10 45 Quantum Invariants

Further quantum knot invariants for 10_45.

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}+3 q^9-3 q^7+4 q^5-3 q^3+q+ q^{-1} -3 q^{-3} +4 q^{-5} -3 q^{-7} +3 q^{-9} - q^{-11} }
2	$q^{32}-3q^{30}-q^{28}+11q^{26}-9q^{24}-11q^{22}+27q^{20}-10q^{18}-28q^{16}+37q^{14}-37q^{10}+27q^{8}+13q^{6}-26q^{4}+q^{2}+19+q^{-2}-26q^{-4}+13q^{-6}+27q^{-8}-37q^{-10}+37q^{-14}-28q^{-16}-10q^{-18}+27q^{-20}-11q^{-22}-9q^{-24}+11q^{-26}-q^{-28}-3q^{-30}+q^{-32}$
3	$-q^{63}+3q^{61}+q^{59}-7q^{57}-6q^{55}+13q^{53}+21q^{51}-24q^{49}-40q^{47}+27q^{45}+75q^{43}-24q^{41}-118q^{39}+5q^{37}+165q^{35}+29q^{33}-202q^{31}-82q^{29}+222q^{27}+141q^{25}-217q^{23}-191q^{21}+184q^{19}+230q^{17}-134q^{15}-239q^{13}+65q^{11}+228q^{9}+6q^{7}-193q^{5}-75q^{3}+140q+140q^{-1}-75q^{-3}-193q^{-5}+6q^{-7}+228q^{-9}+65q^{-11}-239q^{-13}-134q^{-15}+230q^{-17}+184q^{-19}-191q^{-21}-217q^{-23}+141q^{-25}+222q^{-27}-82q^{-29}-202q^{-31}+29q^{-33}+165q^{-35}+5q^{-37}-118q^{-39}-24q^{-41}+75q^{-43}+27q^{-45}-40q^{-47}-24q^{-49}+21q^{-51}+13q^{-53}-6q^{-55}-7q^{-57}+q^{-59}+3q^{-61}-q^{-63}$
4	$q^{104}-3q^{102}-q^{100}+7q^{98}+2q^{96}+2q^{94}-23q^{92}-13q^{90}+33q^{88}+29q^{86}+28q^{84}-89q^{82}-93q^{80}+65q^{78}+135q^{76}+160q^{74}-190q^{72}-334q^{70}-22q^{68}+317q^{66}+553q^{64}-155q^{62}-748q^{60}-450q^{58}+363q^{56}+1210q^{54}+300q^{52}-1027q^{50}-1229q^{48}-76q^{46}+1737q^{44}+1165q^{42}-755q^{40}-1891q^{38}-951q^{36}+1634q^{34}+1906q^{32}+44q^{30}-1906q^{28}-1709q^{26}+898q^{24}+2002q^{22}+864q^{20}-1261q^{18}-1886q^{16}-49q^{14}+1461q^{12}+1334q^{10}-332q^{8}-1524q^{6}-873q^{4}+613q^{2}+1459+613q^{-2}-873q^{-4}-1524q^{-6}-332q^{-8}+1334q^{-10}+1461q^{-12}-49q^{-14}-1886q^{-16}-1261q^{-18}+864q^{-20}+2002q^{-22}+898q^{-24}-1709q^{-26}-1906q^{-28}+44q^{-30}+1906q^{-32}+1634q^{-34}-951q^{-36}-1891q^{-38}-755q^{-40}+1165q^{-42}+1737q^{-44}-76q^{-46}-1229q^{-48}-1027q^{-50}+300q^{-52}+1210q^{-54}+363q^{-56}-450q^{-58}-748q^{-60}-155q^{-62}+553q^{-64}+317q^{-66}-22q^{-68}-334q^{-70}-190q^{-72}+160q^{-74}+135q^{-76}+65q^{-78}-93q^{-80}-89q^{-82}+28q^{-84}+29q^{-86}+33q^{-88}-13q^{-90}-23q^{-92}+2q^{-94}+2q^{-96}+7q^{-98}-q^{-100}-3q^{-102}+q^{-104}$
5	$-q^{155}+3q^{153}+q^{151}-7q^{149}-2q^{147}+2q^{145}+8q^{143}+15q^{141}+4q^{139}-33q^{137}-43q^{135}-q^{133}+58q^{131}+95q^{129}+41q^{127}-98q^{125}-222q^{123}-135q^{121}+165q^{119}+406q^{117}+333q^{115}-139q^{113}-712q^{111}-764q^{109}+23q^{107}+1089q^{105}+1418q^{103}+432q^{101}-1404q^{99}-2455q^{97}-1334q^{95}+1492q^{93}+3692q^{91}+2874q^{89}-1004q^{87}-4953q^{85}-5068q^{83}-319q^{81}+5824q^{79}+7722q^{77}+2646q^{75}-5867q^{73}-10372q^{71}-5922q^{69}+4731q^{67}+12493q^{65}+9707q^{63}-2337q^{61}-13500q^{59}-13387q^{57}-1098q^{55}+13073q^{53}+16317q^{51}+5018q^{49}-11250q^{47}-17911q^{45}-8741q^{43}+8263q^{41}+17990q^{39}+11748q^{37}-4766q^{35}-16633q^{33}-13554q^{31}+1176q^{29}+14178q^{27}+14228q^{25}+2011q^{23}-11137q^{21}-13854q^{19}-4629q^{17}+7850q^{15}+12833q^{13}+6722q^{11}-4616q^{9}-11487q^{7}-8436q^{5}+1525q^{3}+9988q+9988q^{-1}+1525q^{-3}-8436q^{-5}-11487q^{-7}-4616q^{-9}+6722q^{-11}+12833q^{-13}+7850q^{-15}-4629q^{-17}-13854q^{-19}-11137q^{-21}+2011q^{-23}+14228q^{-25}+14178q^{-27}+1176q^{-29}-13554q^{-31}-16633q^{-33}-4766q^{-35}+11748q^{-37}+17990q^{-39}+8263q^{-41}-8741q^{-43}-17911q^{-45}-11250q^{-47}+5018q^{-49}+16317q^{-51}+13073q^{-53}-1098q^{-55}-13387q^{-57}-13500q^{-59}-2337q^{-61}+9707q^{-63}+12493q^{-65}+4731q^{-67}-5922q^{-69}-10372q^{-71}-5867q^{-73}+2646q^{-75}+7722q^{-77}+5824q^{-79}-319q^{-81}-5068q^{-83}-4953q^{-85}-1004q^{-87}+2874q^{-89}+3692q^{-91}+1492q^{-93}-1334q^{-95}-2455q^{-97}-1404q^{-99}+432q^{-101}+1418q^{-103}+1089q^{-105}+23q^{-107}-764q^{-109}-712q^{-111}-139q^{-113}+333q^{-115}+406q^{-117}+165q^{-119}-135q^{-121}-222q^{-123}-98q^{-125}+41q^{-127}+95q^{-129}+58q^{-131}-q^{-133}-43q^{-135}-33q^{-137}+4q^{-139}+15q^{-141}+8q^{-143}+2q^{-145}-2q^{-147}-7q^{-149}+q^{-151}+3q^{-153}-q^{-155}$

