10 69 Quantum Invariants

Further quantum knot invariants for 10_69.

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^5+3 q^3-3 q+4 q^{-1} -3 q^{-3} + q^{-5} +2 q^{-7} -2 q^{-9} +4 q^{-11} -4 q^{-13} +2 q^{-15} - q^{-17} }
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^{16}-3 q^{14}-q^{12}+11 q^{10}-9 q^8-11 q^6+27 q^4-10 q^2-29+37 q^{-2} +3 q^{-4} -37 q^{-6} +26 q^{-8} +17 q^{-10} -25 q^{-12} -3 q^{-14} +18 q^{-16} +2 q^{-18} -28 q^{-20} +12 q^{-22} +29 q^{-24} -36 q^{-26} -2 q^{-28} +38 q^{-30} -26 q^{-32} -13 q^{-34} +26 q^{-36} -8 q^{-38} -10 q^{-40} +8 q^{-42} -2 q^{-46} + q^{-48} }
3	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^{33}+3 q^{31}+q^{29}-7 q^{27}-6 q^{25}+13 q^{23}+21 q^{21}-24 q^{19}-40 q^{17}+27 q^{15}+76 q^{13}-24 q^{11}-122 q^9+2 q^7+171 q^5+40 q^3-208 q-101 q^{-1} +227 q^{-3} +170 q^{-5} -212 q^{-7} -227 q^{-9} +166 q^{-11} +266 q^{-13} -105 q^{-15} -268 q^{-17} +31 q^{-19} +242 q^{-21} +48 q^{-23} -195 q^{-25} -109 q^{-27} +128 q^{-29} +167 q^{-31} -57 q^{-33} -212 q^{-35} -22 q^{-37} +238 q^{-39} +98 q^{-41} -245 q^{-43} -165 q^{-45} +220 q^{-47} +223 q^{-49} -175 q^{-51} -250 q^{-53} +110 q^{-55} +251 q^{-57} -48 q^{-59} -215 q^{-61} -11 q^{-63} +166 q^{-65} +42 q^{-67} -110 q^{-69} -47 q^{-71} +57 q^{-73} +41 q^{-75} -25 q^{-77} -26 q^{-79} +9 q^{-81} +12 q^{-83} -2 q^{-85} -4 q^{-87} +2 q^{-91} - q^{-93} }
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^{56}-3 q^{54}-q^{52}+7 q^{50}+2 q^{48}+2 q^{46}-23 q^{44}-13 q^{42}+33 q^{40}+29 q^{38}+28 q^{36}-89 q^{34}-94 q^{32}+65 q^{30}+139 q^{28}+164 q^{26}-193 q^{24}-350 q^{22}-35 q^{20}+333 q^{18}+593 q^{16}-131 q^{14}-795 q^{12}-538 q^{10}+349 q^8+1324 q^6+445 q^4-1054 q^2-1455-251 q^{-2} +1853 q^{-4} +1509 q^{-6} -591 q^{-8} -2159 q^{-10} -1370 q^{-12} +1556 q^{-14} +2328 q^{-16} +480 q^{-18} -1991 q^{-20} -2216 q^{-22} +544 q^{-24} +2241 q^{-26} +1394 q^{-28} -1067 q^{-30} -2215 q^{-32} -522 q^{-34} +1412 q^{-36} +1715 q^{-38} +15 q^{-40} -1576 q^{-42} -1258 q^{-44} +372 q^{-46} +1604 q^{-48} +963 q^{-50} -712 q^{-52} -1757 q^{-54} -672 q^{-56} +1285 q^{-58} +1781 q^{-60} +265 q^{-62} -1979 q^{-64} -1672 q^{-66} +632 q^{-68} +2260 q^{-70} +1348 q^{-72} -1610 q^{-74} -2315 q^{-76} -389 q^{-78} +1986 q^{-80} +2133 q^{-82} -609 q^{-84} -2128 q^{-86} -1280 q^{-88} +975 q^{-90} +2070 q^{-92} +394 q^{-94} -1173 q^{-96} -1402 q^{-98} -53 q^{-100} +1241 q^{-102} +719 q^{-104} -216 q^{-106} -843 q^{-108} -422 q^{-110} +403 q^{-112} +434 q^{-114} +157 q^{-116} -265 q^{-118} -269 q^{-120} +37 q^{-122} +118 q^{-124} +117 q^{-126} -33 q^{-128} -80 q^{-130} -9 q^{-132} +8 q^{-134} +31 q^{-136} + q^{-138} -13 q^{-140} -2 q^{-144} +4 q^{-146} -2 q^{-150} + q^{-152} }
