// Magma code for the lmfdb family of higher genus curves 15.120-27.0.2-4-60
// 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:=[120,27];
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:=[0,2,4,60];
genus:=15;
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:=[[61, 65, 64, 63, 62, 71, 75, 74, 73, 72, 66, 70, 69, 68, 67, 76, 80, 79, 78, 77, 86, 90, 89, 88, 87, 81, 85, 84, 83, 82, 91, 95, 94, 93, 92, 101, 105, 104, 103, 102, 96, 100, 99, 98, 97, 106, 110, 109, 108, 107, 116, 120, 119, 118, 117, 111, 115, 114, 113, 112, 1, 5, 4, 3, 2, 11, 15, 14, 13, 12, 6, 10, 9, 8, 7, 16, 20, 19, 18, 17, 26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 31, 35, 34, 33, 32, 41, 45, 44, 43, 42, 36, 40, 39, 38, 37, 46, 50, 49, 48, 47, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52], [104, 103, 102, 101, 105, 99, 98, 97, 96, 100, 94, 93, 92, 91, 95, 119, 118, 117, 116, 120, 114, 113, 112, 111, 115, 109, 108, 107, 106, 110, 89, 88, 87, 86, 90, 84, 83, 82, 81, 85, 79, 78, 77, 76, 80, 74, 73, 72, 71, 75, 69, 68, 67, 66, 70, 64, 63, 62, 61, 65, 44, 43, 42, 41, 45, 39, 38, 37, 36, 40, 34, 33, 32, 31, 35, 59, 58, 57, 56, 60, 54, 53, 52, 51, 55, 49, 48, 47, 46, 50, 29, 28, 27, 26, 30, 24, 23, 22, 21, 25, 19, 18, 17, 16, 20, 14, 13, 12, 11, 15, 9, 8, 7, 6, 10, 4, 3, 2, 1, 5], [53, 54, 55, 51, 52, 58, 59, 60, 56, 57, 48, 49, 50, 46, 47, 38, 39, 40, 36, 37, 43, 44, 45, 41, 42, 33, 34, 35, 31, 32, 8, 9, 10, 6, 7, 13, 14, 15, 11, 12, 3, 4, 5, 1, 2, 23, 24, 25, 21, 22, 28, 29, 30, 26, 27, 18, 19, 20, 16, 17, 113, 114, 115, 111, 112, 118, 119, 120, 116, 117, 108, 109, 110, 106, 107, 98, 99, 100, 96, 97, 103, 104, 105, 101, 102, 93, 94, 95, 91, 92, 68, 69, 70, 66, 67, 73, 74, 75, 71, 72, 63, 64, 65, 61, 62, 83, 84, 85, 81, 82, 88, 89, 90, 86, 87, 78, 79, 80, 76, 77]];
cc:=[3,8,30];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105];
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:=[[61, 65, 64, 63, 62, 71, 75, 74, 73, 72, 66, 70, 69, 68, 67, 76, 80, 79, 78, 77, 86, 90, 89, 88, 87, 81, 85, 84, 83, 82, 91, 95, 94, 93, 92, 101, 105, 104, 103, 102, 96, 100, 99, 98, 97, 106, 110, 109, 108, 107, 116, 120, 119, 118, 117, 111, 115, 114, 113, 112, 1, 5, 4, 3, 2, 11, 15, 14, 13, 12, 6, 10, 9, 8, 7, 16, 20, 19, 18, 17, 26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 31, 35, 34, 33, 32, 41, 45, 44, 43, 42, 36, 40, 39, 38, 37, 46, 50, 49, 48, 47, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52], [102, 101, 105, 104, 103, 97, 96, 100, 99, 98, 92, 91, 95, 94, 93, 117, 116, 120, 119, 118, 112, 111, 115, 114, 113, 107, 106, 110, 109, 108, 87, 86, 90, 89, 88, 82, 81, 85, 84, 83, 77, 76, 80, 79, 78, 72, 71, 75, 74, 73, 67, 66, 70, 69, 68, 62, 61, 65, 64, 63, 42, 41, 45, 44, 43, 37, 36, 40, 39, 38, 32, 31, 35, 34, 33, 57, 56, 60, 59, 58, 52, 51, 55, 54, 53, 47, 46, 50, 49, 48, 27, 26, 30, 29, 28, 22, 21, 25, 24, 23, 17, 16, 20, 19, 18, 12, 11, 15, 14, 13, 7, 6, 10, 9, 8, 2, 1, 5, 4, 3], [55, 51, 52, 53, 54, 60, 56, 57, 58, 59, 50, 46, 47, 48, 49, 40, 36, 37, 38, 39, 45, 41, 42, 43, 44, 35, 31, 32, 33, 34, 10, 6, 7, 8, 9, 15, 11, 12, 13, 14, 5, 1, 2, 3, 4, 25, 21, 22, 23, 24, 30, 26, 27, 28, 29, 20, 16, 17, 18, 19, 115, 111, 112, 113, 114, 120, 116, 117, 118, 119, 110, 106, 107, 108, 109, 100, 96, 97, 98, 99, 105, 101, 102, 103, 104, 95, 91, 92, 93, 94, 70, 66, 67, 68, 69, 75, 71, 72, 73, 74, 65, 61, 62, 63, 64, 85, 81, 82, 83, 84, 90, 86, 87, 88, 89, 80, 76, 77, 78, 79]];
