+c^2*e^2*r^2*v2+c^2*e^2*r*s*v1+c^2*e^2*r*t*v0-c*d^3*p*s*v4+c*d^3
*q*s*v3+c*d^3*q*t*v2+2*c*d^2*e*p*r*v4-2*c*d^2*e*p*s*v3-2*c*d^2*e*p*t*v2-2*c*d^2
*e*q*r*v3-2*c*d^2*e*q*s*v2-2*c*d^2*e*q*t*v1+9*c*d*e^2*p*q*v4+2*c*d*e^2*p*r*v3+2
*c*d*e^2*p*s*v2+2*c*d*e^2*p*t*v1+3*c*d*e^2*q^2*v3+3*c*d*e^2*q*r*v2+3*c*d*e^2*q*
s*v1+3*c*d*e^2*q*t*v0+d^4*p*s*v3+d^4*p*t*v2-2*d^3*e*p*r*v3-2*d^3*e*p*s*v2-2*d^3
*e*p*t*v1+6*d^2*e^2*p^2*v4+3*d^2*e^2*p*q*v3+3*d^2*e^2*p*r*v2+3*d^2*e^2*p*s*v1+3
*d^2*e^2*p*t*v0-3*a*d*e^2*t*v4-a*e^3*s*v4-a*e^3*t*v3-3*b*c*e^2*t*v4+2*b*d^2*e*t
*v4-2*b*d*e^2*s*v4+2*b*d*e^2*t*v3-2*b*e^3*r*v4-b*e^3*s*v3-b*e^3*t*v2+2*c^2*d*e*
t*v4-c^2*e^2*s*v4+c^2*e^2*t*v3-c*d^3*t*v4+c*d^2*e*s*v4-3*c*d^2*e*t*v3-c*d*e^2*r
*v4+2*c*d*e^2*s*v3+2*c*d*e^2*t*v2-3*c*e^3*q*v4-c*e^3*r*v3-c*e^3*s*v2-c*e^3*t*v1
+d^4*t*v3-d^3*e*s*v3-d^3*e*t*v2+d^2*e^2*r*v3+d^2*e^2*s*v2+d^2*e^2*t*v1-4*d*e^3*
p*v4-d*e^3*q*v3-d*e^3*r*v2-d*e^3*s*v1-d*e^3*t*v0+e^4*v4




beta[1,2] = a^4*q*t^3*v4+a^4*r*t^3*v3+a^4*s*t^3*v2+a^4*t^4*v1+3*a^3*b*q*s*t^2*
v4-a^3*b*q*t^3*v3+3*a^3*b*r*s*t^2*v3-a^3*b*r*t^3*v2+3*a^3*b*s^2*t^2*v2+2*a^3*b*
s*t^3*v1-a^3*b*t^4*v0+a^3*c*p*t^3*v3+2*a^3*c*q*r*t^2*v4-a^3*c*q*s*t^2*v3+2*a^3*
c*r^2*t^2*v3+a^3*c*r*s*t^2*v2+2*a^3*c*r*t^3*v1-a^3*c*s^2*t^2*v1-a^3*c*s*t^3*v0+
a^3*d*p*s*t^2*v3+a^3*d*p*t^3*v2+a^3*d*q^2*t^2*v4+a^3*d*q*s*t^2*v2+a^3*d*q*t^3*
v1-a^3*d*r^2*t^2*v2-a^3*d*r*s*t^2*v1-a^3*d*r*t^3*v0+a^3*e*p*r*t^2*v3+a^3*e*p*s*
t^2*v2+a^3*e*p*t^3*v1-a^3*e*q^2*t^2*v3-a^3*e*q*r*t^2*v2-a^3*e*q*s*t^2*v1-a^3*e*
q*t^3*v0-a^2*b^2*p*t^3*v3+a^2*b^2*q*r*t^2*v4+3*a^2*b^2*q*s^2*t*v4-2*a^2*b^2*q*s
*t^2*v3+a^2*b^2*r^2*t^2*v3+3*a^2*b^2*r*s^2*t*v3-a^2*b^2*r*s*t^2*v2+a^2*b^2*r*t^
3*v1+3*a^2*b^2*s^3*t*v2+a^2*b^2*s^2*t^2*v1-2*a^2*b^2*s*t^3*v0-2*a^2*b*c*p*t^3*
v2+3*a^2*b*c*q^2*t^2*v4+4*a^2*b*c*q*r*s*t*v4+2*a^2*b*c*q*r*t^2*v3-2*a^2*b*c*q*s
^2*t*v3+3*a^2*b*c*q*s*t^2*v2+3*a^2*b*c*q*t^3*v1+4*a^2*b*c*r^2*s*t*v3-a^2*b*c*r^
2*t^2*v2+2*a^2*b*c*r*s^2*t*v2+3*a^2*b*c*r*s*t^2*v1-a^2*b*c*r*t^3*v0-2*a^2*b*c*s
^3*t*v1-2*a^2*b*c*s^2*t^2*v0+4*a^2*b*d*p*q*t^2*v4+2*a^2*b*d*p*r*t^2*v3+2*a^2*b*
d*p*s^2*t*v3+4*a^2*b*d*p*s*t^2*v2+2*a^2*b*d*p*t^3*v1+2*a^2*b*d*q^2*s*t*v4+2*a^2
*b*d*q*s^2*t*v2+2*a^2*b*d*q*s*t^2*v1-2*a^2*b*d*r^2*s*t*v2-2*a^2*b*d*r*s^2*t*v1-\
2*a^2*b*d*r*s*t^2*v0-a^2*b*e*p*q*t^2*v3+2*a^2*b*e*p*r*s*t*v3-a^2*b*e*p*r*t^2*v2
+2*a^2*b*e*p*s^2*t*v2+a^2*b*e*p*s*t^2*v1-a^2*b*e*p*t^3*v0-2*a^2*b*e*q^2*s*t*v3-\
2*a^2*b*e*q*r*s*t*v2-2*a^2*b*e*q*s^2*t*v1-2*a^2*b*e*q*s*t^2*v0+2*a^2*c^2*p*q*t^
2*v4+3*a^2*c^2*p*r*t^2*v3-a^2*c^2*p*s^2*t*v3+a^2*c^2*p*t^3*v1+a^2*c^2*q^2*s*t*
v4+a^2*c^2*q*r^2*t*v4+a^2*c^2*q*s^2*t*v2+a^2*c^2*q*s*t^2*v1+a^2*c^2*r^3*t*v3+a^
2*c^2*r^2*t^2*v1-a^2*c^2*r*s^2*t*v1-a^2*c^2*r*s*t^2*v0+3*a^2*c*d*p*q*s*t*v4+2*a
^2*c*d*p*r*s*t*v3-a^2*c*d*p*r*t^2*v2+a^2*c*d*p*s^2*t*v2-a^2*c*d*p*s*t^2*v1-2*a^
2*c*d*p*t^3*v0+a^2*c*d*q^2*r*t*v4+a^2*c*d*q*r*s*t*v2+a^2*c*d*q*r*t^2*v1-a^2*c*d
*r^3*t*v2-a^2*c*d*r^2*s*t*v1-a^2*c*d*r^2*t^2*v0+a^2*c*e*p^2*t^2*v3-a^2*c*e*p*q*
s*t*v3+a^2*c*e*p*r^2*t*v3+a^2*c*e*p*r*t^2*v1-a^2*c*e*p*s^2*t*v1-a^2*c*e*p*s*t^2
*v0-a^2*c*e*q^2*r*t*v3-a^2*c*e*q*r^2*t*v2-a^2*c*e*q*r*s*t*v1-a^2*c*e*q*r*t^2*v0
+a^2*d^2*p^2*t^2*v3+a^2*d^2*p*q*r*t*v4+a^2*d^2*p*q*t^2*v2-a^2*d^2*p*r*s*t*v2-a^
2*d^2*p*s^2*t*v1-a^2*d^2*p*s*t^2*v0+a^2*d*e*p^2*s*t*v3+a^2*d*e*p^2*t^2*v2-a^2*d
*e*p*q*r*t*v3-a^2*d*e*p*r^2*t*v2-a^2*d*e*p*r*s*t*v1-a^2*d*e*p*r*t^2*v0-a*b^3*p*
s*t^2*v3+a*b^3*p*t^3*v2-a*b^3*q^2*t^2*v4+2*a*b^3*q*r*s*t*v4-2*a*b^3*q*r*t^2*v3+
a*b^3*q*s^3*v4-a*b^3*q*s^2*t*v3-a*b^3*q*s*t^2*v2-a*b^3*q*t^3*v1+2*a*b^3*r^2*s*t
*v3-a*b^3*r^2*t^2*v2+a*b^3*r*s^3*v3+a*b^3*r*s^2*t*v2+a*b^3*r*s*t^2*v1-a*b^3*r*t
^3*v0+a*b^3*s^4*v2-a*b^3*s^2*t^2*v0-4*a*b^2*c*p*q*t^2*v4-3*a*b^2*c*p*r*t^2*v3-a
*b^2*c*p*s^2*t*v3-3*a*b^2*c*p*s*t^2*v2-a*b^2*c*p*t^3*v1+4*a*b^2*c*q^2*s*t*v4-3*
a*b^2*c*q^2*t^2*v3+2*a*b^2*c*q*r^2*t*v4+2*a*b^2*c*q*r*s^2*v4+2*a*b^2*c*q*r*s*t*
v3-3*a*b^2*c*q*r*t^2*v2-a*b^2*c*q*s^3*v3+4*a*b^2*c*q*s^2*t*v2+a*b^2*c*q*s*t^2*
v1-3*a*b^2*c*q*t^3*v0+2*a*b^2*c*r^3*t*v3+2*a*b^2*c*r^2*s^2*v3+2*a*b^2*c*r^2*t^2
*v1+a*b^2*c*r*s^3*v2-2*a*b^2*c*r*s*t^2*v0-a*b^2*c*s^4*v1-a*b^2*c*s^3*t*v0+5*a*b
^2*d*p*q*s*t*v4-3*a*b^2*d*p*q*t^2*v3+4*a*b^2*d*p*r*s*t*v3+a*b^2*d*p*s^3*v3+4*a*
b^2*d*p*s^2*t*v2+2*a*b^2*d*p*s*t^2*v1-a*b^2*d*p*t^3*v0+a*b^2*d*q^2*r*t*v4+a*b^2
*d*q^2*s^2*v4+a*b^2*d*q*r*s*t*v2+a*b^2*d*q*r*t^2*v1+a*b^2*d*q*s^3*v2+a*b^2*d*q*
s^2*t*v1-a*b^2*d*r^3*t*v2-a*b^2*d*r^2*s^2*v2-a*b^2*d*r^2*s*t*v1-a*b^2*d*r^2*t^2
*v0-a*b^2*d*r*s^3*v1-a*b^2*d*r*s^2*t*v0-a*b^2*e*p^2*t^2*v3-a*b^2*e*p*q*s*t*v3+a
*b^2*e*p*r^2*t*v3+a*b^2*e*p*r*s^2*v3+a*b^2*e*p*r*t^2*v1+a*b^2*e*p*s^3*v2-a*b^2*
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*c^2*d*r*t^2*v0+3*b*c^2*e*p*q*t*v4+b*c^2*e*p*r*s*v4+4*b*c^2*e*p*r*t*v3+b*c^2*e*
p*s^2*v3+2*b*c^2*e*p*s*t*v2+b*c^2*e*p*t^2*v1-3*b*c^2*e*q^2*s*v4+4*b*c^2*e*q^2*t
*v3-4*b*c^2*e*q*r^2*v4-3*b*c^2*e*q*r*s*v3+2*b*c^2*e*q*r*t*v2-3*b*c^2*e*q*s^2*v2
+b*c^2*e*q*s*t*v1+4*b*c^2*e*q*t^2*v0-2*b*c^2*e*r^3*v3-2*b*c^2*e*r^2*t*v1+2*b*c^
2*e*r*s^2*v1+2*b*c^2*e*r*s*t*v0+5*b*c*d^2*p*q*t*v4+b*c*d^2*p*r*s*v4+2*b*c*d^2*p
*s^2*v3+3*b*c*d^2*p*s*t*v2+b*c*d^2*p*t^2*v1-2*b*c*d^2*q^2*s*v4+2*b*c*d^2*q*r^2*
v4+3*b*c*d^2*q*r*t*v2-b*c*d^2*q*s^2*v2+b*c*d^2*q*t^2*v0-b*c*d^2*r^2*s*v2-b*c*d^
2*r*s^2*v1-b*c*d^2*r*s*t*v0+2*b*c*d*e*p^2*t*v4-6*b*c*d*e*p*q*s*v4-2*b*c*d*e*p*r
^2*v4-4*b*c*d*e*p*r*s*v3-3*b*c*d*e*p*s^2*v2-2*b*c*d*e*p*s*t*v1+b*c*d*e*p*t^2*v0
-4*b*c*d*e*q^2*r*v4+2*b*c*d*e*q^2*s*v3-2*b*c*d*e*q*r^2*v3-2*b*c*d*e*q*r*s*v2-4*
b*c*d*e*q*r*t*v1+2*b*c*d*e*q*s^2*v1+2*b*c*d*e*q*s*t*v0+2*b*c*d*e*r^3*v2+2*b*c*d
*e*r^2*s*v1+2*b*c*d*e*r^2*t*v0+2*b*c*e^2*p^2*t*v3-b*c*e^2*p*q*t*v2-2*b*c*e^2*p*
r^2*v3-b*c*e^2*p*r*s*v2-2*b*c*e^2*p*r*t*v1+b*c*e^2*p*s^2*v1+b*c*e^2*p*s*t*v0+4*
b*c*e^2*q^2*r*v3+4*b*c*e^2*q*r^2*v2+4*b*c*e^2*q*r*s*v1+4*b*c*e^2*q*r*t*v0-2*b*d
^3*p*q*s*v4+2*b*d^3*p*r^2*v4-b*d^3*p*s^2*v2-2*b*d^3*p*s*t*v1-b*d^3*p*t^2*v0-b*d
^2*e*p^2*s*v4+b*d^2*e*p^2*t*v3-4*b*d^2*e*p*q*r*v4+2*b*d^2*e*p*q*s*v3-b*d^2*e*p*
q*t*v2-2*b*d^2*e*p*r^2*v3+b*d^2*e*p*r*s*v2-2*b*d^2*e*p*r*t*v1+3*b*d^2*e*p*s^2*
v1+3*b*d^2*e*p*s*t*v0-2*b*d*e^2*p^2*s*v3-2*b*d*e^2*p^2*t*v2+4*b*d*e^2*p*q*r*v3+
4*b*d*e^2*p*r^2*v2+4*b*d*e^2*p*r*s*v1+4*b*d*e^2*p*r*t*v0+c^4*p*s*t*v3+c^4*q^2*t
*v4+2*c^4*q*r*t*v3-c^4*q*s^2*v3+c^4*q*t^2*v1-2*c^3*d*p*q*t*v4-c^3*d*p*s^2*v3-c^
3*d*p*s*t*v2+2*c^3*d*q^2*s*v4-c^3*d*q^2*t*v3+c^3*d*q*r*s*v3-2*c^3*d*q*r*t*v2+c^
3*d*q*s^2*v2-c^3*d*q*s*t*v1-2*c^3*d*q*t^2*v0-c^3*e*p^2*t*v4+2*c^3*e*p*q*s*v4+c^
3*e*p*q*t*v3+c^3*e*p*r*s*v3-c^3*e*p*s*t*v1-c^3*e*p*t^2*v0-3*c^3*e*q^2*r*v4+c^3*
e*q^2*s*v3-c^3*e*q^2*t*v2-2*c^3*e*q*r^2*v3-2*c^3*e*q*r*t*v1+2*c^3*e*q*s^2*v1+2*
c^3*e*q*s*t*v0+2*c^2*d^2*p*q*s*v4-c^2*d^2*p*q*t*v3+c^2*d^2*p*r*s*v3+c^2*d^2*p*s
^2*v2+c^2*d^2*p*s*t*v1+c^2*d^2*q^2*r*v4+c^2*d^2*q^2*t*v2-c^2*d^2*q*r*s*v2-c^2*d
^2*q*s^2*v1-c^2*d^2*q*s*t*v0+c^2*d*e*p^2*s*v4-c^2*d*e*p^2*t*v3-4*c^2*d*e*p*q*r*
v4+2*c^2*d*e*p*q*s*v3+c^2*d*e*p*q*t*v2-2*c^2*d*e*p*r^2*v3-c^2*d*e*p*r*s*v2-2*c^
2*d*e*p*r*t*v1+c^2*d*e*p*s^2*v1+c^2*d*e*p*s*t*v0-3*c^2*d*e*q^3*v4-c^2*d*e*q^2*r
*v3-3*c^2*d*e*q^2*s*v2-3*c^2*d*e*q^2*t*v1+2*c^2*d*e*q*r^2*v2+2*c^2*d*e*q*r*s*v1
+2*c^2*d*e*q*r*t*v0+c^2*e^2*p^2*s*v3+c^2*e^2*p^2*t*v2-2*c^2*e^2*p*q*r*v3-2*c^2*
e^2*p*q*s*v2-2*c^2*e^2*p*q*t*v1+3*c^2*e^2*q^3*v3+3*c^2*e^2*q^2*r*v2+3*c^2*e^2*q
^2*s*v1+3*c^2*e^2*q^2*t*v0+2*c*d^3*p*q*r*v4+c*d^3*p*q*t*v2-c*d^3*p*r*s*v2-c*d^3
*p*s^2*v1-c*d^3*p*s*t*v0-c*d^2*e*p^2*r*v4+c*d^2*e*p^2*s*v3+c*d^2*e*p^2*t*v2-6*c
*d^2*e*p*q^2*v4-2*c*d^2*e*p*q*r*v3-4*c*d^2*e*p*q*s*v2-4*c*d^2*e*p*q*t*v1+2*c*d^
2*e*p*r^2*v2+2*c*d^2*e*p*r*s*v1+2*c*d^2*e*p*r*t*v0-2*c*d*e^2*p^2*r*v3-2*c*d*e^2
*p^2*s*v2-2*c*d*e^2*p^2*t*v1+6*c*d*e^2*p*q^2*v3+6*c*d*e^2*p*q*r*v2+6*c*d*e^2*p*
q*s*v1+6*c*d*e^2*p*q*t*v0+d^4*p^2*r*v4-3*d^3*e*p^2*q*v4-d^3*e*p^2*r*v3-d^3*e*p^
2*s*v2-d^3*e*p^2*t*v1+3*d^2*e^2*p^2*q*v3+3*d^2*e^2*p^2*r*v2+3*d^2*e^2*p^2*s*v1+
3*d^2*e^2*p^2*t*v0+2*a^2*d*e*t^2*v4+a^2*e^2*s*t*v4+a^2*e^2*t^2*v3-a*b*c*e*t^2*
v4-3*a*b*d^2*t^2*v4+a*b*d*e*s*t*v4-a*b*d*e*t^2*v3+2*a*b*e^2*r*t*v4+a*b*e^2*s^2*
v4+3*a*b*e^2*s*t*v3+2*a*b*e^2*t^2*v2+2*a*c^2*d*t^2*v4-2*a*c^2*e*s*t*v4-3*a*c^2*
e*t^2*v3+a*c*d^2*s*t*v4+2*a*c*d^2*t^2*v3+2*a*c*d*e*r*t*v4-2*a*c*d*e*s^2*v4-3*a*
c*d*e*s*t*v3-a*c*d*e*t^2*v2+3*a*c*e^2*q*t*v4+a*c*e^2*r*s*v4+2*a*c*e^2*r*t*v3+a*
c*e^2*s^2*v3+3*a*c*e^2*s*t*v2+2*a*c*e^2*t^2*v1-2*a*d^3*r*t*v4+a*d^3*s^2*v4-a*d^
3*t^2*v2+3*a*d^2*e*q*t*v4-a*d^2*e*r*s*v4+2*a*d^2*e*r*t*v3-a*d^2*e*s^2*v3+a*d^2*
e*s*t*v2+2*a*d^2*e*t^2*v1+2*a*d*e^2*p*t*v4+a*d*e^2*q*s*v4-3*a*d*e^2*q*t*v3+a*d*
e^2*r*s*v3-3*a*d*e^2*r*t*v2+a*d*e^2*s^2*v2-2*a*d*e^2*s*t*v1-3*a*d*e^2*t^2*v0+a*
e^3*p*t*v3-a*e^3*q*s*v3-a*e^3*r*s*v2-a*e^3*s^2*v1-a*e^3*s*t*v0-b^3*e*t^2*v4+2*b
^2*c*d*t^2*v4-b^2*c*e*s*t*v4+2*b^2*c*e*t^2*v3-b^2*d^2*s*t*v4+b^2*d^2*t^2*v3-4*b
^2*d*e*r*t*v4+b^2*d*e*s^2*v4-2*b^2*d*e*s*t*v3-3*b^2*d*e*t^2*v2+2*b^2*e^2*r*s*v4
+2*b^2*e^2*r*t*v3+b^2*e^2*s^2*v3+2*b^2*e^2*s*t*v2+b^2*e^2*t^2*v1-b*c^3*t^2*v4+b
*c^2*d*s*t*v4-3*b*c^2*d*t^2*v3-b*c^2*e*s^2*v4+b*c^2*e*s*t*v3+2*b*c^2*e*t^2*v2+2
*b*c*d^2*r*t*v4+2*b*c*d^2*s*t*v3+2*b*c*d^2*t^2*v2-b*c*d*e*q*t*v4-3*b*c*d*e*r*s*
v4-2*b*c*d*e*r*t*v3-2*b*c*d*e*s^2*v3-3*b*c*d*e*s*t*v2-b*c*d*e*t^2*v1-2*b*c*e^2*
p*t*v4+3*b*c*e^2*q*s*v4-2*b*c*e^2*q*t*v3+2*b*c*e^2*r^2*v4+4*b*c*e^2*r*s*v3-b*c*
e^2*r*t*v2+2*b*c*e^2*s^2*v2-b*c*e^2*s*t*v1-3*b*c*e^2*t^2*v0-3*b*d^3*q*t*v4+b*d^
3*r*s*v4-b*d^3*s*t*v2-b*d^3*t^2*v1-2*b*d^2*e*p*t*v4+2*b*d^2*e*q*s*v4+3*b*d^2*e*
q*t*v3-2*b*d^2*e*r^2*v4-b*d^2*e*r*s*v3+b*d^2*e*s^2*v2+3*b*d^2*e*s*t*v1+2*b*d^2*
e*t^2*v0+2*b*d*e^2*p*s*v4+2*b*d*e^2*q*r*v4-2*b*d*e^2*q*s*v3+2*b*d*e^2*r^2*v3+2*
b*d*e^2*r*t*v1-2*b*d*e^2*s^2*v1-2*b*d*e^2*s*t*v0+b*e^3*p*s*v3+b*e^3*p*t*v2-2*b*
e^3*q*r*v3-2*b*e^3*r^2*v2-2*b*e^3*r*s*v1-2*b*e^3*r*t*v0+c^4*t^2*v3-c^3*d*s*t*v3
-c^3*d*t^2*v2-2*c^3*e*q*t*v4-2*c^3*e*r*t*v3+c^3*e*s^2*v3-c^3*e*t^2*v1+3*c^2*d^2
*q*t*v4+c^2*d^2*r*t*v3+c^2*d^2*s*t*v2+c^2*d^2*t^2*v1+2*c^2*d*e*p*t*v4-4*c^2*d*e
*q*s*v4-c^2*d*e*q*t*v3-c^2*d*e*r*s*v3+2*c^2*d*e*r*t*v2-c^2*d*e*s^2*v2+c^2*d*e*s
*t*v1+2*c^2*d*e*t^2*v0-c^2*e^2*p*s*v4-2*c^2*e^2*p*t*v3+3*c^2*e^2*q*r*v4+c^2*e^2
*q*s*v3+2*c^2*e^2*q*t*v2+c^2*e^2*r^2*v3+c^2*e^2*r*t*v1-c^2*e^2*s^2*v1-c^2*e^2*s
*t*v0+c*d^3*q*s*v4-c*d^3*r*t*v2-c*d^3*s*t*v1-c*d^3*t^2*v0-2*c*d^2*e*p*s*v4+c*d^
2*e*p*t*v3-2*c*d^2*e*q*r*v4-c*d^2*e*q*s*v3-2*c*d^2*e*q*t*v2+c*d^2*e*r*s*v2+c*d^
2*e*s^2*v1+c*d^2*e*s*t*v0+2*c*d*e^2*p*r*v4+3*c*d*e^2*q^2*v4+2*c*d*e^2*q*r*v3+3*
c*d*e^2*q*s*v2+3*c*d*e^2*q*t*v1-c*d*e^2*r^2*v2-c*d*e^2*r*s*v1-c*d*e^2*r*t*v0+c*
e^3*p*r*v3+c*e^3*p*s*v2+c*e^3*p*t*v1-3*c*e^3*q^2*v3-3*c*e^3*q*r*v2-3*c*e^3*q*s*
v1-3*c*e^3*q*t*v0+d^4*p*s*v4-2*d^3*e*p*r*v4-d^3*e*p*s*v3-d^3*e*p*t*v2+3*d^2*e^2
*p*q*v4+2*d^2*e^2*p*r*v3+2*d^2*e^2*p*s*v2+2*d^2*e^2*p*t*v1-3*d*e^3*p*q*v3-3*d*e
^3*p*r*v2-3*d*e^3*p*s*v1-3*d*e^3*p*t*v0-a*e^3*t*v4+2*b*d*e^2*t*v4-b*e^3*s*v4-b*
e^3*t*v3+c^2*e^2*t*v4-3*c*d^2*e*t*v4+2*c*d*e^2*s*v4+2*c*d*e^2*t*v3-c*e^3*r*v4-c
*e^3*s*v3-c*e^3*t*v2+d^4*t*v4-d^3*e*s*v4-d^3*e*t*v3+d^2*e^2*r*v4+d^2*e^2*s*v3+d
^2*e^2*t*v2-d*e^3*q*v4-d*e^3*r*v3-d*e^3*s*v2-d*e^3*t*v1+e^4*q*v3+e^4*r*v2+e^4*s
*v1+e^4*t*v0




beta[1,3] = a^4*r*t^3*v4+a^4*s*t^3*v3+a^4*t^4*v2+3*a^3*b*r*s*t^2*v4-a^3*b*r*t^3
*v3+3*a^3*b*s^2*t^2*v3+2*a^3*b*s*t^3*v2-a^3*b*t^4*v1+2*a^3*c*r^2*t^2*v4+a^3*c*r
*s*t^2*v3+a^3*c*r*t^3*v2-a^3*c*s^2*t^2*v2-2*a^3*c*s*t^3*v1-a^3*c*t^4*v0+a^3*d*p
*t^3*v3+a^3*d*q*r*t^2*v4+a^3*d*q*s*t^2*v3+2*a^3*d*q*t^3*v2-a^3*d*r^2*t^2*v3-2*a
^3*d*r*s*t^2*v2-a^3*d*r*t^3*v1-a^3*d*s^2*t^2*v1-a^3*d*s*t^3*v0+a^3*e*p*s*t^2*v3
+a^3*e*p*t^3*v2-a^3*e*q*r*t^2*v3-a^3*e*r^2*t^2*v2-a^3*e*r*s*t^2*v1-a^3*e*r*t^3*
v0+a^2*b^2*r^2*t^2*v4+3*a^2*b^2*r*s^2*t*v4-a^2*b^2*r*s*t^2*v3+2*a^2*b^2*r*t^3*
v2+3*a^2*b^2*s^3*t*v3+a^2*b^2*s^2*t^2*v2-a^2*b^2*s*t^3*v1+a^2*b^2*t^4*v0-2*a^2*
b*c*p*t^3*v3+3*a^2*b*c*q*r*t^2*v4+3*a^2*b*c*q*s*t^2*v3+a^2*b*c*q*t^3*v2+4*a^2*b
*c*r^2*s*t*v4-a^2*b*c*r^2*t^2*v3+2*a^2*b*c*r*s^2*t*v3+3*a^2*b*c*r*s*t^2*v2-a^2*
b*c*r*t^3*v1-2*a^2*b*c*s^3*t*v2-2*a^2*b*c*s^2*t^2*v1+4*a^2*b*d*p*r*t^2*v4+4*a^2
*b*d*p*s*t^2*v3+2*a^2*b*d*p*t^3*v2+2*a^2*b*d*q*r*s*t*v4+2*a^2*b*d*q*s^2*t*v3+2*
a^2*b*d*q*s*t^2*v2-2*a^2*b*d*q*t^3*v1-2*a^2*b*d*r^2*s*t*v3+2*a^2*b*d*r^2*t^2*v2
-4*a^2*b*d*r*s^2*t*v2+2*a^2*b*d*r*t^3*v0-2*a^2*b*d*s^3*t*v1-2*a^2*b*d*s^2*t^2*
v0-a^2*b*e*p*r*t^2*v3+2*a^2*b*e*p*s^2*t*v3+a^2*b*e*p*s*t^2*v2-a^2*b*e*p*t^3*v1-\
2*a^2*b*e*q*r*s*t*v3-2*a^2*b*e*r^2*s*t*v2-2*a^2*b*e*r*s^2*t*v1-2*a^2*b*e*r*s*t^
2*v0+2*a^2*c^2*p*r*t^2*v4+a^2*c^2*p*t^3*v2+a^2*c^2*q*r*s*t*v4+a^2*c^2*q*s^2*t*
v3-a^2*c^2*q*s*t^2*v2-a^2*c^2*q*t^3*v1+a^2*c^2*r^3*t*v4-2*a^2*c^2*r*s*t^2*v1-a^
2*c^2*r*t^3*v0+a^2*c^2*s^3*t*v1+a^2*c^2*s^2*t^2*v0+3*a^2*c*d*p*r*s*t*v4-a^2*c*d
*p*r*t^2*v3+a^2*c*d*p*s^2*t*v3-a^2*c*d*p*s*t^2*v2-2*a^2*c*d*p*t^3*v1+a^2*c*d*q*
r^2*t*v4+a^2*c*d*q*r*s*t*v3-2*a^2*c*d*q*s^2*t*v2-4*a^2*c*d*q*s*t^2*v1-2*a^2*c*d
*q*t^3*v0-a^2*c*d*r^3*t*v3-a^2*c*d*r^2*t^2*v1+a^2*c*d*r*s^2*t*v1+a^2*c*d*r*s*t^
2*v0-a^2*c*e*p*s^2*t*v2-2*a^2*c*e*p*s*t^2*v1-a^2*c*e*p*t^3*v0-a^2*c*e*q*r^2*t*
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*r*t*v4-b^2*d*e*p*s^2*v4-2*b^2*d*e*p*s*t*v3-b^2*d*e*q*r*s*v4-3*b^2*d*e*q*r*t*v3
-b^2*d*e*q*s^2*v3-2*b^2*d*e*q*s*t*v2-b^2*d*e*r^3*v4+2*b^2*d*e*r^2*s*v3-5*b^2*d*
e*r^2*t*v2+4*b^2*d*e*r*s^2*v2-b^2*d*e*r*s*t*v1-4*b^2*d*e*r*t^2*v0+b^2*d*e*s^3*
v1+b^2*d*e*s^2*t*v0-b^2*e^2*p*s^2*v3+b^2*e^2*p*t^2*v1+b^2*e^2*q*r*s*v3-2*b^2*e^
2*q*r*t*v2-b^2*e^2*q*s*t*v1-b^2*e^2*q*t^2*v0+b^2*e^2*r^3*v3+3*b^2*e^2*r^2*s*v2+
b^2*e^2*r^2*t*v1+2*b^2*e^2*r*s^2*v1+2*b^2*e^2*r*s*t*v0-b*c^3*q*t^2*v3+2*b*c^3*r
^2*t*v4-b*c^3*r*s^2*v4-b*c^3*s*t^2*v1-b*c^3*t^3*v0-3*b*c^2*d*p*s*t*v4-b*c^2*d*p
*t^2*v3-b*c^2*d*q*r*t*v4+2*b*c^2*d*q*s^2*v4+b*c^2*d*q*s*t*v3+2*b*c^2*d*q*t^2*v2
+b*c^2*d*r^2*s*v4-2*b*c^2*d*r^2*t*v3+b*c^2*d*r*s^2*v3-2*b*c^2*d*r*t^2*v1+b*c^2*
d*s^2*t*v1+b*c^2*d*s*t^2*v0+4*b*c^2*e*p*r*t*v4+2*b*c^2*e*p*s*t*v3+b*c^2*e*p*t^2
*v2-5*b*c^2*e*q*r*s*v4+2*b*c^2*e*q*r*t*v3-3*b*c^2*e*q*s^2*v3+2*b*c^2*e*q*t^2*v1
-2*b*c^2*e*r^3*v4-2*b*c^2*e*r^2*t*v2+b*c^2*e*r*s^2*v2+2*b*c^2*e*r*s*t*v1-b*c^2*
e*s^3*v1-b*c^2*e*s^2*t*v0+2*b*c*d^2*p*r*t*v4+2*b*c*d^2*p*s^2*v4+3*b*c*d^2*p*s*t
*v3+b*c*d^2*p*t^2*v2-b*c*d^2*q^2*t*v4+b*c*d^2*q*r*s*v4+3*b*c*d^2*q*r*t*v3-b*c*d
^2*q*s^2*v3-2*b*c*d^2*q*s*t*v2-b*c*d^2*q*t^2*v1-b*c*d^2*r^2*s*v3+2*b*c*d^2*r^2*
t*v2-b*c*d^2*r*s^2*v2+b*c*d^2*r*s*t*v1+2*b*c*d^2*r*t^2*v0-b*c*d*e*p*q*t*v4-7*b*
c*d*e*p*r*s*v4-3*b*c*d*e*p*s^2*v3-2*b*c*d*e*p*s*t*v2+b*c*d*e*p*t^2*v1-4*b*c*d*e
*q*r^2*v4-2*b*c*d*e*q*r*s*v3-3*b*c*d*e*q*r*t*v2+4*b*c*d*e*q*s^2*v2+4*b*c*d*e*q*
s*t*v1+2*b*c*d*e*r^3*v3-b*c*d*e*r^2*s*v2+2*b*c*d*e*r^2*t*v1-3*b*c*d*e*r*s^2*v1-\
3*b*c*d*e*r*s*t*v0-b*c*e^2*p*q*t*v3-b*c*e^2*p*r*s*v3-4*b*c*e^2*p*r*t*v2+b*c*e^2
*p*s^2*v2-b*c*e^2*p*s*t*v1-2*b*c*e^2*p*t^2*v0-b*c*e^2*q^2*t*v2+4*b*c*e^2*q*r^2*
v3+3*b*c*e^2*q*r*s*v2+2*b*c*e^2*q*r*t*v1+b*c*e^2*q*s^2*v1+b*c*e^2*q*s*t*v0+2*b*
c*e^2*r^3*v2+2*b*c*e^2*r^2*s*v1+2*b*c*e^2*r^2*t*v0-b*d^3*p*q*t*v4+b*d^3*p*r*s*
v4-b*d^3*p*s^2*v3-2*b*d^3*p*s*t*v2-b*d^3*p*t^2*v1-3*b*d^3*q*r*t*v2-2*b*d^3*q*s*
t*v1-2*b*d^3*q*t^2*v0+b*d^3*r^2*s*v2+b*d^3*r*s^2*v1+b*d^3*r*s*t*v0-b*d^2*e*p^2*
t*v4-b*d^2*e*p*q*t*v3-4*b*d^2*e*p*r^2*v4+b*d^2*e*p*r*s*v3-4*b*d^2*e*p*r*t*v2+3*
b*d^2*e*p*s^2*v2+b*d^2*e*p*s*t*v1-2*b*d^2*e*p*t^2*v0-b*d^2*e*q^2*t*v2+3*b*d^2*e
*q*r*s*v2+2*b*d^2*e*q*r*t*v1+b*d^2*e*q*s^2*v1+b*d^2*e*q*s*t*v0-2*b*d^2*e*r^3*v2
-2*b*d^2*e*r^2*s*v1-2*b*d^2*e*r^2*t*v0-2*b*d*e^2*p^2*t*v3-2*b*d*e^2*p*q*t*v2+4*
b*d*e^2*p*r^2*v3+6*b*d*e^2*p*r*s*v2+4*b*d*e^2*p*r*t*v1+2*b*d*e^2*p*s^2*v1+2*b*d
*e^2*p*s*t*v0+c^4*p*s*t*v4+2*c^4*q*r*t*v4-c^4*q*s^2*v4-c^3*d*p*s^2*v4-c^3*d*p*s
*t*v3+c^3*d*q^2*t*v4+c^3*d*q*r*s*v4-2*c^3*d*q*r*t*v3+c^3*d*q*s^2*v3-c^3*d*q*t^2
*v1+c^3*e*p*q*t*v4+c^3*e*p*r*s*v4-c^3*e*p*s*t*v2-c^3*e*p*t^2*v1-c^3*e*q^2*s*v4-
c^3*e*q^2*t*v3-2*c^3*e*q*r^2*v4-2*c^3*e*q*r*t*v2+c^3*e*q*s^2*v2-c^3*e*q*t^2*v0+
c^2*d^2*p*q*t*v4+c^2*d^2*p*r*s*v4+c^2*d^2*p*s^2*v3+c^2*d^2*p*s*t*v2+c^2*d^2*q^2
*s*v4+c^2*d^2*q^2*t*v3-c^2*d^2*q*r*s*v3+2*c^2*d^2*q*r*t*v2-c^2*d^2*q*s^2*v2+c^2
*d^2*q*s*t*v1+2*c^2*d^2*q*t^2*v0+c^2*d*e*p^2*t*v4-2*c^2*d*e*p*q*s*v4+c^2*d*e*p*
q*t*v3-2*c^2*d*e*p*r^2*v4-c^2*d*e*p*r*s*v3+c^2*d*e*p*s^2*v2+3*c^2*d*e*p*s*t*v1+
2*c^2*d*e*p*t^2*v0-3*c^2*d*e*q^2*r*v4-3*c^2*d*e*q^2*s*v3+2*c^2*d*e*q*r^2*v3-c^2
*d*e*q*r*s*v2+2*c^2*d*e*q*r*t*v1-3*c^2*d*e*q*s^2*v1-3*c^2*d*e*q*s*t*v0+c^2*e^2*
p^2*t*v3-2*c^2*e^2*p*q*s*v3-c^2*e^2*p*q*t*v2-c^2*e^2*p*r*s*v2-c^2*e^2*p*s^2*v1-
c^2*e^2*p*s*t*v0+3*c^2*e^2*q^2*r*v3+c^2*e^2*q^2*s*v2+c^2*e^2*q^2*t*v1+2*c^2*e^2
*q*r^2*v2+2*c^2*e^2*q*r*s*v1+2*c^2*e^2*q*r*t*v0+2*c*d^3*p*q*s*v4+c*d^3*p*q*t*v3
-c*d^3*p*r*s*v3-c*d^3*p*s^2*v2-c*d^3*p*s*t*v1-c*d^3*q^2*t*v2+c*d^3*q*r*s*v2+c*d
^3*q*s^2*v1+c*d^3*q*s*t*v0-c*d^2*e*p^2*s*v4+c*d^2*e*p^2*t*v3-6*c*d^2*e*p*q*r*v4
-4*c*d^2*e*p*q*s*v3-2*c*d^2*e*p*q*t*v2+2*c*d^2*e*p*r^2*v3+2*c*d^2*e*p*r*t*v1-2*
c*d^2*e*p*s^2*v1-2*c*d^2*e*p*s*t*v0+2*c*d^2*e*q^2*s*v2+2*c*d^2*e*q^2*t*v1-2*c*d
^2*e*q*r^2*v2-2*c*d^2*e*q*r*s*v1-2*c*d^2*e*q*r*t*v0-2*c*d*e^2*p^2*s*v3-2*c*d*e^
2*p^2*t*v2+6*c*d*e^2*p*q*r*v3+4*c*d*e^2*p*q*s*v2+4*c*d*e^2*p*q*t*v1+2*c*d*e^2*p
*r^2*v2+2*c*d*e^2*p*r*s*v1+2*c*d*e^2*p*r*t*v0+d^4*p^2*s*v4-d^4*p*q*t*v2+d^4*p*r
*s*v2+d^4*p*s^2*v1+d^4*p*s*t*v0-3*d^3*e*p^2*r*v4-d^3*e*p^2*s*v3-d^3*e*p^2*t*v2+
2*d^3*e*p*q*s*v2+2*d^3*e*p*q*t*v1-2*d^3*e*p*r^2*v2-2*d^3*e*p*r*s*v1-2*d^3*e*p*r
*t*v0+3*d^2*e^2*p^2*r*v3+3*d^2*e^2*p^2*s*v2+3*d^2*e^2*p^2*t*v1+a^2*e^2*t^2*v4-a
*b*d*e*t^2*v4+3*a*b*e^2*s*t*v4+2*a*b*e^2*t^2*v3-3*a*c^2*e*t^2*v4+2*a*c*d^2*t^2*
v4-3*a*c*d*e*s*t*v4-a*c*d*e*t^2*v3+2*a*c*e^2*r*t*v4+a*c*e^2*s^2*v4+3*a*c*e^2*s*
t*v3+2*a*c*e^2*t^2*v2-a*d^3*t^2*v3+2*a*d^2*e*r*t*v4-a*d^2*e*s^2*v4+a*d^2*e*s*t*
v3+2*a*d^2*e*t^2*v2+a*d*e^2*r*s*v4-3*a*d*e^2*r*t*v3+a*d*e^2*s^2*v3-2*a*d*e^2*s*
t*v2-3*a*d*e^2*t^2*v1-a*e^3*r*s*v3-a*e^3*r*t*v2-a*e^3*s^2*v2-2*a*e^3*s*t*v1-a*e
^3*t^2*v0+2*b^2*c*e*t^2*v4+b^2*d^2*t^2*v4-2*b^2*d*e*s*t*v4-3*b^2*d*e*t^2*v3+2*b
^2*e^2*r*t*v4+b^2*e^2*s^2*v4+2*b^2*e^2*s*t*v3+b^2*e^2*t^2*v2-3*b*c^2*d*t^2*v4+b
*c^2*e*s*t*v4+2*b*c^2*e*t^2*v3+2*b*c*d^2*s*t*v4+2*b*c*d^2*t^2*v3-2*b*c*d*e*r*t*
v4-2*b*c*d*e*s^2*v4-3*b*c*d*e*s*t*v3-b*c*d*e*t^2*v2+b*c*e^2*q*t*v4+4*b*c*e^2*r*
s*v4-b*c*e^2*r*t*v3+2*b*c*e^2*s^2*v3-b*c*e^2*s*t*v2-3*b*c*e^2*t^2*v1-b*d^3*s*t*
v3-b*d^3*t^2*v2+b*d^2*e*q*t*v4-b*d^2*e*r*s*v4+b*d^2*e*s^2*v3+3*b*d^2*e*s*t*v2+2
*b*d^2*e*t^2*v1+2*b*d*e^2*p*t*v4+2*b*d*e^2*r^2*v4+4*b*d*e^2*r*t*v2-2*b*d*e^2*s^
2*v2+2*b*d*e^2*t^2*v0+b*e^3*p*t*v3+b*e^3*q*t*v2-2*b*e^3*r^2*v3-3*b*e^3*r*s*v2-2
*b*e^3*r*t*v1-b*e^3*s^2*v1-b*e^3*s*t*v0+c^4*t^2*v4-c^3*d*s*t*v4-c^3*d*t^2*v3-2*
c^3*e*r*t*v4+c^3*e*s^2*v4-c^3*e*t^2*v2+c^2*d^2*r*t*v4+c^2*d^2*s*t*v3+c^2*d^2*t^
2*v2-3*c^2*d*e*q*t*v4-c^2*d*e*r*s*v4+2*c^2*d*e*r*t*v3-c^2*d*e*s^2*v3+c^2*d*e*s*
t*v2+2*c^2*d*e*t^2*v1-c^2*e^2*p*t*v4+2*c^2*e^2*q*s*v4+2*c^2*e^2*q*t*v3+c^2*e^2*
r^2*v4+2*c^2*e^2*r*t*v2-c^2*e^2*s^2*v2+c^2*e^2*t^2*v0+c*d^3*q*t*v4-c*d^3*r*t*v3
-c*d^3*s*t*v2-c*d^3*t^2*v1-2*c*d^2*e*p*t*v4-2*c*d^2*e*q*s*v4-2*c*d^2*e*q*t*v3+c
*d^2*e*r*s*v3-3*c*d^2*e*r*t*v2+c*d^2*e*s^2*v2-2*c*d^2*e*s*t*v1-3*c*d^2*e*t^2*v0
+2*c*d*e^2*p*s*v4+3*c*d*e^2*q*r*v4+3*c*d*e^2*q*s*v3+c*d*e^2*q*t*v2-c*d*e^2*r^2*
v3+c*d*e^2*r*s*v2-c*d*e^2*r*t*v1+2*c*d*e^2*s^2*v1+2*c*d*e^2*s*t*v0+c*e^3*p*s*v3
+c*e^3*p*t*v2-3*c*e^3*q*r*v3-2*c*e^3*q*s*v2-2*c*e^3*q*t*v1-c*e^3*r^2*v2-c*e^3*r
*s*v1-c*e^3*r*t*v0+d^4*p*t*v4+d^4*r*t*v2+d^4*s*t*v1+d^4*t^2*v0-2*d^3*e*p*s*v4-d
^3*e*p*t*v3+d^3*e*q*t*v2-d^3*e*r*s*v2-d^3*e*s^2*v1-d^3*e*s*t*v0+3*d^2*e^2*p*r*
v4+2*d^2*e^2*p*s*v3+2*d^2*e^2*p*t*v2-d^2*e^2*q*s*v2-d^2*e^2*q*t*v1+d^2*e^2*r^2*
v2+d^2*e^2*r*s*v1+d^2*e^2*r*t*v0-3*d*e^3*p*r*v3-3*d*e^3*p*s*v2-3*d*e^3*p*t*v1-b
*e^3*t*v4+2*c*d*e^2*t*v4-c*e^3*s*v4-c*e^3*t*v3-d^3*e*t*v4+d^2*e^2*s*v4+d^2*e^2*
t*v3-d*e^3*r*v4-d*e^3*s*v3-d*e^3*t*v2+e^4*r*v3+e^4*s*v2+e^4*t*v1




beta[1,4] = a^4*s*t^3*v4+a^4*t^4*v3+3*a^3*b*s^2*t^2*v4+2*a^3*b*s*t^3*v3-a^3*b*t
^4*v2+2*a^3*c*r*s*t^2*v4+2*a^3*c*r*t^3*v3-a^3*c*s^2*t^2*v3-2*a^3*c*s*t^3*v2-a^3
*c*t^4*v1+a^3*d*q*s*t^2*v4+a^3*d*q*t^3*v3-a^3*d*r*s*t^2*v3-a^3*d*r*t^3*v2-a^3*d
*s^2*t^2*v2-2*a^3*d*s*t^3*v1-a^3*d*t^4*v0+a^3*e*p*t^3*v3-a^3*e*q*s*t^2*v3-a^3*e
*r*s*t^2*v2-a^3*e*s^2*t^2*v1-a^3*e*s*t^3*v0+a^2*b^2*r*s*t^2*v4+a^2*b^2*r*t^3*v3
+3*a^2*b^2*s^3*t*v4+a^2*b^2*s^2*t^2*v3-a^2*b^2*s*t^3*v2+a^2*b^2*t^4*v1+3*a^2*b*
c*q*s*t^2*v4+3*a^2*b*c*q*t^3*v3+4*a^2*b*c*r*s^2*t*v4+3*a^2*b*c*r*s*t^2*v3-a^2*b
*c*r*t^3*v2-2*a^2*b*c*s^3*t*v3-2*a^2*b*c*s^2*t^2*v2+2*a^2*b*c*s*t^3*v1+2*a^2*b*
c*t^4*v0+4*a^2*b*d*p*s*t^2*v4+2*a^2*b*d*p*t^3*v3+2*a^2*b*d*q*s^2*t*v4+2*a^2*b*d
*q*s*t^2*v3-2*a^2*b*d*q*t^3*v2-2*a^2*b*d*r*s^2*t*v3-2*a^2*b*d*s^3*t*v2-2*a^2*b*
d*s^2*t^2*v1+a^2*b*e*p*s*t^2*v3-a^2*b*e*p*t^3*v2-2*a^2*b*e*q*s^2*t*v3-2*a^2*b*e
*r*s^2*t*v2-2*a^2*b*e*s^3*t*v1-2*a^2*b*e*s^2*t^2*v0+2*a^2*c^2*p*s*t^2*v4+a^2*c^
2*p*t^3*v3+a^2*c^2*q*s^2*t*v4+a^2*c^2*q*s*t^2*v3-a^2*c^2*q*t^3*v2+a^2*c^2*r^2*s
*t*v4+a^2*c^2*r^2*t^2*v3-a^2*c^2*r*s^2*t*v3-2*a^2*c^2*r*s*t^2*v2-2*a^2*c^2*r*t^
3*v1+a^2*c^2*s^3*t*v2+3*a^2*c^2*s^2*t^2*v1+2*a^2*c^2*s*t^3*v0+3*a^2*c*d*p*s^2*t
*v4-a^2*c*d*p*s*t^2*v3-2*a^2*c*d*p*t^3*v2+a^2*c*d*q*r*s*t*v4+a^2*c*d*q*r*t^2*v3
-4*a^2*c*d*q*s*t^2*v2-2*a^2*c*d*q*t^3*v1-a^2*c*d*r^2*s*t*v3-a^2*c*d*r^2*t^2*v2+
a^2*c*d*r*s^2*t*v2-2*a^2*c*d*r*s*t^2*v1-a^2*c*d*r*t^3*v0+2*a^2*c*d*s^3*t*v1+2*a
^2*c*d*s^2*t^2*v0+a^2*c*e*p*r*t^2*v3-a^2*c*e*p*s^2*t*v3-2*a^2*c*e*p*s*t^2*v2-a^
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p*t^3*v1-a^2*d^2*q*r*t^2*v2-a^2*d^2*q*s^2*t*v2-2*a^2*d^2*q*s*t^2*v1-a^2*d^2*q*t
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2*e*r*s^2*t*v1-a*b^2*e*r*s*t^2*v0-a*b^2*e*s^4*v1-a*b^2*e*s^3*t*v0-a*b*c^2*p*s^2
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t^2*v3+a*b*c^2*q*s^3*v4-3*a*b*c^2*q*s^2*t*v3-2*a*b*c^2*q*s*t^2*v2+a*b*c^2*r^2*s
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2*v1+3*a*b*c^2*r*t^3*v0+a*b*c^2*s^4*v2-a*b*c^2*s^2*t^2*v0+4*a*b*c*d*p*r*s*t*v4+
4*a*b*c*d*p*r*t^2*v3+3*a*b*c*d*p*s^3*v4-2*a*b*c*d*p*s^2*t*v3-a*b*c*d*p*s*t^2*v2
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v4-2*a*b*c*d*q*r*s*t*v3-3*a*b*c*d*q*r*t^2*v2-3*a*b*c*d*q*s^2*t*v2+a*b*c*d*q*t^3
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-a*b*c*d*r*s*t^2*v0+2*a*b*c*d*s^4*v1+2*a*b*c*d*s^3*t*v0+3*a*b*c*e*p*q*t^2*v3+a*
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*c*e*q^2*s*t*v3-a*b*c*e*q*r*s^2*v3-3*a*b*c*e*q*r*s*t*v2-3*a*b*c*e*q*s^2*t*v1-3*
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2*t^2*v3-a*c^2*e*p*q*s*t*v3-a*c^2*e*p*q*t^2*v2-2*a*c^2*e*p*r*s*t*v2-a*c^2*e*p*r
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s^2*t*v2+2*b^2*c*d*p*s*t^2*v1+b^2*c*d*q^2*s^2*v4+b^2*c*d*q^2*s*t*v3+b^2*c*d*q*r
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t^2*v1-b^2*c*d*q*s^3*v2-2*b^2*c*d*q*s^2*t*v1-b^2*c*d*q*s*t^2*v0-b^2*c*d*r^3*s*
v3-b^2*c*d*r^3*t*v2+b^2*c*d*r^2*s^2*v2-2*b^2*c*d*r^2*s*t*v1-b^2*c*d*r^2*t^2*v0+
2*b^2*c*d*r*s^3*v1+2*b^2*c*d*r*s^2*t*v0-b^2*c*e*p^2*t^2*v3+2*b^2*c*e*p*q*s*t*v3
+b^2*c*e*p*r^2*t*v3-b^2*c*e*p*r*s^2*v3+b^2*c*e*p*r*s*t*v2+b^2*c*e*p*r*t^2*v1+b^
2*c*e*p*s^2*t*v1+b^2*c*e*p*s*t^2*v0-b^2*c*e*q^2*s^2*v3-b^2*c*e*q*r^2*s*v3-b^2*c
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s^2*v1-b^2*c*e*r^2*s*t*v0+2*b^2*d^2*p^2*s*t*v4+b^2*d^2*p*q*s^2*v4+2*b^2*d^2*p*q
*s*t*v3-b^2*d^2*p*q*t^2*v2+b^2*d^2*p*r^2*s*v4-2*b^2*d^2*p*r*s^2*v3-b^2*d^2*p*s^
3*v2+b^2*d^2*p*s*t^2*v0+b^2*d^2*q^2*s*t*v2+b^2*d^2*q^2*t^2*v1-b^2*d^2*q*r^2*t*
v2-b^2*d^2*q*r*s^2*v2-2*b^2*d^2*q*r*s*t*v1-b^2*d^2*q*r*t^2*v0+b^2*d^2*r^3*s*v2+
b^2*d^2*r^2*s^2*v1+b^2*d^2*r^2*s*t*v0-b^2*d*e*p^2*t^2*v2-b^2*d*e*p*q*s^2*v3+b^2
*d*e*p*q*s*t*v2+b^2*d*e*p*q*t^2*v1-b^2*d*e*p*r^2*s*v3-b^2*d*e*p*r^2*t*v2-2*b^2*
d*e*p*r*s^2*v2-2*b^2*d*e*p*r*s*t*v1-b^2*d*e*p*r*t^2*v0-b^2*d*e*p*s^3*v1-b^2*d*e
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-b*c^3*p*s^2*t*v2-b*c^3*p*s*t^2*v1+b*c^3*q^2*s^2*v4+2*b*c^3*q*r^2*s*v4+2*b*c^3*
q*r^2*t*v3-2*b*c^3*q*r*s^2*v3-2*b*c^3*q*r*s*t*v2+b*c^3*q*s^3*v2+b*c^3*q*s^2*t*
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c^2*d*p*r*t^2*v1+b*c^2*d*p*s^3*v2-2*b*c^2*d*p*s^2*t*v1-3*b*c^2*d*p*s*t^2*v0+2*b
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2*v3-b*c^2*e*p*q*s*t*v2+b*c^2*e*p*r*s^2*v2+2*b*c^2*e*p*r*s*t*v1+b*c^2*e*p*r*t^2
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r*s*t*v0+3*b*c*d^2*p^2*s^2*v4+b*c*d^2*p^2*s*t*v3+4*b*c*d^2*p*q*r*s*v4+2*b*c*d^2
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^2*p*r*t^2*v0+2*b*c*d^2*p*s^3*v1+2*b*c*d^2*p*s^2*t*v0-2*b*c*d^2*q^2*r*t*v2-b*c*
d^2*q^2*s^2*v2-2*b*c*d^2*q^2*s*t*v1-b*c*d^2*q^2*t^2*v0+2*b*c*d^2*q*r^2*s*v2+2*b
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b*d*e*p*t^2*v4-3*a*b*d*e*q*s*t*v4-3*a*b*d*e*q*t^2*v3-a*b*d*e*r*s^2*v4+a*b*d*e*r
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v3+a*d^3*q*t^2*v2-2*a*d^3*r*s*t*v2-a*d^3*r*t^2*v1+a*d^3*s^3*v2+a*d^3*s^2*t*v1-2
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v2-2*c*d^2*e*p*s^2*v2-4*c*d^2*e*p*s*t*v1-2*c*d^2*e*p*t^2*v0+2*c*d^2*e*q^2*t*v2-\
2*c*d^2*e*q*r*s*v2-2*c*d^2*e*q*s^2*v1-2*c*d^2*e*q*s*t*v0-2*c*d*e^2*p^2*t*v3+6*c
*d*e^2*p*q*s*v3+4*c*d*e^2*p*q*t*v2+2*c*d*e^2*p*r*s*v2+2*c*d*e^2*p*s^2*v1+2*c*d*
e^2*p*s*t*v0+d^4*p^2*t*v4+d^4*p*s^2*v2+2*d^4*p*s*t*v1+d^4*p*t^2*v0-3*d^3*e*p^2*
s*v4-d^3*e*p^2*t*v3+2*d^3*e*p*q*t*v2-2*d^3*e*p*r*s*v2-2*d^3*e*p*s^2*v1-2*d^3*e*
p*s*t*v0+3*d^2*e^2*p^2*s*v3+3*d^2*e^2*p^2*t*v2+2*a*b*e^2*t^2*v4-a*c*d*e*t^2*v4+
3*a*c*e^2*s*t*v4+2*a*c*e^2*t^2*v3-a*d^3*t^2*v4+a*d^2*e*s*t*v4+2*a*d^2*e*t^2*v3+
a*d*e^2*s^2*v4-2*a*d*e^2*s*t*v3-3*a*d*e^2*t^2*v2-a*e^3*s^2*v3-2*a*e^3*s*t*v2-a*
e^3*t^2*v1-3*b^2*d*e*t^2*v4+2*b^2*e^2*s*t*v4+b^2*e^2*t^2*v3+2*b*c^2*e*t^2*v4+2*
b*c*d^2*t^2*v4-3*b*c*d*e*s*t*v4-b*c*d*e*t^2*v3+2*b*c*e^2*r*t*v4+2*b*c*e^2*s^2*
v4-b*c*e^2*s*t*v3-3*b*c*e^2*t^2*v2-b*d^3*s*t*v4-b*d^3*t^2*v3-2*b*d^2*e*r*t*v4+b
*d^2*e*s^2*v4+3*b*d^2*e*s*t*v3+2*b*d^2*e*t^2*v2+2*b*d*e^2*r*s*v4+2*b*d*e^2*r*t*
v3-2*b*d*e^2*s^2*v3+2*b*d*e^2*t^2*v1-2*b*e^3*r*s*v3-2*b*e^3*r*t*v2-b*e^3*s^2*v2
-2*b*e^3*s*t*v1-b*e^3*t^2*v0-c^3*d*t^2*v4-c^3*e*t^2*v3+c^2*d^2*s*t*v4+c^2*d^2*t
^2*v3-c^2*d*e*s^2*v4+c^2*d*e*s*t*v3+2*c^2*d*e*t^2*v2+2*c^2*e^2*q*t*v4+c^2*e^2*r
*s*v4+c^2*e^2*r*t*v3-c^2*e^2*s^2*v3+c^2*e^2*t^2*v1-c*d^3*s*t*v3-c*d^3*t^2*v2-2*
c*d^2*e*q*t*v4+c*d^2*e*s^2*v3-2*c*d^2*e*s*t*v2-3*c*d^2*e*t^2*v1+2*c*d*e^2*p*t*
v4+3*c*d*e^2*q*s*v4+3*c*d*e^2*q*t*v3-c*d*e^2*r*s*v3-c*d*e^2*r*t*v2+2*c*d*e^2*s^
2*v2+4*c*d*e^2*s*t*v1+2*c*d*e^2*t^2*v0+c*e^3*p*t*v3-3*c*e^3*q*s*v3-2*c*e^3*q*t*
v2-c*e^3*r*s*v2-c*e^3*s^2*v1-c*e^3*s*t*v0+d^4*s*t*v2+d^4*t^2*v1-2*d^3*e*p*t*v4-
d^3*e*s^2*v2-2*d^3*e*s*t*v1-d^3*e*t^2*v0+3*d^2*e^2*p*s*v4+2*d^2*e^2*p*t*v3-d^2*
e^2*q*t*v2+d^2*e^2*r*s*v2+d^2*e^2*s^2*v1+d^2*e^2*s*t*v0-3*d*e^3*p*s*v3-3*d*e^3*
p*t*v2-c*e^3*t*v4+d^2*e^2*t*v4-d*e^3*s*v4-d*e^3*t*v3+e^4*s*v3+e^4*t*v2




