syst := [-34992*P1^2*S1^3*S3*nu^12*w+2916*S1^3*S3^2*nu^12*w^2+2916*S1^2*S3^3*nu
^12*w^2+174960*P1^3*P3*S1^2*nu^12+116640*P1^3*S1^2*S3*nu^12-34992*P1^3*S1^2*nu^
12*w+23328*P1^3*S1*S3*nu^12*w+116640*P1^2*P3*S1^3*nu^12-34992*P1^2*P3*S1^2*nu^
12*w+73872*P1^2*S1^3*S3*nu^12+34992*P1^2*S1^3*S3*nu^11*w-69984*P1^2*S1^3*nu^12*
w-93312*P1^2*S1^2*S3*nu^12*w+34992*P1^2*S1^2*nu^12*w^2+5832*P1^2*S1*S3^2*nu^12*
w+34992*P1^2*S1*S3*nu^12*w^2+5832*P1^2*S3^3*nu^12*w-8748*P1*P3*S1^2*S3*nu^12*w-\
8748*P1*P3*S1*S3^2*nu^12*w+1944*P1*S1^2*S3^2*nu^12*w-2916*P1*S1^2*S3*nu^12*w^2+
1944*P1*S1*S3^3*nu^12*w-8748*P1*S1*S3^2*nu^12*w^2-8748*P1*S3^3*nu^12*w^2+5832*
P3^2*S1^3*nu^12*w+5832*P3^2*S1^2*S3*nu^12*w+1944*P3*S1^3*S3*nu^12*w-8748*P3*S1^
3*nu^12*w^2+1944*P3*S1^2*S3^2*nu^12*w-8748*P3*S1^2*S3*nu^12*w^2-2916*P3*S1*S3^2
*nu^12*w^2-1944*S1^3*S3^2*nu^12*w-11664*S1^3*S3^2*nu^11*w^2+2916*S1^3*nu^12*w^3
-1944*S1^2*S3^3*nu^12*w-11664*S1^2*S3^3*nu^11*w^2+4050*S1^2*S3^2*nu^12*w^2+2916
*S1^2*S3*nu^12*w^3+2916*S1*S3^2*nu^12*w^3-11664*S1*S3*nu^12*w^4+2916*S3^3*nu^12
*w^3-116640*P1^4*P3*nu^12-77760*P1^4*S3*nu^12+23328*P1^4*nu^12*w+38880*P1^3*P3*
S1*nu^12-151632*P1^3*P3*nu^12*w-145800*P1^3*S1^2*S3*nu^11+73872*P1^3*S1^2*nu^12
+34992*P1^3*S1^2*nu^11*w+28512*P1^3*S1*S3*nu^12-23328*P1^3*S1*S3*nu^11*w+23328*
P1^3*S1*nu^12*w-69984*P1^3*S3*nu^12*w+11664*P1^3*nu^12*w^2+29160*P1^2*P3^2*S1*
nu^12+29160*P1^2*P3^2*S3*nu^12-145800*P1^2*P3*S1^3*nu^11+151632*P1^2*P3*S1^2*nu
^12+34992*P1^2*P3*S1^2*nu^11*w+15552*P1^2*P3*S1*S3*nu^12-160380*P1^2*P3*S1*nu^
12*w+15552*P1^2*P3*S3^2*nu^12-11664*P1^2*P3*S3*nu^12*w+34992*P1^2*P3*nu^12*w^2-\
178848*P1^2*S1^3*S3*nu^11+44064*P1^2*S1^3*nu^12+157464*P1^2*S1^3*nu^11*w+93312*
P1^2*S1^2*S3*nu^12+157464*P1^2*S1^2*S3*nu^11*w-132192*P1^2*S1^2*nu^12*w-69984*
P1^2*S1^2*nu^11*w^2-1944*P1^2*S1*S3^2*nu^12-17496*P1^2*S1*S3^2*nu^11*w-121500*
P1^2*S1*S3*nu^12*w-69984*P1^2*S1*S3*nu^11*w^2+96228*P1^2*S1*nu^12*w^2-1944*P1^2
*S3^3*nu^12-17496*P1^2*S3^3*nu^11*w+8100*P1^2*S3^2*nu^12*w+75816*P1^2*S3*nu^12*
w^2-34992*P1^2*nu^12*w^3+15552*P1*P3^2*S1^2*nu^12+15552*P1*P3^2*S1*S3*nu^12-\
11664*P1*P3^2*S1*nu^12*w-20412*P1*P3^2*S3*nu^12*w+8100*P1*P3*S1^2*S3*nu^12+
26244*P1*P3*S1^2*S3*nu^11*w-15552*P1*P3*S1^2*nu^12*w+8100*P1*P3*S1*S3^2*nu^12+
26244*P1*P3*S1*S3^2*nu^11*w-31590*P1*P3*S1*S3*nu^12*w+17496*P1*P3*S1*nu^12*w^2-\
15552*P1*P3*S3^2*nu^12*w+17496*P1*P3*S3*nu^12*w^2+58320*P1*P3*nu^12*w^3-648*P1*
S1^2*S3^2*nu^12-8262*P1*S1^2*S3^2*nu^11*w+1944*P1*S1^2*S3*nu^12*w+11664*P1*S1^2
*S3*nu^11*w^2-648*P1*S1*S3^3*nu^12-8262*P1*S1*S3^3*nu^11*w+8532*P1*S1*S3^2*nu^
12*w+34992*P1*S1*S3^2*nu^11*w^2-4050*P1*S1*S3*nu^12*w^2-5832*P1*S1*nu^12*w^3+
5832*P1*S3^3*nu^12*w+34992*P1*S3^3*nu^11*w^2-12150*P1*S3^2*nu^12*w^2+6804*P1*S3
*nu^12*w^3-11664*P1*nu^12*w^4-1944*P3^2*S1^3*nu^12-17496*P3^2*S1^3*nu^11*w-1944
*P3^2*S1^2*S3*nu^12-17496*P3^2*S1^2*S3*nu^11*w+8100*P3^2*S1^2*nu^12*w+1944*P3^2
*S1*S3*nu^12*w+5832*P3^2*S1*nu^12*w^2+2916*P3^2*S3*nu^12*w^2-648*P3*S1^3*S3*nu^
12-8262*P3*S1^3*S3*nu^11*w+5832*P3*S1^3*nu^12*w+34992*P3*S1^3*nu^11*w^2-648*P3*
S1^2*S3^2*nu^12-8262*P3*S1^2*S3^2*nu^11*w+8532*P3*S1^2*S3*nu^12*w+34992*P3*S1^2
*S3*nu^11*w^2-12150*P3*S1^2*nu^12*w^2+1944*P3*S1*S3^2*nu^12*w+11664*P3*S1*S3^2*
