12a
0060
(K12a
0060
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 11 4 6 12 8 1 9
Solving Sequence
3,7
4
8,11
6 9 10 5 2 1 12
c
3
c
7
c
6
c
8
c
10
c
5
c
2
c
1
c
12
c
4
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.82224 × 10
566
u
139
+ 1.76219 × 10
566
u
138
+ ··· + 1.62257 × 10
567
b + 7.22892 × 10
569
,
1.07751 × 10
567
u
139
+ 6.57014 × 10
566
u
138
+ ··· + 1.62257 × 10
567
a + 2.82386 × 10
570
,
u
140
+ u
139
+ ··· + 8192u + 1024i
I
v
1
= ha, 4v
3
− 6v
2
+ b + 25v −8, v
4
− 2v
3
+ 7v
2
− 5v + 1i
I
v
2
= ha, 50v
5
+ 61v
4
+ 196v
3
+ 119v
2
+ 67b + 390v + 59, v
6
+ v
5
+ 4v
4
+ 2v
3
+ 8v
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 150 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
= h2.82 × 10
566
u
139
+ 1.76 × 10
566
u
138
+ · · · + 1.62 × 10
567
b + 7.23 ×
10
569
, 1.08 × 10
567
u
139
+ 6.57 × 10
566
u
138
+ · · · + 1.62 × 10
567
a + 2.82 ×
10
570
, u
140
+ u
139
+ · · · + 8192u + 1024i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
8
=
u
−u
3
+ u
a
11
=
−0.664076u
139
− 0.404921u
138
+ ··· − 9478.56u − 1740.36
−0.173936u
139
− 0.108605u
138
+ ··· − 2458.67u − 445.522
a
6
=
−0.599073u
139
− 0.372142u
138
+ ··· − 8619.84u − 1591.58
−0.0565797u
139
− 0.0188547u
138
+ ··· − 546.416u − 86.8817
a
9
=
0.235557u
139
+ 0.145522u
138
+ ··· + 3360.46u + 608.447
0.204961u
139
+ 0.119227u
138
+ ··· + 2804.73u + 505.380
a
10
=
−0.729961u
139
− 0.437305u
138
+ ··· − 10338.5u − 1897.61
−0.219084u
139
− 0.134689u
138
+ ··· − 3111.68u − 568.463
a
5
=
−0.00229243u
139
− 0.00688234u
138
+ ··· − 119.334u − 22.0563
0.0224336u
139
+ 0.00780471u
138
+ ··· + 256.104u + 43.2884
a
2
=
−0.00229243u
139
− 0.00688234u
138
+ ··· − 119.334u − 22.0563
−0.0265260u
139
− 0.0110130u
138
+ ··· − 296.052u − 47.9885
a
1
=
−0.0288184u
139
− 0.0178953u
138
+ ··· − 415.385u − 70.0448
−0.0265260u
139
− 0.0110130u
138
+ ··· − 296.052u − 47.9885
a
12
=
−0.459995u
139
− 0.286124u
138
+ ··· − 6634.61u − 1213.55
−0.193301u
139
− 0.112910u
138
+ ··· − 2650.68u − 476.747
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.69069u
139
+ 1.00549u
138
+ ··· + 23555.4u + 4256.25
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
140
+ 69u
139
+ ··· + 221u + 1
c
2
, c
4
u
140
− 11u
139
+ ··· − 5u + 1
c
3
, c
7
u
140
− u
139
+ ··· − 8192u + 1024
c
5
u
140
+ 2u
139
+ ··· − 10624u + 1216
c
6
u
140
− 2u
139
+ ··· − 24012u + 5887
c
8
u
140
− 10u
139
+ ··· − 2u + 1
c
9
, c
12
u
140
+ 2u
139
+ ··· + 14u + 1
c
10
u
140
+ 14u
139
+ ··· + 2u + 1
c
11
u
140
+ 58u
139
+ ··· + 14u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
140
+ 15y
139
+ ··· − 2817y + 1
c
2
, c
4
y
140
− 69y
139
+ ··· − 221y + 1
c
3
, c
7
y
140
− 63y
139
+ ··· − 25690112y + 1048576
c
5
y
140
+ 150y
139
+ ··· + 35716096y + 1478656
c
6
y
140
+ 142y
139
+ ··· + 261556046y + 34656769
