11n
157
(K11n
157
)
A knot diagram
1
Linearized knot diagam
6 7 1 11 8 9 4 2 1 8 7
Solving Sequence
7,9 1,6
2 3 4 8 11 5 10
c
6
c
1
c
2
c
3
c
8
c
11
c
4
c
10
c
5
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h6371u
14
+ 7974u
13
+ ··· + 2417b + 9214, −7643u
14
− 6072u
13
+ ··· + 2417a − 4421,
u
15
+ 2u
14
+ u
13
− u
12
+ 5u
11
+ 12u
10
+ 11u
9
+ 5u
8
+ 8u
7
+ 14u
6
+ 11u
5
+ 5u
4
+ 2u
3
+ 3u
2
+ 3u + 1i
I
u
2
= h−8.78150 × 10
28
u
27
+ 5.66569 × 10
28
u
26
+ ··· + 6.30688 × 10
29
b − 6.14221 × 10
29
,
3.22564 × 10
28
u
27
− 1.12906 × 10
28
u
26
+ ··· + 3.94180 × 10
28
a + 5.37899 × 10
29
, u
28
− 3u
26
+ ··· + 15u + 7i
I
u
3
= hu
8
− 2u
7
− u
6
+ 3u
5
+ 2u
4
− 6u
3
− 4u
2
+ 3b + 5u, 2u
8
− 2u
7
− 3u
6
+ 4u
5
+ 7u
4
− 5u
3
− 8u
2
+ 3a + 8u + 4,
u
9
− u
8
− u
7
+ u
6
+ 3u
5
− u
4
− 3u
3
+ u
2
+ 1i
I
u
4
= h−u
3
− 2u
2
+ 2b − 4u − 1, a, u
4
+ u
3
+ 2u
2
− u + 1i
I
u
5
= hb − u, a, u
2
− u + 1i
* 5 irreducible components of dim
C
= 0, with total 58 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
= h6371u
14
+ 7974u
13
+ · · · + 2417b + 9214, −7643u
14
− 6072u
13
+
· · · + 2417a − 4421, u
15
+ 2u
14
+ · · · + 3u + 1i
(i) Arc colorings
a
7
=
1
0
a
9
=
0
u
a
1
=
3.16218u
14
+ 2.51221u
13
+ ··· + 8.43235u + 1.82913
−2.63591u
14
− 3.29913u
13
+ ··· − 7.27431u − 3.81216
a
6
=
1
−u
2
a
2
=
3.16218u
14
+ 2.51221u
13
+ ··· + 7.43235u + 1.82913
−2.63591u
14
− 3.29913u
13
+ ··· − 7.27431u − 3.81216
a
3
=
0.526272u
14
− 0.786926u
13
+ ··· + 0.158047u − 1.98304
−2.63591u
14
− 3.29913u
13
+ ··· − 7.27431u − 3.81216
a
4
=
−2.88829u
14
− 1.53496u
13
+ ··· − 10.3910u − 1.51055
2.07654u
14
+ 3.02234u
13
+ ··· + 6.23211u + 2.68722
a
8
=
−14.2950u
14
− 17.2429u
13
+ ··· − 37.4675u − 19.5999
3.86512u
14
+ 5.89036u
13
+ ··· + 12.4721u + 7.53496
a
11
=
5.79810u
14
+ 5.81134u
13
+ ··· + 15.7067u + 5.64129
−2.63591u
14
− 3.29913u
13
+ ··· − 7.27431u − 3.81216
a
5
=
9.56144u
14
+ 16.6558u
13
+ ··· + 17.5350u + 18.8192
1.10716u
14
+ 1.23128u
13
+ ··· + 2.12495u − 1.23790
a
10
=
−19.5668u
14
− 23.8411u
13
+ ··· − 54.0161u − 27.2242
6.56103u
14
+ 10.1800u
13
+ ··· + 19.0364u + 11.4803
a
10
=
−19.5668u
14
− 23.8411u
13
+ ··· − 54.0161u − 27.2242
6.56103u
14
+ 10.1800u
13
