/* 7/12/2006 Here's the Humbert component of discriminant 13 (degree 40) I found: It was found by using observed symmetries for the discriminant 5 Humbert component and correctly conjecturing that these symmetries would occur for discriminant 13 (currently conjectured for numbers congruent to 5 mod 8). These symmetries allowed me to deduce that certain monomials lying in a any symmetry orbit have the same coefficient, reducing the size of the linear algebra problem enough for the computation to complete in roughly 11 days. */ //R:=PolynomialRing(Rationals(),3); h13:= e1^20*e2^10*e3^10 - 10*e1^20*e2^9*e3^10 + 45*e1^20*e2^8*e3^10 - 120*e1^20*e2^7*e3^10 + 210*e1^20*e2^6*e3^10 - 252*e1^20*e2^5*e3^10 + 210*e1^20*e2^4*e3^10 - 120*e1^20*e2^3*e3^10 + 45*e1^20*e2^2*e3^10 - 10*e1^20*e2*e3^10 + e1^20*e3^10 - 10*e1^19*e2^11*e3^10 + 266*e1^19*e2^11*e3^9 - 768*e1^19*e2^11*e3^8 + 512*e1^19*e2^11*e3^7 - 442*e1^19*e2^10*e3^10 + 176*e1^19*e2^10*e3^9 + 3328*e1^19*e2^10*e3^8 - 3072*e1^19*e2^10*e3^7 + 266*e1^19*e2^9*e3^11 + 1868*e1^19*e2^9*e3^10 - 6642*e1^19*e2^9*e3^9 - 2560*e1^19*e2^9*e3^8 + 7168*e1^19*e2^9*e3^7 - 1626*e1^19*e2^8*e3^11 - 392*e1^19*e2^8*e3^10 + 19488*e1^19*e2^8*e3^9 - 10752*e1^19*e2^8*e3^8 - 7168*e1^19*e2^8*e3^7 + 3944*e1^19*e2^7*e3^11 - 10332*e1^19*e2^7*e3^10 - 21084*e1^19*e2^7*e3^9 + 28672*e1^19*e2^7*e3^8 - 4424*e1^19*e2^6*e3^11 + 23828*e1^19*e2^6*e3^10 - 28672*e1^19*e2^6*e3^8 + 7168*e1^19*e2^6*e3^7 + 1260*e1^19*e2^5*e3^11 - 23408*e1^19*e2^5*e3^10 + 21084*e1^19*e2^5*e3^9 + 10752*e1^19*e2^5*e3^8 - 7168*e1^19*e2^5*e3^7 + 2324*e1^19*e2^4*e3^11 + 9432*e1^19*e2^4*e3^10 - 19488*e1^19*e2^4*e3^9 + 2560*e1^19*e2^4*e3^8 + 3072*e1^19*e2^4*e3^7 - 2744*e1^19*e2^3*e3^11 + 1142*e1^19*e2^3*e3^10 + 6642*e1^19*e2^3*e3^9 - 3328*e1^19*e2^3*e3^8 - 512*e1^19*e2^3*e3^7 + 1176*e1^19*e2^2*e3^11 - 2218*e1^19*e2^2*e3^10 - 176*e1^19*e2^2*e3^9 + 768*e1^19*e2^2*e3^8 - 166*e1^19*e2*e3^11 + 532*e1^19*e2*e3^10 - 266*e1^19*e2*e3^9 - 10*e1^19*e3^11 + 45*e1^18*e2^12*e3^10 - 1626*e1^18*e2^12*e3^9 + 23341*e1^18*e2^12*e3^8 - 106752*e1^18*e2^12*e3^7 + 216064*e1^18*e2^12*e3^6 - 196608*e1^18*e2^12*e3^5 + 65536*e1^18*e2^12*e3^4 + 1868*e1^18*e2^11*e3^10 - 54058*e1^18*e2^11*e3^9 + 176350*e1^18*e2^11*e3^8 - 5376*e1^18*e2^11*e3^7 - 708608*e1^18*e2^11*e3^6 + 983040*e1^18*e2^11*e3^5 - 393216*e1^18*e2^11*e3^4 + 176*e1^18*e2^10*e3^11 + 62504*e1^18*e2^10*e3^10 - 71572*e1^18*e2^10*e3^9 - 637719*e1^18*e2^10*e3^8 + 1437184*e1^18*e2^10*e3^7 - 4096*e1^18*e2^10*e3^6 - 1769472*e1^18*e2^10*e3^5 + 983040*e1^18*e2^10*e3^4 - 768*e1^18*e2^9*e3^12 - 54058*e1^18*e2^9*e3^11 - 6840*e1^18*e2^9*e3^10 + 576184*e1^18*e2^9*e3^9 + 99944*e1^18*e2^9*e3^8 - 3224064*e1^18*e2^9*e3^7 + 2936832*e1^18*e2^9*e3^6 + 983040*e1^18*e2^9*e3^5 - 1310720*e1^18*e2^9*e3^4 + 23341*e1^18*e2^8*e3^12 + 64400*e1^18*e2^8*e3^11 - 322178*e1^18*e2^8*e3^10 - 739900*e1^18*e2^8*e3^9 + 1958378*e1^18*e2^8*e3^8 + 1932288*e1^18*e2^8*e3^7 - 4880384*e1^18*e2^8*e3^6 + 983040*e1^18*e2^8*e3^5 + 983040*e1^18*e2^8*e3^4 - 56936*e1^18*e2^7*e3^12 + 146920*e1^18*e2^7*e3^11 + 295680*e1^18*e2^7*e3^10 + 292596*e1^18*e2^7*e3^9 - 3289740*e1^18*e2^7*e3^8 + 1831936*e1^18*e2^7*e3^7 + 2936832*e1^18*e2^7*e3^6 - 1769472*e1^18*e2^7*e3^5 - 393216*e1^18*e2^7*e3^4 + 25580*e1^18*e2^6*e3^12 - 211888*e1^18*e2^6*e3^11 - 43212*e1^18*e2^6*e3^10 + 320400*e1^18*e2^6*e3^9 + 2076650*e1^18*e2^6*e3^8 - 3202560*e1^18*e2^6*e3^7 - 4096*e1^18*e2^6*e3^6 + 983040*e1^18*e2^6*e3^5 + 65536*e1^18*e2^6*e3^4 + 28456*e1^18*e2^5*e3^12 - 29692*e1^18*e2^5*e3^11 + 236296*e1^18*e2^5*e3^10 - 831208*e1^18*e2^5*e3^9 + 23144*e1^18*e2^5*e3^8 + 1466880*e1^18*e2^5*e3^7 - 708608*e1^18*e2^5*e3^6 - 196608*e1^18*e2^5*e3^5 - 4786*e1^18*e2^4*e3^12 + 57712*e1^18*e2^4*e3^11 - 249315*e1^18*e2^4*e3^10 + 666406*e1^18*e2^4*e3^9 - 649239*e1^18*e2^4*e3^8 - 27392*e1^18*e2^4*e3^7 + 216064*e1^18*e2^4*e3^6 - 26840*e1^18*e2^3*e3^12 + 74984*e1^18*e2^3*e3^11 - 52332*e1^18*e2^3*e3^10 - 101530*e1^18*e2^3*e3^9 + 202462*e1^18*e2^3*e3^8 - 102144*e1^18*e2^3*e3^7 + 10732*e1^18*e2^2*e3^12 - 46336*e1^18*e2^2*e3^11 + 77660*e1^18*e2^2*e3^10 - 56460*e1^18*e2^2*e3^9 + 16429*e1^18*e2^2*e3^8 + 1176*e1^18*e2*e3^12 - 2218*e1^18*e2*e3^11 - 176*e1^18*e2*e3^10 + 768*e1^18*e2*e3^9 + 45*e1^18*e3^12 - 120*e1^17*e2^13*e3^10 + 3944*e1^17*e2^13*e3^9 - 56936*e1^17*e2^13*e3^8 + 371832*e1^17*e2^13*e3^7 - 1047296*e1^17*e2^13*e3^6 + 1318400*e1^17*e2^13*e3^5 - 720896*e1^17*e2^13*e3^4 + 131072*e1^17*e2^13*e3^3 - 392*e1^17*e2^12*e3^10 + 64400*e1^17*e2^12*e3^9 - 1222792*e1^17*e2^12*e3^8 + 5210496*e1^17*e2^12*e3^7 - 9699072*e1^17*e2^12*e3^6 + 9907200*e1^17*e2^12*e3^5 - 5832704*e1^17*e2^12*e3^4 + 1572864*e1^17*e2^12*e3^3 - 6642*e1^17*e2^11*e3^11 - 6840*e1^17*e2^11*e3^10 + 3368530*e1^17*e2^11*e3^9 - 17415888*e1^17*e2^11*e3^8 + 35981096*e1^17*e2^11*e3^7 - 36019712*e1^17*e2^11*e3^6 + 13509632*e1^17*e2^11*e3^5 + 4128768*e1^17*e2^11*e3^4 - 3538944*e1^17*e2^11*e3^3 + 3328*e1^17*e2^10*e3^12 - 71572*e1^17*e2^10*e3^11 - 5036610*e1^17*e2^10*e3^10 + 24691518*e1^17*e2^10*e3^9 - 39630816*e1^17*e2^10*e3^8 + 6249216*e1^17*e2^10*e3^7 + 53854720*e1^17*e2^10*e3^6 - 60834816*e1^17*e2^10*e3^5 + 20774912*e1^17*e2^10*e3^4 + 512*e1^17*e2^9*e3^13 + 176350*e1^17*e2^9*e3^12 + 3368530*e1^17*e2^9*e3^11 - 12420456*e1^17*e2^9*e3^10 - 4799000*e1^17*e2^9*e3^9 + 82407120*e1^17*e2^9*e3^8 - 145498064*e1^17*e2^9*e3^7 + 92691456*e1^17*e2^9*e3^6 - 1310720*e1^17*e2^9*e3^5 - 18153472*e1^17*e2^9*e3^4 + 3538944*e1^17*e2^9*e3^3 - 106752*e1^17*e2^8*e3^13 - 1222792*e1^17*e2^8*e3^12 + 417128*e1^17*e2^8*e3^11 + 26482832*e1^17*e2^8*e3^10 - 84364248*e1^17*e2^8*e3^9 + 89268816*e1^17*e2^8*e3^8 + 9695232*e1^17*e2^8*e3^7 - 87051264*e1^17*e2^8*e3^6 + 57295872*e1^17*e2^8*e3^5 - 8847360*e1^17*e2^8*e3^4 - 1572864*e1^17*e2^8*e3^3 + 371832*e1^17*e2^7*e3^13 + 912240*e1^17*e2^7*e3^12 - 11285948*e1^17*e2^7*e3^11 + 21523608*e1^17*e2^7*e3^10 + 15447468*e1^17*e2^7*e3^9 - 99214848*e1^17*e2^7*e3^8 + 126783440*e1^17*e2^7*e3^7 - 59560448*e1^17*e2^7*e3^6 - 3286016*e1^17*e2^7*e3^5 + 8454144*e1^17*e2^7*e3^4 - 131072*e1^17*e2^7*e3^3 - 337992*e1^17*e2^6*e3^13 + 1738232*e1^17*e2^6*e3^12 + 2012160*e1^17*e2^6*e3^11 - 28283988*e1^17*e2^6*e3^10 + 67952916*e1^17*e2^6*e3^9 - 65767392*e1^17*e2^6*e3^8 + 7374080*e1^17*e2^6*e3^7 + 31944192*e1^17*e2^6*e3^6 - 16854016*e1^17*e2^6*e3^5 + 196608*e1^17*e2^6*e3^4 - 121384*e1^17*e2^5*e3^13 - 1253764*e1^17*e2^5*e3^12 + 8701372*e1^17*e2^5*e3^11 - 16719808*e1^17*e2^5*e3^10 + 3546400*e1^17*e2^5*e3^9 + 30373080*e1^17*e2^5*e3^8 - 40318760*e1^17*e2^5*e3^7 + 15568640*e1^17*e2^5*e3^6 + 254464*e1^17*e2^5*e3^5 + 267416*e1^17*e2^4*e3^13 - 1246296*e1^17*e2^4*e3^12 - 77160*e1^17*e2^4*e3^11 + 9513256*e1^17*e2^4*e3^10 - 22332648*e1^17*e2^4*e3^9 + 20843768*e1^17*e2^4*e3^8 - 6312320*e1^17*e2^4*e3^7 - 681216*e1^17*e2^4*e3^6 - 43928*e1^17*e2^3*e3^13 + 816576*e1^17*e2^3*e3^12 - 3012178*e1^17*e2^3*e3^11 + 5053376*e1^17*e2^3*e3^10 - 3781230*e1^17*e2^3*e3^9 + 518032*e1^17*e2^3*e3^8 + 463752*e1^17*e2^3*e3^7 - 26840*e1^17*e2^2*e3^13 + 74984*e1^17*e2^2*e3^12 - 52332*e1^17*e2^2*e3^11 - 101530*e1^17*e2^2*e3^10 + 202462*e1^17*e2^2*e3^9 - 102144*e1^17*e2^2*e3^8 - 2744*e1^17*e2*e3^13 + 1142*e1^17*e2*e3^12 + 6642*e1^17*e2*e3^11 - 3328*e1^17*e2*e3^10 - 512*e1^17*e2*e3^9 - 120*e1^17*e3^13 + 210*e1^16*e2^14*e3^10 - 4424*e1^16*e2^14*e3^9 + 25580*e1^16*e2^14*e3^8 - 337992*e1^16*e2^14*e3^7 + 1641938*e1^16*e2^14*e3^6 - 2941184*e1^16*e2^14*e3^5 + 2271232*e1^16*e2^14*e3^4 - 720896*e1^16*e2^14*e3^3 + 65536*e1^16*e2^14*e3^2 - 10332*e1^16*e2^13*e3^10 + 146920*e1^16*e2^13*e3^9 + 912240*e1^16*e2^13*e3^8 - 10572328*e1^16*e2^13*e3^7 + 30714412*e1^16*e2^13*e3^6 - 40646912*e1^16*e2^13*e3^5 + 25681920*e1^16*e2^13*e3^4 - 5832704*e1^16*e2^13*e3^3 - 393216*e1^16*e2^13*e3^2 + 19488*e1^16*e2^12*e3^11 - 322178*e1^16*e2^12*e3^10 + 417128*e1^16*e2^12*e3^9 + 19623712*e1^16*e2^12*e3^8 - 84358416*e1^16*e2^12*e3^7 + 130477290*e1^16*e2^12*e3^6 - 80578048*e1^16*e2^12*e3^5 + 9609216*e1^16*e2^12*e3^4 + 4128768*e1^16*e2^12*e3^3 + 983040*e1^16*e2^12*e3^2 - 2560*e1^16*e2^11*e3^12 + 576184*e1^16*e2^11*e3^11 - 12420456*e1^16*e2^11*e3^10 + 17564288*e1^16*e2^11*e3^9 + 53380480*e1^16*e2^11*e3^8 - 106192224*e1^16*e2^11*e3^7 - 16752624*e1^16*e2^11*e3^6 + 139270656*e1^16*e2^11*e3^5 - 94887936*e1^16*e2^11*e3^4 + 20774912*e1^16*e2^11*e3^3 - 1310720*e1^16*e2^11*e3^2 - 3072*e1^16*e2^10*e3^13 - 637719*e1^16*e2^10*e3^12 + 24691518*e1^16*e2^10*e3^11 - 56535785*e1^16*e2^10*e3^10 - 17774792*e1^16*e2^10*e3^9 + 67028872*e1^16*e2^10*e3^8 + 167554704*e1^16*e2^10*e3^7 - 384153020*e1^16*e2^10*e3^6 + 242399232*e1^16*e2^10*e3^5 - 25399296*e1^16*e2^10*e3^4 - 18153472*e1^16*e2^10*e3^3 + 983040*e1^16*e2^10*e3^2 - 5376*e1^16*e2^9*e3^13 - 17415888*e1^16*e2^9*e3^12 + 17564288*e1^16*e2^9*e3^11 + 113417100*e1^16*e2^9*e3^10 - 181819368*e1^16*e2^9*e3^9 - 145115296*e1^16*e2^9*e3^8 + 449139856*e1^16*e2^9*e3^7 - 189017720*e1^16*e2^9*e3^6 - 154957824*e1^16*e2^9*e3^5 + 117448704*e1^16*e2^9*e3^4 - 8847360*e1^16*e2^9*e3^3 - 393216*e1^16*e2^9*e3^2 + 216064*e1^16*e2^8*e3^14 + 5210496*e1^16*e2^8*e3^13 + 19623712*e1^16*e2^8*e3^12 - 129391600*e1^16*e2^8*e3^11 + 136796430*e1^16*e2^8*e3^10 + 194746424*e1^16*e2^8*e3^9 - 393323600*e1^16*e2^8*e3^8 - 61512448*e1^16*e2^8*e3^7 + 455650372*e1^16*e2^8*e3^6 - 238402048*e1^16*e2^8*e3^5 + 1875968*e1^16*e2^8*e3^4 + 8454144*e1^16*e2^8*e3^3 + 65536*e1^16*e2^8*e3^2 - 1047296*e1^16*e2^7*e3^14 - 10572328*e1^16*e2^7*e3^13 + 36656440*e1^16*e2^7*e3^12 + 25883008*e1^16*e2^7*e3^11 - 251897176*e1^16*e2^7*e3^10 + 258597416*e1^16*e2^7*e3^9 + 253167744*e1^16*e2^7*e3^8 - 543929184*e1^16*e2^7*e3^7 + 200543248*e1^16*e2^7*e3^6 + 68036096*e1^16*e2^7*e3^5 - 35659776*e1^16*e2^7*e3^4 + 196608*e1^16*e2^7*e3^3 + 1641938*e1^16*e2^6*e3^14 + 1046128*e1^16*e2^6*e3^13 - 41156126*e1^16*e2^6*e3^12 + 124841548*e1^16*e2^6*e3^11 - 52158762*e1^16*e2^6*e3^10 - 269506512*e1^16*e2^6*e3^9 + 349211628*e1^16*e2^6*e3^8 - 15814152*e1^16*e2^6*e3^7 - 164158998*e1^16*e2^6*e3^6 + 67037440*e1^16*e2^6*e3^5 - 940032*e1^16*e2^6*e3^4 - 740588*e1^16*e2^5*e3^14 + 7725480*e1^16*e2^5*e3^13 - 15862496*e1^16*e2^5*e3^12 - 39071712*e1^16*e2^5*e3^11 + 150942136*e1^16*e2^5*e3^10 - 106795424*e1^16*e2^5*e3^9 - 106228048*e1^16*e2^5*e3^8 + 174500696*e1^16*e2^5*e3^7 - 65305556*e1^16*e2^5*e3^6 + 782592*e1^16*e2^5*e3^5 - 335282*e1^16*e2^4*e3^14 - 2222176*e1^16*e2^4*e3^13 + 19140600*e1^16*e2^4*e3^12 - 35294944*e1^16*e2^4*e3^11 - 4832372*e1^16*e2^4*e3^10 + 83611968*e1^16*e2^4*e3^9 - 92587056*e1^16*e2^4*e3^8 + 32202704*e1^16*e2^4*e3^7 + 360658*e1^16*e2^4*e3^6 + 267416*e1^16*e2^3*e3^14 - 1246296*e1^16*e2^3*e3^13 - 77160*e1^16*e2^3*e3^12 + 9513256*e1^16*e2^3*e3^11 - 22332648*e1^16*e2^3*e3^10 + 20843768*e1^16*e2^3*e3^9 - 6312320*e1^16*e2^3*e3^8 - 681216*e1^16*e2^3*e3^7 - 4786*e1^16*e2^2*e3^14 + 57712*e1^16*e2^2*e3^13 - 249315*e1^16*e2^2*e3^12 + 666406*e1^16*e2^2*e3^11 - 649239*e1^16*e2^2*e3^10 - 27392*e1^16*e2^2*e3^9 + 216064*e1^16*e2^2*e3^8 + 2324*e1^16*e2*e3^14 + 9432*e1^16*e2*e3^13 - 19488*e1^16*e2*e3^12 + 2560*e1^16*e2*e3^11 + 3072*e1^16*e2*e3^10 + 210*e1^16*e3^14 - 252*e1^15*e2^15*e3^10 + 1260*e1^15*e2^15*e3^9 + 28456*e1^15*e2^15*e3^8 - 121384*e1^15*e2^15*e3^7 - 740588*e1^15*e2^15*e3^6 + 2651900*e1^15*e2^15*e3^5 - 2941184*e1^15*e2^15*e3^4 + 1318400*e1^15*e2^15*e3^3 - 196608*e1^15*e2^15*e3^2 + 23828*e1^15*e2^14*e3^10 - 211888*e1^15*e2^14*e3^9 + 1738232*e1^15*e2^14*e3^8 + 1046128*e1^15*e2^14*e3^7 - 24461932*e1^15*e2^14*e3^6 + 51622304*e1^15*e2^14*e3^5 - 40646912*e1^15*e2^14*e3^4 + 9907200*e1^15*e2^14*e3^3 + 