12n
0880
(K12n
0880
)
A knot diagram
1
Linearized knot diagam
4 10 11 9 2 3 1 4 12 6 7 9
Solving Sequence
4,9 2,5
6 1 8 7 12 10 11 3
c
4
c
5
c
1
c
8
c
7
c
12
c
9
c
11
c
3
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −1.08548 × 10
25
u
28
− 9.54353 × 10
24
u
27
+ ··· + 2.18894 × 10
25
a − 1.64519 × 10
26
,
u
29
+ 2u
28
+ ··· − 13u
2
− 1i
I
u
2
= h3.30161 × 10
299
u
69
+ 1.46925 × 10
300
u
68
+ ··· + 1.12043 × 10
304
b + 1.34425 × 10
304
,
9.23538 × 10
303
u
69
+ 3.54679 × 10
304
u
68
+ ··· + 8.20265 × 10
307
a − 3.71102 × 10
308
,
u
70
+ 4u
69
+ ··· − 25055u + 7321i
I
u
3
= hb + u, 559u
16
+ 807u
15
+ ··· + 229a − 7206, u
17
− 2u
16
+ ··· + 7u − 1i
I
u
4
= h−33628u
15
+ 98620u
14
+ ··· + 332531b + 154483,
− 311649u
15
+ 1539315u
14
+ ··· + 332531a − 733442, u
16
− 5u
15
+ ··· − u + 1i
* 4 irreducible components of dim
C
= 0, with total 132 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, −1.09 × 10
25
u
28
− 9.54 × 10
24
u
27
+ · · · + 2.19 × 10
25
a −
1.65 × 10
26
, u
29
+ 2u
28
+ · · · − 13u
2
− 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
0.495891u
28
+ 0.435988u
27
+ ··· − 9.79192u + 7.51592
u
a
5
=
1
u
2
a
6
=
−0.236452u
28
− 0.866910u
27
+ ··· + 0.968434u + 5.19398
−0.00914076u
28
+ 0.0683031u
27
+ ··· + 0.555793u − 0.105732
a
1
=
0.495891u
28
+ 0.435988u
27
+ ··· − 8.79192u + 7.51592
u
a
8
=
u
u
a
7
=
3.59236u
28
+ 7.49492u
27
+ ··· − 29.5652u − 5.99169
−0.105732u
28
− 0.220604u
27
+ ··· + 0.504109u + 0.555793
a
12
=
0.495891u
28
+ 0.435988u
27
+ ··· − 8.79192u + 7.51592
0.105732u
28
+ 0.220604u
27
+ ··· + 1.49589u − 0.555793
a
10
=
−3.48663u
28
− 7.27432u
27
+ ··· + 31.0611u + 5.43590
0.432299u
28
+ 0.854537u
27
+ ··· − 1.99074u − 0.856852
a
11
=
−4.79535u
28
− 10.1485u
27
+ ··· + 37.3810u + 9.72731
0.567598u
28
+ 1.08259u
27
+ ··· − 2.27410u − 0.965582
a
3
=
−4.76966u
28
− 9.82306u
27
+ ··· + 37.4134u + 7.57843
0.536273u
28
+ 1.28218u
27
+ ··· − 3.23320u − 1.87683
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
15517893495020098849975116
21889407595733348190792803
u
28
−
54924211629619166277092344
21889407595733348190792803
u
27
+
··· −
191772394078626200464288803
21889407595733348190792803
u +
272223026286751222003122765
21889407595733348190792803
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
8
u
29
+ 2u
28
+ ··· − 13u
2
− 1
c
2
, c
11
u
29
− u
28
+ ··· + 6u − 1
c
3
, c
10
u
29
− u
28
+ ··· + 3u − 1
c
5
u
29
− 2u
28
+ ··· + 15u − 1
c
6
u
29
− 19u
28
+ ··· − 36u + 8
c
7
u
29
− 25u
28
+ ··· + 26368u − 2560
c
9
, c
12
u
29
+ 13u
28
+ ··· − 544u − 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
y
29
+ 38y
28
+ ··· − 26y −1
c
2
, c
11
y
29
− 3y
28
+ ··· + 8y −1
c
3
, c
10
y
29
− 7y
28
+ ··· + 11y −1
c
5
y
29
+ 2y
28
+ ··· + 99y −1
c
6
y
29
+ 3y
28
+ ··· − 1264y −64
c
7
y
29
− 17y
28
+ ··· − 26279936y −6553600
c
9
, c
12
y
29
+ 17y
28
+ ··· − 52736y −4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.642235 + 0.726664I
a = −0.949259 + 0.155912I
b = −0.642235 + 0.726664I
−3.06174 − 3.25839I −7.69069 + 6.26564I
u = −0.642235 − 0.726664I
a = −0.949259 − 0.155912I
b = −0.642235 − 0.726664I
−3.06174 + 3.25839I −7.69069 − 6.26564I
u = −0.032170 + 0.801563I
a = 1.55712 − 0.56759I
b = −0.032170 + 0.801563I
