10 61 Quantum Invariants

Further quantum knot invariants for 10_61.

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- q^{-1} - q^{-5} + q^{-9} - q^{-11} + 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^{18}-q^{14}+2 q^{12}+2 q^{10}-3 q^8+2 q^4-3 q^2-2+2 q^{-2} - q^{-6} +3 q^{-8} +3 q^{-10} - q^{-12} - q^{-14} +2 q^{-16} - q^{-18} -3 q^{-20} +2 q^{-22} + q^{-24} - q^{-26} + q^{-30} - q^{-32} - q^{-34} + q^{-36} - q^{-38} + q^{-40} - q^{-44} + q^{-46} }
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^{39}-q^{35}-q^{33}+2 q^{31}+3 q^{29}-5 q^{25}-2 q^{23}+4 q^{21}+5 q^{19}-3 q^{17}-7 q^{15}-3 q^{13}+5 q^{11}+5 q^9-2 q^7-5 q^5-q^3+7 q+6 q^{-1} - q^{-3} -5 q^{-5} + q^{-7} +5 q^{-9} +2 q^{-11} -6 q^{-13} -3 q^{-15} +3 q^{-17} +3 q^{-19} -4 q^{-21} -4 q^{-23} +5 q^{-25} +6 q^{-27} -5 q^{-29} -8 q^{-31} +3 q^{-33} +8 q^{-35} -8 q^{-39} -4 q^{-41} +3 q^{-43} +7 q^{-45} +3 q^{-47} -6 q^{-49} -6 q^{-51} +6 q^{-53} +9 q^{-55} -3 q^{-57} -8 q^{-59} +5 q^{-63} -3 q^{-67} + q^{-69} + q^{-71} -2 q^{-75} + q^{-79} - q^{-85} + q^{-87} }
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^{68}-q^{64}-q^{62}-q^{60}+3 q^{58}+3 q^{56}+q^{54}-2 q^{52}-8 q^{50}-2 q^{48}+4 q^{46}+9 q^{44}+7 q^{42}-7 q^{40}-11 q^{38}-11 q^{36}+2 q^{34}+16 q^{32}+11 q^{30}+2 q^{28}-16 q^{26}-18 q^{24}-q^{22}+13 q^{20}+25 q^{18}+9 q^{16}-14 q^{14}-21 q^{12}-14 q^{10}+15 q^8+28 q^6+12 q^4-11 q^2-31-17 q^{-2} +13 q^{-4} +26 q^{-6} +17 q^{-8} -15 q^{-10} -29 q^{-12} -12 q^{-14} +14 q^{-16} +29 q^{-18} +12 q^{-20} -17 q^{-22} -22 q^{-24} -5 q^{-26} +21 q^{-28} +17 q^{-30} -7 q^{-32} -17 q^{-34} -9 q^{-36} +13 q^{-38} +13 q^{-40} -9 q^{-42} -16 q^{-44} -2 q^{-46} +22 q^{-48} +20 q^{-50} -14 q^{-52} -28 q^{-54} -12 q^{-56} +21 q^{-58} +34 q^{-60} +6 q^{-62} -25 q^{-64} -32 q^{-66} -10 q^{-68} +25 q^{-70} +33 q^{-72} +11 q^{-74} -21 q^{-76} -40 q^{-78} -12 q^{-80} +26 q^{-82} +37 q^{-84} +11 q^{-86} -33 q^{-88} -32 q^{-90} +2 q^{-92} +29 q^{-94} +22 q^{-96} -14 q^{-98} -21 q^{-100} -4 q^{-102} +12 q^{-104} +14 q^{-106} -4 q^{-108} -7 q^{-110} -3 q^{-112} +2 q^{-114} +4 q^{-116} -4 q^{-118} + q^{-120} + q^{-122} -3 q^{-128} +2 q^{-130} - q^{-138} + q^{-140} }
