// Magma code for the lmfdb family of higher genus curves 14.16-1.0.8-8-16-16
// The results are stored in a list of records called 'data'

RecFormat:=recformat<group,gp_id, signature,gen_vectors,conj_classes,genus,dimension,r,g0, passport_label,gen_vect_label, is_hyperelliptic, hyp_involution, is_cyclic_trigonal,cyc_auto,full_auto, full_sign,topological_class,braid_class>;

data:=[];

// Create group as a permutation group, and generate data which is the same for all entries.
gp_id:=[16,1];
H:=SmallGroup(gp_id[1],gp_id[2]); n:=#H; LP:=[]; LG:=[g : g in H]; for i in [1..n] do x:=LG[i]; Tx:=[LG[j]*x : j in [1..n]]; permL:=[]; for j in [1..n] do for k in [1..n] do if Tx[j] eq LG[k] then permL[j]:=k;  break; end if; end for; end for; Append(~LP,permL); end for; G:=PermutationGroup<n|LP>; 
signature:=[0,8,8,16,16];
genus:=14;
r:=#signature-1;
g0:=signature[1];
dim:=3*g0-3+r;
S:=Sym(gp_id[1]);

// Here we add an action to data.
gen_vectors:=[[5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [9, 10, 11, 12, 13, 14, 15, 16, 5, 6, 7, 8, 3, 4, 2, 1], [14, 13, 16, 15, 12, 11, 9, 10, 4, 3, 1, 2, 8, 7, 5, 6]];
cc:=[5,5,9,14];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [13, 14, 15, 16, 11, 12, 10, 9, 3, 4, 2, 1, 7, 8, 6, 5], [10, 9, 12, 11, 14, 13, 16, 15, 6, 5, 8, 7, 4, 3, 1, 2]];
cc:=[5,5,10,13];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [11, 12, 10, 9, 15, 16, 14, 13, 7, 8, 6, 5, 2, 1, 4, 3], [15, 16, 14, 13, 10, 9, 12, 11, 2, 1, 4, 3, 6, 5, 8, 7]];
cc:=[5,5,11,12];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=3;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [12, 11, 9, 10, 16, 15, 13, 14, 8, 7, 5, 6, 1, 2, 3, 4], [16, 15, 13, 14, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8]];
cc:=[5,5,15,16];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=4;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [9, 10, 11, 12, 13, 14, 15, 16, 5, 6, 7, 8, 3, 4, 2, 1], [15, 16, 14, 13, 10, 9, 12, 11, 2, 1, 4, 3, 6, 5, 8, 7]];
cc:=[5,6,9,12];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=5;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [13, 14, 15, 16, 11, 12, 10, 9, 3, 4, 2, 1, 7, 8, 6, 5], [11, 12, 10, 9, 15, 16, 14, 13, 7, 8, 6, 5, 2, 1, 4, 3]];
cc:=[5,6,10,11];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=6;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [10, 9, 12, 11, 14, 13, 16, 15, 6, 5, 8, 7, 4, 3, 1, 2], [16, 15, 13, 14, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8]];
cc:=[5,6,13,16];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=7;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [14, 13, 16, 15, 12, 11, 9, 10, 4, 3, 1, 2, 8, 7, 5, 6], [12, 11, 9, 10, 16, 15, 13, 14, 8, 7, 5, 6, 1, 2, 3, 4]];
cc:=[5,6,14,15];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=8;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [9, 10, 11, 12, 13, 14, 15, 16, 5, 6, 7, 8, 3, 4, 2, 1], [13, 14, 15, 16, 11, 12, 10, 9, 3, 4, 2, 1, 7, 8, 6, 5]];
cc:=[5,7,9,10];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=9;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [11, 12, 10, 9, 15, 16, 14, 13, 7, 8, 6, 5, 2, 1, 4, 3], [16, 15, 13, 14, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8]];
cc:=[5,7,11,16];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=10;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [15, 16, 14, 13, 10, 9, 12, 11, 2, 1, 4, 3, 6, 5, 8, 7], [12, 11, 9, 10, 16, 15, 13, 14, 8, 7, 5, 6, 1, 2, 3, 4]];
cc:=[5,7,12,15];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=11;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [10, 9, 12, 11, 14, 13, 16, 15, 6, 5, 8, 7, 4, 3, 1, 2], [14, 13, 16, 15, 12, 11, 9, 10, 4, 3, 1, 2, 8, 7, 5, 6]];