nu^11*w^2-4050*P3*S1*S3*nu^12*w^2+6804*P3*S1*nu^12*w^3-5832*P3*S3*nu^12*w^3-\
11664*P3*nu^12*w^4+324*S1^3*S3^2*nu^12+9720*S1^3*S3^2*nu^11*w+17496*S1^3*S3^2*
nu^10*w^2-2916*S1^3*nu^12*w^2-14580*S1^3*nu^11*w^3+324*S1^2*S3^3*nu^12+9720*S1^
2*S3^3*nu^11*w+17496*S1^2*S3^3*nu^10*w^2-2700*S1^2*S3^2*nu^12*w-15552*S1^2*S3^2
*nu^11*w^2-2916*S1^2*S3*nu^12*w^2-14580*S1^2*S3*nu^11*w^3+4050*S1^2*nu^12*w^3-\
2916*S1*S3^2*nu^12*w^2-14580*S1*S3^2*nu^11*w^3+16686*S1*S3*nu^12*w^3+46656*S1*
S3*nu^11*w^4-8748*S1*nu^12*w^4-2916*S3^3*nu^12*w^2-14580*S3^3*nu^11*w^3+4050*S3
^2*nu^12*w^3-8748*S3*nu^12*w^4+11664*nu^12*w^5+97200*P1^4*S3*nu^11-49248*P1^4*
nu^12-23328*P1^4*nu^11*w+213840*P1^3*P3*S1*nu^11-34668*P1^3*P3*nu^12+151632*P1^
3*P3*nu^11*w+29160*P1^3*S1^2*S3*nu^10-178848*P1^3*S1^2*nu^11+99792*P1^3*S1*S3*
nu^11+19872*P1^3*S1*nu^12-104976*P1^3*S1*nu^11*w-19656*P1^3*S3*nu^12+157464*P1^
3*S3*nu^11*w-19764*P1^3*nu^12*w-23328*P1^3*nu^11*w^2-58320*P1^2*P3^2*S1*nu^11-\
58320*P1^2*P3^2*S3*nu^11+24948*P1^2*P3^2*nu^12+29160*P1^2*P3*S1^3*nu^10-198288*
P1^2*P3*S1^2*nu^11-50544*P1^2*P3*S1*S3*nu^11+70956*P1^2*P3*S1*nu^12+323676*P1^2
*P3*S1*nu^11*w-50544*P1^2*P3*S3^2*nu^11+25488*P1^2*P3*S3*nu^12+34992*P1^2*P3*S3
*nu^11*w-89586*P1^2*P3*nu^12*w-69984*P1^2*P3*nu^11*w^2+139968*P1^2*S1^3*S3*nu^
10-153576*P1^2*S1^3*nu^11-104976*P1^2*S1^3*nu^10*w-223560*P1^2*S1^2*S3*nu^11-\
34992*P1^2*S1^2*S3*nu^10*w+54000*P1^2*S1^2*nu^12+346032*P1^2*S1^2*nu^11*w+34992
*P1^2*S1^2*nu^10*w^2+7776*P1^2*S1*S3^2*nu^11+17496*P1^2*S1*S3^2*nu^10*w+34884*
P1^2*S1*S3*nu^12+288198*P1^2*S1*S3*nu^11*w+34992*P1^2*S1*S3*nu^10*w^2-108864*P1
^2*S1*nu^12*w-262440*P1^2*S1*nu^11*w^2+7776*P1^2*S3^3*nu^11+17496*P1^2*S3^3*nu^
10*w-2700*P1^2*S3^2*nu^12-23004*P1^2*S3^2*nu^11*w-51084*P1^2*S3*nu^12*w-250776*
P1^2*S3*nu^11*w^2+92502*P1^2*nu^12*w^2+104976*P1^2*nu^11*w^3-50544*P1*P3^2*S1^2
*nu^11-50544*P1*P3^2*S1*S3*nu^11+25488*P1*P3^2*S1*nu^12+34992*P1*P3^2*S1*nu^11*
w+11988*P1*P3^2*S3*nu^12+61236*P1*P3^2*S3*nu^11*w-12798*P1*P3^2*nu^12*w-34992*
P1*P3*S1^2*S3*nu^11-26244*P1*P3*S1^2*S3*nu^10*w+5184*P1*P3*S1^2*nu^12+66096*P1*
P3*S1^2*nu^11*w-34992*P1*P3*S1*S3^2*nu^11-26244*P1*P3*S1*S3^2*nu^10*w+17730*P1*
P3*S1*S3*nu^12+117126*P1*P3*S1*S3*nu^11*w-33264*P1*P3*S1*nu^12*w-69984*P1*P3*S1
*nu^11*w^2+5184*P1*P3*S3^2*nu^12+66096*P1*P3*S3^2*nu^11*w-33264*P1*P3*S3*nu^12*
w-69984*P1*P3*S3*nu^11*w^2-1620*P1*P3*nu^12*w^2-174960*P1*P3*nu^11*w^3+3402*P1*
S1^2*S3^2*nu^11+13608*P1*S1^2*S3^2*nu^10*w-324*P1*S1^2*S3*nu^12-9720*P1*S1^2*S3
*nu^11*w-17496*P1*S1^2*S3*nu^10*w^2+3402*P1*S1*S3^3*nu^11+13608*P1*S1*S3^3*nu^
10*w-1872*P1*S1*S3^2*nu^12-40203*P1*S1*S3^2*nu^11*w-52488*P1*S1*S3^2*nu^10*w^2+
2700*P1*S1*S3*nu^12*w+15552*P1*S1*S3*nu^11*w^2+5832*P1*S1*nu^12*w^2+29160*P1*S1
*nu^11*w^3-972*P1*S3^3*nu^12-29160*P1*S3^3*nu^11*w-52488*P1*S3^3*nu^10*w^2+8100
*P1*S3^2*nu^12*w+46656*P1*S3^2*nu^11*w^2-6804*P1*S3*nu^12*w^2-4860*P1*S3*nu^11*
w^3+8586*P1*nu^12*w^3+46656*P1*nu^11*w^4+7776*P3^2*S1^3*nu^11+17496*P3^2*S1^3*
nu^10*w+7776*P3^2*S1^2*S3*nu^11+17496*P3^2*S1^2*S3*nu^10*w-2700*P3^2*S1^2*nu^12
-23004*P3^2*S1^2*nu^11*w-648*P3^2*S1*S3*nu^12-8262*P3^2*S1*S3*nu^11*w-1188*P3^2
*S1*nu^12*w-23328*P3^2*S1*nu^11*w^2-1944*P3^2*S3*nu^12*w-11664*P3^2*S3*nu^11*w^