c
8
y
140
+ 14y
139
+ ··· + 10y + 1
c
9
, c
12
y
140
+ 58y
139
+ ··· + 14y + 1
c
10
y
140
+ 10y
139
+ ··· + 14y + 1
c
11
y
140
+ 50y
139
+ ··· − 2010y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000760 + 0.012534I
a = −0.306225 + 0.320226I
b = −1.40232 + 0.29598I
0.24476 − 4.35802I 0
u = 1.000760 − 0.012534I
a = −0.306225 − 0.320226I
b = −1.40232 − 0.29598I
0.24476 + 4.35802I 0
u = −0.836596 + 0.555007I
a = 1.006110 − 0.475231I
b = 2.42428 + 0.23434I
−6.69476 − 2.77249I 0
u = −0.836596 − 0.555007I
a = 1.006110 + 0.475231I
b = 2.42428 − 0.23434I
−6.69476 + 2.77249I 0
u = −0.421062 + 0.872083I
a = 0.206555 − 0.622102I
b = 2.25386 − 0.11399I
−1.36351 + 5.67921I 0
u = −0.421062 − 0.872083I
a = 0.206555 + 0.622102I
b = 2.25386 + 0.11399I
−1.36351 − 5.67921I 0
u = 0.189163 + 1.024150I
a = 0.531321 + 1.025970I
b = 0.786265 + 0.856529I
1.66936 − 3.03245I 0
u = 0.189163 − 1.024150I
a = 0.531321 − 1.025970I
b = 0.786265 − 0.856529I
1.66936 + 3.03245I 0
u = −0.797095 + 0.513895I
a = 0.215390 − 1.374710I
b = 0.997714 + 0.916821I
−6.83212 − 1.55059I 0
u = −0.797095 − 0.513895I
a = 0.215390 + 1.374710I
b = 0.997714 − 0.916821I
−6.83212 + 1.55059I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.682457 + 0.821355I
a = 0.276201 − 0.036517I
b = −0.249515 + 0.258948I
0.47320 − 1.54565I 0
u = −0.682457 − 0.821355I
a = 0.276201 + 0.036517I
b = −0.249515 − 0.258948I
0.47320 + 1.54565I 0
u = −0.992021 + 0.397301I
a = −1.195460 + 0.435861I
b = −1.70698 − 0.28925I
−0.77366 − 5.05718I 0
u = −0.992021 − 0.397301I
a = −1.195460 − 0.435861I
b = −1.70698 + 0.28925I
−0.77366 + 5.05718I 0
u = 0.357797 + 0.844946I
a = −0.364638 − 0.836942I
b = −0.852570 − 0.691242I
−1.82288 − 1.42035I 0
u = 0.357797 − 0.844946I
a = −0.364638 + 0.836942I
b = −0.852570 + 0.691242I
−1.82288 + 1.42035I 0
u = −1.002640 + 0.433199I
a = 0.191557 − 0.047478I
b = 1.55074 + 0.59070I
−0.811795 + 0.033701I 0
u = −1.002640 − 0.433199I
a = 0.191557 + 0.047478I
b = 1.55074 − 0.59070I
−0.811795 − 0.033701I 0
u = −0.575665 + 0.936495I
a = 0.395098 − 0.932422I
b = 1.249570 + 0.340721I
−6.19030 + 5.36695I 0
u = −0.575665 − 0.936495I
a = 0.395098 + 0.932422I
b = 1.249570 − 0.340721I
−6.19030 − 5.36695I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.068570 + 0.259692I
a = 0.56267 − 2.76229I
b = 1.49656 + 0.99735I
2.38264 + 1.08657I 0
u = −1.068570 − 0.259692I
a = 0.56267 + 2.76229I
b = 1.49656 − 0.99735I
2.38264 − 1.08657I 0
u = 0.798347 + 0.415330I
a = −0.679635 − 1.152670I
b = −0.486148 + 0.821596I
−2.17880 + 4.32767I 0
u = 0.798347 − 0.415330I
a = −0.679635 + 1.152670I
b = −0.486148 − 0.821596I
−2.17880 − 4.32767I 0
u = −0.299839 + 0.848133I
a = 0.150645 + 0.978113I
b = 0.744768 + 0.363732I
0.79500 + 3.33230I 0
u = −0.299839 − 0.848133I
a = 0.150645 − 0.978113I
