# Degree-12 polynomials (compositions g(h(x)), composita alpha + c beta, x^12 + a x^k + b,
# random ones), one or two per Galois group seen, labeled nTk by Magma (GaloisGroup +
# TransitiveGroupIdentification), used as an oracle.  Per line: nTk magma c0,c1,...,c12
12T2 magma 2017,972,1485,1108,795,390,299,150,51,20,15,6,1
12T10 magma -332807,-573084,-481026,362040,430437,-24660,-88150,108,5622,-12,-132,0,1
12T193 magma 4094,0,-6144,0,3840,0,-1280,0,240,0,-24,0,1
12T299 magma 2,12,9,-12,-18,-4,7,6,6,-6,1,-2,1
12T42 magma 7,0,0,0,0,0,-5,0,0,0,0,0,1
12T28 magma -7,0,0,0,0,0,0,0,0,0,0,0,1
12T293 magma 725,0,1457,0,1215,0,540,0,135,0,18,0,1
12T294 magma -66,0,-144,-48,-60,-72,33,-3,6,17,-6,-3,1
12T83 magma 28208,88704,-6720,-21008,-1224,4104,-576,468,-441,122,0,-6,1
12T301 magma -2,0,0,2,0,0,1,-1,1,0,2,-1,1
12T301 magma -2,1,0,-1,0,-2,-1,1,0,0,0,0,1
12T45 magma 13,159,-458,335,-79,352,-654,386,27,-134,64,-13,1
12T81 magma 5,0,0,0,0,0,1,0,0,0,0,0,1
12T294 magma 25,27,9,1,27,18,3,0,9,3,0,0,1
12T289 magma 8,27,63,99,39,-108,-101,36,54,-4,-12,0,1
12T222 magma -1,0,0,0,300,0,-1060,0,303,0,-30,0,1
12T286 magma 15485,0,-18726,0,9375,0,-2500,0,375,0,-30,0,1
12T61 magma -1,0,0,0,-1,0,0,0,2,0,0,0,1
12T185 magma 2,0,0,0,-1,0,0,0,0,0,0,0,1
12T28 magma -2,0,0,0,0,0,0,0,0,0,0,0,1
12T274 magma 386,1056,24,-2026,-1017,1368,984,-324,-351,-18,42,12,1
12T293 magma -1,0,0,0,0,0,0,0,0,0,2,0,1
12T3 magma 121,0,168,0,420,0,-154,0,60,0,-12,0,1
12T185 magma -18,0,0,0,25,0,0,0,-9,0,0,0,1
12T14 magma 159,-54,327,-469,420,-372,429,-168,-75,59,0,-6,1
12T289 magma -3,24,-27,-35,99,27,-111,-9,54,1,-12,0,1
12T299 magma 1,2,4,2,8,0,3,-4,0,-4,0,0,1
12T180 magma 438336,-2027520,436032,-30720,-76560,27648,-2720,1536,60,0,-12,0,1
12T11 magma 1,-27,190,-104,27,-6,-43,6,27,-2,-2,3,1
12T10 magma -1031,-3008,-792,-1516,-1586,624,-698,12,249,4,-26,0,1
12T193 magma -1,0,-6,0,15,0,-20,0,15,0,-6,0,1
12T14 magma 223,-92,248,-292,271,-124,126,-76,-2,24,-2,-4,1
12T83 magma 511,-417,35,65,313,-806,815,-497,298,-174,66,-13,1
12T119 magma -1,0,0,4,0,0,2,0,0,-4,0,0,1
12T180 magma -1279,-2286,-1371,-510,630,666,169,54,-30,-10,9,6,1
12T23 magma 4,4,64,138,119,76,59,46,40,30,17,6,1
12T81 magma 10,0,0,0,0,0,3,0,0,0,0,0,1
12T15 magma 43,36,387,356,216,-180,-57,0,36,8,-9,0,1
12T219 magma -47,156,-12,246,-714,354,275,-240,-48,66,-3,-6,1
12T11 magma -136,96,384,-160,252,0,-88,0,54,-8,-12,0,1
12T285 magma 1,0,0,0,0,0,0,0,0,0,1,0,1
12T7 magma 9,54,144,210,189,132,115,102,84,50,21,6,1
12T292 magma 1,-2,-1,3,0,-5,2,5,-7,2,3,-3,1
12T258 magma 7,0,0,1,0,0,0,0,0,0,0,0,1
12T274 magma 14,32,24,40,49,24,28,24,6,8,4,0,1
12T219 magma -718,-17063,-2557,-6109,-8339,-1229,36,-374,119,248,97,16,1
12T1 magma 526891,430249,360686,153728,66148,21032,7320,1772,511,99,19,5,1
12T2 magma 181,18,120,170,27,0,99,54,-18,-10,9,6,1
