
// Title : On pairs of 17-congruent elliptic curves
// Author : T. Fisher
// Version : June 2021

// This is a MAGMA file containing some formulae related to
// the paper.

/////////////////////////////////////////////////////////////

// The polynomials F_1(T,x,y) and F_3(T,x,y) in Appendix A. These
// define the double covers Z(17,1) -> W(17,1) and Z(17,3) -> W(17,3).

function Z17Equation(k,T,x,y);
  assert k in {1,3};
  if k eq 1 then
    F := x^10 - 2*T*(T - 1)*x^8*y + T*(T^3 - 2*T^2 - 11*T + 4)*x^9 -
      T^2*(T^4 - 3*T^3 - 3*T^2 + 3*T - 10)*x^7*y + T^2*(8*T^4 + 58*T^3
      + 15*T^2 - 64*T + 5)*x^8 - T^3*(8*T^5 + 51*T^4 + 80*T^3 + 51*T^2
      - 2*T - 20)*x^6*y - 2*T^4*(16*T^4 - 41*T^3 - 205*T^2 - 97*T +
      71)*x^7 + 2*T^4*(16*T^6 + 49*T^5 - 13*T^4 - 142*T^3 - 113*T^2 -
      T + 10)*x^5*y - T^4*(149*T^6 + 576*T^5 + 180*T^4 - 956*T^3 -
      579*T^2 + 148*T + 5)*x^6 - 2*T^5*(13*T^7 - 39*T^6 - 229*T^5 -
      202*T^4 + 126*T^3 + 169*T^2 + 9*T - 5)*x^4*y + T^5*(80*T^8 +
      318*T^7 - 192*T^6 - 1800*T^5 - 1376*T^4 + 819*T^3 + 750*T^2 -
      67*T - 4)*x^5 - T^6*(T + 1)*(24*T^7 + 156*T^6 - 24*T^5 - 558*T^4
      - 285*T^3 + 192*T^2 + 21*T - 2)*x^3*y - T^6*(16*T^10 + 72*T^9 -
      239*T^8 - 1300*T^7 - 870*T^6 + 1952*T^5 + 2295*T^4 + 18*T^3 -
      449*T^2 + 4*T + 1)*x^4 + T^8*(T + 1)^2*(12*T^6 - 50*T^5 -
      226*T^4 + 36*T^3 + 292*T^2 - 31*T - 6)*x^2*y - T^8*(T +
      1)*(76*T^8 + 273*T^7 - 275*T^6 - 1505*T^5 - 631*T^4 + 1016*T^3 +
      472*T^2 - 94*T - 4)*x^3 - T^10*(T + 1)^3*(T^5 - 14*T^4 + 55*T^3
      + 118*T^2 - 68*T - 4)*x*y - T^10*(T + 1)^2*(131*T^6 + 328*T^5 -
      234*T^4 - 700*T^3 - 18*T^2 + 138*T + 3)*x^2 - T^13*(T +
      1)^4*(T^2 - 2*T + 28)*y - 2*T^13*(T + 1)^3*(49*T^3 + 63*T^2 -
      63*T - 27)*x - 27*T^16*(T + 1)^4;
  else
    F := x^10 - 14*T*x^8*y - T*(4*T^2 - 71*T - 16)*x^9 + T^2*(17*T^2 -
      89*T - 18)*x^7*y - T^2*(14*T^4 + 288*T^3 + 165*T^2 - 220*T -
      19)*x^8 + T^3*(76*T^4 + 480*T^3 + 545*T^2 - 176*T - 4)*x^6*y +
      T^3*(94*T^6 + 513*T^5 + 234*T^4 - 1412*T^3 - 732*T^2 + 242*T +
      4)*x^7 - T^5*(163*T^5 + 837*T^4 + 1320*T^3 - 72*T^2 - 898*T +
      106)*x^5*y - T^5*(159*T^7 + 590*T^6 - 103*T^5 - 3276*T^4 -
      3150*T^3 + 1326*T^2 + 820*T - 112)*x^6 + T^6*(80*T^7 + 418*T^6 +
      501*T^5 - 936*T^4 - 2496*T^3 - 948*T^2 + 390*T - 4)*x^4*y +
      T^6*(98*T^9 + 386*T^8 - 350*T^7 - 3439*T^6 - 3894*T^5 + 3010*T^4
      + 4872*T^3 - 306*T^2 - 284*T + 4)*x^5 + T^8*(4*T^8 + 130*T^7 +
      917*T^6 + 2787*T^5 + 4078*T^4 + 2292*T^3 - 482*T^2 - 480*T -
      60)*x^3*y - T^8*(27*T^10 + 122*T^9 - 177*T^8 - 1496*T^7 -
      987*T^6 + 5032*T^5 + 8446*T^4 + 1124*T^3 - 2621*T^2 + 54*T -
      61)*x^4 - T^10*(10*T^9 + 132*T^8 + 738*T^7 + 2126*T^6 + 3179*T^5
      + 1902*T^4 - 718*T^3 - 1376*T^2 - 482*T - 256)*x^2*y +
      T^10*(T^10 - 48*T^9 - 122*T^8 + 882*T^7 + 4304*T^6 + 6244*T^5 +
      973*T^4 - 4506*T^3 - 1714*T^2 + 428*T - 242)*x^3 - T^12*(T^10 -
      T^9 - 70*T^8 - 368*T^7 - 814*T^6 - 714*T^5 + 237*T^4 + 963*T^3 +
      800*T^2 + 522*T + 312)*x*y - T^12*(26*T^9 + 283*T^8 + 1018*T^7 +
      1256*T^6 - 810*T^5 - 3237*T^4 - 1848*T^3 + 648*T^2 + 108*T -
      265)*x^2 - T^14*(T + 2)*(T^8 + 12*T^7 + 44*T^6 + 74*T^5 + 64*T^4
      + 20*T^3 - 43*T^2 - 92*T - 60)*y - 2*T^14*(10*T^8 + 94*T^7 +
      323*T^6 + 471*T^5 + 129*T^4 - 367*T^3 - 263*T^2 + 69*T + 36)*x +
      T^16*(T^8 + 4*T^7 - 8*T^6 - 66*T^5 - 120*T^4 - 56*T^3 + 53*T^2 +
      36*T - 16);
  end if;
  return F;
end function;

// The rational functions j1 + j2 and j1*j2 on W(17,1) and W(17,3)

