12a
0465
(K12a
0465
)
A knot diagram
1
Linearized knot diagam
3 6 11 7 9 2 12 5 1 4 10 8
Solving Sequence
3,11 4,6
2 7 1 10 12 9 5 8
c
3
c
2
c
6
c
1
c
10
c
11
c
9
c
5
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.94916 × 10
307
u
131
− 3.65279 × 10
307
u
130
+ ··· + 2.01785 × 10
308
b − 1.09127 × 10
309
,
− 3.70110 × 10
309
u
131
+ 8.38178 × 10
309
u
130
+ ··· + 2.68374 × 10
310
a + 3.35444 × 10
311
,
u
132
− 2u
131
+ ··· − 476u + 76i
I
u
2
= h3au + 9b + 12a + 5u + 11, 18a
2
+ 3au + 48a + u + 37, u
2
+ 2i
I
u
3
= h−9au + 7b + 3a + 2u − 3, 9a
2
− 6au − 5u − 11, u
2
− u + 1i
I
u
4
= hb, a + u, u
2
+ u + 1i
I
v
1
= ha, b + v, v
2
− v + 1i
* 5 irreducible components of dim
C
= 0, with total 144 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
= h1.95 × 10
307
u
131
− 3.65 × 10
307
u
130
+ · · · + 2.02 × 10
308
b − 1.09 ×
10
309
, −3.70 × 10
309
u
131
+ 8.38 × 10
309
u
130
+ · · · + 2.68 × 10
310
a + 3.35 ×
10
311
, u
132
− 2u
131
+ · · · − 476u + 76i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
6
=
0.137909u
131
− 0.312317u
130
+ ··· + 84.5087u − 12.4991
−0.0965960u
131
+ 0.181024u
130
+ ··· − 30.2730u + 5.40808
a
2
=
0.199343u
131
− 0.396256u
130
+ ··· + 127.923u − 23.4017
−0.0527294u
131
+ 0.131771u
130
+ ··· − 4.97262u − 1.02232
a
7
=
0.112731u
131
− 0.391881u
130
+ ··· + 143.590u − 27.1262
−0.0759172u
131
+ 0.171870u
130
+ ··· − 15.7531u + 0.451833
a
1
=
0.146613u
131
− 0.264486u
130
+ ··· + 122.951u − 24.4240
−0.0527294u
131
+ 0.131771u
130
+ ··· − 4.97262u − 1.02232
a
10
=
u
u
3
+ u
a
12
=
u
3
u
5
+ u
3
+ u
a
9
=
0.0624762u
131
− 0.0629818u
130
+ ··· + 131.166u − 24.5816
0.159767u
131
− 0.280127u
130
+ ··· + 76.3670u − 13.7238
a
5
=
0.0225291u
131
− 0.145369u
130
+ ··· − 32.5467u + 5.91958
−0.106550u
131
+ 0.113212u
130
+ ··· − 20.2316u + 3.42718
a
8
=
0.0687231u
131
− 0.262340u
130
+ ··· + 119.942u − 23.4880
−0.0149219u
131
+ 0.0644011u
130
+ ··· + 1.87048u − 1.24755
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.497123u
131
+ 0.474012u
130
+ ··· − 20.8223u − 10.5378
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
132
+ 64u
131
+ ··· + 14800u + 5776
c
2
, c
6
u
132
− 2u
131
+ ··· − 476u + 76
c
3
, c
10
u
132
+ 2u
131
+ ··· + 476u + 76
c
4
2401(2401u
132
+ 37730u
131
+ ··· + 8199247u + 3800453)
c
5
, c
8
u
132
+ 3u
131
+ ··· + 9208u + 1228
c
7
, c
12
u
132
− 3u
131
+ ··· − 9208u + 1228
c
9
2401(2401u
132
− 37730u
131
+ ··· − 8199247u + 3800453)
c
11
u
132
− 64u
131
+ ··· − 14800u + 5776
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
132
+ 16y
131
+ ··· + 422881536y + 33362176
c
2
, c
3
, c
6
c
10
y
132
+ 64y
131
+ ··· + 14800y + 5776
c
4
, c
9
5764801(5764801y
132
− 1.97886 × 10
8
y
131
+ ··· − 2.94420 × 10
14
y + 1.44434 × 10
13
)
c
5
, c
7
, c
8
c
12
y
132
− 65y
131
+ ··· − 1106432y + 1507984
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.823198 + 0.569211I
