11n
165
(K11n
165
)
A knot diagram
1
Linearized knot diagam
8 5 1 11 3 10 3 4 7 5 9
Solving Sequence
1,4 3,9
8 7 11 5 2 10 6
c
3
c
8
c
7
c
11
c
4
c
2
c
10
c
6
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−766790u
19
+ 10314727u
18
+ ··· + 1340393b − 9262246,
− 9262246u
19
+ 139639714u
18
+ ··· + 17425109a + 534767514, u
20
− 14u
19
+ ··· − 140u + 13i
I
u
2
= h−a
3
u
3
+ 4u
3
a
2
+ ··· + 75a − 12,
− a
3
u
2
+ a
4
− 2a
3
u + 3a
2
u
2
− 2u
3
a − 2a
3
+ 5a
2
u − 4u
2
a + u
3
+ 5a
2
− 5au − u
2
− a − 3u − 6,
u
4
+ u
3
+ u
2
− u + 1i
I
u
3
= h25u
11
+ 234u
10
+ ··· + 167b + 63, −63u
11
− 416u
10
+ ··· + 167a + 55,
u
12
+ 7u
11
+ 26u
10
+ 60u
9
+ 91u
8
+ 87u
7
+ 46u
6
+ 5u
5
− 5u
4
− u
3
+ u
2
+ 1i
I
u
4
= hu
3
− au + u
2
+ b − 1, −u
3
a − 3u
2
a − u
3
+ a
2
− 3au − 3u
2
− a − 4u − 2, u
4
+ 2u
3
+ 2u
2
+ u + 1i
I
u
5
= h−u
3
− au − 2u
2
+ b − 2u, u
2
a + a
2
+ 2au + 2a − 1, u
4
+ 2u
3
+ 2u
2
+ u + 1i
I
v
1
= ha, b
2
+ b + 1, v −1i
* 6 irreducible components of dim
C
= 0, with total 66 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
=
h−7.67×10
5
u
19
+1.03×10
7
u
18
+· · ·+1.34×10
6
b−9.26×10
6
, −9.26×10
6
u
19
+
1.40 × 10
8
u
18
+ · · · + 1.74 × 10
7
a + 5.35 × 10
8
, u
20
− 14u
19
+ · · · − 140u + 13i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
9
=
0.531546u
19
− 8.01371u
18
+ ··· + 299.293u − 30.6895
0.572064u
19
− 7.69530u
18
+ ··· − 43.7270u + 6.91010
a
8
=
1.10361u
19
− 15.7090u
18
+ ··· + 255.567u − 23.7794
0.572064u
19
− 7.69530u
18
+ ··· − 43.7270u + 6.91010
a
7
=
1.60433u
19
− 22.5319u
18
+ ··· + 349.827u − 34.0496
1.31746u
19
− 15.8315u
18
+ ··· − 63.4249u + 9.34363
a
11
=
1.03159u
19
− 13.4015u
18
+ ··· + 183.124u − 20.5381
−1.04074u
19
+ 13.5128u
18
+ ··· − 122.884u + 13.4107
a
5
=
1.71042u
19
− 22.8588u
18
+ ··· + 203.782u − 20.2563
−0.0294787u
19
+ 1.23697u
18
+ ··· − 85.9094u + 8.70582
a
2
=
0.00767507u
19
− 0.391944u
18
+ ··· + 67.6479u − 7.24644
0.0168279u
19
− 0.503255u
18
+ ··· + 9.40885u − 0.118987
a
10
=
−0.0194671u
19
− 1.23452u
18
+ ··· + 309.121u − 35.2533
1.74036u
19
− 23.1238u
18
+ ··· + 166.693u − 14.1659
a
6
=
−1.77426u
19
+ 23.5639u
18
+ ··· − 159.740u + 14.8304
−0.0610127u
19
− 0.487643u
18
+ ··· + 111.512u − 11.1602
a
6
=
−1.77426u
19
+ 23.5639u
18
+ ··· − 159.740u + 14.8304
−0.0610127u
19
− 0.487643u
18
+ ··· + 111.512u − 11.1602
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
2833789
1340393
u
19
+
38974772
1340393
u
18
+ ··· −
300276118
1340393
u +
19362744
1340393
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− u
19
+ ··· − 4u + 1
c
2
, c
5
u
20
+ u
19
+ ··· + 2u + 1
c
3
u
20
− 14u
19
+ ··· − 140u + 13
c
4
, c
10
u
20
− 14u
19
+ ··· − 2560u + 256
c
6
, c
9
u
20
+ 9u
19
+ ··· + 28u + 13
c
7
u
20
+ u
19
