12n
0314
(K12n
0314
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 8 2 12 11 7 6 5 10
Solving Sequence
2,7
6 3
4,10
11 1 9 5 8 12
c
6
c
2
c
3
c
10
c
1
c
9
c
4
c
8
c
12
c
5
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h26419u
19
+ 221467u
18
+ ··· + 81793b + 229898,
655714u
19
+ 5585712u
18
+ ··· + 1717653a + 17248644, u
20
+ 9u
19
+ ··· + 105u + 21i
I
u
2
= hu
14
− 5u
13
+ ··· + 13b − 16, 3u
14
− 2u
13
+ ··· + 13a + 56, u
15
+ 4u
14
+ ··· − 4u − 1i
I
u
3
= h179u
6
a
3
+ 84u
6
a
2
+ ··· + 240a − 68, 2u
6
a
3
+ 5u
6
a
2
+ ··· − a + 5, u
7
− 2u
6
+ 2u
5
+ u
2
− 2u + 1i
I
u
4
= hb + u, a
2
− au + 2a + 1, u
2
− u + 1i
I
u
5
= hb − u + 1, a
2
− au − a + u − 1, u
2
− u + 1i
I
v
1
= ha, b
2
+ b + 1, v + 1i
* 6 irreducible components of dim
C
= 0, with total 73 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
= h26419u
19
+ 221467u
18
+ · · · + 81793b + 229898, 6.56 × 10
5
u
19
+
5.59 × 10
6
u
18
+ · · · + 1.72 × 10
6
a + 1.72 × 10
7
, u
20
+ 9u
19
+ · · · + 105u + 21i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
10
=
−0.381750u
19
− 3.25194u
18
+ ··· − 46.7992u − 10.0420
−0.322998u
19
− 2.70765u
18
+ ··· − 17.1281u − 2.81073
a
11
=
−0.0499612u
19
− 0.781440u
18
+ ··· − 40.9540u − 11.0912
0.183805u
19
+ 1.66304u
18
+ ··· + 30.0418u + 8.01675
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
−0.0587517u
19
− 0.544292u
18
+ ··· − 29.6712u − 7.23125
−0.322998u
19
− 2.70765u
18
+ ··· − 17.1281u − 2.81073
a
5
=
0.0265624u
19
− 0.108474u
18
+ ··· − 14.3377u − 5.90838
0.320040u
19
+ 2.54825u
18
+ ··· + 6.84217u + 0.951341
a
8
=
0.737673u
19
+ 5.54575u
18
+ ··· + 12.8313u + 2.55517
−0.998753u
19
− 6.14769u
18
+ ··· + 5.47587u + 3.09776
a
12
=
0.274738u
19
+ 2.46057u
18
+ ··· + 14.2381u + 2.03681
−0.436358u
19
− 2.67451u
18
+ ··· + 2.33972u + 1.20475
(ii) Obstruction class = −1
(iii) Cusp Shapes =
34565
81793
u
19
+
528526
81793
u
18
+ ··· +
18069450
81793
u +
4396806
81793
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
+ 5u
19
+ ··· + 2751u + 441
c
2
, c
6
u
20
− 9u
19
+ ··· − 105u + 21
c
3
u
20
+ 9u
19
+ ··· − 123711u + 33789
c
4
, c
10
u
20
+ u
19
+ ··· + 3u + 1
c
5
, c
11
u
20
+ 2u
19
+ ··· + u + 1
c
7
u
20
+ 16u
19
+ ··· + 160u + 32
c
8
u
20
+ 22u
19
+ ··· + 273u + 21
c
9
, c
12
u
20
− u
19
+ ··· − 21u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
+ 53y
19
+ ··· + 2156931y + 194481
c
2
, c
6
y
20
+ 5y
19
