Copy of parking functions - generating function edition

3932 days ago by butler

x=var('x') 
       
def recurse_find_parking_function(T,root): if T.order()==1: return (exp(x)-1)/x else: temp_T=copy(T) temp_T.delete_vertex(root) poly(x)=1 for v in T.neighbors(root): poly(x)=poly*recurse_find_parking_function(temp_T.subgraph(temp_T.connected_component_containing_vertex(v)),v) pt=poly.limit(x=0) p=(exp(x)*poly-pt)/x return p.rational_simplify() 
       
%time html('<!--notruncate-->') for num_vertices in range(2,9): for T in graphs.trees(num_vertices): T.show() for v in T.automorphism_group().orbits(): s=recurse_find_parking_function(T,v[0]).limit(x=0)*factorial(T.order()) print "Placing the root at "+str(v[0]%T.order())+": "+str(s(x=0)) print recurse_find_parking_function(T,v[0]) print "" orbited=[] for b in T.automorphism_group().orbits(): orbited.extend(b) for i in range(T.order()): if (i not in orbited) and ((i+T.order()) not in orbited): s=recurse_find_parking_function(T,i).limit(x=0)*factorial(T.order()) print "Placing the root at "+str(i)+": "+str(s(x=0)) print recurse_find_parking_function(T,i) print "" 
       
Placing the root at 1:  3
x |--> -(x - e^(2*x) + e^x)/x^2

Placing the root at 1:  16
x |--> -1/2*(3*x^2 + 2*x*e^x + 2*e^(2*x) - 2*e^(3*x))/x^3

Placing the root at 0:  12
x |--> -(x^2 + 2*e^(2*x) - e^(3*x) - e^x)/x^3

Placing the root at 1:  82
x |--> -1/2*(3*x^3 + 2*(x - 1)*e^(2*x) - 2*x*e^x + 4*e^(3*x) -
2*e^(4*x))/x^4

Placing the root at 2:  125
x |--> -1/6*(16*x^3 + 9*x^2*e^x + 6*x*e^(2*x) + 6*e^(3*x) -
6*e^(4*x))/x^4

Placing the root at 1:  98
x |--> -(2*x^3 + x^2*e^x - e^(2*x) + 2*e^(3*x) - e^(4*x))/x^4

Placing the root at 0:  60
x |--> -(x^3 - 3*e^(2*x) + 3*e^(3*x) - e^(4*x) + e^x)/x^4

Placing the root at 1:  785
x |--> -1/6*(16*x^4 - 9*x^2*e^x + 6*(x - 1)*e^(3*x) + 3*(3*x^2 -
2*x)*e^(2*x) + 12*e^(4*x) - 6*e^(5*x))/x^5

Placing the root at 2:  1296
x |--> -1/24*(125*x^4 + 64*x^3*e^x + 36*x^2*e^(2*x) + 24*x*e^(3*x) +
24*e^(4*x) - 24*e^(5*x))/x^5

Placing the root at 0:  690
x |--> -1/4*(9*x^4 - 4*x^2*e^x + 4*(2*x - 1)*e^(3*x) - 8*x*e^(2*x) +
8*e^(4*x) - 4*e^(5*x))/x^5

Placing the root at 1:  610
x |--> -(2*x^4 - x^2*e^x + (x^2 + 1)*e^(2*x) - 3*e^(3*x) + 3*e^(4*x)
- e^(5*x))/x^5

Placing the root at 2:  1040
x |--> -1/12*(49*x^4 + 24*x^3*e^x + 12*x^2*e^(2*x) - 12*e^(3*x) +
24*e^(4*x) - 12*e^(5*x))/x^5

Placing the root at 3:  905
x |--> -1/12*(41*x^4 + 18*x^3*e^x + 12*(x - 1)*e^(3*x) - 12*x*e^(2*x)
+ 24*e^(4*x) - 12*e^(5*x))/x^5

Placing the root at 0:  500
x |--> -1/2*(3*x^4 + 2*(x - 3)*e^(3*x) - 2*(2*x - 1)*e^(2*x) +
2*x*e^x + 6*e^(4*x) - 2*e^(5*x))/x^5

Placing the root at 1:  690
x |--> -1/2*(5*x^4 + 2*x^3*e^x + 2*e^(2*x) - 6*e^(3*x) + 6*e^(4*x) -
2*e^(5*x))/x^5

Placing the root at 0:  360
x |--> -(x^4 + 4*e^(2*x) - 6*e^(3*x) + 4*e^(4*x) - e^(5*x) - e^x)/x^5

Placing the root at 1:  7865
x |--> -1/2*(8*x^5 - 3*x^3*e^x - 5*x^2*e^(2*x) + 2*(2*x - 1)*e^(4*x)
+ (3*x^2 - 4*x)*e^(3*x) + 4*e^(5*x) - 2*e^(6*x))/x^6

Placing the root at 2:  9651
x |--> -1/24*(125*x^5 - 64*x^3*e^x + 24*(x - 1)*e^(4*x) + 12*(3*x^2 -
2*x)*e^(3*x) + 4*(16*x^3 - 9*x^2)*e^(2*x) + 48*e^(5*x) - 24*e^(6*x))/x^6

Placing the root at 3:  16807
x |--> -1/120*(1296*x^5 + 625*x^4*e^x + 320*x^3*e^(2*x) +
180*x^2*e^(3*x) + 120*x*e^(4*x) + 120*e^(5*x) - 120*e^(6*x))/x^6

Placing the root at 1:  5670
x |--> -1/6*(16*x^5 + 9*x^2*e^x + 6*(x - 3)*e^(4*x) + 3*(3*x^2 - 4*x
+ 2)*e^(3*x) - 6*(3*x^2 - x)*e^(2*x) + 18*e^(5*x) - 6*e^(6*x))/x^6

Placing the root at 2:  10931
x |--> -1/24*(157*x^5 + 64*x^4*e^x - 36*x^2*e^(2*x) + 24*(x -
1)*e^(4*x) + 12*(3*x^2 - 2*x)*e^(3*x) + 48*e^(5*x) - 24*e^(6*x))/x^6

Placing the root at 0:  6090
x |--> -(3*x^5 - x^3*e^x + (x - 3)*e^(4*x) + (x^2 - 2*x + 1)*e^(3*x)
- (x^2 - x)*e^(2*x) + 3*e^(5*x) - e^(6*x))/x^6

Placing the root at 4:  7710
x |--> -1/12*(49*x^5 - 24*x^3*e^x + 12*(x^2 + 1)*e^(3*x) + 12*(2*x^3
- x^2)*e^(2*x) - 36*e^(4*x) + 36*e^(5*x) - 12*e^(6*x))/x^6

Placing the root at 5:  13682
x |--> -1/12*(104*x^5 + 49*x^4*e^x + 24*x^3*e^(2*x) + 12*x^2*e^(3*x)
- 12*e^(4*x) + 24*e^(5*x) - 12*e^(6*x))/x^6

Placing the root at 1:  4380
x |--> -(2*x^5 + x^2*e^x + (x^2 + 4)*e^(3*x) - (2*x^2 + 1)*e^(2*x) -
6*e^(4*x) + 4*e^(5*x) - e^(6*x))/x^6

Placing the root at 2:  8670
x |--> -1/12*(61*x^5 + 24*x^4*e^x - 12*x^2*e^(2*x) + 12*(x^2 +
1)*e^(3*x) - 36*e^(4*x) + 36*e^(5*x) - 12*e^(6*x))/x^6

Placing the root at 1:  6660
x |--> -1/12*(41*x^5 - 18*x^3*e^x + 12*(x - 3)*e^(4*x) - 12*(2*x -
1)*e^(3*x) + 6*(3*x^3 + 2*x)*e^(2*x) + 36*e^(5*x) - 12*e^(6*x))/x^6

Placing the root at 2:  12146
x |--> -1/24*(181*x^5 + 82*x^4*e^x + 36*x^3*e^(2*x) + 24*(x -
1)*e^(4*x) - 24*x*e^(3*x) + 48*e^(5*x) - 24*e^(6*x))/x^6

Placing the root at 0:  4950
x |--> -1/4*(9*x^5 + 4*x^2*e^x + 4*(2*x - 3)*e^(4*x) - 4*(4*x -
1)*e^(3*x) - 4*(x^2 - 2*x)*e^(2*x) + 12*e^(5*x) - 4*e^(6*x))/x^6

Placing the root at 5:  9800
x |--> -1/4*(23*x^5 + 9*x^4*e^x - 4*x^2*e^(2*x) + 4*(2*x - 1)*e^(4*x)
- 8*x*e^(3*x) + 8*e^(5*x) - 4*e^(6*x))/x^6

Placing the root at 1:  5040
x |--> -1/2*(5*x^5 - 2*x^3*e^x + 2*(x^3 - 1)*e^(2*x) + 8*e^(3*x) -
12*e^(4*x) + 8*e^(5*x) - 2*e^(6*x))/x^6

Placing the root at 2:  9480
x |--> -1/4*(23*x^5 + 10*x^4*e^x + 4*x^3*e^(2*x) + 4*e^(3*x) -
12*e^(4*x) + 12*e^(5*x) - 4*e^(6*x))/x^6

Placing the root at 3:  7380
x |--> -1/6*(25*x^5 + 9*x^4*e^x + 6*(x - 3)*e^(4*x) - 6*(2*x -
1)*e^(3*x) + 6*x*e^(2*x) + 18*e^(5*x) - 6*e^(6*x))/x^6

Placing the root at 0:  3540
x |--> -1/2*(3*x^5 + 2*(x - 6)*e^(4*x) - 2*(3*x - 4)*e^(3*x) + 2*(3*x
- 1)*e^(2*x) - 2*x*e^x + 8*e^(5*x) - 2*e^(6*x))/x^6

Placing the root at 1:  5520
x |--> -(3*x^5 + x^4*e^x - e^(2*x) + 4*e^(3*x) - 6*e^(4*x) +
4*e^(5*x) - e^(6*x))/x^6

Placing the root at 0:  2520
x |--> -(x^5 - 5*e^(2*x) + 10*e^(3*x) - 10*e^(4*x) + 5*e^(5*x) -
e^(6*x) + e^x)/x^6

Placing the root at 1:  112273
x |--> -1/48*(375*x^6 - 128*x^4*e^x - 200*x^3*e^(2*x) + 48*(2*x -
1)*e^(5*x) + 24*(3*x^2 - 4*x)*e^(4*x) + 8*(16*x^3 - 15*x^2)*e^(3*x) +
96*e^(6*x) - 48*e^(7*x))/x^7

Placing the root at 2:  144865
x |--> -1/120*(1296*x^6 - 625*x^4*e^x + 120*(x - 1)*e^(5*x) +
60*(3*x^2 - 2*x)*e^(4*x) + 20*(16*x^3 - 9*x^2)*e^(3*x) + 5*(125*x^4 -
64*x^3)*e^(2*x) + 240*e^(6*x) - 120*e^(7*x))/x^7

Placing the root at 3:  262144
x |--> -1/720*(16807*x^6 + 7776*x^5*e^x + 3750*x^4*e^(2*x) +
1920*x^3*e^(3*x) + 1080*x^2*e^(4*x) + 720*x*e^(5*x) + 720*e^(6*x) -
720*e^(7*x))/x^7

Placing the root at 0:  104160
x |--> -1/36*(256*x^6 - 81*x^4*e^x - 108*x^3*e^(2*x) -
144*x^2*e^(3*x) + 36*(2*x - 1)*e^(5*x) + 36*(3*x^2 - 2*x)*e^(4*x) +
72*e^(6*x) - 36*e^(7*x))/x^7

Placing the root at 1:  89530
x |--> -1/8*(49*x^6 - 16*x^4*e^x - 24*x^3*e^(2*x) + 8*(x - 3)*e^(5*x)
+ 8*(x^2 - 2*x + 1)*e^(4*x) + 8*(2*x^3 - x^2 + x)*e^(3*x) + 24*e^(6*x) -
8*e^(7*x))/x^7

Placing the root at 2:  117614
x |--> -1/12*(104*x^6 - 49*x^4*e^x + 12*(x^2 + 1)*e^(4*x) + 12*(2*x^3
- x^2)*e^(3*x) + (49*x^4 - 24*x^3)*e^(2*x) - 36*e^(5*x) + 36*e^(6*x) -
12*e^(7*x))/x^7

Placing the root at 3:  215488
x |--> -1/360*(6841*x^6 + 3120*x^5*e^x + 1470*x^4*e^(2*x) +
720*x^3*e^(3*x) + 360*x^2*e^(4*x) - 360*e^(5*x) + 720*e^(6*x) -
360*e^(7*x))/x^7

Placing the root at 4:  80682
x |--> -1/24*(125*x^6 + 64*x^3*e^x + 24*(x - 3)*e^(5*x) + 12*(3*x^2 -
4*x + 2)*e^(4*x) - 4*(32*x^3 - 9*x^2)*e^(2*x) + 8*(8*x^3 - 9*x^2 +
3*x)*e^(3*x) + 72*e^(6*x) - 24*e^(7*x))/x^7

Placing the root at 5:  162365
x |--> -1/240*(3217*x^6 + 1250*x^5*e^x - 640*x^3*e^(2*x) + 240*(x -
1)*e^(5*x) + 120*(3*x^2 - 2*x)*e^(4*x) + 40*(16*x^3 - 9*x^2)*e^(3*x) +
480*e^(6*x) - 240*e^(7*x))/x^7

Placing the root at 0:  80500
x |--> -1/6*(32*x^6 - 9*x^4*e^x + 6*(x - 3)*e^(5*x) - 6*(4*x^2 -
x)*e^(3*x) + 3*(5*x^2 - 4*x + 2)*e^(4*x) - 3*(2*x^3 - 3*x^2)*e^(2*x) +
18*e^(6*x) - 6*e^(7*x))/x^7

Placing the root at 1:  77105
x |--> -1/8*(41*x^6 - 12*x^4*e^x + 8*(2*x - 3)*e^(5*x) - 8*(4*x -
1)*e^(4*x) - 4*(3*x^3 - 2*x^2)*e^(2*x) + 4*(3*x^3 - 2*x^2 + 4*x)*e^(3*x)
+ 24*e^(6*x) - 8*e^(7*x))/x^7

Placing the root at 0:  65135
x |--> -1/2*(8*x^6 + 3*x^3*e^x + 2*(2*x - 3)*e^(5*x) - 4*(2*x^2 -
x)*e^(3*x) + (3*x^2 - 8*x + 2)*e^(4*x) - (3*x^3 - 5*x^2)*e^(2*x) +
6*e^(6*x) - 2*e^(7*x))/x^7

Placing the root at 2:  104027
x |--> -1/24*(181*x^6 - 82*x^4*e^x + 24*(x - 3)*e^(5*x) - 24*(2*x -
1)*e^(4*x) + 12*(3*x^3 + 2*x)*e^(3*x) + 2*(41*x^4 - 18*x^3)*e^(2*x) +
72*e^(6*x) - 24*e^(7*x))/x^7

Placing the root at 3:  193613
x |--> -1/360*(6073*x^6 + 2715*x^5*e^x + 1230*x^4*e^(2*x) +
540*x^3*e^(3*x) + 360*(x - 1)*e^(5*x) - 360*x*e^(4*x) + 720*e^(6*x) -
360*e^(7*x))/x^7

Placing the root at 4:  93002
x |--> -1/24*(157*x^6 - 64*x^4*e^x + 24*(x - 3)*e^(5*x) + 12*(3*x^2 -
4*x + 2)*e^(4*x) - 24*(3*x^2 - x)*e^(3*x) + 4*(16*x^4 + 9*x^2)*e^(2*x) +
72*e^(6*x) - 24*e^(7*x))/x^7

Placing the root at 5:  177485
x |--> -1/720*(10931*x^6 + 4710*x^5*e^x + 1920*x^4*e^(2*x) -
1080*x^2*e^(3*x) + 720*(x - 1)*e^(5*x) + 360*(3*x^2 - 2*x)*e^(4*x) +
1440*e^(6*x) - 720*e^(7*x))/x^7

Placing the root at 6:  136353
x |--> -1/144*(1573*x^6 + 576*x^5*e^x - 216*x^3*e^(2*x) -
360*x^2*e^(3*x) + 144*(2*x - 1)*e^(5*x) + 72*(3*x^2 - 4*x)*e^(4*x) +
288*e^(6*x) - 144*e^(7*x))/x^7

Placing the root at 1:  46410
x |--> -1/6*(16*x^6 - 9*x^2*e^x + 6*(x - 6)*e^(5*x) + 3*(3*x^2 - 6*x
+ 8)*e^(4*x) - 3*(9*x^2 - 6*x + 2)*e^(3*x) + 3*(9*x^2 - 2*x)*e^(2*x) +
24*e^(6*x) - 6*e^(7*x))/x^7

Placing the root at 2:  101962
x |--> -1/24*(189*x^6 + 64*x^5*e^x + 36*x^2*e^(2*x) + 24*(x -
3)*e^(5*x) + 12*(3*x^2 - 4*x + 2)*e^(4*x) - 24*(3*x^2 - x)*e^(3*x) +
72*e^(6*x) - 24*e^(7*x))/x^7

Placing the root at 0:  58170
x |--> -1/4*(15*x^6 - 4*x^4*e^x + 4*(x - 6)*e^(5*x) - 4*(3*x -
4)*e^(4*x) - 4*(x^3 + x)*e^(2*x) + 4*(x^3 + 3*x - 1)*e^(3*x) +
16*e^(6*x) - 4*e^(7*x))/x^7

Placing the root at 5:  80850
x |--> -1/4*(23*x^6 - 10*x^4*e^x + 4*(x^3 - 1)*e^(3*x) + 2*(5*x^4 -
2*x^3)*e^(2*x) + 16*e^(4*x) - 24*e^(5*x) + 16*e^(6*x) - 4*e^(7*x))/x^7

