systS1S3 := [185093021028188160*S1^13*S3^3*nu^28+777390688318390272*S1^12*S3^4*
nu^28-4368195296265240576*S1^11*S3^5*nu^28-19175636978520293376*S1^10*S3^6*nu^
28+32909539138811854848*S1^9*S3^7*nu^28+181280104795007483904*S1^8*S3^8*nu^28+
22803460190672781312*S1^7*S3^9*nu^28-907400026288589635584*S1^6*S3^10*nu^28-\
1554189078969490341888*S1^5*S3^11*nu^28+3487448665004710035456*S1^4*S3^12*nu^28
+6065128113051669626880*S1^3*S3^13*nu^28-9704204980882671403008*S1^2*S3^14*nu^
28+1573290678739599360*S1^13*S3^2*nu^28+244219958301081600*S1^13*S3*nu^28*w+
16067102519808000*S1^13*nu^28*w^2+10878328163651125248*S1^12*S3^3*nu^28+
1766095908977295360*S1^12*S3^2*nu^28*w+112469717638656000*S1^12*S3*nu^28*w^2-\
12977591510479159296*S1^11*S3^4*nu^28+8706570050253717504*S1^11*S3^3*nu^28*w+
696026881158082560*S1^11*S3^2*nu^28*w^2-196531255580449554432*S1^10*S3^5*nu^28+
35394927093395914752*S1^10*S3^4*nu^28*w+4140042440483966976*S1^10*S3^3*nu^28*w^
2-73390411132237873152*S1^9*S3^6*nu^28+18547863148866355200*S1^9*S3^5*nu^28*w+
15871726553167134720*S1^9*S3^4*nu^28*w^2+1389081991034101432320*S1^8*S3^7*nu^28
-313200528207322890240*S1^8*S3^6*nu^28*w+49374591653830459392*S1^8*S3^5*nu^28*w
^2+1925351486711790354432*S1^7*S3^8*nu^28-849114233966813184000*S1^7*S3^7*nu^28
*w+130650993776430415872*S1^7*S3^6*nu^28*w^2-5716400007752547287040*S1^6*S3^9*
nu^28-192566665899481890816*S1^6*S3^8*nu^28*w+193483904648132689920*S1^6*S3^7*
nu^28*w^2-18174538751808989822976*S1^5*S3^10*nu^28+3188930640690448171008*S1^5*
S3^9*nu^28*w-108982770781397188608*S1^5*S3^8*nu^28*w^2+26916835868299392712704*
S1^4*S3^11*nu^28+1040864433984648511488*S1^4*S3^10*nu^28*w-\
1397822494804876984320*S1^4*S3^9*nu^28*w^2+69130877778850914238464*S1^3*S3^12*
nu^28-7890984388751599337472*S1^3*S3^11*nu^28*w-3297913411471845359616*S1^3*S3^
10*nu^28*w^2-104739287049522496143360*S1^2*S3^13*nu^28+14101422862845131882496*
S1^2*S3^12*nu^28*w-2729307650873251332096*S1^2*S3^11*nu^28*w^2-\
6469469987255114268672*S1*S3^14*nu^28+10917230603493005328384*S1*S3^13*nu^28*w-\
925465105140940800*S1^13*S3^2*nu^27+2547207024145827840*S1^13*S3*nu^28-\
51414728063385600*S1^13*S3*nu^27*w+236900500486502400*S1^13*nu^28*w-\
5048926295824465920*S1^12*S3^3*nu^27+31178383822114301952*S1^12*S3^2*nu^28-\
416459297313423360*S1^12*S3^2*nu^27*w+4340938349457192960*S1^12*S3*nu^28*w+
167811959651328000*S1^12*nu^28*w^2+16762229643224973312*S1^11*S3^4*nu^27+
20021752020016742400*S1^11*S3^3*nu^28-4210352081110646784*S1^11*S3^3*nu^27*w+
35991552166964785152*S1^11*S3^2*nu^28*w+3067102757014548480*S1^11*S3*nu^28*w^2+