+ ··· + 2751y + 441
c
3
y
20
+ 107y
19
+ ··· + 4904181177y + 1141696521
c
4
, c
10
y
20
+ 31y
19
+ ··· − 9y + 1
c
5
, c
11
y
20
− 6y
19
+ ··· + y + 1
c
7
y
20
+ 42y
18
+ ··· + 15872y + 1024
c
8
y
20
− 16y
19
+ ··· − 3423y + 441
c
9
, c
12
y
20
− 49y
19
+ ··· − 81y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.211126 + 0.952456I
a = 0.747076 − 0.491514I
b = 0.116391 + 0.783403I
−3.11229 − 1.03633I −6.44153 + 1.75193I
u = 0.211126 − 0.952456I
a = 0.747076 + 0.491514I
b = 0.116391 − 0.783403I
−3.11229 + 1.03633I −6.44153 − 1.75193I
u = 0.519530 + 0.750364I
a = 0.898033 + 0.618882I
b = −0.484563 + 1.044830I
0.63548 − 1.96108I 4.25150 + 5.47708I
u = 0.519530 − 0.750364I
a = 0.898033 − 0.618882I
b = −0.484563 − 1.044830I
0.63548 + 1.96108I 4.25150 − 5.47708I
u = −0.523090 + 0.979837I
a = 0.414457 − 0.445713I
b = −0.1256290 − 0.0436326I
0.13882 − 2.55024I 1.45356 − 0.37856I
u = −0.523090 − 0.979837I
a = 0.414457 + 0.445713I
b = −0.1256290 + 0.0436326I
0.13882 + 2.55024I 1.45356 + 0.37856I
u = −0.577826 + 0.618275I
a = 0.017905 + 0.660573I
b = −0.253132 + 0.138016I
1.22469 − 1.87328I 5.09006 + 3.79292I
u = −0.577826 − 0.618275I
a = 0.017905 − 0.660573I
b = −0.253132 − 0.138016I
1.22469 + 1.87328I 5.09006 − 3.79292I
u = 0.713575 + 1.077000I
a = −0.756489 − 0.141468I
b = 0.306890 − 1.351890I
−0.16430 + 7.31617I 2.67024 − 6.35722I
u = 0.713575 − 1.077000I
a = −0.756489 + 0.141468I
b = 0.306890 + 1.351890I
−0.16430 − 7.31617I 2.67024 + 6.35722I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351235 + 0.606197I
a = 0.973122 − 0.073477I
b = −0.040017 + 0.338792I
0.08352 − 1.47554I 0.46232 + 5.22837I
u = −0.351235 − 0.606197I
a = 0.973122 + 0.073477I
b = −0.040017 − 0.338792I
0.08352 + 1.47554I 0.46232 − 5.22837I
u = −1.06324 + 1.11292I
a = 1.23198 + 0.99332I
b = 2.62262 − 0.87571I
15.6693 − 14.8627I 4.85498 + 6.94268I
u = −1.06324 − 1.11292I
a = 1.23198 − 0.99332I
b = 2.62262 + 0.87571I
15.6693 + 14.8627I 4.85498 − 6.94268I
u = −1.14401 + 1.05029I
a = 0.913221 + 1.067070I
b = 2.78508 + 0.08218I
15.9439 + 6.7947I 5.34960 − 3.11489I
u = −1.14401 − 1.05029I
a = 0.913221 − 1.067070I
b = 2.78508 − 0.08218I
15.9439 − 6.7947I 5.34960 + 3.11489I
u = −1.22782 + 0.99971I
a = −0.933207 − 0.875787I
b = −2.92684 − 0.10703I
14.3487 − 2.4918I 8.82559 − 1.44733I
u = −1.22782 − 0.99971I
a = −0.933207 + 0.875787I
b = −2.92684 + 0.10703I
14.3487 + 2.4918I 8.82559 + 1.44733I
