centers of Mandelbrot componentsof period i for Fx(z) = z^2 + x computed in Polynomial web solver : http://www.hvks.com/Numerical/websolver.htm ------------------------------------------ Adam Majewski fraktal.republika.pl 2007.07.28 --------------- solutions are not tested, it may be wrong !!!! ------------------------------------------ polynomials were computed in Maxima see http://fraktal.republika.pl/mandelbrot_map.html P(n):=if n=0 then z else P(n-1)^2+c; for m:0 thru 6 step 1 do display(z:ratsimp(P(m))); -------------------------------------------- we must remove * and change c to x it can be done in any text editor with replace function ------------------------------------------- solutions ************************************************** period = 2 equation: x^2+x=0 For the real Polynomial: +1x^2+1x The Solutions are: X1=-1 X2=0 ------------------------ period 3 For the real Polynomial: +1x^4+2x^3+1x^2+1x The Solutions are: X1=-1.7548776662466927 X2=(-0.1225611668766536-i0.7448617666197443) X3=(-0.1225611668766536+i0.7448617666197443) X4=0 -------------------------------------- period 4 For the real Polynomial: +1x^8+4x^7+6x^6+6x^5+5x^4+2x^3+1x^2+1x The Solutions are: X1=-1.9407998065294851 X2=(-0.15652016683375503+i1.032247108922832) X3=(-0.15652016683375503-i1.032247108922832) X4=-1.0000000000000013 X5=(0.28227139076691404-i0.5300606175785253) X6=(0.28227139076691404+i0.5300606175785253) X7=-1.310702641336832 X8=0 ------------------------------------------------ period 5 For the real Polynomial: +1x^16+8x^15+28x^14+60x^13+94x^12+116x^11+114x^10+94x^9+69x^8+44x^7+26x^6+14x^5+5x^4+2x^3+1x^2+1x The Solutions are: X1=(-0.1980420993642531+i1.100269537292699) X2=(-0.1980420993642531-i1.100269537292699) X3=(-1.2563679300681783+i0.380320963472715) X4=(-1.2563679300681783-i0.380320963472715) X5=(0.3592592247580094-i0.6425137371385428) X6=(0.3592592247580094+i0.6425137371385428) X7=-1.9854242530543293 X8=(-0.044212357704071566+i0.9865809762808933) X9=(-0.044212357704071566-i0.9865809762808933) X10=-1.6254137251234502 X11=-1.8607825222045917 X12=(0.3795135880159238-i0.3349323055974976) X13=(0.3795135880159238+i0.3349323055974976) X14=(-0.504340175446244+i0.5627657614529818) X15=(-0.504340175446244-i0.5627657614529818) X16=0 -------------------------------------------------------------- period 6 For the real Polynomial: +1x^32+16x^31+120x^30+568x^29+1932x^28+5096x^27+10948x^26+19788x^25+30782x^24+41944x^23+50788x^22+55308x^21+54746x^20+49700x^19+41658x^18+32398x^17+23461x^16+15864x^15+10068x^14+6036x^13+3434x^12+1860x^11+958x^10+470x^9+221x^8+100x^7+42x^6+14x^5+5x^4+2x^3+1x^2+1x The Solutions are: X1=-1.9667728693864583 X2=(-0.21752674626230376+i1.1144542692378163) X3=(-0.21752674626230376-i1.1144542692378163) X4=(-0.16359825821446478+i1.0977806384703692) X5=(-0.16359825821446478-i1.0977806384703692) X6=-1.772891709191541 X7=(0.35989273755342205-i0.6847620206701639) X8=(0.35989273755342205+i0.6847620206701639) X9=(-0.015570385249629755-i1.0204973635355805) X10=(-0.015570385249629755+i1.0204973635355805) X11=(-1.2840849106076628-i0.42726889728016715) X12=(-1.2840849106076628+i0.42726889728016715) X13=-1.9963762917295835 X14=(0.443325633871087-i0.3729624169672307) X15=(0.443325633871087+i0.3729624169672307) X16=(-0.5968916489632466+i0.6629807383295685) X17=(-0.5968916489632466-i0.6629807383295685) X18=(0.3965345711757607-i0.604181811747153) X19=(0.3965345711757607+i0.604181811747153) X20=(-1.1380007146217779-i0.24033232015293732) X21=(-1.1380007146217779+i0.24033232015293732) X22=(-0.11341866726149594+i0.8605694778360563) X23=(-0.11341866726149594-i0.8605694778360563) X24=-1.75487878723474 X25=-1.4760144955691137 X26=-1.9072804171174427 X27=(0.3890068405697362+i0.21585065087083882) X28=(0.3890068405697362-i0.21585065087083882) X29=(-0.12256116687656166-i0.7448617666196015) X30=(-0.12256116687656166+i0.7448617666196015) X31=-0.9999999999968479 X32=0 -------------------------------------------------------- Problem : Mandelbrot set contains points c : Abs(c)<=2, but roots computed with WebSolver are x: Abs(x)> 2 . Answer : The reason you get roots bigger than 2 is that the coefficients can not be calculated without loss of precision. Notices that the problem first occurs with a polynomial with a degree of 64. With n=64 some of your coefficient is over 10^21 and can’t