12a
0314
(K12a
0314
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 2 9 4 1 12 5 10 7
Solving Sequence
4,11 5,7
8 3 10 12 1 2 9 6
c
4
c
7
c
3
c
10
c
11
c
12
c
1
c
9
c
6
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h3.08859 × 10
177
u
134
+ 4.12913 × 10
177
u
133
+ ··· + 2.92373 × 10
177
b − 6.46265 × 10
177
,
− 5.20487 × 10
177
u
134
− 7.50538 × 10
177
u
133
+ ··· + 2.92373 × 10
177
a − 2.04516 × 10
178
,
u
135
+ u
134
+ ··· − 10u − 1i
I
u
2
= h−u
25
− 5u
23
+ ··· + b + u, u
26
− 3u
25
+ ··· + a + 1, u
27
+ 6u
25
+ ··· + 4u + 1i
* 2 irreducible components of dim
C
= 0, with total 162 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
= h3.09 × 10
177
u
134
+ 4.13 × 10
177
u
133
+ · · · + 2.92 × 10
177
b − 6.46 ×
10
177
, −5.20 × 10
177
u
134
− 7.51 × 10
177
u
133
+ · · · + 2.92 × 10
177
a − 2.05 ×
10
178
, u
135
+ u
134
+ · · · − 10u − 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
u
2
a
7
=
1.78022u
134
+ 2.56706u
133
+ ··· + 1.72860u + 6.99504
−1.05639u
134
− 1.41228u
133
+ ··· + 18.8557u + 2.21042
a
8
=
2.83661u
134
+ 3.97934u
133
+ ··· − 17.1271u + 4.78462
−1.05639u
134
− 1.41228u
133
+ ··· + 18.8557u + 2.21042
a
3
=
0.667462u
134
+ 1.65680u
133
+ ··· − 88.1836u − 9.43511
0.245974u
134
+ 0.777931u
133
+ ··· − 18.2752u − 0.373464
a
10
=
u
u
3
+ u
a
12
=
u
3
u
5
+ u
3
+ u
a
1
=
−1.83805u
134
− 0.271778u
133
+ ··· − 95.8499u − 4.55202
1.08576u
134
+ 0.642890u
133
+ ··· − 0.00908748u + 0.935550
a
2
=
1.69714u
134
+ 2.70494u
133
+ ··· + 8.51473u − 3.45506
−0.898715u
134
− 2.04841u
133
+ ··· + 5.14031u − 0.604629
a
9
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
6
=
2.94174u
134
+ 4.34609u
133
+ ··· − 7.34893u + 6.24805
−1.64723u
134
− 2.09134u
133
+ ··· + 23.2895u + 2.65403
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.06282u
134
+ 5.04217u
133
+ ··· − 3.18528u − 6.72246
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
135
+ 56u
134
+ ··· + 282415u + 5041
c
2
, c
5
u
135
+ 2u
134
+ ··· − 183u + 71
c
3
, c
7
u
135
+ u
134
+ ··· + 14458u + 16279
c
4
, c
10
u
135
− u
134
+ ··· − 10u + 1
c
6
u
135
− 20u
134
+ ··· + 12813u + 3131
c
8
u
135
− 12u
134
+ ··· − 359245u + 99529
c
9
, c
11
u
135
− 45u
134
+ ··· − 76u + 1
c
12
u
135
+ 2u
134
+ ··· − 115u + 457
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
135
+ 60y
134
+ ··· + 2060543075y −25411681
c
2
, c
5
y
135
− 56y
134
+ ··· + 282415y −5041
c
3
, c
7
y
135
+ 97y
134
+ ··· − 11715822106y −265005841
c
4
, c
10
y
135
+ 45y
134
+ ··· − 76y −1
c
6
y
135
− 22y
134
+ ··· + 518733671y −9803161
c
8
y
135
+ 26y
134
+ ··· − 71452162795y −9906021841
c
9
, c
11
y
135
+ 101y
134
+ ··· + 1848y −1
c
12
y
135
− 10y
134
+ ··· + 12233405y −208849
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.182191 + 0.978011I
a = 0.053526 + 0.498105I
b = −0.913562 − 0.305391I
2.78439 − 2.21481I 0
u = 0.182191 − 0.978011I
a = 0.053526 − 0.498105I
b = −0.913562 + 0.305391I
