11a
228
(K11a
228
)
A knot diagram
1
Linearized knot diagam
7 1 9 8 10 2 6 11 3 5 4
Solving Sequence
2,6
7 8 1
3,10
5 11 4 9
c
6
c
7
c
1
c
2
c
5
c
10
c
4
c
9
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−15u
25
− 53u
24
+ ··· + 4b + 140, −29u
25
− 269u
24
+ ··· + 8a − 580, u
26
+ 7u
25
+ ··· + 12u + 8i
I
u
2
= h8.51292 × 10
18
a
5
u
8
− 1.75570 × 10
19
a
4
u
8
+ ··· + 2.60029 × 10
20
a − 4.53756 × 10
20
,
− 2u
8
a
4
− 7u
8
a
3
+ ··· − 9a + 6, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
I
u
3
= hu
11
+ 2u
9
+ 4u
7
− u
6
+ 5u
5
− u
4
+ 3u
3
− u
2
+ b + 2u,
− u
13
− u
12
− 3u
11
− 2u
10
− 7u
9
− 3u
8
− 9u
7
− 2u
6
− 9u
5
+ u
4
− 6u
3
+ u
2
+ a − 2u + 2,
u
14
+ 3u
12
+ 7u
10
− u
9
+ 11u
8
− 2u
7
+ 12u
6
− 3u
5
+ 10u
4
− 2u
3
+ 5u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 94 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−15u
25
− 53u
24
+ · · · + 4b + 140, −29u
25
− 269u
24
+ · · · + 8a −
580, u
26
+ 7u
25
+ · · · + 12u + 8i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
8
=
u
2
+ 1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
10
=
3.62500u
25
+ 33.6250u
24
+ ··· + 49.2500u + 72.5000
15
4
u
25
+
53
4
u
24
+ ··· + 5u − 35
a
5
=
63
8
u
25
+
371
8
u
24
+ ··· +
197
4
u + 24
−
25
4
u
25
−
161
4
u
24
+ ··· −
97
2
u − 37
a
11
=
41
8
u
25
+
335
8
u
24
+ ··· +
119
2
u + 85
6u
25
+
53
2
u
24
+ ··· +
45
2
u − 41
a
4
=
9
8
u
25
+
61
8
u
24
+ ··· +
59
4
u + 1
−
1
4
u
25
−
13
4
u
24
+ ··· −
25
2
u − 9
a
9
=
−3.37500u
25
− 27.3750u
24
+ ··· − 38.7500u − 55.5000
−
21
4
u
25
−
103
4
u
24
+ ··· − 27u + 27
a
9
=
−3.37500u
25
− 27.3750u
24
+ ··· − 38.7500u − 55.5000
−
21
4
u
25
−
103
4
u
24
+ ··· − 27u + 27
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −12u
25
− 78u
24
− 301u
23
− 809u
22
− 1723u
21
− 2988u
20
− 4360u
19
− 5258u
18
−
5163u
17
− 3679u
16
− 1188u
15
+ 1603u
14
+ 3423u
13
+ 3726u
12
+ 2364u
11
+ 364u
10
−
1475u
9
− 2219u
8
− 2061u
7
− 1330u
6
− 696u
5
− 201u
4
− 18u
3
− 43u
2
− 116u − 58
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
26
+ 7u
25
+ ··· + 12u + 8
c
2
, c
7
u
26
+ 9u
25
+ ··· + 48u + 64
c
3
, c
5
, c
9
c
10
u
26
+ 8u
24
+ ··· + 2u + 1
c
4
, c
11
u
26
− u
25
+ ··· − 3u + 1
c
8
u
26
− 21u
25
+ ··· − 6912u + 512
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
26
+ 9y
25
+ ··· + 48y + 64
c
2
, c
7
y
26
+ 17y
25
+ ··· + 60160y + 4096
c
3
, c
5
, c
9
c
10
y
26
+ 16y
25
+ ··· − 2y + 1
c
4
, c
11
y
26
+ 9y
25
+ ··· + 19y + 1
c
8
y
26
− 5y
25
+ ··· + 196608y + 262144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.837651 + 0.572406I
a = 0.835566 + 0.354168I
b = −0.531846 − 0.873998I
1.84430 + 3.12249I 4.20356 − 5.13534I
u = −0.837651 − 0.572406I
a = 0.835566 − 0.354168I
b = −0.531846 + 0.873998I
1.84430 − 3.12249I 4.20356 + 5.13534I
