10 12 Quantum Invariants

Further quantum knot invariants for 10_12.

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+q^3-q+3 q^{-1} - q^{-3} + q^{-5} + q^{-7} - q^{-9} +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^{16}-q^{14}-q^{12}+2 q^{10}-3 q^8-2 q^6+6 q^4-2 q^2-5+10 q^{-2} -9 q^{-6} +8 q^{-8} +3 q^{-10} -6 q^{-12} +2 q^{-14} +4 q^{-16} -6 q^{-20} +4 q^{-22} +5 q^{-24} -10 q^{-26} + q^{-28} +8 q^{-30} -8 q^{-32} -2 q^{-34} +7 q^{-36} -3 q^{-38} -2 q^{-40} +3 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^{33}+q^{31}+q^{29}-q^{25}+q^{23}+q^{21}-3 q^{19}-2 q^{17}+4 q^{15}+3 q^{13}-8 q^{11}-7 q^9+7 q^7+15 q^5-6 q^3-19 q- q^{-1} +29 q^{-3} +9 q^{-5} -28 q^{-7} -18 q^{-9} +27 q^{-11} +27 q^{-13} -21 q^{-15} -26 q^{-17} +14 q^{-19} +25 q^{-21} -5 q^{-23} -21 q^{-25} -2 q^{-27} +16 q^{-29} +9 q^{-31} -11 q^{-33} -19 q^{-35} +6 q^{-37} +25 q^{-39} -32 q^{-43} -6 q^{-45} +31 q^{-47} +14 q^{-49} -29 q^{-51} -20 q^{-53} +21 q^{-55} +24 q^{-57} -13 q^{-59} -21 q^{-61} +3 q^{-63} +18 q^{-65} +2 q^{-67} -12 q^{-69} -3 q^{-71} +6 q^{-73} +3 q^{-75} -3 q^{-77} - q^{-79} +2 q^{-81} -2 q^{-85} + q^{-89} + 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}-q^{54}-q^{52}-q^{48}+3 q^{46}-q^{44}+q^{42}+2 q^{40}-5 q^{38}+2 q^{36}-3 q^{34}+4 q^{32}+11 q^{30}-7 q^{28}-5 q^{26}-16 q^{24}+2 q^{22}+27 q^{20}+6 q^{18}-2 q^{16}-40 q^{14}-23 q^{12}+29 q^{10}+37 q^8+40 q^6-41 q^4-70 q^2-21+40 q^{-2} +113 q^{-4} +16 q^{-6} -89 q^{-8} -99 q^{-10} -19 q^{-12} +143 q^{-14} +97 q^{-16} -40 q^{-18} -132 q^{-20} -92 q^{-22} +103 q^{-24} +124 q^{-26} +21 q^{-28} -96 q^{-30} -107 q^{-32} +35 q^{-34} +88 q^{-36} +50 q^{-38} -39 q^{-40} -79 q^{-42} -15 q^{-44} +44 q^{-46} +58 q^{-48} +5 q^{-50} -51 q^{-52} -63 q^{-54} +10 q^{-56} +78 q^{-58} +51 q^{-60} -32 q^{-62} -116 q^{-64} -33 q^{-66} +90 q^{-68} +106 q^{-70} +12 q^{-72} -143 q^{-74} -87 q^{-76} +55 q^{-78} +127 q^{-80} +78 q^{-82} -102 q^{-84} -112 q^{-86} -23 q^{-88} +81 q^{-90} +113 q^{-92} -21 q^{-94} -71 q^{-96} -65 q^{-98} +3 q^{-100} +78 q^{-102} +27 q^{-104} -4 q^{-106} -44 q^{-108} -33 q^{-110} +22 q^{-112} +15 q^{-114} +21 q^{-116} -6 q^{-118} -18 q^{-120} -6 q^{-124} +10 q^{-126} +4 q^{-128} -2 q^{-130} +3 q^{-132} -7 q^{-134} +4 q^{-142} - q^{-144} - q^{-148} - 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}+q^{83}+q^{81}+q^{77}-q^{75}-3 q^{73}-q^{71}+q^{69}+4 q^{65}+4 q^{63}-3 q^{61}-7 q^{59}-5 q^{57}-q^{55}+8 q^{53}+16 q^{51}+8 q^{49}-13 q^{47}-22 q^{45}-17 q^{43}+7 q^{41}+34 q^{39}+39 q^{37}+4 q^{35}-45 q^{33}-61 q^{31}-32 q^{29}+33 q^{27}+87 q^{25}+76 q^{23}-6 q^{21}-94 q^{19}-130 q^{17}-67 q^{15}+68 q^{13}+171 q^{11}+160 q^9+26 q^7-174 q^5-268 q^3-154 q+106 q^{-1} +332 q^{-3} +336 q^{-5} +34 q^{-7} -350 q^{-9} -478 q^{-11} -219 q^{-13} +263 q^{-15} +583 q^{-17} +426 q^{-19} -124 q^{-21} -595 q^{-23} -574 q^{-25} -54 