beta[1,5] = t*(a^4*t^3*v4+3*a^3*b*s*t^2*v4-a^3*b*t^3*v3+2*a^3*c*r*t^2*v4-a^3*c*
s*t^2*v3-a^3*c*t^3*v2+a^3*d*q*t^2*v4-a^3*d*r*t^2*v3-a^3*d*s*t^2*v2-a^3*d*t^3*v1
-a^3*e*q*t^2*v3-a^3*e*r*t^2*v2-a^3*e*s*t^2*v1-a^3*e*t^3*v0+a^2*b^2*r*t^2*v4+3*a
^2*b^2*s^2*t*v4-2*a^2*b^2*s*t^2*v3+a^2*b^2*t^3*v2+3*a^2*b*c*q*t^2*v4+4*a^2*b*c*
r*s*t*v4-a^2*b*c*r*t^2*v3-2*a^2*b*c*s^2*t*v3+2*a^2*b*c*t^3*v1+4*a^2*b*d*p*t^2*
v4+2*a^2*b*d*q*s*t*v4-2*a^2*b*d*r*s*t*v3+2*a^2*b*d*r*t^2*v2-2*a^2*b*d*s^2*t*v2+
2*a^2*b*d*t^3*v0-a^2*b*e*p*t^2*v3-2*a^2*b*e*q*s*t*v3-2*a^2*b*e*r*s*t*v2-2*a^2*b
*e*s^2*t*v1-2*a^2*b*e*s*t^2*v0+2*a^2*c^2*p*t^2*v4+a^2*c^2*q*s*t*v4+a^2*c^2*r^2*
t*v4-a^2*c^2*r*s*t*v3-a^2*c^2*r*t^2*v2+a^2*c^2*s^2*t*v2+2*a^2*c^2*s*t^2*v1+a^2*
c^2*t^3*v0+3*a^2*c*d*p*s*t*v4-2*a^2*c*d*p*t^2*v3+a^2*c*d*q*r*t*v4-2*a^2*c*d*q*t
^2*v2-a^2*c*d*r^2*t*v3+a^2*c*d*r*s*t*v2-a^2*c*d*r*t^2*v1+2*a^2*c*d*s^2*t*v1+2*a
^2*c*d*s*t^2*v0-a^2*c*e*p*s*t*v3-a^2*c*e*p*t^2*v2-a^2*c*e*q*r*t*v3-a^2*c*e*r^2*
t*v2-a^2*c*e*r*s*t*v1-a^2*c*e*r*t^2*v0+a^2*d^2*p*r*t*v4-a^2*d^2*p*s*t*v3-a^2*d^
2*p*t^2*v2-a^2*d^2*q*s*t*v2-a^2*d^2*q*t^2*v1+a^2*d^2*r^2*t*v2+a^2*d^2*r*s*t*v1+
a^2*d^2*r*t^2*v0-a^2*d*e*p*r*t*v3-a^2*d*e*p*s*t*v2-a^2*d*e*p*t^2*v1-a*b^3*q*t^2
*v4+2*a*b^3*r*s*t*v4-a*b^3*r*t^2*v3+a*b^3*s^3*v4-a*b^3*s^2*t*v3+a*b^3*s*t^2*v2-
a*b^3*t^3*v1-4*a*b^2*c*p*t^2*v4+4*a*b^2*c*q*s*t*v4-3*a*b^2*c*q*t^2*v3+2*a*b^2*c
*r^2*t*v4+2*a*b^2*c*r*s^2*v4-2*a*b^2*c*r*s*t*v3-a*b^2*c*r*t^2*v2-a*b^2*c*s^3*v3
+a*b^2*c*s^2*t*v2-a*b^2*c*s*t^2*v1-3*a*b^2*c*t^3*v0+5*a*b^2*d*p*s*t*v4-a*b^2*d*
p*t^2*v3+a*b^2*d*q*r*t*v4+a*b^2*d*q*s^2*v4+2*a*b^2*d*q*t^2*v2-a*b^2*d*r^2*t*v3-
a*b^2*d*r*s^2*v3+a*b^2*d*r*s*t*v2-a*b^2*d*r*t^2*v1-a*b^2*d*s^3*v2+a*b^2*d*s^2*t
*v1+2*a*b^2*d*s*t^2*v0-a*b^2*e*p*s*t*v3+a*b^2*e*p*t^2*v2-a*b^2*e*q*r*t*v3-a*b^2
*e*q*s^2*v3-a*b^2*e*r^2*t*v2-a*b^2*e*r*s^2*v2-a*b^2*e*r*s*t*v1-a*b^2*e*r*t^2*v0
-a*b^2*e*s^3*v1-a*b^2*e*s^2*t*v0-a*b*c^2*p*s*t*v4+a*b*c^2*p*t^2*v3+5*a*b*c^2*q*
r*t*v4+a*b*c^2*q*s^2*v4-4*a*b*c^2*q*s*t*v3+a*b*c^2*r^2*s*v4-a*b*c^2*r*s^2*v3-a*
b*c^2*r*s*t*v2+3*a*b*c^2*r*t^2*v1+a*b*c^2*s^3*v2-a*b*c^2*s^2*t*v1-2*a*b*c^2*s*t
^2*v0+4*a*b*c*d*p*r*t*v4+3*a*b*c*d*p*s^2*v4-3*a*b*c*d*p*s*t*v3+2*a*b*c*d*p*t^2*
v2+3*a*b*c*d*q^2*t*v4+a*b*c*d*q*r*s*v4-3*a*b*c*d*q*r*t*v3-a*b*c*d*q*s*t*v2+a*b*
c*d*q*t^2*v1-a*b*c*d*r^2*s*v3+a*b*c*d*r*s^2*v2-a*b*c*d*r*s*t*v1+2*a*b*c*d*s^3*
v1+2*a*b*c*d*s^2*t*v0-a*b*c*e*p*s^2*v3+a*b*c*e*p*s*t*v2+2*a*b*c*e*p*t^2*v1-3*a*
b*c*e*q^2*t*v3-a*b*c*e*q*r*s*v3-3*a*b*c*e*q*r*t*v2-3*a*b*c*e*q*s*t*v1-3*a*b*c*e
*q*t^2*v0-a*b*c*e*r^2*s*v2-a*b*c*e*r*s^2*v1-a*b*c*e*r*s*t*v0+3*a*b*d^2*p*q*t*v4
+a*b*d^2*p*r*s*v4-2*a*b*d^2*p*r*t*v3-a*b*d^2*p*s^2*v3-2*a*b*d^2*p*s*t*v2-a*b*d^
2*p*t^2*v1+a*b*d^2*q*r*t*v2-a*b*d^2*q*s^2*v2+a*b*d^2*q*t^2*v0+a*b*d^2*r^2*s*v2+
a*b*d^2*r*s^2*v1+a*b*d^2*r*s*t*v0-3*a*b*d*e*p*q*t*v3-a*b*d*e*p*r*s*v3-2*a*b*d*e
*p*r*t*v2-a*b*d*e*p*s^2*v2-3*a*b*d*e*p*s*t*v1-2*a*b*d*e*p*t^2*v0+2*a*c^3*p*r*t*
v4-a*c^3*p*s^2*v4-a*c^3*p*t^2*v2+a*c^3*q^2*t*v4+a*c^3*q*r*s*v4-a*c^3*q*s^2*v3+a
*c^3*q*s*t*v2+a*c^3*q*t^2*v1+2*a*c^3*r*s*t*v1+a*c^3*r*t^2*v0-a*c^3*s^3*v1-a*c^3
*s^2*t*v0+5*a*c^2*d*p*q*t*v4+a*c^2*d*p*r*s*v4-2*a*c^2*d*p*r*t*v3+a*c^2*d*p*s*t*
v2+a*c^2*d*p*t^2*v1+a*c^2*d*q^2*s*v4-a*c^2*d*q*r*s*v3+a*c^2*d*q*s^2*v2+3*a*c^2*
d*q*s*t*v1+2*a*c^2*d*q*t^2*v0-2*a*c^2*e*p*q*t*v3-2*a*c^2*e*p*r*t*v2+a*c^2*e*p*s
^2*v2-a*c^2*e*p*t^2*v0-a*c^2*e*q^2*s*v3-a*c^2*e*q*r*s*v2-a*c^2*e*q*s^2*v1-a*c^2
*e*q*s*t*v0+4*a*c*d^2*p^2*t*v4+2*a*c*d^2*p*q*s*v4-a*c*d^2*p*q*t*v3-a*c*d^2*p*r*
s*v3+2*a*c*d^2*p*r*t*v2+3*a*c*d^2*p*s*t*v1+3*a*c*d^2*p*t^2*v0-a*c*d^2*q^2*t*v2+
a*c*d^2*q*r*s*v2+a*c*d^2*q*s^2*v1+a*c*d^2*q*s*t*v0-2*a*c*d*e*p^2*t*v3-2*a*c*d*e
*p*q*s*v3-a*c*d*e*p*q*t*v2-a*c*d*e*p*r*s*v2-a*c*d*e*p*s^2*v1-a*c*d*e*p*s*t*v0+a
*d^3*p^2*s*v4-a*d^3*p^2*t*v3-a*d^3*p*q*t*v2+a*d^3*p*r*s*v2+a*d^3*p*s^2*v1+a*d^3
*p*s*t*v0-a*d^2*e*p^2*s*v3-a*d^2*e*p^2*t*v2+b^4*p*t^2*v4-b^4*q*s*t*v4+b^4*q*t^2
*v3+b^4*r*s^2*v4-b^4*r*s*t*v3+b^4*r*t^2*v2+b^4*t^3*v0-b^3*c*p*s*t*v4-b^3*c*q*r*
t*v4+b^3*c*q*s^2*v4+2*b^3*c*r^2*s*v4-b^3*c*r^2*t*v3-b^3*c*r*s^2*v3+b^3*c*r*s*t*
v2-b^3*c*r*t^2*v1+2*b^3*d*p*r*t*v4+b^3*d*p*s^2*v4-b^3*d*p*s*t*v3-b^3*d*q^2*t*v4
+b^3*d*q*r*s*v4+b^3*d*q*r*t*v3+b^3*d*q*s*t*v2-b^3*d*q*t^2*v1-b^3*d*r^2*s*v3+2*b
^3*d*r^2*t*v2-b^3*d*r*s^2*v2+b^3*d*r*s*t*v1+2*b^3*d*r*t^2*v0-b^3*e*p*r*t*v3-b^3
*e*p*t^2*v1+b^3*e*q^2*t*v3-b^3*e*q*r*s*v3+b^3*e*q*r*t*v2+b^3*e*q*s*t*v1+b^3*e*q
*t^2*v0-b^3*e*r^2*s*v2-b^3*e*r*s^2*v1-b^3*e*r*s*t*v0-3*b^2*c^2*p*r*t*v4+b^2*c^2
*p*s*t*v3+3*b^2*c^2*q*r*s*v4-2*b^2*c^2*q*r*t*v3-b^2*c^2*q*s^2*v3+b^2*c^2*r^3*v4
-b^2*c^2*r^2*s*v3-b^2*c^2*r^2*t*v2+b^2*c^2*r*s^2*v2-b^2*c^2*r*s*t*v1-2*b^2*c^2*
r*t^2*v0-b^2*c*d*p*q*t*v4+5*b^2*c*d*p*r*s*v4-b^2*c*d*p*r*t*v3-b^2*c*d*p*s^2*v3+
2*b^2*c*d*p*s*t*v2+b^2*c*d*q^2*s*v4+b^2*c*d*q*r^2*v4-b^2*c*d*q*r*s*v3+2*b^2*c*d
*q*r*t*v2-b^2*c*d*q*s^2*v2-b^2*c*d*q*s*t*v1-b^2*c*d*r^3*v3+b^2*c*d*r^2*s*v2-b^2
*c*d*r^2*t*v1+2*b^2*c*d*r*s^2*v1+2*b^2*c*d*r*s*t*v0+b^2*c*e*p*q*t*v3-b^2*c*e*p*
r*s*v3+2*b^2*c*e*p*r*t*v2+b^2*c*e*p*s*t*v1+b^2*c*e*p*t^2*v0-b^2*c*e*q^2*s*v3-b^
2*c*e*q*r^2*v3-b^2*c*e*q*r*s*v2-b^2*c*e*q*s^2*v1-b^2*c*e*q*s*t*v0-b^2*c*e*r^3*
v2-b^2*c*e*r^2*s*v1-b^2*c*e*r^2*t*v0+2*b^2*d^2*p^2*t*v4+b^2*d^2*p*q*s*v4+b^2*d^
2*p*q*t*v3+b^2*d^2*p*r^2*v4-2*b^2*d^2*p*r*s*v3+2*b^2*d^2*p*r*t*v2-b^2*d^2*p*s^2
*v2+b^2*d^2*p*s*t*v1+2*b^2*d^2*p*t^2*v0+b^2*d^2*q^2*t*v2-b^2*d^2*q*r*s*v2-b^2*d
^2*q*r*t*v1+b^2*d^2*r^3*v2+b^2*d^2*r^2*s*v1+b^2*d^2*r^2*t*v0-b^2*d*e*p^2*t*v3-b
^2*d*e*p*q*s*v3+b^2*d*e*p*q*t*v2-b^2*d*e*p*r^2*v3-2*b^2*d*e*p*r*s*v2-b^2*d*e*p*
r*t*v1-b^2*d*e*p*s^2*v1-b^2*d*e*p*s*t*v0-b*c^3*p*q*t*v4-b*c^3*p*r*s*v4+b*c^3*p*
r*t*v3-b*c^3*p*s*t*v2+b*c^3*q^2*s*v4-b*c^3*q^2*t*v3+2*b*c^3*q*r^2*v4-2*b*c^3*q*
r*s*v3-b*c^3*q*r*t*v2+b*c^3*q*s^2*v2-b*c^3*q*t^2*v0+b*c^3*r^2*t*v1-b*c^3*r*s^2*
v1-b*c^3*r*s*t*v0-4*b*c^2*d*p^2*t*v4+4*b*c^2*d*p*q*s*v4-3*b*c^2*d*p*q*t*v3+2*b*
c^2*d*p*r^2*v4-b*c^2*d*p*r*s*v3-2*b*c^2*d*p*r*t*v2+b*c^2*d*p*s^2*v2-3*b*c^2*d*p
*s*t*v1-4*b*c^2*d*p*t^2*v0+2*b*c^2*d*q^2*r*v4-2*b*c^2*d*q*r^2*v3+2*b*c^2*d*q*r*
s*v2+2*b*c^2*d*q*s^2*v1+2*b*c^2*d*q*s*t*v0+b*c^2*e*p^2*t*v3-b*c^2*e*p*q*s*v3+b*
c^2*e*p*r*s*v2+b*c^2*e*p*r*t*v1-2*b*c^2*e*q^2*r*v3-2*b*c^2*e*q*r^2*v2-2*b*c^2*e
*q*r*s*v1-2*b*c^2*e*q*r*t*v0+3*b*c*d^2*p^2*s*v4+4*b*c*d^2*p*q*r*v4-b*c*d^2*p*q*
s*v3+2*b*c*d^2*p*q*t*v2-2*b*c*d^2*p*r^2*v3+b*c*d^2*p*r*s*v2-b*c*d^2*p*r*t*v1+2*
b*c*d^2*p*s^2*v1+2*b*c*d^2*p*s*t*v0-b*c*d^2*q^2*s*v2-b*c*d^2*q^2*t*v1+2*b*c*d^2
*q*r^2*v2+2*b*c*d^2*q*r*s*v1+2*b*c*d^2*q*r*t*v0-b*c*d*e*p^2*s*v3+2*b*c*d*e*p^2*
t*v2-4*b*c*d*e*p*q*r*v3-b*c*d*e*p*q*s*v2-b*c*d*e*p*q*t*v1-2*b*c*d*e*p*r^2*v2-2*
b*c*d*e*p*r*s*v1-2*b*c*d*e*p*r*t*v0+2*b*d^3*p^2*r*v4-b*d^3*p^2*s*v3-b*d^3*p*q*s
*v2-b*d^3*p*q*t*v1+2*b*d^3*p*r^2*v2+2*b*d^3*p*r*s*v1+2*b*d^3*p*r*t*v0-2*b*d^2*e
*p^2*r*v3-b*d^2*e*p^2*s*v2-b*d^2*e*p^2*t*v1+c^4*p^2*t*v4-c^4*p*q*s*v4+c^4*p*q*t
*v3+c^4*p*s*t*v1+c^4*p*t^2*v0+c^4*q^2*r*v4-c^4*q^2*s*v3+c^4*q*r*t*v1-c^4*q*s^2*
v1-c^4*q*s*t*v0-c^3*d*p^2*s*v4+2*c^3*d*p*q*r*v4-c^3*d*p*q*s*v3-c^3*d*p*q*t*v2+c
^3*d*p*r*t*v1-c^3*d*p*s^2*v1-c^3*d*p*s*t*v0+c^3*d*q^3*v4-c^3*d*q^2*r*v3+c^3*d*q
^2*s*v2+c^3*d*q^2*t*v1-c^3*e*p^2*t*v2+c^3*e*p*q*s*v2+c^3*e*p*q*t*v1-c^3*e*q^3*
v3-c^3*e*q^2*r*v2-c^3*e*q^2*s*v1-c^3*e*q^2*t*v0+c^2*d^2*p^2*r*v4+3*c^2*d^2*p*q^
2*v4-2*c^2*d^2*p*q*r*v3+c^2*d^2*p*q*s*v2+c^2*d^2*p*q*t*v1+c^2*d^2*q^2*r*v2+c^2*
d^2*q^2*s*v1+c^2*d^2*q^2*t*v0+c^2*d*e*p^2*s*v2+c^2*d*e*p^2*t*v1-3*c^2*d*e*p*q^2
*v3-2*c^2*d*e*p*q*r*v2-2*c^2*d*e*p*q*s*v1-2*c^2*d*e*p*q*t*v0+3*c*d^3*p^2*q*v4-c
*d^3*p^2*r*v3+2*c*d^3*p*q*r*v2+2*c*d^3*p*q*s*v1+2*c*d^3*p*q*t*v0-3*c*d^2*e*p^2*
q*v3-c*d^2*e*p^2*r*v2-c*d^2*e*p^2*s*v1-c*d^2*e*p^2*t*v0+d^4*p^3*v4+d^4*p^2*r*v2
+d^4*p^2*s*v1+d^4*p^2*t*v0-d^3*e*p^3*v3-3*a^2*b*e*t^2*v4-3*a^2*c*d*t^2*v4-2*a^2
*c*e*s*t*v4+2*a^2*c*e*t^2*v3-a^2*d^2*s*t*v4+a^2*d^2*t^2*v3-a^2*d*e*r*t*v4+2*a^2
*d*e*s*t*v3+2*a^2*d*e*t^2*v2+a^2*e^2*r*t*v3+a^2*e^2*s*t*v2+a^2*e^2*t^2*v1+2*a*b
^2*d*t^2*v4-4*a*b^2*e*s*t*v4+2*a*b^2*e*t^2*v3+2*a*b*c^2*t^2*v4-a*b*c*d*s*t*v4-a
*b*c*d*t^2*v3-4*a*b*c*e*r*t*v4-2*a*b*c*e*s^2*v4+5*a*b*c*e*s*t*v3-a*b*c*e*t^2*v2
-a*b*d^2*s^2*v4-3*a*b*d^2*t^2*v2-3*a*b*d*e*q*t*v4-a*b*d*e*r*s*v4+2*a*b*d*e*r*t*
v3+2*a*b*d*e*s^2*v3+a*b*d*e*s*t*v2-a*b*d*e*t^2*v1+3*a*b*e^2*q*t*v3+a*b*e^2*r*s*
v3+2*a*b*e^2*r*t*v2+a*b*e^2*s^2*v2+3*a*b*e^2*s*t*v1+2*a*b*e^2*t^2*v0+a*c^3*s*t*
v4-a*c^3*t^2*v3-2*a*c^2*d*r*t*v4+a*c^2*d*s^2*v4-a*c^2*d*s*t*v3+2*a*c^2*d*t^2*v2
-3*a*c^2*e*q*t*v4-a*c^2*e*r*s*v4+a*c^2*e*s^2*v3-2*a*c^2*e*s*t*v2-3*a*c^2*e*t^2*
v1-2*a*c*d^2*q*t*v4+2*a*c*d^2*r*t*v3-a*c*d^2*s^2*v3+a*c*d^2*s*t*v2+2*a*c*d^2*t^
2*v1-6*a*c*d*e*p*t*v4-2*a*c*d*e*q*s*v4+3*a*c*d*e*q*t*v3+a*c*d*e*r*s*v3+2*a*c*d*
e*r*t*v2-2*a*c*d*e*s^2*v2-3*a*c*d*e*s*t*v1-a*c*d*e*t^2*v0+2*a*c*e^2*p*t*v3+2*a*
c*e^2*q*s*v3+a*c*e^2*q*t*v2+a*c*e^2*r*s*v2+a*c*e^2*s^2*v1+a*c*e^2*s*t*v0-2*a*d^
3*p*t*v4-2*a*d^3*r*t*v2+a*d^3*s^2*v2-a*d^3*t^2*v0-2*a*d^2*e*p*s*v4+4*a*d^2*e*p*
t*v3+a*d^2*e*q*t*v2-a*d^2*e*r*s*v2-a*d^2*e*s^2*v1-a*d^2*e*s*t*v0+2*a*d*e^2*p*s*
v3+2*a*d*e^2*p*t*v2-b^3*c*t^2*v4+b^3*d*s*t*v4-b^3*d*t^2*v3-b^3*e*r*t*v4-b^3*e*s
^2*v4+b^3*e*s*t*v3-b^3*e*t^2*v2+b^2*c^2*t^2*v3+b^2*c*d*r*t*v4-b^2*c*d*s*t*v3+2*
b^2*c*d*t^2*v2-4*b^2*c*e*r*s*v4+4*b^2*c*e*r*t*v3+b^2*c*e*s^2*v3-b^2*c*e*s*t*v2+
2*b^2*c*e*t^2*v1+2*b^2*d^2*q*t*v4-b^2*d^2*r*s*v4-b^2*d^2*r*t*v3-b^2*d^2*s*t*v2+
b^2*d^2*t^2*v1-3*b^2*d*e*p*t*v4-b^2*d*e*q*s*v4-3*b^2*d*e*q*t*v3-b^2*d*e*r^2*v4+
3*b^2*d*e*r*s*v3-4*b^2*d*e*r*t*v2+b^2*d*e*s^2*v2-2*b^2*d*e*s*t*v1-3*b^2*d*e*t^2
*v0+b^2*e^2*p*t*v3+b^2*e^2*q*s*v3-b^2*e^2*q*t*v2+b^2*e^2*r^2*v3+2*b^2*e^2*r*s*
v2+b^2*e^2*r*t*v1+b^2*e^2*s^2*v1+b^2*e^2*s*t*v0+b*c^3*r*t*v4-b*c^3*t^2*v2-b*c^2
*d*q*t*v4+b*c^2*d*r*s*v4-2*b*c^2*d*r*t*v3+b*c^2*d*s*t*v2-3*b*c^2*d*t^2*v1+3*b*c
^2*e*p*t*v4-3*b*c^2*e*q*s*v4+4*b*c^2*e*q*t*v3-2*b*c^2*e*r^2*v4+2*b*c^2*e*r*s*v3
-b*c^2*e*s^2*v2+b*c^2*e*s*t*v1+2*b*c^2*e*t^2*v0+3*b*c*d^2*p*t*v4-b*c*d^2*q*s*v4
+b*c*d^2*q*t*v3-b*c*d^2*r*s*v3+2*b*c*d^2*r*t*v2+2*b*c*d^2*s*t*v1+2*b*c*d^2*t^2*
v0-5*b*c*d*e*p*s*v4+b*c*d*e*p*t*v3-4*b*c*d*e*q*r*v4+2*b*c*d*e*q*s*v3+2*b*c*d*e*
r^2*v3-3*b*c*d*e*r*s*v2-b*c*d*e*r*t*v1-2*b*c*d*e*s^2*v1-2*b*c*d*e*s*t*v0+b*c*e^
2*p*s*v3-2*b*c*e^2*p*t*v2+4*b*c*e^2*q*r*v3+b*c*e^2*q*s*v2+b*c*e^2*q*t*v1+2*b*c*
e^2*r^2*v2+2*b*c*e^2*r*s*v1+2*b*c*e^2*r*t*v0-b*d^3*p*s*v4-b*d^3*p*t*v3-2*b*d^3*
q*t*v2+b*d^3*r*s*v2+b*d^3*r*t*v1-4*b*d^2*e*p*r*v4+3*b*d^2*e*p*s*v3-2*b*d^2*e*p*
t*v2+b*d^2*e*q*s*v2+b*d^2*e*q*t*v1-2*b*d^2*e*r^2*v2-2*b*d^2*e*r*s*v1-2*b*d^2*e*
r*t*v0+4*b*d*e^2*p*r*v3+2*b*d*e^2*p*s*v2+2*b*d*e^2*p*t*v1+c^4*q*t*v4+c^4*t^2*v1
-c^3*d*p*t*v4+c^3*d*q*s*v4-2*c^3*d*q*t*v3-c^3*d*s*t*v1-c^3*d*t^2*v0+c^3*e*p*s*
v4-c^3*e*p*t*v3-2*c^3*e*q*r*v4+2*c^3*e*q*s*v3-c^3*e*q*t*v2-c^3*e*r*t*v1+c^3*e*s
^2*v1+c^3*e*s*t*v0+c^2*d^2*p*s*v4-c^2*d^2*q*s*v3+2*c^2*d^2*q*t*v2-2*c^2*d*e*p*r
*v4+c^2*d*e*p*s*v3+2*c^2*d*e*p*t*v2-3*c^2*d*e*q^2*v4+2*c^2*d*e*q*r*v3-3*c^2*d*e
*q*s*v2-3*c^2*d*e*q*t*v1-c^2*e^2*p*s*v2-c^2*e^2*p*t*v1+3*c^2*e^2*q^2*v3+2*c^2*e
^2*q*r*v2+2*c^2*e^2*q*s*v1+2*c^2*e^2*q*t*v0-c*d^3*p*s*v3+c*d^3*q*s*v2+c*d^3*q*t
*v1-6*c*d^2*e*p*q*v4+2*c*d^2*e*p*r*v3-2*c*d^2*e*p*s*v2-2*c*d^2*e*p*t*v1-2*c*d^2
*e*q*r*v2-2*c*d^2*e*q*s*v1-2*c*d^2*e*q*t*v0+6*c*d*e^2*p*q*v3+2*c*d*e^2*p*r*v2+2
*c*d*e^2*p*s*v1+2*c*d*e^2*p*t*v0+d^4*p*s*v2+d^4*p*t*v1-3*d^3*e*p^2*v4-2*d^3*e*p
*r*v2-2*d^3*e*p*s*v1-2*d^3*e*p*t*v0+3*d^2*e^2*p^2*v3+2*a*c*e^2*t*v4+2*a*d^2*e*t
*v4+a*d*e^2*s*v4-3*a*d*e^2*t*v3-a*e^3*s*v3-a*e^3*t*v2+b^2*e^2*t*v4-b*c*d*e*t*v4
+2*b*c*e^2*s*v4-3*b*c*e^2*t*v3-b*d^3*t*v4+b*d^2*e*s*v4+2*b*d^2*e*t*v3+2*b*d*e^2
*r*v4-2*b*d*e^2*s*v3+2*b*d*e^2*t*v2-2*b*e^3*r*v3-b*e^3*s*v2-b*e^3*t*v1-c^3*e*t*
v4+c^2*d^2*t*v4-c^2*d*e*s*v4+2*c^2*d*e*t*v3+c^2*e^2*r*v4-c^2*e^2*s*v3+c^2*e^2*t
*v2-c*d^3*t*v3+c*d^2*e*s*v3-3*c*d^2*e*t*v2+3*c*d*e^2*q*v4-c*d*e^2*r*v3+2*c*d*e^
2*s*v2+2*c*d*e^2*t*v1-3*c*e^3*q*v3-c*e^3*r*v2-c*e^3*s*v1-c*e^3*t*v0+d^4*t*v2-d^
3*e*s*v2-d^3*e*t*v1+3*d^2*e^2*p*v4+d^2*e^2*r*v2+d^2*e^2*s*v1+d^2*e^2*t*v0-3*d*e
^3*p*v3-d*e^3*v4+e^4*v3)




beta[2,1] = a^4*t^3*v4+3*a^3*b*s*t^2*v4-a^3*b*t^3*v3+2*a^3*c*r*t^2*v4-a^3*c*s*t
^2*v3-a^3*c*t^3*v2+a^3*d*q*t^2*v4-a^3*d*r*t^2*v3-a^3*d*s*t^2*v2-a^3*d*t^3*v1-a^
3*e*q*t^2*v3-a^3*e*r*t^2*v2-a^3*e*s*t^2*v1-a^3*e*t^3*v0+a^2*b^2*r*t^2*v4+3*a^2*
b^2*s^2*t*v4-2*a^2*b^2*s*t^2*v3+a^2*b^2*t^3*v2+3*a^2*b*c*q*t^2*v4+4*a^2*b*c*r*s
*t*v4-a^2*b*c*r*t^2*v3-2*a^2*b*c*s^2*t*v3+2*a^2*b*c*t^3*v1+4*a^2*b*d*p*t^2*v4+2
*a^2*b*d*q*s*t*v4-2*a^2*b*d*r*s*t*v3+2*a^2*b*d*r*t^2*v2-2*a^2*b*d*s^2*t*v2+2*a^
2*b*d*t^3*v0-a^2*b*e*p*t^2*v3-2*a^2*b*e*q*s*t*v3-2*a^2*b*e*r*s*t*v2-2*a^2*b*e*s
^2*t*v1-2*a^2*b*e*s*t^2*v0+2*a^2*c^2*p*t^2*v4+a^2*c^2*q*s*t*v4+a^2*c^2*r^2*t*v4
-a^2*c^2*r*s*t*v3-a^2*c^2*r*t^2*v2+a^2*c^2*s^2*t*v2+2*a^2*c^2*s*t^2*v1+a^2*c^2*
t^3*v0+3*a^2*c*d*p*s*t*v4-2*a^2*c*d*p*t^2*v3+a^2*c*d*q*r*t*v4-2*a^2*c*d*q*t^2*
v2-a^2*c*d*r^2*t*v3+a^2*c*d*r*s*t*v2-a^2*c*d*r*t^2*v1+2*a^2*c*d*s^2*t*v1+2*a^2*
c*d*s*t^2*v0-a^2*c*e*p*s*t*v3-a^2*c*e*p*t^2*v2-a^2*c*e*q*r*t*v3-a^2*c*e*r^2*t*
v2-a^2*c*e*r*s*t*v1-a^2*c*e*r*t^2*v0+a^2*d^2*p*r*t*v4-a^2*d^2*p*s*t*v3-a^2*d^2*
p*t^2*v2-a^2*d^2*q*s*t*v2-a^2*d^2*q*t^2*v1+a^2*d^2*r^2*t*v2+a^2*d^2*r*s*t*v1+a^
2*d^2*r*t^2*v0-a^2*d*e*p*r*t*v3-a^2*d*e*p*s*t*v2-a^2*d*e*p*t^2*v1-a*b^3*q*t^2*
v4+2*a*b^3*r*s*t*v4-a*b^3*r*t^2*v3+a*b^3*s^3*v4-a*b^3*s^2*t*v3+a*b^3*s*t^2*v2-a
*b^3*t^3*v1-4*a*b^2*c*p*t^2*v4+4*a*b^2*c*q*s*t*v4-3*a*b^2*c*q*t^2*v3+2*a*b^2*c*
r^2*t*v4+2*a*b^2*c*r*s^2*v4-2*a*b^2*c*r*s*t*v3-a*b^2*c*r*t^2*v2-a*b^2*c*s^3*v3+
a*b^2*c*s^2*t*v2-a*b^2*c*s*t^2*v1-3*a*b^2*c*t^3*v0+5*a*b^2*d*p*s*t*v4-a*b^2*d*p
*t^2*v3+a*b^2*d*q*r*t*v4+a*b^2*d*q*s^2*v4+2*a*b^2*d*q*t^2*v2-a*b^2*d*r^2*t*v3-a
*b^2*d*r*s^2*v3+a*b^2*d*r*s*t*v2-a*b^2*d*r*t^2*v1-a*b^2*d*s^3*v2+a*b^2*d*s^2*t*
v1+2*a*b^2*d*s*t^2*v0-a*b^2*e*p*s*t*v3+a*b^2*e*p*t^2*v2-a*b^2*e*q*r*t*v3-a*b^2*
e*q*s^2*v3-a*b^2*e*r^2*t*v2-a*b^2*e*r*s^2*v2-a*b^2*e*r*s*t*v1-a*b^2*e*r*t^2*v0-
a*b^2*e*s^3*v1-a*b^2*e*s^2*t*v0-a*b*c^2*p*s*t*v4+a*b*c^2*p*t^2*v3+5*a*b*c^2*q*r
*t*v4+a*b*c^2*q*s^2*v4-4*a*b*c^2*q*s*t*v3+a*b*c^2*r^2*s*v4-a*b*c^2*r*s^2*v3-a*b
*c^2*r*s*t*v2+3*a*b*c^2*r*t^2*v1+a*b*c^2*s^3*v2-a*b*c^2*s^2*t*v1-2*a*b*c^2*s*t^
2*v0+4*a*b*c*d*p*r*t*v4+3*a*b*c*d*p*s^2*v4-3*a*b*c*d*p*s*t*v3+2*a*b*c*d*p*t^2*
v2+3*a*b*c*d*q^2*t*v4+a*b*c*d*q*r*s*v4-3*a*b*c*d*q*r*t*v3-a*b*c*d*q*s*t*v2+a*b*
c*d*q*t^2*v1-a*b*c*d*r^2*s*v3+a*b*c*d*r*s^2*v2-a*b*c*d*r*s*t*v1+2*a*b*c*d*s^3*
v1+2*a*b*c*d*s^2*t*v0-a*b*c*e*p*s^2*v3+a*b*c*e*p*s*t*v2+2*a*b*c*e*p*t^2*v1-3*a*
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2*v4-2*c^2*d^2*p*q*r*v3+c^2*d^2*p*q*s*v2+c^2*d^2*p*q*t*v1+c^2*d^2*q^2*r*v2+c^2*
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v1-2*a*c*d^2*q*t*v4+2*a*c*d^2*r*t*v3-a*c*d^2*s^2*v3+a*c*d^2*s*t*v2+2*a*c*d^2*t^
2*v1-6*a*c*d*e*p*t*v4-2*a*c*d*e*q*s*v4+3*a*c*d*e*q*t*v3+a*c*d*e*r*s*v3+2*a*c*d*
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c*e^2*q*s*v3+a*c*e^2*q*t*v2+a*c*e^2*r*s*v2+a*c*e^2*s^2*v1+a*c*e^2*s*t*v0-2*a*d^
3*p*t*v4-2*a*d^3*r*t*v2+a*d^3*s^2*v2-a*d^3*t^2*v0-2*a*d^2*e*p*s*v4+4*a*d^2*e*p*
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v3+2*a*d*e^2*p*t*v2-b^3*c*t^2*v4+b^3*d*s*t*v4-b^3*d*t^2*v3-b^3*e*r*t*v4-b^3*e*s
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2*b^2*c*e*t^2*v1+2*b^2*d^2*q*t*v4-b^2*d^2*r*s*v4-b^2*d^2*r*t*v3-b^2*d^2*s*t*v2+
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3*b^2*d*e*r*s*v3-4*b^2*d*e*r*t*v2+b^2*d*e*s^2*v2-2*b^2*d*e*s*t*v1-3*b^2*d*e*t^2
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t*v2+b*d^2*e*q*s*v2+b*d^2*e*q*t*v1-2*b*d^2*e*r^2*v2-2*b*d^2*e*r*s*v1-2*b*d^2*e*
r*t*v0+4*b*d*e^2*p*r*v3+2*b*d*e^2*p*s*v2+2*b*d*e^2*p*t*v1+c^4*q*t*v4+c^4*t^2*v1
-c^3*d*p*t*v4+c^3*d*q*s*v4-2*c^3*d*q*t*v3-c^3*d*s*t*v1-c^3*d*t^2*v0+c^3*e*p*s*
v4-c^3*e*p*t*v3-2*c^3*e*q*r*v4+2*c^3*e*q*s*v3-c^3*e*q*t*v2-c^3*e*r*t*v1+c^3*e*s
^2*v1+c^3*e*s*t*v0+c^2*d^2*p*s*v4-c^2*d^2*q*s*v3+2*c^2*d^2*q*t*v2-2*c^2*d*e*p*r
*v4+c^2*d*e*p*s*v3+2*c^2*d*e*p*t*v2-3*c^2*d*e*q^2*v4+2*c^2*d*e*q*r*v3-3*c^2*d*e
*q*s*v2-3*c^2*d*e*q*t*v1-c^2*e^2*p*s*v2-c^2*e^2*p*t*v1+3*c^2*e^2*q^2*v3+2*c^2*e
^2*q*r*v2+2*c^2*e^2*q*s*v1+2*c^2*e^2*q*t*v0-c*d^3*p*s*v3+c*d^3*q*s*v2+c*d^3*q*t
*v1-6*c*d^2*e*p*q*v4+2*c*d^2*e*p*r*v3-2*c*d^2*e*p*s*v2-2*c*d^2*e*p*t*v1-2*c*d^2
*e*q*r*v2-2*c*d^2*e*q*s*v1-2*c*d^2*e*q*t*v0+6*c*d*e^2*p*q*v3+2*c*d*e^2*p*r*v2+2
*c*d*e^2*p*s*v1+2*c*d*e^2*p*t*v0+d^4*p*s*v2+d^4*p*t*v1-3*d^3*e*p^2*v4-2*d^3*e*p
*r*v2-2*d^3*e*p*s*v1-2*d^3*e*p*t*v0+3*d^2*e^2*p^2*v3+2*a*c*e^2*t*v4+2*a*d^2*e*t
*v4+a*d*e^2*s*v4-3*a*d*e^2*t*v3-a*e^3*s*v3-a*e^3*t*v2+b^2*e^2*t*v4-b*c*d*e*t*v4
+2*b*c*e^2*s*v4-3*b*c*e^2*t*v3-b*d^3*t*v4+b*d^2*e*s*v4+2*b*d^2*e*t*v3+2*b*d*e^2
*r*v4-2*b*d*e^2*s*v3+2*b*d*e^2*t*v2-2*b*e^3*r*v3-b*e^3*s*v2-b*e^3*t*v1-c^3*e*t*
v4+c^2*d^2*t*v4-c^2*d*e*s*v4+2*c^2*d*e*t*v3+c^2*e^2*r*v4-c^2*e^2*s*v3+c^2*e^2*t
*v2-c*d^3*t*v3+c*d^2*e*s*v3-3*c*d^2*e*t*v2+3*c*d*e^2*q*v4-c*d*e^2*r*v3+2*c*d*e^
2*s*v2+2*c*d*e^2*t*v1-3*c*e^3*q*v3-c*e^3*r*v2-c*e^3*s*v1-c*e^3*t*v0+d^4*t*v2-d^
3*e*s*v2-d^3*e*t*v1+3*d^2*e^2*p*v4+d^2*e^2*r*v2+d^2*e^2*s*v1+d^2*e^2*t*v0-3*d*e
^3*p*v3-d*e^3*v4+e^4*v3




beta[2,2] = a^4*q*t^3*v3+a^4*r*t^3*v2+a^4*s*t^3*v1+a^4*t^4*v0+a^3*b*p*t^3*v3+3*
a^3*b*q*s*t^2*v3+3*a^3*b*r*s*t^2*v2+3*a^3*b*s^2*t^2*v1+3*a^3*b*s*t^3*v0+a^3*c*p
*s*t^2*v3+a^3*c*p*t^3*v2+2*a^3*c*q*r*t^2*v3+2*a^3*c*r^2*t^2*v2+2*a^3*c*r*s*t^2*
v1+2*a^3*c*r*t^3*v0+a^3*d*p*r*t^2*v3+a^3*d*p*s*t^2*v2+a^3*d*p*t^3*v1+a^3*d*q^2*
t^2*v3+a^3*d*q*r*t^2*v2+a^3*d*q*s*t^2*v1+a^3*d*q*t^3*v0+a^3*e*p*q*t^2*v3+a^3*e*
p*r*t^2*v2+a^3*e*p*s*t^2*v1+a^3*e*p*t^3*v0+2*a^2*b^2*p*s*t^2*v3-a^2*b^2*p*t^3*
v2+a^2*b^2*q*r*t^2*v3+3*a^2*b^2*q*s^2*t*v3+a^2*b^2*r^2*t^2*v2+3*a^2*b^2*r*s^2*t
*v2+a^2*b^2*r*s*t^2*v1+a^2*b^2*r*t^3*v0+3*a^2*b^2*s^3*t*v1+3*a^2*b^2*s^2*t^2*v0
+a^2*b*c*p*r*t^2*v3+2*a^2*b*c*p*s^2*t*v3-2*a^2*b*c*p*t^3*v1+3*a^2*b*c*q^2*t^2*
v3+4*a^2*b*c*q*r*s*t*v3+3*a^2*b*c*q*r*t^2*v2+3*a^2*b*c*q*s*t^2*v1+3*a^2*b*c*q*t
^3*v0+4*a^2*b*c*r^2*s*t*v2+4*a^2*b*c*r*s^2*t*v1+4*a^2*b*c*r*s*t^2*v0+4*a^2*b*d*
p*q*t^2*v3+2*a^2*b*d*p*r*s*t*v3+2*a^2*b*d*p*r*t^2*v2+2*a^2*b*d*p*s^2*t*v2+4*a^2
*b*d*p*s*t^2*v1+2*a^2*b*d*p*t^3*v0+2*a^2*b*d*q^2*s*t*v3+2*a^2*b*d*q*r*s*t*v2+2*
a^2*b*d*q*s^2*t*v1+2*a^2*b*d*q*s*t^2*v0+a^2*b*e*p^2*t^2*v3+2*a^2*b*e*p*q*s*t*v3
+2*a^2*b*e*p*r*s*t*v2+2*a^2*b*e*p*s^2*t*v1+2*a^2*b*e*p*s*t^2*v0+2*a^2*c^2*p*q*t
^2*v3+a^2*c^2*p*r*s*t*v3+3*a^2*c^2*p*r*t^2*v2-a^2*c^2*p*s^2*t*v2+a^2*c^2*p*t^3*
v0+a^2*c^2*q^2*s*t*v3+a^2*c^2*q*r^2*t*v3+a^2*c^2*q*r*s*t*v2+a^2*c^2*q*s^2*t*v1+
a^2*c^2*q*s*t^2*v0+a^2*c^2*r^3*t*v2+a^2*c^2*r^2*s*t*v1+a^2*c^2*r^2*t^2*v0+2*a^2
*c*d*p^2*t^2*v3+3*a^2*c*d*p*q*s*t*v3+2*a^2*c*d*p*q*t^2*v2+a^2*c*d*p*r^2*t*v3+2*
a^2*c*d*p*r*s*t*v2+a^2*c*d*p*r*t^2*v1+a^2*c*d*p*s^2*t*v1+a^2*c*d*p*s*t^2*v0+a^2
*c*d*q^2*r*t*v3+a^2*c*d*q*r^2*t*v2+a^2*c*d*q*r*s*t*v1+a^2*c*d*q*r*t^2*v0+a^2*c*
e*p^2*s*t*v3+a^2*c*e*p^2*t^2*v2+a^2*c*e*p*q*r*t*v3+a^2*c*e*p*r^2*t*v2+a^2*c*e*p
*r*s*t*v1+a^2*c*e*p*r*t^2*v0+a^2*d^2*p^2*s*t*v3+a^2*d^2*p^2*t^2*v2+a^2*d^2*p*q*
r*t*v3+a^2*d^2*p*q*s*t*v2+a^2*d^2*p*q*t^2*v1+a^2*d*e*p^2*r*t*v3+a^2*d*e*p^2*s*t
*v2+a^2*d*e*p^2*t^2*v1+a*b^3*p*r*t^2*v3+a*b^3*p*s^2*t*v3-a*b^3*p*s*t^2*v2+a*b^3
*p*t^3*v1-a*b^3*q^2*t^2*v3+2*a*b^3*q*r*s*t*v3-a*b^3*q*r*t^2*v2+a*b^3*q*s^3*v3-a
*b^3*q*s*t^2*v1-a*b^3*q*t^3*v0+2*a*b^3*r^2*s*t*v2+a*b^3*r*s^3*v2+2*a*b^3*r*s^2*
t*v1+2*a*b^3*r*s*t^2*v0+a*b^3*s^4*v1+a*b^3*s^3*t*v0-a*b^2*c*p*q*t^2*v3+2*a*b^2*
c*p*r*s*t*v3-3*a*b^2*c*p*r*t^2*v2+a*b^2*c*p*s^3*v3-a*b^2*c*p*s^2*t*v2-3*a*b^2*c
*p*s*t^2*v1-a*b^2*c*p*t^3*v0+4*a*b^2*c*q^2*s*t*v3+2*a*b^2*c*q*r^2*t*v3+2*a*b^2*
c*q*r*s^2*v3+4*a*b^2*c*q*r*s*t*v2+4*a*b^2*c*q*s^2*t*v1+4*a*b^2*c*q*s*t^2*v0+2*a
*b^2*c*r^3*t*v2+2*a*b^2*c*r^2*s^2*v2+2*a*b^2*c*r^2*s*t*v1+2*a*b^2*c*r^2*t^2*v0+
2*a*b^2*c*r*s^3*v1+2*a*b^2*c*r*s^2*t*v0+a*b^2*d*p^2*t^2*v3+5*a*b^2*d*p*q*s*t*v3
-2*a*b^2*d*p*q*t^2*v2+a*b^2*d*p*r^2*t*v3+a*b^2*d*p*r*s^2*v3+4*a*b^2*d*p*r*s*t*
v2+a*b^2*d*p*r*t^2*v1+a*b^2*d*p*s^3*v2+4*a*b^2*d*p*s^2*t*v1+3*a*b^2*d*p*s*t^2*
v0+a*b^2*d*q^2*r*t*v3+a*b^2*d*q^2*s^2*v3+a*b^2*d*q*r^2*t*v2+a*b^2*d*q*r*s^2*v2+
a*b^2*d*q*r*s*t*v1+a*b^2*d*q*r*t^2*v0+a*b^2*d*q*s^3*v1+a*b^2*d*q*s^2*t*v0+a*b^2
*e*p^2*s*t*v3-a*b^2*e*p^2*t^2*v2+a*b^2*e*p*q*r*t*v3+a*b^2*e*p*q*s^2*v3+a*b^2*e*
p*r^2*t*v2+a*b^2*e*p*r*s^2*v2+a*b^2*e*p*r*s*t*v1+a*b^2*e*p*r*t^2*v0+a*b^2*e*p*s
^3*v1+a*b^2*e*p*s^2*t*v0-a*b*c^2*p^2*t^2*v3+3*a*b*c^2*p*q*s*t*v3+a*b*c^2*p*r*s^
2*v3-3*a*b*c^2*p*r*t^2*v1-a*b*c^2*p*s^3*v2+a*b*c^2*p*s*t^2*v0+5*a*b*c^2*q^2*r*t
*v3+a*b*c^2*q^2*s^2*v3+a*b*c^2*q*r^2*s*v3+5*a*b*c^2*q*r^2*t*v2+a*b*c^2*q*r*s^2*
v2+5*a*b*c^2*q*r*s*t*v1+5*a*b*c^2*q*r*t^2*v0+a*b*c^2*q*s^3*v1+a*b*c^2*q*s^2*t*
v0+a*b*c^2*r^3*s*v2+a*b*c^2*r^2*s^2*v1+a*b*c^2*r^2*s*t*v0+3*a*b*c*d*p^2*s*t*v3-\
2*a*b*c*d*p^2*t^2*v2+7*a*b*c*d*p*q*r*t*v3+3*a*b*c*d*p*q*s^2*v3+a*b*c*d*p*q*s*t*
v2-a*b*c*d*p*q*t^2*v1+a*b*c*d*p*r^2*s*v3+4*a*b*c*d*p*r^2*t*v2+2*a*b*c*d*p*r*s^2
*v2+5*a*b*c*d*p*r*s*t*v1+4*a*b*c*d*p*r*t^2*v0+a*b*c*d*p*s^3*v1+a*b*c*d*p*s^2*t*
v0+3*a*b*c*d*q^3*t*v3+a*b*c*d*q^2*r*s*v3+3*a*b*c*d*q^2*r*t*v2+3*a*b*c*d*q^2*s*t
*v1+3*a*b*c*d*q^2*t^2*v0+a*b*c*d*q*r^2*s*v2+a*b*c*d*q*r*s^2*v1+a*b*c*d*q*r*s*t*
v0+a*b*c*e*p^2*s^2*v3-a*b*c*e*p^2*s*t*v2-2*a*b*c*e*p^2*t^2*v1+3*a*b*c*e*p*q^2*t
*v3+a*b*c*e*p*q*r*s*v3+3*a*b*c*e*p*q*r*t*v2+3*a*b*c*e*p*q*s*t*v1+3*a*b*c*e*p*q*
t^2*v0+a*b*c*e*p*r^2*s*v2+a*b*c*e*p*r*s^2*v1+a*b*c*e*p*r*s*t*v0+2*a*b*d^2*p^2*r
*t*v3+a*b*d^2*p^2*s^2*v3+2*a*b*d^2*p^2*s*t*v2+a*b*d^2*p^2*t^2*v1+3*a*b*d^2*p*q^
2*t*v3+a*b*d^2*p*q*r*s*v3+2*a*b*d^2*p*q*r*t*v2+a*b*d^2*p*q*s^2*v2+3*a*b*d^2*p*q
*s*t*v1+2*a*b*d^2*p*q*t^2*v0+3*a*b*d*e*p^2*q*t*v3+a*b*d*e*p^2*r*s*v3+2*a*b*d*e*
p^2*r*t*v2+a*b*d*e*p^2*s^2*v2+3*a*b*d*e*p^2*s*t*v1+2*a*b*d*e*p^2*t^2*v0+a*c^3*p
^2*t^2*v2+2*a*c^3*p*q*r*t*v3-a*c^3*p*q*s*t*v2-a*c^3*p*q*t^2*v1+2*a*c^3*p*r^2*t*
v2-a*c^3*p*r*s^2*v2+a*c^3*p*r*t^2*v0+a*c^3*q^3*t*v3+a*c^3*q^2*r*s*v3+a*c^3*q^2*
r*t*v2+a*c^3*q^2*s*t*v1+a*c^3*q^2*t^2*v0+a*c^3*q*r^2*s*v2+a*c^3*q*r*s^2*v1+a*c^
3*q*r*s*t*v0+2*a*c^2*d*p^2*r*t*v3-a*c^2*d*p^2*s*t*v2-a*c^2*d*p^2*t^2*v1+5*a*c^2
*d*p*q^2*t*v3+2*a*c^2*d*p*q*r*s*v3+5*a*c^2*d*p*q*r*t*v2-a*c^2*d*p*q*s^2*v2+2*a*
c^2*d*p*q*s*t*v1+3*a*c^2*d*p*q*t^2*v0+a*c^2*d*p*r^2*s*v2+a*c^2*d*p*r*s^2*v1+a*c
^2*d*p*r*s*t*v0+a*c^2*d*q^3*s*v3+a*c^2*d*q^2*r*s*v2+a*c^2*d*q^2*s^2*v1+a*c^2*d*
q^2*s*t*v0+2*a*c^2*e*p^2*q*t*v3+2*a*c^2*e*p^2*r*t*v2-a*c^2*e*p^2*s^2*v2+a*c^2*e
*p^2*t^2*v0+a*c^2*e*p*q^2*s*v3+a*c^2*e*p*q*r*s*v2+a*c^2*e*p*q*s^2*v1+a*c^2*e*p*
q*s*t*v0+5*a*c*d^2*p^2*q*t*v3+a*c*d^2*p^2*r*s*v3+2*a*c*d^2*p^2*r*t*v2+a*c*d^2*p
^2*s*t*v1+a*c*d^2*p^2*t^2*v0+2*a*c*d^2*p*q^2*s*v3+a*c*d^2*p*q^2*t*v2+a*c*d^2*p*
q*r*s*v2+a*c*d^2*p*q*s^2*v1+a*c*d^2*p*q*s*t*v0+2*a*c*d*e*p^3*t*v3+2*a*c*d*e*p^2
*q*s*v3+a*c*d*e*p^2*q*t*v2+a*c*d*e*p^2*r*s*v2+a*c*d*e*p^2*s^2*v1+a*c*d*e*p^2*s*
t*v0+a*d^3*p^3*t*v3+a*d^3*p^2*q*s*v3+a*d^3*p^2*q*t*v2+a*d^2*e*p^3*s*v3+a*d^2*e*
p^3*t*v2+b^4*p*r*s*t*v3+b^4*p*s*t^2*v1-b^4*q^2*s*t*v3+b^4*q*r*s^2*v3-b^4*q*r*s*
t*v2-b^4*q*s^2*t*v1-b^4*q*s*t^2*v0+b^4*r^2*s^2*v2+b^4*r*s^3*v1+b^4*r*s^2*t*v0-b
^3*c*p*q*s*t*v3+b^3*c*p*r^2*t*v3+b^3*c*p*r*s^2*v3-2*b^3*c*p*r*s*t*v2+b^3*c*p*r*
t^2*v1-b^3*c*p*s^2*t*v1-b^3*c*p*s*t^2*v0-b^3*c*q^2*r*t*v3+b^3*c*q^2*s^2*v3+2*b^
3*c*q*r^2*s*v3-b^3*c*q*r^2*t*v2+b^3*c*q*r*s^2*v2-b^3*c*q*r*s*t*v1-b^3*c*q*r*t^2
*v0+b^3*c*q*s^3*v1+b^3*c*q*s^2*t*v0+2*b^3*c*r^3*s*v2+2*b^3*c*r^2*s^2*v1+2*b^3*c
*r^2*s*t*v0+b^3*d*p^2*s*t*v3+b^3*d*p*q*r*t*v3+b^3*d*p*q*s^2*v3-b^3*d*p*q*s*t*v2
+b^3*d*p*q*t^2*v1+b^3*d*p*r^2*s*v3+2*b^3*d*p*r*s^2*v2+b^3*d*p*r*s*t*v1+b^3*d*p*
s^3*v1+b^3*d*p*s^2*t*v0-b^3*d*q^3*t*v3+b^3*d*q^2*r*s*v3-b^3*d*q^2*r*t*v2-b^3*d*
q^2*s*t*v1-b^3*d*q^2*t^2*v0+b^3*d*q*r^2*s*v2+b^3*d*q*r*s^2*v1+b^3*d*q*r*s*t*v0+
b^3*e*p^2*r*t*v3+b^3*e*p^2*t^2*v1-b^3*e*p*q^2*t*v3+b^3*e*p*q*r*s*v3-b^3*e*p*q*r
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q*r*s^2*v1+3*b^2*c^2*q*r*s*t*v0+b^2*c^2*r^4*v2+b^2*c^2*r^3*s*v1+b^2*c^2*r^3*t*
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e*p^2*s*t*v1-b^2*c*e*p^2*t^2*v0+b^2*c*e*p*q^2*s*v3+b^2*c*e*p*q*r^2*v3+b^2*c*e*p
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s*v1+b^2*c*e*p*r^2*t*v0+b^2*d^2*p^2*q*t*v3+2*b^2*d^2*p^2*r*s*v3+b^2*d^2*p^2*s^2
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b^2*d*e*p^3*t*v3+b^2*d*e*p^2*q*s*v3-b^2*d*e*p^2*q*t*v2+b^2*d*e*p^2*r^2*v3+2*b^2
*d*e*p^2*r*s*v2+b^2*d*e*p^2*r*t*v1+b^2*d*e*p^2*s^2*v1+b^2*d*e*p^2*s*t*v0-b*c^3*
p^2*r*t*v3+b*c^3*p^2*s*t*v2+b*c^3*p*q*r*s*v3-b*c^3*p*q*s^2*v2-b*c^3*p*q*s*t*v1-
b*c^3*p*r^2*s*v2-b*c^3*p*r^2*t*v1+b*c^3*q^3*s*v3+2*b*c^3*q^2*r^2*v3+b*c^3*q^2*r
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2*d*p^2*s^2*v2-b*c^2*d*p^2*s*t*v1+4*b*c^2*d*p*q^2*s*v3+4*b*c^2*d*p*q*r^2*v3+2*b
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2*b*c^2*d*p*r^2*s*v1+2*b*c^2*d*p*r^2*t*v0+2*b*c^2*d*q^3*r*v3+2*b*c^2*d*q^2*r^2*
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2*q*t*v2+2*b*c*d^2*p^2*r^2*v3+2*b*c*d^2*p^2*r*s*v2+b*c*d^2*p^2*r*t*v1+b*c*d^2*p
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q^2*t*v1+2*b*c*d^2*p*q*r^2*v2+2*b*c*d^2*p*q*r*s*v1+2*b*c*d^2*p*q*r*t*v0+b*c*d*e
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*d*p^2*r*s*v2-c^3*d*p^2*r*t*v1+3*c^3*d*p*q^2*r*v3-c^3*d*p*q^2*s*v2-c^3*d*p*q^2*
t*v1+2*c^3*d*p*q*r^2*v2+2*c^3*d*p*q*r*s*v1+2*c^3*d*p*q*r*t*v0+c^3*d*q^4*v3+c^3*
d*q^3*r*v2+c^3*d*q^3*s*v1+c^3*d*q^3*t*v0+c^3*e*p^3*t*v2-c^3*e*p^2*q*s*v2-c^3*e*
p^2*q*t*v1+c^3*e*p*q^3*v3+c^3*e*p*q^2*r*v2+c^3*e*p*q^2*s*v1+c^3*e*p*q^2*t*v0+3*
c^2*d^2*p^2*q*r*v3-c^2*d^2*p^2*q*s*v2-c^2*d^2*p^2*q*t*v1+c^2*d^2*p^2*r^2*v2+c^2
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2*d^2*p*q^2*s*v1+2*c^2*d^2*p*q^2*t*v0-c^2*d*e*p^3*s*v2-c^2*d*e*p^3*t*v1+3*c^2*d
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d^3*p^3*r*v3+3*c*d^3*p^2*q^2*v3+c*d^3*p^2*q*r*v2+c*d^3*p^2*q*s*v1+c*d^3*p^2*q*t
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3*d*s*t^2*v3-a^3*d*t^3*v2-a^3*e*q*t^2*v4-a^3*e*r*t^2*v3-a^3*e*s*t^2*v2-a^3*e*t^
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2*b*c*t^3*v2-2*a^2*b*d*r*s*t*v4+2*a^2*b*d*r*t^2*v3-2*a^2*b*d*s^2*t*v3+2*a^2*b*d
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v3-3*a^2*b*e*r*t^2*v2-2*a^2*b*e*s^2*t*v2-5*a^2*b*e*s*t^2*v1-3*a^2*b*e*t^3*v0-a^
2*c^2*r*s*t*v4-a^2*c^2*r*t^2*v3+a^2*c^2*s^2*t*v3+2*a^2*c^2*s*t^2*v2+a^2*c^2*t^3
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s*t*v4-3*a^2*c*e*p*t^2*v3-a^2*c*e*q*r*t*v4-2*a^2*c*e*q*s*t*v3-a^2*c*e*r^2*t*v3-\
3*a^2*c*e*r*s*t*v2-a^2*c*e*r*t^2*v1-2*a^2*c*e*s^2*t*v1-2*a^2*c*e*s*t^2*v0-a^2*d
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t*v3+a^2*d^2*r*t^2*v1-a^2*d^2*s^2*t*v1-a^2*d^2*s*t^2*v0-a^2*d*e*p*r*t*v4-3*a^2*
d*e*p*s*t*v3-3*a^2*d*e*p*t^2*v2-a^2*d*e*q*r*t*v3-a^2*d*e*r^2*t*v2-a^2*d*e*r*s*t
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2*v4+a*b^2*d*r*s*t*v3+a*b^2*d*r*t^2*v2-a*b^2*d*s^3*v3+a*b^2*d*s^2*t*v2+4*a*b^2*
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2*a*b*c*e*s^2*t*v0-2*a*b*d^2*p*r*t*v4-a*b*d^2*p*s^2*v4-2*a*b*d^2*p*s*t*v3+2*a*b
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3*e*p^3*v4-3*d^3*e*p^2*q*v3-d^3*e*p^2*r*v2-d^3*e*p^2*s*v1-d^3*e*p^2*t*v0-3*d^2*
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-b*d^2*e*r*s*v2-2*b*d^2*e*r*t*v1+b*d^2*e*s^2*v1+b*d^2*e*s*t*v0+4*b*d*e^2*p*r*v4
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d*e*q*t*v2-c^2*d*e*r*s*v2-c^2*d*e*s^2*v1-c^2*d*e*s*t*v0-2*c^2*e^2*p*t*v2+3*c^2*
e^2*q^2*v4+3*c^2*e^2*q*r*v3+2*c^2*e^2*q*s*v2+2*c^2*e^2*q*t*v1+c^2*e^2*r^2*v2+c^
2*e^2*r*s*v1+c^2*e^2*r*t*v0-c*d^3*p*s*v4+c*d^3*p*t*v3+c*d^3*q*s*v3+c*d^3*q*t*v2
+2*c*d^2*e*p*r*v4-3*c*d^2*e*p*s*v3+c*d^2*e*p*t*v2-2*c*d^2*e*q*r*v3-2*c*d^2*e*q*
s*v2-2*c*d^2*e*q*t*v1+6*c*d*e^2*p*q*v4+3*c*d*e^2*p*r*v3+3*c*d*e^2*q^2*v3+3*c*d*
e^2*q*r*v2+3*c*d*e^2*q*s*v1+3*c*d*e^2*q*t*v0+3*c*e^3*p*q*v3+c*e^3*p*r*v2+c*e^3*
p*s*v1+c*e^3*p*t*v0+d^4*p*s*v3-2*d^3*e*p*r*v3-d^3*e*p*s*v2-d^3*e*p*t*v1+3*d^2*e
^2*p^2*v4+3*d^2*e^2*p*q*v3+2*d^2*e^2*p*r*v2+2*d^2*e^2*p*s*v1+2*d^2*e^2*p*t*v0+3
*d*e^3*p^2*v3-3*a*d*e^2*t*v4-a*e^3*s*v4-a*e^3*t*v3-3*b*c*e^2*t*v4+2*b*d^2*e*t*
v4-2*b*d*e^2*s*v4+2*b*d*e^2*t*v3-2*b*e^3*r*v4-b*e^3*s*v3-b*e^3*t*v2+2*c^2*d*e*t
*v4-c^2*e^2*s*v4+c^2*e^2*t*v3-c*d^3*t*v4+c*d^2*e*s*v4-3*c*d^2*e*t*v3-c*d*e^2*r*
v4+2*c*d*e^2*s*v3+2*c*d*e^2*t*v2-3*c*e^3*q*v4-c*e^3*r*v3-c*e^3*s*v2-c*e^3*t*v1+
d^4*t*v3-d^3*e*s*v3-d^3*e*t*v2+d^2*e^2*r*v3+d^2*e^2*s*v2+d^2*e^2*t*v1-3*d*e^3*p
*v4-d*e^3*q*v3-d*e^3*r*v2-d*e^3*s*v1-d*e^3*t*v0-e^4*p*v3+e^4*v4




