10 27 Quantum Invariants

Further quantum knot invariants for 10_27.

A1 Invariants.

Weight	Invariant
1	$-q^{17}+2q^{15}-3q^{13}+3q^{11}-2q^{9}+q^{7}+q^{5}-2q^{3}+4q-2q^{-1}+2q^{-3}-q^{-5}$
2	$q^{48}-2q^{46}-q^{44}+7q^{42}-6q^{40}-8q^{38}+18q^{36}-5q^{34}-19q^{32}+23q^{30}+2q^{28}-24q^{26}+15q^{24}+9q^{22}-16q^{20}-q^{18}+11q^{16}+2q^{14}-17q^{12}+7q^{10}+19q^{8}-23q^{6}-q^{4}+25q^{2}-15-6q^{-2}+16q^{-4}-6q^{-6}-6q^{-8}+6q^{-10}-q^{-12}-2q^{-14}+q^{-16}$
3	$-q^{93}+2q^{91}+q^{89}-3q^{87}-4q^{85}+6q^{83}+11q^{81}-11q^{79}-22q^{77}+12q^{75}+39q^{73}-7q^{71}-62q^{69}-4q^{67}+84q^{65}+26q^{63}-98q^{61}-58q^{59}+104q^{57}+87q^{55}-95q^{53}-112q^{51}+74q^{49}+126q^{47}-45q^{45}-126q^{43}+14q^{41}+112q^{39}+18q^{37}-88q^{35}-48q^{33}+56q^{31}+77q^{29}-22q^{27}-98q^{25}-17q^{23}+111q^{21}+52q^{19}-113q^{17}-87q^{15}+106q^{13}+107q^{11}-80q^{9}-117q^{7}+51q^{5}+117q^{3}-23q-95q^{-1}-q^{-3}+76q^{-5}+13q^{-7}-49q^{-9}-19q^{-11}+30q^{-13}+15q^{-15}-16q^{-17}-12q^{-19}+8q^{-21}+6q^{-23}-3q^{-25}-3q^{-27}+q^{-29}+2q^{-31}-q^{-33}$
4	$q^{152}-2q^{150}-q^{148}+3q^{146}+4q^{142}-9q^{140}-6q^{138}+12q^{136}+6q^{134}+17q^{132}-33q^{130}-36q^{128}+25q^{126}+41q^{124}+72q^{122}-71q^{120}-130q^{118}-13q^{116}+103q^{114}+240q^{112}-42q^{110}-288q^{108}-204q^{106}+82q^{104}+505q^{102}+186q^{100}-348q^{98}-529q^{96}-174q^{94}+662q^{92}+566q^{90}-145q^{88}-743q^{86}-572q^{84}+520q^{82}+819q^{80}+232q^{78}-654q^{76}-828q^{74}+169q^{72}+759q^{70}+510q^{68}-342q^{66}-780q^{64}-172q^{62}+465q^{60}+584q^{58}+13q^{56}-528q^{54}-418q^{52}+103q^{50}+531q^{48}+344q^{46}-202q^{44}-609q^{42}-272q^{40}+412q^{38}+637q^{36}+167q^{34}-698q^{32}-627q^{30}+170q^{28}+796q^{26}+559q^{24}-566q^{22}-826q^{20}-182q^{18}+667q^{16}+798q^{14}-209q^{12}-711q^{10}-459q^{8}+296q^{6}+723q^{4}+121q^{2}-360-459q^{-2}-35q^{-4}+416q^{-6}+208q^{-8}-54q^{-10}-266q^{-12}-138q^{-14}+146q^{-16}+118q^{-18}+53q^{-20}-93q^{-22}-90q^{-24}+32q^{-26}+33q^{-28}+40q^{-30}-21q^{-32}-33q^{-34}+8q^{-36}+3q^{-38}+14q^{-40}-3q^{-42}-9q^{-44}+3q^{-46}+3q^{-50}-q^{-52}-2q^{-54}+q^{-56}$
5	$-q^{225}+2q^{223}+q^{221}-3q^{219}-q^{213}+4q^{211}+5q^{209}-8q^{207}-9q^{205}+2q^{203}+8q^{201}+18q^{199}+11q^{197}-22q^{195}-52q^{193}-27q^{191}+46q^{189}+100q^{187}+81q^{185}-47q^{183}-197q^{181}-209q^{179}+14q^{177}+323q^{175}+420q^{173}+134q^{171}-413q^{169}-756q^{167}-468q^{165}+403q^{163}+1157q^{161}+1012q^{159}-140q^{157}-1494q^{155}-1785q^{153}-463q^{151}+1622q^{149}+2652q^{147}+1415q^{145}-1357q^{143}-3394q^{141}-2665q^{139}+621q^{137}+3830q^{135}+3964q^{133}+516q^{131}-3746q^{129}-5056q^{127}-1930q^{125}+3156q^{123}+5727q^{121}+3304q^{119}-2140q^{117}-5816q^{115}-4414q^{113}+895q^{111}+5379q^{109}+5066q^{107}+328q^{105}-4528q^{103}-5210q^{101}-1351q^{99}+3432q^{97}+4936q^{95}+2093q^{93}-2306q^{91}-4367q^{89}-2550q^{87}+1242q^{85}+3658q^{83}+2838q^{81}-284q^{79}-2964q^{77}-3032q^{75}-594q^{73}+2291q^{71}+3251q^{69}+1472q^{67}-1657q^{65}-3511q^{63}-2387q^{61}+967q^{59}+3766q^{57}+3378q^{55}-154q^{53}-3890q^{51}-4390q^{49}-844q^{47}+3782q^{45}+5257q^{43}+1987q^{41}-3270q^{39}-5835q^{37}-3212q^{35}+2406q^{33}+5936q^{31}+4234q^{29}-1168q^{27}-5475q^{25}-4935q^{23}-182q^{21}+4512q^{19}+5098q^{17}+1384q^{15}-3165q^{13}-4701q^{11}-2265q^{9}+1751q^{7}+3884q^{5}+2613q^{3}-514q-2766q^{-1}-2529q^{-3}-364q^{-5}+1708q^{-7}+2072q^{-9}+809q^{-11}-805q^{-13}-1487q^{-15}-902q^{-17}+225q^{-19}+909q^{-21}+769q^{-23}+92q^{-25}-486q^{-27}-543q^{-29}-187q^{-31}+195q^{-33}+335q^{-35}+184q^{-37}-66q^{-39}-181q^{-41}-121q^{-43}+3q^{-45}+81q^{-47}+78q^{-49}+11q^{-51}-40q^{-53}-36q^{-55}-5q^{-57}+13q^{-59}+14q^{-61}+8q^{-63}-7q^{-65}-10q^{-67}+2q^{-69}+4q^{-71}-3q^{-79}+q^{-81}+2q^{-83}-q^{-85}$

