//////////////////////////////////////////////////////////////
// Modifications for Type VI Graph: Non-generic x^3 and x^4 //
//////////////////////////////////////////////////////////////

// The following contains an example for the modified Type VI graph in R^3 (with one genus 1 component with a node). The curve can be visualized by means of projections. 

// Since our modifications involve square roots, we take our branch points to be squares, resp. negative of squares, for computational convenience.

// The parameters w2,..., w5 satisfy w2 < w3 = w4 = w5 with no cancellations.

// Our choice of refined modification is such that 0< e < e' < min{w4-w2/2, w4 + val(A3+A4)}
// In our case e =1, e' = 2, w2/2=14 and val(A3 + A4) =18

LIB "all.lib";
LIB "poly.lib";
LIB "all.lib";
LIB "tropical.lib";
LIB "elim.lib";
LIB "primitiv.lib";

ring R = 0, (s), dp;
def r1 = splitring(s^2+1);

setring r1; basering;

ring S = r1, (t), dp;

setring S;

ring rr = S, (b2,b3,b4,b5, x,y,z),dp;
poly f=y^2-x*(x-b2^2)*(x-b3^2)*(x-b4^2)*(x+b5^2);
// f;
// b2^2*b3^2*b4^2*b5^2*x+b2^2*b3^2*b4^2*x^2-b2^2*b3^2*b5^2*x^2-b2^2*b4^2*b5^2*x^2-b3^2*b4^2*b5^2*x^2-b2^2*b3^2*x^3-b2^2*b4^2*x^3-b3^2*b4^2*x^3+b2^2*b5^2*x^3+b3^2*b5^2*x^3+b4^2*b5^2*x^3+b2^2*x^4+b3^2*x^4+b4^2*x^4-b5^2*x^4-x^5+y^2

poly g = substitute(f, y, y+b3*b4*b5*(1+t)*x-b5*(1+t^2)*x^2);
// g;
// b2^2*b3^2*b4^2*b5^2*x+b2^2*b3^2*b4^2*x^2-b2^2*b3^2*b5^2*x^2-b2^2*b4^2*b5^2*x^2+(t^2+2*t)*b3^2*b4^2*b5^2*x^2-b2^2*b3^2*x^3-b2^2*b4^2*x^3-b3^2*b4^2*x^3+b2^2*b5^2*x^3+b3^2*b5^2*x^3+(-2*t^3-2*t^2-2*t-2)*b3*b4*b5^2*x^3+b4^2*b5^2*x^3+b2^2*x^4+b3^2*x^4+b4^2*x^4+(t^4+2*t^2)*b5^2*x^4-x^5+(2*t+2)*b3*b4*b5*x*y+(-2*t^2-2)*b5*x^2*y+y^2

matrix m = coef(g,xy);
// m;
// m[1,1]=x^5
// m[1,2]=x^4
// m[1,3]=x^3
// m[1,4]=x^2*y
// m[1,5]=x^2
// m[1,6]=x*y
// m[1,7]=y^2
// m[1,8]=x
// m[2,1]=-1
// m[2,2]=b2^2+b3^2+b4^2+(t^4+2*t^2)*b5^2
// m[2,3]=-b2^2*b3^2-b2^2*b4^2-b3^2*b4^2+b2^2*b5^2+b3^2*b5^2+(-2*t^3-2*t^2-2*t-2)*b3*b4*b5^2+b4^2*b5^2
// m[2,4]=(-2*t^2-2)*b5
// m[2,5]=b2^2*b3^2*b4^2-b2^2*b3^2*b5^2-b2^2*b4^2*b5^2+(t^2+2*t)*b3^2*b4^2*b5^2
// m[2,6]=(2*t+2)*b3*b4*b5
// m[2,7]=1
// m[2,8]=b2^2*b3^2*b4^2*b5^2

setring(S);
poly B2 = (5*t^14+t^16);
poly B3 = ((a-1)+t^18);
poly B4 = ((1+a));
poly B5 = (1);

poly A2 = B2^2;
poly A3 = B3^2;
poly A4 = B4^2;
poly A5 = -1*B5^2;

// coeff x^4
// B2^2+B3^2+B4^2+(t^4+2*t^2)*B5^2;
// t36+t32+10*t30+25*t28+(2a-2)*t18+t4+2*t2

// coeff x^3
// -B2^2*B3^2-B2^2*B4^2-B3^2*B4^2+B2^2*B5^2+B3^2*B5^2+(-2*t^3-2*t^2-2*t-2)*B3*B4*B5^2+B4^2*B5^2;
// -t68-10*t66-25*t64+(-2a+2)*t50+(-20a+20)*t48+(-50a+50)*t46+(-2a+1)*t36+t32+10*t30+25*t28+(-2a-2)*t21+(-2a-2)*t20+(-2a-2)*t19+(4a)*t18+4*t3+4*t2+4*t

// coeff x^2
// B2^2*B3^2*B4^2-B2^2*B3^2*B5^2-B2^2*B4^2*B5^2+(t^2+2*t)*B3^2*B4^2*B5^2;
// (2a-1)*t68+(20a-10)*t66+(50a-25)*t64+(-6a-2)*t50+(-60a-20)*t48+(-150a-50)*t46+(2a)*t38+(4a)*t37+4*t32+40*t30+100*t28+(-4a-4)*t20+(-8a-8)*t19+4*t2+8*t

// A5;
// (-1)
// A4;
// (2*a)
// A3;
// (t^36+(2*a-2)*t^18+(-2*a))

// non-generic for x^3
// A3+A4;
// (t^36+(2*a-2)*t^18)


// non-generic for x^4
// A5*(B3-B4)^2+A3*A4;
// ((2*a-1)*t^36+(-4*a)*t^18)

// -A2*(A3+A4)*A5 -  A2*A3*A4 + A3*A4*A5*t*(2+t);
// ((-2*a+1)*t^68+(-20*a+10)*t^66+(-50*a+25)*t^64+(6*a+2)*t^50+(60*a+20)*t^48+(150*a+50)*t^46+(-2*a)*t^38+(-4*a)*t^37-4*t^32-40*t^30-100*t^28+(4*a+4)*t^20+(8*a+8)*t^19-4*t^2-8*t)

setring(rr);
poly B2 = (5*t^14+t^16);
poly B3 = ((a-1)+t^18);
poly B4 = ((1+a));
poly B5 = (1);

map P2 = rr, B2, B3, B4, B5, x, y, z;

poly ff = P2(f);
// ff;
// -x^5+(t^36+t^32+10*t^30+25*t^28+(2*a-2)*t^18-1)*x^4+(-t^68-10*t^66-25*t^64+(-2*a+2)*t^50+(-20*a+20)*t^48+(-50*a+50)*t^46+(-2*a+1)*t^36+t^32+10*t^30+25*t^28+(6*a+2)*t^18-4)*x^3+((2*a-1)*t^68+(20*a-10)*t^66+(50*a-25)*t^64+(-6*a-2)*t^50+(-60*a-20)*t^48+(-150*a-50)*t^46+(-2*a)*t^36+4*t^32+40*t^30+100*t^28+(4*a+4)*t^18-4)*x^2+y^2+((2*a)*t^68+(20*a)*t^66+(50*a)*t^64+(-4*a-4)*t^50+(-40*a-40)*t^48+(-100*a-100)*t^46+4*t^32+40*t^30+100*t^28)*x

ring r = S,(x,y),dp;
setring(r);
map newP2 = rr, 0,0,0,0,x,y,0;

poly f2 = newP2(ff);
// f2;
// -x5+(t36+t32+10*t30+25*t28+(2a-2)*t18-1)*x4+(-t68-10*t66-25*t64+(-2a+2)*t50+(-20a+20)*t48+(-50a+50)*t46+(-2a+1)*t36+t32+10*t30+25*t28+(6a+2)*t18-4)*x3+((2a-1)*t68+(20a-10)*t66+(50a-25)*t64+(-6a-2)*t50+(-60a-20)*t48+(-150a-50)*t46+(-2a)*t36+4*t32+40*t30+100*t28+(4a+4)*t18-4)*x2+y2+((2a)*t68+(20a)*t66+(50a)*t64+(-4a-4)*t50+(-40a-40)*t48+(-100a-100)*t46+4*t32+40*t30+100*t28)*x


///////////////////
// XZ-projection //
///////////////////

poly B2 = newP2(B2);
poly B3 = newP2(B3);
poly B4 = newP2(B4);
poly B5 = newP2(B5);

poly g2xz = substitute(f2, y, y+B3*B4*B5*(1+t)*x-B5*(1+t^2)*x^2);
// g2xz;
// -x5+(t36+t32+10*t30+25*t28+(2a-2)*t18+t4+2*t2)*x4+(-t68-10*t66-25*t64+(-2a+2)*t50+(-20a+20)*t48+(-50a+50)*t46+(-2a+1)*t36+t32+10*t30+25*t28+(-2a-2)*t21+(-2a-2)*t20+(-2a-2)*t19+(4a)*t18+4*t3+4*t2+4*t)*x3+(-2*t2-2)*x2y+((2a-1)*t68+(20a-10)*t66+(50a-25)*t64+(-6a-2)*t50+(-60a-20)*t48+(-150a-50)*t46+(2a)*t38+(4a)*t37+4*t32+40*t30+100*t28+(-4a-4)*t20+(-8a-8)*t19+4*t2+8*t)*x2+((2a+2)*t19+(2a+2)*t18-4*t-4)*xy+y2+((2a)*t68+(20a)*t66+(50a)*t64+(-4a-4)*t50+(-40a-40)*t48+(-100a-100)*t46+4*t32+40*t30+100*t28)*x


/////////////////////
// Z_4Y-projection //
/////////////////////

poly B2 = newP2(B2);
poly B3 = newP2(B3);
poly B4 = newP2(B4);
poly B5 = newP2(B5);
poly A4 = B4^2;

poly g2z4y = substitute(f2, x, x+A4);
// g2z4y;
// -x5+(t36+t32+10*t30+25*t28+(2a-2)*t18+(-10a-1))*x4+(-t68-10*t66-25*t64+(-2a+2)*t50+(-20a+20)*t48+(-50a+50)*t46+(6a+1)*t36+(8a+1)*t32+(80a+10)*t30+(200a+25)*t28+(-10a-14)*t18+(-8a+36))*x3+((-4a-1)*t68+(-40a-10)*t66+(-100a-25)*t64+(6a+10)*t50+(60a+100)*t48+(150a+250)*t46+(4a-12)*t36+(6a-20)*t32+(60a-200)*t30+(150a-500)*t28+(-32a+16)*t18+(56a+20))*x2+y2+((-2a+4)*t68+(-20a+40)*t66+(-50a+100)*t64+(12a-4)*t50+(120a-40)*t48+(300a-100)*t46+(-8a-4)*t36+(-16a-8)*t32+(-160a-80)*t30+(-400a-200)*t28+(8a+24)*t18+(16a-32))*x


/////////////////////
// Z_4Z-projection //
/////////////////////

poly gz4z = substitute(substitute(f2, y, y+B3*B4*B5*(1+t)*x-B5*(1+t^2)*x^2),x, x + A4); 
// gz4z;
// -x5+(t36+t32+10*t30+25*t28+(2a-2)*t18+t4+2*t2+(-10a))*x4+(-t68-10*t66-25*t64+(-2a+2)*t50+(-20a+20)*t48+(-50a+50)*t46+(6a+1)*t36+(8a+1)*t32+(80a+10)*t30+(200a+25)*t28+(-2a-2)*t21+(-2a-2)*t20+(-2a-2)*t19+(-12a-16)*t18+(8a)*t4+4*t3+(16a+4)*t2+4*t+40)*x3+(-2*t2-2)*x2y+((-4a-1)*t68+(-40a-10)*t66+(-100a-25)*t64+(6a+10)*t50+(60a+100)*t48+(150a+250)*t46+(2a)*t38+(4a)*t37+(6a-12)*t36+(6a-20)*t32+(60a-200)*t30+(150a-500)*t28+(-12a+12)*t21+(-16a+8)*t20+(-20a+4)*t19+(-48a+24)*t18-24*t4+(24a)*t3+(24a-44)*t2+(24a+8)*t+(80a))*x2+((2a+2)*t19+(2a+2)*t18+(-8a)*t2-4*t+(-8a-4))*xy+y2+((-2a+4)*t68+(-20a+40)*t66+(-50a+100)*t64+(12a-4)*t50+(120a-40)*t48+(300a-100)*t46-8*t38-16*t37+(-8a-12)*t36+(-16a-8)*t32+(-160a-80)*t30+(-400a-200)*t28+(24a+24)*t21+(8a+40)*t20+(-8a+56)*t19+(16a+64)*t18+(-32a)*t4-48*t3+(-48a-48)*t2+(32a-48)*t-80)*x+((4a-4)*t19+(4a-4)*t18+8*t2+(-8a)*t+(-8a+8))*y+((-8a)*t38+(-16a)*t37+(-8a)*t36+(16a-16)*t21+(32a)*t20+(48a+16)*t19+(32a)*t18+16*t4+(-32a)*t3+(-32a+16)*t2+(-32a-32)*t+(-32a))


/////////////////////
// Z_3Y-projection //
/////////////////////

poly A3 = B3^2;

poly h2 = substitute(f2, x, x+A3);
// h2;
// -x5+(-4*t36+t32+10*t30+25*t28+(-8a+8)*t18+(10a-1))*x4+(-6*t72+3*t68+30*t66+75*t64+(-24a+24)*t54+(6a-6)*t50+(60a-60)*t48+(150a-150)*t46+(78a-3)*t36+(-8a+1)*t32+(-80a+10)*t30+(-200a+25)*t28+(-66a-54)*t18+(8a+36))*x3+(-4*t108+3*t104+30*t102+75*t100+(-24a+24)*t90+(12a-12)*t86+(120a-120)*t84+(300a-300)*t82+(126a-3)*t72+(-40a+2)*t68+(-400a+20)*t66+(-1000a+50)*t64+(-196a-172)*t54+(36a+28)*t50+(360a+280)*t48+(900a+700)*t46+(40a+312)*t36+(-6a-20)*t32+(-60a-200)*t30+(-150a-500)*t28+(112a-176)*t18+(-56a+20))*x2+y2+(-t144+t140+10*t138+25*t136+(-8a+8)*t126+(6a-6)*t122+(60a-60)*t120+(150a-150)*t118+(58a-1)*t108+(-32a+1)*t104+(-320a+10)*t102+(-800a+25)*t100+(-130a-118)*t90+(52a+44)*t86+(520a+440)*t84+(1300a+1100)*t82+(32a+340)*t72+(-14a-84)*t68+(-140a-840)*t66+(-350a-2100)*t64+(256a-352)*t54+(-28a+52)*t50+(-280a+520)*t48+(-700a+1300)*t46+(-344a+84)*t36+(16a-8)*t32+(160a-80)*t30+(400a-200)*t28+(152a+72)*t18+(-16a-32))*x