12T217 magma 79,-324,810,-1404,1863,-1944,1620,-1080,567,-228,66,-12,1
12T13 magma -3,0,0,0,0,0,0,0,0,0,0,0,1
12T87 magma 1,0,6,0,-13,0,-8,0,8,0,6,0,1
12T260 magma 3,0,9,0,9,0,-3,0,-6,0,0,0,1
12T51 magma -3,0,0,0,9,0,0,0,-6,0,0,0,1
12T45 magma 466399,478212,380835,126499,34308,9342,3543,-36,297,85,-12,0,1
12T4 magma 806417533,586168476,168725646,20419672,3341781,1213164,159306,-36,2970,652,-12,0,1
12T7 magma 289,0,9222,0,5199,0,276,0,-81,0,6,0,1
12T167 magma 13,0,0,7,0,0,8,0,0,2,0,0,1
12T39 magma 2,0,0,0,0,0,-4,0,0,0,0,0,1
12T121 magma 1,0,0,1,0,0,2,0,0,2,0,0,1
12T250 magma 30,0,-270,0,927,0,-1180,0,309,0,-30,0,1
12T261 magma -23,16,64,-16,-122,52,94,-64,-23,28,-2,-4,1
12T25 magma 1,0,42,0,129,0,62,0,42,0,12,0,1
12T89 magma 1,0,0,0,-2,0,0,0,-1,0,0,0,1
12T286 magma -43,0,18,0,15,0,-20,0,15,0,-6,0,1
12T261 magma -8,-144,396,-276,-183,324,-64,-108,54,12,-12,0,1
12T3 magma 4,0,96,0,-75,0,26,0,15,0,6,0,1
12T43 magma 261312,-363648,700416,-262144,177840,-27072,12864,-3456,900,-72,48,0,1
12T292 magma 41,0,-114,-114,137,198,6,-147,-43,27,18,-9,1
12T217 magma 7,0,0,6,0,0,7,0,0,2,0,0,1
12T135 magma 4,-18,129,-450,690,-18,-911,18,690,450,129,18,1
12T167 magma 7,0,0,4,0,0,5,0,0,2,0,0,1
12T13 magma -12,0,0,0,0,0,0,0,0,0,0,0,1
12T258 magma 12,0,0,-1,0,0,0,0,0,0,0,0,1
12T125 magma -2,0,0,0,1,0,4,0,6,0,4,0,1
12T203 magma 1,0,-3,0,9,0,1,0,-6,0,0,0,1
12T135 magma 67,0,192,0,240,0,160,0,60,0,12,0,1
12T264 magma 1,-3,9,-26,75,27,-107,-9,54,1,-12,0,1
12T50 magma 6,0,0,0,-3,0,0,0,0,0,0,0,1
12T280 magma 12,-24,0,8,81,0,-108,0,54,0,-12,0,1
12T77 magma 386,-996,1433,-1334,1117,-736,405,-210,115,-56,23,-6,1
12T250 magma 3,0,-40,0,304,0,-1060,0,303,0,-30,0,1
12T186 magma 6,0,-48,0,108,0,-112,0,54,0,-12,0,1
12T186 magma -2,0,0,0,0,0,-1,0,3,0,-3,0,1
12T43 magma 1296,0,2592,-864,432,1728,504,0,36,16,0,0,1
12T42 magma 3,0,0,0,0,0,3,0,0,0,0,0,1
12T226 magma 1,0,-30,0,3,0,-1000,0,300,0,-30,0,1
12T264 magma 2,-32,64,32,-140,40,100,-64,-23,28,-2,-4,1
12T260 magma 2,0,-6,0,9,0,2,0,-6,0,0,0,1
12T188 magma -3,0,48,-112,12,168,-76,-168,15,100,54,12,1
12T213 magma -1,0,0,-1,0,0,0,0,0,0,0,0,1
12T15 magma 3,0,0,0,0,0,0,0,0,0,0,0,1
12T156 magma -1,0,0,-4,0,0,6,0,0,-4,0,0,1
12T213 magma -1,0,0,0,0,0,0,0,0,-2,0,0,1
12T48 magma 1,0,0,0,9,0,0,0,-6,0,0,0,1
12T20 magma 1681,-584,956,1948,1422,-324,458,-52,-47,48,-2,-4,1
12T1 magma 1,24,40,-172,-166,436,42,-292,39,64,-14,-4,1
12T134 magma 43,0,-135,0,179,0,-127,0,51,0,-11,0,1
12T114 magma -1,0,0,0,4,0,0,0,-3,0,0,0,1
12T125 magma 26,0,-90,0,141,0,-118,0,54,0,-12,0,1
12T134 magma 757,0,1485,0,1224,0,541,0,135,0,18,0,1
12T20 magma 2561,-3688,8284,-6404,3230,-1700,682,-244,97,0,-2,-4,1
12T38 magma -3,0,0,0,0,0,1,0,0,0,0,0,1
12T138 magma 1,0,0,0,-1,0,0,0,0,0,0,0,1
12T138 magma 1,0,0,0,1,0,0,0,0,0,0,0,1
12T86 magma 2,0,0,0,5,0,0,0,0,0,0,0,1
