12a
0908
(K12a
0908
)
A knot diagram
1
Linearized knot diagam
4 6 8 1 12 11 10 5 2 7 3 9
Solving Sequence
6,11 3,7
12 2 5 10 8 4 1 9
c
6
c
11
c
2
c
5
c
10
c
7
c
3
c
1
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.64139 × 10
24
u
52
− 1.07961 × 10
26
u
51
+ ··· + 7.39787 × 10
23
b + 6.82500 × 10
25
,
− 3.41250 × 10
25
u
52
− 4.26342 × 10
26
u
51
+ ··· + 1.47957 × 10
24
a + 2.88944 × 10
26
,
u
53
+ 13u
52
+ ··· − 18u − 4i
I
u
2
= h56634753u
22
a
3
− 240804262u
22
a
2
+ ··· − 330550633a − 132611191,
− u
22
a
3
+ 5u
22
a
2
+ ··· − 4a + 51, u
23
− 5u
22
+ ··· − 6u
2
+ 1i
I
u
3
= h59u
27
− 471u
26
+ ··· + 47b − 50, 50u
27
− 341u
26
+ ··· + 47a + 58, u
28
− 8u
27
+ ··· − 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 173 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−8.64 × 10
24
u
52
− 1.08 × 10
26
u
51
+ · · · + 7.40 × 10
23
b + 6.83 ×
10
25
, −3.41 × 10
25
u
52
− 4.26 × 10
26
u
51
+ · · · + 1.48 × 10
24
a + 2.89 ×
10
26
, u
53
+ 13u
52
+ · · · − 18u − 4i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
23.0641u
52
+ 288.152u
51
+ ··· − 461.727u − 195.289
11.6809u
52
+ 145.935u
51
+ ··· − 219.864u − 92.2563
a
7
=
1
u
2
a
12
=
34.8240u
52
+ 435.869u
51
+ ··· − 659.197u − 297.311
16.8427u
52
+ 210.735u
51
+ ··· − 328.520u − 139.296
a
2
=
11.3832u
52
+ 142.217u
51
+ ··· − 241.863u − 103.033
11.6809u
52
+ 145.935u
51
+ ··· − 219.864u − 92.2563
a
5
=
−38.2045u
52
− 480.262u
51
+ ··· + 774.344u + 369.617
−24.6163u
52
− 310.110u
51
+ ··· + 482.937u + 220.189
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
21.0832u
52
+ 263.927u
51
+ ··· − 431.740u − 179.708
9.66738u
52
+ 121.370u
51
+ ··· − 192.750u − 83.0710
a
1
=
40.8118u
52
+ 510.563u
51
+ ··· − 813.034u − 355.160
25.5389u
52
+ 319.906u
51
+ ··· − 495.955u − 211.836
a
9
=
3.42379u
52
+ 43.8595u
51
+ ··· − 53.5420u − 34.9635
1.13831u
52
+ 14.3096u
51
+ ··· − 27.9059u − 18.2484
(ii) Obstruction class = −1
(iii) Cusp Shapes =
7813885398705379548002022
369893658631687521362639
u
52
+
97738403535384698831973970
369893658631687521362639
u
51
+ ··· −
144011829016585325244113120
369893658631687521362639
u −
67086585797972419521829478
369893658631687521362639
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
53
− 21u
52
+ ··· − 3256u + 192
c
2
, c
11
u
53
− 3u
52
+ ··· + 7u + 1
c
3
, c
9
u
53
− u
52
+ ··· − 12u + 1
c
5
u
53
− 38u
52
+ ··· − 150994944u + 8388608
c
6
, c
7
, c
10
u
53
− 13u
52
+ ··· − 18u + 4
c
8
, c
12
u
53
+ u
52
+ ··· + 18u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
53
+ 39y
52
+ ··· + 230080y −36864
c
2
, c
11
y
53
− 25y
52
+ ··· − 89y −1
c
3
, c
9
y
53
− 5y
52
+ ··· + 10y −1
c
5
y
53
+ 16y
52
+ ··· + 140737488355328y −70368744177664
c
6
, c
7
, c
10
y
53
+ 51y
52
+ ··· + 764y −16
c
8
, c
12
y
53
+ 17y
52
+ ··· − 36y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.705381 + 0.706977I
a = 0.940947 + 0.011228I
b = 0.671664 − 0.657308I
−3.12391 − 4.65185I 0
u = −0.705381 − 0.706977I
a = 0.940947 − 0.011228I
b = 0.671664 + 0.657308I
−3.12391 + 4.65185I 0
u = −0.846780 + 0.538162I
a = −0.299959 − 1.372480I
b = −0.992613 − 1.000760I
−0.0493 + 15.5803I 0
u = −0.846780 − 0.538162I
a = −0.299959 + 1.372480I
b = −0.992613 + 1.000760I
−0.0493 − 15.5803I 0
u = −0.921335 + 0.403223I
a = 0.731872 + 0.584881I
b = 0.910136 + 0.243764I
4.18006 + 7.18781I 0
u = −0.921335 − 0.403223I
a = 0.731872 − 0.584881I
b = 0.910136 − 0.243764I
4.18006 − 7.18781I 0
u = −0.537871 + 0.784035I
a = 0.278841 + 0.943890I