function Z17ModuliInformation(k,T,x,y);
  assert k in {1,3};
//                    j1*j2 = A^3/D
//  (j1 - 1728)*(j2 - 1728) = B^2/D     where D = D1*D17^17
  if k eq 1 then
    D1 := -T^13*x^4*(x - T^3 - T^2)^3*(y - (T + 1)*x + T^3)^2
      *(y + (T^2 - T - 1)*x + T^3)^2/(x + T)^2/(y + (T^2 - 1)*x
      + T^3)^3/(x - T^2)^2;
    D17 := (x + T - T^3)*(y - x + T^2) - T*(x + T)^2
      + (T^4 + T^3)*(x + T) + T^5;
    A := ((-6*T^2 - 2*T)*x^16 + (-35*T^6 - 15*T^5 + 277*T^4 - 19*T^3 -
      18*T^2)*x^15 + (-56*T^10 + 3700*T^8 + 4555*T^7 + 1302*T^6 +
      2019*T^5 + 64*T^4 - 72*T^3)*x^14 + (-36*T^14 + 28*T^13 +
      8372*T^12 + 13448*T^11 - 3410*T^10 + 7270*T^9 + 20127*T^8 +
      6869*T^7 + 6254*T^6 + 476*T^5 - 168*T^4)*x^13 + (-10*T^18 +
      18*T^17 + 6592*T^16 + 9192*T^15 - 30712*T^14 - 31004*T^13 -
      6120*T^12 - 81522*T^11 - 63724*T^10 + 15725*T^9 + 12248*T^8 +
      10516*T^7 + 1204*T^6 - 252*T^5)*x^12 + (-T^22 + 3*T^21 +
      2099*T^20 + 1651*T^19 - 30180*T^18 - 33854*T^17 - 13256*T^16 -
      194736*T^15 - 319514*T^14 - 264086*T^13 - 376940*T^12 -
      311240*T^11 - 66180*T^10 + 3928*T^9 + 9926*T^8 + 1694*T^7 -
      252*T^6)*x^11 + (232*T^24 - 23*T^23 - 9530*T^22 - 7031*T^21 +
      8676*T^20 - 123462*T^19 - 240988*T^18 - 202644*T^17 -
      563948*T^16 - 946034*T^15 - 860316*T^14 - 839564*T^13 -
      624892*T^12 - 188756*T^11 - 16808*T^10 + 4354*T^9 + 1456*T^8 -
      168*T^7)*x^10 + (-956*T^26 - 16*T^25 + 3043*T^24 - 41543*T^23 -
      77462*T^22 - 44780*T^21 - 333710*T^20 - 766342*T^19 -
      868378*T^18 - 1332462*T^17 - 1872870*T^16 - 1633894*T^15 -
      1197152*T^14 - 731932*T^13 - 228108*T^12 - 27908*T^11 - 616*T^10
      + 764*T^9 - 72*T^8)*x^9 + (-8*T^28 - 5424*T^27 - 8012*T^26 -
      4231*T^25 - 121628*T^24 - 301368*T^23 - 341678*T^22 -
      704472*T^21 - 1339480*T^20 - 1572902*T^19 - 2007888*T^18 -
      2544470*T^17 - 2124032*T^16 - 1243008*T^15 - 573640*T^14 -
      158348*T^13 - 20176*T^12 - 1676*T^11 + 226*T^10 - 18*T^9)*x^8 +
      (-70*T^30 - 1842*T^29 - 20308*T^28 - 43516*T^27 - 48313*T^26 -
      186461*T^25 - 410479*T^24 - 381827*T^23 - 412140*T^22 -
      603314*T^21 - 514710*T^20 - 831842*T^19 - 1611994*T^18 -
      1595498*T^17 - 879252*T^16 - 314904*T^15 - 68825*T^14 -
      7657*T^13 - 739*T^12 + 29*T^11 - 2*T^10)*x^7 + (-232*T^32 -
      1246*T^31 - 7024*T^30 - 37196*T^29 - 74360*T^28 - 70223*T^27 -
      132874*T^26 - 203841*T^25 + 77680*T^24 + 533358*T^23 +
      963676*T^22 + 1493650*T^21 + 1361996*T^20 + 334034*T^19 -
      365688*T^18 - 313540*T^17 - 105360*T^16 - 18535*T^15 - 1462*T^14
      - 109*T^13)*x^6 + (4*T^34 - 472*T^33 - 2560*T^32 - 11840*T^31 -
      43748*T^30 - 68560*T^29 - 30803*T^28 - 31569*T^27 - 75442*T^26 +
      113720*T^25 + 479852*T^24 + 868828*T^23 + 1369800*T^22 +
      1506092*T^21 + 911984*T^20 + 244900*T^19 + 4226*T^18 - 9802*T^17
      - 2131*T^16 - 113*T^15 + 2*T^14)*x^5 + (8*T^36 + 40*T^35 -
      274*T^34 - 1410*T^33 - 8348*T^32 - 33856*T^31 - 50282*T^30 -
      6375*T^29 + 11480*T^28 - 79736*T^27 - 141430*T^26 - 129594*T^25
      - 90688*T^24 + 93428*T^23 + 310834*T^22 + 288054*T^21 +
      121368*T^20 + 25218*T^19 + 3308*T^18 + 207*T^17)*x^4 + (-T^38 +
      23*T^37 + 129*T^36 + 49*T^35 - 321*T^34 - 3247*T^33 - 16067*T^32
      - 24279*T^31 + 7017*T^30 + 43199*T^29 + 17283*T^28 - 36589*T^27
      - 80267*T^26 - 130245*T^25 - 137425*T^24 - 74221*T^23 -
      15484*T^22 + 286*T^21 + 112*T^20)*x^3 + (-3*T^39 + 18*T^38 +
      155*T^37 + 240*T^36 - 217*T^35 - 2242*T^34 - 7565*T^33 -
      10248*T^32 + 4157*T^31 + 30118*T^30 + 43537*T^29 + 44616*T^28 +
      44597*T^27 + 34762*T^26 + 15265*T^25 + 2576*T^24 - 86*T^23)*x^2
      + (-3*T^40 - T^39 + 60*T^38 + 170*T^37 + 107*T^36 - 419*T^35 -
      1458*T^34 - 1924*T^33 + 83*T^32 + 3273*T^31 + 3264*T^30 +
      58*T^29 - 1819*T^28 - 1157*T^27 - 234*T^26)*x - T^41 - 4*T^40 -
      2*T^39 + 12*T^38 + 17*T^37 - 8*T^36 - 28*T^35 - 8*T^34 + 17*T^33
      + 12*T^32 - 2*T^31 - 4*T^30 - T^29)*y + x^18 + (15*T^4 + 10*T^3
      - T^2 + 12*T)*x^17 + (35*T^8 + 20*T^7 - 1230*T^6 - 1146*T^5 -
      258*T^4 - 46*T^3 + 63*T^2)*x^16 + (28*T^12 - 4784*T^10 -
      9140*T^9 - 6682*T^8 - 12088*T^7 - 9949*T^6 - 2190*T^5 - 334*T^4
      + 192*T^3)*x^15 + (9*T^16 - 8*T^15 - 4948*T^14 - 10128*T^13 +
      4608*T^12 + 2352*T^11 - 7044*T^10 + 116*T^9 - 30674*T^8 -
      33240*T^7 - 7105*T^6 - 1136*T^5 + 378*T^4)*x^14 + (T^20 - 2*T^19
      - 1867*T^18 - 3088*T^17 + 17318*T^16 + 32764*T^15 + 53224*T^14 +
      169500*T^13 + 244798*T^12 + 236320*T^11 + 180160*T^10 +
      10912*T^9 - 55452*T^8 - 12188*T^7 - 2254*T^6 + 504*T^5)*x^13 +
      (-232*T^22 - 210*T^21 + 7901*T^20 + 13990*T^19 + 20825*T^18 +
      121740*T^17 + 251545*T^16 + 405252*T^15 + 775098*T^14 +
      1045300*T^13 + 994983*T^12 + 682744*T^11 + 185788*T^10 -
      43576*T^9 - 11536*T^8 - 2828*T^7 + 462*T^6)*x^12 + (956*T^24 +
      1204*T^23 + 507*T^22 + 33006*T^21 + 77562*T^20 + 130784*T^19 +
      389522*T^18 + 755000*T^17 + 1164566*T^16 + 1835720*T^15 +
      2233258*T^14 + 1943044*T^13 + 1214008*T^12 + 386792*T^11 -
      552*T^10 - 4844*T^9 - 2296*T^8 + 288*T^7)*x^11 + (8*T^26 +
      4476*T^25 + 10274*T^24 + 20968*T^23 + 117207*T^22 + 290416*T^21
      + 526973*T^20 + 1060380*T^19 + 1772750*T^18 + 2509116*T^17 +
      3304384*T^16 + 3373388*T^15 + 2426772*T^14 + 1281536*T^13 +
      411264*T^12 + 28896*T^11 + 1130*T^10 - 1184*T^9 + 117*T^8)*x^10
      + (70*T^28 + 1904*T^27 + 17636*T^26 + 47692*T^25 + 95369*T^24 +
      235890*T^23 + 408783*T^22 + 507048*T^21 + 791870*T^20 +
      1491808*T^19 + 2692874*T^18 + 3940264*T^17 + 3793978*T^16 +
      2239240*T^15 + 900496*T^14 + 260836*T^13 + 24685*T^12 +
      2290*T^11 - 361*T^10 + 28*T^9)*x^9 + (232*T^30 + 1408*T^29 +
      6926*T^28 + 27460*T^27 + 48318*T^26 + 38162*T^25 - 3654*T^24 -
      298702*T^23 - 1222443*T^22 - 2469756*T^21 - 2836328*T^20 -
      1223496*T^19 + 1438548*T^18 + 2458104*T^17 + 1450958*T^16 +
      444820*T^15 + 104042*T^14 + 9258*T^13 + 1002*T^12 - 54*T^11 +
      3*T^10)*x^8 + (-4*T^32 + 236*T^31 + 1156*T^30 + 5344*T^29 +
      17000*T^28 + 10680*T^27 - 31639*T^26 - 55226*T^25 - 321030*T^24
      - 1625028*T^23 - 4111712*T^22 - 6065924*T^21 - 5218120*T^20 -
      2051880*T^19 + 248632*T^18 + 477340*T^17 + 135834*T^16 +
      25928*T^15 + 1509*T^14 + 154*T^13 - 2*T^12)*x^7 + (-8*T^34 -
      44*T^33 - 19*T^32 - 320*T^31 + 266*T^30 + 4336*T^29 - 295*T^28 +
      51792*T^27 + 432127*T^26 + 1121008*T^25 + 1161957*T^24 -
      407688*T^23 - 2743352*T^22 - 3562264*T^21 - 2209883*T^20 -
      591656*T^19 - 19018*T^18 + 9548*T^17 + 3002*T^16 + 64*T^15 -
      T^14)*x^6 + (T^36 - 14*T^35 - 89*T^34 - 108*T^33 + 79*T^32 +
      1878*T^31 + 591*T^30 - 36712*T^29 - 71043*T^28 + 198914*T^27 +
      1031829*T^26 + 1957860*T^25 + 1980921*T^24 + 875570*T^23 -
      268947*T^22 - 513092*T^21 - 223798*T^20 - 39596*T^19 - 5032*T^18
      - 188*T^17)*x^5 + (2*T^37 - 3*T^36 - 42*T^35 - 51*T^34 + 54*T^33
      + 1107*T^32 - 3614*T^31 - 56425*T^30 - 198074*T^29 - 324850*T^28
      - 203334*T^27 + 215793*T^26 + 601106*T^25 + 594970*T^24 +
      298898*T^23 + 68529*T^22 + 4596*T^21 + 522*T^20)*x^4 + (T^38 +
      2*T^37 + 4*T^36 + 44*T^35 + 131*T^34 + 1562*T^33 + 6802*T^32 +
      6036*T^31 - 32137*T^30 - 124290*T^29 - 221232*T^28 - 236420*T^27
      - 153083*T^26 - 53466*T^25 - 6246*T^24 + 772*T^23)*x^3 + (-T^38
      - 4*T^37 - 2*T^36 + 12*T^35 + 849*T^34 + 5944*T^33 + 19556*T^32
      + 39096*T^31 + 51857*T^30 + 46284*T^29 + 26750*T^28 + 9020*T^27
      + 1343*T^26)*x^2;
    B := ((9*T^2 + 3*T)*x^25 + (120*T^6 + 72*T^5 + 420*T^4 + 61*T^3 +
      42*T^2)*x^24 + (462*T^10 + 210*T^9 + 17316*T^8 + 20836*T^7 +
      3736*T^6 + 5010*T^5 - 29*T^4 + 273*T^3)*x^23 + (792*T^14 +
      104076*T^12 + 175686*T^11 - 89568*T^10 - 26256*T^9 + 150920*T^8
      + 33958*T^7 + 27632*T^6 - 1833*T^5 + 1092*T^4)*x^22 + (715*T^18
      - 495*T^17 + 232452*T^16 + 399816*T^15 - 1314936*T^14 -
      2278164*T^13 - 969495*T^12 - 1918257*T^11 - 1439178*T^10 +
      344070*T^9 + 147975*T^8 + 93681*T^7 - 9815*T^6 + 3003*T^5)*x^21
      + (364*T^22 - 572*T^21 + 251460*T^20 + 355135*T^19 -
      3988026*T^18 - 8575452*T^17 - 5567220*T^16 - 13413288*T^15 -
      22881078*T^14 - 14357983*T^13 - 12138016*T^12 - 8753664*T^11 -
      351564*T^10 + 382027*T^9 + 219216*T^8 - 29315*T^7 +
      6006*T^6)*x^20 + (105*T^26 - 273*T^25 + 146250*T^24 +
      123506*T^23 - 4991393*T^22 - 10932805*T^21 - 2017449*T^20 -
      15649815*T^19 - 50698587*T^18 - 34152651*T^17 - 40049025*T^16 -
      76159461*T^15 - 53129171*T^14 - 36578695*T^13 - 26620490*T^12 -
      3905548*T^11 + 624418*T^10 + 377432*T^9 - 58773*T^8 +
      9009*T^7)*x^19 + (16*T^30 - 60*T^29 + 46746*T^28 + 3401*T^27 -
      3130704*T^26 - 6119466*T^25 + 7465006*T^24 - 3869139*T^23 -
      51836724*T^22 - 6806017*T^21 + 6934242*T^20 - 111064641*T^19 -
      77943698*T^18 - 32542935*T^17 - 108077874*T^16 - 84790375*T^15 -
      55880034*T^14 - 47942436*T^13 - 10817584*T^12 + 626340*T^11 +
      498300*T^10 - 84513*T^9 + 10296*T^8)*x^18 + (T^34 - 5*T^33 +
      7728*T^32 - 6666*T^31 - 1042633*T^30 - 1550697*T^29 +
      7575845*T^28 - 1195305*T^27 - 40312413*T^26 + 15418751*T^25 +
      28913063*T^24 - 197879403*T^23 - 211393203*T^22 - 143989187*T^21
      - 416548824*T^20 - 375497822*T^19 - 101140965*T^18 -
      79244415*T^17 - 42352757*T^16 - 26771687*T^15 - 51301794*T^14 -
      17494370*T^13 + 273141*T^12 + 518859*T^11 - 89661*T^10 +
      9009*T^9)*x^17 + (516*T^36 - 997*T^35 - 176864*T^34 -
      144892*T^33 + 2746654*T^32 - 2073463*T^31 - 19859606*T^30 +
      16625481*T^29 + 5474130*T^28 - 237041577*T^27 - 316339460*T^26 -
      407492461*T^25 - 1261580990*T^24 - 1932656269*T^23 -
      2073855878*T^22 - 2480518132*T^21 - 2182494696*T^20 -
      1072943715*T^19 - 319037802*T^18 + 7523663*T^17 + 48693202*T^16
      - 25571080*T^15 - 18908700*T^14 - 218955*T^13 + 433092*T^12 -
      70785*T^11 + 6006*T^10)*x^16 + (-12078*T^38 + 204*T^37 +
      423749*T^36 - 824043*T^35 - 4790118*T^34 + 8145510*T^33 -
      6707676*T^32 - 133883082*T^31 - 166540112*T^30 - 278388114*T^29
      - 1154113353*T^28 - 2058148161*T^27 - 2762502285*T^26 -
      4757706129*T^25 - 6900610865*T^24 - 7790512323*T^23 -
      8111320455*T^22 - 6865655225*T^21 - 3915790248*T^20 -
      1374561024*T^19 - 163606292*T^18 + 88368558*T^17 + 9153306*T^16
      - 14363748*T^15 - 515196*T^14 + 290202*T^13 - 41327*T^12 +
      3003*T^11)*x^15 + (23140*T^40 - 90056*T^39 - 492276*T^38 +
      1620137*T^37 - 3973820*T^36 - 37120548*T^35 - 36370210*T^34 -
      94914452*T^33 - 523309452*T^32 - 913374748*T^31 -
      1224890186*T^30 - 2767473141*T^29 - 4745986982*T^28 -
      5978896059*T^27 - 8278475292*T^26 - 11388973397*T^25 -
      13397489234*T^24 - 14029488417*T^23 - 12051294074*T^22 -
      7386283872*T^21 - 2912144598*T^20 - 575099424*T^19 +
      35625444*T^18 + 24226776*T^17 - 7920536*T^16 - 503690*T^15 +
      153384*T^14 - 17459*T^13 + 1092*T^12)*x^14 + (-18705*T^42 +
      94151*T^41 - 672821*T^40 - 4803811*T^39 - 3581863*T^38 -
      22956227*T^37 - 136787920*T^36 - 213236332*T^35 - 301575992*T^34
      - 1001555380*T^33 - 1800821074*T^32 - 1950847370*T^31 -
      2814624286*T^30 - 4207987368*T^29 - 4350252879*T^28 -
      4541407989*T^27 - 6395270605*T^26 - 9410734409*T^25 -
      12085822504*T^24 - 11858663394*T^23 - 8057959497*T^22 -
      3518260821*T^21 - 851754711*T^20 - 48799011*T^19 + 17114514*T^18
      - 3310366*T^17 - 322943*T^16 + 61415*T^15 - 5109*T^14 +
      273*T^13)*x^13 + (-26808*T^44 - 243657*T^43 - 241614*T^42 -
      3457557*T^41 - 19379940*T^40 - 28054271*T^39 - 60467766*T^38 -
      271197816*T^37 - 480465748*T^36 - 498557322*T^35 -
      1004380614*T^34 - 1804923178*T^33 - 1562414166*T^32 -
      721191594*T^31 + 53618740*T^30 + 1927884249*T^29 +
      4824056592*T^28 + 6047042931*T^27 + 3312600288*T^26 -
      1853981604*T^25 - 5253216446*T^24 - 4870348641*T^23 -
      2512682436*T^22 - 709196835*T^21 - 76682388*T^20 + 5605536*T^19
      - 1108740*T^18 - 146667*T^17 + 17352*T^16 - 953*T^15 +
      42*T^14)*x^12 + (-5188*T^46 - 209584*T^45 - 1217340*T^44 -
      1932520*T^43 - 8949981*T^42 - 45133659*T^41 - 81087905*T^40 -
      109748849*T^39 - 331312824*T^38 - 660275566*T^37 -
      640804586*T^36 - 580628388*T^35 - 928343191*T^34 -
      828944303*T^33 + 396501981*T^32 + 1985370999*T^31 +
      3898615319*T^30 + 7365943803*T^29 + 10867193403*T^28 +
      10416388303*T^27 + 5828720658*T^26 + 1084578874*T^25 -
      1037669838*T^24 - 957069810*T^23 - 342055033*T^22 -
      48043471*T^21 + 467898*T^20 - 292020*T^19 - 46430*T^18 +
      3036*T^17 - 95*T^16 + 3*T^15)*x^11 + (3624*T^48 - 488*T^47 -
      655360*T^46 - 3689372*T^45 - 7011114*T^44 - 16062873*T^43 -
      67176660*T^42 - 145158559*T^41 - 169702424*T^40 - 249552214*T^39
      - 495990268*T^38 - 489430784*T^37 + 93102032*T^36 +
      585036695*T^35 + 622649926*T^34 + 1070229965*T^33 +
      1691387722*T^32 + 1598532725*T^31 + 2445802312*T^30 +
      5094507731*T^29 + 6564687664*T^28 + 5057807636*T^27 +
      2374984362*T^26 + 535761834*T^25 - 82147026*T^24 - 83339969*T^23
      - 15422146*T^22 - 165380*T^21 - 45184*T^20 - 9248*T^19 +
      236*T^18 - 3*T^17)*x^10 + (1455*T^50 + 19257*T^49 + 27166*T^48 -
      1231608*T^47 - 7425438*T^46 - 16961232*T^45 - 25646169*T^44 -
      63253065*T^43 - 152233410*T^42 - 183756402*T^41 - 71835612*T^40
      - 5586310*T^39 + 75222615*T^38 + 769169607*T^37 +
      1829389817*T^36 + 2304220707*T^35 + 2592862164*T^34 +
      2880212684*T^33 + 1919302776*T^32 + 435044286*T^31 +
      417314688*T^30 + 1281382680*T^29 + 1468858596*T^28 +
      955030418*T^27 + 381275928*T^26 + 72019128*T^25 - 2981293*T^24 -
      2190141*T^23 - 11334*T^22 + 1082*T^21 - 861*T^20 - 3*T^19)*x^9 +
      (-460*T^52 + 2729*T^51 + 34092*T^50 + 21710*T^49 - 1579350*T^48
      - 9995010*T^47 - 26910718*T^46 - 36568609*T^45 - 34416696*T^44 -
      63196704*T^43 - 83118968*T^42 + 70985148*T^41 + 283964126*T^40 +
      302434273*T^39 + 471215334*T^38 + 947802469*T^37 +
      1141604448*T^36 + 1327294032*T^35 + 2036274218*T^34 +
      2223564188*T^33 + 1281027648*T^32 + 324500116*T^31 +
      35872118*T^30 + 60732540*T^29 + 88236458*T^28 + 64391568*T^27 +
      22294368*T^26 + 2489491*T^25 - 33662*T^24 + 6216*T^23 +
      1204*T^22 + 3*T^21)*x^8 + (18*T^54 - 1628*T^53 - 5347*T^52 -
      12803*T^51 - 126672*T^50 - 1268238*T^49 - 7864347*T^48 -
      25965857*T^47 - 40855525*T^46 - 17678327*T^45 + 22888625*T^44 +
      40717567*T^43 + 113769422*T^42 + 205832264*T^41 + 55584817*T^40
      - 285282037*T^39 - 632104422*T^38 - 1158368880*T^37 -
      1546139214*T^36 - 1065430298*T^35 - 90435403*T^34 +
      408296371*T^33 + 337753393*T^32 + 137418953*T^31 + 19556176*T^30
      - 9882036*T^29 - 3019941*T^28 + 867495*T^27 + 246818*T^26 +
      5326*T^25 - 526*T^24)*x^7 + (-12*T^56 + 48*T^55 - 1548*T^54 -
      15867*T^53 - 117240*T^52 - 435216*T^51 - 688050*T^50 -
      2038779*T^49 - 11663986*T^48 - 28166769*T^47 - 21063420*T^46 +
      19451595*T^45 + 51541980*T^44 + 77275236*T^43 + 99943982*T^42 +
      15184899*T^41 - 191465538*T^40 - 459490472*T^39 - 900294684*T^38
      - 1410650418*T^37 - 1494598638*T^36 - 1025902311*T^35 -
      450891462*T^34 - 112173711*T^33 + 1846260*T^32 + 12693882*T^31 +
      2992690*T^30 - 300759*T^29 - 114702*T^28 - 5726*T^27)*x^6 +
      (T^58 - 59*T^57 - 105*T^56 + 661*T^55 - 7575*T^54 - 141249*T^53
      - 587589*T^52 - 521961*T^51 + 1524558*T^50 + 1363304*T^49 -
      8210110*T^48 - 17410230*T^47 - 9880389*T^46 + 5487109*T^45 +
      22722936*T^44 + 54025592*T^43 + 89915194*T^42 + 134079438*T^41 +
      191034827*T^40 + 162356425*T^39 - 19404822*T^38 - 211320148*T^37
      - 252988391*T^36 - 173723571*T^35 - 81862657*T^34 -
      26810699*T^33 - 5319792*T^32 - 459812*T^31 - 11286*T^30)*x^5 +
      (5*T^59 - 110*T^58 - 541*T^57 + 1476*T^56 + 8367*T^55 -
      58440*T^54 - 374445*T^53 - 415014*T^52 + 1416450*T^51 +
      3930358*T^50 + 1131050*T^49 - 7682420*T^48 - 13267615*T^47 -
      10628372*T^46 - 1806340*T^45 + 13470464*T^44 + 34943854*T^43 +
      67809266*T^42 + 119279123*T^41 + 163572160*T^40 + 157940288*T^39
      + 106369052*T^38 + 51851053*T^37 + 19207574*T^36 + 5288411*T^35
      + 885574*T^34 + 51908*T^33)*x^4 + (10*T^60 - 90*T^59 - 774*T^58
      - 284*T^57 + 8418*T^56 + 906*T^55 - 113578*T^54 - 183258*T^53 +
      505782*T^52 + 1910740*T^51 + 1714860*T^50 - 1650588*T^49 -
      5205072*T^48 - 5114508*T^47 - 1939716*T^46 + 667344*T^45 -
      689814*T^44 - 5640714*T^43 - 8702070*T^42 - 6343128*T^41 -
      2102370*T^40 - 120814*T^39 - 1026*T^38 - 73446*T^37 -
      22490*T^36)*x^3 + (10*T^61 - 20*T^60 - 468*T^59 - 1176*T^58 +
      1160*T^57 + 4200*T^56 - 18716*T^55 - 57898*T^54 + 43542*T^53 +
      361786*T^52 + 458846*T^51 - 158058*T^50 - 1000622*T^49 -
      1023118*T^48 - 80418*T^47 + 995602*T^46 + 1425512*T^45 +
      1033938*T^44 + 278814*T^43 - 190694*T^42 - 211554*T^41 -
      79826*T^40 - 11370*T^39)*x^2 + (5*T^62 + 13*T^61 - 91*T^60 -
      473*T^59 - 622*T^58 + 100*T^57 - 1196*T^56 - 7300*T^55 -
      5762*T^54 + 18934*T^53 + 39446*T^52 + 7474*T^51 - 50312*T^50 -
      51340*T^49 + 5764*T^48 + 40012*T^47 + 22133*T^46 - 3803*T^45 -
      8851*T^44 - 3617*T^43 - 514*T^42)*x + (T^63 + 6*T^62 + 9*T^61 -
      16*T^60 - 60*T^59 - 24*T^58 + 116*T^57 + 144*T^56 - 66*T^55 -
      220*T^54 - 66*T^53 + 144*T^52 + 116*T^51 - 24*T^50 - 60*T^49 -
      16*T^48 + 9*T^47 + 6*T^46 + T^45))*y - x^27 + (-36*T^4 - 24*T^3
      - 18*T)*x^26 + (-210*T^8 - 168*T^7 - 3876*T^6 - 3214*T^5 -
      620*T^4 + 68*T^3 - 147*T^2)*x^25 + (-462*T^12 - 252*T^11 -
      41706*T^10 - 72548*T^9 - 25134*T^8 - 50676*T^7 - 38931*T^6 -
      5492*T^5 + 890*T^4 - 728*T^3)*x^24 + (-495*T^16 - 126792*T^14 -
      263088*T^13 + 263508*T^12 + 454608*T^11 + 77733*T^10 +
      137988*T^9 - 208374*T^8 - 224994*T^7 - 26621*T^6 + 5382*T^5 -
      2457*T^4)*x^23 + (-286*T^20 + 220*T^19 - 167530*T^18 -
      332190*T^17 + 1718658*T^16 + 4379028*T^15 + 4875339*T^14 +
      8619810*T^13 + 9977385*T^12 + 5747536*T^11 + 2973860*T^10 -
      80354*T^9 - 789613*T^8 - 83996*T^7 + 19916*T^6 - 6006*T^5)*x^22
      + (-91*T^24 + 156*T^23 - 112410*T^22 - 176638*T^21 +
      2993575*T^20 + 8309300*T^19 + 9106413*T^18 + 20939664*T^17 +
      40055007*T^16 + 43394974*T^15 + 53896287*T^14 + 55999650*T^13 +
      34318313*T^12 + 16255256*T^11 + 2274622*T^10 - 1860272*T^9 -
      189134*T^8 + 50336*T^7 - 11011*T^6)*x^21 + (-15*T^28 + 42*T^27 -
      40041*T^26 - 36654*T^25 + 2294745*T^24 + 6164178*T^23 +
      2589714*T^22 + 11516614*T^21 + 38359683*T^20 + 34170864*T^19 +
      53091996*T^18 + 106176438*T^17 + 110348124*T^16 + 131674158*T^15
      + 145691004*T^14 + 96723384*T^13 + 47093603*T^12 + 9812556*T^11
      - 3090243*T^10 - 322520*T^9 + 91806*T^8 - 15444*T^7)*x^20 +
      (-T^32 + 4*T^31 - 7210*T^30 - 488*T^29 + 876611*T^28 +
      2053870*T^27 - 2792595*T^26 + 686112*T^25 + 21045915*T^24 +
      528484*T^23 + 2967779*T^22 + 89408368*T^21 + 89054837*T^20 +
      93024292*T^19 + 156545822*T^18 + 97891800*T^17 + 98778633*T^16 +
      170211516*T^15 + 144762767*T^14 + 83008096*T^13 + 22275602*T^12
      - 3697254*T^11 - 434379*T^10 + 124410*T^9 - 16731*T^8)*x^19 +
      (-516*T^34 + 482*T^33 + 164233*T^32 + 292310*T^31 - 1826462*T^30
      + 25604*T^29 + 11099518*T^28 - 4080158*T^27 + 8172717*T^26 +
      138606732*T^25 + 238937043*T^24 + 439525544*T^23 +
      931309882*T^22 + 1242781958*T^21 + 1277595352*T^20 +
      1054378964*T^19 + 401127297*T^18 - 41089638*T^17 - 5562969*T^16
      + 85089426*T^15 + 89884450*T^14 + 33062582*T^13 - 3177053*T^12 -
      474672*T^11 + 126984*T^10 - 14014*T^9)*x^18 + (12078*T^36 +
      12390*T^35 - 364029*T^34 + 299944*T^33 + 3517596*T^32 -
      2330250*T^31 + 9910160*T^30 + 97906620*T^29 + 192254094*T^28 +
      444179316*T^27 + 1192269843*T^26 + 2204779740*T^25 +
      3600212015*T^24 + 5646003222*T^23 + 7254991347*T^22 +
      7483198966*T^21 + 5916866709*T^20 + 2894844294*T^19 +
      503458980*T^18 - 189249918*T^17 - 77894052*T^16 + 51093784*T^15
      + 34410582*T^14 - 1879416*T^13 - 424512*T^12 + 97812*T^11 -
      9009*T^10)*x^17 + (-23140*T^38 + 54838*T^37 + 457661*T^36 -
      678106*T^35 + 3731761*T^34 + 30779300*T^33 + 59572937*T^32 +
      168097732*T^31 + 552428609*T^30 + 1118034278*T^29 +
      2058188686*T^28 + 3978528962*T^27 + 6611148939*T^26 +
      10033714290*T^25 + 14715205923*T^24 + 19044588074*T^23 +
      20303771464*T^22 + 16535700878*T^21 + 9045025098*T^20 +
      2687858490*T^19 + 91065771*T^18 - 185000436*T^17 - 2597667*T^16
      + 25967604*T^15 - 637681*T^14 - 307076*T^13 + 56342*T^12 -
      4368*T^11)*x^16 + (18705*T^40 - 52306*T^39 + 599419*T^38 +
      4491038*T^37 + 8582119*T^36 + 33844252*T^35 + 134403434*T^34 +
      272988818*T^33 + 530508682*T^32 + 1186344770*T^31 +
      2013834628*T^30 + 2900310598*T^29 + 4313809628*T^28 +
      6077394840*T^27 + 8861961693*T^26 + 14684869662*T^25 +
      22973677749*T^24 + 28598431222*T^23 + 25710649046*T^22 +
      15424536574*T^21 + 5551904739*T^20 + 837232242*T^19 -
      122637929*T^18 - 28511916*T^17 + 14572830*T^16 + 33426*T^15 -
      174275*T^14 + 23738*T^13 - 1547*T^12)*x^15 + (26808*T^42 +
      251760*T^41 + 575403*T^40 + 3864868*T^39 + 18197346*T^38 +
      37682328*T^37 + 87830083*T^36 + 248687220*T^35 + 439788513*T^34
      + 603969268*T^33 + 882721119*T^32 + 854301618*T^31 -
      148018343*T^30 - 2440495548*T^29 - 6403243494*T^28 -
      10231186482*T^27 - 8288438310*T^26 + 2966016552*T^25 +
      16948860661*T^24 + 21811390506*T^23 + 15429984651*T^22 +
      6413931300*T^21 + 1343858901*T^20 + 15452004*T^19 -
      22112640*T^18 + 6276522*T^17 + 189825*T^16 - 74012*T^15 +
      7020*T^14 - 378*T^13)*x^14 + (5188*T^44 + 187964*T^43 +
      1140736*T^42 + 2647260*T^41 + 9518601*T^40 + 36496728*T^39 +
      74429921*T^38 + 128156278*T^37 + 266138600*T^36 + 409804472*T^35
      + 403010056*T^34 + 269435426*T^33 - 202376251*T^32 -
      1715962616*T^31 - 5687218405*T^30 - 14226935936*T^29 -
      26431355977*T^28 - 33621470390*T^27 - 25870633423*T^26 -
      7294034090*T^25 + 6482051048*T^24 + 8389597596*T^23 +
      4373552034*T^22 + 1129956132*T^21 + 79667653*T^20 - 7907560*T^19
      + 2140906*T^18 + 125816*T^17 - 21926*T^16 + 1352*T^15 -
      57*T^14)*x^13 + (-3624*T^46 - 8324*T^45 + 448091*T^44 +
      2785414*T^43 + 6861315*T^42 + 16643184*T^41 + 49403451*T^40 +
      100452734*T^39 + 143951863*T^38 + 194247872*T^37 +
      222949104*T^36 + 122080540*T^35 - 16205548*T^34 + 356495764*T^33
      + 1735317817*T^32 + 2754119138*T^31 - 1212309615*T^30 -
      13772391772*T^29 - 28242062819*T^28 - 30712318826*T^27 -
      18828524030*T^26 - 5100672130*T^25 + 1190939485*T^24 +
      1576001718*T^23 + 544745760*T^22 + 56422592*T^21 - 1136251*T^20
      + 562036*T^19 + 47047*T^18 - 4016*T^17 + 146*T^16 - 4*T^15)*x^12
      + (-1455*T^48 - 17088*T^47 - 35676*T^46 + 712076*T^45 +
      4622400*T^44 + 12386310*T^43 + 23040567*T^42 + 43305798*T^41 +
      69437232*T^40 + 49471066*T^39 - 84618774*T^38 - 375961644*T^37 -
      970539521*T^36 - 1973212572*T^35 - 2533331103*T^34 -
      548346110*T^33 + 4986054486*T^32 + 9995776344*T^31 +
      6938423546*T^30 - 4253485290*T^29 - 12815520708*T^28 -
      11694281924*T^27 - 5639904456*T^26 - 1292839872*T^25 +
      102467928*T^24 + 135383046*T^23 + 18689421*T^22 - 25048*T^21 +
      91782*T^20 + 10230*T^19 - 341*T^18 + 6*T^17)*x^11 + (460*T^50 -
      814*T^49 - 15425*T^48 + 15498*T^47 + 873222*T^46 + 5000178*T^45
      + 13644763*T^44 + 19820726*T^43 + 12626842*T^42 - 13965226*T^41
      - 93786647*T^40 - 273915886*T^39 - 516800806*T^38 -
      935929250*T^37 - 2120121406*T^36 - 4341098628*T^35 -
      5971128606*T^34 - 3844127400*T^33 + 2320158136*T^32 +
      6942047252*T^31 + 5229689926*T^30 + 300854866*T^29 -
      2277164551*T^28 - 1871019428*T^27 - 743906910*T^26 -
      128819364*T^25 + 7525563*T^24 + 2685482*T^23 - 45062*T^22 +
      2498*T^21 + 1005*T^20)*x^10 + (-18*T^52 + 1150*T^51 + 6803*T^50
      + 40048*T^49 + 199114*T^48 + 695352*T^47 + 2349855*T^46 +
      5958380*T^45 + 4839605*T^44 - 13750364*T^43 - 43773051*T^42 -
      67003766*T^41 - 28216822*T^40 + 322995800*T^39 + 1281929695*T^38
      + 2429582510*T^37 + 2286153722*T^36 - 163747248*T^35 -
      3115995786*T^34 - 3284722970*T^33 - 699965179*T^32 +
      1305572998*T^31 + 1218691459*T^30 + 373837004*T^29 -
      72879110*T^28 - 110916396*T^27 - 37925685*T^26 - 3050496*T^25 +
      63984*T^24 - 14720*T^23 - 1306*T^22 - 2*T^21)*x^9 + (12*T^54 -
      18*T^53 + 423*T^52 + 7790*T^51 + 80319*T^50 + 319542*T^49 +
      349503*T^48 - 591408*T^47 - 2027055*T^46 - 5564392*T^45 -
      15794460*T^44 - 25526970*T^43 - 30692762*T^42 - 36290934*T^41 +
      137404704*T^40 + 1075461772*T^39 + 3287090856*T^38 +
      5923236336*T^37 + 6676287093*T^36 + 4446816078*T^35 +
      1238843961*T^34 - 426018208*T^33 - 446260887*T^32 -
      73943760*T^31 + 72042134*T^30 + 49704906*T^29 + 9005811*T^28 -
      1598910*T^27 - 318141*T^26 + 240*T^25 + 553*T^24)*x^8 + (-T^56 +
      46*T^55 + 155*T^54 - 786*T^53 - 2265*T^52 + 41034*T^51 +
      187167*T^50 + 6840*T^49 - 1245786*T^48 - 2525846*T^47 -
      2245336*T^46 - 2141318*T^45 - 6530863*T^44 - 51743930*T^43 -
      272731906*T^42 - 806110528*T^41 - 1353604946*T^40 -
      992611894*T^39 + 807395573*T^38 + 2941045684*T^37 +
      3614285918*T^36 + 2571954518*T^35 + 1116992749*T^34 +
      255927686*T^33 - 6480673*T^32 - 21620540*T^31 - 2823970*T^30 +
      1150950*T^29 + 180888*T^28 + 4788*T^27)*x^7 + (-4*T^57 + 61*T^56
      + 380*T^55 - 290*T^54 - 4974*T^53 + 4233*T^52 + 40398*T^51 -
      130227*T^50 - 743802*T^49 - 680556*T^48 + 2018396*T^47 +
      7999822*T^46 + 20428528*T^45 + 33455155*T^44 - 44299090*T^43 -
      436828593*T^42 - 1242037382*T^41 - 2016998686*T^40 -
      2023926018*T^39 - 1155755504*T^38 - 148485928*T^37 +
      336731285*T^36 + 324475228*T^35 + 160889465*T^34 + 48837694*T^33
      + 8013004*T^32 + 394142*T^31 - 1601*T^30)*x^6 + (-6*T^58 +
      28*T^57 + 300*T^56 + 390*T^55 - 978*T^54 + 3036*T^53 +
      15966*T^52 - 38442*T^51 - 183036*T^50 + 142296*T^49 +
      1882538*T^48 + 6297546*T^47 + 22271970*T^46 + 74678806*T^45 +
      169855650*T^44 + 220037418*T^43 + 77069500*T^42 - 259083714*T^41
      - 554043942*T^40 - 590942168*T^39 - 410233824*T^38 -
      199400658*T^37 - 69269936*T^36 - 16471704*T^35 - 2231274*T^34 -
      89906*T^33)*x^5 + (-4*T^59 - 2*T^58 + 68*T^57 + 76*T^56 -
      256*T^55 + 1069*T^54 + 4198*T^53 - 10963*T^52 - 46610*T^51 +
      29122*T^50 + 252818*T^49 + 119866*T^48 + 1243318*T^47 +
      14467232*T^46 + 57020422*T^45 + 126044332*T^44 + 180856382*T^43
      + 178551184*T^42 + 124540082*T^41 + 62408074*T^40 +
      22968482*T^39 + 6367971*T^38 + 1277580*T^37 + 138519*T^36)*x^4 +
      (-T^60 - 2*T^59 - T^58 - 76*T^57 - 376*T^56 - 536*T^55 - 84*T^54
      - 1600*T^53 - 7310*T^52 - 10924*T^51 - 93166*T^50 - 743768*T^49
      - 2906028*T^48 - 6737176*T^47 - 10072676*T^46 - 9845472*T^45 -
      5915353*T^44 - 1568354*T^43 + 495783*T^42 + 581572*T^41 +
      198284*T^40 + 25408*T^39)*x^3 + (T^60 + 6*T^59 + 9*T^58 -
      16*T^57 - 60*T^56 - 24*T^55 + 116*T^54 + 144*T^53 + 1662*T^52 +
      17060*T^51 + 77694*T^50 + 207504*T^49 + 362996*T^48 +
      435432*T^47 + 362820*T^46 + 207344*T^45 + 77769*T^44 +
      17286*T^43 + 1729*T^42)*x^2;
  else // k = 3
    D1 := -(T/x)^11*(f - T*x)^5*f^6 where f is y + (T^2 - 1)*x + T^3;
    D17 := (T*(T + 2)*x + T^2)*y - x^3 - T*(T^2 + 2*T + 3)*x^2 - T^2*x;
    A := ((-T^2 - 17*T)*x^19 + (230*T^5 + 3012*T^4 - 431*T^3 -
      140*T^2)*x^18 + (-723*T^8 - 9345*T^7 + 40511*T^6 + 20213*T^5 -
      3332*T^4 - 508*T^3)*x^17 + (-248*T^11 + 3176*T^10 - 168107*T^9 -
      119646*T^8 + 287423*T^7 + 58908*T^6 - 11436*T^5 - 1064*T^4)*x^16
      + (259*T^14 + 5439*T^13 + 276656*T^12 + 222048*T^11 -
      1307098*T^10 - 638718*T^9 + 920120*T^8 + 98128*T^7 - 22754*T^6 -
      1414*T^5)*x^15 + (966*T^17 + 6516*T^16 - 194355*T^15 -
      188760*T^14 + 2263940*T^13 + 1914604*T^12 - 4520018*T^11 -
      1867380*T^10 + 1725472*T^9 + 103944*T^8 - 28910*T^7 -
      1232*T^6)*x^14 + (259*T^20 - 4483*T^19 + 57186*T^18 + 66484*T^17
      - 1777458*T^16 - 2193794*T^15 + 7925766*T^14 + 7426078*T^13 -
      9073518*T^12 - 3293926*T^11 + 2082899*T^10 + 73975*T^9 -
      24360*T^8 - 700*T^7)*x^13 + (-488*T^23 - 4848*T^22 - 20817*T^21
      + 15734*T^20 + 760424*T^19 + 1011954*T^18 - 6616586*T^17 -
      9615980*T^16 + 15412554*T^15 + 16504256*T^14 - 11798706*T^13 -
      3601932*T^12 + 1673405*T^11 + 35918*T^10 - 13672*T^9 -
      248*T^8)*x^12 + (-243*T^26 - 51*T^25 + 6936*T^24 - 23340*T^23 -
      289869*T^22 - 243465*T^21 + 3211949*T^20 + 5378563*T^19 -
      13127351*T^18 - 23100607*T^17 + 17949552*T^16 + 23212936*T^15 -
      10672940*T^14 - 2361796*T^13 + 890033*T^12 + 10683*T^11 -
      4981*T^10 - 49*T^9)*x^11 + (-10*T^29 + 604*T^28 + 387*T^27 -
      2496*T^26 + 71890*T^25 + 117272*T^24 - 1007419*T^23 -
      1882312*T^22 + 6427817*T^21 + 13978824*T^20 - 15080593*T^19 -
      34827564*T^18 + 12232264*T^17 + 21832088*T^16 - 7107096*T^15 -
      788912*T^14 + 298585*T^13 + 488*T^12 - 1099*T^11 - 4*T^10)*x^10
      + (-T^32 - 3*T^31 - 758*T^30 + 1312*T^29 + 4373*T^28 -
      45029*T^27 + 123254*T^26 + 700620*T^25 - 1257551*T^24 -
      4457505*T^23 + 7663787*T^22 + 22269181*T^21 - 9315612*T^20 -
      35705228*T^19 + 3219072*T^18 + 14238772*T^17 - 3439151*T^16 -
      23245*T^15 + 54042*T^14 - 1076*T^13 - 124*T^12)*x^9 + (-9*T^33 +
      202*T^32 - 4340*T^31 - 5726*T^30 + 19833*T^29 - 160046*T^28 -
      283008*T^27 + 812498*T^26 - 749719*T^25 - 5459826*T^24 +
      7235335*T^23 + 26210672*T^22 + 952288*T^21 - 26001544*T^20 -
      3188980*T^19 + 6271928*T^18 - 890875*T^17 + 67434*T^16 +
      744*T^15 - 382*T^14 - 4*T^13)*x^8 + (-36*T^34 + 1724*T^33 -
      9351*T^32 - 28421*T^31 + 85716*T^30 - 79444*T^29 - 1024861*T^28
      - 1061323*T^27 - 2570753*T^26 - 6877765*T^25 + 4713642*T^24 +
      24982390*T^23 + 10857949*T^22 - 12174939*T^21 - 5052344*T^20 +
      1155992*T^19 + 169422*T^18 + 21818*T^17 - 2261*T^16 -
      35*T^15)*x^7 + (-84*T^35 + 6160*T^34 - 5509*T^33 - 55244*T^32 +
      217356*T^31 + 623680*T^30 - 471449*T^29 - 2787972*T^28 -
      6767171*T^27 - 11936672*T^26 - 3361224*T^25 + 16156808*T^24 +
      14406059*T^23 - 822484*T^22 - 3126340*T^21 - 723580*T^20 +
      202914*T^19 + 7460*T^18 - 515*T^17)*x^6 + (-126*T^36 +
      12446*T^35 + 13266*T^34 - 68198*T^33 + 274917*T^32 +
      1522723*T^31 + 1870433*T^30 - 596949*T^29 - 6529675*T^28 -
      14039677*T^27 - 11585567*T^26 + 2735051*T^25 + 8956726*T^24 +
      3332202*T^23 - 512830*T^22 - 576458*T^21 + 39848*T^20 +
      2236*T^19)*x^5 + (-126*T^37 + 15652*T^36 + 32070*T^35 -
      67752*T^34 + 115761*T^33 + 1515614*T^32 + 3328565*T^31 +
      3148932*T^30 - 769999*T^29 - 7600178*T^28 - 10251163*T^27 -
      4396232*T^26 + 1627042*T^25 + 1879192*T^24 + 335426*T^23 -
      121224*T^22 - 2272*T^21)*x^4 + (-84*T^38 + 12572*T^37 +
      32158*T^36 - 57562*T^35 - 109251*T^34 + 618125*T^33 +
      2224566*T^32 + 3458262*T^31 + 2785403*T^30 - 293085*T^29 -
      3236556*T^28 - 2913388*T^27 - 788809*T^26 + 195119*T^25 +
      119056*T^24 + 1880*T^23)*x^3 + (-36*T^39 + 6304*T^38 +
      17660*T^37 - 35952*T^36 - 162121*T^35 - 65892*T^34 + 495972*T^33
      + 1274068*T^32 + 1707185*T^31 + 1279764*T^30 + 259142*T^29 -
      348620*T^28 - 266375*T^27 - 62108*T^26 - 3688*T^25)*x^2 +
      (-9*T^40 + 1805*T^39 + 5201*T^38 - 13329*T^37 - 78053*T^36 -
      138615*T^35 - 110869*T^34 + 21037*T^33 + 200113*T^32 +
      300723*T^31 + 235919*T^30 + 99705*T^29 + 21568*T^28 +
      2544*T^27)*x - T^41 + 226*T^40 + 645*T^39 - 2128*T^38 -
      13757*T^37 - 33150*T^36 - 52013*T^35 - 61600*T^34 - 54027*T^33 -
      31598*T^32 - 10753*T^31 - 1800*T^30 - 144*T^29)*y + x^21 +
      (-230*T^3 + 127*T^2 + 26*T)*x^20 + (723*T^6 - 17708*T^5 -
      3709*T^4 + 1504*T^3 + 176*T^2)*x^19 + (248*T^9 + 96345*T^8 -
      30768*T^7 - 173131*T^6 - 17910*T^5 + 7386*T^4 + 592*T^3)*x^18 +
      (-259*T^12 - 213796*T^11 + 146892*T^10 + 1101888*T^9 -
      198206*T^8 - 734736*T^7 - 42276*T^6 + 20360*T^5 + 1190*T^4)*x^17
      + (-966*T^15 + 258757*T^14 - 214238*T^13 - 2646600*T^12 +
      742496*T^11 + 5414164*T^10 - 456940*T^9 - 1804254*T^8 -
      56360*T^7 + 35382*T^6 + 1540*T^5)*x^16 + (-259*T^18 -
      198880*T^17 + 94614*T^16 + 3204704*T^15 - 820018*T^14 -
      13940068*T^13 + 465754*T^12 + 15248088*T^11 - 390974*T^10 -
      2861860*T^9 - 43701*T^8 + 40852*T^7 + 1316*T^6)*x^15 + (488*T^21
      + 95334*T^20 + 30792*T^19 - 2176937*T^18 + 86260*T^17 +
      17076630*T^16 + 2085064*T^15 - 41629028*T^14 - 5472528*T^13 +
      27473103*T^12 + 186440*T^11 - 3077888*T^10 - 17814*T^9 +
      31948*T^8 + 736*T^7)*x^14 + (243*T^24 - 20548*T^23 - 16416*T^22
      + 892088*T^21 + 422965*T^20 - 10915350*T^19 - 3817205*T^18 +
      52184728*T^17 + 21344255*T^16 - 77846000*T^15 - 19547020*T^14 +
      33316636*T^13 + 631952*T^12 - 2274654*T^11 - 469*T^10 +
      16836*T^9 + 257*T^8)*x^13 + (10*T^27 + 1389*T^26 - 1378*T^25 -
      195292*T^24 - 187050*T^23 + 3869625*T^22 + 2304378*T^21 -
      33829064*T^20 - 24693470*T^19 + 99007787*T^18 + 65636258*T^17 -
      93716060*T^16 - 32899448*T^15 + 27789254*T^14 + 388500*T^13 -
      1134614*T^12 + 4734*T^11 + 5795*T^10 + 50*T^9)*x^12 + (T^30 +
      4*T^29 + 818*T^28 + 15980*T^27 - 1257*T^26 - 749600*T^25 -
      388754*T^24 + 11907488*T^23 + 10703571*T^22 - 67945614*T^21 -
      75890069*T^20 + 114520868*T^19 + 111257260*T^18 - 70591488*T^17
      - 32675376*T^16 + 15908248*T^15 - 104069*T^14 - 358354*T^13 +
      4090*T^12 + 1212*T^11 + 4*T^10)*x^11 + (8*T^31 + 249*T^30 +
      7352*T^29 + 63492*T^28 - 100388*T^27 - 2190351*T^26 -
      662468*T^25 + 27322640*T^24 + 36513328*T^23 - 82480931*T^22 -
      136055490*T^21 + 67029362*T^20 + 114265416*T^19 - 28643514*T^18
      - 19614712*T^17 + 5914337*T^16 - 250204*T^15 - 58565*T^14 +
      1944*T^13 + 130*T^12)*x^10 + (28*T^32 + 3110*T^31 + 44679*T^30 +
      186012*T^29 - 623832*T^28 - 5990254*T^27 - 4965047*T^26 +
      41029332*T^25 + 77360373*T^24 - 43706972*T^23 - 147210058*T^22 -
      6520700*T^21 + 69431679*T^20 - 868824*T^19 - 6125808*T^18 +
      1008084*T^17 - 130538*T^16 + 1030*T^15 + 465*T^14 + 4*T^13)*x^9
      + (280*T^33 + 17328*T^32 + 183904*T^31 + 600068*T^30 -
      1253988*T^29 - 12231360*T^28 - 18372666*T^27 + 32124681*T^26 +
      98041766*T^25 + 24513712*T^24 - 90158770*T^23 - 41704871*T^22 +
      19486274*T^21 + 5381934*T^20 + 308904*T^19 - 275018*T^18 -
      34920*T^17 + 2692*T^16 + 36*T^15)*x^8 + (1434*T^34 + 52494*T^33
      + 478930*T^32 + 1596508*T^31 - 316713*T^30 - 15439038*T^29 -
      33020815*T^28 - 147748*T^27 + 70649351*T^26 + 57919788*T^25 -
      20429083*T^24 - 30511372*T^23 - 3722178*T^22 + 2587612*T^21 +
      1288814*T^20 - 208312*T^19 - 8824*T^18 + 522*T^17)*x^7 + (T^36 +
      3516*T^35 + 94480*T^34 + 786396*T^33 + 2770342*T^32 +
      2632372*T^31 - 10289777*T^30 - 32359834*T^29 - 24499583*T^28 +
      22617656*T^27 + 41206055*T^26 + 10498922*T^25 - 9656580*T^24 -
      5581972*T^23 + 196686*T^22 + 589640*T^21 - 35801*T^20 -
      2044*T^19)*x^6 + (4*T^37 + 4712*T^36 + 104312*T^35 + 814770*T^34
      + 2986872*T^33 + 4728575*T^32 - 1474316*T^31 - 16970658*T^30 -
      22044744*T^29 - 3468911*T^28 + 13846100*T^27 + 9601784*T^26 -
      235272*T^25 - 2105623*T^24 - 259124*T^23 + 99704*T^22 +
      1752*T^21)*x^5 + (6*T^38 + 3580*T^37 + 69564*T^36 + 518114*T^35
      + 1943953*T^34 + 3774634*T^33 + 2601848*T^32 - 3602102*T^31 -
      8590121*T^30 - 5197846*T^29 + 1513776*T^28 + 3040010*T^27 +
      844835*T^26 - 272706*T^25 - 71290*T^24 - 1640*T^23)*x^4 +
      (4*T^39 + 1457*T^38 + 25796*T^37 + 185081*T^36 + 702484*T^35 +
      1511393*T^34 + 1703412*T^33 + 407303*T^32 - 1322240*T^31 -
      1501717*T^30 - 357432*T^29 + 338347*T^28 + 209260*T^27 +
      16516*T^26 + 3816*T^25)*x^3 + (T^40 + 248*T^39 + 4095*T^38 +
      28502*T^37 + 108613*T^36 + 247168*T^35 + 334641*T^34 +
      229394*T^33 - 8125*T^32 - 144348*T^31 - 104651*T^30 - 27966*T^29
      - 3624*T^28 - 2448*T^27)*x^2;
    B := (x^30 + (T^4 + 544*T^3 + 285*T^2 + 13*T)*x^29 + (519*T^7 -
      180*T^6 + 103151*T^5 + 13267*T^4 + 3566*T^3 + 78*T^2)*x^28 +
      (-11046*T^10 - 189046*T^9 - 1649376*T^8 + 1621881*T^7 +
      1165200*T^6 + 117588*T^5 + 20577*T^4 + 286*T^3)*x^27 +
      (10556*T^13 + 300569*T^12 + 3454800*T^11 - 23159639*T^10 -
      17266708*T^9 + 17924508*T^8 + 6017493*T^7 + 576493*T^6 +
      72516*T^5 + 715*T^4)*x^26 + (-4683*T^16 - 100458*T^15 -
      1629803*T^14 + 93189215*T^13 + 62479615*T^12 - 259587797*T^11 -
      85996858*T^10 + 90977818*T^9 + 18780410*T^8 + 1830928*T^7 +
      174185*T^6 + 1287*T^5)*x^25 + (-5943*T^19 + 38545*T^18 +
      510669*T^17 - 175628352*T^16 - 90016545*T^15 + 1137454428*T^14 +
      500777076*T^13 - 1402566151*T^12 - 270600462*T^11 +
      280805019*T^10 + 39431497*T^9 + 4075218*T^8 + 301290*T^7 +
      1716*T^6)*x^24 + (16135*T^22 + 179128*T^21 - 407688*T^20 +
      201408458*T^19 + 68096794*T^18 - 2422819227*T^17 -
      1249632074*T^16 + 6563936163*T^15 + 2391066393*T^14 -
      4722493719*T^13 - 598082835*T^12 + 587623137*T^11 +
      58625292*T^10 + 6642009*T^9 + 386397*T^8 + 1716*T^7)*x^23 +
      (33327*T^25 + 148581*T^24 - 119788*T^23 - 167674310*T^22 -
      69083872*T^21 + 3016995758*T^20 + 1734383314*T^19 -
      15160998628*T^18 - 8447304273*T^17 + 23551003200*T^16 +
      7662573933*T^15 - 11043180408*T^14 - 970330248*T^13 +
      878818803*T^12 + 63174603*T^11 + 8127966*T^10 + 372504*T^9 +
      1287*T^8)*x^22 + (-23247*T^28 - 567466*T^27 - 2788983*T^26 +
      95320482*T^25 + 86345268*T^24 - 2421298758*T^23 -
      1752689739*T^22 + 20104030518*T^21 + 15488085090*T^20 -
      56979163044*T^19 - 34762835020*T^18 + 58878151227*T^17 +
      17603039862*T^16 - 19049283335*T^15 - 1165259511*T^14 +
      962264373*T^13 + 49509277*T^12 + 7564491*T^11 + 270567*T^10 +
      715*T^9)*x^21 + (-30247*T^31 - 151903*T^30 + 1364931*T^29 -
      32225723*T^28 - 59935696*T^27 + 1263783591*T^26 +
      1279956925*T^25 - 16507707340*T^24 - 17120377020*T^23 +
      77784837583*T^22 + 73955836664*T^21 - 144446427513*T^20 -
      97298572104*T^19 + 109405090576*T^18 + 30280798797*T^17 -
      25220518657*T^16 - 1004546111*T^15 + 773135820*T^14 +
      27697655*T^13 + 5373511*T^12 + 146850*T^11 + 286*T^10)*x^20 +
      (-1113*T^34 + 237348*T^33 + 1622266*T^32 + 10617638*T^31 +
      18000919*T^30 - 419622470*T^29 - 477798277*T^28 +
      8883107311*T^27 + 11671649668*T^26 - 65168805829*T^25 -
      86854673972*T^24 + 195462394045*T^23 + 224210156813*T^22 -
      264507512387*T^21 - 198307727140*T^20 + 157902300058*T^19 +
      40365889544*T^18 - 26400671248*T^17 - 543814892*T^16 +
      443871995*T^15 + 10417301*T^14 + 2899534*T^13 + 58355*T^12 +
      78*T^11)*x^19 + (11739*T^37 + 136468*T^36 - 201582*T^35 -
      4542714*T^34 - 2533005*T^33 + 115424880*T^32 + 61866789*T^31 -
      3287984785*T^30 - 4423076082*T^29 + 36725158125*T^28 +
      61600688928*T^27 - 160886008734*T^26 - 268137364299*T^25 +
      343612709220*T^24 + 475625287638*T^23 - 368597027907*T^22 -
      309663396910*T^21 + 182875842762*T^20 + 43033166880*T^19 -
      22380306525*T^18 - 49143543*T^17 + 165199797*T^16 + 2138331*T^15
      + 1171857*T^14 + 16356*T^13 + 13*T^12)*x^18 + (3556*T^40 -
      22478*T^39 - 333900*T^38 + 944045*T^37 + 7659937*T^36 -
      16892082*T^35 - 19574606*T^34 + 853165035*T^33 + 834286029*T^32
      - 15042023372*T^31 - 28009862879*T^30 + 88555256475*T^29 +
      191319279314*T^28 - 265444264688*T^27 - 556891539321*T^26 +
      456769653971*T^25 + 760169183467*T^24 - 407780259543*T^23 -
      386733716121*T^22 + 173527137650*T^21 + 37793608317*T^20 -
      15643604597*T^19 + 234318200*T^18 + 23318640*T^17 - 77784*T^16 +
      345478*T^15 + 3027*T^14 + T^13)*x^17 + (462*T^43 - 7947*T^42 +
      68252*T^41 + 568825*T^40 - 2703253*T^39 - 11065132*T^38 +
      16808122*T^37 - 56402962*T^36 - 46597065*T^35 + 4253171640*T^34
      + 8700348591*T^33 - 35348062723*T^32 - 93985430348*T^31 +
      122382745886*T^30 + 366768511295*T^29 - 337630999910*T^28 -
      855599279527*T^27 + 501866680082*T^26 + 979107978655*T^25 -
      363622389433*T^24 - 399359649527*T^23 + 135408477059*T^22 +
      27922181254*T^21 - 9081417545*T^20 + 263987312*T^19 -
      13981265*T^18 - 188365*T^17 + 70948*T^16 + 326*T^15)*x^16 +
      (-15*T^46 - 1702*T^45 + 5400*T^44 - 181527*T^43 - 660214*T^42 +
      4903563*T^41 + 6146046*T^40 - 63214559*T^39 - 128207574*T^38 -
      622268898*T^37 - 1653923477*T^36 + 9839085555*T^35 +
      35278330944*T^34 - 28673694206*T^33 - 159212428233*T^32 +
      114943563402*T^31 + 467175451217*T^30 - 432226718289*T^29 -
      1096010869161*T^28 + 467240888303*T^27 + 1067949982665*T^26 -
      247191712596*T^25 - 345405593631*T^24 + 85402815750*T^23 +
      17318309985*T^22 - 4323290283*T^21 + 163450029*T^20 -
      10891137*T^19 - 48530*T^18 + 9333*T^17 + 15*T^16)*x^15 + (-T^49
      - 4*T^48 + 1380*T^47 - 14607*T^46 + 143674*T^45 - 432141*T^44 -
      8249720*T^43 + 4197891*T^42 + 87921174*T^41 + 20238550*T^40 -
      303663563*T^39 - 2200341630*T^38 - 9633782876*T^37 -
      90829059*T^36 + 56707567503*T^35 + 32206235113*T^34 -
      93082932773*T^33 + 202836769251*T^32 + 506081485997*T^31 -
      577189155017*T^30 - 1291423267767*T^29 + 305477065943*T^28 +
      989378398339*T^27 - 100008881460*T^26 - 246136090057*T^25 +
      42015292660*T^24 + 8676071325*T^23 - 1615631498*T^22 +
      64895778*T^21 - 3821799*T^20 - 1995*T^19 + 660*T^18)*x^14 +
      (-14*T^50 - 577*T^49 + 15643*T^48 - 98971*T^47 + 933076*T^46 +
      4131011*T^45 - 28500177*T^44 - 73551747*T^43 + 205485438*T^42 +
      712403756*T^41 + 1230765748*T^40 - 234740161*T^39 -
      19250245653*T^38 - 47117344803*T^37 - 15350430324*T^36 +
      28803281900*T^35 + 83516052121*T^34 + 512755256756*T^33 +
      696760400990*T^32 - 568013359586*T^31 - 1358721042535*T^30 +
      26857177202*T^29 + 740702431492*T^28 + 11849198903*T^27 -
      138606070774*T^26 + 15521269663*T^25 + 3217069052*T^24 -
      431906721*T^23 + 16071201*T^22 - 797895*T^21 + 1440*T^20 +
      15*T^19)*x^13 + (-91*T^51 - 7137*T^50 + 81486*T^49 - 575526*T^48
      + 1728441*T^47 + 28601544*T^46 - 20102116*T^45 - 327719976*T^44
      - 158515578*T^43 + 1444025869*T^42 + 5701929381*T^41 +
      14934530379*T^40 + 1618756796*T^39 - 83958394209*T^38 -
      194653060839*T^37 - 211778876533*T^36 + 54231923160*T^35 +
      770330565903*T^34 + 1016904231799*T^33 - 227588960559*T^32 -
      1119980586510*T^31 - 201728549589*T^30 + 415259882952*T^29 +
      48075370212*T^28 - 58434778274*T^27 + 4414069602*T^26 +
      725513073*T^25 - 66310035*T^24 + 2113782*T^23 - 97482*T^22 +
      238*T^21)*x^12 + (-364*T^52 - 42094*T^51 + 280473*T^50 -
      2189864*T^49 - 5178886*T^48 + 76721601*T^47 + 136915730*T^46 -
      581900634*T^45 - 1596914748*T^44 - 520531243*T^43 +
      7033417532*T^42 + 36707793504*T^41 + 72266942475*T^40 -
      5091779993*T^39 - 274104030243*T^38 - 534232464734*T^37 -
      314340140856*T^36 + 561633147501*T^35 + 1052671601705*T^34 +
      192370881512*T^33 - 630846001443*T^32 - 231366424651*T^31 +
      161708690160*T^30 + 31444296726*T^29 - 17617315254*T^28 +
      1261713342*T^27 + 26127492*T^26 - 785984*T^25 + 63730*T^24 -
      5580*T^23 + T^22)*x^11 + (-1001*T^53 - 153010*T^52 + 754600*T^51
      - 4898993*T^50 - 35463520*T^49 + 89155378*T^48 + 482698410*T^47
      - 258920400*T^46 - 3167324634*T^45 - 6047108984*T^44 -
      3687737299*T^43 + 32641801729*T^42 + 128813882381*T^41 +
      163663693696*T^40 - 83980992490*T^39 - 529197878838*T^38 -
      600776465145*T^37 + 50730800361*T^36 + 641927125015*T^35 +
      312108388052*T^34 - 209580734252*T^33 - 125296079577*T^32 +
      43650989832*T^31 + 9207616200*T^30 - 3945591480*T^29 +
      461468649*T^28 - 34684842*T^27 + 1415822*T^26 - 11183*T^25 +
      11*T^24)*x^10 + (-2002*T^54 - 380523*T^53 + 1699995*T^52 -
      5123569*T^51 - 90793548*T^50 - 36998412*T^49 + 734273050*T^48 +
      820263240*T^47 - 2624564277*T^46 - 9537444390*T^45 -
      19255152411*T^44 - 7487170146*T^43 + 87795213951*T^42 +
      225466869981*T^41 + 169856082744*T^40 - 179989587372*T^39 -
      444491617725*T^38 - 213055505118*T^37 + 179802433310*T^36 +
      164187160059*T^35 - 36568808430*T^34 - 35406828913*T^33 +
      12193581117*T^32 + 795778530*T^31 - 868734986*T^30 +
      137161965*T^29 - 8141598*T^28 + 137594*T^27 - 552*T^26)*x^9 +
      (-3003*T^55 - 682539*T^54 + 3177306*T^53 + 3437149*T^52 -
      133160840*T^51 - 295203255*T^50 + 482496053*T^49 +
      1662503869*T^48 + 32221395*T^47 - 5674850697*T^46 -
      19641531313*T^45 - 38438515098*T^44 - 9245620948*T^43 +
      106415765268*T^42 + 190726059273*T^41 + 85149675525*T^40 -
      106665817038*T^39 - 123107827899*T^38 + 1146954878*T^37 +
      29861126012*T^36 - 13082381301*T^35 - 7309495746*T^34 +
      5071331164*T^33 + 24402570*T^32 - 200415694*T^31 + 18774919*T^30
      - 410760*T^29 - 500*T^28)*x^8 + (-3432*T^56 - 907764*T^55 +
      4740747*T^54 + 21560423*T^53 - 111916088*T^52 - 491450233*T^51 -
      199738144*T^50 + 1184954416*T^49 + 1623828911*T^48 +
      887584882*T^47 - 3818247982*T^46 - 24260582165*T^45 -
      47219031945*T^44 - 24018208188*T^43 + 43429557978*T^42 +
      73348372422*T^41 + 35214633006*T^40 + 3018792021*T^39 +
      7453443415*T^38 + 2171036822*T^37 - 9562291364*T^36 -
      3865868839*T^35 + 1357368400*T^34 + 110849576*T^33 -
      20655325*T^32 + 102247*T^31 + 3920*T^30)*x^7 + (-3003*T^57 -
      906048*T^56 + 5463876*T^55 + 38672457*T^54 - 30920088*T^53 -
      445771398*T^52 - 705670263*T^51 - 116869632*T^50 +
      477468300*T^49 + 2171547743*T^48 + 7217363715*T^47 +
      6013637232*T^46 - 14070550694*T^45 - 38021844660*T^44 -
      36414972036*T^43 - 11929875093*T^42 + 8266431753*T^41 +
      15981678087*T^40 + 15493908428*T^39 + 6491800149*T^38 -
      1658948670*T^37 - 1597928952*T^36 + 29482041*T^35 +
      18492015*T^34 + 1862676*T^33 + 2856*T^32)*x^6 + (-2002*T^58 -
      678535*T^57 + 4750185*T^56 + 41913805*T^55 + 45029258*T^54 -
      220901778*T^53 - 651558952*T^52 - 838681917*T^51 -
      1210804548*T^50 - 918761717*T^49 + 4272206029*T^48 +
      13443232527*T^47 + 14581000462*T^46 + 355317756*T^45 -
      17370925980*T^44 - 22411236495*T^43 - 14324927964*T^42 -
      3144470406*T^41 + 3347622026*T^40 + 3250433633*T^39 +
      759144165*T^38 - 131655422*T^37 - 29958643*T^36 - 3971328*T^35 -
      31504*T^34)*x^5 + (-1001*T^59 - 376519*T^58 + 3044290*T^57 +
      30479743*T^56 + 65746628*T^55 - 25608269*T^54 - 290427138*T^53 -
      608583636*T^52 - 1319455953*T^51 - 2465457193*T^50 -
      1568940476*T^49 + 3980346404*T^48 + 10864528362*T^47 +
      11739604794*T^46 + 5127126852*T^45 - 2451956487*T^44 -
      5333647416*T^43 - 3857483241*T^42 - 1274853059*T^41 +
      78598277*T^40 + 180151249*T^39 + 37072045*T^38 + 3486764*T^37 +
      57448*T^36)*x^4 + (-364*T^60 - 150462*T^59 + 1392363*T^58 +
      15071245*T^57 + 43396374*T^56 + 39696087*T^55 - 33245350*T^54 -
      148908204*T^53 - 487244463*T^52 - 1379847330*T^51 -
      2280413736*T^50 - 1617496062*T^49 + 1049235425*T^48 +
      3676778550*T^47 + 4053069447*T^46 + 2444669981*T^45 +
      654707349*T^44 - 234929025*T^43 - 314331260*T^42 -
      129386052*T^41 - 22437648*T^40 - 1416400*T^39 - 44640*T^38)*x^3
      + (-91*T^61 - 41002*T^60 + 429936*T^59 + 4894369*T^58 +
      16660916*T^57 + 27015615*T^56 + 28088461*T^55 + 35328773*T^54 +
      9707754*T^53 - 211967000*T^52 - 686259289*T^51 - 1080377499*T^50
      - 953211377*T^49 - 351946768*T^48 + 219246021*T^47 +
      419846158*T^46 + 324946532*T^45 + 155724771*T^44 + 45036758*T^43
      + 6415956*T^42 + 260712*T^41 + 12960*T^40)*x^2 + (-14*T^62 -
      6829*T^61 + 80353*T^60 + 945961*T^59 + 3601910*T^58 +
      7579027*T^57 + 13282273*T^56 + 28156610*T^55 + 54864397*T^54 +
      64712740*T^53 + 13128185*T^52 - 94772618*T^51 - 186186533*T^50 -
      198562027*T^49 - 144348788*T^48 - 76576979*T^47 - 29433397*T^46
      - 7435919*T^45 - 983412*T^44 - 34992*T^43)*x - T^63 - 525*T^62 +
      6870*T^61 + 82736*T^60 + 341823*T^59 + 846249*T^58 +
      1869833*T^57 + 4707135*T^56 + 11131911*T^55 + 20346545*T^54 +
      27386817*T^53 + 27204987*T^52 + 20209868*T^51 + 11443458*T^50 +
      5011287*T^49 + 1650419*T^48 + 360180*T^47 + 37584*T^46)*y +
      (-T^2 - 26*T - 1)*x^31 + (-519*T^5 - 11385*T^4 - 2515*T^3 -
      629*T^2 - 13*T)*x^30 + (11046*T^8 + 210648*T^7 - 579423*T^6 -
      254742*T^5 - 38352*T^4 - 5672*T^3 - 78*T^2)*x^29 + (-10556*T^11
      - 315808*T^10 + 10126024*T^9 + 778648*T^8 - 8283301*T^7 -
      2103068*T^6 - 265597*T^5 - 28481*T^4 - 286*T^3)*x^28 +
      (4683*T^14 + 99198*T^13 - 45294644*T^12 + 24001712*T^11 +
      144308596*T^10 - 6703508*T^9 - 53149171*T^8 - 9596276*T^7 -
      1112070*T^6 - 92822*T^5 - 715*T^4)*x^27 + (5943*T^17 -
      16467*T^16 + 108982083*T^15 - 131349483*T^14 - 758826528*T^13 +
      284420741*T^12 + 960021279*T^11 - 63126756*T^10 - 203935966*T^9
      - 28210230*T^8 - 3158043*T^7 - 211937*T^6 - 1287*T^5)*x^26 +
      (-16135*T^20 - 161936*T^19 - 179090557*T^18 + 270187592*T^17 +
      2039447803*T^16 - 1373867128*T^15 - 5731481670*T^14 +
      1433785332*T^13 + 3935570292*T^12 - 245950458*T^11 -
      525059769*T^10 - 57634068*T^9 - 6456795*T^8 - 353628*T^7 -
      1716*T^6)*x^25 + (-33327*T^23 - 205155*T^22 + 208756564*T^21 -
      282191768*T^20 - 3382066408*T^19 + 2793937030*T^18 +
      16836470371*T^17 - 5917144474*T^16 - 26133455104*T^15 +
      4169832459*T^14 + 11117564388*T^13 - 594416411*T^12 -
      961714431*T^11 - 85276230*T^10 - 9833714*T^9 - 441309*T^8 -
      1716*T^7)*x^24 + (23247*T^26 + 560466*T^25 - 169541907*T^24 +
      164138574*T^23 + 3773048274*T^22 - 2861233616*T^21 -
      28865396055*T^20 + 10500439590*T^19 + 82219320541*T^18 -
      11921061078*T^17 - 81148431459*T^16 + 7609183830*T^15 +
      22982071062*T^14 - 1012553946*T^13 - 1292060886*T^12 -
      93404880*T^11 - 11373549*T^10 - 416262*T^9 - 1287*T^8)*x^23 +
      (30247*T^29 + 181037*T^28 + 98422129*T^27 - 43026431*T^26 -
      2910916516*T^25 + 1479696058*T^24 + 31808109493*T^23 -
      8354122411*T^22 - 145668987662*T^21 + 7798262026*T^20 +
      268667306354*T^19 - 1296818234*T^18 - 183437456773*T^17 +
      8399328010*T^16 + 36103497968*T^15 - 1308880093*T^14 -
      1288042940*T^13 - 76405003*T^12 - 10082380*T^11 - 296879*T^10 -
      715*T^9)*x^22 + (1113*T^32 - 224496*T^31 - 40560348*T^30 -
      10003654*T^29 + 1549392892*T^28 - 249544800*T^27 -
      23700077665*T^26 + 978745198*T^25 + 160567996073*T^24 +
      18505028198*T^23 - 486276785852*T^22 - 79682892404*T^21 +
      630139382234*T^20 + 60336894106*T^19 - 315272518412*T^18 +
      3396604006*T^17 + 44254706438*T^16 - 1362950240*T^15 -
      945048986*T^14 - 46571290*T^13 - 6858478*T^12 - 158576*T^11 -
      286*T^10)*x^21 + (-11739*T^35 - 144651*T^34 + 9755970*T^33 +
      8966580*T^32 - 558909465*T^31 - 122297749*T^30 +
      12089041953*T^29 + 3156391359*T^28 - 116839735771*T^27 -
      43278441750*T^26 + 533844702447*T^25 + 214871303486*T^24 -
      1148089572480*T^23 - 376506795063*T^22 + 1112637402635*T^21 +
      191295455472*T^20 - 425238220176*T^19 - 6270662174*T^18 +
      43174898766*T^17 - 1207554498*T^16 - 489022478*T^15 -
      20856741*T^14 - 3556785*T^13 - 62099*T^12 - 78*T^11)*x^20 +
      (-3556*T^38 + 19384*T^37 - 1020538*T^36 - 1047310*T^35 +
      125567206*T^34 + 43273028*T^33 - 4204250061*T^32 -
      2385538416*T^31 + 57681810243*T^30 + 40093495166*T^29 -
      378591564182*T^28 - 271661057932*T^27 + 1238340493919*T^26 +
      786344083354*T^25 - 2015389733416*T^24 - 933699821122*T^23 +
      1534609700641*T^22 + 357526013138*T^21 - 461186186075*T^20 -
      15376014484*T^19 + 34034218675*T^18 - 946740080*T^17 -
      152924026*T^16 - 6655964*T^15 - 1384852*T^14 - 17162*T^13 -
      13*T^12)*x^19 + (-462*T^41 + 7470*T^40 + 18968*T^39 -
      868802*T^38 - 17257720*T^37 + 12161397*T^36 + 969123940*T^35 +
      635949854*T^34 - 19583322786*T^33 - 20242870725*T^32 +
      179684290389*T^31 + 198396108411*T^30 - 842277750233*T^29 -
      859844070946*T^28 + 2108330782359*T^27 + 1769771375227*T^26 -
      2751027696928*T^25 - 1608925607389*T^24 + 1702562212552*T^23 +
      485842751189*T^22 - 409155153155*T^21 - 19158091969*T^20 +
      21896549011*T^19 - 658633094*T^18 - 4019806*T^17 - 1427456*T^16
      - 393927*T^15 - 3131*T^14 - T^13)*x^18 + (15*T^44 + 1716*T^43 -
      4926*T^42 + 211764*T^41 + 2225256*T^40 - 6020240*T^39 -
      147734334*T^38 - 22034070*T^37 + 4571969677*T^36 +
      5852101380*T^35 - 58156057191*T^34 - 89438197200*T^33 +
      374023415784*T^32 + 560491386294*T^31 - 1345259162582*T^30 -
      1743430966380*T^29 + 2803909051983*T^28 + 2871731146840*T^27 -
      3040988161494*T^26 - 2137517353854*T^25 + 1546987183588*T^24 +
      518262282426*T^23 - 299348118489*T^22 - 16808078938*T^21 +
      11523906000*T^20 - 390472602*T^19 + 24321515*T^18 - 187128*T^17
      - 78135*T^16 - 332*T^15)*x^17 + (T^47 + 5*T^46 - 1388*T^45 +
      11486*T^44 - 195017*T^43 + 390770*T^42 + 18605625*T^41 +
      4119654*T^40 - 697184919*T^39 - 986131084*T^38 +
      12991183759*T^37 + 26460614039*T^36 - 108609908391*T^35 -
      231552547380*T^34 + 526843941093*T^33 + 992005047521*T^32 -
      1690008356093*T^31 - 2535028122931*T^30 + 3148254136226*T^29 +
      3705399905899*T^28 - 2781611299486*T^27 - 2317274516101*T^26 +
      1149460303537*T^25 + 447791863523*T^24 - 180123555967*T^23 -
      11005481513*T^22 + 4902219044*T^21 - 184312959*T^20 +
      14251269*T^19 - 18360*T^18 - 9936*T^17 - 15*T^16)*x^16 +
      (13*T^48 + 584*T^47 - 13649*T^46 + 71198*T^45 - 1492007*T^44 -
      5742796*T^43 + 72774854*T^42 + 191084652*T^41 - 1874040312*T^40
      - 5621375834*T^39 + 20248282864*T^38 + 67066370942*T^37 -
      112445939346*T^36 - 345549393768*T^35 + 551490725874*T^34 +
      1133728870384*T^33 - 1990124101289*T^32 - 2993306241712*T^31 +
      3131518623653*T^30 + 4078066076110*T^29 - 2052628808143*T^28 -
      2094015940502*T^27 + 679421601616*T^26 + 313620878510*T^25 -
      88136251869*T^24 - 5259300410*T^23 + 1620532136*T^22 -
      63735098*T^21 + 4520022*T^20 - 5808*T^19 - 680*T^18)*x^15 +
      (78*T^49 + 6617*T^48 - 61641*T^47 + 380400*T^46 - 5472512*T^45 -
      39843171*T^44 + 172982055*T^43 + 1064395230*T^42 -
      2306476458*T^41 - 16250104014*T^40 + 4514718340*T^39 +
      88306112901*T^38 - 27093891111*T^37 - 205701710580*T^36 +
      655937221857*T^35 + 919029481863*T^34 - 2444674318964*T^33 -
      3314736396474*T^32 + 2613101684019*T^31 + 3898604667013*T^30 -
      1096670727420*T^29 - 1557798039834*T^28 + 302235217705*T^27 +
      174310252140*T^26 - 34709160999*T^25 - 1631206748*T^24 +
      377314398*T^23 - 14407761*T^22 + 884007*T^21 - 1926*T^20 -
      15*T^19)*x^14 + (286*T^50 + 35672*T^49 - 198749*T^48 +
      922810*T^47 - 14954263*T^46 - 142452572*T^45 + 258342921*T^44 +
      3476763294*T^43 + 2762168433*T^42 - 26061156014*T^41 -
      54656266573*T^40 - 1233817286*T^39 + 34395164240*T^38 +
      224013341146*T^37 + 1153421869166*T^36 + 876223763466*T^35 -
      2692027925412*T^34 - 3561019078902*T^33 + 1523861735878*T^32 +
      3106279755614*T^31 - 289052787638*T^30 - 923187266088*T^29 +
      92973868323*T^28 + 74455880826*T^27 - 11142167394*T^26 -
      176336982*T^25 + 45659748*T^24 - 1681060*T^23 + 102079*T^22 -
      244*T^21)*x^13 + (715*T^51 + 117689*T^50 - 585278*T^49 -
      914554*T^48 - 45789559*T^47 - 395013356*T^46 + 66332012*T^45 +
      7710065088*T^44 + 19475142879*T^43 - 13037828414*T^42 -
      129279766861*T^41 - 238539345971*T^40 - 150544411356*T^39 +
      529862087989*T^38 + 1807609203554*T^37 + 1364621613182*T^36 -
      2106413140134*T^35 - 3286155847245*T^34 + 322685321269*T^33 +
      1927204874927*T^32 + 107812026649*T^31 - 421473719432*T^30 +
      17962299972*T^29 + 23787738822*T^28 - 3101689566*T^27 +
      96698604*T^26 - 2714262*T^25 - 9932*T^24 + 5509*T^23 -
      T^22)*x^12 + (1287*T^52 + 262592*T^51 - 1575432*T^50 -
      12627150*T^49 - 142794976*T^48 - 961101462*T^47 -
      1077131145*T^46 + 11530716168*T^45 + 46292331603*T^44 +
      42158380686*T^43 - 134170624588*T^42 - 474078629604*T^41 -
      570759281340*T^40 + 284760981742*T^39 + 1882969490040*T^38 +
      1845732696426*T^37 - 869349648459*T^36 - 2272219752822*T^35 -
      344983448910*T^34 + 872001677846*T^33 + 153460688397*T^32 -
      146559512724*T^31 + 2754750231*T^30 + 5756029284*T^29 -
      791766753*T^28 + 48688152*T^27 - 1645485*T^26 + 14040*T^25 -
      11*T^24)*x^11 + (1716*T^53 + 414939*T^52 - 3420369*T^51 -
      40330648*T^50 - 343488980*T^49 - 1954519606*T^48 -
      3902799985*T^47 + 10068880477*T^46 + 66564933065*T^45 +
      118937848951*T^44 - 22384947217*T^43 - 477896930699*T^42 -
      851552371593*T^41 - 291197361204*T^40 + 1163375410887*T^39 +
      1625081936253*T^38 + 101338162602*T^37 - 1064885259876*T^36 -
      382840107737*T^35 + 272904388844*T^34 + 79009882138*T^33 -
      40421035795*T^32 + 843948514*T^31 + 1161730964*T^30 -
      162210313*T^29 + 8380366*T^28 - 137608*T^27 + 552*T^26)*x^10 +
      (1717*T^54 + 472770*T^53 - 5550324*T^52 - 74845966*T^51 -
      583877732*T^50 - 3065825200*T^49 - 7797745766*T^48 +
      979895584*T^47 + 60571673405*T^46 + 157807730636*T^45 +
      123592553651*T^44 - 237309024098*T^43 - 708234287527*T^42 -
      589730979300*T^41 + 302014061352*T^40 + 877062293544*T^39 +
      342564502656*T^38 - 302026027542*T^37 - 186000095689*T^36 +
      58311221660*T^35 + 25762832794*T^34 - 9433764238*T^33 +
      127515448*T^32 + 197737994*T^31 - 17522843*T^30 + 365830*T^29 +
      500*T^28)*x^9 + (1293*T^55 + 387627*T^54 - 6554091*T^53 -
      92166822*T^52 - 696279983*T^51 - 3539895528*T^50 -
      10244593215*T^49 - 10241372705*T^48 + 30445460010*T^47 +
      125645983422*T^46 + 176092250672*T^45 + 10753072845*T^44 -
      325137997056*T^43 - 437576305704*T^42 - 98089624866*T^41 +
      261838489146*T^40 + 188428572774*T^39 - 40621886799*T^38 -
      54116153802*T^37 + 9048526916*T^36 + 6755661417*T^35 -
      1609840890*T^34 - 51021407*T^33 + 14597313*T^32 - 3327*T^31 -
      3920*T^30)*x^8 + (730*T^56 + 223808*T^55 - 5549228*T^54 -
      78049970*T^53 - 581228620*T^52 - 2927426312*T^51 -
      9180506637*T^50 - 14880700854*T^49 + 959211708*T^48 +
      58121092694*T^47 + 120280606900*T^46 + 91581564350*T^45 -
      52484804793*T^44 - 163869414444*T^43 - 102506710323*T^42 +
      27739633812*T^41 + 49879935930*T^40 + 75066750*T^39 -
      11683335632*T^38 + 438687350*T^37 + 1390555909*T^36 -
      73840238*T^35 - 6239260*T^34 - 1778540*T^33 - 2856*T^32)*x^7 +
      (306*T^57 + 86657*T^56 - 3290399*T^55 - 45194886*T^54 -
      333264376*T^53 - 1680962756*T^52 - 5575654725*T^51 -
      11183901378*T^50 - 9845414268*T^49 + 10629540039*T^48 +
      43882284799*T^47 + 54993586670*T^46 + 20717297972*T^45 -
      24749222214*T^44 - 29906445213*T^43 - 4006853698*T^42 +
      7756460154*T^41 + 1186081086*T^40 - 2077482994*T^39 -
      446701225*T^38 + 81126061*T^37 + 15024267*T^36 + 3356084*T^35 +
      31504*T^34)*x^6 + (93*T^58 + 20330*T^57 - 1303410*T^56 -
      17127816*T^55 - 124791316*T^54 - 634107522*T^53 -
      2197397970*T^52 - 4977579606*T^51 - 6718763136*T^50 -
      3107639346*T^49 + 6374282044*T^48 + 13834407546*T^47 +
      10857728352*T^46 + 1308708264*T^45 - 3321937440*T^44 -
      936944226*T^43 + 1292481069*T^42 + 708745848*T^41 -
      41750814*T^40 - 79864324*T^39 - 24163545*T^38 - 2539020*T^37 -
      57448*T^36)*x^5 + (19*T^59 + 2243*T^58 - 312893*T^57 -
      3804566*T^56 - 27094537*T^55 - 139609760*T^54 - 504093977*T^53 -
      1237366315*T^52 - 2006849714*T^51 - 1951781234*T^50 -
      630491587*T^49 + 954968209*T^48 + 1257844471*T^47 +
      292057313*T^46 - 456786092*T^45 - 308276219*T^44 + 57583193*T^43
      + 129571108*T^42 + 59351916*T^41 + 14284212*T^40 + 785616*T^39 +
      44640*T^38)*x^4 + (2*T^60 + 20*T^59 - 35807*T^58 - 357542*T^57 -
      2358850*T^56 - 12660014*T^55 - 48914949*T^54 - 128357284*T^53 -
      226778441*T^52 - 263274598*T^51 - 181912345*T^50 - 51636980*T^49
      - 6140103*T^48 - 67275946*T^47 - 126013802*T^46 - 110281670*T^45
      - 56716375*T^44 - 18092240*T^43 - 3164808*T^42 - 105912*T^41 -
      12960*T^40)*x^3 + (-T^60 - 525*T^59 + 6870*T^58 + 82736*T^57 +
      341823*T^56 + 846249*T^55 + 1869833*T^54 + 4707135*T^53 +
      11131911*T^52 + 20346545*T^51 + 27386817*T^50 + 27204987*T^49 +
      20209868*T^48 + 11443458*T^47 + 5011287*T^46 + 1650419*T^45 +
      360180*T^44 + 37584*T^43)*x^2;
  end if;
  return A,B,D1,D17;
end function;

