12a
0199
(K12a
0199
)
A knot diagram
1
Linearized knot diagam
3 5 11 7 2 10 12 4 6 9 1 8
Solving Sequence
2,5
3
6,10
7 1 4 9 11 8 12
c
2
c
5
c
6
c
1
c
4
c
9
c
10
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.05186 × 10
25
u
29
− 1.43266 × 10
24
u
28
+ ··· + 3.83777 × 10
26
b + 2.01209 × 10
26
,
1.20840 × 10
25
u
29
+ 2.78546 × 10
25
u
28
+ ··· + 3.83777 × 10
26
a − 1.47083 × 10
27
, u
30
+ u
29
+ ··· − 136u + 16i
I
u
2
= h8301956774068u
47
a − 1716498814000922u
47
+ ··· − 18605403975840a + 3278970716047515,
24902419266u
47
a + 25380336871u
47
+ ··· + 44502374232a − 179167125090,
u
48
− 2u
47
+ ··· + 16u
2
+ 1i
I
u
3
= h2au + b − a, 4a
2
− 2au + u + 1, u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 130 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−1.05 × 10
25
u
29
− 1.43 × 10
24
u
28
+ · · · + 3.84 × 10
26
b + 2.01 ×
10
26
, 1.21 × 10
25
u
29
+ 2.79 × 10
25
u
28
+ · · · + 3.84 × 10
26
a − 1.47 ×
10
27
, u
30
+ u
29
+ · · · − 136u + 16i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
−u
2
a
6
=
u
u
a
10
=
−0.0314870u
29
− 0.0725802u
28
+ ··· − 3.16309u + 3.83250
0.0274082u
29
+ 0.00373306u
28
+ ··· + 1.51313u − 0.524287
a
7
=
0.00441977u
29
+ 0.0255666u
28
+ ··· − 0.244085u − 1.67888
−0.0228435u
29
+ 0.0213127u
28
+ ··· − 5.26346u + 0.973918
a
1
=
u
2
+ 1
−u
4
a
4
=
0.00435453u
29
+ 0.00268953u
28
+ ··· + 1.16324u + 0.264419
−0.00450085u
29
− 0.00348346u
28
+ ··· + 1.15275u − 0.0963126
a
9
=
−0.0381470u
29
− 0.0678968u
28
+ ··· − 1.73655u + 3.55381
0.0207481u
29
+ 0.00841644u
28
+ ··· + 2.93967u − 0.802977
a
11
=
−0.0397231u
29
− 0.0645166u
28
+ ··· − 4.17765u + 2.94412
−0.00367619u
29
− 0.0461053u
28
+ ··· + 1.65856u − 0.467412
a
8
=
−0.0204362u
29
− 0.0555509u
28
+ ··· − 0.715574u + 3.27528
0.0267068u
29
− 0.0127292u
28
+ ··· + 6.08279u − 1.17219
a
12
=
−0.0286036u
29
− 0.0437086u
28
+ ··· − 2.32665u + 2.99514
−0.00925796u
29
− 0.0455321u
28
+ ··· + 3.42484u − 0.697592
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
12790684592978423102182111
95944166907326703898487264
u
29
+
24283871709880963319867825
95944166907326703898487264
u
28
+
··· −
443477214659957979551419763
11993020863415837987310908
u −
42761849795147821338360495
5996510431707918993655454
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
+ 11u
29
+ ··· − 12320u + 256
c
2
, c
5
u
30
− u
29
+ ··· + 136u + 16
c
3
, c
4
16(16u
30
− 24u
29
+ ··· + u + 1)
c
6
, c
7
, c
9
c
12
u
30
− 2u
29
+ ··· + 3u − 1
c
8
u
30
+ 5u
29
+ ··· − 9216u − 1024
c
10
, c
11
u
30
+ 16u
29
+ ··· + 9u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ 15y
29
+ ··· − 173031936y + 65536
c
2
, c
5
y
30
+ 11y
29
+ ··· − 12320y + 256
c
3
, c
4
256(256y
30
+ 2752y
29
+ ··· + y + 1)
c
6
, c
7
, c
9
c
12
y
30
− 16y
29
+ ··· − 9y + 1
c
8
y
30
+ 5y
29
