10 145 Quantum Invariants
From Knot Atlas
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A1 Invariants.
Weight
Invariant
1
−
q
21
+
q
13
+
q
5
+
q
3
{\displaystyle -q^{21}+q^{13}+q^{5}+q^{3}}
2
q
60
−
q
56
−
q
46
+
q
44
+
q
42
−
q
40
−
q
34
−
q
32
−
q
30
−
q
28
+
q
26
+
q
24
+
2
q
22
−
q
18
+
2
q
16
−
q
12
+
q
10
+
q
8
+
q
6
{\displaystyle q^{60}-q^{56}-q^{46}+q^{44}+q^{42}-q^{40}-q^{34}-q^{32}-q^{30}-q^{28}+q^{26}+q^{24}+2q^{22}-q^{18}+2q^{16}-q^{12}+q^{10}+q^{8}+q^{6}}
3
−
q
117
+
q
113
+
q
111
−
q
107
+
q
97
−
q
95
−
2
q
93
+
2
q
89
+
2
q
87
−
q
85
−
q
83
+
q
79
+
2
q
77
−
2
q
73
−
q
71
+
q
69
+
q
67
−
2
q
65
−
q
63
+
q
61
−
q
57
−
q
55
+
q
53
−
q
49
−
q
47
−
q
41
−
q
39
+
2
q
35
+
2
q
33
−
q
29
+
2
q
25
+
2
q
23
−
q
19
−
q
17
+
q
15
+
q
13
+
q
11
+
q
9
{\displaystyle -q^{117}+q^{113}+q^{111}-q^{107}+q^{97}-q^{95}-2q^{93}+2q^{89}+2q^{87}-q^{85}-q^{83}+q^{79}+2q^{77}-2q^{73}-q^{71}+q^{69}+q^{67}-2q^{65}-q^{63}+q^{61}-q^{57}-q^{55}+q^{53}-q^{49}-q^{47}-q^{41}-q^{39}+2q^{35}+2q^{33}-q^{29}+2q^{25}+2q^{23}-q^{19}-q^{17}+q^{15}+q^{13}+q^{11}+q^{9}}
A2 Invariants.
Weight
Invariant
1,0
−
q
32
−
q
30
+
q
24
+
q
14
+
q
10
+
q
8
+
q
6
{\displaystyle -q^{32}-q^{30}+q^{24}+q^{14}+q^{10}+q^{8}+q^{6}}
1,1
q
84
+
2
q
80
−
2
q
74
−
4
q
72
−
2
q
68
+
2
q
66
+
2
q
64
+
2
q
62
+
6
q
60
−
2
q
58
−
4
q
54
−
3
q
52
−
2
q
50
−
2
q
48
+
2
q
46
−
2
q
44
+
2
q
42
−
4
q
40
+
2
q
38
−
4
q
36
+
2
q
34
+
2
q
32
−
2
q
30
+
4
q
28
+
4
q
24
+
q
20
+
2
q
18
+
2
q
16
+
2
q
14
+
q
12
{\displaystyle q^{84}+2q^{80}-2q^{74}-4q^{72}-2q^{68}+2q^{66}+2q^{64}+2q^{62}+6q^{60}-2q^{58}-4q^{54}-3q^{52}-2q^{50}-2q^{48}+2q^{46}-2q^{44}+2q^{42}-4q^{40}+2q^{38}-4q^{36}+2q^{34}+2q^{32}-2q^{30}+4q^{28}+4q^{24}+q^{20}+2q^{18}+2q^{16}+2q^{14}+q^{12}}
2,0
q
82
+
q
80
+
q
78
−
q
76
−
q
74
−
q
72
−
q
70
+
q
64
+
q
60
+
q
58
−
q
56
−
q
54
−
q
52
−
2
q
48
−
2
q
46
−
q
44
−
2
q
42
−
q
40
+
2
q
36
+
q
34
+
2
q
32
+
2
q
30
+
q
28
+
q
26
+
q
24
+
q
22
+
2
q
16
+
q
14
+
q
12
{\displaystyle q^{82}+q^{80}+q^{78}-q^{76}-q^{74}-q^{72}-q^{70}+q^{64}+q^{60}+q^{58}-q^{56}-q^{54}-q^{52}-2q^{48}-2q^{46}-q^{44}-2q^{42}-q^{40}+2q^{36}+q^{34}+2q^{32}+2q^{30}+q^{28}+q^{26}+q^{24}+q^{22}+2q^{16}+q^{14}+q^{12}}
A3 Invariants.