b = 0.744768 − 0.363732I
0.79500 − 3.33230I 0
u = −1.047890 + 0.343169I
a = −0.88012 + 3.01481I
b = −2.29815 − 1.00177I
2.07851 − 3.32587I 0
u = −1.047890 − 0.343169I
a = −0.88012 − 3.01481I
b = −2.29815 + 1.00177I
2.07851 + 3.32587I 0
u = −0.866740 + 0.208182I
a = −0.58859 + 1.77401I
b = −1.389370 − 0.112852I
1.10254 + 1.14634I 0
u = −0.866740 − 0.208182I
a = −0.58859 − 1.77401I
b = −1.389370 + 0.112852I
1.10254 − 1.14634I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.650609 + 0.588985I
a = 0.354024 − 0.405783I
b = −0.1023010 + 0.0046218I
0.44265 − 1.56279I 0
u = −0.650609 − 0.588985I
a = 0.354024 + 0.405783I
b = −0.1023010 − 0.0046218I
0.44265 + 1.56279I 0
u = 0.661212 + 0.572663I
a = 0.921225 + 0.672046I
b = 0.279894 − 0.814023I
−4.97493 + 8.44093I 0
u = 0.661212 − 0.572663I
a = 0.921225 − 0.672046I
b = 0.279894 + 0.814023I
−4.97493 − 8.44093I 0
u = 1.114470 + 0.173765I
a = −0.712327 + 0.632019I
b = −0.397554 − 1.170360I
3.91294 − 3.33139I 0
u = 1.114470 − 0.173765I
a = −0.712327 − 0.632019I
b = −0.397554 + 1.170360I
3.91294 + 3.33139I 0
u = 0.286617 + 1.097040I
a = −0.578658 − 1.101670I
b = −1.32911 − 0.99991I
−0.05649 − 8.46319I 0
u = 0.286617 − 1.097040I
a = −0.578658 + 1.101670I
b = −1.32911 + 0.99991I
−0.05649 + 8.46319I 0
u = 0.427712 + 0.750160I
a = −0.704498 − 1.018660I
b = −1.081150 + 0.346220I
−3.82479 − 1.32683I 0
u = 0.427712 − 0.750160I
a = −0.704498 + 1.018660I
b = −1.081150 − 0.346220I
−3.82479 + 1.32683I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.435388 + 0.743385I
a = 3.24340 + 2.10472I
b = 6.13829 + 0.59251I
−1.93443 − 3.19824I 0
u = 0.435388 − 0.743385I
a = 3.24340 − 2.10472I
b = 6.13829 − 0.59251I
−1.93443 + 3.19824I 0
u = 1.018440 + 0.525386I
a = 1.32268 + 1.57773I
b = 2.52977 − 1.33691I
−0.66742 + 3.20117I 0
u = 1.018440 − 0.525386I
a = 1.32268 − 1.57773I
b = 2.52977 + 1.33691I
−0.66742 − 3.20117I 0
u = −0.213477 + 0.816553I
a = 0.173255 + 0.561079I
b = −1.064580 − 0.152324I
1.043390 + 0.077155I 0
u = −0.213477 − 0.816553I
a = 0.173255 − 0.561079I
b = −1.064580 + 0.152324I
1.043390 − 0.077155I 0
u = −1.062380 + 0.456587I
a = 1.228930 − 0.504376I
b = 1.68579 + 0.64955I
−2.70777 − 10.63070I 0
u = −1.062380 − 0.456587I
a = 1.228930 + 0.504376I
b = 1.68579 − 0.64955I
−2.70777 + 10.63070I 0
u = −1.121250 + 0.296975I
a = 1.149810 − 0.253365I
b = 0.471235 + 0.734948I
2.53463 − 1.34948I 0
u = −1.121250 − 0.296975I
a = 1.149810 + 0.253365I
b = 0.471235 − 0.734948I
2.53463 + 1.34948I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.150790 + 0.258089I
a = 0.554520 + 0.096579I
b = 1.03502 − 1.39865I
5.51111 − 0.29685I 0
u = 1.150790 − 0.258089I
a = 0.554520 − 0.096579I
b = 1.03502 + 1.39865I
5.51111 + 0.29685I 0
u = 1.112440 + 0.403471I
a = −0.580315 − 0.363099I
b = −0.98833 + 1.94189I
