12n
0259
(K12n
0259
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 11 9 12 4 6 1 8 6
Solving Sequence
4,8
9
3,12
7 6 1 11 5 2 10
c
8
c
3
c
7
c
6
c
12
c
11
c
5
c
2
c
10
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h8.06424 × 10
33
u
29
− 3.08706 × 10
34
u
28
+ ··· + 2.02678 × 10
35
b + 8.88012 × 10
34
,
− 1.10182 × 10
35
u
29
+ 5.35345 × 10
35
u
28
+ ··· + 2.02678 × 10
36
a − 5.52972 × 10
36
,
u
30
− 5u
29
+ ··· + 208u − 64i
I
u
2
= h−50322u
16
+ 60651u
15
+ ··· + 148714b + 159141,
− 2740465u
16
+ 777157u
15
+ ··· + 297428a + 8444609,
u
17
+ 3u
15
− 2u
14
+ 5u
13
− 9u
12
+ 2u
11
− 20u
10
− 2u
9
− 25u
8
+ u
7
− 17u
6
+ 6u
5
+ 3u
3
+ 2u
2
− 3u − 1i
I
u
3
= h−158244u
8
a
3
− 40800u
8
a
2
+ ··· + 813522a − 91963, 2u
8
a
3
− u
8
a
2
+ ··· + 94a + 520,
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
I
v
1
= ha, b + 2v + 2, 4v
2
+ 6v + 1i
* 4 irreducible components of dim
C
= 0, with total 85 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
= h8.06 × 10
33
u
29
− 3.09 × 10
34
u
28
+ · · · + 2.03 × 10
35
b + 8.88 ×
10
34
, −1.10 × 10
35
u
29
+ 5.35 × 10
35
u
28
+ · · · + 2.03 × 10
36
a − 5.53 ×
10
36
, u
30
− 5u
29
+ · · · + 208u − 64i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
3
=
u
u
3
+ u
a
12
=
0.0543630u
29
− 0.264136u
28
+ ··· − 10.6974u + 2.72833
−0.0397885u
29
+ 0.152314u
28
+ ··· − 0.205764u − 0.438140
a
7
=
0.0394700u
29
− 0.200918u
28
+ ··· − 9.53676u + 4.27030
−0.0378177u
29
+ 0.199367u
28
+ ··· + 10.9483u − 5.71363
a
6
=
0.0249093u
29
− 0.112539u
28
+ ··· − 1.85669u − 1.21498
−0.0341130u
29
+ 0.167188u
28
+ ··· + 6.77674u − 4.71681
a
1
=
0.0984923u
29
− 0.480645u
28
+ ··· − 18.1702u + 6.77214
0.0129199u
29
− 0.117465u
28
+ ··· − 13.8793u + 11.1867
a
11
=
0.0145745u
29
− 0.111822u
28
+ ··· − 10.9032u + 2.29019
−0.0397885u
29
+ 0.152314u
28
+ ··· − 0.205764u − 0.438140
a
5
=
0.0265616u
29
− 0.114090u
28
+ ··· − 0.445179u − 3.65831
−0.0719307u
29
+ 0.366555u
28
+ ··· + 17.7250u − 10.4304
a
2
=
−0.0766915u
29
+ 0.396957u
28
+ ··· + 20.3635u − 7.97007
−0.00269807u
29
+ 0.0505818u
28
+ ··· + 12.2023u − 10.7644
a
10
=
0.0441293u
29
− 0.216509u
28
+ ··· − 7.47278u + 5.04380
0.0527084u
29
− 0.269779u
28
+ ··· − 13.6736u + 11.6248
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.171902u
29
+ 0.740462u
28
+ ··· + 32.2278u − 42.5665
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
+ 17u
29
+ ··· + 6768u + 256
c
2
, c
4
u
30
− 3u
29
+ ··· − 44u − 16
c
3
, c
8
u
30
− 5u
29
+ ··· + 208u − 64
c
5
, c
7
, c
11
u
30
− u
29
+ ··· + 2u
2
− 1
c
6
, c
9
, c
12
u
30
− 30u
28
+ ··· − u + 1
c
10
u
30
− 19u
29
+ ··· + 2048u − 512
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
− 5y
29
+ ··· − 31895296y + 65536
c
2
, c
4
y
30
− 17y
29
+ ··· − 6768y + 256