2+4050*P3^2*nu^12*w^2+3402*P3*S1^3*S3*nu^11+13608*P3*S1^3*S3*nu^10*w-972*P3*S1^
3*nu^12-29160*P3*S1^3*nu^11*w-52488*P3*S1^3*nu^10*w^2+3402*P3*S1^2*S3^2*nu^11+
13608*P3*S1^2*S3^2*nu^10*w-1872*P3*S1^2*S3*nu^12-40203*P3*S1^2*S3*nu^11*w-52488
*P3*S1^2*S3*nu^10*w^2+8100*P3*S1^2*nu^12*w+46656*P3*S1^2*nu^11*w^2-324*P3*S1*S3
^2*nu^12-9720*P3*S1*S3^2*nu^11*w-17496*P3*S1*S3^2*nu^10*w^2+2700*P3*S1*S3*nu^12
*w+15552*P3*S1*S3*nu^11*w^2-6804*P3*S1*nu^12*w^2-4860*P3*S1*nu^11*w^3+5832*P3*
S3*nu^12*w^2+29160*P3*S3*nu^11*w^3+8586*P3*nu^12*w^3+46656*P3*nu^11*w^4-1944*S1
^3*S3^2*nu^11-19440*S1^3*S3^2*nu^10*w-11664*S1^3*S3^2*nu^9*w^2+972*S1^3*nu^12*w
+17496*S1^3*nu^11*w^2+29160*S1^3*nu^10*w^3-1944*S1^2*S3^3*nu^11-19440*S1^2*S3^3
*nu^10*w-11664*S1^2*S3^3*nu^9*w^2+450*S1^2*S3^2*nu^12+13068*S1^2*S3^2*nu^11*w+
18468*S1^2*S3^2*nu^10*w^2+972*S1^2*S3*nu^12*w+17496*S1^2*S3*nu^11*w^2+29160*S1^
2*S3*nu^10*w^3-4050*S1^2*nu^12*w^2-19602*S1^2*nu^11*w^3+972*S1*S3^2*nu^12*w+
17496*S1*S3^2*nu^11*w^2+29160*S1*S3^2*nu^10*w^3-8910*S1*S3*nu^12*w^2-75006*S1*
S3*nu^11*w^3-69984*S1*S3*nu^10*w^4+10692*S1*nu^12*w^3+34992*S1*nu^11*w^4+972*S3
^3*nu^12*w+17496*S3^3*nu^11*w^2+29160*S3^3*nu^10*w^3-4050*S3^2*nu^12*w^2-19602*
S3^2*nu^11*w^3+10692*S3*nu^12*w^3+34992*S3*nu^11*w^4-16524*nu^12*w^4-58320*nu^
11*w^5-19440*P1^4*S3*nu^10+119232*P1^4*nu^11-252720*P1^3*P3*S1*nu^10+206712*P1^
3*P3*nu^11+139968*P1^3*S1^2*nu^10-326592*P1^3*S1*S3*nu^10+32400*P1^3*S1*nu^11+
139968*P1^3*S1*nu^10*w+148554*P1^3*S3*nu^11-104976*P1^3*S3*nu^10*w-10260*P1^3*
nu^12+46332*P1^3*nu^11*w+11664*P1^3*nu^10*w^2+29160*P1^2*P3^2*S1*nu^10+29160*P1
^2*P3^2*S3*nu^10-23976*P1^2*P3^2*nu^11-93312*P1^2*P3*S1^2*nu^10+58320*P1^2*P3*
S1*S3*nu^10-74358*P1^2*P3*S1*nu^11-166212*P1^2*P3*S1*nu^10*w+58320*P1^2*P3*S3^2
*nu^10-82296*P1^2*P3*S3*nu^11-34992*P1^2*P3*S3*nu^10*w+17622*P1^2*P3*nu^12+
252558*P1^2*P3*nu^11*w+34992*P1^2*P3*nu^10*w^2-38880*P1^2*S1^3*S3*nu^9+200232*
P1^2*S1^3*nu^10+17496*P1^2*S1^3*nu^9*w+75816*P1^2*S1^2*S3*nu^10-29160*P1^2*S1^2
*S3*nu^9*w-181872*P1^2*S1^2*nu^11-225504*P1^2*S1^2*nu^10*w-11664*P1^2*S1*S3^2*
nu^10-5832*P1^2*S1*S3^2*nu^9*w-47574*P1^2*S1*S3*nu^11-127332*P1^2*S1*S3*nu^10*w
+20412*P1^2*S1*nu^12+320274*P1^2*S1*nu^11*w+209952*P1^2*S1*nu^10*w^2-11664*P1^2
*S3^3*nu^10-5832*P1^2*S3^3*nu^9*w+10368*P1^2*S3^2*nu^11+13932*P1^2*S3^2*nu^10*w
+3420*P1^2*S3*nu^12+184167*P1^2*S3*nu^11*w+297432*P1^2*S3*nu^10*w^2-34452*P1^2*
nu^12*w-377136*P1^2*nu^11*w^2-104976*P1^2*nu^10*w^3+58320*P1*P3^2*S1^2*nu^10+
58320*P1*P3^2*S1*S3*nu^10-82296*P1*P3^2*S1*nu^11-34992*P1*P3^2*S1*nu^10*w-50544
*P1*P3^2*S3*nu^11-61236*P1*P3^2*S3*nu^10*w+11466*P1*P3^2*nu^12+14418*P1*P3^2*nu
^11*w+59292*P1*P3*S1^2*S3*nu^10+8748*P1*P3*S1^2*S3*nu^9*w-27216*P1*P3*S1^2*nu^
11-108864*P1*P3*S1^2*nu^10*w+59292*P1*P3*S1*S3^2*nu^10+8748*P1*P3*S1*S3^2*nu^9*
w-80820*P1*P3*S1*S3*nu^11-156978*P1*P3*S1*S3*nu^10*w+9144*P1*P3*S1*nu^12+146664
*P1*P3*S1*nu^11*w+104976*P1*P3*S1*nu^10*w^2-27216*P1*P3*S3^2*nu^11-108864*P1*P3
*S3^2*nu^10*w+9144*P1*P3*S3*nu^12+146664*P1*P3*S3*nu^11*w+104976*P1*P3*S3*nu^10
*w^2-18360*P1*P3*nu^12*w+15552*P1*P3*nu^11*w^2+174960*P1*P3*nu^10*w^3-7290*P1*
S1^2*S3^2*nu^10-10692*P1*S1^2*S3^2*nu^9*w+1944*P1*S1^2*S3*nu^11+19440*P1*S1^2*
S3*nu^10*w+11664*P1*S1^2*S3*nu^9*w^2-7290*P1*S1*S3^3*nu^10-10692*P1*S1*S3^3*nu^
