11a
349
(K11a
349
)
A knot diagram
1
Linearized knot diagam
6 5 1 10 9 4 11 3 2 8 7
Solving Sequence
7,11
8
1,4
3 6 2 10 5 9
c
7
c
11
c
3
c
6
c
1
c
10
c
4
c
9
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−8794u
30
− 59427u
29
+ ··· + 14648b − 565817,
1207779u
30
+ 10072486u
29
+ ··· + 1069304a − 32922272, u
31
+ 9u
30
+ ··· − 608u − 73i
I
u
2
= h1245599508u
14
a
3
+ 2019297822u
14
a
2
+ ··· + 2559076525a + 1076862186,
u
14
a
2
− 3u
14
+ ··· − a + 8,
u
15
− 3u
14
+ 12u
13
− 25u
12
+ 52u
11
− 78u
10
+ 104u
9
− 109u
8
+ 94u
7
− 58u
6
+ 24u
5
+ 2u
4
− 8u
3
+ 4u
2
− 1i
I
u
3
= h−u
15
+ 5u
14
+ ··· + 2b + 3u, u
15
− 6u
14
+ ··· + 2a + 3, u
16
− 4u
15
+ ··· + 2u
2
+ 1i
I
v
1
= ha, b
2
− b + 1, v −1i
* 4 irreducible components of dim
C
= 0, with total 109 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−8794u
30
− 59427u
29
+ · · · + 14648b − 565817, 1.21 × 10
6
u
30
+
1.01 × 10
7
u
29
+ · · · + 1.07 × 10
6
a − 3.29 × 10
7
, u
31
+ 9u
30
+ · · · − 608u − 73i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
1
=
−u
u
a
4
=
−1.12950u
30
− 9.41967u
29
+ ··· + 251.970u + 30.7885
0.600355u
30
+ 4.05700u
29
+ ··· + 252.304u + 38.6276
a
3
=
0.216690u
30
+ 2.67536u
29
+ ··· − 151.674u − 13.0374
−0.745836u
30
− 8.03803u
29
+ ··· + 655.948u + 82.4535
a
6
=
0.742167u
30
+ 6.23678u
29
+ ··· − 18.8469u + 1.55985
−0.689719u
30
− 5.07503u
29
+ ··· − 28.6196u − 3.82871
a
2
=
−1.15640u
30
− 8.25807u
29
+ ··· − 113.632u − 15.8600
−0.265838u
30
− 5.40866u
29
+ ··· + 1150.58u + 154.173
a
10
=
u
u
3
+ u
a
5
=
−0.757026u
30
− 7.25316u
29
+ ··· + 294.147u + 32.3085
1.10930u
30
+ 9.99788u
29
+ ··· − 399.270u − 46.4128
a
9
=
0.261828u
30
+ 1.90356u
29
+ ··· − 25.4736u − 4.38300
0.0106499u
30
+ 0.585131u
29
+ ··· − 179.751u − 22.5472
a
9
=
0.261828u
30
+ 1.90356u
29
+ ··· − 25.4736u − 4.38300
0.0106499u
30
+ 0.585131u
29
+ ··· − 179.751u − 22.5472
(ii) Obstruction class = −1
(iii) Cusp Shapes =
102043
14648
u
30
+
113248
1831
u
29
+ ··· −
59622049
14648
u −
4091199
7324
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
− 24u
30
+ ··· − 360448u + 32768
c
2
u
31
− 22u
30
+ ··· + 419u − 73
c
3
, c
6
u
31
+ u
30
+ ··· + 14u + 1
c
4
, c
8
u
31
− u
30
+ ··· − 2u + 1
c
5
, c
9
u
31
+ u
29
+ ··· + 2u + 1
c
7
, c
10
, c
11
u
31
− 9u
30
+ ··· − 608u + 73
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
+ 10y
30
+ ··· − 2147483648y − 1073741824
c
2
y
31
+ 46y
29
+ ··· + 42263y − 5329
c
3
, c
6
y
31
+ 15y
30
+ ··· + 110y − 1
c
4
, c
8
y
31
+ 7y
30
+ ··· − 40y − 1
c
5
, c
9
y
31
+ 2y
30
+ ··· − 6y − 1
c
7
, c
10
, c
11
y
31
+ 31y
30
