12n
0228
(K12n
0228
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 9 11 4 6 12 8 5 10
Solving Sequence
6,11 4,7
8 9 3 5 12 2 1 10
c
6
c
7
c
8
c
3
c
5
c
11
c
2
c
1
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−9861446311968u
17
+ 13967634545632u
16
+ ··· + 5212485204695b − 26164458415624,
− 35356917620792u
17
+ 9192459205168u
16
+ ··· + 5212485204695a + 53817437592104,
u
18
− u
17
+ ··· − u − 1i
I
u
2
= hu
8
+ u
6
+ 2u
4
+ u
2
+ b + u, u
8
+ u
7
+ 3u
6
+ u
5
+ 4u
4
+ u
3
+ 4u
2
+ a + 2,
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
I
u
3
= h−1.81728 × 10
21
u
17
+ 1.12182 × 10
21
u
16
+ ··· + 3.70892 × 10
24
b − 2.85100 × 10
23
,
6.07558 × 10
21
u
17
− 6.65651 × 10
21
u
16
+ ··· + 3.70892 × 10
24
a − 7.70911 × 10
24
,
u
18
− u
17
+ ··· − 1024u + 512i
I
v
1
= ha, 16726v
8
+ 41423v
7
+ ··· + 11959b + 26601,
v
9
+ 3v
8
− 2v
7
+ 6v
6
+ 25v
5
+ 11v
4
− 9v
3
− 2v
2
+ 3v + 1i
* 4 irreducible components of dim
C
= 0, with total 54 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−9.86×10
12
u
17
+1.40×10
13
u
16
+· · ·+5.21×10
12
b−2.62×10
13
, −3.54×
10
13
u
17
+9.19×10
12
u
16
+· · ·+5.21×10
12
a+5.38×10
13
, u
18
−u
17
+· · ·−u−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
6.78312u
17
− 1.76355u
16
+ ··· − 14.7181u − 10.3247
1.89189u
17
− 2.67965u
16
+ ··· + 10.8027u + 5.01957
a
7
=
1
u
2
a
8
=
−5.01957u
17
+ 3.12769u
16
+ ··· + 3.54160u − 5.78312
0.787760u
17
+ 0.523498u
16
+ ··· − 6.91146u − 1.89189
a
9
=
−4.23181u
17
+ 3.65118u
16
+ ··· − 3.36987u − 7.67501
0.787760u
17
+ 0.523498u
16
+ ··· − 6.91146u − 1.89189
a
3
=
8.67501u
17
− 4.44320u
16
+ ··· − 3.91541u − 5.30514
0.580631u
17
− 1.87796u
16
+ ··· + 11.9068u + 4.23181
a
5
=
−0.182502u
17
− 1.66573u
16
+ ··· + 14.4199u + 6.60470
−0.872414u
17
+ 0.452638u
16
+ ··· + 1.36048u − 0.117197
a
12
=
9.81987u
17
− 10.3086u
16
+ ··· + 26.3092u + 18.8999
−2.15014u
17
− 0.0100325u
16
+ ··· + 10.2859u + 1.01350
a
2
=
8.04847u
17
− 1.60224u
16
+ ··· − 21.8507u − 13.9296
2.27885u
17
− 3.00234u
16
+ ··· + 11.9846u + 5.66748
a
1
=
0.307849u
17
+ 0.749387u
16
+ ··· − 5.26730u − 4.18442
0.509570u
17
− 0.575614u
16
+ ··· + 2.09902u + 1.31126
a
10
=
7.61379u
17
− 7.71164u
16
+ ··· + 21.1440u + 12.3571
−1.42846u
17
+ 0.0464712u
16
+ ··· + 7.41181u + 0.689913
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
33036266987992
5212485204695
u
17
−
83885068578828
5212485204695
u
16
+ ··· +
600947759550584
5212485204695
u −
154008499337594
5212485204695
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 11u
17
+ ··· + 3u + 1
c
2
, c
4
, c
9
c
12
u
18
− 7u
17
+ ··· − u + 1
c
3
, c
6
, c
7
u
18
+ u
17
+ ··· + u − 1
c
5
, c
8
u
18
+ u
17
+ ··· + 3u − 1
c
10
u
18
− 3u
17
+ ··· + 517u − 1
c
11
u
18
− 5u
17
+ ··· + 77u − 23
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 41y
17
+ ··· − 47y + 1
c
2
, c
4
, c
9
c
12
y
18
− 11y
17
+ ··· − 3y + 1
c
3
, c
6
, c
7
y
18
+ 21y
17
+ ··· − 7y + 1
c
5
, c
8
y
18
+ 13y
