gap_nr := 136;
gl := 23*x^3 - 22*x^2*y + 5*x^2*z - 36*x^2*w - 15*x*y^2 + 48*x*y*z + 5*x*y*w
- 33*x*z^2 -70*x*z*w - 3*x*w^2 + 39*y^3 - 24*y^2*z - 31*y*z^2 - 5*y*z*w + y*w^2 
- 79*z^3 + 25*z^2*w -20*z*w^2 + w^3;
pol1 := -tt^3 - 6*tt^2 - 3*tt + 1;
pol2 := -2*tt^3 + 15*tt^2 - 69*tt + 20;
ch_pol_sm := tt^2 - 135*tt;
h1_gal := 1;
rk_pic := 1;
ord_gal := 18;
Elt := [ 6 ];
bp := [ 3, 19, 37, 1543 ];

gap_nr := 145;
gl := -5*x^3 - 3*x^2*y + 3*x^2*z + 6*x^2*w + 6*x*y^2 - 3*x*y*z + 6*x*y*w 
+6*x*z^2 + 9*x*z*w+ 3*x*w^2 - 3*y^3 + 3*y^2*w + y*z^2 - 5*y*z*w + 4*y*w^2
- 7*z^3 - 3*z^2*w +w^3;
pol1 := 3*tt^3 + 75;
pol2 := -2*tt^3 + 150*tt - 250;
ch_pol_sm := tt^2 - 135*tt;
h1_gal := 1;
rk_pic := 1;
ord_gal := 18;
Elt := [ 6 ];
bp := [ 2, 3, 5, 739 ];

gap_nr := 213;
gl := 5*x^3 + 21*x^2*y - 15*x^2*z - 21*x^2*w - 39*x*y^2 + 45*x*y*z - 15*x*y*w 
+ 30*x*z^2 + 6*x*z*w + 70*x*w^2 + 15*y^3 + 129*y^2*z + 15*y^2*w - 3*y*z^2 
+ 84*y*z*w - 10*y*w^2 + 37*z^3 - 6*z^2*w - 12*z*w^2 - 28*w^3;
pol1 := 2*tt^3 - 30*tt - 60;
pol2 := tt^3 + 2*tt^2 - 17*tt - 99;
ch_pol_sm := tt^2 - 135*tt;
h1_gal := 1;
rk_pic := 1;
ord_gal := 36;
Elt := [ 2, 2 ];
bp := [ 2, 3, 5, 7, 13, 19, 227 ];

gap_nr := 243;
gl := -95*x^3 + 25*x^2*y + 30*x^2*z + 26*x^2*w - 20*x*y^2 - 21*x*y*z - 22*x*y*w 
+ 9*x*z^2 - 66*x*z*w + 12*x*w^2 + 83*y^3 - 63*y^2*z + 2*y^2*w - 6*y*z*w 
- 12*y*w^2 + 9*z^3 + 18*z^2*w - 36*z*w^2 - 2*w^3;
pol1 := 2*tt^3 + 18*tt - 162;
pol2 := -3*tt^3 + 45*tt^2 - 162*tt + 171;
ch_pol_sm := tt^2 - 135*tt;
h1_gal := 1;
rk_pic := 1;
ord_gal := 54;
Elt := [ 6 ];
bp := [ 2, 3, 5, 13, 19, 88903 ];

gap_nr := 244;
gl := 131*x^3 + 49*x^2*y + 55*x^2*z - 50*x^2*w + 58*x*y^2 + 81*x*y*z + 48*x*y*w 
+ 44*x*z^2 - 41*x*z*w - 61*x*w^2 - 87*y^3 + 92*y^2*z + 83*y^2*w - 25*y*z^2 
+ 37*y*z*w - 4*y*w^2 + 5*z^3 + 27*z^2*w - 60*z*w^2 + 55*w^3;
pol1 := 2*tt^3 - 8*tt^2 + 134*tt - 90;
pol2 := tt^3 + 18*tt^2 + 51*tt - 19;
ch_pol_sm := tt^2 - 135*tt;
h1_gal := 1;
rk_pic := 1;
ord_gal := 54;
Elt := [ 3, 6 ];
bp := [ 2, 3, 7, 13, 19, 71, 197, 433 ];

gap_nr := 281; /* gerade */
res_36_type := [ 3, 6, 27 ];
res_45_type := [ 3, 3, 12, 27 ];
res_72_type := [ 6, 12, 54 ];
gl := -9*x^3 + 112*x^2*y + x^2*z - 323*x^2*w + 191*x*y^2 + 29*x*y*z - 50*x*y*w 
+ 5*x*z^2 + 90*x*z*w + 256*x*w^2 + 130*y^3 + 18*y^2*z + 293*y^2*w + 149*y*z*w 
- 213*y*w^2 - z^3 + 5*z^2*w + 281*z*w^2 + 77*w^3;
pol1 := 2*tt^3 + 270*tt + 1080;
pol2 := 3*tt^3 - 3*tt^2 - 27;
ch_pol_sm := tt^2 - 135*tt;
h1_gal := 1;
rk_pic := 1;
ord_gal := 108;
Elt := [ 2, 6 ];
bp := [ 2, 3, 5, 7, 13, 19, 29, 71, 337 ];