beta[2,3] = a^4*r*t^3*v3+a^4*s*t^3*v2+a^4*t^4*v1+3*a^3*b*r*s*t^2*v3-a^3*b*r*t^3
*v2+3*a^3*b*s^2*t^2*v2+2*a^3*b*s*t^3*v1-a^3*b*t^4*v0+a^3*c*p*t^3*v3+a^3*c*q*t^3
*v2+2*a^3*c*r^2*t^2*v3+a^3*c*r*s*t^2*v2+2*a^3*c*r*t^3*v1-a^3*c*s^2*t^2*v1-a^3*c
*s*t^3*v0+a^3*d*p*s*t^2*v3+a^3*d*p*t^3*v2+a^3*d*q*r*t^2*v3+2*a^3*d*q*s*t^2*v2+2
*a^3*d*q*t^3*v1-a^3*d*r^2*t^2*v2-a^3*d*r*s*t^2*v1-a^3*d*r*t^3*v0+a^3*e*p*r*t^2*
v3+a^3*e*p*s*t^2*v2+a^3*e*p*t^3*v1-a^2*b^2*p*t^3*v3-a^2*b^2*q*t^3*v2+a^2*b^2*r^
2*t^2*v3+3*a^2*b^2*r*s^2*t*v3-a^2*b^2*r*s*t^2*v2+a^2*b^2*r*t^3*v1+3*a^2*b^2*s^3
*t*v2+a^2*b^2*s^2*t^2*v1-2*a^2*b^2*s*t^3*v0-2*a^2*b*c*p*t^3*v2+3*a^2*b*c*q*r*t^
2*v3+3*a^2*b*c*q*s*t^2*v2+a^2*b*c*q*t^3*v1+4*a^2*b*c*r^2*s*t*v3-a^2*b*c*r^2*t^2
*v2+2*a^2*b*c*r*s^2*t*v2+3*a^2*b*c*r*s*t^2*v1-a^2*b*c*r*t^3*v0-2*a^2*b*c*s^3*t*
v1-2*a^2*b*c*s^2*t^2*v0+2*a^2*b*d*p*r*t^2*v3+2*a^2*b*d*p*s^2*t*v3+4*a^2*b*d*p*s
*t^2*v2+2*a^2*b*d*p*t^3*v1+2*a^2*b*d*q*r*s*t*v3-2*a^2*b*d*q*r*t^2*v2+4*a^2*b*d*
q*s^2*t*v2+2*a^2*b*d*q*s*t^2*v1-2*a^2*b*d*q*t^3*v0-2*a^2*b*d*r^2*s*t*v2-2*a^2*b
*d*r*s^2*t*v1-2*a^2*b*d*r*s*t^2*v0+2*a^2*b*e*p*r*s*t*v3-a^2*b*e*p*r*t^2*v2+2*a^
2*b*e*p*s^2*t*v2+a^2*b*e*p*s*t^2*v1-a^2*b*e*p*t^3*v0+3*a^2*c^2*p*r*t^2*v3-a^2*c
^2*p*s^2*t*v3+a^2*c^2*p*t^3*v1+a^2*c^2*q*r*s*t*v3+a^2*c^2*q*r*t^2*v2-a^2*c^2*q*
s*t^2*v1-a^2*c^2*q*t^3*v0+a^2*c^2*r^3*t*v3+a^2*c^2*r^2*t^2*v1-a^2*c^2*r*s^2*t*
v1-a^2*c^2*r*s*t^2*v0+2*a^2*c*d*p*q*t^2*v3+2*a^2*c*d*p*r*s*t*v3-a^2*c*d*p*r*t^2
*v2+a^2*c*d*p*s^2*t*v2-a^2*c*d*p*s*t^2*v1-2*a^2*c*d*p*t^3*v0+2*a^2*c*d*q^2*t^2*
v2+a^2*c*d*q*r^2*t*v3+2*a^2*c*d*q*r*t^2*v1-2*a^2*c*d*q*s^2*t*v1-2*a^2*c*d*q*s*t
^2*v0-a^2*c*d*r^3*t*v2-a^2*c*d*r^2*s*t*v1-a^2*c*d*r^2*t^2*v0+a^2*c*e*p^2*t^2*v3
+a^2*c*e*p*q*t^2*v2+a^2*c*e*p*r^2*t*v3+a^2*c*e*p*r*t^2*v1-a^2*c*e*p*s^2*t*v1-a^
2*c*e*p*s*t^2*v0+a^2*d^2*p^2*t^2*v3+a^2*d^2*p*q*s*t*v3+2*a^2*d^2*p*q*t^2*v2-a^2
*d^2*p*r*s*t*v2-a^2*d^2*p*s^2*t*v1-a^2*d^2*p*s*t^2*v0+a^2*d^2*q^2*s*t*v2+a^2*d^
2*q^2*t^2*v1-a^2*d^2*q*r^2*t*v2-a^2*d^2*q*r*s*t*v1-a^2*d^2*q*r*t^2*v0+a^2*d*e*p
^2*s*t*v3+a^2*d*e*p^2*t^2*v2+a^2*d*e*p*q*s*t*v2+a^2*d*e*p*q*t^2*v1-a^2*d*e*p*r^
2*t*v2-a^2*d*e*p*r*s*t*v1-a^2*d*e*p*r*t^2*v0-a*b^3*p*s*t^2*v3+a*b^3*p*t^3*v2-a*
b^3*q*r*t^2*v3-2*a*b^3*q*s*t^2*v2+2*a*b^3*r^2*s*t*v3-a*b^3*r^2*t^2*v2+a*b^3*r*s
^3*v3+a*b^3*r*s^2*t*v2+a*b^3*r*s*t^2*v1-a*b^3*r*t^3*v0+a*b^3*s^4*v2-a*b^3*s^2*t
^2*v0-3*a*b^2*c*p*r*t^2*v3-a*b^2*c*p*s^2*t*v3-3*a*b^2*c*p*s*t^2*v2-a*b^2*c*p*t^
3*v1+4*a*b^2*c*q*r*s*t*v3-2*a*b^2*c*q*r*t^2*v2+3*a*b^2*c*q*s^2*t*v2+2*a*b^2*c*q
*s*t^2*v1+2*a*b^2*c*r^3*t*v3+2*a*b^2*c*r^2*s^2*v3+2*a*b^2*c*r^2*t^2*v1+a*b^2*c*
r*s^3*v2-2*a*b^2*c*r*s*t^2*v0-a*b^2*c*s^4*v1-a*b^2*c*s^3*t*v0-2*a*b^2*d*p*q*t^2
*v3+4*a*b^2*d*p*r*s*t*v3+a*b^2*d*p*s^3*v3+4*a*b^2*d*p*s^2*t*v2+2*a*b^2*d*p*s*t^
2*v1-a*b^2*d*p*t^3*v0-2*a*b^2*d*q^2*t^2*v2+a*b^2*d*q*r^2*t*v3+a*b^2*d*q*r*s^2*
v3+2*a*b^2*d*q*r*t^2*v1+2*a*b^2*d*q*s^3*v2-2*a*b^2*d*q*s*t^2*v0-a*b^2*d*r^3*t*
v2-a*b^2*d*r^2*s^2*v2-a*b^2*d*r^2*s*t*v1-a*b^2*d*r^2*t^2*v0-a*b^2*d*r*s^3*v1-a*
b^2*d*r*s^2*t*v0-a*b^2*e*p^2*t^2*v3-a*b^2*e*p*q*t^2*v2+a*b^2*e*p*r^2*t*v3+a*b^2
*e*p*r*s^2*v3+a*b^2*e*p*r*t^2*v1+a*b^2*e*p*s^3*v2-a*b^2*e*p*s*t^2*v0-2*a*b*c^2*
p*r*t^2*v2-a*b*c^2*p*s^3*v3+2*a*b*c^2*p*s*t^2*v1+a*b*c^2*p*t^3*v0+5*a*b*c^2*q*r
^2*t*v3+a*b*c^2*q*r*s^2*v3+2*a*b*c^2*q*r*s*t*v2+2*a*b*c^2*q*r*t^2*v1-2*a*b*c^2*
q*s^2*t*v1-2*a*b*c^2*q*s*t^2*v0+a*b*c^2*r^3*s*v3+a*b*c^2*r^2*s*t*v1-a*b*c^2*r*s
^3*v1-a*b*c^2*r*s^2*t*v0-2*a*b*c*d*p^2*t^2*v3+a*b*c*d*p*q*s*t*v3-3*a*b*c*d*p*q*
t^2*v2+4*a*b*c*d*p*r^2*t*v3+2*a*b*c*d*p*r*s^2*v3+2*a*b*c*d*p*r*s*t*v2+4*a*b*c*d
*p*r*t^2*v1+a*b*c*d*p*s^3*v2-2*a*b*c*d*p*s^2*t*v1-3*a*b*c*d*p*s*t^2*v0+3*a*b*c*
d*q^2*r*t*v3+4*a*b*c*d*q^2*s*t*v2+2*a*b*c*d*q^2*t^2*v1+a*b*c*d*q*r^2*s*v3-3*a*b
*c*d*q*r^2*t*v2-a*b*c*d*q*r*s*t*v1-3*a*b*c*d*q*r*t^2*v0-2*a*b*c*d*q*s^3*v1-2*a*
b*c*d*q*s^2*t*v0-a*b*c*d*r^3*s*v2-a*b*c*d*r^2*s^2*v1-a*b*c*d*r^2*s*t*v0-a*b*c*e
*p^2*s*t*v3-2*a*b*c*e*p^2*t^2*v2+3*a*b*c*e*p*q*r*t*v3+2*a*b*c*e*p*q*s*t*v2+a*b*
c*e*p*q*t^2*v1+a*b*c*e*p*r^2*s*v3+a*b*c*e*p*r*s*t*v1-a*b*c*e*p*s^3*v1-a*b*c*e*p
*s^2*t*v0+2*a*b*d^2*p^2*s*t*v3+a*b*d^2*p^2*t^2*v2+2*a*b*d^2*p*q*r*t*v3+a*b*d^2*
p*q*s^2*v3+5*a*b*d^2*p*q*s*t*v2+3*a*b*d^2*p*q*t^2*v1-2*a*b*d^2*p*r^2*t*v2-a*b*d
^2*p*r*s^2*v2-2*a*b*d^2*p*r*s*t*v1-2*a*b*d^2*p*r*t^2*v0-a*b*d^2*p*s^3*v1-a*b*d^
2*p*s^2*t*v0-a*b*d^2*q^2*r*t*v2+a*b*d^2*q^2*s^2*v2-a*b*d^2*q^2*t^2*v0-a*b*d^2*q
*r^2*s*v2-a*b*d^2*q*r*s^2*v1-a*b*d^2*q*r*s*t*v0+2*a*b*d*e*p^2*r*t*v3+a*b*d*e*p^
2*s^2*v3+3*a*b*d*e*p^2*s*t*v2+2*a*b*d*e*p^2*t^2*v1-a*b*d*e*p*q*r*t*v2+a*b*d*e*p
*q*s^2*v2-a*b*d*e*p*q*t^2*v0-a*b*d*e*p*r^2*s*v2-a*b*d*e*p*r*s^2*v1-a*b*d*e*p*r*
s*t*v0+a*c^3*p^2*t^2*v3-a*c^3*p*q*s*t*v3+2*a*c^3*p*r^2*t*v3-a*c^3*p*r*s^2*v3+a*
c^3*p*r*t^2*v1+a*c^3*q^2*r*t*v3+a*c^3*q*r^2*s*v3-a*c^3*q*r*s*t*v1-a*c^3*q*r*t^2
*v0-a*c^2*d*p^2*s*t*v3-a*c^2*d*p^2*t^2*v2+5*a*c^2*d*p*q*r*t*v3-a*c^2*d*p*q*s^2*
v3+a*c^2*d*p*q*s*t*v2+2*a*c^2*d*p*q*t^2*v1+a*c^2*d*p*r^2*s*v3-2*a*c^2*d*p*r^2*t
*v2+a*c^2*d*p*r*s^2*v2-a*c^2*d*p*r*s*t*v1-2*a*c^2*d*p*r*t^2*v0+a*c^2*d*q^2*r*s*
v3-2*a*c^2*d*q^2*s*t*v1-2*a*c^2*d*q^2*t^2*v0-a*c^2*d*q*r^2*s*v2-a*c^2*d*q*r*s^2
*v1-a*c^2*d*q*r*s*t*v0+2*a*c^2*e*p^2*r*t*v3-a*c^2*e*p^2*s^2*v3+a*c^2*e*p^2*t^2*
v1+a*c^2*e*p*q*r*s*v3-a*c^2*e*p*q*s*t*v1-a*c^2*e*p*q*t^2*v0+2*a*c*d^2*p^2*r*t*
v3+a*c*d^2*p^2*s*t*v2+a*c*d^2*p^2*t^2*v1+a*c*d^2*p*q^2*t*v3+a*c*d^2*p*q*r*s*v3-\
3*a*c*d^2*p*q*r*t*v2+a*c*d^2*p*q*s^2*v2-3*a*c*d^2*p*q*s*t*v1-4*a*c*d^2*p*q*t^2*
v0-a*c*d^2*p*r^2*s*v2-a*c*d^2*p*r*s^2*v1-a*c*d^2*p*r*s*t*v0+a*c*d^2*q^3*t*v2-a*
c*d^2*q^2*r*s*v2-a*c*d^2*q^2*s^2*v1-a*c*d^2*q^2*s*t*v0+a*c*d*e*p^2*q*t*v3+a*c*d
*e*p^2*r*s*v3-2*a*c*d*e*p^2*r*t*v2+a*c*d*e*p^2*s^2*v2-a*c*d*e*p^2*s*t*v1-2*a*c*
d*e*p^2*t^2*v0+a*c*d*e*p*q^2*t*v2-a*c*d*e*p*q*r*s*v2-a*c*d*e*p*q*s^2*v1-a*c*d*e
*p*q*s*t*v0+a*d^3*p^2*q*t*v3-a*d^3*p^2*r*t*v2-a*d^3*p^2*s*t*v1-a*d^3*p^2*t^2*v0
+a*d^3*p*q^2*t*v2-a*d^3*p*q*r*s*v2-a*d^3*p*q*s^2*v1-a*d^3*p*q*s*t*v0+a*d^2*e*p^
3*t*v3+a*d^2*e*p^2*q*t*v2-a*d^2*e*p^2*r*s*v2-a*d^2*e*p^2*s^2*v1-a*d^2*e*p^2*s*t
*v0+b^4*p*s*t^2*v2-b^4*q*r*s*t*v3-b^4*q*s^2*t*v2+b^4*r^2*s^2*v3-b^4*r^2*s*t*v2+
b^4*r*s^3*v2-b^4*r*s*t^2*v0-2*b^3*c*p*r*s*t*v3+b^3*c*p*r*t^2*v2-b^3*c*p*s^2*t*
v2-b^3*c*p*s*t^2*v1-b^3*c*q*r^2*t*v3+b^3*c*q*r*s^2*v3-2*b^3*c*q*r*s*t*v2+b^3*c*
q*s^3*v2+b^3*c*q*s^2*t*v1+2*b^3*c*r^3*s*v3-b^3*c*r^3*t*v2+b^3*c*r^2*s^2*v2+b^3*
c*r^2*s*t*v1-b^3*c*r^2*t^2*v0-b^3*c*r*s^3*v1-b^3*c*r*s^2*t*v0-b^3*d*p*q*s*t*v3+
b^3*d*p*q*t^2*v2+2*b^3*d*p*r*s^2*v3+b^3*d*p*s^3*v2-b^3*d*p*s*t^2*v0-b^3*d*q^2*r
*t*v3-2*b^3*d*q^2*s*t*v2+b^3*d*q*r^2*s*v3-b^3*d*q*r^2*t*v2+2*b^3*d*q*r*s^2*v2+b
^3*d*q*r*s*t*v1-b^3*d*q*r*t^2*v0-b^3*d*r^3*s*v2-b^3*d*r^2*s^2*v1-b^3*d*r^2*s*t*
v0+b^3*e*p^2*t^2*v2-b^3*e*p*q*r*t*v3-b^3*e*p*q*s*t*v2+b^3*e*p*r^2*s*v3-b^3*e*p*
r^2*t*v2+b^3*e*p*r*s^2*v2-b^3*e*p*r*t^2*v0-2*b^2*c^2*p*r^2*t*v3-b^2*c^2*p*r*s^2
*v3-b^2*c^2*p*r*s*t*v2-b^2*c^2*p*r*t^2*v1+b^2*c^2*p*s^2*t*v1+b^2*c^2*p*s*t^2*v0
+3*b^2*c^2*q*r^2*s*v3-b^2*c^2*q*r^2*t*v2+b^2*c^2*q*r*s^2*v2+2*b^2*c^2*q*r*s*t*
v1-b^2*c^2*q*s^3*v1-b^2*c^2*q*s^2*t*v0+b^2*c^2*r^4*v3+b^2*c^2*r^3*t*v1-b^2*c^2*
r^2*s^2*v1-b^2*c^2*r^2*s*t*v0-2*b^2*c*d*p^2*s*t*v3-3*b^2*c*d*p*q*r*t*v3+b^2*c*d
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c*d*p*r*s^2*v2+2*b^2*c*d*p*r*s*t*v1-b^2*c*d*p*r*t^2*v0-b^2*c*d*p*s^3*v1-b^2*c*d
*p*s^2*t*v0+b^2*c*d*q^2*r*s*v3-2*b^2*c*d*q^2*r*t*v2+2*b^2*c*d*q^2*s^2*v2+2*b^2*
c*d*q^2*s*t*v1+b^2*c*d*q*r^3*v3-b^2*c*d*q*r^2*s*v2+2*b^2*c*d*q*r^2*t*v1-3*b^2*c
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t*v0-2*b^2*c*e*p^2*r*t*v3-b^2*c*e*p^2*s*t*v2-b^2*c*e*p^2*t^2*v1+b^2*c*e*p*q*r*s
*v3-b^2*c*e*p*q*r*t*v2+b^2*c*e*p*q*s^2*v2+b^2*c*e*p*q*s*t*v1+b^2*c*e*p*r^3*v3+b
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d^2*p^2*s*t*v2-b^2*d^2*p*q^2*t*v3+2*b^2*d^2*p*q*r*s*v3+2*b^2*d^2*p*q*s^2*v2+b^2
*d^2*p*q*s*t*v1-b^2*d^2*p*q*t^2*v0-2*b^2*d^2*p*r^2*s*v2-2*b^2*d^2*p*r*s^2*v1-2*
b^2*d^2*p*r*s*t*v0-b^2*d^2*q^3*t*v2+b^2*d^2*q^2*r*s*v2+b^2*d^2*q^2*r*t*v1-b^2*d
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*r*s*v2+b^2*d*e*p*q*r*t*v1-b^2*d*e*p*r^3*v2-b^2*d*e*p*r^2*s*v1-b^2*d*e*p*r^2*t*
v0+b*c^3*p^2*s*t*v3-b*c^3*p*q*s^2*v3-b*c^3*p*r^2*s*v3+b*c^3*p*r*s*t*v1+b*c^3*p*
r*t^2*v0+b*c^3*q^2*r*s*v3+2*b*c^3*q*r^3*v3+b*c^3*q*r^2*t*v1-b*c^3*q*r*s^2*v1-b*
c^3*q*r*s*t*v0-2*b*c^2*d*p^2*r*t*v3-b*c^2*d*p^2*s^2*v3-b*c^2*d*p^2*s*t*v2+2*b*c
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2*d*p*q*t^2*v0+2*b*c^2*d*p*r^3*v3+b*c^2*d*p*r^2*s*v2+2*b*c^2*d*p*r^2*t*v1-b*c^2
*d*p*r*s^2*v1-b*c^2*d*p*r*s*t*v0+2*b*c^2*d*q^2*r^2*v3+2*b*c^2*d*q^2*r*t*v1-2*b*
c^2*d*q^2*s^2*v1-2*b*c^2*d*q^2*s*t*v0-2*b*c^2*d*q*r^3*v2-2*b*c^2*d*q*r^2*s*v1-2
*b*c^2*d*q*r^2*t*v0-b*c^2*e*p^2*r*s*v3+b*c^2*e*p^2*s*t*v1+b*c^2*e*p^2*t^2*v0+2*
b*c^2*e*p*q*r^2*v3+b*c^2*e*p*q*r*t*v1-b*c^2*e*p*q*s^2*v1-b*c^2*e*p*q*s*t*v0-2*b
*c*d^2*p^2*q*t*v3+2*b*c*d^2*p^2*r*s*v3+b*c*d^2*p^2*r*t*v2+b*c*d^2*p^2*s^2*v2+b*
c*d^2*p^2*s*t*v1+b*c*d^2*p*q^2*s*v3-b*c*d^2*p*q^2*t*v2+2*b*c*d^2*p*q*r^2*v3+3*b
*c*d^2*p*q*r*t*v1-3*b*c*d^2*p*q*s^2*v1-3*b*c*d^2*p*q*s*t*v0-2*b*c*d^2*p*r^3*v2-\
2*b*c*d^2*p*r^2*s*v1-2*b*c*d^2*p*r^2*t*v0+b*c*d^2*q^3*s*v2+b*c*d^2*q^3*t*v1-2*b
*c*d^2*q^2*r^2*v2-2*b*c*d^2*q^2*r*s*v1-2*b*c*d^2*q^2*r*t*v0-2*b*c*d*e*p^3*t*v3+
b*c*d*e*p^2*q*s*v3-b*c*d*e*p^2*q*t*v2+2*b*c*d*e*p^2*r^2*v3+b*c*d*e*p^2*r*s*v2+2
*b*c*d*e*p^2*r*t*v1-b*c*d*e*p^2*s^2*v1-b*c*d*e*p^2*s*t*v0+b*c*d*e*p*q^2*s*v2+b*
c*d*e*p*q^2*t*v1-2*b*c*d*e*p*q*r^2*v2-2*b*c*d*e*p*q*r*s*v1-2*b*c*d*e*p*q*r*t*v0
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s*t*v0+b*d^3*p*q^2*s*v2+b*d^3*p*q^2*t*v1-2*b*d^3*p*q*r^2*v2-2*b*d^3*p*q*r*s*v1-\
2*b*d^3*p*q*r*t*v0+b*d^2*e*p^3*s*v3+b*d^2*e*p^3*t*v2+b*d^2*e*p^2*q*s*v2+b*d^2*e
*p^2*q*t*v1-2*b*d^2*e*p^2*r^2*v2-2*b*d^2*e*p^2*r*s*v1-2*b*d^2*e*p^2*r*t*v0+c^4*
p^2*r*t*v3-c^4*p*q*r*s*v3+c^4*q^2*r^2*v3+c^3*d*p^2*q*t*v3-c^3*d*p^2*r*s*v3-c^3*
d*p^2*r*t*v2-c^3*d*p*q^2*s*v3+2*c^3*d*p*q*r^2*v3+c^3*d*p*q*r*s*v2+c^3*d*p*q*r*t
*v1+c^3*d*q^3*r*v3-c^3*d*q^2*r^2*v2-c^3*d*q^2*r*s*v1-c^3*d*q^2*r*t*v0+c^3*e*p^3
*t*v3-c^3*e*p^2*q*s*v3+c^3*e*p*q^2*r*v3-c^2*d^2*p^2*q*s*v3-c^2*d^2*p^2*q*t*v2+c
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2*d^2*p*q^2*s*v2+c^2*d^2*p*q^2*t*v1-2*c^2*d^2*p*q*r^2*v2-2*c^2*d^2*p*q*r*s*v1-2
*c^2*d^2*p*q*r*t*v0-c^2*d^2*q^3*r*v2-c^2*d^2*q^3*s*v1-c^2*d^2*q^3*t*v0-c^2*d*e*
p^3*s*v3-c^2*d*e*p^3*t*v2+2*c^2*d*e*p^2*q*r*v3+c^2*d*e*p^2*q*s*v2+c^2*d*e*p^2*q
*t*v1-c^2*d*e*p*q^2*r*v2-c^2*d*e*p*q^2*s*v1-c^2*d*e*p*q^2*t*v0+c*d^3*p^2*q*r*v3
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r*t*v0-2*c*d^3*p*q^2*r*v2-2*c*d^3*p*q^2*s*v1-2*c*d^3*p*q^2*t*v0+c*d^2*e*p^3*r*
v3+c*d^2*e*p^3*s*v2+c*d^2*e*p^3*t*v1-2*c*d^2*e*p^2*q*r*v2-2*c*d^2*e*p^2*q*s*v1-\
2*c*d^2*e*p^2*q*t*v0-d^4*p^2*q*r*v2-d^4*p^2*q*s*v1-d^4*p^2*q*t*v0-d^3*e*p^3*r*
v2-d^3*e*p^3*s*v1-d^3*e*p^3*t*v0-a^3*c*t^3*v4-a^3*d*s*t^2*v4-a^3*d*t^3*v3-a^3*e
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2*v3-2*a^2*b*e*s^2*t*v3-5*a^2*b*e*s*t^2*v2-3*a^2*b*e*t^3*v1-a^2*c^2*r*t^2*v4+a^
2*c^2*s^2*t*v4+2*a^2*c^2*s*t^2*v3+a^2*c^2*t^3*v2-2*a^2*c*d*q*t^2*v4+a^2*c*d*r*s
*t*v4-4*a^2*c*d*r*t^2*v3+2*a^2*c*d*s^2*t*v3-a^2*c*d*s*t^2*v2-3*a^2*c*d*t^3*v1-a
^2*c*e*p*t^2*v4-a^2*c*e*r^2*t*v4-3*a^2*c*e*r*s*t*v3+a^2*c*e*r*t^2*v2-2*a^2*c*e*
s^2*t*v2+2*a^2*c*e*t^3*v0-a^2*d^2*p*t^2*v4-a^2*d^2*q*s*t*v4-a^2*d^2*q*t^2*v3+a^
2*d^2*r^2*t*v4+2*a^2*d^2*r*t^2*v2-a^2*d^2*s^2*t*v2+a^2*d^2*t^3*v0-a^2*d*e*p*s*t
*v4-3*a^2*d*e*p*t^2*v3-2*a^2*d*e*q*t^2*v2-a^2*d*e*r^2*t*v3+a^2*d*e*r*s*t*v2-a^2
*d*e*r*t^2*v1+2*a^2*d*e*s^2*t*v1+2*a^2*d*e*s*t^2*v0-a^2*e^2*p*s*t*v3-a^2*e^2*p*
t^2*v2-a^2*e^2*q*s*t*v2-a^2*e^2*q*t^2*v1+a^2*e^2*r^2*t*v2+a^2*e^2*r*s*t*v1+a^2*
e^2*r*t^2*v0+a*b^3*s*t^2*v4-a*b^3*t^3*v3-a*b^2*c*r*t^2*v4+a*b^2*c*s^2*t*v4-a*b^
2*c*s*t^2*v3-3*a*b^2*c*t^3*v2+2*a*b^2*d*q*t^2*v4+a*b^2*d*r*s*t*v4+a*b^2*d*r*t^2
*v3-a*b^2*d*s^3*v4+a*b^2*d*s^2*t*v3+4*a*b^2*d*s*t^2*v2+2*a*b^2*d*t^3*v1+a*b^2*e
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-a*b^2*e*s^3*v3-5*a*b^2*e*s^2*t*v2-2*a*b^2*e*s*t^2*v1+2*a*b^2*e*t^3*v0-a*b*c^2*
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*b*c*d*t^3*v0+a*b*c*e*p*s*t*v4+3*a*b*c*e*p*t^2*v3-3*a*b*c*e*q*r*t*v4-3*a*b*c*e*
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*v3-4*a*b*c*e*r*t^2*v1-2*a*b*c*e*s^3*v2+3*a*b*c*e*s^2*t*v1+5*a*b*c*e*s*t^2*v0-2
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2*q*t^2*v2+a*b*d^2*r^2*s*v4+a*b*d^2*r*s*t*v2-a*b*d^2*s^3*v2-a*b*d^2*s^2*t*v1-2*
a*b*d*e*p*r*t*v4-a*b*d*e*p*s^2*v4-4*a*b*d*e*p*s*t*v3-a*b*d*e*p*t^2*v2-3*a*b*d*e
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t*v2+a*b*d*e*r*s^2*v2+a*b*d*e*r*s*t*v1+2*a*b*d*e*r*t^2*v0+2*a*b*d*e*s^3*v1+2*a*
b*d*e*s^2*t*v0-2*a*b*e^2*p*r*t*v3-a*b*e^2*p*s^2*v3-3*a*b*e^2*p*s*t*v2-2*a*b*e^2
*p*t^2*v1+a*b*e^2*q*r*t*v2-a*b*e^2*q*s^2*v2+a*b*e^2*q*t^2*v0+a*b*e^2*r^2*s*v2+a
*b*e^2*r*s^2*v1+a*b*e^2*r*s*t*v0-a*c^3*p*t^2*v4+a*c^3*q*s*t*v4+a*c^3*q*t^2*v3+3
*a*c^3*r*s*t*v3-a*c^3*s^3*v3-a*c^3*t^3*v0+a*c^2*d*p*s*t*v4-a*c^2*d*p*t^2*v3+a*c
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2*p*t^2*v2-a*c*d^2*q^2*t*v4+a*c*d^2*q*r*s*v4-2*a*c*d^2*q*r*t*v3+a*c*d^2*q*s^2*
v3-2*a*c*d^2*q*s*t*v2-4*a*c*d^2*q*t^2*v1+2*a*c*d^2*r^2*t*v2-a*c*d^2*r*s^2*v2+2*
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*t*v4-a*c*d*e*p*r*s*v4-8*a*c*d*e*p*r*t*v3+a*c*d*e*p*s^2*v3-4*a*c*d*e*p*s*t*v2-5
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d*e*q*t^2*v0+a*c*d*e*r^2*s*v2+a*c*d*e*r*s^2*v1+a*c*d*e*r*s*t*v0-a*c*e^2*p*q*t*
v3-a*c*e^2*p*r*s*v3+2*a*c*e^2*p*r*t*v2-a*c*e^2*p*s^2*v2+a*c*e^2*p*s*t*v1+2*a*c*
e^2*p*t^2*v0-a*c*e^2*q^2*t*v2+a*c*e^2*q*r*s*v2+a*c*e^2*q*s^2*v1+a*c*e^2*q*s*t*
v0-a*d^3*p*q*t*v4+a*d^3*p*r*s*v4-a*d^3*p*s*t*v2-a*d^3*p*t^2*v1+2*a*d^3*q*r*t*v2
-a*d^3*q*s^2*v2+a*d^3*q*t^2*v0-a*d^2*e*p^2*t*v4-a*d^2*e*p*q*t*v3-a*d^2*e*p*r*s*
v3+4*a*d^2*e*p*r*t*v2-a*d^2*e*p*s^2*v2+3*a*d^2*e*p*s*t*v1+4*a*d^2*e*p*t^2*v0-a*
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v0+b^4*r*t^2*v4+b^4*t^3*v2+b^3*c*r*s*t*v4-2*b^3*c*r*t^2*v3-b^3*c*s*t^2*v2-b^3*c
*t^3*v1+b^3*d*q*s*t*v4-b^3*d*q*t^2*v3+2*b^3*d*r^2*t*v4-b^3*d*r*s^2*v4+2*b^3*d*r
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v3+2*b^3*e*q*t^2*v2-b^3*e*r^2*s*v4-b^3*e*r^2*t*v3-2*b^3*e*r*s^2*v3-b^3*e*r*s*t*
v2-b^3*e*r*t^2*v1-b^3*e*s^3*v2+b^3*e*s*t^2*v0-b^2*c^2*r^2*t*v4+b^2*c^2*r*s^2*v4
-b^2*c^2*r*s*t*v3-b^2*c^2*r*t^2*v2+b^2*c^2*s*t^2*v1+b^2*c^2*t^3*v0+2*b^2*c*d*p*
s*t*v4-2*b^2*c*d*p*t^2*v3+2*b^2*c*d*q*r*t*v4-b^2*c*d*q*s^2*v4-b^2*c*d*q*s*t*v3-\
2*b^2*c*d*q*t^2*v2+b^2*c*d*r^2*s*v4+2*b^2*c*d*r*s^2*v3+2*b^2*c*d*r*s*t*v2+b^2*c
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v2+b^2*e^2*p*t^2*v0+b^2*e^2*q^2*t*v2-b^2*e^2*q*r*s*v2-b^2*e^2*q*r*t*v1+b^2*e^2*
r^3*v2+b^2*e^2*r^2*s*v1+b^2*e^2*r^2*t*v0-b*c^3*p*s*t*v4+b*c^3*p*t^2*v3-b*c^3*q*
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p*r*t*v4+b*c^2*d*p*s^2*v4-4*b*c^2*d*p*s*t*v3-b*c^2*d*p*t^2*v2+2*b*c^2*d*q*r*s*
v4-b*c^2*d*q*r*t*v3+2*b*c^2*d*q*s^2*v3+2*b*c^2*d*q*t^2*v1+b*c^2*d*r^2*s*v3-2*b*
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*b*c^2*e*q*r^2*v4-5*b*c^2*e*q*r*s*v3+2*b*c^2*e*q*r*t*v2-2*b*c^2*e*q*s^2*v2+2*b*
c^2*e*q*t^2*v0-2*b*c^2*e*r^3*v3-2*b*c^2*e*r^2*t*v1+2*b*c^2*e*r*s^2*v1+2*b*c^2*e
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t*v2+b*c*d^2*p*t^2*v1-b*c*d^2*q^2*s*v4-b*c*d^2*q^2*t*v3+2*b*c*d^2*q*r^2*v4+b*c*
d^2*q*r*s*v3+b*c*d^2*q*r*t*v2-b*c*d^2*q*s^2*v2-2*b*c*d^2*q*s*t*v1-b*c*d^2*q*t^2
*v0-b*c*d^2*r^2*s*v2-b*c*d^2*r*s^2*v1-b*c*d^2*r*s*t*v0+2*b*c*d*e*p^2*t*v4-b*c*d
*e*p*q*s*v4-b*c*d*e*p*q*t*v3-2*b*c*d*e*p*r^2*v4-4*b*c*d*e*p*r*s*v3-3*b*c*d*e*p*
s^2*v2-2*b*c*d*e*p*s*t*v1+b*c*d*e*p*t^2*v0-4*b*c*d*e*q*r^2*v3+b*c*d*e*q*r*s*v2-\
3*b*c*d*e*q*r*t*v1+4*b*c*d*e*q*s^2*v1+4*b*c*d*e*q*s*t*v0+2*b*c*d*e*r^3*v2+2*b*c
*d*e*r^2*s*v1+2*b*c*d*e*r^2*t*v0+2*b*c*e^2*p^2*t*v3-b*c*e^2*p*q*s*v3+b*c*e^2*p*
q*t*v2-2*b*c*e^2*p*r^2*v3-b*c*e^2*p*r*s*v2-2*b*c*e^2*p*r*t*v1+b*c*e^2*p*s^2*v1+
b*c*e^2*p*s*t*v0-b*c*e^2*q^2*s*v2-b*c*e^2*q^2*t*v1+2*b*c*e^2*q*r^2*v2+2*b*c*e^2
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-2*b*d^2*e*p*r^2*v3+b*d^2*e*p*r*s*v2-2*b*d^2*e*p*r*t*v1+3*b*d^2*e*p*s^2*v1+3*b*
d^2*e*p*s*t*v0-b*d^2*e*q^2*s*v2-b*d^2*e*q^2*t*v1+2*b*d^2*e*q*r^2*v2+2*b*d^2*e*q
*r*s*v1+2*b*d^2*e*q*r*t*v0-2*b*d*e^2*p^2*s*v3-2*b*d*e^2*p^2*t*v2-2*b*d*e^2*p*q*
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v0+c^4*p*s*t*v3+2*c^4*q*r*t*v3-c^4*q*s^2*v3-c^3*d*p*q*t*v4-c^3*d*p*s^2*v3-c^3*d
*p*s*t*v2+c^3*d*q^2*s*v4+c^3*d*q^2*t*v3+c^3*d*q*r*s*v3-2*c^3*d*q*r*t*v2+c^3*d*q
*s^2*v2-c^3*d*q*t^2*v0-c^3*e*p^2*t*v4+c^3*e*p*q*s*v4+2*c^3*e*p*q*t*v3+c^3*e*p*r
*s*v3-c^3*e*p*s*t*v1-c^3*e*p*t^2*v0-c^3*e*q^2*r*v4-c^3*e*q^2*s*v3-2*c^3*e*q*r^2
*v3-c^3*e*q*r*t*v1+c^3*e*q*s^2*v1+c^3*e*q*s*t*v0+c^2*d^2*p*q*s*v4-c^2*d^2*p*q*t
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q*t*v2-2*c^2*d*e*p*r^2*v3-c^2*d*e*p*r*s*v2-2*c^2*d*e*p*r*t*v1+c^2*d*e*p*s^2*v1+
c^2*d*e*p*s*t*v0-3*c^2*d*e*q^2*r*v3+2*c^2*d*e*q*r^2*v2+2*c^2*d*e*q*r*s*v1+2*c^2
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s*v2-c^2*e^2*p*q*t*v1+c^2*e^2*q^2*r*v2+c^2*e^2*q^2*s*v1+c^2*e^2*q^2*t*v0+2*c*d^
3*p*q*r*v4+c*d^3*p*q*s*v3+c*d^3*p*q*t*v2-c*d^3*p*r*s*v2-c*d^3*p*s^2*v1-c*d^3*p*
s*t*v0-c*d^3*q^2*s*v2-c*d^3*q^2*t*v1-c*d^2*e*p^2*r*v4+c*d^2*e*p^2*s*v3+c*d^2*e*
p^2*t*v2-4*c*d^2*e*p*q*r*v3-2*c*d^2*e*p*q*s*v2-2*c*d^2*e*p*q*t*v1+2*c*d^2*e*p*r
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v1+2*c*d^2*e*q^2*t*v0-2*c*d*e^2*p^2*r*v3-2*c*d*e^2*p^2*s*v2-2*c*d*e^2*p^2*t*v1+
4*c*d*e^2*p*q*r*v2+4*c*d*e^2*p*q*s*v1+4*c*d*e^2*p*q*t*v0+d^4*p^2*r*v4-d^4*p*q*s
*v2-d^4*p*q*t*v1-d^3*e*p^2*r*v3-d^3*e*p^2*s*v2-d^3*e*p^2*t*v1+2*d^3*e*p*q*r*v2+
2*d^3*e*p*q*s*v1+2*d^3*e*p*q*t*v0+3*d^2*e^2*p^2*r*v2+3*d^2*e^2*p^2*s*v1+3*d^2*e
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t*v3-a*c*d*e*t^2*v2+a*c*e^2*q*t*v4+a*c*e^2*r*s*v4+2*a*c*e^2*r*t*v3+a*c*e^2*s^2*
v3+3*a*c*e^2*s*t*v2+2*a*c*e^2*t^2*v1-2*a*d^3*r*t*v4+a*d^3*s^2*v4-a*d^3*t^2*v2+a
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v3-3*b^2*d*e*t^2*v2-b^2*e^2*q*t*v4+2*b^2*e^2*r*s*v4+2*b^2*e^2*r*t*v3+b^2*e^2*s^
2*v3+2*b^2*e^2*s*t*v2+b^2*e^2*t^2*v1-b*c^3*t^2*v4+b*c^2*d*s*t*v4-3*b*c^2*d*t^2*
v3-b*c^2*e*s^2*v4+b*c^2*e*s*t*v3+2*b*c^2*e*t^2*v2+2*b*c*d^2*r*t*v4+2*b*c*d^2*s*
t*v3+2*b*c*d^2*t^2*v2-3*b*c*d*e*r*s*v4-2*b*c*d*e*r*t*v3-2*b*c*d*e*s^2*v3-3*b*c*
d*e*s*t*v2-b*c*d*e*t^2*v1-2*b*c*e^2*p*t*v4+b*c*e^2*q*s*v4+b*c*e^2*q*t*v3+2*b*c*
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c*e^2*t^2*v0-2*b*d^3*q*t*v4+b*d^3*r*s*v4-b*d^3*s*t*v2-b*d^3*t^2*v1-2*b*d^2*e*p*
t*v4+b*d^2*e*q*s*v4+b*d^2*e*q*t*v3-2*b*d^2*e*r^2*v4-b*d^2*e*r*s*v3+b*d^2*e*s^2*
v2+3*b*d^2*e*s*t*v1+2*b*d^2*e*t^2*v0+2*b*d*e^2*p*s*v4-2*b*d*e^2*q*t*v2+2*b*d*e^
2*r^2*v3+2*b*d*e^2*r*t*v1-2*b*d*e^2*s^2*v1-2*b*d*e^2*s*t*v0+b*e^3*p*s*v3+b*e^3*
p*t*v2+b*e^3*q*s*v2+b*e^3*q*t*v1-2*b*e^3*r^2*v2-2*b*e^3*r*s*v1-2*b*e^3*r*t*v0+c
^4*t^2*v3-c^3*d*s*t*v3-c^3*d*t^2*v2-c^3*e*q*t*v4-2*c^3*e*r*t*v3+c^3*e*s^2*v3-c^
3*e*t^2*v1+2*c^2*d^2*q*t*v4+c^2*d^2*r*t*v3+c^2*d^2*s*t*v2+c^2*d^2*t^2*v1+2*c^2*
d*e*p*t*v4-3*c^2*d*e*q*s*v4-3*c^2*d*e*q*t*v3-c^2*d*e*r*s*v3+2*c^2*d*e*r*t*v2-c^
2*d*e*s^2*v2+c^2*d*e*s*t*v1+2*c^2*d*e*t^2*v0-c^2*e^2*p*s*v4-2*c^2*e^2*p*t*v3+2*
c^2*e^2*q*r*v4+2*c^2*e^2*q*s*v3+c^2*e^2*q*t*v2+c^2*e^2*r^2*v3+c^2*e^2*r*t*v1-c^
2*e^2*s^2*v1-c^2*e^2*s*t*v0+c*d^3*q*s*v4+c*d^3*q*t*v3-c*d^3*r*t*v2-c*d^3*s*t*v1
-c*d^3*t^2*v0-2*c*d^2*e*p*s*v4+c*d^2*e*p*t*v3-2*c*d^2*e*q*r*v4-2*c*d^2*e*q*s*v3
+c*d^2*e*q*t*v2+c*d^2*e*r*s*v2+c*d^2*e*s^2*v1+c*d^2*e*s*t*v0+2*c*d*e^2*p*r*v4+3
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v1-2*c*e^3*q*t*v0+d^4*p*s*v4-d^4*q*t*v2-2*d^3*e*p*r*v4-d^3*e*p*s*v3-d^3*e*p*t*
v2+d^3*e*q*s*v2+d^3*e*q*t*v1+2*d^2*e^2*p*r*v3+2*d^2*e^2*p*s*v2+2*d^2*e^2*p*t*v1
-d^2*e^2*q*r*v2-d^2*e^2*q*s*v1-d^2*e^2*q*t*v0-3*d*e^3*p*r*v2-3*d*e^3*p*s*v1-3*d
*e^3*p*t*v0-a*e^3*t*v4+2*b*d*e^2*t*v4-b*e^3*s*v4-b*e^3*t*v3+c^2*e^2*t*v4-3*c*d^
2*e*t*v4+2*c*d*e^2*s*v4+2*c*d*e^2*t*v3-c*e^3*r*v4-c*e^3*s*v3-c*e^3*t*v2+d^4*t*
v4-d^3*e*s*v4-d^3*e*t*v3+d^2*e^2*r*v4+d^2*e^2*s*v3+d^2*e^2*t*v2-d*e^3*r*v3-d*e^
3*s*v2-d*e^3*t*v1+e^4*r*v2+e^4*s*v1+e^4*t*v0




beta[2,4] = a^4*s*t^3*v3+a^4*t^4*v2+3*a^3*b*s^2*t^2*v3+2*a^3*b*s*t^3*v2-a^3*b*t
^4*v1+2*a^3*c*r*s*t^2*v3+2*a^3*c*r*t^3*v2-a^3*c*s^2*t^2*v2-2*a^3*c*s*t^3*v1-a^3
*c*t^4*v0+a^3*d*p*t^3*v3+a^3*d*q*s*t^2*v3+2*a^3*d*q*t^3*v2-a^3*d*r*s*t^2*v2-a^3
*d*s^2*t^2*v1-a^3*d*s*t^3*v0+a^3*e*p*s*t^2*v3+a^3*e*p*t^3*v2+a^2*b^2*r*s*t^2*v3
+a^2*b^2*r*t^3*v2+3*a^2*b^2*s^3*t*v3+a^2*b^2*s^2*t^2*v2-a^2*b^2*s*t^3*v1+a^2*b^
2*t^4*v0-2*a^2*b*c*p*t^3*v3+3*a^2*b*c*q*s*t^2*v3+a^2*b*c*q*t^3*v2+4*a^2*b*c*r*s
^2*t*v3+3*a^2*b*c*r*s*t^2*v2-3*a^2*b*c*r*t^3*v1-2*a^2*b*c*s^3*t*v2-2*a^2*b*c*s^
2*t^2*v1+4*a^2*b*d*p*s*t^2*v3+2*a^2*b*d*p*t^3*v2+2*a^2*b*d*q*s^2*t*v3+2*a^2*b*d
*q*s*t^2*v2-2*a^2*b*d*q*t^3*v1-2*a^2*b*d*r*s^2*t*v2-2*a^2*b*d*s^3*t*v1-2*a^2*b*
d*s^2*t^2*v0+2*a^2*b*e*p*s^2*t*v3+a^2*b*e*p*s*t^2*v2-a^2*b*e*p*t^3*v1+a^2*c^2*p
*t^3*v2+a^2*c^2*q*s^2*t*v3-a^2*c^2*q*s*t^2*v2-a^2*c^2*q*t^3*v1+a^2*c^2*r^2*s*t*
v3+a^2*c^2*r^2*t^2*v2-a^2*c^2*r*s^2*t*v2-4*a^2*c^2*r*s*t^2*v1-2*a^2*c^2*r*t^3*
v0+a^2*c^2*s^3*t*v1+a^2*c^2*s^2*t^2*v0+a^2*c*d*p*r*t^2*v3+a^2*c*d*p*s^2*t*v3-a^
2*c*d*p*s*t^2*v2-2*a^2*c*d*p*t^3*v1+a^2*c*d*q*r*s*t*v3+2*a^2*c*d*q*r*t^2*v2-2*a
^2*c*d*q*s^2*t*v2-4*a^2*c*d*q*s*t^2*v1-2*a^2*c*d*q*t^3*v0-a^2*c*d*r^2*s*t*v2-a^
2*c*d*r*s^2*t*v1-a^2*c*d*r*s*t^2*v0+a^2*c*e*p*r*s*t*v3+a^2*c*e*p*r*t^2*v2-a^2*c
*e*p*s^2*t*v2-2*a^2*c*e*p*s*t^2*v1-a^2*c*e*p*t^3*v0+a^2*d^2*p*q*t^2*v3-a^2*d^2*
p*s^2*t*v2-2*a^2*d^2*p*s*t^2*v1-a^2*d^2*p*t^3*v0+a^2*d^2*q^2*t^2*v2-a^2*d^2*q*r
*s*t*v2-a^2*d^2*q*s^2*t*v1-a^2*d^2*q*s*t^2*v0+a^2*d*e*p^2*t^2*v3+a^2*d*e*p*q*t^
2*v2-a^2*d*e*p*r*s*t*v2-a^2*d*e*p*s^2*t*v1-a^2*d*e*p*s*t^2*v0+a*b^3*p*t^3*v3-a*
b^3*q*s*t^2*v3+2*a*b^3*r*s^2*t*v3+a*b^3*r*s*t^2*v2+a*b^3*s^4*v3+a*b^3*s*t^3*v0-\
3*a*b^2*c*p*s*t^2*v3-a*b^2*c*p*t^3*v2+4*a*b^2*c*q*s^2*t*v3+2*a*b^2*c*q*s*t^2*v2
+2*a*b^2*c*r^2*s*t*v3+2*a*b^2*c*r^2*t^2*v2+2*a*b^2*c*r*s^3*v3-2*a*b^2*c*r*s*t^2
*v1+2*a*b^2*c*r*t^3*v0-a*b^2*c*s^4*v2+a*b^2*c*s^2*t^2*v0+a*b^2*d*p*r*t^2*v3+4*a
*b^2*d*p*s^2*t*v3+2*a*b^2*d*p*s*t^2*v2-a*b^2*d*p*t^3*v1+a*b^2*d*q*r*s*t*v3+2*a*
b^2*d*q*r*t^2*v2+a*b^2*d*q*s^3*v3+2*a*b^2*d*q*t^3*v0-a*b^2*d*r^2*s*t*v2-a*b^2*d
*r*s^3*v2-a*b^2*d*r*s^2*t*v1-a*b^2*d*r*s*t^2*v0-a*b^2*d*s^4*v1-a*b^2*d*s^3*t*v0
+a*b^2*e*p*r*s*t*v3+a*b^2*e*p*r*t^2*v2+a*b^2*e*p*s^3*v3+a*b^2*e*p*t^3*v0-3*a*b*
c^2*p*r*t^2*v3+2*a*b*c^2*p*s*t^2*v2+a*b*c^2*p*t^3*v1+5*a*b*c^2*q*r*s*t*v3+2*a*b
*c^2*q*r*t^2*v2+a*b*c^2*q*s^3*v3-2*a*b*c^2*q*s^2*t*v2-2*a*b*c^2*q*s*t^2*v1+a*b*
c^2*r^2*s^2*v3+a*b*c^2*r^2*s*t*v2-3*a*b*c^2*r^2*t^2*v1-a*b*c^2*r*s^3*v2-a*b*c^2
*r*s^2*t*v1+a*b*c^2*r*s*t^2*v0+a*b*c^2*s^4*v1+a*b*c^2*s^3*t*v0-a*b*c*d*p*q*t^2*
v3+5*a*b*c*d*p*r*s*t*v3+4*a*b*c*d*p*r*t^2*v2+a*b*c*d*p*s^3*v3-2*a*b*c*d*p*s^2*t
*v2-a*b*c*d*p*s*t^2*v1+2*a*b*c*d*p*t^3*v0+3*a*b*c*d*q^2*s*t*v3+2*a*b*c*d*q^2*t^
2*v2+a*b*c*d*q*r*s^2*v3-a*b*c*d*q*r*s*t*v2-4*a*b*c*d*q*r*t^2*v1-2*a*b*c*d*q*s^3
*v2-3*a*b*c*d*q*s^2*t*v1-a*b*c*d*q*s*t^2*v0-a*b*c*d*r^2*s^2*v2-a*b*c*d*r*s^3*v1
-a*b*c*d*r*s^2*t*v0-2*a*b*c*e*p^2*t^2*v3+3*a*b*c*e*p*q*s*t*v3+a*b*c*e*p*q*t^2*
v2+a*b*c*e*p*r*s^2*v3+a*b*c*e*p*r*s*t*v2-2*a*b*c*e*p*r*t^2*v1-a*b*c*e*p*s^3*v2+
a*b*c*e*p*s*t^2*v0+a*b*d^2*p^2*t^2*v3+3*a*b*d^2*p*q*s*t*v3+3*a*b*d^2*p*q*t^2*v2
-2*a*b*d^2*p*r*s*t*v2-a*b*d^2*p*r*t^2*v1-a*b*d^2*p*s^3*v2-3*a*b*d^2*p*s^2*t*v1-\
2*a*b*d^2*p*s*t^2*v0-a*b*d^2*q^2*t^2*v1-a*b*d^2*q*r*s^2*v2-a*b*d^2*q*s^3*v1-a*b
*d^2*q*s^2*t*v0+3*a*b*d*e*p^2*s*t*v3+2*a*b*d*e*p^2*t^2*v2-a*b*d*e*p*q*t^2*v1-a*
b*d*e*p*r*s^2*v2-a*b*d*e*p*s^3*v1-a*b*d*e*p*s^2*t*v0-a*c^3*p*q*t^2*v3+a*c^3*p*r
*t^2*v2-a*c^3*p*s*t^2*v1-a*c^3*p*t^3*v0+a*c^3*q^2*s*t*v3+a*c^3*q*r*s^2*v3-a*c^3
*q*r*s*t*v2-2*a*c^3*q*r*t^2*v1+a*c^3*q*s^2*t*v1+a*c^3*q*s*t^2*v0-2*a*c^3*r^2*s*
t*v1-a*c^3*r^2*t^2*v0+a*c^3*r*s^3*v1+a*c^3*r*s^2*t*v0-a*c^2*d*p^2*t^2*v3+2*a*c^
2*d*p*q*s*t*v3+2*a*c^2*d*p*q*t^2*v2+a*c^2*d*p*r*s^2*v3-a*c^2*d*p*r*s*t*v2-3*a*c
^2*d*p*r*t^2*v1+a*c^2*d*p*s^2*t*v1+a*c^2*d*p*s*t^2*v0+a*c^2*d*q^2*s^2*v3-2*a*c^
2*d*q^2*s*t*v2-2*a*c^2*d*q^2*t^2*v1-a*c^2*d*q*r*s^2*v2-4*a*c^2*d*q*r*s*t*v1-2*a
*c^2*d*q*r*t^2*v0+a*c^2*d*q*s^3*v1+a*c^2*d*q*s^2*t*v0+a*c^2*e*p^2*t^2*v2+a*c^2*
e*p*q*s^2*v3-a*c^2*e*p*q*s*t*v2-a*c^2*e*p*q*t^2*v1-2*a*c^2*e*p*r*s*t*v1-a*c^2*e
*p*r*t^2*v0+a*c^2*e*p*s^3*v1+a*c^2*e*p*s^2*t*v0+a*c*d^2*p^2*s*t*v3+a*c*d^2*p^2*
t^2*v2+a*c*d^2*p*q*s^2*v3-3*a*c*d^2*p*q*s*t*v2-4*a*c*d^2*p*q*t^2*v1-a*c*d^2*p*r
*s^2*v2-2*a*c*d^2*p*r*s*t*v1-a*c*d^2*p*r*t^2*v0-a*c*d^2*q^2*s^2*v2-2*a*c*d^2*q^
2*s*t*v1-a*c*d^2*q^2*t^2*v0+a*c*d*e*p^2*s^2*v3-a*c*d*e*p^2*s*t*v2-2*a*c*d*e*p^2
*t^2*v1-a*c*d*e*p*q*s^2*v2-2*a*c*d*e*p*q*s*t*v1-a*c*d*e*p*q*t^2*v0-a*d^3*p^2*s*
t*v2-a*d^3*p^2*t^2*v1-a*d^3*p*q*s^2*v2-2*a*d^3*p*q*s*t*v1-a*d^3*p*q*t^2*v0-a*d^
2*e*p^2*s^2*v2-2*a*d^2*e*p^2*s*t*v1-a*d^2*e*p^2*t^2*v0+b^4*p*s*t^2*v3-b^4*q*s^2
*t*v3+b^4*r*s^3*v3+b^3*c*p*r*t^2*v3-b^3*c*p*s^2*t*v3-b^3*c*p*s*t^2*v2-b^3*c*q*r
*s*t*v3+b^3*c*q*s^3*v3+b^3*c*q*s^2*t*v2+2*b^3*c*r^2*s^2*v3+b^3*c*r^2*s*t*v2-b^3
*c*r*s^3*v2+b^3*c*r*s*t^2*v0+b^3*d*p*q*t^2*v3+b^3*d*p*r*s*t*v3+b^3*d*p*s^3*v3-b
^3*d*p*s*t^2*v1-b^3*d*q^2*s*t*v3+b^3*d*q*r*s^2*v3+b^3*d*q*r*s*t*v2+b^3*d*q*s^2*
t*v1+b^3*d*q*s*t^2*v0-b^3*d*r^2*s^2*v2-b^3*d*r*s^3*v1-b^3*d*r*s^2*t*v0+b^3*e*p^
2*t^2*v3-b^3*e*p*q*s*t*v3+b^3*e*p*r*s^2*v3-2*b^2*c^2*p*r*s*t*v3-b^2*c^2*p*r*t^2
*v2+b^2*c^2*p*s^2*t*v2+b^2*c^2*p*s*t^2*v1+3*b^2*c^2*q*r*s^2*v3+2*b^2*c^2*q*r*s*
t*v2-b^2*c^2*q*s^3*v2-b^2*c^2*q*s^2*t*v1+b^2*c^2*r^3*s*v3+b^2*c^2*r^3*t*v2-b^2*
c^2*r^2*s^2*v2-b^2*c^2*r^2*s*t*v1+b^2*c^2*r^2*t^2*v0+b^2*c^2*r*s^3*v1+b^2*c^2*r
*s^2*t*v0-b^2*c*d*p*q*t^2*v2+b^2*c*d*p*r^2*t*v3+3*b^2*c*d*p*r*s^2*v3+2*b^2*c*d*
p*r*s*t*v2-b^2*c*d*p*r*t^2*v1-b^2*c*d*p*s^3*v2+b^2*c*d*p*s^2*t*v1+2*b^2*c*d*p*s
*t^2*v0+b^2*c*d*q^2*s^2*v3+2*b^2*c*d*q^2*s*t*v2+b^2*c*d*q*r^2*s*v3+2*b^2*c*d*q*
r^2*t*v2-3*b^2*c*d*q*r*s^2*v2+2*b^2*c*d*q*r*t^2*v0-b^2*c*d*q*s^3*v1-b^2*c*d*q*s
^2*t*v0-b^2*c*d*r^3*s*v2-b^2*c*d*r^2*s^2*v1-b^2*c*d*r^2*s*t*v0-b^2*c*e*p^2*s*t*
v3-b^2*c*e*p^2*t^2*v2+b^2*c*e*p*q*s^2*v3+b^2*c*e*p*q*s*t*v2+b^2*c*e*p*r^2*s*v3+
b^2*c*e*p*r^2*t*v2-b^2*c*e*p*r*s^2*v2+b^2*c*e*p*r*t^2*v0+b^2*d^2*p^2*s*t*v3+b^2
*d^2*p*q*r*t*v3+b^2*d^2*p*q*s^2*v3+b^2*d^2*p*q*s*t*v2-b^2*d^2*p*q*t^2*v1-2*b^2*
d^2*p*r*s^2*v2-b^2*d^2*p*r*s*t*v1-b^2*d^2*p*s^3*v1-b^2*d^2*p*s^2*t*v0+b^2*d^2*q
^2*r*t*v2+b^2*d^2*q^2*s*t*v1+b^2*d^2*q^2*t^2*v0-b^2*d^2*q*r^2*s*v2-b^2*d^2*q*r*
s^2*v1-b^2*d^2*q*r*s*t*v0+b^2*d*e*p^2*r*t*v3+b^2*d*e*p^2*s^2*v3-b^2*d*e*p^2*t^2
*v1+b^2*d*e*p*q*r*t*v2+b^2*d*e*p*q*s*t*v1+b^2*d*e*p*q*t^2*v0-b^2*d*e*p*r^2*s*v2
-b^2*d*e*p*r*s^2*v1-b^2*d*e*p*r*s*t*v0-b*c^3*p*q*s*t*v3-b*c^3*p*r^2*t*v3+b*c^3*
p*r*s*t*v2+b*c^3*p*r*t^2*v1-b*c^3*p*s^2*t*v1-b*c^3*p*s*t^2*v0+b*c^3*q^2*s^2*v3+
2*b*c^3*q*r^2*s*v3+b*c^3*q*r^2*t*v2-b*c^3*q*r*s^2*v2-2*b*c^3*q*r*s*t*v1+b*c^3*q
*s^3*v1+b*c^3*q*s^2*t*v0-b*c^3*r^3*t*v1+b*c^3*r^2*s^2*v1+b*c^3*r^2*s*t*v0-b*c^2
*d*p^2*s*t*v3+2*b*c^2*d*p*q*s^2*v3+2*b*c^2*d*p*q*s*t*v2+b*c^2*d*p*q*t^2*v1+2*b*
c^2*d*p*r^2*s*v3+2*b*c^2*d*p*r^2*t*v2-b*c^2*d*p*r*s^2*v2+2*b*c^2*d*p*r*t^2*v0+b
*c^2*d*p*s^3*v1+b*c^2*d*p*s^2*t*v0+2*b*c^2*d*q^2*r*s*v3+2*b*c^2*d*q^2*r*t*v2-2*
b*c^2*d*q^2*s^2*v2-2*b*c^2*d*q^2*s*t*v1-2*b*c^2*d*q*r^2*s*v2-2*b*c^2*d*q*r^2*t*
v1-b*c^2*e*p^2*r*t*v3+b*c^2*e*p^2*s*t*v2+b*c^2*e*p^2*t^2*v1+2*b*c^2*e*p*q*r*s*
v3+b*c^2*e*p*q*r*t*v2-b*c^2*e*p*q*s^2*v2-b*c^2*e*p*q*s*t*v1-b*c^2*e*p*r^2*t*v1+
b*c^2*e*p*r*s^2*v1+b*c^2*e*p*r*s*t*v0+b*c*d^2*p^2*r*t*v3+b*c*d^2*p^2*s^2*v3+b*c
*d^2*p^2*s*t*v2+b*c*d^2*p*q^2*t*v3+2*b*c*d^2*p*q*r*s*v3+3*b*c*d^2*p*q*r*t*v2-3*
b*c*d^2*p*q*s^2*v2-b*c*d^2*p*q*s*t*v1+2*b*c*d^2*p*q*t^2*v0-2*b*c*d^2*p*r^2*s*v2
-b*c*d^2*p*r^2*t*v1-b*c*d^2*p*r*s^2*v1-b*c*d^2*p*r*s*t*v0+b*c*d^2*q^3*t*v2-2*b*
c*d^2*q^2*r*s*v2-b*c*d^2*q^2*r*t*v1-b*c*d^2*q^2*s^2*v1-b*c*d^2*q^2*s*t*v0+b*c*d
*e*p^2*q*t*v3+2*b*c*d*e*p^2*r*s*v3+2*b*c*d*e*p^2*r*t*v2-b*c*d*e*p^2*s^2*v2+b*c*
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2*s^2*v2-b*d^3*p^2*s*t*v1+b*d^3*p*q^2*t*v2-2*b*d^3*p*q*r*s*v2-b*d^3*p*q*r*t*v1-
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*s*t*v1+2*c^2*d*e*p*t^2*v0-3*c^2*d*e*q^2*s*v3+2*c^2*d*e*q*r*s*v2+5*c^2*d*e*q*r*
t*v1-3*c^2*d*e*q*s^2*v1-3*c^2*d*e*q*s*t*v0+c^2*e^2*p^2*t*v3-2*c^2*e^2*p*q*s*v3-
c^2*e^2*p*q*t*v2+c^2*e^2*p*r*t*v1-c^2*e^2*p*s^2*v1-c^2*e^2*p*s*t*v0+c^2*e^2*q^2
*s*v2+c^2*e^2*q^2*t*v1+2*c*d^3*p*q*s*v4+c*d^3*p*q*t*v3-c*d^3*p*s^2*v2-c*d^3*p*s
*t*v1-c*d^3*q^2*t*v2-c*d^3*q*r*t*v1+c*d^3*q*s^2*v1+c*d^3*q*s*t*v0-c*d^2*e*p^2*s
*v4+c*d^2*e*p^2*t*v3-4*c*d^2*e*p*q*s*v3-2*c*d^2*e*p*q*t*v2+2*c*d^2*e*p*r*s*v2+4
*c*d^2*e*p*r*t*v1-2*c*d^2*e*p*s^2*v1-2*c*d^2*e*p*s*t*v0+2*c*d^2*e*q^2*s*v2+2*c*
d^2*e*q^2*t*v1-2*c*d*e^2*p^2*s*v3-2*c*d*e^2*p^2*t*v2+4*c*d*e^2*p*q*s*v2+4*c*d*e
^2*p*q*t*v1+d^4*p^2*s*v4-d^4*p*q*t*v2-d^4*p*r*t*v1+d^4*p*s^2*v1+d^4*p*s*t*v0-d^
3*e*p^2*s*v3-d^3*e*p^2*t*v2+2*d^3*e*p*q*s*v2+2*d^3*e*p*q*t*v1+3*d^2*e^2*p^2*s*
v2+3*d^2*e^2*p^2*t*v1+a^2*e^2*t^2*v4-a*b*d*e*t^2*v4+3*a*b*e^2*s*t*v4+2*a*b*e^2*
t^2*v3-3*a*c^2*e*t^2*v4+2*a*c*d^2*t^2*v4-3*a*c*d*e*s*t*v4-a*c*d*e*t^2*v3+a*c*e^
2*s^2*v4+3*a*c*e^2*s*t*v3+2*a*c*e^2*t^2*v2-a*d^3*t^2*v3-a*d^2*e*s^2*v4+a*d^2*e*
s*t*v3+2*a*d^2*e*t^2*v2+a*d*e^2*s^2*v3-2*a*d*e^2*s*t*v2-3*a*d*e^2*t^2*v1-a*e^3*
s^2*v2-2*a*e^3*s*t*v1-a*e^3*t^2*v0+2*b^2*c*e*t^2*v4+b^2*d^2*t^2*v4-2*b^2*d*e*s*
t*v4-3*b^2*d*e*t^2*v3+b^2*e^2*r*t*v4+b^2*e^2*s^2*v4+2*b^2*e^2*s*t*v3+b^2*e^2*t^
2*v2-3*b*c^2*d*t^2*v4+b*c^2*e*s*t*v4+2*b*c^2*e*t^2*v3+2*b*c*d^2*s*t*v4+2*b*c*d^
2*t^2*v3-b*c*d*e*r*t*v4-2*b*c*d*e*s^2*v4-3*b*c*d*e*s*t*v3-b*c*d*e*t^2*v2+b*c*e^
2*q*t*v4+2*b*c*e^2*r*s*v4+2*b*c*e^2*r*t*v3+2*b*c*e^2*s^2*v3-b*c*e^2*s*t*v2-3*b*
c*e^2*t^2*v1+b*d^3*r*t*v4-b*d^3*s*t*v3-b*d^3*t^2*v2+b*d^2*e*q*t*v4-2*b*d^2*e*r*
s*v4-2*b*d^2*e*r*t*v3+b*d^2*e*s^2*v3+3*b*d^2*e*s*t*v2+2*b*d^2*e*t^2*v1+2*b*d*e^
2*p*t*v4+2*b*d*e^2*r*s*v3+2*b*d*e^2*r*t*v2-2*b*d*e^2*s^2*v2+2*b*d*e^2*t^2*v0+b*
e^3*p*t*v3+b*e^3*q*t*v2-2*b*e^3*r*s*v2-b*e^3*r*t*v1-b*e^3*s^2*v1-b*e^3*s*t*v0+c
^4*t^2*v4-c^3*d*s*t*v4-c^3*d*t^2*v3-c^3*e*r*t*v4+c^3*e*s^2*v4-c^3*e*t^2*v2+c^2*
d^2*s*t*v3+c^2*d^2*t^2*v2-3*c^2*d*e*q*t*v4-c^2*d*e*s^2*v3+c^2*d*e*s*t*v2+2*c^2*
d*e*t^2*v1-c^2*e^2*p*t*v4+2*c^2*e^2*q*s*v4+2*c^2*e^2*q*t*v3+c^2*e^2*r*s*v3+c^2*
e^2*r*t*v2-c^2*e^2*s^2*v2+c^2*e^2*t^2*v0+c*d^3*q*t*v4-c*d^3*s*t*v2-c*d^3*t^2*v1
-2*c*d^2*e*p*t*v4-2*c*d^2*e*q*s*v4-2*c*d^2*e*q*t*v3+c*d^2*e*s^2*v2-2*c*d^2*e*s*
t*v1-3*c*d^2*e*t^2*v0+2*c*d*e^2*p*s*v4+3*c*d*e^2*q*s*v3+c*d*e^2*q*t*v2-c*d*e^2*
r*s*v2-3*c*d*e^2*r*t*v1+2*c*d*e^2*s^2*v1+2*c*d*e^2*s*t*v0+c*e^3*p*s*v3+c*e^3*p*
t*v2-2*c*e^3*q*s*v2-2*c*e^3*q*t*v1+d^4*p*t*v4+d^4*s*t*v1+d^4*t^2*v0-2*d^3*e*p*s
*v4-d^3*e*p*t*v3+d^3*e*q*t*v2+d^3*e*r*t*v1-d^3*e*s^2*v1-d^3*e*s*t*v0+2*d^2*e^2*
p*s*v3+2*d^2*e^2*p*t*v2-d^2*e^2*q*s*v2-d^2*e^2*q*t*v1-3*d*e^3*p*s*v2-3*d*e^3*p*
t*v1-b*e^3*t*v4+2*c*d*e^2*t*v4-c*e^3*s*v4-c*e^3*t*v3-d^3*e*t*v4+d^2*e^2*s*v4+d^
2*e^2*t*v3-d*e^3*s*v3-d*e^3*t*v2+e^4*s*v2+e^4*t*v1




