// Magma code for the lmfdb family of higher genus curves 13.104-5.0.2-4-52
// 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:=[104,5];
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:=[0,2,4,52];
genus:=13;
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:=[[53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41], [89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 91, 90, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 104, 103, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 78, 77, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 65, 64, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 39, 38, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 52, 51, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 26, 25, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 12], [43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 40, 41, 42, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 27, 28, 29, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 14, 15, 16, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 92, 93, 94, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 79, 80, 81, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 53, 54, 55, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 66, 67, 68]];
cc:=[3,7,22];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41], [85, 84, 83, 82, 81, 80, 79, 91, 90, 89, 88, 87, 86, 98, 97, 96, 95, 94, 93, 92, 104, 103, 102, 101, 100, 99, 72, 71, 70, 69, 68, 67, 66, 78, 77, 76, 75, 74, 73, 59, 58, 57, 56, 55, 54, 53, 65, 64, 63, 62, 61, 60, 33, 32, 31, 30, 29, 28, 27, 39, 38, 37, 36, 35, 34, 46, 45, 44, 43, 42, 41, 40, 52, 51, 50, 49, 48, 47, 20, 19, 18, 17, 16, 15, 14, 26, 25, 24, 23, 22, 21, 7, 6, 5, 4, 3, 2, 1, 13, 12, 11, 10, 9, 8], [47, 48, 49, 50, 51, 52, 40, 41, 42, 43, 44, 45, 46, 34, 35, 36, 37, 38, 39, 27, 28, 29, 30, 31, 32, 33, 8, 9, 10, 11, 12, 13, 1, 2, 3, 4, 5, 6, 7, 21, 22, 23, 24, 25, 26, 14, 15, 16, 17, 18, 19, 20, 99, 100, 101, 102, 103, 104, 92, 93, 94, 95, 96, 97, 98, 86, 87, 88, 89, 90, 91, 79, 80, 81, 82, 83, 84, 85, 60, 61, 62, 63, 64, 65, 53, 54, 55, 56, 57, 58, 59, 73, 74, 75, 76, 77, 78, 66, 67, 68, 69, 70, 71, 72]];
cc:=[3,7,24];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41], [81, 80, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 94, 93, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 68, 67, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 55, 54, 53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 29, 28, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 42, 41, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 16, 15, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 3, 2, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4], [51, 52, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 38, 39, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 12, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 25, 26, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 103, 104, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 90, 91, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 64, 65, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 77, 78, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76]];
cc:=[3,7,26];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=3;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41], [91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 40, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 27, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 14, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 92, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 79, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 53, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 66]];
cc:=[3,7,29];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=4;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41], [87, 86, 85, 84, 83, 82, 81, 80, 79, 91, 90, 89, 88, 100, 99, 98, 97, 96, 95, 94, 93, 92, 104, 103, 102, 101, 74, 73, 72, 71, 70, 69, 68, 67, 66, 78, 77, 76, 75, 61, 60, 59, 58, 57, 56, 55, 54, 53, 65, 64, 63, 62, 35, 34, 33, 32, 31, 30, 29, 28, 27, 39, 38, 37, 36, 48, 47, 46, 45, 44, 43, 42, 41, 40, 52, 51, 50, 49, 22, 21, 20, 19, 18, 17, 16, 15, 14, 26, 25, 24, 23, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 12, 11, 10], [45, 46, 47, 48, 49, 50, 51, 52, 40, 41, 42, 43, 44, 32, 33, 34, 35, 36, 37, 38, 39, 27, 28, 29, 30, 31, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3, 4, 5, 19, 20, 21, 22, 23, 24, 25, 26, 14, 15, 16, 17, 18, 97, 98, 99, 100, 101, 102, 103, 104, 92, 93, 94, 95, 96, 84, 85, 86, 87, 88, 89, 90, 91, 79, 80, 81, 82, 83, 58, 59, 60, 61, 62, 63, 64, 65, 53, 54, 55, 56, 57, 71, 72, 73, 74, 75, 76, 77, 78, 66, 67, 68, 69, 70]];