+ ··· + 21626880y + 1048576
c
10
, c
11
y
30
− 48y
28
+ ··· + 87y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.513843 + 0.871891I
a = −0.446146 − 0.725334I
b = 0.38934 − 2.10569I
−8.85186 + 2.07542I 33.6724 − 61.7857I
u = 0.513843 − 0.871891I
a = −0.446146 + 0.725334I
b = 0.38934 + 2.10569I
−8.85186 − 2.07542I 33.6724 + 61.7857I
u = −0.355475 + 0.904157I
a = 0.411047 − 0.455694I
b = 0.035443 − 0.584835I
−0.39684 − 1.65663I −3.61734 + 2.59404I
u = −0.355475 − 0.904157I
a = 0.411047 + 0.455694I
b = 0.035443 + 0.584835I
−0.39684 + 1.65663I −3.61734 − 2.59404I
u = 0.886842 + 0.643141I
a = 0.108219 + 0.207785I
b = 0.056684 − 0.750111I
7.28214 − 1.89713I −1.79602 − 0.99400I
u = 0.886842 − 0.643141I
a = 0.108219 − 0.207785I
b = 0.056684 + 0.750111I
7.28214 + 1.89713I −1.79602 + 0.99400I
u = −0.270910 + 1.074590I
a = −1.07328 + 1.52289I
b = −0.72130 + 2.24404I
−3.48392 − 0.63227I −16.5794 + 0.3609I
u = −0.270910 − 1.074590I
a = −1.07328 − 1.52289I
b = −0.72130 − 2.24404I
−3.48392 + 0.63227I −16.5794 − 0.3609I
u = 0.989431 + 0.528893I
a = 2.04634 − 0.16797I
b = 0.906269 − 0.257371I
4.1464 − 13.5352I −6.25412 + 8.07209I
u = 0.989431 − 0.528893I
a = 2.04634 + 0.16797I
b = 0.906269 + 0.257371I
4.1464 + 13.5352I −6.25412 − 8.07209I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.333835 + 1.072850I
a = 0.15424 − 1.54650I
b = 0.33154 − 2.61604I
−8.69259 + 3.42736I −19.7102 − 3.7396I
u = 0.333835 − 1.072850I
a = 0.15424 + 1.54650I
b = 0.33154 + 2.61604I
−8.69259 − 3.42736I −19.7102 + 3.7396I
u = −0.369336 + 1.114300I
a = 0.386505 − 0.563344I
b = −0.127883 − 0.862401I
−0.33657 − 1.57944I −6.03935 + 1.36982I
u = −0.369336 − 1.114300I
a = 0.386505 + 0.563344I
b = −0.127883 + 0.862401I
−0.33657 + 1.57944I −6.03935 − 1.36982I
u = −1.146190 + 0.299068I
a = 1.55316 + 0.09412I
b = 0.749359 + 0.445987I
4.59032 + 3.09332I 1.17313 − 4.12974I
u = −1.146190 − 0.299068I
a = 1.55316 − 0.09412I
b = 0.749359 − 0.445987I
4.59032 − 3.09332I 1.17313 + 4.12974I
u = 0.727436 + 1.053530I
a = −0.047464 + 0.176285I
b = 0.776365 + 0.265918I
6.01261 + 7.86778I −3.60910 − 3.95992I
u = 0.727436 − 1.053530I
a = −0.047464 − 0.176285I
b = 0.776365 − 0.265918I
6.01261 − 7.86778I −3.60910 + 3.95992I
u = −1.136890 + 0.641709I
a = −0.623817 + 0.518365I
b = −0.279528 + 1.274650I
4.21761 − 6.91864I −0.34998 + 9.53979I
u = −1.136890 − 0.641709I
a = −0.623817 − 0.518365I
b = −0.279528 − 1.274650I
4.21761 + 6.91864I −0.34998 − 9.53979I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.720787 + 1.140920I
a = −0.21243 + 2.06553I
b = −0.22299 + 3.04110I
2.2432 + 19.7483I −8.5481 − 11.6447I
u = 0.720787 − 1.140920I
a = −0.21243 − 2.06553I
b = −0.22299 − 3.04110I
2.2432 − 19.7483I −8.5481 + 11.6447I
u = 0.646093
a = −1.97921
b = −0.298708
−5.53280 −15.4870
u = −0.901122 + 1.028260I
