12a
0977
(K12a
0977
)
A knot diagram
1
Linearized knot diagam
4 6 11 7 10 2 12 1 5 3 9 8
Solving Sequence
3,10
11
4,6
2 7 1 5 9 12 8
c
10
c
3
c
2
c
6
c
1
c
5
c
9
c
11
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −6.57813 × 10
24
u
37
+ 6.93409 × 10
24
u
36
+ ··· + 1.58961 × 10
25
a − 1.79176 × 10
25
,
u
38
− u
37
+ ··· − 2u − 1i
I
u
2
= h−3.41732 × 10
236
u
71
− 6.79357 × 10
235
u
70
+ ··· + 4.34076 × 10
236
b + 1.29907 × 10
241
,
4.33939 × 10
191
u
71
+ 8.92073 × 10
190
u
70
+ ··· + 5.46565 × 10
191
a − 1.64326 × 10
196
,
u
72
− u
71
+ ··· + 27418u + 45671i
I
u
3
= hb + u, −29744507u
22
+ 20395822u
21
+ ··· + 15493951a − 35668774, u
23
− u
22
+ ··· + 2u − 1i
* 3 irreducible components of dim
C
= 0, with total 133 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
= hb − u, −6.58 × 10
24
u
37
+ 6.93 × 10
24
u
36
+ · · · + 1.59 × 10
25
a −
1.79 × 10
25
, u
38
− u
37
+ · · · − 2u − 1i
(i) Arc colorings
a
3
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
4
=
−u
−u
3
+ u
a
6
=
0.413821u
37
− 0.436214u
36
+ ··· − 1.50019u + 1.12717
u
a
2
=
0.116083u
37
− 0.0485543u
36
+ ··· − 2.44812u − 1.74726
−0.0852640u
37
− 0.0336343u
36
+ ··· + 0.630964u + 0.0223927
a
7
=
−0.230273u
37
+ 0.259709u
36
+ ··· + 1.51707u + 1.86697
−0.0298691u
37
+ 0.209123u
36
+ ··· + 0.379824u − 0.0451359
a
1
=
−0.0235968u
37
+ 0.113861u
36
+ ··· − 1.86834u − 1.50048
0.0600474u
37
− 0.161614u
36
+ ··· − 0.0430228u − 0.201654
a
5
=
0.413821u
37
− 0.436214u
36
+ ··· − 0.500191u + 1.12717
u
a
9
=
0.0223927u
37
− 0.107657u
36
+ ··· − 1.95481u + 0.586179
−u
2
a
12
=
−0.231100u
37
+ 0.0117291u
36
+ ··· + 0.254712u + 1.24608
−0.144821u
37
+ 0.0158346u
36
+ ··· − 0.0732163u + 0.0228410
a
8
=
−0.252060u
37
− 0.112582u
36
+ ··· + 0.324884u + 1.39835
−0.124431u
37
+ 0.0520392u
36
+ ··· − 0.454891u − 0.274698
(ii) Obstruction class = −1
(iii) Cusp Shapes =
30044921907723853376224412
15896073949776978916320991
u
37
−
55405836824956460952841385
15896073949776978916320991
u
36
+
··· −
101017582556204696388328298
15896073949776978916320991
u −
126386542644867906673421663
15896073949776978916320991
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
38
− 2u
37
+ ··· + 4u + 1
c
2
, c
6
u
38
− 26u
37
+ ··· + 65536u − 4096
c
3
, c
5
, c
9
c
10
u
38
− u
37
+ ··· − 2u − 1
c
7
, c
8
, c
12
u
38
+ 9u
37
+ ··· − 28u + 8
c
11
u
38
− 30u
37
+ ··· + 43124u − 3512
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
38
− 4y
37
+ ··· − 94y + 1
c
2
, c
6
y
38
+ 26y
37
+ ··· − 125829120y + 16777216
c
3
, c
5
, c
9
c
10
y
38
− 33y
37
+ ··· + 2y + 1
c
7
, c
8
, c
12
y
38
− 33y
37
+ ··· − 80y + 64
c
11
y
38
+ 6y
37
+ ··· − 103314128y + 12334144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.642582 + 0.529294I
a = −0.362091 − 0.970748I
b = −0.642582 + 0.529294I
−0.62981 + 3.65009I −8.45785 − 7.32483I
u = −0.642582 − 0.529294I