gap_nr := 282;
res_36_type := [ 3, 6, 27 ];
res_45_type := [ 3, 3, 12, 27 ];
res_72_type := [ 3, 3, 12, 54 ];
gl := -147*x^3 - 234*x^2*y - 6*x^2*z + 273*x^2*w + 47*x*y^2 + 135*x*y*z 
- 50*x*y*w + 21*x*z^2 - 21*x*z*w + 239*x*w^2 - 58*y^3 + 51*y^2*z - 23*y^2*w 
+ 18*y*z^2 + 57*y*z*w - 163*y*w^2 + z^3 + 6*z^2*w + 177*z*w^2 + 193*w^3;
pol1 := tt^3 - 45*tt + 680;
pol2 := -3*tt^3 + 12*tt^2 + 297*tt + 1215;
ch_pol_sm := tt^2 - 135*tt;
h1_gal := 1;
rk_pic := 1;
ord_gal := 108;
Elt := [ 2, 2 ];
bp := [ 2, 3, 5, 13, 19, 59, 107, 96857 ];

gap_nr := 288;
res_36_type := [ 3, 6, 27 ];
res_45_type := [ 3, 3, 6, 6, 27 ];
res_72_type := [ 6, 12, 54 ];
gl := 6*x^3 - 24*x^2*y - 42*x^2*z + 21*x^2*w - 48*x*y^2 + 12*x*y*z - 126*x*y*w 
+ 78*x*z^2 - 63*x*z*w + 147*x*w^2 - 41*y^3 - 59*y^2*w + 57*y*z^2 - 11*y*z*w 
- 110*y*w^2 - 101*z^3 - 182*z^2*w - 76*z*w^2 - 52*w^3;
pol1 := tt^3 + 135*tt + 540;
pol2 := -3*tt^3 - 12*tt^2 + 123*tt + 567;
ch_pol_sm := tt^2 - 135*tt;
h1_gal := 1;
rk_pic := 1;
ord_gal := 108;
Elt := [ 2, 2 ];
bp := [ 2, 3, 5, 13, 19, 31, 8264387 ];

gap_nr := 290; /* ungerade */
res_36_type := [ 3, 6, 27 ];
res_45_type := [ 3, 3, 12, 27 ];
res_72_type := [ 6, 6, 6, 54 ];
gl := 4*x^3 + 36*x^2*y - 6*x^2*z + 66*x^2*w - 9*x*y^2 - 42*x*y*z - 93*x*y*w 
+ 2*x*z^2 - 91*x*z*w - 190*x*w^2 + 45*y^3 - 9*y^2*z - 108*y^2*w + 24*y*z^2 
- 27*y*z*w + 66*y*w^2 - z^3 + 32*z^2*w - 91*z*w^2 + 10*w^3;
pol1 := tt^3 - 6*tt^2 + 99*tt + 81;
pol2 := 3*tt^3 + 54*tt^2 + 243*tt + 243;
ch_pol_sm := tt^2 - 135*tt;
h1_gal := 1;
rk_pic := 1;
ord_gal := 108;
Elt := [ 2, 6 ];
bp := [ 2, 3, 13, 19, 3571 ];

gap_nr := 318;
gl := 3*x^3 + 10*x^2*y + 3*x^2*z - 19*x^2*w - 8*x*y^2 - 29*x*y*z - 75*x*y*w 
+ 12*x*z^2 + 47*x*z*w + 76*x*w^2 - 38*y^3 - 103*y^2*z - 65*y^2*w + 10*y*z^2 
+ 36*y*z*w - 144*y*w^2 + 66*z^3 + 59*z^2*w + 44*z*w^2 - 46*w^3;
pol1 := tt^3 + 135*tt + 540;
pol2 := 3*tt^3 - 18*tt^2 + 297*tt + 243;
ch_pol_sm := tt^2 - 135*tt;
h1_gal := 1;
rk_pic := 1;
ord_gal := 216;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 5, 13, 19, 137, 941 ];