a = −0.918924 − 0.071187I
b = −0.226436 + 0.036666I
3.03751 − 0.25657I −1.246747 + 0.314424I
u = −0.901122 − 1.028260I
a = −0.918924 + 0.071187I
b = −0.226436 − 0.036666I
3.03751 + 0.25657I −1.246747 − 0.314424I
u = −0.095565 + 1.384150I
a = 0.39805 + 1.76502I
b = 0.02520 + 2.54016I
−3.39765 − 10.83270I −11.6079 + 10.7508I
u = −0.095565 − 1.384150I
a = 0.39805 − 1.76502I
b = 0.02520 − 2.54016I
−3.39765 + 10.83270I −11.6079 − 10.7508I
u = −0.78951 + 1.26116I
a = −0.08887 − 1.76517I
b = −0.07406 − 2.52275I
1.73617 − 9.98872I −5.29929 + 12.58752I
u = −0.78951 − 1.26116I
a = −0.08887 + 1.76517I
b = −0.07406 + 2.52275I
1.73617 + 9.98872I −5.29929 − 12.58752I
u = 0.139554
a = 3.43594
b = −0.437309
−0.810611 −12.3890
7
II. I
u
2
= h8.30 × 10
12
au
47
− 1.72 × 10
15
u
47
+ · · · − 1.86 × 10
13
a + 3.28 ×
10
15
, 2.49 × 10
10
au
47
+ 2.54 × 10
10
u
47
+ · · · + 4.45 × 10
10
a − 1.79 ×
10
11
, u
48
− 2u
47
+ · · · + 16u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
−u
2
a
6
=
u
u
a
10
=
a
−0.00768508au
47
+ 1.58895u
47
+ ··· + 0.0172229a − 3.03533
a
7
=
0.913597au
47
− 1.12318u
47
+ ··· − 3.05186a − 4.32727
1.69606au
47
− 2.47177u
47
+ ··· + 1.67376a + 0.0264682
a
1
=
u
2
+ 1
−u
4
a
4
=
−0.895600au
47
+ 1.48267u
47
+ ··· + 1.88285a + 10.0601
−0.805141au
47
+ 0.416548u
47
+ ··· − 0.739690a + 0.986881
a
9
=
0.222411au
47
+ 0.533718u
47
+ ··· + 1.07881a − 1.01638
0.214726au
47
+ 2.12267u
47
+ ··· + 0.0960309a − 4.05170
a
11
=
2.20533au
47
− 1.56856u
47
+ ··· − 4.28442a − 7.99229
2.65700au
47
− 0.108542u
47
+ ··· − 0.172526a − 3.38343
a
8
=
0.391848au
47
+ 0.489312u
47
+ ··· + 0.237285a − 5.57041
0.391848au
47
+ 2.93394u
47
+ ··· + 0.237285a − 4.59756
a
12
=
−1.89258au
47
− 1.52697u
47
+ ··· − 0.347615a − 7.31396
−1.43205au
47
+ 1.08570u
47
+ ··· + 2.37872a − 4.96729
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
17136040638
3523750753
u
47
+
40416089808
3523750753
u
46
+ ···−
10188595612
3523750753
u −
39541667460
3523750753
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
48
+ 18u
47
+ ··· + 32u + 1)
2
c
2
, c
5
(u
48
+ 2u
47
+ ··· + 16u
2
+ 1)
2
c
3
, c
4
u
96
− 9u
95
+ ··· + 130810298u + 122183483
c
6
, c
7
, c
9
c
12
u
96
+ 5u
95
+ ··· + 2u + 1
c
8
(u
48
− 2u
47
+ ··· + 2u + 1)
2
c
10
, c
11
u
96
+ 37u
95
+ ··· + 408u
3
+ 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
48
+ 26y
47
+ ··· − 264y + 1)
2
c
2
, c
5
(y
48
+ 18y
47
+ ··· + 32y + 1)
2
c
3
, c
4
y
96
+ 47y
95
+ ··· + 239047203594444768y + 14928803518011289
c
6
, c
7
, c
9
c
12
y
96
− 37y
95
+ ··· − 408y
3
+ 1
c
8
(y
48
+ 10y
47
+ ··· + 20y + 1)
2
c
10
, c
11
y
96
+ 43y
95
+ ··· + 2144y
2
+ 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.484781 + 0.850953I
a = −3.37504 + 5.83345I
b = −3.33055 + 4.82375I
−0.02738 − 1.96363I 2.8944 + 51.2708I
u = −0.484781 + 0.850953I