/////////////////////
// Z_3Z-projection //
/////////////////////

poly gz3z = substitute(substitute(f2, y, y+B3*B4*B5*(1+t)*x-B5*(1+t^2)*x^2),x, x + A3); 
// gz3z;
// -x5+(-4*t36+t32+10*t30+25*t28+(-8a+8)*t18+t4+2*t2+(10a))*x4+(-6*t72+3*t68+30*t66+75*t64+(-24a+24)*t54+(6a-6)*t50+(60a-60)*t48+(150a-150)*t46+4*t40+8*t38+(78a+1)*t36+(-8a+1)*t32+(-80a+10)*t30+(-200a+25)*t28+(8a-8)*t22+(-2a-2)*t21+(14a-18)*t20+(-2a-2)*t19+(-60a-64)*t18+(-8a)*t4+4*t3+(-16a+4)*t2+4*t+40)*x3+(-2*t2-2)*x2y+(-4*t108+3*t104+30*t102+75*t100+(-24a+24)*t90+(12a-12)*t86+(120a-120)*t84+(300a-300)*t82+6*t76+12*t74+(126a+3)*t72+(-40a+2)*t68+(-400a+20)*t66+(-1000a+50)*t64+(24a-24)*t58+(-6a-6)*t57+(42a-54)*t56+(-6a-6)*t55+(-178a-202)*t54+(36a+28)*t50+(360a+280)*t48+(900a+700)*t46+(-72a)*t40+36*t39+(-142a+36)*t38+(4a+36)*t37+(-30a+348)*t36+(-6a-20)*t32+(-60a-200)*t30+(-150a-500)*t28+(48a+48)*t22+(36a-36)*t21+(128a+56)*t20+(28a-44)*t19+(192a-168)*t18-24*t4+(-24a)*t3+(-24a-44)*t2+(-24a+8)*t+(-80a))*x2+(-4*t38-4*t36+(-8a+8)*t20+(2a+2)*t19+(-6a+10)*t18+(8a)*t2-4*t+(8a-4))*xy+y2+(-t144+t140+10*t138+25*t136+(-8a+8)*t126+(6a-6)*t122+(60a-60)*t120+(150a-150)*t118+4*t112+8*t110+(58a+3)*t108+(-32a+1)*t104+(-320a+10)*t102+(-800a+25)*t100+(24a-24)*t94+(-6a-6)*t93+(42a-54)*t92+(-6a-6)*t91+(-112a-148)*t90+(52a+44)*t86+(520a+440)*t84+(1300a+1100)*t82+(-120a)*t76+60*t75+(-236a+60)*t74+(8a+60)*t73+(-84a+400)*t72+(-14a-84)*t68+(-140a-840)*t66+(-350a-2100)*t64+(160a+160)*t58+(120a-120)*t57+(424a+184)*t56+(88a-152)*t55+(520a-328)*t54+(-28a+52)*t50+(-280a+520)*t48+(-700a+1300)*t46-240*t40+(-240a)*t39+(-240a-432)*t38+(-240a+96)*t37+(-584a-108)*t36+(16a-8)*t32+(160a-80)*t30+(400a-200)*t28+(-96a+96)*t22+(120a+120)*t21+(-40a+280)*t20+(184a+56)*t19+(208a+256)*t18+(32a)*t4-48*t3+(48a-48)*t2+(-32a-48)*t-80)*x+(-2*t74-2*t72+(-8a+8)*t56+(2a+2)*t55+(-6a+10)*t54+(24a)*t38-12*t37+(24a-12)*t36+(-16a-16)*t20+(-12a+12)*t19+(-28a-4)*t18+8*t2+(8a)*t+(8a+8))*y+(t148+2*t146+t144+(8a-8)*t130+(-2a-2)*t129+(14a-18)*t128+(-2a-2)*t127+(6a-10)*t126+(-56a)*t112+28*t111+(-110a+28)*t110+(4a+28)*t109+(-54a+28)*t108+(112a+112)*t94+(84a-84)*t93+(296a+128)*t92+(60a-108)*t91+(184a+16)*t90-280*t76+(-280a)*t75+(-280a-500)*t74+(-280a+120)*t73+(-280a-220)*t72+(-224a+224)*t58+(280a+280)*t57+(-88a+648)*t56+(440a+120)*t55+(136a+424)*t54+(224a)*t40-336*t39+(328a-336)*t38+(-240a-336)*t37+(104a-336)*t36+(-64a-64)*t22+(-112a+112)*t21+(-192a+32)*t20+(-16a+208)*t19+(-128a+96)*t18+16*t4+(32a)*t3+(32a+16)*t2+(32a-32)*t+(32a))


///////////////////
// ZY-projection //
///////////////////

ring ss = S,(x,y,z),dp;
map P = r, x,y;
poly ff= P(f2);

poly B3 = P(B3);
poly B4 = P(B4);
poly B5 = P(B5);

ideal I = (ff,z-y+B3*B4*B5*(1+t)*x-B5*(1+t^2)*x^2);
// I;
// I[1]=-x5+(t36+t32+10*t30+25*t28+(2a-2)*t18-1)*x4+(-t68-10*t66-25*t64+(-2a+2)*t50+(-20a+20)*t48+(-50a+50)*t46+(-2a+1)*t36+t32+10*t30+25*t28+(6a+2)*t18-4)*x3+((2a-1)*t68+(20a-10)*t66+(50a-25)*t64+(-6a-2)*t50+(-60a-20)*t48+(-150a-50)*t46+(-2a)*t36+4*t32+40*t30+100*t28+(4a+4)*t18-4)*x2+y2+((2a)*t68+(20a)*t66+(50a)*t64+(-4a-4)*t50+(-40a-40)*t48+(-100a-100)*t46+4*t32+40*t30+100*t28)*x
// I[2]=(-t2-1)*x2+((a+1)*t19+(a+1)*t18-2*t-2)*x-y+z




LIB "all.lib";
LIB "poly.lib";
LIB "all.lib";
LIB "tropical.lib";
LIB "elim.lib";
LIB "primitiv.lib";

ring R = 0, (s), dp;


def r1 = splitring(s^2+1);

setring r1; basering;

ring S = r1, (t), dp;

ring ss = (0,t), (a,x,y,z), dp;

ideal I =  (-x5+(t36+t32+10*t30+25*t28+(2a-2)*t18-1)*x4+(-t68-10*t66-25*t64+(-2a+2)*t50+(-20a+20)*t48+(-50a+50)*t46+(-2a+1)*t36+t32+10*t30+25*t28+(6a+2)*t18-4)*x3+((2a-1)*t68+(20a-10)*t66+(50a-25)*t64+(-6a-2)*t50+(-60a-20)*t48+(-150a-50)*t46+(-2a)*t36+4*t32+40*t30+100*t28+(4a+4)*t18-4)*x2+y2+((2a)*t68+(20a)*t66+(50a)*t64+(-4a-4)*t50+(-40a-40)*t48+(-100a-100)*t46+4*t32+40*t30+100*t28)*x,(-t2-1)*x2+((a+1)*t19+(a+1)*t18-2*t-2)*x-y+z);

ideal J = eliminate(I,x);

poly fnox= J[1];