9*w+10413*P1*S1*S3^2*nu^11+73224*P1*S1*S3^2*nu^10*w+34992*P1*S1*S3^2*nu^9*w^2-\
450*P1*S1*S3*nu^12-13068*P1*S1*S3*nu^11*w-18468*P1*S1*S3*nu^10*w^2-1944*P1*S1*
nu^12*w-34992*P1*S1*nu^11*w^2-58320*P1*S1*nu^10*w^3+5832*P1*S3^3*nu^11+58320*P1
*S3^3*nu^10*w+34992*P1*S3^3*nu^9*w^2-1350*P1*S3^2*nu^12-39204*P1*S3^2*nu^11*w-\
55404*P1*S3^2*nu^10*w^2+2268*P1*S3*nu^12*w+11664*P1*S3*nu^11*w^2-48600*P1*S3*nu
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49320*P1*P3^2*nu^9+103680*P1*P3^2*nu^8*w-3888*P1*P3*S1^2*S3*nu^7+38880*P1*P3*S1
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42228*P1^3*nu^6+14382*P1^2*P3*nu^6+6696*P1^2*S1^2*nu^5-6264*P1^2*S1*S3*nu^5-\
74520*P1^2*S1*nu^6+972*P1^2*S1*nu^5*w+39303*P1^2*S3*nu^6+6696*P1^2*S3*nu^5*w+
156996*P1^2*nu^7-82404*P1^2*nu^6*w-28710*P1*P3^2*nu^6+4392*P1*P3*S1*S3*nu^5-\
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13014*S1*S3*nu^5*w-648*S1*S3*nu^4*w^2-15318*S1*nu^7-77112*S1*nu^6*w-30861*S1*nu
^5*w^2+2592*S1*nu^4*w^3+864*S3^3*nu^5+5544*S3^2*nu^6+22842*S3^2*nu^5*w+3240*S3^
2*nu^4*w^2-15318*S3*nu^7-77112*S3*nu^6*w-30861*S3*nu^5*w^2+2592*S3*nu^4*w^3+
6840*nu^8+60480*nu^7*w+42336*nu^6*w^2-45360*nu^5*w^3-3888*nu^4*w^4+1296*P1^3*nu
^4+936*P1^2*P3*nu^4+9315*P1^2*S1*nu^4+11223*P1^2*S3*nu^4-38160*P1^2*nu^5-14256*
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*nu^6-32670*P1*nu^5*w-7128*P1*nu^4*w^2+180*P3^2*S1*nu^4+2232*P3^2*nu^5+1080*P3*
S1^2*nu^4+360*P3*S1*S3*nu^4-5544*P3*S1*nu^5-1728*P3*S3*nu^5-504*P3*nu^6-32670*
P3*nu^5*w-7128*P3*nu^4*w^2-108*S1^3*nu^4-108*S1^2*S3*nu^4-6192*S1^2*nu^5-7776*
S1^2*nu^4*w-108*S1*S3^2*nu^4-5904*S1*S3*nu^5-1296*S1*S3*nu^4*w+16758*S1*nu^6+
35316*S1*nu^5*w-2673*S1*nu^4*w^2-324*S1*nu^3*w^3-108*S3^3*nu^4-6192*S3^2*nu^5-\
7776*S3^2*nu^4*w+16758*S3*nu^6+35316*S3*nu^5*w-2673*S3*nu^4*w^2-324*S3*nu^3*w^3
-11376*nu^7-48384*nu^6*w+19008*nu^5*w^2+25920*nu^4*w^3-1620*P1^2*S1*nu^3-1620*
P1^2*S3*nu^3+23076*P1^2*nu^4+1296*P1^2*nu^3*w-5040*P1*P3*nu^4+216*P1*S1*nu^4+
828*P1*S3*nu^4+6480*P1*nu^5+14256*P1*nu^4*w-360*P3^2*nu^4+828*P3*S1*nu^4+216*P3
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2*nu^4+1080*S3^2*nu^3*w-10764*S3*nu^5-4860*S3*nu^4*w+2916*S3*nu^3*w^2+11592*nu^
6+13824*nu^5*w-33480*nu^4*w^2-5184*nu^3*w^3+108*P1^2*S1*nu^2+108*P1^2*S3*nu^2-\
5184*P1^2*nu^3-5166*P1*nu^4-2376*P1*nu^3*w-5166*P3*nu^4-2376*P3*nu^3*w-984*S1^2
*nu^3-120*S1*S3*nu^3+3492*S1*nu^4-2511*S1*nu^3*w-324*S1*nu^2*w^2-984*S3^2*nu^3+
3492*S3*nu^4-2511*S3*nu^3*w-324*S3*nu^2*w^2-6624*nu^5+9504*nu^4*w+15552*nu^3*w^
2+432*P1^2*nu^2+1848*P1*nu^3+1848*P3*nu^3+120*S1^2*nu^2-24*S1*S3*nu^2+27*S1*nu^
3+1080*S1*nu^2*w+120*S3^2*nu^2+27*S3*nu^3+1080*S3*nu^2*w+900*nu^4-10656*nu^3*w-\
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S3*nu*w+1560*nu^3+4032*nu^2*w+132*S1*nu+132*S3*nu-1212*nu^2-576*nu*w-12*S1-12*
S3+384*nu-48, -34992*S1^5*S3*nu^12*w+174960*P1*P3*S1^4*nu^12+116640*P1*S1^4*S3*
nu^12-34992*P1*S1^4*nu^12*w+116640*P3*S1^5*nu^12-34992*P3*S1^4*nu^12*w+73872*S1
^5*S3*nu^12+34992*S1^5*S3*nu^11*w-69984*S1^5*nu^12*w-93312*S1^4*S3*nu^12*w+
34992*S1^4*nu^12*w^2-8748*S1^3*S3^2*nu^12*w+34992*S1^3*S3*nu^12*w^2-8748*S1^2*
S3^3*nu^12*w+34992*P1^2*S1*S3*nu^12*w+116640*P1*P3*S1^3*nu^12+43740*P1*P3*S1^2*