+ ··· − 37092y − 5329
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.852991 + 0.499323I
a = −0.379018 − 0.633422I
b = −0.994010 + 0.988244I
−3.36735 + 13.70180I −6.58812 − 9.58074I
u = −0.852991 − 0.499323I
a = −0.379018 + 0.633422I
b = −0.994010 − 0.988244I
−3.36735 − 13.70180I −6.58812 + 9.58074I
u = −0.316579 + 0.888214I
a = −1.097970 + 0.312101I
b = 0.721245 + 0.634191I
−0.90699 − 1.43155I −3.87159 + 9.73821I
u = −0.316579 − 0.888214I
a = −1.097970 − 0.312101I
b = 0.721245 − 0.634191I
−0.90699 + 1.43155I −3.87159 − 9.73821I
u = −0.886962 + 0.303700I
a = 0.332501 + 0.072745I
b = 0.235798 − 0.956055I
1.08264 + 5.12278I −0.41195 − 8.68112I
u = −0.886962 − 0.303700I
a = 0.332501 − 0.072745I
b = 0.235798 + 0.956055I
1.08264 − 5.12278I −0.41195 + 8.68112I
u = −0.844232 + 0.691840I
a = 0.578588 − 0.200674I
b = −0.675443 − 0.657436I
−2.87005 − 8.08181I −6.17763 + 7.71756I
u = −0.844232 − 0.691840I
a = 0.578588 + 0.200674I
b = −0.675443 + 0.657436I
−2.87005 + 8.08181I −6.17763 − 7.71756I
u = 1.18811
a = −0.163592
b = 0.0888281
−2.36361 35.4320
u = −0.722698 + 0.301514I
a = 0.681450 + 0.287166I
b = 0.960625 − 1.037040I
−2.64536 + 5.39096I −12.5250 − 11.7577I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.722698 − 0.301514I
a = 0.681450 − 0.287166I
b = 0.960625 + 1.037040I
−2.64536 − 5.39096I −12.5250 + 11.7577I
u = −0.403264 + 0.649558I
a = −0.871610 − 0.575987I
b = −0.277793 + 0.861904I
2.96693 − 0.69018I 2.10294 + 0.24214I
u = −0.403264 − 0.649558I
a = −0.871610 + 0.575987I
b = −0.277793 − 0.861904I
2.96693 + 0.69018I 2.10294 − 0.24214I
u = −0.281651 + 1.296450I
a = −0.574322 − 0.910235I
b = −0.150654 + 0.951529I
3.76674 − 0.82301I 0
u = −0.281651 − 1.296450I
a = −0.574322 + 0.910235I
b = −0.150654 − 0.951529I
3.76674 + 0.82301I 0
u = 0.013670 + 1.401210I
a = −0.09185 + 1.89114I
b = 0.94670 − 1.20717I
4.82828 + 1.90483I 0
u = 0.013670 − 1.401210I
a = −0.09185 − 1.89114I
b = 0.94670 + 1.20717I
4.82828 − 1.90483I 0
u = 0.297730 + 0.511306I
a = −0.978614 − 0.248724I
b = 0.260483 + 0.340007I
−0.38522 − 1.41061I −2.90382 + 5.08297I
u = 0.297730 − 0.511306I
a = −0.978614 + 0.248724I
b = 0.260483 − 0.340007I
−0.38522 + 1.41061I −2.90382 − 5.08297I
u = 0.06166 + 1.42151I
a = −0.130706 − 1.235920I
b = −0.471500 + 0.878105I
5.49366 − 2.37184I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.06166 − 1.42151I
a = −0.130706 + 1.235920I
b = −0.471500 − 0.878105I
5.49366 + 2.37184I 0
u = −0.26782 + 1.43933I
a = −0.00779 + 1.93679I
b = 1.07459 − 1.38869I
2.96780 + 8.97601I 0
u = −0.26782 − 1.43933I
a = −0.00779 − 1.93679I