Placing the root at 6:  153426
x |--> -1/12*(158*x^6 + 69*x^5*e^x + 30*x^4*e^(2*x) + 12*x^3*e^(3*x)
+ 12*e^(4*x) - 36*e^(5*x) + 36*e^(6*x) - 12*e^(7*x))/x^7

Placing the root at 1:  64260
x |--> -1/12*(49*x^6 + 24*x^3*e^x + 12*(x^2 + 4)*e^(4*x) + 12*(2*x^3
- 2*x^2 - 1)*e^(3*x) - 12*(4*x^3 - x^2)*e^(2*x) - 72*e^(5*x) +
48*e^(6*x) - 12*e^(7*x))/x^7

Placing the root at 2:  131334
x |--> -1/24*(257*x^6 + 98*x^5*e^x - 48*x^3*e^(2*x) + 24*(x^2 +
1)*e^(4*x) + 24*(2*x^3 - x^2)*e^(3*x) - 72*e^(5*x) + 72*e^(6*x) -
24*e^(7*x))/x^7

Placing the root at 0:  62160
x |--> -(4*x^6 - x^4*e^x + 2*x^2*e^(2*x) + 2*(x^2 + 2)*e^(4*x) -
(4*x^2 + 1)*e^(3*x) - 6*e^(5*x) + 4*e^(6*x) - e^(7*x))/x^7

Placing the root at 1:  55230
x |--> -1/12*(41*x^6 + 18*x^3*e^x + 12*(x - 6)*e^(5*x) - 12*(3*x -
4)*e^(4*x) - 12*(3*x^3 + x)*e^(2*x) + 6*(3*x^3 + 6*x - 2)*e^(3*x) +
48*e^(6*x) - 12*e^(7*x))/x^7

Placing the root at 2:  115507
x |--> -1/12*(111*x^6 + 41*x^5*e^x - 18*x^3*e^(2*x) + 12*(x -
3)*e^(5*x) - 12*(2*x - 1)*e^(4*x) + 6*(3*x^3 + 2*x)*e^(3*x) + 36*e^(6*x)
- 12*e^(7*x))/x^7

Placing the root at 0:  50190
x |--> -(3*x^6 + x^3*e^x + (x - 6)*e^(5*x) + (x^2 - 3*x + 4)*e^(4*x)
- (2*x^2 - 3*x + 1)*e^(3*x) - (x^3 - x^2 + x)*e^(2*x) + 4*e^(6*x) -
e^(7*x))/x^7

Placing the root at 4:  73500
x |--> -1/12*(61*x^6 - 24*x^4*e^x + 12*(x^2 + 4)*e^(4*x) - 12*(2*x^2
+ 1)*e^(3*x) + 12*(2*x^4 + x^2)*e^(2*x) - 72*e^(5*x) + 48*e^(6*x) -
12*e^(7*x))/x^7

Placing the root at 5:  142674
x |--> -1/24*(289*x^6 + 122*x^5*e^x + 48*x^4*e^(2*x) - 24*x^2*e^(3*x)
+ 24*(x^2 + 1)*e^(4*x) - 72*e^(5*x) + 72*e^(6*x) - 24*e^(7*x))/x^7

Placing the root at 6:  107590
x |--> -1/24*(203*x^6 + 72*x^5*e^x - 24*x^3*e^(2*x) + 24*(x -
3)*e^(5*x) + 24*(x^2 - 2*x + 1)*e^(4*x) - 24*(x^2 - x)*e^(3*x) +
72*e^(6*x) - 24*e^(7*x))/x^7

Placing the root at 1:  41580
x |--> -1/2*(5*x^6 + 2*x^3*e^x + 2*(x^3 - 5)*e^(3*x) - 2*(2*x^3 -
1)*e^(2*x) + 20*e^(4*x) - 20*e^(5*x) + 10*e^(6*x) - 2*e^(7*x))/x^7

Placing the root at 2:  89250
x |--> -1/2*(14*x^6 + 5*x^5*e^x - 2*x^3*e^(2*x) + 2*(x^3 - 1)*e^(3*x)
+ 8*e^(4*x) - 12*e^(5*x) + 8*e^(6*x) - 2*e^(7*x))/x^7

Placing the root at 4:  80220
x |--> -1/12*(73*x^6 + 24*x^5*e^x + 12*x^2*e^(2*x) + 12*(x^2 +
4)*e^(4*x) - 12*(2*x^2 + 1)*e^(3*x) - 72*e^(5*x) + 48*e^(6*x) -
12*e^(7*x))/x^7

Placing the root at 0:  35700
x |--> -(2*x^6 - x^2*e^x + (x^2 + 10)*e^(4*x) + (3*x^2 + 1)*e^(2*x) -
(3*x^2 + 5)*e^(3*x) - 10*e^(5*x) + 5*e^(6*x) - e^(7*x))/x^7

Placing the root at 1:  83090
x |--> -1/4*(23*x^6 - 9*x^4*e^x + 4*(2*x - 3)*e^(5*x) - 4*(4*x -
1)*e^(4*x) - 4*(x^2 - 2*x)*e^(3*x) + (9*x^4 + 4*x^2)*e^(2*x) +
12*e^(6*x) - 4*e^(7*x))/x^7

Placing the root at 2:  160986
x |--> -1/36*(490*x^6 + 207*x^5*e^x + 81*x^4*e^(2*x) - 36*x^2*e^(3*x)
+ 36*(2*x - 1)*e^(5*x) - 72*x*e^(4*x) + 72*e^(6*x) - 36*e^(7*x))/x^7

Placing the root at 0:  56700
x |--> -1/8*(27*x^6 + 8*x^3*e^x + 24*x^2*e^(2*x) + 24*(x - 1)*e^(5*x)
- 8*(6*x - 1)*e^(4*x) - 24*(x^2 - x)*e^(3*x) + 24*e^(6*x) -
8*e^(7*x))/x^7

Placing the root at 1:  62160
x |--> -1/6*(25*x^6 - 9*x^4*e^x + 6*(x - 6)*e^(5*x) - 6*(3*x -
4)*e^(4*x) + 6*(3*x - 1)*e^(3*x) + 3*(3*x^4 - 2*x)*e^(2*x) + 24*e^(6*x)
- 6*e^(7*x))/x^7

Placing the root at 2:  124012
x |--> -1/12*(123*x^6 + 50*x^5*e^x + 18*x^4*e^(2*x) + 12*(x -
3)*e^(5*x) - 12*(2*x - 1)*e^(4*x) + 12*x*e^(3*x) + 36*e^(6*x) -
12*e^(7*x))/x^7

Placing the root at 5:  90650
x |--> -1/8*(55*x^6 + 18*x^5*e^x + 8*x^2*e^(2*x) + 8*(2*x -
3)*e^(5*x) - 8*(4*x - 1)*e^(4*x) - 8*(x^2 - 2*x)*e^(3*x) + 24*e^(6*x) -
8*e^(7*x))/x^7

Placing the root at 0:  40320
x |--> -1/4*(9*x^6 - 4*x^2*e^x + 8*(x - 3)*e^(5*x) - 8*(3*x -
2)*e^(4*x) - 4*(x^2 - 6*x + 1)*e^(3*x) + 8*(x^2 - x)*e^(2*x) +
16*e^(6*x) - 4*e^(7*x))/x^7

Placing the root at 1:  46200
x |--> -(3*x^6 - x^4*e^x + (x^4 + 1)*e^(2*x) - 5*e^(3*x) + 10*e^(4*x)
- 10*e^(5*x) + 5*e^(6*x) - e^(7*x))/x^7

Placing the root at 2:  94920
x |--> -1/3*(23*x^6 + 9*x^5*e^x + 3*x^4*e^(2*x) - 3*e^(3*x) +
12*e^(4*x) - 18*e^(5*x) + 12*e^(6*x) - 3*e^(7*x))/x^7

Placing the root at 3:  67200
x |--> -1/12*(59*x^6 + 18*x^5*e^x + 12*(x - 6)*e^(5*x) - 12*(3*x -
4)*e^(4*x) + 12*(3*x - 1)*e^(3*x) - 12*x*e^(2*x) + 48*e^(6*x) -
12*e^(7*x))/x^7

Placing the root at 0:  28560
x |--> -1/2*(3*x^6 + 2*(x - 10)*e^(5*x) - 4*(2*x - 5)*e^(4*x) -
2*(4*x - 1)*e^(2*x) + 2*(6*x - 5)*e^(3*x) + 2*x*e^x + 10*e^(6*x) -
2*e^(7*x))/x^7

Placing the root at 1:  49560
x |--> -1/2*(7*x^6 + 2*x^5*e^x + 2*e^(2*x) - 10*e^(3*x) + 20*e^(4*x)
- 20*e^(5*x) + 10*e^(6*x) - 2*e^(7*x))/x^7

Placing the root at 0:  20160
x |--> -(x^6 + 6*e^(2*x) - 15*e^(3*x) + 20*e^(4*x) - 15*e^(5*x) +
6*e^(6*x) - e^(7*x) - e^x)/x^7

Placing the root at 1:  1694966
x |--> -1/36*(500*x^7 - 144*x^5*e^x - 177*x^4*e^(2*x) -
204*x^3*e^(3*x) + 36*(2*x - 1)*e^(6*x) + 36*(3*x^2 - 2*x)*e^(5*x) +
48*(2*x^3 - 3*x^2)*e^(4*x) + 72*e^(7*x) - 36*e^(8*x))/x^8

Placing the root at 2:  1919820
x |--> -1/120*(1944*x^7 - 625*x^5*e^x - 945*x^4*e^(2*x) + 120*(2*x -
1)*e^(6*x) + 60*(3*x^2 - 4*x)*e^(5*x) + 20*(16*x^3 - 15*x^2)*e^(4*x) +
125*(5*x^4 - 4*x^3)*e^(3*x) + 240*e^(7*x) - 120*e^(8*x))/x^8

Placing the root at 3:  2567748
x |--> -1/720*(16807*x^7 - 7776*x^5*e^x + 720*(x - 1)*e^(6*x) +
360*(3*x^2 - 2*x)*e^(5*x) + 120*(16*x^3 - 9*x^2)*e^(4*x) + 30*(125*x^4 -
64*x^3)*e^(3*x) + 6*(1296*x^5 - 625*x^4)*e^(2*x) + 1440*e^(7*x) -
720*e^(8*x))/x^8

Placing the root at 4:  4782969
x |--> -1/5040*(262144*x^7 + 117649*x^6*e^x + 54432*x^5*e^(2*x) +
26250*x^4*e^(3*x) + 13440*x^3*e^(4*x) + 7560*x^2*e^(5*x) +
5040*x*e^(6*x) + 5040*e^(7*x) - 5040*e^(8*x))/x^8

Placing the root at 1:  1308412
x |--> -1/12*(125*x^7 - 32*x^5*e^x + 12*(x - 3)*e^(6*x) + 6*(5*x^2 -
4*x + 2)*e^(5*x) - 2*(38*x^3 - 9*x^2)*e^(3*x) - 2*(9*x^4 -
16*x^3)*e^(2*x) + 4*(8*x^3 - 12*x^2 + 3*x)*e^(4*x) + 36*e^(7*x) -
12*e^(8*x))/x^8

Placing the root at 2:  1376648
x |--> -1/120*(1296*x^7 + 625*x^4*e^x + 120*(x - 3)*e^(6*x) +
60*(3*x^2 - 4*x + 2)*e^(5*x) - 10*(125*x^4 - 32*x^3)*e^(2*x) + 40*(8*x^3
- 9*x^2 + 3*x)*e^(4*x) + 5*(125*x^4 - 128*x^3 + 36*x^2)*e^(3*x) +
360*e^(7*x) - 120*e^(8*x))/x^8

Placing the root at 3:  2858052
x |--> -1/720*(20695*x^7 + 7776*x^6*e^x - 3750*x^4*e^(2*x) + 720*(x -
1)*e^(6*x) + 360*(3*x^2 - 2*x)*e^(5*x) + 120*(16*x^3 - 9*x^2)*e^(4*x) +
30*(125*x^4 - 64*x^3)*e^(3*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8

Placing the root at 0:  1350300
x |--> -1/18*(196*x^7 - 54*x^5*e^x - 63*x^4*e^(2*x) + 18*(x -
3)*e^(6*x) + 9*(5*x^2 - 4*x + 2)*e^(5*x) - 27*(2*x^3 - x^2)*e^(3*x) +
18*(2*x^3 - 4*x^2 + x)*e^(4*x) + 54*e^(7*x) - 18*e^(8*x))/x^8

Placing the root at 5:  1556968
x |--> -1/12*(156*x^7 - 49*x^5*e^x - 73*x^4*e^(2*x) + 12*(x -
3)*e^(6*x) + 12*(x^2 - 2*x + 1)*e^(5*x) + (49*x^4 - 36*x^3)*e^(3*x) +
12*(2*x^3 - x^2 + x)*e^(4*x) + 36*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 6:  2107000
x |--> -1/360*(6841*x^7 - 3120*x^5*e^x + 360*(x^2 + 1)*e^(5*x) +
360*(2*x^3 - x^2)*e^(4*x) + 30*(49*x^4 - 24*x^3)*e^(3*x) + 30*(104*x^5 -
49*x^4)*e^(2*x) - 1080*e^(6*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8

Placing the root at 7:  3959426
x |--> -1/360*(15392*x^7 + 6841*x^6*e^x + 3120*x^5*e^(2*x) +
1470*x^4*e^(3*x) + 720*x^3*e^(4*x) + 360*x^2*e^(5*x) - 360*e^(6*x) +
720*e^(7*x) - 360*e^(8*x))/x^8

Placing the root at 1:  1041880
x |--> -1/6*(49*x^7 - 12*x^5*e^x + 12*(x^2 + 2)*e^(5*x) + 6*(2*x^3 -
4*x^2 - 1)*e^(4*x) - 12*(2*x^3 - x^2)*e^(3*x) - 6*(x^4 - 2*x^3)*e^(2*x)
- 36*e^(6*x) + 24*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 2:  1115632
x |--> -1/12*(104*x^7 + 49*x^4*e^x + 12*(x^2 + 4)*e^(5*x) + 12*(2*x^3
- 2*x^2 - 1)*e^(4*x) - 2*(49*x^4 - 12*x^3)*e^(2*x) + (49*x^4 - 48*x^3 +
12*x^2)*e^(3*x) - 72*e^(6*x) + 48*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 3:  2339960
x |--> -1/360*(8401*x^7 + 3120*x^6*e^x - 1470*x^4*e^(2*x) + 360*(x^2
+ 1)*e^(5*x) + 360*(2*x^3 - x^2)*e^(4*x) + 30*(49*x^4 - 24*x^3)*e^(3*x)
- 1080*e^(6*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8

Placing the root at 1:  1055684
x |--> -1/48*(375*x^7 + 128*x^4*e^x + 48*(2*x - 3)*e^(6*x) +
24*(3*x^2 - 8*x + 2)*e^(5*x) - 8*(41*x^3 - 15*x^2)*e^(3*x) - 8*(16*x^4 -
25*x^3)*e^(2*x) + 32*(4*x^3 - 6*x^2 + 3*x)*e^(4*x) + 144*e^(7*x) -
48*e^(8*x))/x^8

Placing the root at 0:  1161020
x |--> -1/36*(328*x^7 - 81*x^5*e^x + 36*(2*x - 3)*e^(6*x) + 18*(3*x^2
- 8*x + 2)*e^(5*x) - 18*(6*x^3 - 5*x^2)*e^(3*x) - 54*(x^4 - x^3)*e^(2*x)
+ 18*(3*x^3 - 8*x^2 + 4*x)*e^(4*x) + 108*e^(7*x) - 36*e^(8*x))/x^8

Placing the root at 2:  1569148
x |--> -1/240*(3217*x^7 - 1250*x^5*e^x + 240*(x - 3)*e^(6*x) +
120*(3*x^2 - 4*x + 2)*e^(5*x) - 40*(32*x^3 - 9*x^2)*e^(3*x) +
10*(125*x^5 + 64*x^3)*e^(2*x) + 80*(8*x^3 - 9*x^2 + 3*x)*e^(4*x) +
720*e^(7*x) - 240*e^(8*x))/x^8

Placing the root at 3:  3094302
x |--> -1/720*(23195*x^7 + 9651*x^6*e^x + 3750*x^5*e^(2*x) -
1920*x^3*e^(3*x) + 720*(x - 1)*e^(6*x) + 360*(3*x^2 - 2*x)*e^(5*x) +
120*(16*x^3 - 9*x^2)*e^(4*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8

Placing the root at 4:  2296070
x |--> -1/720*(16039*x^7 + 5625*x^6*e^x - 1920*x^4*e^(2*x) -
3000*x^3*e^(3*x) + 720*(2*x - 1)*e^(6*x) + 360*(3*x^2 - 4*x)*e^(5*x) +
120*(16*x^3 - 15*x^2)*e^(4*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8

Placing the root at 5:  1375024
x |--> -1/48*(543*x^7 - 164*x^5*e^x - 236*x^4*e^(2*x) + 48*(2*x -
3)*e^(6*x) - 48*(4*x - 1)*e^(5*x) + 24*(3*x^3 - 2*x^2 + 4*x)*e^(4*x) +
4*(41*x^4 - 18*x^3 + 12*x^2)*e^(3*x) + 144*e^(7*x) - 48*e^(8*x))/x^8

Placing the root at 6:  1888992
x |--> -1/360*(6073*x^7 - 2715*x^5*e^x + 360*(x - 3)*e^(6*x) -
360*(2*x - 1)*e^(5*x) + 180*(3*x^3 + 2*x)*e^(4*x) + 30*(41*x^4 -
18*x^3)*e^(3*x) + 15*(181*x^5 - 82*x^4)*e^(2*x) + 1080*e^(7*x) -
360*e^(8*x))/x^8