/* Examples with 3 orbits */

gap_nr := 71;
gl := x^3 - 4*x^2*y - x^2*w + 7*x*y^2 - x*y*z - 3*x*z^2 - x*z*w - 4*x*w^2 +
7*y^3 - 7*y^2*z+ 7*y^2*w - 4*y*z^2 + y*w^2 + 5*z^3 - 7*z^2*w - 2*z*w^2 + 5*w^3;
pol1 := -tt^3 + 9*tt^2 - 18*tt + 9;
pol2 := -2*tt^3 + 15*tt^2 - 27*tt + 12;
ch_pol_sm := tt^3 - 81*tt^2;
h1_gal := 3;
rk_pic := 1;
ord_gal := 9;
Elt := [ 3, 3 ];
bp := [ 3, 7 ];

gap_nr := 137;
gl := 2*x^3 - 3*x^2*y + 3*x^2*z - 6*x^2*w + 6*x*y^2 - 3*x*y*z + 6*x*y*w 
-4*x*z^2 - 4*x*z*w+ 5*x*w^2 - y^3 + 6*y^2*z + y*z^2 - 2*y*z*w + 7*y*w^2 
- 2*z^3 - 7*z^2*w +5*z*w^2 - 3*w^3;
pol1 := 2*tt^3 - 12*tt^2 + 24*tt - 6;
pol2 := tt^3 - 6*tt^2 + 12*tt + 7;
ch_pol_sm := tt^3 - 81*tt^2;
h1_gal := 3;
rk_pic := 1;
ord_gal := 18;
Elt := [ 2 ];
bp := [ 2, 3, 5 ];

gap_nr := 178;
gl := 45*x^3 + 24*x^2*y - x^2*z + 8*x^2*w - 33*x*y^2 + 32*x*y*z + 17*x*y*w 
- 5*x*z^2 + 106*x*z*w + 31*x*w^2 + 15*y^3 - 4*y^2*z + 47*y^2*w - 4*y*z^2 
+ 2*y*z*w - 22*y*w^2 + z^3 - 18*z^2*w - 3*z*w^2 - 7*w^3;
pol1 := 3*tt^3 + 54*tt^2 + 243*tt + 243;
pol2 := 2*tt^3 - 18*tt^2 - 648*tt + 648;
ch_pol_sm := tt^3 - 81*tt^2;
h1_gal := 3;
rk_pic := 1;
ord_gal := 27;
Elt := [ 3, 3, 3 ];
bp := [ 2, 3, 5, 13, 31, 109 ];

gap_nr := 240;
gl := x^3 - 5*x^2*y + 5*x^2*z + 16*x^2*w - 2*x*y^2 + 4*x*y*z + 6*x*y*w 
- 2*x*z^2 + 6*x*z*w - 13*x*w^2 + 4*y^3 + 5*y^2*w + 5*y*z*w + 17*y*w^2 
- z^2*w + 4*z*w^2 - 13*w^3;
pol1 := 3*tt^3 + 405*tt + 1620;
pol2 := 2*tt^3 - 162*tt - 648;
ch_pol_sm := tt^3 - 81*tt^2;
h1_gal := 3;
rk_pic := 1;
ord_gal := 54;
Elt := [ 2 ];
bp := [ 2, 3, 5, 7 ];

gap_nr := 241;
gl := -x^3 - 15*x^2*y + 9*x^2*z + 18*x^2*w - 12*x*y^2 - 18*x*y*z - 3*x*z*w 
+ 7*x*w^2 + 4*y^3 - 18*y^2*w - 18*y*z^2 + 3*y*z*w + 20*y*w^2 - 12*z^3 
- 6*z*w^2 - 14*w^3;
pol1 := tt^3 + 135*tt + 540;
pol2 := 3*tt^3 - 243*tt - 972;
ch_pol_sm := tt^3 - 81*tt^2;
h1_gal := 3;
rk_pic := 1;
ord_gal := 54;
Elt := [ 6 ];
bp := [ 2, 3, 5, 7 ];

gap_nr := 242;
gl := -6*x^3 + 111*x^2*y - 39*x^2*z - 54*x^2*w + 24*x*y^2 + 99*x*y*z - 24*x*y*w 
- 33*x*z^2 - 48*x*z*w + 6*x*w^2 + 20*y^3 - 19*y^2*z + 37*y^2*w - 55*y*z^2 
+ 19*y*z*w - 35*y*w^2 - 27*z^3 + 70*z^2*w + 74*z*w^2 - 77*w^3;
pol1 := tt^3 + 18*tt^2 + 81*tt + 81;
pol2 := 3*tt^3 + 702*tt^2 + 42120*tt + 134784;
ch_pol_sm := tt^3 - 81*tt^2;
h1_gal := 3;
rk_pic := 1;
ord_gal := 54;
Elt := [ 3, 6 ];
bp := [ 2, 3, 13, 109, 577, 34919, 836289647 ];