be represented accurately with 64bit floating point. If you have a need for higher precision you would need to use arbitrary precision for n=64 and higher. Henrik Vestermark, www.hvks.com ================================================================================================================== period 7 ( probably bad roots !!!!!!!!!!! ) see above For the real Polynomial: +1x^64+32x^63+496x^62+4976x^61+36440x^60+208336x^59+971272x^58+3807704x^57+12843980x^56+37945904x^55+99582920x^54+234813592x^53+502196500x^52+981900168x^51+1766948340x^50+2943492972x^49+4562339774x^48+6609143792x^47+8984070856x^46+11500901864x^45+13910043524x^44+15941684776x^43+17357937708x^42+17999433372x^41+17813777994x^40+16859410792x^39+15286065700x^38+13299362332x^37+11120136162x^36+8948546308x^35+6939692682x^34+5193067630x^33+3754272037x^32+2625062128x^31+1777171560x^30+1166067016x^29+742179284x^28+458591432x^27+275276716x^26+160617860x^25+91143114x^24+50323496x^23+27049196x^22+14162220x^21+7228014x^20+3598964x^19+1749654x^18+831014x^17+385741x^16+175048x^15+77684x^14+33708x^13+14290x^12+5916x^11+2398x^10+950x^9+365x^8+132x^7+42x^6+14x^5+5x^4+2x^3+1x^2+1x The Solutions are: X1=(-0.2741686558488794+i1.1061932623403614) X2=(-0.2741686558488794-i1.1061932623403614) X3=(-1.3503885045724444-i0.4751678298930445) X4=(-1.3503885045724444+i0.4751678298930445) X5=(0.3575626071274554+i0.7422141884075043) X6=(0.3575626071274554-i0.7422141884075043) X7=(-2.0742311692231725+i0.2397723724252332) X8=(-2.0742311692231725-i0.2397723724252332) X9=(0.5186955960640173+i0.29545464596918314) X10=(0.5186955960640173-i0.29545464596918314) X11=(-0.6550383703376352+i0.7505452909198996) X12=(-0.6550383703376352-i0.7505452909198996) X13=(-1.653693251795596-i0.33259826101587026) X14=(-1.653693251795596+i0.33259826101587026) X15=(0.45946866241956236+i0.621165721924777) X16=(0.45946866241956236-i0.621165721924777) X17=(-0.22800779538584237-i1.1515905815623673) X18=(-0.22800779538584237+i1.1515905815623673) X19=(-2.1795165564156087+i0.08776283582849274) X20=(-2.1795165564156087-i0.08776283582849274) X21=(0.03980603032101611+i1.0377139443019532) X22=(0.03980603032101611-i1.0377139443019532) X23=(-0.33905759022989274+i0.9884919446253708) X24=(-0.33905759022989274-i0.9884919446253708) X25=(-0.021552668019327058+i1.0854350041134186) X26=(-0.021552668019327058-i1.0854350041134186) X27=(-1.8885094298802314+i0.32881811692372165) X28=(-1.8885094298802314-i0.32881811692372165) X29=(0.5033850346465291-i0.16801257306295508) X30=(0.5033850346465291+i0.16801257306295508) X31=(-1.0746190004171252+i0.5258934625436418) X32=(-1.0746190004171252-i0.5258934625436418) X33=-1.9530375714184323 X34=(0.20233745459415164+i0.7837919115884039) X35=(0.20233745459415164-i0.7837919115884039) X36=(-0.10379342871218612-i1.1287444721923696) X37=(-0.10379342871218612+i1.1287444721923696) X38=(0.5145336972494401-i0.400872844563007) X39=(0.5145336972494401+i0.400872844563007) X40=(-1.4412300387473775+i0.37146805634686114) X41=(-1.4412300387473775-i0.37146805634686114) X42=(-0.1687775166702839+i1.155104381463612) X43=(-0.1687775166702839-i1.155104381463612) X44=(-1.5529401927121083+i0.2020862076628329) X45=(-1.5529401927121083-i0.2020862076628329) X46=(0.4203428027380649+i0.695295997828589) X47=(0.4203428027380649-i0.695295997828589) X48=(0.09117144819159687+i0.9372477035243342) X49=(0.09117144819159687-i0.9372477035243342) X50=(-0.8098954382820235+i0.5915551330005684) X51=(-0.8098954382820235-i0.5915551330005684) X52=0.4741778913653919 X53=(-1.2459390492833922+i0.5155817238610794) X54=(-1.2459390492833922-i0.5155817238610794) X55=(-0.483611279985452+i0.8396875661799417) X56=(-0.483611279985452-i0.8396875661799417) X57=(0.47560248578841574-i0.5146604655395266) X58=(0.47560248578841574+i0.5146604655395266) X59=-1.594525067334121 X60=(0.12119278611409451+i0.610611692228492) X61=(0.12119278611409451-i0.610611692228492) X62=(-0.6224362950421879+i0.4248784364819922) X63=(-0.6224362950421879-i0.4248784364819922) X64=0 =========================================== period 8 ( probably bad roots !!!!!!!!!!! ) see above For the real Polynomial: +1x^128+64x^127+2016x^126+41696x^125+637360x^124+7685024x^123+76185104x^122+639097008x^121+4634116312x^120+29524775520x^119+167453394320x^118+854515874096x^117+3958458557608x^116+16771945556496x^115+65418624260840x^114+236221241425176x^113+793548088258508x^112+2490875091238112x^111+7333879739219600x^110+20324543852025936x^109+53181959591958024x^108+131760770157606220x^107+309881648709683140x^106+693434955498545800x^105+1479594496462756400x^104+3016191418506637300x^103+5884917700519129000x^102+11008161481780603000x^101+19772322481956975000x^100+34150590308701282000x^99+56796799826096530000x^98+91071943593142470000x^97+140960183546144740000x^96+210835921361505580000x^95+305060580205223740000x^94+427417353874088260000x^93+580430565842543250000x^92+764655844340519800000x^91+978057923319151300000x^90+1.2156044111615272e+21x^89+1.469189341596552e+21x^88+1.7279585216304647e+21x^87+1.9790454080732723e+21x^86+2.2086534878322607e+21x^85+2.40335441894389e+21x^84+2.5514255916439574e+21x^83+2.6440369709363086e+21x^82+2.6761185429789726e+21x^81+2.6467918122462075e+21x^80+2.5593202759882837e+21x^79+2.4206096463352514e+21x^78+2.2403538973044622e+21x^77+2.0299665953207943e+21x^76+1.8014527514029557e+21x^75+1.566365198635996e+21x^74+1.3349570927521004e+21x^73+1.1155975817333279e+21x^72+914470757914434600000x^71+735537050036491900000x^70+580706779030058430000x^69+450159936955994400000x^68+342743629811082460000x^67+256386228250001080000x^66+188481251186354000000x^65+136210493669590630000x^64+96791719611591970000x^63+67649247253332560000x^62+46514944583399580000x^61+31472438318100877000x^60+20959276151880730000x^59+13741246529612442000x^58+8870996681171367000x^57+5640327912922026000x^56+3532711259225506300x^55+2180053774442766600x^54+1325752376790240300x^53+794643418760272900x^52+469540646039042560x^51+273551721580800400x^50+157160523515654620x^49+89054473147697360x^48+49778848242964940x^47+27452211062573400x^46+14938862548001560x^45+8022825031835276x^44+4252710138415640x^43+2225301467579844x^42+1149605839249820x^41+586400982013486x^40+295372837865192x^39+146932182777116x^38+72188854953372x^37+35031835376454x^36+16792863663700x^35+7952125694214x^34+3720187393990x^33+1719477330477x^32+785248461712x^31+354347339496x^30+158015533208x^29+69640352964x^28+30336029592x^27+13062923500x^26+5560968284x^25+2340595778x^24+974083128x^23+400844588x^22+163107044x^21+65626918x^20+26108844x^19+10269590x^18+3993030x^17+1534301x^16+582408x^15+218324x^14+80812x^13+29538x^12+10652x^11+3774x^10+1302x^9+429x^8+132x^7+42x^6+14x^5+5x^4+2x^3+1x^2+1x The Solutions are: X1=(-0.3153378434487797+i1.3940173779784981) X2=(-0.3153378434487797-i1.3940173779784981) X3=(-3.1250333183178407-i1.1342944962786994) X4=(-3.1250333183178407+i1.1342944962786994) X5=(-0.03821314639256769+i1.3161582904056865) X6=(-0.03821314639256769-i1.3161582904056865) X7=(-2.3157317047333463-i1.6350549616979169) X8=(-2.3157317047333463+i1.6350549616979169) X9=(-3.3111704253073944+i0.647484987808723) X10=(-3.3111704253073944-i0.647484987808723) X11=(0.4791600607887792-i0.6442144172772161) X12=(0.4791600607887792+i0.6442144172772161) X13=(-1.4802925278266175-i1.6008881606895369) X14=(-1.4802925278266175+i1.6008881606895369) X15=(-2.751129095828013-i1.460885490092461) X16=(-2.751129095828013+i1.460885490092461) X17=(0.5415936822803569+i0.3837434011022276) X18=(0.5415936822803569-i0.3837434011022276) X19=(-0.8530555049432682-i1.3270365966682853) X20=(-0.8530555049432682+i1.3270365966682853) X21=(-3.3137105867745618+i0.4641936022237693) X22=(-3.3137105867745618-i0.4641936022237693) X23=(-1.878612505504788+i1.673229167364006) X24=(-1.878612505504788-i1.673229167364006) X25=(0.03573563666182565+i1.2353671810617628) X26=(0.03573563666182565-i1.2353671810617628) X27=-3.5176687122332373 X28=(0.3609450571071498-i0.7768111945859396) X29=(0.3609450571071498+i0.7768111945859396) X30=(-1.6522034917812722-i0.7176263167436057) X31=(-1.6522034917812722+i0.7176263167436057) X32=(-1.1503374322308169-i1.4579130443098776) X33=(-1.1503374322308169+i1.4579130443098776) X34=(-0.154366928314452+i1.3787925455299208) X35=(-0.154366928314452-i1.3787925455299208) X36=-2.1524363128270445 X37=(0.5348987051667825+i0.21366796323933912) X38=(0.5348987051667825-i0.21366796323933912) X39=(-0.5229320172630343-i1.3377196404144287) X40=(-0.5229320172630343+i1.3377196404144287) X41=-1.3828089722108914 