u = 0.881347 + 0.183622I
a = −0.573452 − 0.801837I
b = 0.396890 + 1.190540I
−3.96770 + 6.65430I −0.65787 − 6.33935I
u = 0.881347 − 0.183622I
a = −0.573452 + 0.801837I
b = 0.396890 − 1.190540I
−3.96770 − 6.65430I −0.65787 + 6.33935I
u = 0.297455 + 0.831482I
a = 0.191314 + 0.562862I
b = 0.504051 − 0.077620I
−0.64079 + 1.97179I 1.39932 − 4.26013I
u = 0.297455 − 0.831482I
a = 0.191314 − 0.562862I
b = 0.504051 + 0.077620I
−0.64079 − 1.97179I 1.39932 + 4.26013I
u = −0.899623 + 0.665417I
a = −0.786099 − 0.972145I
b = 0.63545 + 1.32692I
−1.14356 + 10.71300I 0.33526 − 5.40937I
u = −0.899623 − 0.665417I
a = −0.786099 + 0.972145I
b = 0.63545 − 1.32692I
−1.14356 − 10.71300I 0.33526 + 5.40937I
u = −0.800652 + 0.839278I
a = 1.244260 + 0.159972I
b = −0.866677 + 0.161865I
5.83701 − 0.85262I 7.15266 + 0.82662I
u = −0.800652 − 0.839278I
a = 1.244260 − 0.159972I
b = −0.866677 − 0.161865I
5.83701 + 0.85262I 7.15266 − 0.82662I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.201343 + 1.171450I
a = 0.634705 − 1.046330I
b = −0.44754 − 1.35708I
−8.67640 + 10.06980I −5.88892 − 7.31379I
u = 0.201343 − 1.171450I
a = 0.634705 + 1.046330I
b = −0.44754 + 1.35708I
−8.67640 − 10.06980I −5.88892 + 7.31379I
u = −0.093471 + 1.199340I
a = −0.073401 + 0.980820I
b = 0.239568 + 0.837324I
−4.09225 + 1.31670I 5.84188 − 2.64117I
u = −0.093471 − 1.199340I
a = −0.073401 − 0.980820I
b = 0.239568 − 0.837324I
−4.09225 − 1.31670I 5.84188 + 2.64117I
u = −0.781122 + 0.922042I
a = −0.938819 − 0.875292I
b = 0.846844 + 0.063440I
5.58632 − 5.07870I 6.80297 + 4.99584I
u = −0.781122 − 0.922042I
a = −0.938819 + 0.875292I
b = 0.846844 − 0.063440I
5.58632 + 5.07870I 6.80297 − 4.99584I
u = 0.439531 + 1.186270I
a = −0.784277 + 0.187768I
b = −0.232529 + 1.203110I
−7.23748 − 1.85191I −5.27925 + 3.38649I
u = 0.439531 − 1.186270I
a = −0.784277 − 0.187768I
b = −0.232529 − 1.203110I
−7.23748 + 1.85191I −5.27925 − 3.38649I
u = −0.698499 + 1.080440I
a = −1.60109 − 0.59030I
b = 0.513688 − 0.994028I
0.31911 − 8.88087I 0.68625 + 10.27634I
u = −0.698499 − 1.080440I
a = −1.60109 + 0.59030I
b = 0.513688 + 0.994028I
0.31911 + 8.88087I 0.68625 − 10.27634I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.749005 + 1.057380I
a = 2.09827 + 0.24225I
b = −0.65034 + 1.38923I
−2.3566 − 16.8090I −1.24843 + 9.63879I
u = −0.749005 − 1.057380I
a = 2.09827 − 0.24225I
b = −0.65034 − 1.38923I
−2.3566 + 16.8090I −1.24843 − 9.63879I
u = −0.932872 + 0.931207I
a = −0.472447 + 0.573546I
b = 0.053787 − 0.847257I
3.75978 − 3.40349I −4.66696 + 3.91131I
u = −0.932872 − 0.931207I
a = −0.472447 − 0.573546I
b = 0.053787 + 0.847257I
3.75978 + 3.40349I −4.66696 − 3.91131I
u = 0.473220 + 0.303991I
a = 0.975471 + 0.017379I
b = −0.461342 − 0.420051I
0.898620 + 0.817519I 6.81953 − 4.33053I
