12a
0374
(K12a
0374
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 2 12 1 5 11 4 8 7
Solving Sequence
4,10 2,5
6 11 9 3 1 8 12 7
c
4
c
5
c
10
c
9
c
3
c
1
c
8
c
11
c
7
c
2
, c
6
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
69
+ 4u
68
+ ··· + 4b − 4, −2u
70
− u
69
+ ··· + 4a − 2, u
71
+ 2u
70
+ ··· − 4u − 2i
I
u
2
= h−20u
3
a
2
− 83u
3
a + ··· − 210a + 142,
− 2u
3
a
2
+ u
3
a + a
3
− 2a
2
u − 3u
2
a − u
3
− 2a
2
− au − 2u
2
+ 2a − u + 1, u
4
+ u
2
+ u + 1i
I
u
3
= h−u
3
+ b − u + 1, −u
3
+ 2u
2
+ 2a + 4, u
4
+ 2u
2
+ 2i
I
u
4
= h−5u
5
a
2
+ 15u
5
a + ··· − 30a + 24, −2u
4
a
2
− u
4
a − 2a
2
u
2
+ 3u
3
a − u
4
+ a
3
+ u
3
+ 2au − u
2
+ 1,
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
I
v
1
= ha, b + 1, v −1i
* 5 irreducible components of dim
C
= 0, with total 106 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
= h3u
69
+4u
68
+· · ·+4b−4, −2u
70
−u
69
+· · ·+4a−2, u
71
+2u
70
+· · ·−4u−2i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
1
2
u
70
+
1
4
u
69
+ ··· −
3
2
u +
1
2
−
3
4
u
69
− u
68
+ ··· +
1
2
u + 1
a
5
=
1
−u
2
a
6
=
−
1
2
u
70
− u
69
+ ··· + u +
3
2
−u
70
− u
69
+ ··· +
3
2
u + 1
a
11
=
u
u
a
9
=
u
3
u
3
+ u
a
3
=
−u
6
− u
4
+ 1
−u
6
− 2u
4
− u
2
a
1
=
1
2
u
70
+
17
2
u
68
+ ··· − 2u −
1
2
−u
69
− u
68
+ ··· +
1
2
u + 1
a
8
=
u
5
+ 2u
3
+ u
−u
7
− u
5
+ u
a
12
=
u
13
+ 4u
11
+ 7u
9
+ 6u
7
+ 2u
5
+ u
−u
15
− 3u
13
− 4u
11
− u
9
+ 2u
7
+ 2u
5
+ u
a
7
=
1
4
u
56
+
13
4
u
54
+ ··· +
1
2
u +
1
2
1
4
u
56
+
7
2
u
54
+ ··· −
1
2
u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
70
− 4u
69
+ ··· + 4u
2
− 2u
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
71
+ 34u
70
+ ··· + 9u + 1
c
2
, c
5
u
71
+ 2u
70
+ ··· + u + 1
c
3
u
71
+ 2u
70
+ ··· + 2308u + 202
c
4
, c
10
u
71
− 2u
70
+ ··· − 4u + 2
c
6
, c
7
, c
12
u
71
− 2u
70
+ ··· + 13u + 1
c
8
u
71
− 10u
70
+ ··· − 1608u + 86
c
9
u
71
+ 34u
70
+ ··· + 8u − 4
c
11
u
71
+ 6u
70
+ ··· + 3584u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
71
+ 14y
70
+ ··· − 39y −1
c
2
, c
5
y
71
− 34y
70
+ ··· + 9y −1
c
3
y
71
− 22y
70
+ ··· + 2098096y −40804
c
4
, c
10
y
71
+ 34y
70
+ ··· + 8y −4
c
6
, c
7
, c
12
y
71
− 66y
70
+ ··· − 71y −1
c
8
y
71
+ 2y
70
+ ··· − 2565048y −7396
c
9
y
71
+ 6y
70
+ ··· + 160y −16
c
11
y
71
+ 30y
70
+ ··· − 3604480y −65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.513487 + 0.874485I
a = −0.612533 − 0.514676I
b = −1.80080 − 0.15793I
−1.85439 − 1.13692I −1.95543 + 1.42420I
u = 0.513487 − 0.874485I
a = −0.612533 + 0.514676I
b = −1.80080 + 0.15793I
−1.85439 + 1.13692I −1.95543 − 1.42420I
u = −0.063916 + 1.045220I