S3*nu^12-174960*P1*P3*S1^2*nu^12*w+43740*P1*P3*S1*S3^2*nu^12-145800*P1*S1^4*S3*
nu^11+73872*P1*S1^4*nu^12+34992*P1*S1^4*nu^11*w+77760*P1*S1^3*S3*nu^12-23328*P1
*S1^3*nu^12*w+29160*P1*S1^2*S3^2*nu^12-148716*P1*S1^2*S3*nu^12*w+34992*P1*S1^2*
nu^12*w^2+29160*P1*S1*S3^3*nu^12+8748*P1*S1*S3^2*nu^12*w+69984*P1*S1*S3*nu^12*w
^2+8748*P1*S3^3*nu^12*w-145800*P3*S1^5*nu^11+151632*P3*S1^4*nu^12+34992*P3*S1^4
*nu^11*w+29160*P3*S1^3*S3*nu^12-131220*P3*S1^3*nu^12*w+29160*P3*S1^2*S3^2*nu^12
+8748*P3*S1^2*S3*nu^12*w+34992*P3*S1^2*nu^12*w^2-8748*P3*S1*S3^2*nu^12*w-178848
*S1^5*S3*nu^11+44064*S1^5*nu^12+157464*S1^5*nu^11*w+93312*S1^4*S3*nu^12+157464*
S1^4*S3*nu^11*w-132192*S1^4*nu^12*w-69984*S1^4*nu^11*w^2+18468*S1^3*S3^2*nu^12+
26244*S1^3*S3^2*nu^11*w-123444*S1^3*S3*nu^12*w-69984*S1^3*S3*nu^11*w^2+84564*S1
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12*w+61236*S1^2*S3*nu^12*w^2-34992*S1^2*nu^12*w^3-8748*S1*S3^2*nu^12*w^2+34992*
S1*S3*nu^12*w^3-8748*S3^3*nu^12*w^2-174960*P1^3*P3*nu^12-116640*P1^3*S3*nu^12+
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*S1^2*S3*nu^11+92340*P1*P3*S1^2*nu^12+174960*P1*P3*S1^2*nu^11*w-87480*P1*P3*S1*
S3^2*nu^11+2430*P1*P3*S1*S3*nu^12-274104*P1*P3*S1*nu^12*w-17496*P1*P3*S3*nu^12*
w-104976*P1*P3*nu^12*w^2+29160*P1*S1^4*S3*nu^10-178848*P1*S1^4*nu^11-19440*P1*
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12+288684*P1*S1^2*S3*nu^11*w-123444*P1*S1^2*nu^12*w-69984*P1*S1^2*nu^11*w^2-\
94770*P1*S1*S3^3*nu^11+22032*P1*S1*S3^2*nu^12-26244*P1*S1*S3^2*nu^11*w-212382*
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*nu^12-26244*P1*S3^3*nu^11*w+12150*P1*S3^2*nu^12*w+32076*P1*S3*nu^12*w^2-34992*
P1*nu^12*w^3+29160*P3^2*S1*S3*nu^12-8748*P3^2*S3*nu^12*w+29160*P3*S1^5*nu^10-\
198288*P3*S1^4*nu^11-94770*P3*S1^3*S3*nu^11+40500*P3*S1^3*nu^12+236196*P3*S1^3*
nu^11*w-94770*P3*S1^2*S3^2*nu^11+22032*P3*S1^2*S3*nu^12-26244*P3*S1^2*S3*nu^11*
w-64638*P3*S1^2*nu^12*w-69984*P3*S1^2*nu^11*w^2+18468*P3*S1*S3^2*nu^12+26244*P3
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12*w^2+34992*P3*nu^12*w^3+139968*S1^5*S3*nu^10-153576*S1^5*nu^11-104976*S1^5*nu
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nu^11*w+34992*S1^4*nu^10*w^2-81648*S1^3*S3^2*nu^11-26244*S1^3*S3^2*nu^10*w+
35532*S1^3*S3*nu^12+296460*S1^3*S3*nu^11*w+34992*S1^3*S3*nu^10*w^2-85536*S1^3*
nu^12*w-215784*S1^3*nu^11*w^2-81648*S1^2*S3^3*nu^11-26244*S1^2*S3^3*nu^10*w+
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34992*S1*S3^2*nu^11*w^2-100602*S1*S3*nu^12*w^2-104976*S1*S3*nu^11*w^3+26244*S1*
nu^12*w^3+21384*S3^3*nu^12*w+34992*S3^3*nu^11*w^2-12150*S3^2*nu^12*w^2+26244*S3
*nu^12*w^3-34992*nu^12*w^4+145800*P1^3*S3*nu^11-73872*P1^3*nu^12-34992*P1^3*nu^
11*w+174960*P1^2*P3*S1*nu^11+16038*P1^2*P3*nu^12+314928*P1^2*P3*nu^11*w+64638*
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+367416*P1^2*S3*nu^11*w-80190*P1^2*nu^12*w-69984*P1^2*nu^11*w^2-87480*P1*P3^2*
S3*nu^11+60750*P1*P3^2*nu^12-233280*P1*P3*S1^3*nu^10+43740*P1*P3*S1^2*S3*nu^10+
68040*P1*P3*S1^2*nu^11+43740*P1*P3*S1*S3^2*nu^10+77760*P1*P3*S1*S3*nu^11+105624
*P1*P3*S1*nu^12+577368*P1*P3*S1*nu^11*w+36936*P1*P3*S3*nu^12+52488*P1*P3*S3*nu^
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^11*w+69984*P1*S1*S3*nu^10*w^2-199584*P1*S1*nu^12*w-548208*P1*S1*nu^11*w^2+