c
3
, c
8
y
30
+ 9y
29
+ ··· − 21248y + 4096
c
5
, c
7
, c
11
y
30
+ y
29
+ ··· − 4y + 1
c
6
, c
9
, c
12
y
30
− 60y
29
+ ··· − 63y + 1
c
10
y
30
− 23y
29
+ ··· − 3145728y + 262144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.920671 + 0.215050I
a = 0.474770 + 0.236439I
b = 0.185709 − 0.495074I
−0.678358 − 0.594987I −11.14828 − 1.26949I
u = −0.920671 − 0.215050I
a = 0.474770 − 0.236439I
b = 0.185709 + 0.495074I
−0.678358 + 0.594987I −11.14828 + 1.26949I
u = 0.997695 + 0.376702I
a = 0.437212 + 0.126971I
b = 0.612963 − 0.562757I
−1.30376 + 3.43482I −13.9978 − 7.1058I
u = 0.997695 − 0.376702I
a = 0.437212 − 0.126971I
b = 0.612963 + 0.562757I
−1.30376 − 3.43482I −13.9978 + 7.1058I
u = 0.316298 + 0.849109I
a = 0.425852 + 0.030660I
b = 0.918017 − 0.164528I
−2.07471 − 1.64401I −10.99207 + 2.69705I
u = 0.316298 − 0.849109I
a = 0.425852 − 0.030660I
b = 0.918017 + 0.164528I
−2.07471 + 1.64401I −10.99207 − 2.69705I
u = 0.250072 + 0.795467I
a = 0.08474 + 1.97666I
b = −0.528572 − 0.417784I
−2.30189 − 1.11843I −12.20818 + 6.54898I
u = 0.250072 − 0.795467I
a = 0.08474 − 1.97666I
b = −0.528572 + 0.417784I
−2.30189 + 1.11843I −12.20818 − 6.54898I
u = −0.439076 + 1.238770I
a = −0.341907 − 1.274950I
b = −0.664768 + 0.726793I
3.50589 + 3.81678I −10.18184 − 5.51966I
u = −0.439076 − 1.238770I
a = −0.341907 + 1.274950I
b = −0.664768 − 0.726793I
3.50589 − 3.81678I −10.18184 + 5.51966I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.672305 + 0.131504I
a = 0.465097 − 0.014978I
b = −1.333120 + 0.111490I
−10.75090 − 0.00550I −26.5001 + 2.7456I
u = 0.672305 − 0.131504I
a = 0.465097 + 0.014978I
b = −1.333120 − 0.111490I
−10.75090 + 0.00550I −26.5001 − 2.7456I
u = 0.673336 + 1.153840I
a = −0.01039 − 1.60109I
b = 0.938705 + 0.985912I
−8.26944 − 5.68185I −13.8804 + 4.5637I
u = 0.673336 − 1.153840I
a = −0.01039 + 1.60109I
b = 0.938705 − 0.985912I
−8.26944 + 5.68185I −13.8804 − 4.5637I
u = −1.195980 + 0.596147I
a = 0.433700 + 0.140568I
b = −0.804031 − 0.882885I
−5.01474 − 3.34334I −11.59669 + 2.94079I
u = −1.195980 − 0.596147I
a = 0.433700 − 0.140568I
b = −0.804031 + 0.882885I
−5.01474 + 3.34334I −11.59669 − 2.94079I
u = 1.165670 + 0.733627I
a = 0.464934 − 0.150862I
b = −0.96952 + 1.09583I
−7.65940 + 8.88821I −13.8511 − 5.5347I
u = 1.165670 − 0.733627I
a = 0.464934 + 0.150862I
b = −0.96952 − 1.09583I
−7.65940 − 8.88821I −13.8511 + 5.5347I
u = 0.221400 + 1.363400I
a = 0.015740 − 1.022660I
b = −0.132717 + 0.871865I
4.53000 − 0.32057I −7.71560 − 1.10595I
u = 0.221400 − 1.363400I
a = 0.015740 + 1.022660I
b = −0.132717 − 0.871865I
4.53000 + 0.32057I −7.71560 + 1.10595I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.647790 + 1.222820I
a = −0.535702 + 1.224120I
b = −0.802016 − 0.702401I
