10 83 Quantum Invariants

Further quantum knot invariants for 10_83.

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} -2 q^{-3} + q^{-5} + q^{-7} -3 q^{-9} +4 q^{-11} -3 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}+10 q^{10}-9 q^8-10 q^6+26 q^4-7 q^2-27+32 q^{-2} +6 q^{-4} -34 q^{-6} +18 q^{-8} +17 q^{-10} -21 q^{-12} -5 q^{-14} +17 q^{-16} +4 q^{-18} -26 q^{-20} +9 q^{-22} +28 q^{-24} -32 q^{-26} -5 q^{-28} +34 q^{-30} -19 q^{-32} -13 q^{-34} +21 q^{-36} -4 q^{-38} -9 q^{-40} +6 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}-6 q^{27}-5 q^{25}+10 q^{23}+16 q^{21}-22 q^{19}-30 q^{17}+27 q^{15}+62 q^{13}-25 q^{11}-105 q^9+5 q^7+152 q^5+41 q^3-179 q-110 q^{-1} +185 q^{-3} +177 q^{-5} -155 q^{-7} -226 q^{-9} +99 q^{-11} +250 q^{-13} -35 q^{-15} -237 q^{-17} -28 q^{-19} +201 q^{-21} +79 q^{-23} -146 q^{-25} -125 q^{-27} +85 q^{-29} +160 q^{-31} -19 q^{-33} -188 q^{-35} -46 q^{-37} +201 q^{-39} +116 q^{-41} -196 q^{-43} -179 q^{-45} +168 q^{-47} +218 q^{-49} -111 q^{-51} -237 q^{-53} +44 q^{-55} +222 q^{-57} +16 q^{-59} -172 q^{-61} -59 q^{-63} +115 q^{-65} +70 q^{-67} -60 q^{-69} -59 q^{-71} +22 q^{-73} +38 q^{-75} -5 q^{-77} -20 q^{-79} + q^{-81} +8 q^{-83} -3 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}+6 q^{50}+q^{48}+4 q^{46}-16 q^{44}-8 q^{42}+23 q^{40}+8 q^{38}+14 q^{36}-63 q^{34}-43 q^{32}+79 q^{30}+86 q^{28}+73 q^{26}-197 q^{24}-246 q^{22}+66 q^{20}+324 q^{18}+444 q^{16}-213 q^{14}-724 q^{12}-426 q^{10}+374 q^8+1197 q^6+431 q^4-922 q^2-1396-390 q^{-2} +1579 q^{-4} +1586 q^{-6} -179 q^{-8} -1908 q^{-10} -1628 q^{-12} +920 q^{-14} +2177 q^{-16} +1032 q^{-18} -1358 q^{-20} -2226 q^{-22} -220 q^{-24} +1707 q^{-26} +1667 q^{-28} -327 q^{-30} -1830 q^{-32} -964 q^{-34} +761 q^{-36} +1550 q^{-38} +472 q^{-40} -1037 q^{-42} -1246 q^{-44} -76 q^{-46} +1197 q^{-48} +1044 q^{-50} -277 q^{-52} -1453 q^{-54} -852 q^{-56} +834 q^{-58} +1619 q^{-60} +570 q^{-62} -1532 q^{-64} -1695 q^{-66} +150 q^{-68} +1939 q^{-70} +1592 q^{-72} -1005 q^{-74} -2178 q^{-76} -915 q^{-78} +1419 q^{-80} +2198 q^{-82} +141 q^{-84} -1666 q^{-86} -1634 q^{-88} +203 q^{-90} +1738 q^{-92} +973 q^{-94} -464 q^{-96} -1314 q^{-98} -641 q^{-100} +641 q^{-102} +828 q^{-104} +319 q^{-106} -475 q^{-108} -575 q^{-110} -32 q^{-112} +267 q^{-114} +318 q^{-116} -10 q^{-118} -199 q^{-120} -95 q^{-122} +104 q^{-126} +35 q^{-128} -31 q^{-130} -18 q^{-132} -17 q^{-134} +18 q^{-136} +7 q^{-138} -6 q^{-140} + q^{-142} -3 q^{-144} +3 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}-6 q^{79}-q^{77}+2 q^{73}+8 q^{71}+7 q^{69}-13 q^{67}-13 q^{65}+11 q^{63}+22 q^{61}+12 q^{59}-27 q^{57}-69 q^{55}-72 q^{53}+54 q^{51}+221 q^{49}+210 q^{47}-29 q^{45}-391 q^{43}-584 q^{41}-262 q^{39}+564 q^{37}+1216 q^{35}+941 q^{33}-353 q^{31}-1913 q^{29}-2287 q^{27}-603 