17
+ ··· − 43y + 1
c
10
y
18
+ 29y
17
+ ··· − 268915y + 1
c
11
y
18
+ y
17
+ ··· − 5331y + 529
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.557323 + 0.726879I
a = −0.078908 − 0.132094I
b = 0.467481 − 0.634184I
−5.49927 + 7.93492I −11.8455 − 13.1993I
u = −0.557323 − 0.726879I
a = −0.078908 + 0.132094I
b = 0.467481 + 0.634184I
−5.49927 − 7.93492I −11.8455 + 13.1993I
u = −0.781322 + 0.060789I
a = −1.67426 − 2.33250I
b = −0.456133 − 1.317030I
−3.91966 − 2.10303I −13.59813 + 2.08848I
u = −0.781322 − 0.060789I
a = −1.67426 + 2.33250I
b = −0.456133 + 1.317030I
−3.91966 + 2.10303I −13.59813 − 2.08848I
u = 0.136626 + 0.709955I
a = 0.134891 + 0.049791I
b = −0.211757 − 0.707953I
0.64686 − 2.83787I 0.86568 + 9.86296I
u = 0.136626 − 0.709955I
a = 0.134891 − 0.049791I
b = −0.211757 + 0.707953I
0.64686 + 2.83787I 0.86568 − 9.86296I
u = 0.367491 + 0.554636I
a = −0.073321 + 0.530685I
b = −0.571171 − 0.676106I
−0.53975 − 1.77290I −3.88757 + 3.00933I
u = 0.367491 − 0.554636I
a = −0.073321 − 0.530685I
b = −0.571171 + 0.676106I
−0.53975 + 1.77290I −3.88757 − 3.00933I
u = 0.344494 + 0.511075I
a = 2.56907 − 7.38757I
b = 1.89070 + 1.44645I
−5.78192 + 0.83339I −4.3200 + 13.4737I
u = 0.344494 − 0.511075I
a = 2.56907 + 7.38757I
b = 1.89070 − 1.44645I
−5.78192 − 0.83339I −4.3200 − 13.4737I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.604129
a = 1.66056
b = 0.00192836
−1.09450 −7.23730
u = −0.318928
a = −11.2006
b = −0.820343
−3.03100 −72.2820
u = 0.74883 + 1.97520I
a = 0.448418 − 0.789734I
b = 0.08933 + 1.98953I
9.51613 − 3.71804I −9.22156 + 1.51475I
u = 0.74883 − 1.97520I
a = 0.448418 + 0.789734I
b = 0.08933 − 1.98953I
9.51613 + 3.71804I −9.22156 − 1.51475I
u = −0.83783 + 2.05810I
a = −0.421019 − 0.873213I
b = −0.68580 + 2.47962I
13.3797 + 9.0997I −6.48039 − 4.12934I
u = −0.83783 − 2.05810I
a = −0.421019 + 0.873213I
b = −0.68580 − 2.47962I
13.3797 − 9.0997I −6.48039 + 4.12934I
u = 0.93643 + 2.07951I
a = 0.365142 − 0.919671I
b = 1.38656 + 2.51311I
9.0651 − 14.3484I −9.75296 + 6.52825I
u = 0.93643 − 2.07951I
a = 0.365142 + 0.919671I
b = 1.38656 − 2.51311I
9.0651 + 14.3484I −9.75296 − 6.52825I
6
II. I
u
2
= hu
8
+ u
6
+ 2u
4
+ u
2
+ b + u, u
8
+ u
7
+ 3u
6
+ u
5
+ 4u
4
+ u
3
+ 4u
2
+
a + 2, u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
−u
8
− u
7
− 3u
6
− u
5
− 4u
4
− u
3
− 4u
2
− 2
−u
8
− u
6
− 2u
4
− u
2
− u
a
7
=
1
u
2
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
3
=
−u
8
− u
7
− 3u
6
− u
5
− 4u
4
− u
3
− 4u
2
− 2
−u
8
− u
6
− 2u
4
− u
2
− u
a
5
=
u
4
+ u
2
+ 1
u
4
a
12
=
u
8
+ u
6
+ u
4
− 1
u
8
+ u
7
+ u
6
+ 2u
5
+ u
4
+ 2u
3
+ 2u − 1
a
2
=
−u
8
− u
7
− 3u
6
− u
5
− 5u
4
− u
3
− 5u
2
− 3
−u
8
− u
6
− 3u
4
− u
2
− u
a
1
=
−u
4
− u
2
− 1
−u
4
a
10
=
u
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
8
+ 5u
6
+ u
5
+ 9u
4
+ 5u
2
+ 4u − 8
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
6
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
8
