// Magma code for the lmfdb family of higher genus curves 8.336-208.0.2-3-8
// 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:=[336,208];
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:=[0,2,3,8];
genus:=8;
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:=[[199, 259, 186, 284, 174, 229, 273, 296, 207, 267, 194, 300, 214, 261, 249, 288, 191, 227, 210, 292, 222, 253, 241, 312, 183, 235, 202, 316, 190, 269, 225, 304, 215, 251, 170, 308, 182, 277, 233, 328, 223, 243, 178, 332, 198, 237, 257, 320, 175, 275, 218, 324, 206, 245, 265, 336, 255, 315, 242, 172, 230, 285, 329, 184, 263, 323, 250, 188, 270, 317, 305, 176, 247, 283, 266, 180, 278, 309, 297, 200, 239, 291, 258, 204, 246, 325, 281, 192, 271, 307, 226, 196, 238, 333, 289, 216, 279, 299, 234, 220, 254, 293, 313, 208, 231, 331, 274, 212, 262, 301, 321, 224, 311, 203, 298, 228, 286, 173, 217, 240, 319, 211, 306, 244, 326, 205, 193, 232, 303, 171, 322, 236, 334, 197, 185, 256, 295, 179, 314, 260, 302, 213, 169, 248, 327, 195, 282, 252, 294, 221, 177, 272, 335, 187, 290, 276, 310, 181, 201, 264, 287, 219, 330, 268, 318, 189, 209, 280, 143, 35, 130, 60, 118, 5, 49, 72, 151, 43, 138, 76, 158, 37, 25, 64, 135, 3, 154, 68, 166, 29, 17, 88, 127, 11, 146, 92, 134, 45, 1, 80, 159, 27, 114, 84, 126, 53, 9, 104, 167, 19, 122, 108, 142, 13, 33, 96, 119, 51, 162, 100, 150, 21, 41, 112, 31, 91, 18, 116, 6, 61, 105, 128, 39, 99, 26, 132, 46, 93, 81, 120, 23, 59, 42, 124, 54, 85, 73, 144, 15, 67, 34, 148, 22, 101, 57, 136, 47, 83, 2, 140, 14, 109, 65, 160, 55, 75, 10, 164, 30, 69, 89, 152, 7, 107, 50, 156, 38, 77, 97, 168, 87, 147, 74, 4, 62, 117, 161, 16, 95, 155, 82, 20, 102, 149, 137, 8, 79, 115, 98, 12, 110, 141, 129, 32, 71, 123, 90, 36, 78, 157, 113, 24, 103, 139, 58, 28, 70, 165, 121, 48, 111, 131, 66, 52, 86, 125, 145, 40, 63, 163, 106, 44, 94, 133, 153, 56], [261, 114, 209, 312, 11, 110, 164, 191, 269, 138, 185, 296, 27, 70, 132, 199, 229, 146, 169, 328, 3, 62, 140, 215, 237, 162, 193, 288, 43, 94, 124, 207, 253, 154, 217, 336, 19, 102, 116, 175, 245, 130, 201, 304, 51, 86, 156, 183, 277, 122, 177, 320, 35, 78, 148, 223, 317, 2, 265, 200, 67, 166, 52, 247, 325, 26, 241, 184, 83, 126, 20, 255, 285, 34, 225, 216, 59, 118, 28, 271, 293, 50, 249, 176, 99, 150, 12, 263, 309, 42, 273, 224, 75, 158, 4, 231, 301, 18, 257, 192, 107, 142, 44, 239, 333, 10, 233, 208, 91, 134, 36, 279, 205, 58, 321, 256, 123, 54, 108, 303, 213, 82, 297, 240, 139, 14, 76, 311, 173, 90, 281, 