12a
0051
(K12a
0051
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 4 11 12 6 1 9 8
Solving Sequence
9,11
12 8 1
4,7
3 2 6 10 5
c
11
c
8
c
12
c
7
c
3
c
1
c
6
c
10
c
5
c
2
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h5.08396 × 10
34
u
109
+ 2.87987 × 10
35
u
108
+ ··· + 2.07043 × 10
34
b + 1.00700 × 10
35
,
− 2.40150 × 10
34
u
109
− 7.91502 × 10
34
u
108
+ ··· + 2.07043 × 10
34
a − 1.21324 × 10
35
,
u
110
+ 5u
109
+ ··· − 7u + 1i
I
u
2
= hau − u
2
+ b + a, −u
2
a + a
2
+ 1, u
3
− u
2
+ 2u − 1i
I
u
3
= h−u
2
+ b − u − 2, 2u
2
+ a + u + 4, u
3
+ 2u − 1i
I
u
4
= h−u
2
+ b, −u
3
+ a − u, u
4
+ u
3
+ 2u
2
+ 2u + 1i
I
u
5
= hu
2
+ b + u, −u
2
+ a − 2, u
3
− u
2
+ 2u − 1i
* 5 irreducible components of dim
C
= 0, with total 126 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
= h5.08 × 10
34
u
109
+ 2.88 × 10
35
u
108
+ · · · + 2.07 × 10
34
b + 1.01 ×
10
35
, −2.40 × 10
34
u
109
− 7.92 × 10
34
u
108
+ · · · + 2.07 × 10
34
a − 1.21 ×
10
35
, u
110
+ 5u
109
+ · · · − 7u + 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
8
=
−u
u
3
+ u
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
4
=
1.15991u
109
+ 3.82290u
108
+ ··· + 17.5984u + 5.85986
−2.45551u
109
− 13.9096u
108
+ ··· + 31.6055u − 4.86375
a
7
=
−u
3
− 2u
u
3
+ u
a
3
=
1.25426u
109
+ 2.47074u
108
+ ··· + 28.5308u + 4.84333
−4.21354u
109
− 19.7876u
108
+ ··· + 21.4988u − 3.81138
a
2
=
−1.32122u
109
− 5.24754u
108
+ ··· − 10.3151u − 3.64345
0.442881u
109
+ 4.21484u
108
+ ··· − 18.3658u + 2.99673
a
6
=
−3.93346u
109
− 15.5438u
108
+ ··· + 29.5005u − 0.0441834
4.97771u
109
+ 20.9442u
108
+ ··· − 6.60421u + 0.827017
a
10
=
−u
6
− 3u
4
− 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
a
5
=
−1.46652u
109
− 8.11160u
108
+ ··· + 30.3922u + 0.400062
0.0103310u
109
+ 0.286370u
108
+ ··· − 2.69149u + 0.0323288
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.61410u
109
+ 7.48255u
108
+ ··· − 53.0640u − 4.23776
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
110
+ 53u
109
+ ··· + 874u + 1
c
2
, c
4
u
110
− 11u
109
+ ··· + 20u + 1
c
3
, c
6
u
110
− 4u
109
+ ··· + 1344u − 128
c
5
, c
9
u
110
− 2u
109
+ ··· − 1024u − 512
c
7
u
110
− 5u
109
+ ··· − 3176u + 292
c
8
, c
11
, c
12
u
110
+ 5u
109
+ ··· − 7u + 1
c
10
u
110
+ 23u
109
+ ··· − 3335609u + 61891
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
110
+ 19y
109
+ ··· − 806974y + 1
c
2
, c
4
y
110
− 53y
109
+ ··· − 874y + 1
c
3
, c
6
y
110
+ 54y
109
+ ··· − 192512y + 16384
c
5
, c
9
y
110
+ 56y
109
+ ··· + 2228224y + 262144
c
7
y
110
+ 9y
109
+ ··· − 11413240y + 85264
c
8
, c
11
, c
12
y
110
+ 101y
109
+ ··· − 147y + 1