a = 0.889660 + 0.779506I
b = −0.190681 + 1.006910I
−1.53863 + 0.67688I 0
u = 0.823198 − 0.569211I
a = 0.889660 − 0.779506I
b = −0.190681 − 1.006910I
−1.53863 − 0.67688I 0
u = 0.559179 + 0.825258I
a = 4.50642 + 0.70465I
b = 0.440469 + 0.792376I
0.105725 − 0.171371I 0
u = 0.559179 − 0.825258I
a = 4.50642 − 0.70465I
b = 0.440469 − 0.792376I
0.105725 + 0.171371I 0
u = −0.424632 + 0.889847I
a = 1.42271 − 0.04850I
b = −0.03946 − 1.50799I
−5.98533 + 1.74123I 0
u = −0.424632 − 0.889847I
a = 1.42271 + 0.04850I
b = −0.03946 + 1.50799I
−5.98533 − 1.74123I 0
u = 0.936127 + 0.405809I
a = −0.808074 + 0.587728I
b = 0.624017 + 1.147650I
−2.30779 + 13.83220I 0
u = 0.936127 − 0.405809I
a = −0.808074 − 0.587728I
b = 0.624017 − 1.147650I
−2.30779 − 13.83220I 0
u = 0.305623 + 0.975415I
a = −2.36155 + 0.30402I
b = 0.725974 − 0.852806I
3.22670 − 3.10282I 0
u = 0.305623 − 0.975415I
a = −2.36155 − 0.30402I
b = 0.725974 + 0.852806I
3.22670 + 3.10282I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.190681 + 1.006910I
a = 1.87153 − 0.08400I
b = −0.823198 + 0.569211I
1.53863 + 0.67688I 0
u = 0.190681 − 1.006910I
a = 1.87153 + 0.08400I
b = −0.823198 − 0.569211I
1.53863 − 0.67688I 0
u = −0.065305 + 1.027270I
a = 1.121830 − 0.587024I
b = 0.065305 + 1.027270I
3.95402I 0
u = −0.065305 − 1.027270I
a = 1.121830 + 0.587024I
b = 0.065305 − 1.027270I
− 3.95402I 0
u = −0.840683 + 0.484130I
a = −0.764027 − 0.676827I
b = 0.312065 − 1.072640I
−5.44129 + 1.88998I 0
u = −0.840683 − 0.484130I
a = −0.764027 + 0.676827I
b = 0.312065 + 1.072640I
−5.44129 − 1.88998I 0
u = 0.780358 + 0.686992I
a = −0.500434 − 0.041443I
b = 0.615963 + 0.235511I
−1.84741 − 4.70427I 0
u = 0.780358 − 0.686992I
a = −0.500434 + 0.041443I
b = 0.615963 − 0.235511I
−1.84741 + 4.70427I 0
u = −0.875820 + 0.380654I
a = −0.525655 + 0.011559I
b = 0.875820 + 0.380654I
− 8.30339I 0
u = −0.875820 − 0.380654I
a = −0.525655 − 0.011559I
b = 0.875820 − 0.380654I
8.30339I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.542091 + 0.784398I
a = −1.78393 − 1.81238I
b = −0.542091 + 0.784398I
− 4.28914I 0
u = 0.542091 − 0.784398I
a = −1.78393 + 1.81238I
b = −0.542091 − 0.784398I
4.28914I 0
u = 0.994492 + 0.335966I
a = 0.826490 − 0.442222I
b = −0.576215 − 1.069210I
0.91777 + 7.31895I 0
u = 0.994492 − 0.335966I
a = 0.826490 + 0.442222I
b = −0.576215 + 1.069210I
0.91777 − 7.31895I 0
u = 0.817201 + 0.484524I
a = −0.544788 − 0.554708I
b = 0.453821 − 1.077520I
−5.47754 − 4.53124I 0
u = 0.817201 − 0.484524I
a = −0.544788 + 0.554708I
b = 0.453821 + 1.077520I
−5.47754 + 4.53124I 0
u = −0.134345 + 0.932428I
a = −1.58441 + 1.51602I
b = 0.667796 − 0.832412I
3.26894 − 2.20224I 0
u = −0.134345 − 0.932428I
a = −1.58441 − 1.51602I
b = 0.667796 + 0.832412I
3.26894 + 2.20224I 0
u = −0.778502 + 0.520876I
a = 0.594890 + 0.559060I
b = −0.536423 + 1.037550I
−1.65135 − 3.15049I 0