2.78439 + 2.21481I 0
u = −0.257952 + 0.978394I
a = −0.207563 + 0.191828I
b = 1.040760 − 0.132048I
1.69152 + 7.21546I 0
u = −0.257952 − 0.978394I
a = −0.207563 − 0.191828I
b = 1.040760 + 0.132048I
1.69152 − 7.21546I 0
u = 0.297927 + 0.935277I
a = 0.554906 + 0.972744I
b = −0.375896 + 0.194038I
2.04642 − 3.11861I 0
u = 0.297927 − 0.935277I
a = 0.554906 − 0.972744I
b = −0.375896 − 0.194038I
2.04642 + 3.11861I 0
u = 0.048541 + 1.020490I
a = −0.281366 + 0.850989I
b = −0.229769 − 0.550795I
2.37651 − 1.33885I 0
u = 0.048541 − 1.020490I
a = −0.281366 − 0.850989I
b = −0.229769 + 0.550795I
2.37651 + 1.33885I 0
u = 0.624839 + 0.743352I
a = 1.36143 + 0.58880I
b = 0.33558 + 1.44289I
1.44939 − 4.62743I 0
u = 0.624839 − 0.743352I
a = 1.36143 − 0.58880I
b = 0.33558 − 1.44289I
1.44939 + 4.62743I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.687698 + 0.766698I
a = 1.22927 + 1.70192I
b = 0.93164 + 1.16301I
1.08282 − 3.99338I 0
u = −0.687698 − 0.766698I
a = 1.22927 − 1.70192I
b = 0.93164 − 1.16301I
1.08282 + 3.99338I 0
u = 0.322455 + 0.986690I
a = 1.30133 − 0.65999I
b = 0.288260 + 1.111700I
1.00007 − 5.31249I 0
u = 0.322455 − 0.986690I
a = 1.30133 + 0.65999I
b = 0.288260 − 1.111700I
1.00007 + 5.31249I 0
u = −0.784066 + 0.556358I
a = 0.394134 − 0.253532I
b = 0.030061 + 0.779063I
−3.06388 + 0.25442I 0
u = −0.784066 − 0.556358I
a = 0.394134 + 0.253532I
b = 0.030061 − 0.779063I
−3.06388 − 0.25442I 0
u = 0.017373 + 0.959928I
a = −0.26438 + 1.69451I
b = −0.66691 − 1.45421I
5.75111 − 4.49804I 0
u = 0.017373 − 0.959928I
a = −0.26438 − 1.69451I
b = −0.66691 + 1.45421I
5.75111 + 4.49804I 0
u = 0.690019 + 0.794749I
a = −0.70119 + 1.83083I
b = −0.733382 + 1.200060I
1.64624 − 1.58894I 0
u = 0.690019 − 0.794749I
a = −0.70119 − 1.83083I
b = −0.733382 − 1.200060I
1.64624 + 1.58894I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.124250 + 1.052510I
a = −0.374282 + 1.019370I
b = 0.242021 − 0.356502I
2.47481 − 1.46151I 0
u = −0.124250 − 1.052510I
a = −0.374282 − 1.019370I
b = 0.242021 + 0.356502I
2.47481 + 1.46151I 0
u = 0.730207 + 0.768827I
a = 1.38692 − 0.88175I
b = 0.083254 − 1.033660I
1.61638 + 0.94446I 0
u = 0.730207 − 0.768827I
a = 1.38692 + 0.88175I
b = 0.083254 + 1.033660I
1.61638 − 0.94446I 0
u = −0.672932 + 0.819553I
a = −1.43281 − 0.80589I
b = 0.040967 − 0.796293I
0.78023 + 5.76542I 0
u = −0.672932 − 0.819553I
a = −1.43281 + 0.80589I
b = 0.040967 + 0.796293I
0.78023 − 5.76542I 0
u = −0.781702 + 0.719098I
a = 1.184710 + 0.338601I
b = 0.786645 + 0.475694I
−3.44393 − 1.01362I 0
u = −0.781702 − 0.719098I
a = 1.184710 − 0.338601I
b = 0.786645 − 0.475694I
−3.44393 + 1.01362I 0
u = −0.073144 + 0.932715I
a = −2.00962 − 2.39100I
b = −0.051227 + 1.230250I
6.80128 + 1.87487I 0
u = −0.073144 − 0.932715I
a = −2.00962 + 2.39100I
b = −0.051227 − 1.230250I
6.80128 − 1.87487I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.886558 + 0.603387I
a = −0.355164 + 0.151303I