−0.504140 + 0.951000I 1.54358 − 2.27904I
u = −0.032170 − 0.801563I
a = 1.55712 + 0.56759I
b = −0.032170 − 0.801563I
−0.504140 − 0.951000I 1.54358 + 2.27904I
u = 0.198126 + 0.740818I
a = −0.655188 + 0.248714I
b = 0.198126 + 0.740818I
2.37624 + 4.78664I 2.73963 − 5.44891I
u = 0.198126 − 0.740818I
a = −0.655188 − 0.248714I
b = 0.198126 − 0.740818I
2.37624 − 4.78664I 2.73963 + 5.44891I
u = −0.661536 + 0.319149I
a = 1.41580 − 1.68650I
b = −0.661536 + 0.319149I
−4.19456 + 0.95591I −0.74396 − 10.67777I
u = −0.661536 − 0.319149I
a = 1.41580 + 1.68650I
b = −0.661536 − 0.319149I
−4.19456 − 0.95591I −0.74396 + 10.67777I
u = 0.363420 + 0.611313I
a = −2.25022 − 1.12399I
b = 0.363420 + 0.611313I
−2.25137 + 9.11530I 0.91619 − 5.98946I
u = 0.363420 − 0.611313I
a = −2.25022 + 1.12399I
b = 0.363420 − 0.611313I
−2.25137 − 9.11530I 0.91619 + 5.98946I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.36313 + 1.47042I
a = 0.008827 − 1.188710I
b = −0.36313 + 1.47042I
2.73712 + 3.34248I −3.35900 − 2.79422I
u = −0.36313 − 1.47042I
a = 0.008827 + 1.188710I
b = −0.36313 − 1.47042I
2.73712 − 3.34248I −3.35900 + 2.79422I
u = −0.064814 + 0.477187I
a = 1.022190 − 0.598774I
b = −0.064814 + 0.477187I
0.008337 + 1.334080I 0.34791 − 4.25043I
u = −0.064814 − 0.477187I
a = 1.022190 + 0.598774I
b = −0.064814 − 0.477187I
0.008337 − 1.334080I 0.34791 + 4.25043I
u = 0.44900 + 1.45880I
a = 0.178143 − 0.845770I
b = 0.44900 + 1.45880I
−0.088337 − 0.453344I −3.53660 + 0.I
u = 0.44900 − 1.45880I
a = 0.178143 + 0.845770I
b = 0.44900 − 1.45880I
−0.088337 + 0.453344I −3.53660 + 0.I
u = −0.42651 + 1.53556I
a = 0.063635 − 0.740740I
b = −0.42651 + 1.53556I
1.85990 + 6.10163I 0. − 6.71936I
u = −0.42651 − 1.53556I
a = 0.063635 + 0.740740I
b = −0.42651 − 1.53556I
1.85990 − 6.10163I 0. + 6.71936I
u = −0.00700 + 1.64434I
a = 0.387864 − 1.087010I
b = −0.00700 + 1.64434I
5.36503 + 3.15379I 0. − 5.21676I
u = −0.00700 − 1.64434I
a = 0.387864 + 1.087010I
b = −0.00700 − 1.64434I
5.36503 − 3.15379I 0. + 5.21676I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.035016 + 0.329660I
a = 3.92347 − 1.51601I
b = −0.035016 + 0.329660I
−2.64525 + 3.58389I 5.38204 − 3.13101I
u = −0.035016 − 0.329660I
a = 3.92347 + 1.51601I
b = −0.035016 − 0.329660I
−2.64525 − 3.58389I 5.38204 + 3.13101I
u = 0.308534
a = 2.18209
b = 0.308534
1.77894 6.13630
u = 0.02951 + 1.77011I
a = −0.345581 − 0.914758I
b = 0.02951 + 1.77011I
7.48152 − 10.06130I 0
u = 0.02951 − 1.77011I
a = −0.345581 + 0.914758I
b = 0.02951 − 1.77011I
7.48152 + 10.06130I 0
u = −0.52214 + 1.75074I
a = 0.049722 − 1.179220I
b = −0.52214 + 1.75074I
3.80541 + 9.37886I 0
u = −0.52214 − 1.75074I
a = 0.049722 + 1.179220I
b = −0.52214 − 1.75074I
3.80541 − 9.37886I 0
u = 0.56023 + 1.75971I
a = 0.002425 − 1.091640I
b = 0.56023 + 1.75971I
4.6717 − 18.2246I 0
u = 0.56023 − 1.75971I
a = 0.002425 + 1.091640I
b = 0.56023 − 1.75971I
4.6717 + 18.2246I 0
7
II. I
u
2
= h3.30 × 10
299
u
69
+ 1.47 × 10
300
u
68
+ · · · + 1.12 × 10
304
b + 1.34 ×
10
304
, 9.24 × 10
303
u
69
+ 3.55 × 10
304
u
68
+ · · · + 8.20 × 10
307
a − 3.71 ×
10
308
, u
70
+ 4u
69
+ · · · − 25055u + 7321i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
−0.000112590u
69
− 0.000432396u
68
+ ··· + 39.3655u + 4.52418
−0.0000294674u
69
− 0.000131133u