matrix m = coef(fnox,yz);
// m;
// m[1,1]=y5
// m[1,2]=y4z
// m[1,3]=y3z2
// m[1,4]=y2z3
// m[1,5]=yz4
// m[1,6]=z5
// m[1,7]=y4
// m[1,8]=y3z
// m[1,9]=y2z2
// m[1,10]=yz3
// m[1,11]=z4
// m[1,12]=y3
// m[1,13]=y2z
// m[1,14]=yz2
// m[1,15]=z3
// m[1,16]=y2
// m[1,17]=yz
// m[1,18]=z2
// m[1,19]=y
// m[1,20]=z
// m[2,1]=1
// m[2,2]=-5
// m[2,3]=10
// m[2,4]=-10
// m[2,5]=5
// m[2,6]=-1
// m[2,7]=(4t38-2t37+2t36)*a2+(4t56-t55+3t54-t51-t50-10t49-10t48-25t47-25t46-12t38-12t36+4t24-5t23+7t22-10t21+10t20+12t18)*a+(t74+t72+t66+21t64+170t62+650t60+1125t58+621t56-t55-5t54-t51-t50-10t49-10t48-25t47-25t46+2t42+6t40+12t38+4t37+36t36+116t34+2t33+214t32+20t31+190t30+50t29+100t28-4t24-5t23-17t22-10t21-14t20-8t19-4t18+t10+5t8+8t6+10t5+14t4+20t3+12t2+8t)
// m[2,8]=(-16t38+8t37-8t36)*a2+(-16t56+4t55-12t54+4t51+4t50+40t49+40t48+100t47+100t46+48t38+48t36-8t24+10t23-14t22+20t21-36t20-10t19-50t18)*a+(-4t74-4t72-4t66-84t64-680t62-2600t60-4500t58-2484t56+4t55+20t54+4t51+4t50+40t49+40t48+100t47+100t46-4t42-12t40-32t38-16t37-88t36-232t34-8t33-432t32-80t31-420t30-200t29-300t28+8t24+10t23+34t22+20t21+12t20+22t19-2t18+4t6-20t5-8t4-40t3-12t+20)
// m[2,9]=(24t38-12t37+12t36)*a2+(24t56-6t55+18t54-6t51-6t50-60t49-60t48-150t47-150t46-72t38-72t36+4t24-5t23+7t22-10t21+50t20+25t19+77t18)*a+(6t74+6t72+6t66+126t64+1020t62+3900t60+6750t58+3726t56-6t55-30t54-6t51-6t50-60t49-60t48-150t47-150t46+2t42+6t40+32t38+24t37+76t36+116t34+12t33+224t32+120t31+290t30+300t29+350t28-4t24-5t23-17t22-10t21+26t20-23t19+21t18-2t6+10t5+4t4+20t3-28t2-2t-46)
// m[2,10]=(-16t38+8t37-8t36)*a2+(-16t56+4t55-12t54+4t51+4t50+40t49+40t48+100t47+100t46+48t38+48t36-32t20-20t19-52t18)*a+(-4t74-4t72-4t66-84t64-680t62-2600t60-4500t58-2484t56+4t55+20t54+4t51+4t50+40t49+40t48+100t47+100t46-16t38-16t37-32t36-8t33-8t32-80t31-80t30-200t29-200t28-32t20+12t19-20t18+28t2+8t+36)
// m[2,11]=(4t38-2t37+2t36)*a2+(4t56-t55+3t54-t51-t50-10t49-10t48-25t47-25t46-12t38-12t36+8t20+5t19+13t18)*a+(t74+t72+t66+21t64+170t62+650t60+1125t58+621t56-t55-5t54-t51-t50-10t49-10t48-25t47-25t46+4t38+4t37+8t36+2t33+2t32+20t31+20t30+50t29+50t28+8t20-3t19+5t18-7t2-2t-9)
// m[2,12]=(-4t89-2t88-40t87-22t86-100t85-70t84-50t82-4t75-2t74-2t72-8t60-11t59-9t58+2t56-t55+3t54)*a3+(-4t107-3t106-42t105-29t104-122t103-19t102-92t101+647t100-340t99+2940t98-1300t97+5800t96-2250t95+4750t94-1252t93+1248t92-2t91-2t90+8t89+10t88+92t87+110t86+320t85+350t84+300t83+250t82-4t78-8t77-8t76-2t75+9t74+76t73+37t72+252t71+107t70+250t69+113t68-150t67-145t66-500t65-175t64+6t61-2t60+17t59+23t58+54t57+8t56-t55-17t54-18t43+18t42-12t41-16t40-56t39-24t38-6t37+10t36)*a2+(-t125-t124-11t123-7t122-36t121+52t120-46t119+718t118-170t117+3110t116-650t115+6450t114-1125t113+5875t112-625t111+1875t110+2t106+4t105+10t104+40t103-194t102+100t101-2242t100-9840t98-21300t96-21000t94+2t93-7498t92+38t91+38t90+190t89+184t88+482t87+436t86+700t85+786t84+280t83+1958t82+850t81+7410t80+3250t79+17442t78+5609t77+19597t76+3109t75+8053t74-16t73-380t72-232t71-1162t70-1180t69-2074t68-2400t67-2590t66-1500t65-1350t64+3t61+27t60+72t59+126t58+105t57+227t56-140t55+836t54-463t53+2061t52+159t51+2783t50+1690t49+2630t48+1600t47+1200t46+4t44-36t43-12t42-152t41-204t40-276t39-148t38-64t37+40t36-8t26+48t25-32t24+108t23+108t22+188t21+116t20+48t19-16t18)*a+(t140+22t138+191t136+820t134+1775t132+1750t130+625t128-t125-t124-11t123-15t122-36t121-124t120-46t119-810t118-170t117-3450t116-650t115-7750t114-1125t113-8125t112-625t111-3125t110+6t107+7t106+68t105+81t104+234t103+337t102+284t101+1023t100+680t99+3960t98+2600t97+9700t96+4500t95+11500t94+2504t93+5004t92+40t91+40t90+162t89+156t88+174t87+128t86-288t85-202t84-588t83+1090t82-510t81+6050t80-1950t79+12246t78-3383t77+10616t76-1905t75+3124t74-176t73-72t72-792t71-589t70-1618t69-1200t68-1282t67-911t66+8t65-1454t64-340t63-6080t62-1303t61-13704t60-2206t59-14422t58-1143t57-5476t56+204t55+624t54+929t53+2125t52+2671t51+3623t50+3410t49+3230t48+1400t47+1200t46-44t42-118t41-210t40-254t39-290t38-80t37-708t36-50t35-1910t34-998t33-2786t32-1980t31-2360t30-1200t29-900t28-8t26+24t25+8t24+164t23+228t22+332t21+212t20+144t19+8t8-24t7+24t6-80t5-88t4-152t3-104t2-64t)
// m[2,13]=(12t89+6t88+120t87+66t86+300t85+210t84+150t82+12t75+6t74+6t72+8t60+11t59+9t58-24t57-14t56+t55-15t54)*a3+(12t107+9t106+126t105+87t104+366t103+57t102+276t101-1941t100+1020t99-8820t98+3900t97-17400t96+6750t95-14250t94+3756t93-3744t92+6t91+6t90-24t89-30t88-276t87-330t86-960t85-1050t84-900t83-750t82+4t78+8t77-14t75-47t74-104t73-67t72-252t71-89t70-214t69+85t68+510t67+775t66+1400t65+625t64-6t61+2t60-17t59+9t58-70t57+84t56+73t55+77t54+18t43-18t42+12t41-24t40+108t39-60t38-54t37-54t36)*a2+(3t125+3t124+33t123+21t122+108t121-156t120+138t119-2154t118+510t117-9330t116+1950t115-19350t114+3375t113-17625t112+1875t111-5625t110-6t106-12t105-30t104-120t103+582t102-300t101+6726t100+29520t98+63900t96+63000t94+22500t92-36t91-36t90-222t89-204t88-810t87-672t86-1590t85-1848t84-690t83-5724t82-2550t81-22230t80-9750t79-52342t78-16859t77-58847t76-9391t75-24335t74-16t73+348t72+312t71+1246t70+2068t69+2998t68+5280t67+5530t66+3700t65+3450t64-3t61-27t60-72t59-102t58-15t57-61t56+286t55-694t54+417t53-2131t52-713t51-3553t50-3780t49-5080t48-3950t47-2950t46-4t44+36t43+12t42+152t41+132t40+196t39-172t38-208t37-288t36+8t26-48t25+32t24-108t23-60t22-180t21+68t20+120t19+152t18)*a+(-3t140-66t138-573t136-2460t134-5325t132-5250t130-1875t128+3t125+3t124+33t123+45t122+108t121+372t120+138t119+2430t118+510t117+10350t116+1950t115+23250t114+3375t113+24375t112+1875t111+9375t110-18t107-21t106-204t105-243t104-702t103-1011t102-852t101-3069t100-2040t99-11880t98-7800t97-29100t96-13500t95-34500t94-7506t93-15006t92-42t91-42t90-138t89-120t88+114t87+252t86+1374t85+1116t84+1914t83-3120t82+1530t81-18150t80+5850t79-36746t78+10133t77-31868t76+5659t75-9372t74+184t73+76t72+792t71+567t70+1574t69+972t68+846t67+453t66-1024t65+3662t64+1020t63+18240t62+3903t61+41154t60+6706t59+43430t58+3661t57+16756t56-194t55-602t54-975t53-2163t52-3161t51-4041t50-4860t49-4560t48-2150t47-2150t46+44t42+118t41+170t40+182t39+122t38-24t37+580t36+78t35+1946t34+1322t33+3182t32+3120t31+3620t30+2300t29+1800t28+8t26-24t25-8t24-164t23-180t22-244t21+20t20+40t19+184t18-8t8+24t7-24t6+80t5+72t4+120t3+8t2-32t-80)
// m[2,14]=(-12t89-6t88-120t87-66t86-300t85-210t84-150t82-12t75-6t74-6t72+36t57+18t56+18t54)*a3+(-12t107-9t106-126t105-87t104-366t103-57t102-276t101+1941t100-1020t99+8820t98-3900t97+17400t96-6750t95+14250t94-3756t93+3744t92-6t91-6t90+24t89+30t88+276t87+330t86+960t85+1050t84+900t83+750t82+12t76+24t75+57t74+42t73+45t72-27t70-54t69-297t68-540t67-945t66-1350t65-675t64-48t58+24t57-138t56-108t55-90t54+60t40-78t39+126t38+90t37+66t36)*a2+(-3t125-3t124-33t123-21t122-108t121+156t120-138t119+2154t118-510t117+9330t116-1950t115+19350t114-3375t113+17625t112-1875t111+5625t110+6t106+12t105+30t104+120t103-582t102+300t101-6726t100-29520t98-63900t96-63000t94-3t93-22503t92-3t91-3t90+48t89+30t88+492t87+354t86+1335t85+1593t84+615t83+5649t82+2550t81+22230t80+9750t79+52350t78+16875t77+58875t76+9423t75+24423t74+48t73+48t72-120t71-126t70-1332t69-1386t68-4320t67-4410t66-3300t65-3150t64-36t58-135t57-249t56-219t55-213t54+69t53+105t52+831t51+1155t50+3135t49+3675t48+3525t47+2625t46+108t40+120t39+480t38+408t37+372t36-72t22-12t21-276t20-252t19-204t18)*a+(3t140+66t138+573t136+2460t134+5325t132+5250t130+1875t128-3t125-3t124-33t123-45t122-108t121-372t120-138t119-2430t118-510t117-10350t116-1950t115-23250t114-3375t113-24375t112-1875t111-9375t110+18t107+21t106+204t105+243t104+702t103+1011t102+852t101+3069t100+2040t99+11880t98+7800t97+29100t96+13500t95+34500t94+7503t93+15003t92+3t91+3t90-36t89-54t88-432t87-570t86-1629t85-1371t84-1989t83+3045t82-1530t81+18150t80-5850t79+36750t78-10125t77+31878t76-5631t75+9372t74-12t73-6t72+33t70+66t69+342t68+654t67+687t66+1524t65-3312t64-1020t63-18240t62-3900t61-41175t60-6750t59-43512t58-3777t57-16920t56-15t55-33t54+69t53+57t52+735t51+627t50+2175t49+1995t48+1125t47+1425t46+60t40+108t39+252t38+156t37+192t36-42t35-54t34-486t33-594t32-1710t31-1890t30-1650t29-1350t28-72t22-132t21-348t20-276t19-276t18+24t4+48t3+144t2+144t+120)
// m[2,15]=(4t89+2t88+40t87+22t86+100t85+70t84+50t82+4t75+2t74+2t72-12t57-6t56-6t54)*a3+(4t107+3t106+42t105+29t104+122t103+19t102+92t101-647t100+340t99-2940t98+1300t97-5800t96+2250t95-4750t94+1252t93-1248t92+2t91+2t90-8t89-10t88-92t87-110t86-320t85-350t84-300t83-250t82-4t76-8t75-19t74-14t73-15t72+9t70+18t69+99t68+180t67+315t66+450t65+225t64+16t58-8t57+46t56+36t55+30t54-20t40+26t39-42t38-30t37-22t36)*a2+(t125+t124+11t123+7t122+36t121-52t120+46t119-718t118+170t117-3110t116+650t115-6450t114+1125t113-5875t112+625t111-1875t110-2t106-4t105-10t104-40t103+194t102-100t101+2242t100+9840t98+21300t96+21000t94+t93+7501t92+t91+t90-16t89-10t88-164t87-118t86-445t85-531t84-205t83-1883t82-850t81-7410t80-3250t79-17450t78-5625t77-19625t76-3141t75-8141t74-16t73-16t72+40t71+42t70+444t69+462t68+1440t67+1470t66+1100t65+1050t64+12t58+45t57+83t56+73t55+71t54-23t53-35t52-277t51-385t50-1045t49-1225t48-1175t47-875t46-36t40-40t39-160t38-136t37-124t36+24t22+4t21+92t20+84t19+68t18)*a+(-t140-22t138-191t136-820t134-1775t132-1750t130-625t128+t125+t124+11t123+15t122+36t121+124t120+46t119+810t118+170t117+3450t116+650t115+7750t114+1125t113+8125t112+625t111+3125t110-6t107-7t106-68t105-81t104-234t103-337t102-284t101-1023t100-680t99-3960t98-2600t97-9700t96-4500t95-11500t94-2501t93-5001t92-t91-t90+12t89+18t88+144t87+190t86+543t85+457t84+663t83-1015t82+510t81-6050t80+1950t79-12250t78+3375t77-10626t76+1877t75-3124t74+4t73+2t72-11t70-22t69-114t68-218t67-229t66-508t65+1104t64+340t63+6080t62+1300t61+13725t60+2250t59+14504t58+1259t57+5640t56+5t55+11t54-23t53-19t52-245t51-209t50-725t49-665t48-375t47-475t46-20t40-36t39-84t38-52t37-64t36+14t35+18t34+162t33+198t32+570t31+630t30+550t29+450t28+24t22+44t21+116t20+92t19+92t18-8t4-16t3-48t2-48t-40)
// m[2,16]=(2t96+7t95+9t94+6t93+4t92+3t91+t90)*a5+(4t126+6t125+42t124+62t123+122t122+170t121+70t120+50t119+50t118+t114+4t113+7t112+6t111+2t110-22t109-68t108-134t107-324t106-398t105-572t104-680t103-295t102-200t101-175t100-2t97+9t95-t94-22t93-20t92-9t91-3t90+6t79+t78-28t77-19t76+18t75+15t74+4t73+3t72)*a4+(2t144+4t143+24t142+40t141+90t140+56t139+76t138-580t137-332t136-2600t135-1640t134-4500t133-3550t132-2500t131-3500t130-t129-1253t128-19t127-45t126-143t125-261t124-523t123-743t122-748t121-908t120+1290t119+796t118+7800t117+4920t116+13500t115+10654t114+7516t113+10528t112+28t111+3794t110+36t109+52t108+264t107+88t106+904t105+902t104+1240t103+2420t102+1600t101+550t100-5t97-19t96-47t95-115t94-152t93-180t92-72t91-60t90-194t89+390t88-510t87-36t86-175t85-1985t84-1125t83-275t82-2t80+28t79+52t78+24t77+174t76+324t75+244t74+112t73+20t72+4t62-32t61-48t60+32t59-84t58-220t57-148t56-68t55-12t54)*a3+(-2t159-2t158-44t157-44t156-382t155-382t154-1640t153-1640t152-3550t151-3550t150-3500t149-3500t148-1250t147-1250t146+3t144+6t143+40t142+74t141+241t140+392t139+1274t138+1804t137+6220t136+7580t135+19400t134+18100t133+33625t132+20750t131+28750t130+8747t129+9366t128-49t127-143t126-353t125-859t124-1425t123-2625t122-2848t121-6296t120-1346t119-19800t118-920t117-53000t116-14400t115-81244t114-35476t113-62459t112-22448t111-18650t110+244t109+628t108+1708t107+3218t106+6270t105+9263t104+10844t103+15464t102+4110t101+24252t100-11800t99+53540t98-9753t97+74013t96+17367t95+50739t94+18462t93+13250t92-492t91-1368t90-3318t89-4870t88-11292t87-14010t86-17945t85-19975t84-13425t83-5875t82-4t80+34t79+132t78+278t77+680t76+832t75+954t74+432t73+1038t72+2052t71+2364t70+6784t69+7420t68+9690t67+12150t66+7850t65+3250t64+20t62-80t61-224t60-200t59-828t58-1164t57-868t56-348t55-20t54-20t44+56t43+136t42+380t40+568t39+408t38+160t37+8t36)*a2+(-t159-t158-22t157-22t156-191t155-191t154-820t153-820t152-1775t151-1775t150-1750t149-1750t148-625t147-625t146+16t141+16t140+352t139+352t138+3056t137+3056t136+13120t135+13120t134+28400t133+28400t132+28000t131+28000t130+9997t129+9991t128-46t127-128t126-289t125-663t124-1024t123-1764t122-2758t121-5194t120-10158t119-23876t118-41660t117-79520t116-98075t115-147021t114-110234t113-131724t112-45581t111-44299t110+284t109+764t108+1880t107+4104t106+6728t105+10580t104+12856t103+19644t102+16856t101+56554t100+49120t99+165580t98+133401t97+283073t96+177880t95+239282t94+84742t93+77040t92-803t91-2293t90-5546t89-10794t88-19588t87-27458t86-33433t85-36575t84-23669t83-42343t82-16880t81-98362t80-59092t79-162596t78-96620t77-133238t76-51688t75-41240t74+824t73+3196t72+6776t71+12456t70+24756t69+32340t68+40860t67+39700t66+27400t65+12000t64+20t62-44t61-244t60-564t59-1400t58-1620t57-1724t56-460t55-1588t54-2728t53-4904t52-10884t51-13548t50-17740t49-18180t48-12600t47-5200t46-48t44+64t43+288t42+320t41+1328t40+1664t39+1312t38+448t37+32t26-32t25-128t24-16t23-496t22-624t21-496t20-160t19)*a+(t159+t158+22t157+22t156+191t155+191t154+820t153+820t152+1775t151+1775t150+1750t149+1750t148+625t147+625t146-t144-2t143-11t142-24t141-26t140-116t139+87t138-474t137+413t136-1980t135+135t134-4850t133-1800t132-5750t131-2875t130-2501t129-1253t128-16t127-34t126-85t125-115t124-152t123-156t122-124t121-876t120-1460t119-5306t118-6700t117-16120t116-13375t115-26524t114-11246t113-21744t112-3111t111-6857t110+108t109+254t108+666t107+1278t106+1926t105+2749t104+3008t103+6703t102+7962t101+28999t100+32240t99+87980t98+74301t97+148593t96+80964t95+124438t94+32406t93+39884t92-387t91-933t90-2486t89-4958t88-8174t87-11300t86-12991t85-16233t84-15537t83-40127t82-44240t81-118040t80-109304t79-205273t78-130854t77-175725t76-57182t75-57049t74+604t73+1851t72+4596t71+9292t70+16528t69+22280t68+26554t67+24998t66+18778t65+21050t64+18560t63+47004t62+49204t61+84932t60+63684t59+74344t58+29292t57+24092t56-292t55-1724t54-3624t53-7944t52-15172t51-20412t50-25420t49-22820t48-15800t47-6800t46-20t44+112t42+344t41+916t40+1064t39+1064t38+144t37+600t36+944t35+2416t34+5080t33+6856t32+9000t31+8360t30+6000t29+2400t28+32t26-96t24-144t23-688t22-848t21-720t20-224t19-16t8+32t6+208t4+256t3+224t2+64t)
// m[2,17]=(-8t126-12t125-84t124-124t123-244t122-340t121-140t120-100t119-100t118+24t108+36t107+252t106+372t105+732t104+1020t103+420t102+300t101+300t100+8t94+12t93+4t92+4t91+4t90-16t76-24t75-8t74-8t73-8t72)*a4+(-4t144-8t143-48t142-80t141-180t140-112t139-152t138+1160t137+664t136+5200t135+3280t134+9000t133+7100t132+5000t131+7000t130+2500t128+8t127+16t126+122t125+222t124+650t123+1034t122+1086t121+1546t120-2730t119-1642t118-15600t117-9840t116-27000t115-21300t114-15000t113-20996t112+8t111-7492t110-24t109+28t108-336t107+96t106-1072t105-880t104-1520t103-4000t102-2800t101-1000t100-8t95-8t94-28t93-52t92-4t91-80t90+360t89-480t88+680t87-280t86-200t85+3200t84+2000t83+500t82+40t77-28t76+112t74+72t73+28t72-48t59+40t58+24t57-88t56-40t55-16t54)*a3+(4t159+4t158+88t157+88t156+764t155+764t154+3280t153+3280t152+7100t151+7100t150+7000t149+7000t148+2500t147+2500t146-6t144-12t143-80t142-148t141-482t140-784t139-2548t138-3608t137-12440t136-15160t135-38800t134-36200t133-67250t132-41500t131-57500t130-17500t129-18750t128+8t127+64t126+214t125+818t124+1662t123+3894t122+4466t121+11782t120+2242t119+39450t118+1840t117+106000t116+28800t115+162500t114+71000t113+125008t112+45016t111+37516t110-56t109-170t108-1160t107-2428t106-6684t105-11716t104-15328t103-26428t102-5820t101-47754t100+23600t99-107080t98+19500t97-148100t96-35004t95-102052t94-37616t93-27640t92+40t91+108t90+2344t89+2784t88+11128t87+15352t86+23480t85+30720t84+22200t83+10300t82-8t78+72t77+80t76+304t75+472t74+296t73+160t72-1536t71-960t70-6272t69-7424t68-11520t67-18240t66-12800t65-5600t64+32t60-224t59+24t58-360t57-696t56-568t55-256t54-32t42+176t41-88t40+160t39+352t38+272t37+120t36)*a2+(2t159+2t158+44t157+44t156+382t155+382t154+1640t153+1640t152+3550t151+3550t150+3500t149+3500t148+1250t147+1250t146-32t141-32t140-704t139-704t138-6112t137-6112t136-26240t135-26240t134-56800t133-56800t132-56000t131-56000t130-20000t129-20000t128+2t127+34t126+86t125+426t124+860t123+2172t122+4286t121+9578t120+19866t119+47602t118+83320t117+159040t116+196150t115+294050t114+220500t113+263504t112+91258t111+88758t110-24t109-200t108-752t107-2592t106-5648t105-11960t104-17232t103-33488t102-30512t101-112108t100-98240t99-331160t98-266800t97-566200t96-355996t95-479044t94-170092t93-155100t92+56t91+444t90+2752t89+6456t88+16856t87+29032t86+42416t85+55960t84+38088t83+81836t82+33760t81+196720t80+118200t79+325400t78+194000t77+268156t76+105368t75+85480t74+240t73-284t72-3712t71-6912t70-20832t69-32736t68-49920t67-56960t66-42800t65-20400t64+32t60-136t59-176t58-760t57-1096t56-944t55-296t54+1632t53+2496t52+8704t51+13312t50+20640t49+25920t48+19600t47+8800t46-96t42+320t41-64t40+768t39+1120t38+1088t37+448t36+64t24-192t23+128t22-288t21-416t20-416t19-160t18)*a+(-2t159-2t158-44t157-44t156-382t155-382t154-1640t153-1640t152-3550t151-3550t150-3500t149-3500t148-1250t147-1250t146+2t144+4t143+22t142+48t141+52t140+232t139-174t138+948t137-826t136+3960t135-270t134+9700t133+3600t132+11500t131+5750t130+5000t129+2500t128+2t127-6t126+6t125-70t124-92t123-140t122-162t121+1482t120+2770t119+10562t118+13400t117+32240t116+26750t115+53050t114+22500t113+43500t112+6250t111+13750t110-12t109-22t108-156t107-280t106-740t105-1772t104-2596t103-11096t102-14624t101-57598t100-64480t99-175960t98-148600t97-297200t96-162000t95-249008t94-65016t93-80016t92+40t91+156t90+896t89+2040t88+5144t87+9032t86+13392t85+23736t84+26224t83+78804t82+88480t81+236080t80+218600t79+410600t78+261992t77+352048t76+115104t75+115120t74-304t72-2080t71-4576t70-12064t69-19472t68-29088t67-33216t66-28256t65-39400t64-37120t63-94000t62-98400t61-170000t60-127992t59-150128t58-60312t57-50424t56-320t55+136t54+1888t53+4224t52+11392t51+18688t50+28320t49+30080t48+22800t47+11200t46-32t42+64t41+88t40+512t39+704t38+704t37+200t36-576t35-1344t34-3712t33-6400t32-9920t31-11200t30-8800t29-4000t28+64t24-128t23+64t22-416t21-544t20-608t19-224t18-32t6+64t5-64t4+128t3+160t2+192t+64)
// m[2,18]=(4t126+6t125+42t124+62t123+122t122+170t121+70t120+50t119+50t118-12t108-18t107-126t106-186t105-366t104-510t103-210t102-150t101-150t100-4t94-6t93-2t92-2t91-2t90+8t76+12t75+4t74+4t73+4t72)*a4+(2t144+4t143+24t142+40t141+90t140+56t139+76t138-580t137-332t136-2600t135-1640t134-4500t133-3550t132-2500t131-3500t130-1250t128-4t127-8t126-61t125-111t124-325t123-517t122-543t121-773t120+1365t119+821t118+7800t117+4920t116+13500t115+10650t114+7500t113+10498t112-4t111+3746t110+12t109-14t108+168t107-48t106+536t105+440t104+760t103+2000t102+1400t101+500t100+4t95+4t94+14t93+26t92+2t91+40t90-180t89+240t88-340t87+140t86+100t85-1600t84-1000t83-250t82-20t77+14t76-56t74-36t73-14t72+24t59-20t58-12t57+44t56+20t55+8t54)*a3+(-2t159-2t158-44t157-44t156-382t155-382t154-1640t153-1640t152-3550t151-3550t150-3500t149-3500t148-1250t147-1250t146+3t144+6t143+40t142+74t141+241t140+392t139+1274t138+1804t137+6220t136+7580t135+19400t134+18100t133+33625t132+20750t131+28750t130+8750t129+9375t128-4t127-32t126-107t125-409t124-831t123-1947t122-2233t121-5891t120-1121t119-19725t118-920t117-53000t116-14400t115-81250t114-35500t113-62504t112-22508t111-18758t110+28t109+85t108+580t107+1214t106+3342t105+5858t104+7664t103+13214t102+2910t101+23877t100-11800t99+53540t98-9750t97+74050t96+17502t95+51026t94+18808t93+13820t92-20t91-54t90-1172t89-1392t88-5564t87-7676t86-11740t85-15360t84-11100t83-5150t82+4t78-36t77-40t76-152t75-236t74-148t73-80t72+768t71+480t70+3136t69+3712t68+5760t67+9120t66+6400t65+2800t64-16t60+112t59-12t58+180t57+348t56+284t55+128t54+16t42-88t41+44t40-80t39-176t38-136t37-60t36)*a2+(-t159-t158-22t157-22t156-191t155-191t154-820t153-820t152-1775t151-1775t150-1750t149-1750t148-625t147-625t146+16t141+16t140+352t139+352t138+3056t137+3056t136+13120t135+13120t134+28400t133+28400t132+28000t131+28000t130+10000t129+10000t128-t127-17t126-43t125-213t124-430t123-1086t122-2143t121-4789t120-9933t119-23801t118-41660t117-79520t116-98075t115-147025t114-110250t113-131752t112-45629t111-44379t110+12t109+100t108+376t107+1296t106+2824t105+5980t104+8616t103+16744t102+15256t101+56054t100+49120t99+165580t98+133400t97+283100t96+177998t95+239522t94+85046t93+77550t92-28t91-222t90-1376t89-3228t88-8428t87-14516t86-21208t85-27980t84-19044t83-40918t82-16880t81-98360t80-59100t79-162700t78-97000t77-134078t76-52684t75-42740t74-120t73+142t72+1856t71+3456t70+10416t69+16368t68+24960t67+28480t66+21400t65+10200t64-16t60+68t59+88t58+380t57+548t56+472t55+148t54-816t53-1248t52-4352t51-6656t50-10320t49-12960t48-9800t47-4400t46+48t42-160t41+32t40-384t39-560t38-544t37-224t36-32t24+96t23-64t22+144t21+208t20+208t19+80t18)*a+(t159+t158+22t157+22t156+191t155+191t154+820t153+820t152+1775t151+1775t150+1750t149+1750t148+625t147+625t146-t144-2t143-11t142-24t141-26t140-116t139+87t138-474t137+413t136-1980t135+135t134-4850t133-1800t132-5750t131-2875t130-2500t129-1250t128-t127+3t126-3t125+35t124+46t123+70t122+81t121-741t120-1385t119-5281t118-6700t117-16120t116-13375t115-26525t114-11250t113-21750t112-3125t111-6875t110+6t109+11t108+78t107+140t106+370t105+886t104+1298t103+5548t102+7312t101+28799t100+32240t99+87980t98+74300t97+148600t96+81000t95+124504t94+32508t93+40008t92-20t91-78t90-448t89-1020t88-2572t87-4516t86-6696t85-11868t84-13112t83-39402t82-44240t81-118040t80-109300t79-205300t78-130996t77-176024t76-57552t75-57560t74+152t72+1040t71+2288t70+6032t69+9736t68+14544t67+16608t66+14128t65+19700t64+18560t63+47000t62+49200t61+85000t60+63996t59+75064t58+30156t57+25212t56+160t55-68t54-944t53-2112t52-5696t51-9344t50-14160t49-15040t48-11400t47-5600t46+16t42-32t41-44t40-256t39-352t38-352t37-100t36+288t35+672t34+1856t33+3200t32+4960t31+5600t30+4400t29+2000t28-32t24+64t23-32t22+208t21+272t20+304t19+112t18+16t6-32t5+32t4-64t3-80t2-96t-32)
// m[2,19]=(4t145+10t144+48t143+104t142+184t141+292t140+240t139+120t138+100t137+50t136-8t127-20t126-96t125-208t124-368t123-584t122-480t121-240t120-200t119-100t118)*a5+(2t163+6t162+28t161+64t160+130t159+146t158+132t157-504t156-912t155-2932t154-4240t153-6140t152-8050t151-6050t150-6000t149-3500t148-1250t147-1254t146-4t145-48t144-72t143-216t142-436t141-476t140-824t139+268t138+1424t137+5764t136+8480t135+12280t134+16100t133+12100t132+12000t131+7000t130+2500t129+2520t128-10t127+146t126-76t125+36t124+24t123-584t122+940t121+1960t120+850t119+150t118-24t110+12t109-168t108+120t107+72t106+288t105+1320t104-120t103-1200t102-300t101)*a4+(-2t178-4t177-46t176-88t175-426t174-764t173-2022t172-3280t171-5190t170-7100t169-7050t168-7000t167-4750t166-2500t165-1250t164+6t163+18t162+88t161+208t160+506t159+806t158+1776t157+1896t156+5892t155+7380t154+17340t153+23100t152+32550t151+38250t150+33500t149+27500t148+13750t147+6244t146-40t145-174t144-604t143-1478t142-3404t141-4678t140-9476t139-4320t138-17356t137-1864t136-28620t135-23030t134-35900t133-63350t132-40500t131-50750t130-22504t129-8690t128+58t127+814t126+1428t125+4256t124+8604t123+11464t122+21168t121+14732t120+24530t119-2102t118+22600t117+7460t116+14500t115+42200t114+15000t113+36500t112+12516t111+4840t110+44t109-1708t108-1432t107-5960t106-10160t105-11664t104-22200t103-23640t102-13500t101-4100t100-16t93+120t92-108t91+1172t90+440t89+3160t88+4752t87+3776t86+10520t85+11760t84+6300t83+1900t82)*a3+(-4t178-8t177-92t176-176t175-852t174-1528t173-4044t172-6560t171-10380t170-14200t169-14100t168-14000t167-9500t166-5000t165-2500t164+6t163+18t162+86t161+230t160+508t159+1312t158+2406t157+6582t156+13038t155+29622t154+51510t153+80190t152+110700t151+115800t150+112750t149+79750t148+42500t147+20000t146-56t145-172t144-852t143-1988t142-5068t141-7580t140-17924t139-16692t138-58692t137-65236t136-175340t135-212220t134-331300t133-352900t132-333500t131-255500t130-132504t129-59964t128+170t127+966t126+3180t125+7976t124+19316t123+25232t122+58344t121+27756t120+130714t119+42698t118+291280t117+224460t116+457100t115+467200t114+432000t113+361500t112+177540t111+79788t110-8t109-3124t108-5400t107-17724t106-36232t105-48620t104-90416t103-56456t102-118256t101+1720t100-174120t99-65100t98-233400t97-209500t96-203000t95-177500t94-85096t93-37124t92-588t91+4484t90+3576t89+19320t88+33648t87+45440t86+74280t85+72400t84+44700t83+13500t82+64t75-208t74+520t73-2232t72-464t71-7760t70-12320t69-14400t68-28400t67-28000t66-17000t65-5000t64)*a2+(-2t178-4t177-46t176-88t175-426t174-764t173-2022t172-3280t171-5190t170-7100t169-7050t168-7000t167-4750t166-2500t165-1250t164+2t163+6t162+26t161+90t160+140t159+744t158+938t157+5034t156+7762t155+23354t154+36490t153+61330t152+84300t151+85600t150+87250t149+58250t148+32500t147+15002t146-28t145-72t144-408t143-1082t142-2264t141-5550t140-8304t139-22076t138-38820t137-94526t136-160400t135-261770t134-363000t133-387650t132-385000t131-269250t130-150000t129-66258t128+138t127+378t126+2176t125+5100t124+13128t123+19788t122+44168t121+38316t120+134638t119+141698t118+413260t117+483960t116+813200t115+819700t114+831500t113+599000t112+330016t111+142452t110-212t109-1644t108-5624t107-14744t106-36240t105-47200t104-106968t103-42264t102-224604t101-38404t100-522080t99-336080t98-885600t97-755600t96-852000t95-602000t94-340096t93-139768t92-444t91+3876t90+6264t89+24920t88+51936t87+73712t86+132712t85+80448t84+161148t83-19860t82+236960t81+56800t80+357200t79+246000t78+324000t77+220000t76+130160t75+49680t74+1280t73-4160t72-1920t71-20800t70-37440t69-56640t68-90400t67-86400t66-56000t65-16000t64-80t57+144t56-736t55+1632t54-512t53+6528t52+10784t51+15072t50+28240t49+27120t48+17600t47+4800t46)*a+(4t160+8t159+92t158+176t157+852t156+1528t155+4044t154+6560t153+10380t152+14200t151+14100t150+14000t149+9500t148+5000t147+2500t146-4t145-12t144-52t143-160t142-240t141-1028t140-996t139-5808t138-7884t137-26488t136-40180t135-70760t134-97600t133-100700t132-104500t131-69000t130-40000t129-17504t128+28t127+60t126+420t125+1120t124+2328t123+5652t122+7572t121+19684t120+31356t119+80472t118+133620t117+225440t116+313400t115+338300t114+340500t113+236000t112+135000t111+57512t110-100t109-236t108-1624t107-3804t106-9840t105-14764t104-30904t103-23000t102-84348t101-77248t100-264960t99-293460t98-547200t97-519700t96-574000t95-386500t94-230016t93-92492t92+36t91+788t90+2968t89+8472t88+21024t87+28752t86+60472t85+22304t84+111644t83+92t82+258880t81+139840t80+471600t79+358800t78+472000t77+296000t76+190064t75+69936t74+456t73-1400t72-1968t71-11008t70-23744t69-36656t68-63760t67-40352t66-69896t65+14328t64-93920t63-11440t62-154400t61-90800t60-148000t59-86000t58-60080t57-19920t56-736t55+1184t54-256t53+7168t52+13600t51+23136t50+37200t49+35760t48+24000t47+6400t46+32t39-32t38+320t37-384t36+512t35-1792t34-3136t33-5184t32-9760t31-9440t30-6400t29-1600t28)
// m[2,20]=(-4t145-10t144-48t143-104t142-184t141-292t140-240t139-120t138-100t137-50t136+8t127+20t126+96t125+208t124+368t123+584t122+480t121+240t120+200t119+100t118)*a5+(-2t163-6t162-28t161-64t160-130t159-146t158-132t157+504t156+912t155+2932t154+4240t153+6140t152+8050t151+6050t150+6000t149+3500t148+1250t147+1254t146+4t145+48t144+72t143+216t142+436t141+476t140+824t139-268t138-1424t137-5764t136-8480t135-12280t134-16100t133-12100t132-12000t131-7000t130-2500t129-2520t128+10t127-146t126+76t125-36t124-24t123+584t122-940t121-1960t120-850t119-150t118+24t110-12t109+168t108-120t107-72t106-288t105-1320t104+120t103+1200t102+300t101)*a4+(2t178+4t177+46t176+88t175+426t174+764t173+2022t172+3280t171+5190t170+7100t169+7050t168+7000t167+4750t166+2500t165+1250t164-6t163-18t162-88t161-208t160-506t159-806t158-1776t157-1896t156-5892t155-7380t154-17340t153-23100t152-32550t151-38250t150-33500t149-27500t148-13750t147-6244t146+40t145+174t144+604t143+1478t142+3404t141+4678t140+9476t139+4320t138+17356t137+1864t136+28620t135+23030t134+35900t133+63350t132+40500t131+50750t130+22504t129+8690t128-58t127-814t126-1428t125-4256t124-8604t123-11464t122-21168t121-14732t120-24530t119+2102t118-22600t117-7460t116-14500t115-42200t114-15000t113-36500t112-12516t111-4840t110-44t109+1708t108+1432t107+5960t106+10160t105+11664t104+22200t103+23640t102+13500t101+4100t100+16t93-120t92+108t91-1172t90-440t89-3160t88-4752t87-3776t86-10520t85-11760t84-6300t83-1900t82)*a3+(4t178+8t177+92t176+176t175+852t174+1528t173+4044t172+6560t171+10380t170+14200t169+14100t168+14000t167+9500t166+5000t165+2500t164-6t163-18t162-86t161-230t160-508t159-1312t158-2406t157-6582t156-13038t155-29622t154-51510t153-80190t152-110700t151-115800t150-112750t149-79750t148-42500t147-20000t146+56t145+172t144+852t143+1988t142+5068t141+7580t140+17924t139+16692t138+58692t137+65236t136+175340t135+212220t134+331300t133+352900t132+333500t131+255500t130+132504t129+59964t128-170t127-966t126-3180t125-7976t124-19316t123-25232t122-58344t121-27756t120-130714t119-42698t118-291280t117-224460t116-457100t115-467200t114-432000t113-361500t112-177540t111-79788t110+8t109+3124t108+5400t107+17724t106+36232t105+48620t104+90416t103+56456t102+118256t101-1720t100+174120t99+65100t98+233400t97+209500t96+203000t95+177500t94+85096t93+37124t92+588t91-4484t90-3576t89-19320t88-33648t87-45440t86-74280t85-72400t84-44700t83-13500t82-64t75+208t74-520t73+2232t72+464t71+7760t70+12320t69+14400t68+28400t67+28000t66+17000t65+5000t64)*a2+(2t178+4t177+46t176+88t175+426t174+764t173+2022t172+3280t171+5190t170+7100t169+7050t168+7000t167+4750t166+2500t165+1250t164-2t163-6t162-26t161-90t160-140t159-744t158-938t157-5034t156-7762t155-23354t154-36490t153-61330t152-84300t151-85600t150-87250t149-58250t148-32500t147-15002t146+28t145+72t144+408t143+1082t142+2264t141+5550t140+8304t139+22076t138+38820t137+94526t136+160400t135+261770t134+363000t133+387650t132+385000t131+269250t130+150000t129+66258t128-138t127-378t126-2176t125-5100t124-13128t123-19788t122-44168t121-38316t120-134638t119-141698t118-413260t117-483960t116-813200t115-819700t114-831500t113-599000t112-330016t111-142452t110+212t109+1644t108+5624t107+14744t106+36240t105+47200t104+106968t103+42264t102+224604t101+38404t100+522080t99+336080t98+885600t97+755600t96+852000t95+602000t94+340096t93+139768t92+444t91-3876t90-6264t89-24920t88-51936t87-73712t86-132712t85-80448t84-161148t83+19860t82-236960t81-56800t80-357200t79-246000t78-324000t77-220000t76-130160t75-49680t74-1280t73+4160t72+1920t71+20800t70+37440t69+56640t68+90400t67+86400t66+56000t65+16000t64+80t57-144t56+736t55-1632t54+512t53-6528t52-10784t51-15072t50-28240t49-27120t48-17600t47-4800t46)*a+(-4t160-8t159-92t158-176t157-852t156-1528t155-4044t154-6560t153-10380t152-14200t151-14100t150-14000t149-9500t148-5000t147-2500t146+4t145+12t144+52t143+160t142+240t141+1028t140+996t139+5808t138+7884t137+26488t136+40180t135+70760t134+97600t133+100700t132+104500t131+69000t130+40000t129+17504t128-28t127-60t126-420t125-1120t124-2328t123-5652t122-7572t121-19684t120-31356t119-80472t118-133620t117-225440t116-313400t115-338300t114-340500t113-236000t112-135000t111-57512t110+100t109+236t108+1624t107+3804t106+9840t105+14764t104+30904t103+23000t102+84348t101+77248t100+264960t99+293460t98+547200t97+519700t96+574000t95+386500t94+230016t93+92492t92-36t91-788t90-2968t89-8472t88-21024t87-28752t86-60472t85-22304t84-111644t83-92t82-258880t81-139840t80-471600t79-358800t78-472000t77-296000t76-190064t75-69936t74-456t73+1400t72+1968t71+11008t70+23744t69+36656t68+63760t67+40352t66+69896t65-14328t64+93920t63+11440t62+154400t61+90800t60+148000t59+86000t58+60080t57+19920t56+736t55-1184t54+256t53-7168t52-13600t51-23136t50-37200t49-35760t48-24000t47-6400t46-32t39+32t38-320t37+384t36-512t35+1792t34+3136t33+5184t32+9760t31+9440t30+6400t29+1600t28)