cc:=[3,8,31];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105];
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:=[[61, 65, 64, 63, 62, 71, 75, 74, 73, 72, 66, 70, 69, 68, 67, 76, 80, 79, 78, 77, 86, 90, 89, 88, 87, 81, 85, 84, 83, 82, 91, 95, 94, 93, 92, 101, 105, 104, 103, 102, 96, 100, 99, 98, 97, 106, 110, 109, 108, 107, 116, 120, 119, 118, 117, 111, 115, 114, 113, 112, 1, 5, 4, 3, 2, 11, 15, 14, 13, 12, 6, 10, 9, 8, 7, 16, 20, 19, 18, 17, 26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 31, 35, 34, 33, 32, 41, 45, 44, 43, 42, 36, 40, 39, 38, 37, 46, 50, 49, 48, 47, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52], [103, 102, 101, 105, 104, 98, 97, 96, 100, 99, 93, 92, 91, 95, 94, 118, 117, 116, 120, 119, 113, 112, 111, 115, 114, 108, 107, 106, 110, 109, 88, 87, 86, 90, 89, 83, 82, 81, 85, 84, 78, 77, 76, 80, 79, 73, 72, 71, 75, 74, 68, 67, 66, 70, 69, 63, 62, 61, 65, 64, 43, 42, 41, 45, 44, 38, 37, 36, 40, 39, 33, 32, 31, 35, 34, 58, 57, 56, 60, 59, 53, 52, 51, 55, 54, 48, 47, 46, 50, 49, 28, 27, 26, 30, 29, 23, 22, 21, 25, 24, 18, 17, 16, 20, 19, 13, 12, 11, 15, 14, 8, 7, 6, 10, 9, 3, 2, 1, 5, 4], [54, 55, 51, 52, 53, 59, 60, 56, 57, 58, 49, 50, 46, 47, 48, 39, 40, 36, 37, 38, 44, 45, 41, 42, 43, 34, 35, 31, 32, 33, 9, 10, 6, 7, 8, 14, 15, 11, 12, 13, 4, 5, 1, 2, 3, 24, 25, 21, 22, 23, 29, 30, 26, 27, 28, 19, 20, 16, 17, 18, 114, 115, 111, 112, 113, 119, 120, 116, 117, 118, 109, 110, 106, 107, 108, 99, 100, 96, 97, 98, 104, 105, 101, 102, 103, 94, 95, 91, 92, 93, 69, 70, 66, 67, 68, 74, 75, 71, 72, 73, 64, 65, 61, 62, 63, 84, 85, 81, 82, 83, 89, 90, 86, 87, 88, 79, 80, 76, 77, 78]];
cc:=[3,8,34];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=3;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105];
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:=[[61, 65, 64, 63, 62, 71, 75, 74, 73, 72, 66, 70, 69, 68, 67, 76, 80, 79, 78, 77, 86, 90, 89, 88, 87, 81, 85, 84, 83, 82, 91, 95, 94, 93, 92, 101, 105, 104, 103, 102, 96, 100, 99, 98, 97, 106, 110, 109, 108, 107, 116, 120, 119, 118, 117, 111, 115, 114, 113, 112, 1, 5, 4, 3, 2, 11, 15, 14, 13, 12, 6, 10, 9, 8, 7, 16, 20, 19, 18, 17, 26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 31, 35, 34, 33, 32, 41, 45, 44, 43, 42, 36, 40, 39, 38, 37, 46, 50, 49, 48, 47, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52], [105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 30, 29, 28, 27, 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], [52, 53, 54, 55, 51, 57, 58, 59, 60, 56, 47, 48, 49, 50, 46, 37, 38, 39, 40, 36, 42, 43, 44, 45, 41, 32, 33, 34, 35, 31, 7, 8, 9, 10, 6, 12, 13, 14, 15, 11, 2, 3, 4, 5, 1, 22, 23, 24, 25, 21, 27, 28, 29, 30, 26, 17, 18, 19, 20, 16, 112, 113, 114, 115, 111, 117, 118, 119, 120, 116, 107, 108, 109, 110, 106, 97, 98, 99, 100, 96, 102, 103, 104, 105, 101, 92, 93, 94, 95, 91, 67, 68, 69, 70, 66, 72, 73, 74, 75, 71, 62, 63, 64, 65, 61, 82, 83, 84, 85, 81, 87, 88, 89, 90, 86, 77, 78, 79, 80, 76]];
