// Magma code for the lmfdb family of higher genus curves 13.128-71.0.2-4-16
// 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:=[128,71];
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:=[0,2,4,16];
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:=[[33, 34, 36, 35, 38, 37, 39, 40, 48, 47, 46, 45, 44, 43, 42, 41, 51, 52, 49, 50, 56, 55, 54, 53, 61, 62, 64, 63, 57, 58, 60, 59, 1, 2, 4, 3, 6, 5, 7, 8, 16, 15, 14, 13, 12, 11, 10, 9, 19, 20, 17, 18, 24, 23, 22, 21, 29, 30, 32, 31, 25, 26, 28, 27, 97, 98, 100, 99, 102, 101, 103, 104, 112, 111, 110, 109, 108, 107, 106, 105, 115, 116, 113, 114, 120, 119, 118, 117, 125, 126, 128, 127, 121, 122, 124, 123, 65, 66, 68, 67, 70, 69, 71, 72, 80, 79, 78, 77, 76, 75, 74, 73, 83, 84, 81, 82, 88, 87, 86, 85, 93, 94, 96, 95, 89, 90, 92, 91], [70, 69, 71, 72, 65, 66, 68, 67, 78, 77, 79, 80, 73, 74, 76, 75, 81, 82, 84, 83, 85, 86, 88, 87, 89, 90, 92, 91, 93, 94, 96, 95, 118, 117, 119, 120, 113, 114, 116, 115, 126, 125, 127, 128, 121, 122, 124, 123, 100, 99, 98, 97, 104, 103, 102, 101, 108, 107, 106, 105, 112, 111, 110, 109, 14, 13, 15, 16, 9, 10, 12, 11, 6, 5, 7, 8, 1, 2, 4, 3, 26, 25, 27, 28, 30, 29, 31, 32, 18, 17, 19, 20, 22, 21, 23, 24, 59, 60, 57, 58, 63, 64, 61, 62, 51, 52, 49, 50, 55, 56, 53, 54, 46, 45, 47, 48, 41, 42, 44, 43, 38, 37, 39, 40, 33, 34, 36, 35], [108, 107, 105, 106, 111, 112, 110, 109, 102, 101, 104, 103, 98, 97, 100, 99, 126, 125, 128, 127, 122, 121, 124, 123, 116, 115, 113, 114, 119, 120, 118, 117, 89, 90, 91, 92, 94, 93, 96, 95, 88, 87, 85, 86, 84, 83, 81, 82, 78, 77, 80, 79, 74, 73, 76, 75, 68, 67, 65, 66, 71, 72, 70, 69, 38, 37, 40, 39, 34, 33, 36, 35, 44, 43, 41, 42, 47, 48, 46, 45, 51, 52, 50, 49, 56, 55, 53, 54, 61, 62, 63, 64, 57, 58, 59, 60, 18, 17, 20, 19, 21, 22, 23, 24, 31, 32, 30, 29, 27, 28, 26, 25, 6, 5, 8, 7, 2, 1, 4, 3, 12, 11, 9, 10, 15, 16, 14, 13]];
cc:=[5,9,18];
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:=[[33, 34, 36, 35, 38, 37, 39, 40, 48, 47, 46, 45, 44, 43, 42, 41, 51, 52, 49, 50, 56, 55, 54, 53, 61, 62, 64, 63, 57, 58, 60, 59, 1, 2, 4, 3, 6, 5, 7, 8, 16, 15, 14, 13, 12, 11, 10, 9, 19, 20, 17, 18, 24, 23, 22, 21, 29, 30, 32, 31, 25, 26, 28, 27, 97, 98, 100, 99, 102, 101, 103, 104, 112, 111, 110, 109, 108, 107, 106, 105, 115, 116, 