// Next, we replace every occurrence of a^2 by -1 and reconstruct the coefficients as cij (where corresponding to the monomial y^i*z^j)



poly c50 = m[2,1];
poly c41 = m[2,2];
poly c32 = m[2,3];
poly c23 = m[2,4];
poly c14 = m[2,5];
poly c05 = m[2,6];
poly c40 = m[2,7];
poly c31 = m[2,8];
poly c22 = m[2,9];
poly c13 = m[2,10];
poly c04 = m[2,11];
poly c30 = m[2,12];
poly c21 = m[2,13];
poly c12 = m[2,14];
poly c03 = m[2,15];
poly c20 = m[2,16];
poly c11 = m[2,17];
poly c02 = m[2,18];
poly c10 = m[2,19];
poly c01 = m[2,20];

// Replace c40:

poly c40 = (4t38-2t37+2t36)*(-1)+(4t56-t55+3t54-t51-t50-10t49-10t48-25t47-25t46-12t38-12t36+4t24-5t23+7t22-10t21+10t20+12t18)*a+(t74+t72+t66+21t64+170t62+650t60+1125t58+621t56-t55-5t54-t51-t50-10t49-10t48-25t47-25t46+2t42+6t40+12t38+4t37+36t36+116t34+2t33+214t32+20t31+190t30+50t29+100t28-4t24-5t23-17t22-10t21-14t20-8t19-4t18+t10+5t8+8t6+10t5+14t4+20t3+12t2+8t);

// c40;
// (4t56-t55+3t54-t51-t50-10t49-10t48-25t47-25t46-12t38-12t36+4t24-5t23+7t22-10t21+10t20+12t18)*a+(t74+t72+t66+21t64+170t62+650t60+1125t58+621t56-t55-5t54-t51-t50-10t49-10t48-25t47-25t46+2t42+6t40+8t38+6t37+34t36+116t34+2t33+214t32+20t31+190t30+50t29+100t28-4t24-5t23-17t22-10t21-14t20-8t19-4t18+t10+5t8+8t6+10t5+14t4+20t3+12t2+8t)

poly c31 = (-16t38+8t37-8t36)*(-1)+(-16t56+4t55-12t54+4t51+4t50+40t49+40t48+100t47+100t46+48t38+48t36-8t24+10t23-14t22+20t21-36t20-10t19-50t18)*a+(-4t74-4t72-4t66-84t64-680t62-2600t60-4500t58-2484t56+4t55+20t54+4t51+4t50+40t49+40t48+100t47+100t46-4t42-12t40-32t38-16t37-88t36-232t34-8t33-432t32-80t31-420t30-200t29-300t28+8t24+10t23+34t22+20t21+12t20+22t19-2t18+4t6-20t5-8t4-40t3-12t+20);

