12n
0690
(K12n
0690
)
A knot diagram
1
Linearized knot diagam
4 5 8 2 9 11 3 12 5 8 6 10
Solving Sequence
2,5
4
1,10
9 6 12 8 3 7 11
c
4
c
1
c
9
c
5
c
12
c
8
c
3
c
7
c
11
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.93346 × 10
17
u
21
+ 1.10518 × 10
18
u
20
+ ··· + 6.77435 × 10
18
b + 2.05511 × 10
18
,
− 4.34516 × 10
16
u
21
+ 5.25657 × 10
17
u
20
+ ··· + 6.77435 × 10
18
a − 3.58257 × 10
19
,
u
22
− 5u
21
+ ··· + 108u + 16i
I
u
2
= h−u
4
a
2
+ 5u
4
a + ··· + 3a − 3, u
4
a
3
+ 5u
4
a
2
+ ··· + 27a + 31, u
5
− 2u
4
+ 2u
3
+ u
2
− u + 1i
I
u
3
= h2a
2
+ 2b + 3a + 2, 4a
3
+ 4a
2
+ 5a + 4, u + 1i
I
u
4
= hu
12
− 3u
11
+ u
10
+ 6u
9
− 6u
8
− 5u
7
+ 7u
6
+ 2u
5
− 2u
4
+ 2u
3
− u
2
+ b − 3u − 1,
− u
12
+ 4u
11
− 5u
10
− 2u
9
+ 12u
8
− 12u
7
+ 3u
6
+ 6u
5
− 12u
4
+ 7u
3
+ a + 1,
u
13
− 5u
12
+ 8u
11
+ u
10
− 18u
9
+ 18u
8
+ 2u
7
− 13u
6
+ 10u
5
− 5u
4
− 3u
3
+ 3u
2
+ u + 1i
I
u
5
= hb
2
+ ba − a, a
2
+ a + 1, u + 1i
* 5 irreducible components of dim
C
= 0, with total 62 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−2.93 × 10
17
u
21
+ 1.11 × 10
18
u
20
+ · · · + 6.77 × 10
18
b + 2.06 ×
10
18
, −4.35 × 10
16
u
21
+ 5.26 × 10
17
u
20
+ · · · + 6.77 × 10
18
a − 3.58 ×
10
19
, u
22
− 5u
21
+ · · · + 108u + 16i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
1
=
u
−u
3
+ u
a
10
=
0.00641415u
21
− 0.0775953u
20
+ ··· + 4.28301u + 5.28844
0.0433025u
21
− 0.163141u
20
+ ··· − 5.64620u − 0.303366
a
9
=
−0.0368883u
21
+ 0.0855460u
20
+ ··· + 9.92921u + 5.59180
0.0433025u
21
− 0.163141u
20
+ ··· − 5.64620u − 0.303366
a
6
=
−0.0252335u
21
+ 0.102422u
20
+ ··· + 0.204852u − 0.803579
0.0147201u
21
− 0.0585005u
20
+ ··· − 0.406958u − 0.266094
a
12
=
0.0213809u
21
− 0.116096u
20
+ ··· + 1.68488u + 3.12427
−0.0129002u
21
+ 0.0465450u
20
+ ··· + 0.617134u + 0.230969
a
8
=
0.0620474u
21
− 0.266688u
20
+ ··· − 4.65907u + 1.63431
−0.0435486u
21
+ 0.186762u
20
+ ··· + 5.06681u + 0.992758
a
3
=
−u
u
a
7
=
0.0771001u
21
− 0.323949u
20
+ ··· − 6.31235u + 1.43322
−0.0586013u
21
+ 0.244022u
20
+ ··· + 6.72009u + 1.19384
a
11
=
0.122920u
21
− 0.520465u
20
+ ··· − 8.71637u + 2.14038
−0.0963555u
21
+ 0.373312u
20
+ ··· + 10.0845u + 1.56072
(ii) Obstruction class = −1
(iii) Cusp Shapes =
14355148220565440769
27097382097032209472
u
21
−
32455260689474630771
13548691048516104736
u
20
+ ··· −
224275806594788262169
6774345524258052368
u +
14951472397892805561
1693586381064513092
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
22
− 5u
21
+ ··· + 108u + 16
c
3
, c
7
u
22
− 6u
21
+ ··· + 160u − 128
c
5
, c
6
, c
9
c
11
u
22
+ 6u
20