983040*e1^15*e2^14*e3^2 - 21084*e1^15*e2^13*e3^11 + 295680*e1^15*e2^13*e3^10 - 11285948*e1^15*e2^13*e3^9 + 36656440*e1^15*e2^13*e3^8 + 10576932*e1^15*e2^13*e3^7 - 146226136*e1^15*e2^13*e3^6 + 178842004*e1^15*e2^13*e3^5 - 80578048*e1^15*e2^13*e3^4 + 13509632*e1^15*e2^13*e3^3 - 1769472*e1^15*e2^13*e3^2 - 10752*e1^15*e2^12*e3^12 - 739900*e1^15*e2^12*e3^11 + 26482832*e1^15*e2^12*e3^10 - 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11285948*e1^3*e2^9*e3^13 + 417128*e1^3*e2^9*e3^12 + 3368530*e1^3*e2^9*e3^11 - 71572*e1^3*e2^9*e3^10 - 6642*e1^3*e2^9*e3^9 + 1142*e1^3*e2^8*e3^19 + 74984*e1^3*e2^8*e3^18 + 816576*e1^3*e2^8*e3^17 - 1246296*e1^3*e2^8*e3^16 - 1253764*e1^3*e2^8*e3^15 + 1738232*e1^3*e2^8*e3^14 + 912240*e1^3*e2^8*e3^13 - 1222792*e1^3*e2^8*e3^12 + 176350*e1^3*e2^8*e3^11 + 3328*e1^3*e2^8*e3^10 - 120*e1^3*e2^7*e3^20 - 2744*e1^3*e2^7*e3^19 - 26840*e1^3*e2^7*e3^18 - 43928*e1^3*e2^7*e3^17 + 267416*e1^3*e2^7*e3^16 - 121384*e1^3*e2^7*e3^15 - 337992*e1^3*e2^7*e3^14 + 371832*e1^3*e2^7*e3^13 - 106752*e1^3*e2^7*e3^12 + 512*e1^3*e2^7*e3^11 + 65536*e1^2*e2^16*e3^14 - 393216*e1^2*e2^16*e3^13 + 983040*e1^2*e2^16*e3^12 - 1310720*e1^2*e2^16*e3^11 + 983040*e1^2*e2^16*e3^10 - 393216*e1^2*e2^16*e3^9 + 65536*e1^2*e2^16*e3^8 - 196608*e1^2*e2^15*e3^15 + 983040*e1^2*e2^15*e3^14 - 1769472*e1^2*e2^15*e3^13 + 983040*e1^2*e2^15*e3^12 + 983040*e1^2*e2^15*e3^11 - 1769472*e1^2*e2^15*e3^10 + 983040*e1^2*e2^15*e3^9 - 196608*e1^2*e2^15*e3^8 + 216064*e1^2*e2^14*e3^16 - 708608*e1^2*e2^14*e3^15 - 4096*e1^2*e2^14*e3^14 + 2936832*e1^2*e2^14*e3^13 - 4880384*e1^2*e2^14*e3^12 + 2936832*e1^2*e2^14*e3^11 - 4096*e1^2*e2^14*e3^10 - 708608*e1^2*e2^14*e3^9 + 216064*e1^2*e2^14*e3^8 - 102144*e1^2*e2^13*e3^17 - 27392*e1^2*e2^13*e3^16 + 1466880*e1^2*e2^13*e3^15 - 3202560*e1^2*e2^13*e3^14 + 1831936*e1^2*e2^13*e3^13 + 1932288*e1^2*e2^13*e3^12 - 3224064*e1^2*e2^13*e3^11 + 1437184*e1^2*e2^13*e3^10 - 5376*e1^2*e2^13*e3^9 - 106752*e1^2*e2^13*e3^8 + 16429*e1^2*e2^12*e3^18 + 202462*e1^2*e2^12*e3^17 - 649239*e1^2*e2^12*e3^16 + 23144*e1^2*e2^12*e3^15 + 2076650*e1^2*e2^12*e3^14 - 3289740*e1^2*e2^12*e3^13 + 1958378*e1^2*e2^12*e3^12 + 99944*e1^2*e2^12*e3^11 - 637719*e1^2*e2^12*e3^10 + 176350*e1^2*e2^12*e3^9 + 23341*e1^2*e2^12*e3^8 + 768*e1^2*e2^11*e3^19 - 56460*e1^2*e2^11*e3^18 - 