+ ··· + 19.0364u + 11.4803
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1121
2417
u
14
−
15391
2417
u
13
+ ··· +
7549
2417
u −
21392
2417
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
15
− 2u
14
+ ··· + 3u − 1
c
2
, c
5
u
15
+ 4u
13
+ ··· + 21u − 7
c
3
, c
10
u
15
− u
14
+ ··· + 9u + 1
c
4
, c
11
u
15
− u
14
+ ··· + 3u − 1
c
7
u
15
− 9u
14
+ ··· + 89u − 13
c
8
u
15
− 16u
14
+ ··· − 384u + 64
c
9
u
15
− 18u
14
+ ··· + 166u − 13
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
15
− 2y
14
+ ··· + 3y −1
c
2
, c
5
y
15
+ 8y
14
+ ··· − 371y −49
c
3
, c
10
y
15
− 23y
14
+ ··· + 143y −1
c
4
, c
11
y
15
+ 17y
14
+ ··· − 9y −1
c
7
y
15
− 3y
14
+ ··· − 633y −169
c
8
y
15
− 6y
14
+ ··· + 49152y −4096
c
9
y
15
− 14y
14
+ ··· + 1972y −169
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.612704 + 0.756856I
a = 0.341418 − 0.122016I
b = 0.566944 + 0.416117I
0.01045 − 1.91554I 0.97885 + 4.27627I
u = 0.612704 − 0.756856I
a = 0.341418 + 0.122016I
b = 0.566944 − 0.416117I
0.01045 + 1.91554I 0.97885 − 4.27627I
u = −0.749863 + 0.844909I
a = −0.867808 − 0.597101I
b = −0.124797 − 0.345224I
3.80312 + 4.84275I 6.83327 − 2.97437I
u = −0.749863 − 0.844909I
a = −0.867808 + 0.597101I
b = −0.124797 + 0.345224I
3.80312 − 4.84275I 6.83327 + 2.97437I
u = −0.864919
a = −0.417102
b = −0.552891
1.96166 8.66210
u = −0.330359 + 0.744277I
a = −0.712671 + 0.196118I
b = −0.743805 + 0.481051I
1.29784 − 0.91531I 6.30482 + 3.51826I
u = −0.330359 − 0.744277I
a = −0.712671 − 0.196118I
b = −0.743805 − 0.481051I
1.29784 + 0.91531I 6.30482 − 3.51826I
u = 0.551581 + 0.527918I
a = 3.41165 − 0.50064I
b = 0.17287 − 1.44617I
−7.32770 − 5.27705I −2.66781 + 10.56442I
u = 0.551581 − 0.527918I
a = 3.41165 + 0.50064I
b = 0.17287 + 1.44617I
−7.32770 + 5.27705I −2.66781 − 10.56442I
u = −0.620336 + 0.202077I
a = −3.98780 + 1.70604I
b = 0.32367 − 1.38455I
−8.37106 − 3.72407I −11.66592 − 1.71457I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.620336 − 0.202077I
a = −3.98780 − 1.70604I
b = 0.32367 + 1.38455I
−8.37106 + 3.72407I −11.66592 + 1.71457I
u = 1.19608 + 0.93854I
a = 1.153170 − 0.195631I
b = 0.12290 − 1.54294I
−10.07790 − 6.40199I −2.27236 + 3.45803I
u = 1.19608 − 0.93854I
