10 40 Quantum Invariants

Further quantum knot invariants for 10_40.

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+2 q^3-3 q+4 q^{-1} - q^{-3} +2 q^{-5} + q^{-7} -3 q^{-9} +3 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}-2 q^{14}-q^{12}+7 q^{10}-7 q^8-8 q^6+20 q^4-7 q^2-21+28 q^{-2} +2 q^{-4} -26 q^{-6} +20 q^{-8} +11 q^{-10} -18 q^{-12} +12 q^{-16} -20 q^{-20} +9 q^{-22} +21 q^{-24} -27 q^{-26} - q^{-28} +27 q^{-30} -20 q^{-32} -8 q^{-34} +19 q^{-36} -7 q^{-38} -6 q^{-40} +7 q^{-42} - q^{-44} -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}+2 q^{31}+q^{29}-3 q^{27}-4 q^{25}+7 q^{23}+11 q^{21}-14 q^{19}-23 q^{17}+17 q^{15}+44 q^{13}-15 q^{11}-74 q^9+3 q^7+105 q^5+20 q^3-126 q-61 q^{-1} +143 q^{-3} +98 q^{-5} -131 q^{-7} -132 q^{-9} +112 q^{-11} +153 q^{-13} -71 q^{-15} -156 q^{-17} +32 q^{-19} +143 q^{-21} +9 q^{-23} -115 q^{-25} -55 q^{-27} +80 q^{-29} +87 q^{-31} -37 q^{-33} -124 q^{-35} -2 q^{-37} +141 q^{-39} +54 q^{-41} -151 q^{-43} -95 q^{-45} +141 q^{-47} +126 q^{-49} -114 q^{-51} -145 q^{-53} +78 q^{-55} +145 q^{-57} -40 q^{-59} -127 q^{-61} +8 q^{-63} +98 q^{-65} +12 q^{-67} -67 q^{-69} -18 q^{-71} +39 q^{-73} +17 q^{-75} -20 q^{-77} -12 q^{-79} +10 q^{-81} +6 q^{-83} -4 q^{-85} -3 q^{-87} + q^{-89} +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}-2 q^{54}-q^{52}+3 q^{50}+4 q^{46}-10 q^{44}-6 q^{42}+15 q^{40}+8 q^{38}+15 q^{36}-42 q^{34}-40 q^{32}+38 q^{30}+57 q^{28}+77 q^{26}-101 q^{24}-166 q^{22}-q^{20}+157 q^{18}+296 q^{16}-86 q^{14}-399 q^{12}-244 q^{10}+172 q^8+676 q^6+190 q^4-542 q^2-701-119 q^{-2} +964 q^{-4} +712 q^{-6} -341 q^{-8} -1061 q^{-10} -648 q^{-12} +852 q^{-14} +1117 q^{-16} +152 q^{-18} -1013 q^{-20} -1053 q^{-22} +391 q^{-24} +1103 q^{-26} +585 q^{-28} -608 q^{-30} -1069 q^{-32} -119 q^{-34} +735 q^{-36} +764 q^{-38} -96 q^{-40} -788 q^{-42} -516 q^{-44} +247 q^{-46} +763 q^{-48} +394 q^{-50} -390 q^{-52} -834 q^{-54} -262 q^{-56} +665 q^{-58} +836 q^{-60} +82 q^{-62} -1017 q^{-64} -772 q^{-66} +381 q^{-68} +1117 q^{-70} +624 q^{-72} -891 q^{-74} -1112 q^{-76} -97 q^{-78} +1016 q^{-80} +1014 q^{-82} -427 q^{-84} -1042 q^{-86} -533 q^{-88} +545 q^{-90} +1003 q^{-92} +64 q^{-94} -605 q^{-96} -617 q^{-98} +57 q^{-100} +631 q^{-102} +250 q^{-104} -159 q^{-106} -389 q^{-108} -142 q^{-110} +244 q^{-112} +163 q^{-114} +34 q^{-116} -141 