b = 1.07459 + 1.38869I
2.96780 − 8.97601I 0
u = −0.14638 + 1.50740I
a = −0.13509 − 1.58317I
b = −0.698585 + 1.200690I
9.90733 + 1.39993I 0
u = −0.14638 − 1.50740I
a = −0.13509 + 1.58317I
b = −0.698585 − 1.200690I
9.90733 − 1.39993I 0
u = −0.33955 + 1.47960I
a = 0.39739 + 1.41421I
b = 0.499587 − 1.282410I
6.87874 + 9.56615I 0
u = −0.33955 − 1.47960I
a = 0.39739 − 1.41421I
b = 0.499587 + 1.282410I
6.87874 − 9.56615I 0
u = −0.30764 + 1.52681I
a = 0.13457 − 1.85476I
b = −1.10902 + 1.32474I
3.1915 + 17.9314I 0
u = −0.30764 − 1.52681I
a = 0.13457 + 1.85476I
b = −1.10902 − 1.32474I
3.1915 − 17.9314I 0
u = −0.09735 + 1.67029I
a = 0.203729 + 0.617797I
b = 0.133556 − 0.557496I
5.63925 − 4.20521I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.09735 − 1.67029I
a = 0.203729 − 0.617797I
b = 0.133556 + 0.557496I
5.63925 + 4.20521I 0
8
II. I
u
2
= h1.25 × 10
9
a
3
u
14
+ 2.02 × 10
9
a
2
u
14
+ · · · + 2.56 × 10
9
a + 1.08 ×
10
9
, u
14
a
2
− 3u
14
+ · · · − a + 8, u
15
− 3u
14
+ · · · + 4u
2
− 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
1
=
−u
u
a
4
=
a
−0.817912a
3
u
14
− 1.32595a
2
u
14
+ ··· − 1.68039a − 0.707112
a
3
=
−0.471824a
3
u
14
+ 0.346733a
2
u
14
+ ··· + 0.195001a − 0.931134
−0.346088a
3
u
14
− 1.67269a
2
u
14
+ ··· − 0.875395a + 0.224022
a
6
=
−0.0699739a
3
u
14
− 0.319988a
2
u
14
+ ··· + 0.0210967a + 0.491055
−0.0602705a
3
u
14
− 0.0972240a
2
u
14
+ ··· − 0.701805a + 0.161294
a
2
=
−0.548073a
3
u
14
− 0.225684a
2
u
14
+ ··· − 0.0705041a + 0.0289120
0.417828a
3
u
14
− 0.191528a
2
u
14
+ ··· − 0.610204a + 0.623437
a
10
=
u
u
3
+ u
a
5
=
−0.471824a
3
u
14
+ 0.346733a
2
u
14
+ ··· + 0.195001a − 0.931134
−1.19479a
3
u
14
− 1.41931a
2
u
14
+ ··· − 1.33430a − 0.154021
a
9
=
−0.923492a
3
u
14
+ 0.378846a
2
u
14
+ ··· − 0.912625a − 0.744597
0.765493a
3
u
14
− 1.51930a
2
u
14
+ ··· − 0.488395a + 1.38890
a
9
=
−0.923492a
3
u
14
+ 0.378846a
2
u
14
+ ··· − 0.912625a − 0.744597
0.765493a
3
u
14
− 1.51930a
2
u
14
+ ··· − 0.488395a + 1.38890
(ii) Obstruction class = −1
(iii) Cusp Shapes =
271921296
138445675
u
14
a
3
+
88680364
138445675
u
14
a
2
+ ··· +
17490488
5537827
a −
1797460618
138445675
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)
30
c
2
(u
15
+ 7u
14
+ ··· − 4u
2
+ 1)
4
c
3
, c
6
u
60
+ u
59
+ ··· + 12u + 7
c
4
, c
8
u
60
− u
59
+ ··· − 19478u + 3673
c
5
, c
9
u
60
− u
59
+ ··· + 6u + 1
c
7
, c
10
, c
11
(u
15
+ 3u
14
+ ··· − 4u
2
+ 1)
4
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
30
c
2
(y
15
− y
14
+ ··· + 8y − 1)
4
c
3
, c
6
y
60
− 9y
59
+ ··· − 256y + 49
c
4
, c
8
y
60
+ 15y
59
