11n
156
(K11n
156
)
A knot diagram
1
Linearized knot diagam
10 5 1 11 10 3 4 5 3 8 7
Solving Sequence
4,11 5,7
8 1 3 2 6 10 9
c
4
c
7
c
11
c
3
c
2
c
6
c
10
c
9
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h286u
13
+ 1025u
12
+ ··· + 189b + 494, a − 1,
2u
14
+ 3u
13
+ 6u
12
+ u
11
+ 11u
10
+ 5u
9
+ 20u
8
− 2u
7
+ 15u
6
− 5u
5
+ 11u
4
− 7u
3
+ 7u
2
− 3u + 1i
I
u
2
= h2u
7
− 14u
6
− 8u
5
− 21u
4
+ 25u
3
− 19u
2
+ 9b + 30u − 14, a + 1,
2u
8
+ 2u
6
− 5u
5
+ 4u
4
− 6u
3
+ 5u
2
− 2u + 1i
I
u
3
= h−1.76422 × 10
54
u
35
− 3.41094 × 10
54
u
34
+ ··· + 1.61573 × 10
53
b + 2.47914 × 10
53
,
3.12290 × 10
54
u
35
+ 4.43281 × 10
54
u
34
+ ··· + 2.30819 × 10
52
a − 3.74791 × 10
54
, 2u
36
+ 2u
35
+ ··· − 14u + 1i
I
u
4
= h4u
3
+ 6u
2
+ 3b + 4u + 1, 4u
3
+ 12u
2
+ 3a + 10u + 1, 2u
4
+ 4u
3
+ 2u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 62 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
= h286u
13
+ 1025u
12
+ · · · + 189b + 494, a − 1, 2u
14
+ 3u
13
+ · · · − 3u + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
7
=
1
−1.51323u
13
− 5.42328u
12
+ ··· − 0.164021u − 2.61376
a
8
=
−1.51323u
13
− 5.42328u
12
+ ··· − 0.164021u − 1.61376
−1.51323u
13
− 5.42328u
12
+ ··· − 0.164021u − 2.61376
a
1
=
u
−3.15344u
13
− 6.81481u
12
+ ··· − 3.88360u + 0.756614
a
3
=
2.08466u
13
+ 3.32804u
12
+ ··· + 3.97354u − 0.576720
2.06349u
13
+ 2.26984u
12
+ ··· + 5.63492u − 2.73016
a
2
=
3.56614u
13
+ 4.35450u
12
+ ··· + 8.86772u − 3.40741
3.43915u
13
+ 4.67196u
12
+ ··· + 8.16931u − 3.32804
a
6
=
−4.79365u
13
− 11.9206u
12
+ ··· − 4.74603u − 0.777778
−5.22751u
13
− 10.4550u
12
+ ··· − 8.65608u + 1.37037
a
10
=
−5.46032u
13
− 10.2540u
12
+ ··· − 9.41270u + 2.55556
−2.30688u
13
− 3.43915u
12
+ ··· − 4.52910u + 1.79894
a
9
=
2.08466u
13
+ 3.32804u
12
+ ··· + 3.97354u − 0.576720
−3.01587u
13
− 7.50794u
12
+ ··· − 3.39683u − 0.936508
a
9
=
2.08466u
13
+ 3.32804u
12
+ ··· + 3.97354u − 0.576720
−3.01587u
13
− 7.50794u
12
+ ··· − 3.39683u − 0.936508
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
136
27
u
13
−
1550
189
u
12
−
2491
189
u
11
+
248
189
u
10
−
1103
63
u
9
−
2428
189
u
8
−
2563
63
u
7
+
1360
189
u
6
−
1738
189
u
5
+
1937
189
u
4
−
1363
63
u
3
−
16
27
u
2
−
2242
189
u −
176
189
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
4(4u
14
+ 43u
13
+ ··· + 336u + 64)
c
2
, c
5
2(2u
14
− u
13
+ ··· + 9u
2
+ 1)
c
3
, c
10
u
14
− 2u
13
+ ··· − 3u + 2
c
4
, c
11
2(2u
14
− 3u
13
+ ··· + 3u + 1)
c
6
, c
8
u
14
− u
13
+ ··· − 13u + 2
c
7
u
14
− 9u
13
+ ··· − 24u + 8
c
9
u
14
− 10u
13
+ ··· − 80u + 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
16(16y
14
− 105y
13
+ ··· + 16128y + 4096)
c
2
, c
5
4(4y