c
10
y
110
+ 41y
109
+ ··· − 17639818908843y + 3830495881
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.087769 + 1.071150I
a = −1.248980 − 0.465454I
b = −1.37873 − 0.37865I
2.25688 + 0.90789I 0
u = −0.087769 − 1.071150I
a = −1.248980 + 0.465454I
b = −1.37873 + 0.37865I
2.25688 − 0.90789I 0
u = 0.267272 + 1.065890I
a = −1.50466 − 0.67505I
b = −0.984660 + 0.847043I
1.22660 + 4.08841I 0
u = 0.267272 − 1.065890I
a = −1.50466 + 0.67505I
b = −0.984660 − 0.847043I
1.22660 − 4.08841I 0
u = −0.467803 + 0.703618I
a = 2.29074 − 0.39775I
b = −0.223957 + 0.915152I
−2.03455 + 9.47276I 0
u = −0.467803 − 0.703618I
a = 2.29074 + 0.39775I
b = −0.223957 − 0.915152I
−2.03455 − 9.47276I 0
u = 0.326859 + 1.111260I
a = 1.47565 + 0.59737I
b = 0.842871 − 0.962044I
−0.76167 + 9.32773I 0
u = 0.326859 − 1.111260I
a = 1.47565 − 0.59737I
b = 0.842871 + 0.962044I
−0.76167 − 9.32773I 0
u = 0.044918 + 1.159940I
a = 0.485785 + 0.353856I
b = 0.012116 − 1.098570I
−2.74728 + 0.22494I 0
u = 0.044918 − 1.159940I
a = 0.485785 − 0.353856I
b = 0.012116 + 1.098570I
−2.74728 − 0.22494I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.213857 + 1.147760I
a = −0.609333 − 0.547444I
b = −0.276527 + 1.333880I
−3.24169 + 3.96546I 0
u = 0.213857 − 1.147760I
a = −0.609333 + 0.547444I
b = −0.276527 − 1.333880I
−3.24169 − 3.96546I 0
u = −0.122184 + 1.171470I
a = 0.937221 + 0.413575I
b = 1.70265 + 0.66436I
1.13228 − 4.77677I 0
u = −0.122184 − 1.171470I
a = 0.937221 − 0.413575I
b = 1.70265 − 0.66436I
1.13228 + 4.77677I 0
u = −0.751985 + 0.316865I
a = −0.19275 − 2.67863I
b = 0.28939 + 2.30634I
−0.69158 − 13.75370I 0. + 9.91597I
u = −0.751985 − 0.316865I
a = −0.19275 + 2.67863I
b = 0.28939 − 2.30634I
−0.69158 + 13.75370I 0. − 9.91597I
u = −0.682778 + 0.437855I
a = 0.140125 + 0.021845I
b = 0.306524 − 0.099329I
−4.92429 − 1.07894I 0
u = −0.682778 − 0.437855I
a = 0.140125 − 0.021845I
b = 0.306524 + 0.099329I
−4.92429 + 1.07894I 0
u = −0.608747 + 0.529637I
a = −0.156738 + 0.093345I
b = −0.147370 + 0.361143I
−5.26321 − 3.26086I 0. + 8.42000I
u = −0.608747 − 0.529637I
a = −0.156738 − 0.093345I
b = −0.147370 − 0.361143I
−5.26321 + 3.26086I 0. − 8.42000I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.133764 + 1.201670I
a = 1.70456 + 1.05818I
b = 2.18770 − 1.16206I
−4.25280 + 2.01271I 0
u = 0.133764 − 1.201670I
a = 1.70456 − 1.05818I
b = 2.18770 + 1.16206I
−4.25280 − 2.01271I 0
u = −0.393997 + 0.682907I
a = −2.30080 + 0.11323I
b = 0.155381 − 0.647926I
0.47353 + 4.02638I 2.00000 − 1.65162I
u = −0.393997 − 0.682907I
a = −2.30080 − 0.11323I
b = 0.155381 + 0.647926I
0.47353 − 4.02638I 2.00000 + 1.65162I
