12a
0812
(K12a
0812
)
A knot diagram
1
Linearized knot diagam
4 5 7 2 9 12 3 11 1 6 8 10
Solving Sequence
1,4
2
5,9
6 10 11 8 12 7 3
c
1
c
4
c
5
c
9
c
10
c
8
c
12
c
6
c
3
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.08509 × 10
47
u
41
+ 2.04550 × 10
47
u
40
+ ··· + 6.21177 × 10
47
b − 1.86338 × 10
48
,
5.29448 × 10
46
u
41
+ 1.94560 × 10
47
u
40
+ ··· + 2.48471 × 10
48
a − 1.28814 × 10
49
,
u
42
+ 3u
41
+ ··· − 193u − 16i
I
u
2
= h−19470u
34
a + 16063u
34
+ ··· + 14876a − 16265, 5u
34
a − 2u
34
+ ··· − 3a − 42,
u
35
+ 3u
34
+ ··· + u − 1i
I
u
3
= h4a
2
+ b − 5a + 2, 4a
3
− 5a
2
+ 3a − 1, u − 1i
I
u
4
= hb + 1, 2u
3
+ 2u
2
+ 2a − 2u + 1, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
I
u
5
= h−a
3
+ 3a
2
+ b − 5a + 2, a
4
− 3a
3
+ 5a
2
− 3a + 1, u − 1i
* 5 irreducible components of dim
C
= 0, with total 124 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
=
h1.09×10
47
u
41
+2.05×10
47
u
40
+· · ·+6.21×10
47
b−1.86×10
48
, 5.29×10
46
u
41
+
1.95 × 10
47
u
40
+ · · · + 2.48 × 10
48
a − 1.29 × 10
49
, u
42
+ 3u
41
+ · · · − 193u − 16i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
−0.0213082u
41
− 0.0783029u
40
+ ··· − 15.6524u + 5.18428
−0.174683u
41
− 0.329294u
40
+ ··· + 27.4193u + 2.99976
a
6
=
0.0226884u
41
+ 0.0558900u
40
+ ··· − 11.7167u + 1.98961
0.101268u
41
+ 0.188266u
40
+ ··· − 17.0252u − 1.36379
a
10
=
0.153375u
41
+ 0.250991u
40
+ ··· − 43.0717u + 2.18452
−0.174683u
41
− 0.329294u
40
+ ··· + 27.4193u + 2.99976
a
11
=
0.0127553u
41
− 0.0150214u
40
+ ··· − 16.9996u + 2.86365
0.0542267u
41
+ 0.114915u
40
+ ··· − 8.87829u − 0.362657
a
8
=
−0.0348739u
41
− 0.0901865u
40
+ ··· − 4.77020u + 3.86624
0.483980u
41
+ 0.895391u
40
+ ··· − 78.1740u − 6.66305
a
12
=
0.0139183u
41
+ 0.0517931u
40
+ ··· + 8.25026u − 1.43381
−0.100313u
41
− 0.210125u
40
+ ··· + 16.6956u + 1.23646
a
7
=
−0.0504330u
41
− 0.0839435u
40
+ ··· + 1.76064u + 4.15274
0.481308u
41
+ 0.909837u
40
+ ··· − 80.3209u − 6.90973
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.241704u
41
− 0.550405u
40
+ ··· + 15.5978u − 9.77163
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
42
− 3u
41
+ ··· + 193u − 16
c
3
, c
7
u
42
+ 9u
40
+ ··· + 432u + 128
c
5
, c
6
32(32u
42
+ 48u
41
+ ··· + 2u − 1)
c
8
, c
9
, c
11
c
12
u
42
+ 5u
41
+ ··· + 5u + 1
c
10
u
42
− 6u
41
+ ··· + 15360u − 4096
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
42
− 37y
41
+ ··· − 56545y + 256
c
3
, c
7
y
42
+ 18y
41
+ ··· − 83200y + 16384
c
5
, c
6
1024(1024y
42
+ 12032y
41
+ ··· − 26y + 1)
c
8
, c
9
, c
11
c
12
y
42
+ 21y
41
+ ··· − 7y + 1
c
10
y
42
+ 12y
41
+ ··· + 133169152y + 16777216
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.248224 + 0.954180I
a = −0.848722 + 0.859465I
b = −0.54514 − 1.34283I
6.4028 − 14.0443I −4.40019 + 8.75993I
u = 0.248224 − 0.954180I
a = −0.848722 − 0.859465I
b = −0.54514 + 1.34283I