q^{-118} -106 q^{-120} +58 q^{-122} +48 q^{-124} +40 q^{-126} -31 q^{-128} -37 q^{-130} +13 q^{-132} +4 q^{-134} +13 q^{-136} -5 q^{-138} -9 q^{-140} +4 q^{-142} +3 q^{-146} - q^{-148} -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}+2 q^{83}+q^{81}-3 q^{79}-q^{73}+5 q^{71}+5 q^{69}-11 q^{67}-11 q^{65}+3 q^{63}+14 q^{61}+26 q^{59}+11 q^{57}-37 q^{55}-73 q^{53}-31 q^{51}+72 q^{49}+144 q^{47}+107 q^{45}-80 q^{43}-283 q^{41}-283 q^{39}+42 q^{37}+465 q^{35}+579 q^{33}+155 q^{31}-620 q^{29}-1064 q^{27}-594 q^{25}+656 q^{23}+1665 q^{21}+1348 q^{19}-380 q^{17}-2253 q^{15}-2449 q^{13}-355 q^{11}+2611 q^9+3785 q^7+1599 q^5-2504 q^3-5039 q-3344 q^{-1} +1729 q^{-3} +6007 q^{-5} +5293 q^{-7} -362 q^{-9} -6264 q^{-11} -7097 q^{-13} -1569 q^{-15} +5830 q^{-17} +8422 q^{-19} +3582 q^{-21} -4630 q^{-23} -8958 q^{-25} -5426 q^{-27} +2974 q^{-29} +8706 q^{-31} +6700 q^{-33} -1125 q^{-35} -7733 q^{-37} -7320 q^{-39} -580 q^{-41} +6274 q^{-43} +7284 q^{-45} +1973 q^{-47} -4621 q^{-49} -6754 q^{-51} -3012 q^{-53} +2965 q^{-55} +5952 q^{-57} +3734 q^{-59} -1413 q^{-61} -5048 q^{-63} -4329 q^{-65} -15 q^{-67} +4204 q^{-69} +4832 q^{-71} +1421 q^{-73} -3322 q^{-75} -5445 q^{-77} -2848 q^{-79} +2460 q^{-81} +5951 q^{-83} +4377 q^{-85} -1339 q^{-87} -6388 q^{-89} -5964 q^{-91} +31 q^{-93} +6427 q^{-95} +7401 q^{-97} +1632 q^{-99} -5976 q^{-101} -8513 q^{-103} -3423 q^{-105} +4919 q^{-107} +9000 q^{-109} +5127 q^{-111} -3279 q^{-113} -8721 q^{-115} -6463 q^{-117} +1319 q^{-119} +7658 q^{-121} +7130 q^{-123} +625 q^{-125} -5937 q^{-127} -7025 q^{-129} -2212 q^{-131} +3925 q^{-133} +6190 q^{-135} +3164 q^{-137} -1998 q^{-139} -4835 q^{-141} -3419 q^{-143} +452 q^{-145} +3317 q^{-147} +3096 q^{-149} +512 q^{-151} -1942 q^{-153} -2396 q^{-155} -934 q^{-157} +892 q^{-159} +1624 q^{-161} +955 q^{-163} -262 q^{-165} -950 q^{-167} -741 q^{-169} -50 q^{-171} +466 q^{-173} +490 q^{-175} +143 q^{-177} -199 q^{-179} -271 q^{-181} -118 q^{-183} +60 q^{-185} +125 q^{-187} +80 q^{-189} -9 q^{-191} -57 q^{-193} -37 q^{-195} +2 q^{-197} +17 q^{-199} +11 q^{-201} +6 q^{-203} -7 q^{-205} -9 q^{-207} +4 q^{-209} +4 q^{-211} - q^{-213} -3 q^{-219} + q^{-221} +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+q^4-q^2-1+3 q^{-2} - q^{-4} +4 q^{-6} + q^{-8} + q^{-12} -3 q^{-14} +2 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}-4 