3.275 \(\int \frac {1}{(d+e x^2)^2 (a+b x^2+c x^4)^2} \, dx\)

Optimal. Leaf size=1077 \[ \frac {x e^4}{2 d \left (c d^2-b e d+a e^2\right )^2 \left (e x^2+d\right )}+\frac {\tan ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {d}}\right ) e^{7/2}}{2 d^{3/2} \left (c d^2-b e d+a e^2\right )^2}+\frac {2 (2 c d-b e) \tan ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {d}}\right ) e^{7/2}}{\sqrt {d} \left (c d^2-b e d+a e^2\right )^3}+\frac {\sqrt {2} \sqrt {c} \left (3 c^2 d^2+b \left (b+\sqrt {b^2-4 a c}\right ) e^2-c e \left (3 b d+2 \sqrt {b^2-4 a c} d+a e\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right ) e^2}{\sqrt {b^2-4 a c} \sqrt {b-\sqrt {b^2-4 a c}} \left (c d^2-b e d+a e^2\right )^3}-\frac {\sqrt {2} \sqrt {c} \left (3 c^2 d^2+b \left (b-\sqrt {b^2-4 a c}\right ) e^2-c e \left (3 b d-2 \sqrt {b^2-4 a c} d+a e\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b+\sqrt {b^2-4 a c}}}\right ) e^2}{\sqrt {b^2-4 a c} \sqrt {b+\sqrt {b^2-4 a c}} \left (c d^2-b e d+a e^2\right )^3}+\frac {\sqrt {c} \left (e^2 b^4-e \left (2 c d-\sqrt {b^2-4 a c} e\right ) b^3+c \left (c d^2-e \left (2 \sqrt {b^2-4 a c} d+9 a e\right )\right ) b^2-c \left (3 a \sqrt {b^2-4 a c} e^2-c d \left (\sqrt {b^2-4 a c} d+16 a e\right )\right ) b-4 a c^2 \left (3 c d^2-e \left (\sqrt {b^2-4 a c} d+3 a e\right )\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{2 \sqrt {2} a \left (b^2-4 a c\right )^{3/2} \sqrt {b-\sqrt {b^2-4 a c}} \left (c d^2-b e d+a e^2\right )^2}-\frac {\sqrt {c} \left (e^2 b^4-e \left (2 c d+\sqrt {b^2-4 a c} e\right ) b^3+c \left (c d^2+e \left (2 \sqrt {b^2-4 a c} d-9 a e\right )\right ) b^2+c \left (3 a \sqrt {b^2-4 a c} e^2-c d \left (\sqrt {b^2-4 a c} d-16 a e\right )\right ) b-4 a c^2 \left (3 c d^2+e \left (\sqrt {b^2-4 a c} d-3 a e\right )\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b+\sqrt {b^2-4 a c}}}\right )}{2 \sqrt {2} a \left (b^2-4 a c\right )^{3/2} \sqrt {b+\sqrt {b^2-4 a c}} \left (c d^2-b e d+a e^2\right )^2}+\frac {x \left (-c \left (-e^2 b^3+2 c d e b^2-c \left (c d^2-3 a e^2\right ) b-4 a c^2 d e\right ) x^2+a b c e (2 c d-b e)+\left (b^2-2 a c\right ) \left (c^2 d^2+b^2 e^2-c e (2 b d+a e)\right )\right )}{2 a \left (b^2-4 a c\right ) \left (c d^2-b e d+a e^2\right )^2 \left (c x^4+b x^2+a\right )} \]

[Out]

1/2*e^4*x/d/(a*e^2-b*d*e+c*d^2)^2/(e*x^2+d)+1/2*x*(a*b*c*e*(-b*e+2*c*d)+(-2*a*c+b^2)*(c^2*d^2+b^2*e^2-c*e*(a*e
+2*b*d))-c*(2*b^2*c*d*e-4*a*c^2*d*e-b^3*e^2-b*c*(-3*a*e^2+c*d^2))*x^2)/a/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)^2/(c
*x^4+b*x^2+a)+1/2*e^(7/2)*arctan(x*e^(1/2)/d^(1/2))/d^(3/2)/(a*e^2-b*d*e+c*d^2)^2+2*e^(7/2)*(-b*e+2*c*d)*arcta
n(x*e^(1/2)/d^(1/2))/(a*e^2-b*d*e+c*d^2)^3/d^(1/2)+e^2*arctan(x*2^(1/2)*c^(1/2)/(b-(-4*a*c+b^2)^(1/2))^(1/2))*
2^(1/2)*c^(1/2)*(3*c^2*d^2+b*e^2*(b+(-4*a*c+b^2)^(1/2))-c*e*(3*b*d+a*e+2*d*(-4*a*c+b^2)^(1/2)))/(a*e^2-b*d*e+c
*d^2)^3/(-4*a*c+b^2)^(1/2)/(b-(-4*a*c+b^2)^(1/2))^(1/2)+1/4*arctan(x*2^(1/2)*c^(1/2)/(b-(-4*a*c+b^2)^(1/2))^(1
/2))*c^(1/2)*(b^4*e^2-b^3*e*(2*c*d-e*(-4*a*c+b^2)^(1/2))-4*a*c^2*(3*c*d^2-e*(3*a*e+d*(-4*a*c+b^2)^(1/2)))-b*c*
(3*a*e^2*(-4*a*c+b^2)^(1/2)-c*d*(16*a*e+d*(-4*a*c+b^2)^(1/2)))+b^2*c*(c*d^2-e*(9*a*e+2*d*(-4*a*c+b^2)^(1/2))))
/a/(-4*a*c+b^2)^(3/2)/(a*e^2-b*d*e+c*d^2)^2*2^(1/2)/(b-(-4*a*c+b^2)^(1/2))^(1/2)-e^2*arctan(x*2^(1/2)*c^(1/2)/
(b+(-4*a*c+b^2)^(1/2))^(1/2))*2^(1/2)*c^(1/2)*(3*c^2*d^2+b*e^2*(b-(-4*a*c+b^2)^(1/2))-c*e*(3*b*d+a*e-2*d*(-4*a
*c+b^2)^(1/2)))/(a*e^2-b*d*e+c*d^2)^3/(-4*a*c+b^2)^(1/2)/(b+(-4*a*c+b^2)^(1/2))^(1/2)-1/4*arctan(x*2^(1/2)*c^(
1/2)/(b+(-4*a*c+b^2)^(1/2))^(1/2))*c^(1/2)*(b^4*e^2-b^3*e*(2*c*d+e*(-4*a*c+b^2)^(1/2))+b*c*(3*a*e^2*(-4*a*c+b^
2)^(1/2)-c*d*(-16*a*e+d*(-4*a*c+b^2)^(1/2)))-4*a*c^2*(3*c*d^2+e*(-3*a*e+d*(-4*a*c+b^2)^(1/2)))+b^2*c*(c*d^2+e*
(-9*a*e+2*d*(-4*a*c+b^2)^(1/2))))/a/(-4*a*c+b^2)^(3/2)/(a*e^2-b*d*e+c*d^2)^2*2^(1/2)/(b+(-4*a*c+b^2)^(1/2))^(1
/2)

________________________________________________________________________________________

Rubi [A]  time = 12.64, antiderivative size = 1077, normalized size of antiderivative = 1.00, number of steps used = 12, number of rules used = 5, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.208, Rules used = {1238, 199, 205, 1178, 1166} \[ \frac {x e^4}{2 d \left (c d^2-b e d+a e^2\right )^2 \left (e x^2+d\right )}+\frac {\tan ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {d}}\right ) e^{7/2}}{2 d^{3/2} \left (c d^2-b e d+a e^2\right )^2}+\frac {2 (2 c d-b e) \tan ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {d}}\right ) e^{7/2}}{\sqrt {d} \left (c d^2-b e d+a e^2\right )^3}+\frac {\sqrt {2} \sqrt {c} \left (3 c^2 d^2+b \left (b+\sqrt {b^2-4 a c}\right ) e^2-c e \left (3 b d+2 \sqrt {b^2-4 a c} d+a e\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right ) e^2}{\sqrt {b^2-4 a c} \sqrt {b-\sqrt {b^2-4 a c}} \left (c d^2-b e d+a e^2\right )^3}-\frac {\sqrt {2} \sqrt {c} \left (3 c^2 d^2+b \left (b-\sqrt {b^2-4 a c}\right ) e^2-c e \left (3 b d-2 \sqrt {b^2-4 a c} d+a e\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b+\sqrt {b^2-4 a c}}}\right ) e^2}{\sqrt {b^2-4 a c} \sqrt {b+\sqrt {b^2-4 a c}} \left (c d^2-b e d+a e^2\right )^3}+\frac {\sqrt {c} \left (e^2 b^4-e \left (2 c d-\sqrt {b^2-4 a c} e\right ) b^3+c \left (c d^2-e \left (2 \sqrt {b^2-4 a c} d+9 a e\right )\right ) b^2-c \left (3 a \sqrt {b^2-4 a c} e^2-c d \left (\sqrt {b^2-4 a c} d+16 a e\right )\right ) b-4 a c^2 \left (3 c d^2-e \left (\sqrt {b^2-4 a c} d+3 a e\right )\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{2 \sqrt {2} a \left (b^2-4 a c\right )^{3/2} \sqrt {b-\sqrt {b^2-4 a c}} \left (c d^2-b e d+a e^2\right )^2}-\frac {\sqrt {c} \left (e^2 b^4-e \left (2 c d+\sqrt {b^2-4 a c} e\right ) b^3+c \left (c d^2+e \left (2 \sqrt {b^2-4 a c} d-9 a e\right )\right ) b^2+c \left (3 a \sqrt {b^2-4 a c} e^2-c d \left (\sqrt {b^2-4 a c} d-16 a e\right )\right ) b-4 a c^2 \left (3 c d^2+e \left (\sqrt {b^2-4 a c} d-3 a e\right )\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b+\sqrt {b^2-4 a c}}}\right )}{2 \sqrt {2} a \left (b^2-4 a c\right )^{3/2} \sqrt {b+\sqrt {b^2-4 a c}} \left (c d^2-b e d+a e^2\right )^2}+\frac {x \left (-c \left (-e^2 b^3+2 c d e b^2-c \left (c d^2-3 a e^2\right ) b-4 a c^2 d e\right ) x^2+a b c e (2 c d-b e)+\left (b^2-2 a c\right ) \left (c^2 d^2+b^2 e^2-c e (2 b d+a e)\right )\right )}{2 a \left (b^2-4 a c\right ) \left (c d^2-b e d+a e^2\right )^2 \left (c x^4+b x^2+a\right )} \]

Antiderivative was successfully verified.

[In]

Int[1/((d + e*x^2)^2*(a + b*x^2 + c*x^4)^2),x]

[Out]

(e^4*x)/(2*d*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x^2)) + (x*(a*b*c*e*(2*c*d - b*e) + (b^2 - 2*a*c)*(c^2*d^2 + b^2
*e^2 - c*e*(2*b*d + a*e)) - c*(2*b^2*c*d*e - 4*a*c^2*d*e - b^3*e^2 - b*c*(c*d^2 - 3*a*e^2))*x^2))/(2*a*(b^2 -
4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x^2 + c*x^4)) + (Sqrt[2]*Sqrt[c]*e^2*(3*c^2*d^2 + b*(b + Sqrt[b^2 - 4*
a*c])*e^2 - c*e*(3*b*d + 2*Sqrt[b^2 - 4*a*c]*d + a*e))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]]
)/(Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]*(c*d^2 - b*d*e + a*e^2)^3) + (Sqrt[c]*(b^4*e^2 - b^3*e*(2*c*d
- Sqrt[b^2 - 4*a*c]*e) - 4*a*c^2*(3*c*d^2 - e*(Sqrt[b^2 - 4*a*c]*d + 3*a*e)) + b^2*c*(c*d^2 - e*(2*Sqrt[b^2 -
4*a*c]*d + 9*a*e)) - b*c*(3*a*Sqrt[b^2 - 4*a*c]*e^2 - c*d*(Sqrt[b^2 - 4*a*c]*d + 16*a*e)))*ArcTan[(Sqrt[2]*Sq
rt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*(c*d^2 - b
*d*e + a*e^2)^2) - (Sqrt[2]*Sqrt[c]*e^2*(3*c^2*d^2 + b*(b - Sqrt[b^2 - 4*a*c])*e^2 - c*e*(3*b*d - 2*Sqrt[b^2 -
4*a*c]*d + a*e))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^
2 - 4*a*c]]*(c*d^2 - b*d*e + a*e^2)^3) - (Sqrt[c]*(b^4*e^2 - b^3*e*(2*c*d + Sqrt[b^2 - 4*a*c]*e) + b*c*(3*a*Sq
rt[b^2 - 4*a*c]*e^2 - c*d*(Sqrt[b^2 - 4*a*c]*d - 16*a*e)) + b^2*c*(c*d^2 + e*(2*Sqrt[b^2 - 4*a*c]*d - 9*a*e))
- 4*a*c^2*(3*c*d^2 + e*(Sqrt[b^2 - 4*a*c]*d - 3*a*e)))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]]
)/(2*Sqrt[2]*a*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*(c*d^2 - b*d*e + a*e^2)^2) + (2*e^(7/2)*(2*c*d
- b*e)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*(c*d^2 - b*d*e + a*e^2)^3) + (e^(7/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]]
)/(2*d^(3/2)*(c*d^2 - b*d*e + a*e^2)^2)

Rule 199

Int[((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> -Simp[(x*(a + b*x^n)^(p + 1))/(a*n*(p + 1)), x] + Dist[(n*(p +
1) + 1)/(a*n*(p + 1)), Int[(a + b*x^n)^(p + 1), x], x] /; FreeQ[{a, b}, x] && IGtQ[n, 0] && LtQ[p, -1] && (In
tegerQ[2*p] || (n == 2 && IntegerQ[4*p]) || (n == 2 && IntegerQ[3*p]) || Denominator[p + 1/n] < Denominator[p]
)

Rule 205

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(Rt[a/b, 2]*ArcTan[x/Rt[a/b, 2]])/a, x] /; FreeQ[{a, b}, x]
&& PosQ[a/b]

Rule 1166

Int[((d_) + (e_.)*(x_)^2)/((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4), x_Symbol] :> With[{q = Rt[b^2 - 4*a*c, 2]}, Di
st[e/2 + (2*c*d - b*e)/(2*q), Int[1/(b/2 - q/2 + c*x^2), x], x] + Dist[e/2 - (2*c*d - b*e)/(2*q), Int[1/(b/2 +
q/2 + c*x^2), x], x]] /; FreeQ[{a, b, c, d, e}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - a*e^2, 0] && PosQ[b^
2 - 4*a*c]

Rule 1178

Int[((d_) + (e_.)*(x_)^2)*((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4)^(p_), x_Symbol] :> Simp[(x*(a*b*e - d*(b^2 - 2*
a*c) - c*(b*d - 2*a*e)*x^2)*(a + b*x^2 + c*x^4)^(p + 1))/(2*a*(p + 1)*(b^2 - 4*a*c)), x] + Dist[1/(2*a*(p + 1)
*(b^2 - 4*a*c)), Int[Simp[(2*p + 3)*d*b^2 - a*b*e - 2*a*c*d*(4*p + 5) + (4*p + 7)*(d*b - 2*a*e)*c*x^2, x]*(a +
b*x^2 + c*x^4)^(p + 1), x], x] /; FreeQ[{a, b, c, d, e}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e
^2, 0] && LtQ[p, -1] && IntegerQ[2*p]

Rule 1238

Int[((d_) + (e_.)*(x_)^2)^(q_)*((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4)^(p_), x_Symbol] :> Int[ExpandIntegrand[(d
+ e*x^2)^q*(a + b*x^2 + c*x^4)^p, x], x] /; FreeQ[{a, b, c, d, e, p, q}, x] && NeQ[b^2 - 4*a*c, 0] && ((Intege
rQ[p] && IntegerQ[q]) || IGtQ[p, 0] || IGtQ[q, 0])

Rubi steps

\begin {align*} \int \frac {1}{\left (d+e x^2\right )^2 \left (a+b x^2+c x^4\right )^2} \, dx &=\int \left (\frac {e^4}{\left (c d^2-b d e+a e^2\right )^2 \left (d+e x^2\right )^2}-\frac {2 e^4 (-2 c d+b e)}{\left (c d^2-b d e+a e^2\right )^3 \left (d+e x^2\right )}+\frac {c^2 d^2+b^2 e^2-c e (2 b d+a e)-c e (2 c d-b e) x^2}{\left (c d^2-b d e+a e^2\right )^2 \left (a+b x^2+c x^4\right )^2}+\frac {e^2 \left (3 c^2 d^2+2 b^2 e^2-c e (5 b d+a e)-2 c e (2 c d-b e) x^2\right )}{\left (c d^2-b d e+a e^2\right )^3 \left (a+b x^2+c x^4\right )}\right ) \, dx\\ &=\frac {e^2 \int \frac {3 c^2 d^2+2 b^2 e^2-c e (5 b d+a e)-2 c e (2 c d-b e) x^2}{a+b x^2+c x^4} \, dx}{\left (c d^2-b d e+a e^2\right )^3}+\frac {\left (2 e^4 (2 c d-b e)\right ) \int \frac {1}{d+e x^2} \, dx}{\left (c d^2-b d e+a e^2\right )^3}+\frac {\int \frac {c^2 d^2+b^2 e^2-c e (2 b d+a e)-c e (2 c d-b e) x^2}{\left (a+b x^2+c x^4\right )^2} \, dx}{\left (c d^2-b d e+a e^2\right )^2}+\frac {e^4 \int \frac {1}{\left (d+e x^2\right )^2} \, dx}{\left (c d^2-b d e+a e^2\right )^2}\\ &=\frac {e^4 x}{2 d \left (c d^2-b d e+a e^2\right )^2 \left (d+e x^2\right )}+\frac {x \left (a b c e (2 c d-b e)+\left (b^2-2 a c\right ) \left (c^2 d^2+b^2 e^2-c e (2 b d+a e)\right )-c \left (2 b^2 c d e-4 a c^2 d e-b^3 e^2-b c \left (c d^2-3 a e^2\right )\right ) x^2\right )}{2 a \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right )^2 \left (a+b x^2+c x^4\right )}+\frac {2 e^{7/2} (2 c d-b e) \tan ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {d}}\right )}{\sqrt {d} \left (c d^2-b d e+a e^2\right )^3}-\frac {\int \frac {2 b^3 c d e-10 a b c^2 d e-b^4 e^2-b^2 c \left (c d^2-6 a e^2\right )+6 a c^2 \left (c d^2-a e^2\right )+c \left (2 b^2 c d e-4 a c^2 d e-b^3 e^2-b c \left (c d^2-3 a e^2\right )\right ) x^2}{a+b x^2+c x^4} \, dx}{2 a \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right )^2}+\frac {e^4 \int \frac {1}{d+e x^2} \, dx}{2 d \left (c d^2-b d e+a e^2\right )^2}-\frac {\left (c e^2 \left (3 c^2 d^2+b \left (b-\sqrt {b^2-4 a c}\right ) e^2-c e \left (3 b d-2 \sqrt {b^2-4 a c} d+a e\right )\right )\right ) \int \frac {1}{\frac {b}{2}+\frac {1}{2} \sqrt {b^2-4 a c}+c x^2} \, dx}{\sqrt {b^2-4 a c} \left (c d^2-b d e+a e^2\right )^3}+\frac {\left (c e^2 \left (3 c^2 d^2+b \left (b+\sqrt {b^2-4 a c}\right ) e^2-c e \left (3 b d+2 \sqrt {b^2-4 a c} d+a e\right )\right )\right ) \int \frac {1}{\frac {b}{2}-\frac {1}{2} \sqrt {b^2-4 a c}+c x^2} \, dx}{\sqrt {b^2-4 a c} \left (c d^2-b d e+a e^2\right )^3}\\ &=\frac {e^4 x}{2 d \left (c d^2-b d e+a e^2\right )^2 \left (d+e x^2\right )}+\frac {x \left (a b c e (2 c d-b e)+\left (b^2-2 a c\right ) \left (c^2 d^2+b^2 e^2-c e (2 b d+a e)\right )-c \left (2 b^2 c d e-4 a c^2 d e-b^3 e^2-b c \left (c d^2-3 a e^2\right )\right ) x^2\right )}{2 a \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right )^2 \left (a+b x^2+c x^4\right )}+\frac {\sqrt {2} \sqrt {c} e^2 \left (3 c^2 d^2+b \left (b+\sqrt {b^2-4 a c}\right ) e^2-c e \left (3 b d+2 \sqrt {b^2-4 a c} d+a e\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{\sqrt {b^2-4 a c} \sqrt {b-\sqrt {b^2-4 a c}} \left (c d^2-b d e+a e^2\right )^3}-\frac {\sqrt {2} \sqrt {c} e^2 \left (3 c^2 d^2+b \left (b-\sqrt {b^2-4 a c}\right ) e^2-c e \left (3 b d-2 \sqrt {b^2-4 a c} d+a e\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b+\sqrt {b^2-4 a c}}}\right )}{\sqrt {b^2-4 a c} \sqrt {b+\sqrt {b^2-4 a c}} \left (c d^2-b d e+a e^2\right )^3}+\frac {2 e^{7/2} (2 c d-b e) \tan ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {d}}\right )}{\sqrt {d} \left (c d^2-b d e+a e^2\right )^3}+\frac {e^{7/2} \tan ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {d}}\right )}{2 d^{3/2} \left (c d^2-b d e+a e^2\right )^2}-\frac {\left (c \left (b^4 e^2-b^3 e \left (2 c d+\sqrt {b^2-4 a c} e\right )+b c \left (3 a \sqrt {b^2-4 a c} e^2-c d \left (\sqrt {b^2-4 a c} d-16 a e\right )\right )+b^2 c \left (c d^2+e \left (2 \sqrt {b^2-4 a c} d-9 a e\right )\right )-4 a c^2 \left (3 c d^2+e \left (\sqrt {b^2-4 a c} d-3 a e\right )\right )\right )\right ) \int \frac {1}{\frac {b}{2}+\frac {1}{2} \sqrt {b^2-4 a c}+c x^2} \, dx}{4 a \left (b^2-4 a c\right )^{3/2} \left (c d^2-b d e+a e^2\right )^2}+\frac {\left (c \left (b^4 e^2-b^3 e \left (2 c d-\sqrt {b^2-4 a c} e\right )-4 a c^2 \left (3 c d^2-e \left (\sqrt {b^2-4 a c} d+3 a e\right )\right )+b^2 c \left (c d^2-e \left (2 \sqrt {b^2-4 a c} d+9 a e\right )\right )-b c \left (3 a \sqrt {b^2-4 a c} e^2-c d \left (\sqrt {b^2-4 a c} d+16 a e\right )\right )\right )\right ) \int \frac {1}{\frac {b}{2}-\frac {1}{2} \sqrt {b^2-4 a c}+c x^2} \, dx}{4 a \left (b^2-4 a c\right )^{3/2} \left (c d^2-b d e+a e^2\right )^2}\\ &=\frac {e^4 x}{2 d \left (c d^2-b d e+a e^2\right )^2 \left (d+e x^2\right )}+\frac {x \left (a b c e (2 c d-b e)+\left (b^2-2 a c\right ) \left (c^2 d^2+b^2 e^2-c e (2 b d+a e)\right )-c \left (2 b^2 c d e-4 a c^2 d e-b^3 e^2-b c \left (c d^2-3 a e^2\right )\right ) x^2\right )}{2 a \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right )^2 \left (a+b x^2+c x^4\right )}+\frac {\sqrt {2} \sqrt {c} e^2 \left (3 c^2 d^2+b \left (b+\sqrt {b^2-4 a c}\right ) e^2-c e \left (3 b d+2 \sqrt {b^2-4 a c} d+a e\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{\sqrt {b^2-4 a c} \sqrt {b-\sqrt {b^2-4 a c}} \left (c d^2-b d e+a e^2\right )^3}+\frac {\sqrt {c} \left (b^4 e^2-b^3 e \left (2 c d-\sqrt {b^2-4 a c} e\right )-4 a c^2 \left (3 c d^2-e \left (\sqrt {b^2-4 a c} d+3 a e\right )\right )+b^2 c \left (c d^2-e \left (2 \sqrt {b^2-4 a c} d+9 a e\right )\right )-b c \left (3 a \sqrt {b^2-4 a c} e^2-c d \left (\sqrt {b^2-4 a c} d+16 a e\right )\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{2 \sqrt {2} a \left (b^2-4 a c\right )^{3/2} \sqrt {b-\sqrt {b^2-4 a c}} \left (c d^2-b d e+a e^2\right )^2}-\frac {\sqrt {2} \sqrt {c} e^2 \left (3 c^2 d^2+b \left (b-\sqrt {b^2-4 a c}\right ) e^2-c e \left (3 b d-2 \sqrt {b^2-4 a c} d+a e\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b+\sqrt {b^2-4 a c}}}\right )}{\sqrt {b^2-4 a c} \sqrt {b+\sqrt {b^2-4 a c}} \left (c d^2-b d e+a e^2\right )^3}-\frac {\sqrt {c} \left (b^4 e^2-b^3 e \left (2 c d+\sqrt {b^2-4 a c} e\right )+b c \left (3 a \sqrt {b^2-4 a c} e^2-c d \left (\sqrt {b^2-4 a c} d-16 a e\right )\right )+b^2 c \left (c d^2+e \left (2 \sqrt {b^2-4 a c} d-9 a e\right )\right )-4 a c^2 \left (3 c d^2+e \left (\sqrt {b^2-4 a c} d-3 a e\right )\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b+\sqrt {b^2-4 a c}}}\right )}{2 \sqrt {2} a \left (b^2-4 a c\right )^{3/2} \sqrt {b+\sqrt {b^2-4 a c}} \left (c d^2-b d e+a e^2\right )^2}+\frac {2 e^{7/2} (2 c d-b e) \tan ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {d}}\right )}{\sqrt {d} \left (c d^2-b d e+a e^2\right )^3}+\frac {e^{7/2} \tan ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {d}}\right )}{2 d^{3/2} \left (c d^2-b d e+a e^2\right )^2}\\ \end {align*}

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Mathematica [A]  time = 5.84, size = 1020, normalized size = 0.95 \[ \frac {1}{4} \left (\frac {2 x e^4}{d \left (c d^2+e (a e-b d)\right )^2 \left (e x^2+d\right )}+\frac {2 \left (9 c d^2+e (a e-5 b d)\right ) \tan ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {d}}\right ) e^{7/2}}{d^{3/2} \left (c d^2+e (a e-b d)\right )^3}-\frac {2 x \left (e^2 b^4+c e \left (e x^2-2 d\right ) b^3+c \left (c d \left (d-2 e x^2\right )-4 a e^2\right ) b^2+c^2 \left (c d^2 x^2-3 a e \left (e x^2-2 d\right )\right ) b+2 a c^2 \left (a e^2-c d \left (d-2 e x^2\right )\right )\right )}{a \left (4 a c-b^2\right ) \left (c d^2+e (a e-b d)\right )^2 \left (c x^4+b x^2+a\right )}+\frac {\sqrt {2} \sqrt {c} \left (d e^3 b^5+e^2 \left (e \left (\sqrt {b^2-4 a c} d-5 a e\right )-3 c d^2\right ) b^4+e \left (c d-\sqrt {b^2-4 a c} e\right ) \left (3 c d^2+5 a e^2\right ) b^3+c \left (-c^2 d^4+3 c e \left (\sqrt {b^2-4 a c} d+4 a e\right ) d^2+a e^3 \left (7 \sqrt {b^2-4 a c} d+29 a e\right )\right ) b^2-c \left (-19 a^2 \sqrt {b^2-4 a c} e^4+2 a c d \left (26 a e-3 \sqrt {b^2-4 a c} d\right ) e^2+c^2 d^3 \left (\sqrt {b^2-4 a c} d+28 a e\right )\right ) b-4 a c^2 \left (-3 c^2 d^4+c e \left (\sqrt {b^2-4 a c} d-12 a e\right ) d^2+a e^3 \left (9 \sqrt {b^2-4 a c} d+7 a e\right )\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{a \left (b^2-4 a c\right )^{3/2} \sqrt {b-\sqrt {b^2-4 a c}} \left (e (b d-a e)-c d^2\right )^3}-\frac {\sqrt {2} \sqrt {c} \left (d e^3 b^5-e^2 \left (3 c d^2+e \left (\sqrt {b^2-4 a c} d+5 a e\right )\right ) b^4+e \left (c d+\sqrt {b^2-4 a c} e\right ) \left (3 c d^2+5 a e^2\right ) b^3-c \left (c^2 d^4+3 c e \left (\sqrt {b^2-4 a c} d-4 a e\right ) d^2+a e^3 \left (7 \sqrt {b^2-4 a c} d-29 a e\right )\right ) b^2+c \left (-19 a^2 \sqrt {b^2-4 a c} e^4-2 a c d \left (3 \sqrt {b^2-4 a c} d+26 a e\right ) e^2+c^2 d^3 \left (\sqrt {b^2-4 a c} d-28 a e\right )\right ) b+4 a c^2 \left (3 c^2 d^4+c e \left (\sqrt {b^2-4 a c} d+12 a e\right ) d^2+a e^3 \left (9 \sqrt {b^2-4 a c} d-7 a e\right )\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b+\sqrt {b^2-4 a c}}}\right )}{a \left (b^2-4 a c\right )^{3/2} \sqrt {b+\sqrt {b^2-4 a c}} \left (e (b d-a e)-c d^2\right )^3}\right ) \]

Antiderivative was successfully verified.