1.35480 − 9.44263I −13.2001 + 10.5014I
u = 0.647790 − 1.222820I
a = −0.535702 − 1.224120I
b = −0.802016 + 0.702401I
1.35480 + 9.44263I −13.2001 − 10.5014I
u = 1.40325
a = 0.323081
b = −0.580884
−10.9270 −40.4210
u = −0.79217 + 1.21119I
a = 0.24417 + 1.46527I
b = 0.94680 − 1.23179I
−2.95388 + 10.39440I −10.10326 − 5.62687I
u = −0.79217 − 1.21119I
a = 0.24417 − 1.46527I
b = 0.94680 + 1.23179I
−2.95388 − 10.39440I −10.10326 + 5.62687I
u = 0.86453 + 1.17030I
a = 0.39716 − 1.50383I
b = 1.07853 + 1.31263I
−6.1786 − 16.1705I −12.9056 + 8.4851I
u = 0.86453 − 1.17030I
a = 0.39716 + 1.50383I
b = 1.07853 − 1.31263I
−6.1786 + 16.1705I −12.9056 − 8.4851I
u = −0.43744 + 1.41584I
a = −0.014032 + 1.010380I
b = 0.154110 − 0.976877I
3.27546 + 6.39941I −8.60195 − 5.42628I
u = −0.43744 − 1.41584I
a = −0.014032 − 1.010380I
b = 0.154110 + 0.976877I
3.27546 − 6.39941I −8.60195 + 5.42628I
u = −0.450762
a = 0.594234
b = 0.380692
−0.635586 −15.5630
7
II.
I
u
2
= h−5.03 × 10
4
u
16
+ 6.07 × 10
4
u
15
+ · · · + 1.49 × 10
5
b + 1.59 × 10
5
, −2.74 ×
10
6
u
16
+7.77×10
5
u
15
+· · · +2.97×10
5
a+8.44×10
6
, u
17
+3u
15
+· · · − 3u −1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
3
=
u
u
3
+ u
a
12
=
9.21388u
16
− 2.61292u
15
+ ··· + 9.55963u − 28.3921
0.338381u
16
− 0.407837u
15
+ ··· + 0.429865u − 1.07011
a
7
=
8.05673u
16
− 2.39322u
15
+ ··· + 5.18074u − 23.8643
0.240774u
16
+ 0.356863u
15
+ ··· + 0.945237u − 0.542810
a
6
=
7.15244u
16
− 2.00192u
15
+ ··· + 5.24891u − 22.0139
0.161686u
16
+ 0.219011u
15
+ ··· + 1.21485u − 0.151512
a
1
=
1.06597u
16
− 0.172287u
15
+ ··· + 1.14668u − 3.00192
−0.00475409u
16
− 0.200035u
15
+ ··· + 0.818719u + 0.219011
a
11
=
9.55226u
16
− 3.02076u
15
+ ··· + 9.98950u − 29.4622
0.338381u
16
− 0.407837u
15
+ ··· + 0.429865u − 1.07011
a
5
=
−1.14506u
16
+ 0.0344352u
15
+ ··· − 0.877073u + 3.39322
−0.0790880u
16
− 0.137852u
15
+ ··· + 0.269611u + 0.391298
a
2
=
1.11352u
16
− 0.409703u
15
+ ··· + 2.18844u − 3.03636
0.179102u
16
− 0.186802u
15
+ ··· + 1.19578u − 0.0528397
a
10
=
8.14791u
16
− 2.44064u
15
+ ··· + 8.41295u − 24.3902
0.343135u
16
− 0.207802u
15
+ ··· − 0.388854u − 1.28913
(ii) Obstruction class = 1
(iii) Cusp Shapes =
6794471
297428
u
16
−
1681861
297428
u
15
+ ··· +
571348
74357
u −
25623465
297428
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 10u
16
+ ··· + 17u − 1
c
2
u
17
+ 4u
16
+ ··· − u + 1
c
3
u
17
+ 3u
15
+ ··· − 3u + 1
c
4
u
17
− 4u
16
+ ··· − u − 1
c
5
, c
11
u
17
+ 6u
15
+ ··· − 3u − 1
c
6
, c
12
u
17
− 3u
16
+ ··· + 6u
2
+ 1
c
7
u
17
+ 6u
15
+ ··· − 3u + 1
c
8
u
17
+ 3u
15
+ ··· − 3u − 1
c
9
u
17
+ 3u
16
+ ··· − 6u
2
− 1
c
10
u
17
− 5u
16
+ ··· + 5u − 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 2y
16
+ ··· + 157y −1
c
2
, c
4
y
17
− 10y
16
