12a
0041
(K12a
0041
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 8 11 4 12 1 6 10 9
Solving Sequence
8,12
9 1
4,10
7 3 11 6 5 2
c
8
c
12
c
9
c
7
c
3
c
11
c
6
c
5
c
2
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.44805 × 10
35
u
105
+ 9.77658 × 10
35
u
104
+ ··· + 1.67026 × 10
34
b + 1.04667 × 10
35
,
− 3.36641 × 10
36
u
105
+ 2.29468 × 10
37
u
104
+ ··· + 1.67026 × 10
34
a + 2.84093 × 10
36
,
u
106
− 8u
105
+ ··· − 8u + 1i
I
u
2
= hb, u
7
− 2u
6
− 2u
5
+ 4u
4
+ 2u
3
− u
2
+ a − u − 3, u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
I
u
3
= h−a
5
+ a
4
− 2a
2
+ b + a + 1, a
6
− a
5
+ 2a
3
− a
2
− a + 1, u + 1i
* 3 irreducible components of dim
C
= 0, with total 120 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−1.45 × 10
35
u
105
+ 9.78 × 10
35
u
104
+ · · · + 1.67 × 10
34
b + 1.05 ×
10
35
, −3.37 × 10
36
u
105
+ 2.29 × 10
37
u
104
+ · · · + 1.67 × 10
34
a + 2.84 ×
10
36
, u
106
− 8u
105
+ · · · − 8u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
201.551u
105
− 1373.85u
104
+ ··· + 1189.54u − 170.089
8.66963u
105
− 58.5334u
104
+ ··· + 49.7451u − 6.26650
a
10
=
−u
2
+ 1
u
4
− 2u
2
a
7
=
−89.0641u
105
+ 593.235u
104
+ ··· − 494.775u + 66.5949
144.038u
105
− 1011.28u
104
+ ··· + 967.142u − 136.266
a
3
=
173.819u
105
− 1206.87u
104
+ ··· + 1110.50u − 161.594
68.8034u
105
− 417.555u
104
+ ··· + 217.759u − 26.4940
a
11
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
6
=
31.9491u
105
− 240.754u
104
+ ··· + 266.507u − 40.0703
48.9374u
105
− 391.734u
104
+ ··· + 508.341u − 73.9905
a
5
=
−16.9883u
105
+ 150.980u
104
+ ··· − 241.834u + 33.9202
48.9374u
105
− 391.734u
104
+ ··· + 508.341u − 73.9905
a
2
=
193.608u
105
− 1303.08u
104
+ ··· + 1072.35u − 154.685
51.6786u
105
− 376.900u
104
+ ··· + 402.827u − 56.7005
(ii) Obstruction class = −1
(iii) Cusp Shapes = 187.107u
105
− 1299.22u
104
+ ··· + 1186.54u − 169.352
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
106
+ 50u
105
+ ··· + 115u + 1
c
2
, c
4
u
106
− 10u
105
+ ··· − 11u + 1
c
3
, c
7
u
106
− 2u
105
+ ··· − 2176u + 256
c
5
u
106
+ 3u
105
+ ··· + 3191795u + 338425
c
6
, c
10
u
106
+ 2u
105
+ ··· + 128u + 64
c
8
, c
9
, c
12
u
106
+ 8u
105
+ ··· + 8u + 1
c
11
u
106
− 42u
105
+ ··· − 40960u + 4096
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
106
+ 22y
105
+ ··· − 9623y + 1
c
2
, c
4
y
106
− 50y
105
+ ··· − 115y + 1
c
3
, c
7
y
106
− 54y
105
+ ··· − 2015232y + 65536
c
5
y
106
− 25y
105
+ ··· − 3787599470175y + 114531480625
c
6
, c
10
y
106
− 42y
105
+ ··· − 40960y + 4096
c
8
, c
9
, c
12
y
106
− 92y
105
+ ··· − 20y + 1
c
11
y
106
+ 34y
105
+ ··· − 511705088y + 16777216
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.975597 + 0.332760I