+ ··· − u − 1
c
8
u
22
− 14u
21
+ ··· − 464u + 32
c
10
, c
12
u
22
+ 3u
21
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
22
− 11y
21
+ ··· − 10352y + 256
c
3
, c
7
y
22
+ 12y
21
+ ··· − 289792y + 16384
c
5
, c
6
, c
9
c
11
y
22
+ 12y
21
+ ··· − 15y + 1
c
8
y
22
+ 6y
21
+ ··· − 36608y + 1024
c
10
, c
12
y
22
− 37y
21
+ ··· − 141y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.593822 + 0.658603I
a = −0.232154 + 0.275565I
b = −0.443126 + 0.548064I
−1.76571 + 0.41277I −1.52576 − 0.47761I
u = −0.593822 − 0.658603I
a = −0.232154 − 0.275565I
b = −0.443126 − 0.548064I
−1.76571 − 0.41277I −1.52576 + 0.47761I
u = −0.871168
a = −0.718681
b = −0.283731
−1.22854 −10.9960
u = 1.143630 + 0.105102I
a = −0.057070 − 0.907033I
b = −0.19308 + 1.40671I
−11.40350 − 5.37019I −14.2310 + 9.8207I
u = 1.143630 − 0.105102I
a = −0.057070 + 0.907033I
b = −0.19308 − 1.40671I
−11.40350 + 5.37019I −14.2310 − 9.8207I
u = −0.551985 + 0.412677I
a = 2.14943 − 0.33347I
b = 0.514816 + 0.271439I
0.924854 + 0.158726I 4.34440 − 6.69903I
u = −0.551985 − 0.412677I
a = 2.14943 + 0.33347I
b = 0.514816 − 0.271439I
0.924854 − 0.158726I 4.34440 + 6.69903I
u = −0.864951 + 1.007370I
a = −1.007060 + 0.230412I
b = −0.863800 − 0.926848I
−1.67557 + 5.53623I −0.55960 − 5.41231I
u = −0.864951 − 1.007370I
a = −1.007060 − 0.230412I
b = −0.863800 + 0.926848I
−1.67557 − 5.53623I −0.55960 + 5.41231I
u = 0.636703 + 1.182420I
a = −0.620154 − 0.137775I
b = −0.861446 − 0.939694I
7.30571 − 0.11649I 1.357790 − 0.220682I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.636703 − 1.182420I
a = −0.620154 + 0.137775I
b = −0.861446 + 0.939694I
7.30571 + 0.11649I 1.357790 + 0.220682I
u = 1.46880 + 0.23288I
a = 0.344293 + 0.498724I
b = −0.233614 − 0.763468I
−8.21433 − 3.59803I −0.94605 + 7.25200I
u = 1.46880 − 0.23288I
a = 0.344293 − 0.498724I
b = −0.233614 + 0.763468I
−8.21433 + 3.59803I −0.94605 − 7.25200I
u = 1.29164 + 0.77827I
a = −1.062860 − 0.754268I
b = −0.540251 + 1.195250I
5.05931 − 7.06255I −1.67212 + 4.37965I
u = 1.29164 − 0.77827I
a = −1.062860 + 0.754268I
b = −0.540251 − 1.195250I
5.05931 + 7.06255I −1.67212 − 4.37965I
u = −1.51290 + 0.00522I
a = −0.178858 + 0.739842I
b = 0.667548 − 0.729025I
−3.75642 − 2.26076I −0.68469 + 3.46770I
u = −1.51290 − 0.00522I
a = −0.178858 − 0.739842I
b = 0.667548 + 0.729025I
−3.75642 + 2.26076I −0.68469 − 3.46770I
u = 0.65142 + 1.38092I
a = 0.480434 + 0.328699I
b = 1.05295 + 1.31649I
5.55369 + 6.92717I 0.41712 − 3.63279I
u = 0.65142 − 1.38092I
a = 0.480434 − 0.328699I
b = 1.05295 − 1.31649I
5.55369 − 6.92717I 0.41712 + 3.63279I