u = 0.473220 − 0.303991I
a = 0.975471 − 0.017379I
b = −0.461342 + 0.420051I
0.898620 − 0.817519I 6.81953 + 4.33053I
7
II. I
u
2
= h8.51 × 10
18
a
5
u
8
− 1.76 × 10
19
a
4
u
8
+ · · · + 2.60 × 10
20
a − 4.54 ×
10
20
, −2u
8
a
4
−7u
8
a
3
+· · ·−9a+6, u
9
−u
8
+2u
7
−u
6
+3u
5
−u
4
+2u
3
+u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
8
=
u
2
+ 1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
10
=
a
−0.0501691a
5
u
8
+ 0.103468a
4
u
8
+ ··· − 1.53242a + 2.67411
a
5
=
0.0104893a
5
u
8
+ 0.300793a
4
u
8
+ ··· − 1.19290a + 4.00869
0.0757787a
5
u
8
+ 0.141035a
4
u
8
+ ··· + 2.09572a − 3.59647
a
11
=
−0.0191376a
5
u
8
+ 0.302267a
4
u
8
+ ··· + 0.192227a − 0.0413771
0.0842588a
5
u
8
− 0.190487a
4
u
8
+ ··· − 1.41715a + 1.39892
a
4
=
−0.0505824a
5
u
8
− 0.230088a
4
u
8
+ ··· + 0.271748a + 0.149238
0.0624037a
5
u
8
+ 0.372711a
4
u
8
+ ··· + 1.33349a − 2.66894
a
9
=
−0.117790a
5
u
8
+ 0.236604a
4
u
8
+ ··· + 0.487696a − 0.491448
0.144583a
5
u
8
+ 0.0202877a
4
u
8
+ ··· − 1.10453a + 2.79806
a
9
=
−0.117790a
5
u
8
+ 0.236604a
4
u
8
+ ··· + 0.487696a − 0.491448
0.144583a
5
u
8
+ 0.0202877a
4
u
8
+ ··· − 1.10453a + 2.79806
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1848468244326230304
24240666886441401379
u
8
a
5
+
7769797230450955500
24240666886441401379
u
8
a
4
+ ··· −
86732149638444774432
24240666886441401379
a +
198450488198204972058
24240666886441401379
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
6
c
2
, c
7
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
6
c
3
, c
5
, c
9
c
10
u
54
− u
53
+ ··· + 2026u + 167
c
4
, c
11
u
54
− 3u
53
+ ··· − 88u + 7
c
8
(u
3
+ u
2
− 1)
18
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
6
c
2
, c
7
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
6
c
3
, c
5
, c
9
c
10
y
54
+ 39y
53
+ ··· − 756660y + 27889
c
4
, c
11
y
54
− 13y
53
+ ··· − 772y + 49
c
8
(y
3
− y
2
+ 2y −1)
18
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140343 + 0.966856I
a = −0.789673 + 0.879642I
b = 0.197045 + 0.055587I
−3.69411 + 0.73475I −5.00524 + 1.18338I
u = −0.140343 + 0.966856I
a = 0.80190 + 1.19171I
b = −0.51815 + 1.57690I
−7.83169 − 2.09337I −11.53450 + 4.16283I
u = −0.140343 + 0.966856I
a = 0.32744 + 1.40287I
b = 0.303816 + 1.064500I
−3.69411 + 0.73475I −5.00524 + 1.18338I
u = −0.140343 + 0.966856I
a = 0.158893 + 0.006810I
b = −1.104640 + 0.259039I
−3.69411 − 4.92150I −5.00524 + 7.14228I
u = −0.140343 + 0.966856I
a = −1.80300 − 1.22850I
b = 0.077708 − 1.286090I
−7.83169 − 2.09337I −11.53450 + 4.16283I
u = −0.140343 + 0.966856I
a = −0.45237 − 2.31709I
b = 0.271297 − 1.159590I
−3.69411 − 4.92150I −5.00524 + 7.14228I
u = −0.140343 − 0.966856I
a = −0.789673 − 0.879642I
b = 0.197045 − 0.055587I
−3.69411 − 0.73475I −5.00524 − 1.18338I
u = −0.140343 − 0.966856I