gap_nr := 284;
res_36_type := [ 3, 3, 3, 27 ];
res_45_type := [ 3, 3, 6, 6, 27 ];
res_72_type := [ 6, 6, 6, 27, 27 ];
gl := x^3 - 9*x^2*y + 5*x^2*z - 17*x^2*w - 9*x*y^2 - 21*x*y*z + 3*x*y*w 
+ x*z^2 - 7*x*z*w + 24*x*w^2 - 6*y^3 - 9*y^2*w - 12*y*z^2 + 3*y*z*w 
- 14*z^3 - 2*z^2*w - 9*z*w^2 + 11*w^3;
pol1 := tt^3 + 135*tt + 540;
pol2 := 3*tt^3 + 243*tt + 486;
ch_pol_sm := tt^3 - 81*tt^2;
h1_gal := 3;
rk_pic := 1;
ord_gal := 108;
Elt := [ 2, 2 ];
bp := [ 2, 3, 5, 11, 17 ];

gap_nr := 139;
gl := -3*x^3 + 9*x^2*z - 5*x^2*w + 3*x*y^2 - 3*x*y*z - 6*x*z^2 - 6*x*z*w 
- 29*x*w^2 + y^3 - 3*y^2*z + 18*y^2*w + 3*y*z*w + z^3 + 12*z^2*w 
- 3*z*w^2 + 5*w^3;
pol1 := tt^3 + 6*tt^2 - 9*tt - 17;
pol2 := 3*tt^3 + 54*tt;
ch_pol_sm := tt^3 - 123*tt^2;
h1_gal := 1;
rk_pic := 1;
ord_gal := 18;
Elt := [ 6 ];
bp := [ 2, 3, 17, 19, 89 ];

gap_nr := 142;
gl := 3*x^3 + 18*x^2*y - 9*x^2*z + 27*x*y^2 - 18*x*y*z - 27*x*y*w - 3*x*z^2
+ 12*x*z*w - 39*x*w^2 + 16*y^3 + 5*y^2*z - 4*y^2*w - 11*y*z^2 - 31*y*z*w 
+ 7*y*w^2 - 11*z^3 - 15*z^2*w - 15*z*w^2 - 20*w^3;
pol1 := 12*tt^3 - 36*tt + 12;
pol2 := 11*tt^3 + 3*tt - 14;
ch_pol_sm := tt^3 - 123*tt^2;
h1_gal := 1;
rk_pic := 1;
ord_gal := 18;
Elt := [ 3, 6 ];
bp := [ 2, 3, 5, 11, 13, 34919 ];

gap_nr := 204; /* Galois-Group has 12 conjugacy classes */
res_36_type := [ 3, 6, 9, 18 ];
res_45_type := [ 1, 2, 3, 6, 6, 9, 18 ];
res_72_type := [ 6, 12, 18, 36 ];
gl := 15*x^3 - 3*x^2*y - 8*x^2*z + 6*x^2*w + 9*x*y^2 - 8*x*y*z - 12*x*y*w 
+ 8*x*z^2 - 12*x*z*w + 6*x*w^2 + 5*y^3 + 4*y^2*z + 3*y^2*w + 4*y*z^2 
+ 8*z^3 + 6*z^2*w - w^3;
pol1 := 3*t^3 - 27*t^2 + 54*t - 36;
pol2 := t^3 - 9*t^2 + 8;
ch_pol_sm := tt^3 - 123*tt^2;
h1_gal := 1;
rk_pic := 1;
ord_gal := 36;
Elt := [ 2, 2 ];
bp := [ 2, 3, 5, 317 ];

gap_nr := 205; /* Galois-Group has 9 conjugacy classes */
res_36_type := [ 3, 6, 9, 18 ];
res_45_type := [ 1, 2, 3, 6, 6, 9, 18 ];
res_72_type := [ 6, 12, 18, 36 ];
gl := -x^3 - 4*x^2*y - 2*x^2*z + 6*x^2*w + 2*x*y^2 + 7*x*y*z - 27*x*y*w 
- x*z^2 - x*z*w - 13*x*w^2 + 14*y^3 + 26*y^2*z + y^2*w + 11*y*z^2 - y*z*w 
- 26*y*w^2 + 9*z^3 - z^2*w + 10*z*w^2 + 7*w^3;
pol1 := tt^3 - 2*tt^2 + 37*tt - 81;
pol2 := 3*tt^3 + 6*tt;
ch_pol_sm := tt^3 - 123*tt^2;
h1_gal := 1;
rk_pic := 1;
ord_gal := 36;
Elt := [ 2, 2 ];
bp := [ 2, 3, 5, 7, 13, 19 ];