2.99181 + 5.97516I 0
u = 1.112440 − 0.403471I
a = −0.580315 + 0.363099I
b = −0.98833 − 1.94189I
2.99181 − 5.97516I 0
u = 1.145340 + 0.322180I
a = 0.799528 − 0.226577I
b = 0.887250 + 0.424942I
5.25058 + 3.26329I 0
u = 1.145340 − 0.322180I
a = 0.799528 + 0.226577I
b = 0.887250 − 0.424942I
5.25058 − 3.26329I 0
u = −0.502968 + 1.083090I
a = −0.332049 + 1.189060I
b = −1.45374 + 0.78148I
0.11630 + 7.78284I 0
u = −0.502968 − 1.083090I
a = −0.332049 − 1.189060I
b = −1.45374 − 0.78148I
0.11630 − 7.78284I 0
u = 0.651482 + 0.461118I
a = −0.659951 − 0.466565I
b = −1.082100 − 0.435986I
−2.43454 − 0.65211I 0
u = 0.651482 − 0.461118I
a = −0.659951 + 0.466565I
b = −1.082100 + 0.435986I
−2.43454 + 0.65211I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073680 + 0.545137I
a = −0.835240 − 0.325325I
b = −1.83968 + 0.59135I
−1.88588 + 6.17613I 0
u = 1.073680 − 0.545137I
a = −0.835240 + 0.325325I
b = −1.83968 − 0.59135I
−1.88588 − 6.17613I 0
u = 0.329298 + 0.722391I
a = −2.66753 − 1.82474I
b = −5.11037 − 1.17767I
−1.66193 + 0.85450I 0
u = 0.329298 − 0.722391I
a = −2.66753 + 1.82474I
b = −5.11037 + 1.17767I
−1.66193 − 0.85450I 0
u = −1.116010 + 0.465367I
a = 0.632935 + 0.748697I
b = 0.011210 − 0.645952I
2.54912 − 1.64137I 0
u = −1.116010 − 0.465367I
a = 0.632935 − 0.748697I
b = 0.011210 + 0.645952I
2.54912 + 1.64137I 0
u = 0.182675 + 1.199720I
a = −0.515031 − 0.404484I
b = −1.067950 − 0.429971I
−1.95759 − 0.96618I 0
u = 0.182675 − 1.199720I
a = −0.515031 + 0.404484I
b = −1.067950 + 0.429971I
−1.95759 + 0.96618I 0
u = −0.704978 + 0.343098I
a = 0.02805 + 1.80042I
b = −0.796426 − 0.591122I
−1.78233 + 1.83282I 0
u = −0.704978 − 0.343098I
a = 0.02805 − 1.80042I
b = −0.796426 + 0.591122I
−1.78233 − 1.83282I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.505815 + 0.581629I
a = 3.01807 + 1.77462I
b = 4.63447 − 0.19221I
−2.16722 + 1.22909I 0
u = 0.505815 − 0.581629I
a = 3.01807 − 1.77462I
b = 4.63447 + 0.19221I
−2.16722 − 1.22909I 0
u = 1.112810 + 0.525316I
a = −0.61949 − 2.26822I
b = −2.68143 + 1.16589I
0.69005 + 3.86115I 0
u = 1.112810 − 0.525316I
a = −0.61949 + 2.26822I
b = −2.68143 − 1.16589I
0.69005 − 3.86115I 0
u = 1.228410 + 0.219366I
a = 0.019605 + 0.557187I
b = 0.345202 + 0.145747I
−3.90155 + 1.70271I 0
u = 1.228410 − 0.219366I
a = 0.019605 − 0.557187I
b = 0.345202 − 0.145747I
−3.90155 − 1.70271I 0
u = 1.104490 + 0.586240I
a = 1.07594 + 2.50607I
b = 3.53051 − 1.54348I
0.07853 + 8.28625I 0
u = 1.104490 − 0.586240I
a = 1.07594 − 2.50607I
b = 3.53051 + 1.54348I
0.07853 − 8.28625I 0
u = −0.554796 + 1.126340I
a = 0.421885 − 1.233660I
b = 1.95442 − 0.79674I
−1.85183 + 13.51530I 0
u = −0.554796 − 1.126340I
a = 0.421885 + 1.233660I
b = 1.95442 + 0.79674I
−1.85183 − 13.51530I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.459461 + 1.173470I