+ ··· + 17u + 21
c
8
, c
11
u
20
− 2u
19
+ ··· − 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
− 5y
19
+ ··· − 14y + 1
c
2
, c
5
y
20
+ 23y
19
+ ··· + 10y + 1
c
3
y
20
+ 4y
19
+ ··· + 498y + 169
c
4
, c
10
y
20
+ 12y
19
+ ··· − 65536y + 65536
c
6
, c
9
y
20
+ 9y
19
+ ··· + 698y + 169
c
7
y
20
− 19y
19
+ ··· − 2641y + 441
c
8
, c
11
y
20
+ 20y
18
+ ··· + 4y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.643832 + 0.539702I
a = −1.74604 + 0.04327I
b = 1.14751 + 0.91448I
−7.56901 − 4.35325I 6.00959 − 2.36650I
u = 0.643832 − 0.539702I
a = −1.74604 − 0.04327I
b = 1.14751 − 0.91448I
−7.56901 + 4.35325I 6.00959 + 2.36650I
u = 1.198930 + 0.321628I
a = 0.470312 − 0.608504I
b = −0.759582 + 0.578288I
0.87661 + 1.80368I −0.33009 − 3.39562I
u = 1.198930 − 0.321628I
a = 0.470312 + 0.608504I
b = −0.759582 − 0.578288I
0.87661 − 1.80368I −0.33009 + 3.39562I
u = 0.808778 + 1.074790I
a = 1.154450 − 0.190358I
b = −1.13829 − 1.08683I
2.70163 − 8.25419I 1.74639 + 5.26030I
u = 0.808778 − 1.074790I
a = 1.154450 + 0.190358I
b = −1.13829 + 1.08683I
2.70163 + 8.25419I 1.74639 − 5.26030I
u = −0.081606 + 0.559081I
a = −1.233730 + 0.525348I
b = 0.193032 + 0.732624I
1.06285 + 1.12930I 5.13966 − 4.07834I
u = −0.081606 − 0.559081I
a = −1.233730 − 0.525348I
b = 0.193032 − 0.732624I
1.06285 − 1.12930I 5.13966 + 4.07834I
u = 0.80616 + 1.24885I
a = −0.724968 − 0.008424I
b = 0.573922 + 0.912168I
6.49001 − 1.26443I 4.97798 + 1.96291I
u = 0.80616 − 1.24885I
a = −0.724968 + 0.008424I
b = 0.573922 − 0.912168I
6.49001 + 1.26443I 4.97798 − 1.96291I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.01334 + 1.17077I
a = −1.029040 + 0.119371I
b = 1.18252 + 1.08380I
1.5683 − 15.8169I −0.23034 + 8.70601I
u = 1.01334 − 1.17077I
a = −1.029040 − 0.119371I
b = 1.18252 − 1.08380I
1.5683 + 15.8169I −0.23034 − 8.70601I
u = 0.307600 + 0.248640I
a = 2.41339 + 0.42231I
b = −0.637356 − 0.729970I
−0.01507 − 1.86524I 0.60762 + 4.36679I
u = 0.307600 − 0.248640I
a = 2.41339 − 0.42231I
b = −0.637356 + 0.729970I
−0.01507 + 1.86524I 0.60762 − 4.36679I
u = −0.34327 + 1.61845I
a = 0.214787 + 0.114493I
b = 0.259032 − 0.308320I
−4.19435 + 1.15765I 2.14031 − 7.95914I
u = −0.34327 − 1.61845I
a = 0.214787 − 0.114493I
b = 0.259032 + 0.308320I
−4.19435 − 1.15765I 2.14031 + 7.95914I
u = 1.15645 + 1.28057I
a = 0.604483 + 0.080235I
b = −0.596309 − 0.866871I
5.15014 − 7.97058I 2.89077 + 7.60145I
u = 1.15645 − 1.28057I
a = 0.604483 − 0.080235I
b = −0.596309 + 0.866871I
5.15014 + 7.97058I 2.89077 − 7.60145I
u = 1.48978 + 0.91920I
a = −0.277498 + 0.393931I
b = 0.775515 − 0.331794I
0.50861 + 7.39141I −3.95189 − 9.17426I
u = 1.48978 − 0.91920I
a = −0.277498 − 0.393931I
b = 0.775515 + 0.331794I
0.50861 − 7.39141I −3.95189 + 9.17426I
6
II.
