12n
0496
(K12n
0496
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 12 4 7 5 9 6 7
Solving Sequence
4,7
8
9,12
1 3 6 2 5 11 10
c
7
c
8
c
12
c
3
c
6
c
2
c
5
c
11
c
10
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
12
+ u
11
+ 4u
10
− 5u
9
+ 3u
8
− u
7
+ 3u
6
− 5u
5
− 7u
4
+ 2u
2
+ 8b + 8u + 6,
− u
11
− 2u
9
+ u
8
− 4u
7
+ u
6
− 4u
5
+ 5u
4
− 2u
3
+ 4u
2
+ 4a − 2u + 2,
u
13
+ 3u
11
− 3u
10
+ 6u
9
− 6u
8
+ 10u
7
− 10u
6
+ 8u
5
− 9u
4
+ 6u
3
− 2u
2
+ 2u + 2i
I
u
2
= h−12498270u
19
− 27347075u
18
+ ··· + 27481697b − 99369926,
− 80173179u
19
− 177871512u
18
+ ··· + 274816970a − 993207167, u
20
+ 3u
19
+ ··· + 18u + 5i
I
u
3
= h−u
6
− 2u
4
− u
2
a − u
3
− 2u
2
+ b − a − u,
2u
6
a + 2u
5
a + 3u
6
+ 6u
4
a + u
5
+ 4u
3
a + 5u
4
+ 8u
2
a + 4u
3
+ 2a
2
+ 4au + 6u
2
+ 2a + u − 1,
u
7
+ 2u
5
+ u
4
+ 2u
3
+ u
2
+ 1i
I
u
4
= hb + 1, −u
2
+ 2a + u + 2, u
4
+ u
2
+ 2i
I
u
5
= h−u
11
+ u
10
− 4u
9
+ 4u
8
− 7u
7
+ 7u
6
− 5u
5
+ 5u
4
− u
2
a − u
3
+ u
2
+ b − a, 2u
11
− u
10
+ ··· + a
2
+ 2,
u
12
− u
11
+ 4u
10
− 4u
9
+ 7u
8
− 7u
7
+ 5u
6
− 5u
5
+ u
4
− u
3
+ 1i
I
u
6
= hb + u, 2a − u + 1, u
2
+ 1i
I
u
7
= hb − 1, u
3
+ u
2
+ 2a + u − 3, u
4
+ 1i
I
v
1
= ha, b − 1, v + 1i
* 8 irreducible components of dim
C
= 0, with total 82 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
1
I.
I
u
1
= h3u
12
+u
11
+· · ·+8b+6, −u
11
−2u
9
+· · ·+4a+2, u
13
+3u
11
+· · ·+2u+2i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
12
=
1
4
u
11
+
1
2
u
9
+ ··· +
1
2
u −
1
2
−
3
8
u
12
−
1
8
u
11
+ ··· − u −
3
4
a
1
=
3
8
u
12
+
3
8
u
11
+ ··· +
3
2
u +
1
4
−
3
8
u
12
−
1
8
u
11
+ ··· − u −
3
4
a
3
=
u
u
3
+ u
a
6
=
1
4
u
11
+
1
2
u
9
+ ··· −
1
2
u +
1
2
−
3
8
u
12
+
3
8
u
11
+ ··· −
5
4
u
2
+
1
4
a
2
=
−
1
4
u
11
−
1
2
u
9
+ ··· +
1
2
u −
1
2
−
1
8
u
12
−
3
8
u
11
+ ··· −
3
4
u
2
−
1
4
a
5
=
−u
−
1
2
u
12
+
1
2
u
11
+ ··· + u + 1
a
11
=
−u
4
− u
2
− 1
−
1
2
u
12
−
1
2
u
11
+ ··· − 2u − 1
a
10
=
−1
−
1
2
u
12
−
1
2
u
11
+ ··· − 2u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
1
2
u
12
+
5
2
u
11
+
9
2
u
9
−
13
2
u
8
+
21
2
u
7
−
21
2
u
6
+
25
2
u
5
−
39
2
u
4
+ 10u
3
− 9u
2
+ 8u − 9
in decimal forms when there is not enough margin.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
+ u
12
+ ··· + 45u + 4
c
2
, c
5
, c
6
c
11
, c
12
u
13
+ 3u
12
+ ··· + 3u + 2
c
3
, c
4
, c
7
c
9
u
13
+ 3u
11
+ ··· + 2u + 2
c
8
, c
10
u
13
− 6u
12
+ ··· + 12u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
+ 11y
12
+ ··· + 913y −16
c
2
, c