q^{18}+12 q^{16}-28 q^{14}+58 q^{12}-110 q^{10}+186 q^8-290 q^6+417 q^4-566 q^2+704-810 q^{-2} +856 q^{-4} -816 q^{-6} +678 q^{-8} -412 q^{-10} +73 q^{-12} +342 q^{-14} -758 q^{-16} +1158 q^{-18} -1472 q^{-20} +1666 q^{-22} -1722 q^{-24} +1616 q^{-26} -1389 q^{-28} +1042 q^{-30} -640 q^{-32} +214 q^{-34} +181 q^{-36} -490 q^{-38} +708 q^{-40} -822 q^{-42} +835 q^{-44} -770 q^{-46} +652 q^{-48} -518 q^{-50} +385 q^{-52} -264 q^{-54} +170 q^{-56} -102 q^{-58} +56 q^{-60} -28 q^{-62} +12 q^{-64} -4 q^{-66} + q^{-68} }
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}-q^{16}-2 q^{14}+3 q^{12}+3 q^{10}-5 q^8-6 q^6+6 q^4+6 q^2-12-6 q^{-2} +14 q^{-4} +4 q^{-6} -10 q^{-8} +4 q^{-10} +15 q^{-12} - q^{-14} -4 q^{-16} +8 q^{-18} +3 q^{-20} -12 q^{-22} +2 q^{-24} +6 q^{-26} -11 q^{-28} -4 q^{-30} +12 q^{-32} +2 q^{-34} -14 q^{-36} - q^{-38} +11 q^{-40} -2 q^{-42} -10 q^{-44} +3 q^{-46} +7 q^{-48} -2 q^{-50} -3 q^{-52} + q^{-54} +2 q^{-56} - q^{-58} - q^{-60} + q^{-62} }

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^{14}-2 q^{12}+q^{10}+4 q^8-9 q^6+2 q^4+10 q^2-19+3 q^{-2} +19 q^{-4} -21 q^{-6} +5 q^{-8} +24 q^{-10} -11 q^{-12} -2 q^{-14} +14 q^{-16} -2 q^{-18} -8 q^{-20} -3 q^{-22} +12 q^{-24} -5 q^{-26} -17 q^{-28} +20 q^{-30} - q^{-32} -23 q^{-34} +18 q^{-36} +3 q^{-38} -17 q^{-40} +11 q^{-42} +3 q^{-44} -8 q^{-46} +4 q^{-48} + q^{-50} -2 q^{-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+q^5-2 q^3+q-2 q^{-1} +3 q^{-3} - q^{-5} +4 q^{-7} +2 q^{-9} +2 q^{-11} + q^{-13} - q^{-15} + q^{-17} -3 q^{-19} +2 q^{-21} -2 q^{-23} + q^{-25} -2 q^{-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}-q^{14}+3 q^{10}-q^8-5 q^6+2 q^4+3 q^2-9-8 q^{-2} +8 q^{-4} +5 q^{-6} -15 q^{-8} +2 q^{-10} +23 q^{-12} +3 q^{-14} -9 q^{-16} +18 q^{-18} +15 q^{-20} -11 q^{-22} -4 q^{-24} +13 q^{-26} -5 q^{-28} -16 q^{-30} +10 q^{-32} +8 q^{-34} -18 q^{-36} -4 q^{-38} +16 q^{-40} -8 q^{-42} -17 q^{-44} +7 q^{-46} +10 q^{-48} -9 q^{-50} -7 q^{-52} +9 q^{-54} +4 q^{-56} -6 q^{-58} +4 q^{-62} - 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+q^6-2 q^4-2 q^{-2} +3 q^{-4} - q^{-6} +4 q^{-8} +2 q^{-10} +3 q^{-12} +2 q^{-14} + q^{-16} - q^{-20} + q^{-22} -3 q^{-24} +2 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}+2 q^{12}-5 q^{10}+8 q^8-13 q^6+18 q^4-22 q^2+25-25 q^{-2} +23 