[In]

Integrate[1/((d + e*x^2)^2*(a + b*x^2 + c*x^4)^2),x]

[Out]

((2*e^4*x)/(d*(c*d^2 + e*(-(b*d) + a*e))^2*(d + e*x^2)) - (2*x*(b^4*e^2 + b^3*c*e*(-2*d + e*x^2) + 2*a*c^2*(a*
e^2 - c*d*(d - 2*e*x^2)) + b^2*c*(-4*a*e^2 + c*d*(d - 2*e*x^2)) + b*c^2*(c*d^2*x^2 - 3*a*e*(-2*d + e*x^2))))/(
a*(-b^2 + 4*a*c)*(c*d^2 + e*(-(b*d) + a*e))^2*(a + b*x^2 + c*x^4)) + (Sqrt[2]*Sqrt[c]*(b^5*d*e^3 + b^3*e*(c*d
- Sqrt[b^2 - 4*a*c]*e)*(3*c*d^2 + 5*a*e^2) + b^4*e^2*(-3*c*d^2 + e*(Sqrt[b^2 - 4*a*c]*d - 5*a*e)) - 4*a*c^2*(-
3*c^2*d^4 + c*d^2*e*(Sqrt[b^2 - 4*a*c]*d - 12*a*e) + a*e^3*(9*Sqrt[b^2 - 4*a*c]*d + 7*a*e)) - b*c*(-19*a^2*Sqr
t[b^2 - 4*a*c]*e^4 + 2*a*c*d*e^2*(-3*Sqrt[b^2 - 4*a*c]*d + 26*a*e) + c^2*d^3*(Sqrt[b^2 - 4*a*c]*d + 28*a*e)) +
b^2*c*(-(c^2*d^4) + 3*c*d^2*e*(Sqrt[b^2 - 4*a*c]*d + 4*a*e) + a*e^3*(7*Sqrt[b^2 - 4*a*c]*d + 29*a*e)))*ArcTan
[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(a*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*(-(c*d^2
) + e*(b*d - a*e))^3) - (Sqrt[2]*Sqrt[c]*(b^5*d*e^3 + b^3*e*(c*d + Sqrt[b^2 - 4*a*c]*e)*(3*c*d^2 + 5*a*e^2) -
b^2*c*(c^2*d^4 + a*e^3*(7*Sqrt[b^2 - 4*a*c]*d - 29*a*e) + 3*c*d^2*e*(Sqrt[b^2 - 4*a*c]*d - 4*a*e)) - b^4*e^2*(
3*c*d^2 + e*(Sqrt[b^2 - 4*a*c]*d + 5*a*e)) + 4*a*c^2*(3*c^2*d^4 + a*e^3*(9*Sqrt[b^2 - 4*a*c]*d - 7*a*e) + c*d^
2*e*(Sqrt[b^2 - 4*a*c]*d + 12*a*e)) + b*c*(-19*a^2*Sqrt[b^2 - 4*a*c]*e^4 + c^2*d^3*(Sqrt[b^2 - 4*a*c]*d - 28*a
*e) - 2*a*c*d*e^2*(3*Sqrt[b^2 - 4*a*c]*d + 26*a*e)))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/
(a*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*(-(c*d^2) + e*(b*d - a*e))^3) + (2*e^(7/2)*(9*c*d^2 + e*(-5
*b*d + a*e))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(d^(3/2)*(c*d^2 + e*(-(b*d) + a*e))^3))/4

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fricas [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x^2+d)^2/(c*x^4+b*x^2+a)^2,x, algorithm="fricas")

[Out]

Timed out

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x^2+d)^2/(c*x^4+b*x^2+a)^2,x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 0.08, size = 5709, normalized size = 5.30 \[ \text {output too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(e*x^2+d)^2/(c*x^4+b*x^2+a)^2,x)

[Out]

result too large to display

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x^2+d)^2/(c*x^4+b*x^2+a)^2,x, algorithm="maxima")

[Out]

1/2*(9*c*d^2*e^4 - 5*b*d*e^5 + a*e^6)*arctan(e*x/sqrt(d*e))/((c^3*d^7 - 3*b*c^2*d^6*e - 3*a^2*b*d^2*e^5 + a^3*
d*e^6 + 3*(b^2*c + a*c^2)*d^5*e^2 - (b^3 + 6*a*b*c)*d^4*e^3 + 3*(a*b^2 + a^2*c)*d^3*e^4)*sqrt(d*e)) + 1/2*((b*
c^3*d^3*e - 2*(b^2*c^2 - 2*a*c^3)*d^2*e^2 + (b^3*c - 3*a*b*c^2)*d*e^3 + (a*b^2*c - 4*a^2*c^2)*e^4)*x^5 + (b*c^
3*d^4 - (b^2*c^2 - 2*a*c^3)*d^3*e - (b^3*c - 3*a*b*c^2)*d^2*e^2 + (b^4 - 4*a*b^2*c + 2*a^2*c^2)*d*e^3 + (a*b^3
- 4*a^2*b*c)*e^4)*x^3 + ((b^2*c^2 - 2*a*c^3)*d^4 - 2*(b^3*c - 3*a*b*c^2)*d^3*e + (b^4 - 4*a*b^2*c + 2*a^2*c^2
)*d^2*e^2 + (a^2*b^2 - 4*a^3*c)*e^4)*x)/((a^2*b^2*c^2 - 4*a^3*c^3)*d^6 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^5*e + (
a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^4*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d^3*e^3 + (a^4*b^2 - 4*a^5*c)*d^2*e^4 + (
(a*b^2*c^3 - 4*a^2*c^4)*d^5*e - 2*(a*b^3*c^2 - 4*a^2*b*c^3)*d^4*e^2 + (a*b^4*c - 2*a^2*b^2*c^2 - 8*a^3*c^3)*d^
3*e^3 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^2*e^4 + (a^3*b^2*c - 4*a^4*c^2)*d*e^5)*x^6 + ((a*b^2*c^3 - 4*a^2*c^4)*d^
6 - (a*b^3*c^2 - 4*a^2*b*c^3)*d^5*e - (a*b^4*c - 6*a^2*b^2*c^2 + 8*a^3*c^3)*d^4*e^2 + (a*b^5 - 4*a^2*b^3*c)*d^
3*e^3 - (2*a^2*b^4 - 9*a^3*b^2*c + 4*a^4*c^2)*d^2*e^4 + (a^3*b^3 - 4*a^4*b*c)*d*e^5)*x^4 + ((a*b^3*c^2 - 4*a^2
*b*c^3)*d^6 - (2*a*b^4*c - 9*a^2*b^2*c^2 + 4*a^3*c^3)*d^5*e + (a*b^5 - 4*a^2*b^3*c)*d^4*e^2 - (a^2*b^4 - 6*a^3
*b^2*c + 8*a^4*c^2)*d^3*e^3 - (a^3*b^3 - 4*a^4*b*c)*d^2*e^4 + (a^4*b^2 - 4*a^5*c)*d*e^5)*x^2) - 1/2*integrate(
-((b^2*c^3 - 6*a*c^4)*d^4 - (3*b^3*c^2 - 16*a*b*c^3)*d^3*e + 3*(b^4*c - 3*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - (b^
5 + 6*a*b^3*c - 44*a^2*b*c^2)*d*e^3 + (5*a*b^4 - 24*a^2*b^2*c + 14*a^3*c^2)*e^4 + (b*c^4*d^4 - (3*b^2*c^3 - 4*
a*c^4)*d^3*e + 3*(b^3*c^2 - 2*a*b*c^3)*d^2*e^2 - (b^4*c + 7*a*b^2*c^2 - 36*a^2*c^3)*d*e^3 + (5*a*b^3*c - 19*a^
2*b*c^2)*e^4)*x^2)/(c*x^4 + b*x^2 + a), x)/((a*b^2*c^3 - 4*a^2*c^4)*d^6 - 3*(a*b^3*c^2 - 4*a^2*b*c^3)*d^5*e +
3*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^4*e^2 - (a*b^5 + 2*a^2*b^3*c - 24*a^3*b*c^2)*d^3*e^3 + 3*(a^2*b^4 -
3*a^3*b^2*c - 4*a^4*c^2)*d^2*e^4 - 3*(a^3*b^3 - 4*a^4*b*c)*d*e^5 + (a^4*b^2 - 4*a^5*c)*e^6)

________________________________________________________________________________________

mupad [B]  time = 17.81, size = 97073, normalized size = 90.13 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((d + e*x^2)^2*(a + b*x^2 + c*x^4)^2),x)

[Out]

