12a
1216
(K12a
1216
)
A knot diagram
1
Linearized knot diagam
5 6 7 10 9 11 12 1 2 4 3 8
Solving Sequence
1,5 2,9
6 3 10 4 8 12 7 11
c
1
c
5
c
2
c
9
c
4
c
8
c
12
c
7
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.07110 × 10
55
u
35
+ 3.11578 × 10
55
u
34
+ ··· + 1.21007 × 10
57
b − 2.38367 × 10
57
,
− 3.06823 × 10
57
u
35
− 8.48330 × 10
57
u
34
+ ··· + 2.92837 × 10
58
a − 3.15010 × 10
57
,
u
36
+ 3u
35
+ ··· + 31u + 11i
I
u
2
= h1.96215 × 10
378
u
83
− 5.73830 × 10
378
u
82
+ ··· + 2.31304 × 10
381
b + 1.14245 × 10
383
,
− 2.55618 × 10
383
u
83
+ 1.36720 × 10
384
u
82
+ ··· + 3.72608 × 10
385
a − 4.36737 × 10
387
,
u
84
− 6u
83
+ ··· + 75402u + 16109i
I
u
3
= h−1.41646 × 10
18
u
23
− 1.09158 × 10
19
u
22
+ ··· + 9.42892 × 10
19
b − 2.23684 × 10
20
,
− 2.41868 × 10
19
u
23
− 2.30045 × 10
19
u
22
+ ··· + 3.45727 × 10
20
a + 9.65371 × 10
20
,
u
24
+ u
23
+ ··· − 44u + 11i
I
u
4
= h−u
2
+ b + u − 1, u
3
− u
2
+ a + 2u, u
5
− u
4
+ 3u
3
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 149 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
= h3.07 × 10
55
u
35
+ 3.12 × 10
55
u
34
+ · · · + 1.21 × 10
57
b − 2.38 ×
10
57
, −3.07 × 10
57
u
35
− 8.48 × 10
57
u
34
+ · · · + 2.93 × 10
58
a − 3.15 ×
10
57
, u
36
+ 3u
35
+ · · · + 31u + 11i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
9
=
0.104776u
35
+ 0.289694u
34
+ ··· + 8.06655u + 0.107572
−0.0253796u
35
− 0.0257488u
34
+ ··· + 2.33690u + 1.96987
a
6
=
−0.0430439u
35
− 0.0980154u
34
+ ··· − 1.26891u + 1.90110
−0.0282150u
35
− 0.0943192u
34
+ ··· − 1.90756u − 0.940844
a
3
=
0.0194838u
35
+ 0.0845787u
34
+ ··· + 2.21756u + 2.39922
−0.00642062u
35
− 0.0145250u
34
+ ··· − 0.611763u − 0.128826
a
10
=
0.119201u
35
+ 0.286732u
34
+ ··· + 5.34079u − 1.59131
−0.0176093u
35
+ 0.0122805u
34
+ ··· + 3.61154u + 2.47846
a
4
=
−0.0321006u
35
− 0.0871705u
34
+ ··· + 1.07521u + 2.34185
0.0515844u
35
+ 0.171749u
34
+ ··· + 1.14236u + 0.0573708
a
8
=
0.130156u
35
+ 0.315443u
34
+ ··· + 5.72965u − 1.86229
−0.0253796u
35
− 0.0257488u
34
+ ··· + 2.33690u + 1.96987
a
12
=
0.0218056u
35
+ 0.0861969u
34
+ ··· + 5.45506u + 0.366809
0.0637256u
35
+ 0.142182u
34
+ ··· + 0.735110u + 0.377098
a
7
=
−0.00521553u
35
+ 0.0359378u
34
+ ··· + 6.08640u + 0.980678
0.0169269u
35
− 0.00722416u
34
+ ··· − 4.32230u − 1.22939
a
11
=
−0.0405255u
35
− 0.0987638u
34
+ ··· − 0.0270432u − 1.57349
0.0588225u
35
+ 0.139014u
34
+ ··· + 1.58649u + 0.520172
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.343599u
35
+ 0.938842u
34
+ ··· + 7.99255u + 3.25096
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