101530*e1^2*e2^11*e3^17 + 666406*e1^2*e2^11*e3^16 - 831208*e1^2*e2^11*e3^15 + 320400*e1^2*e2^11*e3^14 + 292596*e1^2*e2^11*e3^13 - 739900*e1^2*e2^11*e3^12 + 576184*e1^2*e2^11*e3^11 - 71572*e1^2*e2^11*e3^10 - 54058*e1^2*e2^11*e3^9 - 1626*e1^2*e2^11*e3^8 - 176*e1^2*e2^10*e3^19 + 77660*e1^2*e2^10*e3^18 - 52332*e1^2*e2^10*e3^17 - 249315*e1^2*e2^10*e3^16 + 236296*e1^2*e2^10*e3^15 - 43212*e1^2*e2^10*e3^14 + 295680*e1^2*e2^10*e3^13 - 322178*e1^2*e2^10*e3^12 - 6840*e1^2*e2^10*e3^11 + 62504*e1^2*e2^10*e3^10 + 1868*e1^2*e2^10*e3^9 + 45*e1^2*e2^10*e3^8 - 2218*e1^2*e2^9*e3^19 - 46336*e1^2*e2^9*e3^18 + 74984*e1^2*e2^9*e3^17 + 57712*e1^2*e2^9*e3^16 - 29692*e1^2*e2^9*e3^15 - 211888*e1^2*e2^9*e3^14 + 146920*e1^2*e2^9*e3^13 + 64400*e1^2*e2^9*e3^12 - 54058*e1^2*e2^9*e3^11 + 176*e1^2*e2^9*e3^10 + 45*e1^2*e2^8*e3^20 + 1176*e1^2*e2^8*e3^19 + 10732*e1^2*e2^8*e3^18 - 26840*e1^2*e2^8*e3^17 - 4786*e1^2*e2^8*e3^16 + 28456*e1^2*e2^8*e3^15 + 25580*e1^2*e2^8*e3^14 - 56936*e1^2*e2^8*e3^13 + 23341*e1^2*e2^8*e3^12 - 768*e1^2*e2^8*e3^11 - 512*e1*e2^13*e3^17 + 3072*e1*e2^13*e3^16 - 7168*e1*e2^13*e3^15 + 7168*e1*e2^13*e3^14 - 7168*e1*e2^13*e3^12 + 7168*e1*e2^13*e3^11 - 3072*e1*e2^13*e3^10 + 512*e1*e2^13*e3^9 + 768*e1*e2^12*e3^18 - 3328*e1*e2^12*e3^17 + 2560*e1*e2^12*e3^16 + 10752*e1*e2^12*e3^15 - 28672*e1*e2^12*e3^14 + 28672*e1*e2^12*e3^13 - 10752*e1*e2^12*e3^12 - 2560*e1*e2^12*e3^11 + 3328*e1*e2^12*e3^10 - 768*e1*e2^12*e3^9 - 266*e1*e2^11*e3^19 - 176*e1*e2^11*e3^18 + 6642*e1*e2^11*e3^17 - 19488*e1*e2^11*e3^16 + 21084*e1*e2^11*e3^15 - 21084*e1*e2^11*e3^13 + 19488*e1*e2^11*e3^12 - 6642*e1*e2^11*e3^11 + 176*e1*e2^11*e3^10 + 266*e1*e2^11*e3^9 + 532*e1*e2^10*e3^19 - 2218*e1*e2^10*e3^18 + 1142*e1*e2^10*e3^17 + 9432*e1*e2^10*e3^16 - 23408*e1*e2^10*e3^15 + 23828*e1*e2^10*e3^14 - 10332*e1*e2^10*e3^13 - 392*e1*e2^10*e3^12 + 1868*e1*e2^10*e3^11 - 442*e1*e2^10*e3^10 - 10*e1*e2^10*e3^9 - 10*e1*e2^9*e3^20 - 166*e1*e2^9*e3^19 + 1176*e1*e2^9*e3^18 - 2744*e1*e2^9*e3^17 + 2324*e1*e2^9*e3^16 + 1260*e1*e2^9*e3^15 - 4424*e1*e2^9*e3^14 + 3944*e1*e2^9*e3^13 - 1626*e1*e2^9*e3^12 + 266*e1*e2^9*e3^11 + e2^10*e3^20 - 10*e2^10*e3^19 + 45*e2^10*e3^18 - 120*e2^10*e3^17 + 210*e2^10*e3^16 - 252*e2^10*e3^15 + 210*e2^10*e3^14 - 120*e2^10*e3^13 + 45*e2^10*e3^12 - 10*e2^10*e3^11 + e2^10*e3^10 ;