// The polynomials in Section 3 defining the genus 2 curve C
// and the morphisms C -> E1 and C -> E2 of degree 17. 

function Genus2Polynomials(R)
  x := R.1;
  f1 := 196081931*x^3 + 1143338037*x^2 - 801791940*x + 135616700;
  f2 := -25996*x^3 + 1698260*x^2 - 6845267*x + 3822078;
  g1 := 236763018258074528726022224160448100*x^7 -
    3794325575568062742976281587502971846*x^6 -
    1080208147430600140075373460493938652584*x^5 -
    19017800672966218380727078734003916071656*x^4 -
    73200250374301711398797185974409420166528*x^3 +
    83264039009703906130870248178745098841696*x^2 -
    28349180827278931095415942183384251232384*x +
    3147455900074724953476040820631141774976;
  g2 := 5876397603392*x^7 - 40086060833344*x^6 - 61207842693648*x^5 +
    393394368265600*x^4 - 589745130068900*x^3 + 350852746253100*x^2 -
    85742272798975*x + 6838002651350;
  h1 := -45917679365932685522619607936109208458858231011676371239295\
    42004269000483181765505704*x^17 +
    2816136835648844585896058859612521058062022987755739571655928111\
    8573713617743582448668*x^16 - 2111041671501494580038811582144422\
    3720112893766090874685967996689570917894639241291964094*x^15 -
    1490541758843661485865592197877049435360025583722866026035176368\
    47225325319834715413071339*x^14 +
    5178661297580833277301500400452485139743563925625331336686067424\
    1278149041673806333743294204*x^13 +
    1997342961406499664961498000424825990309475711591485319637560693\
    895188000786514882254131339484*x^12 +
    3077658047960968730213727846564768937841985227539720211858154959\
    2575161930269215215601339583168*x^11 +
    2220751051494883547975382860984812107502895948550231739919071054\
    98189537856118191627400087065552*x^10 +
    6238827887023913301652190390069178656789966025015986937315452215\
    63648132296422461316181140382528*x^9 -
    3364451175690329069182278591379574844384404498007105467501013764\
    46845119814430092770811462281792*x^8 -
    2491267877852677661079428077550776751186244740949640475353746018\
    667648438104520603999947631418880*x^7 +
    4300115060566047730803565892229334863625051596053438499686039855\
    867551026069146001093788572948224*x^6 -
    3309698912225155687006027479594815727637540976143756450781951333\
    352897895149464104429592768814080*x^5 +
    1477249125829583519211856904398974352010999690419727818957907285\
    247476887757178555418940206380032*x^4 -
    4083529919379739965878722249473805060106043207100950874838059290\
    58364279437629085612100060119040*x^3 +
    6935318604465080109807383369334051140198048115190920416266908344\
    9929018156280842320513302884352*x^2 -
    6664947453768979956478013860968797463548833669368135610095900156\
    970019238746089698478805565440*x +
    2785624856186028870015508647919792756030252553984925903318670068\
    32583485639996916859894579200;
  h2 := 603895888203833054860999967569066131456*x^17 -
    15552966090024642865703834388520902918144*x^16 +
    234330612838017541393764435436079189639168*x^15 -
    535883868745315981402437353754070174269440*x^14 -
    11501888972781813809879007934129947085107200*x^13 +
    112002909124873196739033995066429742283116544*x^12 -
    531366824128254809851741172445447958417028096*x^11 +
    1680378127800969298275232300446441379790374912*x^10 -
    3787839702984766035120353072313296659093331200*x^9 +
    6105940086717207320065501323064086324724128000*x^8 -
    7039719217281115111293331010477951712861451200*x^7 +
    5832788645834985064298018223915074165542534400*x^6 -
    3479641594410433230478046854938656455410549200*x^5 +
    1482259510469171940005980207778358421786270000*x^4 -
    439669993499461149480502084396124415258657500*x^3 +
    86150795139208944593959400580741607995205000*x^2 -
    10002826162013847461887340929380361268930000*x +
    520034275872064560764502402936169538780000;
  return f1,f2,g1,g2,h1,h2;
end function;

// Additional equations for the curve C1 in Proposition 4.1

function ExtraQuarticsForACurve(R)
  x0,x1,x2,x3,x4,x5,x6,x7,x8 := Explode([R.i : i in [1..9]]);  
  qq := [
    x0^4 + x1*x3*x5*x7, x0^3*x1 + x0*x1*x4*x8 + x0*x6^2*x8 +
    x1*x3*x8^2, x0^2*x1^2 + x0^2*x4*x7 + x0*x3*x4*x6 - x1*x4*x5*x7,
    x0^2*x1^2 + x0^2*x4*x7 + x0*x1*x5*x8 - x2*x3*x4*x5, x0*x1*x3*x4 -
    x0*x6*x8^2 + x1*x3^2*x8 - x4*x6*x7*x8, x0*x1*x3*x5 + x0*x3*x4*x8 +
    x1^2*x3*x4 - x1*x4^2*x5 - x4^3*x8, x0*x1^2*x2 + x0*x3*x5^2 +
    x1*x2*x5*x8 - x1*x4*x6*x7 - x4^2*x5^2, x0*x1*x3*x5 + x0*x2*x3*x6 -
    x2*x3*x7^2 + x2*x4^2*x6 - x2*x4*x7*x8, x0*x1*x2*x3 + x0*x2*x4*x5 +
    x2*x3*x5*x8 - x2*x4*x6^2 - x3*x4*x6*x7, x0^2*x2*x6 - x0^2*x4*x8 +
    x1^2*x5^2 - x1*x2^2*x4 + x1*x2*x5*x6 - x5*x6^2*x8, x0^2*x6*x8 -
    x0*x1^2*x6 - x1*x5*x6*x8 - x2^2*x3^2 - x2*x4*x5*x7 - x2*x6^2*x8,
    x0^2*x1*x2 + x0*x2*x5*x8 + x0*x7^2*x8 + x1*x2*x4*x8 + x2*x6^2*x8 +
    x3*x6*x7*x8, x0^2*x1*x3 + x0*x1*x2*x7 + x0*x3*x5*x8 + x2*x4*x5*x6
    + x2*x5*x7*x8 + x3*x4*x5*x7, x0^2*x1*x2 + x0*x2*x5*x8 - x2^2*x3^2
    - x2*x4*x5*x7 - x2*x6^2*x8 - x3^2*x5*x8 - x3*x5^3, x0^3*x1 -
    x0*x1*x2*x6 - x0*x2*x3^2 + x1*x2^2*x5 + x1*x5^2*x8 + x2^3*x6 +
    x2*x5*x6*x8 - x4*x6^2*x7, x0^2*x1*x2 - x0^2*x6*x8 + x0*x1^2*x6 +
    x0*x1*x3^2 - x0*x3*x4*x5 - x0*x4*x6*x7 - x1*x2*x4*x8 + x4^3*x5 ];
  return qq;
end function;

// Equations for the surfaces Sigma_1 (in P^10) and Sigma_3 (in P^9)
// defined in Sections 5 and 6

