10 140 Quantum Invariants
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A1 Invariants.
Weight
Invariant
1
−
q
15
+
q
9
+
q
7
+
q
−
1
{\displaystyle -q^{15}+q^{9}+q^{7}+q^{-1}}
2
q
44
−
q
40
−
q
34
−
q
32
+
q
28
+
q
26
+
q
22
−
q
18
−
q
14
−
q
12
+
q
10
+
q
8
+
q
6
+
q
2
+
2
−
q
−
4
{\displaystyle q^{44}-q^{40}-q^{34}-q^{32}+q^{28}+q^{26}+q^{22}-q^{18}-q^{14}-q^{12}+q^{10}+q^{8}+q^{6}+q^{2}+2-q^{-4}}
3
−
q
87
+
q
83
+
q
81
−
q
77
+
q
73
+
q
71
−
q
67
−
2
q
65
−
q
63
+
q
59
−
q
55
+
2
q
51
+
2
q
49
−
q
45
+
q
41
−
2
q
37
−
2
q
35
−
q
29
+
q
25
+
q
23
+
q
17
+
q
15
−
q
11
−
q
9
+
2
q
7
+
3
q
5
−
2
q
+
3
q
−
3
+
q
−
5
−
q
−
7
−
q
−
9
{\displaystyle -q^{87}+q^{83}+q^{81}-q^{77}+q^{73}+q^{71}-q^{67}-2q^{65}-q^{63}+q^{59}-q^{55}+2q^{51}+2q^{49}-q^{45}+q^{41}-2q^{37}-2q^{35}-q^{29}+q^{25}+q^{23}+q^{17}+q^{15}-q^{11}-q^{9}+2q^{7}+3q^{5}-2q+3q^{-3}+q^{-5}-q^{-7}-q^{-9}}
A2 Invariants.
Weight
Invariant
1,0
−
q
22
−
q
20
−
q
18
+
2
q
14
+
2
q
12
+
2
q
10
−
q
6
−
q
4
+
1
+
q
−
2
{\displaystyle -q^{22}-q^{20}-q^{18}+2q^{14}+2q^{12}+2q^{10}-q^{6}-q^{4}+1+q^{-2}}
1,1
q
60
+
2
q
56
−
2
q
54
+
2
q
52
−
2
q
50
−
2
q
46
−
4
q
44
−
4
q
40
+
2
q
38
+
q
36
+
4
q
34
+
4
q
32
+
4
q
30
+
q
28
−
2
q
26
−
4
q
24
−
4
q
22
−
4
q
20
−
2
q
18
+
6
q
14
+
2
q
12
+
6
q
10
+
2
q
8
+
2
q
4
−
2
q
2
+
2
−
2
q
−
2
+
q
−
4
{\displaystyle q^{60}+2q^{56}-2q^{54}+2q^{52}-2q^{50}-2q^{46}-4q^{44}-4q^{40}+2q^{38}+q^{36}+4q^{34}+4q^{32}+4q^{30}+q^{28}-2q^{26}-4q^{24}-4q^{22}-4q^{20}-2q^{18}+6q^{14}+2q^{12}+6q^{10}+2q^{8}+2q^{4}-2q^{2}+2-2q^{-2}+q^{-4}}
2,0
q
58
+
q
56
+
q
54
−
q
48
−
2
q
46
−
4
q
44
−
4
q
42
−
3
q
40
+
4
q
36
+
4
q
34
+
6
q
32
+
4
q
30
+
3
q
28
−
2
q
26
−
4
q
24
−
5
q
22
−
5
q
20
−
3
q
18
+
4
q
14
+
4
q
12
+
5
q
10
+
2
q
8
+
1
−
q
−
2
{\displaystyle q^{58}+q^{56}+q^{54}-q^{48}-2q^{46}-4q^{44}-4q^{42}-3q^{40}+4q^{36}+4q^{34}+6q^{32}+4q^{30}+3q^{28}-2q^{26}-4q^{24}-5q^{22}-5q^{20}-3q^{18}+4q^{14}+4q^{12}+5q^{10}+2q^{8}+1-q^{-2}}
A3 Invariants.
Weight
Invariant
0,1,0
q
46
+
q
42
−
q
38
−
2
q
36
−
2
q
34
−
2
q
32
−
3
q
30
+
2
q
24
+
2
q
22
+
4
q
20
+
3
q
18
+
2
q
16
+
2
q
14
−
q
10
−
2
q
8
−
q
6
−
q
4
+
2
+
q
−
2
+
q
−
4
{\displaystyle q^{46}+q^{42}-q^{38}-2q^{36}-2q^{34}-2q^{32}-3q^{30}+2q^{24}+2q^{22}+4q^{20}+3q^{18}+2q^{16}+2q^{14}-q^{10}-2q^{8}-q^{6}-q^{4}+2+q^{-2}+q^{-4}}
1,0,0
−
q
29
−
q
27
−
2
q
25
−
q
23
+
2
q
19
+
3
q
17
+
3
q
15
+
2
q
13
−
q
9
−
2
q
7
−
q
5
+
q
+
q
−
1
+
q
−
3
{\displaystyle -q^{29}-q^{27}-2q^{25}-q^{23}+2q^{19}+3q^{17}+3q^{15}+2q^{13}-q^{9}-2q^{7}-q^{5}+q+q^{-1}+q^{-3}}
A4 Invariants.