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^{85}+3 q^{83}+q^{81}-7 q^{79}-2 q^{77}+2 q^{75}+8 q^{73}+15 q^{71}+4 q^{69}-33 q^{67}-43 q^{65}-q^{63}+58 q^{61}+95 q^{59}+42 q^{57}-98 q^{55}-226 q^{53}-139 q^{51}+167 q^{49}+419 q^{47}+351 q^{45}-136 q^{43}-745 q^{41}-823 q^{39}-7 q^{37}+1144 q^{35}+1555 q^{33}+546 q^{31}-1453 q^{29}-2717 q^{27}-1638 q^{25}+1465 q^{23}+4103 q^{21}+3502 q^{19}-723 q^{17}-5462 q^{15}-6166 q^{13}-1115 q^{11}+6247 q^9+9339 q^7+4252 q^5-5844 q^3-12391 q-8571 q^{-1} +3809 q^{-3} +14563 q^{-5} +13421 q^{-7} -96 q^{-9} -15055 q^{-11} -17894 q^{-13} -4872 q^{-15} +13525 q^{-17} +21057 q^{-19} +10203 q^{-21} -10166 q^{-23} -22157 q^{-25} -14879 q^{-27} +5525 q^{-29} +21093 q^{-31} +18124 q^{-33} -590 q^{-35} -18204 q^{-37} -19422 q^{-39} -3902 q^{-41} +14133 q^{-43} +18999 q^{-45} +7395 q^{-47} -9700 q^{-49} -17272 q^{-51} -9699 q^{-53} +5399 q^{-55} +14814 q^{-57} +11177 q^{-59} -1575 q^{-61} -12261 q^{-63} -12095 q^{-65} -1803 q^{-67} +9744 q^{-69} +12940 q^{-71} +5020 q^{-73} -7435 q^{-75} -13829 q^{-77} -8277 q^{-79} +5020 q^{-81} +14706 q^{-83} +11762 q^{-85} -2198 q^{-87} -15282 q^{-89} -15339 q^{-91} -1250 q^{-93} +15027 q^{-95} +18637 q^{-97} +5399 q^{-99} -13533 q^{-101} -21098 q^{-103} -9887 q^{-105} +10536 q^{-107} +22050 q^{-109} +14178 q^{-111} -6236 q^{-113} -21050 q^{-115} -17417 q^{-117} +1110 q^{-119} +18082 q^{-121} +18967 q^{-123} +3828 q^{-125} -13500 q^{-127} -18371 q^{-129} -7804 q^{-131} +8192 q^{-133} +15916 q^{-135} +9953 q^{-137} -3176 q^{-139} -12057 q^{-141} -10227 q^{-143} -723 q^{-145} +7853 q^{-147} +8911 q^{-149} +2955 q^{-151} -4092 q^{-153} -6647 q^{-155} -3682 q^{-157} +1358 q^{-159} +4271 q^{-161} +3311 q^{-163} +145 q^{-165} -2274 q^{-167} -2393 q^{-169} -747 q^{-171} +955 q^{-173} +1466 q^{-175} +753 q^{-177} -270 q^{-179} -745 q^{-181} -529 q^{-183} -11 q^{-185} +314 q^{-187} +304 q^{-189} +75 q^{-191} -119 q^{-193} -139 q^{-195} -50 q^{-197} +30 q^{-199} +49 q^{-201} +34 q^{-203} -7 q^{-205} -24 q^{-207} -6 q^{-209} +3 q^{-211} + q^{-213} +4 q^{-215} +2 q^{-217} -4 q^{-219} +2 q^{-223} - q^{-225} }