a = 0.654592 + 0.217537I
b = −0.109398 + 0.923327I
3.27038 + 2.34753I 0. − 3.27632I
u = −0.063916 − 1.045220I
a = 0.654592 − 0.217537I
b = −0.109398 − 0.923327I
3.27038 − 2.34753I 0. + 3.27632I
u = −0.662691 + 0.682395I
a = 0.22635 + 2.15514I
b = −0.804600 + 0.848680I
3.81746 − 9.62606I 3.94934 + 8.10898I
u = −0.662691 − 0.682395I
a = 0.22635 − 2.15514I
b = −0.804600 − 0.848680I
3.81746 + 9.62606I 3.94934 − 8.10898I
u = −0.598790 + 0.882849I
a = −0.751708 + 0.316001I
b = −1.75329 − 0.07900I
3.22141 + 4.73439I 0
u = −0.598790 − 0.882849I
a = −0.751708 − 0.316001I
b = −1.75329 + 0.07900I
3.22141 − 4.73439I 0
u = 0.653038 + 0.634669I
a = 0.89558 + 1.18479I
b = 1.300590 + 0.058600I
6.19918 + 4.37861I 7.35250 − 4.00415I
u = 0.653038 − 0.634669I
a = 0.89558 − 1.18479I
b = 1.300590 − 0.058600I
6.19918 − 4.37861I 7.35250 + 4.00415I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.609895 + 0.669378I
a = 0.27854 − 2.39600I
b = −0.846051 − 0.904470I
−1.24344 + 5.64932I −0.28766 − 7.43545I
u = 0.609895 − 0.669378I
a = 0.27854 + 2.39600I
b = −0.846051 + 0.904470I
−1.24344 − 5.64932I −0.28766 + 7.43545I
u = 0.574306 + 0.932793I
a = 0.411839 + 1.347550I
b = 1.26857 + 1.08036I
5.32142 + 0.41145I 0
u = 0.574306 − 0.932793I
a = 0.411839 − 1.347550I
b = 1.26857 − 1.08036I
5.32142 − 0.41145I 0
u = 0.228446 + 0.838614I
a = 0.200792 − 0.458390I
b = −0.952126 − 0.674209I
−1.97287 − 0.88244I −5.64875 + 2.81510I
u = 0.228446 − 0.838614I
a = 0.200792 + 0.458390I
b = −0.952126 + 0.674209I
−1.97287 + 0.88244I −5.64875 − 2.81510I
u = 0.705528 + 0.505545I
a = 0.73725 − 1.67660I
b = −0.629527 − 0.851578I
8.46014 + 1.47314I 8.26420 − 2.78831I
u = 0.705528 − 0.505545I
a = 0.73725 + 1.67660I
b = −0.629527 + 0.851578I
8.46014 − 1.47314I 8.26420 + 2.78831I
u = −0.728728 + 0.451672I
a = 0.79061 − 1.61875I
b = 1.64604 + 0.34130I
8.18636 + 3.92680I 7.58253 − 3.44941I
u = −0.728728 − 0.451672I
a = 0.79061 + 1.61875I
b = 1.64604 − 0.34130I
8.18636 − 3.92680I 7.58253 + 3.44941I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.791382 + 0.314323I
a = 0.08069 + 1.75753I
b = 2.01785 − 0.39007I
1.92417 − 11.86780I 2.47956 + 7.18622I
u = 0.791382 − 0.314323I
a = 0.08069 − 1.75753I
b = 2.01785 + 0.39007I
1.92417 + 11.86780I 2.47956 − 7.18622I
u = −0.231462 + 1.132740I
a = 0.214026 + 0.113049I
b = −0.010233 − 0.583159I
0.12300 + 3.78560I 0
u = −0.231462 − 1.132740I
a = 0.214026 − 0.113049I
b = −0.010233 + 0.583159I
0.12300 − 3.78560I 0
u = −0.767148 + 0.333935I
a = 0.624267 + 1.096350I
b = −0.599647 + 0.673879I
4.70435 + 6.54204I 5.79038 − 3.77114I
u = −0.767148 − 0.333935I