36
− 3u
35
+ ··· − 31u + 11
c
2
u
36
− 7u
35
+ ··· − 12071u + 1268
c
4
, c
10
11(11u
36
− 27u
35
+ ··· − 224u + 64)
c
5
, c
11
11(11u
36
− 5u
35
+ ··· + 11u + 1)
c
6
, c
9
u
36
+ u
35
+ ··· + 17u + 11
c
7
, c
8
, c
12
u
36
+ 4u
35
+ ··· − 71u + 28
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
36
+ 17y
35
+ ··· + 1525y + 121
c
2
y
36
− 5y
35
+ ··· − 32055665y + 1607824
c
4
, c
10
121(121y
36
+ 4177y
35
+ ··· − 52224y + 4096)
c
5
, c
11
121(121y
36
− 179y
35
+ ··· − 15y + 1)
c
6
, c
9
y
36
− 9y
35
+ ··· − 993y + 121
c
7
, c
8
, c
12
y
36
− 42y
35
+ ··· − 10025y + 784
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.626439 + 0.821744I
a = −0.014200 + 0.915314I
b = 0.285946 + 1.359990I
5.67717 − 7.19089I 6.77872 + 10.51894I
u = 0.626439 − 0.821744I
a = −0.014200 − 0.915314I
b = 0.285946 − 1.359990I
5.67717 + 7.19089I 6.77872 − 10.51894I
u = −0.735513 + 0.847069I
a = −0.061617 − 1.306230I
b = −0.731247 − 0.579536I
1.25199 + 9.16761I 2.00321 − 10.89319I
u = −0.735513 − 0.847069I
a = −0.061617 + 1.306230I
b = −0.731247 + 0.579536I
1.25199 − 9.16761I 2.00321 + 10.89319I
u = 0.772732 + 0.874210I
a = 0.194851 + 0.728325I
b = −0.486450 + 0.481309I
−1.16285 − 3.35532I −5.76129 + 8.10680I
u = 0.772732 − 0.874210I
a = 0.194851 − 0.728325I
b = −0.486450 − 0.481309I
−1.16285 + 3.35532I −5.76129 − 8.10680I
u = −0.805692 + 0.116635I
a = 0.617278 − 1.109470I
b = 0.337006 − 0.262138I
2.93111 − 1.00501I −2.25229 + 5.18116I
u = −0.805692 − 0.116635I
a = 0.617278 + 1.109470I
b = 0.337006 + 0.262138I
2.93111 + 1.00501I −2.25229 − 5.18116I
u = −0.165485 + 0.766453I
a = 1.42439 − 0.22806I
b = −1.69610 + 0.07451I
11.30080 + 0.97216I 1.38322 − 7.38671I
u = −0.165485 − 0.766453I
a = 1.42439 + 0.22806I
b = −1.69610 − 0.07451I
11.30080 − 0.97216I 1.38322 + 7.38671I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.696880 + 0.295020I
a = 0.096744 − 0.480185I
b = −0.400914 − 0.336417I
−1.319370 − 0.296330I −6.81999 − 0.16370I
u = 0.696880 − 0.295020I
a = 0.096744 + 0.480185I
b = −0.400914 + 0.336417I
−1.319370 + 0.296330I −6.81999 + 0.16370I
u = −0.737714 + 1.001740I
a = −0.073548 − 0.249450I
b = 0.589463 − 0.458452I
2.89931 + 3.69822I 0.38877 − 1.68665I
u = −0.737714 − 1.001740I
a = −0.073548 + 0.249450I
b = 0.589463 + 0.458452I
2.89931 − 3.69822I 0.38877 + 1.68665I
u = −0.405498 + 0.604340I
a = −0.253574 + 1.341290I
b = −0.285857 + 0.818526I
−0.18794 + 4.61110I −1.49697 − 10.53385I
u = −0.405498 − 0.604340I
a = −0.253574 − 1.341290I
b = −0.285857 − 0.818526I
−0.18794 − 4.61110I −1.49697 + 10.53385I
u = −0.018649 + 0.720074I
a = 0.212930 − 0.920994I