a = 1.66268 − 0.43076I
b = −0.719953 − 0.291088I
−0.664937 + 0.060812I 0
u = −0.975597 − 0.332760I
a = 1.66268 + 0.43076I
b = −0.719953 + 0.291088I
−0.664937 − 0.060812I 0
u = −0.787729 + 0.530832I
a = −1.025870 − 0.880599I
b = 1.235030 − 0.231770I
5.70804 − 0.97860I 0
u = −0.787729 − 0.530832I
a = −1.025870 + 0.880599I
b = 1.235030 + 0.231770I
5.70804 + 0.97860I 0
u = −0.971534 + 0.424156I
a = 0.554238 + 0.741710I
b = −0.381199 + 0.952283I
0.22721 + 2.28278I 0
u = −0.971534 − 0.424156I
a = 0.554238 − 0.741710I
b = −0.381199 − 0.952283I
0.22721 − 2.28278I 0
u = −0.719478 + 0.572631I
a = 0.97434 + 1.13046I
b = −1.226880 + 0.499611I
4.23697 − 6.46219I 0
u = −0.719478 − 0.572631I
a = 0.97434 − 1.13046I
b = −1.226880 − 0.499611I
4.23697 + 6.46219I 0
u = −0.965180 + 0.494632I
a = −0.734599 − 0.110481I
b = 1.206320 + 0.413402I
4.90799 + 2.58638I 0
u = −0.965180 − 0.494632I
a = −0.734599 + 0.110481I
b = 1.206320 − 0.413402I
4.90799 − 2.58638I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.220211 + 0.865620I
a = 0.41270 + 1.60488I
b = −1.216810 + 0.674505I
0.38915 − 12.96150I 0
u = −0.220211 − 0.865620I
a = 0.41270 − 1.60488I
b = −1.216810 − 0.674505I
0.38915 + 12.96150I 0
u = −0.239845 + 0.842650I
a = −0.49567 − 1.38558I
b = 1.227260 − 0.486133I
2.68174 − 7.33219I 0
u = −0.239845 − 0.842650I
a = −0.49567 + 1.38558I
b = 1.227260 + 0.486133I
2.68174 + 7.33219I 0
u = −1.014630 + 0.504575I
a = 0.488720 − 0.061862I
b = −1.206960 − 0.630482I
2.81598 + 8.10504I 0
u = −1.014630 − 0.504575I
a = 0.488720 + 0.061862I
b = −1.206960 + 0.630482I
2.81598 − 8.10504I 0
u = −1.125830 + 0.181268I
a = −0.899054 − 0.314000I
b = 0.196548 − 0.484159I
1.40723 − 0.85274I 0
u = −1.125830 − 0.181268I
a = −0.899054 + 0.314000I
b = 0.196548 + 0.484159I
1.40723 + 0.85274I 0
u = −0.755747 + 0.391839I
a = −0.452972 − 0.622080I
b = −0.159790 − 0.860727I
0.91081 − 1.47380I 0
u = −0.755747 − 0.391839I
a = −0.452972 + 0.622080I
b = −0.159790 + 0.860727I
0.91081 + 1.47380I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.217080 + 0.816392I
a = −0.723684 − 0.838932I
b = −0.435106 − 1.030610I
−2.10087 − 6.75943I 0
u = −0.217080 − 0.816392I
a = −0.723684 + 0.838932I
b = −0.435106 + 1.030610I
−2.10087 + 6.75943I 0
u = −0.332885 + 0.758781I
a = −0.328189 − 0.525794I
b = 1.268420 + 0.119140I
4.32160 − 3.56949I 0
u = −0.332885 − 0.758781I
a = −0.328189 + 0.525794I
b = 1.268420 − 0.119140I
4.32160 + 3.56949I 0
u = −0.100955 + 0.814954I
a = −0.779621 − 0.254715I
b = −0.776258 − 0.307494I
−3.44339 − 1.35942I 0
u = −0.100955 − 0.814954I
a = −0.779621 + 0.254715I
b = −0.776258 + 0.307494I
−3.44339 + 1.35942I 0
u = −0.396637 + 0.712421I
