w2:=sqrt(2); w3:=sqrt(3); w5:=sqrt(5); w31:=sqrt(31); I:=sqrt(-1); w10:=w2*w5; w15:=w3*w5; w62:=w2*w31; w155:=w5*w31; w310:=w10*w31; r1:=sqrt((w5-1)/2); r2:=sqrt(6+w5); a:=(31*(3*I*w15-43))^(1/3); r3:=-1/496*a^2*I*w15-43/1488*a^2+a/3-1/3; t:=cos(2*Pi/31); s1:=16384*t^14 - 53248*t^12 + 66560*t^10 - 39936*t^8 + 128*t^7 + 11712*t^6 - 224*t^5 - 1552*t^4 + 120*t^3 + 88*t^2 - 20*t - 2; s2:=-64*t^6 - 32*t^5 + 96*t^4 + 40*t^3 - 36*t^2 - 12*t + 2; fid124:=[ ((9300*w155 + 19220*w5 - 26660*w31 - 19220)*r3^2 + (44640*w155 + 115320*w5 - 120280*w31 - 153760)*r3 - 88660*w155 + 19220*w5 + 313100*w31 - 672700)*I + (-76880*w10 + 9300*w155 + 230640*w2 - 19220*w5 - 26660*w31 + 19220)*r3^2 + (-269080*w10 + 44640*w155 + 884120*w2 - 115320*w5 - 120280*w31 + 153760)*r3 + 961000*w10 - 88660*w155 - 3267400*w2 - 19220*w5 + 313100*w31 + 672700, (((86*w155 - 358*w5 - 142*w31 + 970)*r1*r2*r3^2 + (476*w155 - 1496*w5 - 816*w31 + 4140)*r1*r2*r3 + (1271*w10 - 4061*w2)*r1*r3^2 + (805*w10 - 1513*w2)*r2*r3^2 + (-2179*w155 + 9003*w5 + 3665*w31 - 24165)*r1*r2 + (5735*w10 - 18383*w2)*r1*r3 + (3058*w10 - 5824*w2)*r2*r3 + (-130*w155 + 496*w5 + 570*w31 - 620)*r3^2 + (-32891*w10 + 99355*w2)*r1 + (-19630*w10 + 37180*w2)*r2 + (-128*w155 + 4464*w5 + 1620*w31 - 8060)*r3 + (2035*w155 - 17825*w5 - 10735*w31 + 27745))*s1^2*s2^4 + ((52*w155 - 376*w5 - 144*w31 + 520)*r1*r2*r3^2 + (262*w155 - 1222*w5 - 662*w31 + 1070)*r1*r2*r3 + (-403*w10 - 1147*w2)*r1*r3^2 + (385*w10 - 481*w2)*r2*r3^2 + (-1623*w155 + 8311*w5 + 4205*w31 - 11705)*r1*r2 + (-775*w10 - 6541*w2)*r1*r3 + (856*w10 - 238*w2)*r2*r3 + (40*w155 - 558*w5 - 80*w31 + 930)*r3^2 + (8153*w10 + 27435*w2)*r1 + (-8620*w10 + 11110*w2)*r2 + (254*w155 - 1922*w5 - 570*w31 + 2790)*r3 - 1425*w155 + 17515*w5 + 3005*w31 - 33635)*s1^2*s2^3 + ((-174*w155 - 590*w5 + 322*w31 + 1494)*r1*r2*r3^2 + (-628*w155 - 3436*w5 + 1036*w31 + 8092)*r1*r2*r3 + (1891*w10 - 3813*w2)*r1*r3^2 + (1415*w10 - 3623*w2)*r2*r3^2 + (4071*w155 + 17193*w5 - 7645*w31 - 42615)*r1*r2 + (6727*w10 - 13299*w2)*r1*r3 + (7784*w10 - 20354*w2)*r2*r3 + (260*w155 - 2790*w5 - 616*w31 + 7006)*r3^2 + (-45601*w10 + 92845*w2)*r1 + (-37556*w10 + 91850*w2)*r2 + (814*w155 - 14322*w5 - 1878*w31 + 34658)*r3 - 7387*w155 + 64449*w5 + 18535*w31 - 159185)*s1*s2^4 + ((-881*w155 + 3383*w5 + 1337*w31 - 9975)*r1*r2*r3^2 + (-4856*w155 + 14576*w5 + 7876*w31 - 44180)*r1*r2*r3 + (-15376*w10 + 45136*w2)*r1*r3^2 + (-8230*w10 + 15838*w2)*r2*r3^2 + (21369*w155 - 88283*w5 - 32865*w31 + 250915)*r1*r2 + (-68200*w10 + 203608*w2)*r1*r3 + (-32188*w10 + 63424*w2)*r2*r3 + (1370*w155 - 5766*w5 - 6120*w31 + 7440)*r3^2 + (394816*w10 - 1106080*w2)*r1 + (201860*w10 - 390280*w2)*r2 + (1368*w155 - 48484*w5 - 17720*w31 + 87420)*r3 - 21410*w155 + 203050*w5 + 115260*w31 - 319920)*s1^2*s2^2 + ((-248*w155 - 540*w5 + 484*w31 + 388)*r1*r2*r3^2 + (-1086*w155 - 3522*w5 + 2142*w31 + 3834)*r1*r2*r3 + (837*w10 - 651*w2)*r1*r3^2 + (205*w10 - 1261*w2)*r2*r3^2 + (5557*w155 + 11131*w5 - 10815*w31 - 9405)*r1*r2 + (1209*w10 + 3627*w2)*r1*r3 + (2968*w10 - 10678*w2)*r2*r3 + (80*w155 - 1550*w5 - 232*w31 + 4402)*r3^2 + (-17267*w10 + 14415*w2)*r1 + (-7772*w10 + 33550*w2)*r2 + (198*w155 - 7874*w5 - 506*w31 + 21886)*r3 - 3749*w155 + 38223*w5 + 10745*w31 - 103695)*s1*s2^3 + ((-958*w155 - 26*w5 + 2042*w31 - 2138)*r1*r2*r3^2 + (-4634*w155 - 5574*w5 + 9906*w31 + 1886)*r1*r2*r3 + (-8184*w10 + 31248*w2)*r1*r3^2 + (-2580*w10 + 1716*w2)*r2*r3^2 + (22720*w155 - 560*w5 - 49260*w31 + 44900)*r1*r2 + (-35712*w10 + 134664*w2)*r1*r3 + (-1968*w10 - 14232*w2)*r2*r3 + (418*w155 + 2418*w5 - 2418*w31 - 10106)*r3^2 + (212412*w10 - 758260*w2)*r1 + (52992*w10 - 33000*w2)*r2 + (-424*w155 - 5208*w5 - 6324*w31 - 7068)*r3 - 4142*w155 - 40486*w5 + 40610*w31 + 208010)*s2^4 + ((298*w155 - 1064*w5 + 4*w31 + 6570)*r1*r2*r3^2 + (2178*w155 - 8288*w5 - 2008*w31 + 39250)*r1*r2*r3 + (17298*w10 - 33728*w2)*r1*r3^2 + (6015*w10 - 14049*w2)*r2*r3^2 + (-5887*w155 + 34559*w5 - 2355*w31 - 175145)*r1*r2 + (68820*w10 - 139934*w2)*r1*r3 + (29709*w10 - 72327*w2)*r2*r3 + (-1465*w155 + 10633*w5 + 6235*w31 - 15655)*r3^2 + (-426963*w10 + 831265*w2)*r1 + (-155365*w10 + 353265*w2)*r2 + (-1979*w155 + 65937*w5 + 18985*w31 - 113615)*r3 + (29735*w155 - 366885*w5 - 133055*w31 + 642785))*s1^2*s2 + ((1709*w155 + 5345*w5 - 2977*w31 - 14989)*r1*r2*r3^2 + (6068*w155 + 30136*w5 - 8876*w31 - 77152)*r1*r2*r3 + (-20646*w10 + 42718*w2)*r1*r3^2 + (-14890*w10 + 37198*w2)*r2*r3^2 + (-40921*w155 - 164493*w5 + 72345*w31 + 431965)*r1*r2 + (-77562*w10 + 161014*w2)*r1*r3 + (-79594*w10 + 204454*w2)*r2*r3 + (-2740*w155 + 29140*w5 + 6526*w31 - 72106)*r3^2 + (503316*w10 - 1045320*w2)*r1 + (392266*w10 - 941050*w2)*r2 + (-8254*w155 + 150102*w5 + 19458*w31 - 357058)*r3 + (73882*w155 - 684914*w5 - 186260*w31 + 1672760))*s1*s2^2 + ((-1316*w155 - 2632*w5 + 3244*w31 + 4384)*r1*r2*r3^2 + (-5728*w155 - 20148*w5 + 13892*w31 + 38552)*r1*r2*r3 + (1922*w10 + 13206*w2)*r1*r3^2 + (2540*w10 - 11768*w2)*r2*r3^2 + (34820*w155 + 66020*w5 - 83320*w31 - 113400)*r1*r2 + (8246*w10 + 56358*w2)*r1*r3 + (27134*w10 - 91814*w2)*r2*r3 + (-1204*w155 + 7316*w5 + 3004*w31 - 17732)*r3^2 + (-35836*w10 - 301320*w2)*r1 + (-84086*w10 + 309650*w2)*r2 + (-4998*w155 + 26474*w5 + 12522*w31 - 64046)*r3 + (27346*w155 - 202182*w5 - 69430*w31 + 491970))*s2^3 + ((85*w155 + 1465*w5 - 115*w31 - 1195)*r1*r2*r3^2 + (200*w155 + 7030*w5 - 420*w31 - 5910)*r1*r2*r3 + (6820*w10 - 23870*w2)*r1*r3^2 + (-775*w10 + 1705*w2)*r2*r3^2 + (80*w155 - 23360*w5 - 1900*w31 + 17400)*r1*r2 + (30070*w10 - 110360*w2)*r1*r3 + (-3565*w10 + 8215*w2)*r2*r3 + (745*w155 - 2945*w5 - 1185*w31 + 7285)*r3^2 + (-180265*w10 + 577375*w2)*r1 + (19685*w10 - 42625*w2)*r2 + (3390*w155 - 11160*w5 - 5130*w31 + 24180)*r3 - 19430*w155 + 91760*w5 + 34950*w31 - 232500)*s1^2 + ((308*w155 - 3210*w5 - 674*w31 + 15912)*r1*r2*r3^2 + (3086*w155 - 14288*w5 - 7712*w31 + 70166)*r1*r2*r3 + (12338*w10 - 36084*w2)*r1*r3^2 + (15945*w10 - 33639*w2)*r2*r3^2 + (-5747*w155 + 124399*w5 + 11565*w31 - 455645)*r1*r2 + (53816*w10 - 164982*w2)*r1*r3 + (69747*w10 - 153897*w2)*r2*r3 + (3165*w155 - 17205*w5 - 7163*w31 + 39463)*r3^2 + (-318773*w10 + 879935*w2)*r1 + (-400443*w10 + 837375*w2)*r2 + (12247*w155 - 90861*w5 - 27829*w31 + 198059)*r3 - 72271*w155 + 375317*w5 + 167355*w31 - 854205)*s1*s2 + ((8688*w155 - 2824*w5 - 17492*w31 + 30708)*r1*r2*r3^2 + (42584*w155 + 33584*w5 - 87256*w31 + 43024)*r1*r2*r3 + (94364*w10 - 334428*w2)*r1*r3^2 + (31980*w10 - 36756*w2)*r2*r3^2 + (-197440*w155 + 109000*w5 + 406460*w31 - 706700)*r1*r2 + (412052*w10 - 1453404*w2)*r1*r3 + (63108*w10 + 13812*w2)*r2*r3 + (-5378*w155 - 19778*w5 + 28358*w31 + 92566)*r3^2 + (-2438832*w10 + 8133160*w2)*r1 + (-705892*w10 + 834900*w2)*r2 + (-196*w155 + 75268*w5 + 80244*w31 + 21948)*r3 + (62422*w155 + 277326*w5 - 484610*w31 - 1832410))*s2^2 + ((-1355*w155 + 2785*w5 + 1625*w31 - 4775)*r1*r2*r3^2 + (-5950*w155 + 14400*w5 + 6150*w31 - 27500)*r1*r2*r3 + (3410*w10 - 4340*w2)*r1*r3^2 + (-775*w10 - 155*w2)*r2*r3^2 + (33930*w155 - 60110*w5 - 40950*w31 + 106150)*r1*r2 + (17360*w10 - 23870*w2)*r1*r3 + (1085*w10 - 11315*w2)*r2*r3 + (-85*w155 - 6975*w5 - 735*w31 + 15655)*r3^2 + (-84165*w10 + 118575*w2)*r1 + (13795*w10 + 8525*w2)*r2 + (-3260*w155 - 35650*w5 + 2920*w31 + 77190)*r3 + (11650*w155 + 254200*w5 - 3750*w31 - 595200))*s1 + ((1916*w155 + 21692*w5 - 7384*w31 - 60464)*r1*r2*r3^2 + (2388*w155 + 114468*w5 - 17012*w31 - 319892)*r1*r2*r3 + (-114762*w10 + 241614*w2)*r1*r3^2 + (-52290*w10 + 128298*w2)*r2*r3^2 + (-73290*w155 - 537830*w5 + 213170*w31 + 1443550)*r1*r2 + (-506106*w10 + 1052202*w2)*r1*r3 + (-273684*w10 + 693504*w2)*r2*r3 + (11434*w155 - 43586*w5 - 45454*w31 + 60822)*r3^2 + (2843506*w10 - 6064530*w2)*r1 + (1370156*w10 - 3240600*w2)*r2 + (17708*w155 - 298964*w5 - 135372*w31 + 528116)*r3 - 225436*w155 + 1576412*w5 + 950280*w31 - 2669720)*s2 + ((-1160*w155 - 14700*w5 + 2440*w31 + 780)*r1*r2*r3^2 + (-5280*w155 - 67660*w5 + 14820*w31 + 5440)*r1*r2*r3 + (-17670*w10 + 123070*w2)*r1*r3^2 + (-6200*w10 + 11780*w2)*r2*r3^2 + (13460*w155 + 180580*w5 - 19400*w31 + 208600)*r1*r2 + (-53010*w10 + 539710*w2)*r1*r3 + (-23870*w10 + 46190*w2)*r2*r3 + (-4520*w155 + 57040*w5 + 12080*w31 - 151280)*r3^2 + (520180*w10 - 2845800*w2)*r1 + (151590*w10 - 289850*w2)*r2 + (-6010*w155 + 207390*w5 + 21590*w31 - 557690)*r3 + (111890*w155 - 1529230*w5 - 318750*w31 + 4028450)))*I + ((86*w155 + 358*w5 - 142*w31 - 970)*r1*r2*r3^2 + (476*w155 + 1496*w5 - 816*w31 - 4140)*r1*r2*r3 + (-27*w310 + 49*w62)*r1*r3^2 + (-85*w310 + 241*w62)*r2*r3^2 + (-2179*w155 - 9003*w5 + 3665*w31 + 24165)*r1*r2 + (-483*w310 + 787*w62)*r1*r3 + (-526*w310 + 1468*w62)*r2*r3 + (-130*w155 - 496*w5 + 570*w31 + 620)*r3^2 + (803*w310 - 2075*w62)*r1 + (2330*w310 - 6160*w62)*r2 + (-128*w155 - 4464*w5 + 1620*w31 + 8060)*r3 + (2035*w155 + 17825*w5 - 10735*w31 - 27745))*s1^2*s2^4 + ((52*w155 + 376*w5 - 144*w31 - 520)*r1*r2*r3^2 + (262*w155 + 1222*w5 - 662*w31 - 1070)*r1*r2*r3 + (91*w310 - 397*w62)*r1*r3^2 + (-145*w310 + 337*w62)*r2*r3^2 + (-1623*w155 - 8311*w5 + 4205*w31 + 11705)*r1*r2 + (319*w310 - 2011*w62)*r1*r3 + (-712*w310 + 1726*w62)*r2*r3 + (40*w155 + 558*w5 - 80*w31 - 930)*r3^2 + (-2649*w310 + 9125*w62)*r1 + (3740*w310 - 8470*w62)*r2 + (254*w155 + 1922*w5 - 570*w31 - 2790)*r3 - 1425*w155 - 17515*w5 + 3005*w31 + 33635)*s1^2*s2^3 + ((-174*w155 + 590*w5 + 322*w31 - 1494)*r1*r2*r3^2 + (-628*w155 + 3436*w5 + 1036*w31 - 8092)*r1*r2*r3 + (-315*w310 + 733*w62)*r1*r3^2 + (265*w310 - 457*w62)*r2*r3^2 + (4071*w155 - 17193*w5 - 7645*w31 + 42615)*r1*r2 + (-1791*w310 + 4219*w62)*r1*r3 + (904*w310 - 1486*w62)*r2*r3 + (260*w155 + 2790*w5 - 616*w31 - 7006)*r3^2 + (8273*w310 - 18925*w62)*r1 + (-6332*w310 + 11110*w62)*r2 + (814*w155 + 14322*w5 - 1878*w31 - 34658)*r3 - 7387*w155 - 64449*w5 + 18535*w31 + 159185)*s1*s2^4 + ((-881*w155 - 3383*w5 + 1337*w31 + 9975)*r1*r2*r3^2 + (-4856*w155 - 14576*w5 + 7876*w31 + 44180)*r1*r2*r3 + (352*w310 - 1024*w62)*r1*r3^2 + (710*w310 - 2126*w62)*r2*r3^2 + (21369*w155 + 88283*w5 - 32865*w31 - 250915)*r1*r2 + (5608*w310 - 11512*w62)*r1*r3 + (4676*w310 - 13448*w62)*r2*r3 + (1370*w155 + 5766*w5 - 6120*w31 - 7440)*r3^2 + (-10928*w310 + 34000*w62)*r1 + (-19820*w310 + 54560*w62)*r2 + (1368*w155 + 48484*w5 - 17720*w31 - 87420)*r3 - 21410*w155 - 203050*w5 + 115260*w31 + 319920)*s1^2*s2^2 + ((-248*w155 + 540*w5 + 484*w31 - 388)*r1*r2*r3^2 + (-1086*w155 + 3522*w5 + 2142*w31 - 3834)*r1*r2*r3 + (-485*w310 + 971*w62)*r1*r3^2 + (355*w310 - 739*w62)*r2*r3^2 + (5557*w155 - 11131*w5 - 10815*w31 + 9405)*r1*r2 + (-2297*w310 + 4853*w62)*r1*r3 + (1528*w310 - 3322*w62)*r2*r3 + (80*w155 + 1550*w5 - 232*w31 - 4402)*r3^2 + (12291*w310 - 24575*w62)*r1 + (-8884*w310 + 18370*w62)*r2 + (198*w155 + 7874*w5 - 506*w31 - 21886)*r3 - 3749*w155 - 38223*w5 + 10745*w31 + 103695)*s1*s2^3 + ((-958*w155 + 26*w5 + 2042*w31 + 2138)*r1*r2*r3^2 + (-4634*w155 + 5574*w5 + 9906*w31 - 1886)*r1*r2*r3 + (704*w310 - 760*w62)*r1*r3^2 + (1620*w310 - 3636*w62)*r2*r3^2 + (22720*w155 + 560*w5 - 49260*w31 - 44900)*r1*r2 + (6008*w310 - 7120*w62)*r1*r3 + (7632*w310 - 17928*w62)*r2*r3 + (418*w155 - 2418*w5 - 2418*w31 + 10106)*r3^2 + (-17516*w310 + 27540*w62)*r1 + (-41376*w310 + 91080*w62)*r2 + (-424*w155 + 5208*w5 - 6324*w31 + 7068)*r3 - 4142*w155 + 40486*w5 + 40610*w31 - 208010)*s2^4 + ((298*w155 + 1064*w5 + 4*w31 - 6570)*r1*r2*r3^2 + (2178*w155 + 8288*w5 - 2008*w31 - 