5
, c
6
c
11
, c
12
y
13
− y
12
+ ··· + 45y −4
c
3
, c
4
, c
7
c
9
y
13
+ 6y
12
+ ··· + 12y −4
c
8
, c
10
y
13
+ 6y
12
+ ··· + 592y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.929226 + 0.280059I
a = −1.57901 + 0.35078I
b = −1.020380 + 0.665255I
−0.97155 + 5.22971I −12.23690 − 3.97423I
u = 0.929226 − 0.280059I
a = −1.57901 − 0.35078I
b = −1.020380 − 0.665255I
−0.97155 − 5.22971I −12.23690 + 3.97423I
u = 0.167516 + 0.866699I
a = −0.245529 + 0.584083I
b = 0.173060 − 1.267070I
4.28319 − 0.90080I −9.45658 + 7.47152I
u = 0.167516 − 0.866699I
a = −0.245529 − 0.584083I
b = 0.173060 + 1.267070I
4.28319 + 0.90080I −9.45658 − 7.47152I
u = 0.796399 + 0.915905I
a = 1.57817 − 0.32207I
b = 0.871377 + 0.416192I
−3.44917 − 7.30520I −10.1022 + 10.2949I
u = 0.796399 − 0.915905I
a = 1.57817 + 0.32207I
b = 0.871377 − 0.416192I
−3.44917 + 7.30520I −10.1022 − 10.2949I
u = −0.369074 + 1.182800I
a = 0.137445 + 0.036300I
b = −0.850920 − 1.124830I
8.13648 + 2.11284I −3.39753 − 3.18179I
u = −0.369074 − 1.182800I
a = 0.137445 − 0.036300I
b = −0.850920 + 1.124830I
8.13648 − 2.11284I −3.39753 + 3.18179I
u = −0.741404 + 0.995026I
a = 1.037390 + 0.553915I
b = 0.730597 + 0.204654I
−2.95235 + 4.56373I −7.10603 − 0.26574I
u = −0.741404 − 0.995026I
a = 1.037390 − 0.553915I
b = 0.730597 − 0.204654I
−2.95235 − 4.56373I −7.10603 + 0.26574I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.577273 + 1.253670I
a = −1.44865 − 1.14989I
b = −1.22052 + 0.78529I
5.1437 + 16.4022I −7.06197 − 9.59363I
u = −0.577273 − 1.253670I
a = −1.44865 + 1.14989I
b = −1.22052 − 0.78529I
5.1437 − 16.4022I −7.06197 + 9.59363I
u = −0.410781
a = −0.959635
b = −0.366431
−0.641398 −15.2780
6
II.
I
u
2
= h−1.25 × 10
7
u
19
− 2.73 × 10
7
u
18
+ · · · + 2.75 × 10
7
b − 9.94 × 10
7
, −8.02 ×
10
7
u
19
−1.78×10
8
u
18
+· · ·+2.75×10
8
a−9.93×10
8
, u
20
+3u
19
+· · ·+18u+5i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
12
=
0.291733u
19
+ 0.647236u
18
+ ··· + 4.92689u + 3.61407
0.454785u
19
+ 0.995101u
18
+ ··· + 7.42465u + 3.61586
a
1
=
−0.163052u
19
− 0.347865u
18
+ ··· − 2.49775u − 0.00179062
0.454785u
19
+ 0.995101u
18
+ ··· + 7.42465u + 3.61586
a
3
=
u
u
3
+ u
a
6
=
−0.864463u
19
− 1.98643u
18
+ ··· − 16.6818u − 6.40771
−0.595689u
19
− 1.29703u
18
+ ··· − 9.53604u − 3.85004
a
2
=
−0.653089u
19
− 1.43379u
18
+ ··· − 9.37011u − 2.98023
−0.349978u
19
− 0.737864u
18
+ ··· − 3.91291u − 1.28352
a
5
=
−0.821168u
19
− 2.00657u
18
+ ··· − 18.8114u − 8.21548
−0.621168u
19
