(* This Mathematica file accompanies the paper "Division Polynomials with Galois Group SU_3(3).2 = G_2(2)". Many of the formulas here were cut from LaTeX source for this paper and then tested to guard against accidental errors in the paper. Other formulas are here only, because they are too long to be printed in the paper. For example, the list of 376 number fields in Section 8.1 is given here only. This file is just meant to provide some support for readers of the paper. Not everything which could be here is. For example, all the L-function computations involved Magma and none of them correspond to material here. The material here is organized as follows. The eight section headers of the paper are repeated here twice. The first headers are followed by a short amount of material associated to the section. This material is easily read by scrolling. The second headers are followed by a much longer amount of material. Here perhaps the best way to look at this material is to search for equal signs. The first headers also have some forward references to the material following the second headers. The notation here is very close to that of the paper and so our comments as to the meaning of the material here are very brief. *) (* Before getting to the material in the individual sections, we first give some explicit directions so that readers unfamiliar with Mathematica can still begin to use this file. Also we show some sample uses of Pari and Magma. *) (* Mathematica does not currently have a Galois theory package. As a substitute, we use the following two commands. *) factorpattern[poly_, p_] := Module[{fl, tab}, fl = FactorList[poly, Modulus -> p]; tab = Reverse[Sort[Table[Exponent[fl[[k,1]], x], {k, 1, Length[fl]}]]]; Select[tab, #1 > 0 & ]] factpats[polys_, a_, b_] := Module[{degs, dat, datu, gooddatu, ans}, degs = Table[Exponent[polys[[j]], x], {j, 1, Length[polys]}]; dat = Table[factorpattern[polys[[j]], Prime[k]], {k, a, b}, {j, 1, Length[polys]}]; datu = Union[dat]; gooddatu = Select[datu, Table[Plus @@ #1[[j]], {j, 1, Length[#1]}] == degs & ]; ans = Table[{gooddatu[[j]], Count[dat, gooddatu[[j]]]}, {j, 1, Length[gooddatu]}]; TableForm[ans, TableDirections -> {Column, Row, Row, Row}, TableSpacing -> {0, 2, 1, 0}]] (* After loading this file (or even just the few relevant parts) into Mathematica, typing factpats[{x^2+1,f28[4,x],f36[4,x]},1,1000] returns 2 8 8 84 8 8 844211 17 2 121231 121266 15 2 6 6 6631 6 6 666321 16 2 4 4 44441111 4 4 4444222222 2 2 2 2 22222222221111 2 2 222222222222221111 1 11 7 7 77 7 7 7771 18 11 121231 121266 5 11 6 6 6631 6 6 663333 2 11 8 8 8211 8 8 8444 15 11 4 4 444422 4 4 444422221111 1 11 3 3 33333331 3 3 3333333333 1 11 3 3 33333331 3 3 333333333111 3 11 4 4 44441111 4 4 4444222222 1 11 2 2 22222222221111 2 2 2222222222111111111111 1 This information is an approximation to the paper's Table 2.1. The highly structured factorization patterns reflect the fact that f28[4,x] has Galois group G.2, x^2+1 corresponds to the .2, and f36[4,x] is indeed a resolvent. Similarly, typing FactorInteger[Discriminant[f36[4,x],x]] shows that the polynomial discriminant of f36[4,x] is 2^294 3^372. This implies that the field discriminants of both f28[4,x] and f36[4,x] have the form 2^a 3^b. *) (* Many of the computations of this paper used Pari and or Magma. As a two-part Pari example, suppose the expanded polynomial f28[4,x] is input as f in Pari. Then polredabs(f,16) returns (with the 16 for a speed-up) the polynomial called lightram below, i.e. {lightram = 4 + 32*x + 24*x^2 - 192*x^3 - 216*x^4 - 240*x^5 + 1800*x^6 + 672*x^7 - 1116*x^8 - 4680*x^9 + 1752*x^10 + 3768*x^11 - 1068*x^12 + 3072*x^13 - 4920*x^14 + 1464*x^15 - 657*x^16 - 756*x^17 + 2478*x^18 - 2292*x^19 + 2040*x^20 - 1440*x^21 + 798*x^22 - 420*x^23 + 165*x^24 - 60*x^25 + 18*x^26 - 4*x^27 + x^28} Then factor(nfdisc(lightram)) shows almost instantaneously that the field discriminant of f28[4,x] is 2^66 3^46. As a Magma example, after initializing the variable x with e.g. _:=PolynomialRing(Integers()); the commands lightram := 4 + 32*x + 24*x^2 - 192*x^3 - 216*x^4 - 240*x^5 + 1800*x^6 + 672*x^7 - 1116*x^8 - 4680*x^9 + 1752*x^10 + 3768*x^11 - 1068*x^12 + 3072*x^13 - 4920*x^14 + 1464*x^15 - 657*x^16 - 756*x^17 + 2478*x^18 - 2292*x^19 + 2040*x^20 - 1440*x^21 + 798*x^22 - 420*x^23 + 165*x^24 - 60*x^25 + 18*x^26 - 4*x^27 + x^28; G := GaloisGroup(lightram); G; confirm that the Galois group of lightram is indeed SU_3(3).2 = G_2(2). *) (* Section 1. Introduction. *) (* Section 2. Background. *) (* The Malle-Matzat polynomial. *) m[t_,x_] := -(x^6-6 x^5-435 x^4-308 x^3+15x^2+66 x+19)^4 (x^4+20 x^3+114 x^2+68 x+13) + t 2^2 3^9 (x^2+4 x+1)^12 (2x+1) (* Section 3. Rigid Covers of U311 and U32. *) (* The map from U to U311*) sig1[{u_,v_}] := {3(2u-v+1)/(u-v+2)^2,3 u (u-v+2)/(2u-v+1)^2} (* The map from U to U32 *) sig2[{u_,v_}] := Module[{Del,W}, Del = u^2 + v^2 + 1 - 2 u - 2 v - 2 u v; W := u^2 - 10 u v + 6 u + 9 v^2 - 18 v + 9; {-768 u^3/W^2,9 Del/W}] (* Section 4. 3-Division polynomials of Deligne-Mostow covers. Degree 28 polynomials f0, f1, f2, g0, g1, g2 are in the second part. *) (* The map from X0 to U *) pi0[{x_,y_}] := Module[{g4,g6a,g6b,g7a,g7b,g9,g10,g17,g18}, g4 = 15 x^2-4 y x-4 x+5; g6a = 9 x y^2+y^2+18 x y-18 y-66 x+6; g6b = 225 x^2-30 y x-30 x-2 y^2+6 y+33; g7a = 15 y x^2+65 x^2-2 y^2 x-4 y x-2 x+5 y+5; g7b = 45 y x^2-105 x^2+6 y^2 x-8 y x-14 x-5 y-5; g9 = 225 x^3-30 y x^2-105 x^2+y^2 x+22 y x+21 x+y^2-8 y-9; g10 = 225 x^2 y^2+1200 x^2 y+2850 x^2+250 x y^2-1500 x+2 y^4+8 y^3+37 y^2 -192 y +402; g17 = (2025 x^3 y^2+24300 x^3 y+39150 x^3+540 x^2 y^3+1845 x^2 y^2-180 x^2 y -29610 x^2-18 x y^4+168 x y^3-213 x y^2-252 x y+9522 x+10 y^4 +60 y^3-105 y^2+900 y-2070); g18 = ( 50625 x^5-3375 y x^4+30375 x^4-675 y^2 x^3+2025 y x^3+2700 x^3+75 y^3 x^2 +2025 y x^2+5850 x^2-2 y^4 x-18 y^3 x+33 y^2 x-513 y x+63 x +15 y^3 -30 y^2+270 y+315); {(g6b^6 x^4 (x+1))/(25 g6a^3 g7a^2 (9 x^2-2x+1)), (g18^2 g4^2 g9)/(25 g6a^3 g7a^2 (9x^2-2 x+1))}] (* The map from X0 to X1 *) Sig1[{x_,y_}] := Module[{g4,g6a,g6b,g9,g10,g17,g18}, g4 = 15 x^2-4 y x-4 x+5; g6a = 9 x y^2+y^2+18 x y-18 y-66 x+6; g6b = 225 x^2-30 y x-30 x-2 y^2+6 y+33; g9 = 225 x^3-30 y x^2-105 x^2+y^2 x+22 y x+21 x+y^2-8 y-9; g10 = 225 x^2 y^2+1200 x^2 y+2850 x^2+250 x y^2-1500 x+2 y^4+8 y^3+37 y^2 -192 y +402; g17 = (2025 x^3 y^2+24300 x^3 y+39150 x^3+540 x^2 y^3+1845 x^2 y^2-180 x^2 y -29610 x^2-18 x y^4+168 x y^3-213 x y^2-252 x y+9522 x+10 y^4 +60 y^3-105 y^2+900 y-2070); {-g17/(g6a g6b),45 g10 (x+1) (9 x^2 - 2 x + 1)/(g4 g6a g6b)} ] (* The map from X0 to X2 *) Sig2[{x_,y_}] := Module[{g4,g7a,g7b}, g4 = 15 x^2-4 y x-4 x+5; g7a = 15 y x^2+65 x^2-2 y^2 x-4 y x-2 x+5 y+5; g7b = 45 y x^2-105 x^2+6 y^2 x-8 y x-14 x-5 y-5; {1/((x+1)),g4 g7a/(5 g7b (x+1)^2)}] (* The map from X1 to U311 *) pi1[{x_,y_}] := Module[{h11,h26}, h11 = 2 x^5+4 x^4-12 x^3 y+8 x^3+9 x^2 y+16 x^2-24 x y+8 x+3 y^3+18 y+16; h26 = 4 x^7+48 x^6 y+7 x^6-72 x^5 y^2+24 x^5+48 x^4 y^3-63 x^4 y^2+288 x^4 y +42 x^4-12 x^3 y^4-288 x^3 y^2+48 x^3-3 x^2 y^4+192 x^2 y^3-252 x^2 y^2 +576 x^2 y+84 x^2-24 x y^4-288 x y^2+32 x+ 3 y^6-6 y^4+192 y^3-252 y^2 +384 y+56; (* returns (p,q) *) {(3 h26/h11^2), (3 h11 y (3 x^2-y^2+6)^4)/(h26^2)} ] (* The map from X2 to U32 *) pi2[{x_,y_}] := Module[{f9,f14}, f9 = 144 x^3 y-408 x^2 y-12 x^2+8 x y^2+388 x y+20 x-9 y^2-126 y-9; f14 = 36 x^4 y^2-288 x^3 y^2-504 x^3 y+816 x^2 y^2+1236 x^2 y-12 x^2+2 x y^3 -840 x y^2-1038 x y+20 x-9 y^3+297 y^2+297 y-9; (* returns (a,b) *) {(3 f9^3)/(f14^2 (12 x^2-20 x+9)), (36 x^4 y^2)/(f14)}] (* A check that the left parallelogram in Figure~3.2 indeed commutes as entering commute1[{x,y}] indeed returns {1,1} *) commute1[{x_,y_}] := Factor[pi1[Sig1[{x,y}]]/sig1[pi0[{x,y}]]] (* A check that the right parallelogram in Figure~3.2 indeed commutes as entering commute2[{x,y}] indeed returns {1,1} *) commute2[{x_,y_}] := Factor[pi2[Sig2[{x,y}]]/sig2[pi0[{x,y}]]] (* Section 5. 2-Division polynomials of Shioda quartics. The Shioda polynomial shioda[{r1_,r3_,r4_,r5_,r6_,r7_,r9_}, z_] is in the second part *) (* Shioda expression for the Malle-Matzat cover *) indsm[t_] := {0,-27 t^2, -81 t^2, 243 t^3, 243 t^3, -729 t^4, 729 t^5} sm[t_,z_] := shioda[indsm[t],z] (* Shioda expression for X0->U *) inds0[{u_,v_}] := {1,u-v+1,-3 u,0,u(-u+v-1),u(-u+v-1),-u^2} s0[{u_,v_},z_] := shioda[inds0[{u,v}],z] (* Shioda expression for X1->U311 *) inds1[{p_,q_}] := Module[{d}, d = p^2 q^2 - 6 p q + 4 p + 4 q - 3; {0, d^2 p, 3 d^2 p^2 (q-1), 3 d^3 p^2, -d^3 p^2 (3 p^2 q^2-9 p q+4 q+2 p), -3 d^4 p^3 (q-1), d^5 p^4 (2 p q^2-3 q+1) }] s1[{p_,q_},z_] := shioda[inds1[{p,q}],z] (* Shioda expression for X2->U32 *) inds2[{a_,b_}] := Module[{A=256/a,B=(b-1)/8}, { 1, 3 (A B^2+2), -3 (8 A B^2+A B+1), -3 (5 A B^2+A B-4), -8 A^2 B^4-A^2 B^3-184 A B^2-31 A B-A-2, -56 A^2 B^4-7 A^2 B^3-199 A B^2-58 A B-4 A+10, -440 A^2 B^4-103 A^2 B^3-6 A^2 B^2-693 A B^2-183 A B-12 A+3} ] s2[{a_,b_},z_] := shioda[inds2[{a,b}],z] (* Three different expressions for the same cover of U. For example, typing Factor[three0[{-3,-4}],Modulus->97] gives three polynomials factoring in the form 1+3+12+12, and this is a spot check on the agreement of the three covers. *) three0[{u_,v_}] := {f0[{u,v},x],g0[{u,v},x],s0[{u,v},x]} (* Three different expressions for the same cover of U311 *) three1[{p_,q_}] := {f1[{p,q},x],g1[{p,q},x],s1[{p,q},x]} (* Three different expressions for the same cover of U32 *) three2[{a_,b_}] := {f2[{a,b},x],g2[{a,b},x],s2[{a,b},x]} (* Section 6. 2-division polynomials of Dettweiler-Reiter G2 motives *) (* matrixcheck returns the identity matrix as it should *) matrixcheck := Module[{a,b,c,d}, a = { {1,0,0,0,0,0,0}, {0,1,0,0,0,0,0}, {0,0,1,0,0,0,0}, {-3,-1,0,1,0,0,0}, {3,-1,0,0,1,0,0}, {9,-3,0,0,0,1,0}, {-1,0,3,-1,2,-1,1} }; b = { {1,0,0,0,3,-1,0}, {0,1,0,0,9,-3,0}, {0,0,-2,1,0,0,0}, {0,0,-9,4,0,0,0}, {0,0,0,0,1,0,0}, {0,0,0,0,0,1,0}, {0,0,-3,1,0,0,1}}; c = { {1,-1,0,0,0,0,-3}, {3,-2,0,0,0,0,0}, {0,0,1,-1,0,0,3}, {0,0,3,-2,0,0,6}, {0,0,0,0,1,-1,-3}, {0,0,0,0,3,-2,0}, {0,0,0,0,0,0,1}}; d = { {10,-5,0,0,9,-5,-6}, {15,-8,0,0,18,-9,-9}, {0,0,1,0,0,0,0}, {-3,4,-3,1,-6,3,3}, {9,-5,0,0,10,-5,-6}, {18,-9,0,0,15,-8,-9}, {-2,1,0,0,-2,1,1} }; a.b.c.d] (* Section 7. Specialization to three-point covers *) (* Labels and parametrizations for base curves, ordered as in Table 7.1 *) params = {{{"H''", 311, {3/4, (8*t)/9}}}, {{"I''", 311, {16/(-5 + 9*t)^2, (-5 + 9*t)/4}}}, {{"B*", 311, {-3*t, -3/t}}, {"B", 32, {-48*(-1 + t), 9}}}, {{"M", 32, {-16*t, 1}}}, {{"G", 32, {(-1 + t)^2, t}}}, {{"H'", 311, {(8*t)/9, 3/4}}, {"G''", 311, {1, t}}}, {{"L'", 311, {(3*(4 + t))/16, (24*t)/(4 + t)^2}}, {"E", 32, {(-4*t^3)/(3*(-3 + t)^2), (3*(-1 + t))/(-3 + t)}}, {"K", 32, {(4*(-1 + t)^3)/(3*(2 + t)^2), (3*t)/(2 + t)}}}, {{"G'", 311, {t, 1}}, {"H", 32, {(4*(-1 + t)*t)/9, (2*t)/3}}}, {{"K'", 311, {(2 + t)/3, (9*t)/(2 + t)^2}}, {"A", 32, {(-48*t^3)/(-9 + 5*t)^2, (9*(-1 + t))/(-9 + 5*t)}}}, {{"K''", 311, {(9*t)/(2 + t)^2, (2 + t)/3}}, {"C", 32, {(-48*t)/(-1 + 5*t)^2, (9*(-1 + t))/(-1 + 5*t)}}, {"I", 32, {(729*(-1 + t)^2*t)/(-5 + 9*t)^2, 4/(-5 + 9*t)}}}, {{"L''", 311, {(24*t)/(4 + t)^2, (3*(4 + t))/16}}}, {{"F*", 311, {3/(-1 + 4*t), 3/(-1 + 4*t)}}, {"I'", 311, {(-5 + 9*t)/4, 16/(-5 + 9*t)^2}}, {"F", 32, {-3/(1 - 7*t + 9*t^2)^2, (9*(-1 + t)*t)/(1 - 7*t + 9*t^2)}}}, {{"J'", 311, {(3 + t)/4, (16*t)/(3 + t)^2}}}, {{"L", 32, {(3*(-1 + t)*t^2)/(4*(4 + t)^2), (9*t)/(2*(4 + t))}}}, {{"M*", 311, {t, t^(-1)}}, {"J", 32, {((-1 + t)^2*t)/(3 + t)^2, (4*t)/(3 + t)}}}, {{"J''", 311, {(16*t)/(3 + t)^2, (3 + t)/4}}}} (*Explicit polynomials for the unique cover, corresponding to B*, pursued more explicitly *) f28[t_,x_] := 19683*(1 - t)*t*(-2 + x)^8*x^2*(8 + x^2)*(-1 - 2*x + x^2)^8 + 1024*(1 - t)*(1 + 4*x)*(1 + 18*x + 48*x^2 + 18*x^3 + 9*x^4)^6 - t*(-5 - 692*x + 222*x^2 - 252*x^3 + 3*x^4)* (-32 + 576*x + 8952*x^2 + 52752*x^3 + 184140*x^4 + 400896*x^5 + 618759*x^6 + 574938*x^7 + 268515*x^8 + 73332*x^9 + 26001*x^10 + 2106*x^11 + 81*x^12)^2 f36[t_,x_] := -19683*t*(-1 + x)^4*(-1 + 2*x^2)^8*(1 - 2*x + 2*x^2)^4 + (-3 + 4*x^4)^3*(-3 + 12*x - 12*x^2 + 4*x^4)^6 (* Section 8. Specialization to number fields. Polynomials for other number fields are in the second part. *) (* A polynomial defining the most lightly ramified of all our SU_3(3)=G_2(2).2 fields *) lightram = 4 + 32*x + 24*x^2 - 192*x^3 - 216*x^4 - 240*x^5 + 1800*x^6 + 672*x^7 - 1116*x^8 - 4680*x^9 + 1752*x^10 + 3768*x^11 - 1068*x^12 + 3072*x^13 - 4920*x^14 + 1464*x^15 - 657*x^16 - 756*x^17 + 2478*x^18 - 2292*x^19 + 2040*x^20 - 1440*x^21 + 798*x^22 - 420*x^23 + 165*x^24 - 60*x^25 + 18*x^26 - 4*x^27 + x^28 (* NOW COMES THE SECOND PART, WHERE THE INFORMATION IS TOO BIG TO BE EASILY HUMAN-READ *) (* Section 1. Introduction *) (* Section 2. Background *) (* Section 3. Rigid Covers of U311 and U32 *) (* Section 4. 