+ ··· + 17y −1
c
3
, c
8
y
17
+ 6y
16
+ ··· + 13y −1
c
5
, c
7
, c
11
y
17
+ 12y
16
+ ··· + 5y −1
c
6
, c
9
, c
12
y
17
− 5y
16
+ ··· − 12y −1
c
10
y
17
− 17y
16
+ ··· + 11y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.222868 + 0.957169I
a = 0.937935 − 0.366003I
b = 0.975905 + 0.087227I
−3.24280 + 2.04185I −17.4447 − 3.6628I
u = −0.222868 − 0.957169I
a = 0.937935 + 0.366003I
b = 0.975905 − 0.087227I
−3.24280 − 2.04185I −17.4447 + 3.6628I
u = −0.143073 + 1.125680I
a = −0.06490 + 1.65937I
b = −0.240226 − 1.383230I
6.60440 − 0.23148I −4.66739 − 0.18271I
u = −0.143073 − 1.125680I
a = −0.06490 − 1.65937I
b = −0.240226 + 1.383230I
6.60440 + 0.23148I −4.66739 + 0.18271I
u = −0.934717 + 0.786177I
a = −0.460802 − 0.068107I
b = 0.102794 + 0.830593I
0.49138 − 1.47201I −4.39198 + 2.32537I
u = −0.934717 − 0.786177I
a = −0.460802 + 0.068107I
b = 0.102794 − 0.830593I
0.49138 + 1.47201I −4.39198 − 2.32537I
u = 0.463922 + 1.145870I
a = 0.43983 − 1.42671I
b = −0.17875 + 1.49824I
5.30175 − 4.82160I −8.88387 + 5.04151I
u = 0.463922 − 1.145870I
a = 0.43983 + 1.42671I
b = −0.17875 − 1.49824I
5.30175 + 4.82160I −8.88387 − 5.04151I
u = 0.622575 + 1.114960I
a = −0.632046 + 0.809570I
b = −0.340268 − 0.934275I
4.76952 − 2.66666I −3.51429 + 3.01636I
u = 0.622575 − 1.114960I
a = −0.632046 − 0.809570I
b = −0.340268 + 0.934275I
4.76952 + 2.66666I −3.51429 − 3.01636I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621513 + 0.226133I
a = 3.17814 + 0.77491I
b = 0.068320 + 1.335540I
2.59448 + 0.58189I −16.1225 − 5.9646I
u = 0.621513 − 0.226133I
a = 3.17814 − 0.77491I
b = 0.068320 − 1.335540I
2.59448 − 0.58189I −16.1225 + 5.9646I
u = −0.76282 + 1.20700I
a = −0.450462 − 0.871861I
b = −0.529361 + 0.773457I
1.99341 + 8.23287I −9.38259 − 6.87786I
u = −0.76282 − 1.20700I
a = −0.450462 + 0.871861I
b = −0.529361 − 0.773457I
1.99341 − 8.23287I −9.38259 + 6.87786I
u = −0.509710
a = −3.08687
b = 0.727999
−4.29378 −7.87230
u = 1.53136
a = −0.327837
b = 0.362879
−10.7956 20.7800
u = −0.310720
a = −25.4807
b = −0.807701
−5.48556 −72.0930
12
III. I
u
3
= h−1.58 × 10
5
a
3
u
8
− 4.08 × 10
4
a
2
u
8
+ · · · + 8.14 × 10
5
a − 9.20 ×
10
4
, 2u
8
a
3
−u
8
a
2
+· · ·+94a +520, u
9
+u
8
+2u
7
+u
6
+3u
5
+u
4
+2u
3
+u−1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
3
=
u
u
3
+ u
a
12
=
a
0.250587a
3
u
8
+ 0.0646088a
2
u
8
+ ··· − 1.28825a + 0.145628
a
7
=
0.0695431a
3
u
8
− 0.0718551a
2
u
8
+ ··· − 0.741380a + 2.26000
−0.0275854a
3
u
8
+ 0.352029a
2
u
8
+ ··· + 1.67727a + 0.105629
a
6
=
−0.0695431a
3
u
8
+ 0.0718551a
2
u
8
+ ··· + 0.741380a + 1.74000
−0.250587a
3
u
8
− 0.0646088a
2
u
8
+ ··· + 1.28825a + 0.854372
a
1
=
−u
2
− 1
−u
2
a
11
=
0.250587a
3
u
8
+ 0.0646088a
2
u
8
+ ··· − 0.288252a + 0.145628
0.250587a
3
u
8
+ 0.0646088a
2
u
8
+ ··· − 1.28825a + 0.145628
a
5
=
−u
4
− u
2
− 1
−u
4
a
2
=
u
6
+ u
4
+ 2u
2
+ 1
u
8
+ 2u
6
+ 2u
4
+ 2u
2
a
10
=
0.324754a
3
u
8
+ 0.342471a
2
u
8
+ ··· − 0.326854a + 0.340849
0.0741671a
3
u
8
+ 0.277862a
2
u
8
+ ··· − 0.0386022a + 0.195221
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
− 4u
6
− 4u
5
− 4u
4
− 8u
3
− 4u
2
− 14
13
(iv) u-Polynomials at the component
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)
4
c
2
, c
4
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
4
c
3
, c
8
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
4
c
5
, c
7
, c
11
u
36
+ 3u
35
+ ··· − 136u − 31
c
6
, c
9
, c
12
u
36
− 3u
35
+ ··· + 18264u − 3559
c
10
(u
2
+ u − 1)
18
14
(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)
4
c
2
, c
4
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
4
c
3
, c
8
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
4
c
5
, c
7
, c
11
y
36
+ 11y
35
+ ··· + 16224y + 961
c
6
, c
9
, c
12
y
36
− 25y
35
+ ··· + 545224y + 12666481
c
10
(y
2
− 3y + 1)
18
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140343 + 0.966856I
a = −0.61869 + 1.39310I
b = −0.42993 − 1.44275I
5.73128 − 2.09337I −7.48501 + 4.16283I
u = 0.140343 + 0.966856I
a = 1.38851 + 0.80504I
b = 0.128913 − 0.359883I
−2.16441 − 2.09337I −7.48501 + 4.16283I
u = 0.140343 + 0.966856I
a = 0.243842 + 0.158886I
b = 1.351770 − 0.079224I
−2.16441 − 2.09337I −7.48501 + 4.16283I
u = 0.140343 + 0.966856I
a = −0.00482 − 1.76129I
b = −0.13564 + 1.61047I
5.73128 − 2.09337I −7.48501 + 4.16283I
u = 0.140343 − 0.966856I
a = −0.61869 − 1.39310I
b = −0.42993 + 1.44275I
5.73128 + 2.09337I −7.48501 − 4.16283I
u = 0.140343 − 0.966856I
a = 1.38851 − 0.80504I
b = 0.128913 + 0.359883I
−2.16441 + 2.09337I −7.48501 − 4.16283I
u = 0.140343 − 0.966856I
a = 0.243842 − 0.158886I
b = 1.351770 + 0.079224I
−2.16441 + 2.09337I −7.48501 − 4.16283I
u = 0.140343 − 0.966856I
a = −0.00482 + 1.76129I
b = −0.13564 − 1.61047I
5.73128 + 2.09337I −7.48501 − 4.16283I
u = 0.628449 + 0.875112I
a = −0.525443 + 0.462550I
b = 1.30414 − 0.74950I
−4.56478 − 2.45442I −10.32792 + 2.91298I
u = 0.628449 + 0.875112I
a = 0.763452 − 1.086660I
b = 0.294073 + 1.242760I
3.33090 − 2.45442I −10.32792 + 2.91298I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.628449 + 0.875112I
a = −0.485650 + 0.077610I
b = −0.523285 − 0.562963I
3.33090 − 2.45442I −10.32792 + 2.91298I
u = 0.628449 + 0.875112I
a = −0.20185 + 2.17919I
b = −0.704050 − 1.030220I
−4.56478 − 2.45442I −10.32792 + 2.91298I
u = 0.628449 − 0.875112I
a = −0.525443 − 0.462550I
b = 1.30414 + 0.74950I
−4.56478 + 2.45442I −10.32792 − 2.91298I
u = 0.628449 − 0.875112I
a = 0.763452 + 1.086660I
b = 0.294073 − 1.242760I
3.33090 + 2.45442I −10.32792 − 2.91298I