function SigmakEquations(k,R)
  if k eq 1 then 
  z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11 := Explode([R.i : i in [1..11]]);
  quads := [ 2*z1^2 - 16*z1*z2 - 5*z1*z3 - z1*z4 - 2*z1*z7 - z1*z11 -
    10*z2^2 + 14*z2*z3 + 5*z2*z4 - 4*z2*z5 - z2*z6 + 6*z2*z8 -
    4*z2*z10 + 2*z2*z11 + 6*z3^2 + 2*z3*z7 - z3*z8 + 2*z3*z11 + 6*z4^2
    + 2*z4*z6 + 2*z4*z7 - z4*z8 + 3*z4*z11 + z6*z11 + 2*z7*z11 -
    z8*z11, 5*z1^2 - 2*z1*z2 - 8*z1*z3 + 5*z1*z4 + z1*z5 + 2*z1*z8 -
    z1*z9 - 7*z2^2 - 7*z2*z3 + 2*z2*z4 + z2*z5 + 6*z2*z7 + 10*z2*z8 -
    z2*z10 - 2*z2*z11 + 14*z3^2 - 14*z3*z4 - 2*z3*z6 - 6*z3*z7 +
    3*z3*z8 + 3*z3*z9 + 5*z3*z11 + z4*z5 - 2*z4*z8 - 3*z4*z9 - z5*z8 -
    z6*z9 - 4*z7*z8 - 3*z8^2 + z8*z9 + z8*z10 - z8*z11, 27*z1^2 +
    6*z1*z2 - 17*z1*z3 - 4*z1*z4 + 2*z1*z5 + 2*z1*z6 - 13*z1*z7 -
    22*z1*z8 + 7*z1*z10 - 6*z1*z11 - 3*z2^2 + 9*z2*z3 - 7*z2*z5 -
    3*z2*z6 - 8*z2*z7 - 8*z2*z8 - 4*z2*z9 - 5*z2*z10 - 3*z3*z4 + z3*z6
    + 4*z3*z7 + 7*z3*z8 - 3*z3*z9 + z4*z5 + z4*z7 + 5*z4*z8 + 4*z7*z8
    + z7*z11 + 4*z8^2 - 2*z8*z10 + 4*z8*z11, 5*z1^2 + 8*z1*z2 -
    22*z1*z3 + 6*z1*z4 + 2*z1*z5 - z1*z6 + 4*z1*z7 + z1*z8 - 5*z1*z11
    + 3*z2^2 - 9*z2*z3 - z2*z4 + 2*z2*z5 + z2*z6 + 2*z2*z7 - z2*z8 +
    z2*z9 + 2*z2*z10 - 4*z2*z11 + 39*z3^2 - 6*z3*z5 + 3*z3*z6 -
    16*z3*z7 - 5*z3*z8 + 2*z3*z9 + 17*z3*z11 - 9*z4^2 - 3*z4*z6 -
    7*z4*z7 - 3*z5*z11 - 7*z7*z11 - z8*z11, 2*z1^2 - 3*z1*z2 -
    15*z1*z3 - 5*z1*z4 + z1*z5 - 3*z1*z6 - 4*z1*z11 - z2^2 + 7*z2*z3 -
    2*z2*z4 - z2*z5 - z2*z6 - 4*z2*z7 - 2*z2*z8 + z2*z11 + 25*z3^2 +
    13*z3*z4 - 4*z3*z5 + 6*z3*z6 - 4*z3*z7 - 7*z3*z8 + 11*z3*z11 -
    2*z4*z7 + z4*z8 + 6*z4*z11 - 2*z5*z11 + 2*z6*z11 + 2*z7*z8 -
    2*z7*z11 + 2*z8^2 - z8*z10 - 2*z8*z11, 10*z1^2 - 3*z1*z3 +
    16*z1*z4 - 7*z1*z7 - 3*z1*z8 + 2*z1*z10 - 2*z1*z11 - 8*z2^2 +
    8*z2*z3 - z2*z5 + 2*z2*z7 + 7*z2*z8 + 2*z2*z9 - z2*z10 - 4*z2*z11
    + 41*z3^2 - 17*z3*z4 - 4*z3*z5 + 4*z3*z6 - 20*z3*z7 - 14*z3*z8 +
    4*z3*z9 + 17*z3*z11 - 12*z4^2 + 3*z4*z5 - 4*z4*z6 - 6*z4*z7 +
    2*z4*z8 - 2*z5*z11 - 6*z7*z11 - 2*z8*z11, 16*z1*z2 + 5*z1*z3 -
    11*z1*z4 - 3*z1*z6 - 5*z1*z7 - 7*z1*z8 + 3*z1*z11 + 10*z2^2 -
    5*z2*z3 - 8*z2*z4 + 3*z2*z5 - 7*z2*z7 - 12*z2*z8 + 4*z2*z10 +
    z2*z11 - 8*z3^2 + 20*z3*z4 + z3*z5 + 6*z3*z6 + 8*z3*z7 - 6*z3*z11
    - 3*z4*z5 - 2*z4*z7 + z4*z8 - z5*z6 - z5*z7 - z5*z8 + z5*z11 -
    z6*z7 - z6*z8 + 4*z7*z8 + z7*z11 + 4*z8^2 - 2*z8*z10, 3*z1^2 +
    4*z1*z2 + 4*z1*z4 - z1*z5 + 3*z1*z6 - 2*z1*z7 - 2*z1*z8 - 4*z1*z9
    + z1*z11 - z2^2 - 2*z2*z3 + 2*z2*z4 + z2*z6 + z2*z8 - z2*z9 -
    5*z3^2 + 2*z3*z5 + 6*z3*z7 + z3*z8 + 6*z3*z9 + z3*z10 - 8*z3*z11 +
    z4*z5 - z4*z7 - 5*z4*z8 + 3*z4*z10 + z5*z7 - z5*z9 + 2*z5*z11 -
    2*z6*z7 - 2*z6*z8 + z6*z10 - z7*z8 + z7*z10 + 6*z7*z11 + z8*z11,
    12*z1^2 - 12*z1*z3 + 6*z1*z4 + z1*z5 + 3*z1*z6 - 5*z1*z7 -
    12*z1*z8 + z1*z10 - 2*z1*z11 - 4*z2^2 + 9*z2*z3 + 6*z2*z4 -
    3*z2*z5 + z2*z6 - 3*z2*z7 - 4*z2*z8 - 2*z2*z10 + 12*z3^2 - 2*z3*z4
    + z3*z8 + z3*z9 + z3*z10 + 3*z3*z11 - 3*z4*z7 - 3*z4*z8 + 3*z4*z10
    - z5*z8 - z6*z7 - 2*z6*z8 + z6*z10 + 3*z7*z8 + z7*z10 + z7*z11 +
    4*z8^2 - 2*z8*z10, 5*z1^2 - 6*z1*z2 - 3*z1*z3 + 10*z1*z4 - 6*z1*z7
    - 2*z1*z8 - z1*z10 + 2*z1*z11 - 11*z2^2 + 7*z2*z3 + 4*z2*z4 +
    z2*z6 + 4*z2*z7 + 10*z2*z8 + 4*z2*z9 - z2*z10 - 2*z2*z11 + 32*z3^2
    - 15*z3*z4 - 2*z3*z5 - z3*z6 - 14*z3*z7 - 7*z3*z8 + 5*z3*z9 +
    12*z3*z11 + z4*z5 + z4*z7 - z4*z8 - z5*z8 - z5*z11 + z6*z7 +
    2*z7^2 + z7*z8 - 3*z7*z11 - 4*z8*z11, z1^2 - 4*z1*z2 - 18*z1*z3 -
    2*z1*z4 + z1*z5 + 3*z1*z6 + 3*z1*z7 + 5*z1*z8 - 8*z1*z11 - z2^2 +
    2*z2*z4 - z2*z5 + 2*z2*z6 - z2*z7 + z2*z8 - 3*z2*z11 + 10*z3^2 +
    11*z3*z4 - 2*z3*z5 + 2*z3*z7 - 2*z3*z8 - z3*z10 + 4*z3*z11 -
    2*z4*z5 - z4*z6 - 4*z4*z7 - 4*z4*z8 + z4*z10 + 2*z4*z11 + z5*z8 -
    z5*z11 - 3*z6*z7 - 2*z6*z8 + z6*z10 + z7*z8 - z7*z10 + 4*z7*z11 +
    2*z8*z11 - z10*z11, 7*z1^2 - 14*z1*z3 - 3*z1*z4 + 2*z1*z5 +
    2*z1*z7 + z1*z8 + z1*z9 + z1*z10 - 3*z1*z11 - z2^2 - z2*z3 + z2*z4
    - z2*z5 - z2*z6 + z2*z7 + 3*z2*z8 + z2*z9 - 2*z2*z10 + 14*z3^2 +
    3*z3*z4 + 4*z3*z6 - 2*z3*z7 + 2*z3*z8 + 5*z3*z9 + 6*z3*z10 -
    z3*z11 - z4*z8 + z4*z11 - z6*z7 + z6*z9 + z6*z11 - 3*z7*z8 -
    2*z7*z9 - z7*z10 + 2*z7*z11 - 3*z8^2 - 3*z8*z9 + z8*z10 + 2*z8*z11
    + 2*z9*z10 + z10*z11 - z11^2, z1^2 + z1*z2 + 5*z1*z4 - 2*z1*z5 +
    2*z1*z6 + z1*z7 + 2*z1*z8 + z1*z9 - z1*z10 - z1*z11 + 2*z2^2 +
    4*z2*z3 + 6*z2*z4 - 3*z2*z5 + z2*z7 - z2*z8 + 2*z2*z9 - 2*z2*z10 +
    z2*z11 - z3^2 + 8*z3*z4 - 2*z3*z5 - 7*z3*z8 - z3*z9 + 2*z3*z10 +
    2*z3*z11 - 2*z4^2 - 5*z4*z7 - 6*z4*z8 + 2*z4*z9 + 2*z4*z10 + z5*z7
    + 3*z5*z8 - z5*z9 + z6*z9 - 2*z7^2 - z7*z8 - 2*z7*z9 + 2*z7*z10 -
    2*z7*z11 - z8^2 - 3*z8*z9 + 2*z8*z10 + z10*z11 + z11^2 ];
  cubics := [ 2*z1^3 - 3*z1^2*z2 - 3*z1^2*z3 + 10*z1^2*z5 + z1^2*z6 +
    4*z1^2*z7 + z1^2*z9 + 2*z1^2*z11 - 6*z1*z2*z3 + 3*z1*z2*z4 +
    2*z1*z2*z5 - 3*z1*z2*z6 - z1*z2*z9 - 6*z1*z2*z10 + 2*z1*z2*z11 -
    2*z1*z3^2 + z1*z3*z4 - z1*z3*z5 + 6*z1*z3*z6 + 3*z1*z3*z7 +
    7*z1*z3*z8 - 2*z1*z3*z9 + 2*z1*z3*z10 - 10*z1*z3*z11 - 3*z1*z4^2 -
    z1*z4*z5 - 2*z1*z4*z6 + 2*z1*z4*z7 + 12*z1*z4*z8 + 3*z1*z4*z10 -
    z1*z5*z7 + z1*z5*z8 + 6*z1*z5*z9 + z1*z5*z10 + 3*z1*z5*z11 +
    z1*z6^2 - 2*z1*z6*z7 + 3*z1*z6*z8 + 3*z1*z6*z11 + z1*z7*z8 +
    z1*z7*z10 + z1*z7*z11 - 5*z1*z8*z9 + 2*z1*z8*z11 + z1*z9^2 +
    2*z1*z9*z10 - z1*z9*z11 - 7*z1*z11^2 + z2^3 - z2^2*z3 + 2*z2^2*z4
    - 6*z2^2*z5 - 4*z2^2*z6 + 3*z2^2*z7 - z2^2*z8 + z2^2*z10 -
    5*z2*z3^2 - 4*z2*z3*z4 + z2*z3*z5 - 17*z2*z3*z6 - 2*z2*z3*z7 +
    8*z2*z3*z8 + z2*z3*z10 - 9*z2*z3*z11 - 3*z2*z4^2 - 5*z2*z4*z5 +
    z2*z4*z6 + 3*z2*z4*z8 - z2*z4*z9 - z2*z4*z11 + 6*z2*z5*z7 +
    9*z2*z5*z8 + 8*z2*z5*z9 + z2*z5*z10 - z2*z5*z11 + 6*z2*z6*z8 +
    z2*z6*z9 + 2*z2*z7^2 + z2*z7*z9 - 6*z2*z7*z10 + 5*z2*z7*z11 -
    5*z2*z8*z9 - z2*z8*z10 + 2*z2*z8*z11 + 2*z2*z9^2 + z2*z9*z10 -
    2*z2*z9*z11 - 2*z2*z10^2 - 3*z2*z10*z11 - 2*z2*z11^2 - 3*z3^2*z5 -
    z3^2*z6 - z3^2*z7 + 5*z3^2*z8 - 5*z3^2*z9 + 6*z3^2*z10 +
    10*z3^2*z11 - z3*z4*z5 - 3*z3*z4*z6 - 8*z3*z4*z7 - 18*z3*z4*z8 +
    4*z3*z4*z9 + 6*z3*z4*z10 - 3*z3*z4*z11 + 7*z3*z5*z6 + 7*z3*z5*z7 -
    2*z3*z5*z8 - z3*z5*z9 - z3*z5*z10 + 2*z3*z5*z11 + 7*z3*z6*z7 -
    3*z3*z6*z9 + 15*z3*z6*z10 + 28*z3*z7*z8 + 6*z3*z7*z11 + 5*z3*z8^2
    + 8*z3*z8*z9 - 14*z3*z9*z10 - 8*z3*z10^2 + 10*z3*z10*z11 +
    5*z3*z11^2 - z4^3 + z4^2*z5 + z4^2*z6 - 13*z4^2*z7 - 3*z4^2*z8 +
    2*z4^2*z9 + 8*z4^2*z10 + 29*z4^2*z11 + z4*z5^2 + z4*z5*z6 -
    3*z4*z5*z7 + 3*z4*z5*z8 - 11*z4*z5*z9 + 5*z4*z5*z10 - 7*z4*z6*z7 +
    z4*z6*z8 + z4*z6*z10 + 3*z4*z6*z11 + 3*z4*z7*z8 + 5*z4*z7*z9 +
    5*z4*z7*z10 + 10*z4*z7*z11 - 8*z4*z8^2 - 6*z4*z8*z9 + 2*z4*z8*z10
    - z4*z8*z11 + 8*z4*z9^2 + 2*z4*z10^2 - 2*z4*z10*z11 + 10*z4*z11^2
    + z5^2*z8 + z5*z6^2 - 5*z5*z6*z7 - z5*z6*z8 - 2*z5*z6*z9 +
    z5*z6*z10 - 4*z5*z7^2 + z5*z7*z8 - 4*z5*z7*z9 - z5*z7*z10 +
    2*z5*z7*z11 + z5*z8^2 - 2*z5*z8*z9 - 3*z5*z8*z10 - 5*z5*z8*z11 -
    z5*z9^2 + 2*z5*z9*z10 + 7*z5*z9*z11 - 3*z5*z10*z11 - 3*z5*z11^2 -
    5*z6^2*z7 - z6^2*z8 + z6^2*z10 + z6*z7^2 - z6*z7*z8 + 4*z6*z7*z9 -
    9*z6*z7*z10 + 8*z6*z7*z11 - 4*z6*z8^2 - 2*z6*z8*z9 - 4*z6*z8*z10 +
    z6*z9^2 + z6*z9*z10 - z6*z9*z11 + 2*z6*z10^2 - z6*z10*z11 +
    z6*z11^2 + 2*z7^3 + 3*z7^2*z8 + 6*z7^2*z9 + 2*z7^2*z10 -
    6*z7^2*z11 + z7*z8^2 + 18*z7*z8*z9 + 6*z7*z8*z10 + 4*z7*z8*z11 +
    2*z7*z9^2 + 6*z7*z9*z10 + 6*z7*z9*z11 - z7*z10^2 - 6*z7*z11^2 +
    3*z8^3 + 12*z8^2*z9 - 2*z8^2*z11 + z8*z9^2 + 2*z8*z9*z10 -
    z8*z9*z11 - z8*z10^2 - 4*z8*z10*z11 - 4*z9^2*z10 - 2*z9*z10^2 +
    2*z9*z10*z11 + 3*z9*z11^2 - 3*z10^2*z11 - 5*z11^3, 4*z1^2*z2 +
    8*z1^2*z4 - z1^2*z5 - 3*z1^2*z9 - z1^2*z11 - 7*z1*z2^2 -
    7*z1*z2*z3 - 2*z1*z2*z4 + 4*z1*z2*z5 - z1*z2*z6 + z1*z2*z9 +
    2*z1*z2*z11 + 8*z1*z3^2 + z1*z3*z4 + 13*z1*z3*z5 - 5*z1*z3*z6 -
    3*z1*z3*z7 - 6*z1*z3*z8 + 17*z1*z3*z10 + 19*z1*z3*z11 - 2*z1*z4^2
    + 4*z1*z4*z5 + z1*z4*z6 + z1*z4*z7 + 2*z1*z4*z8 - z1*z4*z10 +
    z1*z4*z11 + z1*z5*z6 - z1*z5*z7 + z1*z5*z8 - 6*z1*z5*z9 -
    z1*z5*z10 - 2*z1*z5*z11 + 3*z1*z6^2 + 2*z1*z6*z7 - 8*z1*z6*z8 +
    2*z1*z6*z9 + z1*z6*z10 + 4*z1*z6*z11 - 3*z1*z7*z8 - 16*z1*z7*z10 +
    z1*z7*z11 - 6*z1*z8*z9 + 11*z1*z8*z11 - 4*z1*z9^2 + 6*z1*z9*z10 +
    4*z1*z9*z11 + 3*z1*z11^2 - 9*z2^3 + 3*z2^2*z3 + 6*z2^2*z4 +
    4*z2^2*z5 + z2^2*z6 - z2^2*z7 + 2*z2^2*z8 + 5*z2^2*z9 - 3*z2^2*z10
    + 3*z2^2*z11 - 4*z2*z3^2 + z2*z3*z4 - z2*z3*z5 + 17*z2*z3*z6 -
    2*z2*z3*z7 - 5*z2*z3*z8 - 2*z2*z3*z10 + 2*z2*z3*z11 + z2*z4^2 +
    2*z2*z4*z5 - 3*z2*z4*z6 - 13*z2*z4*z8 - 2*z2*z4*z9 + 3*z2*z4*z11 -
    2*z2*z5*z7 - 3*z2*z5*z8 - 14*z2*z5*z9 + z2*z5*z10 - 3*z2*z6*z8 +
    4*z2*z6*z9 + z2*z7^2 - 3*z2*z7*z9 + 5*z2*z7*z10 - 2*z2*z7*z11 +
    5*z2*z8^2 - z2*z8*z9 + 3*z2*z8*z10 + 2*z2*z8*z11 + 5*z2*z9^2 +
    6*z2*z9*z11 - z2*z10^2 - 6*z2*z10*z11 + z2*z11^2 - 9*z3^2*z5 +
    2*z3^2*z6 + z3^2*z7 + 12*z3^2*z8 - 10*z3^2*z9 + 16*z3^2*z10 +
    12*z3^2*z11 - 2*z3*z4*z5 + 5*z3*z4*z6 - 2*z3*z4*z7 + 14*z3*z4*z8 +
    4*z3*z4*z9 + 2*z3*z5*z6 + z3*z5*z7 - 4*z3*z5*z8 - 9*z3*z5*z9 +
    2*z3*z5*z10 + 14*z3*z6*z9 + 5*z3*z6*z10 - 14*z3*z7*z8 -
    4*z3*z7*z11 - z3*z8^2 - 3*z3*z8*z9 - 20*z3*z8*z10 + 17*z3*z9*z10 +
    3*z3*z9*z11 + 10*z3*z10^2 + 6*z3*z10*z11 - 8*z3*z11^2 - 4*z4^3 +
    22*z4^2*z5 - 6*z4^2*z6 + 4*z4^2*z7 + 4*z4^2*z8 + 8*z4^2*z9 -
    6*z4^2*z10 - 14*z4^2*z11 + z4*z5^2 + 15*z4*z5*z6 + 2*z4*z5*z7 -
    17*z4*z5*z8 + 6*z4*z5*z11 + 17*z4*z6*z7 + 3*z4*z6*z9 + 5*z4*z6*z10
    - 3*z4*z6*z11 - 7*z4*z7^2 - 16*z4*z7*z8 + 17*z4*z7*z9 +
    4*z4*z7*z10 - 20*z4*z7*z11 - 4*z4*z8^2 + 5*z4*z8*z9 + z4*z8*z10 -
    16*z4*z8*z11 + 8*z4*z9^2 + z4*z9*z10 - z4*z9*z11 - 2*z4*z10^2 -
    4*z4*z10*z11 - 11*z4*z11^2 + z5^2*z8 + 2*z5*z6^2 + 7*z5*z6*z7 -
    8*z5*z6*z8 - 3*z5*z6*z9 + 2*z5*z6*z10 + 5*z5*z6*z11 - 2*z5*z7^2 -
    2*z5*z7*z8 + 6*z5*z7*z9 + 2*z5*z7*z10 - z5*z7*z11 - 2*z5*z8^2 +
    10*z5*z8*z9 + 8*z5*z8*z11 - 3*z5*z9^2 - z5*z9*z11 + 4*z6^2*z7 +
    2*z6^2*z9 + z6^2*z10 + z6^2*z11 + 4*z6*z7^2 + 2*z6*z7*z8 -
    3*z6*z7*z9 + 6*z6*z7*z10 - 5*z6*z8*z9 - z6*z8*z10 - 9*z6*z8*z11 +
    4*z6*z9^2 + 4*z6*z9*z10 + 2*z6*z9*z11 + 3*z6*z10*z11 - 2*z7^3 +
    2*z7^2*z8 + 2*z7^2*z9 + z7^2*z10 + 3*z7^2*z11 + 3*z7*z8^2 +
    3*z7*z8*z9 + z7*z8*z10 - 9*z7*z8*z11 - 4*z7*z9^2 - 4*z7*z9*z10 -
    z7*z9*z11 - 4*z7*z10^2 + 2*z7*z10*z11 + z7*z11^2 - 2*z8^2*z10 -
    7*z8^2*z11 - 8*z8*z9^2 - 6*z8*z9*z10 - z8*z9*z11 + z8*z10^2 +
    5*z8*z10*z11 + 6*z8*z11^2 + 2*z9^2*z10 + 4*z9*z10^2 + 6*z9*z10*z11
    + z10^2*z11 - 3*z11^3, 2*z1^3 + 3*z1^2*z2 + 13*z1^2*z3 -
    16*z1^2*z4 - z1^2*z6 - z1^2*z7 + 4*z1^2*z11 - z1*z2^2 -
    12*z1*z2*z3 + 4*z1*z2*z4 - 4*z1*z2*z5 + 4*z1*z2*z6 - 2*z1*z2*z9 +
    z1*z2*z10 - 2*z1*z2*z11 - z1*z3^2 + 2*z1*z3*z4 + z1*z3*z5 +
    2*z1*z3*z6 + 14*z1*z3*z7 + 14*z1*z3*z8 + 2*z1*z3*z9 + 7*z1*z3*z10
    - 21*z1*z3*z11 - 5*z1*z4^2 + 6*z1*z4*z5 + 2*z1*z4*z7 + 12*z1*z4*z8
    - 6*z1*z4*z10 - z1*z4*z11 - 2*z1*z5*z6 + z1*z5*z9 + 10*z1*z6^2 -
    2*z1*z6*z7 + 12*z1*z6*z8 - 2*z1*z6*z9 - 3*z1*z6*z10 - 4*z1*z6*z11
    - 5*z1*z7^2 - 2*z1*z7*z8 + 14*z1*z7*z10 + 4*z1*z7*z11 + 5*z1*z8*z9
    + 12*z1*z8*z11 - 4*z1*z9^2 + 9*z1*z9*z10 - 6*z1*z9*z11 +
    7*z1*z11^2 - 2*z2^3 + 12*z2^2*z4 - 6*z2^2*z5 + 8*z2^2*z6 +
    4*z2^2*z7 + 3*z2^2*z8 + 6*z2^2*z9 + z2^2*z10 - 2*z2^2*z11 +
    6*z2*z3^2 - z2*z3*z4 - 5*z2*z3*z5 - z2*z3*z6 + z2*z3*z7 +
    15*z2*z3*z8 - z2*z3*z10 - 17*z2*z3*z11 - 7*z2*z4^2 + 10*z2*z4*z5 -
    15*z2*z4*z8 + z2*z4*z9 + z2*z5^2 + 6*z2*z5*z7 + 5*z2*z5*z8 +
    6*z2*z5*z9 - 3*z2*z5*z10 - 2*z2*z5*z11 - 4*z2*z6*z8 + 6*z2*z6*z9 -
    z2*z7^2 - z2*z7*z9 + z2*z7*z10 - 2*z2*z7*z11 - 2*z2*z8^2 -
    3*z2*z8*z9 - z2*z8*z10 + 3*z2*z8*z11 - 4*z2*z9^2 + z2*z9*z10 -
    5*z2*z9*z11 - 3*z2*z10^2 + 5*z2*z10*z11 - z2*z11^2 + 6*z3^2*z5 -
    2*z3^2*z6 + 5*z3^2*z7 - 5*z3^2*z8 - 2*z3^2*z9 - 11*z3^2*z10 +
    26*z3^2*z11 + 2*z3*z4*z5 + 11*z3*z4*z6 - 4*z3*z4*z7 - 6*z3*z4*z8 +
    6*z3*z4*z9 - 3*z3*z4*z10 - 7*z3*z4*z11 + 8*z3*z5*z6 + 3*z3*z5*z7 -
    z3*z5*z8 + 2*z3*z5*z11 + 5*z3*z6*z7 + 10*z3*z6*z9 + 19*z3*z6*z10 -
    3*z3*z6*z11 - 4*z3*z7*z8 - 2*z3*z8^2 + z3*z8*z9 + z3*z8*z10 -
    4*z3*z9^2 - 5*z3*z9*z10 + z3*z9*z11 - z3*z10*z11 - z3*z11^2 +
    3*z4^3 + 7*z4^2*z5 - 16*z4^2*z6 + z4^2*z7 - 4*z4^2*z8 - 2*z4^2*z9
    + 8*z4^2*z10 + 8*z4^2*z11 + z4*z5^2 + 18*z4*z5*z6 + 11*z4*z5*z7 -
    3*z4*z5*z8 + 6*z4*z5*z9 - 6*z4*z5*z10 - 3*z4*z5*z11 - 7*z4*z6^2 +
    18*z4*z6*z7 - 4*z4*z6*z8 + 5*z4*z6*z9 + 11*z4*z6*z10 - 2*z4*z6*z11
    + 6*z4*z7^2 - 6*z4*z7*z8 + 3*z4*z7*z9 + 6*z4*z7*z10 - 16*z4*z7*z11
    - z4*z8^2 - 5*z4*z8*z9 - 3*z4*z8*z10 - 18*z4*z8*z11 + 2*z4*z9^2 -
    9*z4*z9*z10 + 3*z4*z9*z11 - 11*z4*z11^2 + 8*z5*z6^2 + 7*z5*z6*z7 +
    z5*z6*z8 + z5*z6*z9 - 3*z5*z6*z11 + 4*z5*z7^2 + 6*z5*z7*z8 +
    4*z5*z7*z9 - 5*z5*z7*z10 - z5*z7*z11 + 2*z5*z8^2 - 4*z5*z8*z9 +
    2*z5*z8*z10 - 2*z5*z9^2 + 2*z5*z9*z10 + 6*z5*z9*z11 - 2*z5*z10*z11
    - 5*z5*z11^2 - z6^2*z7 + 5*z6^2*z9 + 4*z6^2*z10 + z6^2*z11 +
    5*z6*z7^2 - 17*z6*z7*z8 - 2*z6*z7*z9 - 3*z6*z7*z10 + 12*z6*z7*z11
    - 8*z6*z8^2 - 10*z6*z8*z9 + z6*z8*z11 + 4*z6*z9*z10 + 4*z6*z10*z11
    - 5*z6*z11^2 - 7*z7^2*z8 - 2*z7^2*z9 - 3*z7^2*z10 - 2*z7^2*z11 -
    6*z7*z8^2 - 4*z7*z8*z9 + z7*z8*z10 + 6*z7*z9*z11 - 4*z7*z10*z11 -
    14*z7*z11^2 + z8^3 - z8^2*z9 - 2*z8^2*z10 + 5*z8^2*z11 +
    2*z8*z9*z10 + 12*z8*z9*z11 + z8*z10^2 - 5*z8*z10*z11 - z8*z11^2 -
    2*z9^2*z10 + 4*z9*z10*z11 + 2*z9*z11^2 - z10*z11^2 - 9*z11^3,
    4*z1^3 + 5*z1^2*z2 + 5*z1^2*z3 + 8*z1^2*z4 + 2*z1^2*z5 + 5*z1^2*z6
    + z1^2*z7 + z1^2*z9 + 5*z1^2*z11 - 4*z1*z2^2 + 8*z1*z2*z3 -
    3*z1*z2*z5 + 5*z1*z2*z6 - z1*z2*z9 - 5*z1*z2*z10 + 3*z1*z2*z11 -
    z1*z3^2 + 4*z1*z3*z4 - 5*z1*z3*z5 - 9*z1*z3*z6 + 7*z1*z3*z7 -
    6*z1*z3*z8 - 5*z1*z3*z9 + 3*z1*z3*z10 - 20*z1*z3*z11 + 3*z1*z4*z6
    + 6*z1*z4*z7 - 11*z1*z4*z8 + 3*z1*z4*z11 - z1*z5*z6 - 4*z1*z5*z8 +
    3*z1*z5*z9 + 4*z1*z5*z10 + 2*z1*z5*z11 - z1*z6*z8 - z1*z6*z9 -
    3*z1*z6*z10 - 2*z1*z6*z11 - 6*z1*z7^2 + 4*z1*z7*z8 + 12*z1*z7*z10
    + 2*z1*z7*z11 + 15*z1*z8*z11 - 3*z1*z9^2 + 13*z1*z9*z10 -
    z1*z9*z11 + 7*z1*z11^2 + z2^3 + 6*z2^2*z3 - 3*z2^2*z4 - 3*z2^2*z6
    - 2*z2^2*z7 - 4*z2^2*z8 - 7*z2^2*z9 + z2^2*z10 - z2^2*z11 +
    11*z2*z3^2 - 4*z2*z3*z4 - 4*z2*z3*z5 - 8*z2*z3*z6 - 3*z2*z3*z7 -
    4*z2*z3*z10 - 3*z2*z3*z11 + 5*z2*z4^2 + 5*z2*z4*z6 - 7*z2*z4*z8 +
    2*z2*z4*z9 - 5*z2*z4*z11 - 4*z2*z5^2 - 11*z2*z5*z7 - 8*z2*z5*z8 -
    2*z2*z5*z9 - 4*z2*z5*z10 + 2*z2*z5*z11 + 13*z2*z6*z8 - z2*z6*z9 -
    9*z2*z7^2 + z2*z7*z9 - z2*z7*z10 - 6*z2*z7*z11 - 2*z2*z8^2 +
    9*z2*z8*z9 - z2*z8*z10 + 4*z2*z8*z11 + 4*z2*z9^2 - 3*z2*z9*z10 -
    z2*z10^2 + z2*z10*z11 + 3*z2*z11^2 - z3^2*z4 + z3^2*z5 - 5*z3^2*z6
    + 3*z3^2*z7 - 2*z3^2*z8 + 13*z3^2*z9 + 8*z3^2*z10 - 7*z3^2*z11 +
    6*z3*z4*z5 - 5*z3*z4*z6 - 16*z3*z4*z8 - 7*z3*z4*z10 - 7*z3*z4*z11
    - 13*z3*z5*z6 - 7*z3*z5*z7 - 4*z3*z5*z8 - z3*z5*z9 + 3*z3*z5*z10 -
    3*z3*z5*z11 - 3*z3*z6*z9 - 6*z3*z6*z10 - z3*z6*z11 - 10*z3*z7*z8 +
    9*z3*z7*z11 - 2*z3*z8^2 + z3*z8*z9 + 3*z3*z8*z10 + 5*z3*z9^2 -
    11*z3*z9*z10 + 5*z3*z9*z11 + 19*z3*z10*z11 - 8*z3*z11^2 + 8*z4^3 -
    13*z4^2*z5 - 12*z4^2*z6 - 15*z4^2*z7 - 14*z4^2*z8 - 3*z4^2*z9 -
    9*z4^2*z10 - 8*z4^2*z11 - 4*z4*z5^2 - 3*z4*z5*z6 + 2*z4*z5*z7 +
    4*z4*z5*z8 + 3*z4*z5*z9 - 10*z4*z5*z10 + 7*z4*z5*z11 - 5*z4*z6^2 -
    10*z4*z6*z7 - 16*z4*z6*z8 - 16*z4*z6*z9 - z4*z6*z10 + 2*z4*z7^2 +
    z4*z7*z8 + 2*z4*z7*z9 - 7*z4*z7*z10 + 12*z4*z8^2 - 6*z4*z8*z9 +
    z4*z8*z10 - 3*z4*z8*z11 - 2*z4*z9^2 - 7*z4*z9*z10 - 4*z4*z10^2 -
    3*z4*z10*z11 + 5*z4*z11^2 + 2*z5^2*z6 + z5^2*z7 + z5^2*z8 +
    z5^2*z9 - 2*z5^2*z11 + 6*z5*z6*z7 + 6*z5*z6*z8 + z5*z6*z9 +
    z5*z6*z10 + 3*z5*z6*z11 + 7*z5*z7^2 + 12*z5*z7*z8 - 6*z5*z7*z10 +
    4*z5*z8^2 - 3*z5*z8*z9 - 4*z5*z8*z11 - 3*z5*z9^2 + 7*z5*z9*z10 +
    z5*z9*z11 - 6*z5*z10*z11 - 4*z6^2*z7 - 3*z6^2*z9 + z6^2*z11 -
    4*z6*z7^2 - 11*z6*z7*z8 - 3*z6*z7*z9 + 6*z6*z7*z10 + 10*z6*z7*z11
    - 6*z6*z8^2 - 3*z6*z8*z9 + 8*z6*z8*z10 + z6*z9^2 - 2*z6*z10^2 +
    2*z6*z10*z11 + 3*z6*z11^2 - 2*z7^3 - 7*z7^2*z8 - 8*z7^2*z9 -
    6*z7^2*z10 + z7^2*z11 - 2*z7*z8^2 - 14*z7*z8*z9 - 6*z7*z9^2 +
    5*z7*z9*z10 + 2*z7*z9*z11 - 16*z7*z10*z11 + 4*z7*z11^2 + 4*z8^3 -
    3*z8^2*z9 - 2*z8^2*z10 - 3*z8^2*z11 - 7*z8*z9^2 + 3*z8*z9*z10 +
    6*z8*z9*z11 - 7*z8*z11^2 + 2*z9^2*z10 + 3*z9*z10*z11 + z9*z11^2 +
    z10^2*z11 - 2*z11^3, 6*z1^3 - 2*z1^2*z2 - 8*z1^2*z3 + 5*z1^2*z4 -
    12*z1^2*z5 + 2*z1^2*z6 + 4*z1^2*z7 - 5*z1^2*z11 + 3*z1*z2^2 +
    7*z1*z2*z3 - z1*z2*z4 - z1*z2*z5 - 6*z1*z2*z6 + 3*z1*z2*z9 -
    z1*z2*z10 + 3*z1*z2*z11 + 4*z1*z3^2 - z1*z3*z4 + 6*z1*z3*z5 -
    4*z1*z3*z6 + 9*z1*z3*z7 - z1*z3*z8 - 4*z1*z3*z9 - 2*z1*z3*z10 -
    10*z1*z3*z11 - 10*z1*z4*z6 + 4*z1*z4*z10 + 3*z1*z5*z9 - z1*z5*z10
    + z1*z5*z11 - 3*z1*z6^2 + 3*z1*z6*z7 + 15*z1*z6*z8 + z1*z6*z9 +
    z1*z6*z10 - 8*z1*z6*z11 - z1*z7^2 + z1*z7*z8 + 8*z1*z8*z9 +
    2*z1*z9^2 - 6*z1*z9*z10 - 3*z1*z9*z11 - z1*z11^2 + z2^3 - z2^2*z3
    - z2^2*z4 + 6*z2^2*z5 + 10*z2^2*z6 + 6*z2^2*z7 + 7*z2^2*z8 +
    10*z2^2*z9 - 2*z2^2*z10 + 3*z2^2*z11 + z2*z3^2 - 3*z2*z3*z4 +
    6*z2*z3*z6 - z2*z3*z7 - 5*z2*z3*z8 + 2*z2*z3*z10 + 5*z2*z3*z11 -
    4*z2*z4^2 - 3*z2*z4*z5 + 11*z2*z4*z8 + 5*z2*z5^2 + 2*z2*z5*z7 -
    4*z2*z5*z8 + 16*z2*z5*z9 + 5*z2*z5*z10 + 3*z2*z5*z11 + 2*z2*z6*z8
    - z2*z6*z9 + 2*z2*z7^2 - 3*z2*z7*z9 - 10*z2*z7*z10 - 7*z2*z8^2 -
    6*z2*z8*z9 + 2*z2*z8*z10 + z2*z8*z11 + 3*z2*z9^2 + 2*z2*z10^2 +
    z2*z10*z11 - 2*z2*z11^2 - z3^2*z5 - 2*z3^2*z6 + z3^2*z7 - z3^2*z8
    + z3^2*z9 - 4*z3^2*z10 - 2*z3^2*z11 - 20*z3*z4*z6 + z3*z4*z10 -
    3*z3*z5*z6 + 11*z3*z5*z7 - 2*z3*z5*z8 + 5*z3*z5*z9 - 2*z3*z5*z10 +
    2*z3*z5*z11 + z3*z6*z7 + 5*z3*z6*z9 + 4*z3*z6*z10 - 2*z3*z7*z8 +
    2*z3*z7*z11 + z3*z8^2 - 7*z3*z8*z9 + z3*z8*z10 - 2*z3*z9^2 -
    3*z3*z9*z10 - z3*z9*z11 - 6*z3*z10^2 + 5*z3*z10*z11 - 3*z3*z11^2 -
    10*z4^3 + 11*z4^2*z5 - 6*z4^2*z6 - 6*z4^2*z7 + 11*z4^2*z8 -
    4*z4^2*z9 + 7*z4^2*z10 - 12*z4^2*z11 - 10*z4*z5^2 + 4*z4*z5*z6 +
    7*z4*z5*z7 - 15*z4*z5*z8 - 2*z4*z5*z9 - 2*z4*z5*z10 - 7*z4*z5*z11
    + z4*z6^2 - 8*z4*z6*z7 + 2*z4*z6*z8 - 17*z4*z6*z9 + 4*z4*z6*z10 -
    z4*z6*z11 - 3*z4*z7^2 - 5*z4*z7*z8 + z4*z7*z9 + z4*z7*z10 -
    3*z4*z7*z11 - 6*z4*z8^2 + 7*z4*z8*z9 - 8*z4*z8*z10 + 8*z4*z9^2 -
    3*z4*z9*z10 - 13*z4*z9*z11 + 4*z4*z10^2 - 8*z4*z10*z11 -
    5*z4*z11^2 - 4*z5^2*z6 - 3*z5^2*z7 - 3*z5^2*z8 - z5^2*z9 +
    3*z5^2*z11 - 4*z5*z6^2 + 7*z5*z6*z7 - 7*z5*z6*z8 - 2*z5*z6*z9 -
    4*z5*z6*z10 + 2*z5*z6*z11 - z5*z7*z8 + 2*z5*z7*z9 + 2*z5*z7*z10 -
    7*z5*z7*z11 + z5*z8^2 - 8*z5*z8*z9 - 2*z5*z8*z10 + 2*z5*z9^2 -
    z5*z9*z10 - 4*z5*z9*z11 + 2*z5*z10*z11 + 6*z5*z11^2 - 6*z6^2*z7 -
    2*z6^2*z8 - 5*z6^2*z9 - z6^2*z10 + 2*z6*z7^2 - 15*z6*z7*z8 -
    5*z6*z7*z9 - z6*z7*z10 + 13*z6*z7*z11 - 5*z6*z8^2 + 2*z6*z8*z9 -
    7*z6*z8*z10 + 4*z6*z8*z11 + 2*z6*z9^2 - 3*z6*z9*z10 - 3*z6*z9*z11
    + 2*z6*z10^2 - 3*z6*z10*z11 + 3*z6*z11^2 - 4*z7^3 - 8*z7^2*z8 +
    2*z7^2*z9 + 4*z7^2*z10 - 7*z7^2*z11 - 2*z7*z8^2 + 4*z7*z8*z9 +
    2*z7*z8*z10 + 5*z7*z8*z11 + 4*z7*z9^2 - 3*z7*z9*z10 - 4*z7*z9*z11
    + z7*z10^2 + 4*z7*z10*z11 - 5*z7*z11^2 + 2*z8^2*z10 - 3*z8^2*z11 +
    2*z8*z9^2 + 3*z8*z9*z10 - 4*z8*z9*z11 - z8*z10^2 + 4*z8*z10*z11 +
    4*z8*z11^2 - 2*z9*z10^2 - 2*z9*z11^2 - 2*z10^2*z11 + 3*z10*z11^2,
    z1^3 + 5*z1^2*z2 - 4*z1^2*z3 + 9*z1^2*z4 + z1^2*z5 + z1^2*z6 -
    4*z1^2*z7 - 5*z1^2*z9 - 3*z1^2*z11 + 7*z1*z2^2 - 4*z1*z2*z4 +
    3*z1*z2*z6 + z1*z2*z9 - 5*z1*z2*z11 + 6*z1*z3^2 - 2*z1*z3*z5 -
    5*z1*z3*z6 - 8*z1*z3*z7 - 3*z1*z3*z8 + 9*z1*z3*z9 + 4*z1*z3*z10 +
    15*z1*z3*z11 + z1*z4^2 + 3*z1*z4*z5 - 5*z1*z4*z6 - 7*z1*z4*z8 -
    5*z1*z4*z10 - z1*z4*z11 + z1*z5*z6 + z1*z5*z8 - 4*z1*z5*z9 -
    2*z1*z5*z10 - 2*z1*z5*z11 + 3*z1*z6^2 + 5*z1*z6*z7 - 4*z1*z6*z8 +
    z1*z6*z9 + 2*z1*z6*z10 + 4*z1*z6*z11 + 2*z1*z7^2 - 3*z1*z7*z8 -
    8*z1*z7*z10 - z1*z7*z11 - 4*z1*z8*z9 + 2*z1*z8*z11 + 4*z1*z9^2 -
    3*z1*z9*z10 + z1*z9*z11 + z1*z11^2 + z2^3 - 6*z2^2*z4 + 2*z2^2*z5
    + z2^2*z6 - 9*z2^2*z7 - 6*z2^2*z8 + 3*z2^2*z9 - 4*z2^2*z10 -
    11*z2*z3^2 + 4*z2*z3*z4 + 4*z2*z3*z5 + 2*z2*z3*z6 + 5*z2*z3*z7 -
    11*z2*z3*z8 - 3*z2*z3*z10 + 10*z2*z3*z11 + 4*z2*z4^2 - z2*z4*z6 -
    13*z2*z4*z8 + z2*z4*z11 - z2*z5^2 + 2*z2*z5*z7 - 3*z2*z5*z9 -
    z2*z5*z11 + 2*z2*z6*z8 + 5*z2*z6*z9 + 5*z2*z7^2 - z2*z7*z9 +
    7*z2*z7*z10 + 8*z2*z8^2 - z2*z8*z9 + 4*z2*z8*z10 + 6*z2*z9^2 +
    z2*z9*z10 + 7*z2*z9*z11 + 2*z2*z10^2 - 3*z2*z10*z11 + z2*z11^2 -
    7*z3^2*z5 + z3^2*z6 + z3^2*z7 + 2*z3^2*z8 - 7*z3^2*z9 + z3^2*z10 +
    z3^2*z11 - 4*z3*z4*z5 + 13*z3*z4*z6 - z3*z4*z7 + 6*z3*z4*z8 +
    z3*z4*z9 - 2*z3*z4*z10 - 4*z3*z5*z6 - 5*z3*z5*z7 - 7*z3*z5*z8 +
    3*z3*z5*z9 - z3*z5*z10 + z3*z5*z11 - z3*z6*z7 + 3*z3*z6*z9 -
    9*z3*z6*z11 - 11*z3*z7*z8 - 14*z3*z7*z11 - z3*z8^2 - 3*z3*z8*z9 -
    4*z3*z8*z10 + 8*z3*z9^2 + 22*z3*z9*z10 - 2*z3*z9*z11 - z3*z10^2 +
    6*z3*z10*z11 - 6*z3*z11^2 + 10*z4^3 + 5*z4^2*z5 + z4^2*z6 +
    10*z4^2*z7 + z4^2*z8 + 14*z4^2*z9 + 4*z4^2*z10 - z4^2*z11 +
    6*z4*z5*z8 + 11*z4*z5*z9 + 8*z4*z5*z11 - 2*z4*z6^2 + z4*z6*z7 +
    10*z4*z6*z9 - z4*z6*z10 - 6*z4*z6*z11 - 12*z4*z7^2 + 6*z4*z7*z8 +
    12*z4*z7*z9 + 2*z4*z7*z10 + 8*z4*z7*z11 + 10*z4*z8^2 + 5*z4*z8*z9
    + z4*z8*z10 + 7*z4*z8*z11 + 3*z4*z9^2 + 2*z4*z9*z10 + 12*z4*z9*z11
    - 3*z4*z10^2 + 10*z4*z10*z11 + 4*z4*z11^2 + z5^2*z7 + z5^2*z8 -
    z5^2*z9 + z5^2*z11 + z5*z6^2 + 4*z5*z6*z8 + 4*z5*z6*z9 + z5*z6*z10
    + 2*z5*z6*z11 + 5*z5*z7^2 + 6*z5*z7*z8 + 5*z5*z7*z9 + 7*z5*z7*z11
    - z5*z8^2 + 2*z5*z8*z9 + z5*z8*z10 - 2*z5*z8*z11 - 2*z5*z9*z10 -
    3*z5*z9*z11 + z5*z10*z11 + 2*z5*z11^2 - 3*z6^2*z7 + z6^2*z8 +
    3*z6^2*z9 - 2*z6^2*z11 - 4*z6*z7^2 + z6*z7*z8 - 2*z6*z7*z9 -
    z6*z7*z10 + 5*z6*z7*z11 - z6*z8^2 - 2*z6*z8*z9 + 3*z6*z8*z10 +
    4*z6*z8*z11 + 4*z6*z9^2 + 3*z6*z9*z10 + 7*z6*z9*z11 - z6*z10^2 +
    3*z6*z10*z11 - 2*z7^3 + 5*z7^2*z8 + 6*z7^2*z9 + 2*z7^2*z10 +
    9*z7^2*z11 + 3*z7*z8^2 + 5*z7*z8*z9 - 8*z7*z8*z11 - 6*z7*z9^2 -
    3*z7*z9*z10 - z7*z10^2 + 4*z7*z10*z11 + 10*z7*z11^2 - 2*z8^3 -
    2*z8^2*z9 + 2*z8^2*z10 - 3*z8^2*z11 - 10*z8*z9^2 + z8*z9*z10 -
    4*z8*z9*z11 - z8*z10^2 - 3*z8*z10*z11 + 2*z8*z11^2 + 6*z9^2*z10 +
    4*z9*z10*z11 - 3*z9*z11^2 + z10*z11^2 + z11^3, 3*z1^3 - z1^2*z2 -
    2*z1^2*z3 + 2*z1^2*z4 + z1^2*z5 + 4*z1^2*z6 + 7*z1^2*z7 -
    2*z1^2*z9 - 5*z1^2*z11 - 5*z1*z2^2 + 5*z1*z2*z4 - z1*z2*z5 +
    3*z1*z2*z6 + 2*z1*z2*z9 - 7*z1*z2*z10 - 4*z1*z2*z11 - 11*z1*z3^2 +
    z1*z3*z4 - 10*z1*z3*z5 - 7*z1*z3*z6 - z1*z3*z7 + 18*z1*z3*z9 -
    4*z1*z3*z10 - 11*z1*z3*z11 - z1*z4^2 + 4*z1*z4*z5 + 6*z1*z4*z6 +
    4*z1*z4*z7 + z1*z4*z8 - z1*z4*z9 - z1*z4*z10 + z1*z4*z11 +
    5*z1*z5*z6 + 3*z1*z5*z7 + 6*z1*z5*z9 + 4*z1*z5*z10 + 8*z1*z6^2 +
    3*z1*z6*z7 + 6*z1*z6*z8 + 2*z1*z6*z10 - 10*z1*z6*z11 - 6*z1*z7^2 +
    8*z1*z7*z8 + 8*z1*z7*z10 - z1*z7*z11 - 4*z1*z8*z11 + 6*z1*z9^2 +
    8*z1*z9*z10 - 4*z1*z9*z11 - 5*z2^3 + 5*z2^2*z3 - 2*z2^2*z4 +
    6*z2^2*z6 + z2^2*z7 + 7*z2^2*z9 - 3*z2^2*z10 - 5*z2^2*z11 -
    z2*z3^2 - 3*z2*z3*z4 + z2*z3*z5 - 4*z2*z3*z6 + 4*z2*z3*z8 +
    3*z2*z3*z10 - 2*z2*z3*z11 + 3*z2*z4^2 - z2*z4*z5 - 2*z2*z4*z8 +
    z2*z4*z9 - 9*z2*z5*z7 - 3*z2*z5*z8 + 3*z2*z5*z9 - z2*z5*z10 +
    6*z2*z5*z11 - 5*z2*z6*z8 - z2*z6*z9 - 12*z2*z7^2 - 2*z2*z7*z9 -
    13*z2*z7*z10 + 3*z2*z7*z11 + 3*z2*z8^2 - 4*z2*z8*z9 + 3*z2*z8*z10
    + 2*z2*z8*z11 + 2*z2*z9^2 - 4*z2*z9*z11 - z2*z10^2 + 5*z3^2*z5 -
    6*z3^2*z6 + 3*z3^2*z7 - 12*z3^2*z8 + 6*z3^2*z9 - 35*z3^2*z10 -
    3*z3^2*z11 + 2*z3*z4*z5 + 3*z3*z4*z6 - 2*z3*z4*z7 - 20*z3*z4*z8 +
    4*z3*z4*z9 - 2*z3*z4*z11 - 2*z3*z5*z6 + 4*z3*z5*z7 + 2*z3*z5*z8 +
    5*z3*z5*z9 - 2*z3*z5*z10 - 5*z3*z5*z11 + 2*z3*z6*z7 + 5*z3*z6*z9 +
    5*z3*z6*z10 - 3*z3*z6*z11 + 19*z3*z7*z8 - 15*z3*z7*z11 + 2*z3*z8^2
    - 5*z3*z8*z9 + 4*z3*z8*z10 + 5*z3*z9^2 - 24*z3*z9*z10 +
    6*z3*z9*z11 - 15*z3*z10^2 + 4*z3*z10*z11 - 2*z3*z11^2 + 2*z4^3 +
    z4^2*z6 + 2*z4^2*z7 + 2*z4^2*z8 - 9*z4^2*z9 + 14*z4^2*z10 +
    27*z4^2*z11 - 8*z4*z5*z6 + 11*z4*z5*z7 + 18*z4*z5*z8 - 7*z4*z5*z9
    + 7*z4*z5*z11 - z4*z6^2 - 9*z4*z6*z7 + 8*z4*z6*z8 + 9*z4*z6*z9 -
    5*z4*z6*z10 + 3*z4*z6*z11 + 21*z4*z7^2 + 15*z4*z7*z8 - 4*z4*z7*z9
    + 7*z4*z7*z10 + 25*z4*z7*z11 + 5*z4*z8^2 - 5*z4*z8*z9 +
    2*z4*z8*z10 + 25*z4*z8*z11 - 2*z4*z9^2 - 10*z4*z9*z10 +
    6*z4*z9*z11 - z4*z10^2 - 2*z4*z10*z11 + 12*z4*z11^2 - 3*z5^2*z8 -
    z5*z6^2 + 8*z5*z6*z8 - 2*z5*z6*z10 - 3*z5*z6*z11 + 3*z5*z7*z8 -
    7*z5*z7*z9 + z5*z7*z10 - z5*z7*z11 + 2*z5*z8^2 - 5*z5*z8*z10 -
    11*z5*z8*z11 + z5*z9^2 + 2*z5*z9*z10 - 2*z5*z10*z11 + z5*z11^2 -
    3*z6^2*z7 + z6^2*z8 + 4*z6^2*z9 - z6^2*z10 - 3*z6*z7^2 +
    2*z6*z7*z8 + 4*z6*z7*z9 - 8*z6*z7*z10 - 3*z6*z8^2 - 3*z6*z8*z9 +
    13*z6*z8*z11 - 3*z6*z9*z10 + 2*z6*z9*z11 + z6*z10^2 - 4*z6*z10*z11
    - 2*z6*z11^2 + 10*z7^3 + z7^2*z8 + 2*z7^2*z9 - 2*z7^2*z10 +
    13*z7^2*z11 - 9*z7*z8^2 + 4*z7*z8*z9 + 9*z7*z8*z10 + 15*z7*z8*z11
    - 2*z7*z9^2 + 3*z7*z9*z10 - 4*z7*z9*z11 - z7*z10^2 - 4*z7*z10*z11
    - 6*z7*z11^2 + 4*z8^3 + 4*z8^2*z9 - z8^2*z10 - z8^2*z11 -
    2*z8*z9^2 + 9*z8*z9*z10 - 2*z8*z9*z11 - 2*z8*z10^2 - 10*z8*z10*z11
    + z9^2*z10 - 4*z9*z10^2 - 4*z10^2*z11 + z10*z11^2 + z11^3, z1^3 -
    4*z1^2*z2 + z1^2*z3 - 3*z1^2*z4 - 6*z1^2*z5 + 3*z1^2*z6 -
    12*z1^2*z7 - z1^2*z11 - 6*z1*z2^2 - z1*z2*z3 + z1*z2*z5 -
    4*z1*z2*z6 + 2*z1*z2*z9 - 3*z1*z2*z10 - 2*z1*z2*z11 - 6*z1*z3^2 +
    z1*z3*z5 - 15*z1*z3*z6 - z1*z3*z7 - 6*z1*z3*z8 + 4*z1*z3*z9 +
    8*z1*z3*z10 + z1*z3*z11 + z1*z4^2 - 3*z1*z4*z5 - 15*z1*z4*z6 -
    z1*z4*z7 - 12*z1*z4*z8 + z1*z4*z10 + z1*z4*z11 - z1*z5*z6 -
    3*z1*z5*z8 - 6*z1*z5*z11 - 7*z1*z6^2 - z1*z6*z7 + 3*z1*z6*z9 -
    2*z1*z6*z11 + 5*z1*z7^2 - z1*z7*z8 - 11*z1*z7*z10 - 6*z1*z7*z11 -
    13*z1*z8*z9 + 10*z1*z8*z11 - 3*z1*z9^2 + 3*z1*z9*z10 - z1*z9*z11 -
    4*z1*z11^2 - 5*z2^3 - 9*z2^2*z3 + z2^2*z4 + 7*z2^2*z5 + z2^2*z7 -
    z2^2*z8 - 4*z2^2*z9 - 3*z2^2*z10 - z2^2*z11 + 10*z2*z3^2 +
    2*z2*z3*z4 - z2*z3*z5 + 2*z2*z3*z6 - 4*z2*z3*z7 + 5*z2*z3*z8 +
    z2*z3*z10 + 18*z2*z3*z11 + z2*z4^2 + 5*z2*z4*z5 + z2*z4*z6 +
    z2*z4*z8 - 2*z2*z4*z9 - z2*z4*z11 + z2*z5^2 + 10*z2*z5*z7 +
    11*z2*z5*z9 + z2*z5*z10 - 4*z2*z5*z11 + 10*z2*z6*z8 - 2*z2*z6*z9 -
    3*z2*z7*z9 - 4*z2*z7*z10 - z2*z7*z11 + 10*z2*z8^2 + 3*z2*z8*z10 -
    5*z2*z9^2 - 3*z2*z9*z10 + z2*z10^2 - 4*z2*z11^2 - 2*z3^2*z5 +
    3*z3^2*z6 + 2*z3^2*z8 + 15*z3^2*z10 - 16*z3^2*z11 - 5*z3*z4*z6 +
    z3*z4*z7 + z3*z4*z8 - 6*z3*z4*z9 - 4*z3*z4*z10 + 8*z3*z4*z11 -
    14*z3*z5*z6 + 23*z3*z5*z7 + 6*z3*z5*z8 - 2*z3*z5*z9 + z3*z5*z10 +
    4*z3*z5*z11 - 7*z3*z6*z7 - 14*z3*z6*z9 - 6*z3*z6*z10 + z3*z6*z11 -
    7*z3*z7*z8 + 6*z3*z7*z11 - 6*z3*z8*z9 - 6*z3*z8*z10 - 2*z3*z9^2 -
    2*z3*z9*z10 - 3*z3*z9*z11 + 5*z3*z10*z11 - 30*z4^3 - 3*z4^2*z5 -
    z4^2*z6 - 15*z4^2*z7 - z4^2*z8 - 13*z4^2*z9 - z4^2*z10 -
    22*z4^2*z11 - 8*z4*z5^2 - z4*z5*z6 + z4*z5*z7 + 6*z4*z5*z9 -
    z4*z5*z10 + z4*z5*z11 - 7*z4*z6*z7 + 2*z4*z6*z8 - 17*z4*z6*z9 -
    9*z4*z6*z10 + 16*z4*z6*z11 - 13*z4*z7^2 - 19*z4*z7*z8 -
    24*z4*z7*z9 + z4*z7*z10 - 13*z4*z7*z11 - 4*z4*z8^2 - 15*z4*z8*z9 +
    11*z4*z8*z11 - 11*z4*z9^2 + 2*z4*z9*z10 - 4*z4*z9*z11 +
    5*z4*z10*z11 + 7*z4*z11^2 - 2*z5^2*z6 - 2*z5^2*z7 - 2*z5^2*z8 +
    z5^2*z11 - 3*z5*z6^2 + 4*z5*z6*z7 + 2*z5*z6*z8 + 2*z5*z6*z9 -
    3*z5*z6*z10 + 3*z5*z6*z11 - 3*z5*z7^2 - 12*z5*z7*z8 + 9*z5*z7*z9 -
    2*z5*z7*z10 + 6*z5*z7*z11 - 8*z5*z8^2 - 10*z5*z8*z9 - 2*z5*z8*z10
    + 3*z5*z8*z11 + z5*z9^2 + z5*z9*z10 - 6*z5*z9*z11 + z5*z10*z11 +
    3*z5*z11^2 - 4*z6^2*z7 + z6^2*z8 - 5*z6^2*z9 - 2*z6^2*z10 +
    2*z6^2*z11 - 8*z6*z7^2 - 14*z6*z7*z8 - 12*z6*z7*z9 + 2*z6*z7*z10 +
    5*z6*z7*z11 - 8*z6*z8^2 - 6*z6*z8*z9 + 2*z6*z8*z10 + 3*z6*z8*z11 -
    3*z6*z9^2 - 4*z6*z9*z10 - z6*z9*z11 - 3*z6*z10*z11 + 6*z6*z11^2 -
    4*z7^3 - 11*z7^2*z8 - 8*z7^2*z9 - 5*z7^2*z10 + 2*z7^2*z11 -
    10*z7*z8^2 - 10*z7*z8*z9 - 7*z7*z8*z10 - 4*z7*z8*z11 + 4*z7*z9*z10
    - 3*z7*z10*z11 + 7*z7*z11^2 - 4*z8^3 + 3*z8^2*z9 - 4*z8^2*z11 +
    3*z8*z9^2 - z8*z9*z10 - z8*z9*z11 - z8*z10^2 - 4*z8*z10*z11 +
    5*z8*z11^2 + 2*z9^2*z10 - 4*z9*z10*z11 - 2*z9*z11^2 - z10*z11^2 +
    7*z11^3, z1^2*z2 - 3*z1^2*z3 - 4*z1^2*z4 + z1^2*z5 - 4*z1^2*z6 +
    2*z1^2*z7 + 2*z1^2*z9 + 2*z1^2*z11 + 4*z1*z2^2 - z1*z2*z4 +
    3*z1*z2*z6 - z1*z2*z9 + 2*z1*z2*z10 + z1*z2*z11 - 4*z1*z3^2 +
    z1*z3*z4 + z1*z3*z5 + 14*z1*z3*z6 - 13*z1*z3*z7 + 7*z1*z3*z8 +
    z1*z3*z9 + 18*z1*z3*z10 + 8*z1*z3*z11 + 2*z1*z4^2 - 3*z1*z4*z5 +
    11*z1*z4*z6 + 2*z1*z4*z7 + 7*z1*z4*z8 + 2*z1*z4*z10 + z1*z4*z11 -
    2*z1*z5*z6 + 2*z1*z5*z8 + 7*z1*z5*z9 - 2*z1*z5*z10 - 5*z1*z5*z11 -
    z1*z6^2 - 15*z1*z6*z7 - 2*z1*z6*z8 + z1*z6*z9 - 4*z1*z6*z10 +
    9*z1*z6*z11 + 5*z1*z7^2 - 4*z1*z7*z8 - 6*z1*z7*z10 - 3*z1*z7*z11 -
    7*z1*z8*z9 - 9*z1*z8*z11 - 5*z1*z9^2 + 13*z1*z9*z10 + z1*z9*z11 +
    10*z1*z11^2 + 3*z2^3 + 2*z2^2*z4 - z2^2*z5 + 4*z2^2*z6 - 6*z2^2*z7
    - 4*z2^2*z8 - 2*z2^2*z9 + 2*z2^2*z10 + 2*z2^2*z11 - 13*z2*z3^2 +
    3*z2*z3*z5 - z2*z3*z6 + z2*z3*z8 + z2*z3*z10 + 2*z2*z3*z11 +
    7*z2*z4^2 - 9*z2*z4*z5 - 4*z2*z4*z6 + 2*z2*z4*z8 + 4*z2*z4*z11 -
    3*z2*z5*z7 - z2*z5*z8 + 3*z2*z5*z9 - 2*z2*z5*z10 + z2*z5*z11 -
    13*z2*z6*z8 + 5*z2*z7^2 + z2*z7*z9 + 2*z2*z7*z10 + 3*z2*z7*z11 +
    6*z2*z8^2 + z2*z8*z9 - 2*z2*z8*z10 - 4*z2*z8*z11 - z2*z9^2 +
    z2*z9*z10 + z2*z9*z11 - z2*z10^2 - 4*z2*z10*z11 - 10*z3^2*z5 +
    2*z3^2*z6 - 3*z3^2*z7 + 2*z3^2*z8 + 5*z3^2*z9 - 3*z3^2*z10 +
    13*z3^2*z11 - 4*z3*z4*z5 + 2*z3*z4*z6 - 2*z3*z4*z7 + 9*z3*z4*z8 -
    2*z3*z4*z9 + 8*z3*z4*z11 + 7*z3*z5*z6 - 10*z3*z5*z7 + 2*z3*z5*z8 -
    z3*z5*z9 - z3*z5*z10 + z3*z5*z11 + 2*z3*z6*z10 + z3*z6*z11 +
    3*z3*z7*z8 - 2*z3*z8*z9 + 7*z3*z8*z10 + 10*z3*z9^2 - 3*z3*z9*z10 -
    z3*z9*z11 + 2*z3*z10^2 - z3*z10*z11 - 2*z3*z11^2 - 6*z4^3 +
    2*z4^2*z6 - 8*z4^2*z7 - 13*z4^2*z8 + 11*z4^2*z10 + 21*z4^2*z11 -
    z4*z5^2 - 10*z4*z5*z6 - 10*z4*z5*z7 + 17*z4*z5*z8 - 13*z4*z5*z9 +
    3*z4*z5*z10 + 7*z4*z5*z11 + z4*z6^2 - 4*z4*z6*z7 + 4*z4*z6*z8 +
    10*z4*z6*z9 - 6*z4*z6*z10 - 9*z4*z6*z11 - 11*z4*z7^2 - 4*z4*z7*z8
    + 6*z4*z7*z10 + 15*z4*z7*z11 - 6*z4*z8^2 + 4*z4*z8*z9 +
    10*z4*z8*z10 + 11*z4*z8*z11 + 9*z4*z9^2 - z4*z9*z10 + 8*z4*z9*z11
    - 4*z4*z10^2 + 3*z4*z10*z11 + 3*z4*z11^2 - 3*z5*z6^2 - 16*z5*z6*z7
    + 3*z5*z6*z8 - 2*z5*z6*z9 + 3*z5*z6*z10 + 5*z5*z6*z11 + z5*z7^2 +
    6*z5*z7*z8 - 6*z5*z7*z9 - 5*z5*z7*z10 + 11*z5*z7*z11 + 4*z5*z8^2 -
    7*z5*z8*z11 - 2*z5*z9^2 + 4*z5*z9*z10 + 4*z5*z9*z11 - 6*z5*z10*z11
    + z5*z11^2 - 2*z6^2*z7 + z6^2*z8 + 2*z6^2*z9 - 2*z6^2*z10 -
    5*z6^2*z11 - 8*z6*z7^2 + 7*z6*z7*z8 + 6*z6*z7*z9 - 8*z6*z7*z10 +
    6*z6*z7*z11 + 3*z6*z8^2 + 4*z6*z8*z9 + 3*z6*z8*z10 + 2*z6*z8*z11 +
    3*z6*z9^2 - z6*z9*z10 + 3*z6*z9*z11 + z6*z11^2 - 2*z7^3 + z7^2*z8
    - 2*z7^2*z10 + 4*z7^2*z11 - z7*z8^2 + z7*z8*z9 - 2*z7*z8*z10 +
    z7*z8*z11 + 5*z7*z9*z10 + 5*z7*z9*z11 - 5*z7*z10^2 + 3*z7*z10*z11
    - 7*z7*z11^2 - 3*z8^3 + 6*z8^2*z11 - 3*z8*z9^2 + z8*z9*z10 +
    3*z8*z9*z11 - z8*z10^2 - 2*z8*z10*z11 - 3*z8*z11^2 + 2*z9*z10^2 +
    2*z9*z10*z11 - z10^2*z11 - 2*z10*z11^2 - 3*z11^3, 4*z1^2*z2 -
    10*z1^2*z3 + 10*z1^2*z4 + 12*z1^2*z5 - 2*z1^2*z6 + 9*z1^2*z7 +
    4*z1^2*z9 + 3*z1^2*z11 + 2*z1*z2^2 + 8*z1*z2*z3 - z1*z2*z4 -
    z1*z2*z6 + 2*z1*z2*z9 + 3*z1*z2*z10 + 5*z1*z2*z11 - 2*z1*z3^2 -
    2*z1*z3*z4 - 16*z1*z3*z5 + 3*z1*z3*z6 - 4*z1*z3*z7 + 9*z1*z3*z8 -
    2*z1*z3*z9 - 3*z1*z3*z10 - 3*z1*z3*z11 - 2*z1*z4^2 - z1*z4*z5 -
    7*z1*z4*z6 + z1*z4*z7 - z1*z4*z8 - z1*z4*z10 + 2*z1*z4*z11 -
    2*z1*z5*z7 - z1*z5*z9 - z1*z5*z10 + 3*z1*z5*z11 + z1*z6^2 +
    4*z1*z6*z7 + z1*z6*z8 - z1*z6*z9 + 2*z1*z6*z10 + 7*z1*z6*z11 -
    2*z1*z7^2 - 3*z1*z7*z8 + z1*z7*z10 + 3*z1*z7*z11 + 5*z1*z8*z9 +
    2*z1*z8*z11 + 2*z1*z9^2 + 5*z1*z9*z10 - z1*z11^2 + 2*z2^3 -
    8*z2^2*z4 - 6*z2^2*z5 + z2^2*z6 - 5*z2^2*z7 - 4*z2^2*z8 -
    3*z2^2*z9 - 2*z2^2*z10 - 5*z2*z3^2 - 4*z2*z3*z4 + 2*z2*z3*z5 -
    23*z2*z3*z6 - 2*z2*z3*z8 - 3*z2*z3*z10 - 3*z2*z3*z11 + 7*z2*z4^2 -
    6*z2*z4*z5 + 3*z2*z4*z9 - 4*z2*z5^2 - 7*z2*z5*z7 - 7*z2*z5*z9 +
    2*z2*z5*z10 + 2*z2*z6*z8 - z2*z6*z9 + z2*z7^2 - 4*z2*z7*z9 -
    z2*z7*z10 - 4*z2*z7*z11 + 3*z2*z8^2 + 3*z2*z8*z9 + 2*z2*z8*z10 +
    z2*z8*z11 - z2*z9^2 - 3*z2*z9*z10 + z2*z9*z11 + 2*z2*z10^2 +
    3*z2*z10*z11 + z2*z11^2 - 4*z3^2*z5 + 3*z3^2*z7 + 9*z3^2*z8 +
    2*z3^2*z11 - 3*z3*z4*z5 + 8*z3*z4*z6 - z3*z4*z8 + 3*z3*z4*z9 +
    3*z3*z4*z10 - 4*z3*z4*z11 - 9*z3*z5*z6 - 2*z3*z5*z7 - 11*z3*z5*z8
    - 2*z3*z5*z9 - z3*z5*z11 - 4*z3*z6*z7 - 12*z3*z6*z9 + 6*z3*z6*z10
    - 8*z3*z6*z11 - 5*z3*z7*z8 - 18*z3*z7*z11 - z3*z8^2 + 8*z3*z8*z10
    + 5*z3*z9^2 + z3*z9*z10 + z3*z9*z11 + 8*z3*z10*z11 - z3*z11^2 +
    4*z4^3 - 3*z4^2*z5 - 13*z4^2*z6 + 14*z4^2*z7 - 12*z4^2*z8 +
    z4^2*z9 - 5*z4^2*z10 + 11*z4^2*z11 + 5*z4*z5*z6 - 4*z4*z5*z7 +
    20*z4*z5*z8 + 6*z4*z5*z9 + z4*z5*z10 - z4*z5*z11 - 8*z4*z6^2 -
    6*z4*z6*z7 + 7*z4*z6*z8 + 5*z4*z6*z9 - 5*z4*z6*z10 - 3*z4*z6*z11 -
    z4*z7^2 + 11*z4*z7*z8 + 4*z4*z7*z9 - 12*z4*z7*z10 + 16*z4*z7*z11 +
    16*z4*z8^2 + 10*z4*z8*z9 - z4*z8*z10 - 5*z4*z8*z11 + z4*z9^2 -
    3*z4*z9*z10 + 2*z4*z9*z11 + 6*z4*z10*z11 + 6*z4*z11^2 + 2*z5^2*z6
    + 2*z5^2*z7 + 4*z5^2*z8 - z5^2*z11 + 6*z5*z6^2 + 2*z5*z6*z7 +
    11*z5*z6*z8 + 7*z5*z6*z9 + 2*z5*z6*z10 - 8*z5*z6*z11 + 4*z5*z7^2 +
    16*z5*z7*z8 + 4*z5*z7*z9 - 2*z5*z7*z10 + 3*z5*z7*z11 + 6*z5*z8^2 +
    8*z5*z8*z9 - 3*z5*z8*z10 - 12*z5*z8*z11 + z5*z9^2 - z5*z9*z10 -
    4*z5*z9*z11 + z5*z11^2 - 3*z6^2*z7 + 2*z6^2*z8 + 2*z6^2*z9 +
    2*z6^2*z10 - z6^2*z11 - 2*z6*z7^2 + 6*z6*z7*z9 - 7*z6*z7*z10 -
    2*z6*z7*z11 + 4*z6*z8^2 + 8*z6*z8*z9 - z6*z8*z10 + 3*z6*z8*z11 +
    2*z6*z9^2 + 3*z6*z9*z10 + 3*z6*z9*z11 - z6*z10*z11 - 6*z6*z11^2 -
    2*z7^3 + 2*z7^2*z9 - z7^2*z10 + 3*z7^2*z11 - 3*z7*z8^2 -
    7*z7*z8*z10 - 5*z7*z8*z11 - 2*z7*z9^2 - 2*z7*z9*z10 - 7*z7*z9*z11
    - z7*z10*z11 + 8*z7*z11^2 - z8^3 - 3*z8^2*z9 - z8^2*z10 - z8^2*z11
    - 4*z8*z9^2 + 7*z8*z9*z10 - z8*z9*z11 - 3*z8*z10^2 - 5*z8*z10*z11
    - 2*z8*z11^2 + 4*z9^2*z10 + z9*z10*z11 - 3*z9*z11^2 + 3*z11^3,
    z1^3 + 2*z1^2*z2 + z1^2*z5 - 2*z1^2*z6 + 7*z1^2*z7 + 4*z1^2*z9 +
    3*z1^2*z11 - z1*z2^2 + 3*z1*z2*z3 + 2*z1*z2*z4 - 5*z1*z2*z5 +
    4*z1*z2*z6 + z1*z2*z9 + 6*z1*z2*z11 + 7*z1*z3^2 - z1*z3*z5 +
    10*z1*z3*z6 - 6*z1*z3*z7 + z1*z3*z8 - 2*z1*z3*z9 + 2*z1*z3*z10 -
    2*z1*z3*z11 + z1*z4^2 - 2*z1*z4*z5 + 18*z1*z4*z6 + 6*z1*z4*z8 +