a = 0.088469 + 0.208203I
b = −1.226060 − 0.398992I
3.29218 + 1.91305I 0
u = −0.396637 − 0.712421I
a = 0.088469 − 0.208203I
b = −1.226060 + 0.398992I
3.29218 − 1.91305I 0
u = −0.204708 + 0.788783I
a = 1.15366 + 1.32172I
b = −0.897435 + 0.329928I
−3.03362 − 4.24411I 0
u = −0.204708 − 0.788783I
a = 1.15366 − 1.32172I
b = −0.897435 − 0.329928I
−3.03362 + 4.24411I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.779771
a = 3.27362
b = −0.476085
−0.441751 0
u = −1.159330 + 0.387775I
a = 0.269576 + 0.833513I
b = −0.867224 + 0.343872I
−0.21010 − 2.97299I 0
u = −1.159330 − 0.387775I
a = 0.269576 − 0.833513I
b = −0.867224 − 0.343872I
−0.21010 + 2.97299I 0
u = −0.226322 + 0.738094I
a = 0.435071 + 0.984632I
b = 0.071439 + 0.904117I
−0.86368 − 2.44093I 0
u = −0.226322 − 0.738094I
a = 0.435071 − 0.984632I
b = 0.071439 − 0.904117I
−0.86368 + 2.44093I 0
u = 1.216950 + 0.180245I
a = −0.520675 − 0.270816I
b = 1.071960 − 0.662084I
2.00198 − 4.54056I 0
u = 1.216950 − 0.180245I
a = −0.520675 + 0.270816I
b = 1.071960 + 0.662084I
2.00198 + 4.54056I 0
u = −0.014428 + 0.766161I
a = 0.931288 − 0.294098I
b = 0.836190 − 0.399287I
−3.81217 − 4.28264I 0
u = −0.014428 − 0.766161I
a = 0.931288 + 0.294098I
b = 0.836190 + 0.399287I
−3.81217 + 4.28264I 0
u = 1.274170 + 0.165295I
a = 0.704589 + 0.152345I
b = −0.963662 + 0.557506I
4.57161 + 0.34047I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.274170 − 0.165295I
a = 0.704589 − 0.152345I
b = −0.963662 − 0.557506I
4.57161 − 0.34047I 0
u = −1.242310 + 0.335443I
a = 0.137119 − 0.855612I
b = 0.830272 + 0.297989I
−0.019244 + 0.300241I 0
u = −1.242310 − 0.335443I
a = 0.137119 + 0.855612I
b = 0.830272 − 0.297989I
−0.019244 − 0.300241I 0
u = −1.276760 + 0.174071I
a = −1.067710 + 0.598894I
b = 0.026372 − 0.883725I
1.95886 − 0.66619I 0
u = −1.276760 − 0.174071I
a = −1.067710 − 0.598894I
b = 0.026372 + 0.883725I
1.95886 + 0.66619I 0
u = 1.279740 + 0.211946I
a = −0.686542 + 0.674004I
b = 0.612218 + 0.892040I
0.504812 + 1.217070I 0
u = 1.279740 − 0.211946I
a = −0.686542 − 0.674004I
b = 0.612218 − 0.892040I
0.504812 − 1.217070I 0
u = −1.283730 + 0.231052I
a = −2.85407 − 1.47162I
b = 0.849304 − 0.283050I
0.00191 − 2.41011I 0
u = −1.283730 − 0.231052I
a = −2.85407 + 1.47162I
b = 0.849304 + 0.283050I
0.00191 + 2.41011I 0
u = 1.273370 + 0.311313I
a = −0.325712 + 0.595994I
b = 0.837898 + 0.492250I
0.18004 + 8.16321I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.273370 − 0.311313I
a = −0.325712 − 0.595994I
b = 0.837898 − 0.492250I
0.18004 − 8.16321I 0
u = 1.293690 + 0.236811I
a = −1.038820 − 0.511092I
b = 0.818163 − 0.593568I
0.11121 + 3.81256I 0
u = 1.293690 − 0.236811I
a = −1.038820 + 0.511092I