Placing the root at 7:  3586178
x |--> -1/720*(27659*x^7 + 12146*x^6*e^x + 5430*x^5*e^(2*x) +
2460*x^4*e^(3*x) + 1080*x^3*e^(4*x) + 720*(x - 1)*e^(6*x) -
720*x*e^(5*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8

Placing the root at 1:  839720
x |--> -1/8*(49*x^7 + 16*x^4*e^x + 8*(x - 6)*e^(6*x) + 8*(x^2 - 3*x +
4)*e^(5*x) - 8*(2*x^4 - 3*x^3)*e^(2*x) + 8*(2*x^3 - 2*x^2 + 3*x -
1)*e^(4*x) - 8*(5*x^3 - x^2 + x)*e^(3*x) + 32*e^(7*x) - 8*e^(8*x))/x^8

Placing the root at 2:  1266552
x |--> -1/24*(257*x^7 - 98*x^5*e^x + 24*(x^2 + 4)*e^(5*x) + 24*(2*x^3
- 2*x^2 - 1)*e^(4*x) - 24*(4*x^3 - x^2)*e^(3*x) + 2*(49*x^5 +
24*x^3)*e^(2*x) - 144*e^(6*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 3:  2525180
x |--> -1/120*(3127*x^7 + 1285*x^6*e^x + 490*x^5*e^(2*x) -
240*x^3*e^(3*x) + 120*(x^2 + 1)*e^(5*x) + 120*(2*x^3 - x^2)*e^(4*x) -
360*e^(6*x) + 360*e^(7*x) - 120*e^(8*x))/x^8

Placing the root at 4:  1851948
x |--> -1/72*(1279*x^7 + 441*x^6*e^x - 144*x^4*e^(2*x) -
216*x^3*e^(3*x) + 72*(x - 3)*e^(6*x) + 72*(x^2 - 2*x + 1)*e^(5*x) +
72*(2*x^3 - x^2 + x)*e^(4*x) + 216*e^(7*x) - 72*e^(8*x))/x^8

Placing the root at 5:  984256
x |--> -1/24*(181*x^7 + 82*x^4*e^x + 24*(x - 6)*e^(6*x) - 24*(3*x -
4)*e^(5*x) + 12*(3*x^3 + 6*x - 2)*e^(4*x) - 4*(41*x^4 - 9*x^3)*e^(2*x) +
2*(41*x^4 - 36*x^3 - 12*x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 6:  2091712
x |--> -1/720*(14861*x^7 + 5430*x^6*e^x - 2460*x^4*e^(2*x) + 720*(x -
3)*e^(6*x) - 720*(2*x - 1)*e^(5*x) + 360*(3*x^3 + 2*x)*e^(4*x) +
60*(41*x^4 - 18*x^3)*e^(3*x) + 2160*e^(7*x) - 720*e^(8*x))/x^8

Placing the root at 0:  895160
x |--> -1/6*(41*x^7 - 9*x^5*e^x + 15*x^3*e^(2*x) + 6*(x - 6)*e^(6*x)
+ 6*(x^2 - 3*x + 4)*e^(5*x) + 3*(3*x^3 - 4*x^2 + 6*x - 2)*e^(4*x) -
6*(4*x^3 - x^2 + x)*e^(3*x) + 24*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 1:  720160
x |--> -1/8*(41*x^7 + 12*x^4*e^x + 16*(x - 3)*e^(6*x) - 16*(3*x -
2)*e^(5*x) - 8*(3*x^3 - 2*x^2 + 2*x)*e^(3*x) + 4*(3*x^3 - 2*x^2 + 12*x -
2)*e^(4*x) - 4*(3*x^4 - 3*x^3 + 2*x^2)*e^(2*x) + 32*e^(7*x) -
8*e^(8*x))/x^8

Placing the root at 2:  1110536
x |--> -1/12*(111*x^7 - 41*x^5*e^x + 12*(x - 6)*e^(6*x) - 12*(3*x -
4)*e^(5*x) - 12*(3*x^3 + x)*e^(3*x) + 6*(3*x^3 + 6*x - 2)*e^(4*x) +
(41*x^5 + 18*x^3)*e^(2*x) + 48*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 3:  2246692
x |--> -1/720*(16501*x^7 + 6660*x^6*e^x + 2460*x^5*e^(2*x) -
1080*x^3*e^(3*x) + 720*(x - 3)*e^(6*x) - 720*(2*x - 1)*e^(5*x) +
360*(3*x^3 + 2*x)*e^(4*x) + 2160*e^(7*x) - 720*e^(8*x))/x^8

Placing the root at 4:  1621844
x |--> -1/144*(2203*x^7 + 738*x^6*e^x - 216*x^4*e^(2*x) + 144*(2*x -
3)*e^(6*x) - 144*(4*x - 1)*e^(5*x) - 72*(3*x^3 - 2*x^2)*e^(3*x) +
72*(3*x^3 - 2*x^2 + 4*x)*e^(4*x) + 432*e^(7*x) - 144*e^(8*x))/x^8

Placing the root at 1:  1225924
x |--> -1/48*(471*x^7 - 128*x^5*e^x + 48*(2*x - 3)*e^(6*x) -
96*(2*x^2 - x)*e^(4*x) + 24*(3*x^2 - 8*x + 2)*e^(5*x) - 8*(16*x^4 -
9*x^3)*e^(2*x) + 8*(16*x^4 - 9*x^3 + 15*x^2)*e^(3*x) + 144*e^(7*x) -
48*e^(8*x))/x^8

Placing the root at 2:  1725948
x |--> -1/720*(10931*x^7 - 4710*x^5*e^x + 720*(x - 3)*e^(6*x) +
360*(3*x^2 - 4*x + 2)*e^(5*x) - 720*(3*x^2 - x)*e^(4*x) + 120*(16*x^4 +
9*x^2)*e^(3*x) + 30*(157*x^5 - 64*x^4)*e^(2*x) + 2160*e^(7*x) -
720*e^(8*x))/x^8

Placing the root at 3:  3323678
x |--> -1/720*(25355*x^7 + 10931*x^6*e^x + 4710*x^5*e^(2*x) +
1920*x^4*e^(3*x) - 1080*x^2*e^(4*x) + 720*(x - 1)*e^(6*x) + 360*(3*x^2 -
2*x)*e^(5*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8

Placing the root at 0:  976640
x |--> -1/36*(256*x^7 + 81*x^4*e^x + 36*(2*x - 3)*e^(6*x) + 36*(3*x^2
- 4*x + 1)*e^(5*x) - 36*(7*x^2 - 2*x)*e^(4*x) - 36*(3*x^3 -
4*x^2)*e^(3*x) - 27*(3*x^4 - 4*x^3)*e^(2*x) + 108*e^(7*x) -
36*e^(8*x))/x^8

Placing the root at 7:  2152822
x |--> -1/36*(744*x^7 + 256*x^6*e^x - 81*x^4*e^(2*x) -
108*x^3*e^(3*x) - 144*x^2*e^(4*x) + 36*(2*x - 1)*e^(6*x) + 36*(3*x^2 -
2*x)*e^(5*x) + 72*e^(7*x) - 36*e^(8*x))/x^8

Placing the root at 1:  1066800
x |--> -1/8*(69*x^7 - 20*x^5*e^x - 28*x^4*e^(2*x) + 8*(x - 6)*e^(6*x)
- 8*(3*x - 4)*e^(5*x) + 8*(x^3 + 3*x - 1)*e^(4*x) + 4*(5*x^4 - 2*x^3 -
2*x)*e^(3*x) + 32*e^(7*x) - 8*e^(8*x))/x^8

Placing the root at 2:  1492848
x |--> -1/12*(158*x^7 - 69*x^5*e^x + 12*(x^3 - 1)*e^(4*x) + 6*(5*x^4
- 2*x^3)*e^(3*x) + 3*(23*x^5 - 10*x^4)*e^(2*x) + 48*e^(5*x) - 72*e^(6*x)
+ 48*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 3:  2872212
x |--> -1/120*(3653*x^7 + 1580*x^6*e^x + 690*x^5*e^(2*x) +
300*x^4*e^(3*x) + 120*x^3*e^(4*x) + 120*e^(5*x) - 360*e^(6*x) +
360*e^(7*x) - 120*e^(8*x))/x^8

Placing the root at 4:  750456
x |--> -1/24*(125*x^7 - 64*x^3*e^x + 24*(x - 6)*e^(6*x) + 12*(3*x^2 -
6*x + 8)*e^(5*x) + 12*(16*x^3 - 3*x^2)*e^(2*x) + 4*(16*x^3 - 27*x^2 +
18*x - 6)*e^(4*x) - 12*(16*x^3 - 9*x^2 + 2*x)*e^(3*x) + 96*e^(7*x) -
24*e^(8*x))/x^8

Placing the root at 5:  1709148
x |--> -1/120*(1921*x^7 + 625*x^6*e^x + 320*x^3*e^(2*x) + 120*(x -
3)*e^(6*x) + 60*(3*x^2 - 4*x + 2)*e^(5*x) - 20*(32*x^3 - 9*x^2)*e^(3*x)
+ 40*(8*x^3 - 9*x^2 + 3*x)*e^(4*x) + 360*e^(7*x) - 120*e^(8*x))/x^8

Placing the root at 0:  874440
x |--> -1/6*(40*x^7 - 9*x^5*e^x + 6*(x - 6)*e^(6*x) + 3*(3*x^2 - 6*x
+ 8)*e^(5*x) - 3*(2*x^4 + 3*x^2)*e^(2*x) - 3*(2*x^3 - 9*x^2 +
2*x)*e^(3*x) + 3*(2*x^3 - 9*x^2 + 6*x - 2)*e^(4*x) + 24*e^(7*x) -
6*e^(8*x))/x^8

Placing the root at 1:  967400
x |--> -1/8*(61*x^7 - 16*x^5*e^x + 8*(x - 6)*e^(6*x) + 8*(x^2 - 3*x +
4)*e^(5*x) - 8*(2*x^2 - 3*x + 1)*e^(4*x) - 8*(2*x^4 - x^3)*e^(2*x) +
8*(2*x^4 - x^3 + x^2 - x)*e^(3*x) + 32*e^(7*x) - 8*e^(8*x))/x^8

Placing the root at 2:  1384152
x |--> -1/24*(289*x^7 - 122*x^5*e^x + 24*(x^2 + 4)*e^(5*x) -
24*(2*x^2 + 1)*e^(4*x) + 24*(2*x^4 + x^2)*e^(3*x) + 2*(61*x^5 -
24*x^4)*e^(2*x) - 144*e^(6*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 3:  2697212
x |--> -1/120*(3397*x^7 + 1445*x^6*e^x + 610*x^5*e^(2*x) +
240*x^4*e^(3*x) - 120*x^2*e^(4*x) + 120*(x^2 + 1)*e^(5*x) - 360*e^(6*x)
+ 360*e^(7*x) - 120*e^(8*x))/x^8

Placing the root at 4:  875896
x |--> -1/24*(157*x^7 + 64*x^4*e^x + 24*(x - 6)*e^(6*x) + 12*(3*x^2 -
6*x + 8)*e^(5*x) - 12*(9*x^2 - 6*x + 2)*e^(4*x) - 4*(32*x^4 +
9*x^2)*e^(2*x) + 4*(16*x^4 + 27*x^2 - 6*x)*e^(3*x) + 96*e^(7*x) -
24*e^(8*x))/x^8

Placing the root at 5:  1901788
x |--> -1/360*(6643*x^7 + 2355*x^6*e^x - 960*x^4*e^(2*x) + 360*(x -
3)*e^(6*x) + 180*(3*x^2 - 4*x + 2)*e^(5*x) - 360*(3*x^2 - x)*e^(4*x) +
60*(16*x^4 + 9*x^2)*e^(3*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8

Placing the root at 0:  751520
x |--> -1/6*(32*x^7 + 9*x^4*e^x + 6*(x - 6)*e^(6*x) + 3*(5*x^2 - 6*x
+ 8)*e^(5*x) - 3*(13*x^2 - 6*x + 2)*e^(4*x) - 3*(2*x^3 - 11*x^2 +
2*x)*e^(3*x) - 3*(3*x^4 - 2*x^3 + 3*x^2)*e^(2*x) + 24*e^(7*x) -
6*e^(8*x))/x^8

Placing the root at 7:  1693692
x |--> -1/36*(575*x^7 + 192*x^6*e^x - 54*x^4*e^(2*x) + 36*(x -
3)*e^(6*x) - 36*(4*x^2 - x)*e^(4*x) + 18*(5*x^2 - 4*x + 2)*e^(5*x) -
18*(2*x^3 - 3*x^2)*e^(3*x) + 108*e^(7*x) - 36*e^(8*x))/x^8

Placing the root at 1:  1093680
x |--> -1/8*(69*x^7 - 18*x^5*e^x + 24*(x - 1)*e^(6*x) - 8*(6*x -
1)*e^(5*x) - 24*(x^2 - x)*e^(4*x) + 6*(3*x^4 + 4*x^2)*e^(3*x) - 2*(9*x^4
- 4*x^3)*e^(2*x) + 24*e^(7*x) - 8*e^(8*x))/x^8

Placing the root at 2:  1562288
x |--> -1/36*(490*x^7 - 207*x^5*e^x + 36*(2*x - 3)*e^(6*x) - 36*(4*x
- 1)*e^(5*x) - 36*(x^2 - 2*x)*e^(4*x) + 9*(9*x^4 + 4*x^2)*e^(3*x) +
9*(23*x^5 - 9*x^4)*e^(2*x) + 108*e^(7*x) - 36*e^(8*x))/x^8

Placing the root at 3:  3037930
x |--> -1/360*(11499*x^7 + 4900*x^6*e^x + 2070*x^5*e^(2*x) +
810*x^4*e^(3*x) - 360*x^2*e^(4*x) + 360*(2*x - 1)*e^(6*x) -
720*x*e^(5*x) + 720*e^(7*x) - 360*e^(8*x))/x^8

Placing the root at 4:  1311044
x |--> -1/144*(1573*x^7 - 576*x^5*e^x + 144*(2*x - 3)*e^(6*x) -
288*(2*x^2 - x)*e^(4*x) + 72*(3*x^2 - 8*x + 2)*e^(5*x) - 72*(3*x^3 -
5*x^2)*e^(3*x) + 72*(8*x^5 + 3*x^3)*e^(2*x) + 432*e^(7*x) -
144*e^(8*x))/x^8

Placing the root at 5:  2646406
x |--> -1/720*(19479*x^7 + 7865*x^6*e^x + 2880*x^5*e^(2*x) -
1080*x^3*e^(3*x) - 1800*x^2*e^(4*x) + 720*(2*x - 1)*e^(6*x) + 360*(3*x^2
- 4*x)*e^(5*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8

Placing the root at 0:  848820
x |--> -1/2*(12*x^7 + 3*x^4*e^x + 8*x^3*e^(2*x) + 6*(x - 1)*e^(6*x) -
6*(2*x^2 - x)*e^(4*x) + (3*x^2 - 12*x + 2)*e^(5*x) - 3*(2*x^3 -
3*x^2)*e^(3*x) + 6*e^(7*x) - 2*e^(8*x))/x^8

Placing the root at 1:  815920
x |--> -1/4*(25*x^7 - 6*x^5*e^x + 8*(x - 3)*e^(6*x) - 8*(3*x -
2)*e^(5*x) - 4*(x^2 - 6*x + 1)*e^(4*x) - 2*(3*x^4 + 2*x^2)*e^(2*x) +
2*(3*x^4 + 4*x^2 - 4*x)*e^(3*x) + 16*e^(7*x) - 4*e^(8*x))/x^8

Placing the root at 2:  1198736
x |--> -1/12*(123*x^7 - 50*x^5*e^x + 12*(x - 6)*e^(6*x) - 12*(3*x -
4)*e^(5*x) + 12*(3*x - 1)*e^(4*x) + 6*(3*x^4 - 2*x)*e^(3*x) + 2*(25*x^5
- 9*x^4)*e^(2*x) + 48*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 3:  2375716
x |--> -1/180*(4429*x^7 + 1845*x^6*e^x + 750*x^5*e^(2*x) +
270*x^4*e^(3*x) + 180*(x - 3)*e^(6*x) - 180*(2*x - 1)*e^(5*x) +
180*x*e^(4*x) + 540*e^(7*x) - 180*e^(8*x))/x^8

Placing the root at 4:  974456
x |--> -1/24*(189*x^7 - 64*x^5*e^x + 24*(x - 6)*e^(6*x) + 12*(3*x^2 -
6*x + 8)*e^(5*x) - 12*(9*x^2 - 6*x + 2)*e^(4*x) + 12*(9*x^2 -
2*x)*e^(3*x) + 4*(16*x^5 - 9*x^2)*e^(2*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 5:  2022748
x |--> -1/360*(7283*x^7 + 2835*x^6*e^x + 960*x^5*e^(2*x) +
540*x^2*e^(3*x) + 360*(x - 3)*e^(6*x) + 180*(3*x^2 - 4*x + 2)*e^(5*x) -
360*(3*x^2 - x)*e^(4*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8

Placing the root at 6:  1418564
x |--> -1/144*(1861*x^7 + 576*x^6*e^x + 216*x^3*e^(2*x) + 144*(2*x -
3)*e^(6*x) - 288*(2*x^2 - x)*e^(4*x) + 72*(3*x^2 - 8*x + 2)*e^(5*x) -
72*(3*x^3 - 5*x^2)*e^(3*x) + 432*e^(7*x) - 144*e^(8*x))/x^8

Placing the root at 0:  601720
x |--> -1/2*(8*x^7 - 3*x^3*e^x + 4*(x - 3)*e^(6*x) + (3*x^2 - 12*x +
8)*e^(5*x) - (11*x^2 - 12*x + 2)*e^(4*x) + (6*x^3 - 5*x^2)*e^(2*x) -
(3*x^3 - 13*x^2 + 4*x)*e^(3*x) + 8*e^(7*x) - 2*e^(8*x))/x^8

