gap_nr := 331;
K := NumberField(tt^2 - 7);
pol1 :=  (1+K.1)*u^3 + u^2 + (1+ K.1) * u - 1 + K.1;
pol2 :=  (1-K.1)*u^3 + u^2 + (1- K.1) * u - 1 - K.1;
gl := -15*x^3 - 53*x^2*y + 55*x^2*z + 20*x^2*w - 143*x*y^2 + 172*x*y*z 
      - 195*x*y*w - 232*x*z^2 - 159*x*z*w - 158*x*w^2 + 137*y^3 + 9*y^2*z 
      + 74*y^2*w - 96*y*z^2 - 115*y*z*w - 79*y*w^2 - 40*z^3 - 95*z^2*w 
      - 64*z*w^2 - 122*w^3;
ch_pol_sm := tt^2 - 135*tt;
h1_gal := 1;
rk_pic := 1;
ord_gal := 432;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 7, 17, 31, 47, 2633 ];


gap_nr := 321;
K := NumberField(tt^2 - 7);
pol1 := (K.1 + 1)*u^3 + u^2 + (-3*K.1 + 1)*u - K.1 - 1;
pol2 := (-K.1 + 1)*u^3 + u^2 + (3*K.1 + 1)*u + K.1 - 1;
gl := 46*x^3 + 235*x^2*y + 125*x^2*z + 417*x^2*w - 105*x*y^2 + 232*x*y*z 
      - 399*x*y*w - 30*x*z^2 - 166*x*z*w - 112*x*w^2 - 127*y^3 + 201*y^2*z 
      - 170*y^2*w - 156*y*z^2 + 534*y*z*w - 37*y*w^2 + 6*z^3 + 48*z^2*w 
      - 510*z*w^2 - 130*w^3;
ch_pol_sm := tt^2 - 135*tt;
h1_gal := 1;
rk_pic := 1;
ord_gal := 216;
Elt := [ 2, 6 ];
bp := [ 2, 3, 7, 37, 53, 50929 ];


gap_nr := 320;
K := NumberField(tt^2-2);
pol1 := (2*K.1 + 3)*u^3 + 3*u^2 + (-9*K.1 + 3)*u + 9*K.1 - 13;
pol2 := (-2*K.1 + 3)*u^3 + 3*u^2 + (9*K.1 + 3)*u - 9*K.1 - 13;
gl := -x^2*y - x^2*z - 2*x^2*w - 4*x*y*z - x*y*w + 4*x*z^2 - 2*x*w^2 - y^3 
      - 4*y^2*z - 6*y^2*w - 4*y*z^2 + 3*y*z*w - y*w^2 + 3*z^3 - 3*z*w^2 - 4*w^3;
ch_pol_sm := tt^2 - 135*tt;
h1_gal := 1;
rk_pic := 1;
ord_gal := 216;
Elt := [ 2, 2 ];
bp := [ 2, 3, 3191 ];
res_36_type := [ 3, 6, 27 ];
res_45_type := [ 6, 12, 27 ];
res_72_type := [ 3, 3, 12, 54 ];


gap_nr := 316;
K := NumberField(tt^2-2);
pol1 := K.1*u^3 - 18*K.1*u^2 + (78*K.1 + 6)*u + 28*K.1 - 88;
pol2 := -K.1*u^3 + 18*K.1*u^2 + (-78*K.1 + 6)*u - 28*K.1 - 88;
gl := 3*x^3 + 3*x^2*y + 5*x^2*z - 3*x^2*w + 3*x*y^2 + 2*x*y*z - 4*x*z^2 
      + 4*x*w^2 + 2*y^2*z + 3*y^2*w + y*z^2 - 6*y*z*w + 2*y*w^2 - z^3 
      - 4*z^2*w + 4*z*w^2 + 2*w^3;
ch_pol_sm := tt^2 - 135*tt;
h1_gal := 1;
rk_pic := 1;
ord_gal := 216;
Elt := [ 2, 2 ];
bp := [ 2, 3, 37, 83 ];
res_36_type := [ 3, 6, 27 ];
res_45_type := [ 6, 12, 27 ];
res_72_type := [ 6, 12, 54 ];