14
+ 83y
13
+ ··· + 18y + 1)
c
3
, c
10
y
14
+ 4y
13
+ ··· − 5y + 4
c
4
, c
11
4(4y
14
+ 15y
13
+ ··· + 5y + 1)
c
6
, c
8
y
14
+ 7y
13
+ ··· − 33y + 4
c
7
y
14
+ 3y
13
+ ··· − 96y + 64
c
9
y
14
− 10y
13
+ ··· + 5376y + 1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.747471 + 0.736656I
a = 1.00000
b = −1.190140 + 0.650810I
2.08139 − 2.02696I 1.83038 + 2.57438I
u = −0.747471 − 0.736656I
a = 1.00000
b = −1.190140 − 0.650810I
2.08139 + 2.02696I 1.83038 − 2.57438I
u = 0.068372 + 0.773508I
a = 1.00000
b = 0.483737 − 0.312119I
0.50090 − 2.66807I 3.96052 + 3.99756I
u = 0.068372 − 0.773508I
a = 1.00000
b = 0.483737 + 0.312119I
0.50090 + 2.66807I 3.96052 − 3.99756I
u = 0.863068 + 0.906873I
a = 1.00000
b = −1.23002 − 1.06519I
1.01240 + 7.85357I 1.37704 − 6.81636I
u = 0.863068 − 0.906873I
a = 1.00000
b = −1.23002 + 1.06519I
1.01240 − 7.85357I 1.37704 + 6.81636I
u = −0.606706 + 1.104340I
a = 1.00000
b = −0.474186 + 0.465380I
2.86726 − 1.52978I −3.12219 + 1.19653I
u = −0.606706 − 1.104340I
a = 1.00000
b = −0.474186 − 0.465380I
2.86726 + 1.52978I −3.12219 − 1.19653I
u = 0.376941 + 0.517480I
a = 1.00000
b = −0.75145 + 1.71976I
6.55927 + 6.69837I −2.55381 − 9.47495I
u = 0.376941 − 0.517480I
a = 1.00000
b = −0.75145 − 1.71976I
6.55927 − 6.69837I −2.55381 + 9.47495I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.387427 + 0.358801I
a = 1.00000
b = −0.081855 − 1.118280I
−1.68063 + 1.15707I −4.41586 − 6.34189I
u = 0.387427 − 0.358801I
a = 1.00000
b = −0.081855 + 1.118280I
−1.68063 − 1.15707I −4.41586 + 6.34189I
u = −1.09163 + 1.20653I
a = 1.00000
b = −1.25608 + 0.97829I
8.3986 − 15.3972I 1.29891 + 7.67212I
u = −1.09163 − 1.20653I
a = 1.00000
b = −1.25608 − 0.97829I
8.3986 + 15.3972I 1.29891 − 7.67212I
6
II.
I
u
2
= h2u
7
−14u
6
+· · ·+9b−14, a+1, 2u
8
+2u
6
−5u
5
+4u
4
−6u
3
+5u
2
−2u+1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
7
=
−1
−
2
9
u
7
+
14
9
u
6
+ ··· −
10
3
u +
14
9
a
8
=
−
2
9
u
7
+
14
9
u
6
+ ··· −
10
3
u +
5
9
−
2
9
u
7
+
14
9
u
6
+ ··· −
10
3
u +
14
9
a
1
=
u
−
14
9
u
7
−
10
9
u
6
+ ··· −
1
3
u −
1
9
a
3
=
10
9
u
7
+
2
9
u
6
+ ··· +
5
3
u +
2
9
2
3
u
7
+ 2u
5
+ ··· +
5
3
u −
4
3
a
2
=
20
9
u
7
+
10
9
u
6
+ ··· + 3u −
11
9
−
4
9
u
7
−
8
9
u
6
+ ··· +
4
3
u −
8
9
a
6
=
2
3
u
6
+
2
3
u
5
+ ··· −
4
3
u +
1
3
2
3
u
6
+
2
3
u
5
+ ··· −
4
3
u +
1
3
a
10
=
−
8
3
u
7
−
2
3
u
6
+ ··· −
10
3
u + 1
−
10
9
u
7
+
4
9
u
6
+ ··· − 2u +
10
9
a
9
=
−
10
9
u
7
−
2
9
u
6
+ ··· −
5
3
u −
2
9
4
3
u
7
+
8
3
u
6
+ ··· − 2u +
2
3
a
9
=
−
10
9
u
7
−
2
9
u
6
+ ··· −
5
3
u −
2
9
4
3
u
7
+
8
3
u
6
+ ··· − 2u +
2
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
166
9
u
7
−
92
9
u
6
−
194
9
u
5
+
103
3
u
4