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^{105}-q^{101}-q^{99}-q^{97}+3 q^{93}+4 q^{91}+q^{89}-2 q^{87}-5 q^{85}-8 q^{83}-3 q^{81}+6 q^{79}+12 q^{77}+11 q^{75}+3 q^{73}-11 q^{71}-20 q^{69}-17 q^{67}-2 q^{65}+17 q^{63}+28 q^{61}+22 q^{59}+q^{57}-25 q^{55}-39 q^{53}-27 q^{51}+3 q^{49}+34 q^{47}+49 q^{45}+35 q^{43}-7 q^{41}-46 q^{39}-57 q^{37}-33 q^{35}+14 q^{33}+61 q^{31}+70 q^{29}+30 q^{27}-31 q^{25}-74 q^{23}-75 q^{21}-23 q^{19}+49 q^{17}+88 q^{15}+67 q^{13}+3 q^{11}-70 q^9-99 q^7-58 q^5+24 q^3+92 q+97 q^{-1} +35 q^{-3} -55 q^{-5} -106 q^{-7} -81 q^{-9} +5 q^{-11} +91 q^{-13} +114 q^{-15} +49 q^{-17} -51 q^{-19} -116 q^{-21} -91 q^{-23} +5 q^{-25} +99 q^{-27} +112 q^{-29} +38 q^{-31} -66 q^{-33} -116 q^{-35} -73 q^{-37} +30 q^{-39} +104 q^{-41} +88 q^{-43} +5 q^{-45} -78 q^{-47} -90 q^{-49} -24 q^{-51} +51 q^{-53} +71 q^{-55} +28 q^{-57} -33 q^{-59} -48 q^{-61} -16 q^{-63} +29 q^{-65} +31 q^{-67} -12 q^{-69} -45 q^{-71} -26 q^{-73} +29 q^{-75} +73 q^{-77} +49 q^{-79} -33 q^{-81} -99 q^{-83} -81 q^{-85} +9 q^{-87} +99 q^{-89} +117 q^{-91} +43 q^{-93} -66 q^{-95} -127 q^{-97} -94 q^{-99} +2 q^{-101} +96 q^{-103} +127 q^{-105} +74 q^{-107} -37 q^{-109} -129 q^{-111} -128 q^{-113} -35 q^{-115} +93 q^{-117} +155 q^{-119} +94 q^{-121} -42 q^{-123} -145 q^{-125} -124 q^{-127} -2 q^{-129} +110 q^{-131} +125 q^{-133} +32 q^{-135} -78 q^{-137} -108 q^{-139} -41 q^{-141} +51 q^{-143} +82 q^{-145} +38 q^{-147} -32 q^{-149} -61 q^{-151} -28 q^{-153} +24 q^{-155} +39 q^{-157} +16 q^{-159} -15 q^{-161} -25 q^{-163} -9 q^{-165} +12 q^{-167} +15 q^{-169} +3 q^{-171} -6 q^{-173} -5 q^{-175} - q^{-177} + q^{-179} +2 q^{-181} - q^{-185} + q^{-187} - q^{-191} - q^{-193} + q^{-195} - q^{-203} + q^{-205} }