cc:=[3,8,36];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=4;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105];
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:=[[61, 65, 64, 63, 62, 71, 75, 74, 73, 72, 66, 70, 69, 68, 67, 76, 80, 79, 78, 77, 86, 90, 89, 88, 87, 81, 85, 84, 83, 82, 91, 95, 94, 93, 92, 101, 105, 104, 103, 102, 96, 100, 99, 98, 97, 106, 110, 109, 108, 107, 116, 120, 119, 118, 117, 111, 115, 114, 113, 112, 1, 5, 4, 3, 2, 11, 15, 14, 13, 12, 6, 10, 9, 8, 7, 16, 20, 19, 18, 17, 26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 31, 35, 34, 33, 32, 41, 45, 44, 43, 42, 36, 40, 39, 38, 37, 46, 50, 49, 48, 47, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52], [120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16], [37, 38, 39, 40, 36, 42, 43, 44, 45, 41, 32, 33, 34, 35, 31, 52, 53, 54, 55, 51, 57, 58, 59, 60, 56, 47, 48, 49, 50, 46, 22, 23, 24, 25, 21, 27, 28, 29, 30, 26, 17, 18, 19, 20, 16, 7, 8, 9, 10, 6, 12, 13, 14, 15, 11, 2, 3, 4, 5, 1, 97, 98, 99, 100, 96, 102, 103, 104, 105, 101, 92, 93, 94, 95, 91, 112, 113, 114, 115, 111, 117, 118, 119, 120, 116, 107, 108, 109, 110, 106, 82, 83, 84, 85, 81, 87, 88, 89, 90, 86, 77, 78, 79, 80, 76, 67, 68, 69, 70, 66, 72, 73, 74, 75, 71, 62, 63, 64, 65, 61]];
cc:=[3,9,29];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=5;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105];
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:=[[61, 65, 64, 63, 62, 71, 75, 74, 73, 72, 66, 70, 69, 68, 67, 76, 80, 79, 78, 77, 86, 90, 89, 88, 87, 81, 85, 84, 83, 82, 91, 95, 94, 93, 92, 101, 105, 104, 103, 102, 96, 100, 99, 98, 97, 106, 110, 109, 108, 107, 116, 120, 119, 118, 117, 111, 115, 114, 113, 112, 1, 5, 4, 3, 2, 11, 15, 14, 13, 12, 6, 10, 9, 8, 7, 16, 20, 19, 18, 17, 26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 31, 35, 34, 33, 32, 41, 45, 44, 43, 42, 36, 40, 39, 38, 37, 46, 50, 49, 48, 47, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52], [118, 117, 116, 120, 119, 113, 112, 111, 115, 114, 108, 107, 106, 110, 109, 103, 102, 101, 105, 104, 98, 97, 96, 100, 99, 93, 92, 91, 95, 94, 73, 72, 71, 75, 74, 68, 67, 66, 70, 69, 63, 62, 61, 65, 64, 88, 87, 86, 90, 89, 83, 82, 81, 85, 84, 78, 77, 76, 80, 79, 58, 57, 56, 60, 59, 53, 52, 51, 55, 54, 48, 47, 46, 50, 49, 43, 42, 41, 45, 44, 38, 37, 36, 40, 39, 33, 32, 31, 35, 34, 13, 12, 11, 15, 14, 8, 7, 6, 10, 9, 3, 2, 1, 5, 4, 28, 27, 26, 30, 29, 23, 22, 21, 25, 24, 18, 17, 16, 20, 19], [39, 40, 36, 37, 38, 44, 45, 41, 42, 43, 34, 35, 31, 32, 33, 54, 55, 51, 52, 53, 59, 60, 56, 57, 58, 49, 50, 46, 47, 48, 24, 25, 21, 22, 23, 29, 30, 26, 27, 28, 19, 20, 16, 17, 18, 9, 10, 6, 7, 8, 14, 15, 11, 12, 13, 4, 5, 1, 2, 3, 99, 100, 96, 97, 98, 104, 105, 101, 102, 103, 94, 95, 91, 92, 93, 114, 115, 111, 112, 113, 119, 120, 116, 117, 118, 109, 110, 106, 107, 108, 84, 85, 81, 82, 83, 89, 90, 86, 87, 88, 79, 80, 76, 77, 78, 69, 70, 66, 67, 68, 74, 75, 71, 72, 73, 64, 65, 61, 62, 63]];
cc:=[3,9,32];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=6;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105];