Weight
Invariant
0,1,0
q
66
+
q
62
+
q
60
−
2
q
56
−
q
54
−
2
q
52
−
3
q
50
−
q
46
+
2
q
40
+
q
38
+
q
34
−
q
30
−
q
28
+
q
26
+
q
22
+
3
q
20
+
q
18
+
2
q
16
+
q
14
+
q
12
{\displaystyle q^{66}+q^{62}+q^{60}-2q^{56}-q^{54}-2q^{52}-3q^{50}-q^{46}+2q^{40}+q^{38}+q^{34}-q^{30}-q^{28}+q^{26}+q^{22}+3q^{20}+q^{18}+2q^{16}+q^{14}+q^{12}}
1,0,0
−
q
43
−
q
41
−
q
39
+
q
33
+
q
31
−
q
25
+
q
19
+
q
17
+
q
15
+
q
13
+
q
11
+
q
9
{\displaystyle -q^{43}-q^{41}-q^{39}+q^{33}+q^{31}-q^{25}+q^{19}+q^{17}+q^{15}+q^{13}+q^{11}+q^{9}}
A4 Invariants.
Weight
Invariant
0,1,0,0
q
88
+
q
86
+
q
84
+
q
82
+
q
80
−
q
74
−
2
q
72
−
2
q
70
−
2
q
68
−
3
q
66
−
3
q
64
−
2
q
62
−
2
q
60
−
2
q
58
−
q
56
+
2
q
54
+
2
q
52
+
3
q
50
+
4
q
48
+
2
q
46
−
q
42
−
2
q
40
−
3
q
38
−
q
36
+
q
34
+
2
q
32
+
3
q
30
+
3
q
28
+
4
q
26
+
2
q
24
+
2
q
22
+
q
20
+
q
18
{\displaystyle q^{88}+q^{86}+q^{84}+q^{82}+q^{80}-q^{74}-2q^{72}-2q^{70}-2q^{68}-3q^{66}-3q^{64}-2q^{62}-2q^{60}-2q^{58}-q^{56}+2q^{54}+2q^{52}+3q^{50}+4q^{48}+2q^{46}-q^{42}-2q^{40}-3q^{38}-q^{36}+q^{34}+2q^{32}+3q^{30}+3q^{28}+4q^{26}+2q^{24}+2q^{22}+q^{20}+q^{18}}
1,0,0,0
−
q
54
−
q
52
−
q
50
−
q
48
+
q
42
+
q
40
+
q
38
−
q
32
−
q
30
+
q
24
+
q
22
+
2
q
20
+
q
18
+
q
16
+
q
14
+
q
12
{\displaystyle -q^{54}-q^{52}-q^{50}-q^{48}+q^{42}+q^{40}+q^{38}-q^{32}-q^{30}+q^{24}+q^{22}+2q^{20}+q^{18}+q^{16}+q^{14}+q^{12}}
B2 Invariants.
Weight
Invariant
0,1
−
q
66
−
q
62
−
q
60
+
q
54
+
q
50
+
q
46
−
q
38
−
q
34
−
q
30
+
q
28
+
q
26
+
q
22
+
q
20
+
q
18
+
q
14
+
q
12
{\displaystyle -q^{66}-q^{62}-q^{60}+q^{54}+q^{50}+q^{46}-q^{38}-q^{34}-q^{30}+q^{28}+q^{26}+q^{22}+q^{20}+q^{18}+q^{14}+q^{12}}
1,0
q
108
+
q
100
−
q
90
−
2
q
88
−
q
82
−
q
80
−
q
72
+
q
56
+
q
48
−
q
44
+
q
42
+
q
40
−
q
36
+
q
34
+
q
32
+
q
30
+
q
26
+
q
24
+
q
22
+
q
18
{\displaystyle q^{108}+q^{100}-q^{90}-2q^{88}-q^{82}-q^{80}-q^{72}+q^{56}+q^{48}-q^{44}+q^{42}+q^{40}-q^{36}+q^{34}+q^{32}+q^{30}+q^{26}+q^{24}+q^{22}+q^{18}}
G2 Invariants.
Weight
Invariant
1,0
q
156
+
q
152
−
q
148
+
q
142
−
2
q
138
−
q
130
−
3
q
128
−
q
126
+
q
124
−
q
122
−
q
120
−
q
118
−
2
q
116
+
2
q
114
−
2
q
112
−
q
110
+
q
108
+
2
q
104
+
2
q
102
+
q
98
+
q
96
+
2
q
92
+
q
88
+
2
q
82
−
q
78
−
3
q
76
+
q
74
−
q
72
−
3
q
66
+
2
q
64
+
q
62
−
2
q
60
−
q
54
+
3
q
52
+
2
q
48
+
q
46
+
3
q
42
+
q
38
+
q
32
+
q
30
{\displaystyle q^{156}+q^{152}-q^{148}+q^{142}-2q^{138}-q^{130}-3q^{128}-q^{126}+q^{124}-q^{122}-q^{120}-q^{118}-2q^{116}+2q^{114}-2q^{112}-q^{110}+q^{108}+2q^{104}+2q^{102}+q^{98}+q^{96}+2q^{92}+q^{88}+2q^{82}-q^{78}-3q^{76}+q^{74}-q^{72}-3q^{66}+2q^{64}+q^{62}-2q^{60}-q^{54}+3q^{52}+2q^{48}+q^{46}+3q^{42}+q^{38}+q^{32}+q^{30}}
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