b = 0.890023 + 0.289070I
5.74699 − 1.95135I 0
u = −0.537871 − 0.784035I
a = 0.278841 − 0.943890I
b = 0.890023 − 0.289070I
5.74699 + 1.95135I 0
u = −0.795408 + 0.442380I
a = 0.43381 + 1.47445I
b = 0.997322 + 0.980880I
−3.88201 + 9.72876I 0
u = −0.795408 − 0.442380I
a = 0.43381 − 1.47445I
b = 0.997322 − 0.980880I
−3.88201 − 9.72876I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.884649 + 0.636725I
a = −0.861899 + 0.160096I
b = −0.660540 + 0.690422I
0.16418 − 9.89272I 0
u = −0.884649 − 0.636725I
a = −0.861899 − 0.160096I
b = −0.660540 − 0.690422I
0.16418 + 9.89272I 0
u = 1.166540 + 0.234114I
a = −0.0096401 + 0.0930633I
b = 0.0330331 − 0.1063050I
−1.01570 − 1.08166I 0
u = 1.166540 − 0.234114I
a = −0.0096401 − 0.0930633I
b = 0.0330331 + 0.1063050I
−1.01570 + 1.08166I 0
u = 0.132150 + 1.227450I
a = −0.614846 + 0.058087I
b = 0.152551 + 0.747014I
2.82416 − 2.70237I 0
u = 0.132150 − 1.227450I
a = −0.614846 − 0.058087I
b = 0.152551 − 0.747014I
2.82416 + 2.70237I 0
u = −0.056333 + 1.254440I
a = −0.168258 + 0.728529I
b = 0.904418 + 0.252110I
5.40952 − 2.59372I 0
u = −0.056333 − 1.254440I
a = −0.168258 − 0.728529I
b = 0.904418 − 0.252110I
5.40952 + 2.59372I 0
u = −0.586615 + 0.265441I
a = −1.03974 − 1.14731I
b = −0.914471 − 0.397042I
1.49476 + 1.54837I 1.89519 − 3.54470I
u = −0.586615 − 0.265441I
a = −1.03974 + 1.14731I
b = −0.914471 + 0.397042I
1.49476 − 1.54837I 1.89519 + 3.54470I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.521207 + 0.343252I
a = −0.40504 − 2.22925I
b = −0.976303 − 1.022870I
1.59267 + 3.97075I 8.04998 − 10.15076I
u = −0.521207 − 0.343252I
a = −0.40504 + 2.22925I
b = −0.976303 + 1.022870I
1.59267 − 3.97075I 8.04998 + 10.15076I
u = −0.041141 + 1.384110I
a = 0.621792 − 0.871465I
b = −1.18062 − 0.89648I
5.84394 + 2.71782I 0
u = −0.041141 − 1.384110I
a = 0.621792 + 0.871465I
b = −1.18062 + 0.89648I
5.84394 − 2.71782I 0
u = 0.04414 + 1.42109I
a = −0.703415 + 0.845262I
b = 1.23224 + 0.96230I
6.72507 + 1.35266I 0
u = 0.04414 − 1.42109I
a = −0.703415 − 0.845262I
b = 1.23224 − 0.96230I
6.72507 − 1.35266I 0
u = −0.36334 + 1.37838I
a = −0.221898 − 0.637733I
b = −0.959664 + 0.074146I
5.57512 + 2.07297I 0
u = −0.36334 − 1.37838I
a = −0.221898 + 0.637733I
b = −0.959664 − 0.074146I
5.57512 − 2.07297I 0
u = 0.08011 + 1.44842I
a = 0.388708 − 0.632540I
b = −0.947321 − 0.512342I
7.93090 − 3.01833I 0
u = 0.08011 − 1.44842I
a = 0.388708 + 0.632540I
b = −0.947321 + 0.512342I
7.93090 + 3.01833I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.19568 + 1.44259I
a = 0.702045 − 1.064010I
b = −1.39755 − 1.22097I
7.37959 + 6.62771I 0
u = −0.19568 − 1.44259I
a = 0.702045 + 1.064010I
b = −1.39755 + 1.22097I
7.37959 − 6.62771I 0
u = 0.536362
a = −0.412615
b = 0.221311
−0.915843 −11.2030
u = −0.24997 + 1.44388I
a = 0.287466 − 1.002230I
b = −1.37525 − 0.66560I
7.08466 + 4.78253I 0
u = −0.24997 − 1.44388I
a = 0.287466 + 1.002230I
b = −1.37525 + 0.66560I
7.08466 − 4.78253I 0
u = −0.04329 + 1.49707I
a = −0.162493 + 0.458582I
b = 0.679495 + 0.263116I
4.90382 − 2.29725I 0
u = −0.04329 − 1.49707I
a = −0.162493 − 0.458582I
b = 0.679495 − 0.263116I
4.90382 + 2.29725I 0
u = −0.28675 + 1.49647I
a = −0.546695 + 1.000300I
b = 1.34014 + 1.10495I
2.39051 + 13.65630I 0
u = −0.28675 − 1.49647I
a = −0.546695 − 1.000300I
b = 1.34014 − 1.10495I
2.39051 − 13.65630I 0
u = −0.473148 + 0.012404I
a = −1.73924 − 1.18472I
b = −0.837614 − 0.538973I
1.37401 + 1.60518I 0.98727 − 1.76402I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.473148 − 0.012404I