a = 0.80190 − 1.19171I
b = −0.51815 − 1.57690I
−7.83169 + 2.09337I −11.53450 − 4.16283I
u = −0.140343 − 0.966856I
a = 0.32744 − 1.40287I
b = 0.303816 − 1.064500I
−3.69411 − 0.73475I −5.00524 − 1.18338I
u = −0.140343 − 0.966856I
a = 0.158893 − 0.006810I
b = −1.104640 − 0.259039I
−3.69411 + 4.92150I −5.00524 − 7.14228I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140343 − 0.966856I
a = −1.80300 + 1.22850I
b = 0.077708 + 1.286090I
−7.83169 + 2.09337I −11.53450 − 4.16283I
u = −0.140343 − 0.966856I
a = −0.45237 + 2.31709I
b = 0.271297 + 1.159590I
−3.69411 + 4.92150I −5.00524 − 7.14228I
u = −0.628449 + 0.875112I
a = 0.942165 + 0.601863I
b = 0.02614 + 1.49190I
−5.43132 − 2.45442I −8.69159 + 2.91298I
u = −0.628449 + 0.875112I
a = −1.262370 − 0.229556I
b = 0.173732 + 0.700808I
−1.29373 − 5.28254I −2.16232 + 5.89242I
u = −0.628449 + 0.875112I
a = 1.08622 + 1.35134I
b = −0.923600 − 0.879737I
−1.293730 + 0.373705I −2.16232 − 0.06647I
u = −0.628449 + 0.875112I
a = −1.52683 + 0.97782I
b = −0.10677 − 1.91340I
−5.43132 − 2.45442I −8.69159 + 2.91298I
u = −0.628449 + 0.875112I
a = 2.31670 + 0.58603I
b = −0.073681 + 0.905589I
−1.293730 + 0.373705I −2.16232 − 0.06647I
u = −0.628449 + 0.875112I
a = −2.58190 − 0.51535I
b = 0.762688 − 1.044840I
−1.29373 − 5.28254I −2.16232 + 5.89242I
u = −0.628449 − 0.875112I
a = 0.942165 − 0.601863I
b = 0.02614 − 1.49190I
−5.43132 + 2.45442I −8.69159 − 2.91298I
u = −0.628449 − 0.875112I
a = −1.262370 + 0.229556I
b = 0.173732 − 0.700808I
−1.29373 + 5.28254I −2.16232 − 5.89242I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.628449 − 0.875112I
a = 1.08622 − 1.35134I
b = −0.923600 + 0.879737I
−1.293730 − 0.373705I −2.16232 + 0.06647I
u = −0.628449 − 0.875112I
a = −1.52683 − 0.97782I
b = −0.10677 + 1.91340I
−5.43132 + 2.45442I −8.69159 − 2.91298I
u = −0.628449 − 0.875112I
a = 2.31670 − 0.58603I
b = −0.073681 − 0.905589I
−1.293730 − 0.373705I −2.16232 + 0.06647I
u = −0.628449 − 0.875112I
a = −2.58190 + 0.51535I
b = 0.762688 + 1.044840I
−1.29373 + 5.28254I −2.16232 − 5.89242I
u = 0.796005 + 0.733148I
a = 0.713362 − 0.505363I
b = −0.502274 + 1.249400I
2.46068 − 4.16429I 2.79385 + 3.68120I
u = 0.796005 + 0.733148I
a = 1.238440 + 0.048506I
b = −0.648327 − 0.667502I
2.46068 + 1.49195I 2.79385 − 2.27770I
u = 0.796005 + 0.733148I
a = 0.765974 − 1.136570I
b = −0.118171 + 0.986357I
−1.67691 − 1.33617I −3.73542 + 0.70175I
u = 0.796005 + 0.733148I
a = −0.181650 + 0.241266I
b = 0.388994 − 0.951181I
2.46068 + 1.49195I 2.79385 − 2.27770I
u = 0.796005 + 0.733148I
a = −0.81516 + 1.60536I
b = 0.78711 − 1.20948I
−1.67691 − 1.33617I −3.73542 + 0.70175I
u = 0.796005 + 0.733148I
a = −1.80729 + 0.56948I
b = 1.266580 + 0.200850I
2.46068 − 4.16429I 2.79385 + 3.68120I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.796005 − 0.733148I