−
128
9
u
3
+
344
9
u
2
− 18u −
59
9
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
4(4u
8
− 8u
7
+ 17u
5
− 13u
4
− 2u
3
+ 13u
2
− 3u + 1)
c
2
, c
5
2(2u
8
− 2u
7
+ 4u
6
+ u
5
− 11u
4
+ 5u
3
+ 6u
2
− 5u + 1)
c
3
, c
10
u
8
+ 2u
7
+ 3u
6
+ 2u
5
+ 2u
4
+ 3u
3
+ 6u
2
+ 6u + 2
c
4
, c
11
2(2u
8
+ 2u
6
− 5u
5
+ 4u
4
− 6u
3
+ 5u
2
− 2u + 1)
c
6
, c
8
u
8
+ u
7
+ u
6
+ 4u
5
+ 7u
4
− u
3
− 2u
2
+ 8u + 6
c
7
u
8
+ 4u
7
+ 9u
6
+ 11u
5
+ 9u
4
+ 3u
3
− 2u + 1
c
9
u
8
− u
7
− 3u
6
− 2u
5
+ 5u
4
+ 6u
3
+ 4u
2
+ u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
16
· (16y
8
− 64y
7
+ 168y
6
− 217y
5
+ 197y
4
− 240y
3
+ 131y
2
+ 17y + 1)
c
2
, c
5
4(4y
8
+ 12y
7
− 24y
6
− 45y
5
+ 143y
4
− 139y
3
+ 64y
2
− 13y + 1)
c
3
, c
10
y
8
+ 2y
7
+ 5y
6
+ 8y
5
+ 8y
4
+ 3y
3
+ 8y
2
− 12y + 4
c
4
, c
11
4(4y
8
+ 8y
7
+ 20y
6
+ 11y
5
− 20y
4
− 12y
3
+ 9y
2
+ 6y + 1)
c
6
, c
8
y
8
+ y
7
+ 7y
6
− 4y
5
+ 49y
4
− 81y
3
+ 104y
2
− 88y + 36
c
7
y
8
+ 2y
7
+ 11y
6
+ 17y
5
+ 33y
4
+ 53y
3
+ 30y
2
− 4y + 1
c
9
y
8
− 7y
7
+ 15y
6
− 14y
5
+ 29y
4
+ 2y
3
+ 14y
2
+ 7y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.081144 + 0.964537I
a = −1.00000
b = −0.344131 − 0.211497I
−0.11790 + 2.52032I −8.47313 − 1.37245I
u = −0.081144 − 0.964537I
a = −1.00000
b = −0.344131 + 0.211497I
−0.11790 − 2.52032I −8.47313 + 1.37245I
u = 0.876567 + 0.170950I
a = −1.00000
b = 0.186359 + 1.054490I
7.53561 + 5.92481I 2.17560 − 4.89559I
u = 0.876567 − 0.170950I
a = −1.00000
b = 0.186359 − 1.054490I
7.53561 − 5.92481I 2.17560 + 4.89559I
u = 0.120498 + 0.535479I
a = −1.00000
b = 1.02903 − 1.25354I
−2.49208 + 1.02158I −16.3238 − 6.0123I
u = 0.120498 − 0.535479I
a = −1.00000
b = 1.02903 + 1.25354I
−2.49208 − 1.02158I −16.3238 + 6.0123I
u = −0.91592 + 1.17562I
a = −1.00000
b = 1.12874 − 0.87067I
−1.63576 − 8.28057I −4.87863 + 7.63527I
u = −0.91592 − 1.17562I
a = −1.00000
b = 1.12874 + 0.87067I
−1.63576 + 8.28057I −4.87863 − 7.63527I
10
III. I
u
3
= h−1.76 × 10
54
u
35
− 3.41 × 10
54
u
34
+ · · · + 1.62 × 10
53
b + 2.48 ×
10
53
, 3.12 × 10
54
u
35
+ 4.43 × 10
54
u
34
+ · · · + 2.31 × 10
52
a − 3.75 ×
10
54
, 2u
36
+ 2u
35
+ · · · − 14u + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
7
=
−135.297u
35
− 192.047u
34
+ ··· − 1894.64u + 162.375
10.9190u
35
+ 21.1108u
34
+ ··· + 23.6339u − 1.53438
a
8
=
−124.378u
35
− 170.936u
34
+ ··· − 1871.00u + 160.840
10.9190u
35
+ 21.1108u
34
+ ··· + 23.6339u − 1.53438
a
1
=
140.578u
35
+ 183.175u
34
+ ··· + 2437.80u − 225.735
−22.7951u
35
− 26.5223u
34
+ ··· − 458.196u + 42.0517
a
3
=
−203.081u
35
− 272.115u
34
+ ··· − 3148.94u + 274.459
46.8092u
35
+ 61.5248u
34
+ ··· + 699.352u − 58.6705
a
2
=
−177.136u
35