I
u
2
= h−a
3
u
3
+4u
3
a
2
+· · ·+75a−12, −2u
3
a+u
3
+· · ·−a−6, u
4
+u
3
+u
2
−u+1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
9
=
a
1
45
a
3
u
3
−
4
45
u
3
a
2
+ ··· −
5
3
a +
4
15
a
8
=
1
45
a
3
u
3
−
4
45
u
3
a
2
+ ··· −
2
3
a +
4
15
1
45
a
3
u
3
−
4
45
u
3
a
2
+ ··· −
5
3
a +
4
15
a
7
=
0.244444a
3
u
3
+ 0.0222222a
2
u
3
+ ··· + 0.666667a − 0.0666667
7
15
a
3
u
3
−
13
15
u
3
a
2
+ ··· − a +
3
5
a
11
=
a
2
u
−0.244444a
3
u
3
− 0.0222222a
2
u
3
+ ··· + 0.333333a − 0.933333
a
5
=
2
45
a
3
u
3
−
8
45
u
3
a
2
+ ··· −
1
3
a +
8
15
−0.244444a
3
u
3
− 0.0222222a
2
u
3
+ ··· + 0.333333a + 0.0666667
a
2
=
−0.688889a
3
u
3
− 0.244444a
2
u
3
+ ··· − 0.333333a − 0.266667
−
4
9
a
3
u
3
−
2
9
u
3
a
2
+ ··· −
2
3
a +
2
3
a
10
=
0.288889a
3
u
3
− 0.155556a
2
u
3
+ ··· − 0.666667a + 0.466667
−0.244444a
3
u
3
− 0.0222222a
2
u
3
+ ··· + 0.333333a + 0.0666667
a
6
=
2
9
a
3
u
3
+
1
9
u
3
a
2
+ ··· +
1
3
a −
1
3
0.177778a
3
u
3
− 0.711111a
2
u
3
+ ··· − 0.333333a + 0.133333
a
6
=
2
9
a
3
u
3
+
1
9
u
3
a
2
+ ··· +
1
3
a −
1
3
0.177778a
3
u
3
− 0.711111a
2
u
3
+ ··· − 0.333333a + 0.133333
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
44
45
a
3
u
3
−
76
45
a
3
u
2
−
4
45
u
3
a
2
+
16
15
a
3
u +
124
45
a
2
u
2
−
4
3
u
3
a −
52
45
a
3
−
4
15
a
2
u −
8
3
u
2
a +
68
15
u
3
+
28
45
a
2
− 4au +
172
15
u
2
+
4
3
a +
48
5
u −
26
15
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
+ 2u
15
+ ··· + 10u + 25
c
2
, c
5
u
16
− u
15
+ ··· − 12u + 3
c
3
(u
4
+ u
3
+ u
2
− u + 1)
4
c
4
, c
10
(u
2
+ u + 1)
8
c
6
, c
9
(u
4
− u
3
+ u
2
+ u + 1)
4
c
7
u
16
− 2u
15
+ ··· + 264u + 111
c
8
, c
11
u
16
+ u
15
+ ··· − 12u + 3
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ 34y
14
+ ··· − 4150y + 625
c
2
, c
5
y
16
+ 3y
15
+ ··· + 402y + 9
c
3
, c
6
, c
9
(y
4
+ y
3
+ 5y
2
+ y + 1)
4
c
4
, c
10
(y
2
+ y + 1)
8
c
7
y
16
− 16y
15
+ ··· − 83682y + 12321
c
8
, c
11
y
16
− 5y
15
+ ··· − 102y + 9
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.433380 + 0.525827I
a = −0.671245 + 0.201645I
b = 1.22825 − 1.67883I
2.24108 − 6.71592I 1.29059 + 13.74348I
u = 0.433380 + 0.525827I
a = 1.48035 + 0.37541I
b = −1.59236 + 0.24028I
2.24108 − 2.65615I 1.29059 + 6.81528I
u = 0.433380 + 0.525827I
a = 1.21416 − 2.02760I
b = −0.444152 − 0.941106I
2.24108 − 2.65615I 1.29059 + 6.81528I
u = 0.433380 + 0.525827I
a = 0.75482 + 2.95796I
b = 0.396935 + 0.265570I
2.24108 − 6.71592I 1.29059 + 13.74348I
u = 0.433380 − 0.525827I
a = −0.671245 − 0.201645I
b = 1.22825 + 1.67883I
2.24108 + 6.71592I 1.29059 − 13.74348I
u = 0.433380 − 0.525827I
a = 1.48035 − 0.37541I
b = −1.59236 − 0.24028I
2.24108 + 2.65615I 1.29059 − 6.81528I
u = 0.433380 − 0.525827I
a = 1.21416 + 2.02760I
b = −0.444152 + 0.941106I