a = 0.713362 + 0.505363I
b = −0.502274 − 1.249400I
2.46068 + 4.16429I 2.79385 − 3.68120I
u = 0.796005 − 0.733148I
a = 1.238440 − 0.048506I
b = −0.648327 + 0.667502I
2.46068 − 1.49195I 2.79385 + 2.27770I
u = 0.796005 − 0.733148I
a = 0.765974 + 1.136570I
b = −0.118171 − 0.986357I
−1.67691 + 1.33617I −3.73542 − 0.70175I
u = 0.796005 − 0.733148I
a = −0.181650 − 0.241266I
b = 0.388994 + 0.951181I
2.46068 − 1.49195I 2.79385 + 2.27770I
u = 0.796005 − 0.733148I
a = −0.81516 − 1.60536I
b = 0.78711 + 1.20948I
−1.67691 + 1.33617I −3.73542 − 0.70175I
u = 0.796005 − 0.733148I
a = −1.80729 − 0.56948I
b = 1.266580 − 0.200850I
2.46068 + 4.16429I 2.79385 − 3.68120I
u = 0.728966 + 0.986295I
a = −0.387701 + 0.616336I
b = 0.688581 − 0.531471I
1.68745 + 4.25680I 1.08656 − 2.93390I
u = 0.728966 + 0.986295I
a = 1.337780 − 0.309242I
b = −0.286685 − 1.108740I
1.68745 + 4.25680I 1.08656 − 2.93390I
u = 0.728966 + 0.986295I
a = 1.29786 − 1.11923I
b = −1.368850 + 0.117343I
1.68745 + 9.91305I 1.08656 − 8.89280I
u = 0.728966 + 0.986295I
a = −2.09945 + 0.52391I
b = 0.462600 + 1.307620I
1.68745 + 9.91305I 1.08656 − 8.89280I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.728966 + 0.986295I
a = −2.12891 − 0.45451I
b = 0.202583 + 1.039430I
−2.45013 + 7.08493I −5.44271 − 5.91335I
u = 0.728966 + 0.986295I
a = 2.32561 + 0.07270I
b = −0.87070 − 1.32457I
−2.45013 + 7.08493I −5.44271 − 5.91335I
u = 0.728966 − 0.986295I
a = −0.387701 − 0.616336I
b = 0.688581 + 0.531471I
1.68745 − 4.25680I 1.08656 + 2.93390I
u = 0.728966 − 0.986295I
a = 1.337780 + 0.309242I
b = −0.286685 + 1.108740I
1.68745 − 4.25680I 1.08656 + 2.93390I
u = 0.728966 − 0.986295I
a = 1.29786 + 1.11923I
b = −1.368850 − 0.117343I
1.68745 − 9.91305I 1.08656 + 8.89280I
u = 0.728966 − 0.986295I
a = −2.09945 − 0.52391I
b = 0.462600 − 1.307620I
1.68745 − 9.91305I 1.08656 + 8.89280I
u = 0.728966 − 0.986295I
a = −2.12891 + 0.45451I
b = 0.202583 − 1.039430I
−2.45013 − 7.08493I −5.44271 + 5.91335I
u = 0.728966 − 0.986295I
a = 2.32561 − 0.07270I
b = −0.87070 + 1.32457I
−2.45013 − 7.08493I −5.44271 + 5.91335I
u = −0.512358
a = 0.969937 + 0.067507I
b = −0.426633 − 0.992210I
−0.71223 + 2.82812I 4.16210 − 2.97945I
u = −0.512358
a = 0.969937 − 0.067507I
b = −0.426633 + 0.992210I
−0.71223 − 2.82812I 4.16210 + 2.97945I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.512358
a = −0.74455 + 1.43727I
b = 0.604275 + 0.087401I
−0.71223 − 2.82812I 4.16210 + 2.97945I
u = −0.512358
a = −0.74455 − 1.43727I
b = 0.604275 − 0.087401I
−0.71223 + 2.82812I 4.16210 − 2.97945I
u = −0.512358
a = 0.29857 + 2.09521I
b = 0.235325 − 1.259830I
−4.84981 −2.36716 + 0.I
u = −0.512358
a = 0.29857 − 2.09521I
b = 0.235325 + 1.259830I
−4.84981 −2.36716 + 0.I
16
III.