Weight
Invariant
0,1,0,0
q
60
+
q
58
+
2
q
56
+
2
q
54
+
q
52
−
q
50
−
3
q
48
−
6
q
46
−
7
q
44
−
6
q
42
−
4
q
40
−
q
38
+
2
q
36
+
6
q
34
+
6
q
32
+
5
q
30
+
4
q
28
+
3
q
26
+
q
22
+
q
20
+
q
18
+
q
16
+
q
14
−
2
q
10
−
2
q
8
−
q
6
−
q
4
+
2
+
2
q
−
2
+
q
−
4
+
q
−
6
{\displaystyle q^{60}+q^{58}+2q^{56}+2q^{54}+q^{52}-q^{50}-3q^{48}-6q^{46}-7q^{44}-6q^{42}-4q^{40}-q^{38}+2q^{36}+6q^{34}+6q^{32}+5q^{30}+4q^{28}+3q^{26}+q^{22}+q^{20}+q^{18}+q^{16}+q^{14}-2q^{10}-2q^{8}-q^{6}-q^{4}+2+2q^{-2}+q^{-4}+q^{-6}}
1,0,0,0
−
q
36
−
q
34
−
2
q
32
−
2
q
30
−
q
28
+
2
q
24
+
3
q
22
+
4
q
20
+
3
q
18
+
2
q
16
−
q
12
−
2
q
10
−
2
q
8
−
q
6
+
q
2
+
1
+
q
−
2
+
q
−
4
{\displaystyle -q^{36}-q^{34}-2q^{32}-2q^{30}-q^{28}+2q^{24}+3q^{22}+4q^{20}+3q^{18}+2q^{16}-q^{12}-2q^{10}-2q^{8}-q^{6}+q^{2}+1+q^{-2}+q^{-4}}
B2 Invariants.
Weight
Invariant
0,1
−
q
46
−
q
42
−
q
38
+
q
30
+
2
q
26
+
2
q
22
+
q
18
−
q
10
−
q
6
+
q
4
+
q
−
2
+
q
−
4
{\displaystyle -q^{46}-q^{42}-q^{38}+q^{30}+2q^{26}+2q^{22}+q^{18}-q^{10}-q^{6}+q^{4}+q^{-2}+q^{-4}}
1,0
q
76
+
q
68
−
q
64
−
q
62
−
q
58
−
2
q
56
−
q
54
−
q
48
+
q
42
+
q
38
+
q
34
+
q
32
+
q
30
+
q
26
+
2
q
24
+
q
22
+
q
16
−
q
12
−
q
10
−
q
4
+
1
+
q
−
2
+
q
−
6
{\displaystyle q^{76}+q^{68}-q^{64}-q^{62}-q^{58}-2q^{56}-q^{54}-q^{48}+q^{42}+q^{38}+q^{34}+q^{32}+q^{30}+q^{26}+2q^{24}+q^{22}+q^{16}-q^{12}-q^{10}-q^{4}+1+q^{-2}+q^{-6}}
G2 Invariants.
Weight
Invariant
1,0
q
108
+
q
104
−
q
102
−
q
96
+
q
94
−
q
92
−
q
90
−
q
88
−
q
86
−
q
82
−
4
q
80
−
4
q
70
+
q
68
+
3
q
66
−
q
62
−
q
60
+
3
q
58
+
5
q
56
+
2
q
54
−
q
52
+
q
50
+
3
q
48
+
4
q
46
−
2
q
42
+
q
40
+
3
q
38
+
q
36
−
q
34
−
2
q
30
+
q
28
−
3
q
24
−
q
20
−
q
18
+
q
16
−
q
14
−
q
12
−
q
8
+
q
6
+
2
+
q
−
4
+
q
−
6
+
q
−
10
{\displaystyle q^{108}+q^{104}-q^{102}-q^{96}+q^{94}-q^{92}-q^{90}-q^{88}-q^{86}-q^{82}-4q^{80}-4q^{70}+q^{68}+3q^{66}-q^{62}-q^{60}+3q^{58}+5q^{56}+2q^{54}-q^{52}+q^{50}+3q^{48}+4q^{46}-2q^{42}+q^{40}+3q^{38}+q^{36}-q^{34}-2q^{30}+q^{28}-3q^{24}-q^{20}-q^{18}+q^{16}-q^{14}-q^{12}-q^{8}+q^{6}+2+q^{-4}+q^{-6}+q^{-10}}
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