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

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^{12}+3 q^8+2 q^6+2 q^4+3 q^2+1- q^{-2} -2 q^{-6} -4 q^{-8} -2 q^{-10} -4 q^{-12} -2 q^{-14} +2 q^{-20} +4 q^{-22} +3 q^{-24} + q^{-26} - q^{-32} -2 q^{-34} + q^{-36} + q^{-38} - q^{-40} + q^{-42} + q^{-44} -2 q^{-46} +2 q^{-50} - q^{-52} - q^{-54} + q^{-56} }
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+3 q^3+2 q+3 q^{-1} - q^{-5} -4 q^{-7} -3 q^{-9} -3 q^{-11} - q^{-13} + q^{-15} + q^{-17} +2 q^{-19} + q^{-23} - q^{-25} + 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^{14}+q^{12}+3 q^{10}+5 q^8+6 q^6+6 q^4+7 q^2+2- q^{-2} -5 q^{-4} -9 q^{-6} -12 q^{-8} -10 q^{-10} -6 q^{-12} -5 q^{-14} +6 q^{-18} +8 q^{-20} +2 q^{-22} +6 q^{-24} +6 q^{-26} + q^{-28} + q^{-30} +2 q^{-32} + q^{-34} -2 q^{-36} - q^{-38} -2 q^{-40} -3 q^{-42} -3 q^{-44} + q^{-46} + q^{-48} - q^{-50} +2 q^{-52} +2 q^{-54} - q^{-58} + q^{-62} - q^{-66} + q^{-70} }
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+3 q^4+3 q^2+3+3 q^{-2} - q^{-6} -4 q^{-8} -4 q^{-10} -4 q^{-12} -3 q^{-14} - q^{-16} +2 q^{-20} + q^{-22} +2 q^{-24} + q^{-28} + 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^{12}+3 q^8-2 q^6+4 q^4-3 q^2+5-3 q^{-2} +4 q^{-4} -2 q^{-6} -4 q^{-12} +4 q^{-14} -8 q^{-16} +6 q^{-18} -8 q^{-20} +6 q^{-22} -7 q^{-24} +5 q^{-26} -2 q^{-28} +2 q^{-30} + q^{-32} +3 q^{-36} -3 q^{-38} +3 q^{-40} -3 q^{-42} +3 q^{-44} -2 q^{-46} +2 q^{-48} -2 q^{-50} + q^{-52} - q^{-54} + q^{-56} }
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^{22}+3 q^{14}+2 q^{12}-q^{10}-q^8+3 q^6+3 q^4-4- q^{-2} +2 q^{-4} +2 q^{-6} -3 q^{-8} -5 q^{-10} +3 q^{-14} + q^{-16} -4 q^{-18} -3 q^{-20} + q^{-22} +3 q^{-24} - q^{-26} -2 q^{-28} +3 q^{-32} - q^{-36} + q^{-38} +4 q^{-40} +2 q^{-42} -2 q^{-44} -2 q^{-46} + q^{-48} +3 q^{-50} - q^{-52} -3 q^{-54} -2 q^{-56} +2 q^{-58} +2 q^{-60} - q^{-62} -2 q^{-64} +2 q^{-68} +2 q^{-70} - q^{-72} -2 q^{-74} - q^{-76} + q^{-78} +2 q^{-80} - q^{-84} - q^{-86} + q^{-90} }

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^{14}+3 q^{10}+6 q^6+6 q^2+6 q^{-2} -2 q^{-4} +2 q^{-6} -4 q^{-8} -2 q^{-10} -5 q^{-12} -7 q^{-14} -3 q^{-16} -7 q^{-18} + q^{-20} -7 q^{-22} +6 q^{-24} -3 q^{-26} +10 q^{-28} -2 q^{-30} +8 q^{-32} -2 q^{-34} +5 q^{-36} -2 q^{-38} + q^{-40} -2 q^{-42} - q^{-44} + q^{-46} - q^{-48} +2 q^{-50} -2 q^{-52} +3 q^{-54} -2 q^{-56} +2 q^{-58} -2 q^{-60} +2 q^{-62} -2 q^{-64} + q^{-66} - q^{-68} +2 q^{-70} - q^{-72} - q^{-76} + q^{-78} }

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^{26}+3 q^{22}-3 q^{20}+3 q^{18}-q^{16}+7 q^{12}-9 q^{10}+10 q^8-3 q^6+q^4+8 q^2-12+11 q^{-2} -2 q^{-4} +5 q^{-8} -9 q^{-10} +4 q^{-12} +5 q^{-14} -4 q^{-16} + q^{-18} -5 q^{-20} - q^{-22} +4 q^{-24} -8 q^{-26} +4 q^{-28} -9 q^{-30} +5 q^{-32} + q^{-34} -7 q^{-36} +6 q^{-38} -12 q^{-40} +8 q^{-42} -5 q^{-44} -3 q^{-46} +7 q^{-48} -9 q^{-50} +5 q^{-52} +3 q^{-54} -3 q^{-56} +4 q^{-58} - q^{-60} -4 q^{-62} +6 q^{-64} -3 q^{-66} +3 q^{-68} + q^{-70} -2 q^{-72} +6 q^{-74} -3 q^{-76} +3 q^{-78} - q^{-80} + q^{-82} - q^{-84} + q^{-86} + q^{-88} -2 q^{-90} +4 q^{-92} -3 q^{-94} +2 q^{-96} - q^{-98} - q^{-100} -3 q^{-104} +3 q^{-106} - q^{-108} + q^{-110} - q^{-114} +2 q^{-116} -2 q^{-118} +2 q^{-120} - q^{-122} - q^{-128} + q^{-130} - q^{-132} + q^{-134} }