6.4028 + 14.0443I −4.40019 − 8.75993I
u = 0.074743 + 1.078940I
a = 0.152006 − 0.668014I
b = 0.207853 + 1.064410I
3.92510 − 4.77662I −2.81528 + 10.95479I
u = 0.074743 − 1.078940I
a = 0.152006 + 0.668014I
b = 0.207853 − 1.064410I
3.92510 + 4.77662I −2.81528 − 10.95479I
u = −0.632717 + 0.661126I
a = 0.509452 − 0.199959I
b = −0.209062 − 1.245590I
7.73166 − 3.41034I 1.10803 + 3.48014I
u = −0.632717 − 0.661126I
a = 0.509452 + 0.199959I
b = −0.209062 + 1.245590I
7.73166 + 3.41034I 1.10803 − 3.48014I
u = 1.09752
a = −0.739117
b = 0.169294
−2.12730 0.370320
u = −1.109190 + 0.023523I
a = −0.247206 − 0.450213I
b = −0.23649 − 1.51407I
7.52656 − 5.05499I −19.5152 − 0.7337I
u = −1.109190 − 0.023523I
a = −0.247206 + 0.450213I
b = −0.23649 + 1.51407I
7.52656 + 5.05499I −19.5152 + 0.7337I
u = −0.323062 + 0.739421I
a = −1.228070 − 0.642588I
b = −0.407229 + 1.331930I
8.66776 + 7.85288I −1.05755 − 5.46989I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.323062 − 0.739421I
a = −1.228070 + 0.642588I
b = −0.407229 − 1.331930I
8.66776 − 7.85288I −1.05755 + 5.46989I
u = 0.710359 + 0.992141I
a = −0.515262 + 0.317448I
b = −0.197546 − 0.956092I
1.34229 − 4.08963I −9.0363 + 12.2471I
u = 0.710359 − 0.992141I
a = −0.515262 − 0.317448I
b = −0.197546 + 0.956092I
1.34229 + 4.08963I −9.0363 − 12.2471I
u = 1.231670 + 0.094353I
a = 2.38664 − 0.99295I
b = 1.099420 − 0.250933I
−4.19721 − 0.35644I −7.83557 + 11.50691I
u = 1.231670 − 0.094353I
a = 2.38664 + 0.99295I
b = 1.099420 + 0.250933I
−4.19721 + 0.35644I −7.83557 − 11.50691I
u = 1.062770 + 0.640101I
a = 0.050170 + 0.246213I
b = −0.487427 + 1.277770I
3.96174 + 8.50579I −6.69220 − 5.52259I
u = 1.062770 − 0.640101I
a = 0.050170 − 0.246213I
b = −0.487427 − 1.277770I
3.96174 − 8.50579I −6.69220 + 5.52259I
u = 0.236961 + 0.636493I
a = −0.206766 + 0.041993I
b = 1.260010 − 0.175724I
−1.70101 − 1.91356I 0.02681 + 10.10782I
u = 0.236961 − 0.636493I
a = −0.206766 − 0.041993I
b = 1.260010 + 0.175724I
−1.70101 + 1.91356I 0.02681 − 10.10782I
u = 0.520974 + 0.404635I
a = 0.109786 − 1.228840I
b = 0.894996 + 0.377632I
−2.74179 − 1.37249I −17.0129 − 1.6205I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.520974 − 0.404635I
a = 0.109786 + 1.228840I
b = 0.894996 − 0.377632I
−2.74179 + 1.37249I −17.0129 + 1.6205I
u = 0.392865 + 0.454143I
a = −0.597332 − 0.349954I
b = −0.103400 + 0.198098I
−0.466654 − 1.208450I −5.65241 + 4.78210I
u = 0.392865 − 0.454143I
a = −0.597332 + 0.349954I
b = −0.103400 − 0.198098I
−0.466654 + 1.208450I −5.65241 − 4.78210I
u = 1.271940 + 0.603035I
a = 0.604222 − 0.251023I
b = 0.161484 + 0.882187I
−0.37856 − 2.57914I −8.00000 + 9.43410I
u = 1.271940 − 0.603035I
a = 0.604222 + 0.251023I
b = 0.161484 − 0.882187I
−0.37856 + 2.57914I −8.00000 − 9.43410I
u = −1.386130 + 0.262729I
a = 1.40638 + 0.89464I
b = 1.43050 + 0.28539I
−6.85298 + 5.22980I −8.00000 − 7.21139I
u = −1.386130 − 0.262729I