A2 Invariants.

Weight	Invariant
1,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{24}+q^{22}-q^{20}-q^{18}+2 q^{16}-2 q^{14}+2 q^{12}+2 q^6-2 q^4+3 q^2+ q^{-4} - q^{-6} }
1,1	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{68}-4 q^{66}+12 q^{64}-28 q^{62}+56 q^{60}-102 q^{58}+168 q^{56}-252 q^{54}+351 q^{52}-462 q^{50}+560 q^{48}-622 q^{46}+639 q^{44}-592 q^{42}+466 q^{40}-252 q^{38}-18 q^{36}+318 q^{34}-636 q^{32}+920 q^{30}-1141 q^{28}+1266 q^{26}-1286 q^{24}+1198 q^{22}-1011 q^{20}+748 q^{18}-446 q^{16}+132 q^{14}+156 q^{12}-374 q^{10}+534 q^8-612 q^6+626 q^4-570 q^2+488-394 q^{-2} +296 q^{-4} -204 q^{-6} +132 q^{-8} -84 q^{-10} +46 q^{-12} -22 q^{-14} +10 q^{-16} -4 q^{-18} + q^{-20} }
2,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{62}-q^{60}-q^{58}+2 q^{56}+q^{54}-3 q^{52}-3 q^{50}+5 q^{48}+3 q^{46}-8 q^{44}-q^{42}+10 q^{40}-10 q^{36}+2 q^{34}+10 q^{32}-5 q^{30}-9 q^{28}+6 q^{26}+2 q^{24}-10 q^{22}+2 q^{20}+7 q^{18}-6 q^{16}-2 q^{14}+11 q^{12}+3 q^{10}-9 q^8+3 q^6+13 q^4-4 q^2-7+6 q^{-2} +5 q^{-4} -6 q^{-6} -4 q^{-8} +3 q^{-10} +2 q^{-12} -2 q^{-14} - q^{-16} + q^{-18} }

A3 Invariants.

Weight	Invariant
0,1,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{54}-2 q^{52}+q^{50}+4 q^{48}-8 q^{46}+3 q^{44}+10 q^{42}-16 q^{40}+4 q^{38}+15 q^{36}-21 q^{34}+16 q^{30}-14 q^{28}-4 q^{26}+11 q^{24}-5 q^{20}-q^{18}+13 q^{16}-3 q^{14}-13 q^{12}+19 q^{10}-19 q^6+17 q^4+3 q^2-13+10 q^{-2} +3 q^{-4} -7 q^{-6} +3 q^{-8} -2 q^{-12} + q^{-14} }
1,0,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{31}+q^{29}-2 q^{27}+q^{25}-2 q^{23}+2 q^{21}-2 q^{19}+2 q^{17}+q^{13}+q^{11}+2 q^7-2 q^5+3 q^3-q+2 q^{-1} - q^{-3} + q^{-5} - q^{-7} }

A4 Invariants.