68
+ ··· + 10.9533u − 1.19976
a
5
=
1
u
2
a
6
=
−0.000220172u
69
− 0.000838330u
68
+ ··· + 22.3863u + 3.16969
0.000123302u
69
+ 0.000461935u
68
+ ··· − 0.298297u + 1.15154
a
1
=
−0.000142058u
69
− 0.000563529u
68
+ ··· + 50.3188u + 3.32441
−0.0000294674u
69
− 0.000131133u
68
+ ··· + 10.9533u − 1.19976
a
8
=
u
u
a
7
=
−0.0000101216u
69
− 0.000129726u
68
+ ··· − 18.3646u − 6.84743
8.90333 × 10
−6
u
69
+ 0.0000205847u
68
+ ··· + 2.62665u − 1.06858
a
12
=
−0.000142058u
69
− 0.000563529u
68
+ ··· + 50.3188u + 3.32441
2.71889 × 10
−6
u
69
− 0.0000339701u
68
+ ··· + 12.1111u − 1.23418
a
10
=
−0.0000424653u
69
− 0.0000800391u
68
+ ··· + 22.4206u + 6.90329
−0.000106669u
69
− 0.000435892u
68
+ ··· + 6.61734u − 0.601728
a
11
=
−0.000135005u
69
− 0.000501852u
68
+ ··· − 2.82311u − 1.87464
0.0000112497u
69
− 0.0000185942u
68
+ ··· + 9.85186u − 1.86309
a
3
=
0.0000677057u
69
+ 0.000381037u
68
+ ··· − 9.38177u + 4.29494
−0.000159969u
69
− 0.000628642u
68
+ ··· + 1.07104u − 0.793122
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.000428326u
69
− 0.00153541u
68
+ ··· + 42.7410u + 1.53991
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
8
u
70
+ 4u
69
+ ··· − 25055u + 7321
c
2
, c
11
u
70
+ 3u
69
+ ··· + 4797u + 373
c
3
, c
10
u
70
+ 7u
68
+ ··· − 28u + 1
c
5
u
70
+ 3u
69
+ ··· + 13827u − 2381
c
6
(u
35
+ 8u
34
+ ··· + 4u + 1)
2
c
7
(u
35
+ 13u
34
+ ··· − 28u − 1)
2
c
9
, c
12
(u
35
− 10u
34
+ ··· + 29u − 7)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
y
70
+ 64y
69
+ ··· − 6291205415y + 53597041
c
2
, c
11
y
70
− y
69
+ ··· − 4085189y + 139129
c
3
, c
10
y
70
+ 14y
69
+ ··· − 416y + 1
c
5
y
70
+ 19y
69
+ ··· − 521935401y + 5669161
c
6
(y
35
− 2y
34
+ ··· + 18y −1)
2
c
7
(y
35
− 45y
34
+ ··· + 92y −1)
2
c
9
, c
12
(y
35
+ 12y
34
+ ··· − 825y −49)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.058400 + 0.079730I
a = 0.545962 + 0.044088I
b = 0.173597 + 0.712167I
0.26528 + 2.69707I 5.39503 − 6.85723I
u = 1.058400 − 0.079730I
a = 0.545962 − 0.044088I
b = 0.173597 − 0.712167I
0.26528 − 2.69707I 5.39503 + 6.85723I
u = −0.024911 + 0.911364I
a = 0.715176 − 0.576738I
b = −1.51437 + 0.36342I
−2.44566 − 0.09156I −4.00202 − 0.79327I
u = −0.024911 − 0.911364I
a = 0.715176 + 0.576738I
b = −1.51437 − 0.36342I
−2.44566 + 0.09156I −4.00202 + 0.79327I
u = −0.842982 + 0.298449I
a = −0.21865 + 1.68444I
b = −0.352984 − 0.459182I
−4.03807 − 1.26323I −2.43296 + 8.36038I
u = −0.842982 − 0.298449I
a = −0.21865 − 1.68444I
b = −0.352984 + 0.459182I
−4.03807 + 1.26323I −2.43296 − 8.36038I
u = −0.106910 + 1.108100I
a = 0.42598 + 1.51358I
b = −0.02176 − 1.91547I
5.12124 − 4.17998I 0
u = −0.106910 − 1.108100I
a = 0.42598 − 1.51358I
b = −0.02176 + 1.91547I
5.12124 + 4.17998I 0
u = −0.345458 + 0.796183I
a = 0.0813893 + 0.0438662I
b = −1.279940 − 0.228114I
−1.55070 − 2.22046I 3.51989 + 4.80032I
u = −0.345458 − 0.796183I
a = 0.0813893 − 0.0438662I
b = −1.279940 + 0.228114I
−1.55070 + 2.22046I 3.51989 − 4.80032I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.332881 + 0.736341I
a = 0.809113 + 0.578377I
b = −1.332510 + 0.087336I
−2.58048 + 2.08849I −4.91472 − 12.36677I
u = −0.332881 − 0.736341I
a = 0.809113 − 0.578377I
b = −1.332510 − 0.087336I
−2.58048 − 2.08849I −4.91472 + 12.36677I
