# LMOV invariants made from HOMFLY polynomials. They are defined as Nh[knot,representation]:=[lowest degree of A, Matrix of coefficients with powers of A changing in horizontal direction and powers of z changing in vertical direction with a step of 2] Nh[[3, 1],[1]]:=[A,Matrix(2, 3, [[-2,3,-1],[-1,1,0]])]: Nh[[3, 1],[2]]:=[A^2,Matrix(4, 5, [[4,-16,24,-16,4],[4,-20,32,-20,4],[1,-8,14,-8,1],[0,-1,2,-1,0]])]: Nh[[3, 1],[1, 1]]:=[A^2,Matrix(3, 5, [[2,-8,12,-8,2],[1,-6,10,-6,1],[0,-1,2,-1,0]])]: Nh[[3, 1],[3]]:=[A^3,Matrix(9, 7, [[-12,108,-352,568,-492,220,-40],[-26,306,-1180,2136,-2006,950,-180],[-22,366,-1740,3618,-3728,1864,-358],[-8,230,-1431,3504,-3978,2066,-383],[-1,79,-698,2077,-2603,1378,-232],[0,14,-200,761,-1057,561,-79],[0,1,-31,167,-259,136,-14],[0,0,-2,20,-35,18,-1],[0,0,0,1,-2,1,0]])]: Nh[[3, 1],[2, 1]]:=[A^3,Matrix(8, 7, [[-11,99,-332,558,-507,239,-46],[-15,201,-842,1627,-1612,796,-155],[-7,164,-910,2080,-2275,1172,-224],[-1,66,-528,1475,-1792,947,-167],[0,13,-171,614,-833,443,-66],[0,1,-29,148,-226,119,-13],[0,0,-2,19,-33,17,-1],[0,0,0,1,-2,1,0]])]: Nh[[3, 1],[1, 1, 1]]:=[A^3,Matrix(6, 7, [[-2,18,-64,116,-114,58,-12],[-1,21,-106,232,-251,131,-26],[0,8,-67,187,-227,121,-22],[0,1,-19,74,-103,55,-8],[0,0,-2,14,-23,12,-1],[0,0,0,1,-2,1,0]])]: Nh[[3, 1],[4]]:=[A^4,Matrix(17, 9, [[60,-846,4524,-12646,20784,-20906,12700,-4290,620],[240,-4350,27966,-90362,167326,-186290,123670,-45230,7030],[427,-10539,83874,-318863,672636,-833811,605570,-238823,39529],[421,-15376,156829,-713834,1729859,-2392452,1894389,-798398,138562],[242,-14638,199205,-1106168,3104497,-4795389,4120517,-1836715,328449],[80,-9367,178413,-1235365,4052713,-7001996,6499897,-3033382,549007],[14,-4046,114462,-1015219,3937519,-7629617,7623214,-3690120,663793],[1,-1160,52716,-620012,2883889,-6294872,6751265,-3361594,589767],[0,-211,17249,-281866,1601225,-3964185,4555464,-2315960,388284],[0,-22,3906,-94785,673388,-1910177,2349643,-1211664,189711],[0,-1,581,-23201,212778,-702062,924073,-480546,68378],[0,0,51,-4010,49647,-194901,274547,-143235,17901],[0,0,2,-463,8289,-40111,60501,-31522,3304],[0,0,0,-32,936,-5924,9575,-4962,407],[0,0,0,-1,64,-593,1028,-528,30],[0,0,0,0,2,-36,67,-34,1],[0,0,0,0,0,-1,2,-1,0]])]: Nh[[3, 1],[2, 2]]:=[A^4,Matrix(15, 9, [[32,-489,2807,-8389,14703,-15739,10157,-3639,557],[76,-1696,12481,-44684,90011,-107684,76111,-29416,4801],[76,-2722,26645,-116605,273272,-367835,285260,-118502,20411],[39,-2582,35151,-191966,528559,-802646,680712,-301036,53769],[10,-1548,31051,-216945,709228,-1217397,1123804,-523154,94951],[1,-590,18872,-174286,685561,-1334254,1334940,-647042,116798],[0,-138,7902,-100898,486019,-1078226,1165515,-582384,102210],[0,-18,2235,-42111,254324,-648754,756178,-386119,64265],[0,-1,407,-12523,97925,-291148,365616,-189308,29032],[0,0,43,-2582,27365,-96853,131043,-68335,9319],[0,0,2,-350,5393,-23503,34287,-17899,2070],[0,0,0,-28,710,-4036,6356,-3304,302],[0,0,0,-1,56,-464,790,-407,26],[0,0,0,0,2,-32,59,-30,1],[0,0,0,0,0,-1,2,-1,0]])]: Nh[[3, 1],[3, 1]]:=[A^4,Matrix(16, 9, [[76,-1122,6271,-18274,31257,-32694,20649,-7254,1091],[220,-4502,31455,-108340,211509,-246534,170503,-64716,10405],[275,-8423,76046,-315516,711193,-929381,704583,-287730,48953],[184,-9402,114069,-580921,1525148,-2238880,1853607,-806633,142828],[68,-6758,115495,-737392,2274981,-3755874,3379244,-1550038,280274],[13,-3197,81636,-670669,2457748,-4572393,4450568,-2129145,385439],[1,-987,40709,-445118,1964306,-4133137,4336747,-2143070,380549],[0,-191,14241,-216966,1173657,-2810067,3170450,-1604606,273482],[0,-21,3415,-77421,525469,-1445222,1750606,-900660,143834],[0,-1,534,-19946,175283,-561806,730079,-379339,55196],[0,0,49,-3605,42888,-163759,228281,-119106,15252],[0,0,2,-433,7469,-35178,52622,-27433,2951],[0,0,0,-31,876,-5397,8669,-4496,379],[0,0,0,-1,62,-559,965,-496,29],[0,0,0,0,2,-35,65,-33,1],[0,0,0,0,0,-1,2,-1,0]])]: Nh[[3, 1],[2, 1, 1]]:=[A^4,Matrix(14, 9, [[26,-417,2501,-7757,14049,-15507,10311,-3807,601],[45,-1177,9470,-36021,75996,-94451,68990,-27447,4595],[30,-1492,16892,-80757,201305,-283807,228119,-97400,17110],[9,-1078,18231,-112451,335178,-537847,474113,-215054,38899],[1,-469,12848,-105646,381662,-699215,672944,-320474,58349],[0,-121,6034,-69168,308225,-647801,678061,-335136,59906],[0,-17,1869,-31864,179316,-435797,494738,-251124,42879],[0,-1,366,-10265,75334,-214421,263599,-136135,21523],[0,0,41,-2259,22630,-76976,102420,-53383,7527],[0,0,2,-323,4737,-19901,28666,-14974,1793],[0,0,0,-27,656,-3603,5623,-2926,277],[0,0,0,-1,54,-433,733,-378,25],[0,0,0,0,2,-31,57,-29,1],[0,0,0,0,0,-1,2,-1,0]])]: Nh[[3, 1],[1, 1, 1, 1]]:=[A^4,Matrix(11, 9, [[2,-39,266,-915,1812,-2165,1546,-609,102],[1,-61,661,-3003,7189,-9843,7761,-3281,576],[0,-37,722,-4541,13460,-21386,18708,-8466,1540],[0,-10,435,-4034,15197,-28297,27439,-13145,2415],[0,-1,149,-2248,11143,-24599,26386,-13194,2364],[0,0,27,-790,5416,-14423,17093,-8793,1470],[0,0,2,-169,1729,-5716,7487,-3909,576],[0,0,0,-20,348,-1504,2181,-1142,137],[0,0,0,-1,40,-251,404,-210,18],[0,0,0,0,2,-24,43,-22,1],[0,0,0,0,0,-1,2,-1,0]])]: Nh[[4, 1],[1]]:=[1/A^3,Matrix(2, 4, [[-1,2,-2,1],[0,1,-1,0]])]: Nh[[4, 1],[2]]:=[1/A^6,Matrix(3, 7, [[1,-3,4,-6,9,-7,2],[0,-1,2,-5,9,-6,1],[0,0,0,-1,2,-1,0]])]: Nh[[4, 1],[1, 1]]:=[1/A^6,Matrix(3, 7, [[2,-7,9,-6,4,-3,1],[1,-6,9,-5,2,-1,0],[0,-1,2,-1,0,0,0]])]: Nh[[4, 1],[3]]:=[1/A^9,Matrix(6, 10, [[-2,8,-13,15,-24,50,-85,91,-52,12],[-1,6,-11,12,-26,87,-192,225,-126,26],[0,1,-2,2,-9,59,-171,218,-120,22],[0,0,0,0,-1,18,-72,102,-55,8],[0,0,0,0,0,2,-14,23,-12,1],[0,0,0,0,0,0,-1,2,-1,0]])]: Nh[[4, 1],[2, 1]]:=[1/A^9,Matrix(5, 10, [[-11,46,-79,81,-71,71,-81,79,-46,11],[-15,75,-134,124,-92,92,-124,134,-75,15],[-7,44,-81,66,-38,38,-66,81,-44,7],[-1,11,-21,14,-5,5,-14,21,-11,1],[0,1,-2,1,0,0,-1,2,-1,0]])]: Nh[[4, 1],[1, 1, 1]]:=[1/A^9,Matrix(6, 10, [[-12,52,-91,85,-50,24,-15,13,-8,2],[-26,126,-225,192,-87,26,-12,11,-6,1],[-22,120,-218,171,-59,9,-2,2,-1,0],[-8,55,-102,72,-18,1,0,0,0,0],[-1,12,-23,14,-2,0,0,0,0,0],[0,1,-2,1,0,0,0,0,0,0]])]: Nh[[4, 1],[4]]:=[1/A^12,Matrix(11, 13, [[7,-33,65,-79,90,-144,318,-718,1293,-1611,1261,-551,102],[11,-56,109,-116,114,-223,757,-2460,5631,-8093,6850,-3100,576],[6,-36,68,-60,46,-127,787,-3893,11423,-18956,17422,-8220,1540],[1,-10,19,-13,6,-32,454,-3619,13733,-26422,26438,-12970,2415],[0,-1,2,-1,0,-3,151,-2101,10530,-23745,25931,-13127,2364],[0,0,0,0,0,0,27,-763,5268,-14195,16973,-8780,1470],[0,0,0,0,0,0,2,-167,1710,-5683,7470,-3908,576],[0,0,0,0,0,0,0,-20,347,-1502,2180,-1142,137],[0,0,0,0,0,0,0,-1,40,-251,404,-210,18],[0,0,0,0,0,0,0,0,2,-24,43,-22,1],[0,0,0,0,0,0,0,0,0,-1,2,-1,0]])]: Nh[[4, 1],[2, 2]]:=[1/A^12,Matrix(9, 13, [[67,-346,755,-948,837,-658,586,-658,837,-948,755,-346,67],[251,-1315,2784,-3168,2315,-1437,1140,-1437,2315,-3168,2784,-1315,251],[433,-2299,4681,-4793,2830,-1270,836,-1270,2830,-4793,4681,-2299,433],[422,-2334,4591,-4215,1977,-582,282,-582,1977,-4215,4591,-2334,422],[242,-1467,2820,-2316,846,-146,42,-146,846,-2316,2820,-1467,242],[80,-576,1097,-803,220,-19,2,-19,220,-803,1097,-576,80],[14,-137,262,-170,32,-1,0,-1,32,-170,262,-137,14],[1,-18,35,-20,2,0,0,0,2,-20,35,-18,1],[0,-1,2,-1,0,0,0,0,0,-1,2,-1,0]])]: Nh[[4, 1],[3, 1]]:=[1/A^12,Matrix(10, 13, [[61,-305,649,-823,808,-814,982,-1366,1897,-2169,1697,-763,146],[185,-951,1963,-2229,1823,-1629,2114,-3594,6246,-8442,7245,-3371,640],[247,-1315,2613,-2617,1694,-1265,1838,-4065,9266,-15047,14254,-6907,1304],[175,-1010,1949,-1708,830,-475,819,-2533,7967,-15756,16510,-8292,1524],[67,-456,868,-663,227,-86,195,-926,4291,-10502,12183,-6279,1081],[13,-120,229,-152,33,-6,23,-196,1473,-4573,5882,-3075,469],[1,-17,33,-19,2,0,1,-22,314,-1294,1850,-970,121],[0,-1,2,-1,0,0,0,-1,38,-229,365,-190,17],[0,0,0,0,0,0,0,0,2,-23,41,-21,1],[0,0,0,0,0,0,0,0,0,-1,2,-1,0]])]: Nh[[4, 1],[2, 1, 1]]:=[1/A^12,Matrix(10, 13, [[146,-763,1697,-2169,1897,-1366,982,-814,808,-823,649,-305,61],[640,-3371,7245,-8442,6246,-3594,2114,-1629,1823,-2229,1963,-951,185],[1304,-6907,14254,-15047,9266,-4065,1838,-1265,1694,-2617,2613,-1315,247],[1524,-8292,16510,-15756,7967,-2533,819,-475,830,-1708,1949,-1010,175],[1081,-6279,12183,-10502,4291,-926,195,-86,227,-663,868,-456,67],[469,-3075,5882,-4573,1473,-196,23,-6,33,-152,229,-120,13],[121,-970,1850,-1294,314,-22,1,0,2,-19,33,-17,1],[17,-190,365,-229,38,-1,0,0,0,-1,2,-1,0],[1,-21,41,-23,2,0,0,0,0,0,0,0,0],[0,-1,2,-1,0,0,0,0,0,0,0,0,0]])]: Nh[[4, 1],[1, 1, 1, 1]]:=[1/A^12,Matrix(11, 13, [[102,-551,1261,-1611,1293,-718,318,-144,90,-79,65,-33,7],[576,-3100,6850,-8093,5631,-2460,757,-223,114,-116,109,-56,11],[1540,-8220,17422,-18956,11423,-3893,787,-127,46,-60,68,-36,6],[2415,-12970,26438,-26422,13733,-3619,454,-32,6,-13,19,-10,1],[2364,-13127,25931,-23745,10530,-2101,151,-3,0,-1,2,-1,0],[1470,-8780,16973,-14195,5268,-763,27,0,0,0,0,0,0],[576,-3908,7470,-5683,1710,-167,2,0,0,0,0,0,0],[137,-1142,2180,-1502,347,-20,0,0,0,0,0,0,0],[18,-210,404,-251,40,-1,0,0,0,0,0,0,0],[1,-22,43,-24,2,0,0,0,0,0,0,0,0],[0,-1,2,-1,0,0,0,0,0,0,0,0,0]])]: Nh[[5, 1],[1]]:=[A^3,Matrix(3, 3, [[-3,5,-2],[-4,5,-1],[-1,1,0]])]: Nh[[5, 1],[2]]:=[A^6,Matrix(8, 5, [[30,-120,180,-120,30],[115,-490,750,-490,115],[176,-819,1286,-819,176],[137,-724,1174,-724,137],[57,-365,616,-365,57],[12,-105,186,-105,12],[1,-16,30,-16,1],[0,-1,2,-1,0]])]: Nh[[5, 1],[1, 1]]:=[A^6,Matrix(7, 5, [[20,-80,120,-80,20],[60,-260,400,-260,60],[69,-336,534,-336,69],[38,-221,366,-221,38],[10,-78,136,-78,10],[1,-14,26,-14,1],[0,-1,2,-1,0]])]: Nh[[5, 1],[3]]:=[A^9,Matrix(18, 7, [[-612,4282,-12170,18100,-14920,6482,-1162],[-5506,42271,-129215,203600,-175690,79121,-14581],[-23192,198031,-657139,1103915,-1000889,467586,-88312],[-59384,572273,-2078169,3736000,-3559209,1718033,-329544],[-101720,1124627,-4504027,8688844,-8685457,4307675,-829942],[-121996,1578123,-7029420,14594746,-15285709,7746221,-1481965],[-104816,1625710,-8134469,18248211,-20007137,10307863,-1935362],[-65114,1249175,-7106311,17316684,-19871498,10362997,-1885933],[-29205,721405,-4735067,12623787,-15169790,7976692,-1387822],[-9339,313241,-2415866,7114329,-8962560,4735426,-775231],[-2071,101529,-941668,3102690,-4104397,2172177,-328260],[-302,24156,-277825,1042441,-1450978,766965,-104457],[-26,4090,-60907,266857,-391757,206277,-24534],[-1,466,-9605,51024,-79211,41446,-4119],[0,32,-1029,7046,-11600,6018,-467],[0,1,-67,663,-1161,596,-32],[0,0,-2,38,-71,36,-1],[0,0,0,1,-2,1,0]])]: Nh[[5, 1],[2, 1]]:=[A^9,Matrix(17, 7, [[-778,5483,-15755,23750,-19880,8783,-1603],[-5929,46514,-145060,232875,-204460,93539,-17479],[-20986,186222,-636631,1095250,-1012006,479592,-91441],[-44960,458386,-1732046,3205225,-3116781,1523901,-293725],[-64066,764419,-3219215,6427475,-6569210,3295156,-634559],[-63300,905137,-4290087,9275345,-9951953,5092334,-967476],[-44151,780483,-4213699,9914620,-11161326,5796079,-1072006],[-21814,496526,-3099128,7990833,-9440203,4952673,-878887],[-7564,233985,-1719912,4905169,-6086843,3213286,-538121],[-1795,81304,-720501,2301847,-3004880,1590473,-246448],[-277,20526,-226187,823741,-1133523,599603,-83883],[-25,3656,-52319,222684,-323786,170666,-20876],[-1,435,-8643,44635,-68760,36018,-3684],[0,31,-964,6421,-10510,5458,-436],[0,1,-65,626,-1092,561,-31],[0,0,-2,37,-69,35,-1],[0,0,0,1,-2,1,0]])]: Nh[[5, 1],[1, 1, 1]]:=[A^9,Matrix(15, 7, [[-232,1652,-4820,7400,-6320,2852,-532],[-1436,11626,-37290,61400,-55140,25726,-4886],[-4046,38060,-135824,241510,-228824,110390,-21266],[-6781,75590,-303114,584700,-584729,290550,-56216],[-7384,100086,-456013,958591,-1011218,514589,-98651],[-5384,92128,-483836,1115009,-1240265,642511,-120163],[-2636,60064,-370471,943863,-1107524,580839,-104135],[-851,27853,-206727,589169,-730275,385792,-64961],[-173,9107,-83995,272258,-357280,189269,-29186],[-20,2048,-24548,92689,-129164,68333,-9338],[-1,301,-5020,22898,-34006,17899,-2071],[0,26,-681,3984,-6331,3304,-302],[0,1,-55,462,-789,407,-26],[0,0,-2,32,-59,30,-1],[0,0,0,1,-2,1,0]])]: Nh[[5, 1],[4]]:=[A^12,Matrix(33, 9, [[18882,-189335,809110,-1934307,2839900,-2629397,1502550,-485345,67942],[321486,-3539415,16401115,-42105861,65872875,-64580621,38872575,-13168155,1926001],[2758456,-33612937,169894732,-470436261,786697010,-818290284,519266370,-184414104,28137018],[15467566,-210195306,1164338856,-3486948776,6240381140,-6885488415,4599459160,-1707640277,270626052],[62315675,-951763898,5803567721,-18839697039,36101945476,-42216284471,29617817532,-11453662800,1875761804],[189152664,-3273950765,22077700905,-77863146109,159845311048,-197902412473,145481918379,-58383884373,9829310724],[445129083,-8810295135,66033724423,-253659289690,558271575060,-731241074294,562049805104,-233257552373,40167977822],[827873656,-18925050021,158525893456,-665214256032,1571198879160,-2176174804221,1745647618244,-746798060142,130911905900],[1233605159,-32933410512,310190232534,-1426648637817,3621205863336,-5302429084199,4432002682560,-1948774739674,346153488613],[1487320657,-46952415103,500599422712,-2533115375857,6921435695158,-10715512084595,9320193178190,-4200844199749,752708458587],[1461120399,-55312005857,672521089513,-3760178669755,11082613188382,-18147220771523,16407065852849,-7561660255153,1360710451145],[1174982008,-54190602507,757551000538,-4702740494863,14987106190546,-25972311135988,24386368601644,-11465897724936,2062939183558],[775418799,-44360679665,719470640324,-4986014565659,17228772476164,-31627432860543,30817477803253,-14750176535919,2641488303246],[420158953,-30434892907,578464650374,-4502865727885,16923725595316,-32948614346942,33297547212732,-16190930049996,2872687400355],[186616691,-17527207222,394811257944,-3476172825323,14261758800663,-29491199391743,30896620780540,-15233484492526,2665006460976],[67668900,-8472736596,229077921902,-2299579902950,10340710274676,-22753089133389,24703177368926,-12327728648079,2115837186610],[19893113,-3432410343,113014763332,-1305339271144,6463305723528,-15166100923384,17059771013546,-8601986