a = 1.40638 − 0.89464I
b = 1.43050 − 0.28539I
−6.85298 − 5.22980I −8.00000 + 7.21139I
u = −1.42771 + 0.10441I
a = 1.61787 − 0.00916I
b = 1.033580 − 0.727245I
−8.95280 + 3.04983I −8.00000 + 0.I
u = −1.42771 − 0.10441I
a = 1.61787 + 0.00916I
b = 1.033580 + 0.727245I
−8.95280 − 3.04983I −8.00000 + 0.I
u = 1.42833 + 0.29979I
a = −1.90675 − 0.45833I
b = −0.529519 − 1.302180I
3.09440 − 11.65060I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42833 − 0.29979I
a = −1.90675 + 0.45833I
b = −0.529519 + 1.302180I
3.09440 + 11.65060I 0
u = −1.39218 + 0.45224I
a = 1.148140 + 0.058065I
b = 0.348492 − 1.178060I
−0.77197 + 10.13610I 0
u = −1.39218 − 0.45224I
a = 1.148140 − 0.058065I
b = 0.348492 + 1.178060I
−0.77197 − 10.13610I 0
u = −1.45716 + 0.20775I
a = −0.735467 − 0.263115I
b = −0.392117 − 0.291228I
−6.51306 + 3.82462I 0
u = −1.45716 − 0.20775I
a = −0.735467 + 0.263115I
b = −0.392117 + 0.291228I
−6.51306 − 3.82462I 0
u = −1.43751 + 0.39844I
a = −1.86696 + 0.05479I
b = −0.60360 + 1.37108I
1.0500 + 18.8951I 0
u = −1.43751 − 0.39844I
a = −1.86696 − 0.05479I
b = −0.60360 − 1.37108I
1.0500 − 18.8951I 0
u = 1.55911 + 0.19525I
a = −0.459593 − 0.364526I
b = −0.066400 − 0.822655I
−1.24848 − 0.86846I 0
u = 1.55911 − 0.19525I
a = −0.459593 + 0.364526I
b = −0.066400 + 0.822655I
−1.24848 + 0.86846I 0
u = −1.58720 + 0.14260I
a = −1.035690 + 0.554995I
b = −0.504339 + 0.985200I
−6.73705 + 7.84823I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.58720 − 0.14260I
a = −1.035690 − 0.554995I
b = −0.504339 − 0.985200I
−6.73705 − 7.84823I 0
u = −0.0676965
a = 6.25293
b = 0.522564
−0.864294 −11.0520
9
II. I
u
2
= h−1.95 × 10
4
au
34
+ 1.61 × 10
4
u
34
+ · · · + 1.49 × 10
4
a − 1.63 ×
10
4
, 5u
34
a − 2u
34
+ · · · − 3a − 42, u
35
+ 3u
34
+ · · · + u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
a
3.97509au
34
− 3.27950u
34
+ ··· − 3.03716a + 3.32074
a
6
=
8.89506au
34
− 13.8579u
34
+ ··· − 8.77950a + 2.19559
−4.35790au
34
+ 4.53716u
34
+ ··· + 3.69559a − 5.08391
a
10
=
−3.97509au
34
+ 3.27950u
34
+ ··· + 4.03716a − 3.32074
3.97509au
34
− 3.27950u
34
+ ··· − 3.03716a + 3.32074
a
11
=
3.27950au
34
− 5.69559u
34
+ ··· − 3.32074a + 5.71641
−1
a
8
=
3u
34
+ 5u
33
+ ··· + u − 3
−
5
2
u
34
− 4u
33
+ ··· − 2u +
3
2
a
12
=
−4.52491au
34
+ 1.72050u
34
+ ··· + 4.46284a − 0.679257
3.74541au
34
+ 4.47509u
34
+ ··· − 2.64210a − 2.53716
a
7
=
u
33
+ u
32
+ ··· − 3u − 1
−
11
2
u
34
− 10u
33
+ ··· − 7u +
9
2
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 7u
34
+ 7u
33
− 100u
32
− 67u
31
+ 665u
30
+ 193u
29
− 2656u
28
+ 332u
27
+ 6763u
26
−
4013u
25
− 10334u
24
+ 13042u
23
+ 5838u
22
− 22006u
21
+ 10452u
20
+ 17336u
19
−
25367u
18
+ 3521u
17
+ 19332u
16
−18920u
15
+ 1888u
14
+ 11508u
13
−11034u
12
+ 2874u
11
+
3024u
10
−4152u
9
+ 2538u
8
−542u
7
−450u
6
+ 658u
5
−514u
4
+ 230u
3
−79u
2
+ 25u −12
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