I
u
3
= hu
11
+2u
9
+· · ·+ b +2u, −u
13
−u
12
+· · ·+ a +2, u
14
+3u
12
+· · ·− u +1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
8
=
u
2
+ 1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
10
=
u
13
+ u
12
+ ··· + 2u − 2
−u
11
− 2u
9
− 4u
7
+ u
6
− 5u
5
+ u
4
− 3u
3
+ u
2
− 2u
a
5
=
−u
13
+ u
12
+ ··· + u + 2
u
12
+ 3u
10
+ 7u
8
− u
7
+ 10u
6
− 2u
5
+ 10u
4
− 3u
3
+ 7u
2
− u + 1
a
11
=
u
13
− u
12
+ ··· − 7u
2
− 3
−u
13
− u
12
+ ··· − u − 1
a
4
=
−u
13
+ u
12
+ ··· + 2u + 1
u
13
+ u
12
+ 2u
11
+ 3u
10
+ 4u
9
+ 6u
8
+ 4u
7
+ 9u
6
+ 2u
5
+ 9u
4
+ 7u
2
+ 1
a
9
=
u
13
+ 3u
11
+ ··· + 3u − 3
−u
11
− 2u
9
− 4u
7
+ u
6
− 5u
5
+ u
4
− 3u
3
− 2u
a
9
=
u
13
+ 3u
11
+ ··· + 3u − 3
−u
11
− 2u
9
− 4u
7
+ u
6
− 5u
5
+ u
4
− 3u
3
− 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −4u
13
−12u
11
−2u
10
−29u
9
−4u
8
−45u
7
−5u
6
−45u
5
−10u
4
−32u
3
−8u
2
−11u −7
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
+ 3u
12
+ ··· + u + 1
c
2
, c
7
u
14
+ 6u
13
+ ··· + 9u + 1
c
3
, c
10
u
14
+ 7u
12
+ ··· − u + 1
c
4
, c
11
u
14
− u
13
− 3u
10
+ 3u
9
+ u
8
+ 2u
6
− 4u
5
− 2u
4
+ u
2
+ 2u + 1
c
5
, c
9
u
14
+ 7u
12
+ ··· + u + 1
c
6
u
14
+ 3u
12
+ ··· − u + 1
c
8
u
14
− 6u
13
+ ··· − 4u
2
+ 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
14
+ 6y
13
+ ··· + 9y + 1
c
2
, c
7
y
14
+ 10y
13
+ ··· + y + 1
c
3
, c
5
, c
9
c
10
y
14
+ 14y
13
+ ··· + 13y + 1
c
4
, c
11
y
14
− y
13
+ ··· − 2y + 1
c
8
y
14
− 4y
13
+ ··· − 8y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.726429 + 0.738003I
a = 1.33833 − 1.17422I
b = −0.584789 + 0.795162I
−0.01062 − 1.94202I 2.00932 + 3.37456I
u = 0.726429 − 0.738003I
a = 1.33833 + 1.17422I
b = −0.584789 − 0.795162I
−0.01062 + 1.94202I 2.00932 − 3.37456I
u = −0.653577 + 0.866508I
a = 1.194500 − 0.206474I
b = 0.04408 + 1.69162I
−4.68531 − 2.54104I 4.65327 + 4.19412I
u = −0.653577 − 0.866508I
a = 1.194500 + 0.206474I
b = 0.04408 − 1.69162I
−4.68531 + 2.54104I 4.65327 − 4.19412I
u = −0.252602 + 0.846708I
a = −1.68568 − 0.55564I
b = 0.10455 − 1.45717I
−6.98963 − 1.12261I −6.65272 − 1.37335I
u = −0.252602 − 0.846708I
a = −1.68568 + 0.55564I
b = 0.10455 + 1.45717I
−6.98963 + 1.12261I −6.65272 + 1.37335I
u = 0.164460 + 1.120840I
a = −0.012063 − 1.300920I
b = 0.258541 − 0.856843I
−4.52958 − 1.45474I −11.85219 + 6.68999I