a = 0.20739 − 7.60050I
b = −0.64315 − 8.14498I
−0.02738 − 1.96363I 2.8944 + 51.2708I
u = −0.484781 − 0.850953I
a = −3.37504 − 5.83345I
b = −3.33055 − 4.82375I
−0.02738 + 1.96363I 2.8944 − 51.2708I
u = −0.484781 − 0.850953I
a = 0.20739 + 7.60050I
b = −0.64315 + 8.14498I
−0.02738 + 1.96363I 2.8944 − 51.2708I
u = 0.097067 + 1.022650I
a = −0.406779 + 0.448418I
b = 0.253041 + 0.768046I
−3.99758 + 0.49161I −13.81533 − 0.65955I
u = 0.097067 + 1.022650I
a = −0.72794 + 1.49597I
b = −0.61571 + 2.57000I
−3.99758 + 0.49161I −13.81533 − 0.65955I
u = 0.097067 − 1.022650I
a = −0.406779 − 0.448418I
b = 0.253041 − 0.768046I
−3.99758 − 0.49161I −13.81533 + 0.65955I
u = 0.097067 − 1.022650I
a = −0.72794 − 1.49597I
b = −0.61571 − 2.57000I
−3.99758 − 0.49161I −13.81533 + 0.65955I
u = 0.716038 + 0.740578I
a = −1.58024 + 0.04054I
b = −0.327130 − 0.220538I
4.67401 − 3.43632I −1.94110 + 3.09138I
u = 0.716038 + 0.740578I
a = 0.292211 − 0.016004I
b = −0.626333 − 0.371523I
4.67401 − 3.43632I −1.94110 + 3.09138I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.716038 − 0.740578I
a = −1.58024 − 0.04054I
b = −0.327130 + 0.220538I
4.67401 + 3.43632I −1.94110 − 3.09138I
u = 0.716038 − 0.740578I
a = 0.292211 + 0.016004I
b = −0.626333 + 0.371523I
4.67401 + 3.43632I −1.94110 − 3.09138I
u = −0.685446 + 0.778575I
a = −0.298304 − 0.757635I
b = −0.444479 − 0.452774I
1.43924 − 0.31691I −6.77030 + 0.34002I
u = −0.685446 + 0.778575I
a = −1.15899 − 1.04942I
b = −0.234179 − 0.846072I
1.43924 − 0.31691I −6.77030 + 0.34002I
u = −0.685446 − 0.778575I
a = −0.298304 + 0.757635I
b = −0.444479 + 0.452774I
1.43924 + 0.31691I −6.77030 − 0.34002I
u = −0.685446 − 0.778575I
a = −1.15899 + 1.04942I
b = −0.234179 + 0.846072I
1.43924 + 0.31691I −6.77030 − 0.34002I
u = 0.636609 + 0.849934I
a = 0.078084 + 1.162150I
b = −0.09338 + 2.45454I
2.20823 + 2.48736I −1.52867 − 3.91872I
u = 0.636609 + 0.849934I
a = 1.311060 + 0.127836I
b = 0.091787 + 0.556421I
2.20823 + 2.48736I −1.52867 − 3.91872I
u = 0.636609 − 0.849934I
a = 0.078084 − 1.162150I
b = −0.09338 − 2.45454I
2.20823 − 2.48736I −1.52867 + 3.91872I
u = 0.636609 − 0.849934I
a = 1.311060 − 0.127836I
b = 0.091787 − 0.556421I
2.20823 − 2.48736I −1.52867 + 3.91872I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.936905 + 0.579477I
a = −0.055387 − 0.251475I
b = −0.074157 + 0.690139I
5.72343 − 7.74189I −4.00692 + 3.57032I
u = 0.936905 + 0.579477I
a = −1.97766 + 0.12581I
b = −0.810338 + 0.148751I
5.72343 − 7.74189I −4.00692 + 3.57032I
u = 0.936905 − 0.579477I
a = −0.055387 + 0.251475I
b = −0.074157 − 0.690139I
5.72343 + 7.74189I −4.00692 − 3.57032I
u = 0.936905 − 0.579477I
a = −1.97766 − 0.12581I
b = −0.810338 − 0.148751I
5.72343 + 7.74189I −4.00692 − 3.57032I
u = 0.717956 + 0.851849I
a = 0.251023 − 0.019875I
b = −0.076809 − 0.959910I