(u
35
− 3u
34
+ ··· + u + 1)
2
c
3
, c
7
(u
35
− u
34
+ ··· − 8u + 4)
2
c
5
, c
6
u
70
− 2u
69
+ ··· − 5401216u + 7036657
c
8
, c
9
, c
11
c
12
u
70
− 12u
69
+ ··· − 4u + 1
c
10
(u
35
+ 2u
34
+ ··· − 2u
2
+ 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y
35
− 31y
34
+ ··· − 17y −1)
2
c
3
, c
7
(y
35
+ 15y
34
+ ··· − 72y −16)
2
c
5
, c
6
y
70
+ 34y
69
+ ··· + 937785468713840y + 49514541735649
c
8
, c
9
, c
11
c
12
y
70
+ 46y
69
+ ··· + 40y
2
+ 1
c
10
(y
35
+ 12y
34
+ ··· + 4y −1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.827242 + 0.510777I
a = −0.212545 − 0.733799I
b = −0.255434 + 0.179971I
−0.32534 − 1.86508I −12.01949 + 2.70414I
u = 0.827242 + 0.510777I
a = 0.201230 − 0.318451I
b = 0.161759 + 0.922833I
−0.32534 − 1.86508I −12.01949 + 2.70414I
u = 0.827242 − 0.510777I
a = −0.212545 + 0.733799I
b = −0.255434 − 0.179971I
−0.32534 + 1.86508I −12.01949 − 2.70414I
u = 0.827242 − 0.510777I
a = 0.201230 + 0.318451I
b = 0.161759 − 0.922833I
−0.32534 + 1.86508I −12.01949 − 2.70414I
u = 0.943343 + 0.501099I
a = −0.806313 + 1.002030I
b = −0.892934 − 0.050732I
0.19294 + 3.49535I −10.37889 − 3.75014I
u = 0.943343 + 0.501099I
a = −0.392801 − 0.250034I
b = 0.473353 − 1.238280I
0.19294 + 3.49535I −10.37889 − 3.75014I
u = 0.943343 − 0.501099I
a = −0.806313 − 1.002030I
b = −0.892934 + 0.050732I
0.19294 − 3.49535I −10.37889 + 3.75014I
u = 0.943343 − 0.501099I
a = −0.392801 + 0.250034I
b = 0.473353 + 1.238280I
0.19294 − 3.49535I −10.37889 + 3.75014I
u = 0.253334 + 0.839514I
a = 0.732491 − 0.990248I
b = 0.57430 + 1.36050I
2.31683 − 8.24742I −6.56945 + 7.59916I
u = 0.253334 + 0.839514I
a = −0.236166 + 0.144804I
b = −1.099950 + 0.040721I
2.31683 − 8.24742I −6.56945 + 7.59916I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.253334 − 0.839514I
a = 0.732491 + 0.990248I
b = 0.57430 − 1.36050I
2.31683 + 8.24742I −6.56945 − 7.59916I
u = 0.253334 − 0.839514I
a = −0.236166 − 0.144804I
b = −1.099950 − 0.040721I
2.31683 + 8.24742I −6.56945 − 7.59916I
u = 1.15725
a = 8.02935 + 5.32139I
b = 0.059906 − 1.005370I
1.07873 −8.02480
u = 1.15725
a = 8.02935 − 5.32139I
b = 0.059906 + 1.005370I
1.07873 −8.02480
u = 0.295449 + 0.784598I
a = 0.131977 + 0.656606I
b = 0.272386 − 0.009768I
1.31903 − 2.68874I −8.58889 + 2.89622I
u = 0.295449 + 0.784598I
a = −0.99423 + 1.03224I
b = −0.138135 − 1.022530I
1.31903 − 2.68874I −8.58889 + 2.89622I
u = 0.295449 − 0.784598I
a = 0.131977 − 0.656606I
b = 0.272386 + 0.009768I
1.31903 + 2.68874I −8.58889 − 2.89622I
u = 0.295449 − 0.784598I
a = −0.99423 − 1.03224I
b = −0.138135 + 1.022530I
1.31903 + 2.68874I −8.58889 − 2.89622I
u = 1.164960 + 0.288871I
a = 0.174184 + 1.133140I
b = −0.401753 + 1.320700I
3.90189 − 1.16771I −3.40537 + 0.48242I
u = 1.164960 + 0.288871I
a = −2.78171 − 0.27519I
b = −0.507904 − 1.221810I
3.90189 − 1.16771I −3.40537 + 0.48242I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.164960 − 0.288871I