a = −0.362091 + 0.970748I
b = −0.642582 − 0.529294I
−0.62981 − 3.65009I −8.45785 + 7.32483I
u = −0.311299 + 0.761183I
a = −0.085459 − 0.793774I
b = −0.311299 + 0.761183I
−1.66830 − 2.81679I −7.20948 + 0.94774I
u = −0.311299 − 0.761183I
a = −0.085459 + 0.793774I
b = −0.311299 − 0.761183I
−1.66830 + 2.81679I −7.20948 − 0.94774I
u = −1.199830 + 0.197665I
a = −0.39774 − 1.71231I
b = −1.199830 + 0.197665I
−5.74703 + 1.70191I −30.1093 − 4.4341I
u = −1.199830 − 0.197665I
a = −0.39774 + 1.71231I
b = −1.199830 − 0.197665I
−5.74703 − 1.70191I −30.1093 + 4.4341I
u = −1.214180 + 0.163826I
a = −1.142910 − 0.562138I
b = −1.214180 + 0.163826I
−3.58346 + 2.28431I −12.26521 − 5.93080I
u = −1.214180 − 0.163826I
a = −1.142910 + 0.562138I
b = −1.214180 − 0.163826I
−3.58346 − 2.28431I −12.26521 + 5.93080I
u = 0.441998 + 0.630000I
a = 0.143471 − 0.902436I
b = 0.441998 + 0.630000I
2.72467 − 0.41534I −1.86874 + 2.50646I
u = 0.441998 − 0.630000I
a = 0.143471 + 0.902436I
b = 0.441998 − 0.630000I
2.72467 + 0.41534I −1.86874 − 2.50646I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.125697 + 0.754675I
a = 1.46136 − 0.33666I
b = 0.125697 + 0.754675I
−4.16749 + 6.80742I −11.39539 − 4.57055I
u = 0.125697 − 0.754675I
a = 1.46136 + 0.33666I
b = 0.125697 − 0.754675I
−4.16749 − 6.80742I −11.39539 + 4.57055I
u = 0.319015 + 0.661353I
a = −1.13060 − 0.90619I
b = 0.319015 + 0.661353I
−5.30082 + 0.18015I −13.27778 + 1.55316I
u = 0.319015 − 0.661353I
a = −1.13060 + 0.90619I
b = 0.319015 − 0.661353I
−5.30082 − 0.18015I −13.27778 − 1.55316I
u = 1.262990 + 0.084911I
a = 0.66371 − 1.32119I
b = 1.262990 + 0.084911I
−11.45280 + 3.42761I −20.1823 − 6.5471I
u = 1.262990 − 0.084911I
a = 0.66371 + 1.32119I
b = 1.262990 − 0.084911I
−11.45280 − 3.42761I −20.1823 + 6.5471I
u = 1.263310 + 0.274194I
a = 0.921270 − 0.499067I
b = 1.263310 + 0.274194I
−2.35527 − 7.30757I −10.63293 + 7.72113I
u = 1.263310 − 0.274194I
a = 0.921270 + 0.499067I
b = 1.263310 − 0.274194I
−2.35527 + 7.30757I −10.63293 − 7.72113I
u = 1.255600 + 0.363345I
a = −0.019509 − 1.407240I
b = 1.255600 + 0.363345I
−8.61451 − 7.26588I −15.9503 + 10.7715I
u = 1.255600 − 0.363345I
a = −0.019509 + 1.407240I
b = 1.255600 − 0.363345I
−8.61451 + 7.26588I −15.9503 − 10.7715I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.33470
a = 1.18898
b = 1.33470
−12.3935 −21.7990
u = −1.335100 + 0.309048I
a = −0.853516 − 0.422112I
b = −1.335100 + 0.309048I
−8.15095 + 11.42250I −14.3546 − 7.5460I
u = −1.335100 − 0.309048I
a = −0.853516 + 0.422112I
b = −1.335100 − 0.309048I
−8.15095 − 11.42250I −14.3546 + 7.5460I
u = −0.170696 + 0.593684I
a = −1.78466 − 0.26897I
b = −0.170696 + 0.593684I
0.71316 − 3.70227I −4.70598 + 2.17127I
u = −0.170696 − 0.593684I
a = −1.78466 + 0.26897I
b = −0.170696 − 0.593684I
0.71316 + 3.70227I −4.70598 − 2.17127I
u = 0.441678 + 0.391338I