u = −1.05700 + 1.19896I
a = −1.00610 − 1.04385I
b = −2.50080 + 0.96199I
13.6274 − 5.8207I 6.48369 + 6.53505I
u = −1.05700 − 1.19896I
a = −1.00610 + 1.04385I
b = −2.50080 − 0.96199I
13.6274 + 5.8207I 6.48369 − 6.53505I
6
II. I
u
2
=
hu
14
−5u
13
+· · ·+13b−16, 3u
14
−2u
13
+· · ·+13a+56, u
15
+4u
14
+· · ·−4u−1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
10
=
−0.230769u
14
+ 0.153846u
13
+ ··· − 10.3077u − 4.30769
−0.0769231u
14
+ 0.384615u
13
+ ··· + 0.230769u + 1.23077
a
11
=
0.153846u
14
+ 0.230769u
13
+ ··· − 6.46154u − 4.46154
1.07692u
14
+ 4.61538u
13
+ ··· − 5.23077u − 0.230769
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
−0.153846u
14
− 0.230769u
13
+ ··· − 10.5385u − 5.53846
−0.0769231u
14
+ 0.384615u
13
+ ··· + 0.230769u + 1.23077
a
5
=
2.23077u
14
+ 7.84615u
13
+ ··· − 8.69231u + 0.307692
−0.384615u
14
− 2.07692u
13
+ ··· + 6.15385u + 1.15385
a
8
=
−3.15385u
14
− 11.2308u
13
+ ··· + 13.4615u + 3.46154
−0.0769231u
14
+ 0.384615u
13
+ ··· − 1.76923u − 0.769231
a
12
=
0.769231u
14
+ 2.15385u
13
+ ··· + 0.692308u + 1.69231
−0.0769231u
14
− 0.615385u
13
+ ··· + 3.23077u + 0.230769
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
4
13
u
14
+
20
13
u
13
+
49
13
u
12
+
207
13
u
11
+
331
13
u
10
+
590
13
u
9
+
503
13
u
8
+
567
13
u
7
+
150
13
u
6
+
2
13
u
5
− 24u
4
−
489
13
u
3
−
307
13
u
2
−
274
13
u −
1
13
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 6u
14
+ ··· − 6u + 1
c
2
u
15
− 4u
14
+ ··· − 4u + 1
c
3
u
15
+ 4u
14
+ ··· − 6u + 1
c
4
, c
10
u
15
+ 8u
13
+ ··· + 4u − 1
c
5
, c
11
u
15
+ u
14
+ ··· + 2u + 1
c
6
u
15
+ 4u
14
+ ··· − 4u − 1
c
7
u
15
+ 6u
14
+ ··· + 5u + 1
c
8
u
15
+ 11u
14
+ ··· + 1118u + 169
c
9
, c
12
u
15
− 8u
14
+ ··· + 2u − 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
+ 6y
14
+ ··· + 2y − 1
c
2
, c
6
y
15
+ 6y
14
+ ··· − 6y − 1
c
3
y
15
+ 12y
14
+ ··· − 224y
2
− 1
c
4
, c
10
y
15
+ 16y
14
+ ··· − 6y − 1
c
5
, c
11
y
15
− 5y
14
+ ··· + 8y − 1
c
7
y
15
− 2y
13
+ ··· + 7y − 1
c
8
y
15
− 11y
14
+ ··· + 118300y − 28561
c
9
, c
12
y
15
− 16y
14
+ ··· − 2y − 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.119628 + 0.929628I
a = 1.085450 + 0.734281I
b = −0.896569 + 0.439913I
1.32926 − 1.15840I 10.02147 + 1.35486I
u = 0.119628 − 0.929628I
a = 1.085450 − 0.734281I
b = −0.896569 − 0.439913I
1.32926 + 1.15840I 10.02147 − 1.35486I
u = 0.927045
a = −1.23357
b = −1.65358