113, 114, 120, 119, 118, 117, 125, 126, 128, 127, 121, 122, 124, 123, 65, 66, 68, 67, 70, 69, 71, 72, 80, 79, 78, 77, 76, 75, 74, 73, 83, 84, 81, 82, 88, 87, 86, 85, 93, 94, 96, 95, 89, 90, 92, 91], [65, 66, 68, 67, 69, 70, 72, 71, 73, 74, 76, 75, 77, 78, 80, 79, 85, 86, 88, 87, 82, 81, 83, 84, 93, 94, 96, 95, 90, 89, 91, 92, 113, 114, 116, 115, 117, 118, 120, 119, 121, 122, 124, 123, 125, 126, 128, 127, 104, 103, 102, 101, 99, 100, 97, 98, 112, 111, 110, 109, 107, 108, 105, 106, 9, 10, 12, 11, 13, 14, 16, 15, 1, 2, 4, 3, 5, 6, 8, 7, 30, 29, 31, 32, 25, 26, 28, 27, 22, 21, 23, 24, 17, 18, 20, 19, 63, 64, 61, 62, 60, 59, 58, 57, 55, 56, 53, 54, 52, 51, 50, 49, 41, 42, 44, 43, 45, 46, 48, 47, 33, 34, 36, 35, 37, 38, 40, 39], [112, 111, 109, 110, 108, 107, 105, 106, 97, 98, 99, 100, 102, 101, 104, 103, 121, 122, 123, 124, 126, 125, 128, 127, 120, 119, 117, 118, 116, 115, 113, 114, 93, 94, 95, 96, 89, 90, 91, 92, 83, 84, 82, 81, 88, 87, 85, 86, 73, 74, 75, 76, 78, 77, 80, 79, 72, 71, 69, 70, 68, 67, 65, 66, 33, 34, 35, 36, 38, 37, 40, 39, 48, 47, 45, 46, 44, 43, 41, 42, 55, 56, 54, 53, 51, 52, 50, 49, 58, 57, 60, 59, 61, 62, 63, 64, 22, 21, 24, 23, 18, 17, 20, 19, 28, 27, 25, 26, 31, 32, 30, 29, 1, 2, 3, 4, 6, 5, 8, 7, 16, 15, 13, 14, 12, 11, 9, 10]];
cc:=[5,9,20];
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:=[[33, 34, 36, 35, 38, 37, 39, 40, 48, 47, 46, 45, 44, 43, 42, 41, 51, 52, 49, 50, 56, 55, 54, 53, 61, 62, 64, 63, 57, 58, 60, 59, 1, 2, 4, 3, 6, 5, 7, 8, 16, 15, 14, 13, 12, 11, 10, 9, 19, 20, 17, 18, 24, 23, 22, 21, 29, 30, 32, 31, 25, 26, 28, 27, 97, 98, 100, 99, 102, 101, 103, 104, 112, 111, 110, 109, 108, 107, 106, 105, 115, 116, 113, 114, 120, 119, 118, 117, 125, 126, 128, 127, 121, 122, 124, 123, 65, 66, 68, 67, 70, 69, 71, 72, 80, 79, 78, 77, 76, 75, 74, 73, 83, 84, 81, 82, 88, 87, 86, 85, 93, 94, 96, 95, 89, 90, 92, 91], [73, 74, 76, 75, 77, 78, 80, 79, 65, 66, 68, 67, 69, 70, 72, 71, 93, 94, 96, 95, 90, 89, 91, 92, 85, 86, 88, 87, 82, 81, 83, 84, 121, 122, 124, 123, 125, 126, 128, 127, 113, 114, 116, 115, 117, 118, 120, 119, 112, 111, 110, 109, 107, 108, 105, 106, 104, 103, 102, 101, 99, 100, 97, 98, 1, 2, 4, 3, 5, 6, 8, 7, 9, 10, 12, 11, 13, 14, 16, 15, 22, 21, 23, 24, 17, 18, 20, 19, 30, 29, 31, 32, 25, 26, 28, 27, 