// c31;
// (-16t56+4t55-12t54+4t51+4t50+40t49+40t48+100t47+100t46+48t38+48t36-8t24+10t23-14t22+20t21-36t20-10t19-50t18)*a+(-4t74-4t72-4t66-84t64-680t62-2600t60-4500t58-2484t56+4t55+20t54+4t51+4t50+40t49+40t48+100t47+100t46-4t42-12t40-16t38-24t37-80t36-232t34-8t33-432t32-80t31-420t30-200t29-300t28+8t24+10t23+34t22+20t21+12t20+22t19-2t18+4t6-20t5-8t4-40t3-12t+20)


poly c22 = (24t38-12t37+12t36)*(-1)+(24t56-6t55+18t54-6t51-6t50-60t49-60t48-150t47-150t46-72t38-72t36+4t24-5t23+7t22-10t21+50t20+25t19+77t18)*a+(6t74+6t72+6t66+126t64+1020t62+3900t60+6750t58+3726t56-6t55-30t54-6t51-6t50-60t49-60t48-150t47-150t46+2t42+6t40+32t38+24t37+76t36+116t34+12t33+224t32+120t31+290t30+300t29+350t28-4t24-5t23-17t22-10t21+26t20-23t19+21t18-2t6+10t5+4t4+20t3-28t2-2t-46);

// c22;
// (24t56-6t55+18t54-6t51-6t50-60t49-60t48-150t47-150t46-72t38-72t36+4t24-5t23+7t22-10t21+50t20+25t19+77t18)*a+(6t74+6t72+6t66+126t64+1020t62+3900t60+6750t58+3726t56-6t55-30t54-6t51-6t50-60t49-60t48-150t47-150t46+2t42+6t40+8t38+36t37+64t36+116t34+12t33+224t32+120t31+290t30+300t29+350t28-4t24-5t23-17t22-10t21+26t20-23t19+21t18-2t6+10t5+4t4+20t3-28t2-2t-46)

poly c13 = (-16t38+8t37-8t36)*(-1)+(-16t56+4t55-12t54+4t51+4t50+40t49+40t48+100t47+100t46+48t38+48t36-32t20-20t19-52t18)*a+(-4t74-4t72-4t66-84t64-680t62-2600t60-4500t58-2484t56+4t55+20t54+4t51+4t50+40t49+40t48+100t47+100t46-16t38-16t37-32t36-8t33-8t32-80t31-80t30-200t29-200t28-32t20+12t19-20t18+28t2+8t+36);

// c13;
// (-16t56+4t55-12t54+4t51+4t50+40t49+40t48+100t47+100t46+48t38+48t36-32t20-20t19-52t18)*a+(-4t74-4t72-4t66-84t64-680t62-2600t60-4500t58-2484t56+4t55+20t54+4t51+4t50+40t49+40t48+100t47+100t46-24t37-24t36-8t33-8t32-80t31-80t30-200t29-200t28-32t20+12t19-20t18+28t2+8t+36)

poly c04 = (4t38-2t37+2t36)*(-1)+(4t56-t55+3t54-t51-t50-10t49-10t48-25t47-25t46-12t38-12t36+8t20+5t19+13t18)*a+(t74+t72+t66+21t64+170t62+650t60+1125t58+621t56-t55-5t54-t51-t50-10t49-10t48-25t47-25t46+4t38+4t37+8t36+2t33+2t32+20t31+20t30+50t29+50t28+8t20-3t19+5t18-7t2-2t-9);

// c04;
// (4t56-t55+3t54-t51-t50-10t49-10t48-25t47-25t46-12t38-12t36+8t20+5t19+13t18)*a+(t74+t72+t66+21t64+170t62+650t60+1125t58+621t56-t55-5t54-t51-t50-10t49-10t48-25t47-25t46+6t37+6t36+2t33+2t32+20t31+20t30+50t29+50t28+8t20-3t19+5t18-7t2-2t-9)

poly c30 = (-4t89-2t88-40t87-22t86-100t85-70t84-50t82-4t75-2t74-2t72-8t60-11t59-9t58+2t56-t55+3t54)*(-1*a)+(-4t107-3t106-42t105-29t104-122t103-19t102-92t101+647t100-340t99+2940t98-1300t97+5800t96-2250t95+4750t94-1252t93+1248t92-2t91-2t90+8t89+10t88+92t87+110t86+320t85+350t84+300t83+250t82-4t78-8t77-8t76-2t75+9t74+76t73+37t72+252t71+107t70+250t69+113t68-150t67-145t66-500t65-175t64+6t61-2t60+17t59+23t58+54t57+8t56-t55-17t54-18t43+18t42-12t41-16t40-56t39-24t38-6t37+10t36)*(-1)+(-t125-t124-11t123-7t122-36t121+52t120-46t119+718t118-170t117+3110t116-650t115+6450t114-1125t113+5875t112-625t111+1875t110+2t106+4t105+10t104+40t103-194t102+100t101-2242t100-9840t98-21300t96-21000t94+2t93-7498t92+38t91+38t90+190t89+184t88+482t87+436t86+700t85+786t84+280t83+1958t82+850t81+7410t80+3250t79+17442t78+5609t77+19597t76+3109t75+8053t74-16t73-380t72-232t71-1162t70-1180t69-2074t68-2400t67-2590t66-1500t65-1350t64+3t61+27t60+72t59+126t58+105t57+227t56-140t55+836t54-463t53+2061t52+159t51+2783t50+1690t49+2630t48+1600t47+1200t46+4t44-36t43-12t42-152t41-204t40-276t39-148t38-64t37+40t36-8t26+48t25-32t24+108t23+108t22+188t21+116t20+48t19-16t18)*a+(t140+22t138+191t136+820t134+1775t132+1750t130+625t128-t125-t124-11t123-15t122-36t121-124t120-46t119-810t118-170t117-3450t116-650t115-7750t114-1125t113-8125t112-625t111-3125t110+6t107+7t106+68t105+81t104+234t103+337t102+284t101+1023t100+680t99+3960t98+2600t97+9700t96+4500t95+11500t94+2504t93+5004t92+40t91+40t90+162t89+156t88+174t87+128t86-288t85-202t84-588t83+1090t82-510t81+6050t80-1950t79+12246t78-3383t77+10616t76-1905t75+3124t74-176t73-72t72-792t71-589t70-1618t69-1200t68-1282t67-911t66+8t65-1454t64-340t63-6080t62-1303t61-13704t60-2206t59-14422t58-1143t57-5476t56+204t55+624t54+929t53+2125t52+2671t51+3623t50+3410t49+3230t48+1400t47+1200t46-44t42-118t41-210t40-254t39-290t38-80t37-708t36-50t35-1910t34-998t33-2786t32-1980t31-2360t30-1200t29-900t28-8t26+24t25+8t24+164t23+228t22+332t21+212t20+144t19+8t8-24t7+24t6-80t5-88t4-152t3-104t2-64t);

// c30;
// (-t125-t124-11t123-7t122-36t121+52t120-46t119+718t118-170t117+3110t116-650t115+6450t114-1125t113+5875t112-625t111+1875t110+2t106+4t105+10t104+40t103-194t102+100t101-2242t100-9840t98-21300t96-21000t94+2t93-7498t92+38t91+38t90+194t89+186t88+522t87+458t86+800t85+856t84+280t83+2008t82+850t81+7410t80+3250t79+17442t78+5609t77+19597t76+3113t75+8055t74-16t73-378t72-232t71-1162t70-1180t69-2074t68-2400t67-2590t66-1500t65-1350t64+3t61+35t60+83t59+135t58+105t57+225t56-139t55+833t54-463t53+2061t52+159t51+2783t50+1690t49+2630t48+1600t47+1200t46+4t44-36t43-12t42-152t41-204t40-276t39-148t38-64t37+40t36-8t26+48t25-32t24+108t23+108t22+188t21+116t20+48t19-16t18)*a+(t140+22t138+191t136+820t134+1775t132+1750t130+625t128-t125-t124-11t123-15t122-36t121-124t120-46t119-810t118-170t117-3450t116-650t115-7750t114-1125t113-8125t112-625t111-3125t110+10t107+10t106+110t105+110t104+356t103+356t102+376t101+376t100+1020t99+1020t98+3900t97+3900t96+6750t95+6750t94+3756t93+3756t92+42t91+42t90+154t89+146t88+82t87+18t86-608t85-552t84-888t83+840t82-510t81+6050t80-1950t79+12250t78-3375t77+10624t76-1903t75+3115t74-252t73-109t72-1044t71-696t70-1868t69-1313t68-1132t67-766t66+508t65-1279t64-340t63-6080t62-1309t61-13702t60-2223t59-14445t58-1197t57-5484t56+205t55+641t54+929t53+2125t52+2671t51+3623t50+3410t49+3230t48+1400t47+1200t46+18t43-62t42-106t41-194t40-198t39-266t38-74t37-718t36-50t35-1910t34-998t33-2786t32-1980t31-2360t30-1200t29-900t28-8t26+24t25+8t24+164t23+228t22+332t21+212t20+144t19+8t8-24t7+24t6-80t5-88t4-152t3-104t2-64t)

poly c21 = (12t89+6t88+120t87+66t86+300t85+210t84+150t82+12t75+6t74+6t72+8t60+11t59+9t58-24t57-14t56+t55-15t54)*(-1*a)+(12t107+9t106+126t105+87t104+366t103+57t102+276t101-1941t100+1020t99-8820t98+3900t97-17400t96+6750t95-14250t94+3756t93-3744t92+6t91+6t90-24t89-30t88-276t87-330t86-960t85-1050t84-900t83-750t82+4t78+8t77-14t75-47t74-104t73-67t72-252t71-89t70-214t69+85t68+510t67+775t66+1400t65+625t64-6t61+2t60-17t59+9t58-70t57+84t56+73t55+77t54+18t43-18t42+12t41-24t40+108t39-60t38-54t37-54t36)*(-1)+(3t125+3t124+33t123+21t122+108t121-156t120+138t119-2154t118+510t117-9330t116+1950t115-19350t114+3375t113-17625t112+1875t111-5625t110-6t106-12t105-30t104-120t103+582t102-300t101+6726t100+29520t98+63900t96+63000t94+22500t92-36t91-36t90-222t89-204t88-810t87-672t86-1590t85-1848t84-690t83-5724t82-2550t81-22230t80-9750t79-52342t78-16859t77-58847t76-9391t75-24335t74-16t73+348t72+312t71+1246t70+2068t69+2998t68+5280t67+5530t66+3700t65+3450t64-3t61-27t60-72t59-102t58-15t57-61t56+286t55-694t54+417t53-2131t52-713t51-3553t50-3780t49-5080t48-3950t47-2950t46-4t44+36t43+12t42+152t41+132t40+196t39-172t38-208t37-288t36+8t26-48t25+32t24-108t23-60t22-180t21+68t20+120t19+152t18)*a+(-3t140-66t138-573t136-2460t134-5325t132-5250t130-1875t128+3t125+3t124+33t123+45t122+108t121+372t120+138t119+2430t118+510t117+10350t116+1950t115+23250t114+3375t113+24375t112+1875t111+9375t110-18t107-21t106-204t105-243t104-702t103-1011t102-852t101-3069t100-2040t99-11880t98-7800t97-29100t96-13500t95-34500t94-7506t93-15006t92-42t91-42t90-138t89-120t88+114t87+252t86+1374t85+1116t84+1914t83-3120t82+1530t81-18150t80+5850t79-36746t78+10133t77-31868t76+5659t75-9372t74+184t73+76t72+792t71+567t70+1574t69+972t68+846t67+453t66-1024t65+3662t64+1020t63+18240t62+3903t61+41154t60+6706t59+43430t58+3661t57+16756t56-194t55-602t54-975t53-2163t52-3161t51-4041t50-4860t49-4560t48-2150t47-2150t46+44t42+118t41+170t40+182t39+122t38-24t37+580t36+78t35+1946t34+1322t33+3182t32+3120t31+3620t30+2300t29+1800t28+8t26-24t25-8t24-164t23-180t22-244t21+20t20+40t19+184t18-8t8+24t7-24t6+80t5+72t4+120t3+8t2-32t-80);

// c21;
// (3t125+3t124+33t123+21t122+108t121-156t120+138t119-2154t118+510t117-9330t116+1950t115-19350t114+3375t113-17625t112+1875t111-5625t110-6t106-12t105-30t104-120t103+582t102-300t101+6726t100+29520t98+63900t96+63000t94+22500t92-36t91-36t90-234t89-210t88-930t87-738t86-1890t85-2058t84-690t83-5874t82-2550t81-22230t80-9750t79-52342t78-16859t77-58847t76-9403t75-24341t74-16t73+342t72+312t71+1246t70+2068t69+2998t68+5280t67+5530t66+3700t65+3450t64-3t61-35t60-83t59-111t58+9t57-47t56+285t55-679t54+417t53-2131t52-713t51-3553t50-3780t49-5080t48-3950t47-2950t46-4t44+36t43+12t42+152t41+132t40+196t39-172t38-208t37-288t36+8t26-48t25+32t24-108t23-60t22-180t21+68t20+120t19+152t18)*a+(-3t140-66t138-573t136-2460t134-5325t132-5250t130-1875t128+3t125+3t124+33t123+45t122+108t121+372t120+138t119+2430t118+510t117+10350t116+1950t115+23250t114+3375t113+24375t112+1875t111+9375t110-30t107-30t106-330t105-330t104-1068t103-1068t102-1128t101-1128t100-3060t99-3060t98-11700t97-11700t96-20250t95-20250t94-11262t93-11262t92-48t91-48t90-114t89-90t88+390t87+582t86+2334t85+2166t84+2814t83-2370t82+1530t81-18150t80+5850t79-36750t78+10125t77-31868t76+5673t75-9325t74+288t73+143t72+1044t71+656t70+1788t69+887t68+336t67-322t66-2424t65+3037t64+1020t63+18240t62+3909t61+41152t60+6723t59+43421t58+3731t57+16672t56-267t55-679t54-975t53-2163t52-3161t51-4041t50-4860t49-4560t48-2150t47-2150t46-18t43+62t42+106t41+194t40+74t39+182t38+30t37+634t36+78t35+1946t34+1322t33+3182t32+3120t31+3620t30+2300t29+1800t28+8t26-24t25-8t24-164t23-180t22-244t21+20t20+40t19+184t18-8t8+24t7-24t6+80t5+72t4+120t3+8t2-32t-80)

poly c12 = (-12t89-6t88-120t87-66t86-300t85-210t84-150t82-12t75-6t74-6t72+36t57+18t56+18t54)*(-1*a)+(-12t107-9t106-126t105-87t104-366t103-57t102-276t101+1941t100-1020t99+8820t98-3900t97+17400t96-6750t95+14250t94-3756t93+3744t92-6t91-6t90+24t89+30t88+276t87+330t86+960t85+1050t84+900t83+750t82+12t76+24t75+57t74+42t73+45t72-27t70-54t69-297t68-540t67-945t66-1350t65-675t64-48t58+24t57-138t56-108t55-90t54+60t40-78t39+126t38+90t37+66t36)*(-1)+(-3t125-3t124-33t123-21t122-108t121+156t120-138t119+2154t118-510t117+9330t116-1950t115+19350t114-3375t113+17625t112-1875t111+5625t110+6t106+12t105+30t104+120t103-582t102+300t101-6726t100-29520t98-63900t96-63000t94-3t93-22503t92-3t91-3t90+48t89+30t88+492t87+354t86+1335t85+1593t84+615t83+5649t82+2550t81+22230t80+9750t79+52350t78+16875t77+58875t76+9423t75+24423t74+48t73+48t72-120t71-126t70-1332t69-1386t68-4320t67-4410t66-3300t65-3150t64-36t58-135t57-249t56-219t55-213t54+69t53+105t52+831t51+1155t50+3135t49+3675t48+3525t47+2625t46+108t40+120t39+480t38+408t37+372t36-72t22-12t21-276t20-252t19-204t18)*a+(3t140+66t138+573t136+2460t134+5325t132+5250t130+1875t128-3t125-3t124-33t123-45t122-108t121-372t120-138t119-2430t118-510t117-10350t116-1950t115-23250t114-3375t113-24375t112-1875t111-9375t110+18t107+21t106+204t105+243t104+702t103+1011t102+852t101+3069t100+2040t99+11880t98+7800t97+29100t96+13500t95+34500t94+7503t93+15003t92+3t91+3t90-36t89-54t88-432t87-570t86-1629t85-1371t84-1989t83+3045t82-1530t81+18150t80-5850t79+36750t78-10125t77+31878t76-5631t75+9372t74-12t73-6t72+33t70+66t69+342t68+654t67+687t66+1524t65-3312t64-1020t63-18240t62-3900t61-41175t60-6750t59-43512t58-3777t57-16920t56-15t55-33t54+69t53+57t52+735t51+627t50+2175t49+1995t48+1125t47+1425t46+60t40+108t39+252t38+156t37+192t36-42t35-54t34-486t33-594t32-1710t31-1890t30-1650t29-1350t28-72t22-132t21-348t20-276t19-276t18+24t4+48t3+144t2+144t+120);

// c12;
// (-3t125-3t124-33t123-21t122-108t121+156t120-138t119+2154t118-510t117+9330t116-1950t115+19350t114-3375t113+17625t112-1875t111+5625t110+6t106+12t105+30t104+120t103-582t102+300t101-6726t100-29520t98-63900t96-63000t94-3t93-22503t92-3t91-3t90+60t89+36t88+612t87+420t86+1635t85+1803t84+615t83+5799t82+2550t81+22230t80+9750t79+52350t78+16875t77+58875t76+9435t75+24429t74+48t73+54t72-120t71-126t70-1332t69-1386t68-4320t67-4410t66-3300t65-3150t64-36t58-171t57-267t56-219t55-231t54+69t53+105t52+831t51+1155t50+3135t49+3675t48+3525t47+2625t46+108t40+120t39+480t38+408t37+372t36-72t22-12t21-276t20-252t19-204t18)*a+(3t140+66t138+573t136+2460t134+5325t132+5250t130+1875t128-3t125-3t124-33t123-45t122-108t121-372t120-138t119-2430t118-510t117-10350t116-1950t115-23250t114-3375t113-24375t112-1875t111-9375t110+30t107+30t106+330t105+330t104+1068t103+1068t102+1128t101+1128t100+3060t99+3060t98+11700t97+11700t96+20250t95+20250t94+11259t93+11259t92+9t91+9t90-60t89-84t88-708t87-900t86-2589t85-2421t84-2889t83+2295t82-1530t81+18150t80-5850t79+36750t78-10125t77+31866t76-5655t75+9315t74-54t73-51t72+60t70+120t69+639t68+1194t67+1632t66+2874t65-2637t64-1020t63-18240t62-3900t61-41175t60-6750t59-43464t58-3801t57-16782t56+93t55+57t54+69t53+57t52+735t51+627t50+2175t49+1995t48+1125t47+1425t46+186t39+126t38+66t37+126t36-42t35-54t34-486t33-594t32-1710t31-1890t30-1650t29-1350t28-72t22-132t21-348t20-276t19-276t18+24t4+48t3+144t2+144t+120)

poly c03 = (4t89+2t88+40t87+22t86+100t85+70t84+50t82+4t75+2t74+2t72-12t57-6t56-6t54)*(-1*a)+(4t107+3t106+42t105+29t104+122t103+19t102+92t101-647t100+340t99-2940t98+1300t97-5800t96+2250t95-4750t94+1252t93-1248t92+2t91+2t90-8t89-10t88-92t87-110t86-320t85-350t84-300t83-250t82-4t76-8t75-19t74-14t73-15t72+9t70+18t69+99t68+180t67+315t66+450t65+225t64+16t58-8t57+46t56+36t55+30t54-20t40+26t39-42t38-30t37-22t36)*(-1)+(t125+t124+11t123+7t122+36t121-52t120+46t119-718t118+170t117-3110t116+650t115-6450t114+1125t113-5875t112+625t111-1875t110-2t106-4t105-10t104-40t103+194t102-100t101+2242t100+9840t98+21300t96+21000t94+t93+7501t92+t91+t90-16t89-10t88-164t87-118t86-445t85-531t84-205t83-1883t82-850t81-7410t80-3250t79-17450t78-5625t77-19625t76-3141t75-8141t74-16t73-16t72+40t71+42t70+444t69+462t68+1440t67+1470t66+1100t65+1050t64+12t58+45t57+83t56+73t55+71t54-23t53-35t52-277t51-385t50-1045t49-1225t48-1175t47-875t46-36t40-40t39-160t38-136t37-124t36+24t22+4t21+92t20+84t19+68t18)*a+(-t140-22t138-191t136-820t134-1775t132-1750t130-625t128+t125+t124+11t123+15t122+36t121+124t120+46t119+810t118+170t117+3450t116+650t115+7750t114+1125t113+8125t112+625t111+3125t110-6t107-7t106-68t105-81t104-234t103-337t102-284t101-1023t100-680t99-3960t98-2600t97-9700t96-4500t95-11500t94-2501t93-5001t92-t91-t90+12t89+18t88+144t87+190t86+543t85+457t84+663t83-1015t82+510t81-6050t80+1950t79-12250t78+3375t77-10626t76+1877t75-3124t74+4t73+2t72-11t70-22t69-114t68-218t67-229t66-508t65+1104t64+340t63+6080t62+1300t61+13725t60+2250t59+14504t58+1259t57+5640t56+5t55+11t54-23t53-19t52-245t51-209t50-725t49-665t48-375t47-475t46-20t40-36t39-84t38-52t37-64t36+14t35+18t34+162t33+198t32+570t31+630t30+550t29+450t28+24t22+44t21+116t20+92t19+92t18-8t4-16t3-48t2-48t-40);

// c03;
// (t125+t124+11t123+7t122+36t121-52t120+46t119-718t118+170t117-3110t116+650t115-6450t114+1125t113-5875t112+625t111-1875t110-2t106-4t105-10t104-40t103+194t102-100t101+2242t100+9840t98+21300t96+21000t94+t93+7501t92+t91+t90-20t89-12t88-204t87-140t86-545t85-601t84-205t83-1933t82-850t81-7410t80-3250t79-17450t78-5625t77-19625t76-3145t75-8143t74-16t73-18t72+40t71+42t70+444t69+462t68+1440t67+1470t66+1100t65+1050t64+12t58+57t57+89t56+73t55+77t54-23t53-35t52-277t51-385t50-1045t49-1225t48-1175t47-875t46-36t40-40t39-160t38-136t37-124t36+24t22+4t21+92t20+84t19+68t18)*a+(-t140-22t138-191t136-820t134-1775t132-1750t130-625t128+t125+t124+11t123+15t122+36t121+124t120+46t119+810t118+170t117+3450t116+650t115+7750t114+1125t113+8125t112+625t111+3125t110-10t107-10t106-110t105-110t104-356t103-356t102-376t101-376t100-1020t99-1020t98-3900t97-3900t96-6750t95-6750t94-3753t93-3753t92-3t91-3t90+20t89+28t88+236t87+300t86+863t85+807t84+963t83-765t82+510t81-6050t80+1950t79-12250t78+3375t77-10622t76+1885t75-3105t74+18t73+17t72-20t70-40t69-213t68-398t67-544t66-958t65+879t64+340t63+6080t62+1300t61+13725t60+2250t59+14488t58+1267t57+5594t56-31t55-19t54-23t53-19t52-245t51-209t50-725t49-665t48-375t47-475t46-62t39-42t38-22t37-42t36+14t35+18t34+162t33+198t32+570t31+630t30+550t29+450t28+24t22+44t21+116t20+92t19+92t18-8t4-16t3-48t2-48t-40)

poly c20 = (2t96+7t95+9t94+6t93+4t92+3t91+t90)*a+(4t126+6t125+42t124+62t123+122t122+170t121+70t120+50t119+50t118+t114+4t113+7t112+6t111+2t110-22t109-68t108-134t107-324t106-398t105-572t104-680t103-295t102-200t101-175t100-2t97+9t95-t94-22t93-20t92-9t91-3t90+6t79+t78-28t77-19t76+18t75+15t74+4t73+3t72)*(1)+(2t144+4t143+24t142+40t141+90t140+56t139+76t138-580t137-332t136-2600t135-1640t134-4500t133-3550t132-2500t131-3500t130-t129-1253t128-19t127-45t126-143t125-261t124-523t123-743t122-748t121-908t120+1290t119+796t118+7800t117+4920t116+13500t115+10654t114+7516t113+10528t112+28t111+3794t110+36t109+52t108+264t107+88t106+904t105+902t104+1240t103+2420t102+1600t101+550t100-5t97-19t96-47t95-115t94-152t93-180t92-72t91-60t90-194t89+390t88-510t87-36t86-175t85-1985t84-1125t83-275t82-2t80+28t79+52t78+24t77+174t76+324t75+244t74+112t73+20t72+4t62-32t61-48t60+32t59-84t58-220t57-148t56-68t55-12t54)*(-1*a)+(-2t159-2t158-44t157-44t156-382t155-382t154-1640t153-1640t152-3550t151-3550t150-3500t149-3500t148-1250t147-1250t146+3t144+6t143+40t142+74t141+241t140+392t139+1274t138+1804t137+6220t136+7580t135+19400t134+18100t133+33625t132+20750t131+28750t130+8747t129+9366t128-49t127-143t126-353t125-859t124-1425t123-2625t122-2848t121-6296t120-1346t119-19800t118-920t117-53000t116-14400t115-81244t114-35476t113-62459t112-22448t111-18650t110+244t109+628t108+1708t107+3218t106+6270t105+9263t104+10844t103+15464t102+4110t101+24252t100-11800t99+53540t98-9753t97+74013t96+17367t95+50739t94+18462t93+13250t92-492t91-1368t90-3318t89-4870t88-11292t87-14010t86-17945t85-19975t84-13425t83-5875t82-4t80+34t79+132t78+278t77+680t76+832t75+954t74+432t73+1038t72+2052t71+2364t70+6784t69+7420t68+9690t67+12150t66+7850t65+3250t64+20t62-80t61-224t60-200t59-828t58-1164t57-868t56-348t55-20t54-20t44+56t43+136t42+380t40+568t39+408t38+160t37+8t36)*(-1)+(-t159-t158-22t157-22t156-191t155-191t154-820t153-820t152-1775t151-1775t150-1750t149-1750t148-625t147-625t146+16t141+16t140+352t139+352t138+3056t137+3056t136+13120t135+13120t134+28400t133+28400t132+28000t131+28000t130+9997t129+9991t128-46t127-128t126-289t125-663t124-1024t123-1764t122-2758t121-5194t120-10158t119-23876t118-41660t117-79520t116-98075t115-147021t114-110234t113-131724t112-45581t111-44299t110+284t109+764t108+1880t107+4104t106+6728t105+10580t104+12856t103+19644t102+16856t101+56554t100+49120t99+165580t98+133401t97+283073t96+177880t95+239282t94+84742t93+77040t92-803t91-2293t90-5546t89-10794t88-19588t87-27458t86-33433t85-36575t84-23669t83-42343t82-16880t81-98362t80-59092t79-162596t78-96620t77-133238t76-51688t75-41240t74+824t73+3196t72+6776t71+12456t70+24756t69+32340t68+40860t67+39700t66+27400t65+12000t64+20t62-44t61-244t60-564t59-1400t58-1620t57-1724t56-460t55-1588t54-2728t53-4904t52-10884t51-13548t50-17740t49-18180t48-12600t47-5200t46-48t44+64t43+288t42+320t41+1328t40+1664t39+1312t38+448t37+32t26-32t25-128t24-16t23-496t22-624t21-496t20-160t19)*a+(t159+t158+22t157+22t156+191t155+191t154+820t153+820t152+1775t151+1775t150+1750t149+1750t148+625t147+625t146-t144-2t143-11t142-24t141-26t140-116t139+87t138-474t137+413t136-1980t135+135t134-4850t133-1800t132-5750t131-2875t130-2501t129-1253t128-16t127-34t126-85t125-115t124-152t123-156t122-124t121-876t120-1460t119-5306t118-6700t117-16120t116-13375t115-26524t114-11246t113-21744t112-3111t111-6857t110+108t109+254t108+666t107+1278t106+1926t105+2749t104+3008t103+6703t102+7962t101+28999t100+32240t99+87980t98+74301t97+148593t96+80964t95+124438t94+32406t93+39884t92-387t91-933t90-2486t89-4958t88-8174t87-11300t86-12991t85-16233t84-15537t83-40127t82-44240t81-118040t80-109304t79-205273t78-130854t77-175725t76-57182t75-57049t74+604t73+1851t72+4596t71+9292t70+16528t69+22280t68+26554t67+24998t66+18778t65+21050t64+18560t63+47004t62+49204t61+84932t60+63684t59+74344t58+29292t57+24092t56-292t55-1724t54-3624t53-7944t52-15172t51-20412t50-25420t49-22820t48-15800t47-6800t46-20t44+112t42+344t41+916t40+1064t39+1064t38+144t37+600t36+944t35+2416t34+5080t33+6856t32+9000t31+8360t30+6000t29+2400t28+32t26-96t24-144t23-688t22-848t21-720t20-224t19-16t8+32t6+208t4+256t3+224t2+64t);

// c20;
// (-t159-t158-22t157-22t156-191t155-191t154-820t153-820t152-1775t151-1775t150-1750t149-1750t148-625t147-625t146-2t144-4t143-24t142-24t141-74t140+296t139+276t138+3636t137+3388t136+15720t135+14760t134+32900t133+31950t132+30500t131+31500t130+9998t129+11244t128-27t127-83t126-146t125-402t124-501t123-1021t122-2010t121-4286t120-11448t119-24672t118-49460t117-84440t116-111575t115-157675t114-117750t113-142252t112-45609t111-48093t110+248t109+712t108+1616t107+4016t106+5824t105+9678t104+11616t103+17224t102+15256t101+56004t100+49120t99+165580t98+133406t97+283094t96+177934t95+239406t94+84900t93+77224t92-728t91-2232t90-5352t89-11184t88-19078t87-27422t86-33258t85-34590t84-22544t83-42068t82-16880t81-98360t80-59120t79-162648t78-96644t77-133412t76-52012t75-41484t74+712t73+3176t72+6776t71+12456t70+24756t69+32340t68+40860t67+39700t66+27400t65+12000t64+16t62-12t61-196t60-596t59-1316t58-1400t57-1576t56-392t55-1576t54-2728t53-4904t52-10884t51-13548t50-17740t49-18180t48-12600t47-5200t46-48t44+64t43+288t42+320t41+1328t40+1664t39+1312t38+448t37+32t26-32t25-128t24-16t23-496t22-624t21-496t20-160t19)*a+(3t159+3t158+66t157+66t156+573t155+573t154+2460t153+2460t152+5325t151+5325t150+5250t149+5250t148+1875t147+1875t146-4t144-8t143-51t142-98t141-267t140-508t139-1187t138-2278t137-5807t136-9560t135-19265t134-22950t133-35425t132-26500t131-31625t130-11248t129-10619t128+33t127+113t126+274t125+786t124+1335t123+2591t122+2894t121+5490t120-64t119+14544t118-5780t117+36880t116+1025t115+54721t114+24234t113+40722t112+19343t111+11795t110-158t109-442t108-1176t107-2264t106-4742t105-7086t104-8516t103-9056t102+3652t101+4572t100+44040t99+34440t98+84052t97+74580t96+63606t95+73698t94+13922t93+26614t92+96t91+432t90+832t89-88t88+3118t87+2710t86+4954t85+3742t84-2112t83-34252t82-44240t81-118036t80-109332t79-205404t78-131160t77-176424t76-57996t75-57988t74+176t73+816t72+2544t71+6928t70+9744t69+14860t68+16864t67+12848t66+10928t65+17800t64+18560t63+46984t62+49284t61+85156t60+63884t59+75172t58+30456t57+24960t56+56t55-1704t54-3624t53-7944t52-15172t51-20412t50-25420t49-22820t48-15800t47-6800t46-56t43-24t42+344t41+536t40+496t39+656t38-16t37+592t36+944t35+2416t34+5080t33+6856t32+9000t31+8360t30+6000t29+2400t28+32t26-96t24-144t23-688t22-848t21-720t20-224t19-16t8+32t6+208t4+256t3+224t2+64t)


