u2:=u+1;
u3:=2*u+1;
u4:=3*u+1;
u5:=u;
u6:=u;
u7:=3*u^3-9*u^2-3*u+1;
u8:=7*u^2+2*u-1;
u9:=3*u-1;
u10:=7*u^3-4*u^2-2*u+1;
u11:=5*u^2-1;
u12:=5*u^2-1;
u13:=u^8-24*u^7-12*u^6+8*u^5+38*u^4+24*u^3-12*u^2-8*u+1;
u14:=4*u^4-2*u^3+3*u^2-1;
u15:=13*u^5-u^4+6*u^3+2*u^2-3*u-1;
u16:=23*u^6+6*u^5+5*u^4+4*u^3-3*u^2-2*u-1;
u17:=4*u^10-92*u^9+24*u^8+128*u^7-58*u^6-78*u^5+35*u^4+32*u^3-4*u^2-6*u-1;
u18:=216*u^11+108*u^10+118*u^9+209*u^8-100*u^7-160*u^6+40*u^5+46*u^4-20*u^3-12*u^2+2*u+1;
# u19 unknown
u20:=21*u^3-9*u^2-5*u+1;
# u21 -- u23  unknown
u24:=7*u^3+u^2-3*u-1;
# u25 -- u26  unknown
u27 := 16*u^24-128*u^23+536*u^22-2088*u^21+4977*u^20-12258*u^19+20672*u^18-\
36126*u^17+51043*u^16-73408*u^15+104128*u^14-137928*u^13+175090*u^12-181700*u^
11+155936*u^10-92916*u^9+32222*u^8+6608*u^7-16568*u^6+8192*u^5-1843*u^4-490*u^
3+128*u^2+2*u-1;
# u28 -- u29  unknown
u30 := 21508124014*u^29+32054106929*u^28-17306462662*u^27-25038151480*u^26+
45587477052*u^25+38755887413*u^24-43255133604*u^23-45501640088*u^22+
10460524458*u^21+17929512405*u^20-4828786226*u^19-5447284224*u^18+4496890016*u
^17+4235161545*u^16-436447576*u^15-1539874224*u^14-487336414*u^13+100621747*u^
12+97938998*u^11+20609352*u^10+665516*u^9+320703*u^8+272188*u^7-6712*u^6-34298
*u^5-7289*u^4+386*u^3+368*u^2+56*u+3;
# u31  unknown
u32 := 6561*u^22-4374*u^21-94041*u^20+1289844*u^19+3605067*u^18-4301046*u^17+
6019389*u^16+238896*u^15-10407366*u^14+7894164*u^13+7975830*u^12-7790088*u^11-\
3481466*u^10+3831332*u^9+843658*u^8-1303376*u^7-311819*u^6+148290*u^5+39667*u^
4-3660*u^3-1185*u^2+18*u+9;
# u33 -- u37  unknown
# note that u38 (next) is even and it factors over Q(sqrt(3))
u38:=363*u^14+7685*u^12+34299*u^10-77139*u^8+68985*u^6-31833*u^4+6561*u^2-729;
# u39 -- u47  unknown
u48:=34*u^5+15*u^4-12*u^3-14*u^2-6*u-1;
# u49 unknown
u50:=386*u^12+1679*u^11+6433*u^10-743*u^9-2287*u^8-19290*u^7+8490*u^6+19170*u^5-5580*u^4-6885*u^3-1755*u^2+2997*u-567;
# u51 unknown
u52:=448001*u^16+1243448*u^15+2260200*u^14+2517944*u^13+1365340*u^12-424904*u^11-1782664*u^10-1847944*u^9-864186*u^8-12568*u^7+192280*u^6+95976*u^5+19676*u^4+936*u^3-248*u^2-24*u+1;
# u53 -- u119  unknown
#
# note that u120 (next) factors over Q(sqrt(5))
u120:=1364*u^10+1230*u^9-709*u^8-1468*u^7-688*u^6+136*u^5+286*u^4+108*u^3+4*u^2-6*u-1;
#
# note:  u_n factors over Q(sqrt(2)) for n=8, 16
#        u_n factors over Q(sqrt(3)) for n=38
#        u_n factors over Q(sqrt(5)) for n=11, 12, 120
#        u_n factors over Q(9th roots of unity) for n=7.