a = 0.624267 − 1.096350I
b = −0.599647 − 0.673879I
4.70435 − 6.54204I 5.79038 + 3.77114I
u = −0.365604 + 1.116320I
a = −0.259723 + 0.097301I
b = −0.298705 − 0.667149I
−1.29499 − 3.68632I 0
u = −0.365604 − 1.116320I
a = −0.259723 − 0.097301I
b = −0.298705 + 0.667149I
−1.29499 + 3.68632I 0
u = −0.259361 + 1.146110I
a = 1.42463 + 0.50253I
b = 0.30824 + 1.96322I
−7.44510 + 4.53951I 0
u = −0.259361 − 1.146110I
a = 1.42463 − 0.50253I
b = 0.30824 − 1.96322I
−7.44510 − 4.53951I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.444604 + 1.090210I
a = −1.08820 − 1.03201I
b = −1.056750 − 0.021697I
−4.15088 + 3.62944I 0
u = 0.444604 − 1.090210I
a = −1.08820 + 1.03201I
b = −1.056750 + 0.021697I
−4.15088 − 3.62944I 0
u = −0.762418 + 0.303958I
a = 0.05370 − 1.95721I
b = 2.03025 + 0.46470I
−2.99313 + 7.49280I −1.58304 − 5.99856I
u = −0.762418 − 0.303958I
a = 0.05370 + 1.95721I
b = 2.03025 − 0.46470I
−2.99313 − 7.49280I −1.58304 + 5.99856I
u = 0.539794 + 1.054410I
a = −0.00276 + 2.26244I
b = 1.81446 + 2.37519I
−0.18858 + 6.80979I 0
u = 0.539794 − 1.054410I
a = −0.00276 − 2.26244I
b = 1.81446 − 2.37519I
−0.18858 − 6.80979I 0
u = 0.586595 + 1.034960I
a = −1.157370 − 0.316824I
b = −1.92458 + 0.42111I
6.90012 + 3.48785I 0
u = 0.586595 − 1.034960I
a = −1.157370 + 0.316824I
b = −1.92458 − 0.42111I
6.90012 − 3.48785I 0
u = −0.319539 + 1.145970I
a = −1.74893 + 0.70644I
b = −1.45388 − 0.03347I
−8.13430 − 3.88779I 0
u = −0.319539 − 1.145970I
a = −1.74893 − 0.70644I
b = −1.45388 + 0.03347I
−8.13430 + 3.88779I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.238257 + 1.165620I
a = 1.373680 − 0.332254I
b = 0.41998 − 1.74584I
−2.75297 − 8.88088I 0
u = 0.238257 − 1.165620I
a = 1.373680 + 0.332254I
b = 0.41998 + 1.74584I
−2.75297 + 8.88088I 0
u = −0.515095 + 1.084290I
a = −1.366990 + 0.207634I
b = −1.80978 − 0.87821I
−0.42638 − 3.61243I 0
u = −0.515095 − 1.084290I
a = −1.366990 − 0.207634I
b = −1.80978 + 0.87821I
−0.42638 + 3.61243I 0
u = −0.587342 + 1.068190I
a = 0.60859 − 2.11445I
b = 2.25733 − 1.62807I
6.37174 − 8.94657I 0
u = −0.587342 − 1.068190I
a = 0.60859 + 2.11445I
b = 2.25733 + 1.62807I
6.37174 + 8.94657I 0
u = 0.344494 + 1.171720I
a = −1.65618 − 0.61457I
b = −1.44820 + 0.09476I
−4.05007 + 7.75611I 0
u = 0.344494 − 1.171720I
a = −1.65618 + 0.61457I
b = −1.44820 − 0.09476I
−4.05007 − 7.75611I 0
u = −0.450939 + 1.138550I
a = −1.100670 + 0.417658I
b = −1.152270 − 0.460227I
−0.84961 − 3.91539I 0
u = −0.450939 − 1.138550I
a = −1.100670 − 0.417658I
b = −1.152270 + 0.460227I
−0.84961 + 3.91539I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.754204 + 0.167987I
