10 131 Quantum Invariants
From Knot Atlas
Revision as of 18:39, 15 September 2005 by
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A1 Invariants.
Weight
Invariant
1
q
19
−
q
17
+
q
15
−
2
q
13
+
2
q
5
−
q
3
+
2
q
{\displaystyle q^{19}-q^{17}+q^{15}-2q^{13}+2q^{5}-q^{3}+2q}
2
q
54
−
q
52
−
2
q
50
+
3
q
48
+
q
46
−
5
q
44
+
2
q
42
+
4
q
40
−
5
q
38
+
5
q
34
−
2
q
32
−
3
q
30
+
4
q
28
+
q
26
−
4
q
24
+
3
q
20
−
2
q
18
−
5
q
16
+
5
q
14
+
q
12
−
5
q
10
+
4
q
8
+
2
q
6
−
2
q
4
+
2
q
2
+
1
{\displaystyle q^{54}-q^{52}-2q^{50}+3q^{48}+q^{46}-5q^{44}+2q^{42}+4q^{40}-5q^{38}+5q^{34}-2q^{32}-3q^{30}+4q^{28}+q^{26}-4q^{24}+3q^{20}-2q^{18}-5q^{16}+5q^{14}+q^{12}-5q^{10}+4q^{8}+2q^{6}-2q^{4}+2q^{2}+1}
3
q
105
−
q
103
−
2
q
101
+
4
q
97
+
3
q
95
−
5
q
93
−
7
q
91
+
3
q
89
+
11
q
87
+
2
q
85
−
13
q
83
−
9
q
81
+
11
q
79
+
14
q
77
−
4
q
75
−
17
q
73
−
q
71
+
15
q
69
+
8
q
67
−
14
q
65
−
12
q
63
+
11
q
61
+
14
q
59
−
8
q
57
−
16
q
55
+
6
q
53
+
16
q
51
−
3
q
49
−
16
q
47
+
q
45
+
13
q
43
+
7
q
41
−
11
q
39
−
11
q
37
+
3
q
35
+
16
q
33
+
3
q
31
−
17
q
29
−
10
q
27
+
15
q
25
+
14
q
23
−
11
q
21
−
14
q
19
+
5
q
17
+
10
q
15
−
q
13
−
6
q
11
+
q
9
+
4
q
7
−
q
5
+
q
3
+
2
q
−
1
{\displaystyle q^{105}-q^{103}-2q^{101}+4q^{97}+3q^{95}-5q^{93}-7q^{91}+3q^{89}+11q^{87}+2q^{85}-13q^{83}-9q^{81}+11q^{79}+14q^{77}-4q^{75}-17q^{73}-q^{71}+15q^{69}+8q^{67}-14q^{65}-12q^{63}+11q^{61}+14q^{59}-8q^{57}-16q^{55}+6q^{53}+16q^{51}-3q^{49}-16q^{47}+q^{45}+13q^{43}+7q^{41}-11q^{39}-11q^{37}+3q^{35}+16q^{33}+3q^{31}-17q^{29}-10q^{27}+15q^{25}+14q^{23}-11q^{21}-14q^{19}+5q^{17}+10q^{15}-q^{13}-6q^{11}+q^{9}+4q^{7}-q^{5}+q^{3}+2q^{-1}}
A2 Invariants.
Weight
Invariant
1,0
q
28
+
q
22
−
2
q
20
−
q
18
−
q
16
−
q
14
+
q
12
+
2
q
8
+
q
6
+
2
q
2
{\displaystyle q^{28}+q^{22}-2q^{20}-q^{18}-q^{16}-q^{14}+q^{12}+2q^{8}+q^{6}+2q^{2}}
1,1
q
76
−
2
q
74
+
6
q
72
−
14
q
70
+
21
q
68
−
32
q
66
+
44
q
64
−
48
q
62
+
47
q
60
−
40
q
58
+
28
q
56
−
6
q
54
−
22
q
52
+
38
q
50
−
60
q
48
+
76
q
46
−
84
q
44
+
88
q
42
−
74
q
40
+
66
q
38
−
40
q
36
+
18
q
34
+
4
q
32
−
26
q
30
+
36
q
28
−
46
q
26
+
36
q
24
−
38
q
22
+
28
q
20
−
24
q
18
+
14
q
16
−
8
q
14
+
13
q
12
+
4
q
8
+
2
q
4
+
2
q
2
{\displaystyle q^{76}-2q^{74}+6q^{72}-14q^{70}+21q^{68}-32q^{66}+44q^{64}-48q^{62}+47q^{60}-40q^{58}+28q^{56}-6q^{54}-22q^{52}+38q^{50}-60q^{48}+76q^{46}-84q^{44}+88q^{42}-74q^{40}+66q^{38}-40q^{36}+18q^{34}+4q^{32}-26q^{30}+36q^{28}-46q^{26}+36q^{24}-38q^{22}+28q^{20}-24q^{18}+14q^{16}-8q^{14}+13q^{12}+4q^{8}+2q^{4}+2q^{2}}
2,0
q
72
−
q
68
−
q
66
+
q
64
+
2
q
62
−
2
q
60
−
2
q
58
+
q
56
+
q
54
−
2
q
52
−
3
q
50
+
2
q
48
+
4
q
46
+
2
q
40
+
2
q
38
−
q
30
−
2
q
28
−
q
26
−
4
q
24
−
6
q
22
+
q
20
+
2
q
18
−
q
16
+
5
q
12
+
5
q
10
−
q
6
+
3
q
4
+
q
2
{\displaystyle q^{72}-q^{68}-q^{66}+q^{64}+2q^{62}-2q^{60}-2q^{58}+q^{56}+q^{54}-2q^{52}-3q^{50}+2q^{48}+4q^{46}+2q^{40}+2q^{38}-q^{30}-2q^{28}-q^{26}-4q^{24}-6q^{22}+q^{20}+2q^{18}-q^{16}+5q^{12}+5q^{10}-q^{6}+3q^{4}+q^{2}}
A3 Invariants.