− 1.40657u
18
+ ··· − 10.8114u − 4.61548
a
11
=
−0.361356u
19
− 0.786551u
18
+ ··· − 5.44322u + 0.633834
0.104807u
19
+ 0.257238u
18
+ ··· + 2.51174u + 2.33233
a
10
=
−0.923097u
19
− 2.14812u
18
+ ··· − 14.5205u − 4.80434
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
7065492
27481697
u
19
−
31839998
27481697
u
18
+ ··· +
103205694
27481697
u −
125331692
27481697
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
10
+ 3u
9
+ 11u
8
+ 18u
7
+ 33u
6
+ 32u
5
+ 34u
4
+ 18u
3
+ 8u
2
+ u + 1)
2
c
2
, c
5
, c
6
c
11
, c
12
(u
10
− u
9
− u
8
+ 2u
7
+ 3u
6
− 4u
5
+ 4u
3
− u + 1)
2
c
3
, c
4
, c
7
c
9
u
20
+ 3u
19
+ ··· + 18u + 5
c
8
, c
10
u
20
− 11u
19
+ ··· − 76u + 25
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
10
+ 13y
9
+ ··· + 15y + 1)
2
c
2
, c
5
, c
6
c
11
, c
12
(y
10
− 3y
9
+ 11y
8
− 18y
7
+ 33y
6
− 32y
5
+ 34y
4
− 18y
3
+ 8y
2
− y + 1)
2
c
3
, c
4
, c
7
c
9
y
20
+ 11y
19
+ ··· + 76y + 25
c
8
, c
10
y
20
− 5y
19
+ ··· − 2276y + 625
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.979461 + 0.188210I
a = 1.59751 + 0.26897I
b = 1.142330 + 0.733576I
1.87405 − 10.79660I −9.84814 + 6.97307I
u = −0.979461 − 0.188210I
a = 1.59751 − 0.26897I
b = 1.142330 − 0.733576I
1.87405 + 10.79660I −9.84814 − 6.97307I
u = −0.843090 + 0.709533I
a = −1.51303 − 0.11033I
b = −0.773203 + 0.317670I
−3.82303 + 1.33139I −9.94848 − 5.33149I
u = −0.843090 − 0.709533I
a = −1.51303 + 0.11033I
b = −0.773203 − 0.317670I
−3.82303 − 1.33139I −9.94848 + 5.33149I
u = 0.813642 + 0.789464I
a = −1.203100 + 0.561936I
b = −0.773203 + 0.317670I
−3.82303 + 1.33139I −9.94848 − 5.33149I
u = 0.813642 − 0.789464I
a = −1.203100 − 0.561936I
b = −0.773203 − 0.317670I
−3.82303 − 1.33139I −9.94848 + 5.33149I
u = 0.004473 + 1.188620I
a = 0.166971 + 0.462136I
b = 0.351677 − 0.481849I
3.14663 + 1.17971I −5.77268 − 5.86187I
u = 0.004473 − 1.188620I
a = 0.166971 − 0.462136I
b = 0.351677 + 0.481849I
3.14663 − 1.17971I −5.77268 + 5.86187I
u = −0.709802 + 0.215491I
a = 1.80898 + 0.45664I
b = 0.794058 + 0.823254I
4.23778 − 1.45588I −7.02190 + 1.71983I
u = −0.709802 − 0.215491I
a = 1.80898 − 0.45664I
b = 0.794058 − 0.823254I
4.23778 + 1.45588I −7.02190 − 1.71983I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.540050 + 1.155880I
a = −1.79606 − 1.06825I
b = −1.014860 + 0.798709I
6.90157 + 6.23908I −5.40880 − 5.42921I
u = −0.540050 − 1.155880I
a = −1.79606 + 1.06825I
b = −1.014860 − 0.798709I
6.90157 − 6.23908I −5.40880 + 5.42921I
u = 0.256269 + 1.270830I