55, 56, 53, 54, 52, 51, 50, 49, 63, 64, 61, 62, 60, 59, 58, 57, 33, 34, 36, 35, 37, 38, 40, 39, 41, 42, 44, 43, 45, 46, 48, 47], [97, 98, 99, 100, 102, 101, 104, 103, 112, 111, 109, 110, 108, 107, 105, 106, 120, 119, 117, 118, 116, 115, 113, 114, 121, 122, 123, 124, 126, 125, 128, 127, 83, 84, 82, 81, 88, 87, 85, 86, 93, 94, 95, 96, 89, 90, 91, 92, 72, 71, 69, 70, 68, 67, 65, 66, 73, 74, 75, 76, 78, 77, 80, 79, 48, 47, 45, 46, 44, 43, 41, 42, 33, 34, 35, 36, 38, 37, 40, 39, 58, 57, 60, 59, 61, 62, 63, 64, 55, 56, 54, 53, 51, 52, 50, 49, 28, 27, 25, 26, 31, 32, 30, 29, 22, 21, 24, 23, 18, 17, 20, 19, 16, 15, 13, 14, 12, 11, 9, 10, 1, 2, 3, 4, 6, 5, 8, 7]];
cc:=[5,10,17];
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:=[[33, 34, 36, 35, 38, 37, 39, 40, 48, 47, 46, 45, 44, 43, 42, 41, 51, 52, 49, 50, 56, 55, 54, 53, 61, 62, 64, 63, 57, 58, 60, 59, 1, 2, 4, 3, 6, 5, 7, 8, 16, 15, 14, 13, 12, 11, 10, 9, 19, 20, 17, 18, 24, 23, 22, 21, 29, 30, 32, 31, 25, 26, 28, 27, 97, 98, 100, 99, 102, 101, 103, 104, 112, 111, 110, 109, 108, 107, 106, 105, 115, 116, 113, 114, 120, 119, 118, 117, 125, 126, 128, 127, 121, 122, 124, 123, 65, 66, 68, 67, 70, 69, 71, 72, 80, 79, 78, 77, 76, 75, 74, 73, 83, 84, 81, 82, 88, 87, 86, 85, 93, 94, 96, 95, 89, 90, 92, 91], [77, 78, 80, 79, 74, 73, 75, 76, 69, 70, 72, 71, 66, 65, 67, 68, 90, 89, 91, 92, 94, 93, 95, 96, 82, 81, 83, 84, 86, 85, 87, 88, 125, 126, 128, 127, 122, 121, 123, 124, 117, 118, 120, 119, 114, 113, 115, 116, 107, 108, 105, 106, 111, 112, 109, 110, 99, 100, 97, 98, 103, 104, 101, 102, 5, 6, 8, 7, 2, 1, 3, 4, 13, 14, 16, 15, 10, 9, 11, 12, 17, 18, 20, 19, 21, 22, 24, 23, 25, 26, 28, 27, 29, 30, 32, 31, 52, 51, 50, 49, 56, 55, 54, 53, 60, 59, 58, 57, 64, 63, 62, 61, 37, 38, 40, 39, 34, 33, 35, 36, 45, 46, 48, 47, 42, 41, 43, 44], [101, 102, 103, 104, 97, 98, 99, 100, 107, 108, 106, 105, 112, 111, 109, 110, 115, 116, 114, 113, 120, 119, 117, 118, 125, 126, 127, 128, 121, 122, 123, 124, 87, 88, 86, 85, 83, 84, 82, 81, 90, 89, 92, 91, 93, 94, 95, 96, 67, 68, 66, 65, 72, 71, 69, 70, 77, 78, 79, 80, 73, 74, 75, 76, 43, 44, 42, 41, 48, 47, 45, 46, 37, 38, 39, 40, 33, 34, 35, 36, 62, 61, 64, 63, 58, 57, 60, 59, 52, 51, 49, 50, 55, 56, 54, 53, 32, 31, 29, 30, 28, 27, 25, 26, 17, 18, 19, 20, 22, 21, 24, 23, 11, 12, 10, 9, 16, 15, 13, 14, 5, 6, 7, 8, 1, 2, 3, 4]];