cc:=[3,7,31];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=5;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41], [83, 82, 81, 80, 79, 91, 90, 89, 88, 87, 86, 85, 84, 96, 95, 94, 93, 92, 104, 103, 102, 101, 100, 99, 98, 97, 70, 69, 68, 67, 66, 78, 77, 76, 75, 74, 73, 72, 71, 57, 56, 55, 54, 53, 65, 64, 63, 62, 61, 60, 59, 58, 31, 30, 29, 28, 27, 39, 38, 37, 36, 35, 34, 33, 32, 44, 43, 42, 41, 40, 52, 51, 50, 49, 48, 47, 46, 45, 18, 17, 16, 15, 14, 26, 25, 24, 23, 22, 21, 20, 19, 5, 4, 3, 2, 1, 13, 12, 11, 10, 9, 8, 7, 6], [49, 50, 51, 52, 40, 41, 42, 43, 44, 45, 46, 47, 48, 36, 37, 38, 39, 27, 28, 29, 30, 31, 32, 33, 34, 35, 10, 11, 12, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 23, 24, 25, 26, 14, 15, 16, 17, 18, 19, 20, 21, 22, 101, 102, 103, 104, 92, 93, 94, 95, 96, 97, 98, 99, 100, 88, 89, 90, 91, 79, 80, 81, 82, 83, 84, 85, 86, 87, 62, 63, 64, 65, 53, 54, 55, 56, 57, 58, 59, 60, 61, 75, 76, 77, 78, 66, 67, 68, 69, 70, 71, 72, 73, 74]];
cc:=[3,7,32];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=6;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41], [104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14], [28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 27, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 40, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 14, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 79, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 92, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 66, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 53]];
cc:=[3,8,21];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=7;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41], [100, 99, 98, 97, 96, 95, 94, 93, 92, 104, 103, 102, 101, 87, 86, 85, 84, 83, 82, 81, 80, 79, 91, 90, 89, 88, 61, 60, 59, 58, 57, 56, 55, 54, 53, 65, 64, 63, 62, 74, 73, 72, 71, 70, 69, 68, 67, 66, 78, 77, 76, 75, 48, 47, 46, 45, 44, 43, 42, 41, 40, 52, 51, 50, 49, 35, 34, 33, 32, 31, 30, 29, 28, 27, 39, 38, 37, 36, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 12, 11, 10, 22, 21, 20, 19, 18, 17, 16, 15, 14, 26, 25, 24, 23], [32, 33, 34, 35, 36, 37, 38, 39, 27, 28, 29, 30, 31, 45, 46, 47, 48, 49, 50, 51, 52, 40, 41, 42, 43, 44, 19, 20, 21, 22, 23, 24, 25, 26, 14, 15, 16, 17, 18, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3, 4, 5, 84, 85, 86, 87, 88, 89, 90, 91, 79, 80, 81, 82, 83, 97, 98, 99, 100, 101, 102, 103, 104, 92, 93, 94, 95, 96, 71, 72, 73, 74, 75, 76, 77, 78, 66, 67, 68, 69, 70, 58, 59, 60, 61, 62, 63, 64, 65, 53, 54, 55, 56, 57]];
cc:=[3,8,23];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=8;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41], [96, 95, 94, 93, 92, 104, 103, 102, 101, 100, 99, 98, 97, 83, 82, 81, 80, 79, 91, 90, 89, 88, 87, 86, 85, 84, 57, 56, 55, 54, 53, 65, 64, 63, 62, 61, 60, 59, 58, 70, 69, 68, 67, 66, 78, 77, 76, 75, 74, 73, 72, 71, 44, 43, 42, 41, 40, 52, 51, 50, 49, 48, 47, 46, 45, 31, 30, 29, 28, 27, 39, 38, 37, 36, 35, 34, 33, 32, 5, 4, 3, 2, 1, 13, 12, 11, 10, 9, 8, 7, 6, 18, 17, 16, 15, 14, 26, 25, 24, 23, 22, 21, 20, 19], [36, 37, 38, 39, 27, 28, 29, 30, 31, 32, 33, 34, 35, 49, 50, 51, 52, 40, 41, 42, 43, 44, 45, 46, 47, 48, 23, 24, 25, 26, 14, 15, 16, 17, 18, 19, 20, 21, 22, 10, 11, 12, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 88, 89, 90, 91, 79, 80, 81, 82, 83, 84, 85, 86, 87, 101, 102, 103, 104, 92, 93, 94, 95, 96, 97, 98, 99, 100, 75, 76, 77, 78, 66, 67, 68, 69, 70, 71, 72, 73, 74, 62, 63, 64, 65, 53, 54, 55, 56, 57, 58, 59, 60, 61]];
cc:=[3,8,25];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=9;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41], [94, 93, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 81, 80, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 55, 54, 53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 68, 67, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 42, 41, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 29, 28, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 3, 2, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 16, 15, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [38, 39, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 51, 52, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 25, 26, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 12, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 90, 91, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 103, 104, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 77, 78, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 64, 65, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63]];