39250)*r1*r2*r3 + (-1156*w310 + 4042*w62)*r1*r3^2 + (545*w310 - 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186*w10*r1*r3^2 + (-575*w10 + 1373*w2)*r2*r3^2 + (1671*w155 + 7373*w5 - 2465*w31 - 13455)*r1*r2 + (-1860*w10 + 2790*w2)*r1*r3 + (-2915*w10 + 7229*w2)*r2*r3 + (-539*w155 - 217*w5 + 1341*w31 + 651)*r3^2 + (5487*w10 - 2325*w2)*r1 + (14947*w10 - 34595*w2)*r2 + (-2519*w155 + 1085*w5 + 6133*w31 - 1147)*r3 + (10549*w155 + 1457*w5 - 26325*w31 - 8525))*s1^2*s2^3 + ((152*w155 + 10*w5 - 402*w31 + 64)*r1*r2*r3^2 + (782*w155 + 1288*w5 - 1976*w31 - 2458)*r1*r2*r3 + (-620*w10 + 62*w2)*r1*r3^2 + (-355*w10 - 71*w2)*r2*r3^2 + (-4149*w155 - 3247*w5 + 10935*w31 + 3145)*r1*r2 + (-3038*w10 + 1736*w2)*r1*r3 + (497*w10 - 5183*w2)*r2*r3 + (431*w155 - 1643*w5 - 1153*w31 + 2697)*r3^2 + (15221*w10 - 3875*w2)*r1 + (6319*w10 + 3905*w2)*r2 + (1455*w155 - 12369*w5 - 4189*w31 + 22351)*r3 - 10065*w155 + 40455*w5 + 27145*w31 - 65875)*s1*s2^4 + ((965*w155 - 2747*w5 - 1021*w31 + 8515)*r1*r2*r3^2 + (5160*w155 - 19264*w5 - 5708*w31 + 54700)*r1*r2*r3 + (-682*w10 - 310*w2)*r1*r3^2 + (-6000*w10 + 12936*w2)*r2*r3^2 + (-28663*w155 + 70881*w5 + 32395*w31 - 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2495*w31 - 4495)*r3^2 + (1395*w10 + 6800*w155 + 1705*w2 + 7130*w5 - 12410*w31 - 14260)*r3 + (6045*w10 - 29660*w155 - 58125*w2 - 33170*w5 + 54300*w31 + 94550))*s1^2 + ((7804*w10 - 288*w155 - 17622*w2 - 13778*w5 - 238*w31 + 23148)*r1*r2*r3^2 + (38562*w10 - 2586*w155 - 83936*w2 - 58972*w5 + 1256*w31 + 97214)*r1*r2*r3 + (-187567*w10 + 3159*w155 + 460545*w2 + 306943*w5 + 6495*w31 - 503605)*r1*r2 + (-4619*w10 + 1351*w155 + 18197*w2 - 13733*w5 - 617*w31 + 33759)*r3^2 + (1891*w10 + 11513*w155 + 27311*w2 - 60977*w5 - 13731*w31 + 155527)*r3 + (155403*w10 - 43987*w155 - 566215*w2 + 342891*w5 + 45095*w31 - 835915))*s1*s2 + ((5730*w10 - 6210*w155 - 28490*w2 - 25814*w5 + 14094*w31 + 39130)*r1*r2*r3^2 + (-6208*w10 - 31648*w155 - 48560*w2 - 64440*w5 + 68392*w31 + 59280)*r1*r2*r3 + (-185234*w10 + 158326*w155 + 804690*w2 + 476162*w5 - 376850*w31 - 670790)*r1*r2 + (-20708*w10 + 14166*w155 + 46872*w2 + 123194*w5 - 30278*w31 - 297290)*r3^2 + (-132680*w10 + 55696*w155 + 227416*w2 + 555272*w5 - 114384*w31 - 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