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11*w-72576*P1*S3*nu^12*w-110808*P1*S3*nu^11*w^2+100602*P1*nu^12*w^2+104976*P1*
nu^11*w^3-94770*P3^2*S1*S3*nu^11+40500*P3^2*S1*nu^12+18468*P3^2*S3*nu^12+26244*
P3^2*S3*nu^11*w-12150*P3^2*nu^12*w-93312*P3*S1^4*nu^10+109350*P3*S1^3*S3*nu^10+
57834*P3*S1^3*nu^11-78732*P3*S1^3*nu^10*w+109350*P3*S1^2*S3^2*nu^10-43497*P3*S1
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+34992*P3*S1^2*nu^10*w^2-81648*P3*S1*S3^2*nu^11-26244*P3*S1*S3^2*nu^10*w+25650*
P3*S1*S3*nu^12+34506*P3*S1*S3*nu^11*w+27216*P3*S1*nu^12*w+344088*P3*S1*nu^11*w^
2-42768*P3*S3*nu^12*w-69984*P3*S3*nu^11*w^2-76302*P3*nu^12*w^2-104976*P3*nu^11*
w^3-38880*S1^5*S3*nu^9+200232*S1^5*nu^10+17496*S1^5*nu^9*w+75816*S1^4*S3*nu^10-\
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nu^12+195858*S1^3*nu^11*w+139968*S1^3*nu^10*w^2+142884*S1^2*S3^3*nu^10+8748*S1^
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^2-78732*S3*nu^11*w^3+100116*nu^12*w^3+139968*nu^11*w^4-29160*P1^3*S3*nu^10+
178848*P1^3*nu^11-218700*P1^2*P3*S1*nu^10+242028*P1^2*P3*nu^11-263898*P1^2*S1*
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*P1*P3^2*S3*nu^10-111780*P1*P3^2*nu^11-393660*P1*P3*S1^2*nu^10-225990*P1*P3*S1*
S3*nu^10-140940*P1*P3*S1*nu^11-332424*P1*P3*S1*nu^10*w-163296*P1*P3*S3*nu^11-\
52488*P1*P3*S3*nu^10*w+58752*P1*P3*nu^12+443232*P1*P3*nu^11*w-104976*P1*P3*nu^
10*w^2-38880*P1*S1^4*nu^9+213840*P1*S1^3*S3*nu^9-124416*P1*S1^3*nu^10-46656*P1*
S1^3*nu^9*w-51030*P1*S1^2*S3^2*nu^9-158922*P1*S1^2*S3*nu^10-8748*P1*S1^2*S3*nu^
9*w-50976*P1*S1^2*nu^11-140940*P1*S1^2*nu^10*w-51030*P1*S1*S3^3*nu^9-44469*P1*
S1*S3^2*nu^10-8748*P1*S1*S3^2*nu^9*w-138240*P1*S1*S3*nu^11-431082*P1*S1*S3*nu^
10*w+36072*P1*S1*nu^12+715716*P1*S1*nu^11*w+559872*P1*S1*nu^10*w^2-142884*P1*S3
^3*nu^10-8748*P1*S3^3*nu^9*w+109296*P1*S3^2*nu^11+20898*P1*S3^2*nu^10*w+10260*
P1*S3*nu^12+337446*P1*S3*nu^11*w+139968*P1*S3*nu^10*w^2-61452*P1*nu^12*w-408240
*P1*nu^11*w^2-104976*P1*nu^10*w^3+109350*P3^2*S1*S3*nu^10-125145*P3^2*S1*nu^11-\
81648*P3^2*S3*nu^11-26244*P3^2*S3*nu^10*w+25650*P3^2*nu^12+34506*P3^2*nu^11*w+
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^9*w-51030*P3*S1^2*S3^2*nu^9-44469*P3*S1^2*S3*nu^10-8748*P3*S1^2*S3*nu^9*w+
131328*P3*S1^2*nu^11-248346*P3*S1^2*nu^10*w+142884*P3*S1*S3^2*nu^10+8748*P3*S1*
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104976*P3*S3*nu^10*w^2+2052*P3*nu^12*w+314928*P3*nu^11*w^2+104976*P3*nu^10*w^3+
3888*S1^5*S3*nu^8-120204*S1^5*nu^9+185652*S1^4*S3*nu^9+162864*S1^4*nu^10-77760*
S1^4*nu^9*w-124416*S1^3*S3^2*nu^9-173124*S1^3*S3*nu^10-121500*S1^3*S3*nu^9*w-\
7398*S1^3*nu^11+104004*S1^3*nu^10*w+29160*S1^3*nu^9*w^2-124416*S1^2*S3^3*nu^9+
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39528*S3^3*nu^11+253692*S3^3*nu^10*w+34992*S3^3*nu^9*w^2-8550*S3^2*nu^12-154548
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2*nu^10*w-7290*P1*P3^2*nu^10+213840*P1*P3*S1^2*nu^9+208980*P1*P3*S1*S3*nu^9-\
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18900*P3^2*nu^8-72414*P3^2*nu^7*w-2916*P3*S1^3*nu^6+26865*P3*S1^2*S3*nu^6-\
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w^2+113400*P3*S3*nu^8+151632*P3*S3*nu^7*w+5832*P3*S3*nu^6*w^2-104166*P3*nu^9-\
