12a
0673
(K12a
0673
)
A knot diagram
1
Linearized knot diagam
3 7 11 9 10 8 2 1 12 6 4 5
Solving Sequence
9,12 5,10
6 1 4 8 7 11 3 2
c
9
c
5
c
12
c
4
c
8
c
6
c
11
c
3
c
2
c
1
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−579387u
39
− 23275447u
38
+ ··· + 8192b − 8251727872,
− 1007291u
39
− 40140157u
38
+ ··· + 16384a − 16662396928,
u
40
+ 41u
39
+ ··· + 401408u + 16384i
I
u
2
= h−3.50204 × 10
97
a
27
u
2
+ 1.27267 × 10
97
a
26
u
2
+ ··· − 3.32558 × 10
97
a − 9.43161 × 10
94
,
a
27
u
2
− 5a
26
u
2
+ ··· + 285596a + 148877, u
3
− u
2
+ 1i
I
u
3
= h−13u
22
+ 66u
21
+ ··· + b + 11, −11u
22
+ 53u
21
+ ··· + a + 1, u
23
− 6u
22
+ ··· − 4u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 147 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−5.79×10
5
u
39
−2.33×10
7
u
38
+· · ·+8192b−8.25×10
9
, −1.01×10
6
u
39
−
4.01×10
7
u
38
+· · ·+1.64×10
4
a−1.67×10
10
, u
40
+41u
39
+· · ·+401408u+16384i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
5
=
61.4802u
39
+ 2449.96u
38
+ ··· + 2.36167 × 10
7
u + 1016992
70.7260u
39
+ 2841.24u
38
+ ··· + 2.36616 × 10
7
u + 1007291
a
10
=
1
u
2
a
6
=
49.2772u
39
+ 2035.73u
38
+ ··· + 2.73378 × 10
7
u + 1168475
−140.846u
39
− 5495.21u
38
+ ··· − 1.06948 × 10
7
u − 403173
a
1
=
−1.00781u
39
− 40.3125u
38
+ ··· − 386593u − 16447.5
−1.00781u
39
− 40.3203u
38
+ ··· − 388096.u − 16512
a
4
=
−9.24579u
39
− 391.280u
38
+ ··· − 44895.3u + 9701
70.7260u
39
+ 2841.24u
38
+ ··· + 2.36616 × 10
7
u + 1007291
a
8
=
−8.96484u
39
− 359.707u
38
+ ··· − 3.84858 × 10
6
u − 164479
−6.85156u
39
− 275.133u
38
+ ··· − 3046048u − 130368
a
7
=
115.111u
39
+ 4531.45u
38
+ ··· + 1.61831 × 10
7
u + 643411
135.594u
39
+ 5527.05u
38
+ ··· + 5.94395 × 10
7
u + 2503924
a
11
=
1
128
u
39
+
5
16
u
38
+ ··· + 1568u +
129
2
−0.00781250u
39
− 0.304688u
38
+ ··· − 1503.50u
2
− 63.5000u
a
3
=
−21.4449u
39
− 742.195u
38
+ ··· + 1.96811 × 10
7
u + 856786.
−128.012u
39
− 5132.03u
38
+ ··· − 3.03051 × 10
7
u − 1238166
a
2
=
−2.46484u
39
− 99.5313u
38
+ ··· − 783425.u − 32640
11.0078u
39
+ 439.559u
38
+ ··· + 3859393u + 163968
(ii) Obstruction class = −1
(iii) Cusp Shapes =
313701
2048
u
39
+
12529453
2048
u
38
+ ··· + 15458438u + 553758
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
40
+ 13u
39
+ ··· + 32u + 64
c
2
, c
7
u
40
+ 7u
39
+ ··· + 2u
2
+ 8
c
3
, c
5
, c
10
c
11
u
40
+ u
39
+ ··· + 2u + 1
c
4
, c
12
u
40
+ 3u
38
+ ··· + 3u + 1
c
8
u
40
− 35u
39
+ ··· − 4086976u + 307752
c
9
u
40
− 41u
39
+ ··· − 401408u + 16384
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
40
+ 25y
39
+ ··· − 27136y + 4096
c
2
, c
7
y
40
+ 13y
39
+ ··· + 32y + 64
c
3
, c
5
, c
10
c
11
y
40
− 35y
39
+ ··· + 20y + 1
c
4
, c
12
y
40
+ 6y
39
+ ··· + 5y + 1
c
8
y
40
+ 17y
39
+ ··· + 373353571616y + 94711293504
c
9
y
40
− 7y
39
+ ··· − 1409286144y + 268435456
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.386041 + 0.781738I
a = 0.327982 + 0.912189I
b = 0.839708 + 0.095747I
4.29895 − 4.62297I 0
u = −0.386041 − 0.781738I
a = 0.327982 − 0.912189I