symsum(log(root(128723189760*a^14*b^4*c^9*d^13*e^14*z^6 + 128723189760*a^12*b^4*c^11*d^17*e^10*z^6 - 843245568
0*a^11*b^12*c^4*d^11*e^16*z^6 - 8432455680*a^7*b^12*c^8*d^19*e^8*z^6 + 12673351680*a^11*b^11*c^5*d^12*e^15*z^6
+ 12673351680*a^8*b^11*c^8*d^18*e^9*z^6 - 72637480960*a^12*b^9*c^6*d^12*e^15*z^6 - 72637480960*a^9*b^9*c^9*d^
18*e^9*z^6 - 21048344576*a^9*b^12*c^6*d^15*e^12*z^6 - 16609443840*a^17*b^3*c^7*d^8*e^19*z^6 - 16609443840*a^10
*b^3*c^14*d^22*e^5*z^6 + 145332633600*a^13*b^5*c^9*d^14*e^13*z^6 + 145332633600*a^12*b^5*c^10*d^16*e^11*z^6 +
123740356608*a^14*b^5*c^8*d^12*e^15*z^6 + 123740356608*a^11*b^5*c^11*d^18*e^9*z^6 + 3460300800*a^17*b^5*c^5*d^
6*e^21*z^6 + 3460300800*a^8*b^5*c^14*d^24*e^3*z^6 - 7751073792*a^15*b^7*c^5*d^8*e^19*z^6 - 7751073792*a^8*b^7*
c^12*d^22*e^5*z^6 + 12041846784*a^14*b^7*c^6*d^10*e^17*z^6 + 12041846784*a^9*b^7*c^11*d^20*e^7*z^6 - 325545099
264*a^14*b^3*c^10*d^14*e^13*z^6 - 325545099264*a^13*b^3*c^11*d^16*e^11*z^6 - 3330539520*a^13*b^10*c^4*d^9*e^18
*z^6 - 3330539520*a^7*b^10*c^10*d^21*e^6*z^6 + 157789716480*a^12*b^7*c^8*d^14*e^13*z^6 + 157789716480*a^11*b^7
*c^9*d^16*e^11*z^6 + 37492359168*a^11*b^10*c^6*d^13*e^14*z^6 + 37492359168*a^9*b^10*c^8*d^17*e^10*z^6 + 301989
888*a^8*b^3*c^16*d^26*e*z^6 - 7266631680*a^17*b^4*c^6*d^7*e^20*z^6 - 7266631680*a^9*b^4*c^14*d^23*e^4*z^6 - 20
1326592*a^20*b*c^6*d^4*e^23*z^6 - 188743680*a^7*b^5*c^15*d^26*e*z^6 + 45747339264*a^13*b^8*c^6*d^11*e^16*z^6 +
45747339264*a^9*b^8*c^10*d^19*e^8*z^6 - 74612736*a^10*b^16*c*d^9*e^18*z^6 - 2768240640*a^16*b^7*c^4*d^6*e^21*
z^6 - 2768240640*a^7*b^7*c^13*d^24*e^3*z^6 + 69746688*a^11*b^15*c*d^8*e^19*z^6 + 62914560*a^6*b^7*c^14*d^26*e*
z^6 + 2752020480*a^10*b^13*c^4*d^12*e^15*z^6 + 2752020480*a^7*b^13*c^7*d^18*e^9*z^6 + 55148544*a^9*b^17*c*d^10
*e^17*z^6 - 45957120*a^12*b^14*c*d^7*e^20*z^6 - 2724986880*a^14*b^9*c^4*d^8*e^19*z^6 - 2724986880*a^7*b^9*c^11
*d^22*e^5*z^6 - 25952256*a^8*b^18*c*d^11*e^16*z^6 + 21086208*a^13*b^13*c*d^6*e^21*z^6 - 11796480*a^5*b^9*c^13*
d^26*e*z^6 - 6438912*a^14*b^12*c*d^5*e^22*z^6 + 5406720*a^7*b^19*c*d^12*e^15*z^6 + 1622016*a^6*b^20*c*d^13*e^1
4*z^6 - 1523712*a^5*b^21*c*d^14*e^13*z^6 + 1179648*a^15*b^11*c*d^4*e^23*z^6 + 1179648*a^4*b^11*c^12*d^26*e*z^6
+ 442368*a^4*b^22*c*d^15*e^12*z^6 - 98304*a^16*b^10*c*d^3*e^24*z^6 - 49152*a^3*b^23*c*d^16*e^11*z^6 - 49152*a
^3*b^13*c^11*d^26*e*z^6 + 6897106944*a^9*b^13*c^5*d^14*e^13*z^6 + 6897106944*a^8*b^13*c^6*d^16*e^11*z^6 - 2422
210560*a^16*b^6*c^5*d^7*e^20*z^6 - 2422210560*a^8*b^6*c^13*d^23*e^4*z^6 + 255785435136*a^14*b^2*c^11*d^15*e^12
*z^6 + 41004564480*a^15*b^4*c^8*d^11*e^16*z^6 + 41004564480*a^11*b^4*c^12*d^19*e^8*z^6 + 2270822400*a^13*b^11*
c^3*d^8*e^19*z^6 + 2270822400*a^6*b^11*c^10*d^22*e^5*z^6 + 23677108224*a^14*b^8*c^5*d^9*e^18*z^6 + 23677108224
*a^8*b^8*c^11*d^21*e^6*z^6 + 212600881152*a^15*b^2*c^10*d^13*e^14*z^6 + 212600881152*a^13*b^2*c^12*d^17*e^10*z
^6 + 75157733376*a^15*b^5*c^7*d^10*e^17*z^6 + 75157733376*a^10*b^5*c^12*d^20*e^7*z^6 - 251217838080*a^13*b^6*c
^8*d^13*e^14*z^6 - 251217838080*a^11*b^6*c^10*d^17*e^10*z^6 - 1952907264*a^14*b^10*c^3*d^7*e^20*z^6 - 19529072
64*a^6*b^10*c^11*d^23*e^4*z^6 - 27691057152*a^13*b^9*c^5*d^10*e^17*z^6 - 27691057152*a^8*b^9*c^10*d^20*e^7*z^6
- 1902673920*a^8*b^15*c^4*d^14*e^13*z^6 - 1902673920*a^7*b^15*c^5*d^16*e^11*z^6 + 10465050624*a^10*b^11*c^6*d
^14*e^13*z^6 + 10465050624*a^9*b^11*c^7*d^16*e^11*z^6 + 1613905920*a^9*b^14*c^4*d^13*e^14*z^6 + 1613905920*a^7
*b^14*c^6*d^17*e^10*z^6 - 33218887680*a^17*b*c^9*d^10*e^17*z^6 - 33218887680*a^12*b*c^14*d^20*e^7*z^6 + 152469
5040*a^10*b^14*c^3*d^11*e^16*z^6 + 1524695040*a^6*b^14*c^7*d^19*e^8*z^6 - 1472200704*a^18*b^4*c^5*d^5*e^22*z^6
- 1472200704*a^8*b^4*c^15*d^25*e^2*z^6 - 83047219200*a^16*b^3*c^8*d^10*e^17*z^6 - 83047219200*a^11*b^3*c^13*d
^20*e^7*z^6 + 44291850240*a^17*b^2*c^8*d^9*e^18*z^6 + 44291850240*a^11*b^2*c^14*d^21*e^6*z^6 + 1308131328*a^8*
b^14*c^5*d^15*e^12*z^6 - 201326592*a^9*b*c^17*d^26*e*z^6 + 48530718720*a^12*b^8*c^7*d^13*e^14*z^6 + 4853071872
0*a^10*b^8*c^9*d^17*e^10*z^6 - 1242644480*a^12*b^12*c^3*d^9*e^18*z^6 - 1242644480*a^6*b^12*c^9*d^21*e^6*z^6 +
9813196800*a^12*b^10*c^5*d^11*e^16*z^6 + 9813196800*a^8*b^10*c^9*d^19*e^8*z^6 - 93012885504*a^15*b*c^11*d^14*e
^13*z^6 - 93012885504*a^14*b*c^12*d^16*e^11*z^6 + 177305812992*a^13*b^4*c^10*d^15*e^12*z^6 + 52730658816*a^10*
b^10*c^7*d^15*e^12*z^6 - 1180106752*a^9*b^15*c^3*d^12*e^15*z^6 - 1180106752*a^6*b^15*c^6*d^18*e^9*z^6 + 102367
2320*a^15*b^9*c^3*d^6*e^21*z^6 + 1023672320*a^6*b^9*c^12*d^24*e^3*z^6 + 975175680*a^17*b^6*c^4*d^5*e^22*z^6 +
975175680*a^7*b^6*c^14*d^25*e^2*z^6 - 11072962560*a^18*b*c^8*d^8*e^19*z^6 - 11072962560*a^11*b*c^15*d^22*e^5*z
^6 + 9412018176*a^18*b^2*c^7*d^7*e^20*z^6 + 9412018176*a^10*b^2*c^15*d^23*e^4*z^6 + 805306368*a^19*b^2*c^6*d^5
*e^22*z^6 + 805306368*a^9*b^2*c^16*d^25*e^2*z^6 - 133809831936*a^14*b^6*c^7*d^11*e^16*z^6 - 133809831936*a^10*
b^6*c^11*d^19*e^8*z^6 - 2214592512*a^19*b*c^7*d^6*e^21*z^6 - 2214592512*a^10*b*c^16*d^24*e^3*z^6 + 82216747008
*a^13*b^7*c^7*d^12*e^15*z^6 + 82216747008*a^10*b^7*c^10*d^18*e^9*z^6 - 586629120*a^12*b^13*c^2*d^8*e^19*z^6 -
586629120*a^5*b^13*c^9*d^22*e^5*z^6 + 568565760*a^7*b^16*c^4*d^15*e^12*z^6 - 4844421120*a^16*b^4*c^7*d^9*e^18*
z^6 - 4844421120*a^10*b^4*c^13*d^21*e^6*z^6 + 531210240*a^11*b^14*c^2*d^9*e^18*z^6 + 531210240*a^5*b^14*c^8*d^
21*e^6*z^6 - 527155200*a^11*b^13*c^3*d^10*e^17*z^6 - 527155200*a^6*b^13*c^8*d^20*e^7*z^6 + 43470028800*a^11*b^
8*c^8*d^15*e^12*z^6 - 107874877440*a^11*b^9*c^7*d^14*e^13*z^6 - 107874877440*a^10*b^9*c^8*d^16*e^11*z^6 + 9018
408960*a^12*b^11*c^4*d^10*e^17*z^6 + 9018408960*a^7*b^11*c^9*d^20*e^7*z^6 + 421994496*a^13*b^12*c^2*d^7*e^20*z
^6 + 421994496*a^5*b^12*c^10*d^23*e^4*z^6 - 66437775360*a^16*b*c^10*d^12*e^15*z^6 - 66437775360*a^13*b*c^13*d^
18*e^9*z^6 + 26159874048*a^16*b^5*c^6*d^8*e^19*z^6 + 26159874048*a^9*b^5*c^13*d^22*e^5*z^6 - 369098752*a^18*b^
3*c^6*d^6*e^21*z^6 - 369098752*a^9*b^3*c^15*d^24*e^3*z^6 + 351436800*a^8*b^16*c^3*d^13*e^14*z^6 + 351436800*a^
6*b^16*c^5*d^17*e^10*z^6 - 334233600*a^16*b^8*c^3*d^5*e^22*z^6 - 334233600*a^6*b^8*c^13*d^25*e^2*z^6 + 3019898
88*a^19*b^3*c^5*d^4*e^23*z^6 - 266010624*a^10*b^15*c^2*d^10*e^17*z^6 - 266010624*a^5*b^15*c^7*d^20*e^7*z^6 - 3
05198530560*a^12*b^6*c^9*d^15*e^12*z^6 - 203292672*a^14*b^11*c^2*d^6*e^21*z^6 - 203292672*a^5*b^11*c^11*d^24*e
^3*z^6 - 188743680*a^18*b^5*c^4*d^4*e^23*z^6 + 120418467840*a^16*b^2*c^9*d^11*e^16*z^6 + 120418467840*a^12*b^2
*c^13*d^19*e^8*z^6 - 17293934592*a^10*b^12*c^5*d^13*e^14*z^6 - 17293934592*a^8*b^12*c^7*d^17*e^10*z^6 + 104890
368*a^8*b^17*c^2*d^12*e^15*z^6 + 104890368*a^5*b^17*c^5*d^18*e^9*z^6 + 4390256640*a^15*b^8*c^4*d^7*e^20*z^6 +
4390256640*a^7*b^8*c^12*d^23*e^4*z^6 - 91750400*a^6*b^18*c^3*d^15*e^12*z^6 + 79134720*a^7*b^17*c^3*d^14*e^13*z
^6 + 79134720*a^6*b^17*c^4*d^16*e^11*z^6 - 74612736*a^4*b^16*c^7*d^21*e^6*z^6 - 72990720*a^7*b^18*c^2*d^13*e^1
4*z^6 - 72990720*a^5*b^18*c^4*d^17*e^10*z^6 + 69746688*a^4*b^15*c^8*d^22*e^5*z^6 + 63700992*a^15*b^10*c^2*d^5*
e^22*z^6 + 63700992*a^5*b^10*c^12*d^25*e^2*z^6 + 62914560*a^17*b^7*c^3*d^4*e^23*z^6 + 55148544*a^4*b^17*c^6*d^
20*e^7*z^6 - 45957120*a^4*b^14*c^9*d^23*e^4*z^6 - 25952256*a^4*b^18*c^5*d^19*e^8*z^6 - 25165824*a^20*b^2*c^5*d
^3*e^24*z^6 + 21086208*a^4*b^13*c^10*d^24*e^3*z^6 + 20643840*a^6*b^19*c^2*d^14*e^13*z^6 + 20643840*a^5*b^19*c^
3*d^16*e^11*z^6 + 15728640*a^19*b^4*c^4*d^3*e^24*z^6 - 11796480*a^16*b^9*c^2*d^4*e^23*z^6 - 6438912*a^4*b^12*c
^11*d^25*e^2*z^6 + 5406720*a^4*b^19*c^4*d^18*e^9*z^6 - 5242880*a^18*b^6*c^3*d^3*e^24*z^6 + 3784704*a^3*b^18*c^
6*d^21*e^6*z^6 - 3244032*a^3*b^19*c^5*d^20*e^7*z^6 - 3244032*a^3*b^17*c^7*d^22*e^5*z^6 + 2027520*a^3*b^20*c^4*
d^19*e^8*z^6 + 2027520*a^3*b^16*c^8*d^23*e^4*z^6 - 1622016*a^9*b^16*c^2*d^11*e^16*z^6 - 1622016*a^5*b^16*c^6*d
^19*e^8*z^6 + 1622016*a^4*b^20*c^3*d^17*e^10*z^6 - 1523712*a^4*b^21*c^2*d^16*e^11*z^6 + 983040*a^17*b^8*c^2*d^
3*e^24*z^6 - 901120*a^3*b^21*c^3*d^18*e^9*z^6 - 901120*a^3*b^15*c^9*d^24*e^3*z^6 + 270336*a^3*b^22*c^2*d^17*e^
10*z^6 + 270336*a^3*b^14*c^10*d^25*e^2*z^6 + 172032*a^5*b^20*c^2*d^15*e^12*z^6 - 38593888256*a^15*b^6*c^6*d^9*
e^18*z^6 - 38593888256*a^9*b^6*c^12*d^21*e^6*z^6 - 210386288640*a^15*b^3*c^9*d^12*e^15*z^6 - 210386288640*a^12
*b^3*c^12*d^18*e^9*z^6 + 15502147584*a^15*c^12*d^15*e^12*z^6 + 1107296256*a^19*c^8*d^7*e^20*z^6 + 1107296256*a
^11*c^16*d^23*e^4*z^6 + 13287555072*a^16*c^11*d^13*e^14*z^6 + 13287555072*a^14*c^13*d^17*e^10*z^6 + 201326592*
a^20*c^7*d^5*e^22*z^6 + 201326592*a^10*c^17*d^25*e^2*z^6 + 16777216*a^21*c^6*d^3*e^24*z^6 + 3784704*a^9*b^18*d
^9*e^18*z^6 - 3244032*a^10*b^17*d^8*e^19*z^6 - 3244032*a^8*b^19*d^10*e^17*z^6 + 2027520*a^11*b^16*d^7*e^20*z^6
+ 2027520*a^7*b^20*d^11*e^16*z^6 - 901120*a^12*b^15*d^6*e^21*z^6 - 901120*a^6*b^21*d^12*e^15*z^6 + 270336*a^1
3*b^14*d^5*e^22*z^6 + 270336*a^5*b^22*d^13*e^14*z^6 - 49152*a^14*b^13*d^4*e^23*z^6 - 49152*a^4*b^23*d^14*e^13*
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80*a^6*b^12*c^5*d^10*e^13*z^4 - 9714364416*a^7*b^8*c^8*d^12*e^11*z^4 - 16777216*a^16*b*c^6*d*e^22*z^4 + 98304*
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0*c^9*d^16*e^7*z^4 + 984087552*a^5*b^12*c^6*d^12*e^11*z^4 - 9564585984*a^9*b^7*c^7*d^9*e^14*z^4 - 5266857984*a
^10*b^7*c^6*d^7*e^16*z^4 - 892145664*a^7*b^11*c^5*d^9*e^14*z^4 - 2444623872*a^11*b*c^11*d^11*e^12*z^4 + 768540
672*a^12*b^3*c^8*d^7*e^16*z^4 + 5048322048*a^8*b^9*c^6*d^9*e^14*z^4 + 5047612416*a^6*b^9*c^8*d^13*e^10*z^4 - 7
32492288*a^4*b^11*c^8*d^15*e^8*z^4 + 9266921472*a^7*b^6*c^10*d^14*e^9*z^4 - 645857280*a^6*b^6*c^11*d^16*e^7*z^
4 - 623867904*a^4*b^9*c^10*d^17*e^6*z^4 - 622067712*a^6*b^3*c^14*d^19*e^4*z^4 + 582617088*a^10*b^8*c^5*d^6*e^1
7*z^4 + 577119744*a^7*b^12*c^4*d^8*e^15*z^4 + 552566784*a^12*b^6*c^5*d^4*e^19*z^4 + 549224448*a^9*b^8*c^6*d^8*
e^15*z^4 - 526565376*a^9*b^10*c^4*d^6*e^17*z^4 + 511520256*a^10*b^9*c^4*d^5*e^18*z^4 + 13393723392*a^9*b^3*c^1
1*d^13*e^10*z^4 - 2066350080*a^14*b*c^8*d^5*e^18*z^4 + 4718592000*a^13*b^2*c^8*d^6*e^17*z^4 - 314572800*a^7*b^
2*c^14*d^18*e^5*z^4 + 287250432*a^4*b^13*c^6*d^13*e^10*z^4 + 4565827584*a^10*b^5*c^8*d^9*e^14*z^4 - 250785792*
a^4*b^14*c^5*d^12*e^11*z^4 + 235536384*a^13*b^3*c^7*d^5*e^18*z^4 - 232683264*a^8*b^11*c^4*d^7*e^16*z^4 - 19962
7776*a^5*b^14*c^4*d^10*e^13*z^4 - 190267392*a^12*b^7*c^4*d^3*e^20*z^4 + 184891392*a^6*b^10*c^7*d^12*e^11*z^4 +
180502528*a^4*b^7*c^12*d^19*e^4*z^4 + 178877952*a^3*b^13*c^7*d^15*e^8*z^4 + 172490752*a^14*b^3*c^6*d^3*e^20*z
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2*e^21*z^4 - 116767488*a^3*b^9*c^11*d^19*e^4*z^4 - 108985344*a^3*b^14*c^6*d^14*e^9*z^4 - 106223616*a^6*b^13*c^
4*d^9*e^14*z^4 + 106119168*a^3*b^10*c^10*d^18*e^5*z^4 + 102432768*a^5*b^4*c^14*d^20*e^3*z^4 + 102113280*a^4*b^
12*c^7*d^14*e^9*z^4 + 100674048*a^5*b^9*c^9*d^15*e^8*z^4 + 90439680*a^13*b^6*c^4*d^2*e^21*z^4 - 86808576*a^6*b
^14*c^3*d^8*e^15*z^4 + 86245376*a^6*b^2*c^15*d^20*e^3*z^4 + 79011840*a^4*b^8*c^11*d^18*e^5*z^4 + 78345216*a^4*
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3*b^8*c^12*d^20*e^3*z^4 + 67108864*a^15*b^2*c^6*d^2*e^21*z^4 - 61590528*a^10*b^10*c^3*d^4*e^19*z^4 + 61559808*
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2176*a^7*b^14*c^2*d^6*e^17*z^4 - 23248896*a^3*b^7*c^13*d^21*e^2*z^4 + 20929536*a^3*b^15*c^5*d^13*e^10*z^4 + 18
428928*a^9*b^12*c^2*d^4*e^19*z^4 + 18026496*a^6*b^15*c^2*d^7*e^16*z^4 - 16261632*a^10*b^11*c^2*d^3*e^20*z^4 +
15128064*a^3*b^16*c^4*d^12*e^11*z^4 - 14060544*a^2*b^10*c^11*d^20*e^3*z^4 + 13178880*a^2*b^16*c^5*d^14*e^9*z^4
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4 - 7045632*a^2*b^17*c^4*d^13*e^10*z^4 - 6285312*a^2*b^14*c^7*d^16*e^7*z^4 + 5996544*a^11*b^10*c^2*d^2*e^21*z^
4 + 4558336*a^2*b^9*c^12*d^21*e^2*z^4 + 4478976*a^11*b^8*c^4*d^4*e^19*z^4 + 2850816*a^4*b^16*c^3*d^10*e^13*z^4
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^5*b*c^17*d^23*z^4 - 6912*a*b^9*c^13*d^23*z^4 + 1824522240*a^13*c^10*d^8*e^15*z^4 + 1730150400*a^12*c^11*d^10*
e^13*z^4 + 958922752*a^14*c^9*d^6*e^17*z^4 - 537919488*a^9*c^14*d^16*e^7*z^4 + 508559360*a^11*c^12*d^12*e^11*z
^4 - 500170752*a^10*c^13*d^14*e^9*z^4 + 246939648*a^15*c^8*d^4*e^19*z^4 - 199229440*a^8*c^15*d^18*e^5*z^4 - 29
884416*a^7*c^16*d^20*e^3*z^4 + 25165824*a^16*c^7*d^2*e^21*z^4 + 236544*b^17*c^6*d^17*e^6*z^4 - 202752*b^18*c^5
*d^16*e^7*z^4 - 202752*b^16*c^7*d^18*e^5*z^4 + 126720*b^19*c^4*d^15*e^8*z^4 + 126720*b^15*c^8*d^19*e^4*z^4 - 5
6320*b^20*c^3*d^14*e^9*z^4 - 56320*b^14*c^9*d^20*e^3*z^4 + 16896*b^21*c^2*d^13*e^10*z^4 + 16896*b^13*c^10*d^21
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6*c^3*e^23*z^4 + 61440*a^13*b^8*c^2*e^23*z^4 + 983040*a^4*b^3*c^16*d^23*z^4 - 385024*a^3*b^5*c^15*d^23*z^4 + 7
3728*a^2*b^7*c^14*d^23*z^4 + 256*b^23*d^11*e^12*z^4 + 1048576*a^17*c^6*e^23*z^4 + 256*b^11*c^12*d^23*z^4 + 256
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^2*e^17*z^2 + 29675520*a^8*b^6*c^5*d*e^18*z^2 - 24170496*a^9*b^4*c^6*d*e^18*z^2 - 17202816*a^7*b^8*c^4*d*e^18*
z^2 - 14561280*a^4*b*c^14*d^14*e^5*z^2 + 5532416*a^6*b^10*c^3*d*e^18*z^2 + 4128768*a^10*b^2*c^7*d*e^18*z^2 - 2
662400*a^3*b*c^15*d^16*e^3*z^2 + 1184512*a*b^12*c^6*d^9*e^10*z^2 - 1136160*a*b^13*c^5*d^8*e^11*z^2 - 1017600*a
^5*b^12*c^2*d*e^18*z^2 - 744768*a*b^11*c^7*d^10*e^9*z^2 + 607872*a*b^14*c^4*d^7*e^12*z^2 - 424064*a*b^6*c^12*d
^15*e^4*z^2 + 408576*a*b^5*c^13*d^16*e^3*z^2 + 361152*a*b^10*c^8*d^11*e^8*z^2 - 287408*a*b^9*c^9*d^12*e^7*z^2
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e^16*z^2 + 1824135552*a^7*b^4*c^8*d^5*e^14*z^2 - 1457252352*a^8*b^2*c^9*d^5*e^14*z^2 - 1405209600*a^7*b^5*c^7*
d^4*e^15*z^2 - 184320*a^2*b*c^16*d^18*e*z^2 + 100608*a^4*b^14*c*d*e^18*z^2 + 53248*a*b^3*c^15*d^18*e*z^2 + 264
48*a*b^17*c*d^4*e^15*z^2 + 1067599872*a^8*b^3*c^8*d^4*e^15*z^2 - 930828288*a^7*b^3*c^9*d^6*e^13*z^2 + 92076000
0*a^6*b^4*c^9*d^7*e^12*z^2 - 806639616*a^6*b^3*c^10*d^8*e^11*z^2 - 791052480*a^6*b^6*c^7*d^5*e^14*z^2 + 772237
824*a^6*b^7*c^6*d^4*e^15*z^2 - 701025408*a^5*b^6*c^8*d^7*e^12*z^2 + 443340288*a^5*b^5*c^9*d^8*e^11*z^2 + 43304
7552*a^7*b^6*c^6*d^3*e^16*z^2 + 405741312*a^5*b^7*c^7*d^6*e^13*z^2 + 293652480*a^6*b^2*c^11*d^9*e^10*z^2 - 276
962688*a^6*b^8*c^5*d^3*e^16*z^2 - 247804272*a^8*b^4*c^7*d^3*e^16*z^2 + 213564384*a^4*b^8*c^7*d^7*e^12*z^2 - 20
2596816*a^5*b^9*c^5*d^4*e^15*z^2 - 182520896*a^4*b^9*c^6*d^6*e^13*z^2 - 153489408*a^5*b^3*c^11*d^10*e^9*z^2 -
152151552*a^7*b^2*c^10*d^7*e^12*z^2 + 115859712*a^5*b^2*c^12*d^11*e^8*z^2 + 108085248*a^9*b^3*c^7*d^2*e^17*z^2
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47614464*a^3*b^8*c^8*d^9*e^10*z^2 + 35604480*a^4*b^2*c^13*d^13*e^6*z^2 + 33983040*a^3*b^11*c^5*d^6*e^13*z^2 -
33515520*a^4*b^3*c^12*d^12*e^7*z^2 - 33463808*a^3*b^7*c^9*d^10*e^9*z^2 - 25128864*a^4*b^4*c^11*d^11*e^8*z^2 -
23193728*a^3*b^10*c^6*d^7*e^12*z^2 + 21015456*a^6*b^9*c^4*d^2*e^17*z^2 + 19924176*a^4*b^11*c^4*d^4*e^15*z^2 -
19251216*a^3*b^9*c^7*d^8*e^11*z^2 - 16434048*a^5*b^4*c^10*d^9*e^10*z^2 - 16289664*a^3*b^12*c^4*d^5*e^14*z^2 -
15059328*a^4*b^12*c^3*d^3*e^16*z^2 - 10766016*a^2*b^10*c^7*d^9*e^10*z^2 - 10453632*a^5*b^11*c^3*d^2*e^17*z^2
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7077888*a^3*b^5*c^11*d^12*e^7*z^2 + 6798240*a^2*b^9*c^8*d^10*e^9*z^2 - 3589440*a^2*b^6*c^11*d^13*e^6*z^2 + 354
4320*a^3*b^6*c^10*d^11*e^8*z^2 + 3128064*a^2*b^5*c^12*d^14*e^5*z^2 + 2346336*a^4*b^13*c^2*d^2*e^17*z^2 - 22615
68*a^2*b^8*c^9*d^11*e^8*z^2 - 2125824*a^2*b^13*c^4*d^6*e^13*z^2 + 2002560*a^3*b^4*c^12*d^13*e^6*z^2 + 1927680*
a^2*b^7*c^10*d^12*e^7*z^2 + 1814784*a^2*b^14*c^3*d^5*e^14*z^2 - 1807104*a^2*b^12*c^5*d^7*e^12*z^2 + 1637808*a^
3*b^13*c^3*d^4*e^15*z^2 + 1083456*a^3*b^14*c^2*d^3*e^16*z^2 - 792384*a^2*b^4*c^13*d^15*e^4*z^2 - 657408*a^2*b^
3*c^14*d^16*e^3*z^2 + 608256*a^7*b^7*c^5*d^2*e^17*z^2 + 595968*a^2*b^2*c^15*d^17*e^2*z^2 - 498624*a^2*b^15*c^2
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^16*d*e^18*z^2 - 4160*a*b^18*d^3*e^16*z^2 - 1290240*a^11*b*c^7*e^19*z^2 - 9840*a^5*b^13*c*e^19*z^2 - 5760*a*b^
2*c^16*d^19*z^2 - 280581120*a^8*c^11*d^7*e^12*z^2 + 110278656*a^9*c^10*d^5*e^14*z^2 - 89479168*a^7*c^12*d^9*e^
10*z^2 + 34464000*a^10*c^9*d^3*e^16*z^2 + 54240*b^15*c^4*d^8*e^11*z^2 + 54240*b^8*c^11*d^15*e^4*z^2 - 49920*b^
14*c^5*d^9*e^10*z^2 - 49920*b^9*c^10*d^14*e^5*z^2 - 37376*b^16*c^3*d^7*e^12*z^2 - 37376*b^7*c^12*d^16*e^3*z^2
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7*e^2*z^2 - 7920*b^12*c^7*d^11*e^8*z^2 - 7920*b^11*c^8*d^12*e^7*z^2 + 7489536*a^5*c^14*d^13*e^6*z^2 + 6084096*
a^6*c^13*d^11*e^8*z^2 + 2280448*a^4*c^15*d^15*e^4*z^2 + 350208*a^3*c^16*d^17*e^2*z^2 + 11616*a^2*b^17*d^2*e^17
*z^2 - 3515904*a^9*b^5*c^5*e^19*z^2 + 3440640*a^10*b^3*c^6*e^19*z^2 + 1870848*a^8*b^7*c^4*e^19*z^2 - 572272*a^
7*b^9*c^3*e^19*z^2 + 101856*a^6*b^11*c^2*e^19*z^2 + 400*b^19*d^4*e^15*z^2 + 400*b^4*c^15*d^19*z^2 + 20736*a^2*
c^17*d^19*z^2 + 400*a^4*b^15*e^19*z^2 - 3969216*a^4*b*c^10*d^3*e^12 - 3001536*a^3*b*c^11*d^5*e^10 - 419904*a^2
*b*c^12*d^7*e^8 + 184608*a^4*b^3*c^8*d*e^14 - 153036*a*b^4*c^10*d^6*e^9 + 127008*a*b^3*c^11*d^7*e^8 + 63108*a*
b^6*c^8*d^4*e^11 - 29160*a*b^2*c^12*d^8*e^7 - 21060*a^3*b^5*c^7*d*e^14 - 21060*a*b^7*c^7*d^3*e^12 + 5460*a*b^5
*c^9*d^5*e^10 - 404544*a^5*b*c^9*d*e^14 + 1251872*a^3*b^3*c^9*d^3*e^12 + 844224*a^4*b^2*c^9*d^2*e^13 + 820512*
a^2*b^3*c^10*d^5*e^10 + 750672*a^3*b^2*c^10*d^4*e^11 - 657498*a^2*b^4*c^9*d^4*e^11 - 487116*a^3*b^4*c^8*d^2*e^
13 + 160704*a^2*b^2*c^11*d^6*e^9 + 58806*a^2*b^6*c^7*d^2*e^13 + 13140*a^2*b^5*c^8*d^3*e^12 + 15286*b^6*c^9*d^6
*e^9 - 9540*b^7*c^8*d^5*e^10 - 9540*b^5*c^10*d^7*e^8 + 2025*b^8*c^7*d^4*e^11 + 2025*b^4*c^11*d^8*e^7 + 3367008
*a^4*c^11*d^4*e^11 + 1166400*a^3*c^12*d^6*e^9 + 705600*a^5*c^10*d^2*e^13 + 104976*a^2*c^13*d^8*e^7 - 17640*a^5
*b^2*c^8*e^15 + 2025*a^4*b^4*c^7*e^15 + 38416*a^6*c^9*e^15, z, k)*(root(128723189760*a^14*b^4*c^9*d^13*e^14*z^
6 + 128723189760*a^12*b^4*c^11*d^17*e^10*z^6 - 8432455680*a^11*b^12*c^4*d^11*e^16*z^6 - 8432455680*a^7*b^12*c^
8*d^19*e^8*z^6 + 12673351680*a^11*b^11*c^5*d^12*e^15*z^6 + 12673351680*a^8*b^11*c^8*d^18*e^9*z^6 - 72637480960
*a^12*b^9*c^6*d^12*e^15*z^6 - 72637480960*a^9*b^9*c^9*d^18*e^9*z^6 - 21048344576*a^9*b^12*c^6*d^15*e^12*z^6 -
16609443840*a^17*b^3*c^7*d^8*e^19*z^6 - 16609443840*a^10*b^3*c^14*d^22*e^5*z^6 + 145332633600*a^13*b^5*c^9*d^1
4*e^13*z^6 + 145332633600*a^12*b^5*c^10*d^16*e^11*z^6 + 123740356608*a^14*b^5*c^8*d^12*e^15*z^6 + 123740356608
*a^11*b^5*c^11*d^18*e^9*z^6 + 3460300800*a^17*b^5*c^5*d^6*e^21*z^6 + 3460300800*a^8*b^5*c^14*d^24*e^3*z^6 - 77
51073792*a^15*b^7*c^5*d^8*e^19*z^6 - 7751073792*a^8*b^7*c^12*d^22*e^5*z^6 + 12041846784*a^14*b^7*c^6*d^10*e^17
*z^6 + 12041846784*a^9*b^7*c^11*d^20*e^7*z^6 - 325545099264*a^14*b^3*c^10*d^14*e^13*z^6 - 325545099264*a^13*b^
3*c^11*d^16*e^11*z^6 - 3330539520*a^13*b^10*c^4*d^9*e^18*z^6 - 3330539520*a^7*b^10*c^10*d^21*e^6*z^6 + 1577897
16480*a^12*b^7*c^8*d^14*e^13*z^6 + 157789716480*a^11*b^7*c^9*d^16*e^11*z^6 + 37492359168*a^11*b^10*c^6*d^13*e^
14*z^6 + 37492359168*a^9*b^10*c^8*d^17*e^10*z^6 + 301989888*a^8*b^3*c^16*d^26*e*z^6 - 7266631680*a^17*b^4*c^6*
d^7*e^20*z^6 - 7266631680*a^9*b^4*c^14*d^23*e^4*z^6 - 201326592*a^20*b*c^6*d^4*e^23*z^6 - 188743680*a^7*b^5*c^
15*d^26*e*z^6 + 45747339264*a^13*b^8*c^6*d^11*e^16*z^6 + 45747339264*a^9*b^8*c^10*d^19*e^8*z^6 - 74612736*a^10
*b^16*c*d^9*e^18*z^6 - 2768240640*a^16*b^7*c^4*d^6*e^21*z^6 - 2768240640*a^7*b^7*c^13*d^24*e^3*z^6 + 69746688*
a^11*b^15*c*d^8*e^19*z^6 + 62914560*a^6*b^7*c^14*d^26*e*z^6 + 2752020480*a^10*b^13*c^4*d^12*e^15*z^6 + 2752020
480*a^7*b^13*c^7*d^18*e^9*z^6 + 55148544*a^9*b^17*c*d^10*e^17*z^6 - 45957120*a^12*b^14*c*d^7*e^20*z^6 - 272498
6880*a^14*b^9*c^4*d^8*e^19*z^6 - 2724986880*a^7*b^9*c^11*d^22*e^5*z^6 - 25952256*a^8*b^18*c*d^11*e^16*z^6 + 21
086208*a^13*b^13*c*d^6*e^21*z^6 - 11796480*a^5*b^9*c^13*d^26*e*z^6 - 6438912*a^14*b^12*c*d^5*e^22*z^6 + 540672
0*a^7*b^19*c*d^12*e^15*z^6 + 1622016*a^6*b^20*c*d^13*e^14*z^6 - 1523712*a^5*b^21*c*d^14*e^13*z^6 + 1179648*a^1
5*b^11*c*d^4*e^23*z^6 + 1179648*a^4*b^11*c^12*d^26*e*z^6 + 442368*a^4*b^22*c*d^15*e^12*z^6 - 98304*a^16*b^10*c
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c^13*d^23*e^4*z^6 + 255785435136*a^14*b^2*c^11*d^15*e^12*z^6 + 41004564480*a^15*b^4*c^8*d^11*e^16*z^6 + 410045
64480*a^11*b^4*c^12*d^19*e^8*z^6 + 2270822400*a^13*b^11*c^3*d^8*e^19*z^6 + 2270822400*a^6*b^11*c^10*d^22*e^5*z
^6 + 23677108224*a^14*b^8*c^5*d^9*e^18*z^6 + 23677108224*a^8*b^8*c^11*d^21*e^6*z^6 + 212600881152*a^15*b^2*c^1
0*d^13*e^14*z^6 + 212600881152*a^13*b^2*c^12*d^17*e^10*z^6 + 75157733376*a^15*b^5*c^7*d^10*e^17*z^6 + 75157733
376*a^10*b^5*c^12*d^20*e^7*z^6 - 251217838080*a^13*b^6*c^8*d^13*e^14*z^6 - 251217838080*a^11*b^6*c^10*d^17*e^1
0*z^6 - 1952907264*a^14*b^10*c^3*d^7*e^20*z^6 - 1952907264*a^6*b^10*c^11*d^23*e^4*z^6 - 27691057152*a^13*b^9*c
^5*d^10*e^17*z^6 - 27691057152*a^8*b^9*c^10*d^20*e^7*z^6 - 1902673920*a^8*b^15*c^4*d^14*e^13*z^6 - 1902673920*
a^7*b^15*c^5*d^16*e^11*z^6 + 10465050624*a^10*b^11*c^6*d^14*e^13*z^6 + 10465050624*a^9*b^11*c^7*d^16*e^11*z^6