gap_nr := 207;
res_36_type := [3, 6, 9, 18];
res_45_type := [1, 2, 3, 9, 12, 18];
res_72_type := [ 3, 3, 12, 18, 36 ];
gl := -5*x^3 - 31*x^2*y - 11*x^2*z + 5*x^2*w + 66*x*y^2 - 22*x*y*z - 9*x*y*w 
+ 16*x*z^2 - 79*x*z*w + 16*x*w^2 + y^3 + 61*y^2*z + 12*y^2*w + 39*y*z^2 
- 36*y*z*w + 49*y*w^2 - 25*z^3 - 16*z^2*w - 31*z*w^2 + 65*w^3;
pol1 := 2*tt^3 + 16*tt^2 + 32*tt - 1152;
pol2 := tt^3 + 73*tt^2 + 1314*tt - 1388;
ch_pol_sm := tt^3 - 123*tt^2;
h1_gal := 1;
rk_pic := 1;
ord_gal := 36;
Elt := [ 2, 2 ];
bp := [ 2, 5, 7, 11, 13, 19, 29, 43, 5869 ];

gap_nr := 209;
res_36_type := [ 3, 6, 9, 18 ];
res_45_type := [ 1, 2, 3, 9, 12, 18 ];
res_72_type := [ 6, 6, 6, 18, 18, 18 ];
gl := -6*x^3 + 7*x^2*y + 9*x^2*z + 14*x^2*w + 4*x*y^2 - 4*x*y*z + 4*x*y*w 
+ 3*x*z^2 - 5*x*z*w + 4*x*w^2 - 4*y^3 + 4*y^2*z - 8*y*z^2 - 2*y*z*w 
+ 7*z^3 + 8*z^2*w + z*w^2 + w^3;
pol1 := tt^3 + 18*tt^2 + 81*tt + 81;
pol2 := 3*tt^3 - 36*tt^2 + 162*tt;
ch_pol_sm := tt^3 - 123*tt^2;
h1_gal := 1;
rk_pic := 1;
ord_gal := 36;
Elt := [ 2, 6 ];
bp := [ 2, 3, 17, 89 ];

gap_nr := 210;
res_36_type := [ 3, 6, 9, 18 ];
res_45_type := [ 1, 2, 3, 9, 12, 18 ];
res_72_type := [ 6, 12, 18, 36 ];
gl := -17*x^3 + 40*x^2*y + 4*x^2*z - 22*x^2*w - 31*x*y^2 - 10*x*y*z + 10*x*y*w 
+ 85*x*z^2 + 10*x*z*w + 39*x*w^2 - 10*y^3 + 6*y^2*z - 16*y^2*w - 6*y*z^2 
- 24*y*z*w - 30*y*w^2 + 27*z^3 + 18*z^2*w - 2*z*w^2 + 36*w^3;
pol1 := 3*tt^3 - 12*tt^2 + 201*tt - 135;
pol2 := 2*tt^3 - 28*tt^2 + 136*tt - 176;
ch_pol_sm := tt^3 - 123*tt^2;
h1_gal := 1;
rk_pic := 1;
ord_gal := 36;
Elt := [ 2, 6 ];
bp := [ 2, 3, 13, 19, 61, 23753 ];

gap_nr := 264;
gl := -11*x^3 - 20*x^2*y - 5*x^2*z + 7*x^2*w - 15*x*y^2 - 17*x*y*z + x*y*w 
- 4*x*z^2 + 23*x*z*w - 15*x*w^2 + y^3 - 4*y^2*z - 21*y^2*w - 3*y*z^2 
- 73*y*z*w - 35*y*w^2 - z^3 + 16*z^2*w - 19*z*w^2 + 35*w^3;
pol1 := tt^3 - 6*tt^2 + 99*tt + 81;
pol2 := 3*tt^3 - 36*tt^2 + 162*tt;
ch_pol_sm := tt^3 - 123*tt^2;
h1_gal := 1;
rk_pic := 1;
ord_gal := 72;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 11, 13, 19, 37 ];

/* Examplex with 4 Orbits */

gap_nr := 138;
gl := 2*x^3 - 4*x^2*y + 13*x^2*z + 28*x^2*w + 4*x*y^2 + 9*x*y*z + 18*x*y*w 
+ 5*x*z^2 - 23*x*z*w + 23*x*w^2 + 2*y^3 + 2*y^2*z - 7*y^2*w + y*z^2 
- 13*y*z*w - 23*y*w^2 - 6*z^2*w + 12*z*w^2 + 5*w^3;
pol1 := 101*tt^3 + 8181*tt + 16362;
pol2 := 162*tt^3 + 16416*tt - 16578;
ch_pol_sm := tt^4 - 69*tt^3;
h1_gal := 3;
rk_pic := 1;
ord_gal := 18;
Elt := [ 2 ];
bp := [ 2, 3, 5, 61, 101, 853 ];