u = 0.771829
a = 1.06093
b = 0.0837624
1.61445 9.96300
u = −0.198870 + 0.719238I
a = 0.841225 − 0.931153I
b = 0.715177 + 0.075240I
−2.56135 + 4.30729I −4.11547 − 11.98740I
u = −0.198870 − 0.719238I
a = 0.841225 + 0.931153I
b = 0.715177 − 0.075240I
−2.56135 − 4.30729I −4.11547 + 11.98740I
u = 0.173597 + 0.712167I
a = 0.305095 − 0.732082I
b = 1.058400 + 0.079730I
0.26528 + 2.69707I 5.39503 − 6.85723I
u = 0.173597 − 0.712167I
a = 0.305095 + 0.732082I
b = 1.058400 − 0.079730I
0.26528 − 2.69707I 5.39503 + 6.85723I
u = 0.715177 + 0.075240I
a = 0.809801 + 1.019730I
b = −0.198870 + 0.719238I
−2.56135 + 4.30729I −4.11547 − 11.98740I
u = 0.715177 − 0.075240I
a = 0.809801 − 1.019730I
b = −0.198870 − 0.719238I
−2.56135 − 4.30729I −4.11547 + 11.98740I
u = 0.030698 + 0.717655I
a = −0.490991 + 0.799569I
b = 1.56053 + 0.16062I
−1.79291 − 10.37620I 1.00185 + 8.04577I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.030698 − 0.717655I
a = −0.490991 − 0.799569I
b = 1.56053 − 0.16062I
−1.79291 + 10.37620I 1.00185 − 8.04577I
u = −1.255260 + 0.308189I
a = 0.398382 − 0.072693I
b = −0.165206 − 0.197590I
−2.66687 + 0.36120I 0
u = −1.255260 − 0.308189I
a = 0.398382 + 0.072693I
b = −0.165206 + 0.197590I
−2.66687 − 0.36120I 0
u = −1.279940 + 0.228114I
a = 0.0410374 + 0.0461021I
b = −0.345458 − 0.796183I
−1.55070 + 2.22046I 0
u = −1.279940 − 0.228114I
a = 0.0410374 − 0.0461021I
b = −0.345458 + 0.796183I
−1.55070 − 2.22046I 0
u = 1.132590 + 0.686893I
a = −0.601873 − 0.054832I
b = −0.134777 − 0.571016I
−3.12149 − 5.64463I 0
u = 1.132590 − 0.686893I
a = −0.601873 + 0.054832I
b = −0.134777 + 0.571016I
−3.12149 + 5.64463I 0
u = −1.332510 + 0.087336I
a = 0.539255 − 0.267281I
b = −0.332881 + 0.736341I
−2.58048 + 2.08849I 0
u = −1.332510 − 0.087336I
a = 0.539255 + 0.267281I
b = −0.332881 − 0.736341I
−2.58048 − 2.08849I 0
u = 0.355920 + 1.345040I
a = −0.593513 + 0.907048I
b = 0.02059 − 1.72427I
5.20790 − 1.91522I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.355920 − 1.345040I
a = −0.593513 − 0.907048I
b = 0.02059 + 1.72427I
5.20790 + 1.91522I 0
u = −0.134777 + 0.571016I
a = 1.040980 + 0.882131I
b = 1.132590 − 0.686893I
−3.12149 + 5.64463I 0.09455 − 3.89255I
u = −0.134777 − 0.571016I
a = 1.040980 − 0.882131I
b = 1.132590 + 0.686893I
−3.12149 − 5.64463I 0.09455 + 3.89255I
u = −0.352984 + 0.459182I
a = 2.36810 − 1.12701I
b = −0.842982 − 0.298449I
−4.03807 + 1.26323I −2.43296 − 8.36038I
u = −0.352984 − 0.459182I
a = 2.36810 + 1.12701I
b = −0.842982 + 0.298449I
−4.03807 − 1.26323I −2.43296 + 8.36038I
u = −0.42198 + 1.39834I
a = −0.53394 − 1.33567I
b = 0.00672 + 1.90303I
7.29297 + 6.22548I 0
u = −0.42198 − 1.39834I
a = −0.53394 + 1.33567I
b = 0.00672 − 1.90303I
7.29297 − 6.22548I 0
u = 0.54051 + 1.43484I
a = −0.141799 + 1.049770I
b = −0.04610 − 1.73166I
6.40155 − 4.67956I 0
u = 0.54051 − 1.43484I
a = −0.141799 − 1.049770I
b = −0.04610 + 1.73166I
6.40155 + 4.67956I 0
u = 0.32270 + 1.50213I
a = 0.003594 + 1.213610I
b = −0.70316 − 1.74818I
2.39979 − 8.51124I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.32270 − 1.50213I
a = 0.003594 − 1.213610I
b = −0.70316 + 1.74818I
2.39979 + 8.51124I 0
u = −1.51437 + 0.36342I
a = −0.217248 − 0.492021I
b = −0.024911 + 0.911364I
−2.44566 − 0.09156I 0