a = 0.174184 − 1.133140I
b = −0.401753 − 1.320700I
3.90189 + 1.16771I −3.40537 − 0.48242I
u = 1.164960 − 0.288871I
a = −2.78171 + 0.27519I
b = −0.507904 + 1.221810I
3.90189 + 1.16771I −3.40537 − 0.48242I
u = 0.098834 + 0.725130I
a = −0.388983 + 0.814875I
b = −0.62501 − 1.28751I
7.12278 − 2.53588I −0.15314 + 3.83326I
u = 0.098834 + 0.725130I
a = −0.637467 − 1.226900I
b = −0.44854 + 1.43678I
7.12278 − 2.53588I −0.15314 + 3.83326I
u = 0.098834 − 0.725130I
a = −0.388983 − 0.814875I
b = −0.62501 + 1.28751I
7.12278 + 2.53588I −0.15314 − 3.83326I
u = 0.098834 − 0.725130I
a = −0.637467 + 1.226900I
b = −0.44854 − 1.43678I
7.12278 + 2.53588I −0.15314 − 3.83326I
u = −1.275860 + 0.152636I
a = −1.19877 − 0.84816I
b = −1.066620 − 0.552500I
0.525136 − 0.811264I −10.02594 + 0.I
u = −1.275860 + 0.152636I
a = −0.233286 + 0.448211I
b = 0.19793 + 1.59412I
0.525136 − 0.811264I −10.02594 + 0.I
u = −1.275860 − 0.152636I
a = −1.19877 + 0.84816I
b = −1.066620 + 0.552500I
0.525136 + 0.811264I −10.02594 + 0.I
u = −1.275860 − 0.152636I
a = −0.233286 − 0.448211I
b = 0.19793 − 1.59412I
0.525136 + 0.811264I −10.02594 + 0.I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.343360 + 0.175547I
a = −1.29193 − 0.61731I
b = −0.067487 − 0.890816I
−1.47991 − 0.62379I −10.88558 + 0.I
u = 1.343360 + 0.175547I
a = −0.045410 + 0.417751I
b = 0.103890 − 0.197377I
−1.47991 − 0.62379I −10.88558 + 0.I
u = 1.343360 − 0.175547I
a = −1.29193 + 0.61731I
b = −0.067487 + 0.890816I
−1.47991 + 0.62379I −10.88558 + 0.I
u = 1.343360 − 0.175547I
a = −0.045410 − 0.417751I
b = 0.103890 + 0.197377I
−1.47991 + 0.62379I −10.88558 + 0.I
u = −1.328700 + 0.290772I
a = 0.100120 − 0.714272I
b = −0.40483 − 1.60095I
2.63440 + 6.20108I −5.95124 − 5.89177I
u = −1.328700 + 0.290772I
a = −1.92740 + 0.20238I
b = −0.81198 + 1.27967I
2.63440 + 6.20108I −5.95124 − 5.89177I
u = −1.328700 − 0.290772I
a = 0.100120 + 0.714272I
b = −0.40483 + 1.60095I
2.63440 − 6.20108I −5.95124 + 5.89177I
u = −1.328700 − 0.290772I
a = −1.92740 − 0.20238I
b = −0.81198 − 1.27967I
2.63440 − 6.20108I −5.95124 + 5.89177I
u = 1.349650 + 0.231790I
a = −1.67459 + 0.63239I
b = −1.013470 + 0.079471I
−0.71766 − 6.15318I −9.27676 + 5.00692I
u = 1.349650 + 0.231790I
a = 2.10621 + 0.67470I
b = 0.552167 + 1.289800I
−0.71766 − 6.15318I −9.27676 + 5.00692I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.349650 − 0.231790I
a = −1.67459 − 0.63239I
b = −1.013470 − 0.079471I
−0.71766 + 6.15318I −9.27676 − 5.00692I
u = 1.349650 − 0.231790I
a = 2.10621 − 0.67470I
b = 0.552167 − 1.289800I
−0.71766 + 6.15318I −9.27676 − 5.00692I
u = −1.360060 + 0.198169I
a = 0.714600 + 1.125270I
b = 0.117959 − 1.223150I
−1.87781 + 3.59908I −12.99233 − 3.96847I
u = −1.360060 + 0.198169I
a = 1.72670 + 0.67818I
b = 0.362424 + 0.868364I
−1.87781 + 3.59908I −12.99233 − 3.96847I
u = −1.360060 − 0.198169I