A2 Invariants.

Weight	Invariant
1,0	$-q^{16}+q^{14}+2q^{12}-2q^{10}+3q^{8}-2q^{4}+2q^{2}-3+2q^{-2}-2q^{-4}+3q^{-8}-2q^{-10}+2q^{-12}+q^{-14}-q^{-16}$
1,1	$q^{44}-6q^{42}+20q^{40}-50q^{38}+105q^{36}-198q^{34}+336q^{32}-524q^{30}+755q^{28}-1002q^{26}+1248q^{24}-1436q^{22}+1518q^{20}-1454q^{18}+1210q^{16}-784q^{14}+187q^{12}+522q^{10}-1274q^{8}+1984q^{6}-2565q^{4}+2950q^{2}-3078+2950q^{-2}-2565q^{-4}+1984q^{-6}-1274q^{-8}+522q^{-10}+187q^{-12}-784q^{-14}+1210q^{-16}-1454q^{-18}+1518q^{-20}-1436q^{-22}+1248q^{-24}-1002q^{-26}+755q^{-28}-524q^{-30}+336q^{-32}-198q^{-34}+105q^{-36}-50q^{-38}+20q^{-40}-6q^{-42}+q^{-44}$
2,0	$q^{42}-q^{40}-3q^{38}+6q^{34}+3q^{32}-10q^{30}-2q^{28}+15q^{26}+4q^{24}-19q^{22}-5q^{20}+21q^{18}+4q^{16}-24q^{14}+20q^{10}-6q^{8}-12q^{6}+8q^{4}+6q^{2}-6+6q^{-2}+8q^{-4}-12q^{-6}-6q^{-8}+20q^{-10}-24q^{-14}+4q^{-16}+21q^{-18}-5q^{-20}-19q^{-22}+4q^{-24}+15q^{-26}-2q^{-28}-10q^{-30}+3q^{-32}+6q^{-34}-3q^{-38}-q^{-40}+q^{-42}$

A3 Invariants.