a = 0.0612993 + 0.1044580I
b = 0.794058 − 0.823254I
4.23778 + 1.45588I −7.02190 − 1.71983I
u = 0.256269 − 1.270830I
a = 0.0612993 − 0.1044580I
b = 0.794058 + 0.823254I
4.23778 − 1.45588I −7.02190 + 1.71983I
u = 0.242436 + 0.610608I
a = 1.73616 + 1.08804I
b = 0.351677 + 0.481849I
3.14663 − 1.17971I −5.77268 + 5.86187I
u = 0.242436 − 0.610608I
a = 1.73616 − 1.08804I
b = 0.351677 − 0.481849I
3.14663 + 1.17971I −5.77268 − 5.86187I
u = 0.595640 + 1.211330I
a = 1.53920 − 1.03480I
b = 1.142330 + 0.733576I
1.87405 − 10.79660I −9.84814 + 6.97307I
u = 0.595640 − 1.211330I
a = 1.53920 + 1.03480I
b = 1.142330 − 0.733576I
1.87405 + 10.79660I −9.84814 − 6.97307I
u = −0.340059 + 1.345340I
a = −0.0979292 − 0.0498685I
b = −1.014860 − 0.798709I
6.90157 − 6.23908I −5.40880 + 5.42921I
u = −0.340059 − 1.345340I
a = −0.0979292 + 0.0498685I
b = −1.014860 + 0.798709I
6.90157 + 6.23908I −5.40880 − 5.42921I
11
III. I
u
3
= h−u
6
− 2u
4
− u
2
a − u
3
− 2u
2
+ b − a − u, 2u
6
a + 3u
6
+ · · · + 2a −
1, u
7
+ 2u
5
+ u
4
+ 2u
3
+ u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
12
=
a
u
6
+ 2u
4
+ u
2
a + u
3
+ 2u
2
+ a + u
a
1
=
−u
6
− 2u
4
− u
2
a − u
3
− 2u
2
− u
u
6
+ 2u
4
+ u
2
a + u
3
+ 2u
2
+ a + u
a
3
=
u
u
3
+ u
a
6
=
u
6
a + u
6
+ 2u
4
a + 2u
4
+ 2u
2
a + 2u
2
− u
−u
5
a + u
6
− 2u
3
a + 2u
4
− au + 2u
2
a
2
=
−u
6
a − u
6
− 2u
4
a − 2u
4
− 2u
2
a − 2u
2
+ u
−u
6
a + u
5
a + u
6
− u
4
a + u
5
+ u
3
a + 2u
4
+ 4u
3
+ au + 2u
2
+ a + 3u
a
5
=
−u
−u
6
+ u
5
− u
4
+ 1
a
11
=
−u
4
− u
2
− 1
−u
6
− u
5
− 2u
4
− 2u
3
− 2u
2
− u − 1
a
10
=
−1
−u
6
− u
5
− u
4
− 2u
3
− 2u
2
− u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
6
+ 4u
5
+ 4u
4
+ 8u
3
+ 8u
2
+ 4u − 10
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
+ 7u
13
+ ··· + 254u + 121
c
2
, c
5
, c
6
c
11
, c
12
u
14
+ 3u
13
+ ··· + 34u + 11
c
3
, c
4
, c
7
c
9
(u
7
+ 2u
5
+ u
4
+ 2u
3
+ u
2
+ 1)
2
c
8
, c
10
(u
7
− 4u
6
+ 8u
5
− 7u
4
+ 2u
3
+ 3u
2
− 2u + 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
+ y
13
+ ··· + 56242y + 14641
c
2
, c
5
, c
6
c
11
, c
12
y
14
− 7y
13
+ ··· − 254y + 121
c
3
, c
4
, c
7
c
9
(y
7
+ 4y
6
+ 8y
5
+ 7y
4
+ 2y
3
− 3y
2
− 2y −1)
2
c
8
, c
10
(y
7
+ 12y
5
+ 3y
4
+ 22y
3
− 3y
2
− 2y −1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.468927 + 1.008510I
a = −0.137111 − 0.945771I
b = −0.543255 + 0.753172I
−1.13946 + 6.00484I −7.73392 − 8.08638I
u = −0.468927 + 1.008510I
a = 1.15206 + 0.83449I
b = 1.402030 − 0.105113I