cc:=[5,7,13,14];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=12;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [9, 10, 11, 12, 13, 14, 15, 16, 5, 6, 7, 8, 3, 4, 2, 1], [16, 15, 13, 14, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8]];
cc:=[5,8,9,16];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=13;
gen_vect_label:=1;
full_auto:=[32,18];
full_sign:=[0,2,2,8,16];
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [13, 14, 15, 16, 11, 12, 10, 9, 3, 4, 2, 1, 7, 8, 6, 5], [12, 11, 9, 10, 16, 15, 13, 14, 8, 7, 5, 6, 1, 2, 3, 4]];
cc:=[5,8,10,15];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=14;
gen_vect_label:=1;
full_auto:=[32,18];
full_sign:=[0,2,2,8,16];
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [11, 12, 10, 9, 15, 16, 14, 13, 7, 8, 6, 5, 2, 1, 4, 3], [14, 13, 16, 15, 12, 11, 9, 10, 4, 3, 1, 2, 8, 7, 5, 6]];
cc:=[5,8,11,14];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=15;
gen_vect_label:=1;
full_auto:=[32,18];
full_sign:=[0,2,2,8,16];
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9], [8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [15, 16, 14, 13, 10, 9, 12, 11, 2, 1, 4, 3, 6, 5, 8, 7], [10, 9, 12, 11, 14, 13, 16, 15, 6, 5, 8, 7, 4, 3, 1, 2]];
cc:=[5,8,12,13];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=16;
gen_vect_label:=1;
full_auto:=[32,18];
full_sign:=[0,2,2,8,16];
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [9, 10, 11, 12, 13, 14, 15, 16, 5, 6, 7, 8, 3, 4, 2, 1], [13, 14, 15, 16, 11, 12, 10, 9, 3, 4, 2, 1, 7, 8, 6, 5]];
cc:=[6,6,9,10];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=17;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [11, 12, 10, 9, 15, 16, 14, 13, 7, 8, 6, 5, 2, 1, 4, 3], [16, 15, 13, 14, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8]];
cc:=[6,6,11,16];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=18;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [15, 16, 14, 13, 10, 9, 12, 11, 2, 1, 4, 3, 6, 5, 8, 7], [12, 11, 9, 10, 16, 15, 13, 14, 8, 7, 5, 6, 1, 2, 3, 4]];
cc:=[6,6,12,15];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=19;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [10, 9, 12, 11, 14, 13, 16, 15, 6, 5, 8, 7, 4, 3, 1, 2], [14, 13, 16, 15, 12, 11, 9, 10, 4, 3, 1, 2, 8, 7, 5, 6]];
cc:=[6,6,13,14];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=20;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [9, 10, 11, 12, 13, 14, 15, 16, 5, 6, 7, 8, 3, 4, 2, 1], [16, 15, 13, 14, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8]];
cc:=[6,7,9,16];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=21;
gen_vect_label:=1;
full_auto:=[32,18];
full_sign:=[0,2,2,8,16];
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [13, 14, 15, 16, 11, 12, 10, 9, 3, 4, 2, 1, 7, 8, 6, 5], [12, 11, 9, 10, 16, 15, 13, 14, 8, 7, 5, 6, 1, 2, 3, 4]];
cc:=[6,7,10,15];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=22;
gen_vect_label:=1;
full_auto:=[32,18];
full_sign:=[0,2,2,8,16];
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [11, 12, 10, 9, 15, 16, 14, 13, 7, 8, 6, 5, 2, 1, 4, 3], [14, 13, 16, 15, 12, 11, 9, 10, 4, 3, 1, 2, 8, 7, 5, 6]];
cc:=[6,7,11,14];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=23;
gen_vect_label:=1;
full_auto:=[32,18];
full_sign:=[0,2,2,8,16];
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [15, 16, 14, 13, 10, 9, 12, 11, 2, 1, 4, 3, 6, 5, 8, 7], [10, 9, 12, 11, 14, 13, 16, 15, 6, 5, 8, 7, 4, 3, 1, 2]];
cc:=[6,7,12,13];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=24;
gen_vect_label:=1;
full_auto:=[32,18];
full_sign:=[0,2,2,8,16];
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [9, 10, 11, 12, 13, 14, 15, 16, 5, 6, 7, 8, 3, 4, 2, 1], [14, 13, 16, 15, 12, 11, 9, 10, 4, 3, 1, 2, 8, 7, 5, 6]];
cc:=[6,8,9,14];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=25;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [13, 14, 15, 16, 11, 12, 10, 9, 3, 4, 2, 1, 7, 8, 6, 5], [10, 9, 12, 11, 14, 13, 16, 15, 6, 5, 8, 7, 4, 3, 1, 2]];