a = 1.153170 + 0.195631I
b = 0.12290 + 1.54294I
−10.07790 + 6.40199I −2.27236 − 3.45803I
u = −1.22735 + 1.00294I
a = −1.129410 − 0.049047I
b = −0.54134 − 1.75302I
−9.9244 + 14.7471I −1.34191 − 7.45505I
u = −1.22735 − 1.00294I
a = −1.129410 + 0.049047I
b = −0.54134 + 1.75302I
−9.9244 − 14.7471I −1.34191 + 7.45505I
6
II. I
u
2
= h−8.78 × 10
28
u
27
+ 5.67 × 10
28
u
26
+ · · · + 6.31 × 10
29
b − 6.14 ×
10
29
, 3.23 × 10
28
u
27
− 1.13 × 10
28
u
26
+ · · · + 3.94 × 10
28
a + 5.38 ×
10
29
, u
28
− 3u
26
+ · · · + 15u + 7i
(i) Arc colorings
a
7
=
1
0
a
9
=
0
u
a
1
=
−0.818316u
27
+ 0.286432u
26
+ ··· − 4.31215u − 13.6460
0.139237u
27
− 0.0898334u
26
+ ··· − 1.14880u + 0.973891
a
6
=
1
−u
2
a
2
=
−0.778079u
27
+ 0.383226u
26
+ ··· − 4.59508u − 12.6149
0.198461u
27
− 0.197076u
26
+ ··· + 0.584769u + 1.65145
a
3
=
−0.579618u
27
+ 0.186150u
26
+ ··· − 4.01031u − 10.9634
0.198461u
27
− 0.197076u
26
+ ··· + 0.584769u + 1.65145
a
4
=
−0.554453u
27
+ 0.463290u
26
+ ··· − 15.3130u − 5.98983
−0.0847239u
27
+ 0.0398120u
26
+ ··· − 4.10503u + 2.09476
a
8
=
−0.920936u
27
+ 0.383226u
26
+ ··· + 5.69064u − 14.7577
0.000248909u
27
+ 0.0199758u
26
+ ··· − 1.85550u − 3.21584
a
11
=
−0.957553u
27
+ 0.376265u
26
+ ··· − 3.16334u − 14.6199
0.139237u
27
− 0.0898334u
26
+ ··· − 1.14880u + 0.973891
a
5
=
−0.530531u
27
+ 0.278934u
26
+ ··· + 1.71271u − 9.93905
−0.307348u
27
+ 0.0603723u
26
+ ··· − 5.15516u − 3.44204
a
10
=
−1.47268u
27
+ 0.509623u
26
+ ··· + 8.66934u − 25.3019
−0.0298670u
27
− 0.135246u
26
+ ··· + 3.47164u − 1.07835
a
10
=
−1.47268u
27
+ 0.509623u
26
+ ··· + 8.66934u − 25.3019
−0.0298670u
27
− 0.135246u
26
+ ··· + 3.47164u − 1.07835
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.21687u
27
+ 1.77020u
26
+ ··· − 21.5171u − 59.2310
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
28
− 3u
26
+ ··· − 15u + 7
c
2
, c
5
u
28
+ 14u
26
+ ··· + 18426u + 5476
c
3
, c
10
u
28
+ 3u
27
+ ··· + 702u + 189
c
4
, c
11
u
28
+ 15u
26
+ ··· + 1651u + 211
c
7
(u
7
+ 2u
6
+ 2u
5
− u
4
− 2u
3
− 3u
2
− 2u − 1)
4
c
8
(u
2
+ u + 1)
14
c
9
(u
7
+ 3u
6
+ 3u
5
− 2u
4
− 6u
3
− 3u
2
+ 3u + 2)
4
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
28
− 6y
27
+ ··· − 1233y + 49
c
2
, c
5
y
28