beta[2,5] = t*(a^4*t^3*v3+3*a^3*b*s*t^2*v3-a^3*b*t^3*v2+2*a^3*c*r*t^2*v3-a^3*c*
s*t^2*v2-a^3*c*t^3*v1+a^3*d*q*t^2*v3-a^3*d*r*t^2*v2-a^3*d*s*t^2*v1-a^3*d*t^3*v0
+a^3*e*p*t^2*v3+a^2*b^2*r*t^2*v3+3*a^2*b^2*s^2*t*v3-2*a^2*b^2*s*t^2*v2+a^2*b^2*
t^3*v1+3*a^2*b*c*q*t^2*v3+4*a^2*b*c*r*s*t*v3-a^2*b*c*r*t^2*v2-2*a^2*b*c*s^2*t*
v2+2*a^2*b*c*t^3*v0+2*a^2*b*d*p*t^2*v3+2*a^2*b*d*q*s*t*v3-2*a^2*b*d*q*t^2*v2-2*
a^2*b*d*r*s*t*v2-2*a^2*b*d*s^2*t*v1-2*a^2*b*d*s*t^2*v0+2*a^2*b*e*p*s*t*v3-a^2*b
*e*p*t^2*v2+a^2*c^2*p*t^2*v3+a^2*c^2*q*s*t*v3-a^2*c^2*q*t^2*v2+a^2*c^2*r^2*t*v3
-a^2*c^2*r*s*t*v2-2*a^2*c^2*r*t^2*v1+a^2*c^2*s^2*t*v1+a^2*c^2*s*t^2*v0+a^2*c*d*
p*s*t*v3-2*a^2*c*d*p*t^2*v2+a^2*c*d*q*r*t*v3-2*a^2*c*d*q*s*t*v2-2*a^2*c*d*q*t^2
*v1-a^2*c*d*r^2*t*v2-a^2*c*d*r*s*t*v1-a^2*c*d*r*t^2*v0+a^2*c*e*p*r*t*v3-a^2*c*e
*p*s*t*v2-a^2*c*e*p*t^2*v1-a^2*d^2*p*s*t*v2-a^2*d^2*p*t^2*v1-a^2*d^2*q*r*t*v2-a
^2*d^2*q*s*t*v1-a^2*d^2*q*t^2*v0-a^2*d*e*p*r*t*v2-a^2*d*e*p*s*t*v1-a^2*d*e*p*t^
2*v0-a*b^3*q*t^2*v3+2*a*b^3*r*s*t*v3-a*b^3*r*t^2*v2+a*b^3*s^3*v3-a*b^3*s^2*t*v2
+a*b^3*s*t^2*v1-a*b^3*t^3*v0-a*b^2*c*p*t^2*v3+4*a*b^2*c*q*s*t*v3+2*a*b^2*c*r^2*
t*v3+2*a*b^2*c*r*s^2*v3-2*a*b^2*c*r*s*t*v2+2*a*b^2*c*r*t^2*v1-a*b^2*c*s^3*v2+a*
b^2*c*s^2*t*v1+2*a*b^2*c*s*t^2*v0+3*a*b^2*d*p*s*t*v3-a*b^2*d*p*t^2*v2+a*b^2*d*q
*r*t*v3+a*b^2*d*q*s^2*v3-2*a*b^2*d*q*s*t*v2+2*a*b^2*d*q*t^2*v1-a*b^2*d*r^2*t*v2
-a*b^2*d*r*s^2*v2-a*b^2*d*r*s*t*v1-a*b^2*d*r*t^2*v0-a*b^2*d*s^3*v1-a*b^2*d*s^2*
t*v0+a*b^2*e*p*r*t*v3+a*b^2*e*p*s^2*v3-a*b^2*e*p*s*t*v2+a*b^2*e*p*t^2*v1+a*b*c^
2*p*s*t*v3+a*b*c^2*p*t^2*v2+5*a*b*c^2*q*r*t*v3+a*b*c^2*q*s^2*v3-2*a*b*c^2*q*s*t
*v2+a*b*c^2*r^2*s*v3-a*b*c^2*r*s^2*v2+a*b*c^2*r*s*t*v1+3*a*b*c^2*r*t^2*v0+a*b*c
^2*s^3*v1+a*b*c^2*s^2*t*v0+4*a*b*c*d*p*r*t*v3+a*b*c*d*p*s^2*v3-3*a*b*c*d*p*s*t*
v2+2*a*b*c*d*p*t^2*v1+3*a*b*c*d*q^2*t*v3+a*b*c*d*q*r*s*v3-3*a*b*c*d*q*r*t*v2-2*
a*b*c*d*q*s^2*v2-a*b*c*d*q*s*t*v1+a*b*c*d*q*t^2*v0-a*b*c*d*r^2*s*v2-a*b*c*d*r*s
^2*v1-a*b*c*d*r*s*t*v0+3*a*b*c*e*p*q*t*v3+a*b*c*e*p*r*s*v3-a*b*c*e*p*s^2*v2+a*b
*c*e*p*s*t*v1+2*a*b*c*e*p*t^2*v0+2*a*b*d^2*p*q*t*v3-2*a*b*d^2*p*r*t*v2-a*b*d^2*
p*s^2*v2-2*a*b*d^2*p*s*t*v1-a*b*d^2*p*t^2*v0-a*b*d^2*q^2*t*v2-a*b*d^2*q*r*s*v2-
a*b*d^2*q*s^2*v1-a*b*d^2*q*s*t*v0+2*a*b*d*e*p^2*t*v3-a*b*d*e*p*q*t*v2-a*b*d*e*p
*r*s*v2-a*b*d*e*p*s^2*v1-a*b*d*e*p*s*t*v0+a*c^3*p*r*t*v3-a*c^3*p*t^2*v1+a*c^3*q
^2*t*v3+a*c^3*q*r*s*v3-a*c^3*q*r*t*v2+a*c^3*q*s*t*v1+a*c^3*q*t^2*v0-a*c^3*r^2*t
*v1+a*c^3*r*s^2*v1+a*c^3*r*s*t*v0+3*a*c^2*d*p*q*t*v3+a*c^2*d*p*r*s*v3-2*a*c^2*d
*p*r*t*v2+a*c^2*d*p*s*t*v1+a*c^2*d*p*t^2*v0+a*c^2*d*q^2*s*v3-2*a*c^2*d*q^2*t*v2
-a*c^2*d*q*r*s*v2-2*a*c^2*d*q*r*t*v1+a*c^2*d*q*s^2*v1+a*c^2*d*q*s*t*v0+a*c^2*e*
p^2*t*v3+a*c^2*e*p*q*s*v3-a*c^2*e*p*q*t*v2-a*c^2*e*p*r*t*v1+a*c^2*e*p*s^2*v1+a*
c^2*e*p*s*t*v0+a*c*d^2*p^2*t*v3+a*c*d^2*p*q*s*v3-4*a*c*d^2*p*q*t*v2-a*c*d^2*p*r
*s*v2-a*c*d^2*p*r*t*v1-a*c*d^2*q^2*s*v2-a*c*d^2*q^2*t*v1+a*c*d*e*p^2*s*v3-2*a*c
*d*e*p^2*t*v2-a*c*d*e*p*q*s*v2-a*c*d*e*p*q*t*v1-a*d^3*p^2*t*v2-a*d^3*p*q*s*v2-a
*d^3*p*q*t*v1-a*d^2*e*p^2*s*v2-a*d^2*e*p^2*t*v1-b^4*q*s*t*v3+b^4*r*s^2*v3-b^4*r
*s*t*v2-b^4*s*t^2*v0-b^3*c*p*s*t*v3-b^3*c*q*r*t*v3+b^3*c*q*s^2*v3+2*b^3*c*r^2*s
*v3-b^3*c*r^2*t*v2-b^3*c*r*s^2*v2+b^3*c*r*s*t*v1-b^3*c*r*t^2*v0+b^3*d*p*s^2*v3-
b^3*d*p*s*t*v2-b^3*d*q^2*t*v3+b^3*d*q*r*s*v3-b^3*d*q*r*t*v2+b^3*d*q*s*t*v1-b^3*
d*q*t^2*v0-b^3*d*r^2*s*v2-b^3*d*r*s^2*v1-b^3*d*r*s*t*v0-b^3*e*p*q*t*v3+b^3*e*p*
r*s*v3-b^3*e*p*r*t*v2-b^3*e*p*t^2*v0-b^2*c^2*p*r*t*v3+b^2*c^2*p*s*t*v2+3*b^2*c^
2*q*r*s*v3-b^2*c^2*q*s^2*v2+b^2*c^2*r^3*v3-b^2*c^2*r^2*s*v2+b^2*c^2*r^2*t*v1+b^
2*c^2*r*s^2*v1+b^2*c^2*r*s*t*v0-b^2*c*d*p*q*t*v3+3*b^2*c*d*p*r*s*v3-b^2*c*d*p*r
*t*v2-b^2*c*d*p*s^2*v2+2*b^2*c*d*p*s*t*v1+b^2*c*d*q^2*s*v3+b^2*c*d*q*r^2*v3-3*b
^2*c*d*q*r*s*v2+2*b^2*c*d*q*r*t*v1-b^2*c*d*q*s^2*v1-b^2*c*d*q*s*t*v0-b^2*c*d*r^
3*v2-b^2*c*d*r^2*s*v1-b^2*c*d*r^2*t*v0-b^2*c*e*p^2*t*v3+b^2*c*e*p*q*s*v3+b^2*c*
e*p*r^2*v3-b^2*c*e*p*r*s*v2+b^2*c*e*p*r*t*v1+b^2*d^2*p*q*s*v3-b^2*d^2*p*q*t*v2-\
2*b^2*d^2*p*r*s*v2-b^2*d^2*p*s^2*v1-b^2*d^2*p*s*t*v0+b^2*d^2*q^2*t*v1-b^2*d^2*q
*r^2*v2-b^2*d^2*q*r*s*v1-b^2*d^2*q*r*t*v0+b^2*d*e*p^2*s*v3-b^2*d*e*p^2*t*v2+b^2
*d*e*p*q*t*v1-b^2*d*e*p*r^2*v2-b^2*d*e*p*r*s*v1-b^2*d*e*p*r*t*v0+b*c^3*p*r*t*v2
-b*c^3*p*s*t*v1+b*c^3*q^2*s*v3+2*b*c^3*q*r^2*v3-b*c^3*q*r*s*v2+b*c^3*q*s^2*v1+b
*c^3*q*s*t*v0+b*c^3*r^2*s*v1+b*c^3*r^2*t*v0+2*b*c^2*d*p*q*s*v3+b*c^2*d*p*q*t*v2
+2*b*c^2*d*p*r^2*v3-b*c^2*d*p*r*s*v2+2*b*c^2*d*p*r*t*v1+b*c^2*d*p*s^2*v1+b*c^2*
d*p*s*t*v0+2*b*c^2*d*q^2*r*v3-2*b*c^2*d*q^2*s*v2-2*b*c^2*d*q*r^2*v2+b*c^2*e*p^2
*t*v2+2*b*c^2*e*p*q*r*v3-b*c^2*e*p*q*s*v2+b*c^2*e*p*r*s*v1+b*c^2*e*p*r*t*v0+b*c
*d^2*p^2*s*v3+2*b*c*d^2*p*q*r*v3-3*b*c*d^2*p*q*s*v2+2*b*c*d^2*p*q*t*v1-2*b*c*d^
2*p*r^2*v2-b*c*d^2*p*r*s*v1-b*c*d^2*p*r*t*v0-2*b*c*d^2*q^2*r*v2-b*c*d^2*q^2*s*
v1-b*c*d^2*q^2*t*v0+2*b*c*d*e*p^2*r*v3-b*c*d*e*p^2*s*v2+2*b*c*d*e*p^2*t*v1-2*b*
c*d*e*p*q*r*v2-b*c*d*e*p*q*s*v1-b*c*d*e*p*q*t*v0-b*d^3*p^2*s*v2-2*b*d^3*p*q*r*
v2-b*d^3*p*q*s*v1-b*d^3*p*q*t*v0-2*b*d^2*e*p^2*r*v2-b*d^2*e*p^2*s*v1-b*d^2*e*p^
2*t*v0-c^4*p*r*t*v1+c^4*q^2*r*v3+c^4*q*r*s*v1+c^4*q*r*t*v0+2*c^3*d*p*q*r*v3-c^3
*d*p*q*t*v1+c^3*d*p*r*s*v1+c^3*d*p*r*t*v0+c^3*d*q^3*v3-c^3*d*q^2*r*v2+c^3*d*q^2
*s*v1+c^3*d*q^2*t*v0-c^3*e*p^2*t*v1+c^3*e*p*q^2*v3+c^3*e*p*q*s*v1+c^3*e*p*q*t*
v0+c^2*d^2*p^2*r*v3+2*c^2*d^2*p*q^2*v3-2*c^2*d^2*p*q*r*v2+c^2*d^2*p*q*s*v1+c^2*
d^2*p*q*t*v0-c^2*d^2*q^3*v2+2*c^2*d*e*p^2*q*v3+c^2*d*e*p^2*s*v1+c^2*d*e*p^2*t*
v0-c^2*d*e*p*q^2*v2+c*d^3*p^2*q*v3-c*d^3*p^2*r*v2-2*c*d^3*p*q^2*v2+c*d^2*e*p^3*
v3-2*c*d^2*e*p^2*q*v2-d^4*p^2*q*v2-d^3*e*p^3*v2-a^3*e*t^2*v4+2*a^2*b*d*t^2*v4-2
*a^2*b*e*s*t*v4-3*a^2*b*e*t^2*v3+a^2*c^2*t^2*v4+2*a^2*c*d*s*t*v4-3*a^2*c*d*t^2*
v3-a^2*c*e*r*t*v4-2*a^2*c*e*s*t*v3+2*a^2*c*e*t^2*v2+a^2*d^2*r*t*v4-a^2*d^2*s*t*
v3+a^2*d^2*t^2*v2-a^2*d*e*r*t*v3+2*a^2*d*e*s*t*v2+2*a^2*d*e*t^2*v1+a^2*e^2*r*t*
v2+a^2*e^2*s*t*v1+a^2*e^2*t^2*v0-3*a*b^2*c*t^2*v4+2*a*b^2*d*s*t*v4+2*a*b^2*d*t^
2*v3-a*b^2*e*r*t*v4-a*b^2*e*s^2*v4-4*a*b^2*e*s*t*v3+2*a*b^2*e*t^2*v2-2*a*b*c^2*
s*t*v4+2*a*b*c^2*t^2*v3+2*a*b*c*d*s^2*v4-a*b*c*d*s*t*v3-a*b*c*d*t^2*v2-3*a*b*c*
e*q*t*v4-a*b*c*e*r*s*v4-4*a*b*c*e*r*t*v3-2*a*b*c*e*s^2*v3+5*a*b*c*e*s*t*v2-a*b*
c*e*t^2*v1+a*b*d^2*q*t*v4+a*b*d^2*r*s*v4-a*b*d^2*s^2*v3-3*a*b*d^2*t^2*v1-2*a*b*
d*e*p*t*v4-3*a*b*d*e*q*t*v3-a*b*d*e*r*s*v3+2*a*b*d*e*r*t*v2+2*a*b*d*e*s^2*v2+a*
b*d*e*s*t*v1-a*b*d*e*t^2*v0-2*a*b*e^2*p*t*v3+a*b*e^2*q*t*v2+a*b*e^2*r*s*v2+a*b*
e^2*s^2*v1+a*b*e^2*s*t*v0+a*c^3*r*t*v4-a*c^3*s^2*v4+a*c^3*s*t*v3-a*c^3*t^2*v2+2
*a*c^2*d*q*t*v4-2*a*c^2*d*r*t*v3+a*c^2*d*s^2*v3-a*c^2*d*s*t*v2+2*a*c^2*d*t^2*v1
-a*c^2*e*p*t*v4-a*c^2*e*q*s*v4-3*a*c^2*e*q*t*v3-a*c^2*e*r*s*v3+a*c^2*e*s^2*v2-2
*a*c^2*e*s*t*v1-3*a*c^2*e*t^2*v0+3*a*c*d^2*p*t*v4+a*c*d^2*q*s*v4-2*a*c*d^2*q*t*
v3+2*a*c*d^2*r*t*v2-a*c*d^2*s^2*v2+a*c*d^2*s*t*v1+2*a*c*d^2*t^2*v0-a*c*d*e*p*s*
v4-5*a*c*d*e*p*t*v3-2*a*c*d*e*q*s*v3+4*a*c*d*e*q*t*v2+a*c*d*e*r*s*v2+3*a*c*d*e*
r*t*v1-2*a*c*d*e*s^2*v1-2*a*c*d*e*s*t*v0-a*c*e^2*p*s*v3+2*a*c*e^2*p*t*v2+a*c*e^
2*q*s*v2+a*c*e^2*q*t*v1+a*d^3*p*s*v4-a*d^3*p*t*v3+a*d^3*q*t*v2-a*d^3*r*t*v1+a*d
^3*s^2*v1+a*d^3*s*t*v0-a*d^2*e*p*s*v3+4*a*d^2*e*p*t*v2+a*d^2*e*q*s*v2+a*d^2*e*q
*t*v1+2*a*d*e^2*p*s*v2+2*a*d*e^2*p*t*v1+b^4*t^2*v4-b^3*c*t^2*v3+2*b^3*d*r*t*v4+
b^3*d*s*t*v3-b^3*d*t^2*v2+b^3*e*q*t*v4-b^3*e*r*s*v4-b^3*e*r*t*v3-b^3*e*s^2*v3+b
^3*e*s*t*v2-b^3*e*t^2*v1-2*b^2*c^2*r*t*v4+b^2*c^2*t^2*v2+2*b^2*c*d*r*s*v4+b^2*c
*d*r*t*v3-b^2*c*d*s*t*v2+2*b^2*c*d*t^2*v1+b^2*c*e*p*t*v4-b^2*c*e*q*s*v4-b^2*c*e
*r^2*v4-4*b^2*c*e*r*s*v3+4*b^2*c*e*r*t*v2+b^2*c*e*s^2*v2-b^2*c*e*s*t*v1+2*b^2*c
*e*t^2*v0+2*b^2*d^2*p*t*v4+2*b^2*d^2*q*t*v3+b^2*d^2*r^2*v4-b^2*d^2*r*s*v3-b^2*d
^2*r*t*v2-b^2*d^2*s*t*v1+b^2*d^2*t^2*v0-b^2*d*e*p*s*v4-b^2*d*e*q*s*v3-b^2*d*e*r
^2*v3+3*b^2*d*e*r*s*v2-b^2*d*e*r*t*v1+b^2*d*e*s^2*v1+b^2*d*e*s*t*v0-b^2*e^2*p*s
*v3+b^2*e^2*p*t*v2-b^2*e^2*q*t*v1+b^2*e^2*r^2*v2+b^2*e^2*r*s*v1+b^2*e^2*r*t*v0-
b*c^3*q*t*v4-b*c^3*r*s*v4+b*c^3*r*t*v3-b*c^3*t^2*v1-4*b*c^2*d*p*t*v4+2*b*c^2*d*
q*s*v4-b*c^2*d*q*t*v3+b*c^2*d*r*s*v3-2*b*c^2*d*r*t*v2+b*c^2*d*s*t*v1-3*b*c^2*d*
t^2*v0+b*c^2*e*p*t*v3-2*b*c^2*e*q*r*v4-3*b*c^2*e*q*s*v3+2*b*c^2*e*q*t*v2-2*b*c^
2*e*r^2*v3+2*b*c^2*e*r*s*v2-2*b*c^2*e*r*t*v1-b*c^2*e*s^2*v1-b*c^2*e*s*t*v0+2*b*
c*d^2*p*s*v4+b*c*d^2*p*t*v3+2*b*c*d^2*q*r*v4-b*c*d^2*q*s*v3-b*c*d^2*q*t*v2-b*c*
d^2*r*s*v2-2*b*c*d*e*p*r*v4-3*b*c*d*e*p*s*v3+b*c*d*e*p*t*v2-4*b*c*d*e*q*r*v3+4*
b*c*d*e*q*s*v2+2*b*c*d*e*r^2*v2-b*c*d*e*r*s*v1-b*c*d*e*r*t*v0-2*b*c*e^2*p*r*v3+
b*c*e^2*p*s*v2-2*b*c*e^2*p*t*v1+2*b*c*e^2*q*r*v2+b*c*e^2*q*s*v1+b*c*e^2*q*t*v0+
2*b*d^3*p*r*v4-b*d^3*p*s*v3-b*d^3*p*t*v2-2*b*d^3*q*t*v1+b*d^3*r*s*v1+b*d^3*r*t*
v0-2*b*d^2*e*p*r*v3+3*b*d^2*e*p*s*v2-2*b*d^2*e*p*t*v1+2*b*d^2*e*q*r*v2+b*d^2*e*
q*s*v1+b*d^2*e*q*t*v0+4*b*d*e^2*p*r*v2+2*b*d*e^2*p*s*v1+2*b*d*e^2*p*t*v0+c^4*p*
t*v4-c^4*q*s*v4+c^4*q*t*v3+c^4*t^2*v0-c^3*d*p*s*v4+c^3*d*q*s*v3-c^3*d*q*t*v2+c^
3*d*r*t*v1-c^3*e*p*t*v2-c^3*e*q^2*v4-2*c^3*e*q*r*v3+c^3*e*q*s*v2-c^3*e*q*t*v1-c
^3*e*r*s*v1-c^3*e*r*t*v0+c^2*d^2*p*s*v3+c^2*d^2*q^2*v4-c^2*d^2*q*s*v2+2*c^2*d^2
*q*t*v1-2*c^2*d*e*p*q*v4-2*c^2*d*e*p*r*v3+c^2*d*e*p*s*v2+2*c^2*d*e*p*t*v1-3*c^2
*d*e*q^2*v3+2*c^2*d*e*q*r*v2-3*c^2*d*e*q*s*v1-3*c^2*d*e*q*t*v0-2*c^2*e^2*p*q*v3
-c^2*e^2*p*s*v1-c^2*e^2*p*t*v0+c^2*e^2*q^2*v2+2*c*d^3*p*q*v4-c*d^3*p*s*v2+c*d^3
*q*s*v1+c*d^3*q*t*v0-c*d^2*e*p^2*v4-4*c*d^2*e*p*q*v3+2*c*d^2*e*p*r*v2-2*c*d^2*e
*p*s*v1-2*c*d^2*e*p*t*v0+2*c*d^2*e*q^2*v2-2*c*d*e^2*p^2*v3+4*c*d*e^2*p*q*v2+d^4
*p^2*v4+d^4*p*s*v1+d^4*p*t*v0-d^3*e*p^2*v3+2*d^3*e*p*q*v2+3*d^2*e^2*p^2*v2+2*a*
b*e^2*t*v4-a*c*d*e*t*v4+a*c*e^2*s*v4+2*a*c*e^2*t*v3-a*d^3*t*v4-a*d^2*e*s*v4+2*a
*d^2*e*t*v3+a*d*e^2*s*v3-3*a*d*e^2*t*v2-a*e^3*s*v2-a*e^3*t*v1-3*b^2*d*e*t*v4+b^
2*e^2*s*v4+b^2*e^2*t*v3+2*b*c^2*e*t*v4+2*b*c*d^2*t*v4-2*b*c*d*e*s*v4-b*c*d*e*t*
v3+2*b*c*e^2*r*v4+2*b*c*e^2*s*v3-3*b*c*e^2*t*v2-b*d^3*t*v3-2*b*d^2*e*r*v4+b*d^2
*e*s*v3+2*b*d^2*e*t*v2+2*b*d*e^2*r*v3-2*b*d*e^2*s*v2+2*b*d*e^2*t*v1-2*b*e^3*r*
v2-b*e^3*s*v1-b*e^3*t*v0-c^3*d*t*v4+c^3*e*s*v4-c^3*e*t*v3+c^2*d^2*t*v3-c^2*d*e*
s*v3+2*c^2*d*e*t*v2+2*c^2*e^2*q*v4+c^2*e^2*r*v3-c^2*e^2*s*v2+c^2*e^2*t*v1-c*d^3
*t*v2-2*c*d^2*e*q*v4+c*d^2*e*s*v2-3*c*d^2*e*t*v1+2*c*d*e^2*p*v4+3*c*d*e^2*q*v3-
c*d*e^2*r*v2+2*c*d*e^2*s*v1+2*c*d*e^2*t*v0+c*e^3*p*v3-2*c*e^3*q*v2+d^4*t*v1-2*d
^3*e*p*v4-d^3*e*s*v1-d^3*e*t*v0+2*d^2*e^2*p*v3-d^2*e^2*q*v2-3*d*e^3*p*v2-c*e^3*
v4+d^2*e^2*v4-d*e^3*v3+e^4*v2)




beta[3,1] = a^4*t^3*v3+3*a^3*b*s*t^2*v3-a^3*b*t^3*v2+2*a^3*c*r*t^2*v3-a^3*c*s*t
^2*v2-a^3*c*t^3*v1+a^3*d*q*t^2*v3-a^3*d*r*t^2*v2-a^3*d*s*t^2*v1-a^3*d*t^3*v0+a^
3*e*p*t^2*v3+a^2*b^2*r*t^2*v3+3*a^2*b^2*s^2*t*v3-2*a^2*b^2*s*t^2*v2+a^2*b^2*t^3
*v1+3*a^2*b*c*q*t^2*v3+4*a^2*b*c*r*s*t*v3-a^2*b*c*r*t^2*v2-2*a^2*b*c*s^2*t*v2+2
*a^2*b*c*t^3*v0+2*a^2*b*d*p*t^2*v3+2*a^2*b*d*q*s*t*v3-2*a^2*b*d*q*t^2*v2-2*a^2*
b*d*r*s*t*v2-2*a^2*b*d*s^2*t*v1-2*a^2*b*d*s*t^2*v0+2*a^2*b*e*p*s*t*v3-a^2*b*e*p
*t^2*v2+a^2*c^2*p*t^2*v3+a^2*c^2*q*s*t*v3-a^2*c^2*q*t^2*v2+a^2*c^2*r^2*t*v3-a^2
*c^2*r*s*t*v2-2*a^2*c^2*r*t^2*v1+a^2*c^2*s^2*t*v1+a^2*c^2*s*t^2*v0+a^2*c*d*p*s*
t*v3-2*a^2*c*d*p*t^2*v2+a^2*c*d*q*r*t*v3-2*a^2*c*d*q*s*t*v2-2*a^2*c*d*q*t^2*v1-
a^2*c*d*r^2*t*v2-a^2*c*d*r*s*t*v1-a^2*c*d*r*t^2*v0+a^2*c*e*p*r*t*v3-a^2*c*e*p*s
*t*v2-a^2*c*e*p*t^2*v1-a^2*d^2*p*s*t*v2-a^2*d^2*p*t^2*v1-a^2*d^2*q*r*t*v2-a^2*d
^2*q*s*t*v1-a^2*d^2*q*t^2*v0-a^2*d*e*p*r*t*v2-a^2*d*e*p*s*t*v1-a^2*d*e*p*t^2*v0
-a*b^3*q*t^2*v3+2*a*b^3*r*s*t*v3-a*b^3*r*t^2*v2+a*b^3*s^3*v3-a*b^3*s^2*t*v2+a*b
^3*s*t^2*v1-a*b^3*t^3*v0-a*b^2*c*p*t^2*v3+4*a*b^2*c*q*s*t*v3+2*a*b^2*c*r^2*t*v3
+2*a*b^2*c*r*s^2*v3-2*a*b^2*c*r*s*t*v2+2*a*b^2*c*r*t^2*v1-a*b^2*c*s^3*v2+a*b^2*
c*s^2*t*v1+2*a*b^2*c*s*t^2*v0+3*a*b^2*d*p*s*t*v3-a*b^2*d*p*t^2*v2+a*b^2*d*q*r*t
*v3+a*b^2*d*q*s^2*v3-2*a*b^2*d*q*s*t*v2+2*a*b^2*d*q*t^2*v1-a*b^2*d*r^2*t*v2-a*b
^2*d*r*s^2*v2-a*b^2*d*r*s*t*v1-a*b^2*d*r*t^2*v0-a*b^2*d*s^3*v1-a*b^2*d*s^2*t*v0
+a*b^2*e*p*r*t*v3+a*b^2*e*p*s^2*v3-a*b^2*e*p*s*t*v2+a*b^2*e*p*t^2*v1+a*b*c^2*p*
s*t*v3+a*b*c^2*p*t^2*v2+5*a*b*c^2*q*r*t*v3+a*b*c^2*q*s^2*v3-2*a*b*c^2*q*s*t*v2+
a*b*c^2*r^2*s*v3-a*b*c^2*r*s^2*v2+a*b*c^2*r*s*t*v1+3*a*b*c^2*r*t^2*v0+a*b*c^2*s
^3*v1+a*b*c^2*s^2*t*v0+4*a*b*c*d*p*r*t*v3+a*b*c*d*p*s^2*v3-3*a*b*c*d*p*s*t*v2+2
*a*b*c*d*p*t^2*v1+3*a*b*c*d*q^2*t*v3+a*b*c*d*q*r*s*v3-3*a*b*c*d*q*r*t*v2-2*a*b*
c*d*q*s^2*v2-a*b*c*d*q*s*t*v1+a*b*c*d*q*t^2*v0-a*b*c*d*r^2*s*v2-a*b*c*d*r*s^2*
v1-a*b*c*d*r*s*t*v0+3*a*b*c*e*p*q*t*v3+a*b*c*e*p*r*s*v3-a*b*c*e*p*s^2*v2+a*b*c*
e*p*s*t*v1+2*a*b*c*e*p*t^2*v0+2*a*b*d^2*p*q*t*v3-2*a*b*d^2*p*r*t*v2-a*b*d^2*p*s
^2*v2-2*a*b*d^2*p*s*t*v1-a*b*d^2*p*t^2*v0-a*b*d^2*q^2*t*v2-a*b*d^2*q*r*s*v2-a*b
*d^2*q*s^2*v1-a*b*d^2*q*s*t*v0+2*a*b*d*e*p^2*t*v3-a*b*d*e*p*q*t*v2-a*b*d*e*p*r*
s*v2-a*b*d*e*p*s^2*v1-a*b*d*e*p*s*t*v0+a*c^3*p*r*t*v3-a*c^3*p*t^2*v1+a*c^3*q^2*
t*v3+a*c^3*q*r*s*v3-a*c^3*q*r*t*v2+a*c^3*q*s*t*v1+a*c^3*q*t^2*v0-a*c^3*r^2*t*v1
+a*c^3*r*s^2*v1+a*c^3*r*s*t*v0+3*a*c^2*d*p*q*t*v3+a*c^2*d*p*r*s*v3-2*a*c^2*d*p*
r*t*v2+a*c^2*d*p*s*t*v1+a*c^2*d*p*t^2*v0+a*c^2*d*q^2*s*v3-2*a*c^2*d*q^2*t*v2-a*
c^2*d*q*r*s*v2-2*a*c^2*d*q*r*t*v1+a*c^2*d*q*s^2*v1+a*c^2*d*q*s*t*v0+a*c^2*e*p^2
*t*v3+a*c^2*e*p*q*s*v3-a*c^2*e*p*q*t*v2-a*c^2*e*p*r*t*v1+a*c^2*e*p*s^2*v1+a*c^2
*e*p*s*t*v0+a*c*d^2*p^2*t*v3+a*c*d^2*p*q*s*v3-4*a*c*d^2*p*q*t*v2-a*c*d^2*p*r*s*
v2-a*c*d^2*p*r*t*v1-a*c*d^2*q^2*s*v2-a*c*d^2*q^2*t*v1+a*c*d*e*p^2*s*v3-2*a*c*d*
e*p^2*t*v2-a*c*d*e*p*q*s*v2-a*c*d*e*p*q*t*v1-a*d^3*p^2*t*v2-a*d^3*p*q*s*v2-a*d^
3*p*q*t*v1-a*d^2*e*p^2*s*v2-a*d^2*e*p^2*t*v1-b^4*q*s*t*v3+b^4*r*s^2*v3-b^4*r*s*
t*v2-b^4*s*t^2*v0-b^3*c*p*s*t*v3-b^3*c*q*r*t*v3+b^3*c*q*s^2*v3+2*b^3*c*r^2*s*v3
-b^3*c*r^2*t*v2-b^3*c*r*s^2*v2+b^3*c*r*s*t*v1-b^3*c*r*t^2*v0+b^3*d*p*s^2*v3-b^3
*d*p*s*t*v2-b^3*d*q^2*t*v3+b^3*d*q*r*s*v3-b^3*d*q*r*t*v2+b^3*d*q*s*t*v1-b^3*d*q
*t^2*v0-b^3*d*r^2*s*v2-b^3*d*r*s^2*v1-b^3*d*r*s*t*v0-b^3*e*p*q*t*v3+b^3*e*p*r*s
*v3-b^3*e*p*r*t*v2-b^3*e*p*t^2*v0-b^2*c^2*p*r*t*v3+b^2*c^2*p*s*t*v2+3*b^2*c^2*q
*r*s*v3-b^2*c^2*q*s^2*v2+b^2*c^2*r^3*v3-b^2*c^2*r^2*s*v2+b^2*c^2*r^2*t*v1+b^2*c
^2*r*s^2*v1+b^2*c^2*r*s*t*v0-b^2*c*d*p*q*t*v3+3*b^2*c*d*p*r*s*v3-b^2*c*d*p*r*t*
v2-b^2*c*d*p*s^2*v2+2*b^2*c*d*p*s*t*v1+b^2*c*d*q^2*s*v3+b^2*c*d*q*r^2*v3-3*b^2*
c*d*q*r*s*v2+2*b^2*c*d*q*r*t*v1-b^2*c*d*q*s^2*v1-b^2*c*d*q*s*t*v0-b^2*c*d*r^3*
v2-b^2*c*d*r^2*s*v1-b^2*c*d*r^2*t*v0-b^2*c*e*p^2*t*v3+b^2*c*e*p*q*s*v3+b^2*c*e*
p*r^2*v3-b^2*c*e*p*r*s*v2+b^2*c*e*p*r*t*v1+b^2*d^2*p*q*s*v3-b^2*d^2*p*q*t*v2-2*
b^2*d^2*p*r*s*v2-b^2*d^2*p*s^2*v1-b^2*d^2*p*s*t*v0+b^2*d^2*q^2*t*v1-b^2*d^2*q*r
^2*v2-b^2*d^2*q*r*s*v1-b^2*d^2*q*r*t*v0+b^2*d*e*p^2*s*v3-b^2*d*e*p^2*t*v2+b^2*d
*e*p*q*t*v1-b^2*d*e*p*r^2*v2-b^2*d*e*p*r*s*v1-b^2*d*e*p*r*t*v0+b*c^3*p*r*t*v2-b
*c^3*p*s*t*v1+b*c^3*q^2*s*v3+2*b*c^3*q*r^2*v3-b*c^3*q*r*s*v2+b*c^3*q*s^2*v1+b*c
^3*q*s*t*v0+b*c^3*r^2*s*v1+b*c^3*r^2*t*v0+2*b*c^2*d*p*q*s*v3+b*c^2*d*p*q*t*v2+2
*b*c^2*d*p*r^2*v3-b*c^2*d*p*r*s*v2+2*b*c^2*d*p*r*t*v1+b*c^2*d*p*s^2*v1+b*c^2*d*
p*s*t*v0+2*b*c^2*d*q^2*r*v3-2*b*c^2*d*q^2*s*v2-2*b*c^2*d*q*r^2*v2+b*c^2*e*p^2*t
*v2+2*b*c^2*e*p*q*r*v3-b*c^2*e*p*q*s*v2+b*c^2*e*p*r*s*v1+b*c^2*e*p*r*t*v0+b*c*d
^2*p^2*s*v3+2*b*c*d^2*p*q*r*v3-3*b*c*d^2*p*q*s*v2+2*b*c*d^2*p*q*t*v1-2*b*c*d^2*
p*r^2*v2-b*c*d^2*p*r*s*v1-b*c*d^2*p*r*t*v0-2*b*c*d^2*q^2*r*v2-b*c*d^2*q^2*s*v1-
b*c*d^2*q^2*t*v0+2*b*c*d*e*p^2*r*v3-b*c*d*e*p^2*s*v2+2*b*c*d*e*p^2*t*v1-2*b*c*d
*e*p*q*r*v2-b*c*d*e*p*q*s*v1-b*c*d*e*p*q*t*v0-b*d^3*p^2*s*v2-2*b*d^3*p*q*r*v2-b
*d^3*p*q*s*v1-b*d^3*p*q*t*v0-2*b*d^2*e*p^2*r*v2-b*d^2*e*p^2*s*v1-b*d^2*e*p^2*t*
v0-c^4*p*r*t*v1+c^4*q^2*r*v3+c^4*q*r*s*v1+c^4*q*r*t*v0+2*c^3*d*p*q*r*v3-c^3*d*p
*q*t*v1+c^3*d*p*r*s*v1+c^3*d*p*r*t*v0+c^3*d*q^3*v3-c^3*d*q^2*r*v2+c^3*d*q^2*s*
v1+c^3*d*q^2*t*v0-c^3*e*p^2*t*v1+c^3*e*p*q^2*v3+c^3*e*p*q*s*v1+c^3*e*p*q*t*v0+c
^2*d^2*p^2*r*v3+2*c^2*d^2*p*q^2*v3-2*c^2*d^2*p*q*r*v2+c^2*d^2*p*q*s*v1+c^2*d^2*
p*q*t*v0-c^2*d^2*q^3*v2+2*c^2*d*e*p^2*q*v3+c^2*d*e*p^2*s*v1+c^2*d*e*p^2*t*v0-c^
2*d*e*p*q^2*v2+c*d^3*p^2*q*v3-c*d^3*p^2*r*v2-2*c*d^3*p*q^2*v2+c*d^2*e*p^3*v3-2*
c*d^2*e*p^2*q*v2-d^4*p^2*q*v2-d^3*e*p^3*v2-a^3*e*t^2*v4+2*a^2*b*d*t^2*v4-2*a^2*
b*e*s*t*v4-3*a^2*b*e*t^2*v3+a^2*c^2*t^2*v4+2*a^2*c*d*s*t*v4-3*a^2*c*d*t^2*v3-a^
2*c*e*r*t*v4-2*a^2*c*e*s*t*v3+2*a^2*c*e*t^2*v2+a^2*d^2*r*t*v4-a^2*d^2*s*t*v3+a^
2*d^2*t^2*v2-a^2*d*e*r*t*v3+2*a^2*d*e*s*t*v2+2*a^2*d*e*t^2*v1+a^2*e^2*r*t*v2+a^
2*e^2*s*t*v1+a^2*e^2*t^2*v0-3*a*b^2*c*t^2*v4+2*a*b^2*d*s*t*v4+2*a*b^2*d*t^2*v3-
a*b^2*e*r*t*v4-a*b^2*e*s^2*v4-4*a*b^2*e*s*t*v3+2*a*b^2*e*t^2*v2-2*a*b*c^2*s*t*
v4+2*a*b*c^2*t^2*v3+2*a*b*c*d*s^2*v4-a*b*c*d*s*t*v3-a*b*c*d*t^2*v2-3*a*b*c*e*q*
t*v4-a*b*c*e*r*s*v4-4*a*b*c*e*r*t*v3-2*a*b*c*e*s^2*v3+5*a*b*c*e*s*t*v2-a*b*c*e*
t^2*v1+a*b*d^2*q*t*v4+a*b*d^2*r*s*v4-a*b*d^2*s^2*v3-3*a*b*d^2*t^2*v1-2*a*b*d*e*
p*t*v4-3*a*b*d*e*q*t*v3-a*b*d*e*r*s*v3+2*a*b*d*e*r*t*v2+2*a*b*d*e*s^2*v2+a*b*d*
e*s*t*v1-a*b*d*e*t^2*v0-2*a*b*e^2*p*t*v3+a*b*e^2*q*t*v2+a*b*e^2*r*s*v2+a*b*e^2*
s^2*v1+a*b*e^2*s*t*v0+a*c^3*r*t*v4-a*c^3*s^2*v4+a*c^3*s*t*v3-a*c^3*t^2*v2+2*a*c
^2*d*q*t*v4-2*a*c^2*d*r*t*v3+a*c^2*d*s^2*v3-a*c^2*d*s*t*v2+2*a*c^2*d*t^2*v1-a*c
^2*e*p*t*v4-a*c^2*e*q*s*v4-3*a*c^2*e*q*t*v3-a*c^2*e*r*s*v3+a*c^2*e*s^2*v2-2*a*c
^2*e*s*t*v1-3*a*c^2*e*t^2*v0+3*a*c*d^2*p*t*v4+a*c*d^2*q*s*v4-2*a*c*d^2*q*t*v3+2
*a*c*d^2*r*t*v2-a*c*d^2*s^2*v2+a*c*d^2*s*t*v1+2*a*c*d^2*t^2*v0-a*c*d*e*p*s*v4-5
*a*c*d*e*p*t*v3-2*a*c*d*e*q*s*v3+4*a*c*d*e*q*t*v2+a*c*d*e*r*s*v2+3*a*c*d*e*r*t*
v1-2*a*c*d*e*s^2*v1-2*a*c*d*e*s*t*v0-a*c*e^2*p*s*v3+2*a*c*e^2*p*t*v2+a*c*e^2*q*
s*v2+a*c*e^2*q*t*v1+a*d^3*p*s*v4-a*d^3*p*t*v3+a*d^3*q*t*v2-a*d^3*r*t*v1+a*d^3*s
^2*v1+a*d^3*s*t*v0-a*d^2*e*p*s*v3+4*a*d^2*e*p*t*v2+a*d^2*e*q*s*v2+a*d^2*e*q*t*
v1+2*a*d*e^2*p*s*v2+2*a*d*e^2*p*t*v1+b^4*t^2*v4-b^3*c*t^2*v3+2*b^3*d*r*t*v4+b^3
*d*s*t*v3-b^3*d*t^2*v2+b^3*e*q*t*v4-b^3*e*r*s*v4-b^3*e*r*t*v3-b^3*e*s^2*v3+b^3*
e*s*t*v2-b^3*e*t^2*v1-2*b^2*c^2*r*t*v4+b^2*c^2*t^2*v2+2*b^2*c*d*r*s*v4+b^2*c*d*
r*t*v3-b^2*c*d*s*t*v2+2*b^2*c*d*t^2*v1+b^2*c*e*p*t*v4-b^2*c*e*q*s*v4-b^2*c*e*r^
2*v4-4*b^2*c*e*r*s*v3+4*b^2*c*e*r*t*v2+b^2*c*e*s^2*v2-b^2*c*e*s*t*v1+2*b^2*c*e*
t^2*v0+2*b^2*d^2*p*t*v4+2*b^2*d^2*q*t*v3+b^2*d^2*r^2*v4-b^2*d^2*r*s*v3-b^2*d^2*
r*t*v2-b^2*d^2*s*t*v1+b^2*d^2*t^2*v0-b^2*d*e*p*s*v4-b^2*d*e*q*s*v3-b^2*d*e*r^2*
v3+3*b^2*d*e*r*s*v2-b^2*d*e*r*t*v1+b^2*d*e*s^2*v1+b^2*d*e*s*t*v0-b^2*e^2*p*s*v3
+b^2*e^2*p*t*v2-b^2*e^2*q*t*v1+b^2*e^2*r^2*v2+b^2*e^2*r*s*v1+b^2*e^2*r*t*v0-b*c
^3*q*t*v4-b*c^3*r*s*v4+b*c^3*r*t*v3-b*c^3*t^2*v1-4*b*c^2*d*p*t*v4+2*b*c^2*d*q*s
*v4-b*c^2*d*q*t*v3+b*c^2*d*r*s*v3-2*b*c^2*d*r*t*v2+b*c^2*d*s*t*v1-3*b*c^2*d*t^2
*v0+b*c^2*e*p*t*v3-2*b*c^2*e*q*r*v4-3*b*c^2*e*q*s*v3+2*b*c^2*e*q*t*v2-2*b*c^2*e
*r^2*v3+2*b*c^2*e*r*s*v2-2*b*c^2*e*r*t*v1-b*c^2*e*s^2*v1-b*c^2*e*s*t*v0+2*b*c*d
^2*p*s*v4+b*c*d^2*p*t*v3+2*b*c*d^2*q*r*v4-b*c*d^2*q*s*v3-b*c*d^2*q*t*v2-b*c*d^2
*r*s*v2-2*b*c*d*e*p*r*v4-3*b*c*d*e*p*s*v3+b*c*d*e*p*t*v2-4*b*c*d*e*q*r*v3+4*b*c
*d*e*q*s*v2+2*b*c*d*e*r^2*v2-b*c*d*e*r*s*v1-b*c*d*e*r*t*v0-2*b*c*e^2*p*r*v3+b*c
*e^2*p*s*v2-2*b*c*e^2*p*t*v1+2*b*c*e^2*q*r*v2+b*c*e^2*q*s*v1+b*c*e^2*q*t*v0+2*b
*d^3*p*r*v4-b*d^3*p*s*v3-b*d^3*p*t*v2-2*b*d^3*q*t*v1+b*d^3*r*s*v1+b*d^3*r*t*v0-\
2*b*d^2*e*p*r*v3+3*b*d^2*e*p*s*v2-2*b*d^2*e*p*t*v1+2*b*d^2*e*q*r*v2+b*d^2*e*q*s
*v1+b*d^2*e*q*t*v0+4*b*d*e^2*p*r*v2+2*b*d*e^2*p*s*v1+2*b*d*e^2*p*t*v0+c^4*p*t*
v4-c^4*q*s*v4+c^4*q*t*v3+c^4*t^2*v0-c^3*d*p*s*v4+c^3*d*q*s*v3-c^3*d*q*t*v2+c^3*
d*r*t*v1-c^3*e*p*t*v2-c^3*e*q^2*v4-2*c^3*e*q*r*v3+c^3*e*q*s*v2-c^3*e*q*t*v1-c^3
*e*r*s*v1-c^3*e*r*t*v0+c^2*d^2*p*s*v3+c^2*d^2*q^2*v4-c^2*d^2*q*s*v2+2*c^2*d^2*q
*t*v1-2*c^2*d*e*p*q*v4-2*c^2*d*e*p*r*v3+c^2*d*e*p*s*v2+2*c^2*d*e*p*t*v1-3*c^2*d
*e*q^2*v3+2*c^2*d*e*q*r*v2-3*c^2*d*e*q*s*v1-3*c^2*d*e*q*t*v0-2*c^2*e^2*p*q*v3-c
^2*e^2*p*s*v1-c^2*e^2*p*t*v0+c^2*e^2*q^2*v2+2*c*d^3*p*q*v4-c*d^3*p*s*v2+c*d^3*q
*s*v1+c*d^3*q*t*v0-c*d^2*e*p^2*v4-4*c*d^2*e*p*q*v3+2*c*d^2*e*p*r*v2-2*c*d^2*e*p
*s*v1-2*c*d^2*e*p*t*v0+2*c*d^2*e*q^2*v2-2*c*d*e^2*p^2*v3+4*c*d*e^2*p*q*v2+d^4*p
^2*v4+d^4*p*s*v1+d^4*p*t*v0-d^3*e*p^2*v3+2*d^3*e*p*q*v2+3*d^2*e^2*p^2*v2+2*a*b*
e^2*t*v4-a*c*d*e*t*v4+a*c*e^2*s*v4+2*a*c*e^2*t*v3-a*d^3*t*v4-a*d^2*e*s*v4+2*a*d
^2*e*t*v3+a*d*e^2*s*v3-3*a*d*e^2*t*v2-a*e^3*s*v2-a*e^3*t*v1-3*b^2*d*e*t*v4+b^2*
e^2*s*v4+b^2*e^2*t*v3+2*b*c^2*e*t*v4+2*b*c*d^2*t*v4-2*b*c*d*e*s*v4-b*c*d*e*t*v3
+2*b*c*e^2*r*v4+2*b*c*e^2*s*v3-3*b*c*e^2*t*v2-b*d^3*t*v3-2*b*d^2*e*r*v4+b*d^2*e
*s*v3+2*b*d^2*e*t*v2+2*b*d*e^2*r*v3-2*b*d*e^2*s*v2+2*b*d*e^2*t*v1-2*b*e^3*r*v2-
b*e^3*s*v1-b*e^3*t*v0-c^3*d*t*v4+c^3*e*s*v4-c^3*e*t*v3+c^2*d^2*t*v3-c^2*d*e*s*
v3+2*c^2*d*e*t*v2+2*c^2*e^2*q*v4+c^2*e^2*r*v3-c^2*e^2*s*v2+c^2*e^2*t*v1-c*d^3*t
*v2-2*c*d^2*e*q*v4+c*d^2*e*s*v2-3*c*d^2*e*t*v1+2*c*d*e^2*p*v4+3*c*d*e^2*q*v3-c*
d*e^2*r*v2+2*c*d*e^2*s*v1+2*c*d*e^2*t*v0+c*e^3*p*v3-2*c*e^3*q*v2+d^4*t*v1-2*d^3
*e*p*v4-d^3*e*s*v1-d^3*e*t*v0+2*d^2*e^2*p*v3-d^2*e^2*q*v2-3*d*e^3*p*v2-c*e^3*v4
+d^2*e^2*v4-d*e^3*v3+e^4*v2




beta[3,2] = -a^4*p*t^3*v3-3*a^3*b*p*s*t^2*v3+a^3*b*p*t^3*v2-2*a^3*c*p*r*t^2*v3+
a^3*c*p*s*t^2*v2+a^3*c*p*t^3*v1-a^3*d*p*q*t^2*v3+a^3*d*p*r*t^2*v2+a^3*d*p*s*t^2
*v1+a^3*d*p*t^3*v0-a^3*e*p^2*t^2*v3-a^2*b^2*p*r*t^2*v3-3*a^2*b^2*p*s^2*t*v3+2*a
^2*b^2*p*s*t^2*v2-a^2*b^2*p*t^3*v1-3*a^2*b*c*p*q*t^2*v3-4*a^2*b*c*p*r*s*t*v3+a^
2*b*c*p*r*t^2*v2+2*a^2*b*c*p*s^2*t*v2-2*a^2*b*c*p*t^3*v0-2*a^2*b*d*p^2*t^2*v3-2
*a^2*b*d*p*q*s*t*v3+2*a^2*b*d*p*q*t^2*v2+2*a^2*b*d*p*r*s*t*v2+2*a^2*b*d*p*s^2*t
*v1+2*a^2*b*d*p*s*t^2*v0-2*a^2*b*e*p^2*s*t*v3+a^2*b*e*p^2*t^2*v2-a^2*c^2*p^2*t^
2*v3-a^2*c^2*p*q*s*t*v3+a^2*c^2*p*q*t^2*v2-a^2*c^2*p*r^2*t*v3+a^2*c^2*p*r*s*t*
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*v3-4*a*b*c*e*p*s*t*v2+3*a*b*c*e*p*t^2*v1-3*a*b*c*e*q^2*t*v3-a*b*c*e*q*r*s*v3-3
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e*r*s^2*v1-a*b*c*e*r*s*t*v0+2*a*b*d^2*p*q*t*v4-2*a*b*d^2*p*r*t*v3-2*a*b*d^2*p*s
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r*t*v2-3*a*b*d*e*p*s^2*v2-4*a*b*d*e*p*s*t*v1-a*b*d*e*p*t^2*v0+2*a*b*e^2*p^2*t*
v3-a*b*e^2*p*q*t*v2-a*b*e^2*p*r*s*v2-a*b*e^2*p*s^2*v1-a*b*e^2*p*s*t*v0+a*c^3*p*
r*t*v4-a*c^3*p*s*t*v3+a*c^3*q^2*t*v4+a*c^3*q*r*s*v4-a*c^3*q*s^2*v3+a*c^3*q*s*t*
v2+a*c^3*q*t^2*v1+2*a*c^3*r*s*t*v1+a*c^3*r*t^2*v0-a*c^3*s^3*v1-a*c^3*s^2*t*v0+3
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p*t^2*v1+a*c^2*d*q^2*s*v4-a*c^2*d*q*r*s*v3+a*c^2*d*q*s^2*v2+3*a*c^2*d*q*s*t*v1+
2*a*c^2*d*q*t^2*v0+a*c^2*e*p^2*t*v4+a*c^2*e*p*q*s*v4+a*c^2*e*p*q*t*v3+a*c^2*e*p
*r*s*v3-2*a*c^2*e*p*r*t*v2+2*a*c^2*e*p*s*t*v1+2*a*c^2*e*p*t^2*v0-a*c^2*e*q^2*s*
v3-a*c^2*e*q*r*s*v2-a*c^2*e*q*s^2*v1-a*c^2*e*q*s*t*v0+a*c*d^2*p^2*t*v4+a*c*d^2*
p*q*s*v4+a*c*d^2*p*q*t*v3-a*c*d^2*p*r*s*v3+a*c*d^2*p*s^2*v2+2*a*c*d^2*p*s*t*v1+
a*c*d^2*p*t^2*v0-a*c*d^2*q^2*t*v2+a*c*d^2*q*r*s*v2+a*c*d^2*q*s^2*v1+a*c*d^2*q*s
*t*v0+a*c*d*e*p^2*s*v4+3*a*c*d*e*p^2*t*v3-5*a*c*d*e*p*q*t*v2-2*a*c*d*e*p*r*s*v2
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2*p^2*t*v2-a*c*e^2*p*q*s*v2-a*c*e^2*p*q*t*v1-2*a*d^3*p*q*t*v2+a*d^3*p*r*s*v2+a*
d^3*p*r*t*v1-5*a*d^2*e*p^2*t*v2-a*d^2*e*p*q*s*v2-a*d^2*e*p*q*t*v1-2*a*d*e^2*p^2
*s*v2-2*a*d*e^2*p^2*t*v1-b^4*q*s*t*v4+b^4*q*t^2*v3+b^4*r*s^2*v4-b^4*r*s*t*v3+b^
4*r*t^2*v2+b^4*t^3*v0-b^3*c*p*s*t*v4+b^3*c*p*t^2*v3-b^3*c*q*r*t*v4+b^3*c*q*s^2*
v4+2*b^3*c*r^2*s*v4-b^3*c*r^2*t*v3-b^3*c*r*s^2*v3+b^3*c*r*s*t*v2-b^3*c*r*t^2*v1
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v1+2*b^2*c*d*r*s*t*v0-b^2*c*e*p^2*t*v4+b^2*c*e*p*q*s*v4+b^2*c*e*p*q*t*v3+b^2*c*
e*p*r^2*v4+3*b^2*c*e*p*r*s*v3-2*b^2*c*e*p*r*t*v2-b^2*c*e*p*s^2*v2+2*b^2*c*e*p*s
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*e*q*s^2*v1-b^2*c*e*q*s*t*v0-b^2*c*e*r^3*v2-b^2*c*e*r^2*s*v1-b^2*c*e*r^2*t*v0+b
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s^2*v2+2*b^2*d^2*p*s*t*v1+b^2*d^2*p*t^2*v0+b^2*d^2*q^2*t*v2-b^2*d^2*q*r*s*v2-b^
2*d^2*q*r*t*v1+b^2*d^2*r^3*v2+b^2*d^2*r^2*s*v1+b^2*d^2*r^2*t*v0+b^2*d*e*p^2*s*
v4-b^2*d*e*p^2*t*v3+b^2*d*e*p*q*t*v2-5*b^2*d*e*p*r*s*v2-2*b^2*d*e*p*s^2*v1-2*b^
2*d*e*p*s*t*v0+b^2*e^2*p^2*s*v3-b^2*e^2*p^2*t*v2+b^2*e^2*p*q*t*v1-b^2*e^2*p*r^2
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*v2-b*c^3*q*t^2*v0+b*c^3*r^2*t*v1-b*c^3*r*s^2*v1-b*c^3*r*s*t*v0+2*b*c^2*d*p*q*s
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2*d*q*r*s*v2+2*b*c^2*d*q*s^2*v1+2*b*c^2*d*q*s*t*v0+2*b*c^2*e*p*q*r*v4+2*b*c^2*e
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t*v1+b*c^2*e*p*s^2*v1+b*c^2*e*p*s*t*v0-2*b*c^2*e*q^2*r*v3-2*b*c^2*e*q*r^2*v2-2*
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t*v1+2*b*c*d^2*p*s^2*v1+2*b*c*d^2*p*s*t*v0-b*c*d^2*q^2*s*v2-b*c*d^2*q^2*t*v1+2*
b*c*d^2*q*r^2*v2+2*b*c*d^2*q*r*s*v1+2*b*c*d^2*q*r*t*v0+2*b*c*d*e*p^2*r*v4+2*b*c
*d*e*p^2*s*v3+b*c*d*e*p^2*t*v2-5*b*c*d*e*p*q*s*v2-b*c*d*e*p*q*t*v1-4*b*c*d*e*p*
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b*c*e^2*p^2*t*v1-2*b*c*e^2*p*q*r*v2-b*c*e^2*p*q*s*v1-b*c*e^2*p*q*t*v0+b*d^3*p^2
*t*v2-b*d^3*p*q*s*v2+b*d^3*p*q*t*v1+2*b*d^3*p*r^2*v2+b*d^3*p*r*s*v1+b*d^3*p*r*t
*v0-4*b*d^2*e*p^2*s*v2+b*d^2*e*p^2*t*v1-2*b*d^2*e*p*q*r*v2-b*d^2*e*p*q*s*v1-b*d
^2*e*p*q*t*v0-4*b*d*e^2*p^2*r*v2-2*b*d*e^2*p^2*s*v1-2*b*d*e^2*p^2*t*v0+c^4*p*s*
t*v1+c^4*q^2*r*v4-c^4*q^2*s*v3+c^4*q*r*t*v1-c^4*q*s^2*v1-c^4*q*s*t*v0+2*c^3*d*p
*q*r*v4-2*c^3*d*p*q*s*v3-c^3*d*p*s^2*v1-c^3*d*p*s*t*v0+c^3*d*q^3*v4-c^3*d*q^2*r
*v3+c^3*d*q^2*s*v2+c^3*d*q^2*t*v1+c^3*e*p*q^2*v4+2*c^3*e*p*q*r*v3+2*c^3*e*p*q*t
*v1+c^3*e*p*r*s*v1+c^3*e*p*r*t*v0-c^3*e*q^3*v3-c^3*e*q^2*r*v2-c^3*e*q^2*s*v1-c^
3*e*q^2*t*v0+c^2*d^2*p^2*r*v4-c^2*d^2*p^2*s*v3+2*c^2*d^2*p*q^2*v4-2*c^2*d^2*p*q
*r*v3+2*c^2*d^2*p*q*s*v2-c^2*d^2*p*q*t*v1+c^2*d^2*q^2*r*v2+c^2*d^2*q^2*s*v1+c^2
*d^2*q^2*t*v0+2*c^2*d*e*p^2*q*v4+2*c^2*d*e*p^2*r*v3-c^2*d*e*p^2*t*v1-4*c^2*d*e*
p*q*r*v2+c^2*d*e*p*q*s*v1+c^2*d*e*p*q*t*v0+2*c^2*e^2*p^2*q*v3+c^2*e^2*p^2*s*v1+
c^2*e^2*p^2*t*v0-c^2*e^2*p*q^2*v2+c*d^3*p^2*q*v4-c*d^3*p^2*r*v3+c*d^3*p^2*s*v2+
2*c*d^3*p*q*r*v2+c*d^3*p*q*s*v1+c*d^3*p*q*t*v0+c*d^2*e*p^3*v4+c*d^2*e*p^2*q*v3-\
3*c*d^2*e*p^2*r*v2+c*d^2*e*p^2*s*v1+c*d^2*e*p^2*t*v0-2*c*d^2*e*p*q^2*v2+2*c*d*e
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^2*b*e*t^2*v4-3*a^2*c*d*t^2*v4-2*a^2*c*e*s*t*v4+2*a^2*c*e*t^2*v3-a^2*d^2*s*t*v4
+a^2*d^2*t^2*v3-a^2*d*e*r*t*v4+2*a^2*d*e*s*t*v3+2*a^2*d*e*t^2*v2+a^2*e^2*r*t*v3
+a^2*e^2*s*t*v2+a^2*e^2*t^2*v1+2*a*b^2*d*t^2*v4-4*a*b^2*e*s*t*v4+2*a*b^2*e*t^2*
v3+2*a*b*c^2*t^2*v4-a*b*c*d*s*t*v4-a*b*c*d*t^2*v3-4*a*b*c*e*r*t*v4-2*a*b*c*e*s^
2*v4+5*a*b*c*e*s*t*v3-a*b*c*e*t^2*v2-a*b*d^2*s^2*v4-3*a*b*d^2*t^2*v2-3*a*b*d*e*
q*t*v4-a*b*d*e*r*s*v4+2*a*b*d*e*r*t*v3+2*a*b*d*e*s^2*v3+a*b*d*e*s*t*v2-a*b*d*e*
t^2*v1-2*a*b*e^2*p*t*v4+3*a*b*e^2*q*t*v3+a*b*e^2*r*s*v3+2*a*b*e^2*r*t*v2+a*b*e^
2*s^2*v2+3*a*b*e^2*s*t*v1+2*a*b*e^2*t^2*v0+a*c^3*s*t*v4-a*c^3*t^2*v3-2*a*c^2*d*
r*t*v4+a*c^2*d*s^2*v4-a*c^2*d*s*t*v3+2*a*c^2*d*t^2*v2-3*a*c^2*e*q*t*v4-a*c^2*e*
r*s*v4+a*c^2*e*s^2*v3-2*a*c^2*e*s*t*v2-3*a*c^2*e*t^2*v1-2*a*c*d^2*q*t*v4+2*a*c*
d^2*r*t*v3-a*c*d^2*s^2*v3+a*c*d^2*s*t*v2+2*a*c*d^2*t^2*v1-5*a*c*d*e*p*t*v4-2*a*
c*d*e*q*s*v4+3*a*c*d*e*q*t*v3+a*c*d*e*r*s*v3+2*a*c*d*e*r*t*v2-2*a*c*d*e*s^2*v2-\
3*a*c*d*e*s*t*v1-a*c*d*e*t^2*v0-a*c*e^2*p*s*v4+2*a*c*e^2*q*s*v3+a*c*e^2*q*t*v2+
a*c*e^2*r*s*v2+a*c*e^2*s^2*v1+a*c*e^2*s*t*v0-a*d^3*p*t*v4-2*a*d^3*r*t*v2+a*d^3*
s^2*v2-a*d^3*t^2*v0-a*d^2*e*p*s*v4+2*a*d^2*e*p*t*v3+a*d^2*e*q*t*v2-a*d^2*e*r*s*
v2-a*d^2*e*s^2*v1-a*d^2*e*s*t*v0+a*d*e^2*p*s*v3+5*a*d*e^2*p*t*v2+a*e^3*p*s*v2+a
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3*e*s*t*v3-b^3*e*t^2*v2+b^2*c^2*t^2*v3+b^2*c*d*r*t*v4-b^2*c*d*s*t*v3+2*b^2*c*d*
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e*t^2*v1+2*b^2*d^2*q*t*v4-b^2*d^2*r*s*v4-b^2*d^2*r*t*v3-b^2*d^2*s*t*v2+b^2*d^2*
t^2*v1-b^2*d*e*q*s*v4-3*b^2*d*e*q*t*v3-b^2*d*e*r^2*v4+3*b^2*d*e*r*s*v3-4*b^2*d*
e*r*t*v2+b^2*d*e*s^2*v2-2*b^2*d*e*s*t*v1-3*b^2*d*e*t^2*v0-b^2*e^2*p*s*v4+b^2*e^
2*q*s*v3-b^2*e^2*q*t*v2+b^2*e^2*r^2*v3+2*b^2*e^2*r*s*v2+b^2*e^2*r*t*v1+b^2*e^2*
s^2*v1+b^2*e^2*s*t*v0+b*c^3*r*t*v4-b*c^3*t^2*v2-b*c^2*d*q*t*v4+b*c^2*d*r*s*v4-2
*b*c^2*d*r*t*v3+b*c^2*d*s*t*v2-3*b*c^2*d*t^2*v1+b*c^2*e*p*t*v4-3*b*c^2*e*q*s*v4
+4*b*c^2*e*q*t*v3-2*b*c^2*e*r^2*v4+2*b*c^2*e*r*s*v3-b*c^2*e*s^2*v2+b*c^2*e*s*t*
v1+2*b*c^2*e*t^2*v0+b*c*d^2*p*t*v4-b*c*d^2*q*s*v4+b*c*d^2*q*t*v3-b*c*d^2*r*s*v3
+2*b*c*d^2*r*t*v2+2*b*c*d^2*s*t*v1+2*b*c*d^2*t^2*v0-3*b*c*d*e*p*s*v4+2*b*c*d*e*
p*t*v3-4*b*c*d*e*q*r*v4+2*b*c*d*e*q*s*v3+2*b*c*d*e*r^2*v3-3*b*c*d*e*r*s*v2-b*c*
d*e*r*t*v1-2*b*c*d*e*s^2*v1-2*b*c*d*e*s*t*v0-2*b*c*e^2*p*r*v4-b*c*e^2*p*s*v3+b*
c*e^2*p*t*v2+4*b*c*e^2*q*r*v3+b*c*e^2*q*s*v2+b*c*e^2*q*t*v1+2*b*c*e^2*r^2*v2+2*
b*c*e^2*r*s*v1+2*b*c*e^2*r*t*v0-b*d^3*p*s*v4-2*b*d^3*q*t*v2+b*d^3*r*s*v2+b*d^3*
r*t*v1-2*b*d^2*e*p*r*v4+2*b*d^2*e*p*s*v3-4*b*d^2*e*p*t*v2+b*d^2*e*q*s*v2+b*d^2*
e*q*t*v1-2*b*d^2*e*r^2*v2-2*b*d^2*e*r*s*v1-2*b*d^2*e*r*t*v0+2*b*d*e^2*p*r*v3+4*
b*d*e^2*p*s*v2+2*b*e^3*p*r*v2+b*e^3*p*s*v1+b*e^3*p*t*v0+c^4*q*t*v4+c^4*t^2*v1+c
^3*d*q*s*v4-2*c^3*d*q*t*v3-c^3*d*s*t*v1-c^3*d*t^2*v0-2*c^3*e*q*r*v4+2*c^3*e*q*s
*v3-c^3*e*q*t*v2-c^3*e*r*t*v1+c^3*e*s^2*v1+c^3*e*s*t*v0+c^2*d^2*p*s*v4-c^2*d^2*
p*t*v3-c^2*d^2*q*s*v3+2*c^2*d^2*q*t*v2-2*c^2*d*e*p*r*v4+2*c^2*d*e*p*s*v3-3*c^2*
d*e*q^2*v4+2*c^2*d*e*q*r*v3-3*c^2*d*e*q*s*v2-3*c^2*d*e*q*t*v1-2*c^2*e^2*p*q*v4-
c^2*e^2*p*r*v3-2*c^2*e^2*p*t*v1+3*c^2*e^2*q^2*v3+2*c^2*e^2*q*r*v2+2*c^2*e^2*q*s
*v1+2*c^2*e^2*q*t*v0-c*d^3*p*s*v3+c*d^3*p*t*v2+c*d^3*q*s*v2+c*d^3*q*t*v1-4*c*d^
2*e*p*q*v4+2*c*d^2*e*p*r*v3-3*c*d^2*e*p*s*v2+c*d^2*e*p*t*v1-2*c*d^2*e*q*r*v2-2*
c*d^2*e*q*s*v1-2*c*d^2*e*q*t*v0-2*c*d*e^2*p^2*v4+3*c*d*e^2*p*q*v3+3*c*d*e^2*p*r
*v2-c*e^3*p^2*v3+2*c*e^3*p*q*v2+d^4*p*s*v2-d^3*e*p^2*v4-2*d^3*e*p*r*v2-d^3*e*p*
s*v1-d^3*e*p*t*v0+d^2*e^2*p^2*v3+d^2*e^2*p*q*v2+3*d*e^3*p^2*v2+2*a*c*e^2*t*v4+2
*a*d^2*e*t*v4+a*d*e^2*s*v4-3*a*d*e^2*t*v3-a*e^3*s*v3-a*e^3*t*v2+b^2*e^2*t*v4-b*
c*d*e*t*v4+2*b*c*e^2*s*v4-3*b*c*e^2*t*v3-b*d^3*t*v4+b*d^2*e*s*v4+2*b*d^2*e*t*v3
+2*b*d*e^2*r*v4-2*b*d*e^2*s*v3+2*b*d*e^2*t*v2-2*b*e^3*r*v3-b*e^3*s*v2-b*e^3*t*
v1-c^3*e*t*v4+c^2*d^2*t*v4-c^2*d*e*s*v4+2*c^2*d*e*t*v3+c^2*e^2*r*v4-c^2*e^2*s*
v3+c^2*e^2*t*v2-c*d^3*t*v3+c*d^2*e*s*v3-3*c*d^2*e*t*v2+3*c*d*e^2*q*v4-c*d*e^2*r
*v3+2*c*d*e^2*s*v2+2*c*d*e^2*t*v1+c*e^3*p*v4-3*c*e^3*q*v3-c*e^3*r*v2-c*e^3*s*v1
-c*e^3*t*v0+d^4*t*v2-d^3*e*s*v2-d^3*e*t*v1+2*d^2*e^2*p*v4+d^2*e^2*r*v2+d^2*e^2*
s*v1+d^2*e^2*t*v0-2*d*e^3*p*v3-e^4*p*v2-d*e^3*v4+e^4*v3