gap_nr := 143;
gl := x^3 - 3*x^2*y + 8*x^2*z - 2*x^2*w - 8*x*y^2 + 2*x*y*z - 14*x*y*w 
+ 14*x*z^2 + 11*x*z*w + 15*x*w^2 + 3*y^3 + 2*y^2*z + 18*y*z*w + 3*y*w^2 
+ 8*z^3 + 8*z^2*w + 2*z*w^2 - 9*w^3;
pol1 := tt^3 + 6*tt^2 + 67*tt - 165;
pol2 := 2*tt^3 - 14*tt^2 + 156*tt - 272;
ch_pol_sm := tt^4 - 69*tt^3;
h1_gal := 3;
rk_pic := 1;
ord_gal := 18;
Elt := [ 6 ];
bp := [ 2, 11, 13, 19, 785347 ];

gap_nr := 211;
gl := -9*x^3 - 66*x^2*y - 27*x^2*z + 141*x^2*w - 178*x*y^2 - 141*x*y*z 
+ 1444*x*y*w - 28*x*z^2 + 274*x*z*w + 220*x*w^2 - 359*y^3 - 300*y^2*z 
- 364*y^2*w - 95*y*z^2 + 575*y*z*w + 81*y*w^2 - 11*z^3 + 81*z^2*w 
- 1050*z*w^2 + 449*w^3;
pol1 := tt^3 - 6*tt^2 + 99*tt + 81;
pol2 := 3*tt^3 - 747*tt^2 + 46686*tt;
ch_pol_sm := tt^4 - 69*tt^3;
h1_gal := 3;
rk_pic := 1;
ord_gal := 36;
Elt := [ 2, 2 ];
bp := [ 3, 5, 13, 19, 89, 227, 15248304311, 31858990363 ];

gap_nr := 92;
gl := -24*x^3 + 19*x^2*y + 15*x^2*z - 18*x^2*w + 4*x*y^2 + 37*x*y*z 
-15*x*y*w - 16*x*z^2 -5*x*z*w - 10*x*w^2 - 11*y^3 - 13*y^2*z - 3*y^2*w 
- 15*y*z^2 - 8*y*z*w -y*w^2 - 14*z^3 -16*z^2*w - 5*z*w^2 - 6*w^3;
pol1 := 2*tt^3 - 12*tt^2 - 6*tt + 104;
pol2 := tt^3 - 9*tt^2 - 24*tt + 140;
ch_pol_sm := tt^4 - 75*tt^3;
h1_gal := 1;
rk_pic := 1;
ord_gal := 12;
Elt := [ 2, 2 ];
bp := [ 2, 3, 5, 19, 199, 211 ];

gap_nr := 131;
gl := -x^3 + x^2*y - 10*x^2*z - 4*x^2*w - 36*x*y*z + 55*x*y*w + 36*x*z^2 
- 43*x*z*w - 50*x*w^2 + 9*y^3 + 18*y^2*z + 3*y^2*w + 81*y*z^2 + 18*y*z*w 
- 13*y*w^2 - 44*z^3 + 43*z^2*w - 55*z*w^2 + 3*w^3;
pol1 := 3*tt^3 + 6*tt^2 - 51*tt - 297;
pol2 := 2*tt^3 - 2*tt;
ch_pol_sm := tt^4 - 117*tt^3;
h1_gal := 1;
rk_pic := 1;
ord_gal := 18;
Elt := [ 6 ];
bp := [ 2, 3, 11, 13, 19, 61, 113 ];

gap_nr := 132;
gl := -x^3 - x^2*y + 4*x^2*z - x*y^2 - 3*x*y*z + 8*x*y*w - x*z^2 - 3*x*z*w-2*x*w^2 
+ y^3 - 2*y^2*z + 3*y^2*w + 5*y*z^2 - 3*y*z*w + y*w^2 + z^2*w - 5*z*w^2 - 5*w^3;
pol1 := tt^3 - 15*tt + 30;
pol2 := -3*tt^3 + 21*tt - 18;
ch_pol_sm := tt^4 - 117*tt^3;
h1_gal := 1;
rk_pic := 1;
ord_gal := 18;
Elt := [ 2 ];
bp := [ 2, 3, 5 ];

gap_nr := 198;
gl := 23*x^2*y + 24*x^2*z - 21*x^2*w + 13*x*y^2 - 28*x*y*z - 27*x*y*w 
+ 9*x*z^2 - 59*x*z*w - x*w^2 - y^3 - 25*y^2*z + 21*y^2*w + 28*y*z^2 
+ 43*y*z*w + 56*y*w^2 + 13*z^3 - 17*z^2*w - 20*z*w^2 - 9*w^3;
pol1 := tt^3 - 6*tt^2 + 99*tt + 81;
pol2 := 3*tt^3 + 12*tt^2 - 15*tt;
ch_pol_sm := tt^4 - 117*tt^3;
h1_gal := 1;
rk_pic := 1;
ord_gal := 36;
Elt := [ 2, 2 ];
bp := [ 2, 3, 5, 7, 13, 19, 53, 449, 479 ];