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e^17*z^6 - 33218887680*a^12*b*c^14*d^20*e^7*z^6 + 1524695040*a^10*b^14*c^3*d^11*e^16*z^6 + 1524695040*a^6*b^14
*c^7*d^19*e^8*z^6 - 1472200704*a^18*b^4*c^5*d^5*e^22*z^6 - 1472200704*a^8*b^4*c^15*d^25*e^2*z^6 - 83047219200*
a^16*b^3*c^8*d^10*e^17*z^6 - 83047219200*a^11*b^3*c^13*d^20*e^7*z^6 + 44291850240*a^17*b^2*c^8*d^9*e^18*z^6 +
44291850240*a^11*b^2*c^14*d^21*e^6*z^6 + 1308131328*a^8*b^14*c^5*d^15*e^12*z^6 - 201326592*a^9*b*c^17*d^26*e*z
^6 + 48530718720*a^12*b^8*c^7*d^13*e^14*z^6 + 48530718720*a^10*b^8*c^9*d^17*e^10*z^6 - 1242644480*a^12*b^12*c^
3*d^9*e^18*z^6 - 1242644480*a^6*b^12*c^9*d^21*e^6*z^6 + 9813196800*a^12*b^10*c^5*d^11*e^16*z^6 + 9813196800*a^
8*b^10*c^9*d^19*e^8*z^6 - 93012885504*a^15*b*c^11*d^14*e^13*z^6 - 93012885504*a^14*b*c^12*d^16*e^11*z^6 + 1773
05812992*a^13*b^4*c^10*d^15*e^12*z^6 + 52730658816*a^10*b^10*c^7*d^15*e^12*z^6 - 1180106752*a^9*b^15*c^3*d^12*
e^15*z^6 - 1180106752*a^6*b^15*c^6*d^18*e^9*z^6 + 1023672320*a^15*b^9*c^3*d^6*e^21*z^6 + 1023672320*a^6*b^9*c^
12*d^24*e^3*z^6 + 975175680*a^17*b^6*c^4*d^5*e^22*z^6 + 975175680*a^7*b^6*c^14*d^25*e^2*z^6 - 11072962560*a^18
*b*c^8*d^8*e^19*z^6 - 11072962560*a^11*b*c^15*d^22*e^5*z^6 + 9412018176*a^18*b^2*c^7*d^7*e^20*z^6 + 9412018176
*a^10*b^2*c^15*d^23*e^4*z^6 + 805306368*a^19*b^2*c^6*d^5*e^22*z^6 + 805306368*a^9*b^2*c^16*d^25*e^2*z^6 - 1338
09831936*a^14*b^6*c^7*d^11*e^16*z^6 - 133809831936*a^10*b^6*c^11*d^19*e^8*z^6 - 2214592512*a^19*b*c^7*d^6*e^21
*z^6 - 2214592512*a^10*b*c^16*d^24*e^3*z^6 + 82216747008*a^13*b^7*c^7*d^12*e^15*z^6 + 82216747008*a^10*b^7*c^1
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8*e^5*z^4 - 31293440*a^12*b^8*c^3*d^2*e^21*z^4 + 29933568*a^5*b^13*c^5*d^11*e^12*z^4 + 27793920*a^2*b^11*c^10*
d^19*e^4*z^4 + 27168768*a^2*b^13*c^8*d^17*e^6*z^4 - 23602176*a^7*b^14*c^2*d^6*e^17*z^4 - 23248896*a^3*b^7*c^13
*d^21*e^2*z^4 + 20929536*a^3*b^15*c^5*d^13*e^10*z^4 + 18428928*a^9*b^12*c^2*d^4*e^19*z^4 + 18026496*a^6*b^15*c
^2*d^7*e^16*z^4 - 16261632*a^10*b^11*c^2*d^3*e^20*z^4 + 15128064*a^3*b^16*c^4*d^12*e^11*z^4 - 14060544*a^2*b^1
0*c^11*d^20*e^3*z^4 + 13178880*a^2*b^16*c^5*d^14*e^9*z^4 - 11244288*a^3*b^17*c^3*d^11*e^12*z^4 - 10509312*a^2*
b^15*c^6*d^15*e^8*z^4 - 7262208*a^4*b^17*c^2*d^9*e^14*z^4 - 7045632*a^2*b^17*c^4*d^13*e^10*z^4 - 6285312*a^2*b
^14*c^7*d^16*e^7*z^4 + 5996544*a^11*b^10*c^2*d^2*e^21*z^4 + 4558336*a^2*b^9*c^12*d^21*e^2*z^4 + 4478976*a^11*b
^8*c^4*d^4*e^19*z^4 + 2850816*a^4*b^16*c^3*d^10*e^13*z^4 + 2629632*a^3*b^11*c^9*d^17*e^6*z^4 + 2503680*a^3*b^1
8*c^2*d^10*e^13*z^4 + 1627136*a^2*b^18*c^3*d^12*e^11*z^4 + 1605120*a^8*b^13*c^2*d^5*e^18*z^4 + 1483776*a^5*b^1
6*c^2*d^8*e^15*z^4 + 139776*a^2*b^19*c^2*d^11*e^12*z^4 - 8542224384*a^10*b^2*c^11*d^12*e^11*z^4 - 3072*b^22*c*
d^12*e^11*z^4 - 3072*b^12*c^11*d^22*e*z^4 - 1572864*a^6*c^17*d^22*e*z^4 - 4096*a^10*b^13*d*e^22*z^4 - 4096*a*b
^22*d^10*e^13*z^4 - 6144*a^12*b^10*c*e^23*z^4 - 983040*a^5*b*c^17*d^23*z^4 - 6912*a*b^9*c^13*d^23*z^4 + 182452
2240*a^13*c^10*d^8*e^15*z^4 + 1730150400*a^12*c^11*d^10*e^13*z^4 + 958922752*a^14*c^9*d^6*e^17*z^4 - 537919488
*a^9*c^14*d^16*e^7*z^4 + 508559360*a^11*c^12*d^12*e^11*z^4 - 500170752*a^10*c^13*d^14*e^9*z^4 + 246939648*a^15
*c^8*d^4*e^19*z^4 - 199229440*a^8*c^15*d^18*e^5*z^4 - 29884416*a^7*c^16*d^20*e^3*z^4 + 25165824*a^16*c^7*d^2*e
^21*z^4 + 236544*b^17*c^6*d^17*e^6*z^4 - 202752*b^18*c^5*d^16*e^7*z^4 - 202752*b^16*c^7*d^18*e^5*z^4 + 126720*
b^19*c^4*d^15*e^8*z^4 + 126720*b^15*c^8*d^19*e^4*z^4 - 56320*b^20*c^3*d^14*e^9*z^4 - 56320*b^14*c^9*d^20*e^3*z
^4 + 16896*b^21*c^2*d^13*e^10*z^4 + 16896*b^13*c^10*d^21*e^2*z^4 + 110080*a^7*b^16*d^4*e^19*z^4 + 110080*a^4*b
^19*d^7*e^16*z^4 - 75520*a^8*b^15*d^3*e^20*z^4 - 75520*a^3*b^20*d^8*e^15*z^4 - 56320*a^6*b^17*d^5*e^18*z^4 - 5
6320*a^5*b^18*d^6*e^17*z^4 + 25600*a^9*b^14*d^2*e^21*z^4 + 25600*a^2*b^21*d^9*e^14*z^4 - 1572864*a^16*b^2*c^5*
e^23*z^4 + 983040*a^15*b^4*c^4*e^23*z^4 - 327680*a^14*b^6*c^3*e^23*z^4 + 61440*a^13*b^8*c^2*e^23*z^4 + 983040*
a^4*b^3*c^16*d^23*z^4 - 385024*a^3*b^5*c^15*d^23*z^4 + 73728*a^2*b^7*c^14*d^23*z^4 + 256*b^23*d^11*e^12*z^4 +
1048576*a^17*c^6*e^23*z^4 + 256*b^11*c^12*d^23*z^4 + 256*a^11*b^12*e^23*z^4 + 948695040*a^8*b*c^10*d^6*e^13*z^
2 + 348917760*a^7*b*c^11*d^8*e^11*z^2 - 125030400*a^9*b*c^9*d^4*e^15*z^2 - 50728960*a^6*b*c^12*d^10*e^9*z^2 -
44298240*a^5*b*c^13*d^12*e^7*z^2 - 36495360*a^10*b*c^8*d^2*e^17*z^2 + 29675520*a^8*b^6*c^5*d*e^18*z^2 - 241704
96*a^9*b^4*c^6*d*e^18*z^2 - 17202816*a^7*b^8*c^4*d*e^18*z^2 - 14561280*a^4*b*c^14*d^14*e^5*z^2 + 5532416*a^6*b
^10*c^3*d*e^18*z^2 + 4128768*a^10*b^2*c^7*d*e^18*z^2 - 2662400*a^3*b*c^15*d^16*e^3*z^2 + 1184512*a*b^12*c^6*d^
9*e^10*z^2 - 1136160*a*b^13*c^5*d^8*e^11*z^2 - 1017600*a^5*b^12*c^2*d*e^18*z^2 - 744768*a*b^11*c^7*d^10*e^9*z^
2 + 607872*a*b^14*c^4*d^7*e^12*z^2 - 424064*a*b^6*c^12*d^15*e^4*z^2 + 408576*a*b^5*c^13*d^16*e^3*z^2 + 361152*
a*b^10*c^8*d^11*e^8*z^2 - 287408*a*b^9*c^9*d^12*e^7*z^2 - 260448*a^3*b^15*c*d^2*e^17*z^2 - 203904*a*b^4*c^14*d
^17*e^2*z^2 + 200832*a*b^8*c^10*d^13*e^6*z^2 + 126720*a*b^7*c^11*d^14*e^5*z^2 - 123968*a*b^15*c^3*d^6*e^13*z^2
- 39168*a*b^16*c^2*d^5*e^14*z^2 + 11904*a^2*b^16*c*d^3*e^16*z^2 + 1824135552*a^7*b^4*c^8*d^5*e^14*z^2 - 14572
52352*a^8*b^2*c^9*d^5*e^14*z^2 - 1405209600*a^7*b^5*c^7*d^4*e^15*z^2 - 184320*a^2*b*c^16*d^18*e*z^2 + 100608*a
^4*b^14*c*d*e^18*z^2 + 53248*a*b^3*c^15*d^18*e*z^2 + 26448*a*b^17*c*d^4*e^15*z^2 + 1067599872*a^8*b^3*c^8*d^4*
e^15*z^2 - 930828288*a^7*b^3*c^9*d^6*e^13*z^2 + 920760000*a^6*b^4*c^9*d^7*e^12*z^2 - 806639616*a^6*b^3*c^10*d^
8*e^11*z^2 - 791052480*a^6*b^6*c^7*d^5*e^14*z^2 + 772237824*a^6*b^7*c^6*d^4*e^15*z^2 - 701025408*a^5*b^6*c^8*d
^7*e^12*z^2 + 443340288*a^5*b^5*c^9*d^8*e^11*z^2 + 433047552*a^7*b^6*c^6*d^3*e^16*z^2 + 405741312*a^5*b^7*c^7*
d^6*e^13*z^2 + 293652480*a^6*b^2*c^11*d^9*e^10*z^2 - 276962688*a^6*b^8*c^5*d^3*e^16*z^2 - 247804272*a^8*b^4*c^
7*d^3*e^16*z^2 + 213564384*a^4*b^8*c^7*d^7*e^12*z^2 - 202596816*a^5*b^9*c^5*d^4*e^15*z^2 - 182520896*a^4*b^9*c
^6*d^6*e^13*z^2 - 153489408*a^5*b^3*c^11*d^10*e^9*z^2 - 152151552*a^7*b^2*c^10*d^7*e^12*z^2 + 115859712*a^5*b^
2*c^12*d^11*e^8*z^2 + 108085248*a^9*b^3*c^7*d^2*e^17*z^2 + 105536256*a^4*b^5*c^10*d^10*e^9*z^2 - 98323200*a^6*
b^5*c^8*d^6*e^13*z^2 - 93564992*a^4*b^6*c^9*d^9*e^10*z^2 + 89464512*a^5*b^10*c^4*d^3*e^16*z^2 - 75930624*a^8*b
^5*c^6*d^2*e^17*z^2 + 68315904*a^5*b^8*c^6*d^5*e^14*z^2 - 64157184*a^4*b^7*c^8*d^8*e^11*z^2 - 62951040*a^9*b^2
*c^8*d^3*e^16*z^2 + 49056768*a^4*b^10*c^5*d^5*e^14*z^2 + 47614464*a^3*b^8*c^8*d^9*e^10*z^2 + 35604480*a^4*b^2*
c^13*d^13*e^6*z^2 + 33983040*a^3*b^11*c^5*d^6*e^13*z^2 - 33515520*a^4*b^3*c^12*d^12*e^7*z^2 - 33463808*a^3*b^7
*c^9*d^10*e^9*z^2 - 25128864*a^4*b^4*c^11*d^11*e^8*z^2 - 23193728*a^3*b^10*c^6*d^7*e^12*z^2 + 21015456*a^6*b^9
*c^4*d^2*e^17*z^2 + 19924176*a^4*b^11*c^4*d^4*e^15*z^2 - 19251216*a^3*b^9*c^7*d^8*e^11*z^2 - 16434048*a^5*b^4*
c^10*d^9*e^10*z^2 - 16289664*a^3*b^12*c^4*d^5*e^14*z^2 - 15059328*a^4*b^12*c^3*d^3*e^16*z^2 - 10766016*a^2*b^1
0*c^7*d^9*e^10*z^2 - 10453632*a^5*b^11*c^3*d^2*e^17*z^2 - 9940992*a^3*b^3*c^13*d^14*e^5*z^2 + 8373696*a^2*b^11
*c^6*d^8*e^11*z^2 + 7776768*a^3*b^2*c^14*d^15*e^4*z^2 + 7077888*a^3*b^5*c^11*d^12*e^7*z^2 + 6798240*a^2*b^9*c^
8*d^10*e^9*z^2 - 3589440*a^2*b^6*c^11*d^13*e^6*z^2 + 3544320*a^3*b^6*c^10*d^11*e^8*z^2 + 3128064*a^2*b^5*c^12*
d^14*e^5*z^2 + 2346336*a^4*b^13*c^2*d^2*e^17*z^2 - 2261568*a^2*b^8*c^9*d^11*e^8*z^2 - 2125824*a^2*b^13*c^4*d^6
*e^13*z^2 + 2002560*a^3*b^4*c^12*d^13*e^6*z^2 + 1927680*a^2*b^7*c^10*d^12*e^7*z^2 + 1814784*a^2*b^14*c^3*d^5*e
^14*z^2 - 1807104*a^2*b^12*c^5*d^7*e^12*z^2 + 1637808*a^3*b^13*c^3*d^4*e^15*z^2 + 1083456*a^3*b^14*c^2*d^3*e^1
6*z^2 - 792384*a^2*b^4*c^13*d^15*e^4*z^2 - 657408*a^2*b^3*c^14*d^16*e^3*z^2 + 608256*a^7*b^7*c^5*d^2*e^17*z^2
+ 595968*a^2*b^2*c^15*d^17*e^2*z^2 - 498624*a^2*b^15*c^2*d^4*e^15*z^2 - 3840*b^18*c*d^5*e^14*z^2 - 3840*b^5*c^
14*d^18*e*z^2 + 2064384*a^11*c^8*d*e^18*z^2 - 4160*a^3*b^16*d*e^18*z^2 - 4160*a*b^18*d^3*e^16*z^2 - 1290240*a^
11*b*c^7*e^19*z^2 - 9840*a^5*b^13*c*e^19*z^2 - 5760*a*b^2*c^16*d^19*z^2 - 280581120*a^8*c^11*d^7*e^12*z^2 + 11
0278656*a^9*c^10*d^5*e^14*z^2 - 89479168*a^7*c^12*d^9*e^10*z^2 + 34464000*a^10*c^9*d^3*e^16*z^2 + 54240*b^15*c
^4*d^8*e^11*z^2 + 54240*b^8*c^11*d^15*e^4*z^2 - 49920*b^14*c^5*d^9*e^10*z^2 - 49920*b^9*c^10*d^14*e^5*z^2 - 37
376*b^16*c^3*d^7*e^12*z^2 - 37376*b^7*c^12*d^16*e^3*z^2 + 28480*b^13*c^6*d^10*e^9*z^2 + 28480*b^10*c^9*d^13*e^
6*z^2 + 15936*b^17*c^2*d^6*e^13*z^2 + 15936*b^6*c^13*d^17*e^2*z^2 - 7920*b^12*c^7*d^11*e^8*z^2 - 7920*b^11*c^8
*d^12*e^7*z^2 + 7489536*a^5*c^14*d^13*e^6*z^2 + 6084096*a^6*c^13*d^11*e^8*z^2 + 2280448*a^4*c^15*d^15*e^4*z^2
+ 350208*a^3*c^16*d^17*e^2*z^2 + 11616*a^2*b^17*d^2*e^17*z^2 - 3515904*a^9*b^5*c^5*e^19*z^2 + 3440640*a^10*b^3
*c^6*e^19*z^2 + 1870848*a^8*b^7*c^4*e^19*z^2 - 572272*a^7*b^9*c^3*e^19*z^2 + 101856*a^6*b^11*c^2*e^19*z^2 + 40
0*b^19*d^4*e^15*z^2 + 400*b^4*c^15*d^19*z^2 + 20736*a^2*c^17*d^19*z^2 + 400*a^4*b^15*e^19*z^2 - 3969216*a^4*b*
c^10*d^3*e^12 - 3001536*a^3*b*c^11*d^5*e^10 - 419904*a^2*b*c^12*d^7*e^8 + 184608*a^4*b^3*c^8*d*e^14 - 153036*a
*b^4*c^10*d^6*e^9 + 127008*a*b^3*c^11*d^7*e^8 + 63108*a*b^6*c^8*d^4*e^11 - 29160*a*b^2*c^12*d^8*e^7 - 21060*a^
3*b^5*c^7*d*e^14 - 21060*a*b^7*c^7*d^3*e^12 + 5460*a*b^5*c^9*d^5*e^10 - 404544*a^5*b*c^9*d*e^14 + 1251872*a^3*
b^3*c^9*d^3*e^12 + 844224*a^4*b^2*c^9*d^2*e^13 + 820512*a^2*b^3*c^10*d^5*e^10 + 750672*a^3*b^2*c^10*d^4*e^11 -
657498*a^2*b^4*c^9*d^4*e^11 - 487116*a^3*b^4*c^8*d^2*e^13 + 160704*a^2*b^2*c^11*d^6*e^9 + 58806*a^2*b^6*c^7*d
^2*e^13 + 13140*a^2*b^5*c^8*d^3*e^12 + 15286*b^6*c^9*d^6*e^9 - 9540*b^7*c^8*d^5*e^10 - 9540*b^5*c^10*d^7*e^8 +
2025*b^8*c^7*d^4*e^11 + 2025*b^4*c^11*d^8*e^7 + 3367008*a^4*c^11*d^4*e^11 + 1166400*a^3*c^12*d^6*e^9 + 705600
*a^5*c^10*d^2*e^13 + 104976*a^2*c^13*d^8*e^7 - 17640*a^5*b^2*c^8*e^15 + 2025*a^4*b^4*c^7*e^15 + 38416*a^6*c^9*
e^15, z, k)*((57344*a^12*c^9*e^21 - 80*a^5*b^14*c^2*e^21 + 1824*a^6*b^12*c^3*e^21 - 17296*a^7*b^10*c^4*e^21 +
87520*a^8*b^8*c^5*e^21 - 250880*a^9*b^6*c^6*e^21 + 394240*a^10*b^4*c^7*e^21 - 290816*a^11*b^2*c^8*e^21 + 18432
*a^3*c^18*d^18*e^3 + 210944*a^4*c^17*d^16*e^5 + 878592*a^5*c^16*d^14*e^7 + 4749312*a^6*c^15*d^12*e^9 + 2051891
2*a^7*c^14*d^10*e^11 + 12306432*a^8*c^13*d^8*e^13 - 22743040*a^9*c^12*d^6*e^15 - 20076544*a^10*c^11*d^4*e^17 -
1425408*a^11*c^10*d^2*e^19 - 80*b^5*c^16*d^19*e^2 + 704*b^6*c^15*d^18*e^3 - 2688*b^7*c^14*d^17*e^4 + 5824*b^8
*c^13*d^16*e^5 - 7840*b^9*c^12*d^15*e^6 + 6720*b^10*c^11*d^14*e^7 - 3728*b^11*c^10*d^13*e^8 + 2176*b^12*c^9*d^
12*e^9 - 3728*b^13*c^8*d^11*e^10 + 6720*b^14*c^7*d^10*e^11 - 7840*b^15*c^6*d^9*e^12 + 5824*b^16*c^5*d^8*e^13 -
2688*b^17*c^4*d^7*e^14 + 704*b^18*c^3*d^6*e^15 - 80*b^19*c^2*d^5*e^16 + 12288*a^2*b^2*c^17*d^18*e^3 - 1536*a^
2*b^3*c^16*d^17*e^4 - 131712*a^2*b^4*c^15*d^16*e^5 + 410112*a^2*b^5*c^14*d^15*e^6 - 576576*a^2*b^6*c^13*d^14*e
^7 + 342720*a^2*b^7*c^12*d^13*e^8 + 298464*a^2*b^8*c^11*d^12*e^9 - 1248672*a^2*b^9*c^10*d^11*e^10 + 2177920*a^
2*b^10*c^9*d^10*e^11 - 2309120*a^2*b^11*c^8*d^9*e^12 + 1389888*a^2*b^12*c^7*d^8*e^13 - 314048*a^2*b^13*c^6*d^7
*e^14 - 120896*a^2*b^14*c^5*d^6*e^15 + 88128*a^2*b^15*c^4*d^5*e^16 - 14240*a^2*b^16*c^3*d^4*e^17 - 416*a^2*b^1
7*c^2*d^3*e^18 + 621568*a^3*b^2*c^16*d^16*e^5 - 953344*a^3*b^3*c^15*d^15*e^6 + 196224*a^3*b^4*c^14*d^14*e^7 +
1667904*a^3*b^5*c^13*d^13*e^8 - 3981824*a^3*b^6*c^12*d^12*e^9 + 7617920*a^3*b^7*c^11*d^11*e^10 - 11899456*a^3*
b^8*c^10*d^10*e^11 + 11500496*a^3*b^9*c^9*d^9*e^12 - 4599536*a^3*b^10*c^8*d^8*e^13 - 1951936*a^3*b^11*c^7*d^7*
e^14 + 2953152*a^3*b^12*c^6*d^6*e^15 - 1134960*a^3*b^13*c^5*d^5*e^16 + 98960*a^3*b^14*c^4*d^4*e^17 + 21920*a^3
*b^15*c^3*d^3*e^18 - 416*a^3*b^16*c^2*d^2*e^19 + 4509696*a^4*b^2*c^15*d^14*e^7 - 6720000*a^4*b^3*c^14*d^13*e^8
+ 8231808*a^4*b^4*c^13*d^12*e^9 - 17138976*a^4*b^5*c^12*d^11*e^10 + 30880320*a^4*b^6*c^11*d^10*e^11 - 2488345
6*a^4*b^7*c^10*d^9*e^12 - 6291360*a^4*b^8*c^9*d^8*e^13 + 28429152*a^4*b^9*c^8*d^7*e^14 - 21523072*a^4*b^10*c^7
*d^6*e^15 + 5834928*a^4*b^11*c^6*d^5*e^16 + 339872*a^4*b^12*c^5*d^4*e^17 - 325216*a^4*b^13*c^4*d^3*e^18 + 1344
*a^4*b^14*c^3*d^2*e^19 + 5483520*a^5*b^2*c^14*d^12*e^9 + 14537472*a^5*b^3*c^13*d^11*e^10 - 39383680*a^5*b^4*c^
12*d^10*e^11 + 5513408*a^5*b^5*c^11*d^9*e^12 + 84582144*a^5*b^6*c^10*d^8*e^13 - 124246848*a^5*b^7*c^9*d^7*e^14
+ 70979712*a^5*b^8*c^8*d^6*e^15 - 8326320*a^5*b^9*c^7*d^5*e^16 - 7484656*a^5*b^10*c^6*d^4*e^17 + 2142272*a^5*
b^11*c^5*d^3*e^18 + 83520*a^5*b^12*c^4*d^2*e^19 + 25849856*a^6*b^2*c^13*d^10*e^11 + 67294720*a^6*b^3*c^12*d^9*
e^12 - 216767360*a^6*b^4*c^11*d^8*e^13 + 237211008*a^6*b^5*c^10*d^7*e^14 - 88839360*a^6*b^6*c^9*d^6*e^15 - 359
29920*a^6*b^7*c^8*d^5*e^16 + 37859616*a^6*b^8*c^7*d^4*e^17 - 6475552*a^6*b^9*c^6*d^3*e^18 - 1055296*a^6*b^10*c
^5*d^2*e^19 + 190669824*a^7*b^2*c^12*d^8*e^13 - 143425536*a^7*b^3*c^11*d^7*e^14 - 47908992*a^7*b^4*c^10*d^6*e^
15 + 154814400*a^7*b^5*c^9*d^5*e^16 - 83642880*a^7*b^6*c^8*d^4*e^17 + 4534272*a^7*b^7*c^7*d^3*e^18 + 5525568*a
^7*b^8*c^6*d^2*e^19 + 165122048*a^8*b^2*c^11*d^6*e^15 - 187467264*a^8*b^3*c^10*d^5*e^16 + 66920064*a^8*b^4*c^9
*d^4*e^17 + 21356016*a^8*b^5*c^8*d^3*e^18 - 14644224*a^8*b^6*c^7*d^2*e^19 + 16114688*a^9*b^2*c^10*d^4*e^17 - 4
8695936*a^9*b^3*c^9*d^3*e^18 + 18757632*a^9*b^4*c^8*d^2*e^19 - 8060928*a^10*b^2*c^9*d^2*e^19 + 1257472*a^11*b*
c^9*d*e^20 + 896*a*b^3*c^17*d^19*e^2 - 7040*a*b^4*c^16*d^18*e^3 + 22080*a*b^5*c^15*d^17*e^4 - 32512*a*b^6*c^14
*d^16*e^5 + 12736*a*b^7*c^13*d^15*e^6 + 31104*a*b^8*c^12*d^14*e^7 - 51472*a*b^9*c^11*d^13*e^8 + 10864*a*b^10*c
^10*d^12*e^9 + 85440*a*b^11*c^9*d^11*e^10 - 186560*a*b^12*c^8*d^10*e^11 + 215904*a*b^13*c^7*d^9*e^12 - 151008*
a*b^14*c^6*d^8*e^13 + 59776*a*b^15*c^5*d^7*e^14 - 9408*a*b^16*c^4*d^6*e^15 - 1296*a*b^17*c^3*d^5*e^16 + 496*a*
b^18*c^2*d^4*e^17 - 2304*a^2*b*c^18*d^19*e^2 - 175104*a^3*b*c^17*d^17*e^4 - 1556480*a^4*b*c^16*d^15*e^6 + 496*
a^4*b^15*c^2*d*e^20 - 4746240*a^5*b*c^15*d^13*e^8 - 10256*a^5*b^13*c^3*d*e^20 - 24033792*a^6*b*c^14*d^11*e^10
+ 84512*a^6*b^11*c^4*d*e^20 - 100332544*a^7*b*c^13*d^9*e^12 - 341264*a^7*b^9*c^5*d*e^20 - 65824768*a^8*b*c^12*
d^7*e^14 + 621568*a^8*b^7*c^6*d*e^20 + 39738368*a^9*b*c^11*d^5*e^16 - 68096*a^9*b^5*c^7*d*e^20 + 27159296*a^10
*b*c^10*d^3*e^18 - 1310720*a^10*b^3*c^8*d*e^20)/(32*(16*a^3*b^6*c^9*d^18 - a^2*b^8*c^8*d^18 - 256*a^6*c^12*d^1
8 - 96*a^4*b^4*c^10*d^18 + 256*a^5*b^2*c^11*d^18 - a^2*b^16*d^10*e^8 + 8*a^3*b^15*d^9*e^9 - 28*a^4*b^14*d^8*e^
10 + 56*a^5*b^13*d^7*e^11 - 70*a^6*b^12*d^6*e^12 + 56*a^7*b^11*d^5*e^13 - 28*a^8*b^10*d^4*e^14 + 8*a^9*b^9*d^3
*e^15 - a^10*b^8*d^2*e^16 - 2048*a^7*c^11*d^16*e^2 - 7168*a^8*c^10*d^14*e^4 - 14336*a^9*c^9*d^12*e^6 - 17920*a
^10*c^8*d^10*e^8 - 14336*a^11*c^7*d^8*e^10 - 7168*a^12*c^6*d^6*e^12 - 2048*a^13*c^5*d^4*e^14 - 256*a^14*c^4*d^
2*e^16 - 28*a^2*b^10*c^6*d^16*e^2 + 56*a^2*b^11*c^5*d^15*e^3 - 70*a^2*b^12*c^4*d^14*e^4 + 56*a^2*b^13*c^3*d^13
*e^5 - 28*a^2*b^14*c^2*d^12*e^6 + 440*a^3*b^8*c^7*d^16*e^2 - 840*a^3*b^9*c^6*d^15*e^3 + 952*a^3*b^10*c^5*d^14*
e^4 - 616*a^3*b^11*c^4*d^13*e^5 + 168*a^3*b^12*c^3*d^12*e^6 + 40*a^3*b^13*c^2*d^11*e^7 - 2560*a^4*b^6*c^8*d^16
*e^2 + 4480*a^4*b^7*c^7*d^15*e^3 - 4060*a^4*b^8*c^6*d^14*e^4 + 1064*a^4*b^9*c^5*d^13*e^5 + 1372*a^4*b^10*c^4*d
^12*e^6 - 1360*a^4*b^11*c^3*d^11*e^7 + 380*a^4*b^12*c^2*d^10*e^8 + 6400*a^5*b^4*c^9*d^16*e^2 - 8960*a^5*b^5*c^
8*d^15*e^3 + 2240*a^5*b^6*c^7*d^14*e^4 + 9856*a^5*b^7*c^6*d^13*e^5 - 13048*a^5*b^8*c^5*d^12*e^6 + 5400*a^5*b^9
*c^4*d^11*e^7 + 1040*a^5*b^10*c^3*d^10*e^8 - 1360*a^5*b^11*c^2*d^9*e^9 - 5120*a^6*b^2*c^10*d^16*e^2 + 22400*a^
6*b^4*c^8*d^14*e^4 - 41216*a^6*b^5*c^7*d^13*e^5 + 25088*a^6*b^6*c^6*d^12*e^6 + 8320*a^6*b^7*c^5*d^11*e^7 - 173
50*a^6*b^8*c^4*d^10*e^8 + 5400*a^6*b^9*c^3*d^9*e^9 + 1372*a^6*b^10*c^2*d^8*e^10 - 35840*a^7*b^2*c^9*d^14*e^4 +
28672*a^7*b^3*c^8*d^13*e^5 + 30464*a^7*b^4*c^7*d^12*e^6 - 73472*a^7*b^5*c^6*d^11*e^7 + 40544*a^7*b^6*c^5*d^10
*e^8 + 8320*a^7*b^7*c^4*d^9*e^9 - 13048*a^7*b^8*c^3*d^8*e^10 + 1064*a^7*b^9*c^2*d^7*e^11 - 93184*a^8*b^2*c^8*d
^12*e^6 + 71680*a^8*b^3*c^7*d^11*e^7 + 29120*a^8*b^4*c^6*d^10*e^8 - 73472*a^8*b^5*c^5*d^9*e^9 + 25088*a^8*b^6*
c^4*d^8*e^10 + 9856*a^8*b^7*c^3*d^7*e^11 - 4060*a^8*b^8*c^2*d^6*e^12 - 125440*a^9*b^2*c^7*d^10*e^8 + 71680*a^9
*b^3*c^6*d^9*e^9 + 30464*a^9*b^4*c^5*d^8*e^10 - 41216*a^9*b^5*c^4*d^7*e^11 + 2240*a^9*b^6*c^3*d^6*e^12 + 4480*
a^9*b^7*c^2*d^5*e^13 - 93184*a^10*b^2*c^6*d^8*e^10 + 28672*a^10*b^3*c^5*d^7*e^11 + 22400*a^10*b^4*c^4*d^6*e^12
- 8960*a^10*b^5*c^3*d^5*e^13 - 2560*a^10*b^6*c^2*d^4*e^14 - 35840*a^11*b^2*c^5*d^6*e^12 + 6400*a^11*b^4*c^3*d
^4*e^14 + 768*a^11*b^5*c^2*d^3*e^15 - 5120*a^12*b^2*c^4*d^4*e^14 - 2048*a^12*b^3*c^3*d^3*e^15 - 96*a^12*b^4*c^
2*d^2*e^16 + 256*a^13*b^2*c^3*d^2*e^16 + 2048*a^6*b*c^11*d^17*e + 8*a^2*b^9*c^7*d^17*e + 8*a^2*b^15*c*d^11*e^7
- 128*a^3*b^7*c^8*d^17*e - 40*a^3*b^14*c*d^10*e^8 + 768*a^4*b^5*c^9*d^17*e + 40*a^4*b^13*c*d^9*e^9 - 2048*a^5
*b^3*c^10*d^17*e + 168*a^5*b^12*c*d^8*e^10 - 616*a^6*b^11*c*d^7*e^11 + 14336*a^7*b*c^10*d^15*e^3 + 952*a^7*b^1
0*c*d^6*e^12 + 43008*a^8*b*c^9*d^13*e^5 - 840*a^8*b^9*c*d^5*e^13 + 71680*a^9*b*c^8*d^11*e^7 + 440*a^9*b^8*c*d^
4*e^14 + 71680*a^10*b*c^7*d^9*e^9 - 128*a^10*b^7*c*d^3*e^15 + 43008*a^11*b*c^6*d^7*e^11 + 16*a^11*b^6*c*d^2*e^
16 + 14336*a^12*b*c^5*d^5*e^13 + 2048*a^13*b*c^4*d^3*e^15)) - root(128723189760*a^14*b^4*c^9*d^13*e^14*z^6 + 1
28723189760*a^12*b^4*c^11*d^17*e^10*z^6 - 8432455680*a^11*b^12*c^4*d^11*e^16*z^6 - 8432455680*a^7*b^12*c^8*d^1
9*e^8*z^6 + 12673351680*a^11*b^11*c^5*d^12*e^15*z^6 + 12673351680*a^8*b^11*c^8*d^18*e^9*z^6 - 72637480960*a^12
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443840*a^17*b^3*c^7*d^8*e^19*z^6 - 16609443840*a^10*b^3*c^14*d^22*e^5*z^6 + 145332633600*a^13*b^5*c^9*d^14*e^1
3*z^6 + 145332633600*a^12*b^5*c^10*d^16*e^11*z^6 + 123740356608*a^14*b^5*c^8*d^12*e^15*z^6 + 123740356608*a^11
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792*a^15*b^7*c^5*d^8*e^19*z^6 - 7751073792*a^8*b^7*c^12*d^22*e^5*z^6 + 12041846784*a^14*b^7*c^6*d^10*e^17*z^6
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6 + 37492359168*a^9*b^10*c^8*d^17*e^10*z^6 + 301989888*a^8*b^3*c^16*d^26*e*z^6 - 7266631680*a^17*b^4*c^6*d^7*e
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26*e*z^6 + 45747339264*a^13*b^8*c^6*d^11*e^16*z^6 + 45747339264*a^9*b^8*c^10*d^19*e^8*z^6 - 74612736*a^10*b^16
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10*e^17*z^6 - 27691057152*a^8*b^9*c^10*d^20*e^7*z^6 - 1902673920*a^8*b^15*c^4*d^14*e^13*z^6 - 1902673920*a^7*b
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48530718720*a^12*b^8*c^7*d^13*e^14*z^6 + 48530718720*a^10*b^8*c^9*d^17*e^10*z^6 - 1242644480*a^12*b^12*c^3*d^9
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8*e^9*z^6 + 4390256640*a^15*b^8*c^4*d^7*e^20*z^6 + 4390256640*a^7*b^8*c^12*d^23*e^4*z^6 - 91750400*a^6*b^18*c^
3*d^15*e^12*z^6 + 79134720*a^7*b^17*c^3*d^14*e^13*z^6 + 79134720*a^6*b^17*c^4*d^16*e^11*z^6 - 74612736*a^4*b^1
6*c^7*d^21*e^6*z^6 - 72990720*a^7*b^18*c^2*d^13*e^14*z^6 - 72990720*a^5*b^18*c^4*d^17*e^10*z^6 + 69746688*a^4*
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6480*a^16*b^9*c^2*d^4*e^23*z^6 - 6438912*a^4*b^12*c^11*d^25*e^2*z^6 + 5406720*a^4*b^19*c^4*d^18*e^9*z^6 - 5242
880*a^18*b^6*c^3*d^3*e^24*z^6 + 3784704*a^3*b^18*c^6*d^21*e^6*z^6 - 3244032*a^3*b^19*c^5*d^20*e^7*z^6 - 324403
2*a^3*b^17*c^7*d^22*e^5*z^6 + 2027520*a^3*b^20*c^4*d^19*e^8*z^6 + 2027520*a^3*b^16*c^8*d^23*e^4*z^6 - 1622016*
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8640*a^15*b^3*c^9*d^12*e^15*z^6 - 210386288640*a^12*b^3*c^12*d^18*e^9*z^6 + 15502147584*a^15*c^12*d^15*e^12*z^
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16777216*a^21*c^6*d^3*e^24*z^6 + 3784704*a^9*b^18*d^9*e^18*z^6 - 3244032*a^10*b^17*d^8*e^19*z^6 - 3244032*a^8*
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21*z^6 - 901120*a^6*b^21*d^12*e^15*z^6 + 270336*a^13*b^14*d^5*e^22*z^6 + 270336*a^5*b^22*d^13*e^14*z^6 - 49152
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0*a^5*b^8*c^14*d^27*z^6 - 98304*a^4*b^10*c^13*d^27*z^6 + 4096*a^3*b^12*c^12*d^27*z^6 + 8304721920*a^17*c^10*d^
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7*d^11*e^12*z^4 - 7782137856*a^8*b^7*c^8*d^11*e^12*z^4 + 7780433920*a^12*b^2*c^9*d^8*e^15*z^4 - 12020465664*a^
7*b^5*c^11*d^15*e^8*z^4 + 3176792064*a^8*b^3*c^12*d^15*e^8*z^4 - 322633728*a^15*b*c^7*d^3*e^20*z^4 + 210829312
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62336*a^8*b^6*c^9*d^12*e^11*z^4 - 15333588992*a^10*b^4*c^9*d^10*e^13*z^4 + 6702170112*a^7*b^4*c^12*d^16*e^7*z^
4 + 15167913984*a^10*b^3*c^10*d^11*e^12*z^4 - 2256638976*a^5*b^11*c^7*d^13*e^10*z^4 + 2254307328*a^5*b^7*c^11*
d^17*e^6*z^4 - 2200633344*a^6*b^5*c^12*d^17*e^6*z^4 + 6457131008*a^11*b^3*c^9*d^9*e^14*z^4 - 2128785408*a^5*b^
8*c^10*d^16*e^7*z^4 - 2126057472*a^6*b^11*c^6*d^11*e^12*z^4 + 2038349824*a^12*b^5*c^6*d^5*e^18*z^4 + 203784192
0*a^5*b^10*c^8*d^14*e^9*z^4 + 3615621120*a^9*b*c^13*d^15*e^8*z^4 + 1900019712*a^11*b^2*c^10*d^10*e^13*z^4 + 18