u = −0.778502 − 0.520876I
a = 0.594890 − 0.559060I
b = −0.536423 − 1.037550I
−1.65135 + 3.15049I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.794043 + 0.494894I
a = −0.652893 − 0.992228I
b = 0.144394 − 1.255500I
−5.60411 + 5.29311I 0
u = 0.794043 − 0.494894I
a = −0.652893 + 0.992228I
b = 0.144394 + 1.255500I
−5.60411 − 5.29311I 0
u = −0.804376 + 0.473745I
a = −0.445827 − 0.606987I
b = 0.600283 − 1.174750I
−5.40534 − 7.86857I 0
u = −0.804376 − 0.473745I
a = −0.445827 + 0.606987I
b = 0.600283 + 1.174750I
−5.40534 + 7.86857I 0
u = −0.667796 + 0.832412I
a = 0.390266 − 0.930903I
b = 0.134345 − 0.932428I
−3.26894 + 2.20224I 0
u = −0.667796 − 0.832412I
a = 0.390266 + 0.930903I
b = 0.134345 + 0.932428I
−3.26894 − 2.20224I 0
u = −0.887707 + 0.281785I
a = 0.698511 − 0.047066I
b = −0.685230 − 0.439467I
2.75162 − 2.43503I 0
u = −0.887707 − 0.281785I
a = 0.698511 + 0.047066I
b = −0.685230 + 0.439467I
2.75162 + 2.43503I 0
u = 0.363712 + 1.014900I
a = 0.732029 + 0.614356I
b = −0.662951 − 1.106910I
3.62233 + 0.99937I 0
u = 0.363712 − 1.014900I
a = 0.732029 − 0.614356I
b = −0.662951 + 1.106910I
3.62233 − 0.99937I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.340852 + 0.844220I
a = 2.92738 − 1.67284I
b = 0.340852 + 0.844220I
3.77961I 0
u = −0.340852 − 0.844220I
a = 2.92738 + 1.67284I
b = 0.340852 − 0.844220I
− 3.77961I 0
u = 0.286052 + 0.862830I
a = 0.128517 − 0.772851I
b = −0.440853 − 1.054770I
2.69897 + 1.03309I 0
u = 0.286052 − 0.862830I
a = 0.128517 + 0.772851I
b = −0.440853 + 1.054770I
2.69897 − 1.03309I 0
u = −0.440469 + 0.792376I
a = 5.56339 − 1.16074I
b = −0.559179 + 0.825258I
−0.105725 − 0.171371I 0
u = −0.440469 − 0.792376I
a = 5.56339 + 1.16074I
b = −0.559179 − 0.825258I
−0.105725 + 0.171371I 0
u = −0.030760 + 1.094590I
a = 1.33123 − 1.16689I
b = −0.639482 + 1.037190I
0.11969 − 6.11919I 0
u = −0.030760 − 1.094590I
a = 1.33123 + 1.16689I
b = −0.639482 − 1.037190I
0.11969 + 6.11919I 0
u = 0.416162 + 1.021470I
a = −2.51719 − 0.44595I
b = 0.674582 − 1.079680I
3.66958 − 3.73337I 0
u = 0.416162 − 1.021470I
a = −2.51719 + 0.44595I
b = 0.674582 + 1.079680I
3.66958 + 3.73337I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.312065 + 1.072640I
a = −0.76927 + 1.36764I
b = 0.840683 − 0.484130I
5.44129 − 1.88998I 0
u = −0.312065 − 1.072640I
a = −0.76927 − 1.36764I
b = 0.840683 + 0.484130I
5.44129 + 1.88998I 0
u = −0.551641 + 0.972164I
a = −0.892713 − 0.064231I
b = −0.21137 + 1.45409I
−7.03788 + 3.12317I 0
u = −0.551641 − 0.972164I
a = −0.892713 + 0.064231I
b = −0.21137 − 1.45409I
−7.03788 − 3.12317I 0
u = −0.725974 + 0.852806I
a = 1.21922 − 0.99635I
b = −0.305623 − 0.975415I
−3.22670 + 3.10282I 0
u = −0.725974 − 0.852806I
a = 1.21922 + 0.99635I
b = −0.305623 + 0.975415I
−3.22670 − 3.10282I 0
u = −0.593570 + 0.641593I
a = −1.31728 + 0.93688I
b = 0.253656 + 1.348810I
−8.03402 + 1.43434I 0
u = −0.593570 − 0.641593I
