3 1 Quantum Invariants

Because the braid index of 3_1 is only 2, it's easy to calculate lots of quantum invariants.

A1 Invariants.

Weight	Invariant
1	[math]\displaystyle{ -q^9+q^5+q^3+q }[/math]
2	[math]\displaystyle{ q^{24}-q^{20}-q^{18}-q^{16}+q^{10}+q^8+q^6+q^4+q^2 }[/math]
3	[math]\displaystyle{ -q^{45}+q^{41}+q^{39}+q^{37}-q^{31}-q^{29}-q^{27}-q^{25}-q^{23}+q^{15}+q^{13}+q^{11}+q^9+q^7+q^5+q^3 }[/math]
4	[math]\displaystyle{ q^{72}-q^{68}-q^{66}-q^{64}+q^{58}+q^{56}+q^{54}+q^{52}+q^{50}-q^{42}-q^{40}-q^{38}-q^{36}-q^{34}-q^{32}-q^{30}+q^{20}+q^{18}+q^{16}+q^{14}+q^{12}+q^{10}+q^8+q^6+q^4 }[/math]
5	[math]\displaystyle{ -q^{105}+q^{101}+q^{99}+q^{97}-q^{91}-q^{89}-q^{87}-q^{85}-q^{83}+q^{75}+q^{73}+q^{71}+q^{69}+q^{67}+q^{65}+q^{63}-q^{53}-q^{51}-q^{49}-q^{47}-q^{45}-q^{43}-q^{41}-q^{39}-q^{37}+q^{25}+q^{23}+q^{21}+q^{19}+q^{17}+q^{15}+q^{13}+q^{11}+q^9+q^7+q^5 }[/math]

A2 Invariants.

Weight	Invariant
1,0	[math]\displaystyle{ -q^{14}-q^{12}+q^8+2 q^6+q^4+q^2 }[/math]
1,1	[math]\displaystyle{ q^{36}-2 q^{24}-2 q^{22}-3 q^{20}-2 q^{18}+2 q^{14}+3 q^{12}+4 q^{10}+4 q^8+2 q^6+q^4 }[/math]
2,0	[math]\displaystyle{ q^{34}+q^{32}+q^{30}-q^{28}-2 q^{26}-3 q^{24}-3 q^{22}-q^{20}+2 q^{16}+2 q^{14}+3 q^{12}+2 q^{10}+2 q^8+q^6+q^4 }[/math]
3,0	[math]\displaystyle{ -q^{60}-q^{58}-q^{56}+2 q^{52}+3 q^{50}+4 q^{48}+3 q^{46}+2 q^{44}-q^{42}-3 q^{40}-5 q^{38}-5 q^{36}-5 q^{34}-4 q^{32}-2 q^{30}-q^{28}+q^{26}+2 q^{24}+3 q^{22}+3 q^{20}+4 q^{18}+3 q^{16}+3 q^{14}+2 q^{12}+2 q^{10}+q^8+q^6 }[/math]

A3 Invariants.

Weight	Invariant
0,1,0	[math]\displaystyle{ q^{30}-q^{24}-2 q^{22}-2 q^{20}-2 q^{18}+q^{14}+3 q^{12}+3 q^{10}+3 q^8+q^6+q^4 }[/math]
1,0,0	[math]\displaystyle{ -q^{19}-q^{17}-q^{15}+q^{11}+2 q^9+2 q^7+q^5+q^3 }[/math]
1,0,1	[math]\displaystyle{ q^{48}+q^{38}+q^{36}+q^{34}-q^{32}-3 q^{30}-5 q^{28}-6 q^{26}-6 q^{24}-3 q^{22}+q^{20}+4 q^{18}+7 q^{16}+8 q^{14}+7 q^{12}+5 q^{10}+2 q^8+q^6 }[/math]

A4 Invariants.

Weight	Invariant
0,1,0,0	[math]\displaystyle{ q^{40}+q^{38}+q^{36}-q^{32}-3 q^{30}-4 q^{28}-4 q^{26}-3 q^{24}-q^{22}+q^{20}+4 q^{18}+4 q^{16}+5 q^{14}+4 q^{12}+3 q^{10}+q^8+q^6 }[/math]
1,0,0,0	[math]\displaystyle{ -q^{24}-q^{22}-q^{20}-q^{18}+q^{14}+2 q^{12}+2 q^{10}+2 q^8+q^6+q^4 }[/math]

B2 Invariants.

Weight	Invariant
0,1	[math]\displaystyle{ -q^{30}-q^{24}+q^{14}+q^{12}+q^{10}+q^8+q^6+q^4 }[/math]
1,0	[math]\displaystyle{ q^{48}-q^{38}-q^{36}-q^{34}-q^{32}-q^{30}-q^{28}+q^{22}+q^{20}+2 q^{18}+q^{16}+2 q^{14}+q^{12}+q^{10}+q^6 }[/math]

D4 Invariants.

Weight	Invariant
0,1,0,0	[math]\displaystyle{ q^{72}-q^{64}-q^{62}+2 q^{56}+4 q^{54}+5 q^{52}+4 q^{50}+3 q^{48}-q^{46}-5 q^{44}-9 q^{42}-13 q^{40}-14 q^{38}-13 q^{36}-9 q^{34}-4 q^{32}+2 q^{30}+7 q^{28}+12 q^{26}+12 q^{24}+14 q^{22}+11 q^{20}+9 q^{18}+6 q^{16}+4 q^{14}+q^{12}+q^{10} }[/math]
1,0,0,0	[math]\displaystyle{ q^{42}-q^{34}-q^{32}-2 q^{30}-2 q^{28}-2 q^{26}-q^{24}+q^{20}+2 q^{18}+3 q^{16}+3 q^{14}+3 q^{12}+2 q^{10}+q^8+q^6 }[/math]

G2 Invariants.

Weight	Invariant
1,0	[math]\displaystyle{ q^{72}-q^{64}-q^{62}-q^{56}-2 q^{54}-q^{52}+q^{50}-q^{46}-2 q^{44}+2 q^{40}+q^{38}-q^{36}+2 q^{32}+2 q^{30}+q^{28}+2 q^{22}+2 q^{20}+q^{14}+q^{12}+q^{10} }[/math]