4.01270 10.3920
u = 0.396806 + 1.009340I
a = −0.100376 + 0.697396I
b = −0.762363 − 0.345807I
0.57283 + 3.31790I 5.20563 − 6.98486I
u = 0.396806 − 1.009340I
a = −0.100376 − 0.697396I
b = −0.762363 + 0.345807I
0.57283 − 3.31790I 5.20563 + 6.98486I
u = −0.838508 + 0.071078I
a = 0.057971 − 0.286484I
b = 0.417658 + 1.125080I
2.88845 − 5.01567I 6.54273 + 3.81231I
u = −0.838508 − 0.071078I
a = 0.057971 + 0.286484I
b = 0.417658 − 1.125080I
2.88845 + 5.01567I 6.54273 − 3.81231I
u = −0.323439 + 1.178010I
a = 0.640201 + 0.826390I
b = −0.313721 − 0.616088I
−1.15408 + 0.99595I 2.36087 − 3.16141I
u = −0.323439 − 1.178010I
a = 0.640201 − 0.826390I
b = −0.313721 + 0.616088I
−1.15408 − 0.99595I 2.36087 + 3.16141I
u = −0.493362 + 1.123440I
a = −0.974071 − 0.249094I
b = 0.251285 + 0.447031I
−0.15694 − 9.16119I 0.57307 + 9.40240I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.493362 − 1.123440I
a = −0.974071 + 0.249094I
b = 0.251285 − 0.447031I
−0.15694 + 9.16119I 0.57307 − 9.40240I
u = −0.228765 + 0.477425I
a = −1.52624 − 1.56710I
b = 0.739527 − 0.375189I
2.35397 + 5.43215I 3.98759 − 5.23601I
u = −0.228765 − 0.477425I
a = −1.52624 + 1.56710I
b = 0.739527 + 0.375189I
2.35397 − 5.43215I 3.98759 + 5.23601I
u = −1.09588 + 1.06775I
a = −1.06614 − 0.98430I
b = −2.60903 + 0.37822I
13.54430 − 3.99769I 5.11287 + 2.07343I
u = −1.09588 − 1.06775I
a = −1.06614 + 0.98430I
b = −2.60903 − 0.37822I
13.54430 + 3.99769I 5.11287 − 2.07343I
11
III. I
u
3
= h179u
6
a
3
+ 84u
6
a
2
+ · · · + 240a − 68, 2u
6
a
3
+ 5u
6
a
2
+ · · · − a +
5, u
7
− 2u
6
+ 2u
5
+ u
2
− 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
10
=
a
−0.650909a
3
u
6
− 0.305455a
2
u
6
+ ··· − 0.872727a + 0.247273
a
11
=
0.650909a
3
u
6
+ 0.305455a
2
u
6
+ ··· + 1.87273a − 0.247273
−0.738182a
3
u
6
− 0.229091a
2
u
6
+ ··· − 0.654545a + 0.185455
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
0.650909a
3
u
6
+ 0.305455a
2
u
6
+ ··· + 1.87273a − 0.247273
−0.650909a
3
u
6
− 0.305455a
2
u
6
+ ··· − 0.872727a + 0.247273
a
5
=
u
5
− u
4
− a
2
u + u
2
+ u + 1
0.0581818a
3
u
6
− 1.05091a
2
u
6
+ ··· + 1.85455a − 0.625455
a
8
=
0.0581818a
3
u
6
+ 0.949091a
2
u
6
+ ··· − 0.145455a + 1.37455
0.0436364a
3
u
6
− 0.538182a
2
u
6
+ ··· + 1.89091a − 0.469091
a
12
=
0.0145455a
3
u
6
− 0.512727a
2
u
6
+ ··· − 0.0363636a − 1.15636
−0.0436364a
3
u
6
+ 0.538182a
2
u
6
+ ··· − 1.89091a − 0.530909
(ii) Obstruction class = −1