12T48 magma 7749,-11466,21246,4422,-3329,-4644,27,1806,-272,-270,117,-18,1
12T51 magma 3,0,0,0,9,0,0,0,6,0,0,0,1
12T226 magma 4,0,-10,0,-299,0,-940,0,297,0,-30,0,1
12T114 magma -1,0,0,0,0,0,0,0,1,0,0,0,1
12T280 magma 597,-1476,1350,-1032,981,-540,258,-180,54,-20,12,0,1
12T188 magma 4047,0,-6120,0,3837,0,-1280,0,240,0,-24,0,1
12T61 magma -3,0,48,208,492,792,924,792,495,220,66,12,1
12T156 magma -3,0,0,0,0,0,1,0,0,2,0,0,1
12T37 magma 2,0,0,4,0,0,6,0,0,4,0,0,1
12T187 magma 1,0,8,0,-18,0,-56,0,47,0,-12,0,1
12T234 magma 12,0,0,-24,0,0,24,0,0,-8,0,0,1
12T285 magma 1,0,1,0,-1,0,0,0,1,0,0,0,1
12T23 magma 3673,12160,21352,26712,25282,18020,10030,4424,1549,420,86,12,1
12T168 magma 82,0,0,-108,0,0,54,0,0,-12,0,0,1
12T106 magma 4,0,-6,0,15,0,-20,0,15,0,-6,0,1
12T86 magma 6,0,0,0,12,0,0,0,6,0,0,0,1
12T89 magma 1,0,0,0,3,0,0,0,-4,0,0,0,1
12T170 magma 194,0,0,-224,0,0,92,0,0,-16,0,0,1
12T92 magma -3,0,0,0,12,0,-20,0,15,0,-6,0,1
12T4 magma 4157,-2748,2574,3688,1269,1044,522,36,90,20,-12,0,1
12T222 magma -1,0,0,0,48,0,-88,0,51,0,-12,0,1
12T168 magma 2,-12,42,-4,-153,-72,276,504,423,212,66,12,1
12T142 magma -1,0,18,0,-15,0,-16,0,6,0,6,0,1
12T237 magma 5,0,-5,0,16,0,-11,0,11,0,-6,0,1
12T234 magma 236,0,0,-248,0,0,96,0,0,-16,0,0,1
12T119 magma -1,0,0,-4,0,0,2,0,0,4,0,0,1
12T77 magma 1,0,-10,0,-19,0,-6,0,6,0,4,0,1
12T87 magma 1,0,0,0,-12,0,4,0,9,0,-6,0,1
12T18 magma 1,0,0,4,0,0,5,0,0,2,0,0,1
12T236 magma 1,0,12,0,9,0,-4,0,-6,0,0,0,1
12T170 magma 205,0,0,-215,0,0,85,0,0,-15,0,0,1
12T227 magma 24,0,-108,0,171,0,-136,0,57,0,-12,0,1
12T236 magma 1,0,3,0,9,0,-1,0,-6,0,0,0,1
12T147 magma -3,0,0,0,3,0,0,0,-3,0,0,0,1
12T243 magma -1,27,108,153,9,-162,-96,54,54,-6,-12,0,1
12T237 magma 2,0,-4,0,1,0,4,0,-2,0,0,0,1
12T141 magma -19,0,0,0,24,0,0,0,-9,0,0,0,1
12T37 magma -8,0,0,16,0,0,-4,0,0,-4,0,0,1
12T67 magma 1,0,0,0,-1,0,-1,0,-1,0,0,0,1
12T203 magma 1,0,-2,0,2,0,0,0,-1,0,0,0,1
12T25 magma 1,0,-3,0,12,0,-19,0,15,0,-6,0,1
12T78 magma 17,0,-72,0,129,0,-116,0,54,0,-12,0,1
12T149 magma 31,0,0,0,28,0,0,0,9,0,0,0,1
12T141 magma 3,0,0,0,0,0,0,0,-3,0,0,0,1
12T39 magma 2,0,0,0,0,0,4,0,0,0,0,0,1
12T106 magma 4,0,6,0,15,0,20,0,15,0,6,0,1
12T147 magma -3,0,0,0,21,0,0,0,-9,0,0,0,1
12T24 magma 484,0,-384,0,684,0,-180,0,33,0,-6,0,1
12T202 magma 4,0,9,0,9,0,-3,0,-6,0,0,0,1
12T90 magma 1,0,-60,0,506,0,-1100,0,305,0,-30,0,1
12T92 magma -1,0,-12,12,-3,0,64,-192,240,-160,60,-12,1
12T227 magma 87,0,-232,0,266,0,-168,0,61,0,-12,0,1
12T187 magma 1,0,20,0,-102,0,-980,0,299,0,-30,0,1
12T142 magma -7,0,-42,0,-49,0,15,0,20,0,-9,0,1
12T38 magma 33,0,0,0,0,0,11,0,0,0,0,0,1
12T78 magma 21,0,-81,0,135,0,-117,0,54,0,-12,0,1
12T139 magma 1,0,-20,0,-298,0,-940,0,297,0,-30,0,1
12T240 magma 69,204,42,-331,-177,255,140,-126,-45,40,3,-6,1
12T133 magma 12,0,24,8,0,0,0,0,81,108,54,12,1
12T79 magma 2,0,-4,0,-7,0,0,0,6,0,4,0,1