    2*z1*z4*z10 + z1*z4*z11 - 2*z1*z5*z6 + z1*z5*z7 - 4*z1*z5*z8 +
    9*z1*z5*z9 - z1*z5*z10 - 2*z1*z5*z11 + 4*z1*z6^2 - 18*z1*z6*z7 -
    z1*z6*z8 + 2*z1*z6*z9 - 4*z1*z6*z10 - 4*z1*z6*z11 - 3*z1*z7^2 -
    3*z1*z7*z8 - 4*z1*z7*z10 - 2*z1*z7*z11 + 5*z1*z8*z9 - 7*z1*z8*z11
    - z1*z9^2 - 4*z1*z9*z11 + 8*z1*z11^2 - 2*z2^3 + 4*z2^2*z3 -
    3*z2^2*z4 - 4*z2^2*z5 - 2*z2^2*z6 - z2^2*z7 + 2*z2^2*z8 +
    2*z2^2*z10 + 3*z2^2*z11 - 3*z2*z3^2 - 3*z2*z3*z4 - 2*z2*z3*z5 +
    z2*z3*z6 - 4*z2*z3*z7 - 2*z2*z3*z8 + 4*z2*z3*z10 - 7*z2*z3*z11 +
    5*z2*z4^2 - 2*z2*z4*z5 + 5*z2*z4*z8 + z2*z4*z9 - z2*z5^2 -
    5*z2*z5*z7 - 5*z2*z5*z8 - 3*z2*z5*z9 - z2*z5*z10 + 5*z2*z5*z11 -
    8*z2*z6*z8 + z2*z6*z9 + 2*z2*z7^2 - z2*z7*z9 + 3*z2*z7*z10 -
    2*z2*z8*z10 - z2*z8*z11 - z2*z9^2 - 2*z2*z9*z11 - z2*z10^2 +
    5*z2*z10*z11 + 2*z2*z11^2 + 7*z3^2*z5 + 2*z3^2*z6 - 3*z3^2*z8 -
    z3^2*z9 + 6*z3^2*z10 + 4*z3^2*z11 + 3*z3*z4*z5 - 2*z3*z4*z6 +
    4*z3*z4*z7 + 11*z3*z4*z8 + z3*z4*z10 + 3*z3*z4*z11 - 13*z3*z5*z7 +
    3*z3*z5*z8 - 3*z3*z5*z9 + z3*z5*z10 + z3*z5*z11 - 3*z3*z6*z9 +
    3*z3*z6*z10 + 5*z3*z6*z11 - 2*z3*z7^2 - 4*z3*z7*z8 + 14*z3*z7*z11
    - 2*z3*z8^2 - 5*z3*z8*z9 + 11*z3*z8*z10 + z3*z9^2 - 2*z3*z9*z10 +
    z3*z9*z11 - z3*z10^2 + 7*z3*z10*z11 - 2*z3*z11^2 - 5*z4^3 -
    5*z4^2*z5 - 3*z4^2*z6 - 13*z4^2*z7 - 13*z4^2*z8 + z4^2*z9 -
    4*z4^2*z10 - 14*z4^2*z11 - 6*z4*z5*z6 - 4*z4*z5*z7 + 12*z4*z5*z8 -
    6*z4*z5*z9 + z4*z5*z10 - z4*z5*z11 - z4*z6^2 - 9*z4*z6*z7 -
    4*z4*z6*z8 + 7*z4*z6*z9 - 3*z4*z6*z10 - 17*z4*z6*z11 - z4*z7^2 +
    2*z4*z7*z8 + 11*z4*z7*z9 + z4*z7*z10 + 9*z4*z7*z11 - 2*z4*z8^2 +
    7*z4*z8*z9 + 9*z4*z8*z10 + 3*z4*z8*z11 + 4*z4*z9^2 + 6*z4*z9*z10 +
    7*z4*z9*z11 - 3*z4*z10^2 - 6*z4*z10*z11 + 2*z5^2*z6 - z5^2*z8 +
    2*z5^2*z9 - 3*z5^2*z11 - z5*z6^2 - 9*z5*z6*z7 + 4*z5*z6*z8 +
    z5*z6*z10 + 2*z5*z6*z11 + 6*z5*z7*z8 - 6*z5*z7*z9 - 4*z5*z7*z10 +
    z5*z7*z11 + 5*z5*z8^2 + 2*z5*z8*z9 - z5*z8*z10 - 3*z5*z8*z11 -
    z5*z9^2 + 3*z5*z9*z10 + 5*z5*z9*z11 - 3*z5*z10*z11 - 5*z5*z11^2 -
    z6^2*z8 + 2*z6^2*z9 - 4*z6^2*z11 - 6*z6*z7^2 + z6*z7*z8 +
    4*z6*z7*z9 - 2*z6*z7*z10 - 3*z6*z7*z11 + 2*z6*z8^2 + 3*z6*z8*z9 +
    4*z6*z8*z10 + 4*z6*z8*z11 + z6*z9^2 + 2*z6*z9*z10 + 2*z6*z9*z11 -
    z6*z10^2 - 2*z6*z10*z11 + z6*z11^2 + 4*z7^2*z8 - 2*z7^2*z10 +
    3*z7^2*z11 - 2*z7*z8*z9 - 4*z7*z8*z10 + 8*z7*z8*z11 + 4*z7*z9*z10
    + 11*z7*z9*z11 - z7*z10^2 - 8*z7*z10*z11 - 4*z7*z11^2 - 2*z8^3 -
    5*z8^2*z9 - 2*z8^2*z10 + 5*z8^2*z11 - z8*z9^2 + 5*z8*z9*z10 +
    3*z8*z9*z11 + z8*z10^2 - 3*z8*z11^2 - z9^2*z10 + 2*z9*z10*z11 +
    z9*z11^2 - 4*z11^3, z1^2*z2 - 3*z1^2*z3 + 10*z1^2*z4 - 8*z1^2*z5 -
    z1^2*z6 - 6*z1^2*z7 + 3*z1^2*z11 - 6*z1*z2^2 + 2*z1*z2*z3 -
    z1*z2*z4 + z1*z2*z5 + 10*z1*z2*z6 + z1*z2*z9 - z1*z2*z10 -
    z1*z2*z11 - 8*z1*z3^2 + z1*z3*z4 + 9*z1*z3*z5 - z1*z3*z6 -
    2*z1*z3*z7 - 5*z1*z3*z8 - 11*z1*z3*z9 + 6*z1*z3*z10 + 7*z1*z3*z11
    - z1*z4^2 + z1*z4*z5 - 11*z1*z4*z6 - z1*z4*z7 + z1*z4*z8 +
    2*z1*z4*z10 - z1*z5*z6 - z1*z5*z7 + 2*z1*z5*z8 - 3*z1*z5*z9 -
    z1*z5*z10 - z1*z5*z11 - 8*z1*z6^2 + z1*z6*z7 - 10*z1*z6*z8 +
    4*z1*z6*z11 + 3*z1*z7^2 - 4*z1*z7*z8 - z1*z7*z10 - 3*z1*z8*z9 +
    6*z1*z8*z11 - 4*z1*z9^2 + 3*z1*z9*z10 + 5*z1*z9*z11 + 3*z1*z11^2 -
    7*z2^3 - 5*z2^2*z3 - 3*z2^2*z4 + 9*z2^2*z5 + 6*z2^2*z7 + 6*z2^2*z8
    - z2^2*z9 - z2^2*z10 - z2^2*z11 + 8*z2*z3^2 + z2*z3*z4 +
    3*z2*z3*z5 - 2*z2*z3*z6 - z2*z3*z7 - 4*z2*z3*z8 + 8*z2*z3*z11 -
    5*z2*z4^2 + 5*z2*z4*z8 - z2*z4*z9 - 5*z2*z5*z7 - 7*z2*z5*z8 -
    9*z2*z5*z9 - 2*z2*z5*z10 + 3*z2*z6*z8 - z2*z6*z9 + 2*z2*z7^2 -
    z2*z7*z9 + 3*z2*z7*z10 - z2*z7*z11 + 2*z2*z8^2 + 5*z2*z8*z9 +
    z2*z8*z10 - 3*z2*z8*z11 - 2*z2*z9*z10 - 2*z2*z9*z11 - 2*z2*z10^2 -
    4*z2*z10*z11 - 2*z2*z11^2 - 6*z3^2*z5 + 2*z3^2*z6 - z3^2*z7 +
    2*z3^2*z8 + z3^2*z9 + 15*z3^2*z10 - 8*z3^2*z11 - 5*z3*z4*z5 -
    5*z3*z4*z6 + z3*z4*z7 + 10*z3*z4*z8 - 3*z3*z4*z9 - 2*z3*z4*z10 +
    5*z3*z4*z11 - 4*z3*z5*z6 + 9*z3*z5*z7 - 3*z3*z5*z8 - 8*z3*z5*z9 +
    2*z3*z5*z10 - 3*z3*z6*z7 - 11*z3*z6*z9 + 2*z3*z6*z10 - z3*z6*z11 +
    7*z3*z7*z11 - 10*z3*z8*z9 - 7*z3*z8*z10 - 7*z3*z9^2 + 8*z3*z9*z10
    + 8*z3*z10^2 + 4*z3*z10*z11 - 3*z3*z11^2 - 16*z4^3 - 3*z4^2*z5 +
    14*z4^2*z6 - 7*z4^2*z7 - z4^2*z8 - 5*z4^2*z9 + 9*z4^2*z10 -
    z4^2*z11 + z4*z5^2 - z4*z5*z6 - 9*z4*z5*z7 - 2*z4*z5*z8 +
    2*z4*z5*z9 + 2*z4*z5*z10 - 4*z4*z5*z11 + 6*z4*z6^2 + 9*z4*z6*z7 +
    z4*z6*z8 - 4*z4*z6*z9 - 2*z4*z6*z10 + 20*z4*z6*z11 - 17*z4*z7^2 -
    30*z4*z7*z8 - 7*z4*z7*z9 - 4*z4*z7*z10 - 16*z4*z7*z11 + 2*z4*z8*z9
    - z4*z8*z11 + 2*z4*z9*z10 - 11*z4*z9*z11 - 2*z4*z10^2 - z4*z11^2 -
    z5^2*z7 + z5^2*z9 - z5^2*z11 - z5*z6^2 - 6*z5*z6*z7 + 2*z5*z6*z8 +
    2*z5*z6*z9 - z5*z6*z11 - 8*z5*z7^2 - 11*z5*z7*z8 + 5*z5*z7*z9 -
    3*z5*z7*z10 + 9*z5*z7*z11 - z5*z8^2 + 8*z5*z8*z9 - z5*z8*z10 +
    2*z5*z8*z11 + 2*z5*z9^2 + z5*z9*z10 - 8*z5*z9*z11 + z5*z11^2 +
    z6^2*z7 + 3*z6^2*z8 - z6^2*z9 - 2*z6^2*z10 + 5*z6^2*z11 -
    2*z6*z7^2 - 2*z6*z7*z9 - z6*z7*z10 + 2*z6*z7*z11 + z6*z8^2 +
    2*z6*z8*z9 + 4*z6*z8*z10 - 3*z6*z8*z11 + 2*z6*z9*z10 - 2*z6*z9*z11
    - 2*z6*z10^2 - 2*z6*z10*z11 + z6*z11^2 - 8*z7^3 - 16*z7^2*z8 -
    4*z7^2*z9 - 8*z7^2*z10 - 9*z7^2*z11 - 5*z7*z8^2 - 3*z7*z8*z9 -
    12*z7*z8*z10 - 4*z7*z8*z11 + 4*z7*z9^2 - 3*z7*z9*z10 + z7*z10^2 -
    2*z7*z10*z11 - 2*z7*z11^2 + 4*z8^2*z9 - 2*z8^2*z10 - 5*z8^2*z11 +
    4*z8*z9^2 - 6*z8*z9*z10 - 4*z8*z9*z11 - z8*z10^2 + 5*z8*z10*z11 +
    2*z8*z11^2 + 2*z9^2*z10 + 2*z9*z10^2 - 2*z9*z10*z11 - 4*z9*z11^2 +
    3*z10^2*z11 + 3*z10*z11^2 + 3*z11^3, 4*z1^3 + 2*z1^2*z2 + z1^2*z3
    + z1^2*z4 + z1^2*z5 - 3*z1^2*z6 - 7*z1^2*z7 - z1^2*z9 + z1^2*z11 +
    5*z1*z2^2 + 8*z1*z2*z3 - 2*z1*z2*z4 - 4*z1*z2*z5 + 5*z1*z2*z6 -
    z1*z2*z8 - 2*z1*z2*z11 + 9*z1*z3^2 + 2*z1*z3*z4 + 7*z1*z3*z5 -
    6*z1*z3*z6 + 2*z1*z3*z7 + z1*z3*z8 - 13*z1*z3*z9 + z1*z3*z10 -
    8*z1*z3*z11 - 3*z1*z4^2 + 5*z1*z4*z5 - 4*z1*z4*z6 + 4*z1*z4*z7 -
    13*z1*z4*z8 - z1*z4*z11 - 3*z1*z5*z6 - z1*z5*z10 - 5*z1*z6^2 +
    22*z1*z6*z7 - 7*z1*z6*z8 - 3*z1*z6*z10 - 2*z1*z6*z11 - 2*z1*z7^2 -
    z1*z7*z8 - 12*z1*z7*z10 + 3*z1*z7*z11 - 2*z1*z8*z9 + 5*z1*z9^2 -
    18*z1*z9*z10 - 13*z1*z11^2 + 5*z2^3 + 4*z2^2*z3 + z2^2*z6 +
    z2^2*z7 - 4*z2^2*z8 - 6*z2^2*z9 - 2*z2^2*z11 + z2*z3^2 +
    4*z2*z3*z4 + 2*z2*z3*z5 - 18*z2*z3*z6 + 8*z2*z3*z7 - 5*z2*z3*z8 -
    3*z2*z3*z10 + z2*z3*z11 + z2*z4^2 - 5*z2*z4*z5 - 15*z2*z4*z8 +
    2*z2*z4*z9 - 2*z2*z5^2 + 5*z2*z5*z7 + 5*z2*z5*z8 + 4*z2*z5*z9 -
    2*z2*z5*z10 + 2*z2*z5*z11 + 10*z2*z6*z8 + 5*z2*z6*z9 + 4*z2*z7^2 +
    2*z2*z7*z9 - 3*z2*z7*z10 + 3*z2*z7*z11 - 3*z2*z8^2 + 4*z2*z8*z9 -
    z2*z8*z11 + 9*z2*z9^2 + z2*z9*z10 + z2*z9*z11 + 2*z2*z10^2 -
    z2*z10*z11 + 2*z2*z11^2 + 6*z3^2*z5 + 3*z3^2*z6 + z3^2*z7 -
    9*z3^2*z8 + 5*z3^2*z9 + 11*z3^2*z10 + 2*z3*z4*z5 - 9*z3*z4*z6 -
    2*z3*z4*z7 - 5*z3*z4*z8 + 3*z3*z4*z9 - 5*z3*z4*z10 - 2*z3*z4*z11 +
    6*z3*z5*z6 - 2*z3*z5*z7 + 5*z3*z5*z8 + 6*z3*z5*z9 - 7*z3*z6*z9 -
    z3*z6*z10 - 2*z3*z6*z11 + 24*z3*z7*z8 - z3*z8^2 + 15*z3*z8*z9 -
    5*z3*z8*z10 + 4*z3*z9^2 + 12*z3*z9*z10 - 13*z3*z10^2 +
    5*z3*z10*z11 + 5*z3*z11^2 + 17*z4^3 + z4^2*z5 + 5*z4^2*z6 +
    15*z4^2*z7 + 6*z4^2*z8 + 11*z4^2*z9 - 7*z4^2*z10 + 13*z4^2*z11 -
    3*z4*z5^2 + 8*z4*z5*z6 - 5*z4*z5*z7 + z4*z5*z8 + 20*z4*z5*z9 -
    6*z4*z5*z11 - z4*z6^2 - 5*z4*z6*z7 + 6*z4*z6*z8 + 2*z4*z6*z9 +
    9*z4*z6*z11 - 12*z4*z7^2 + 3*z4*z7*z8 - 3*z4*z7*z9 - 14*z4*z7*z10
    + 17*z4*z7*z11 + 21*z4*z8^2 + 4*z4*z8*z9 - 12*z4*z8*z10 +
    z4*z8*z11 - z4*z9^2 + 10*z4*z9*z10 + 7*z4*z9*z11 + 3*z4*z10^2 -
    6*z4*z10*z11 + 18*z4*z11^2 - 4*z5^2*z6 - 2*z5^2*z7 - 2*z5^2*z8 -
    2*z5^2*z9 + 4*z5^2*z11 + z5*z6^2 - z5*z6*z7 - 2*z5*z6*z8 +
    6*z5*z6*z9 - 6*z5*z6*z10 - z5*z6*z11 - 2*z5*z7^2 - 8*z5*z7*z8 +
    3*z5*z7*z9 + 3*z5*z7*z10 - z5*z7*z11 - 6*z5*z8^2 - 6*z5*z8*z9 -
    z5*z8*z10 + 2*z5*z8*z11 + 3*z5*z9^2 - 6*z5*z9*z10 - 5*z5*z9*z11 +
    9*z5*z10*z11 + z6^2*z8 - z6^2*z9 - z6^2*z11 + z6*z7^2 - 7*z6*z7*z9
    + z6*z7*z10 - 7*z6*z7*z11 + 2*z6*z8^2 - z6*z8*z9 - 5*z6*z8*z10 +
    3*z6*z8*z11 + z6*z9^2 - z6*z9*z10 + 2*z6*z9*z11 - z6*z10^2 -
    5*z6*z10*z11 + 8*z6*z11^2 - 10*z7^3 - 7*z7^2*z8 + 2*z7^2*z9 +
    10*z7^2*z10 - 14*z7^2*z11 + 8*z7*z8^2 + 11*z7*z8*z9 + 4*z7*z8*z10
    + 3*z7*z8*z11 - 3*z7*z9*z10 + 10*z7*z9*z11 + 8*z7*z10^2 -
    4*z7*z10*z11 + 20*z7*z11^2 + 5*z8^3 + 8*z8^2*z9 + 4*z8^2*z10 -
    4*z8^2*z11 - z8*z9^2 - 4*z8*z9*z11 - z8*z10^2 - 8*z8*z11^2 +
    4*z9^2*z10 - 6*z9*z10^2 - 4*z9*z10*z11 - 4*z9*z11^2 + 3*z10*z11^2
    + 3*z11^3, 2*z1^3 - 2*z1^2*z2 + 4*z1^2*z3 - 2*z1^2*z4 - 2*z1^2*z5
    + z1^2*z6 + 3*z1^2*z7 - z1^2*z9 - 7*z1^2*z11 - 4*z1*z2^2 -
    6*z1*z2*z3 + 2*z1*z2*z4 + 4*z1*z2*z5 - 10*z1*z2*z6 - 4*z1*z2*z9 +
    4*z1*z2*z10 + 3*z1*z2*z11 - z1*z3^2 - 2*z1*z3*z4 + 7*z1*z3*z5 -
    8*z1*z3*z6 - 6*z1*z3*z7 + 2*z1*z3*z8 + 6*z1*z3*z9 + 4*z1*z3*z10 +
    13*z1*z3*z11 + 3*z1*z4^2 - z1*z4*z5 - 8*z1*z4*z6 + 4*z1*z4*z7 -
    2*z1*z4*z10 + z1*z4*z11 + 2*z1*z5*z6 + 2*z1*z5*z7 + 3*z1*z5*z8 -
    3*z1*z5*z9 + 4*z1*z5*z10 - z1*z5*z11 + 2*z1*z6*z7 - 2*z1*z6*z8 +
    3*z1*z6*z9 - 6*z1*z6*z10 + 10*z1*z6*z11 + 3*z1*z7^2 + 5*z1*z7*z8 +
    16*z1*z7*z10 - z1*z7*z11 + 4*z1*z8*z9 + z1*z8*z11 + 3*z1*z9^2 +
    11*z1*z9*z10 + z1*z9*z11 + 2*z2^3 - 5*z2^2*z3 - 2*z2^2*z4 +
    z2^2*z5 - 7*z2^2*z6 + 3*z2^2*z9 - 5*z2^2*z10 - z2^2*z11 +
    13*z2*z3^2 + 10*z2*z3*z6 + 8*z2*z3*z7 + 11*z2*z3*z8 - 4*z2*z3*z10
    - 4*z2*z3*z11 - 4*z2*z4^2 + 4*z2*z4*z5 - 3*z2*z4*z6 + 6*z2*z4*z8 +
    3*z2*z4*z9 + 3*z2*z4*z11 + 2*z2*z5^2 - 6*z2*z5*z7 - z2*z5*z8 +
    9*z2*z5*z10 + 4*z2*z5*z11 + 8*z2*z6*z8 - 4*z2*z6*z9 - 7*z2*z7^2 +
    3*z2*z7*z11 - 7*z2*z8^2 + 2*z2*z8*z9 + 5*z2*z8*z10 + 3*z2*z8*z11 -
    z2*z9^2 - z2*z9*z10 + 16*z2*z9*z11 + 8*z2*z10^2 - 7*z2*z10*z11 -
    3*z2*z11^2 - 15*z3^2*z5 - z3^2*z6 + 4*z3^2*z7 + z3^2*z8 -
    2*z3^2*z9 - 3*z3^2*z10 - 13*z3^2*z11 + 13*z3*z4*z6 - 3*z3*z4*z7 +
    7*z3*z4*z9 + 3*z3*z4*z10 + 6*z3*z4*z11 - 8*z3*z5*z6 - 5*z3*z5*z7 -
    z3*z5*z8 + 4*z3*z5*z10 - 7*z3*z5*z11 - 3*z3*z6*z7 + 7*z3*z6*z9 -
    2*z3*z6*z10 - 11*z3*z6*z11 - 4*z3*z7*z8 + 4*z3*z8^2 + 13*z3*z8*z9
    - 12*z3*z8*z10 - 7*z3*z9^2 + 2*z3*z9*z10 + 14*z3*z10*z11 -
    12*z3*z11^2 + 15*z4^3 + 5*z4^2*z5 + 18*z4^2*z6 + 10*z4^2*z7 +
    z4^2*z8 + 5*z4^2*z9 + 22*z4^2*z11 + z4*z5^2 - z4*z5*z6 +
    7*z4*z5*z7 - 11*z4*z5*z8 + 3*z4*z5*z10 + 12*z4*z5*z11 + 4*z4*z6^2
    + 16*z4*z6*z7 + 3*z4*z6*z8 + 2*z4*z6*z9 - 4*z4*z6*z10 +
    16*z4*z6*z11 + 7*z4*z7^2 - 5*z4*z7*z8 + 5*z4*z7*z9 - 7*z4*z7*z10 -
    9*z4*z7*z11 + 3*z4*z8^2 + 10*z4*z8*z9 - 9*z4*z8*z10 - 8*z4*z8*z11
    + 10*z4*z9^2 - 14*z4*z9*z10 + 3*z4*z9*z11 + 4*z4*z10^2 +
    9*z4*z10*z11 - 3*z4*z11^2 + 2*z5^2*z6 + 3*z5^2*z7 + z5^2*z8 -
    z5^2*z9 - 2*z5*z6^2 + 9*z5*z6*z7 + z5*z6*z9 + 2*z5*z6*z10 +
    9*z5*z6*z11 + 7*z5*z7^2 + 2*z5*z7*z8 + 2*z5*z7*z9 + z5*z7*z10 -
    z5*z7*z11 + 2*z5*z8^2 + 4*z5*z8*z9 - 2*z5*z8*z10 - 6*z5*z8*z11 +
    2*z5*z9^2 + 2*z5*z9*z10 - 8*z5*z9*z11 - z5*z10*z11 + 2*z5*z11^2 -
    z6^2*z10 + 2*z6^2*z11 + 4*z6*z7^2 + 6*z6*z7*z8 + 5*z6*z7*z9 +
    11*z6*z7*z11 + 2*z6*z8^2 + 5*z6*z8*z9 - 3*z6*z8*z10 - z6*z8*z11 +
    5*z6*z9^2 - 5*z6*z9*z10 + 5*z6*z9*z11 + 2*z6*z10^2 + 2*z6*z10*z11
    + z6*z11^2 - 2*z7^3 - 13*z7^2*z8 - 4*z7^2*z9 - 6*z7^2*z10 -
    4*z7^2*z11 - 2*z7*z8^2 - 12*z7*z8*z9 - z7*z8*z10 - 14*z7*z9*z11 +
    4*z8^3 - 5*z8^2*z9 + 3*z8^2*z10 - 3*z8^2*z11 - 5*z8*z9^2 +
    3*z8*z9*z10 - 4*z8*z10^2 - z8*z11^2 + 5*z9^2*z10 + 4*z9*z10*z11 -
    5*z9*z11^2 - z10^2*z11 + z10*z11^2 - z11^3, 4*z1^3 - z1^2*z2 -
    5*z1^2*z3 + z1^2*z4 + 3*z1^2*z5 - z1^2*z6 + z1^2*z7 - z1^2*z9 +
    5*z1*z2^2 - 6*z1*z2*z3 - 2*z1*z2*z4 - z1*z2*z5 + z1*z2*z6 -
    5*z1*z2*z9 - 4*z1*z2*z10 - z1*z2*z11 + 3*z1*z3^2 + 2*z1*z3*z5 -
    10*z1*z3*z6 - 7*z1*z3*z7 + 4*z1*z3*z8 - 13*z1*z3*z9 - 3*z1*z3*z10
    + z1*z3*z11 - 3*z1*z4^2 + 2*z1*z4*z5 + 7*z1*z4*z7 + 3*z1*z4*z8 +
    3*z1*z4*z10 + z1*z4*z11 + z1*z5*z7 - z1*z5*z8 - z1*z5*z9 -
    3*z1*z5*z11 - z1*z6^2 + z1*z6*z7 - 3*z1*z6*z8 + 2*z1*z6*z9 +
    z1*z6*z10 - z1*z6*z11 + 2*z1*z7^2 - z1*z7*z8 - 13*z1*z7*z10 +
    3*z1*z7*z11 + z1*z8*z9 - z1*z8*z11 + 2*z1*z9^2 - 5*z1*z9*z10 +
    z1*z9*z11 - 7*z1*z11^2 + 8*z2^3 - 2*z2^2*z3 - z2^2*z5 + 4*z2^2*z6
    - 6*z2^2*z7 - 6*z2^2*z8 - 2*z2^2*z9 - 2*z2^2*z10 + 2*z2^2*z11 +
    4*z2*z3^2 + z2*z3*z5 - 2*z2*z3*z6 + z2*z3*z8 - 3*z2*z3*z10 -
    z2*z3*z11 - 8*z2*z4^2 + 5*z2*z4*z5 + 3*z2*z4*z8 - z2*z4*z9 -
    z2*z5^2 + 3*z2*z5*z7 + 4*z2*z5*z8 + 3*z2*z5*z9 - 4*z2*z5*z10 +
    3*z2*z6*z9 + 7*z2*z7^2 + 2*z2*z7*z9 - 4*z2*z7*z10 - 3*z2*z7*z11 -
    4*z2*z8^2 - 5*z2*z8*z9 + 2*z2*z8*z10 + z2*z8*z11 - 2*z2*z9*z10 +
    3*z2*z9*z11 - z2*z10^2 - 10*z2*z10*z11 - 3*z2*z11^2 - 4*z3^2*z6 +
    2*z3^2*z7 + 2*z3^2*z8 - 2*z3^2*z9 + 10*z3^2*z10 + 15*z3^2*z11 +
    4*z3*z4*z6 - 4*z3*z4*z7 - 7*z3*z4*z8 + 2*z3*z4*z9 - 4*z3*z4*z10 -
    2*z3*z4*z11 - 3*z3*z5*z6 + 8*z3*z5*z7 + 3*z3*z5*z8 - 2*z3*z5*z9 +
    4*z3*z5*z11 + 4*z3*z6*z7 - 9*z3*z6*z9 - 3*z3*z6*z10 + 5*z3*z6*z11
    + z3*z7*z8 + 13*z3*z7*z11 - z3*z8^2 + 5*z3*z8*z9 + 3*z3*z8*z10 -
    10*z3*z9^2 - 5*z3*z9*z10 + 2*z3*z9*z11 - 8*z3*z10^2 +
    21*z3*z10*z11 + 2*z3*z11^2 - 8*z4^3 + 10*z4^2*z5 - 5*z4^2*z6 -
    11*z4^2*z7 - z4^2*z8 - 2*z4^2*z9 + 2*z4^2*z10 - 7*z4^2*z11 +
    z4*z5^2 + 10*z4*z5*z6 + 2*z4*z5*z7 - 15*z4*z5*z8 - 4*z4*z5*z9 +
    4*z4*z5*z10 - 3*z4*z5*z11 - z4*z6^2 - 8*z4*z6*z7 + z4*z6*z8 -
    4*z4*z6*z9 + z4*z6*z10 + 4*z4*z6*z11 - 16*z4*z7^2 - 19*z4*z7*z8 -
    6*z4*z7*z9 - 5*z4*z7*z10 - 5*z4*z7*z11 - 9*z4*z8^2 - 4*z4*z8*z9 -
    3*z4*z8*z10 - 13*z4*z8*z11 + 4*z4*z9^2 - 7*z4*z9*z10 - 6*z4*z9*z11
    - 2*z4*z10^2 - 5*z4*z10*z11 - 4*z4*z11^2 + z5^2*z7 - z5^2*z9 +
    z5^2*z11 - z5*z6*z7 - 5*z5*z6*z8 - 4*z5*z6*z9 + 6*z5*z6*z11 -
    z5*z7^2 - 6*z5*z7*z8 + z5*z7*z10 + 6*z5*z7*z11 - 4*z5*z8^2 -
    4*z5*z8*z9 + 3*z5*z8*z10 + 4*z5*z8*z11 - 2*z5*z9*z10 + 4*z5*z9*z11
    + 2*z5*z10*z11 - 5*z5*z11^2 - 4*z6^2*z7 - z6^2*z9 - 2*z6*z7^2 -
    7*z6*z7*z8 - 7*z6*z7*z9 - 4*z6*z7*z10 + 6*z6*z7*z11 - 5*z6*z8^2 -
    6*z6*z8*z9 - 2*z6*z8*z10 - z6*z8*z11 - 5*z6*z9*z10 - z6*z9*z11 -
    3*z6*z10*z11 + 6*z6*z11^2 - 6*z7^3 - z7^2*z8 - 2*z7^2*z9 +
    4*z7^2*z10 - 11*z7^2*z11 + 7*z7*z8^2 + 6*z7*z8*z9 + 3*z7*z8*z10 -
    4*z7*z8*z11 + 2*z7*z9^2 - 2*z7*z9*z10 - z7*z10^2 + 2*z7*z10*z11 +
    2*z8^3 + 4*z8^2*z9 - 3*z8^2*z11 + 2*z8*z9^2 + z8*z9*z10 -
    3*z8*z9*z11 + z8*z10^2 + 7*z8*z10*z11 + 5*z8*z11^2 - 3*z9^2*z10 -
    2*z9*z10^2 + 5*z9*z10*z11 + 2*z9*z11^2 - 2*z10^2*z11 + 4*z10*z11^2
    - 6*z11^3, z1^3 - z1^2*z2 - z1^2*z3 - 6*z1^2*z4 + 2*z1^2*z5 -
    4*z1^2*z6 - 6*z1^2*z7 + 2*z1^2*z9 + 2*z1^2*z11 - 7*z1*z2^2 +
    5*z1*z2*z3 - 2*z1*z2*z4 - 3*z1*z2*z5 - z1*z2*z6 + 2*z1*z2*z9 +
    z1*z2*z10 - z1*z2*z11 + 4*z1*z3^2 - 9*z1*z3*z5 + 4*z1*z3*z6 -
    3*z1*z3*z7 + 4*z1*z3*z8 + 4*z1*z3*z9 - 9*z1*z3*z10 - 4*z1*z3*z11 -
    3*z1*z4^2 - 4*z1*z4*z5 - 7*z1*z4*z6 - 5*z1*z4*z7 + 6*z1*z4*z8 +
    3*z1*z4*z10 - 2*z1*z4*z11 - 4*z1*z5*z6 + z1*z5*z7 - 2*z1*z5*z8 +
    11*z1*z5*z9 - z1*z5*z10 - z1*z5*z11 - 2*z1*z6^2 - 9*z1*z6*z7 +
    7*z1*z6*z8 - 2*z1*z6*z10 - 4*z1*z7*z8 - 7*z1*z7*z10 - z1*z7*z11 -
    7*z1*z8*z9 - 9*z1*z8*z11 - z1*z9^2 - z1*z9*z10 + 3*z1*z11^2 -
    9*z2^3 + z2^2*z3 + z2^2*z4 - 5*z2^2*z5 - 3*z2^2*z6 + 4*z2^2*z7 -
    5*z2^2*z9 + 3*z2^2*z10 - 3*z2^2*z11 - 8*z2*z3^2 + z2*z3*z4 -
    2*z2*z3*z5 - 2*z2*z3*z6 - 5*z2*z3*z7 - 2*z2*z3*z8 + 5*z2*z3*z10 +
    2*z2*z3*z11 + 6*z2*z4^2 + 7*z2*z4*z5 + 3*z2*z4*z6 + 5*z2*z4*z8 -
    3*z2*z4*z11 + z2*z5^2 + 11*z2*z5*z7 + 7*z2*z5*z8 + 16*z2*z5*z9 -
    7*z2*z6*z8 + 3*z2*z6*z9 - 3*z2*z7^2 - z2*z7*z9 - 3*z2*z7*z10 +
    z2*z7*z11 + 11*z2*z8^2 + 4*z2*z8*z9 - 3*z2*z8*z10 - 2*z2*z8*z11 +
    2*z2*z9^2 + 2*z2*z9*z10 - 3*z2*z9*z11 - 2*z2*z10^2 + 6*z2*z10*z11
    - 2*z2*z11^2 - 6*z3^2*z5 + 2*z3^2*z6 - 6*z3^2*z7 - 2*z3^2*z8 +
    9*z3^2*z9 - 9*z3^2*z10 + 6*z3^2*z11 + 5*z3*z4*z5 + 17*z3*z4*z6 +
    z3*z4*z7 + 7*z3*z4*z8 - 3*z3*z4*z9 + 2*z3*z4*z10 + 2*z3*z4*z11 +
    3*z3*z5*z6 + 7*z3*z5*z7 + 8*z3*z5*z8 - 6*z3*z5*z9 + 7*z3*z5*z11 +
    z3*z6*z7 + 5*z3*z6*z9 - z3*z6*z10 + 2*z3*z6*z11 + 6*z3*z7*z8 +
    4*z3*z7*z11 - 6*z3*z8^2 + 9*z3*z8*z10 + 11*z3*z9^2 - 5*z3*z9*z10 -
    4*z3*z9*z11 + 4*z3*z10^2 - 18*z3*z10*z11 + 3*z3*z11^2 - 26*z4^3 -
    6*z4^2*z5 + 12*z4^2*z6 - 10*z4^2*z7 + 5*z4^2*z8 - 2*z4^2*z9 -
    7*z4^2*z10 - 11*z4^2*z11 - 4*z4*z5*z6 + 2*z4*z5*z7 + 7*z4*z5*z8 -
    2*z4*z5*z9 + 6*z4*z5*z10 - 10*z4*z5*z11 + 7*z4*z6^2 - z4*z6*z7 +
    5*z4*z6*z9 - 3*z4*z6*z10 - 2*z4*z6*z11 + 8*z4*z7^2 + 3*z4*z7*z8 +
    5*z4*z7*z9 + 10*z4*z7*z10 + 2*z4*z7*z11 - 9*z4*z8^2 + 8*z4*z8*z10
    + 9*z4*z8*z11 - 2*z4*z9^2 + 11*z4*z9*z10 + 4*z4*z9*z11 +
    2*z4*z10^2 - 14*z4*z10*z11 - 3*z4*z11^2 - z5^2*z8 - 2*z5*z6^2 +
    6*z5*z6*z7 - z5*z6*z9 - 2*z5*z7^2 - 4*z5*z7*z8 - z5*z7*z9 +
    5*z5*z7*z10 - 15*z5*z7*z11 - 2*z5*z8^2 - 10*z5*z8*z9 - 3*z5*z8*z10
    - z5*z8*z11 + z5*z9^2 + 4*z5*z11^2 + z6^2*z7 - 2*z6^2*z8 -
    z6^2*z11 + 4*z6*z7^2 + z6*z7*z9 + 2*z6*z7*z10 + 4*z6*z7*z11 +
    z6*z8^2 - 2*z6*z8*z10 - 2*z6*z8*z11 - z6*z9^2 + z6*z9*z11 +
    2*z6*z10^2 - 6*z6*z10*z11 + 2*z7^3 + 2*z7^2*z8 + 4*z7^2*z9 +
    7*z7^2*z10 - 6*z7^2*z11 - 3*z7*z8^2 + 4*z7*z8*z9 - 2*z7*z8*z10 +
    2*z7*z8*z11 + 2*z7*z9^2 + 2*z7*z9*z10 + 8*z7*z9*z11 - 3*z7*z10^2 +
    z7*z10*z11 - 8*z7*z11^2 - 2*z8^3 + 3*z8^2*z9 - 3*z8^2*z10 +
    2*z8^2*z11 + 3*z8*z9^2 - z8*z9*z10 - 7*z8*z9*z11 - z8*z10^2 -
    4*z8*z10*z11 + 7*z8*z11^2 + 2*z9*z10^2 - 3*z9*z10*z11 - z9*z11^2 -
    z10^2*z11 - 4*z10*z11^2 + 3*z11^3, 3*z1^3 - 4*z1^2*z2 + z1^2*z3 -
    2*z1^2*z4 - 5*z1^2*z5 + 4*z1^2*z6 + 3*z1^2*z7 - 3*z1^2*z11 -
    5*z1*z2^2 + z1*z2*z3 + 3*z1*z2*z4 + z1*z2*z6 + z1*z2*z7 +
    2*z1*z2*z9 + z1*z2*z11 + 6*z1*z3^2 - 7*z1*z3*z5 - 7*z1*z3*z6 +
    9*z1*z3*z7 + 3*z1*z3*z8 + 3*z1*z3*z9 + 2*z1*z3*z10 - 9*z1*z3*z11 +
    2*z1*z4^2 - z1*z4*z6 + 4*z1*z4*z7 + 2*z1*z4*z8 - 2*z1*z4*z10 +
    z1*z4*z11 - z1*z5*z6 - z1*z5*z8 - 3*z1*z5*z9 - 2*z1*z5*z10 -
    5*z1*z5*z11 + 2*z1*z6^2 - z1*z6*z7 + 11*z1*z6*z8 - 4*z1*z6*z10 -
    4*z1*z7^2 + 2*z1*z7*z8 - 7*z1*z7*z10 - 2*z1*z7*z11 - 2*z1*z8*z9 -
    5*z1*z8*z11 + 2*z1*z9^2 + 6*z1*z9*z10 - 7*z1*z9*z11 + z1*z11^2 -
    2*z2^3 + 2*z2^2*z3 + 3*z2^2*z4 + 3*z2^2*z5 + 10*z2^2*z6 +
    2*z2^2*z7 + 8*z2^2*z9 + z2^2*z11 + 2*z2*z3^2 - z2*z3*z4 -
    4*z2*z3*z5 - z2*z3*z6 + 3*z2*z3*z7 + 2*z2*z3*z8 + z2*z3*z10 +
    6*z2*z3*z11 - 4*z2*z4^2 - 4*z2*z4*z5 - z2*z4*z6 - z2*z4*z8 +
    z2*z4*z11 + 2*z2*z5^2 - 6*z2*z5*z7 - 8*z2*z5*z8 + z2*z5*z9 +
    3*z2*z5*z10 - 2*z2*z6*z8 + 3*z2*z6*z9 - 2*z2*z7^2 - 4*z2*z7*z9 -
    14*z2*z7*z10 - z2*z7*z11 + 3*z2*z8^2 - 12*z2*z8*z9 + 3*z2*z8*z11 +
    3*z2*z9*z10 - 3*z2*z9*z11 + z2*z10^2 + 4*z2*z10*z11 + 3*z2*z11^2 -
    3*z3^2*z5 + z3^2*z6 + 2*z3^2*z7 - 3*z3^2*z8 + 11*z3^2*z9 -
    9*z3^2*z10 + 7*z3^2*z11 + 2*z3*z4*z5 - 5*z3*z4*z6 - 2*z3*z4*z7 -
    z3*z4*z8 - z3*z4*z9 - 2*z3*z4*z10 + 2*z3*z4*z11 - 8*z3*z5*z6 -
    2*z3*z5*z7 - 2*z3*z5*z8 + 10*z3*z5*z9 - 4*z3*z5*z11 + z3*z6*z7 +
    5*z3*z6*z9 + 13*z3*z6*z10 - 5*z3*z6*z11 - 13*z3*z7*z8 -
    15*z3*z7*z11 - 2*z3*z8^2 - 4*z3*z8*z9 + 5*z3*z8*z10 + 3*z3*z9^2 -
    14*z3*z9*z10 - 2*z3*z9*z11 + 5*z3*z10^2 + 5*z3*z10*z11 +
    8*z3*z11^2 - 23*z4^3 + 5*z4^2*z5 - 25*z4^2*z6 - 18*z4^2*z9 -
    12*z4^2*z10 - 19*z4^2*z11 - 11*z4*z5^2 + 3*z4*z5*z6 + 3*z4*z5*z7 +
    4*z4*z5*z8 + z4*z5*z9 - 5*z4*z5*z10 + 8*z4*z5*z11 - 5*z4*z6^2 -
    2*z4*z6*z7 + 5*z4*z6*z8 - 11*z4*z6*z9 - 6*z4*z6*z10 - 7*z4*z6*z11
    + 2*z4*z7^2 - 2*z4*z7*z8 - 11*z4*z7*z9 + z4*z7*z10 + 4*z4*z7*z11 +
    5*z4*z8^2 + 10*z4*z8*z9 - z4*z8*z10 + 12*z4*z8*z11 - z4*z9^2 -
    6*z4*z9*z10 - 2*z4*z9*z11 + z4*z10^2 - 7*z4*z10*z11 - z4*z11^2 -
    6*z5^2*z6 - 3*z5^2*z7 - 3*z5^2*z8 - 3*z5^2*z9 + 6*z5^2*z11 -
    z5*z6^2 + 7*z5*z6*z7 + 2*z5*z6*z8 - z5*z6*z9 - 6*z5*z6*z10 -
    z5*z6*z11 + z5*z7^2 + 6*z5*z7*z8 - 6*z5*z7*z9 + 3*z5*z7*z10 -
    4*z5*z7*z11 + z5*z8^2 - 7*z5*z8*z9 - 3*z5*z8*z10 + z5*z8*z11 +
    z5*z9^2 + z5*z9*z10 - 4*z5*z9*z11 + 2*z5*z10*z11 + 6*z5*z11^2 -
    z6^2*z7 + z6^2*z8 - z6^2*z9 - z6^2*z10 - z6*z7^2 - 6*z6*z7*z8 -
    6*z6*z7*z9 - 2*z6*z7*z10 + 4*z6*z7*z11 - z6*z8^2 - 4*z6*z8*z10 +
    7*z6*z8*z11 + z6*z10^2 - 2*z6*z10*z11 - z6*z11^2 - 2*z7^3 -
    6*z7^2*z8 - 4*z7^2*z9 + 5*z7^2*z10 + 3*z7^2*z11 - 12*z7*z8^2 -
    2*z7*z8*z9 + 2*z7*z8*z10 - 6*z7*z9*z10 - 5*z7*z9*z11 - 2*z7*z10^2
    - z7*z10*z11 - 7*z7*z11^2 - 4*z8^3 - 2*z8^2*z9 - 2*z8^2*z10 -
    z8^2*z11 - 3*z8*z9*z11 + 3*z8*z11^2 + z9^2*z10 + 2*z9*z10^2 -
    z9*z10*z11 - z9*z11^2 + 3*z11^3, 6*z1^3 + 4*z1^2*z2 - 2*z1^2*z3 -
    3*z1^2*z4 + z1^2*z5 - z1^2*z7 - 5*z1^2*z9 + 12*z1*z2^2 - z1*z2*z4
    + 2*z1*z2*z6 - 3*z1*z2*z9 - 2*z1*z2*z10 + 8*z1*z3^2 - 7*z1*z3*z5 -
    6*z1*z3*z6 - 14*z1*z3*z7 + 5*z1*z3*z8 - 6*z1*z3*z9 + 17*z1*z3*z10
    + 3*z1*z3*z11 - 3*z1*z4^2 + z1*z4*z5 + 2*z1*z4*z6 + 3*z1*z4*z7 +
    5*z1*z4*z8 - 3*z1*z4*z10 - z1*z4*z11 + 2*z1*z5*z8 - 3*z1*z5*z9 -
    z1*z5*z10 + z1*z5*z11 + 4*z1*z6^2 - z1*z6*z7 + 6*z1*z6*z8 +
    z1*z6*z10 - 2*z1*z6*z11 + 2*z1*z7*z10 + 3*z1*z7*z11 + 16*z1*z8*z9
    + 8*z1*z8*z11 + 7*z1*z9^2 - 3*z1*z9*z10 - 2*z1*z11^2 + 6*z2^3 -
    5*z2^2*z3 + 6*z2^2*z4 + 5*z2^2*z5 - z2^2*z6 - 4*z2^2*z7 - z2^2*z8
    + 11*z2^2*z9 - 3*z2^2*z10 - 2*z2^2*z11 - 3*z2*z3^2 - z2*z3*z4 +
    5*z2*z3*z5 + 9*z2*z3*z6 + 3*z2*z3*z7 + z2*z3*z8 - 3*z2*z3*z10 -
    15*z2*z3*z11 - 2*z2*z4*z5 - z2*z4*z6 - 16*z2*z4*z8 + 2*z2*z4*z9 +
    z2*z4*z11 - z2*z5^2 - z2*z5*z8 - 3*z2*z5*z10 + 14*z2*z6*z8 +
    3*z2*z6*z9 - z2*z7^2 + 3*z2*z7*z9 + 5*z2*z7*z10 + 2*z2*z7*z11 -
    5*z2*z8^2 + 4*z2*z8*z9 + 3*z2*z8*z10 + 5*z2*z8*z11 + 11*z2*z9^2 -
    4*z2*z9*z10 + 5*z2*z9*z11 - 5*z2*z10*z11 - 3*z2*z11^2 + 9*z3^2*z5
    - 7*z3^2*z6 + 5*z3^2*z7 - 2*z3^2*z8 - 10*z3^2*z9 - 5*z3^2*z10 +
    12*z3^2*z11 - 5*z3*z4*z5 - z3*z4*z6 - 2*z3*z4*z7 - 5*z3*z4*z8 +
    z3*z4*z9 - z3*z4*z10 - 7*z3*z4*z11 - 3*z3*z5*z6 - 4*z3*z5*z7 -
    7*z3*z5*z8 + 3*z3*z5*z9 + 2*z3*z5*z10 + 5*z3*z5*z11 + 6*z3*z6*z7 -
    z3*z6*z10 - 11*z3*z6*z11 + 3*z3*z7*z8 - 3*z3*z7*z11 + 2*z3*z8^2 +
    11*z3*z8*z9 - 10*z3*z8*z10 + 5*z3*z9^2 + 11*z3*z9*z10 - 4*z3*z10^2
    + 18*z3*z10*z11 - 9*z3*z11^2 + 15*z4^3 + 9*z4^2*z6 + 12*z4^2*z7 -
    3*z4^2*z8 + 13*z4^2*z9 + 24*z4^2*z10 + 5*z4^2*z11 - 3*z4*z5^2 -
    5*z4*z5*z6 + 8*z4*z5*z7 - 5*z4*z5*z8 + 8*z4*z5*z9 - z4*z5*z10 -
    12*z4*z5*z11 + 4*z4*z6*z7 - 9*z4*z6*z8 + 6*z4*z6*z9 + 5*z4*z6*z10
    - 3*z4*z6*z11 + 7*z4*z7^2 - 6*z4*z7*z8 + 22*z4*z7*z9 + 7*z4*z7*z10
    - 2*z4*z7*z11 + 3*z4*z8^2 + z4*z8*z9 - 8*z4*z8*z10 - z4*z8*z11 +
    14*z4*z9^2 - 7*z4*z9*z10 + 5*z4*z9*z11 + 2*z4*z10^2 +
    13*z4*z10*z11 - 3*z4*z11^2 - 2*z5*z6^2 - 9*z5*z6*z7 - 2*z5*z6*z8 +
    2*z5*z6*z10 + 5*z5*z6*z11 + 9*z5*z7^2 + 3*z5*z7*z8 + 2*z5*z7*z9 -
    7*z5*z7*z10 + 13*z5*z7*z11 - z5*z8^2 + z5*z8*z9 + 2*z5*z8*z10 +
    4*z5*z8*z11 - 4*z5*z9^2 + 2*z5*z9*z10 + 9*z5*z9*z11 - 2*z5*z10*z11
    - 6*z5*z11^2 - 7*z6^2*z7 + 2*z6^2*z9 - z6^2*z10 - 2*z6^2*z11 -
    z6*z7^2 - 11*z6*z7*z8 + z6*z7*z9 - 3*z6*z7*z10 + 8*z6*z7*z11 -
    13*z6*z8^2 - 3*z6*z8*z9 + 5*z6*z8*z10 + 5*z6*z8*z11 + 7*z6*z9^2 -
    3*z6*z9*z10 + 3*z6*z9*z11 + 8*z6*z10*z11 + 4*z6*z11^2 + 4*z7^3 +
    6*z7^2*z8 + 6*z7^2*z9 + 4*z7^2*z11 + 11*z7*z8^2 + 4*z7*z8*z9 +
    4*z7*z8*z10 + z7*z8*z11 - 10*z7*z9^2 + z7*z9*z10 - z7*z9*z11 +
    3*z7*z10^2 - 6*z7*z10*z11 + 14*z7*z11^2 + 4*z8^3 - 9*z8^2*z9 +
    4*z8^2*z10 - 3*z8^2*z11 - 17*z8*z9^2 + 9*z8*z9*z10 + 8*z8*z9*z11 -
    z8*z10*z11 - z8*z11^2 + 2*z9^2*z10 - 2*z9*z10^2 + 11*z9*z10*z11 +
    3*z9*z11^2 - 10*z11^3, 2*z1^3 + z1^2*z3 + 4*z1^2*z4 - 12*z1^2*z7 -
    3*z1^2*z9 + 2*z1^2*z11 + 6*z1*z2^2 - 6*z1*z2*z3 - 2*z1*z2*z4 -
    3*z1*z2*z5 + 8*z1*z2*z6 - 3*z1*z2*z9 - z1*z2*z10 - 4*z1*z2*z11 -
    18*z1*z3^2 - 12*z1*z3*z5 - 5*z1*z3*z6 + z1*z3*z7 - z1*z3*z8 +
    9*z1*z3*z9 - 10*z1*z3*z10 - z1*z3*z11 + z1*z4^2 + 2*z1*z4*z5 -
    15*z1*z4*z6 - z1*z4*z7 + 3*z1*z4*z8 - 2*z1*z4*z10 - 2*z1*z4*z11 -
    z1*z5*z6 + 2*z1*z5*z7 - z1*z5*z8 + 2*z1*z5*z9 - 2*z1*z6^2 +
    5*z1*z6*z7 - 4*z1*z6*z8 - z1*z6*z9 - 2*z1*z6*z10 + z1*z6*z11 +
    7*z1*z7^2 + z1*z7*z8 + 16*z1*z7*z10 - z1*z7*z11 - 4*z1*z8*z9 -
    5*z1*z8*z11 + z1*z9^2 + 2*z1*z9*z10 + 2*z1*z9*z11 - z1*z11^2 +
    6*z2^3 - 9*z2^2*z3 - 8*z2^2*z4 - 8*z2^2*z7 - 7*z2^2*z8 - 7*z2^2*z9
    - 4*z2^2*z11 + 3*z2*z3^2 + 5*z2*z3*z4 + 6*z2*z3*z5 - 9*z2*z3*z6 +
    6*z2*z3*z7 + 3*z2*z3*z8 - 3*z2*z3*z10 + 2*z2*z3*z11 - 3*z2*z4^2 +
    4*z2*z4*z5 + z2*z4*z8 - z2*z4*z9 - z2*z5^2 + 9*z2*z5*z7 +
    4*z2*z5*z8 + 11*z2*z5*z9 - 3*z2*z5*z10 - 2*z2*z5*z11 + 5*z2*z6*z8
    + 8*z2*z7^2 + 4*z2*z7*z9 + 8*z2*z7*z10 + 3*z2*z7*z11 + z2*z8^2 +
    5*z2*z8*z9 - z2*z8*z11 + z2*z9*z10 + 5*z2*z9*z11 + 2*z2*z10^2 -
    4*z2*z10*z11 - 3*z2*z11^2 - 14*z3^2*z5 - z3^2*z6 - 8*z3^2*z8 -
    z3^2*z9 - 18*z3^2*z10 - 4*z3^2*z11 - 4*z3*z4*z5 + 10*z3*z4*z6 -
    2*z3*z4*z7 - 11*z3*z4*z8 - 3*z3*z4*z9 - 2*z3*z4*z10 + 13*z3*z5*z7
    - z3*z5*z8 + z3*z5*z10 - z3*z6*z9 - z3*z6*z10 - 14*z3*z6*z11 +
    7*z3*z7*z8 - 5*z3*z7*z11 + 3*z3*z8^2 + z3*z8*z9 + 2*z3*z8*z10 +
    7*z3*z9^2 + z3*z9*z10 - 5*z3*z9*z11 - 6*z3*z10^2 - 3*z3*z11^2 +
    15*z4^3 + 4*z4^2*z5 + 16*z4^2*z6 + 10*z4^2*z7 - 2*z4^2*z8 +
    15*z4^2*z9 + 14*z4^2*z10 + 20*z4^2*z11 + 8*z4*z5^2 - 4*z4*z5*z6 +
    10*z4*z5*z7 + 13*z4*z5*z8 + 18*z4*z5*z9 + 2*z4*z5*z10 -
    6*z4*z5*z11 + 3*z4*z6^2 - 3*z4*z6*z7 - 6*z4*z6*z8 + 7*z4*z6*z9 +
    3*z4*z6*z10 + z4*z6*z11 - 10*z4*z7^2 + 2*z4*z7*z8 + 5*z4*z7*z9 -
    5*z4*z7*z10 + 5*z4*z8^2 - 3*z4*z8*z9 + 6*z4*z8*z10 + 4*z4*z8*z11 +
    z4*z9*z10 - 4*z4*z10^2 + 13*z4*z10*z11 + 8*z4*z11^2 + 4*z5^2*z6 +
    2*z5^2*z7 + 2*z5^2*z9 - 4*z5^2*z11 + z5*z6*z7 + 8*z5*z6*z8 +
    9*z5*z6*z9 + 3*z5*z6*z10 - 3*z5*z6*z11 + 2*z5*z7^2 - 4*z5*z7*z8 +
    11*z5*z7*z9 - 5*z5*z7*z10 + 4*z5*z7*z11 - 2*z5*z8^2 - 7*z5*z8*z9 +
    z5*z8*z10 - 9*z5*z8*z11 + 3*z5*z9^2 + 3*z5*z9*z10 - 6*z5*z9*z11 -
    4*z5*z10*z11 + 4*z5*z11^2 - 8*z6^2*z7 + z6^2*z9 - z6^2*z11 +
    2*z6*z7^2 + 2*z6*z7*z8 + 3*z6*z7*z9 - 3*z6*z7*z10 + 10*z6*z7*z11 -
    z6*z8*z9 + 5*z6*z8*z10 + 3*z6*z8*z11 + z6*z9^2 + 2*z6*z9*z10 +
    2*z6*z9*z11 - 2*z6*z10^2 + 3*z6*z10*z11 - 2*z6*z11^2 - 4*z7^3 -
    8*z7^2*z8 + 6*z7^2*z9 - 6*z7^2*z10 - 4*z7^2*z11 + z7*z8^2 +
    3*z7*z8*z9 - 4*z7*z8*z10 - 5*z7*z8*z11 + 2*z7*z9^2 + 2*z7*z9*z10 -
    3*z7*z9*z11 + z7*z10^2 - z7*z10*z11 + 9*z7*z11^2 + 3*z8^3 +
    6*z8^2*z9 + 2*z8^2*z10 + z8*z9^2 - z8*z9*z10 - 4*z8*z9*z11 -
    3*z8*z10^2 - 5*z8*z10*z11 - 2*z8*z11^2 + 4*z9^2*z10 - 2*z9*z10^2 -
    2*z9*z10*z11 - 5*z9*z11^2 + z10*z11^2 + 4*z11^3, 2*z1^3 +
    2*z1^2*z2 - z1^2*z3 - 5*z1^2*z4 - z1^2*z5 + 4*z1^2*z6 - 2*z1^2*z7
    + 4*z1^2*z9 + 3*z1^2*z11 + 4*z1*z2^2 - z1*z2*z3 + z1*z2*z4 -
    6*z1*z2*z5 + 7*z1*z2*z6 + 3*z1*z2*z9 - 3*z1*z2*z10 - 5*z1*z3^2 +
    2*z1*z3*z4 - 9*z1*z3*z5 - 4*z1*z3*z6 - 10*z1*z3*z7 - 5*z1*z3*z8 +
    7*z1*z3*z9 + 7*z1*z3*z10 - 4*z1*z3*z11 + 6*z1*z4^2 + z1*z4*z6 +
    2*z1*z4*z7 + 2*z1*z4*z8 - z1*z4*z11 - 2*z1*z5*z6 + 2*z1*z5*z7 -
    6*z1*z5*z8 + 5*z1*z5*z9 + z1*z5*z10 - 3*z1*z5*z11 - 19*z1*z6*z7 -
    8*z1*z6*z8 + z1*z6*z9 - 3*z1*z6*z10 + 5*z1*z6*z11 + z1*z7^2 +
    z1*z7*z8 + 9*z1*z7*z10 - 6*z1*z7*z11 - 7*z1*z8*z9 - 4*z1*z8*z11 +
    7*z1*z9^2 + 12*z1*z9*z10 + z1*z9*z11 + 2*z2^3 - 5*z2^2*z3 -
    10*z2^2*z4 - 4*z2^2*z6 - 8*z2^2*z7 - 5*z2^2*z8 - 2*z2^2*z10 +
    z2^2*z11 + 6*z2*z3^2 + 4*z2*z3*z4 + 3*z2*z3*z5 + 3*z2*z3*z6 +
    3*z2*z3*z8 + 3*z2*z3*z10 + 4*z2*z3*z11 - 5*z2*z4^2 + 8*z2*z4*z5 +
    2*z2*z4*z8 - z2*z4*z9 - 2*z2*z5^2 - 5*z2*z5*z8 - 2*z2*z5*z10 +
    z2*z5*z11 + 2*z2*z6*z8 + 2*z2*z7^2 - 2*z2*z7*z9 + 11*z2*z7*z10 +
    3*z2*z7*z11 + 5*z2*z8^2 - 5*z2*z8*z9 + 2*z2*z8*z10 - 2*z2*z8*z11 -
    3*z2*z9^2 + 3*z2*z9*z10 + 4*z2*z9*z11 + z2*z10^2 - 4*z2*z10*z11 -
    11*z3^2*z5 + 3*z3^2*z6 - 2*z3^2*z7 - 9*z3^2*z8 + 5*z3^2*z9 -
    9*z3^2*z10 + 3*z3^2*z11 + 15*z3*z4*z6 - 2*z3*z4*z7 + 8*z3*z4*z8 -
    3*z3*z4*z9 - z3*z4*z10 + 10*z3*z4*z11 - 12*z3*z5*z6 + 5*z3*z5*z7 +
    5*z3*z5*z8 + 2*z3*z5*z9 - 6*z3*z5*z11 - 5*z3*z6*z7 - 16*z3*z6*z9 -
    3*z3*z6*z10 - 4*z3*z6*z11 - 14*z3*z7*z8 + 8*z3*z7*z11 + 3*z3*z8^2
    - 3*z3*z8*z9 - 4*z3*z9*z10 - 3*z3*z9*z11 - 2*z3*z10^2 +
    15*z3*z10*z11 + 4*z3*z11^2 - 3*z4^3 - 7*z4^2*z5 + 6*z4^2*z6 -
    12*z4^2*z7 - 15*z4^2*z8 - z4^2*z9 + 4*z4^2*z10 + 14*z4^2*z11 -
    z4*z5^2 - 11*z4*z5*z6 + 14*z4*z5*z8 - 4*z4*z5*z10 + 10*z4*z5*z11 -
    z4*z6^2 + 5*z4*z6*z7 + 12*z4*z6*z9 - 13*z4*z6*z10 + 4*z4*z6*z11 -
    12*z4*z7^2 - 12*z4*z7*z8 - 7*z4*z7*z9 - z4*z7*z10 + 3*z4*z7*z11 -
    z4*z8^2 - 6*z4*z8*z9 + 12*z4*z8*z10 + 13*z4*z8*z11 - 2*z4*z9^2 +
    2*z4*z9*z11 - 6*z4*z10^2 + 9*z4*z10*z11 + 17*z4*z11^2 + 2*z5^2*z6
    - 2*z5^2*z8 + 2*z5^2*z9 - 3*z5^2*z11 - z5*z6^2 - 7*z5*z6*z7 +
    11*z5*z6*z8 + 5*z5*z6*z9 + z5*z6*z11 + z5*z7*z8 + z5*z7*z9 -
    9*z5*z7*z10 + 12*z5*z7*z11 + z5*z8^2 - 2*z5*z8*z9 - 3*z5*z8*z10 -
    8*z5*z8*z11 + 4*z5*z9^2 + 5*z5*z9*z10 - 3*z5*z9*z11 - 5*z5*z10*z11
    - 3*z5*z11^2 + z6^2*z7 + 3*z6^2*z8 + 3*z6^2*z9 - 2*z6^2*z10 -
    2*z6^2*z11 - 9*z6*z7^2 - z6*z7*z8 + 4*z6*z7*z9 - 4*z6*z7*z10 -
    4*z6*z8^2 - z6*z8*z9 + 10*z6*z8*z10 + 7*z6*z8*z11 + z6*z9^2 +
    4*z6*z9*z11 - 2*z6*z10^2 - 3*z6*z10*z11 + 3*z6*z11^2 - 2*z7^3 -
    7*z7^2*z8 - 4*z7^2*z9 - 14*z7^2*z10 + 10*z7^2*z11 - 9*z7*z8^2 -
    10*z7*z8*z9 - 9*z7*z8*z10 - 3*z7*z8*z11 + 5*z7*z9*z10 - 2*z7*z10^2
    - 9*z7*z10*z11 - z7*z11^2 - 2*z8^3 + z8^2*z9 - z8^2*z10 +
    2*z8^2*z11 - z8*z9^2 + z8*z9*z10 - 3*z8*z9*z11 - 2*z8*z10^2 -
    8*z8*z10*z11 + 5*z9^2*z10 + z9*z10*z11 - 5*z9*z11^2 + 2*z10*z11^2
    + 3*z11^3, 5*z1^3 + 3*z1^2*z2 - 3*z1^2*z3 - z1^2*z4 + z1^2*z5 +
    z1^2*z6 - 7*z1^2*z7 - 3*z1^2*z9 + z1^2*z11 + 9*z1*z2^2 -
    5*z1*z2*z3 - 4*z1*z2*z4 - 3*z1*z2*z5 + 3*z1*z2*z6 + 3*z1*z2*z9 -
    4*z1*z2*z10 - 3*z1*z2*z11 + 4*z1*z3^2 + 2*z1*z3*z4 - 6*z1*z3*z6 +
    4*z1*z3*z7 + z1*z3*z9 + 7*z1*z3*z10 - 3*z1*z3*z11 - 3*z1*z4^2 +
    4*z1*z4*z5 - 5*z1*z4*z6 + 2*z1*z4*z7 - 2*z1*z5*z6 - z1*z5*z7 -
    2*z1*z5*z8 + 2*z1*z5*z9 - 3*z1*z5*z10 - z1*z5*z11 - z1*z6^2 +
    9*z1*z6*z8 + 2*z1*z6*z10 + z1*z6*z11 - 3*z1*z7*z8 - 17*z1*z7*z10 -
    5*z1*z8*z9 + 4*z1*z9^2 - 4*z1*z9*z10 - z1*z9*z11 + 3*z2^3 +
    4*z2^2*z4 + 2*z2^2*z5 + 7*z2^2*z6 - 3*z2^2*z7 - 6*z2^2*z8 +
    9*z2^2*z9 + 2*z2^2*z11 - 11*z2*z3^2 + 2*z2*z3*z4 + 3*z2*z3*z5 +
    5*z2*z3*z6 - 9*z2*z3*z8 + z2*z3*z10 + 6*z2*z3*z11 - 4*z2*z4^2 +
    7*z2*z4*z5 - 13*z2*z4*z8 - 3*z2*z4*z9 - z2*z5^2 + 10*z2*z5*z7 +
    4*z2*z5*z8 + 10*z2*z5*z9 - 6*z2*z5*z10 - z2*z5*z11 + 3*z2*z6*z8 +
    8*z2*z6*z9 + 6*z2*z7^2 - 3*z2*z7*z9 + z2*z7*z10 - z2*z7*z11 +
    7*z2*z8^2 - 9*z2*z8*z9 + 6*z2*z9^2 + 3*z2*z9*z10 - 3*z2*z10^2 -
    4*z2*z10*z11 + 3*z2*z11^2 - 10*z3^2*z5 - z3^2*z7 - z3^2*z8 +
    z3^2*z9 - 5*z3^2*z10 + 25*z3^2*z11 - z3*z4*z5 + z3*z4*z6 -
    4*z3*z4*z7 + 6*z3*z4*z8 - 4*z3*z4*z9 - 5*z3*z4*z10 - z3*z4*z11 +
    z3*z5*z6 + 12*z3*z5*z7 - 3*z3*z5*z8 + z3*z5*z9 - 3*z3*z5*z10 +
    5*z3*z5*z11 + 4*z3*z6*z7 + 9*z3*z6*z9 - 4*z3*z6*z10 - 2*z3*z6*z11
    - 12*z3*z7*z8 - 5*z3*z7*z11 - 2*z3*z8^2 - 2*z3*z8*z9 - 7*z3*z8*z10
    + 4*z3*z9^2 + 12*z3*z9*z10 - 3*z3*z9*z11 - 3*z3*z10^2 +
    5*z3*z10*z11 + 2*z3*z11^2 - 10*z4^3 + 12*z4^2*z5 - 7*z4^2*z6 -
    6*z4^2*z7 + 9*z4^2*z8 + 5*z4^2*z10 - 18*z4^2*z11 - 6*z4*z5^2 +
    8*z4*z5*z6 + 5*z4*z5*z7 - 15*z4*z5*z8 + 5*z4*z5*z9 - 2*z4*z5*z10 -
    10*z4*z5*z11 - 3*z4*z6*z7 - z4*z6*z9 + 3*z4*z6*z10 - 9*z4*z6*z11 -
    13*z4*z7^2 - 6*z4*z7*z8 + 6*z4*z7*z9 + 10*z4*z7*z10 - 6*z4*z7*z11
    - 5*z4*z8^2 + z4*z8*z9 + 4*z4*z8*z10 - 4*z4*z8*z11 + 4*z4*z9^2 +
    4*z4*z9*z10 - 5*z4*z9*z11 - 5*z4*z10^2 - 3*z4*z10*z11 - 6*z4*z11^2
    - 4*z5^2*z6 - 2*z5^2*z7 - z5^2*z8 - 2*z5^2*z9 + 4*z5^2*z11 -
    2*z5*z6^2 + 4*z5*z6*z7 - 8*z5*z6*z8 - 3*z5*z6*z9 - 3*z5*z6*z10 +
    5*z5*z6*z11 - 2*z5*z7*z8 + 2*z5*z7*z9 + 3*z5*z7*z10 - 2*z5*z7*z11
    - 6*z5*z8^2 - 12*z5*z8*z9 + 3*z5*z8*z10 + 8*z5*z8*z11 -
    3*z5*z9*z10 + 3*z5*z9*z11 + 3*z5*z10*z11 + z5*z11^2 - 4*z6^2*z7 -
    z6^2*z10 - 3*z6^2*z11 - z6*z7^2 - 11*z6*z7*z8 - 8*z6*z7*z9 +
    2*z6*z7*z10 + 10*z6*z7*z11 - 10*z6*z8^2 - 8*z6*z8*z9 + z6*z8*z10 -
    z6*z8*z11 + 2*z6*z9^2 - z6*z9*z10 - z6*z10^2 + 6*z6*z11^2 - 2*z7^3
    + 7*z7^2*z8 + 4*z7^2*z9 + 8*z7^2*z10 + 3*z7^2*z11 + 4*z7*z8^2 +
    8*z7*z8*z9 + 9*z7*z8*z10 - 8*z7*z8*z11 - 2*z7*z9^2 - 5*z7*z9*z10 +
    3*z7*z9*z11 - 3*z7*z10^2 + 5*z7*z10*z11 - z7*z11^2 - 2*z8^3 +
    2*z8^2*z9 + z8^2*z10 - 2*z8^2*z11 - 4*z8*z9^2 - 4*z8*z9*z10 -
    2*z8*z9*z11 + 2*z8*z10^2 + z8*z10*z11 + 6*z8*z11^2 + z9^2*z10 +
    5*z9*z10*z11 - z10^2*z11 + 2*z10*z11^2 - 4*z11^3 ];
  else
  z1,z2,z3,z4,z5,z6,z7,z8,z9,z10 := Explode([R.i : i in [1..10]]);
  quads := [ z1*z6 + z1*z7 - z2*z5 + z2*z7 + z4*z7, z1*z7 - z2*z5 -
    z2*z6 + z3*z6 - z5*z7 - z6*z7, z3*z7 - z4*z6 + z4*z7 + z5*z8 +
    z5*z10 + z6*z9, z1*z2 - z2*z9 + z3*z5 + z3*z9 - z4*z9 + z5*z10,
    z1*z2 - z2*z8 - z2*z10 + z3*z5 + z3*z8 - z4*z9 - z4*z10 - z6*z10,
    z1*z3 + 2*z1*z7 + z1*z10 + z2^2 + z2*z7 - z3^2 + z3*z4 - z3*z5 +
    z3*z9, z1*z5 + z1*z6 + z2*z5 - z3*z5 + z4*z5 + z5^2 + z5*z6 -
    z5*z7 + z5*z8 + z6*z9, z1*z7 - z1*z8 + z2^2 - z2*z3 + z2*z7 -
    z3*z5 + z3*z9 + z6*z10 - z7*z8 + z7*z9, z1*z4 - z1*z6 + z2^2 -
    z2*z3 + 2*z2*z4 + z2*z5 - z3*z4 - z3*z5 + z4^2 + z4*z5, z1*z6 -
    z1*z7 + z2*z6 - z2*z7 - z3*z6 + 2*z3*z7 + z5*z10 + z6*z10 - z7*z8
    + z7*z9, z1*z2 + 2*z1*z7 + 2*z2^2 - 2*z2*z3 + z2*z4 - z2*z10 -
    z3*z5 + z3*z7 - z4*z10 - z5*z7 - z6*z7, z1^2 + 2*z1*z2 - z1*z3 +
    z1*z4 + z1*z5 + z1*z6 + z1*z8 + z1*z10 - z2*z8 + z2*z9 + z3*z8 -
    z6*z10, z2*z3 + z2*z6 + z2*z8 + z2*z10 + z3*z5 + z3*z6 - z3*z7 +
    z4*z6 + z4*z8 + z4*z10 + z5*z6 + z6^2 - z6*z7, z1*z2 + z1*z7 +
    z1*z10 + z2^2 - z2*z3 + z2*z7 + z2*z9 - z3*z10 + z4*z8 - z4*z9 -
    z4*z10 + z5*z8 + z6*z9 ];
  cubics := [ z1*z2*z10 + z1*z6*z10 + z2^2*z10 - z2*z3*z7 + z2*z4*z10
    - z2*z5*z10 + z2*z6*z7 - z2*z7*z9 + z2*z8*z10 - z2*z9*z10 +
    z2*z10^2 + z3*z5*z10 + z4*z5*z8 - z4*z6^2 + z4*z6*z7 + z4*z8*z10 +
    z4*z10^2 + z5*z8*z9 + z6*z8*z9 - z6*z9*z10 + z7^3 - z7*z8*z9 -
    z7*z9*z10 - z8*z9*z10 - z9*z10^2, z1^2*z8 - z1*z2*z6 + z1*z2*z9 +
    z1*z2*z10 - z1*z3*z8 + z1*z4*z7 + z1*z4*z8 + z1*z6*z7 + z1*z8^2 -
    z1*z8*z9 + z1*z8*z10 + z1*z9^2 - z2^2*z7 - z2*z3*z9 - z2*z3*z10 +
    z2*z4*z6 + z2*z5*z9 + z2*z6*z8 - z3*z5*z6 - z3*z5*z7 - z3*z6*z7 -
    z3*z6*z8 - z3*z7*z8 - z3*z7*z9 + z3*z7*z10 + z4^2*z7 + z4*z5*z7 +
    z4*z6*z9 + z5*z7*z9 - z5*z8*z9 + z5*z9^2 + z5*z9*z10 + z5*z10^2 +
    z6*z7*z9 + z6*z7*z10 + z7^3 - z7*z9^2 - z7*z9*z10 - z9^2*z10 -
    z9*z10^2 ];
  end if;
  return quads,cubics;
end function;