poly c11 = (-8t126-12t125-84t124-124t123-244t122-340t121-140t120-100t119-100t118+24t108+36t107+252t106+372t105+732t104+1020t103+420t102+300t101+300t100+8t94+12t93+4t92+4t91+4t90-16t76-24t75-8t74-8t73-8t72)*(1)+(-4t144-8t143-48t142-80t141-180t140-112t139-152t138+1160t137+664t136+5200t135+3280t134+9000t133+7100t132+5000t131+7000t130+2500t128+8t127+16t126+122t125+222t124+650t123+1034t122+1086t121+1546t120-2730t119-1642t118-15600t117-9840t116-27000t115-21300t114-15000t113-20996t112+8t111-7492t110-24t109+28t108-336t107+96t106-1072t105-880t104-1520t103-4000t102-2800t101-1000t100-8t95-8t94-28t93-52t92-4t91-80t90+360t89-480t88+680t87-280t86-200t85+3200t84+2000t83+500t82+40t77-28t76+112t74+72t73+28t72-48t59+40t58+24t57-88t56-40t55-16t54)*(-1*a)+(4t159+4t158+88t157+88t156+764t155+764t154+3280t153+3280t152+7100t151+7100t150+7000t149+7000t148+2500t147+2500t146-6t144-12t143-80t142-148t141-482t140-784t139-2548t138-3608t137-12440t136-15160t135-38800t134-36200t133-67250t132-41500t131-57500t130-17500t129-18750t128+8t127+64t126+214t125+818t124+1662t123+3894t122+4466t121+11782t120+2242t119+39450t118+1840t117+106000t116+28800t115+162500t114+71000t113+125008t112+45016t111+37516t110-56t109-170t108-1160t107-2428t106-6684t105-11716t104-15328t103-26428t102-5820t101-47754t100+23600t99-107080t98+19500t97-148100t96-35004t95-102052t94-37616t93-27640t92+40t91+108t90+2344t89+2784t88+11128t87+15352t86+23480t85+30720t84+22200t83+10300t82-8t78+72t77+80t76+304t75+472t74+296t73+160t72-1536t71-960t70-6272t69-7424t68-11520t67-18240t66-12800t65-5600t64+32t60-224t59+24t58-360t57-696t56-568t55-256t54-32t42+176t41-88t40+160t39+352t38+272t37+120t36)*(-1)+(2t159+2t158+44t157+44t156+382t155+382t154+1640t153+1640t152+3550t151+3550t150+3500t149+3500t148+1250t147+1250t146-32t141-32t140-704t139-704t138-6112t137-6112t136-26240t135-26240t134-56800t133-56800t132-56000t131-56000t130-20000t129-20000t128+2t127+34t126+86t125+426t124+860t123+2172t122+4286t121+9578t120+19866t119+47602t118+83320t117+159040t116+196150t115+294050t114+220500t113+263504t112+91258t111+88758t110-24t109-200t108-752t107-2592t106-5648t105-11960t104-17232t103-33488t102-30512t101-112108t100-98240t99-331160t98-266800t97-566200t96-355996t95-479044t94-170092t93-155100t92+56t91+444t90+2752t89+6456t88+16856t87+29032t86+42416t85+55960t84+38088t83+81836t82+33760t81+196720t80+118200t79+325400t78+194000t77+268156t76+105368t75+85480t74+240t73-284t72-3712t71-6912t70-20832t69-32736t68-49920t67-56960t66-42800t65-20400t64+32t60-136t59-176t58-760t57-1096t56-944t55-296t54+1632t53+2496t52+8704t51+13312t50+20640t49+25920t48+19600t47+8800t46-96t42+320t41-64t40+768t39+1120t38+1088t37+448t36+64t24-192t23+128t22-288t21-416t20-416t19-160t18)*a+(-2t159-2t158-44t157-44t156-382t155-382t154-1640t153-1640t152-3550t151-3550t150-3500t149-3500t148-1250t147-1250t146+2t144+4t143+22t142+48t141+52t140+232t139-174t138+948t137-826t136+3960t135-270t134+9700t133+3600t132+11500t131+5750t130+5000t129+2500t128+2t127-6t126+6t125-70t124-92t123-140t122-162t121+1482t120+2770t119+10562t118+13400t117+32240t116+26750t115+53050t114+22500t113+43500t112+6250t111+13750t110-12t109-22t108-156t107-280t106-740t105-1772t104-2596t103-11096t102-14624t101-57598t100-64480t99-175960t98-148600t97-297200t96-162000t95-249008t94-65016t93-80016t92+40t91+156t90+896t89+2040t88+5144t87+9032t86+13392t85+23736t84+26224t83+78804t82+88480t81+236080t80+218600t79+410600t78+261992t77+352048t76+115104t75+115120t74-304t72-2080t71-4576t70-12064t69-19472t68-29088t67-33216t66-28256t65-39400t64-37120t63-94000t62-98400t61-170000t60-127992t59-150128t58-60312t57-50424t56-320t55+136t54+1888t53+4224t52+11392t51+18688t50+28320t49+30080t48+22800t47+11200t46-32t42+64t41+88t40+512t39+704t38+704t37+200t36-576t35-1344t34-3712t33-6400t32-9920t31-11200t30-8800t29-4000t28+64t24-128t23+64t22-416t21-544t20-608t19-224t18-32t6+64t5-64t4+128t3+160t2+192t+64);

// c11;
// (2t159+2t158+44t157+44t156+382t155+382t154+1640t153+1640t152+3550t151+3550t150+3500t149+3500t148+1250t147+1250t146+4t144+8t143+48t142+48t141+148t140-592t139-552t138-7272t137-6776t136-31440t135-29520t134-65800t133-63900t132-61000t131-63000t130-20000t129-22500t128-6t127+18t126-36t125+204t124+210t123+1138t122+3200t121+8032t120+22596t119+49244t118+98920t117+168880t116+223150t115+315350t114+235500t113+284500t112+91250t111+96250t110-228t108-416t107-2688t106-4576t105-11080t104-15712t103-29488t102-27712t101-111108t100-98240t99-331160t98-266800t97-566200t96-355988t95-479036t94-170064t93-155048t92+60t91+524t90+2392t89+6936t88+16176t87+29312t86+42616t85+52760t84+36088t83+81336t82+33760t81+196720t80+118200t79+325400t78+193960t77+268184t76+105368t75+85368t74+168t73-312t72-3712t71-6912t70-20832t69-32736t68-49920t67-56960t66-42800t65-20400t64+32t60-88t59-216t58-784t57-1008t56-904t55-280t54+1632t53+2496t52+8704t51+13312t50+20640t49+25920t48+19600t47+8800t46-96t42+320t41-64t40+768t39+1120t38+1088t37+448t36+64t24-192t23+128t22-288t21-416t20-416t19-160t18)*a+(-6t159-6t158-132t157-132t156-1146t155-1146t154-4920t153-4920t152-10650t151-10650t150-10500t149-10500t148-3750t147-3750t146+8t144+16t143+102t142+196t141+534t140+1016t139+2374t138+4556t137+11614t136+19120t135+38530t134+45900t133+70850t132+53000t131+63250t130+22500t129+21250t128-6t127-78t126-220t125-972t124-1878t123-4278t122-4968t121-10440t120+428t119-28988t118+11560t117-73760t116-2050t115-109450t114-48500t113-81508t112-38766t111-23766t110+44t109+172t108+1040t107+2400t106+6316t105+10676t104+13752t103+15752t102-8504t101-9544t100-88080t99-68880t98-168100t97-149100t96-126996t95-146948t94-27388t93-52372t92+4t91+52t90-1448t89-744t88-5984t87-6320t86-10088t85-6984t84+4024t83+68504t82+88480t81+236080t80+218600t79+410608t78+261920t77+351952t76+114776t75+114640t74-304t73-472t72-544t71-3616t70-5792t69-12048t68-17568t67-14976t66-15456t65-33800t64-37120t63-94000t62-98400t61-170032t60-127768t59-150152t58-59952t57-49728t56+248t55+392t54+1888t53+4224t52+11392t51+18688t50+28320t49+30080t48+22800t47+11200t46-112t41+176t40+352t39+352t38+432t37+80t36-576t35-1344t34-3712t33-6400t32-9920t31-11200t30-8800t29-4000t28+64t24-128t23+64t22-416t21-544t20-608t19-224t18-32t6+64t5-64t4+128t3+160t2+192t+64)

poly c02 = (4t126+6t125+42t124+62t123+122t122+170t121+70t120+50t119+50t118-12t108-18t107-126t106-186t105-366t104-510t103-210t102-150t101-150t100-4t94-6t93-2t92-2t91-2t90+8t76+12t75+4t74+4t73+4t72)*(1)+(2t144+4t143+24t142+40t141+90t140+56t139+76t138-580t137-332t136-2600t135-1640t134-4500t133-3550t132-2500t131-3500t130-1250t128-4t127-8t126-61t125-111t124-325t123-517t122-543t121-773t120+1365t119+821t118+7800t117+4920t116+13500t115+10650t114+7500t113+10498t112-4t111+3746t110+12t109-14t108+168t107-48t106+536t105+440t104+760t103+2000t102+1400t101+500t100+4t95+4t94+14t93+26t92+2t91+40t90-180t89+240t88-340t87+140t86+100t85-1600t84-1000t83-250t82-20t77+14t76-56t74-36t73-14t72+24t59-20t58-12t57+44t56+20t55+8t54)*(-1*a)+(-2t159-2t158-44t157-44t156-382t155-382t154-1640t153-1640t152-3550t151-3550t150-3500t149-3500t148-1250t147-1250t146+3t144+6t143+40t142+74t141+241t140+392t139+1274t138+1804t137+6220t136+7580t135+19400t134+18100t133+33625t132+20750t131+28750t130+8750t129+9375t128-4t127-32t126-107t125-409t124-831t123-1947t122-2233t121-5891t120-1121t119-19725t118-920t117-53000t116-14400t115-81250t114-35500t113-62504t112-22508t111-18758t110+28t109+85t108+580t107+1214t106+3342t105+5858t104+7664t103+13214t102+2910t101+23877t100-11800t99+53540t98-9750t97+74050t96+17502t95+51026t94+18808t93+13820t92-20t91-54t90-1172t89-1392t88-5564t87-7676t86-11740t85-15360t84-11100t83-5150t82+4t78-36t77-40t76-152t75-236t74-148t73-80t72+768t71+480t70+3136t69+3712t68+5760t67+9120t66+6400t65+2800t64-16t60+112t59-12t58+180t57+348t56+284t55+128t54+16t42-88t41+44t40-80t39-176t38-136t37-60t36)*(-1)+(-t159-t158-22t157-22t156-191t155-191t154-820t153-820t152-1775t151-1775t150-1750t149-1750t148-625t147-625t146+16t141+16t140+352t139+352t138+3056t137+3056t136+13120t135+13120t134+28400t133+28400t132+28000t131+28000t130+10000t129+10000t128-t127-17t126-43t125-213t124-430t123-1086t122-2143t121-4789t120-9933t119-23801t118-41660t117-79520t116-98075t115-147025t114-110250t113-131752t112-45629t111-44379t110+12t109+100t108+376t107+1296t106+2824t105+5980t104+8616t103+16744t102+15256t101+56054t100+49120t99+165580t98+133400t97+283100t96+177998t95+239522t94+85046t93+77550t92-28t91-222t90-1376t89-3228t88-8428t87-14516t86-21208t85-27980t84-19044t83-40918t82-16880t81-98360t80-59100t79-162700t78-97000t77-134078t76-52684t75-42740t74-120t73+142t72+1856t71+3456t70+10416t69+16368t68+24960t67+28480t66+21400t65+10200t64-16t60+68t59+88t58+380t57+548t56+472t55+148t54-816t53-1248t52-4352t51-6656t50-10320t49-12960t48-9800t47-4400t46+48t42-160t41+32t40-384t39-560t38-544t37-224t36-32t24+96t23-64t22+144t21+208t20+208t19+80t18)*a+(t159+t158+22t157+22t156+191t155+191t154+820t153+820t152+1775t151+1775t150+1750t149+1750t148+625t147+625t146-t144-2t143-11t142-24t141-26t140-116t139+87t138-474t137+413t136-1980t135+135t134-4850t133-1800t132-5750t131-2875t130-2500t129-1250t128-t127+3t126-3t125+35t124+46t123+70t122+81t121-741t120-1385t119-5281t118-6700t117-16120t116-13375t115-26525t114-11250t113-21750t112-3125t111-6875t110+6t109+11t108+78t107+140t106+370t105+886t104+1298t103+5548t102+7312t101+28799t100+32240t99+87980t98+74300t97+148600t96+81000t95+124504t94+32508t93+40008t92-20t91-78t90-448t89-1020t88-2572t87-4516t86-6696t85-11868t84-13112t83-39402t82-44240t81-118040t80-109300t79-205300t78-130996t77-176024t76-57552t75-57560t74+152t72+1040t71+2288t70+6032t69+9736t68+14544t67+16608t66+14128t65+19700t64+18560t63+47000t62+49200t61+85000t60+63996t59+75064t58+30156t57+25212t56+160t55-68t54-944t53-2112t52-5696t51-9344t50-14160t49-15040t48-11400t47-5600t46+16t42-32t41-44t40-256t39-352t38-352t37-100t36+288t35+672t34+1856t33+3200t32+4960t31+5600t30+4400t29+2000t28-32t24+64t23-32t22+208t21+272t20+304t19+112t18+16t6-32t5+32t4-64t3-80t2-96t-32);

// c02;
// (-t159-t158-22t157-22t156-191t155-191t154-820t153-820t152-1775t151-1775t150-1750t149-1750t148-625t147-625t146-2t144-4t143-24t142-24t141-74t140+296t139+276t138+3636t137+3388t136+15720t135+14760t134+32900t133+31950t132+30500t131+31500t130+10000t129+11250t128+3t127-9t126+18t125-102t124-105t123-569t122-1600t121-4016t120-11298t119-24622t118-49460t117-84440t116-111575t115-157675t114-117750t113-142250t112-45625t111-48125t110+114t108+208t107+1344t106+2288t105+5540t104+7856t103+14744t102+13856t101+55554t100+49120t99+165580t98+133400t97+283100t96+177994t95+239518t94+85032t93+77524t92-30t91-262t90-1196t89-3468t88-8088t87-14656t86-21308t85-26380t84-18044t83-40668t82-16880t81-98360t80-59100t79-162700t78-96980t77-134092t76-52684t75-42684t74-84t73+156t72+1856t71+3456t70+10416t69+16368t68+24960t67+28480t66+21400t65+10200t64-16t60+44t59+108t58+392t57+504t56+452t55+140t54-816t53-1248t52-4352t51-6656t50-10320t49-12960t48-9800t47-4400t46+48t42-160t41+32t40-384t39-560t38-544t37-224t36-32t24+96t23-64t22+144t21+208t20+208t19+80t18)*a+(3t159+3t158+66t157+66t156+573t155+573t154+2460t153+2460t152+5325t151+5325t150+5250t149+5250t148+1875t147+1875t146-4t144-8t143-51t142-98t141-267t140-508t139-1187t138-2278t137-5807t136-9560t135-19265t134-22950t133-35425t132-26500t131-31625t130-11250t129-10625t128+3t127+39t126+110t125+486t124+939t123+2139t122+2484t121+5220t120-214t119+14494t118-5780t117+36880t116+1025t115+54725t114+24250t113+40754t112+19383t111+11883t110-22t109-86t108-520t107-1200t106-3158t105-5338t104-6876t103-7876t102+4252t101+4772t100+44040t99+34440t98+84050t97+74550t96+63498t95+73474t94+13694t93+26186t92-2t91-26t90+724t89+372t88+2992t87+3160t86+5044t85+3492t84-2012t83-34252t82-44240t81-118040t80-109300t79-205304t78-130960t77-175976t76-57388t75-57320t74+152t73+236t72+272t71+1808t70+2896t69+6024t68+8784t67+7488t66+7728t65+16900t64+18560t63+47000t62+49200t61+85016t60+63884t59+75076t58+29976t57+24864t56-124t55-196t54-944t53-2112t52-5696t51-9344t50-14160t49-15040t48-11400t47-5600t46+56t41-88t40-176t39-176t38-216t37-40t36+288t35+672t34+1856t33+3200t32+4960t31+5600t30+4400t29+2000t28-32t24+64t23-32t22+208t21+272t20+304t19+112t18+16t6-32t5+32t4-64t3-80t2-96t-32)