b = −2.00932 − 0.41237I
12.86020 + 1.02559I 15.7606 − 6.4698I
u = −0.018649 − 0.720074I
a = 0.212930 + 0.920994I
b = −2.00932 + 0.41237I
12.86020 − 1.02559I 15.7606 + 6.4698I
u = 0.570273 + 0.403483I
a = 0.797604 − 0.529762I
b = 1.71444 − 0.17611I
6.75055 − 0.27364I 3.68665 + 13.40425I
u = 0.570273 − 0.403483I
a = 0.797604 + 0.529762I
b = 1.71444 + 0.17611I
6.75055 + 0.27364I 3.68665 − 13.40425I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.896164 + 1.034610I
a = 0.190031 + 1.352920I
b = 1.62048 + 0.16576I
9.2208 + 11.9404I 5.14110 − 9.30022I
u = −0.896164 − 1.034610I
a = 0.190031 − 1.352920I
b = 1.62048 − 0.16576I
9.2208 − 11.9404I 5.14110 + 9.30022I
u = −1.379280 + 0.100054I
a = −0.551599 + 0.192022I
b = −1.48860 − 0.03556I
8.76113 − 1.33737I 5.81278 + 5.28943I
u = −1.379280 − 0.100054I
a = −0.551599 − 0.192022I
b = −1.48860 + 0.03556I
8.76113 + 1.33737I 5.81278 − 5.28943I
u = 0.85971 + 1.17187I
a = −0.049347 − 0.951517I
b = 0.903388 − 0.869869I
7.7128 − 14.1526I 5.37015 + 9.64601I
u = 0.85971 − 1.17187I
a = −0.049347 + 0.951517I
b = 0.903388 + 0.869869I
7.7128 + 14.1526I 5.37015 − 9.64601I
u = −0.156302 + 0.359262I
a = −0.90151 + 1.91392I
b = 0.858883 + 0.215221I
1.63286 + 0.71455I 2.07561 − 1.46762I
u = −0.156302 − 0.359262I
a = −0.90151 − 1.91392I
b = 0.858883 − 0.215221I
1.63286 − 0.71455I 2.07561 + 1.46762I
u = 0.77773 + 1.43937I
a = −0.327351 − 0.665051I
b = 1.51996 − 0.13931I
5.50525 − 5.57144I 0
u = 0.77773 − 1.43937I
a = −0.327351 + 0.665051I
b = 1.51996 + 0.13931I
5.50525 + 5.57144I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.91981 + 1.44541I
a = 0.083609 + 0.983332I
b = −1.68386 + 0.26413I
16.3072 − 18.5095I 0
u = 0.91981 − 1.44541I
a = 0.083609 − 0.983332I
b = −1.68386 − 0.26413I
16.3072 + 18.5095I 0
u = −0.71477 + 1.57778I
a = −0.255474 + 0.443114I
b = 0.529759 + 0.323204I
2.68916 + 6.34722I 0
u = −0.71477 − 1.57778I
a = −0.255474 − 0.443114I
b = 0.529759 − 0.323204I
2.68916 − 6.34722I 0
u = −0.70851 + 2.00785I
a = 0.374916 − 0.443328I
b = −1.57698 − 0.08807I
9.97824 + 7.80433I 0
u = −0.70851 − 2.00785I
a = 0.374916 + 0.443328I
b = −1.57698 + 0.08807I
9.97824 − 7.80433I 0
8
II. I
u
2
= h1.96 × 10
378
u
83
− 5.74 × 10
378
u
82
+ · · · + 2.31 × 10
381
b + 1.14 ×
10
383
, −2.56 × 10
383
u
83
+ 1.37 × 10
384
u
82
+ · · · + 3.73 × 10
385
a − 4.37 ×
10
387
, u
84
− 6u
83
+ · · · + 75402u + 16109i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
9
=
0.00686023u
83
− 0.0366927u
82
+ ··· + 770.784u + 117.211
−0.000848300u
83
+ 0.00248085u
82
+ ··· − 242.928u − 49.3918
a
6
=
−0.0168256u
83
+ 0.122202u