125680446377164800*S1^11*nu^28*w^3+105045430906303119360*S1^10*S3^5*nu^27-\
644241252959195258880*S1^10*S3^4*nu^28-18105696487521239040*S1^10*S3^4*nu^27*w+
198042891431119810560*S1^10*S3^3*nu^28*w+25373453936658923520*S1^10*S3^2*nu^28*
w^2+980307481741885440*S1^10*S3*nu^28*w^3-117001411770162806784*S1^9*S3^6*nu^27
-1267421940740656429056*S1^9*S3^5*nu^28+18748380588313559040*S1^9*S3^5*nu^27*w+
311978707181437704192*S1^9*S3^4*nu^28*w+121410210419729215488*S1^9*S3^3*nu^28*w
^2+5018762988693946368*S1^9*S3^2*nu^28*w^3-928973646183986233344*S1^8*S3^7*nu^
27+3915879631814986868736*S1^8*S3^6*nu^28+238126798878289772544*S1^8*S3^6*nu^27
*w-1656350579228439177216*S1^8*S3^5*nu^28*w+390992954101396586496*S1^8*S3^4*nu^
28*w^2+22709085600938655744*S1^8*S3^3*nu^28*w^3-334996773875233947648*S1^7*S3^8
*nu^27+13300878108736283258880*S1^7*S3^7*nu^28+283371245426788466688*S1^7*S3^7*
nu^27*w-7414151061372367306752*S1^7*S3^6*nu^28*w+969006353131126407168*S1^7*S3^
5*nu^28*w^2+57642765456130375680*S1^7*S3^4*nu^28*w^3+5115698603160384798720*S1^
6*S3^9*nu^27-9512229570074049540096*S1^6*S3^8*nu^28-981367310669698695168*S1^6*
S3^8*nu^27*w-6230314208285849272320*S1^6*S3^7*nu^28*w+1421673958535908442112*S1
^6*S3^6*nu^28*w^2+15356550977972011008*S1^6*S3^5*nu^28*w^3+
11357274864863664930816*S1^5*S3^10*nu^27-88697366092460527386624*S1^5*S3^9*nu^
28-3151023589983875235840*S1^5*S3^9*nu^27*w+24875755141572154589184*S1^5*S3^8*
nu^28*w-1779173073677790609408*S1^5*S3^7*nu^28*w^2-243384983117332217856*S1^5*
S3^6*nu^28*w^3-25791930976411456634880*S1^4*S3^11*nu^27+76854915574951967981568
*S1^4*S3^10*nu^28+3507981650804103708672*S1^4*S3^10*nu^27*w+
24149991009996771065856*S1^4*S3^9*nu^28*w-11792173540249740902400*S1^4*S3^8*nu^
28*w^2-154885839996387852288*S1^4*S3^7*nu^28*w^3-52364378656607557386240*S1^3*
S3^12*nu^27+350637520790870883827712*S1^3*S3^11*nu^28+13349599690498102001664*
S1^3*S3^11*nu^27*w-56576929917019902050304*S1^3*S3^10*nu^28*w-\
27544605584775085817856*S1^3*S3^9*nu^28*w^2+1769785429863123910656*S1^3*S3^8*nu
^28*w^3+88176011838011599749120*S1^2*S3^13*nu^27-520844631664363359436800*S1^2*
S3^12*nu^28-14101422862845131882496*S1^2*S3^12*nu^27*w+140332296580844532793344
*S1^2*S3^11*nu^28*w-51277578247981957644288*S1^2*S3^10*nu^28*w^2+
4349834068579244310528*S1^2*S3^9*nu^28*w^3+8086837484068892835840*S1*S3^14*nu^
27-73060926359975887896576*S1*S3^13*nu^28-10917230603493005328384*S1*S3^13*nu^
27*w+133651573758922579771392*S1*S3^12*nu^28*w-28899387782423541448704*S1*S3^11