Weight
Invariant
0,1,0
q
60
−
q
58
+
q
56
−
4
q
52
+
q
50
−
q
48
−
2
q
46
+
5
q
44
+
3
q
42
+
6
q
38
+
q
36
−
4
q
34
−
2
q
32
−
3
q
30
−
3
q
28
−
4
q
26
−
q
24
+
2
q
22
−
3
q
20
+
5
q
16
−
2
q
14
+
2
q
12
+
6
q
10
+
3
q
4
{\displaystyle q^{60}-q^{58}+q^{56}-4q^{52}+q^{50}-q^{48}-2q^{46}+5q^{44}+3q^{42}+6q^{38}+q^{36}-4q^{34}-2q^{32}-3q^{30}-3q^{28}-4q^{26}-q^{24}+2q^{22}-3q^{20}+5q^{16}-2q^{14}+2q^{12}+6q^{10}+3q^{4}}
1,0,0
q
37
+
q
33
+
q
29
−
2
q
27
−
q
25
−
2
q
23
−
q
21
−
q
19
+
q
15
+
2
q
11
+
q
9
+
2
q
7
+
2
q
3
{\displaystyle q^{37}+q^{33}+q^{29}-2q^{27}-q^{25}-2q^{23}-q^{21}-q^{19}+q^{15}+2q^{11}+q^{9}+2q^{7}+2q^{3}}
A4 Invariants.
Weight
Invariant
0,1,0,0
q
78
+
2
q
72
−
4
q
68
−
2
q
66
−
q
64
−
5
q
62
−
5
q
60
+
3
q
58
+
8
q
56
+
3
q
54
+
6
q
52
+
12
q
50
+
6
q
48
−
3
q
46
−
q
44
−
4
q
42
−
10
q
40
−
8
q
38
−
4
q
36
−
4
q
34
−
6
q
32
+
q
30
+
3
q
28
−
3
q
26
−
q
24
+
5
q
22
+
3
q
20
+
3
q
16
+
6
q
14
+
4
q
12
+
q
10
+
q
8
+
3
q
6
{\displaystyle q^{78}+2q^{72}-4q^{68}-2q^{66}-q^{64}-5q^{62}-5q^{60}+3q^{58}+8q^{56}+3q^{54}+6q^{52}+12q^{50}+6q^{48}-3q^{46}-q^{44}-4q^{42}-10q^{40}-8q^{38}-4q^{36}-4q^{34}-6q^{32}+q^{30}+3q^{28}-3q^{26}-q^{24}+5q^{22}+3q^{20}+3q^{16}+6q^{14}+4q^{12}+q^{10}+q^{8}+3q^{6}}
1,0,0,0
q
46
+
q
42
+
q
40
+
q
36
−
2
q
34
−
q
32
−
2
q
30
−
2
q
28
−
q
26
−
q
24
+
q
18
+
2
q
14
+
q
12
+
2
q
10
+
2
q
8
+
2
q
4
{\displaystyle q^{46}+q^{42}+q^{40}+q^{36}-2q^{34}-q^{32}-2q^{30}-2q^{28}-q^{26}-q^{24}+q^{18}+2q^{14}+q^{12}+2q^{10}+2q^{8}+2q^{4}}
B2 Invariants.