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8*z^4 - 232683264*a^8*b^11*c^4*d^7*e^16*z^4 - 199627776*a^5*b^14*c^4*d^10*e^13*z^4 - 190267392*a^12*b^7*c^4*d^
3*e^20*z^4 + 184891392*a^6*b^10*c^7*d^12*e^11*z^4 + 180502528*a^4*b^7*c^12*d^19*e^4*z^4 + 178877952*a^3*b^13*c
^7*d^15*e^8*z^4 + 172490752*a^14*b^3*c^6*d^3*e^20*z^4 + 163946496*a^13*b^5*c^5*d^3*e^20*z^4 + 155839488*a^8*b^
12*c^3*d^6*e^17*z^4 + 155000832*a^5*b^5*c^13*d^19*e^4*z^4 - 152076288*a^4*b^6*c^13*d^20*e^3*z^4 - 137592576*a^
3*b^12*c^8*d^16*e^7*z^4 - 133693440*a^14*b^4*c^5*d^2*e^21*z^4 - 116767488*a^3*b^9*c^11*d^19*e^4*z^4 - 10898534
4*a^3*b^14*c^6*d^14*e^9*z^4 - 106223616*a^6*b^13*c^4*d^9*e^14*z^4 + 106119168*a^3*b^10*c^10*d^18*e^5*z^4 + 102
432768*a^5*b^4*c^14*d^20*e^3*z^4 + 102113280*a^4*b^12*c^7*d^14*e^9*z^4 + 100674048*a^5*b^9*c^9*d^15*e^8*z^4 +
90439680*a^13*b^6*c^4*d^2*e^21*z^4 - 86808576*a^6*b^14*c^3*d^8*e^15*z^4 + 86245376*a^6*b^2*c^15*d^20*e^3*z^4 +
79011840*a^4*b^8*c^11*d^18*e^5*z^4 + 78345216*a^4*b^15*c^4*d^11*e^12*z^4 + 78006528*a^11*b^9*c^3*d^3*e^20*z^4
- 73253376*a^9*b^11*c^3*d^5*e^18*z^4 + 67524608*a^3*b^8*c^12*d^20*e^3*z^4 + 67108864*a^15*b^2*c^6*d^2*e^21*z^
4 - 61590528*a^10*b^10*c^3*d^4*e^19*z^4 + 61559808*a^5*b^15*c^3*d^9*e^14*z^4 - 59637760*a^5*b^3*c^15*d^21*e^2*
z^4 + 58638336*a^4*b^5*c^14*d^21*e^2*z^4 - 40828416*a^7*b^13*c^3*d^7*e^16*z^4 - 35639296*a^2*b^12*c^9*d^18*e^5
*z^4 - 31293440*a^12*b^8*c^3*d^2*e^21*z^4 + 29933568*a^5*b^13*c^5*d^11*e^12*z^4 + 27793920*a^2*b^11*c^10*d^19*
e^4*z^4 + 27168768*a^2*b^13*c^8*d^17*e^6*z^4 - 23602176*a^7*b^14*c^2*d^6*e^17*z^4 - 23248896*a^3*b^7*c^13*d^21
*e^2*z^4 + 20929536*a^3*b^15*c^5*d^13*e^10*z^4 + 18428928*a^9*b^12*c^2*d^4*e^19*z^4 + 18026496*a^6*b^15*c^2*d^
7*e^16*z^4 - 16261632*a^10*b^11*c^2*d^3*e^20*z^4 + 15128064*a^3*b^16*c^4*d^12*e^11*z^4 - 14060544*a^2*b^10*c^1
1*d^20*e^3*z^4 + 13178880*a^2*b^16*c^5*d^14*e^9*z^4 - 11244288*a^3*b^17*c^3*d^11*e^12*z^4 - 10509312*a^2*b^15*
c^6*d^15*e^8*z^4 - 7262208*a^4*b^17*c^2*d^9*e^14*z^4 - 7045632*a^2*b^17*c^4*d^13*e^10*z^4 - 6285312*a^2*b^14*c
^7*d^16*e^7*z^4 + 5996544*a^11*b^10*c^2*d^2*e^21*z^4 + 4558336*a^2*b^9*c^12*d^21*e^2*z^4 + 4478976*a^11*b^8*c^
4*d^4*e^19*z^4 + 2850816*a^4*b^16*c^3*d^10*e^13*z^4 + 2629632*a^3*b^11*c^9*d^17*e^6*z^4 + 2503680*a^3*b^18*c^2
*d^10*e^13*z^4 + 1627136*a^2*b^18*c^3*d^12*e^11*z^4 + 1605120*a^8*b^13*c^2*d^5*e^18*z^4 + 1483776*a^5*b^16*c^2
*d^8*e^15*z^4 + 139776*a^2*b^19*c^2*d^11*e^12*z^4 - 8542224384*a^10*b^2*c^11*d^12*e^11*z^4 - 3072*b^22*c*d^12*
e^11*z^4 - 3072*b^12*c^11*d^22*e*z^4 - 1572864*a^6*c^17*d^22*e*z^4 - 4096*a^10*b^13*d*e^22*z^4 - 4096*a*b^22*d
^10*e^13*z^4 - 6144*a^12*b^10*c*e^23*z^4 - 983040*a^5*b*c^17*d^23*z^4 - 6912*a*b^9*c^13*d^23*z^4 + 1824522240*
a^13*c^10*d^8*e^15*z^4 + 1730150400*a^12*c^11*d^10*e^13*z^4 + 958922752*a^14*c^9*d^6*e^17*z^4 - 537919488*a^9*
c^14*d^16*e^7*z^4 + 508559360*a^11*c^12*d^12*e^11*z^4 - 500170752*a^10*c^13*d^14*e^9*z^4 + 246939648*a^15*c^8*
d^4*e^19*z^4 - 199229440*a^8*c^15*d^18*e^5*z^4 - 29884416*a^7*c^16*d^20*e^3*z^4 + 25165824*a^16*c^7*d^2*e^21*z
^4 + 236544*b^17*c^6*d^17*e^6*z^4 - 202752*b^18*c^5*d^16*e^7*z^4 - 202752*b^16*c^7*d^18*e^5*z^4 + 126720*b^19*
c^4*d^15*e^8*z^4 + 126720*b^15*c^8*d^19*e^4*z^4 - 56320*b^20*c^3*d^14*e^9*z^4 - 56320*b^14*c^9*d^20*e^3*z^4 +
16896*b^21*c^2*d^13*e^10*z^4 + 16896*b^13*c^10*d^21*e^2*z^4 + 110080*a^7*b^16*d^4*e^19*z^4 + 110080*a^4*b^19*d
^7*e^16*z^4 - 75520*a^8*b^15*d^3*e^20*z^4 - 75520*a^3*b^20*d^8*e^15*z^4 - 56320*a^6*b^17*d^5*e^18*z^4 - 56320*
a^5*b^18*d^6*e^17*z^4 + 25600*a^9*b^14*d^2*e^21*z^4 + 25600*a^2*b^21*d^9*e^14*z^4 - 1572864*a^16*b^2*c^5*e^23*
z^4 + 983040*a^15*b^4*c^4*e^23*z^4 - 327680*a^14*b^6*c^3*e^23*z^4 + 61440*a^13*b^8*c^2*e^23*z^4 + 983040*a^4*b
^3*c^16*d^23*z^4 - 385024*a^3*b^5*c^15*d^23*z^4 + 73728*a^2*b^7*c^14*d^23*z^4 + 256*b^23*d^11*e^12*z^4 + 10485
76*a^17*c^6*e^23*z^4 + 256*b^11*c^12*d^23*z^4 + 256*a^11*b^12*e^23*z^4 + 948695040*a^8*b*c^10*d^6*e^13*z^2 + 3
48917760*a^7*b*c^11*d^8*e^11*z^2 - 125030400*a^9*b*c^9*d^4*e^15*z^2 - 50728960*a^6*b*c^12*d^10*e^9*z^2 - 44298
240*a^5*b*c^13*d^12*e^7*z^2 - 36495360*a^10*b*c^8*d^2*e^17*z^2 + 29675520*a^8*b^6*c^5*d*e^18*z^2 - 24170496*a^
9*b^4*c^6*d*e^18*z^2 - 17202816*a^7*b^8*c^4*d*e^18*z^2 - 14561280*a^4*b*c^14*d^14*e^5*z^2 + 5532416*a^6*b^10*c
^3*d*e^18*z^2 + 4128768*a^10*b^2*c^7*d*e^18*z^2 - 2662400*a^3*b*c^15*d^16*e^3*z^2 + 1184512*a*b^12*c^6*d^9*e^1
0*z^2 - 1136160*a*b^13*c^5*d^8*e^11*z^2 - 1017600*a^5*b^12*c^2*d*e^18*z^2 - 744768*a*b^11*c^7*d^10*e^9*z^2 + 6
07872*a*b^14*c^4*d^7*e^12*z^2 - 424064*a*b^6*c^12*d^15*e^4*z^2 + 408576*a*b^5*c^13*d^16*e^3*z^2 + 361152*a*b^1
0*c^8*d^11*e^8*z^2 - 287408*a*b^9*c^9*d^12*e^7*z^2 - 260448*a^3*b^15*c*d^2*e^17*z^2 - 203904*a*b^4*c^14*d^17*e
^2*z^2 + 200832*a*b^8*c^10*d^13*e^6*z^2 + 126720*a*b^7*c^11*d^14*e^5*z^2 - 123968*a*b^15*c^3*d^6*e^13*z^2 - 39
168*a*b^16*c^2*d^5*e^14*z^2 + 11904*a^2*b^16*c*d^3*e^16*z^2 + 1824135552*a^7*b^4*c^8*d^5*e^14*z^2 - 1457252352
*a^8*b^2*c^9*d^5*e^14*z^2 - 1405209600*a^7*b^5*c^7*d^4*e^15*z^2 - 184320*a^2*b*c^16*d^18*e*z^2 + 100608*a^4*b^
14*c*d*e^18*z^2 + 53248*a*b^3*c^15*d^18*e*z^2 + 26448*a*b^17*c*d^4*e^15*z^2 + 1067599872*a^8*b^3*c^8*d^4*e^15*
z^2 - 930828288*a^7*b^3*c^9*d^6*e^13*z^2 + 920760000*a^6*b^4*c^9*d^7*e^12*z^2 - 806639616*a^6*b^3*c^10*d^8*e^1
1*z^2 - 791052480*a^6*b^6*c^7*d^5*e^14*z^2 + 772237824*a^6*b^7*c^6*d^4*e^15*z^2 - 701025408*a^5*b^6*c^8*d^7*e^
12*z^2 + 443340288*a^5*b^5*c^9*d^8*e^11*z^2 + 433047552*a^7*b^6*c^6*d^3*e^16*z^2 + 405741312*a^5*b^7*c^7*d^6*e
^13*z^2 + 293652480*a^6*b^2*c^11*d^9*e^10*z^2 - 276962688*a^6*b^8*c^5*d^3*e^16*z^2 - 247804272*a^8*b^4*c^7*d^3
*e^16*z^2 + 213564384*a^4*b^8*c^7*d^7*e^12*z^2 - 202596816*a^5*b^9*c^5*d^4*e^15*z^2 - 182520896*a^4*b^9*c^6*d^
6*e^13*z^2 - 153489408*a^5*b^3*c^11*d^10*e^9*z^2 - 152151552*a^7*b^2*c^10*d^7*e^12*z^2 + 115859712*a^5*b^2*c^1
2*d^11*e^8*z^2 + 108085248*a^9*b^3*c^7*d^2*e^17*z^2 + 105536256*a^4*b^5*c^10*d^10*e^9*z^2 - 98323200*a^6*b^5*c
^8*d^6*e^13*z^2 - 93564992*a^4*b^6*c^9*d^9*e^10*z^2 + 89464512*a^5*b^10*c^4*d^3*e^16*z^2 - 75930624*a^8*b^5*c^
6*d^2*e^17*z^2 + 68315904*a^5*b^8*c^6*d^5*e^14*z^2 - 64157184*a^4*b^7*c^8*d^8*e^11*z^2 - 62951040*a^9*b^2*c^8*
d^3*e^16*z^2 + 49056768*a^4*b^10*c^5*d^5*e^14*z^2 + 47614464*a^3*b^8*c^8*d^9*e^10*z^2 + 35604480*a^4*b^2*c^13*
d^13*e^6*z^2 + 33983040*a^3*b^11*c^5*d^6*e^13*z^2 - 33515520*a^4*b^3*c^12*d^12*e^7*z^2 - 33463808*a^3*b^7*c^9*
d^10*e^9*z^2 - 25128864*a^4*b^4*c^11*d^11*e^8*z^2 - 23193728*a^3*b^10*c^6*d^7*e^12*z^2 + 21015456*a^6*b^9*c^4*
d^2*e^17*z^2 + 19924176*a^4*b^11*c^4*d^4*e^15*z^2 - 19251216*a^3*b^9*c^7*d^8*e^11*z^2 - 16434048*a^5*b^4*c^10*
d^9*e^10*z^2 - 16289664*a^3*b^12*c^4*d^5*e^14*z^2 - 15059328*a^4*b^12*c^3*d^3*e^16*z^2 - 10766016*a^2*b^10*c^7
*d^9*e^10*z^2 - 10453632*a^5*b^11*c^3*d^2*e^17*z^2 - 9940992*a^3*b^3*c^13*d^14*e^5*z^2 + 8373696*a^2*b^11*c^6*
d^8*e^11*z^2 + 7776768*a^3*b^2*c^14*d^15*e^4*z^2 + 7077888*a^3*b^5*c^11*d^12*e^7*z^2 + 6798240*a^2*b^9*c^8*d^1
0*e^9*z^2 - 3589440*a^2*b^6*c^11*d^13*e^6*z^2 + 3544320*a^3*b^6*c^10*d^11*e^8*z^2 + 3128064*a^2*b^5*c^12*d^14*
e^5*z^2 + 2346336*a^4*b^13*c^2*d^2*e^17*z^2 - 2261568*a^2*b^8*c^9*d^11*e^8*z^2 - 2125824*a^2*b^13*c^4*d^6*e^13
*z^2 + 2002560*a^3*b^4*c^12*d^13*e^6*z^2 + 1927680*a^2*b^7*c^10*d^12*e^7*z^2 + 1814784*a^2*b^14*c^3*d^5*e^14*z
^2 - 1807104*a^2*b^12*c^5*d^7*e^12*z^2 + 1637808*a^3*b^13*c^3*d^4*e^15*z^2 + 1083456*a^3*b^14*c^2*d^3*e^16*z^2
- 792384*a^2*b^4*c^13*d^15*e^4*z^2 - 657408*a^2*b^3*c^14*d^16*e^3*z^2 + 608256*a^7*b^7*c^5*d^2*e^17*z^2 + 595
968*a^2*b^2*c^15*d^17*e^2*z^2 - 498624*a^2*b^15*c^2*d^4*e^15*z^2 - 3840*b^18*c*d^5*e^14*z^2 - 3840*b^5*c^14*d^
18*e*z^2 + 2064384*a^11*c^8*d*e^18*z^2 - 4160*a^3*b^16*d*e^18*z^2 - 4160*a*b^18*d^3*e^16*z^2 - 1290240*a^11*b*
c^7*e^19*z^2 - 9840*a^5*b^13*c*e^19*z^2 - 5760*a*b^2*c^16*d^19*z^2 - 280581120*a^8*c^11*d^7*e^12*z^2 + 1102786
56*a^9*c^10*d^5*e^14*z^2 - 89479168*a^7*c^12*d^9*e^10*z^2 + 34464000*a^10*c^9*d^3*e^16*z^2 + 54240*b^15*c^4*d^
8*e^11*z^2 + 54240*b^8*c^11*d^15*e^4*z^2 - 49920*b^14*c^5*d^9*e^10*z^2 - 49920*b^9*c^10*d^14*e^5*z^2 - 37376*b
^16*c^3*d^7*e^12*z^2 - 37376*b^7*c^12*d^16*e^3*z^2 + 28480*b^13*c^6*d^10*e^9*z^2 + 28480*b^10*c^9*d^13*e^6*z^2
+ 15936*b^17*c^2*d^6*e^13*z^2 + 15936*b^6*c^13*d^17*e^2*z^2 - 7920*b^12*c^7*d^11*e^8*z^2 - 7920*b^11*c^8*d^12
*e^7*z^2 + 7489536*a^5*c^14*d^13*e^6*z^2 + 6084096*a^6*c^13*d^11*e^8*z^2 + 2280448*a^4*c^15*d^15*e^4*z^2 + 350
208*a^3*c^16*d^17*e^2*z^2 + 11616*a^2*b^17*d^2*e^17*z^2 - 3515904*a^9*b^5*c^5*e^19*z^2 + 3440640*a^10*b^3*c^6*
e^19*z^2 + 1870848*a^8*b^7*c^4*e^19*z^2 - 572272*a^7*b^9*c^3*e^19*z^2 + 101856*a^6*b^11*c^2*e^19*z^2 + 400*b^1
9*d^4*e^15*z^2 + 400*b^4*c^15*d^19*z^2 + 20736*a^2*c^17*d^19*z^2 + 400*a^4*b^15*e^19*z^2 - 3969216*a^4*b*c^10*
d^3*e^12 - 3001536*a^3*b*c^11*d^5*e^10 - 419904*a^2*b*c^12*d^7*e^8 + 184608*a^4*b^3*c^8*d*e^14 - 153036*a*b^4*
c^10*d^6*e^9 + 127008*a*b^3*c^11*d^7*e^8 + 63108*a*b^6*c^8*d^4*e^11 - 29160*a*b^2*c^12*d^8*e^7 - 21060*a^3*b^5
*c^7*d*e^14 - 21060*a*b^7*c^7*d^3*e^12 + 5460*a*b^5*c^9*d^5*e^10 - 404544*a^5*b*c^9*d*e^14 + 1251872*a^3*b^3*c
^9*d^3*e^12 + 844224*a^4*b^2*c^9*d^2*e^13 + 820512*a^2*b^3*c^10*d^5*e^10 + 750672*a^3*b^2*c^10*d^4*e^11 - 6574
98*a^2*b^4*c^9*d^4*e^11 - 487116*a^3*b^4*c^8*d^2*e^13 + 160704*a^2*b^2*c^11*d^6*e^9 + 58806*a^2*b^6*c^7*d^2*e^
13 + 13140*a^2*b^5*c^8*d^3*e^12 + 15286*b^6*c^9*d^6*e^9 - 9540*b^7*c^8*d^5*e^10 - 9540*b^5*c^10*d^7*e^8 + 2025
*b^8*c^7*d^4*e^11 + 2025*b^4*c^11*d^8*e^7 + 3367008*a^4*c^11*d^4*e^11 + 1166400*a^3*c^12*d^6*e^9 + 705600*a^5*
c^10*d^2*e^13 + 104976*a^2*c^13*d^8*e^7 - 17640*a^5*b^2*c^8*e^15 + 2025*a^4*b^4*c^7*e^15 + 38416*a^6*c^9*e^15,
z, k)*(root(128723189760*a^14*b^4*c^9*d^13*e^14*z^6 + 128723189760*a^12*b^4*c^11*d^17*e^10*z^6 - 8432455680*a
^11*b^12*c^4*d^11*e^16*z^6 - 8432455680*a^7*b^12*c^8*d^19*e^8*z^6 + 12673351680*a^11*b^11*c^5*d^12*e^15*z^6 +
12673351680*a^8*b^11*c^8*d^18*e^9*z^6 - 72637480960*a^12*b^9*c^6*d^12*e^15*z^6 - 72637480960*a^9*b^9*c^9*d^18*
e^9*z^6 - 21048344576*a^9*b^12*c^6*d^15*e^12*z^6 - 16609443840*a^17*b^3*c^7*d^8*e^19*z^6 - 16609443840*a^10*b^
3*c^14*d^22*e^5*z^6 + 145332633600*a^13*b^5*c^9*d^14*e^13*z^6 + 145332633600*a^12*b^5*c^10*d^16*e^11*z^6 + 123
740356608*a^14*b^5*c^8*d^12*e^15*z^6 + 123740356608*a^11*b^5*c^11*d^18*e^9*z^6 + 3460300800*a^17*b^5*c^5*d^6*e
^21*z^6 + 3460300800*a^8*b^5*c^14*d^24*e^3*z^6 - 7751073792*a^15*b^7*c^5*d^8*e^19*z^6 - 7751073792*a^8*b^7*c^1
2*d^22*e^5*z^6 + 12041846784*a^14*b^7*c^6*d^10*e^17*z^6 + 12041846784*a^9*b^7*c^11*d^20*e^7*z^6 - 325545099264
*a^14*b^3*c^10*d^14*e^13*z^6 - 325545099264*a^13*b^3*c^11*d^16*e^11*z^6 - 3330539520*a^13*b^10*c^4*d^9*e^18*z^
6 - 3330539520*a^7*b^10*c^10*d^21*e^6*z^6 + 157789716480*a^12*b^7*c^8*d^14*e^13*z^6 + 157789716480*a^11*b^7*c^
9*d^16*e^11*z^6 + 37492359168*a^11*b^10*c^6*d^13*e^14*z^6 + 37492359168*a^9*b^10*c^8*d^17*e^10*z^6 + 301989888
*a^8*b^3*c^16*d^26*e*z^6 - 7266631680*a^17*b^4*c^6*d^7*e^20*z^6 - 7266631680*a^9*b^4*c^14*d^23*e^4*z^6 - 20132
6592*a^20*b*c^6*d^4*e^23*z^6 - 188743680*a^7*b^5*c^15*d^26*e*z^6 + 45747339264*a^13*b^8*c^6*d^11*e^16*z^6 + 45
747339264*a^9*b^8*c^10*d^19*e^8*z^6 - 74612736*a^10*b^16*c*d^9*e^18*z^6 - 2768240640*a^16*b^7*c^4*d^6*e^21*z^6
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22*e^5*z^6 - 25952256*a^8*b^18*c*d^11*e^16*z^6 + 21086208*a^13*b^13*c*d^6*e^21*z^6 - 11796480*a^5*b^9*c^13*d^2
6*e*z^6 - 6438912*a^14*b^12*c*d^5*e^22*z^6 + 5406720*a^7*b^19*c*d^12*e^15*z^6 + 1622016*a^6*b^20*c*d^13*e^14*z
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442368*a^4*b^22*c*d^15*e^12*z^6 - 98304*a^16*b^10*c*d^3*e^24*z^6 - 49152*a^3*b^23*c*d^16*e^11*z^6 - 49152*a^3*
b^13*c^11*d^26*e*z^6 + 6897106944*a^9*b^13*c^5*d^14*e^13*z^6 + 6897106944*a^8*b^13*c^6*d^16*e^11*z^6 - 2422210
560*a^16*b^6*c^5*d^7*e^20*z^6 - 2422210560*a^8*b^6*c^13*d^23*e^4*z^6 + 255785435136*a^14*b^2*c^11*d^15*e^12*z^
6 + 41004564480*a^15*b^4*c^8*d^11*e^16*z^6 + 41004564480*a^11*b^4*c^12*d^19*e^8*z^6 + 2270822400*a^13*b^11*c^3
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8*b^8*c^11*d^21*e^6*z^6 + 212600881152*a^15*b^2*c^10*d^13*e^14*z^6 + 212600881152*a^13*b^2*c^12*d^17*e^10*z^6
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d^13*e^14*z^6 - 251217838080*a^11*b^6*c^10*d^17*e^10*z^6 - 1952907264*a^14*b^10*c^3*d^7*e^20*z^6 - 1952907264*
a^6*b^10*c^11*d^23*e^4*z^6 - 27691057152*a^13*b^9*c^5*d^10*e^17*z^6 - 27691057152*a^8*b^9*c^10*d^20*e^7*z^6 -
1902673920*a^8*b^15*c^4*d^14*e^13*z^6 - 1902673920*a^7*b^15*c^5*d^16*e^11*z^6 + 10465050624*a^10*b^11*c^6*d^14
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14*c^6*d^17*e^10*z^6 - 33218887680*a^17*b*c^9*d^10*e^17*z^6 - 33218887680*a^12*b*c^14*d^20*e^7*z^6 + 152469504
0*a^10*b^14*c^3*d^11*e^16*z^6 + 1524695040*a^6*b^14*c^7*d^19*e^8*z^6 - 1472200704*a^18*b^4*c^5*d^5*e^22*z^6 -
1472200704*a^8*b^4*c^15*d^25*e^2*z^6 - 83047219200*a^16*b^3*c^8*d^10*e^17*z^6 - 83047219200*a^11*b^3*c^13*d^20
*e^7*z^6 + 44291850240*a^17*b^2*c^8*d^9*e^18*z^6 + 44291850240*a^11*b^2*c^14*d^21*e^6*z^6 + 1308131328*a^8*b^1
4*c^5*d^15*e^12*z^6 - 201326592*a^9*b*c^17*d^26*e*z^6 + 48530718720*a^12*b^8*c^7*d^13*e^14*z^6 + 48530718720*a
^10*b^8*c^9*d^17*e^10*z^6 - 1242644480*a^12*b^12*c^3*d^9*e^18*z^6 - 1242644480*a^6*b^12*c^9*d^21*e^6*z^6 + 981
3196800*a^12*b^10*c^5*d^11*e^16*z^6 + 9813196800*a^8*b^10*c^9*d^19*e^8*z^6 - 93012885504*a^15*b*c^11*d^14*e^13
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0*c^7*d^15*e^12*z^6 - 1180106752*a^9*b^15*c^3*d^12*e^15*z^6 - 1180106752*a^6*b^15*c^6*d^18*e^9*z^6 + 102367232
0*a^15*b^9*c^3*d^6*e^21*z^6 + 1023672320*a^6*b^9*c^12*d^24*e^3*z^6 + 975175680*a^17*b^6*c^4*d^5*e^22*z^6 + 975
175680*a^7*b^6*c^14*d^25*e^2*z^6 - 11072962560*a^18*b*c^8*d^8*e^19*z^6 - 11072962560*a^11*b*c^15*d^22*e^5*z^6
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22*z^6 + 805306368*a^9*b^2*c^16*d^25*e^2*z^6 - 133809831936*a^14*b^6*c^7*d^11*e^16*z^6 - 133809831936*a^10*b^6
*c^11*d^19*e^8*z^6 - 2214592512*a^19*b*c^7*d^6*e^21*z^6 - 2214592512*a^10*b*c^16*d^24*e^3*z^6 + 82216747008*a^
13*b^7*c^7*d^12*e^15*z^6 + 82216747008*a^10*b^7*c^10*d^18*e^9*z^6 - 586629120*a^12*b^13*c^2*d^8*e^19*z^6 - 586
629120*a^5*b^13*c^9*d^22*e^5*z^6 + 568565760*a^7*b^16*c^4*d^15*e^12*z^6 - 4844421120*a^16*b^4*c^7*d^9*e^18*z^6
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e^6*z^6 - 527155200*a^11*b^13*c^3*d^10*e^17*z^6 - 527155200*a^6*b^13*c^8*d^20*e^7*z^6 + 43470028800*a^11*b^8*c
^8*d^15*e^12*z^6 - 107874877440*a^11*b^9*c^7*d^14*e^13*z^6 - 107874877440*a^10*b^9*c^8*d^16*e^11*z^6 + 9018408
960*a^12*b^11*c^4*d^10*e^17*z^6 + 9018408960*a^7*b^11*c^9*d^20*e^7*z^6 + 421994496*a^13*b^12*c^2*d^7*e^20*z^6
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e^9*z^6 + 26159874048*a^16*b^5*c^6*d^8*e^19*z^6 + 26159874048*a^9*b^5*c^13*d^22*e^5*z^6 - 369098752*a^18*b^3*c
^6*d^6*e^21*z^6 - 369098752*a^9*b^3*c^15*d^24*e^3*z^6 + 351436800*a^8*b^16*c^3*d^13*e^14*z^6 + 351436800*a^6*b
^16*c^5*d^17*e^10*z^6 - 334233600*a^16*b^8*c^3*d^5*e^22*z^6 - 334233600*a^6*b^8*c^13*d^25*e^2*z^6 + 301989888*
a^19*b^3*c^5*d^4*e^23*z^6 - 266010624*a^10*b^15*c^2*d^10*e^17*z^6 - 266010624*a^5*b^15*c^7*d^20*e^7*z^6 - 3051
98530560*a^12*b^6*c^9*d^15*e^12*z^6 - 203292672*a^14*b^11*c^2*d^6*e^21*z^6 - 203292672*a^5*b^11*c^11*d^24*e^3*
z^6 - 188743680*a^18*b^5*c^4*d^4*e^23*z^6 + 120418467840*a^16*b^2*c^9*d^11*e^16*z^6 + 120418467840*a^12*b^2*c^
13*d^19*e^8*z^6 - 17293934592*a^10*b^12*c^5*d^13*e^14*z^6 - 17293934592*a^8*b^12*c^7*d^17*e^10*z^6 + 104890368
*a^8*b^17*c^2*d^12*e^15*z^6 + 104890368*a^5*b^17*c^5*d^18*e^9*z^6 + 4390256640*a^15*b^8*c^4*d^7*e^20*z^6 + 439
0256640*a^7*b^8*c^12*d^23*e^4*z^6 - 91750400*a^6*b^18*c^3*d^15*e^12*z^6 + 79134720*a^7*b^17*c^3*d^14*e^13*z^6
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^6 - 72990720*a^5*b^18*c^4*d^17*e^10*z^6 + 69746688*a^4*b^15*c^8*d^22*e^5*z^6 + 63700992*a^15*b^10*c^2*d^5*e^2
2*z^6 + 63700992*a^5*b^10*c^12*d^25*e^2*z^6 + 62914560*a^17*b^7*c^3*d^4*e^23*z^6 + 55148544*a^4*b^17*c^6*d^20*
e^7*z^6 - 45957120*a^4*b^14*c^9*d^23*e^4*z^6 - 25952256*a^4*b^18*c^5*d^19*e^8*z^6 - 25165824*a^20*b^2*c^5*d^3*
e^24*z^6 + 21086208*a^4*b^13*c^10*d^24*e^3*z^6 + 20643840*a^6*b^19*c^2*d^14*e^13*z^6 + 20643840*a^5*b^19*c^3*d
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*d^25*e^2*z^6 + 5406720*a^4*b^19*c^4*d^18*e^9*z^6 - 5242880*a^18*b^6*c^3*d^3*e^24*z^6 + 3784704*a^3*b^18*c^6*d
^21*e^6*z^6 - 3244032*a^3*b^19*c^5*d^20*e^7*z^6 - 3244032*a^3*b^17*c^7*d^22*e^5*z^6 + 2027520*a^3*b^20*c^4*d^1
9*e^8*z^6 + 2027520*a^3*b^16*c^8*d^23*e^4*z^6 - 1622016*a^9*b^16*c^2*d^11*e^16*z^6 - 1622016*a^5*b^16*c^6*d^19
*e^8*z^6 + 1622016*a^4*b^20*c^3*d^17*e^10*z^6 - 1523712*a^4*b^21*c^2*d^16*e^11*z^6 + 983040*a^17*b^8*c^2*d^3*e
^24*z^6 - 901120*a^3*b^21*c^3*d^18*e^9*z^6 - 901120*a^3*b^15*c^9*d^24*e^3*z^6 + 270336*a^3*b^22*c^2*d^17*e^10*
z^6 + 270336*a^3*b^14*c^10*d^25*e^2*z^6 + 172032*a^5*b^20*c^2*d^15*e^12*z^6 - 38593888256*a^15*b^6*c^6*d^9*e^1
8*z^6 - 38593888256*a^9*b^6*c^12*d^21*e^6*z^6 - 210386288640*a^15*b^3*c^9*d^12*e^15*z^6 - 210386288640*a^12*b^
3*c^12*d^18*e^9*z^6 + 15502147584*a^15*c^12*d^15*e^12*z^6 + 1107296256*a^19*c^8*d^7*e^20*z^6 + 1107296256*a^11
*c^16*d^23*e^4*z^6 + 13287555072*a^16*c^11*d^13*e^14*z^6 + 13287555072*a^14*c^13*d^17*e^10*z^6 + 201326592*a^2
0*c^7*d^5*e^22*z^6 + 201326592*a^10*c^17*d^25*e^2*z^6 + 16777216*a^21*c^6*d^3*e^24*z^6 + 3784704*a^9*b^18*d^9*
e^18*z^6 - 3244032*a^10*b^17*d^8*e^19*z^6 - 3244032*a^8*b^19*d^10*e^17*z^6 + 2027520*a^11*b^16*d^7*e^20*z^6 +
2027520*a^7*b^20*d^11*e^16*z^6 - 901120*a^12*b^15*d^6*e^21*z^6 - 901120*a^6*b^21*d^12*e^15*z^6 + 270336*a^13*b
^14*d^5*e^22*z^6 + 270336*a^5*b^22*d^13*e^14*z^6 - 49152*a^14*b^13*d^4*e^23*z^6 - 49152*a^4*b^23*d^14*e^13*z^6
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^4*c^16*d^27*z^6 - 5242880*a^6*b^6*c^15*d^27*z^6 + 983040*a^5*b^8*c^14*d^27*z^6 - 98304*a^4*b^10*c^13*d^27*z^6
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987520*a^18*c^9*d^9*e^18*z^6 + 3690987520*a^12*c^15*d^21*e^6*z^6 + 16777216*a^9*c^18*d^27*z^6 - 8493371392*a^6
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6*a^9*b^5*c^9*d^11*e^12*z^4 - 5588058112*a^13*b*c^9*d^7*e^16*z^4 - 3892838400*a^8*b^2*c^13*d^16*e^7*z^4 - 3611
713536*a^8*b^8*c^7*d^10*e^13*z^4 + 7819006464*a^7*b^9*c^7*d^11*e^12*z^4 - 7782137856*a^8*b^7*c^8*d^11*e^12*z^4
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89464512*a^5*b^10*c^4*d^3*e^16*z^2 - 75930624*a^8*b^5*c^6*d^2*e^17*z^2 + 68315904*a^5*b^8*c^6*d^5*e^14*z^2 - 6
4157184*a^4*b^7*c^8*d^8*e^11*z^2 - 62951040*a^9*b^2*c^8*d^3*e^16*z^2 + 49056768*a^4*b^10*c^5*d^5*e^14*z^2 + 47
614464*a^3*b^8*c^8*d^9*e^10*z^2 + 35604480*a^4*b^2*c^13*d^13*e^6*z^2 + 33983040*a^3*b^11*c^5*d^6*e^13*z^2 - 33
515520*a^4*b^3*c^12*d^12*e^7*z^2 - 33463808*a^3*b^7*c^9*d^10*e^9*z^2 - 25128864*a^4*b^4*c^11*d^11*e^8*z^2 - 23
193728*a^3*b^10*c^6*d^7*e^12*z^2 + 21015456*a^6*b^9*c^4*d^2*e^17*z^2 + 19924176*a^4*b^11*c^4*d^4*e^15*z^2 - 19
251216*a^3*b^9*c^7*d^8*e^11*z^2 - 16434048*a^5*b^4*c^10*d^9*e^10*z^2 - 16289664*a^3*b^12*c^4*d^5*e^14*z^2 - 15
059328*a^4*b^12*c^3*d^3*e^16*z^2 - 10766016*a^2*b^10*c^7*d^9*e^10*z^2 - 10453632*a^5*b^11*c^3*d^2*e^17*z^2 - 9
940992*a^3*b^3*c^13*d^14*e^5*z^2 + 8373696*a^2*b^11*c^6*d^8*e^11*z^2 + 7776768*a^3*b^2*c^14*d^15*e^4*z^2 + 707
7888*a^3*b^5*c^11*d^12*e^7*z^2 + 6798240*a^2*b^9*c^8*d^10*e^9*z^2 - 3589440*a^2*b^6*c^11*d^13*e^6*z^2 + 354432
0*a^3*b^6*c^10*d^11*e^8*z^2 + 3128064*a^2*b^5*c^12*d^14*e^5*z^2 + 2346336*a^4*b^13*c^2*d^2*e^17*z^2 - 2261568*
a^2*b^8*c^9*d^11*e^8*z^2 - 2125824*a^2*b^13*c^4*d^6*e^13*z^2 + 2002560*a^3*b^4*c^12*d^13*e^6*z^2 + 1927680*a^2
*b^7*c^10*d^12*e^7*z^2 + 1814784*a^2*b^14*c^3*d^5*e^14*z^2 - 1807104*a^2*b^12*c^5*d^7*e^12*z^2 + 1637808*a^3*b
^13*c^3*d^4*e^15*z^2 + 1083456*a^3*b^14*c^2*d^3*e^16*z^2 - 792384*a^2*b^4*c^13*d^15*e^4*z^2 - 657408*a^2*b^3*c
^14*d^16*e^3*z^2 + 608256*a^7*b^7*c^5*d^2*e^17*z^2 + 595968*a^2*b^2*c^15*d^17*e^2*z^2 - 498624*a^2*b^15*c^2*d^
4*e^15*z^2 - 3840*b^18*c*d^5*e^14*z^2 - 3840*b^5*c^14*d^18*e*z^2 + 2064384*a^11*c^8*d*e^18*z^2 - 4160*a^3*b^16
*d*e^18*z^2 - 4160*a*b^18*d^3*e^16*z^2 - 1290240*a^11*b*c^7*e^19*z^2 - 9840*a^5*b^13*c*e^19*z^2 - 5760*a*b^2*c
^16*d^19*z^2 - 280581120*a^8*c^11*d^7*e^12*z^2 + 110278656*a^9*c^10*d^5*e^14*z^2 - 89479168*a^7*c^12*d^9*e^10*
z^2 + 34464000*a^10*c^9*d^3*e^16*z^2 + 54240*b^15*c^4*d^8*e^11*z^2 + 54240*b^8*c^11*d^15*e^4*z^2 - 49920*b^14*
c^5*d^9*e^10*z^2 - 49920*b^9*c^10*d^14*e^5*z^2 - 37376*b^16*c^3*d^7*e^12*z^2 - 37376*b^7*c^12*d^16*e^3*z^2 + 2
8480*b^13*c^6*d^10*e^9*z^2 + 28480*b^10*c^9*d^13*e^6*z^2 + 15936*b^17*c^2*d^6*e^13*z^2 + 15936*b^6*c^13*d^17*e
^2*z^2 - 7920*b^12*c^7*d^11*e^8*z^2 - 7920*b^11*c^8*d^12*e^7*z^2 + 7489536*a^5*c^14*d^13*e^6*z^2 + 6084096*a^6
*c^13*d^11*e^8*z^2 + 2280448*a^4*c^15*d^15*e^4*z^2 + 350208*a^3*c^16*d^17*e^2*z^2 + 11616*a^2*b^17*d^2*e^17*z^
2 - 3515904*a^9*b^5*c^5*e^19*z^2 + 3440640*a^10*b^3*c^6*e^19*z^2 + 1870848*a^8*b^7*c^4*e^19*z^2 - 572272*a^7*b
^9*c^3*e^19*z^2 + 101856*a^6*b^11*c^2*e^19*z^2 + 400*b^19*d^4*e^15*z^2 + 400*b^4*c^15*d^19*z^2 + 20736*a^2*c^1