b = −0.296286 + 1.079330I
−3.81694 + 3.79135I 0
u = 0.886558 − 0.603387I
a = −0.355164 − 0.151303I
b = −0.296286 − 1.079330I
−3.81694 − 3.79135I 0
u = 0.721149 + 0.797335I
a = 0.206670 + 0.515003I
b = 0.241979 − 1.324930I
0.03808 + 3.51542I 0
u = 0.721149 − 0.797335I
a = 0.206670 − 0.515003I
b = 0.241979 + 1.324930I
0.03808 − 3.51542I 0
u = −0.712957 + 0.814314I
a = −1.33242 + 0.66330I
b = −0.18819 + 1.77652I
1.68930 + 0.74766I 0
u = −0.712957 − 0.814314I
a = −1.33242 − 0.66330I
b = −0.18819 − 1.77652I
1.68930 − 0.74766I 0
u = −0.801154 + 0.742049I
a = 1.55777 + 0.32439I
b = 1.060750 + 0.043144I
−3.59680 − 1.35599I 0
u = −0.801154 − 0.742049I
a = 1.55777 − 0.32439I
b = 1.060750 − 0.043144I
−3.59680 + 1.35599I 0
u = −0.650109 + 0.880076I
a = 0.84298 + 1.23027I
b = −0.014753 − 1.331240I
3.78897 + 2.52031I 0
u = −0.650109 − 0.880076I
a = 0.84298 − 1.23027I
b = −0.014753 + 1.331240I
3.78897 − 2.52031I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.028887 + 0.899858I
a = 1.42340 − 3.31692I
b = −0.128305 + 1.165830I
4.74784 + 4.74110I 0
u = −0.028887 − 0.899858I
a = 1.42340 + 3.31692I
b = −0.128305 − 1.165830I
4.74784 − 4.74110I 0
u = −0.002396 + 0.896636I
a = 0.60825 + 1.82878I
b = 0.48954 − 1.57452I
6.04754 − 0.54483I 0
u = −0.002396 − 0.896636I
a = 0.60825 − 1.82878I
b = 0.48954 + 1.57452I
6.04754 + 0.54483I 0
u = 0.863693 + 0.692591I
a = 0.897732 − 0.804504I
b = 0.52708 − 1.32870I
0.56808 + 6.92229I 0
u = 0.863693 − 0.692591I
a = 0.897732 + 0.804504I
b = 0.52708 + 1.32870I
0.56808 − 6.92229I 0
u = −0.894065 + 0.688028I
a = −0.840171 − 0.806541I
b = −0.65417 − 1.37472I
−1.49753 − 12.96880I 0
u = −0.894065 − 0.688028I
a = −0.840171 + 0.806541I
b = −0.65417 + 1.37472I
−1.49753 + 12.96880I 0
u = −0.197669 + 1.111950I
a = −0.88725 − 1.44321I
b = −0.403719 + 1.351080I
7.76949 + 6.79943I 0
u = −0.197669 − 1.111950I
a = −0.88725 + 1.44321I
b = −0.403719 − 1.351080I
7.76949 − 6.79943I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.840905 + 0.754988I
a = −1.65520 + 0.40132I
b = −1.346250 − 0.168487I
−5.37206 + 6.09957I 0
u = 0.840905 − 0.754988I
a = −1.65520 − 0.40132I
b = −1.346250 + 0.168487I
−5.37206 − 6.09957I 0
u = 0.851238 + 0.147950I
a = −0.718097 − 0.554840I
b = −0.530662 − 1.202540I
1.65967 − 9.19748I 0
u = 0.851238 − 0.147950I
a = −0.718097 + 0.554840I
b = −0.530662 + 1.202540I
1.65967 + 9.19748I 0
u = −0.681150 + 0.910444I
a = 2.83794 − 0.14278I
b = 0.011720 − 0.931068I
1.066200 − 0.522589I 0
u = −0.681150 − 0.910444I
a = 2.83794 + 0.14278I
b = 0.011720 + 0.931068I
1.066200 + 0.522589I 0
u = 0.793490 + 0.819836I
a = −1.84178 + 0.28996I
b = −0.869259 − 0.565594I
−7.86699 − 0.96280I 0
u = 0.793490 − 0.819836I
a = −1.84178 − 0.28996I
b = −0.869259 + 0.565594I
−7.86699 + 0.96280I 0
u = 0.876571 + 0.732191I
a = −0.611541 + 0.448689I
b = −0.745897 + 0.893684I
−4.74494 − 1.40898I 0
u = 0.876571 − 0.732191I
a = −0.611541 − 0.448689I