X42=(0.5034736392287467+i0.547822894184506) X43=(0.5034736392287467-i0.547822894184506) X44=(-0.4085756220411622+i1.0019786349946802) X45=(-0.4085756220411622-i1.0019786349946802) X46=(0.1338590444327253+i0.9491550610983123) X47=(0.1338590444327253-i0.9491550610983123) X48=(-0.9356599974655856+i0.5796710635241921) X49=(-0.9356599974655856-i0.5796710635241921) X50=(0.08218878863665756-i1.1576210400674753) X51=(0.08218878863665756+i1.1576210400674753) X52=(-0.9902416307412252+i0.7704801398266679) X53=(-0.9902416307412252-i0.7704801398266679) X54=(0.5412616494798888+i0.27410562541543626) X55=(0.5412616494798888-i0.27410562541543626) X56=(0.11276698083127987+i1.0789859488045919) X57=(0.11276698083127987-i1.0789859488045919) X58=(-0.9209248386997396+i0.32301474136206115) X59=(-0.9209248386997396-i0.32301474136206115) X60=(0.43414690499305714-i0.7207219616523057) X61=(0.43414690499305714+i0.7207219616523057) X62=(-0.6001436435153691+i0.8035244615365473) X63=(-0.6001436435153691-i0.8035244615365473) X64=(-0.11107596091286277-i0.973514904653001) X65=(-0.11107596091286277+i0.973514904653001) X66=(0.45938537275652436-i0.6845520112168386) X67=(0.45938537275652436+i0.6845520112168386) X68=(-0.8206397427766251+i0.567038388775588) X69=(-0.8206397427766251-i0.567038388775588) X70=(0.11646109870013077-i0.9992756926017785) X71=(0.11646109870013077+i0.9992756926017785) X72=(-0.279471680655295+i0.9353621386130231) X73=(-0.279471680655295-i0.9353621386130231) X74=(-0.9659230161134319+i0.0805462510520349) X75=(-0.9659230161134319-i0.0805462510520349) X76=(0.5109537396100541-i0.07975262843221655) X77=(0.5109537396100541+i0.07975262843221655) X78=(-0.7095164179476493+i0.7025187054724679) X79=(-0.7095164179476493-i0.7025187054724679) X80=(0.5162134262696109-i0.4907064163439118) X81=(0.5162134262696109+i0.4907064163439118) X82=(-0.4450628147443532-i0.8788426017282867) X83=(-0.4450628147443532+i0.8788426017282867) X84=(0.24267124872650606+i0.8397131256176332) X85=(0.24267124872650606-i0.8397131256176332) X86=(-0.9413752920339894+i0.2422111873304941) X87=(-0.9413752920339894-i0.2422111873304941) X88=(0.49300997630834165+i0.599391306052551) X89=(0.49300997630834165-i0.599391306052551) X90=(-0.1958877990748069-i0.9588683628640147) X91=(-0.1958877990748069+i0.9588683628640147) X92=(0.30645133028868893-i0.8022848005501885) X93=(0.30645133028868893+i0.8022848005501885) X94=(-0.8633057930285172+i0.48417545354513575) X95=(-0.8633057930285172-i0.48417545354513575) X96=(0.05151777985816809-i0.9793513795410506) X97=(0.05151777985816809+i0.9793513795410506) X98=(-0.6549293912507504+i0.7601888684621326) X99=(-0.6549293912507504-i0.7601888684621326) X100=(0.5242262309304714-i0.15014108841661888) X101=(0.5242262309304714+i0.15014108841661888) X102=(-0.8946216668244085+i0.40327933536946936) X103=(-0.8946216668244085-i0.40327933536946936) X104=(0.4023188287919155-i0.7513356658252952) X105=(0.4023188287919155+i0.7513356658252952) X106=(-0.5270055040205295-i0.8396202118401351) X107=(-0.5270055040205295+i0.8396202118401351) X108=(-0.36036261667347597+i0.9093397061706036) X109=(-0.36036261667347597-i0.9093397061706036) X110=(0.5444033058235214-i0.33098563994698665) X111=(0.5444033058235214+i0.33098563994698665) X112=(-0.9561344253571543+i0.16128332224646436) X113=(-0.9561344253571543-i0.16128332224646436) X114=(0.1834609000093228-i0.892518593286507) X115=(0.1834609000093228+i0.892518593286507) X116=(-0.028369160340762804-i0.9788718566453424) X117=(-0.028369160340762804+i0.9788718566453424) X118=-0.6866453215788658 X119=0.503563224551449 X120=0.11462723499696824 X121=(-0.766505398647787+i0.6396028566692163) X122=(-0.766505398647787-i0.6396028566692163) X123=(0.5313760720995985-i0.43558194102773734) X124=(0.5313760720995985+i0.43558194102773734) X125=-0.9696629177738161 X126=(-0.3591046297101545+i0.6173487636666921) X127=(-0.3591046297101545-i0.6173487636666921) X128=0 ============================================= period 9 ( probably bad roots !!!!!!!!!!! ) see above For the real Polynomial: +1x^256+128x^255+8128x^254+341440x^253+10676064x^252+265070400x^251+5444445216x^250+95166629216x^249+1445348279984x^248+19378537561280x^247+232268682367776x^246+2514273632010848x^245+24788919621401424x^244+224191664094990370x^243+1871297598686042600x^242+14491605396979153000x^241+104602447595513700000x^240+706618798086250400000x^239+4.483505696773631e+21x^238+2.6806924022759844e+22x^237+1.5147526317091358e+23x^236+8.110580813779278e+23x^235+4.125012901912075e+24x^234+1.997194460379286e+25x^233+9.223966618378913e+25x^232+4.071265506462485e+26x^231+1.720309814938175e+27x^230+6.970220391424263e+27x^229+2.7120492587985475e+28x^228+1.0147637258180529e+29x^227+3.656068971029832e+29x^226+1.2699192517382172e+30x^225+4.257434387934555e+30x^224+1.379108078241045e+31x^223+4.320843158980755e+31x^222+1.3106152258165564e+32x^221+3.85223108926963e+32x^220+1.0981276615394526e+33x^219+3.038437621115521e+33x^218+8.166585853663073e+33x^217+2.133745334757832e+34x^216+5.423257299456389e+34x^215+1.3417846127232617e+35x^214+3.2336010162083995e+35x^213+7.595120897671362e+35x^212+1.7397208105862568e+36x^211+3.888321184608781e+36x^210+8.48424729413649e+36x^209+1.8082333476489765e+37x^208+3.7661532090006723e+37x^207+7.669160026615687e+37x^206+1.527565865882524e+38x^205+2.9774396518452634e+38x^204+5.681439267049956e+38x^203+1.0617468868231017e+39x^202+1.944014108104146e+39x^201+3.488640599323216e+39x^200+6.138304551418968e+39x^199+1.0593211860911769e+40x^198+1.793661484274345e+40x^197+2.9807713640365373e+40x^196+4.863281281625551e+40x^195+7.792476087136796e+40x^194+1.22657922928895e+41x^193+1.897205982803946e+41x^192+2.884383805383309e+41x^191+4.3115022227853235e+41x^190+6.3380410328185975e+41x^189+9.165220128563138e+41x^188+1.3040659661714854e+42x^187+1.8261202540122225e+42x^186+2.5172929877396005e+42x^185+3.4167355345421657e+42x^184+4.5672848793159376e+42x^183+6.014053930340374e+42x^182+7.802429718010215e+42x^181+9.975488936723065e+42x^180+1.2570901757592986e+43x^179+1.5617463352691422e+43x^178+1.9131461054431363e+43x^177+2.311314496359107e+43x^176+2.7543612052598816e+43x^175+3.2382430080344296e+43x^174+3.756631173520194e+43x^173+4.300909846226485e+43x^172+4.860322868993083e+43x^171+5.422275242262181e+43x^170+5.972782334382791e+43x^169+6.497046378337308e+43x^168+6.980127188809167e+43x^167+7.407663859867006e+43x^166+7.766597689806514e+43x^165+8.045844569150479e+43x^164+8.236867894706779e+43x^163+8.334110511333074e+43x^162+8.335255474799097e+43x^161+8.241299381198167e+43x^160+8.056437150635257e+43x^159+7.787771926829333e+43x^158+7.444876705817495e+43x^157+7.039244256249501e+43x^156+6.583668058600301e+43x^155+6.0915990501386155e+43x^154+5.576521056994244e+43x^153+5.051382467485111e+43x^152+4.528113795742205e+43x^151+4.0172513173808543e+43x^150+3.5276769831415485e+43x^149+3.066475301914884e+43x^148+2.6388996224287917e+43x^147+2.248433785329757e+43x^146+1.8969307550404378e+43x^145+1.5848076139733748e+43x^144+1.3112760387937096e+43x^143+1.0745887515313572e+43x^142+8.72285026277122e+42x^141+7.014216818665685e+42x^140+5.587796699064813e+42x^139+4.410400032648403e+42x^138+3.449260745731498e+42x^137+2.673121933311782e+42x^136+2.0530032136692418e+42x^135+1.562684870749208e+42x^134+1.1789524904021462e+42x^133+8.816494249129489e+41x^132+6.535838482116545e+41x^131+4.803335418960428e+41x^130+3.499859788313721e+41x^129+2.528447069666606e+41x^128+1.8112625357187405e+41x^127+1.286653375926709e+41x^126+9.064046785865054e+40x^125+6.332721962595584e+40x^124+4.388268710597122e+40x^123+3.016177110037234e+40x^122+2.0563979211389322e+40x^121+1.390815625231185e+40x^120+9.331877019067401e+39x^119+6.21197942895509e+39x^118+4.102765146235919e+39x^117+2.688639819941138e+39x^116+1.7483210378914757e+39x^115+1.1281457184292358e+39x^114+7.224156685215784e+38x^113+4.591019723609199e+38x^112+2.895695797043167e+38x^111+1.8127581036540613e+38x^110+1.1263955501110858e+38x^109+6.947472011591809e+37x^108+4.253709292829882e+37x^107+2.585436624753953e+37x^106+1.560072245439443e+37x^105+9.345865932333407e+36x^104+5.558752947317759e+36x^103+3.2827425698464324e+36x^102+1.9249356699235142e+36x^101+1.1208139717289263e+36x^100+6.480468913364954e+35x^99+3.720936318816738e+35x^98+2.121719446901434e+35x^97+1.2015179583514156e+35x^96+6.75764718089223e+34x^95+3.774850160022868e+34x^94+2.094394883027613e+34x^93+1.1542168939148693e+34x^92+6.318315736467813e+33x^91+3.4356978664587893e+33x^90+1.8558493768589205e+33x^89+9.958608449152775e+32x^88+5.3088015471949996e+32x^87+2.8115747803588815e+32x^86+1.4793509022208807e+32x^85+7.7334622168103465e+31x^84+4.016709566908882e+31x^83+2.0728734298657763e+31x^82+1.062901304005033e+31x^81+5.415549467449775e+30x^80+2.7417819208644753e+30x^79+1.379352239359451e+30x^78+6.895729284706297e+29x^77+3.425772908031025e+29x^76+1.691300019512475e+29x^75+8.298060411061537e+28x^74+4.04609709076319e+28x^73+1.9606924238994356