/* Examples with 5 orbits */

gap_nr := 26;
gl := -3*x^2*z - x^2*w - 6*x*y*z - 2*x*y*w + 3*x*z^2 - 2*x*z*w - 11*x*w^2 +
y^3 + 2*y^2*w -3*y*z^2 + 13*y*z*w + y*w^2 - 11*z^3 + 2*z^2*w - 5*z*w^2 + 3*w^3;
pol1 := -tt^3 + 15*tt^2 - 54*tt + 37;
pol2 := -2*tt^3 + 15*tt^2 - 51*tt + 38;
ch_pol_sm := tt^5 - 51*tt^4;
h1_gal := 1;
rk_pic := 1;
ord_gal := 6;
Elt := [ 6 ];
bp := [ 3, 5, 17, 19 ];

gap_nr := 72;
gl := -x^3 + 3*x^2*y - 12*x^2*z - 6*x*y*z + 3*x*y*w + 4*x*z^2 - 6*x*z*w 
+ 3*x*w^2 - 3*y^3 + 27*y^2*z - 9*y^2*w + 6*y*z*w - 6*y*w^2 - 8*z^3 
+ 8*z^2*w + 9*z*w^2 + w^3;
pol1 := tt^3 + 12*tt^2 + 27*tt + 17;
pol2 := 2*tt^3 + 8*tt^2 + 6*tt;
ch_pol_sm := tt^5 - 63*tt^4;
h1_gal := 3;
rk_pic := 1;
ord_gal := 9;
Elt := [ 3, 3 ];
bp := [ 2, 3, 17, 79 ];

gap_nr := 129;
gl := -x^3 + 3*x^2*y - 11*x^2*z + 6*x^2*w + 12*x*y*z - 3*x*y*w + 12*x*z^2 
+ 5*x*z*w - 3*x*w^2 - y^3 + 18*y^2*z + 3*y*z^2 + 12*y*z*w + 3*y*w^2 + 8*z^3 
- 24*z^2*w - 29*z*w^2 - w^3;
pol1 := tt^3 + 18*tt^2 + 81*tt + 81;
pol2 := 3*tt^3 + 12*tt^2 - 15*tt;
ch_pol_sm := tt^5 - 63*tt^4;
h1_gal := 3;
rk_pic := 1;
ord_gal := 18;
Elt := [ 6 ];
bp := [ 2, 3, 19, 127, 181 ];

/* Examples with 6 orbits */

gap_nr := 37;
gl := x^3 - 6*x^2*y - x^2*z + 4*x^2*w + 5*x*y*z + 4*x*y*w - x*z^2 + 2*x*z*w
- 4*x*w^2 -6*y^3 + 3*y^2*z + 6*y^2*w - 5*y*z^2 + 9*y*z*w + 2*y*w^2 - 6*z^3 
- 6*z^2*w -5*z*w^2 - 3*w^3;
pol1 := 2*tt^3 - 12*tt^2 + 144*tt - 576;
pol2 := tt^3 - 12*tt^2 + 84*tt - 416;
ch_pol_sm := tt^6 - 45*tt^5;
h1_gal := 3;
rk_pic := 1;
ord_gal := 6;
Elt := [ 2 ];
bp := [ 2, 3, 5, 13, 127 ];

gap_nr := 83;
gl := -x^2*y + x^2*z + x^2*w + x*y^2 - x*w^2 - y*z^2 + 2*y*z*w + y*w^2 + z^2*w 
+ 2*z*w^2 - w^3;
pol1 := 2*tt^3 - 12*tt^2 + 36*tt;
pol2 := 3*tt^3 - 6*tt^2 - 36*tt - 216;
ch_pol_sm := tt^6 - 39*tt^5 - 1844*tt^4;
h1_gal := 1;
rk_pic := 2;
ord_gal := 12;
Elt := [ 2, 6 ];
bp := [ 2, 7, 41 ];

gap_nr := 85;
res_36_type := [ 2, 3, 3, 4, 6, 6, 12 ];
res_45_type := [ 1, 1, 2, 2, 3, 6, 6, 12, 12 ];
res_72_type := [ 3, 3, 4, 4, 4, 6, 12, 12, 12, 12 ];
gl := 2*x^2*w - 3*x*y*z + 3*x*y*w - 2*x*z^2 + 4*x*z*w - x*w^2 - 2*y^3 - 2*y*z^2 
- 6*y*z*w - 3*y*w^2 - z^3 + z^2*w - z*w^2 - w^3;
pol1 := tt^3 - 6*tt^2 + 18*tt;
pol2 := 3*tt^3 - 54*tt^2 + 369*tt - 804;
ch_pol_sm := tt^6 - 39*tt^5 - 1844*tt^4;
h1_gal := 1;
rk_pic := 2;
ord_gal := 12;
Elt := [ 2, 2 ];
bp := [ 2, 3, 5, 11, 67, 1201 ];