u = 0.628449 − 0.875112I
a = −0.485650 − 0.077610I
b = −0.523285 + 0.562963I
3.33090 + 2.45442I −10.32792 − 2.91298I
u = 0.628449 − 0.875112I
a = −0.20185 − 2.17919I
b = −0.704050 + 1.030220I
−4.56478 + 2.45442I −10.32792 − 2.91298I
u = −0.796005 + 0.733148I
a = −0.880986 − 0.487136I
b = 0.964779 + 0.981447I
−8.31919 − 1.33617I −15.2841 + 0.7017I
u = −0.796005 + 0.733148I
a = 0.892032 + 0.347149I
b = −0.127108 − 1.007800I
−0.423507 − 1.336170I −15.2841 + 0.7017I
u = −0.796005 + 0.733148I
a = −0.187374 + 0.704738I
b = 0.186512 + 0.286438I
−0.423507 − 1.336170I −15.2841 + 0.7017I
u = −0.796005 + 0.733148I
a = −0.96383 − 2.26674I
b = −1.12030 + 0.90709I
−8.31919 − 1.33617I −15.2841 + 0.7017I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.796005 − 0.733148I
a = −0.880986 + 0.487136I
b = 0.964779 − 0.981447I
−8.31919 + 1.33617I −15.2841 − 0.7017I
u = −0.796005 − 0.733148I
a = 0.892032 − 0.347149I
b = −0.127108 + 1.007800I
−0.423507 + 1.336170I −15.2841 − 0.7017I
u = −0.796005 − 0.733148I
a = −0.187374 − 0.704738I
b = 0.186512 − 0.286438I
−0.423507 + 1.336170I −15.2841 − 0.7017I
u = −0.796005 − 0.733148I
a = −0.96383 + 2.26674I
b = −1.12030 − 0.90709I
−8.31919 + 1.33617I −15.2841 − 0.7017I
u = −0.728966 + 0.986295I
a = 0.501545 + 1.033540I
b = 0.646764 − 1.177390I
0.34972 + 7.08493I −13.5768 − 5.9133I
u = −0.728966 + 0.986295I
a = −0.593832 − 0.265649I
b = 1.49815 + 0.97115I
−7.54597 + 7.08493I −13.5768 − 5.9133I
u = −0.728966 + 0.986295I
a = −0.124651 − 0.247951I
b = −0.919556 + 0.288684I
0.34972 + 7.08493I −13.5768 − 5.9133I
u = −0.728966 + 0.986295I
a = −0.39289 − 1.79104I
b = −0.78397 + 1.35550I
−7.54597 + 7.08493I −13.5768 − 5.9133I
u = −0.728966 − 0.986295I
a = 0.501545 − 1.033540I
b = 0.646764 + 1.177390I
0.34972 − 7.08493I −13.5768 + 5.9133I
u = −0.728966 − 0.986295I
a = −0.593832 + 0.265649I
b = 1.49815 − 0.97115I
−7.54597 − 7.08493I −13.5768 + 5.9133I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.728966 − 0.986295I
a = −0.124651 + 0.247951I
b = −0.919556 − 0.288684I
0.34972 − 7.08493I −13.5768 + 5.9133I
u = −0.728966 − 0.986295I
a = −0.39289 + 1.79104I
b = −0.78397 − 1.35550I
−7.54597 − 7.08493I −13.5768 + 5.9133I
u = 0.512358
a = −4.03622
b = 0.558485
−5.14629 −16.6520
u = 0.512358
a = 2.66334 + 4.93805I
b = 0.081120 + 1.296290I
2.74940 −16.6520
u = 0.512358
a = 2.66334 − 4.93805I
b = 0.081120 − 1.296290I
2.74940 −16.6520
u = 0.512358
a = −9.90920
b = −0.983236
−5.14629 −16.6520
19
IV. I
v
1
= ha, b + 2v + 2, 4v
2
+ 6v + 1i
(i) Arc colorings
a
4
=
v
0
a
8
=
1
0
a
9
=
1
0
a
3
=
v
0
a
12
=
0
−2v − 2
a
7
=
1
−2v − 3
a
6
=
−2v − 2
−2v − 3
a
1
=
4v + 5
4v + 6
a
11
=
−2v − 2
−2v − 2
a
5
=
−4v − 5
−4v − 6
a
2
=
5v + 5
4v + 6
a
10
=
4v + 6
6v + 8
(ii) Obstruction class = 1