q^{-4} -15 q^{-6} +7 q^{-8} +6 q^{-10} -17 q^{-12} +32 q^{-14} -40 q^{-16} +48 q^{-18} -48 q^{-20} +47 q^{-22} -40 q^{-24} +29 q^{-26} -17 q^{-28} +2 q^{-30} +7 q^{-32} -17 q^{-34} +22 q^{-36} -25 q^{-38} +25 q^{-40} -21 q^{-42} +17 q^{-44} -12 q^{-46} +8 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}-2 q^{20}-2 q^{18}+3 q^{16}+6 q^{14}-q^{12}-11 q^{10}-7 q^8+11 q^6+16 q^4-5 q^2-24-9 q^{-2} +22 q^{-4} +22 q^{-6} -12 q^{-8} -26 q^{-10} +27 q^{-14} +13 q^{-16} -15 q^{-18} -14 q^{-20} +13 q^{-22} +17 q^{-24} -5 q^{-26} -17 q^{-28} +2 q^{-30} +16 q^{-32} + q^{-34} -18 q^{-36} -6 q^{-38} +17 q^{-40} +10 q^{-42} -17 q^{-44} -18 q^{-46} +13 q^{-48} +24 q^{-50} -3 q^{-52} -28 q^{-54} -11 q^{-56} +21 q^{-58} +21 q^{-60} -9 q^{-62} -23 q^{-64} -4 q^{-66} +16 q^{-68} +11 q^{-70} -6 q^{-72} -10 q^{-74} - q^{-76} +6 q^{-78} +3 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}-2 q^{16}+3 q^{14}-4 q^{12}+7 q^{10}-11 q^8+11 q^6-15 q^4+17 q^2-22+17 q^{-2} -19 q^{-4} +20 q^{-6} -13 q^{-8} +9 q^{-10} + q^{-12} +4 q^{-14} +16 q^{-16} -17 q^{-18} +25 q^{-20} -27 q^{-22} +37 q^{-24} -38 q^{-26} +34 q^{-28} -38 q^{-30} +36 q^{-32} -28 q^{-34} +21 q^{-36} -20 q^{-38} +9 q^{-40} -6 q^{-44} +6 q^{-46} -16 q^{-48} +19 q^{-50} -18 q^{-52} +18 q^{-54} -20 q^{-56} +18 q^{-58} -13 q^{-60} +11 q^{-62} -10 q^{-64} +7 q^{-66} -4 q^{-68} +3 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}-2 q^{30}+5 q^{28}-8 q^{26}+8 q^{24}-7 q^{22}-2 q^{20}+16 q^{18}-33 q^{16}+47 q^{14}-51 q^{12}+33 q^{10}+2 q^8-50 q^6+101 q^4-129 q^2+121-72 q^{-2} -17 q^{-4} +104 q^{-6} -167 q^{-8} +180 q^{-10} -128 q^{-12} +42 q^{-14} +60 q^{-16} -129 q^{-18} +140 q^{-20} -83 q^{-22} -4 q^{-24} +84 q^{-26} -117 q^{-28} +87 q^{-30} +6 q^{-32} -105 q^{-34} +189 q^{-36} -204 q^{-38} +146 q^{-40} -22 q^{-42} -125 q^{-44} +230 q^{-46} -268 q^{-48} +222 q^{-50} -104 q^{-52} -35 q^{-54} +148 q^{-56} -201 q^{-58} +176 q^{-60} -92 q^{-62} -19 q^{-64} +94 q^{-66} -114 q^{-68} +68 q^{-70} +21 q^{-72} -98 q^{-74} +142 q^{-76} -123 q^{-78} +47 q^{-80} +49 q^{-82} -139 q^{-84} +179 q^{-86} -159 q^{-88} +92 q^{-90} -5 q^{-92} -71 q^{-94} +115 q^{-96} -120 q^{-98} +93 q^{-100} -47 q^{-102} - q^{-104} +31 q^{-106} -47 q^{-108} +43 q^{-110} -30 q^{-112} +17 q^{-114} -2 q^{-116} -6 q^{-118} +8 q^{-120} -8 q^{-122} +5 q^{-124} -2 q^{-126} + q^{-128} }