b = 0.839708 − 0.095747I
4.29895 + 4.62297I 0
u = −0.424468 + 0.716698I
a = −0.337606 − 1.005260I
b = −0.863768 − 0.184738I
4.71501 + 0.92897I 0
u = −0.424468 − 0.716698I
a = −0.337606 + 1.005260I
b = −0.863768 + 0.184738I
4.71501 − 0.92897I 0
u = −0.688781 + 0.410406I
a = 0.50871 + 1.50198I
b = 0.966812 + 0.825756I
2.54965 + 8.13634I 0
u = −0.688781 − 0.410406I
a = 0.50871 − 1.50198I
b = 0.966812 − 0.825756I
2.54965 − 8.13634I 0
u = −0.654557 + 0.438339I
a = −0.47237 − 1.45216I
b = −0.945733 − 0.743460I
3.41551 + 2.50598I 0
u = −0.654557 − 0.438339I
a = −0.47237 + 1.45216I
b = −0.945733 + 0.743460I
3.41551 − 2.50598I 0
u = −0.607234 + 0.303704I
a = 0.34044 + 1.61539I
b = 0.697328 + 0.877527I
−2.53281 + 2.82471I 0
u = −0.607234 − 0.303704I
a = 0.34044 − 1.61539I
b = 0.697328 − 0.877527I
−2.53281 − 2.82471I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.445048 + 0.401866I
a = −0.184660 − 1.394420I
b = −0.642554 − 0.546377I
1.01499 + 1.04142I 0
u = −0.445048 − 0.401866I
a = −0.184660 + 1.394420I
b = −0.642554 + 0.546377I
1.01499 − 1.04142I 0
u = 0.079057 + 0.565866I
a = −0.254159 + 0.764745I
b = 0.452836 + 0.083361I
−0.513730 − 1.280700I 0
u = 0.079057 − 0.565866I
a = −0.254159 − 0.764745I
b = 0.452836 − 0.083361I
−0.513730 + 1.280700I 0
u = −0.530557 + 0.081357I
a = 0.07376 + 1.79161I
b = 0.184894 + 0.944550I
−0.04537 − 2.31418I 0
u = −0.530557 − 0.081357I
a = 0.07376 − 1.79161I
b = 0.184894 − 0.944550I
−0.04537 + 2.31418I 0
u = −1.29444 + 0.91899I
a = −0.059482 − 1.047590I
b = −1.03972 − 1.30139I
−7.1554 + 18.5968I 0
u = −1.29444 − 0.91899I
a = −0.059482 + 1.047590I
b = −1.03972 + 1.30139I
−7.1554 − 18.5968I 0
u = −1.30733 + 0.91344I
a = 0.076070 + 1.022580I
b = 1.03351 + 1.26737I
−5.82110 + 12.79620I 0
u = −1.30733 − 0.91344I
a = 0.076070 − 1.022580I
b = 1.03351 − 1.26737I
−5.82110 − 12.79620I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.31965 + 0.94989I
a = −0.009169 − 0.979688I
b = −0.94269 − 1.28413I
−12.4391 + 11.8677I 0
u = −1.31965 − 0.94989I
a = −0.009169 + 0.979688I
b = −0.94269 + 1.28413I
−12.4391 − 11.8677I 0
u = −1.36530 + 0.94019I
a = 0.052407 + 0.903121I
b = 0.92065 + 1.18375I
−7.44660 + 9.43936I 0
u = −1.36530 − 0.94019I
a = 0.052407 − 0.903121I
b = 0.92065 − 1.18375I
−7.44660 − 9.43936I 0
u = −1.37313 + 0.98630I
a = 0.016734 − 0.861988I
b = −0.82720 − 1.20013I
−9.66748 + 4.61526I 0
u = −1.37313 − 0.98630I
a = 0.016734 + 0.861988I
b = −0.82720 + 1.20013I
−9.66748 − 4.61526I 0
u = −1.58176 + 0.75718I
a = 0.318816 + 0.640437I
b = 0.989214 + 0.771613I
0.26052 + 9.55635I 0
u = −1.58176 − 0.75718I
a = 0.318816 − 0.640437I
b = 0.989214 − 0.771613I
0.26052 − 9.55635I 0
u = −1.67866 + 0.73710I
a = −0.323543 − 0.544420I
b = −0.944411 − 0.675412I
0.62354 + 3.38801I 0
u = −1.67866 − 0.73710I
a = −0.323543 + 0.544420I
b = −0.944411 + 0.675412I
0.62354 − 3.38801I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.91638 + 1.89680I
a = −0.306375 + 0.043826I
b = −0.197627 + 0.621294I
−4.94081 − 9.75847I 0
u = −0.91638 − 1.89680I
a = −0.306375 − 0.043826I