a = 1.83459 + 0.60874I
b = 0.441678 + 0.391338I
−2.20747 + 1.18529I −14.4340 + 4.4751I
u = 0.441678 − 0.391338I
a = 1.83459 − 0.60874I
b = 0.441678 − 0.391338I
−2.20747 − 1.18529I −14.4340 − 4.4751I
u = −1.50663 + 0.36313I
a = −0.112277 − 1.068330I
b = −1.50663 + 0.36313I
−17.9039 + 7.3787I 0
u = −1.50663 − 0.36313I
a = −0.112277 + 1.068330I
b = −1.50663 − 0.36313I
−17.9039 − 7.3787I 0
u = 1.46940 + 0.49385I
a = −0.023597 − 1.058640I
b = 1.46940 + 0.49385I
−10.00620 − 8.86952I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46940 − 0.49385I
a = −0.023597 + 1.058640I
b = 1.46940 − 0.49385I
−10.00620 + 8.86952I 0
u = −0.207067 + 0.387382I
a = 1.30451 − 1.62960I
b = −0.207067 + 0.387382I
−0.46850 + 1.50335I −4.10768 − 5.04879I
u = −0.207067 − 0.387382I
a = 1.30451 + 1.62960I
b = −0.207067 − 0.387382I
−0.46850 − 1.50335I −4.10768 + 5.04879I
u = −0.415323
a = 0.953137
b = −0.415323
−0.837431 −10.5390
u = −1.52626 + 0.54197I
a = 0.036058 − 0.993072I
b = −1.52626 + 0.54197I
−8.3844 + 13.5000I 0
u = −1.52626 − 0.54197I
a = 0.036058 + 0.993072I
b = −1.52626 − 0.54197I
−8.3844 − 13.5000I 0
u = 1.57427 + 0.55070I
a = −0.023672 − 0.956443I
b = 1.57427 + 0.55070I
−13.9247 − 17.5662I 0
u = 1.57427 − 0.55070I
a = −0.023672 + 0.956443I
b = 1.57427 − 0.55070I
−13.9247 + 17.5662I 0
8
II. I
u
2
= h−3.42 × 10
236
u
71
− 6.79 × 10
235
u
70
+ · · · + 4.34 × 10
236
b + 1.30 ×
10
241
, 4.34 × 10
191
u
71
+ 8.92 × 10
190
u
70
+ · · · + 5.47 × 10
191
a − 1.64 ×
10
196
, u
72
− u
71
+ · · · + 27418u + 45671i
(i) Arc colorings
a
3
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
4
=
−u
−u
3
+ u
a
6
=
−0.793938u
71
− 0.163215u
70
+ ··· + 42952.0u + 30065.3
0.787262u
71
+ 0.156506u
70
+ ··· − 42815.4u − 29927.2
a
2
=
−0.408138u
71
− 0.0889949u
70
+ ··· + 21707.3u + 15292.2
0.267218u
71
+ 0.0807519u
70
+ ··· − 12557.3u − 9274.97
a
7
=
0.385823u
71
+ 0.0741978u
70
+ ··· − 21244.3u − 14772.5
0.617782u
71
+ 0.138655u
70
+ ··· − 32712.3u − 23063.8
a
1
=
0.328655u
71
+ 0.0965080u
70
+ ··· − 15531.5u − 11457.2
0.679992u
71
+ 0.171566u
70
+ ··· − 34256.0u − 24647.7
a
5
=
−0.00667606u
71
− 0.00670817u
70
+ ··· + 136.624u + 138.090
0.787262u
71
+ 0.156506u
70
+ ··· − 42815.4u − 29927.2
a
9
=
0.325476u
71
+ 0.0478554u
70
+ ··· − 18634.3u − 12815.3
0.122394u
71
− 0.0162808u
70
+ ··· − 9238.65u − 5826.11
a
12
=
0.101849u
71
+ 0.0284827u
70
+ ··· − 4604.86u − 3500.59
0.256426u
71
+ 0.0412224u
70
+ ··· − 14192.2u − 9911.86
a
8
=
0.398346u
71
+ 0.0956167u
70
+ ··· − 20161.7u − 14516.7
0.631835u
71
+ 0.123936u
70
+ ··· − 34126.4u − 23950.8
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.19731u
71
− 0.498944u
70
+ ··· + 116066.u + 81882.3
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
72
− 13u
71
+ ··· − 19474u + 1151
c
2
, c
6
(u
3
+ u
2
+ 2u + 1)
24
c
3
, c
5
, c
9
c
10
u
72
− u
71