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
9
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
10
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
11
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
12
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
7
y
9
c
5
, c
8
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
6
, c
10
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
9
, c
12
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
11
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140343 + 0.966856I
a = 0.483566 + 0.305056I
b = −0.525305 − 0.147929I
0.13850 − 2.09337I −6.02684 + 1.69698I
u = 0.140343 − 0.966856I
a = 0.483566 − 0.305056I
b = −0.525305 + 0.147929I
0.13850 + 2.09337I −6.02684 − 1.69698I
u = 0.628449 + 0.875112I
a = −1.022450 + 0.246780I
b = 0.107759 − 1.216140I
−2.26187 − 2.45442I −8.53903 + 2.82066I
u = 0.628449 − 0.875112I
a = −1.022450 − 0.246780I
b = 0.107759 + 1.216140I
−2.26187 + 2.45442I −8.53903 − 2.82066I
u = −0.796005 + 0.733148I
a = 1.23246 + 1.62704I
b = 2.01751 − 1.28212I
−6.01628 − 1.33617I −16.4774 + 4.4812I
u = −0.796005 − 0.733148I
a = 1.23246 − 1.62704I
b = 2.01751 + 1.28212I
−6.01628 + 1.33617I −16.4774 − 4.4812I
u = −0.728966 + 0.986295I
a = −0.411691 + 0.129409I
b = 0.367799 + 0.534872I
−5.24306 + 7.08493I −9.02021 − 2.94778I
u = −0.728966 − 0.986295I
a = −0.411691 − 0.129409I
b = 0.367799 − 0.534872I
−5.24306 − 7.08493I −9.02021 + 2.94778I
u = 0.512358
a = −3.56378
b = −0.935531
−2.84338 −3.87310
10
III. I
u
3
= h−1.82 × 10
21
u
17
+ 1.12 × 10
21
u
16
+ · · · + 3.71 × 10
24
b − 2.85 ×
10
23
, 6.08 × 10
21
u
17
− 6.66 × 10
21
u
16
+ · · · + 3.71 × 10
24
a − 7.71 ×
10
24
, u
18
− u
17
+ · · · − 1024u + 512i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
−0.00163810u
17
+ 0.00179473u
16
+ ··· − 2.49995u + 2.07853
0.000489974u
17
− 0.000302464u
16
+ ··· − 1.00081u + 0.0768688
a
7
=
1
u
2
a
8
=
−0.000647148u
17
+ 0.00137895u
16
+ ··· − 2.62281u − 0.193950
−0.000380983u
17
+ 0.000549244u
16
+ ··· − 1.73916u + 0.608978
a
9
=
−0.00102813u
17
+ 0.00192819u
16
+ ··· − 4.36197u + 0.415028
−0.000380983u
17
+ 0.000549244u
16
+ ··· − 1.73916u + 0.608978
a
3
=
−0.00322523u
17
+ 0.00350611u
16
+ ··· − 2.41456u + 1.38902
−0.0000152880u
17
+ 0.000660040u
16
+ ··· − 2.70270u + 0.0251916
a
5
=
−0.00137194u
17
+ 0.000914778u
16
+ ··· + 3.57480u − 0.897464
−0.000606358u
17
+ 0.000539657u
16
+ ··· + 0.359893u − 0.400830
a
12
=
−0.00177283u
17
+ 0.00280042u
16
+ ··· − 7.34159u + 0.997270
−0.000412612u
17
+ 0.000733802u
16
+ ··· − 2.73715u + 0.865009
a
2
=
−0.000957173u
17
+ 0.00142033u
16
+ ··· − 4.42822u + 2.32273
0.000900583u
17
− 0.000630850u
16
+ ··· − 1.88345u + 0.230042
a
1
=
0.00197317u
17
− 0.00315915u
16
+ ··· + 8.61298u − 1.34243
0.000666946u
17
− 0.000742761u
16
+ ··· + 3.18723u − 1.06981
a
10
=
−0.00115375u
17
+ 0.00192948u
16
+ ··· − 2.60407u + 0.0364046
−0.000390462u
17
+ 0.000755167u
16
