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

A2 Invariants.

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

A3 Invariants.

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

A4 Invariants.

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

B2 Invariants.

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

D4 Invariants.

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

G2 Invariants.

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