10 81 Quantum Invariants

Further quantum knot invariants for 10_81.

A1 Invariants.

Weight	Invariant
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^{11}+2 q^9-4 q^7+4 q^5-2 q^3+2 q+2 q^{-1} -2 q^{-3} +4 q^{-5} -4 q^{-7} +2 q^{-9} - q^{-11} }
2	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^{32}-2 q^{30}+8 q^{26}-10 q^{24}-8 q^{22}+26 q^{20}-13 q^{18}-27 q^{16}+38 q^{14}-38 q^{10}+26 q^8+15 q^6-26 q^4+q^2+21+ q^{-2} -26 q^{-4} +15 q^{-6} +26 q^{-8} -38 q^{-10} +38 q^{-14} -27 q^{-16} -13 q^{-18} +26 q^{-20} -8 q^{-22} -10 q^{-24} +8 q^{-26} -2 q^{-30} + q^{-32} }
3	$-q^{63}+2q^{61}-4q^{57}-2q^{55}+12q^{53}+9q^{51}-26q^{49}-25q^{47}+41q^{45}+58q^{43}-47q^{41}-113q^{39}+41q^{37}+173q^{35}-3q^{33}-226q^{31}-68q^{29}+260q^{27}+140q^{25}-250q^{23}-215q^{21}+207q^{19}+260q^{17}-137q^{15}-277q^{13}+64q^{11}+255q^{9}+21q^{7}-215q^{5}-91q^{3}+159q+159q^{-1}-91q^{-3}-215q^{-5}+21q^{-7}+255q^{-9}+64q^{-11}-277q^{-13}-137q^{-15}+260q^{-17}+207q^{-19}-215q^{-21}-250q^{-23}+140q^{-25}+260q^{-27}-68q^{-29}-226q^{-31}-3q^{-33}+173q^{-35}+41q^{-37}-113q^{-39}-47q^{-41}+58q^{-43}+41q^{-45}-25q^{-47}-26q^{-49}+9q^{-51}+12q^{-53}-2q^{-55}-4q^{-57}+2q^{-61}-q^{-63}$
4	$q^{104}-2q^{102}+4q^{98}-2q^{96}-13q^{92}+q^{90}+31q^{88}+8q^{86}-9q^{84}-80q^{82}-34q^{80}+117q^{78}+121q^{76}+39q^{74}-273q^{72}-277q^{70}+153q^{68}+456q^{66}+436q^{64}-420q^{62}-907q^{60}-292q^{58}+744q^{56}+1385q^{54}+71q^{52}-1490q^{50}-1436q^{48}+256q^{46}+2270q^{44}+1356q^{42}-1174q^{40}-2491q^{38}-1058q^{36}+2127q^{34}+2496q^{32}+51q^{30}-2484q^{28}-2193q^{26}+1010q^{24}+2579q^{22}+1212q^{20}-1509q^{18}-2375q^{16}-229q^{14}+1776q^{12}+1719q^{10}-323q^{8}-1855q^{6}-1131q^{4}+741q^{2}+1799+741q^{-2}-1131q^{-4}-1855q^{-6}-323q^{-8}+1719q^{-10}+1776q^{-12}-229q^{-14}-2375q^{-16}-1509q^{-18}+1212q^{-20}+2579q^{-22}+1010q^{-24}-2193q^{-26}-2484q^{-28}+51q^{-30}+2496q^{-32}+2127q^{-34}-1058q^{-36}-2491q^{-38}-1174q^{-40}+1356q^{-42}+2270q^{-44}+256q^{-46}-1436q^{-48}-1490q^{-50}+71q^{-52}+1385q^{-54}+744q^{-56}-292q^{-58}-907q^{-60}-420q^{-62}+436q^{-64}+456q^{-66}+153q^{-68}-277q^{-70}-273q^{-72}+39q^{-74}+121q^{-76}+117q^{-78}-34q^{-80}-80q^{-82}-9q^{-84}+8q^{-86}+31q^{-88}+q^{-90}-13q^{-92}-2q^{-96}+4q^{-98}-2q^{-102}+q^{-104}$
