10 111 Quantum Invariants
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Further quantum knot invariants for 10_111.
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-2 q^{-1} +4 q^{-3} -2 q^{-5} +3 q^{-7} - q^{-9} - q^{-11} +2 q^{-13} -4 q^{-15} +3 q^{-17} -2 q^{-19} + q^{-21} } |
| 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^6-2 q^4-q^2+9-5 q^{-2} -13 q^{-4} +20 q^{-6} +5 q^{-8} -27 q^{-10} +15 q^{-12} +20 q^{-14} -27 q^{-16} +23 q^{-20} -13 q^{-22} -12 q^{-24} +14 q^{-26} +7 q^{-28} -19 q^{-30} -4 q^{-32} +27 q^{-34} -14 q^{-36} -20 q^{-38} +29 q^{-40} -2 q^{-42} -20 q^{-44} +14 q^{-46} +3 q^{-48} -8 q^{-50} +4 q^{-52} -2 q^{-56} + q^{-58} } |
| 3 | |
| 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^{28}-2 q^{26}-q^{24}+4 q^{22}+q^{20}+3 q^{18}-14 q^{16}-13 q^{14}+18 q^{12}+28 q^{10}+39 q^8-48 q^6-105 q^4-36 q^2+77+235 q^{-2} +81 q^{-4} -207 q^{-6} -342 q^{-8} -196 q^{-10} +385 q^{-12} +565 q^{-14} +197 q^{-16} -481 q^{-18} -899 q^{-20} -186 q^{-22} +729 q^{-24} +1079 q^{-26} +279 q^{-28} -1115 q^{-30} -1227 q^{-32} -137 q^{-34} +1339 q^{-36} +1440 q^{-38} -238 q^{-40} -1562 q^{-42} -1334 q^{-44} +558 q^{-46} +1841 q^{-48} +888 q^{-50} -940 q^{-52} -1780 q^{-54} -397 q^{-56} +1376 q^{-58} +1351 q^{-60} -187 q^{-62} -1488 q^{-64} -820 q^{-66} +761 q^{-68} +1266 q^{-70} +225 q^{-72} -1053 q^{-74} -933 q^{-76} +282 q^{-78} +1145 q^{-80} +592 q^{-82} -625 q^{-84} -1151 q^{-86} -392 q^{-88} +964 q^{-90} +1206 q^{-92} +173 q^{-94} -1266 q^{-96} -1391 q^{-98} +251 q^{-100} +1594 q^{-102} +1336 q^{-104} -641 q^{-106} -1978 q^{-108} -916 q^{-110} +1025 q^{-112} +1946 q^{-114} +507 q^{-116} -1405 q^{-118} -1474 q^{-120} -104 q^{-122} +1345 q^{-124} +1034 q^{-126} -301 q^{-128} -949 q^{-130} -607 q^{-132} +372 q^{-134} +637 q^{-136} +192 q^{-138} -230 q^{-140} -367 q^{-142} -30 q^{-144} +166 q^{-146} +118 q^{-148} +17 q^{-150} -101 q^{-152} -31 q^{-154} +17 q^{-156} +19 q^{-158} +22 q^{-160} -20 q^{-162} -5 q^{-164} + q^{-166} - q^{-168} +7 q^{-170} -3 q^{-172} + q^{-174} -2 q^{-178} + q^{-180} } |
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 1- q^{-2} + q^{-4} +2 q^{-6} - q^{-8} +4 q^{-10} - q^{-12} + q^{-14} -3 q^{-18} + q^{-20} -3 q^{-22} + q^{-24} + q^{-26} - q^{-28} + q^{-30} } |