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:=[[61, 65, 64, 63, 62, 71, 75, 74, 73, 72, 66, 70, 69, 68, 67, 76, 80, 79, 78, 77, 86, 90, 89, 88, 87, 81, 85, 84, 83, 82, 91, 95, 94, 93, 92, 101, 105, 104, 103, 102, 96, 100, 99, 98, 97, 106, 110, 109, 108, 107, 116, 120, 119, 118, 117, 111, 115, 114, 113, 112, 1, 5, 4, 3, 2, 11, 15, 14, 13, 12, 6, 10, 9, 8, 7, 16, 20, 19, 18, 17, 26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 31, 35, 34, 33, 32, 41, 45, 44, 43, 42, 36, 40, 39, 38, 37, 46, 50, 49, 48, 47, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52], [119, 118, 117, 116, 120, 114, 113, 112, 111, 115, 109, 108, 107, 106, 110, 104, 103, 102, 101, 105, 99, 98, 97, 96, 100, 94, 93, 92, 91, 95, 74, 73, 72, 71, 75, 69, 68, 67, 66, 70, 64, 63, 62, 61, 65, 89, 88, 87, 86, 90, 84, 83, 82, 81, 85, 79, 78, 77, 76, 80, 59, 58, 57, 56, 60, 54, 53, 52, 51, 55, 49, 48, 47, 46, 50, 44, 43, 42, 41, 45, 39, 38, 37, 36, 40, 34, 33, 32, 31, 35, 14, 13, 12, 11, 15, 9, 8, 7, 6, 10, 4, 3, 2, 1, 5, 29, 28, 27, 26, 30, 24, 23, 22, 21, 25, 19, 18, 17, 16, 20], [38, 39, 40, 36, 37, 43, 44, 45, 41, 42, 33, 34, 35, 31, 32, 53, 54, 55, 51, 52, 58, 59, 60, 56, 57, 48, 49, 50, 46, 47, 23, 24, 25, 21, 22, 28, 29, 30, 26, 27, 18, 19, 20, 16, 17, 8, 9, 10, 6, 7, 13, 14, 15, 11, 12, 3, 4, 5, 1, 2, 98, 99, 100, 96, 97, 103, 104, 105, 101, 102, 93, 94, 95, 91, 92, 113, 114, 115, 111, 112, 118, 119, 120, 116, 117, 108, 109, 110, 106, 107, 83, 84, 85, 81, 82, 88, 89, 90, 86, 87, 78, 79, 80, 76, 77, 68, 69, 70, 66, 67, 73, 74, 75, 71, 72, 63, 64, 65, 61, 62]];
cc:=[3,9,33];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=7;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105];
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:=[[61, 65, 64, 63, 62, 71, 75, 74, 73, 72, 66, 70, 69, 68, 67, 76, 80, 79, 78, 77, 86, 90, 89, 88, 87, 81, 85, 84, 83, 82, 91, 95, 94, 93, 92, 101, 105, 104, 103, 102, 96, 100, 99, 98, 97, 106, 110, 109, 108, 107, 116, 120, 119, 118, 117, 111, 115, 114, 113, 112, 1, 5, 4, 3, 2, 11, 15, 14, 13, 12, 6, 10, 9, 8, 7, 16, 20, 19, 18, 17, 26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 31, 35, 34, 33, 32, 41, 45, 44, 43, 42, 36, 40, 39, 38, 37, 46, 50, 49, 48, 47, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52], [117, 116, 120, 119, 118, 112, 111, 115, 114, 113, 107, 106, 110, 109, 108, 102, 101, 105, 104, 103, 97, 96, 100, 99, 98, 92, 91, 95, 94, 93, 72, 71, 75, 74, 73, 67, 66, 70, 69, 68, 62, 61, 65, 64, 63, 87, 86, 90, 89, 88, 82, 81, 85, 84, 83, 77, 76, 80, 79, 78, 57, 56, 60, 59, 58, 52, 51, 55, 54, 53, 47, 46, 50, 49, 48, 42, 41, 45, 44, 43, 37, 36, 40, 39, 38, 32, 31, 35, 34, 33, 12, 11, 15, 14, 13, 7, 6, 10, 9, 8, 2, 1, 5, 4, 3, 27, 26, 30, 29, 28, 22, 21, 25, 24, 23, 17, 16, 20, 19, 18], [40, 36, 37, 38, 39, 45, 41, 42, 43, 44, 35, 31, 32, 33, 34, 55, 51, 52, 53, 54, 60, 56, 57, 58, 59, 50, 46, 47, 48, 49, 25, 21, 22, 23, 24, 30, 26, 27, 28, 29, 20, 16, 17, 18, 19, 10, 6, 7, 8, 9, 15, 11, 12, 13, 14, 5, 1, 2, 3, 4, 100, 96, 97, 98, 99, 105, 101, 102, 103, 104, 95, 91, 92, 93, 94, 115, 111, 112, 113, 114, 120, 116, 117, 118, 119, 110, 106, 107, 108, 109, 85, 81, 82, 83, 84, 90, 86, 87, 88, 89, 80, 76, 77, 78, 79, 70, 66, 67, 68, 69, 75, 71, 72, 73, 74, 65, 61, 62, 63, 64]];
cc:=[3,9,35];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=8;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105];