u = −0.728838 + 0.296790I
a = 0.43006 + 2.61474I
b = −0.35716 − 2.24164I
1.88370 − 8.04851I 4.66389 + 6.64940I
u = −0.728838 − 0.296790I
a = 0.43006 − 2.61474I
b = −0.35716 + 2.24164I
1.88370 + 8.04851I 4.66389 − 6.64940I
u = 0.777005 + 0.085415I
a = −0.01227 + 2.08995I
b = −0.29493 − 1.78626I
2.37677 − 5.29652I 3.30695 + 5.27195I
u = 0.777005 − 0.085415I
a = −0.01227 − 2.08995I
b = −0.29493 + 1.78626I
2.37677 + 5.29652I 3.30695 − 5.27195I
u = −0.702649 + 0.316627I
a = 0.203452 + 0.089662I
b = 0.504761 + 0.070122I
−2.93391 − 7.17237I 0. + 7.42213I
u = −0.702649 − 0.316627I
a = 0.203452 − 0.089662I
b = 0.504761 − 0.070122I
−2.93391 + 7.17237I 0. − 7.42213I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.676292 + 0.325580I
a = −0.92125 − 3.03516I
b = 0.62862 + 2.30011I
−3.81916 − 4.42307I 0.33207 + 6.45804I
u = −0.676292 − 0.325580I
a = −0.92125 + 3.03516I
b = 0.62862 − 2.30011I
−3.81916 + 4.42307I 0.33207 − 6.45804I
u = 0.737560 + 0.128821I
a = −0.23433 − 2.21989I
b = 0.34707 + 1.87285I
4.05943 − 0.32957I 7.05242 + 0.19707I
u = 0.737560 − 0.128821I
a = −0.23433 + 2.21989I
b = 0.34707 − 1.87285I
4.05943 + 0.32957I 7.05242 − 0.19707I
u = 0.666718 + 0.321526I
a = 1.00379 + 1.71314I
b = −0.57519 − 1.79009I
1.83773 + 7.20528I 3.32675 − 7.67477I
u = 0.666718 − 0.321526I
a = 1.00379 − 1.71314I
b = −0.57519 + 1.79009I
1.83773 − 7.20528I 3.32675 + 7.67477I
u = −0.422080 + 0.598409I
a = −0.305176 + 0.223190I
b = −0.003864 + 0.654541I
−4.06310 + 3.25446I −2.82924 − 1.68811I
u = −0.422080 − 0.598409I
a = −0.305176 − 0.223190I
b = −0.003864 − 0.654541I
−4.06310 − 3.25446I −2.82924 + 1.68811I
u = 0.673412 + 0.257531I
a = −0.90832 − 1.97279I
b = 0.55569 + 1.85787I
3.75181 + 2.12756I 7.14555 − 2.70279I
u = 0.673412 − 0.257531I
a = −0.90832 + 1.97279I
b = 0.55569 − 1.85787I
3.75181 − 2.12756I 7.14555 + 2.70279I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.633760 + 0.307440I
a = −0.191099 − 0.147798I
b = −0.453297 − 0.191626I
−1.35364 − 2.39156I 1.35494 + 3.44541I
u = −0.633760 − 0.307440I
a = −0.191099 + 0.147798I
b = −0.453297 + 0.191626I
−1.35364 + 2.39156I 1.35494 − 3.44541I
u = −0.442645 + 0.534598I
a = 2.95117 + 0.09459I
b = −0.765044 + 0.351218I
−4.73490 + 0.63177I −2.64133 − 0.41353I
u = −0.442645 − 0.534598I
a = 2.95117 − 0.09459I
b = −0.765044 − 0.351218I
−4.73490 − 0.63177I −2.64133 + 0.41353I
u = 0.238477 + 1.301950I
a = 1.94233 − 0.22816I
b = −0.30674 − 2.02821I
−4.24078 + 2.59768I 0
u = 0.238477 − 1.301950I
a = 1.94233 + 0.22816I
b = −0.30674 + 2.02821I
−4.24078 − 2.59768I 0
u = 0.668764 + 0.067218I
a = −1.01044 − 2.15829I