u = −1.51437 − 0.36342I
a = −0.217248 + 0.492021I
b = −0.024911 − 0.911364I
−2.44566 + 0.09156I 0
u = 1.56053 + 0.16062I
a = −0.394801 − 0.169432I
b = 0.030698 + 0.717655I
−1.79291 − 10.37620I 0
u = 1.56053 − 0.16062I
a = −0.394801 + 0.169432I
b = 0.030698 − 0.717655I
−1.79291 + 10.37620I 0
u = 0.54090 + 1.55613I
a = 0.415824 − 1.126470I
b = −0.07039 + 1.65458I
7.79835 + 1.50555I 0
u = 0.54090 − 1.55613I
a = 0.415824 + 1.126470I
b = −0.07039 − 1.65458I
7.79835 − 1.50555I 0
u = −0.07039 + 1.65458I
a = −0.027974 − 1.194190I
b = 0.54090 + 1.55613I
7.79835 + 1.50555I 0
u = −0.07039 − 1.65458I
a = −0.027974 + 1.194190I
b = 0.54090 − 1.55613I
7.79835 − 1.50555I 0
u = 0.55556 + 1.62154I
a = −0.171442 + 1.034380I
b = −0.44556 − 1.78830I
5.47181 − 9.13625I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.55556 − 1.62154I
a = −0.171442 − 1.034380I
b = −0.44556 + 1.78830I
5.47181 + 9.13625I 0
u = 0.02059 + 1.72427I
a = 0.265797 + 0.833243I
b = 0.355920 − 1.345040I
5.20790 + 1.91522I 0
u = 0.02059 − 1.72427I
a = 0.265797 − 0.833243I
b = 0.355920 + 1.345040I
5.20790 − 1.91522I 0
u = −0.04610 + 1.73166I
a = −0.185709 + 0.919029I
b = 0.54051 − 1.43484I
6.40155 + 4.67956I 0
u = −0.04610 − 1.73166I
a = −0.185709 − 0.919029I
b = 0.54051 + 1.43484I
6.40155 − 4.67956I 0
u = −0.165206 + 0.197590I
a = 0.55212 + 1.95585I
b = −1.255260 − 0.308189I
−2.66687 − 0.36120I −3.12875 − 5.49495I
u = −0.165206 − 0.197590I
a = 0.55212 − 1.95585I
b = −1.255260 + 0.308189I
−2.66687 + 0.36120I −3.12875 + 5.49495I
u = 0.00841 + 1.79105I
a = 0.132285 + 0.808176I
b = 0.14593 − 1.82319I
8.77775 − 0.37906I 0
u = 0.00841 − 1.79105I
a = 0.132285 − 0.808176I
b = 0.14593 + 1.82319I
8.77775 + 0.37906I 0
u = 0.14593 + 1.82319I
a = −0.195925 + 0.777639I
b = 0.00841 − 1.79105I
8.77775 + 0.37906I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.14593 − 1.82319I
a = −0.195925 − 0.777639I
b = 0.00841 + 1.79105I
8.77775 − 0.37906I 0
u = −0.44556 + 1.78830I
a = 0.076328 + 0.972168I
b = 0.55556 − 1.62154I
5.47181 + 9.13625I 0
u = −0.44556 − 1.78830I
a = 0.076328 − 0.972168I
b = 0.55556 + 1.62154I
5.47181 − 9.13625I 0
u = −0.70316 + 1.74818I
a = 0.165319 + 0.975638I
b = 0.32270 − 1.50213I
2.39979 + 8.51124I 0
u = −0.70316 − 1.74818I
a = 0.165319 − 0.975638I
b = 0.32270 + 1.50213I
2.39979 − 8.51124I 0
u = 0.00672 + 1.90303I
a = −0.092277 − 1.100180I
b = −0.42198 + 1.39834I
7.29297 + 6.22548I 0
u = 0.00672 − 1.90303I
a = −0.092277 + 1.100180I
b = −0.42198 − 1.39834I
7.29297 − 6.22548I 0
u = −0.02176 + 1.91547I
a = −0.151716 + 0.901109I
b = −0.106910 − 1.108100I
5.12124 + 4.17998I 0
u = −0.02176 − 1.91547I
a = −0.151716 − 0.901109I
b = −0.106910 + 1.108100I
5.12124 − 4.17998I 0
u = 0.0837624
a = 9.77593
b = 0.771829
1.61445 9.96300
17
III.
I
u
3
= hb + u, 559u
16
+ 807u
15
+ · · · + 229a − 7206, u
17
− 2u
16
+ · · · + 7u − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
−2.44105u
16
− 3.52402u
15
+ ··· − 80.4192u + 31.4672
−u
a
5
=
1
u
2
a
6
=
−19.2445u
16
+ 23.7293u
15
+ ··· + 195.183u − 48.6419
−1.23581u
16
+ 5.09607u
15
+ ··· + 32.6769u − 5.86900
a
1
=
−2.44105u
16
− 3.52402u
15
+ ··· − 81.4192u + 31.4672
−u
a
8
=
u
u
a
7
=
−57.9520u
16
+ 87.0175u
15
+ ··· + 617.214u − 129.249
−5.86900u
16
+ 10.5022u
15