+ ··· + 27418u + 45671
c
7
, c
8
, c
12
(u
12
− u
11
− 5u
10
+ 4u
9
+ 9u
8
− 4u
7
− 6u
6
− 2u
5
+ 3u
3
+ u
2
+ 1)
6
c
11
(u
12
+ 3u
11
+ ··· + 4u + 1)
6
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
72
− 17y
71
+ ··· − 39129988y + 1324801
c
2
, c
6
(y
3
+ 3y
2
+ 2y −1)
24
c
3
, c
5
, c
9
c
10
y
72
− 65y
71
+ ··· + 1084775528y + 2085840241
c
7
, c
8
, c
12
(y
12
− 11y
11
+ ··· + 2y + 1)
6
c
11
(y
12
+ y
11
+ ··· − 2y + 1)
6
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.016904 + 0.938793I
a = −1.396040 + 0.203966I
b = 1.209300 + 0.005604I
−4.84384 + 2.73451I 0
u = 0.016904 − 0.938793I
a = −1.396040 − 0.203966I
b = 1.209300 − 0.005604I
−4.84384 − 2.73451I 0
u = 0.941410 + 0.511838I
a = −0.467200 + 0.254013I
b = 0.102703 − 0.669479I
1.31764 − 3.88480I 0
u = 0.941410 − 0.511838I
a = −0.467200 − 0.254013I
b = 0.102703 + 0.669479I
1.31764 + 3.88480I 0
u = 0.709464 + 0.503759I
a = 0.66819 + 1.36798I
b = −1.64033 − 0.08580I
−11.07400 − 2.92173I 0
u = 0.709464 − 0.503759I
a = 0.66819 − 1.36798I
b = −1.64033 + 0.08580I
−11.07400 + 2.92173I 0
u = −0.108050 + 1.182640I
a = −1.079650 + 0.280505I
b = 1.239000 − 0.126036I
−4.84384 + 2.92173I 0
u = −0.108050 − 1.182640I
a = −1.079650 − 0.280505I
b = 1.239000 + 0.126036I
−4.84384 − 2.92173I 0
u = −1.053450 + 0.548334I
a = 0.425615 + 0.221538I
b = 0.003969 − 0.768800I
−3.82135 + 7.58818I 0
u = −1.053450 − 0.548334I
a = 0.425615 − 0.221538I
b = 0.003969 + 0.768800I
−3.82135 − 7.58818I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.163260 + 0.267260I
a = 0.420845 − 1.027000I
b = −0.205919 + 0.579765I
−2.81995 + 1.05668I 0
u = −1.163260 − 0.267260I
a = 0.420845 + 1.027000I
b = −0.205919 − 0.579765I
−2.81995 − 1.05668I 0
u = 1.209300 + 0.005604I
a = −0.182860 − 1.080060I
b = 0.016904 + 0.938793I
−4.84384 + 2.73451I 0
u = 1.209300 − 0.005604I
a = −0.182860 + 1.080060I
b = 0.016904 − 0.938793I
−4.84384 − 2.73451I 0
u = 1.203930 + 0.129844I
a = −0.060845 + 1.092290I
b = −1.94643 − 0.60072I
−13.09790 + 1.05668I 0
u = 1.203930 − 0.129844I
a = −0.060845 − 1.092290I
b = −1.94643 + 0.60072I
−13.09790 − 1.05668I 0
u = 1.182150 + 0.267603I
a = −0.458540 + 0.103800I
b = −1.354490 + 0.112254I
−3.82135 − 1.20211I 0
u = 1.182150 − 0.267603I
a = −0.458540 − 0.103800I
b = −1.354490 − 0.112254I
−3.82135 + 1.20211I 0
u = −0.697309 + 0.362810I
a = 0.643103 + 0.334607I
b = −0.316643 − 0.411076I
−0.706253 + 0.093609I −8.00000 + 0.I
u = −0.697309 − 0.362810I
a = 0.643103 − 0.334607I
b = −0.316643 + 0.411076I
−0.706253 − 0.093609I −8.00000 + 0.I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.196300 + 0.253597I
a = −0.049609 + 1.082140I
b = 1.77144 − 0.52507I
−7.95893 + 1.62601I 0
u = −1.196300 − 0.253597I
a = −0.049609 − 1.082140I
b = 1.77144 + 0.52507I
−7.95893 − 1.62601I 0
u = 0.003969 + 0.768800I
a = −0.003826 + 0.741188I
b = −1.053450 − 0.548334I