u = 1.35088 + 0.88382I
a = 1.167610 + 0.664320I
b = 0.82472 − 1.52688I
3.1876 − 14.9988I −1.61073 + 7.00884I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.35088 − 0.88382I
a = 1.167610 − 0.664320I
b = 0.82472 + 1.52688I
3.1876 + 14.9988I −1.61073 − 7.00884I
u = −0.167658
a = 4.50144
b = 0.434292
0.927721 12.4670
7
II. I
u
2
= h−u
4
a
2
+ 5u
4
a + · · · + 3a − 3, u
4
a
3
+ 5u
4
a
2
+ · · · + 27a + 31, u
5
−
2u
4
+ 2u
3
+ u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
1
=
u
−u
3
+ u
a
10
=
a
1
2
u
4
a
2
−
5
2
u
4
a + ··· −
3
2
a +
3
2
a
9
=
−
1
2
u
4
a
2
+
5
2
u
4
a + ··· +
5
2
a −
3
2
1
2
u
4
a
2
−
5
2
u
4
a + ··· −
3
2
a +
3
2
a
6
=
2u
4
a
3
− 3u
4
a
2
+ ··· − a
2
− 6
−
5
2
u
4
a
3
+
7
2
u
4
a
2
+ ··· −
9
2
a + 5
a
12
=
−
1
2
u
4
a
3
+
1
2
u
4
a
2
+ ··· −
7
2
a − 7
3
2
u
4
a
3
−
5
2
u
4
a
2
+ ··· +
5
2
a − 5
a
8
=
−u
4
+ 2u
3
− u
2
− 2u + 1
−u
3
+ u
2
− 1
a
3
=
−u
u
a
7
=
−u
4
+ 3u
3
− u
2
− 2u + 2
−2u
3
+ u
2
− 2
a
11
=
−
3
2
u
4
a
2
+
3
2
u
4
a + ··· +
1
2
a −
21
2
u
4
a
3
− u
4
a
2
+ ··· − 4a
2
+ 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
4
a
2
− 4a
3
u − 4a
2
u
2
+ 4u
3
a − 16u
4
− 4a
3
+ 12a
2
u − 8u
2
a +
26u
3
+ 8a
2
+ 16au − 28u
2
− 4a − 2u − 24
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
(u
5
− 2u
4
+ 2u
3
+ u
2
− u + 1)
4
c
3
, c
7
(u
5
+ u
4
+ 5u
3
+ u
2
+ 2u − 2)
4
c
5
, c
6
, c
9
c
11
u
20
− 2u
19
+ ··· + 150u + 103
c
8
(u
2
+ u + 1)
10
c
10
, c
12
u
20
+ 2u
19
+ ··· + 13224u + 2521
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y
5
+ 6y
3
− y
2
− y − 1)
4
c
3
, c
7
(y
5
+ 9y
4
+ 27y
3
+ 23y
2
+ 8y − 4)
4
c
5
, c
6
, c
9
c
11
y
20
+ 6y
19
+ ··· + 110988y + 10609
c
8
(y
2
+ y + 1)
10
c
10
, c
12
y
20
− 18y
19
+ ··· + 37696544y + 6355441
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.833800
a = −2.41812 + 0.15016I
b = −0.272476 − 1.364140I
−6.13845 + 2.02988I −10.94304 − 3.46410I
u = −0.833800
a = −2.41812 − 0.15016I
b = −0.272476 + 1.364140I
−6.13845 − 2.02988I −10.94304 + 3.46410I
u = −0.833800
a = −0.91730 + 5.62696I
b = 0.409925 + 1.126070I
−6.13845 + 2.02988I −10.94304 − 3.46410I
u = −0.833800
a = −0.91730 − 5.62696I
b = 0.409925 − 1.126070I
−6.13845 − 2.02988I −10.94304 + 3.46410I
u = 0.317129 + 0.618084I
a = −1.226670 − 0.088438I
b = −0.05655 + 1.55273I
−3.08342 + 0.92097I 0.36548 − 1.42298I
u = 0.317129 + 0.618084I
a = −1.283840 − 0.195995I
b = −1.102440 + 0.773065I
−3.08342 − 3.13880I 0.36548 + 5.50523I
u = 0.317129 + 0.618084I
a = 1.42128 − 0.76900I
b = −0.035904 − 0.509258I
−3.08342 + 0.92097I 0.36548 − 1.42298I
u = 0.317129 + 0.618084I
