9 15 Quantum Invariants
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Further quantum knot invariants for 9_15.
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^3-q+2 q^{-1} -2 q^{-3} + q^{-5} + q^{-7} +2 q^{-11} -2 q^{-13} + 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^{10}-q^8-q^6+3 q^4-3 q^2-2+9 q^{-2} -4 q^{-4} -6 q^{-6} +11 q^{-8} - q^{-10} -7 q^{-12} +5 q^{-14} +2 q^{-16} -3 q^{-18} -3 q^{-20} +5 q^{-22} +2 q^{-24} -8 q^{-26} +5 q^{-28} +6 q^{-30} -10 q^{-32} + q^{-34} +7 q^{-36} -6 q^{-38} -2 q^{-40} +4 q^{-42} - q^{-44} - 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^{21}-q^{19}-q^{17}+2 q^{13}-q^{11}-2 q^9+4 q^7+4 q^5-7 q^3-8 q+11 q^{-1} +16 q^{-3} -14 q^{-5} -25 q^{-7} +13 q^{-9} +33 q^{-11} -5 q^{-13} -38 q^{-15} +38 q^{-19} +8 q^{-21} -28 q^{-23} -14 q^{-25} +21 q^{-27} +16 q^{-29} -9 q^{-31} -19 q^{-33} -2 q^{-35} +17 q^{-37} +11 q^{-39} -19 q^{-41} -21 q^{-43} +19 q^{-45} +27 q^{-47} -14 q^{-49} -33 q^{-51} +10 q^{-53} +36 q^{-55} -37 q^{-59} -7 q^{-61} +28 q^{-63} +15 q^{-65} -21 q^{-67} -18 q^{-69} +12 q^{-71} +16 q^{-73} -3 q^{-75} -12 q^{-77} - q^{-79} +7 q^{-81} +2 q^{-83} -3 q^{-85} - q^{-87} + q^{-89} + q^{-91} - q^{-93} } |
| 4 | |
| 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^{55}-q^{53}-q^{51}-q^{47}+q^{45}+4 q^{43}+q^{41}-2 q^{39}-5 q^{35}-5 q^{33}+3 q^{31}+6 q^{29}+7 q^{27}+6 q^{25}-5 q^{23}-20 q^{21}-19 q^{19}+2 q^{17}+30 q^{15}+45 q^{13}+21 q^{11}-37 q^9-88 q^7-68 q^5+34 q^3+137 q+146 q^{-1} +8 q^{-3} -182 q^{-5} -260 q^{-7} -97 q^{-9} +206 q^{-11} +382 q^{-13} +235 q^{-15} -169 q^{-17} -487 q^{-19} -410 q^{-21} +67 q^{-23} +553 q^{-25} +581 q^{-27} +84 q^{-29} -529 q^{-31} -704 q^{-33} -266 q^{-35} +436 q^{-37} +765 q^{-39} +412 q^{-41} -287 q^{-43} -721 q^{-45} -510 q^{-47} +116 q^{-49} +604 q^{-51} +547 q^{-53} +28 q^{-55} -451 q^{-57} -501 q^{-59} -150 q^{-61} +277 q^{-63} +434 q^{-65} +222 q^{-67} -136 q^{-69} -336 q^{-71} -267 q^{-73} +5 q^{-75} +263 q^{-77} +298 q^{-79} +91 q^{-81} -198 q^{-83} -334 q^{-85} -181 q^{-87} +156 q^{-89} +385 q^{-91} +269 q^{-93} -125 q^{-95} -443 q^{-97} -366 q^{-99} +79 q^{-101} +496 q^{-103} +476 q^{-105} -16 q^{-107} -530 q^{-109} -576 q^{-111} -88 q^{-113} +522 q^{-115} +667 q^{-117} +208 q^{-119} -441 q^{-121} -711 q^{-123} -352 q^{-125} +317 q^{-127} +695 q^{-129} +462 q^{-131} -137 q^{-133} -595 q^{-135} -548 q^{-137} -43 q^{-139} +449 q^{-141} +534 q^{-143} +195 q^{-145} -252 q^{-147} -461 q^{-149} -292 q^{-151} +79 q^{-153} +328 q^{-155} +302 q^{-157} +61 q^{-159} -178 q^{-161} -252 q^{-163} -137 q^{-165} +57 q^{-167} +168 q^{-169} +141 q^{-171} +26 q^{-173} -80 q^{-175} -110 q^{-177} -59 q^{-179} +21 q^{-181} +63 q^{-183} +54 q^{-185} +9 q^{-187} -25 q^{-189} -34 q^{-191} -19 q^{-193} +7 q^{-195} +18 q^{-197} +11 q^{-199} -4 q^{-203} -7 q^{-205} -3 q^{-207} +4 q^{-209} +2 q^{-211} - q^{-213} - q^{-219} + q^{-221} + 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^4+2 q^{-2} -2 q^{-4} +2 q^{-12} +2 q^{-16} - q^{-20} + q^{-22} - q^{-24} - q^{-26} } |
