12a
0665
(K12a
0665
)
A knot diagram
1
Linearized knot diagam
3 7 10 1 11 2 5 12 4 6 9 8
Solving Sequence
2,6
7
3,10
4 11 1 5 8 9 12
c
6
c
2
c
3
c
10
c
1
c
5
c
7
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h3349u
42
− 43719u
41
+ ··· + 64b + 14656, −3589u
42
+ 50017u
41
+ ··· + 128a − 81280,
u
43
− 15u
42
+ ··· − 1216u + 128i
I
u
2
= h−4164019282a
5
u
5
− 75372960680u
5
a
4
+ ··· − 521321653767a − 34419126350,
− u
5
a
4
− 3u
5
a
3
+ ··· + 3a + 4, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
u
3
= h2.29399 × 10
20
a
7
u
5
− 2.53388 × 10
20
a
6
u
5
+ ··· − 6.52305 × 10
21
a − 2.07651 × 10
21
,
− a
7
u
5
− 3a
6
u
5
+ ··· − 26a
2
− 4a, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
u
4
= hu
29
+ 6u
28
+ ··· + b − 21, 25u
29
− 4u
28
+ ··· + 2a + 57, u
30
− 9u
28
+ ··· + 5u + 2i
* 4 irreducible components of dim
C
= 0, with total 157 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
= h3349u
42
− 43719u
41
+ · · · + 64b + 14656, −3589u
42
+ 50017u
41
+
· · · + 128a − 81280, u
43
− 15u
42
+ · · · − 1216u + 128i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
28.0391u
42
− 390.758u
41
+ ··· − 1241u + 635
−52.3281u
42
+ 683.109u
41
+ ··· − 2048.50u − 229
a
4
=
7.89844u
42
− 92.9609u
41
+ ··· − 4368.25u + 604
17.3281u
42
− 251.203u
41
+ ··· + 19808.5u − 2255
a
11
=
−24.2891u
42
+ 292.352u
41
+ ··· − 3289.50u + 406
−52.3281u
42
+ 683.109u
41
+ ··· − 2048.50u − 229
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
−25.2266u
42
+ 344.164u
41
+ ··· − 15440.3u + 1652
−17.3281u
42
+ 251.203u
41
+ ··· − 19807.5u + 2255
a
8
=
45.3984u
42
− 584.070u
41
+ ··· + 5029u − 163
69.8125u
42
− 962.781u
41
+ ··· + 51693.5u − 5699
a
9
=
153.563u
42
− 2048.64u
41
+ ··· + 62357u − 6237
40.8281u
42
− 599.109u
41
+ ··· + 56436u − 6624
a
12
=
125.570u
42
− 1848.51u
41
+ ··· + 166307.u − 19206.5
−66.1094u
42
+ 840.391u
41
+ ··· − 3085u − 203
(ii) Obstruction class = −1
(iii) Cusp Shapes =
493
4
u
42
−
14343
8
u
41
+ ··· + 118988u − 12926
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
43
+ 21u
42
+ ··· − 36864u + 16384
c
2
, c
6
u
43
− 15u
42
+ ··· − 1216u + 128
c
3
, c
5
, c
9
c
10
u
43
+ 13u
41
+ ··· + u + 1
c
4
, c
7
u
43
− u
42
+ ··· − 11u + 1
c
8
, c
11
, c
12
u
43
− 15u
42
+ ··· + 1184u − 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
43
+ 3y
42
+ ··· − 352321536y −268435456
c
2
, c
6
y
43
− 21y
42
+ ··· − 36864y −16384
c
3
, c
5
, c
9
c
10
y
43
+ 26y
42
+ ··· − 3y −1
c
4
, c
7
y
43
+ 27y
42
+ ··· + 9y −1
c
8
, c
11
, c
12
y
43
+ 37y
42
+ ··· + 37888y −4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.358058 + 0.942581I
a = −0.814671 − 0.995400I
b = 0.64470 + 1.33116I
2.90969 + 12.64310I 0
u = 0.358058 − 0.942581I
a = −0.814671 + 0.995400I
b = 0.64470 − 1.33116I
2.90969 − 12.64310I 0
u = 0.743017 + 0.654264I
a = −1.023650 − 0.133058I
b = 0.675954 − 0.243151I
2.67794 − 1.15193I 0
u = 0.743017 − 0.654264I
a = −1.023650 + 0.133058I
b = 0.675954 + 0.243151I
2.67794 + 1.15193I 0
u = −0.999110 + 0.173940I
a = 0.351404 − 0.168789I
b = 0.603212 − 0.515281I
2.90024 + 0.90114I 0
u = −0.999110 − 0.173940I
a = 0.351404 + 0.168789I
b = 0.603212 + 0.515281I
2.90024 − 0.90114I 0
u = 0.235936 + 0.987451I
a = −0.680042 − 0.624157I
b = 0.460174 + 1.075750I
−1.43821 + 3.02141I 0
u = 0.235936 − 0.987451I
a = −0.680042 + 0.624157I
b = 0.460174 − 1.075750I
−1.43821 − 3.02141I 0
u = 0.326612 + 0.969222I
a = 0.720618 + 0.864498I
b = −0.544872 − 1.244440I
−2.99115 + 8.30522I 0
u = 0.326612 − 0.969222I