b = 0.17342 + 1.51996I
−0.004153 − 0.660121I −0.81116 + 3.72545I
u = 0.668764 − 0.067218I
a = −1.01044 + 2.15829I
b = 0.17342 − 1.51996I
−0.004153 + 0.660121I −0.81116 − 3.72545I
u = 0.327530 + 1.290810I
a = −0.880564 − 0.599152I
b = −0.39051 + 2.00378I
−1.90814 − 1.31421I 0
u = 0.327530 − 1.290810I
a = −0.880564 + 0.599152I
b = −0.39051 − 2.00378I
−1.90814 + 1.31421I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.431721 + 0.498945I
a = 1.38512 + 1.26258I
b = 0.329753 − 0.717428I
0.96271 − 3.52397I 1.82648 + 1.71517I
u = 0.431721 − 0.498945I
a = 1.38512 − 1.26258I
b = 0.329753 + 0.717428I
0.96271 + 3.52397I 1.82648 − 1.71517I
u = −0.625020 + 0.195335I
a = 1.02317 + 1.71908I
b = −0.30780 − 1.78368I
4.65417 − 3.79918I 5.60561 + 9.12001I
u = −0.625020 − 0.195335I
a = 1.02317 − 1.71908I
b = −0.30780 + 1.78368I
4.65417 + 3.79918I 5.60561 − 9.12001I
u = 0.158715 + 1.337860I
a = 0.527912 − 0.390102I
b = −0.670480 − 0.244495I
−3.43387 + 2.25266I 0
u = 0.158715 − 1.337860I
a = 0.527912 + 0.390102I
b = −0.670480 + 0.244495I
−3.43387 − 2.25266I 0
u = 0.300858 + 1.330050I
a = 1.015650 + 0.572458I
b = 0.43639 − 2.22756I
−0.51775 + 3.42145I 0
u = 0.300858 − 1.330050I
a = 1.015650 − 0.572458I
b = 0.43639 + 2.22756I
−0.51775 − 3.42145I 0
u = 0.590275 + 0.237552I
a = 1.14216 + 1.56879I
b = 0.028965 − 0.993228I
−0.45742 + 2.08316I 1.71834 − 4.71563I
u = 0.590275 − 0.237552I
a = 1.14216 − 1.56879I
b = 0.028965 + 0.993228I
−0.45742 − 2.08316I 1.71834 + 4.71563I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.448708 + 0.424163I
a = 0.087098 − 0.355565I
b = −0.189088 − 0.505206I
−2.04918 − 1.01718I −0.77645 + 4.39237I
u = −0.448708 − 0.424163I
a = 0.087098 + 0.355565I
b = −0.189088 + 0.505206I
−2.04918 + 1.01718I −0.77645 − 4.39237I
u = −0.213217 + 1.374140I
a = −0.077328 + 0.925196I
b = −1.84754 − 2.39610I
−0.811385 − 0.560255I 0
u = −0.213217 − 1.374140I
a = −0.077328 − 0.925196I
b = −1.84754 + 2.39610I
−0.811385 + 0.560255I 0
u = 0.232900 + 0.562056I
a = −1.68860 − 1.12075I
b = −0.368435 + 0.504187I
2.28204 + 1.25980I 3.87420 − 3.95142I
u = 0.232900 − 0.562056I
a = −1.68860 + 1.12075I
b = −0.368435 − 0.504187I
2.28204 − 1.25980I 3.87420 + 3.95142I
u = 0.096418 + 1.393080I
a = 0.667863 + 0.044755I
b = −0.504387 − 0.413403I
−3.56329 + 2.49031I 0
u = 0.096418 − 1.393080I
a = 0.667863 − 0.044755I
b = −0.504387 + 0.413403I
−3.56329 − 2.49031I 0
u = 0.205762 + 1.386790I
a = −1.46276 − 0.03865I
b = 0.01850 + 3.00217I
−6.10565 + 2.87492I 0
u = 0.205762 − 1.386790I
a = −1.46276 + 0.03865I
b = 0.01850 − 3.00217I
−6.10565 − 2.87492I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.239877 + 1.381360I