+ 28y
27
+ ··· + 251529108y + 29986576
c
3
, c
10
y
28
− 31y
27
+ ··· + 442746y + 35721
c
4
, c
11
y
28
+ 30y
27
+ ··· − 141473y + 44521
c
7
(y
7
+ 4y
5
− y
4
− 6y
3
− 3y
2
− 2y −1)
4
c
8
(y
2
+ y + 1)
14
c
9
(y
7
− 3y
6
+ 9y
5
− 16y
4
+ 30y
3
− 37y
2
+ 21y −4)
4
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.926441 + 0.302933I
a = 0.835660 − 0.395936I
b = 0.18430 − 1.56542I
−8.81923 + 1.88726I −4.79602 + 0.46086I
u = 0.926441 − 0.302933I
a = 0.835660 + 0.395936I
b = 0.18430 + 1.56542I
−8.81923 − 1.88726I −4.79602 − 0.46086I
u = 0.882336 + 0.398262I
a = −1.25789 − 0.69503I
b = −0.127775 + 1.222770I
−1.98093 − 2.69340I 1.01907 + 5.70877I
u = 0.882336 − 0.398262I
a = −1.25789 + 0.69503I
b = −0.127775 − 1.222770I
−1.98093 + 2.69340I 1.01907 − 5.70877I
u = −0.955589 + 0.447693I
a = 1.361010 − 0.102924I
b = 0.398158 + 0.190766I
−3.77470 + 4.56872I −6.86344 − 5.27495I
u = −0.955589 − 0.447693I
a = 1.361010 + 0.102924I
b = 0.398158 − 0.190766I
−3.77470 − 4.56872I −6.86344 + 5.27495I
u = 1.030270 + 0.444143I
a = −0.777103 + 1.021880I
b = 0.933329 − 0.035309I
−3.77470 + 0.50896I −6.86344 + 1.65325I
u = 1.030270 − 0.444143I
a = −0.777103 − 1.021880I
b = 0.933329 + 0.035309I
−3.77470 − 0.50896I −6.86344 − 1.65325I
u = −0.764988 + 0.333203I
a = −1.036830 − 0.303027I
b = −0.52562 − 1.87875I
−8.81923 + 5.94703I −4.79602 − 6.46734I
u = −0.764988 − 0.333203I
a = −1.036830 + 0.303027I
b = −0.52562 + 1.87875I
−8.81923 − 5.94703I −4.79602 + 6.46734I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.832170 + 1.011860I
a = −1.060780 − 0.049088I
b = −1.76309 + 1.00644I
−1.98093 − 6.75317I 1.01907 + 12.63698I
u = 0.832170 − 1.011860I
a = −1.060780 + 0.049088I
b = −1.76309 − 1.00644I
−1.98093 + 6.75317I 1.01907 − 12.63698I
u = −0.673430 + 0.136605I
a = 1.99394 − 0.64637I
b = 0.282129 + 1.092080I
−3.77470 + 0.50896I −6.86344 + 1.65325I
u = −0.673430 − 0.136605I
a = 1.99394 + 0.64637I
b = 0.282129 − 1.092080I
−3.77470 − 0.50896I −6.86344 − 1.65325I
u = 0.418095 + 0.243425I
a = −1.095220 + 0.637666I
b = −0.84642 − 1.28005I
1.18584 − 2.02988I −7.71921 + 3.46410I
u = 0.418095 − 0.243425I
a = −1.095220 − 0.637666I
b = −0.84642 + 1.28005I
1.18584 + 2.02988I −7.71921 − 3.46410I