647827,1440747859179],[4690461,-1161277395,47352139974,-635997708646,3485662341900,-8745535477144,10190654353884,-5183384522473,842405459439],[872886,-326272961,16805342737,-265761526435,1621835953712,-4364899160852,5268262920789,-2698919670478,423001540602],[125176,-75489638,5029950777,-95050843803,650316080082,-1884624429021,2356045748278,-1213880589410,182239447559],[13331,-14210832,1261499408,-28998455952,224200405238,-702890205514,910171210802,-470950773526,67220517045],[992,-2139440,262698259,-7508808524,66215504086,-225851781316,302946667300,-157217185786,21155044429],[46,-251223,44849378,-1638677320,16665443392,-62277210721,86541701732,-44987496344,5651641060],[1,-22153,6166675,-298511580,3548671972,-14656170408,21102332079,-10975127909,1272661323],[0,-1379,665638,-44798153,633055148,-2921877713,4359702388,-2265985639,239239710],[0,-54,54280,-5438525,93357937,-488547517,755556236,-392034346,37051989],[0,-1,3142,-520432,11174085,-67591296,108368648,-56076433,4642287],[0,0,115,-37765,1057532,-7595721,12627822,-6510474,458491],[0,0,2,-1952,76122,-675395,1164561,-597677,34339],[0,0,0,-64,3914,-45701,81748,-41729,1832],[0,0,0,-1,128,-2210,4102,-2081,62],[0,0,0,0,2,-68,131,-66,1],[0,0,0,0,0,-1,2,-1,0]])]: Nh[[5, 1],[2, 2]]:=[A^12,Matrix(31, 9, 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Nh[[6, 3],[1]]:=[1/A^3,Matrix(3, 4, [[1,-4,4,-1],[1,-4,4,-1],[0,-1,1,0]])]: Nh[[6, 3],[2]]:=[1/A^6,Matrix(6, 7, [[1,-9,28,-42,33,-13,2],[5,-27,72,-113,104,-52,11],[5,-26,65,-114,127,-72,15],[1,-9,24,-54,74,-43,7],[0,-1,3,-12,20,-11,1],[0,0,0,-1,2,-1,0]])]: Nh[[6, 3],[1, 1]]:=[1/A^6,Matrix(6, 7, [[2,-13,33,-42,28,-9,1],[11,-52,104,-113,72,-27,5],[15,-72,127,-114,65,-26,5],[7,-43,74,-54,24,-9,1],[1,-11,20,-12,3,-1,0],[0,-1,2,-1,0,0,0]])]: Nh[[6, 3],[3]]:=[1/A^9,Matrix(12, 10, 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Nh[[7, 1],[1]]:=[A^5,Matrix(4, 3, [[-4,7,-3],[-10,14,-4],[-6,7,-1],[-1,1,0]])]: Nh[[7, 1],[2]]:=[A^10,Matrix(12, 5, [[112,-448,672,-448,112],[896,-3696,5600,-3696,896],[3052,-13104,20104,-13104,3052],[5812,-26300,40976,-26300,5812],[6844,-33188,52688,-33188,6844],[5212,-27692,44960,-27692,5212],[2607,-15640,26066,-15640,2607],[849,-6003,10308,-6003,849],[173,-1541,2736,-1541,173],[20,-253,466,-253,20],[1,-24,46,-24,1],[0,-1,2,-1,0]])]: Nh[[7, 1],[1, 1]]:=[A^10,Matrix(11, 5, [[84,-336,504,-336,84],[574,-2380,3612,-2380,574],[1652,-7182,11060,-7182,1652],[2623,-12144,19042,-12144,2623],[2529,-12739,20420,-12739,2529],[1536,-8673,14274,-8673,1536],[589,-3892,6606,-3892,589],[138,-1141,2006,-1141,138],[18,-210,384,-210,18],[1,-22,42,-22,1],[0,-1,2,-1,0]])]: Nh[[7, 1],[3]]:=[A^15,Matrix(27, 7, 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Nh[[4, 1],Zua[11][1]]:=[A^Zua[11][3],Zua[11][7]]: