12n
0450
(K12n
0450
)
A knot diagram
1
Linearized knot diagam
3 6 12 11 2 11 1 4 3 1 9 8
Solving Sequence
4,8 9,12
1 3 2 7 11 5 6 10
c
8
c
12
c
3
c
1
c
7
c
11
c
4
c
6
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.60444 × 10
22
u
28
+ 2.55663 × 10
22
u
27
+ ··· + 2.54971 × 10
22
b − 4.79237 × 10
21
, a − 1,
u
29
− 2u
28
+ ··· − 3u + 1i
I
u
2
= h−101u
19
+ 163u
18
+ ··· + 83b − 171, a + 1, u
20
+ u
19
+ ··· − 2u + 1i
I
u
3
= h−3.73965 × 10
51
u
39
− 8.54778 × 10
51
u
38
+ ··· + 4.04316 × 10
50
b + 1.36063 × 10
52
,
− 3.50215 × 10
83
u
39
− 8.75016 × 10
83
u
38
+ ··· + 9.39462 × 10
81
a + 3.79380 × 10
83
,
u
40
+ 2u
39
+ ··· − 13u + 1i
I
u
4
= h−u
3
− 2u
2
+ 2b − 2u + 1, u
3
+ 2a − 5, u
4
+ u
3
+ 2u
2
− u + 1i
I
u
5
= hb + u + 1, a − 1, u
2
+ u + 1i
* 5 irreducible components of dim
C
= 0, with total 95 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−1.60 × 10
22
u
28
+ 2.56 × 10
22
u
27
+ · · · + 2.55 × 10
22
b − 4.79 ×
10
21
, a − 1, u
29
− 2u
28
+ · · · − 3u + 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
12
=
1
0.629264u
28
− 1.00271u
27
+ ··· + 4.09043u + 0.187957
a
1
=
0.629264u
28
− 1.00271u
27
+ ··· + 4.09043u + 1.18796
0.629264u
28
− 1.00271u
27
+ ··· + 4.09043u + 0.187957
a
3
=
u
0.255815u
28
− 0.468311u
27
+ ··· + 3.07575u − 0.629264
a
2
=
0.572071u
28
− 0.965425u
27
+ ··· + 3.54331u + 0.766462
0.0578442u
28
− 0.0712994u
27
+ ··· + 0.481981u + 0.447834
a
7
=
1.81161u
28
− 3.20172u
27
+ ··· + 12.3104u − 1.73946
1.18234u
28
− 2.19901u
27
+ ··· + 8.21997u − 2.92741
a
11
=
0.629264u
28
− 1.00271u
27
+ ··· + 4.09043u + 1.18796
0.672582u
28
− 1.03859u
27
+ ··· + 4.22861u − 0.0678573
a
5
=
0.575794u
28
− 1.20888u
27
+ ··· + 6.02284u − 2.35424
0.299202u
28
− 0.691078u
27
+ ··· + 3.19943u − 1.66768
a
6
=
1.13473u
28
− 2.13653u
27
+ ··· + 8.11688u − 1.69516
0.493538u
28
− 1.13834u
27
+ ··· + 4.35556u − 1.96801
a
10
=
−0.0433177u
28
+ 0.0358776u
27
+ ··· − 0.138180u + 1.25581
0.0355816u
28
− 0.0476050u
27
+ ··· + 0.517900u + 0.626552
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1968133132746250507567
25497116697596300834899
u
28
+
51952197439902261991497
25497116697596300834899
u
27
+ ··· −
276922517104029225550000
25497116697596300834899
u +
47895990870458513606664
25497116697596300834899
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
29
+ 9u
28
+ ··· − 861u + 441
c
2
, c
5
u
29
+ 9u
28
+ ··· + 105u + 21
c
3
, c
8
u
29
− 2u
28
+ ··· − 3u + 1
c
4
, c
9
u
29
− u
28
+ ··· + 19u + 17
c
6
, c
10
u
29
+ 3u
28
+ ··· + 29u + 1
c
7
, c
12
u
29
− 18u
28
+ ··· − 2560u + 512
c
11
u
29
− 18u
28
+ ··· + 294u − 21
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
+ 31y
28
+ ··· + 2190447y −194481
c
2
, c
5
y
29
− 9y
28
+ ··· − 861y −441
c
3
, c
8
y
29
+ 28y
27
+ ··· − 11y −1
c
4
, c
9
y
29
− 15y
28
+ ··· + 3183y −289
c
6
, c
10
y
29
+ 45y
28
+ ··· + 331y −1
c
7
, c
12
y
29
+ 12y
28
+ ··· + 7864320y −262144
c
11
y
29
+ 4y
28
+ ··· + 1344y −441
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.553569 + 0.834452I
a = 1.00000
b = −1.086080 − 0.257296I
1.07593 + 3.51673I −0.88547 − 6.06083I
u = −0.553569 − 0.834452I
a = 1.00000
b = −1.086080 + 0.257296I
1.07593 − 3.51673I −0.88547 + 6.06083I
u = −0.898744 + 0.481411I
a = 1.00000
b = −1.04286 − 1.29908I
4.54760 + 1.43626I −5.55282 − 2.76214I
u = −0.898744 − 0.481411I
a = 1.00000
b = −1.04286 + 1.29908I
4.54760 − 1.43626I −5.55282 + 2.76214I
u = 0.885586 + 0.378627I
a = 1.00000
b = −1.05204 + 1.35554I
4.49815 − 7.86181I −6.63470 + 7.85058I
u = 0.885586 − 0.378627I
a = 1.00000
b = −1.05204 − 1.35554I
4.49815 + 7.86181I −6.63470 − 7.85058I
u = 0.390658 + 0.859931I
a = 1.00000
b = −0.766543 − 0.146226I
2.79783 + 0.59845I 2.09571 − 1.89566I
u = 0.390658 − 0.859931I
a = 1.00000
b = −0.766543 + 0.146226I
2.79783 − 0.59845I 2.09571 + 1.89566I
u = −0.631994 + 0.882834I
a = 1.00000
b = −1.47686 + 0.36781I
9.81309 + 8.93318I −1.43468 − 7.09429I
u = −0.631994 − 0.882834I
a = 1.00000
b = −1.47686 − 0.36781I
9.81309 − 8.93318I −1.43468 + 7.09429I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.622317 + 0.918963I
a = 1.00000
b = −1.37238 − 0.35412I
10.54740 − 2.08899I −0.28693 + 2.13318I
u = 0.622317 − 0.918963I
a = 1.00000
b = −1.37238 + 0.35412I
10.54740 + 2.08899I −0.28693 − 2.13318I
u = −0.246064 + 0.681299I
a = 1.00000
b = −0.291258 − 0.850239I
−0.06368 + 1.78512I −1.17437 − 4.76019I
u = −0.246064 − 0.681299I
a = 1.00000
b = −0.291258 + 0.850239I
−0.06368 − 1.78512I −1.17437 + 4.76019I
u = 1.040160 + 0.774644I
a = 1.00000
b = 0.003744 + 1.185610I
−4.83952 + 0.52966I −8.94722 − 4.42653I
u = 1.040160 − 0.774644I
a = 1.00000
b = 0.003744 − 1.185610I
−4.83952 − 0.52966I −8.94722 + 4.42653I
u = −0.662685
a = 1.00000
b = 0.179578
−1.45974 −5.50510
u = −0.954244 + 0.980591I
a = 1.00000
b = −0.384074 − 1.189700I
−0.41230 + 3.60972I −1.66995 − 2.14870I
u = −0.954244 − 0.980591I
a = 1.00000
b = −0.384074 + 1.189700I
−0.41230 − 3.60972I −1.66995 + 2.14870I
u = 0.447072 + 0.358702I
a = 1.00000
b = −0.44229 + 1.60778I
−2.94431 − 4.31709I −9.8550 + 12.7269I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.447072 − 0.358702I
a = 1.00000
b = −0.44229 − 1.60778I
−2.94431 + 4.31709I −9.8550 − 12.7269I
u = 1.08646 + 1.01922I
a = 1.00000
b = −0.47265 + 1.42228I
−4.10333 − 8.99973I −2.77388 + 6.56416I
u = 1.08646 − 1.01922I
a = 1.00000
b = −0.47265 − 1.42228I
−4.10333 + 8.99973I −2.77388 − 6.56416I
u = −1.16230 + 1.12800I
a = 1.00000
b = −0.74251 − 1.33081I
7.38506 + 9.34813I −2.85483 − 4.48281I
u = −1.16230 − 1.12800I
a = 1.00000
b = −0.74251 + 1.33081I
7.38506 − 9.34813I −2.85483 + 4.48281I
u = 0.117027 + 0.360629I
a = 1.00000
b = 0.817618 + 0.957619I
−2.13866 + 1.52424I −4.33983 − 3.48956I
u = 0.117027 − 0.360629I
a = 1.00000
b = 0.817618 − 0.957619I
−2.13866 − 1.52424I −4.33983 + 3.48956I
u = 1.18898 + 1.11285I
a = 1.00000
b = −0.78159 + 1.34575I
6.6428 − 16.5676I −4.00000 + 8.49370I
u = 1.18898 − 1.11285I
a = 1.00000
b = −0.78159 − 1.34575I
6.6428 + 16.5676I −4.00000 − 8.49370I
7
II. I
u
2
= h−101u
19
+ 163u
18
+ · · · + 83b − 171, a + 1, u
20
+ u
19
+ · · · − 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
12
=
−1
1.21687u
19
− 1.96386u
18
+ ··· − 10.1928u + 2.06024
a
1
=
1.21687u
19
− 1.96386u
18
+ ··· − 10.1928u + 1.06024
1.21687u
19
− 1.96386u
18
+ ··· − 10.1928u + 2.06024
a
3
=
u
3.18072u
19
+ 2.53012u
18
+ ··· − 3.49398u + 1.21687
a
2
=
2.16867u
19
− 2.63855u
18
+ ··· − 15.9277u + 4.60241
2.15663u
19
− 3.80723u
18
+ ··· − 19.3614u + 8.98795
a
7
=
1.34940u
19
+ 4.89157u
18
+ ··· + 7.57831u − 11.1807
2.56627u
19
+ 2.92771u
18
+ ··· − 2.61446u − 10.1205
a
11
=
1.21687u
19
− 1.96386u
18
+ ··· − 10.1928u + 1.06024
1.86747u
19
− 3.85542u
18
+ ··· − 17.7711u + 5.24096
a
5
=
1.63855u
19
+ 1.93976u
18
+ ··· − 4.01205u − 1.43373
−0.626506u
19
+ 0.228916u
18
+ ··· − 0.554217u − 2.95181
a
6
=
−0.168675u
19
+ 5.63855u
18
+ ··· + 15.9277u − 10.6024
−0.156627u
19
+ 6.80723u
18
+ ··· + 19.3614u − 15.9880
a
10
=
0.650602u
19
− 1.89157u
18
+ ··· − 7.57831u + 4.18072
0.650602u
19
− 1.89157u
18
+ ··· − 7.57831u + 4.18072
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1728
83
u
19
−
2529
83
u
18
+ ··· −
290
83
u −
148
83
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− 8u
19
+ ··· − 10u + 1
c
2
u
20
+ 4u
19
+ ··· + 4u + 1
c
3
, c
8
u
20
+ u
19
+ ··· − 2u + 1
c
4
, c
9
u
20
− 3u
18
+ ··· − 4u + 5
c
5
u
20
− 4u
19
+ ··· − 4u + 1
c
6
, c
10
u
20
− 2u
19
+ ··· + 2u + 1
c
7
u
20
− 6u
19
+ ··· − 11u + 5
c
11
u
20
+ 13u
19
+ ··· + 125u + 25
c
12
u
20
+ 6u
19
+ ··· + 11u + 5
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
+ 16y
19
+ ··· + 14y + 1
c
2
, c
5
y
20
− 8y
19
+ ··· − 10y + 1
c
3
, c
8
y
20
− 7y
19
+ ··· − 16y + 1
c
4
, c
9
y
20
− 6y
19
+ ··· + 314y + 25
c
6
, c
10
y
20
+ 6y
19
+ ··· − 14y + 1
c
7
, c
12
y
20
+ 12y
19
+ ··· + 329y + 25
c
11
y
20
+ y
19
+ ··· + 1525y + 625
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.749177 + 0.792993I
a = −1.00000
b = −0.461335 − 0.696929I
7.15083 + 6.18840I −3.23960 − 2.72855I
u = 0.749177 − 0.792993I
a = −1.00000
b = −0.461335 + 0.696929I
7.15083 − 6.18840I −3.23960 + 2.72855I
u = −0.856996 + 0.013947I
a = −1.00000
b = 0.097835 + 0.598647I
−2.80631 − 0.60538I −10.53109 − 0.51236I
u = −0.856996 − 0.013947I
a = −1.00000
b = 0.097835 − 0.598647I
−2.80631 + 0.60538I −10.53109 + 0.51236I
u = −0.838006 + 0.822643I
a = −1.00000
b = −0.378604 + 0.720129I
7.53299 + 0.99079I −2.61556 − 1.90284I
u = −0.838006 − 0.822643I
a = −1.00000
b = −0.378604 − 0.720129I
7.53299 − 0.99079I −2.61556 + 1.90284I
u = −0.665108 + 0.324125I
a = −1.00000
b = 1.117190 − 0.608940I
−1.83782 + 3.01831I −10.5178 − 9.5148I
u = −0.665108 − 0.324125I
a = −1.00000
b = 1.117190 + 0.608940I
−1.83782 − 3.01831I −10.5178 + 9.5148I
u = −1.081860 + 0.842780I
a = −1.00000
b = 0.605583 + 0.877015I
−2.54111 + 5.42929I −4.17139 − 2.92908I
u = −1.081860 − 0.842780I
a = −1.00000
b = 0.605583 − 0.877015I
−2.54111 − 5.42929I −4.17139 + 2.92908I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.126260 + 0.824230I
a = −1.00000
b = −0.055343 − 1.135190I
−4.70013 − 0.25170I −6.72415 + 4.83979I
u = 1.126260 − 0.824230I
a = −1.00000
b = −0.055343 + 1.135190I
−4.70013 + 0.25170I −6.72415 − 4.83979I
u = 0.582150 + 0.090727I
a = −1.00000
b = 0.015486 − 1.370700I
−3.30705 + 3.54726I −12.80442 − 5.42208I
u = 0.582150 − 0.090727I
a = −1.00000
b = 0.015486 + 1.370700I
−3.30705 − 3.54726I −12.80442 + 5.42208I
u = −1.11790 + 0.86654I
a = −1.00000
b = 0.225749 + 0.939626I
−1.68131 + 5.33977I −5.49082 − 5.51223I
u = −1.11790 − 0.86654I
a = −1.00000
b = 0.225749 − 0.939626I
−1.68131 − 5.33977I −5.49082 + 5.51223I
u = 1.11605 + 0.91718I
a = −1.00000
b = 0.51806 − 1.34055I
−5.18149 − 8.81978I −10.79868 + 6.59356I
u = 1.11605 − 0.91718I
a = −1.00000
b = 0.51806 + 1.34055I
−5.18149 + 8.81978I −10.79868 − 6.59356I
u = 0.486237 + 0.221311I
a = −1.00000
b = 1.31538 + 1.29746I
−2.49821 + 1.18090I −17.1065 + 7.0501I
u = 0.486237 − 0.221311I
a = −1.00000
b = 1.31538 − 1.29746I
−2.49821 − 1.18090I −17.1065 − 7.0501I
12
III. I
u
3
= h−3.74 × 10
51
u
39
− 8.55 × 10
51
u
38
+ · · · + 4.04 × 10
50
b + 1.36 ×
10
52
, −3.50 × 10
83
u
39
− 8.75 × 10
83
u
38
+ · · · + 9.39 × 10
81
a + 3.79 ×
10
83
, u
40
+ 2u
39
+ · · · − 13u + 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
12
=
37.2782u
39
+ 93.1401u
38
+ ··· + 658.285u − 40.3827
9.24932u
39
+ 21.1413u
38
+ ··· + 315.076u − 33.6527
a
1
=
46.5275u
39
+ 114.281u
38
+ ··· + 973.362u − 74.0354
9.24932u
39
+ 21.1413u
38
+ ··· + 315.076u − 33.6527
a
3
=
30.1491u
39
+ 59.6821u
38
+ ··· + 1673.11u − 208.172
31.8912u
39
+ 73.1587u
38
+ ··· + 1019.79u − 101.577
a
2
=
15.0952u
39
+ 42.4578u
38
+ ··· − 102.381u + 42.5474
−14.6995u
39
− 33.0619u
38
+ ··· − 518.350u + 54.3768
a
7
=
110.826u
39
+ 256.187u
38
+ ··· + 3415.02u − 335.365
9.24932u
39
+ 21.1413u
38
+ ··· + 315.076u − 34.6527
a
11
=
38.9331u
39
+ 96.3096u
38
+ ··· + 769.052u − 55.4517
9.11106u
39
+ 20.8265u
38
+ ··· + 311.597u − 33.5123
a
5
=
96.4146u
39
+ 213.222u
38
+ ··· + 3675.88u − 401.553
35.0020u
39
+ 80.3933u
38
+ ··· + 1115.52u − 111.581
a
6
=
85.2631u
39
+ 194.465u
38
+ ··· + 2845.50u − 291.046
14.2530u
39
+ 33.9549u
38
+ ··· + 366.582u − 31.9756
a
10
=
−17.9587u
39
− 38.4998u
38
+ ··· − 749.953u + 80.2253
16.5567u
39
+ 36.5186u
38
+ ··· + 649.966u − 72.1059
(ii) Obstruction class = −1
(iii) Cusp Shapes = 32.1094u
39
+ 63.6905u
38
+ ··· + 1775.28u − 226.798
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
10
+ 2u
9
+ 9u
8
+ 15u
7
+ 28u
6
+ 36u
5
+ 35u
4
+ 22u
3
+ 15u
2
+ 6u + 1)
4
c
2
, c
5
(u
10
− 2u
9
+ u
8
+ 3u
7
− 2u
6
− 2u
5
+ 3u
4
+ 2u
3
− u
2
− 2u + 1)
4
c
3
, c
8
u
40
+ 2u
39
+ ··· − 13u + 1
c
4
, c
9
u
40
+ 2u
39
+ ··· + 556819u + 78541
c
6
, c
10
u
40
− 3u
39
+ ··· + 59250u + 16729
c
7
, c
12
(u
2
+ u + 1)
20
c
11
(u
10
+ 3u
9
+ 6u
8
+ 7u
7
+ 9u
6
+ 9u
5
+ 10u
4
+ 6u
3
+ 5u
2
+ 3u + 2)
4
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
10
+ 14y
9
+ ··· − 6y + 1)
4
c
2
, c
5
(y
10
− 2y
9
+ 9y
8
− 15y
7
+ 28y
6
− 36y
5
+ 35y
4
− 22y
3
+ 15y
2
− 6y + 1)
4
c
3
, c
8
y
40
− 6y
39
+ ··· − 41y + 1
c
4
, c
9
y
40
− 18y
39
+ ··· + 798086907y + 6168688681
c
6
, c
10
y
40
+ 41y
39
+ ··· + 1832579726y + 279859441
c
7
, c
12
(y
2
+ y + 1)
20
c
11
(y
10
+ 3y
9
+ ··· + 11y + 4)
4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.180275 + 0.992664I
a = 0.000968 − 0.299992I
b = 0.500000 + 0.866025I
−2.22682 + 1.42904I −7.31849 − 0.06369I
u = −0.180275 − 0.992664I
a = 0.000968 + 0.299992I
b = 0.500000 − 0.866025I
−2.22682 − 1.42904I −7.31849 + 0.06369I
u = −0.825169 + 0.581665I
a = −0.269230 − 0.089195I
b = 0.500000 − 0.866025I
−0.55514 + 2.55647I −1.79322 − 3.96020I
u = −0.825169 − 0.581665I
a = −0.269230 + 0.089195I
b = 0.500000 + 0.866025I
−0.55514 − 2.55647I −1.79322 + 3.96020I
u = −0.927681 + 0.025135I
a = −0.677736 − 0.206020I
b = 0.500000 + 0.866025I
−3.21269 − 1.90262I −14.2791 + 3.2498I
u = −0.927681 − 0.025135I
a = −0.677736 + 0.206020I
b = 0.500000 − 0.866025I
−3.21269 + 1.90262I −14.2791 − 3.2498I
u = 0.150588 + 1.186930I
a = −0.279685 − 1.340970I
b = 0.500000 + 0.866025I
7.82170 + 3.78328I 0. − 2.61377I
u = 0.150588 − 1.186930I
a = −0.279685 + 1.340970I
b = 0.500000 − 0.866025I
7.82170 − 3.78328I 0. + 2.61377I
u = 0.510475 + 0.619539I
a = −2.17116 + 0.59425I
b = 0.500000 − 0.866025I
−2.22682 − 2.63073I −7.31849 + 6.86451I
u = 0.510475 − 0.619539I
a = −2.17116 − 0.59425I
b = 0.500000 + 0.866025I
−2.22682 + 2.63073I −7.31849 − 6.86451I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.332577 + 1.177620I
a = −0.010519 + 1.274250I
b = 0.500000 − 0.866025I
7.22009 + 3.33409I −4.00000 − 3.04149I
u = −0.332577 − 1.177620I
a = −0.010519 − 1.274250I
b = 0.500000 + 0.866025I
7.22009 − 3.33409I −4.00000 + 3.04149I
u = −0.693076 + 1.011640I
a = −1.172690 − 0.580972I
b = 0.500000 + 0.866025I
−0.55514 + 6.61623I 0. − 10.88840I
u = −0.693076 − 1.011640I
a = −1.172690 + 0.580972I
b = 0.500000 − 0.866025I
−0.55514 − 6.61623I 0. + 10.88840I
u = 1.110860 + 0.660478I
a = −1.157050 − 0.225323I
b = 0.500000 − 0.866025I
−3.21269 − 5.96239I −14.2791 + 10.1780I
u = 1.110860 − 0.660478I
a = −1.157050 + 0.225323I
b = 0.500000 + 0.866025I
−3.21269 + 5.96239I −14.2791 − 10.1780I
u = 0.633901 + 0.174086I
a = −1.350690 + 0.410587I
b = 0.500000 + 0.866025I
−3.21269 − 1.90262I −14.2791 + 3.2498I
u = 0.633901 − 0.174086I
a = −1.350690 − 0.410587I
b = 0.500000 − 0.866025I
−3.21269 + 1.90262I −14.2791 − 3.2498I
u = 0.353320 + 0.370137I
a = −0.61494 − 3.83881I
b = 0.500000 − 0.866025I
7.22009 − 7.39385I −2.50388 + 9.96969I
u = 0.353320 − 0.370137I
a = −0.61494 + 3.83881I
b = 0.500000 + 0.866025I
7.22009 + 7.39385I −2.50388 − 9.96969I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.13650 + 1.01451I
a = −0.832688 − 0.162157I
b = 0.500000 + 0.866025I
−3.21269 + 5.96239I 0
u = −1.13650 − 1.01451I
a = −0.832688 + 0.162157I
b = 0.500000 − 0.866025I
−3.21269 − 5.96239I 0
u = −0.264091 + 0.371106I
a = −1.24764 + 3.99076I
b = 0.500000 + 0.866025I
7.82170 + 0.27648I −0.60526 − 4.31443I
u = −0.264091 − 0.371106I
a = −1.24764 − 3.99076I
b = 0.500000 − 0.866025I
7.82170 − 0.27648I −0.60526 + 4.31443I
u = −1.49707 + 0.43617I
a = −0.006478 + 0.784725I
b = 0.500000 + 0.866025I
7.22009 − 3.33409I 0
u = −1.49707 − 0.43617I
a = −0.006478 − 0.784725I
b = 0.500000 − 0.866025I
7.22009 + 3.33409I 0
u = 1.40050 + 0.78368I
a = −0.684691 − 0.339208I
b = 0.500000 − 0.866025I
−0.55514 − 6.61623I 0
u = 1.40050 − 0.78368I
a = −0.684691 + 0.339208I
b = 0.500000 + 0.866025I
−0.55514 + 6.61623I 0
u = 1.54952 + 0.53390I
a = −0.149052 − 0.714642I
b = 0.500000 − 0.866025I
7.82170 − 3.78328I 0
u = 1.54952 − 0.53390I
a = −0.149052 + 0.714642I
b = 0.500000 + 0.866025I
7.82170 + 3.78328I 0
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.297617 + 0.055042I
a = 0.01076 + 3.33339I
b = 0.500000 + 0.866025I
−2.22682 + 1.42904I −7.31849 − 0.06369I
u = 0.297617 − 0.055042I
a = 0.01076 − 3.33339I
b = 0.500000 − 0.866025I
−2.22682 − 1.42904I −7.31849 + 0.06369I
u = 0.274042 + 0.083001I
a = −3.34695 − 1.10883I
b = 0.500000 + 0.866025I
−0.55514 − 2.55647I −1.79322 + 3.96020I
u = 0.274042 − 0.083001I
a = −3.34695 + 1.10883I
b = 0.500000 − 0.866025I
−0.55514 + 2.55647I −1.79322 − 3.96020I
u = −1.47649 + 1.04177I
a = −0.428484 + 0.117277I
b = 0.500000 + 0.866025I
−2.22682 + 2.63073I 0
u = −1.47649 − 1.04177I
a = −0.428484 − 0.117277I
b = 0.500000 − 0.866025I
−2.22682 − 2.63073I 0
u = −1.15150 + 1.51693I
a = −0.071364 + 0.228268I
b = 0.500000 − 0.866025I
7.82170 − 0.27648I 0
u = −1.15150 − 1.51693I
a = −0.071364 − 0.228268I
b = 0.500000 + 0.866025I
7.82170 + 0.27648I 0
u = 1.20361 + 1.58394I
a = −0.040685 − 0.253980I
b = 0.500000 + 0.866025I
7.22009 + 7.39385I 0
u = 1.20361 − 1.58394I
a = −0.040685 + 0.253980I
b = 0.500000 − 0.866025I
7.22009 − 7.39385I 0
19
IV. I
u
4
= h−u
3
− 2u
2
+ 2b − 2u + 1, u
3
+ 2a − 5, u
4
+ u
3
+ 2u
2
− u + 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
12
=
−
1
2
u
3
+
5
2
1
2
u
3
+ u
2
+ u −
1
2
a
1
=
u
2
+ u + 2
1
2
u
3
+ u
2
+ u −
1
2
a
3
=
3
2
u
3
+ 3u
2
+ 5u +
3
2
1
2
u
3
+ u −
3
2
a
2
=
3
2
u
3
+ 4u
2
+ 6u +
7
2
u
3
+ u
2
+ 2u − 2
a
7
=
u
3
+ u
2
+ 2u − 1
−
1
2
u
3
− u
2
− u −
1
2
a
11
=
−
1
2
u
3
+
5
2
1
2
u
3
+ u
2
+ u −
1
2
a
5
=
3
2
u
3
+ 3u
2
+ 5u +
3
2
1
2
u
3
+ u −
3
2
a
6
=
−u
2
− u − 2
−
1
2
u
3
− u
2
− u +
1
2
a
10
=
−
3
2
u
3
− 2u
2
− 3u +
5
2
1
2
u
3
+ u
2
+ u +
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
3
+ 4u
2
+ 4u − 1
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
4
, c
8
c
9
u
4
+ u
3
+ 2u
2
− u + 1
c
5
(u + 1)
4
c
6
, c
10
, c
12
(u
2
− u + 1)
2
c
7
(u
2
+ u + 1)
2
c
11
u
4
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
, c
8
c
9
y
4
+ 3y
3
+ 8y
2
+ 3y + 1
c
6
, c
7
, c
10
c
12
(y
2
+ y + 1)
2
c
11
y
4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.309017 + 0.535233I
a = 2.61803
b = −0.500000 + 0.866025I
−1.64493 − 2.02988I −1.00000 + 3.46410I
u = 0.309017 − 0.535233I
a = 2.61803
b = −0.500000 − 0.866025I
−1.64493 + 2.02988I −1.00000 − 3.46410I
u = −0.80902 + 1.40126I
a = 0.381966
b = −0.500000 − 0.866025I
−1.64493 + 2.02988I −1.00000 − 3.46410I
u = −0.80902 − 1.40126I
a = 0.381966
b = −0.500000 + 0.866025I
−1.64493 − 2.02988I −1.00000 + 3.46410I
23
V. I
u
5
= hb + u + 1, a − 1, u
2
+ u + 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
−u − 1
a
12
=
1
−u − 1
a
1
=
−u
−u − 1
a
3
=
u
u + 1
a
2
=
−u
−u − 1
a
7
=
0
u
a
11
=
1
−u − 1
a
5
=
u
u + 1
a
6
=
u
u + 1
a
10
=
u + 2
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u − 2
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
11
u
2
c
3
, c
4
, c
6
c
8
, c
9
, c
10
u
2
+ u + 1
c
7
, c
12
u
2
− u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