u = −1.32892 + 0.76374I
a = 0.833463 − 0.359442I
b = 0.576049 + 1.105100I
−1.98093 + 6.75317I 1.00000 − 12.63698I
u = −1.32892 − 0.76374I
a = 0.833463 + 0.359442I
b = 0.576049 − 1.105100I
−1.98093 − 6.75317I 1.00000 + 12.63698I
u = −0.419083 + 0.092128I
a = 2.45375 − 2.11929I
b = 0.635857 + 0.145439I
−1.98093 + 2.69340I 1.01907 − 5.70877I
u = −0.419083 − 0.092128I
a = 2.45375 + 2.11929I
b = 0.635857 − 0.145439I
−1.98093 − 2.69340I 1.01907 + 5.70877I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.28011 + 1.04710I
a = −0.858059 + 0.149052I
b = −0.09070 + 1.77177I
−3.77470 − 4.56872I −6.86344 + 5.27495I
u = 1.28011 − 1.04710I
a = −0.858059 − 0.149052I
b = −0.09070 − 1.77177I
−3.77470 + 4.56872I −6.86344 − 5.27495I
u = 1.04709 + 1.39986I
a = 0.358425 − 0.370628I
b = 0.14931 − 1.67361I
−8.81923 − 1.88726I −4.79602 + 0.I
u = 1.04709 − 1.39986I
a = 0.358425 + 0.370628I
b = 0.14931 + 1.67361I
−8.81923 + 1.88726I −4.79602 + 0.I
u = −1.10276 + 1.42931I
a = 0.207467 + 0.268901I
b = −0.258042 + 0.632924I
1.18584 + 2.02988I −7.71921 + 0.I
u = −1.10276 − 1.42931I
a = 0.207467 − 0.268901I
b = −0.258042 − 0.632924I
1.18584 − 2.02988I −7.71921 + 0.I
u = −1.17174 + 1.49387I
a = −0.243547 − 0.407503I
b = 0.45250 − 1.53573I
−8.81923 − 5.94703I 0
u = −1.17174 − 1.49387I
a = −0.243547 + 0.407503I
b = 0.45250 + 1.53573I
−8.81923 + 5.94703I 0
12
III. I
u
3
= hu
8
− 2u
7
+ · · · + 3b + 5u, 2u
8
− 2u
7
+ · · · + 3a + 4, u
9
− u
8
− u
7
+
u
6
+ 3u
5
− u
4
− 3u
3
+ u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
9
=
0
u
a
1
=
−
2
3
u
8
+
2
3
u
7
+ ··· −
8
3
u −
4
3
−
1
3
u
8
+
2
3
u
7
+ ··· +
4
3
u
2
−
5
3
u
a
6
=
1
−u
2
a
2
=
−
2
3
u
8
+
2
3
u
7
+ ··· −
5
3
u −
4
3
−
1
3
u
8
+
2
3
u
7
+ ··· +
4
3
u
2
−
5
3
u
a
3
=
−u
8
+
4
3
u
7
+ ··· −
10
3
u −
4
3
−
1
3
u
8
+
2
3
u
7
+ ··· +
4
3
u
2
−
5
3
u
a
4
=
u
8
−
2
3
u
7
+ ··· +
5
3
u −
1
3
−
2
3
u
7
+
1
3
u
6
+ ··· +
5
3
u −
1
3
a
8
=
u
8
−
2
3
u
7
+ ··· +
2
3
u +
5
3
2
3
u
8
−
2
3
u
7
+ ··· +
8
3
u +
1
3
a
11
=
−
1
3
u
8
+
2
3
u
6
+ ··· − u −
4
3
−
1
3
u
8
+
2
3
u
7
+ ··· +
4
3
u
2
−
5
3
u
a
5
=
u
8
− 2u
7
+ 2u
5
+ 2u
4
− 4u
3
− 2u
2
+ 5u − 1
−
1
3
u
8
−
1
3
u
7
+ ··· +
4
3
u − 2
a
10
=
5
3
u
8
− 2u
7
+ ··· + 2u +
5
3
4
3
u