198288*P3*nu^8*w+184842*P3*nu^7*w^2+38556*S1^3*nu^7+19440*S1^3*nu^6*w-32994*S1^
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432*S1*S3*nu^3*w-61128*S1*nu^5-3726*S1*nu^4*w+3888*S1*nu^3*w^2+17982*S3^2*nu^4+
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-47412*nu^3*w-3888*nu^2*w^2-792*P1*nu^2-792*P3*nu^2-2385*S1*nu^2-216*S1*nu*w-\
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+265383*S3*nu^8*w^2+276426*S3*nu^7*w^3+14580*S3*nu^6*w^4-3504*nu^10*w-106704*nu
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+37980*P1^2*P3*nu^7-162*P1^2*S1*S3*nu^6-1296*P1^2*S1*nu^7+2160*P1^2*S3^2*nu^6-\
3897*P1^2*S3*nu^7-3348*P1^2*S3*nu^6*w+2052*P1^2*nu^8-5076*P1^2*nu^7*w-3240*P1^2
*nu^6*w^2-4320*P1*P3^2*S1*nu^6-972*P1*P3^2*S3*nu^6+294804*P1*P3^2*nu^7+1296*P1*
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1296*P1*P3*S3^2*nu^6+2664*P1*P3*S3*nu^7+26784*P1*P3*S3*nu^6*w+28728*P1*P3*nu^8-\
71064*P1*P3*nu^7*w-45360*P1*P3*nu^6*w^2-324*P1*S1^2*S3*nu^6+1755*P1*S1*S3^2*nu^
6+540*P1*S1*S3^2*nu^5*w-72*P1*S1*S3*nu^7-6912*P1*S1*S3*nu^6*w+3240*P1*S1*nu^8+
19440*P1*S1*nu^7*w+5832*P1*S1*nu^6*w^2-972*P1*S3^3*nu^6-216*P1*S3^2*nu^7-20736*
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P1*nu^9-119556*P1*nu^8*w-192456*P1*nu^7*w^2+6480*P3^3*S1*nu^6-7776*P3^3*S3*nu^6
+256824*P3^3*nu^7+2160*P3^2*S1^2*nu^6-105462*P3^2*S1*S3*nu^6+517194*P3^2*S1*nu^
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6*w-548136*P3^2*nu^8-877824*P3^2*nu^7*w+4536*P3^2*nu^6*w^2-972*P3*S1^3*nu^6+
1755*P3*S1^2*S3*nu^6+540*P3*S1^2*S3*nu^5*w-216*P3*S1^2*nu^7-20736*P3*S1^2*nu^6*
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106920*P3*S1*nu^7*w+32076*P3*S1*nu^6*w^2+3240*P3*S3*nu^8+19440*P3*S3*nu^7*w+
5832*P3*S3*nu^6*w^2-6804*P3*nu^9-119556*P3*nu^8*w-192456*P3*nu^7*w^2+2160*S1^3*
nu^7+4860*S1^3*nu^6*w-1998*S1^2*S3^2*nu^6-2160*S1^2*S3^2*nu^5*w+2160*S1^2*S3*nu
^7+4860*S1^2*S3*nu^6*w-1986*S1^2*nu^8-5940*S1^2*nu^7*w+17982*S1^2*nu^6*w^2+3240
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*S3*nu^7*w+98658*S1*S3*nu^6*w^2+648*S1*S3*nu^5*w^3-3781*S1*nu^9-101034*S1*nu^8*
w-356454*S1*nu^7*w^2-140184*S1*nu^6*w^3+2160*S3^3*nu^7+4860*S3^3*nu^6*w-1986*S3
^2*nu^8-5940*S3^2*nu^7*w+17982*S3^2*nu^6*w^2+3240*S3^2*nu^5*w^3-3781*S3*nu^9-\
101034*S3*nu^8*w-356454*S3*nu^7*w^2-140184*S3*nu^6*w^3+292*nu^10+27216*nu^9*w+
307368*nu^8*w^2+540000*nu^7*w^3+80676*nu^6*w^4-21006*P1^2*P3*nu^6+324*P1^2*S1*
nu^6+3375*P1^2*S3*nu^6+540*P1^2*S3*nu^5*w+72*P1^2*nu^7+6912*P1^2*nu^6*w-58266*
P1*P3^2*nu^6+3672*P1*P3*S1*S3*nu^5-19872*P1*P3*S1*nu^6-4320*P1*P3*S1*nu^5*w-\
19872*P1*P3*S3*nu^6-4320*P1*P3*S3*nu^5*w+1008*P1*P3*nu^7+96768*P1*P3*nu^6*w-\
1296*P1*S1*S3^2*nu^5+1998*P1*S1*S3*nu^6+2160*P1*S1*S3*nu^5*w-4320*P1*S1*nu^7-\
9720*P1*S1*nu^6*w+5994*P1*S3^2*nu^6+6480*P1*S3^2*nu^5*w-23760*P1*S3*nu^7-53460*
P1*S3*nu^6*w+19062*P1*nu^8+140940*P1*nu^7*w+62694*P1*nu^6*w^2-5832*P1*nu^5*w^3-\
37260*P3^3*nu^6+7128*P3^2*S1*S3*nu^5-208098*P3^2*S1*nu^6+4428*P3^2*S1*nu^5*w+
9720*P3^2*S3^2*nu^5-358893*P3^2*S3*nu^6-3888*P3^2*S3*nu^5*w+608616*P3^2*nu^7+
311364*P3^2*nu^6*w-1296*P3*S1^2*S3*nu^5+5994*P3*S1^2*nu^6+6480*P3*S1^2*nu^5*w+
1998*P3*S1*S3*nu^6+2160*P3*S1*S3*nu^5*w-23760*P3*S1*nu^7-53460*P3*S1*nu^6*w-\