a = 0.363803 − 1.007460I
b = 1.83084 + 2.64228I
−0.37974 − 6.94098I 0
u = −0.239877 − 1.381360I
a = 0.363803 + 1.007460I
b = 1.83084 − 2.64228I
−0.37974 + 6.94098I 0
u = 0.23220 + 1.39528I
a = −1.080520 + 0.161583I
b = 0.376710 + 0.711456I
−5.68295 + 5.10949I 0
u = 0.23220 − 1.39528I
a = −1.080520 − 0.161583I
b = 0.376710 − 0.711456I
−5.68295 − 5.10949I 0
u = −0.557111 + 0.152288I
a = −1.16889 − 1.17714I
b = 0.13263 + 1.54331I
4.09579 + 2.24249I 2.09249 + 6.49191I
u = −0.557111 − 0.152288I
a = −1.16889 + 1.17714I
b = 0.13263 − 1.54331I
4.09579 − 2.24249I 2.09249 − 6.49191I
u = 0.26322 + 1.40067I
a = 1.150470 + 0.262478I
b = 0.12209 − 2.54689I
−1.53483 + 5.53884I 0
u = 0.26322 − 1.40067I
a = 1.150470 − 0.262478I
b = 0.12209 + 2.54689I
−1.53483 − 5.53884I 0
u = −0.24822 + 1.42034I
a = 0.125478 + 0.107540I
b = 0.746609 − 0.398952I
−6.88313 − 5.63183I 0
u = −0.24822 − 1.42034I
a = 0.125478 − 0.107540I
b = 0.746609 + 0.398952I
−6.88313 + 5.63183I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.17484 + 1.43130I
a = 0.024046 + 0.220816I
b = 0.936174 + 0.364235I
−7.94217 − 3.35665I 0
u = −0.17484 − 1.43130I
a = 0.024046 − 0.220816I
b = 0.936174 − 0.364235I
−7.94217 + 3.35665I 0
u = −0.10527 + 1.44541I
a = 0.853980 + 0.625681I
b = −1.59490 − 0.51909I
−6.16042 + 2.51482I 0
u = −0.10527 − 1.44541I
a = 0.853980 − 0.625681I
b = −1.59490 + 0.51909I
−6.16042 − 2.51482I 0
u = 0.16355 + 1.44140I
a = −0.879236 + 0.029819I
b = 0.413235 + 0.411153I
−5.14995 − 1.32551I 0
u = 0.16355 − 1.44140I
a = −0.879236 − 0.029819I
b = 0.413235 − 0.411153I
−5.14995 + 1.32551I 0
u = 0.25844 + 1.42833I
a = −1.084660 − 0.164757I
b = 0.01462 + 2.51096I
−3.76654 + 10.58860I 0
u = 0.25844 − 1.42833I
a = −1.084660 + 0.164757I
b = 0.01462 − 2.51096I
−3.76654 − 10.58860I 0
u = −0.28605 + 1.42369I
a = 1.02941 − 1.09734I
b = 1.18408 + 3.15876I
−3.61534 − 11.73800I 0
u = −0.28605 − 1.42369I
a = 1.02941 + 1.09734I
b = 1.18408 − 3.15876I
−3.61534 + 11.73800I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.26157 + 1.42986I
a = −0.95968 + 1.43576I
b = −1.58657 − 3.53860I
−9.44015 − 7.84845I 0
u = −0.26157 − 1.42986I
a = −0.95968 − 1.43576I
b = −1.58657 + 3.53860I
−9.44015 + 7.84845I 0
u = −0.15325 + 1.44673I
a = −0.921050 − 0.964047I
b = 2.34445 + 0.68813I
−10.99480 − 1.49755I 0
u = −0.15325 − 1.44673I
a = −0.921050 + 0.964047I
b = 2.34445 − 0.68813I
−10.99480 + 1.49755I 0
u = −0.27283 + 1.42929I
a = −0.147225 − 0.080722I
b = −0.629275 + 0.574116I
−8.52249 − 10.72670I 0
u = −0.27283 − 1.42929I
a = −0.147225 + 0.080722I
b = −0.629275 − 0.574116I