beta[3,3] = a^4*r*t^3*v2+a^4*s*t^3*v1+a^4*t^4*v0+a^3*b*p*t^3*v3+a^3*b*q*t^3*v2+
3*a^3*b*r*s*t^2*v2+3*a^3*b*s^2*t^2*v1+3*a^3*b*s*t^3*v0+a^3*c*p*s*t^2*v3+a^3*c*p
*t^3*v2+a^3*c*q*s*t^2*v2+a^3*c*q*t^3*v1+2*a^3*c*r^2*t^2*v2+2*a^3*c*r*s*t^2*v1+2
*a^3*c*r*t^3*v0+a^3*d*p*r*t^2*v3+a^3*d*p*s*t^2*v2+a^3*d*p*t^3*v1+2*a^3*d*q*r*t^
2*v2+2*a^3*d*q*s*t^2*v1+2*a^3*d*q*t^3*v0+a^3*e*p*r*t^2*v2+a^3*e*p*s*t^2*v1+a^3*
e*p*t^3*v0+2*a^2*b^2*p*s*t^2*v3-a^2*b^2*p*t^3*v2+2*a^2*b^2*q*s*t^2*v2-a^2*b^2*q
*t^3*v1+a^2*b^2*r^2*t^2*v2+3*a^2*b^2*r*s^2*t*v2+a^2*b^2*r*s*t^2*v1+a^2*b^2*r*t^
3*v0+3*a^2*b^2*s^3*t*v1+3*a^2*b^2*s^2*t^2*v0+a^2*b*c*p*r*t^2*v3+2*a^2*b*c*p*s^2
*t*v3-2*a^2*b*c*p*t^3*v1+4*a^2*b*c*q*r*t^2*v2+2*a^2*b*c*q*s^2*t*v2+3*a^2*b*c*q*
s*t^2*v1+a^2*b*c*q*t^3*v0+4*a^2*b*c*r^2*s*t*v2+4*a^2*b*c*r*s^2*t*v1+4*a^2*b*c*r
*s*t^2*v0+2*a^2*b*d*p*q*t^2*v3+2*a^2*b*d*p*r*s*t*v3+2*a^2*b*d*p*r*t^2*v2+2*a^2*
b*d*p*s^2*t*v2+4*a^2*b*d*p*s*t^2*v1+2*a^2*b*d*p*t^3*v0+2*a^2*b*d*q^2*t^2*v2+4*a
^2*b*d*q*r*s*t*v2+4*a^2*b*d*q*s^2*t*v1+4*a^2*b*d*q*s*t^2*v0+a^2*b*e*p^2*t^2*v3+
a^2*b*e*p*q*t^2*v2+2*a^2*b*e*p*r*s*t*v2+2*a^2*b*e*p*s^2*t*v1+2*a^2*b*e*p*s*t^2*
v0+a^2*c^2*p*q*t^2*v3+a^2*c^2*p*r*s*t*v3+3*a^2*c^2*p*r*t^2*v2-a^2*c^2*p*s^2*t*
v2+a^2*c^2*p*t^3*v0+a^2*c^2*q^2*t^2*v2+2*a^2*c^2*q*r*s*t*v2+2*a^2*c^2*q*r*t^2*
v1+a^2*c^2*r^3*t*v2+a^2*c^2*r^2*s*t*v1+a^2*c^2*r^2*t^2*v0+2*a^2*c*d*p^2*t^2*v3+
2*a^2*c*d*p*q*s*t*v3+4*a^2*c*d*p*q*t^2*v2+a^2*c*d*p*r^2*t*v3+2*a^2*c*d*p*r*s*t*
v2+a^2*c*d*p*r*t^2*v1+a^2*c*d*p*s^2*t*v1+a^2*c*d*p*s*t^2*v0+2*a^2*c*d*q^2*s*t*
v2+2*a^2*c*d*q^2*t^2*v1+2*a^2*c*d*q*r^2*t*v2+2*a^2*c*d*q*r*s*t*v1+2*a^2*c*d*q*r
*t^2*v0+a^2*c*e*p^2*s*t*v3+a^2*c*e*p^2*t^2*v2+a^2*c*e*p*q*s*t*v2+a^2*c*e*p*q*t^
2*v1+a^2*c*e*p*r^2*t*v2+a^2*c*e*p*r*s*t*v1+a^2*c*e*p*r*t^2*v0+a^2*d^2*p^2*s*t*
v3+a^2*d^2*p^2*t^2*v2+a^2*d^2*p*q*r*t*v3+2*a^2*d^2*p*q*s*t*v2+2*a^2*d^2*p*q*t^2
*v1+a^2*d^2*q^2*r*t*v2+a^2*d^2*q^2*s*t*v1+a^2*d^2*q^2*t^2*v0+a^2*d*e*p^2*r*t*v3
+a^2*d*e*p^2*s*t*v2+a^2*d*e*p^2*t^2*v1+a^2*d*e*p*q*r*t*v2+a^2*d*e*p*q*s*t*v1+a^
2*d*e*p*q*t^2*v0+a*b^3*p*r*t^2*v3+a*b^3*p*s^2*t*v3-a*b^3*p*s*t^2*v2+a*b^3*p*t^3
*v1+a*b^3*q*s^2*t*v2-2*a*b^3*q*s*t^2*v1+2*a*b^3*r^2*s*t*v2+a*b^3*r*s^3*v2+2*a*b
^3*r*s^2*t*v1+2*a*b^3*r*s*t^2*v0+a*b^3*s^4*v1+a*b^3*s^3*t*v0+2*a*b^2*c*p*r*s*t*
v3-3*a*b^2*c*p*r*t^2*v2+a*b^2*c*p*s^3*v3-a*b^2*c*p*s^2*t*v2-3*a*b^2*c*p*s*t^2*
v1-a*b^2*c*p*t^3*v0+6*a*b^2*c*q*r*s*t*v2-2*a*b^2*c*q*r*t^2*v1+a*b^2*c*q*s^3*v2+
3*a*b^2*c*q*s^2*t*v1+2*a*b^2*c*q*s*t^2*v0+2*a*b^2*c*r^3*t*v2+2*a*b^2*c*r^2*s^2*
v2+2*a*b^2*c*r^2*s*t*v1+2*a*b^2*c*r^2*t^2*v0+2*a*b^2*c*r*s^3*v1+2*a*b^2*c*r*s^2
*t*v0+a*b^2*d*p^2*t^2*v3+2*a*b^2*d*p*q*s*t*v3-a*b^2*d*p*q*t^2*v2+a*b^2*d*p*r^2*
t*v3+a*b^2*d*p*r*s^2*v3+4*a*b^2*d*p*r*s*t*v2+a*b^2*d*p*r*t^2*v1+a*b^2*d*p*s^3*
v2+4*a*b^2*d*p*s^2*t*v1+3*a*b^2*d*p*s*t^2*v0+2*a*b^2*d*q^2*s*t*v2-2*a*b^2*d*q^2
*t^2*v1+2*a*b^2*d*q*r^2*t*v2+2*a*b^2*d*q*r*s^2*v2+2*a*b^2*d*q*r*s*t*v1+2*a*b^2*
d*q*r*t^2*v0+2*a*b^2*d*q*s^3*v1+2*a*b^2*d*q*s^2*t*v0+a*b^2*e*p^2*s*t*v3-a*b^2*e
*p^2*t^2*v2+a*b^2*e*p*q*s*t*v2-a*b^2*e*p*q*t^2*v1+a*b^2*e*p*r^2*t*v2+a*b^2*e*p*
r*s^2*v2+a*b^2*e*p*r*s*t*v1+a*b^2*e*p*r*t^2*v0+a*b^2*e*p*s^3*v1+a*b^2*e*p*s^2*t
*v0-a*b*c^2*p^2*t^2*v3+2*a*b*c^2*p*q*s*t*v3-a*b*c^2*p*q*t^2*v2+a*b*c^2*p*r*s^2*
v3-3*a*b*c^2*p*r*t^2*v1-a*b*c^2*p*s^3*v2+a*b*c^2*p*s*t^2*v0+2*a*b*c^2*q^2*s*t*
v2+5*a*b*c^2*q*r^2*t*v2+2*a*b*c^2*q*r*s^2*v2+4*a*b*c^2*q*r*s*t*v1+2*a*b*c^2*q*r
*t^2*v0+a*b*c^2*r^3*s*v2+a*b*c^2*r^2*s^2*v1+a*b*c^2*r^2*s*t*v0+3*a*b*c*d*p^2*s*
t*v3-2*a*b*c*d*p^2*t^2*v2+3*a*b*c*d*p*q*r*t*v3+2*a*b*c*d*p*q*s^2*v3+4*a*b*c*d*p
*q*s*t*v2-3*a*b*c*d*p*q*t^2*v1+a*b*c*d*p*r^2*s*v3+4*a*b*c*d*p*r^2*t*v2+2*a*b*c*
d*p*r*s^2*v2+5*a*b*c*d*p*r*s*t*v1+4*a*b*c*d*p*r*t^2*v0+a*b*c*d*p*s^3*v1+a*b*c*d
*p*s^2*t*v0+6*a*b*c*d*q^2*r*t*v2+2*a*b*c*d*q^2*s^2*v2+4*a*b*c*d*q^2*s*t*v1+2*a*
b*c*d*q^2*t^2*v0+2*a*b*c*d*q*r^2*s*v2+2*a*b*c*d*q*r*s^2*v1+2*a*b*c*d*q*r*s*t*v0
+a*b*c*e*p^2*s^2*v3-a*b*c*e*p^2*s*t*v2-2*a*b*c*e*p^2*t^2*v1+3*a*b*c*e*p*q*r*t*
v2+a*b*c*e*p*q*s^2*v2+2*a*b*c*e*p*q*s*t*v1+a*b*c*e*p*q*t^2*v0+a*b*c*e*p*r^2*s*
v2+a*b*c*e*p*r*s^2*v1+a*b*c*e*p*r*s*t*v0+2*a*b*d^2*p^2*r*t*v3+a*b*d^2*p^2*s^2*
v3+2*a*b*d^2*p^2*s*t*v2+a*b*d^2*p^2*t^2*v1+a*b*d^2*p*q^2*t*v3+a*b*d^2*p*q*r*s*
v3+4*a*b*d^2*p*q*r*t*v2+2*a*b*d^2*p*q*s^2*v2+5*a*b*d^2*p*q*s*t*v1+3*a*b*d^2*p*q
*t^2*v0+a*b*d^2*q^3*t*v2+a*b*d^2*q^2*r*s*v2+a*b*d^2*q^2*s^2*v1+a*b*d^2*q^2*s*t*
v0+a*b*d*e*p^2*q*t*v3+a*b*d*e*p^2*r*s*v3+2*a*b*d*e*p^2*r*t*v2+a*b*d*e*p^2*s^2*
v2+3*a*b*d*e*p^2*s*t*v1+2*a*b*d*e*p^2*t^2*v0+a*b*d*e*p*q^2*t*v2+a*b*d*e*p*q*r*s
*v2+a*b*d*e*p*q*s^2*v1+a*b*d*e*p*q*s*t*v0+a*c^3*p^2*t^2*v2+a*c^3*p*q*r*t*v3-a*c
^3*p*q*s*t*v2+2*a*c^3*p*r^2*t*v2-a*c^3*p*r*s^2*v2+a*c^3*p*r*t^2*v0+2*a*c^3*q^2*
r*t*v2+a*c^3*q*r^2*s*v2+a*c^3*q*r^2*t*v1+2*a*c^2*d*p^2*r*t*v3-a*c^2*d*p^2*s*t*
v2-a*c^2*d*p^2*t^2*v1+2*a*c^2*d*p*q^2*t*v3+a*c^2*d*p*q*r*s*v3+7*a*c^2*d*p*q*r*t
*v2-a*c^2*d*p*q*s^2*v2+a*c^2*d*p*q*s*t*v1+2*a*c^2*d*p*q*t^2*v0+a*c^2*d*p*r^2*s*
v2+a*c^2*d*p*r*s^2*v1+a*c^2*d*p*r*s*t*v0+2*a*c^2*d*q^3*t*v2+2*a*c^2*d*q^2*r*s*
v2+2*a*c^2*d*q^2*r*t*v1+a*c^2*e*p^2*q*t*v3+2*a*c^2*e*p^2*r*t*v2-a*c^2*e*p^2*s^2
*v2+a*c^2*e*p^2*t^2*v0+a*c^2*e*p*q^2*t*v2+a*c^2*e*p*q*r*s*v2+a*c^2*e*p*q*r*t*v1
+4*a*c*d^2*p^2*q*t*v3+a*c*d^2*p^2*r*s*v3+2*a*c*d^2*p^2*r*t*v2+a*c*d^2*p^2*s*t*
v1+a*c*d^2*p^2*t^2*v0+a*c*d^2*p*q^2*s*v3+5*a*c*d^2*p*q^2*t*v2+2*a*c*d^2*p*q*r*s
*v2+a*c*d^2*p*q*r*t*v1+a*c*d^2*p*q*s^2*v1+a*c*d^2*p*q*s*t*v0+a*c*d^2*q^3*s*v2+a
*c*d^2*q^3*t*v1+2*a*c*d*e*p^3*t*v3+a*c*d*e*p^2*q*s*v3+3*a*c*d*e*p^2*q*t*v2+a*c*
d*e*p^2*r*s*v2+a*c*d*e*p^2*s^2*v1+a*c*d*e*p^2*s*t*v0+a*c*d*e*p*q^2*s*v2+a*c*d*e
*p*q^2*t*v1+a*d^3*p^3*t*v3+a*d^3*p^2*q*s*v3+2*a*d^3*p^2*q*t*v2+a*d^3*p*q^2*s*v2
+a*d^3*p*q^2*t*v1+a*d^2*e*p^3*s*v3+a*d^2*e*p^3*t*v2+a*d^2*e*p^2*q*s*v2+a*d^2*e*
p^2*q*t*v1+b^4*p*r*s*t*v3+b^4*p*s*t^2*v1-b^4*q*s^2*t*v1+b^4*r^2*s^2*v2+b^4*r*s^
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*v1+b^3*c*q*s^3*v1+b^3*c*q*s^2*t*v0+2*b^3*c*r^3*s*v2+2*b^3*c*r^2*s^2*v1+2*b^3*c
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3*p*q^2*t*v0+2*b*d^2*e*p^3*r*v3+b*d^2*e*p^3*s*v2+b*d^2*e*p^3*t*v1+2*b*d^2*e*p^2
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t*v4+4*b*c*d*e*q*s*v4+2*b*c*d*e*r^2*v4-3*b*c*d*e*r*s*v3-2*b*c*d*e*r*t*v2-2*b*c*
d*e*s^2*v2-3*b*c*d*e*s*t*v1-b*c*d*e*t^2*v0+b*c*e^2*p*s*v4+b*c*e^2*p*t*v3+2*b*c*
e^2*q*r*v4+b*c*e^2*q*s*v3+4*b*c*e^2*q*t*v2+2*b*c*e^2*r^2*v3+4*b*c*e^2*r*s*v2+2*
b*c*e^2*r*t*v1+2*b*c*e^2*s^2*v1+2*b*c*e^2*s*t*v0-b*d^3*p*t*v4-2*b*d^3*q*t*v3+b*
d^3*r*s*v3-b*d^3*s*t*v1-b*d^3*t^2*v0+3*b*d^2*e*p*s*v4-4*b*d^2*e*p*t*v3+2*b*d^2*
e*q*r*v4+b*d^2*e*q*s*v3-b*d^2*e*q*t*v2-2*b*d^2*e*r^2*v3-b*d^2*e*r*s*v2-2*b*d^2*
e*r*t*v1+b*d^2*e*s^2*v1+b*d^2*e*s*t*v0+4*b*d*e^2*p*r*v4+4*b*d*e^2*p*s*v3+2*b*d*
e^2*q*s*v2-2*b*d*e^2*q*t*v1+2*b*d*e^2*r^2*v2+2*b*d*e^2*r*s*v1+2*b*d*e^2*r*t*v0+
2*b*e^3*p*r*v3+b*e^3*p*s*v2+b*e^3*p*t*v1+2*b*e^3*q*r*v2+b*e^3*q*s*v1+b*e^3*q*t*
v0+c^4*t^2*v2-c^3*d*q*t*v4-c^3*d*s*t*v2-c^3*d*t^2*v1-c^3*e*p*t*v4+c^3*e*q*s*v4-
c^3*e*q*t*v3-2*c^3*e*r*t*v2+c^3*e*s^2*v2-c^3*e*t^2*v0-c^2*d^2*q*s*v4+2*c^2*d^2*
q*t*v3+c^2*d^2*r*t*v2+c^2*d^2*s*t*v1+c^2*d^2*t^2*v0+c^2*d*e*p*s*v4+2*c^2*d*e*q*
r*v4-3*c^2*d*e*q*s*v3-5*c^2*d*e*q*t*v2-c^2*d*e*r*s*v2-c^2*d*e*s^2*v1-c^2*d*e*s*
t*v0-2*c^2*e^2*p*t*v2+c^2*e^2*q^2*v4+2*c^2*e^2*q*r*v3+3*c^2*e^2*q*s*v2+c^2*e^2*
q*t*v1+c^2*e^2*r^2*v2+c^2*e^2*r*s*v1+c^2*e^2*r*t*v0-c*d^3*p*s*v4+c*d^3*p*t*v3+c
*d^3*q*s*v3+2*c*d^3*q*t*v2+2*c*d^2*e*p*r*v4-3*c*d^2*e*p*s*v3+c*d^2*e*p*t*v2+2*c
*d^2*e*q^2*v4-2*c*d^2*e*q*r*v3-3*c*d^2*e*q*s*v2+c*d^2*e*q*t*v1+4*c*d*e^2*p*q*v4
+3*c*d*e^2*p*r*v3+4*c*d*e^2*q*r*v2+c*d*e^2*q*s*v1+c*d*e^2*q*t*v0+2*c*e^3*p*q*v3
+c*e^3*p*r*v2+c*e^3*p*s*v1+c*e^3*p*t*v0+2*c*e^3*q^2*v2+d^4*p*s*v3-d^4*q*t*v1+2*
d^3*e*p*q*v4-2*d^3*e*p*r*v3-d^3*e*p*s*v2-d^3*e*p*t*v1+d^3*e*q*s*v1+d^3*e*q*t*v0
+3*d^2*e^2*p^2*v4+d^2*e^2*p*q*v3+2*d^2*e^2*p*r*v2+2*d^2*e^2*p*s*v1+2*d^2*e^2*p*
t*v0+d^2*e^2*q^2*v2+3*d*e^3*p^2*v3+3*d*e^3*p*q*v2-3*a*d*e^2*t*v4-a*e^3*s*v4-a*e
^3*t*v3-3*b*c*e^2*t*v4+2*b*d^2*e*t*v4-2*b*d*e^2*s*v4+2*b*d*e^2*t*v3-2*b*e^3*r*
v4-b*e^3*s*v3-b*e^3*t*v2+2*c^2*d*e*t*v4-c^2*e^2*s*v4+c^2*e^2*t*v3-c*d^3*t*v4+c*
d^2*e*s*v4-3*c*d^2*e*t*v3-c*d*e^2*r*v4+2*c*d*e^2*s*v3+2*c*d*e^2*t*v2-2*c*e^3*q*
v4-c*e^3*r*v3-c*e^3*s*v2-c*e^3*t*v1+d^4*t*v3-d^3*e*s*v3-d^3*e*t*v2-d^2*e^2*q*v4
+d^2*e^2*r*v3+d^2*e^2*s*v2+d^2*e^2*t*v1-3*d*e^3*p*v4-d*e^3*r*v2-d*e^3*s*v1-d*e^
3*t*v0-e^4*p*v3-e^4*q*v2+e^4*v4




beta[3,4] = a^4*s*t^3*v2+a^4*t^4*v1+3*a^3*b*s^2*t^2*v2+2*a^3*b*s*t^3*v1-a^3*b*t
^4*v0+a^3*c*p*t^3*v3+a^3*c*q*t^3*v2+2*a^3*c*r*s*t^2*v2+3*a^3*c*r*t^3*v1-a^3*c*s
^2*t^2*v1-a^3*c*s*t^3*v0+a^3*d*p*s*t^2*v3+a^3*d*p*t^3*v2+2*a^3*d*q*s*t^2*v2+2*a
^3*d*q*t^3*v1+a^3*e*p*s*t^2*v2+a^3*e*p*t^3*v1-a^2*b^2*p*t^3*v3-a^2*b^2*q*t^3*v2
+a^2*b^2*r*s*t^2*v2+3*a^2*b^2*s^3*t*v2+a^2*b^2*s^2*t^2*v1-2*a^2*b^2*s*t^3*v0-2*
a^2*b*c*p*t^3*v2+3*a^2*b*c*q*s*t^2*v2+a^2*b*c*q*t^3*v1+4*a^2*b*c*r*s^2*t*v2+3*a
^2*b*c*r*s*t^2*v1-3*a^2*b*c*r*t^3*v0-2*a^2*b*c*s^3*t*v1-2*a^2*b*c*s^2*t^2*v0+2*
a^2*b*d*p*s^2*t*v3+4*a^2*b*d*p*s*t^2*v2+2*a^2*b*d*p*t^3*v1+4*a^2*b*d*q*s^2*t*v2
+2*a^2*b*d*q*s*t^2*v1-2*a^2*b*d*q*t^3*v0+2*a^2*b*e*p*s^2*t*v2+a^2*b*e*p*s*t^2*
v1-a^2*b*e*p*t^3*v0+2*a^2*c^2*p*r*t^2*v3-a^2*c^2*p*s^2*t*v3+a^2*c^2*p*t^3*v1+2*
a^2*c^2*q*r*t^2*v2-a^2*c^2*q*s*t^2*v1-a^2*c^2*q*t^3*v0+a^2*c^2*r^2*s*t*v2+3*a^2
*c^2*r^2*t^2*v1-2*a^2*c^2*r*s^2*t*v1-2*a^2*c^2*r*s*t^2*v0+2*a^2*c*d*p*q*t^2*v3+
a^2*c*d*p*r*s*t*v3+a^2*c*d*p*r*t^2*v2+a^2*c*d*p*s^2*t*v2-a^2*c*d*p*s*t^2*v1-2*a
^2*c*d*p*t^3*v0+2*a^2*c*d*q^2*t^2*v2+2*a^2*c*d*q*r*s*t*v2+4*a^2*c*d*q*r*t^2*v1-\
2*a^2*c*d*q*s^2*t*v1-2*a^2*c*d*q*s*t^2*v0+a^2*c*e*p^2*t^2*v3+a^2*c*e*p*q*t^2*v2
+a^2*c*e*p*r*s*t*v2+2*a^2*c*e*p*r*t^2*v1-a^2*c*e*p*s^2*t*v1-a^2*c*e*p*s*t^2*v0+
a^2*d^2*p^2*t^2*v3+a^2*d^2*p*q*s*t*v3+2*a^2*d^2*p*q*t^2*v2+a^2*d^2*p*r*t^2*v1-a
^2*d^2*p*s^2*t*v1-a^2*d^2*p*s*t^2*v0+a^2*d^2*q^2*s*t*v2+a^2*d^2*q^2*t^2*v1+a^2*
d*e*p^2*s*t*v3+a^2*d*e*p^2*t^2*v2+a^2*d*e*p*q*s*t*v2+a^2*d*e*p*q*t^2*v1-a*b^3*p
*s*t^2*v3+a*b^3*p*t^3*v2-2*a*b^3*q*s*t^2*v2+2*a*b^3*r*s^2*t*v2+a*b^3*s^4*v2-a*b
^3*s^2*t^2*v0-2*a*b^2*c*p*r*t^2*v3-a*b^2*c*p*s^2*t*v3-3*a*b^2*c*p*s*t^2*v2-a*b^
2*c*p*t^3*v1-2*a*b^2*c*q*r*t^2*v2+3*a*b^2*c*q*s^2*t*v2+2*a*b^2*c*q*s*t^2*v1+2*a
*b^2*c*r^2*s*t*v2+2*a*b^2*c*r*s^3*v2-a*b^2*c*r*s^2*t*v1-4*a*b^2*c*r*s*t^2*v0-a*
b^2*c*s^4*v1-a*b^2*c*s^3*t*v0-2*a*b^2*d*p*q*t^2*v3+a*b^2*d*p*r*s*t*v3+a*b^2*d*p
*r*t^2*v2+a*b^2*d*p*s^3*v3+4*a*b^2*d*p*s^2*t*v2+2*a*b^2*d*p*s*t^2*v1-a*b^2*d*p*
t^3*v0-2*a*b^2*d*q^2*t^2*v2+2*a*b^2*d*q*r*s*t*v2+2*a*b^2*d*q*s^3*v2-2*a*b^2*d*q
*s*t^2*v0-a*b^2*e*p^2*t^2*v3-a*b^2*e*p*q*t^2*v2+a*b^2*e*p*r*s*t*v2+a*b^2*e*p*s^
3*v2-a*b^2*e*p*s*t^2*v0-a*b*c^2*p*r*s*t*v3-3*a*b*c^2*p*r*t^2*v2-a*b*c^2*p*s^3*
v3+2*a*b*c^2*p*s*t^2*v1+a*b*c^2*p*t^3*v0+4*a*b*c^2*q*r*s*t*v2+2*a*b*c^2*q*r*t^2
*v1-2*a*b*c^2*q*s^2*t*v1-2*a*b*c^2*q*s*t^2*v0+a*b*c^2*r^2*s^2*v2-3*a*b*c^2*r^2*
t^2*v0-2*a*b*c^2*r*s^3*v1-2*a*b*c^2*r*s^2*t*v0-2*a*b*c*d*p^2*t^2*v3+a*b*c*d*p*q
*s*t*v3-3*a*b*c*d*p*q*t^2*v2+a*b*c*d*p*r*s^2*v3+5*a*b*c*d*p*r*s*t*v2+2*a*b*c*d*
p*r*t^2*v1+a*b*c*d*p*s^3*v2-2*a*b*c*d*p*s^2*t*v1-3*a*b*c*d*p*s*t^2*v0+4*a*b*c*d
*q^2*s*t*v2+2*a*b*c*d*q^2*t^2*v1+2*a*b*c*d*q*r*s^2*v2-4*a*b*c*d*q*r*t^2*v0-2*a*
b*c*d*q*s^3*v1-2*a*b*c*d*q*s^2*t*v0-a*b*c*e*p^2*s*t*v3-2*a*b*c*e*p^2*t^2*v2+2*a
*b*c*e*p*q*s*t*v2+a*b*c*e*p*q*t^2*v1+a*b*c*e*p*r*s^2*v2-2*a*b*c*e*p*r*t^2*v0-a*
b*c*e*p*s^3*v1-a*b*c*e*p*s^2*t*v0+2*a*b*d^2*p^2*s*t*v3+a*b*d^2*p^2*t^2*v2+a*b*d
^2*p*q*s^2*v3+5*a*b*d^2*p*q*s*t*v2+3*a*b*d^2*p*q*t^2*v1-a*b*d^2*p*r*t^2*v0-a*b*
d^2*p*s^3*v1-a*b*d^2*p*s^2*t*v0+a*b*d^2*q^2*s^2*v2-a*b*d^2*q^2*t^2*v0+a*b*d*e*p
^2*s^2*v3+3*a*b*d*e*p^2*s*t*v2+2*a*b*d*e*p^2*t^2*v1+a*b*d*e*p*q*s^2*v2-a*b*d*e*
p*q*t^2*v0+a*c^3*p^2*t^2*v3-a*c^3*p*q*s*t*v3+a*c^3*p*r^2*t*v3-a*c^3*p*r*s^2*v3+
2*a*c^3*p*r*t^2*v1+a*c^3*q*r^2*t*v2-2*a*c^3*q*r*s*t*v1-2*a*c^3*q*r*t^2*v0+a*c^3
*r^3*t*v1-a*c^3*r^2*s^2*v1-a*c^3*r^2*s*t*v0-a*c^2*d*p^2*s*t*v3-a*c^2*d*p^2*t^2*
v2+2*a*c^2*d*p*q*r*t*v3-a*c^2*d*p*q*s^2*v3+a*c^2*d*p*q*s*t*v2+2*a*c^2*d*p*q*t^2
*v1+a*c^2*d*p*r*s^2*v2-2*a*c^2*d*p*r*s*t*v1-3*a*c^2*d*p*r*t^2*v0+2*a*c^2*d*q^2*
r*t*v2-2*a*c^2*d*q^2*s*t*v1-2*a*c^2*d*q^2*t^2*v0+2*a*c^2*d*q*r^2*t*v1-2*a*c^2*d
*q*r*s^2*v1-2*a*c^2*d*q*r*s*t*v0+a*c^2*e*p^2*r*t*v3-a*c^2*e*p^2*s^2*v3+a*c^2*e*
p^2*t^2*v1+a*c^2*e*p*q*r*t*v2-a*c^2*e*p*q*s*t*v1-a*c^2*e*p*q*t^2*v0+a*c^2*e*p*r
^2*t*v1-a*c^2*e*p*r*s^2*v1-a*c^2*e*p*r*s*t*v0+a*c*d^2*p^2*r*t*v3+a*c*d^2*p^2*s*
t*v2+a*c*d^2*p^2*t^2*v1+a*c*d^2*p*q^2*t*v3+a*c*d^2*p*q*r*t*v2+a*c*d^2*p*q*s^2*
v2-3*a*c*d^2*p*q*s*t*v1-4*a*c*d^2*p*q*t^2*v0+a*c*d^2*p*r^2*t*v1-a*c*d^2*p*r*s^2
*v1-a*c*d^2*p*r*s*t*v0+a*c*d^2*q^3*t*v2+a*c*d^2*q^2*r*t*v1-a*c*d^2*q^2*s^2*v1-a
*c*d^2*q^2*s*t*v0+a*c*d*e*p^2*q*t*v3+a*c*d*e*p^2*s^2*v2-a*c*d*e*p^2*s*t*v1-2*a*
c*d*e*p^2*t^2*v0+a*c*d*e*p*q^2*t*v2+a*c*d*e*p*q*r*t*v1-a*c*d*e*p*q*s^2*v1-a*c*d
*e*p*q*s*t*v0+a*d^3*p^2*q*t*v3-a*d^3*p^2*s*t*v1-a*d^3*p^2*t^2*v0+a*d^3*p*q^2*t*
v2+a*d^3*p*q*r*t*v1-a*d^3*p*q*s^2*v1-a*d^3*p*q*s*t*v0+a*d^2*e*p^3*t*v3+a*d^2*e*
p^2*q*t*v2+a*d^2*e*p^2*r*t*v1-a*d^2*e*p^2*s^2*v1-a*d^2*e*p^2*s*t*v0+b^4*p*s*t^2
*v2-b^4*q*s^2*t*v2+b^4*r*s^3*v2-b^3*c*p*r*s*t*v3+b^3*c*p*r*t^2*v2-b^3*c*p*s^2*t
*v2-b^3*c*p*s*t^2*v1-2*b^3*c*q*r*s*t*v2+b^3*c*q*s^3*v2+b^3*c*q*s^2*t*v1+2*b^3*c
*r^2*s^2*v2-b^3*c*r*s^3*v1-b^3*c*r*s^2*t*v0-b^3*d*p*q*s*t*v3+b^3*d*p*q*t^2*v2+b
^3*d*p*r*s^2*v3+b^3*d*p*r*s*t*v2+b^3*d*p*s^3*v2-b^3*d*p*s*t^2*v0-2*b^3*d*q^2*s*
t*v2+2*b^3*d*q*r*s^2*v2+b^3*e*p^2*t^2*v2-b^3*e*p*q*s*t*v2+b^3*e*p*r*s^2*v2-b^2*
c^2*p*r^2*t*v3-b^2*c^2*p*r*s^2*v3-2*b^2*c^2*p*r*s*t*v2-b^2*c^2*p*r*t^2*v1+b^2*c
^2*p*s^2*t*v1+b^2*c^2*p*s*t^2*v0-b^2*c^2*q*r^2*t*v2+2*b^2*c^2*q*r*s^2*v2+2*b^2*
c^2*q*r*s*t*v1-b^2*c^2*q*s^3*v1-b^2*c^2*q*s^2*t*v0+b^2*c^2*r^3*s*v2-2*b^2*c^2*r
^2*s^2*v1-2*b^2*c^2*r^2*s*t*v0-2*b^2*c*d*p^2*s*t*v3-2*b^2*c*d*p*q*r*t*v3+b^2*c*
d*p*q*s^2*v3-2*b^2*c*d*p*q*s*t*v2-b^2*c*d*p*q*t^2*v1+b^2*c*d*p*r^2*s*v3+b^2*c*d
*p*r^2*t*v2+3*b^2*c*d*p*r*s^2*v2-b^2*c*d*p*r*t^2*v0-b^2*c*d*p*s^3*v1-b^2*c*d*p*
s^2*t*v0-2*b^2*c*d*q^2*r*t*v2+2*b^2*c*d*q^2*s^2*v2+2*b^2*c*d*q^2*s*t*v1+2*b^2*c
*d*q*r^2*s*v2-2*b^2*c*d*q*r*s^2*v1-2*b^2*c*d*q*r*s*t*v0-b^2*c*e*p^2*r*t*v3-b^2*
c*e*p^2*s*t*v2-b^2*c*e*p^2*t^2*v1-b^2*c*e*p*q*r*t*v2+b^2*c*e*p*q*s^2*v2+b^2*c*e
*p*q*s*t*v1+b^2*c*e*p*r^2*s*v2-b^2*c*e*p*r*s^2*v1-b^2*c*e*p*r*s*t*v0+b^2*d^2*p^
2*s^2*v3+b^2*d^2*p^2*s*t*v2-b^2*d^2*p*q^2*t*v3+b^2*d^2*p*q*r*s*v3+b^2*d^2*p*q*r
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2*v1-a*b*e^2*q*s^2*v2+a*b*e^2*q*t^2*v0-a*c^3*p*t^2*v4+a*c^3*q*s*t*v4+a*c^3*q*t^
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v2-b^2*e^2*q*r*s*v2-b*c^3*p*s*t*v4+b*c^3*p*t^2*v3+b*c^3*q*s^2*v4+b*c^3*r^2*s*v4
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2*v4-4*b*c^2*d*p*s*t*v3-b*c^2*d*p*t^2*v2+2*b*c^2*d*q*s^2*v3+2*b*c^2*d*q*t^2*v1+
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*p*r*t*v3+b*c^2*e*p*s^2*v3+2*b*c^2*e*p*s*t*v2+b*c^2*e*p*t^2*v1-2*b*c^2*e*q*r*s*
v3-2*b*c^2*e*q*s^2*v2+2*b*c^2*e*q*t^2*v0-2*b*c^2*e*r^2*s*v2+3*b*c^2*e*r*s^2*v1+
3*b*c^2*e*r*s*t*v0+2*b*c*d^2*p*q*t*v4-b*c*d^2*p*r*s*v4-b*c*d^2*p*r*t*v3+2*b*c*d
^2*p*s^2*v3+3*b*c*d^2*p*s*t*v2+b*c*d^2*p*t^2*v1-b*c*d^2*q^2*s*v4-b*c*d^2*q^2*t*
v3+2*b*c*d^2*q*r*s*v3+2*b*c*d^2*q*r*t*v2-b*c*d^2*q*s^2*v2-2*b*c*d^2*q*s*t*v1-b*
c*d^2*q*t^2*v0-b*c*d^2*r*s^2*v1-b*c*d^2*r*s*t*v0+2*b*c*d*e*p^2*t*v4-b*c*d*e*p*q
*s*v4-b*c*d*e*p*q*t*v3-b*c*d*e*p*r*s*v3-b*c*d*e*p*r*t*v2-3*b*c*d*e*p*s^2*v2-2*b
*c*d*e*p*s*t*v1+b*c*d*e*p*t^2*v0-3*b*c*d*e*q*r*s*v2-3*b*c*d*e*q*r*t*v1+4*b*c*d*
e*q*s^2*v1+4*b*c*d*e*q*s*t*v0+3*b*c*d*e*r^2*s*v1+3*b*c*d*e*r^2*t*v0+2*b*c*e^2*p
^2*t*v3-b*c*e^2*p*q*s*v3+b*c*e^2*p*q*t*v2-2*b*c*e^2*p*r*s*v2+b*c*e^2*p*s^2*v1+b
*c*e^2*p*s*t*v0-b*c*e^2*q^2*s*v2-b*c*e^2*q^2*t*v1+b*c*e^2*q*r*s*v1+b*c*e^2*q*r*
t*v0-b*d^3*p*q*s*v4+b*d^3*p*q*t*v3+b*d^3*p*r*s*v3+b*d^3*p*r*t*v2-b*d^3*p*s^2*v2
-2*b*d^3*p*s*t*v1-b*d^3*p*t^2*v0+2*b*d^3*q^2*t*v2-b*d^3*q*r*s*v2+b*d^3*q*r*t*v1
-b*d^3*r^2*s*v1-b*d^3*r^2*t*v0-b*d^2*e*p^2*s*v4+b*d^2*e*p^2*t*v3-b*d^2*e*p*q*s*
v3+b*d^2*e*p*q*t*v2-2*b*d^2*e*p*r*s*v2+3*b*d^2*e*p*s^2*v1+3*b*d^2*e*p*s*t*v0-b*
d^2*e*q^2*s*v2-b*d^2*e*q^2*t*v1+b*d^2*e*q*r*s*v1+b*d^2*e*q*r*t*v0-2*b*d*e^2*p^2
*s*v3-2*b*d*e^2*p^2*t*v2-2*b*d*e^2*p*q*s*v2-2*b*d*e^2*p*q*t*v1+2*b*d*e^2*p*r*s*
v1+2*b*d*e^2*p*r*t*v0-c^4*p*r*t*v4+c^4*p*s*t*v3+c^4*q*r*s*v4+c^4*q*r*t*v3-c^4*q
*s^2*v3-c^4*r*t^2*v0-c^3*d*p*q*t*v4+c^3*d*p*r*s*v4-c^3*d*p*s^2*v3-c^3*d*p*s*t*
v2+c^3*d*q^2*s*v4+c^3*d*q^2*t*v3-c^3*d*q*r*t*v2+c^3*d*q*s^2*v2-c^3*d*q*t^2*v0-c
^3*d*r^2*t*v1-c^3*e*p^2*t*v4+c^3*e*p*q*s*v4+2*c^3*e*p*q*t*v3+c^3*e*p*r*s*v3+c^3
*e*p*r*t*v2-c^3*e*p*s*t*v1-c^3*e*p*t^2*v0-c^3*e*q^2*s*v3-c^3*e*q*r*s*v2+c^3*e*q
*s^2*v1+c^3*e*q*s*t*v0+c^3*e*r^2*s*v1+c^3*e*r^2*t*v0+c^2*d^2*p*q*s*v4-c^2*d^2*p
*q*t*v3+c^2*d^2*p*s^2*v2+c^2*d^2*p*s*t*v1+c^2*d^2*q^2*s*v3-c^2*d^2*q^2*t*v2-2*c
^2*d^2*q*r*t*v1-c^2*d^2*q*s^2*v1-c^2*d^2*q*s*t*v0+c^2*d*e*p^2*s*v4-c^2*d*e*p^2*
t*v3+c^2*d*e*p*q*s*v3-c^2*d*e*p*q*t*v2-2*c^2*d*e*p*r*s*v2-4*c^2*d*e*p*r*t*v1+c^
2*d*e*p*s^2*v1+c^2*d*e*p*s*t*v0+5*c^2*d*e*q*r*s*v1+5*c^2*d*e*q*r*t*v0+c^2*e^2*p
^2*s*v3+c^2*e^2*p^2*t*v2-c^2*e^2*p*q*s*v2-c^2*e^2*p*q*t*v1+c^2*e^2*p*r*s*v1+c^2
*e^2*p*r*t*v0+c^2*e^2*q^2*s*v1+c^2*e^2*q^2*t*v0+c*d^3*p*q*s*v3+c*d^3*p*q*t*v2-c
*d^3*p*s^2*v1-c*d^3*p*s*t*v0-c*d^3*q^2*s*v2-c*d^3*q^2*t*v1-c*d^3*q*r*s*v1-c*d^3
*q*r*t*v0+c*d^2*e*p^2*s*v3+c*d^2*e*p^2*t*v2-2*c*d^2*e*p*q*s*v2-2*c*d^2*e*p*q*t*
v1+4*c*d^2*e*p*r*s*v1+4*c*d^2*e*p*r*t*v0+2*c*d^2*e*q^2*s*v1+2*c*d^2*e*q^2*t*v0-\
2*c*d*e^2*p^2*s*v2-2*c*d*e^2*p^2*t*v1+4*c*d*e^2*p*q*s*v1+4*c*d*e^2*p*q*t*v0-d^4
*p*q*s*v2-d^4*p*q*t*v1-d^4*p*r*s*v1-d^4*p*r*t*v0-d^3*e*p^2*s*v2-d^3*e*p^2*t*v1+
2*d^3*e*p*q*s*v1+2*d^3*e*p*q*t*v0+3*d^2*e^2*p^2*s*v1+3*d^2*e^2*p^2*t*v0+2*a^2*d
*e*t^2*v4+a^2*e^2*s*t*v4+a^2*e^2*t^2*v3-a*b*c*e*t^2*v4-3*a*b*d^2*t^2*v4+a*b*d*e
*s*t*v4-a*b*d*e*t^2*v3+a*b*e^2*s^2*v4+3*a*b*e^2*s*t*v3+2*a*b*e^2*t^2*v2+2*a*c^2
*d*t^2*v4-2*a*c^2*e*s*t*v4-3*a*c^2*e*t^2*v3+a*c*d^2*s*t*v4+2*a*c*d^2*t^2*v3+3*a
*c*d*e*r*t*v4-2*a*c*d*e*s^2*v4-3*a*c*d*e*s*t*v3-a*c*d*e*t^2*v2+a*c*e^2*q*t*v4+a
*c*e^2*s^2*v3+3*a*c*e^2*s*t*v2+2*a*c*e^2*t^2*v1-a*d^3*r*t*v4+a*d^3*s^2*v4-a*d^3
*t^2*v2+a*d^2*e*q*t*v4-a*d^2*e*s^2*v3+a*d^2*e*s*t*v2+2*a*d^2*e*t^2*v1+2*a*d*e^2
*p*t*v4+a*d*e^2*s^2*v2-2*a*d*e^2*s*t*v1-3*a*d*e^2*t^2*v0+a*e^3*p*t*v3+a*e^3*q*t
*v2+a*e^3*r*t*v1-a*e^3*s^2*v1-a*e^3*s*t*v0-b^3*e*t^2*v4+2*b^2*c*d*t^2*v4-b^2*c*
e*s*t*v4+2*b^2*c*e*t^2*v3-b^2*d^2*s*t*v4+b^2*d^2*t^2*v3-b^2*d*e*r*t*v4+b^2*d*e*
s^2*v4-2*b^2*d*e*s*t*v3-3*b^2*d*e*t^2*v2-b^2*e^2*q*t*v4+b^2*e^2*r*s*v4+b^2*e^2*
r*t*v3+b^2*e^2*s^2*v3+2*b^2*e^2*s*t*v2+b^2*e^2*t^2*v1-b*c^3*t^2*v4+b*c^2*d*s*t*
v4-3*b*c^2*d*t^2*v3-2*b*c^2*e*r*t*v4-b*c^2*e*s^2*v4+b*c^2*e*s*t*v3+2*b*c^2*e*t^
2*v2+2*b*c*d^2*s*t*v3+2*b*c*d^2*t^2*v2-b*c*d*e*r*s*v4-b*c*d*e*r*t*v3-2*b*c*d*e*
s^2*v3-3*b*c*d*e*s*t*v2-b*c*d*e*t^2*v1-2*b*c*e^2*p*t*v4+b*c*e^2*q*s*v4+b*c*e^2*
q*t*v3+2*b*c*e^2*r*s*v3+2*b*c*e^2*r*t*v2+2*b*c*e^2*s^2*v2-b*c*e^2*s*t*v1-3*b*c*
e^2*t^2*v0-2*b*d^3*q*t*v4+b*d^3*r*s*v4+b*d^3*r*t*v3-b*d^3*s*t*v2-b*d^3*t^2*v1-2
*b*d^2*e*p*t*v4+b*d^2*e*q*s*v4+b*d^2*e*q*t*v3-2*b*d^2*e*r*s*v3-2*b*d^2*e*r*t*v2
+b*d^2*e*s^2*v2+3*b*d^2*e*s*t*v1+2*b*d^2*e*t^2*v0+2*b*d*e^2*p*s*v4-2*b*d*e^2*q*
t*v2+2*b*d*e^2*r*s*v2-2*b*d*e^2*s^2*v1-2*b*d*e^2*s*t*v0+b*e^3*p*s*v3+b*e^3*p*t*
v2+b*e^3*q*s*v2+b*e^3*q*t*v1-b*e^3*r*s*v1-b*e^3*r*t*v0+c^4*t^2*v3+c^3*d*r*t*v4-
c^3*d*s*t*v3-c^3*d*t^2*v2-c^3*e*q*t*v4-c^3*e*r*s*v4-c^3*e*r*t*v3+c^3*e*s^2*v3-c
^3*e*t^2*v1+2*c^2*d^2*q*t*v4+c^2*d^2*s*t*v2+c^2*d^2*t^2*v1+2*c^2*d*e*p*t*v4-3*c
^2*d*e*q*s*v4-3*c^2*d*e*q*t*v3-c^2*d*e*s^2*v2+c^2*d*e*s*t*v1+2*c^2*d*e*t^2*v0-c
^2*e^2*p*s*v4-2*c^2*e^2*p*t*v3+2*c^2*e^2*q*s*v3+c^2*e^2*q*t*v2+c^2*e^2*r*s*v2-c
^2*e^2*s^2*v1-c^2*e^2*s*t*v0+c*d^3*q*s*v4+c*d^3*q*t*v3-c*d^3*s*t*v1-c*d^3*t^2*
v0-2*c*d^2*e*p*s*v4+c*d^2*e*p*t*v3-2*c*d^2*e*q*s*v3+c*d^2*e*q*t*v2+3*c*d^2*e*r*
t*v1+c*d^2*e*s^2*v1+c*d^2*e*s*t*v0+c*d*e^2*q*s*v2+c*d*e^2*q*t*v1-3*c*d*e^2*r*s*
v1-3*c*d*e^2*r*t*v0+c*e^3*p*s*v2+c*e^3*p*t*v1-2*c*e^3*q*s*v1-2*c*e^3*q*t*v0+d^4
*p*s*v4-d^4*q*t*v2-d^4*r*t*v1-d^3*e*p*s*v3-d^3*e*p*t*v2+d^3*e*q*s*v2+d^3*e*q*t*
v1+d^3*e*r*s*v1+d^3*e*r*t*v0+2*d^2*e^2*p*s*v2+2*d^2*e^2*p*t*v1-d^2*e^2*q*s*v1-d
^2*e^2*q*t*v0-3*d*e^3*p*s*v1-3*d*e^3*p*t*v0-a*e^3*t*v4+2*b*d*e^2*t*v4-b*e^3*s*
v4-b*e^3*t*v3+c^2*e^2*t*v4-3*c*d^2*e*t*v4+2*c*d*e^2*s*v4+2*c*d*e^2*t*v3-c*e^3*s
*v3-c*e^3*t*v2+d^4*t*v4-d^3*e*s*v4-d^3*e*t*v3+d^2*e^2*s*v3+d^2*e^2*t*v2-d*e^3*s
*v2-d*e^3*t*v1+e^4*s*v1+e^4*t*v0




beta[3,5] = t*(a^4*t^3*v2+3*a^3*b*s*t^2*v2-a^3*b*t^3*v1+2*a^3*c*r*t^2*v2-a^3*c*
s*t^2*v1-a^3*c*t^3*v0+a^3*d*p*t^2*v3+2*a^3*d*q*t^2*v2+a^3*e*p*t^2*v2+a^2*b^2*r*
t^2*v2+3*a^2*b^2*s^2*t*v2-2*a^2*b^2*s*t^2*v1+a^2*b^2*t^3*v0-2*a^2*b*c*p*t^2*v3+
a^2*b*c*q*t^2*v2+4*a^2*b*c*r*s*t*v2-3*a^2*b*c*r*t^2*v1-2*a^2*b*c*s^2*t*v1-2*a^2
*b*c*s*t^2*v0+2*a^2*b*d*p*s*t*v3+2*a^2*b*d*p*t^2*v2+4*a^2*b*d*q*s*t*v2-2*a^2*b*
d*q*t^2*v1+2*a^2*b*e*p*s*t*v2-a^2*b*e*p*t^2*v1-a^2*c^2*p*s*t*v3+a^2*c^2*p*t^2*
v2-a^2*c^2*q*t^2*v1+a^2*c^2*r^2*t*v2-2*a^2*c^2*r*s*t*v1-2*a^2*c^2*r*t^2*v0+a^2*
c*d*p*r*t*v3+a^2*c*d*p*s*t*v2-2*a^2*c*d*p*t^2*v1+2*a^2*c*d*q*r*t*v2-2*a^2*c*d*q
*s*t*v1-2*a^2*c*d*q*t^2*v0+a^2*c*e*p*r*t*v2-a^2*c*e*p*s*t*v1-a^2*c*e*p*t^2*v0+a
^2*d^2*p*q*t*v3-a^2*d^2*p*s*t*v1-a^2*d^2*p*t^2*v0+a^2*d^2*q^2*t*v2+a^2*d*e*p^2*
t*v3+a^2*d*e*p*q*t*v2+a*b^3*p*t^2*v3+2*a*b^3*r*s*t*v2+a*b^3*s^3*v2-a*b^3*s^2*t*
v1+2*a*b^3*s*t^2*v0-2*a*b^2*c*p*s*t*v3-a*b^2*c*p*t^2*v2+2*a*b^2*c*q*s*t*v2+2*a*
b^2*c*r^2*t*v2+2*a*b^2*c*r*s^2*v2-4*a*b^2*c*r*s*t*v1+2*a*b^2*c*r*t^2*v0-a*b^2*c
*s^3*v1-a*b^2*c*s^2*t*v0+a*b^2*d*p*r*t*v3+a*b^2*d*p*s^2*v3+3*a*b^2*d*p*s*t*v2-a
*b^2*d*p*t^2*v1+2*a*b^2*d*q*r*t*v2+2*a*b^2*d*q*s^2*v2-2*a*b^2*d*q*s*t*v1+2*a*b^
2*d*q*t^2*v0+a*b^2*e*p*r*t*v2+a*b^2*e*p*s^2*v2-a*b^2*e*p*s*t*v1+a*b^2*e*p*t^2*
v0-3*a*b*c^2*p*r*t*v3-a*b*c^2*p*s^2*v3+a*b*c^2*p*s*t*v2+a*b*c^2*p*t^2*v1+2*a*b*
c^2*q*r*t*v2-2*a*b*c^2*q*s*t*v1+a*b*c^2*r^2*s*v2-3*a*b*c^2*r^2*t*v1-2*a*b*c^2*r
*s^2*v1-2*a*b*c^2*r*s*t*v0-a*b*c*d*p*q*t*v3+a*b*c*d*p*r*s*v3+4*a*b*c*d*p*r*t*v2
+a*b*c*d*p*s^2*v2-3*a*b*c*d*p*s*t*v1+2*a*b*c*d*p*t^2*v0+2*a*b*c*d*q^2*t*v2+2*a*
b*c*d*q*r*s*v2-4*a*b*c*d*q*r*t*v1-2*a*b*c*d*q*s^2*v1-2*a*b*c*d*q*s*t*v0-2*a*b*c
*e*p^2*t*v3+a*b*c*e*p*q*t*v2+a*b*c*e*p*r*s*v2-2*a*b*c*e*p*r*t*v1-a*b*c*e*p*s^2*
v1-a*b*c*e*p*s*t*v0+a*b*d^2*p^2*t*v3+a*b*d^2*p*q*s*v3+3*a*b*d^2*p*q*t*v2-a*b*d^
2*p*r*t*v1-a*b*d^2*p*s^2*v1-a*b*d^2*p*s*t*v0+a*b*d^2*q^2*s*v2-a*b*d^2*q^2*t*v1+
a*b*d*e*p^2*s*v3+2*a*b*d*e*p^2*t*v2+a*b*d*e*p*q*s*v2-a*b*d*e*p*q*t*v1-a*c^3*p*q
*t*v3-a*c^3*p*r*s*v3+a*c^3*p*r*t*v2-a*c^3*p*t^2*v0-2*a*c^3*q*r*t*v1-a*c^3*r^2*s
*v1-a*c^3*r^2*t*v0-a*c^2*d*p^2*t*v3-a*c^2*d*p*q*s*v3+2*a*c^2*d*p*q*t*v2+a*c^2*d
*p*r*s*v2-3*a*c^2*d*p*r*t*v1-2*a*c^2*d*q^2*t*v1-2*a*c^2*d*q*r*s*v1-2*a*c^2*d*q*
r*t*v0-a*c^2*e*p^2*s*v3+a*c^2*e*p^2*t*v2-a*c^2*e*p*q*t*v1-a*c^2*e*p*r*s*v1-a*c^
2*e*p*r*t*v0+a*c*d^2*p^2*t*v2+a*c*d^2*p*q*s*v2-4*a*c*d^2*p*q*t*v1-a*c*d^2*p*r*s
*v1-a*c*d^2*p*r*t*v0-a*c*d^2*q^2*s*v1-a*c*d^2*q^2*t*v0+a*c*d*e*p^2*s*v2-2*a*c*d
*e*p^2*t*v1-a*c*d*e*p*q*s*v1-a*c*d*e*p*q*t*v0-a*d^3*p^2*t*v1-a*d^3*p*q*s*v1-a*d
^3*p*q*t*v0-a*d^2*e*p^2*s*v1-a*d^2*e*p^2*t*v0+b^4*p*s*t*v3+b^4*r*s^2*v2+b^4*s^2
*t*v0+b^3*c*p*r*t*v3-b^3*c*p*s*t*v2+b^3*c*q*s^2*v2+2*b^3*c*r^2*s*v2-b^3*c*r*s^2
*v1+2*b^3*c*r*s*t*v0+b^3*d*p*q*t*v3+b^3*d*p*r*s*v3+b^3*d*p*s^2*v2-b^3*d*p*s*t*
v1+2*b^3*d*q*r*s*v2+2*b^3*d*q*s*t*v0+b^3*e*p^2*t*v3+b^3*e*p*r*s*v2+b^3*e*p*s*t*
v0-b^2*c^2*p*r*s*v3-b^2*c^2*p*r*t*v2+b^2*c^2*p*s*t*v1+2*b^2*c^2*q*r*s*v2-b^2*c^
2*q*s^2*v1+b^2*c^2*r^3*v2-2*b^2*c^2*r^2*s*v1+b^2*c^2*r^2*t*v0+b^2*c*d*p*q*s*v3-
b^2*c*d*p*q*t*v2+b^2*c*d*p*r^2*v3+3*b^2*c*d*p*r*s*v2-b^2*c*d*p*r*t*v1-b^2*c*d*p
*s^2*v1+2*b^2*c*d*p*s*t*v0+2*b^2*c*d*q^2*s*v2+2*b^2*c*d*q*r^2*v2-2*b^2*c*d*q*r*
s*v1+2*b^2*c*d*q*r*t*v0-b^2*c*e*p^2*t*v2+b^2*c*e*p*q*s*v2+b^2*c*e*p*r^2*v2-b^2*
c*e*p*r*s*v1+b^2*c*e*p*r*t*v0+b^2*d^2*p^2*s*v3+b^2*d^2*p*q*r*v3+2*b^2*d^2*p*q*s
*v2-b^2*d^2*p*q*t*v1-b^2*d^2*p*r*s*v1+b^2*d^2*q^2*r*v2+b^2*d^2*q^2*t*v0+b^2*d*e
*p^2*r*v3+b^2*d*e*p^2*s*v2-b^2*d*e*p^2*t*v1+b^2*d*e*p*q*r*v2+b^2*d*e*p*q*t*v0-b
*c^3*p*q*s*v3-b*c^3*p*r^2*v3+b*c^3*p*r*t*v1-b*c^3*p*s*t*v0+b*c^3*q*r^2*v2-2*b*c
^3*q*r*s*v1-b*c^3*r^3*v1-b*c^2*d*p^2*s*v3+b*c^2*d*p*q*s*v2+b*c^2*d*p*q*t*v1+2*b
*c^2*d*p*r^2*v2-2*b*c^2*d*p*r*s*v1+2*b*c^2*d*p*r*t*v0+2*b*c^2*d*q^2*r*v2-2*b*c^
2*d*q^2*s*v1-2*b*c^2*d*q*r^2*v1-b*c^2*e*p^2*r*v3+b*c^2*e*p^2*t*v1+b*c^2*e*p*q*r
*v2-b*c^2*e*p*q*s*v1-b*c^2*e*p*r^2*v1+b*c*d^2*p^2*r*v3+b*c*d^2*p^2*s*v2+b*c*d^2
*p*q^2*v3+3*b*c*d^2*p*q*r*v2-3*b*c*d^2*p*q*s*v1+2*b*c*d^2*p*q*t*v0-b*c*d^2*p*r^
2*v1+b*c*d^2*q^3*v2-b*c*d^2*q^2*r*v1+b*c*d*e*p^2*q*v3+2*b*c*d*e*p^2*r*v2-b*c*d*
e*p^2*s*v1+2*b*c*d*e*p^2*t*v0+b*c*d*e*p*q^2*v2-b*c*d*e*p*q*r*v1+b*d^3*p^2*q*v3-
b*d^3*p^2*s*v1+b*d^3*p*q^2*v2-b*d^3*p*q*r*v1+b*d^2*e*p^3*v3+b*d^2*e*p^2*q*v2-b*
d^2*e*p^2*r*v1-c^4*p*q*r*v3-c^4*p*r*t*v0-c^4*q*r^2*v1-c^3*d*p^2*r*v3-c^3*d*p*q^
2*v3+c^3*d*p*q*r*v2-c^3*d*p*q*t*v0-c^3*d*p*r^2*v1-2*c^3*d*q^2*r*v1-c^3*e*p^2*q*
v3-c^3*e*p^2*t*v0-c^3*e*p*q*r*v1-c^2*d^2*p^2*q*v3+c^2*d^2*p^2*r*v2+c^2*d^2*p*q^
2*v2-3*c^2*d^2*p*q*r*v1-c^2*d^2*q^3*v1-c^2*d*e*p^3*v3+c^2*d*e*p^2*q*v2-c^2*d*e*
p^2*r*v1-c^2*d*e*p*q^2*v1+c*d^3*p^2*q*v2-c*d^3*p^2*r*v1-2*c*d^3*p*q^2*v1+c*d^2*
e*p^3*v2-2*c*d^2*e*p^2*q*v1-d^4*p^2*q*v1-d^3*e*p^3*v1-a^3*d*t^2*v4-a^3*e*t^2*v3
+2*a^2*b*c*t^2*v4-2*a^2*b*d*s*t*v4+2*a^2*b*d*t^2*v3-2*a^2*b*e*s*t*v3-3*a^2*b*e*
t^2*v2+a^2*c^2*s*t*v4+a^2*c^2*t^2*v3-a^2*c*d*r*t*v4+2*a^2*c*d*s*t*v3-3*a^2*c*d*
t^2*v2-a^2*c*e*r*t*v3-2*a^2*c*e*s*t*v2+2*a^2*c*e*t^2*v1-a^2*d^2*q*t*v4+a^2*d^2*
r*t*v3-a^2*d^2*s*t*v2+a^2*d^2*t^2*v1-a^2*d*e*p*t*v4-a^2*d*e*r*t*v2+2*a^2*d*e*s*
t*v1+2*a^2*d*e*t^2*v0-a^2*e^2*p*t*v3-a^2*e^2*q*t*v2-a*b^3*t^2*v4+2*a*b^2*c*s*t*
v4-3*a*b^2*c*t^2*v3-a*b^2*d*r*t*v4-a*b^2*d*s^2*v4+2*a*b^2*d*s*t*v3+2*a*b^2*d*t^
2*v2-a*b^2*e*r*t*v3-a*b^2*e*s^2*v3-4*a*b^2*e*s*t*v2+2*a*b^2*e*t^2*v1+3*a*b*c^2*
r*t*v4+a*b*c^2*s^2*v4-2*a*b*c^2*s*t*v3+2*a*b*c^2*t^2*v2+a*b*c*d*q*t*v4-a*b*c*d*
r*s*v4+2*a*b*c*d*s^2*v3-a*b*c*d*s*t*v2-a*b*c*d*t^2*v1+2*a*b*c*e*p*t*v4-3*a*b*c*
e*q*t*v3-a*b*c*e*r*s*v3-4*a*b*c*e*r*t*v2-2*a*b*c*e*s^2*v2+5*a*b*c*e*s*t*v1-a*b*
c*e*t^2*v0-a*b*d^2*p*t*v4-a*b*d^2*q*s*v4+a*b*d^2*q*t*v3+a*b*d^2*r*s*v3-a*b*d^2*
s^2*v2-3*a*b*d^2*t^2*v0-a*b*d*e*p*s*v4-a*b*d*e*p*t*v3-2*a*b*d*e*q*t*v2-a*b*d*e*
r*s*v2+3*a*b*d*e*r*t*v1+2*a*b*d*e*s^2*v1+2*a*b*d*e*s*t*v0-a*b*e^2*p*s*v3-2*a*b*
e^2*p*t*v2-a*b*e^2*q*s*v2+a*b*e^2*q*t*v1+a*c^3*q*t*v4+a*c^3*r*s*v4+a*c^3*r*t*v3
-a*c^3*s^2*v3+a*c^3*s*t*v2-a*c^3*t^2*v1+a*c^2*d*p*t*v4+a*c^2*d*q*s*v4+2*a*c^2*d
*q*t*v3-2*a*c^2*d*r*t*v2+a*c^2*d*s^2*v2-a*c^2*d*s*t*v1+2*a*c^2*d*t^2*v0+a*c^2*e
*p*s*v4+2*a*c^2*e*p*t*v3-a*c^2*e*q*s*v3-a*c^2*e*r*s*v2+3*a*c^2*e*r*t*v1+a*c^2*e
*s^2*v1+a*c^2*e*s*t*v0+a*c*d^2*p*t*v3+a*c*d^2*q*s*v3-4*a*c*d^2*q*t*v2-a*c*d^2*s
^2*v1-a*c*d^2*s*t*v0+a*c*d*e*p*s*v3-5*a*c*d*e*p*t*v2+4*a*c*d*e*q*t*v1+3*a*c*d*e
*r*s*v1+3*a*c*d*e*r*t*v0-a*c*e^2*p*s*v2+2*a*c*e^2*p*t*v1+a*c*e^2*q*s*v1+a*c*e^2
*q*t*v0-a*d^3*p*t*v2-a*d^3*q*s*v2+a*d^3*q*t*v1-a*d^3*r*s*v1-a*d^3*r*t*v0-a*d^2*
e*p*s*v2+4*a*d^2*e*p*t*v1+a*d^2*e*q*s*v1+a*d^2*e*q*t*v0+2*a*d*e^2*p*s*v1+2*a*d*
e^2*p*t*v0-b^4*s*t*v4+b^4*t^2*v3-b^3*c*r*t*v4-b^3*c*t^2*v2-b^3*d*q*t*v4-b^3*d*r
*s*v4+2*b^3*d*r*t*v3+b^3*d*s*t*v2-b^3*d*t^2*v1-b^3*e*p*t*v4+b^3*e*q*t*v3-b^3*e*
r*s*v3-b^3*e*r*t*v2-b^3*e*s^2*v2+b^3*e*s*t*v1-b^3*e*t^2*v0+b^2*c^2*r*s*v4-2*b^2
*c^2*r*t*v3+b^2*c^2*t^2*v1-b^2*c*d*q*s*v4-b^2*c*d*r^2*v4+2*b^2*c*d*r*s*v3+b^2*c
*d*r*t*v2-b^2*c*d*s*t*v1+2*b^2*c*d*t^2*v0-b^2*c*e*p*t*v3-b^2*c*e*q*s*v3-2*b^2*c
*e*q*t*v2-b^2*c*e*r^2*v3-4*b^2*c*e*r*s*v2+2*b^2*c*e*r*t*v1+b^2*c*e*s^2*v1-3*b^2
*c*e*s*t*v0-b^2*d^2*p*s*v4+b^2*d^2*p*t*v3-b^2*d^2*q*r*v4+b^2*d^2*q*t*v2+b^2*d^2
*r^2*v3-b^2*d^2*r*s*v2-2*b^2*d^2*r*t*v1-2*b^2*d^2*s*t*v0-b^2*d*e*p*r*v4-2*b^2*d
*e*p*s*v3-2*b^2*d*e*q*s*v2-b^2*d*e*r^2*v2+2*b^2*d*e*r*s*v1-b^2*d*e*r*t*v0-b^2*e
^2*p*r*v3-b^2*e^2*p*s*v2+b^2*e^2*p*t*v1-b^2*e^2*q*r*v2-b^2*e^2*q*t*v0+b*c^3*q*s
*v4-b*c^3*q*t*v3+b*c^3*r^2*v4-b*c^3*r*s*v3+b*c^3*r*t*v2-b*c^3*t^2*v0+b*c^2*d*p*
s*v4-b*c^2*d*p*t*v3+2*b*c^2*d*q*s*v3+2*b*c^2*d*q*t*v2+b*c^2*d*r*s*v2+b*c^2*d*r*
t*v1+4*b*c^2*d*s*t*v0+b*c^2*e*p*r*v4+b*c^2*e*p*s*v3+b*c^2*e*p*t*v2-2*b*c^2*e*q*
r*v3-2*b*c^2*e*q*s*v2+2*b*c^2*e*q*t*v1-2*b*c^2*e*r^2*v2+3*b*c^2*e*r*s*v1-2*b*c^
2*e*r*t*v0-b*c*d^2*p*r*v4+2*b*c*d^2*p*s*v3+b*c*d^2*p*t*v2-b*c*d^2*q^2*v4+2*b*c*
d^2*q*r*v3-b*c*d^2*q*s*v2-b*c*d^2*q*t*v1-b*c*d^2*r*s*v1-b*c*d*e*p*q*v4-b*c*d*e*
p*r*v3-3*b*c*d*e*p*s*v2+b*c*d*e*p*t*v1-3*b*c*d*e*q*r*v2+4*b*c*d*e*q*s*v1+3*b*c*
d*e*r^2*v1-b*c*e^2*p*q*v3-2*b*c*e^2*p*r*v2+b*c*e^2*p*s*v1-2*b*c*e^2*p*t*v0-b*c*
e^2*q^2*v2+b*c*e^2*q*r*v1-b*d^3*p*q*v4+b*d^3*p*r*v3-b*d^3*p*s*v2-b*d^3*p*t*v1-b
*d^3*q*r*v2-2*b*d^3*q*t*v0-b*d^3*r^2*v1-b*d^2*e*p^2*v4-b*d^2*e*p*q*v3-2*b*d^2*e
*p*r*v2+3*b*d^2*e*p*s*v1-2*b*d^2*e*p*t*v0-b*d^2*e*q^2*v2+b*d^2*e*q*r*v1-2*b*d*e
^2*p^2*v3-2*b*d*e^2*p*q*v2+2*b*d*e^2*p*r*v1+c^4*q*r*v4-c^4*q*s*v3-c^4*r*t*v1-c^
4*s*t*v0+c^3*d*p*r*v4-c^3*d*p*s*v3+c^3*d*q^2*v4+c^3*d*q*s*v2-c^3*d*q*t*v1+c^3*d
*r*t*v0+c^3*e*p*q*v4+c^3*e*p*r*v3-c^3*e*p*t*v1-c^3*e*q^2*v3-c^3*e*q*r*v2+c^3*e*
q*s*v1-c^3*e*q*t*v0+c^3*e*r^2*v1+c^2*d^2*p*q*v4+c^2*d^2*p*s*v2+c^2*d^2*q^2*v3-c
^2*d^2*q*s*v1+2*c^2*d^2*q*t*v0+c^2*d*e*p^2*v4+c^2*d*e*p*q*v3-2*c^2*d*e*p*r*v2+c
^2*d*e*p*s*v1+2*c^2*d*e*p*t*v0+5*c^2*d*e*q*r*v1+c^2*e^2*p^2*v3-c^2*e^2*p*q*v2+c
^2*e^2*p*r*v1+c^2*e^2*q^2*v1+c*d^3*p*q*v3-c*d^3*p*s*v1-c*d^3*q^2*v2-c*d^3*q*r*
v1+c*d^2*e*p^2*v3-2*c*d^2*e*p*q*v2+4*c*d^2*e*p*r*v1+2*c*d^2*e*q^2*v1-2*c*d*e^2*
p^2*v2+4*c*d*e^2*p*q*v1-d^4*p*q*v2-d^4*p*r*v1-d^3*e*p^2*v2+2*d^3*e*p*q*v1+3*d^2
*e^2*p^2*v1+a^2*e^2*t*v4-a*b*d*e*t*v4+a*b*e^2*s*v4+2*a*b*e^2*t*v3-3*a*c^2*e*t*
v4+2*a*c*d^2*t*v4-2*a*c*d*e*s*v4-a*c*d*e*t*v3+a*c*e^2*s*v3+2*a*c*e^2*t*v2+a*d^3
*s*v4-a*d^3*t*v3-a*d^2*e*s*v3+2*a*d^2*e*t*v2+a*d*e^2*s*v2-3*a*d*e^2*t*v1-a*e^3*
s*v1-a*e^3*t*v0+2*b^2*c*e*t*v4+b^2*d^2*t*v4+b^2*d*e*s*v4-3*b^2*d*e*t*v3+b^2*e^2
*r*v4+b^2*e^2*s*v3+b^2*e^2*t*v2-3*b*c^2*d*t*v4-b*c^2*e*s*v4+2*b*c^2*e*t*v3+2*b*
c*d^2*t*v3-b*c*d*e*r*v4-2*b*c*d*e*s*v3-b*c*d*e*t*v2+b*c*e^2*q*v4+2*b*c*e^2*r*v3
+2*b*c*e^2*s*v2-3*b*c*e^2*t*v1+b*d^3*r*v4-b*d^3*t*v2+b*d^2*e*q*v4-2*b*d^2*e*r*
v3+b*d^2*e*s*v2+2*b*d^2*e*t*v1+2*b*d*e^2*p*v4+2*b*d*e^2*r*v2-2*b*d*e^2*s*v1+2*b
*d*e^2*t*v0+b*e^3*p*v3+b*e^3*q*v2-b*e^3*r*v1+c^4*t*v4-c^3*d*t*v3-c^3*e*r*v4+c^3
*e*s*v3-c^3*e*t*v2+c^2*d^2*t*v2-3*c^2*d*e*q*v4-c^2*d*e*s*v2+2*c^2*d*e*t*v1-c^2*
e^2*p*v4+2*c^2*e^2*q*v3+c^2*e^2*r*v2-c^2*e^2*s*v1+c^2*e^2*t*v0+c*d^3*q*v4-c*d^3
*t*v1-2*c*d^2*e*p*v4-2*c*d^2*e*q*v3+c*d^2*e*s*v1-3*c*d^2*e*t*v0+c*d*e^2*q*v2-3*
c*d*e^2*r*v1+c*e^3*p*v2-2*c*e^3*q*v1+d^4*p*v4+d^4*t*v0-d^3*e*p*v3+d^3*e*q*v2+d^
3*e*r*v1+2*d^2*e^2*p*v2-d^2*e^2*q*v1-3*d*e^3*p*v1-b*e^3*v4+2*c*d*e^2*v4-c*e^3*
v3-d^3*e*v4+d^2*e^2*v3-d*e^3*v2+e^4*v1)