// The quadric intersections in the proofs of Propositions 5.3 and 6.2

function QuadricIntersection(k,T,z1,z2,z3,z4)
  if k eq 1 then 
    q1 := 2*T*z1^2 + 3*T*z1*z2 - (5*T - 2)*z1*z3 - 3*T^2*z1*z4
      + T*z2^2 - 4*T*z2*z3 - 2*T^2*z2*z4 + 2*(2*T - 1)*z3^2
      + T*(4*T - 1)*z3*z4 + T^3*z4^2;
    q2 := (T + 1)^2*z1^2 + T*(2*T + 1)*z1*z2 - (T + 1)^2*z1*z3
      - T*(T + 1)^2*z1*z4 + T^2*z2^2 - 2*T^2*z2*z3 - T^3*z2*z4;
  else
    q1 := z1^2 - T*z1*z2 + T*z1*z3 + T*z2*z3 - T*z3^2 + T*z3*z4;
    q2 := z1*z3 - T*z2*z3 + 2*(T + 1)*z1*z4 - (T^2 - 1)*z2*z4
        + (T + 1)*z4^2;
  end if;
  return [q1,q2];
end function;
  
function QI_Simplified(k,T,u1,u2,u3,u4)
  if k eq 1 then 
    q1 := u1*u2 + u1*u3 + (T + 1)*u2^2 - u3*u4;
    q2 := u1*u4 + T*u2^2 - T^2*u2*u4 - T*u3*u4;
  else
    q1 := u1^2 + T*u1*u2 + T*u2*u3 - T*u1*u4;
    q2 := u1*u3 + T*u1*u4 + u2*u4 + u3*u4;
  end if;
  return [q1,q2];
end function;

// The inverses for the maps Sigma_1 -> Sigma and Sigma_3 -> Sigma
// as promised at the end of the proofs of Propositions 5.3 and 6.2

function InverseMap(k,T,x,y);
  if k eq 1 then 
  zz := [ 1, (-T - 1)/(x^2 - T^2*x)*y + (-T^3 - T^2 + T + 1)/(x -
    T^2), (T*x - T^4 - T^3)/(x^3 - 2*T^2*x^2 + T^4*x)*y + ((T^3 -
    2*T^2 - 2*T)*x^2 + (-T^6 + 4*T^4 + 2*T^3)*x - T^7 - T^6)/(x^3 -
    2*T^2*x^2 + T^4*x), (-2*x + (2*T^3 + 2*T^2))/(x^3 - 2*T^2*x^2 +
    T^4*x)*y + (1/T*x^3 + (-2*T^2 + T + 3)*x^2 + (2*T^5 - 5*T^3 -
    2*T^2)*x + (2*T^6 + T^5 - T^4))/(x^3 - 2*T^2*x^2 + T^4*x),
    (7*T*x^3 + (-12*T^4 - 12*T^3 + 7*T^2)*x^2 + (4*T^7 + 15*T^6 -
    2*T^5 - 13*T^4)*x + (T^10 - 3*T^9 - 3*T^8 + 7*T^7 + 6*T^6))/(x^5 +
    (-T^3 - 3*T^2 + T)*x^4 + (3*T^5 + 3*T^4 - 3*T^3)*x^3 + (-3*T^7 -
    T^6 + 3*T^5)*x^2 + (T^9 - T^7)*x)*y + (-4*x^5 + (11*T^3 + T^2 -
    15*T)*x^4 + (-12*T^6 - 9*T^5 + 34*T^4 + 18*T^3 - 11*T^2)*x^3 +
    (4*T^9 + 12*T^8 - 24*T^7 - 38*T^6 + 15*T^5 + 18*T^4)*x^2 + (T^12 -
    4*T^11 + 2*T^10 + 23*T^9 + T^8 - 19*T^7 - 4*T^6)*x + (T^13 -
    3*T^12 - 2*T^11 + 6*T^10 + T^9 - 3*T^8))/(x^5 + (-T^3 - 3*T^2 +
    T)*x^4 + (3*T^5 + 3*T^4 - 3*T^3)*x^3 + (-3*T^7 - T^6 + 3*T^5)*x^2
    + (T^9 - T^7)*x), (7*x^3 + (-12*T^3 - 12*T^2 + 7*T)*x^2 + (4*T^6 +
    15*T^5 - 2*T^4 - 13*T^3)*x + (T^9 - 3*T^8 - 3*T^7 + 7*T^6 +
    6*T^5))/(x^5 + (-T^3 - 3*T^2 + T)*x^4 + (3*T^5 + 3*T^4 -
    3*T^3)*x^3 + (-3*T^7 - T^6 + 3*T^5)*x^2 + (T^9 - T^7)*x)*y +
    (-4/T*x^5 + (11*T^2 + T - 15)*x^4 + (-12*T^5 - 9*T^4 + 34*T^3 +
    18*T^2 - 11*T)*x^3 + (4*T^8 + 12*T^7 - 24*T^6 - 38*T^5 + 15*T^4 +
    18*T^3)*x^2 + (T^11 - 4*T^10 + 2*T^9 + 23*T^8 + T^7 - 19*T^6 -
    4*T^5)*x + (T^12 - 3*T^11 - 2*T^10 + 6*T^9 + T^8 - 3*T^7))/(x^5 +
    (-T^3 - 3*T^2 + T)*x^4 + (3*T^5 + 3*T^4 - 3*T^3)*x^3 + (-3*T^7 -
    T^6 + 3*T^5)*x^2 + (T^9 - T^7)*x), (-T*x^3 + (2*T^4 + T^3 -
    2*T^2)*x^2 + (-T^7 - T^6 + 3*T^5 + 2*T^4 - T^3)*x - 2*T^8 - 3*T^7
    + T^5)/(x^5 + (-T^3 - 3*T^2 + T)*x^4 + (3*T^5 + 3*T^4 - 3*T^3)*x^3
    + (-3*T^7 - T^6 + 3*T^5)*x^2 + (T^9 - T^7)*x)*y + (x^5 + (-2*T^3 -
    T^2 + 3*T)*x^4 + (2*T^6 + T^5 - 5*T^4 - 2*T^3 + 3*T^2)*x^3 + (-T^9
    + 5*T^7 - 7*T^5 - 2*T^4 + T^3)*x^2 + (-3*T^10 - T^9 + 8*T^8 +
    4*T^7 - 3*T^6 - T^5)*x - 2*T^11 - 2*T^10 + 2*T^9 + 2*T^8)/(x^5 +
    (-T^3 - 3*T^2 + T)*x^4 + (3*T^5 + 3*T^4 - 3*T^3)*x^3 + (-3*T^7 -
    T^6 + 3*T^5)*x^2 + (T^9 - T^7)*x), (-2*T*x^3 + (2*T^4 + 2*T^3 -
    T^2)*x^2 + (-2*T^6 - T^5 + 2*T^4 + T^3)*x + (T^8 + T^7 - T^6 -
    T^5))/(x^5 + (-T^3 - 3*T^2 + T)*x^4 + (3*T^5 + 3*T^4 - 3*T^3)*x^3
    + (-3*T^7 - T^6 + 3*T^5)*x^2 + (T^9 - T^7)*x)*y + ((T - 1)/T*x^4 +
    (-3*T^3 - T^2 + 3*T - 2)*x^3 + (2*T^6 + 4*T^5 - T^4 + 3*T^2 -
    T)*x^2 + (-2*T^8 - 3*T^7 + T^3)*x + (T^10 + 2*T^9 - 2*T^7 -
    T^6))/(x^4 + (-T^3 - 3*T^2 + T)*x^3 + (3*T^5 + 3*T^4 - 3*T^3)*x^2
    + (-3*T^7 - T^6 + 3*T^5)*x + (T^9 - T^7)), (2/T^2*x^3 + (-4*T^2 -
    2*T + 2)/T*x^2 + (3*T^4 + 5*T^3 - 2*T^2 - 3*T)*x - 2*T^6 - T^5 +
    2*T^4 + T^3)/(x^4 - 3*T^2*x^3 + 3*T^4*x^2 - T^6*x)*y + (-1/T^3*x^5
    + (2*T^2 - T - 4)/T^2*x^4 + (-4*T^4 + 5*T^3 + 13*T^2 + 3*T -
    3)/T*x^3 + (3*T^6 + 2*T^5 - 19*T^4 - 12*T^3 + 7*T^2 + 5*T)*x^2 +
    (-2*T^8 + 4*T^7 + 12*T^6 - T^5 - 7*T^4 - 2*T^3)*x - 2*T^9 - T^8 +
    2*T^7 + T^6)/(x^4 - 3*T^2*x^3 + 3*T^4*x^2 - T^6*x), ((-6*T -
    1)*x^4 + (10*T^4 + 9*T^3 - 5*T^2 - T)*x^3 + (-4*T^7 - 9*T^6 +
    5*T^5 + 11*T^4 + T^3)*x^2 + (T^9 - 3*T^8 - 8*T^7 - 3*T^6 + T^5)*x
    + (T^11 + 2*T^10 - 2*T^8 - T^7))/(x^6 + (-T^3 - 3*T^2 + T)*x^5 +
    (3*T^5 + 3*T^4 - 3*T^3)*x^4 + (-3*T^7 - T^6 + 3*T^5)*x^3 + (T^9 -
    T^7)*x^2)*y + (2*x^6 + (-8*T^3 + 3*T^2 + 11*T + 1)*x^5 + (10*T^6 +
    T^5 - 31*T^4 - 7*T^3 + 10*T^2 + T)*x^4 + (-4*T^9 - 5*T^8 + 27*T^7
    + 21*T^6 - 27*T^5 - 16*T^4 + T^3)*x^3 + (T^11 - 8*T^10 - 13*T^9 +
    18*T^8 + 24*T^7 - 3*T^6 - 5*T^5)*x^2 + (T^13 + 2*T^12 - 7*T^11 -
    13*T^10 + T^9 + 9*T^8 + 3*T^7)*x + (T^14 + 2*T^13 - 2*T^11 -
    T^10))/(x^6 + (-T^3 - 3*T^2 + T)*x^5 + (3*T^5 + 3*T^4 - 3*T^3)*x^4
    + (-3*T^7 - T^6 + 3*T^5)*x^3 + (T^9 - T^7)*x^2), (-1/T^2*x^2 +
    (-3*T^2 - 1)/T*x + (2*T^4 + 2*T^3 + T^2 + T))/(x^3 - 2*T^2*x^2 +
    T^4*x)*y + ((T^2 + T + 1)/T^2*x^3 + (-3*T^4 + T^3 + 3*T^2 + T +
    1)/T*x^2 + (2*T^6 - 6*T^4 - 5*T^3 - 4*T^2 - T)*x + (2*T^7 + 2*T^6
    + 2*T^5 + 2*T^4))/(x^3 - 2*T^2*x^2 + T^4*x) ];
  else // k = 3
  zz := [ ((T + 2)*x^2 + (T^4 + T^3 + T)*x + (T^5 + T^4))*y - 1/T*x^4
    + (-T^2 - 2*T - 3)*x^3 - T*x^2, (-x^2 - T*x + T^3)*y + (2*T +
    1)*x^3 + (T^3 + 3*T^2 + T)*x^2, ((T^3 + T^2)*x^3 + (T^7 + 2*T^6 -
    T^5 - 3*T^4 - T^3)*x^2 + (2*T^8 + 4*T^7 - 3*T^5 - T^4)*x + (T^9 +
    2*T^8 + T^7))*y + (-T^5 - 3*T^4 - 2*T^3)*x^4 + (-T^6 - T^5 + 2*T^4
    + 2*T^3)*x^3 + (T^6 + 2*T^5 + T^4)*x^2, ((T^2 + T)*x^4 + (2*T^6 +
    6*T^5 + 4*T^4)*x^3 + (-T^8 + T^7 + 9*T^6 + 9*T^5 + 2*T^4)*x^2 +
    (-2*T^9 - 3*T^8 + 2*T^7 + 4*T^6 + T^5)*x - T^10 - 2*T^9 - T^8)/(x
    - T^2)*y + ((-2*T^4 - 6*T^3 - 5*T^2 - T)*x^5 + (T^6 - 5*T^4 -
    4*T^3)*x^4 + (T^7 - 4*T^5 - 3*T^4)*x^3 + (-T^7 - 2*T^6 -
    T^5)*x^2)/(x - T^2), ((T^6 + 3*T^5 + 2*T^4 - T^3 - T^2)*x^2 + (T^7
    + 3*T^6 + 3*T^5 + T^4)*x)*y + (-T^4 - 2*T^3 - T^2)*x^4 + (T^4 +
    2*T^3 + T^2)*x^3, ((T^5 + 2*T^4 + T^3)*x^3 + (T^9 + 2*T^8 - 2*T^7
    - 6*T^6 - 3*T^5)*x^2 + (2*T^10 + 5*T^9 + T^8 - 6*T^7 - 5*T^6 -
    T^5)*x + (T^11 + 3*T^10 + 3*T^9 + T^8))/(x - T^2)*y + ((-T^7 -
    3*T^6 - 3*T^5 - T^4)*x^4 + (-T^8 - 2*T^7 + 2*T^5 + T^4)*x^3 + (T^8
    + 3*T^7 + 3*T^6 + T^5)*x^2)/(x - T^2), ((-2*T^3 - 4*T^2)*x^4 +
    (-T^7 - 4*T^6 - 2*T^5 + 2*T^4 - 3*T^3)*x^3 + (-T^8 - 7*T^7 - 7*T^6
    + 2*T^5)*x^2 + (T^9 - 2*T^8 - 5*T^7 - T^6)*x + (T^10 + T^9))/(x -
    T^2)*y + (T*x^6 + (T^5 + 5*T^4 + 7*T^3 + 5*T^2)*x^5 + (3*T^5 +
    5*T^4 + 3*T^3)*x^4 + (-T^7 + T^5)*x^3 + (T^7 + T^6)*x^2)/(x -
    T^2), ((-2*T^2 - 4*T)*x^4 + (-T^6 - 4*T^5 - 2*T^4 + 2*T^3 -
    3*T^2)*x^3 + (-T^7 - 7*T^6 - 7*T^5 + 2*T^4)*x^2 + (T^8 - 2*T^7 -
    5*T^6 - T^5)*x + (T^9 + T^8))/(x - T^2)*y + (x^6 + (T^4 + 5*T^3 +
    7*T^2 + 5*T)*x^5 + (3*T^4 + 5*T^3 + 3*T^2)*x^4 + (-T^6 + T^4)*x^3
    + (T^6 + T^5)*x^2)/(x - T^2), ((-T^2 - T)*x^4 + (-T^6 - 4*T^5 -
    3*T^4 - T^3 - T^2)*x^3 + (-T^7 - 7*T^6 - 7*T^5 - T^4)*x^2 + (T^8 -
    2*T^7 - 4*T^6 - T^5)*x + (T^9 + T^8))/(x - T^2)*y + ((T^4 + 4*T^3
    + 4*T^2 + T)*x^5 + (T^5 + 6*T^4 + 6*T^3 + T^2)*x^4 + (3*T^5 +
    3*T^4)*x^3 + (T^6 + T^5)*x^2)/(x - T^2), (-1/T*x^4 + (2*T - 1)*x^3
    + (-3*T^3 + T^2)*x^2 + (T^5 - 3*T^4 - T^3)*x + T^6)*y + (2*T +
    1)/T*x^5 + (-T^3 - 3*T^2 + 2*T + 1)*x^4 + (-T^4 - 3*T^3 + T^2)*x^3
    + T^3*x^2, (x^4 + (T^4 + 2*T^3 - T^2 + T)*x^3 + (-T^6 + T^5 +
    7*T^4 + T^3)*x^2 + (-2*T^7 - 2*T^6 + 5*T^5 + 2*T^4)*x - T^8 -
    2*T^7)*y + (-T^2 - 3*T - 1)*x^5 + (T^4 - 5*T^2 - T)*x^4 + (T^5 -
    4*T^3)*x^3 + (-T^5 - 2*T^4)*x^2, ((-T^3 - 2*T^2 - T)*x^3 + (-3*T^4
    - 5*T^3 - 2*T^2)*x^2 + (T^6 - T^5 - 3*T^4 - T^3)*x + (T^7 +
    T^6))*y + (T + 1)*x^5 + (3*T^2 + 3*T)*x^4 + (3*T^3 + 3*T^2)*x^3 +
    (T^4 + T^3)*x^2 ];
  end if;
  return zz;
end function;

// Some polynomials used in computing the j-maps on Z(17,1)