b = −0.745897 − 0.893684I
−4.74494 + 1.40898I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.790320 + 0.825636I
a = 0.961027 + 0.336341I
b = 0.329707 + 0.756995I
−2.17948 − 2.71087I 0
u = 0.790320 − 0.825636I
a = 0.961027 − 0.336341I
b = 0.329707 − 0.756995I
−2.17948 + 2.71087I 0
u = −0.852083 + 0.765794I
a = −0.894156 − 0.987576I
b = −0.486242 − 1.010700I
−6.42768 − 3.99066I 0
u = −0.852083 − 0.765794I
a = −0.894156 + 0.987576I
b = −0.486242 + 1.010700I
−6.42768 + 3.99066I 0
u = 0.655478 + 0.942520I
a = 1.152080 + 0.765922I
b = −0.40671 + 1.56053I
2.05184 − 0.42331I 0
u = 0.655478 − 0.942520I
a = 1.152080 − 0.765922I
b = −0.40671 − 1.56053I
2.05184 + 0.42331I 0
u = 0.689876 + 0.924925I
a = 2.63892 + 0.23797I
b = 0.76308 + 1.35140I
2.04503 − 3.73553I 0
u = 0.689876 − 0.924925I
a = 2.63892 − 0.23797I
b = 0.76308 − 1.35140I
2.04503 + 3.73553I 0
u = −0.702748 + 0.919564I
a = −1.24798 + 0.76455I
b = 0.28362 + 1.80278I
2.01595 + 4.68054I 0
u = −0.702748 − 0.919564I
a = −1.24798 − 0.76455I
b = 0.28362 − 1.80278I
2.01595 − 4.68054I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.884733 + 0.752880I
a = −0.531180 + 0.206844I
b = −0.200453 + 0.496698I
−5.74291 − 1.34202I 0
u = −0.884733 − 0.752880I
a = −0.531180 − 0.206844I
b = −0.200453 − 0.496698I
−5.74291 + 1.34202I 0
u = 0.158242 + 1.155000I
a = −0.349033 + 0.640872I
b = 0.028732 − 0.815651I
2.19994 − 1.27262I 0
u = 0.158242 − 1.155000I
a = −0.349033 − 0.640872I
b = 0.028732 + 0.815651I
2.19994 + 1.27262I 0
u = −0.684601 + 0.945585I
a = −2.77824 − 0.26400I
b = −0.94746 + 1.30952I
1.63233 + 9.30140I 0
u = −0.684601 − 0.945585I
a = −2.77824 + 0.26400I
b = −0.94746 − 1.30952I
1.63233 − 9.30140I 0
u = 0.706799 + 0.930995I
a = −1.69494 + 1.17271I
b = −0.194351 − 1.328060I
0.44874 − 8.98252I 0
u = 0.706799 − 0.930995I
a = −1.69494 − 1.17271I
b = −0.194351 + 1.328060I
0.44874 + 8.98252I 0
u = 0.221920 + 1.151170I
a = 0.69674 − 1.35373I
b = 0.51132 + 1.34118I
6.10373 − 12.62740I 0
u = 0.221920 − 1.151170I
a = 0.69674 + 1.35373I
b = 0.51132 − 1.34118I
6.10373 + 12.62740I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.437000 + 1.100790I
a = 0.864126 + 0.513330I
b = −0.264139 − 1.258760I
6.37212 + 0.50399I 0
u = −0.437000 − 1.100790I
a = 0.864126 − 0.513330I
b = −0.264139 + 1.258760I
6.37212 − 0.50399I 0
u = 0.708667 + 0.949566I
a = −2.83413 − 0.15041I
b = −0.128903 − 1.089500I
2.16540 − 6.44695I 0
u = 0.708667 − 0.949566I
a = −2.83413 + 0.15041I
b = −0.128903 + 1.089500I
2.16540 + 6.44695I 0
u = 0.741269 + 0.929721I
a = −0.056422 + 0.467169I
b = −0.332085 + 0.578033I
−1.85034 − 3.06303I 0
u = 0.741269 − 0.929721I
a = −0.056422 − 0.467169I
b = −0.332085 − 0.578033I
−1.85034 + 3.06303I 0
u = −0.198998 + 0.780233I
a = 0.716435 + 0.210614I
b = 0.764763 + 0.174582I
−1.97377 + 1.53826I 0
u = −0.198998 − 0.780233I
a = 0.716435 − 0.210614I
b = 0.764763 − 0.174582I
−1.97377 − 1.53826I 0