a = 0.714600 − 1.125270I
b = 0.117959 + 1.223150I
−1.87781 − 3.59908I −12.99233 + 3.96847I
u = −1.360060 − 0.198169I
a = 1.72670 − 0.67818I
b = 0.362424 − 0.868364I
−1.87781 − 3.59908I −12.99233 + 3.96847I
u = −0.130391 + 0.566931I
a = −0.564679 − 0.532687I
b = −0.926527 + 0.182651I
3.98776 + 3.19845I −2.93735 − 3.08489I
u = −0.130391 + 0.566931I
a = 1.47355 + 1.17244I
b = 0.36381 − 1.36753I
3.98776 + 3.19845I −2.93735 − 3.08489I
u = −0.130391 − 0.566931I
a = −0.564679 + 0.532687I
b = −0.926527 − 0.182651I
3.98776 − 3.19845I −2.93735 + 3.08489I
u = −0.130391 − 0.566931I
a = 1.47355 − 1.17244I
b = 0.36381 + 1.36753I
3.98776 − 3.19845I −2.93735 + 3.08489I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42263 + 0.31147I
a = 0.773954 − 0.130107I
b = 0.562971 + 0.001188I
−4.15268 + 6.65019I −12.04335 + 0.I
u = −1.42263 + 0.31147I
a = −1.47708 − 0.09128I
b = −0.281937 + 1.111930I
−4.15268 + 6.65019I −12.04335 + 0.I
u = −1.42263 − 0.31147I
a = 0.773954 + 0.130107I
b = 0.562971 − 0.001188I
−4.15268 − 6.65019I −12.04335 + 0.I
u = −1.42263 − 0.31147I
a = −1.47708 + 0.09128I
b = −0.281937 − 1.111930I
−4.15268 − 6.65019I −12.04335 + 0.I
u = −1.41674 + 0.34279I
a = −1.32972 − 0.72964I
b = −1.224650 − 0.094256I
−2.99525 + 12.51090I 0. − 8.16035I
u = −1.41674 + 0.34279I
a = 1.85441 − 0.13441I
b = 0.67176 − 1.40948I
−2.99525 + 12.51090I 0. − 8.16035I
u = −1.41674 − 0.34279I
a = −1.32972 + 0.72964I
b = −1.224650 + 0.094256I
−2.99525 − 12.51090I 0. + 8.16035I
u = −1.41674 − 0.34279I
a = 1.85441 + 0.13441I
b = 0.67176 + 1.40948I
−2.99525 − 12.51090I 0. + 8.16035I
u = −1.49697 + 0.02263I
a = 0.938878 − 0.712892I
b = 0.671118 − 0.890248I
−8.17684 + 3.01120I −14.10437 + 0.I
u = −1.49697 + 0.02263I
a = −1.316410 − 0.089350I
b = −0.794357 − 0.531549I
−8.17684 + 3.01120I −14.10437 + 0.I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.49697 − 0.02263I
a = 0.938878 + 0.712892I
b = 0.671118 + 0.890248I
−8.17684 − 3.01120I −14.10437 + 0.I
u = −1.49697 − 0.02263I
a = −1.316410 + 0.089350I
b = −0.794357 + 0.531549I
−8.17684 − 3.01120I −14.10437 + 0.I
u = 0.223261 + 0.425121I
a = 4.06387 − 1.81746I
b = 0.055017 − 0.848791I
3.05354 − 1.15463I −7.51275 + 5.51426I
u = 0.223261 + 0.425121I
a = −2.95799 − 5.46989I
b = 0.023876 + 1.105990I
3.05354 − 1.15463I −7.51275 + 5.51426I
u = 0.223261 − 0.425121I
a = 4.06387 + 1.81746I
b = 0.055017 + 0.848791I
3.05354 + 1.15463I −7.51275 − 5.51426I
u = 0.223261 − 0.425121I
a = −2.95799 + 5.46989I
b = 0.023876 − 1.105990I
3.05354 + 1.15463I −7.51275 − 5.51426I
u = −0.146719 + 0.318162I
a = 0.31286 − 2.35336I
b = −0.331846 − 0.386611I
3.17896 − 1.46996I −3.05083 + 3.34118I
u = −0.146719 + 0.318162I
a = −3.36692 + 0.15962I
b = 0.068722 + 1.183220I
3.17896 − 1.46996I −3.05083 + 3.34118I
u = −0.146719 − 0.318162I
a = 0.31286 + 2.35336I
b = −0.331846 + 0.386611I
3.17896 + 1.46996I −3.05083 − 3.34118I