q^{-27} +524 q^{-29} +655 q^{-31} +223 q^{-33} -403 q^{-35} -650 q^{-37} -324 q^{-39} +247 q^{-41} +566 q^{-43} +376 q^{-45} -109 q^{-47} -447 q^{-49} -364 q^{-51} +8 q^{-53} +312 q^{-55} +316 q^{-57} +64 q^{-59} -200 q^{-61} -265 q^{-63} -107 q^{-65} +115 q^{-67} +220 q^{-69} +142 q^{-71} -54 q^{-73} -208 q^{-75} -196 q^{-77} +4 q^{-79} +224 q^{-81} +261 q^{-83} +60 q^{-85} -241 q^{-87} -366 q^{-89} -142 q^{-91} +255 q^{-93} +465 q^{-95} +258 q^{-97} -220 q^{-99} -553 q^{-101} -399 q^{-103} +145 q^{-105} +589 q^{-107} +528 q^{-109} -5 q^{-111} -554 q^{-113} -618 q^{-115} -158 q^{-117} +429 q^{-119} +647 q^{-121} +316 q^{-123} -255 q^{-125} -579 q^{-127} -419 q^{-129} +45 q^{-131} +440 q^{-133} +455 q^{-135} +116 q^{-137} -260 q^{-139} -392 q^{-141} -224 q^{-143} +79 q^{-145} +283 q^{-147} +250 q^{-149} +45 q^{-151} -148 q^{-153} -207 q^{-155} -111 q^{-157} +37 q^{-159} +135 q^{-161} +121 q^{-163} +25 q^{-165} -60 q^{-167} -89 q^{-169} -54 q^{-171} +8 q^{-173} +51 q^{-175} +50 q^{-177} +16 q^{-179} -18 q^{-181} -32 q^{-183} -22 q^{-185} -3 q^{-187} +16 q^{-189} +20 q^{-191} +7 q^{-193} -4 q^{-195} -9 q^{-197} -10 q^{-199} -4 q^{-201} +6 q^{-203} +6 q^{-205} +2 q^{-207} +2 q^{-209} -2 q^{-211} -4 q^{-213} - q^{-215} + q^{-217} + 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^6+2 q^{-2} - q^{-4} +2 q^{-6} + q^{-8} + q^{-10} +2 q^{-12} - q^{-14} + q^{-16} - q^{-18} - q^{-20} - 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}-2 q^{18}+4 q^{16}-8 q^{14}+15 q^{12}-22 q^{10}+28 q^8-42 q^6+55 q^4-70 q^2+78-96 q^{-2} +105 q^{-4} -98 q^{-6} +90 q^{-8} -56 q^{-10} +29 q^{-12} +30 q^{-14} -76 q^{-16} +128 q^{-18} -171 q^{-20} +202 q^{-22} -216 q^{-24} +214 q^{-26} -199 q^{-28} +162 q^{-30} -118 q^{-32} +64 q^{-34} -19 q^{-36} -32 q^{-38} +70 q^{-40} -92 q^{-42} +100 q^{-44} -102 q^{-46} +96 q^{-48} -80 q^{-50} +66 q^{-52} -54 q^{-54} +40 q^{-56} -28 q^{-58} +19 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^{18}-q^{14}+q^{10}-2 q^8-4 q^6+q^4+3 q^2-2-2 q^{-2} +5 q^{-4} +2 q^{-6} -3 q^{-8} + q^{-10} +4 q^{-12} +5 q^{-18} +4 q^{-20} -2 q^{-22} +4 q^{-24} +4 q^{-26} -3 q^{-28} -3 q^{-30} +2 q^{-32} - q^{-34} -6 q^{-36} -3 q^{-38} + q^{-40} - q^{-42} -3 q^{-44} + q^{-46} +2 q^{-48} + 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}-q^{12}+q^8-3 q^6+2 q^2-6+7 q^{-4} -7 q^{-6} +2 q^{-8} +10 q^{-10} -2 q^{-12} + q^{-14} +7 q^{-16} + q^{-18} - q^{-20} + q^{-22} +4 q^{-24} -2 q^{-26} -6 q^{-28} +5 q^{-30} - q^{-32} -10 q^{-34} +5 q^{-36} + q^{-38} -7 q^{-40} +3 q^{-42} + q^{-44} -3 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^7-q^3+q- q^{-1} +2 q^{-3} - q^{-5} +2 q^{-7} + q^{-9} +2 q^{-11} +2 q^{-13} + q^{-15} +2 q^{-17} - q^{-19} + q^{-21} -2 q^{-23} -2 q^{-27} - 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^6-q^4-q^2-3-3 q^{-2} - q^{-4} + q^{-6} -5 q^{-8} + q^{-10} +8 