7*d^19*z^2 + 400*a^4*b^15*e^19*z^2 - 3969216*a^4*b*c^10*d^3*e^12 - 3001536*a^3*b*c^11*d^5*e^10 - 419904*a^2*b*
c^12*d^7*e^8 + 184608*a^4*b^3*c^8*d*e^14 - 153036*a*b^4*c^10*d^6*e^9 + 127008*a*b^3*c^11*d^7*e^8 + 63108*a*b^6
*c^8*d^4*e^11 - 29160*a*b^2*c^12*d^8*e^7 - 21060*a^3*b^5*c^7*d*e^14 - 21060*a*b^7*c^7*d^3*e^12 + 5460*a*b^5*c^
9*d^5*e^10 - 404544*a^5*b*c^9*d*e^14 + 1251872*a^3*b^3*c^9*d^3*e^12 + 844224*a^4*b^2*c^9*d^2*e^13 + 820512*a^2
*b^3*c^10*d^5*e^10 + 750672*a^3*b^2*c^10*d^4*e^11 - 657498*a^2*b^4*c^9*d^4*e^11 - 487116*a^3*b^4*c^8*d^2*e^13
+ 160704*a^2*b^2*c^11*d^6*e^9 + 58806*a^2*b^6*c^7*d^2*e^13 + 13140*a^2*b^5*c^8*d^3*e^12 + 15286*b^6*c^9*d^6*e^
9 - 9540*b^7*c^8*d^5*e^10 - 9540*b^5*c^10*d^7*e^8 + 2025*b^8*c^7*d^4*e^11 + 2025*b^4*c^11*d^8*e^7 + 3367008*a^
4*c^11*d^4*e^11 + 1166400*a^3*c^12*d^6*e^9 + 705600*a^5*c^10*d^2*e^13 + 104976*a^2*c^13*d^8*e^7 - 17640*a^5*b^
2*c^8*e^15 + 2025*a^4*b^4*c^7*e^15 + 38416*a^6*c^9*e^15, z, k)*((1048576*a^17*c^8*d*e^24 - 393216*a^6*c^19*d^2
3*e^2 - 3407872*a^7*c^18*d^21*e^4 - 5636096*a^8*c^17*d^19*e^6 + 31457280*a^9*c^16*d^17*e^8 + 175374336*a^10*c^
15*d^15*e^10 + 407371776*a^11*c^14*d^13*e^12 + 556007424*a^12*c^13*d^11*e^14 + 481296384*a^13*c^12*d^9*e^16 +
265420800*a^14*c^11*d^7*e^18 + 88866816*a^15*c^10*d^5*e^20 + 15859712*a^16*c^9*d^3*e^22 - 5632*a^2*b^8*c^15*d^
23*e^2 + 67584*a^2*b^9*c^14*d^22*e^3 - 368640*a^2*b^10*c^13*d^21*e^4 + 1205248*a^2*b^11*c^12*d^20*e^5 - 261888
0*a^2*b^12*c^11*d^19*e^6 + 3953664*a^2*b^13*c^10*d^18*e^7 - 4190208*a^2*b^14*c^9*d^17*e^8 + 3041280*a^2*b^15*c
^8*d^16*e^9 - 1368576*a^2*b^16*c^7*d^15*e^10 + 225280*a^2*b^17*c^6*d^14*e^11 + 135168*a^2*b^18*c^5*d^13*e^12 -
101376*a^2*b^19*c^4*d^12*e^13 + 28160*a^2*b^20*c^3*d^11*e^14 - 3072*a^2*b^21*c^2*d^10*e^15 + 49152*a^3*b^6*c^
16*d^23*e^2 - 589824*a^3*b^7*c^15*d^22*e^3 + 3181568*a^3*b^8*c^14*d^21*e^4 - 10121216*a^3*b^9*c^13*d^20*e^5 +
20854016*a^3*b^10*c^12*d^19*e^6 - 28504064*a^3*b^11*c^11*d^18*e^7 + 24727808*a^3*b^12*c^10*d^17*e^8 - 10510336
*a^3*b^13*c^9*d^16*e^9 - 3040768*a^3*b^14*c^8*d^15*e^10 + 7405568*a^3*b^15*c^7*d^14*e^11 - 4684288*a^3*b^16*c^
6*d^13*e^12 + 1314816*a^3*b^17*c^5*d^12*e^13 - 12032*a^3*b^18*c^4*d^11*e^14 - 86016*a^3*b^19*c^3*d^10*e^15 + 1
5616*a^3*b^20*c^2*d^9*e^16 - 212992*a^4*b^4*c^17*d^23*e^2 + 2555904*a^4*b^5*c^16*d^22*e^3 - 13549568*a^4*b^6*c
^15*d^21*e^4 + 41189376*a^4*b^7*c^14*d^20*e^5 - 76867072*a^4*b^8*c^13*d^19*e^6 + 83304448*a^4*b^9*c^12*d^18*e^
7 - 29710336*a^4*b^10*c^11*d^17*e^8 - 53473280*a^4*b^11*c^10*d^16*e^9 + 94751744*a^4*b^12*c^9*d^15*e^10 - 6896
8448*a^4*b^13*c^8*d^14*e^11 + 20899840*a^4*b^14*c^7*d^13*e^12 + 4022272*a^4*b^15*c^6*d^12*e^13 - 5248512*a^4*b
^16*c^5*d^11*e^14 + 1310720*a^4*b^17*c^4*d^10*e^15 + 40960*a^4*b^18*c^3*d^9*e^16 - 45056*a^4*b^19*c^2*d^8*e^17
+ 458752*a^5*b^2*c^18*d^23*e^2 - 5505024*a^5*b^3*c^17*d^22*e^3 + 28213248*a^5*b^4*c^16*d^21*e^4 - 77725696*a^
5*b^5*c^15*d^20*e^5 + 109985792*a^5*b^6*c^14*d^19*e^6 - 16252928*a^5*b^7*c^13*d^18*e^7 - 236929024*a^5*b^8*c^1
2*d^17*e^8 + 460423168*a^5*b^9*c^11*d^16*e^9 - 412556800*a^5*b^10*c^10*d^15*e^10 + 137754624*a^5*b^11*c^9*d^14
*e^11 + 80635904*a^5*b^12*c^8*d^13*e^12 - 102774784*a^5*b^13*c^7*d^12*e^13 + 36015104*a^5*b^14*c^6*d^11*e^14 +
1345536*a^5*b^15*c^5*d^10*e^15 - 3577856*a^5*b^16*c^4*d^9*e^16 + 407552*a^5*b^17*c^3*d^8*e^17 + 82432*a^5*b^1
8*c^2*d^7*e^18 - 21757952*a^6*b^2*c^17*d^21*e^4 + 39059456*a^6*b^3*c^16*d^20*e^5 + 44351488*a^6*b^4*c^15*d^19*
e^6 - 381681664*a^6*b^5*c^14*d^18*e^7 + 872808448*a^6*b^6*c^13*d^17*e^8 - 981073920*a^6*b^7*c^12*d^16*e^9 + 32
9307136*a^6*b^8*c^11*d^15*e^10 + 558870528*a^6*b^9*c^10*d^14*e^11 - 809418752*a^6*b^10*c^9*d^13*e^12 + 3944591
36*a^6*b^11*c^8*d^12*e^13 + 10594304*a^6*b^12*c^7*d^11*e^14 - 84887552*a^6*b^13*c^6*d^10*e^15 + 23650304*a^6*b
^14*c^5*d^9*e^16 + 2762752*a^6*b^15*c^4*d^8*e^17 - 1268736*a^6*b^16*c^3*d^7*e^18 - 100352*a^6*b^17*c^2*d^6*e^1
9 - 192217088*a^7*b^2*c^16*d^19*e^6 + 514850816*a^7*b^3*c^15*d^18*e^7 - 691208192*a^7*b^4*c^14*d^17*e^8 + 8388
608*a^7*b^5*c^13*d^16*e^9 + 1583054848*a^7*b^6*c^12*d^15*e^10 - 2597715968*a^7*b^7*c^11*d^14*e^11 + 1705592832
*a^7*b^8*c^10*d^13*e^12 + 65314816*a^7*b^9*c^9*d^12*e^13 - 792112640*a^7*b^10*c^8*d^11*e^14 + 396832768*a^7*b^
11*c^7*d^10*e^15 + 5305856*a^7*b^12*c^6*d^9*e^16 - 47955968*a^7*b^13*c^5*d^8*e^17 + 4476416*a^7*b^14*c^4*d^7*e
^18 + 1921024*a^7*b^15*c^3*d^6*e^19 + 82432*a^7*b^16*c^2*d^5*e^20 - 472383488*a^8*b^2*c^15*d^17*e^8 + 15529410
56*a^8*b^3*c^14*d^16*e^9 - 2815066112*a^8*b^4*c^13*d^15*e^10 + 2329542656*a^8*b^5*c^12*d^14*e^11 + 631472128*a
^8*b^6*c^11*d^13*e^12 - 3123511296*a^8*b^7*c^10*d^12*e^13 + 2406024192*a^8*b^8*c^9*d^11*e^14 - 253763584*a^8*b
^9*c^8*d^10*e^15 - 535957504*a^8*b^10*c^7*d^9*e^16 + 196169728*a^8*b^11*c^6*d^8*e^17 + 27567104*a^8*b^12*c^5*d
^7*e^18 - 13180928*a^8*b^13*c^4*d^6*e^19 - 1767424*a^8*b^14*c^3*d^5*e^20 - 45056*a^8*b^15*c^2*d^4*e^21 - 26345
472*a^9*b^2*c^14*d^15*e^10 + 1757937664*a^9*b^3*c^13*d^14*e^11 - 4680646656*a^9*b^4*c^12*d^13*e^12 + 497837670
4*a^9*b^5*c^11*d^12*e^13 - 1037008896*a^9*b^6*c^10*d^11*e^14 - 2360082432*a^9*b^7*c^9*d^10*e^15 + 1791750144*a
^9*b^8*c^8*d^9*e^16 - 76677120*a^9*b^9*c^7*d^8*e^17 - 263758592*a^9*b^10*c^6*d^7*e^18 + 28357632*a^9*b^11*c^5*
d^6*e^19 + 14978560*a^9*b^12*c^4*d^5*e^20 + 1029120*a^9*b^13*c^3*d^4*e^21 + 15616*a^9*b^14*c^2*d^3*e^22 + 1853
358080*a^10*b^2*c^13*d^13*e^12 + 106430464*a^10*b^3*c^12*d^12*e^13 - 4433149952*a^10*b^4*c^11*d^11*e^14 + 5213
257728*a^10*b^5*c^10*d^10*e^15 - 1239613440*a^10*b^6*c^9*d^9*e^16 - 1399455744*a^10*b^7*c^8*d^8*e^17 + 7215191
04*a^10*b^8*c^7*d^7*e^18 + 92768256*a^10*b^9*c^6*d^6*e^19 - 60235776*a^10*b^10*c^5*d^5*e^20 - 9616384*a^10*b^1
1*c^4*d^4*e^21 - 369152*a^10*b^12*c^3*d^3*e^22 - 3072*a^10*b^13*c^2*d^2*e^23 + 3744333824*a^11*b^2*c^12*d^11*e
^14 - 1445986304*a^11*b^3*c^11*d^10*e^15 - 2945974272*a^11*b^4*c^10*d^9*e^16 + 3180331008*a^11*b^5*c^9*d^8*e^1
7 - 344997888*a^11*b^6*c^8*d^7*e^18 - 607715328*a^11*b^7*c^7*d^6*e^19 + 91261952*a^11*b^8*c^6*d^5*e^20 + 46288
896*a^11*b^9*c^5*d^4*e^21 + 3619072*a^11*b^10*c^4*d^3*e^22 + 73728*a^11*b^11*c^3*d^2*e^23 + 3567255552*a^12*b^
2*c^11*d^9*e^16 - 1152385024*a^12*b^3*c^10*d^8*e^17 - 1550467072*a^12*b^4*c^9*d^7*e^18 + 1052180480*a^12*b^5*c
^8*d^6*e^19 + 114114560*a^12*b^6*c^7*d^5*e^20 - 115572736*a^12*b^7*c^6*d^4*e^21 - 18767360*a^12*b^8*c^5*d^3*e^
22 - 737280*a^12*b^9*c^4*d^2*e^23 + 1821048832*a^13*b^2*c^10*d^7*e^18 - 236191744*a^13*b^3*c^9*d^6*e^19 - 5445
71392*a^13*b^4*c^8*d^5*e^20 + 114688000*a^13*b^5*c^7*d^4*e^21 + 53821440*a^13*b^6*c^6*d^3*e^22 + 3932160*a^13*
b^7*c^5*d^2*e^23 + 460587008*a^14*b^2*c^9*d^5*e^20 + 57933824*a^14*b^3*c^8*d^4*e^21 - 78659584*a^14*b^4*c^7*d^
3*e^22 - 11796480*a^14*b^5*c^6*d^2*e^23 + 38207488*a^15*b^2*c^8*d^3*e^22 + 18874368*a^15*b^3*c^7*d^2*e^23 + 25
6*a*b^10*c^14*d^23*e^2 - 3072*a*b^11*c^13*d^22*e^3 + 16896*a*b^12*c^12*d^21*e^4 - 56320*a*b^13*c^11*d^20*e^5 +
126720*a*b^14*c^10*d^19*e^6 - 202752*a*b^15*c^9*d^18*e^7 + 236544*a*b^16*c^8*d^17*e^8 - 202752*a*b^17*c^7*d^1
6*e^9 + 126720*a*b^18*c^6*d^15*e^10 - 56320*a*b^19*c^5*d^14*e^11 + 16896*a*b^20*c^4*d^13*e^12 - 3072*a*b^21*c^
3*d^12*e^13 + 256*a*b^22*c^2*d^11*e^14 + 4718592*a^6*b*c^18*d^22*e^3 + 38797312*a^7*b*c^17*d^20*e^5 + 77594624
*a^8*b*c^16*d^18*e^7 - 159383552*a^9*b*c^15*d^16*e^9 - 1020264448*a^10*b*c^14*d^14*e^11 - 2128609280*a^11*b*c^
13*d^12*e^13 + 256*a^11*b^12*c^2*d*e^24 - 2451570688*a^12*b*c^12*d^10*e^15 - 6144*a^12*b^10*c^3*d*e^24 - 16944
98816*a^13*b*c^11*d^8*e^17 + 61440*a^13*b^8*c^4*d*e^24 - 691535872*a^14*b*c^10*d^6*e^19 - 327680*a^14*b^6*c^5*
d*e^24 - 149946368*a^15*b*c^9*d^4*e^21 + 983040*a^15*b^4*c^6*d*e^24 - 12582912*a^16*b*c^8*d^2*e^23 - 1572864*a
^16*b^2*c^7*d*e^24)/(32*(16*a^3*b^6*c^9*d^18 - a^2*b^8*c^8*d^18 - 256*a^6*c^12*d^18 - 96*a^4*b^4*c^10*d^18 + 2
56*a^5*b^2*c^11*d^18 - a^2*b^16*d^10*e^8 + 8*a^3*b^15*d^9*e^9 - 28*a^4*b^14*d^8*e^10 + 56*a^5*b^13*d^7*e^11 -
70*a^6*b^12*d^6*e^12 + 56*a^7*b^11*d^5*e^13 - 28*a^8*b^10*d^4*e^14 + 8*a^9*b^9*d^3*e^15 - a^10*b^8*d^2*e^16 -
2048*a^7*c^11*d^16*e^2 - 7168*a^8*c^10*d^14*e^4 - 14336*a^9*c^9*d^12*e^6 - 17920*a^10*c^8*d^10*e^8 - 14336*a^1
1*c^7*d^8*e^10 - 7168*a^12*c^6*d^6*e^12 - 2048*a^13*c^5*d^4*e^14 - 256*a^14*c^4*d^2*e^16 - 28*a^2*b^10*c^6*d^1
6*e^2 + 56*a^2*b^11*c^5*d^15*e^3 - 70*a^2*b^12*c^4*d^14*e^4 + 56*a^2*b^13*c^3*d^13*e^5 - 28*a^2*b^14*c^2*d^12*
e^6 + 440*a^3*b^8*c^7*d^16*e^2 - 840*a^3*b^9*c^6*d^15*e^3 + 952*a^3*b^10*c^5*d^14*e^4 - 616*a^3*b^11*c^4*d^13*
e^5 + 168*a^3*b^12*c^3*d^12*e^6 + 40*a^3*b^13*c^2*d^11*e^7 - 2560*a^4*b^6*c^8*d^16*e^2 + 4480*a^4*b^7*c^7*d^15
*e^3 - 4060*a^4*b^8*c^6*d^14*e^4 + 1064*a^4*b^9*c^5*d^13*e^5 + 1372*a^4*b^10*c^4*d^12*e^6 - 1360*a^4*b^11*c^3*
d^11*e^7 + 380*a^4*b^12*c^2*d^10*e^8 + 6400*a^5*b^4*c^9*d^16*e^2 - 8960*a^5*b^5*c^8*d^15*e^3 + 2240*a^5*b^6*c^
7*d^14*e^4 + 9856*a^5*b^7*c^6*d^13*e^5 - 13048*a^5*b^8*c^5*d^12*e^6 + 5400*a^5*b^9*c^4*d^11*e^7 + 1040*a^5*b^1
0*c^3*d^10*e^8 - 1360*a^5*b^11*c^2*d^9*e^9 - 5120*a^6*b^2*c^10*d^16*e^2 + 22400*a^6*b^4*c^8*d^14*e^4 - 41216*a
^6*b^5*c^7*d^13*e^5 + 25088*a^6*b^6*c^6*d^12*e^6 + 8320*a^6*b^7*c^5*d^11*e^7 - 17350*a^6*b^8*c^4*d^10*e^8 + 54
00*a^6*b^9*c^3*d^9*e^9 + 1372*a^6*b^10*c^2*d^8*e^10 - 35840*a^7*b^2*c^9*d^14*e^4 + 28672*a^7*b^3*c^8*d^13*e^5
+ 30464*a^7*b^4*c^7*d^12*e^6 - 73472*a^7*b^5*c^6*d^11*e^7 + 40544*a^7*b^6*c^5*d^10*e^8 + 8320*a^7*b^7*c^4*d^9*
e^9 - 13048*a^7*b^8*c^3*d^8*e^10 + 1064*a^7*b^9*c^2*d^7*e^11 - 93184*a^8*b^2*c^8*d^12*e^6 + 71680*a^8*b^3*c^7*
d^11*e^7 + 29120*a^8*b^4*c^6*d^10*e^8 - 73472*a^8*b^5*c^5*d^9*e^9 + 25088*a^8*b^6*c^4*d^8*e^10 + 9856*a^8*b^7*
c^3*d^7*e^11 - 4060*a^8*b^8*c^2*d^6*e^12 - 125440*a^9*b^2*c^7*d^10*e^8 + 71680*a^9*b^3*c^6*d^9*e^9 + 30464*a^9
*b^4*c^5*d^8*e^10 - 41216*a^9*b^5*c^4*d^7*e^11 + 2240*a^9*b^6*c^3*d^6*e^12 + 4480*a^9*b^7*c^2*d^5*e^13 - 93184
*a^10*b^2*c^6*d^8*e^10 + 28672*a^10*b^3*c^5*d^7*e^11 + 22400*a^10*b^4*c^4*d^6*e^12 - 8960*a^10*b^5*c^3*d^5*e^1
3 - 2560*a^10*b^6*c^2*d^4*e^14 - 35840*a^11*b^2*c^5*d^6*e^12 + 6400*a^11*b^4*c^3*d^4*e^14 + 768*a^11*b^5*c^2*d
^3*e^15 - 5120*a^12*b^2*c^4*d^4*e^14 - 2048*a^12*b^3*c^3*d^3*e^15 - 96*a^12*b^4*c^2*d^2*e^16 + 256*a^13*b^2*c^
3*d^2*e^16 + 2048*a^6*b*c^11*d^17*e + 8*a^2*b^9*c^7*d^17*e + 8*a^2*b^15*c*d^11*e^7 - 128*a^3*b^7*c^8*d^17*e -
40*a^3*b^14*c*d^10*e^8 + 768*a^4*b^5*c^9*d^17*e + 40*a^4*b^13*c*d^9*e^9 - 2048*a^5*b^3*c^10*d^17*e + 168*a^5*b
^12*c*d^8*e^10 - 616*a^6*b^11*c*d^7*e^11 + 14336*a^7*b*c^10*d^15*e^3 + 952*a^7*b^10*c*d^6*e^12 + 43008*a^8*b*c
^9*d^13*e^5 - 840*a^8*b^9*c*d^5*e^13 + 71680*a^9*b*c^8*d^11*e^7 + 440*a^9*b^8*c*d^4*e^14 + 71680*a^10*b*c^7*d^
9*e^9 - 128*a^10*b^7*c*d^3*e^15 + 43008*a^11*b*c^6*d^7*e^11 + 16*a^11*b^6*c*d^2*e^16 + 14336*a^12*b*c^5*d^5*e^
13 + 2048*a^13*b*c^4*d^3*e^15)) + (root(128723189760*a^14*b^4*c^9*d^13*e^14*z^6 + 128723189760*a^12*b^4*c^11*d
^17*e^10*z^6 - 8432455680*a^11*b^12*c^4*d^11*e^16*z^6 - 8432455680*a^7*b^12*c^8*d^19*e^8*z^6 + 12673351680*a^1
1*b^11*c^5*d^12*e^15*z^6 + 12673351680*a^8*b^11*c^8*d^18*e^9*z^6 - 72637480960*a^12*b^9*c^6*d^12*e^15*z^6 - 72
637480960*a^9*b^9*c^9*d^18*e^9*z^6 - 21048344576*a^9*b^12*c^6*d^15*e^12*z^6 - 16609443840*a^17*b^3*c^7*d^8*e^1
9*z^6 - 16609443840*a^10*b^3*c^14*d^22*e^5*z^6 + 145332633600*a^13*b^5*c^9*d^14*e^13*z^6 + 145332633600*a^12*b
^5*c^10*d^16*e^11*z^6 + 123740356608*a^14*b^5*c^8*d^12*e^15*z^6 + 123740356608*a^11*b^5*c^11*d^18*e^9*z^6 + 34
60300800*a^17*b^5*c^5*d^6*e^21*z^6 + 3460300800*a^8*b^5*c^14*d^24*e^3*z^6 - 7751073792*a^15*b^7*c^5*d^8*e^19*z
^6 - 7751073792*a^8*b^7*c^12*d^22*e^5*z^6 + 12041846784*a^14*b^7*c^6*d^10*e^17*z^6 + 12041846784*a^9*b^7*c^11*
d^20*e^7*z^6 - 325545099264*a^14*b^3*c^10*d^14*e^13*z^6 - 325545099264*a^13*b^3*c^11*d^16*e^11*z^6 - 333053952
0*a^13*b^10*c^4*d^9*e^18*z^6 - 3330539520*a^7*b^10*c^10*d^21*e^6*z^6 + 157789716480*a^12*b^7*c^8*d^14*e^13*z^6
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8*d^17*e^10*z^6 + 301989888*a^8*b^3*c^16*d^26*e*z^6 - 7266631680*a^17*b^4*c^6*d^7*e^20*z^6 - 7266631680*a^9*b^
4*c^14*d^23*e^4*z^6 - 201326592*a^20*b*c^6*d^4*e^23*z^6 - 188743680*a^7*b^5*c^15*d^26*e*z^6 + 45747339264*a^13
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0*a^16*b^7*c^4*d^6*e^21*z^6 - 2768240640*a^7*b^7*c^13*d^24*e^3*z^6 + 69746688*a^11*b^15*c*d^8*e^19*z^6 + 62914
560*a^6*b^7*c^14*d^26*e*z^6 + 2752020480*a^10*b^13*c^4*d^12*e^15*z^6 + 2752020480*a^7*b^13*c^7*d^18*e^9*z^6 +
55148544*a^9*b^17*c*d^10*e^17*z^6 - 45957120*a^12*b^14*c*d^7*e^20*z^6 - 2724986880*a^14*b^9*c^4*d^8*e^19*z^6 -
2724986880*a^7*b^9*c^11*d^22*e^5*z^6 - 25952256*a^8*b^18*c*d^11*e^16*z^6 + 21086208*a^13*b^13*c*d^6*e^21*z^6
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2016*a^6*b^20*c*d^13*e^14*z^6 - 1523712*a^5*b^21*c*d^14*e^13*z^6 + 1179648*a^15*b^11*c*d^4*e^23*z^6 + 1179648*
a^4*b^11*c^12*d^26*e*z^6 + 442368*a^4*b^22*c*d^15*e^12*z^6 - 98304*a^16*b^10*c*d^3*e^24*z^6 - 49152*a^3*b^23*c
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c^6*d^16*e^11*z^6 - 2422210560*a^16*b^6*c^5*d^7*e^20*z^6 - 2422210560*a^8*b^6*c^13*d^23*e^4*z^6 + 255785435136
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9*e^18*z^6 + 23677108224*a^8*b^8*c^11*d^21*e^6*z^6 + 212600881152*a^15*b^2*c^10*d^13*e^14*z^6 + 212600881152*a
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65050624*a^10*b^11*c^6*d^14*e^13*z^6 + 10465050624*a^9*b^11*c^7*d^16*e^11*z^6 + 1613905920*a^9*b^14*c^4*d^13*e
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14*d^20*e^7*z^6 + 1524695040*a^10*b^14*c^3*d^11*e^16*z^6 + 1524695040*a^6*b^14*c^7*d^19*e^8*z^6 - 1472200704*a
^18*b^4*c^5*d^5*e^22*z^6 - 1472200704*a^8*b^4*c^15*d^25*e^2*z^6 - 83047219200*a^16*b^3*c^8*d^10*e^17*z^6 - 830
47219200*a^11*b^3*c^13*d^20*e^7*z^6 + 44291850240*a^17*b^2*c^8*d^9*e^18*z^6 + 44291850240*a^11*b^2*c^14*d^21*e
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13*e^14*z^6 + 48530718720*a^10*b^8*c^9*d^17*e^10*z^6 - 1242644480*a^12*b^12*c^3*d^9*e^18*z^6 - 1242644480*a^6*
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85504*a^15*b*c^11*d^14*e^13*z^6 - 93012885504*a^14*b*c^12*d^16*e^11*z^6 + 177305812992*a^13*b^4*c^10*d^15*e^12
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z^6 - 133809831936*a^10*b^6*c^11*d^19*e^8*z^6 - 2214592512*a^19*b*c^7*d^6*e^21*z^6 - 2214592512*a^10*b*c^16*d^
24*e^3*z^6 + 82216747008*a^13*b^7*c^7*d^12*e^15*z^6 + 82216747008*a^10*b^7*c^10*d^18*e^9*z^6 - 586629120*a^12*
b^13*c^2*d^8*e^19*z^6 - 586629120*a^5*b^13*c^9*d^22*e^5*z^6 + 568565760*a^7*b^16*c^4*d^15*e^12*z^6 - 484442112
0*a^16*b^4*c^7*d^9*e^18*z^6 - 4844421120*a^10*b^4*c^13*d^21*e^6*z^6 + 531210240*a^11*b^14*c^2*d^9*e^18*z^6 + 5
31210240*a^5*b^14*c^8*d^21*e^6*z^6 - 527155200*a^11*b^13*c^3*d^10*e^17*z^6 - 527155200*a^6*b^13*c^8*d^20*e^7*z
^6 + 43470028800*a^11*b^8*c^8*d^15*e^12*z^6 - 107874877440*a^11*b^9*c^7*d^14*e^13*z^6 - 107874877440*a^10*b^9*
c^8*d^16*e^11*z^6 + 9018408960*a^12*b^11*c^4*d^10*e^17*z^6 + 9018408960*a^7*b^11*c^9*d^20*e^7*z^6 + 421994496*
a^13*b^12*c^2*d^7*e^20*z^6 + 421994496*a^5*b^12*c^10*d^23*e^4*z^6 - 66437775360*a^16*b*c^10*d^12*e^15*z^6 - 66
437775360*a^13*b*c^13*d^18*e^9*z^6 + 26159874048*a^16*b^5*c^6*d^8*e^19*z^6 + 26159874048*a^9*b^5*c^13*d^22*e^5
*z^6 - 369098752*a^18*b^3*c^6*d^6*e^21*z^6 - 369098752*a^9*b^3*c^15*d^24*e^3*z^6 + 351436800*a^8*b^16*c^3*d^13
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2*c*d^2*e^21*z^4 - 440832*a*b^11*c^11*d^21*e^2*z^4 + 275968*a*b^19*c^3*d^13*e^10*z^4 - 159744*a^2*b^20*c*d^10*
e^13*z^4 - 153600*a*b^20*c^2*d^12*e^11*z^4 + 64512*a^3*b^19*c*d^9*e^14*z^4 + 19746062336*a^8*b^6*c^9*d^12*e^11
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b^19*c^2*d^11*e^12*z^4 - 8542224384*a^10*b^2*c^11*d^12*e^11*z^4 - 3072*b^22*c*d^12*e^11*z^4 - 3072*b^12*c^11*d
^22*e*z^4 - 1572864*a^6*c^17*d^22*e*z^4 - 4096*a^10*b^13*d*e^22*z^4 - 4096*a*b^22*d^10*e^13*z^4 - 6144*a^12*b^
10*c*e^23*z^4 - 983040*a^5*b*c^17*d^23*z^4 - 6912*a*b^9*c^13*d^23*z^4 + 1824522240*a^13*c^10*d^8*e^15*z^4 + 17
30150400*a^12*c^11*d^10*e^13*z^4 + 958922752*a^14*c^9*d^6*e^17*z^4 - 537919488*a^9*c^14*d^16*e^7*z^4 + 5085593
60*a^11*c^12*d^12*e^11*z^4 - 500170752*a^10*c^13*d^14*e^9*z^4 + 246939648*a^15*c^8*d^4*e^19*z^4 - 199229440*a^
8*c^15*d^18*e^5*z^4 - 29884416*a^7*c^16*d^20*e^3*z^4 + 25165824*a^16*c^7*d^2*e^21*z^4 + 236544*b^17*c^6*d^17*e
^6*z^4 - 202752*b^18*c^5*d^16*e^7*z^4 - 202752*b^16*c^7*d^18*e^5*z^4 + 126720*b^19*c^4*d^15*e^8*z^4 + 126720*b
^15*c^8*d^19*e^4*z^4 - 56320*b^20*c^3*d^14*e^9*z^4 - 56320*b^14*c^9*d^20*e^3*z^4 + 16896*b^21*c^2*d^13*e^10*z^
4 + 16896*b^13*c^10*d^21*e^2*z^4 + 110080*a^7*b^16*d^4*e^19*z^4 + 110080*a^4*b^19*d^7*e^16*z^4 - 75520*a^8*b^1
5*d^3*e^20*z^4 - 75520*a^3*b^20*d^8*e^15*z^4 - 56320*a^6*b^17*d^5*e^18*z^4 - 56320*a^5*b^18*d^6*e^17*z^4 + 256
00*a^9*b^14*d^2*e^21*z^4 + 25600*a^2*b^21*d^9*e^14*z^4 - 1572864*a^16*b^2*c^5*e^23*z^4 + 983040*a^15*b^4*c^4*e
^23*z^4 - 327680*a^14*b^6*c^3*e^23*z^4 + 61440*a^13*b^8*c^2*e^23*z^4 + 983040*a^4*b^3*c^16*d^23*z^4 - 385024*a
^3*b^5*c^15*d^23*z^4 + 73728*a^2*b^7*c^14*d^23*z^4 + 256*b^23*d^11*e^12*z^4 + 1048576*a^17*c^6*e^23*z^4 + 256*
b^11*c^12*d^23*z^4 + 256*a^11*b^12*e^23*z^4 + 948695040*a^8*b*c^10*d^6*e^13*z^2 + 348917760*a^7*b*c^11*d^8*e^1
1*z^2 - 125030400*a^9*b*c^9*d^4*e^15*z^2 - 50728960*a^6*b*c^12*d^10*e^9*z^2 - 44298240*a^5*b*c^13*d^12*e^7*z^2
- 36495360*a^10*b*c^8*d^2*e^17*z^2 + 29675520*a^8*b^6*c^5*d*e^18*z^2 - 24170496*a^9*b^4*c^6*d*e^18*z^2 - 1720
2816*a^7*b^8*c^4*d*e^18*z^2 - 14561280*a^4*b*c^14*d^14*e^5*z^2 + 5532416*a^6*b^10*c^3*d*e^18*z^2 + 4128768*a^1
0*b^2*c^7*d*e^18*z^2 - 2662400*a^3*b*c^15*d^16*e^3*z^2 + 1184512*a*b^12*c^6*d^9*e^10*z^2 - 1136160*a*b^13*c^5*
d^8*e^11*z^2 - 1017600*a^5*b^12*c^2*d*e^18*z^2 - 744768*a*b^11*c^7*d^10*e^9*z^2 + 607872*a*b^14*c^4*d^7*e^12*z
^2 - 424064*a*b^6*c^12*d^15*e^4*z^2 + 408576*a*b^5*c^13*d^16*e^3*z^2 + 361152*a*b^10*c^8*d^11*e^8*z^2 - 287408
*a*b^9*c^9*d^12*e^7*z^2 - 260448*a^3*b^15*c*d^2*e^17*z^2 - 203904*a*b^4*c^14*d^17*e^2*z^2 + 200832*a*b^8*c^10*
d^13*e^6*z^2 + 126720*a*b^7*c^11*d^14*e^5*z^2 - 123968*a*b^15*c^3*d^6*e^13*z^2 - 39168*a*b^16*c^2*d^5*e^14*z^2
+ 11904*a^2*b^16*c*d^3*e^16*z^2 + 1824135552*a^7*b^4*c^8*d^5*e^14*z^2 - 1457252352*a^8*b^2*c^9*d^5*e^14*z^2 -
1405209600*a^7*b^5*c^7*d^4*e^15*z^2 - 184320*a^2*b*c^16*d^18*e*z^2 + 100608*a^4*b^14*c*d*e^18*z^2 + 53248*a*b
^3*c^15*d^18*e*z^2 + 26448*a*b^17*c*d^4*e^15*z^2 + 1067599872*a^8*b^3*c^8*d^4*e^15*z^2 - 930828288*a^7*b^3*c^9
*d^6*e^13*z^2 + 920760000*a^6*b^4*c^9*d^7*e^12*z^2 - 806639616*a^6*b^3*c^10*d^8*e^11*z^2 - 791052480*a^6*b^6*c
^7*d^5*e^14*z^2 + 772237824*a^6*b^7*c^6*d^4*e^15*z^2 - 701025408*a^5*b^6*c^8*d^7*e^12*z^2 + 443340288*a^5*b^5*
c^9*d^8*e^11*z^2 + 433047552*a^7*b^6*c^6*d^3*e^16*z^2 + 405741312*a^5*b^7*c^7*d^6*e^13*z^2 + 293652480*a^6*b^2
*c^11*d^9*e^10*z^2 - 276962688*a^6*b^8*c^5*d^3*e^16*z^2 - 247804272*a^8*b^4*c^7*d^3*e^16*z^2 + 213564384*a^4*b
^8*c^7*d^7*e^12*z^2 - 202596816*a^5*b^9*c^5*d^4*e^15*z^2 - 182520896*a^4*b^9*c^6*d^6*e^13*z^2 - 153489408*a^5*
b^3*c^11*d^10*e^9*z^2 - 152151552*a^7*b^2*c^10*d^7*e^12*z^2 + 115859712*a^5*b^2*c^12*d^11*e^8*z^2 + 108085248*
a^9*b^3*c^7*d^2*e^17*z^2 + 105536256*a^4*b^5*c^10*d^10*e^9*z^2 - 98323200*a^6*b^5*c^8*d^6*e^13*z^2 - 93564992*
a^4*b^6*c^9*d^9*e^10*z^2 + 89464512*a^5*b^10*c^4*d^3*e^16*z^2 - 75930624*a^8*b^5*c^6*d^2*e^17*z^2 + 68315904*a
^5*b^8*c^6*d^5*e^14*z^2 - 64157184*a^4*b^7*c^8*d^8*e^11*z^2 - 62951040*a^9*b^2*c^8*d^3*e^16*z^2 + 49056768*a^4
*b^10*c^5*d^5*e^14*z^2 + 47614464*a^3*b^8*c^8*d^9*e^10*z^2 + 35604480*a^4*b^2*c^13*d^13*e^6*z^2 + 33983040*a^3
*b^11*c^5*d^6*e^13*z^2 - 33515520*a^4*b^3*c^12*d^12*e^7*z^2 - 33463808*a^3*b^7*c^9*d^10*e^9*z^2 - 25128864*a^4
*b^4*c^11*d^11*e^8*z^2 - 23193728*a^3*b^10*c^6*d^7*e^12*z^2 + 21015456*a^6*b^9*c^4*d^2*e^17*z^2 + 19924176*a^4
*b^11*c^4*d^4*e^15*z^2 - 19251216*a^3*b^9*c^7*d^8*e^11*z^2 - 16434048*a^5*b^4*c^10*d^9*e^10*z^2 - 16289664*a^3
*b^12*c^4*d^5*e^14*z^2 - 15059328*a^4*b^12*c^3*d^3*e^16*z^2 - 10766016*a^2*b^10*c^7*d^9*e^10*z^2 - 10453632*a^
5*b^11*c^3*d^2*e^17*z^2 - 9940992*a^3*b^3*c^13*d^14*e^5*z^2 + 8373696*a^2*b^11*c^6*d^8*e^11*z^2 + 7776768*a^3*
b^2*c^14*d^15*e^4*z^2 + 7077888*a^3*b^5*c^11*d^12*e^7*z^2 + 6798240*a^2*b^9*c^8*d^10*e^9*z^2 - 3589440*a^2*b^6
*c^11*d^13*e^6*z^2 + 3544320*a^3*b^6*c^10*d^11*e^8*z^2 + 3128064*a^2*b^5*c^12*d^14*e^5*z^2 + 2346336*a^4*b^13*
c^2*d^2*e^17*z^2 - 2261568*a^2*b^8*c^9*d^11*e^8*z^2 - 2125824*a^2*b^13*c^4*d^6*e^13*z^2 + 2002560*a^3*b^4*c^12
*d^13*e^6*z^2 + 1927680*a^2*b^7*c^10*d^12*e^7*z^2 + 1814784*a^2*b^14*c^3*d^5*e^14*z^2 - 1807104*a^2*b^12*c^5*d
^7*e^12*z^2 + 1637808*a^3*b^13*c^3*d^4*e^15*z^2 + 1083456*a^3*b^14*c^2*d^3*e^16*z^2 - 792384*a^2*b^4*c^13*d^15
*e^4*z^2 - 657408*a^2*b^3*c^14*d^16*e^3*z^2 + 608256*a^7*b^7*c^5*d^2*e^17*z^2 + 595968*a^2*b^2*c^15*d^17*e^2*z
^2 - 498624*a^2*b^15*c^2*d^4*e^15*z^2 - 3840*b^18*c*d^5*e^14*z^2 - 3840*b^5*c^14*d^18*e*z^2 + 2064384*a^11*c^8
*d*e^18*z^2 - 4160*a^3*b^16*d*e^18*z^2 - 4160*a*b^18*d^3*e^16*z^2 - 1290240*a^11*b*c^7*e^19*z^2 - 9840*a^5*b^1
3*c*e^19*z^2 - 5760*a*b^2*c^16*d^19*z^2 - 280581120*a^8*c^11*d^7*e^12*z^2 + 110278656*a^9*c^10*d^5*e^14*z^2 -