e+28x^72+9.442904099029667e+27x^71+4.5199525891545277e+27x^70+2.1503215257084464e+27x^69+1.0167705248948402e+27x^68+4.778604357477038e+26x^67+2.2322667273654017e+26x^66+1.036492135501938e+26x^65+4.783751196614701e+25x^64+2.1946295142986957e+25x^63+1.0008084544181525e+25x^62+4.536746451258604e+24x^61+2.044316329571573e+24x^60+9.157301866900901e+23x^59+4.0776327628043235e+23x^58+1.8049892042374278e+23x^57+7.942756312655764e+22x^56+3.4745744569472475e+22x^55+1.5110150073211914e+22x^54+6.532435099515038e+21x^53+2.8075169497670133e+21x^52+1.1995319437992528e+21x^51+509499807078842800000x^50+215138987697889480000x^49+90310195379140130000x^48+37687412945772085000x^47+15634961825829063000x^46+6448181040666496000x^45+2643726144349102000x^44+1077540604058822500x^43+436604408356041200x^42+175865084154629020x^41+70422002837291224x^40+28033353858438104x^39+11093812898913788x^38+4364426595039604x^37+1706930089807390x^36+663663412897100x^35+256521909225414x^34+98570133024230x^33+37653810688701x^32+14299203591952x^31+5398194738600x^30+2025867409304x^29+755767816996x^28+280263417112x^27+103306269964x^26+37848254300x^25+13781448434x^24+4986986168x^23+1793215404x^22+640655364x^21+227377494x^20+80152748x^19+28056886x^18+9750118x^17+3363133x^16+1151240x^15+390964x^14+131596x^13+43810x^12+14364x^11+4606x^10+1430x^9+429x^8+132x^7+42x^6+14x^5+5x^4+2x^3+1x^2+1x The Solutions are: X1=(-0.7007039049868906+i3.124085847082636) X2=(-0.7007039049868906-i3.124085847082636) X3=(-5.575154724946352-i2.9676021751460446) X4=(-5.575154724946352+i2.9676021751460446) X5=(-3.9089062206992815-i3.859207758212847) X6=(-3.9089062206992815+i3.859207758212847) X7=(0.5085866241855378-i1.5750018688607252) X8=(0.5085866241855378+i1.5750018688607252) X9=(-6.737319144845511+i1.237772418780232) X10=(-6.737319144845511-i1.237772418780232) X11=(-2.457710174690323-i3.8713394767573863) X12=(-2.457710174690323+i3.8713394767573863) X13=(0.1327996281397198+i2.3818882883057073) X14=(0.1327996281397198-i2.3818882883057073) X15=(-4.788837297802911+i3.5096037148995856) X16=(-4.788837297802911-i3.5096037148995856) X17=(-6.252592218454132+i2.236426287255418) X18=(-6.252592218454132-i2.236426287255418) X19=(-1.3764515168389215-i3.592888461574985) X20=(-1.3764515168389215+i3.592888461574985) X21=-6.881718410879269 X22=(0.39231391710866975-i1.9561381501835) X23=(0.39231391710866975+i1.9561381501835) X24=(-3.0897602295664455+i3.952822838581382) X25=(-3.0897602295664455-i3.952822838581382) X26=(-1.9083347944242628+i3.7887356008345265) X27=(-1.9083347944242628-i3.7887356008345265) X28=(-3.9118563990552717+i2.7314711108200345) X29=(-3.9118563990552717-i2.7314711108200345) X30=-5.9506528206375275 X31=(0.4603056837263181+i0.326899504414351) X32=(0.4603056837263181-i0.326899504414351) X33=(-0.3607863081289777+i2.9097281490912934) X34=(-0.3607863081289777-i2.9097281490912934) X35=(-0.08332412634122079+i2.6398090496826647) X36=(-0.08332412634122079-i2.6398090496826647) X37=(-2.9552765464074975+i0.7179302050329736) X38=(-2.9552765464074975-i0.7179302050329736) X39=(-0.9911061664679548+i3.311233689141533) X40=(-0.9911061664679548-i3.311233689141533) X41=(0.2864670198605454+i2.1596889725641772) X42=(0.2864670198605454-i2.1596889725641772) X43=-3.0046451800334744 X44=(0.5659091797459681-i1.297465863102758) X45=(0.5659091797459681+i1.297465863102758) X46=(0.457104844829094-i1.7596381870250226) X47=(0.457104844829094+i1.7596381870250226) X48=(-1.6428318705855613+i1.5253501479938236) X49=(-1.6428318705855613-i1.5253501479938236) X50=(-1.1268453159085334+i2.161720111715668) X51=(-1.1268453159085334-i2.161720111715668) X52=(0.5462028860550315-i0.9519206764782964) X53=(0.5462028860550315+i0.9519206764782964) X54=(-2.2176797719245105+i0.8904377435337225) X55=(-2.2176797719245105-i0.8904377435337225) X56=(-0.28712888819472293+i2.2601648282675364) X57=(-0.28712888819472293-i2.2601648282675364) X58=(-0.42008415316043274+i1.4891443873506611) X59=(-0.42008415316043274-i1.4891443873506611) X60=(0.5506266699538993-i0.6733115894640584) X61=(0.5506266699538993+i0.6733115894640584) X62=(-1.5360181246833677+i0.9856780141102516) X63=(-1.5360181246833677-i0.9856780141102516) X64=-1.70563502650579 