82
+ ··· + 1670.97u + 450.926
0.00649536u
83
− 0.0484208u
82
+ ··· − 918.996u − 236.276
a
3
=
0.0354912u
83
− 0.232975u
82
+ ··· − 748.044u − 335.703
−0.0188856u
83
+ 0.133648u
82
+ ··· + 1425.41u + 406.752
a
10
=
0.00459288u
83
− 0.0233944u
82
+ ··· + 566.251u + 94.6163
−0.000548050u
83
+ 0.000304096u
82
+ ··· − 183.346u − 44.4657
a
4
=
−0.0108581u
83
+ 0.0775995u
82
+ ··· + 1106.74u + 294.456
0.00419775u
83
− 0.0306150u
82
+ ··· − 609.826u − 150.118
a
8
=
0.00770853u
83
− 0.0391735u
82
+ ··· + 1013.71u + 166.603
−0.000848300u
83
+ 0.00248085u
82
+ ··· − 242.928u − 49.3918
a
12
=
0.0217802u
83
− 0.121456u
82
+ ··· + 1657.93u + 239.097
−0.00711285u
83
+ 0.0399474u
82
+ ··· − 415.961u − 52.1460
a
7
=
−0.0111339u
83
+ 0.0504405u
82
+ ··· − 2063.90u − 380.414
0.00551466u
83
− 0.0250079u
82
+ ··· + 1064.17u + 192.856
a
11
=
−0.0165383u
83
+ 0.0810880u
82
+ ··· − 2538.50u − 468.124
0.0147464u
83
− 0.0845715u
82
+ ··· + 1055.87u + 156.995
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0487492u
83
− 0.270054u
82
+ ··· + 2871.27u + 426.180
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
84
+ 6u
83
+ ··· − 75402u + 16109
c
2
(u
42
+ 7u
41
+ ··· + 3649u + 1139)
2
c
4
, c
10
(u
42
+ u
41
+ ··· − 42u + 11)
2
c
5
, c
11
u
84
− 21u
82
+ ··· − 44416u + 6119
c
6
, c
9
u
84
− u
83
+ ··· − 2672u + 2143
c
7
, c
8
, c
12
(u
42
− 2u
41
+ ··· + 22u + 19)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
84
+ 32y
83
+ ··· + 5914049372y + 259499881
c
2
(y
42
− 41y
41
+ ··· + 6170811y + 1297321)
2
c
4
, c
10
(y
42
+ 39y
41
+ ··· − 5570y + 121)
2
c
5
, c
11
y
84
− 42y
83
+ ··· − 2518510190y + 37442161
c
6
, c
9
y
84
+ 33y
83
+ ··· + 197735502y + 4592449
c
7
, c
8
, c
12
(y
42
− 50y
41
+ ··· − 7704y + 361)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.412080 + 0.913638I
a = 0.263346 + 1.103990I
b = −0.437900 + 0.497668I
6.35842 + 3.57446I 0
u = −0.412080 − 0.913638I
a = 0.263346 − 1.103990I
b = −0.437900 − 0.497668I
6.35842 − 3.57446I 0
u = −0.088801 + 0.946124I
a = 1.47719 − 1.37886I
b = −1.62572 + 0.17083I
13.87510 − 0.52912I 0
u = −0.088801 − 0.946124I
a = 1.47719 + 1.37886I
b = −1.62572 − 0.17083I
13.87510 + 0.52912I 0
u = 0.325109 + 1.007640I
a = 0.544570 + 1.150320I
b = −0.549752 + 0.104184I
1.71215 − 3.87199I 0
u = 0.325109 − 1.007640I
a = 0.544570 − 1.150320I
b = −0.549752 − 0.104184I
1.71215 + 3.87199I 0
u = 0.691646 + 0.804712I
a = −0.000664 − 0.793299I
b = 0.066574 − 0.604668I
−1.43965 − 2.16802I 0
u = 0.691646 − 0.804712I
a = −0.000664 + 0.793299I
b = 0.066574 + 0.604668I
−1.43965 + 2.16802I 0
u = 0.759609 + 0.743113I