a = 0.720618 − 0.864498I
b = −0.544872 + 1.244440I
−2.99115 − 8.30522I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.651470 + 0.725080I
a = 1.233230 − 0.174675I
b = −0.890002 + 0.402380I
8.73286 + 0.70670I 0
u = 0.651470 − 0.725080I
a = 1.233230 + 0.174675I
b = −0.890002 − 0.402380I
8.73286 − 0.70670I 0
u = 0.903670 + 0.651098I
a = 0.599159 + 0.652153I
b = −0.648967 − 0.018284I
2.20727 − 3.90000I 0
u = 0.903670 − 0.651098I
a = 0.599159 − 0.652153I
b = −0.648967 + 0.018284I
2.20727 + 3.90000I 0
u = −0.842879
a = −0.225488
b = −0.350256
−1.50335 −5.12250
u = 0.972657 + 0.671565I
a = −0.355935 − 1.042540I
b = 0.831839 + 0.271950I
7.79870 − 6.02479I 0
u = 0.972657 − 0.671565I
a = −0.355935 + 1.042540I
b = 0.831839 − 0.271950I
7.79870 + 6.02479I 0
u = 0.751407 + 0.931725I
a = −0.609054 + 0.646477I
b = 0.339629 − 0.967304I
5.45582 − 7.81547I 0
u = 0.751407 − 0.931725I
a = −0.609054 − 0.646477I
b = 0.339629 + 0.967304I
5.45582 + 7.81547I 0
u = 0.272176 + 0.746094I
a = 1.192810 + 0.389893I
b = −0.767728 − 0.699776I
6.98629 + 1.56790I 2.80133 − 2.46354I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.272176 − 0.746094I
a = 1.192810 − 0.389893I
b = −0.767728 + 0.699776I
6.98629 − 1.56790I 2.80133 + 2.46354I
u = 0.872394 + 0.921013I
a = 0.501488 − 0.537298I
b = −0.112657 + 0.859584I
0.69776 − 3.31768I 0
u = 0.872394 − 0.921013I
a = 0.501488 + 0.537298I
b = −0.112657 − 0.859584I
0.69776 + 3.31768I 0
u = 1.172660 + 0.517851I
a = −1.31313 − 0.88547I
b = 0.703150 − 0.856659I
4.29326 − 6.36705I 0
u = 1.172660 − 0.517851I
a = −1.31313 + 0.88547I
b = 0.703150 + 0.856659I
4.29326 + 6.36705I 0
u = 0.997676 + 0.861165I
a = −0.505629 + 0.623433I
b = −0.158233 − 0.897192I
4.73833 + 1.30717I 0
u = 0.997676 − 0.861165I
a = −0.505629 − 0.623433I
b = −0.158233 + 0.897192I
4.73833 − 1.30717I 0
u = −1.322220 + 0.148081I
a = −0.209261 + 0.407512I
b = −0.41802 + 1.35525I
−2.99573 − 9.16073I 0
u = −1.322220 − 0.148081I
a = −0.209261 − 0.407512I
b = −0.41802 − 1.35525I
−2.99573 + 9.16073I 0
u = 1.180550 + 0.633598I
a = 1.76187 + 0.42869I
b = −0.70145 + 1.43870I
0.3978 − 18.3824I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.180550 − 0.633598I
a = 1.76187 − 0.42869I
b = −0.70145 − 1.43870I
0.3978 + 18.3824I 0
u = 1.197870 + 0.631514I
a = −1.61675 − 0.39727I
b = 0.61173 − 1.36078I
−5.6553 − 14.0973I 0
u = 1.197870 − 0.631514I
a = −1.61675 + 0.39727I
b = 0.61173 + 1.36078I
−5.6553 + 14.0973I 0
u = 1.227120 + 0.611490I
a = 1.40925 + 0.45940I
b = −0.542711 + 1.209440I
−4.44568 − 8.75769I 0
u = 1.227120 − 0.611490I
a = 1.40925 − 0.45940I
b = −0.542711 − 1.209440I
−4.44568 + 8.75769I 0
u = 1.359510 + 0.190320I
a = 0.488834 + 1.162540I
b = −0.159126 + 0.686027I
−4.99250 − 3.53030I 0
u = 1.359510 − 0.190320I
a = 0.488834 − 1.162540I
b = −0.159126 − 0.686027I
−4.99250 + 3.53030I 0
u = −1.376440 + 0.184461I
a = 0.171191 − 0.354840I
b = 0.308507 − 1.267130I
−8.89743 − 4.41324I 0
u = −1.376440 − 0.184461I
a = 0.171191 + 0.354840I
b = 0.308507 + 1.267130I
−8.89743 + 4.41324I 0
u = −1.41517 + 0.31880I
a = −0.175777 + 0.270332I
b = −0.252812 + 1.111140I
−6.86433 + 1.58891I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41517 − 0.31880I
a = −0.175777 − 0.270332I
b = −0.252812 − 1.111140I
−6.86433 − 1.58891I 0
u = −0.188410 + 0.452205I
a = −0.763214 + 0.333478I
b = 0.192803 + 0.481657I
−0.071939 + 1.056770I −1.07955 − 6.08510I
u = −0.188410 − 0.452205I
a = −0.763214 − 0.333478I
b = 0.192803 − 0.481657I