a = 1.92910 + 0.79325I
b = 0.244995 − 1.374870I
−3.08342 − 3.13880I 0.36548 + 5.50523I
u = 0.317129 − 0.618084I
a = −1.226670 + 0.088438I
b = −0.05655 − 1.55273I
−3.08342 − 0.92097I 0.36548 + 1.42298I
u = 0.317129 − 0.618084I
a = −1.283840 + 0.195995I
b = −1.102440 − 0.773065I
−3.08342 + 3.13880I 0.36548 − 5.50523I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.317129 − 0.618084I
a = 1.42128 + 0.76900I
b = −0.035904 + 0.509258I
−3.08342 − 0.92097I 0.36548 + 1.42298I
u = 0.317129 − 0.618084I
a = 1.92910 − 0.79325I
b = 0.244995 + 1.374870I
−3.08342 + 3.13880I 0.36548 − 5.50523I
u = 1.09977 + 1.12945I
a = 0.969002 + 0.567215I
b = 1.49281 − 1.00208I
6.97511 − 2.09502I −0.89396 − 1.30967I
u = 1.09977 + 1.12945I
a = −1.097140 − 0.256413I
b = −0.722774 + 1.025520I
6.97511 − 6.15479I −0.89396 + 5.61853I
u = 1.09977 + 1.12945I
a = 0.555611 + 0.563935I
b = 1.77894 + 0.45753I
6.97511 − 6.15479I −0.89396 + 5.61853I
u = 1.09977 + 1.12945I
a = −0.431917 − 0.251999I
b = −0.736535 − 0.654115I
6.97511 − 2.09502I −0.89396 − 1.30967I
u = 1.09977 − 1.12945I
a = 0.969002 − 0.567215I
b = 1.49281 + 1.00208I
6.97511 + 2.09502I −0.89396 + 1.30967I
u = 1.09977 − 1.12945I
a = −1.097140 + 0.256413I
b = −0.722774 − 1.025520I
6.97511 + 6.15479I −0.89396 − 5.61853I
u = 1.09977 − 1.12945I
a = 0.555611 − 0.563935I
b = 1.77894 − 0.45753I
6.97511 + 6.15479I −0.89396 − 5.61853I
u = 1.09977 − 1.12945I
a = −0.431917 + 0.251999I
b = −0.736535 + 0.654115I
6.97511 + 2.09502I −0.89396 + 1.30967I
12
III. I
u
3
= h2a
2
+ 2b + 3a + 2, 4a
3
+ 4a
2
+ 5a + 4, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
4
=
1
−1
a
1
=
−1
0
a
10
=
a
−a
2
−
3
2
a − 1
a
9
=
a
2
+
5
2
a + 1
−a
2
−
3
2
a − 1
a
6
=
3
2
a
2
−
3
4
a − 1
−a
2
+
1
2
a + 1
a
12
=
1
2
a
2
−
1
4
a − 2
−a
2
+
1
2
a + 1
a
8
=
−2a
2
− a + 1
2a
2
+ a − 1
a
3
=
1
−1
a
7
=
−2a
2
− a + 1
2a
2
+ a − 1
a
11
=
−2a
2
− 4a − 3
a
2
+
7
2
a + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes =
19
4
a
2
−
11
8
a +
17
2
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
7
u
3
c
4
(u + 1)
3
c
5
, c
6
u
3
+ 2u + 1
c
8
u
3
+ 3u
2
+ 5u + 2
c
9
, c
10
, c
11
c
12
u
3
+ 2u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
3
c
3
, c
7
y
3
c
5
, c
6
, c
9
c
10
, c
11
, c
12
y
3
+ 4y
2
+ 4y − 1
c
8
y
3
+ y
2
+ 13y − 4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.061957 + 1.066580I
b = 0.22670 − 1.46771I
−11.08570 − 5.13794I 3.19982 − 2.09434I
u = −1.00000
a = −0.061957 − 1.066580I
b = 0.22670 + 1.46771I
−11.08570 + 5.13794I 3.19982 + 2.09434I
u = −1.00000
a = −0.876086
b = −0.453398
−0.857735 13.3500
16
IV.
