11a
199
(K11a
199
)
A knot diagram
1
Linearized knot diagam
7 1 8 11 10 2 4 3 5 6 9
Solving Sequence
5,9
10 6 11
1,3
2 4 8 7
c
9
c
5
c
10
c
11
c
2
c
4
c
8
c
7
c
1
, c
3
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= h2u
39
− 2u
38
+ ··· + 4b − 2, −u
38
+ 17u
36
+ ··· + 4a + 2, u
40
− 2u
39
+ ··· + u + 2i
I
u
2
= h7u
4
a
2
+ 43u
4
a + ··· − 99a + 30,
2u
4
a
2
+ 2u
3
a
2
− u
4
a − 2a
2
u
2
+ 4u
3
a + a
3
− 2a
2
u + 3u
2
a − 7au + 2a + u − 2, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
I
u
3
= h−u
5
+ 2u
3
+ b − u, u
3
− u
2
+ a − u + 1, u
6
− 3u
4
+ 2u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 61 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= h2u
39
−2u
38
+· · ·+4b−2, −u
38
+17u
36
+· · ·+4a+2, u
40
−2u
39
+· · ·+u+2i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
6
=
u
−u
3
+ u
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
3
=
1
4
u
38
−
17
4
u
36
+ ··· −
1
2
u −
1
2
−
1
2
u
39
+
1
2
u
38
+ ··· +
5
4
u +
1
2
a
2
=
1
2
u
39
−
33
4
u
37
+ ··· −
1
4
u − 2
−u
39
+ u
38
+ ··· +
3
2
u + 1
a
4
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
8
=
−
1
4
u
33
+
7
2
u
31
+ ··· +
5
4
u + 1
1
4
u
33
−
15
4
u
31
+ ··· −
1
2
u
2
+
1
2
u
a
7
=
−
1
2
u
39
+ 9u
37
+ ··· +
13
4
u + 2
−
3
4
u
36
+ 12u
34
+ ··· +
1
2
u − 1
a
7
=
−
1
2
u
39
+ 9u
37
+ ··· +
13
4
u + 2
−
3
4
u
36
+ 12u
34
+ ··· +
1
2
u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −2u
39
+ 36u
37
+ 4u
36
− 292u
35
− 68u
34
+ 1400u
33
+ 516u
32
− 4364u
31
− 2288u
30
+
9120u
29
+ 6502u
28
−12568u
27
−12162u
26
+ 10398u
25
+ 14642u
24
−3354u
23
−10260u
22
−
1742u
21
+ 2820u
20
+ 1100u
19
+ 554u
18
+ 1126u
17
+ 310u
16
−880u
15
−734u
14
−336u
13
−
82u
12
+ 494u
11
+ 512u
10
−42u
9
−430u
8
−250u
7
+ 90u
6
+ 172u
5
+ 102u
4
+ 6u
3
−2u
2
+ 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
40
+ u
39
+ ··· + 16u + 5
c
2
u
40
+ 15u
39
+ ··· + 224u + 25
c
3
, c
7
, c
8
u
40
+ u
39
+ ··· + 26u + 5
c
4
u
40
+ 6u
39
+ ··· + 160u + 128
c
5
, c
9
, c
10
u
40
− 2u
39
+ ··· + u + 2
c
11
u
40
− 8u
39
+ ··· − 3945u + 1016
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
40
+ 15y
39
+ ··· + 224y + 25
c
2
y
40
+ 27y
39
+ ··· + 14224y + 625
c
3
, c
7
, c
8
y
40
+ 43y
39
+ ··· − 576y + 25
c
4
y
40
− 4y
39
+ ··· + 23552y + 16384
c
5
, c
9
, c
10
y
40
− 36y
39
+ ··· + 19y + 4
c
11
y
40
+ 16y
39
+ ··· + 17349279y + 1032256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.132680 + 0.164833I
a = −0.558909 − 0.184032I
b = −0.608652 − 0.139154I
−0.49925 − 3.31648I −1.64724 + 4.89716I
u = −1.132680 − 0.164833I