X65=(0.5462816858272322+i1.4308881482989284) X66=(0.5462816858272322-i1.4308881482989284) X67=(0.3570961175579061-i1.6275868152543984) X68=(0.3570961175579061+i1.6275868152543984) X69=(-0.9841603739721687+i1.3224762639524585) X70=(-0.9841603739721687-i1.3224762639524585) X71=(-1.2868457324305553+i0.4252153625193221) X72=(-1.2868457324305553-i0.4252153625193221) X73=(0.48178951841612044+i0.5444005645025989) X74=(0.48178951841612044-i0.5444005645025989) X75=(-0.3175752247349443+i1.1541327357466606) X76=(-0.3175752247349443-i1.1541327357466606) X77=(0.454164238918465-i1.1052516373053307) X78=(0.454164238918465+i1.1052516373053307) X79=(-1.1096626405760217+i0.8027628710037247) X80=(-1.1096626405760217-i0.8027628710037247) X81=(0.20393492672311472+i1.261780009873258) X82=(0.20393492672311472-i1.261780009873258) X83=(0.5626743914624156-i0.8038664291206359) X84=(0.5626743914624156+i0.8038664291206359) X85=(-0.6795604587568789+i0.883190641045306) X86=(-0.6795604587568789-i0.883190641045306) X87=(0.5664179355570752-i1.1675265982839833) X88=(0.5664179355570752+i1.1675265982839833) X89=(-1.1963839056681453+i0.23586325329811444) X90=(-1.1963839056681453-i0.23586325329811444) X91=(0.558489522409599+i1.0433259441676446) X92=(0.558489522409599-i1.0433259441676446) X93=(-0.895297201557029-i0.522734949358673) X94=(-0.895297201557029+i0.522734949358673) X95=(-0.2609717842884895-i0.9880558567438502) X96=(-0.2609717842884895+i0.9880558567438502) X97=(0.12289539495792566-i0.9999261899996964) X98=(0.12289539495792566+i0.9999261899996964) X99=(0.4051982678341523+i0.14085177561009354) X100=(0.4051982678341523-i0.14085177561009354) X101=(0.5352439700146511-i0.6226543511702295) X102=(0.5352439700146511+i0.6226543511702295) X103=(-0.8265763567757363+i0.24019954827975132) X104=(-0.8265763567757363-i0.24019954827975132) X105=(-0.4700653235077925+i0.8058882306317116) X106=(-0.4700653235077925-i0.8058882306317116) X107=(-0.12023289944287907+i0.9003730477987565) X108=(-0.12023289944287907-i0.9003730477987565) X109=(0.5545805020890305-i0.8826154769675215) X110=(0.5545805020890305+i0.8826154769675215) X111=(-0.7180366967722276+i0.48810638474237544) X112=(-0.7180366967722276-i0.48810638474237544) X113=(0.45628211989426226+i0.4103496288402397) X114=(0.45628211989426226-i0.4103496288402397) X115=(0.560170583960945+i0.7332665619606243) X116=(0.560170583960945-i0.7332665619606243) X117=(-0.877120111713245-i0.15163234235762055) X118=(-0.877120111713245+i0.15163234235762055) X119=(-0.26385873339094534+i0.7776116496984558) X120=(-0.26385873339094534-i0.7776116496984558) X121=(0.44665207192714224-i0.2436358578038517) X122=(0.44665207192714224+i0.2436358578038517) X123=(-0.6705670746404108+i0.4806236336026044) X124=(-0.6705670746404108-i0.4806236336026044) X125=(-0.11641050008509947-i0.8030109291733984) X126=(-0.11641050008509947+i0.8030109291733984) X127=(0.2335436668167368+i0.6685475140159926) X128=(0.2335436668167368-i0.6685475140159926) X129=(0.39445448745560335+i0.7166577003685537) X130=(0.39445448745560335-i0.7166577003685537) X131=(-0.6628782518497396-i0.18365453963297887) X132=(-0.6628782518497396+i0.18365453963297887) X133=(0.5135033376530523+i0.579625343193569) X134=(0.5135033376530523-i0.579625343193569) X135=(-0.4396168918409238+i0.4755843809175498) X136=(-0.4396168918409238-i0.4755843809175498) X137=(0.049597031518581296-i0.6836261530818308) X138=(0.049597031518581296+i0.6836261530818308) X139=(-0.35779819968847826+i0.6018423799828644) X140=(-0.35779819968847826-i0.6018423799828644) X141=(0.4334267156770133-i0.5074823355869046) X142=(0.4334267156770133+i0.5074823355869046) X143=-0.6555706848530993 X144=(-0.21848700452386394+i0.5620671043232068) X145=(-0.21848700452386394-i0.5620671043232068) X146=(0.441674702537725-i0.22859505080646528) X147=(0.441674702537725+i0.22859505080646528) X148=(-0.5399868372774212+i0.383715447683622) X149=(-0.5399868372774212-i0.383715447683622) X150=(0.47155623438093697+i0.3574601332952856) X151=(0.47155623438093697-i0.3574601332952856) X152=(0.4528851072034209+i0.5418883823081684) X153=(0.4528851072034209-i0.5418883823081684) X154=(-0.5918613078895278+i0.13128190249340538) X155=(-0.5918613078895278-i0.13128190249340538) X156=(0.12877822843989334+i0.6384189512713739) X157=(0.12877822843989334-i0.6384189512713739) X158=(-0.12345573135445091-i0.6039942405347092) X159=(-0.12345573135445091+i0.6039942405347092) X160=(0.20461474160560175-i0.5764653793646193) X161=(0.20461474160560175+i0.5764653793646193) X162=(-0.5452210382546214