a = −1.31728 − 0.93688I
b = 0.253656 − 1.348810I
−8.03402 − 1.43434I 0
u = 0.442482 + 1.047020I
a = −0.775241 − 1.125380I
b = 0.811066 + 0.953448I
3.44590 − 2.80937I 0
u = 0.442482 − 1.047020I
a = −0.775241 + 1.125380I
b = 0.811066 − 0.953448I
3.44590 + 2.80937I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.676144 + 0.920637I
a = 0.838781 + 0.502579I
b = −0.446567 + 0.118673I
−1.140000 − 0.761652I 0
u = 0.676144 − 0.920637I
a = 0.838781 − 0.502579I
b = −0.446567 − 0.118673I
−1.140000 + 0.761652I 0
u = 0.440853 + 1.054770I
a = 0.13764 + 1.46787I
b = −0.286052 − 0.862830I
−2.69897 − 1.03309I 0
u = 0.440853 − 1.054770I
a = 0.13764 − 1.46787I
b = −0.286052 + 0.862830I
−2.69897 + 1.03309I 0
u = −0.372131 + 1.084960I
a = 0.513198 − 0.809836I
b = −0.762411 + 0.144170I
5.98400 + 2.64260I 0
u = −0.372131 − 1.084960I
a = 0.513198 + 0.809836I
b = −0.762411 − 0.144170I
5.98400 − 2.64260I 0
u = −0.905060 + 0.710796I
a = −1.045390 + 0.744286I
b = 0.504598 + 1.087370I
−4.18406 + 9.03796I 0
u = −0.905060 − 0.710796I
a = −1.045390 − 0.744286I
b = 0.504598 − 1.087370I
−4.18406 − 9.03796I 0
u = 0.488416 + 1.049830I
a = 1.98084 + 0.74828I
b = −0.527973 + 1.235020I
2.76109 − 7.52450I 0
u = 0.488416 − 1.049830I
a = 1.98084 − 0.74828I
b = −0.527973 − 1.235020I
2.76109 + 7.52450I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.536423 + 1.037550I
a = −0.577248 − 1.143850I
b = 0.778502 + 0.520876I
1.65135 − 3.15049I 0
u = 0.536423 − 1.037550I
a = −0.577248 + 1.143850I
b = 0.778502 − 0.520876I
1.65135 + 3.15049I 0
u = −0.453821 + 1.077520I
a = 1.324010 + 0.107331I
b = −0.817201 − 0.484524I
5.47754 + 4.53124I 0
u = −0.453821 − 1.077520I
a = 1.324010 − 0.107331I
b = −0.817201 + 0.484524I
5.47754 − 4.53124I 0
u = 0.685230 + 0.439467I
a = −0.418480 − 0.367370I
b = 0.887707 − 0.281785I
−2.75162 + 2.43503I 0
u = 0.685230 − 0.439467I
a = −0.418480 + 0.367370I
b = 0.887707 + 0.281785I
−2.75162 − 2.43503I 0
u = −0.504598 + 1.087370I
a = −1.83060 + 0.10230I
b = 0.905060 + 0.710796I
4.18406 + 9.03796I 0
u = −0.504598 − 1.087370I
a = −1.83060 − 0.10230I
b = 0.905060 − 0.710796I
4.18406 − 9.03796I 0
u = −0.482158 + 1.109660I
a = 1.18731 − 0.84176I
b = −0.465532 + 0.253242I
−0.72270 + 3.54697I 0
u = −0.482158 − 1.109660I
a = 1.18731 + 0.84176I
b = −0.465532 − 0.253242I
−0.72270 − 3.54697I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.576215 + 1.069210I
a = 0.732912 + 1.102690I
b = −0.994492 − 0.335966I
−0.91777 − 7.31895I 0
u = 0.576215 − 1.069210I
a = 0.732912 − 1.102690I
b = −0.994492 + 0.335966I
−0.91777 + 7.31895I 0
u = 0.639482 + 1.037190I
a = 0.479761 + 0.412159I
b = 0.030760 + 1.094590I
−0.11969 − 6.11919I 0
u = 0.639482 − 1.037190I
a = 0.479761 − 0.412159I
b = 0.030760 − 1.094590I
−0.11969 + 6.11919I 0
u = 0.762411 + 0.144170I
a = −1.037450 + 0.166443I
b = 0.372131 + 1.084960I
−5.98400 + 2.64260I −7.53031 − 4.30612I