8
−
4
3
u
7
+ ··· +
10
3
u −
1
3
a
10
=
5
3
u
8
− 2u
7
+ ··· + 2u +
5
3
4
3
u
8
−
4
3
u
7
+ ··· +
10
3
u −
1
3
(ii) Obstruction class = 1
(iii) Cusp Shapes =
11
3
u
8
− 2u
7
−
16
3
u
6
+
11
3
u
5
+
31
3
u
4
+
2
3
u
3
−
26
3
u
2
+ u −
13
3
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
9
− u
8
− u
7
+ u
6
+ 3u
5
− u
4
− 3u
3
+ u
2
+ 1
c
2
, c
5
u
9
− u
8
+ 2u
7
− 2u
6
− 3u
5
+ 6u
4
− 9u
3
+ 12u
2
− 6u + 1
c
3
, c
10
u
9
+ 4u
8
+ 4u
7
− 3u
6
− 6u
5
+ 2u
4
+ 9u
3
+ 5u
2
+ 2u + 1
c
4
, c
11
u
9
+ 4u
7
+ 8u
5
+ 4u
4
+ 10u
3
+ 5u
2
+ 4u + 1
c
7
u
9
+ 4u
8
+ 6u
7
+ 2u
6
− 6u
5
− 9u
4
− 9u
3
− 9u
2
− 4u − 1
c
8
u
9
− 2u
8
− u
7
+ 6u
6
− 2u
5
− 6u
4
+ 9u
3
− 4u
2
− u + 1
c
9
u
9
− 5u
8
+ 7u
7
+ 10u
6
− 43u
5
+ 40u
4
+ 32u
3
− 101u
2
+ 85u − 25
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
9
− 3y
8
+ 9y
7
− 15y
6
+ 19y
5
− 19y
4
+ 9y
3
+ y
2
− 2y − 1
c
2
, c
5
y
9
+ 3y
8
− 6y
7
− 22y
6
+ 9y
5
+ 44y
4
− 23y
3
− 48y
2
+ 12y − 1
c
3
, c
10
y
9
− 8y
8
+ 28y
7
− 55y
6
+ 84y
5
− 74y
4
+ 43y
3
+ 7y
2
− 6y − 1
c
4
, c
11
y
9
+ 8y
8
+ 32y
7
+ 84y
6
+ 152y
5
+ 176y
4
+ 124y
3
+ 47y
2
+ 6y − 1
c
7
y
9
− 4y
8
+ 8y
7
− 22y
6
+ 28y
5
+ 23y
4
− 29y
3
− 27y
2
− 2y − 1
c
8
y
9
− 6y
8
+ 21y
7
− 38y
6
+ 40y
5
− 18y
4
+ 25y
3
− 22y
2
+ 9y − 1
c
9
y
9
− 11y
8
+ ··· + 2175y − 625
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.925729 + 0.298901I
a = −1.65967 − 0.29203I
b = 0.186675 + 0.843739I
−3.44968 − 2.27918I −6.79542 + 4.07405I
u = 0.925729 − 0.298901I
a = −1.65967 + 0.29203I
b = 0.186675 − 0.843739I
−3.44968 + 2.27918I −6.79542 − 4.07405I
u = −1.06290
a = 0.677227
b = 0.297798
1.40144 −6.42530
u = −0.835681 + 0.887260I
a = 1.154510 + 0.429518I
b = 0.301332 + 0.862970I
3.17057 + 5.55556I 0.67256 − 7.78739I
u = −0.835681 − 0.887260I
a = 1.154510 − 0.429518I
b = 0.301332 − 0.862970I
3.17057 − 5.55556I 0.67256 + 7.78739I
u = 1.117240 + 0.844025I
a = −1.015900 − 0.192244I
b = −0.93544 + 1.17493I
−2.48959 − 5.91665I −4.21171 + 4.65114I
u = 1.117240 − 0.844025I
a = −1.015900 + 0.192244I
b = −0.93544 − 1.17493I
−2.48959 + 5.91665I −4.21171 − 4.65114I
u = −0.175840 + 0.557149I
a = −1.31756 − 2.50559I
b = 0.29853 − 1.51561I
−7.80162 − 4.26526I −1.95279 + 3.52841I