Placing the root at 1:  425040
x |--> -1/6*(16*x^7 + 9*x^2*e^x + 6*(x - 10)*e^(6*x) + 3*(3*x^2 - 8*x
+ 20)*e^(5*x) - 6*(6*x^2 - 6*x + 5)*e^(4*x) - 6*(6*x^2 - x)*e^(2*x) +
6*(9*x^2 - 4*x + 1)*e^(3*x) + 30*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 2:  1046136
x |--> -1/24*(221*x^7 + 64*x^6*e^x - 36*x^2*e^(2*x) + 24*(x -
6)*e^(6*x) + 12*(3*x^2 - 6*x + 8)*e^(5*x) - 12*(9*x^2 - 6*x + 2)*e^(4*x)
+ 12*(9*x^2 - 2*x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 0:  604800
x |--> -1/2*(9*x^7 - 2*x^5*e^x + 2*(x - 10)*e^(6*x) - 4*(2*x -
5)*e^(5*x) + 2*(6*x - 5)*e^(4*x) + 2*(x^4 - 4*x + 1)*e^(3*x) - 2*(x^4 -
x)*e^(2*x) + 10*e^(7*x) - 2*e^(8*x))/x^8

Placing the root at 6:  913920
x |--> -1/3*(23*x^7 - 9*x^5*e^x + 3*(x^4 + 1)*e^(3*x) + 3*(3*x^5 -
x^4)*e^(2*x) - 15*e^(4*x) + 30*e^(5*x) - 30*e^(6*x) + 15*e^(7*x) -
3*e^(8*x))/x^8

Placing the root at 7:  1846824
x |--> -1/6*(113*x^7 + 46*x^6*e^x + 18*x^5*e^(2*x) + 6*x^4*e^(3*x) -
6*e^(4*x) + 24*e^(5*x) - 36*e^(6*x) + 24*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 1:  596400
x |--> -1/12*(49*x^7 - 24*x^3*e^x + 12*(x^2 + 10)*e^(5*x) + 12*(2*x^3
- 3*x^2 - 5)*e^(4*x) - 12*(6*x^3 - 3*x^2 - 1)*e^(3*x) + 12*(6*x^3 -
x^2)*e^(2*x) - 120*e^(6*x) + 60*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 2:  1376312
x |--> -1/12*(153*x^7 + 49*x^6*e^x + 24*x^3*e^(2*x) + 12*(x^2 +
4)*e^(5*x) + 12*(2*x^3 - 2*x^2 - 1)*e^(4*x) - 12*(4*x^3 - x^2)*e^(3*x) -
72*e^(6*x) + 48*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 5:  762720
x |--> -1/4*(23*x^7 + 10*x^4*e^x + 4*(x^3 - 5)*e^(4*x) + 2*(5*x^4 -
4*x^3 + 2)*e^(3*x) - 4*(5*x^4 - x^3)*e^(2*x) + 40*e^(5*x) - 40*e^(6*x) +
20*e^(7*x) - 4*e^(8*x))/x^8

Placing the root at 6:  1647408
x |--> -1/24*(385*x^7 + 138*x^6*e^x - 60*x^4*e^(2*x) + 24*(x^3 -
1)*e^(4*x) + 12*(5*x^4 - 2*x^3)*e^(3*x) + 96*e^(5*x) - 144*e^(6*x) +
96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 0:  673680
x |--> -(5*x^7 - x^5*e^x + (x^2 + 10)*e^(5*x) + (x^3 - 3*x^2 -
5)*e^(4*x) + (x^3 - x^2)*e^(2*x) - (2*x^3 - 3*x^2 - 1)*e^(3*x) -
10*e^(6*x) + 5*e^(7*x) - e^(8*x))/x^8

Placing the root at 1:  510720
x |--> -1/12*(41*x^7 - 18*x^3*e^x + 12*(x - 10)*e^(6*x) - 24*(2*x -
5)*e^(5*x) + 6*(3*x^3 + 12*x - 10)*e^(4*x) + 6*(9*x^3 + 2*x)*e^(2*x) -
6*(9*x^3 + 8*x - 2)*e^(3*x) + 60*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 2:  1202376
x |--> -1/24*(263*x^7 + 82*x^6*e^x + 36*x^3*e^(2*x) + 24*(x -
6)*e^(6*x) - 24*(3*x - 4)*e^(5*x) - 24*(3*x^3 + x)*e^(3*x) + 12*(3*x^3 +
6*x - 2)*e^(4*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 0:  540960
x |--> -1/4*(15*x^7 + 4*x^4*e^x + 4*(x - 10)*e^(6*x) - 8*(2*x -
5)*e^(5*x) + 4*(x^3 + 6*x - 5)*e^(4*x) - 4*(2*x^3 + 4*x - 1)*e^(3*x) -
4*(x^4 - x^3 - x)*e^(2*x) + 20*e^(7*x) - 4*e^(8*x))/x^8

Placing the root at 5:  855120
x |--> -1/2*(14*x^7 - 5*x^5*e^x + 2*(x^3 - 5)*e^(4*x) - 2*(2*x^3 -
1)*e^(3*x) + (5*x^5 + 2*x^3)*e^(2*x) + 20*e^(5*x) - 20*e^(6*x) +
10*e^(7*x) - 2*e^(8*x))/x^8

Placing the root at 6:  1760808
x |--> -1/24*(425*x^7 + 168*x^6*e^x + 60*x^5*e^(2*x) - 24*x^3*e^(3*x)
+ 24*(x^3 - 1)*e^(4*x) + 96*e^(5*x) - 144*e^(6*x) + 96*e^(7*x) -
24*e^(8*x))/x^8

Placing the root at 7:  1247400
x |--> -1/24*(277*x^7 + 90*x^6*e^x - 24*x^4*e^(2*x) + 24*(x -
6)*e^(6*x) - 24*(3*x - 4)*e^(5*x) - 24*(x^3 + x)*e^(3*x) + 24*(x^3 + 3*x
- 1)*e^(4*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 1:  383040
x |--> -1/2*(5*x^7 - 2*x^3*e^x + 2*(x^3 - 15)*e^(4*x) - 6*(x^3 -
2)*e^(3*x) + 2*(3*x^3 - 1)*e^(2*x) + 40*e^(5*x) - 30*e^(6*x) +
12*e^(7*x) - 2*e^(8*x))/x^8

Placing the root at 2:  922320
x |--> -1/4*(33*x^7 + 10*x^6*e^x + 4*x^3*e^(2*x) + 4*(x^3 -
5)*e^(4*x) - 4*(2*x^3 - 1)*e^(3*x) + 40*e^(5*x) - 40*e^(6*x) +
20*e^(7*x) - 4*e^(8*x))/x^8

Placing the root at 1:  690480
x |--> -1/12*(61*x^7 + 24*x^4*e^x + 12*(x^2 + 10)*e^(5*x) - 12*(3*x^2
+ 5)*e^(4*x) + 12*(2*x^4 + 3*x^2 + 1)*e^(3*x) - 12*(4*x^4 + x^2)*e^(2*x)
- 120*e^(6*x) + 60*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 2:  1520792
x |--> -1/12*(175*x^7 + 61*x^6*e^x - 24*x^4*e^(2*x) + 12*(x^2 +
4)*e^(5*x) - 12*(2*x^2 + 1)*e^(4*x) + 12*(2*x^4 + x^2)*e^(3*x) -
72*e^(6*x) + 48*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 0:  577920
x |--> -(4*x^7 + x^4*e^x + 2*(x^2 + 5)*e^(5*x) + (6*x^2 + 1)*e^(3*x)
- (6*x^2 + 5)*e^(4*x) - (x^4 + 2*x^2)*e^(2*x) - 10*e^(6*x) + 5*e^(7*x) -
e^(8*x))/x^8

Placing the root at 7:  1330840
x |--> -1/3*(37*x^7 + 12*x^6*e^x - 3*x^4*e^(2*x) + 6*x^2*e^(3*x) +
6*(x^2 + 2)*e^(5*x) - 3*(4*x^2 + 1)*e^(4*x) - 18*e^(6*x) + 12*e^(7*x) -
3*e^(8*x))/x^8

Placing the root at 1:  780640
x |--> -1/4*(23*x^7 + 9*x^4*e^x + 8*(x - 3)*e^(6*x) - 8*(3*x -
2)*e^(5*x) - 4*(x^2 - 6*x + 1)*e^(4*x) - 2*(9*x^4 + 2*x^2)*e^(2*x) +
(9*x^4 + 8*x^2 - 8*x)*e^(3*x) + 16*e^(7*x) - 4*e^(8*x))/x^8

Placing the root at 2:  1716848
x |--> -1/72*(1187*x^7 + 414*x^6*e^x - 162*x^4*e^(2*x) + 72*(2*x -
3)*e^(6*x) - 72*(4*x - 1)*e^(5*x) - 72*(x^2 - 2*x)*e^(4*x) + 18*(9*x^4 +
4*x^2)*e^(3*x) + 216*e^(7*x) - 72*e^(8*x))/x^8

Placing the root at 4:  1031240
x |--> -1/24*(203*x^7 - 72*x^5*e^x + 24*(x - 6)*e^(6*x) + 24*(x^2 -
3*x + 4)*e^(5*x) - 24*(2*x^2 - 3*x + 1)*e^(4*x) + 24*(3*x^5 +
x^3)*e^(2*x) - 24*(x^3 - x^2 + x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 5:  2114700
x |--> -1/72*(1537*x^7 + 609*x^6*e^x + 216*x^5*e^(2*x) -
72*x^3*e^(3*x) + 72*(x - 3)*e^(6*x) + 72*(x^2 - 2*x + 1)*e^(5*x) -
72*(x^2 - x)*e^(4*x) + 216*e^(7*x) - 72*e^(8*x))/x^8

Placing the root at 0:  652680
x |--> -1/2*(9*x^7 + 2*x^4*e^x + 4*(x - 3)*e^(6*x) + 2*(x^2 - 6*x +
4)*e^(5*x) - 2*(3*x^2 - 6*x + 1)*e^(4*x) + 2*(2*x^3 - x^2)*e^(2*x) -
2*(2*x^3 - 3*x^2 + 2*x)*e^(3*x) + 8*e^(7*x) - 2*e^(8*x))/x^8

Placing the root at 1:  581280
x |--> -1/6*(25*x^7 + 9*x^4*e^x + 6*(x - 10)*e^(6*x) - 12*(2*x -
5)*e^(5*x) + 6*(6*x - 5)*e^(4*x) + 3*(3*x^4 - 8*x + 2)*e^(3*x) -
6*(3*x^4 - x)*e^(2*x) + 30*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 2:  1310736
x |--> -1/6*(74*x^7 + 25*x^6*e^x - 9*x^4*e^(2*x) + 6*(x - 6)*e^(6*x)
- 6*(3*x - 4)*e^(5*x) + 6*(3*x - 1)*e^(4*x) + 3*(3*x^4 - 2*x)*e^(3*x) +
24*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 4:  764400
x |--> -1/12*(73*x^7 - 24*x^5*e^x + 12*(x^2 + 10)*e^(5*x) + 12*(3*x^2
+ 1)*e^(3*x) - 12*(3*x^2 + 5)*e^(4*x) + 12*(2*x^5 - x^2)*e^(2*x) -
120*e^(6*x) + 60*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 5:  1611512
x |--> -1/12*(191*x^7 + 73*x^6*e^x + 24*x^5*e^(2*x) + 12*x^2*e^(3*x)
+ 12*(x^2 + 4)*e^(5*x) - 12*(2*x^2 + 1)*e^(4*x) - 72*e^(6*x) +
48*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 6:  1111880
x |--> -1/24*(239*x^7 + 72*x^6*e^x + 24*x^3*e^(2*x) + 24*(x -
6)*e^(6*x) + 24*(x^2 - 3*x + 4)*e^(5*x) - 24*(2*x^2 - 3*x + 1)*e^(4*x) -
24*(x^3 - x^2 + x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 0:  462000
x |--> -(3*x^7 - x^3*e^x + (x - 10)*e^(6*x) + (x^2 - 4*x +
10)*e^(5*x) - (3*x^2 - 6*x + 5)*e^(4*x) - (x^3 - 3*x^2 + 4*x -
1)*e^(3*x) + (2*x^3 - x^2 + x)*e^(2*x) + 5*e^(7*x) - e^(8*x))/x^8

Placing the root at 1:  430080
x |--> -(3*x^7 + x^4*e^x + (x^4 + 6)*e^(3*x) - (2*x^4 + 1)*e^(2*x) -
15*e^(4*x) + 20*e^(5*x) - 15*e^(6*x) + 6*e^(7*x) - e^(8*x))/x^8

Placing the root at 2:  994560
x |--> -1/6*(55*x^7 + 18*x^6*e^x - 6*x^4*e^(2*x) + 6*(x^4 +
1)*e^(3*x) - 30*e^(4*x) + 60*e^(5*x) - 60*e^(6*x) + 30*e^(7*x) -
6*e^(8*x))/x^8

Placing the root at 4:  818160
x |--> -1/12*(85*x^7 + 24*x^6*e^x - 12*x^2*e^(2*x) + 12*(x^2 +
10)*e^(5*x) + 12*(3*x^2 + 1)*e^(3*x) - 12*(3*x^2 + 5)*e^(4*x) -
120*e^(6*x) + 60*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 0:  325920
x |--> -(2*x^7 + x^2*e^x + 6*(x^2 + 1)*e^(3*x) + (x^2 + 20)*e^(5*x) -
(4*x^2 + 1)*e^(2*x) - (4*x^2 + 15)*e^(4*x) - 15*e^(6*x) + 6*e^(7*x) -
e^(8*x))/x^8

Placing the root at 1:  863800
x |--> -1/8*(55*x^7 - 18*x^5*e^x + 16*(x - 3)*e^(6*x) - 16*(3*x -
2)*e^(5*x) - 8*(x^2 - 6*x + 1)*e^(4*x) + 16*(x^2 - x)*e^(3*x) + 2*(9*x^5
- 4*x^2)*e^(2*x) + 32*e^(7*x) - 8*e^(8*x))/x^8

Placing the root at 2:  1818908
x |--> -1/72*(1295*x^7 + 495*x^6*e^x + 162*x^5*e^(2*x) +
72*x^2*e^(3*x) + 72*(2*x - 3)*e^(6*x) - 72*(4*x - 1)*e^(5*x) - 72*(x^2 -
2*x)*e^(4*x) + 216*e^(7*x) - 72*e^(8*x))/x^8

Placing the root at 0:  521640
x |--> -1/8*(27*x^7 - 8*x^3*e^x + 24*(x - 2)*e^(6*x) - 8*(9*x -
4)*e^(5*x) + 24*(2*x^2 - x)*e^(3*x) - 8*(3*x^2 - 9*x + 1)*e^(4*x) +
8*(x^3 - 3*x^2)*e^(2*x) + 32*e^(7*x) - 8*e^(8*x))/x^8

Placing the root at 7:  1256220
x |--> -1/8*(90*x^7 + 27*x^6*e^x + 8*x^3*e^(2*x) + 24*x^2*e^(3*x) +
24*(x - 1)*e^(6*x) - 8*(6*x - 1)*e^(5*x) - 24*(x^2 - x)*e^(4*x) +
24*e^(7*x) - 8*e^(8*x))/x^8

Placing the root at 1:  636720
x |--> -1/12*(59*x^7 - 18*x^5*e^x + 12*(x - 10)*e^(6*x) - 24*(2*x -
5)*e^(5*x) - 12*(4*x - 1)*e^(3*x) + 12*(6*x - 5)*e^(4*x) + 6*(3*x^5 +
2*x)*e^(2*x) + 60*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 2:  1378776
x |--> -1/12*(160*x^7 + 59*x^6*e^x + 18*x^5*e^(2*x) + 12*(x -
6)*e^(6*x) - 12*(3*x - 4)*e^(5*x) + 12*(3*x - 1)*e^(4*x) - 12*x*e^(3*x)
+ 48*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 5:  924280
x |--> -1/4*(32*x^7 + 9*x^6*e^x - 4*x^2*e^(2*x) + 8*(x - 3)*e^(6*x) -
8*(3*x - 2)*e^(5*x) - 4*(x^2 - 6*x + 1)*e^(4*x) + 8*(x^2 - x)*e^(3*x) +
16*e^(7*x) - 4*e^(8*x))/x^8

Placing the root at 0:  367920
x |--> -1/4*(9*x^7 + 4*x^2*e^x + 8*(x - 5)*e^(6*x) - 8*(4*x -
5)*e^(5*x) - 4*(x^2 - 12*x + 5)*e^(4*x) + 4*(3*x^2 - 8*x + 1)*e^(3*x) -
4*(3*x^2 - 2*x)*e^(2*x) + 20*e^(7*x) - 4*e^(8*x))/x^8

Placing the root at 1:  467040
x |--> -1/2*(7*x^7 - 2*x^5*e^x + 2*(x^5 - 1)*e^(2*x) + 12*e^(3*x) -
30*e^(4*x) + 40*e^(5*x) - 30*e^(6*x) + 12*e^(7*x) - 2*e^(8*x))/x^8

Placing the root at 2:  1039920
x |--> -1/6*(59*x^7 + 21*x^6*e^x + 6*x^5*e^(2*x) + 6*e^(3*x) -
30*e^(4*x) + 60*e^(5*x) - 60*e^(6*x) + 30*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 3:  677040
x |--> -1/6*(34*x^7 + 9*x^6*e^x + 6*(x - 10)*e^(6*x) - 12*(2*x -
5)*e^(5*x) - 6*(4*x - 1)*e^(3*x) + 6*(6*x - 5)*e^(4*x) + 6*x*e^(2*x) +
30*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 0:  258720
x |--> -1/2*(3*x^7 + 2*(x - 15)*e^(6*x) - 10*(x - 4)*e^(5*x) +
10*(2*x - 3)*e^(4*x) - 4*(5*x - 3)*e^(3*x) + 2*(5*x - 1)*e^(2*x) -
2*x*e^x + 12*e^(7*x) - 2*e^(8*x))/x^8