function ExtraRelationsforJmap1(S)
  u,v,w,z4,z5,z6,z7,z8,z9,z10,z11 := Explode([S.i : i in [1..11]]);
  gg := [ -z4, 2*u*v - u*w + z5 - z6 + 2*z8 + z9 + 2*z11, -u^7*v +
    2*u^3*v^3 + 2*u^7*w - u^5*v*w - 8*u^3*v^2*w - u*v^3*w - 5*u^5*w^2
    + 15*u^3*v*w^2 + 4*u*v^2*w^2 - 4*u^3*w^3 - u*v*w^3 - 3*u*w^4 -
    3*u^4*v*z4 - 2*u^2*v^2*z4 + 4*u^4*w*z4 + 3*u^2*v*w*z4 - 3*v^2*w*z4
    - 5*u^2*w^2*z4 + 2*v*w^2*z4 + w^3*z4 + u^3*z4^2 + u*v*z4^2 -
    4*u*w*z4^2 - 2*u^4*v*z5 + 2*u^2*v^2*z5 - u^4*w*z5 + 8*u^2*v*w*z5 +
    2*v^2*w*z5 - 10*u^2*w^2*z5 + 2*v*w^2*z5 - w^3*z5 + 2*u^3*z4*z5 +
    2*u*v*z4*z5 - 6*u*w*z4*z5 - 3*z4^2*z5 + u^3*z5^2 - 4*u*w*z5^2 -
    3*z4*z5^2 + 3*z5^3 + u^6*z6 - 3*u^4*v*z6 + u^2*v^2*z6 + u^2*v*w*z6
    + v^2*w*z6 + 7*u^2*w^2*z6 + v*w^2*z6 - 2*w^3*z6 + 7*u^3*z4*z6 -
    10*u*v*z4*z6 + u*w*z4*z6 - 2*z4^2*z6 - u*w*z5*z6 - 3*z4*z5*z6 -
    u^3*z6^2 + u*v*z6^2 - z4*z6^2 + z5*z6^2 - u^4*v*z7 + u^2*v^2*z7 -
    2*u^4*w*z7 + u^2*v*w*z7 - v^2*w*z7 + 2*u^2*w^2*z7 + v*w^2*z7 -
    u^3*z4*z7 - u*v*z4*z7 + 7*u*w*z4*z7 - z4^2*z7 - u^3*z5*z7 +
    u*v*z5*z7 - u*w*z5*z7 + 3*z4*z5*z7 + u*v*z6*z7 + 4*z4*z6*z7 +
    u*v*z7^2 + u*w*z7^2 + z4*z7^2 + u^4*v*z8 + u^2*v^2*z8 - 3*u^4*w*z8
    - 9*u^2*v*w*z8 + 2*v^2*w*z8 + 8*u^2*w^2*z8 + v*w^2*z8 - w^3*z8 +
    2*u^3*z4*z8 + u*v*z4*z8 - 6*u*w*z4*z8 - 2*z4^2*z8 - 2*u*v*z5*z8 +
    3*u*w*z5*z8 - 2*z4*z5*z8 + 2*z5^2*z8 - u^3*z6*z8 + 3*u*v*z6*z8 -
    2*u*w*z6*z8 - 2*z4*z6*z8 - z5*z6*z8 + z6^2*z8 - u*v*z7*z8 +
    4*u*w*z7*z8 + z5*z7*z8 + z7^2*z8 + u*v*z8^2 - u*w*z8^2 - 4*z4*z8^2
    - z5*z8^2 + z6*z8^2 - u^4*v*z9 + u^2*v^2*z9 + 3*u^2*v*w*z9 +
    v^2*w*z9 + u^2*w^2*z9 - 2*w^3*z9 + 4*u*w*z4*z9 - 2*z4^2*z9 +
    u^3*z5*z9 - u*v*z5*z9 - z4*z5*z9 + u^3*z6*z9 - 2*u*v*z6*z9 +
    2*u*w*z6*z9 + z4*z6*z9 + z5*z6*z9 - u*v*z7*z9 + 2*u*w*z7*z9 +
    5*z4*z7*z9 + z7^2*z9 - 2*u*w*z8*z9 + z5*z8*z9 - z7*z8*z9 + z8^2*z9
    + u^3*z9^2 - u*v*z9^2 + u*w*z9^2 + z4*z9^2 - z5*z9^2 - z6*z9^2 +
    z7*z9^2 - 2*z8*z9^2 - u^6*z10 + 2*u^4*v*z10 - u^2*v^2*z10 + u^4*w*z10
    - 3*u^2*v*w*z10 - 2*v^2*w*z10 + v*w^2*z10 - 3*w^3*z10 - 2*u^3*z4*z10 +
    4*u*v*z4*z10 - 6*u*w*z4*z10 - u^3*z5*z10 + u*v*z5*z10 - z4*z5*z10 -
    u*v*z6*z10 + u*w*z6*z10 - 8*z4*z6*z10 + u*w*z7*z10 - z4*z7*z10 +
    u^3*z8*z10 - u*v*z8*z10 - u*w*z8*z10 + 3*z4*z8*z10 + z7*z8*z10 +
    z8^2*z10 + u^3*z9*z10 - 2*u*v*z9*z10 + 2*u*w*z9*z10 - 2*z4*z9*z10 -
    z5*z9*z10 - z6*z9*z10 + 2*z7*z9*z10 - 2*z8*z9*z10 + z9^2*z10 - u*v*z10^2
    + u*w*z10^2 + z4*z10^2 - z6*z10^2 + z9*z10^2 + 2*u^2*v^2*z11 - u^4*w*z11
    - u^2*v*w*z11 - u^2*w^2*z11 + u^3*z4*z11 + u*v*z4*z11 - 4*u*w*z4*z11 -
    u^3*z5*z11 + 3*u*v*z5*z11 - 2*u*w*z5*z11 - 4*z4*z5*z11 + z5^2*z11 -
    u*w*z6*z11 - 6*z4*z6*z11 - u*v*z7*z11 + u*w*z7*z11 - 2*z4*z7*z11 -
    z5*z7*z11 + z6*z7*z11 + z7^2*z11 - 3*z4*z8*z11 + z5*z8*z11 - u*w*z9*z11
    + z6*z9*z11 - z7*z9*z11 + z8*z9*z11 + u^3*z10*z11 - u*v*z10*z11 +
    2*z4*z10*z11 - z5*z10*z11 + 2*z6*z10*z11 + z7*z10*z11 + z8*z10*z11 -
    z9*z10*z11 + 2*z5*z11^2, 6869166055942531/32*u^13*v +
    7196619633587825/32*u^11*v^2 - 16475965851601*u^9*v^3 -
    2250304378573*u^7*v^4 - 23808555372*u^5*v^5 + 242547012*u^3*v^6 -
    127532*u*v^7 + 826479632338399/16*u^13*w +
    3280652757178235/16*u^11*v*w - 8116027750341159/16*u^9*v^2*w -
    58675940334149/4*u^7*v^3*w + 298542609313/2*u^5*v^4*w +
    1743711641*u^3*v^5*w + 24156624*u*v^6*w -
    115947252674637933/64*u^11*w^2 + 8210391836719603/32*u^9*v*w^2 +
    195160020304131/8*u^9*w^3 - 1930198590997/2*u^7*w^4 +
    7557617686*u^5*w^5 - 78594280*u^3*w^6 + 13944*u*w^7 -
    40736952907494745/256*u^12*z4 + 2691548567697509/16*u^10*v*z4 +
    50756548949889/8*u^8*v^2*z4 + 4399820610071/8*u^6*v^3*z4 +
    27637712515/4*u^4*v^4*z4 - 137924397/2*u^2*v^5*z4 + 47241*v^6*z4 +
    33055623731911525/256*u^10*w*z4 - 29465933039483/8*u^8*w^2*z4 -
    253872679817/2*u^6*w^3*z4 + 615398608*u^4*w^4*z4 -
    354958*u^2*w^5*z4 + 5280*w^6*z4 - 5938156556697595/512*u^9*z4^2 -
    56496104671431/32*u^7*v*z4^2 + 27927285585/16*u^5*v^2*z4^2 -
    721651443/8*u^3*v^3*z4^2 + 990230*u*v^4*z4^2 +
    13554698457017/32*u^7*w*z4^2 + 2564646799/8*u^5*w^2*z4^2 +
    274648411/8*u^3*w^3*z4^2 - 22118*u*w^4*z4^2 +
    889364118043/32*u^6*z4^3 + 23506807745/32*u^4*v*z4^3 -
    30460317/8*u^2*v^2*z4^3 + 23549/8*v^3*z4^3 -
    2908263593/16*u^4*w*z4^3 - 135933/16*u^2*w^2*z4^3 -
    12233/16*w^3*z4^3 - 420729335/32*u^3*z4^4 - 4082233/128*u*v*z4^4 +
    8697/32*u*w*z4^4 - 2207/32*z4^5 - 5355034231662065/16*u^12*z5 -
    24149117300247419/32*u^10*v*z5 + 175577367057997/8*u^8*v^2*z5 +
    4099644806965/4*u^6*v^3*z5 + 22550793567/2*u^4*v^4*z5 -
    166430285*u^2*v^5*z5 + 63654*v^6*z5 -
    31110544689408595/32*u^10*w*z5 - 36315418433825/2*u^8*w^2*z5 -
    208372013265*u^6*w^3*z5 + 1040588074*u^4*w^4*z5 -
    470024*u^2*w^5*z5 + 9620*w^6*z5 + 12315406786657043/128*u^9*z4*z5
    - 9726236274075/2*u^7*v*z4*z5 + 27895120573/8*u^5*v^2*z4*z5 -
    1382579027/4*u^3*v^3*z4*z5 + 9012393/2*u*v^4*z4*z5 +
    1795728236795/8*u^7*w*z4*z5 + 9466610441*u^5*w^2*z4*z5 +
    5476418*u^3*w^3*z4*z5 - 99222*u*w^4*z4*z5 +
    739769352501/4*u^6*z4^2*z5 + 2452339511*u^4*v*z4^2*z5 -
    34004049/2*u^2*v^2*z4^2*z5 + 23473/2*v^3*z4^2*z5 -
    491948816*u^4*w*z4^2*z5 - 1081891/4*u^2*w^2*z4^2*z5 -
    18887/4*w^3*z4^2*z5 - 1666696577/16*u^3*z4^3*z5 -
    1004519/32*u*v*z4^3*z5 - 264119/32*u*w*z4^3*z5 - 13539/64*z4^4*z5
    + 6525810070031885/64*u^9*z5^2 + 10984368269331265/16*u^12*z6 -
    9624982487340047/8*u^10*v*z6 - 28389893776447/8*u^8*v^2*z6 +
    14499540163929/4*u^6*v^3*z6 + 69538439055/2*u^4*v^4*z6 -
    268581395*u^2*v^5*z6 + 129922*v^6*z6 -
    24387558557233471/8*u^10*w*z6 - 23615619530926*u^8*w^2*z6 -
    4604075204*u^6*w^3*z6 - 942204920*u^4*w^4*z6 + 404452*u^2*w^5*z6 +
    1892*w^6*z6 + 10727984348789253/256*u^9*z4*z6 -
    10359062715576*u^7*v*z4*z6 + 5597074947*u^5*v^2*z4*z6 -
    31398287*u^3*v^3*z4*z6 - 43596*u*v^4*z4*z6 -
    980421081695/8*u^7*w*z4*z6 + 25955469583/2*u^5*w^2*z4*z6 +
    6761190*u^3*w^3*z4*z6 - 83184*u*w^4*z4*z6 +
    4684620162687/32*u^6*z4^2*z6 + 5186601331/8*u^4*v*z4^2*z6 +
    25479435/4*u^2*v^2*z4^2*z6 - 24941/4*v^3*z4^2*z6 -
    10086106979/8*u^4*w*z4^2*z6 - 173415*u^2*w^2*z4^2*z6 -
    4865/2*w^3*z4^2*z6 - 491258039/8*u^3*z4^3*z6 -
    2620557/16*u*v*z4^3*z6 - 503913/32*u*w*z4^3*z6 + 87349/128*z4^4*z6
    - 2414404417403233/16*u^9*z5*z6 - 3168629837885/8*u^6*z4*z5*z6 +
    2303768663/8*u^3*z4^2*z5*z6 + 74887/32*z4^3*z5*z6 -
    25953301007317605/32*u^10*v*z7 + 6649997753408267/32*u^10*w*z7 +
    9348097564532081/128*u^9*z4*z7 - 14705467087087/16*u^7*v*z4*z7 +
    422001543389/4*u^7*w*z4*z7 + 140430844753/2*u^6*z4^2*z7 -
    240880271*u^4*v*z4^2*z7 - 1702553531/2*u^4*w*z4^2*z7 -
    562745779/16*u^3*z4^3*z7 - 1493427/32*u*v*z4^3*z7 -
    7050*u*w*z4^3*z7 + 18369/64*z4^4*z7 + 463225785949585/8*u^9*z5*z7
    + 27396037816783/4*u^12*z8 + 2031238057714913/8*u^10*v*z8 -
    10358328144443/8*u^8*v^2*z8 + 4527363006753/4*u^6*v^3*z8 +
    24375134859/2*u^4*v^4*z8 - 120465387*u^2*v^5*z8 + 94482*v^6*z8 +
    11792395004162287/32*u^10*w*z8 - 472511830307635/256*u^9*z4*z8 -
    61702171911415/16*u^7*v*z4*z8 + 15763302901/4*u^5*v^2*z4*z8 -
    101223476*u^3*v^3*z4*z8 + 1279378*u*v^4*z4*z8 +
    453214132229/8*u^6*z4^2*z8 + 4840009111/4*u^4*v*z4^2*z8 -
    62991853/8*u^2*v^2*z4^2*z8 + 23549/4*v^3*z4^2*z8 -
    420594155/16*u^3*z4^3*z8 - 523709/8*u*v*z4^3*z8 - 2207/16*z4^4*z8
    - 639523099584475/4*u^9*z6*z8 + 2830062084285*u^7*v*z6*z8 +
    26015630163*u^5*v^2*z6*z8 - 660235442*u^3*v^3*z6*z8 +
    6134260*u*v^4*z6*z8 + 5305955273*u^6*z4*z6*z8 +
    2235836504*u^4*v*z4*z6*z8 - 11688636*u^2*v^2*z4*z6*z8 -
    283*v^3*z4*z6*z8 + 369691662214677/8*u^9*z8^2 -
    5954651475239/4*u^7*v*z8^2 - 26574235149/2*u^5*v^2*z8^2 +
    220900223*u^3*v^3*z8^2 - 1545762*u*v^4*z8^2 +
    2450195607885997/32*u^12*z9 - 9285930328681679/32*u^10*v*z9 -
    239975084494767/8*u^8*v^2*z9 + 4874371122021/4*u^6*v^3*z9 +
    27231842927/2*u^4*v^4*z9 - 91346185*u^2*v^5*z9 + 63766*v^6*z9 -
    2884691799873629/8*u^10*w*z9 - 20974382706882*u^8*w^2*z9 -
    107090690470*u^6*w^3*z9 - 861775000*u^4*w^4*z9 - 23264*u^2*w^5*z9
    + 5706389278306749/256*u^9*z4*z9 + 4291544822203/16*u^7*v*z4*z9 -
    1167303245031/8*u^7*w*z4*z9 + 5304336548*u^5*w^2*z4*z9 +
    116193222*u^3*w^3*z4*z9 + 3073*u*w^4*z4*z9 +
    158660326865/8*u^6*z4^2*z9 + 111372370*u^4*v*z4^2*z9 +
    246476021/2*u^4*w*z4^2*z9 - 1557461/4*u^2*w^2*z4^2*z9 +
    1189/2*w^3*z4^2*z9 - 455578443/32*u^3*z4^3*z9 +
    407039/16*u*v*z4^3*z9 - 28163/8*u*w*z4^3*z9 - 961/8*z4^4*z9 -
    20563450465553/8*u^9*z5*z9 - 96967149807*u^6*z4*z5*z9 +
    83710747*u^3*z4^2*z5*z9 - 99/16*z4^3*z5*z9 -
    178793492487/2*u^9*z9^2 + 114942035801*u^7*v*z9^2 -
    528723578*u^5*v^2*z9^2 + 591204*u^3*v^3*z9^2 + 4*u*v^4*z9^2 -
    203472516738*u^7*w*z9^2 - 2013474044*u^5*w^2*z9^2 -
    41495908*u^3*w^3*z9^2 + 16*u*w^4*z9^2 - 45985223699/2*u^6*z4*z9^2
    + 46037715/2*u^3*z4^2*z9^2 - 19/16*z4^3*z9^2 +
    17232801158*u^6*z5*z9^2 - 51835159*u^3*z4*z5*z9^2 +
    13/4*z4^2*z5*z9^2 - 205230580*u^6*z9^3 + 37411568*u^4*v*z9^3 +
    4*u^2*v^2*z9^3 + 4*v^3*z9^3 - 73716956*u^4*w*z9^3 -
    904*u^2*w^2*z9^3 + 4*w^3*z9^3 - 9212914*u^3*z4*z9^3 -
    3/4*z4^2*z9^3 + 4602488*u^3*z5*z9^3 - 2*z4*z5*z9^3 - 48*u^3*z9^4 +
    8*u*w*z9^4 + z4*z9^4 - 1517982428183333/8*u^12*z10 -
    8528503888154557/32*u^10*v*z10 - 74491782076373/8*u^8*v^2*z10 -
    4517251965489/4*u^6*v^3*z10 - 22656222651/2*u^4*v^4*z10 +
    115433567*u^2*v^5*z10 - 63766*v^6*z10 +
    23619983410333747/32*u^10*w*z10 + 1482842714865927/256*u^9*z4*z10 +
    70132580371187/16*u^7*v*z4*z10 - 635670891467/32*u^6*z4^2*z10 -
    2245584791/8*u^4*v*z4^2*z10 - 115215363/32*u^3*z4^3*z10 +
    1942341/32*u*v*z4^3*z10 - 44565/128*z4^4*z10 +
    375929005276089/16*u^9*z5*z10 + 1357092885451/8*u^6*z4*z5*z10 -
    595034787/4*u^3*z4^2*z5*z10 - 59499/32*z4^3*z5*z10 -
    77118992998015/2*u^9*z9*z10 - 1428389324*u^6*z9^2*z10 -
    888*u^3*z9^3*z10 + 27396037816783/4*u^12*z11 +
    2801783691241259/32*u^10*v*z11 - 48894671927579/4*u^8*v^2*z11 -
    35522171581/2*u^6*v^3*z11 + 820290143*u^4*v^4*z11 -
    5065546*u^2*v^5*z11 + 30716*v^6*z11 + 17282286825545487/32*u^10*w*z11
    + 4754567439275/4*u^8*v*w*z11 + 179231627927*u^6*v^2*w*z11 +
    2082964452*u^4*v^3*w*z11 + 1940242*u^2*v^4*w*z11 - 140124*v^5*w*z11 +
    933515279875/4*u^8*w^2*z11 - 8571251562*u^6*w^3*z11 -
    44647940*u^4*w^4*z11 + 4236*u^2*w^5*z11 - 8*w^6*z11 +
    14391689617735/32*u^9*z4*z11 + 11559767319749/16*u^7*v*z4*z11 +
    63144988929/8*u^5*v^2*z4*z11 - 117492569/4*u^3*v^3*z4*z11 -
    238321/2*u*v^4*z4*z11 + 314558517341/2*u^7*w*z4*z11 -
    6313498901/2*u^5*w^2*z4*z11 + 9235015*u^3*w^3*z4*z11 +
    28316*u*w^4*z4*z11 + 4894904171/4*u^6*z4^2*z11 -
    393035817/4*u^4*v*z4^2*z11 - 19735843/8*u^2*v^2*z4^2*z11 -
    24317/4*v^3*z4^2*z11 - 838093879/4*u^4*w*z4^2*z11 +
    152455/4*u^2*w^2*z4^2*z11 + 4737/4*w^3*z4^2*z11 +
    51820701/16*u^3*z4^3*z11 - 523003/32*u*v*z4^3*z11 +
    2431/16*u*w*z4^3*z11 + 3887/32*z4^4*z11 + 13833863737459/8*u^9*z5*z11
    + 263965337685/4*u^7*v*z5*z11 + 31376918263/2*u^5*v^2*z5*z11 +
    587852173*u^3*v^3*z5*z11 - 5263262*u*v^4*z5*z11 +
    27396037817295/4*u^9*z6*z11 - 1236486416725/2*u^7*v*z6*z11 -
    424837896477/2*u^7*w*z6*z11 + 854852630*u^5*w^2*z6*z11 +
    12176936*u^3*w^3*z6*z11 - 15236*u*w^4*z6*z11 - 6670634683*u^9*z11^2 +
    136827672558*u^7*v*z11^2 - 1605090268*u^5*v^2*z11^2 -
    164785670*u^3*v^3*z11^2 + 1481660*u*v^4*z11^2 +
    101359715573/2*u^7*w*z11^2 + 1239348839*u^5*v*w*z11^2 +
    185739494*u^3*v^2*w*z11^2 - 1505372*u*v^3*w*z11^2 -
    493176370*u^5*w^2*z11^2 + 5243080*u^3*w^3*z11^2 + 2880*u*w^4*z11^2 -
    4544442314*u^6*z4*z11^2 + 689632483/2*u^4*v*z4*z11^2 -
    2453344*u^2*v^2*z4*z11^2 + 289593*u^3*z4^2*z11^2 +
    39587/2*u*v*z4^2*z11^2 - 18376494388*u^6*z5*z11^2 -
    585727842*u^4*v*z5*z11^2 + 6194632*u^2*v^2*z5*z11^2 +
    31168*v^3*z5*z11^2 - 6670634559*u^6*z6*z11^2 -
    622769374*u^4*v*z6*z11^2 - 80314528*u^4*w*z6*z11^2 -
    18112*u^2*w^2*z6*z11^2 + 40044*u^6*z11^3 + 225544068*u^4*v*z11^3 -
    1568444*u^2*v^2*z11^3 - 56*v^3*z11^3 + 17490208*u^4*w*z11^3 +
    38540*u^2*v*w*z11^3 + 52*v^2*w*z11^3 - 7660*u^2*w^2*z11^3 -
    1150672*u^3*z4*z11^3 + 7807*u*v*z4*z11^3 - 1/4*z4^2*z11^3 -
    4602628*u^3*z5*z11^3 - 240*u*v*z5*z11^3 + 40096*u^3*z6*z11^3 +
    816*u*v*z6*z11^3 + 12*u*w*z6*z11^3 - 8*u^3*z11^4 + 48*u*v*z11^4,
    -18521026619165/4*u^13*v - 19714573337023/4*u^11*v^2 +
    345360335800*u^9*v^3 + 50930733168*u^7*v^4 + 586244840*u^5*v^5 -
    5224880*u^3*v^6 + 1184*u*v^7 - 2097143570281/2*u^13*w -
    7983005133389/2*u^11*v*w + 21659707213889/2*u^9*v^2*w +
    301158101642*u^7*v^3*w - 2963225844*u^5*v^4*w - 15440176*u^3*v^5*w
    - 661432*u*v^6*w + 307249025299731/8*u^11*w^2 -
    21738838150045/4*u^9*v*w^2 - 520941608705*u^9*w^3 +
    21768545268*u^7*w^4 - 137120752*u^5*w^5 + 1144832*u^3*w^6 -
    1456*u*w^7 + 108933095847719/32*u^12*z4 -
    7108401643139/2*u^10*v*z4 - 136324710501*u^8*v^2*z4 -
    12736792885*u^6*v^3*z4 - 166282984*u^4*v^4*z4 + 1460016*u^2*v^5*z4
    - 384*v^6*z4 - 90913836999099/32*u^10*w*z4 +
    71082844735*u^8*w^2*z4 + 2802410000*u^6*w^3*z4 -
    8986184*u^4*w^4*z4 + 580*u^2*w^5*z4 + 56*w^6*z4 +
    15911355277797/64*u^9*z4^2 + 38069522200*u^7*v*z4^2 -
    28642156*u^5*v^2*z4^2 + 1988958*u^3*v^3*z4^2 - 15300*u*v^4*z4^2 -
    36357111787/4*u^7*w*z4^2 - 2517395*u^5*w^2*z4^2 -
    988941/2*u^3*w^3*z4^2 + 73*u*w^4*z4^2 - 5115482923/8*u^6*z4^3 -
    120232819/8*u^4*v*z4^3 + 260841/4*u^2*v^2*z4^3 - 19/2*v^3*z4^3 +
    5514049/2*u^4*w*z4^3 + 3421*u^2*w^2*z4^3 - 5*w^3*z4^3 +
    3450437/16*u^3*z4^4 + 50211/32*u*v*z4^4 + 141/4*u*w*z4^4 +
    3/8*z4^5 + 14324537884391/2*u^12*z5 + 64878890309493/4*u^10*v*z5 -
    470896095055*u^8*v^2*z5 - 23934013478*u^6*v^3*z5 -
    302557620*u^4*v^4*z5 + 3618832*u^2*v^5*z5 - 592*v^6*z5 +
    82463320150989/4*u^10*w*z5 + 391585613116*u^8*w^2*z5 +
    4115012912*u^6*w^3*z5 - 14610168*u^4*w^4*z5 + 7936*u^2*w^5*z5 -
    33336919853917/16*u^9*z4*z5 + 98324814655*u^7*v*z4*z5 -
    2857697*u^5*v^2*z4*z5 + 8091520*u^3*v^3*z4*z5 - 67568*u*v^4*z4*z5
    - 7268100664*u^7*w*z4*z5 - 127373404*u^5*w^2*z4*z5 -
    129300*u^3*w^3*z4*z5 - 580*u*w^4*z4*z5 - 3861483620*u^6*z4^2*z5 -
    116922357/2*u^4*v*z4^2*z5 + 297307*u^2*v^2*z4^2*z5 -
    55*v^3*z4^2*z5 + 9059675*u^4*w*z4^2*z5 + 16947*u^2*w^2*z4^2*z5 -
    23*w^3*z4^2*z5 + 1630131*u^3*z4^3*z5 + 23719/8*u*v*z4^3*z5 -
    2575/8*u*w*z4^3*z5 + 7/8*z4^4*z5 - 17695292539443/8*u^9*z5^2 -
    29438834982383/2*u^12*z6 + 25941214079641*u^10*v*z6 +
    112774274673*u^8*v^2*z6 - 79677853598*u^6*v^3*z6 -
    815322716*u^4*v^4*z6 + 5692760*u^2*v^5*z6 - 1424*v^6*z6 +
    65188308768933*u^10*w*z6 + 517324026048*u^8*w^2*z6 -
    172336400*u^6*w^3*z6 + 14450624*u^4*w^4*z6 + 3488*u^2*w^5*z6 -
    272*w^6*z6 - 29761142225499/32*u^9*z4*z6 +
    210733320584*u^7*v*z4*z6 - 104785578*u^5*v^2*z4*z6 +
    962052*u^3*v^3*z4*z6 + 3184*u*v^4*z4*z6 + 711342858*u^7*w*z4*z6 -
    219950918*u^5*w^2*z4*z6 - 205328*u^3*w^3*z4*z6 - 1800*u*w^4*z4*z6
    - 5503593893/2*u^6*z4^2*z6 - 22639711/2*u^4*v*z4^2*z6 -
    123086*u^2*v^2*z4^2*z6 + 16*v^3*z4^2*z6 + 43010605/2*u^4*w*z4^2*z6
    + 13479*u^2*w^2*z4^2*z6 - 15*w^3*z4^2*z6 + 3350685/4*u^3*z4^3*z6 +
    7460*u*v*z4^3*z6 - 6247/8*u*w*z4^3*z6 - 7/32*z4^4*z6 +
    6377695932183/2*u^9*z5*z6 + 8769477146*u^6*z4*z5*z6 -
    9519081/2*u^3*z4^2*z5*z6 + 65/8*z4^3*z5*z6 +
    69283202884155/4*u^10*v*z7 - 17953849002261/4*u^10*w*z7 -
    25309856957151/16*u^9*z4*z7 + 30978351963/2*u^7*v*z4*z7 -
    2918717784*u^7*w*z4*z7 - 1340816279*u^6*z4^2*z7 +
    2238805*u^4*v*z4^2*z7 + 13865518*u^4*w*z4^2*z7 +
    479517*u^3*z4^3*z7 + 7029/8*u*v*z4^3*z7 - 1623/4*u*w*z4^3*z7 -
    9/4*z4^4*z7 - 1266651115195*u^9*z5*z7 - 141794404226*u^12*z8 -
    5329301506499*u^10*v*z8 + 27943875081*u^8*v^2*z8 -
    25846464542*u^6*v^3*z8 - 296022932*u^4*v^4*z8 + 2641944*u^2*v^5*z8
    - 768*v^6*z8 - 32323526809521/4*u^10*w*z8 +
    1471440042925/32*u^9*z4*z8 + 164975514381/2*u^7*v*z4*z8 -
    59483638*u^5*v^2*z4*z8 + 2151718*u^3*v^3*z4*z8 - 19572*u*v^4*z4*z8
    - 2591480043/2*u^6*z4^2*z8 - 51559427/2*u^4*v*z4^2*z8 +
    285601/2*u^2*v^2*z4^2*z8 - 19*v^3*z4^2*z8 + 1726459/4*u^3*z4^3*z8
    + 6301/2*u*v*z4^3*z8 + 3/4*z4^4*z8 + 3471334508402*u^9*z6*z8 -
    57414702800*u^7*v*z6*z8 - 506962992*u^5*v^2*z6*z8 +
    14747632*u^3*v^3*z6*z8 - 91072*u*v^4*z6*z8 -
    238697608*u^6*z4*z6*z8 - 50354076*u^4*v*z4*z6*z8 +
    198380*u^2*v^2*z4*z6*z8 - 4*v^3*z4*z6*z8 - 990661891179*u^9*z8^2 +
    31513762258*u^7*v*z8^2 + 287407996*u^5*v^2*z8^2 -
    4801712*u^3*v^3*z8^2 + 22832*u*v^4*z8^2 - 6577221113507/4*u^12*z9
    + 24986374471665/4*u^10*v*z9 + 650736135341*u^8*v^2*z9 -
    26849785286*u^6*v^3*z9 - 306537604*u^4*v^4*z9 + 1858896*u^2*v^5*z9
    - 592*v^6*z9 + 7705866628059*u^10*w*z9 + 456566617008*u^8*w^2*z9 +
    2067584616*u^6*w^3*z9 + 13639776*u^4*w^4*z9 - 6880*u^2*w^5*z9 -
    320*w^6*z9 - 15252287946883/32*u^9*z4*z9 -
    17671691253/2*u^7*v*z4*z9 + 2952019981*u^7*w*z4*z9 -
    72795854*u^5*w^2*z4*z9 - 1845180*u^3*w^3*z4*z9 - 252*u*w^4*z4*z9 -
    823948815/2*u^6*z4^2*z9 - 6116022*u^4*v*z4^2*z9 -
    1206708*u^4*w*z4^2*z9 + 15155*u^2*w^2*z4^2*z9 + 25*w^3*z4^2*z9 +
    1919447/8*u^3*z4^3*z9 - 1709/4*u*v*z4^3*z9 - 3/4*u*w*z4^3*z9 +
    25/8*z4^4*z9 + 60553513367*u^9*z5*z9 + 2052345276*u^6*z4*z5*z9 -
    1264336*u^3*z4^2*z5*z9 + 2*z4^3*z5*z9 + 1561755508*u^9*z9^2 -
    1913653592*u^7*v*z9^2 + 10290176*u^5*v^2*z9^2 - 4416*u^3*v^3*z9^2
    - 16*u*v^4*z9^2 + 3691715600*u^7*w*z9^2 + 32366592*u^5*w^2*z9^2 +
    616864*u^3*w^3*z9^2 - 1664*u*w^4*z9^2 + 486934634*u^6*z4*z9^2 -
    347688*u^3*z4^2*z9^2 - 69/4*z4^3*z9^2 - 364120488*u^6*z5*z9^2 +
    782468*u^3*z4*z5*z9^2 - 23*z4^2*z5*z9^2 + 4682448*u^6*z9^3 -
    556864*u^4*v*z9^3 - 720*u^2*v^2*z9^3 + 16*v^3*z9^3 +
    1107616*u^4*w*z9^3 - 3264*u^2*w^2*z9^3 - 48*w^3*z9^3 +
    139240*u^3*z4*z9^3 + 33*z4^2*z9^3 - 69408*u^3*z5*z9^3 +
    40*z4*z5*z9^3 + 32*u^3*z9^4 + 80*u*v*z9^4 - 112*u*w*z9^4 -
    12*z4*z9^4 + 4034523161555*u^12*z10 + 22417746730371/4*u^10*v*z10 +
    192646640819*u^8*v^2*z10 + 25482813958*u^6*v^3*z10 +
    280054180*u^4*v^4*z10 - 2519752*u^2*v^5*z10 + 592*v^6*z10 -
    62631373563533/4*u^10*w*z10 - 3619949222841/32*u^9*z4*z10 -
    185758806255/2*u^7*v*z4*z10 + 286461904*u^6*z4^2*z10 +
    6053607/2*u^4*v*z4^2*z10 + 850097/8*u^3*z4^3*z10 -
    25375/8*u*v*z4^3*z10 - 117/32*z4^4*z10 - 964177506439/2*u^9*z5*z10 -
    4146639480*u^6*z4*z5*z10 + 2588566*u^3*z4^2*z5*z10 -
    103/8*z4^3*z5*z10 + 841964582924*u^9*z9*z10 + 23350400*u^6*z9^2*z10 -
    2592*u^3*z9^3*z10 - 141794404226*u^12*z11 -
    7527120671349/4*u^10*v*z11 + 253458766686*u^8*v^2*z11 +
    1579708*u^6*v^3*z11 - 14577456*u^4*v^4*z11 + 122624*u^2*v^5*z11 -
    176*v^6*z11 - 46322178531905/4*u^10*w*z11 - 24750274874*u^8*v*w*z11 -
    2728180920*u^6*v^2*w*z11 - 64399192*u^4*v^3*w*z11 -
    347768*u^2*v^4*w*z11 + 1264*v^5*w*z11 - 7451505898*u^8*w^2*z11 +
    167983208*u^6*w^3*z11 + 992656*u^4*w^4*z11 - 1600*u^2*w^5*z11 -
    41585271801/4*u^9*z4*z11 - 31996773289/2*u^7*v*z4*z11 -
    198004809*u^5*v^2*z4*z11 + 410642*u^3*v^3*z4*z11 + 4184*u*v^4*z4*z11
    - 3080138712*u^7*w*z4*z11 + 53553660*u^5*w^2*z4*z11 -
    125876*u^3*w^3*z4*z11 + 364*u*w^4*z4*z11 - 25909107*u^6*z4^2*z11 -
    508846*u^4*v*z4^2*z11 + 90489/2*u^2*v^2*z4^2*z11 + 47*v^3*z4^2*z11 +
    3011007*u^4*w*z4^2*z11 - 268*u^2*w^2*z4^2*z11 + 10*w^3*z4^2*z11 -
    294343/4*u^3*z4^3*z11 + 2199/8*u*v*z4^3*z11 - 3*u*w*z4^3*z11 -
    11/16*z4^4*z11 - 40883244669*u^9*z5*z11 - 3664377550*u^7*v*z5*z11 -
    325937852*u^5*v^2*z5*z11 - 13257480*u^3*v^3*z5*z11 +
    91664*u*v^4*z5*z11 - 141794404306*u^9*z6*z11 +
    12954245892*u^7*v*z6*z11 + 5635054996*u^7*w*z6*z11 +
    1090760*u^5*w^2*z6*z11 - 202400*u^3*w^3*z6*z11 + 128*u*w^4*z6*z11 +
    130615768*u^9*z11^2 - 2290239072*u^7*v*z11^2 + 24546640*u^5*v^2*z11^2
    + 3766264*u^3*v^3*z11^2 - 22240*u*v^4*z11^2 - 1214709964*u^7*w*z11^2
    - 29573928*u^5*v*w*z11^2 - 4364976*u^3*v^2*w*z11^2 +
    22304*u*v^3*w*z11^2 + 7762776*u^5*w^2*z11^2 - 71440*u^3*w^3*z11^2 +
    95545960*u^6*z4*z11^2 - 7761274*u^4*v*z4*z11^2 +
    36076*u^2*v^2*z4*z11^2 - 4355*u^3*z4^2*z11^2 - 124*u*v*z4^2*z11^2 +
    386765456*u^6*z5*z11^2 + 14564424*u^4*v*z5*z11^2 -
    93616*u^2*v^2*z5*z11^2 - 176*v^3*z5*z11^2 + 130615704*u^6*z6*z11^2 +
    14380960*u^4*v*z6*z11^2 + 1282192*u^4*w*z6*z11^2 +
    112*u^2*w^2*z6*z11^2 - 208*u^6*z11^3 - 4986592*u^4*v*z11^3 +
    22960*u^2*v^2*z11^3 - 265168*u^4*w*z11^3 - 176*u^2*v*w*z11^3 +
    32*u^2*w^2*z11^3 + 17380*u^3*z4*z11^3 - 44*u*v*z4*z11^3 +
    69520*u^3*z5*z11^3 - 224*u^3*z6*z11^3 ];
  hh := [ 1, 1, z5, v*z5 - w*z5 + w*z8, u*z8 ];
  return gg,hh;
end function;

// Some polynomials used in computing the j-maps on Z(17,3)

function ExtraRelationsforJmap3(S)
  v,w,z1,z2,z3,z4,z5,z6,z7,z8,z9,z10 := Explode([S.i : i in [1..12]]);
  gg := [ 4*z1 - 4*z2 - 4*z6, -9*z1^2 + 10*z1*z2 - 5*z2^2 - 7*z1*z3 -
    16*z3^2 - 24*z1*z4 + 23*z2*z4 - 29*z3*z4 - 9*z4^2 + 2*z1*z5 +
    5*z2*z5 - 3*z3*z5 - 9*z4*z5 + 10*z1*z6 + z4*z6 - 7*z1*z7 - 2*z2*z7
    - 15*z4*z7 - 8*z6*z7 + 21*z1*z8 + 4*z2*z8 - 9*z3*z8 - 6*z7*z8 -
    16*z1*z9 - 11*z2*z9 - 11*z3*z9 - 17*z4*z9 - 20*z7*z9 + 18*z1*z10 -
    12*z2*z10 - 21*z6*z10, -v*z1^2 - v*z1*z4 + 2*v*z1*z7 + 2*v*z1*z10,
    -12*v*w^3 + 12*w*z1^2 - 22*v*z1*z2 - 10*v*z2^2 - 2*w*z2^2 +
    8*w*z1*z3 + 42*v*z2*z3 - 14*v*z3^2 + 10*w*z1*z4 - 16*v*z2*z4 -
    10*w*z2*z4 - 14*v*z1*z5 - 34*w*z1*z5 + 10*v*z2*z5 - 14*v*z3*z5 +
    18*w*z4*z5 + 2*w*z5^2 - 58*v*z1*z6 - 12*w*z1*z6 - 38*v*z4*z6 +
    26*v*z1*z7 + 4*w*z1*z7 + 42*v*z2*z7 + 4*w*z2*z7 + 28*v*z4*z7 -
    16*v*z6*z7 - 16*v*z7^2 + 14*v*z1*z8 - 36*w*z1*z8 + 12*v*z2*z8 -
    12*v*z6*z8 + 12*v*z8^2 + 18*v*z1*z9 + 12*w*z1*z9 - 28*v*z2*z9 +
    28*v*z4*z9 - 26*v*z5*z9 - 26*v*z6*z9 + 14*v*z1*z10 - 26*w*z1*z10 +
    64*v*z2*z10 + 18*v*z6*z10 - 28*v*z7*z10, -32*v^4*w^2 + 53*v^3*w^3
    - 11*v^2*w^4 + 3*v^3*z1^2 + 41*v^2*w*z1^2 + 90*v*w^2*z1^2 +
    141*v^3*z1*z2 + 8*v^2*w*z1*z2 - 10*v*w^2*z1*z2 - 234*z1^3*z2 +
    84*v^3*z2^2 + 9*v^2*w*z2^2 + v*w^2*z2^2 - 83*z1^2*z2^2 - 8*z1*z2^3
    - 111*v^3*z1*z3 + 112*v^2*w*z1*z3 + 25*v*w^2*z1*z3 - 178*z1^3*z3 -
    173*v^3*z2*z3 - 15*z1^2*z2*z3 + 4*z1*z2^2*z3 + 19*v^3*z3^2 -
    32*z1^2*z3^2 - 157*v^2*w*z1*z4 - 33*v*w^2*z1*z4 + 3*z1^3*z4 -
    51*v^3*z2*z4 + 49*v^2*w*z2*z4 - 12*v*w^2*z2*z4 - 51*z1^2*z2*z4 -
    v^3*z3*z4 + 6*z1^2*z3*z4 - 23*v^2*w*z4^2 + 3*z1^2*z4^2 -
    45*v^3*z1*z5 - 72*v^2*w*z1*z5 + 31*v*w^2*z1*z5 + 4*z1^3*z5 -
    127*v^3*z2*z5 + 93*z1^2*z2*z5 + 8*z1*z2^2*z5 - 48*v^3*z3*z5 -
    9*z1^2*z3*z5 - 3*v^3*z4*z5 - 61*v^2*w*z4*z5 + 18*v*w^2*z4*z5 -
    13*z1^2*z4*z5 - 4*v^2*w*z5^2 + 2*v*w^2*z5^2 + 182*v^3*z1*z6 -
    21*v^2*w*z1*z6 - 22*v*w^2*z1*z6 - 317*z1^3*z6 + 178*v^3*z4*z6 -
    130*z1^2*z4*z6 + 32*v^3*z5*z6 + 96*z1^2*z5*z6 + 31*v^3*z6^2 -
    11*v^2*w*z6^2 + 94*z1^2*z6^2 - 169*v^3*z1*z7 + 60*v^2*w*z1*z7 -
    4*v*w^2*z1*z7 - 192*z1^3*z7 - 165*v^3*z2*z7 + 50*v^2*w*z2*z7 -
    v*w^2*z2*z7 + 186*z1^2*z2*z7 - 152*v^3*z4*z7 - 91*z1^2*z4*z7 +
    63*v^3*z6*z7 + 186*z1^2*z6*z7 + 32*v^3*z7^2 - 10*v^2*w*z7^2 -
    171*v^3*z1*z8 - 70*v^2*w*z1*z8 - 22*v*w^2*z1*z8 + 214*z1^3*z8 -
    246*v^3*z2*z8 + 91*z1^2*z2*z8 - 4*z1*z2^2*z8 - 57*v^3*z3*z8 +
    171*z1^2*z3*z8 + 30*v^3*z6*z8 + 47*v^2*w*z6*z8 - 39*v^3*z8^2 +
    11*v^2*w*z8^2 - 94*z1^2*z8^2 + 186*v^3*z1*z9 - 98*v^2*w*z1*z9 +
    47*v*w^2*z1*z9 - 289*z1^3*z9 + 135*v^3*z2*z9 + 34*z1^2*z2*z9 +
    8*z1*z2^2*z9 + 14*v^3*z3*z9 - 149*z1^2*z3*z9 - 115*v^3*z4*z9 -
    123*z1^2*z4*z9 + 86*v^3*z5*z9 - 97*z1^2*z5*z9 + 72*v^3*z6*z9 +
    14*v^2*w*z6*z9 - 94*z1^2*z9^2 - 134*v^3*z1*z10 + 127*v^2*w*z1*z10
    + 10*v*w^2*z1*z10 - 146*z1^3*z10 - 389*v^3*z2*z10 +
    419*z1^2*z2*z10 - 25*v^3*z6*z10 + 425*z1^2*z6*z10 + 132*v^3*z7*z10
    - 18*v^2*w*z7*z10, v^6*z5*z6 + v^6*z6^2 + v^3*z6^4 + z2*z5*z6^4 +
    z5*z6^5 + 8*v^6*z6*z7 + 243*v^6*z7^2 - 479*v^5*w*z7^2 +
    456*v^3*z6^2*z7^2 + 225*z6^4*z7^2 + 188*v^3*z6*z7^3 +
    991*z6^3*z7^3 + 72*v^3*z7^4 + 304*v^2*w*z7^4 + 894*z6^2*z7^4 +
    177*z5*z7^5 + 305*z6*z7^5 - 754*z7^5*z8 + 1399*z7^4*z8^2 -
    402*z5*z8^5 - 645*z7*z8^5 + 4*z1*z4^4*z9 + 4*z4^5*z9 + v^6*z5*z9 +
    485*z4^4*z5*z9 - 1102*z2*z5*z6^3*z9 - 1099*z2*z6^4*z9 +
    730*z3*z6^4*z9 - 329*z4*z6^4*z9 - 2*z5*z6^4*z9 + 1440*z5*z7^4*z9 +
    1227*z6*z7^4*z9 + 766*z7^5*z9 - 6666*z7^4*z8*z9 +
    13025*z7^3*z8^2*z9 - 389*z5*z8^4*z9 - 6169*z7*z8^4*z9 - 2*v^6*z9^2
    + 2*z1^4*z9^2 + 4779*z1*z4^3*z9^2 + 5262*z4^4*z9^2 +
    6937*z4^3*z5*z9^2 - 3*v^3*z5^2*z9^2 - 578*z2*z5*z6^2*z9^2 -
    2009*z2*z6^3*z9^2 - 4808*z3*z6^3*z9^2 + 8281*z4*z6^3*z9^2 +
    7808*z5*z7^3*z9^2 + 9482*z6*z7^3*z9^2 + 8529*z7^4*z9^2 -
    38907*z7^3*z8*z9^2 + 88992*z7^2*z8^2*z9^2 - 5983*z5*z8^3*z9^2 -
    49881*z7*z8^3*z9^2 + 4*z1^3*z9^3 - 5496*z1*z4^2*z9^3 +
    1914*z4^3*z9^3 + 241*v^3*z5*z9^3 - 8639*z4^2*z5*z9^3 +
    450*z2*z5*z6*z9^3 + 8152*z2*z6^2*z9^3 - 534*z3*z6^2*z9^3 +
    15273*z4*z6^2*z9^3 + 2*z5*z6^2*z9^3 + 7738*z5*z7^2*z9^3 +
    40852*z6*z7^2*z9^3 + 42060*z7^3*z9^3 - 45750*z7^2*z8*z9^3 +
    54835*z4*z8^2*z9^3 - 527*z5*z8^2*z9^3 + 85867*z7*z8^2*z9^3 -
    1922*v^3*z9^4 - 2*z1^2*z9^4 + 5474*z1*z4*z9^4 + 4243*z4^2*z9^4 +
    20882*z2*z5*z9^4 + 21902*z3*z5*z9^4 + 11045*z4*z5*z9^4 -
    4795*z5^2*z9^4 + 36615*z2*z6*z9^4 + 3320*z3*z6*z9^4 +
    565*z4*z6*z9^4 - 4796*z5*z6*z9^4 + 29951*z5*z7*z9^4 +
    49249*z6*z7*z9^4 + 76025*z7^2*z9^4 - 12544*z2*z8*z9^4 +
    27157*z3*z8*z9^4 - 12902*z4*z8*z9^4 + 10497*z5*z8*z9^4 +
    14402*z7*z8*z9^4 + 5740*z1*z9^5 + 6856*z2*z9^5 + 15544*z4*z9^5 +
    35984*z7*z9^5 + 2*z1*z4^4*z10 + 3*z4^4*z5*z10 + 5*v^6*z6*z10 -
    7*v^3*z6^3*z10 - 12*z2*z5*z6^3*z10 + 2*z3*z6^4*z10 + z4*z6^4*z10 -
    12*z5*z6^4*z10 + z6^5*z10 + 467*v^6*z7*z10 - 755*v^5*w*z7*z10 +
    2544*v^3*z6^2*z7*z10 - 496*z6^4*z7*z10 + 331*v^3*z6*z7^2*z10 -
    1290*z6^3*z7^2*z10 + 4376*v^3*z7^3*z10 + 4893*v^2*w*z7^3*z10 -
    1364*w^3*z7^3*z10 - 2662*z6^2*z7^3*z10 + 7604*z5*z7^4*z10 +
    4668*z6*z7^4*z10 - 1364*z7^5*z10 - 7107*z7^4*z8*z10 +
    11379*z7^3*z8^2*z10 - 145*z5*z8^4*z10 + 243*z6*z8^4*z10 -
    1864*z7*z8^4*z10 - 1046*z8^5*z10 - 233*v^6*z9*z10 + z1^4*z9*z10 +
    3115*z1*z4^3*z9*z10 + 972*z4^4*z9*z10 + 4672*z4^3*z5*z9*z10 -
    1908*v^3*z5^2*z9*z10 - 1966*z2*z5*z6^2*z9*z10 -
    1998*z2*z6^3*z9*z10 - 2002*z3*z6^3*z9*z10 - 1900*z4*z6^3*z9*z10 +
    21*z5*z6^3*z9*z10 - 3*z6^4*z9*z10 + 34437*z5*z7^3*z9*z10 +
    53210*z6*z7^3*z9*z10 + 26809*z7^4*z9*z10 - 66173*z7^3*z8*z9*z10 +
    70561*z7^2*z8^2*z9*z10 + 5515*z5*z8^3*z9*z10 + 3945*z6*z8^3*z9*z10
    - 18464*z7*z8^3*z9*z10 - 7289*z8^4*z9*z10 - 1/2*z1^3*z9^2*z10 +
    3298*z1*z4^2*z9^2*z10 + 23113/2*z4^3*z9^2*z10 +
    3817*v^3*z5*z9^2*z10 + 55781/4*z4^2*z5*z9^2*z10 -
    23608*z2*z5*z6*z9^2*z10 - 28671*z2*z6^2*z9^2*z10 -
    36955/2*z3*z6^2*z9^2*z10 + 10949*z4*z6^2*z9^2*z10 +
    1565*z5*z6^2*z9^2*z10 + 1431*z6^3*z9^2*z10 +
    139517/2*z5*z7^2*z9^2*z10 + 228971*z6*z7^2*z9^2*z10 +
    146635*z7^3*z9^2*z10 - 117030*z7^2*z8*z9^2*z10 +
    562651/4*z4*z8^2*z9^2*z10 + 42401/2*z5*z8^2*z9^2*z10 +
    49777*z6*z8^2*z9^2*z10 + 887851/4*z7*z8^2*z9^2*z10 -
    45998*z8^3*z9^2*z10 - 9586*v^3*z9^3*z10 + 197/4*z1^2*z9^3*z10 +
    55879/4*z1*z4*z9^3*z10 + 102103/4*z4^2*z9^3*z10 -
    88527/2*z2*z5*z9^3*z10 + 73374*z3*z5*z9^3*z10 +
    187665/4*z4*z5*z9^3*z10 + 3367*z5^2*z9^3*z10 -
    94189/2*z2*z6*z9^3*z10 + 8498*z3*z6*z9^3*z10 +
    246651/2*z4*z6*z9^3*z10 + 47643*z5*z6*z9^3*z10 +
    40817*z6^2*z9^3*z10 + 173227*z5*z7*z9^3*z10 +
    458119*z6*z7*z9^3*z10 + 959211/2*z7^2*z9^3*z10 -
    1044929/4*z2*z8*z9^3*z10 + 689125/2*z3*z8*z9^3*z10 +
    92395/4*z4*z8*z9^3*z10 + 296113/2*z5*z8*z9^3*z10 -
    30953*z6*z8*z9^3*z10 + 460423/2*z7*z8*z9^3*z10 +
    31087*z8^2*z9^3*z10 + 37379/4*z1*z9^4*z10 - 78135/2*z2*z9^4*z10 -
    11134*z3*z9^4*z10 + 312421/4*z4*z9^4*z10 + 99204*z5*z9^4*z10 +
    110477*z6*z9^4*z10 + 755169/2*z7*z9^4*z10 + 14402*z8*z9^4*z10 +
    8827*z9^5*z10 - 954*v^5*w*z10^2 + 1/2*z1^3*z4*z10^2 -
    117*z1^2*z4^2*z10^2 + 248*z1*z4^3*z10^2 - z4^4*z10^2 -
    464*z4^3*z5*z10^2 + 4505*v^3*z5*z6*z10^2 + 4915*v^3*z6^2*z10^2 -
    1769*z2*z5*z6^2*z10^2 + 101*z2*z6^3*z10^2 + 1381/2*z3*z6^3*z10^2 +
    1035/2*z4*z6^3*z10^2 - 1349*z5*z6^3*z10^2 - 211*z6^4*z10^2 -
    4095*v^3*z6*z7*z10^2 - 8495*z6^3*z7*z10^2 + 13646*v^3*z7^2*z10^2 +
    11731*v^2*w*z7^2*z10^2 - 17652*w^3*z7^2*z10^2 -
    4821*z6^2*z7^2*z10^2 + 57161/2*z5*z7^3*z10^2 + 30519*z6*z7^3*z10^2
    - 21439*z7^4*z10^2 - 11882*z7^3*z8*z10^2 + 62431/2*z7^2*z8^2*z10^2
    + 23633/2*z5*z8^3*z10^2 + 5205*z6*z8^3*z10^2 + 3074*z7*z8^3*z10^2
    - 604*z8^4*z10^2 - 2*z1^3*z9*z10^2 - 3767/4*z1*z4^2*z9*z10^2 -
    6110*z4^3*z9*z10^2 - 993*v^3*z5*z9*z10^2 -
    90261/8*z4^2*z5*z9*z10^2 + 14511/2*z2*z5*z6*z9*z10^2 +
    2472*z2*z6^2*z9*z10^2 + 10027/4*z3*z6^2*z9*z10^2 -
    104685/2*z4*z6^2*z9*z10^2 - 39547*z5*z6^2*z9*z10^2 -
    41584*z6^3*z9*z10^2 + 875679/4*z5*z7^2*z9*z10^2 +
    477979*z6*z7^2*z9*z10^2 + 255509/2*z7^3*z9*z10^2 -
    694689/2*z7^2*z8*z9*z10^2 + 1754599/8*z4*z8^2*z9*z10^2 +
    247727/4*z5*z8^2*z9*z10^2 + 58958*z6*z8^2*z9*z10^2 +
    3595781/8*z7*z8^2*z9*z10^2 - 23509*z8^3*z9*z10^2 -
    8916*v^3*z9^2*z10^2 + 5393/8*z1^2*z9^2*z10^2 -
    169337/8*z1*z4*z9^2*z10^2 - 289923/8*z4^2*z9^2*z10^2 +
    29319/4*z2*z5*z9^2*z10^2 + 22465/4*z3*z5*z9^2*z10^2 -
    33847/8*z4*z5*z9^2*z10^2 + 5406*z5^2*z9^2*z10^2 +
    10071/4*z2*z6*z9^2*z10^2 + 17223/2*z3*z6*z9^2*z10^2 +
    583287/4*z4*z6*z9^2*z10^2 + 121350*z5*z6*z9^2*z10^2 +
    113124*z6^2*z9^2*z10^2 + 1695321/4*z5*z7*z9^2*z10^2 +
    3336481/2*z6*z7*z9^2*z10^2 + 4499693/4*z7^2*z9^2*z10^2 -
    10891669/8*z2*z8*z9^2*z10^2 + 1976817/2*z3*z8*z9^2*z10^2 +
    1346757/8*z4*z8*z9^2*z10^2 + 603101*z5*z8*z9^2*z10^2 +
    13719/2*z6*z8*z9^2*z10^2 + 2565611/4*z7*z8*z9^2*z10^2 -
    469609/4*z8^2*z9^2*z10^2 + 18703/8*z1*z9^3*z10^2 +
    409*z2*z9^3*z10^2 + 196825/4*z3*z9^3*z10^2 - 50343/8*z4*z9^3*z10^2
    + 717903/4*z5*z9^3*z10^2 + 1508309/4*z6*z9^3*z10^2 +
    2412583/2*z7*z9^3*z10^2 + 586347/2*z8*z9^3*z10^2 -
    10151*z9^4*z10^2 - z1^3*z10^3 - 2199/8*z1^2*z4*z10^3 -
    1882*z1*z4^2*z10^3 - 249*z4^3*z10^3 + 215*z4^2*z5*z10^3 -
    5584*v^3*z6*z10^3 + 17087/8*z2*z5*z6*z10^3 - 9505/8*z2*z6^2*z10^3
    + 2279*z3*z6^2*z10^3 - 29401*z4*z6^2*z10^3 - 23145*z5*z6^2*z10^3 -
    34563*z6^3*z10^3 + 13055*v^3*z7*z10^3 + 16990*v^2*w*z7*z10^3 -
    79261*w^3*z7*z10^3 + 92785*z6^2*z7*z10^3 + 161781/2*z5*z7^2*z10^3
    + 264163/2*z6*z7^2*z10^3 - 131042*z7^3*z10^3 + 56704*z7^2*z8*z10^3
    - 10912*z4*z8^2*z10^3 + 62841/2*z5*z8^2*z10^3 +
    29202*z6*z8^2*z10^3 + 516349/8*z7*z8^2*z10^3 + 725*z8^3*z10^3 -
    976*v^3*z9*z10^3 + 1179*z1^2*z9*z10^3 - 36069/4*z1*z4*z9*z10^3 -
    24365/4*z4^2*z9*z10^3 - 248353/4*z2*z5*z9*z10^3 -
    357273/8*z3*z5*z9*z10^3 + 43*z4*z5*z9*z10^3 - 13906*z5^2*z9*z10^3
    - 461031/8*z2*z6*z9*z10^3 - 106969/2*z3*z6*z9*z10^3 +
    3132295/4*z4*z6*z9*z10^3 + 732263*z5*z6*z9*z10^3 +
    1519521/2*z6^2*z9*z10^3 + 3268167/2*z5*z7*z9*z10^3 +
    23657449/8*z6*z7*z9*z10^3 + 452242*z7^2*z9*z10^3 -
    4589361/2*z2*z8*z9*z10^3 + 5536769/8*z3*z8*z9*z10^3 +
    4253269/8*z4*z8*z9*z10^3 - 3976063/8*z5*z8*z9*z10^3 -
    158814*z6*z8*z9*z10^3 + 1206248*z7*z8*z9*z10^3 -
    3894919/8*z8^2*z9*z10^3 + 54375/4*z1*z9^2*z10^3 -
    52693*z2*z9^2*z10^3 - 585549/8*z3*z9^2*z10^3 +
    168973/8*z4*z9^2*z10^3 + 4809973/8*z5*z9^2*z10^3 +
    13700981/8*z6*z9^2*z10^3 + 1187468*z7*z9^2*z10^3 +
    1177823/2*z8*z9^2*z10^3 + 235131/4*z9^3*z10^3 - 25334*v^2*w*z10^4
    - 427141/2*v*w^2*z10^4 + 952*z1^2*z10^4 + 4017/4*z1*z4*z10^4 +
    1999*z4^2*z10^4 + 231387/4*z2*z5*z10^4 + 412941/2*z3*z5*z10^4 +
    15415*z4*z5*z10^4 + 244383/4*z2*z6*z10^4 - 765795/4*z3*z6*z10^4 +
    6022293/8*z4*z6*z10^4 + 5897935/8*z5*z6*z10^4 +
    6687799/8*z6^2*z10^4 + 9804755/8*z5*z7*z10^4 + 871993*z6*z7*z10^4
    - 271103*z7^2*z10^4 - 3940843/8*z2*z8*z10^4 - 864203/4*z3*z8*z10^4
    - 525083/2*z4*z8*z10^4 - 11808105/8*z5*z8*z10^4 -
    836911/4*z6*z8*z10^4 + 873795/2*z7*z8*z10^4 - 2579519/4*z8^2*z10^4
    + 456215*z1*z9*z10^4 + 892951/8*z2*z9*z10^4 - 874751/8*z3*z9*z10^4
    + 3827269/8*z4*z9*z10^4 + 322377/4*z5*z9*z10^4 +
    1134596*z6*z9*z10^4 - 3353619/4*z7*z9*z10^4 +
    5826441/8*z8*z9*z10^4 - 91865/2*z9^2*z10^4 + 475325/2*z1*z10^5 -
    8322*z2*z10^5 - 524171/2*z3*z10^5 - 5839/8*z4*z10^5 +
    382603/2*z5*z10^5 - 1764147/8*z6*z10^5 - 852317/2*z7*z10^5 -
    1166165/4*z8*z10^5 - 634897*z9*z10^5 - 500699*z10^6, 8*w^3*z1^4 +
    8*z4^5*z5 - 56*z2*z5*z6^4 - 56*z2*z6^5 + 272*z3*z6^5 + 280*z4*z6^5
    - 272*z5*z7^5 + 1080*z7^5*z8 - 2736*z7^4*z8^2 + 272*z5*z8^5 +
    1656*z7*z8^5 - 16*z1^5*z9 - 120*z1*z4^4*z9 - 64*z4^5*z9 +
    64*z4^4*z5*z9 + 2080*z2*z5*z6^3*z9 + 2288*z2*z6^4*z9 +
    2816*z3*z6^4*z9 - 1376*z4*z6^4*z9 + 8*z5*z6^4*z9 + 1112*z5*z7^4*z9
    - 1912*z6*z7^4*z9 - 1576*z7^5*z9 - 6960*z7^4*z8*z9 +
    17952*z7^3*z8^2*z9 + 2808*z5*z8^4*z9 - 13240*z7*z8^4*z9 +
    112*z1^4*z9^2 + 440*z1*z4^3*z9^2 + 336*z4^4*z9^2 -
    1048*z4^3*z5*z9^2 + 6792*z2*z5*z6^2*z9^2 + 7432*z2*z6^3*z9^2 +
    3272*z3*z6^3*z9^2 - 11680*z4*z6^3*z9^2 - 8*z5*z6^3*z9^2 +
    4376*z5*z7^3*z9^2 + 15296*z6*z7^3*z9^2 + 10128*z7^4*z9^2 -
    21008*z7^3*z8*z9^2 + 37208*z7^2*z8^2*z9^2 + 3280*z5*z8^3*z9^2 -
    6584*z7*z8^3*z9^2 - 136*z1^3*z9^3 + 2928*z1*z4^2*z9^3 +
    1928*z4^3*z9^3 + 2652*z4^2*z5*z9^3 - 6728*z2*z5*z6*z9^3 -
    11896*z2*z6^2*z9^3 - 7048*z3*z6^2*z9^3 - 9056*z4*z6^2*z9^3 +
    2664*z5*z7^2*z9^3 + 21744*z6*z7^2*z9^3 + 29600*z7^3*z9^3 +
    1488*z7^2*z8*z9^3 + 25100*z4*z8^2*z9^3 - 7048*z5*z8^2*z9^3 +
    14884*z7*z8^2*z9^3 + 8*v^3*z9^4 + 788*z1^2*z9^4 - 11884*z1*z4*z9^4
    - 10804*z4^2*z9^4 - 30088*z2*z5*z9^4 - 16032*z3*z5*z9^4 +
    692*z4*z5*z9^4 - 72*z5^2*z9^4 - 46488*z2*z6*z9^4 + 5024*z3*z6*z9^4
    + 9512*z4*z6*z9^4 - 72*z5*z6*z9^4 - 40712*z5*z7*z9^4 -
    25280*z6*z7*z9^4 + 13040*z7^2*z9^4 + 9164*z2*z8*z9^4 +
    36560*z3*z8*z9^4 - 23244*z4*z8*z9^4 + 57608*z5*z8*z9^4 +
    51032*z7*z8*z9^4 - 9244*z1*z9^5 - 23856*z2*z9^5 - 6436*z4*z9^5 +
    5448*z7*z9^5 - 40*w^3*z1^3*z10 - 32*z1^4*z4*z10 - 96*z1^3*z4^2*z10
    + 304*z1^2*z4^3*z10 - 112*z1*z4^4*z10 + 8*z4^5*z10 +
    40*z4^4*z5*z10 - 1320*z2*z5*z6^3*z10 - 1328*z2*z6^4*z10 -
    1192*z3*z6^4*z10 + 408*z4*z6^4*z10 + 16*z5*z6^4*z10 +
    16*v^5*w*z7*z10 - 32*v^3*z6^2*z7*z10 - 64*z6^4*z7*z10 +
    176*v^3*z6*z7^2*z10 - 752*z6^3*z7^2*z10 - 368*v^3*z7^3*z10 -
    520*v^2*w*z7^3*z10 + 1072*w^3*z7^3*z10 - 1480*z6^2*z7^3*z10 -
    4408*z5*z7^4*z10 - 1160*z6*z7^4*z10 + 1072*z7^5*z10 +
    5752*z7^4*z8*z10 - 10808*z7^3*z8^2*z10 - 1560*z5*z8^4*z10 -
    1656*z6*z8^4*z10 + 2320*z7*z8^4*z10 + 2152*z8^5*z10 +
    232*z1^4*z9*z10 + 184*z1*z4^3*z9*z10 - 208*z4^4*z9*z10 +
    88*z4^3*z5*z9*z10 + 8*v^3*z5^2*z9*z10 - 9128*z2*z5*z6^2*z9*z10 -
    9496*z2*z6^3*z9*z10 + 704*z3*z6^3*z9*z10 + 9808*z4*z6^3*z9*z10 -
    536*z5*z6^3*z9*z10 - 216*z6^4*z9*z10 + 11544*z5*z7^3*z9*z10 -
    44800*z6*z7^3*z9*z10 - 36240*z7^4*z9*z10 + 27592*z7^3*z8*z9*z10 -
    31496*z7^2*z8^2*z9*z10 + 25304*z5*z8^3*z9*z10 +
    16840*z6*z8^3*z9*z10 + 49656*z7*z8^3*z9*z10 - 12928*z8^4*z9*z10 -
    336*z1^3*z9^2*z10 + 1756*z1*z4^2*z9^2*z10 - 672*z4^3*z9^2*z10 +
    72*v^3*z5*z9^2*z10 + 2506*z4^2*z5*z9^2*z10 +
    17480*z2*z5*z6*z9^2*z10 + 19944*z2*z6^2*z9^2*z10 +
    31564*z3*z6^2*z9^2*z10 - 23240*z4*z6^2*z9^2*z10 -
    5184*z5*z6^2*z9^2*z10 - 976*z6^3*z9^2*z10 + 65196*z5*z7^2*z9^2*z10
    + 71760*z6*z7^2*z9^2*z10 - 45560*z7^3*z9^2*z10 -
    157264*z7^2*z8*z9^2*z10 - 40310*z4*z8^2*z9^2*z10 +
    48372*z5*z8^2*z9^2*z10 + 14216*z6*z8^2*z9^2*z10 +
    112502*z7*z8^2*z9^2*z10 - 6232*z8^3*z9^2*z10 + 192*v^3*z9^3*z10 +
    1086*z1^2*z9^3*z10 - 5374*z1*z4*z9^3*z10 + 2582*z4^2*z9^3*z10 +
    45068*z2*z5*z9^3*z10 - 18732*z3*z5*z9^3*z10 - 18954*z4*z5*z9^3*z10
    - 128*z5^2*z9^3*z10 + 44044*z2*z6*z9^3*z10 + 5384*z3*z6*z9^3*z10 -
    100548*z4*z6*z9^3*z10 - 29608*z5*z6*z9^3*z10 - 23096*z6^2*z9^3*z10
    - 1692*z5*z7*z9^3*z10 + 218480*z6*z7*z9^3*z10 +
    169108*z7^2*z9^3*z10 - 180270*z2*z8*z9^3*z10 +
    130344*z3*z8*z9^3*z10 + 39254*z4*z8*z9^3*z10 +
    148200*z5*z8*z9^3*z10 - 4128*z6*z8*z9^3*z10 - 89908*z7*z8*z9^3*z10
    + 40892*z8^2*z9^3*z10 - 3406*z1*z9^4*z10 - 18952*z2*z9^4*z10 +
    22204*z3*z9^4*z10 - 10074*z4*z9^4*z10 - 52892*z5*z9^4*z10 -
    49956*z6*z9^4*z10 + 203576*z7*z9^4*z10 + 51032*z8*z9^4*z10 -
    31112*z9^5*z10 + 8*v^5*w*z10^2 + 96*w^3*z1^2*z10^2 + 88*z1^4*z10^2
    + 80*z1^3*z4*z10^2 + 240*z1^2*z4^2*z10^2 - 504*z1*z4^3*z10^2 +
    96*z4^4*z10^2 + 16*z4^3*z5*z10^2 - 16*v^3*z5*z6*z10^2 -
    24*v^3*z6^2*z10^2 + 6520*z2*z5*z6^2*z10^2 + 6496*z2*z6^3*z10^2 +
    4272*z3*z6^3*z10^2 - 3984*z4*z6^3*z10^2 + 1832*z5*z6^3*z10^2 +
    1912*z6^4*z10^2 + 608*v^3*z6*z7*z10^2 - 15576*z6^3*z7*z10^2 -
    8016*v^3*z7^2*z10^2 - 46880*v^2*w*z7^2*z10^2 + 7440*w^3*z7^2*z10^2
    - 91104*z6^2*z7^2*z10^2 - 18376*z5*z7^3*z10^2 -
    76712*z6*z7^3*z10^2 + 10664*z7^4*z10^2 - 25976*z7^3*z8*z10^2 -
    5128*z7^2*z8^2*z10^2 - 4688*z5*z8^3*z10^2 - 3240*z6*z8^3*z10^2 +
    18312*z7*z8^3*z10^2 + 2160*z8^4*z10^2 - 608*z1^3*z9*z10^2 +
    1458*z1*z4^2*z9*z10^2 - 352*z4^3*z9*z10^2 + 16*v^3*z5*z9*z10^2 -
    1013*z4^2*z5*z9*z10^2 - 3248*z2*z5*z6*z9*z10^2 -
    5208*z2*z6^2*z9*z10^2 - 8622*z3*z6^2*z9*z10^2 -
    15352*z4*z6^2*z9*z10^2 - 10960*z5*z6^2*z9*z10^2 -
    13552*z6^3*z9*z10^2 - 55254*z5*z7^2*z9*z10^2 -
    187576*z6*z7^2*z9*z10^2 - 13528*z7^3*z9*z10^2 +
    70756*z7^2*z8*z9*z10^2 - 11433*z4*z8^2*z9*z10^2 +
    4226*z5*z8^2*z9*z10^2 - 18688*z6*z8^2*z9*z10^2 -
    183823*z7*z8^2*z9*z10^2 + 64048*z8^3*z9*z10^2 + 496*v^3*z9^2*z10^2
    + 16*w^3*z9^2*z10^2 + 1341*z1^2*z9^2*z10^2 + 4147*z1*z4*z9^2*z10^2
    + 4337*z4^2*z9^2*z10^2 - 42286*z2*z5*z9^2*z10^2 +
    16730*z3*z5*z9^2*z10^2 + 2389*z4*z5*z9^2*z10^2 -
    192*z5^2*z9^2*z10^2 - 46710*z2*z6*z9^2*z10^2 +
    8060*z3*z6*z9^2*z10^2 + 208354*z4*z6*z9^2*z10^2 +
    138432*z5*z6*z9^2*z10^2 + 139360*z6^2*z9^2*z10^2 +
    421022*z5*z7*z9^2*z10^2 + 478208*z6*z7*z9^2*z10^2 -
    42374*z7^2*z9^2*z10^2 - 366301*z2*z8*z9^2*z10^2 -
    31900*z3*z8*z9^2*z10^2 + 65333*z4*z8*z9^2*z10^2 -
    233360*z5*z8*z9^2*z10^2 - 82344*z6*z8*z9^2*z10^2 +
    199362*z7*z8*z9^2*z10^2 - 110850*z8^2*z9^2*z10^2 -
    2889*z1*z9^3*z10^2 + 12180*z2*z9^3*z10^2 - 51174*z3*z9^3*z10^2 -
    23*z4*z9^3*z10^2 + 170358*z5*z9^3*z10^2 + 428006*z6*z9^3*z10^2 +
    92548*z7*z9^3*z10^2 - 35720*z8*z9^3*z10^2 + 71220*z9^4*z10^2 -
    160*w^3*z1*z10^3 - 224*z1^3*z10^3 - 371*z1^2*z4*z10^3 +
    48*z1*z4^2*z10^3 + 208*z4^3*z10^3 - 192*z4^2*z5*z10^3 +
    392*v^3*z6*z10^3 - 4309*z2*z5*z6*z10^3 - 3797*z2*z6^2*z10^3 +
    15616*z3*z6^2*z10^3 + 94088*z4*z6^2*z10^3 + 91256*z5*z6^2*z10^3 +
    76016*z6^3*z10^3 - 1328*v^3*z7*z10^3 + 103400*v^2*w*z7*z10^3 +
    104568*w^3*z7*z10^3 + 155696*z6^2*z7*z10^3 - 82184*z5*z7^2*z10^3 +
    163296*z6*z7^2*z10^3 + 129568*z7^3*z10^3 + 196168*z7^2*z8*z10^3 -
    78672*z4*z8^2*z10^3 - 68936*z5*z8^2*z10^3 - 106088*z6*z8^2*z10^3 -
    440835*z7*z8^2*z10^3 + 35744*z8^3*z10^3 + 8*v^3*z9*z10^3 -
    112*w^3*z9*z10^3 + 1744*z1^2*z9*z10^3 + 1402*z1*z4*z9*z10^3 -
    378*z4^2*z9*z10^3 + 8650*z2*z5*z9*z10^3 + 6819*z3*z5*z9*z10^3 +
    1392*z4*z5*z9*z10^3 + 2016*z5^2*z9*z10^3 - 10899*z2*z6*z9*z10^3 -
    52420*z3*z6*z9*z10^3 + 29190*z4*z6*z9*z10^3 +
    166252*z5*z6*z9*z10^3 + 166452*z6^2*z9*z10^3 -
    119608*z5*z7*z9*z10^3 - 34423*z6*z7*z9*z10^3 +
    191580*z7^2*z9*z10^3 + 526684*z2*z8*z9*z10^3 -
    444431*z3*z8*z9*z10^3 + 43653*z4*z8*z9*z10^3 -
    438247*z5*z8*z9*z10^3 + 115784*z6*z8*z9*z10^3 -
    240836*z7*z8*z9*z10^3 - 131683*z8^2*z9*z10^3 - 2298*z1*z9^2*z10^3
    + 13564*z2*z9^2*z10^3 + 22571*z3*z9^2*z10^3 - 2631*z4*z9^2*z10^3 -
    34635*z5*z9^2*z10^3 + 19357*z6*z9^2*z10^3 - 101464*z7*z9^2*z10^3 +
    68792*z8*z9^2*z10^3 - 5138*z9^3*z10^3 + 3344*v^2*w*z10^4 +
    110464*v*w^2*z10^4 + 96*w^3*z10^4 + 568*z1^2*z10^4 +
    534*z1*z4*z10^4 - 192*z4^2*z10^4 - 87094*z2*z5*z10^4 -
    104400*z3*z5*z10^4 - 1424*z4*z5*z10^4 - 80950*z2*z6*z10^4 -
    120726*z3*z6*z10^4 - 270715*z4*z6*z10^4 - 246377*z5*z6*z10^4 +
    6215*z6^2*z10^4 - 345017*z5*z7*z10^4 - 37468*z6*z7*z10^4 +
    289424*z7^2*z10^4 + 69433*z2*z8*z10^4 - 27542*z3*z8*z10^4 +
    317656*z4*z8*z10^4 + 426491*z5*z8*z10^4 + 210838*z6*z8*z10^4 +
    188892*z7*z8*z10^4 - 188722*z8^2*z10^4 - 226744*z1*z9*z10^4 +
    68547*z2*z9*z10^4 + 130973*z3*z9*z10^4 - 226399*z4*z9*z10^4 -
    6754*z5*z9*z10^4 + 50196*z6*z9*z10^4 + 575626*z7*z9*z10^4 -
    365887*z8*z9*z10^4 + 457560*z9^2*z10^4 - 114664*z1*z10^5 -
    12960*z2*z10^5 + 317560*z3*z10^5 - 211*z4*z10^5 - 102848*z5*z10^5
    - 121619*z6*z10^5 + 480560*z7*z10^5 - 76694*z8*z10^5 +
    623568*z9*z10^5 + 431792*z10^6 ];
  hh := [ 1, v, z1 + z3, w, v*z2 + v*z6 - 3*v*z9, v*z2*z5 + v*z2*z6 -
    v*z4*z6 - v*z5*z7 - v*z6*z7 + v*z5*z8, z2*z3 - z2*z6 - 2*z2*z9 +
    z4*z9 - z6*z10 ];
  gg[6] *:= 4;
  gg[7] *:= 2;
  return gg,hh;
end function;