a = −0.024470 + 0.354598I
b = −0.979566 + 0.287647I
−0.06219 + 4.14718I 1.27520 − 4.45466I
u = 0.754204 − 0.167987I
a = −0.024470 − 0.354598I
b = −0.979566 − 0.287647I
−0.06219 − 4.14718I 1.27520 + 4.45466I
u = 0.618925 + 0.436315I
a = 1.37547 + 1.71414I
b = 1.35948 − 0.60832I
1.60270 − 2.22709I 4.83541 + 5.16175I
u = 0.618925 − 0.436315I
a = 1.37547 − 1.71414I
b = 1.35948 + 0.60832I
1.60270 + 2.22709I 4.83541 − 5.16175I
u = −0.718360 + 0.226691I
a = −0.077274 − 0.287120I
b = −1.027460 − 0.246380I
−4.12951 − 0.62986I −4.18016 + 0.87931I
u = −0.718360 − 0.226691I
a = −0.077274 + 0.287120I
b = −1.027460 + 0.246380I
−4.12951 + 0.62986I −4.18016 − 0.87931I
u = −0.525110 + 1.137140I
a = −0.558679 + 1.098690I
b = −0.696208 + 0.110571I
−6.74053 − 4.06635I 0
u = −0.525110 − 1.137140I
a = −0.558679 − 1.098690I
b = −0.696208 − 0.110571I
−6.74053 + 4.06635I 0
u = −0.569447 + 1.127590I
a = −1.277050 + 0.206790I
b = −1.71725 − 0.54419I
2.36963 − 11.57700I 0
u = −0.569447 − 1.127590I
a = −1.277050 − 0.206790I
b = −1.71725 + 0.54419I
2.36963 + 11.57700I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.559285 + 1.134790I
a = 1.32203 − 2.59601I
b = 3.42052 − 1.38075I
−5.42747 − 12.46830I 0
u = −0.559285 − 1.134790I
a = 1.32203 + 2.59601I
b = 3.42052 + 1.38075I
−5.42747 + 12.46830I 0
u = 0.507677 + 1.159500I
a = −0.512282 − 0.989208I
b = −0.641800 − 0.033222I
−2.94176 + 0.53130I 0
u = 0.507677 − 1.159500I
a = −0.512282 + 0.989208I
b = −0.641800 + 0.033222I
−2.94176 − 0.53130I 0
u = 0.570790 + 1.141150I
a = 1.34343 + 2.41774I
b = 3.26126 + 1.18859I
−0.5177 + 16.9633I 0
u = 0.570790 − 1.141150I
a = 1.34343 − 2.41774I
b = 3.26126 − 1.18859I
−0.5177 − 16.9633I 0
u = −0.582646 + 0.406188I
a = 1.51368 + 1.21207I
b = −0.328432 + 0.887581I
1.57381 − 0.78601I 6.17132 + 3.59193I
u = −0.582646 − 0.406188I
a = 1.51368 − 1.21207I
b = −0.328432 − 0.887581I
1.57381 + 0.78601I 6.17132 − 3.59193I
u = −0.656905 + 0.092000I
a = 0.529384 + 0.412476I
b = −0.595806 + 0.310286I
2.09873 − 0.21123I 4.89242 − 0.61064I
u = −0.656905 − 0.092000I
a = 0.529384 − 0.412476I
b = −0.595806 − 0.310286I
2.09873 + 0.21123I 4.89242 + 0.61064I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.486728
a = 0.0713723
b = −0.936469
−1.48811 −6.39640
12
II. I
u
2
=
h−20u
3
a
2
−83u
3
a+· · ·−210a+142, −2u
3
a
2
+u
3
a+· · ·+2a+1, u
4
+u
2
+u+1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
a
0.0947867a
2
u
3
+ 0.393365au
3
+ ··· + 0.995261a − 0.672986
a
5
=
1
−u
2
a
6
=
−0.0426540a
2
u
3
− 0.327014au
3
+ ··· + 0.0521327a + 1.40284
−0.0568720a
2
u
3
− 0.436019au
3
+ ··· − 0.597156a + 1.20379