2.24108 + 2.65615I 1.29059 − 6.81528I
u = 0.433380 − 0.525827I
a = 0.75482 − 2.95796I
b = 0.396935 − 0.265570I
2.24108 + 6.71592I 1.29059 − 13.74348I
u = −0.93338 + 1.13249I
a = 0.937489 + 0.356410I
b = −0.928296 + 1.033700I
−2.24108 + 6.71592I −1.29059 − 13.74348I
u = −0.93338 + 1.13249I
a = −0.945855 − 0.040136I
b = 1.27866 − 0.72903I
−2.24108 + 6.71592I −1.29059 − 13.74348I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.93338 + 1.13249I
a = −0.556441 − 0.371428I
b = 0.500964 − 0.132390I
−2.24108 + 2.65615I −1.29059 − 6.81528I
u = −0.93338 + 1.13249I
a = 0.286722 + 0.206045I
b = −0.940007 + 0.283478I
−2.24108 + 2.65615I −1.29059 − 6.81528I
u = −0.93338 − 1.13249I
a = 0.937489 − 0.356410I
b = −0.928296 − 1.033700I
−2.24108 − 6.71592I −1.29059 + 13.74348I
u = −0.93338 − 1.13249I
a = −0.945855 + 0.040136I
b = 1.27866 + 0.72903I
−2.24108 − 6.71592I −1.29059 + 13.74348I
u = −0.93338 − 1.13249I
a = −0.556441 + 0.371428I
b = 0.500964 + 0.132390I
−2.24108 − 2.65615I −1.29059 + 6.81528I
u = −0.93338 − 1.13249I
a = 0.286722 − 0.206045I
b = −0.940007 − 0.283478I
−2.24108 − 2.65615I −1.29059 + 6.81528I
11
III. I
u
3
= h25u
11
+ 234u
10
+ · · · + 167b + 63, −63u
11
− 416u
10
+ · · · + 167a +
55, u
12
+ 7u
11
+ · · · + u
2
+ 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
9
=
0.377246u
11
+ 2.49102u
10
+ ··· − 1.97006u − 0.329341
−0.149701u
11
− 1.40120u
10
+ ··· − 0.329341u − 0.377246
a
8
=
0.227545u
11
+ 1.08982u
10
+ ··· − 2.29940u − 0.706587
−0.149701u
11
− 1.40120u
10
+ ··· − 0.329341u − 0.377246
a
7
=
−0.155689u
11
− 1.37725u
10
+ ··· − 1.74251u − 0.832335
0.221557u
11
+ 1.11377u
10
+ ··· − 0.712575u − 0.161677
a
11
=
−0.119760u
11
− 1.52096u
10
+ ··· − 0.263473u − 2.10180
−0.682635u
11
− 4.26946u
10
+ ··· − 1.10180u + 0.119760
a
5
=
−2.01198u
11
− 12.9521u
10
+ ··· − 0.826347u + 1.08982
0.622754u
11
+ 4.50898u
10
+ ··· − 0.0299401u + 1.32934
a
2
=
−0.976048u
11
− 7.09581u
10
+ ··· − 4.34731u − 1.17964
−0.173653u
11
− 1.30539u
10
+ ··· − 0.982036u + 0.802395
a
10
=
1.14970u
11
+ 8.40120u
10
+ ··· + 0.329341u − 0.622754
0.712575u
11
+ 4.14970u
10
+ ··· − 0.832335u + 0.155689
a
6
=
−2.18563u
11
− 14.2575u
10
+ ··· − 2.80838u + 0.892216
0.634731u
11
+ 4.46108u
10
+ ··· − 0.203593u + 1.23952
a
6
=
−2.18563u
11
− 14.2575u
10
+ ··· − 2.80838u + 0.892216
0.634731u
11
+ 4.46108u
10
+ ··· − 0.203593u + 1.23952
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
790
167
u
11
−
5023
167
u
10
−
17057
167
u
9
−
34789
167
u
8
−
43919
167
u
7
−
28839
167
u
6
−
2343
167
u
5
+
9799
167
u
4
+
2707
167
u
3
−
263
167
u
2
+
99
167
u −
421
167
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
− u
10
+ 3u
8
+ 3u
7
− 3u
6
+ 4u
5
+ 2u
4
− 6u
3
+ 9u
2
− 4u + 3
c
2
u
12
− 2u
11
+ 3u