− 236.734u
34
+ ··· − 2831.29u + 250.306
44.3327u
35
+ 58.6254u
34
+ ··· + 646.276u − 53.9528
a
6
=
28.2278u
35
+ 40.0599u
34
+ ··· + 373.025u − 32.8519
−6.91942u
35
− 4.84581u
34
+ ··· − 223.697u + 19.9655
a
10
=
104.432u
35
+ 141.715u
34
+ ··· + 1653.06u − 152.962
−13.3506u
35
− 14.9377u
34
+ ··· − 324.539u + 30.7209
a
9
=
−117.271u
35
− 167.192u
34
+ ··· − 1630.91u + 139.095
14.3939u
35
+ 26.3816u
34
+ ··· + 50.7212u − 3.21539
a
9
=
−117.271u
35
− 167.192u
34
+ ··· − 1630.91u + 139.095
14.3939u
35
+ 26.3816u
34
+ ··· + 50.7212u − 3.21539
(ii) Obstruction class = −1
(iii) Cusp Shapes = −284.262u
35
− 374.406u
34
+ ··· − 4742.13u + 418.350
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
4(2u
18
− 16u
17
+ ··· − 7u + 7)
2
c
2
, c
5
2(2u
36
+ 2u
35
+ ··· + 1164u + 139)
c
3
, c
10
u
36
− 5u
35
+ ··· − 20u + 2
c
4
, c
11
2(2u
36
− 2u
35
+ ··· + 14u + 1)
c
6
, c
8
u
36
+ u
35
+ ··· + 804u + 346
c
7
(u
18
+ 4u
17
+ ··· + 2u + 1)
2
c
9
(u
18
+ 6u
17
+ ··· − 17u − 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
16(4y
18
− 72y
17
+ ··· − 553y + 49)
2
c
2
, c
5
4(4y
36
+ 156y
35
+ ··· − 52188y + 19321)
c
3
, c
10
y
36
+ 7y
35
+ ··· + 344y + 4
c
4
, c
11
4(4y
36
− 20y
35
+ ··· − 8y + 1)
c
6
, c
8
y
36
+ 15y
35
+ ··· − 174472y + 119716
c
7
(y
18
− 2y
17
+ ··· − 12y + 1)
2
c
9
(y
18
− 24y
17
+ ··· − 197y + 1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.961570 + 0.451207I
a = −0.99137 + 1.45940I
b = 0.705308 + 0.173824I
9.41487 + 6.35338I 6.10831 − 5.82519I
u = 0.961570 − 0.451207I
a = −0.99137 − 1.45940I
b = 0.705308 − 0.173824I
9.41487 − 6.35338I 6.10831 + 5.82519I
u = 0.802634 + 0.723579I
a = −0.970908 + 0.553934I
b = 1.09375 + 1.07152I
9.34056 + 3.99785I 4.89270 − 3.37103I
u = 0.802634 − 0.723579I
a = −0.970908 − 0.553934I
b = 1.09375 − 1.07152I
9.34056 − 3.99785I 4.89270 + 3.37103I
u = 1.045790 + 0.309537I
a = 0.012525 − 0.502541I
b = 0.201172 + 0.954404I
−1.66631 − 0.81812I −4.46509 + 7.48163I
u = 1.045790 − 0.309537I
a = 0.012525 + 0.502541I
b = 0.201172 − 0.954404I
−1.66631 + 0.81812I −4.46509 − 7.48163I
u = −0.313395 + 0.785869I
a = 1.82670 + 0.98006I
b = −0.590040 + 0.925318I
5.29155 − 6.58230I −1.74185 + 7.38738I
u = −0.313395 − 0.785869I
a = 1.82670 − 0.98006I
b = −0.590040 − 0.925318I
5.29155 + 6.58230I −1.74185 − 7.38738I
u = −1.146610 + 0.289938I
a = 0.879803 + 0.475338I
b = −0.771930
2.09741 6.92265 + 0.I
u = −1.146610 − 0.289938I
a = 0.879803 − 0.475338I
b = −0.771930
2.09741 6.92265 + 0.I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.925613 + 0.773706I
a = 0.177368 − 0.984145I
b = −0.377469
0.191595 0
u = 0.925613 − 0.773706I
a = 0.177368 + 0.984145I
b = −0.377469
0.191595 0