6.27413 + 2.73487I 0. − 3.17064I
u = 0.717956 + 0.851849I
a = −0.220056 + 0.082656I
b = 0.693660 + 0.338468I
6.27413 + 2.73487I 0. − 3.17064I
u = 0.717956 − 0.851849I
a = 0.251023 + 0.019875I
b = −0.076809 + 0.959910I
6.27413 − 2.73487I 0. + 3.17064I
u = 0.717956 − 0.851849I
a = −0.220056 − 0.082656I
b = 0.693660 − 0.338468I
6.27413 − 2.73487I 0. + 3.17064I
u = −0.684569 + 0.885432I
a = 0.497504 + 0.678613I
b = 0.594605 + 0.365341I
1.11254 − 4.96052I −8.00000 + 5.40900I
u = −0.684569 + 0.885432I
a = 1.10653 + 0.94980I
b = 1.18189 + 1.90242I
1.11254 − 4.96052I −8.00000 + 5.40900I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.684569 − 0.885432I
a = 0.497504 − 0.678613I
b = 0.594605 − 0.365341I
1.11254 + 4.96052I −8.00000 − 5.40900I
u = −0.684569 − 0.885432I
a = 1.10653 − 0.94980I
b = 1.18189 − 1.90242I
1.11254 + 4.96052I −8.00000 − 5.40900I
u = −0.420414 + 0.772149I
a = 3.55803 + 1.71143I
b = 2.51087 + 1.16971I
−0.14530 + 2.51169I −9.91381 + 1.94946I
u = −0.420414 + 0.772149I
a = −2.15258 + 3.37249I
b = −1.24231 + 4.05910I
−0.14530 + 2.51169I −9.91381 + 1.94946I
u = −0.420414 − 0.772149I
a = 3.55803 − 1.71143I
b = 2.51087 − 1.16971I
−0.14530 − 2.51169I −9.91381 − 1.94946I
u = −0.420414 − 0.772149I
a = −2.15258 − 3.37249I
b = −1.24231 − 4.05910I
−0.14530 − 2.51169I −9.91381 − 1.94946I
u = 0.733465 + 0.467600I
a = −1.65111 − 0.38305I
b = −0.445586 − 1.014770I
−0.96653 − 6.30841I −9.45390 + 5.38910I
u = 0.733465 + 0.467600I
a = 1.86018 − 0.33304I
b = 0.410288 − 0.363694I
−0.96653 − 6.30841I −9.45390 + 5.38910I
u = 0.733465 − 0.467600I
a = −1.65111 + 0.38305I
b = −0.445586 + 1.014770I
−0.96653 + 6.30841I −9.45390 − 5.38910I
u = 0.733465 − 0.467600I
a = 1.86018 + 0.33304I
b = 0.410288 + 0.363694I
−0.96653 + 6.30841I −9.45390 − 5.38910I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.605495 + 0.621445I
a = 1.241810 + 0.446110I
b = 0.123749 + 1.329770I
0.278716 − 0.472036I −6.31074 + 2.15424I
u = 0.605495 + 0.621445I
a = −0.463331 − 0.287948I
b = −0.267791 + 0.963683I
0.278716 − 0.472036I −6.31074 + 2.15424I
u = 0.605495 − 0.621445I
a = 1.241810 − 0.446110I
b = 0.123749 − 1.329770I
0.278716 + 0.472036I −6.31074 − 2.15424I
u = 0.605495 − 0.621445I
a = −0.463331 + 0.287948I
b = −0.267791 − 0.963683I
0.278716 + 0.472036I −6.31074 − 2.15424I
u = −0.490818 + 1.023000I
a = 0.994900 − 0.202633I
b = 0.826814 − 0.594067I
−0.41863 − 1.44578I −8.00000 − 1.12617I
u = −0.490818 + 1.023000I
a = −0.116576 − 0.595943I
b = −0.743474 − 0.981271I
−0.41863 − 1.44578I −8.00000 − 1.12617I
u = −0.490818 − 1.023000I
a = 0.994900 + 0.202633I
b = 0.826814 + 0.594067I
−0.41863 + 1.44578I −8.00000 + 1.12617I
u = −0.490818 − 1.023000I
a = −0.116576 + 0.595943I
b = −0.743474 + 0.981271I
−0.41863 + 1.44578I −8.00000 + 1.12617I
u = 0.679611 + 0.941578I