−1.13946 + 6.00484I −7.73392 − 8.08638I
u = −0.468927 − 1.008510I
a = −0.137111 + 0.945771I
b = −0.543255 − 0.753172I
−1.13946 − 6.00484I −7.73392 + 8.08638I
u = −0.468927 − 1.008510I
a = 1.15206 − 0.83449I
b = 1.402030 + 0.105113I
−1.13946 − 6.00484I −7.73392 + 8.08638I
u = −0.824481
a = −1.134300 + 0.394235I
b = −0.692469 + 0.662223I
0.0577569 −10.7630
u = −0.824481
a = −1.134300 − 0.394235I
b = −0.692469 − 0.662223I
0.0577569 −10.7630
u = 0.391915 + 0.631080I
a = −0.915562 − 0.479802I
b = −1.164390 + 0.328250I
−3.69786 − 1.46776I −13.4123 + 4.8542I
u = 0.391915 + 0.631080I
a = 1.23572 − 1.87006I
b = 1.148250 + 0.342291I
−3.69786 − 1.46776I −13.4123 + 4.8542I
u = 0.391915 − 0.631080I
a = −0.915562 + 0.479802I
b = −1.164390 − 0.328250I
−3.69786 + 1.46776I −13.4123 − 4.8542I
u = 0.391915 − 0.631080I
a = 1.23572 + 1.87006I
b = 1.148250 − 0.342291I
−3.69786 + 1.46776I −13.4123 − 4.8542I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.489252 + 1.239920I
a = −1.10571 + 0.94503I
b = −1.09240 − 0.92531I
7.27584 − 9.47458I −4.47246 + 6.21855I
u = 0.489252 + 1.239920I
a = 0.404899 + 0.133299I
b = −0.557760 + 1.149380I
7.27584 − 9.47458I −4.47246 + 6.21855I
u = 0.489252 − 1.239920I
a = −1.10571 − 0.94503I
b = −1.09240 + 0.92531I
7.27584 + 9.47458I −4.47246 − 6.21855I
u = 0.489252 − 1.239920I
a = 0.404899 − 0.133299I
b = −0.557760 − 1.149380I
7.27584 + 9.47458I −4.47246 − 6.21855I
16
IV. I
u
4
= hb + 1, −u
2
+ 2a + u + 2, u
4
+ u
2
+ 2i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
12
=
1
2
u
2
−
1
2
u − 1
−1
a
1
=
1
2
u
2
−
1
2
u
−1
a
3
=
u
u
3
+ u
a
6
=
1
2
u
2
−
1
2
u
−1
a
2
=
1
2
u
2
+
1
2
u
u
3
+ u − 1
a
5
=
−u
−u
3
− u
a
11
=
−1
0
a
10
=
1
u
2
+ 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
− 12
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
11
c
12
(u − 1)
4
c
2
, c
6
(u + 1)
4
c
3
, c
4
, c
7
c
9
u
4
+ u
2
+ 2
c
8
, c
10
(u
2
− u + 2)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y −1)
4
c
3
, c
4
, c
7
c
9
(y
2
+ y + 2)
2
c
8
, c
10
(y
2
+ 3y + 4)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.676097 + 0.978318I
a = −1.58805 + 0.17228I
b = −1.00000
−4.11234 − 5.33349I −14.0000 + 5.2915I
u = 0.676097 − 0.978318I
a = −1.58805 − 0.17228I
b = −1.00000
−4.11234 + 5.33349I −14.0000 − 5.2915I
u = −0.676097 + 0.978318I
a = −0.91195 − 1.15060I
b = −1.00000
−4.11234 + 5.33349I −14.0000 − 5.2915I
u = −0.676097 − 0.978318I
a = −0.91195 + 1.15060I
b = −1.00000
−4.11234 − 5.33349I −14.0000 + 5.2915I
20
V.