(iii) Cusp Shapes =
45
2
v +
55
4
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
8
u
2
c
4
(u + 1)
2
c
5
, c
7
, c
10
u
2
+ u − 1
c
6
u
2
− 3u + 1
c
9
, c
12
u
2
+ 3u + 1
c
11
u
2
− u − 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
8
y
2
c
5
, c
7
, c
10
c
11
y
2
− 3y + 1
c
6
, c
9
, c
12
y
2
− 7y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.30902
a = 0
b = 0.618034
−2.63189 −15.7030
v = −0.190983
a = 0
b = −1.61803
−10.5276 9.45290
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
4
· (u
17
− 10u
16
+ ··· + 17u − 1)(u
30
+ 17u
29
+ ··· + 6768u + 256)
c
2
(u − 1)
2
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
4
· (u
17
+ 4u
16
+ ··· − u + 1)(u
30
− 3u
29
+ ··· − 44u − 16)
c
3
u
2
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
4
· (u
17
+ 3u
15
+ ··· − 3u + 1)(u
30
− 5u
29
+ ··· + 208u − 64)
c
4
(u + 1)
2
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
4
· (u
17
− 4u
16
+ ··· − u − 1)(u
30
− 3u
29
+ ··· − 44u − 16)
c
5
(u
2
+ u − 1)(u
17
+ 6u
15
+ ··· − 3u − 1)(u
30
− u
29
+ ··· + 2u
2
− 1)
· (u
36
+ 3u
35
+ ··· − 136u − 31)
c
6
(u
2
− 3u + 1)(u
17
− 3u
16
+ ··· + 6u
2
+ 1)(u
30
− 30u
28
+ ··· − u + 1)
· (u
36
− 3u
35
+ ··· + 18264u − 3559)
c
7
(u
2
+ u − 1)(u
17
+ 6u
15
+ ··· − 3u + 1)(u
30
− u
29
+ ··· + 2u
2
− 1)
· (u
36
+ 3u
35
+ ··· − 136u − 31)
c
8
u
2
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
4
· (u
17
+ 3u
15
+ ··· − 3u − 1)(u
30
− 5u
29
+ ··· + 208u − 64)
c
9
(u
2
+ 3u + 1)(u
17
+ 3u
16
+ ··· − 6u
2
− 1)(u
30
− 30u
28
+ ··· − u + 1)
· (u
36
− 3u
35
+ ··· + 18264u − 3559)
c
10
((u
2
+ u − 1)
19
)(u
17
− 5u
16
+ ··· + 5u − 1)
· (u
30
− 19u
29
+ ··· + 2048u − 512)
c
11
(u
2
− u − 1)(u
17
+ 6u
15
+ ··· − 3u − 1)(u
30
− u
29
+ ··· + 2u
2
− 1)
· (u
36
+ 3u
35
+ ··· − 136u − 31)
c
12
(u
2
+ 3u + 1)(u
17
− 3u
16
+ ··· + 6u
2
+ 1)(u
30
− 30u
28
+ ··· − u + 1)
· (u
36
− 3u
35
+ ··· + 18264u − 3559)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
2
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
4
· (y
17
− 2y
16
+ ··· + 157y − 1)(y
30
− 5y
29
+ ··· − 31895296y + 65536)
c
2
, c
4
(y − 1)
2
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
4
· (y
17
− 10y
16
+ ··· + 17y − 1)(y
30
− 17y
29
+ ··· − 6768y + 256)
c
3
, c
8
y
2
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
4
· (y
17
+ 6y
16
+ ··· + 13y − 1)(y
30
+ 9y
29
+ ··· − 21248y + 4096)
c
5
, c
7
, c
11
(y
2
− 3y + 1)(y
17
+ 12y
16
+ ··· + 5y − 1)(y
30
+ y
29
+ ··· − 4y + 1)
· (y
36
+ 11y
35
+ ··· + 16224y + 961)
c
6
, c
9
, c
12
(y
2
− 7y + 1)(y
17
− 5y
16
+ ··· − 12y − 1)(y
30
− 60y
29
+ ··· − 63y + 1)
· (y
36
− 25y
35
+ ··· + 545224y + 12666481)
c
10
((y
2
− 3y + 1)
19
)(y
17
− 17y
16
+ ··· + 11y − 1)
· (y
30
− 23y
29
+ ··· − 3145728y + 262144)
25