a = −1.73924 + 1.18472I
b = −0.837614 + 0.538973I
1.37401 − 1.60518I 0.98727 + 1.76402I
u = −0.33123 + 1.51592I
a = −0.164815 + 0.861559I
b = 1.251470 + 0.535219I
10.4327 + 11.7049I 0
u = −0.33123 − 1.51592I
a = −0.164815 − 0.861559I
b = 1.251470 − 0.535219I
10.4327 − 11.7049I 0
u = −0.15501 + 1.54465I
a = −0.350654 + 0.808638I
b = 1.194710 + 0.666986I
13.27140 + 0.47929I 0
u = −0.15501 − 1.54465I
a = −0.350654 − 0.808638I
b = 1.194710 − 0.666986I
13.27140 − 0.47929I 0
u = −0.30052 + 1.54210I
a = 0.534893 − 0.962600I
b = −1.32368 − 1.11414I
6.7038 + 19.7778I 0
u = −0.30052 − 1.54210I
a = 0.534893 + 0.962600I
b = −1.32368 + 1.11414I
6.7038 − 19.7778I 0
u = 0.124193 + 0.376004I
a = 0.04375 − 1.87558I
b = −0.710661 + 0.216483I
1.99587 − 1.98789I 0.55073 + 4.64963I
u = 0.124193 − 0.376004I
a = 0.04375 + 1.87558I
b = −0.710661 − 0.216483I
1.99587 + 1.98789I 0.55073 − 4.64963I
u = −0.16302 + 1.72258I
a = 0.012987 − 0.317247I
b = −0.544367 − 0.074090I
8.35128 − 5.41960I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.16302 − 1.72258I
a = 0.012987 + 0.317247I
b = −0.544367 + 0.074090I
8.35128 + 5.41960I 0
u = 0.143374 + 0.069582I
a = −6.73222 − 0.17863I
b = 0.952798 + 0.494051I
1.60714 + 1.98817I 0.01145 − 3.39198I
u = 0.143374 − 0.069582I
a = −6.73222 + 0.17863I
b = 0.952798 − 0.494051I
1.60714 − 1.98817I 0.01145 + 3.39198I
10
II. I
u
2
= h5.66 × 10
7
a
3
u
22
− 2.41 × 10
8
a
2
u
22
+ · · · − 3.31 × 10
8
a − 1.33 ×
10
8
, −u
22
a
3
+ 5u
22
a
2
+ · · · − 4a + 51, u
23
− 5u
22
+ · · · − 6u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
a
−0.100953a
3
u
22
+ 0.429241a
2
u
22
+ ··· + 0.589216a + 0.236383
a
7
=
1
u
2
a
12
=
a
2
u
0.118983a
3
u
22
+ 0.100953a
2
u
22
+ ··· − 0.597423a + 0.441808
a
2
=
0.100953a
3
u
22
− 0.429241a
2
u
22
+ ··· + 0.410784a − 0.236383
−0.100953a
3
u
22
+ 0.429241a
2
u
22
+ ··· + 0.589216a + 0.236383
a
5
=
0.100514a
3
u
22
− 0.245183a
2
u
22
+ ··· + 0.346239a + 0.178354
0.118983a
3
u
22
+ 0.100953a
2
u
22
+ ··· − 0.597423a − 0.558192
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
0.216382a
3
u
22
+ 0.0434821a
2
u
22
+ ··· + 0.114127a − 0.297301
−0.171643a
3
u
22
− 0.00407502a
2
u
22
+ ··· + 0.141712a − 0.0148777
a
1
=
−0.155470a
3
u
22
− 0.104587a
2
u
22
+ ··· + 0.455317a + 0.456813
0.295891a
3
u
22
− 0.206190a
2
u
22
+ ··· + 1.13295a − 0.333330
a
9
=
0.155444a
3
u
22
+ 0.0144758a
2
u
22
+ ··· + 0.745033a − 0.122273
0.126936a
3
u
22
− 0.0925502a
2
u
22
+ ··· + 0.139554a − 0.879438
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
266998012
561000751
u
22
a
3
−
226539012
561000751
u
22
a
2
+ ···+
1340618208
561000751
a −
11089432646
561000751
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
23
+ 7u
22
+ ··· + 4u + 1)
4
c
2
, c
11
u
92
− 7u
91
+ ··· + 206u + 37
c
3
, c
9
u
92
+ u
91
+ ··· − 141040u + 27037
c
5
(u
2
+ u + 1)
46
c
6
, c
7
, c
10
(u
23
+ 5u
22
+ ··· + 6u
2
− 1)
4
c
8
, c
12
u
92
− u
91
+ ··· + 2u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
23
+ 15y
22
+ ··· − 12y −1)
4
c
2
, c
11
y
92
+ 15y
91
+ ··· + 12324y + 1369
c
3
, c
9
y
92
− 9y
91
+ ··· − 4059414400y + 730999369
c
5
(y
2
+ y + 1)
46
c
6
, c
7
, c
10
(y
23
+ 23y
22
+ ··· + 12y −1)
4
c
8
, c
12
y
92
− 21y
91
+ ··· − 8y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.816909 + 0.632975I
a = −0.132905 − 1.127110I
b = 0.955647 − 0.890603I
−1.16253 − 5.71950I −10.3146 + 14.3306I
u = 0.816909 + 0.632975I
a = 0.656732 + 0.473901I
b = 0.160095 + 0.441907I