−0.071939 − 1.056770I −1.07955 + 6.08510I
9
II. I
u
2
= h−4.16 × 10
9
a
5
u
5
− 7.54 × 10
10
a
4
u
5
+ · · · − 5.21 × 10
11
a − 3.44 ×
10
10
, −u
5
a
4
− 3u
5
a
3
+ · · · + 3a + 4, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
a
0.0115886a
5
u
5
+ 0.209765a
4
u
5
+ ··· + 1.45085a + 0.0957893
a
4
=
−0.196344a
5
u
5
− 0.127790a
4
u
5
+ ··· + 0.258519a − 0.540133
0.0469600a
5
u
5
+ 0.0904674a
4
u
5
+ ··· − 0.272263a − 0.624194
a
11
=
0.0115886a
5
u
5
+ 0.209765a
4
u
5
+ ··· + 2.45085a + 0.0957893
0.0115886a
5
u
5
+ 0.209765a
4
u
5
+ ··· + 1.45085a + 0.0957893
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
0.0392084a
5
u
5
− 0.139324a
4
u
5
+ ··· − 0.209846a − 1.53310
−0.170556a
5
u
5
− 0.129475a
4
u
5
+ ··· − 1.69553a − 2.16257
a
8
=
−0.0509717a
5
u
5
+ 0.281923a
4
u
5
+ ··· + 2.38699a + 0.810462
0.0585370a
5
u
5
+ 0.228983a
4
u
5
+ ··· + 2.21950a + 0.271504
a
9
=
0.0352420a
5
u
5
+ 0.0936125a
4
u
5
+ ··· + 1.34226a − 0.0657213
−0.0552255a
5
u
5
+ 0.0897440a
4
u
5
+ ··· + 0.929944a + 0.941941
a
12
=
−0.00266510a
5
u
5
+ 0.138334a
4
u
5
+ ··· − 1.66833a + 1.57218
0.0788189a
5
u
5
+ 0.229555a
4
u
5
+ ··· + 1.98983a + 1.26999
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
154930048320
359321316539
a
5
u
5
−
7843205684
359321316539
u
5
a
4
+ ··· +
1582962992116
359321316539
a −
1022275344910
359321316539
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
6
c
2
, c
6
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
6
c
3
, c
5
, c
9
c
10
u
36
+ 9u
34
+ ··· − 118u + 31
c
4
, c
7
u
36
− 2u
35
+ ··· − 986u + 227
c
8
, c
11
, c
12
(u
3
+ 2u − 1)
12
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
6
c
2
, c
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
6
c
3
, c
5
, c
9
c
10
y
36
+ 18y
35
+ ··· + 92716y + 961
c
4
, c
7
y
36
+ 6y
35
+ ··· − 656212y + 51529
c
8
, c
11
, c
12
(y
3
+ 4y
2
+ 4y −1)
12
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −0.013507 − 1.079530I
b = −0.09167 − 1.43449I
−7.61261 − 0.92430I −18.3526 + 0.7942I
u = 1.002190 + 0.295542I
a = 0.777995 + 0.206131I
b = 0.28584 + 1.73579I
−7.61261 − 0.92430I −18.3526 + 0.7942I
u = 1.002190 + 0.295542I
a = 0.77699 + 1.31113I
b = −1.262930 − 0.434196I
2.61533 + 4.21364I −6.39878 − 2.41479I
u = 1.002190 + 0.295542I
a = −1.67565 − 0.70869I
b = 0.027573 + 0.143090I
2.61533 − 6.06225I −6.39878 + 4.00324I
u = 1.002190 + 0.295542I
a = −1.53392 − 1.32936I
b = 0.850685 − 0.922276I
2.61533 − 6.06225I −6.39878 + 4.00324I
u = 1.002190 + 0.295542I
a = 1.66809 + 1.60033I
b = 0.190509 + 0.912085I
2.61533 + 4.21364I −6.39878 − 2.41479I
u = 1.002190 − 0.295542I
a = −0.013507 + 1.079530I
b = −0.09167 + 1.43449I
−7.61261 + 0.92430I −18.3526 − 0.7942I
u = 1.002190 − 0.295542I
a = 0.777995 − 0.206131I
b = 0.28584 − 1.73579I
−7.61261 + 0.92430I −18.3526 − 0.7942I
u = 1.002190 − 0.295542I
a = 0.77699 − 1.31113I
b = −1.262930 + 0.434196I
2.61533 − 4.21364I −6.39878 + 2.41479I
u = 1.002190 − 0.295542I
a = −1.67565 + 0.70869I
b = 0.027573 − 0.143090I
2.61533 + 6.06225I −6.39878 − 4.00324I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 − 0.295542I
a = −1.53392 + 1.32936I
b = 0.850685 + 0.922276I
2.61533 + 6.06225I −6.39878 − 4.00324I
u = 1.002190 − 0.295542I
a = 1.66809 − 1.60033I
b = 0.190509 − 0.912085I
2.61533 − 4.21364I −6.39878 + 2.41479I
u = −0.428243 + 0.664531I
a = 0.864083 − 0.103468I
b = −0.578826 + 1.138480I
6.39654 − 6.06225I 1.03465 + 4.00324I
u = −0.428243 + 0.664531I
a = −0.343617 − 0.544568I
b = 0.580767 − 0.599442I