272, 115, 6, 84, 327, 181, 106, 305, 232, 155, 38, 68, 319, 197, 98, 329, 280, 131, 46, 60, 287, 189, 74, 313, 248, 163, 30, 100, 295, 221, 66, 289, 264, 147, 22, 92, 335, 37, 282, 153, 88, 179, 278, 332, 135, 45, 306, 129, 72, 195, 238, 300, 143, 5, 314, 113, 104, 171, 230, 308, 159, 13, 330, 137, 64, 211, 262, 292, 151, 29, 322, 161, 112, 187, 270, 284, 119, 21, 298, 145, 80, 219, 254, 324, 127, 53, 290, 121, 96, 203, 246, 316, 167, 93, 170, 41, 144, 235, 334, 220, 23, 101, 194, 17, 128, 251, 294, 188, 31, 61, 202, 1, 160, 227, 286, 196, 47, 69, 218, 25, 120, 267, 318, 180, 39, 85, 210, 49, 168, 243, 326, 172, 7, 77, 186, 33, 136, 275, 310, 212, 15, 109, 178, 9, 152, 259, 302, 204, 55, 149, 226, 97, 32, 291, 222, 276, 79, 157, 250, 73, 16, 307, 182, 244, 87, 117, 258, 57, 48, 283, 174, 252, 103, 125, 274, 81, 8, 323, 206, 236, 95, 141, 266, 105, 56, 299, 214, 228, 63, 133, 242, 89, 24, 331, 198, 268, 71, 165, 234, 65, 40, 315, 190, 260, 111], [42, 315, 222, 289, 135, 197, 160, 36, 50, 331, 174, 281, 127, 205, 152, 20, 26, 299, 182, 305, 167, 189, 128, 52, 34, 323, 214, 297, 159, 181, 120, 4, 10, 283, 206, 321, 143, 213, 136, 44, 18, 307, 190, 313, 151, 221, 144, 12, 2, 291, 198, 329, 119, 173, 168, 28, 98, 203, 278, 177, 23, 253, 48, 92, 106, 219, 230, 169, 15, 261, 40, 76, 82, 187, 238, 193, 55, 245, 16, 108, 90, 211, 270, 185, 47, 237, 8, 60, 66, 171, 262, 209, 31, 269, 24, 100, 74, 195, 246, 201, 39, 277, 32, 68, 58, 179, 254, 217, 7, 229, 56, 84, 154, 259, 334, 233, 79, 309, 104, 148, 162, 275, 286, 225, 71, 317, 96, 132, 138, 243, 294, 249, 111, 301, 72, 164, 146, 267, 326, 241, 103, 293, 64, 116, 122, 227, 318, 265, 87, 325, 80, 156, 130, 251, 302, 257, 95, 333, 88, 124, 114, 235, 310, 273, 63, 285, 112, 140, 210, 91, 166, 65, 303, 141, 328, 204, 218, 107, 118, 57, 295, 149, 320, 188, 194, 75, 126, 81, 335, 133, 296, 220, 202, 99, 158, 73, 327, 125, 288, 172, 178, 59, 150, 97, 311, 157, 304, 212, 186, 83, 134, 89, 319, 165, 312, 180, 170, 67, 142, 105, 287, 117, 336, 196, 266, 147, 54, 121, 191, 29, 216, 260, 274, 163, 6, 113, 183, 37, 208, 244, 250, 131, 14, 137, 223, 21, 184, 276, 258, 155, 46, 129, 215, 13, 176, 228, 234, 115, 38, 153, 199, 45, 192, 268, 242, 139, 22, 145, 207, 53, 200, 236, 226, 123, 30, 161, 175, 5, 224, 252, 322, 35, 110, 9, 247, 85, 272, 316, 330, 51, 62, 1, 239, 93, 264, 300, 306, 19, 70, 25, 279, 77, 240, 332, 314, 43, 102, 17, 271, 69, 232, 284, 290, 3, 94, 41, 255, 101, 248, 324, 298, 27, 78, 33, 263, 109, 256, 292, 282, 11, 86, 49, 231, 61, 280, 308]];