cc:=[5,10,19];
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:=[[33, 34, 36, 35, 38, 37, 39, 40, 48, 47, 46, 45, 44, 43, 42, 41, 51, 52, 49, 50, 56, 55, 54, 53, 61, 62, 64, 63, 57, 58, 60, 59, 1, 2, 4, 3, 6, 5, 7, 8, 16, 15, 14, 13, 12, 11, 10, 9, 19, 20, 17, 18, 24, 23, 22, 21, 29, 30, 32, 31, 25, 26, 28, 27, 97, 98, 100, 99, 102, 101, 103, 104, 112, 111, 110, 109, 108, 107, 106, 105, 115, 116, 113, 114, 120, 119, 118, 117, 125, 126, 128, 127, 121, 122, 124, 123, 65, 66, 68, 67, 70, 69, 71, 72, 80, 79, 78, 77, 76, 75, 74, 73, 83, 84, 81, 82, 88, 87, 86, 85, 93, 94, 96, 95, 89, 90, 92, 91], [67, 68, 65, 66, 71, 72, 69, 70, 75, 76, 73, 74, 79, 80, 77, 78, 87, 88, 85, 86, 84, 83, 82, 81, 95, 96, 93, 94, 92, 91, 90, 89, 115, 116, 113, 114, 119, 120, 117, 118, 123, 124, 121, 122, 127, 128, 125, 126, 101, 102, 104, 103, 98, 97, 99, 100, 109, 110, 112, 111, 106, 105, 107, 108, 11, 12, 9, 10, 15, 16, 13, 14, 3, 4, 1, 2, 7, 8, 5, 6, 32, 31, 30, 29, 27, 28, 25, 26, 24, 23, 22, 21, 19, 20, 17, 18, 62, 61, 63, 64, 57, 58, 60, 59, 54, 53, 55, 56, 49, 50, 52, 51, 43, 44, 41, 42, 47, 48, 45, 46, 35, 36, 33, 34, 39, 40, 37, 38], [110, 109, 112, 111, 106, 105, 108, 107, 100, 99, 97, 98, 103, 104, 102, 101, 124, 123, 121, 122, 127, 128, 126, 125, 118, 117, 120, 119, 114, 113, 116, 115, 96, 95, 93, 94, 92, 91, 89, 90, 81, 82, 83, 84, 86, 85, 88, 87, 76, 75, 73, 74, 79, 80, 78, 77, 70, 69, 72, 71, 66, 65, 68, 67, 36, 35, 33, 34, 39, 40, 38, 37, 46, 45, 48, 47, 42, 41, 44, 43, 53, 54, 55, 56, 49, 50, 51, 52, 59, 60, 58, 57, 64, 63, 61, 62, 23, 24, 22, 21, 19, 20, 18, 17, 26, 25, 28, 27, 29, 30, 31, 32, 4, 3, 1, 2, 7, 8, 6, 5, 14, 13, 16, 15, 10, 9, 12, 11]];
cc:=[5,11,18];
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:=[[33, 34, 36, 35, 38, 37, 39, 40, 48, 47, 46, 45, 44, 43, 42, 41, 51, 52, 49, 50, 56, 55, 54, 53, 61, 62, 64, 63, 57, 58, 60, 59, 1, 2, 4, 3, 6, 5, 7, 8, 16, 15, 14, 13, 12, 11, 10, 9, 19, 20, 17, 18, 24, 23, 22, 21, 29, 30, 32, 31, 25, 26, 28, 27, 97, 98, 100, 99, 102, 101, 103, 104, 112, 111, 110, 109, 108, 107, 106, 105, 115, 116, 113, 114, 120, 119, 118, 117, 125, 126, 128, 127, 121, 122, 124, 123, 65, 66, 68, 67, 70, 69, 71, 72, 80, 79, 78, 77, 76, 75, 74, 73, 