u = 0.762411 − 0.144170I
a = −1.037450 − 0.166443I
b = 0.372131 − 1.084960I
−5.98400 − 2.64260I −7.53031 + 4.30612I
u = −0.621647 + 1.066320I
a = −2.20563 + 0.57148I
b = 0.621647 + 1.066320I
8.43624I 0
u = −0.621647 − 1.066320I
a = −2.20563 − 0.57148I
b = 0.621647 − 1.066320I
− 8.43624I 0
u = 0.627948 + 1.077210I
a = −0.872641 − 0.106447I
b = −0.100526 − 1.320640I
−3.85813 − 10.63980I 0
u = 0.627948 − 1.077210I
a = −0.872641 + 0.106447I
b = −0.100526 + 1.320640I
−3.85813 + 10.63980I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.811066 + 0.953448I
a = 0.077919 + 0.139152I
b = −0.442482 + 1.047020I
−3.44590 − 2.80937I 0
u = −0.811066 − 0.953448I
a = 0.077919 − 0.139152I
b = −0.442482 − 1.047020I
−3.44590 + 2.80937I 0
u = −0.627262 + 1.090270I
a = 2.17043 − 0.55484I
b = −0.648802 − 1.200400I
−3.55819 + 13.23950I 0
u = −0.627262 − 1.090270I
a = 2.17043 + 0.55484I
b = −0.648802 + 1.200400I
−3.55819 − 13.23950I 0
u = −0.144394 + 1.255500I
a = 1.66491 + 0.37293I
b = −0.794043 − 0.494894I
5.60411 − 5.29311I 0
u = −0.144394 − 1.255500I
a = 1.66491 − 0.37293I
b = −0.794043 + 0.494894I
5.60411 + 5.29311I 0
u = 0.426260 + 0.593011I
a = 0.747594 + 0.224902I
b = −0.463849 + 0.281567I
0.056199 − 1.099450I 1.88449 + 5.07932I
u = 0.426260 − 0.593011I
a = 0.747594 − 0.224902I
b = −0.463849 − 0.281567I
0.056199 + 1.099450I 1.88449 − 5.07932I
u = −0.674582 + 1.079680I
a = 2.00622 − 0.52033I
b = −0.416162 − 1.021470I
−3.66958 + 3.73337I 0
u = −0.674582 − 1.079680I
a = 2.00622 + 0.52033I
b = −0.416162 + 1.021470I
−3.66958 − 3.73337I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.662951 + 1.106910I
a = −0.136573 + 0.392511I
b = −0.363712 − 1.014900I
−3.62233 − 0.99937I 0
u = 0.662951 − 1.106910I
a = −0.136573 − 0.392511I
b = −0.363712 + 1.014900I
−3.62233 + 0.99937I 0
u = −0.577404 + 0.412181I
a = −0.864830 − 0.502017I
b = 0.588134 − 0.056662I
−2.83155 + 0.71775I −2.72776 + 0.85165I
u = −0.577404 − 0.412181I
a = −0.864830 + 0.502017I
b = 0.588134 + 0.056662I
−2.83155 − 0.71775I −2.72776 − 0.85165I
u = −0.624017 + 1.147650I
a = 0.721774 − 1.156220I
b = −0.936127 + 0.405809I
2.30779 + 13.83220I 0
u = −0.624017 − 1.147650I
a = 0.721774 + 1.156220I
b = −0.936127 − 0.405809I
2.30779 − 13.83220I 0
u = −0.600283 + 1.174750I
a = −0.768502 + 1.005460I
b = 0.804376 − 0.473745I
5.40534 + 7.86857I 0
u = −0.600283 − 1.174750I
a = −0.768502 − 1.005460I
b = 0.804376 + 0.473745I
5.40534 − 7.86857I 0
u = 0.100526 + 1.320640I
a = 1.41079 + 0.80869I
b = −0.627948 − 1.077210I
3.85813 + 10.63980I 0
u = 0.100526 − 1.320640I
a = 1.41079 − 0.80869I
b = −0.627948 + 1.077210I
3.85813 − 10.63980I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.652855 + 1.162310I
a = 2.26946 + 0.51022I
b = −0.652855 + 1.162310I
− 19.6345I 0
u = 0.652855 − 1.162310I
a = 2.26946 − 0.51022I
b = −0.652855 − 1.162310I
19.6345I 0