(iii) Cusp Shapes =
48
275
u
6
a
3
−
592
275
u
6
a
2
+ ··· +
416
55
a +
4709
275
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
7
+ 4u
5
− 4u
3
− u
2
+ 2u − 1)
4
c
2
, c
6
(u
7
+ 2u
6
+ 2u
5
− u
2
− 2u − 1)
4
c
3
(u
7
− 2u
6
+ 10u
5
+ 8u
4
− 18u
3
− 39u
2
− 22u − 5)
4
c
4
, c
10
u
28
+ 23u
26
+ ··· + 1459u + 4993
c
5
, c
11
u
28
− 3u
26
+ ··· − 21u + 13
c
7
(u
2
− u + 1)
14
c
8
(u
7
− 3u
6
+ 2u
5
+ 5u
4
− 9u
3
+ u
2
+ 6u − 4)
4
c
9
, c
12
u
28
− 5u
27
+ ··· + 21416u + 10543
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
7
+ 8y
6
+ 8y
5
− 28y
4
+ 32y
3
− 17y
2
+ 2y − 1)
4
c
2
, c
6
(y
7
+ 4y
5
− 4y
3
− y
2
+ 2y − 1)
4
c
3
(y
7
+ 16y
6
+ 96y
5
− 624y
4
+ 488y
3
− 649y
2
+ 94y − 25)
4
c
4
, c
10
y
28
+ 46y
27
+ ··· + 280734755y + 24930049
c
5
, c
11
y
28
− 6y
27
+ ··· − 3561y + 169
c
7
(y
2
+ y + 1)
14
c
8
(y
7
− 5y
6
+ 16y
5
− 43y
4
+ 71y
3
− 69y
2
+ 44y − 16)
4
c
9
, c
12
y
28
− 53y
27
+ ··· + 543656868y + 111154849
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.234558 + 0.938347I
a = 0.557581 + 0.629769I
b = −0.005594 + 0.375241I
0.141984 − 1.068600I 1.62838 + 2.98348I
u = −0.234558 + 0.938347I
a = 1.48963 + 0.01254I
b = −0.834015 − 0.189579I
0.141984 − 1.068600I 1.62838 + 2.98348I
u = −0.234558 + 0.938347I
a = 0.289555 + 0.078561I
b = 1.047710 − 0.498808I
0.14198 − 5.12837I 1.62838 + 9.91169I
u = −0.234558 + 0.938347I
a = −0.75691 − 2.17265I
b = −0.467113 + 1.133100I
0.14198 − 5.12837I 1.62838 + 9.91169I
u = −0.234558 − 0.938347I
a = 0.557581 − 0.629769I
b = −0.005594 − 0.375241I
0.141984 + 1.068600I 1.62838 − 2.98348I
u = −0.234558 − 0.938347I
a = 1.48963 − 0.01254I
b = −0.834015 + 0.189579I
0.141984 + 1.068600I 1.62838 − 2.98348I
u = −0.234558 − 0.938347I
a = 0.289555 − 0.078561I
b = 1.047710 + 0.498808I
0.14198 + 5.12837I 1.62838 − 9.91169I
u = −0.234558 − 0.938347I
a = −0.75691 + 2.17265I
b = −0.467113 − 1.133100I
0.14198 + 5.12837I 1.62838 − 9.91169I
u = −0.954563
a = −0.978481 + 0.427663I
b = −1.94430 + 1.59422I
4.10408 − 2.02988I 10.25058 + 3.46410I
u = −0.954563
a = −0.978481 − 0.427663I
b = −1.94430 − 1.59422I
4.10408 + 2.02988I 10.25058 − 3.46410I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.954563
a = 1.031960 + 0.520296I
b = 0.869450 − 0.267482I
4.10408 + 2.02988I 10.25058 − 3.46410I
u = −0.954563
a = 1.031960 − 0.520296I
b = 0.869450 + 0.267482I
4.10408 − 2.02988I 10.25058 + 3.46410I