cc:=[3,8,27];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=10;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41], [102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 104, 103, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 91, 90, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 65, 64, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 78, 77, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 52, 51, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 39, 38, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 12, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 26, 25], [30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 27, 28, 29, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 40, 41, 42, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 14, 15, 16, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 79, 80, 81, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 92, 93, 94, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 66, 67, 68, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 53, 54, 55]];
cc:=[3,8,28];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=11;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41], [98, 97, 96, 95, 94, 93, 92, 104, 103, 102, 101, 100, 99, 85, 84, 83, 82, 81, 80, 79, 91, 90, 89, 88, 87, 86, 59, 58, 57, 56, 55, 54, 53, 65, 64, 63, 62, 61, 60, 72, 71, 70, 69, 68, 67, 66, 78, 77, 76, 75, 74, 73, 46, 45, 44, 43, 42, 41, 40, 52, 51, 50, 49, 48, 47, 33, 32, 31, 30, 29, 28, 27, 39, 38, 37, 36, 35, 34, 7, 6, 5, 4, 3, 2, 1, 13, 12, 11, 10, 9, 8, 20, 19, 18, 17, 16, 15, 14, 26, 25, 24, 23, 22, 21], [34, 35, 36, 37, 38, 39, 27, 28, 29, 30, 31, 32, 33, 47, 48, 49, 50, 51, 52, 40, 41, 42, 43, 44, 45, 46, 21, 22, 23, 24, 25, 26, 14, 15, 16, 17, 18, 19, 20, 8, 9, 10, 11, 12, 13, 1, 2, 3, 4, 5, 6, 7, 86, 87, 88, 89, 90, 91, 79, 80, 81, 82, 83, 84, 85, 99, 100, 101, 102, 103, 104, 92, 93, 94, 95, 96, 97, 98, 73, 74, 75, 76, 77, 78, 66, 67, 68, 69, 70, 71, 72, 60, 61, 62, 63, 64, 65, 53, 54, 55, 56, 57, 58, 59]];
cc:=[3,8,30];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=12;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 27, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 40, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 14, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 79, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 92, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 66, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 53]];
cc:=[4,7,21];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=13;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [87, 86, 85, 84, 83, 82, 81, 80, 79, 91, 90, 89, 88, 100, 99, 98, 97, 96, 95, 94, 93, 92, 104, 103, 102, 101, 74, 73, 72, 71, 70, 69, 68, 67, 66, 78, 77, 76, 75, 61, 60, 59, 58, 57, 56, 55, 54, 53, 65, 64, 63, 62, 35, 34, 33, 32, 31, 30, 29, 28, 27, 39, 38, 37, 36, 48, 47, 46, 45, 44, 43, 42, 41, 40, 52, 51, 50, 49, 22, 21, 20, 19, 18, 17, 16, 15, 14, 26, 25, 24, 23, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 12, 11, 10], [32, 33, 34, 35, 36, 37, 38, 39, 27, 28, 29, 30, 31, 45, 46, 47, 48, 49, 50, 51, 52, 40, 41, 42, 43, 44, 19, 20, 21, 22, 23, 24, 25, 26, 14, 15, 16, 17, 18, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3, 4, 5, 84, 85, 86, 87, 88, 89, 90, 91, 79, 80, 81, 82, 83, 97, 98, 99, 100, 101, 102, 103, 104, 92, 93, 94, 95, 96, 71, 72, 73, 74, 75, 76, 77, 78, 66, 67, 68, 69, 70, 58, 59, 60, 61, 62, 63, 64, 65, 53, 54, 55, 56, 57]];
cc:=[4,7,23];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=14;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [83, 82, 81, 80, 79, 91, 90, 89, 88, 87, 86, 85, 84, 96, 95, 94, 93, 92, 104, 103, 102, 101, 100, 99, 98, 97, 70, 69, 68, 67, 66, 78, 77, 76, 75, 74, 73, 72, 71, 57, 56, 55, 54, 53, 65, 64, 63, 62, 61, 60, 59, 58, 31, 30, 29, 28, 27, 39, 38, 37, 36, 35, 34, 33, 32, 44, 43, 42, 41, 40, 52, 51, 50, 49, 48, 47, 46, 45, 18, 17, 16, 15, 14, 26, 25, 24, 23, 22, 21, 20, 19, 5, 4, 3, 2, 1, 13, 12, 11, 10, 9, 8, 7, 6], [36, 37, 38, 39, 27, 28, 29, 30, 31, 32, 33, 34, 35, 49, 50, 51, 52, 40, 41, 42, 43, 44, 45, 46, 47, 48, 23, 24, 25, 26, 14, 15, 16, 17, 18, 19, 20, 21, 22, 10, 11, 12, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 88, 89, 90, 91, 79, 80, 81, 82, 83, 84, 85, 86, 87, 101, 102, 103, 104, 92, 93, 94, 95, 96, 97, 98, 99, 100, 75, 76, 77, 78, 66, 67, 68, 69, 70, 71, 72, 73, 74, 62, 63, 64, 65, 53, 54, 55, 56, 57, 58, 59, 60, 61]];