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:=[[76, 80, 79, 78, 77, 86, 90, 89, 88, 87, 81, 85, 84, 83, 82, 61, 65, 64, 63, 62, 71, 75, 74, 73, 72, 66, 70, 69, 68, 67, 106, 110, 109, 108, 107, 116, 120, 119, 118, 117, 111, 115, 114, 113, 112, 91, 95, 94, 93, 92, 101, 105, 104, 103, 102, 96, 100, 99, 98, 97, 16, 20, 19, 18, 17, 26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 1, 5, 4, 3, 2, 11, 15, 14, 13, 12, 6, 10, 9, 8, 7, 46, 50, 49, 48, 47, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52, 31, 35, 34, 33, 32, 41, 45, 44, 43, 42, 36, 40, 39, 38, 37], [105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 30, 29, 28, 27, 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], [37, 38, 39, 40, 36, 42, 43, 44, 45, 41, 32, 33, 34, 35, 31, 52, 53, 54, 55, 51, 57, 58, 59, 60, 56, 47, 48, 49, 50, 46, 22, 23, 24, 25, 21, 27, 28, 29, 30, 26, 17, 18, 19, 20, 16, 7, 8, 9, 10, 6, 12, 13, 14, 15, 11, 2, 3, 4, 5, 1, 97, 98, 99, 100, 96, 102, 103, 104, 105, 101, 92, 93, 94, 95, 91, 112, 113, 114, 115, 111, 117, 118, 119, 120, 116, 107, 108, 109, 110, 106, 82, 83, 84, 85, 81, 87, 88, 89, 90, 86, 77, 78, 79, 80, 76, 67, 68, 69, 70, 66, 72, 73, 74, 75, 71, 62, 63, 64, 65, 61]];
cc:=[4,8,29];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=9;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105];
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:=[[76, 80, 79, 78, 77, 86, 90, 89, 88, 87, 81, 85, 84, 83, 82, 61, 65, 64, 63, 62, 71, 75, 74, 73, 72, 66, 70, 69, 68, 67, 106, 110, 109, 108, 107, 116, 120, 119, 118, 117, 111, 115, 114, 113, 112, 91, 95, 94, 93, 92, 101, 105, 104, 103, 102, 96, 100, 99, 98, 97, 16, 20, 19, 18, 17, 26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 1, 5, 4, 3, 2, 11, 15, 14, 13, 12, 6, 10, 9, 8, 7, 46, 50, 49, 48, 47, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52, 31, 35, 34, 33, 32, 41, 45, 44, 43, 42, 36, 40, 39, 38, 37], [103, 102, 101, 105, 104, 98, 97, 96, 100, 99, 93, 92, 91, 95, 94, 118, 117, 116, 120, 119, 113, 112, 111, 115, 114, 108, 107, 106, 110, 109, 88, 87, 86, 90, 89, 83, 82, 81, 85, 84, 78, 77, 76, 80, 79, 73, 72, 71, 75, 74, 68, 67, 66, 70, 69, 63, 62, 61, 65, 64, 43, 42, 41, 45, 44, 38, 37, 36, 40, 39, 33, 32, 31, 35, 34, 58, 57, 56, 60, 59, 53, 52, 51, 55, 54, 48, 47, 46, 50, 49, 28, 27, 26, 30, 29, 23, 22, 21, 25, 24, 18, 17, 16, 20, 19, 13, 12, 11, 15, 14, 8, 7, 6, 10, 9, 3, 2, 1, 5, 4], [39, 40, 36, 37, 38, 44, 45, 41, 42, 43, 34, 35, 31, 32, 33, 54, 55, 51, 52, 53, 59, 60, 56, 57, 58, 49, 50, 46, 47, 48, 24, 25, 21, 22, 23, 29, 30, 26, 27, 28, 19, 20, 16, 17, 18, 9, 10, 6, 7, 8, 14, 15, 11, 12, 13, 4, 5, 1, 2, 3, 99, 100, 96, 97, 98, 104, 105, 101, 102, 103, 94, 95, 91, 92, 93, 114, 115, 111, 112, 113, 119, 120, 116, 117, 118, 109, 110, 106, 107, 108, 84, 85, 81, 82, 83, 89, 90, 86, 87, 88, 79, 80, 76, 77, 78, 69, 70, 66, 67, 68, 74, 75, 71, 72, 73, 64, 65, 61, 62, 63]];
cc:=[4,8,32];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=10;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105];