b = −0.197627 − 0.621294I
−4.94081 + 9.75847I 0
u = −1.66153 + 1.30418I
a = −0.074448 + 0.424186I
b = 0.429519 + 0.801889I
−8.50425 + 5.60885I 0
u = −1.66153 − 1.30418I
a = −0.074448 − 0.424186I
b = 0.429519 − 0.801889I
−8.50425 − 5.60885I 0
u = −1.43142 + 1.78513I
a = −0.217267 + 0.216904I
b = 0.076202 + 0.698329I
−10.59290 − 2.39404I 0
u = −1.43142 − 1.78513I
a = −0.217267 − 0.216904I
b = 0.076202 − 0.698329I
−10.59290 + 2.39404I 0
u = −0.94045 + 2.13875I
a = 0.233463 − 0.037102I
b = 0.140206 − 0.534212I
−3.38165 − 3.78335I 0
u = −0.94045 − 2.13875I
a = 0.233463 + 0.037102I
b = 0.140206 + 0.534212I
−3.38165 + 3.78335I 0
u = −1.97234 + 1.58931I
a = 0.040698 − 0.256368I
b = −0.327178 − 0.570325I
−5.52208 + 0.87397I 0
u = −1.97234 − 1.58931I
a = 0.040698 + 0.256368I
b = −0.327178 + 0.570325I
−5.52208 − 0.87397I 0
8
II. I
u
2
= h−3.50 × 10
97
a
27
u
2
+ 1.27 × 10
97
a
26
u
2
+ · · · − 3.33 × 10
97
a − 9.43 ×
10
94
, a
27
u
2
− 5a
26
u
2
+ · · · + 285596a + 148877, u
3
− u
2
+ 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
5
=
a
10.2657a
27
u
2
− 3.73064a
26
u
2
+ ··· + 9.74846a + 0.0276474
a
10
=
1
u
2
a
6
=
−10.2657a
27
u
2
+ 3.73064a
26
u
2
+ ··· − 8.74846a − 0.0276474
17.0710a
27
u
2
− 5.63123a
26
u
2
+ ··· − 1.53110a − 0.821207
a
1
=
a
2
u
−2.14419a
27
u
2
− 3.82791a
26
u
2
+ ··· + 14.6111a + 5.85525
a
4
=
−10.2657a
27
u
2
+ 3.73064a
26
u
2
+ ··· − 8.74846a − 0.0276474
10.2657a
27
u
2
− 3.73064a
26
u
2
+ ··· + 9.74846a + 0.0276474
a
8
=
3.13258a
27
u
2
+ 1.11366a
26
u
2
+ ··· + 8.60740a + 4.83529
−2.20805a
27
u
2
+ 3.25415a
26
u
2
+ ··· + 6.88820a − 1.57925
a
7
=
−17.2876a
27
u
2
+ 3.16256a
26
u
2
+ ··· − 22.6088a − 10.3492
3.39639a
27
u
2
− 2.26539a
26
u
2
+ ··· − 5.45361a + 4.59514
a
11
=
−5.04547a
27
u
2
+ 8.36584a
26
u
2
+ ··· + 5.97337a + 0.330067
7.18966a
27
u
2
− 4.53793a
26
u
2
+ ··· − 20.5845a − 6.18532
a
3
=
−5.05099a
27
u
2
− 0.537079a
26
u
2
+ ··· + 17.4477a + 3.50841
−13.3963a
27
u
2
+ 8.75813a
26
u
2
+ ··· − 5.43958a − 4.39989
a
2
=
2.77771a
27
u
2
− 7.24386a
26
u
2
+ ··· + 19.9178a + 0.0502453
−16.1715a
27
u
2
+ 19.3292a
26
u
2
+ ··· − 8.66336a − 1.90620
(ii) Obstruction class = −1
(iii) Cusp Shapes = 135.121a
27
u
2
− 4.70834a
26
u
2
+ ··· − 47.4051a − 38.0609
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
(u
14
+ 5u
13
+ ··· + 3u + 1)
6
c
2
, c
7
(u
14
− u
13
+ ··· + u + 1)
6
c
3
, c
5
, c
10
c
11
u
84
− u
83
+ ··· − 36600u + 3721
c
4
, c
12
u
84
− 3u
83
+ ··· − 16116u + 6737
c
9
(u
3
+ u
2
− 1)
28
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
(y
14
+ 9y
13
+ ··· + 15y + 1)
6
c
2
, c
7
(y
14
+ 5y
13
+ ··· + 3y + 1)
6
c
3
, c
5
, c
10
c
11
y
84
− 69y
83
+ ··· + 118923160y + 13845841
c
4
, c
12
y
84
+ 23y
83
+ ··· + 2095745328y + 45387169
c
9
(y
3
− y
2
+ 2y − 1)
28
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.120006 − 0.991776I
b = 0.72497 − 1.60540I
−3.10096 + 0.58459I −6.59625 + 0.35429I
u = 0.877439 + 0.744862I
a = 0.986237 − 0.087553I
b = 0.123059 + 0.619630I
−1.91067 + 6.10773I −4.49024 − 4.28133I
u = 0.877439 + 0.744862I
a = −0.006942 − 0.989783I
b = 0.96956 − 1.57337I
−6.55340 − 5.59559I −9.90787 + 6.19322I
u = 0.877439 + 0.744862I
a = 0.084543 − 0.980700I
b = 1.15049 − 1.52825I
−1.91067 − 11.76400I −4.49024 + 10.24022I
u = 0.877439 + 0.744862I
a = 0.954989 + 0.177300I
b = −0.023799 + 0.748491I
−6.55340 − 0.06065I −9.90787 − 0.23433I
u = 0.877439 + 0.744862I
a = 0.929113 + 0.489507I
b = −0.162423 + 0.898869I
−3.10096 − 6.24083I −6.59625 + 5.60461I
u = 0.877439 + 0.744862I
a = −0.075925 + 0.944213I
b = −1.12272 + 1.45979I
−0.72038 − 6.24083I −2.38424 + 5.60461I
u = 0.877439 + 0.744862I
a = −0.345086 + 1.036840I
b = −0.452684 + 0.317394I
2.73205 − 0.06065I 0.927378 − 0.234326I
u = 0.877439 + 0.744862I
a = 0.178079 + 0.886248I
b = −0.58485 + 1.35446I
−1.93349 − 4.20582I −5.37614 + 7.10152I
u = 0.877439 + 0.744862I
a = −0.633327 − 0.629672I
b = 0.343438 − 0.886961I
−1.93349 − 1.45042I −5.37614 − 1.14262I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.873175 + 0.094296I
b = −0.063434 − 0.555802I
−0.720385 + 0.584589I −2.38424 + 0.35429I
u = 0.877439 + 0.744862I
a = 0.095249 + 0.871209I
b = −0.77182 + 1.33732I
−1.88785 − 4.20582I −3.60435 + 7.10152I
u = 0.877439 + 0.744862I
a = 0.271240 + 0.780595I
b = 0.086688 + 1.024240I
−1.93349 − 1.45042I −5.37614 − 1.14262I
u = 0.877439 + 0.744862I
a = 0.297573 − 1.147490I
b = 0.527326 − 0.393396I
2.73205 − 5.59559I 0.92738 + 6.19322I
u = 0.877439 + 0.744862I
a = −0.397833 − 0.686701I
b = −0.450625 − 1.121570I
−3.10096 − 6.24083I −6.59625 + 5.60461I
u = 0.877439 + 0.744862I
a = −0.601889 − 0.410389I
b = 0.317647 − 0.754765I
−1.88785 − 1.45042I −3.60435 − 1.14262I
u = 0.877439 + 0.744862I
a = −0.374205 − 1.225980I
b = 0.503878 − 0.910272I
−1.93349 − 4.20582I −5.37614 + 7.10152I
u = 0.877439 + 0.744862I
a = 0.213993 + 0.678532I
b = 0.222438 + 0.808416I
−1.88785 − 1.45042I −3.60435 − 1.14262I
u = 0.877439 + 0.744862I
a = −0.240729 − 1.319760I
b = 0.565355 − 0.835380I
−1.88785 − 4.20582I −3.60435 + 7.10152I
u = 0.877439 + 0.744862I
a = −0.405098 − 0.509151I
b = −0.705881 − 0.866905I
−6.55340 − 0.06065I −9.90787 − 0.23433I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.128081 + 0.557074I
b = −1.115820 + 0.785201I
2.73205 − 5.59559I 0.92738 + 6.19322I
u = 0.877439 + 0.744862I
a = −0.429915 − 0.341224I
b = −0.930577 − 0.657788I
−1.91067 + 6.10773I −4.49024 − 4.28133I
u = 0.877439 + 0.744862I
a = 0.354532 + 0.332473I
b = 0.836395 + 0.567656I
−0.720385 + 0.584589I −2.38424 + 0.35429I
u = 0.877439 + 0.744862I
a = 0.121375 − 0.464764I
b = 1.075100 − 0.652723I
2.73205 − 0.06065I 0.927378 − 0.234326I
u = 0.877439 + 0.744862I
a = 0.42250 + 1.47099I
b = −0.633438 + 0.959610I
−3.10096 + 0.58459I 0
u = 0.877439 + 0.744862I
a = −0.07716 − 1.59819I
b = 0.769927 − 0.771935I
−0.72038 − 6.24083I 0
u = 0.877439 + 0.744862I
a = 0.24248 + 1.58730I
b = −0.731161 + 0.873645I
−6.55340 − 5.59559I 0
u = 0.877439 + 0.744862I
a = 0.09727 + 1.65915I
b = −0.804668 + 0.797531I
−1.91067 − 11.76400I 0
u = 0.877439 − 0.744862I
a = −0.120006 + 0.991776I
b = 0.72497 + 1.60540I
−3.10096 − 0.58459I −6.59625 − 0.35429I
u = 0.877439 − 0.744862I
a = 0.986237 + 0.087553I
b = 0.123059 − 0.619630I
−1.91067 − 6.10773I −4.49024 + 4.28133I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 − 0.744862I
a = −0.006942 + 0.989783I
b = 0.96956 + 1.57337I
−6.55340 + 5.59559I −9.90787 − 6.19322I
u = 0.877439 − 0.744862I
a = 0.084543 + 0.980700I
b = 1.15049 + 1.52825I
−1.91067 + 11.76400I −4.49024 − 10.24022I
u = 0.877439 − 0.744862I
a = 0.954989 − 0.177300I
b = −0.023799 − 0.748491I
−6.55340 + 0.06065I −9.90787 + 0.23433I
u = 0.877439 − 0.744862I
a = 0.929113 − 0.489507I
b = −0.162423 − 0.898869I
−3.10096 + 6.24083I −6.59625 − 5.60461I
u = 0.877439 − 0.744862I
a = −0.075925 − 0.944213I
b = −1.12272 − 1.45979I
−0.72038 + 6.24083I −2.38424 − 5.60461I
u = 0.877439 − 0.744862I
a = −0.345086 − 1.036840I
b = −0.452684 − 0.317394I
2.73205 + 0.06065I 0.927378 + 0.234326I
u = 0.877439 − 0.744862I
a = 0.178079 − 0.886248I
b = −0.58485 − 1.35446I
−1.93349 + 4.20582I −5.37614 − 7.10152I
u = 0.877439 − 0.744862I
a = −0.633327 + 0.629672I
b = 0.343438 + 0.886961I
−1.93349 + 1.45042I −5.37614 + 1.14262I
u = 0.877439 − 0.744862I
a = −0.873175 − 0.094296I
b = −0.063434 + 0.555802I
−0.720385 − 0.584589I −2.38424 − 0.35429I
u = 0.877439 − 0.744862I
a = 0.095249 − 0.871209I
b = −0.77182 − 1.33732I
−1.88785 + 4.20582I −3.60435 − 7.10152I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 − 0.744862I
a = 0.271240 − 0.780595I
b = 0.086688 − 1.024240I
−1.93349 + 1.45042I −5.37614 + 1.14262I
u = 0.877439 − 0.744862I
a = 0.297573 + 1.147490I
b = 0.527326 + 0.393396I
2.73205 + 5.59559I 0.92738 − 6.19322I
u = 0.877439 − 0.744862I
a = −0.397833 + 0.686701I
b = −0.450625 + 1.121570I
−3.10096 + 6.24083I −6.59625 − 5.60461I
u = 0.877439 − 0.744862I
a = −0.601889 + 0.410389I
b = 0.317647 + 0.754765I
−1.88785 + 1.45042I −3.60435 + 1.14262I
u = 0.877439 − 0.744862I
a = −0.374205 + 1.225980I
b = 0.503878 + 0.910272I
−1.93349 + 4.20582I −5.37614 − 7.10152I
u = 0.877439 − 0.744862I
a = 0.213993 − 0.678532I
b = 0.222438 − 0.808416I
−1.88785 + 1.45042I −3.60435 + 1.14262I
u = 0.877439 − 0.744862I
a = −0.240729 + 1.319760I
b = 0.565355 + 0.835380I
−1.88785 + 4.20582I −3.60435 − 7.10152I
u = 0.877439 − 0.744862I
a = −0.405098 + 0.509151I
b = −0.705881 + 0.866905I
−6.55340 + 0.06065I −9.90787 + 0.23433I
u = 0.877439 − 0.744862I
a = −0.128081 − 0.557074I
b = −1.115820 − 0.785201I
2.73205 + 5.59559I 0.92738 − 6.19322I
u = 0.877439 − 0.744862I
a = −0.429915 + 0.341224I
b = −0.930577 + 0.657788I
−1.91067 − 6.10773I −4.49024 + 4.28133I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 − 0.744862I
a = 0.354532 − 0.332473I
b = 0.836395 − 0.567656I
−0.720385 − 0.584589I −2.38424 − 0.35429I
u = 0.877439 − 0.744862I
a = 0.121375 + 0.464764I
b = 1.075100 + 0.652723I
2.73205 + 0.06065I 0.927378 + 0.234326I
u = 0.877439 − 0.744862I
a = 0.42250 − 1.47099I
b = −0.633438 − 0.959610I
−3.10096 − 0.58459I 0
u = 0.877439 − 0.744862I
a = −0.07716 + 1.59819I
b = 0.769927 + 0.771935I
−0.72038 + 6.24083I 0
u = 0.877439 − 0.744862I
a = 0.24248 − 1.58730I
b = −0.731161 − 0.873645I
−6.55340 + 5.59559I 0
u = 0.877439 − 0.744862I
a = 0.09727 − 1.65915I
b = −0.804668 − 0.797531I
−1.91067 + 11.76400I 0
u = −0.754878
a = 0.023468 + 0.988160I
b = −1.70900 + 1.25529I
−10.69100 + 2.76747I −16.4371 − 3.2138I
u = −0.754878
a = 0.023468 − 0.988160I
b = −1.70900 − 1.25529I
−10.69100 − 2.76747I −16.4371 + 3.2138I
u = −0.754878
a = −0.351285 + 0.840493I
b = 1.41371 + 0.90881I
−6.02544 − 1.37770I −10.13361 + 4.12207I
u = −0.754878
a = −0.351285 − 0.840493I
b = 1.41371 − 0.90881I
−6.02544 + 1.37770I −10.13361 − 4.12207I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754878
a = 0.010172 + 1.172770I
b = −1.59712 + 1.49891I
−6.04826 + 8.93586I −11.01951 − 7.26077I
u = −0.754878
a = 0.010172 − 1.172770I
b = −1.59712 − 1.49891I
−6.04826 − 8.93586I −11.01951 + 7.26077I
u = −0.754878
a = −0.082088 + 1.172510I
b = 1.50842 + 1.44210I
−4.85797 − 3.41271I −8.91351 + 2.62516I
u = −0.754878
a = −0.082088 − 1.172510I
b = 1.50842 − 1.44210I
−4.85797 + 3.41271I −8.91351 − 2.62516I
u = −0.754878
a = 0.039321 + 0.722074I
b = −1.82506 + 0.91144I
−7.23855 − 3.41271I −13.12551 + 2.62516I
u = −0.754878
a = 0.039321 − 0.722074I
b = −1.82506 − 0.91144I
−7.23855 + 3.41271I −13.12551 − 2.62516I
u = −0.754878
a = −0.377459 + 0.576451I
b = 1.48695 + 0.62139I
−6.07108 − 1.37770I −11.90541 + 4.12207I
u = −0.754878
a = −0.377459 − 0.576451I
b = 1.48695 − 0.62139I
−6.07108 + 1.37770I −11.90541 − 4.12207I
u = −0.754878
a = −0.70608 + 1.61550I
b = 0.64975 + 1.28372I
−1.40553 − 2.76747I 0
u = −0.754878
a = −0.70608 − 1.61550I
b = 0.64975 − 1.28372I
−1.40553 + 2.76747I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754878
a = 0.86074 + 1.70056I
b = −0.533004 + 1.219510I
−1.40553 − 2.76747I 0
u = −0.754878
a = 0.86074 − 1.70056I
b = −0.533004 − 1.219510I
−1.40553 + 2.76747I 0
u = −0.754878
a = 1.96979 + 0.82317I
b = −0.284936 + 0.435150I
−6.07108 − 1.37770I 0
u = −0.754878
a = 1.96979 − 0.82317I
b = −0.284936 − 0.435150I
−6.07108 + 1.37770I 0
u = −0.754878
a = 1.87277 + 1.20392I
b = −0.265177 + 0.634469I
−6.02544 − 1.37770I 0
u = −0.754878
a = 1.87277 − 1.20392I
b = −0.265177 − 0.634469I
−6.02544 + 1.37770I 0
u = −0.754878
a = −2.41769 + 1.20740I
b = 0.029682 + 0.545077I
−7.23855 − 3.41271I 0
u = −0.754878
a = −2.41769 − 1.20740I
b = 0.029682 − 0.545077I
−7.23855 + 3.41271I 0
u = −0.754878
a = 1.99823 + 1.91037I
b = −0.061966 + 0.885098I
−4.85797 − 3.41271I 0
u = −0.754878
a = 1.99823 − 1.91037I
b = −0.061966 − 0.885098I
−4.85797 + 3.41271I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754878
a = −2.26395 + 1.66291I
b = 0.017716 + 0.745940I
−10.69100 + 2.76747I 0
u = −0.754878
a = −2.26395 − 1.66291I
b = 0.017716 − 0.745940I
−10.69100 − 2.76747I 0
u = −0.754878
a = −2.11574 + 1.98563I
b = 0.007679 + 0.885300I
−6.04826 + 8.93586I 0
u = −0.754878
a = −2.11574 − 1.98563I
b = 0.007679 − 0.885300I
−6.04826 − 8.93586I 0
20
III. I
u
3
= h−13u
22
+ 66u
21
+ · · · + b + 11, −11u
22
+ 53u
21
+ · · · + a +
1, u
23
− 6u
22
+ · · · − 4u
2
+ 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
5
=
11u
22
− 53u
21
+ ··· + 8u − 1
13u
22
− 66u
21
+ ··· − u − 11
a
10
=
1
u
2
a
6
=
10u
22
− 54u
21
+ ··· − 2u − 3
6u
22
− 30u
21
+ ··· + 22u
2
− 4
a
1
=
−u
20
+ 5u
19
+ ··· − 2u − 4
−u
21
+ 5u
20
+ ··· − 2u
2
− 3u
a
4
=
−2u
22
+ 13u
21
+ ··· + 9u + 10
13u
22
− 66u
21
+ ··· − u − 11
a
8
=
2u
22
− 7u
21
+ ··· + 6u + 1
4u
22
− 20u
21
+ ··· + 11u
2
− 2
a
7
=
−25u
22
+ 128u
21
+ ··· + 11u + 25
u
22
+ u
21
+ ··· + 8u + 5
a
11
=
−u
22
+ 7u
21
+ ··· + 6u − 4
u
22
− 6u
21
+ ··· + 2u
2
− 3u
a
3
=
−10u
22
+ 58u
21
+ ··· + 9u + 9
4u
22
− 18u
21
+ ··· + 7u
2
+ 6u
a
2
=
−6u
22
+ 34u
21
+ ··· − u − 1
u
21
− 3u
20
+ ··· + 4u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −33u
22
+164u
21
−310u
20
+202u
19
+165u
18
−486u
17
+718u
16
−847u
15
+485u
14
+66u
13
+
52u
12
−376u
11
+17u
10
+267u
9
−16u
8
+28u
7
−185u
6
−94u
5
+220u
4
+15u
3
−93u
2
−5u+12
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
23
− 8u
22
+ ··· − 8u + 1
c
2
u
23
+ 4u
21
+ ··· − 4u
2
− 1
c
3
, c
10
u
23
− u
22
+ ··· − u + 1
c
4
, c
12
u
23
+ 3u
21
+ ··· + 2u
3
− 1
c
5
, c
11
u
23
+ u
22
+ ··· − u − 1
c
7
u
23
+ 4u
21
+ ··· + 4u
2
+ 1
c
8
u
23
+ 4u
21
+ ··· + 7u
2
+ 1
c
9
u
23
− 6u
22
+ ··· − 4u
2
+ 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
23
+ 16y
22
+ ··· − 56y
2
− 1
c
2
, c
7
y
23
+ 8y
22
+ ··· − 8y − 1
c
3
, c
5
, c
10
c
11
y
23
− 23y
22
+ ··· + 17y − 1
c
4
, c
12
y
23
+ 6y
22
+ ··· + 2y
2
− 1
c
8
y
23
+ 8y
22
+ ··· − 14y − 1
c
9
y
23
− 6y
22
+ ··· + 8y − 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.787420 + 0.529100I
a = 0.41407 + 1.37209I
b = −0.399927 + 1.299500I
−0.434887 + 0.785370I −2.68661 + 0.75939I
u = 0.787420 − 0.529100I
a = 0.41407 − 1.37209I
b = −0.399927 − 1.299500I
−0.434887 − 0.785370I −2.68661 − 0.75939I
u = 0.736005 + 0.575876I
a = −0.573964 − 1.266750I
b = 0.307052 − 1.262870I
−0.07310 − 4.42137I −0.74349 + 7.07462I
u = 0.736005 − 0.575876I
a = −0.573964 + 1.266750I
b = 0.307052 + 1.262870I
−0.07310 + 4.42137I −0.74349 − 7.07462I
u = −0.161987 + 0.897096I
a = 0.710005 − 0.628569I
b = 0.448875 + 0.738762I
−4.44482 − 8.70555I −5.21496 + 5.50164I
u = −0.161987 − 0.897096I
a = 0.710005 + 0.628569I
b = 0.448875 − 0.738762I
−4.44482 + 8.70555I −5.21496 − 5.50164I
u = −0.601154 + 0.655701I
a = −0.120426 − 0.898075I
b = 0.661263 + 0.460918I
−9.35112 − 2.26227I −9.29651 + 0.96913I
u = −0.601154 − 0.655701I
a = −0.120426 + 0.898075I
b = 0.661263 − 0.460918I
−9.35112 + 2.26227I −9.29651 − 0.96913I
u = 0.980139 + 0.570303I
a = 0.024628 + 1.095960I
b = −0.600892 + 1.088240I
−3.78789 − 3.52111I −11.37828 + 4.82801I
u = 0.980139 − 0.570303I
a = 0.024628 − 1.095960I
b = −0.600892 − 1.088240I
−3.78789 + 3.52111I −11.37828 − 4.82801I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.178274 + 1.165150I
a = −0.492915 + 0.354316I
b = −0.324955 − 0.637483I
−3.07900 − 3.10823I −3.91996 + 0.06213I
u = −0.178274 − 1.165150I