b = 0.818163 + 0.593568I
0.11121 − 3.81256I 0
u = 1.32993
a = 0.358643
b = −0.620045
5.73362 0
u = 0.137302 + 0.654097I
a = −0.53263 + 2.08724I
b = 1.162830 + 0.643339I
−1.12935 + 7.49600I 3.17543 − 5.19190I
u = 0.137302 − 0.654097I
a = −0.53263 − 2.08724I
b = 1.162830 − 0.643339I
−1.12935 − 7.49600I 3.17543 + 5.19190I
u = −1.312530 + 0.242030I
a = 0.769040 − 0.906565I
b = 0.399807 + 1.008790I
0.97390 − 4.81466I 0
u = −1.312530 − 0.242030I
a = 0.769040 + 0.906565I
b = 0.399807 − 1.008790I
0.97390 + 4.81466I 0
u = 1.328650 + 0.255478I
a = 0.673459 − 0.353384I
b = −0.450231 − 0.779449I
3.07140 + 5.25471I 0
u = 1.328650 − 0.255478I
a = 0.673459 + 0.353384I
b = −0.450231 + 0.779449I
3.07140 − 5.25471I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.347830 + 0.147998I
a = 2.48621 + 1.07165I
b = −1.264040 − 0.176666I
6.98793 − 1.47827I 0
u = −1.347830 − 0.147998I
a = 2.48621 − 1.07165I
b = −1.264040 + 0.176666I
6.98793 + 1.47827I 0
u = −0.110509 + 0.632808I
a = −0.386174 + 1.058420I
b = −0.269146 + 0.693777I
−1.45150 − 2.00619I 4.67683 + 5.18706I
u = −0.110509 − 0.632808I
a = −0.386174 − 1.058420I
b = −0.269146 − 0.693777I
−1.45150 + 2.00619I 4.67683 − 5.18706I
u = −1.354850 + 0.102000I
a = −2.35075 − 0.99307I
b = 1.238120 + 0.451792I
5.73583 + 4.04891I 0
u = −1.354850 − 0.102000I
a = −2.35075 + 0.99307I
b = 1.238120 − 0.451792I
5.73583 − 4.04891I 0
u = −1.344860 + 0.242958I
a = 2.49790 + 1.35461I
b = −1.229600 + 0.451056I
5.76007 − 5.25979I 0
u = −1.344860 − 0.242958I
a = 2.49790 − 1.35461I
b = −1.229600 − 0.451056I
5.76007 + 5.25979I 0
u = −0.009420 + 0.629939I
a = −0.99744 + 1.99085I
b = 0.779932 + 0.446948I
−3.95789 − 0.68802I 1.63493 − 0.69608I
u = −0.009420 − 0.629939I
a = −0.99744 − 1.99085I
b = 0.779932 − 0.446948I
−3.95789 + 0.68802I 1.63493 + 0.69608I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.348810 + 0.269511I
a = −2.40893 − 1.39590I
b = 1.220420 − 0.653105I
3.57407 − 10.87410I 0
u = −1.348810 − 0.269511I
a = −2.40893 + 1.39590I
b = 1.220420 + 0.653105I
3.57407 + 10.87410I 0
u = 1.332360 + 0.348313I
a = −0.133187 − 0.496674I
b = −0.707308 + 0.275029I
1.05711 + 5.54164I 0
u = 1.332360 − 0.348313I
a = −0.133187 + 0.496674I
b = −0.707308 − 0.275029I
1.05711 − 5.54164I 0
u = 0.047760 + 0.612339I
a = 1.12247 − 0.95080I
b = 0.476521 − 0.921710I
−3.31230 + 1.70372I 0.96529 − 1.53746I
u = 0.047760 − 0.612339I
a = 1.12247 + 0.95080I
b = 0.476521 + 0.921710I
−3.31230 − 1.70372I 0.96529 + 1.53746I
u = 0.123677 + 0.589119I
a = 0.59271 − 1.97345I
b = −1.124350 − 0.445004I
1.10125 + 2.18817I 6.14918 − 1.16320I
u = 0.123677 − 0.589119I
a = 0.59271 + 1.97345I
b = −1.124350 + 0.445004I
1.10125 − 2.18817I 6.14918 + 1.16320I
