8 15 Quantum Invariants

Further quantum knot invariants for 8_15.

A1 Invariants.

Weight	Invariant
1	$q^{21}-2q^{19}+q^{17}-2q^{15}+q^{11}+3q^{7}-q^{5}+q^{3}$
2	$q^{58}-2q^{56}-2q^{54}+6q^{52}-2q^{50}-6q^{48}+9q^{46}+q^{44}-9q^{42}+6q^{40}+3q^{38}-6q^{36}-q^{34}+2q^{32}-7q^{28}+2q^{26}+7q^{24}-8q^{22}+10q^{18}-5q^{16}-2q^{14}+6q^{12}-q^{8}+q^{6}$
3	$q^{111}-2q^{109}-2q^{107}+3q^{105}+6q^{103}-2q^{101}-13q^{99}+2q^{97}+18q^{95}+4q^{93}-25q^{91}-13q^{89}+27q^{87}+22q^{85}-27q^{83}-29q^{81}+20q^{79}+35q^{77}-12q^{75}-32q^{73}+7q^{71}+27q^{69}+4q^{67}-21q^{65}-9q^{63}+10q^{61}+17q^{59}-5q^{57}-21q^{55}-7q^{53}+27q^{51}+13q^{49}-30q^{47}-23q^{45}+27q^{43}+27q^{41}-22q^{39}-32q^{37}+12q^{35}+32q^{33}-6q^{31}-23q^{29}-2q^{27}+19q^{25}+7q^{23}-8q^{21}-4q^{19}+4q^{17}+3q^{15}-q^{11}+q^{9}$
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^{180}-2 q^{178}-2 q^{176}+3 q^{174}+3 q^{172}+6 q^{170}-9 q^{168}-13 q^{166}+2 q^{164}+11 q^{162}+30 q^{160}-11 q^{158}-41 q^{156}-22 q^{154}+14 q^{152}+80 q^{150}+22 q^{148}-62 q^{146}-83 q^{144}-27 q^{142}+123 q^{140}+97 q^{138}-31 q^{136}-135 q^{134}-108 q^{132}+102 q^{130}+151 q^{128}+41 q^{126}-124 q^{124}-159 q^{122}+38 q^{120}+138 q^{118}+88 q^{116}-63 q^{114}-137 q^{112}-19 q^{110}+80 q^{108}+92 q^{106}-2 q^{104}-81 q^{102}-57 q^{100}+17 q^{98}+75 q^{96}+49 q^{94}-23 q^{92}-93 q^{90}-46 q^{88}+62 q^{86}+102 q^{84}+34 q^{82}-121 q^{80}-107 q^{78}+32 q^{76}+141 q^{74}+101 q^{72}-112 q^{70}-148 q^{68}-28 q^{66}+124 q^{64}+148 q^{62}-49 q^{60}-133 q^{58}-86 q^{56}+53 q^{54}+136 q^{52}+19 q^{50}-62 q^{48}-83 q^{46}-12 q^{44}+70 q^{42}+38 q^{40}-38 q^{36}-24 q^{34}+16 q^{32}+14 q^{30}+11 q^{28}-5 q^{26}-7 q^{24}+2 q^{22}+q^{20}+3 q^{18}-q^{14}+q^{12}}
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^{265}-2 q^{263}-2 q^{261}+3 q^{259}+3 q^{257}+3 q^{255}-q^{253}-9 q^{251}-13 q^{249}+2 q^{247}+20 q^{245}+23 q^{243}+6 q^{241}-27 q^{239}-49 q^{237}-33 q^{235}+37 q^{233}+92 q^{231}+71 q^{229}-21 q^{227}-131 q^{225}-155 q^{223}-29 q^{221}+172 q^{219}+255 q^{217}+121 q^{215}-157 q^{213}-369 q^{211}-275 q^{209}+93 q^{207}+447 q^{205}+449 q^{203}+42 q^{201}-464 q^{199}-612 q^{197}-218 q^{195}+403 q^{193}+725 q^{191}+409 q^{189}-288 q^{187}-747 q^{185}-557 q^{183}+129 q^{181}+696 q^{179}+645 q^{177}+23 q^{175}-589 q^{173}-647 q^{171}-147 q^{169}+441 q^{167}+591 q^{165}+229 q^{163}-299 q^{161}-511 q^{159}-260 q^{157}+162 q^{155}+395 q^{153}+289 q^{151}-49 q^{149}-310 q^{147}-287 q^{145}-48 q^{143}+215 q^{141}+319 q^{139}+152 q^{137}-156 q^{135}-340 q^{133}-254 q^{131}+77 q^{129}+394 q^{127}+373 q^{125}-7 q^{123}-426 q^{121}-499 q^{119}-98 q^{117}+448 q^{115}+620 q^{113}+214 q^{111}-413 q^{109}-712 q^{107}-360 q^{105}+339 q^{103}+747 q^{101}+494 q^{99}-202 q^{97}-709 q^{95}-595 q^{93}+27 q^{91}+607 q^{89}+634 q^{87}+132 q^{85}-435 q^{83}-592 q^{81}-272 q^{79}+239 q^{77}+496 q^{75}+313 q^{73}-70 q^{71}-337 q^{69}-309 q^{67}-55 q^{65}+194 q^{63}+240 q^{61}+101 q^{59}-72 q^{57}-154 q^{55}-101 q^{53}+6 q^{51}+77 q^{49}+74 q^{47}+18 q^{45}-27 q^{43}-36 q^{41}-14 q^{39}+4 q^{37}+17 q^{35}+12 q^{33}-q^{31}-4 q^{29}-q^{27}-q^{25}+q^{23}+3 q^{21}-q^{17}+q^{15}}