89479168*a^7*c^12*d^9*e^10*z^2 + 34464000*a^10*c^9*d^3*e^16*z^2 + 54240*b^15*c^4*d^8*e^11*z^2 + 54240*b^8*c^11
*d^15*e^4*z^2 - 49920*b^14*c^5*d^9*e^10*z^2 - 49920*b^9*c^10*d^14*e^5*z^2 - 37376*b^16*c^3*d^7*e^12*z^2 - 3737
6*b^7*c^12*d^16*e^3*z^2 + 28480*b^13*c^6*d^10*e^9*z^2 + 28480*b^10*c^9*d^13*e^6*z^2 + 15936*b^17*c^2*d^6*e^13*
z^2 + 15936*b^6*c^13*d^17*e^2*z^2 - 7920*b^12*c^7*d^11*e^8*z^2 - 7920*b^11*c^8*d^12*e^7*z^2 + 7489536*a^5*c^14
*d^13*e^6*z^2 + 6084096*a^6*c^13*d^11*e^8*z^2 + 2280448*a^4*c^15*d^15*e^4*z^2 + 350208*a^3*c^16*d^17*e^2*z^2 +
11616*a^2*b^17*d^2*e^17*z^2 - 3515904*a^9*b^5*c^5*e^19*z^2 + 3440640*a^10*b^3*c^6*e^19*z^2 + 1870848*a^8*b^7*
c^4*e^19*z^2 - 572272*a^7*b^9*c^3*e^19*z^2 + 101856*a^6*b^11*c^2*e^19*z^2 + 400*b^19*d^4*e^15*z^2 + 400*b^4*c^
15*d^19*z^2 + 20736*a^2*c^17*d^19*z^2 + 400*a^4*b^15*e^19*z^2 - 3969216*a^4*b*c^10*d^3*e^12 - 3001536*a^3*b*c^
11*d^5*e^10 - 419904*a^2*b*c^12*d^7*e^8 + 184608*a^4*b^3*c^8*d*e^14 - 153036*a*b^4*c^10*d^6*e^9 + 127008*a*b^3
*c^11*d^7*e^8 + 63108*a*b^6*c^8*d^4*e^11 - 29160*a*b^2*c^12*d^8*e^7 - 21060*a^3*b^5*c^7*d*e^14 - 21060*a*b^7*c
^7*d^3*e^12 + 5460*a*b^5*c^9*d^5*e^10 - 404544*a^5*b*c^9*d*e^14 + 1251872*a^3*b^3*c^9*d^3*e^12 + 844224*a^4*b^
2*c^9*d^2*e^13 + 820512*a^2*b^3*c^10*d^5*e^10 + 750672*a^3*b^2*c^10*d^4*e^11 - 657498*a^2*b^4*c^9*d^4*e^11 - 4
87116*a^3*b^4*c^8*d^2*e^13 + 160704*a^2*b^2*c^11*d^6*e^9 + 58806*a^2*b^6*c^7*d^2*e^13 + 13140*a^2*b^5*c^8*d^3*
e^12 + 15286*b^6*c^9*d^6*e^9 - 9540*b^7*c^8*d^5*e^10 - 9540*b^5*c^10*d^7*e^8 + 2025*b^8*c^7*d^4*e^11 + 2025*b^
4*c^11*d^8*e^7 + 3367008*a^4*c^11*d^4*e^11 + 1166400*a^3*c^12*d^6*e^9 + 705600*a^5*c^10*d^2*e^13 + 104976*a^2*
c^13*d^8*e^7 - 17640*a^5*b^2*c^8*e^15 + 2025*a^4*b^4*c^7*e^15 + 38416*a^6*c^9*e^15, z, k)*x*(1048576*a^8*c^19*
d^24*e^3 + 9437184*a^9*c^18*d^22*e^5 + 36700160*a^10*c^17*d^20*e^7 + 78643200*a^11*c^16*d^18*e^9 + 94371840*a^
12*c^15*d^16*e^11 + 44040192*a^13*c^14*d^14*e^13 - 44040192*a^14*c^13*d^12*e^15 - 94371840*a^15*c^12*d^10*e^17
- 78643200*a^16*c^11*d^8*e^19 - 36700160*a^17*c^10*d^6*e^21 - 9437184*a^18*c^9*d^4*e^23 - 1048576*a^19*c^8*d^
2*e^25 - 256*a^2*b^11*c^14*d^25*e^2 + 3072*a^2*b^12*c^13*d^24*e^3 - 16896*a^2*b^13*c^12*d^23*e^4 + 56320*a^2*b
^14*c^11*d^22*e^5 - 126720*a^2*b^15*c^10*d^21*e^6 + 202752*a^2*b^16*c^9*d^20*e^7 - 236544*a^2*b^17*c^8*d^19*e^
8 + 202752*a^2*b^18*c^7*d^18*e^9 - 126720*a^2*b^19*c^6*d^17*e^10 + 56320*a^2*b^20*c^5*d^16*e^11 - 16896*a^2*b^
21*c^4*d^15*e^12 + 3072*a^2*b^22*c^3*d^14*e^13 - 256*a^2*b^23*c^2*d^13*e^14 + 5120*a^3*b^9*c^15*d^25*e^2 - 624
64*a^3*b^10*c^14*d^24*e^3 + 346368*a^3*b^11*c^13*d^23*e^4 - 1152256*a^3*b^12*c^12*d^22*e^5 + 2553600*a^3*b^13*
c^11*d^21*e^6 - 3951360*a^3*b^14*c^10*d^20*e^7 + 4336128*a^3*b^15*c^9*d^19*e^8 - 3334656*a^3*b^16*c^8*d^18*e^9
+ 1700352*a^3*b^17*c^7*d^17*e^10 - 473600*a^3*b^18*c^6*d^16*e^11 - 8960*a^3*b^19*c^5*d^15*e^12 + 59136*a^3*b^
20*c^4*d^14*e^13 - 19712*a^3*b^21*c^3*d^13*e^14 + 2304*a^3*b^22*c^2*d^12*e^15 - 40960*a^4*b^7*c^16*d^25*e^2 +
512000*a^4*b^8*c^15*d^24*e^3 - 2872320*a^4*b^9*c^14*d^23*e^4 + 9519104*a^4*b^10*c^13*d^22*e^5 - 20581120*a^4*b
^11*c^12*d^21*e^6 + 30087680*a^4*b^12*c^11*d^20*e^7 - 29433600*a^4*b^13*c^10*d^19*e^8 + 17602560*a^4*b^14*c^9*
d^18*e^9 - 3798528*a^4*b^15*c^8*d^17*e^10 - 3077120*a^4*b^16*c^7*d^16*e^11 + 3028480*a^4*b^17*c^6*d^15*e^12 -
1075200*a^4*b^18*c^5*d^14*e^13 + 98560*a^4*b^19*c^4*d^13*e^14 + 39424*a^4*b^20*c^3*d^12*e^15 - 8960*a^4*b^21*c
^2*d^11*e^16 + 163840*a^5*b^5*c^17*d^25*e^2 - 2129920*a^5*b^6*c^16*d^24*e^3 + 12165120*a^5*b^7*c^15*d^23*e^4 -
39997440*a^5*b^8*c^14*d^22*e^5 + 82611200*a^5*b^9*c^13*d^21*e^6 - 107627520*a^5*b^10*c^12*d^20*e^7 + 78140160
*a^5*b^11*c^11*d^19*e^8 - 6831360*a^5*b^12*c^10*d^18*e^9 - 46586880*a^5*b^13*c^9*d^17*e^10 + 47436800*a^5*b^14
*c^8*d^16*e^11 - 20088320*a^5*b^15*c^7*d^15*e^12 + 1128960*a^5*b^16*c^6*d^14*e^13 + 2365440*a^5*b^17*c^5*d^13*
e^14 - 788480*a^5*b^18*c^4*d^12*e^15 + 19200*a^5*b^19*c^3*d^11*e^16 + 19200*a^5*b^20*c^2*d^10*e^17 - 327680*a^
6*b^3*c^18*d^25*e^2 + 4587520*a^6*b^4*c^17*d^24*e^3 - 27033600*a^6*b^5*c^16*d^23*e^4 + 87162880*a^6*b^6*c^15*d
^22*e^5 - 161996800*a^6*b^7*c^14*d^21*e^6 + 149237760*a^6*b^8*c^13*d^20*e^7 + 27202560*a^6*b^9*c^12*d^19*e^8 -
251750400*a^6*b^10*c^11*d^18*e^9 + 305948160*a^6*b^11*c^10*d^17*e^10 - 160153600*a^6*b^12*c^9*d^16*e^11 + 143
360*a^6*b^13*c^8*d^15*e^12 + 46018560*a^6*b^14*c^7*d^14*e^13 - 21683200*a^6*b^15*c^6*d^13*e^14 + 1576960*a^6*b
^16*c^5*d^12*e^15 + 1305600*a^6*b^17*c^4*d^11*e^16 - 215040*a^6*b^18*c^3*d^10*e^17 - 23040*a^6*b^19*c^2*d^9*e^
18 - 4456448*a^7*b^2*c^18*d^24*e^3 + 28114944*a^7*b^3*c^17*d^23*e^4 - 84869120*a^7*b^4*c^16*d^22*e^5 + 1043660
80*a^7*b^5*c^15*d^21*e^6 + 97943552*a^7*b^6*c^14*d^20*e^7 - 549986304*a^7*b^7*c^13*d^19*e^8 + 841961472*a^7*b^
8*c^12*d^18*e^9 - 549795840*a^7*b^9*c^11*d^17*e^10 - 68823040*a^7*b^10*c^10*d^16*e^11 + 375613952*a^7*b^11*c^9
*d^15*e^12 - 240167424*a^7*b^12*c^8*d^14*e^13 + 32840192*a^7*b^13*c^7*d^13*e^14 + 27399680*a^7*b^14*c^6*d^12*e
^15 - 10703360*a^7*b^15*c^5*d^11*e^16 - 81408*a^7*b^16*c^4*d^10*e^17 + 370176*a^7*b^17*c^3*d^9*e^18 + 10752*a^
7*b^18*c^2*d^8*e^19 + 14680064*a^8*b^2*c^17*d^22*e^5 + 80281600*a^8*b^3*c^16*d^21*e^6 - 440401920*a^8*b^4*c^15
*d^20*e^7 + 888373248*a^8*b^5*c^14*d^19*e^8 - 703266816*a^8*b^6*c^13*d^18*e^9 - 394149888*a^8*b^7*c^12*d^17*e^
10 + 1358438400*a^8*b^8*c^11*d^16*e^11 - 1129891840*a^8*b^9*c^10*d^15*e^12 + 225189888*a^8*b^10*c^9*d^14*e^13
+ 246045184*a^8*b^11*c^8*d^13*e^14 - 164082688*a^8*b^12*c^7*d^12*e^15 + 18009600*a^8*b^13*c^6*d^11*e^16 + 1065
9840*a^8*b^14*c^5*d^10*e^17 - 2099712*a^8*b^15*c^4*d^9*e^18 - 193536*a^8*b^16*c^3*d^8*e^19 + 10752*a^8*b^17*c^
2*d^7*e^20 + 239861760*a^9*b^2*c^16*d^20*e^7 - 172032000*a^9*b^3*c^15*d^19*e^8 - 704839680*a^9*b^4*c^14*d^18*e
^9 + 2013069312*a^9*b^5*c^13*d^17*e^10 - 2086993920*a^9*b^6*c^12*d^16*e^11 + 424427520*a^9*b^7*c^11*d^15*e^12
+ 1074585600*a^9*b^8*c^10*d^14*e^13 - 997877760*a^9*b^9*c^9*d^13*e^14 + 234493952*a^9*b^10*c^8*d^12*e^15 + 957
61920*a^9*b^11*c^7*d^11*e^16 - 55288320*a^9*b^12*c^6*d^10*e^17 + 3916800*a^9*b^13*c^5*d^9*e^18 + 1704960*a^9*b
^14*c^4*d^8*e^19 - 250368*a^9*b^15*c^3*d^7*e^20 - 23040*a^9*b^16*c^2*d^6*e^21 + 857210880*a^10*b^2*c^15*d^18*e
^9 - 1036124160*a^10*b^3*c^14*d^17*e^10 - 255590400*a^10*b^4*c^13*d^16*e^11 + 2195128320*a^10*b^5*c^12*d^15*e^
12 - 2422210560*a^10*b^6*c^11*d^14*e^13 + 813711360*a^10*b^7*c^10*d^13*e^14 + 420372480*a^10*b^8*c^9*d^12*e^15
- 428595200*a^10*b^9*c^8*d^11*e^16 + 106106880*a^10*b^10*c^7*d^10*e^17 + 8866560*a^10*b^11*c^6*d^9*e^18 - 110
74560*a^10*b^12*c^5*d^8*e^19 + 1989120*a^10*b^13*c^4*d^7*e^20 + 537600*a^10*b^14*c^3*d^6*e^21 + 19200*a^10*b^1
5*c^2*d^5*e^22 + 1454899200*a^11*b^2*c^14*d^16*e^11 - 1747845120*a^11*b^3*c^13*d^15*e^12 + 454164480*a^11*b^4*
c^12*d^14*e^13 + 1135411200*a^11*b^5*c^11*d^13*e^14 - 1286799360*a^11*b^6*c^10*d^12*e^15 + 527155200*a^11*b^7*
c^9*d^11*e^16 - 41902080*a^11*b^8*c^8*d^10*e^17 - 74849280*a^11*b^9*c^7*d^9*e^18 + 53222400*a^11*b^10*c^6*d^8*
e^19 - 4023040*a^11*b^11*c^5*d^7*e^20 - 4972800*a^11*b^12*c^4*d^6*e^21 - 456960*a^11*b^13*c^3*d^5*e^22 - 8960*
a^11*b^14*c^2*d^4*e^23 + 1189085184*a^12*b^2*c^13*d^14*e^13 - 1241382912*a^12*b^3*c^12*d^13*e^14 + 605552640*a
^12*b^4*c^11*d^12*e^15 - 97320960*a^12*b^5*c^10*d^11*e^16 - 142737408*a^12*b^6*c^9*d^10*e^17 + 278716416*a^12*
b^7*c^8*d^9*e^18 - 144764928*a^12*b^8*c^7*d^8*e^19 - 28779520*a^12*b^9*c^6*d^7*e^20 + 22077440*a^12*b^10*c^5*d
^6*e^21 + 4456704*a^12*b^11*c^4*d^5*e^22 + 215552*a^12*b^12*c^3*d^4*e^23 + 2304*a^12*b^13*c^2*d^3*e^24 + 12111
0528*a^13*b^2*c^12*d^12*e^15 - 108134400*a^13*b^3*c^11*d^11*e^16 + 454164480*a^13*b^4*c^10*d^10*e^17 - 5871697
92*a^13*b^5*c^9*d^9*e^18 + 98402304*a^13*b^6*c^8*d^8*e^19 + 184819712*a^13*b^7*c^7*d^7*e^20 - 39424000*a^13*b^
8*c^6*d^6*e^21 - 22471680*a^13*b^9*c^5*d^5*e^22 - 2151424*a^13*b^10*c^4*d^4*e^23 - 55552*a^13*b^11*c^3*d^3*e^2
4 - 256*a^13*b^12*c^2*d^2*e^25 - 644874240*a^14*b^2*c^11*d^10*e^17 + 339148800*a^14*b^3*c^10*d^9*e^18 + 371589
120*a^14*b^4*c^9*d^8*e^19 - 367689728*a^14*b^5*c^8*d^7*e^20 - 32112640*a^14*b^6*c^7*d^6*e^21 + 59351040*a^14*b
^7*c^6*d^5*e^22 + 11366400*a^14*b^8*c^5*d^4*e^23 + 558080*a^14*b^9*c^4*d^3*e^24 + 6144*a^14*b^10*c^3*d^2*e^25
- 578027520*a^15*b^2*c^10*d^8*e^19 + 135331840*a^15*b^3*c^9*d^7*e^20 + 217907200*a^15*b^4*c^8*d^6*e^21 - 65372
160*a^15*b^5*c^7*d^5*e^22 - 33259520*a^15*b^6*c^6*d^4*e^23 - 2990080*a^15*b^7*c^5*d^3*e^24 - 61440*a^15*b^8*c^
4*d^2*e^25 - 209715200*a^16*b^2*c^9*d^6*e^21 - 20643840*a^16*b^3*c^8*d^5*e^22 + 49807360*a^16*b^4*c^7*d^4*e^23
+ 9011200*a^16*b^5*c^6*d^3*e^24 + 327680*a^16*b^6*c^5*d^2*e^25 - 25427968*a^17*b^2*c^8*d^4*e^23 - 14483456*a^
17*b^3*c^7*d^3*e^24 - 983040*a^17*b^4*c^6*d^2*e^25 + 1572864*a^18*b^2*c^7*d^2*e^25 + 262144*a^7*b*c^19*d^25*e^
2 - 8650752*a^8*b*c^18*d^23*e^4 - 79953920*a^9*b*c^17*d^21*e^6 - 287047680*a^10*b*c^16*d^19*e^8 - 542638080*a^
11*b*c^15*d^17*e^10 - 539492352*a^12*b*c^14*d^15*e^12 - 143130624*a^13*b*c^13*d^13*e^14 + 306708480*a^14*b*c^1
2*d^11*e^16 + 420741120*a^15*b*c^11*d^9*e^18 + 250347520*a^16*b*c^10*d^7*e^20 + 76283904*a^17*b*c^9*d^5*e^22 +
9699328*a^18*b*c^8*d^3*e^24))/(8*(16*a^3*b^6*c^9*d^18 - a^2*b^8*c^8*d^18 - 256*a^6*c^12*d^18 - 96*a^4*b^4*c^1
0*d^18 + 256*a^5*b^2*c^11*d^18 - a^2*b^16*d^10*e^8 + 8*a^3*b^15*d^9*e^9 - 28*a^4*b^14*d^8*e^10 + 56*a^5*b^13*d
^7*e^11 - 70*a^6*b^12*d^6*e^12 + 56*a^7*b^11*d^5*e^13 - 28*a^8*b^10*d^4*e^14 + 8*a^9*b^9*d^3*e^15 - a^10*b^8*d
^2*e^16 - 2048*a^7*c^11*d^16*e^2 - 7168*a^8*c^10*d^14*e^4 - 14336*a^9*c^9*d^12*e^6 - 17920*a^10*c^8*d^10*e^8 -
14336*a^11*c^7*d^8*e^10 - 7168*a^12*c^6*d^6*e^12 - 2048*a^13*c^5*d^4*e^14 - 256*a^14*c^4*d^2*e^16 - 28*a^2*b^
10*c^6*d^16*e^2 + 56*a^2*b^11*c^5*d^15*e^3 - 70*a^2*b^12*c^4*d^14*e^4 + 56*a^2*b^13*c^3*d^13*e^5 - 28*a^2*b^14
*c^2*d^12*e^6 + 440*a^3*b^8*c^7*d^16*e^2 - 840*a^3*b^9*c^6*d^15*e^3 + 952*a^3*b^10*c^5*d^14*e^4 - 616*a^3*b^11
*c^4*d^13*e^5 + 168*a^3*b^12*c^3*d^12*e^6 + 40*a^3*b^13*c^2*d^11*e^7 - 2560*a^4*b^6*c^8*d^16*e^2 + 4480*a^4*b^
7*c^7*d^15*e^3 - 4060*a^4*b^8*c^6*d^14*e^4 + 1064*a^4*b^9*c^5*d^13*e^5 + 1372*a^4*b^10*c^4*d^12*e^6 - 1360*a^4
*b^11*c^3*d^11*e^7 + 380*a^4*b^12*c^2*d^10*e^8 + 6400*a^5*b^4*c^9*d^16*e^2 - 8960*a^5*b^5*c^8*d^15*e^3 + 2240*
a^5*b^6*c^7*d^14*e^4 + 9856*a^5*b^7*c^6*d^13*e^5 - 13048*a^5*b^8*c^5*d^12*e^6 + 5400*a^5*b^9*c^4*d^11*e^7 + 10
40*a^5*b^10*c^3*d^10*e^8 - 1360*a^5*b^11*c^2*d^9*e^9 - 5120*a^6*b^2*c^10*d^16*e^2 + 22400*a^6*b^4*c^8*d^14*e^4
- 41216*a^6*b^5*c^7*d^13*e^5 + 25088*a^6*b^6*c^6*d^12*e^6 + 8320*a^6*b^7*c^5*d^11*e^7 - 17350*a^6*b^8*c^4*d^1
0*e^8 + 5400*a^6*b^9*c^3*d^9*e^9 + 1372*a^6*b^10*c^2*d^8*e^10 - 35840*a^7*b^2*c^9*d^14*e^4 + 28672*a^7*b^3*c^8
*d^13*e^5 + 30464*a^7*b^4*c^7*d^12*e^6 - 73472*a^7*b^5*c^6*d^11*e^7 + 40544*a^7*b^6*c^5*d^10*e^8 + 8320*a^7*b^
7*c^4*d^9*e^9 - 13048*a^7*b^8*c^3*d^8*e^10 + 1064*a^7*b^9*c^2*d^7*e^11 - 93184*a^8*b^2*c^8*d^12*e^6 + 71680*a^
8*b^3*c^7*d^11*e^7 + 29120*a^8*b^4*c^6*d^10*e^8 - 73472*a^8*b^5*c^5*d^9*e^9 + 25088*a^8*b^6*c^4*d^8*e^10 + 985
6*a^8*b^7*c^3*d^7*e^11 - 4060*a^8*b^8*c^2*d^6*e^12 - 125440*a^9*b^2*c^7*d^10*e^8 + 71680*a^9*b^3*c^6*d^9*e^9 +
30464*a^9*b^4*c^5*d^8*e^10 - 41216*a^9*b^5*c^4*d^7*e^11 + 2240*a^9*b^6*c^3*d^6*e^12 + 4480*a^9*b^7*c^2*d^5*e^
13 - 93184*a^10*b^2*c^6*d^8*e^10 + 28672*a^10*b^3*c^5*d^7*e^11 + 22400*a^10*b^4*c^4*d^6*e^12 - 8960*a^10*b^5*c
^3*d^5*e^13 - 2560*a^10*b^6*c^2*d^4*e^14 - 35840*a^11*b^2*c^5*d^6*e^12 + 6400*a^11*b^4*c^3*d^4*e^14 + 768*a^11
*b^5*c^2*d^3*e^15 - 5120*a^12*b^2*c^4*d^4*e^14 - 2048*a^12*b^3*c^3*d^3*e^15 - 96*a^12*b^4*c^2*d^2*e^16 + 256*a
^13*b^2*c^3*d^2*e^16 + 2048*a^6*b*c^11*d^17*e + 8*a^2*b^9*c^7*d^17*e + 8*a^2*b^15*c*d^11*e^7 - 128*a^3*b^7*c^8
*d^17*e - 40*a^3*b^14*c*d^10*e^8 + 768*a^4*b^5*c^9*d^17*e + 40*a^4*b^13*c*d^9*e^9 - 2048*a^5*b^3*c^10*d^17*e +
168*a^5*b^12*c*d^8*e^10 - 616*a^6*b^11*c*d^7*e^11 + 14336*a^7*b*c^10*d^15*e^3 + 952*a^7*b^10*c*d^6*e^12 + 430
08*a^8*b*c^9*d^13*e^5 - 840*a^8*b^9*c*d^5*e^13 + 71680*a^9*b*c^8*d^11*e^7 + 440*a^9*b^8*c*d^4*e^14 + 71680*a^1
0*b*c^7*d^9*e^9 - 128*a^10*b^7*c*d^3*e^15 + 43008*a^11*b*c^6*d^7*e^11 + 16*a^11*b^6*c*d^2*e^16 + 14336*a^12*b*
c^5*d^5*e^13 + 2048*a^13*b*c^4*d^3*e^15))) - (x*(49152*a^14*b*c^8*e^23 - 65536*a^14*c^9*d*e^22 + 16*a^8*b^13*c
^2*e^23 - 368*a^9*b^11*c^3*e^23 + 3520*a^10*b^9*c^4*e^23 - 17920*a^11*b^7*c^5*e^23 + 51200*a^12*b^5*c^6*e^23 -
77824*a^13*b^3*c^7*e^23 + 18432*a^4*c^19*d^21*e^2 + 243712*a^5*c^18*d^19*e^4 + 1253376*a^6*c^17*d^17*e^6 + 22
52800*a^7*c^16*d^15*e^8 - 7835648*a^8*c^15*d^13*e^10 - 35516416*a^9*c^14*d^11*e^12 - 50487296*a^10*c^13*d^9*e^
14 - 30416896*a^11*c^12*d^7*e^16 - 5797888*a^12*c^11*d^5*e^18 + 522240*a^13*c^10*d^3*e^20 + 16*b^8*c^15*d^21*e
^2 - 160*b^9*c^14*d^20*e^3 + 720*b^10*c^13*d^19*e^4 - 1904*b^11*c^12*d^18*e^5 + 3200*b^12*c^11*d^17*e^6 - 3312
*b^13*c^10*d^16*e^7 + 1440*b^14*c^9*d^15*e^8 + 1440*b^15*c^8*d^14*e^9 - 3312*b^16*c^7*d^13*e^10 + 3200*b^17*c^
6*d^12*e^11 - 1904*b^18*c^5*d^11*e^12 + 720*b^19*c^4*d^10*e^13 - 160*b^20*c^3*d^9*e^14 + 16*b^21*c^2*d^8*e^15
+ 3200*a^2*b^4*c^17*d^21*e^2 - 30336*a^2*b^5*c^16*d^20*e^3 + 123296*a^2*b^6*c^15*d^19*e^4 - 269568*a^2*b^7*c^1
4*d^18*e^5 + 295872*a^2*b^8*c^13*d^17*e^6 + 16576*a^2*b^9*c^12*d^16*e^7 - 582688*a^2*b^10*c^11*d^15*e^8 + 9446
40*a^2*b^11*c^10*d^14*e^9 - 761856*a^2*b^12*c^9*d^13*e^10 + 243456*a^2*b^13*c^8*d^12*e^11 + 126048*a^2*b^14*c^
7*d^11*e^12 - 164096*a^2*b^15*c^6*d^10*e^13 + 58304*a^2*b^16*c^5*d^9*e^14 + 3264*a^2*b^17*c^4*d^8*e^15 - 7648*
a^2*b^18*c^3*d^7*e^16 + 1536*a^2*b^19*c^2*d^6*e^17 - 12800*a^3*b^2*c^18*d^21*e^2 + 119296*a^3*b^3*c^17*d^20*e^
3 - 448896*a^3*b^4*c^16*d^19*e^4 + 783872*a^3*b^5*c^15*d^18*e^5 - 197504*a^3*b^6*c^14*d^17*e^6 - 1977216*a^3*b
^7*c^13*d^16*e^7 + 4413568*a^3*b^8*c^12*d^15*e^8 - 4435520*a^3*b^9*c^11*d^14*e^9 + 1422432*a^3*b^10*c^10*d^13*
e^10 + 1795872*a^3*b^11*c^9*d^12*e^11 - 2349888*a^3*b^12*c^8*d^11*e^12 + 800352*a^3*b^13*c^7*d^10*e^13 + 42668
8*a^3*b^14*c^6*d^9*e^14 - 478112*a^3*b^15*c^5*d^8*e^15 + 145344*a^3*b^16*c^4*d^7*e^16 - 3104*a^3*b^17*c^3*d^6*
e^17 - 4384*a^3*b^18*c^2*d^5*e^18 + 519680*a^4*b^2*c^17*d^19*e^4 - 122880*a^4*b^3*c^16*d^18*e^5 - 3229184*a^4*
b^4*c^15*d^17*e^6 + 9323008*a^4*b^5*c^14*d^16*e^7 - 11702656*a^4*b^6*c^13*d^15*e^8 + 3460864*a^4*b^7*c^12*d^14
*e^9 + 10917472*a^4*b^8*c^11*d^13*e^10 - 16615488*a^4*b^9*c^10*d^12*e^11 + 7102272*a^4*b^10*c^9*d^11*e^12 + 58
42272*a^4*b^11*c^8*d^10*e^13 - 8942080*a^4*b^12*c^7*d^9*e^14 + 4203232*a^4*b^13*c^6*d^8*e^15 - 364736*a^4*b^14
*c^5*d^7*e^16 - 309472*a^4*b^15*c^4*d^6*e^17 + 63136*a^4*b^16*c^3*d^5*e^18 + 6112*a^4*b^17*c^2*d^4*e^19 + 6961
152*a^5*b^2*c^16*d^17*e^6 - 10246144*a^5*b^3*c^15*d^16*e^7 - 747008*a^5*b^4*c^14*d^15*e^8 + 29979648*a^5*b^5*c
^13*d^14*e^9 - 52869952*a^5*b^6*c^12*d^13*e^10 + 32791616*a^5*b^7*c^11*d^12*e^11 + 25176960*a^5*b^8*c^10*d^11*
e^12 - 62955552*a^5*b^9*c^9*d^10*e^13 + 45989472*a^5*b^10*c^8*d^9*e^14 - 9362688*a^5*b^11*c^7*d^8*e^15 - 58244
80*a^5*b^12*c^6*d^7*e^16 + 3196768*a^5*b^13*c^5*d^6*e^17 - 132768*a^5*b^14*c^4*d^5*e^18 - 119680*a^5*b^15*c^3*
d^4*e^19 - 4384*a^5*b^16*c^2*d^3*e^20 + 32086016*a^6*b^2*c^15*d^15*e^8 - 57880576*a^6*b^3*c^14*d^14*e^9 + 4468
3008*a^6*b^4*c^13*d^13*e^10 + 49481984*a^6*b^5*c^12*d^12*e^11 - 175788864*a^6*b^6*c^11*d^11*e^12 + 194611968*a
^6*b^7*c^10*d^10*e^13 - 73867584*a^6*b^8*c^9*d^9*e^14 - 38225280*a^6*b^9*c^8*d^8*e^15 + 45450144*a^6*b^10*c^7*
d^7*e^16 - 10588672*a^6*b^11*c^6*d^6*e^17 - 2519296*a^6*b^12*c^5*d^5*e^18 + 864384*a^6*b^13*c^4*d^4*e^19 + 962
24*a^6*b^14*c^3*d^3*e^20 + 1536*a^6*b^15*c^2*d^2*e^21 + 67527680*a^7*b^2*c^14*d^13*e^10 - 181466112*a^7*b^3*c^
13*d^12*e^11 + 278696704*a^7*b^4*c^12*d^11*e^12 - 171431936*a^7*b^5*c^11*d^10*e^13 - 104909184*a^7*b^6*c^10*d^
9*e^14 + 231100032*a^7*b^7*c^9*d^8*e^15 - 116105856*a^7*b^8*c^8*d^7*e^16 - 5653568*a^7*b^9*c^7*d^6*e^17 + 1955
6768*a^7*b^10*c^6*d^5*e^18 - 2291488*a^7*b^11*c^5*d^4*e^19 - 855936*a^7*b^12*c^4*d^3*e^20 - 35168*a^7*b^13*c^3
*d^2*e^21 - 40418304*a^8*b^2*c^13*d^11*e^12 - 155127808*a^8*b^3*c^12*d^10*e^13 + 421659136*a^8*b^4*c^11*d^9*e^
14 - 366294528*a^8*b^5*c^10*d^8*e^15 + 42953856*a^8*b^6*c^9*d^7*e^16 + 115841280*a^8*b^7*c^8*d^6*e^17 - 543016
80*a^8*b^8*c^7*d^5*e^18 - 3139616*a^8*b^9*c^6*d^4*e^19 + 3850352*a^8*b^10*c^5*d^3*e^20 + 333840*a^8*b^11*c^4*d
^2*e^21 - 262465536*a^9*b^2*c^12*d^9*e^14 + 49444864*a^9*b^3*c^11*d^8*e^15 + 255840768*a^9*b^4*c^10*d^7*e^16 -
241492992*a^9*b^5*c^9*d^6*e^17 + 41574816*a^9*b^6*c^8*d^5*e^18 + 32344416*a^9*b^7*c^7*d^4*e^19 - 8542208*a^9*
b^8*c^6*d^3*e^20 - 1677872*a^9*b^9*c^5*d^2*e^21 - 270632960*a^10*b^2*c^11*d^7*e^16 + 105492480*a^10*b^3*c^10*d
^6*e^17 + 71796864*a^10*b^4*c^9*d^5*e^18 - 66791040*a^10*b^5*c^8*d^4*e^19 + 5437088*a^10*b^6*c^7*d^3*e^20 + 46
84288*a^10*b^7*c^6*d^2*e^21 - 105693696*a^11*b^2*c^10*d^5*e^18 + 38220288*a^11*b^3*c^9*d^4*e^19 + 10967680*a^1
1*b^4*c^8*d^3*e^20 - 6778368*a^11*b^5*c^7*d^2*e^21 - 15811072*a^12*b^2*c^9*d^3*e^20 + 3633152*a^12*b^3*c^8*d^2
*e^21 - 352*a*b^6*c^16*d^21*e^2 + 3424*a*b^7*c^15*d^20*e^3 - 14720*a*b^8*c^14*d^19*e^4 + 36048*a*b^9*c^13*d^18
*e^5 - 52384*a*b^10*c^12*d^17*e^6 + 36464*a*b^11*c^11*d^16*e^7 + 17952*a*b^12*c^10*d^15*e^8 - 75360*a*b^13*c^9
*d^14*e^9 + 91104*a*b^14*c^8*d^13*e^10 - 60992*a*b^15*c^7*d^12*e^11 + 20288*a*b^16*c^6*d^11*e^12 + 1424*a*b^17
*c^5*d^10*e^13 - 4320*a*b^18*c^4*d^9*e^14 + 1648*a*b^19*c^3*d^8*e^15 - 224*a*b^20*c^2*d^7*e^16 - 169984*a^4*b*
c^18*d^20*e^3 - 2076672*a^5*b*c^17*d^18*e^5 - 9658368*a^6*b*c^16*d^16*e^7 - 16384000*a^7*b*c^15*d^14*e^9 - 224
*a^7*b^14*c^2*d*e^22 + 42463232*a^8*b*c^14*d^12*e^11 + 5120*a^8*b^12*c^3*d*e^22 + 170631168*a^9*b*c^13*d^10*e^
13 - 48576*a^9*b^10*c^4*d*e^22 + 199843840*a^10*b*c^12*d^8*e^15 + 244480*a^10*b^8*c^5*d*e^22 + 95387648*a^11*b
*c^11*d^6*e^17 - 686080*a^11*b^6*c^6*d*e^22 + 15722496*a^12*b*c^10*d^4*e^19 + 1007616*a^12*b^4*c^7*d*e^22 + 69
2224*a^13*b*c^9*d^2*e^21 - 573440*a^13*b^2*c^8*d*e^22))/(8*(16*a^3*b^6*c^9*d^18 - a^2*b^8*c^8*d^18 - 256*a^6*c
^12*d^18 - 96*a^4*b^4*c^10*d^18 + 256*a^5*b^2*c^11*d^18 - a^2*b^16*d^10*e^8 + 8*a^3*b^15*d^9*e^9 - 28*a^4*b^14
*d^8*e^10 + 56*a^5*b^13*d^7*e^11 - 70*a^6*b^12*d^6*e^12 + 56*a^7*b^11*d^5*e^13 - 28*a^8*b^10*d^4*e^14 + 8*a^9*
b^9*d^3*e^15 - a^10*b^8*d^2*e^16 - 2048*a^7*c^11*d^16*e^2 - 7168*a^8*c^10*d^14*e^4 - 14336*a^9*c^9*d^12*e^6 -
17920*a^10*c^8*d^10*e^8 - 14336*a^11*c^7*d^8*e^10 - 7168*a^12*c^6*d^6*e^12 - 2048*a^13*c^5*d^4*e^14 - 256*a^14
*c^4*d^2*e^16 - 28*a^2*b^10*c^6*d^16*e^2 + 56*a^2*b^11*c^5*d^15*e^3 - 70*a^2*b^12*c^4*d^14*e^4 + 56*a^2*b^13*c
^3*d^13*e^5 - 28*a^2*b^14*c^2*d^12*e^6 + 440*a^3*b^8*c^7*d^16*e^2 - 840*a^3*b^9*c^6*d^15*e^3 + 952*a^3*b^10*c^
5*d^14*e^4 - 616*a^3*b^11*c^4*d^13*e^5 + 168*a^3*b^12*c^3*d^12*e^6 + 40*a^3*b^13*c^2*d^11*e^7 - 2560*a^4*b^6*c
^8*d^16*e^2 + 4480*a^4*b^7*c^7*d^15*e^3 - 4060*a^4*b^8*c^6*d^14*e^4 + 1064*a^4*b^9*c^5*d^13*e^5 + 1372*a^4*b^1
0*c^4*d^12*e^6 - 1360*a^4*b^11*c^3*d^11*e^7 + 380*a^4*b^12*c^2*d^10*e^8 + 6400*a^5*b^4*c^9*d^16*e^2 - 8960*a^5
*b^5*c^8*d^15*e^3 + 2240*a^5*b^6*c^7*d^14*e^4 + 9856*a^5*b^7*c^6*d^13*e^5 - 13048*a^5*b^8*c^5*d^12*e^6 + 5400*
a^5*b^9*c^4*d^11*e^7 + 1040*a^5*b^10*c^3*d^10*e^8 - 1360*a^5*b^11*c^2*d^9*e^9 - 5120*a^6*b^2*c^10*d^16*e^2 + 2
2400*a^6*b^4*c^8*d^14*e^4 - 41216*a^6*b^5*c^7*d^13*e^5 + 25088*a^6*b^6*c^6*d^12*e^6 + 8320*a^6*b^7*c^5*d^11*e^
7 - 17350*a^6*b^8*c^4*d^10*e^8 + 5400*a^6*b^9*c^3*d^9*e^9 + 1372*a^6*b^10*c^2*d^8*e^10 - 35840*a^7*b^2*c^9*d^1
4*e^4 + 28672*a^7*b^3*c^8*d^13*e^5 + 30464*a^7*b^4*c^7*d^12*e^6 - 73472*a^7*b^5*c^6*d^11*e^7 + 40544*a^7*b^6*c
^5*d^10*e^8 + 8320*a^7*b^7*c^4*d^9*e^9 - 13048*a^7*b^8*c^3*d^8*e^10 + 1064*a^7*b^9*c^2*d^7*e^11 - 93184*a^8*b^
2*c^8*d^12*e^6 + 71680*a^8*b^3*c^7*d^11*e^7 + 29120*a^8*b^4*c^6*d^10*e^8 - 73472*a^8*b^5*c^5*d^9*e^9 + 25088*a
^8*b^6*c^4*d^8*e^10 + 9856*a^8*b^7*c^3*d^7*e^11 - 4060*a^8*b^8*c^2*d^6*e^12 - 125440*a^9*b^2*c^7*d^10*e^8 + 71
680*a^9*b^3*c^6*d^9*e^9 + 30464*a^9*b^4*c^5*d^8*e^10 - 41216*a^9*b^5*c^4*d^7*e^11 + 2240*a^9*b^6*c^3*d^6*e^12
+ 4480*a^9*b^7*c^2*d^5*e^13 - 93184*a^10*b^2*c^6*d^8*e^10 + 28672*a^10*b^3*c^5*d^7*e^11 + 22400*a^10*b^4*c^4*d
^6*e^12 - 8960*a^10*b^5*c^3*d^5*e^13 - 2560*a^10*b^6*c^2*d^4*e^14 - 35840*a^11*b^2*c^5*d^6*e^12 + 6400*a^11*b^
4*c^3*d^4*e^14 + 768*a^11*b^5*c^2*d^3*e^15 - 5120*a^12*b^2*c^4*d^4*e^14 - 2048*a^12*b^3*c^3*d^3*e^15 - 96*a^12
*b^4*c^2*d^2*e^16 + 256*a^13*b^2*c^3*d^2*e^16 + 2048*a^6*b*c^11*d^17*e + 8*a^2*b^9*c^7*d^17*e + 8*a^2*b^15*c*d
^11*e^7 - 128*a^3*b^7*c^8*d^17*e - 40*a^3*b^14*c*d^10*e^8 + 768*a^4*b^5*c^9*d^17*e + 40*a^4*b^13*c*d^9*e^9 - 2
048*a^5*b^3*c^10*d^17*e + 168*a^5*b^12*c*d^8*e^10 - 616*a^6*b^11*c*d^7*e^11 + 14336*a^7*b*c^10*d^15*e^3 + 952*
a^7*b^10*c*d^6*e^12 + 43008*a^8*b*c^9*d^13*e^5 - 840*a^8*b^9*c*d^5*e^13 + 71680*a^9*b*c^8*d^11*e^7 + 440*a^9*b
^8*c*d^4*e^14 + 71680*a^10*b*c^7*d^9*e^9 - 128*a^10*b^7*c*d^3*e^15 + 43008*a^11*b*c^6*d^7*e^11 + 16*a^11*b^6*c
*d^2*e^16 + 14336*a^12*b*c^5*d^5*e^13 + 2048*a^13*b*c^4*d^3*e^15)))) + (x*(25*a^4*b^10*c^5*e^19 - 6272*a^9*c^1