−1.16253 − 1.65973I −10.31455 + 7.40239I
u = 0.816909 + 0.632975I
a = −0.203134 + 1.247610I
b = −0.604864 + 1.004880I
−1.16253 − 5.71950I −10.3146 + 14.3306I
u = 0.816909 + 0.632975I
a = −0.384363 − 0.243129I
b = −0.236523 − 0.802829I
−1.16253 − 1.65973I −10.31455 + 7.40239I
u = 0.816909 − 0.632975I
a = −0.132905 + 1.127110I
b = 0.955647 + 0.890603I
−1.16253 + 5.71950I −10.3146 − 14.3306I
u = 0.816909 − 0.632975I
a = 0.656732 − 0.473901I
b = 0.160095 − 0.441907I
−1.16253 + 1.65973I −10.31455 − 7.40239I
u = 0.816909 − 0.632975I
a = −0.203134 − 1.247610I
b = −0.604864 − 1.004880I
−1.16253 + 5.71950I −10.3146 − 14.3306I
u = 0.816909 − 0.632975I
a = −0.384363 + 0.243129I
b = −0.236523 + 0.802829I
−1.16253 + 1.65973I −10.31455 − 7.40239I
u = 0.801341 + 0.397729I
a = −0.918744 − 0.455551I
b = −0.207708 − 0.570360I
−1.84456 + 0.33069I −13.29306 − 2.86632I
u = 0.801341 + 0.397729I
a = −0.173679 + 1.071300I
b = −0.877581 + 1.010140I
−1.84456 − 3.72908I −13.29306 + 4.06189I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.801341 + 0.397729I
a = 0.491411 + 0.467855I
b = 0.555041 + 0.730463I
−1.84456 + 0.33069I −13.29306 − 2.86632I
u = 0.801341 + 0.397729I
a = 0.37669 − 1.44753I
b = 0.565262 − 0.789396I
−1.84456 − 3.72908I −13.29306 + 4.06189I
u = 0.801341 − 0.397729I
a = −0.918744 + 0.455551I
b = −0.207708 + 0.570360I
−1.84456 − 0.33069I −13.29306 + 2.86632I
u = 0.801341 − 0.397729I
a = −0.173679 − 1.071300I
b = −0.877581 − 1.010140I
−1.84456 + 3.72908I −13.29306 − 4.06189I
u = 0.801341 − 0.397729I
a = 0.491411 − 0.467855I
b = 0.555041 − 0.730463I
−1.84456 − 0.33069I −13.29306 + 2.86632I
u = 0.801341 − 0.397729I
a = 0.37669 + 1.44753I
b = 0.565262 + 0.789396I
−1.84456 + 3.72908I −13.29306 − 4.06189I
u = 0.183062 + 0.717931I
a = −0.573742 − 1.227590I
b = 0.150561 + 0.314245I
2.40316 − 2.52933I −0.58287 + 2.63457I
u = 0.183062 + 0.717931I
a = −0.461198 + 0.092116I
b = −0.776293 + 0.636632I
2.40316 − 2.52933I −0.58287 + 2.63457I
u = 0.183062 + 0.717931I
a = 0.01885 − 1.53818I
b = 0.59714 − 1.28539I
2.40316 − 6.58910I −0.58287 + 9.56277I
u = 0.183062 + 0.717931I
a = 1.48197 + 1.20963I
b = −1.107760 + 0.268048I
2.40316 − 6.58910I −0.58287 + 9.56277I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.183062 − 0.717931I
a = −0.573742 + 1.227590I
b = 0.150561 − 0.314245I
2.40316 + 2.52933I −0.58287 − 2.63457I
u = 0.183062 − 0.717931I
a = −0.461198 − 0.092116I
b = −0.776293 − 0.636632I
2.40316 + 2.52933I −0.58287 − 2.63457I
u = 0.183062 − 0.717931I
a = 0.01885 + 1.53818I
b = 0.59714 + 1.28539I
2.40316 + 6.58910I −0.58287 − 9.56277I
u = 0.183062 − 0.717931I
a = 1.48197 − 1.20963I
b = −1.107760 − 0.268048I
2.40316 + 6.58910I −0.58287 − 9.56277I
u = 0.111985 + 1.275990I
a = −0.924330 − 0.026533I
b = 0.326257 + 0.347377I
2.88331 − 2.69431I −6.87243 + 2.20033I
u = 0.111985 + 1.275990I
a = 0.714488 + 0.420155I
b = −1.97889 + 0.53671I
2.88331 − 6.75407I −6.87243 + 9.12853I
u = 0.111985 + 1.275990I
a = −0.28234 − 1.57564I
b = 0.456102 − 0.958731I
2.88331 − 6.75407I −6.87243 + 9.12853I
u = 0.111985 + 1.275990I
a = −0.292428 + 0.230025I
b = 0.069655 + 1.182410I
2.88331 − 2.69431I −6.87243 + 2.20033I
u = 0.111985 − 1.275990I
a = −0.924330 + 0.026533I
b = 0.326257 − 0.347377I
2.88331 + 2.69431I −6.87243 − 2.20033I
u = 0.111985 − 1.275990I
a = 0.714488 − 0.420155I
b = −1.97889 − 0.53671I
2.88331 + 6.75407I −6.87243 − 9.12853I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.111985 − 1.275990I