*nu^28*w^2+3070471107232407748608*S1*S3^10*nu^28*w^3-1078244997875852378112*S3^
14*nu^28+3639076867831001776128*S3^13*nu^28*w-3070471107232407748608*S3^12*nu^
28*w^2-3372520523579965440*S1^13*S3*nu^27+1159986285939479040*S1^13*nu^28-\
231366276285235200*S1^13*nu^27*w-1044747274247995392*S1^12*S3^3*nu^26-\
31302314739550420992*S1^12*S3^2*nu^27+32671843217570976768*S1^12*S3*nu^28-\
2959131828081438720*S1^12*S3*nu^27*w+2549880907379988480*S1^12*nu^28*w-\
35704672266240000*S1^12*nu^27*w^2-2576906170536886272*S1^11*S3^4*nu^26+
51701022407485218816*S1^11*S3^3*nu^27+96606263758873307904*S1^11*S3^2*nu^28-\
35853782118558271488*S1^11*S3^2*nu^27*w+46138047613953500160*S1^11*S3*nu^28*w-\
2428488988860579840*S1^11*S3*nu^27*w^2+2334549996128102400*S1^11*nu^28*w^2-\
125680446377164800*S1^11*nu^27*w^3+27883235323335278592*S1^10*S3^5*nu^26+
860106160115746578432*S1^10*S3^4*nu^27-955888854350066664192*S1^10*S3^3*nu^28-\
222857502978401998848*S1^10*S3^3*nu^27*w+401180776913096312832*S1^10*S3^2*nu^28
*w-22793748519816364032*S1^10*S3^2*nu^27*w^2+43583108941387708416*S1^10*S3*nu^
28*w^2-980307481741885440*S1^10*S3*nu^27*w^3+1476459607553556480*S1^10*nu^28*w^
3+64505431975604207616*S1^9*S3^6*nu^26+556200015119130968064*S1^9*S3^5*nu^27-\
3978605008941632004096*S1^9*S3^4*nu^28-123924769091554793472*S1^9*S3^4*nu^27*w+
1178102402637241890816*S1^9*S3^3*nu^28*w-115392702056535097344*S1^9*S3^3*nu^27*
w^2+302579949692450267136*S1^9*S3^2*nu^28*w^2-5018762988693946368*S1^9*S3^2*nu^
27*w^3+12278484506260242432*S1^9*S3*nu^28*w^3+25707364031692800*S1^9*nu^28*w^4-\
257010400201410035712*S1^8*S3^7*nu^26-6677454330531487973376*S1^8*S3^6*nu^27+
4476912509777831087616*S1^8*S3^5*nu^28+2869964443455293859840*S1^8*S3^5*nu^27*w
-3155770298445206501376*S1^8*S3^4*nu^28*w-371999211005269426176*S1^8*S3^4*nu^27
*w^2+1216000102686866878464*S1^8*S3^3*nu^28*w^2-22709085600938655744*S1^8*S3^3*
nu^27*w^3+86585924919738286080*S1^8*S3^2*nu^28*w^3+920323632334602240*S1^8*S3*
nu^28*w^4-615728901310528831488*S1^7*S3^8*nu^26-12605646484884521115648*S1^7*S3
^7*nu^27+40760023228558668460800*S1^7*S3^6*nu^28+8347324034034668371968*S1^7*S3
^6*nu^27*w-25764680316402757942272*S1^7*S3^5*nu^28*w-717028083747706798080*S1^7
*S3^5*nu^27*w^2+3476992001879588751360*S1^7*S3^4*nu^28*w^2-57642765456130375680
*S1^7*S3^4*nu^27*w^3+376562458545813651456*S1^7*S3^3*nu^28*w^3+
5335820478418157568*S1^7*S3^2*nu^28*w^4+914915317089614708736*S1^6*S3^9*nu^26+
25523142861633877794816*S1^6*S3^8*nu^27+18743393043209162854656*S1^6*S3^7*nu^28