Placing the root at 1:  493920
x |--> -(4*x^7 + x^6*e^x - e^(2*x) + 6*e^(3*x) - 15*e^(4*x) +
20*e^(5*x) - 15*e^(6*x) + 6*e^(7*x) - e^(8*x))/x^8

Placing the root at 0:  181440
x |--> -(x^7 - 7*e^(2*x) + 21*e^(3*x) - 35*e^(4*x) + 35*e^(5*x) -
21*e^(6*x) + 7*e^(7*x) - e^(8*x) + e^x)/x^8

CPU time: 1185.43 s,  Wall time: 1188.21 s
Placing the root at 1:  3
x |--> -(x - e^(2*x) + e^x)/x^2

Placing the root at 1:  16
x |--> -1/2*(3*x^2 + 2*x*e^x + 2*e^(2*x) - 2*e^(3*x))/x^3

Placing the root at 0:  12
x |--> -(x^2 + 2*e^(2*x) - e^(3*x) - e^x)/x^3

Placing the root at 1:  82
x |--> -1/2*(3*x^3 + 2*(x - 1)*e^(2*x) - 2*x*e^x + 4*e^(3*x) - 2*e^(4*x))/x^4

Placing the root at 2:  125
x |--> -1/6*(16*x^3 + 9*x^2*e^x + 6*x*e^(2*x) + 6*e^(3*x) - 6*e^(4*x))/x^4

Placing the root at 1:  98
x |--> -(2*x^3 + x^2*e^x - e^(2*x) + 2*e^(3*x) - e^(4*x))/x^4

Placing the root at 0:  60
x |--> -(x^3 - 3*e^(2*x) + 3*e^(3*x) - e^(4*x) + e^x)/x^4

Placing the root at 1:  785
x |--> -1/6*(16*x^4 - 9*x^2*e^x + 6*(x - 1)*e^(3*x) + 3*(3*x^2 - 2*x)*e^(2*x) + 12*e^(4*x) - 6*e^(5*x))/x^5

Placing the root at 2:  1296
x |--> -1/24*(125*x^4 + 64*x^3*e^x + 36*x^2*e^(2*x) + 24*x*e^(3*x) + 24*e^(4*x) - 24*e^(5*x))/x^5

Placing the root at 0:  690
x |--> -1/4*(9*x^4 - 4*x^2*e^x + 4*(2*x - 1)*e^(3*x) - 8*x*e^(2*x) + 8*e^(4*x) - 4*e^(5*x))/x^5

Placing the root at 1:  610
x |--> -(2*x^4 - x^2*e^x + (x^2 + 1)*e^(2*x) - 3*e^(3*x) + 3*e^(4*x) - e^(5*x))/x^5

Placing the root at 2:  1040
x |--> -1/12*(49*x^4 + 24*x^3*e^x + 12*x^2*e^(2*x) - 12*e^(3*x) + 24*e^(4*x) - 12*e^(5*x))/x^5

Placing the root at 3:  905
x |--> -1/12*(41*x^4 + 18*x^3*e^x + 12*(x - 1)*e^(3*x) - 12*x*e^(2*x) + 24*e^(4*x) - 12*e^(5*x))/x^5

Placing the root at 0:  500
x |--> -1/2*(3*x^4 + 2*(x - 3)*e^(3*x) - 2*(2*x - 1)*e^(2*x) + 2*x*e^x + 6*e^(4*x) - 2*e^(5*x))/x^5

Placing the root at 1:  690
x |--> -1/2*(5*x^4 + 2*x^3*e^x + 2*e^(2*x) - 6*e^(3*x) + 6*e^(4*x) - 2*e^(5*x))/x^5

Placing the root at 0:  360
x |--> -(x^4 + 4*e^(2*x) - 6*e^(3*x) + 4*e^(4*x) - e^(5*x) - e^x)/x^5

Placing the root at 1:  7865
x |--> -1/2*(8*x^5 - 3*x^3*e^x - 5*x^2*e^(2*x) + 2*(2*x - 1)*e^(4*x) + (3*x^2 - 4*x)*e^(3*x) + 4*e^(5*x) - 2*e^(6*x))/x^6

Placing the root at 2:  9651
x |--> -1/24*(125*x^5 - 64*x^3*e^x + 24*(x - 1)*e^(4*x) + 12*(3*x^2 - 2*x)*e^(3*x) + 4*(16*x^3 - 9*x^2)*e^(2*x) + 48*e^(5*x) - 24*e^(6*x))/x^6

Placing the root at 3:  16807
x |--> -1/120*(1296*x^5 + 625*x^4*e^x + 320*x^3*e^(2*x) + 180*x^2*e^(3*x) + 120*x*e^(4*x) + 120*e^(5*x) - 120*e^(6*x))/x^6

Placing the root at 1:  5670
x |--> -1/6*(16*x^5 + 9*x^2*e^x + 6*(x - 3)*e^(4*x) + 3*(3*x^2 - 4*x + 2)*e^(3*x) - 6*(3*x^2 - x)*e^(2*x) + 18*e^(5*x) - 6*e^(6*x))/x^6

Placing the root at 2:  10931
x |--> -1/24*(157*x^5 + 64*x^4*e^x - 36*x^2*e^(2*x) + 24*(x - 1)*e^(4*x) + 12*(3*x^2 - 2*x)*e^(3*x) + 48*e^(5*x) - 24*e^(6*x))/x^6

Placing the root at 0:  6090
x |--> -(3*x^5 - x^3*e^x + (x - 3)*e^(4*x) + (x^2 - 2*x + 1)*e^(3*x) - (x^2 - x)*e^(2*x) + 3*e^(5*x) - e^(6*x))/x^6

Placing the root at 4:  7710
x |--> -1/12*(49*x^5 - 24*x^3*e^x + 12*(x^2 + 1)*e^(3*x) + 12*(2*x^3 - x^2)*e^(2*x) - 36*e^(4*x) + 36*e^(5*x) - 12*e^(6*x))/x^6

Placing the root at 5:  13682
x |--> -1/12*(104*x^5 + 49*x^4*e^x + 24*x^3*e^(2*x) + 12*x^2*e^(3*x) - 12*e^(4*x) + 24*e^(5*x) - 12*e^(6*x))/x^6

Placing the root at 1:  4380
x |--> -(2*x^5 + x^2*e^x + (x^2 + 4)*e^(3*x) - (2*x^2 + 1)*e^(2*x) - 6*e^(4*x) + 4*e^(5*x) - e^(6*x))/x^6

Placing the root at 2:  8670
x |--> -1/12*(61*x^5 + 24*x^4*e^x - 12*x^2*e^(2*x) + 12*(x^2 + 1)*e^(3*x) - 36*e^(4*x) + 36*e^(5*x) - 12*e^(6*x))/x^6

Placing the root at 1:  6660
x |--> -1/12*(41*x^5 - 18*x^3*e^x + 12*(x - 3)*e^(4*x) - 12*(2*x - 1)*e^(3*x) + 6*(3*x^3 + 2*x)*e^(2*x) + 36*e^(5*x) - 12*e^(6*x))/x^6

Placing the root at 2:  12146
x |--> -1/24*(181*x^5 + 82*x^4*e^x + 36*x^3*e^(2*x) + 24*(x - 1)*e^(4*x) - 24*x*e^(3*x) + 48*e^(5*x) - 24*e^(6*x))/x^6

Placing the root at 0:  4950
x |--> -1/4*(9*x^5 + 4*x^2*e^x + 4*(2*x - 3)*e^(4*x) - 4*(4*x - 1)*e^(3*x) - 4*(x^2 - 2*x)*e^(2*x) + 12*e^(5*x) - 4*e^(6*x))/x^6

Placing the root at 5:  9800
x |--> -1/4*(23*x^5 + 9*x^4*e^x - 4*x^2*e^(2*x) + 4*(2*x - 1)*e^(4*x) - 8*x*e^(3*x) + 8*e^(5*x) - 4*e^(6*x))/x^6

Placing the root at 1:  5040
x |--> -1/2*(5*x^5 - 2*x^3*e^x + 2*(x^3 - 1)*e^(2*x) + 8*e^(3*x) - 12*e^(4*x) + 8*e^(5*x) - 2*e^(6*x))/x^6

Placing the root at 2:  9480
x |--> -1/4*(23*x^5 + 10*x^4*e^x + 4*x^3*e^(2*x) + 4*e^(3*x) - 12*e^(4*x) + 12*e^(5*x) - 4*e^(6*x))/x^6

Placing the root at 3:  7380
x |--> -1/6*(25*x^5 + 9*x^4*e^x + 6*(x - 3)*e^(4*x) - 6*(2*x - 1)*e^(3*x) + 6*x*e^(2*x) + 18*e^(5*x) - 6*e^(6*x))/x^6

Placing the root at 0:  3540
x |--> -1/2*(3*x^5 + 2*(x - 6)*e^(4*x) - 2*(3*x - 4)*e^(3*x) + 2*(3*x - 1)*e^(2*x) - 2*x*e^x + 8*e^(5*x) - 2*e^(6*x))/x^6

Placing the root at 1:  5520
x |--> -(3*x^5 + x^4*e^x - e^(2*x) + 4*e^(3*x) - 6*e^(4*x) + 4*e^(5*x) - e^(6*x))/x^6

Placing the root at 0:  2520
x |--> -(x^5 - 5*e^(2*x) + 10*e^(3*x) - 10*e^(4*x) + 5*e^(5*x) - e^(6*x) + e^x)/x^6

Placing the root at 1:  112273
x |--> -1/48*(375*x^6 - 128*x^4*e^x - 200*x^3*e^(2*x) + 48*(2*x - 1)*e^(5*x) + 24*(3*x^2 - 4*x)*e^(4*x) + 8*(16*x^3 - 15*x^2)*e^(3*x) + 96*e^(6*x) - 48*e^(7*x))/x^7

Placing the root at 2:  144865
x |--> -1/120*(1296*x^6 - 625*x^4*e^x + 120*(x - 1)*e^(5*x) + 60*(3*x^2 - 2*x)*e^(4*x) + 20*(16*x^3 - 9*x^2)*e^(3*x) + 5*(125*x^4 - 64*x^3)*e^(2*x) + 240*e^(6*x) - 120*e^(7*x))/x^7

Placing the root at 3:  262144
x |--> -1/720*(16807*x^6 + 7776*x^5*e^x + 3750*x^4*e^(2*x) + 1920*x^3*e^(3*x) + 1080*x^2*e^(4*x) + 720*x*e^(5*x) + 720*e^(6*x) - 720*e^(7*x))/x^7

Placing the root at 0:  104160
x |--> -1/36*(256*x^6 - 81*x^4*e^x - 108*x^3*e^(2*x) - 144*x^2*e^(3*x) + 36*(2*x - 1)*e^(5*x) + 36*(3*x^2 - 2*x)*e^(4*x) + 72*e^(6*x) - 36*e^(7*x))/x^7

Placing the root at 1:  89530
x |--> -1/8*(49*x^6 - 16*x^4*e^x - 24*x^3*e^(2*x) + 8*(x - 3)*e^(5*x) + 8*(x^2 - 2*x + 1)*e^(4*x) + 8*(2*x^3 - x^2 + x)*e^(3*x) + 24*e^(6*x) - 8*e^(7*x))/x^7

Placing the root at 2:  117614
x |--> -1/12*(104*x^6 - 49*x^4*e^x + 12*(x^2 + 1)*e^(4*x) + 12*(2*x^3 - x^2)*e^(3*x) + (49*x^4 - 24*x^3)*e^(2*x) - 36*e^(5*x) + 36*e^(6*x) - 12*e^(7*x))/x^7

Placing the root at 3:  215488
x |--> -1/360*(6841*x^6 + 3120*x^5*e^x + 1470*x^4*e^(2*x) + 720*x^3*e^(3*x) + 360*x^2*e^(4*x) - 360*e^(5*x) + 720*e^(6*x) - 360*e^(7*x))/x^7

Placing the root at 4:  80682
x |--> -1/24*(125*x^6 + 64*x^3*e^x + 24*(x - 3)*e^(5*x) + 12*(3*x^2 - 4*x + 2)*e^(4*x) - 4*(32*x^3 - 9*x^2)*e^(2*x) + 8*(8*x^3 - 9*x^2 + 3*x)*e^(3*x) + 72*e^(6*x) - 24*e^(7*x))/x^7

Placing the root at 5:  162365
x |--> -1/240*(3217*x^6 + 1250*x^5*e^x - 640*x^3*e^(2*x) + 240*(x - 1)*e^(5*x) + 120*(3*x^2 - 2*x)*e^(4*x) + 40*(16*x^3 - 9*x^2)*e^(3*x) + 480*e^(6*x) - 240*e^(7*x))/x^7

Placing the root at 0:  80500
x |--> -1/6*(32*x^6 - 9*x^4*e^x + 6*(x - 3)*e^(5*x) - 6*(4*x^2 - x)*e^(3*x) + 3*(5*x^2 - 4*x + 2)*e^(4*x) - 3*(2*x^3 - 3*x^2)*e^(2*x) + 18*e^(6*x) - 6*e^(7*x))/x^7

Placing the root at 1:  77105
x |--> -1/8*(41*x^6 - 12*x^4*e^x + 8*(2*x - 3)*e^(5*x) - 8*(4*x - 1)*e^(4*x) - 4*(3*x^3 - 2*x^2)*e^(2*x) + 4*(3*x^3 - 2*x^2 + 4*x)*e^(3*x) + 24*e^(6*x) - 8*e^(7*x))/x^7

Placing the root at 0:  65135
x |--> -1/2*(8*x^6 + 3*x^3*e^x + 2*(2*x - 3)*e^(5*x) - 4*(2*x^2 - x)*e^(3*x) + (3*x^2 - 8*x + 2)*e^(4*x) - (3*x^3 - 5*x^2)*e^(2*x) + 6*e^(6*x) - 2*e^(7*x))/x^7

Placing the root at 2:  104027
x |--> -1/24*(181*x^6 - 82*x^4*e^x + 24*(x - 3)*e^(5*x) - 24*(2*x - 1)*e^(4*x) + 12*(3*x^3 + 2*x)*e^(3*x) + 2*(41*x^4 - 18*x^3)*e^(2*x) + 72*e^(6*x) - 24*e^(7*x))/x^7

Placing the root at 3:  193613
x |--> -1/360*(6073*x^6 + 2715*x^5*e^x + 1230*x^4*e^(2*x) + 540*x^3*e^(3*x) + 360*(x - 1)*e^(5*x) - 360*x*e^(4*x) + 720*e^(6*x) - 360*e^(7*x))/x^7

Placing the root at 4:  93002
x |--> -1/24*(157*x^6 - 64*x^4*e^x + 24*(x - 3)*e^(5*x) + 12*(3*x^2 - 4*x + 2)*e^(4*x) - 24*(3*x^2 - x)*e^(3*x) + 4*(16*x^4 + 9*x^2)*e^(2*x) + 72*e^(6*x) - 24*e^(7*x))/x^7

Placing the root at 5:  177485
x |--> -1/720*(10931*x^6 + 4710*x^5*e^x + 1920*x^4*e^(2*x) - 1080*x^2*e^(3*x) + 720*(x - 1)*e^(5*x) + 360*(3*x^2 - 2*x)*e^(4*x) + 1440*e^(6*x) - 720*e^(7*x))/x^7

Placing the root at 6:  136353
x |--> -1/144*(1573*x^6 + 576*x^5*e^x - 216*x^3*e^(2*x) - 360*x^2*e^(3*x) + 144*(2*x - 1)*e^(5*x) + 72*(3*x^2 - 4*x)*e^(4*x) + 288*e^(6*x) - 144*e^(7*x))/x^7

Placing the root at 1:  46410
x |--> -1/6*(16*x^6 - 9*x^2*e^x + 6*(x - 6)*e^(5*x) + 3*(3*x^2 - 6*x + 8)*e^(4*x) - 3*(9*x^2 - 6*x + 2)*e^(3*x) + 3*(9*x^2 - 2*x)*e^(2*x) + 24*e^(6*x) - 6*e^(7*x))/x^7

Placing the root at 2:  101962
x |--> -1/24*(189*x^6 + 64*x^5*e^x + 36*x^2*e^(2*x) + 24*(x - 3)*e^(5*x) + 12*(3*x^2 - 4*x + 2)*e^(4*x) - 24*(3*x^2 - x)*e^(3*x) + 72*e^(6*x) - 24*e^(7*x))/x^7

Placing the root at 0:  58170
x |--> -1/4*(15*x^6 - 4*x^4*e^x + 4*(x - 6)*e^(5*x) - 4*(3*x - 4)*e^(4*x) - 4*(x^3 + x)*e^(2*x) + 4*(x^3 + 3*x - 1)*e^(3*x) + 16*e^(6*x) - 4*e^(7*x))/x^7

Placing the root at 5:  80850
x |--> -1/4*(23*x^6 - 10*x^4*e^x + 4*(x^3 - 1)*e^(3*x) + 2*(5*x^4 - 2*x^3)*e^(2*x) + 16*e^(4*x) - 24*e^(5*x) + 16*e^(6*x) - 4*e^(7*x))/x^7

Placing the root at 6:  153426
x |--> -1/12*(158*x^6 + 69*x^5*e^x + 30*x^4*e^(2*x) + 12*x^3*e^(3*x) + 12*e^(4*x) - 36*e^(5*x) + 36*e^(6*x) - 12*e^(7*x))/x^7