u = −1.180100 + 0.257922I
a = −0.777034 + 0.443323I
b = 1.09375 − 1.07152I
9.34056 − 3.99785I 4.89270 + 3.37103I
u = −1.180100 − 0.257922I
a = −0.777034 − 0.443323I
b = 1.09375 + 1.07152I
9.34056 + 3.99785I 4.89270 − 3.37103I
u = 0.445688 + 1.214900I
a = 0.262519 − 0.268046I
b = −1.212220 + 0.386817I
7.83132 + 1.16760I 4.47566 + 0.I
u = 0.445688 − 1.214900I
a = 0.262519 + 0.268046I
b = −1.212220 − 0.386817I
7.83132 − 1.16760I 4.47566 + 0.I
u = 0.242297 + 0.574880I
a = −0.483632 − 0.551179I
b = 0.620071 − 1.035940I
−1.91252 + 0.92110I 0.62272 − 2.27597I
u = 0.242297 − 0.574880I
a = −0.483632 + 0.551179I
b = 0.620071 + 1.035940I
−1.91252 − 0.92110I 0.62272 + 2.27597I
u = 0.168654 + 0.521676I
a = 0.04956 − 1.98865I
b = 0.201172 − 0.954404I
−1.66631 + 0.81812I −4.46509 − 7.48163I
u = 0.168654 − 0.521676I
a = 0.04956 + 1.98865I
b = 0.201172 + 0.954404I
−1.66631 − 0.81812I −4.46509 + 7.48163I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.04555 + 1.04502I
a = −1.025980 − 0.149246I
b = 1.129710 + 0.820643I
−0.40495 + 7.64175I 0
u = 1.04555 − 1.04502I
a = −1.025980 + 0.149246I
b = 1.129710 − 0.820643I
−0.40495 − 7.64175I 0
u = −0.61317 + 1.38045I
a = −0.131546 − 0.191009I
b = 0.626954 − 0.364844I
0.56981 − 3.14278I 0
u = −0.61317 − 1.38045I
a = −0.131546 + 0.191009I
b = 0.626954 + 0.364844I
0.56981 + 3.14278I 0
u = 0.442651 + 0.199469I
a = 1.86494 + 1.90421I
b = −1.212220 + 0.386817I
7.83132 + 1.16760I 4.47566 − 0.91080I
u = 0.442651 − 0.199469I
a = 1.86494 − 1.90421I
b = −1.212220 − 0.386817I
7.83132 − 1.16760I 4.47566 + 0.91080I
u = −0.91675 + 1.22821I
a = −0.954477 − 0.138844I
b = 1.129710 − 0.820643I
−0.40495 − 7.64175I 0
u = −0.91675 − 1.22821I
a = −0.954477 + 0.138844I
b = 1.129710 + 0.820643I
−0.40495 + 7.64175I 0
u = 0.199679 + 0.411580I
a = −0.899448 − 1.025070I
b = 0.620071 + 1.035940I
−1.91252 − 0.92110I 0.62272 + 2.27597I
u = 0.199679 − 0.411580I
a = −0.899448 + 1.025070I
b = 0.620071 − 1.035940I
−1.91252 + 0.92110I 0.62272 − 2.27597I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.344338 + 0.064471I
a = −2.44560 − 3.55110I
b = 0.626954 + 0.364844I
0.56981 + 3.14278I 0.19751 − 9.10915I
u = 0.344338 − 0.064471I
a = −2.44560 + 3.55110I
b = 0.626954 − 0.364844I
0.56981 − 3.14278I 0.19751 + 9.10915I
u = −1.34267 + 1.12840I
a = 0.425077 − 0.228061I
b = −0.590040 + 0.925318I
5.29155 − 6.58230I 0
u = −1.34267 − 1.12840I
a = 0.425077 + 0.228061I
b = −0.590040 − 0.925318I
5.29155 + 6.58230I 0
u = −1.61177 + 0.95600I
a = −0.318496 − 0.468858I
b = 0.705308 + 0.173824I
9.41487 + 6.35338I 0
u = −1.61177 − 0.95600I
a = −0.318496 + 0.468858I
b = 0.705308 − 0.173824I
9.41487 − 6.35338I 0
17
IV.