u = −0.146719 − 0.318162I
a = −3.36692 − 0.15962I
b = 0.068722 − 1.183220I
3.17896 + 1.46996I −3.05083 − 3.34118I
19
III. I
u
3
= h4a
2
+ b − 5a + 2, 4a
3
− 5a
2
+ 3a − 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
5
=
−1
0
a
9
=
a
−4a
2
+ 5a − 2
a
6
=
−a
−4a
2
+ a + 1
a
10
=
4a
2
− 4a + 2
−4a
2
+ 5a − 2
a
11
=
4a
2
− 2a + 1
8a
2
− 6a
a
8
=
0
4a
2
− 9a + 4
a
12
=
4a
2
− 2a + 1
−4a
2
+ a + 1
a
7
=
0
4a
2
− 9a + 4
a
3
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −93a
2
+ 67a − 30
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
7
u
3
c
4
(u + 1)
3
c
5
, c
6
, c
8
c
9
u
3
+ 2u − 1
c
10
u
3
+ 3u
2
+ 5u + 2
c
11
, c
12
u
3
+ 2u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
7
y
3
c
5
, c
6
, c
8
c
9
, c
11
, c
12
y
3
+ 4y
2
+ 4y −1
c
10
y
3
+ y
2
+ 13y −4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.688043
b = −0.453398
−2.43213 −27.9280
u = 1.00000
a = 0.280979 + 0.533292I
b = 0.22670 + 1.46771I
7.79580 − 5.13794I 7.93256 + 7.85966I
u = 1.00000
a = 0.280979 − 0.533292I
b = 0.22670 − 1.46771I
7.79580 + 5.13794I 7.93256 − 7.85966I
23
IV. I
u
4
= hb + 1, 2u
3
+ 2u
2
+ 2a − 2u + 1, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
−u
3
− u
2
+ u −
1
2
−1
a
6
=
1
4
u
3
−
3
4
u
−
1
2
u
3
+
1
2
u
a
10
=
−u
3
− u
2
+ u +
1
2
−1
a
11
=
−u
3
− u
2
+ u +
1
2
−1
a
8
=
−1
0
a
12
=
−u
3
− u
2
+ u +
3
2
−1
a
7
=
u
3
− 2u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =
17
4
u
4
+
15
4
u
3
−
17
4
u
2
+
1
2
u −
41
4
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
3
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
4
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
5
32(32u
5
− 48u
4
+ 32u
3
− 4u
2
− 2u + 1)
c
6
32(32u
5
+ 48u
4
+ 32u
3
+ 4u
2
− 2u − 1)
c
7
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
8
, c
9
(u − 1)
5
c
10
u
5
c
11
, c
12
(u + 1)
5
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
3
, c
7
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
5
, c
6
1024(1024y
5
− 256y
4
+ 512y
3
− 48y
2
+ 12y −1)
c
8
, c
9
, c
11
c
12
(y −1)
5
c
10
y
5
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21774
a = −2.57090
b = −1.00000
−4.04602 0.173700
u = 0.309916 + 0.549911I
a = 0.267660 + 0.216900I
b = −1.00000
−1.97403 − 1.53058I −10.47354 − 1.80092I
u = 0.309916 − 0.549911I
a = 0.267660 − 0.216900I
b = −1.00000
−1.97403 + 1.53058I −10.47354 + 1.80092I
u = −1.41878 + 0.21917I
a = −1.232210 − 0.471915I
b = −1.00000
−7.51750 + 4.40083I −14.4883 − 2.7105I
u = −1.41878 − 0.21917I
a = −1.232210 + 0.471915I
b = −1.00000
−7.51750 − 4.40083I −14.4883 + 2.7105I
27
V. I
u
5
= h−a
3
+ 3a
2
+ b − 5a + 2, a
4
− 3a
3
+ 5a
2
− 3a + 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
5
=
−1
0
a
9
=
a
a
3
− 3a
2
+ 5a − 2
a
6
=
−a
a
3
− 2a
2
+ 2a + 1
a
10
=
−a
3
+ 3a
2
− 4a + 2
a
3
− 3a
2
+ 5a − 2
a
11
=
−a
3
+ 2a
2
− 3a + 1
1
a
8
=
0
a
3
− 3a
2
+ 4a − 1
a