a = −0.438511 − 0.287298I
b = −0.134749 − 0.946354I
−0.51232 − 5.68304I 0
u = −0.459461 − 1.173470I
a = −0.438511 + 0.287298I
b = −0.134749 + 0.946354I
−0.51232 + 5.68304I 0
u = −0.643765 + 0.361947I
a = 0.734544 + 0.051006I
b = 1.28036 + 1.97188I
−2.03338 − 3.54410I 0
u = −0.643765 − 0.361947I
a = 0.734544 − 0.051006I
b = 1.28036 − 1.97188I
−2.03338 + 3.54410I 0
u = 1.143750 + 0.534995I
a = −1.323960 − 0.415383I
b = −1.03519 + 1.56419I
0.79510 + 6.48971I 0
u = 1.143750 − 0.534995I
a = −1.323960 + 0.415383I
b = −1.03519 − 1.56419I
0.79510 − 6.48971I 0
u = 1.028740 + 0.737591I
a = 0.298060 − 0.180542I
b = 0.489256 − 0.256264I
−2.64106 + 6.15310I 0
u = 1.028740 − 0.737591I
a = 0.298060 + 0.180542I
b = 0.489256 + 0.256264I
−2.64106 − 6.15310I 0
u = −1.157490 + 0.513108I
a = −0.439738 + 0.144931I
b = −1.21838 − 1.57254I
3.90851 − 4.89501I 0
u = −1.157490 − 0.513108I
a = −0.439738 − 0.144931I
b = −1.21838 + 1.57254I
3.90851 + 4.89501I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.160600 + 0.558977I
a = −0.813277 − 0.320613I
b = −0.783174 − 0.123363I
3.42764 − 8.49889I 0
u = −1.160600 − 0.558977I
a = −0.813277 + 0.320613I
b = −0.783174 + 0.123363I
3.42764 + 8.49889I 0
u = −1.145230 + 0.613504I
a = 0.481101 − 0.353014I
b = 1.18208 + 2.04523I
0.88219 − 11.18370I 0
u = −1.145230 − 0.613504I
a = 0.481101 + 0.353014I
b = 1.18208 − 2.04523I
0.88219 + 11.18370I 0
u = −0.586133 + 0.375681I
a = 0.21752 − 2.06189I
b = 0.909065 + 0.437397I
−4.37037 + 6.99484I 0
u = −0.586133 − 0.375681I
a = 0.21752 + 2.06189I
b = 0.909065 − 0.437397I
−4.37037 − 6.99484I 0
u = −0.101004 + 0.684568I
a = −0.653162 − 1.215450I
b = −2.07348 − 0.96157I
−0.28743 − 2.46726I 0. + 4.44531I
u = −0.101004 − 0.684568I
a = −0.653162 + 1.215450I
b = −2.07348 + 0.96157I
−0.28743 + 2.46726I 0. − 4.44531I
u = 0.628929 + 0.266306I
a = 0.96771 + 1.53296I
b = 0.299913 − 0.898642I
−5.78935 + 0.68606I −2.49507 − 6.39155I
u = 0.628929 − 0.266306I
a = 0.96771 − 1.53296I
b = 0.299913 + 0.898642I
−5.78935 − 0.68606I −2.49507 + 6.39155I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.121170 + 0.694244I
a = 0.890693 − 0.238226I
b = 1.91995 + 1.01176I
−4.44426 − 11.38070I 0
u = −1.121170 − 0.694244I
a = 0.890693 + 0.238226I
b = 1.91995 − 1.01176I
−4.44426 + 11.38070I 0
u = 0.881465 + 1.004630I
a = 0.142382 + 0.010281I
b = −0.007897 − 0.568997I
−3.36270 + 0.14216I 0
u = 0.881465 − 1.004630I
a = 0.142382 − 0.010281I
b = −0.007897 + 0.568997I
−3.36270 − 0.14216I 0
u = 1.117470 + 0.736926I
a = −0.038687 + 0.285469I
b = 0.610468 + 0.504985I
−3.69249 − 3.37191I 0
u = 1.117470 − 0.736926I
a = −0.038687 − 0.285469I
b = 0.610468 − 0.504985I
−3.69249 + 3.37191I 0
u = 1.231700 + 0.570330I
a = 1.145330 + 0.252408I
b = 1.22493 − 1.24831I
4.92055 + 8.62646I 0
u = 1.231700 − 0.570330I