6.39654 + 4.21364I 1.03465 − 2.41479I
u = −0.428243 + 0.664531I
a = 1.54434 + 0.21164I
b = −0.787341 − 0.938487I
6.39654 + 4.21364I 1.03465 − 2.41479I
u = −0.428243 + 0.664531I
a = −0.69400 + 1.41167I
b = 0.044354 − 1.079790I
−3.83140 − 0.92430I −10.91915 + 0.79423I
u = −0.428243 + 0.664531I
a = 0.53759 − 1.75844I
b = −0.498746 + 1.213790I
−3.83140 − 0.92430I −10.91915 + 0.79423I
u = −0.428243 + 0.664531I
a = −1.90839 + 0.78316I
b = 1.239790 + 0.265446I
6.39654 − 6.06225I 1.03465 + 4.00324I
u = −0.428243 − 0.664531I
a = 0.864083 + 0.103468I
b = −0.578826 − 1.138480I
6.39654 + 6.06225I 1.03465 − 4.00324I
u = −0.428243 − 0.664531I
a = −0.343617 + 0.544568I
b = 0.580767 + 0.599442I
6.39654 − 4.21364I 1.03465 + 2.41479I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428243 − 0.664531I
a = 1.54434 − 0.21164I
b = −0.787341 + 0.938487I
6.39654 − 4.21364I 1.03465 + 2.41479I
u = −0.428243 − 0.664531I
a = −0.69400 − 1.41167I
b = 0.044354 + 1.079790I
−3.83140 + 0.92430I −10.91915 − 0.79423I
u = −0.428243 − 0.664531I
a = 0.53759 + 1.75844I
b = −0.498746 − 1.213790I
−3.83140 + 0.92430I −10.91915 − 0.79423I
u = −0.428243 − 0.664531I
a = −1.90839 − 0.78316I
b = 1.239790 − 0.265446I
6.39654 + 6.06225I 1.03465 − 4.00324I
u = −1.073950 + 0.558752I
a = 0.633332 − 0.905497I
b = −0.262746 − 0.891123I
4.50593 + 0.55508I −2.68207 − 2.30155I
u = −1.073950 + 0.558752I
a = 0.914818 − 1.037650I
b = −1.53217 + 0.17763I
4.50593 + 10.83100I −2.68207 − 8.71959I
u = −1.073950 + 0.558752I
a = −0.027013 + 0.573159I
b = 0.839369 − 0.811794I
4.50593 + 0.55508I −2.68207 − 2.30155I
u = −1.073950 + 0.558752I
a = −1.94384 + 0.16468I
b = 0.74634 + 1.38128I
−5.72200 + 5.69302I −14.6359 − 5.5106I
u = −1.073950 + 0.558752I
a = −1.59315 + 1.17157I
b = 0.468622 + 1.271950I
4.50593 + 10.83100I −2.68207 − 8.71959I
u = −1.073950 + 0.558752I
a = 2.01585 + 0.03374I
b = −0.259409 − 1.127950I
−5.72200 + 5.69302I −14.6359 − 5.5106I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.073950 − 0.558752I
a = 0.633332 + 0.905497I
b = −0.262746 + 0.891123I
4.50593 − 0.55508I −2.68207 + 2.30155I
u = −1.073950 − 0.558752I
a = 0.914818 + 1.037650I
b = −1.53217 − 0.17763I
4.50593 − 10.83100I −2.68207 + 8.71959I
u = −1.073950 − 0.558752I
a = −0.027013 − 0.573159I
b = 0.839369 + 0.811794I
4.50593 − 0.55508I −2.68207 + 2.30155I
u = −1.073950 − 0.558752I
a = −1.94384 − 0.16468I
b = 0.74634 − 1.38128I
−5.72200 − 5.69302I −14.6359 + 5.5106I
u = −1.073950 − 0.558752I
a = −1.59315 − 1.17157I
b = 0.468622 − 1.271950I
4.50593 − 10.83100I −2.68207 + 8.71959I
u = −1.073950 − 0.558752I
a = 2.01585 − 0.03374I
b = −0.259409 + 1.127950I
−5.72200 − 5.69302I −14.6359 + 5.5106I
16
III. I
u
3
= h2.29 × 10
20
a
7
u
5
− 2.53 × 10
20
a
6
u
5
+ · · · − 6.52 × 10
21
a − 2.08 ×
10
21
, −a
7
u
5
− 3a
6
u
5
+ · · · − 26a
2
− 4a, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
a
−0.0876714a
7
u
5
+ 0.0968394a
6
u
5
+ ··· + 2.49297a + 0.793595
a
4
=
0.00979694a
7
u
5
+ 0.0892583a
6
u
5
+ ··· + 0.236224a − 1.71364
−0.0205307a
7
u
5
+ 0.0739253a
6
u
5
+ ··· − 0.187546a − 0.432373
a
11
=
−0.0876714a
7
u
5
+ 0.0968394a
6
u
5
+ ··· + 3.49297a + 0.793595
−0.0876714a
7
u
5
+ 0.0968394a
6
u
5
+ ··· + 2.49297a + 0.793595
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
0.0778071a
7
u
5
− 0.0824931a
6
u
5
+ ··· − 2.81597a − 0.435778
0.0745886a
7
u
5
+ 0.0901752a
6
u
5
+ ··· − 0.377816a − 1.90604
a
8
=
−0.0901512a
7
u
5
+ 0.0564587a
6
u
5
+ ··· + 0.205725a + 0.247001
0.0204009a
7
u
5