-1490156662492069281792*S1^6*S3^7*nu^27*w-39493794170306205075456*S1^6*S3^6*nu^
28*w-112288052266165370880*S1^6*S3^6*nu^27*w^2+5738229708698371811328*S1^6*S3^5
*nu^28*w^2-15356550977972011008*S1^6*S3^5*nu^27*w^3+544814794864250486784*S1^6*
S3^4*nu^28*w^3+10487576230369394688*S1^6*S3^3*nu^28*w^4+3073942629671247544320*
S1^5*S3^10*nu^26+121261277605457908924416*S1^5*S3^9*nu^27-\
239500983061496424554496*S1^5*S3^8*nu^28-47688387034201736380416*S1^5*S3^8*nu^
27*w+78012758065090494210048*S1^5*S3^7*nu^28*w+4601579772009390538752*S1^5*S3^7
*nu^27*w^2-8122619735447032922112*S1^5*S3^6*nu^28*w^2+243384983117332217856*S1^
5*S3^6*nu^27*w^3-806725190032528048128*S1^5*S3^5*nu^28*w^3+34994920509062774784
*S1^5*S3^4*nu^28*w^4-1409207772187233091584*S1^4*S3^11*nu^26-\
168787344344240243146752*S1^4*S3^10*nu^27+57547144395658069475328*S1^4*S3^9*nu^
28+547210035662296743936*S1^4*S3^9*nu^27*w+158663972880665446440960*S1^4*S3^8*
nu^28*w+8862196262334218108928*S1^4*S3^8*nu^27*w^2-50712736388242457198592*S1^4
*S3^7*nu^28*w^2+154885839996387852288*S1^4*S3^7*nu^27*w^3-\
2421335486362694123520*S1^4*S3^6*nu^28*w^3+130305486803844464640*S1^4*S3^5*nu^
28*w^4-7668806952665852411904*S1^3*S3^12*nu^26-543227730522627560177664*S1^3*S3
^11*nu^27+1036703927530270723276800*S1^3*S3^10*nu^28+164176814524879480946688*
S1^3*S3^10*nu^27*w-140305881769197179682816*S1^3*S3^9*nu^28*w+
11287614078105145049088*S1^3*S3^9*nu^27*w^2-120027523449699113582592*S1^3*S3^8*
nu^28*w^2-1769785429863123910656*S1^3*S3^8*nu^27*w^3+8938734283118496448512*S1^
3*S3^7*nu^28*w^3+9772911510288334848*S1^3*S3^6*nu^28*w^4+5646044608017891065856
*S1^2*S3^13*nu^26+884818260921088512884736*S1^2*S3^12*nu^27-\
1587960178438788756799488*S1^2*S3^11*nu^28-248036494131117938442240*S1^2*S3^11*
nu^27*w+668602356613033682534400*S1^2*S3^10*nu^28*w+54792272605682016976896*S1^
2*S3^10*nu^27*w^2-344638869350468768612352*S1^2*S3^9*nu^28*w^2-\
4349834068579244310528*S1^2*S3^9*nu^27*w^3+46905162830837274378240*S1^2*S3^8*nu
^28*w^3+2665339502805909504*S1^2*S3^7*nu^28*w^4-1617367496813778567168*S1*S3^14
*nu^26+152334046150096538566656*S1*S3^13*nu^27-384472115545078392422400*S1*S3^
12*nu^28-250842800478738916048896*S1*S3^12*nu^27*w+754503516724073808789504*S1*
S3^11*nu^28*w+44152237310480826236928*S1*S3^11*nu^27*w^2-\
305383655064190977441792*S1*S3^10*nu^28*w^2-3070471107232407748608*S1*S3^10*nu^
27*w^3+50362478352018595381248*S1*S3^9*nu^28*w^3+2238885182356963983360*S1*S3^8
*nu^28*w^4+2695612494689630945280*S3^14*nu^27-12491309184376438259712*S3^13*nu^
28-8187922952619753996288*S3^13*nu^27*w+43666026736487491436544*S3^12*nu^28*w+