10
− u
9
− u
8
+ u
7
+ 2u
6
− 5u
5
+ 8u
4
− 3u
3
− 3u
2
+ 2u + 1
c
3
u
12
+ 7u
11
+ ··· + u
2
+ 1
c
4
u
12
+ 2u
11
+ ··· + 5u + 3
c
5
u
12
+ 2u
11
+ 3u
10
+ u
9
− u
8
− u
7
+ 2u
6
+ 5u
5
+ 8u
4
+ 3u
3
− 3u
2
− 2u + 1
c
6
u
12
+ 4u
11
+ ··· + 5u
2
+ 1
c
7
u
12
− 2u
10
+ ··· + 11u + 13
c
8
, c
11
u
12
+ u
11
+ ··· − 2u + 1
c
9
u
12
− 4u
11
+ ··· + 5u
2
+ 1
c
10
u
12
− 2u
11
+ ··· − 5u + 3
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 2y
11
+ ··· + 38y + 9
c
2
, c
5
y
12
+ 2y
11
+ ··· − 10y + 1
c
3
y
12
+ 3y
11
+ ··· + 2y + 1
c
4
, c
10
y
12
+ 12y
11
+ ··· + 35y + 9
c
6
, c
9
y
12
+ 8y
11
+ ··· + 10y + 1
c
7
y
12
− 4y
11
+ ··· + 139y + 169
c
8
, c
11
y
12
− 5y
11
+ ··· − 12y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.766436 + 0.608986I
a = 1.50954 + 0.04369I
b = −1.18358 + 0.88580I
−7.90320 + 4.59198I −10.36791 − 8.72045I
u = −0.766436 − 0.608986I
a = 1.50954 − 0.04369I
b = −1.18358 − 0.88580I
−7.90320 − 4.59198I −10.36791 + 8.72045I
u = −0.99500 + 1.07131I
a = −0.940323 − 0.168055I
b = 1.115660 − 0.840164I
−2.52113 + 5.90216I −4.45034 − 3.90745I
u = −0.99500 − 1.07131I
a = −0.940323 + 0.168055I
b = 1.115660 + 0.840164I
−2.52113 − 5.90216I −4.45034 + 3.90745I
u = −1.27015 + 0.78597I
a = −0.549722 − 0.184546I
b = 0.843277 − 0.197663I
−3.20993 + 2.02643I −9.74479 − 3.88837I
u = −1.27015 − 0.78597I
a = −0.549722 + 0.184546I
b = 0.843277 + 0.197663I
−3.20993 − 2.02643I −9.74479 + 3.88837I
u = 0.031039 + 0.489412I
a = −1.34512 − 1.99487I
b = 0.934560 − 0.720234I
2.75349 + 1.52030I 2.99434 − 1.95006I
u = 0.031039 − 0.489412I
a = −1.34512 + 1.99487I
b = 0.934560 + 0.720234I
2.75349 − 1.52030I 2.99434 + 1.95006I
u = 0.422290 + 0.201900I
a = −0.80651 + 1.96505I
b = −0.737321 + 0.666987I
2.29385 − 5.81227I 0.92217 + 3.42975I
u = 0.422290 − 0.201900I
a = −0.80651 − 1.96505I
b = −0.737321 − 0.666987I
2.29385 + 5.81227I 0.92217 − 3.42975I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.92174 + 1.81742I
a = 0.132122 + 0.193032I
b = −0.472602 + 0.062197I
−4.57255 + 1.04234I −18.3535 − 2.2196I
u = −0.92174 − 1.81742I
a = 0.132122 − 0.193032I
b = −0.472602 − 0.062197I
−4.57255 − 1.04234I −18.3535 + 2.2196I
16
IV.
I
u
4
= hu
3
− au + u
2
+ b − 1, −u
3
a − u
3
+ · · · − a − 2, u
4
+ 2u
3
+ 2u
2
+ u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
9
=
a
−u
3
+ au − u
2
+ 1
a
8
=
−u
3
+ au − u
2
+ a + 1
−u
3
+ au − u
2
+ 1
a
7
=
−u
3
a − u
2
a + a + 1
u
3
a + u
2
a − u
3
+ au − 2u
2
+ a
a
11
=
u
3
a + u
2
a + u
3
+ 2u
2
− a + u − 1
−u
2
− u − 1
a
5
=
−u
2
a − 2au − u
2
− a − 2u − 1
−u
2
− u
a
2
=
u
3
a + u
2
a + u
3
+ u
2
− 2a − u − 2
−a + u
a
10
=
−u
2
a − 2au − a − u − 1
−u
2
− u
a
6
=
2u
2
a + 3au + u
2
+ 2a + 2u + 2
u
3
a + u
2
a + au + a + u
a
6
=
2u