u = 0.760414 + 0.933967I
a = 1.058620 − 0.882520I
b = 0.928936 − 0.502379I
−7.51384 − 4.88368I 0
u = 0.760414 − 0.933967I
a = 1.058620 + 0.882520I
b = 0.928936 + 0.502379I
−7.51384 + 4.88368I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.826433 + 0.884407I
a = 0.502926 + 0.497730I
b = 0.716200 + 0.483626I
−5.32606 − 0.60628I 0
u = −0.826433 − 0.884407I
a = 0.502926 − 0.497730I
b = 0.716200 − 0.483626I
−5.32606 + 0.60628I 0
u = −0.762596 + 0.167367I
a = 0.796811 − 0.619266I
b = 0.374725 − 1.239250I
3.51291 + 3.79183I −8.00000 − 3.66278I
u = −0.762596 − 0.167367I
a = 0.796811 + 0.619266I
b = 0.374725 + 1.239250I
3.51291 − 3.79183I −8.00000 + 3.66278I
u = −0.717460 + 0.991265I
a = −1.61017 − 0.78407I
b = −0.785319 + 0.609006I
−2.61535 + 6.68659I 0
u = −0.717460 − 0.991265I
a = −1.61017 + 0.78407I
b = −0.785319 − 0.609006I
−2.61535 − 6.68659I 0
u = −0.737356 + 0.983139I
a = −1.34639 − 1.08442I
b = −1.122400 + 0.095325I
−2.86184 + 7.14763I 0
u = −0.737356 − 0.983139I
a = −1.34639 + 1.08442I
b = −1.122400 − 0.095325I
−2.86184 − 7.14763I 0
u = −0.025837 + 1.233540I
a = −0.059316 + 1.259640I
b = 0.106338 − 1.025650I
2.97005 + 2.13809I 0
u = −0.025837 − 1.233540I
a = −0.059316 − 1.259640I
b = 0.106338 + 1.025650I
2.97005 − 2.13809I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.847510 + 0.896957I
a = −1.069150 − 0.156979I
b = −0.667049 + 0.655089I
−5.30570 + 6.81308I 0
u = −0.847510 − 0.896957I
a = −1.069150 + 0.156979I
b = −0.667049 − 0.655089I
−5.30570 − 6.81308I 0
u = 0.417407 + 1.173910I
a = −0.785299 + 0.387509I
b = 0.387239 − 1.149160I
4.97232 + 4.61880I 0
u = 0.417407 − 1.173910I
a = −0.785299 − 0.387509I
b = 0.387239 + 1.149160I
4.97232 − 4.61880I 0
u = −0.286583 + 0.697207I
a = 1.24082 + 0.82984I
b = 0.04312 − 1.41819I
4.08895 + 1.36538I −8.00000 − 3.72323I
u = −0.286583 − 0.697207I
a = 1.24082 − 0.82984I
b = 0.04312 + 1.41819I
4.08895 − 1.36538I −8.00000 + 3.72323I
u = 0.761348 + 0.992134I
a = 1.18922 − 1.23499I
b = 1.402570 − 0.090730I
−4.63912 − 12.08370I 0
u = 0.761348 − 0.992134I
a = 1.18922 + 1.23499I
b = 1.402570 + 0.090730I
−4.63912 + 12.08370I 0
u = −0.772167 + 0.990529I
a = 2.08639 − 0.10299I
b = 0.500777 − 1.055170I
−5.73047 + 10.04250I 0
u = −0.772167 − 0.990529I
a = 2.08639 + 0.10299I
b = 0.500777 + 1.055170I
−5.73047 − 10.04250I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.733219 + 0.082682I
a = −0.431782 + 0.836904I
b = −0.245045 + 0.909165I
−1.94022 + 1.78020I −11.45430 − 3.94650I
u = 0.733219 − 0.082682I
a = −0.431782 − 0.836904I
b = −0.245045 − 0.909165I
−1.94022 − 1.78020I −11.45430 + 3.94650I
u = −0.690336 + 1.061470I
a = −1.41515 − 0.54700I
b = −0.125386 + 0.916784I
−1.60825 + 5.34108I 0
u = −0.690336 − 1.061470I
a = −1.41515 + 0.54700I
b = −0.125386 − 0.916784I
−1.60825 − 5.34108I 0
u = 0.747130 + 1.031610I
a = −2.28323 + 0.30120I
b = −0.53260 − 1.36857I
1.60981 − 12.91710I 0