u = 0.656474 + 0.273636I
a = −0.931267 + 0.317916I
b = −0.97436 − 1.34239I
3.33504 + 2.23752I 9.53857 − 3.70520I
u = 0.656474 + 0.273636I
a = 1.244040 − 0.363481I
b = 1.83972 − 1.54468I
3.33504 + 6.29728I 9.5386 − 10.6334I
u = 0.656474 + 0.273636I
a = −1.95049 − 0.33453I
b = −1.232480 + 0.014553I
3.33504 + 2.23752I 9.53857 − 3.70520I
u = 0.656474 + 0.273636I
a = 0.21122 − 2.12389I
b = 0.413640 + 0.297426I
3.33504 + 6.29728I 9.5386 − 10.6334I
u = 0.656474 − 0.273636I
a = −0.931267 − 0.317916I
b = −0.97436 + 1.34239I
3.33504 − 2.23752I 9.53857 + 3.70520I
u = 0.656474 − 0.273636I
a = 1.244040 + 0.363481I
b = 1.83972 + 1.54468I
3.33504 − 6.29728I 9.5386 + 10.6334I
u = 0.656474 − 0.273636I
a = −1.95049 + 0.33453I
b = −1.232480 − 0.014553I
3.33504 − 2.23752I 9.53857 + 3.70520I
u = 0.656474 − 0.273636I
a = 0.21122 + 2.12389I
b = 0.413640 − 0.297426I
3.33504 − 6.29728I 9.5386 + 10.6334I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.05537 + 1.04881I
a = 0.973714 − 0.891961I
b = 2.24383 − 0.01181I
14.2101 + 5.9023I 7.20776 − 5.84206I
u = 1.05537 + 1.04881I
a = 1.13442 − 0.89114I
b = 2.03850 + 0.56037I
14.2101 + 1.8425I 7.20776 + 1.08615I
u = 1.05537 + 1.04881I
a = −0.84886 + 1.29485I
b = −2.83247 + 0.38149I
14.2101 + 1.8425I 7.20776 + 1.08615I
u = 1.05537 + 1.04881I
a = −1.46612 + 0.93741I
b = −2.66251 − 1.14672I
14.2101 + 5.9023I 7.20776 − 5.84206I
u = 1.05537 − 1.04881I
a = 0.973714 + 0.891961I
b = 2.24383 + 0.01181I
14.2101 − 5.9023I 7.20776 + 5.84206I
u = 1.05537 − 1.04881I
a = 1.13442 + 0.89114I
b = 2.03850 − 0.56037I
14.2101 − 1.8425I 7.20776 − 1.08615I
u = 1.05537 − 1.04881I
a = −0.84886 − 1.29485I
b = −2.83247 − 0.38149I
14.2101 − 1.8425I 7.20776 − 1.08615I
u = 1.05537 − 1.04881I
a = −1.46612 − 0.93741I
b = −2.66251 + 1.14672I
14.2101 − 5.9023I 7.20776 + 5.84206I
17
IV. I
u
4
= hb + u, a
2
− au + 2a + 1, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u − 1
a
3
=
u
u − 1
a
4
=
1
u − 1
a
10
=
a
−u
a
11
=
au + u
−au − u − 1
a
1
=
−1
0
a
9
=
a + u
−u
a
5
=
au + a + u + 1
−a + u − 2
a
8
=
a + u
−u
a
12
=
au − 1
−u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u + 5
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
9
, c
12
(u
2
− u + 1)
2
c
2
(u
2
+ u + 1)
2
c
4
, c
5
, c
10
c
11
u
4
− 2u
3
+ 2u
2
− u + 1
c
8
u
4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
9
c
12
(y
2
+ y + 1)
2
c
4
, c
5
, c
10
c
11
y
4
+ 2y
2
+ 3y + 1
c
8