I
u
4
= hu
12
−3u
11
+· · ·+b−1, −u
12
+4u
11
+· · ·+a+1, u
13
−5u
12
+· · ·+u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
1
=
u
−u
3
+ u
a
10
=
u
12
− 4u
11
+ 5u
10
+ 2u
9
− 12u
8
+ 12u
7
− 3u
6
− 6u
5
+ 12u
4
− 7u
3
− 1
−u
12
+ 3u
11
+ ··· + 3u + 1
a
9
=
2u
12
− 7u
11
+ ··· − 3u − 2
−u
12
+ 3u
11
+ ··· + 3u + 1
a
6
=
u
12
− 6u
11
+ ··· + 3u + 1
u
11
− 4u
10
+ 5u
9
+ 2u
8
− 11u
7
+ 8u
6
+ 2u
5
− 5u
4
+ 4u
3
− u
2
− u + 1
a
12
=
−u
11
+ 5u
10
− 9u
9
+ 4u
8
+ 9u
7
− 14u
6
+ 7u
5
− u
4
− 3u
3
+ 5u
2
− u + 1
−u
3
+ u
2
− 1
a
8
=
−2u
12
+ 8u
11
+ ··· + u + 1
2u
12
− 8u
11
+ ··· − 3u − 2
a
3
=
−u
u
a
7
=
−2u
12
+ 7u
11
+ ··· + u + 1
2u
12
− 7u
11
+ ··· − 3u − 2
a
11
=
u
12
− 4u
11
+ ··· + u
2
− 2
−u
12
+ 3u
11
+ ··· + 4u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 11u
11
− 46u
10
+ 62u
9
+ 11u
8
− 114u
7
+ 98u
6
− 4u
5
− 36u
4
+ 51u
3
− 26u
2
− 10u − 9
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
13
+ 5u
12
+ ··· + u − 1
c
3
u
13
− u
12
+ ··· − u − 1
c
4
u
13
− 5u
12
+ ··· + u + 1
c
5
, c
11
u
13
+ 5u
11
+ ··· + 8u − 1
c
6
, c
9
u
13
+ 5u
11
+ ··· + 8u + 1
c
7
u
13
+ u
12
+ ··· − u + 1
c
8
u
13
− 2u
12
+ ··· + 3u + 1
c
10
, c
12
u
13
− 3u
12
+ ··· − 2u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
13
− 9y
12
+ ··· − 5y − 1
c
3
, c
7
y
13
+ 3y
12
+ ··· − y − 1
c
5
, c
6
, c
9
c
11
y
13
+ 10y
12
+ ··· + 62y − 1
c
8
y
13
+ 4y
12
+ ··· + 3y − 1
c
10
, c
12
y
13
− 3y
12
+ ··· − 4y − 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.071790 + 0.063918I
a = 3.89373 + 0.86609I
b = −0.350540 + 1.237350I
−6.72126 − 1.88681I 0.50306 + 13.63564I
u = −1.071790 − 0.063918I
a = 3.89373 − 0.86609I
b = −0.350540 − 1.237350I
−6.72126 + 1.88681I 0.50306 − 13.63564I
u = 0.130382 + 0.815929I
a = 1.43598 − 0.50475I
b = 0.570608 − 1.217040I
−3.69895 − 1.30722I −2.19900 + 1.04986I
u = 0.130382 − 0.815929I
a = 1.43598 + 0.50475I
b = 0.570608 + 1.217040I
−3.69895 + 1.30722I −2.19900 − 1.04986I
u = −0.672448
a = 2.97967
b = 0.122783
0.610906 −22.4950
u = 1.384340 + 0.198421I
a = 0.111997 + 1.000200I
b = 0.163145 − 1.174190I
−9.90727 − 5.10044I −4.52290 + 4.82780I
u = 1.384340 − 0.198421I
a = 0.111997 − 1.000200I
b = 0.163145 + 1.174190I
−9.90727 + 5.10044I −4.52290 − 4.82780I
u = 1.44789 + 0.30492I
a = −0.265186 − 0.255350I
b = 0.378653 + 0.878868I
−8.51258 − 3.08878I −7.58668 − 3.50114I
u = 1.44789 − 0.30492I
a = −0.265186 + 0.255350I
b = 0.378653 − 0.878868I
−8.51258 + 3.08878I −7.58668 + 3.50114I
u = 1.10155 + 1.08640I
a = −0.805723 − 0.406507I
b = −1.082570 + 0.295127I
7.14389 − 4.01026I −0.32249 + 2.61344I
20
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.10155 − 1.08640I
a = −0.805723 + 0.406507I
b = −1.082570 − 0.295127I
7.14389 + 4.01026I −0.32249 − 2.61344I
u = −0.156146 + 0.399949I
a = −1.36064 + 0.71418I
b = 0.259312 + 1.270730I
−4.92823 + 2.67880I −0.12459 − 4.50580I
u = −0.156146 − 0.399949I
a = −1.36064 − 0.71418I
b = 0.259312 − 1.270730I
−4.92823 − 2.67880I −0.12459 + 4.50580I
21
V. I
u
5
= hb
2
+ ba − a, a
2
+ a + 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
4
=
1
−1
a
1
=
−1
0
a