u = 0.747130 − 1.031610I
a = −2.28323 − 0.30120I
b = −0.53260 + 1.36857I
1.60981 + 12.91710I 0
u = −0.785444 + 1.004640I
a = 0.056048 + 0.131552I
b = 0.169789 + 0.357159I
−4.96281 + 7.52395I 0
u = −0.785444 − 1.004640I
a = 0.056048 − 0.131552I
b = 0.169789 − 0.357159I
−4.96281 − 7.52395I 0
u = 0.779412 + 1.017680I
a = 1.48728 − 0.47472I
b = 0.679389 + 1.033730I
−3.86949 − 4.73325I 0
u = 0.779412 − 1.017680I
a = 1.48728 + 0.47472I
b = 0.679389 − 1.033730I
−3.86949 + 4.73325I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.757416 + 1.046400I
a = 2.19473 + 0.40576I
b = 0.64594 − 1.41898I
−0.3875 + 19.0826I 0
u = −0.757416 − 1.046400I
a = 2.19473 − 0.40576I
b = 0.64594 + 1.41898I
−0.3875 − 19.0826I 0
u = 0.728582 + 1.081060I
a = 1.45635 − 0.52465I
b = 0.273313 + 1.158300I
−2.36888 − 9.78045I 0
u = 0.728582 − 1.081060I
a = 1.45635 + 0.52465I
b = 0.273313 − 1.158300I
−2.36888 + 9.78045I 0
u = −0.670414 + 0.061548I
a = −0.883943 − 0.504311I
b = −0.846187 + 0.248725I
−1.25905 − 4.10688I −12.29238 + 5.14366I
u = −0.670414 − 0.061548I
a = −0.883943 + 0.504311I
b = −0.846187 − 0.248725I
−1.25905 + 4.10688I −12.29238 − 5.14366I
u = −0.373579 + 0.451382I
a = −0.17418 − 2.00459I
b = −0.301836 + 0.404575I
−3.12408 + 0.64190I −10.3906 − 9.6269I
u = −0.373579 − 0.451382I
a = −0.17418 + 2.00459I
b = −0.301836 − 0.404575I
−3.12408 − 0.64190I −10.3906 + 9.6269I
u = 0.555860 + 0.079655I
a = 0.986163 + 0.461106I
b = 0.717460 + 0.092449I
−0.436395 + 0.147603I −10.87352 + 0.55690I
u = 0.555860 − 0.079655I
a = 0.986163 − 0.461106I
b = 0.717460 − 0.092449I
−0.436395 − 0.147603I −10.87352 − 0.55690I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.397375
a = 0.961032
b = 0.451366
−0.689241 −14.2140
u = −0.199448 + 0.110060I
a = 3.73682 − 2.06229I
b = −0.157294 − 1.269930I
3.89546 + 0.90103I −5.37105 − 2.93314I
u = −0.199448 − 0.110060I
a = 3.73682 + 2.06229I
b = −0.157294 + 1.269930I
3.89546 − 0.90103I −5.37105 + 2.93314I
u = −0.038914 + 0.138913I
a = 6.81455 + 1.81439I
b = 0.428741 + 1.175730I
2.55492 − 4.41403I −7.39626 + 1.76727I
u = −0.038914 − 0.138913I
a = 6.81455 − 1.81439I
b = 0.428741 − 1.175730I
2.55492 + 4.41403I −7.39626 − 1.76727I
18
II.
I
u
2
= h−u
25
−5u
23
+· · ·+b+u, u
26
−3u
25
+· · ·+a+1, u
27
+6u
25
+· · ·+4u+1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
u
2
a
7
=
−u
26
+ 3u
25
+ ··· + 3u − 1
u
25
+ 5u
23
+ ··· + u
2
− u
a
8
=
−u
26
+ 2u
25
+ ··· + 4u − 1
u
25
+ 5u
23
+ ··· + u
2
− u
a
3
=
u
23
+ 2u
22
+ ··· + 7u + 3
2u
26
+ 12u
24
+ ··· + 7u
2
+ 2u
a
10
=
u
u
3
+ u
a
12
=
u
3
u
5
+ u
3
+ u
a
1
=
u
26
+ 6u
24
+ ··· + 11u
2
− 6u
−2u
25
− 11u
23
+ ··· − 10u − 3
a
2
=
−3u
26
− 2u
25
+ ··· − 4u + 3
2u
26
+ 3u
25
+ ··· + 8u + 1
a
9
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
6
=
−u
26
+ 3u
25
+ ··· − 2u − 2
−u
23
− 6u
21
+ ··· − 6u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
26
+ 8u
25
− 36u
24
+ 42u
23
− 132u
22
+ 137u
21
