// found a 30-smooth decomposition: T = g^47233*T0 = lc*X^230*poly, row = 1384, leading coeff=1:
poly:=X^255+u^295*X^254+u^477*X^253+u^214*X^252+u^557*X^251+u^50*X^250+u^273*X^249+u^51*X^248+u^725*X^247+u^619*X^246
+u^374*X^245+u^66*X^244+u^591*X^243+u^410*X^242+u^132*X^241+u^619*X^240+u^546*X^239+u^484*X^238+u^618*X^237+u^638*X^236
+u^399*X^235+u^598*X^234+u^701*X^233+u^647*X^232+u^663*X^231+u^78*X^230+u^43*X^229+u^520*X^228+u^151*X^227+u^726*X^226
+u^238*X^225+u^321*X^224+u^415*X^223+u^170*X^222+u^63*X^221+u^615*X^220+u^634*X^219+u^10*X^218+u^126*X^217+u^160*X^216
+u^579*X^215+u^425*X^214+u^93*X^213+u^436*X^212+u^191*X^211+u^573*X^210+u^725*X^209+u^336*X^208+u^19*X^207+u^580*X^206
+u^563*X^205+u^45*X^204+u^330*X^203+u^349*X^202+u^50*X^201+u^166*X^200+u^260*X^199+u^670*X^198+u^44*X^197+u^477*X^196
+u^476*X^195+u^492*X^194+u^71*X^193+X^192+u^277*X^191+u^60*X^190+u^103*X^189+u^403*X^188+u^112*X^187+u^213*X^186
+u^314*X^185+u^404*X^184+u^193*X^183+u^189*X^182+u^727*X^181+u^610*X^180+u^178*X^179+u^432*X^178+u^495*X^177+u^285*X^176
+u^577*X^175+u^444*X^174+u^715*X^173+u^416*X^172+u^644*X^171+u^629*X^170+u^468*X^169+u^293*X^168+u^724*X^167+u^502*X^166
+u^697*X^165+u^272*X^164+u^10*X^163+u^575*X^162+u^411*X^161+u^49*X^160+u^182*X^159+u^285*X^158+u^143*X^157+u^380*X^156
+u^594*X^155+u^349*X^154+u^141*X^153+u^683*X^152+u^102*X^151+u^523*X^150+u^410*X^149+u^300*X^148+u^450*X^147+u^16*X^146
+u^423*X^145+u^159*X^144+u^722*X^143+u^379*X^142+u^465*X^141+u^621*X^140+u^104*X^139+u^293*X^138+u^137*X^137+u^551*X^136
+u^627*X^135+u^158*X^134+u^426*X^133+u^150*X^132+u^484*X^131+u^677*X^130+u^120*X^129+u^75*X^128+u^223*X^127+u^186*X^126
+u^566*X^125+u^258*X^124+u^405*X^123+u^344*X^122+u^82*X^121+u^445*X^120+u^79*X^119+u^215*X^118+u^65*X^117+u^191*X^116
+u^251*X^115+u^169*X^114+u^282*X^113+u^510*X^112+u^617*X^111+u^116*X^110+u^639*X^109+u^552*X^108+u^468*X^107+u^340*X^106
+u^514*X^105+u^527*X^104+u^581*X^103+u^280*X^102+u^360*X^101+u^442*X^100+u^197*X^99+u^696*X^98+u^129*X^97+u^74*X^96
+u^720*X^95+u^235*X^94+u^479*X^93+u^382*X^92+u^308*X^91+u^547*X^90+u^716*X^89+u^35*X^88+u^117*X^87+u^548*X^86+u^94*X^85
+u^133*X^84+u^200*X^83+u^156*X^82+u^212*X^81+u^270*X^80+u^608*X^79+u^418*X^78+u^197*X^77+u^656*X^76+u^255*X^75+u^75*X^74
+u^651*X^73+u^462*X^72+u^285*X^71+u^24*X^70+u^306*X^69+u^396*X^68+u^10*X^67+u^87*X^66+u^656*X^65+u^672*X^64+u^500*X^63
+u^243*X^62+u^700*X^61+u^216*X^60+u^58*X^59+u^471*X^58+u^395*X^57+u^14*X^56+u^184*X^55+u^582*X^54+u^440*X^53+u^131*X^52
+u^137*X^51+u^386*X^50+u^422*X^49+u^79*X^48+u^371*X^47+u^680*X^46+u^321*X^45+u^34*X^44+u^258*X^43+u^23*X^42+u^525*X^41
+u^47*X^40+u^258*X^39+u^246*X^38+u^594*X^37+u^658*X^36+u^490*X^35+u^306*X^34+u^300*X^33+u^61*X^32+u^692*X^31+u^632*X^30
+u^198*X^29+u^485*X^28+u^594*X^27+u^252*X^26+u^342*X^25+u^112*X^24+u^92*X^23+u^455*X^22+u^559*X^21+u^241*X^20+u^656*X^19
+u^45*X^18+u^366*X^17+u^677*X^16+u^61*X^15+u^42*X^14+u^363*X^13+u^681*X^12+u^457*X^11+u^610*X^10+u^573*X^9+u^624*X^8