a = −0.492915 − 0.354316I
b = −0.324955 + 0.637483I
−3.07900 + 3.10823I −3.91996 − 0.06213I
u = 0.838487 + 0.908902I
a = −0.389816 − 0.648774I
b = 0.262816 − 0.898293I
−2.26839 − 2.40878I −8.74665 + 6.47811I
u = 0.838487 − 0.908902I
a = −0.389816 + 0.648774I
b = 0.262816 + 0.898293I
−2.26839 + 2.40878I −8.74665 − 6.47811I
u = 1.202560 + 0.483097I
a = −0.374092 + 0.858532I
b = −0.864624 + 0.851716I
1.30147 − 7.92747I −3.76396 + 6.76222I
u = 1.202560 − 0.483097I
a = −0.374092 − 0.858532I
b = −0.864624 − 0.851716I
1.30147 + 7.92747I −3.76396 − 6.76222I
u = −0.617636 + 0.146970I
a = 1.43119 + 0.59789I
b = −0.971827 − 0.158937I
−5.39009 − 0.99265I −0.41096 − 2.40382I
u = −0.617636 − 0.146970I
a = 1.43119 − 0.59789I
b = −0.971827 + 0.158937I
−5.39009 + 0.99265I −0.41096 + 2.40382I
u = −0.575316 + 0.265705I
a = −1.16602 − 1.04883I
b = 0.949508 + 0.293589I
−6.27868 + 3.82032I −4.15429 − 6.73059I
u = −0.575316 − 0.265705I
a = −1.16602 + 1.04883I
b = 0.949508 − 0.293589I
−6.27868 − 3.82032I −4.15429 + 6.73059I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.36816
a = 0.406059
b = −0.555554
−5.28477 −6.39140
u = 1.273830 + 0.530353I
a = 0.334310 − 0.725242I
b = 0.810489 − 0.746535I
1.90529 − 2.16291I −1.48866 + 2.24531I
u = 1.273830 − 0.530353I
a = 0.334310 + 0.725242I
b = 0.810489 + 0.746535I
1.90529 + 2.16291I −1.48866 − 2.24531I
26
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
((u
14
+ 5u
13
+ ··· + 3u + 1)
6
)(u
23
− 8u
22
+ ··· − 8u + 1)
· (u
40
+ 13u
39
+ ··· + 32u + 64)
c
2
((u
14
− u
13
+ ··· + u + 1)
6
)(u
23
+ 4u
21
+ ··· − 4u
2
− 1)
· (u
40
+ 7u
39
+ ··· + 2u
2
+ 8)
c
3
, c
10
(u
23
− u
22
+ ··· − u + 1)(u
40
+ u
39
+ ··· + 2u + 1)
· (u
84
− u
83
+ ··· − 36600u + 3721)
c
4
, c
12
(u
23
+ 3u
21
+ ··· + 2u
3
− 1)(u
40
+ 3u
38
+ ··· + 3u + 1)
· (u
84
− 3u
83
+ ··· − 16116u + 6737)
c
5
, c
11
(u
23
+ u
22
+ ··· − u − 1)(u
40
+ u
39
+ ··· + 2u + 1)
· (u
84
− u
83
+ ··· − 36600u + 3721)
c
7
((u
14
− u
13
+ ··· + u + 1)
6
)(u
23
+ 4u
21
+ ··· + 4u
2
+ 1)
· (u
40
+ 7u
39
+ ··· + 2u
2
+ 8)
c
8
((u
14
+ 5u
13
+ ··· + 3u + 1)
6
)(u
23
+ 4u
21
+ ··· + 7u
2
+ 1)
· (u
40
− 35u
39
+ ··· − 4086976u + 307752)
c
9
((u
3
+ u
2
− 1)
28
)(u
23
− 6u
22
+ ··· − 4u
2
+ 1)
· (u
40
− 41u
39
+ ··· − 401408u + 16384)
27
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
((y
14
+ 9y
13
+ ··· + 15y + 1)
6
)(y
23
+ 16y
22
+ ··· − 56y
2
− 1)
· (y
40
+ 25y
39
+ ··· − 27136y + 4096)
c
2
, c
7
((y
14
+ 5y
13
+ ··· + 3y + 1)
6
)(y
23
+ 8y
22
+ ··· − 8y − 1)
· (y
40
+ 13y
39
+ ··· + 32y + 64)
c
3
, c
5
, c
10
c
11
(y
23
− 23y
22
+ ··· + 17y − 1)(y
40
− 35y
39
+ ··· + 20y + 1)
· (y
84
− 69y
83
+ ··· + 118923160y + 13845841)
c
4
, c
12
(y
23
+ 6y
22
+ ··· + 2y
2
− 1)(y
40
+ 6y
39
+ ··· + 5y + 1)
· (y
84
+ 23y
83
+ ··· + 2095745328y + 45387169)
c
8
((y
14
+ 9y
13
+ ··· + 15y + 1)
6
)(y
23
+ 8y
22
+ ··· − 14y − 1)
· (y
40
+ 17y
39
+ ··· + 373353571616y + 94711293504)
c
9
((y
3
− y
2
+ 2y − 1)
28
)(y
23
− 6y
22
+ ··· + 8y − 1)
· (y
40
− 7y
39
+ ··· − 1409286144y + 268435456)
28