− 0.284621a
6
u
5
+ ··· − 0.854018a + 0.155365
a
9
=
0.0453767a
7
u
5
+ 0.0806940a
6
u
5
+ ··· − 1.12856a − 1.58783
0.00277812a
7
u
5
+ 0.0567067a
6
u
5
+ ··· + 0.609646a − 1.08214
a
12
=
−0.264406a
7
u
5
− 0.106883a
6
u
5
+ ··· + 5.27344a + 1.47780
0.0400965a
7
u
5
− 0.227368a
6
u
5
+ ··· + 3.33193a + 1.68322
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
12869602086720
31969293098417
a
7
u
5
+
7770591958420
31969293098417
a
6
u
5
+ ··· −
105347813841252
31969293098417
a −
216568031551418
31969293098417
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
8
c
2
, c
6
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
8
c
3
, c
5
, c
9
c
10
u
48
+ u
47
+ ··· + 2816u + 1429
c
4
, c
7
u
48
− 5u
47
+ ··· + 20u + 31
c
8
, c
11
, c
12
(u
4
+ u
3
+ 2u
2
+ 2u + 1)
12
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
8
c
2
, c
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
8
c
3
, c
5
, c
9
c
10
y
48
+ 45y
47
+ ··· + 29429920y + 2042041
c
4
, c
7
y
48
− 15y
47
+ ··· − 8212y + 961
c
8
, c
11
, c
12
(y
4
+ 3y
3
+ 2y
2
+ 1)
12
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −0.630240 + 0.910708I
b = 0.017438 + 1.293140I
−3.53554 − 2.95419I −9.71672 + 4.25833I
u = 1.002190 + 0.295542I
a = −0.817208 − 0.972776I
b = 0.891703 + 0.533613I
−3.53554 + 1.10558I −9.71672 − 2.66988I
u = 1.002190 + 0.295542I
a = −0.574575 + 0.362328I
b = −0.65090 − 1.70065I
−3.53554 + 1.10558I −9.71672 − 2.66988I
u = 1.002190 + 0.295542I
a = −1.266850 − 0.455916I
b = 0.00909 − 1.89499I
−3.53554 − 2.95419I −9.71672 + 4.25833I
u = 1.002190 + 0.295542I
a = 1.223620 + 0.678825I
b = −0.400778 − 0.388180I
−3.53554 − 2.95419I −9.71672 + 4.25833I
u = 1.002190 + 0.295542I
a = 0.37497 + 1.57827I
b = 0.09185 + 1.47616I
−3.53554 + 1.10558I −9.71672 − 2.66988I
u = 1.002190 + 0.295542I
a = 1.49867 + 1.28979I
b = −0.415377 + 1.028640I
−3.53554 − 2.95419I −9.71672 + 4.25833I
u = 1.002190 + 0.295542I
a = −1.49452 − 1.46488I
b = 0.028724 − 1.012260I
−3.53554 + 1.10558I −9.71672 − 2.66988I
u = 1.002190 − 0.295542I
a = −0.630240 − 0.910708I
b = 0.017438 − 1.293140I
−3.53554 + 2.95419I −9.71672 − 4.25833I
u = 1.002190 − 0.295542I
a = −0.817208 + 0.972776I
b = 0.891703 − 0.533613I
−3.53554 − 1.10558I −9.71672 + 2.66988I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 − 0.295542I
a = −0.574575 − 0.362328I
b = −0.65090 + 1.70065I
−3.53554 − 1.10558I −9.71672 + 2.66988I
u = 1.002190 − 0.295542I
a = −1.266850 + 0.455916I
b = 0.00909 + 1.89499I
−3.53554 + 2.95419I −9.71672 − 4.25833I
u = 1.002190 − 0.295542I
a = 1.223620 − 0.678825I
b = −0.400778 + 0.388180I
−3.53554 + 2.95419I −9.71672 − 4.25833I
u = 1.002190 − 0.295542I
a = 0.37497 − 1.57827I
b = 0.09185 − 1.47616I
−3.53554 − 1.10558I −9.71672 + 2.66988I
u = 1.002190 − 0.295542I
a = 1.49867 − 1.28979I
b = −0.415377 − 1.028640I
−3.53554 + 2.95419I −9.71672 − 4.25833I
u = 1.002190 − 0.295542I
a = −1.49452 + 1.46488I
b = 0.028724 + 1.012260I
−3.53554 − 1.10558I −9.71672 + 2.66988I
u = −0.428243 + 0.664531I
a = −1.160570 + 0.252579I
b = 0.564310 + 0.561072I
0.245672 + 1.105580I −2.28328 − 2.66988I
u = −0.428243 + 0.664531I
a = −0.573726 + 0.214251I
b = 0.421958 − 1.070860I
0.24567 − 2.95419I −2.28328 + 4.25833I
u = −0.428243 + 0.664531I
a = 0.81080 − 1.25860I
b = −0.072000 + 1.291420I
0.24567 − 2.95419I −2.28328 + 4.25833I
u = −0.428243 + 0.664531I
a = 0.62738 − 1.46301I
b = 0.160009 + 0.836205I
0.245672 + 1.105580I −2.28328 − 2.66988I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428243 + 0.664531I