| 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^4-4 q^2+14-36 q^{-2} +80 q^{-4} -146 q^{-6} +254 q^{-8} -392 q^{-10} +548 q^{-12} -682 q^{-14} +786 q^{-16} -808 q^{-18} +720 q^{-20} -514 q^{-22} +216 q^{-24} +150 q^{-26} -543 q^{-28} +906 q^{-30} -1206 q^{-32} +1396 q^{-34} -1471 q^{-36} +1408 q^{-38} -1222 q^{-40} +940 q^{-42} -589 q^{-44} +216 q^{-46} +126 q^{-48} -396 q^{-50} +574 q^{-52} -656 q^{-54} +650 q^{-56} -578 q^{-58} +486 q^{-60} -388 q^{-62} +292 q^{-64} -216 q^{-66} +161 q^{-68} -118 q^{-70} +82 q^{-72} -54 q^{-74} +34 q^{-76} -20 q^{-78} +10 q^{-80} -4 q^{-82} + q^{-84} } |
| 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^4-q^2-2+3 q^{-2} +5 q^{-4} - q^{-6} -7 q^{-8} +2 q^{-10} +13 q^{-12} -3 q^{-14} -10 q^{-16} +6 q^{-18} +11 q^{-20} -5 q^{-22} -8 q^{-24} +7 q^{-26} +3 q^{-28} -7 q^{-30} + q^{-32} +5 q^{-34} -7 q^{-36} -4 q^{-38} +9 q^{-40} -7 q^{-42} -10 q^{-44} +6 q^{-46} +11 q^{-48} -6 q^{-50} -9 q^{-52} +11 q^{-54} +6 q^{-56} -6 q^{-58} -5 q^{-60} +5 q^{-62} +2 q^{-64} -2 q^{-66} - q^{-68} - q^{-74} + q^{-76} } |
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 1-2 q^{-2} +2 q^{-4} +4 q^{-6} -8 q^{-8} +7 q^{-10} +7 q^{-12} -15 q^{-14} +17 q^{-16} +8 q^{-18} -17 q^{-20} +16 q^{-22} +7 q^{-24} -20 q^{-26} + q^{-28} +3 q^{-30} -11 q^{-32} -6 q^{-34} +2 q^{-36} +11 q^{-38} -8 q^{-40} -3 q^{-42} +23 q^{-44} -13 q^{-46} -9 q^{-48} +22 q^{-50} -11 q^{-52} -10 q^{-54} +13 q^{-56} -3 q^{-58} -6 q^{-60} +5 q^{-62} -2 q^{-66} + q^{-68} } |
| 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^{-1} - q^{-3} +2 q^{-5} - q^{-7} +3 q^{-9} - q^{-11} +4 q^{-13} +2 q^{-17} - q^{-21} - q^{-23} -4 q^{-25} + q^{-27} -3 q^{-29} +2 q^{-31} - q^{-33} +2 q^{-35} - q^{-37} + q^{-39} } |
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^{-2} - q^{-4} +4 q^{-8} - q^{-10} -3 q^{-12} +6 q^{-14} +4 q^{-16} -6 q^{-18} +2 q^{-20} +16 q^{-22} +2 q^{-24} -7 q^{-26} +15 q^{-28} +19 q^{-30} -16 q^{-32} -12 q^{-34} +13 q^{-36} -11 q^{-38} -31 q^{-40} -3 q^{-42} +7 q^{-44} -16 q^{-46} -5 q^{-48} +22 q^{-50} +6 q^{-52} -10 q^{-54} +16 q^{-56} +17 q^{-58} -13 q^{-60} -6 q^{-62} +15 q^{-64} -2 q^{-66} -16 q^{-68} +9 q^{-72} -4 q^{-74} -7 q^{-76} +4 q^{-78} +4 q^{-80} -2 q^{-82} - q^{-84} + q^{-86} } |
| 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^{-2} - q^{-4} +2 q^{-6} +3 q^{-12} - q^{-14} +4 q^{-16} +3 q^{-20} + q^{-22} - q^{-26} -2 q^{-28} -2 q^{-30} -4 q^{-32} + q^{-34} -3 q^{-36} +2 q^{-38} +2 q^{-44} - q^{-46} + q^{-48} } |
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 1-2 q^{-2} +6 q^{-4} -10 q^{-6} +16 q^{-8} -21 q^{-10} +27 q^{-12} -27 q^{-14} +27 q^{-16} -22 q^{-18} +15 q^{-20} -2 q^{-22} -11 q^{-24} +26 q^{-26} -37 q^{-28} +47 q^{-30} -53 q^{-32} +52 q^{-34} -48 q^{-36} +37 q^{-38} -26 q^{-40} +11 q^{-42} + q^{-44} -13 q^{-46} +21 q^{-48} -26 q^{-50} +27 q^{-52} -24 q^{-54} +21 q^{-56} -15 q^{-58} +10 q^{-60} -7 q^{-62} +4 q^{-64} -2 q^{-66} + q^{-68} } |