gap_nr := 315;
K := NumberField(tt^2 - 7);
pol1 := (K.1 + 1)*u^3 + 9*K.1*u^2 - 7*K.1*u - 7*K.1;
pol2 := (-K.1 + 1)*u^3 - 9*K.1*u^2 + 7*K.1*u + 7*K.1;
gl := -773*x^3 - 520*x^2*y + 1442*x^2*z - 5400*x^2*w - 306*x*y^2 
      + 757*x*y*z + 349*x*y*w - 83*x*z^2 + 6466*x*z*w + 4946*x*w^2 
      - y^3 + 405*y^2*z + 2926*y^2*w - 88*y*z^2 + 5343*y*z*w 
      - 5882*y*w^2 - 622*z^3 + 3701*z^2*w + 6521*z*w^2 - 285*w^3;
ch_pol_sm := tt^2 - 135*tt;
h1_gal := 1;
rk_pic := 1;
ord_gal := 216;
Elt := [ 2, 2 ];
bp := [ 2, 3, 7, 17, 47, 148957 ];


gap_nr := 314;
K := NumberField(tt^2-2);
pol1 := (K.1 + 1)*u^3 + 1/2*(-3*K.1 - 6)*u + K.1 + 2;
pol2 := (-K.1 + 1)*u^3 + 1/2*(3*K.1 - 6)*u - K.1 + 2;
gl := 4*x^3 + x^2*y - 2*x^2*z - 2*x^2*w - 2*x*y*z + 2*x*y*w + 2*x*z^2 
      + 2*x*w^2 + 2*y^2*z - y*z*w + y*w^2 + z^3 - z^2*w + z*w^2 - w^3;
ch_pol_sm := tt^2 - 135*tt;
h1_gal := 1;
rk_pic := 1;
ord_gal := 216;
Elt :=[ 2, 4 ];
bp := [ 2, 3 ];


gap_nr := 287;
K := NumberField(tt^2-2);
pol1 :=  (K.1 + 1)*u^3 + (3*K.1 + 6)*u^2 + 9/2*u - K.1 + 2;
pol2 := (-K.1 + 1)*u^3 + (-3*K.1 + 6)*u^2 + 9/2*u + K.1 + 2;
gl := 2*x^2*y - 2*x^2*w + 2*x*y^2 - 2*x*y*z + 2*x*z^2 - 4*x*z*w - y^3 
      + 2*y^2*z + 2*y^2*w - 4*y*w^2 + 2*z^3 - z^2*w;
ch_pol_sm := tt^2 - 135*tt;
h1_gal := 1;
rk_pic := 1;
ord_gal := 108;
Elt := [ 12 ];
bp := [ 2, 3, 37 ];


gap_nr := 285;
K := NumberField(tt^2-2);
pol1 := (K.1 + 5)*u^3 + 1/2*(-15*K.1 - 6)*u + 5*K.1 + 2;
pol2 := (-K.1 + 5)*u^3 + 1/2*(15*K.1 - 6)*u - 5*K.1 + 2;
gl := -x^3 + x^2*y - 6*x^2*z - 6*x^2*w + 5*x*y^2 + 2*x*y*z - 8*x*y*w 
      + 5*x*z^2 + 5*x*z*w - 10*x*w^2 + y^3 - y^2*z - 11*y^2*w + 7*y*z^2 
      + 13*y*z*w - 2*y*w^2 - 2*z^3 + 6*z^2*w + 3*z*w^2 + 11*w^3;
ch_pol_sm := tt^2 - 135*tt;
h1_gal := 1;
rk_pic := 1;
ord_gal := 108;
Elt := [ 4 ];
bp := [ 2, 3, 5, 23 ];

/* 3 Orbits */

gap_nr := 312;
K := NumberField(tt^2 - 7);
pol1 := K.1*u^3 + (K.1 - 7)*u^2 + (-K.1 + 7)*u + 5*K.1 - 7;
pol2 := -K.1*u^3 + (-K.1 - 7)*u^2 + (K.1 + 7)*u - 5*K.1 - 7;
gl := -5*x^3 + 5*x^2*y + 5*x^2*z + 3*x*y^2 - 5*x*y*z + 5*x*y*w 
      + 4*x*z^2 - x*z*w - 6*x*w^2 - 6*y^3 - 3*y^2*z - 6*y^2*w 
      + 2*y*z^2 + 2*y*z*w - 4*y*w^2 - 5*z^3 - 4*z^2*w - 4*z*w^2 - 2*w^3;
ch_pol_sm := tt^3 - 81*tt^2;
h1_gal := 3;
rk_pic := 1;
ord_gal := 216;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 5, 7, 13 ];