a = 0.01271 − 1.46261I
b = 0.11344 − 2.62787I
4.06736 + 8.78436I −3.69204 − 9.06876I
u = 0.679611 + 0.941578I
a = −0.239559 + 0.117695I
b = 0.175598 + 0.973145I
4.06736 + 8.78436I −3.69204 − 9.06876I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.679611 − 0.941578I
a = 0.01271 + 1.46261I
b = 0.11344 + 2.62787I
4.06736 − 8.78436I −3.69204 + 9.06876I
u = 0.679611 − 0.941578I
a = −0.239559 − 0.117695I
b = 0.175598 − 0.973145I
4.06736 − 8.78436I −3.69204 + 9.06876I
u = 0.618516 + 0.996648I
a = 0.70483 + 1.36867I
b = 0.13252 + 2.33095I
−0.83388 + 5.37086I −8.00000 − 6.82742I
u = 0.618516 + 0.996648I
a = 0.155618 − 0.259413I
b = −0.791151 − 0.314501I
−0.83388 + 5.37086I −8.00000 − 6.82742I
u = 0.618516 − 0.996648I
a = 0.70483 − 1.36867I
b = 0.13252 − 2.33095I
−0.83388 − 5.37086I −8.00000 + 6.82742I
u = 0.618516 − 0.996648I
a = 0.155618 + 0.259413I
b = −0.791151 + 0.314501I
−0.83388 − 5.37086I −8.00000 + 6.82742I
u = 0.092633 + 1.183130I
a = 0.407430 + 1.310510I
b = −0.13398 + 2.18038I
−6.20332 − 4.21770I −16.5470 + 3.6832I
u = 0.092633 + 1.183130I
a = 0.70859 − 1.82338I
b = 0.66013 − 2.74184I
−6.20332 − 4.21770I −16.5470 + 3.6832I
u = 0.092633 − 1.183130I
a = 0.407430 − 1.310510I
b = −0.13398 − 2.18038I
−6.20332 + 4.21770I −16.5470 − 3.6832I
u = 0.092633 − 1.183130I
a = 0.70859 + 1.82338I
b = 0.66013 + 2.74184I
−6.20332 + 4.21770I −16.5470 − 3.6832I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.453428 + 1.117910I
a = −1.45632 + 0.78848I
b = −1.23263 + 1.33171I
−1.33452 − 5.77158I −8.00000 + 6.31105I
u = −0.453428 + 1.117910I
a = −0.19465 − 2.16584I
b = −0.06297 − 3.08092I
−1.33452 − 5.77158I −8.00000 + 6.31105I
u = −0.453428 − 1.117910I
a = −1.45632 − 0.78848I
b = −1.23263 − 1.33171I
−1.33452 + 5.77158I −8.00000 − 6.31105I
u = −0.453428 − 1.117910I
a = −0.19465 + 2.16584I
b = −0.06297 + 3.08092I
−1.33452 + 5.77158I −8.00000 − 6.31105I
u = −1.140860 + 0.475100I
a = 0.830481 − 0.288484I
b = 0.383709 − 1.036000I
4.44182 − 1.91664I 0
u = −1.140860 + 0.475100I
a = −1.53836 − 0.13415I
b = −0.738598 − 0.364252I
4.44182 − 1.91664I 0
u = −1.140860 − 0.475100I
a = 0.830481 + 0.288484I
b = 0.383709 + 1.036000I
4.44182 + 1.91664I 0
u = −1.140860 − 0.475100I
a = −1.53836 + 0.13415I
b = −0.738598 + 0.364252I
4.44182 + 1.91664I 0
u = 0.628445 + 1.067610I
a = −0.68712 − 1.58177I
b = −0.18687 − 2.48633I
−2.68228 + 11.51390I 0
u = 0.628445 + 1.067610I
a = −0.37642 + 1.72589I
b = −0.34089 + 2.80245I
−2.68228 + 11.51390I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.628445 − 1.067610I
a = −0.68712 + 1.58177I
b = −0.18687 + 2.48633I
−2.68228 − 11.51390I 0
u = 0.628445 − 1.067610I
a = −0.37642 − 1.72589I
b = −0.34089 − 2.80245I
−2.68228 − 11.51390I 0
u = −0.178050 + 1.254860I
a = −0.395666 + 0.536799I
b = 0.133593 + 0.820738I