2
a + 3au + u
2
+ 2a + 2u + 2
u
3
a + u
2
a + au + a + u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u
3
− 16u
2
− 8u − 2
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− 2u
7
− 3u
6
+ u
5
+ 9u
4
+ 16u
3
+ 14u
2
+ 6u + 1
c
2
, c
5
u
8
+ 3u
7
+ 6u
6
+ 13u
5
+ 22u
4
+ 27u
3
+ 22u
2
+ 8u + 1
c
3
(u
4
+ 2u
3
+ 2u
2
+ u + 1)
2
c
4
, c
10
(u
2
+ u + 1)
4
c
6
, c
9
(u
4
− 2u
3
+ 2u
2
− u + 1)
2
c
7
u
8
+ 2u
7
− u
6
− 7u
5
− 9u
4
+ 12u
2
+ 14u + 7
c
8
, c
11
u
8
− 3u
7
+ 2u
6
+ u
5
+ u
3
− 2u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 10y
7
+ 31y
6
+ 37y
5
− 9y
4
− 22y
3
+ 22y
2
− 8y + 1
c
2
, c
5
y
8
+ 3y
7
+ 2y
6
− 23y
5
+ 43y
3
+ 96y
2
− 20y + 1
c
3
, c
6
, c
9
(y
4
+ 2y
2
+ 3y + 1)
2
c
4
, c
10
(y
2
+ y + 1)
4
c
7
y
8
− 6y
7
+ 11y
6
− 7y
5
+ 15y
4
− 34y
3
+ 18y
2
− 28y + 49
c
8
, c
11
y
8
− 5y
7
+ 10y
6
+ 5y
5
− 12y
4
+ 7y
3
+ 4y
2
− 4y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.070696 + 0.758745I
a = −1.235260 − 0.133925I
b = 1.70673 − 0.62857I
3.39192 + 4.62527I 7.53952 − 4.38302I
u = 0.070696 + 0.758745I
a = 0.61352 + 2.30657I
b = −0.014287 + 0.946719I
3.39192 + 4.62527I 7.53952 − 4.38302I
u = 0.070696 − 0.758745I
a = −1.235260 + 0.133925I
b = 1.70673 + 0.62857I
3.39192 − 4.62527I 7.53952 + 4.38302I
u = 0.070696 − 0.758745I
a = 0.61352 − 2.30657I
b = −0.014287 − 0.946719I
3.39192 − 4.62527I 7.53952 + 4.38302I
u = −1.070700 + 0.758745I
a = −0.337294 − 0.598758I
b = 0.623004 − 0.162710I
−3.39192 + 0.56550I −7.53952 + 2.54518I
u = −1.070700 + 0.758745I
a = 0.459039 + 0.173330I
b = −0.815445 − 0.385168I
−3.39192 + 0.56550I −7.53952 + 2.54518I
u = −1.070700 − 0.758745I
a = −0.337294 + 0.598758I
b = 0.623004 + 0.162710I
−3.39192 − 0.56550I −7.53952 − 2.54518I
u = −1.070700 − 0.758745I
a = 0.459039 − 0.173330I
b = −0.815445 + 0.385168I
−3.39192 − 0.56550I −7.53952 − 2.54518I
20
V.
I
u
5
= h−u
3
−au −2u
2
+b −2u, u
2
a + a
2
+2au +2a −1, u
4
+2u
3
+2u
2
+u +1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
9
=
a
u
3
+ au + 2u
2
+ 2u
a
8
=
u
3
+ au + 2u
2
+ a + 2u
u
3
+ au + 2u
2
+ 2u
a
7
=
−u
3
a − u
2
a + u
2
+ a + u
u
3
a + u
2
a + 2u
3
+ au + 3u
2
+ a + 2u + 1
a
11
=
−u
3
a − 2u
2
a − 2au + u
u
2
+ u
a
5
=
−u
2
a − u
3
− 2au − u
2
− a + 1
u
2
+ u + 1
a
2
=
−u
3
a − 3u
2
a − 3au + 1
−u
2
a − au − u
2
+ 1
a
10
=
−u
2
a − u
3
− 2au − 2u
2
− a − u
u
2
+ u + 1
a
6
=
2u
2
a + u
3
+ 3au + 2u
2
+ 2a + u − 1
u
3
a + u
2
a + u
3
+ au + u
2
+ a
a
6
=
2u
2
a + u
3
+ 3au + 2u
2
+ 2a + u − 1
u
3
a + u
2
a + u
3
+ au + u
2
+ a
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u
3
− 8u
2
+ 2
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
+ u
7
+ 3u
6
− 2u
5
+ 3u
4
− 5u
3
− 7u
2
+ 6u + 7
c
2
, c
5
u
8
− 3u
7
+ 9u
6
− 17u
5
+ 25u
4