+ ··· − 1.28059u + 0.391978
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
335010846082545701
542874601956974270032
u
17
+
62587569732089869
4342996815655794160256
u
16
+ ··· +
240047666391711939473
67859325244621783754
u −
317868067795007140580
33929662622310891877
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 10u
17
+ ··· + 18u + 1
c
2
, c
4
, c
9
c
12
u
18
− 4u
17
+ ··· − 9u
2
+ 1
c
3
, c
6
, c
7
u
18
+ u
17
+ ··· + 1024u + 512
c
5
, c
8
(u
9
+ u
8
+ 4u
7
+ 3u
6
+ 5u
5
+ 3u
4
− 3u − 1)
2
c
10
u
18
+ 4u
17
+ ··· + 1179u − 199
c
11
u
18
− 3u
17
+ ··· + 3241u + 1303
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 38y
17
+ ··· − 206y + 1
c
2
, c
4
, c
9
c
12
y
18
+ 10y
17
+ ··· − 18y + 1
c
3
, c
6
, c
7
y
18
+ 39y
17
+ ··· − 262144y + 262144
c
5
, c
8
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ y
5
− 31y
4
− 24y
3
+ 6y
2
+ 9y −1)
2
c
10
y
18
+ 40y
17
+ ··· − 5352529y + 39601
c
11
y
18
+ 33y
17
+ ··· − 7027677y + 1697809
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.595275 + 1.147110I
a = −0.404894 − 0.038279I
b = −1.081020 + 0.780899I
0.11314 + 3.86354I −7.87583 − 4.20503I
u = 0.595275 − 1.147110I
a = −0.404894 + 0.038279I
b = −1.081020 − 0.780899I
0.11314 − 3.86354I −7.87583 + 4.20503I
u = −1.015350 + 0.875548I
a = −0.464440 − 0.716594I
b = −1.196010 + 0.177321I
−4.49282 − 1.55423I −10.08319 + 1.78109I
u = −1.015350 − 0.875548I
a = −0.464440 + 0.716594I
b = −1.196010 − 0.177321I
−4.49282 + 1.55423I −10.08319 − 1.78109I
u = 0.606622
a = 1.43188
b = 0.0937213
−1.08370 −8.12940
u = −0.200843 + 0.459012I
a = −0.29240 − 2.26629I
b = 0.647304 − 0.435564I
−4.49282 − 1.55423I −10.08319 + 1.78109I
u = −0.200843 − 0.459012I
a = −0.29240 + 2.26629I
b = 0.647304 + 0.435564I
−4.49282 + 1.55423I −10.08319 − 1.78109I
u = 0.433195
a = 2.00512
b = −0.230345
−1.08370 −8.12940
u = −0.96197 + 1.32057I
a = 0.120599 + 0.165555I
b = 1.28388 + 0.87865I
3.85626 −3.50861 + 0.I
u = −0.96197 − 1.32057I
a = 0.120599 − 0.165555I
b = 1.28388 − 0.87865I
3.85626 −3.50861 + 0.I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52260 + 1.29705I
a = 0.082950 + 0.249345I
b = −1.52738 + 1.63332I
0.11314 − 3.86354I −7.87583 + 4.20503I
u = 1.52260 − 1.29705I
a = 0.082950 − 0.249345I
b = −1.52738 − 1.63332I
0.11314 + 3.86354I −7.87583 − 4.20503I
u = 0.15107 + 2.32872I
a = 0.021091 + 0.902669I
b = −0.76230 − 2.19908I
10.52390 − 4.99486I −8.55415 + 3.07435I
u = 0.15107 − 2.32872I
a = 0.021091 − 0.902669I
b = −0.76230 + 2.19908I
10.52390 + 4.99486I −8.55415 − 3.07435I
u = −0.12400 + 2.50290I
a = 0.042253 + 0.852894I
b = 0.38934 − 2.85319I
14.5478 −5.33565 + 0.I
u = −0.12400 − 2.50290I
a = 0.042253 − 0.852894I
b = 0.38934 + 2.85319I
14.5478 −5.33565 + 0.I
u = 0.01330 + 2.66058I
a = −0.073656 + 0.788510I
b = 0.31450 − 3.25798I
10.52390 + 4.99486I −8.55415 − 3.07435I
u = 0.01330 − 2.66058I
a = −0.073656 − 0.788510I
b = 0.31450 + 3.25798I
10.52390 − 4.99486I −8.55415 + 3.07435I
15
IV.