a = 1.53104 − 0.75811I
b = −0.930131 − 0.202650I
0.24567 − 2.95419I −2.28328 + 4.25833I
u = −0.428243 + 0.664531I
a = −0.07592 + 1.78653I
b = 0.33288 − 1.46152I
0.245672 + 1.105580I −2.28328 − 2.66988I
u = −0.428243 + 0.664531I
a = 0.119257 + 0.105054I
b = −0.300160 + 0.784396I
0.245672 + 1.105580I −2.28328 − 2.66988I
u = −0.428243 + 0.664531I
a = −0.93329 + 1.88611I
b = 0.825323 − 1.033610I
0.24567 − 2.95419I −2.28328 + 4.25833I
u = −0.428243 − 0.664531I
a = −1.160570 − 0.252579I
b = 0.564310 − 0.561072I
0.245672 − 1.105580I −2.28328 + 2.66988I
u = −0.428243 − 0.664531I
a = −0.573726 − 0.214251I
b = 0.421958 + 1.070860I
0.24567 + 2.95419I −2.28328 − 4.25833I
u = −0.428243 − 0.664531I
a = 0.81080 + 1.25860I
b = −0.072000 − 1.291420I
0.24567 + 2.95419I −2.28328 − 4.25833I
u = −0.428243 − 0.664531I
a = 0.62738 + 1.46301I
b = 0.160009 − 0.836205I
0.245672 − 1.105580I −2.28328 + 2.66988I
u = −0.428243 − 0.664531I
a = 1.53104 + 0.75811I
b = −0.930131 + 0.202650I
0.24567 + 2.95419I −2.28328 − 4.25833I
u = −0.428243 − 0.664531I
a = −0.07592 − 1.78653I
b = 0.33288 + 1.46152I
0.245672 − 1.105580I −2.28328 + 2.66988I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428243 − 0.664531I
a = 0.119257 − 0.105054I
b = −0.300160 − 0.784396I
0.245672 − 1.105580I −2.28328 + 2.66988I
u = −0.428243 − 0.664531I
a = −0.93329 − 1.88611I
b = 0.825323 + 1.033610I
0.24567 + 2.95419I −2.28328 − 4.25833I
u = −1.073950 + 0.558752I
a = −0.920921 + 0.716645I
b = 1.222720 − 0.072136I
−1.64493 + 7.72290I −6.00000 − 8.97467I
u = −1.073950 + 0.558752I
a = −1.123580 + 0.626202I
b = 0.215578 + 1.163690I
−1.64493 + 3.66314I −6.00000 − 2.04647I
u = −1.073950 + 0.558752I
a = 0.571084 − 0.365384I
b = −0.814908 + 0.307580I
−1.64493 + 3.66314I −6.00000 − 2.04647I
u = −1.073950 + 0.558752I
a = 1.51209 − 0.87090I
b = −0.361891 − 1.263090I
−1.64493 + 7.72290I −6.00000 − 8.97467I
u = −1.073950 + 0.558752I
a = −1.85013 − 0.34826I
b = 0.117199 + 0.847786I
−1.64493 + 3.66314I −6.00000 − 2.04647I
u = −1.073950 + 0.558752I
a = 1.94420 + 0.00617I
b = −0.53874 − 1.66837I
−1.64493 + 3.66314I −6.00000 − 2.04647I
u = −1.073950 + 0.558752I
a = 1.92851 − 0.39187I
b = −1.12635 − 1.19985I
−1.64493 + 7.72290I −6.00000 − 8.97467I
u = −1.073950 + 0.558752I
a = −2.22009 + 0.18976I
b = 0.212442 + 1.325630I
−1.64493 + 7.72290I −6.00000 − 8.97467I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.073950 − 0.558752I
a = −0.920921 − 0.716645I
b = 1.222720 + 0.072136I
−1.64493 − 7.72290I −6.00000 + 8.97467I
u = −1.073950 − 0.558752I
a = −1.123580 − 0.626202I
b = 0.215578 − 1.163690I
−1.64493 − 3.66314I −6.00000 + 2.04647I
u = −1.073950 − 0.558752I
a = 0.571084 + 0.365384I
b = −0.814908 − 0.307580I
−1.64493 − 3.66314I −6.00000 + 2.04647I
u = −1.073950 − 0.558752I
a = 1.51209 + 0.87090I
b = −0.361891 + 1.263090I
−1.64493 − 7.72290I −6.00000 + 8.97467I
u = −1.073950 − 0.558752I
a = −1.85013 + 0.34826I
b = 0.117199 − 0.847786I
−1.64493 − 3.66314I −6.00000 + 2.04647I
u = −1.073950 − 0.558752I
a = 1.94420 − 0.00617I
b = −0.53874 + 1.66837I
−1.64493 − 3.66314I −6.00000 + 2.04647I
u = −1.073950 − 0.558752I
a = 1.92851 + 0.39187I
b = −1.12635 + 1.19985I
−1.64493 − 7.72290I −6.00000 + 8.97467I
u = −1.073950 − 0.558752I
a = −2.22009 − 0.18976I
b = 0.212442 − 1.325630I
−1.64493 − 7.72290I −6.00000 + 8.97467I
24
IV. I
u
4
=
hu
29
+6u
28
+· · · +b−21, 25u
29
−4u
28
+· · · +2a+57, u
30
−9u
28
+· · · +5u+2i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