y
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.378256 − 0.440597I
b = −0.500000 − 0.866025I
4.05977I 2.50000 − 4.33013I
u = 0.500000 + 0.866025I
a = −1.12174 + 1.30662I
b = −0.500000 − 0.866025I
4.05977I 2.50000 − 4.33013I
u = 0.500000 − 0.866025I
a = −0.378256 + 0.440597I
b = −0.500000 + 0.866025I
− 4.05977I 2.50000 + 4.33013I
u = 0.500000 − 0.866025I
a = −1.12174 − 1.30662I
b = −0.500000 + 0.866025I
− 4.05977I 2.50000 + 4.33013I
21
V. I
u
5
= hb − u + 1, a
2
− au − a + u − 1, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u − 1
a
3
=
u
u − 1
a
4
=
1
u − 1
a
10
=
a
u − 1
a
11
=
au − u + 1
−au + 2u − 1
a
1
=
−1
0
a
9
=
a − u + 1
u − 1
a
5
=
−2au + a
au
a
8
=
a − u + 1
u − 1
a
12
=
−au + a − 1
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u + 1
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
9
, c
12
(u
2
− u + 1)
2
c
2
(u
2
+ u + 1)
2
c
4
, c
5
, c
10
c
11
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
8
u
4
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
9
c
12
(y
2
+ y + 1)
2
c
4
, c
5
, c
10
c
11
y
4
+ 3y
3
+ 2y
2
+ 1
c
8
y
4
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.192440 + 0.547877I
b = −0.500000 + 0.866025I
0 2.50000 + 2.59808I
u = 0.500000 + 0.866025I
a = 1.69244 + 0.31815I
b = −0.500000 + 0.866025I
0 2.50000 + 2.59808I
u = 0.500000 − 0.866025I
a = −0.192440 − 0.547877I
b = −0.500000 − 0.866025I
0 2.50000 − 2.59808I
u = 0.500000 − 0.866025I
a = 1.69244 − 0.31815I
b = −0.500000 − 0.866025I
0 2.50000 − 2.59808I
25
VI. I
v
1
= ha, b
2
+ b + 1, v + 1i
(i) Arc colorings
a
2
=
−1
0
a
7
=
1
0
a
6
=
1
0
a
3
=
−1
0
a
4
=
−1
0
a
10
=
0
b
a
11
=
−b
b
a
1
=
−1
0
a
9
=
−b
b
a
5
=
−b − 2
b + 1
a
8
=
−b
b
a
12
=
−1
b + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4b + 2
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
8
u
2
c
4
, c
5
, c
9
c
10
, c
11
, c
12
u
2
− u + 1
c
7
u
2
+ u + 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
8
y
2
c
4
, c
5
, c
7
c
9
, c
10
, c
11
c
12
y
2
+ y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −0.500000 + 0.866025I
− 2.02988I 0. + 3.46410I
v = −1.00000
a = 0
b = −0.500000 − 0.866025I
2.02988I 0. − 3.46410I
29
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u
2
− u + 1)
4
(u
7
+ 4u
5
− 4u
3
− u
2
+ 2u − 1)
4
· (u
15
− 6u
14
+ ··· − 6u + 1)(u
20
+ 5u
19
+ ··· + 2751u + 441)
c
2
u
2
(u
2
+ u + 1)
4
(u
7
+ 2u
6
+ 2u
5
− u
2
− 2u − 1)
4