83, 84, 81, 82, 88, 87, 86, 85, 93, 94, 96, 95, 89, 90, 92, 91], [72, 71, 70, 69, 67, 68, 65, 66, 80, 79, 78, 77, 75, 76, 73, 74, 83, 84, 81, 82, 87, 88, 85, 86, 91, 92, 89, 90, 95, 96, 93, 94, 120, 119, 118, 117, 115, 116, 113, 114, 128, 127, 126, 125, 123, 124, 121, 122, 97, 98, 100, 99, 101, 102, 104, 103, 105, 106, 108, 107, 109, 110, 112, 111, 16, 15, 14, 13, 11, 12, 9, 10, 8, 7, 6, 5, 3, 4, 1, 2, 28, 27, 26, 25, 32, 31, 30, 29, 20, 19, 18, 17, 24, 23, 22, 21, 58, 57, 59, 60, 62, 61, 63, 64, 50, 49, 51, 52, 54, 53, 55, 56, 48, 47, 46, 45, 43, 44, 41, 42, 40, 39, 38, 37, 35, 36, 33, 34], [106, 105, 108, 107, 109, 110, 111, 112, 103, 104, 102, 101, 99, 100, 98, 97, 127, 128, 126, 125, 123, 124, 122, 121, 114, 113, 116, 115, 117, 118, 119, 120, 92, 91, 89, 90, 95, 96, 94, 93, 86, 85, 88, 87, 82, 81, 84, 83, 79, 80, 78, 77, 75, 76, 74, 73, 66, 65, 68, 67, 69, 70, 71, 72, 39, 40, 38, 37, 35, 36, 34, 33, 42, 41, 44, 43, 45, 46, 47, 48, 49, 50, 51, 52, 54, 53, 56, 55, 64, 63, 61, 62, 60, 59, 57, 58, 19, 20, 18, 17, 24, 23, 21, 22, 29, 30, 31, 32, 25, 26, 27, 28, 7, 8, 6, 5, 3, 4, 2, 1, 10, 9, 12, 11, 13, 14, 15, 16]];
cc:=[5,11,20];
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:=[[33, 34, 36, 35, 38, 37, 39, 40, 48, 47, 46, 45, 44, 43, 42, 41, 51, 52, 49, 50, 56, 55, 54, 53, 61, 62, 64, 63, 57, 58, 60, 59, 1, 2, 4, 3, 6, 5, 7, 8, 16, 15, 14, 13, 12, 11, 10, 9, 19, 20, 17, 18, 24, 23, 22, 21, 29, 30, 32, 31, 25, 26, 28, 27, 97, 98, 100, 99, 102, 101, 103, 104, 112, 111, 110, 109, 108, 107, 106, 105, 115, 116, 113, 114, 120, 119, 118, 117, 125, 126, 128, 127, 121, 122, 124, 123, 65, 66, 68, 67, 70, 69, 71, 72, 80, 79, 78, 77, 76, 75, 74, 73, 83, 84, 81, 82, 88, 87, 86, 85, 93, 94, 96, 95, 89, 90, 92, 91], [79, 80, 77, 78, 76, 75, 74, 73, 71, 72, 69, 70, 68, 67, 66, 65, 92, 91, 90, 89, 96, 95, 94, 93, 84, 83, 82, 81, 88, 87, 86, 85, 127, 128, 125, 126, 124, 123, 122, 121, 119, 120, 117, 118, 116, 115, 114, 113, 106, 105, 107, 108, 110, 109, 111, 112, 98, 97, 99, 100, 102, 101, 103, 104, 7, 8, 5, 6, 4, 3, 2, 1, 15, 16, 13, 14, 12, 11, 10, 9, 19, 20, 17, 18, 23, 24, 21, 22, 27, 28, 25, 26, 31, 32, 29, 30, 49, 50, 52, 51, 53, 54, 56, 55, 57, 58, 60, 59, 61, 62, 64, 63, 39, 40, 37, 38, 36, 35, 34, 33, 47, 48, 45, 46, 44, 43, 42, 41], [104, 