0*e^19 - 440*a^5*b^8*c^6*e^19 + 2986*a^6*b^6*c^7*e^19 - 9560*a^7*b^4*c^8*e^19 + 13792*a^8*b^2*c^9*e^19 + 1296*
a^2*c^17*d^14*e^5 + 19296*a^3*c^16*d^12*e^7 + 195952*a^4*c^15*d^10*e^9 + 938176*a^5*c^14*d^8*e^11 + 1838832*a^
6*c^13*d^6*e^13 - 20896*a^7*c^12*d^4*e^15 - 57200*a^8*c^11*d^2*e^17 + 25*b^4*c^15*d^14*e^5 - 190*b^5*c^14*d^13
*e^6 + 591*b^6*c^13*d^12*e^7 - 964*b^7*c^12*d^11*e^8 + 952*b^8*c^11*d^10*e^9 - 828*b^9*c^10*d^9*e^10 + 952*b^1
0*c^9*d^8*e^11 - 964*b^11*c^8*d^7*e^12 + 591*b^12*c^7*d^6*e^13 - 190*b^13*c^6*d^5*e^14 + 25*b^14*c^5*d^4*e^15
+ 18816*a^2*b^2*c^15*d^12*e^7 - 464*a^2*b^3*c^14*d^11*e^8 - 33441*a^2*b^4*c^13*d^10*e^9 - 9780*a^2*b^5*c^12*d^
9*e^10 + 98620*a^2*b^6*c^11*d^8*e^11 - 74420*a^2*b^7*c^10*d^7*e^12 - 25327*a^2*b^8*c^9*d^6*e^13 + 51944*a^2*b^
9*c^8*d^5*e^14 - 19162*a^2*b^10*c^7*d^4*e^15 + 376*a^2*b^11*c^6*d^3*e^16 + 726*a^2*b^12*c^5*d^2*e^17 + 132104*
a^3*b^2*c^14*d^10*e^9 + 202944*a^3*b^3*c^13*d^9*e^10 - 496916*a^3*b^4*c^12*d^8*e^11 + 62420*a^3*b^5*c^11*d^7*e
^12 + 477560*a^3*b^6*c^10*d^6*e^13 - 367184*a^3*b^7*c^9*d^5*e^14 + 42920*a^3*b^8*c^8*d^4*e^15 + 41584*a^3*b^9*
c^7*d^3*e^16 - 11716*a^3*b^10*c^6*d^2*e^17 + 774624*a^4*b^2*c^13*d^8*e^11 + 1091488*a^4*b^3*c^12*d^7*e^12 - 20
78409*a^4*b^4*c^11*d^6*e^13 + 759546*a^4*b^5*c^10*d^5*e^14 + 436579*a^4*b^6*c^9*d^4*e^15 - 373848*a^4*b^7*c^8*
d^3*e^16 + 68053*a^4*b^8*c^7*d^2*e^17 + 2519400*a^5*b^2*c^12*d^6*e^13 + 1051760*a^5*b^3*c^11*d^5*e^14 - 249424
2*a^5*b^4*c^10*d^4*e^15 + 1223634*a^5*b^5*c^9*d^3*e^16 - 153022*a^5*b^6*c^8*d^2*e^17 + 3717952*a^6*b^2*c^11*d^
4*e^15 - 1366224*a^6*b^3*c^10*d^3*e^16 + 23697*a^6*b^4*c^9*d^2*e^17 + 268408*a^7*b^2*c^10*d^2*e^17 + 43136*a^8
*b*c^10*d*e^18 - 360*a*b^2*c^16*d^14*e^5 + 2608*a*b^3*c^15*d^13*e^6 - 7218*a*b^4*c^14*d^12*e^7 + 8922*a*b^5*c^
13*d^11*e^8 - 4786*a*b^6*c^12*d^10*e^9 + 4722*a*b^7*c^11*d^9*e^10 - 12250*a*b^8*c^10*d^8*e^11 + 13434*a*b^9*c^
9*d^7*e^12 - 4918*a*b^10*c^8*d^6*e^13 - 1202*a*b^11*c^7*d^5*e^14 + 1308*a*b^12*c^6*d^4*e^15 - 260*a*b^13*c^5*d
^3*e^16 - 8928*a^2*b*c^16*d^13*e^6 - 107360*a^3*b*c^15*d^11*e^8 - 260*a^3*b^11*c^5*d*e^18 - 846912*a^4*b*c^14*
d^9*e^10 + 4518*a^4*b^9*c^6*d*e^18 - 3155136*a^5*b*c^13*d^7*e^12 - 30034*a^5*b^7*c^7*d*e^18 - 4176736*a^6*b*c^
12*d^5*e^14 + 92664*a^6*b^5*c^8*d*e^18 - 154080*a^7*b*c^11*d^3*e^16 - 123488*a^7*b^3*c^9*d*e^18))/(8*(16*a^3*b
^6*c^9*d^18 - a^2*b^8*c^8*d^18 - 256*a^6*c^12*d^18 - 96*a^4*b^4*c^10*d^18 + 256*a^5*b^2*c^11*d^18 - a^2*b^16*d
^10*e^8 + 8*a^3*b^15*d^9*e^9 - 28*a^4*b^14*d^8*e^10 + 56*a^5*b^13*d^7*e^11 - 70*a^6*b^12*d^6*e^12 + 56*a^7*b^1
1*d^5*e^13 - 28*a^8*b^10*d^4*e^14 + 8*a^9*b^9*d^3*e^15 - a^10*b^8*d^2*e^16 - 2048*a^7*c^11*d^16*e^2 - 7168*a^8
*c^10*d^14*e^4 - 14336*a^9*c^9*d^12*e^6 - 17920*a^10*c^8*d^10*e^8 - 14336*a^11*c^7*d^8*e^10 - 7168*a^12*c^6*d^
6*e^12 - 2048*a^13*c^5*d^4*e^14 - 256*a^14*c^4*d^2*e^16 - 28*a^2*b^10*c^6*d^16*e^2 + 56*a^2*b^11*c^5*d^15*e^3
- 70*a^2*b^12*c^4*d^14*e^4 + 56*a^2*b^13*c^3*d^13*e^5 - 28*a^2*b^14*c^2*d^12*e^6 + 440*a^3*b^8*c^7*d^16*e^2 -
840*a^3*b^9*c^6*d^15*e^3 + 952*a^3*b^10*c^5*d^14*e^4 - 616*a^3*b^11*c^4*d^13*e^5 + 168*a^3*b^12*c^3*d^12*e^6 +
40*a^3*b^13*c^2*d^11*e^7 - 2560*a^4*b^6*c^8*d^16*e^2 + 4480*a^4*b^7*c^7*d^15*e^3 - 4060*a^4*b^8*c^6*d^14*e^4
+ 1064*a^4*b^9*c^5*d^13*e^5 + 1372*a^4*b^10*c^4*d^12*e^6 - 1360*a^4*b^11*c^3*d^11*e^7 + 380*a^4*b^12*c^2*d^10*
e^8 + 6400*a^5*b^4*c^9*d^16*e^2 - 8960*a^5*b^5*c^8*d^15*e^3 + 2240*a^5*b^6*c^7*d^14*e^4 + 9856*a^5*b^7*c^6*d^1
3*e^5 - 13048*a^5*b^8*c^5*d^12*e^6 + 5400*a^5*b^9*c^4*d^11*e^7 + 1040*a^5*b^10*c^3*d^10*e^8 - 1360*a^5*b^11*c^
2*d^9*e^9 - 5120*a^6*b^2*c^10*d^16*e^2 + 22400*a^6*b^4*c^8*d^14*e^4 - 41216*a^6*b^5*c^7*d^13*e^5 + 25088*a^6*b
^6*c^6*d^12*e^6 + 8320*a^6*b^7*c^5*d^11*e^7 - 17350*a^6*b^8*c^4*d^10*e^8 + 5400*a^6*b^9*c^3*d^9*e^9 + 1372*a^6
*b^10*c^2*d^8*e^10 - 35840*a^7*b^2*c^9*d^14*e^4 + 28672*a^7*b^3*c^8*d^13*e^5 + 30464*a^7*b^4*c^7*d^12*e^6 - 73
472*a^7*b^5*c^6*d^11*e^7 + 40544*a^7*b^6*c^5*d^10*e^8 + 8320*a^7*b^7*c^4*d^9*e^9 - 13048*a^7*b^8*c^3*d^8*e^10
+ 1064*a^7*b^9*c^2*d^7*e^11 - 93184*a^8*b^2*c^8*d^12*e^6 + 71680*a^8*b^3*c^7*d^11*e^7 + 29120*a^8*b^4*c^6*d^10
*e^8 - 73472*a^8*b^5*c^5*d^9*e^9 + 25088*a^8*b^6*c^4*d^8*e^10 + 9856*a^8*b^7*c^3*d^7*e^11 - 4060*a^8*b^8*c^2*d
^6*e^12 - 125440*a^9*b^2*c^7*d^10*e^8 + 71680*a^9*b^3*c^6*d^9*e^9 + 30464*a^9*b^4*c^5*d^8*e^10 - 41216*a^9*b^5
*c^4*d^7*e^11 + 2240*a^9*b^6*c^3*d^6*e^12 + 4480*a^9*b^7*c^2*d^5*e^13 - 93184*a^10*b^2*c^6*d^8*e^10 + 28672*a^
10*b^3*c^5*d^7*e^11 + 22400*a^10*b^4*c^4*d^6*e^12 - 8960*a^10*b^5*c^3*d^5*e^13 - 2560*a^10*b^6*c^2*d^4*e^14 -
35840*a^11*b^2*c^5*d^6*e^12 + 6400*a^11*b^4*c^3*d^4*e^14 + 768*a^11*b^5*c^2*d^3*e^15 - 5120*a^12*b^2*c^4*d^4*e
^14 - 2048*a^12*b^3*c^3*d^3*e^15 - 96*a^12*b^4*c^2*d^2*e^16 + 256*a^13*b^2*c^3*d^2*e^16 + 2048*a^6*b*c^11*d^17
*e + 8*a^2*b^9*c^7*d^17*e + 8*a^2*b^15*c*d^11*e^7 - 128*a^3*b^7*c^8*d^17*e - 40*a^3*b^14*c*d^10*e^8 + 768*a^4*
b^5*c^9*d^17*e + 40*a^4*b^13*c*d^9*e^9 - 2048*a^5*b^3*c^10*d^17*e + 168*a^5*b^12*c*d^8*e^10 - 616*a^6*b^11*c*d
^7*e^11 + 14336*a^7*b*c^10*d^15*e^3 + 952*a^7*b^10*c*d^6*e^12 + 43008*a^8*b*c^9*d^13*e^5 - 840*a^8*b^9*c*d^5*e
^13 + 71680*a^9*b*c^8*d^11*e^7 + 440*a^9*b^8*c*d^4*e^14 + 71680*a^10*b*c^7*d^9*e^9 - 128*a^10*b^7*c*d^3*e^15 +
43008*a^11*b*c^6*d^7*e^11 + 16*a^11*b^6*c*d^2*e^16 + 14336*a^12*b*c^5*d^5*e^13 + 2048*a^13*b*c^4*d^3*e^15)))
- (3920*a^6*b*c^10*e^17 + 32144*a^6*c^11*d*e^16 + 225*a^4*b^5*c^8*e^17 - 1880*a^5*b^3*c^9*e^17 + 11664*a^2*c^1
5*d^9*e^8 + 46656*a^3*c^14*d^7*e^10 - 40608*a^4*c^13*d^5*e^12 + 284224*a^5*c^12*d^3*e^14 + 225*b^4*c^13*d^9*e^
8 - 755*b^5*c^12*d^8*e^9 + 530*b^6*c^11*d^7*e^10 + 530*b^7*c^10*d^6*e^11 - 755*b^8*c^9*d^5*e^12 + 225*b^9*c^8*
d^4*e^13 + 27648*a^2*b^2*c^13*d^7*e^10 + 4576*a^2*b^3*c^12*d^6*e^11 + 24438*a^2*b^4*c^11*d^5*e^12 - 44262*a^2*
b^5*c^10*d^4*e^13 + 4042*a^2*b^6*c^9*d^3*e^14 + 6534*a^2*b^7*c^8*d^2*e^15 - 23408*a^3*b^2*c^12*d^5*e^12 + 4187
2*a^3*b^3*c^11*d^4*e^13 + 100948*a^3*b^4*c^10*d^3*e^14 - 60416*a^3*b^5*c^9*d^2*e^15 - 384384*a^4*b^2*c^11*d^3*
e^14 + 165216*a^4*b^3*c^10*d^2*e^15 - 3240*a*b^2*c^14*d^9*e^8 + 11016*a*b^3*c^13*d^8*e^9 - 8812*a*b^4*c^12*d^7
*e^10 - 1992*a*b^5*c^11*d^6*e^11 + 408*a*b^6*c^10*d^5*e^12 + 5216*a*b^7*c^9*d^4*e^13 - 2340*a*b^8*c^8*d^3*e^14
- 40176*a^2*b*c^14*d^8*e^9 - 63360*a^3*b*c^13*d^6*e^11 - 2340*a^3*b^6*c^8*d*e^16 + 120608*a^4*b*c^12*d^4*e^13
+ 21281*a^4*b^4*c^9*d*e^16 - 114432*a^5*b*c^11*d^2*e^15 - 55656*a^5*b^2*c^10*d*e^16)/(32*(16*a^3*b^6*c^9*d^18
- a^2*b^8*c^8*d^18 - 256*a^6*c^12*d^18 - 96*a^4*b^4*c^10*d^18 + 256*a^5*b^2*c^11*d^18 - a^2*b^16*d^10*e^8 + 8
*a^3*b^15*d^9*e^9 - 28*a^4*b^14*d^8*e^10 + 56*a^5*b^13*d^7*e^11 - 70*a^6*b^12*d^6*e^12 + 56*a^7*b^11*d^5*e^13
- 28*a^8*b^10*d^4*e^14 + 8*a^9*b^9*d^3*e^15 - a^10*b^8*d^2*e^16 - 2048*a^7*c^11*d^16*e^2 - 7168*a^8*c^10*d^14*
e^4 - 14336*a^9*c^9*d^12*e^6 - 17920*a^10*c^8*d^10*e^8 - 14336*a^11*c^7*d^8*e^10 - 7168*a^12*c^6*d^6*e^12 - 20
48*a^13*c^5*d^4*e^14 - 256*a^14*c^4*d^2*e^16 - 28*a^2*b^10*c^6*d^16*e^2 + 56*a^2*b^11*c^5*d^15*e^3 - 70*a^2*b^
12*c^4*d^14*e^4 + 56*a^2*b^13*c^3*d^13*e^5 - 28*a^2*b^14*c^2*d^12*e^6 + 440*a^3*b^8*c^7*d^16*e^2 - 840*a^3*b^9
*c^6*d^15*e^3 + 952*a^3*b^10*c^5*d^14*e^4 - 616*a^3*b^11*c^4*d^13*e^5 + 168*a^3*b^12*c^3*d^12*e^6 + 40*a^3*b^1
3*c^2*d^11*e^7 - 2560*a^4*b^6*c^8*d^16*e^2 + 4480*a^4*b^7*c^7*d^15*e^3 - 4060*a^4*b^8*c^6*d^14*e^4 + 1064*a^4*
b^9*c^5*d^13*e^5 + 1372*a^4*b^10*c^4*d^12*e^6 - 1360*a^4*b^11*c^3*d^11*e^7 + 380*a^4*b^12*c^2*d^10*e^8 + 6400*
a^5*b^4*c^9*d^16*e^2 - 8960*a^5*b^5*c^8*d^15*e^3 + 2240*a^5*b^6*c^7*d^14*e^4 + 9856*a^5*b^7*c^6*d^13*e^5 - 130
48*a^5*b^8*c^5*d^12*e^6 + 5400*a^5*b^9*c^4*d^11*e^7 + 1040*a^5*b^10*c^3*d^10*e^8 - 1360*a^5*b^11*c^2*d^9*e^9 -
5120*a^6*b^2*c^10*d^16*e^2 + 22400*a^6*b^4*c^8*d^14*e^4 - 41216*a^6*b^5*c^7*d^13*e^5 + 25088*a^6*b^6*c^6*d^12
*e^6 + 8320*a^6*b^7*c^5*d^11*e^7 - 17350*a^6*b^8*c^4*d^10*e^8 + 5400*a^6*b^9*c^3*d^9*e^9 + 1372*a^6*b^10*c^2*d
^8*e^10 - 35840*a^7*b^2*c^9*d^14*e^4 + 28672*a^7*b^3*c^8*d^13*e^5 + 30464*a^7*b^4*c^7*d^12*e^6 - 73472*a^7*b^5
*c^6*d^11*e^7 + 40544*a^7*b^6*c^5*d^10*e^8 + 8320*a^7*b^7*c^4*d^9*e^9 - 13048*a^7*b^8*c^3*d^8*e^10 + 1064*a^7*
b^9*c^2*d^7*e^11 - 93184*a^8*b^2*c^8*d^12*e^6 + 71680*a^8*b^3*c^7*d^11*e^7 + 29120*a^8*b^4*c^6*d^10*e^8 - 7347
2*a^8*b^5*c^5*d^9*e^9 + 25088*a^8*b^6*c^4*d^8*e^10 + 9856*a^8*b^7*c^3*d^7*e^11 - 4060*a^8*b^8*c^2*d^6*e^12 - 1
25440*a^9*b^2*c^7*d^10*e^8 + 71680*a^9*b^3*c^6*d^9*e^9 + 30464*a^9*b^4*c^5*d^8*e^10 - 41216*a^9*b^5*c^4*d^7*e^
11 + 2240*a^9*b^6*c^3*d^6*e^12 + 4480*a^9*b^7*c^2*d^5*e^13 - 93184*a^10*b^2*c^6*d^8*e^10 + 28672*a^10*b^3*c^5*
d^7*e^11 + 22400*a^10*b^4*c^4*d^6*e^12 - 8960*a^10*b^5*c^3*d^5*e^13 - 2560*a^10*b^6*c^2*d^4*e^14 - 35840*a^11*
b^2*c^5*d^6*e^12 + 6400*a^11*b^4*c^3*d^4*e^14 + 768*a^11*b^5*c^2*d^3*e^15 - 5120*a^12*b^2*c^4*d^4*e^14 - 2048*
a^12*b^3*c^3*d^3*e^15 - 96*a^12*b^4*c^2*d^2*e^16 + 256*a^13*b^2*c^3*d^2*e^16 + 2048*a^6*b*c^11*d^17*e + 8*a^2*
b^9*c^7*d^17*e + 8*a^2*b^15*c*d^11*e^7 - 128*a^3*b^7*c^8*d^17*e - 40*a^3*b^14*c*d^10*e^8 + 768*a^4*b^5*c^9*d^1
7*e + 40*a^4*b^13*c*d^9*e^9 - 2048*a^5*b^3*c^10*d^17*e + 168*a^5*b^12*c*d^8*e^10 - 616*a^6*b^11*c*d^7*e^11 + 1
4336*a^7*b*c^10*d^15*e^3 + 952*a^7*b^10*c*d^6*e^12 + 43008*a^8*b*c^9*d^13*e^5 - 840*a^8*b^9*c*d^5*e^13 + 71680
*a^9*b*c^8*d^11*e^7 + 440*a^9*b^8*c*d^4*e^14 + 71680*a^10*b*c^7*d^9*e^9 - 128*a^10*b^7*c*d^3*e^15 + 43008*a^11
*b*c^6*d^7*e^11 + 16*a^11*b^6*c*d^2*e^16 + 14336*a^12*b*c^5*d^5*e^13 + 2048*a^13*b*c^4*d^3*e^15)))*root(128723
189760*a^14*b^4*c^9*d^13*e^14*z^6 + 128723189760*a^12*b^4*c^11*d^17*e^10*z^6 - 8432455680*a^11*b^12*c^4*d^11*e
^16*z^6 - 8432455680*a^7*b^12*c^8*d^19*e^8*z^6 + 12673351680*a^11*b^11*c^5*d^12*e^15*z^6 + 12673351680*a^8*b^1
1*c^8*d^18*e^9*z^6 - 72637480960*a^12*b^9*c^6*d^12*e^15*z^6 - 72637480960*a^9*b^9*c^9*d^18*e^9*z^6 - 210483445
76*a^9*b^12*c^6*d^15*e^12*z^6 - 16609443840*a^17*b^3*c^7*d^8*e^19*z^6 - 16609443840*a^10*b^3*c^14*d^22*e^5*z^6
+ 145332633600*a^13*b^5*c^9*d^14*e^13*z^6 + 145332633600*a^12*b^5*c^10*d^16*e^11*z^6 + 123740356608*a^14*b^5*
c^8*d^12*e^15*z^6 + 123740356608*a^11*b^5*c^11*d^18*e^9*z^6 + 3460300800*a^17*b^5*c^5*d^6*e^21*z^6 + 346030080
0*a^8*b^5*c^14*d^24*e^3*z^6 - 7751073792*a^15*b^7*c^5*d^8*e^19*z^6 - 7751073792*a^8*b^7*c^12*d^22*e^5*z^6 + 12
041846784*a^14*b^7*c^6*d^10*e^17*z^6 + 12041846784*a^9*b^7*c^11*d^20*e^7*z^6 - 325545099264*a^14*b^3*c^10*d^14
*e^13*z^6 - 325545099264*a^13*b^3*c^11*d^16*e^11*z^6 - 3330539520*a^13*b^10*c^4*d^9*e^18*z^6 - 3330539520*a^7*
b^10*c^10*d^21*e^6*z^6 + 157789716480*a^12*b^7*c^8*d^14*e^13*z^6 + 157789716480*a^11*b^7*c^9*d^16*e^11*z^6 + 3
7492359168*a^11*b^10*c^6*d^13*e^14*z^6 + 37492359168*a^9*b^10*c^8*d^17*e^10*z^6 + 301989888*a^8*b^3*c^16*d^26*
e*z^6 - 7266631680*a^17*b^4*c^6*d^7*e^20*z^6 - 7266631680*a^9*b^4*c^14*d^23*e^4*z^6 - 201326592*a^20*b*c^6*d^4
*e^23*z^6 - 188743680*a^7*b^5*c^15*d^26*e*z^6 + 45747339264*a^13*b^8*c^6*d^11*e^16*z^6 + 45747339264*a^9*b^8*c
^10*d^19*e^8*z^6 - 74612736*a^10*b^16*c*d^9*e^18*z^6 - 2768240640*a^16*b^7*c^4*d^6*e^21*z^6 - 2768240640*a^7*b
^7*c^13*d^24*e^3*z^6 + 69746688*a^11*b^15*c*d^8*e^19*z^6 + 62914560*a^6*b^7*c^14*d^26*e*z^6 + 2752020480*a^10*
b^13*c^4*d^12*e^15*z^6 + 2752020480*a^7*b^13*c^7*d^18*e^9*z^6 + 55148544*a^9*b^17*c*d^10*e^17*z^6 - 45957120*a
^12*b^14*c*d^7*e^20*z^6 - 2724986880*a^14*b^9*c^4*d^8*e^19*z^6 - 2724986880*a^7*b^9*c^11*d^22*e^5*z^6 - 259522
56*a^8*b^18*c*d^11*e^16*z^6 + 21086208*a^13*b^13*c*d^6*e^21*z^6 - 11796480*a^5*b^9*c^13*d^26*e*z^6 - 6438912*a
^14*b^12*c*d^5*e^22*z^6 + 5406720*a^7*b^19*c*d^12*e^15*z^6 + 1622016*a^6*b^20*c*d^13*e^14*z^6 - 1523712*a^5*b^
21*c*d^14*e^13*z^6 + 1179648*a^15*b^11*c*d^4*e^23*z^6 + 1179648*a^4*b^11*c^12*d^26*e*z^6 + 442368*a^4*b^22*c*d
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6 + 6897106944*a^9*b^13*c^5*d^14*e^13*z^6 + 6897106944*a^8*b^13*c^6*d^16*e^11*z^6 - 2422210560*a^16*b^6*c^5*d^
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217838080*a^11*b^6*c^10*d^17*e^10*z^6 - 1952907264*a^14*b^10*c^3*d^7*e^20*z^6 - 1952907264*a^6*b^10*c^11*d^23*
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6 - 33218887680*a^17*b*c^9*d^10*e^17*z^6 - 33218887680*a^12*b*c^14*d^20*e^7*z^6 + 1524695040*a^10*b^14*c^3*d^1
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240*a^17*b^2*c^8*d^9*e^18*z^6 + 44291850240*a^11*b^2*c^14*d^21*e^6*z^6 + 1308131328*a^8*b^14*c^5*d^15*e^12*z^6
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10*z^6 - 1242644480*a^12*b^12*c^3*d^9*e^18*z^6 - 1242644480*a^6*b^12*c^9*d^21*e^6*z^6 + 9813196800*a^12*b^10*c
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107874877440*a^11*b^9*c^7*d^14*e^13*z^6 - 107874877440*a^10*b^9*c^8*d^16*e^11*z^6 + 9018408960*a^12*b^11*c^4*d
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^6 - 334233600*a^16*b^8*c^3*d^5*e^22*z^6 - 334233600*a^6*b^8*c^13*d^25*e^2*z^6 + 301989888*a^19*b^3*c^5*d^4*e^
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^9*d^15*e^12*z^6 - 203292672*a^14*b^11*c^2*d^6*e^21*z^6 - 203292672*a^5*b^11*c^11*d^24*e^3*z^6 - 188743680*a^1
8*b^5*c^4*d^4*e^23*z^6 + 120418467840*a^16*b^2*c^9*d^11*e^16*z^6 + 120418467840*a^12*b^2*c^13*d^19*e^8*z^6 - 1
7293934592*a^10*b^12*c^5*d^13*e^14*z^6 - 17293934592*a^8*b^12*c^7*d^17*e^10*z^6 + 104890368*a^8*b^17*c^2*d^12*
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2*d^23*e^4*z^6 - 91750400*a^6*b^18*c^3*d^15*e^12*z^6 + 79134720*a^7*b^17*c^3*d^14*e^13*z^6 + 79134720*a^6*b^17
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^18*c^4*d^17*e^10*z^6 + 69746688*a^4*b^15*c^8*d^22*e^5*z^6 + 63700992*a^15*b^10*c^2*d^5*e^22*z^6 + 63700992*a^
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8640*a^19*b^4*c^4*d^3*e^24*z^6 - 11796480*a^16*b^9*c^2*d^4*e^23*z^6 - 6438912*a^4*b^12*c^11*d^25*e^2*z^6 + 540
6720*a^4*b^19*c^4*d^18*e^9*z^6 - 5242880*a^18*b^6*c^3*d^3*e^24*z^6 + 3784704*a^3*b^18*c^6*d^21*e^6*z^6 - 32440
32*a^3*b^19*c^5*d^20*e^7*z^6 - 3244032*a^3*b^17*c^7*d^22*e^5*z^6 + 2027520*a^3*b^20*c^4*d^19*e^8*z^6 + 2027520
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a^4*b^20*c^3*d^17*e^10*z^6 - 1523712*a^4*b^21*c^2*d^16*e^11*z^6 + 983040*a^17*b^8*c^2*d^3*e^24*z^6 - 901120*a^
3*b^21*c^3*d^18*e^9*z^6 - 901120*a^3*b^15*c^9*d^24*e^3*z^6 + 270336*a^3*b^22*c^2*d^17*e^10*z^6 + 270336*a^3*b^
14*c^10*d^25*e^2*z^6 + 172032*a^5*b^20*c^2*d^15*e^12*z^6 - 38593888256*a^15*b^6*c^6*d^9*e^18*z^6 - 38593888256
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11*e^16*z^6 - 901120*a^12*b^15*d^6*e^21*z^6 - 901120*a^6*b^21*d^12*e^15*z^6 + 270336*a^13*b^14*d^5*e^22*z^6 +
270336*a^5*b^22*d^13*e^14*z^6 - 49152*a^14*b^13*d^4*e^23*z^6 - 49152*a^4*b^23*d^14*e^13*z^6 + 4096*a^15*b^12*d
^3*e^24*z^6 + 4096*a^3*b^24*d^15*e^12*z^6 - 25165824*a^8*b^2*c^17*d^27*z^6 + 15728640*a^7*b^4*c^16*d^27*z^6 -
5242880*a^6*b^6*c^15*d^27*z^6 + 983040*a^5*b^8*c^14*d^27*z^6 - 98304*a^4*b^10*c^13*d^27*z^6 + 4096*a^3*b^12*c^
12*d^27*z^6 + 8304721920*a^17*c^10*d^11*e^16*z^6 + 8304721920*a^13*c^14*d^19*e^8*z^6 + 3690987520*a^18*c^9*d^9
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d^10*e^13*z^4 + 7819006464*a^7*b^9*c^7*d^11*e^12*z^4 - 7782137856*a^8*b^7*c^8*d^11*e^12*z^4 + 7780433920*a^12*
b^2*c^9*d^8*e^15*z^4 - 12020465664*a^7*b^5*c^11*d^15*e^8*z^4 + 3176792064*a^8*b^3*c^12*d^15*e^8*z^4 - 32263372
8*a^15*b*c^7*d^3*e^20*z^4 + 210829312*a^7*b*c^15*d^19*e^4*z^4 + 15623258112*a^9*b^6*c^8*d^10*e^13*z^4 + 251658
24*a^15*b^3*c^5*d*e^22*z^4 - 15728640*a^14*b^5*c^4*d*e^22*z^4 + 12582912*a^5*b^2*c^16*d^22*e*z^4 - 11730944*a^
4*b^4*c^15*d^22*e*z^4 + 5242880*a^13*b^7*c^3*d*e^22*z^4 - 4561920*a*b^15*c^7*d^17*e^6*z^4 + 4521984*a^3*b^6*c^
14*d^22*e*z^4 + 4460544*a*b^14*c^8*d^18*e^5*z^4 + 3538944*a^6*b*c^16*d^21*e^2*z^4 + 3108864*a*b^16*c^6*d^16*e^
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56320*a^6*b^17*d^5*e^18*z^4 - 56320*a^5*b^18*d^6*e^17*z^4 + 25600*a^9*b^14*d^2*e^21*z^4 + 25600*a^2*b^21*d^9*
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^2 + 1067599872*a^8*b^3*c^8*d^4*e^15*z^2 - 930828288*a^7*b^3*c^9*d^6*e^13*z^2 + 920760000*a^6*b^4*c^9*d^7*e^12
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15*z^2 - 701025408*a^5*b^6*c^8*d^7*e^12*z^2 + 443340288*a^5*b^5*c^9*d^8*e^11*z^2 + 433047552*a^7*b^6*c^6*d^3*e
^16*z^2 + 405741312*a^5*b^7*c^7*d^6*e^13*z^2 + 293652480*a^6*b^2*c^11*d^9*e^10*z^2 - 276962688*a^6*b^8*c^5*d^3
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4*e^15*z^2 - 182520896*a^4*b^9*c^6*d^6*e^13*z^2 - 153489408*a^5*b^3*c^11*d^10*e^9*z^2 - 152151552*a^7*b^2*c^10
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^10*d^10*e^9*z^2 - 98323200*a^6*b^5*c^8*d^6*e^13*z^2 - 93564992*a^4*b^6*c^9*d^9*e^10*z^2 + 89464512*a^5*b^10*c
^4*d^3*e^16*z^2 - 75930624*a^8*b^5*c^6*d^2*e^17*z^2 + 68315904*a^5*b^8*c^6*d^5*e^14*z^2 - 64157184*a^4*b^7*c^8
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d^9*e^10*z^2 + 35604480*a^4*b^2*c^13*d^13*e^6*z^2 + 33983040*a^3*b^11*c^5*d^6*e^13*z^2 - 33515520*a^4*b^3*c^12
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d^8*e^11*z^2 - 16434048*a^5*b^4*c^10*d^9*e^10*z^2 - 16289664*a^3*b^12*c^4*d^5*e^14*z^2 - 15059328*a^4*b^12*c^3
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^12*e^7*z^2 + 6798240*a^2*b^9*c^8*d^10*e^9*z^2 - 3589440*a^2*b^6*c^11*d^13*e^6*z^2 + 3544320*a^3*b^6*c^10*d^11
*e^8*z^2 + 3128064*a^2*b^5*c^12*d^14*e^5*z^2 + 2346336*a^4*b^13*c^2*d^2*e^17*z^2 - 2261568*a^2*b^8*c^9*d^11*e^
8*z^2 - 2125824*a^2*b^13*c^4*d^6*e^13*z^2 + 2002560*a^3*b^4*c^12*d^13*e^6*z^2 + 1927680*a^2*b^7*c^10*d^12*e^7*
z^2 + 1814784*a^2*b^14*c^3*d^5*e^14*z^2 - 1807104*a^2*b^12*c^5*d^7*e^12*z^2 + 1637808*a^3*b^13*c^3*d^4*e^15*z^
2 + 1083456*a^3*b^14*c^2*d^3*e^16*z^2 - 792384*a^2*b^4*c^13*d^15*e^4*z^2 - 657408*a^2*b^3*c^14*d^16*e^3*z^2 +
608256*a^7*b^7*c^5*d^2*e^17*z^2 + 595968*a^2*b^2*c^15*d^17*e^2*z^2 - 498624*a^2*b^15*c^2*d^4*e^15*z^2 - 3840*b
^18*c*d^5*e^14*z^2 - 3840*b^5*c^14*d^18*e*z^2 + 2064384*a^11*c^8*d*e^18*z^2 - 4160*a^3*b^16*d*e^18*z^2 - 4160*
a*b^18*d^3*e^16*z^2 - 1290240*a^11*b*c^7*e^19*z^2 - 9840*a^5*b^13*c*e^19*z^2 - 5760*a*b^2*c^16*d^19*z^2 - 2805
81120*a^8*c^11*d^7*e^12*z^2 + 110278656*a^9*c^10*d^5*e^14*z^2 - 89479168*a^7*c^12*d^9*e^10*z^2 + 34464000*a^10
*c^9*d^3*e^16*z^2 + 54240*b^15*c^4*d^8*e^11*z^2 + 54240*b^8*c^11*d^15*e^4*z^2 - 49920*b^14*c^5*d^9*e^10*z^2 -
49920*b^9*c^10*d^14*e^5*z^2 - 37376*b^16*c^3*d^7*e^12*z^2 - 37376*b^7*c^12*d^16*e^3*z^2 + 28480*b^13*c^6*d^10*
e^9*z^2 + 28480*b^10*c^9*d^13*e^6*z^2 + 15936*b^17*c^2*d^6*e^13*z^2 + 15936*b^6*c^13*d^17*e^2*z^2 - 7920*b^12*
c^7*d^11*e^8*z^2 - 7920*b^11*c^8*d^12*e^7*z^2 + 7489536*a^5*c^14*d^13*e^6*z^2 + 6084096*a^6*c^13*d^11*e^8*z^2
+ 2280448*a^4*c^15*d^15*e^4*z^2 + 350208*a^3*c^16*d^17*e^2*z^2 + 11616*a^2*b^17*d^2*e^17*z^2 - 3515904*a^9*b^5
*c^5*e^19*z^2 + 3440640*a^10*b^3*c^6*e^19*z^2 + 1870848*a^8*b^7*c^4*e^19*z^2 - 572272*a^7*b^9*c^3*e^19*z^2 + 1
01856*a^6*b^11*c^2*e^19*z^2 + 400*b^19*d^4*e^15*z^2 + 400*b^4*c^15*d^19*z^2 + 20736*a^2*c^17*d^19*z^2 + 400*a^
4*b^15*e^19*z^2 - 3969216*a^4*b*c^10*d^3*e^12 - 3001536*a^3*b*c^11*d^5*e^10 - 419904*a^2*b*c^12*d^7*e^8 + 1846
08*a^4*b^3*c^8*d*e^14 - 153036*a*b^4*c^10*d^6*e^9 + 127008*a*b^3*c^11*d^7*e^8 + 63108*a*b^6*c^8*d^4*e^11 - 291
60*a*b^2*c^12*d^8*e^7 - 21060*a^3*b^5*c^7*d*e^14 - 21060*a*b^7*c^7*d^3*e^12 + 5460*a*b^5*c^9*d^5*e^10 - 404544
*a^5*b*c^9*d*e^14 + 1251872*a^3*b^3*c^9*d^3*e^12 + 844224*a^4*b^2*c^9*d^2*e^13 + 820512*a^2*b^3*c^10*d^5*e^10
+ 750672*a^3*b^2*c^10*d^4*e^11 - 657498*a^2*b^4*c^9*d^4*e^11 - 487116*a^3*b^4*c^8*d^2*e^13 + 160704*a^2*b^2*c^
11*d^6*e^9 + 58806*a^2*b^6*c^7*d^2*e^13 + 13140*a^2*b^5*c^8*d^3*e^12 + 15286*b^6*c^9*d^6*e^9 - 9540*b^7*c^8*d^
5*e^10 - 9540*b^5*c^10*d^7*e^8 + 2025*b^8*c^7*d^4*e^11 + 2025*b^4*c^11*d^8*e^7 + 3367008*a^4*c^11*d^4*e^11 + 1
166400*a^3*c^12*d^6*e^9 + 705600*a^5*c^10*d^2*e^13 + 104976*a^2*c^13*d^8*e^7 - 17640*a^5*b^2*c^8*e^15 + 2025*a
^4*b^4*c^7*e^15 + 38416*a^6*c^9*e^15, z, k), k, 1, 6) - ((x*(a^2*b^2*e^4 - 4*a^3*c*e^4 - 2*a*c^3*d^4 + b^2*c^2
*d^4 + b^4*d^2*e^2 + 2*a^2*c^2*d^2*e^2 - 2*b^3*c*d^3*e + 6*a*b*c^2*d^3*e - 4*a*b^2*c*d^2*e^2))/(2*a*d*(4*a*c^3
*d^4 + 4*a^3*c*e^4 - a^2*b^2*e^4 - b^2*c^2*d^4 - b^4*d^2*e^2 + 8*a^2*c^2*d^2*e^2 + 2*a*b^3*d*e^3 + 2*b^3*c*d^3
*e - 8*a*b*c^2*d^3*e - 8*a^2*b*c*d*e^3 + 2*a*b^2*c*d^2*e^2)) + (x^3*(a*b^3*e^4 + b*c^3*d^4 + b^4*d*e^3 + 2*a^2
*c^2*d*e^3 - b^2*c^2*d^3*e - b^3*c*d^2*e^2 - 4*a^2*b*c*e^4 + 2*a*c^3*d^3*e - 4*a*b^2*c*d*e^3 + 3*a*b*c^2*d^2*e
^2))/(2*a*d*(4*a*c^3*d^4 + 4*a^3*c*e^4 - a^2*b^2*e^4 - b^2*c^2*d^4 - b^4*d^2*e^2 + 8*a^2*c^2*d^2*e^2 + 2*a*b^3
*d*e^3 + 2*b^3*c*d^3*e - 8*a*b*c^2*d^3*e - 8*a^2*b*c*d*e^3 + 2*a*b^2*c*d^2*e^2)) + (c*e*x^5*(a*b^2*e^3 + b*c^2
*d^3 - 4*a^2*c*e^3 + b^3*d*e^2 + 4*a*c^2*d^2*e - 2*b^2*c*d^2*e - 3*a*b*c*d*e^2))/(2*a*d*(4*a*c^3*d^4 + 4*a^3*c
*e^4 - a^2*b^2*e^4 - b^2*c^2*d^4 - b^4*d^2*e^2 + 8*a^2*c^2*d^2*e^2 + 2*a*b^3*d*e^3 + 2*b^3*c*d^3*e - 8*a*b*c^2
*d^3*e - 8*a^2*b*c*d*e^3 + 2*a*b^2*c*d^2*e^2)))/(a*d + x^2*(a*e + b*d) + x^4*(b*e + c*d) + c*e*x^6)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x**2+d)**2/(c*x**4+b*x**2+a)**2,x)

[Out]

Timed out

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