+i0.2676146437822288) X163=(-0.5452210382546214-i0.2676146437822288) X164=(0.3706552499447791-i0.10101753623495831) X165=(0.3706552499447791+i0.10101753623495831) X166=(-0.40856093498062995-i0.4532072792846689) X167=(-0.40856093498062995+i0.4532072792846689) X168=(0.015884964285275634+i0.6044942255886885) X169=(0.015884964285275634-i0.6044942255886885) X170=(0.3888671921809587+i0.5020444348479068) X171=(0.3888671921809587-i0.5020444348479068) X172=(-0.5957796218337377+i0.09175108913884059) X173=(-0.5957796218337377-i0.09175108913884059) X174=(0.46716600532884567+i0.38277233342683964) X175=(0.46716600532884567-i0.38277233342683964) X176=(-0.29465219113755003-i0.5493715295938079) X177=(-0.29465219113755003+i0.5493715295938079) X178=(-0.3758119491741923-i0.4749043800574368) X179=(-0.3758119491741923+i0.4749043800574368) X180=(0.28012995922435835-i0.5464461308338956) X181=(0.28012995922435835+i0.5464461308338956) X182=(-0.09071687803363587-i0.6045852908222767) X183=(-0.09071687803363587+i0.6045852908222767) X184=-0.6383954703655252 X185=(0.4266482475110936+i0.21546623930397343) X186=(0.4266482475110936-i0.21546623930397343) X187=(-0.46544542325240307+i0.396977995070071) X188=(-0.46544542325240307-i0.396977995070071) X189=(0.3460544337065776-i0.5134198767412984) X190=(0.3460544337065776+i0.5134198767412984) X191=(0.4668148580509692-i0.3966312752961633) X192=(0.4668148580509692+i0.3966312752961633) X193=(-0.5602687690905381+i0.23418346866240936) X194=(-0.5602687690905381-i0.23418346866240936) X195=(-0.18353728010127843+i0.5774672397259287) X196=(-0.18353728010127843-i0.5774672397259287) X197=(0.08066775763891837-i0.6095945353819846) X198=(0.08066775763891837+i0.6095945353819846) X199=(-0.05214875806925636-i0.6064215729932745) X200=(-0.05214875806925636+i0.6064215729932745) X201=(-0.5129219591102157-i0.33471959762662856) X202=(-0.5129219591102157+i0.33471959762662856) X203=(0.44084132619031974+i0.20705851325166064) X204=(0.44084132619031974-i0.20705851325166064) X205=(0.3152881096831578+i0.5318355863324926) X206=(0.3152881096831578-i0.5318355863324926) X207=(-0.5746424646985783+i0.20095376766351064) X208=(-0.5746424646985783-i0.20095376766351064) X209=(-0.312488813884519-i0.5171013357655939) X210=(-0.312488813884519+i0.5171013357655939) X211=(0.47095553940261375+i0.3449914301624679) X212=(0.47095553940261375-i0.3449914301624679) X213=(0.16550247151617284-i0.591189980144925) X214=(0.16550247151617284+i0.591189980144925) X215=(-0.49107648632397155+i0.36742216723346693) X216=(-0.49107648632397155-i0.36742216723346693) X217=(0.12313596222735473-i0.6043586059017971) X218=(0.12313596222735473+i0.6043586059017971) X219=(0.44223774717479114-i0.41166216144828743) X220=(0.44223774717479114+i0.41166216144828743) X221=(-0.6013906233143527+i0.049558017366327624) X222=(-0.6013906233143527-i0.049558017366327624) X223=(-0.013548050961732158+i0.6070787491122847) X224=(-0.013548050961732158-i0.6070787491122847) X225=(-0.2524281492846016+i0.5433567001327814) X226=(-0.2524281492846016-i0.5433567001327814) X227=(0.4065893397684931-i0.1502465763212361) X228=(0.4065893397684931+i0.1502465763212361) X229=(0.3535157561301442+i0.49590438547663274) X230=(0.3535157561301442-i0.49590438547663274) X231=(-0.5859551123852098+i0.16744274509041573) X232=(-0.5859551123852098-i0.16744274509041573) X233=(0.4310864873337161+i0.31872004064932496) X234=(0.4310864873337161-i0.31872004064932496) X235=(-0.43906480435611284+i0.4255145365353073) X236=(-0.43906480435611284-i0.4255145365353073) X237=(0.04282477783458463-i0.6099060929231175) X238=(0.04282477783458463+i0.6099060929231175) X239=(-0.3443697899596327+i0.49563205541341104) X240=(-0.3443697899596327-i0.49563205541341104) X241=(0.24259495984198637-i0.5615515291302183) X242=(0.24259495984198637+i0.5615515291302183) X243=(-0.529788182574507-i0.30120290110446774) X244=(-0.529788182574507+i0.30120290110446774) X245=(-0.150157463984143+i0.5928369452618341) X246=(-0.150157463984143-i0.5928369452618341) X247=-0.6092453125363864 X248=(0.3450755034213706+i0.0909141459509047) X249=(0.3450755034213706-i0.0909141459509047) X250=(-0.27254253352686336+i0.5297545355184442) X251=(-0.27254253352686336-i0.5297545355184442) X252=(0.2756542698705202-i0.44468761621810143) X253=(0.2756542698705202+i0.44468761621810143) X254=-0.49954273871159294 X255=-0.506151262613412 X256=0