− 339u
20
+
318u
19
−669u
18
+ 557u
17
−1060u
16
+ 791u
15
−1376u
14
+ 897u
13
−1484u
12
+ 842u
11
−
1326u
10
+ 633u
9
− 970u
8
+ 371u
7
− 556u
6
+ 158u
5
− 236u
4
+ 37u
3
− 54u
2
− 3u − 6
19
(iv) u-Polynomials at the component
20
Crossings u-Polynomials at each crossing
c
1
u
27
− 13u
26
+ ··· + 13u − 1
c
2
u
27
+ u
26
+ ··· − u − 1
c
3
u
27
+ 14u
25
+ ··· + 4u − 1
c
4
u
27
+ 6u
25
+ ··· + 4u + 1
c
5
u
27
− u
26
+ ··· − u + 1
c
6
u
27
+ u
26
+ ··· + 3u − 1
c
7
u
27
+ 14u
25
+ ··· + 4u + 1
c
8
u
27
+ 5u
26
+ ··· − u − 1
c
9
u
27
+ 12u
26
+ ··· + 2u − 1
c
10
u
27
+ 6u
25
+ ··· + 4u − 1
c
11
u
27
− 12u
26
+ ··· + 2u + 1
c
12
u
27
− u
26
+ ··· − 5u + 1
21
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
+ 15y
26
+ ··· − 7y −1
c
2
, c
5
y
27
− 13y
26
+ ··· + 13y −1
c
3
, c
7
y
27
+ 28y
26
+ ··· + 128y
2
− 1
c
4
, c
10
y
27
+ 12y
26
+ ··· + 2y −1
c
6
y
27
− 7y
26
+ ··· + 5y −1
c
8
y
27
− 7y
26
+ ··· − y −1
c
9
, c
11
y
27
+ 16y
26
+ ··· + 198y −1
c
12
y
27
+ y
26
+ ··· + 7y −1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.761479 + 0.640887I
a = 0.910448 − 0.166609I
b = 0.579634 + 0.474240I
−4.02360 − 0.21116I −16.7658 − 0.3372I
u = −0.761479 − 0.640887I
a = 0.910448 + 0.166609I
b = 0.579634 − 0.474240I
−4.02360 + 0.21116I −16.7658 + 0.3372I
u = −0.198504 + 0.997767I
a = 1.12532 + 1.56160I
b = −0.260908 − 1.127740I
4.21139 − 3.20224I −3.85581 + 2.20635I
u = −0.198504 − 0.997767I
a = 1.12532 − 1.56160I
b = −0.260908 + 1.127740I
4.21139 + 3.20224I −3.85581 − 2.20635I
u = −0.690133 + 0.811068I
a = 1.097110 + 0.487259I
b = 0.449305 + 1.221140I
0.71077 − 2.64443I −6.47183 + 0.74363I
u = −0.690133 − 0.811068I
a = 1.097110 − 0.487259I
b = 0.449305 − 1.221140I
0.71077 + 2.64443I −6.47183 − 0.74363I
u = 0.226267 + 0.902043I
a = −1.08139 + 1.64350I
b = 0.096987 − 1.351070I
5.09894 − 1.89183I −2.01080 + 5.17175I
u = 0.226267 − 0.902043I
a = −1.08139 − 1.64350I
b = 0.096987 + 1.351070I
5.09894 + 1.89183I −2.01080 − 5.17175I
u = 0.664641 + 0.849545I
a = 0.418217 + 0.828352I
b = −0.22181 + 1.55034I
2.37091 − 3.03914I −4.82866 + 3.51658I
u = 0.664641 − 0.849545I
a = 0.418217 − 0.828352I
b = −0.22181 − 1.55034I
2.37091 + 3.03914I −4.82866 − 3.51658I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.663771 + 0.885311I
a = 1.96946 + 0.14600I
b = 0.15156 + 1.55129I
2.48434 − 2.11146I −4.79115 + 2.62168I
u = 0.663771 − 0.885311I
a = 1.96946 − 0.14600I
b = 0.15156 − 1.55129I
2.48434 + 2.11146I −4.79115 − 2.62168I
u = 0.883289 + 0.721673I
a = −0.525680 + 0.315492I
b = −0.295318 + 0.501734I
−5.69432 + 2.18099I −12.30398 − 4.36845I
u = 0.883289 − 0.721673I
a = −0.525680 − 0.315492I
b = −0.295318 − 0.501734I
−5.69432 − 2.18099I −12.30398 + 4.36845I
u = −0.680382 + 0.924373I
a = −2.53920 − 0.70489I
b = −0.409343 + 1.262820I
1.06768 + 7.93216I −6.00345 − 6.85178I
u = −0.680382 − 0.924373I
a = −2.53920 + 0.70489I
b = −0.409343 − 1.262820I