a = −0.558909 + 0.184032I
b = −0.608652 + 0.139154I
−0.49925 + 3.31648I −1.64724 − 4.89716I
u = 0.665458 + 0.491027I
a = 0.181179 + 0.948992I
b = −0.26041 − 1.45828I
5.75631 − 5.93546I 5.14838 + 2.56129I
u = 0.665458 − 0.491027I
a = 0.181179 − 0.948992I
b = −0.26041 + 1.45828I
5.75631 + 5.93546I 5.14838 − 2.56129I
u = 0.336380 + 0.742311I
a = 1.85503 + 0.61503I
b = 0.31157 − 1.46130I
4.58807 + 10.21880I 2.84113 − 7.75802I
u = 0.336380 − 0.742311I
a = 1.85503 − 0.61503I
b = 0.31157 + 1.46130I
4.58807 − 10.21880I 2.84113 + 7.75802I
u = 1.148420 + 0.314124I
a = −1.045320 − 0.767765I
b = −0.184002 + 1.355880I
4.23075 + 6.09808I 4.98979 − 6.57054I
u = 1.148420 − 0.314124I
a = −1.045320 + 0.767765I
b = −0.184002 − 1.355880I
4.23075 − 6.09808I 4.98979 + 6.57054I
u = −0.379059 + 0.695927I
a = −1.66096 + 0.88347I
b = −0.20263 − 1.47527I
6.64060 − 4.34123I 5.66048 + 3.73746I
u = −0.379059 − 0.695927I
a = −1.66096 − 0.88347I
b = −0.20263 + 1.47527I
6.64060 + 4.34123I 5.66048 − 3.73746I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.564420 + 0.541568I
a = −0.566896 + 1.146240I
b = 0.13026 − 1.47688I
7.33749 + 0.16034I 7.10861 + 2.53050I
u = −0.564420 − 0.541568I
a = −0.566896 − 1.146240I
b = 0.13026 + 1.47688I
7.33749 − 0.16034I 7.10861 − 2.53050I
u = 0.056460 + 0.762597I
a = 0.009786 + 0.725772I
b = 0.115987 + 1.331210I
0.89197 − 2.16729I 1.73023 + 3.02653I
u = 0.056460 − 0.762597I
a = 0.009786 − 0.725772I
b = 0.115987 − 1.331210I
0.89197 + 2.16729I 1.73023 − 3.02653I
u = −0.311434 + 0.675248I
a = 1.124050 − 0.679341I
b = 0.808027 + 0.336204I
−1.19660 − 6.15509I −0.81548 + 8.05631I
u = −0.311434 − 0.675248I
a = 1.124050 + 0.679341I
b = 0.808027 − 0.336204I
−1.19660 + 6.15509I −0.81548 − 8.05631I
u = −1.267540 + 0.308667I
a = 0.914279 − 0.732791I
b = −0.048919 + 1.307620I
4.99451 − 1.70471I 6.96107 + 0.I
u = −1.267540 − 0.308667I
a = 0.914279 + 0.732791I
b = −0.048919 − 1.307620I
4.99451 + 1.70471I 6.96107 + 0.I
u = −1.334840 + 0.143127I
a = 0.664581 − 1.202350I
b = 0.284491 + 0.929637I
5.15475 − 3.01598I 9.37714 + 4.67947I
u = −1.334840 − 0.143127I
a = 0.664581 + 1.202350I
b = 0.284491 − 0.929637I
5.15475 + 3.01598I 9.37714 − 4.67947I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.117413 + 0.644564I
a = 0.825462 − 1.029330I
b = 0.429397 − 0.050528I
−3.45598 + 0.23711I −7.22744 + 0.24322I
u = −0.117413 − 0.644564I
a = 0.825462 + 1.029330I
b = 0.429397 + 0.050528I
−3.45598 − 0.23711I −7.22744 − 0.24322I
u = −0.525465 + 0.378936I
a = −0.201594 + 0.316704I
b = −0.675269 + 0.380878I
−0.15865 + 2.49460I 1.76474 − 2.69354I