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:=[[76, 80, 79, 78, 77, 86, 90, 89, 88, 87, 81, 85, 84, 83, 82, 61, 65, 64, 63, 62, 71, 75, 74, 73, 72, 66, 70, 69, 68, 67, 106, 110, 109, 108, 107, 116, 120, 119, 118, 117, 111, 115, 114, 113, 112, 91, 95, 94, 93, 92, 101, 105, 104, 103, 102, 96, 100, 99, 98, 97, 16, 20, 19, 18, 17, 26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 1, 5, 4, 3, 2, 11, 15, 14, 13, 12, 6, 10, 9, 8, 7, 46, 50, 49, 48, 47, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52, 31, 35, 34, 33, 32, 41, 45, 44, 43, 42, 36, 40, 39, 38, 37], [104, 103, 102, 101, 105, 99, 98, 97, 96, 100, 94, 93, 92, 91, 95, 119, 118, 117, 116, 120, 114, 113, 112, 111, 115, 109, 108, 107, 106, 110, 89, 88, 87, 86, 90, 84, 83, 82, 81, 85, 79, 78, 77, 76, 80, 74, 73, 72, 71, 75, 69, 68, 67, 66, 70, 64, 63, 62, 61, 65, 44, 43, 42, 41, 45, 39, 38, 37, 36, 40, 34, 33, 32, 31, 35, 59, 58, 57, 56, 60, 54, 53, 52, 51, 55, 49, 48, 47, 46, 50, 29, 28, 27, 26, 30, 24, 23, 22, 21, 25, 19, 18, 17, 16, 20, 14, 13, 12, 11, 15, 9, 8, 7, 6, 10, 4, 3, 2, 1, 5], [38, 39, 40, 36, 37, 43, 44, 45, 41, 42, 33, 34, 35, 31, 32, 53, 54, 55, 51, 52, 58, 59, 60, 56, 57, 48, 49, 50, 46, 47, 23, 24, 25, 21, 22, 28, 29, 30, 26, 27, 18, 19, 20, 16, 17, 8, 9, 10, 6, 7, 13, 14, 15, 11, 12, 3, 4, 5, 1, 2, 98, 99, 100, 96, 97, 103, 104, 105, 101, 102, 93, 94, 95, 91, 92, 113, 114, 115, 111, 112, 118, 119, 120, 116, 117, 108, 109, 110, 106, 107, 83, 84, 85, 81, 82, 88, 89, 90, 86, 87, 78, 79, 80, 76, 77, 68, 69, 70, 66, 67, 73, 74, 75, 71, 72, 63, 64, 65, 61, 62]];
cc:=[4,8,33];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=11;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105];
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:=[[76, 80, 79, 78, 77, 86, 90, 89, 88, 87, 81, 85, 84, 83, 82, 61, 65, 64, 63, 62, 71, 75, 74, 73, 72, 66, 70, 69, 68, 67, 106, 110, 109, 108, 107, 116, 120, 119, 118, 117, 111, 115, 114, 113, 112, 91, 95, 94, 93, 92, 101, 105, 104, 103, 102, 96, 100, 99, 98, 97, 16, 20, 19, 18, 17, 26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 1, 5, 4, 3, 2, 11, 15, 14, 13, 12, 6, 10, 9, 8, 7, 46, 50, 49, 48, 47, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52, 31, 35, 34, 33, 32, 41, 45, 44, 43, 42, 36, 40, 39, 38, 37], [102, 101, 105, 104, 103, 97, 96, 100, 99, 98, 92, 91, 95, 94, 93, 117, 116, 120, 119, 118, 112, 111, 115, 114, 113, 107, 106, 110, 109, 108, 87, 86, 90, 89, 88, 82, 81, 85, 84, 83, 77, 76, 80, 79, 78, 72, 71, 75, 74, 73, 67, 66, 70, 69, 68, 62, 61, 65, 64, 63, 42, 41, 45, 44, 43, 37, 36, 40, 39, 38, 32, 31, 35, 34, 33, 57, 56, 60, 59, 58, 52, 51, 55, 54, 53, 47, 46, 50, 49, 48, 27, 26, 30, 29, 28, 22, 21, 25, 24, 23, 17, 16, 20, 19, 18, 12, 11, 15, 14, 13, 7, 6, 10, 9, 8, 2, 1, 5, 4, 3], [40, 36, 37, 38, 39, 45, 41, 42, 43, 44, 35, 31, 32, 33, 34, 55, 51, 52, 53, 54, 60, 56, 57, 58, 59, 50, 46, 47, 48, 49, 25, 21, 22, 23, 24, 30, 26, 27, 28, 29, 20, 16, 17, 18, 19, 10, 6, 7, 8, 9, 15, 11, 12, 13, 14, 5, 1, 2, 3, 4, 100, 96, 97, 98, 99, 105, 101, 102, 103, 104, 95, 91, 92, 93, 94, 115, 111, 112, 113, 114, 120, 116, 117, 118, 119, 110, 106, 107, 108, 109, 85, 81, 82, 83, 84, 90, 86, 87, 88, 89, 80, 76, 77, 78, 79, 70, 66, 67, 68, 69, 75, 71, 72, 73, 74, 65, 61, 62, 63, 64]];
cc:=[4,8,35];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=12;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105];