q^{25}+2312 q^{23}+4072 q^{21}+2646 q^{19}-1668 q^{17}-5785 q^{15}-5789 q^{13}-569 q^{11}+6511 q^9+9429 q^7+4551 q^5-5341 q^3-12417 q-9807 q^{-1} +1848 q^{-3} +13649 q^{-5} +15086 q^{-7} +3554 q^{-9} -12267 q^{-11} -18976 q^{-13} -9829 q^{-15} +8410 q^{-17} +20440 q^{-19} +15417 q^{-21} -2946 q^{-23} -19085 q^{-25} -19083 q^{-27} -2865 q^{-29} +15506 q^{-31} +20234 q^{-33} +7669 q^{-35} -10717 q^{-37} -18969 q^{-39} -10775 q^{-41} +5823 q^{-43} +16153 q^{-45} +12024 q^{-47} -1731 q^{-49} -12649 q^{-51} -11901 q^{-53} -1280 q^{-55} +9345 q^{-57} +11120 q^{-59} +3352 q^{-61} -6687 q^{-63} -10396 q^{-65} -4949 q^{-67} +4705 q^{-69} +10165 q^{-71} +6662 q^{-73} -3041 q^{-75} -10577 q^{-77} -8895 q^{-79} +1213 q^{-81} +11221 q^{-83} +11801 q^{-85} +1384 q^{-87} -11546 q^{-89} -15119 q^{-91} -4966 q^{-93} +10785 q^{-95} +18087 q^{-97} +9477 q^{-99} -8335 q^{-101} -19843 q^{-103} -14283 q^{-105} +4164 q^{-107} +19482 q^{-109} +18241 q^{-111} +1365 q^{-113} -16608 q^{-115} -20358 q^{-117} -7051 q^{-119} +11571 q^{-121} +19788 q^{-123} +11543 q^{-125} -5318 q^{-127} -16576 q^{-129} -13816 q^{-131} -603 q^{-133} +11564 q^{-135} +13373 q^{-137} +4890 q^{-139} -6004 q^{-141} -10790 q^{-143} -6880 q^{-145} +1372 q^{-147} +7111 q^{-149} +6652 q^{-151} +1575 q^{-153} -3548 q^{-155} -5062 q^{-157} -2709 q^{-159} +972 q^{-161} +3075 q^{-163} +2516 q^{-165} +388 q^{-167} -1412 q^{-169} -1743 q^{-171} -798 q^{-173} +417 q^{-175} +955 q^{-177} +659 q^{-179} +22 q^{-181} -402 q^{-183} -400 q^{-185} -129 q^{-187} +137 q^{-189} +193 q^{-191} +86 q^{-193} -29 q^{-195} -68 q^{-197} -47 q^{-199} -2 q^{-201} +30 q^{-203} +16 q^{-205} -5 q^{-207} -4 q^{-209} -2 q^{-211} -3 q^{-213} +2 q^{-215} +3 q^{-217} -3 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+3 q^{-2} -3 q^{-4} +2 q^{-6} - q^{-8} +2 q^{-12} -2 q^{-14} +3 q^{-16} - q^{-18} - q^{-20} + q^{-22} - q^{-24} }
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^{20}-6 q^{18}+20 q^{16}-50 q^{14}+99 q^{12}-178 q^{10}+294 q^8-442 q^6+613 q^4-794 q^2+964-1062 q^{-2} +1072 q^{-4} -960 q^{-6} +708 q^{-8} -308 q^{-10} -188 q^{-12} +728 q^{-14} -1258 q^{-16} +1712 q^{-18} -2029 q^{-20} +2164 q^{-22} -2116 q^{-24} +1886 q^{-26} -1497 q^{-28} +1006 q^{-30} -468 q^{-32} -54 q^{-34} +505 q^{-36} -832 q^{-38} +1014 q^{-40} -1070 q^{-42} +1012 q^{-44} -868 q^{-46} +690 q^{-48} -518 q^{-50} +365 q^{-52} -236 q^{-54} +144 q^{-56} -88 q^{-58} +48 q^{-60} -22 q^{-62} +10 q^{-64} -4 q^{-66} + q^{-68} }
2,0	$q^{18}-2q^{16}-3q^{14}+5q^{12}+4q^{10}-7q^{8}-7q^{6}+10q^{4}+11q^{2}-12-7q^{-2}+17q^{-4}+4q^{-6}-14q^{-8}+q^{-10}+12q^{-12}-3q^{-14}-6q^{-16}+6q^{-18}+2q^{-20}-12q^{-22}+5q^{-24}+8q^{-26}-14q^{-28}-4q^{-30}+15q^{-32}+4q^{-34}-14q^{-36}+14q^{-40}+q^{-42}-12q^{-44}+7q^{-48}-2q^{-50}-3q^{-52}-q^{-54}+2q^{-56}-q^{-60}+q^{-62}$