| 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^{12}-2 q^{10}+6 q^8-10 q^6+17 q^4-26 q^2+36-52 q^{-2} +68 q^{-4} -82 q^{-6} +98 q^{-8} -102 q^{-10} +106 q^{-12} -82 q^{-14} +52 q^{-16} -8 q^{-18} -47 q^{-20} +102 q^{-22} -156 q^{-24} +194 q^{-26} -217 q^{-28} +220 q^{-30} -204 q^{-32} +174 q^{-34} -126 q^{-36} +72 q^{-38} -12 q^{-40} -38 q^{-42} +78 q^{-44} -108 q^{-46} +118 q^{-48} -116 q^{-50} +98 q^{-52} -80 q^{-54} +58 q^{-56} -38 q^{-58} +23 q^{-60} -12 q^{-62} +6 q^{-64} -2 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^{12}-q^8+2 q^4-4+7 q^{-4} - q^{-6} -6 q^{-8} +3 q^{-10} +7 q^{-12} + q^{-14} -4 q^{-16} +3 q^{-18} +3 q^{-20} -3 q^{-22} - q^{-24} -3 q^{-28} - q^{-30} +5 q^{-32} - q^{-34} -2 q^{-36} +3 q^{-38} +6 q^{-40} -2 q^{-42} -6 q^{-44} +2 q^{-46} +3 q^{-48} -3 q^{-50} -5 q^{-52} +3 q^{-56} -2 q^{-60} + q^{-64} + q^{-66} } |
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^8-q^6+q^4+3 q^2-3+6 q^{-4} -6 q^{-6} -2 q^{-8} +9 q^{-10} -5 q^{-12} -2 q^{-14} +6 q^{-16} -2 q^{-18} -2 q^{-20} + q^{-22} +4 q^{-24} -2 q^{-28} +6 q^{-30} +3 q^{-32} -8 q^{-34} +4 q^{-36} +2 q^{-38} -9 q^{-40} +2 q^{-42} + q^{-44} -4 q^{-46} +2 q^{-48} + q^{-50} - 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^5+q+2 q^{-3} -2 q^{-5} - q^{-9} + q^{-15} +2 q^{-17} +2 q^{-21} + q^{-25} - q^{-27} + 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^8-q^6+3 q^4-3 q^2+5-6 q^{-2} +8 q^{-4} -8 q^{-6} +6 q^{-8} -5 q^{-10} + q^{-12} +2 q^{-14} -6 q^{-16} +10 q^{-18} -12 q^{-20} +15 q^{-22} -14 q^{-24} +14 q^{-26} -10 q^{-28} +8 q^{-30} -3 q^{-32} +4 q^{-36} -6 q^{-38} +7 q^{-40} -8 q^{-42} +7 q^{-44} -6 q^{-46} +4 q^{-48} -3 q^{-50} + 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^{14}-q^{10}-q^8+2 q^6+3 q^4-4-3 q^{-2} +3 q^{-4} +7 q^{-6} -8 q^{-10} -4 q^{-12} +6 q^{-14} +8 q^{-16} -2 q^{-18} -7 q^{-20} +7 q^{-24} +2 q^{-26} -6 q^{-28} -3 q^{-30} +4 q^{-32} +4 q^{-34} -3 q^{-36} -4 q^{-38} +2 q^{-40} +6 q^{-42} -4 q^{-46} +7 q^{-50} +3 q^{-52} -6 q^{-54} -7 q^{-56} +4 q^{-58} +8 q^{-60} - q^{-62} -9 q^{-64} -5 q^{-66} +5 q^{-68} +5 q^{-70} -2 q^{-72} -5 q^{-74} - q^{-76} +3 q^{-78} +2 q^{-80} - q^{-82} - 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^{18}-q^{16}+3 q^{14}-3 q^{12}+2 q^{10}-3 q^6+8 q^4-9 q^2+11-9 q^{-2} +5 q^{-4} +4 q^{-6} -13 q^{-8} +23 q^{-10} -26 q^{-12} +21 q^{-14} -13 q^{-16} -5 q^{-18} +20 q^{-20} -31 q^{-22} +33 q^{-24} -20 q^{-26} +2 q^{-28} +14 q^{-30} -23 q^{-32} +15 q^{-34} -2 q^{-36} -13 q^{-38} +24 q^{-40} -23 q^{-42} +9 q^{-44} +17 q^{-46} -34 q^{-48} +46 q^{-50} -42 q^{-52} +21 q^{-54} +6 q^{-56} -28 q^{-58} +43 q^{-60} -44 q^{-62} +36 q^{-64} -11 q^{-66} -11 q^{-68} +26 q^{-70} -30 q^{-72} +20 q^{-74} - q^{-76} -15 q^{-78} +21 q^{-80} -15 q^{-82} +3 q^{-84} +18 q^{-86} -31 q^{-88} +33 q^{-90} -23 q^{-92} +18 q^{-96} -32 q^{-98} +33 q^{-100} -24 q^{-102} +10 q^{-104} +3 q^{-106} -15 q^{-108} +17 q^{-110} -15 q^{-112} +9 q^{-114} -3 q^{-116} -2 q^{-118} +3 q^{-120} -4 q^{-122} +3 q^{-124} - q^{-126} + q^{-128} } |