a = −0.65385 + 1.91886I
b = −1.58084
8.77057 0
u = 0.759609 − 0.743113I
a = −0.65385 − 1.91886I
b = −1.58084
8.77057 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.075329 + 0.925694I
a = −0.124605 + 1.122850I
b = 1.72261 + 0.32384I
15.3392 + 9.3793I 0
u = −0.075329 − 0.925694I
a = −0.124605 − 1.122850I
b = 1.72261 − 0.32384I
15.3392 − 9.3793I 0
u = 0.090374 + 1.067480I
a = 0.114307 + 0.819229I
b = −1.62572 + 0.17083I
13.87510 − 0.52912I 0
u = 0.090374 − 1.067480I
a = 0.114307 − 0.819229I
b = −1.62572 − 0.17083I
13.87510 + 0.52912I 0
u = −0.351633 + 1.028510I
a = 0.076516 − 0.845833I
b = 0.576821 − 0.583368I
6.28954 + 2.36144I 0
u = −0.351633 − 1.028510I
a = 0.076516 + 0.845833I
b = 0.576821 + 0.583368I
6.28954 − 2.36144I 0
u = 0.114981 + 0.901161I
a = −1.19186 − 1.83232I
b = 1.58370 − 0.06665I
13.30610 − 1.90744I 0
u = 0.114981 − 0.901161I
a = −1.19186 + 1.83232I
b = 1.58370 + 0.06665I
13.30610 + 1.90744I 0
u = 0.038364 + 0.900051I
a = −0.32415 − 1.54825I
b = 1.57184 − 0.14261I
13.28250 + 1.24407I 0
u = 0.038364 − 0.900051I
a = −0.32415 + 1.54825I
b = 1.57184 + 0.14261I
13.28250 − 1.24407I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.381897 + 0.812659I
a = 1.59666 − 0.56281I
b = −0.655015 + 0.430426I
7.13711 − 6.82425I 0
u = 0.381897 − 0.812659I
a = 1.59666 + 0.56281I
b = −0.655015 − 0.430426I
7.13711 + 6.82425I 0
u = −0.479320 + 0.757238I
a = −0.150258 + 1.328570I
b = 0.637898 + 0.738470I
2.17073 + 2.60369I 0
u = −0.479320 − 0.757238I
a = −0.150258 − 1.328570I
b = 0.637898 − 0.738470I
2.17073 − 2.60369I 0
u = 0.368717 + 0.802163I
a = 0.103264 − 0.959262I
b = −0.775794 − 1.149540I
6.99281 + 3.81110I 0
u = 0.368717 − 0.802163I
a = 0.103264 + 0.959262I
b = −0.775794 + 1.149540I
6.99281 − 3.81110I 0
u = −0.495002 + 1.016410I
a = −0.508573 − 0.313164I
b = −0.549752 + 0.104184I
1.71215 − 3.87199I 0
u = −0.495002 − 1.016410I
a = −0.508573 + 0.313164I
b = −0.549752 − 0.104184I
1.71215 + 3.87199I 0
u = −0.525684 + 0.690822I
a = −0.21351 + 1.57522I
b = 1.097370 + 0.361003I
1.50059 + 1.26218I 0
u = −0.525684 − 0.690822I
a = −0.21351 − 1.57522I
b = 1.097370 − 0.361003I
1.50059 − 1.26218I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.534465 + 1.016380I
a = −1.057290 + 0.230653I
b = 0.576821 − 0.583368I
6.28954 + 2.36144I 0
u = 0.534465 − 1.016380I
a = −1.057290 − 0.230653I
b = 0.576821 + 0.583368I
6.28954 − 2.36144I 0
u = −0.864888 + 0.782442I
a = −0.548158 − 0.772833I
b = −1.51839
8.58416 0
u = −0.864888 − 0.782442I
a = −0.548158 + 0.772833I
b = −1.51839
8.58416 0
u = −0.047743 + 0.824577I
a = −1.92274 + 1.75421I