beta[4,1] = a^4*t^3*v2+3*a^3*b*s*t^2*v2-a^3*b*t^3*v1+2*a^3*c*r*t^2*v2-a^3*c*s*t
^2*v1-a^3*c*t^3*v0+a^3*d*p*t^2*v3+2*a^3*d*q*t^2*v2+a^3*e*p*t^2*v2+a^2*b^2*r*t^2
*v2+3*a^2*b^2*s^2*t*v2-2*a^2*b^2*s*t^2*v1+a^2*b^2*t^3*v0-2*a^2*b*c*p*t^2*v3+a^2
*b*c*q*t^2*v2+4*a^2*b*c*r*s*t*v2-3*a^2*b*c*r*t^2*v1-2*a^2*b*c*s^2*t*v1-2*a^2*b*
c*s*t^2*v0+2*a^2*b*d*p*s*t*v3+2*a^2*b*d*p*t^2*v2+4*a^2*b*d*q*s*t*v2-2*a^2*b*d*q
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*p^2*v3-2*b*d*e^2*p*q*v2+2*b*d*e^2*p*r*v1+c^4*q*r*v4-c^4*q*s*v3-c^4*r*t*v1-c^4*
s*t*v0+c^3*d*p*r*v4-c^3*d*p*s*v3+c^3*d*q^2*v4+c^3*d*q*s*v2-c^3*d*q*t*v1+c^3*d*r
*t*v0+c^3*e*p*q*v4+c^3*e*p*r*v3-c^3*e*p*t*v1-c^3*e*q^2*v3-c^3*e*q*r*v2+c^3*e*q*
s*v1-c^3*e*q*t*v0+c^3*e*r^2*v1+c^2*d^2*p*q*v4+c^2*d^2*p*s*v2+c^2*d^2*q^2*v3-c^2
*d^2*q*s*v1+2*c^2*d^2*q*t*v0+c^2*d*e*p^2*v4+c^2*d*e*p*q*v3-2*c^2*d*e*p*r*v2+c^2
*d*e*p*s*v1+2*c^2*d*e*p*t*v0+5*c^2*d*e*q*r*v1+c^2*e^2*p^2*v3-c^2*e^2*p*q*v2+c^2
*e^2*p*r*v1+c^2*e^2*q^2*v1+c*d^3*p*q*v3-c*d^3*p*s*v1-c*d^3*q^2*v2-c*d^3*q*r*v1+
c*d^2*e*p^2*v3-2*c*d^2*e*p*q*v2+4*c*d^2*e*p*r*v1+2*c*d^2*e*q^2*v1-2*c*d*e^2*p^2
*v2+4*c*d*e^2*p*q*v1-d^4*p*q*v2-d^4*p*r*v1-d^3*e*p^2*v2+2*d^3*e*p*q*v1+3*d^2*e^
2*p^2*v1+a^2*e^2*t*v4-a*b*d*e*t*v4+a*b*e^2*s*v4+2*a*b*e^2*t*v3-3*a*c^2*e*t*v4+2
*a*c*d^2*t*v4-2*a*c*d*e*s*v4-a*c*d*e*t*v3+a*c*e^2*s*v3+2*a*c*e^2*t*v2+a*d^3*s*
v4-a*d^3*t*v3-a*d^2*e*s*v3+2*a*d^2*e*t*v2+a*d*e^2*s*v2-3*a*d*e^2*t*v1-a*e^3*s*
v1-a*e^3*t*v0+2*b^2*c*e*t*v4+b^2*d^2*t*v4+b^2*d*e*s*v4-3*b^2*d*e*t*v3+b^2*e^2*r
*v4+b^2*e^2*s*v3+b^2*e^2*t*v2-3*b*c^2*d*t*v4-b*c^2*e*s*v4+2*b*c^2*e*t*v3+2*b*c*
d^2*t*v3-b*c*d*e*r*v4-2*b*c*d*e*s*v3-b*c*d*e*t*v2+b*c*e^2*q*v4+2*b*c*e^2*r*v3+2
*b*c*e^2*s*v2-3*b*c*e^2*t*v1+b*d^3*r*v4-b*d^3*t*v2+b*d^2*e*q*v4-2*b*d^2*e*r*v3+
b*d^2*e*s*v2+2*b*d^2*e*t*v1+2*b*d*e^2*p*v4+2*b*d*e^2*r*v2-2*b*d*e^2*s*v1+2*b*d*
e^2*t*v0+b*e^3*p*v3+b*e^3*q*v2-b*e^3*r*v1+c^4*t*v4-c^3*d*t*v3-c^3*e*r*v4+c^3*e*
s*v3-c^3*e*t*v2+c^2*d^2*t*v2-3*c^2*d*e*q*v4-c^2*d*e*s*v2+2*c^2*d*e*t*v1-c^2*e^2
*p*v4+2*c^2*e^2*q*v3+c^2*e^2*r*v2-c^2*e^2*s*v1+c^2*e^2*t*v0+c*d^3*q*v4-c*d^3*t*
v1-2*c*d^2*e*p*v4-2*c*d^2*e*q*v3+c*d^2*e*s*v1-3*c*d^2*e*t*v0+c*d*e^2*q*v2-3*c*d
*e^2*r*v1+c*e^3*p*v2-2*c*e^3*q*v1+d^4*p*v4+d^4*t*v0-d^3*e*p*v3+d^3*e*q*v2+d^3*e
*r*v1+2*d^2*e^2*p*v2-d^2*e^2*q*v1-3*d*e^3*p*v1-b*e^3*v4+2*c*d*e^2*v4-c*e^3*v3-d
^3*e*v4+d^2*e^2*v3-d*e^3*v2+e^4*v1




beta[4,2] = -a^4*p*t^3*v2-3*a^3*b*p*s*t^2*v2+a^3*b*p*t^3*v1-2*a^3*c*p*r*t^2*v2+
a^3*c*p*s*t^2*v1+a^3*c*p*t^3*v0-a^3*d*p^2*t^2*v3-2*a^3*d*p*q*t^2*v2-a^3*e*p^2*t
^2*v2-a^2*b^2*p*r*t^2*v2-3*a^2*b^2*p*s^2*t*v2+2*a^2*b^2*p*s*t^2*v1-a^2*b^2*p*t^
3*v0+2*a^2*b*c*p^2*t^2*v3-a^2*b*c*p*q*t^2*v2-4*a^2*b*c*p*r*s*t*v2+3*a^2*b*c*p*r
*t^2*v1+2*a^2*b*c*p*s^2*t*v1+2*a^2*b*c*p*s*t^2*v0-2*a^2*b*d*p^2*s*t*v3-2*a^2*b*
d*p^2*t^2*v2-4*a^2*b*d*p*q*s*t*v2+2*a^2*b*d*p*q*t^2*v1-2*a^2*b*e*p^2*s*t*v2+a^2
*b*e*p^2*t^2*v1+a^2*c^2*p^2*s*t*v3-a^2*c^2*p^2*t^2*v2+a^2*c^2*p*q*t^2*v1-a^2*c^
2*p*r^2*t*v2+2*a^2*c^2*p*r*s*t*v1+2*a^2*c^2*p*r*t^2*v0-a^2*c*d*p^2*r*t*v3-a^2*c
*d*p^2*s*t*v2+2*a^2*c*d*p^2*t^2*v1-2*a^2*c*d*p*q*r*t*v2+2*a^2*c*d*p*q*s*t*v1+2*
a^2*c*d*p*q*t^2*v0-a^2*c*e*p^2*r*t*v2+a^2*c*e*p^2*s*t*v1+a^2*c*e*p^2*t^2*v0-a^2
*d^2*p^2*q*t*v3+a^2*d^2*p^2*s*t*v1+a^2*d^2*p^2*t^2*v0-a^2*d^2*p*q^2*t*v2-a^2*d*
e*p^3*t*v3-a^2*d*e*p^2*q*t*v2-a*b^3*p^2*t^2*v3-2*a*b^3*p*r*s*t*v2-a*b^3*p*s^3*
v2+a*b^3*p*s^2*t*v1-2*a*b^3*p*s*t^2*v0+2*a*b^2*c*p^2*s*t*v3+a*b^2*c*p^2*t^2*v2-\
2*a*b^2*c*p*q*s*t*v2-2*a*b^2*c*p*r^2*t*v2-2*a*b^2*c*p*r*s^2*v2+4*a*b^2*c*p*r*s*
t*v1-2*a*b^2*c*p*r*t^2*v0+a*b^2*c*p*s^3*v1+a*b^2*c*p*s^2*t*v0-a*b^2*d*p^2*r*t*
v3-a*b^2*d*p^2*s^2*v3-3*a*b^2*d*p^2*s*t*v2+a*b^2*d*p^2*t^2*v1-2*a*b^2*d*p*q*r*t
*v2-2*a*b^2*d*p*q*s^2*v2+2*a*b^2*d*p*q*s*t*v1-2*a*b^2*d*p*q*t^2*v0-a*b^2*e*p^2*
r*t*v2-a*b^2*e*p^2*s^2*v2+a*b^2*e*p^2*s*t*v1-a*b^2*e*p^2*t^2*v0+3*a*b*c^2*p^2*r
*t*v3+a*b*c^2*p^2*s^2*v3-a*b*c^2*p^2*s*t*v2-a*b*c^2*p^2*t^2*v1-2*a*b*c^2*p*q*r*
t*v2+2*a*b*c^2*p*q*s*t*v1-a*b*c^2*p*r^2*s*v2+3*a*b*c^2*p*r^2*t*v1+2*a*b*c^2*p*r
*s^2*v1+2*a*b*c^2*p*r*s*t*v0+a*b*c*d*p^2*q*t*v3-a*b*c*d*p^2*r*s*v3-4*a*b*c*d*p^
2*r*t*v2-a*b*c*d*p^2*s^2*v2+3*a*b*c*d*p^2*s*t*v1-2*a*b*c*d*p^2*t^2*v0-2*a*b*c*d
*p*q^2*t*v2-2*a*b*c*d*p*q*r*s*v2+4*a*b*c*d*p*q*r*t*v1+2*a*b*c*d*p*q*s^2*v1+2*a*
b*c*d*p*q*s*t*v0+2*a*b*c*e*p^3*t*v3-a*b*c*e*p^2*q*t*v2-a*b*c*e*p^2*r*s*v2+2*a*b
*c*e*p^2*r*t*v1+a*b*c*e*p^2*s^2*v1+a*b*c*e*p^2*s*t*v0-a*b*d^2*p^3*t*v3-a*b*d^2*
p^2*q*s*v3-3*a*b*d^2*p^2*q*t*v2+a*b*d^2*p^2*r*t*v1+a*b*d^2*p^2*s^2*v1+a*b*d^2*p
^2*s*t*v0-a*b*d^2*p*q^2*s*v2+a*b*d^2*p*q^2*t*v1-a*b*d*e*p^3*s*v3-2*a*b*d*e*p^3*
t*v2-a*b*d*e*p^2*q*s*v2+a*b*d*e*p^2*q*t*v1+a*c^3*p^2*q*t*v3+a*c^3*p^2*r*s*v3-a*
c^3*p^2*r*t*v2+a*c^3*p^2*t^2*v0+2*a*c^3*p*q*r*t*v1+a*c^3*p*r^2*s*v1+a*c^3*p*r^2
*t*v0+a*c^2*d*p^3*t*v3+a*c^2*d*p^2*q*s*v3-2*a*c^2*d*p^2*q*t*v2-a*c^2*d*p^2*r*s*
v2+3*a*c^2*d*p^2*r*t*v1+2*a*c^2*d*p*q^2*t*v1+2*a*c^2*d*p*q*r*s*v1+2*a*c^2*d*p*q
*r*t*v0+a*c^2*e*p^3*s*v3-a*c^2*e*p^3*t*v2+a*c^2*e*p^2*q*t*v1+a*c^2*e*p^2*r*s*v1
+a*c^2*e*p^2*r*t*v0-a*c*d^2*p^3*t*v2-a*c*d^2*p^2*q*s*v2+4*a*c*d^2*p^2*q*t*v1+a*
c*d^2*p^2*r*s*v1+a*c*d^2*p^2*r*t*v0+a*c*d^2*p*q^2*s*v1+a*c*d^2*p*q^2*t*v0-a*c*d
*e*p^3*s*v2+2*a*c*d*e*p^3*t*v1+a*c*d*e*p^2*q*s*v1+a*c*d*e*p^2*q*t*v0+a*d^3*p^3*
t*v1+a*d^3*p^2*q*s*v1+a*d^3*p^2*q*t*v0+a*d^2*e*p^3*s*v1+a*d^2*e*p^3*t*v0-b^4*p^
2*s*t*v3-b^4*p*r*s^2*v2-b^4*p*s^2*t*v0-b^3*c*p^2*r*t*v3+b^3*c*p^2*s*t*v2-b^3*c*
p*q*s^2*v2-2*b^3*c*p*r^2*s*v2+b^3*c*p*r*s^2*v1-2*b^3*c*p*r*s*t*v0-b^3*d*p^2*q*t
*v3-b^3*d*p^2*r*s*v3-b^3*d*p^2*s^2*v2+b^3*d*p^2*s*t*v1-2*b^3*d*p*q*r*s*v2-2*b^3
*d*p*q*s*t*v0-b^3*e*p^3*t*v3-b^3*e*p^2*r*s*v2-b^3*e*p^2*s*t*v0+b^2*c^2*p^2*r*s*
v3+b^2*c^2*p^2*r*t*v2-b^2*c^2*p^2*s*t*v1-2*b^2*c^2*p*q*r*s*v2+b^2*c^2*p*q*s^2*
v1-b^2*c^2*p*r^3*v2+2*b^2*c^2*p*r^2*s*v1-b^2*c^2*p*r^2*t*v0-b^2*c*d*p^2*q*s*v3+
b^2*c*d*p^2*q*t*v2-b^2*c*d*p^2*r^2*v3-3*b^2*c*d*p^2*r*s*v2+b^2*c*d*p^2*r*t*v1+b
^2*c*d*p^2*s^2*v1-2*b^2*c*d*p^2*s*t*v0-2*b^2*c*d*p*q^2*s*v2-2*b^2*c*d*p*q*r^2*
v2+2*b^2*c*d*p*q*r*s*v1-2*b^2*c*d*p*q*r*t*v0+b^2*c*e*p^3*t*v2-b^2*c*e*p^2*q*s*
v2-b^2*c*e*p^2*r^2*v2+b^2*c*e*p^2*r*s*v1-b^2*c*e*p^2*r*t*v0-b^2*d^2*p^3*s*v3-b^
2*d^2*p^2*q*r*v3-2*b^2*d^2*p^2*q*s*v2+b^2*d^2*p^2*q*t*v1+b^2*d^2*p^2*r*s*v1-b^2
*d^2*p*q^2*r*v2-b^2*d^2*p*q^2*t*v0-b^2*d*e*p^3*r*v3-b^2*d*e*p^3*s*v2+b^2*d*e*p^
3*t*v1-b^2*d*e*p^2*q*r*v2-b^2*d*e*p^2*q*t*v0+b*c^3*p^2*q*s*v3+b*c^3*p^2*r^2*v3-
b*c^3*p^2*r*t*v1+b*c^3*p^2*s*t*v0-b*c^3*p*q*r^2*v2+2*b*c^3*p*q*r*s*v1+b*c^3*p*r
^3*v1+b*c^2*d*p^3*s*v3-b*c^2*d*p^2*q*s*v2-b*c^2*d*p^2*q*t*v1-2*b*c^2*d*p^2*r^2*
v2+2*b*c^2*d*p^2*r*s*v1-2*b*c^2*d*p^2*r*t*v0-2*b*c^2*d*p*q^2*r*v2+2*b*c^2*d*p*q
^2*s*v1+2*b*c^2*d*p*q*r^2*v1+b*c^2*e*p^3*r*v3-b*c^2*e*p^3*t*v1-b*c^2*e*p^2*q*r*
v2+b*c^2*e*p^2*q*s*v1+b*c^2*e*p^2*r^2*v1-b*c*d^2*p^3*r*v3-b*c*d^2*p^3*s*v2-b*c*
d^2*p^2*q^2*v3-3*b*c*d^2*p^2*q*r*v2+3*b*c*d^2*p^2*q*s*v1-2*b*c*d^2*p^2*q*t*v0+b
*c*d^2*p^2*r^2*v1-b*c*d^2*p*q^3*v2+b*c*d^2*p*q^2*r*v1-b*c*d*e*p^3*q*v3-2*b*c*d*
e*p^3*r*v2+b*c*d*e*p^3*s*v1-2*b*c*d*e*p^3*t*v0-b*c*d*e*p^2*q^2*v2+b*c*d*e*p^2*q
*r*v1-b*d^3*p^3*q*v3+b*d^3*p^3*s*v1-b*d^3*p^2*q^2*v2+b*d^3*p^2*q*r*v1-b*d^2*e*p
^4*v3-b*d^2*e*p^3*q*v2+b*d^2*e*p^3*r*v1+c^4*p^2*q*r*v3+c^4*p^2*r*t*v0+c^4*p*q*r
^2*v1+c^3*d*p^3*r*v3+c^3*d*p^2*q^2*v3-c^3*d*p^2*q*r*v2+c^3*d*p^2*q*t*v0+c^3*d*p
^2*r^2*v1+2*c^3*d*p*q^2*r*v1+c^3*e*p^3*q*v3+c^3*e*p^3*t*v0+c^3*e*p^2*q*r*v1+c^2
*d^2*p^3*q*v3-c^2*d^2*p^3*r*v2-c^2*d^2*p^2*q^2*v2+3*c^2*d^2*p^2*q*r*v1+c^2*d^2*
p*q^3*v1+c^2*d*e*p^4*v3-c^2*d*e*p^3*q*v2+c^2*d*e*p^3*r*v1+c^2*d*e*p^2*q^2*v1-c*
d^3*p^3*q*v2+c*d^3*p^3*r*v1+2*c*d^3*p^2*q^2*v1-c*d^2*e*p^4*v2+2*c*d^2*e*p^3*q*
v1+d^4*p^3*q*v1+d^3*e*p^4*v1+a^4*t^3*v3+3*a^3*b*s*t^2*v3-a^3*b*t^3*v2+2*a^3*c*r
*t^2*v3-a^3*c*s*t^2*v2-a^3*c*t^3*v1+a^3*d*p*t^2*v4+a^3*d*q*t^2*v3-a^3*d*r*t^2*
v2-a^3*d*s*t^2*v1-a^3*d*t^3*v0+2*a^3*e*p*t^2*v3+a^2*b^2*r*t^2*v3+3*a^2*b^2*s^2*
t*v3-2*a^2*b^2*s*t^2*v2+a^2*b^2*t^3*v1-2*a^2*b*c*p*t^2*v4+3*a^2*b*c*q*t^2*v3+4*
a^2*b*c*r*s*t*v3-a^2*b*c*r*t^2*v2-2*a^2*b*c*s^2*t*v2+2*a^2*b*c*t^3*v0+2*a^2*b*d
*p*s*t*v4+2*a^2*b*d*q*s*t*v3-2*a^2*b*d*q*t^2*v2-2*a^2*b*d*r*s*t*v2-2*a^2*b*d*s^
2*t*v1-2*a^2*b*d*s*t^2*v0+4*a^2*b*e*p*s*t*v3+2*a^2*b*e*p*t^2*v2-a^2*c^2*p*s*t*
v4+a^2*c^2*q*s*t*v3-a^2*c^2*q*t^2*v2+a^2*c^2*r^2*t*v3-a^2*c^2*r*s*t*v2-2*a^2*c^
2*r*t^2*v1+a^2*c^2*s^2*t*v1+a^2*c^2*s*t^2*v0+a^2*c*d*p*r*t*v4-a^2*c*d*p*s*t*v3+
a^2*c*d*p*t^2*v2+a^2*c*d*q*r*t*v3-2*a^2*c*d*q*s*t*v2-2*a^2*c*d*q*t^2*v1-a^2*c*d
*r^2*t*v2-a^2*c*d*r*s*t*v1-a^2*c*d*r*t^2*v0+2*a^2*c*e*p*r*t*v3+a^2*c*e*p*s*t*v2
-3*a^2*c*e*p*t^2*v1+a^2*d^2*p*q*t*v4-a^2*d^2*p*r*t*v3-2*a^2*d^2*p*t^2*v1-a^2*d^
2*q*r*t*v2-a^2*d^2*q*s*t*v1-a^2*d^2*q*t^2*v0+a^2*d*e*p^2*t*v4-3*a^2*d*e*p*s*t*
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*d^3*s^2*v1+a*d^3*s*t*v0+2*a*d^2*e*p*t*v2+a*d^2*e*q*s*v2+a*d^2*e*q*t*v1+a*d*e^2
*p*s*v2+5*a*d*e^2*p*t*v1+a*e^3*p*s*v1+a*e^3*p*t*v0+b^4*t^2*v4-b^3*c*t^2*v3+2*b^
3*d*r*t*v4+b^3*d*s*t*v3-b^3*d*t^2*v2+b^3*e*q*t*v4-b^3*e*r*s*v4-b^3*e*r*t*v3-b^3
*e*s^2*v3+b^3*e*s*t*v2-b^3*e*t^2*v1-2*b^2*c^2*r*t*v4+b^2*c^2*t^2*v2+2*b^2*c*d*r
*s*v4+b^2*c*d*r*t*v3-b^2*c*d*s*t*v2+2*b^2*c*d*t^2*v1-b^2*c*e*p*t*v4-b^2*c*e*q*s
*v4-b^2*c*e*r^2*v4-4*b^2*c*e*r*s*v3+4*b^2*c*e*r*t*v2+b^2*c*e*s^2*v2-b^2*c*e*s*t
*v1+2*b^2*c*e*t^2*v0+b^2*d^2*p*t*v4+2*b^2*d^2*q*t*v3+b^2*d^2*r^2*v4-b^2*d^2*r*s
*v3-b^2*d^2*r*t*v2-b^2*d^2*s*t*v1+b^2*d^2*t^2*v0-2*b^2*d*e*p*s*v4+3*b^2*d*e*p*t
*v3-b^2*d*e*q*s*v3-b^2*d*e*r^2*v3+3*b^2*d*e*r*s*v2-b^2*d*e*r*t*v1+b^2*d*e*s^2*
v1+b^2*d*e*s*t*v0-b^2*e^2*p*r*v4-2*b^2*e^2*p*s*v3-b^2*e^2*q*t*v1+b^2*e^2*r^2*v2
+b^2*e^2*r*s*v1+b^2*e^2*r*t*v0-b*c^3*q*t*v4-b*c^3*r*s*v4+b*c^3*r*t*v3-b*c^3*t^2
*v1-b*c^2*d*p*t*v4+2*b*c^2*d*q*s*v4-b*c^2*d*q*t*v3+b*c^2*d*r*s*v3-2*b*c^2*d*r*t
*v2+b*c^2*d*s*t*v1-3*b*c^2*d*t^2*v0+b*c^2*e*p*s*v4-b*c^2*e*p*t*v3-2*b*c^2*e*q*r
*v4-3*b*c^2*e*q*s*v3+2*b*c^2*e*q*t*v2-2*b*c^2*e*r^2*v3+2*b*c^2*e*r*s*v2-2*b*c^2
*e*r*t*v1-b*c^2*e*s^2*v1-b*c^2*e*s*t*v0+2*b*c*d^2*p*s*v4-b*c*d^2*p*t*v3+2*b*c*d
^2*q*r*v4-b*c*d^2*q*s*v3-b*c*d^2*q*t*v2-b*c*d^2*r*s*v2-b*c*d*e*p*r*v4-b*c*d*e*p
*s*v3+2*b*c*d*e*p*t*v2-4*b*c*d*e*q*r*v3+4*b*c*d*e*q*s*v2+2*b*c*d*e*r^2*v2-b*c*d
*e*r*s*v1-b*c*d*e*r*t*v0-b*c*e^2*p*q*v4-4*b*c*e^2*p*r*v3-b*c*e^2*p*s*v2+b*c*e^2
*p*t*v1+2*b*c*e^2*q*r*v2+b*c*e^2*q*s*v1+b*c*e^2*q*t*v0+b*d^3*p*r*v4-b*d^3*p*s*
v3-2*b*d^3*q*t*v1+b*d^3*r*s*v1+b*d^3*r*t*v0-b*d^2*e*p*q*v4+2*b*d^2*e*p*s*v2-4*b
*d^2*e*p*t*v1+2*b*d^2*e*q*r*v2+b*d^2*e*q*s*v1+b*d^2*e*q*t*v0-2*b*d*e^2*p^2*v4+2
*b*d*e^2*p*r*v2+4*b*d*e^2*p*s*v1-b*e^3*p^2*v3-b*e^3*p*q*v2+b*e^3*p*r*v1-c^4*q*s
*v4+c^4*q*t*v3+c^4*t^2*v0-c^3*d*p*s*v4+c^3*d*p*t*v3+c^3*d*q*s*v3-c^3*d*q*t*v2+c
^3*d*r*t*v1+c^3*e*p*r*v4-c^3*e*p*s*v3-c^3*e*q^2*v4-2*c^3*e*q*r*v3+c^3*e*q*s*v2-
c^3*e*q*t*v1-c^3*e*r*s*v1-c^3*e*r*t*v0+c^2*d^2*p*s*v3-c^2*d^2*p*t*v2+c^2*d^2*q^
2*v4-c^2*d^2*q*s*v2+2*c^2*d^2*q*t*v1+c^2*d*e*p*q*v4-2*c^2*d*e*p*r*v3+2*c^2*d*e*
p*s*v2-3*c^2*d*e*q^2*v3+2*c^2*d*e*q*r*v2-3*c^2*d*e*q*s*v1-3*c^2*d*e*q*t*v0+c^2*
e^2*p^2*v4-4*c^2*e^2*p*q*v3-c^2*e^2*p*r*v2-2*c^2*e^2*p*t*v0+c^2*e^2*q^2*v2+c*d^
3*p*q*v4-c*d^3*p*s*v2+c*d^3*p*t*v1+c*d^3*q*s*v1+c*d^3*q*t*v0+c*d^2*e*p^2*v4-2*c
*d^2*e*p*q*v3+2*c*d^2*e*p*r*v2-3*c*d^2*e*p*s*v1+c*d^2*e*p*t*v0+2*c*d^2*e*q^2*v2
-2*c*d*e^2*p^2*v3+3*c*d*e^2*p*q*v2+3*c*d*e^2*p*r*v1-c*e^3*p^2*v2+2*c*e^3*p*q*v1
+d^4*p*s*v1+d^3*e*p*q*v2-d^3*e*p*r*v1+d^2*e^2*p^2*v2+d^2*e^2*p*q*v1+3*d*e^3*p^2
*v1+2*a*b*e^2*t*v4-a*c*d*e*t*v4+a*c*e^2*s*v4+2*a*c*e^2*t*v3-a*d^3*t*v4-a*d^2*e*
s*v4+2*a*d^2*e*t*v3+a*d*e^2*s*v3-3*a*d*e^2*t*v2-a*e^3*s*v2-a*e^3*t*v1-3*b^2*d*e
*t*v4+b^2*e^2*s*v4+b^2*e^2*t*v3+2*b*c^2*e*t*v4+2*b*c*d^2*t*v4-2*b*c*d*e*s*v4-b*
c*d*e*t*v3+2*b*c*e^2*r*v4+2*b*c*e^2*s*v3-3*b*c*e^2*t*v2-b*d^3*t*v3-2*b*d^2*e*r*
v4+b*d^2*e*s*v3+2*b*d^2*e*t*v2+2*b*d*e^2*r*v3-2*b*d*e^2*s*v2+2*b*d*e^2*t*v1+b*e
^3*p*v4-2*b*e^3*r*v2-b*e^3*s*v1-b*e^3*t*v0-c^3*d*t*v4+c^3*e*s*v4-c^3*e*t*v3+c^2
*d^2*t*v3-c^2*d*e*s*v3+2*c^2*d*e*t*v2+2*c^2*e^2*q*v4+c^2*e^2*r*v3-c^2*e^2*s*v2+
c^2*e^2*t*v1-c*d^3*t*v2-2*c*d^2*e*q*v4+c*d^2*e*s*v2-3*c*d^2*e*t*v1+3*c*d*e^2*q*
v3-c*d*e^2*r*v2+2*c*d*e^2*s*v1+2*c*d*e^2*t*v0+2*c*e^3*p*v3-2*c*e^3*q*v2+d^4*t*
v1-d^3*e*p*v4-d^3*e*s*v1-d^3*e*t*v0+d^2*e^2*p*v3-d^2*e^2*q*v2-2*d*e^3*p*v2-e^4*
p*v1-c*e^3*v4+d^2*e^2*v4-d*e^3*v3+e^4*v2




beta[4,3] = -a^4*p*t^3*v3-a^4*q*t^3*v2-3*a^3*b*p*s*t^2*v3+a^3*b*p*t^3*v2-3*a^3*
b*q*s*t^2*v2+a^3*b*q*t^3*v1-2*a^3*c*p*r*t^2*v3+a^3*c*p*s*t^2*v2+a^3*c*p*t^3*v1-\
2*a^3*c*q*r*t^2*v2+a^3*c*q*s*t^2*v1+a^3*c*q*t^3*v0-2*a^3*d*p*q*t^2*v3+a^3*d*p*r
*t^2*v2+a^3*d*p*s*t^2*v1+a^3*d*p*t^3*v0-2*a^3*d*q^2*t^2*v2-a^3*e*p^2*t^2*v3-a^3
*e*p*q*t^2*v2-a^2*b^2*p*r*t^2*v3-3*a^2*b^2*p*s^2*t*v3+2*a^2*b^2*p*s*t^2*v2-a^2*
b^2*p*t^3*v1-a^2*b^2*q*r*t^2*v2-3*a^2*b^2*q*s^2*t*v2+2*a^2*b^2*q*s*t^2*v1-a^2*b
^2*q*t^3*v0-a^2*b*c*p*q*t^2*v3-4*a^2*b*c*p*r*s*t*v3+a^2*b*c*p*r*t^2*v2+2*a^2*b*
c*p*s^2*t*v2-2*a^2*b*c*p*t^3*v0-a^2*b*c*q^2*t^2*v2-4*a^2*b*c*q*r*s*t*v2+3*a^2*b
*c*q*r*t^2*v1+2*a^2*b*c*q*s^2*t*v1+2*a^2*b*c*q*s*t^2*v0-2*a^2*b*d*p^2*t^2*v3-4*
a^2*b*d*p*q*s*t*v3+2*a^2*b*d*p*r*s*t*v2+2*a^2*b*d*p*s^2*t*v1+2*a^2*b*d*p*s*t^2*
v0-4*a^2*b*d*q^2*s*t*v2+2*a^2*b*d*q^2*t^2*v1-2*a^2*b*e*p^2*s*t*v3+a^2*b*e*p^2*t
^2*v2-2*a^2*b*e*p*q*s*t*v2+a^2*b*e*p*q*t^2*v1-a^2*c^2*p^2*t^2*v3-a^2*c^2*p*r^2*
t*v3+a^2*c^2*p*r*s*t*v2+2*a^2*c^2*p*r*t^2*v1-a^2*c^2*p*s^2*t*v1-a^2*c^2*p*s*t^2
*v0+a^2*c^2*q^2*t^2*v1-a^2*c^2*q*r^2*t*v2+2*a^2*c^2*q*r*s*t*v1+2*a^2*c^2*q*r*t^
2*v0-a^2*c*d*p^2*s*t*v3+2*a^2*c*d*p^2*t^2*v2-2*a^2*c*d*p*q*r*t*v3+a^2*c*d*p*q*s
*t*v2+4*a^2*c*d*p*q*t^2*v1+a^2*c*d*p*r^2*t*v2+a^2*c*d*p*r*s*t*v1+a^2*c*d*p*r*t^
2*v0-2*a^2*c*d*q^2*r*t*v2+2*a^2*c*d*q^2*s*t*v1+2*a^2*c*d*q^2*t^2*v0-a^2*c*e*p^2
*r*t*v3+a^2*c*e*p^2*s*t*v2+a^2*c*e*p^2*t^2*v1-a^2*c*e*p*q*r*t*v2+a^2*c*e*p*q*s*
t*v1+a^2*c*e*p*q*t^2*v0+a^2*d^2*p^2*s*t*v2+a^2*d^2*p^2*t^2*v1-a^2*d^2*p*q^2*t*
v3+a^2*d^2*p*q*r*t*v2+2*a^2*d^2*p*q*s*t*v1+2*a^2*d^2*p*q*t^2*v0-a^2*d^2*q^3*t*
v2-a^2*d*e*p^2*q*t*v3+a^2*d*e*p^2*r*t*v2+a^2*d*e*p^2*s*t*v1+a^2*d*e*p^2*t^2*v0-
a^2*d*e*p*q^2*t*v2-2*a*b^3*p*r*s*t*v3+a*b^3*p*r*t^2*v2-a*b^3*p*s^3*v3+a*b^3*p*s
^2*t*v2-a*b^3*p*s*t^2*v1+a*b^3*p*t^3*v0-2*a*b^3*q*r*s*t*v2-a*b^3*q*s^3*v2+a*b^3
*q*s^2*t*v1-2*a*b^3*q*s*t^2*v0+a*b^2*c*p^2*t^2*v3-2*a*b^2*c*p*q*s*t*v3+a*b^2*c*
p*q*t^2*v2-2*a*b^2*c*p*r^2*t*v3-2*a*b^2*c*p*r*s^2*v3+2*a*b^2*c*p*r*s*t*v2-2*a*b
^2*c*p*r*t^2*v1+a*b^2*c*p*s^3*v2-a*b^2*c*p*s^2*t*v1-2*a*b^2*c*p*s*t^2*v0-2*a*b^
2*c*q^2*s*t*v2-2*a*b^2*c*q*r^2*t*v2-2*a*b^2*c*q*r*s^2*v2+4*a*b^2*c*q*r*s*t*v1-2
*a*b^2*c*q*r*t^2*v0+a*b^2*c*q*s^3*v1+a*b^2*c*q*s^2*t*v0-3*a*b^2*d*p^2*s*t*v3+a*
b^2*d*p^2*t^2*v2-2*a*b^2*d*p*q*r*t*v3-2*a*b^2*d*p*q*s^2*v3-a*b^2*d*p*q*s*t*v2-a
*b^2*d*p*q*t^2*v1+a*b^2*d*p*r^2*t*v2+a*b^2*d*p*r*s^2*v2+a*b^2*d*p*r*s*t*v1+a*b^
2*d*p*r*t^2*v0+a*b^2*d*p*s^3*v1+a*b^2*d*p*s^2*t*v0-2*a*b^2*d*q^2*r*t*v2-2*a*b^2
*d*q^2*s^2*v2+2*a*b^2*d*q^2*s*t*v1-2*a*b^2*d*q^2*t^2*v0-a*b^2*e*p^2*r*t*v3-a*b^
2*e*p^2*s^2*v3+a*b^2*e*p^2*s*t*v2-a*b^2*e*p^2*t^2*v1-a*b^2*e*p*q*r*t*v2-a*b^2*e
*p*q*s^2*v2+a*b^2*e*p*q*s*t*v1-a*b^2*e*p*q*t^2*v0-a*b*c^2*p^2*s*t*v3-a*b*c^2*p^
2*t^2*v2-2*a*b*c^2*p*q*r*t*v3+a*b*c^2*p*q*s*t*v2-a*b*c^2*p*q*t^2*v1-a*b*c^2*p*r
^2*s*v3+a*b*c^2*p*r*s^2*v2-a*b*c^2*p*r*s*t*v1-3*a*b*c^2*p*r*t^2*v0-a*b*c^2*p*s^
3*v1-a*b*c^2*p*s^2*t*v0-2*a*b*c^2*q^2*r*t*v2+2*a*b*c^2*q^2*s*t*v1-a*b*c^2*q*r^2
*s*v2+3*a*b*c^2*q*r^2*t*v1+2*a*b*c^2*q*r*s^2*v1+2*a*b*c^2*q*r*s*t*v0-4*a*b*c*d*
p^2*r*t*v3-a*b*c*d*p^2*s^2*v3+3*a*b*c*d*p^2*s*t*v2-2*a*b*c*d*p^2*t^2*v1-2*a*b*c
*d*p*q^2*t*v3-2*a*b*c*d*p*q*r*s*v3-a*b*c*d*p*q*r*t*v2+a*b*c*d*p*q*s^2*v2+4*a*b*
c*d*p*q*s*t*v1-3*a*b*c*d*p*q*t^2*v0+a*b*c*d*p*r^2*s*v2+a*b*c*d*p*r*s^2*v1+a*b*c
*d*p*r*s*t*v0-2*a*b*c*d*q^3*t*v2-2*a*b*c*d*q^2*r*s*v2+4*a*b*c*d*q^2*r*t*v1+2*a*
b*c*d*q^2*s^2*v1+2*a*b*c*d*q^2*s*t*v0-a*b*c*e*p^2*q*t*v3-a*b*c*e*p^2*r*s*v3+a*b
*c*e*p^2*s^2*v2-a*b*c*e*p^2*s*t*v1-2*a*b*c*e*p^2*t^2*v0-a*b*c*e*p*q^2*t*v2-a*b*
c*e*p*q*r*s*v2+2*a*b*c*e*p*q*r*t*v1+a*b*c*e*p*q*s^2*v1+a*b*c*e*p*q*s*t*v0-3*a*b
*d^2*p^2*q*t*v3+2*a*b*d^2*p^2*r*t*v2+a*b*d^2*p^2*s^2*v2+2*a*b*d^2*p^2*s*t*v1+a*
b*d^2*p^2*t^2*v0-a*b*d^2*p*q^2*s*v3-2*a*b*d^2*p*q^2*t*v2+a*b*d^2*p*q*r*s*v2+a*b
*d^2*p*q*r*t*v1+2*a*b*d^2*p*q*s^2*v1+2*a*b*d^2*p*q*s*t*v0-a*b*d^2*q^3*s*v2+a*b*
d^2*q^3*t*v1-2*a*b*d*e*p^3*t*v3-a*b*d*e*p^2*q*s*v3-a*b*d*e*p^2*q*t*v2+a*b*d*e*p
^2*r*s*v2+a*b*d*e*p^2*s^2*v1+a*b*d*e*p^2*s*t*v0-a*b*d*e*p*q^2*s*v2+a*b*d*e*p*q^
2*t*v1-a*c^3*p^2*r*t*v3+a*c^3*p^2*t^2*v1-a*c^3*p*q*s*t*v1+a*c^3*p*r^2*t*v1-a*c^
3*p*r*s^2*v1-a*c^3*p*r*s*t*v0+2*a*c^3*q^2*r*t*v1+a*c^3*q*r^2*s*v1+a*c^3*q*r^2*t
*v0-2*a*c^2*d*p^2*q*t*v3-a*c^2*d*p^2*r*s*v3+2*a*c^2*d*p^2*r*t*v2-a*c^2*d*p^2*s*
t*v1-a*c^2*d*p^2*t^2*v0+5*a*c^2*d*p*q*r*t*v1-a*c^2*d*p*q*s^2*v1-a*c^2*d*p*q*s*t
*v0+2*a*c^2*d*q^3*t*v1+2*a*c^2*d*q^2*r*s*v1+2*a*c^2*d*q^2*r*t*v0-a*c^2*e*p^3*t*
v3+a*c^2*e*p^2*r*t*v1-a*c^2*e*p^2*s^2*v1-a*c^2*e*p^2*s*t*v0+a*c^2*e*p*q^2*t*v1+
a*c^2*e*p*q*r*s*v1+a*c^2*e*p*q*r*t*v0-a*c*d^2*p^3*t*v3-a*c*d^2*p^2*q*s*v3+3*a*c
*d^2*p^2*q*t*v2+a*c*d^2*p^2*r*s*v2+a*c*d^2*p^2*r*t*v1+5*a*c*d^2*p*q^2*t*v1+a*c*
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d*e*p*t*v3-3*b*c*d*e*q*r*v4+4*b*c*d*e*q*s*v3+b*c*d*e*q*t*v2+2*b*c*d*e*r^2*v3-3*
b*c*d*e*r*s*v2-b*c*d*e*r*t*v1-2*b*c*d*e*s^2*v1-2*b*c*d*e*s*t*v0-2*b*c*e^2*p*r*
v4-b*c*e^2*p*s*v3+b*c*e^2*p*t*v2-b*c*e^2*q^2*v4+2*b*c*e^2*q*r*v3-b*c*e^2*q*s*v2
+4*b*c*e^2*q*t*v1+2*b*c*e^2*r^2*v2+2*b*c*e^2*r*s*v1+2*b*c*e^2*r*t*v0-b*d^3*p*s*
v4-b*d^3*q*r*v4-b*d^3*q*t*v2+b*d^3*r*s*v2+b*d^3*r*t*v1-2*b*d^2*e*p*r*v4+2*b*d^2
*e*p*s*v3-4*b*d^2*e*p*t*v2-b*d^2*e*q^2*v4+2*b*d^2*e*q*r*v3-b*d^2*e*q*t*v1-2*b*d
^2*e*r^2*v2-2*b*d^2*e*r*s*v1-2*b*d^2*e*r*t*v0-2*b*d*e^2*p*q*v4+2*b*d*e^2*p*r*v3
+4*b*d*e^2*p*s*v2-2*b*d*e^2*q*r*v2+2*b*d*e^2*q*s*v1-2*b*d*e^2*q*t*v0-b*e^3*p*q*
v3+2*b*e^3*p*r*v2+b*e^3*p*s*v1+b*e^3*p*t*v0-b*e^3*q^2*v2+b*e^3*q*r*v1+c^4*t^2*
v1+c^3*d*q*s*v4-c^3*d*q*t*v3-c^3*d*s*t*v1-c^3*d*t^2*v0-c^3*e*q*r*v4+c^3*e*q*s*
v3-c^3*e*r*t*v1+c^3*e*s^2*v1+c^3*e*s*t*v0+c^2*d^2*p*s*v4-c^2*d^2*p*t*v3-c^2*d^2
*q*s*v3+c^2*d^2*q*t*v2-2*c^2*d*e*p*r*v4+2*c^2*d*e*p*s*v3+2*c^2*d*e*q*r*v3-2*c^2
*d*e*q*s*v2-5*c^2*d*e*q*t*v1-c^2*e^2*p*q*v4-c^2*e^2*p*r*v3-2*c^2*e^2*p*t*v1+c^2
*e^2*q^2*v3+c^2*e^2*q*r*v2+3*c^2*e^2*q*s*v1+c^2*e^2*q*t*v0-c*d^3*p*s*v3+c*d^3*p
*t*v2-c*d^3*q^2*v4+c*d^3*q*s*v2+2*c*d^3*q*t*v1-2*c*d^2*e*p*q*v4+2*c*d^2*e*p*r*
v3-3*c*d^2*e*p*s*v2+c*d^2*e*p*t*v1+2*c*d^2*e*q^2*v3-2*c*d^2*e*q*r*v2-3*c*d^2*e*
q*s*v1+c*d^2*e*q*t*v0-2*c*d*e^2*p^2*v4+3*c*d*e^2*p*q*v3+3*c*d*e^2*p*r*v2-c*d*e^
2*q^2*v2+3*c*d*e^2*q*r*v1-c*e^3*p^2*v3+c*e^3*p*q*v2+2*c*e^3*q^2*v1-d^4*p*q*v4+d
^4*p*s*v2-d^4*q*t*v0-d^3*e*p^2*v4+d^3*e*p*q*v3-2*d^3*e*p*r*v2-d^3*e*p*s*v1-d^3*
e*p*t*v0-d^3*e*q^2*v2-d^3*e*q*r*v1+d^2*e^2*p^2*v3-d^2*e^2*p*q*v2+d^2*e^2*q^2*v1
+3*d*e^3*p^2*v2+3*d*e^3*p*q*v1+2*a*c*e^2*t*v4+2*a*d^2*e*t*v4+a*d*e^2*s*v4-3*a*d
*e^2*t*v3-a*e^3*s*v3-a*e^3*t*v2+b^2*e^2*t*v4-b*c*d*e*t*v4+2*b*c*e^2*s*v4-3*b*c*
e^2*t*v3-b*d^3*t*v4+b*d^2*e*s*v4+2*b*d^2*e*t*v3+2*b*d*e^2*r*v4-2*b*d*e^2*s*v3+2
*b*d*e^2*t*v2+b*e^3*q*v4-2*b*e^3*r*v3-b*e^3*s*v2-b*e^3*t*v1-c^3*e*t*v4+c^2*d^2*
t*v4-c^2*d*e*s*v4+2*c^2*d*e*t*v3+c^2*e^2*r*v4-c^2*e^2*s*v3+c^2*e^2*t*v2-c*d^3*t
*v3+c*d^2*e*s*v3-3*c*d^2*e*t*v2+c*d*e^2*q*v4-c*d*e^2*r*v3+2*c*d*e^2*s*v2+2*c*d*
e^2*t*v1+c*e^3*p*v4-2*c*e^3*q*v3-c*e^3*r*v2-c*e^3*s*v1-c*e^3*t*v0+d^4*t*v2+d^3*
e*q*v4-d^3*e*s*v2-d^3*e*t*v1+2*d^2*e^2*p*v4-d^2*e^2*q*v3+d^2*e^2*r*v2+d^2*e^2*s
*v1+d^2*e^2*t*v0-2*d*e^3*p*v3+d*e^3*q*v2-e^4*p*v2-e^4*q*v1-d*e^3*v4+e^4*v3




beta[4,4] = a^4*s*t^3*v1+a^4*t^4*v0+a^3*b*p*t^3*v3+a^3*b*q*t^3*v2+a^3*b*r*t^3*
v1+3*a^3*b*s^2*t^2*v1+3*a^3*b*s*t^3*v0+a^3*c*p*s*t^2*v3+a^3*c*p*t^3*v2+a^3*c*q*
s*t^2*v2+a^3*c*q*t^3*v1+3*a^3*c*r*s*t^2*v1+3*a^3*c*r*t^3*v0+a^3*d*p*s*t^2*v2+a^
3*d*p*t^3*v1+2*a^3*d*q*s*t^2*v1+2*a^3*d*q*t^3*v0+a^3*e*p*s*t^2*v1+a^3*e*p*t^3*
v0+2*a^2*b^2*p*s*t^2*v3-a^2*b^2*p*t^3*v2+2*a^2*b^2*q*s*t^2*v2-a^2*b^2*q*t^3*v1+
3*a^2*b^2*r*s*t^2*v1+3*a^2*b^2*s^3*t*v1+3*a^2*b^2*s^2*t^2*v0+3*a^2*b*c*p*r*t^2*
v3+2*a^2*b*c*p*s^2*t*v3-2*a^2*b*c*p*t^3*v1+3*a^2*b*c*q*r*t^2*v2+2*a^2*b*c*q*s^2
*t*v2+3*a^2*b*c*q*s*t^2*v1+a^2*b*c*q*t^3*v0+3*a^2*b*c*r^2*t^2*v1+6*a^2*b*c*r*s^
2*t*v1+6*a^2*b*c*r*s*t^2*v0+2*a^2*b*d*p*q*t^2*v3+2*a^2*b*d*p*s^2*t*v2+4*a^2*b*d
*p*s*t^2*v1+2*a^2*b*d*p*t^3*v0+2*a^2*b*d*q^2*t^2*v2+2*a^2*b*d*q*r*t^2*v1+4*a^2*
b*d*q*s^2*t*v1+4*a^2*b*d*q*s*t^2*v0+a^2*b*e*p^2*t^2*v3+a^2*b*e*p*q*t^2*v2+a^2*b
*e*p*r*t^2*v1+2*a^2*b*e*p*s^2*t*v1+2*a^2*b*e*p*s*t^2*v0+a^2*c^2*p*q*t^2*v3+2*a^
2*c^2*p*r*s*t*v3+2*a^2*c^2*p*r*t^2*v2-a^2*c^2*p*s^2*t*v2+a^2*c^2*p*t^3*v0+a^2*c
^2*q^2*t^2*v2+2*a^2*c^2*q*r*s*t*v2+3*a^2*c^2*q*r*t^2*v1+3*a^2*c^2*r^2*s*t*v1+3*
a^2*c^2*r^2*t^2*v0+2*a^2*c*d*p^2*t^2*v3+2*a^2*c*d*p*q*s*t*v3+4*a^2*c*d*p*q*t^2*
v2+a^2*c*d*p*r*s*t*v2+3*a^2*c*d*p*r*t^2*v1+a^2*c*d*p*s^2*t*v1+a^2*c*d*p*s*t^2*
v0+2*a^2*c*d*q^2*s*t*v2+2*a^2*c*d*q^2*t^2*v1+4*a^2*c*d*q*r*s*t*v1+4*a^2*c*d*q*r
*t^2*v0+a^2*c*e*p^2*s*t*v3+a^2*c*e*p^2*t^2*v2+a^2*c*e*p*q*s*t*v2+a^2*c*e*p*q*t^
2*v1+2*a^2*c*e*p*r*s*t*v1+2*a^2*c*e*p*r*t^2*v0+a^2*d^2*p^2*s*t*v3+a^2*d^2*p^2*t
^2*v2+2*a^2*d^2*p*q*s*t*v2+2*a^2*d^2*p*q*t^2*v1+a^2*d^2*p*r*s*t*v1+a^2*d^2*p*r*
t^2*v0+a^2*d^2*q^2*s*t*v1+a^2*d^2*q^2*t^2*v0+a^2*d*e*p^2*s*t*v2+a^2*d*e*p^2*t^2
*v1+a^2*d*e*p*q*s*t*v1+a^2*d*e*p*q*t^2*v0+a*b^3*p*s^2*t*v3-a*b^3*p*s*t^2*v2+a*b
^3*p*t^3*v1+a*b^3*q*s^2*t*v2-2*a*b^3*q*s*t^2*v1+3*a*b^3*r*s^2*t*v1+a*b^3*s^4*v1
+a*b^3*s^3*t*v0+4*a*b^2*c*p*r*s*t*v3-2*a*b^2*c*p*r*t^2*v2+a*b^2*c*p*s^3*v3-a*b^
2*c*p*s^2*t*v2-3*a*b^2*c*p*s*t^2*v1-a*b^2*c*p*t^3*v0+4*a*b^2*c*q*r*s*t*v2-2*a*b
^2*c*q*r*t^2*v1+a*b^2*c*q*s^3*v2+3*a*b^2*c*q*s^2*t*v1+2*a*b^2*c*q*s*t^2*v0+6*a*
b^2*c*r^2*s*t*v1+3*a*b^2*c*r*s^3*v1+3*a*b^2*c*r*s^2*t*v0+a*b^2*d*p^2*t^2*v3+2*a
*b^2*d*p*q*s*t*v3-a*b^2*d*p*q*t^2*v2+a*b^2*d*p*r*s*t*v2+2*a*b^2*d*p*r*t^2*v1+a*
b^2*d*p*s^3*v2+4*a*b^2*d*p*s^2*t*v1+3*a*b^2*d*p*s*t^2*v0+2*a*b^2*d*q^2*s*t*v2-2
*a*b^2*d*q^2*t^2*v1+4*a*b^2*d*q*r*s*t*v1+2*a*b^2*d*q*s^3*v1+2*a*b^2*d*q*s^2*t*
v0+a*b^2*e*p^2*s*t*v3-a*b^2*e*p^2*t^2*v2+a*b^2*e*p*q*s*t*v2-a*b^2*e*p*q*t^2*v1+
2*a*b^2*e*p*r*s*t*v1+a*b^2*e*p*s^3*v1+a*b^2*e*p*s^2*t*v0-a*b*c^2*p^2*t^2*v3+2*a
*b*c^2*p*q*s*t*v3-a*b*c^2*p*q*t^2*v2+3*a*b*c^2*p*r^2*t*v3+2*a*b*c^2*p*r*s^2*v3-
a*b*c^2*p*r*s*t*v2-4*a*b*c^2*p*r*t^2*v1-a*b*c^2*p*s^3*v2+a*b*c^2*p*s*t^2*v0+2*a
*b*c^2*q^2*s*t*v2+3*a*b*c^2*q*r^2*t*v2+2*a*b*c^2*q*r*s^2*v2+6*a*b*c^2*q*r*s*t*
v1+2*a*b*c^2*q*r*t^2*v0+3*a*b*c^2*r^3*t*v1+3*a*b*c^2*r^2*s^2*v1+3*a*b*c^2*r^2*s
*t*v0+3*a*b*c*d*p^2*s*t*v3-2*a*b*c*d*p^2*t^2*v2+4*a*b*c*d*p*q*r*t*v3+2*a*b*c*d*
p*q*s^2*v3+4*a*b*c*d*p*q*s*t*v2-3*a*b*c*d*p*q*t^2*v1+a*b*c*d*p*r*s^2*v2+8*a*b*c
*d*p*r*s*t*v1+2*a*b*c*d*p*r*t^2*v0+a*b*c*d*p*s^3*v1+a*b*c*d*p*s^2*t*v0+4*a*b*c*
d*q^2*r*t*v2+2*a*b*c*d*q^2*s^2*v2+4*a*b*c*d*q^2*s*t*v1+2*a*b*c*d*q^2*t^2*v0+4*a
*b*c*d*q*r^2*t*v1+4*a*b*c*d*q*r*s^2*v1+4*a*b*c*d*q*r*s*t*v0+2*a*b*c*e*p^2*r*t*
v3+a*b*c*e*p^2*s^2*v3-a*b*c*e*p^2*s*t*v2-2*a*b*c*e*p^2*t^2*v1+2*a*b*c*e*p*q*r*t
*v2+a*b*c*e*p*q*s^2*v2+2*a*b*c*e*p*q*s*t*v1+a*b*c*e*p*q*t^2*v0+2*a*b*c*e*p*r^2*
t*v1+2*a*b*c*e*p*r*s^2*v1+2*a*b*c*e*p*r*s*t*v0+a*b*d^2*p^2*r*t*v3+a*b*d^2*p^2*s
^2*v3+2*a*b*d^2*p^2*s*t*v2+a*b*d^2*p^2*t^2*v1+a*b*d^2*p*q^2*t*v3+a*b*d^2*p*q*r*
t*v2+2*a*b*d^2*p*q*s^2*v2+5*a*b*d^2*p*q*s*t*v1+3*a*b*d^2*p*q*t^2*v0+a*b*d^2*p*r
^2*t*v1+a*b*d^2*p*r*s^2*v1+a*b*d^2*p*r*s*t*v0+a*b*d^2*q^3*t*v2+a*b*d^2*q^2*r*t*
v1+a*b*d^2*q^2*s^2*v1+a*b*d^2*q^2*s*t*v0+a*b*d*e*p^2*q*t*v3+a*b*d*e*p^2*s^2*v2+
3*a*b*d*e*p^2*s*t*v1+2*a*b*d*e*p^2*t^2*v0+a*b*d*e*p*q^2*t*v2+a*b*d*e*p*q*r*t*v1
+a*b*d*e*p*q*s^2*v1+a*b*d*e*p*q*s*t*v0+a*c^3*p^2*t^2*v2+2*a*c^3*p*q*r*t*v3-a*c^
3*p*q*s*t*v2+a*c^3*p*r^2*s*v3+a*c^3*p*r^2*t*v2-a*c^3*p*r*s^2*v2+2*a*c^3*p*r*t^2
*v0+2*a*c^3*q^2*r*t*v2+a*c^3*q*r^2*s*v2+3*a*c^3*q*r^2*t*v1+a*c^3*r^3*s*v1+a*c^3
*r^3*t*v0+3*a*c^2*d*p^2*r*t*v3-a*c^2*d*p^2*s*t*v2-a*c^2*d*p^2*t^2*v1+2*a*c^2*d*
p*q^2*t*v3+2*a*c^2*d*p*q*r*s*v3+5*a*c^2*d*p*q*r*t*v2-a*c^2*d*p*q*s^2*v2+a*c^2*d
*p*q*s*t*v1+2*a*c^2*d*p*q*t^2*v0+3*a*c^2*d*p*r^2*t*v1+a*c^2*d*p*r*s^2*v1+a*c^2*
d*p*r*s*t*v0+2*a*c^2*d*q^3*t*v2+2*a*c^2*d*q^2*r*s*v2+4*a*c^2*d*q^2*r*t*v1+2*a*c
^2*d*q*r^2*s*v1+2*a*c^2*d*q*r^2*t*v0+a*c^2*e*p^2*q*t*v3+a*c^2*e*p^2*r*s*v3+a*c^
2*e*p^2*r*t*v2-a*c^2*e*p^2*s^2*v2+a*c^2*e*p^2*t^2*v0+a*c^2*e*p*q^2*t*v2+a*c^2*e
*p*q*r*s*v2+2*a*c^2*e*p*q*r*t*v1+a*c^2*e*p*r^2*s*v1+a*c^2*e*p*r^2*t*v0+4*a*c*d^
2*p^2*q*t*v3+a*c*d^2*p^2*r*s*v3+a*c*d^2*p^2*r*t*v2+a*c*d^2*p^2*s*t*v1+a*c*d^2*p
^2*t^2*v0+a*c*d^2*p*q^2*s*v3+5*a*c*d^2*p*q^2*t*v2+a*c*d^2*p*q*r*s*v2+5*a*c*d^2*
p*q*r*t*v1+a*c*d^2*p*q*s^2*v1+a*c*d^2*p*q*s*t*v0+a*c*d^2*p*r^2*s*v1+a*c*d^2*p*r
^2*t*v0+a*c*d^2*q^3*s*v2+a*c*d^2*q^3*t*v1+a*c*d^2*q^2*r*s*v1+a*c*d^2*q^2*r*t*v0
+2*a*c*d*e*p^3*t*v3+a*c*d*e*p^2*q*s*v3+3*a*c*d*e*p^2*q*t*v2+2*a*c*d*e*p^2*r*t*
v1+a*c*d*e*p^2*s^2*v1+a*c*d*e*p^2*s*t*v0+a*c*d*e*p*q^2*s*v2+a*c*d*e*p*q^2*t*v1+
a*c*d*e*p*q*r*s*v1+a*c*d*e*p*q*r*t*v0+a*d^3*p^3*t*v3+a*d^3*p^2*q*s*v3+2*a*d^3*p
^2*q*t*v2+a*d^3*p^2*r*t*v1+a*d^3*p*q^2*s*v2+a*d^3*p*q^2*t*v1+a*d^3*p*q*r*s*v1+a
*d^3*p*q*r*t*v0+a*d^2*e*p^3*s*v3+a*d^2*e*p^3*t*v2+a*d^2*e*p^2*q*s*v2+a*d^2*e*p^
2*q*t*v1+a*d^2*e*p^2*r*s*v1+a*d^2*e*p^2*r*t*v0+b^4*p*s*t^2*v1-b^4*q*s^2*t*v1+b^
4*r*s^3*v1+b^3*c*p*r*s^2*v3-b^3*c*p*r*s*t*v2+b^3*c*p*r*t^2*v1-b^3*c*p*s^2*t*v1-
b^3*c*p*s*t^2*v0+b^3*c*q*r*s^2*v2-2*b^3*c*q*r*s*t*v1+b^3*c*q*s^3*v1+b^3*c*q*s^2
*t*v0+3*b^3*c*r^2*s^2*v1+b^3*d*p^2*s*t*v3+b^3*d*p*q*t^2*v1+b^3*d*p*r*s^2*v2+2*b
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2*c^2*q*r^2*s*v2-b^2*c^2*q*r^2*t*v1+3*b^2*c^2*q*r*s^2*v1+2*b^2*c^2*q*r*s*t*v0+3
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-b^2*c*d*p*q*t^2*v0+b^2*c*d*p*r^2*s*v2+2*b^2*c*d*p*r^2*t*v1+4*b^2*c*d*p*r*s^2*
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b*c^2*d*p^2*s^2*v2-b*c^2*d*p^2*s*t*v1+2*b*c^2*d*p*q^2*s*v3-b*c^2*d*p*q^2*t*v2+2
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v1+b*c^2*d*p*q*s*t*v0+4*b*c^2*d*p*r^2*s*v1+2*b*c^2*d*q^3*s*v2+2*b*c^2*d*q^2*r^2
*v2+4*b*c^2*d*q^2*r*s*v1+2*b*c^2*d*q^2*r*t*v0+2*b*c^2*d*q*r^3*v1-b*c^2*e*p^3*t*
v3+b*c^2*e*p^2*q*s*v3-b*c^2*e*p^2*q*t*v2+b*c^2*e*p^2*r^2*v3-b*c^2*e*p^2*r*s*v2-\
2*b*c^2*e*p^2*r*t*v1+b*c^2*e*p*q^2*s*v2+b*c^2*e*p*q*r^2*v2+2*b*c^2*e*p*q*r*s*v1
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3*v1+2*c^3*d*q^3*r*v2+2*c^3*d*q^2*r^2*v1+c^3*e*p^3*t*v2+c^3*e*p^2*q*r*v3-c^3*e*
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+c^2*d^2*p*q^3*v3+3*c^2*d^2*p*q^2*r*v2+c^2*d^2*p*q^2*s*v1+c^2*d^2*p*q^2*t*v0+3*
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3*p^3*r*v3+2*c*d^3*p^2*q^2*v3+c*d^3*p^2*q*r*v2+c*d^3*p^2*q*s*v1+c*d^3*p^2*q*t*
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a^3*b*t^3*v4-a^3*c*s*t^2*v4-a^3*c*t^3*v3-a^3*d*s*t^2*v3-a^3*d*t^3*v2-a^3*e*s*t^
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s*t^2*v2+a^2*c^2*t^3*v1-2*a^2*c*d*p*t^2*v4-2*a^2*c*d*q*s*t*v4-2*a^2*c*d*q*t^2*
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*v2-3*a^2*c*e*r*t^2*v1-2*a^2*c*e*s^2*t*v1-2*a^2*c*e*s*t^2*v0-a^2*d^2*p*s*t*v4-2
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*p*r*v4+4*b*d*e^2*p*s*v3+2*b*d*e^2*q*s*v2-2*b*d*e^2*q*t*v1+4*b*d*e^2*r*s*v1+b*e
^3*p*r*v3+b*e^3*p*s*v2+b*e^3*p*t*v1+b*e^3*q*r*v2+b*e^3*q*s*v1+b*e^3*q*t*v0+b*e^
3*r^2*v1-c^4*r*t*v4+c^4*t^2*v2-c^3*d*q*t*v4+c^3*d*r*t*v3-c^3*d*s*t*v2-c^3*d*t^2
*v1-c^3*e*p*t*v4+c^3*e*q*s*v4-c^3*e*q*t*v3+c^3*e*r^2*v4-c^3*e*r*s*v3-c^3*e*r*t*
v2+c^3*e*s^2*v2-c^3*e*t^2*v0-c^2*d^2*q*s*v4+2*c^2*d^2*q*t*v3+c^2*d^2*s*t*v1+c^2
*d^2*t^2*v0+c^2*d*e*p*s*v4+5*c^2*d*e*q*r*v4-3*c^2*d*e*q*s*v3-5*c^2*d*e*q*t*v2-2
*c^2*d*e*r*t*v1-c^2*d*e*s^2*v1-c^2*d*e*s*t*v0+c^2*e^2*p*r*v4-2*c^2*e^2*p*t*v2+c
^2*e^2*q^2*v4+3*c^2*e^2*q*s*v2+c^2*e^2*q*t*v1+2*c^2*e^2*r*s*v1-c*d^3*p*s*v4+c*d
^3*p*t*v3-c*d^3*q*r*v4+c*d^3*q*s*v3+2*c*d^3*q*t*v2+c*d^3*r*t*v1+4*c*d^2*e*p*r*
v4-3*c*d^2*e*p*s*v3+c*d^2*e*p*t*v2+2*c*d^2*e*q^2*v4-3*c*d^2*e*q*s*v2+c*d^2*e*q*
t*v1-c*d^2*e*r*s*v1+3*c*d^2*e*r*t*v0+4*c*d*e^2*p*q*v4+3*c*d*e^2*p*r*v3+3*c*d*e^
2*q*r*v2+c*d*e^2*q*s*v1+c*d*e^2*q*t*v0+3*c*d*e^2*r^2*v1+2*c*e^3*p*q*v3+c*e^3*p*
s*v1+c*e^3*p*t*v0+2*c*e^3*q^2*v2+2*c*e^3*q*r*v1-d^4*p*r*v4+d^4*p*s*v3-d^4*q*t*
v1-d^4*r*t*v0+2*d^3*e*p*q*v4-d^3*e*p*r*v3-d^3*e*p*s*v2-d^3*e*p*t*v1-d^3*e*q*r*
v2+d^3*e*q*s*v1+d^3*e*q*t*v0-d^3*e*r^2*v1+3*d^2*e^2*p^2*v4+d^2*e^2*p*q*v3+2*d^2
*e^2*p*s*v1+2*d^2*e^2*p*t*v0+d^2*e^2*q^2*v2+d^2*e^2*q*r*v1+3*d*e^3*p^2*v3+3*d*e
^3*p*q*v2+3*d*e^3*p*r*v1-3*a*d*e^2*t*v4-a*e^3*s*v4-a*e^3*t*v3-3*b*c*e^2*t*v4+2*
b*d^2*e*t*v4-2*b*d*e^2*s*v4+2*b*d*e^2*t*v3-b*e^3*r*v4-b*e^3*s*v3-b*e^3*t*v2+2*c
^2*d*e*t*v4-c^2*e^2*s*v4+c^2*e^2*t*v3-c*d^3*t*v4+c*d^2*e*s*v4-3*c*d^2*e*t*v3-3*
c*d*e^2*r*v4+2*c*d*e^2*s*v3+2*c*d*e^2*t*v2-2*c*e^3*q*v4-c*e^3*s*v2-c*e^3*t*v1+d
^4*t*v3+d^3*e*r*v4-d^3*e*s*v3-d^3*e*t*v2-d^2*e^2*q*v4+d^2*e^2*s*v2+d^2*e^2*t*v1
-3*d*e^3*p*v4-d*e^3*s*v1-d*e^3*t*v0-e^4*p*v3-e^4*q*v2-e^4*r*v1+e^4*v4