−
25
2
u
29
+ 2u
28
+ ··· − 18u −
57
2
−u
29
− 6u
28
+ ··· + 49u + 21
a
4
=
1
2
u
29
− u
28
+ ··· − 3u +
5
2
u
26
− 8u
24
+ ··· + 5u + 1
a
11
=
−
27
2
u
29
− 4u
28
+ ··· + 31u −
15
2
−u
29
− 6u
28
+ ··· + 49u + 21
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
1
2
u
29
− u
28
+ ··· + 2u +
9
2
u
26
− 8u
24
+ ··· + 4u + 1
a
8
=
7
2
u
29
+ 3u
28
+ ··· + 4u +
1
2
u
29
+ 4u
28
+ ··· − 14u − 5
a
9
=
3u
29
+ 6u
28
+ ··· − 69u − 37
5u
29
+ 3u
28
+ ··· − 30u − 4
a
12
=
−
11
2
u
29
− 17u
28
+ ··· + 91u +
59
2
−9u
29
− 8u
28
+ ··· + 63u + 21
(ii) Obstruction class = 1
(iii) Cusp Shapes =
21u
29
−12u
28
−177u
27
+124u
26
+747u
25
−603u
24
−2073u
23
+1827u
22
+4215u
21
−3835u
20
−
6692u
19
+5859u
18
+8734u
17
−6614u
16
−9721u
15
+5392u
14
+9405u
13
−2806u
12
−7806u
11
+
246u
10
+5402u
9
+1198u
8
−2968u
7
−1360u
6
+1236u
5
+809u
4
−337u
3
−276u
2
+49u + 42
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
− 18u
29
+ ··· − 57u + 4
c
2
u
30
− 9u
28
+ ··· − 5u + 2
c
3
, c
10
u
30
+ 15u
28
+ ··· + 12u
2
+ 1
c
4
, c
7
u
30
+ u
29
+ ··· − 8u + 1
c
5
, c
9
u
30
+ 15u
28
+ ··· + 12u
2
+ 1
c
6
u
30
− 9u
28
+ ··· + 5u + 2
c
8
u
30
− 4u
29
+ ··· + 3u
2
+ 1
c
11
, c
12
u
30
+ 4u
29
+ ··· + 3u
2
+ 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ 2y
29
+ ··· + 31y + 16
c
2
, c
6
y
30
− 18y
29
+ ··· − 57y + 4
c
3
, c
5
, c
9
c
10
y
30
+ 30y
29
+ ··· + 24y + 1
c
4
, c
7
y
30
− y
29
+ ··· − 28y + 1
c
8
, c
11
, c
12
y
30
+ 30y
29
+ ··· + 6y + 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.952145 + 0.286252I
a = 0.398837 + 0.697047I
b = 0.12915 + 1.57008I
−7.01292 − 1.14021I −3.38655 + 6.37988I
u = 0.952145 − 0.286252I
a = 0.398837 − 0.697047I
b = 0.12915 − 1.57008I
−7.01292 + 1.14021I −3.38655 − 6.37988I
u = 0.965248 + 0.373546I
a = −0.553231 − 0.601657I
b = −0.31364 − 1.66297I
−2.92587 + 0.16877I −3.75310 + 4.51294I
u = 0.965248 − 0.373546I
a = −0.553231 + 0.601657I
b = −0.31364 + 1.66297I
−2.92587 − 0.16877I −3.75310 − 4.51294I
u = 0.798652 + 0.725690I
a = −0.099222 − 0.283628I
b = 0.444314 − 0.445083I
6.25118 − 6.66463I −1.05506 + 5.08784I
u = 0.798652 − 0.725690I
a = −0.099222 + 0.283628I
b = 0.444314 + 0.445083I
6.25118 + 6.66463I −1.05506 − 5.08784I
u = −0.604930 + 0.647300I
a = −0.15994 + 1.85503I
b = 0.357229 − 1.198860I
−0.164048 − 1.136400I −3.89887 − 0.20909I
u = −0.604930 − 0.647300I
a = −0.15994 − 1.85503I
b = 0.357229 + 1.198860I
−0.164048 + 1.136400I −3.89887 + 0.20909I
u = −1.057750 + 0.371785I
a = 1.93959 − 1.25031I
b = −0.668159 − 0.707939I
2.86251 + 7.19350I −4.55086 − 11.56979I
u = −1.057750 − 0.371785I
a = 1.93959 + 1.25031I
b = −0.668159 + 0.707939I
2.86251 − 7.19350I −4.55086 + 11.56979I
28
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.825694 + 0.282075I
a = −0.419225 − 0.902735I
b = 0.07654 − 1.60255I
−2.28876 − 2.99583I −1.16764 + 5.09061I
u = 0.825694 − 0.282075I
a = −0.419225 + 0.902735I
b = 0.07654 + 1.60255I
−2.28876 + 2.99583I −1.16764 − 5.09061I
u = −1.021850 + 0.570454I
a = 2.15586 + 0.17936I
b = −0.54662 − 1.33793I
−1.45873 + 5.91291I −4.59524 − 4.83976I
u = −1.021850 − 0.570454I
a = 2.15586 − 0.17936I
b = −0.54662 + 1.33793I
−1.45873 − 5.91291I −4.59524 + 4.83976I
u = 0.868569 + 0.797714I
a = 0.162609 + 0.097391I
b = −0.052215 + 0.451138I
1.38771 − 2.98700I 0.28532 + 1.40240I
u = 0.868569 − 0.797714I
a = 0.162609 − 0.097391I
b = −0.052215 − 0.451138I
1.38771 + 2.98700I 0.28532 − 1.40240I
u = −0.272134 + 0.763114I
a = 0.727677 − 1.024560I
b = −0.211575 + 1.052660I