− 30u
3
+ 25u
2
− 16u + 7
c
3
(u
4
+ 2u
3
+ 2u
2
+ u + 1)
2
c
4
, c
10
(u
2
+ u + 1)
4
c
6
, c
9
(u
4
− 2u
3
+ 2u
2
− u + 1)
2
c
7
u
8
− u
7
+ 5u
6
− 4u
5
− 3u
4
− 3u
3
+ 9u
2
+ 2u + 1
c
8
, c
11
u
8
+ 3u
7
+ 5u
6
+ u
5
− 3u
4
− 2u
3
+ 9u
2
+ 4u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
+ 5y
7
+ 19y
6
+ 10y
5
− 51y
4
− y
3
+ 151y
2
− 134y + 49
c
2
, c
5
y
8
+ 9y
7
+ 29y
6
+ 31y
5
− 27y
4
− 68y
3
+ 15y
2
+ 94y + 49
c
3
, c
6
, c
9
(y
4
+ 2y
2
+ 3y + 1)
2
c
4
, c
10
(y
2
+ y + 1)
4
c
7
y
8
+ 9y
7
+ 11y
6
− 34y
5
+ 81y
4
− 37y
3
+ 87y
2
+ 14y + 1
c
8
, c
11
y
8
+ y
7
+ 13y
6
− y
5
+ 81y
4
− 56y
3
+ 91y
2
+ 2y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.070696 + 0.758745I
a = 0.344185 − 0.247546I
b = −0.90959 + 1.55027I
3.39192 + 0.56550I 7.53952 + 2.54518I
u = 0.070696 + 0.758745I
a = −1.91488 − 1.37722I
b = −0.212157 − 0.243648I
3.39192 + 0.56550I 7.53952 + 2.54518I
u = 0.070696 − 0.758745I
a = 0.344185 + 0.247546I
b = −0.90959 − 1.55027I
3.39192 − 0.56550I 7.53952 − 2.54518I
u = 0.070696 − 0.758745I
a = −1.91488 + 1.37722I
b = −0.212157 + 0.243648I
3.39192 − 0.56550I 7.53952 − 2.54518I
u = −1.070700 + 0.758745I
a = 0.806781 + 0.042368I
b = −1.27422 + 1.00737I
−3.39192 + 4.62527I −7.53952 − 4.38302I
u = −1.070700 + 0.758745I
a = −1.236090 + 0.064913I
b = 0.895964 − 0.566778I
−3.39192 + 4.62527I −7.53952 − 4.38302I
u = −1.070700 − 0.758745I
a = 0.806781 − 0.042368I
b = −1.27422 − 1.00737I
−3.39192 − 4.62527I −7.53952 + 4.38302I
u = −1.070700 − 0.758745I
a = −1.236090 − 0.064913I
b = 0.895964 + 0.566778I
−3.39192 − 4.62527I −7.53952 + 4.38302I
24
VI. I
v
1
= ha, b
2
+ b + 1, v − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
1
0
a
3
=
1
0
a
9
=
0
b
a
8
=
b
b
a
7
=
0
b
a
11
=
1
b + 1
a
5
=
−b
−b
a
2
=
b + 2
b + 1
a
10
=
0
b
a
6
=
0
b
a
6
=
0
b
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4b − 2
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
8
, c
11
u
2
+ u + 1
c
3
, c
6
, c
9
u
2
c
4
, c
10
u
2
− u + 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
8
c
10
, c
11
y
2
+ y + 1
c
3
, c
6
, c
9
y
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −0.500000 + 0.866025I
2.02988I 0. − 3.46410I
v = 1.00000
a = 0
b = −0.500000 − 0.866025I
− 2.02988I 0. + 3.46410I
28
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)(u
8
− 2u
7
− 3u
6
+ u
5
+ 9u
4
+ 16u
3
+ 14u
2
+ 6u + 1)
· (u
8
+ u
7
+ 3u
6
− 2u
5
+ 3u
4
− 5u
3
− 7u
2
+ 6u + 7)
· (u
12
− u
10
+ 3u
8
+ 3u
7
− 3u
6
+ 4u
5
+ 2u
4
− 6u
3
+ 9u
2
− 4u + 3)
· (u
16
+ 2u
15
+ ··· + 10u + 25)(u
20
− u
19
+ ··· − 4u + 1)
c
2
(u
2
+ u + 1)(u
8
− 3u
7
+ ··· − 16u + 7)
· (u
8
+ 3u
7
+ 6u
6
+ 13u
5
+ 22u
4
+ 27u
3
+ 22u
2
+ 8u + 1)
· (u
12
− 2u
11
+ 3u
10
− u
9
− u
8
+ u
7
+ 2u
6
− 5u
5