I
u
5
= h−u
11
+u
10
+· · ·+b −a, 2u
11
−u
10
+· · ·+a
2
+2, u
12
−u
11
+· · ·−u
3
+1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
12
=
a
u
11
− u
10
+ 4u
9
− 4u
8
+ 7u
7
− 7u
6
+ 5u
5
− 5u
4
+ u
2
a + u
3
− u
2
+ a
a
1
=
−u
11
+ u
10
− 4u
9
+ 4u
8
− 7u
7
+ 7u
6
− 5u
5
+ 5u
4
− u
2
a − u
3
+ u
2
u
11
− u
10
+ 4u
9
− 4u
8
+ 7u
7
− 7u
6
+ 5u
5
− 5u
4
+ u
2
a + u
3
− u
2
+ a
a
3
=
u
u
3
+ u
a
6
=
u
11
a − u
10
a + ··· + u + 2
−u
5
a + u
6
− 2u
3
a + 2u
4
− au + 2u
2
a
2
=
−u
11
+ u
10
+ ··· + u
2
+ 2u
u
11
− u
10
+ ··· + a + 2u
a
5
=
u
10
+ 3u
8
+ 4u
6
+ u
4
− u
2
− 1
u
11
+ 4u
9
− u
8
+ 7u
7
− 3u
6
+ 5u
5
− 4u
4
+ u
3
− 2u
2
− 1
a
11
=
u
7
+ 2u
5
+ 2u
3
u
9
+ 3u
7
+ 3u
5
− u
a
10
=
−u
11
− 4u
9
− 6u
7
− 2u
5
+ 3u
3
+ 2u + 1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
9
− 12u
7
− 12u
5
+ 4u
3
+ 8u − 6
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
12
+ 5u
11
+ ··· + 40u + 9)
2
c
2
, c
5
, c
6
c
11
, c
12
(u
12
− u
11
− 2u
10
+ 4u
9
+ u
8
− 5u
7
− u
6
+ 7u
5
− u
4
− 9u
3
+ 6u
2
+ 2u − 3)
2
c
3
, c
4
, c
7
c
9
(u
12
− u
11
+ 4u
10
− 4u
9
+ 7u
8
− 7u
7
+ 5u
6
− 5u
5
+ u
4
− u
3
+ 1)
2
c
8
, c
10
(u
12
− 7u
11
+ ··· + 2u
2
+ 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
12
+ 3y
11
+ ··· − 196y + 81)
2
c
2
, c
5
, c
6
c
11
, c
12
(y
12
− 5y
11
+ ··· − 40y + 9)
2
c
3
, c
4
, c
7
c
9
(y
12
+ 7y
11
+ ··· + 2y
2
+ 1)
2
c
8
, c
10
(y
12
− 5y
11
+ ··· + 4y + 1)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.386547 + 0.899125I
a = −1.49862 + 0.55245I
b = −1.298590 + 0.085372I
−2.96024 − 1.97241I −11.42428 + 3.68478I
u = 0.386547 + 0.899125I
a = 0.16732 − 1.65718I
b = 0.805413 + 0.489916I
−2.96024 − 1.97241I −11.42428 + 3.68478I
u = 0.386547 − 0.899125I
a = −1.49862 − 0.55245I
b = −1.298590 − 0.085372I
−2.96024 + 1.97241I −11.42428 − 3.68478I
u = 0.386547 − 0.899125I
a = 0.16732 + 1.65718I
b = 0.805413 − 0.489916I
−2.96024 + 1.97241I −11.42428 − 3.68478I
u = −0.206575 + 1.062080I
a = 2.35205 − 1.46291I
b = −0.666209
0.738851 −2.58322 + 0.I
u = −0.206575 + 1.062080I
a = 1.57640 + 2.52499I
b = 1.14988
0.738851 −2.58322 + 0.I
u = −0.206575 − 1.062080I
a = 2.35205 + 1.46291I
b = −0.666209
0.738851 −2.58322 + 0.I
u = −0.206575 − 1.062080I
a = 1.57640 − 2.52499I
b = 1.14988
0.738851 −2.58322 + 0.I
u = 0.869654 + 0.049931I
a = 0.988080 + 0.457240I
b = 0.547085 + 0.953523I
3.69558 + 4.59213I −7.41886 − 3.20482I
u = 0.869654 + 0.049931I
a = 1.181660 − 0.546728I
b = 0.973781 − 0.790428I
3.69558 + 4.59213I −7.41886 − 3.20482I
24
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.869654 − 0.049931I
a = 0.988080 − 0.457240I
b = 0.547085 − 0.953523I
3.69558 − 4.59213I −7.41886 + 3.20482I
u = 0.869654 − 0.049931I
a = 1.181660 + 0.546728I
b = 0.973781 + 0.790428I
3.69558 − 4.59213I −7.41886 + 3.20482I
u = −0.460851 + 1.226450I
a = 1.09714 + 0.90713I