+ ··· + 261046488y + 13490929
c
5
, c
9
y
60
− 21y
59
+ ··· − 228y
2
+ 1
c
7
, c
10
, c
11
(y
15
+ 15y
14
+ ··· + 8y − 1)
4
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.825834 + 0.538674I
a = 0.179032 − 0.898220I
b = 0.942665 + 0.900730I
−2.77564 − 4.75250I −17.6934 + 11.6845I
u = 0.825834 + 0.538674I
a = 0.064202 + 0.531611I
b = −0.515882 + 0.190551I
−2.77564 − 0.69273I −17.6934 + 4.7563I
u = 0.825834 + 0.538674I
a = −0.374874 + 0.363480I
b = −0.924983 − 0.606302I
−2.77564 − 4.75250I −17.6934 + 11.6845I
u = 0.825834 + 0.538674I
a = −0.429379 − 0.094637I
b = 0.762023 − 0.353078I
−2.77564 − 0.69273I −17.6934 + 4.7563I
u = 0.825834 − 0.538674I
a = 0.179032 + 0.898220I
b = 0.942665 − 0.900730I
−2.77564 + 4.75250I −17.6934 − 11.6845I
u = 0.825834 − 0.538674I
a = 0.064202 − 0.531611I
b = −0.515882 − 0.190551I
−2.77564 + 0.69273I −17.6934 − 4.7563I
u = 0.825834 − 0.538674I
a = −0.374874 − 0.363480I
b = −0.924983 + 0.606302I
−2.77564 + 4.75250I −17.6934 − 11.6845I
u = 0.825834 − 0.538674I
a = −0.429379 + 0.094637I
b = 0.762023 + 0.353078I
−2.77564 + 0.69273I −17.6934 − 4.7563I
u = −0.000696 + 1.255430I
a = −0.537288 + 0.318620I
b = −1.054520 − 0.277320I
0.17890 − 4.56727I −8.44510 + 5.18626I
u = −0.000696 + 1.255430I
a = −1.53790 − 0.07369I
b = 1.74600 + 0.26986I
0.178899 − 0.507500I −8.44510 − 1.74195I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.000696 + 1.255430I
a = −0.46059 + 1.65199I
b = 0.246412 − 0.261109I
0.178899 − 0.507500I −8.44510 − 1.74195I
u = −0.000696 + 1.255430I
a = 0.16969 − 2.83852I
b = 0.05074 + 1.99842I
0.17890 − 4.56727I −8.44510 + 5.18626I
u = −0.000696 − 1.255430I
a = −0.537288 − 0.318620I
b = −1.054520 + 0.277320I
0.17890 + 4.56727I −8.44510 − 5.18626I
u = −0.000696 − 1.255430I
a = −1.53790 + 0.07369I
b = 1.74600 − 0.26986I
0.178899 + 0.507500I −8.44510 + 1.74195I
u = −0.000696 − 1.255430I
a = −0.46059 − 1.65199I
b = 0.246412 + 0.261109I
0.178899 + 0.507500I −8.44510 + 1.74195I
u = −0.000696 − 1.255430I
a = 0.16969 + 2.83852I
b = 0.05074 − 1.99842I
0.17890 + 4.56727I −8.44510 − 5.18626I
u = 0.374558 + 0.641779I
a = −1.242750 − 0.072310I
b = 0.404571 − 0.052904I
−0.331160 − 1.366830I −2.47200 + 4.73263I
u = 0.374558 + 0.641779I
a = −0.211923 + 0.547582I
b = −1.227140 − 0.690327I
−0.33116 − 5.42660I −2.47200 + 11.66083I
u = 0.374558 + 0.641779I
a = −0.446534 − 0.078718I
b = 0.233588 + 0.584828I
−0.331160 − 1.366830I −2.47200 + 4.73263I
u = 0.374558 + 0.641779I
a = 1.18736 − 1.93503I
b = 0.447402 + 0.977027I
−0.33116 − 5.42660I −2.47200 + 11.66083I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.374558 − 0.641779I