u = −0.175840 − 0.557149I
a = −1.31756 + 2.50559I
b = 0.29853 + 1.51561I
−7.80162 + 4.26526I −1.95279 − 3.52841I
16
IV. I
u
4
= h−u
3
− 2u
2
+ 2b − 4u − 1, a, u
4
+ u
3
+ 2u
2
− u + 1i
(i) Arc colorings
a
7
=
1
0
a
9
=
0
u
a
1
=
0
1
2
u
3
+ u
2
+ 2u +
1
2
a
6
=
1
−u
2
a
2
=
−
1
2
u
3
− u
2
− 2u −
1
2
u
3
+ u
2
+ 2u
a
3
=
1
2
u
3
−
1
2
u
3
+ u
2
+ 2u
a
4
=
1
2
u
3
−
1
2
1
a
8
=
−
1
2
u
3
+
3
2
−1
a
11
=
−
1
2
u
3
− u
2
− 2u −
1
2
1
2
u
3
+ u
2
+ 2u +
1
2
a
5
=
u
3
+ u
2
+ u − 1
−
1
2
u
3
− u
2
− u +
3
2
a
10
=
0
u
a
10
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
3
+ 4u
2
+ 4u + 11
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
11
u
4
+ u
3
+ 2u
2
− u + 1
c
2
, c
5
u
4
+ 3u
3
+ 5u
2
+ 6u + 4
c
3
, c
8
, c
10
(u
2
+ u + 1)
2
c
7
(u − 1)
4
c
9
u
4
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
11
y
4
+ 3y
3
+ 8y
2
+ 3y + 1
c
2
, c
5
y
4
+ y
3
− 3y
2
+ 4y + 16
c
3
, c
8
, c
10
(y
2
+ y + 1)
2
c
7
(y − 1)
4
c
9
y
4
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.309017 + 0.535233I
a = 0
b = 0.80902 + 1.40126I
1.64493 − 2.02988I 11.00000 + 3.46410I
u = 0.309017 − 0.535233I
a = 0
b = 0.80902 − 1.40126I
1.64493 + 2.02988I 11.00000 − 3.46410I
u = −0.80902 + 1.40126I
a = 0
b = −0.309017 + 0.535233I
1.64493 + 2.02988I 11.00000 − 3.46410I
u = −0.80902 − 1.40126I
a = 0
b = −0.309017 − 0.535233I
1.64493 − 2.02988I 11.00000 + 3.46410I
20
V. I
u
5
= hb − u, a, u
2
− u + 1i
(i) Arc colorings
a
7
=
1
0
a
9
=
0
u
a
1
=
0
u
a
6
=
1
−u + 1
a
2
=
−u
u − 1
a
3
=
−1
u − 1
a
4
=
−1
0
a
8
=
1
0
a
11
=
−u
u
a
5
=
−u
u − 1
a
10
=
0
u
a
10
=
0
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u − 2
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
10
, c
11
u
2
+ u + 1
c
2
, c
5
, c
8
u
2
− u + 1
c
7
, c
9
u
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
8
, c
10
, c
11
y
2
+ y + 1
c
7
, c
9
y
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0
b = 0.500000 + 0.866025I
− 2.02988I 0. + 3.46410I
u = 0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
2.02988I 0. − 3.46410I
24
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
2
+ u + 1)(u
4
+ u
3
+ 2u
2
− u + 1)
· (u
9
− u
8
+ ··· + u
2
+ 1)(u
15
− 2u
14
+ ··· + 3u − 1)
· (u
28
− 3u
26