u = 1.38946 + 0.30667I
a = 0.725871 + 0.247775I
b = 0.100534 − 1.013670I
4.25836 + 6.24602I 0
u = 1.38946 − 0.30667I
a = 0.725871 − 0.247775I
b = 0.100534 + 1.013670I
4.25836 − 6.24602I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38676 + 0.32750I
a = 2.22145 − 1.24393I
b = −0.979090 − 0.325843I
2.01147 + 8.28093I 0
u = 1.38676 − 0.32750I
a = 2.22145 + 1.24393I
b = −0.979090 + 0.325843I
2.01147 − 8.28093I 0
u = 1.39547 + 0.33838I
a = −0.661353 − 0.483166I
b = −0.445124 + 1.086220I
3.01346 + 10.92650I 0
u = 1.39547 − 0.33838I
a = −0.661353 + 0.483166I
b = −0.445124 − 1.086220I
3.01346 − 10.92650I 0
u = 1.44467
a = 2.73857
b = −0.965678
6.54061 0
u = 1.40543 + 0.36177I
a = 1.88322 − 1.36604I
b = −1.23603 − 0.69987I
5.5453 + 17.3785I 0
u = 1.40543 − 0.36177I
a = 1.88322 + 1.36604I
b = −1.23603 + 0.69987I
5.5453 − 17.3785I 0
u = 1.41017 + 0.34686I
a = −1.92773 + 1.29284I
b = 1.264080 + 0.521279I
7.92299 + 11.61900I 0
u = 1.41017 − 0.34686I
a = −1.92773 − 1.29284I
b = 1.264080 − 0.521279I
7.92299 − 11.61900I 0
u = 1.43097 + 0.25547I
a = 1.54652 − 0.79475I
b = −1.317580 + 0.343849I
9.11890 + 1.51931I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43097 − 0.25547I
a = 1.54652 + 0.79475I
b = −1.317580 − 0.343849I
9.11890 − 1.51931I 0
u = 1.42784 + 0.28880I
a = −1.75788 + 0.93117I
b = 1.354820 − 0.083923I
9.93949 + 7.33761I 0
u = 1.42784 − 0.28880I
a = −1.75788 − 0.93117I
b = 1.354820 + 0.083923I
9.93949 − 7.33761I 0
u = 1.45803 + 0.02469I
a = 0.144641 − 0.749887I
b = −0.202758 + 1.076270I
8.08502 + 2.33225I 0
u = 1.45803 − 0.02469I
a = 0.144641 + 0.749887I
b = −0.202758 − 1.076270I
8.08502 − 2.33225I 0
u = 1.49012 + 0.06818I
a = 2.23140 − 0.17523I
b = −1.30879 − 0.56563I
11.6664 + 8.2496I 0
u = 1.49012 − 0.06818I
a = 2.23140 + 0.17523I
b = −1.30879 + 0.56563I
11.6664 − 8.2496I 0
u = 1.49130 + 0.03892I
a = −2.34660 + 0.12553I
b = 1.343590 + 0.329120I
13.37820 + 2.34517I 0
u = 1.49130 − 0.03892I
a = −2.34660 − 0.12553I
b = 1.343590 − 0.329120I
13.37820 − 2.34517I 0
u = 0.328828 + 0.206242I
a = −1.19831 + 1.44333I
b = 1.113270 − 0.511888I
0.55693 − 5.26669I 2.17022 + 4.89770I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.328828 − 0.206242I
a = −1.19831 − 1.44333I
b = 1.113270 + 0.511888I
0.55693 + 5.26669I 2.17022 − 4.89770I
u = 0.216080 + 0.303403I
a = 0.86930 − 1.86344I
b = −1.080150 + 0.204268I
2.12093 − 0.33420I 5.91854 − 0.05388I
u = 0.216080 − 0.303403I
a = 0.86930 + 1.86344I
b = −1.080150 − 0.204268I
2.12093 + 0.33420I 5.91854 + 0.05388I
u = −0.363030
a = −0.676170
b = −0.314526
0.730740 14.1320
u = 0.1057060 + 0.0875681I
a = −4.78981 + 0.25440I
b = 0.338389 + 0.624293I
−1.73093 − 0.78651I −2.83553 + 1.26176I