Weight
Invariant
0,1
q
60
−
q
58
+
3
q
56
−
4
q
54
+
4
q
52
−
5
q
50
+
5
q
48
−
4
q
46
+
3
q
44
−
q
42
−
2
q
40
+
4
q
38
−
7
q
36
+
8
q
34
−
10
q
32
+
9
q
30
−
9
q
28
+
6
q
26
−
5
q
24
+
2
q
22
+
q
20
−
2
q
18
+
5
q
16
−
4
q
14
+
6
q
12
−
4
q
10
+
4
q
8
−
2
q
6
+
3
q
4
{\displaystyle q^{60}-q^{58}+3q^{56}-4q^{54}+4q^{52}-5q^{50}+5q^{48}-4q^{46}+3q^{44}-q^{42}-2q^{40}+4q^{38}-7q^{36}+8q^{34}-10q^{32}+9q^{30}-9q^{28}+6q^{26}-5q^{24}+2q^{22}+q^{20}-2q^{18}+5q^{16}-4q^{14}+6q^{12}-4q^{10}+4q^{8}-2q^{6}+3q^{4}}
1,0
q
98
−
q
94
−
q
92
+
2
q
90
+
2
q
88
−
3
q
86
−
4
q
84
+
4
q
80
+
q
78
−
5
q
76
−
3
q
74
+
4
q
72
+
6
q
70
+
q
68
−
4
q
66
+
5
q
62
+
4
q
60
−
2
q
58
−
3
q
56
+
q
54
+
2
q
52
−
3
q
50
−
5
q
48
−
q
46
+
3
q
44
−
q
42
−
5
q
40
−
3
q
38
+
3
q
36
+
3
q
34
−
3
q
32
−
4
q
30
+
q
28
+
6
q
26
+
q
24
−
3
q
22
−
2
q
20
+
4
q
18
+
5
q
16
+
q
14
−
2
q
12
−
q
10
+
q
8
+
3
q
6
{\displaystyle q^{98}-q^{94}-q^{92}+2q^{90}+2q^{88}-3q^{86}-4q^{84}+4q^{80}+q^{78}-5q^{76}-3q^{74}+4q^{72}+6q^{70}+q^{68}-4q^{66}+5q^{62}+4q^{60}-2q^{58}-3q^{56}+q^{54}+2q^{52}-3q^{50}-5q^{48}-q^{46}+3q^{44}-q^{42}-5q^{40}-3q^{38}+3q^{36}+3q^{34}-3q^{32}-4q^{30}+q^{28}+6q^{26}+q^{24}-3q^{22}-2q^{20}+4q^{18}+5q^{16}+q^{14}-2q^{12}-q^{10}+q^{8}+3q^{6}}
G2 Invariants.
Weight
Invariant
1,0
q
142
−
q
140
+
3
q
138
−
5
q
136
+
3
q
134
−
2
q
132
−
4
q
130
+
10
q
128
−
14
q
126
+
14
q
124
−
7
q
122
−
4
q
120
+
14
q
118
−
19
q
116
+
18
q
114
−
8
q
112
−
2
q
110
+
13
q
108
−
15
q
106
+
12
q
104
+
q
102
−
8
q
100
+
14
q
98
−
11
q
96
+
2
q
94
+
7
q
92
−
15
q
90
+
19
q
88
−
18
q
86
+
9
q
84
+
2
q
82
−
17
q
80
+
21
q
78
−
25
q
76
+
14
q
74
−
4
q
72
−
11
q
70
+
16
q
68
−
18
q
66
+
11
q
64
+
q
62
−
12
q
60
+
14
q
58
−
9
q
56
−
q
54
+
11
q
52
−
15
q
50
+
14
q
48
−
4
q
46
−
3
q
44
+
10
q
42
−
14
q
40
+
14
q
38
−
7
q
36
+
2
q
34
+
4
q
32
−
7
q
30
+
8
q
28
−
5
q
26
+
6
q
24
−
q
22
+
2
q
18
−
2
q
16
+
3
q
14
−
q
12
+
2
q
10
+
q
8
{\displaystyle q^{142}-q^{140}+3q^{138}-5q^{136}+3q^{134}-2q^{132}-4q^{130}+10q^{128}-14q^{126}+14q^{124}-7q^{122}-4q^{120}+14q^{118}-19q^{116}+18q^{114}-8q^{112}-2q^{110}+13q^{108}-15q^{106}+12q^{104}+q^{102}-8q^{100}+14q^{98}-11q^{96}+2q^{94}+7q^{92}-15q^{90}+19q^{88}-18q^{86}+9q^{84}+2q^{82}-17q^{80}+21q^{78}-25q^{76}+14q^{74}-4q^{72}-11q^{70}+16q^{68}-18q^{66}+11q^{64}+q^{62}-12q^{60}+14q^{58}-9q^{56}-q^{54}+11q^{52}-15q^{50}+14q^{48}-4q^{46}-3q^{44}+10q^{42}-14q^{40}+14q^{38}-7q^{36}+2q^{34}+4q^{32}-7q^{30}+8q^{28}-5q^{26}+6q^{24}-q^{22}+2q^{18}-2q^{16}+3q^{14}-q^{12}+2q^{10}+q^{8}}
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