−1.79384 − 6.04938I 0
u = −0.178050 + 1.254860I
a = −0.18971 − 1.75408I
b = 0.14118 − 2.61617I
−1.79384 − 6.04938I 0
u = −0.178050 − 1.254860I
a = −0.395666 − 0.536799I
b = 0.133593 − 0.820738I
−1.79384 + 6.04938I 0
u = −0.178050 − 1.254860I
a = −0.18971 + 1.75408I
b = 0.14118 + 2.61617I
−1.79384 + 6.04938I 0
u = 0.722062 + 1.101140I
a = 0.004104 − 0.197466I
b = −0.795178 − 0.256311I
4.1071 + 13.8241I 0
u = 0.722062 + 1.101140I
a = 0.15676 − 1.95744I
b = 0.18592 − 2.96149I
4.1071 + 13.8241I 0
u = 0.722062 − 1.101140I
a = 0.004104 + 0.197466I
b = −0.795178 + 0.256311I
4.1071 − 13.8241I 0
u = 0.722062 − 1.101140I
a = 0.15676 + 1.95744I
b = 0.18592 + 2.96149I
4.1071 − 13.8241I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.197836 + 0.635066I
a = 1.62396 − 0.06057I
b = 1.78812 − 1.67082I
−0.31620 − 5.25869I −10.26177 + 8.82936I
u = −0.197836 + 0.635066I
a = 0.43158 − 2.15416I
b = −0.109316 − 0.694850I
−0.31620 − 5.25869I −10.26177 + 8.82936I
u = −0.197836 − 0.635066I
a = 1.62396 + 0.06057I
b = 1.78812 + 1.67082I
−0.31620 + 5.25869I −10.26177 − 8.82936I
u = −0.197836 − 0.635066I
a = 0.43158 + 2.15416I
b = −0.109316 + 0.694850I
−0.31620 + 5.25869I −10.26177 − 8.82936I
u = −0.597205 + 0.122097I
a = 0.047679 − 1.266580I
b = −0.062307 − 0.611788I
1.90373 − 2.42418I −2.94951 + 3.72567I
u = −0.597205 + 0.122097I
a = 1.53323 + 1.07170I
b = 0.385306 − 0.194369I
1.90373 − 2.42418I −2.94951 + 3.72567I
u = −0.597205 − 0.122097I
a = 0.047679 + 1.266580I
b = −0.062307 + 0.611788I
1.90373 + 2.42418I −2.94951 − 3.72567I
u = −0.597205 − 0.122097I
a = 1.53323 − 1.07170I
b = 0.385306 + 0.194369I
1.90373 + 2.42418I −2.94951 − 3.72567I
u = −0.84747 + 1.14529I
a = 0.784607 − 0.096523I
b = 0.142080 − 0.240249I
2.44671 − 5.11859I 0
u = −0.84747 + 1.14529I
a = 0.11082 + 1.54830I
b = 0.15082 + 2.32934I
2.44671 − 5.11859I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.84747 − 1.14529I
a = 0.784607 + 0.096523I
b = 0.142080 + 0.240249I
2.44671 + 5.11859I 0
u = −0.84747 − 1.14529I
a = 0.11082 − 1.54830I
b = 0.15082 − 2.32934I
2.44671 + 5.11859I 0
u = −0.003925 + 0.294268I
a = −0.09066 − 2.76849I
b = −1.231110 + 0.466867I
−0.218311 − 0.283540I −10.30249 + 1.71239I
u = −0.003925 + 0.294268I
a = −3.05863 − 2.20591I
b = −0.918738 + 0.418014I
−0.218311 − 0.283540I −10.30249 + 1.71239I
u = −0.003925 − 0.294268I
a = −0.09066 + 2.76849I
b = −1.231110 − 0.466867I
−0.218311 + 0.283540I −10.30249 − 1.71239I
u = −0.003925 − 0.294268I
a = −3.05863 + 2.20591I
b = −0.918738 − 0.418014I
−0.218311 + 0.283540I −10.30249 − 1.71239I
20
III. I
u
3
= h2au + b − a, 4a
2
− 2au + u + 1, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u + 1
a
6
=
u
u
a
10
=
a
−2au + a
a
7
=
−a +
1
2
u
2au − a −
1
2
u − 1
a
1
=
−u
−u
a
4
=
1
2
au +
1
2
a +
1
2
1
2
au −
1
2
a + u +
1
2
a
9
=
−a