a
11
=
u
u
a
9
=
u
3
u
3
+ u
a
3
=
u
3
+ u
2
+ 1
u
3
+ u
2
+ u + 1
a
1
=
0.554502a
2
u
3
+ 0.251185au
3
+ ··· + 2.32227a − 0.236967
0.388626a
2
u
3
+ 0.312796au
3
+ ··· + 2.08057a − 0.559242
a
8
=
u
3
− u
2
u
3
− u
2
− 1
a
12
=
−u
3
− u
2
− 1
−u
3
− u
2
− u − 1
a
7
=
0.0568720a
2
u
3
− 0.563981au
3
+ ··· − 0.402844a + 2.79621
0.175355a
2
u
3
− 1.32227au
3
+ ··· − 0.658768a + 2.45498
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
− 4u
2
+ 2
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ 8u
11
+ ··· − u + 1
c
2
, c
5
, c
6
c
7
, c
12
u
12
− 4u
10
+ 6u
8
− 3u
6
− u
4
+ u
3
+ u
2
− u + 1
c
3
(u
4
− 3u
3
+ 4u
2
− 3u + 2)
3
c
4
, c
10
, c
11
(u
4
+ u
2
− u + 1)
3
c
8
, c
9
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
3
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 8y
11
+ ··· + y + 1
c
2
, c
5
, c
6
c
7
, c
12
y
12
− 8y
11
+ ··· + y + 1
c
3
(y
4
− y
3
+ 2y
2
+ 7y + 4)
3
c
4
, c
10
, c
11
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
3
c
8
, c
9
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
3
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547424 + 0.585652I
a = 1.07789 − 1.00535I
b = 0.987548 + 0.089110I
0.98010 − 1.39709I 3.77019 + 3.86736I
u = −0.547424 + 0.585652I
a = −0.293671 + 0.061787I
b = −1.287260 − 0.020553I
0.98010 − 1.39709I 3.77019 + 3.86736I
u = −0.547424 + 0.585652I
a = 0.91940 + 2.76614I
b = −0.795135 + 1.102750I
0.98010 − 1.39709I 3.77019 + 3.86736I
u = −0.547424 − 0.585652I
a = 1.07789 + 1.00535I
b = 0.987548 − 0.089110I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = −0.547424 − 0.585652I
a = −0.293671 − 0.061787I
b = −1.287260 + 0.020553I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = −0.547424 − 0.585652I
a = 0.91940 − 2.76614I
b = −0.795135 − 1.102750I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = 0.547424 + 1.120870I
a = −1.287880 − 0.217456I
b = −1.70041 + 0.60693I
−2.62503 + 7.64338I −1.77019 − 6.51087I
u = 0.547424 + 1.120870I
a = −0.550722 − 1.202610I
b = −0.710961 − 0.189039I
−2.62503 + 7.64338I −1.77019 − 6.51087I
u = 0.547424 + 1.120870I
a = 1.13499 + 2.86075I
b = 3.50622 + 1.82385I
−2.62503 + 7.64338I −1.77019 − 6.51087I
u = 0.547424 − 1.120870I
a = −1.287880 + 0.217456I
b = −1.70041 − 0.60693I
−2.62503 − 7.64338I −1.77019 + 6.51087I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547424 − 1.120870I
a = −0.550722 + 1.202610I
b = −0.710961 + 0.189039I
−2.62503 − 7.64338I −1.77019 + 6.51087I
u = 0.547424 − 1.120870I
a = 1.13499 − 2.86075I
b = 3.50622 − 1.82385I
−2.62503 − 7.64338I −1.77019 + 6.51087I
17
III. I
u
3
= h−u
3
+ b − u + 1, −u