poly c10 = (4t145+10t144+48t143+104t142+184t141+292t140+240t139+120t138+100t137+50t136-8t127-20t126-96t125-208t124-368t123-584t122-480t121-240t120-200t119-100t118)*a+(2t163+6t162+28t161+64t160+130t159+146t158+132t157-504t156-912t155-2932t154-4240t153-6140t152-8050t151-6050t150-6000t149-3500t148-1250t147-1254t146-4t145-48t144-72t143-216t142-436t141-476t140-824t139+268t138+1424t137+5764t136+8480t135+12280t134+16100t133+12100t132+12000t131+7000t130+2500t129+2520t128-10t127+146t126-76t125+36t124+24t123-584t122+940t121+1960t120+850t119+150t118-24t110+12t109-168t108+120t107+72t106+288t105+1320t104-120t103-1200t102-300t101)*(1)+(-2t178-4t177-46t176-88t175-426t174-764t173-2022t172-3280t171-5190t170-7100t169-7050t168-7000t167-4750t166-2500t165-1250t164+6t163+18t162+88t161+208t160+506t159+806t158+1776t157+1896t156+5892t155+7380t154+17340t153+23100t152+32550t151+38250t150+33500t149+27500t148+13750t147+6244t146-40t145-174t144-604t143-1478t142-3404t141-4678t140-9476t139-4320t138-17356t137-1864t136-28620t135-23030t134-35900t133-63350t132-40500t131-50750t130-22504t129-8690t128+58t127+814t126+1428t125+4256t124+8604t123+11464t122+21168t121+14732t120+24530t119-2102t118+22600t117+7460t116+14500t115+42200t114+15000t113+36500t112+12516t111+4840t110+44t109-1708t108-1432t107-5960t106-10160t105-11664t104-22200t103-23640t102-13500t101-4100t100-16t93+120t92-108t91+1172t90+440t89+3160t88+4752t87+3776t86+10520t85+11760t84+6300t83+1900t82)*(-1*a)+(-4t178-8t177-92t176-176t175-852t174-1528t173-4044t172-6560t171-10380t170-14200t169-14100t168-14000t167-9500t166-5000t165-2500t164+6t163+18t162+86t161+230t160+508t159+1312t158+2406t157+6582t156+13038t155+29622t154+51510t153+80190t152+110700t151+115800t150+112750t149+79750t148+42500t147+20000t146-56t145-172t144-852t143-1988t142-5068t141-7580t140-17924t139-16692t138-58692t137-65236t136-175340t135-212220t134-331300t133-352900t132-333500t131-255500t130-132504t129-59964t128+170t127+966t126+3180t125+7976t124+19316t123+25232t122+58344t121+27756t120+130714t119+42698t118+291280t117+224460t116+457100t115+467200t114+432000t113+361500t112+177540t111+79788t110-8t109-3124t108-5400t107-17724t106-36232t105-48620t104-90416t103-56456t102-118256t101+1720t100-174120t99-65100t98-233400t97-209500t96-203000t95-177500t94-85096t93-37124t92-588t91+4484t90+3576t89+19320t88+33648t87+45440t86+74280t85+72400t84+44700t83+13500t82+64t75-208t74+520t73-2232t72-464t71-7760t70-12320t69-14400t68-28400t67-28000t66-17000t65-5000t64)*(-1)+(-2t178-4t177-46t176-88t175-426t174-764t173-2022t172-3280t171-5190t170-7100t169-7050t168-7000t167-4750t166-2500t165-1250t164+2t163+6t162+26t161+90t160+140t159+744t158+938t157+5034t156+7762t155+23354t154+36490t153+61330t152+84300t151+85600t150+87250t149+58250t148+32500t147+15002t146-28t145-72t144-408t143-1082t142-2264t141-5550t140-8304t139-22076t138-38820t137-94526t136-160400t135-261770t134-363000t133-387650t132-385000t131-269250t130-150000t129-66258t128+138t127+378t126+2176t125+5100t124+13128t123+19788t122+44168t121+38316t120+134638t119+141698t118+413260t117+483960t116+813200t115+819700t114+831500t113+599000t112+330016t111+142452t110-212t109-1644t108-5624t107-14744t106-36240t105-47200t104-106968t103-42264t102-224604t101-38404t100-522080t99-336080t98-885600t97-755600t96-852000t95-602000t94-340096t93-139768t92-444t91+3876t90+6264t89+24920t88+51936t87+73712t86+132712t85+80448t84+161148t83-19860t82+236960t81+56800t80+357200t79+246000t78+324000t77+220000t76+130160t75+49680t74+1280t73-4160t72-1920t71-20800t70-37440t69-56640t68-90400t67-86400t66-56000t65-16000t64-80t57+144t56-736t55+1632t54-512t53+6528t52+10784t51+15072t50+28240t49+27120t48+17600t47+4800t46)*a+(4t160+8t159+92t158+176t157+852t156+1528t155+4044t154+6560t153+10380t152+14200t151+14100t150+14000t149+9500t148+5000t147+2500t146-4t145-12t144-52t143-160t142-240t141-1028t140-996t139-5808t138-7884t137-26488t136-40180t135-70760t134-97600t133-100700t132-104500t131-69000t130-40000t129-17504t128+28t127+60t126+420t125+1120t124+2328t123+5652t122+7572t121+19684t120+31356t119+80472t118+133620t117+225440t116+313400t115+338300t114+340500t113+236000t112+135000t111+57512t110-100t109-236t108-1624t107-3804t106-9840t105-14764t104-30904t103-23000t102-84348t101-77248t100-264960t99-293460t98-547200t97-519700t96-574000t95-386500t94-230016t93-92492t92+36t91+788t90+2968t89+8472t88+21024t87+28752t86+60472t85+22304t84+111644t83+92t82+258880t81+139840t80+471600t79+358800t78+472000t77+296000t76+190064t75+69936t74+456t73-1400t72-1968t71-11008t70-23744t69-36656t68-63760t67-40352t66-69896t65+14328t64-93920t63-11440t62-154400t61-90800t60-148000t59-86000t58-60080t57-19920t56-736t55+1184t54-256t53+7168t52+13600t51+23136t50+37200t49+35760t48+24000t47+6400t46+32t39-32t38+320t37-384t36+512t35-1792t34-3136t33-5184t32-9760t31-9440t30-6400t29-1600t28);

// c10;
// (-4t163-12t162-62t161-118t160-366t159-62t158-838t157+3138t156+1870t155+15974t154+19150t153+38230t152+51750t151+47350t150+53750t149+30750t148+18750t147+8758t146+16t145+112t144+244t143+500t142+1324t141-580t140+1412t139-17636t138-21364t137-92612t136-131780t135-238740t134-327100t133-324300t132-344500t131-218500t130-127496t129-57568t128+72t127-456t126+652t125+636t124+4156t123+7740t122+22520t121+23344t120+109908t119+143700t118+390660t117+476500t116+798700t115+777500t114+816500t113+562500t112+317500t111+137612t110-256t109+64t108-4192t107-8784t106-26080t105-35536t104-84768t103-18624t102-211104t101-34304t100-522080t99-336080t98-885600t97-755600t96-852000t95-602000t94-340080t93-139888t92-336t91+2704t90+5824t89+21760t88+47184t87+69936t86+122192t85+68688t84+154848t83-21760t82+236960t81+56800t80+357200t79+246000t78+324000t77+220000t76+130160t75+49680t74+1280t73-4160t72-1920t71-20800t70-37440t69-56640t68-90400t67-86400t66-56000t65-16000t64-80t57+144t56-736t55+1632t54-512t53+6528t52+10784t51+15072t50+28240t49+27120t48+17600t47+4800t46)*a+(4t178+8t177+92t176+176t175+852t174+1528t173+4044t172+6560t171+10380t170+14200t169+14100t168+14000t167+9500t166+5000t165+2500t164-4t163-12t162-58t161-162t160-370t159-1074t158-2098t157-6234t156-12422t155-28510t154-49190t153-75950t152-104550t151-107750t150-104750t149-73750t148-38750t147-18754t146+48t145+112t144+728t143+1612t142+4392t141+6076t140+16104t139+11152t138+52232t137+44512t136+143640t135+153740t134+249800t133+264300t132+241000t131+193500t130+95004t129+44980t128-152t127-760t126-2836t125-6820t124-16964t123-20164t122-49832t121-6112t120-98508t119+37924t118-157660t117+980t116-143700t115-128900t114-91500t113-125500t112-42540t111-22300t110-80t109+2720t108+3896t107+13992t106+26680t105+35176t104+59392t103+32256t102+33608t101-78968t100-90840t99-228360t98-313800t97-310200t96-371000t95-209000t94-144920t93-55368t92+624t91-3696t90-608t89-10848t88-12624t87-16688t86-13808t85-50096t84+66944t83-13408t82+258880t81+139840t80+471600t79+358800t78+472000t77+296000t76+190000t75+70144t74-64t73+832t72-1504t71-3248t70-11424t69-22256t68-35360t67-12352t66-52896t65+19328t64-93920t63-11440t62-154400t61-90800t60-148000t59-86000t58-60080t57-19920t56-736t55+1184t54-256t53+7168t52+13600t51+23136t50+37200t49+35760t48+24000t47+6400t46+32t39-32t38+320t37-384t36+512t35-1792t34-3136t33-5184t32-9760t31-9440t30-6400t29-1600t28)


poly c01 = (-4t145-10t144-48t143-104t142-184t141-292t140-240t139-120t138-100t137-50t136+8t127+20t126+96t125+208t124+368t123+584t122+480t121+240t120+200t119+100t118)*a+(-2t163-6t162-28t161-64t160-130t159-146t158-132t157+504t156+912t155+2932t154+4240t153+6140t152+8050t151+6050t150+6000t149+3500t148+1250t147+1254t146+4t145+48t144+72t143+216t142+436t141+476t140+824t139-268t138-1424t137-5764t136-8480t135-12280t134-16100t133-12100t132-12000t131-7000t130-2500t129-2520t128+10t127-146t126+76t125-36t124-24t123+584t122-940t121-1960t120-850t119-150t118+24t110-12t109+168t108-120t107-72t106-288t105-1320t104+120t103+1200t102+300t101)*(1)+(2t178+4t177+46t176+88t175+426t174+764t173+2022t172+3280t171+5190t170+7100t169+7050t168+7000t167+4750t166+2500t165+1250t164-6t163-18t162-88t161-208t160-506t159-806t158-1776t157-1896t156-5892t155-7380t154-17340t153-23100t152-32550t151-38250t150-33500t149-27500t148-13750t147-6244t146+40t145+174t144+604t143+1478t142+3404t141+4678t140+9476t139+4320t138+17356t137+1864t136+28620t135+23030t134+35900t133+63350t132+40500t131+50750t130+22504t129+8690t128-58t127-814t126-1428t125-4256t124-8604t123-11464t122-21168t121-14732t120-24530t119+2102t118-22600t117-7460t116-14500t115-42200t114-15000t113-36500t112-12516t111-4840t110-44t109+1708t108+1432t107+5960t106+10160t105+11664t104+22200t103+23640t102+13500t101+4100t100+16t93-120t92+108t91-1172t90-440t89-3160t88-4752t87-3776t86-10520t85-11760t84-6300t83-1900t82)*(-1*a)+(4t178+8t177+92t176+176t175+852t174+1528t173+4044t172+6560t171+10380t170+14200t169+14100t168+14000t167+9500t166+5000t165+2500t164-6t163-18t162-86t161-230t160-508t159-1312t158-2406t157-6582t156-13038t155-29622t154-51510t153-80190t152-110700t151-115800t150-112750t149-79750t148-42500t147-20000t146+56t145+172t144+852t143+1988t142+5068t141+7580t140+17924t139+16692t138+58692t137+65236t136+175340t135+212220t134+331300t133+352900t132+333500t131+255500t130+132504t129+59964t128-170t127-966t126-3180t125-7976t124-19316t123-25232t122-58344t121-27756t120-130714t119-42698t118-291280t117-224460t116-457100t115-467200t114-432000t113-361500t112-177540t111-79788t110+8t109+3124t108+5400t107+17724t106+36232t105+48620t104+90416t103+56456t102+118256t101-1720t100+174120t99+65100t98+233400t97+209500t96+203000t95+177500t94+85096t93+37124t92+588t91-4484t90-3576t89-19320t88-33648t87-45440t86-74280t85-72400t84-44700t83-13500t82-64t75+208t74-520t73+2232t72+464t71+7760t70+12320t69+14400t68+28400t67+28000t66+17000t65+5000t64)*(-1)+(2t178+4t177+46t176+88t175+426t174+764t173+2022t172+3280t171+5190t170+7100t169+7050t168+7000t167+4750t166+2500t165+1250t164-2t163-6t162-26t161-90t160-140t159-744t158-938t157-5034t156-7762t155-23354t154-36490t153-61330t152-84300t151-85600t150-87250t149-58250t148-32500t147-15002t146+28t145+72t144+408t143+1082t142+2264t141+5550t140+8304t139+22076t138+38820t137+94526t136+160400t135+261770t134+363000t133+387650t132+385000t131+269250t130+150000t129+66258t128-138t127-378t126-2176t125-5100t124-13128t123-19788t122-44168t121-38316t120-134638t119-141698t118-413260t117-483960t116-813200t115-819700t114-831500t113-599000t112-330016t111-142452t110+212t109+1644t108+5624t107+14744t106+36240t105+47200t104+106968t103+42264t102+224604t101+38404t100+522080t99+336080t98+885600t97+755600t96+852000t95+602000t94+340096t93+139768t92+444t91-3876t90-6264t89-24920t88-51936t87-73712t86-132712t85-80448t84-161148t83+19860t82-236960t81-56800t80-357200t79-246000t78-324000t77-220000t76-130160t75-49680t74-1280t73+4160t72+1920t71+20800t70+37440t69+56640t68+90400t67+86400t66+56000t65+16000t64+80t57-144t56+736t55-1632t54+512t53-6528t52-10784t51-15072t50-28240t49-27120t48-17600t47-4800t46)*a+(-4t160-8t159-92t158-176t157-852t156-1528t155-4044t154-6560t153-10380t152-14200t151-14100t150-14000t149-9500t148-5000t147-2500t146+4t145+12t144+52t143+160t142+240t141+1028t140+996t139+5808t138+7884t137+26488t136+40180t135+70760t134+97600t133+100700t132+104500t131+69000t130+40000t129+17504t128-28t127-60t126-420t125-1120t124-2328t123-5652t122-7572t121-19684t120-31356t119-80472t118-133620t117-225440t116-313400t115-338300t114-340500t113-236000t112-135000t111-57512t110+100t109+236t108+1624t107+3804t106+9840t105+14764t104+30904t103+23000t102+84348t101+77248t100+264960t99+293460t98+547200t97+519700t96+574000t95+386500t94+230016t93+92492t92-36t91-788t90-2968t89-8472t88-21024t87-28752t86-60472t85-22304t84-111644t83-92t82-258880t81-139840t80-471600t79-358800t78-472000t77-296000t76-190064t75-69936t74-456t73+1400t72+1968t71+11008t70+23744t69+36656t68+63760t67+40352t66+69896t65-14328t64+93920t63+11440t62+154400t61+90800t60+148000t59+86000t58+60080t57+19920t56+736t55-1184t54+256t53-7168t52-13600t51-23136t50-37200t49-35760t48-24000t47-6400t46-32t39+32t38-320t37+384t36-512t35+1792t34+3136t33+5184t32+9760t31+9440t30+6400t29+1600t28);

// c01;
// (4t163+12t162+62t161+118t160+366t159+62t158+838t157-3138t156-1870t155-15974t154-19150t153-38230t152-51750t151-47350t150-53750t149-30750t148-18750t147-8758t146-16t145-112t144-244t143-500t142-1324t141+580t140-1412t139+17636t138+21364t137+92612t136+131780t135+238740t134+327100t133+324300t132+344500t131+218500t130+127496t129+57568t128-72t127+456t126-652t125-636t124-4156t123-7740t122-22520t121-23344t120-109908t119-143700t118-390660t117-476500t116-798700t115-777500t114-816500t113-562500t112-317500t111-137612t110+256t109-64t108+4192t107+8784t106+26080t105+35536t104+84768t103+18624t102+211104t101+34304t100+522080t99+336080t98+885600t97+755600t96+852000t95+602000t94+340080t93+139888t92+336t91-2704t90-5824t89-21760t88-47184t87-69936t86-122192t85-68688t84-154848t83+21760t82-236960t81-56800t80-357200t79-246000t78-324000t77-220000t76-130160t75-49680t74-1280t73+4160t72+1920t71+20800t70+37440t69+56640t68+90400t67+86400t66+56000t65+16000t64+80t57-144t56+736t55-1632t54+512t53-6528t52-10784t51-15072t50-28240t49-27120t48-17600t47-4800t46)*a+(-4t178-8t177-92t176-176t175-852t174-1528t173-4044t172-6560t171-10380t170-14200t169-14100t168-14000t167-9500t166-5000t165-2500t164+4t163+12t162+58t161+162t160+370t159+1074t158+2098t157+6234t156+12422t155+28510t154+49190t153+75950t152+104550t151+107750t150+104750t149+73750t148+38750t147+18754t146-48t145-112t144-728t143-1612t142-4392t141-6076t140-16104t139-11152t138-52232t137-44512t136-143640t135-153740t134-249800t133-264300t132-241000t131-193500t130-95004t129-44980t128+152t127+760t126+2836t125+6820t124+16964t123+20164t122+49832t121+6112t120+98508t119-37924t118+157660t117-980t116+143700t115+128900t114+91500t113+125500t112+42540t111+22300t110+80t109-2720t108-3896t107-13992t106-26680t105-35176t104-59392t103-32256t102-33608t101+78968t100+90840t99+228360t98+313800t97+310200t96+371000t95+209000t94+144920t93+55368t92-624t91+3696t90+608t89+10848t88+12624t87+16688t86+13808t85+50096t84-66944t83+13408t82-258880t81-139840t80-471600t79-358800t78-472000t77-296000t76-190000t75-70144t74+64t73-832t72+1504t71+3248t70+11424t69+22256t68+35360t67+12352t66+52896t65-19328t64+93920t63+11440t62+154400t61+90800t60+148000t59+86000t58+60080t57+19920t56+736t55-1184t54+256t53-7168t52-13600t51-23136t50-37200t49-35760t48-24000t47-6400t46-32t39+32t38-320t37+384t36-512t35+1792t34+3136t33+5184t32+9760t31+9440t30+6400t29+1600t28)


// We rewrite the polynomial in the x, y variables:

poly newfnox = c50*x^5 + c41*x^4*y + c32*x^3*y^2 + c23*x^2*y^3+c14*x*y^4 + c05*y^5 + c40*x^4 + c31*x^3*y+ c22*x^2*y^2 + c13*x*y^3 + c04*y^4 + c30*x^3 + c21*x^2*y + c12*x*y^2 + c03*y^3 + c20*x^2 + c11*x*y + c02*y^2 + c10*x + c01*y;

// newfnox;
// 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// We copy this data into a separate Singular file and replace a by a random integer so as not to affect the valuations of the coefficients.