beta[4,5] = t*(a^4*t^3*v1+3*a^3*b*s*t^2*v1-a^3*b*t^3*v0+a^3*c*p*t^2*v3+a^3*c*q*
t^2*v2+3*a^3*c*r*t^2*v1+a^3*d*p*t^2*v2+2*a^3*d*q*t^2*v1+a^3*e*p*t^2*v1-a^2*b^2*
p*t^2*v3-a^2*b^2*q*t^2*v2+3*a^2*b^2*s^2*t*v1-3*a^2*b^2*s*t^2*v0+2*a^2*b*c*p*s*t
*v3-2*a^2*b*c*p*t^2*v2+2*a^2*b*c*q*s*t*v2+a^2*b*c*q*t^2*v1+6*a^2*b*c*r*s*t*v1-3
*a^2*b*c*r*t^2*v0+2*a^2*b*d*p*s*t*v2+2*a^2*b*d*p*t^2*v1+4*a^2*b*d*q*s*t*v1-2*a^
2*b*d*q*t^2*v0+2*a^2*b*e*p*s*t*v1-a^2*b*e*p*t^2*v0+2*a^2*c^2*p*r*t*v3-a^2*c^2*p
*s*t*v2+a^2*c^2*p*t^2*v1+2*a^2*c^2*q*r*t*v2-a^2*c^2*q*t^2*v0+3*a^2*c^2*r^2*t*v1
+2*a^2*c*d*p*q*t*v3+a^2*c*d*p*r*t*v2+a^2*c*d*p*s*t*v1-2*a^2*c*d*p*t^2*v0+2*a^2*
c*d*q^2*t*v2+4*a^2*c*d*q*r*t*v1+a^2*c*e*p^2*t*v3+a^2*c*e*p*q*t*v2+2*a^2*c*e*p*r
*t*v1+a^2*d^2*p^2*t*v3+2*a^2*d^2*p*q*t*v2+a^2*d^2*p*r*t*v1+a^2*d^2*q^2*t*v1+a^2
*d*e*p^2*t*v2+a^2*d*e*p*q*t*v1-2*a*b^3*p*s*t*v3+a*b^3*p*t^2*v2-2*a*b^3*q*s*t*v2
+a*b^3*s^3*v1-3*a*b^3*s^2*t*v0-2*a*b^2*c*p*r*t*v3+a*b^2*c*p*s^2*v3-2*a*b^2*c*p*
s*t*v2-a*b^2*c*p*t^2*v1-2*a*b^2*c*q*r*t*v2+a*b^2*c*q*s^2*v2+2*a*b^2*c*q*s*t*v1+
3*a*b^2*c*r*s^2*v1-6*a*b^2*c*r*s*t*v0-2*a*b^2*d*p*q*t*v3+a*b^2*d*p*r*t*v2+a*b^2
*d*p*s^2*v2+3*a*b^2*d*p*s*t*v1-a*b^2*d*p*t^2*v0-2*a*b^2*d*q^2*t*v2+2*a*b^2*d*q*
s^2*v1-4*a*b^2*d*q*s*t*v0-a*b^2*e*p^2*t*v3-a*b^2*e*p*q*t*v2+a*b^2*e*p*s^2*v1-2*
a*b^2*e*p*s*t*v0+2*a*b*c^2*p*r*s*v3-3*a*b*c^2*p*r*t*v2-a*b*c^2*p*s^2*v2+a*b*c^2
*p*s*t*v1+a*b*c^2*p*t^2*v0+2*a*b*c^2*q*r*s*v2+2*a*b*c^2*q*r*t*v1-2*a*b*c^2*q*s*
t*v0+3*a*b*c^2*r^2*s*v1-3*a*b*c^2*r^2*t*v0-2*a*b*c*d*p^2*t*v3+2*a*b*c*d*p*q*s*
v3-3*a*b*c*d*p*q*t*v2+a*b*c*d*p*r*s*v2+2*a*b*c*d*p*r*t*v1+a*b*c*d*p*s^2*v1-5*a*
b*c*d*p*s*t*v0+2*a*b*c*d*q^2*s*v2+2*a*b*c*d*q^2*t*v1+4*a*b*c*d*q*r*s*v1-4*a*b*c
*d*q*r*t*v0+a*b*c*e*p^2*s*v3-2*a*b*c*e*p^2*t*v2+a*b*c*e*p*q*s*v2+a*b*c*e*p*q*t*
v1+2*a*b*c*e*p*r*s*v1-2*a*b*c*e*p*r*t*v0+a*b*d^2*p^2*s*v3+a*b*d^2*p^2*t*v2+2*a*
b*d^2*p*q*s*v2+3*a*b*d^2*p*q*t*v1+a*b*d^2*p*r*s*v1-a*b*d^2*p*r*t*v0+a*b*d^2*q^2
*s*v1-a*b*d^2*q^2*t*v0+a*b*d*e*p^2*s*v2+2*a*b*d*e*p^2*t*v1+a*b*d*e*p*q*s*v1-a*b
*d*e*p*q*t*v0+a*c^3*p^2*t*v3+a*c^3*p*r^2*v3-a*c^3*p*r*s*v2+2*a*c^3*p*r*t*v1+a*c
^3*p*s*t*v0+a*c^3*q*r^2*v2-2*a*c^3*q*r*t*v0+a*c^3*r^3*v1-a*c^2*d*p^2*t*v2+2*a*c
^2*d*p*q*r*v3-a*c^2*d*p*q*s*v2+2*a*c^2*d*p*q*t*v1+a*c^2*d*p*r*s*v1-3*a*c^2*d*p*
r*t*v0+2*a*c^2*d*q^2*r*v2-2*a*c^2*d*q^2*t*v0+2*a*c^2*d*q*r^2*v1+a*c^2*e*p^2*r*
v3-a*c^2*e*p^2*s*v2+a*c^2*e*p^2*t*v1+a*c^2*e*p*q*r*v2-a*c^2*e*p*q*t*v0+a*c^2*e*
p*r^2*v1+a*c*d^2*p^2*r*v3+a*c*d^2*p^2*t*v1+a*c*d^2*p*q^2*v3+a*c*d^2*p*q*r*v2+a*
c*d^2*p*q*s*v1-4*a*c*d^2*p*q*t*v0+a*c*d^2*p*r^2*v1+a*c*d^2*q^3*v2+a*c*d^2*q^2*r
*v1+a*c*d*e*p^2*q*v3+a*c*d*e*p^2*s*v1-2*a*c*d*e*p^2*t*v0+a*c*d*e*p*q^2*v2+a*c*d
*e*p*q*r*v1+a*d^3*p^2*q*v3-a*d^3*p^2*t*v0+a*d^3*p*q^2*v2+a*d^3*p*q*r*v1+a*d^2*e
*p^3*v3+a*d^2*e*p^2*q*v2+a*d^2*e*p^2*r*v1-b^4*p*s^2*v3+b^4*p*s*t*v2-b^4*q*s^2*
v2-b^4*s^3*v0-2*b^3*c*p*r*s*v3+b^3*c*p*r*t*v2-b^3*c*p*s*t*v1-2*b^3*c*q*r*s*v2+b
^3*c*q*s^2*v1-3*b^3*c*r*s^2*v0-2*b^3*d*p*q*s*v3+b^3*d*p*q*t*v2+b^3*d*p*r*s*v2+b
^3*d*p*s^2*v1-b^3*d*p*s*t*v0-2*b^3*d*q^2*s*v2-2*b^3*d*q*s^2*v0-b^3*e*p^2*s*v3+b
^3*e*p^2*t*v2-b^3*e*p*q*s*v2-b^3*e*p*s^2*v0-b^2*c^2*p*r^2*v3-b^2*c^2*p*r*s*v2-b
^2*c^2*p*r*t*v1+b^2*c^2*p*s*t*v0-b^2*c^2*q*r^2*v2+2*b^2*c^2*q*r*s*v1-b^2*c^2*q*
s^2*v0-3*b^2*c^2*r^2*s*v0-2*b^2*c*d*p^2*s*v3-2*b^2*c*d*p*q*r*v3-b^2*c*d*p*q*s*
v2-b^2*c*d*p*q*t*v1+b^2*c*d*p*r^2*v2+b^2*c*d*p*r*s*v1-b^2*c*d*p*r*t*v0-3*b^2*c*
d*p*s^2*v0-2*b^2*c*d*q^2*r*v2+2*b^2*c*d*q^2*s*v1-4*b^2*c*d*q*r*s*v0-b^2*c*e*p^2
*r*v3-b^2*c*e*p^2*t*v1-b^2*c*e*p*q*r*v2+b^2*c*e*p*q*s*v1-2*b^2*c*e*p*r*s*v0+b^2
*d^2*p^2*s*v2-b^2*d^2*p*q^2*v3+b^2*d^2*p*q*r*v2+2*b^2*d^2*p*q*s*v1-b^2*d^2*p*q*
t*v0-b^2*d^2*p*r*s*v0-b^2*d^2*q^3*v2-b^2*d^2*q^2*s*v0-b^2*d*e*p^2*q*v3+b^2*d*e*
p^2*r*v2+b^2*d*e*p^2*s*v1-b^2*d*e*p^2*t*v0-b^2*d*e*p*q^2*v2-b^2*d*e*p*q*s*v0+b*
c^3*p^2*s*v3-b*c^3*p*r^2*v2+b*c^3*p*r*s*v1+b*c^3*p*r*t*v0+b*c^3*p*s^2*v0+b*c^3*
q*r^2*v1-2*b*c^3*q*r*s*v0-b*c^3*r^3*v0-2*b*c^2*d*p^2*r*v3-b*c^2*d*p^2*s*v2-2*b*
c^2*d*p*q*r*v2+b*c^2*d*p*q*s*v1+b*c^2*d*p*q*t*v0-4*b*c^2*d*p*r*s*v0+2*b*c^2*d*q
^2*r*v1-2*b*c^2*d*q^2*s*v0-2*b*c^2*d*q*r^2*v0-b*c^2*e*p^2*r*v2+b*c^2*e*p^2*t*v0
+b*c^2*e*p*q*r*v1-b*c^2*e*p*q*s*v0-b*c^2*e*p*r^2*v0-2*b*c*d^2*p^2*q*v3+b*c*d^2*
p^2*r*v2+b*c*d^2*p^2*s*v1-b*c*d^2*p*q^2*v2+b*c*d^2*p*q*r*v1-5*b*c*d^2*p*q*s*v0-
b*c*d^2*p*r^2*v0+b*c*d^2*q^3*v1-b*c*d^2*q^2*r*v0-2*b*c*d*e*p^3*v3-b*c*d*e*p^2*q
*v2-3*b*c*d*e*p^2*s*v0+b*c*d*e*p*q^2*v1-b*c*d*e*p*q*r*v0+b*d^3*p^2*q*v2-b*d^3*p
^2*s*v0+b*d^3*p*q^2*v1-b*d^3*p*q*r*v0+b*d^2*e*p^3*v2+b*d^2*e*p^2*q*v1-b*d^2*e*p
^2*r*v0+c^4*p^2*r*v3+c^4*p*r^2*v1+c^4*p*r*s*v0-c^4*q*r^2*v0+c^3*d*p^2*q*v3-c^3*
d*p^2*r*v2+2*c^3*d*p*q*r*v1+c^3*d*p*q*s*v0-c^3*d*p*r^2*v0-2*c^3*d*q^2*r*v0+c^3*
e*p^3*v3+c^3*e*p^2*r*v1+c^3*e*p^2*s*v0-c^3*e*p*q*r*v0-c^2*d^2*p^2*q*v2+c^2*d^2*
p^2*r*v1+c^2*d^2*p*q^2*v1-3*c^2*d^2*p*q*r*v0-c^2*d^2*q^3*v0-c^2*d*e*p^3*v2+c^2*
d*e*p^2*q*v1-c^2*d*e*p^2*r*v0-c^2*d*e*p*q^2*v0+c*d^3*p^2*q*v1-c*d^3*p^2*r*v0-2*
c*d^3*p*q^2*v0+c*d^2*e*p^3*v1-2*c*d^2*e*p^2*q*v0-d^4*p^2*q*v0-d^3*e*p^3*v0-a^3*
c*t^2*v4-a^3*d*t^2*v3-a^3*e*t^2*v2+a^2*b^2*t^2*v4-2*a^2*b*c*s*t*v4+2*a^2*b*c*t^
2*v3-2*a^2*b*d*s*t*v3+2*a^2*b*d*t^2*v2-2*a^2*b*e*s*t*v2-3*a^2*b*e*t^2*v1-2*a^2*
c^2*r*t*v4+a^2*c^2*s*t*v3+a^2*c^2*t^2*v2-2*a^2*c*d*q*t*v4-a^2*c*d*r*t*v3+2*a^2*
c*d*s*t*v2-3*a^2*c*d*t^2*v1-a^2*c*e*p*t*v4-a^2*c*e*r*t*v2-2*a^2*c*e*s*t*v1+2*a^
2*c*e*t^2*v0-a^2*d^2*p*t*v4-a^2*d^2*q*t*v3+a^2*d^2*r*t*v2-a^2*d^2*s*t*v1+a^2*d^
2*t^2*v0-3*a^2*d*e*p*t*v3-2*a^2*d*e*q*t*v2-3*a^2*d*e*r*t*v1-a^2*e^2*p*t*v2-a^2*
e^2*q*t*v1+2*a*b^3*s*t*v4-a*b^3*t^2*v3+2*a*b^2*c*r*t*v4-a*b^2*c*s^2*v4+2*a*b^2*
c*s*t*v3-3*a*b^2*c*t^2*v2+2*a*b^2*d*q*t*v4-a*b^2*d*r*t*v3-a*b^2*d*s^2*v3+2*a*b^
2*d*s*t*v2+2*a*b^2*d*t^2*v1+a*b^2*e*p*t*v4-a*b^2*e*r*t*v2-a*b^2*e*s^2*v2-4*a*b^
2*e*s*t*v1+2*a*b^2*e*t^2*v0-2*a*b*c^2*r*s*v4+3*a*b*c^2*r*t*v3+a*b*c^2*s^2*v3-2*
a*b*c^2*s*t*v2+2*a*b*c^2*t^2*v1+2*a*b*c*d*p*t*v4-2*a*b*c*d*q*s*v4+a*b*c*d*q*t*
v3-a*b*c*d*r*s*v3+2*a*b*c*d*s^2*v2-a*b*c*d*s*t*v1-a*b*c*d*t^2*v0-a*b*c*e*p*s*v4
+3*a*b*c*e*p*t*v3-2*a*b*c*e*q*t*v2-a*b*c*e*r*s*v2-3*a*b*c*e*r*t*v1-2*a*b*c*e*s^
2*v1+6*a*b*c*e*s*t*v0-a*b*d^2*p*s*v4+2*a*b*d^2*p*t*v3-a*b*d^2*q*s*v3+4*a*b*d^2*
q*t*v2+a*b*d^2*r*s*v2+3*a*b*d^2*r*t*v1-a*b*d^2*s^2*v1+3*a*b*d^2*s*t*v0-3*a*b*d*
e*p*s*v3-a*b*d*e*p*t*v2-2*a*b*d*e*q*s*v2-2*a*b*d*e*q*t*v1-3*a*b*d*e*r*s*v1+3*a*
b*d*e*r*t*v0-a*b*e^2*p*s*v2-2*a*b*e^2*p*t*v1-a*b*e^2*q*s*v1+a*b*e^2*q*t*v0-a*c^
3*p*t*v4+a*c^3*q*t*v3-a*c^3*r^2*v4+a*c^3*r*s*v3+a*c^3*r*t*v2-a*c^3*s^2*v2+a*c^3
*s*t*v1-a*c^3*t^2*v0-a*c^2*d*p*t*v3-2*a*c^2*d*q*r*v4+a*c^2*d*q*s*v3-4*a*c^2*d*r
*t*v1+a*c^2*d*s^2*v1-3*a*c^2*d*s*t*v0-a*c^2*e*p*r*v4+2*a*c^2*e*p*t*v2-2*a*c^2*e
*q*s*v2-2*a*c^2*e*r*s*v1+3*a*c^2*e*r*t*v0-a*c*d^2*p*r*v4+a*c*d^2*p*s*v3+a*c*d^2
*p*t*v2-a*c*d^2*q^2*v4+2*a*c*d^2*q*s*v2-4*a*c*d^2*q*t*v1+a*c*d^2*r*s*v1-a*c*d*e
*p*q*v4-3*a*c*d*e*p*r*v3+a*c*d*e*p*s*v2-5*a*c*d*e*p*t*v1-3*a*c*d*e*q*r*v2+4*a*c
*d*e*q*t*v0-3*a*c*d*e*r^2*v1-a*c*e^2*p*q*v3-a*c*e^2*p*s*v1+2*a*c*e^2*p*t*v0-a*c
*e^2*q^2*v2-a*c*e^2*q*r*v1-a*d^3*p*q*v4+a*d^3*p*r*v3-a*d^3*p*t*v1+a*d^3*q*r*v2-
a*d^3*q*s*v1+a*d^3*q*t*v0+a*d^3*r^2*v1-a*d^2*e*p^2*v4-a*d^2*e*p*q*v3-a*d^2*e*p*
s*v1+4*a*d^2*e*p*t*v0-a*d^2*e*q^2*v2-a*d^2*e*q*r*v1-2*a*d*e^2*p^2*v3-2*a*d*e^2*
p*q*v2-2*a*d*e^2*p*r*v1+b^4*s^2*v4-b^4*s*t*v3+b^4*t^2*v2+2*b^3*c*r*s*v4-b^3*c*r
*t*v3-b^3*c*t^2*v1+2*b^3*d*q*s*v4-b^3*d*q*t*v3-b^3*d*r*s*v3+2*b^3*d*r*t*v2+b^3*
d*s*t*v1-b^3*d*t^2*v0+b^3*e*p*s*v4+2*b^3*e*q*t*v2-b^3*e*r*s*v2-b^3*e*s^2*v1+2*b
^3*e*s*t*v0+b^2*c^2*r^2*v4+b^2*c^2*r*s*v3-2*b^2*c^2*r*t*v2+b^2*c^2*t^2*v0+2*b^2
*c*d*p*s*v4-2*b^2*c*d*p*t*v3+2*b^2*c*d*q*r*v4-b^2*c*d*q*s*v3-2*b^2*c*d*q*t*v2-b
^2*c*d*r^2*v3+2*b^2*c*d*r*s*v2-b^2*c*d*r*t*v1-3*b^2*c*d*s*t*v0+b^2*c*e*p*r*v4+3
*b^2*c*e*p*s*v3-b^2*c*e*p*t*v2+2*b^2*c*e*q*s*v2-2*b^2*c*e*q*t*v1-b^2*c*e*r^2*v2
-b^2*c*e*r*s*v1+2*b^2*c*e*r*t*v0+4*b^2*c*e*s^2*v0+b^2*d^2*p*s*v3+b^2*d^2*p*t*v2
+b^2*d^2*q^2*v4-b^2*d^2*q*r*v3+2*b^2*d^2*q*s*v2+b^2*d^2*q*t*v1+b^2*d^2*r^2*v2+b
^2*d^2*r*s*v1-2*b^2*d^2*r*t*v0+2*b^2*d^2*s^2*v0+b^2*d*e*p*q*v4-2*b^2*d*e*p*s*v2
+b^2*d*e*q*r*v2-2*b^2*d*e*q*s*v1+3*b^2*d*e*r*s*v0+b^2*e^2*p*q*v3-b^2*e^2*p*r*v2
-b^2*e^2*p*s*v1+b^2*e^2*p*t*v0+b^2*e^2*q^2*v2+b^2*e^2*q*s*v0-b*c^3*p*s*v4+b*c^3
*p*t*v3+b*c^3*q*s*v3+b*c^3*r^2*v3-b*c^3*r*s*v2+2*b*c^3*r*t*v1+b*c^3*s*t*v0+2*b*
c^2*d*p*r*v4-3*b*c^2*d*p*s*v3-b*c^2*d*p*t*v2-2*b*c^2*d*q*s*v2+2*b*c^2*d*q*t*v1-\
3*b*c^2*d*r*s*v1+b*c^2*d*r*t*v0-4*b*c^2*d*s^2*v0+3*b*c^2*e*p*r*v3+b*c^2*e*p*s*
v2+b*c^2*e*p*t*v1-2*b*c^2*e*q*s*v1+2*b*c^2*e*q*t*v0+5*b*c^2*e*r*s*v0+2*b*c*d^2*
p*q*v4-b*c*d^2*p*r*v3+2*b*c*d^2*p*s*v2+b*c*d^2*p*t*v1-b*c*d^2*q^2*v3+2*b*c*d^2*
q*r*v2-b*c*d^2*q*s*v1-b*c*d^2*q*t*v0-b*c*d^2*r*s*v0+2*b*c*d*e*p^2*v4-b*c*d*e*p*
q*v3-b*c*d*e*p*r*v2-3*b*c*d*e*p*s*v1+b*c*d*e*p*t*v0-3*b*c*d*e*q*r*v1+4*b*c*d*e*
q*s*v0+3*b*c*d*e*r^2*v0+2*b*c*e^2*p^2*v3+b*c*e^2*p*q*v2+3*b*c*e^2*p*s*v0-b*c*e^
2*q^2*v1+b*c*e^2*q*r*v0+b*d^3*p*q*v3+b*d^3*p*r*v2-b*d^3*p*s*v1-b*d^3*p*t*v0+2*b
*d^3*q^2*v2+b*d^3*q*r*v1+2*b*d^3*q*s*v0-b*d^3*r^2*v0+b*d^2*e*p^2*v3+b*d^2*e*p*q
*v2+5*b*d^2*e*p*s*v0-b*d^2*e*q^2*v1+b*d^2*e*q*r*v0-2*b*d*e^2*p^2*v2-2*b*d*e^2*p
*q*v1+2*b*d*e^2*p*r*v0-c^4*p*r*v4+c^4*p*s*v3+c^4*q*r*v3+c^4*r*s*v1-c^4*r*t*v0+c
^4*s^2*v0-c^3*d*p*q*v4-c^3*d*p*s*v2+c^3*d*q^2*v3-c^3*d*q*r*v2+c^3*d*q*s*v1-c^3*
d*q*t*v0-c^3*d*r^2*v1-c^3*d*r*s*v0-c^3*e*p^2*v4+2*c^3*e*p*q*v3+c^3*e*p*r*v2-c^3
*e*p*t*v0+2*c^3*e*q*s*v0+c^3*e*r^2*v0-c^2*d^2*p*q*v3+c^2*d^2*p*s*v1-c^2*d^2*q^2
*v2-2*c^2*d^2*q*r*v1-3*c^2*d^2*q*s*v0-c^2*d*e*p^2*v3-c^2*d*e*p*q*v2-4*c^2*d*e*p
*r*v1-c^2*d*e*p*s*v0+5*c^2*d*e*q*r*v0+c^2*e^2*p^2*v2-c^2*e^2*p*q*v1+c^2*e^2*p*r
*v0+c^2*e^2*q^2*v0+c*d^3*p*q*v2-c*d^3*p*s*v0-c*d^3*q^2*v1-c*d^3*q*r*v0+c*d^2*e*
p^2*v2-2*c*d^2*e*p*q*v1+4*c*d^2*e*p*r*v0+2*c*d^2*e*q^2*v0-2*c*d*e^2*p^2*v1+4*c*
d*e^2*p*q*v0-d^4*p*q*v1-d^4*p*r*v0-d^3*e*p^2*v1+2*d^3*e*p*q*v0+3*d^2*e^2*p^2*v0
+2*a^2*d*e*t*v4+a^2*e^2*t*v3-a*b*c*e*t*v4-3*a*b*d^2*t*v4+2*a*b*d*e*s*v4-a*b*d*e
*t*v3+a*b*e^2*s*v3+2*a*b*e^2*t*v2+2*a*c^2*d*t*v4+a*c^2*e*s*v4-3*a*c^2*e*t*v3-a*
c*d^2*s*v4+2*a*c*d^2*t*v3+3*a*c*d*e*r*v4-2*a*c*d*e*s*v3-a*c*d*e*t*v2+a*c*e^2*q*
v4+a*c*e^2*s*v2+2*a*c*e^2*t*v1-a*d^3*r*v4+a*d^3*s*v3-a*d^3*t*v2+a*d^2*e*q*v4-a*
d^2*e*s*v2+2*a*d^2*e*t*v1+2*a*d*e^2*p*v4+a*d*e^2*s*v1-3*a*d*e^2*t*v0+a*e^3*p*v3
+a*e^3*q*v2+a*e^3*r*v1-b^3*e*t*v4+2*b^2*c*d*t*v4-3*b^2*c*e*s*v4+2*b^2*c*e*t*v3-\
2*b^2*d^2*s*v4+b^2*d^2*t*v3-b^2*d*e*r*v4+b^2*d*e*s*v3-3*b^2*d*e*t*v2-b^2*e^2*q*
v4+b^2*e^2*r*v3+b^2*e^2*s*v2+b^2*e^2*t*v1-b*c^3*t*v4+4*b*c^2*d*s*v4-3*b*c^2*d*t
*v3-2*b*c^2*e*r*v4-b*c^2*e*s*v3+2*b*c^2*e*t*v2+2*b*c*d^2*t*v2-b*c*d*e*r*v3-2*b*
c*d*e*s*v2-b*c*d*e*t*v1-2*b*c*e^2*p*v4+b*c*e^2*q*v3+2*b*c*e^2*r*v2+2*b*c*e^2*s*
v1-3*b*c*e^2*t*v0-2*b*d^3*q*v4+b*d^3*r*v3-b*d^3*t*v1-2*b*d^2*e*p*v4+b*d^2*e*q*
v3-2*b*d^2*e*r*v2+b*d^2*e*s*v1+2*b*d^2*e*t*v0-2*b*d*e^2*q*v2-4*b*d*e^2*s*v0+b*e
^3*p*v2+b*e^3*q*v1-b*e^3*r*v0-c^4*s*v4+c^4*t*v3+c^3*d*r*v4-c^3*d*t*v2-c^3*e*q*
v4-c^3*e*r*v3+c^3*e*s*v2-c^3*e*t*v1+2*c^2*d^2*q*v4+c^2*d^2*t*v1+2*c^2*d*e*p*v4-\
3*c^2*d*e*q*v3-c^2*d*e*s*v1+2*c^2*d*e*t*v0-2*c^2*e^2*p*v3+c^2*e^2*q*v2-2*c^2*e^
2*s*v0+c*d^3*q*v3-c*d^3*t*v0+c*d^2*e*p*v3+c*d^2*e*q*v2+3*c*d^2*e*r*v1+4*c*d^2*e
*s*v0+c*d*e^2*q*v1-3*c*d*e^2*r*v0+c*e^3*p*v1-2*c*e^3*q*v0-d^4*q*v2-d^4*r*v1-d^4
*s*v0-d^3*e*p*v2+d^3*e*q*v1+d^3*e*r*v0+2*d^2*e^2*p*v1-d^2*e^2*q*v0-3*d*e^3*p*v0
-a*e^3*v4+2*b*d*e^2*v4-b*e^3*v3+c^2*e^2*v4-3*c*d^2*e*v4+2*c*d*e^2*v3-c*e^3*v2+d
^4*v4-d^3*e*v3+d^2*e^2*v2-d*e^3*v1+e^4*v0)




beta[5,1] = a^4*t^3*v1+3*a^3*b*s*t^2*v1-a^3*b*t^3*v0+a^3*c*p*t^2*v3+a^3*c*q*t^2
*v2+3*a^3*c*r*t^2*v1+a^3*d*p*t^2*v2+2*a^3*d*q*t^2*v1+a^3*e*p*t^2*v1-a^2*b^2*p*t
^2*v3-a^2*b^2*q*t^2*v2+3*a^2*b^2*s^2*t*v1-3*a^2*b^2*s*t^2*v0+2*a^2*b*c*p*s*t*v3
-2*a^2*b*c*p*t^2*v2+2*a^2*b*c*q*s*t*v2+a^2*b*c*q*t^2*v1+6*a^2*b*c*r*s*t*v1-3*a^
2*b*c*r*t^2*v0+2*a^2*b*d*p*s*t*v2+2*a^2*b*d*p*t^2*v1+4*a^2*b*d*q*s*t*v1-2*a^2*b
*d*q*t^2*v0+2*a^2*b*e*p*s*t*v1-a^2*b*e*p*t^2*v0+2*a^2*c^2*p*r*t*v3-a^2*c^2*p*s*
t*v2+a^2*c^2*p*t^2*v1+2*a^2*c^2*q*r*t*v2-a^2*c^2*q*t^2*v0+3*a^2*c^2*r^2*t*v1+2*
a^2*c*d*p*q*t*v3+a^2*c*d*p*r*t*v2+a^2*c*d*p*s*t*v1-2*a^2*c*d*p*t^2*v0+2*a^2*c*d
*q^2*t*v2+4*a^2*c*d*q*r*t*v1+a^2*c*e*p^2*t*v3+a^2*c*e*p*q*t*v2+2*a^2*c*e*p*r*t*
v1+a^2*d^2*p^2*t*v3+2*a^2*d^2*p*q*t*v2+a^2*d^2*p*r*t*v1+a^2*d^2*q^2*t*v1+a^2*d*
e*p^2*t*v2+a^2*d*e*p*q*t*v1-2*a*b^3*p*s*t*v3+a*b^3*p*t^2*v2-2*a*b^3*q*s*t*v2+a*
b^3*s^3*v1-3*a*b^3*s^2*t*v0-2*a*b^2*c*p*r*t*v3+a*b^2*c*p*s^2*v3-2*a*b^2*c*p*s*t
*v2-a*b^2*c*p*t^2*v1-2*a*b^2*c*q*r*t*v2+a*b^2*c*q*s^2*v2+2*a*b^2*c*q*s*t*v1+3*a
*b^2*c*r*s^2*v1-6*a*b^2*c*r*s*t*v0-2*a*b^2*d*p*q*t*v3+a*b^2*d*p*r*t*v2+a*b^2*d*
p*s^2*v2+3*a*b^2*d*p*s*t*v1-a*b^2*d*p*t^2*v0-2*a*b^2*d*q^2*t*v2+2*a*b^2*d*q*s^2
*v1-4*a*b^2*d*q*s*t*v0-a*b^2*e*p^2*t*v3-a*b^2*e*p*q*t*v2+a*b^2*e*p*s^2*v1-2*a*b
^2*e*p*s*t*v0+2*a*b*c^2*p*r*s*v3-3*a*b*c^2*p*r*t*v2-a*b*c^2*p*s^2*v2+a*b*c^2*p*
s*t*v1+a*b*c^2*p*t^2*v0+2*a*b*c^2*q*r*s*v2+2*a*b*c^2*q*r*t*v1-2*a*b*c^2*q*s*t*
v0+3*a*b*c^2*r^2*s*v1-3*a*b*c^2*r^2*t*v0-2*a*b*c*d*p^2*t*v3+2*a*b*c*d*p*q*s*v3-\
3*a*b*c*d*p*q*t*v2+a*b*c*d*p*r*s*v2+2*a*b*c*d*p*r*t*v1+a*b*c*d*p*s^2*v1-5*a*b*c
*d*p*s*t*v0+2*a*b*c*d*q^2*s*v2+2*a*b*c*d*q^2*t*v1+4*a*b*c*d*q*r*s*v1-4*a*b*c*d*
q*r*t*v0+a*b*c*e*p^2*s*v3-2*a*b*c*e*p^2*t*v2+a*b*c*e*p*q*s*v2+a*b*c*e*p*q*t*v1+
2*a*b*c*e*p*r*s*v1-2*a*b*c*e*p*r*t*v0+a*b*d^2*p^2*s*v3+a*b*d^2*p^2*t*v2+2*a*b*d
^2*p*q*s*v2+3*a*b*d^2*p*q*t*v1+a*b*d^2*p*r*s*v1-a*b*d^2*p*r*t*v0+a*b*d^2*q^2*s*
v1-a*b*d^2*q^2*t*v0+a*b*d*e*p^2*s*v2+2*a*b*d*e*p^2*t*v1+a*b*d*e*p*q*s*v1-a*b*d*
e*p*q*t*v0+a*c^3*p^2*t*v3+a*c^3*p*r^2*v3-a*c^3*p*r*s*v2+2*a*c^3*p*r*t*v1+a*c^3*
p*s*t*v0+a*c^3*q*r^2*v2-2*a*c^3*q*r*t*v0+a*c^3*r^3*v1-a*c^2*d*p^2*t*v2+2*a*c^2*
d*p*q*r*v3-a*c^2*d*p*q*s*v2+2*a*c^2*d*p*q*t*v1+a*c^2*d*p*r*s*v1-3*a*c^2*d*p*r*t
*v0+2*a*c^2*d*q^2*r*v2-2*a*c^2*d*q^2*t*v0+2*a*c^2*d*q*r^2*v1+a*c^2*e*p^2*r*v3-a
*c^2*e*p^2*s*v2+a*c^2*e*p^2*t*v1+a*c^2*e*p*q*r*v2-a*c^2*e*p*q*t*v0+a*c^2*e*p*r^
2*v1+a*c*d^2*p^2*r*v3+a*c*d^2*p^2*t*v1+a*c*d^2*p*q^2*v3+a*c*d^2*p*q*r*v2+a*c*d^
2*p*q*s*v1-4*a*c*d^2*p*q*t*v0+a*c*d^2*p*r^2*v1+a*c*d^2*q^3*v2+a*c*d^2*q^2*r*v1+
a*c*d*e*p^2*q*v3+a*c*d*e*p^2*s*v1-2*a*c*d*e*p^2*t*v0+a*c*d*e*p*q^2*v2+a*c*d*e*p
*q*r*v1+a*d^3*p^2*q*v3-a*d^3*p^2*t*v0+a*d^3*p*q^2*v2+a*d^3*p*q*r*v1+a*d^2*e*p^3
*v3+a*d^2*e*p^2*q*v2+a*d^2*e*p^2*r*v1-b^4*p*s^2*v3+b^4*p*s*t*v2-b^4*q*s^2*v2-b^
4*s^3*v0-2*b^3*c*p*r*s*v3+b^3*c*p*r*t*v2-b^3*c*p*s*t*v1-2*b^3*c*q*r*s*v2+b^3*c*
q*s^2*v1-3*b^3*c*r*s^2*v0-2*b^3*d*p*q*s*v3+b^3*d*p*q*t*v2+b^3*d*p*r*s*v2+b^3*d*
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3*e*r*v3+c^3*e*s*v2-c^3*e*t*v1+2*c^2*d^2*q*v4+c^2*d^2*t*v1+2*c^2*d*e*p*v4-3*c^2
*d*e*q*v3-c^2*d*e*s*v1+2*c^2*d*e*t*v0-2*c^2*e^2*p*v3+c^2*e^2*q*v2-2*c^2*e^2*s*
v0+c*d^3*q*v3-c*d^3*t*v0+c*d^2*e*p*v3+c*d^2*e*q*v2+3*c*d^2*e*r*v1+4*c*d^2*e*s*
v0+c*d*e^2*q*v1-3*c*d*e^2*r*v0+c*e^3*p*v1-2*c*e^3*q*v0-d^4*q*v2-d^4*r*v1-d^4*s*
v0-d^3*e*p*v2+d^3*e*q*v1+d^3*e*r*v0+2*d^2*e^2*p*v1-d^2*e^2*q*v0-3*d*e^3*p*v0-a*
e^3*v4+2*b*d*e^2*v4-b*e^3*v3+c^2*e^2*v4-3*c*d^2*e*v4+2*c*d*e^2*v3-c*e^3*v2+d^4*
v4-d^3*e*v3+d^2*e^2*v2-d*e^3*v1+e^4*v0




beta[5,2] = -a^4*p*t^3*v1-3*a^3*b*p*s*t^2*v1+a^3*b*p*t^3*v0-a^3*c*p^2*t^2*v3-a^
3*c*p*q*t^2*v2-3*a^3*c*p*r*t^2*v1-a^3*d*p^2*t^2*v2-2*a^3*d*p*q*t^2*v1-a^3*e*p^2
*t^2*v1+a^2*b^2*p^2*t^2*v3+a^2*b^2*p*q*t^2*v2-3*a^2*b^2*p*s^2*t*v1+3*a^2*b^2*p*
s*t^2*v0-2*a^2*b*c*p^2*s*t*v3+2*a^2*b*c*p^2*t^2*v2-2*a^2*b*c*p*q*s*t*v2-a^2*b*c
*p*q*t^2*v1-6*a^2*b*c*p*r*s*t*v1+3*a^2*b*c*p*r*t^2*v0-2*a^2*b*d*p^2*s*t*v2-2*a^
2*b*d*p^2*t^2*v1-4*a^2*b*d*p*q*s*t*v1+2*a^2*b*d*p*q*t^2*v0-2*a^2*b*e*p^2*s*t*v1
+a^2*b*e*p^2*t^2*v0-2*a^2*c^2*p^2*r*t*v3+a^2*c^2*p^2*s*t*v2-a^2*c^2*p^2*t^2*v1-\
2*a^2*c^2*p*q*r*t*v2+a^2*c^2*p*q*t^2*v0-3*a^2*c^2*p*r^2*t*v1-2*a^2*c*d*p^2*q*t*
v3-a^2*c*d*p^2*r*t*v2-a^2*c*d*p^2*s*t*v1+2*a^2*c*d*p^2*t^2*v0-2*a^2*c*d*p*q^2*t
*v2-4*a^2*c*d*p*q*r*t*v1-a^2*c*e*p^3*t*v3-a^2*c*e*p^2*q*t*v2-2*a^2*c*e*p^2*r*t*
v1-a^2*d^2*p^3*t*v3-2*a^2*d^2*p^2*q*t*v2-a^2*d^2*p^2*r*t*v1-a^2*d^2*p*q^2*t*v1-
a^2*d*e*p^3*t*v2-a^2*d*e*p^2*q*t*v1+2*a*b^3*p^2*s*t*v3-a*b^3*p^2*t^2*v2+2*a*b^3
*p*q*s*t*v2-a*b^3*p*s^3*v1+3*a*b^3*p*s^2*t*v0+2*a*b^2*c*p^2*r*t*v3-a*b^2*c*p^2*
s^2*v3+2*a*b^2*c*p^2*s*t*v2+a*b^2*c*p^2*t^2*v1+2*a*b^2*c*p*q*r*t*v2-a*b^2*c*p*q
*s^2*v2-2*a*b^2*c*p*q*s*t*v1-3*a*b^2*c*p*r*s^2*v1+6*a*b^2*c*p*r*s*t*v0+2*a*b^2*
d*p^2*q*t*v3-a*b^2*d*p^2*r*t*v2-a*b^2*d*p^2*s^2*v2-3*a*b^2*d*p^2*s*t*v1+a*b^2*d
*p^2*t^2*v0+2*a*b^2*d*p*q^2*t*v2-2*a*b^2*d*p*q*s^2*v1+4*a*b^2*d*p*q*s*t*v0+a*b^
2*e*p^3*t*v3+a*b^2*e*p^2*q*t*v2-a*b^2*e*p^2*s^2*v1+2*a*b^2*e*p^2*s*t*v0-2*a*b*c
^2*p^2*r*s*v3+3*a*b*c^2*p^2*r*t*v2+a*b*c^2*p^2*s^2*v2-a*b*c^2*p^2*s*t*v1-a*b*c^
2*p^2*t^2*v0-2*a*b*c^2*p*q*r*s*v2-2*a*b*c^2*p*q*r*t*v1+2*a*b*c^2*p*q*s*t*v0-3*a
*b*c^2*p*r^2*s*v1+3*a*b*c^2*p*r^2*t*v0+2*a*b*c*d*p^3*t*v3-2*a*b*c*d*p^2*q*s*v3+
3*a*b*c*d*p^2*q*t*v2-a*b*c*d*p^2*r*s*v2-2*a*b*c*d*p^2*r*t*v1-a*b*c*d*p^2*s^2*v1
+5*a*b*c*d*p^2*s*t*v0-2*a*b*c*d*p*q^2*s*v2-2*a*b*c*d*p*q^2*t*v1-4*a*b*c*d*p*q*r
*s*v1+4*a*b*c*d*p*q*r*t*v0-a*b*c*e*p^3*s*v3+2*a*b*c*e*p^3*t*v2-a*b*c*e*p^2*q*s*
v2-a*b*c*e*p^2*q*t*v1-2*a*b*c*e*p^2*r*s*v1+2*a*b*c*e*p^2*r*t*v0-a*b*d^2*p^3*s*
v3-a*b*d^2*p^3*t*v2-2*a*b*d^2*p^2*q*s*v2-3*a*b*d^2*p^2*q*t*v1-a*b*d^2*p^2*r*s*
v1+a*b*d^2*p^2*r*t*v0-a*b*d^2*p*q^2*s*v1+a*b*d^2*p*q^2*t*v0-a*b*d*e*p^3*s*v2-2*
a*b*d*e*p^3*t*v1-a*b*d*e*p^2*q*s*v1+a*b*d*e*p^2*q*t*v0-a*c^3*p^3*t*v3-a*c^3*p^2
*r^2*v3+a*c^3*p^2*r*s*v2-2*a*c^3*p^2*r*t*v1-a*c^3*p^2*s*t*v0-a*c^3*p*q*r^2*v2+2
*a*c^3*p*q*r*t*v0-a*c^3*p*r^3*v1+a*c^2*d*p^3*t*v2-2*a*c^2*d*p^2*q*r*v3+a*c^2*d*
p^2*q*s*v2-2*a*c^2*d*p^2*q*t*v1-a*c^2*d*p^2*r*s*v1+3*a*c^2*d*p^2*r*t*v0-2*a*c^2
*d*p*q^2*r*v2+2*a*c^2*d*p*q^2*t*v0-2*a*c^2*d*p*q*r^2*v1-a*c^2*e*p^3*r*v3+a*c^2*
e*p^3*s*v2-a*c^2*e*p^3*t*v1-a*c^2*e*p^2*q*r*v2+a*c^2*e*p^2*q*t*v0-a*c^2*e*p^2*r
^2*v1-a*c*d^2*p^3*r*v3-a*c*d^2*p^3*t*v1-a*c*d^2*p^2*q^2*v3-a*c*d^2*p^2*q*r*v2-a
*c*d^2*p^2*q*s*v1+4*a*c*d^2*p^2*q*t*v0-a*c*d^2*p^2*r^2*v1-a*c*d^2*p*q^3*v2-a*c*
d^2*p*q^2*r*v1-a*c*d*e*p^3*q*v3-a*c*d*e*p^3*s*v1+2*a*c*d*e*p^3*t*v0-a*c*d*e*p^2
*q^2*v2-a*c*d*e*p^2*q*r*v1-a*d^3*p^3*q*v3+a*d^3*p^3*t*v0-a*d^3*p^2*q^2*v2-a*d^3
*p^2*q*r*v1-a*d^2*e*p^4*v3-a*d^2*e*p^3*q*v2-a*d^2*e*p^3*r*v1+b^4*p^2*s^2*v3-b^4
*p^2*s*t*v2+b^4*p*q*s^2*v2+b^4*p*s^3*v0+2*b^3*c*p^2*r*s*v3-b^3*c*p^2*r*t*v2+b^3
*c*p^2*s*t*v1+2*b^3*c*p*q*r*s*v2-b^3*c*p*q*s^2*v1+3*b^3*c*p*r*s^2*v0+2*b^3*d*p^
2*q*s*v3-b^3*d*p^2*q*t*v2-b^3*d*p^2*r*s*v2-b^3*d*p^2*s^2*v1+b^3*d*p^2*s*t*v0+2*
b^3*d*p*q^2*s*v2+2*b^3*d*p*q*s^2*v0+b^3*e*p^3*s*v3-b^3*e*p^3*t*v2+b^3*e*p^2*q*s
*v2+b^3*e*p^2*s^2*v0+b^2*c^2*p^2*r^2*v3+b^2*c^2*p^2*r*s*v2+b^2*c^2*p^2*r*t*v1-b
^2*c^2*p^2*s*t*v0+b^2*c^2*p*q*r^2*v2-2*b^2*c^2*p*q*r*s*v1+b^2*c^2*p*q*s^2*v0+3*
b^2*c^2*p*r^2*s*v0+2*b^2*c*d*p^3*s*v3+2*b^2*c*d*p^2*q*r*v3+b^2*c*d*p^2*q*s*v2+b
^2*c*d*p^2*q*t*v1-b^2*c*d*p^2*r^2*v2-b^2*c*d*p^2*r*s*v1+b^2*c*d*p^2*r*t*v0+3*b^
2*c*d*p^2*s^2*v0+2*b^2*c*d*p*q^2*r*v2-2*b^2*c*d*p*q^2*s*v1+4*b^2*c*d*p*q*r*s*v0
+b^2*c*e*p^3*r*v3+b^2*c*e*p^3*t*v1+b^2*c*e*p^2*q*r*v2-b^2*c*e*p^2*q*s*v1+2*b^2*
c*e*p^2*r*s*v0-b^2*d^2*p^3*s*v2+b^2*d^2*p^2*q^2*v3-b^2*d^2*p^2*q*r*v2-2*b^2*d^2
*p^2*q*s*v1+b^2*d^2*p^2*q*t*v0+b^2*d^2*p^2*r*s*v0+b^2*d^2*p*q^3*v2+b^2*d^2*p*q^
2*s*v0+b^2*d*e*p^3*q*v3-b^2*d*e*p^3*r*v2-b^2*d*e*p^3*s*v1+b^2*d*e*p^3*t*v0+b^2*
d*e*p^2*q^2*v2+b^2*d*e*p^2*q*s*v0-b*c^3*p^3*s*v3+b*c^3*p^2*r^2*v2-b*c^3*p^2*r*s
*v1-b*c^3*p^2*r*t*v0-b*c^3*p^2*s^2*v0-b*c^3*p*q*r^2*v1+2*b*c^3*p*q*r*s*v0+b*c^3
*p*r^3*v0+2*b*c^2*d*p^3*r*v3+b*c^2*d*p^3*s*v2+2*b*c^2*d*p^2*q*r*v2-b*c^2*d*p^2*
q*s*v1-b*c^2*d*p^2*q*t*v0+4*b*c^2*d*p^2*r*s*v0-2*b*c^2*d*p*q^2*r*v1+2*b*c^2*d*p
*q^2*s*v0+2*b*c^2*d*p*q*r^2*v0+b*c^2*e*p^3*r*v2-b*c^2*e*p^3*t*v0-b*c^2*e*p^2*q*
r*v1+b*c^2*e*p^2*q*s*v0+b*c^2*e*p^2*r^2*v0+2*b*c*d^2*p^3*q*v3-b*c*d^2*p^3*r*v2-
b*c*d^2*p^3*s*v1+b*c*d^2*p^2*q^2*v2-b*c*d^2*p^2*q*r*v1+5*b*c*d^2*p^2*q*s*v0+b*c
*d^2*p^2*r^2*v0-b*c*d^2*p*q^3*v1+b*c*d^2*p*q^2*r*v0+2*b*c*d*e*p^4*v3+b*c*d*e*p^
3*q*v2+3*b*c*d*e*p^3*s*v0-b*c*d*e*p^2*q^2*v1+b*c*d*e*p^2*q*r*v0-b*d^3*p^3*q*v2+
b*d^3*p^3*s*v0-b*d^3*p^2*q^2*v1+b*d^3*p^2*q*r*v0-b*d^2*e*p^4*v2-b*d^2*e*p^3*q*
v1+b*d^2*e*p^3*r*v0-c^4*p^3*r*v3-c^4*p^2*r^2*v1-c^4*p^2*r*s*v0+c^4*p*q*r^2*v0-c
^3*d*p^3*q*v3+c^3*d*p^3*r*v2-2*c^3*d*p^2*q*r*v1-c^3*d*p^2*q*s*v0+c^3*d*p^2*r^2*
v0+2*c^3*d*p*q^2*r*v0-c^3*e*p^4*v3-c^3*e*p^3*r*v1-c^3*e*p^3*s*v0+c^3*e*p^2*q*r*
v0+c^2*d^2*p^3*q*v2-c^2*d^2*p^3*r*v1-c^2*d^2*p^2*q^2*v1+3*c^2*d^2*p^2*q*r*v0+c^
2*d^2*p*q^3*v0+c^2*d*e*p^4*v2-c^2*d*e*p^3*q*v1+c^2*d*e*p^3*r*v0+c^2*d*e*p^2*q^2
*v0-c*d^3*p^3*q*v1+c*d^3*p^3*r*v0+2*c*d^3*p^2*q^2*v0-c*d^2*e*p^4*v1+2*c*d^2*e*p
^3*q*v0+d^4*p^3*q*v0+d^3*e*p^4*v0+a^4*t^3*v2+3*a^3*b*s*t^2*v2-a^3*b*t^3*v1+a^3*
c*p*t^2*v4+2*a^3*c*r*t^2*v2-a^3*c*s*t^2*v1-a^3*c*t^3*v0+2*a^3*d*p*t^2*v3+2*a^3*
d*q*t^2*v2+2*a^3*e*p*t^2*v2-a^2*b^2*p*t^2*v4+a^2*b^2*r*t^2*v2+3*a^2*b^2*s^2*t*
v2-2*a^2*b^2*s*t^2*v1+a^2*b^2*t^3*v0+2*a^2*b*c*p*s*t*v4-4*a^2*b*c*p*t^2*v3+a^2*
b*c*q*t^2*v2+4*a^2*b*c*r*s*t*v2-3*a^2*b*c*r*t^2*v1-2*a^2*b*c*s^2*t*v1-2*a^2*b*c
*s*t^2*v0+4*a^2*b*d*p*s*t*v3+4*a^2*b*d*q*s*t*v2-2*a^2*b*d*q*t^2*v1+4*a^2*b*e*p*
s*t*v2+2*a^2*b*e*p*t^2*v1+2*a^2*c^2*p*r*t*v4-2*a^2*c^2*p*s*t*v3-a^2*c^2*q*t^2*
v1+a^2*c^2*r^2*t*v2-2*a^2*c^2*r*s*t*v1-2*a^2*c^2*r*t^2*v0+2*a^2*c*d*p*q*t*v4+2*
a^2*c*d*p*r*t*v3-a^2*c*d*p*s*t*v2+a^2*c*d*p*t^2*v1+2*a^2*c*d*q*r*t*v2-2*a^2*c*d
*q*s*t*v1-2*a^2*c*d*q*t^2*v0+a^2*c*e*p^2*t*v4+2*a^2*c*e*p*r*t*v2+a^2*c*e*p*s*t*
v1-3*a^2*c*e*p*t^2*v0+a^2*d^2*p^2*t*v4+2*a^2*d^2*p*q*t*v3-a^2*d^2*p*r*t*v2-2*a^
2*d^2*p*t^2*v0+a^2*d^2*q^2*t*v2+4*a^2*d*e*p^2*t*v3+3*a^2*d*e*p*q*t*v2+3*a^2*d*e
*p*r*t*v1+a^2*e^2*p^2*t*v2+a^2*e^2*p*q*t*v1-2*a*b^3*p*s*t*v4+2*a*b^3*p*t^2*v3+2
*a*b^3*r*s*t*v2+a*b^3*s^3*v2-a*b^3*s^2*t*v1+2*a*b^3*s*t^2*v0-2*a*b^2*c*p*r*t*v4
+a*b^2*c*p*s^2*v4-4*a*b^2*c*p*s*t*v3+2*a*b^2*c*p*t^2*v2+2*a*b^2*c*q*s*t*v2+2*a*
b^2*c*r^2*t*v2+2*a*b^2*c*r*s^2*v2-4*a*b^2*c*r*s*t*v1+2*a*b^2*c*r*t^2*v0-a*b^2*c
*s^3*v1-a*b^2*c*s^2*t*v0-2*a*b^2*d*p*q*t*v4+2*a*b^2*d*p*r*t*v3+2*a*b^2*d*p*s^2*
v3+a*b^2*d*p*s*t*v2-3*a*b^2*d*p*t^2*v1+2*a*b^2*d*q*r*t*v2+2*a*b^2*d*q*s^2*v2-2*
a*b^2*d*q*s*t*v1+2*a*b^2*d*q*t^2*v0-a*b^2*e*p^2*t*v4+2*a*b^2*e*p*r*t*v2+2*a*b^2
*e*p*s^2*v2+3*a*b^2*e*p*s*t*v1-a*b^2*e*p*t^2*v0+2*a*b*c^2*p*r*s*v4-6*a*b*c^2*p*
r*t*v3-2*a*b*c^2*p*s^2*v3+3*a*b*c^2*p*s*t*v2-a*b*c^2*p*t^2*v1+2*a*b*c^2*q*r*t*
v2-2*a*b*c^2*q*s*t*v1+a*b*c^2*r^2*s*v2-3*a*b*c^2*r^2*t*v1-2*a*b*c^2*r*s^2*v1-2*
a*b*c^2*r*s*t*v0-2*a*b*c*d*p^2*t*v4+2*a*b*c*d*p*q*s*v4-2*a*b*c*d*p*q*t*v3+2*a*b
*c*d*p*r*s*v3+4*a*b*c*d*p*r*t*v2-a*b*c*d*p*s^2*v2-2*a*b*c*d*p*s*t*v1+3*a*b*c*d*
p*t^2*v0+2*a*b*c*d*q^2*t*v2+2*a*b*c*d*q*r*s*v2-4*a*b*c*d*q*r*t*v1-2*a*b*c*d*q*s
^2*v1-2*a*b*c*d*q*s*t*v0+a*b*c*e*p^2*s*v4-5*a*b*c*e*p^2*t*v3+3*a*b*c*e*p*q*t*v2
+2*a*b*c*e*p*r*s*v2+a*b*c*e*p*r*t*v1+a*b*c*e*p*s^2*v1-7*a*b*c*e*p*s*t*v0+a*b*d^
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v0-b*c*d^2*p*r*v4+2*b*c*d^2*p*s*v3-b*c*d^2*p*t*v2-b*c*d^2*q^2*v4+2*b*c*d^2*q*r*
v3-b*c*d^2*q*s*v2-b*c*d^2*q*t*v1-b*c*d^2*r*s*v1-b*c*d*e*p*q*v4-b*c*d*e*p*s*v2+2
*b*c*d*e*p*t*v1-3*b*c*d*e*q*r*v2+4*b*c*d*e*q*s*v1+3*b*c*d*e*r^2*v1+2*b*c*e^2*p^
2*v4-2*b*c*e^2*p*q*v3-4*b*c*e^2*p*r*v2-b*c*e^2*p*s*v1+b*c*e^2*p*t*v0-b*c*e^2*q^
2*v2+b*c*e^2*q*r*v1+b*d^3*p*q*v4-b*d^3*p*s*v2-b*d^3*q*r*v2-2*b*d^3*q*t*v0-b*d^3
*r^2*v1+b*d^2*e*p^2*v4-2*b*d^2*e*p*q*v3+2*b*d^2*e*p*s*v1-4*b*d^2*e*p*t*v0-b*d^2
*e*q^2*v2+b*d^2*e*q*r*v1-2*b*d*e^2*p^2*v3+2*b*d*e^2*p*r*v1+4*b*d*e^2*p*s*v0-b*e
^3*p^2*v2-b*e^3*p*q*v1+b*e^3*p*r*v0+c^4*p*s*v4-c^4*p*t*v3+c^4*q*r*v4-c^4*q*s*v3
-c^4*r*t*v1-c^4*s*t*v0-c^3*d*p*s*v3+c^3*d*p*t*v2+c^3*d*q^2*v4+c^3*d*q*s*v2-c^3*
d*q*t*v1+c^3*d*r*t*v0+2*c^3*e*p*q*v4+2*c^3*e*p*r*v3-c^3*e*p*s*v2-c^3*e*q^2*v3-c
^3*e*q*r*v2+c^3*e*q*s*v1-c^3*e*q*t*v0+c^3*e*r^2*v1-c^2*d^2*p*q*v4+c^2*d^2*p*s*
v2-c^2*d^2*p*t*v1+c^2*d^2*q^2*v3-c^2*d^2*q*s*v1+2*c^2*d^2*q*t*v0-c^2*d*e*p^2*v4
+4*c^2*d*e*p*q*v3-2*c^2*d*e*p*r*v2+2*c^2*d*e*p*s*v1+5*c^2*d*e*q*r*v1+3*c^2*e^2*
p^2*v3-2*c^2*e^2*p*q*v2+c^2*e^2*p*r*v1+2*c^2*e^2*p*s*v0+c^2*e^2*q^2*v1-c*d^3*p*
s*v1+c*d^3*p*t*v0-c*d^3*q^2*v2-c*d^3*q*r*v1-3*c*d^2*e*p*q*v2+c*d^2*e*p*r*v1-4*c
*d^2*e*p*s*v0+2*c*d^2*e*q^2*v1-2*c*d*e^2*p^2*v2+3*c*d*e^2*p*q*v1+3*c*d*e^2*p*r*
v0-c*e^3*p^2*v1+2*c*e^3*p*q*v0+d^4*p*s*v0+d^3*e*p*q*v1-d^3*e*p*r*v0+d^2*e^2*p^2
*v1+d^2*e^2*p*q*v0+3*d*e^3*p^2*v0+a^2*e^2*t*v4-a*b*d*e*t*v4+a*b*e^2*s*v4+2*a*b*
e^2*t*v3-3*a*c^2*e*t*v4+2*a*c*d^2*t*v4-2*a*c*d*e*s*v4-a*c*d*e*t*v3+a*c*e^2*s*v3
+2*a*c*e^2*t*v2+a*d^3*s*v4-a*d^3*t*v3-a*d^2*e*s*v3+2*a*d^2*e*t*v2+a*d*e^2*s*v2-\
3*a*d*e^2*t*v1+a*e^3*p*v4-a*e^3*s*v1-a*e^3*t*v0+2*b^2*c*e*t*v4+b^2*d^2*t*v4+b^2
*d*e*s*v4-3*b^2*d*e*t*v3+b^2*e^2*r*v4+b^2*e^2*s*v3+b^2*e^2*t*v2-3*b*c^2*d*t*v4-
b*c^2*e*s*v4+2*b*c^2*e*t*v3+2*b*c*d^2*t*v3-b*c*d*e*r*v4-2*b*c*d*e*s*v3-b*c*d*e*
t*v2+b*c*e^2*q*v4+2*b*c*e^2*r*v3+2*b*c*e^2*s*v2-3*b*c*e^2*t*v1+b*d^3*r*v4-b*d^3
*t*v2+b*d^2*e*q*v4-2*b*d^2*e*r*v3+b*d^2*e*s*v2+2*b*d^2*e*t*v1+2*b*d*e^2*r*v2-2*
b*d*e^2*s*v1+2*b*d*e^2*t*v0+2*b*e^3*p*v3+b*e^3*q*v2-b*e^3*r*v1+c^4*t*v4-c^3*d*t
*v3-c^3*e*r*v4+c^3*e*s*v3-c^3*e*t*v2+c^2*d^2*t*v2-3*c^2*d*e*q*v4-c^2*d*e*s*v2+2
*c^2*d*e*t*v1-2*c^2*e^2*p*v4+2*c^2*e^2*q*v3+c^2*e^2*r*v2-c^2*e^2*s*v1+c^2*e^2*t
*v0+c*d^3*q*v4-c*d^3*t*v1+c*d^2*e*p*v4-2*c*d^2*e*q*v3+c*d^2*e*s*v1-3*c*d^2*e*t*
v0-2*c*d*e^2*p*v3+c*d*e^2*q*v2-3*c*d*e^2*r*v1+2*c*e^3*p*v2-2*c*e^3*q*v1+d^4*t*
v0+d^3*e*q*v2+d^3*e*r*v1+d^2*e^2*p*v2-d^2*e^2*q*v1-2*d*e^3*p*v1-e^4*p*v0-b*e^3*
v4+2*c*d*e^2*v4-c*e^3*v3-d^3*e*v4+d^2*e^2*v3-d*e^3*v2+e^4*v1