3
+ 2u
2
+ 2a + 4, u
4
+ 2u
2
+ 2i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
1
2
u
3
− u
2
− 2
u
3
+ u − 1
a
5
=
1
−u
2
a
6
=
1
2
u
3
− u
2
− 1
u
3
− u
2
+ u − 1
a
11
=
u
u
a
9
=
u
3
u
3
+ u
a
3
=
−1
u
2
a
1
=
1
2
u
3
− u
2
− 1
u
3
− u
2
+ u − 1
a
8
=
−u
−u
a
12
=
u
u
a
7
=
1
2
u
3
− u
2
− u − 1
u
3
− u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
− 8
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
(u − 1)
4
c
2
, c
12
(u + 1)
4
c
3
, c
8
u
4
− 2u
2
+ 2
c
4
, c
10
u
4
+ 2u
2
+ 2
c
9
(u
2
− 2u + 2)
2
c
11
u
4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
12
(y −1)
4
c
3
, c
8
(y
2
− 2y + 2)
2
c
4
, c
10
(y
2
+ 2y + 2)
2
c
9
(y
2
+ 4)
2
c
11
y
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455090 + 1.098680I
a = −1.77689 − 1.32180I
b = −2.09868 + 0.45509I
−2.46740 + 3.66386I −4.00000 − 4.00000I
u = 0.455090 − 1.098680I
a = −1.77689 + 1.32180I
b = −2.09868 − 0.45509I
−2.46740 − 3.66386I −4.00000 + 4.00000I
u = −0.455090 + 1.098680I
a = −0.223113 + 0.678203I
b = 0.098684 + 0.455090I
−2.46740 − 3.66386I −4.00000 + 4.00000I
u = −0.455090 − 1.098680I
a = −0.223113 − 0.678203I
b = 0.098684 − 0.455090I
−2.46740 + 3.66386I −4.00000 − 4.00000I
21
IV. I
u
4
= h−5u
5
a
2
+ 15u
5
a + · · · − 30a + 24, −2u
4
a
2
− u
4
a + · · · + a
3
+
1, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
a
0.217391a
2
u
5
− 0.652174au
5
+ ··· + 1.30435a − 1.04348
a
5
=
1
−u
2
a
6
=
−0.391304a
2
u
5
+ 0.173913au
5
+ ··· + 0.652174a + 1.47826
−0.0869565a
2
u
5
+ 0.260870au
5
+ ··· − 0.521739a + 1.21739
a
11
=
u
u
a
9
=
u
3
u
3
+ u
a
3
=
−u
5
+ u
4
− 2u
3
+ 2u
2
− 2u + 2
−u
5
− 2u
3
+ u
2
− 2u + 1
a
1
=
0.869565a
2
u
5
− 0.608696au
5
+ ··· + 2.21739a − 2.17391
0.391304a
2
u
5
− 1.17391au
5
+ ··· + 2.34783a − 1.47826
a
8
=
u
5
+ 2u
3
+ u
1
a
12
=
u
5
− u
4
+ 2u
3
− 2u
2
+ 2u − 2
u
5
+ 2u
3
− u
2
+ 2u − 1
a
7
=
−0.826087a
2
u
5
+ 1.47826au
5
+ ··· − 0.956522a + 3.56522
−0.173913a
2
u
5
+ 1.52174au
5
+ ··· − 1.04348a + 2.43478
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 4u − 2
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 12u
17
+ ··· − 2u
3
+ 1
c
2
, c
5
, c
6
c
7
, c
12
u
18
− 6u
16
+ ··· + 2u + 1
c
3
(u
3
+ u
2
− 1)
6
c
4
, c
10
, c
11
(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
c
8
, c
9
(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
3
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 12y
17
+ ··· − 16y
2
+ 1
c
2
, c
5
, c
6
c
7
, c
12
y
18
− 12y
17
+ ··· + 2y
3
+ 1
c
3
(y
3
− y
2
+ 2y − 1)
6
c
4
, c
10
, c
11
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
3
c
8
, c
9