cc:=[3,4,8];
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:=[[199, 259, 186, 284, 174, 229, 273, 296, 207, 267, 194, 300, 214, 261, 249, 288, 191, 227, 210, 292, 222, 253, 241, 312, 183, 235, 202, 316, 190, 269, 225, 304, 215, 251, 170, 308, 182, 277, 233, 328, 223, 243, 178, 332, 198, 237, 257, 320, 175, 275, 218, 324, 206, 245, 265, 336, 255, 315, 242, 172, 230, 285, 329, 184, 263, 323, 250, 188, 270, 317, 305, 176, 247, 283, 266, 180, 278, 309, 297, 200, 239, 291, 258, 204, 246, 325, 281, 192, 271, 307, 226, 196, 238, 333, 289, 216, 279, 299, 234, 220, 254, 293, 313, 208, 231, 331, 274, 212, 262, 301, 321, 224, 311, 203, 298, 228, 286, 173, 217, 240, 319, 211, 306, 244, 326, 205, 193, 232, 303, 171, 322, 236, 334, 197, 185, 256, 295, 179, 314, 260, 302, 213, 169, 248, 327, 195, 282, 252, 294, 221, 177, 272, 335, 187, 290, 276, 310, 181, 201, 264, 287, 219, 330, 268, 318, 189, 209, 280, 143, 35, 130, 60, 118, 5, 49, 72, 151, 43, 138, 76, 158, 37, 25, 64, 135, 3, 154, 68, 166, 29, 17, 88, 127, 11, 146, 92, 134, 45, 1, 80, 159, 27, 114, 84, 126, 53, 9, 104, 167, 19, 122, 108, 142, 13, 33, 96, 119, 51, 162, 100, 150, 21, 41, 112, 31, 91, 18, 116, 6, 61, 105, 128, 39, 99, 26, 132, 46, 93, 81, 120, 23, 59, 42, 124, 54, 85, 73, 144, 15, 67, 34, 148, 22, 101, 57, 136, 47, 83, 2, 140, 14, 109, 65, 160, 55, 75, 10, 164, 30, 69, 89, 152, 7, 107, 50, 156, 38, 77, 97, 168, 87, 147, 74, 4, 62, 117, 161, 16, 95, 155, 82, 20, 102, 149, 137, 8, 79, 115, 98, 12, 110, 141, 129, 32, 71, 123, 90, 36, 78, 157, 113, 24, 103, 139, 58, 28, 70, 165, 121, 48, 111, 131, 66, 52, 86, 125, 145, 40, 63, 163, 106, 44, 94, 133, 153, 56], [113, 86, 204, 63, 85, 112, 211, 66, 137, 78, 180, 111, 77, 72, 187, 90, 145, 94, 196, 103, 93, 64, 171, 106, 161, 102, 220, 71, 101, 96, 195, 82, 153, 70, 188, 79, 69, 104, 219, 58, 129, 62, 172, 95, 61, 88, 203, 74, 121, 110, 212, 87, 109, 80, 179, 98, 1, 142, 260, 119, 141, 168, 267, 122, 25, 134, 236, 167, 133, 128, 243, 146, 33, 150, 252, 159, 149, 120, 227, 162, 49, 158, 276, 127, 157, 152, 251, 138, 41, 126, 244, 135, 125, 160, 275, 114, 17, 118, 228, 151, 117, 144, 259, 130, 9, 166, 268, 143, 165, 136, 235, 154, 57, 30, 316, 7, 29, 56, 323, 10, 81, 22, 292, 55, 21, 16, 299, 34, 89, 38, 308, 47, 37, 8, 283, 50, 105, 46, 332, 15, 45, 40, 307, 26, 97, 14, 300, 23, 13, 48, 331, 2, 73, 6, 284, 39, 5, 32, 315, 18, 65, 54, 324, 31, 53, 24, 291, 