−3.82135 − 7.58818I −8.98049 + 5.13539I
u = 0.003969 − 0.768800I
a = −0.003826 − 0.741188I
b = −1.053450 + 0.548334I
−3.82135 + 7.58818I −8.98049 − 5.13539I
u = 1.239000 + 0.126036I
a = −0.065594 + 1.061670I
b = −0.108050 − 1.182640I
−4.84384 − 2.92173I 0
u = 1.239000 − 0.126036I
a = −0.065594 − 1.061670I
b = −0.108050 + 1.182640I
−4.84384 + 2.92173I 0
u = 1.268300 + 0.097095I
a = −0.446678 + 0.034196I
b = −0.625462 − 0.283222I
−6.93644 + 0.09361I 0
u = 1.268300 − 0.097095I
a = −0.446678 − 0.034196I
b = −0.625462 + 0.283222I
−6.93644 − 0.09361I 0
u = −1.264550 + 0.238133I
a = −0.023731 + 1.029210I
b = 0.20647 − 1.45163I
−2.81995 + 6.71292I 0
u = −1.264550 − 0.238133I
a = −0.023731 − 1.029210I
b = 0.20647 + 1.45163I
−2.81995 − 6.71292I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.625462 + 0.283222I
a = 0.756046 + 0.342354I
b = 1.268300 − 0.097095I
−6.93644 − 0.09361I −10.97137 − 0.76204I
u = −0.625462 − 0.283222I
a = 0.756046 − 0.342354I
b = 1.268300 + 0.097095I
−6.93644 + 0.09361I −10.97137 + 0.76204I
u = 0.102703 + 0.669479I
a = −0.127574 + 0.831599I
b = 0.941410 − 0.511838I
1.31764 + 3.88480I −4.17488 − 4.17140I
u = 0.102703 − 0.669479I
a = −0.127574 − 0.831599I
b = 0.941410 + 0.511838I
1.31764 − 3.88480I −4.17488 + 4.17140I
u = 1.295140 + 0.280941I
a = 0.050487 + 0.998312I
b = −0.29281 − 1.57276I
−7.95893 − 10.41630I 0
u = 1.295140 − 0.280941I
a = 0.050487 − 0.998312I
b = −0.29281 + 1.57276I
−7.95893 + 10.41630I 0
u = −1.275570 + 0.379612I
a = 0.410386 + 0.122131I
b = 1.44696 + 0.17098I
−8.96033 + 3.88480I 0
u = −1.275570 − 0.379612I
a = 0.410386 − 0.122131I
b = 1.44696 − 0.17098I
−8.96033 − 3.88480I 0
u = 1.271480 + 0.448451I
a = −0.472922 − 0.861251I
b = 0.165937 + 0.330843I
−7.95893 − 4.76006I 0
u = 1.271480 − 0.448451I
a = −0.472922 + 0.861251I
b = 0.165937 − 0.330843I
−7.95893 + 4.76006I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.354490 + 0.112254I
a = 0.417835 + 0.034628I
b = 1.182150 + 0.267603I
−3.82135 − 1.20211I 0
u = −1.354490 − 0.112254I
a = 0.417835 − 0.034628I
b = 1.182150 − 0.267603I
−3.82135 + 1.20211I 0
u = −0.205919 + 0.579765I
a = 2.11905 − 0.38166I
b = −1.163260 + 0.267260I
−2.81995 + 1.05668I −10.70414 − 1.19195I
u = −0.205919 − 0.579765I
a = 2.11905 + 0.38166I
b = −1.163260 − 0.267260I
−2.81995 − 1.05668I −10.70414 + 1.19195I
u = 0.906082 + 1.051410I
a = 0.612247 + 0.732186I
b = −1.46963 − 0.20075I
−11.07400 − 2.73451I 0
u = 0.906082 − 1.051410I
a = 0.612247 − 0.732186I
b = −1.46963 + 0.20075I
−11.07400 + 2.73451I 0
u = −1.394260 + 0.162883I
a = 0.044134 + 0.942674I
b = 1.73833 − 0.97198I
−13.0979 + 6.7129I 0
u = −1.394260 − 0.162883I
a = 0.044134 − 0.942674I
b = 1.73833 + 0.97198I
−13.0979 − 6.7129I 0
u = 1.392260 + 0.231638I
a = 0.001675 + 0.938584I
b = −1.56676 − 0.84322I
−7.95893 − 4.03024I 0
u = 1.392260 − 0.231638I