3-Division polynomials of Deligne-Mostow covers *) f0[{u_, v_}, x_] := 26244*u^7 - 59697*u^8 + 40828*u^9 - 7542*u^10 + 168*u^11 - u^12 + 1458*u^7*v - 50004*u^8*v + 21528*u^9*v - 636*u^10*v + 6*u^11*v - 6561*u^6*v^2 + 9396*u^7*v^2 - 20916*u^8*v^2 + 864*u^9*v^2 - 15*u^10*v^2 + 2916*u^6*v^3 + 7416*u^7*v^3 - 456*u^8*v^3 + 20*u^9*v^3 - 486*u^6*v^4 + 24*u^7*v^4 - 15*u^8*v^4 + 36*u^6*v^5 + 6*u^7*v^5 - u^6*v^6 - 227448*u^7*x + 542916*u^8*x - 402272*u^9*x + 85560*u^10*x + 1272*u^11*x - 28*u^12*x - 157464*u^6*v*x + 600696*u^7*v*x + 398880*u^8*v*x - 283296*u^9*v*x - 6024*u^10*v*x + 168*u^11*v*x + 166212*u^6*v^2*x + 152928*u^7*v^2*x + 335184*u^8*v^2*x + 11376*u^9*v^2*x - 420*u^10*v^2*x - 147744*u^6*v^3*x - 162720*u^7*v^3*x - 10704*u^8*v^3*x + 560*u^9*v^3*x + 25272*u^6*v^4*x + 5016*u^7*v^4*x - 420*u^8*v^4*x - 936*u^6*v^5*x + 168*u^7*v^5*x - 28*u^6*v^6*x - 472392*u^6*x^2 + 3210516*u^7*x^2 - 5923854*u^8*x^2 + 4103568*u^9*x^2 - 915948*u^10*x^2 - 1620*u^11*x^2 - 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32942581135143840*u*v^4*x^25 + 12811003774778160*u^2*v^4*x^25 + 3660286792793760*u^3*v^4*x^25 + 2745215094595320*u^4*v^4*x^25 + 3660286792793760*u^5*v^4*x^25 + 12811003774778160*u^6*v^4*x^25 - 32942581135143840*u^7*v^4*x^25 + 15098683020274260*u^8*v^4*x^25 - 24157892832438816*v^5*x^25 + 15373204529733792*u*v^5*x^25 + 5124401509911264*u^2*v^5*x^25 + 3660286792793760*u^3*v^5*x^25 + 3660286792793760*u^4*v^5*x^25 + 5124401509911264*u^5*v^5*x^25 + 15373204529733792*u^6*v^5*x^25 - 24157892832438816*u^7*v^5*x^25 + 28184208304511952*v^6*x^25 + 15373204529733792*u*v^6*x^25 + 12811003774778160*u^2*v^6*x^25 + 12200955975979200*u^3*v^6*x^25 + 12811003774778160*u^4*v^6*x^25 + 15373204529733792*u^5*v^6*x^25 + 28184208304511952*u^6*v^6*x^25 - 24157892832438816*v^7*x^25 - 32942581135143840*u*v^7*x^25 - 36602867927937600*u^2*v^7*x^25 - 36602867927937600*u^3*v^7*x^25 - 32942581135143840*u^4*v^7*x^25 - 24157892832438816*u^5*v^7*x^25 + 15098683020274260*v^8*x^25 + 27452150945953200*u*v^8*x^25 + 32027509436945400*u^2*v^8*x^25 + 27452150945953200*u^3*v^8*x^25 + 15098683020274260*u^4*v^8*x^25 - 6710525786788560*v^9*x^25 - 12811003774778160*u*v^9*x^25 - 12811003774778160*u^2*v^9*x^25 - 6710525786788560*u^3*v^9*x^25 + 2013157736036568*v^10*x^25 + 3294258113514384*u*v^10*x^25 + 2013157736036568*u^2*v^10*x^25 - 366028679279376*v^11*x^25 - 366028679279376*u*v^11*x^25 + 30502389939948*v^12*x^25 + 45753584909922*x^26 - 549043018919064*u*x^26 + 3019736604054852*u^2*x^26 - 10065788680182840*u^3*x^26 + 22648024530411390*u^4*x^26 - 36236839248658224*u^5*x^26 + 42276312456767928*u^6*x^26 - 36236839248658224*u^7*x^26 + 22648024530411390*u^8*x^26 - 10065788680182840*u^9*x^26 + 3019736604054852*u^10*x^26 - 549043018919064*u^11*x^26 + 45753584909922*u^12*x^26 - 549043018919064*v*x^26 + 4941387170271576*u*v*x^26 - 19216505662167240*u^2*v*x^26 + 41178226418929800*u^3*v*x^26 - 49413871702715760*u^4*v*x^26 + 23059806794600688*u^5*v*x^26 + 23059806794600688*u^6*v*x^26 - 49413871702715760*u^7*v*x^26 + 41178226418929800*u^8*v*x^26 - 19216505662167240*u^9*v*x^26 + 4941387170271576*u^10*v*x^26 - 549043018919064*u^11*v*x^26 + 3019736604054852*v^2*x^26 - 19216505662167240*u*v^2*x^26 + 48041264155418100*u^2*v^2*x^26 - 54904301891906400*u^3*v^2*x^26 + 19216505662167240*u^4*v^2*x^26 + 7686602264866896*u^5*v^2*x^26 + 19216505662167240*u^6*v^2*x^26 - 54904301891906400*u^7*v^2*x^26 + 48041264155418100*u^8*v^2*x^26 - 19216505662167240*u^9*v^2*x^26 + 3019736604054852*u^10*v^2*x^26 - 10065788680182840*v^3*x^26 + 41178226418929800*u*v^3*x^26 - 54904301891906400*u^2*v^3*x^26 + 18301433963968800*u^3*v^3*x^26 + 5490430189190640*u^4*v^3*x^26 + 5490430189190640*u^5*v^3*x^26 + 18301433963968800*u^6*v^3*x^26 - 54904301891906400*u^7*v^3*x^26 + 41178226418929800*u^8*v^3*x^26 - 10065788680182840*u^9*v^3*x^26 + 22648024530411390*v^4*x^26 - 49413871702715760*u*v^4*x^26 + 19216505662167240*u^2*v^4*x^26 + 5490430189190640*u^3*v^4*x^26 + 4117822641892980*u^4*v^4*x^26 + 5490430189190640*u^5*v^4*x^26 + 19216505662167240*u^6*v^4*x^26 - 49413871702715760*u^7*v^4*x^26 + 22648024530411390*u^8*v^4*x^26 - 36236839248658224*v^5*x^26 + 23059806794600688*u*v^5*x^26 + 7686602264866896*u^2*v^5*x^26 + 5490430189190640*u^3*v^5*x^26 + 5490430189190640*u^4*v^5*x^26 + 7686602264866896*u^5*v^5*x^26 + 23059806794600688*u^6*v^5*x^26 - 36236839248658224*u^7*v^5*x^26 + 42276312456767928*v^6*x^26 + 23059806794600688*u*v^6*x^26 + 19216505662167240*u^2*v^6*x^26 + 18301433963968800*u^3*v^6*x^26 + 19216505662167240*u^4*v^6*x^26 + 23059806794600688*u^5*v^6*x^26 + 42276312456767928*u^6*v^6*x^26 - 36236839248658224*v^7*x^26 - 49413871702715760*u*v^7*x^26 - 54904301891906400*u^2*v^7*x^26 - 54904301891906400*u^3*v^7*x^26 - 49413871702715760*u^4*v^7*x^26 - 36236839248658224*u^5*v^7*x^26 + 22648024530411390*v^8*x^26 + 41178226418929800*u*v^8*x^26 + 48041264155418100*u^2*v^8*x^26 + 41178226418929800*u^3*v^8*x^26 + 22648024530411390*u^4*v^8*x^26 - 10065788680182840*v^9*x^26 - 19216505662167240*u*v^9*x^26 - 19216505662167240*u^2*v^9*x^26 - 10065788680182840*u^3*v^9*x^26 + 3019736604054852*v^10*x^26 + 4941387170271576*u*v^10*x^26 + 3019736604054852*u^2*v^10*x^26 - 549043018919064*v^11*x^26 - 549043018919064*u*v^11*x^26 + 45753584909922*v^12*x^26 + 30502389939948*x^27 - 366028679279376*u*x^27 + 2013157736036568*u^2*x^27 - 6710525786788560*u^3*x^27 + 15098683020274260*u^4*x^27 - 24157892832438816*u^5*x^27 + 28184208304511952*u^6*x^27 - 24157892832438816*u^7*x^27 + 15098683020274260*u^8*x^27 - 6710525786788560*u^9*x^27 + 2013157736036568*u^10*x^27 - 366028679279376*u^11*x^27 + 30502389939948*u^12*x^27 - 366028679279376*v*x^27 + 3294258113514384*u*v*x^27 - 12811003774778160*u^2*v*x^27 + 27452150945953200*u^3*v*x^27 - 32942581135143840*u^4*v*x^27 + 15373204529733792*u^5*v*x^27 + 15373204529733792*u^6*v*x^27 - 32942581135143840*u^7*v*x^27 + 27452150945953200*u^8*v*x^27 - 12811003774778160*u^9*v*x^27 + 3294258113514384*u^10*v*x^27 - 366028679279376*u^11*v*x^27 + 2013157736036568*v^2*x^27 - 12811003774778160*u*v^2*x^27 + 32027509436945400*u^2*v^2*x^27 - 36602867927937600*u^3*v^2*x^27 + 12811003774778160*u^4*v^2*x^27 + 5124401509911264*u^5*v^2*x^27 + 12811003774778160*u^6*v^2*x^27 - 36602867927937600*u^7*v^2*x^27 + 32027509436945400*u^8*v^2*x^27 - 12811003774778160*u^9*v^2*x^27 + 2013157736036568*u^10*v^2*x^27 - 6710525786788560*v^3*x^27 + 27452150945953200*u*v^3*x^27 - 36602867927937600*u^2*v^3*x^27 + 12200955975979200*u^3*v^3*x^27 + 3660286792793760*u^4*v^3*x^27 + 3660286792793760*u^5*v^3*x^27 + 12200955975979200*u^6*v^3*x^27 - 36602867927937600*u^7*v^3*x^27 + 27452150945953200*u^8*v^3*x^27 - 6710525786788560*u^9*v^3*x^27 + 15098683020274260*v^4*x^27 - 32942581135143840*u*v^4*x^27 + 12811003774778160*u^2*v^4*x^27 + 3660286792793760*u^3*v^4*x^27 + 2745215094595320*u^4*v^4*x^27 + 3660286792793760*u^5*v^4*x^27 + 12811003774778160*u^6*v^4*x^27 - 32942581135143840*u^7*v^4*x^27 + 15098683020274260*u^8*v^4*x^27 - 24157892832438816*v^5*x^27 + 15373204529733792*u*v^5*x^27 + 5124401509911264*u^2*v^5*x^27 + 3660286792793760*u^3*v^5*x^27 + 3660286792793760*u^4*v^5*x^27 + 5124401509911264*u^5*v^5*x^27 + 15373204529733792*u^6*v^5*x^27 - 24157892832438816*u^7*v^5*x^27 + 28184208304511952*v^6*x^27 + 15373204529733792*u*v^6*x^27 + 12811003774778160*u^2*v^6*x^27 + 12200955975979200*u^3*v^6*x^27 + 12811003774778160*u^4*v^6*x^27 + 15373204529733792*u^5*v^6*x^27 + 28184208304511952*u^6*v^6*x^27 - 24157892832438816*v^7*x^27 - 32942581135143840*u*v^7*x^27 - 36602867927937600*u^2*v^7*x^27 - 36602867927937600*u^3*v^7*x^27 - 32942581135143840*u^4*v^7*x^27 - 24157892832438816*u^5*v^7*x^27 + 15098683020274260*v^8*x^27 + 27452150945953200*u*v^8*x^27 + 32027509436945400*u^2*v^8*x^27 + 27452150945953200*u^3*v^8*x^27 + 15098683020274260*u^4*v^8*x^27 - 6710525786788560*v^9*x^27 - 12811003774778160*u*v^9*x^27 - 12811003774778160*u^2*v^9*x^27 - 6710525786788560*u^3*v^9*x^27 + 2013157736036568*v^10*x^27 + 3294258113514384*u*v^10*x^27 + 2013157736036568*u^2*v^10*x^27 - 366028679279376*v^11*x^27 - 366028679279376*u*v^11*x^27 + 30502389939948*v^12*x^27 + 7625597484987*x^28 - 91507169819844*u*x^28 + 503289434009142*u^2*x^28 - 1677631446697140*u^3*x^28 + 3774670755068565*u^4*x^28 - 6039473208109704*u^5*x^28 + 7046052076127988*u^6*x^28 - 6039473208109704*u^7*x^28 + 3774670755068565*u^8*x^28 - 1677631446697140*u^9*x^28 + 503289434009142*u^10*x^28 - 91507169819844*u^11*x^28 + 7625597484987*u^12*x^28 - 91507169819844*v*x^28 + 823564528378596*u*v*x^28 - 3202750943694540*u^2*v*x^28 + 6863037736488300*u^3*v*x^28 - 8235645283785960*u^4*v*x^28 + 3843301132433448*u^5*v*x^28 + 3843301132433448*u^6*v*x^28 - 8235645283785960*u^7*v*x^28 + 6863037736488300*u^8*v*x^28 - 3202750943694540*u^9*v*x^28 + 823564528378596*u^10*v*x^28 - 91507169819844*u^11*v*x^28 + 503289434009142*v^2*x^28 - 3202750943694540*u*v^2*x^28 + 8006877359236350*u^2*v^2*x^28 - 9150716981984400*u^3*v^2*x^28 + 3202750943694540*u^4*v^2*x^28 + 1281100377477816*u^5*v^2*x^28 + 3202750943694540*u^6*v^2*x^28 - 9150716981984400*u^7*v^2*x^28 + 8006877359236350*u^8*v^2*x^28 - 3202750943694540*u^9*v^2*x^28 + 503289434009142*u^10*v^2*x^28 - 1677631446697140*v^3*x^28 + 6863037736488300*u*v^3*x^28 - 9150716981984400*u^2*v^3*x^28 + 3050238993994800*u^3*v^3*x^28 + 915071698198440*u^4*v^3*x^28 + 915071698198440*u^5*v^3*x^28 + 3050238993994800*u^6*v^3*x^28 - 9150716981984400*u^7*v^3*x^28 + 6863037736488300*u^8*v^3*x^28 - 1677631446697140*u^9*v^3*x^28 + 3774670755068565*v^4*x^28 - 8235645283785960*u*v^4*x^28 + 3202750943694540*u^2*v^4*x^28 + 915071698198440*u^3*v^4*x^28 + 686303773648830*u^4*v^4*x^28 + 915071698198440*u^5*v^4*x^28 + 3202750943694540*u^6*v^4*x^28 - 8235645283785960*u^7*v^4*x^28 + 3774670755068565*u^8*v^4*x^28 - 6039473208109704*v^5*x^28 + 3843301132433448*u*v^5*x^28 + 1281100377477816*u^2*v^5*x^28 + 915071698198440*u^3*v^5*x^28 + 915071698198440*u^4*v^5*x^28 + 1281100377477816*u^5*v^5*x^28 + 3843301132433448*u^6*v^5*x^28 - 6039473208109704*u^7*v^5*x^28 + 7046052076127988*v^6*x^28 + 3843301132433448*u*v^6*x^28 + 3202750943694540*u^2*v^6*x^28 + 3050238993994800*u^3*v^6*x^28 + 3202750943694540*u^4*v^6*x^28 + 3843301132433448*u^5*v^6*x^28 + 7046052076127988*u^6*v^6*x^28 - 6039473208109704*v^7*x^28 - 8235645283785960*u*v^7*x^28 - 9150716981984400*u^2*v^7*x^28 - 9150716981984400*u^3*v^7*x^28 - 8235645283785960*u^4*v^7*x^28 - 6039473208109704*u^5*v^7*x^28 + 3774670755068565*v^8*x^28 + 6863037736488300*u*v^8*x^28 + 8006877359236350*u^2*v^8*x^28 + 6863037736488300*u^3*v^8*x^28 + 3774670755068565*u^4*v^8*x^28 - 1677631446697140*v^9*x^28 - 3202750943694540*u*v^9*x^28 - 3202750943694540*u^2*v^9*x^28 - 1677631446697140*u^3*v^9*x^28 + 503289434009142*v^10*x^28 + 823564528378596*u*v^10*x^28 + 503289434009142*u^2*v^10*x^28 - 91507169819844*v^11*x^28 - 91507169819844*u*v^11*x^28 + 7625597484987*v^12*x^28 (* Section 5. 2-Division polynomials of Shioda quartics *) shioda[{r1_,r3_,r4_,r5_,r6_,r7_,r9_},z_] := 64*r1*r3^9 + 320*r1^2*r3^6*r4^2 + 512*r1^4*r3^4*r4^3 - 40*r1*r3^5*r4^3 + r3^4*r4^4 - 768*r1^2*r3^7*r5 - 96*r1*r3^6*r4*r5 - 3328*r1^3*r3^4*r4^2*r5 + 8*r3^5*r4^2*r5 - 4096*r1^5*r3^2*r4^3*r5 + 320*r1^2*r3^3*r4^3*r5 - 8*r1*r3^2*r4^4*r5 + 3072*r1^3*r3^5*r5^2 + 16*r3^6*r5^2 + 1152*r1^2*r3^4*r4*r5^2 + 11264*r1^4*r3^2*r4^2*r5^2 - 64*r1*r3^3*r4^2*r5^2 + 8192*r1^6*r4^3*r5^2 - 640*r1^3*r3*r4^3*r5^2 + 16*r1^2*r4^4*r5^2 - 4096*r1^4*r3^3*r5^3 - 192*r1*r3^4*r5^3 - 4608*r1^3*r3^2*r4*r5^3 - 12288*r1^5*r4^2*r5^3 + 128*r1^2*r3*r4^2*r5^3 + 768*r1^2*r3^2*r5^4 + 6144*r1^4*r4*r5^4 - 1024*r1^3*r5^5 + 192*r1*r3^7*r6 + 3072*r1^3*r3^5*r4*r6 + 4096*r1^5*r3^3*r4^2*r6 - 448*r1^2*r3^4*r4^2*r6 + 8*r1*r3^3*r4^3*r6 - 768*r1^2*r3^5*r5*r6 - 16384*r1^4*r3^3*r4*r5*r6 - 128*r1*r3^4*r4*r5*r6 - 16384*r1^6*r3*r4^2*r5*r6 + 2304*r1^3*r3^2*r4^2*r5*r6 + 8*r3^3*r4^2*r5*r6 - 32*r1^2*r3*r4^3*r5*r6 + 1024*r1^3*r3^3*r5^2*r6 + 32*r3^4*r5^2*r6 + 16384*r1^5*r3*r4*r5^2*r6 - 2048*r1^4*r4^2*r5^2*r6 - 32*r1*r3*r4^2*r5^2*r6 - 4096*r1^4*r3*r5^3*r6 + 2048*r1^3*r4*r5^3*r6 - 512*r1^2*r5^4*r6 + 192*r1*r3^5*r6^2 - 1024*r1^3*r3^3*r4*r6^2 - 256*r1^2*r3^3*r5*r6^2 + 4096*r1^4*r3*r4*r5*r6^2 - 32*r1*r3^2*r4*r5*r6^2 - 2048*r1^3*r3*r5^2*r6^2 + 16*r3^2*r5^2*r6^2 + 128*r1^2*r4*r5^2*r6^2 - 64*r1*r5^3*r6^2 + 64*r1*r3^3*r6^3 - 256*r1^2*r3*r5*r6^3 + 1536*r1^3*r3^6*r7 - 1344*r1^2*r3^5*r4*r7 - 2048*r1^4*r3^3*r4^2*r7 + 152*r1*r3^4*r4^2*r7 - 4*r3^3*r4^3*r7 - 12288*r1^4*r3^4*r5*r7 + 96*r1*r3^5*r5*r7 + 8704*r1^3*r3^3*r4*r5*r7 - 16*r3^4*r4*r5*r7 + 8192*r1^5*r3*r4^2*r5*r7 - 576*r1^2*r3^2*r4^2*r5*r7 + 16*r1*r3*r4^3*r5*r7 + 24576*r1^5*r3^2*r5^2*r7 - 768*r1^2*r3^3*r5^2*r7 - 13312*r1^4*r3*r4*r5^2*r7 - 128*r1^3*r4^2*r5^2*r7 + 1536*r1^3*r3*r5^3*r7 + 256*r1^2*r4*r5^3*r7 - 1536*r1^3*r3^4*r6*r7 + 24576*r1^5*r3^2*r4*r6*r7 + 128*r1^2*r3^3*r4*r6*r7 + 32768*r1^7*r4^2*r6*r7 - 2560*r1^4*r3*r4^2*r6*r7 + 8*r1*r3^2*r4^2*r6*r7 + 64*r1^3*r4^3*r6*r7 + 12288*r1^4*r3^2*r5*r6*r7 + 128*r1*r3^3*r5*r6*r7 - 32768*r1^6*r4*r5*r6*r7 - 2560*r1^3*r3*r4*r5*r6*r7 - 16*r3^2*r4*r5*r6*r7 + 32*r1^2*r4^2*r5*r6*r7 + 8192*r1^5*r5^2*r6*r7 + 64*r1*r4*r5^2*r6*r7 + 1536*r1^3*r3^2*r6^2*r7 - 8192*r1^5*r4*r6^2*r7 - 64*r1^2*r3*r4*r6^2*r7 + 4096*r1^4*r5*r6^2*r7 + 32*r1*r3*r5*r6^2*r7 + 512*r1^3*r6^3*r7 + 12288*r1^5*r3^3*r7^2 + 1152*r1^2*r3^4*r7^2 + 3072*r1^4*r3^2*r4*r7^2 - 184*r1*r3^3*r4*r7^2 + 6*r3^2*r4^2*r7^2 - 49152*r1^6*r3*r5*r7^2 - 3840*r1^3*r3^2*r5*r7^2 + 8*r3^3*r5*r7^2 - 4096*r1^5*r4*r5*r7^2 + 96*r1^2*r3*r4*r5*r7^2 - 8*r1*r4^2*r5*r7^2 + 5120*r1^4*r5^2*r7^2 + 96*r1*r3*r5^2*r7^2 - 24576*r1^5*r3*r6*r7^2 + 576*r1^2*r3^2*r6*r7^2 - 512*r1^4*r4*r6*r7^2 - 