// The quadratics f1, f2 at the end of Section 5, and f1,f2,f3 at
// the end of Section 6, have the same discriminants, up to
// multiplication by squares. Here we record the square roots
// (in the function field Q(Sigma)) needed to check this.

function MySquareRoots(k,T,x,y)
  if k eq 1 then
  c1 := T^2*y - x^2 - T*x + T^3;
  c2 := ((T^2 + 2*T)*x^2 + (-2*T^5 - 9*T^4 - 3*T^3 + 4*T^2)*x +
    (T^8 + 6*T^7 + T^6 - 10*T^5 - 4*T^4 + 2*T^3))*y - x^4 + (2*T^3 -
    T^2 - 5*T)*x^3 + (-T^6 + 11*T^5 + 22*T^4 + 3*T^3 - 7*T^2)*x^2 +
    (-8*T^8 - 19*T^7 + 5*T^6 + 23*T^5 + 4*T^4 - 3*T^3)*x - 7*T^9 -
    12*T^8 - 3*T^7 + 2*T^6;
  c3 := (x^13 + (10*T^4 + 28*T^3 + 24*T^2 + 7*T)*x^12 + (15*T^8 +
    60*T^7 + 140*T^6 + 255*T^5 + 266*T^4 + 155*T^3 + 21*T^2)*x^11 +
    (7*T^12 + 30*T^11 + 155*T^10 + 635*T^9 + 1517*T^8 + 2310*T^7 +
    1941*T^6 + 953*T^5 + 426*T^4 + 35*T^3)*x^10 + (T^16 + 4*T^15 +
    69*T^14 + 405*T^13 + 1307*T^12 + 3126*T^11 + 5446*T^10 + 7478*T^9
    + 8357*T^8 + 5553*T^7 + 1747*T^6 + 645*T^5 + 35*T^4)*x^9 +
    (11*T^18 + 69*T^17 + 284*T^16 + 909*T^15 + 1475*T^14 + 686*T^13 +
    562*T^12 + 3590*T^11 + 7965*T^10 + 10820*T^9 + 7424*T^8 + 1790*T^7
    + 580*T^6 + 21*T^5)*x^8 + (18*T^20 + 104*T^19 + 18*T^18 - 980*T^17
    - 2364*T^16 - 4580*T^15 - 12308*T^14 - 21844*T^13 - 21821*T^12 -
    10882*T^11 + 2016*T^10 + 4621*T^9 + 1008*T^8 + 309*T^7 +
    7*T^6)*x^7 + (-26*T^22 - 142*T^21 - 184*T^20 - 231*T^19 -
    1494*T^18 - 2766*T^17 - 2951*T^16 - 9455*T^15 - 24636*T^14 -
    34806*T^13 - 25833*T^12 - 6963*T^11 + 809*T^10 + 261*T^9 + 90*T^8
    + T^7)*x^6 + (-3*T^24 - 36*T^23 - 177*T^22 - 129*T^21 + 650*T^20 +
    2165*T^19 + 6440*T^18 + 15951*T^17 + 23772*T^16 + 14518*T^15 -
    7746*T^14 - 14774*T^13 - 5550*T^12 - 373*T^11 + 3*T^10 +
    11*T^9)*x^5 + (-T^26 - 7*T^25 - 24*T^24 - 13*T^23 + 290*T^22 +
    1109*T^21 + 2100*T^20 + 3736*T^19 + 11368*T^18 + 26218*T^17 +
    28812*T^16 + 11864*T^15 - 673*T^14 - 1155*T^13 - 128*T^12 -
    8*T^11)*x^4 + (-2*T^26 - 24*T^25 - 114*T^24 - 381*T^23 - 888*T^22
    - 2483*T^21 - 6962*T^20 - 8661*T^19 - 340*T^18 + 7405*T^17 +
    5207*T^16 + 1094*T^15 + 49*T^14)*x^3 + (T^28 + 5*T^27 + 18*T^26 -
    20*T^25 - 415*T^24 - 979*T^23 - 1646*T^22 - 4004*T^21 - 6450*T^20
    - 5000*T^19 - 1688*T^18 - 182*T^17)*x^2 + (56*T^27 + 212*T^26 +
    238*T^25 + 162*T^24 + 383*T^23 + 553*T^22 + 295*T^21 + 45*T^20)*x
    + (32*T^28 + 136*T^27 + 224*T^26 + 176*T^25 + 64*T^24 + 8*T^23))*y
    + (-4*T^2 - 8*T - 1)*x^14 + (-10*T^6 - 42*T^5 - 89*T^4 - 112*T^3 -
    82*T^2 - 7*T)*x^13 + (-6*T^10 - 30*T^9 - 135*T^8 - 465*T^7 -
    954*T^6 - 1058*T^5 - 712*T^4 - 337*T^3 - 21*T^2)*x^12 + (-T^14 -
    5*T^13 - 65*T^12 - 385*T^11 - 1338*T^10 - 3395*T^9 - 6204*T^8 -
    7051*T^7 - 4813*T^6 - 2087*T^5 - 748*T^4 - 35*T^3)*x^11 +
    (-11*T^16 - 79*T^15 - 361*T^14 - 1241*T^13 - 2803*T^12 - 4920*T^11
    - 10903*T^10 - 19438*T^9 - 19529*T^8 - 10579*T^7 - 3385*T^6 -
    995*T^5 - 35*T^4)*x^10 + (-18*T^18 - 111*T^17 - 101*T^16 +
    857*T^15 + 3581*T^14 + 10473*T^13 + 18929*T^12 + 11657*T^11 -
    11918*T^10 - 22304*T^9 - 12049*T^8 - 3204*T^7 - 818*T^6 -
    21*T^5)*x^9 + (26*T^20 + 186*T^19 + 548*T^18 + 1366*T^17 +
    3395*T^16 + 10914*T^15 + 35529*T^14 + 71527*T^13 + 76192*T^12 +
    32657*T^11 - 4934*T^10 - 6620*T^9 - 1722*T^8 - 407*T^7 -
    7*T^6)*x^8 + (3*T^22 + 13*T^21 - 17*T^20 - 555*T^19 - 4272*T^18 -
    16680*T^17 - 32273*T^16 - 19978*T^15 + 39088*T^14 + 85107*T^13 +
    56729*T^12 + 10570*T^11 - 887*T^10 - 447*T^9 - 112*T^8 - T^7)*x^7
    + (T^24 + 5*T^23 + 15*T^22 + 202*T^21 + 687*T^20 - 2758*T^19 -
    23608*T^18 - 72962*T^17 - 111603*T^16 - 68115*T^15 + 12506*T^14 +
    29235*T^13 + 8338*T^12 + 601*T^11 - 17*T^10 - 13*T^9)*x^6 + (-T^25
    + 33*T^24 + 315*T^23 + 1873*T^22 + 7033*T^21 + 19943*T^20 +
    30558*T^19 - 3994*T^18 - 71938*T^17 - 78325*T^16 - 26217*T^15 +
    1671*T^14 + 1679*T^13 + 182*T^12 + 10*T^11)*x^5 + (-12*T^27 -
    84*T^26 - 270*T^25 - 97*T^24 + 876*T^23 + 2653*T^22 + 17569*T^21 +
    50855*T^20 + 55555*T^19 + 12965*T^18 - 15937*T^17 - 10163*T^16 -
    1721*T^15 - 69*T^14)*x^4 + (-T^28 - 124*T^27 - 822*T^26 -
    1537*T^25 - 2374*T^24 - 7144*T^23 - 7552*T^22 + 8850*T^21 +
    22596*T^20 + 15628*T^19 + 4171*T^18 + 345*T^17)*x^3 + (67*T^29 +
    141*T^28 - 479*T^27 - 1465*T^26 - 1947*T^25 - 4316*T^24 -
    7703*T^23 - 6525*T^22 - 2382*T^21 - 279*T^20)*x^2 + (88*T^30 +
    316*T^29 + 262*T^28 - 158*T^27 - 177*T^26 + 145*T^25 + 159*T^24 +
    29*T^23)*x + 32*T^31 + 136*T^30 + 224*T^29 + 176*T^28 + 64*T^27 +
    8*T^26;
  D17 := (x + T - T^3)*(y - x + T^2) - T*(x + T)^2 + (T^4 + T^3)*(x + T)
          + T^5;
  m1 := -2*c2*(y + (T^2 - T - 1)*x + T^3)*(y - (2*T + 1)*x + T^3*(T + 1))
          /(T^6*x^3*(x + T)*(x + T - T^3)*(x - T^2)^4*c1);
  m2 := 16*c3*D17/(T^11*x^7*(x + T - T^3)*(x - T^2)^3*c1^4);
  eps := T^2/(x + T)*(y - x + T^2) + x + T^2*(T^2 - T - 1);
  mm := [eps*m1,eps*m2];
  else
  pi1 := y + (T^2 - 1)*x + T^3;
  pi2 := y + (T^2 - T - 1)*x + T^3;
  pi3 := ((T^2 + 2*T)*x + T^2)*y - x^3 + (-T^3 - 2*T^2 - 3*T)*x^2 - T^2*x;
  pi4 := (T - 1)*y + (T + 1)*x;
  pi5 := y - (2*T + 1)*x - T^2;
  pi6 := ((T^2 + 9*T)*x^5 + (3*T^5 + 21*T^4 + 31*T^3 + 20*T^2)*x^4 +
    (T^8 + 5*T^7 + 12*T^6 + 40*T^5 + 49*T^4 + 13*T^3)*x^3 + (3*T^9 +
    14*T^8 + 14*T^7 + 19*T^6 + 23*T^5 + 2*T^4)*x^2 + (3*T^10 + 13*T^9
    + 11*T^8 + 5*T^7 + 4*T^6)*x + (T^11 + 4*T^10 + 3*T^9 + T^8))*y -
    x^7 + (-5*T^3 - 31*T^2 - 12*T)*x^6 + (2*T^6 - 7*T^5 - 46*T^4 -
    105*T^3 - 23*T^2)*x^5 + (3*T^8 + 11*T^7 + 2*T^6 - 50*T^5 - 108*T^4
    - 14*T^3)*x^4 + (3*T^9 + 13*T^8 + 21*T^7 - T^6 - 39*T^5 -
    2*T^4)*x^3 + (T^9 + 5*T^8 + 4*T^7 - 5*T^6)*x^2;
  pi7 := ((2*T^3 + 4*T^2 - 8*T)*x^16 + (T^7 + 24*T^6 + 25*T^5 - 66*T^4 -
    2*T^3 - 61*T^2)*x^15 + (10*T^10 + 50*T^9 - 10*T^8 + 163*T^7 +
    1007*T^6 + 680*T^5 - 158*T^4 - 201*T^3)*x^14 + (15*T^13 + 60*T^12
    + 135*T^11 + 580*T^10 + 379*T^9 + 530*T^8 + 5726*T^7 + 5006*T^6 -
    656*T^5 - 373*T^4)*x^13 + (10*T^16 - 6*T^15 - 218*T^14 - 836*T^13
    - 1632*T^12 + 807*T^11 + 2050*T^10 - 724*T^9 + 13552*T^8 +
    12698*T^7 - 1269*T^6 - 425*T^5)*x^12 + (-58*T^18 - 275*T^17 -
    458*T^16 - 386*T^15 - 2491*T^14 - 10459*T^13 - 7395*T^12 +
    2476*T^11 - 6901*T^10 + 16728*T^9 + 16812*T^8 - 1392*T^7 -
    303*T^6)*x^11 + (-5*T^22 - 49*T^21 - 88*T^20 + 6*T^19 - 763*T^18 -
    3224*T^17 - 1117*T^16 + 3765*T^15 - 19173*T^14 - 32225*T^13 -
    5152*T^12 - 14403*T^11 + 12439*T^10 + 12687*T^9 - 917*T^8 -
    131*T^7)*x^10 + (-T^25 - 2*T^24 - 2*T^23 - 251*T^22 - 961*T^21 +
    178*T^20 + 2621*T^19 - 5791*T^18 - 9829*T^17 + 19975*T^16 -
    3040*T^15 - 56530*T^14 - 21793*T^13 - 16023*T^12 + 7940*T^11 +
    5244*T^10 - 368*T^9 - 31*T^8)*x^9 + (-9*T^26 - 32*T^25 + 110*T^24
    - 126*T^23 - 3424*T^22 - 3403*T^21 + 12255*T^20 + 6437*T^19 -
    26425*T^18 + 21075*T^17 + 35472*T^16 - 49483*T^15 - 34901*T^14 -
    13833*T^13 + 6379*T^12 + 882*T^11 - 91*T^10 - 3*T^9)*x^8 +
    (-36*T^27 - 184*T^26 + 317*T^25 + 1828*T^24 - 4545*T^23 -
    15522*T^22 + 13294*T^21 + 36669*T^20 - 25563*T^19 - 4297*T^18 +
    53410*T^17 - 15268*T^16 - 30343*T^15 - 11781*T^14 + 4347*T^13 -
    78*T^12 - 14*T^11)*x^7 + (-84*T^28 - 560*T^27 + 21*T^26 +
    5534*T^25 + 1779*T^24 - 27041*T^23 - 8920*T^22 + 52516*T^21 +
    3643*T^20 - 21968*T^19 + 34494*T^18 + 10074*T^17 - 13176*T^16 -
    7944*T^15 + 1610*T^14 - 29*T^13 - T^12)*x^6 + (-126*T^29 -
    1036*T^28 - 1379*T^27 + 7038*T^26 + 13281*T^25 - 20948*T^24 -
    33545*T^23 + 31456*T^22 + 26744*T^21 - 12169*T^20 + 9557*T^19 +
    11253*T^18 - 943*T^17 - 3060*T^16 + 210*T^15 + 2*T^14)*x^5 +
    (-126*T^30 - 1232*T^29 - 3017*T^28 + 3644*T^27 + 17719*T^26 -
    2153*T^25 - 31721*T^24 + 1311*T^23 + 20328*T^22 + 1364*T^21 +
    176*T^20 + 3733*T^19 + 1309*T^18 - 461*T^17 - 11*T^16)*x^4 +
    (-84*T^31 - 952*T^30 - 3225*T^29 - 956*T^28 + 11141*T^27 +
    8088*T^26 - 12992*T^25 - 8096*T^24 + 4878*T^23 + 2919*T^22 -
    219*T^21 + 251*T^20 + 343*T^19 + 9*T^18)*x^3 + (-36*T^32 -
    464*T^31 - 1948*T^30 - 2277*T^29 + 3025*T^28 + 5587*T^27 -
    1361*T^26 - 3718*T^25 - 726*T^24 + 543*T^23 + 45*T^22 -
    61*T^21)*x^2 + (-9*T^33 - 130*T^32 - 639*T^31 - 1131*T^30 -
    36*T^29 + 1318*T^28 + 483*T^27 - 430*T^26 - 375*T^25 - 59*T^24)*x
    - T^34 - 16*T^33 - 89*T^32 - 198*T^31 - 131*T^30 + 60*T^29 +
    86*T^28 + 34*T^27)*y + (-T + 1)*x^18 + (-T^5 - 15*T^4 - 2*T^3 +
    19*T^2 + 16*T)*x^17 + (-10*T^8 - 45*T^7 + 16*T^6 - 38*T^5 -
    155*T^4 + 217*T^3 + 89*T^2)*x^16 + (-15*T^11 - 65*T^10 - 206*T^9 -
    958*T^8 - 1926*T^7 - 3101*T^6 - 1914*T^5 + 933*T^4 + 257*T^3)*x^15
    + (-10*T^14 - 4*T^13 + 161*T^12 + 863*T^11 + 2317*T^10 - 498*T^9 -
    10345*T^8 - 18664*T^7 - 7912*T^6 + 2208*T^5 + 443*T^4)*x^14 +
    (53*T^16 + 281*T^15 + 634*T^14 + 847*T^13 + 3976*T^12 + 17384*T^11
    + 19955*T^10 - 16086*T^9 - 47847*T^8 - 16466*T^7 + 3196*T^6 +
    481*T^5)*x^13 + (5*T^20 + 53*T^19 + 147*T^18 + 191*T^17 + 788*T^16
    + 2410*T^15 - 237*T^14 - 491*T^13 + 42166*T^12 + 79308*T^11 +
    6852*T^10 - 68144*T^9 - 19787*T^8 + 2930*T^7 + 331*T^6)*x^12 +
    (T^23 + 3*T^22 + 2*T^21 + 194*T^20 + 925*T^19 + 880*T^18 -
    172*T^17 + 2660*T^16 - 7300*T^15 - 31434*T^14 + 39178*T^13 +
    141377*T^12 + 53288*T^11 - 60199*T^10 - 14218*T^9 + 1702*T^8 +
    139*T^7)*x^11 + (8*T^24 + 36*T^23 - 62*T^22 - 81*T^21 + 1893*T^20
    + 3260*T^19 - 2076*T^18 + 35*T^17 - 14068*T^16 - 76876*T^15 -
    12076*T^14 + 140757*T^13 + 76970*T^12 - 35817*T^11 - 5808*T^10 +
    613*T^9 + 32*T^8)*x^10 + (28*T^25 + 167*T^24 - 64*T^23 - 1402*T^22
    + 666*T^21 + 6360*T^20 - 837*T^19 - 761*T^18 - 6030*T^17 -
    88484*T^16 - 61851*T^15 + 82608*T^14 + 59837*T^13 - 15999*T^12 -
    1048*T^11 + 133*T^10 + 3*T^9)*x^9 + (56*T^26 + 413*T^25 + 384*T^24
    - 2639*T^23 - 2929*T^22 + 7190*T^21 + 3228*T^20 + 75*T^19 +
    10168*T^18 - 54270*T^17 - 62188*T^16 + 27744*T^15 + 30047*T^14 -
    5860*T^13 + 40*T^12 + 17*T^11)*x^8 + (70*T^27 + 609*T^26 +
    1184*T^25 - 1993*T^24 - 4799*T^23 + 5968*T^22 + 5568*T^21 -
    3111*T^20 + 12683*T^19 - 16472*T^18 - 32966*T^17 + 3528*T^16 +
    10825*T^15 - 1538*T^14 + 24*T^13 + T^12)*x^7 + (56*T^28 + 553*T^27
    + 1462*T^26 - 463*T^25 - 3579*T^24 + 4545*T^23 + 5416*T^22 -
    6758*T^21 + 2875*T^20 - 1780*T^19 - 10431*T^18 - 1626*T^17 +
    2731*T^16 - 165*T^15 - 2*T^14)*x^6 + (28*T^29 + 301*T^28 +
    888*T^27 - 105*T^26 - 2275*T^25 + 2519*T^24 + 4176*T^23 -
    4963*T^22 - 2839*T^21 - 483*T^20 - 1865*T^19 - 1068*T^18 +
    325*T^17 + 11*T^16)*x^5 + (8*T^30 + 87*T^29 + 211*T^28 - 457*T^27
    - 1740*T^26 + 384*T^25 + 2256*T^24 - 1218*T^23 - 1832*T^22 -
    565*T^21 - 91*T^20 - 198*T^19 - 9*T^18)*x^4 + (T^31 + 8*T^30 -
    26*T^29 - 370*T^28 - 923*T^27 - 341*T^26 + 645*T^25 + 161*T^24 -
    258*T^23 - 169*T^22 + 9*T^21)*x^3 + (-T^31 - 16*T^30 - 89*T^29 -
    198*T^28 - 131*T^27 + 60*T^26 + 86*T^25 + 34*T^24)*x^2;
  sqrt1 := -2/T^2*x^4*(x + T)^2/pi1^2/pi2^2*pi3*pi4*pi5;
  sqrt2 := -1/T^3*x^5*(x + T)/pi1^2/pi2^3*pi5^2*pi6;
  sqrt3 := 2^4*x^6*pi3*pi5*pi7/(T^6*(x - T^2)*pi1^2*pi2^4);
  mm := [sqrt1,sqrt2,sqrt3];
  end if;
  return mm;
end function;

// Some randomly chosen points on X(17) over GF(p) where p = 10^9 + 7

random_modp_points := [ [ 536697596, 613227521, 39189966, 158774284,
    126918257, 707094260, 58642768, 839405650, 1 ], [ 899704351,
    260536182, 627816963, 454472733, 231298891, 600681139, 855429071,
    157889016, 1 ], [ 964483236, 635802791, 32303378, 788633195,
    894060016, 568835239, 106638150, 740099290, 1 ], [ 657325310,
    194235055, 461628007, 947824841, 671076343, 887725421, 103052022,
    552618596, 1 ], [ 473892914, 881137028, 233673699, 437702755,
    747116785, 15467, 894647346, 68766173, 1 ], [ 6029066, 526049268,
    922172119, 923151453, 345801948, 775134955, 772016234, 879119088,
    1 ], [ 957170969, 355351660, 451602841, 229981745, 802911909,
    295273721, 467572549, 833310091, 1 ], [ 801828817, 610226221,
    871790070, 846656830, 457959346, 630094737, 599259218, 402424476,
    1 ], [ 201129876, 746014114, 615439048, 539368765, 352228195,
    582183626, 715453803, 779683580, 1 ], [ 103217899, 34527222,
    440034324, 600391092, 894567772, 721252071, 838771874, 418861253,
    1 ], [ 997061532, 913825152, 250668114, 154606946, 875622451,
    685069199, 395325690, 458969017, 1 ], [ 624424600, 995000362,
    342428648, 676010511, 365283102, 347458318, 974559875, 283746215,
    1 ], [ 180564348, 518956692, 636728307, 721170815, 719800074,
    499375255, 623779923, 217299571, 1 ], [ 681661917, 546279852,
    81354269, 272539466, 255617318, 891723579, 607156524, 478040768, 1
    ], [ 649604341, 415199009, 707214132, 233743880, 88581903,
    40282719, 411158512, 358913900, 1 ], [ 436455218, 35606405,
    818523588, 722864316, 746084661, 586665456, 522544730, 853880554,
    1 ], [ 874019583, 604835039, 491182873, 747378798, 46603549,
    101046049, 184046755, 437657682, 1 ], [ 711661813, 10098265,
    382362029, 97660985, 186806684, 246467581, 702253161, 340135336, 1
    ], [ 82961798, 410862257, 478809250, 372285501, 215964850,
    941060907, 290343236, 427927620, 1 ], [ 871351070, 547440615,
    604846347, 402734556, 559985178, 822020257, 240364662, 328924208,
    1 ], [ 898173984, 487128860, 414626836, 473199572, 934163411,
    683509674, 786359026, 168442118, 1 ], [ 737683417, 332057866,
    336873792, 640469308, 211152624, 672720103, 126087970, 869564729,
    1 ], [ 69997997, 539753205, 960585158, 6407168, 665676038,
    669370965, 195169849, 870287424, 1 ], [ 756225615, 992285407,
    565633367, 514063643, 241563214, 559569210, 966676557, 332719507,
    1 ], [ 462483831, 917454572, 898655002, 740440007, 282068396,
    245584060, 206050654, 382221086, 1 ], [ 630587027, 444390026,
    364545712, 153618722, 83159329, 812267305, 73313229, 963159515, 1
    ], [ 186449004, 280585463, 472204947, 743534223, 925039414,
    904962412, 766289970, 327561606, 1 ], [ 76923533, 209407143,
    815351495, 244196647, 61152788, 995515738, 853332443, 895899444, 1
    ], [ 423181553, 856686952, 20056843, 731463519, 376944264,
    522003922, 645572696, 122171714, 1 ], [ 19894807, 66222814,
    90592173, 928395694, 239727671, 236303645, 422103519, 969898392, 1
    ], [ 471405020, 442999385, 735258477, 715634366, 30224480,
    808924718, 353750600, 750776626, 1 ], [ 390599869, 781322302,
    216063023, 905070307, 922312049, 734523357, 202899744, 130061693,
    1 ], [ 760292615, 480667988, 639095161, 609188104, 632049885,
    473476813, 48494362, 2773701, 1 ], [ 557130972, 149819139,
    552895793, 270007575, 72282906, 999436135, 869361069, 819445696, 1
    ], [ 971826651, 533966958, 159421039, 350147712, 548118552,
    419987950, 232126099, 891353397, 1 ], [ 544176887, 12900883,
    776421508, 788088020, 853892111, 669567029, 5507284, 920042966, 1
    ], [ 82823852, 933959620, 421345195, 732291620, 724675921,
    854705573, 112044585, 232331781, 1 ], [ 691890806, 111993924,
    708450317, 109404916, 605599881, 131023598, 127272675, 369562685,
    1 ], [ 822767347, 253934988, 397654311, 657462121, 596807917,
    163942533, 989718031, 546104822, 1 ], [ 728603409, 351358047,
    501629111, 299619643, 69059255, 549054893, 943261643, 202688239, 1
    ], [ 541855925, 969729171, 56929942, 624759898, 18758729,
    79003864, 646666385, 32206917, 1 ], [ 912717194, 793311717,
    645185698, 92515065, 560395221, 274591732, 611057991, 694503873, 1
    ], [ 864927696, 577253500, 426230743, 722231514, 645139425,
    666574546, 700696924, 431764545, 1 ], [ 953302592, 116018132,
    25435167, 943855954, 266312001, 244863826, 961663497, 384414088, 1
    ], [ 71062360, 871335049, 767681547, 362103975, 274553436,
    656077321, 141183595, 758646207, 1 ], [ 940312058, 358205507,
    130030272, 784017001, 274343330, 583209855, 469270689, 886382617,
    1 ], [ 621831908, 618715271, 31883424, 498761032, 327921814,
    579721261, 474123949, 481814000, 1 ], [ 52941332, 138127516,
    975162265, 934966970, 85317150, 894745770, 95478616, 513195678, 1
    ], [ 131723343, 55687301, 35693792, 157649379, 221134795,
    357312344, 320328067, 426842297, 1 ], [ 16363160, 772304271,
    804241890, 668903154, 546141059, 197918677, 629442047, 827538418,
    1 ], [ 108047418, 502596282, 161016390, 517797782, 978141551,
    722328251, 256317938, 450040158, 1 ], [ 982409320, 138924637,
    34992835, 301273269, 630331251, 794543138, 757772225, 811022578, 1
    ], [ 634698203, 613252539, 542251537, 545291898, 124666852,
    603403052, 313399186, 133230597, 1 ], [ 664117140, 651355327,
    437150137, 406066242, 358575437, 555786964, 862029884, 513619330,
    1 ], [ 350075727, 896841377, 173799437, 342710546, 945078727,
    363889456, 16110949, 117545079, 1 ], [ 252312495, 289701570,
    400095806, 198646647, 494260433, 614248994, 467228282, 962406774,
    1 ], [ 643790509, 483118765, 193959511, 784747483, 700917003,
    884386651, 612653809, 63638331, 1 ], [ 980088521, 34893097,
    475285622, 140726199, 563708220, 88570098, 857372534, 91878535, 1
    ], [ 10820430, 388382605, 428290345, 475919567, 161097861,
    42317255, 168202230, 454004049, 1 ], [ 49438423, 479948399,
    771910235, 28232933, 893152835, 560989795, 1715848, 20508948, 1 ],
    [ 88208489, 411873559, 796883213, 211838410, 828968970, 273973904,
    988238544, 602299804, 1 ], [ 585684303, 335707358, 59587030,
    599568413, 392054571, 787566003, 446480184, 925415934, 1 ], [
    948680636, 949435255, 86935684, 281227622, 876218363, 146646032,
    100344327, 451097957, 1 ], [ 817951164, 713100751, 106205913,
    775265933, 981225802, 468918609, 881505705, 258379879, 1 ], [
    598511256, 403565896, 216470854, 817552520, 651469076, 946378554,
    681037987, 583262961, 1 ], [ 335098873, 334289530, 389871490,
    314723451, 980307576, 741988768, 846612202, 674800479, 1 ], [
    840312754, 75205294, 721892861, 899088222, 704203190, 176669091,
    319250741, 341654620, 1 ], [ 632620336, 212807329, 858005623,
    698094645, 79340053, 759676242, 401899648, 856994941, 1 ], [
    775570416, 546015559, 602548708, 326940838, 985133201, 78712610,
    617068232, 442734004, 1 ], [ 938111875, 684253811, 556591720,
    157427486, 708111044, 157143749, 743559973, 736275319, 1 ], [
    303300334, 412634092, 543186481, 314241218, 310092402, 337530790,
    184345105, 315441430, 1 ], [ 839465811, 996668337, 926299387,
    84398168, 361377728, 525706750, 29732507, 28720497, 1 ], [
    336079357, 591998853, 389336821, 121645058, 1307204, 674759589,
    231476478, 260948500, 1 ], [ 947755651, 419330129, 798614666,
    261259107, 644298654, 268929868, 205388922, 739800754, 1 ], [
    460507095, 118647499, 431754840, 347577547, 449800259, 952225529,
    571798639, 559011083, 1 ], [ 29425565, 175823504, 676672031,
    278653347, 421605651, 229286331, 401479329, 367205008, 1 ], [
    266169523, 538902806, 933655834, 678774095, 271679691, 849359100,
    387039396, 663052733, 1 ], [ 73874892, 946590316, 863753323,
    901959979, 368728213, 427392782, 33813218, 692724939, 1 ], [
    880688444, 46905333, 725392737, 508890934, 499803881, 720822926,
    854757461, 687820096, 1 ], [ 504170046, 597574815, 411515099,
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