· (u
15
− 4u
14
+ ··· − 4u + 1)(u
20
− 9u
19
+ ··· − 105u + 21)
c
3
u
2
(u
2
− u + 1)
4
(u
7
− 2u
6
+ 10u
5
+ 8u
4
− 18u
3
− 39u
2
− 22u − 5)
4
· (u
15
+ 4u
14
+ ··· − 6u + 1)(u
20
+ 9u
19
+ ··· − 123711u + 33789)
c
4
, c
10
(u
2
− u + 1)(u
4
− 2u
3
+ 2u
2
− u + 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (u
15
+ 8u
13
+ ··· + 4u − 1)(u
20
+ u
19
+ ··· + 3u + 1)
· (u
28
+ 23u
26
+ ··· + 1459u + 4993)
c
5
, c
11
(u
2
− u + 1)(u
4
− 2u
3
+ 2u
2
− u + 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (u
15
+ u
14
+ ··· + 2u + 1)(u
20
+ 2u
19
+ ··· + u + 1)
· (u
28
− 3u
26
+ ··· − 21u + 13)
c
6
u
2
(u
2
− u + 1)
4
(u
7
+ 2u
6
+ 2u
5
− u
2
− 2u − 1)
4
· (u
15
+ 4u
14
+ ··· − 4u − 1)(u
20
− 9u
19
+ ··· − 105u + 21)
c
7
((u
2
− u + 1)
18
)(u
2
+ u + 1)(u
15
+ 6u
14
+ ··· + 5u + 1)
· (u
20
+ 16u
19
+ ··· + 160u + 32)
c
8
u
10
(u
7
− 3u
6
+ 2u
5
+ 5u
4
− 9u
3
+ u
2
+ 6u − 4)
4
· (u
15
+ 11u
14
+ ··· + 1118u + 169)(u
20
+ 22u
19
+ ··· + 273u + 21)
c
9
, c
12
((u
2
− u + 1)
5
)(u
15
− 8u
14
+ ··· + 2u − 1)(u
20
− u
19
+ ··· − 21u + 1)
· (u
28
− 5u
27
+ ··· + 21416u + 10543)
30
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
2
(y
2
+ y + 1)
4
(y
7
+ 8y
6
+ 8y
5
− 28y
4
+ 32y
3
− 17y
2
+ 2y − 1)
4
· (y
15
+ 6y
14
+ ··· + 2y − 1)(y
20
+ 53y
19
+ ··· + 2156931y + 194481)
c
2
, c
6
y
2
(y
2
+ y + 1)
4
(y
7
+ 4y
5
− 4y
3
− y
2
+ 2y − 1)
4
· (y
15
+ 6y
14
+ ··· − 6y − 1)(y
20
+ 5y
19
+ ··· + 2751y + 441)
c
3
y
2
(y
2
+ y + 1)
4
· (y
7
+ 16y
6
+ 96y
5
− 624y
4
+ 488y
3
− 649y
2
+ 94y − 25)
4
· (y
15
+ 12y
14
+ ··· − 224y
2
− 1)
· (y
20
+ 107y
19
+ ··· + 4904181177y + 1141696521)
c
4
, c
10
(y
2
+ y + 1)(y
4
+ 2y
2
+ 3y + 1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
15
+ 16y
14
+ ··· − 6y − 1)(y
20
+ 31y
19
+ ··· − 9y + 1)
· (y
28
+ 46y
27
+ ··· + 280734755y + 24930049)
c
5
, c
11
(y
2
+ y + 1)(y
4
+ 2y
2
+ 3y + 1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
15
− 5y
14
+ ··· + 8y − 1)(y
20
− 6y
19
+ ··· + y + 1)
· (y
28
− 6y
27
+ ··· − 3561y + 169)
c
7
((y
2
+ y + 1)
19
)(y
15
− 2y
13
+ ··· + 7y − 1)
· (y
20
+ 42y
18
+ ··· + 15872y + 1024)
c
8
y
10
(y
7
− 5y
6
+ 16y
5
− 43y
4
+ 71y
3
− 69y
2
+ 44y − 16)
4
· (y
15
− 11y
14
+ ··· + 118300y − 28561)
· (y
20
− 16y
19
+ ··· − 3423y + 441)
c
9
, c
12
((y
2
+ y + 1)
5
)(y
15
− 16y
14
+ ··· − 2y − 1)(y
20
− 49y
19
+ ··· − 81y + 1)
· (y
28
− 53y
27
+ ··· + 543656868y + 111154849)
31