b = 1.60502 − 0.11915I
14.8937 − 8.8355I 0
u = −0.047743 − 0.824577I
a = −1.92274 − 1.75421I
b = 1.60502 + 0.11915I
14.8937 + 8.8355I 0
u = −0.250947 + 0.751345I
a = 1.35039 + 0.85488I
b = −0.563023 + 0.229679I
5.86017 − 0.82248I 0
u = −0.250947 − 0.751345I
a = 1.35039 − 0.85488I
b = −0.563023 − 0.229679I
5.86017 + 0.82248I 0
u = 0.577765 + 1.102210I
a = −0.35170 − 1.50242I
b = 1.56641 − 0.02917I
8.98118 − 4.39010I 0
u = 0.577765 − 1.102210I
a = −0.35170 + 1.50242I
b = 1.56641 + 0.02917I
8.98118 + 4.39010I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.691788 + 1.044050I
a = 0.00719 − 1.43711I
b = −1.59862 − 0.19607I
9.70426 + 5.93683I 0
u = −0.691788 − 1.044050I
a = 0.00719 + 1.43711I
b = −1.59862 + 0.19607I
9.70426 − 5.93683I 0
u = 0.480853 + 0.566284I
a = 0.73045 − 2.11810I
b = 0.518753
1.41871 0
u = 0.480853 − 0.566284I
a = 0.73045 + 2.11810I
b = 0.518753
1.41871 0
u = 0.200106 + 0.684096I
a = 0.386069 − 0.824872I
b = 0.637898 − 0.738470I
2.17073 − 2.60369I 9.54698 + 6.96810I
u = 0.200106 − 0.684096I
a = 0.386069 + 0.824872I
b = 0.637898 + 0.738470I
2.17073 + 2.60369I 9.54698 − 6.96810I
u = −0.588208 + 0.329396I
a = 0.22454 − 1.42162I
b = 0.066574 − 0.604668I
−1.43965 − 2.16802I −4.95440 + 3.47274I
u = −0.588208 − 0.329396I
a = 0.22454 + 1.42162I
b = 0.066574 + 0.604668I
−1.43965 + 2.16802I −4.95440 − 3.47274I
u = 0.747996 + 1.109260I
a = −0.218898 + 0.650559I
b = −1.59862 + 0.19607I
9.70426 − 5.93683I 0
u = 0.747996 − 1.109260I
a = −0.218898 − 0.650559I
b = −1.59862 − 0.19607I
9.70426 + 5.93683I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.840070 + 1.047900I
a = −0.005954 + 0.918057I
b = −0.775794 + 1.149540I
6.99281 − 3.81110I 0
u = 0.840070 − 1.047900I
a = −0.005954 − 0.918057I
b = −0.775794 − 1.149540I
6.99281 + 3.81110I 0
u = −0.586859 + 1.213690I
a = −0.212588 + 1.012480I
b = 0.521404 + 0.493566I
6.18148 + 6.08971I 0
u = −0.586859 − 1.213690I
a = −0.212588 − 1.012480I
b = 0.521404 − 0.493566I
6.18148 − 6.08971I 0
u = −0.802110 + 1.164690I
a = −0.105102 − 0.915114I
b = −0.655015 − 0.430426I
7.13711 + 6.82425I 0
u = −0.802110 − 1.164690I
a = −0.105102 + 0.915114I
b = −0.655015 + 0.430426I
7.13711 − 6.82425I 0
u = 0.440217 + 0.373005I
a = −0.357777 + 0.355965I
b = 1.097370 + 0.361003I
1.50059 + 1.26218I −4.11625 + 3.56355I
u = 0.440217 − 0.373005I
a = −0.357777 − 0.355965I
b = 1.097370 − 0.361003I
1.50059 − 1.26218I −4.11625 − 3.56355I
u = −0.170731 + 0.447358I
a = 0.96366 + 1.92676I
b = 0.539790
1.75929 7.33658 + 0.I
u = −0.170731 − 0.447358I
a = 0.96366 − 1.92676I
b = 0.539790