+u^584*X^7+u^102*X^6+u^692*X^5+u^273*X^4+u^500*X^3+u^700*X^2+u^232*X+u^445;
factors := [
<X, 230>,
<X+u^224, 1>,
<X+u^440, 1>,
<X^2+u^544*X+u^205, 1>,
<X^3+u^141*X^2+u^567*X+u^486, 1>,
<X^16+u^374*X^15+u^543*X^14+u^477*X^13+u^40*X^12+u^9*X^11+u^149*X^10+u^193*X^9+u^76*X^8+u^579*X^7+u^580*X^6+u^521*X^5
 +u^513*X^4+u^22*X^3+u^431*X^2+u^166*X+u^95, 1>,
<X^20+u^559*X^19+u^230*X^18+u^283*X^17+u^118*X^16+u^529*X^15+u^603*X^14+u^228*X^13+u^618*X^12+u^321*X^11+u^335*X^10
 +u^299*X^9+u^86*X^8+u^138*X^7+u^163*X^6+u^262*X^5+u^571*X^4+u^135*X^3+u^544*X^2+u^361*X+u^21, 1>,
<X^21+u^438*X^20+u^94*X^19+u^474*X^18+u^625*X^17+u^207*X^16+u^146*X^15+u^458*X^14+u^525*X^13+u^590*X^12+u^187*X^11
 +u^94*X^10+u^376*X^9+u^64*X^8+u^544*X^7+u^278*X^6+u^29*X^5+u^612*X^4+u^480*X^3+u^181*X^2+u^52*X+u^63, 1>,
<X^23+u^294*X^22+u^523*X^21+u^5*X^20+u^306*X^19+u^332*X^18+u^467*X^17+u^194*X^16+u^727*X^15+u^335*X^14+u^281*X^13
 +u^472*X^12+u^129*X^11+u^719*X^10+u^582*X^9+u^240*X^8+u^483*X^7+u^102*X^6+u^444*X^5+u^236*X^4+u^212*X^3+u^491*X^2+u^491*X
 +u^641, 1>,
<X^27+u^178*X^26+u^652*X^25+u^717*X^24+u^381*X^23+u^578*X^22+u^523*X^21+u^234*X^20+u^642*X^19+u^306*X^18+u^291*X^17
 +u^73*X^16+u^243*X^15+u^396*X^14+u^723*X^13+u^458*X^12+u^215*X^11+u^700*X^10+u^335*X^9+u^493*X^8+u^642*X^7+u^317*X^6
 +u^727*X^5+u^252*X^4+u^538*X^3+u^87*X^2+u^406*X+u^701, 1>,
<X^27+u^649*X^26+u^405*X^25+u^529*X^24+u^24*X^23+u^257*X^22+u^304*X^21+u^7*X^20+u^324*X^19+u^683*X^18+u^349*X^17
 +u^294*X^16+u^522*X^15+u^456*X^14+u^546*X^13+u^221*X^12+u^601*X^11+u^238*X^10+u^379*X^9+u^12*X^8+u^576*X^7+u^587*X^6
 +u^201*X^5+u^2*X^4+u^103*X^3+u^376*X^2+u^339*X+u^274, 1>,
<X^28+u^37*X^27+u^214*X^26+u^473*X^25+u^249*X^24+u^497*X^23+u^553*X^22+u^485*X^21+u^282*X^20+u^13*X^19+u^308*X^18
 +u^356*X^17+u^190*X^16+u^308*X^15+u^400*X^14+u^504*X^13+u^339*X^12+u^96*X^11+u^532*X^10+u^161*X^9+u^572*X^8+u^116*X^7
 +u^686*X^6+u^420*X^5+u^457*X^4+u^571*X^3+u^230*X^2+u^306*X+u^611, 1>,
<X^28+u^296*X^27+u^311*X^26+u^446*X^25+u^220*X^24+u^217*X^23+u^492*X^22+u^159*X^21+u^408*X^20+u^539*X^19+u*X^18+u^109*X^17
 +u^111*X^16+u^179*X^15+u^354*X^14+u^86*X^13+u^587*X^12+u^569*X^11+u^268*X^10+u^647*X^9+u^134*X^8+u^237*X^7+u^173*X^6
 +u^107*X^5+u^388*X^4+u^58*X^3+u^209*X^2+u^244*X+u^104, 1>,
<X^28+u^642*X^27+u^403*X^26+u^24*X^25+u^412*X^24+u^462*X^23+u^434*X^22+u^229*X^21+u^643*X^20+u^721*X^19+u^524*X^18
 +u^663*X^17+u^469*X^16+u^402*X^15+u^210*X^14+u^183*X^13+u^147*X^12+u^606*X^11+u^410*X^10+u^403*X^9+u^163*X^8+u^81*X^7
 +u^526*X^6+u^627*X^5+u*X^3+u^328*X^2+u^611*X+u^314, 1>,
<X^30+u^94*X^29+u^220*X^28+u^4*X^27+u^14*X^26+u^585*X^25+u^528*X^24+u^448*X^23+u^505*X^22+u^307*X^21+u^412*X^20+u^620*X^19
 +u^449*X^18+u^248*X^17+u^72*X^16+u^499*X^15+u^667*X^14+u^410*X^13+u^268*X^12+u^563*X^11+u^420*X^10+u^377*X^9+u^218*X^8
 +u^698*X^7+u^711*X^6+u^613*X^5+u^30*X^4+u^571*X^3+u^386*X^2+u^600*X+u^634, 1>];