−8.52249 + 10.72670I 0
u = −0.13438 + 1.44948I
a = 0.060062 − 0.292373I
b = −0.956495 − 0.748806I
−10.49970 + 1.35653I 0
u = −0.13438 − 1.44948I
a = 0.060062 + 0.292373I
b = −0.956495 + 0.748806I
−10.49970 − 1.35653I 0
u = −0.29452 + 1.43525I
a = −1.15670 + 1.04114I
b = −0.94490 − 3.18553I
−6.2981 − 17.5562I 0
u = −0.29452 − 1.43525I
a = −1.15670 − 1.04114I
b = −0.94490 + 3.18553I
−6.2981 + 17.5562I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10198 + 1.47999I
a = −1.002820 − 0.545658I
b = 1.56485 + 0.12099I
−9.06430 + 7.73555I 0
u = −0.10198 − 1.47999I
a = −1.002820 + 0.545658I
b = 1.56485 − 0.12099I
−9.06430 − 7.73555I 0
u = 0.485114 + 0.170668I
a = 2.51389 + 2.67178I
b = −1.16833 − 2.03899I
−1.032640 + 0.255032I 3.20255 − 10.10229I
u = 0.485114 − 0.170668I
a = 2.51389 − 2.67178I
b = −1.16833 + 2.03899I
−1.032640 − 0.255032I 3.20255 + 10.10229I
u = −0.24423 + 1.47467I
a = −0.0983331 − 0.0071465I
b = −0.188904 + 0.429077I
−11.10450 − 4.45040I 0
u = −0.24423 − 1.47467I
a = −0.0983331 + 0.0071465I
b = −0.188904 − 0.429077I
−11.10450 + 4.45040I 0
u = −0.19551 + 1.48517I
a = 0.081909 − 0.126058I
b = −0.394609 − 0.545514I
−11.79450 − 6.13180I 0
u = −0.19551 − 1.48517I
a = 0.081909 + 0.126058I
b = −0.394609 + 0.545514I
−11.79450 + 6.13180I 0
u = 0.480020
a = −1.07071
b = 0.420132
0.824866 12.3370
u = 0.0855909
a = 7.24591
b = −0.772916
−1.21018 −9.52400
15
II. I
u
2
= hau − u
2
+ b + a, −u
2
a + a
2
+ 1, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
8
=
−u
u
2
− u + 1
a
1
=
u
2
+ 1
−u
2
+ u − 1
a
4
=
a
−au + u
2
− a
a
7
=
−u
2
− 1
u
2
− u + 1
a
3
=
−u
2
a + au − a + u
−au
a
2
=
−u
2
a + au − a + u
−2u
2
+ 2u − 2
a
6
=
0
au − u
2
− a + 2u − 2
a
10
=
0
u
a
5
=
0
au − u
2
− a + 2u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
2
a + 6au + 6u
2
− 9a − 5u + 6
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
11
c
12
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
, c
7
, c
10
(u
3
− u
2
+ 1)
2
c
5
, c
9
u
6
c
6
, c
8
(u
3
+ u
2
+ 2u + 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
, c
7
c
10
(y
3
− y
2
+ 2y −1)
2
c
5
, c
9
y
6
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.500000 − 0.424452I
b = −1.60964 + 1.73159I
5.65624I −0.00556 − 4.66003I
u = 0.215080 + 1.307140I
a = −1.16236 + 0.98673I
b = 1.039800 + 0.882689I
−4.13758 + 2.82812I −6.5820 − 15.2977I
u = 0.215080 − 1.307140I
a = −0.500000 + 0.424452I
b = −1.60964 − 1.73159I
− 5.65624I −0.00556 + 4.66003I
u = 0.215080 − 1.307140I
a = −1.16236 − 0.98673I
b = 1.039800 − 0.882689I
−4.13758 − 2.82812I −6.5820 + 15.2977I
u = 0.569840
a = 0.162359 + 0.986732I