b = 0.973781 − 0.790428I
3.69558 + 4.59213I −7.41886 − 3.20482I
u = −0.460851 + 1.226450I
a = −0.257899 + 0.179897I
b = 0.547085 + 0.953523I
3.69558 + 4.59213I −7.41886 − 3.20482I
u = −0.460851 − 1.226450I
a = 1.09714 − 0.90713I
b = 0.973781 + 0.790428I
3.69558 − 4.59213I −7.41886 + 3.20482I
u = −0.460851 − 1.226450I
a = −0.257899 − 0.179897I
b = 0.547085 − 0.953523I
3.69558 − 4.59213I −7.41886 + 3.20482I
u = 0.436607 + 1.253750I
a = −1.14929 + 0.87685I
b = −0.769522 − 0.881187I
7.66009 −3.73050 + 0.I
u = 0.436607 + 1.253750I
a = 0.286388 + 0.376891I
b = −0.769522 + 0.881187I
7.66009 −3.73050 + 0.I
u = 0.436607 − 1.253750I
a = −1.14929 − 0.87685I
b = −0.769522 + 0.881187I
7.66009 −3.73050 + 0.I
u = 0.436607 − 1.253750I
a = 0.286388 − 0.376891I
b = −0.769522 − 0.881187I
7.66009 −3.73050 + 0.I
25
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.525382 + 0.335320I
a = −0.341666 − 0.424256I
b = 0.805413 + 0.489916I
−2.96024 − 1.97241I −11.42428 + 3.68478I
u = −0.525382 + 0.335320I
a = −1.90157 − 1.24427I
b = −1.298590 + 0.085372I
−2.96024 − 1.97241I −11.42428 + 3.68478I
u = −0.525382 − 0.335320I
a = −0.341666 + 0.424256I
b = 0.805413 − 0.489916I
−2.96024 + 1.97241I −11.42428 − 3.68478I
u = −0.525382 − 0.335320I
a = −1.90157 + 1.24427I
b = −1.298590 − 0.085372I
−2.96024 + 1.97241I −11.42428 − 3.68478I
26
VI. I
u
6
= hb + u, 2a − u + 1, u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−1
a
9
=
0
−1
a
12
=
1
2
u −
1
2
−u
a
1
=
3
2
u −
1
2
−u
a
3
=
u
0
a
6
=
−
1
2
u +
1
2
1
a
2
=
1
2
u −
1
2
−u
a
5
=
−u
2
a
11
=
−1
−2u
a
10
=
−1
−2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u + 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
11
, c
12
u
2
+ 1
c
8
, c
10
(u − 1)
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
(y − 1)
2
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
11
, c
12
(y + 1)
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.500000 + 0.500000I
b = − 1.000000I
4.93480 0
u = − 1.000000I
a = −0.500000 − 0.500000I
b = 1.000000I
4.93480 0
30
VII. I
u
7
= hb − 1, u
3
+ u
2
+ 2a + u − 3, u
4
+ 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
12
=
−
1
2
u
3
−
1
2
u
2
−
1
2
u +
3
2
1
a
1
=
−
1
2
u
3
−
1
2
u
2
−
1
2
u +
1
2
1
a
3
=
u
u
3
+ u
a
6
=
1
2
u
3
+
1
2
u
2
+
1
2
u −
1
2
−1
a
2
=
−
1
2
u
3
−
1
2
u
2
+
1
2
u +
1
2
u
3
+ u + 1
a
5
=
u
u
3
+ u
a
11
=
1
0
a
10
=
u
2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −16
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
(u − 1)
4
c
3
, c
4
, c
7
c
9
u
4
+ 1
c
5
, c
11
, c
12
(u + 1)
4
c
8
, c
10
(u
2
+ 1)
2
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y − 1)
4
c
3
, c
4
, c
7
c
9
(y
2
+ 1)
2
c
8
, c
10
(y + 1)
4
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707107 + 0.707107I
a = 1.50000 − 1.20711I
b = 1.00000
−4.93480 −16.0000