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:=[[76, 80, 79, 78, 77, 86, 90, 89, 88, 87, 81, 85, 84, 83, 82, 61, 65, 64, 63, 62, 71, 75, 74, 73, 72, 66, 70, 69, 68, 67, 106, 110, 109, 108, 107, 116, 120, 119, 118, 117, 111, 115, 114, 113, 112, 91, 95, 94, 93, 92, 101, 105, 104, 103, 102, 96, 100, 99, 98, 97, 16, 20, 19, 18, 17, 26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 1, 5, 4, 3, 2, 11, 15, 14, 13, 12, 6, 10, 9, 8, 7, 46, 50, 49, 48, 47, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52, 31, 35, 34, 33, 32, 41, 45, 44, 43, 42, 36, 40, 39, 38, 37], [119, 118, 117, 116, 120, 114, 113, 112, 111, 115, 109, 108, 107, 106, 110, 104, 103, 102, 101, 105, 99, 98, 97, 96, 100, 94, 93, 92, 91, 95, 74, 73, 72, 71, 75, 69, 68, 67, 66, 70, 64, 63, 62, 61, 65, 89, 88, 87, 86, 90, 84, 83, 82, 81, 85, 79, 78, 77, 76, 80, 59, 58, 57, 56, 60, 54, 53, 52, 51, 55, 49, 48, 47, 46, 50, 44, 43, 42, 41, 45, 39, 38, 37, 36, 40, 34, 33, 32, 31, 35, 14, 13, 12, 11, 15, 9, 8, 7, 6, 10, 4, 3, 2, 1, 5, 29, 28, 27, 26, 30, 24, 23, 22, 21, 25, 19, 18, 17, 16, 20], [53, 54, 55, 51, 52, 58, 59, 60, 56, 57, 48, 49, 50, 46, 47, 38, 39, 40, 36, 37, 43, 44, 45, 41, 42, 33, 34, 35, 31, 32, 8, 9, 10, 6, 7, 13, 14, 15, 11, 12, 3, 4, 5, 1, 2, 23, 24, 25, 21, 22, 28, 29, 30, 26, 27, 18, 19, 20, 16, 17, 113, 114, 115, 111, 112, 118, 119, 120, 116, 117, 108, 109, 110, 106, 107, 98, 99, 100, 96, 97, 103, 104, 105, 101, 102, 93, 94, 95, 91, 92, 68, 69, 70, 66, 67, 73, 74, 75, 71, 72, 63, 64, 65, 61, 62, 83, 84, 85, 81, 82, 88, 89, 90, 86, 87, 78, 79, 80, 76, 77]];
cc:=[4,9,30];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=13;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105];
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:=[[76, 80, 79, 78, 77, 86, 90, 89, 88, 87, 81, 85, 84, 83, 82, 61, 65, 64, 63, 62, 71, 75, 74, 73, 72, 66, 70, 69, 68, 67, 106, 110, 109, 108, 107, 116, 120, 119, 118, 117, 111, 115, 114, 113, 112, 91, 95, 94, 93, 92, 101, 105, 104, 103, 102, 96, 100, 99, 98, 97, 16, 20, 19, 18, 17, 26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 1, 5, 4, 3, 2, 11, 15, 14, 13, 12, 6, 10, 9, 8, 7, 46, 50, 49, 48, 47, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52, 31, 35, 34, 33, 32, 41, 45, 44, 43, 42, 36, 40, 39, 38, 37], [117, 116, 120, 119, 118, 112, 111, 115, 114, 113, 107, 106, 110, 109, 108, 102, 101, 105, 104, 103, 97, 96, 100, 99, 98, 92, 91, 95, 94, 93, 72, 71, 75, 74, 73, 67, 66, 70, 69, 68, 62, 61, 65, 64, 63, 87, 86, 90, 89, 88, 82, 81, 85, 84, 83, 77, 76, 80, 79, 78, 57, 56, 60, 59, 58, 52, 51, 55, 54, 53, 47, 46, 50, 49, 48, 42, 41, 45, 44, 43, 37, 36, 40, 39, 38, 32, 31, 35, 34, 33, 12, 11, 15, 14, 13, 7, 6, 10, 9, 8, 2, 1, 5, 4, 3, 27, 26, 30, 29, 28, 22, 21, 25, 24, 23, 17, 16, 20, 19, 18], [55, 51, 52, 53, 54, 60, 56, 57, 58, 59, 50, 46, 47, 48, 49, 40, 36, 37, 38, 39, 45, 41, 42, 43, 44, 35, 31, 32, 33, 34, 10, 6, 7, 8, 9, 15, 11, 12, 13, 14, 5, 1, 2, 3, 4, 25, 21, 22, 23, 24, 30, 26, 27, 28, 29, 20, 16, 17, 18, 19, 115, 111, 112, 113, 114, 120, 116, 117, 118, 119, 110, 106, 107, 108, 109, 100, 96, 97, 98, 99, 105, 101, 102, 103, 104, 95, 91, 92, 93, 94, 70, 66, 67, 68, 69, 75, 71, 72, 73, 74, 65, 61, 62, 63, 64, 85, 81, 82, 83, 84, 90, 86, 87, 88, 89, 80, 76, 77, 78, 79]];