a = −0.28234 + 1.57564I
b = 0.456102 + 0.958731I
2.88331 + 6.75407I −6.87243 − 9.12853I
u = 0.111985 − 1.275990I
a = −0.292428 − 0.230025I
b = 0.069655 − 1.182410I
2.88331 + 2.69431I −6.87243 − 2.20033I
u = 0.605875 + 0.307254I
a = 0.657522 + 0.536626I
b = 0.811755 + 0.560398I
−1.67096 + 0.25033I −11.09313 + 1.32660I
u = 0.605875 + 0.307254I
a = −0.377921 + 1.171620I
b = −0.906876 + 1.077900I
−1.67096 − 3.80943I −11.09313 + 8.25480I
u = 0.605875 + 0.307254I
a = −1.43883 − 0.19527I
b = −0.233496 − 0.527155I
−1.67096 + 0.25033I −11.09313 + 1.32660I
u = 0.605875 + 0.307254I
a = 0.47296 − 2.01893I
b = 0.588957 − 0.593734I
−1.67096 − 3.80943I −11.09313 + 8.25480I
u = 0.605875 − 0.307254I
a = 0.657522 − 0.536626I
b = 0.811755 − 0.560398I
−1.67096 − 0.25033I −11.09313 − 1.32660I
u = 0.605875 − 0.307254I
a = −0.377921 − 1.171620I
b = −0.906876 − 1.077900I
−1.67096 + 3.80943I −11.09313 − 8.25480I
u = 0.605875 − 0.307254I
a = −1.43883 + 0.19527I
b = −0.233496 + 0.527155I
−1.67096 − 0.25033I −11.09313 − 1.32660I
u = 0.605875 − 0.307254I
a = 0.47296 + 2.01893I
b = 0.588957 + 0.593734I
−1.67096 + 3.80943I −11.09313 − 8.25480I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.052152 + 1.332210I
a = −0.801782 + 0.035405I
b = 2.05182 + 0.52630I
0.292728 − 0.708872I −10.99704 − 0.88326I
u = −0.052152 + 1.332210I
a = −0.33425 + 1.55325I
b = 0.005352 + 1.069990I
0.292728 − 0.708872I −10.99704 − 0.88326I
u = −0.052152 + 1.332210I
a = 0.121716 − 0.181614I
b = 0.58944 − 2.40808I
0.29273 + 3.35089I −10.99704 − 7.81146I
u = −0.052152 + 1.332210I
a = 1.82212 + 0.37112I
b = −0.235600 − 0.171622I
0.29273 + 3.35089I −10.99704 − 7.81146I
u = −0.052152 − 1.332210I
a = −0.801782 − 0.035405I
b = 2.05182 − 0.52630I
0.292728 + 0.708872I −10.99704 + 0.88326I
u = −0.052152 − 1.332210I
a = −0.33425 − 1.55325I
b = 0.005352 − 1.069990I
0.292728 + 0.708872I −10.99704 + 0.88326I
u = −0.052152 − 1.332210I
a = 0.121716 + 0.181614I
b = 0.58944 + 2.40808I
0.29273 − 3.35089I −10.99704 + 7.81146I
u = −0.052152 − 1.332210I
a = 1.82212 − 0.37112I
b = −0.235600 + 0.171622I
0.29273 − 3.35089I −10.99704 + 7.81146I
u = −0.096870 + 1.402080I
a = 0.334278 − 0.927721I
b = −0.26543 − 1.67133I
5.35246 + 5.29024I −3.16679 − 5.90545I
u = −0.096870 + 1.402080I
a = 1.173360 − 0.270378I
b = −1.268360 − 0.558555I
5.35246 + 5.29024I −3.16679 − 5.90545I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.096870 + 1.402080I
a = −0.045350 + 0.201337I
b = −1.44214 + 2.36016I
5.35246 + 9.35001I −3.16679 − 12.83365I
u = −0.096870 + 1.402080I
a = −1.74605 − 0.90794I
b = 0.277898 + 0.083088I
5.35246 + 9.35001I −3.16679 − 12.83365I
u = −0.096870 − 1.402080I
a = 0.334278 + 0.927721I
b = −0.26543 + 1.67133I
5.35246 − 5.29024I −3.16679 + 5.90545I
u = −0.096870 − 1.402080I
a = 1.173360 + 0.270378I
b = −1.268360 + 0.558555I
5.35246 − 5.29024I −3.16679 + 5.90545I
u = −0.096870 − 1.402080I
a = −0.045350 − 0.201337I
b = −1.44214 − 2.36016I
5.35246 − 9.35001I −3.16679 + 12.83365I
u = −0.096870 − 1.402080I
a = −1.74605 + 0.90794I
b = 0.277898 − 0.083088I
5.35246 − 9.35001I −3.16679 + 12.83365I
u = 0.26164 + 1.48846I
a = 0.541804 + 0.713453I
b = −1.39530 + 1.05281I
4.27121 − 7.43348I −6.73363 + 5.21535I
u = 0.26164 + 1.48846I
a = −0.526279 − 1.029920I
b = 0.920184 − 0.993121I
4.27121 − 7.43348I −6.73363 + 5.21535I
u = 0.26164 + 1.48846I
a = 0.071703 + 0.543174I
b = −0.500478 + 0.630455I
4.27121 − 3.37372I −6.73363 − 1.71285I
u = 0.26164 + 1.48846I
a = −0.353535 − 0.398385I