a = −1.242750 + 0.072310I
b = 0.404571 + 0.052904I
−0.331160 + 1.366830I −2.47200 − 4.73263I
u = 0.374558 − 0.641779I
a = −0.211923 − 0.547582I
b = −1.227140 + 0.690327I
−0.33116 + 5.42660I −2.47200 − 11.66083I
u = 0.374558 − 0.641779I
a = −0.446534 + 0.078718I
b = 0.233588 − 0.584828I
−0.331160 + 1.366830I −2.47200 − 4.73263I
u = 0.374558 − 0.641779I
a = 1.18736 + 1.93503I
b = 0.447402 − 0.977027I
−0.33116 + 5.42660I −2.47200 − 11.66083I
u = 0.678314
a = −0.755171 + 1.008870I
b = −0.575180 + 0.365490I
−2.66135 + 2.02988I −15.2719 − 3.4641I
u = 0.678314
a = −0.755171 − 1.008870I
b = −0.575180 − 0.365490I
−2.66135 − 2.02988I −15.2719 + 3.4641I
u = 0.678314
a = −0.054442 + 0.393425I
b = 0.902396 − 0.932245I
−2.66135 + 2.02988I −15.2719 − 3.4641I
u = 0.678314
a = −0.054442 − 0.393425I
b = 0.902396 + 0.932245I
−2.66135 − 2.02988I −15.2719 + 3.4641I
u = −0.100337 + 1.375660I
a = −0.339092 + 0.510735I
b = 1.44399 − 0.16542I
1.67680 + 3.56562I −5.33049 − 4.32935I
u = −0.100337 + 1.375660I
a = 0.86553 − 2.02688I
b = −0.113467 + 0.277530I
1.67680 + 7.62538I −5.33049 − 11.25756I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.100337 + 1.375660I
a = 2.12438 + 1.14269I
b = −2.33104 − 1.21010I
1.67680 + 7.62538I −5.33049 − 11.25756I
u = −0.100337 + 1.375660I
a = −0.39013 + 2.52070I
b = 0.58590 − 1.48531I
1.67680 + 3.56562I −5.33049 − 4.32935I
u = −0.100337 − 1.375660I
a = −0.339092 − 0.510735I
b = 1.44399 + 0.16542I
1.67680 − 3.56562I −5.33049 + 4.32935I
u = −0.100337 − 1.375660I
a = 0.86553 + 2.02688I
b = −0.113467 − 0.277530I
1.67680 − 7.62538I −5.33049 + 11.25756I
u = −0.100337 − 1.375660I
a = 2.12438 − 1.14269I
b = −2.33104 + 1.21010I
1.67680 − 7.62538I −5.33049 + 11.25756I
u = −0.100337 − 1.375660I
a = −0.39013 − 2.52070I
b = 0.58590 + 1.48531I
1.67680 − 3.56562I −5.33049 + 4.32935I
u = 0.15235 + 1.51729I
a = −0.521531 + 0.526784I
b = −0.380642 − 0.366400I
6.67569 − 3.44689I 2.29813 + 1.92370I
u = 0.15235 + 1.51729I
a = −0.11679 − 1.56879I
b = 0.380795 + 1.344430I
6.67569 − 3.44689I 2.29813 + 1.92370I
u = 0.15235 + 1.51729I
a = 0.36895 − 1.83783I
b = 0.665586 + 0.944764I
6.67569 − 7.50666I 2.29813 + 8.85191I
u = 0.15235 + 1.51729I
a = 0.85260 + 1.80604I
b = −1.51266 − 1.43364I
6.67569 − 7.50666I 2.29813 + 8.85191I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.15235 − 1.51729I
a = −0.521531 − 0.526784I
b = −0.380642 + 0.366400I
6.67569 + 3.44689I 2.29813 − 1.92370I
u = 0.15235 − 1.51729I
a = −0.11679 + 1.56879I
b = 0.380795 − 1.344430I
6.67569 + 3.44689I 2.29813 − 1.92370I