(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
3
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498832 + 1.001300I
a = −0.223235 − 1.354840I
b = 0.72220 − 1.74636I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.498832 + 1.001300I
a = −1.21428 + 0.80097I
b = −2.51209 − 0.18863I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.498832 + 1.001300I
a = −0.92954 + 1.56791I
b = −1.007320 + 0.334757I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.498832 − 1.001300I
a = −0.223235 + 1.354840I
b = 0.72220 + 1.74636I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.498832 − 1.001300I
a = −1.21428 − 0.80097I
b = −2.51209 + 0.18863I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.498832 − 1.001300I
a = −0.92954 − 1.56791I
b = −1.007320 − 0.334757I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.284920 + 1.115140I
a = 1.41549 − 0.81369I
b = −0.00186 − 2.26530I
−4.40332 −5.01951 + 0.I
u = 0.284920 + 1.115140I
a = 0.0617346 − 0.0738124I
b = −0.083715 + 0.613470I
−4.40332 −5.01951 + 0.I
u = 0.284920 + 1.115140I
a = −1.90738 − 0.79608I
b = −1.48427 − 0.03176I
−4.40332 −5.01951 + 0.I
u = 0.284920 − 1.115140I
a = 1.41549 + 0.81369I
b = −0.00186 + 2.26530I
−4.40332 −5.01951 + 0.I
25
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.284920 − 1.115140I
a = 0.0617346 + 0.0738124I
b = −0.083715 − 0.613470I
−4.40332 −5.01951 + 0.I
u = 0.284920 − 1.115140I
a = −1.90738 + 0.79608I
b = −1.48427 + 0.03176I
−4.40332 −5.01951 + 0.I
u = 0.713912 + 0.305839I
a = 0.748472 − 0.975138I
b = −0.538111 − 0.638486I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = 0.713912 + 0.305839I
a = −0.157375 + 0.249093I
b = −1.093530 + 0.232040I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = 0.713912 + 0.305839I
a = 0.20612 + 2.32629I
b = 1.99869 − 0.60760I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = 0.713912 − 0.305839I
a = 0.748472 + 0.975138I
b = −0.538111 + 0.638486I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.713912 − 0.305839I
a = −0.157375 − 0.249093I
b = −1.093530 − 0.232040I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.713912 − 0.305839I
a = 0.20612 − 2.32629I
b = 1.99869 + 0.60760I
−0.26574 + 2.82812I 1.50976 − 2.97945I
26
V. I
v
1
= ha, b + 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
1
0
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
11
=
1
0
a
9
=
1
0
a
3
=
1
0
a
1
=
−1
−1
a
8
=
1
0
a
12
=
1
0
a
7
=
2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
u − 1
c
3
, c
4
, c
8
c
9
, c
10
, c
11
u
c
5
, c
6
, c
7
u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
12
y − 1
c
3
, c
4
, c
