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	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^{152}-2 q^{150}-q^{148}+3 q^{146}+4 q^{142}-9 q^{140}-6 q^{138}+12 q^{136}+6 q^{134}+17 q^{132}-33 q^{130}-36 q^{128}+25 q^{126}+41 q^{124}+72 q^{122}-71 q^{120}-130 q^{118}-13 q^{116}+103 q^{114}+240 q^{112}-42 q^{110}-288 q^{108}-204 q^{106}+82 q^{104}+505 q^{102}+186 q^{100}-348 q^{98}-529 q^{96}-174 q^{94}+662 q^{92}+566 q^{90}-145 q^{88}-743 q^{86}-572 q^{84}+520 q^{82}+819 q^{80}+232 q^{78}-654 q^{76}-828 q^{74}+169 q^{72}+759 q^{70}+510 q^{68}-342 q^{66}-780 q^{64}-172 q^{62}+465 q^{60}+584 q^{58}+13 q^{56}-528 q^{54}-418 q^{52}+103 q^{50}+531 q^{48}+344 q^{46}-202 q^{44}-609 q^{42}-272 q^{40}+412 q^{38}+637 q^{36}+167 q^{34}-698 q^{32}-627 q^{30}+170 q^{28}+796 q^{26}+559 q^{24}-566 q^{22}-826 q^{20}-182 q^{18}+667 q^{16}+798 q^{14}-209 q^{12}-711 q^{10}-459 q^8+296 q^6+723 q^4+121 q^2-360-459 q^{-2} -35 q^{-4} +416 q^{-6} +208 q^{-8} -54 q^{-10} -266 q^{-12} -138 q^{-14} +146 q^{-16} +118 q^{-18} +53 q^{-20} -93 q^{-22} -90 q^{-24} +32 q^{-26} +33 q^{-28} +40 q^{-30} -21 q^{-32} -33 q^{-34} +8 q^{-36} +3 q^{-38} +14 q^{-40} -3 q^{-42} -9 q^{-44} +3 q^{-46} +3 q^{-50} - q^{-52} -2 q^{-54} + q^{-56} }
5	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^{225}+2 q^{223}+q^{221}-3 q^{219}-q^{213}+4 q^{211}+5 q^{209}-8 q^{207}-9 q^{205}+2 q^{203}+8 q^{201}+18 q^{199}+11 q^{197}-22 q^{195}-52 q^{193}-27 q^{191}+46 q^{189}+100 q^{187}+81 q^{185}-47 q^{183}-197 q^{181}-209 q^{179}+14 q^{177}+323 q^{175}+420 q^{173}+134 q^{171}-413 q^{169}-756 q^{167}-468 q^{165}+403 q^{163}+1157 q^{161}+1012 q^{159}-140 q^{157}-1494 q^{155}-1785 q^{153}-463 q^{151}+1622 q^{149}+2652 q^{147}+1415 q^{145}-1357 q^{143}-3394 q^{141}-2665 q^{139}+621 q^{137}+3830 q^{135}+3964 q^{133}+516 q^{131}-3746 q^{129}-5056 q^{127}-1930 q^{125}+3156 q^{123}+5727 q^{121}+3304 q^{119}-2140 q^{117}-5816 q^{115}-4414 q^{113}+895 q^{111}+5379 q^{109}+5066 q^{107}+328 q^{105}-4528 q^{103}-5210 q^{101}-1351 q^{99}+3432 q^{97}+4936 q^{95}+2093 q^{93}-2306 q^{91}-4367 q^{89}-2550 q^{87}+1242 q^{85}+3658 q^{83}+2838 q^{81}-284 q^{79}-2964 q^{77}-3032 q^{75}-594 q^{73}+2291 q^{71}+3251 q^{69}+1472 q^{67}-1657 q^{65}-3511 q^{63}-2387 q^{61}+967 q^{59}+3766 q^{57}+3378 q^{55}-154 q^{53}-3890 q^{51}-4390 q^{49}-844 q^{47}+3782 q^{45}+5257 q^{43}+1987 q^{41}-3270 q^{39}-5835 q^{37}-3212 q^{35}+2406 q^{33}+5936 q^{31}+4234 q^{29}-1168 q^{27}-5475 q^{25}-4935 q^{23}-182 q^{21}+4512 q^{19}+5098 q^{17}+1384 q^{15}-3165 q^{13}-4701 q^{11}-2265 q^9+1751 q^7+3884 q^5+2613 q^3-514 q-2766 q^{-1} -2529 q^{-3} -364 q^{-5} +1708 q^{-7} +2072 q^{-9} +809 q^{-11} -805 q^{-13} -1487 q^{-15} -902 q^{-17} +225 q^{-19} +909 q^{-21} +769 q^{-23} +92 q^{-25} -486 q^{-27} -543 q^{-29} -187 q^{-31} +195 q^{-33} +335 q^{-35} +184 q^{-37} -66 q^{-39} -181 q^{-41} -121 q^{-43} +3 q^{-45} +81 q^{-47} +78 q^{-49} +11 q^{-51} -40 q^{-53} -36 q^{-55} -5 q^{-57} +13 q^{-59} +14 q^{-61} +8 q^{-63} -7 q^{-65} -10 q^{-67} +2 q^{-69} +4 q^{-71} -3 q^{-79} + q^{-81} +2 q^{-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	$-q^{54}+2q^{52}-5q^{50}+8q^{48}-12q^{46}+17q^{44}-20q^{42}+22q^{40}-22q^{38}+19q^{36}-13q^{34}+4q^{32}+6q^{30}-18q^{28}+28q^{26}-37q^{24}+42q^{22}-43q^{20}+41q^{18}-33q^{16}+25q^{14}-13q^{12}+3q^{10}+8q^{8}-15q^{6}+21q^{4}-21q^{2}+21-18q^{-2}+15q^{-4}-11q^{-6}+7q^{-8}-4q^{-10}+2q^{-12}-q^{-14}$
1,0	$q^{88}-2q^{84}-2q^{82}+3q^{80}+6q^{78}-q^{76}-10q^{74}-6q^{72}+11q^{70}+15q^{68}-5q^{66}-21q^{64}-7q^{62}+20q^{60}+18q^{58}-12q^{56}-24q^{54}-q^{52}+21q^{50}+9q^{48}-16q^{46}-13q^{44}+10q^{42}+14q^{40}-6q^{38}-14q^{36}+3q^{34}+15q^{32}+q^{30}-15q^{28}-3q^{26}+16q^{24}+9q^{22}-15q^{20}-14q^{18}+12q^{16}+22q^{14}-3q^{12}-24q^{10}-9q^{8}+20q^{6}+18q^{4}-7q^{2}-19-3q^{-2}+14q^{-4}+10q^{-6}-5q^{-8}-9q^{-10}-q^{-12}+5q^{-14}+2q^{-16}-2q^{-18}-2q^{-20}+q^{-24}$