−2.28671 − 0.83827I −4.66791 + 0.25545I
u = −0.272134 − 0.763114I
a = 0.727677 + 1.024560I
b = −0.211575 − 1.052660I
−2.28671 + 0.83827I −4.66791 − 0.25545I
u = −0.729439 + 0.315278I
a = −1.28485 + 2.32663I
b = 0.717893 − 0.504562I
4.11744 − 4.24974I 1.06780 + 2.13757I
u = −0.729439 − 0.315278I
a = −1.28485 − 2.32663I
b = 0.717893 + 0.504562I
4.11744 + 4.24974I 1.06780 − 2.13757I
29
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.968187 + 0.738073I
a = −0.248401 + 0.007066I
b = −0.353343 − 0.528734I
5.73348 + 1.07614I 2.38900 − 0.71413I
u = 0.968187 − 0.738073I
a = −0.248401 − 0.007066I
b = −0.353343 + 0.528734I
5.73348 − 1.07614I 2.38900 + 0.71413I
u = −1.101080 + 0.549507I
a = −1.77107 + 0.21633I
b = 0.480587 + 1.128710I
−4.64868 + 5.65428I −5.65639 − 4.94967I
u = −1.101080 − 0.549507I
a = −1.77107 − 0.21633I
b = 0.480587 − 1.128710I
−4.64868 − 5.65428I −5.65639 + 4.94967I
u = 1.312340 + 0.224482I
a = 0.140510 + 0.376788I
b = 0.112726 + 1.238740I
−7.27992 − 2.38540I −10.03555 + 4.49833I
u = 1.312340 − 0.224482I
a = 0.140510 − 0.376788I
b = 0.112726 − 1.238740I
−7.27992 + 2.38540I −10.03555 − 4.49833I
u = −1.325000 + 0.188356I
a = −0.61712 + 1.30300I
b = 0.161101 + 0.706679I
−5.13377 + 3.52632I −36.8849 − 5.6431I
u = −1.325000 − 0.188356I
a = −0.61712 − 1.30300I
b = 0.161101 − 0.706679I
−5.13377 − 3.52632I −36.8849 + 5.6431I
u = −0.578657 + 0.221126I
a = 0.87799 − 2.21332I
b = −0.333989 + 0.617317I
−1.95731 − 1.64325I −4.09003 + 4.22173I
u = −0.578657 − 0.221126I
a = 0.87799 + 2.21332I
b = −0.333989 − 0.617317I
−1.95731 + 1.64325I −4.09003 − 4.22173I
30
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
14
)(u
30
− 18u
29
+ ··· − 57u + 4)
· (u
43
+ 21u
42
+ ··· − 36864u + 16384)
c
2
((u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
14
)(u
30
− 9u
28
+ ··· − 5u + 2)
· (u
43
− 15u
42
+ ··· − 1216u + 128)
c
3
, c
10
(u
30
+ 15u
28
+ ··· + 12u
2
+ 1)(u
36
+ 9u
34
+ ··· − 118u + 31)
· (u
43
+ 13u
41
+ ··· + u + 1)(u
48
+ u
47
+ ··· + 2816u + 1429)
c
4
, c
7
(u
30
+ u
29
+ ··· − 8u + 1)(u
36
− 2u
35
+ ··· − 986u + 227)
· (u
43
− u
42
+ ··· − 11u + 1)(u
48
− 5u
47
+ ··· + 20u + 31)
c
5
, c
9
(u
30
+ 15u
28
+ ··· + 12u
2
+ 1)(u
36
+ 9u
34
+ ··· − 118u + 31)
· (u
43
+ 13u
41
+ ··· + u + 1)(u
48
+ u
47
+ ··· + 2816u + 1429)
c
6
((u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
14
)(u
30
− 9u
28
+ ··· + 5u + 2)
· (u
43
− 15u
42
+ ··· − 1216u + 128)
c
8
((u
3
+ 2u − 1)
12
)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
12
(u
30
− 4u
29
+ ··· + 3u
2
+ 1)
· (u
43
− 15u
42
+ ··· + 1184u − 64)
c
11
, c
12
((u
3
+ 2u − 1)
12
)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
12
(u
30
+ 4u
29
+ ··· + 3u
2
+ 1)
· (u
43
− 15u
42
+ ··· + 1184u − 64)
31
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
14
)(y
30
+ 2y
29
+ ··· + 31y + 16)
· (y
43
+ 3y
42
+ ··· − 352321536y −268435456)
c
2
, c
6
((y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
14
)(y
30
− 18y
29
+ ··· − 57y + 4)
· (y
43
− 21y
42
+ ··· − 36864y −16384)
c
3
, c
5
, c
9
c
10
(y
30
+ 30y
29
+ ··· + 24y + 1)(y
36
+ 18y
35
+ ··· + 92716y + 961)
· (y
43
+ 26y
42
+ ··· − 3y −1)
· (y
48
+ 45y
47
+ ··· + 29429920y + 2042041)
c
4
, c
7
(y
30
− y
29
+ ··· − 28y + 1)(y
36
+ 6y
35
+ ··· − 656212y + 51529)
· (y
43
+ 27y
42
+ ··· + 9y −1)(y
48
− 15y
47
+ ··· − 8212y + 961)
c
8
, c
11
, c
12
(y
3
+ 4y
2
+ 4y −1)
12
(y
4
+ 3y
3
+ 2y
2
+ 1)
12
· (y
30
+ 30y
29
+ ··· + 6y + 1)(y
43
+ 37y
42
+ ··· + 37888y −4096)
32