u = −0.525465 − 0.378936I
a = −0.201594 − 0.316704I
b = −0.675269 − 0.380878I
−0.15865 − 2.49460I 1.76474 + 2.69354I
u = 1.335420 + 0.239501I
a = −0.182679 − 1.103330I
b = −0.313407 + 0.070374I
1.11209 + 2.95109I 0
u = 1.335420 − 0.239501I
a = −0.182679 + 1.103330I
b = −0.313407 − 0.070374I
1.11209 − 2.95109I 0
u = 1.42739 + 0.15745I
a = −0.498107 − 0.387169I
b = 0.731038 + 0.551180I
5.86273 − 0.50813I 0
u = 1.42739 − 0.15745I
a = −0.498107 + 0.387169I
b = 0.731038 − 0.551180I
5.86273 + 0.50813I 0
u = 1.42572 + 0.26112I
a = −0.184246 − 1.165150I
b = −0.872768 + 0.360378I
4.36673 + 9.57310I 0
u = 1.42572 − 0.26112I
a = −0.184246 + 1.165150I
b = −0.872768 − 0.360378I
4.36673 − 9.57310I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44310 + 0.28746I
a = −1.64649 + 2.14222I
b = −0.33802 − 1.48174I
10.2925 − 13.9644I 0
u = −1.44310 − 0.28746I
a = −1.64649 − 2.14222I
b = −0.33802 + 1.48174I
10.2925 + 13.9644I 0
u = 1.45342 + 0.26173I
a = 1.46189 + 2.36452I
b = 0.23852 − 1.51103I
12.5309 + 7.8320I 0
u = 1.45342 − 0.26173I
a = 1.46189 − 2.36452I
b = 0.23852 + 1.51103I
12.5309 − 7.8320I 0
u = −1.48259 + 0.12271I
a = −0.23184 + 2.45383I
b = 0.22820 − 1.52392I
12.67960 + 3.94897I 0
u = −1.48259 − 0.12271I
a = −0.23184 − 2.45383I
b = 0.22820 + 1.52392I
12.67960 − 3.94897I 0
u = 1.47893 + 0.16568I
a = 0.54665 + 2.57861I
b = −0.09835 − 1.54844I
13.93280 + 2.32178I 0
u = 1.47893 − 0.16568I
a = 0.54665 − 2.57861I
b = −0.09835 + 1.54844I
13.93280 − 2.32178I 0
u = 0.230955 + 0.365705I
a = −1.055850 + 0.160049I
b = −0.175073 + 0.673486I
0.344977 + 1.063350I 4.35668 − 6.80283I
u = 0.230955 − 0.365705I
a = −1.055850 − 0.160049I
b = −0.175073 − 0.673486I
0.344977 − 1.063350I 4.35668 + 6.80283I
8
II. I
u
2
= h7u
4
a
2
+ 43u
4
a + · · · − 99a + 30, 2u
4
a
2
− u
4
a + · · · + 2a − 2, u
5
+
u
4
− 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
6
=
u
−u
3
+ u
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
3
=
a
−0.0445860a
2
u
4
− 0.273885au
4
+ ··· + 0.630573a − 0.191083
a
2
=
−0.184713a
2
u
4
+ 0.579618au
4
+ ··· − 0.101911a + 0.636943
−0.280255a
2
u
4
− 1.29299au
4
+ ··· + 1.53503a − 0.343949
a
4
=
u
4
− u
2
− 1
−u
4
+ 2u
2
a
8
=
−0.00636943a
2
u
4
+ 0.675159au
4
+ ··· + 0.375796a + 1.40127
−0.312102a
2
u
4
+ 0.0828025au
4
+ ··· + 0.414013a + 0.662420
a
7
=
0.305732a
2
u
4
+ 1.59236au
4
+ ··· − 0.0382166a + 0.738854
−0.707006a
2
u
4
− 0.0573248au
4
+ ··· + 0.713376a + 1.54140
a
7
=
0.305732a
2
u
4
+ 1.59236au
4
+ ··· − 0.0382166a + 0.738854
−0.707006a
2
u
4
− 0.0573248au
4
+ ··· + 0.713376a + 1.54140