a = 1.145330 − 0.252408I
b = 1.22493 + 1.24831I
4.92055 − 8.62646I 0
u = 0.507192 + 1.285270I
a = 0.416315 + 0.282811I
b = 1.097480 − 0.164729I
−2.63922 − 4.76673I 0
u = 0.507192 − 1.285270I
a = 0.416315 − 0.282811I
b = 1.097480 + 0.164729I
−2.63922 + 4.76673I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.387160 + 0.023645I
a = 0.849880 + 0.283511I
b = 0.056347 + 0.145052I
7.67778 + 4.50262I 0
u = 1.387160 − 0.023645I
a = 0.849880 − 0.283511I
b = 0.056347 − 0.145052I
7.67778 − 4.50262I 0
u = −0.606172 + 0.075201I
a = −1.134450 + 0.312248I
b = −2.16618 + 1.31816I
−0.21515 − 1.52425I 12.12024 + 5.88982I
u = −0.606172 − 0.075201I
a = −1.134450 − 0.312248I
b = −2.16618 − 1.31816I
−0.21515 + 1.52425I 12.12024 − 5.88982I
u = 1.244780 + 0.629258I
a = −1.204340 − 0.351088I
b = −1.41993 + 1.59802I
2.9856 + 14.5493I 0
u = 1.244780 − 0.629258I
a = −1.204340 + 0.351088I
b = −1.41993 − 1.59802I
2.9856 − 14.5493I 0
u = −1.207310 + 0.725372I
a = −1.191030 + 0.199433I
b = −1.55697 − 1.71863I
2.3775 − 14.3079I 0
u = −1.207310 − 0.725372I
a = −1.191030 − 0.199433I
b = −1.55697 + 1.71863I
2.3775 + 14.3079I 0
u = −1.396050 + 0.219696I
a = −0.705777 − 0.231654I
b = 0.091109 − 0.644702I
7.30949 − 1.49107I 0
u = −1.396050 − 0.219696I
a = −0.705777 + 0.231654I
b = 0.091109 + 0.644702I
7.30949 + 1.49107I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.24470 + 0.67938I
a = −0.781513 − 0.301806I
b = −1.03733 + 1.16608I
1.14688 + 7.28909I 0
u = 1.24470 − 0.67938I
a = −0.781513 + 0.301806I
b = −1.03733 − 1.16608I
1.14688 − 7.28909I 0
u = −1.33510 + 0.49815I
a = 0.647713 − 0.264716I
b = 0.496765 + 0.861477I
3.40573 − 1.43298I 0
u = −1.33510 − 0.49815I
a = 0.647713 + 0.264716I
b = 0.496765 − 0.861477I
3.40573 + 1.43298I 0
u = −1.20974 + 0.76422I
a = 1.248120 − 0.306679I
b = 1.81363 + 1.98292I
0.2730 − 20.3086I 0
u = −1.20974 − 0.76422I
a = 1.248120 + 0.306679I
b = 1.81363 − 1.98292I
0.2730 + 20.3086I 0
u = 1.44553 + 0.11425I
a = −0.910720 − 0.361032I
b = 0.101745 + 0.296358I
6.51257 + 10.16590I 0
u = 1.44553 − 0.11425I
a = −0.910720 + 0.361032I
b = 0.101745 − 0.296358I
6.51257 − 10.16590I 0
u = 0.397125 + 0.354132I
a = −2.83441 − 0.55123I
b = −3.49550 + 0.86823I
−2.14003 − 2.45951I 10.75971 − 5.86740I
u = 0.397125 − 0.354132I
a = −2.83441 + 0.55123I
b = −3.49550 − 0.86823I
−2.14003 + 2.45951I 10.75971 + 5.86740I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46973 + 0.11223I
a = 0.764122 + 0.301520I
b = −0.362334 + 0.255883I
6.51509 + 3.93547I 0
u = −1.46973 − 0.11223I
a = 0.764122 − 0.301520I
b = −0.362334 − 0.255883I
6.51509 − 3.93547I 0
u = 1.24991 + 0.78752I
a = 0.585591 + 0.363161I
b = 1.35565 − 0.94383I
−0.24586 + 11.98110I 0
u = 1.24991 − 0.78752I
a = 0.585591 − 0.363161I
b = 1.35565 + 0.94383I
−0.24586 − 11.98110I 0
u = −1.32719 + 0.68210I