103, 101, 102, 100, 99, 97, 98, 105, 106, 107, 108, 110, 109, 112, 111, 113, 114, 115, 116, 118, 117, 120, 119, 128, 127, 125, 126, 124, 123, 121, 122, 85, 86, 87, 88, 81, 82, 83, 84, 91, 92, 90, 89, 96, 95, 93, 94, 65, 66, 67, 68, 70, 69, 72, 71, 80, 79, 77, 78, 76, 75, 73, 74, 41, 42, 43, 44, 46, 45, 48, 47, 40, 39, 37, 38, 36, 35, 33, 34, 63, 64, 62, 61, 59, 60, 58, 57, 50, 49, 52, 51, 53, 54, 55, 56, 30, 29, 32, 31, 26, 25, 28, 27, 20, 19, 17, 18, 23, 24, 22, 21, 9, 10, 11, 12, 14, 13, 16, 15, 8, 7, 5, 6, 4, 3, 1, 2]];
cc:=[5,12,17];
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:=[[33, 34, 36, 35, 38, 37, 39, 40, 48, 47, 46, 45, 44, 43, 42, 41, 51, 52, 49, 50, 56, 55, 54, 53, 61, 62, 64, 63, 57, 58, 60, 59, 1, 2, 4, 3, 6, 5, 7, 8, 16, 15, 14, 13, 12, 11, 10, 9, 19, 20, 17, 18, 24, 23, 22, 21, 29, 30, 32, 31, 25, 26, 28, 27, 97, 98, 100, 99, 102, 101, 103, 104, 112, 111, 110, 109, 108, 107, 106, 105, 115, 116, 113, 114, 120, 119, 118, 117, 125, 126, 128, 127, 121, 122, 124, 123, 65, 66, 68, 67, 70, 69, 71, 72, 80, 79, 78, 77, 76, 75, 74, 73, 83, 84, 81, 82, 88, 87, 86, 85, 93, 94, 96, 95, 89, 90, 92, 91], [75, 76, 73, 74, 79, 80, 77, 78, 67, 68, 65, 66, 71, 72, 69, 70, 95, 96, 93, 94, 92, 91, 90, 89, 87, 88, 85, 86, 84, 83, 82, 81, 123, 124, 121, 122, 127, 128, 125, 126, 115, 116, 113, 114, 119, 120, 117, 118, 109, 110, 112, 111, 106, 105, 107, 108, 101, 102, 104, 103, 98, 97, 99, 100, 3, 4, 1, 2, 7, 8, 5, 6, 11, 12, 9, 10, 15, 16, 13, 14, 24, 23, 22, 21, 19, 20, 17, 18, 32, 31, 30, 29, 27, 28, 25, 26, 54, 53, 55, 56, 49, 50, 52, 51, 62, 61, 63, 64, 57, 58, 60, 59, 35, 36, 33, 34, 39, 40, 37, 38, 43, 44, 41, 42, 47, 48, 45, 46], [100, 99, 97, 98, 103, 104, 102, 101, 110, 109, 112, 111, 106, 105, 108, 107, 118, 117, 120, 119, 114, 113, 116, 115, 124, 123, 121, 122, 127, 128, 126, 125, 81, 82, 83, 84, 86, 85, 88, 87, 96, 95, 93, 94, 92, 91, 89, 90, 70, 69, 72, 71, 66, 65, 68, 67, 76, 75, 73, 74, 79, 80, 78, 77, 46, 45, 48, 47, 42, 41, 44, 43, 36, 35, 33, 34, 39, 40, 38, 37, 59, 60, 58, 57, 64, 63, 61, 62, 53, 54, 55, 56, 49, 50, 51, 52, 26, 25, 28, 27, 29, 30, 31, 32, 23, 24, 22, 21, 19, 20, 18, 17, 14, 13, 16, 15, 10, 9, 12, 11, 4, 3, 1, 2, 7, 8, 6, 5]];
cc:=[5,12,19];
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 >);