+ 8u
4
− 3u
3
− 3u
2
+ 2u + 1)
· (u
16
− u
15
+ ··· − 12u + 3)(u
20
+ u
19
+ ··· + 2u + 1)
c
3
u
2
(u
4
+ u
3
+ u
2
− u + 1)
4
(u
4
+ 2u
3
+ 2u
2
+ u + 1)
4
· (u
12
+ 7u
11
+ ··· + u
2
+ 1)(u
20
− 14u
19
+ ··· − 140u + 13)
c
4
(u
2
− u + 1)(u
2
+ u + 1)
16
(u
12
+ 2u
11
+ ··· + 5u + 3)
· (u
20
− 14u
19
+ ··· − 2560u + 256)
c
5
(u
2
+ u + 1)(u
8
− 3u
7
+ ··· − 16u + 7)
· (u
8
+ 3u
7
+ 6u
6
+ 13u
5
+ 22u
4
+ 27u
3
+ 22u
2
+ 8u + 1)
· (u
12
+ 2u
11
+ 3u
10
+ u
9
− u
8
− u
7
+ 2u
6
+ 5u
5
+ 8u
4
+ 3u
3
− 3u
2
− 2u + 1)
· (u
16
− u
15
+ ··· − 12u + 3)(u
20
+ u
19
+ ··· + 2u + 1)
c
6
u
2
(u
4
− 2u
3
+ 2u
2
− u + 1)
4
(u
4
− u
3
+ u
2
+ u + 1)
4
· (u
12
+ 4u
11
+ ··· + 5u
2
+ 1)(u
20
+ 9u
19
+ ··· + 28u + 13)
c
7
(u
2
+ u + 1)(u
8
− u
7
+ 5u
6
− 4u
5
− 3u
4
− 3u
3
+ 9u
2
+ 2u + 1)
· (u
8
+ 2u
7
− u
6
− 7u
5
− 9u
4
+ 12u
2
+ 14u + 7)
· (u
12
− 2u
10
+ ··· + 11u + 13)(u
16
− 2u
15
+ ··· + 264u + 111)
· (u
20
+ u
19
+ ··· + 17u + 21)
c
8
, c
11
(u
2
+ u + 1)(u
8
− 3u
7
+ 2u
6
+ u
5
+ u
3
− 2u + 1)
· (u
8
+ 3u
7
+ 5u
6
+ u
5
− 3u
4
− 2u
3
+ 9u
2
+ 4u + 1)
· (u
12
+ u
11
+ ··· − 2u + 1)(u
16
+ u
15
+ ··· − 12u + 3)
· (u
20
− 2u
19
+ ··· − 4u + 1)
c
9
u
2
(u
4
− 2u
3
+ 2u
2
− u + 1)
4
(u
4
− u
3
+ u
2
+ u + 1)
4
· (u
12
− 4u
11
+ ··· + 5u
2
+ 1)(u
20
+ 9u
19
+ ··· + 28u + 13)
c
10
(u
2
− u + 1)(u
2
+ u + 1)
16
(u
12
− 2u
11
+ ··· − 5u + 3)
· (u
20
− 14u
19
+ ··· − 2560u + 256)
29
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
8
− 10y
7
+ ··· − 8y + 1)
· (y
8
+ 5y
7
+ 19y
6
+ 10y
5
− 51y
4
− y
3
+ 151y
2
− 134y + 49)
· (y
12
− 2y
11
+ ··· + 38y + 9)(y
16
+ 34y
14
+ ··· − 4150y + 625)
· (y
20
− 5y
19
+ ··· − 14y + 1)
c
2
, c
5
(y
2
+ y + 1)(y
8
+ 3y
7
+ 2y
6
− 23y
5
+ 43y
3
+ 96y
2
− 20y + 1)
· (y
8
+ 9y
7
+ 29y
6
+ 31y
5
− 27y
4
− 68y
3
+ 15y
2
+ 94y + 49)
· (y
12
+ 2y
11
+ ··· − 10y + 1)(y
16
+ 3y
15
+ ··· + 402y + 9)
· (y
20
+ 23y
19
+ ··· + 10y + 1)
c
3
y
2
(y
4
+ 2y
2
+ 3y + 1)
4
(y
4
+ y
3
+ 5y
2
+ y + 1)
4
· (y
12
+ 3y
11
+ ··· + 2y + 1)(y
20
+ 4y
19
+ ··· + 498y + 169)
c
4
, c
10
((y
2
+ y + 1)
17
)(y
12
+ 12y
11
+ ··· + 35y + 9)
· (y
20
+ 12y
19
+ ··· − 65536y + 65536)
c
6
, c
9
y
2
(y
4
+ 2y
2
+ 3y + 1)
4
(y
4
+ y
3
+ 5y
2
+ y + 1)
4
· (y
12
+ 8y
11
+ ··· + 10y + 1)(y
20
+ 9y
19
+ ··· + 698y + 169)
c
7
(y
2
+ y + 1)(y
8
− 6y
7
+ ··· − 28y + 49)
· (y
8
+ 9y
7
+ 11y
6
− 34y
5
+ 81y
4
− 37y
3
+ 87y
2
+ 14y + 1)
· (y
12
− 4y
11
+ ··· + 139y + 169)(y
16
− 16y
15
+ ··· − 83682y + 12321)
· (y
20
− 19y
19
+ ··· − 2641y + 441)
c
8
, c
11
(y
2
+ y + 1)(y
8
− 5y
7
+ 10y
6
+ 5y
5
− 12y
4
+ 7y
3
+ 4y
2
− 4y + 1)
· (y
8
+ y
7
+ 13y
6
− y
5
+ 81y
4
− 56y
3
+ 91y
2
+ 2y + 1)
· (y
12
− 5y
11
+ ··· − 12y + 1)(y
16
− 5y
15
+ ··· − 102y + 9)
· (y
20
+ 20y
18
+ ··· + 4y + 1)
30