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^6+2 q^4-q^2+4 q^{-2} -3 q^{-4} +2 q^{-6} - q^{-8} +2 q^{-12} -2 q^{-14} +3 q^{-16} - q^{-18} - q^{-20} +2 q^{-22} - q^{-24} - q^{-26} }
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^{18}-2 q^{16}-2 q^{14}+5 q^{12}+2 q^{10}-7 q^8-4 q^6+13 q^4+6 q^2-19-5 q^{-2} +23 q^{-4} +2 q^{-6} -22 q^{-8} +3 q^{-10} +20 q^{-12} - q^{-14} -11 q^{-16} +8 q^{-18} +6 q^{-20} -11 q^{-22} +4 q^{-24} +5 q^{-26} -14 q^{-28} -4 q^{-30} +18 q^{-32} -18 q^{-36} +4 q^{-38} +20 q^{-40} -3 q^{-42} -19 q^{-44} +4 q^{-46} +13 q^{-48} -3 q^{-50} -11 q^{-52} - q^{-54} +7 q^{-56} + q^{-58} -3 q^{-60} - q^{-62} + q^{-64} + q^{-66} }

A3 Invariants.

Weight	Invariant
0,1,0	$q^{14}-3q^{12}+q^{10}+6q^{8}-12q^{6}+5q^{4}+16q^{2}-23+6q^{-2}+25q^{-4}-30q^{-6}+2q^{-8}+27q^{-10}-21q^{-12}-4q^{-14}+16q^{-16}-q^{-18}-8q^{-20}-3q^{-22}+19q^{-24}-6q^{-26}-21q^{-28}+27q^{-30}-30q^{-34}+25q^{-36}+3q^{-38}-23q^{-40}+15q^{-42}+2q^{-44}-10q^{-46}+5q^{-48}+q^{-50}-2q^{-52}+q^{-54}$
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^7+2 q^5-2 q^3+2 q- q^{-1} +4 q^{-3} -2 q^{-5} +2 q^{-7} - q^{-15} +2 q^{-17} -3 q^{-19} +3 q^{-21} - q^{-23} +2 q^{-25} - q^{-27} +2 q^{-29} - q^{-31} - q^{-33} - q^{-35} }

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^{14}+3 q^{12}-7 q^{10}+12 q^8-18 q^6+25 q^4-30 q^2+35-34 q^{-2} +31 q^{-4} -20 q^{-6} +8 q^{-8} +9 q^{-10} -27 q^{-12} +44 q^{-14} -58 q^{-16} +65 q^{-18} -68 q^{-20} +63 q^{-22} -53 q^{-24} +38 q^{-26} -19 q^{-28} +3 q^{-30} +14 q^{-32} -24 q^{-34} +33 q^{-36} -35 q^{-38} +33 q^{-40} -29 q^{-42} +22 q^{-44} -16 q^{-46} +9 q^{-48} -5 q^{-50} +2 q^{-52} - q^{-54} }
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}-3 q^{20}-3 q^{18}+4 q^{16}+9 q^{14}-q^{12}-15 q^{10}-9 q^8+17 q^6+23 q^4-6 q^2-32-11 q^{-2} +30 q^{-4} +29 q^{-6} -17 q^{-8} -37 q^{-10} - q^{-12} +35 q^{-14} +15 q^{-16} -25 q^{-18} -20 q^{-20} +17 q^{-22} +23 q^{-24} -10 q^{-26} -23 q^{-28} +5 q^{-30} +24 q^{-32} -24 q^{-36} -5 q^{-38} +25 q^{-40} +14 q^{-42} -24 q^{-44} -23 q^{-46} +18 q^{-48} +34 q^{-50} -5 q^{-52} -38 q^{-54} -15 q^{-56} +30 q^{-58} +28 q^{-60} -14 q^{-62} -31 q^{-64} -4 q^{-66} +22 q^{-68} +13 q^{-70} -9 q^{-72} -13 q^{-74} +7 q^{-78} +3 q^{-80} -2 q^{-82} -2 q^{-84} + q^{-88} }

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^{32}-3 q^{30}+7 q^{28}-13 q^{26}+14 q^{24}-12 q^{22}-q^{20}+26 q^{18}-51 q^{16}+77 q^{14}-84 q^{12}+57 q^{10}-q^8-83 q^6+165 q^4-206 q^2+191-107 q^{-2} -23 q^{-4} +170 q^{-6} -269 q^{-8} +282 q^{-10} -199 q^{-12} +45 q^{-14} +111 q^{-16} -215 q^{-18} +217 q^{-20} -120 q^{-22} -17 q^{-24} +156 q^{-26} -210 q^{-28} +145 q^{-30} +6 q^{-32} -193 q^{-34} +324 q^{-36} -341 q^{-38} +228 q^{-40} -18 q^{-42} -207 q^{-44} +382 q^{-46} -429 q^{-48} +337 q^{-50} -147 q^{-52} -86 q^{-54} +260 q^{-56} -320 q^{-58} +260 q^{-60} -108 q^{-62} -54 q^{-64} +173 q^{-66} -190 q^{-68} +100 q^{-70} +42 q^{-72} -183 q^{-74} +249 q^{-76} -204 q^{-78} +69 q^{-80} +100 q^{-82} -232 q^{-84} +292 q^{-86} -249 q^{-88} +132 q^{-90} +7 q^{-92} -133 q^{-94} +191 q^{-96} -182 q^{-98} +127 q^{-100} -49 q^{-102} -15 q^{-104} +55 q^{-106} -69 q^{-108} +56 q^{-110} -35 q^{-112} +14 q^{-114} + q^{-116} -9 q^{-118} +9 q^{-120} -8 q^{-122} +5 q^{-124} -2 q^{-126} + q^{-128} }