b = 0.06984 − 1.54901I
4.13758 + 2.82812I 4.08755 − 6.14773I
u = 0.569840
a = 0.162359 − 0.986732I
b = 0.06984 + 1.54901I
4.13758 − 2.82812I 4.08755 + 6.14773I
19
III. I
u
3
= h−u
2
+ b − u − 2, 2u
2
+ a + u + 4, u
3
+ 2u − 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
8
=
−u
−u + 1
a
1
=
u
2
+ 1
−u
a
4
=
−2u
2
− u − 4
u
2
+ u + 2
a
7
=
−1
−u + 1
a
3
=
−2u
2
− u − 4
u
2
+ u + 2
a
2
=
−u
2
− u − 3
u
2
+ 2
a
6
=
−1
−u + 1
a
10
=
u
u
2
a
5
=
−u
2
− 1
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 11u
2
+ 9u + 22
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
6
u
3
c
4
(u + 1)
3
c
5
, c
8
, c
10
u
3
+ 2u + 1
c
7
u
3
+ 3u
2
+ 5u + 2
c
9
, c
11
, c
12
u
3
+ 2u − 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
6
y
3
c
5
, c
8
, c
9
c
10
, c
11
, c
12
y
3
+ 4y
2
+ 4y −1
c
7
y
3
+ y
2
+ 13y −4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22670 + 1.46771I
a = 0.432268 − 0.136798I
b = −0.329484 + 0.802255I
−11.08570 − 5.13794I −3.17092 + 5.88938I
u = −0.22670 − 1.46771I
a = 0.432268 + 0.136798I
b = −0.329484 − 0.802255I
−11.08570 + 5.13794I −3.17092 − 5.88938I
u = 0.453398
a = −4.86454
b = 2.65897
−0.857735 28.3420
23
IV. I
u
4
= h−u
2
+ b, −u
3
+ a − u, u
4
+ u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
8
=
−u
u
3
+ u
a
1
=
u
2
+ 1
u
3
+ 2u + 1
a
4
=
u
3
+ u
u
2
a
7
=
−u
3
− 2u
u
3
+ u
a
3
=
u
3
+ u
u
2
a
2
=
u
3
+ u
2
+ u + 1
u
3
+ u
2
+ 2u + 1
a
6
=
−u
3
− 2u
u
3
+ u
a
10
=
2u
3
+ u
2
+ 3u + 3
−u
3
− u
2
− u − 2
a
5
=
−u
2
− 1
−u
3
− 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
3
+ 3u
2
+ 7u + 2
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
6
u
4
c
4
(u + 1)
4
c
5
, c
8
, c
10
u
4
− u
3
+ 2u
2
− 2u + 1
c
7
(u
2
− u + 1)
2
c
9
, c
11
, c
12
u
4
+ u
3
+ 2u
2
+ 2u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
6
y
4
c
5
, c
8
, c
9
c
10
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
c
7
(y
2
+ y + 1)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621744 + 0.440597I
a = −0.500000 + 0.866025I
b = 0.192440 − 0.547877I
−4.93480 − 2.02988I −0.92268 + 4.41855I
u = −0.621744 − 0.440597I
a = −0.500000 − 0.866025I
b = 0.192440 + 0.547877I
−4.93480 + 2.02988I −0.92268 − 4.41855I
u = 0.121744 + 1.306620I
a = −0.500000 − 0.866025I
b = −1.69244 + 0.31815I
−4.93480 + 2.02988I −6.57732 − 5.10773I
u = 0.121744 − 1.306620I
a = −0.500000 + 0.866025I
b = −1.69244 − 0.31815I
−4.93480 − 2.02988I −6.57732 + 5.10773I
27
V. I
u
5
= hu
2
+ b + u, −u
2
+ a − 2, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
8
=
−u
u
2
− u + 1
a
1
=
u
2
+ 1
−u
2
+ u − 1
a
4
=
u
2
+ 2
−u
2
− u
a
7
=
−u
2
− 1
u
2
− u + 1
a
3
=