11
y
2
c
3
, c
4
, c
6
c
7
, c
8
, c
9
c
10
, c
12
y
2
+ y + 1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 1.00000
b = −0.500000 − 0.866025I
2.02988I 0. − 3.46410I
u = −0.500000 − 0.866025I
a = 1.00000
b = −0.500000 + 0.866025I
− 2.02988I 0. + 3.46410I
27
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u − 1)
4
· (u
10
+ 2u
9
+ 9u
8
+ 15u
7
+ 28u
6
+ 36u
5
+ 35u
4
+ 22u
3
+ 15u
2
+ 6u + 1)
4
· (u
20
− 8u
19
+ ··· − 10u + 1)(u
29
+ 9u
28
+ ··· − 861u + 441)
c
2
u
2
(u − 1)
4
· (u
10
− 2u
9
+ u
8
+ 3u
7
− 2u
6
− 2u
5
+ 3u
4
+ 2u
3
− u
2
− 2u + 1)
4
· (u
20
+ 4u
19
+ ··· + 4u + 1)(u
29
+ 9u
28
+ ··· + 105u + 21)
c
3
, c
8
(u
2
+ u + 1)(u
4
+ u
3
+ 2u
2
− u + 1)(u
20
+ u
19
+ ··· − 2u + 1)
· (u
29
− 2u
28
+ ··· − 3u + 1)(u
40
+ 2u
39
+ ··· − 13u + 1)
c
4
, c
9
(u
2
+ u + 1)(u
4
+ u
3
+ 2u
2
− u + 1)(u
20
− 3u
18
+ ··· − 4u + 5)
· (u
29
− u
28
+ ··· + 19u + 17)(u
40
+ 2u
39
+ ··· + 556819u + 78541)
c
5
u
2
(u + 1)
4
· (u
10
− 2u
9
+ u
8
+ 3u
7
− 2u
6
− 2u
5
+ 3u
4
+ 2u
3
− u
2
− 2u + 1)
4
· (u
20
− 4u
19
+ ··· − 4u + 1)(u
29
+ 9u
28
+ ··· + 105u + 21)
c
6
, c
10
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
20
− 2u
19
+ ··· + 2u + 1)
· (u
29
+ 3u
28
+ ··· + 29u + 1)(u
40
− 3u
39
+ ··· + 59250u + 16729)
c
7
(u
2
− u + 1)(u
2
+ u + 1)
22
(u
20
− 6u
19
+ ··· − 11u + 5)
· (u
29
− 18u
28
+ ··· − 2560u + 512)
c
11
u
6
(u
10
+ 3u
9
+ 6u
8
+ 7u
7
+ 9u
6
+ 9u
5
+ 10u
4
+ 6u
3
+ 5u
2
+ 3u + 2)
4
· (u
20
+ 13u
19
+ ··· + 125u + 25)(u
29
− 18u
28
+ ··· + 294u − 21)
c
12
((u
2
− u + 1)
3
)(u
2
+ u + 1)
20
(u
20
+ 6u
19
+ ··· + 11u + 5)
· (u
29
− 18u
28
+ ··· − 2560u + 512)
28
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
2
(y −1)
4
(y
10
+ 14y
9
+ ··· − 6y + 1)
4
(y
20
+ 16y
19
+ ··· + 14y + 1)
· (y
29
+ 31y
28
+ ··· + 2190447y −194481)
c
2
, c
5
y
2
(y −1)
4
· (y
10
− 2y
9
+ 9y
8
− 15y
7
+ 28y
6
− 36y
5
+ 35y
4
− 22y
3
+ 15y
2
− 6y + 1)
4
· (y
20
− 8y
19
+ ··· − 10y + 1)(y
29
− 9y
28
+ ··· − 861y −441)
c
3
, c
8
(y
2
+ y + 1)(y
4
+ 3y
3
+ ··· + 3y + 1)(y
20
− 7y
19
+ ··· − 16y + 1)
· (y
29
+ 28y
27
+ ··· − 11y −1)(y
40
− 6y
39
+ ··· − 41y + 1)
c
4
, c
9
(y
2
+ y + 1)(y
4
+ 3y
3
+ ··· + 3y + 1)(y
20
− 6y
19
+ ··· + 314y + 25)
· (y
29
− 15y
28
+ ··· + 3183y −289)
· (y
40
− 18y
39
+ ··· + 798086907y + 6168688681)
c
6
, c
10
((y
2
+ y + 1)
3
)(y
20
+ 6y
19
+ ··· − 14y + 1)
· (y
29
+ 45y
28
+ ··· + 331y −1)
· (y
40
+ 41y
39
+ ··· + 1832579726y + 279859441)
c
7
, c
12
((y
2
+ y + 1)
23
)(y
20
+ 12y
19
+ ··· + 329y + 25)
· (y
29
+ 12y
28
+ ··· + 7864320y −262144)
c
11
y
6
(y
10
+ 3y
9
+ ··· + 11y + 4)
4
(y
20
+ y
19
+ ··· + 1525y + 625)
· (y
29
+ 4y
28
+ ··· + 1344y −441)
29