u = 0.164460 − 1.120840I
a = −0.012063 + 1.300920I
b = 0.258541 + 0.856843I
−4.52958 + 1.45474I −11.85219 − 6.68999I
u = 0.693530 + 0.982336I
a = −2.20489 + 0.21016I
b = 0.590972 + 0.911227I
−0.76823 + 7.39185I −0.21938 − 7.80771I
u = 0.693530 − 0.982336I
a = −2.20489 − 0.21016I
b = 0.590972 − 0.911227I
−0.76823 − 7.39185I −0.21938 + 7.80771I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.890932 + 0.918447I
a = 0.287546 − 0.062061I
b = −0.035727 + 0.562759I
4.35733 − 3.27992I 8.77581 + 1.72593I
u = −0.890932 − 0.918447I
a = 0.287546 + 0.062061I
b = −0.035727 − 0.562759I
4.35733 + 3.27992I 8.77581 − 1.72593I
u = 0.212692 + 0.537116I
a = −1.91774 + 0.45936I
b = −0.377626 − 0.645284I
−2.17837 + 3.22050I −4.21411 − 3.89687I
u = 0.212692 − 0.537116I
a = −1.91774 − 0.45936I
b = −0.377626 + 0.645284I
−2.17837 − 3.22050I −4.21411 + 3.89687I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
9
− u
8
+ ··· + u + 1)
6
)(u
14
+ 3u
12
+ ··· + u + 1)
· (u
26
+ 7u
25
+ ··· + 12u + 8)
c
2
, c
7
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
6
· (u
14
+ 6u
13
+ ··· + 9u + 1)(u
26
+ 9u
25
+ ··· + 48u + 64)
c
3
, c
10
(u
14
+ 7u
12
+ ··· − u + 1)(u
26
+ 8u
24
+ ··· + 2u + 1)
· (u
54
− u
53
+ ··· + 2026u + 167)
c
4
, c
11
(u
14
− u
13
− 3u
10
+ 3u
9
+ u
8
+ 2u
6
− 4u
5
− 2u
4
+ u
2
+ 2u + 1)
· (u
26
− u
25
+ ··· − 3u + 1)(u
54
− 3u
53
+ ··· − 88u + 7)
c
5
, c
9
(u
14
+ 7u
12
+ ··· + u + 1)(u
26
+ 8u
24
+ ··· + 2u + 1)
· (u
54
− u
53
+ ··· + 2026u + 167)
c
6
((u
9
− u
8
+ ··· + u + 1)
6
)(u
14
+ 3u
12
+ ··· − u + 1)
· (u
26
+ 7u
25
+ ··· + 12u + 8)
c
8
((u
3
+ u
2
− 1)
18
)(u
14
− 6u
13
+ ··· − 4u
2
+ 1)
· (u
26
− 21u
25
+ ··· − 6912u + 512)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
6
· (y
14
+ 6y
13
+ ··· + 9y + 1)(y
26
+ 9y
25
+ ··· + 48y + 64)
c
2
, c
7
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
6
· (y
14
+ 10y
13
+ ··· + y + 1)(y
26
+ 17y
25
+ ··· + 60160y + 4096)
c
3
, c
5
, c
9
c
10
(y
14
+ 14y
13
+ ··· + 13y + 1)(y
26
+ 16y
25
+ ··· − 2y + 1)
· (y
54
+ 39y
53
+ ··· − 756660y + 27889)
c
4
, c
11
(y
14
− y
13
+ ··· − 2y + 1)(y
26
+ 9y
25
+ ··· + 19y + 1)
· (y
54
− 13y
53
+ ··· − 772y + 49)
c
8
((y
3
− y
2
+ 2y −1)
18
)(y
14
− 4y
13
+ ··· − 8y + 1)
· (y
26
− 5y
25
+ ··· + 196608y + 262144)
23