−2au − a
a
11
=
3a +
1
2
u
2au + 3a −
1
2
u − 1
a
8
=
−a
−2au − a
a
12
=
a −
1
2
u
2au + a −
3
2
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 64au − 4a −
51
4
u − 30
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
− u + 1)
2
c
2
(u
2
+ u + 1)
2
c
3
16(16u
4
+ 8u
3
+ 8u
2
− 2u + 1)
c
4
16(16u
4
− 8u
3
+ 8u
2
+ 2u + 1)
c
6
, c
7
(u
2
+ u − 1)
2
c
8
u
4
c
9
, c
12
(u
2
− u − 1)
2
c
10
(u
2
+ 3u + 1)
2
c
11
(u
2
− 3u + 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y
2
+ y + 1)
2
c
3
, c
4
256(256y
4
+ 192y
3
+ 128y
2
+ 12y + 1)
c
6
, c
7
, c
9
c
12
(y
2
− 3y + 1)
2
c
8
y
4
c
10
, c
11
(y
2
− 7y + 1)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.404508 + 0.700629I
b = 0.40451 + 2.10189I
−8.88264 − 2.02988I −47.8955 − 58.6846I
u = −0.500000 + 0.866025I
a = 0.154508 − 0.267617I
b = −0.154508 − 0.802850I
−0.98696 − 2.02988I −14.3545 + 7.1561I
u = −0.500000 − 0.866025I
a = −0.404508 − 0.700629I
b = 0.40451 − 2.10189I
−8.88264 + 2.02988I −47.8955 + 58.6846I
u = −0.500000 − 0.866025I
a = 0.154508 + 0.267617I
b = −0.154508 + 0.802850I
−0.98696 + 2.02988I −14.3545 − 7.1561I
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
30
+ 11u
29
+ ··· − 12320u + 256)
· (u
48
+ 18u
47
+ ··· + 32u + 1)
2
c
2
((u
2
+ u + 1)
2
)(u
30
− u
29
+ ··· + 136u + 16)
· (u
48
+ 2u
47
+ ··· + 16u
2
+ 1)
2
c
3
256(16u
4
+ 8u
3
+ ··· − 2u + 1)(16u
30
− 24u
29
+ ··· + u + 1)
· (u
96
− 9u
95
+ ··· + 130810298u + 122183483)
c
4
256(16u
4
− 8u
3
+ ··· + 2u + 1)(16u
30
− 24u
29
+ ··· + u + 1)
· (u
96
− 9u
95
+ ··· + 130810298u + 122183483)
c
5
((u
2
− u + 1)
2
)(u
30
− u
29
+ ··· + 136u + 16)
· (u
48
+ 2u
47
+ ··· + 16u
2
+ 1)
2
c
6
, c
7
((u
2
+ u − 1)
2
)(u
30
− 2u
29
+ ··· + 3u − 1)(u
96
+ 5u
95
+ ··· + 2u + 1)
c
8
u
4
(u
30
+ 5u
29
+ ··· − 9216u − 1024)(u
48
− 2u
47
+ ··· + 2u + 1)
2
c
9
, c
12
((u
2
− u − 1)
2
)(u
30
− 2u
29
+ ··· + 3u − 1)(u
96
+ 5u
95
+ ··· + 2u + 1)
c
10
((u
2
+ 3u + 1)
2
)(u
30
+ 16u
29
+ ··· + 9u + 1)
· (u
96
+ 37u
95
+ ··· + 408u
3
+ 1)
c
11
((u
2
− 3u + 1)
2
)(u
30
+ 16u
29
+ ··· + 9u + 1)
· (u
96
+ 37u
95
+ ··· + 408u
3
+ 1)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
2
)(y
30
+ 15y
29
+ ··· − 1.73032 × 10
8
y + 65536)
· (y
48
+ 26y
47
+ ··· − 264y + 1)
2
c
2
, c
5
((y
2
+ y + 1)
2
)(y
30
+ 11y
29
+ ··· − 12320y + 256)
· (y
48
+ 18y
47
+ ··· + 32y + 1)
2
c
3
, c
4
65536(256y
4
+ 192y
3
+ 128y
2
+ 12y + 1)
· (256y
30
+ 2752y
29
+ ··· + y + 1)
· (y
96
+ 47y
95
+ ··· + 239047203594444768y + 14928803518011289)
c
6
, c
7
, c
9
c
12
((y
2
− 3y + 1)
2
)(y
30
− 16y
29
+ ··· − 9y + 1)
· (y
96
− 37y
95
+ ··· − 408y
3
+ 1)
c
8
y
4
(y
30
+ 5y
29
+ ··· + 2.16269 × 10
7
y + 1048576)
· (y
48
+ 10y
47
+ ··· + 20y + 1)
2
c
10
, c
11
((y
2
− 7y + 1)
2
)(y
30
− 48y
28
+ ··· + 87y + 1)
· (y
96
+ 43y
95
+ ··· + 2144y
2
+ 1)
26