Weight	Invariant
0,1,0,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{68}-q^{66}-q^{64}+4 q^{62}-6 q^{58}+4 q^{56}+8 q^{54}-7 q^{52}-8 q^{50}+9 q^{48}+5 q^{46}-16 q^{44}-6 q^{42}+13 q^{40}-5 q^{38}-15 q^{36}+10 q^{34}+9 q^{32}-11 q^{30}+3 q^{28}+15 q^{26}-3 q^{24}-9 q^{22}+12 q^{20}+8 q^{18}-14 q^{16}-2 q^{14}+15 q^{12}-2 q^{10}-12 q^8+7 q^6+8 q^4-3 q^2-3+5 q^{-2} +2 q^{-4} -3 q^{-6} - q^{-8} + q^{-10} - q^{-12} - q^{-14} + q^{-16} }
1,0,0,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{38}+q^{36}-2 q^{34}-2 q^{28}+2 q^{26}-2 q^{24}+2 q^{22}+q^{18}+q^{16}+q^{14}+q^{12}+2 q^8-2 q^6+3 q^4-q^2+1+ q^{-2} - q^{-4} + q^{-6} - q^{-8} }

B2 Invariants.

Weight	Invariant
0,1	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{54}+2 q^{52}-5 q^{50}+8 q^{48}-12 q^{46}+17 q^{44}-20 q^{42}+22 q^{40}-22 q^{38}+19 q^{36}-13 q^{34}+4 q^{32}+6 q^{30}-18 q^{28}+28 q^{26}-37 q^{24}+42 q^{22}-43 q^{20}+41 q^{18}-33 q^{16}+25 q^{14}-13 q^{12}+3 q^{10}+8 q^8-15 q^6+21 q^4-21 q^2+21-18 q^{-2} +15 q^{-4} -11 q^{-6} +7 q^{-8} -4 q^{-10} +2 q^{-12} - q^{-14} }
1,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{88}-2 q^{84}-2 q^{82}+3 q^{80}+6 q^{78}-q^{76}-10 q^{74}-6 q^{72}+11 q^{70}+15 q^{68}-5 q^{66}-21 q^{64}-7 q^{62}+20 q^{60}+18 q^{58}-12 q^{56}-24 q^{54}-q^{52}+21 q^{50}+9 q^{48}-16 q^{46}-13 q^{44}+10 q^{42}+14 q^{40}-6 q^{38}-14 q^{36}+3 q^{34}+15 q^{32}+q^{30}-15 q^{28}-3 q^{26}+16 q^{24}+9 q^{22}-15 q^{20}-14 q^{18}+12 q^{16}+22 q^{14}-3 q^{12}-24 q^{10}-9 q^8+20 q^6+18 q^4-7 q^2-19-3 q^{-2} +14 q^{-4} +10 q^{-6} -5 q^{-8} -9 q^{-10} - q^{-12} +5 q^{-14} +2 q^{-16} -2 q^{-18} -2 q^{-20} + q^{-24} }

D4 Invariants.

Weight

Invariant

1,0,0,0

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{74}-2 q^{72}+3 q^{70}-4 q^{68}+7 q^{66}-10 q^{64}+11 q^{62}-13 q^{60}+17 q^{58}-18 q^{56}+16 q^{54}-16 q^{52}+16 q^{50}-13 q^{48}+3 q^{46}-3 q^{44}-3 q^{42}+10 q^{40}-20 q^{38}+21 q^{36}-25 q^{34}+34 q^{32}-32 q^{30}+32 q^{28}-31 q^{26}+33 q^{24}-22 q^{22}+19 q^{20}-15 q^{18}+9 q^{16}+2 q^{14}-4 q^{12}+7 q^{10}-14 q^8+18 q^6-15 q^4+16 q^2-16+16 q^{-2} -11 q^{-4} +10 q^{-6} -9 q^{-8} +6 q^{-10} -4 q^{-12} +2 q^{-14} -2 q^{-16} + q^{-18} }

G2 Invariants.

Weight

Invariant

1,0

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{128}-2 q^{126}+5 q^{124}-8 q^{122}+8 q^{120}-6 q^{118}-2 q^{116}+17 q^{114}-31 q^{112}+44 q^{110}-45 q^{108}+26 q^{106}+5 q^{104}-49 q^{102}+90 q^{100}-111 q^{98}+98 q^{96}-52 q^{94}-22 q^{92}+93 q^{90}-138 q^{88}+142 q^{86}-96 q^{84}+21 q^{82}+56 q^{80}-107 q^{78}+104 q^{76}-55 q^{74}-16 q^{72}+76 q^{70}-96 q^{68}+62 q^{66}+14 q^{64}-99 q^{62}+161 q^{60}-167 q^{58}+109 q^{56}-6 q^{54}-110 q^{52}+193 q^{50}-214 q^{48}+172 q^{46}-73 q^{44}-38 q^{42}+126 q^{40}-160 q^{38}+133 q^{36}-60 q^{34}-24 q^{32}+80 q^{30}-87 q^{28}+47 q^{26}+25 q^{24}-86 q^{22}+116 q^{20}-96 q^{18}+31 q^{16}+47 q^{14}-115 q^{12}+145 q^{10}-121 q^8+70 q^6-q^4-59 q^2+94-96 q^{-2} +73 q^{-4} -36 q^{-6} -2 q^{-8} +27 q^{-10} -38 q^{-12} +36 q^{-14} -25 q^{-16} +14 q^{-18} - q^{-20} -6 q^{-22} +6 q^{-24} -7 q^{-26} +4 q^{-28} -2 q^{-30} + q^{-32} }