a = −0.466877 + 0.289109I
b = −0.859626 − 0.809727I
2.52813 − 5.97540I 0
u = −1.32719 − 0.68210I
a = −0.466877 − 0.289109I
b = −0.859626 + 0.809727I
2.52813 + 5.97540I 0
u = −0.388772 + 0.005114I
a = 1.25926 − 2.02427I
b = −0.193919 − 0.468391I
0.82272 − 1.37291I 5.33346 + 4.38312I
u = −0.388772 − 0.005114I
a = 1.25926 + 2.02427I
b = −0.193919 + 0.468391I
0.82272 + 1.37291I 5.33346 − 4.38312I
u = −0.063607 + 0.318230I
a = 0.02848 − 2.88617I
b = −0.711121 − 1.156350I
−0.15035 − 2.79872I 1.55621 + 1.54033I
u = −0.063607 − 0.318230I
a = 0.02848 + 2.88617I
b = −0.711121 + 1.156350I
−0.15035 + 2.79872I 1.55621 − 1.54033I
18
II. I
v
1
= ha, 4v
3
− 6v
2
+ b + 25v − 8, v
4
− 2v
3
+ 7v
2
− 5v + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
v
0
a
4
=
1
0
a
8
=
v
0
a
11
=
0
−4v
3
+ 6v
2
− 25v + 8
a
6
=
v
5v
3
− 8v
2
+ 32v − 12
a
9
=
v
3
− v
2
+ 6v − 2
−1
a
10
=
v
3
− 2v
2
+ 6v − 2
−4v
3
+ 6v
2
− 25v + 8
a
5
=
v
3
− 2v
2
+ 6v − 2
1
a
2
=
−v
3
+ 2v
2
− 6v + 3
−1
a
1
=
−v
3
+ 2v
2
− 6v + 2
−1
a
12
=
2v − 1
−2v
3
+ 3v
2
− 12v + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7v
3
+ 10v
2
− 47v + 12
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
6
, c
9
u
4
+ u
2
+ u + 1
c
8
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
10
, c
12
u
4
+ u
2
− u + 1
c
11
u
4
− 2u
3
+ 3u
2
− u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
4
c
3
, c
7
y
4
c
5
y
4
− y
3
+ 2y
2
+ 7y + 4
c
6
, c
9
, c
10
c
12
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
8
, c
11
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.409261 + 0.055548I
a = 0
b = −1.50411 − 1.22685I
−0.66484 + 1.39709I −6.04449 − 2.35025I
v = 0.409261 − 0.055548I
a = 0
b = −1.50411 + 1.22685I
−0.66484 − 1.39709I −6.04449 + 2.35025I
v = 0.59074 + 2.34806I
a = 0
b = 0.504108 − 0.106312I
−4.26996 + 7.64338I −0.45551 − 9.20433I
v = 0.59074 − 2.34806I
a = 0
b = 0.504108 + 0.106312I
−4.26996 − 7.64338I −0.45551 + 9.20433I
22
III. I
v
2
= ha, 50v
5
+ 61v
4
+ · · · + 67b + 59, v
6
+ v
5
+ 4v
4
+ 2v
3
+ 8v
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
v
0
a
4
=
1
0
a
8
=
v
0
a
11
=
0
−0.746269v
5
− 0.910448v
4
+ ··· − 5.82090v − 0.880597
a
6
=
v
−0.447761v
5
− 0.746269v
4
+ ··· − 3.49254v − 1.32836
a
9
=
0.134328v
5
+ 0.223881v
4
+ ··· + 1.44776v + 0.298507
−1
a
10
=
−0.223881v
5
− 0.373134v
4
+ ··· − 0.746269v − 0.164179
−0.746269v
5
− 0.910448v
4
+ ··· − 5.82090v − 0.880597
a
5
=
0.134328v
5
+ 0.223881v
4
+ ··· + 1.44776v + 0.298507
1
a
2
=
−0.134328v
5
− 0.223881v
4
+ ··· − 1.44776v + 0.701493
−1
a
1
=
−0.134328v
5
− 0.223881v
4
+ ··· − 1.44776v − 0.298507
−1
a
12
=
0.164179v
5
− 0.0597015v
4
+ ··· − 0.119403v − 0.746269
−0.268657v
5
− 0.447761v
4
+ ··· − 2.89552v − 1.59701
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
68
67
v
5
+
43
67
v
4
−
221
67
v
3
+