I
v
1
= ha, 16726v
8
+ 41423v
7
+ · · · + 11959b + 26601, v
9
+ 3v
8
+ · · · + 3v + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
v
0
a
4
=
0
−1.39861v
8
− 3.46375v
7
+ ··· − 3.94598v −2.22435
a
7
=
1
0
a
8
=
1
−1.45213v
8
− 3.82515v
7
+ ··· − 3.73944v −4.14098
a
9
=
−1.45213v
8
− 3.82515v
7
+ ··· − 3.73944v −3.14098
−1.45213v
8
− 3.82515v
7
+ ··· − 3.73944v −4.14098
a
3
=
−1.39861v
8
− 3.46375v
7
+ ··· − 3.94598v −2.22435
−1.77239v
8
− 4.70666v
7
+ ··· − 2.34719v −4.59520
a
5
=
−0.240990v
8
− 0.883686v
7
+ ··· + 1.89882v −1.13396
1.21114v
8
+ 2.94147v
7
+ ··· + 5.63826v + 2.00702
a
12
=
0.920896v
8
+ 2.25955v
7
+ ··· + 4.52404v + 1.68885
2.14408v
8
+ 5.73234v
7
+ ··· + 5.36583v + 5.35212
a
2
=
−0.759010v
8
− 2.11631v
7
+ ··· + 0.101179v −1.86604
0.929844v
8
+ 2.02935v
7
+ ··· + 6.16138v + 0.676478
a
1
=
1.45213v
8
+ 3.82515v
7
+ ··· + 3.73944v + 3.14098
1.45213v
8
+ 3.82515v
7
+ ··· + 3.73944v + 4.14098
a
10
=
−0.531232v
8
− 1.56560v
7
+ ··· + 0.784597v −1.45213
0.691947v
8
+ 1.90718v
7
+ ··· + 1.62639v + 1.21114
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
38011
11959
v
8
−
103132
11959
v
7
+
110061
11959
v
6
−
250712
11959
v
5
−
892353
11959
v
4
−
104528
11959
v
3
+
444297
11959
v
2
−
43711
11959
v−
188057
11959
16
(iv) u-Polynomials at the component
17
Crossings u-Polynomials at each crossing
c
1
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
2
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
3
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
4
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
5
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
6
u
9
c
7
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
8
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
9
(u − 1)
9
c
10
u
9
− 3u
8
+ 3u
7
+ 2u
6
+ u
5
+ 9u
4
+ 3u
3
+ 2u + 1
c
11
u
9
− 2u
8
+ 5u
7
− 22u
6
+ 52u
5
− 63u
4
+ 41u
3
− 10u
2
− 2u + 1
c
12
(u + 1)
9
18
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
2
, c
4
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
3
, c
7
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
5
, c
8
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
6
y
9
c
9
, c
12
(y −1)
9
c
10
y
9
− 3y
8
+ 23y
7
+ 62y
6
− 13y
5
− 57y
4
+ 9y
3
− 6y
2
+ 4y −1
c
11
y
9
+ 6y
8
+ ··· + 24y −1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.022450 + 0.246780I
a = 0
b = −0.628449 − 0.875112I
−2.26187 − 2.45442I −8.53903 + 2.82066I
v = −1.022450 − 0.246780I
a = 0
b = −0.628449 + 0.875112I
−2.26187 + 2.45442I −8.53903 − 2.82066I
v = 0.483566 + 0.305056I
a = 0
b = −0.140343 − 0.966856I
0.13850 − 2.09337I −6.02684 + 1.69698I
v = 0.483566 − 0.305056I
a = 0
b = −0.140343 + 0.966856I
0.13850 + 2.09337I −6.02684 − 1.69698I