5	$-q^{155}+2q^{153}-4q^{149}+2q^{147}+4q^{145}+q^{143}+3q^{141}-6q^{139}-24q^{137}-7q^{135}+34q^{133}+49q^{131}+30q^{129}-49q^{127}-139q^{125}-122q^{123}+73q^{121}+307q^{119}+323q^{117}-3q^{115}-536q^{113}-776q^{111}-304q^{109}+763q^{107}+1544q^{105}+1063q^{103}-721q^{101}-2541q^{99}-2552q^{97}-33q^{95}+3502q^{93}+4831q^{91}+1897q^{89}-3746q^{87}-7535q^{85}-5268q^{83}+2547q^{81}+9987q^{79}+9878q^{77}+624q^{75}-11060q^{73}-14906q^{71}-5906q^{69}+9898q^{67}+19206q^{65}+12485q^{63}-6200q^{61}-21361q^{59}-19110q^{57}+243q^{55}+20810q^{53}+24323q^{51}+6647q^{49}-17440q^{47}-26957q^{45}-13219q^{43}+12096q^{41}+26728q^{39}+18078q^{37}-5902q^{35}-23973q^{33}-20683q^{31}+113q^{29}+19538q^{27}+21025q^{25}+4588q^{23}-14499q^{21}-19760q^{19}-7842q^{17}+9640q^{15}+17570q^{13}+10084q^{11}-5387q^{9}-15327q^{7}-11708q^{5}+1734q^{3}+13340q+13340q^{-1}+1734q^{-3}-11708q^{-5}-15327q^{-7}-5387q^{-9}+10084q^{-11}+17570q^{-13}+9640q^{-15}-7842q^{-17}-19760q^{-19}-14499q^{-21}+4588q^{-23}+21025q^{-25}+19538q^{-27}+113q^{-29}-20683q^{-31}-23973q^{-33}-5902q^{-35}+18078q^{-37}+26728q^{-39}+12096q^{-41}-13219q^{-43}-26957q^{-45}-17440q^{-47}+6647q^{-49}+24323q^{-51}+20810q^{-53}+243q^{-55}-19110q^{-57}-21361q^{-59}-6200q^{-61}+12485q^{-63}+19206q^{-65}+9898q^{-67}-5906q^{-69}-14906q^{-71}-11060q^{-73}+624q^{-75}+9878q^{-77}+9987q^{-79}+2547q^{-81}-5268q^{-83}-7535q^{-85}-3746q^{-87}+1897q^{-89}+4831q^{-91}+3502q^{-93}-33q^{-95}-2552q^{-97}-2541q^{-99}-721q^{-101}+1063q^{-103}+1544q^{-105}+763q^{-107}-304q^{-109}-776q^{-111}-536q^{-113}-3q^{-115}+323q^{-117}+307q^{-119}+73q^{-121}-122q^{-123}-139q^{-125}-49q^{-127}+30q^{-129}+49q^{-131}+34q^{-133}-7q^{-135}-24q^{-137}-6q^{-139}+3q^{-141}+q^{-143}+4q^{-145}+2q^{-147}-4q^{-149}+2q^{-153}-q^{-155}$