D4 Invariants.

Weight	Invariant
1,0,0,0	$q^{74}-2q^{72}+3q^{70}-4q^{68}+7q^{66}-10q^{64}+11q^{62}-13q^{60}+17q^{58}-18q^{56}+16q^{54}-16q^{52}+16q^{50}-13q^{48}+3q^{46}-3q^{44}-3q^{42}+10q^{40}-20q^{38}+21q^{36}-25q^{34}+34q^{32}-32q^{30}+32q^{28}-31q^{26}+33q^{24}-22q^{22}+19q^{20}-15q^{18}+9q^{16}+2q^{14}-4q^{12}+7q^{10}-14q^{8}+18q^{6}-15q^{4}+16q^{2}-16+16q^{-2}-11q^{-4}+10q^{-6}-9q^{-8}+6q^{-10}-4q^{-12}+2q^{-14}-2q^{-16}+q^{-18}$

G2 Invariants.

Weight

Invariant

1,0

$q^{128}-2q^{126}+5q^{124}-8q^{122}+8q^{120}-6q^{118}-2q^{116}+17q^{114}-31q^{112}+44q^{110}-45q^{108}+26q^{106}+5q^{104}-49q^{102}+90q^{100}-111q^{98}+98q^{96}-52q^{94}-22q^{92}+93q^{90}-138q^{88}+142q^{86}-96q^{84}+21q^{82}+56q^{80}-107q^{78}+104q^{76}-55q^{74}-16q^{72}+76q^{70}-96q^{68}+62q^{66}+14q^{64}-99q^{62}+161q^{60}-167q^{58}+109q^{56}-6q^{54}-110q^{52}+193q^{50}-214q^{48}+172q^{46}-73q^{44}-38q^{42}+126q^{40}-160q^{38}+133q^{36}-60q^{34}-24q^{32}+80q^{30}-87q^{28}+47q^{26}+25q^{24}-86q^{22}+116q^{20}-96q^{18}+31q^{16}+47q^{14}-115q^{12}+145q^{10}-121q^{8}+70q^{6}-q^{4}-59q^{2}+94-96q^{-2}+73q^{-4}-36q^{-6}-2q^{-8}+27q^{-10}-38q^{-12}+36q^{-14}-25q^{-16}+14q^{-18}-q^{-20}-6q^{-22}+6q^{-24}-7q^{-26}+4q^{-28}-2q^{-30}+q^{-32}$