u = −0.615963 + 0.235511I
a = 0.063853 − 0.350301I
b = −0.780358 + 0.686992I
1.84741 − 4.70427I 0.08651 + 6.41701I
u = −0.615963 − 0.235511I
a = 0.063853 + 0.350301I
b = −0.780358 − 0.686992I
1.84741 + 4.70427I 0.08651 − 6.41701I
u = 0.527973 + 1.235020I
a = 2.10900 − 0.20973I
b = −0.488416 + 1.049830I
−2.76109 − 7.52450I 0
u = 0.527973 − 1.235020I
a = 2.10900 + 0.20973I
b = −0.488416 − 1.049830I
−2.76109 + 7.52450I 0
u = 0.648802 + 1.200400I
a = −2.11366 − 0.34332I
b = 0.627262 − 1.090270I
3.55819 − 13.23950I 0
u = 0.648802 − 1.200400I
a = −2.11366 + 0.34332I
b = 0.627262 + 1.090270I
3.55819 + 13.23950I 0
u = −0.253656 + 1.348810I
a = −1.57262 − 0.32343I
b = 0.593570 + 0.641593I
8.03402 + 1.43434I 0
u = −0.253656 − 1.348810I
a = −1.57262 + 0.32343I
b = 0.593570 − 0.641593I
8.03402 − 1.43434I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.588134 + 0.056662I
a = 0.623241 + 0.414614I
b = 0.577404 − 0.412181I
2.83155 − 0.71775I 2.72776 − 0.85165I
u = −0.588134 − 0.056662I
a = 0.623241 − 0.414614I
b = 0.577404 + 0.412181I
2.83155 + 0.71775I 2.72776 + 0.85165I
u = 0.463849 + 0.281567I
a = 0.649975 + 0.433633I
b = −0.426260 + 0.593011I
−0.056199 − 1.099450I −1.88449 + 5.07932I
u = 0.463849 − 0.281567I
a = 0.649975 − 0.433633I
b = −0.426260 − 0.593011I
−0.056199 + 1.099450I −1.88449 − 5.07932I
u = 0.21137 + 1.45409I
a = −1.166600 − 0.679942I
b = 0.551641 + 0.972164I
7.03788 + 3.12317I 0
u = 0.21137 − 1.45409I
a = −1.166600 + 0.679942I
b = 0.551641 − 0.972164I
7.03788 − 3.12317I 0
u = 0.465532 + 0.253242I
a = 0.47243 + 2.07301I
b = 0.482158 + 1.109660I
0.72270 + 3.54697I −2.29694 − 5.05715I
u = 0.465532 − 0.253242I
a = 0.47243 − 2.07301I
b = 0.482158 − 1.109660I
0.72270 − 3.54697I −2.29694 + 5.05715I
u = 0.03946 + 1.50799I
a = −1.267500 + 0.495790I
b = 0.424632 − 0.889847I
5.98533 − 1.74123I 0
u = 0.03946 − 1.50799I
a = −1.267500 − 0.495790I
b = 0.424632 + 0.889847I
5.98533 + 1.74123I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.446567 + 0.118673I
a = 1.07579 + 1.46333I
b = −0.676144 + 0.920637I
1.140000 − 0.761652I −1.54281 − 1.70362I
u = 0.446567 − 0.118673I
a = 1.07579 − 1.46333I
b = −0.676144 − 0.920637I
1.140000 + 0.761652I −1.54281 + 1.70362I
18
II. I
u
2
= h3au + 9b + 12a + 5u + 11, 18a
2
+ 3au + 48a + u + 37, u
2
+ 2i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−2
a
6
=
a
−
1
3
au −
4
3
a −
5
9
u −
11
9
a
2
=
0.555556au + 2.22222a + 0.759259u + 3.70370
−
1
3
au −
4
3
a −
5
9
u −
20
9
a
7
=
2
9
au +
8
9
a +
11
54
u +
40
27
−
1
3
au −
4
3
a −
5
9
u −
20
9
a
1
=
2
9
au +
8
9
a +
11
54
u +
40
27
−
1
3
au −
4
3
a −
5
9
u −
20
9
a
10
=
u
−u
a
12
=
−2u
3u
a
9
=
−0.259259au + 0.296296a + 0.734568u + 0.493827
1
3
au −
2
3
a −
7
9
u −
10
9
a
5
=
−0.296296au + 0.481481a − 0.493827u + 1.46914
1
3
au −
2
3
a +
5
9
u −
25
9
a
8
=
2
9
au +
8
9
a +
119
54
u +
40
27
−
1
3
au −
4
3
a −
32
9