40*r1*r3*r4*r6*r7^2 + 1792*r1^3*r5*r6*r7^2 + 8*r3*r5*r6*r7^2 + 192*r1^2*r6^2*r7^2 + 32768*r1^7*r7^3 - 4608*r1^4*r3*r7^3 + 72*r1*r3^2*r7^3 + 64*r1^3*r4*r7^3 - 4*r3*r4*r7^3 + 160*r1^2*r5*r7^3 + 24*r1*r6*r7^3 + r7^4 - 192*r1*r3^6*r9 - 9216*r1^3*r3^4*r4*r9 - 36864*r1^5*r3^2*r4^2*r9 + 1280*r1^2*r3^3*r4^2*r9 - 32768*r1^7*r4^3*r9 + 2560*r1^4*r3*r4^3*r9 - 32*r1*r3^2*r4^3*r9 - 64*r1^3*r4^4*r9 - 768*r1^2*r3^4*r5*r9 + 18432*r1^4*r3^2*r4*r5*r9 + 96*r1*r3^3*r4*r5*r9 + 49152*r1^6*r4^2*r5*r9 - 512*r1^3*r3*r4^2*r5*r9 - 8*r3^2*r4^2*r5*r9 - 3072*r1^3*r3^2*r5^2*r9 - 32*r3^3*r5^2*r9 - 24576*r1^5*r4*r5^2*r9 + 1152*r1^2*r3*r4*r5^2*r9 - 32*r1*r4^2*r5^2*r9 + 4096*r1^4*r5^3*r9 - 384*r1*r3*r5^3*r9 - 384*r1*r3^4*r6*r9 + 1536*r1^3*r3^2*r4*r6*r9 + 8192*r1^5*r4^2*r6*r9 + 64*r1^2*r3*r4^2*r6*r9 - 1536*r1^2*r3^2*r5*r6*r9 - 8192*r1^4*r4*r5*r6*r9 + 32*r1*r3*r4*r5*r6*r9 + 2048*r1^3*r5^2*r6*r9 - 32*r3*r5^2*r6*r9 - 192*r1*r3^2*r6^2*r9 - 512*r1^3*r4*r6^2*r9 + 256*r1^2*r5*r6^2*r9 + 10752*r1^3*r3^3*r7*r9 + 36864*r1^5*r3*r4*r7*r9 - 2112*r1^2*r3^2*r4*r7*r9 + 512*r1^4*r4^2*r7*r9 + 64*r1*r3*r4^2*r7*r9 - 6144*r1^4*r3*r5*r7*r9 - 96*r1*r3^2*r5*r7*r9 - 1024*r1^3*r4*r5*r7*r9 + 16*r3*r4*r5*r7*r9 - 384*r1^2*r5^2*r7*r9 + 1536*r1^3*r3*r6*r7*r9 - 320*r1^2*r4*r6*r7*r9 - 32*r1*r5*r6*r7*r9 - 12288*r1^5*r7^2*r9 + 576*r1^2*r3*r7^2*r9 - 32*r1*r4*r7^2*r9 - 8*r5*r7^2*r9 + 192*r1*r3^3*r9^2 - 4608*r1^3*r3*r4*r9^2 + 128*r1^2*r4^2*r9^2 + 1536*r1^2*r3*r5*r9^2 + 16*r5^2*r9^2 + 192*r1*r3*r6*r9^2 + 1536*r1^3*r7*r9^2 - 64*r1*r9^3 + 64*r3^9*z - 1344*r1^2*r3^7*r4*z + 808*r1*r3^6*r4^2*z - 1088*r1^3*r3^4*r4^3*z - 44*r3^5*r4^3*z - 4096*r1^5*r3^2*r4^4*z + 320*r1^2*r3^3*r4^4*z - 8*r1*r3^2*r4^5*z - 1248*r1*r3^7*r5*z + 13056*r1^3*r3^5*r4*r5*z - 112*r3^6*r4*r5*z - 10272*r1^2*r3^4*r4^2*r5*z + 512*r1^4*r3^2*r4^3*r5*z + 608*r1*r3^3*r4^3*r5*z + 16384*r1^6*r4^4*r5*z - 1280*r1^3*r3*r4^4*r5*z - 8*r3^2*r4^4*r5*z + 32*r1^2*r4^5*r5*z + 5760*r1^2*r3^5*r5^2*z - 39936*r1^4*r3^3*r4*r5^2*z + 2304*r1*r3^4*r4*r5^2*z + 39296*r1^3*r3^2*r4^2*r5^2*z - 64*r3^3*r4^2*r5^2*z + 15360*r1^5*r4^3*r5^2*z - 1728*r1^2*r3*r4^3*r5^2*z + 32*r1*r4^4*r5^2*z - 2560*r1^3*r3^3*r5^3*z - 192*r3^4*r5^3*z + 36864*r1^5*r3*r4*r5^3*z - 13056*r1^2*r3^2*r4*r5^3*z - 44544*r1^4*r4^2*r5^3*z + 256*r1*r3*r4^2*r5^3*z - 18432*r1^4*r3*r5^4*z + 1536*r1*r3^2*r5^4*z + 22528*r1^3*r4*r5^4*z - 3072*r1^2*r5^5*z - 1536*r1^3*r3^6*r6*z + 192*r3^7*r6*z + 10560*r1^2*r3^5*r4*r6*z + 3584*r1^4*r3^3*r4^2*r6*z - 1040*r1*r3^4*r4^2*r6*z - 16384*r1^6*r3*r4^3*r6*z + 2304*r1^3*r3^2*r4^3*r6*z + 12*r3^3*r4^3*r6*z - 32*r1^2*r3*r4^4*r6*z + 12288*r1^4*r3^4*r5*r6*z - 1056*r1*r3^5*r5*r6*z - 76288*r1^3*r3^3*r4*r5*r6*z - 128*r3^4*r4*r5*r6*z - 63488*r1^5*r3*r4^2*r5*r6*z + 7296*r1^2*r3^2*r4^2*r5*r6*z - 4096*r1^4*r4^3*r5*r6*z - 112*r1*r3*r4^3*r5*r6*z - 24576*r1^5*r3^2*r5^2*r6*z + 3840*r1^2*r3^3*r5^2*r6*z + 87040*r1^4*r3*r4*r5^2*r6*z - 3328*r1^3*r4^2*r5^2*r6*z - 32*r3*r4^2*r5^2*r6*z - 27136*r1^3*r3*r5^3*r6*z + 5120*r1^2*r4*r5^3*r6*z - 1024*r1*r5^4*r6*z + 7680*r1^3*r3^4*r6^2*z + 192*r3^5*r6^2*z + 24576*r1^5*r3^2*r4*r6^2*z - 3776*r1^2*r3^3*r4*r6^2*z + 32768*r1^7*r4^2*r6^2*z + 1536*r1^4*r3*r4^2*r6^2*z - 24*r1*r3^2*r4^2*r6^2*z + 64*r1^3*r4^3*r6^2*z - 24576*r1^4*r3^2*r5*r6^2*z - 288*r1*r3^3*r5*r6^2*z - 32768*r1^6*r4*r5*r6^2*z + 12032*r1^3*r3*r4*r5*r6^2*z - 16*r3^2*r4*r5*r6^2*z + 288*r1^2*r4^2*r5*r6^2*z + 8192*r1^5*r5^2*r6^2*z - 6528*r1^2*r3*r5^2*r6^2*z + 128*r1*r4*r5^2*r6^2*z - 64*r5^3*r6^2*z + 1536*r1^3*r3^2*r6^3*z + 64*r3^3*r6^3*z - 8192*r1^5*r4*r6^3*z - 320*r1^2*r3*r4*r6^3*z + 4096*r1^4*r5*r6^3*z - 480*r1*r3*r5*r6^3*z + 512*r1^3*r6^4*z + 6528*r1^2*r3^6*r7*z - 16896*r1^4*r3^4*r4*r7*z - 3312*r1*r3^5*r4*r7*z - 256*r1^3*r3^3*r4^2*r7*z + 172*r3^4*r4^2*r7*z + 8192*r1^5*r3*r4^3*r7*z - 576*r1^2*r3^2*r4^3*r7*z + 16*r1*r3*r4^4*r7*z - 62208*r1^3*r3^4*r5*r7*z + 144*r3^5*r5*r7*z + 86016*r1^5*r3^2*r4*r5*r7*z + 28032*r1^2*r3^3*r4*r5*r7*z + 17408*r1^4*r3*r4^2*r5*r7*z - 1248*r1*r3^2*r4^2*r5*r7*z - 256*r1^3*r4^3*r5*r7*z + 16*r3*r4^3*r5*r7*z + 135168*r1^4*r3^2*r5^2*r7*z - 1920*r1*r3^3*r5^2*r7*z - 73728*r1^6*r4*r5^2*r7*z - 50944*r1^3*r3*r4*r5^2*r7*z + 192*r1^2*r4^2*r5^2*r7*z + 36864*r1^5*r5^3*r7*z + 5376*r1^2*r3*r5^3*r7*z + 512*r1*r4*r5^3*r7*z - 24576*r1^5*r3^3*r6*r7*z - 4992*r1^2*r3^4*r6*r7*z + 159744*r1^4*r3^2*r4*r6*r7*z + 160*r1*r3^3*r4*r6*r7*z + 208896*r1^6*r4^2*r6*r7*z - 13568*r1^3*r3*r4^2*r6*r7*z + 4*r3^2*r4^2*r6*r7*z + 224*r1^2*r4^3*r6*r7*z + 98304*r1^6*r3*r5*r6*r7*z + 59904*r1^3*r3^2*r5*r6*r7*z + 192*r3^3*r5*r6*r7*z - 212992*r1^5*r4*r5*r6*r7*z - 8832*r1^2*r3*r4*r5*r6*r7*z + 176*r1*r4^2*r5*r6*r7*z + 57344*r1^4*r5^2*r6*r7*z + 64*r4*r5^2*r6*r7*z + 24576*r1^5*r3*r6^2*r7*z + 5760*r1^2*r3^2*r6^2*r7*z - 42496*r1^4*r4*r6^2*r7*z - 176*r1*r3*r4*r6^2*r7*z + 20736*r1^3*r5*r6^2*r7*z + 48*r3*r5*r6^2*r7*z + 1920*r1^2*r6^3*r7*z + 78336*r1^4*r3^3*r7^2*z + 2760*r1*r3^4*r7^2*z - 49152*r1^6*r3*r4*r7^2*z + 9600*r1^3*r3^2*r4*r7^2*z - 212*r3^3*r4*r7^2*z - 4096*r1^5*r4^2*r7^2*z + 96*r1^2*r3*r4^2*r7^2*z - 8*r1*r4^3*r7^2*z - 362496*r1^5*r3*r5*r7^2*z - 12096*r1^2*r3^2*r5*r7^2*z - 11776*r1^4*r4*r5*r7^2*z + 336*r1*r3*r4*r5*r7^2*z - 8*r4^2*r5*r7^2*z + 24704*r1^3*r5^2*r7^2*z + 96*r3*r5^2*r7^2*z - 98304*r1^7*r6*r7^2*z - 130560*r1^4*r3*r6*r7^2*z + 1392*r1*r3^2*r6*r7^2*z - 640*r1^3*r4*r6*r7^2*z - 44*r3*r4*r6*r7^2*z + 6336*r1^2*r5*r6*r7^2*z + 456*r1*r6^2*r7^2*z + 241664*r1^6*r7^3*z - 19968*r1^3*r3*r7^3*z + 84*r3^2*r7^3*z + 352*r1^2*r4*r7^3*z + 368*r1*r5*r7^3*z + 28*r6*r7^3*z + 13824*r1^3*r3^5*r9*z - 192*r3^6*r9*z + 36864*r1^5*r3^3*r4*r9*z - 35904*r1^2*r3^4*r4*r9*z - 188928*r1^4*r3^2*r4^2*r9*z + 3040*r1*r3^3*r4^2*r9*z - 192512*r1^6*r4^3*r9*z + 10496*r1^3*r3*r4^3*r9*z - 40*r3^2*r4^3*r9*z - 192*r1^2*r4^4*r9*z - 73728*r1^4*r3^3*r5*r9*z - 1824*r1*r3^4*r5*r9*z - 147456*r1^6*r3*r4*r5*r9*z + 76800*r1^3*r3^2*r4*r5*r9*z + 80*r3^3*r4*r5*r9*z + 276480*r1^5*r4^2*r5*r9*z + 768*r1^2*r3*r4^2*r5*r9*z - 64*r1*r4^3*r5*r9*z + 73728*r1^5*r3*r5^2*r9*z - 16128*r1^2*r3^2*r5^2*r9*z - 113664*r1^4*r4*r5^2*r9*z + 1728*r1*r3*r4*r5^2*r9*z - 32*r4^2*r5^2*r9*z + 11776*r1^3*r5^3*r9*z - 384*r3*r5^3*r9*z - 15360*r1^3*r3^3*r6*r9*z - 384*r3^4*r6*r9*z - 36864*r1^5*r3*r4*r6*r9*z + 2688*r1^2*r3^2*r4*r6*r9*z + 37888*r1^4*r4^2*r6*r9*z + 224*r1*r3*r4^2*r6*r9*z + 24576*r1^4*r3*r5*r6*r9*z - 3264*r1*r3^2*r5*r6*r9*z - 32768*r1^3*r4*r5*r6*r9*z - 16*r3*r4*r5*r6*r9*z + 5376*r1^2*r5^2*r6*r9*z + 1536*r1^3*r3*r6^2*r9*z - 192*r3^2*r6^2*r9*z - 1600*r1^2*r4*r6^2*r9*z + 480*r1*r5*r6^2*r9*z + 110592*r1^5*r3^2*r7*r9*z + 39936*r1^2*r3^3*r7*r9*z + 294912*r1^7*r4*r7*r9*z + 168960*r1^4*r3*r4*r7*r9*z - 4896*r1*r3^2*r4*r7*r9*z + 1792*r1^3*r4^2*r7*r9*z + 80*r3*r4^2*r7*r9*z - 147456*r1^6*r5*r7*r9*z - 27648*r1^3*r3*r5*r7*r9*z - 144*r3^2*r5*r7*r9*z - 3840*r1^2*r4*r5*r7*r9*z - 960*r1*r5^2*r7*r9*z - 12288*r1^5*r6*r7*r9*z + 6144*r1^2*r3*r6*r7*r9*z - 736*r1*r4*r6*r7*r9*z - 48*r5*r6*r7*r9*z - 69120*r1^4*r7^2*r9*z + 1344*r1*r3*r7^2*r9*z - 40*r4*r7^2*r9*z + 27648*r1^3*r3^2*r9^2*z + 192*r3^3*r9^2*z - 36864*r1^5*r4*r9^2*z - 14592*r1^2*r3*r4*r9^2*z + 256*r1*r4^2*r9^2*z + 18432*r1^4*r5*r9^2*z + 3072*r1*r3*r5*r9^2*z + 32*r4*r5*r9^2*z + 3072*r1^3*r6*r9^2*z + 192*r3*r6*r9^2*z + 5376*r1^2*r7*r9^2*z - 64*r9^3*z - 2808*r1*r3^7*r4*z^2 + 9216*r1^3*r3^5*r4^2*z^2 + 486*r3^6*r4^2*z^2 - 7488*r1^2*r3^4*r4^3*z^2 - 10752*r1^4*r3^2*r4^4*z^2 + 672*r1*r3^3*r4^4*z^2 + 8192*r1^6*r4^5*z^2 - 640*r1^3*r3*r4^5*z^2 - 8*r3^2*r4^5*z^2 + 16*r1^2*r4^6*z^2 - 504*r3^7*r5*z^2 + 37152*r1^2*r3^5*r4*r5*z^2 - 61440*r1^4*r3^3*r4^2*r5*z^2 - 10440*r1*r3^4*r4^2*r5*z^2 + 43008*r1^3*r3^2*r4^3*r5*z^2 + 288*r3^3*r4^3*r5*z^2 + 67584*r1^5*r4^4*r5*z^2 - 3840*r1^2*r3*r4^4*r5*z^2 + 64*r1*r4^5*r5*z^2 + 2592*r1*r3^5*r5^2*z^2 - 137856*r1^3*r3^3*r4*r5^2*z^2 + 1152*r3^4*r4*r5^2*z^2 + 98304*r1^5*r3*r4^2*r5^2*z^2 + 50208*r1^2*r3^2*r4^2*r5^2*z^2 - 27648*r1^4*r4^3*r5^2*z^2 - 1536*r1*r3*r4^3*r5^2*z^2 + 16*r4^4*r5^2*z^2 + 15744*r1^2*r3^3*r5^3*z^2 + 136704*r1^4*r3*r4*r5^3*z^2 - 12288*r1*r3^2*r4*r5^3*z^2 - 56704*r1^3*r4^2*r5^3*z^2 + 128*r3*r4^2*r5^3*z^2 - 72192*r1^3*r3*r5^4*z^2 + 768*r3^2*r5^4*z^2 + 30720*r1^2*r4*r5^4*z^2 - 3072*r1*r5^5*z^2 - 9792*r1^2*r3^6*r6*z^2 + 12456*r1*r3^5*r4*r6*z^2 - 36864*r1^3*r3^3*r4^2*r6*z^2 - 612*r3^4*r4^2*r6*z^2 - 79872*r1^5*r3*r4^3*r6*z^2 + 7296*r1^2*r3^2*r4^3*r6*z^2 - 2048*r1^4*r4^4*r6*z^2 - 80*r1*r3*r4^4*r6*z^2 + 78336*r1^3*r3^4*r5*r6*z^2 - 360*r3^5*r5*r6*z^2 - 128448*r1^2*r3^3*r4*r5*r6*z^2 - 55296*r1^4*r3*r4^2*r5*r6*z^2 + 7728*r1*r3^2*r4^2*r5*r6*z^2 - 12800*r1^3*r4^3*r5*r6*z^2 - 80*r3*r4^3*r5*r6*z^2 - 156672*r1^4*r3^2*r5^2*r6*z^2 + 4032*r1*r3^3*r5^2*r6*z^2 + 148608*r1^3*r3*r4*r5^2*r6*z^2 + 1920*r1^2*r4^2*r5^2*r6*z^2 - 53376*r1^2*r3*r5^3*r6*z^2 + 4096*r1*r4*r5^3*r6*z^2 - 512*r5^4*r6*z^2 + 21312*r1^2*r3^4*r6^2*z^2 + 119808*r1^4*r3^2*r4*r6^2*z^2 - 4392*r1*r3^3*r4*r6^2*z^2 + 208896*r1^6*r4^2*r6^2*z^2 + 3072*r1^3*r3*r4^2*r6^2*z^2 - 18*r3^2*r4^2*r6^2*z^2 + 352*r1^2*r4^3*r6^2*z^2 - 82944*r1^3*r3^2*r5*r6^2*z^2 - 72*r3^3*r5*r6^2*z^2 - 208896*r1^5*r4*r5*r6^2*z^2 + 9888*r1^2*r3*r4*r5*r6^2*z^2 + 504*r1*r4^2*r5*r6^2*z^2 + 52224*r1^4*r5^2*r6^2*z^2 - 6624*r1*r3*r5^2*r6^2*z^2 + 49152*r1^5*r3*r6^3*z^2 + 5184*r1^2*r3^2*r6^3*z^2 - 41984*r1^4*r4*r6^3*z^2 - 648*r1*r3*r4*r6^3*z^2 + 18944*r1^3*r5*r6^3*z^2 - 216*r3*r5*r6^3*z^2 + 1728*r1^2*r6^4*z^2 + 9144*r1*r3^6*r7*z^2 - 70848*r1^3*r3^4*r4*r7*z^2 - 1980*r3^5*r4*r7*z^2 + 73728*r1^5*r3^2*r4^2*r7*z^2 + 12096*r1^2*r3^3*r4^2*r7*z^2 + 30720*r1^4*r3*r4^3*r7*z^2 - 1224*r1*r3^2*r4^3*r7*z^2 - 128*r1^3*r4^4*r7*z^2 + 16*r3*r4^4*r7*z^2 - 118368*r1^2*r3^4*r5*r7*z^2 + 400896*r1^4*r3^2*r4*r5*r7*z^2 + 30240*r1*r3^3*r4*r5*r7*z^2 - 196608*r1^6*r4^2*r5*r7*z^2 - 3840*r1^3*r3*r4^2*r5*r7*z^2 - 672*r3^2*r4^2*r5*r7*z^2 - 480*r1^2*r4^3*r5*r7*z^2 + 305280*r1^3*r3^2*r5^2*r7*z^2 - 1152*r3^3*r5^2*r7*z^2 - 273408*r1^5*r4*r5^2*r7*z^2 - 73920*r1^2*r3*r4*r5^2*r7*z^2 + 768*r1*r4^2*r5^2*r7*z^2 + 185856*r1^4*r5^3*r7*z^2 + 6144*r1*r3*r5^3*r7*z^2 + 256*r4*r5^3*r7*z^2 - 156672*r1^4*r3^3*r6*r7*z^2 - 4968*r1*r3^4*r6*r7*z^2 + 411264*r1^3*r3^2*r4*r6*r7*z^2 + 72*r3^3*r4*r6*r7*z^2 + 559104*r1^5*r4^2*r6*r7*z^2 - 26592*r1^2*r3*r4^2*r6*r7*z^2 + 304*r1*r4^3*r6*r7*z^2 + 626688*r1^5*r3*r5*r6*r7*z^2 + 106560*r1^2*r3^2*r5*r6*r7*z^2 - 536064*r1^4*r4*r5*r6*r7*z^2 - 10272*r1*r3*r4*r5*r6*r7*z^2 + 144*r4^2*r5*r6*r7*z^2 + 147840*r1^3*r5^2*r6*r7*z^2 + 119808*r1^4*r3*r6^2*r7*z^2 + 7272*r1*r3^2*r6^2*r7*z^2 - 85440*r1^3*r4*r6^2*r7*z^2 - 108*r3*r4*r6^2*r7*z^2 + 37920*r1^2*r5*r6^2*r7*z^2 + 2376*r1*r6^3*r7*z^2 + 177408*r1^3*r3^3*r7^2*z^2 + 1638*r3^4*r7^2*z^2 - 387072*r1^5*r3*r4*r7^2*z^2 + 13248*r1^2*r3^2*r4*r7^2*z^2 - 16896*r1^4*r4^2*r7^2*z^2 + 192*r1*r3*r4^2*r7^2*z^2 - 8*r4^3*r7^2*z^2 - 1059840*r1^4*r3*r5*r7^2*z^2 - 13536*r1*r3^2*r5*r7^2*z^2 + 768*r1^3*r4*r5*r7^2*z^2 + 240*r3*r4*r5*r7^2*z^2 + 43296*r1^2*r5^2*r7^2*z^2 - 626688*r1^6*r6*r7^2*z^2 - 288000*r1^3*r3*r6*r7^2*z^2 + 828*r3^2*r6*r7^2*z^2 + 2208*r1^2*r4*r6*r7^2*z^2 + 7296*r1*r5*r6*r7^2*z^2 + 270*r6^2*r7^2*z^2 + 792576*r1^5*r7^3*z^2 - 33888*r1^2*r3*r7^3*z^2 + 584*r1*r4*r7^3*z^2 + 208*r5*r7^3*z^2 + 57024*r1^2*r3^5*r9*z^2 + 235008*r1^4*r3^3*r4*r9*z^2 - 45792*r1*r3^4*r4*r9*z^2 - 399744*r1^3*r3^2*r4^2*r9*z^2 + 1800*r3^3*r4^2*r9*z^2 - 479232*r1^5*r4^3*r9*z^2 + 17472*r1^2*r3*r4^3*r9*z^2 - 224*r1*r4^4*r9*z^2 - 304128*r1^3*r3^3*r5*r9*z^2 - 936*r3^4*r5*r9*z^2 - 940032*r1^5*r3*r4*r5*r9*z^2 + 103680*r1^2*r3^2*r4*r5*r9*z^2 + 665088*r1^4*r4^2*r5*r9*z^2 + 3168*r1*r3*r4^2*r5*r9*z^2 - 64*r4^3*r5*r9*z^2 + 304128*r1^4*r3*r5^2*r9*z^2 - 20736*r1*r3^2*r5^2*r9*z^2 - 222720*r1^3*r4*r5^2*r9*z^2 + 576*r3*r4*r5^2*r9*z^2 + 11904*r1^2*r5^3*r9*z^2 - 35712*r1^2*r3^3*r6*r9*z^2 - 179712*r1^4*r3*r4*r6*r9*z^2 + 288*r1*r3^2*r4*r6*r9*z^2 + 69120*r1^3*r4^2*r6*r9*z^2 + 144*r3*r4^2*r6*r9*z^2 + 101376*r1^3*r3*r5*r6*r9*z^2 - 1584*r3^2*r5*r6*r9*z^2 - 50688*r1^2*r4*r5*r6*r9*z^2 + 4608*r1*r5^2*r6*r9*z^2 + 6336*r1^2*r3*r6^2*r9*z^2 - 1728*r1*r4*r6^2*r9*z^2 + 216*r5*r6^2*r9*z^2 + 539136*r1^4*r3^2*r7*r9*z^2 + 48672*r1*r3^3*r7*r9*z^2 + 1880064*r1^6*r4*r7*r9*z^2 + 324864*r1^3*r3*r4*r7*r9*z^2 - 2880*r3^2*r4*r7*r9*z^2 + 1728*r1^2*r4^2*r7*r9*z^2 - 940032*r1^5*r5*r7*r9*z^2 - 48384*r1^2*r3*r5*r7*r9*z^2 - 4896*r1*r4*r5*r7*r9*z^2 - 576*r5^2*r7*r9*z^2 - 78336*r1^4*r6*r7*r9*z^2 + 7776*r1*r3*r6*r7*r9*z^2 - 432*r4*r6*r7*r9*z^2 - 160128*r1^3*r7^2*r9*z^2 + 792*r3*r7^2*r9*z^2 + 331776*r1^5*r3*r9^2*z^2 + 82944*r1^2*r3^2*r9^2*z^2 - 165888*r1^4*r4*r9^2*z^2 - 15552*r1*r3*r4*r9^2*z^2 + 144*r4^2*r9^2*z^2 + 69120*r1^3*r5*r9^2*z^2 + 1440*r3*r5*r9^2*z^2 + 9216*r1^2*r6*r9^2*z^2 + 6336*r1*r7*r9^2*z^2 + 504*r1*r3^8*z^3 - 1452*r3^7*r4*z^3 + 29568*r1^2*r3^5*r4^2*z^3 - 23552*r1^4*r3^3*r4^3*z^3 - 9864*r1*r3^4*r4^3*z^3 - 896*r1^3*r3^2*r4^4*z^3 + 356*r3^3*r4^4*z^3 + 39936*r1^5*r4^5*z^3 - 1984*r1^2*r3*r4^5*z^3 + 32*r1*r4^6*z^3 - 5376*r1^2*r3^6*r5*z^3 + 34704*r1*r3^5*r4*r5*z^3 - 245248*r1^3*r3^3*r4^2*r5*z^3 - 3456*r3^4*r4^2*r5*z^3 + 77824*r1^5*r3*r4^3*r5*z^3 + 85952*r1^2*r3^2*r4^3*r5*z^3 + 102912*r1^4*r4^4*r5*z^3 - 3856*r1*r3*r4^4*r5*z^3 + 32*r4^5*r5*z^3 + 22272*r1^3*r3^4*r5^2*z^3 - 171072*r1^2*r3^3*r4*r5^2*z^3 + 458752*r1^4*r3*r4^2*r5^2*z^3 + 27392*r1*r3^2*r4^2*r5^2*z^3 - 102016*r1^3*r4^3*r5^2*z^3 - 448*r3*r4^3*r5^2*z^3 - 49152*r1^4*r3^2*r5^3*z^3 + 22016*r1*r3^3*r5^3*z^3 + 172800*r1^3*r3*r4*r5^3*z^3 - 3840*r3^2*r4*r5^3*z^3 - 25600*r1^2*r4^2*r5^3*z^3 + 55296*r1^5*r5^4*z^3 - 104448*r1^2*r3*r5^4*z^3 + 18432*r1*r4*r5^4*z^3 - 1024*r5^5*z^3 - 14016*r1*r3^6*r6*z^3 + 37632*r1^3*r3^4*r4*r6*z^3 + 4980*r3^5*r4*r6*z^3 + 49152*r1^5*r3^2*r4^2*r6*z^3 - 93120*r1^2*r3^3*r4^2*r6*z^3 - 146432*r1^4*r3*r4^3*r6*z^3 + 7776*r1*r3^2*r4^3*r6*z^3 - 7424*r1^3*r4^4*r6*z^3 - 48*r3*r4^4*r6*z^3 + 143616*r1^2*r3^4*r5*r6*z^3 - 92160*r1^4*r3^2*r4*r5*r6*z^3 - 94176*r1*r3^3*r4*r5*r6*z^3 - 65536*r1^6*r4^2*r5*r6*z^3 + 57600*r1^3*r3*r4^2*r5*r6*z^3 + 2760*r3^2*r4^2*r5*r6*z^3 - 13696*r1^2*r4^3*r5*r6*z^3 - 322560*r1^3*r3^2*r5^2*r6*z^3 + 1344*r3^3*r5^2*r6*z^3 + 28672*r1^5*r4*r5^2*r6*z^3 + 92224*r1^2*r3*r4*r5^2*r6*z^3 + 5600*r1*r4^2*r5^2*r6*z^3 + 20480*r1^4*r5^3*r6*z^3 - 41728*r1*r3*r5^3*r6*z^3 + 1024*r4*r5^3*r6*z^3 - 73728*r1^4*r3^3*r6^2*z^3 + 20784*r1*r3^4*r6^2*z^3 - 98304*r1^6*r3*r4*r6^2*z^3 + 251904*r1^3*r3^2*r4*r6^2*z^3 - 1668*r3^3*r4*r6^2*z^3 + 563200*r1^5*r4^2*r6^2*z^3 - 1344*r1^2*r3*r4^2*r6^2*z^3 + 504*r1*r4^3*r6^2*z^3 + 196608*r1^5*r3*r5*r6^2*z^3 - 102144*r1^2*r3^2*r5*r6^2*z^3 - 520192*r1^4*r4*r5*r6^2*z^3 + 336*r1*r3*r4*r5*r6^2*z^3 + 216*r4^2*r5*r6^2*z^3 + 121088*r1^3*r5^2*r6^2*z^3 - 2112*r3*r5^2*r6^2*z^3 + 131072*r1^7*r6^3*z^3 + 245760*r1^4*r3*r6^3*z^3 + 6144*r1*r3^2*r6^3*z^3 - 84736*r1^3*r4*r6^3*z^3 - 324*r3*r4*r6^3*z^3 + 31488*r1^2*r5*r6^3*z^3 + 1944*r1*r6^4*z^3 - 2304*r1^3*r3^5*r7*z^3 + 4116*r3^6*r7*z^3 - 113568*r1^2*r3^4*r4*r7*z^3 + 325632*r1^4*r3^2*r4^2*r7*z^3 + 17472*r1*r3^3*r4^2*r7*z^3 - 122880*r1^6*r4^3*r7*z^3 + 48640*r1^3*r3*r4^3*r7*z^3 - 660*r3^2*r4^3*r7*z^3 - 416*r1^2*r4^4*r7*z^3 + 43008*r1^4*r3^3*r5*r7*z^3 - 98928*r1*r3^4*r5*r7*z^3 + 748800*r1^3*r3^2*r4*r5*r7*z^3 + 10848*r3^3*r4*r5*r7*z^3 - 962560*r1^5*r4^2*r5*r7*z^3 - 37120*r1^2*r3*r4^2*r5*r7*z^3 - 176*r1*r4^3*r5*r7*z^3 - 135168*r1^5*r3*r5^2*r7*z^3 + 351168*r1^2*r3^2*r5^2*r7*z^3 - 260608*r1^4*r4*r5^2*r7*z^3 - 48256*r1*r3*r4*r5^2*r7*z^3 + 448*r4^2*r5^2*r7*z^3 + 369408*r1^3*r5^3*r7*z^3 + 2304*r3*r5^3*r7*z^3 - 408576*r1^3*r3^3*r6*r7*z^3 - 1596*r3^4*r6*r7*z^3 - 73728*r1^5*r3*r4*r6*r7*z^3 + 528960*r1^2*r3^2*r4*r6*r7*z^3 + 832000*r1^4*r4^2*r6*r7*z^3 - 23088*r1*r3*r4^2*r6*r7*z^3 + 144*r4^3*r6*r7*z^3 + 1548288*r1^4*r3*r5*r6*r7*z^3 + 82080*r1*r3^2*r5*r6*r7*z^3 - 665344*r1^3*r4*r5*r6*r7*z^3 - 4032*r3*r4*r5*r6*r7*z^3 + 180032*r1^2*r5^2*r6*r7*z^3 - 98304*r1^6*r6^2*r7*z^3 + 220416*r1^3*r3*r6^2*r7*z^3 + 3036*r3^2*r6^2*r7*z^3 - 82848*r1^2*r4*r6^2*r7*z^3 + 29904*r1*r5*r6^2*r7*z^3 + 972*r6^3*r7*z^3 - 36864*r1^5*r3^2*r7^2*z^3 + 181056*r1^2*r3^3*r7^2*z^3 - 1185792*r1^4*r3*r4*r7^2*z^3 + 9360*r1*r3^2*r4*r7^2*z^3 - 23936*r1^3*r4^2*r7^2*z^3 + 108*r3*r4^2*r7^2*z^3 + 245760*r1^6*r5*r7^2*z^3 - 1621248*r1^3*r3*r5*r7^2*z^3 - 5256*r3^2*r5*r7^2*z^3 + 32192*r1^2*r4*r5*r7^2*z^3 + 33056*r1*r5^2*r7^2*z^3 - 1701888*r1^5*r6*r7^2*z^3 - 330432*r1^2*r3*r6*r7^2*z^3 + 4320*r1*r4*r6*r7^2*z^3 + 2760*r5*r6*r7^2*z^3 + 1489408*r1^4*r7^3*z^3 - 26448*r1*r3*r7^3*z^3 + 292*r4*r7^3*z^3 - 82944*r1^4*r3^4*r9*z^3 + 72864*r1*r3^5*r9*z^3 + 624384*r1^3*r3^3*r4*r9*z^3 - 19128*r3^4*r4*r9*z^3 - 73728*r1^5*r3*r4^2*r9*z^3 - 444288*r1^2*r3^2*r4^2*r9*z^3 - 642560*r1^4*r4^3*r9*z^3 + 13920*r1*r3*r4^3*r9*z^3 - 96*r4^4*r9*z^3 + 442368*r1^5*r3^2*r5*r9*z^3 - 445440*r1^2*r3^3*r5*r9*z^3 - 2644992*r1^4*r3*r4*r5*r9*z^3 + 52992*r1*r3^2*r4*r5*r9*z^3 + 864256*r1^3*r4^2*r5*r9*z^3 + 1872*r3*r4^2*r5*r9*z^3 - 442368*r1^6*r5^2*r9*z^3 + 542208*r1^3*r3*r5^2*r9*z^3 - 7776*r3^2*r5^2*r9*z^3 - 228480*r1^2*r4*r5^2*r9*z^3 + 4480*r1*r5^3*r9*z^3 + 165888*r1^4*r3^2*r6*r9*z^3 - 26688*r1*r3^3*r6*r9*z^3 + 147456*r1^6*r4*r6*r9*z^3 - 332544*r1^3*r3*r4*r6*r9*z^3 - 768*r3^2*r4*r6*r9*z^3 + 61056*r1^2*r4^2*r6*r9*z^3 - 147456*r1^5*r5*r6*r9*z^3 + 153600*r1^2*r3*r5*r6*r9*z^3 - 35712*r1*r4*r5*r6*r9*z^3 + 1248*r5^2*r6*r9*z^3 - 9216*r1^4*r6^2*r9*z^3 + 7584*r1*r3*r6^2*r9*z^3 - 648*r4*r6^2*r9*z^3 - 442368*r1^6*r3*r7*r9*z^3 + 997632*r1^3*r3^2*r7*r9*z^3 + 19632*r3^3*r7*r9*z^3 + 5179392*r1^5*r4*r7*r9*z^3 + 328704*r1^2*r3*r4*r7*r9*z^3 + 96*r1*r4^2*r7*r9*z^3 - 2522112*r1^4*r5*r7*r9*z^3 - 38016*r1*r3*r5*r7*r9*z^3 - 2064*r4*r5*r7*r9*z^3 - 201984*r1^3*r6*r7*r9*z^3 + 3216*r3*r6*r7*r9*z^3 - 189696*r1^2*r7^2*r9*z^3 + 884736*r1^7*r9^2*z^3 + 1492992*r1^4*r3*r9^2*z^3 + 84096*r1*r3^2*r9^2*z^3 - 299520*r1^3*r4*r9^2*z^3 - 5664*r3*r4*r9^2*z^3 + 98304*r1^2*r5*r9^2*z^3 + 9600*r1*r6*r9^2*z^3 + 2496*r7*r9^2*z^3 + 513*r3^8*z^4 - 7680*r1^2*r3^6*r4*z^4 + 32496*r1*r3^5*r4^2*z^4 - 100992*r1^3*r3^3*r4^3*z^4 - 3996*r3^4*r4^3*z^4 + 16384*r1^5*r3*r4^4*z^4 + 21920*r1^2*r3^2*r4^4*z^4 + 79872*r1^4*r4^5*z^4 - 2064*r1*r3*r4^5*z^4 + 16*r4^6*z^4 - 8736*r1*r3^6*r5*z^4 + 58368*r1^3*r3^4*r4*r5*z^4 + 10512*r3^5*r4*r5*z^4 - 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37888*r1^4*r3*r4^3*z^9 - 250384*r1*r3^2*r4^3*z^9 + 184960*r1^3*r4^4*z^9 + 25572*r3*r4^4*z^9 - 26880*r1^2*r3^4*r5*z^9 + 274848*r1*r3^3*r4*r5*z^9 - 494848*r1^3*r3*r4^2*r5*z^9 - 143008*r3^2*r4^2*r5*z^9 + 708160*r1^2*r4^3*r5*z^9 + 72192*r1^3*r3^2*r5^2*z^9 + 23552*r3^3*r5^2*z^9 - 833472*r1^2*r3*r4*r5^2*z^9 + 560512*r1*r4^2*r5^2*z^9 - 40960*r1^4*r5^3*z^9 - 199680*r1*r3*r5^3*z^9 + 86016*r4*r5^3*z^9 + 60576*r1*r3^4*r6*z^9 - 761856*r1^3*r3^2*r4*r6*z^9 + 6120*r3^3*r4*r6*z^9 + 151552*r1^5*r4^2*r6*z^9 + 1280576*r1^2*r3*r4^2*r6*z^9 - 279600*r1*r4^3*r6*z^9 - 750720*r1^2*r3^2*r5*r6*z^9 + 2502656*r1^4*r4*r5*r6*z^9 - 187808*r1*r3*r4*r5*r6*z^9 + 32184*r4^2*r5*r6*z^9 + 3223552*r1^3*r5^2*r6*z^9 - 111808*r3*r5^2*r6*z^9 - 239616*r1^4*r3*r6^2*z^9 + 1091424*r1*r3^2*r6^2*z^9 - 3918592*r1^3*r4*r6^2*z^9 - 157788*r3*r4*r6^2*z^9 - 4276864*r1^2*r5*r6^2*z^9 + 184032*r1*r6^3*z^9 - 1536*r1^3*r3^3*r7*z^9 - 12276*r3^4*r7*z^9 + 325248*r1^2*r3^2*r4*r7*z^9 - 154112*r1^4*r4^2*r7*z^9 + 58112*r1*r3*r4^2*r7*z^9 - 57036*r4^3*r7*z^9 - 104448*r1^4*r3*r5*r7*z^9 + 427488*r1*r3^2*r5*r7*z^9 + 719872*r1^3*r4*r5*r7*z^9 - 232672*r3*r4*r5*r7*z^9 + 873408*r1^2*r5^2*r7*z^9 - 4335360*r1^3*r3*r6*r7*z^9 + 237528*r3^2*r6*r7*z^9 + 3153344*r1^2*r4*r6*r7*z^9 + 91808*r1*r5*r6*r7*z^9 - 93636*r6^2*r7*z^9 + 325632*r1^5*r7^2*z^9 - 2734272*r1^2*r3*r7^2*z^9 + 1475456*r1*r4*r7^2*z^9 + 131816*r5*r7^2*z^9 + 331776*r1^4*r3^2*r9*z^9 - 443904*r1*r3^3*r9*z^9 - 1467648*r1^3*r3*r4*r9*z^9 + 405360*r3^2*r4*r9*z^9 - 2046976*r1^2*r4^2*r9*z^9 - 884736*r1^5*r5*r9*z^9 + 321792*r1^2*r3*r5*r9*z^9 - 2324928*r1*r4*r5*r9*z^9 - 181664*r5^2*r9*z^9 + 13160448*r1^4*r6*r9*z^9 - 863232*r1*r3*r6*r9*z^9 + 25920*r4*r6*r9*z^9 + 8565504*r1^3*r7*r9*z^9 - 348336*r3*r7*r9*z^9 + 2889984*r1*r9^2*z^9 + 3612*r3^6*z^10 - 21120*r1^2*r3^4*r4*z^10 + 178592*r1*r3^3*r4^2*z^10 - 151424*r1^3*r3*r4^3*z^10 - 68216*r3^2*r4^3*z^10 + 179488*r1^2*r4^4*z^10 - 43680*r1*r3^4*r5*z^10 + 89088*r1^3*r3^2*r4*r5*z^10 + 85408*r3^3*r4*r5*z^10 - 715008*r1^2*r3*r4^2*r5*z^10 + 339808*r1*r4^3*r5*z^10 + 176832*r1^2*r3^2*r5^2*z^10 - 67584*r1^4*r4*r5^2*z^10 - 483840*r1*r3*r4*r5^2*z^10 + 101344*r4^2*r5^2*z^10 - 145408*r1^3*r5^3*z^10 - 39552*r3*r5^3*z^10 + 70656*r1^3*r3^3*r6*z^10 + 4956*r3^4*r6*z^10 - 976128*r1^2*r3^2*r4*r6*z^10 + 667136*r1^4*r4^2*r6*z^10 + 548896*r1*r3*r4^2*r6*z^10 - 41580*r4^3*r6*z^10 - 282624*r1^4*r3*r5*r6*z^10 - 322176*r1*r3^2*r5*r6*z^10 + 4212224*r1^3*r4*r5*r6*z^10 - 77792*r3*r4*r5*r6*z^10 + 2684736*r1^2*r5^2*r6*z^10 - 738816*r1^3*r3*r6^2*z^10 + 225876*r3^2*r6^2*z^10 - 2256896*r1^2*r4*r6^2*z^10 - 1420896*r1*r5*r6^2*z^10 + 14580*r6^3*z^10 - 54336*r1^2*r3^3*r7*z^10 - 12288*r1^4*r3*r4*r7*z^10 + 250416*r1*r3^2*r4*r7*z^10 - 270976*r1^3*r4^2*r7*z^10 + 784*r3*r4^2*r7*z^10 - 241920*r1^3*r3*r5*r7*z^10 + 112896*r3^2*r5*r7*z^10 + 462528*r1^2*r4*r5*r7*z^10 + 322176*r1*r5^2*r7*z^10 + 565248*r1^5*r6*r7*z^10 - 4386624*r1^2*r3*r6*r7*z^10 + 1399120*r1*r4*r6*r7*z^10 + 36768*r5*r6*r7*z^10 + 1283328*r1^4*r7^2*z^10 - 1313184*r1*r3*r7^2*z^10 + 234724*r4*r7^2*z^10 + 1257984*r1^3*r3^2*r9*z^10 - 175056*r3^3*r9*z^10 - 516096*r1^5*r4*r9*z^10 - 869376*r1^2*r3*r4*r9*z^10 - 791120*r1*r4^2*r9*z^10 - 3612672*r1^4*r5*r9*z^10 + 557760*r1*r3*r5*r9*z^10 - 374992*r4*r5*r9*z^10 + 14336256*r1^3*r6*r9*z^10 - 99888*r3*r6*r9*z^10 + 4940544*r1^2*r7*r9*z^10 + 401808*r9^2*z^10 - 49680*r1*r3^4*r4*z^11 + 29952*r1^3*r3^2*r4^2*z^11 + 65592*r3^3*r4^2*z^11 - 233280*r1^2*r3*r4^3*z^11 + 88800*r1*r4^4*z^11 - 17640*r3^4*r5*z^11 + 252288*r1^2*r3^2*r4*r5*z^11 - 33792*r1^4*r4^2*r5*z^11 - 461088*r1*r3*r4^2*r5*z^11 + 65568*r4^3*r5*z^11 + 139968*r1*r3^2*r5^2*z^11 - 244992*r1^3*r4*r5^2*z^11 - 103104*r3*r4*r5^2*z^11 - 191616*r1^2*r5^3*z^11 + 187776*r1^2*r3^3*r6*z^11 - 138240*r1^4*r3*r4*r6*z^11 - 543744*r1*r3^2*r4*r6*z^11 + 1177344*r1^3*r4^2*r6*z^11 + 92304*r3*r4^2*r6*z^11 - 889344*r1^3*r3*r5*r6*z^11 - 46800*r3^2*r5*r6*z^11 + 3513600*r1^2*r4*r5*r6*z^11 + 1111104*r1*r5^2*r6*z^11 + 276480*r1^5*r6^2*z^11 - 830592*r1^2*r3*r6^2*z^11 - 689904*r1*r4*r6^2*z^11 - 197640*r5*r6^2*z^11 - 81504*r1*r3^3*r7*z^11 + 67896*r3^2*r4*r7*z^11 - 254592*r1^2*r4^2*r7*z^11 - 141696*r1^2*r3*r5*r7*z^11 + 105120*r1*r4*r5*r7*z^11 + 44352*r5^2*r7*z^11 + 2193408*r1^4*r6*r7*z^11 - 2121120*r1*r3*r6*r7*z^11 + 249912*r4*r6*r7*z^11 + 1998720*r1^3*r7^2*z^11 - 242280*r3*r7^2*z^11 + 1627776*r1^2*r3^2*r9*z^11 - 2128896*r1^4*r4*r9*z^11 - 167616*r1*r3*r4*r9*z^11 - 132264*r4^2*r9*z^11 - 5902848*r1^3*r5*r9*z^11 + 167328*r3*r5*r9*z^11 + 8849664*r1^2*r6*r9*z^11 + 1492416*r1*r7*r9*z^11 + 4032*r1*r3^5*z^12 - 28140*r3^4*r4*z^12 + 102432*r1^2*r3^2*r4^2*z^12 - 6656*r1^4*r4^3*z^12 - 164040*r1*r3*r4^3*z^12 + 17985*r4^4*z^12 - 26880*r1^2*r3^3*r5*z^12 + 237312*r1*r3^2*r4*r5*z^12 - 128128*r1^3*r4^2*r5*z^12 - 111864*r3*r4^2*r5*z^12 + 43008*r1^3*r3*r5^2*z^12 + 35568*r3^2*r5^2*z^12 - 330048*r1^2*r4*r5^2*z^12 - 111040*r1*r5^3*z^12 + 153984*r1*r3^3*r6*z^12 - 500352*r1^3*r3*r4*r6*z^12 - 108168*r3^2*r4*r6*z^12 + 1042368*r1^2*r4^2*r6*z^12 - 1041792*r1^2*r3*r5*r6*z^12 + 1451808*r1*r4*r5*r6*z^12 + 183072*r5^2*r6*z^12 + 1071360*r1^4*r6^2*z^12 - 399552*r1*r3*r6^2*z^12 - 89100*r4*r6^2*z^12 + 32256*r1^3*r3^2*r7*z^12 - 29424*r3^3*r7*z^12 + 79104*r1^2*r3*r4*r7*z^12 - 128136*r1*r4^2*r7*z^12 - 86016*r1^4*r5*r7*z^12 + 24480*r1*r3*r5*r7*z^12 - 3120*r4*r5*r7*z^12 + 3357312*r1^3*r6*r7*z^12 - 397488*r3*r6*r7*z^12 + 1536384*r1^2*r7^2*z^12 + 843552*r1*r3^2*r9*z^12 - 3564288*r1^3*r4*r9*z^12 + 21984*r3*r4*r9*z^12 - 4821888*r1^2*r5*r9*z^12 + 2947488*r1*r6*r9*z^12 + 182352*r7*r9*z^12 + 4536*r3^5*z^13 - 12480*r1^2*r3^3*r4*z^13 + 117528*r1*r3^2*r4^2*z^13 - 26304*r1^3*r4^3*z^13 - 44316*r3*r4^3*z^13 - 43680*r1*r3^3*r5*z^13 + 37632*r1^3*r3*r4*r5*z^13 + 73872*r3^2*r4*r5*z^13 - 183072*r1^2*r4^2*r5*z^13 + 108288*r1^2*r3*r5^2*z^13 - 195456*r1*r4*r5^2*z^13 - 23872*r5^3*z^13 + 36864*r1^3*r3^2*r6*z^13 + 37584*r3^3*r6*z^13 - 683904*r1^2*r3*r4*r6*z^13 + 463248*r1*r4^2*r6*z^13 - 98304*r1^4*r5*r6*z^13 - 537888*r1*r3*r5*r6*z^13 + 237600*r4*r5*r6*z^13 + 1646592*r1^3*r6^2*z^13 - 68040*r3*r6^2*z^13 + 32256*r1^2*r3^2*r7*z^13 - 26112*r1^4*r4*r7*z^13 + 104496*r1*r3*r4*r7*z^13 - 27252*r4^2*r7*z^13 - 274176*r1^3*r5*r7*z^13 + 28944*r3*r5*r7*z^13 + 2528448*r1^2*r6*r7*z^13 + 582792*r1*r7^2*z^13 + 262656*r1^3*r3*r9*z^13 + 141264*r3^2*r9*z^13 - 3026496*r1^2*r4*r9*z^13 - 1967712*r1*r5*r9*z^13 + 416016*r6*r9*z^13 - 33480*r1*r3^3*r4*z^14 + 4608*r1^3*r3*r4^2*z^14 + 45018*r3^2*r4^2*z^14 - 40704*r1^2*r4^3*z^14 - 17640*r3^3*r5*z^14 + 106272*r1^2*r3*r4*r5*z^14 - 116808*r1*r4^2*r5*z^14 + 88992*r1*r3*r5^2*z^14 - 42816*r4*r5^2*z^14 + 117504*r1^2*r3^2*r6*z^14 - 18432*r1^4*r4*r6*z^14 - 415512*r1*r3*r4*r6*z^14 + 82620*r4^2*r6*z^14 - 322560*r1^3*r5*r6*z^14 - 103176*r3*r5*r6*z^14 + 1256832*r1^2*r6^2*z^14 - 13176*r1*r3^2*r7*z^14 - 83520*r1^3*r4*r7*z^14 + 37620*r3*r4*r7*z^14 - 318816*r1^2*r5*r7*z^14 + 933912*r1*r6*r7*z^14 + 87462*r7^2*z^14 + 627264*r1^2*r3*r9*z^14 - 1298592*r1*r4*r9*z^14 - 320616*r5*r9*z^14 + 3024*r1*r3^4*z^15 - 20580*r3^3*r4*z^15 + 20928*r1^2*r3*r4^2*z^15 - 29160*r1*r4^3*z^15 - 16128*r1^2*r3^2*r5*z^15 + 99792*r1*r3*r4*r5*z^15 - 28064*r4^2*r5*z^15 + 9984*r1^3*r5^2*z^15 + 23808*r3*r5^2*z^15 + 114048*r1*r3^2*r6*z^15 - 69120*r1^3*r4*r6*z^15 - 93660*r3*r4*r6*z^15 - 395904*r1^2*r5*r6*z^15 + 477936*r1*r6^2*z^15 + 34560*r1^3*r3*r7*z^15 - 13716*r3^2*r7*z^15 - 92640*r1^2*r4*r7*z^15 - 159216*r1*r5*r7*z^15 + 134532*r6*r7*z^15 - 138240*r1^4*r9*z^15 + 488160*r1*r3*r9*z^15 - 223608*r4*r9*z^15 + 3654*r3^4*z^16 - 2304*r1^2*r3^2*r4*z^16 + 29040*r1*r3*r4^2*z^16 - 8108*r4^3*z^16 - 26208*r1*r3^2*r5*z^16 + 6144*r1^3*r4*r5*z^16 + 31056*r3*r4*r5*z^16 + 25632*r1^2*r5^2*z^16 + 33948*r3^2*r6*z^16 - 99744*r1^2*r4*r6*z^16 - 215424*r1*r5*r6*z^16 + 72846*r6^2*z^16 + 65952*r1^2*r3*r7*z^16 - 40152*r1*r4*r7*z^16 - 28512*r5*r7*z^16 - 397440*r1^3*r9*z^16 + 123192*r3*r9*z^16 - 10368*r1*r3^2*r4*z^17 - 1152*r1^3*r4^2*z^17 + 12708*r3*r4^2*z^17 - 10584*r3^2*r5*z^17 + 17280*r1^2*r4*r5*z^17 + 21600*r1*r5^2*z^17 + 13824*r1^2*r3*r6*z^17 - 64944*r1*r4*r6*z^17 - 43848*r5*r6*z^17 + 36720*r1*r3*r7*z^17 - 4932*r4*r7*z^17 - 414720*r1^2*r9*z^17 + 1344*r1*r3^3*z^18 - 7812*r3^2*r4*z^18 - 1840*r1^2*r4^2*z^18 - 5376*r1^2*r3*r5*z^18 + 16176*r1*r4*r5*z^18 + 5968*r5^2*z^18 + 22368*r1*r3*r6*z^18 - 15876*r4*r6*z^18 + 10752*r1^3*r7*z^18 + 5112*r3*r7*z^18 - 184944*r1*r9*z^18 + 1848*r3^3*z^19 + 960*r1^2*r3*r4*z^19 - 56*r1*r4^2*z^19 - 8736*r1*r3*r5*z^19 + 5024*r4*r5*z^19 - 3840*r1^3*r6*z^19 + 8760*r3*r6*z^19 + 23808*r1^2*r7*z^19 - 29496*r9*z^19 - 216*r1*r3*r4*z^20 + 630*r4^2*z^20 - 3528*r3*r5*z^20 - 7200*r1^2*r6*z^20 + 16920*r1*r7*z^20 + 288*r1*r3^2*z^21 - 1092*r3*r4*z^21 - 768*r1^2*r5*z^21 - 3936*r1*r6*z^21 + 3828*r7*z^21 + 540*r3^2*z^22 + 384*r1^2*r4*z^22 - 1248*r1*r5*z^22 - 540*r6*z^22 + 432*r1*r4*z^23 - 504*r5*z^23 + 60*r4*z^24 + 72*r3*z^25 - 8*r1*z^27 + z^28 