6140942214464815497216*S3^12*nu^27*w^2-43176056717578161881088*S3^11*nu^28*w^2+
7644193694047348457472*S3^10*nu^28*w^3+3454279995636458717184*S3^9*nu^28*w^4+
880905674152673280*S1^13*S3*nu^26-2415373472581447680*S1^13*nu^27+
12853682015846400*S1^13*nu^26*w-3600059258998259712*S1^12*S3^2*nu^26-\
52324224848933336064*S1^12*S3*nu^27-1186823306129817600*S1^12*S3*nu^26*w+
11597559136636377600*S1^12*nu^28-3161652696361359360*S1^12*nu^27*w-\
99973082345472000*S1^12*nu^26*w^2-91436295152778706944*S1^11*S3^3*nu^26+
3318565408084836864*S1^11*S3^2*nu^27-58784172419137536*S1^11*S3^2*nu^26*w+
102958845285780414720*S1^11*S3*nu^28-70070650212709988352*S1^11*S3*nu^27*w-\
389895021147340800*S1^11*S3*nu^26*w^2+18852876471858672384*S1^11*nu^28*w-\
3302646479954933760*S1^11*nu^27*w^2-132765681541677465600*S1^10*S3^4*nu^26+
2314118643083236707840*S1^10*S3^3*nu^27+11512271760672669696*S1^10*S3^3*nu^26*w
-682964256656409629184*S1^10*S3^2*nu^28-687018100414270095360*S1^10*S3^2*nu^27*
w-869651561454354432*S1^10*S3^2*nu^26*w^2+347459012378132749056*S1^10*S3*nu^28*
w-69060730069227644928*S1^10*S3*nu^27*w^2+21971454357340523520*S1^10*nu^28*w^2-\
2062301870098022400*S1^10*nu^27*w^3+1063141878661626138624*S1^9*S3^5*nu^26+
5180576657426849682432*S1^9*S3^4*nu^27-225722995732997996544*S1^9*S3^4*nu^26*w-\
5840916040508491436544*S1^9*S3^3*nu^28-1384841145179282512896*S1^9*S3^3*nu^27*w
+2974284890991230976*S1^9*S3^3*nu^26*w^2+1863275713317542499840*S1^9*S3^2*nu^28
*w-496169190264702818304*S1^9*S3^2*nu^27*w^2+311707138105378317312*S1^9*S3*nu^
28*w^2-17025701560812011520*S1^9*S3*nu^27*w^3+7976606407064681472*S1^9*nu^28*w^
3-51414728063385600*S1^9*nu^27*w^4+1754229946733153316864*S1^8*S3^6*nu^26-\
17609228749068914829312*S1^8*S3^5*nu^27-1024436057308981788672*S1^8*S3^5*nu^26*
w-325943553355165149696*S1^8*S3^4*nu^28+9905836086349405857792*S1^8*S3^4*nu^27*
w+14232510767555149824*S1^8*S3^4*nu^26*w^2-2218027779960213367296*S1^8*S3^3*nu^
28*w-2035137029442864261120*S1^8*S3^3*nu^27*w^2+1833421801299799375872*S1^8*S3^
2*nu^28*w^2-138701626151546585088*S1^8*S3^2*nu^27*w^3+108243124824526709760*S1^
8*S3*nu^28*w^3-1840647264669204480*S1^8*S3*nu^27*w^4+1330784544707297280*S1^8*
nu^28*w^4-3875887578207689035776*S1^7*S3^7*nu^26-74082692684322141414912*S1^7*
S3^6*nu^27-340174579756070633472*S1^7*S3^6*nu^26*w+70260065473649947520256*S1^7
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7*S3^5*nu^26*w^2-47060264503803297998592*S1^7*S3^4*nu^28*w-\
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