cc:=[4,7,25];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=15;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [81, 80, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 94, 93, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 68, 67, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 55, 54, 53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 29, 28, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 42, 41, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 16, 15, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 3, 2, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4], [38, 39, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 51, 52, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 25, 26, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 12, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 90, 91, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 103, 104, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 77, 78, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 64, 65, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63]];
cc:=[4,7,27];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=16;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 91, 90, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 104, 103, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 78, 77, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 65, 64, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 39, 38, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 52, 51, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 26, 25, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 12], [30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 27, 28, 29, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 40, 41, 42, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 14, 15, 16, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 79, 80, 81, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 92, 93, 94, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 66, 67, 68, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 53, 54, 55]];
cc:=[4,7,28];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=17;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [85, 84, 83, 82, 81, 80, 79, 91, 90, 89, 88, 87, 86, 98, 97, 96, 95, 94, 93, 92, 104, 103, 102, 101, 100, 99, 72, 71, 70, 69, 68, 67, 66, 78, 77, 76, 75, 74, 73, 59, 58, 57, 56, 55, 54, 53, 65, 64, 63, 62, 61, 60, 33, 32, 31, 30, 29, 28, 27, 39, 38, 37, 36, 35, 34, 46, 45, 44, 43, 42, 41, 40, 52, 51, 50, 49, 48, 47, 20, 19, 18, 17, 16, 15, 14, 26, 25, 24, 23, 22, 21, 7, 6, 5, 4, 3, 2, 1, 13, 12, 11, 10, 9, 8], [34, 35, 36, 37, 38, 39, 27, 28, 29, 30, 31, 32, 33, 47, 48, 49, 50, 51, 52, 40, 41, 42, 43, 44, 45, 46, 21, 22, 23, 24, 25, 26, 14, 15, 16, 17, 18, 19, 20, 8, 9, 10, 11, 12, 13, 1, 2, 3, 4, 5, 6, 7, 86, 87, 88, 89, 90, 91, 79, 80, 81, 82, 83, 84, 85, 99, 100, 101, 102, 103, 104, 92, 93, 94, 95, 96, 97, 98, 73, 74, 75, 76, 77, 78, 66, 67, 68, 69, 70, 71, 72, 60, 61, 62, 63, 64, 65, 53, 54, 55, 56, 57, 58, 59]];
cc:=[4,7,30];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=18;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 104, 103, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 91, 90, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 65, 64, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 78, 77, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 52, 51, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 39, 38, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 12, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 26, 25], [43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 40, 41, 42, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 27, 28, 29, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 14, 15, 16, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 92, 93, 94, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 79, 80, 81, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 53, 54, 55, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 66, 67, 68]];