u = 0.15235 − 1.51729I
a = 0.36895 + 1.83783I
b = 0.665586 − 0.944764I
6.67569 + 7.50666I 2.29813 − 8.85191I
u = 0.15235 − 1.51729I
a = 0.85260 − 1.80604I
b = −1.51266 + 1.43364I
6.67569 + 7.50666I 2.29813 − 8.85191I
u = 0.29798 + 1.53037I
a = −0.206885 + 1.025480I
b = −0.293963 − 0.641758I
3.91480 − 4.81769I −7.00546 + 6.81035I
u = 0.29798 + 1.53037I
a = −0.296418 − 0.758545I
b = 0.736482 + 0.652145I
3.91480 − 4.81769I −7.00546 + 6.81035I
u = 0.29798 + 1.53037I
a = 0.201484 + 1.364530I
b = −1.14931 − 0.94853I
3.91480 − 8.87745I −7.0055 + 13.7386I
u = 0.29798 + 1.53037I
a = −0.18100 − 1.93387I
b = 0.91906 + 1.32657I
3.91480 − 8.87745I −7.0055 + 13.7386I
u = 0.29798 − 1.53037I
a = −0.206885 − 1.025480I
b = −0.293963 + 0.641758I
3.91480 + 4.81769I −7.00546 − 6.81035I
u = 0.29798 − 1.53037I
a = −0.296418 + 0.758545I
b = 0.736482 − 0.652145I
3.91480 + 4.81769I −7.00546 − 6.81035I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.29798 − 1.53037I
a = 0.201484 − 1.364530I
b = −1.14931 + 0.94853I
3.91480 + 8.87745I −7.0055 − 13.7386I
u = 0.29798 − 1.53037I
a = −0.18100 + 1.93387I
b = 0.91906 − 1.32657I
3.91480 + 8.87745I −7.0055 − 13.7386I
u = −0.388845 + 0.104061I
a = −0.406304 + 1.016400I
b = −1.21864 − 1.27940I
−3.07391 + 5.95948I −15.7157 − 11.4516I
u = −0.388845 + 0.104061I
a = 1.27388 + 1.26165I
b = 1.049420 − 0.913569I
−3.07391 + 1.89972I −15.7157 − 4.5234I
u = −0.388845 + 0.104061I
a = 2.16554 − 1.41204I
b = 0.939626 − 0.106413I
−3.07391 + 1.89972I −15.7157 − 4.5234I
u = −0.388845 + 0.104061I
a = −1.44365 − 3.91984I
b = −0.659218 + 0.066827I
−3.07391 + 5.95948I −15.7157 − 11.4516I
u = −0.388845 − 0.104061I
a = −0.406304 − 1.016400I
b = −1.21864 + 1.27940I
−3.07391 − 5.95948I −15.7157 + 11.4516I
u = −0.388845 − 0.104061I
a = 1.27388 − 1.26165I
b = 1.049420 + 0.913569I
−3.07391 − 1.89972I −15.7157 + 4.5234I
u = −0.388845 − 0.104061I
a = 2.16554 + 1.41204I
b = 0.939626 + 0.106413I
−3.07391 − 1.89972I −15.7157 + 4.5234I
u = −0.388845 − 0.104061I
a = −1.44365 + 3.91984I
b = −0.659218 − 0.066827I
−3.07391 − 5.95948I −15.7157 + 11.4516I
17
III. I
u
3
=
h−u
15
+5u
14
+· · ·+2b+3u, u
15
−6u
14
+· · ·+2a+3, u
16
−4u
15
+· · ·+2u
2
+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
1
=
−u
u
a
4
=
−
1
2
u
15
+ 3u
14
+ ··· + 2u −
3
2
1
2
u
15
−
5
2
u
14
+ ··· +
1
2
u
2
−
3
2
u
a
3
=
−u
15
+ 4u
14
+ ··· + 2u − 2
u
15
−
7
2
u
14
+ ··· −
3
2
u +
1
2
a
6
=
1
2
u
15
−
3
2
u
14
+ ··· −
9
2
u + 3
−
1
2
u
14
+
3
2
u
13
+ ··· +
3
2
u −
1
2
a
2
=
u
15
−
11
2
u
14
+ ··· +
15
2
u −
5
2
−u
15
+ 4u
14
+ ··· + 4u
2
− u
a
10
=
u
u
3
+ u
a
5