gap_nr := 283;
K := NumberField(tt^2 - 7);
pol1 := (K.1 + 1)*u^3 + (-93*K.1 - 201)*u + 62*K.1 + 134;
pol2 := (-K.1 + 1)*u^3 + (93*K.1 - 201)*u - 62*K.1 + 134;
gl := -3*x^3 - 160*x^2*y - 21*x^2*z + 194*x^2*w + 278*x*y^2 + 838*x*y*z 
      + 264*x*y*w + 2394*x*z^2 - 755*x*z*w - 653*x*w^2 - 80*y^3 
      - 1306*y^2*z - 908*y^2*w + 1619*y*z^2 + 636*y*z*w +
    1108*y*w^2 - 73*z^3 + 29*z^2*w + 544*z*w^2 - 16*w^3;
ch_pol_sm := tt^3 - 81*tt^2;
h1_gal := 3;
rk_pic := 1;
ord_gal := 108;
Elt := [ 2, 6 ];
bp := [ 2, 3, 5, 7, 31, 373 ];


gap_nr := 280;
K := NumberField(tt^2 + 3);
pol1 := (K.1 + 3)*u^3 + 180*u^2 + 2304*u + 3840*K.1 - 8448;
pol2 := (-K.1 + 3)*u^3 + 180*u^2 + 2304*u - 3840*K.1 - 8448;
gl := -x^2*w - 2*x*y*w + 3*x*z^2 - 30*x*w^2 + 4*y^3 - 6*y^2*z - y^2*w 
      - 3*y*z^2 - 18*y*z*w + 6*y*w^2 + 10*z^3 - 3*w^3;
ch_pol_sm := tt^3 - 81*tt^2;
h1_gal := 3;
rk_pic := 1;
ord_gal := 108;
Elt := [ 2, 2 ];
bp := [ 2, 3, 5, 568049 ];

/* 5 Orbits */

gap_nr := 238;
K := NumberField(tt^2 - 7);
pol1 := (K.1 + 1)*u^3 + K.1*u^2 + (-7*K.1 - 8)*u - 6*K.1;
pol2 := (-K.1 + 1)*u^3 - K.1*u^2 + (7*K.1 - 8)*u + 6*K.1;
gl := 2*x^3 + 2*x^2*y + 5*x^2*z - 9*x^2*w - 12*x*y^2 - 37*x*y*z - 16*x*y*w 
      + 54*x*z^2 - 11*x*w^2 - 2*y^2*z - 31*y^2*w - 10*y*z^2 - 18*y*z*w 
      - 42*y*w^2 + 34*z^3 - 22*z^2*w - 5*z*w^2 + 30*w^3;
ch_pol_sm := tt^5 - 39*tt^4 - 2172*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 24;
Elt := [ 2, 2, 2 ];
bp := [ 2, 3, 7, 29, 31, 1229 ];


gap_nr := 175;
K := NumberField(tt^2 - 7);
pol1 := (K.1 + 1)*u^3 + 9*K.1*u^2 + (-7*K.1 - 63)*u - 7*K.1;
pol2 := (-K.1 + 1)*u^3 - 9*K.1*u^2 + (7*K.1 - 63)*u + 7*K.1;
gl := 8*x^3 - 28*x^2*y - 4*x^2*z + 84*x^2*w - 16*x*y^2 + 56*x*y*z - 78*x*y*w
      + 12*x*z^2 + 9*x*z*w + 18*x*w^2 + 8*y^3 + 58*y^2*z - 87*y^2*w - 51*y*z^2 
      - 84*y*z*w + 81*y*w^2 - 37*z^3 - 155*z^2*w + 21*z*w^2 - 18*w^3;
ch_pol_sm := tt^5 - 39*tt^4 - 2172*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 24;
Elt := [ 2, 2 ];
bp := [ 2, 3, 7, 17, 37, 2939 ];


gap_nr := 174;
K := NumberField(tt^2-5);
pol1 := K.1*u^3 + (3*K.1 - 8)*u^2 + 4*u + 6*K.1 + 14;
pol2 := -K.1*u^3 + (-3*K.1 - 8)*u^2 + 4*u - 6*K.1 + 14;
gl := -x^2*w + x*y*z + 2*x*y*w - 2*x*z^2 + 4*x*w^2 + y^2*z - 2*y^2*w 
      + z^3 + z*w^2;
ch_pol_sm := tt^5 - 39*tt^4 - 2172*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 24;
Elt := [ 2, 2 ];
bp := [ 2, 3, 7, 17, 37, 2939 ];
res_36_type := [ 2, 3, 3, 4, 12, 12 ];
res_45_type := [ 2, 3, 4, 12, 12, 12 ];
res_72_type := [ 4, 4, 4, 6, 6, 12, 12, 24 ];