141
67
v
2
−
450
67
v +
370
67
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
u
6
c
4
(u + 1)
6
c
5
(u
3
− u
2
+ 1)
2
c
6
, c
9
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
8
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
10
, c
12
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
11
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
6
c
3
, c
7
y
6
c
5
(y
3
− y
2
+ 2y − 1)
2
c
6
, c
9
, c
10
c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
8
, c
11
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.42975 + 1.50598I
a = 0
b = −0.702221 + 0.130845I
−1.91067 + 2.82812I −0.06063 − 4.05868I
v = 0.42975 − 1.50598I
a = 0
b = −0.702221 − 0.130845I
−1.91067 − 2.82812I −0.06063 + 4.05868I
v = 0.017526 + 0.363437I
a = 0
b = −0.74506 − 2.00027I
−1.91067 + 2.82812I 5.15973 − 2.26538I
v = 0.017526 − 0.363437I
a = 0
b = −0.74506 + 2.00027I
−1.91067 − 2.82812I 5.15973 + 2.26538I
v = −0.94728 + 1.47725I
a = 0
b = 0.447279 − 0.479689I
−6.04826 −7.59911 + 2.50363I
v = −0.94728 − 1.47725I
a = 0
b = 0.447279 + 0.479689I
−6.04826 −7.59911 − 2.50363I
26
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
140
+ 69u
139
+ ··· + 221u + 1)
c
2
((u − 1)
10
)(u
140
− 11u
139
+ ··· − 5u + 1)
c
3
, c
7
u
10
(u
140
− u
139
+ ··· − 8192u + 1024)
c
4
((u + 1)
10
)(u
140
− 11u
139
+ ··· − 5u + 1)
c
5
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
140
+ 2u
139
+ ··· − 10624u + 1216)
c
6
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
140
− 2u
139
+ ··· − 24012u + 5887)
c
8
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
140
− 10u
139
+ ··· − 2u + 1)
c
9
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
140
+ 2u
139
+ ··· + 14u + 1)
c
10
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
140
+ 14u
139
+ ··· + 2u + 1)
c
11
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
140
+ 58u
139
+ ··· + 14u + 1)
c
12
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
140
+ 2u
139
+ ··· + 14u + 1)
27
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
10
)(y
140
+ 15y
139
+ ··· − 2817y + 1)
c
2
, c
4
((y − 1)
10
)(y
140
− 69y
139
+ ··· − 221y + 1)
c
3
, c
7
y
10
(y
140
− 63y
139
+ ··· − 2.56901 × 10
7
y + 1048576)
c
5
(y
3
− y
2
+ 2y − 1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
140
+ 150y
139
+ ··· + 35716096y + 1478656)
c
6
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
140
+ 142y
139
+ ··· + 261556046y + 34656769)
c
8
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
140
+ 14y
139
+ ··· + 10y + 1)
c
9
, c
12
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
140
+ 58y
139
+ ··· + 14y + 1)
c
10
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
140
+ 10y
139
+ ··· + 14y + 1)
c
11
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
140
+ 50y
139
+ ··· − 2010y + 1)
28