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^{16}+q^{12}-3 q^{10}+2 q^8-q^4+4 q^2-1+4 q^{-2} - q^{-4} +2 q^{-8} -3 q^{-10} + q^{-12} - q^{-16} }
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^{42}-2 q^{38}+5 q^{34}+3 q^{32}-8 q^{30}-5 q^{28}+11 q^{26}+q^{24}-17 q^{22}-6 q^{20}+17 q^{18}+5 q^{16}-20 q^{14}+3 q^{12}+18 q^{10}-5 q^8-10 q^6+9 q^4+6 q^2-6+6 q^{-2} +9 q^{-4} -10 q^{-6} -5 q^{-8} +18 q^{-10} +3 q^{-12} -20 q^{-14} +5 q^{-16} +17 q^{-18} -6 q^{-20} -17 q^{-22} + q^{-24} +11 q^{-26} -5 q^{-28} -8 q^{-30} +3 q^{-32} +5 q^{-34} -2 q^{-38} + q^{-42} }

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^{34}-2 q^{32}+q^{30}+5 q^{28}-10 q^{26}+2 q^{24}+15 q^{22}-23 q^{20}+3 q^{18}+24 q^{16}-31 q^{14}+24 q^{10}-22 q^8-4 q^6+19 q^4+2 q^2-2+2 q^{-2} +19 q^{-4} -4 q^{-6} -22 q^{-8} +24 q^{-10} -31 q^{-14} +24 q^{-16} +3 q^{-18} -23 q^{-20} +15 q^{-22} +2 q^{-24} -10 q^{-26} +5 q^{-28} + q^{-30} -2 q^{-32} + q^{-34} }
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^{21}-q^{17}+q^{15}-3 q^{13}+3 q^{11}-2 q^9+2 q^7-q^5+3 q^3+q+ q^{-1} +3 q^{-3} - q^{-5} +2 q^{-7} -2 q^{-9} +3 q^{-11} -3 q^{-13} + q^{-15} - q^{-17} - q^{-21} }

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^{34}+2 q^{32}-5 q^{30}+9 q^{28}-16 q^{26}+22 q^{24}-29 q^{22}+33 q^{20}-35 q^{18}+32 q^{16}-23 q^{14}+12 q^{12}+6 q^{10}-22 q^8+40 q^6-53 q^4+64 q^2-68+64 q^{-2} -53 q^{-4} +40 q^{-6} -22 q^{-8} +6 q^{-10} +12 q^{-12} -23 q^{-14} +32 q^{-16} -35 q^{-18} +33 q^{-20} -29 q^{-22} +22 q^{-24} -16 q^{-26} +9 q^{-28} -5 q^{-30} +2 q^{-32} - q^{-34} }
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^{56}-2 q^{52}-2 q^{50}+3 q^{48}+7 q^{46}-13 q^{42}-9 q^{40}+13 q^{38}+22 q^{36}-4 q^{34}-31 q^{32}-14 q^{30}+28 q^{28}+29 q^{26}-16 q^{24}-38 q^{22}-4 q^{20}+34 q^{18}+15 q^{16}-25 q^{14}-22 q^{12}+16 q^{10}+24 q^8-6 q^6-22 q^4+5 q^2+27+5 q^{-2} -22 q^{-4} -6 q^{-6} +24 q^{-8} +16 q^{-10} -22 q^{-12} -25 q^{-14} +15 q^{-16} +34 q^{-18} -4 q^{-20} -38 q^{-22} -16 q^{-24} +29 q^{-26} +28 q^{-28} -14 q^{-30} -31 q^{-32} -4 q^{-34} +22 q^{-36} +13 q^{-38} -9 q^{-40} -13 q^{-42} +7 q^{-46} +3 q^{-48} -2 q^{-50} -2 q^{-52} + q^{-56} }

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^{80}-2 q^{78}+5 q^{76}-8 q^{74}+9 q^{72}-9 q^{70}+q^{68}+14 q^{66}-35 q^{64}+56 q^{62}-69 q^{60}+55 q^{58}-16 q^{56}-50 q^{54}+129 q^{52}-183 q^{50}+191 q^{48}-130 q^{46}+4 q^{44}+139 q^{42}-255 q^{40}+293 q^{38}-227 q^{36}+79 q^{34}+91 q^{32}-219 q^{30}+247 q^{28}-166 q^{26}+14 q^{24}+137 q^{22}-214 q^{20}+173 q^{18}-34 q^{16}-147 q^{14}+296 q^{12}-335 q^{10}+249 q^8-55 q^6-172 q^4+360 q^2-427+360 q^{-2} -172 q^{-4} -55 q^{-6} +249 q^{-8} -335 q^{-10} +296 q^{-12} -147 q^{-14} -34 q^{-16} +173 q^{-18} -214 q^{-20} +137 q^{-22} +14 q^{-24} -166 q^{-26} +247 q^{-28} -219 q^{-30} +91 q^{-32} +79 q^{-34} -227 q^{-36} +293 q^{-38} -255 q^{-40} +139 q^{-42} +4 q^{-44} -130 q^{-46} +191 q^{-48} -183 q^{-50} +129 q^{-52} -50 q^{-54} -16 q^{-56} +55 q^{-58} -69 q^{-60} +56 q^{-62} -35 q^{-64} +14 q^{-66} + q^{-68} -9 q^{-70} +9 q^{-72} -8 q^{-74} +5 q^{-76} -2 q^{-78} + q^{-80} }