u = 0.1057060 − 0.0875681I
a = −4.78981 − 0.25440I
b = 0.338389 − 0.624293I
−1.73093 + 0.78651I −2.83553 − 1.26176I
15
II. I
u
2
=
hb, u
7
−2u
6
−2u
5
+4u
4
+2u
3
−u
2
+a−u−3, u
8
−u
7
−3u
6
+2u
5
+3u
4
−2u−1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
−u
7
+ 2u
6
+ 2u
5
− 4u
4
− 2u
3
+ u
2
+ u + 3
0
a
10
=
−u
2
+ 1
u
4
− 2u
2
a
7
=
1
0
a
3
=
−u
7
+ 2u
6
+ 2u
5
− 4u
4
− 2u
3
+ u
2
+ u + 3
0
a
11
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
6
=
u
3
− 2u
u
3
− u
a
5
=
−u
u
3
− u
a
2
=
−u
7
+ 2u
6
+ 2u
5
− 4u
4
− 2u
3
+ u
2
+ 2u + 3
−u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
7
− 2u
6
− 7u
5
+ u
4
+ u
3
+ 4u
2
+ 8u + 3
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
7
u
8
c
4
(u + 1)
8
c
5
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
6
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
8
, c
9
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
10
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
11
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
12
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
8
c
3
, c
7
y
8
c
5
, c
11
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
6
, c
10
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
8
, c
9
, c
12
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.180120 + 0.268597I
a = −0.281371 − 1.128550I
b = 0
−0.604279 − 1.131230I 5.26238 + 0.22273I
u = −1.180120 − 0.268597I
a = −0.281371 + 1.128550I
b = 0
−0.604279 + 1.131230I 5.26238 − 0.22273I
u = −0.108090 + 0.747508I
a = 0.208670 + 0.825203I
b = 0
−3.80435 − 2.57849I 2.12884 + 3.87967I
u = −0.108090 − 0.747508I
a = 0.208670 − 0.825203I
b = 0
−3.80435 + 2.57849I 2.12884 − 3.87967I
u = 1.37100
a = 0.829189
b = 0
4.85780 7.72210
u = 1.334530 + 0.318930I
a = 0.284386 − 0.605794I
b = 0
0.73474 + 6.44354I 7.14098 − 6.66742I
u = 1.334530 − 0.318930I
a = 0.284386 + 0.605794I
b = 0
0.73474 − 6.44354I 7.14098 + 6.66742I
u = −0.463640
a = 2.74744
b = 0
−0.799899 0.213560
19
III. I
u
3
= h−a
5
+ a
4
− 2a
2
+ b + a + 1, a
6
− a
5
+ 2a
3
− a
2
− a + 1, u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
−1
a
9
=
1
−1
a
1
=
−1
0
a
4
=
a
a
5
− a
4
+ 2a
2
− a − 1
a
10
=
0
−1
a
7
=
0
−a
5
+ a
3
− 2a
2
− a + 2
a
3
=
a
−a
5
− a
2
− a
a
11
=
0
−1
a
6
=
0
−a
5
+ a
3
− 2a
2
− a + 2
a
5
=
a
5
− a
3
+ 2a
2
+ a − 2
−a
5
+ a
3
− 2a
2
− a + 2
a
2
=
a
5
− a
3
+ 2a
2
+ a − 2
−2a
5
+ a
3
− 3a
2
− a + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5a
5
− a
3
+ 10a
2
+ 2a + 5
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
, c
7
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
3
, c
4
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
5