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
− 8u + 6
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
8
u
15
+ 5u
13
+ ··· + u − 1
c
2
u
15
+ 10u
14
+ ··· − u − 1
c
4
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
3
c
5
, c
9
, c
10
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
3
c
11
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
3
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
8
y
15
+ 10y
14
+ ··· − y − 1
c
2
y
15
− 10y
14
+ ··· − y − 1
c
4
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
3
c
5
, c
9
, c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
3
c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
3
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21774
a = 0.219220
b = 0.575861
2.40108 3.48110
u = 1.21774
a = −1.41369 + 1.25295I
b = −0.287931 − 1.117460I
2.40108 3.48110
u = 1.21774
a = −1.41369 − 1.25295I
b = −0.287931 + 1.117460I
2.40108 3.48110
u = 0.309916 + 0.549911I
a = −1.058440 − 0.528425I
b = −0.557720 + 0.484088I
0.32910 + 1.53058I 2.51511 − 4.43065I
u = 0.309916 + 0.549911I
a = 0.019615 + 0.534502I
b = 0.472368 + 0.804368I
0.32910 + 1.53058I 2.51511 − 4.43065I
u = 0.309916 + 0.549911I
a = 1.89592 + 2.07247I
b = 0.085352 − 1.288460I
0.32910 + 1.53058I 2.51511 − 4.43065I
u = 0.309916 − 0.549911I
a = −1.058440 + 0.528425I
b = −0.557720 − 0.484088I
0.32910 − 1.53058I 2.51511 + 4.43065I
u = 0.309916 − 0.549911I
a = 0.019615 − 0.534502I
b = 0.472368 − 0.804368I
0.32910 − 1.53058I 2.51511 + 4.43065I
u = 0.309916 − 0.549911I
a = 1.89592 − 2.07247I
b = 0.085352 + 1.288460I
0.32910 − 1.53058I 2.51511 + 4.43065I
u = −1.41878 + 0.21917I
a = 0.620947 − 0.505783I
b = −0.614910 + 0.840475I
5.87256 − 4.40083I 6.74431 + 3.49859I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41878 + 0.21917I
a = 0.243546 − 1.207590I
b = 0.712111 + 0.537643I
5.87256 − 4.40083I 6.74431 + 3.49859I
u = −1.41878 + 0.21917I
a = −1.41751 + 3.16984I
b = −0.097201 − 1.378120I
5.87256 − 4.40083I 6.74431 + 3.49859I
u = −1.41878 − 0.21917I
a = 0.620947 + 0.505783I
b = −0.614910 − 0.840475I
5.87256 + 4.40083I 6.74431 − 3.49859I
u = −1.41878 − 0.21917I
a = 0.243546 + 1.207590I
b = 0.712111 − 0.537643I
5.87256 + 4.40083I 6.74431 − 3.49859I
u = −1.41878 − 0.21917I
a = −1.41751 − 3.16984I
b = −0.097201 + 1.378120I
5.87256 + 4.40083I 6.74431 − 3.49859I
13
III. I
u
3
= h−u
5
+ 2u
3
+ b − u, u
3
− u
2
+ a − u + 1, u
6
− 3u
4
+ 2u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
6
=
u
−u
3
+ u
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
3
=
−u
3
+ u