b = 0.789730 − 0.248843I
4.27121 − 3.37372I −6.73363 − 1.71285I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.26164 − 1.48846I
a = 0.541804 − 0.713453I
b = −1.39530 − 1.05281I
4.27121 + 7.43348I −6.73363 − 5.21535I
u = 0.26164 − 1.48846I
a = −0.526279 + 1.029920I
b = 0.920184 + 0.993121I
4.27121 + 7.43348I −6.73363 − 5.21535I
u = 0.26164 − 1.48846I
a = 0.071703 − 0.543174I
b = −0.500478 − 0.630455I
4.27121 + 3.37372I −6.73363 + 1.71285I
u = 0.26164 − 1.48846I
a = −0.353535 + 0.398385I
b = 0.789730 + 0.248843I
4.27121 + 3.37372I −6.73363 + 1.71285I
u = 0.11855 + 1.54039I
a = −0.281597 − 1.006820I
b = 0.364867 − 0.311396I
9.79790 − 3.98573I 3.34351 + 1.99239I
u = 0.11855 + 1.54039I
a = −0.313354 − 0.661484I
b = 1.34877 − 1.68020I
9.79790 − 8.04549I 3.34351 + 8.92059I
u = 0.11855 + 1.54039I
a = 1.017350 + 0.953900I
b = −0.981796 + 0.561108I
9.79790 − 8.04549I 3.34351 + 8.92059I
u = 0.11855 + 1.54039I
a = 0.182841 + 0.250938I
b = −1.51751 + 0.55313I
9.79790 − 3.98573I 3.34351 + 1.99239I
u = 0.11855 − 1.54039I
a = −0.281597 + 1.006820I
b = 0.364867 + 0.311396I
9.79790 + 3.98573I 3.34351 − 1.99239I
u = 0.11855 − 1.54039I
a = −0.313354 + 0.661484I
b = 1.34877 + 1.68020I
9.79790 + 8.04549I 3.34351 − 8.92059I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.11855 − 1.54039I
a = 1.017350 − 0.953900I
b = −0.981796 − 0.561108I
9.79790 + 8.04549I 3.34351 − 8.92059I
u = 0.11855 − 1.54039I
a = 0.182841 − 0.250938I
b = −1.51751 − 0.55313I
9.79790 + 3.98573I 3.34351 − 1.99239I
u = 0.29767 + 1.56676I
a = −0.647721 − 0.738613I
b = 1.30323 − 0.85409I
5.98402 − 9.89332I −2.38194 + 13.91001I
u = 0.29767 + 1.56676I
a = 0.373610 + 0.902781I
b = −0.96442 + 1.23469I
5.98402 − 9.89332I −2.38194 + 13.91001I
u = 0.29767 + 1.56676I
a = 0.399520 + 0.556339I
b = −0.592520 + 0.307844I
5.98402 − 5.83356I −2.38194 + 6.98181I
u = 0.29767 + 1.56676I
a = −0.120291 − 0.401036I
b = 0.752725 − 0.791559I
5.98402 − 5.83356I −2.38194 + 6.98181I
u = 0.29767 − 1.56676I
a = −0.647721 + 0.738613I
b = 1.30323 + 0.85409I
5.98402 + 9.89332I −2.38194 − 13.91001I
u = 0.29767 − 1.56676I
a = 0.373610 − 0.902781I
b = −0.96442 − 1.23469I
5.98402 + 9.89332I −2.38194 − 13.91001I
u = 0.29767 − 1.56676I
a = 0.399520 − 0.556339I
b = −0.592520 − 0.307844I
5.98402 + 5.83356I −2.38194 − 6.98181I
u = 0.29767 − 1.56676I
a = −0.120291 + 0.401036I
b = 0.752725 + 0.791559I
5.98402 + 5.83356I −2.38194 − 6.98181I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.370862 + 0.160193I
a = −0.37927 + 1.48446I
b = −1.34705 + 1.21058I
0.28220 + 7.76558I −12.5426 − 14.9198I
u = −0.370862 + 0.160193I
a = 0.78273 − 2.65115I
b = −0.818415 − 0.884781I
0.28220 + 3.70582I −12.5426 − 7.9916I
u = −0.370862 + 0.160193I
a = −0.99132 − 2.81394I
b = −0.134412 − 1.108600I
0.28220 + 3.70582I −12.5426 − 7.9916I
u = −0.370862 + 0.160193I
a = −4.24934 + 1.42873I
b = 0.097142 + 0.611286I
0.28220 + 7.76558I −12.5426 − 14.9198I
u = −0.370862 − 0.160193I
a = −0.37927 − 1.48446I
b = −1.34705 − 1.21058I
0.28220 − 7.76558I −12.5426 + 14.9198I
u = −0.370862 − 0.160193I
a = 0.78273 + 2.65115I
b = −0.818415 + 0.884781I
0.28220 − 3.70582I −12.5426 + 7.9916I
u = −0.370862 − 0.160193I
a = −0.99132 + 2.81394I
b = −0.134412 + 1.108600I
0.28220 − 3.70582I −12.5426 + 7.9916I
u = −0.370862 − 0.160193I
a = −4.24934 − 1.42873I
b = 0.097142 − 0.611286I
0.28220 − 7.76558I −12.5426 + 14.9198I
u = −0.354306
a = 0.17563 + 2.02911I
b = 1.09356 + 1.28296I
−3.82984 − 2.02988I −22.7310 + 3.4641I
u = −0.354306