42, 281, 254, 148, 231, 253, 280, 155, 234, 305, 246, 124, 279, 245, 240, 131, 258, 313, 262, 140, 271, 261, 232, 115, 274, 329, 270, 164, 239, 269, 264, 139, 250, 321, 238, 132, 247, 237, 272, 163, 226, 297, 230, 116, 263, 229, 256, 147, 242, 289, 278, 156, 255, 277, 248, 123, 266, 169, 310, 36, 287, 309, 336, 43, 290, 193, 302, 12, 335, 301, 296, 19, 314, 201, 318, 28, 327, 317, 288, 3, 330, 217, 326, 52, 295, 325, 320, 27, 306, 209, 294, 20, 303, 293, 328, 51, 282, 185, 286, 4, 319, 285, 312, 35, 298, 177, 334, 44, 311, 333, 304, 11, 322, 225, 198, 92, 175, 197, 224, 99, 178, 249, 190, 68, 223, 189, 184, 75, 202, 257, 206, 84, 215, 205, 176, 59, 218, 273, 214, 108, 183, 213, 208, 83, 194, 265, 182, 76, 191, 181, 216, 107, 170, 241, 174, 60, 207, 173, 200, 91, 186, 233, 222, 100, 199, 221, 192, 67, 210], [255, 272, 73, 10, 310, 187, 228, 197, 231, 240, 97, 26, 294, 195, 260, 205, 279, 264, 81, 2, 326, 211, 252, 189, 263, 248, 57, 42, 286, 203, 268, 181, 247, 232, 89, 18, 334, 171, 276, 213, 271, 280, 105, 50, 302, 179, 236, 221, 239, 256, 65, 34, 318, 219, 244, 173, 311, 328, 129, 66, 198, 243, 284, 253, 287, 296, 153, 82, 182, 251, 316, 261, 335, 320, 137, 58, 214, 267, 308, 245, 319, 304, 113, 98, 174, 259, 324, 237, 303, 288, 145, 74, 222, 227, 332, 269, 327, 336, 161, 106, 190, 235, 292, 277, 295, 312, 121, 90, 206, 275, 300, 229, 199, 216, 17, 122, 254, 299, 172, 309, 175, 184, 41, 138, 238, 307, 204, 317, 223, 208, 25, 114, 270, 323, 196, 301, 207, 192, 1, 154, 230, 315, 212, 293, 191, 176, 33, 130, 278, 283, 220, 325, 215, 224, 49, 162, 246, 291, 180, 333, 183, 200, 9, 146, 262, 331, 188, 285, 31, 48, 241, 178, 86, 131, 4, 141, 7, 16, 265, 194, 70, 139, 36, 149, 55, 40, 249, 170, 102, 155, 28, 133, 39, 24, 225, 210, 62, 147, 44, 125, 23, 8, 257, 186, 110, 115, 52, 157, 47, 56, 273, 218, 78, 123, 12, 165, 15, 32, 233, 202, 94, 163, 20, 117, 87, 104, 297, 234, 142, 19, 60, 29, 63, 72, 321, 250, 126, 27, 92, 37, 111, 96, 305, 226, 158, 43, 84, 21, 95, 80, 281, 266, 118, 35, 100, 13, 79, 64, 313, 242, 166, 3, 108, 45, 103, 112, 329, 274, 134, 11, 68, 53, 71, 88, 289, 258, 150, 51, 76, 5, 143, 160, 185, 290, 30, 75, 116, 85, 119, 128, 209, 306, 14, 83, 148, 93, 167, 152, 193, 282, 46, 99, 140, 77, 151, 136, 169, 322, 6, 91, 156, 69, 135, 120, 201, 298, 54, 59, 164, 101, 159, 168, 217, 330, 22, 67, 124, 109, 127, 144, 177, 314, 38, 107, 132, 61]];
cc:=[3,4,9];
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 >);