q^{-12} +4 q^{-14} +8 q^{-18} +9 q^{-20} + q^{-24} +7 q^{-26} +4 q^{-28} -3 q^{-30} +4 q^{-32} +5 q^{-34} -6 q^{-36} -3 q^{-38} +2 q^{-40} -6 q^{-42} -10 q^{-44} - q^{-46} -6 q^{-50} -4 q^{-52} +3 q^{-54} +2 q^{-56} -2 q^{-58} +2 q^{-60} +3 q^{-62} + 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^4- q^{-2} +2 q^{-4} - q^{-6} +2 q^{-8} + q^{-10} +2 q^{-12} +2 q^{-14} +2 q^{-16} +2 q^{-18} + q^{-20} +2 q^{-22} - q^{-24} + q^{-26} -2 q^{-28} - q^{-30} - q^{-32} -2 q^{-34} - 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}+q^{12}-2 q^{10}+3 q^8-5 q^6+6 q^4-8 q^2+8-8 q^{-2} +9 q^{-4} -5 q^{-6} +4 q^{-8} +2 q^{-10} -4 q^{-12} +11 q^{-14} -13 q^{-16} +17 q^{-18} -17 q^{-20} +17 q^{-22} -16 q^{-24} +12 q^{-26} -8 q^{-28} +3 q^{-30} + q^{-32} -4 q^{-34} +7 q^{-36} -9 q^{-38} +9 q^{-40} -9 q^{-42} +7 q^{-44} -5 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^{24}-q^{20}-q^{18}+q^{16}+2 q^{14}-q^{12}-4 q^{10}-2 q^8+3 q^6+5 q^4-2 q^2-8-3 q^{-2} +7 q^{-4} +9 q^{-6} -4 q^{-8} -9 q^{-10} - q^{-12} +10 q^{-14} +6 q^{-16} -4 q^{-18} -5 q^{-20} +5 q^{-22} +7 q^{-24} -5 q^{-28} + q^{-30} +6 q^{-32} +2 q^{-34} -5 q^{-36} -3 q^{-38} +5 q^{-40} +4 q^{-42} -5 q^{-44} -7 q^{-46} +3 q^{-48} +8 q^{-50} - q^{-52} -10 q^{-54} -6 q^{-56} +7 q^{-58} +8 q^{-60} -3 q^{-62} -9 q^{-64} -3 q^{-66} +6 q^{-68} +4 q^{-70} -2 q^{-72} -4 q^{-74} - q^{-76} +3 q^{-78} +2 q^{-80} - q^{-82} - 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}-q^{16}+q^{14}-2 q^{12}+3 q^{10}-4 q^8+3 q^6-6 q^4+5 q^2-8+5 q^{-2} -7 q^{-4} +7 q^{-6} -5 q^{-8} +4 q^{-10} + q^{-12} +4 q^{-14} +6 q^{-16} -4 q^{-18} +10 q^{-20} -7 q^{-22} +15 q^{-24} -11 q^{-26} +14 q^{-28} -12 q^{-30} +15 q^{-32} -10 q^{-34} +9 q^{-36} -10 q^{-38} +3 q^{-40} -3 q^{-42} -2 q^{-44} - q^{-46} -6 q^{-48} +5 q^{-50} -7 q^{-52} +6 q^{-54} -8 q^{-56} +7 q^{-58} -6 q^{-60} +4 q^{-62} -4 q^{-64} +4 q^{-66} -2 q^{-68} +2 q^{-70} - 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}-q^{30}+2 q^{28}-3 q^{26}+2 q^{24}-2 q^{22}-2 q^{20}+6 q^{18}-9 q^{16}+9 q^{14}-10 q^{12}+6 q^{10}-10 q^6+17 q^4-23 q^2+23-15 q^{-2} + q^{-4} +14 q^{-6} -26 q^{-8} +38 q^{-10} -30 q^{-12} +14 q^{-14} +6 q^{-16} -23 q^{-18} +30 q^{-20} -21 q^{-22} +8 q^{-24} +12 q^{-26} -20 q^{-28} +21 q^{-30} -6 q^{-32} -14 q^{-34} +32 q^{-36} -39 q^{-38} +30 q^{-40} -9 q^{-42} -16 q^{-44} +40 q^{-46} -49 q^{-48} +48 q^{-50} -29 q^{-52} +3 q^{-54} +23 q^{-56} -40 q^{-58} +42 q^{-60} -27 q^{-62} +9 q^{-64} +13 q^{-66} -23 q^{-68} +22 q^{-70} -8 q^{-72} -10 q^{-74} +24 q^{-76} -29 q^{-78} +14 q^{-80} +4 q^{-82} -23 q^{-84} +34 q^{-86} -34 q^{-88} +22 q^{-90} -7 q^{-92} -13 q^{-94} +22 q^{-96} -28 q^{-98} +23 q^{-100} -14 q^{-102} +4 q^{-104} +4 q^{-106} -11 q^{-108} +13 q^{-110} -11 q^{-112} +8 q^{-114} -3 q^{-116} - q^{-118} +3 q^{-120} -4 q^{-122} +3 q^{-124} - q^{-126} + q^{-128} }