I
u
4
= h4u
3
+ 6u
2
+ 3b + 4u + 1, 4u
3
+ 12u
2
+ 3a + 10u + 1, 2u
4
+ 4u
3
+ 2u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
7
=
−
4
3
u
3
− 4u
2
−
10
3
u −
1
3
−
4
3
u
3
− 2u
2
−
4
3
u −
1
3
a
8
=
−
8
3
u
3
− 6u
2
−
14
3
u −
2
3
−
4
3
u
3
− 2u
2
−
4
3
u −
1
3
a
1
=
−
4
3
u
3
− 4u
2
−
13
3
u −
4
3
−
2
3
u
3
− 2u
2
−
2
3
u −
2
3
a
3
=
−2u
3
− 4u
2
− 2u + 2
−2u
2
a
2
=
−2u
3
− 4u
2
− u + 2
−u
3
− 2u
2
a
6
=
−
4
3
u
3
− 6u
2
−
28
3
u −
13
3
−2u
2
− 2u − 1
a
10
=
−
8
3
u
3
− 8u
2
−
26
3
u −
8
3
−
2
3
u
3
− 2u
2
−
5
3
u −
2
3
a
9
=
−
2
3
u
3
− 4u
2
−
14
3
u −
2
3
−
10
3
u
3
− 4u
2
−
1
3
u −
4
3
a
9
=
−
2
3
u
3
− 4u
2
−
14
3
u −
2
3
−
10
3
u
3
− 4u
2
−
1
3
u −
4
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
4(2u
2
− 2u + 1)
2
c
2
, c
5
2(2u
4
− 4u
3
+ 2u
2
+ 1)
c
3
, c
10
u
4
+ 4u
3
+ 6u
2
+ 4u + 2
c
4
, c
11
2(2u
4
+ 4u
3
+ 2u
2
+ 1)
c
6
, c
8
u
4
+ 2u
2
+ 4u + 2
c
7
, c
9
(u
2
+ 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
16(4y
2
+ 1)
2
c
2
, c
4
, c
5
c
11
4(4y
4
− 8y
3
+ 8y
2
+ 4y + 1)
c
3
, c
10
y
4
− 4y
3
+ 8y
2
+ 8y + 4
c
6
, c
8
y
4
+ 4y
3
+ 8y
2
− 8y + 4
c
7
, c
9
(y + 1)
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.207110 + 0.500000I
a = 0.414214I
b = − 1.000000I
−1.64493 −4.00000
u = −1.207110 − 0.500000I
a = − 0.414214I
b = 1.000000I
−1.64493 −4.00000
u = 0.207107 + 0.500000I
a = − 2.41421I
b = − 1.000000I
−1.64493 −4.00000
u = 0.207107 − 0.500000I
a = 2.41421I
b = 1.000000I
−1.64493 −4.00000
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
256(2u
2
− 2u + 1)
2
(4u
8
− 8u
7
+ ··· − 3u + 1)
· (4u
14
+ 43u
13
+ ··· + 336u + 64)(2u
18
− 16u
17
+ ··· − 7u + 7)
2
c
2
, c
5
16(2u
4
− 4u
3
+ 2u
2
+ 1)
· (2u
8
− 2u
7
+ 4u
6
+ u
5
− 11u
4
+ 5u
3
+ 6u
2
− 5u + 1)
· (2u
14
− u
13
+ ··· + 9u
2
+ 1)(2u
36
+ 2u
35
+ ··· + 1164u + 139)
c
3
, c
10
(u
4
+ 4u
3
+ 6u
2
+ 4u + 2)
· (u
8
+ 2u
7
+ 3u
6
+ 2u