v = −0.411691 + 0.129409I
a = 0
b = 0.728966 − 0.986295I
−5.24306 + 7.08493I −9.02021 − 2.94778I
v = −0.411691 − 0.129409I
a = 0
b = 0.728966 + 0.986295I
−5.24306 − 7.08493I −9.02021 + 2.94778I
v = 1.23246 + 1.62704I
a = 0
b = 0.796005 − 0.733148I
−6.01628 − 1.33617I −16.4774 + 4.4812I
v = 1.23246 − 1.62704I
a = 0
b = 0.796005 + 0.733148I
−6.01628 + 1.33617I −16.4774 − 4.4812I
v = −3.56378
a = 0
b = −0.512358
−2.84338 −3.87310
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
9
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
18
− 10u
17
+ ··· + 18u + 1)(u
18
+ 11u
17
+ ··· + 3u + 1)
c
2
, c
9
(u − 1)
9
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
18
− 7u
17
+ ··· − u + 1)(u
18
− 4u
17
+ ··· − 9u
2
+ 1)
c
3
, c
6
u
9
(u
9
+ u
8
+ ··· + u − 1)(u
18
+ u
17
+ ··· + u − 1)
· (u
18
+ u
17
+ ··· + 1024u + 512)
c
4
, c
12
(u + 1)
9
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
18
− 7u
17
+ ··· − u + 1)(u
18
− 4u
17
+ ··· − 9u
2
+ 1)
c
5
(u
9
+ u
8
+ 4u
7
+ 3u
6
+ 5u
5
+ 3u
4
− 3u − 1)
2
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
2
· (u
18
+ u
17
+ ··· + 3u − 1)
c
7
u
9
(u
9
− u
8
+ ··· + u + 1)(u
18
+ u
17
+ ··· + u − 1)
· (u
18
+ u
17
+ ··· + 1024u + 512)
c
8
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
2
· ((u
9
+ u
8
+ ··· − 3u − 1)
2
)(u
18
+ u
17
+ ··· + 3u − 1)
c
10
(u
9
− 3u
8
+ 3u
7
+ 2u
6
+ u
5
+ 9u
4
+ 3u
3
+ 2u + 1)
· (u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
18
− 3u
17
+ ··· + 517u − 1)(u
18
+ 4u
17
+ ··· + 1179u − 199)
c
11
(u
9
− 2u
8
+ 5u
7
− 22u
6
+ 52u
5
− 63u
4
+ 41u
3
− 10u
2
− 2u + 1)
· (u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
18
− 5u
17
+ ··· + 77u − 23)(u
18
− 3u
17
+ ··· + 3241u + 1303)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
9
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
18
+ 38y
17
+ ··· − 206y + 1)(y
18
+ 41y
17
+ ··· − 47y + 1)
c
2
, c
4
, c
9
c
12
(y −1)
9
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
18
− 11y
17
+ ··· − 3y + 1)(y
18
+ 10y
17
+ ··· − 18y + 1)
c
3
, c
6
, c
7
y
9
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
18
+ 21y
17
+ ··· − 7y + 1)(y
18
+ 39y
17
+ ··· − 262144y + 262144)
c
5
, c
8
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ y
5
− 31y
4
− 24y
3
+ 6y
2
+ 9y −1)
2
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
2
· (y
18
+ 13y
17
+ ··· − 43y + 1)
c
10
(y
9
− 3y
8
+ 23y
7
+ 62y
6
− 13y
5
− 57y
4
+ 9y
3
− 6y
2
+ 4y −1)
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
18
+ 29y
17
+ ··· − 268915y + 1)
· (y
18
+ 40y
17
+ ··· − 5352529y + 39601)
c
11
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
9
+ 6y
8
+ ··· + 24y −1)(y
18
+ y
17
+ ··· − 5331y + 529)
· (y
18
+ 33y
17
+ ··· − 7027677y + 1697809)
23