a = 0.001675 − 0.938584I
b = −1.56676 + 0.84322I
−7.95893 + 4.03024I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44696 + 0.17098I
a = −0.388397 + 0.045894I
b = −1.275570 + 0.379612I
−8.96033 + 3.88480I 0
u = 1.44696 − 0.17098I
a = −0.388397 − 0.045894I
b = −1.275570 − 0.379612I
−8.96033 − 3.88480I 0
u = 0.20647 + 1.45163I
a = 0.861955 + 0.270762I
b = −1.264550 − 0.238133I
−2.81995 − 6.71292I 0
u = 0.20647 − 1.45163I
a = 0.861955 − 0.270762I
b = −1.264550 + 0.238133I
−2.81995 + 6.71292I 0
u = −0.316643 + 0.411076I
a = 0.670151 + 0.870012I
b = −0.697309 − 0.362810I
−0.706253 − 0.093609I −6.98961 − 0.76204I
u = −0.316643 − 0.411076I
a = 0.670151 − 0.870012I
b = −0.697309 + 0.362810I
−0.706253 + 0.093609I −6.98961 + 0.76204I
u = −1.46963 + 0.20075I
a = 0.024396 + 0.892768I
b = 0.906082 − 1.051410I
−11.07400 + 2.73451I 0
u = −1.46963 − 0.20075I
a = 0.024396 − 0.892768I
b = 0.906082 + 1.051410I
−11.07400 − 2.73451I 0
u = −0.29281 + 1.57276I
a = −0.778664 + 0.281724I
b = 1.295140 − 0.280941I
−7.95893 + 10.41630I 0
u = −0.29281 − 1.57276I
a = −0.778664 − 0.281724I
b = 1.295140 + 0.280941I
−7.95893 − 10.41630I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.165937 + 0.330843I
a = −3.41733 − 1.06389I
b = 1.271480 + 0.448451I
−7.95893 − 4.76006I −15.5098 + 2.1559I
u = 0.165937 − 0.330843I
a = −3.41733 + 1.06389I
b = 1.271480 − 0.448451I
−7.95893 + 4.76006I −15.5098 − 2.1559I
u = −1.64033 + 0.08580I
a = 0.089194 + 0.801543I
b = 0.709464 − 0.503759I
−11.07400 + 2.92173I 0
u = −1.64033 − 0.08580I
a = 0.089194 − 0.801543I
b = 0.709464 + 0.503759I
−11.07400 − 2.92173I 0
u = −1.56676 + 0.84322I
a = −0.241722 + 0.704203I
b = 1.392260 − 0.231638I
−7.95893 + 4.03024I 0
u = −1.56676 − 0.84322I
a = −0.241722 − 0.704203I
b = 1.392260 + 0.231638I
−7.95893 − 4.03024I 0
u = 1.77144 + 0.52507I
a = 0.089447 + 0.711385I
b = −1.196300 − 0.253597I
−7.95893 − 1.62601I 0
u = 1.77144 − 0.52507I
a = 0.089447 − 0.711385I
b = −1.196300 + 0.253597I
−7.95893 + 1.62601I 0
u = 1.73833 + 0.97198I
a = 0.226048 + 0.625558I
b = −1.394260 − 0.162883I
−13.0979 − 6.7129I 0
u = 1.73833 − 0.97198I
a = 0.226048 − 0.625558I
b = −1.394260 + 0.162883I
−13.0979 + 6.7129I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.94643 + 0.60072I
a = −0.088346 + 0.644294I
b = 1.203930 − 0.129844I
−13.09790 − 1.05668I 0
u = −1.94643 − 0.60072I
a = −0.088346 − 0.644294I
b = 1.203930 + 0.129844I
−13.09790 + 1.05668I 0
19
III. I
u
3
= hb + u, −2.97 × 10
7
u
22
+ 2.04 × 10
7
u
21
+ · · · + 1.55 × 10
7
a − 3.57 ×
10
7
, u
23
− u
22
+ · · · + 2u − 1i
(i) Arc colorings
a
3
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
4
=
−u
−u
3
+ u
a
6
=
1.91975u
22
− 1.31637u
21
+ ··· − 2.47288u + 2.30211
−u
a
2
=
−1.65430u
22
+ 0.436475u
21
+ ··· − 0.745774u − 1.51994
0.236376u
22
− 0.321252u
21
+ ··· + 1.71300u + 0.603376
a
7
=