+ ··· − 15u + 7)
c
2
, c
5
(u
2
− u + 1)(u
4
+ 3u
3
+ 5u
2
+ 6u + 4)
· (u
9
− u
8
+ 2u
7
− 2u
6
− 3u
5
+ 6u
4
− 9u
3
+ 12u
2
− 6u + 1)
· (u
15
+ 4u
13
+ ··· + 21u − 7)(u
28
+ 14u
26
+ ··· + 18426u + 5476)
c
3
, c
10
((u
2
+ u + 1)
3
)(u
9
+ 4u
8
+ ··· + 2u + 1)
· (u
15
− u
14
+ ··· + 9u + 1)(u
28
+ 3u
27
+ ··· + 702u + 189)
c
4
, c
11
(u
2
+ u + 1)(u
4
+ u
3
+ 2u
2
− u + 1)
· (u
9
+ 4u
7
+ ··· + 4u + 1)(u
15
− u
14
+ ··· + 3u − 1)
· (u
28
+ 15u
26
+ ··· + 1651u + 211)
c
7
u
2
(u − 1)
4
(u
7
+ 2u
6
+ 2u
5
− u
4
− 2u
3
− 3u
2
− 2u − 1)
4
· (u
9
+ 4u
8
+ 6u
7
+ 2u
6
− 6u
5
− 9u
4
− 9u
3
− 9u
2
− 4u − 1)
· (u
15
− 9u
14
+ ··· + 89u − 13)
c
8
(u
2
− u + 1)(u
2
+ u + 1)
16
· (u
9
− 2u
8
− u
7
+ 6u
6
− 2u
5
− 6u
4
+ 9u
3
− 4u
2
− u + 1)
· (u
15
− 16u
14
+ ··· − 384u + 64)
c
9
u
6
(u
7
+ 3u
6
+ 3u
5
− 2u
4
− 6u
3
− 3u
2
+ 3u + 2)
4
· (u
9
− 5u
8
+ 7u
7
+ 10u
6
− 43u
5
+ 40u
4
+ 32u
3
− 101u
2
+ 85u − 25)
· (u
15
− 18u
14
+ ··· + 166u − 13)
25
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
2
+ y + 1)(y
4
+ 3y
3
+ 8y
2
+ 3y + 1)
· (y
9
− 3y
8
+ 9y
7
− 15y
6
+ 19y
5
− 19y
4
+ 9y
3
+ y
2
− 2y − 1)
· (y
15
− 2y
14
+ ··· + 3y − 1)(y
28
− 6y
27
+ ··· − 1233y + 49)
c
2
, c
5
(y
2
+ y + 1)(y
4
+ y
3
− 3y
2
+ 4y + 16)
· (y
9
+ 3y
8
− 6y
7
− 22y
6
+ 9y
5
+ 44y
4
− 23y
3
− 48y
2
+ 12y − 1)
· (y
15
+ 8y
14
+ ··· − 371y − 49)
· (y
28
+ 28y
27
+ ··· + 251529108y + 29986576)
c
3
, c
10
(y
2
+ y + 1)
3
· (y
9
− 8y
8
+ 28y
7
− 55y
6
+ 84y
5
− 74y
4
+ 43y
3
+ 7y
2
− 6y − 1)
· (y
15
− 23y
14
+ ··· + 143y − 1)(y
28
− 31y
27
+ ··· + 442746y + 35721)
c
4
, c
11
(y
2
+ y + 1)(y
4
+ 3y
3
+ 8y
2
+ 3y + 1)
· (y
9
+ 8y
8
+ 32y
7
+ 84y
6
+ 152y
5
+ 176y
4
+ 124y
3
+ 47y
2
+ 6y − 1)
· (y
15
+ 17y
14
+ ··· − 9y − 1)(y
28
+ 30y
27
+ ··· − 141473y + 44521)
c
7
y
2
(y − 1)
4
(y
7
+ 4y
5
− y
4
− 6y
3
− 3y
2
− 2y − 1)
4
· (y
9
− 4y
8
+ 8y
7
− 22y
6
+ 28y
5
+ 23y
4
− 29y
3
− 27y
2
− 2y − 1)
· (y
15
− 3y
14
+ ··· − 633y − 169)
c
8
(y
2
+ y + 1)
17
· (y
9
− 6y
8
+ 21y
7
− 38y
6
+ 40y
5
− 18y
4
+ 25y
3
− 22y
2
+ 9y − 1)
· (y
15
− 6y
14
+ ··· + 49152y − 4096)
c
9
y
6
(y
7
− 3y
6
+ 9y
5
− 16y
4
+ 30y
3
− 37y
2
+ 21y − 4)
4
· (y
9
− 11y
8
+ ··· + 2175y − 625)(y
15
− 14y
14
+ ··· + 1972y − 169)
26