beta[5,3] = -a^4*p*t^3*v2-a^4*q*t^3*v1-3*a^3*b*p*s*t^2*v2+a^3*b*p*t^3*v1-3*a^3*
b*q*s*t^2*v1+a^3*b*q*t^3*v0-a^3*c*p*q*t^2*v3-2*a^3*c*p*r*t^2*v2+a^3*c*p*s*t^2*
v1+a^3*c*p*t^3*v0-a^3*c*q^2*t^2*v2-3*a^3*c*q*r*t^2*v1-a^3*d*p^2*t^2*v3-3*a^3*d*
p*q*t^2*v2-2*a^3*d*q^2*t^2*v1-a^3*e*p^2*t^2*v2-a^3*e*p*q*t^2*v1+a^2*b^2*p*q*t^2
*v3-a^2*b^2*p*r*t^2*v2-3*a^2*b^2*p*s^2*t*v2+2*a^2*b^2*p*s*t^2*v1-a^2*b^2*p*t^3*
v0+a^2*b^2*q^2*t^2*v2-3*a^2*b^2*q*s^2*t*v1+3*a^2*b^2*q*s*t^2*v0+2*a^2*b*c*p^2*t
^2*v3-2*a^2*b*c*p*q*s*t*v3+a^2*b*c*p*q*t^2*v2-4*a^2*b*c*p*r*s*t*v2+3*a^2*b*c*p*
r*t^2*v1+2*a^2*b*c*p*s^2*t*v1+2*a^2*b*c*p*s*t^2*v0-2*a^2*b*c*q^2*s*t*v2-a^2*b*c
*q^2*t^2*v1-6*a^2*b*c*q*r*s*t*v1+3*a^2*b*c*q*r*t^2*v0-2*a^2*b*d*p^2*s*t*v3-2*a^
2*b*d*p^2*t^2*v2-6*a^2*b*d*p*q*s*t*v2-4*a^2*b*d*q^2*s*t*v1+2*a^2*b*d*q^2*t^2*v0
-2*a^2*b*e*p^2*s*t*v2+a^2*b*e*p^2*t^2*v1-2*a^2*b*e*p*q*s*t*v1+a^2*b*e*p*q*t^2*
v0+a^2*c^2*p^2*s*t*v3-a^2*c^2*p^2*t^2*v2-2*a^2*c^2*p*q*r*t*v3+a^2*c^2*p*q*s*t*
v2-a^2*c^2*p*r^2*t*v2+2*a^2*c^2*p*r*s*t*v1+2*a^2*c^2*p*r*t^2*v0-2*a^2*c^2*q^2*r
*t*v2+a^2*c^2*q^2*t^2*v0-3*a^2*c^2*q*r^2*t*v1-a^2*c*d*p^2*r*t*v3-a^2*c*d*p^2*s*
t*v2+2*a^2*c*d*p^2*t^2*v1-2*a^2*c*d*p*q^2*t*v3-3*a^2*c*d*p*q*r*t*v2+a^2*c*d*p*q
*s*t*v1+4*a^2*c*d*p*q*t^2*v0-2*a^2*c*d*q^3*t*v2-4*a^2*c*d*q^2*r*t*v1-a^2*c*e*p^
2*q*t*v3-a^2*c*e*p^2*r*t*v2+a^2*c*e*p^2*s*t*v1+a^2*c*e*p^2*t^2*v0-a^2*c*e*p*q^2
*t*v2-2*a^2*c*e*p*q*r*t*v1-2*a^2*d^2*p^2*q*t*v3+a^2*d^2*p^2*s*t*v1+a^2*d^2*p^2*
t^2*v0-3*a^2*d^2*p*q^2*t*v2-a^2*d^2*p*q*r*t*v1-a^2*d^2*q^3*t*v1-a^2*d*e*p^3*t*
v3-2*a^2*d*e*p^2*q*t*v2-a^2*d*e*p*q^2*t*v1-a*b^3*p^2*t^2*v3+2*a*b^3*p*q*s*t*v3-
a*b^3*p*q*t^2*v2-2*a*b^3*p*r*s*t*v2-a*b^3*p*s^3*v2+a*b^3*p*s^2*t*v1-2*a*b^3*p*s
*t^2*v0+2*a*b^3*q^2*s*t*v2-a*b^3*q*s^3*v1+3*a*b^3*q*s^2*t*v0+2*a*b^2*c*p^2*s*t*
v3+a*b^2*c*p^2*t^2*v2+2*a*b^2*c*p*q*r*t*v3-a*b^2*c*p*q*s^2*v3+a*b^2*c*p*q*t^2*
v1-2*a*b^2*c*p*r^2*t*v2-2*a*b^2*c*p*r*s^2*v2+4*a*b^2*c*p*r*s*t*v1-2*a*b^2*c*p*r
*t^2*v0+a*b^2*c*p*s^3*v1+a*b^2*c*p*s^2*t*v0+2*a*b^2*c*q^2*r*t*v2-a*b^2*c*q^2*s^
2*v2-2*a*b^2*c*q^2*s*t*v1-3*a*b^2*c*q*r*s^2*v1+6*a*b^2*c*q*r*s*t*v0-a*b^2*d*p^2
*r*t*v3-a*b^2*d*p^2*s^2*v3-3*a*b^2*d*p^2*s*t*v2+a*b^2*d*p^2*t^2*v1+2*a*b^2*d*p*
q^2*t*v3-3*a*b^2*d*p*q*r*t*v2-3*a*b^2*d*p*q*s^2*v2-a*b^2*d*p*q*s*t*v1-a*b^2*d*p
*q*t^2*v0+2*a*b^2*d*q^3*t*v2-2*a*b^2*d*q^2*s^2*v1+4*a*b^2*d*q^2*s*t*v0+a*b^2*e*
p^2*q*t*v3-a*b^2*e*p^2*r*t*v2-a*b^2*e*p^2*s^2*v2+a*b^2*e*p^2*s*t*v1-a*b^2*e*p^2
*t^2*v0+a*b^2*e*p*q^2*t*v2-a*b^2*e*p*q*s^2*v1+2*a*b^2*e*p*q*s*t*v0+3*a*b*c^2*p^
2*r*t*v3+a*b*c^2*p^2*s^2*v3-a*b*c^2*p^2*s*t*v2-a*b*c^2*p^2*t^2*v1-2*a*b*c^2*p*q
*r*s*v3+a*b*c^2*p*q*r*t*v2+a*b*c^2*p*q*s^2*v2+a*b*c^2*p*q*s*t*v1-a*b*c^2*p*q*t^
2*v0-a*b*c^2*p*r^2*s*v2+3*a*b*c^2*p*r^2*t*v1+2*a*b*c^2*p*r*s^2*v1+2*a*b*c^2*p*r
*s*t*v0-2*a*b*c^2*q^2*r*s*v2-2*a*b*c^2*q^2*r*t*v1+2*a*b*c^2*q^2*s*t*v0-3*a*b*c^
2*q*r^2*s*v1+3*a*b*c^2*q*r^2*t*v0+3*a*b*c*d*p^2*q*t*v3-a*b*c*d*p^2*r*s*v3-4*a*b
*c*d*p^2*r*t*v2-a*b*c*d*p^2*s^2*v2+3*a*b*c*d*p^2*s*t*v1-2*a*b*c*d*p^2*t^2*v0-2*
a*b*c*d*p*q^2*s*v3+a*b*c*d*p*q^2*t*v2-3*a*b*c*d*p*q*r*s*v2+2*a*b*c*d*p*q*r*t*v1
+a*b*c*d*p*q*s^2*v1+7*a*b*c*d*p*q*s*t*v0-2*a*b*c*d*q^3*s*v2-2*a*b*c*d*q^3*t*v1-\
4*a*b*c*d*q^2*r*s*v1+4*a*b*c*d*q^2*r*t*v0+2*a*b*c*e*p^3*t*v3-a*b*c*e*p^2*q*s*v3
+a*b*c*e*p^2*q*t*v2-a*b*c*e*p^2*r*s*v2+2*a*b*c*e*p^2*r*t*v1+a*b*c*e*p^2*s^2*v1+
a*b*c*e*p^2*s*t*v0-a*b*c*e*p*q^2*s*v2-a*b*c*e*p*q^2*t*v1-2*a*b*c*e*p*q*r*s*v1+2
*a*b*c*e*p*q*r*t*v0-a*b*d^2*p^3*t*v3-2*a*b*d^2*p^2*q*s*v3-4*a*b*d^2*p^2*q*t*v2+
a*b*d^2*p^2*r*t*v1+a*b*d^2*p^2*s^2*v1+a*b*d^2*p^2*s*t*v0-3*a*b*d^2*p*q^2*s*v2-2
*a*b*d^2*p*q^2*t*v1-a*b*d^2*p*q*r*s*v1+a*b*d^2*p*q*r*t*v0-a*b*d^2*q^3*s*v1+a*b*
d^2*q^3*t*v0-a*b*d*e*p^3*s*v3-2*a*b*d*e*p^3*t*v2-2*a*b*d*e*p^2*q*s*v2-a*b*d*e*p
^2*q*t*v1-a*b*d*e*p*q^2*s*v1+a*b*d*e*p*q^2*t*v0+a*c^3*p^2*r*s*v3-a*c^3*p^2*r*t*
v2+a*c^3*p^2*t^2*v0-a*c^3*p*q*r^2*v3+a*c^3*p*q*r*s*v2-a*c^3*p*q*s*t*v0+a*c^3*p*
r^2*s*v1+a*c^3*p*r^2*t*v0-a*c^3*q^2*r^2*v2+2*a*c^3*q^2*r*t*v0-a*c^3*q*r^3*v1+a*
c^2*d*p^3*t*v3+a*c^2*d*p^2*q*s*v3-a*c^2*d*p^2*q*t*v2-a*c^2*d*p^2*r*s*v2+3*a*c^2
*d*p^2*r*t*v1-2*a*c^2*d*p*q^2*r*v3+a*c^2*d*p*q^2*s*v2+a*c^2*d*p*q*r*s*v1+5*a*c^
2*d*p*q*r*t*v0-2*a*c^2*d*q^3*r*v2+2*a*c^2*d*q^3*t*v0-2*a*c^2*d*q^2*r^2*v1+a*c^2
*e*p^3*s*v3-a*c^2*e*p^3*t*v2-a*c^2*e*p^2*q*r*v3+a*c^2*e*p^2*q*s*v2+a*c^2*e*p^2*
r*s*v1+a*c^2*e*p^2*r*t*v0-a*c^2*e*p*q^2*r*v2+a*c^2*e*p*q^2*t*v0-a*c^2*e*p*q*r^2
*v1-a*c*d^2*p^3*t*v2-a*c*d^2*p^2*q*r*v3-a*c*d^2*p^2*q*s*v2+3*a*c*d^2*p^2*q*t*v1
+a*c*d^2*p^2*r*s*v1+a*c*d^2*p^2*r*t*v0-a*c*d^2*p*q^3*v3-a*c*d^2*p*q^2*r*v2+5*a*
c*d^2*p*q^2*t*v0-a*c*d^2*p*q*r^2*v1-a*c*d^2*q^4*v2-a*c*d^2*q^3*r*v1-a*c*d*e*p^3
*s*v2+2*a*c*d*e*p^3*t*v1-a*c*d*e*p^2*q^2*v3+3*a*c*d*e*p^2*q*t*v0-a*c*d*e*p*q^3*
v2-a*c*d*e*p*q^2*r*v1+a*d^3*p^3*t*v1-a*d^3*p^2*q^2*v3+a*d^3*p^2*q*s*v1+2*a*d^3*
p^2*q*t*v0-a*d^3*p*q^3*v2-a*d^3*p*q^2*r*v1-a*d^2*e*p^3*q*v3+a*d^2*e*p^3*s*v1+a*
d^2*e*p^3*t*v0-a*d^2*e*p^2*q^2*v2-a*d^2*e*p^2*q*r*v1-b^4*p^2*s*t*v3+b^4*p*q*s^2
*v3-b^4*p*q*s*t*v2-b^4*p*r*s^2*v2-b^4*p*s^2*t*v0+b^4*q^2*s^2*v2+b^4*q*s^3*v0-b^
3*c*p^2*r*t*v3+b^3*c*p^2*s*t*v2+2*b^3*c*p*q*r*s*v3-b^3*c*p*q*r*t*v2-b^3*c*p*q*s
^2*v2+b^3*c*p*q*s*t*v1-2*b^3*c*p*r^2*s*v2+b^3*c*p*r*s^2*v1-2*b^3*c*p*r*s*t*v0+2
*b^3*c*q^2*r*s*v2-b^3*c*q^2*s^2*v1+3*b^3*c*q*r*s^2*v0-b^3*d*p^2*q*t*v3-b^3*d*p^
2*r*s*v3-b^3*d*p^2*s^2*v2+b^3*d*p^2*s*t*v1+2*b^3*d*p*q^2*s*v3-b^3*d*p*q^2*t*v2-\
3*b^3*d*p*q*r*s*v2-b^3*d*p*q*s^2*v1-b^3*d*p*q*s*t*v0+2*b^3*d*q^3*s*v2+2*b^3*d*q
^2*s^2*v0-b^3*e*p^3*t*v3+b^3*e*p^2*q*s*v3-b^3*e*p^2*q*t*v2-b^3*e*p^2*r*s*v2-b^3
*e*p^2*s*t*v0+b^3*e*p*q^2*s*v2+b^3*e*p*q*s^2*v0+b^2*c^2*p^2*r*s*v3+b^2*c^2*p^2*
r*t*v2-b^2*c^2*p^2*s*t*v1+b^2*c^2*p*q*r^2*v3-b^2*c^2*p*q*r*s*v2+b^2*c^2*p*q*r*t
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3*b^2*c^2*q*r^2*s*v0+b^2*c*d*p^2*q*s*v3+b^2*c*d*p^2*q*t*v2-b^2*c*d*p^2*r^2*v3-3
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2*b^2*c*d*p*q^2*r*v3-b^2*c*d*p*q^2*s*v2+b^2*c*d*p*q^2*t*v1-3*b^2*c*d*p*q*r^2*v2
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2*b^2*c*d*q^3*s*v1+4*b^2*c*d*q^2*r*s*v0+b^2*c*e*p^3*t*v2+b^2*c*e*p^2*q*r*v3-b^2
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e*p^2*r*t*v0+b^2*c*e*p*q^2*r*v2-b^2*c*e*p*q^2*s*v1+2*b^2*c*e*p*q*r*s*v0-b^2*d^2
*p^3*s*v3-b^2*d^2*p^2*q*r*v3-3*b^2*d^2*p^2*q*s*v2+b^2*d^2*p^2*q*t*v1+b^2*d^2*p^
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p*q^3*v2+b^2*d*e*p*q^2*s*v0+b*c^3*p^2*r^2*v3-b*c^3*p^2*r*t*v1+b*c^3*p^2*s*t*v0+
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2*s*t^2*v2+a^2*b^2*t^3*v1-2*a^2*b*c*p*t^2*v4+2*a^2*b*c*q*s*t*v4+a^2*b*c*q*t^2*
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*q^3*v4-3*a*c*d^2*q^2*s*v2+3*a*c*d^2*q^2*t*v1-a*c*d^2*q*r*s*v1+3*a*c*d*e*p^2*t*
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v2+a*c*e^2*q^2*r*v1+a*d^3*p*q^2*v4-a*d^3*p*q*r*v3-a*d^3*p*q*t*v1+a*d^3*p*r*s*v1
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3*v2+a*d^2*e*q^2*r*v1+2*a*d*e^2*p^2*q*v3-2*a*d*e^2*p^2*s*v1-2*a*d*e^2*p^2*t*v0+
2*a*d*e^2*p*q^2*v2+2*a*d*e^2*p*q*r*v1+b^4*p*s*t*v4-b^4*p*t^2*v3-b^4*q*s^2*v4-b^
4*q*t^2*v2+b^4*r*s^2*v3-b^4*r*s*t*v2-b^4*s*t^2*v0+b^3*c*p*r*t*v4-b^3*c*p*s*t*v3
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b*d*e^2*q^2*v2+4*b*d*e^2*q*s*v0-b*e^3*p^2*v3-2*b*e^3*p*q*v2+b*e^3*p*r*v1-b*e^3*
q^2*v1+b*e^3*q*r*v0+c^4*t^2*v0-c^3*d*p*s*v4+c^3*d*p*t*v3-c^3*d*q*r*v4+c^3*d*q*s
*v3+c^3*d*r*t*v1+c^3*e*p*r*v4-c^3*e*p*s*v3-c^3*e*q*r*v3-c^3*e*r*s*v1-c^3*e*r*t*
v0+c^2*d^2*p*s*v3-c^2*d^2*p*t*v2-c^2*d^2*q^2*v4-c^2*d^2*q*s*v2+c^2*d^2*q*t*v1-c
^2*d*e*p*q*v4-2*c^2*d*e*p*r*v3+2*c^2*d*e*p*s*v2+2*c^2*d*e*q*r*v2-2*c^2*d*e*q*s*
v1-5*c^2*d*e*q*t*v0+c^2*e^2*p^2*v4-2*c^2*e^2*p*q*v3-c^2*e^2*p*r*v2-2*c^2*e^2*p*
t*v0+2*c^2*e^2*q*s*v0+c*d^3*p*q*v4-c*d^3*p*s*v2+c*d^3*p*t*v1-c*d^3*q^2*v3+c*d^3
*q*s*v1+2*c*d^3*q*t*v0+c*d^2*e*p^2*v4-3*c*d^2*e*p*q*v3+2*c*d^2*e*p*r*v2-3*c*d^2
*e*p*s*v1+c*d^2*e*p*t*v0+c*d^2*e*q^2*v2-3*c*d^2*e*q*r*v1-4*c*d^2*e*q*s*v0-2*c*d
*e^2*p^2*v3+3*c*d*e^2*p*q*v2+3*c*d*e^2*p*r*v1-c*d*e^2*q^2*v1+3*c*d*e^2*q*r*v0-c
*e^3*p^2*v2+c*e^3*p*q*v1+2*c*e^3*q^2*v0+d^4*p*s*v1+d^4*q^2*v2+d^4*q*r*v1+d^4*q*
s*v0+2*d^3*e*p*q*v2-d^3*e*p*r*v1-d^3*e*q^2*v1-d^3*e*q*r*v0+d^2*e^2*p^2*v2-d^2*e
^2*p*q*v1+d^2*e^2*q^2*v0+3*d*e^3*p^2*v1+3*d*e^3*p*q*v0+2*a*b*e^2*t*v4-a*c*d*e*t
*v4+a*c*e^2*s*v4+2*a*c*e^2*t*v3-a*d^3*t*v4-a*d^2*e*s*v4+2*a*d^2*e*t*v3+a*d*e^2*
s*v3-3*a*d*e^2*t*v2+a*e^3*q*v4-a*e^3*s*v2-a*e^3*t*v1-3*b^2*d*e*t*v4+b^2*e^2*s*
v4+b^2*e^2*t*v3+2*b*c^2*e*t*v4+2*b*c*d^2*t*v4-2*b*c*d*e*s*v4-b*c*d*e*t*v3+2*b*c
*e^2*r*v4+2*b*c*e^2*s*v3-3*b*c*e^2*t*v2-b*d^3*t*v3-2*b*d^2*e*r*v4+b*d^2*e*s*v3+
2*b*d^2*e*t*v2-2*b*d*e^2*q*v4+2*b*d*e^2*r*v3-2*b*d*e^2*s*v2+2*b*d*e^2*t*v1+b*e^
3*p*v4+b*e^3*q*v3-2*b*e^3*r*v2-b*e^3*s*v1-b*e^3*t*v0-c^3*d*t*v4+c^3*e*s*v4-c^3*
e*t*v3+c^2*d^2*t*v3-c^2*d*e*s*v3+2*c^2*d*e*t*v2+c^2*e^2*q*v4+c^2*e^2*r*v3-c^2*e
^2*s*v2+c^2*e^2*t*v1-c*d^3*t*v2+c*d^2*e*q*v4+c*d^2*e*s*v2-3*c*d^2*e*t*v1+c*d*e^
2*q*v3-c*d*e^2*r*v2+2*c*d*e^2*s*v1+2*c*d*e^2*t*v0+2*c*e^3*p*v3-c*e^3*q*v2-d^4*q
*v4+d^4*t*v1-d^3*e*p*v4+d^3*e*q*v3-d^3*e*s*v1-d^3*e*t*v0+d^2*e^2*p*v3-2*d^2*e^2
*q*v2-2*d*e^3*p*v2+d*e^3*q*v1-e^4*p*v1-e^4*q*v0-c*e^3*v4+d^2*e^2*v4-d*e^3*v3+e^
4*v2




beta[5,4] = -a^4*p*t^3*v3-a^4*q*t^3*v2-a^4*r*t^3*v1-3*a^3*b*p*s*t^2*v3+a^3*b*p*
t^3*v2-3*a^3*b*q*s*t^2*v2+a^3*b*q*t^3*v1-3*a^3*b*r*s*t^2*v1+a^3*b*r*t^3*v0-3*a^
3*c*p*r*t^2*v3+a^3*c*p*s*t^2*v2+a^3*c*p*t^3*v1-3*a^3*c*q*r*t^2*v2+a^3*c*q*s*t^2
*v1+a^3*c*q*t^3*v0-3*a^3*c*r^2*t^2*v1-2*a^3*d*p*q*t^2*v3+a^3*d*p*s*t^2*v1+a^3*d
*p*t^3*v0-2*a^3*d*q^2*t^2*v2-2*a^3*d*q*r*t^2*v1-a^3*e*p^2*t^2*v3-a^3*e*p*q*t^2*
v2-a^3*e*p*r*t^2*v1-3*a^2*b^2*p*s^2*t*v3+2*a^2*b^2*p*s*t^2*v2-a^2*b^2*p*t^3*v1-\
3*a^2*b^2*q*s^2*t*v2+2*a^2*b^2*q*s*t^2*v1-a^2*b^2*q*t^3*v0-3*a^2*b^2*r*s^2*t*v1
+3*a^2*b^2*r*s*t^2*v0-a^2*b*c*p*q*t^2*v3-6*a^2*b*c*p*r*s*t*v3+3*a^2*b*c*p*r*t^2
*v2+2*a^2*b*c*p*s^2*t*v2-2*a^2*b*c*p*t^3*v0-a^2*b*c*q^2*t^2*v2-6*a^2*b*c*q*r*s*
t*v2+2*a^2*b*c*q*r*t^2*v1+2*a^2*b*c*q*s^2*t*v1+2*a^2*b*c*q*s*t^2*v0-6*a^2*b*c*r
^2*s*t*v1+3*a^2*b*c*r^2*t^2*v0-2*a^2*b*d*p^2*t^2*v3-4*a^2*b*d*p*q*s*t*v3-2*a^2*
b*d*p*r*t^2*v1+2*a^2*b*d*p*s^2*t*v1+2*a^2*b*d*p*s*t^2*v0-4*a^2*b*d*q^2*s*t*v2+2
*a^2*b*d*q^2*t^2*v1-4*a^2*b*d*q*r*s*t*v1+2*a^2*b*d*q*r*t^2*v0-2*a^2*b*e*p^2*s*t
*v3+a^2*b*e*p^2*t^2*v2-2*a^2*b*e*p*q*s*t*v2+a^2*b*e*p*q*t^2*v1-2*a^2*b*e*p*r*s*
t*v1+a^2*b*e*p*r*t^2*v0-a^2*c^2*p^2*t^2*v3-3*a^2*c^2*p*r^2*t*v3+2*a^2*c^2*p*r*s
*t*v2+a^2*c^2*p*r*t^2*v1-a^2*c^2*p*s^2*t*v1-a^2*c^2*p*s*t^2*v0+a^2*c^2*q^2*t^2*
v1-3*a^2*c^2*q*r^2*t*v2+2*a^2*c^2*q*r*s*t*v1+3*a^2*c^2*q*r*t^2*v0-3*a^2*c^2*r^3
*t*v1-a^2*c*d*p^2*s*t*v3+2*a^2*c*d*p^2*t^2*v2-4*a^2*c*d*p*q*r*t*v3+a^2*c*d*p*q*
s*t*v2+4*a^2*c*d*p*q*t^2*v1+3*a^2*c*d*p*r*t^2*v0-4*a^2*c*d*q^2*r*t*v2+2*a^2*c*d
*q^2*s*t*v1+2*a^2*c*d*q^2*t^2*v0-4*a^2*c*d*q*r^2*t*v1-2*a^2*c*e*p^2*r*t*v3+a^2*
c*e*p^2*s*t*v2+a^2*c*e*p^2*t^2*v1-2*a^2*c*e*p*q*r*t*v2+a^2*c*e*p*q*s*t*v1+a^2*c
*e*p*q*t^2*v0-2*a^2*c*e*p*r^2*t*v1-a^2*d^2*p^2*r*t*v3+a^2*d^2*p^2*s*t*v2+a^2*d^
2*p^2*t^2*v1-a^2*d^2*p*q^2*t*v3-a^2*d^2*p*q*r*t*v2+2*a^2*d^2*p*q*s*t*v1+2*a^2*d
^2*p*q*t^2*v0-a^2*d^2*p*r^2*t*v1-a^2*d^2*q^3*t*v2-a^2*d^2*q^2*r*t*v1-a^2*d*e*p^
2*q*t*v3+a^2*d*e*p^2*s*t*v1+a^2*d*e*p^2*t^2*v0-a^2*d*e*p*q^2*t*v2-a^2*d*e*p*q*r
*t*v1-a*b^3*p*s^3*v3+a*b^3*p*s^2*t*v2-a*b^3*p*s*t^2*v1+a*b^3*p*t^3*v0-a*b^3*q*s
^3*v2+a*b^3*q*s^2*t*v1-2*a*b^3*q*s*t^2*v0-a*b^3*r*s^3*v1+3*a*b^3*r*s^2*t*v0+a*b
^2*c*p^2*t^2*v3-2*a*b^2*c*p*q*s*t*v3+a*b^2*c*p*q*t^2*v2-3*a*b^2*c*p*r*s^2*v3+4*
a*b^2*c*p*r*s*t*v2-a*b^2*c*p*r*t^2*v1+a*b^2*c*p*s^3*v2-a*b^2*c*p*s^2*t*v1-2*a*b
^2*c*p*s*t^2*v0-2*a*b^2*c*q^2*s*t*v2-3*a*b^2*c*q*r*s^2*v2+2*a*b^2*c*q*r*s*t*v1-\
2*a*b^2*c*q*r*t^2*v0+a*b^2*c*q*s^3*v1+a*b^2*c*q*s^2*t*v0-3*a*b^2*c*r^2*s^2*v1+6
*a*b^2*c*r^2*s*t*v0-3*a*b^2*d*p^2*s*t*v3+a*b^2*d*p^2*t^2*v2-2*a*b^2*d*p*q*s^2*
v3-a*b^2*d*p*q*s*t*v2-a*b^2*d*p*q*t^2*v1-2*a*b^2*d*p*r*s*t*v1+2*a*b^2*d*p*r*t^2
*v0+a*b^2*d*p*s^3*v1+a*b^2*d*p*s^2*t*v0-2*a*b^2*d*q^2*s^2*v2+2*a*b^2*d*q^2*s*t*
v1-2*a*b^2*d*q^2*t^2*v0-2*a*b^2*d*q*r*s^2*v1+4*a*b^2*d*q*r*s*t*v0-a*b^2*e*p^2*s
^2*v3+a*b^2*e*p^2*s*t*v2-a*b^2*e*p^2*t^2*v1-a*b^2*e*p*q*s^2*v2+a*b^2*e*p*q*s*t*
v1-a*b^2*e*p*q*t^2*v0-a*b^2*e*p*r*s^2*v1+2*a*b^2*e*p*r*s*t*v0-a*b*c^2*p^2*s*t*
v3-a*b*c^2*p^2*t^2*v2-2*a*b*c^2*p*q*r*t*v3+a*b*c^2*p*q*s*t*v2-a*b*c^2*p*q*t^2*
v1-3*a*b*c^2*p*r^2*s*v3+3*a*b*c^2*p*r^2*t*v2+2*a*b*c^2*p*r*s^2*v2-2*a*b*c^2*p*r
*s*t*v1-4*a*b*c^2*p*r*t^2*v0-a*b*c^2*p*s^3*v1-a*b*c^2*p*s^2*t*v0-2*a*b*c^2*q^2*
r*t*v2+2*a*b*c^2*q^2*s*t*v1-3*a*b*c^2*q*r^2*s*v2+a*b*c^2*q*r^2*t*v1+2*a*b*c^2*q
*r*s^2*v1+4*a*b*c^2*q*r*s*t*v0-3*a*b*c^2*r^3*s*v1+3*a*b*c^2*r^3*t*v0-2*a*b*c*d*
p^2*r*t*v3-a*b*c*d*p^2*s^2*v3+3*a*b*c*d*p^2*s*t*v2-2*a*b*c*d*p^2*t^2*v1-2*a*b*c
*d*p*q^2*t*v3-4*a*b*c*d*p*q*r*s*v3+2*a*b*c*d*p*q*r*t*v2+a*b*c*d*p*q*s^2*v2+4*a*
b*c*d*p*q*s*t*v1-3*a*b*c*d*p*q*t^2*v0-2*a*b*c*d*p*r^2*t*v1+6*a*b*c*d*p*r*s*t*v0
-2*a*b*c*d*q^3*t*v2-4*a*b*c*d*q^2*r*s*v2+2*a*b*c*d*q^2*r*t*v1+2*a*b*c*d*q^2*s^2
*v1+2*a*b*c*d*q^2*s*t*v0-4*a*b*c*d*q*r^2*s*v1+4*a*b*c*d*q*r^2*t*v0-a*b*c*e*p^2*
q*t*v3-2*a*b*c*e*p^2*r*s*v3+2*a*b*c*e*p^2*r*t*v2+a*b*c*e*p^2*s^2*v2-a*b*c*e*p^2
*s*t*v1-2*a*b*c*e*p^2*t^2*v0-a*b*c*e*p*q^2*t*v2-2*a*b*c*e*p*q*r*s*v2+a*b*c*e*p*
q*r*t*v1+a*b*c*e*p*q*s^2*v1+a*b*c*e*p*q*s*t*v0-2*a*b*c*e*p*r^2*s*v1+2*a*b*c*e*p
*r^2*t*v0-3*a*b*d^2*p^2*q*t*v3-a*b*d^2*p^2*r*s*v3+a*b*d^2*p^2*r*t*v2+a*b*d^2*p^
2*s^2*v2+2*a*b*d^2*p^2*s*t*v1+a*b*d^2*p^2*t^2*v0-a*b*d^2*p*q^2*s*v3-2*a*b*d^2*p
*q^2*t*v2-a*b*d^2*p*q*r*s*v2-2*a*b*d^2*p*q*r*t*v1+2*a*b*d^2*p*q*s^2*v1+2*a*b*d^
2*p*q*s*t*v0-a*b*d^2*p*r^2*s*v1+a*b*d^2*p*r^2*t*v0-a*b*d^2*q^3*s*v2+a*b*d^2*q^3
*t*v1-a*b*d^2*q^2*r*s*v1+a*b*d^2*q^2*r*t*v0-2*a*b*d*e*p^3*t*v3-a*b*d*e*p^2*q*s*
v3-a*b*d*e*p^2*q*t*v2-2*a*b*d*e*p^2*r*t*v1+a*b*d*e*p^2*s^2*v1+a*b*d*e*p^2*s*t*
v0-a*b*d*e*p*q^2*s*v2+a*b*d*e*p*q^2*t*v1-a*b*d*e*p*q*r*s*v1+a*b*d*e*p*q*r*t*v0-\
2*a*c^3*p^2*r*t*v3+a*c^3*p^2*t^2*v1-a*c^3*p*q*s*t*v1-a*c^3*p*r^3*v3+a*c^3*p*r^2
*s*v2-a*c^3*p*r^2*t*v1-a*c^3*p*r*s^2*v1-2*a*c^3*p*r*s*t*v0+2*a*c^3*q^2*r*t*v1-a
*c^3*q*r^3*v2+a*c^3*q*r^2*s*v1+3*a*c^3*q*r^2*t*v0-a*c^3*r^4*v1-2*a*c^2*d*p^2*q*
t*v3-a*c^2*d*p^2*r*s*v3+3*a*c^2*d*p^2*r*t*v2-a*c^2*d*p^2*s*t*v1-a*c^2*d*p^2*t^2
*v0-2*a*c^2*d*p*q*r^2*v3+a*c^2*d*p*q*r*s*v2+3*a*c^2*d*p*q*r*t*v1-a*c^2*d*p*q*s^
2*v1-a*c^2*d*p*q*s*t*v0-a*c^2*d*p*r^2*s*v1+3*a*c^2*d*p*r^2*t*v0+2*a*c^2*d*q^3*t
*v1-2*a*c^2*d*q^2*r^2*v2+2*a*c^2*d*q^2*r*s*v1+4*a*c^2*d*q^2*r*t*v0-2*a*c^2*d*q*
r^3*v1-a*c^2*e*p^3*t*v3-a*c^2*e*p^2*r^2*v3+a*c^2*e*p^2*r*s*v2-a*c^2*e*p^2*s^2*
v1-a*c^2*e*p^2*s*t*v0+a*c^2*e*p*q^2*t*v1-a*c^2*e*p*q*r^2*v2+a*c^2*e*p*q*r*s*v1+
2*a*c^2*e*p*q*r*t*v0-a*c^2*e*p*r^3*v1-a*c*d^2*p^3*t*v3-a*c*d^2*p^2*q*s*v3+3*a*c
*d^2*p^2*q*t*v2-a*c*d^2*p^2*r^2*v3+a*c*d^2*p^2*r*s*v2-a*c*d^2*p*q^2*r*v3+5*a*c*
d^2*p*q^2*t*v1-a*c*d^2*p*q*r^2*v2+5*a*c*d^2*p*q*r*t*v0-a*c*d^2*p*r^3*v1-a*c*d^2
*q^3*r*v2+a*c*d^2*q^3*s*v1+a*c*d^2*q^3*t*v0-a*c*d^2*q^2*r^2*v1-a*c*d*e*p^3*s*v3
+2*a*c*d*e*p^3*t*v2-a*c*d*e*p^2*q*r*v3+3*a*c*d*e*p^2*q*t*v1-a*c*d*e*p^2*r*s*v1+
2*a*c*d*e*p^2*r*t*v0-a*c*d*e*p*q^2*r*v2+a*c*d*e*p*q^2*s*v1+a*c*d*e*p*q^2*t*v0-a
*c*d*e*p*q*r^2*v1+a*d^3*p^3*t*v2-a*d^3*p^2*q*r*v3+a*d^3*p^2*q*s*v2+2*a*d^3*p^2*
q*t*v1+a*d^3*p^2*r*t*v0-a*d^3*p*q^2*r*v2+a*d^3*p*q^2*s*v1+a*d^3*p*q^2*t*v0-a*d^
3*p*q*r^2*v1-a*d^2*e*p^3*r*v3+a*d^2*e*p^3*s*v2+a*d^2*e*p^3*t*v1-a*d^2*e*p^2*q*r
*v2+a*d^2*e*p^2*q*s*v1+a*d^2*e*p^2*q*t*v0-a*d^2*e*p^2*r^2*v1+b^4*p*s*t^2*v0-b^4
*q*s^2*t*v0+b^4*r*s^3*v0+b^3*c*p^2*s*t*v3-b^3*c*p*q*s^2*v3+b^3*c*p*q*s*t*v2+b^3
*c*p*r*s^2*v2+b^3*c*p*r*t^2*v0-b^3*c*q^2*s^2*v2-2*b^3*c*q*r*s*t*v0+3*b^3*c*r^2*
s^2*v0-b^3*d*p^2*s^2*v3+b^3*d*p^2*s*t*v2-b^3*d*p*q*s^2*v2+b^3*d*p*q*t^2*v0+2*b^
3*d*p*r*s*t*v0-2*b^3*d*q^2*s*t*v0+2*b^3*d*q*r*s^2*v0+b^3*e*p^2*t^2*v0-b^3*e*p*q
*s*t*v0+b^3*e*p*r*s^2*v0+b^2*c^2*p^2*r*t*v3-b^2*c^2*p^2*s*t*v2-2*b^2*c^2*p*q*r*
s*v3+b^2*c^2*p*q*r*t*v2+b^2*c^2*p*q*s^2*v2-b^2*c^2*p*q*s*t*v1+2*b^2*c^2*p*r^2*s
*v2-b^2*c^2*p*r*s^2*v1-2*b^2*c^2*p*r*s*t*v0-2*b^2*c^2*q^2*r*s*v2+b^2*c^2*q^2*s^
2*v1-b^2*c^2*q*r^2*t*v0+b^2*c^2*q*r*s^2*v0+3*b^2*c^2*r^3*s*v0+b^2*c*d*p^2*q*t*
v3-b^2*c*d*p^2*r*s*v3+b^2*c*d*p^2*r*t*v2+b^2*c*d*p^2*s^2*v2-2*b^2*c*d*p^2*s*t*
v1-2*b^2*c*d*p*q^2*s*v3+b^2*c*d*p*q^2*t*v2+b^2*c*d*p*q*r*s*v2+2*b^2*c*d*p*q*s^2
*v1-b^2*c*d*p*q*s*t*v0+2*b^2*c*d*p*r^2*t*v0+3*b^2*c*d*p*r*s^2*v0-2*b^2*c*d*q^3*
s*v2-2*b^2*c*d*q^2*r*t*v0+4*b^2*c*d*q*r^2*s*v0+b^2*c*e*p^3*t*v3-b^2*c*e*p^2*q*s
*v3+b^2*c*e*p^2*q*t*v2+b^2*c*e*p^2*r*s*v2-b^2*c*e*p*q^2*s*v2-b^2*c*e*p*q*r*t*v0
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v2+b^2*d^2*p^2*s^2*v1+b^2*d^2*p^2*s*t*v0-2*b^2*d^2*p*q^2*s*v2+2*b^2*d^2*p*q*r*t
*v0+b^2*d^2*p*r^2*s*v0-b^2*d^2*q^3*t*v0+b^2*d^2*q^2*r*s*v0-b^2*d*e*p^3*s*v3+b^2
*d*e*p^3*t*v2-b^2*d*e*p^2*q*s*v2+2*b^2*d*e*p^2*r*t*v0-b^2*d*e*p*q^2*t*v0+b^2*d*
e*p*q*r*s*v0-b*c^3*p^2*r*s*v3-b*c^3*p^2*r*t*v2+b*c^3*p^2*s*t*v1-b*c^3*p*q*r^2*
v3+b*c^3*p*q*r*s*v2-b*c^3*p*q*r*t*v1-b*c^3*p*q*s^2*v1+b*c^3*p*r^3*v2-2*b*c^3*p*
r^2*s*v1-2*b*c^3*p*r^2*t*v0-b*c^3*p*r*s^2*v0-b*c^3*q^2*r^2*v2+2*b*c^3*q^2*r*s*
v1+2*b*c^3*q*r^2*s*v0+b*c^3*r^4*v0-b*c^2*d*p^2*q*s*v3-b*c^2*d*p^2*q*t*v2+2*b*c^
2*d*p^2*r*s*v2-2*b*c^2*d*p^2*r*t*v1-b*c^2*d*p^2*s^2*v1-b*c^2*d*p^2*s*t*v0-2*b*c
^2*d*p*q^2*r*v3+b*c^2*d*p*q^2*s*v2-b*c^2*d*p*q^2*t*v1+2*b*c^2*d*p*q*r^2*v2+b*c^
2*d*p*q*r*s*v1-3*b*c^2*d*p*q*r*t*v0+4*b*c^2*d*p*r^2*s*v0-2*b*c^2*d*q^3*r*v2+2*b
*c^2*d*q^3*s*v1+2*b*c^2*d*q^2*r*s*v0+2*b*c^2*d*q*r^3*v0-b*c^2*e*p^3*t*v2-b*c^2*
e*p^2*q*r*v3+b*c^2*e*p^2*q*s*v2-b*c^2*e*p^2*q*t*v1+b*c^2*e*p^2*r^2*v2-b*c^2*e*p
^2*r*s*v1-2*b*c^2*e*p^2*r*t*v0-b*c^2*e*p*q^2*r*v2+b*c^2*e*p*q^2*s*v1+b*c^2*e*p*
q*r*s*v0+b*c^2*e*p*r^3*v0-b*c*d^2*p^3*s*v3-b*c*d^2*p^2*q*r*v3+2*b*c*d^2*p^2*q*s
*v2-2*b*c*d^2*p^2*q*t*v1+b*c*d^2*p^2*r^2*v2+b*c*d^2*p^2*r*t*v0-b*c*d^2*p*q^3*v3
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b*c*d^2*q^4*v2+b*c*d^2*q^2*r^2*v0+b*c*d*e*p^3*s*v2-2*b*c*d*e*p^3*t*v1-b*c*d*e*p
^2*q^2*v3+b*c*d*e*p^2*q*r*v2+2*b*c*d*e*p^2*q*s*v1-b*c*d*e*p^2*q*t*v0+3*b*c*d*e*
p^2*r*s*v0-b*c*d*e*p*q^3*v2+b*c*d*e*p*q*r^2*v0+b*d^3*p^3*s*v2-b*d^3*p^2*q^2*v3+
b*d^3*p^2*q*r*v2+2*b*d^3*p^2*q*s*v1+b*d^3*p^2*q*t*v0+b*d^3*p^2*r*s*v0-b*d^3*p*q
^3*v2+b*d^3*p*q*r^2*v0-b*d^2*e*p^3*q*v3+b*d^2*e*p^3*r*v2+b*d^2*e*p^3*s*v1+b*d^2
*e*p^3*t*v0-b*d^2*e*p^2*q^2*v2+b*d^2*e*p^2*r^2*v0-c^4*p^2*r^2*v3+c^4*p^2*r*t*v1
-c^4*p*q*r*s*v1-c^4*p*r^3*v1-c^4*p*r^2*s*v0+c^4*q^2*r^2*v1+c^4*q*r^3*v0-2*c^3*d
*p^2*q*r*v3+c^3*d*p^2*q*t*v1+c^3*d*p^2*r^2*v2-c^3*d*p^2*r*s*v1-c^3*d*p^2*r*t*v0
-c^3*d*p*q^2*s*v1-c^3*d*p*q*r^2*v1-c^3*d*p*q*r*s*v0+c^3*d*p*r^3*v0+2*c^3*d*q^3*
r*v1+2*c^3*d*q^2*r^2*v0-c^3*e*p^3*r*v3+c^3*e*p^3*t*v1-c^3*e*p^2*q*s*v1-c^3*e*p^
2*r^2*v1-c^3*e*p^2*r*s*v0+c^3*e*p*q^2*r*v1+c^3*e*p*q*r^2*v0-c^2*d^2*p^3*r*v3-c^
2*d^2*p^2*q^2*v3+2*c^2*d^2*p^2*q*r*v2-c^2*d^2*p^2*q*s*v1-c^2*d^2*p^2*q*t*v0-c^2
*d^2*p^2*r^2*v1+2*c^2*d^2*p*q^2*r*v1+3*c^2*d^2*p*q*r^2*v0+c^2*d^2*q^4*v1+c^2*d^
2*q^3*r*v0-c^2*d*e*p^3*q*v3+c^2*d*e*p^3*r*v2-c^2*d*e*p^3*s*v1-c^2*d*e*p^3*t*v0+
c^2*d*e*p^2*r^2*v0+c^2*d*e*p*q^3*v1+c^2*d*e*p*q^2*r*v0-c*d^3*p^3*q*v3+c*d^3*p^3
*r*v2+c*d^3*p^2*q^2*v2+c*d^3*p^2*r^2*v0+2*c*d^3*p*q^3*v1+2*c*d^3*p*q^2*r*v0-c*d
^2*e*p^4*v3+c*d^2*e*p^3*q*v2-c*d^2*e*p^3*r*v1+2*c*d^2*e*p^2*q^2*v1+2*c*d^2*e*p^
2*q*r*v0+d^4*p^3*q*v2+d^4*p^2*q^2*v1+d^4*p^2*q*r*v0+d^3*e*p^4*v2+d^3*e*p^3*q*v1
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*s*t^2*v3-a^3*c*t^3*v2+2*a^3*d*q*t^2*v4-a^3*d*s*t^2*v2-a^3*d*t^3*v1+a^3*e*p*t^2
*v4-a^3*e*s*t^2*v1-a^3*e*t^3*v0+3*a^2*b^2*s^2*t*v4-2*a^2*b^2*s*t^2*v3+a^2*b^2*t
^3*v2+a^2*b*c*q*t^2*v4+6*a^2*b*c*r*s*t*v4-3*a^2*b*c*r*t^2*v3-2*a^2*b*c*s^2*t*v3
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2*b*d*s^2*t*v2+2*a^2*b*d*t^3*v0+2*a^2*b*e*p*s*t*v4+2*a^2*b*e*p*t^2*v3+3*a^2*b*e
*q*t^2*v2+3*a^2*b*e*r*t^2*v1-2*a^2*b*e*s^2*t*v1-2*a^2*b*e*s*t^2*v0+a^2*c^2*p*t^
2*v4-a^2*c^2*q*t^2*v3+3*a^2*c^2*r^2*t*v4-2*a^2*c^2*r*s*t*v3-2*a^2*c^2*r*t^2*v2+
a^2*c^2*s^2*t*v2+2*a^2*c^2*s*t^2*v1+a^2*c^2*t^3*v0+a^2*c*d*p*s*t*v4+a^2*c*d*p*t
^2*v3+4*a^2*c*d*q*r*t*v4-2*a^2*c*d*q*s*t*v3+a^2*c*d*q*t^2*v2-a^2*c*d*r*s*t*v2+2
*a^2*c*d*r*t^2*v1+2*a^2*c*d*s^2*t*v1+2*a^2*c*d*s*t^2*v0+2*a^2*c*e*p*r*t*v4+a^2*
c*e*p*s*t*v3-3*a^2*c*e*p*t^2*v2+2*a^2*c*e*q*s*t*v2-2*a^2*c*e*q*t^2*v1+a^2*c*e*r
*s*t*v1-3*a^2*c*e*r*t^2*v0+a^2*d^2*p*r*t*v4-2*a^2*d^2*p*t^2*v2+a^2*d^2*q^2*t*v4
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2*d*e*p*s*t*v2-3*a^2*d*e*p*t^2*v1+3*a^2*d*e*q*r*t*v2-2*a^2*d*e*q*s*t*v1-2*a^2*d
*e*q*t^2*v0+3*a^2*d*e*r^2*t*v1+a^2*e^2*p*q*t*v3-a^2*e^2*p*s*t*v1-a^2*e^2*p*t^2*
v0+a^2*e^2*q^2*t*v2+a^2*e^2*q*r*t*v1+a*b^3*s^3*v4-a*b^3*s^2*t*v3+a*b^3*s*t^2*v2
-a*b^3*t^3*v1-a*b^2*c*p*t^2*v4+2*a*b^2*c*q*s*t*v4+3*a*b^2*c*r*s^2*v4-4*a*b^2*c*
r*s*t*v3+2*a*b^2*c*r*t^2*v2-a*b^2*c*s^3*v3+a*b^2*c*s^2*t*v2-a*b^2*c*s*t^2*v1-3*
a*b^2*c*t^3*v0+3*a*b^2*d*p*s*t*v4-3*a*b^2*d*p*t^2*v3+2*a*b^2*d*q*s^2*v4-2*a*b^2
*d*q*s*t*v3-a*b^2*d*r*s*t*v2-3*a*b^2*d*r*t^2*v1-a*b^2*d*s^3*v2+a*b^2*d*s^2*t*v1
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2*e*q*s*t*v2-2*a*b^2*e*q*t^2*v1+3*a*b^2*e*r*s*t*v1-3*a*b^2*e*r*t^2*v0-a*b^2*e*s
^3*v1-a*b^2*e*s^2*t*v0+a*b*c^2*p*s*t*v4-a*b*c^2*p*t^2*v3+2*a*b*c^2*q*r*t*v4-2*a
*b*c^2*q*s*t*v3-2*a*b*c^2*q*t^2*v2+3*a*b*c^2*r^2*s*v4-3*a*b*c^2*r^2*t*v3-2*a*b*
c^2*r*s^2*v3+a*b*c^2*r*s*t*v2+a*b*c^2*r*t^2*v1+a*b*c^2*s^3*v2-a*b*c^2*s^2*t*v1-\
2*a*b*c^2*s*t^2*v0+2*a*b*c*d*p*r*t*v4+a*b*c*d*p*s^2*v4-2*a*b*c*d*p*s*t*v3+3*a*b
*c*d*p*t^2*v2+2*a*b*c*d*q^2*t*v4+4*a*b*c*d*q*r*s*v4-4*a*b*c*d*q*r*t*v3-2*a*b*c*
d*q*s^2*v3+2*a*b*c*d*q*t^2*v1-a*b*c*d*r*s^2*v2+a*b*c*d*r*t^2*v0+2*a*b*c*d*s^3*
v1+2*a*b*c*d*s^2*t*v0+a*b*c*e*p*q*t*v4+2*a*b*c*e*p*r*s*v4+a*b*c*e*p*r*t*v3+a*b*
c*e*p*s^2*v3-4*a*b*c*e*p*s*t*v2+3*a*b*c*e*p*t^2*v1+3*a*b*c*e*q*r*t*v2+2*a*b*c*e
*q*s^2*v2-8*a*b*c*e*q*s*t*v1-2*a*b*c*e*q*t^2*v0+3*a*b*c*e*r^2*t*v1+a*b*c*e*r*s^
2*v1-7*a*b*c*e*r*s*t*v0+3*a*b*d^2*p*q*t*v4+a*b*d^2*p*r*s*v4-4*a*b*d^2*p*r*t*v3-\
2*a*b*d^2*p*s*t*v2+2*a*b*d^2*p*t^2*v1+a*b*d^2*q^2*s*v4-a*b*d^2*q^2*t*v3-3*a*b*d
^2*q*r*t*v2+4*a*b*d^2*q*t^2*v0-3*a*b*d^2*r^2*t*v1+2*a*b*d^2*r*s^2*v1-2*a*b*d^2*
r*s*t*v0+2*a*b*d*e*p^2*t*v4+a*b*d*e*p*q*s*v4+a*b*d*e*p*q*t*v3+3*a*b*d*e*p*r*s*
v3-3*a*b*d*e*p*r*t*v2-3*a*b*d*e*p*s^2*v2-4*a*b*d*e*p*s*t*v1-a*b*d*e*p*t^2*v0+2*
a*b*d*e*q^2*t*v2+3*a*b*d*e*q*r*s*v2-a*b*d*e*q*r*t*v1-2*a*b*d*e*q*s^2*v1-2*a*b*d
*e*q*s*t*v0+3*a*b*d*e*r^2*s*v1-3*a*b*d*e*r^2*t*v0+2*a*b*e^2*p^2*t*v3+a*b*e^2*p*
q*s*v3+a*b*e^2*p*q*t*v2+2*a*b*e^2*p*r*t*v1-a*b*e^2*p*s^2*v1-a*b*e^2*p*s*t*v0+a*
b*e^2*q^2*s*v2-a*b*e^2*q^2*t*v1+a*b*e^2*q*r*s*v1-a*b*e^2*q*r*t*v0+2*a*c^3*p*r*t
*v4-a*c^3*p*s*t*v3-2*a*c^3*q*r*t*v3+2*a*c^3*q*t^2*v1+a*c^3*r^3*v4-a*c^3*r^2*s*
v3-a*c^3*r^2*t*v2+a*c^3*r*s^2*v2+a*c^3*r*s*t*v1+2*a*c^3*r*t^2*v0-a*c^3*s^3*v1-a
*c^3*s^2*t*v0+2*a*c^2*d*p*q*t*v4+a*c^2*d*p*r*s*v4+a*c^2*d*p*r*t*v3-a*c^2*d*p*s^
2*v3+2*a*c^2*d*p*s*t*v2-a*c^2*d*p*t^2*v1-2*a*c^2*d*q^2*t*v3+2*a*c^2*d*q*r^2*v4-\
2*a*c^2*d*q*r*s*v3+2*a*c^2*d*q*r*t*v2+4*a*c^2*d*q*s*t*v1+4*a*c^2*d*r^2*t*v1-a*c
^2*d*r*s^2*v1+3*a*c^2*d*r*s*t*v0+a*c^2*e*p^2*t*v4-a*c^2*e*p*q*t*v3+a*c^2*e*p*r^
2*v4+a*c^2*e*p*r*s*v3-4*a*c^2*e*p*r*t*v2+2*a*c^2*e*p*s*t*v1+2*a*c^2*e*p*t^2*v0+
2*a*c^2*e*q*r*s*v2-3*a*c^2*e*q*r*t*v1-2*a*c^2*e*q*s^2*v1-2*a*c^2*e*q*s*t*v0+2*a
*c^2*e*r^2*s*v1-3*a*c^2*e*r^2*t*v0+a*c*d^2*p^2*t*v4+a*c*d^2*p*q*s*v4+a*c*d^2*p*
r^2*v4-2*a*c*d^2*p*r*s*v3-a*c*d^2*p*r*t*v2+a*c*d^2*p*s^2*v2+2*a*c*d^2*p*s*t*v1+
a*c*d^2*p*t^2*v0+a*c*d^2*q^2*r*v4-a*c*d^2*q^2*s*v3+3*a*c*d^2*q^2*t*v2-a*c*d^2*q
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v1-2*b^2*d*e*q*s*v4+2*b^2*d*e*r*s*v3-b^2*d*e*r*t*v2+b^2*d*e*s^2*v2-2*b^2*d*e*s*
t*v1-3*b^2*d*e*t^2*v0-b^2*e^2*p*s*v4-2*b^2*e^2*q*t*v2+b^2*e^2*r*s*v2+b^2*e^2*s^
2*v1+b^2*e^2*s*t*v0+2*b*c^3*r*t*v4-b*c^3*t^2*v2+2*b*c^2*d*q*t*v4-3*b*c^2*d*r*s*
v4+b*c^2*d*r*t*v3+b*c^2*d*s*t*v2-3*b*c^2*d*t^2*v1+b*c^2*e*p*t*v4-2*b*c^2*e*q*s*
v4+2*b*c^2*e*q*t*v3+3*b*c^2*e*r*s*v3-2*b*c^2*e*r*t*v2-b*c^2*e*s^2*v2+b*c^2*e*s*
t*v1+2*b*c^2*e*t^2*v0+b*c*d^2*p*t*v4-b*c*d^2*q*s*v4-b*c*d^2*q*t*v3-b*c*d^2*r*s*
v3+2*b*c*d^2*s*t*v1+2*b*c*d^2*t^2*v0-3*b*c*d*e*p*s*v4+2*b*c*d*e*p*t*v3-3*b*c*d*
e*q*r*v4+4*b*c*d*e*q*s*v3+b*c*d*e*q*t*v2+3*b*c*d*e*r^2*v3-b*c*d*e*r*s*v2-2*b*c*
d*e*s^2*v1-2*b*c*d*e*s*t*v0-b*c*e^2*p*s*v3+b*c*e^2*p*t*v2-b*c*e^2*q^2*v4+b*c*e^
2*q*r*v3-b*c*e^2*q*s*v2+4*b*c*e^2*q*t*v1+5*b*c*e^2*r*t*v0-b*d^3*p*s*v4+b*d^3*q*
r*v4-b*d^3*q*t*v2-b*d^3*r^2*v3+b*d^3*r*s*v2+2*b*d^3*r*t*v1+2*b*d^2*e*p*s*v3-4*b
*d^2*e*p*t*v2-b*d^2*e*q^2*v4+b*d^2*e*q*r*v3-b*d^2*e*q*t*v1-3*b*d^2*e*r*s*v1-4*b
*d^2*e*r*t*v0-2*b*d*e^2*p*q*v4+2*b*d*e^2*p*r*v3+4*b*d*e^2*p*s*v2+2*b*d*e^2*q*s*
v1-2*b*d*e^2*q*t*v0+4*b*d*e^2*r*s*v0-b*e^3*p*q*v3+b*e^3*p*r*v2+b*e^3*p*s*v1+b*e
^3*p*t*v0-b*e^3*q^2*v2+b*e^3*r^2*v0+c^4*r*s*v4-c^4*r*t*v3+c^4*t^2*v1+c^3*d*q*s*
v4-c^3*d*q*t*v3-c^3*d*r^2*v4+c^3*d*r*t*v2-c^3*d*s*t*v1-c^3*d*t^2*v0+c^3*e*q*s*
v3+c^3*e*r^2*v3-c^3*e*r*s*v2+c^3*e*s^2*v1+c^3*e*s*t*v0+c^2*d^2*p*s*v4-c^2*d^2*p
*t*v3-2*c^2*d^2*q*r*v4-c^2*d^2*q*s*v3+c^2*d^2*q*t*v2-c^2*d^2*r*t*v1-4*c^2*d*e*p
*r*v4+2*c^2*d*e*p*s*v3+5*c^2*d*e*q*r*v3-2*c^2*d*e*q*s*v2-5*c^2*d*e*q*t*v1+c^2*d
*e*r*s*v1-2*c^2*d*e*r*t*v0-c^2*e^2*p*q*v4+c^2*e^2*p*r*v3-2*c^2*e^2*p*t*v1+c^2*e
^2*q^2*v3+3*c^2*e^2*q*s*v1+c^2*e^2*q*t*v0+2*c^2*e^2*r*s*v0-c*d^3*p*s*v3+c*d^3*p
*t*v2-c*d^3*q^2*v4-c*d^3*q*r*v3+c*d^3*q*s*v2+2*c*d^3*q*t*v1+c*d^3*r*t*v0-2*c*d^
2*e*p*q*v4+c*d^2*e*p*r*v3-3*c*d^2*e*p*s*v2+c*d^2*e*p*t*v1+2*c*d^2*e*q^2*v3-3*c*
d^2*e*q*r*v2-3*c*d^2*e*q*s*v1+c*d^2*e*q*t*v0-3*c*d^2*e*r^2*v1-4*c*d^2*e*r*s*v0-\
2*c*d*e^2*p^2*v4+3*c*d*e^2*p*q*v3+3*c*d*e^2*p*r*v2-c*d*e^2*q^2*v2+2*c*d*e^2*q*r
*v1+3*c*d*e^2*r^2*v0-c*e^3*p^2*v3+c*e^3*p*q*v2-c*e^3*p*r*v1+2*c*e^3*q^2*v1+2*c*
e^3*q*r*v0-d^4*p*q*v4+d^4*p*s*v2+d^4*q*r*v2-d^4*q*t*v0+d^4*r^2*v1+d^4*r*s*v0-d^
3*e*p^2*v4+d^3*e*p*q*v3-d^3*e*p*r*v2-d^3*e*p*s*v1-d^3*e*p*t*v0-d^3*e*q^2*v2-2*d
^3*e*q*r*v1-d^3*e*r^2*v0+d^2*e^2*p^2*v3-d^2*e^2*p*q*v2-2*d^2*e^2*p*r*v1+d^2*e^2
*q^2*v1+d^2*e^2*q*r*v0+3*d*e^3*p^2*v2+3*d*e^3*p*q*v1+3*d*e^3*p*r*v0+2*a*c*e^2*t
*v4+2*a*d^2*e*t*v4+a*d*e^2*s*v4-3*a*d*e^2*t*v3+a*e^3*r*v4-a*e^3*s*v3-a*e^3*t*v2
+b^2*e^2*t*v4-b*c*d*e*t*v4+2*b*c*e^2*s*v4-3*b*c*e^2*t*v3-b*d^3*t*v4+b*d^2*e*s*
v4+2*b*d^2*e*t*v3-2*b*d*e^2*s*v3+2*b*d*e^2*t*v2+b*e^3*q*v4-b*e^3*r*v3-b*e^3*s*
v2-b*e^3*t*v1-c^3*e*t*v4+c^2*d^2*t*v4-c^2*d*e*s*v4+2*c^2*d*e*t*v3-c^2*e^2*s*v3+
c^2*e^2*t*v2-c*d^3*t*v3+3*c*d^2*e*r*v4+c*d^2*e*s*v3-3*c*d^2*e*t*v2+c*d*e^2*q*v4
-3*c*d*e^2*r*v3+2*c*d*e^2*s*v2+2*c*d*e^2*t*v1+c*e^3*p*v4-2*c*e^3*q*v3-c*e^3*s*
v1-c*e^3*t*v0-d^4*r*v4+d^4*t*v2+d^3*e*q*v4+d^3*e*r*v3-d^3*e*s*v2-d^3*e*t*v1+2*d
^2*e^2*p*v4-d^2*e^2*q*v3+d^2*e^2*s*v1+d^2*e^2*t*v0-2*d*e^3*p*v3+d*e^3*q*v2+d*e^
3*r*v1-e^4*p*v2-e^4*q*v1-e^4*r*v0-d*e^3*v4+e^4*v3




beta[5,5] = a^4*t^4*v0+a^3*b*p*t^3*v3+a^3*b*q*t^3*v2+a^3*b*r*t^3*v1+4*a^3*b*s*t
^3*v0+a^3*c*p*t^3*v2+a^3*c*q*t^3*v1+3*a^3*c*r*t^3*v0+a^3*d*p*t^3*v1+2*a^3*d*q*t
^3*v0+a^3*e*p*t^3*v0+3*a^2*b^2*p*s*t^2*v3-a^2*b^2*p*t^3*v2+3*a^2*b^2*q*s*t^2*v2
-a^2*b^2*q*t^3*v1+3*a^2*b^2*r*s*t^2*v1+6*a^2*b^2*s^2*t^2*v0+3*a^2*b*c*p*r*t^2*
v3+2*a^2*b*c*p*s*t^2*v2-2*a^2*b*c*p*t^3*v1+3*a^2*b*c*q*r*t^2*v2+2*a^2*b*c*q*s*t
^2*v1+a^2*b*c*q*t^3*v0+3*a^2*b*c*r^2*t^2*v1+9*a^2*b*c*r*s*t^2*v0+2*a^2*b*d*p*q*
t^2*v3+2*a^2*b*d*p*s*t^2*v1+2*a^2*b*d*p*t^3*v0+2*a^2*b*d*q^2*t^2*v2+2*a^2*b*d*q
*r*t^2*v1+6*a^2*b*d*q*s*t^2*v0+a^2*b*e*p^2*t^2*v3+a^2*b*e*p*q*t^2*v2+a^2*b*e*p*
r*t^2*v1+3*a^2*b*e*p*s*t^2*v0+a^2*c^2*p*q*t^2*v3+2*a^2*c^2*p*r*t^2*v2-a^2*c^2*p
*s*t^2*v1+a^2*c^2*p*t^3*v0+a^2*c^2*q^2*t^2*v2+3*a^2*c^2*q*r*t^2*v1+a^2*c^2*q*s*
t^2*v0+3*a^2*c^2*r^2*t^2*v0+2*a^2*c*d*p^2*t^2*v3+4*a^2*c*d*p*q*t^2*v2+3*a^2*c*d
*p*r*t^2*v1+3*a^2*c*d*p*s*t^2*v0+2*a^2*c*d*q^2*t^2*v1+4*a^2*c*d*q*r*t^2*v0+a^2*
c*e*p^2*t^2*v2+a^2*c*e*p*q*t^2*v1+2*a^2*c*e*p*r*t^2*v0+a^2*d^2*p^2*t^2*v2+2*a^2
*d^2*p*q*t^2*v1+a^2*d^2*p*r*t^2*v0+a^2*d^2*q^2*t^2*v0+a^2*d*e*p^2*t^2*v1+a^2*d*
e*p*q*t^2*v0+3*a*b^3*p*s^2*t*v3-2*a*b^3*p*s*t^2*v2+a*b^3*p*t^3*v1+3*a*b^3*q*s^2
*t*v2-2*a*b^3*q*s*t^2*v1+3*a*b^3*r*s^2*t*v1+4*a*b^3*s^3*t*v0+6*a*b^2*c*p*r*s*t*
v3-2*a*b^2*c*p*r*t^2*v2+a*b^2*c*p*s^2*t*v2-2*a*b^2*c*p*s*t^2*v1-a*b^2*c*p*t^3*
v0+6*a*b^2*c*q*r*s*t*v2-2*a*b^2*c*q*r*t^2*v1+a*b^2*c*q*s^2*t*v1+2*a*b^2*c*q*s*t
^2*v0+6*a*b^2*c*r^2*s*t*v1+9*a*b^2*c*r*s^2*t*v0+a*b^2*d*p^2*t^2*v3+4*a*b^2*d*p*
q*s*t*v3-a*b^2*d*p*q*t^2*v2+2*a*b^2*d*p*r*t^2*v1+a*b^2*d*p*s^2*t*v1+4*a*b^2*d*p
*s*t^2*v0+4*a*b^2*d*q^2*s*t*v2-2*a*b^2*d*q^2*t^2*v1+4*a*b^2*d*q*r*s*t*v1+6*a*b^
2*d*q*s^2*t*v0+2*a*b^2*e*p^2*s*t*v3-a*b^2*e*p^2*t^2*v2+2*a*b^2*e*p*q*s*t*v2-a*b
^2*e*p*q*t^2*v1+2*a*b^2*e*p*r*s*t*v1+3*a*b^2*e*p*s^2*t*v0-a*b*c^2*p^2*t^2*v3+2*
a*b*c^2*p*q*s*t*v3-a*b*c^2*p*q*t^2*v2+3*a*b*c^2*p*r^2*t*v3+2*a*b*c^2*p*r*s*t*v2
-4*a*b*c^2*p*r*t^2*v1-a*b*c^2*p*s^2*t*v1+2*a*b*c^2*q^2*s*t*v2+3*a*b*c^2*q*r^2*t
*v2+4*a*b*c^2*q*r*s*t*v1+2*a*b*c^2*q*r*t^2*v0+2*a*b*c^2*q*s^2*t*v0+3*a*b*c^2*r^
3*t*v1+6*a*b*c^2*r^2*s*t*v0+5*a*b*c*d*p^2*s*t*v3-2*a*b*c*d*p^2*t^2*v2+4*a*b*c*d
*p*q*r*t*v3+7*a*b*c*d*p*q*s*t*v2-3*a*b*c*d*p*q*t^2*v1+6*a*b*c*d*p*r*s*t*v1+2*a*
b*c*d*p*r*t^2*v0+6*a*b*c*d*p*s^2*t*v0+4*a*b*c*d*q^2*r*t*v2+2*a*b*c*d*q^2*s*t*v1
+2*a*b*c*d*q^2*t^2*v0+4*a*b*c*d*q*r^2*t*v1+8*a*b*c*d*q*r*s*t*v0+2*a*b*c*e*p^2*r
*t*v3+a*b*c*e*p^2*s*t*v2-2*a*b*c*e*p^2*t^2*v1+2*a*b*c*e*p*q*r*t*v2+a*b*c*e*p*q*
s*t*v1+a*b*c*e*p*q*t^2*v0+2*a*b*c*e*p*r^2*t*v1+4*a*b*c*e*p*r*s*t*v0+a*b*d^2*p^2
*r*t*v3+a*b*d^2*p^2*s*t*v2+a*b*d^2*p^2*t^2*v1+a*b*d^2*p*q^2*t*v3+a*b*d^2*p*q*r*
t*v2+2*a*b*d^2*p*q*s*t*v1+3*a*b*d^2*p*q*t^2*v0+a*b*d^2*p*r^2*t*v1+2*a*b*d^2*p*r
*s*t*v0+a*b*d^2*q^3*t*v2+a*b*d^2*q^2*r*t*v1+2*a*b*d^2*q^2*s*t*v0+a*b*d*e*p^2*q*
t*v3+a*b*d*e*p^2*s*t*v1+2*a*b*d*e*p^2*t^2*v0+a*b*d*e*p*q^2*t*v2+a*b*d*e*p*q*r*t
*v1+2*a*b*d*e*p*q*s*t*v0-a*c^3*p^2*s*t*v3+a*c^3*p^2*t^2*v2+2*a*c^3*p*q*r*t*v3-a
*c^3*p*q*s*t*v2+a*c^3*p*r^2*t*v2-2*a*c^3*p*r*s*t*v1+2*a*c^3*p*r*t^2*v0-a*c^3*p*
s^2*t*v0+2*a*c^3*q^2*r*t*v2+3*a*c^3*q*r^2*t*v1+2*a*c^3*q*r*s*t*v0+a*c^3*r^3*t*
v0+3*a*c^2*d*p^2*r*t*v3-a*c^2*d*p^2*t^2*v1+2*a*c^2*d*p*q^2*t*v3+5*a*c^2*d*p*q*r
*t*v2-a*c^2*d*p*q*s*t*v1+2*a*c^2*d*p*q*t^2*v0+3*a*c^2*d*p*r^2*t*v1+4*a*c^2*d*p*
r*s*t*v0+2*a*c^2*d*q^3*t*v2+4*a*c^2*d*q^2*r*t*v1+2*a*c^2*d*q^2*s*t*v0+2*a*c^2*d
*q*r^2*t*v0+a*c^2*e*p^2*q*t*v3+a*c^2*e*p^2*r*t*v2-a*c^2*e*p^2*s*t*v1+a*c^2*e*p^
2*t^2*v0+a*c^2*e*p*q^2*t*v2+2*a*c^2*e*p*q*r*t*v1+a*c^2*e*p*q*s*t*v0+a*c^2*e*p*r
^2*t*v0+4*a*c*d^2*p^2*q*t*v3+a*c*d^2*p^2*r*t*v2+a*c*d^2*p^2*t^2*v0+5*a*c*d^2*p*
q^2*t*v2+5*a*c*d^2*p*q*r*t*v1+5*a*c*d^2*p*q*s*t*v0+a*c*d^2*p*r^2*t*v0+a*c*d^2*q
^3*t*v1+a*c*d^2*q^2*r*t*v0+2*a*c*d*e*p^3*t*v3+3*a*c*d*e*p^2*q*t*v2+2*a*c*d*e*p^
2*r*t*v1+3*a*c*d*e*p^2*s*t*v0+a*c*d*e*p*q^2*t*v1+a*c*d*e*p*q*r*t*v0+a*d^3*p^3*t
*v3+2*a*d^3*p^2*q*t*v2+a*d^3*p^2*r*t*v1+a*d^3*p^2*s*t*v0+a*d^3*p*q^2*t*v1+a*d^3
*p*q*r*t*v0+a*d^2*e*p^3*t*v2+a*d^2*e*p^2*q*t*v1+a*d^2*e*p^2*r*t*v0+b^4*p*s^3*v3
-b^4*p*s^2*t*v2+b^4*p*s*t^2*v1+b^4*q*s^3*v2-b^4*q*s^2*t*v1+b^4*r*s^3*v1+b^4*s^4
*v0+3*b^3*c*p*r*s^2*v3-2*b^3*c*p*r*s*t*v2+b^3*c*p*r*t^2*v1-b^3*c*p*s*t^2*v0+3*b
^3*c*q*r*s^2*v2-2*b^3*c*q*r*s*t*v1+b^3*c*q*s^2*t*v0+3*b^3*c*r^2*s^2*v1+3*b^3*c*
r*s^3*v0+b^3*d*p^2*s*t*v3+2*b^3*d*p*q*s^2*v3-b^3*d*p*q*s*t*v2+b^3*d*p*q*t^2*v1+
2*b^3*d*p*r*s*t*v1+2*b^3*d*p*s^2*t*v0+2*b^3*d*q^2*s^2*v2-2*b^3*d*q^2*s*t*v1+2*b
^3*d*q*r*s^2*v1+2*b^3*d*q*s^3*v0+b^3*e*p^2*s^2*v3-b^3*e*p^2*s*t*v2+b^3*e*p^2*t^
2*v1+b^3*e*p*q*s^2*v2-b^3*e*p*q*s*t*v1+b^3*e*p*r*s^2*v1+b^3*e*p*s^3*v0-b^2*c^2*
p^2*s*t*v3+b^2*c^2*p*q*s^2*v3-b^2*c^2*p*q*s*t*v2+3*b^2*c^2*p*r^2*s*v3-b^2*c^2*p
*r^2*t*v2-2*b^2*c^2*p*r*s*t*v1-b^2*c^2*p*r*t^2*v0-b^2*c^2*p*s^2*t*v0+b^2*c^2*q^
2*s^2*v2+3*b^2*c^2*q*r^2*s*v2-b^2*c^2*q*r^2*t*v1+b^2*c^2*q*r*s^2*v1+2*b^2*c^2*q
*r*s*t*v0+b^2*c^2*q*s^3*v0+3*b^2*c^2*r^3*s*v1+3*b^2*c^2*r^2*s^2*v0+b^2*c*d*p^2*
r*t*v3+3*b^2*c*d*p^2*s^2*v3-2*b^2*c*d*p^2*s*t*v2+4*b^2*c*d*p*q*r*s*v3-b^2*c*d*p
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*v4-3*c*d^2*e*t*v3-3*c*d*e^2*r*v4+2*c*d*e^2*t*v2-2*c*e^3*q*v4-c*e^3*t*v1-d^4*s*
v4+d^4*t*v3+d^3*e*r*v4-d^3*e*t*v2-d^2*e^2*q*v4+d^2*e^2*t*v1-3*d*e^3*p*v4-d*e^3*
t*v0-e^4*p*v3-e^4*q*v2-e^4*r*v1-e^4*s*v0+e^4*v4




                    ----------------------------------------





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          This ends this paper that took, 1.577, seconds to generate