2.38913u
22
− 1.00853u
21
+ ··· + 0.373712u + 2.90053
−0.970927u
22
+ 0.441354u
21
+ ··· − 0.931646u − 1.82120
a
1
=
−1.99583u
22
+ 0.689350u
21
+ ··· − 0.0526426u − 2.20819
0.403903u
22
− 0.280797u
21
+ ··· + 0.855641u + 1.20298
a
5
=
1.91975u
22
− 1.31637u
21
+ ··· − 3.47288u + 2.30211
−u
a
9
=
0.603376u
22
− 0.367000u
21
+ ··· − 1.53739u + 2.91975
−u
2
a
12
=
−0.706876u
22
− 0.0341473u
21
+ ··· + 0.110254u − 0.653981
−0.173528u
22
− 0.105623u
21
+ ··· + 0.125425u − 0.105151
a
8
=
1.64529u
22
− 0.478970u
21
+ ··· − 0.146050u + 2.82677
−0.690842u
22
+ 0.254814u
21
+ ··· − 0.00180316u − 1.64235
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
65051930
15493951
u
22
+
29092423
15493951
u
21
+ ··· +
179315328
15493951
u −
327170903
15493951
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
23
− 2u
22
+ ··· + u
2
− 1
c
2
u
23
− u
22
+ ··· − u − 1
c
3
, c
9
u
23
+ u
22
+ ··· + 2u + 1
c
5
, c
10
u
23
− u
22
+ ··· + 2u − 1
c
6
u
23
+ u
22
+ ··· − u + 1
c
7
, c
8
u
23
+ 2u
22
+ ··· + 3u + 1
c
11
u
23
+ 3u
22
+ ··· + 5u − 1
c
12
u
23
− 2u
22
+ ··· + 3u − 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
23
− 4y
22
+ ··· + 2y − 1
c
2
, c
6
y
23
+ 23y
22
+ ··· − 27y − 1
c
3
, c
5
, c
9
c
10
y
23
− 25y
22
+ ··· − 2y − 1
c
7
, c
8
, c
12
y
23
− 22y
22
+ ··· + 7y − 1
c
11
y
23
+ 5y
22
+ ··· + 23y − 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.022740 + 0.185305I
a = 0.065484 − 0.316927I
b = 1.022740 − 0.185305I
−8.18170 − 0.18078I −19.5491 − 0.2814I
u = −1.022740 − 0.185305I
a = 0.065484 + 0.316927I
b = 1.022740 + 0.185305I
−8.18170 + 0.18078I −19.5491 + 0.2814I
u = 0.596983 + 0.540925I
a = −0.352894 − 0.886196I
b = −0.596983 − 0.540925I
−5.45844 − 8.17580I −15.7018 + 6.8790I
u = 0.596983 − 0.540925I
a = −0.352894 + 0.886196I
b = −0.596983 + 0.540925I
−5.45844 + 8.17580I −15.7018 − 6.8790I
u = 1.21273
a = −0.580501
b = −1.21273
−3.94477 −10.2950
u = −1.139270 + 0.457575I
a = −0.436874 + 1.214120I
b = 1.139270 − 0.457575I
−9.02432 + 6.23311I −18.2377 − 4.9365I
u = −1.139270 − 0.457575I
a = −0.436874 − 1.214120I
b = 1.139270 + 0.457575I
−9.02432 − 6.23311I −18.2377 + 4.9365I
u = 1.217490 + 0.245448I
a = −0.207007 + 1.398780I
b = −1.217490 − 0.245448I
−5.38741 − 1.61647I −7.35891 − 0.92793I
u = 1.217490 − 0.245448I
a = −0.207007 − 1.398780I
b = −1.217490 + 0.245448I
−5.38741 + 1.61647I −7.35891 + 0.92793I
u = −0.492312 + 0.423106I
a = 0.317897 − 1.196720I
b = 0.492312 − 0.423106I
−0.17088 + 4.63461I −11.11237 − 7.01654I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.492312 − 0.423106I
a = 0.317897 + 1.196720I
b = 0.492312 + 0.423106I
−0.17088 − 4.63461I −11.11237 + 7.01654I
u = −1.389650 + 0.114676I
a = 0.350228 + 0.794231I
b = 1.389650 − 0.114676I
−10.91490 − 2.29746I −16.6998 + 0.8164I
u = −1.389650 − 0.114676I
a = 0.350228 − 0.794231I
b = 1.389650 + 0.114676I