Weight	Invariant
0,1,0	$q^{34}-3q^{32}+q^{30}+6q^{28}-12q^{26}+5q^{24}+16q^{22}-23q^{20}+6q^{18}+26q^{16}-30q^{14}+27q^{10}-23q^{8}-7q^{6}+18q^{4}-q^{2}-8-q^{-2}+18q^{-4}-7q^{-6}-23q^{-8}+27q^{-10}-30q^{-14}+26q^{-16}+6q^{-18}-23q^{-20}+16q^{-22}+5q^{-24}-12q^{-26}+6q^{-28}+q^{-30}-3q^{-32}+q^{-34}$
1,0,0	$-q^{21}+q^{19}+2q^{15}-2q^{13}+4q^{11}-q^{9}+2q^{7}-2q^{5}+q^{3}-2q-2q^{-1}+q^{-3}-2q^{-5}+2q^{-7}-q^{-9}+4q^{-11}-2q^{-13}+2q^{-15}+q^{-19}-q^{-21}$

B2 Invariants.

Weight	Invariant
0,1	$-q^{34}+3q^{32}-7q^{30}+12q^{28}-18q^{26}+25q^{24}-30q^{22}+35q^{20}-34q^{18}+32q^{16}-22q^{14}+10q^{12}+7q^{10}-25q^{8}+41q^{6}-56q^{4}+65q^{2}-70+65q^{-2}-56q^{-4}+41q^{-6}-25q^{-8}+7q^{-10}+10q^{-12}-22q^{-14}+32q^{-16}-34q^{-18}+35q^{-20}-30q^{-22}+25q^{-24}-18q^{-26}+12q^{-28}-7q^{-30}+3q^{-32}-q^{-34}$
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}-3 q^{52}-3 q^{50}+4 q^{48}+9 q^{46}-q^{44}-15 q^{42}-9 q^{40}+17 q^{38}+23 q^{36}-6 q^{34}-32 q^{32}-11 q^{30}+30 q^{28}+30 q^{26}-16 q^{24}-38 q^{22}-3 q^{20}+34 q^{18}+16 q^{16}-25 q^{14}-23 q^{12}+14 q^{10}+24 q^8-7 q^6-23 q^4+3 q^2+25+3 q^{-2} -23 q^{-4} -7 q^{-6} +24 q^{-8} +14 q^{-10} -23 q^{-12} -25 q^{-14} +16 q^{-16} +34 q^{-18} -3 q^{-20} -38 q^{-22} -16 q^{-24} +30 q^{-26} +30 q^{-28} -11 q^{-30} -32 q^{-32} -6 q^{-34} +23 q^{-36} +17 q^{-38} -9 q^{-40} -15 q^{-42} - q^{-44} +9 q^{-46} +4 q^{-48} -3 q^{-50} -3 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}-3 q^{78}+7 q^{76}-13 q^{74}+14 q^{72}-12 q^{70}-q^{68}+26 q^{66}-51 q^{64}+77 q^{62}-84 q^{60}+57 q^{58}-82 q^{54}+162 q^{52}-205 q^{50}+193 q^{48}-112 q^{46}-20 q^{44}+163 q^{42}-263 q^{40}+285 q^{38}-209 q^{36}+66 q^{34}+90 q^{32}-201 q^{30}+222 q^{28}-143 q^{26}+10 q^{24}+123 q^{22}-188 q^{20}+146 q^{18}-16 q^{16}-156 q^{14}+293 q^{12}-328 q^{10}+240 q^8-49 q^6-182 q^4+363 q^2-433+363 q^{-2} -182 q^{-4} -49 q^{-6} +240 q^{-8} -328 q^{-10} +293 q^{-12} -156 q^{-14} -16 q^{-16} +146 q^{-18} -188 q^{-20} +123 q^{-22} +10 q^{-24} -143 q^{-26} +222 q^{-28} -201 q^{-30} +90 q^{-32} +66 q^{-34} -209 q^{-36} +285 q^{-38} -263 q^{-40} +163 q^{-42} -20 q^{-44} -112 q^{-46} +193 q^{-48} -205 q^{-50} +162 q^{-52} -82 q^{-54} +57 q^{-58} -84 q^{-60} +77 q^{-62} -51 q^{-64} +26 q^{-66} - q^{-68} -12 q^{-70} +14 q^{-72} -13 q^{-74} +7 q^{-76} -3 q^{-78} + q^{-80} }