u = 0.707107 − 0.707107I
a = 1.50000 + 1.20711I
b = 1.00000
−4.93480 −16.0000
u = −0.707107 + 0.707107I
a = 1.50000 − 0.20711I
b = 1.00000
−4.93480 −16.0000
u = −0.707107 − 0.707107I
a = 1.50000 + 0.20711I
b = 1.00000
−4.93480 −16.0000
34
VIII. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
4
=
−1
0
a
7
=
1
0
a
8
=
1
0
a
9
=
1
0
a
12
=
0
1
a
1
=
−1
1
a
3
=
−1
0
a
6
=
1
−1
a
2
=
−2
1
a
5
=
−1
0
a
11
=
1
0
a
10
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u − 1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
u
c
5
, c
11
, c
12
u + 1
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
y − 1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
y
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−3.28987 −12.0000
38
IX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
9
(u + 1)
2
· (u
10
+ 3u
9
+ 11u
8
+ 18u
7
+ 33u
6
+ 32u
5
+ 34u
4
+ 18u
3
+ 8u
2
+ u + 1)
2
· ((u
12
+ 5u
11
+ ··· + 40u + 9)
2
)(u
13
+ u
12
+ ··· + 45u + 4)
· (u
14
+ 7u
13
+ ··· + 254u + 121)
c
2
, c
6
(u − 1)
5
(u + 1)
4
(u
2
+ 1)
· (u
10
− u
9
− u
8
+ 2u
7
+ 3u
6
− 4u
5
+ 4u
3
− u + 1)
2
· (u
12
− u
11
− 2u
10
+ 4u
9
+ u
8
− 5u
7
− u
6
+ 7u
5
− u
4
− 9u
3
+ 6u
2
+ 2u − 3)
2
· (u
13
+ 3u
12
+ ··· + 3u + 2)(u
14
+ 3u
13
+ ··· + 34u + 11)
c
3
, c
4
, c
7
c
9
u(u
2
+ 1)(u
4
+ 1)(u
4
+ u
2
+ 2)(u
7
+ 2u
5
+ u
4
+ 2u
3
+ u
2
+ 1)
2
· (u
12
− u
11
+ 4u
10
− 4u
9
+ 7u
8
− 7u
7
+ 5u
6
− 5u
5
+ u
4
− u
3
+ 1)
2
· (u
13
+ 3u
11
+ ··· + 2u + 2)(u
20
+ 3u
19
+ ··· + 18u + 5)
c
5
, c
11
, c
12
(u − 1)
4
(u + 1)
5
(u
2
+ 1)
· (u
10
− u
9
− u
8
+ 2u
7
+ 3u
6
− 4u
5
+ 4u
3
− u + 1)
2
· (u
12
− u
11
− 2u
10
+ 4u
9
+ u
8
− 5u
7
− u
6
+ 7u
5
− u
4
− 9u
3
+ 6u
2
+ 2u − 3)
2
· (u
13
+ 3u
12
+ ··· + 3u + 2)(u
14
+ 3u
13
+ ··· + 34u + 11)
c
8
, c
10
u(u − 1)
2
(u
2
+ 1)
2
(u
2
− u + 2)
2
· (u
7
− 4u
6
+ 8u
5
− 7u
4
+ 2u
3
+ 3u
2
− 2u + 1)
2
· ((u
12
− 7u
11
+ ··· + 2u
2
+ 1)
2
)(u
13
− 6u
12
+ ··· + 12u + 4)
· (u
20
− 11u
19
+ ··· − 76u + 25)
39
X. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
11
)(y
10
+ 13y
9
+ ··· + 15y + 1)
2
· ((y
12
+ 3y
11
+ ··· − 196y + 81)
2
)(y
13
+ 11y
12
+ ··· + 913y − 16)
· (y
14
+ y
13
+ ··· + 56242y + 14641)
c
2
, c
5
, c
6
c
11
, c
12
(y − 1)
9
(y + 1)
2
· (y
10
− 3y
9
+ 11y
8
− 18y
7
+ 33y
6
− 32y
5
+ 34y
4
− 18y
3
+ 8y
2
− y + 1)
2
· ((y
12
− 5y
11
+ ··· − 40y + 9)
2
)(y
13
− y
12
+ ··· + 45y − 4)
· (y
14
− 7y
13
+ ··· − 254y + 121)
c
3
, c
4
, c
7
c
9
y(y + 1)
2
(y
2
+ 1)
2
(y
2
+ y + 2)
2
· (y
7
+ 4y
6
+ 8y
5
+ 7y
4
+ 2y
3
− 3y
2
− 2y − 1)
2
· ((y
12
+ 7y
11
+ ··· + 2y
2
+ 1)
2
)(y
13
+ 6y
12
+ ··· + 12y − 4)
· (y
20
+ 11y
19
+ ··· + 76y + 25)
c
8
, c
10
y(y − 1)
2
(y + 1)
4
(y
2
+ 3y + 4)
2
· (y
7
+ 12y
5
+ 3y
4
+ 22y
3
− 3y
2
− 2y − 1)
2
· ((y
12
− 5y
11
+ ··· + 4y + 1)
2
)(y
13
+ 6y
12
+ ··· + 592y − 16)
· (y
20
− 5y
19
+ ··· − 2276y + 625)
40