a = 0.17563 − 2.02911I
b = 1.09356 − 1.28296I
−3.82984 + 2.02988I −22.7310 − 3.4641I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.354306
a = 3.08650 + 3.62106I
b = 0.062227 + 0.718925I
−3.82984 − 2.02988I −22.7310 + 3.4641I
u = −0.354306
a = 3.08650 − 3.62106I
b = 0.062227 − 0.718925I
−3.82984 + 2.02988I −22.7310 − 3.4641I
23
III. I
u
3
= h59u
27
− 471u
26
+ · · · + 47b − 50, 50u
27
− 341u
26
+ · · · + 47a +
58, u
28
− 8u
27
+ · · · − 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−1.06383u
27
+ 7.25532u
26
+ ··· − 3.34043u − 1.23404
−1.25532u
27
+ 10.0213u
26
+ ··· − 3.36170u + 1.06383
a
7
=
1
u
2
a
12
=
0.212766u
27
− 1.85106u
26
+ ··· + 0.468085u − 0.553191
−0.148936u
27
+ 1.59574u
26
+ ··· + 0.872340u − 0.212766
a
2
=
0.191489u
27
− 2.76596u
26
+ ··· + 0.0212766u − 2.29787
−1.25532u
27
+ 10.0213u
26
+ ··· − 3.36170u + 1.06383
a
5
=
0.595745u
27
− 5.38298u
26
+ ··· + 5.51064u − 2.14894
−0.212766u
27
+ 1.85106u
26
+ ··· − 2.46809u − 0.446809
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
−0.787234u
27
+ 4.14894u
26
+ ··· − 0.531915u − 1.55319
−1.51064u
27
+ 12.0426u
26
+ ··· − 3.72340u + 1.12766
a
1
=
0.0425532u
27
− 0.170213u
26
+ ··· + 3.89362u − 2.51064
−0.297872u
27
+ 2.19149u
26
+ ··· − 2.25532u + 0.574468
a
9
=
1.10638u
27
− 8.42553u
26
+ ··· − 2.76596u + 1.72340
0.191489u
27
− 1.76596u
26
+ ··· + 4.02128u − 1.29787
(ii) Obstruction class = 1
(iii) Cusp Shapes =
409
47
u
27
−
2952
47
u
26
+ ··· +
928
47
u −
631
47
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
28
− 10u
27
+ ··· − 87u + 13
c
2
, c
11
u
28
+ 3u
27
+ ··· + 2u + 1
c
3
, c
9
u
28
− u
27
+ ··· − 7u + 1
c
4
u
28
+ 10u
27
+ ··· + 87u + 13
c
5
u
28
− u
27
+ ··· + 6u + 1
c
6
, c
7
u
28
− 8u
27
+ ··· − 2u + 1
c
8
, c
12
u
28
− u
27
+ ··· + u + 1
c
10
u
28
+ 8u
27
+ ··· + 2u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
28
+ 24y
27
+ ··· + 3793y + 169
c
2
, c
11
y
28
+ 7y
27
+ ··· + 12y + 1
c
3
, c
9
y
28
− y
27
+ ··· − 7y + 1
c
5
y
28
+ 15y
27
+ ··· − 20y + 1
c
6
, c
7
, c
10
y
28
+ 28y
27
+ ··· + 8y + 1
c
8
, c
12
y
28
− 11y
27
+ ··· − 17y + 1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.826281 + 0.576167I
a = −0.075421 + 1.153680I
b = −0.727028 + 0.909805I
−1.00522 − 4.77212I −6.00000 + 5.13529I
u = 0.826281 − 0.576167I
a = −0.075421 − 1.153680I
b = −0.727028 − 0.909805I
−1.00522 + 4.77212I −6.00000 − 5.13529I
u = 1.055240 + 0.007074I
a = 0.262407 − 0.362782I
b = 0.279469 − 0.380966I
−1.17311 − 1.21773I −11.7683 + 18.4278I
u = 1.055240 − 0.007074I
a = 0.262407 + 0.362782I
b = 0.279469 + 0.380966I
−1.17311 + 1.21773I −11.7683 − 18.4278I
u = 1.033550 + 0.510555I
a = −0.372133 − 0.276260I
b = −0.243573 − 0.475523I
−1.26351 − 1.00699I −13.3094 − 10.7825I
u = 1.033550 − 0.510555I
a = −0.372133 + 0.276260I
b = −0.243573 + 0.475523I
−1.26351 + 1.00699I −13.3094 + 10.7825I
u = −0.027818 + 1.182340I
a = 0.854342 − 0.070049I
b = 0.059056 + 1.012070I
3.23180 + 3.06600I 5.06709 − 12.60017I
u = −0.027818 − 1.182340I
a = 0.854342 + 0.070049I
b = 0.059056 − 1.012070I
3.23180 − 3.06600I 5.06709 + 12.60017I
u = 0.139552 + 1.302460I
a = −0.646984 − 0.589290I
b = 0.677236 − 0.924903I
2.97091 − 4.72480I −6.00000 + 6.29565I
u = 0.139552 − 1.302460I
a = −0.646984 + 0.589290I
b = 0.677236 + 0.924903I
2.97091 + 4.72480I −6.00000 − 6.29565I
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.006578 + 1.336890I
a = 0.866683 + 0.633813I
b = −0.85304 + 1.15449I
0.59900 + 2.06815I −8.19665 − 3.62924I