=
−u
15
+
9
2
u
14
+ ··· +
3
2
u −
3
2
u
15
−
7
2
u
14
+ ··· −
3
2
u +
1
2
a
9
=
−u
9
+ 3u
8
− 9u
7
+ 17u
6
− 25u
5
+ 30u
4
− 26u
3
+ 18u
2
− 9u + 3
1
2
u
15
−
3
2
u
14
+ ··· −
15
2
u
2
+
5
2
u
a
9
=
−u
9
+ 3u
8
− 9u
7
+ 17u
6
− 25u
5
+ 30u
4
− 26u
3
+ 18u
2
− 9u + 3
1
2
u
15
−
3
2
u
14
+ ··· −
15
2
u
2
+
5
2
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
3
2
u
15
− 4u
14
+
35
2
u
13
− 37u
12
+
171
2
u
11
− 150u
10
+ 239u
9
−
683
2
u
8
+ 402u
7
−
863
2
u
6
+
727
2
u
5
−
503
2
u
4
+
255
2
u
3
−
71
2
u
2
−
19
2
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
+ 5u
14
+ ··· − u + 1
c
2
u
16
− 9u
15
+ ··· − 3u + 1
c
3
, c
6
u
16
+ 4u
15
+ ··· + 4u + 1
c
4
, c
8
u
16
+ 2u
14
+ ··· − 4u + 1
c
5
, c
9
u
16
+ u
15
+ ··· − 2u + 1
c
7
u
16
− 4u
15
+ ··· + 2u
2
+ 1
c
10
, c
11
u
16
+ 4u
15
+ ··· + 2u
2
+ 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ 10y
15
+ ··· − y + 1
c
2
y
16
+ y
15
+ ··· − 7y + 1
c
3
, c
6
y
16
− 4y
15
+ ··· − 10y + 1
c
4
, c
8
y
16
+ 4y
15
+ ··· − 4y + 1
c
5
, c
9
y
16
− 9y
15
+ ··· − 14y + 1
c
7
, c
10
, c
11
y
16
+ 16y
15
+ ··· + 4y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.952498 + 0.131115I
a = 0.0033545 + 0.0725748I
b = −0.484458 + 0.127312I
−2.50830 + 0.01138I −21.2199 − 7.8586I
u = 0.952498 − 0.131115I
a = 0.0033545 − 0.0725748I
b = −0.484458 − 0.127312I
−2.50830 − 0.01138I −21.2199 + 7.8586I
u = 0.125713 + 0.947117I
a = 1.200340 + 0.568422I
b = −0.892721 + 0.414975I
−1.31298 + 1.09614I −16.2051 − 0.8717I
u = 0.125713 − 0.947117I
a = 1.200340 − 0.568422I
b = −0.892721 − 0.414975I
−1.31298 − 1.09614I −16.2051 + 0.8717I
u = 0.714113 + 0.457971I
a = −0.502410 + 0.579452I
b = −0.900844 − 0.800511I
−2.01872 − 4.33323I −6.23875 + 5.22511I
u = 0.714113 − 0.457971I
a = −0.502410 − 0.579452I
b = −0.900844 + 0.800511I
−2.01872 + 4.33323I −6.23875 − 5.22511I
u = 0.054385 + 1.271360I
a = 0.45585 + 1.52893I
b = −1.058410 − 0.722202I
0.41258 − 2.25313I −9.04909 + 3.10995I
u = 0.054385 − 1.271360I
a = 0.45585 − 1.52893I
b = −1.058410 + 0.722202I
0.41258 + 2.25313I −9.04909 − 3.10995I
u = −0.063174 + 1.362500I
a = −0.48160 − 1.76041I
b = 1.11324 + 0.91407I
1.66646 + 6.43037I −4.55872 − 3.61803I
u = −0.063174 − 1.362500I
a = −0.48160 + 1.76041I
b = 1.11324 − 0.91407I
1.66646 − 6.43037I −4.55872 + 3.61803I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.27182 + 1.50460I
a = 0.13400 + 1.67219I
b = −0.99955 − 1.16424I
4.36105 − 7.99836I −2.22876 + 4.36122I
u = 0.27182 − 1.50460I
a = 0.13400 − 1.67219I
b = −0.99955 + 1.16424I
4.36105 + 7.99836I −2.22876 − 4.36122I
u = 0.14710 + 1.63403I