2
+ u − 1
u
5
− 2u
3
+ u
a
2
=
−u
4
− u
3
+ 2u
2
+ u
u
5
+ u
4
− 2u
3
− 2u
2
+ u
a
4
=
−u
5
+ 2u
3
− u
0
a
8
=
u
4
− u
3
− 2u
2
+ 2u + 1
1
a
7
=
u
4
− u
3
− 2u
2
+ 2u
1
a
7
=
u
4
− u
3
− 2u
2
+ 2u
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
4
+ 8u
2
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
8
(u
2
+ 1)
3
c
2
(u + 1)
6
c
4
u
6
+ u
4
+ 2u
2
+ 1
c
5
, c
9
, c
10
u
6
− 3u
4
+ 2u
2
+ 1
c
11
(u
3
− u
2
+ 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
8
(y + 1)
6
c
2
(y − 1)
6
c
4
(y
3
+ y
2
+ 2y + 1)
2
c
5
, c
9
, c
10
(y
3
− 3y
2
+ 2y + 1)
2
c
11
(y
3
− y
2
+ 2y − 1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.307140 + 0.215080I
a = −0.082503 − 0.315159I
b = 1.000000I
3.02413 + 2.82812I 3.50976 − 2.97945I
u = 1.307140 − 0.215080I
a = −0.082503 + 0.315159I
b = − 1.000000I
3.02413 − 2.82812I 3.50976 + 2.97945I
u = −1.307140 + 0.215080I
a = 1.40722 − 1.43972I
b = 1.000000I
3.02413 − 2.82812I 3.50976 + 2.97945I
u = −1.307140 − 0.215080I
a = 1.40722 + 1.43972I
b = − 1.000000I
3.02413 + 2.82812I 3.50976 − 2.97945I
u = 0.569840I
a = −1.32472 + 0.75488I
b = 1.000000I
−1.11345 −3.01950
u = − 0.569840I
a = −1.32472 − 0.75488I
b = − 1.000000I
−1.11345 −3.01950
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
((u
2
+ 1)
3
)(u
15
+ 5u
13
+ ··· + u − 1)(u
40
+ u
39
+ ··· + 16u + 5)
c
2
((u + 1)
6
)(u
15
+ 10u
14
+ ··· − u − 1)(u
40
+ 15u
39
+ ··· + 224u + 25)
c
3
, c
7
, c
8
((u
2
+ 1)
3
)(u
15
+ 5u
13
+ ··· + u − 1)(u
40
+ u
39
+ ··· + 26u + 5)
c
4
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
3
(u
6
+ u
4
+ 2u
2
+ 1)
· (u
40
+ 6u
39
+ ··· + 160u + 128)
c
5
, c
9
, c
10
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
3
(u
6
− 3u
4
+ 2u
2
+ 1)
· (u
40
− 2u
39
+ ··· + u + 2)
c
11
(u
3
− u
2
+ 1)
2
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
3
· (u
40
− 8u
39
+ ··· − 3945u + 1016)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
((y + 1)
6
)(y
15
+ 10y
14
+ ··· − y − 1)(y
40
+ 15y
39
+ ··· + 224y + 25)
c
2
((y − 1)
6
)(y
15
− 10y
14
+ ··· − y − 1)(y
40
+ 27y
39
+ ··· + 14224y + 625)
c
3
, c
7
, c
8
((y + 1)
6
)(y
15
+ 10y
14
+ ··· − y − 1)(y
40
+ 43y
39
+ ··· − 576y + 25)
c
4
(y
3
+ y
2
+ 2y + 1)
2
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
3
· (y
40
− 4y
39
+ ··· + 23552y + 16384)
c
5
, c
9
, c
10
(y
3
− 3y
2
+ 2y + 1)
2
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
3
· (y
40
− 36y
39
+ ··· + 19y + 4)
c
11
(y
3
− y
2
+ 2y − 1)
2
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
3
· (y
40
+ 16y
39
+ ··· + 17349279y + 1032256)
19