cc:=[4,9,31];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=14;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105];
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:=[[76, 80, 79, 78, 77, 86, 90, 89, 88, 87, 81, 85, 84, 83, 82, 61, 65, 64, 63, 62, 71, 75, 74, 73, 72, 66, 70, 69, 68, 67, 106, 110, 109, 108, 107, 116, 120, 119, 118, 117, 111, 115, 114, 113, 112, 91, 95, 94, 93, 92, 101, 105, 104, 103, 102, 96, 100, 99, 98, 97, 16, 20, 19, 18, 17, 26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 1, 5, 4, 3, 2, 11, 15, 14, 13, 12, 6, 10, 9, 8, 7, 46, 50, 49, 48, 47, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52, 31, 35, 34, 33, 32, 41, 45, 44, 43, 42, 36, 40, 39, 38, 37], [118, 117, 116, 120, 119, 113, 112, 111, 115, 114, 108, 107, 106, 110, 109, 103, 102, 101, 105, 104, 98, 97, 96, 100, 99, 93, 92, 91, 95, 94, 73, 72, 71, 75, 74, 68, 67, 66, 70, 69, 63, 62, 61, 65, 64, 88, 87, 86, 90, 89, 83, 82, 81, 85, 84, 78, 77, 76, 80, 79, 58, 57, 56, 60, 59, 53, 52, 51, 55, 54, 48, 47, 46, 50, 49, 43, 42, 41, 45, 44, 38, 37, 36, 40, 39, 33, 32, 31, 35, 34, 13, 12, 11, 15, 14, 8, 7, 6, 10, 9, 3, 2, 1, 5, 4, 28, 27, 26, 30, 29, 23, 22, 21, 25, 24, 18, 17, 16, 20, 19], [54, 55, 51, 52, 53, 59, 60, 56, 57, 58, 49, 50, 46, 47, 48, 39, 40, 36, 37, 38, 44, 45, 41, 42, 43, 34, 35, 31, 32, 33, 9, 10, 6, 7, 8, 14, 15, 11, 12, 13, 4, 5, 1, 2, 3, 24, 25, 21, 22, 23, 29, 30, 26, 27, 28, 19, 20, 16, 17, 18, 114, 115, 111, 112, 113, 119, 120, 116, 117, 118, 109, 110, 106, 107, 108, 99, 100, 96, 97, 98, 104, 105, 101, 102, 103, 94, 95, 91, 92, 93, 69, 70, 66, 67, 68, 74, 75, 71, 72, 73, 64, 65, 61, 62, 63, 84, 85, 81, 82, 83, 89, 90, 86, 87, 88, 79, 80, 76, 77, 78]];
cc:=[4,9,34];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=15;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105];
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:=[[76, 80, 79, 78, 77, 86, 90, 89, 88, 87, 81, 85, 84, 83, 82, 61, 65, 64, 63, 62, 71, 75, 74, 73, 72, 66, 70, 69, 68, 67, 106, 110, 109, 108, 107, 116, 120, 119, 118, 117, 111, 115, 114, 113, 112, 91, 95, 94, 93, 92, 101, 105, 104, 103, 102, 96, 100, 99, 98, 97, 16, 20, 19, 18, 17, 26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 1, 5, 4, 3, 2, 11, 15, 14, 13, 12, 6, 10, 9, 8, 7, 46, 50, 49, 48, 47, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52, 31, 35, 34, 33, 32, 41, 45, 44, 43, 42, 36, 40, 39, 38, 37], [120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16], [52, 53, 54, 55, 51, 57, 58, 59, 60, 56, 47, 48, 49, 50, 46, 37, 38, 39, 40, 36, 42, 43, 44, 45, 41, 32, 33, 34, 35, 31, 7, 8, 9, 10, 6, 12, 13, 14, 15, 11, 2, 3, 4, 5, 1, 22, 23, 24, 25, 21, 27, 28, 29, 30, 26, 17, 18, 19, 20, 16, 112, 113, 114, 115, 111, 117, 118, 119, 120, 116, 107, 108, 109, 110, 106, 97, 98, 99, 100, 96, 102, 103, 104, 105, 101, 92, 93, 94, 95, 91, 67, 68, 69, 70, 66, 72, 73, 74, 75, 71, 62, 63, 64, 65, 61, 82, 83, 84, 85, 81, 87, 88, 89, 90, 86, 77, 78, 79, 80, 76]];
cc:=[4,9,36];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=16;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105];
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 >);