gap_nr := 96;
gl := -x^2*z - x^2*w + 2*x*y^2 + 4*x*z^2 - 4*x*z*w - y^3 + 2*y^2*z + 2*y^2*w 
- y*z^2 + 2*y*z*w - y*w^2 - z^3 - 3*z^2*w - z*w^2 + w^3;
res_36_type := [ 2, 3, 3, 4, 6, 6, 12 ];
res_45_type := [ 1, 1, 2, 2, 3, 6, 6, 6, 6, 12 ];
res_72_type := [ 4, 4, 4, 6, 6, 12, 12, 12, 12 ];
pol1 := tt^3 - 6*tt^2 + 18*tt;
pol2 := 3*tt^3 - 6*tt^2 - 36*tt - 216;
ch_pol_sm := tt^6 - 39*tt^5 - 1844*tt^4;
h1_gal := 1;
rk_pic := 2;
ord_gal := 12;
Elt := [ 2, 2 ];
bp := [ 2, 3, 41 ];

gap_nr := 170;
gl := 3*x^3 - 9*x^2*y + x^2*z + 2*x^2*w + 3*x*y^2 - 2*x*y*z - 8*x*y*w 
+ 11*x*z^2 - 2*x*z*w - 4*x*w^2 + y^3 + y^2*z + 4*y^2*w + 4*y*z^2 - 4*y*z*w 
+ y*w^2 + 4*z^3 + 3*z^2*w + 3*z*w^2 - 5*w^3;
pol1 := tt^3 - 6*tt^2 + 18*tt;
pol2 := 3*tt^3 - 27*tt^2 + 126*tt - 102;
ch_pol_sm := tt^6 - 39*tt^5 - 1844*tt^4;
h1_gal := 1;
rk_pic := 2;
ord_gal := 24;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 13, 17, 179 ];

/* Examples with 9 orbits */

gap_nr := 30;
gl := -x^3 + x^2*y - x^2*w - x*y^2 - 2*x*y*z + 2*x*y*w - x*z^2 + x*w^2 + y^3 
+ 2*y^2*z + y^2*w + y*z^2 + y*w^2 + 3*z^2*w - z*w^2 + w^3;
pol1 := tt^3 + 9*tt;
pol2 := 3*tt^3 + 24*tt^2 + 27*tt - 54;
ch_pol_sm := tt^9 + 3*tt^8 - 1320*tt^7 - 19844*tt^6;
h1_gal := 1;
rk_pic := 3;
ord_gal := 6;
Elt := [ 6 ];
bp := [ 2, 5, 13 ];

gap_nr := 31;
gl := x^2*w + x*y*z - 4*x*y*w + x*z^2 + x*z*w + y^2*z - 4*y^2*w - y*z^2 
- 2*z^3 - 2*z^2*w + 3*z*w^2;
pol1 := -tt^3 - 2*tt^2 + 2*tt + 4;
pol2 := 12*tt^3 - 12*tt;
ch_pol_sm := tt^9 + 3*tt^8 - 1320*tt^7 - 19844*tt^6;
h1_gal := 1;
rk_pic := 3;
ord_gal := 6;
Elt := [ 2 ];
bp := [ 2, 3, 5, 11 ];

gap_nr := 80;
gl := -x^2*y + 3*x^2*z + 4*x^2*w - 4*x*y*w + 2*x*z*w + 4*x*w^2 - y^3 + 3*y^2*z 
+ 4*y^2*w + 4*y*z*w + y*w^2 - 5*z^2*w + 7*z*w^2 + 4*w^3;
pol1 := tt^3 - 6*tt^2 + 18*tt;
pol2 := 3*tt^3 + 18*tt^2 + 9*tt - 30;
ch_pol_sm := tt^9 + 3*tt^8 - 1320*tt^7 - 19844*tt^6;
h1_gal := 1;
rk_pic := 3;
ord_gal := 12;
Elt := [ 2, 2 ];
bp := [ 2, 3, 5, 13, 17, 73, 2851 ];

gap_nr := 6;
gl := x^3 - x^2*z - x^2*w - 2*x*z^2 + x*z*w - y^3 + 3*y^2*z - 3*y*z*w +
3*y*w^2 - z^3 -z^2*w + w^3;
pol1 := tt^3 + 6*tt^2 + 9*tt + 1;
pol2 := 2*tt^3 + 9*tt^2 + 9*tt;
ch_pol_sm := tt^9 - 27*tt^8;
h1_gal := 9;
rk_pic := 1;
ord_gal := 3;
Elt := [ 3 ];
bp := [ 3, 19 ];