Placing the root at 1:  64260
x |--> -1/12*(49*x^6 + 24*x^3*e^x + 12*(x^2 + 4)*e^(4*x) + 12*(2*x^3 - 2*x^2 - 1)*e^(3*x) - 12*(4*x^3 - x^2)*e^(2*x) - 72*e^(5*x) + 48*e^(6*x) - 12*e^(7*x))/x^7

Placing the root at 2:  131334
x |--> -1/24*(257*x^6 + 98*x^5*e^x - 48*x^3*e^(2*x) + 24*(x^2 + 1)*e^(4*x) + 24*(2*x^3 - x^2)*e^(3*x) - 72*e^(5*x) + 72*e^(6*x) - 24*e^(7*x))/x^7

Placing the root at 0:  62160
x |--> -(4*x^6 - x^4*e^x + 2*x^2*e^(2*x) + 2*(x^2 + 2)*e^(4*x) - (4*x^2 + 1)*e^(3*x) - 6*e^(5*x) + 4*e^(6*x) - e^(7*x))/x^7

Placing the root at 1:  55230
x |--> -1/12*(41*x^6 + 18*x^3*e^x + 12*(x - 6)*e^(5*x) - 12*(3*x - 4)*e^(4*x) - 12*(3*x^3 + x)*e^(2*x) + 6*(3*x^3 + 6*x - 2)*e^(3*x) + 48*e^(6*x) - 12*e^(7*x))/x^7

Placing the root at 2:  115507
x |--> -1/12*(111*x^6 + 41*x^5*e^x - 18*x^3*e^(2*x) + 12*(x - 3)*e^(5*x) - 12*(2*x - 1)*e^(4*x) + 6*(3*x^3 + 2*x)*e^(3*x) + 36*e^(6*x) - 12*e^(7*x))/x^7

Placing the root at 0:  50190
x |--> -(3*x^6 + x^3*e^x + (x - 6)*e^(5*x) + (x^2 - 3*x + 4)*e^(4*x) - (2*x^2 - 3*x + 1)*e^(3*x) - (x^3 - x^2 + x)*e^(2*x) + 4*e^(6*x) - e^(7*x))/x^7

Placing the root at 4:  73500
x |--> -1/12*(61*x^6 - 24*x^4*e^x + 12*(x^2 + 4)*e^(4*x) - 12*(2*x^2 + 1)*e^(3*x) + 12*(2*x^4 + x^2)*e^(2*x) - 72*e^(5*x) + 48*e^(6*x) - 12*e^(7*x))/x^7

Placing the root at 5:  142674
x |--> -1/24*(289*x^6 + 122*x^5*e^x + 48*x^4*e^(2*x) - 24*x^2*e^(3*x) + 24*(x^2 + 1)*e^(4*x) - 72*e^(5*x) + 72*e^(6*x) - 24*e^(7*x))/x^7

Placing the root at 6:  107590
x |--> -1/24*(203*x^6 + 72*x^5*e^x - 24*x^3*e^(2*x) + 24*(x - 3)*e^(5*x) + 24*(x^2 - 2*x + 1)*e^(4*x) - 24*(x^2 - x)*e^(3*x) + 72*e^(6*x) - 24*e^(7*x))/x^7

Placing the root at 1:  41580
x |--> -1/2*(5*x^6 + 2*x^3*e^x + 2*(x^3 - 5)*e^(3*x) - 2*(2*x^3 - 1)*e^(2*x) + 20*e^(4*x) - 20*e^(5*x) + 10*e^(6*x) - 2*e^(7*x))/x^7

Placing the root at 2:  89250
x |--> -1/2*(14*x^6 + 5*x^5*e^x - 2*x^3*e^(2*x) + 2*(x^3 - 1)*e^(3*x) + 8*e^(4*x) - 12*e^(5*x) + 8*e^(6*x) - 2*e^(7*x))/x^7

Placing the root at 4:  80220
x |--> -1/12*(73*x^6 + 24*x^5*e^x + 12*x^2*e^(2*x) + 12*(x^2 + 4)*e^(4*x) - 12*(2*x^2 + 1)*e^(3*x) - 72*e^(5*x) + 48*e^(6*x) - 12*e^(7*x))/x^7

Placing the root at 0:  35700
x |--> -(2*x^6 - x^2*e^x + (x^2 + 10)*e^(4*x) + (3*x^2 + 1)*e^(2*x) - (3*x^2 + 5)*e^(3*x) - 10*e^(5*x) + 5*e^(6*x) - e^(7*x))/x^7

Placing the root at 1:  83090
x |--> -1/4*(23*x^6 - 9*x^4*e^x + 4*(2*x - 3)*e^(5*x) - 4*(4*x - 1)*e^(4*x) - 4*(x^2 - 2*x)*e^(3*x) + (9*x^4 + 4*x^2)*e^(2*x) + 12*e^(6*x) - 4*e^(7*x))/x^7

Placing the root at 2:  160986
x |--> -1/36*(490*x^6 + 207*x^5*e^x + 81*x^4*e^(2*x) - 36*x^2*e^(3*x) + 36*(2*x - 1)*e^(5*x) - 72*x*e^(4*x) + 72*e^(6*x) - 36*e^(7*x))/x^7

Placing the root at 0:  56700
x |--> -1/8*(27*x^6 + 8*x^3*e^x + 24*x^2*e^(2*x) + 24*(x - 1)*e^(5*x) - 8*(6*x - 1)*e^(4*x) - 24*(x^2 - x)*e^(3*x) + 24*e^(6*x) - 8*e^(7*x))/x^7

Placing the root at 1:  62160
x |--> -1/6*(25*x^6 - 9*x^4*e^x + 6*(x - 6)*e^(5*x) - 6*(3*x - 4)*e^(4*x) + 6*(3*x - 1)*e^(3*x) + 3*(3*x^4 - 2*x)*e^(2*x) + 24*e^(6*x) - 6*e^(7*x))/x^7

Placing the root at 2:  124012
x |--> -1/12*(123*x^6 + 50*x^5*e^x + 18*x^4*e^(2*x) + 12*(x - 3)*e^(5*x) - 12*(2*x - 1)*e^(4*x) + 12*x*e^(3*x) + 36*e^(6*x) - 12*e^(7*x))/x^7

Placing the root at 5:  90650
x |--> -1/8*(55*x^6 + 18*x^5*e^x + 8*x^2*e^(2*x) + 8*(2*x - 3)*e^(5*x) - 8*(4*x - 1)*e^(4*x) - 8*(x^2 - 2*x)*e^(3*x) + 24*e^(6*x) - 8*e^(7*x))/x^7

Placing the root at 0:  40320
x |--> -1/4*(9*x^6 - 4*x^2*e^x + 8*(x - 3)*e^(5*x) - 8*(3*x - 2)*e^(4*x) - 4*(x^2 - 6*x + 1)*e^(3*x) + 8*(x^2 - x)*e^(2*x) + 16*e^(6*x) - 4*e^(7*x))/x^7

Placing the root at 1:  46200
x |--> -(3*x^6 - x^4*e^x + (x^4 + 1)*e^(2*x) - 5*e^(3*x) + 10*e^(4*x) - 10*e^(5*x) + 5*e^(6*x) - e^(7*x))/x^7

Placing the root at 2:  94920
x |--> -1/3*(23*x^6 + 9*x^5*e^x + 3*x^4*e^(2*x) - 3*e^(3*x) + 12*e^(4*x) - 18*e^(5*x) + 12*e^(6*x) - 3*e^(7*x))/x^7

Placing the root at 3:  67200
x |--> -1/12*(59*x^6 + 18*x^5*e^x + 12*(x - 6)*e^(5*x) - 12*(3*x - 4)*e^(4*x) + 12*(3*x - 1)*e^(3*x) - 12*x*e^(2*x) + 48*e^(6*x) - 12*e^(7*x))/x^7

Placing the root at 0:  28560
x |--> -1/2*(3*x^6 + 2*(x - 10)*e^(5*x) - 4*(2*x - 5)*e^(4*x) - 2*(4*x - 1)*e^(2*x) + 2*(6*x - 5)*e^(3*x) + 2*x*e^x + 10*e^(6*x) - 2*e^(7*x))/x^7

Placing the root at 1:  49560
x |--> -1/2*(7*x^6 + 2*x^5*e^x + 2*e^(2*x) - 10*e^(3*x) + 20*e^(4*x) - 20*e^(5*x) + 10*e^(6*x) - 2*e^(7*x))/x^7

Placing the root at 0:  20160
x |--> -(x^6 + 6*e^(2*x) - 15*e^(3*x) + 20*e^(4*x) - 15*e^(5*x) + 6*e^(6*x) - e^(7*x) - e^x)/x^7

Placing the root at 1:  1694966
x |--> -1/36*(500*x^7 - 144*x^5*e^x - 177*x^4*e^(2*x) - 204*x^3*e^(3*x) + 36*(2*x - 1)*e^(6*x) + 36*(3*x^2 - 2*x)*e^(5*x) + 48*(2*x^3 - 3*x^2)*e^(4*x) + 72*e^(7*x) - 36*e^(8*x))/x^8

Placing the root at 2:  1919820
x |--> -1/120*(1944*x^7 - 625*x^5*e^x - 945*x^4*e^(2*x) + 120*(2*x - 1)*e^(6*x) + 60*(3*x^2 - 4*x)*e^(5*x) + 20*(16*x^3 - 15*x^2)*e^(4*x) + 125*(5*x^4 - 4*x^3)*e^(3*x) + 240*e^(7*x) - 120*e^(8*x))/x^8

Placing the root at 3:  2567748
x |--> -1/720*(16807*x^7 - 7776*x^5*e^x + 720*(x - 1)*e^(6*x) + 360*(3*x^2 - 2*x)*e^(5*x) + 120*(16*x^3 - 9*x^2)*e^(4*x) + 30*(125*x^4 - 64*x^3)*e^(3*x) + 6*(1296*x^5 - 625*x^4)*e^(2*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8

Placing the root at 4:  4782969
x |--> -1/5040*(262144*x^7 + 117649*x^6*e^x + 54432*x^5*e^(2*x) + 26250*x^4*e^(3*x) + 13440*x^3*e^(4*x) + 7560*x^2*e^(5*x) + 5040*x*e^(6*x) + 5040*e^(7*x) - 5040*e^(8*x))/x^8

Placing the root at 1:  1308412
x |--> -1/12*(125*x^7 - 32*x^5*e^x + 12*(x - 3)*e^(6*x) + 6*(5*x^2 - 4*x + 2)*e^(5*x) - 2*(38*x^3 - 9*x^2)*e^(3*x) - 2*(9*x^4 - 16*x^3)*e^(2*x) + 4*(8*x^3 - 12*x^2 + 3*x)*e^(4*x) + 36*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 2:  1376648
x |--> -1/120*(1296*x^7 + 625*x^4*e^x + 120*(x - 3)*e^(6*x) + 60*(3*x^2 - 4*x + 2)*e^(5*x) - 10*(125*x^4 - 32*x^3)*e^(2*x) + 40*(8*x^3 - 9*x^2 + 3*x)*e^(4*x) + 5*(125*x^4 - 128*x^3 + 36*x^2)*e^(3*x) + 360*e^(7*x) - 120*e^(8*x))/x^8

Placing the root at 3:  2858052
x |--> -1/720*(20695*x^7 + 7776*x^6*e^x - 3750*x^4*e^(2*x) + 720*(x - 1)*e^(6*x) + 360*(3*x^2 - 2*x)*e^(5*x) + 120*(16*x^3 - 9*x^2)*e^(4*x) + 30*(125*x^4 - 64*x^3)*e^(3*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8

Placing the root at 0:  1350300
x |--> -1/18*(196*x^7 - 54*x^5*e^x - 63*x^4*e^(2*x) + 18*(x - 3)*e^(6*x) + 9*(5*x^2 - 4*x + 2)*e^(5*x) - 27*(2*x^3 - x^2)*e^(3*x) + 18*(2*x^3 - 4*x^2 + x)*e^(4*x) + 54*e^(7*x) - 18*e^(8*x))/x^8

Placing the root at 5:  1556968
x |--> -1/12*(156*x^7 - 49*x^5*e^x - 73*x^4*e^(2*x) + 12*(x - 3)*e^(6*x) + 12*(x^2 - 2*x + 1)*e^(5*x) + (49*x^4 - 36*x^3)*e^(3*x) + 12*(2*x^3 - x^2 + x)*e^(4*x) + 36*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 6:  2107000
x |--> -1/360*(6841*x^7 - 3120*x^5*e^x + 360*(x^2 + 1)*e^(5*x) + 360*(2*x^3 - x^2)*e^(4*x) + 30*(49*x^4 - 24*x^3)*e^(3*x) + 30*(104*x^5 - 49*x^4)*e^(2*x) - 1080*e^(6*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8

Placing the root at 7:  3959426
x |--> -1/360*(15392*x^7 + 6841*x^6*e^x + 3120*x^5*e^(2*x) + 1470*x^4*e^(3*x) + 720*x^3*e^(4*x) + 360*x^2*e^(5*x) - 360*e^(6*x) + 720*e^(7*x) - 360*e^(8*x))/x^8

Placing the root at 1:  1041880
x |--> -1/6*(49*x^7 - 12*x^5*e^x + 12*(x^2 + 2)*e^(5*x) + 6*(2*x^3 - 4*x^2 - 1)*e^(4*x) - 12*(2*x^3 - x^2)*e^(3*x) - 6*(x^4 - 2*x^3)*e^(2*x) - 36*e^(6*x) + 24*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 2:  1115632
x |--> -1/12*(104*x^7 + 49*x^4*e^x + 12*(x^2 + 4)*e^(5*x) + 12*(2*x^3 - 2*x^2 - 1)*e^(4*x) - 2*(49*x^4 - 12*x^3)*e^(2*x) + (49*x^4 - 48*x^3 + 12*x^2)*e^(3*x) - 72*e^(6*x) + 48*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 3:  2339960
x |--> -1/360*(8401*x^7 + 3120*x^6*e^x - 1470*x^4*e^(2*x) + 360*(x^2 + 1)*e^(5*x) + 360*(2*x^3 - x^2)*e^(4*x) + 30*(49*x^4 - 24*x^3)*e^(3*x) - 1080*e^(6*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8

Placing the root at 1:  1055684
x |--> -1/48*(375*x^7 + 128*x^4*e^x + 48*(2*x - 3)*e^(6*x) + 24*(3*x^2 - 8*x + 2)*e^(5*x) - 8*(41*x^3 - 15*x^2)*e^(3*x) - 8*(16*x^4 - 25*x^3)*e^(2*x) + 32*(4*x^3 - 6*x^2 + 3*x)*e^(4*x) + 144*e^(7*x) - 48*e^(8*x))/x^8

Placing the root at 0:  1161020
x |--> -1/36*(328*x^7 - 81*x^5*e^x + 36*(2*x - 3)*e^(6*x) + 18*(3*x^2 - 8*x + 2)*e^(5*x) - 18*(6*x^3 - 5*x^2)*e^(3*x) - 54*(x^4 - x^3)*e^(2*x) + 18*(3*x^3 - 8*x^2 + 4*x)*e^(4*x) + 108*e^(7*x) - 36*e^(8*x))/x^8

Placing the root at 2:  1569148
x |--> -1/240*(3217*x^7 - 1250*x^5*e^x + 240*(x - 3)*e^(6*x) + 120*(3*x^2 - 4*x + 2)*e^(5*x) - 40*(32*x^3 - 9*x^2)*e^(3*x) + 10*(125*x^5 + 64*x^3)*e^(2*x) + 80*(8*x^3 - 9*x^2 + 3*x)*e^(4*x) + 720*e^(7*x) - 240*e^(8*x))/x^8

Placing the root at 3:  3094302
x |--> -1/720*(23195*x^7 + 9651*x^6*e^x + 3750*x^5*e^(2*x) - 1920*x^3*e^(3*x) + 720*(x - 1)*e^(6*x) + 360*(3*x^2 - 2*x)*e^(5*x) + 120*(16*x^3 - 9*x^2)*e^(4*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8

Placing the root at 4:  2296070
x |--> -1/720*(16039*x^7 + 5625*x^6*e^x - 1920*x^4*e^(2*x) - 3000*x^3*e^(3*x) + 720*(2*x - 1)*e^(6*x) + 360*(3*x^2 - 4*x)*e^(5*x) + 120*(16*x^3 - 15*x^2)*e^(4*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8

Placing the root at 5:  1375024
x |--> -1/48*(543*x^7 - 164*x^5*e^x - 236*x^4*e^(2*x) + 48*(2*x - 3)*e^(6*x) - 48*(4*x - 1)*e^(5*x) + 24*(3*x^3 - 2*x^2 + 4*x)*e^(4*x) + 4*(41*x^4 - 18*x^3 + 12*x^2)*e^(3*x) + 144*e^(7*x) - 48*e^(8*x))/x^8

Placing the root at 6:  1888992
x |--> -1/360*(6073*x^7 - 2715*x^5*e^x + 360*(x - 3)*e^(6*x) - 360*(2*x - 1)*e^(5*x) + 180*(3*x^3 + 2*x)*e^(4*x) + 30*(41*x^4 - 18*x^3)*e^(3*x) + 15*(181*x^5 - 82*x^4)*e^(2*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8

Placing the root at 7:  3586178
x |--> -1/720*(27659*x^7 + 12146*x^6*e^x + 5430*x^5*e^(2*x) + 2460*x^4*e^(3*x) + 1080*x^3*e^(4*x) + 720*(x - 1)*e^(6*x) - 720*x*e^(5*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8