cc:=[6,8,10,13];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=26;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [11, 12, 10, 9, 15, 16, 14, 13, 7, 8, 6, 5, 2, 1, 4, 3], [15, 16, 14, 13, 10, 9, 12, 11, 2, 1, 4, 3, 6, 5, 8, 7]];
cc:=[6,8,11,12];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=27;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11], [8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [12, 11, 9, 10, 16, 15, 13, 14, 8, 7, 5, 6, 1, 2, 3, 4], [16, 15, 13, 14, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8]];
cc:=[6,8,15,16];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=28;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [9, 10, 11, 12, 13, 14, 15, 16, 5, 6, 7, 8, 3, 4, 2, 1], [14, 13, 16, 15, 12, 11, 9, 10, 4, 3, 1, 2, 8, 7, 5, 6]];
cc:=[7,7,9,14];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=29;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [13, 14, 15, 16, 11, 12, 10, 9, 3, 4, 2, 1, 7, 8, 6, 5], [10, 9, 12, 11, 14, 13, 16, 15, 6, 5, 8, 7, 4, 3, 1, 2]];
cc:=[7,7,10,13];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=30;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [11, 12, 10, 9, 15, 16, 14, 13, 7, 8, 6, 5, 2, 1, 4, 3], [15, 16, 14, 13, 10, 9, 12, 11, 2, 1, 4, 3, 6, 5, 8, 7]];
cc:=[7,7,11,12];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=31;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [12, 11, 9, 10, 16, 15, 13, 14, 8, 7, 5, 6, 1, 2, 3, 4], [16, 15, 13, 14, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8]];
cc:=[7,7,15,16];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=32;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [9, 10, 11, 12, 13, 14, 15, 16, 5, 6, 7, 8, 3, 4, 2, 1], [15, 16, 14, 13, 10, 9, 12, 11, 2, 1, 4, 3, 6, 5, 8, 7]];
cc:=[7,8,9,12];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=33;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [13, 14, 15, 16, 11, 12, 10, 9, 3, 4, 2, 1, 7, 8, 6, 5], [11, 12, 10, 9, 15, 16, 14, 13, 7, 8, 6, 5, 2, 1, 4, 3]];
cc:=[7,8,10,11];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=34;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [10, 9, 12, 11, 14, 13, 16, 15, 6, 5, 8, 7, 4, 3, 1, 2], [16, 15, 13, 14, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8]];
cc:=[7,8,13,16];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=35;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10], [8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [14, 13, 16, 15, 12, 11, 9, 10, 4, 3, 1, 2, 8, 7, 5, 6], [12, 11, 9, 10, 16, 15, 13, 14, 8, 7, 5, 6, 1, 2, 3, 4]];
cc:=[7,8,14,15];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=36;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [9, 10, 11, 12, 13, 14, 15, 16, 5, 6, 7, 8, 3, 4, 2, 1], [13, 14, 15, 16, 11, 12, 10, 9, 3, 4, 2, 1, 7, 8, 6, 5]];
cc:=[8,8,9,10];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=37;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [11, 12, 10, 9, 15, 16, 14, 13, 7, 8, 6, 5, 2, 1, 4, 3], [16, 15, 13, 14, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8]];
cc:=[8,8,11,16];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=38;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [15, 16, 14, 13, 10, 9, 12, 11, 2, 1, 4, 3, 6, 5, 8, 7], [12, 11, 9, 10, 16, 15, 13, 14, 8, 7, 5, 6, 1, 2, 3, 4]];
cc:=[8,8,12,15];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=39;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12], [10, 9, 12, 11, 14, 13, 16, 15, 6, 5, 8, 7, 4, 3, 1, 2], [14, 13, 16, 15, 12, 11, 9, 10, 4, 3, 1, 2, 8, 7, 5, 6]];
cc:=[8,8,13,14];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=40;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);