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^{32}+q^{30}-2 q^{28}-q^{26}-2 q^{24}-2 q^{22}+q^{20}+3 q^{16}+q^{14}+q^{12}+2 q^{10}-q^8+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^{84}-4 q^{82}+10 q^{80}-20 q^{78}+34 q^{76}-54 q^{74}+74 q^{72}-92 q^{70}+105 q^{68}-104 q^{66}+90 q^{64}-60 q^{62}+18 q^{60}+36 q^{58}-90 q^{56}+142 q^{54}-176 q^{52}+200 q^{50}-202 q^{48}+182 q^{46}-153 q^{44}+96 q^{42}-52 q^{40}-10 q^{38}+48 q^{36}-86 q^{34}+104 q^{32}-104 q^{30}+99 q^{28}-72 q^{26}+62 q^{24}-34 q^{22}+25 q^{20}-10 q^{18}+6 q^{16}-2 q^{14}+q^{12}}
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^{80}+q^{78}-q^{76}-4 q^{74}-3 q^{72}+2 q^{70}+q^{68}+3 q^{64}+8 q^{62}+4 q^{60}-3 q^{58}+2 q^{54}-4 q^{52}-6 q^{50}-3 q^{48}-3 q^{46}-6 q^{44}-2 q^{42}+q^{40}-3 q^{38}+6 q^{34}+3 q^{32}-3 q^{30}+4 q^{28}+6 q^{26}+q^{24}-2 q^{22}+3 q^{20}+4 q^{18}-q^{16}-q^{14}+q^{12}}

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^{68}-2 q^{66}+3 q^{62}-6 q^{60}+q^{58}+6 q^{56}-5 q^{54}+4 q^{52}+10 q^{50}-3 q^{48}-q^{46}-q^{44}-7 q^{42}-9 q^{40}-7 q^{38}+q^{36}-q^{34}-2 q^{32}+10 q^{30}+5 q^{28}-4 q^{26}+9 q^{24}+2 q^{22}-3 q^{20}+4 q^{18}+q^{16}-q^{14}+q^{12}}
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^{43}+q^{41}+q^{39}-2 q^{37}-q^{35}-4 q^{33}-2 q^{31}-2 q^{29}+q^{27}+q^{25}+2 q^{23}+3 q^{21}+q^{19}+2 q^{17}+2 q^{13}-q^{11}+q^9}

A4 Invariants.