g0[{u_, v_}, y_] := y^28*u^16 - 16*y^28*u^15*v - 176*y^28*u^15 + 120*y^28*u^14*v^2 + 2416*y^28*u^14*v + 8920*y^28*u^14 - 560*y^28*u^13*v^3 - 15344*y^28*u^13*v^2 - 111120*y^28*u^13*v - 106960*y^28*u^13 + 1820*y^28*u^12*v^4 + 59696*y^28*u^12*v^3 + 638664*y^28*u^12*v^2 + 1069168*y^28*u^12*v + 657020*y^28*u^12 - 4368*y^28*u^11*v^5 - 158704*y^28*u^11*v^4 - 2243488*y^28*u^11*v^3 - 4758240*y^28*u^11*v^2 - 5020240*y^28*u^11*v - 2552368*y^28*u^11 + 8008*y^28*u^10*v^6 + 304304*y^28*u^10*v^5 + 5377944*y^28*u^10*v^4 + 12298016*y^28*u^10*v^3 + 16214264*y^28*u^10*v^2 + 14067504*y^28*u^10*v + 6894888*y^28*u^10 - 11440*y^28*u^9*v^7 - 432432*y^28*u^9*v^6 - 9300720*y^28*u^9*v^5 - 20017520*y^28*u^9*v^4 - 28059920*y^28*u^9*v^3 - 30214800*y^28*u^9*v^2 - 25084752*y^28*u^9*v - 13625040*y^28*u^9 + 12870*y^28*u^8*v^8 + 459888*y^28*u^8*v^7 + 11960520*y^28*u^8*v^6 + 20275920*y^28*u^8*v^5 + 26460100*y^28*u^8*v^4 + 30071440*y^28*u^8*v^3 + 30649608*y^28*u^8*v^2 + 27685680*y^28*u^8*v + 20261670*y^28*u^8 - 11440*y^28*u^7*v^9 - 363792*y^28*u^7*v^8 - 11613888*y^28*u^7*v^7 - 10357056*y^28*u^7*v^6 - 10916000*y^28*u^7*v^5 - 11539680*y^28*u^7*v^4 - 12143552*y^28*u^7*v^3 - 12859968*y^28*u^7*v^2 - 14143536*y^28*u^7*v - 23005840*y^28*u^7 + 8008*y^28*u^6*v^10 + 208208*y^28*u^6*v^9 + 8555976*y^28*u^6*v^8 - 2399040*y^28*u^6*v^7 - 168560*y^28*u^6*v^6 + 61152*y^28*u^6*v^5 + 10448*y^28*u^6*v^4 - 252224*y^28*u^6*v^3 - 970200*y^28*u^6*v^2 - 8304560*y^28*u^6*v + 20028008*y^28*u^6 - 4368*y^28*u^5*v^11 - 80080*y^28*u^5*v^10 - 4761328*y^28*u^5*v^9 + 8731728*y^28*u^5*v^8 - 2971808*y^28*u^5*v^7 - 786464*y^28*u^5*v^6 - 559584*y^28*u^5*v^5 - 649568*y^28*u^5*v^4 - 1089872*y^28*u^5*v^3 - 7434768*y^28*u^5*v^2 + 22903760*y^28*u^5*v - 13297648*y^28*u^5 + 1820*y^28*u^4*v^12 + 16016*y^28*u^4*v^11 + 1973400*y^28*u^4*v^10 - 7408880*y^28*u^4*v^9 + 9249220*y^28*u^4*v^8 - 2926560*y^28*u^4*v^7 - 811312*y^28*u^4*v^6 - 656480*y^28*u^4*v^5 - 916380*y^28*u^4*v^4 - 6575280*y^28*u^4*v^3 + 23353880*y^28*u^4*v^2 - 21926064*y^28*u^4*v + 6626620*y^28*u^4 - 560*y^28*u^3*v^13 + 1456*y^28*u^3*v^12 - 592800*y^28*u^3*v^11 + 3537440*y^28*u^3*v^10 - 8496400*y^28*u^3*v^9 + 9319440*y^28*u^3*v^8 - 2988992*y^28*u^3*v^7 - 939840*y^28*u^3*v^6 - 928080*y^28*u^3*v^5 - 6020400*y^28*u^3*v^4 + 21741920*y^28*u^3*v^3 - 24663264*y^28*u^3*v^2 + 12433040*y^28*u^3*v - 2402960*y^28*u^3 + 120*y^28*u^2*v^14 - 1904*y^28*u^2*v^13 + 122824*y^28*u^2*v^12 - 1017312*y^28*u^2*v^11 + 3858680*y^28*u^2*v^10 - 8043280*y^28*u^2*v^9 + 8880648*y^28*u^2*v^8 - 3236928*y^28*u^2*v^7 - 1271256*y^28*u^2*v^6 - 5715600*y^28*u^2*v^5 + 18580760*y^28*u^2*v^4 - 21835744*y^28*u^2*v^3 + 13465704*y^28*u^2*v^2 - 4386032*y^28*u^2*v + 599320*y^28*u^2 - 16*y^28*u*v^15 + 496*y^28*u*v^14 - 15888*y^28*u*v^13 + 164080*y^28*u*v^12 - 888400*y^28*u*v^11 + 2940336*y^28*u*v^10 - 6191952*y^28*u*v^9 + 7840176*y^28*u*v^8 - 3766320*y^28*u*v^7 - 5822000*y^28*u*v^6 + 14188496*y^28*u*v^5 - 15050544*y^28*u*v^4 + 9671312*y^28*u*v^3 - 3874160*y^28*u*v^2 + 896400*y^28*u*v - 92016*y^28*u + y^28*v^16 - 48*y^28*v^15 + 984*y^28*v^14 - 11344*y^28*v^13 + 82044*y^28*v^12 - 396720*y^28*v^11 + 1344552*y^28*v^10 - 3305808*y^28*v^9 + 6035238*y^28*v^8 - 8293648*y^28*v^7 + 8620392*y^28*v^6 - 6749040*y^28*v^5 + 3921724*y^28*v^4 - 1641744*y^28*v^3 + 468504*y^28*v^2 - 81648*y^28*v + 6561*y^28 + 160*y^27*u^17 - 2720*y^27*u^16*v - 27812*y^27*u^16 + 21760*y^27*u^15*v^2 + 409632*y^27*u^15*v + 1391872*y^27*u^15 - 108800*y^27*u^14*v^3 - 2807040*y^27*u^14*v^2 - 18720352*y^27*u^14*v - 16471840*y^27*u^14 + 380800*y^27*u^13*v^4 + 11861920*y^27*u^13*v^3 + 116856768*y^27*u^13*v^2 + 180734240*y^27*u^13*v + 99653120*y^27*u^13 - 990080*y^27*u^12*v^5 - 34529040*y^27*u^12*v^4 - 448887712*y^27*u^12*v^3 - 893000128*y^27*u^12*v^2 - 857235936*y^27*u^12*v - 380227120*y^27*u^12 + 1980160*y^27*u^11*v^6 + 73216416*y^27*u^11*v^5 + 1186127488*y^27*u^11*v^4 + 2603746496*y^27*u^11*v^3 + 3186526080*y^27*u^11*v^2 + 2456501920*y^27*u^11*v + 1005129216*y^27*u^11 - 3111680*y^27*u^10*v^7 - 116532416*y^27*u^10*v^6 - 2282568288*y^27*u^10*v^5 - 4904883808*y^27*u^10*v^4 - 6582907072*y^27*u^10*v^3 - 6470529408*y^27*u^10*v^2 - 4603212768*y^27*u^10*v - 1934096736*y^27*u^10 + 3889600*y^27*u^9*v^8 + 141192480*y^27*u^9*v^7 + 3303203904*y^27*u^9*v^6 + 6054451040*y^27*u^9*v^5 + 7980666240*y^27*u^9*v^4 + 8646262240*y^27*u^9*v^3 + 7864584000*y^27*u^9*v^2 + 5750499744*y^27*u^9*v + 2781430080*y^27*u^9 - 3889600*y^27*u^8*v^9 - 130398840*y^27*u^8*v^8 - 3659019936*y^27*u^8*v^7 - 4493427840*y^27*u^8*v^6 - 5293758240*y^27*u^8*v^5 - 5755668400*y^27*u^8*v^4 - 5822778080*y^27*u^8*v^3 - 5454317376*y^27*u^8*v^2 - 4589676960*y^27*u^8*v - 3023689240*y^27*u^8 + 3111680*y^27*u^7*v^10 + 90627680*y^27*u^7*v^9 + 3127348224*y^27*u^7*v^8 + 984398976*y^27*u^7*v^7 + 1367430912*y^27*u^7*v^6 + 1457555520*y^27*u^7*v^5 + 1514632960*y^27*u^7*v^4 + 1566703744*y^27*u^7*v^3 + 1643060736*y^27*u^7*v^2 + 1873611872*y^27*u^7*v + 2481839360*y^27*u^7 - 1980160*y^27*u^6*v^11 - 45741696*y^27*u^6*v^10 - 2062636576*y^27*u^6*v^9 + 1903115808*y^27*u^6*v^8 - 406062720*y^27*u^6*v^7 - 93054080*y^27*u^6*v^6 - 53004224*y^27*u^6*v^5 - 29806656*y^27*u^6*v^4 + 8353408*y^27*u^6*v^3 + 157068800*y^27*u^6*v^2 + 259327200*y^27*u^6*v - 1514627296*y^27*u^6 + 990080*y^27*u^5*v^12 + 15296736*y^27*u^5*v^11 + 1042000960*y^27*u^5*v^10 - 2592348704*y^27*u^5*v^9 + 2001671424*y^27*u^5*v^8 - 352550464*y^27*u^5*v^7 - 42727552*y^27*u^5*v^6 - 4191552*y^27*u^5*v^5 + 21762176*y^27*u^5*v^4 + 127926624*y^27*u^5*v^3 - 128347584*y^27*u^5*v^2 - 751344800*y^27*u^5*v + 661862656*y^27*u^5 - 380800*y^27*u^4*v^13 - 2351440*y^27*u^4*v^12 - 396675552*y^27*u^4*v^11 + 1727809600*y^27*u^4*v^10 - 2841681440*y^27*u^4*v^9 + 1989832560*y^27*u^4*v^8 - 364530880*y^27*u^4*v^7 - 51905536*y^27*u^4*v^6 - 8763840*y^27*u^4*v^5 + 82108560*y^27*u^4*v^4 - 432947040*y^27*u^4*v^3 + 163400640*y^27*u^4*v^2 + 325549408*y^27*u^4*v - 189464240*y^27*u^4 + 108800*y^27*u^3*v^14 - 514080*y^27*u^3*v^13 + 110551168*y^27*u^3*v^12 - 712289600*y^27*u^3*v^11 + 1948840320*y^27*u^3*v^10 - 2765106400*y^27*u^3*v^9 + 1923057920*y^27*u^3*v^8 - 385570176*y^27*u^3*v^7 - 63006720*y^27*u^3*v^6 + 44489760*y^27*u^3*v^5 - 658108800*y^27*u^3*v^4 + 973434560*y^27*u^3*v^3 - 464331392*y^27*u^3*v^2 + 22199520*y^27*u^3*v + 26245120*y^27*u^3 - 21760*y^27*u^2*v^15 + 375360*y^27*u^2*v^14 - 21428512*y^27*u^2*v^13 + 183513952*y^27*u^2*v^12 - 740496576*y^27*u^2*v^11 + 1723456000*y^27*u^2*v^10 - 2391711840*y^27*u^2*v^9 + 1793629344*y^27*u^2*v^8 - 418191744*y^27*u^2*v^7 - 20689088*y^27*u^2*v^6 - 833564640*y^27*u^2*v^5 + 1490565280*y^27*u^2*v^4 - 1119600832*y^27*u^2*v^3 + 422846592*y^27*u^2*v^2 - 71103136*y^27*u^2*v + 2421600*y^27*u^2 + 2720*y^27*u*v^16 - 85408*y^27*u*v^15 + 2609088*y^27*u*v^14 - 27089504*y^27*u*v^13 + 149895040*y^27*u*v^12 - 517249440*y^27*u*v^11 + 1178280768*y^27*u*v^10 - 1769045856*y^27*u*v^9 + 1590585408*y^27*u*v^8 - 407598560*y^27*u*v^7 - 999903680*y^27*u*v^6 + 1596999648*y^27*u*v^5 - 1237455232*y^27*u*v^4 + 581700896*y^27*u*v^3 - 165775680*y^27*u*v^2 + 25682400*y^27*u*v - 1552608*y^27*u - 160*y^27*v^17 + 7548*y^27*v^16 - 152544*y^27*v^15 + 1741312*y^27*v^14 - 12541152*y^27*v^13 + 60777072*y^27*v^12 - 207719520*y^27*v^11 + 518101056*y^27*v^10 - 965552544*y^27*v^9 + 1364165704*y^27*v^8 - 1470742944*y^27*v^7 + 1208631936*y^27*v^6 - 749871520*y^27*v^5 + 344208432*y^27*v^4 - 112760352*y^27*v^3 + 24743232*y^27*v^2 - 3219264*y^27*v + 183708*y^27 + 61920*y^26*u^17 - 955440*y^26*u^16*v - 6704352*y^26*u^16 + 6865920*y^26*u^15*v^2 + 95365512*y^26*u^15*v + 156162672*y^26*u^15 - 30441600*y^26*u^14*v^3 - 632618640*y^26*u^14*v^2 - 1834733952*y^26*u^14*v - 1529277840*y^26*u^14 + 92937600*y^26*u^13*v^4 + 2597719320*y^26*u^13*v^3 + 9757968768*y^26*u^13*v^2 + 14125557240*y^26*u^13*v + 8619876720*y^26*u^13 - 206256960*y^26*u^12*v^5 - 7391442240*y^26*u^12*v^4 - 30803936112*y^26*u^12*v^3 - 56410008048*y^26*u^12*v^2 - 59587679376*y^26*u^12*v - 32129370000*y^26*u^12 + 341752320*y^26*u^11*v^6 + 15459070536*y^26*u^11*v^5 + 63206780688*y^26*u^11*v^4 + 124311052656*y^26*u^11*v^3 + 165534727680*y^26*u^11*v^2 + 155101284360*y^26*u^11*v + 85215429936*y^26*u^11 - 425842560*y^26*u^10*v^7 - 24605236656*y^26*u^10*v^6 - 85381689888*y^26*u^10*v^5 - 155003726448*y^26*u^10*v^4 - 219973113792*y^26*u^10*v^3 - 262686536208*y^26*u^10*v^2 - 255399442848*y^26*u^10*v - 167781206736*y^26*u^10 + 393307200*y^26*u^9*v^8 + 30447382680*y^26*u^9*v^7 + 68905435104*y^26*u^9*v^6 + 84971948040*y^26*u^9*v^5 + 103902845040*y^26*u^9*v^4 + 137752995240*y^26*u^9*v^3 + 187848028800*y^26*u^9*v^2 + 239703042744*y^26*u^9*v + 251425540080*y^26*u^9 - 254311200*y^26*u^8*v^9 - 29676572640*y^26*u^8*v^8 - 12849849936*y^26*u^8*v^7 + 34879638960*y^26*u^8*v^6 + 62243296560*y^26*u^8*v^5 + 74279156400*y^26*u^8*v^4 + 67813243920*y^26*u^8*v^3 + 37051563024*y^26*u^8*v^2 - 31429751760*y^26*u^8*v - 290670391440*y^26*u^8 + 92252160*y^26*u^7*v^10 + 22945717080*y^26*u^7*v^9 - 46288580976*y^26*u^7*v^8 - 74475746784*y^26*u^7*v^7 - 66401659008*y^26*u^7*v^6 - 69271950960*y^26*u^7*v^5 - 74689100640*y^26*u^7*v^4 - 83980882656*y^26*u^7*v^3 - 104000385024*y^26*u^7*v^2 - 265316292648*y^26*u^7*v + 260517525840*y^26*u^7 + 12055680*y^26*u^6*v^11 - 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1833960645025796792570074488*u^2*v^7 + 2460851870713087251842571024*u^2*v^6 - 2227652404143463946614802040*u^2*v^5 + 1359178851590649589208902560*u^2*v^4 - 542308441253038346230336044*u^2*v^3 + 131561681477915613922656984*u^2*v^2 - 16492955553854141104401372*u^2*v + 672498732901585896048960*u^2 + 1042359477534720*u*v^16 - 2401812323971301376*u*v^15 - 53031538234943483904*u*v^14 + 19717730573865108982272*u*v^13 - 94725539578743856438320*u*v^12 - 2287888840891367877543840*u*v^11 + 24335857970949492818680896*u*v^10 - 110665073827824189206825952*u*v^9 + 300060833304137854226983056*u*v^8 - 540459197992672495372883520*u*v^7 + 677713764901291022013246720*u*v^6 - 602119073148226172942122944*u*v^5 + 377822262453924630555791856*u*v^4 - 163422704393069430602269728*u*v^3 + 46140537669414135603445440*u*v^2 - 7586499706074236871957600*u*v + 542244850353835840162224*u + 1175462461440*v^17 + 882654762295296*v^16 + 261047460140554752*v^15 + 37622385529568290944*v^14 + 2563383070526053591836*v^13 + 55359611319017803992084*v^12 - 878313963428625671842680*v^11 + 5236140667891625643556152*v^10 - 18142708760466061971431628*v^9 + 41763099887620214462525628*v^8 - 67834943441391256425261648*v^7 + 79991514105380355080870352*v^6 - 69113953436230441796666940*v^5 + 43464610963387341192939084*v^4 - 19413361027380195587195064*v^3 + 5847579429794353213644024*v^2 - 1066776289353970432690068*v + 89150985470298500366436 f1[{p_, q_}, x_] := x^28*p^12*q^6 - 3*x^28*p^11*q^4 + 3*x^28*p^10*q^2 - x^28*p^9 - 140*x^27*p^12*q^6 + 1080*x^27*p^11*q^5 - 1092*x^27*p^11*q^4 - 2592*x^27*p^10*q^4 + 5616*x^27*p^10*q^3 - 2580*x^27*p^10*q^2 - 1296*x^27*p^9*q^2 + 1080*x^27*p^9*q - 76*x^27*p^9 + 8370*x^26*p^12*q^6 - 98280*x^26*p^11*q^5 + 85806*x^26*p^11*q^4 + 31104*x^26*p^10*q^5 + 266976*x^26*p^10*q^4 - 506520*x^26*p^10*q^3 + 208278*x^26*p^10*q^2 - 186624*x^26*p^9*q^4 + 342144*x^26*p^9*q^3 - 153252*x^26*p^9*q^2 + 4104*x^26*p^9*q - 2106*x^26*p^9 - 280620*x^25*p^12*q^6 + 3742200*x^25*p^11*q^5 - 2803896*x^25*p^11*q^4 - 1897344*x^25*p^10*q^5 - 10885968*x^25*p^10*q^4 + 18203292*x^25*p^10*q^3 - 6728805*x^25*p^10*q^2 + 12752640*x^25*p^9*q^4 - 19331136*x^25*p^9*q^3 + 7819524*x^25*p^9*q^2 - 295650*x^25*p^9*q - 20160*x^25*p^9 - 2985984*x^25*p^8*q^4 + 4478976*x^25*p^8*q^3 - 2021760*x^25*p^8*q^2 + 256608*x^25*p^8*q - 1917*x^25*p^8 + 5836095*x^24*p^12*q^6 - 79115616*x^24*p^11*q^5 + 53014257*x^24*p^11*q^4 + 48921408*x^24*p^10*q^5 + 231494544*x^24*p^10*q^4 - 354537729*x^24*p^10*q^3 + (476028765*x^24*p^10*q^2)/4 - 330200064*x^24*p^9*q^4 + 449128800*x^24*p^9*q^3 - 155377656*x^24*p^9*q^2 + (2994813*x^24*p^9*q)/2 + 140382*x^24*p^9 + 102269952*x^24*p^8*q^4 - 139968000*x^24*p^8*q^3 + 49027680*x^24*p^8*q^2 - 1041336*x^24*p^8*q - (389259*x^24*p^8)/4 - 78699816*x^23*p^12*q^6 + 1030324752*x^23*p^11*q^5 - 645456168*x^23*p^11*q^4 - 696553344*x^23*p^10*q^5 - 2898641376*x^23*p^10*q^4 + 4224724992*x^23*p^10*q^3 - 1322269002*x^23*p^10*q^2 + 4530235392*x^23*p^9*q^4 - 5832663552*x^23*p^9*q^3 + 1828045584*x^23*p^9*q^2 + 16410492*x^23*p^9*q + 3643056*x^23*p^9 - 1531809792*x^23*p^8*q^4 + 2016658944*x^23*p^8*q^3 - 625454784*x^23*p^8*q^2 - 17185608*x^23*p^8*q - 1309770*x^23*p^8 + 696660516*x^22*p^12*q^6 - 8601418512*x^22*p^11*q^5 + 5248321236*x^22*p^11*q^4 + 6012817920*x^22*p^10*q^5 + 22563532800*x^22*p^10*q^4 - 32554846404*x^22*p^10*q^3 + 9840145761*x^22*p^10*q^2 - 37016642304*x^22*p^9*q^4 + 47216022336*x^22*p^9*q^3 - 14097150792*x^22*p^9*q^2 - 484986366*x^22*p^9*q + 919152*x^22*p^9 + 12899450880*x^22*p^8*q^4 - 17136562176*x^22*p^8*q^3 + 4721737536*x^22*p^8*q^2 + 615216384*x^22*p^8*q + 7969617*x^22*p^8 + 280682496*x^22*p^7*q^2 - 210511872*x^22*p^7*q - 1358208*x^22*p^7 - 3960572616*x^21*p^12*q^6 + 45599253264*x^21*p^11*q^5 - 28294929936*x^21*p^11*q^4 - 31962045312*x^21*p^10*q^5 - 107538024384*x^21*p^10*q^4 + 162830953080*x^21*p^10*q^3 - 49940919036*x^21*p^10*q^2 + 182984562432*x^21*p^9*q^4 - 249968706048*x^21*p^9*q^3 + 79270997112*x^21*p^9*q^2 + 3415642344*x^21*p^9*q - 294007896*x^21*p^9 - 64377815040*x^21*p^8*q^4 + 