u = −0.006578 − 1.336890I
a = 0.866683 − 0.633813I
b = −0.85304 − 1.15449I
0.59900 − 2.06815I −8.19665 + 3.62924I
u = −0.066422 + 1.387730I
a = −0.836610 − 0.634596I
b = 0.93622 − 1.11884I
5.24801 + 8.22321I −6.00000 − 4.19364I
u = −0.066422 − 1.387730I
a = −0.836610 + 0.634596I
b = 0.93622 + 1.11884I
5.24801 − 8.22321I −6.00000 + 4.19364I
u = 0.421190 + 0.370789I
a = −0.18726 − 2.30354I
b = 0.775254 − 1.039660I
1.09986 − 4.14329I −5.4583 + 13.1620I
u = 0.421190 − 0.370789I
a = −0.18726 + 2.30354I
b = 0.775254 + 1.039660I
1.09986 + 4.14329I −5.4583 − 13.1620I
u = 0.18349 + 1.45815I
a = −0.692963 − 0.960195I
b = 1.27296 − 1.18662I
7.08958 − 6.51889I 0
u = 0.18349 − 1.45815I
a = −0.692963 + 0.960195I
b = 1.27296 + 1.18662I
7.08958 + 6.51889I 0
u = 0.31048 + 1.53901I
a = −0.148210 − 0.503925I
b = 0.729529 − 0.384554I
4.77832 − 4.06764I 0
u = 0.31048 − 1.53901I
a = −0.148210 + 0.503925I
b = 0.729529 + 0.384554I
4.77832 + 4.06764I 0
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.29019 + 1.54957I
a = 0.513688 + 0.811901I
b = −1.10903 + 1.03160I
5.89872 − 8.87295I 0
u = 0.29019 − 1.54957I
a = 0.513688 − 0.811901I
b = −1.10903 − 1.03160I
5.89872 + 8.87295I 0
u = 0.06343 + 1.67014I
a = 0.277618 + 0.244945I
b = −0.391482 + 0.479199I
7.78404 − 5.94723I 0
u = 0.06343 − 1.67014I
a = 0.277618 − 0.244945I
b = −0.391482 − 0.479199I
7.78404 + 5.94723I 0
u = 0.008501 + 0.315744I
a = −2.52227 + 1.21558I
b = −0.405253 − 0.786056I
−3.12515 − 2.03402I −8.09076 + 3.19595I
u = 0.008501 − 0.315744I
a = −2.52227 − 1.21558I
b = −0.405253 + 0.786056I
−3.12515 + 2.03402I −8.09076 − 3.19595I
u = −0.231094 + 0.125953I
a = −0.29289 − 3.42985I
b = 0.499686 + 0.755725I
0.76542 − 7.25391I −3.00320 + 4.52417I
u = −0.231094 − 0.125953I
a = −0.29289 + 3.42985I
b = 0.499686 − 0.755725I
0.76542 + 7.25391I −3.00320 − 4.52417I
29
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
23
+ 7u
22
+ ··· + 4u + 1)
4
)(u
28
− 10u
27
+ ··· − 87u + 13)
· (u
53
− 21u
52
+ ··· − 3256u + 192)
c
2
, c
11
(u
28
+ 3u
27
+ ··· + 2u + 1)(u
53
− 3u
52
+ ··· + 7u + 1)
· (u
92
− 7u
91
+ ··· + 206u + 37)
c
3
, c
9
(u
28
− u
27
+ ··· − 7u + 1)(u
53
− u
52
+ ··· − 12u + 1)
· (u
92
+ u
91
+ ··· − 141040u + 27037)
c
4
((u
23
+ 7u
22
+ ··· + 4u + 1)
4
)(u
28
+ 10u
27
+ ··· + 87u + 13)
· (u
53
− 21u
52
+ ··· − 3256u + 192)
c
5
((u
2
+ u + 1)
46
)(u
28
− u
27
+ ··· + 6u + 1)
· (u
53
− 38u
52
+ ··· − 150994944u + 8388608)
c
6
, c
7
((u
23
+ 5u
22
+ ··· + 6u
2
− 1)
4
)(u
28
− 8u
27
+ ··· − 2u + 1)
· (u
53
− 13u
52
+ ··· − 18u + 4)
c
8
, c
12
(u
28
− u
27
+ ··· + u + 1)(u
53
+ u
52
+ ··· + 18u
2
+ 1)
· (u
92
− u
91
+ ··· + 2u + 1)
c
10
((u
23
+ 5u
22
+ ··· + 6u
2
− 1)
4
)(u
28
+ 8u
27
+ ··· + 2u + 1)
· (u
53
− 13u
52
+ ··· − 18u + 4)
30
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
23
+ 15y
22
+ ··· − 12y −1)
4
)(y
28
+ 24y
27
+ ··· + 3793y + 169)
· (y
53
+ 39y
52
+ ··· + 230080y −36864)
c
2
, c
11
(y
28
+ 7y
27
+ ··· + 12y + 1)(y
53
− 25y
52
+ ··· − 89y −1)
· (y
92
+ 15y
91
+ ··· + 12324y + 1369)
c
3
, c
9
(y
28
− y
27
+ ··· − 7y + 1)(y
53
− 5y
52
+ ··· + 10y −1)
· (y
92
− 9y
91
+ ··· − 4059414400y + 730999369)
c
5
((y
2
+ y + 1)
46
)(y
28
+ 15y
27
+ ··· − 20y + 1)
· (y
53
+ 16y
52
+ ··· + 140737488355328y −70368744177664)
c
6
, c
7
, c
10
((y
23
+ 23y
22
+ ··· + 12y −1)
4
)(y
28
+ 28y
27
+ ··· + 8y + 1)
· (y
53
+ 51y
52
+ ··· + 764y −16)
c
8
, c
12
(y
28
− 11y
27
+ ··· − 17y + 1)(y
53
+ 17y
52
+ ··· − 36y −1)
· (y
92
− 21y
91
+ ··· − 8y + 1)
31