Weight	Invariant
0,1,0,0	$q^{90}+q^{88}-q^{86}-3q^{84}-q^{82}-5q^{78}-4q^{76}+6q^{74}+8q^{72}+3q^{70}+9q^{68}+14q^{66}+5q^{64}-5q^{62}-4q^{60}-9q^{58}-20q^{56}-17q^{54}-7q^{52}-10q^{50}-6q^{48}+9q^{46}+9q^{44}+2q^{42}+7q^{40}+12q^{38}+4q^{36}-q^{34}+4q^{32}+6q^{30}-q^{28}+3q^{24}+q^{22}-q^{20}+q^{18}$
1,0,0,0	$q^{54}+q^{52}+q^{50}+q^{48}-2q^{46}-q^{44}-4q^{42}-4q^{40}-2q^{38}-2q^{36}+q^{34}+q^{32}+3q^{30}+2q^{28}+3q^{26}+q^{24}+2q^{22}+q^{20}+2q^{16}-q^{14}+q^{12}$

B2 Invariants.

Weight	Invariant
0,1	$q^{68}-2q^{66}+4q^{64}-5q^{62}+6q^{60}-7q^{58}+6q^{56}-5q^{54}+2q^{52}-5q^{48}+7q^{46}-11q^{44}+11q^{42}-13q^{40}+11q^{38}-9q^{36}+7q^{34}-2q^{32}+5q^{28}-4q^{26}+7q^{24}-6q^{22}+7q^{20}-4q^{18}+3q^{16}-q^{14}+q^{12}$
1,0	$q^{110}-2q^{106}-2q^{104}+2q^{102}+4q^{100}-q^{98}-6q^{96}-3q^{94}+6q^{92}+6q^{90}-2q^{88}-6q^{86}+q^{84}+8q^{82}+5q^{80}-4q^{78}-3q^{76}+3q^{74}+3q^{72}-5q^{70}-7q^{68}-2q^{66}+2q^{64}-3q^{62}-7q^{60}-3q^{58}+3q^{56}+3q^{54}-4q^{52}-3q^{50}+5q^{48}+9q^{46}-5q^{42}-q^{40}+8q^{38}+6q^{36}-2q^{34}-5q^{32}+q^{30}+4q^{28}+2q^{26}-q^{24}-q^{22}+q^{18}$

D4 Invariants.

Weight	Invariant
1,0,0,0	$q^{94}-2q^{92}+2q^{90}-3q^{88}+4q^{86}-6q^{84}+4q^{82}-5q^{80}+6q^{78}-3q^{76}+4q^{74}+2q^{72}+5q^{70}+6q^{68}-4q^{66}+5q^{64}-10q^{62}+4q^{60}-17q^{58}-16q^{54}+4q^{52}-8q^{50}+5q^{48}-2q^{46}+6q^{44}+7q^{42}+2q^{40}+6q^{38}-2q^{36}+8q^{34}-3q^{32}+6q^{30}-4q^{28}+5q^{26}-q^{24}+2q^{22}-q^{20}+q^{18}$

G2 Invariants.

Weight

Invariant

1,0

$q^{162}-2q^{160}+4q^{158}-6q^{156}+3q^{154}-q^{152}-6q^{150}+14q^{148}-18q^{146}+20q^{144}-12q^{142}-q^{140}+17q^{138}-27q^{136}+34q^{134}-24q^{132}+7q^{130}+10q^{128}-21q^{126}+25q^{124}-16q^{122}+q^{120}+14q^{118}-20q^{116}+12q^{114}-24q^{110}+34q^{108}-36q^{106}+18q^{104}-2q^{102}-24q^{100}+40q^{98}-47q^{96}+34q^{94}-18q^{92}-7q^{90}+25q^{88}-33q^{86}+26q^{84}-9q^{82}-2q^{80}+16q^{78}-17q^{76}+9q^{74}+10q^{72}-21q^{70}+29q^{68}-21q^{66}+6q^{64}+17q^{62}-27q^{60}+33q^{58}-23q^{56}+12q^{54}+2q^{52}-14q^{50}+17q^{48}-14q^{46}+10q^{44}-2q^{42}-q^{40}+3q^{38}-3q^{36}+3q^{34}-q^{32}+q^{30}$