A3 Invariants.

Weight	Invariant
0,1,0	$q^{14}-3q^{12}+q^{10}+6q^{8}-11q^{6}+5q^{4}+15q^{2}-20+7q^{-2}+21q^{-4}-28q^{-6}+2q^{-8}+20q^{-10}-18q^{-12}-3q^{-14}+13q^{-16}+2q^{-18}-5q^{-20}-2q^{-22}+17q^{-24}-5q^{-26}-20q^{-28}+23q^{-30}-3q^{-32}-26q^{-34}+22q^{-36}+q^{-38}-17q^{-40}+13q^{-42}+2q^{-44}-7q^{-46}+4q^{-48}-2q^{-52}+q^{-54}$
1,0,0	$-q^{7}+2q^{5}-q^{3}+3q-q^{-1}+3q^{-3}-3q^{-5}+q^{-7}-q^{-9}+q^{-13}+3q^{-17}-2q^{-19}+3q^{-21}-2q^{-23}+q^{-25}-2q^{-27}+q^{-29}-q^{-31}$

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^{16}-2 q^{14}-q^{12}+4 q^{10}-2 q^8-4 q^6+7 q^4+8 q^2-7-4 q^{-2} +15 q^{-4} +5 q^{-6} -22 q^{-8} - q^{-10} +20 q^{-12} -12 q^{-14} -20 q^{-16} +17 q^{-18} +12 q^{-20} -15 q^{-22} +3 q^{-24} +23 q^{-26} -2 q^{-28} -14 q^{-30} +18 q^{-32} +8 q^{-34} -26 q^{-36} -2 q^{-38} +18 q^{-40} -13 q^{-42} -19 q^{-44} +13 q^{-46} +12 q^{-48} -11 q^{-50} -6 q^{-52} +12 q^{-54} +3 q^{-56} -9 q^{-58} + q^{-60} +4 q^{-62} -2 q^{-64} - q^{-66} + q^{-68} }
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^8+2 q^6-q^4+2 q^2+2- q^{-2} +3 q^{-4} -3 q^{-6} + q^{-8} -2 q^{-10} + q^{-16} + q^{-18} + q^{-20} +3 q^{-22} -2 q^{-24} +3 q^{-26} -2 q^{-28} -2 q^{-34} + q^{-36} - q^{-38} }