cc:=[4,8,22];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=19;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [98, 97, 96, 95, 94, 93, 92, 104, 103, 102, 101, 100, 99, 85, 84, 83, 82, 81, 80, 79, 91, 90, 89, 88, 87, 86, 59, 58, 57, 56, 55, 54, 53, 65, 64, 63, 62, 61, 60, 72, 71, 70, 69, 68, 67, 66, 78, 77, 76, 75, 74, 73, 46, 45, 44, 43, 42, 41, 40, 52, 51, 50, 49, 48, 47, 33, 32, 31, 30, 29, 28, 27, 39, 38, 37, 36, 35, 34, 7, 6, 5, 4, 3, 2, 1, 13, 12, 11, 10, 9, 8, 20, 19, 18, 17, 16, 15, 14, 26, 25, 24, 23, 22, 21], [47, 48, 49, 50, 51, 52, 40, 41, 42, 43, 44, 45, 46, 34, 35, 36, 37, 38, 39, 27, 28, 29, 30, 31, 32, 33, 8, 9, 10, 11, 12, 13, 1, 2, 3, 4, 5, 6, 7, 21, 22, 23, 24, 25, 26, 14, 15, 16, 17, 18, 19, 20, 99, 100, 101, 102, 103, 104, 92, 93, 94, 95, 96, 97, 98, 86, 87, 88, 89, 90, 91, 79, 80, 81, 82, 83, 84, 85, 60, 61, 62, 63, 64, 65, 53, 54, 55, 56, 57, 58, 59, 73, 74, 75, 76, 77, 78, 66, 67, 68, 69, 70, 71, 72]];
cc:=[4,8,24];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=20;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [94, 93, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 81, 80, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 55, 54, 53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 68, 67, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 42, 41, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 29, 28, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 3, 2, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 16, 15, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [51, 52, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 38, 39, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 12, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 25, 26, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 103, 104, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 90, 91, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 64, 65, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 77, 78, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76]];
cc:=[4,8,26];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=21;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 40, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 27, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 14, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 92, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 79, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 53, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 66]];
cc:=[4,8,29];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=22;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [100, 99, 98, 97, 96, 95, 94, 93, 92, 104, 103, 102, 101, 87, 86, 85, 84, 83, 82, 81, 80, 79, 91, 90, 89, 88, 61, 60, 59, 58, 57, 56, 55, 54, 53, 65, 64, 63, 62, 74, 73, 72, 71, 70, 69, 68, 67, 66, 78, 77, 76, 75, 48, 47, 46, 45, 44, 43, 42, 41, 40, 52, 51, 50, 49, 35, 34, 33, 32, 31, 30, 29, 28, 27, 39, 38, 37, 36, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 12, 11, 10, 22, 21, 20, 19, 18, 17, 16, 15, 14, 26, 25, 24, 23], [45, 46, 47, 48, 49, 50, 51, 52, 40, 41, 42, 43, 44, 32, 33, 34, 35, 36, 37, 38, 39, 27, 28, 29, 30, 31, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3, 4, 5, 19, 20, 21, 22, 23, 24, 25, 26, 14, 15, 16, 17, 18, 97, 98, 99, 100, 101, 102, 103, 104, 92, 93, 94, 95, 96, 84, 85, 86, 87, 88, 89, 90, 91, 79, 80, 81, 82, 83, 58, 59, 60, 61, 62, 63, 64, 65, 53, 54, 55, 56, 57, 71, 72, 73, 74, 75, 76, 77, 78, 66, 67, 68, 69, 70]];
cc:=[4,8,31];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=23;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [96, 95, 94, 93, 92, 104, 103, 102, 101, 100, 99, 98, 97, 83, 82, 81, 80, 79, 91, 90, 89, 88, 87, 86, 85, 84, 57, 56, 55, 54, 53, 65, 64, 63, 62, 61, 60, 59, 58, 70, 69, 68, 67, 66, 78, 77, 76, 75, 74, 73, 72, 71, 44, 43, 42, 41, 40, 52, 51, 50, 49, 48, 47, 46, 45, 31, 30, 29, 28, 27, 39, 38, 37, 36, 35, 34, 33, 32, 5, 4, 3, 2, 1, 13, 12, 11, 10, 9, 8, 7, 6, 18, 17, 16, 15, 14, 26, 25, 24, 23, 22, 21, 20, 19], [49, 50, 51, 52, 40, 41, 42, 43, 44, 45, 46, 47, 48, 36, 37, 38, 39, 27, 28, 29, 30, 31, 32, 33, 34, 35, 10, 11, 12, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 23, 24, 25, 26, 14, 15, 16, 17, 18, 19, 20, 21, 22, 101, 102, 103, 104, 92, 93, 94, 95, 96, 97, 98, 99, 100, 88, 89, 90, 91, 79, 80, 81, 82, 83, 84, 85, 86, 87, 62, 63, 64, 65, 53, 54, 55, 56, 57, 58, 59, 60, 61, 75, 76, 77, 78, 66, 67, 68, 69, 70, 71, 72, 73, 74]];
cc:=[4,8,32];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=24;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);