12
=
−a
3
+ 2a
2
− 3a + 1
a
3
− 2a
2
+ 2a + 1
a
7
=
0
a
3
− 3a
2
+ 4a − 1
a
3
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
3
+ 12a
2
− 16a − 1
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
, c
6
, c
8
c
9
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
10
(u
2
− u + 1)
2
c
11
, c
12
u
4
− u
3
+ 2u
2
− 2u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
7
y
4
c
5
, c
6
, c
8
c
9
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
c
10
(y
2
+ y + 1)
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.378256 + 0.440597I
b = −0.121744 + 1.306620I
1.64493 + 2.02988I −7.00000 − 3.46410I
u = 1.00000
a = 0.378256 − 0.440597I
b = −0.121744 − 1.306620I
1.64493 − 2.02988I −7.00000 + 3.46410I
u = 1.00000
a = 1.12174 + 1.30662I
b = 0.621744 + 0.440597I
1.64493 − 2.02988I −7.00000 + 3.46410I
u = 1.00000
a = 1.12174 − 1.30662I
b = 0.621744 − 0.440597I
1.64493 + 2.02988I −7.00000 − 3.46410I
31
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
7
)(u
5
+ u
4
+ ··· + u − 1)(u
35
− 3u
34
+ ··· + u + 1)
2
· (u
42
− 3u
41
+ ··· + 193u − 16)
c
3
u
7
(u
5
− u
4
+ ··· + u − 1)(u
35
− u
34
+ ··· − 8u + 4)
2
· (u
42
+ 9u
40
+ ··· + 432u + 128)
c
4
((u + 1)
7
)(u
5
− u
4
+ ··· + u + 1)(u
35
− 3u
34
+ ··· + u + 1)
2
· (u
42
− 3u
41
+ ··· + 193u − 16)
c
5
1024(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (32u
5
− 48u
4
+ ··· − 2u + 1)(32u
42
+ 48u
41
+ ··· + 2u − 1)
· (u
70
− 2u
69
+ ··· − 5401216u + 7036657)
c
6
1024(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (32u
5
+ 48u
4
+ ··· − 2u − 1)(32u
42
+ 48u
41
+ ··· + 2u − 1)
· (u
70
− 2u
69
+ ··· − 5401216u + 7036657)
c
7
u
7
(u
5
+ u
4
+ ··· + u + 1)(u
35
− u
34
+ ··· − 8u + 4)
2
· (u
42
+ 9u
40
+ ··· + 432u + 128)
c
8
, c
9
((u − 1)
5
)(u
3
+ 2u − 1)(u
4
+ u
3
+ ··· + 2u + 1)(u
42
+ 5u
41
+ ··· + 5u + 1)
· (u
70
− 12u
69
+ ··· − 4u + 1)
c
10
u
5
(u
2
− u + 1)
2
(u
3
+ 3u
2
+ 5u + 2)(u
35
+ 2u
34
+ ··· − 2u
2
+ 1)
2
· (u
42
− 6u
41
+ ··· + 15360u − 4096)
c
11
, c
12
((u + 1)
5
)(u
3
+ 2u + 1)(u
4
− u
3
+ ··· − 2u + 1)(u
42
+ 5u
41
+ ··· + 5u + 1)
· (u
70
− 12u
69
+ ··· − 4u + 1)
32
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
((y −1)
7
)(y
5
− 5y
4
+ ··· − y −1)(y
35
− 31y
34
+ ··· − 17y −1)
2
· (y
42
− 37y
41
+ ··· − 56545y + 256)
c
3
, c
7
y
7
(y
5
+ 3y
4
+ ··· − y −1)(y
35
+ 15y
34
+ ··· − 72y −16)
2
· (y
42
+ 18y
41
+ ··· − 83200y + 16384)
c
5
, c
6
1048576(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (1024y
5
− 256y
4
+ 512y
3
− 48y
2
+ 12y −1)
· (1024y
42
+ 12032y
41
+ ··· − 26y + 1)
· (y
70
+ 34y
69
+ ··· + 937785468713840y + 49514541735649)
c
8
, c
9
, c
11
c
12
(y −1)
5
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
42
+ 21y
41
+ ··· − 7y + 1)(y
70
+ 46y
69
+ ··· + 40y
2
+ 1)
c
10
y
5
(y
2
+ y + 1)
2
(y
3
+ y
2
+ 13y −4)(y
35
+ 12y
34
+ ··· + 4y −1)
2
· (y
42
+ 12y
41
+ ··· + 133169152y + 16777216)
33