1.06768 − 7.93216I −6.00345 + 6.85178I
u = 0.247679 + 0.797356I
a = −0.552494 + 0.434314I
b = −0.279994 − 1.357420I
4.69675 − 0.23962I −1.79115 + 0.59356I
u = 0.247679 − 0.797356I
a = −0.552494 − 0.434314I
b = −0.279994 + 1.357420I
4.69675 + 0.23962I −1.79115 − 0.59356I
u = −0.069959 + 1.240000I
a = 0.215684 + 0.785221I
b = −0.096210 − 0.674840I
1.74167 + 1.35927I −19.8098 − 1.0921I
u = −0.069959 − 1.240000I
a = 0.215684 − 0.785221I
b = −0.096210 + 0.674840I
1.74167 − 1.35927I −19.8098 + 1.0921I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.705174 + 1.029550I
a = −1.31848 − 0.83487I
b = −0.611774 + 0.677874I
−2.87133 + 5.81024I −12.36703 − 3.92107I
u = −0.705174 − 1.029550I
a = −1.31848 + 0.83487I
b = −0.611774 − 0.677874I
−2.87133 − 5.81024I −12.36703 + 3.92107I
u = −0.229904 + 0.705974I
a = 0.825900 − 1.141740I
b = 0.413298 − 1.067590I
3.08394 + 5.15702I −1.88648 − 8.37181I
u = −0.229904 − 0.705974I
a = 0.825900 + 1.141740I
b = 0.413298 + 1.067590I
3.08394 − 5.15702I −1.88648 + 8.37181I
u = 0.782849 + 1.022960I
a = 1.086590 − 0.088051I
b = 0.360967 + 0.607311I
−4.77691 − 8.35173I −9.42923 + 9.62881I
u = 0.782849 − 1.022960I
a = 1.086590 + 0.088051I
b = 0.360967 − 0.607311I
−4.77691 + 8.35173I −9.42923 − 9.62881I
u = −0.265919
a = −3.26296
b = 0.247203
−3.04098 −11.3700
26
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
27
− 13u
26
+ ··· + 13u − 1)(u
135
+ 56u
134
+ ··· + 282415u + 5041)
c
2
(u
27
+ u
26
+ ··· − u − 1)(u
135
+ 2u
134
+ ··· − 183u + 71)
c
3
(u
27
+ 14u
25
+ ··· + 4u − 1)(u
135
+ u
134
+ ··· + 14458u + 16279)
c
4
(u
27
+ 6u
25
+ ··· + 4u + 1)(u
135
− u
134
+ ··· − 10u + 1)
c
5
(u
27
− u
26
+ ··· − u + 1)(u
135
+ 2u
134
+ ··· − 183u + 71)
c
6
(u
27
+ u
26
+ ··· + 3u − 1)(u
135
− 20u
134
+ ··· + 12813u + 3131)
c
7
(u
27
+ 14u
25
+ ··· + 4u + 1)(u
135
+ u
134
+ ··· + 14458u + 16279)
c
8
(u
27
+ 5u
26
+ ··· − u − 1)(u
135
− 12u
134
+ ··· − 359245u + 99529)
c
9
(u
27
+ 12u
26
+ ··· + 2u − 1)(u
135
− 45u
134
+ ··· − 76u + 1)
c
10
(u
27
+ 6u
25
+ ··· + 4u − 1)(u
135
− u
134
+ ··· − 10u + 1)
c
11
(u
27
− 12u
26
+ ··· + 2u + 1)(u
135
− 45u
134
+ ··· − 76u + 1)
c
12
(u
27
− u
26
+ ··· − 5u + 1)(u
135
+ 2u
134
+ ··· − 115u + 457)
27
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
27
+ 15y
26
+ ··· − 7y −1)
· (y
135
+ 60y
134
+ ··· + 2060543075y −25411681)
c
2
, c
5
(y
27
− 13y
26
+ ··· + 13y −1)(y
135
− 56y
134
+ ··· + 282415y −5041)
c
3
, c
7
(y
27
+ 28y
26
+ ··· + 128y
2
− 1)
· (y
135
+ 97y
134
+ ··· − 11715822106y −265005841)
c
4
, c
10
(y
27
+ 12y
26
+ ··· + 2y −1)(y
135
+ 45y
134
+ ··· − 76y −1)
c
6
(y
27
− 7y
26
+ ··· + 5y −1)
· (y
135
− 22y
134
+ ··· + 518733671y −9803161)
c
8
(y
27
− 7y
26
+ ··· − y −1)
· (y
135
+ 26y
134
+ ··· − 71452162795y −9906021841)
c
9
, c
11
(y
27
+ 16y
26
+ ··· + 198y −1)(y
135
+ 101y
134
+ ··· + 1848y −1)
c
12
(y
27
+ y
26
+ ··· + 7y −1)(y
135
− 10y
134
+ ··· + 1.22334 × 10
7
y −208849)
28