8
c
9
, c
10
, c
11
y
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
0 0
30
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
12
+ 8u
11
+ ··· − u + 1)(u
18
+ 12u
17
+ ··· − 2u
3
+ 1)
· (u
71
+ 34u
70
+ ··· + 9u + 1)
c
2
(u − 1)(u + 1)
4
(u
12
− 4u
10
+ 6u
8
− 3u
6
− u
4
+ u
3
+ u
2
− u + 1)
· (u
18
− 6u
16
+ ··· + 2u + 1)(u
71
+ 2u
70
+ ··· + u + 1)
c
3
u(u
3
+ u
2
− 1)
6
(u
4
− 2u
2
+ 2)(u
4
− 3u
3
+ 4u
2
− 3u + 2)
3
· (u
71
+ 2u
70
+ ··· + 2308u + 202)
c
4
, c
10
u(u
4
+ u
2
− u + 1)
3
(u
4
+ 2u
2
+ 2)(u
6
+ u
5
+ ··· + 2u + 1)
3
· (u
71
− 2u
70
+ ··· − 4u + 2)
c
5
(u − 1)
4
(u + 1)(u
12
− 4u
10
+ 6u
8
− 3u
6
− u
4
+ u
3
+ u
2
− u + 1)
· (u
18
− 6u
16
+ ··· + 2u + 1)(u
71
+ 2u
70
+ ··· + u + 1)
c
6
, c
7
(u − 1)
4
(u + 1)(u
12
− 4u
10
+ 6u
8
− 3u
6
− u
4
+ u
3
+ u
2
− u + 1)
· (u
18
− 6u
16
+ ··· + 2u + 1)(u
71
− 2u
70
+ ··· + 13u + 1)
c
8
u(u
4
− 2u
2
+ 2)(u
4
+ 2u
3
+ 3u
2
+ u + 1)
3
(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
3
· (u
71
− 10u
70
+ ··· − 1608u + 86)
c
9
u(u
2
− 2u + 2)
2
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
3
(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
3
· (u
71
+ 34u
70
+ ··· + 8u − 4)
c
11
u
5
(u
4
+ u
2
− u + 1)
3
(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
· (u
71
+ 6u
70
+ ··· + 3584u + 256)
c
12
(u − 1)(u + 1)
4
(u
12
− 4u
10
+ 6u
8
− 3u
6
− u
4
+ u
3
+ u
2
− u + 1)
· (u
18
− 6u
16
+ ··· + 2u + 1)(u
71
− 2u
70
+ ··· + 13u + 1)
31
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
5
)(y
12
− 8y
11
+ ··· + y + 1)(y
18
− 12y
17
+ ··· − 16y
2
+ 1)
· (y
71
+ 14y
70
+ ··· − 39y − 1)
c
2
, c
5
((y − 1)
5
)(y
12
− 8y
11
+ ··· + y + 1)(y
18
− 12y
17
+ ··· + 2y
3
+ 1)
· (y
71
− 34y
70
+ ··· + 9y − 1)
c
3
y(y
2
− 2y + 2)
2
(y
3
− y
2
+ 2y − 1)
6
(y
4
− y
3
+ 2y
2
+ 7y + 4)
3
· (y
71
− 22y
70
+ ··· + 2098096y − 40804)
c
4
, c
10
y(y
2
+ 2y + 2)
2
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
3
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
3
· (y
71
+ 34y
70
+ ··· + 8y − 4)
c
6
, c
7
, c
12
((y − 1)
5
)(y
12
− 8y
11
+ ··· + y + 1)(y
18
− 12y
17
+ ··· + 2y
3
+ 1)
· (y
71
− 66y
70
+ ··· − 71y − 1)
c
8
y(y
2
− 2y + 2)
2
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
3
· (y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
3
· (y
71
+ 2y
70
+ ··· − 2565048y − 7396)
c
9
y(y
2
+ 4)
2
(y
4
+ 2y
3
+ ··· + 5y + 1)
3
(y
6
− y
5
+ ··· + 8y
2
+ 1)
3
· (y
71
+ 6y
70
+ ··· + 160y − 16)
c
11
y
5
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
3
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
3
· (y
71
+ 30y
70
+ ··· − 3604480y − 65536)
32