10
=
a
b
a
9
=
−b + a
b
a
6
=
−2ba + a + 1
ba − a
a
12
=
−ba − 1
ba − a
a
8
=
−1
1
a
3
=
1
−1
a
7
=
−1
1
a
11
=
b + 2a
−a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a − 4
22
(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
, c
6
u
4
− u
3
+ 2u
2
− 2u + 1
c
8
(u
2
− u + 1)
2
c
9
, c
10
, c
11
c
12
u
4
+ u
3
+ 2u
2
+ 2u + 1
23
(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
, c
6
, c
9
c
10
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
c
8
(y
2
+ y + 1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.500000 + 0.866025I
b = 0.621744 + 0.440597I
−4.93480 + 2.02988I −2.00000 − 3.46410I
u = −1.00000
a = −0.500000 + 0.866025I
b = −0.121744 − 1.306620I
−4.93480 + 2.02988I −2.00000 − 3.46410I
u = −1.00000
a = −0.500000 − 0.866025I
b = 0.621744 − 0.440597I
−4.93480 − 2.02988I −2.00000 + 3.46410I
u = −1.00000
a = −0.500000 − 0.866025I
b = −0.121744 + 1.306620I
−4.93480 − 2.02988I −2.00000 + 3.46410I
25
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
7
)(u
5
− 2u
4
+ ··· − u + 1)
4
(u
13
+ 5u
12
+ ··· + u − 1)
· (u
22
− 5u
21
+ ··· + 108u + 16)
c
3
u
7
(u
5
+ u
4
+ ··· + 2u − 2)
4
(u
13
− u
12
+ ··· − u − 1)
· (u
22
− 6u
21
+ ··· + 160u − 128)
c
4
((u + 1)
7
)(u
5
− 2u
4
+ ··· − u + 1)
4
(u
13
− 5u
12
+ ··· + u + 1)
· (u
22
− 5u
21
+ ··· + 108u + 16)
c
5
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
13
+ 5u
11
+ ··· + 8u − 1)
· (u
20
− 2u
19
+ ··· + 150u + 103)(u
22
+ 6u
20
+ ··· − u − 1)
c
6
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
13
+ 5u
11
+ ··· + 8u + 1)
· (u
20
− 2u
19
+ ··· + 150u + 103)(u
22
+ 6u
20
+ ··· − u − 1)
c
7
u
7
(u
5
+ u
4
+ ··· + 2u − 2)
4
(u
13
+ u
12
+ ··· − u + 1)
· (u
22
− 6u
21
+ ··· + 160u − 128)
c
8
(u
2
− u + 1)
2
(u
2
+ u + 1)
10
(u
3
+ 3u
2
+ 5u + 2)
· (u
13
− 2u
12
+ ··· + 3u + 1)(u
22
− 14u
21
+ ··· − 464u + 32)
c
9
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
13
+ 5u
11
+ ··· + 8u + 1)
· (u
20
− 2u
19
+ ··· + 150u + 103)(u
22
+ 6u
20
+ ··· − u − 1)
c
10
, c
12
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
13
− 3u
12
+ ··· − 2u − 1)
· (u
20
+ 2u
19
+ ··· + 13224u + 2521)(u
22
+ 3u
21
+ ··· + u + 1)
c
11
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
13
+ 5u
11
+ ··· + 8u − 1)
· (u
20
− 2u
19
+ ··· + 150u + 103)(u
22
+ 6u
20
+ ··· − u − 1)
26
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
((y − 1)
7
)(y
5
+ 6y
3
− y
2
− y − 1)
4
(y
13
− 9y
12
+ ··· − 5y − 1)
· (y
22
− 11y
21
+ ··· − 10352y + 256)
c
3
, c
7
y
7
(y
5
+ 9y
4
+ ··· + 8y − 4)
4
(y
13
+ 3y
12
+ ··· − y − 1)
· (y
22
+ 12y
21
+ ··· − 289792y + 16384)
c
5
, c
6
, c
9
c
11
(y
3
+ 4y
2
+ 4y − 1)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
13
+ 10y
12
+ ··· + 62y − 1)
· (y
20
+ 6y
19
+ ··· + 110988y + 10609)(y
22
+ 12y
21
+ ··· − 15y + 1)
c
8
((y
2
+ y + 1)
12
)(y
3
+ y
2
+ 13y − 4)(y
13
+ 4y
12
+ ··· + 3y − 1)
· (y
22
+ 6y
21
+ ··· − 36608y + 1024)
c
10
, c
12
(y
3
+ 4y
2
+ 4y − 1)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
13
− 3y
12
+ ··· − 4y − 1)
· (y
20
− 18y
19
+ ··· + 37696544y + 6355441)
· (y
22
− 37y
21
+ ··· − 141y + 1)
27