5
+ 2u
4
+ 3u
3
+ 6u
2
+ 6u + 2)
· (u
14
− 2u
13
+ ··· − 3u + 2)(u
36
− 5u
35
+ ··· − 20u + 2)
c
4
, c
11
16(2u
4
+ 4u
3
+ 2u
2
+ 1)(2u
8
+ 2u
6
+ ··· − 2u + 1)
· (2u
14
− 3u
13
+ ··· + 3u + 1)(2u
36
− 2u
35
+ ··· + 14u + 1)
c
6
, c
8
(u
4
+ 2u
2
+ 4u + 2)(u
8
+ u
7
+ u
6
+ 4u
5
+ 7u
4
− u
3
− 2u
2
+ 8u + 6)
· (u
14
− u
13
+ ··· − 13u + 2)(u
36
+ u
35
+ ··· + 804u + 346)
c
7
(u
2
+ 1)
2
(u
8
+ 4u
7
+ 9u
6
+ 11u
5
+ 9u
4
+ 3u
3
− 2u + 1)
· (u
14
− 9u
13
+ ··· − 24u + 8)(u
18
+ 4u
17
+ ··· + 2u + 1)
2
c
9
(u
2
+ 1)
2
(u
8
− u
7
− 3u
6
− 2u
5
+ 5u
4
+ 6u
3
+ 4u
2
+ u + 1)
· (u
14
− 10u
13
+ ··· − 80u + 32)(u
18
+ 6u
17
+ ··· − 17u − 1)
2
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
65536(4y
2
+ 1)
2
· (16y
8
− 64y
7
+ 168y
6
− 217y
5
+ 197y
4
− 240y
3
+ 131y
2
+ 17y + 1)
· (16y
14
− 105y
13
+ ··· + 16128y + 4096)
· (4y
18
− 72y
17
+ ··· − 553y + 49)
2
c
2
, c
5
256(4y
4
− 8y
3
+ 8y
2
+ 4y + 1)
· (4y
8
+ 12y
7
− 24y
6
− 45y
5
+ 143y
4
− 139y
3
+ 64y
2
− 13y + 1)
· (4y
14
+ 83y
13
+ ··· + 18y + 1)
· (4y
36
+ 156y
35
+ ··· − 52188y + 19321)
c
3
, c
10
(y
4
− 4y
3
+ 8y
2
+ 8y + 4)
· (y
8
+ 2y
7
+ 5y
6
+ 8y
5
+ 8y
4
+ 3y
3
+ 8y
2
− 12y + 4)
· (y
14
+ 4y
13
+ ··· − 5y + 4)(y
36
+ 7y
35
+ ··· + 344y + 4)
c
4
, c
11
256(4y
4
− 8y
3
+ 8y
2
+ 4y + 1)
· (4y
8
+ 8y
7
+ 20y
6
+ 11y
5
− 20y
4
− 12y
3
+ 9y
2
+ 6y + 1)
· (4y
14
+ 15y
13
+ ··· + 5y + 1)(4y
36
− 20y
35
+ ··· − 8y + 1)
c
6
, c
8
(y
4
+ 4y
3
+ 8y
2
− 8y + 4)
· (y
8
+ y
7
+ 7y
6
− 4y
5
+ 49y
4
− 81y
3
+ 104y
2
− 88y + 36)
· (y
14
+ 7y
13
+ ··· − 33y + 4)(y
36
+ 15y
35
+ ··· − 174472y + 119716)
c
7
(y + 1)
4
(y
8
+ 2y
7
+ 11y
6
+ 17y
5
+ 33y
4
+ 53y
3
+ 30y
2
− 4y + 1)
· (y
14
+ 3y
13
+ ··· − 96y + 64)(y
18
− 2y
17
+ ··· − 12y + 1)
2
c
9
(y + 1)
4
(y
8
− 7y
7
+ 15y
6
− 14y
5
+ 29y
4
+ 2y
3
+ 14y
2
+ 7y + 1)
· (y
14
− 10y
13
+ ··· + 5376y + 1024)(y
18
− 24y
17
+ ··· − 197y + 1)
2
23