2u
2
− u + 3
−u
2
− 1
a
2
=
2u
2
− u + 3
−2u
2
+ 2u − 2
a
6
=
0
−u
2
+ u
a
10
=
0
u
a
5
=
0
−u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 3u − 4
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
11
c
12
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
, c
7
, c
10
u
3
− u
2
+ 1
c
5
, c
9
u
3
c
6
, c
8
u
3
+ u
2
+ 2u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
, c
11
, c
12
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
, c
7
c
10
y
3
− y
2
+ 2y −1
c
5
, c
9
y
3
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.337641 + 0.562280I
b = 1.44728 − 1.86942I
0 3.29468 + 1.67231I
u = 0.215080 − 1.307140I
a = 0.337641 − 0.562280I
b = 1.44728 + 1.86942I
0 3.29468 − 1.67231I
u = 0.569840
a = 2.32472
b = −0.894558
0 −3.58940
31
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
7
)(u
3
− u
2
+ 2u − 1)
3
(u
110
+ 53u
109
+ ··· + 874u + 1)
c
2
((u − 1)
7
)(u
3
+ u
2
− 1)
3
(u
110
− 11u
109
+ ··· + 20u + 1)
c
3
u
7
(u
3
− u
2
+ 2u − 1)
3
(u
110
− 4u
109
+ ··· + 1344u − 128)
c
4
((u + 1)
7
)(u
3
− u
2
+ 1)
3
(u
110
− 11u
109
+ ··· + 20u + 1)
c
5
u
9
(u
3
+ 2u + 1)(u
4
− u
3
+ ··· − 2u + 1)(u
110
− 2u
109
+ ··· − 1024u − 512)
c
6
u
7
(u
3
+ u
2
+ 2u + 1)
3
(u
110
− 4u
109
+ ··· + 1344u − 128)
c
7
(u
2
− u + 1)
2
(u
3
− u
2
+ 1)
3
(u
3
+ 3u
2
+ 5u + 2)
· (u
110
− 5u
109
+ ··· − 3176u + 292)
c
8
(u
3
+ 2u + 1)(u
3
+ u
2
+ 2u + 1)
3
(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
110
+ 5u
109
+ ··· − 7u + 1)
c
9
u
9
(u
3
+ 2u − 1)(u
4
+ u
3
+ ··· + 2u + 1)(u
110
− 2u
109
+ ··· − 1024u − 512)
c
10
(u
3
+ 2u + 1)(u
3
− u
2
+ 1)
3
(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
110
+ 23u
109
+ ··· − 3335609u + 61891)
c
11
, c
12
(u
3
+ 2u − 1)(u
3
− u
2
+ 2u − 1)
3
(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (u
110
+ 5u
109
+ ··· − 7u + 1)
32
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
7
)(y
3
+ 3y
2
+ 2y −1)
3
(y
110
+ 19y
109
+ ··· − 806974y + 1)
c
2
, c
4
((y −1)
7
)(y
3
− y
2
+ 2y −1)
3
(y
110
− 53y
109
+ ··· − 874y + 1)
c
3
, c
6
y
7
(y
3
+ 3y
2
+ 2y −1)
3
(y
110
+ 54y
109
+ ··· − 192512y + 16384)
c
5
, c
9
y
9
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
110
+ 56y
109
+ ··· + 2228224y + 262144)
c
7
(y
2
+ y + 1)
2
(y
3
− y
2
+ 2y −1)
3
(y
3
+ y
2
+ 13y −4)
· (y
110
+ 9y
109
+ ··· − 11413240y + 85264)
c
8
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
3
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
110
+ 101y
109
+ ··· − 147y + 1)
c
10
(y
3
− y
2
+ 2y −1)
3
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
110
+ 41y
109
+ ··· − 17639818908843y + 3830495881)
33