+ ··· + 57.4017u − 8.40611
a
12
=
−2.44105u
16
− 3.52402u
15
+ ··· − 81.4192u + 31.4672
−5.86900u
16
+ 10.5022u
15
+ ··· + 55.4017u − 8.40611
a
10
=
63.8210u
16
− 97.5197u
15
+ ··· − 672.616u + 137.655
21.2489u
16
− 32.5459u
15
+ ··· − 202.437u + 38.5284
a
11
=
63.8166u
16
− 107.703u
15
+ ··· − 771.362u + 165.769
12.4760u
16
− 25.0087u
15
+ ··· − 189.607u + 41.6245
a
3
=
49.5459u
16
− 84.0742u
15
+ ··· − 617.659u + 133.808
−5.63319u
16
+ 7.40611u
15
+ ··· + 39.7249u − 8.53712
(ii) Obstruction class = 1
(iii) Cusp Shapes =
64360
229
u
16
−
83581
229
u
15
+ ··· −
518407
229
u +
93833
229
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
17
− 2u
16
+ ··· + 7u − 1
c
2
, c
11
u
17
+ u
16
+ ··· − u − 1
c
3
, c
10
u
17
+ u
16
+ ··· + 2u − 1
c
5
u
17
+ 2u
15
+ ··· + 8u + 47
c
6
u
17
+ 10u
16
+ ··· − u − 1
c
7
u
17
− 6u
16
+ ··· + 11u + 11
c
8
u
17
+ 2u
16
+ ··· + 7u + 1
c
9
u
17
+ 6u
16
+ ··· + 36u + 9
c
12
u
17
− 6u
16
+ ··· + 36u − 9
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
y
17
+ 12y
16
+ ··· + 19y − 1
c
2
, c
11
y
17
− y
16
+ ··· − 15y − 1
c
3
, c
10
y
17
+ 3y
16
+ ··· + 12y − 1
c
5
y
17
+ 4y
16
+ ··· + 8524y − 2209
c
6
y
17
+ 4y
16
+ ··· + 15y − 1
c
7
y
17
− 12y
16
+ ··· − 715y − 121
c
9
, c
12
y
17
+ 6y
16
+ ··· − 558y − 81
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.822388 + 0.586206I
a = 0.326639 − 0.274735I
b = 0.822388 − 0.586206I
−4.23946 + 6.27514I −6.90964 − 7.74561I
u = −0.822388 − 0.586206I
a = 0.326639 + 0.274735I
b = 0.822388 + 0.586206I
−4.23946 − 6.27514I −6.90964 + 7.74561I
u = 0.836423 + 0.260647I
a = 0.477439 − 0.492519I
b = −0.836423 − 0.260647I
−3.27504 − 1.05790I −10.74907 + 4.91523I
u = 0.836423 − 0.260647I
a = 0.477439 + 0.492519I
b = −0.836423 + 0.260647I
−3.27504 + 1.05790I −10.74907 − 4.91523I
u = 0.828902 + 0.242494I
a = 1.23115 + 1.40814I
b = −0.828902 − 0.242494I
−4.50436 − 0.81799I −23.5453 + 1.8319I
u = 0.828902 − 0.242494I
a = 1.23115 − 1.40814I
b = −0.828902 + 0.242494I
−4.50436 + 0.81799I −23.5453 − 1.8319I
u = −0.825384 + 0.041955I
a = −0.47468 + 1.37301I
b = 0.825384 − 0.041955I
−3.69121 + 9.90376I −5.08873 − 7.26877I
u = −0.825384 − 0.041955I
a = −0.47468 − 1.37301I
b = 0.825384 + 0.041955I
−3.69121 − 9.90376I −5.08873 + 7.26877I
u = 0.459821
a = 2.00067
b = −0.459821
0.847552 −3.28860
u = 0.430359 + 0.130610I
a = 0.19719 − 2.75683I
b = −0.430359 − 0.130610I
−3.09214 − 3.56138I −12.77052 + 2.44534I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.430359 − 0.130610I
a = 0.19719 + 2.75683I
b = −0.430359 + 0.130610I
−3.09214 + 3.56138I −12.77052 − 2.44534I
u = −0.11773 + 1.61494I
a = 0.192085 + 1.294340I
b = 0.11773 − 1.61494I
7.37277 − 3.06323I 3.30604 + 4.71221I
u = −0.11773 − 1.61494I
a = 0.192085 − 1.294340I
b = 0.11773 + 1.61494I
7.37277 + 3.06323I 3.30604 − 4.71221I
u = 0.48097 + 1.68955I
a = −0.092254 + 1.087490I
b = −0.48097 − 1.68955I
4.36590 − 8.31847I 0.45301 + 5.31811I
u = 0.48097 − 1.68955I
a = −0.092254 − 1.087490I
b = −0.48097 + 1.68955I
4.36590 + 8.31847I 0.45301 − 5.31811I
u = −0.04106 + 1.82490I
a = 0.142096 + 0.733083I
b = 0.04106 − 1.82490I
8.28470 − 0.78469I −3.05154 + 9.47045I
u = −0.04106 − 1.82490I
a = 0.142096 − 0.733083I
b = 0.04106 + 1.82490I
8.28470 + 0.78469I −3.05154 − 9.47045I
22
IV.