Placing the root at 1:  839720
x |--> -1/8*(49*x^7 + 16*x^4*e^x + 8*(x - 6)*e^(6*x) + 8*(x^2 - 3*x + 4)*e^(5*x) - 8*(2*x^4 - 3*x^3)*e^(2*x) + 8*(2*x^3 - 2*x^2 + 3*x - 1)*e^(4*x) - 8*(5*x^3 - x^2 + x)*e^(3*x) + 32*e^(7*x) - 8*e^(8*x))/x^8

Placing the root at 2:  1266552
x |--> -1/24*(257*x^7 - 98*x^5*e^x + 24*(x^2 + 4)*e^(5*x) + 24*(2*x^3 - 2*x^2 - 1)*e^(4*x) - 24*(4*x^3 - x^2)*e^(3*x) + 2*(49*x^5 + 24*x^3)*e^(2*x) - 144*e^(6*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 3:  2525180
x |--> -1/120*(3127*x^7 + 1285*x^6*e^x + 490*x^5*e^(2*x) - 240*x^3*e^(3*x) + 120*(x^2 + 1)*e^(5*x) + 120*(2*x^3 - x^2)*e^(4*x) - 360*e^(6*x) + 360*e^(7*x) - 120*e^(8*x))/x^8

Placing the root at 4:  1851948
x |--> -1/72*(1279*x^7 + 441*x^6*e^x - 144*x^4*e^(2*x) - 216*x^3*e^(3*x) + 72*(x - 3)*e^(6*x) + 72*(x^2 - 2*x + 1)*e^(5*x) + 72*(2*x^3 - x^2 + x)*e^(4*x) + 216*e^(7*x) - 72*e^(8*x))/x^8

Placing the root at 5:  984256
x |--> -1/24*(181*x^7 + 82*x^4*e^x + 24*(x - 6)*e^(6*x) - 24*(3*x - 4)*e^(5*x) + 12*(3*x^3 + 6*x - 2)*e^(4*x) - 4*(41*x^4 - 9*x^3)*e^(2*x) + 2*(41*x^4 - 36*x^3 - 12*x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 6:  2091712
x |--> -1/720*(14861*x^7 + 5430*x^6*e^x - 2460*x^4*e^(2*x) + 720*(x - 3)*e^(6*x) - 720*(2*x - 1)*e^(5*x) + 360*(3*x^3 + 2*x)*e^(4*x) + 60*(41*x^4 - 18*x^3)*e^(3*x) + 2160*e^(7*x) - 720*e^(8*x))/x^8

Placing the root at 0:  895160
x |--> -1/6*(41*x^7 - 9*x^5*e^x + 15*x^3*e^(2*x) + 6*(x - 6)*e^(6*x) + 6*(x^2 - 3*x + 4)*e^(5*x) + 3*(3*x^3 - 4*x^2 + 6*x - 2)*e^(4*x) - 6*(4*x^3 - x^2 + x)*e^(3*x) + 24*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 1:  720160
x |--> -1/8*(41*x^7 + 12*x^4*e^x + 16*(x - 3)*e^(6*x) - 16*(3*x - 2)*e^(5*x) - 8*(3*x^3 - 2*x^2 + 2*x)*e^(3*x) + 4*(3*x^3 - 2*x^2 + 12*x - 2)*e^(4*x) - 4*(3*x^4 - 3*x^3 + 2*x^2)*e^(2*x) + 32*e^(7*x) - 8*e^(8*x))/x^8

Placing the root at 2:  1110536
x |--> -1/12*(111*x^7 - 41*x^5*e^x + 12*(x - 6)*e^(6*x) - 12*(3*x - 4)*e^(5*x) - 12*(3*x^3 + x)*e^(3*x) + 6*(3*x^3 + 6*x - 2)*e^(4*x) + (41*x^5 + 18*x^3)*e^(2*x) + 48*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 3:  2246692
x |--> -1/720*(16501*x^7 + 6660*x^6*e^x + 2460*x^5*e^(2*x) - 1080*x^3*e^(3*x) + 720*(x - 3)*e^(6*x) - 720*(2*x - 1)*e^(5*x) + 360*(3*x^3 + 2*x)*e^(4*x) + 2160*e^(7*x) - 720*e^(8*x))/x^8

Placing the root at 4:  1621844
x |--> -1/144*(2203*x^7 + 738*x^6*e^x - 216*x^4*e^(2*x) + 144*(2*x - 3)*e^(6*x) - 144*(4*x - 1)*e^(5*x) - 72*(3*x^3 - 2*x^2)*e^(3*x) + 72*(3*x^3 - 2*x^2 + 4*x)*e^(4*x) + 432*e^(7*x) - 144*e^(8*x))/x^8

Placing the root at 1:  1225924
x |--> -1/48*(471*x^7 - 128*x^5*e^x + 48*(2*x - 3)*e^(6*x) - 96*(2*x^2 - x)*e^(4*x) + 24*(3*x^2 - 8*x + 2)*e^(5*x) - 8*(16*x^4 - 9*x^3)*e^(2*x) + 8*(16*x^4 - 9*x^3 + 15*x^2)*e^(3*x) + 144*e^(7*x) - 48*e^(8*x))/x^8

Placing the root at 2:  1725948
x |--> -1/720*(10931*x^7 - 4710*x^5*e^x + 720*(x - 3)*e^(6*x) + 360*(3*x^2 - 4*x + 2)*e^(5*x) - 720*(3*x^2 - x)*e^(4*x) + 120*(16*x^4 + 9*x^2)*e^(3*x) + 30*(157*x^5 - 64*x^4)*e^(2*x) + 2160*e^(7*x) - 720*e^(8*x))/x^8

Placing the root at 3:  3323678
x |--> -1/720*(25355*x^7 + 10931*x^6*e^x + 4710*x^5*e^(2*x) + 1920*x^4*e^(3*x) - 1080*x^2*e^(4*x) + 720*(x - 1)*e^(6*x) + 360*(3*x^2 - 2*x)*e^(5*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8

Placing the root at 0:  976640
x |--> -1/36*(256*x^7 + 81*x^4*e^x + 36*(2*x - 3)*e^(6*x) + 36*(3*x^2 - 4*x + 1)*e^(5*x) - 36*(7*x^2 - 2*x)*e^(4*x) - 36*(3*x^3 - 4*x^2)*e^(3*x) - 27*(3*x^4 - 4*x^3)*e^(2*x) + 108*e^(7*x) - 36*e^(8*x))/x^8

Placing the root at 7:  2152822
x |--> -1/36*(744*x^7 + 256*x^6*e^x - 81*x^4*e^(2*x) - 108*x^3*e^(3*x) - 144*x^2*e^(4*x) + 36*(2*x - 1)*e^(6*x) + 36*(3*x^2 - 2*x)*e^(5*x) + 72*e^(7*x) - 36*e^(8*x))/x^8

Placing the root at 1:  1066800
x |--> -1/8*(69*x^7 - 20*x^5*e^x - 28*x^4*e^(2*x) + 8*(x - 6)*e^(6*x) - 8*(3*x - 4)*e^(5*x) + 8*(x^3 + 3*x - 1)*e^(4*x) + 4*(5*x^4 - 2*x^3 - 2*x)*e^(3*x) + 32*e^(7*x) - 8*e^(8*x))/x^8

Placing the root at 2:  1492848
x |--> -1/12*(158*x^7 - 69*x^5*e^x + 12*(x^3 - 1)*e^(4*x) + 6*(5*x^4 - 2*x^3)*e^(3*x) + 3*(23*x^5 - 10*x^4)*e^(2*x) + 48*e^(5*x) - 72*e^(6*x) + 48*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 3:  2872212
x |--> -1/120*(3653*x^7 + 1580*x^6*e^x + 690*x^5*e^(2*x) + 300*x^4*e^(3*x) + 120*x^3*e^(4*x) + 120*e^(5*x) - 360*e^(6*x) + 360*e^(7*x) - 120*e^(8*x))/x^8

Placing the root at 4:  750456
x |--> -1/24*(125*x^7 - 64*x^3*e^x + 24*(x - 6)*e^(6*x) + 12*(3*x^2 - 6*x + 8)*e^(5*x) + 12*(16*x^3 - 3*x^2)*e^(2*x) + 4*(16*x^3 - 27*x^2 + 18*x - 6)*e^(4*x) - 12*(16*x^3 - 9*x^2 + 2*x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 5:  1709148
x |--> -1/120*(1921*x^7 + 625*x^6*e^x + 320*x^3*e^(2*x) + 120*(x - 3)*e^(6*x) + 60*(3*x^2 - 4*x + 2)*e^(5*x) - 20*(32*x^3 - 9*x^2)*e^(3*x) + 40*(8*x^3 - 9*x^2 + 3*x)*e^(4*x) + 360*e^(7*x) - 120*e^(8*x))/x^8

Placing the root at 0:  874440
x |--> -1/6*(40*x^7 - 9*x^5*e^x + 6*(x - 6)*e^(6*x) + 3*(3*x^2 - 6*x + 8)*e^(5*x) - 3*(2*x^4 + 3*x^2)*e^(2*x) - 3*(2*x^3 - 9*x^2 + 2*x)*e^(3*x) + 3*(2*x^3 - 9*x^2 + 6*x - 2)*e^(4*x) + 24*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 1:  967400
x |--> -1/8*(61*x^7 - 16*x^5*e^x + 8*(x - 6)*e^(6*x) + 8*(x^2 - 3*x + 4)*e^(5*x) - 8*(2*x^2 - 3*x + 1)*e^(4*x) - 8*(2*x^4 - x^3)*e^(2*x) + 8*(2*x^4 - x^3 + x^2 - x)*e^(3*x) + 32*e^(7*x) - 8*e^(8*x))/x^8

Placing the root at 2:  1384152
x |--> -1/24*(289*x^7 - 122*x^5*e^x + 24*(x^2 + 4)*e^(5*x) - 24*(2*x^2 + 1)*e^(4*x) + 24*(2*x^4 + x^2)*e^(3*x) + 2*(61*x^5 - 24*x^4)*e^(2*x) - 144*e^(6*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 3:  2697212
x |--> -1/120*(3397*x^7 + 1445*x^6*e^x + 610*x^5*e^(2*x) + 240*x^4*e^(3*x) - 120*x^2*e^(4*x) + 120*(x^2 + 1)*e^(5*x) - 360*e^(6*x) + 360*e^(7*x) - 120*e^(8*x))/x^8

Placing the root at 4:  875896
x |--> -1/24*(157*x^7 + 64*x^4*e^x + 24*(x - 6)*e^(6*x) + 12*(3*x^2 - 6*x + 8)*e^(5*x) - 12*(9*x^2 - 6*x + 2)*e^(4*x) - 4*(32*x^4 + 9*x^2)*e^(2*x) + 4*(16*x^4 + 27*x^2 - 6*x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 5:  1901788
x |--> -1/360*(6643*x^7 + 2355*x^6*e^x - 960*x^4*e^(2*x) + 360*(x - 3)*e^(6*x) + 180*(3*x^2 - 4*x + 2)*e^(5*x) - 360*(3*x^2 - x)*e^(4*x) + 60*(16*x^4 + 9*x^2)*e^(3*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8

Placing the root at 0:  751520
x |--> -1/6*(32*x^7 + 9*x^4*e^x + 6*(x - 6)*e^(6*x) + 3*(5*x^2 - 6*x + 8)*e^(5*x) - 3*(13*x^2 - 6*x + 2)*e^(4*x) - 3*(2*x^3 - 11*x^2 + 2*x)*e^(3*x) - 3*(3*x^4 - 2*x^3 + 3*x^2)*e^(2*x) + 24*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 7:  1693692
x |--> -1/36*(575*x^7 + 192*x^6*e^x - 54*x^4*e^(2*x) + 36*(x - 3)*e^(6*x) - 36*(4*x^2 - x)*e^(4*x) + 18*(5*x^2 - 4*x + 2)*e^(5*x) - 18*(2*x^3 - 3*x^2)*e^(3*x) + 108*e^(7*x) - 36*e^(8*x))/x^8

Placing the root at 1:  1093680
x |--> -1/8*(69*x^7 - 18*x^5*e^x + 24*(x - 1)*e^(6*x) - 8*(6*x - 1)*e^(5*x) - 24*(x^2 - x)*e^(4*x) + 6*(3*x^4 + 4*x^2)*e^(3*x) - 2*(9*x^4 - 4*x^3)*e^(2*x) + 24*e^(7*x) - 8*e^(8*x))/x^8

Placing the root at 2:  1562288
x |--> -1/36*(490*x^7 - 207*x^5*e^x + 36*(2*x - 3)*e^(6*x) - 36*(4*x - 1)*e^(5*x) - 36*(x^2 - 2*x)*e^(4*x) + 9*(9*x^4 + 4*x^2)*e^(3*x) + 9*(23*x^5 - 9*x^4)*e^(2*x) + 108*e^(7*x) - 36*e^(8*x))/x^8

Placing the root at 3:  3037930
x |--> -1/360*(11499*x^7 + 4900*x^6*e^x + 2070*x^5*e^(2*x) + 810*x^4*e^(3*x) - 360*x^2*e^(4*x) + 360*(2*x - 1)*e^(6*x) - 720*x*e^(5*x) + 720*e^(7*x) - 360*e^(8*x))/x^8

Placing the root at 4:  1311044
x |--> -1/144*(1573*x^7 - 576*x^5*e^x + 144*(2*x - 3)*e^(6*x) - 288*(2*x^2 - x)*e^(4*x) + 72*(3*x^2 - 8*x + 2)*e^(5*x) - 72*(3*x^3 - 5*x^2)*e^(3*x) + 72*(8*x^5 + 3*x^3)*e^(2*x) + 432*e^(7*x) - 144*e^(8*x))/x^8

Placing the root at 5:  2646406
x |--> -1/720*(19479*x^7 + 7865*x^6*e^x + 2880*x^5*e^(2*x) - 1080*x^3*e^(3*x) - 1800*x^2*e^(4*x) + 720*(2*x - 1)*e^(6*x) + 360*(3*x^2 - 4*x)*e^(5*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8

Placing the root at 0:  848820
x |--> -1/2*(12*x^7 + 3*x^4*e^x + 8*x^3*e^(2*x) + 6*(x - 1)*e^(6*x) - 6*(2*x^2 - x)*e^(4*x) + (3*x^2 - 12*x + 2)*e^(5*x) - 3*(2*x^3 - 3*x^2)*e^(3*x) + 6*e^(7*x) - 2*e^(8*x))/x^8

Placing the root at 1:  815920
x |--> -1/4*(25*x^7 - 6*x^5*e^x + 8*(x - 3)*e^(6*x) - 8*(3*x - 2)*e^(5*x) - 4*(x^2 - 6*x + 1)*e^(4*x) - 2*(3*x^4 + 2*x^2)*e^(2*x) + 2*(3*x^4 + 4*x^2 - 4*x)*e^(3*x) + 16*e^(7*x) - 4*e^(8*x))/x^8

Placing the root at 2:  1198736
x |--> -1/12*(123*x^7 - 50*x^5*e^x + 12*(x - 6)*e^(6*x) - 12*(3*x - 4)*e^(5*x) + 12*(3*x - 1)*e^(4*x) + 6*(3*x^4 - 2*x)*e^(3*x) + 2*(25*x^5 - 9*x^4)*e^(2*x) + 48*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 3:  2375716
x |--> -1/180*(4429*x^7 + 1845*x^6*e^x + 750*x^5*e^(2*x) + 270*x^4*e^(3*x) + 180*(x - 3)*e^(6*x) - 180*(2*x - 1)*e^(5*x) + 180*x*e^(4*x) + 540*e^(7*x) - 180*e^(8*x))/x^8

Placing the root at 4:  974456
x |--> -1/24*(189*x^7 - 64*x^5*e^x + 24*(x - 6)*e^(6*x) + 12*(3*x^2 - 6*x + 8)*e^(5*x) - 12*(9*x^2 - 6*x + 2)*e^(4*x) + 12*(9*x^2 - 2*x)*e^(3*x) + 4*(16*x^5 - 9*x^2)*e^(2*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 5:  2022748
x |--> -1/360*(7283*x^7 + 2835*x^6*e^x + 960*x^5*e^(2*x) + 540*x^2*e^(3*x) + 360*(x - 3)*e^(6*x) + 180*(3*x^2 - 4*x + 2)*e^(5*x) - 360*(3*x^2 - x)*e^(4*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8

Placing the root at 6:  1418564
x |--> -1/144*(1861*x^7 + 576*x^6*e^x + 216*x^3*e^(2*x) + 144*(2*x - 3)*e^(6*x) - 288*(2*x^2 - x)*e^(4*x) + 72*(3*x^2 - 8*x + 2)*e^(5*x) - 72*(3*x^3 - 5*x^2)*e^(3*x) + 432*e^(7*x) - 144*e^(8*x))/x^8

Placing the root at 0:  601720
x |--> -1/2*(8*x^7 - 3*x^3*e^x + 4*(x - 3)*e^(6*x) + (3*x^2 - 12*x + 8)*e^(5*x) - (11*x^2 - 12*x + 2)*e^(4*x) + (6*x^3 - 5*x^2)*e^(2*x) - (3*x^3 - 13*x^2 + 4*x)*e^(3*x) + 8*e^(7*x) - 2*e^(8*x))/x^8

Placing the root at 1:  425040
x |--> -1/6*(16*x^7 + 9*x^2*e^x + 6*(x - 10)*e^(6*x) + 3*(3*x^2 - 8*x + 20)*e^(5*x) - 6*(6*x^2 - 6*x + 5)*e^(4*x) - 6*(6*x^2 - x)*e^(2*x) + 6*(9*x^2 - 4*x + 1)*e^(3*x) + 30*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 2:  1046136
x |--> -1/24*(221*x^7 + 64*x^6*e^x - 36*x^2*e^(2*x) + 24*(x - 6)*e^(6*x) + 12*(3*x^2 - 6*x + 8)*e^(5*x) - 12*(9*x^2 - 6*x + 2)*e^(4*x) + 12*(9*x^2 - 2*x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 0:  604800
x |--> -1/2*(9*x^7 - 2*x^5*e^x + 2*(x - 10)*e^(6*x) - 4*(2*x - 5)*e^(5*x) + 2*(6*x - 5)*e^(4*x) + 2*(x^4 - 4*x + 1)*e^(3*x) - 2*(x^4 - x)*e^(2*x) + 10*e^(7*x) - 2*e^(8*x))/x^8