100349591040*x^21*p^8*q^3 - 30890522880*x^21*p^8*q^2 - 5728292136*x^21*p^8*q + 245739852*x^21*p^8 - 3869835264*x^21*p^7*q^3 - 273217536*x^21*p^7*q^2 + 2436189696*x^21*p^7*q - 34040736*x^21*p^7 + 13052589345*x^20*p^12*q^6 - 137083313088*x^20*p^11*q^5 + 93370395681*x^20*p^11*q^4 + 95021999424*x^20*p^10*q^5 + 253380142224*x^20*p^10*q^4 - 478338745194*x^20*p^10*q^3 + (329775509439*x^20*p^10*q^2)/2 - 472632869376*x^20*p^9*q^4 + 875531366496*x^20*p^9*q^3 - 393691073544*x^20*p^9*q^2 + 18572888493*x^20*p^9*q - 234073719*x^20*p^9 + 171541794816*x^20*p^8*q^4 - 492679895040*x^20*p^8*q^3 + 290977943328*x^20*p^8*q^2 - 19893538440*x^20*p^8*q - (607023963*x^20*p^8)/2 + 81374035968*x^20*p^7*q^3 - 68319313920*x^20*p^7*q^2 + 5302920960*x^20*p^7*q + 162502848*x^20*p^7 - 13187878788*x^19*p^12*q^6 + 89214046056*x^19*p^11*q^5 - 121274566812*x^19*p^11*q^4 - 67556757888*x^19*p^10*q^5 + 244474595712*x^19*p^10*q^4 + 363956915088*x^19*p^10*q^3 - 268768428138*x^19*p^10*q^2 - 35248711680*x^19*p^9*q^4 - 1876943404800*x^19*p^9*q^3 + 1773487396800*x^19*p^9*q^2 - 364528558980*x^19*p^9*q + 15852388260*x^19*p^9 - 60994363392*x^19*p^8*q^4 + 2088983955456*x^19*p^8*q^3 - 2241809037504*x^19*p^8*q^2 + 581176273320*x^19*p^8*q - 21164022198*x^19*p^8 - 657979490304*x^19*p^7*q^3 + 824883388416*x^19*p^7*q^2 - 253176544512*x^19*p^7*q + 7034283648*x^19*p^7 - 24078974976*x^19*p^6*q^2 + 18059231232*x^19*p^6*q - 411734016*x^19*p^6 - 73641599778*x^18*p^12*q^6 + 959736551400*x^18*p^11*q^5 - 372161191158*x^18*p^11*q^4 - 575136142848*x^18*p^10*q^5 - 3622820000256*x^18*p^10*q^4 + 2971335651876*x^18*p^10*q^3 - 311520553461*x^18*p^10*q^2 + 4344947578368*x^18*p^9*q^4 + 918502820352*x^18*p^9*q^3 - 5237904993804*x^18*p^9*q^2 + 1720888729794*x^18*p^9*q - 14602513506*x^18*p^9 - 1115807145984*x^18*p^8*q^4 - 5427406632960*x^18*p^8*q^3 + 8899144092288*x^18*p^8*q^2 - 3132367844112*x^18*p^8*q + 42577529661*x^18*p^8 + 2200526880768*x^18*p^7*q^3 - 3938225909760*x^18*p^7*q^2 + 1689845607936*x^18*p^7*q - 23384464128*x^18*p^7 + 61917364224*x^18*p^6*q^3 + 271461777408*x^18*p^6*q^2 - 236692979712*x^18*p^6*q + 787387392*x^18*p^6 + 315513679356*x^17*p^12*q^6 - 3567021560280*x^17*p^11*q^5 + 1974658970232*x^17*p^11*q^4 + 2132021502720*x^17*p^10*q^5 + 9439131391920*x^17*p^10*q^4 - 11651169458844*x^17*p^10*q^3 + 2673683247663*x^17*p^10*q^2 - 12106592252928*x^17*p^9*q^4 + 10039348204992*x^17*p^9*q^3 + 4044883216716*x^17*p^9*q^2 - 2201587912026*x^17*p^9*q - 533986886376*x^17*p^9 + 3236818599936*x^17*p^8*q^4 - 162743592960*x^17*p^8*q^3 - 10971971707392*x^17*p^8*q^2 + 4788139042728*x^17*p^8*q + 1004952072591*x^17*p^8 + 611589242880*x^17*p^7*q^3 + 5756741259264*x^17*p^7*q^2 - 3597322606848*x^17*p^7*q - 593525695968*x^17*p^7 - 1013036875776*x^17*p^6*q^3 - 629636530176*x^17*p^6*q^2 + 897261318144*x^17*p^6*q + 113853330432*x^17*p^6 - 407460535929*x^16*p^12*q^6 + 4076776871136*x^16*p^11*q^5 - 3321707370651*x^16*p^11*q^4 - 2522342457216*x^16*p^10*q^5 - 4856008953312*x^16*p^10*q^4 + 17034639546249*x^16*p^10*q^3 - (25289968871493*x^16*p^10*q^2)/4 + 8227846439424*x^16*p^9*q^4 - 38109329706816*x^16*p^9*q^3 + 16842581347968*x^16*p^9*q^2 - (3223634809005*x^16*p^9*q)/2 + 2027001326652*x^16*p^9 - 2170652608512*x^16*p^8*q^4 + 38531337596928*x^16*p^8*q^3 - 17081599806144*x^16*p^8*q^2 + 1806148751616*x^16*p^8*q - (18938856877605*x^16*p^8)/4 - 21243245690880*x^16*p^7*q^3 + 8409941323776*x^16*p^7*q^2 - 49779152640*x^16*p^7*q + 3478920674112*x^16*p^7 + 4903511261184*x^16*p^6*q^3 - 2418909806592*x^16*p^6*q^2 + 146776043520*x^16*p^6*q - 726911801856*x^16*p^6 + 522857742336*x^16*p^5*q^2 - 392143306752*x^16*p^5*q - 39223885824*x^16*p^5 - 130800964464*x^15*p^12*q^6 + 1589270976864*x^15*p^11*q^5 + 2901922564176*x^15*p^11*q^4 - 762398002944*x^15*p^10*q^5 - 10594947213504*x^15*p^10*q^4 - 24750793320192*x^15*p^10*q^3 + 15267828507516*x^15*p^10*q^2 + 6826650181632*x^15*p^9*q^4 + 60644672815104*x^15*p^9*q^3 + 1248837169824*x^15*p^9*q^2 - 34741665322344*x^15*p^9*q + 5524651445760*x^15*p^9 - 1147049828352*x^15*p^8*q^4 - 44856510925824*x^15*p^8*q^3 - 53601313963392*x^15*p^8*q^2 + 79326341715888*x^15*p^8*q - 14628607834212*x^15*p^8 + 13705702391808*x^15*p^7*q^3 + 37153975836672*x^15*p^7*q^2 - 54002110371840*x^15*p^7*q + 14609353466880*x^15*p^7 - 2354006458368*x^15*p^6*q^3 + 3851441602560*x^15*p^6*q^2 + 7375941844992*x^15*p^6*q - 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6560280*y^26*p^13*q^8 + 9362304*y^26*p^12*q^9 + 27744768*y^26*p^12*q^8 + 62688816*y^26*p^12*q^7 - 58521024*y^26*p^12*q^6 - 69859584*y^26*p^11*q^8 - 96764544*y^26*p^11*q^7 - 44116164*y^26*p^11*q^6 + 264131280*y^26*p^11*q^5 - 111340512*y^26*p^11*q^4 + 35831808*y^26*p^10*q^8 + 632406528*y^26*p^10*q^6 - 1330815744*y^26*p^10*q^5 + 956001852*y^26*p^10*q^4 - 296560440*y^26*p^10*q^3 + 39393954*y^26*p^10*q^2 - 358318080*y^26*p^9*q^6 + 806215680*y^26*p^9*q^5 - 661644288*y^26*p^9*q^4 + 239967360*y^26*p^9*q^3 - 35157240*y^26*p^9*q^2 + 460080*y^26*p^9*q - 20916*y^26*p^9 - 15936804*y^25*p^14*q^10 + 1374251832*y^25*p^13*q^9 + 328107078*y^25*p^13*q^8 - 2255302656*y^25*p^12*q^9 - 12479768496*y^25*p^12*q^8 + 3499872786*y^25*p^12*q^7 + 3844889316*y^25*p^12*q^6 + 34968962304*y^25*p^11*q^8 - 736748352*y^25*p^11*q^7 - 17848736532*y^25*p^11*q^6 - 13145727492*y^25*p^11*q^5 + 9666086778*y^25*p^11*q^4 - 19074465792*y^25*p^10*q^8 - 95314599936*y^25*p^10*q^7 + 187535098368*y^25*p^10*q^6 - 110976334848*y^25*p^10*q^5 + 38363725116*y^25*p^10*q^4 - 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12254536494*y^24*p^10*q^2 - 8724328611840*y^24*p^9*q^7 + 14301083713536*y^24*p^9*q^6 - 6147876796416*y^24*p^9*q^5 - 404269076736*y^24*p^9*q^4 + 530075669184*y^24*p^9*q^3 - 28760523552*y^24*p^9*q^2 - 2091055824*y^24*p^9*q - 44333730*y^24*p^9 + 2476694568960*y^24*p^8*q^7 - 4478689345536*y^24*p^8*q^6 + 2197206466560*y^24*p^8*q^5 + 144724672512*y^24*p^8*q^4 - 278971527168*y^24*p^8*q^3 + 29015138304*y^24*p^8*q^2 + 889678080*y^24*p^8*q - 1804032*y^24*p^8 + 453918309192*y^23*p^14*q^10 - 1745682751440*y^23*p^13*q^9 + 3887055802620*y^23*p^13*q^8 - 659620753920*y^23*p^12*q^9 - 31812404203872*y^23*p^12*q^8 + 6433209320220*y^23*p^12*q^7 + 8831121388110*y^23*p^12*q^6 + 62202348320256*y^23*p^11*q^8 + 112321404302976*y^23*p^11*q^7 - 196961553864504*y^23*p^11*q^6 + 58813210872072*y^23*p^11*q^5 + 1977411822156*y^23*p^11*q^4 - 28811159433216*y^23*p^10*q^8 - 337732943814144*y^23*p^10*q^7 + 494209348097472*y^23*p^10*q^6 - 150241927535928*y^23*p^10*q^5 - 27817101396414*y^23*p^10*q^4 + 11416229084340*y^23*p^10*q^3 - 1056474172908*y^23*p^10*q^2 + 287099925037056*y^23*p^9*q^7 - 409884972613632*y^23*p^9*q^6 + 111086361888768*y^23*p^9*q^5 + 52309167427584*y^23*p^9*q^4 - 21922248941856*y^23*p^9*q^3 + 1678537240704*y^23*p^9*q^2 + 42114914604*y^23*p^9*q + 1110916296*y^23*p^9 - 75621740838912*y^23*p^8*q^7 + 111409977360384*y^23*p^8*q^6 - 25601396834304*y^23*p^8*q^5 - 23478266658816*y^23*p^8*q^4 + 9882197157888*y^23*p^8*q^3 - 694242192384*y^23*p^8*q^2 - 13050984960*y^23*p^8*q + 137728512*y^23*p^8 - 22174053285132*y^22*p^14*q^10 + 195243453990576*y^22*p^13*q^9 - 180286769724264*y^22*p^13*q^8 - 77898177711360*y^22*p^12*q^9 + 172783354616640*y^22*p^12*q^8 + 545397575965164*y^22*p^12*q^7 - 379730162675079*y^22*p^12*q^6 - 666541970364672*y^22*p^11*q^8 - 2813801917136832*y^22*p^11*q^7 + 3698243327755296*y^22*p^11*q^6 - 918770772820446*y^22*p^11*q^5 - 51262852751928*y^22*p^11*q^4 + 404356078411776*y^22*p^10*q^8 + 6757856123102208*y^22*p^10*q^7 - 9297361126020672*y^22*p^10*q^6 + 3062388225279312*y^22*p^10*q^5 - 102500361825831*y^22*p^10*q^4 + 48133798340976*y^22*p^10*q^3 + 6626880201024*y^22*p^10*q^2 - 5572932182212608*y^22*p^9*q^7 + 7667489454243840*y^22*p^9*q^6 - 2671185552556032*y^22*p^9*q^5 + 210395399401728*y^22*p^9*q^4 - 119539390207680*y^22*p^9*q^3 - 3798416488752*y^22*p^9*q^2 - 334344838320*y^22*p^9*q - 18665528868*y^22*p^9 + 1444848573874176*y^22*p^8* q^7 - 1989322356031488*y^22*p^8*q^6 + 737399068360704*y^22*p^8*q^5 - 173338235781120*y^22*p^8*q^4 + 83073346937856*y^22*p^8*q^3 + 9816348966912*y^22*p^8*q^2 + 129888912384*y^22*p^8*q - 6033636864*y^22*p^8 - 14529941471232*y^22*p^7*q^6 - 33875677937664*y^22*p^7*q^5 + 68783311945728*y^22*p^7*q^4 - 15956381859840*y^22*p^7*q^3 - 7670845145088*y^22*p^7*q^2 - 127981486080*y^22*p^7*q - 40808448*y^22*p^7 + 545119184999016*y^21*p^14*q^10 - 5719146092747856*y^21*p^13*q^9 + 4318905140577756*y^21*p^13*q^8 + 2884716086950656*y^21*p^12*q^9 + 7019365915184832*y^21*p^12*q^8 - 19889006233029444*y^21*p^12*q^7 + 8590260301240734*y^21*p^12*q^6 - 3244230167659776*y^21*p^11*q^8 + 48298584680845056*y^21*p^11*q^7 - 46158461222285664*y^21*p^11*q^6 + 9877171434229548*y^21*p^11*q^5 + 156784814806140*y^21*p^11*q^4 - 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23853906432*a*b^2*y^26 - 16165254240*a^2*b^2*y^26 - 4545460800*a^3*b^2*y^26 - 459165024*a^4*b^2*y^26 + 12230590464*b^3*y^26 + 109397744640*a*b^3*y^26 + 42578773632*a^2*b^3*y^26 + 2510759808*a^3*b^3*y^26 - 1549271826432*b^4*y^26 + 4354054248960*a*b^4*y^26 + 786406055616*a^2*b^4*y^26 - 218431296*a^3*b^4*y^26 + 7707565228032*b^5*y^26 - 496742823936*a*b^5*y^26 - 1422102904704*a^2*b^5*y^26 - 14914154004480*b^6*y^26 - 12615288841728*a*b^6*y^26 + 330655190688*a^2*b^6*y^26 + 13788461924352*b^7*y^26 + 8900723874816*a*b^7*y^26 - 5648812867584*b^8*y^26 - 228290296320*a*b^8*y^26 + 353922711552*b^9*y^26 + 261667749888*b^10*y^26 - 452984832*b^3*y^27 - 373358592*a*b^3*y^27 - 98470656*a^2*b^3*y^27 - 8116480*a^3*b^3*y^27 + 3170893824*b^4*y^27 + 946667520*a*b^4*y^27 + 63279360*a^2*b^4*y^27 + 1207552*a^3*b^4*y^27 - 9512681472*b^5*y^27 - 53084160*a*b^5*y^27 - 86393088*a^2*b^5*y^27 + 15854469120*b^6*y^27 - 1787166720*a*b^6*y^27 + 121584384*a^2*b^6*y^27 - 15854469120*b^7*y^27 + 1813708800*a*b^7*y^27 + 9512681472*b^8*y^27 - 546766848*a*b^8*y^27 - 3170893824*b^9*y^27 + 452984832*b^10*y^27 + 768*a^3*b^4*y^28 (* Section 6. 2-division polynomials of Dettweiler-Reiter G2 motives *) (* Section 7. Specialization to three-point covers *) (* Section 8. Specialization to number fields *) (* fields376 contains 376 lines, each corresponding to degree 28 field with Galois group SU_3(3)=G_2(2). The lines are sorted by increasing discriminant. Each line has the form {Identifying Number, Defining polynomial in polredabs'd form, list of (u,v)'s from which the field comes, list of new (p,q)'s from which the field comes, list of new (a,b)'s from which the field comes, ord[2,disc], ord[3,disc]} Here a pair is new if it is not the image of a (u,v) *) fields376 = {{1, 4 + 32*x + 24*x^2 - 192*x^3 - 216*x^4 - 240*x^5 + 1800*x^6 + 672*x^7 - 1116*x^8 - 4680*x^9 + 1752*x^10 + 3768*x^11 - 1068*x^12 + 3072*x^13 - 4920*x^14 + 1464*x^15 - 657*x^16 - 756*x^17 + 2478*x^18 - 2292*x^19 + 2040*x^20 - 1440*x^21 + 798*x^22 - 420*x^23 + 165*x^24 - 60*x^25 + 18*x^26 - 4*x^27 + x^28, {{-4, -3}, {-1/2, 1}, {1/2, 3}, {4, -3}, {-32, 1}, {-32/81,49/81}}, {{1, 1/2}}, {{{-27/4, -1/2}}}, 66, 46}, {2, 593 - 1364*x - 4998*x^2 + 20340*x^3 - 27621*x^4 + 13440*x^5 + 6252*x^6 - 4656*x^7 - 12315*x^8 + 15564*x^9 + 2646*x^10 - 17676*x^11 + 13503*x^12 - 3408*x^13 + 1176*x^14 - 3504*x^15 + 3807*x^16 - 3036*x^17 + 2766*x^18 - 2436*x^19 + 1893*x^20 - 1296*x^21 + 780*x^22 - 384*x^23 + 171*x^24 - 60*x^25 + 18*x^26 - 4*x^27 + x^28, {{8, 9}, {8, 1}, {2, 1}, {-8, 81}}, {{40/49, -7/200}}, {}, 84, 36}, {3, 11038 + 58756*x - 20700*x^2 + 84924*x^3 + 8874*x^4 - 191412*x^5 + 53130*x^6 + 13152*x^7 + 11376*x^8 + 15684*x^9 + 20760*x^10 - 10152*x^11 - 33021*x^12 + 42264*x^13 - 37440*x^14 + 19680*x^15 - 1560*x^16 - 7092*x^17 + 11448*x^18 - 9396*x^19 + 4914*x^20 - 1656*x^21 + 342*x^22 - 144*x^23 + 156*x^24 - 96*x^25 + 36*x^26 - 8*x^27 + x^28, {{16, 1}, {1, 1}}, {{-8, 1/64}}, {}, 60, 54}, {4, -18096 + 56640*x - 129168*x^2 + 228528*x^3 - 316008*x^4 + 396720*x^5 - 416520*x^6 + 394416*x^7 - 336312*x^8 + 245340*x^9 - 166428*x^10 + 96192*x^11 - 46377*x^12 + 21024*x^13 - 3402*x^14 - 3924*x^15 + 6228*x^16 - 7236*x^17 + 4950*x^18 - 2592*x^19 + 936*x^20 + 216*x^21 - 414*x^22 + 252*x^23 - 114*x^24 + 12*x^25 + 18*x^26 - 8*x^27 + x^28, {{1/3, 1/3}}, {{-1/9, 3/4}}, {}, 54, 58}, {5, 1 - 28*x + 276*x^2 - 1260*x^3 + 2433*x^4 + 504*x^5 - 7596*x^6 - 576*x^7 + 23871*x^8 + 3180*x^9 - 41388*x^10 - 30252*x^11 + 6543*x^12 - 7152*x^13 - 24120*x^14 - 4800*x^15 + 3567*x^16 - 5316*x^17 - 2868*x^18 + 1308*x^19 + 15*x^20 - 648*x^21 + 228*x^22 - 15*x^24 - 12*x^25 + 12*x^26 - 4*x^27 + x^28, {{12, 6}, {4/9, -2/9}, {3/16, 3/16}}, {{1/2, 1}}, {}, 70, 48}, {6, -41526 - 14364*x + 123120*x^2 - 118476*x^3 - 36315*x^4 + 95904*x^5 - 71064*x^6 + 68688*x^7 - 17496*x^8 + 3348*x^9 + 27216*x^10 + 3780*x^11 - 28233*x^12 - 6192*x^13 - 1728*x^14 + 13104*x^15 + 3330*x^16 - 3780*x^17 - 2016*x^18 + 396*x^19 + 387*x^20 + 336*x^21 - 264*x^22 + 12*x^24 + 12*x^25 - 4*x^27 + x^28, {{16, 27}, {-2, -9/2}, {-1/32, 27/32}}, {}, {{{-1024/7225, -27/85}}}, 76, 46}, {7, -4 - 368*x - 2808*x^2 - 10656*x^3 - 27342*x^4 - 55404*x^5 - 93852*x^6 - 130860*x^7 - 149472*x^8 - 148188*x^9 - 134790*x^10 - 110808*x^11 - 88110*x^12 - 77040*x^13 - 61020*x^14 - 36504*x^15 - 21879*x^16 - 12744*x^17 - 2442*x^18 - 312*x^19 - 1971*x^20 - 504*x^21 + 360*x^22 - 108*x^23 - 81*x^24 + 36*x^25 - 4*x^27 + x^28, {{16/3, 1}, {9/4, -1/2}, {1/12, 1/2}, {3, 1}}, {}, {{{1/16, -1/12}}}, 58, 58}, {8, 1 - 4*x + 6*x^2 - 276*x^3 + 1713*x^4 - 3600*x^5 + 1140*x^6 + 5808*x^7 + 1233*x^8 - 29004*x^9 + 20994*x^10 + 39348*x^11 - 32919*x^12 - 46728*x^13 + 37308*x^14 + 27552*x^15 - 13677*x^16 - 14532*x^17 + 606*x^18 + 4044*x^19 + 2703*x^20 - 1176*x^21 - 408*x^22 - 192*x^23 + 117*x^24 + 12*x^25 + 6*x^26 - 4*x^27 + x^28, {{-8, -9}, {1, 9/2}, {-1/8, 9/8}}, {{-1, 1}}, {{{8/9, 4/3}}}, 84, 42}, {9, 2968 - 18880*x + 50544*x^2 - 81888*x^3 + 100104*x^4 - 38784*x^5 - 187584*x^6 + 453888*x^7 - 610656*x^8 + 629424*x^9 - 496488*x^10 + 271296*x^11 - 3012*x^12 - 222384*x^13 + 342528*x^14 - 356640*x^15 + 296802*x^16 - 213792*x^17 + 133980*x^18 - 73584*x^19 + 35046*x^20 - 14280*x^21 + 5136*x^22 - 1560*x^23 + 462*x^24 - 108*x^25 + 30*x^26 - 4*x^27 + x^28, {{-8, 9}, {-2/9, 1/9}}, {}, {{{4, -1}}}, 84, 42}, {10, -48347 + 79840*x + 49938*x^2 - 76368*x^3 - 154173*x^4 + 144528*x^5 + 164988*x^6 - 132624*x^7 - 221931*x^8 + 170040*x^9 + 172362*x^10 - 121848*x^11 - 134013*x^12 + 105792*x^13 + 58836*x^14 - 73848*x^15 - 2226*x^16 + 29088*x^17 - 10236*x^18 - 3720*x^19 + 3822*x^20 - 792*x^21 - 504*x^22 + 528*x^23 - 219*x^24 + 24*x^25 + 18*x^26 - 8*x^27 + x^28, {{1/4, 3/4}, {16/27, 1/9}}, {{-8/9, 3/4}}, {{{108/49, 4/7}}}, 78, 46}, {11, -368 - 3136*x - 9912*x^2 - 13968*x^3 - 6612*x^4 + 11184*x^5 + 30720*x^6 + 1728*x^7 - 64524*x^8 - 3408*x^9 + 77256*x^10 - 30144*x^11 - 46584*x^12 + 47496*x^13 - 6672*x^14 - 23280*x^15 + 25002*x^16 - 4008*x^17 - 12618*x^18 + 8292*x^19 + 1689*x^20 - 3168*x^21 + 480*x^22 + 456*x^23 - 150*x^24 + 6*x^26 - 4*x^27 + x^28, {{-2, -2}, {2, 6}, {-1/4, 3/4}}, {}, {}, 78, 46}, {12, -926 + 11452*x - 64248*x^2 + 215244*x^3 - 483174*x^4 + 761592*x^5 - 854844*x^6 + 686424*x^7 - 305028*x^8 - 198024*x^9 + 529860*x^10 - 394320*x^11 + 34410*x^12 + 115644*x^13 - 74064*x^14 + 38124*x^15 - 10836*x^16 - 13428*x^17 + 7596*x^18 - 2196*x^19 + 2442*x^20 - 72*x^21 - 216*x^22 + 48*x^23 - 81*x^24 + 18*x^25 - 2*x^27 + x^28, {{-32, -27}, {-1/2, 9/4}, {1/16, 27/16}, {8/27, -1/27}}, {{928/1225, 35/1682}}, {}, 78, 46}, {13, -50000 + 242000*x - 518400*x^2 + 720720*x^3 - 559152*x^4 + 648*x^5 + 468000*x^6 - 454176*x^7 + 224856*x^8 + 4308*x^9 - 202092*x^10 + 155520*x^11 + 48096*x^12 - 105066*x^13 + 16686*x^14 + 32868*x^15 - 18477*x^16 + 3564*x^17 + 1362*x^18 - 2946*x^19 + 2025*x^20 - 288*x^21 - 306*x^22 + 162*x^23 - 45*x^24 + 18*x^25 - 4*x^27 + x^28, {}, {{2/3, -3/4}}, {}, 40, 70}, {14, 4 - 64*x + 72*x^2 - 1908*x^4 + 2304*x^5 - 72*x^6 - 4320*x^7 + 12384*x^8 - 1200*x^9 - 12480*x^10 + 9792*x^11 - 6156*x^12 - 5040*x^13 + 14292*x^14 - 3528*x^15 - 3159*x^16 + 3960*x^17 - 3606*x^18 - 552*x^19 + 1881*x^20 - 432*x^21 - 72*x^22 + 252*x^23 - 18*x^24 + 18*x^26 - 4*x^27 + x^28, {{9/2, 1}, {4/3, -1/3}, {1/6, 1/3}, {32/9, 1}}, {}, {{{-2187/64, -1/8}}}, 66, 54}, {15, 4968 - 12936*x - 13794*x^2 + 65304*x^3 - 61019*x^4 - 56280*x^5 + 55584*x^6 + 5704*x^7 - 19254*x^8 + 75984*x^9 - 54530*x^10 - 18480*x^11 + 3327*x^12 + 18832*x^13 + 47664*x^14 - 51984*x^15 - 25916*x^16 + 27480*x^17 + 4506*x^18 - 1640*x^19 + 3*x^20 - 1848*x^21 + 16*x^22 + 456*x^23 - 6*x^24 - 32*x^25 - 6*x^26 + x^28, {{9/32, 9/32}}, {}, {}, 98, 34}, {16, 576 - 1216*x - 13104*x^2 - 43200*x^3 - 63639*x^4 - 83448*x^5 - 135792*x^6 - 228960*x^7 - 129384*x^8 + 77472*x^9 + 126336*x^10 + 97704*x^11 + 8208*x^12 - 6912*x^13 - 13680*x^14 + 5472*x^15 + 15930*x^16 + 1080*x^17 - 288*x^18 - 1920*x^19 + 936*x^20 - 72*x^23 + 72*x^24 + x^28, {{6, 12}, {-3/4, -3/4}, {-2/9, 4/9}, {-32, 9}}, {}, {}, 76, 48}, {17, -977 - 788*x + 666*x^2 - 6168*x^3 - 24537*x^4 + 94104*x^5 - 99996*x^6 + 335568*x^7 - 488061*x^8 - 484812*x^9 + 1085166*x^10 - 309816*x^11 + 142635*x^12 - 417264*x^13 + 197496*x^14 + 20832*x^15 + 44853*x^16 - 34092*x^17 + 6*x^18 - 6888*x^19 + 3933*x^20 + 1176*x^21 - 732*x^22 + 144*x^23 - 87*x^24 + 12*x^25 + 18*x^26 - 8*x^27 + x^28, {{4, 3}}, {}, {{{8/9, -2/3}}}, 76, 48}, {18, 768 + 2560*x - 2880*x^2 - 14688*x^3 + 32472*x^4 - 58032*x^5 + 115128*x^6 - 145584*x^7 + 62604*x^8 - 29664*x^9 + 87204*x^10 - 53028*x^11 + 6876*x^12 - 29340*x^13 + 28674*x^14 + 2466*x^15 - 1197*x^16 - 4032*x^17 + 1080*x^18 - 474*x^19 - 360*x^20 + 720*x^21 + 36*x^22 - 180*x^23 - 45*x^24 + 54*x^25 - 6*x^27 + x^28, {}, {{1/4, 1}}, {{{-1/12, 1/2}}}, 42, 70}, {19, -8 - 128*x - 336*x^2 + 576*x^3 - 312*x^4 - 7968*x^5 + 21264*x^6 - 15360*x^7 - 3444*x^8 + 4032*x^9 + 18552*x^10 + 16128*x^11 - 172812*x^12 + 288384*x^13 - 209712*x^14 - 3744*x^15 + 139134*x^16 - 108864*x^17 + 12588*x^18 + 33024*x^19 - 20814*x^20 + 1176*x^21 + 3468*x^22 - 1152*x^23 - 117*x^24 + 96*x^25 + 6*x^26 - 8*x^27 + x^28, {}, {}, {{{-1/6, -3/2}}}, 96, 36}, {20, 16421 + 41264*x + 10866*x^2 + 83040*x^3 + 149445*x^4 - 33144*x^5 + 255972*x^6 - 39192*x^7 + 169761*x^8 + 43416*x^9 + 12726*x^10 + 148584*x^11 - 114147*x^12 + 187296*x^13 - 150696*x^14 + 154704*x^15 - 113655*x^16 + 90336*x^17 - 55590*x^18 + 34272*x^19 - 16215*x^20 + 7128*x^21 - 2196*x^22 + 456*x^23 + 21*x^24 - 72*x^25 + 30*x^26 - 8*x^27 + x^28, {{1/2, 1/2}}, {}, {{{1458/169, 4/13}}}, 96, 36}, {21, -163209 - 25844*x - 194994*x^2 + 1555740*x^3 - 587211*x^4 - 5359560*x^5 + 11623572*x^6 - 11620008*x^7 + 6210633*x^8 - 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148359869360*x + 228628584144*x^2 + 545634677232*x^3 - 1063927091880*x^4 - 14679324432*x^5 + 672707021364*x^6 - 99643662000*x^7 - 215603731107*x^8 + 24824119428*x^9 + 51279272418*x^10 - 296151948*x^11 - 9872237187*x^12 - 806552784*x^13 + 1319285952*x^14 + 219651120*x^15 - 111519126*x^16 - 33317640*x^17 + 6177348*x^18 + 2533368*x^19 - 163602*x^20 - 83232*x^21 - 2340*x^22 + 2304*x^23 - 1287*x^24 + 324*x^25 + 18*x^26 - 12*x^27 + x^28, {}, {{1/4, -32}}, {}, 100, 70}, {369, 1964978 - 1013386312*x - 3146603256*x^2 - 10627600320*x^3 - 17161275069*x^4 - 15191856504*x^5 - 16314745932*x^6 - 14415756264*x^7 - 1106818416*x^8 + 764582736*x^9 - 1278809772*x^10 + 3525214680*x^11 - 951907023*x^12 - 694174032*x^13 + 907304544*x^14 - 966829968*x^15 + 487316718*x^16 - 212815800*x^17 + 56854680*x^18 - 12458640*x^19 + 1126215*x^20 + 109224*x^21 - 96156*x^22 + 21816*x^23 - 2844*x^24 + 144*x^25 + 36*x^26 - 8*x^27 + x^28, {}, {{-2, -1/2}}, {{{1/3, 2}}}, 100, 70}, {370, -2097152 - 162529280*x - 1049296896*x^2 - 5126012928*x^3 - 12206596608*x^4 + 9878519808*x^5 + 22519719936*x^6 - 61405396992*x^7 + 30458723328*x^8 - 8561577984*x^9 + 8984561664*x^10 - 3558242304*x^11 + 1481793984*x^12 - 837536256*x^13 + 143479296*x^14 - 109785600*x^15 + 56953440*x^16 - 5553792*x^17 + 3673920*x^18 - 2460480*x^19 + 306126*x^20 - 64224*x^21 + 55224*x^22 - 9504*x^23 + 846*x^24 - 504*x^25 + 108*x^26 - 8*x^27 + x^28, {}, {{1/4, -8}}, {}, 100, 70}, {371, -919135239413 - 3112315778980*x + 5744136506238*x^2 + 24255234184788*x^3 + 26549795819241*x^4 + 13896567309240*x^5 + 5226503050404*x^6 + 2024447489208*x^7 + 843291085257*x^8 + 467423815740*x^9 + 168733346718*x^10 + 45995654340*x^11 + 19331094123*x^12 + 2572118064*x^13 + 1145500488*x^14 + 501961968*x^15 - 34882695*x^16 + 47061828*x^17 - 2006574*x^18 - 413652*x^19 + 882531*x^20 - 230472*x^21 + 46980*x^22 - 4104*x^23 + 27*x^24 + 36*x^25 + 18*x^26 - 4*x^27 + x^28, {}, {{2/3, -3/2}}, {{{1/1323, -2/21}}}, 100, 70}, {372, 7610949476258 - 46106556136136*x + 115164461644452*x^2 - 164612203237080*x^3 + 158560938561240*x^4 - 113992338027960*x^5 + 63579232957140*x^6 - 27139751930664*x^7 + 8473923749925*x^8 - 1571878232796*x^9 - 123310412466*x^10 + 218269344060*x^11 - 87750594027*x^12 + 20299944816*x^13 - 1636215552*x^14 - 594632016*x^15 + 199252764*x^16 - 6307200*x^17 - 10402536*x^18 + 2877600*x^19 - 66582*x^20 - 152280*x^21 + 35100*x^22 - 3240*x^23 + 1701*x^24 - 540*x^25 + 54*x^26 - 4*x^27 + x^28, {}, {{587/588, 344064/344569}}, {}, 100, 70}, {373, 126544687696 + 90218283328*x + 43806505392*x^2 + 402039157824*x^3 + 116623548360*x^4 + 33945299136*x^5 + 143531071632*x^6 + 55647100512*x^7 - 123387298146*x^8 - 42737545896*x^9 - 758746518*x^10 + 36085546152*x^11 - 1423042551*x^12 - 505664208*x^13 - 956946240*x^14 - 172299312*x^15 - 118909152*x^16 + 6633504*x^17 - 4912476*x^18 + 222240*x^19 + 65574*x^20 - 21744*x^21 + 864*x^22 + 5328*x^23 - 1350*x^24 + 72*x^25 + 18*x^26 - 8*x^27 + x^28, {}, {{5/8, 16/25}}, {}, 106, 70}, {374, -4005979460288 - 3617283753728*x + 1191407456448*x^2 + 2781012397824*x^3 + 1319691192768*x^4 - 2641883922432*x^5 - 706738756608*x^6 + 1799623288224*x^7 - 99330908346*x^8 - 613147324776*x^9 + 160406867226*x^10 + 103789686888*x^11 - 46334529567*x^12 - 8679370320*x^13 + 7275984480*x^14 - 278709552*x^15 - 746972568*x^16 + 161047584*x^17 + 34703724*x^18 - 13469280*x^19 + 1061010*x^20 + 293616*x^21 - 70416*x^22 + 4464*x^23 - 486*x^24 + 72*x^25 + 18*x^26 - 8*x^27 + x^28, {}, {{5/8, -32/25}}, {{{1/8255574, 32/1173}}}, 106, 70}, {375, 2737529765986 - 1665356693680*x - 275182699734*x^2 + 2115122061996*x^3 - 2574406365705*x^4 + 1090095036696*x^5 + 118000120536*x^6 - 209280124944*x^7 + 29407389984*x^8 + 6042231240*x^9 + 8414341302*x^10 - 7197481692*x^11 + 1906230483*x^12 - 343442160*x^13 + 220185216*x^14 - 90706752*x^15 + 675522*x^16 + 9275904*x^17 - 2512266*x^18 + 509172*x^19 - 235035*x^20 + 38232*x^21 + 21384*x^22 - 9072*x^23 + 396*x^24 + 360*x^25 - 54*x^26 - 4*x^27 + x^28, {}, {{-1/2, -2}}, {{{1/54, 4/3}}}, 106, 70}, {376, -636588373559 + 958183268156*x - 829466406054*x^2 - 668675184372*x^3 + 2537545393395*x^4 - 3290738387256*x^5 + 1814061486132*x^6 + 183159536328*x^7 - 994271562171*x^8 + 684580096356*x^9 - 191530157874*x^10 - 23308569612*x^11 + 36214604919*x^12 - 9387834192*x^13 - 1289308968*x^14 + 1336752432*x^15 - 222016257*x^16 - 58920588*x^17 + 28583454*x^18 - 1448796*x^19 - 1459755*x^20 + 303336*x^21 + 25956*x^22 - 15768*x^23 + 819*x^24 + 396*x^25 - 54*x^26 - 4*x^27 + x^28, {}, {}, {{{2/3, -1}}}, 106, 70}}; (* fieldsmm contains 42 lines, each corresponding to a degree 28 field with Galois group of index 1 or 2 in SU_3(3).2 = G_2(2). Each field comes from one specialization point in the Malle-Matzat cover. The lines are sorted by increasing discriminant. Each line has the form {Identifying Number, specialization point, square-free part of the discriminant of the associated quadratic algebra, Defining polynomial in polredabs'd form, ord[2,disc], ord[3,disc]} *) fieldsfrommm = {{1, 243, -6, -564 - 5952*x + 13680*x^2 - 14976*x^3 + 61488*x^4 - 127872*x^5 + 42672*x^6 + 134736*x^7 - 25344*x^8 - 391176*x^9 + 533988*x^10 - 100656*x^11 - 380928*x^12 + 354720*x^13 - 20736*x^14 - 142920*x^15 + 78723*x^16 + 3636*x^17 - 19362*x^18 + 8220*x^19 - 777*x^20 - 1176*x^21 + 876*x^22 - 192*x^23 - 87*x^24 + 60*x^25 - 6*x^26 - 4*x^27 + x^28, 72, 46}, {2, -1, -2, -9 - 32*x + 42*x^2 + 276*x^3 - 837*x^4 - 5892*x^5 - 9012*x^6 + 7644*x^7 + 42297*x^8 + 47772*x^9 - 8190*x^10 - 73104*x^11 - 80637*x^12 - 48960*x^13 - 22656*x^14 - 2976*x^15 + 10377*x^16 + 10128*x^17 + 6318*x^18 + 4188*x^19 + 1473*x^20 + 420*x^21 + 180*x^22 - 60*x^23 + 15*x^24 - 12*x^25 + 6*x^26 + x^28, 72, 48}, {3, 2, -2, -3984 + 14627*x - 63090*x^2 + 237027*x^3 - 569583*x^4 + 933324*x^5 - 1079628*x^6 + 825552*x^7 - 238344*x^8 - 363759*x^9 + 640578*x^10 - 520155*x^11 + 221331*x^12 + 17268*x^13 - 112728*x^14 + 103116*x^15 - 52884*x^16 + 9057*x^17 + 8130*x^18 - 7095*x^19 + 2547*x^20 - 96*x^21 - 348*x^22 + 132*x^23 + 12*x^24 - 45*x^25 + 30*x^26 - 9*x^27 + x^28, 72, 48}, {4, 57122, -2, -3984 + 14627*x - 63090*x^2 + 237027*x^3 - 569583*x^4 + 933324*x^5 - 1079628*x^6 + 825552*x^7 - 238344*x^8 - 363759*x^9 + 640578*x^10 - 520155*x^11 + 221331*x^12 + 17268*x^13 - 112728*x^14 + 103116*x^15 - 52884*x^16 + 9057*x^17 + 8130*x^18 - 7095*x^19 + 2547*x^20 - 96*x^21 - 348*x^22 + 132*x^23 + 12*x^24 - 45*x^25 + 30*x^26 - 9*x^27 + x^28, 72, 48}, {5, -14641/243, -1, -4 - 368*x - 2808*x^2 - 10656*x^3 - 27342*x^4 - 55404*x^5 - 93852*x^6 - 130860*x^7 - 149472*x^8 - 148188*x^9 - 134790*x^10 - 110808*x^11 - 88110*x^12 - 77040*x^13 - 61020*x^14 - 36504*x^15 - 21879*x^16 - 12744*x^17 - 2442*x^18 - 312*x^19 - 1971*x^20 - 504*x^21 + 360*x^22 - 108*x^23 - 81*x^24 + 36*x^25 - 4*x^27 + x^28, 58, 58}, {6, 1/2, 1, -14634 - 35108*x - 6420*x^2 + 35832*x^3 + 8235*x^4 - 56496*x^5 - 38904*x^6 + 39912*x^7 + 17676*x^8 - 50508*x^9 + 11280*x^10 - 312*x^11 + 4335*x^12 - 3096*x^13 - 5064*x^14 + 6648*x^15 - 1914*x^16 + 972*x^17 - 1188*x^18 + 768*x^19 + 105*x^20 - 168*x^21 + 72*x^22 - 48*x^23 + 48*x^24 - 12*x^25 + x^28, 84, 42}, {7, -8, -2, 48 - 96*x + 2160*x^2 - 9744*x^3 + 22152*x^4 - 95040*x^5 + 181824*x^6 + 31296*x^7 - 223896*x^8 + 56848*x^9 + 100360*x^10 + 75624*x^11 - 22524*x^12 - 86016*x^13 + 13176*x^14 + 28248*x^15 - 3108*x^16 - 2880*x^17 - 1160*x^18 - 296*x^19 + 48*x^20 + 96*x^21 + 48*x^22 - 36*x^23 + 12*x^25 - 6*x^26 - 2*x^27 + x^28, 78, 46}, {8, -9/16, -1, 54 - 540*x + 1296*x^2 + 324*x^3 - 2106*x^4 - 6480*x^5 + 14904*x^6 + 1944*x^7 - 22842*x^8 + 10368*x^9 + 7776*x^10 - 1728*x^11 + 3402*x^12 - 12528*x^13 - 2160*x^14 + 16308*x^15 - 5238*x^16 - 7236*x^17 + 6138*x^18 - 684*x^19 - 990*x^20 - 468*x^21 + 1404*x^22 - 1080*x^23 + 531*x^24 - 198*x^25 + 54*x^26 - 10*x^27 + x^28, 60, 58}, {9, 4, -3, 144 - 6976*x + 28584*x^2 - 43200*x^3 + 46521*x^4 - 68976*x^5 + 86472*x^6 - 69552*x^7 + 47034*x^8 - 38736*x^9 + 31584*x^10 - 20232*x^11 + 7641*x^12 - 6912*x^13 + 6840*x^14 + 1368*x^15 - 2214*x^16 - 2160*x^17 - 288*x^18 + 960*x^19 + 234*x^20 - 72*x^23 - 36*x^24 + x^28, 60, 58}, {10, -1/8, -1, 576 - 1216*x - 13104*x^2 - 43200*x^3 - 63639*x^4 - 83448*x^5 - 135792*x^6 - 228960*x^7 - 129384*x^8 + 77472*x^9 + 126336*x^10 + 97704*x^11 + 8208*x^12 - 6912*x^13 - 13680*x^14 + 5472*x^15 + 15930*x^16 + 1080*x^17 - 288*x^18 - 1920*x^19 + 936*x^20 - 72*x^23 + 72*x^24 + x^28, 76, 48}, {11, 81/32, -1, -144 - 544*x - 984*x^2 - 1980*x^3 - 4326*x^4 - 7680*x^5 - 10488*x^6 - 19488*x^7 - 19812*x^8 - 10032*x^9 - 33804*x^10 - 6492*x^11 - 9090*x^12 - 31272*x^13 + 31812*x^14 - 35292*x^15 + 19926*x^16 - 2496*x^17 - 4992*x^18 + 8496*x^19 - 3432*x^20 - 72*x^21 + 1128*x^22 - 696*x^23 - 48*x^24 + 120*x^25 - 12*x^26 - 6*x^27 + x^28, 78, 48}, {12, 1/4, 3, -841487 + 3315500*x - 6096006*x^2 + 5982480*x^3 - 2384865*x^4 - 1075356*x^5 + 1759728*x^6 - 517908*x^7 - 609435*x^8 + 1113792*x^9 - 1154130*x^10 + 896724*x^11 - 630333*x^12 + 400680*x^13 - 212400*x^14 + 98328*x^15 - 36777*x^16 + 10980*x^17 - 3450*x^18 + 768*x^19 - 279*x^20 - 108*x^21 + 216*x^22 - 180*x^23 + 111*x^24 - 48*x^25 + 18*x^26 - 4*x^27 + x^28, 60, 60}, {13, 9, -2, 11701 - 11636*x + 15948*x^2 + 37476*x^3 - 118773*x^4 - 67752*x^5 + 42552*x^6 + 417060*x^7 + 420327*x^8 + 12036*x^9 - 147912*x^10 - 82872*x^11 - 35865*x^12 - 33120*x^13 + 50112*x^14 + 59616*x^15 - 8649*x^16 - 32220*x^17 - 9780*x^18 + 6492*x^19 + 4725*x^20 + 936*x^21 - 504*x^22 - 612*x^23 - 27*x^24 + 108*x^25 - 8*x^27 + x^28, 64, 58}, {14, 3/4, 3, 196854 - 145230*x - 901908*x^2 - 417105*x^3 - 355527*x^4 + 848448*x^5 + 2002680*x^6 + 808938*x^7 + 1129032*x^8 - 434880*x^9 - 61866*x^10 + 99927*x^11 - 202131*x^12 + 408312*x^13 - 231624*x^14 + 193932*x^15 - 112122*x^16 + 45018*x^17 - 15840*x^18 + 2853*x^19 + 2331*x^20 - 1620*x^21 + 1260*x^22 - 378*x^23 + 216*x^24 - 36*x^25 + 18*x^26 - x^27 + x^28, 52, 66}, {15, 27/2, -3, 678 + 9048*x + 25740*x^2 - 10944*x^3 - 159714*x^4 - 303480*x^5 - 311568*x^6 - 277728*x^7 - 446688*x^8 - 291984*x^9 + 161076*x^10 - 365760*x^11 + 223044*x^12 - 213816*x^13 + 233172*x^14 - 123408*x^15 - 19494*x^16 + 68040*x^17 - 25656*x^18 - 10104*x^19 + 10752*x^20 - 2088*x^21 - 1416*x^22 + 912*x^23 - 183*x^24 - 36*x^25 + 30*x^26 - 8*x^27 + x^28, 84, 46}, {16, -48, -3, 4014 + 20268*x + 14418*x^2 - 38070*x^3 + 42849*x^4 + 95580*x^5 - 299106*x^6 - 60804*x^7 + 469152*x^8 - 343332*x^9 + 18522*x^10 + 218916*x^11 - 252774*x^12 + 103680*x^13 + 32022*x^14 - 54360*x^15 + 25398*x^16 - 5076*x^17 + 414*x^18 - 450*x^19 - 1179*x^20 + 1800*x^21 - 342*x^22 - 432*x^23 + 162*x^24 + 36*x^25 - 18*x^26 - 2*x^27 + x^28, 54, 66}, {17, -3, -3, 15072 - 223104*x + 1201824*x^2 - 4304736*x^3 + 12250368*x^4 - 26988768*x^5 + 47412504*x^6 - 68353344*x^7 + 80502768*x^8 - 77222736*x^9 + 60305544*x^10 - 37776024*x^11 + 18255420*x^12 - 5975712*x^13 + 500904*x^14 + 837720*x^15 - 632160*x^16 + 261720*x^17 - 67698*x^18 + 12600*x^19 - 1800*x^20 + 828*x^21 - 288*x^22 + 234*x^23 - 99*x^24 + 36*x^25 - 2*x^27 + x^28, 54, 66}, {18, 625/576, -1, 901896 - 2250600*x + 3055536*x^2 - 4784256*x^3 + 2455344*x^4 - 4257576*x^5 + 141444*x^6 - 2007252*x^7 - 832275*x^8 + 63621*x^9 - 144621*x^10 + 763425*x^11 + 298647*x^12 + 531126*x^13 + 215658*x^14 + 194760*x^15 + 62811*x^16 + 44019*x^17 + 8019*x^18 + 4941*x^19 + 963*x^20 - 324*x^21 + 234*x^22 - 18*x^23 + 27*x^24 + 27*x^25 - 9*x^26 - x^27 + x^28, 54, 66}, {19, 2401/192, -1, -758 + 6332*x - 24462*x^2 + 88884*x^3 - 255222*x^4 + 629892*x^5 - 1350054*x^6 + 2601648*x^7 - 4388571*x^8 + 5633448*x^9 - 7466811*x^10 + 9099216*x^11 - 8669349*x^12 + 6087780*x^13 - 2894472*x^14 + 735408*x^15 + 138321*x^16 - 252144*x^17 + 136119*x^18 - 42852*x^19 + 3645*x^20 + 3420*x^21 - 2196*x^22 + 792*x^23 - 153*x^24 + 9*x^26 - 4*x^27 + x^28, 48, 70}, {20, 2401, -6, -64 - 128*x + 1152*x^2 + 3072*x^3 - 16032*x^4 + 2880*x^5 + 45600*x^6 - 37248*x^7 - 28224*x^8 + 50304*x^9 - 95808*x^10 + 153360*x^11 - 15132*x^12 - 223224*x^13 + 314136*x^14 - 266784*x^15 + 157290*x^16 - 24192*x^17 - 52272*x^18 + 44784*x^19 - 12168*x^20 - 1572*x^21 + 924*x^22 + 756*x^23 - 642*x^24 + 192*x^25 - 18*x^26 - 4*x^27 + x^28, 64, 60}, {21, 1/243, 2, 19888 + 109184*x + 404352*x^2 - 341760*x^3 + 2023464*x^4 - 942624*x^5 + 3811200*x^6 + 1480800*x^7 + 1359468*x^8 + 3373056*x^9 + 964368*x^10 + 1403856*x^11 + 933822*x^12 + 449784*x^13 + 394560*x^14 + 157248*x^15 + 57582*x^16 + 45072*x^17 + 21060*x^18 - 5400*x^19 + 684*x^20 + 1848*x^21 - 732*x^22 - 252*x^23 - 6*x^24 + 24*x^25 - 4*x^27 + x^28, 72, 58}, {22, -16/9, -1, 126641 + 843320*x + 735534*x^2 + 866016*x^3 + 5743791*x^4 + 1318428*x^5 - 393984*x^6 + 933912*x^7 - 240633*x^8 + 111000*x^9 + 44850*x^10 + 607572*x^11 + 401139*x^12 - 297216*x^13 - 11232*x^14 + 95868*x^15 - 32688*x^16 + 4176*x^17 + 7836*x^18 - 3936*x^19 + 846*x^20 - 468*x^21 + 144*x^22 + 252*x^23 - 207*x^24 + 36*x^25 + 18*x^26 - 8*x^27 + x^28, 60, 66}, {23, -1/48, -1, -9088 + 61888*x - 250560*x^2 + 552672*x^3 - 800604*x^4 + 499968*x^5 - 568872*x^6 + 369576*x^7 - 240480*x^8 + 79584*x^9 - 119904*x^10 + 414576*x^11 - 610452*x^12 + 651024*x^13 - 425304*x^14 + 18288*x^15 + 229176*x^16 - 258840*x^17 + 168612*x^18 - 70260*x^19 + 19080*x^20 - 1224*x^21 - 1548*x^22 + 828*x^23 - 288*x^24 + 36*x^25 - 4*x^27 + x^28, 54, 70}, {24, 4/3, -1, 104976 - 1726272*x + 6980904*x^2 - 10497600*x^3 + 9454401*x^4 - 9202896*x^5 + 10095192*x^6 - 8223120*x^7 + 4675806*x^8 - 3137616*x^9 + 2558304*x^10 - 1218888*x^11 + 245673*x^12 - 186624*x^13 + 184680*x^14 + 36936*x^15 - 55890*x^16 - 19440*x^17 - 2592*x^18 + 8640*x^19 + 2106*x^20 - 216*x^23 - 108*x^24 + x^28, 54, 70}, {25, -2, -6, 9216 - 217088*x - 907776*x^2 - 1382400*x^3 - 921024*x^4 + 32256*x^5 + 467712*x^6 + 345600*x^7 + 495936*x^8 + 619776*x^9 + 505344*x^10 + 137088*x^11 - 43632*x^12 - 55296*x^13 - 54720*x^14 + 10944*x^15 + 15120*x^16 + 8640*x^17 - 1152*x^18 - 3840*x^19 + 936*x^20 - 144*x^23 + 72*x^24 + x^28, 72, 60}, {26, 9/8, -1, 558414 - 2349324*x + 5254632*x^2 - 11703366*x^3 + 15636321*x^4 - 14976576*x^5 + 10757124*x^6 - 2752704*x^7 - 5816448*x^8 + 4762800*x^9 + 7827516*x^10 - 21306240*x^11 + 25685100*x^12 - 19331136*x^13 + 9055800*x^14 - 1729836*x^15 - 1048302*x^16 + 1039392*x^17 - 404028*x^18 + 41040*x^19 + 36072*x^20 - 19440*x^21 + 3276*x^22 + 648*x^23 - 486*x^24 + 108*x^25 - 6*x^27 + x^28, 76, 58}, {27, 1/9, 2, 1985972 + 4682512*x + 5460912*x^2 + 28083456*x^3 + 32102460*x^4 - 24813432*x^5 - 24869988*x^6 + 36988344*x^7 + 23767992*x^8 - 18170544*x^9 - 5400708*x^10 + 11141172*x^11 + 2647107*x^12 - 3346704*x^13 - 562248*x^14 + 946368*x^15 + 150426*x^16 - 150984*x^17 - 2100*x^18 + 21936*x^19 - 1080*x^20 - 1944*x^21 + 324*x^22 - 216*x^23 - 126*x^24 + 72*x^25 - 4*x^27 + x^28, 64, 66}, {28, -1/3, -1, 19008 + 108800*x + 366912*x^2 + 767232*x^3 + 1108368*x^4 + 1058688*x^5 + 610848*x^6 + 69120*x^7 - 365904*x^8 - 642816*x^9 - 500928*x^10 - 165312*x^11 + 49248*x^12 + 28800*x^13 + 33984*x^14 - 10368*x^15 + 30024*x^16 + 9504*x^17 - 216*x^18 - 1920*x^19 + 252*x^20 - 144*x^22 - 144*x^23 - 108*x^24 + x^28, 58, 70}, {29, -288, -2, 108 - 4568*x + 27144*x^2 - 83448*x^3 + 303843*x^4 - 969336*x^5 + 2438280*x^6 - 5154744*x^7 + 10025550*x^8 - 15752376*x^9 + 20119380*x^10 - 22011840*x^11 + 17000622*x^12 - 9058224*x^13 + 3288996*x^14 - 836280*x^15 + 147108*x^16 + 8064*x^17 - 44460*x^18 + 24048*x^19 - 4671*x^20 - 1080*x^21 + 336*x^22 + 72*x^23 + 54*x^24 - 48*x^25 + x^28, 78, 58}, {30, -2401/10368, -1, 7543952 - 41625160*x + 110033172*x^2 - 165619302*x^3 + 146137710*x^4 - 44515512*x^5 - 60089664*x^6 + 98813112*x^7 - 82906344*x^8 + 51039372*x^9 - 25820556*x^10 + 17559936*x^11 - 22297344*x^12 + 24878496*x^13 - 17379540*x^14 + 5905770*x^15 + 990870*x^16 - 2007072*x^17 + 784176*x^18 + 6180*x^19 - 108396*x^20 + 31692*x^21 + 1596*x^22 - 2340*x^23 + 132*x^24 + 132*x^25 - 18*x^26 - 5*x^27 + x^28, 76, 60}, {31, 32/81, 2, -16259 - 672934*x + 13483890*x^2 - 18293262*x^3 + 1444191*x^4 + 7972992*x^5 + 3924000*x^6 - 18930240*x^7 + 17632800*x^8 - 7092456*x^9 + 799440*x^10 - 1764000*x^11 + 5079486*x^12 - 5735892*x^13 + 4080204*x^14 - 2155212*x^15 + 1046169*x^16 - 521586*x^17 + 265014*x^18 - 124938*x^19 + 47565*x^20 - 13272*x^21 + 4020*x^22 - 1944*x^23 + 819*x^24 - 234*x^25 + 54*x^26 - 10*x^27 + x^28, 78, 60}, {32, -1/2, -3, 37748736 - 209715200*x - 915406848*x^2 - 1415577600*x^3 - 1070530560*x^4 - 540278784*x^5 - 349175808*x^6 - 304349184*x^7 - 4423680*x^8 + 158662656*x^9 + 129368064*x^10 + 47038464*x^11 - 552960*x^12 - 3538944*x^13 - 3502080*x^14 + 700416*x^15 + 1009152*x^16 + 138240*x^17 - 18432*x^18 - 61440*x^19 + 14976*x^20 - 576*x^23 + 288*x^24 + x^28, 84, 58}, {33, 3, -6, -38886723 + 87430644*x + 20609802*x^2 - 258191388*x^3 + 256324419*x^4 - 1129464*x^5 - 127775232*x^6 + 37268424*x^7 + 50959773*x^8 - 37103508*x^9 - 4163454*x^10 + 15083820*x^11 - 5799681*x^12 - 2029536*x^13 + 3087720*x^14 - 1270080*x^15 - 26325*x^16 + 267948*x^17 - 118962*x^18 + 8604*x^19 + 13149*x^20 - 5832*x^21 + 648*x^22 + 216*x^23 + 27*x^24 - 108*x^25 + 54*x^26 - 12*x^27 + x^28, 72, 66}, {34, 83521/1152, -1, -75012528 - 560997688*x - 1453576680*x^2 - 2034883332*x^3 - 2022180138*x^4 - 1726180128*x^5 - 1313161920*x^6 - 777372480*x^7 - 210122748*x^8 + 94014936*x^9 + 83853012*x^10 + 7612956*x^11 - 8816346*x^12 + 4548024*x^13 + 4798548*x^14 - 2063628*x^15 - 1499094*x^16 + 344304*x^17 + 170100*x^18 - 62148*x^19 - 34614*x^20 + 15624*x^21 + 4068*x^22 - 2880*x^23 + 360*x^24 + 36*x^25 - 6*x^27 + x^28, 76, 66}, {35, -24, -6, 41600 + 396800*x + 1395072*x^2 + 2376576*x^3 + 2434752*x^4 + 631296*x^5 - 4381056*x^6 - 5586048*x^7 - 5827104*x^8 + 1158528*x^9 + 3416160*x^10 - 497952*x^11 - 1269072*x^12 - 2802816*x^13 + 407520*x^14 + 257760*x^15 + 795456*x^16 + 14400*x^17 + 56400*x^18 - 74352*x^19 - 3528*x^20 - 4608*x^21 + 3888*x^22 + 576*x^23 + 234*x^24 - 72*x^25 - 18*x^26 - 2*x^27 + x^28, 78, 66}, {36, -1/288, -1, -21165131232 + 13455157728*x + 2659508640*x^2 - 10437765408*x^3 + 4042990872*x^4 + 1633258944*x^5 - 1744575408*x^6 - 3519072*x^7 - 163326888*x^8 + 437381424*x^9 - 69583392*x^10 - 176263344*x^11 + 96972228*x^12 - 2797920*x^13 - 13924368*x^14 + 7337088*x^15 - 3076920*x^16 + 733176*x^17 + 206712*x^18 - 202536*x^19 + 79110*x^20 - 32256*x^21 + 12204*x^22 - 3672*x^23 + 1134*x^24 - 324*x^25 + 72*x^26 - 12*x^27 + x^28, 78, 66}, {37, 8/9, 2, -50688 - 52736*x + 21600*x^2 + 443160*x^3 - 1725903*x^4 + 2471472*x^5 + 179568*x^6 - 2744784*x^7 + 1873692*x^8 + 943632*x^9 - 1831164*x^10 + 149616*x^11 + 812502*x^12 - 211680*x^13 - 212184*x^14 + 69048*x^15 + 37134*x^16 - 11232*x^17 - 5436*x^18 + 1128*x^19 + 117*x^20 + 144*x^21 + 396*x^22 - 72*x^23 - 90*x^24 + x^28, 78, 66}, {38, 1/3, 2, -49545216 + 413138944*x - 1439170560*x^2 + 2802843648*x^3 - 3438673920*x^4 + 2761555968*x^5 - 1393459200*x^6 + 348585984*x^7 - 53968896*x^8 + 106168320*x^9 - 76922880*x^10 + 35979264*x^11 - 26127360*x^12 + 2691072*x^13 + 2055168*x^14 + 1769472*x^15 + 1340928*x^16 - 304128*x^17 + 48384*x^18 + 30720*x^19 + 32256*x^20 + 1152*x^22 - 576*x^23 + 432*x^24 + x^28, 72, 70}, {39, 2/3, 2, 6718464 - 56733696*x + 225068544*x^2 - 335923200*x^3 + 289313856*x^4 - 234026496*x^5 + 235706112*x^6 - 193715712*x^7 + 95598144*x^8 - 50201856*x^9 + 40932864*x^10 - 17822592*x^11 + 2437776*x^12 - 1492992*x^13 + 1477440*x^14 + 295488*x^15 - 439344*x^16 - 77760*x^17 - 10368*x^18 + 34560*x^19 + 8424*x^20 - 432*x^23 - 216*x^24 + x^28, 72, 70}, {40, -1/24, -1, 419904 - 46656*x - 2624400*x^2 - 10497600*x^3 - 13062951*x^4 - 21222648*x^5 - 35726832*x^6 - 59976288*x^7 - 38193768*x^8 + 6275232*x^9 + 10233216*x^10 + 8019000*x^11 + 851472*x^12 - 186624*x^13 - 369360*x^14 + 147744*x^15 + 431082*x^16 + 9720*x^17 - 2592*x^18 - 17280*x^19 + 8424*x^20 - 216*x^23 + 216*x^24 + x^28, 76, 70}, {41, 3/2, -3, -329519340 + 596817936*x + 654056856*x^2 - 2599497360*x^3 + 2454592572*x^4 - 509048064*x^5 - 604047456*x^6 + 268396416*x^7 + 242062020*x^8 - 253117872*x^9 + 53752680*x^10 + 40747536*x^11 - 26158464*x^12 - 2834352*x^13 + 9330552*x^14 - 4072032*x^15 - 17820*x^16 + 784080*x^17 - 356616*x^18 + 42624*x^19 + 24084*x^20 - 11664*x^21 + 1296*x^22 + 432*x^23 - 27*x^24 - 108*x^25 + 54*x^26 - 12*x^27 + x^28, 84, 66}, {42, 625/96, -1, -254971 + 4234274*x - 21324078*x^2 + 23372424*x^3 + 62516817*x^4 - 166056696*x^5 + 65057544*x^6 + 245468304*x^7 - 464217705*x^8 + 360463854*x^9 - 49907130*x^10 - 186225768*x^11 + 222357051*x^12 - 131347584*x^13 + 35353152*x^14 + 10980432*x^15 - 17362089*x^16 + 9786870*x^17 - 3132570*x^18 + 390408*x^19 + 129339*x^20 - 64872*x^21 + 3960*x^22 + 5184*x^23 - 1899*x^24 + 234*x^25 + 18*x^26 - 8*x^27 + x^28, 78, 70}}; (* two more fields in a similar format to those above *) extra = {{1, -2, 1980 + 11024*x - 28872*x^2 - 72552*x^3 + 254658*x^4 - 112488*x^5 - 571908*x^6 + 1384872*x^7 - 1506558*x^8 + 309408*x^9 + 1721196*x^10 - 2982168*x^11 + 2440986*x^12 - 774840*x^13 - 634632*x^14 + 1134528*x^15 - 956928*x^16 + 575880*x^17 - 271020*x^18 + 100788*x^19 - 26829*x^20 + 2112*x^21 + 2934*x^22 - 2292*x^23 + 1041*x^24 - 336*x^25 + 78*x^26 - 12*x^27 + x^28, 78, 48}, {2, 6, 1775479 - 8538914*x + 13655610*x^2 - 4410330*x^3 - 2771817*x^4 - 19688364*x^5 + 43045212*x^6 - 21298668*x^7 - 17822799*x^8 + 19778406*x^9 + 3968502*x^10 - 11618082*x^11 + 2000571*x^12 + 3556212*x^13 - 1389348*x^14 - 638796*x^15 + 401316*x^16 + 52668*x^17 - 62424*x^18 + 1260*x^19 + 4464*x^20 + 372*x^21 - 528*x^22 - 180*x^23 + 129*x^24 + 30*x^25 - 18*x^26 - 2*x^27 + x^28, 78, 54}};