I
u
4
= h−3.36 × 10
4
u
15
+ 9.86 × 10
4
u
14
+ · · · + 3.33 × 10
5
b + 1.54 × 10
5
, −3.12 ×
10
5
u
15
+ 1.54× 10
6
u
14
+ · · · + 3.33 × 10
5
a −7.33 × 10
5
, u
16
− 5u
15
+ · · · − u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
0.937203u
15
− 4.62909u
14
+ ··· − 1.17521u + 2.20563
0.101127u
15
− 0.296574u
14
+ ··· − 0.903362u − 0.464567
a
5
=
1
u
2
a
6
=
−0.501210u
15
+ 2.55767u
14
+ ··· − 0.852218u + 0.136805
0.158770u
15
− 0.409478u
14
+ ··· + 0.726004u + 0.178206
a
1
=
1.03833u
15
− 4.92566u
14
+ ··· − 2.07857u + 1.74107
0.101127u
15
− 0.296574u
14
+ ··· − 0.903362u − 0.464567
a
8
=
u
u
a
7
=
−1.27955u
15
+ 6.69195u
14
+ ··· − 8.52424u + 2.17055
−0.636560u
15
+ 3.07487u
14
+ ··· + 3.40954u − 0.903362
a
12
=
1.03833u
15
− 4.92566u
14
+ ··· − 2.07857u + 1.74107
0.385047u
15
− 1.17822u
14
+ ··· − 1.67570u − 0.730557
a
10
=
2.25646u
15
− 11.0019u
14
+ ··· + 6.92305u − 1.53389
1.49746u
15
− 6.42262u
14
+ ··· − 3.57726u + 0.356262
a
11
=
1.59002u
15
− 7.93196u
14
+ ··· + 6.32355u − 1.43155
0.976913u
15
− 4.30996u
14
+ ··· − 2.60119u + 0.636656
a
3
=
−0.562648u
15
+ 3.34829u
14
+ ··· + 2.37556u − 2.04349
1.25990u
15
− 5.70605u
14
+ ··· + 3.82264u − 0.286361
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1897388
332531
u
15
+
8530028
332531
u
14
+ ··· +
3266028
332531
u −
1136623
332531
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
16
− 5u
15
+ ··· − u + 1
c
2
, c
11
u
16
+ 4u
14
+ ··· + 3u + 1
c
3
, c
10
u
16
+ u
15
+ ··· + 2u + 1
c
5
u
16
+ 2u
15
+ ··· − 3u + 1
c
6
(u
8
− 3u
7
+ 5u
6
− 6u
5
+ 7u
4
− 6u
3
+ 5u
2
− 3u + 1)
2
c
7
(u
8
+ 4u
7
+ 8u
6
+ 14u
5
+ 19u
4
+ 17u
3
+ 11u
2
+ 4u + 1)
2
c
8
u
16
+ 5u
15
+ ··· + u + 1
c
9
(u
8
+ u
7
+ 4u
6
+ u
5
+ 4u
4
− u
3
+ 2u
2
+ 1)
2
c
12
(u
8
− u
7
+ 4u
6
− u
5
+ 4u
4
+ u
3
+ 2u
2
+ 1)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
y
16
+ 5y
15
+ ··· + 9y + 1
c
2
, c
11
y
16
+ 8y
15
+ ··· − 9y + 1
c
3
, c
10
y
16
+ 7y
15
+ ··· − 8y + 1
c
5
y
16
+ 8y
15
+ ··· − 29y + 1
c
6
(y
8
+ y
7
+ 3y
6
+ 8y
5
+ 11y
4
+ 8y
3
+ 3y
2
+ y + 1)
2
c
7
(y
8
− 10y
6
− 6y
5
+ 31y
4
+ 33y
3
+ 23y
2
+ 6y + 1)
2
c
9
, c
12
(y
8
+ 7y
7
+ 22y
6
+ 37y
5
+ 36y
4
+ 23y
3
+ 12y
2
+ 4y + 1)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.843588 + 0.342312I
a = 0.683371 + 0.531641I
b = 0.428384 + 0.721790I
−2.13046 + 3.26530I 2.52059 − 6.28046I
u = 0.843588 − 0.342312I
a = 0.683371 − 0.531641I
b = 0.428384 − 0.721790I
−2.13046 − 3.26530I 2.52059 + 6.28046I
u = −0.428384 + 0.721790I
a = −0.939049 + 0.010775I
b = −0.843588 + 0.342312I
−2.13046 − 3.26530I 2.52059 + 6.28046I
u = −0.428384 − 0.721790I
a = −0.939049 − 0.010775I
b = −0.843588 − 0.342312I
−2.13046 + 3.26530I 2.52059 − 6.28046I
u = −0.298278 + 1.136440I
a = −0.209166 − 1.364500I
b = −0.09497 + 1.91727I
5.17180 + 5.22804I −0.86821 − 8.88887I
u = −0.298278 − 1.136440I
a = −0.209166 + 1.364500I
b = −0.09497 − 1.91727I
5.17180 − 5.22804I −0.86821 + 8.88887I
u = 1.042950 + 0.610170I
a = 0.439205 + 1.152430I
b = 0.207431 − 0.376211I
−4.18130 + 0.80828I −8.44989 + 6.49561I
u = 1.042950 − 0.610170I
a = 0.439205 − 1.152430I
b = 0.207431 + 0.376211I
−4.18130 − 0.80828I −8.44989 − 6.49561I
u = 0.003076 + 0.768345I
a = 0.610401 − 0.306734I
b = −1.44951 − 0.12338I
−2.14992 − 1.35977I 0.79752 + 2.34408I
u = 0.003076 − 0.768345I
a = 0.610401 + 0.306734I