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
6
, c
10
, c
11
u
6
c
8
, c
9
(u + 1)
6
c
12
(u − 1)
6
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
3
, c
4
c
7
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
6
, c
10
, c
11
y
6
c
8
, c
9
, c
12
(y −1)
6
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.917982 + 0.270708I
b = 1.002190 + 0.295542I
3.53554 + 0.92430I 10.88169 − 1.11590I
u = −1.00000
a = −0.917982 − 0.270708I
b = 1.002190 − 0.295542I
3.53554 − 0.92430I 10.88169 + 1.11590I
u = −1.00000
a = 0.732786 + 0.381252I
b = −1.073950 + 0.558752I
1.64493 − 5.69302I 8.89162 + 7.09196I
u = −1.00000
a = 0.732786 − 0.381252I
b = −1.073950 − 0.558752I
1.64493 + 5.69302I 8.89162 − 7.09196I
u = −1.00000
a = 0.685196 + 1.063260I
b = −0.428243 + 0.664531I
−0.245672 + 0.924305I 6.22669 + 0.83820I
u = −1.00000
a = 0.685196 − 1.063260I
b = −0.428243 − 0.664531I
−0.245672 − 0.924305I 6.22669 − 0.83820I
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
8
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
106
+ 50u
105
+ ··· + 115u + 1)
c
2
((u − 1)
8
)(u
6
+ u
5
+ ··· + u + 1)(u
106
− 10u
105
+ ··· − 11u + 1)
c
3
u
8
(u
6
− u
5
+ ··· − u + 1)(u
106
− 2u
105
+ ··· − 2176u + 256)
c
4
((u + 1)
8
)(u
6
− u
5
+ ··· − u + 1)(u
106
− 10u
105
+ ··· − 11u + 1)
c
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
106
+ 3u
105
+ ··· + 3191795u + 338425)
c
6
u
6
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
· (u
106
+ 2u
105
+ ··· + 128u + 64)
c
7
u
8
(u
6
+ u
5
+ ··· + u + 1)(u
106
− 2u
105
+ ··· − 2176u + 256)
c
8
, c
9
((u + 1)
6
)(u
8
− u
7
+ ··· − 2u − 1)(u
106
+ 8u
105
+ ··· + 8u + 1)
c
10
u
6
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
106
+ 2u
105
+ ··· + 128u + 64)
c
11
u
6
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
106
− 42u
105
+ ··· − 40960u + 4096)
c
12
((u − 1)
6
)(u
8
+ u
7
+ ··· + 2u − 1)(u
106
+ 8u
105
+ ··· + 8u + 1)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
8
)(y
6
+ y
5
+ ··· + 3y + 1)(y
106
+ 22y
105
+ ··· − 9623y + 1)
c
2
, c
4
(y −1)
8
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
106
− 50y
105
+ ··· − 115y + 1)
c
3
, c
7
y
8
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
106
− 54y
105
+ ··· − 2015232y + 65536)
c
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
106
− 25y
105
+ ··· − 3787599470175y + 114531480625)
c
6
, c
10
y
6
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
106
− 42y
105
+ ··· − 40960y + 4096)
c
8
, c
9
, c
12
(y −1)
6
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
106
− 92y
105
+ ··· − 20y + 1)
c
11
y
6
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
106
+ 34y
105
+ ··· − 511705088y + 16777216)
25