u −
20
9
(ii) Obstruction class = 1
(iii) Cusp Shapes =
4
3
au +
16
3
a +
20
9
u +
116
9
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u
2
− u + 1)
2
c
3
, c
5
, c
8
c
10
(u
2
+ 2)
2
c
4
27(27u
4
− 18u
3
+ 21u
2
− 6u + 1)
c
6
(u
2
+ u + 1)
2
c
7
(u − 1)
4
c
9
27(27u
4
− 36u
3
+ 12u
2
+ 1)
c
11
(u − 2)
4
c
12
(u + 1)
4
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
(y
2
+ y + 1)
2
c
3
, c
5
, c
8
c
10
(y + 2)
4
c
4
729(729y
4
+ 810y
3
+ 279y
2
+ 6y + 1)
c
7
, c
12
(y −1)
4
c
9
729(729y
4
− 648y
3
+ 198y
2
+ 24y + 1)
c
11
(y −4)
4
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = −1.129210 + 0.459499I
b = 0.500000 − 0.866025I
6.57974 − 2.02988I 6.00000 + 3.46410I
u = 1.414210I
a = −1.53746 − 0.69520I
b = 0.500000 + 0.866025I
6.57974 + 2.02988I 6.00000 − 3.46410I
u = − 1.414210I
a = −1.129210 − 0.459499I
b = 0.500000 + 0.866025I
6.57974 + 2.02988I 6.00000 − 3.46410I
u = − 1.414210I
a = −1.53746 + 0.69520I
b = 0.500000 − 0.866025I
6.57974 − 2.02988I 6.00000 + 3.46410I
22
III. I
u
3
= h−9au + 7b + 3a + 2u − 3, 9a
2
− 6au − 5u − 11, u
2
− u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u − 1
a
6
=
a
9
7
au −
3
7
a −
2
7
u +
3
7
a
2
=
2
7
au −
3
7
a +
43
21
u −
5
21
−2
a
7
=
9
7
au −
10
7
a −
2
7
u +
3
7
−
9
7
au +
3
7
a +
2
7
u −
3
7
a
1
=
2
7
au −
3
7
a +
43
21
u −
47
21
−2
a
10
=
u
u − 1
a
12
=
−1
0
a
9
=
−0.571429au − 0.476190a + 0.349206u − 0.0793651
−0.857143au + 0.285714a + 0.523810u − 0.619048
a
5
=
−0.571429au + 0.523810a + 0.349206u − 0.0793651
3
7
au −
1
7
a +
5
21
u −
4
21
a
8
=
−a
−
9
7
au +
3
7
a +
2
7
u −
3
7
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u − 8
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 2)
4
c
2
, c
6
, c
7
c
12
(u
2
+ 2)
2
c
3
, c
11
(u
2
− u + 1)
2
c
4
27(27u
4
+ 36u
3
+ 12u
2
+ 1)
c
5
(u + 1)
4
c
8
(u − 1)
4
c
9
27(27u
4
+ 18u
3
+ 21u
2
+ 6u + 1)
c
10
(u
2
+ u + 1)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −4)
4
c
2
, c
6
, c
7
c
12
(y + 2)
4
c
3
, c
10
, c
11
(y
2
+ y + 1)
2
c
4
729(729y
4
− 648y
3
+ 198y
2
+ 24y + 1)
c
5
, c
8
(y −1)
4
c
9
729(729y
4
+ 810y
3
+ 279y
2
+ 6y + 1)
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.058080 + 0.052973I
b = − 1.414210I
−6.57974 − 2.02988I −6.00000 + 3.46410I
u = 0.500000 + 0.866025I
a = 1.39141 + 0.52438I
b = 1.414210I
−6.57974 − 2.02988I −6.00000 + 3.46410I
u = 0.500000 − 0.866025I
a = −1.058080 − 0.052973I
b = 1.414210I
−6.57974 + 2.02988I −6.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = 1.39141 − 0.52438I
b = − 1.414210I
−6.57974 + 2.02988I −6.00000 − 3.46410I
26
IV. I
u
4
= hb, a + u, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u − 1
a
6
=
−u
0
a
2
=
1
0
a
7
=
−u
0
a
1
=
1
0
a
10
=
u
u + 1
a
12
=
1
0
a
9
=
−1
u + 1
a
5
=
−u + 1
−u − 1
a
8
=
−u
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u − 2
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