b = −1.44951 + 0.12338I
−2.14992 + 1.35977I 0.79752 − 2.34408I
26
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44951 + 0.12338I
a = 0.189996 + 0.306734I
b = −0.003076 − 0.768345I
−2.14992 − 1.35977I 0.79752 + 2.34408I
u = 1.44951 − 0.12338I
a = 0.189996 − 0.306734I
b = −0.003076 + 0.768345I
−2.14992 + 1.35977I 0.79752 − 2.34408I
u = −0.207431 + 0.376211I
a = 3.27176 − 1.15243I
b = −1.042950 − 0.610170I
−4.18130 + 0.80828I −8.44989 + 6.49561I
u = −0.207431 − 0.376211I
a = 3.27176 + 1.15243I
b = −1.042950 + 0.610170I
−4.18130 − 0.80828I −8.44989 − 6.49561I
u = 0.09497 + 1.91727I
a = −0.046513 − 0.843632I
b = 0.298278 + 1.136440I
5.17180 − 5.22804I −0.86821 + 8.88887I
u = 0.09497 − 1.91727I
a = −0.046513 + 0.843632I
b = 0.298278 − 1.136440I
5.17180 + 5.22804I −0.86821 − 8.88887I
27
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
16
− 5u
15
+ ··· − u + 1)(u
17
− 2u
16
+ ··· + 7u − 1)
· (u
29
+ 2u
28
+ ··· − 13u
2
− 1)(u
70
+ 4u
69
+ ··· − 25055u + 7321)
c
2
, c
11
(u
16
+ 4u
14
+ ··· + 3u + 1)(u
17
+ u
16
+ ··· − u − 1)
· (u
29
− u
28
+ ··· + 6u − 1)(u
70
+ 3u
69
+ ··· + 4797u + 373)
c
3
, c
10
(u
16
+ u
15
+ ··· + 2u + 1)(u
17
+ u
16
+ ··· + 2u − 1)
· (u
29
− u
28
+ ··· + 3u − 1)(u
70
+ 7u
68
+ ··· − 28u + 1)
c
5
(u
16
+ 2u
15
+ ··· − 3u + 1)(u
17
+ 2u
15
+ ··· + 8u + 47)
· (u
29
− 2u
28
+ ··· + 15u − 1)(u
70
+ 3u
69
+ ··· + 13827u − 2381)
c
6
(u
8
− 3u
7
+ 5u
6
− 6u
5
+ 7u
4
− 6u
3
+ 5u
2
− 3u + 1)
2
· (u
17
+ 10u
16
+ ··· − u − 1)(u
29
− 19u
28
+ ··· − 36u + 8)
· (u
35
+ 8u
34
+ ··· + 4u + 1)
2
c
7
(u
8
+ 4u
7
+ 8u
6
+ 14u
5
+ 19u
4
+ 17u
3
+ 11u
2
+ 4u + 1)
2
· (u
17
− 6u
16
+ ··· + 11u + 11)(u
29
− 25u
28
+ ··· + 26368u − 2560)
· (u
35
+ 13u
34
+ ··· − 28u − 1)
2
c
8
(u
16
+ 5u
15
+ ··· + u + 1)(u
17
+ 2u
16
+ ··· + 7u + 1)
· (u
29
+ 2u
28
+ ··· − 13u
2
− 1)(u
70
+ 4u
69
+ ··· − 25055u + 7321)
c
9
((u
8
+ u
7
+ ··· + 2u
2
+ 1)
2
)(u
17
+ 6u
16
+ ··· + 36u + 9)
· (u
29
+ 13u
28
+ ··· − 544u − 64)(u
35
− 10u
34
+ ··· + 29u − 7)
2
c
12
((u
8
− u
7
+ ··· + 2u
2
+ 1)
2
)(u
17
− 6u
16
+ ··· + 36u − 9)
· (u
29
+ 13u
28
+ ··· − 544u − 64)(u
35
− 10u
34
+ ··· + 29u − 7)
2
28
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
(y
16
+ 5y
15
+ ··· + 9y + 1)(y
17
+ 12y
16
+ ··· + 19y − 1)
· (y
29
+ 38y
28
+ ··· − 26y − 1)
· (y
70
+ 64y
69
+ ··· − 6291205415y + 53597041)
c
2
, c
11
(y
16
+ 8y
15
+ ··· − 9y + 1)(y
17
− y
16
+ ··· − 15y − 1)
· (y
29
− 3y
28
+ ··· + 8y − 1)(y
70
− y
69
+ ··· − 4085189y + 139129)
c
3
, c
10
(y
16
+ 7y
15
+ ··· − 8y + 1)(y
17
+ 3y
16
+ ··· + 12y − 1)
· (y
29
− 7y
28
+ ··· + 11y − 1)(y
70
+ 14y
69
+ ··· − 416y + 1)
c
5
(y
16
+ 8y
15
+ ··· − 29y + 1)(y
17
+ 4y
16
+ ··· + 8524y − 2209)
· (y
29
+ 2y
28
+ ··· + 99y − 1)
· (y
70
+ 19y
69
+ ··· − 521935401y + 5669161)
c
6
(y
8
+ y
7
+ 3y
6
+ 8y
5
+ 11y
4
+ 8y
3
+ 3y
2
+ y + 1)
2
· (y
17
+ 4y
16
+ ··· + 15y − 1)(y
29
+ 3y
28
+ ··· − 1264y − 64)
· (y
35
− 2y
34
+ ··· + 18y − 1)
2
c
7
(y
8
− 10y
6
− 6y
5
+ 31y
4
+ 33y
3
+ 23y
2
+ 6y + 1)
2
· (y
17
− 12y
16
+ ··· − 715y − 121)
· (y
29
− 17y
28
+ ··· − 26279936y − 6553600)
· (y
35
− 45y
34
+ ··· + 92y − 1)
2
c
9
, c
12
(y
8
+ 7y
7
+ 22y
6
+ 37y
5
+ 36y
4
+ 23y
3
+ 12y
2
+ 4y + 1)
2
· (y
17
+ 6y
16
+ ··· − 558y − 81)(y
29
+ 17y
28
+ ··· − 52736y − 4096)
· (y
35
+ 12y
34
+ ··· − 825y − 49)
2
29