a = −0.154905 − 0.738372I
b = 0.471140 + 0.478511I
5.13996 − 4.97309I −0.40575 + 9.40850I
u = 0.14710 − 1.63403I
a = −0.154905 + 0.738372I
b = 0.471140 − 0.478511I
5.13996 + 4.97309I −0.40575 − 9.40850I
u = −0.202461 + 0.214174I
a = −3.65462 − 0.29825I
b = 0.751612 − 0.466846I
−2.45018 − 5.54449I −4.59390 + 4.01193I
u = −0.202461 − 0.214174I
a = −3.65462 + 0.29825I
b = 0.751612 + 0.466846I
−2.45018 + 5.54449I −4.59390 − 4.01193I
22
IV. I
v
1
= ha, b
2
− b + 1, v − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
1
0
a
8
=
1
0
a
1
=
1
0
a
4
=
0
b
a
3
=
b
b
a
6
=
1
−b + 1
a
2
=
b
b
a
10
=
1
0
a
5
=
b
b
a
9
=
−b + 2
−b + 1
a
9
=
−b + 2
−b + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4b − 2
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
− u + 1
c
2
, c
7
, c
10
c
11
u
2
c
3
, c
4
, c
5
c
6
, c
8
, c
9
u
2
+ u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
8
c
9
y
2
+ y + 1
c
2
, c
7
, c
10
c
11
y
2
25
(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
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
2
+ u + 1)
30
(u
16
+ 5u
14
+ ··· − u + 1)
· (u
31
− 24u
30
+ ··· − 360448u + 32768)
c
2
u
2
(u
15
+ 7u
14
+ ··· − 4u
2
+ 1)
4
(u
16
− 9u
15
+ ··· − 3u + 1)
· (u
31
− 22u
30
+ ··· + 419u − 73)
c
3
, c
6
(u
2
+ u + 1)(u
16
+ 4u
15
+ ··· + 4u + 1)(u
31
+ u
30
+ ··· + 14u + 1)
· (u
60
+ u
59
+ ··· + 12u + 7)
c
4
, c
8
(u
2
+ u + 1)(u
16
+ 2u
14
+ ··· − 4u + 1)(u
31
− u
30
+ ··· − 2u + 1)
· (u
60
− u
59
+ ··· − 19478u + 3673)
c
5
, c
9
(u
2
+ u + 1)(u
16
+ u
15
+ ··· − 2u + 1)(u
31
+ u
29
+ ··· + 2u + 1)
· (u
60
− u
59
+ ··· + 6u + 1)
c
7
u
2
(u
15
+ 3u
14
+ ··· − 4u
2
+ 1)
4
(u
16
− 4u
15
+ ··· + 2u
2
+ 1)
· (u
31
− 9u
30
+ ··· − 608u + 73)
c
10
, c
11
u
2
(u
15
+ 3u
14
+ ··· − 4u
2
+ 1)
4
(u
16
+ 4u
15
+ ··· + 2u
2
+ 1)
· (u
31
− 9u
30
+ ··· − 608u + 73)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
31
)(y
16
+ 10y
15
+ ··· − y + 1)
· (y
31
+ 10y
30
+ ··· − 2147483648y − 1073741824)
c
2
y
2
(y
15
− y
14
+ ··· + 8y − 1)
4
(y
16
+ y
15
+ ··· − 7y + 1)
· (y
31
+ 46y
29
+ ··· + 42263y − 5329)
c
3
, c
6
(y
2
+ y + 1)(y
16
− 4y
15
+ ··· − 10y + 1)(y
31
+ 15y
30
+ ··· + 110y − 1)
· (y
60
− 9y
59
+ ··· − 256y + 49)
c
4
, c
8
(y
2
+ y + 1)(y
16
+ 4y
15
+ ··· − 4y + 1)(y
31
+ 7y
30
+ ··· − 40y − 1)
· (y
60
+ 15y
59
+ ··· + 261046488y + 13490929)
c
5
, c
9
(y
2
+ y + 1)(y
16
− 9y
15
+ ··· − 14y + 1)(y
31
+ 2y
30
+ ··· − 6y − 1)
· (y
60
− 21y
59
+ ··· − 228y
2
+ 1)
c
7
, c
10
, c
11
y
2
(y
15
+ 15y
14
+ ··· + 8y − 1)
4
(y
16
+ 16y
15
+ ··· + 4y + 1)
· (y
31
+ 31y
30
+ ··· − 37092y − 5329)
28