Placing the root at 6:  913920
x |--> -1/3*(23*x^7 - 9*x^5*e^x + 3*(x^4 + 1)*e^(3*x) + 3*(3*x^5 - x^4)*e^(2*x) - 15*e^(4*x) + 30*e^(5*x) - 30*e^(6*x) + 15*e^(7*x) - 3*e^(8*x))/x^8

Placing the root at 7:  1846824
x |--> -1/6*(113*x^7 + 46*x^6*e^x + 18*x^5*e^(2*x) + 6*x^4*e^(3*x) - 6*e^(4*x) + 24*e^(5*x) - 36*e^(6*x) + 24*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 1:  596400
x |--> -1/12*(49*x^7 - 24*x^3*e^x + 12*(x^2 + 10)*e^(5*x) + 12*(2*x^3 - 3*x^2 - 5)*e^(4*x) - 12*(6*x^3 - 3*x^2 - 1)*e^(3*x) + 12*(6*x^3 - x^2)*e^(2*x) - 120*e^(6*x) + 60*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 2:  1376312
x |--> -1/12*(153*x^7 + 49*x^6*e^x + 24*x^3*e^(2*x) + 12*(x^2 + 4)*e^(5*x) + 12*(2*x^3 - 2*x^2 - 1)*e^(4*x) - 12*(4*x^3 - x^2)*e^(3*x) - 72*e^(6*x) + 48*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 5:  762720
x |--> -1/4*(23*x^7 + 10*x^4*e^x + 4*(x^3 - 5)*e^(4*x) + 2*(5*x^4 - 4*x^3 + 2)*e^(3*x) - 4*(5*x^4 - x^3)*e^(2*x) + 40*e^(5*x) - 40*e^(6*x) + 20*e^(7*x) - 4*e^(8*x))/x^8

Placing the root at 6:  1647408
x |--> -1/24*(385*x^7 + 138*x^6*e^x - 60*x^4*e^(2*x) + 24*(x^3 - 1)*e^(4*x) + 12*(5*x^4 - 2*x^3)*e^(3*x) + 96*e^(5*x) - 144*e^(6*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 0:  673680
x |--> -(5*x^7 - x^5*e^x + (x^2 + 10)*e^(5*x) + (x^3 - 3*x^2 - 5)*e^(4*x) + (x^3 - x^2)*e^(2*x) - (2*x^3 - 3*x^2 - 1)*e^(3*x) - 10*e^(6*x) + 5*e^(7*x) - e^(8*x))/x^8

Placing the root at 1:  510720
x |--> -1/12*(41*x^7 - 18*x^3*e^x + 12*(x - 10)*e^(6*x) - 24*(2*x - 5)*e^(5*x) + 6*(3*x^3 + 12*x - 10)*e^(4*x) + 6*(9*x^3 + 2*x)*e^(2*x) - 6*(9*x^3 + 8*x - 2)*e^(3*x) + 60*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 2:  1202376
x |--> -1/24*(263*x^7 + 82*x^6*e^x + 36*x^3*e^(2*x) + 24*(x - 6)*e^(6*x) - 24*(3*x - 4)*e^(5*x) - 24*(3*x^3 + x)*e^(3*x) + 12*(3*x^3 + 6*x - 2)*e^(4*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 0:  540960
x |--> -1/4*(15*x^7 + 4*x^4*e^x + 4*(x - 10)*e^(6*x) - 8*(2*x - 5)*e^(5*x) + 4*(x^3 + 6*x - 5)*e^(4*x) - 4*(2*x^3 + 4*x - 1)*e^(3*x) - 4*(x^4 - x^3 - x)*e^(2*x) + 20*e^(7*x) - 4*e^(8*x))/x^8

Placing the root at 5:  855120
x |--> -1/2*(14*x^7 - 5*x^5*e^x + 2*(x^3 - 5)*e^(4*x) - 2*(2*x^3 - 1)*e^(3*x) + (5*x^5 + 2*x^3)*e^(2*x) + 20*e^(5*x) - 20*e^(6*x) + 10*e^(7*x) - 2*e^(8*x))/x^8

Placing the root at 6:  1760808
x |--> -1/24*(425*x^7 + 168*x^6*e^x + 60*x^5*e^(2*x) - 24*x^3*e^(3*x) + 24*(x^3 - 1)*e^(4*x) + 96*e^(5*x) - 144*e^(6*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 7:  1247400
x |--> -1/24*(277*x^7 + 90*x^6*e^x - 24*x^4*e^(2*x) + 24*(x - 6)*e^(6*x) - 24*(3*x - 4)*e^(5*x) - 24*(x^3 + x)*e^(3*x) + 24*(x^3 + 3*x - 1)*e^(4*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 1:  383040
x |--> -1/2*(5*x^7 - 2*x^3*e^x + 2*(x^3 - 15)*e^(4*x) - 6*(x^3 - 2)*e^(3*x) + 2*(3*x^3 - 1)*e^(2*x) + 40*e^(5*x) - 30*e^(6*x) + 12*e^(7*x) - 2*e^(8*x))/x^8

Placing the root at 2:  922320
x |--> -1/4*(33*x^7 + 10*x^6*e^x + 4*x^3*e^(2*x) + 4*(x^3 - 5)*e^(4*x) - 4*(2*x^3 - 1)*e^(3*x) + 40*e^(5*x) - 40*e^(6*x) + 20*e^(7*x) - 4*e^(8*x))/x^8

Placing the root at 1:  690480
x |--> -1/12*(61*x^7 + 24*x^4*e^x + 12*(x^2 + 10)*e^(5*x) - 12*(3*x^2 + 5)*e^(4*x) + 12*(2*x^4 + 3*x^2 + 1)*e^(3*x) - 12*(4*x^4 + x^2)*e^(2*x) - 120*e^(6*x) + 60*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 2:  1520792
x |--> -1/12*(175*x^7 + 61*x^6*e^x - 24*x^4*e^(2*x) + 12*(x^2 + 4)*e^(5*x) - 12*(2*x^2 + 1)*e^(4*x) + 12*(2*x^4 + x^2)*e^(3*x) - 72*e^(6*x) + 48*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 0:  577920
x |--> -(4*x^7 + x^4*e^x + 2*(x^2 + 5)*e^(5*x) + (6*x^2 + 1)*e^(3*x) - (6*x^2 + 5)*e^(4*x) - (x^4 + 2*x^2)*e^(2*x) - 10*e^(6*x) + 5*e^(7*x) - e^(8*x))/x^8

Placing the root at 7:  1330840
x |--> -1/3*(37*x^7 + 12*x^6*e^x - 3*x^4*e^(2*x) + 6*x^2*e^(3*x) + 6*(x^2 + 2)*e^(5*x) - 3*(4*x^2 + 1)*e^(4*x) - 18*e^(6*x) + 12*e^(7*x) - 3*e^(8*x))/x^8

Placing the root at 1:  780640
x |--> -1/4*(23*x^7 + 9*x^4*e^x + 8*(x - 3)*e^(6*x) - 8*(3*x - 2)*e^(5*x) - 4*(x^2 - 6*x + 1)*e^(4*x) - 2*(9*x^4 + 2*x^2)*e^(2*x) + (9*x^4 + 8*x^2 - 8*x)*e^(3*x) + 16*e^(7*x) - 4*e^(8*x))/x^8

Placing the root at 2:  1716848
x |--> -1/72*(1187*x^7 + 414*x^6*e^x - 162*x^4*e^(2*x) + 72*(2*x - 3)*e^(6*x) - 72*(4*x - 1)*e^(5*x) - 72*(x^2 - 2*x)*e^(4*x) + 18*(9*x^4 + 4*x^2)*e^(3*x) + 216*e^(7*x) - 72*e^(8*x))/x^8

Placing the root at 4:  1031240
x |--> -1/24*(203*x^7 - 72*x^5*e^x + 24*(x - 6)*e^(6*x) + 24*(x^2 - 3*x + 4)*e^(5*x) - 24*(2*x^2 - 3*x + 1)*e^(4*x) + 24*(3*x^5 + x^3)*e^(2*x) - 24*(x^3 - x^2 + x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 5:  2114700
x |--> -1/72*(1537*x^7 + 609*x^6*e^x + 216*x^5*e^(2*x) - 72*x^3*e^(3*x) + 72*(x - 3)*e^(6*x) + 72*(x^2 - 2*x + 1)*e^(5*x) - 72*(x^2 - x)*e^(4*x) + 216*e^(7*x) - 72*e^(8*x))/x^8

Placing the root at 0:  652680
x |--> -1/2*(9*x^7 + 2*x^4*e^x + 4*(x - 3)*e^(6*x) + 2*(x^2 - 6*x + 4)*e^(5*x) - 2*(3*x^2 - 6*x + 1)*e^(4*x) + 2*(2*x^3 - x^2)*e^(2*x) - 2*(2*x^3 - 3*x^2 + 2*x)*e^(3*x) + 8*e^(7*x) - 2*e^(8*x))/x^8

Placing the root at 1:  581280
x |--> -1/6*(25*x^7 + 9*x^4*e^x + 6*(x - 10)*e^(6*x) - 12*(2*x - 5)*e^(5*x) + 6*(6*x - 5)*e^(4*x) + 3*(3*x^4 - 8*x + 2)*e^(3*x) - 6*(3*x^4 - x)*e^(2*x) + 30*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 2:  1310736
x |--> -1/6*(74*x^7 + 25*x^6*e^x - 9*x^4*e^(2*x) + 6*(x - 6)*e^(6*x) - 6*(3*x - 4)*e^(5*x) + 6*(3*x - 1)*e^(4*x) + 3*(3*x^4 - 2*x)*e^(3*x) + 24*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 4:  764400
x |--> -1/12*(73*x^7 - 24*x^5*e^x + 12*(x^2 + 10)*e^(5*x) + 12*(3*x^2 + 1)*e^(3*x) - 12*(3*x^2 + 5)*e^(4*x) + 12*(2*x^5 - x^2)*e^(2*x) - 120*e^(6*x) + 60*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 5:  1611512
x |--> -1/12*(191*x^7 + 73*x^6*e^x + 24*x^5*e^(2*x) + 12*x^2*e^(3*x) + 12*(x^2 + 4)*e^(5*x) - 12*(2*x^2 + 1)*e^(4*x) - 72*e^(6*x) + 48*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 6:  1111880
x |--> -1/24*(239*x^7 + 72*x^6*e^x + 24*x^3*e^(2*x) + 24*(x - 6)*e^(6*x) + 24*(x^2 - 3*x + 4)*e^(5*x) - 24*(2*x^2 - 3*x + 1)*e^(4*x) - 24*(x^3 - x^2 + x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8

Placing the root at 0:  462000
x |--> -(3*x^7 - x^3*e^x + (x - 10)*e^(6*x) + (x^2 - 4*x + 10)*e^(5*x) - (3*x^2 - 6*x + 5)*e^(4*x) - (x^3 - 3*x^2 + 4*x - 1)*e^(3*x) + (2*x^3 - x^2 + x)*e^(2*x) + 5*e^(7*x) - e^(8*x))/x^8

Placing the root at 1:  430080
x |--> -(3*x^7 + x^4*e^x + (x^4 + 6)*e^(3*x) - (2*x^4 + 1)*e^(2*x) - 15*e^(4*x) + 20*e^(5*x) - 15*e^(6*x) + 6*e^(7*x) - e^(8*x))/x^8

Placing the root at 2:  994560
x |--> -1/6*(55*x^7 + 18*x^6*e^x - 6*x^4*e^(2*x) + 6*(x^4 + 1)*e^(3*x) - 30*e^(4*x) + 60*e^(5*x) - 60*e^(6*x) + 30*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 4:  818160
x |--> -1/12*(85*x^7 + 24*x^6*e^x - 12*x^2*e^(2*x) + 12*(x^2 + 10)*e^(5*x) + 12*(3*x^2 + 1)*e^(3*x) - 12*(3*x^2 + 5)*e^(4*x) - 120*e^(6*x) + 60*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 0:  325920
x |--> -(2*x^7 + x^2*e^x + 6*(x^2 + 1)*e^(3*x) + (x^2 + 20)*e^(5*x) - (4*x^2 + 1)*e^(2*x) - (4*x^2 + 15)*e^(4*x) - 15*e^(6*x) + 6*e^(7*x) - e^(8*x))/x^8

Placing the root at 1:  863800
x |--> -1/8*(55*x^7 - 18*x^5*e^x + 16*(x - 3)*e^(6*x) - 16*(3*x - 2)*e^(5*x) - 8*(x^2 - 6*x + 1)*e^(4*x) + 16*(x^2 - x)*e^(3*x) + 2*(9*x^5 - 4*x^2)*e^(2*x) + 32*e^(7*x) - 8*e^(8*x))/x^8

Placing the root at 2:  1818908
x |--> -1/72*(1295*x^7 + 495*x^6*e^x + 162*x^5*e^(2*x) + 72*x^2*e^(3*x) + 72*(2*x - 3)*e^(6*x) - 72*(4*x - 1)*e^(5*x) - 72*(x^2 - 2*x)*e^(4*x) + 216*e^(7*x) - 72*e^(8*x))/x^8

Placing the root at 0:  521640
x |--> -1/8*(27*x^7 - 8*x^3*e^x + 24*(x - 2)*e^(6*x) - 8*(9*x - 4)*e^(5*x) + 24*(2*x^2 - x)*e^(3*x) - 8*(3*x^2 - 9*x + 1)*e^(4*x) + 8*(x^3 - 3*x^2)*e^(2*x) + 32*e^(7*x) - 8*e^(8*x))/x^8

Placing the root at 7:  1256220
x |--> -1/8*(90*x^7 + 27*x^6*e^x + 8*x^3*e^(2*x) + 24*x^2*e^(3*x) + 24*(x - 1)*e^(6*x) - 8*(6*x - 1)*e^(5*x) - 24*(x^2 - x)*e^(4*x) + 24*e^(7*x) - 8*e^(8*x))/x^8

Placing the root at 1:  636720
x |--> -1/12*(59*x^7 - 18*x^5*e^x + 12*(x - 10)*e^(6*x) - 24*(2*x - 5)*e^(5*x) - 12*(4*x - 1)*e^(3*x) + 12*(6*x - 5)*e^(4*x) + 6*(3*x^5 + 2*x)*e^(2*x) + 60*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 2:  1378776
x |--> -1/12*(160*x^7 + 59*x^6*e^x + 18*x^5*e^(2*x) + 12*(x - 6)*e^(6*x) - 12*(3*x - 4)*e^(5*x) + 12*(3*x - 1)*e^(4*x) - 12*x*e^(3*x) + 48*e^(7*x) - 12*e^(8*x))/x^8

Placing the root at 5:  924280
x |--> -1/4*(32*x^7 + 9*x^6*e^x - 4*x^2*e^(2*x) + 8*(x - 3)*e^(6*x) - 8*(3*x - 2)*e^(5*x) - 4*(x^2 - 6*x + 1)*e^(4*x) + 8*(x^2 - x)*e^(3*x) + 16*e^(7*x) - 4*e^(8*x))/x^8

Placing the root at 0:  367920
x |--> -1/4*(9*x^7 + 4*x^2*e^x + 8*(x - 5)*e^(6*x) - 8*(4*x - 5)*e^(5*x) - 4*(x^2 - 12*x + 5)*e^(4*x) + 4*(3*x^2 - 8*x + 1)*e^(3*x) - 4*(3*x^2 - 2*x)*e^(2*x) + 20*e^(7*x) - 4*e^(8*x))/x^8

Placing the root at 1:  467040
x |--> -1/2*(7*x^7 - 2*x^5*e^x + 2*(x^5 - 1)*e^(2*x) + 12*e^(3*x) - 30*e^(4*x) + 40*e^(5*x) - 30*e^(6*x) + 12*e^(7*x) - 2*e^(8*x))/x^8

Placing the root at 2:  1039920
x |--> -1/6*(59*x^7 + 21*x^6*e^x + 6*x^5*e^(2*x) + 6*e^(3*x) - 30*e^(4*x) + 60*e^(5*x) - 60*e^(6*x) + 30*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 3:  677040
x |--> -1/6*(34*x^7 + 9*x^6*e^x + 6*(x - 10)*e^(6*x) - 12*(2*x - 5)*e^(5*x) - 6*(4*x - 1)*e^(3*x) + 6*(6*x - 5)*e^(4*x) + 6*x*e^(2*x) + 30*e^(7*x) - 6*e^(8*x))/x^8

Placing the root at 0:  258720
x |--> -1/2*(3*x^7 + 2*(x - 15)*e^(6*x) - 10*(x - 4)*e^(5*x) + 10*(2*x - 3)*e^(4*x) - 4*(5*x - 3)*e^(3*x) + 2*(5*x - 1)*e^(2*x) - 2*x*e^x + 12*e^(7*x) - 2*e^(8*x))/x^8

Placing the root at 1:  493920
x |--> -(4*x^7 + x^6*e^x - e^(2*x) + 6*e^(3*x) - 15*e^(4*x) + 20*e^(5*x) - 15*e^(6*x) + 6*e^(7*x) - e^(8*x))/x^8

Placing the root at 0:  181440
x |--> -(x^7 - 7*e^(2*x) + 21*e^(3*x) - 35*e^(4*x) + 35*e^(5*x) - 21*e^(6*x) + 7*e^(7*x) - e^(8*x) + e^x)/x^8

CPU time: 1185.43 s,  Wall time: 1188.21 s