4320*P3*S3*nu^7-9720*P3*S3*nu^6*w+19062*P3*nu^8+140940*P3*nu^7*w+62694*P3*nu^6*
w^2-5832*P3*nu^5*w^3-1620*S1^3*nu^6-972*S1^3*nu^5*w+1512*S1^2*S3^2*nu^5-1620*S1
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^2-1620*S1*S3^2*nu^6-972*S1*S3^2*nu^5*w-25104*S1*S3*nu^7-97470*S1*S3*nu^6*w-\
21384*S1*S3*nu^5*w^2+13275*S1*nu^8+169479*S1*nu^7*w+270810*S1*nu^6*w^2+28755*S1
*nu^5*w^3-1620*S3^3*nu^6-972*S3^3*nu^5*w+1920*S3^2*nu^7-6210*S3^2*nu^6*w-13608*
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^3-2560*nu^9-92016*nu^8*w-486432*nu^7*w^2-365040*nu^6*w^3-7776*nu^5*w^4+3672*P1
^2*P3*nu^5-1296*P1^2*S3*nu^5-1998*P1^2*nu^6-2160*P1^2*nu^5*w+1080*P1*P3^2*nu^5-\
360*P1*P3*S1*S3*nu^4+10368*P1*P3*S1*nu^5+10368*P1*P3*S3*nu^5-27972*P1*P3*nu^6-\
30240*P1*P3*nu^5*w+180*P1*S1*S3^2*nu^4-1512*P1*S1*S3*nu^5+3240*P1*S1*nu^6+1944*
P1*S1*nu^5*w-4536*P1*S3^2*nu^5+17820*P1*S3*nu^6+10692*P1*S3*nu^5*w-28944*P1*nu^
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10692*P3*S1*nu^5*w+3240*P3*S3*nu^6+1944*P3*S3*nu^5*w-28944*P3*nu^7-85050*P3*nu^
6*w+5832*P3*nu^5*w^2+648*S1^3*nu^5-360*S1^2*S3^2*nu^4+648*S1^2*S3*nu^5+30*S1^2*
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40014*S1*S3*nu^5*w+648*S1*S3*nu^4*w^2-26697*S1*nu^7-171288*S1*nu^6*w-110619*S1*
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9936*nu^8+176400*nu^7*w+452520*nu^6*w^2+117936*nu^5*w^3-2592*nu^4*w^4-360*P1^2*
P3*nu^4+180*P1^2*S3*nu^4+1512*P1^2*nu^5+504*P1*P3^2*nu^4-1440*P1*P3*S1*nu^4-\
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576*P3^2*S1*nu^3-576*P3^2*S3*nu^3-10764*P3^2*nu^4+864*P3^2*nu^3*w+1188*P3*S1*nu
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5262*S1*S3*nu^4+216*S1*S3*nu^3*w-27279*S1*nu^5-35586*S1*nu^4*w+432*S1*nu^3*w^2+
1794*S3^2*nu^4+1080*S3^2*nu^3*w-27279*S3*nu^5-35586*S3*nu^4*w+432*S3*nu^3*w^2+
32088*nu^6+154224*nu^5*w+62424*nu^4*w^2-3456*nu^3*w^3+1674*P1*nu^4-1944*P1*nu^3
*w+72*P3^2*S1*nu^2+72*P3^2*S3*nu^2-1440*P3^2*nu^3+1674*P3*nu^4-1944*P3*nu^3*w-\
744*S1^2*nu^3-840*S1*S3*nu^3+13881*S1*nu^4+5049*S1*nu^3*w-216*S1*nu^2*w^2-744*
S3^2*nu^3+13881*S3*nu^4+5049*S3*nu^3*w-216*S3*nu^2*w^2-30240*nu^5-67536*nu^4*w-\
1728*nu^3*w^2+648*P1*nu^3+288*P3^2*nu^2+648*P3*nu^3+120*S1^2*nu^2+24*S1*S3*nu^2
-4035*S1*nu^3+216*S1*nu^2*w+120*S3^2*nu^2-4035*S3*nu^3+216*S3*nu^2*w+18480*nu^4
+14256*nu^3*w-1728*nu^2*w^2-216*P1*nu^2-216*P3*nu^2+477*S1*nu^2-72*S1*nu*w+477*
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nu-32, -2916*S1^3*S3^2*nu^10*w-2916*S1^2*S3^3*nu^10*w+23328*S1*S3^4*nu^10*w+
14580*P1*P3*S1^2*S3*nu^10+14580*P1*P3*S1*S3^2*nu^10-116640*P1*P3*S3^3*nu^10+
9720*P1*S1^2*S3^2*nu^10-2916*P1*S1^2*S3*nu^10*w+9720*P1*S1*S3^3*nu^10+2916*P1*
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222696*nu^8*w-648216*nu^7*w^2-171936*nu^6*w^3-1836*P1^2*S3*nu^5-5454*P1^2*nu^6-\
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w^2+1296*P1*nu^3-192*P3*S3*nu^2+1296*P3*nu^3+120*S1^2*nu^2+24*S1*S3*nu^2-5538*
S1*nu^3+288*S1*nu^2*w+120*S3^2*nu^2-5538*S3*nu^3+288*S3*nu^2*w+35364*nu^4+11556
*nu^3*w-864*nu^2*w^2-216*P1*nu^2-216*P3*nu^2+405*S1*nu^2-48*S1*nu*w+405*S3*nu^2
-48*S3*nu*w-10380*nu^3+864*nu^2*w+56*S1*nu+56*S3*nu+1188*nu^2-288*nu*w-8*S1-8*
S3+128*nu-32];