−10.91490 + 2.29746I −16.6998 − 0.8164I
u = 0.566870 + 0.089301I
a = 0.88106 − 1.21817I
b = −0.566870 − 0.089301I
−1.46405 − 0.87010I −13.9110 + 3.4078I
u = 0.566870 − 0.089301I
a = 0.88106 + 1.21817I
b = −0.566870 + 0.089301I
−1.46405 + 0.87010I −13.9110 − 3.4078I
u = −1.47841 + 0.47470I
a = −0.121772 + 0.812453I
b = 1.47841 − 0.47470I
−7.48689 + 3.06719I −9.94851 − 1.26230I
u = −1.47841 − 0.47470I
a = −0.121772 − 0.812453I
b = 1.47841 + 0.47470I
−7.48689 − 3.06719I −9.94851 + 1.26230I
u = 1.45451 + 0.58040I
a = 0.217296 + 0.784893I
b = −1.45451 − 0.58040I
−11.46970 − 1.01894I −17.6089 − 1.1247I
u = 1.45451 − 0.58040I
a = 0.217296 − 0.784893I
b = −1.45451 + 0.58040I
−11.46970 + 1.01894I −17.6089 + 1.1247I
u = 1.56026 + 0.41054I
a = 0.049018 + 0.755358I
b = −1.56026 − 0.41054I
−12.18930 − 5.38792I −16.7986 + 3.0834I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.56026 − 0.41054I
a = 0.049018 − 0.755358I
b = −1.56026 + 0.41054I
−12.18930 + 5.38792I −16.7986 − 3.0834I
u = 0.019909 + 0.348445I
a = −2.47219 − 1.41321I
b = −0.019909 − 0.348445I
−1.94701 − 1.83327I −9.92563 + 5.88323I
u = 0.019909 − 0.348445I
a = −2.47219 + 1.41321I
b = −0.019909 + 0.348445I
−1.94701 + 1.83327I −9.92563 − 5.88323I
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
23
− 2u
22
+ ··· + u
2
− 1)(u
38
− 2u
37
+ ··· + 4u + 1)
· (u
72
− 13u
71
+ ··· − 19474u + 1151)
c
2
((u
3
+ u
2
+ 2u + 1)
24
)(u
23
− u
22
+ ··· − u − 1)
· (u
38
− 26u
37
+ ··· + 65536u − 4096)
c
3
, c
9
(u
23
+ u
22
+ ··· + 2u + 1)(u
38
− u
37
+ ··· − 2u − 1)
· (u
72
− u
71
+ ··· + 27418u + 45671)
c
5
, c
10
(u
23
− u
22
+ ··· + 2u − 1)(u
38
− u
37
+ ··· − 2u − 1)
· (u
72
− u
71
+ ··· + 27418u + 45671)
c
6
((u
3
+ u
2
+ 2u + 1)
24
)(u
23
+ u
22
+ ··· − u + 1)
· (u
38
− 26u
37
+ ··· + 65536u − 4096)
c
7
, c
8
(u
12
− u
11
− 5u
10
+ 4u
9
+ 9u
8
− 4u
7
− 6u
6
− 2u
5
+ 3u
3
+ u
2
+ 1)
6
· (u
23
+ 2u
22
+ ··· + 3u + 1)(u
38
+ 9u
37
+ ··· − 28u + 8)
c
11
((u
12
+ 3u
11
+ ··· + 4u + 1)
6
)(u
23
+ 3u
22
+ ··· + 5u − 1)
· (u
38
− 30u
37
+ ··· + 43124u − 3512)
c
12
(u
12
− u
11
− 5u
10
+ 4u
9
+ 9u
8
− 4u
7
− 6u
6
− 2u
5
+ 3u
3
+ u
2
+ 1)
6
· (u
23
− 2u
22
+ ··· + 3u − 1)(u
38
+ 9u
37
+ ··· − 28u + 8)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
23
− 4y
22
+ ··· + 2y − 1)(y
38
− 4y
37
+ ··· − 94y + 1)
· (y
72
− 17y
71
+ ··· − 39129988y + 1324801)
c
2
, c
6
((y
3
+ 3y
2
+ 2y − 1)
24
)(y
23
+ 23y
22
+ ··· − 27y − 1)
· (y
38
+ 26y
37
+ ··· − 125829120y + 16777216)
c
3
, c
5
, c
9
c
10
(y
23
− 25y
22
+ ··· − 2y − 1)(y
38
− 33y
37
+ ··· + 2y + 1)
· (y
72
− 65y
71
+ ··· + 1084775528y + 2085840241)
c
7
, c
8
, c
12
((y
12
− 11y
11
+ ··· + 2y + 1)
6
)(y
23
− 22y
22
+ ··· + 7y − 1)
· (y
38
− 33y
37
+ ··· − 80y + 64)
c
11
((y
12
+ y
11
+ ··· − 2y + 1)
6
)(y
23
+ 5y
22
+ ··· + 23y − 1)
· (y
38
+ 6y
37
+ ··· − 103314128y + 12334144)
27