| 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^2-2 q^{-2} -2 q^{-4} +4 q^{-6} +7 q^{-8} -2 q^{-10} -12 q^{-12} -4 q^{-14} +16 q^{-16} +16 q^{-18} -13 q^{-20} -23 q^{-22} +4 q^{-24} +31 q^{-26} +13 q^{-28} -24 q^{-30} -22 q^{-32} +15 q^{-34} +27 q^{-36} - q^{-38} -25 q^{-40} -8 q^{-42} +16 q^{-44} +9 q^{-46} -16 q^{-48} -15 q^{-50} +10 q^{-52} +14 q^{-54} -9 q^{-56} -20 q^{-58} +5 q^{-60} +23 q^{-62} +3 q^{-64} -23 q^{-66} -9 q^{-68} +23 q^{-70} +20 q^{-72} -15 q^{-74} -26 q^{-76} +4 q^{-78} +28 q^{-80} +9 q^{-82} -19 q^{-84} -18 q^{-86} +5 q^{-88} +17 q^{-90} +4 q^{-92} -9 q^{-94} -8 q^{-96} + q^{-98} +6 q^{-100} +2 q^{-102} -2 q^{-104} -2 q^{-106} + q^{-110} } |
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^{-2} -2 q^{-4} +4 q^{-6} -5 q^{-8} +10 q^{-10} -12 q^{-12} +16 q^{-14} -18 q^{-16} +24 q^{-18} -21 q^{-20} +23 q^{-22} -17 q^{-24} +22 q^{-26} -8 q^{-28} +7 q^{-30} +5 q^{-32} -9 q^{-34} +15 q^{-36} -31 q^{-38} +26 q^{-40} -41 q^{-42} +34 q^{-44} -47 q^{-46} +37 q^{-48} -36 q^{-50} +36 q^{-52} -24 q^{-54} +20 q^{-56} -8 q^{-58} +8 q^{-60} +7 q^{-62} -11 q^{-64} +13 q^{-66} -19 q^{-68} +23 q^{-70} -21 q^{-72} +16 q^{-74} -19 q^{-76} +17 q^{-78} -11 q^{-80} +8 q^{-82} -8 q^{-84} +6 q^{-86} -3 q^{-88} +2 q^{-90} -2 q^{-92} + q^{-94} } |
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^{-2} -2 q^{-4} +6 q^{-6} -10 q^{-8} +13 q^{-10} -11 q^{-12} + q^{-14} +20 q^{-16} -43 q^{-18} +67 q^{-20} -74 q^{-22} +48 q^{-24} +8 q^{-26} -84 q^{-28} +152 q^{-30} -169 q^{-32} +131 q^{-34} -35 q^{-36} -85 q^{-38} +181 q^{-40} -207 q^{-42} +155 q^{-44} -36 q^{-46} -85 q^{-48} +163 q^{-50} -153 q^{-52} +71 q^{-54} +49 q^{-56} -142 q^{-58} +171 q^{-60} -123 q^{-62} +10 q^{-64} +117 q^{-66} -214 q^{-68} +239 q^{-70} -182 q^{-72} +57 q^{-74} +88 q^{-76} -213 q^{-78} +259 q^{-80} -226 q^{-82} +114 q^{-84} +29 q^{-86} -152 q^{-88} +201 q^{-90} -163 q^{-92} +57 q^{-94} +65 q^{-96} -143 q^{-98} +139 q^{-100} -64 q^{-102} -48 q^{-104} +143 q^{-106} -173 q^{-108} +137 q^{-110} -44 q^{-112} -60 q^{-114} +134 q^{-116} -157 q^{-118} +131 q^{-120} -68 q^{-122} +2 q^{-124} +50 q^{-126} -77 q^{-128} +77 q^{-130} -60 q^{-132} +38 q^{-134} -12 q^{-136} -9 q^{-138} +21 q^{-140} -28 q^{-142} +24 q^{-144} -17 q^{-146} +10 q^{-148} -2 q^{-150} -3 q^{-152} +5 q^{-154} -6 q^{-156} +4 q^{-158} -2 q^{-160} + q^{-162} } |