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^8-17 q^6+25 q^4-29 q^2+32-31 q^{-2} +27 q^{-4} -16 q^{-6} +4 q^{-8} +12 q^{-10} -28 q^{-12} +43 q^{-14} -55 q^{-16} +60 q^{-18} -61 q^{-20} +56 q^{-22} -45 q^{-24} +31 q^{-26} -14 q^{-28} - q^{-30} +15 q^{-32} -24 q^{-34} +30 q^{-36} -31 q^{-38} +29 q^{-40} -25 q^{-42} +18 q^{-44} -13 q^{-46} +8 q^{-48} -4 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}-14 q^{10}-9 q^8+16 q^6+22 q^4-6 q^2-29-9 q^{-2} +29 q^{-4} +26 q^{-6} -18 q^{-8} -33 q^{-10} + q^{-12} +31 q^{-14} +10 q^{-16} -24 q^{-18} -16 q^{-20} +17 q^{-22} +19 q^{-24} -11 q^{-26} -19 q^{-28} +7 q^{-30} +22 q^{-32} - q^{-34} -22 q^{-36} -3 q^{-38} +24 q^{-40} +11 q^{-42} -24 q^{-44} -21 q^{-46} +18 q^{-48} +30 q^{-50} -7 q^{-52} -35 q^{-54} -11 q^{-56} +28 q^{-58} +23 q^{-60} -13 q^{-62} -26 q^{-64} -2 q^{-66} +19 q^{-68} +10 q^{-70} -7 q^{-72} -10 q^{-74} +6 q^{-78} +2 q^{-80} -2 q^{-82} -2 q^{-84} + q^{-88} }

D4 Invariants.

Weight

Invariant

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^{18}-3 q^{16}+4 q^{14}-6 q^{12}+10 q^{10}-14 q^8+17 q^6-18 q^4+26 q^2-24+25 q^{-2} -22 q^{-4} +23 q^{-6} -17 q^{-8} +4 q^{-10} -2 q^{-12} -7 q^{-14} +17 q^{-16} -30 q^{-18} +33 q^{-20} -37 q^{-22} +50 q^{-24} -45 q^{-26} +47 q^{-28} -42 q^{-30} +45 q^{-32} -30 q^{-34} +23 q^{-36} -20 q^{-38} +6 q^{-40} +3 q^{-42} -12 q^{-44} +11 q^{-46} -23 q^{-48} +25 q^{-50} -23 q^{-52} +23 q^{-54} -23 q^{-56} +21 q^{-58} -14 q^{-60} +12 q^{-62} -10 q^{-64} +7 q^{-66} -4 q^{-68} +2 q^{-70} -2 q^{-72} + q^{-74} }

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}-11 q^{22}-2 q^{20}+25 q^{18}-48 q^{16}+71 q^{14}-74 q^{12}+48 q^{10}+3 q^8-73 q^6+144 q^4-179 q^2+164-87 q^{-2} -33 q^{-4} +156 q^{-6} -232 q^{-8} +235 q^{-10} -149 q^{-12} +11 q^{-14} +123 q^{-16} -200 q^{-18} +178 q^{-20} -72 q^{-22} -68 q^{-24} +173 q^{-26} -193 q^{-28} +109 q^{-30} +43 q^{-32} -201 q^{-34} +297 q^{-36} -286 q^{-38} +167 q^{-40} +19 q^{-42} -207 q^{-44} +329 q^{-46} -341 q^{-48} +249 q^{-50} -77 q^{-52} -102 q^{-54} +230 q^{-56} -260 q^{-58} +190 q^{-60} -50 q^{-62} -91 q^{-64} +173 q^{-66} -161 q^{-68} +62 q^{-70} +79 q^{-72} -189 q^{-74} +222 q^{-76} -162 q^{-78} +27 q^{-80} +114 q^{-82} -217 q^{-84} +239 q^{-86} -178 q^{-88} +72 q^{-90} +38 q^{-92} -119 q^{-94} +146 q^{-96} -127 q^{-98} +79 q^{-100} -24 q^{-102} -20 q^{-104} +42 q^{-106} -47 q^{-108} +39 q^{-110} -24 q^{-112} +12 q^{-114} + q^{-116} -7 q^{-118} +7 q^{-120} -7 q^{-122} +4 q^{-124} -2 q^{-126} + q^{-128} }