gap_nr := 173;
K := NumberField(tt^2-5);
pol1 := (2*K.1 + 1)*u^3 + 1/2*(3*K.1 - 7)*u^2 + (2*K.1 - 1)*u + K.1 + 1;
pol2 := (-2*K.1 + 1)*u^3 + 1/2*(-3*K.1 - 7)*u^2 + (-2*K.1 - 1)*u - K.1 + 1;
gl := 2*x^2*y + 2*x^2*z - x^2*w + x*y^2 - x*z^2 + x*z*w - x*w^2 + y^3 
      + 2*y^2*w + 4*y*z*w + 3*y*w^2 + z^3 - 2*z^2*w + z*w^2 - 3*w^3;
ch_pol_sm := tt^5 - 39*tt^4 - 2172*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 24;
Elt := [ 2, 4 ];
bp := [ 2, 5, 137, 191 ];


gap_nr := 171;
K := NumberField(tt^2-5);
pol1 := K.1*u^3 + (-3*K.1 + 22)*u^2 + (12*K.1 + 12)*u + 8*K.1 + 16;
pol2 := -K.1*u^3 + (3*K.1 + 22)*u^2 + (-12*K.1 + 12)*u - 8*K.1 + 16;
gl := -x^2*w + x*y*z + x*y*w + x*z^2 - 4*x*z*w + 7*x*w^2 - 2*y^2*z 
      + 5*y*z^2 - 4*y*z*w - 5*y*w^2 + 2*z^3 - 3*z^2*w - 9*z*w^2 - 2*w^3;
ch_pol_sm := tt^5 - 39*tt^4 - 2172*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 24;
Elt := [ 2, 2 ];
bp := [ 2, 3, 5, 6761 ];
res_36_type := [ 2, 3, 3, 4, 12, 12 ];
res_45_type := [ 2, 3, 4, 12, 12, 12 ];
res_72_type := [ 3, 3, 4, 4, 4, 6, 12, 12, 24 ];


gap_nr := 167;
K := NumberField(tt^2 - 7);
pol1 := (K.1 + 1)*u^3 + (-3*K.1 - 6)*u - K.1 - 28;
pol2 := (-K.1 + 1)*u^3 + (3*K.1 - 6)*u + K.1 - 28;
gl := -3*x^2*y + 4*x^2*z + x^2*w - x*y^2 + 3*x*y*z + 6*x*y*w + 4*x*z^2 
      - 6*x*z*w - 6*x*w^2 - y^3 - 2*y^2*z + y^2*w + 9*y*z*w + 3*y*w^2 
      - 2*z^3 + z^2*w + 8*z*w^2 - 5*w^3;
ch_pol_sm := tt^5 - 39*tt^4 - 2172*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 24;
Elt := [ 2, 6 ];
bp := [ 2, 3, 7, 19, 31, 37 ];


gap_nr  := 86;
K := NumberField(tt^2 - 5);
pol1 := (K.1 - 3)*u^3 + (17*K.1 - 33)*u^2 + (55*K.1 - 141)*u + 35*K.1 - 59;
pol2 := (-K.1 - 3)*u^3 + (-17*K.1 - 33)*u^2 + (-55*K.1 - 141)*u - 35*K.1 - 59;
gl := -x^3 + x^2*y - x^2*w + 2*x*y*z - x*y*w - x*z^2 - 2*x*z*w - 4*x*w^2 
      - 2*y^2*z + 2*y^2*w - 2*y*z*w - y*w^2 + 2*z^3 + 3*z^2*w - z*w^2 + 3*w^3;
ch_pol_sm := tt^5 - 39*tt^4 - 2172*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 12;
Elt := [ 4 ];
bp := [ 2, 5, 31, 101, 251 ];


gap_nr  := 84;
K := NumberField(tt^2 - 5);
pol1 := (K.1 - 3)*u^3 + (-5*K.1 + 16)*u^2 + (-K.1 - 35)*u + 13*K.1 - 18;
pol2 := (-K.1 - 3)*u^3 + (5*K.1 + 16)*u^2 + (K.1 - 35)*u - 13*K.1 - 18;
gl := -x^2*w - 2*x*y*w + x*z^2 + 7*x*z*w - 28*x*w^2 - y^2*z - 10*y*z^2 
      + 15*y*z*w - 31*z^3 - 18*z^2*w - 5*z*w^2 + 4*w^3;
ch_pol_sm := tt^5 - 39*tt^4 - 2172*tt^3;
h1_gal := 1;
rk_pic := 2;
ord_gal := 12;
Elt := [ 12 ];
bp := [ 2, 5, 7, 7841 ];