12
u
2
c
3
, c
9
u
2
+ u + 1
c
4
, c
5
(u − 1)
2
c
8
(u + 1)
2
c
10
, c
11
u
2
− u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
12
y
2
c
3
, c
9
, c
10
c
11
y
2
+ y + 1
c
4
, c
5
, c
8
(y −1)
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.500000 − 0.866025I
b = 0
−1.64493 + 2.02988I 0. − 3.46410I
u = −0.500000 − 0.866025I
a = 0.500000 + 0.866025I
b = 0
−1.64493 − 2.02988I 0. + 3.46410I
30
V. I
v
1
= ha, b + v, v
2
− v + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
v
0
a
4
=
1
0
a
6
=
0
−v
a
2
=
1
v − 1
a
7
=
−v
−v + 1
a
1
=
v
v − 1
a
10
=
v
0
a
12
=
v
0
a
9
=
0
−v + 1
a
5
=
0
−v
a
8
=
0
−v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v + 2
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
, c
5
, c
8
c
10
, c
11
u
2
c
7
, c
9
(u + 1)
2
c
12
(u − 1)
2
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
y
2
+ y + 1
c
3
, c
5
, c
8
c
10
, c
11
y
2
c
7
, c
9
, c
12
(y − 1)
2
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −0.500000 − 0.866025I
1.64493 + 2.02988I 0. − 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = −0.500000 + 0.866025I
1.64493 − 2.02988I 0. + 3.46410I
34
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u − 2)
4
(u
2
− u + 1)
3
(u
132
+ 64u
131
+ ··· + 14800u + 5776)
c
2
u
2
(u
2
+ 2)
2
(u
2
− u + 1)
2
(u
2
+ u + 1)(u
132
− 2u
131
+ ··· − 476u + 76)
c
3
u
2
(u
2
+ 2)
2
(u
2
− u + 1)
2
(u
2
+ u + 1)(u
132
+ 2u
131
+ ··· + 476u + 76)
c
4
1750329(u − 1)
2
(u
2
− u + 1)(27u
4
− 18u
3
+ 21u
2
− 6u + 1)
· (27u
4
+ 36u
3
+ 12u
2
+ 1)
· (2401u
132
+ 37730u
131
+ ··· + 8199247u + 3800453)
c
5
u
2
(u − 1)
2
(u + 1)
4
(u
2
+ 2)
2
(u
132
+ 3u
131
+ ··· + 9208u + 1228)
c
6
u
2
(u
2
+ 2)
2
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
132
− 2u
131
+ ··· − 476u + 76)
c
7
u
2
(u − 1)
4
(u + 1)
2
(u
2
+ 2)
2
(u
132
− 3u
131
+ ··· − 9208u + 1228)
c
8
u
2
(u − 1)
4
(u + 1)
2
(u
2
+ 2)
2
(u
132
+ 3u
131
+ ··· + 9208u + 1228)
c
9
1750329(u + 1)
2
(u
2
+ u + 1)(27u
4
− 36u
3
+ 12u
2
+ 1)
· (27u
4
+ 18u
3
+ 21u
2
+ 6u + 1)
· (2401u
132
− 37730u
131
+ ··· − 8199247u + 3800453)
c
10
u
2
(u
2
+ 2)
2
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
132
+ 2u
131
+ ··· + 476u + 76)
c
11
u
2
(u − 2)
4
(u
2
− u + 1)
3
(u
132
− 64u
131
+ ··· − 14800u + 5776)
c
12
u
2
(u − 1)
2
(u + 1)
4
(u
2
+ 2)
2
(u
132
− 3u
131
+ ··· − 9208u + 1228)
35
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
2
(y − 4)
4
(y
2
+ y + 1)
3
· (y
132
+ 16y
131
+ ··· + 422881536y + 33362176)
c
2
, c
3
, c
6
c
10
y
2
(y + 2)
4
(y
2
+ y + 1)
3
(y
132
+ 64y
131
+ ··· + 14800y + 5776)
c
4
, c
9
3063651608241(y − 1)
2
(y
2
+ y + 1)
· (729y
4
− 648y
3
+ ··· + 24y + 1)(729y
4
+ 810y
3
+ 279y
2
+ 6y + 1)
· (5.76 × 10
6
y
132
− 1.98 × 10
8
y
131
+ ··· − 2.94 × 10
14
y + 1.44 × 10
13
)
c
5
, c
7
, c
8
c
12
y
2
(y − 1)
6
(y + 2)
4
(y
132
− 65y
131
+ ··· − 1106432y + 1507984)
36