1.75929 7.33658 + 0.I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.81115 + 1.35766I
a = 0.116699 + 0.771146I
b = −1.159800 + 0.191275I
2.23592 − 4.97678I 0
u = 0.81115 − 1.35766I
a = 0.116699 − 0.771146I
b = −1.159800 − 0.191275I
2.23592 + 4.97678I 0
u = −0.67426 + 1.44318I
a = 0.332209 − 1.127350I
b = −1.56368 − 0.13058I
13.2660 + 8.2694I 0
u = −0.67426 − 1.44318I
a = 0.332209 + 1.127350I
b = −1.56368 + 0.13058I
13.2660 − 8.2694I 0
u = 1.13561 + 1.14397I
a = −0.478436 + 0.264820I
b = −0.437900 − 0.497668I
6.35842 − 3.57446I 0
u = 1.13561 − 1.14397I
a = −0.478436 − 0.264820I
b = −0.437900 + 0.497668I
6.35842 + 3.57446I 0
u = −1.14800 + 1.13498I
a = −0.265214 − 0.293687I
b = −0.563023 − 0.229679I
5.86017 + 0.82248I 0
u = −1.14800 − 1.13498I
a = −0.265214 + 0.293687I
b = −0.563023 + 0.229679I
5.86017 − 0.82248I 0
u = −0.338277 + 0.060821I
a = −0.61417 + 2.43408I
b = −1.159800 + 0.191275I
2.23592 − 4.97678I 1.10438 + 6.13491I
u = −0.338277 − 0.060821I
a = −0.61417 − 2.43408I
b = −1.159800 − 0.191275I
2.23592 + 4.97678I 1.10438 − 6.13491I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.14725 + 1.19823I
a = 0.256670 + 0.359569I
b = 1.56641 − 0.02917I
8.98118 − 4.39010I 0
u = −1.14725 − 1.19823I
a = 0.256670 − 0.359569I
b = 1.56641 + 0.02917I
8.98118 + 4.39010I 0
u = 0.94235 + 1.44632I
a = −0.062530 − 0.915398I
b = 1.72261 − 0.32384I
15.3392 − 9.3793I 0
u = 0.94235 − 1.44632I
a = −0.062530 + 0.915398I
b = 1.72261 + 0.32384I
15.3392 + 9.3793I 0
u = −1.01641 + 1.44985I
a = 0.039944 + 0.886627I
b = 1.60502 + 0.11915I
14.8937 + 8.8355I 0
u = −1.01641 − 1.44985I
a = 0.039944 − 0.886627I
b = 1.60502 − 0.11915I
14.8937 − 8.8355I 0
u = 1.60304 + 1.06764I
a = 0.332738 − 0.007652I
b = 0.521404 + 0.493566I
6.18148 + 6.08971I 0
u = 1.60304 − 1.06764I
a = 0.332738 + 0.007652I
b = 0.521404 − 0.493566I
6.18148 − 6.08971I 0
u = −1.61907 + 1.83755I
a = 0.080694 + 0.318163I
b = 1.58370 + 0.06665I
13.30610 + 1.90744I 0
u = −1.61907 − 1.83755I
a = 0.080694 − 0.318163I
b = 1.58370 − 0.06665I
13.30610 − 1.90744I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.69026 + 1.81481I
a = 0.109423 − 0.317057I
b = 1.57184 + 0.14261I
13.28250 − 1.24407I 0
u = 1.69026 − 1.81481I
a = 0.109423 + 0.317057I
b = 1.57184 − 0.14261I
13.28250 + 1.24407I 0
u = 2.59982 + 1.35757I
a = −0.166095 + 0.099938I
b = −1.56368 − 0.13058I
13.2660 + 8.2694I 0
u = 2.59982 − 1.35757I
a = −0.166095 − 0.099938I
b = −1.56368 + 0.13058I
13.2660 − 8.2694I 0
20
III. I
u
3
= h−1.42 × 10
18
u
23
− 1.09 × 10
19
u
22
+ · · · + 9.43 × 10
19
b − 2.24 ×
10
20
, −2.42 × 10
19
u
23
− 2.30 × 10
19
u
22
+ · · · + 3.46 × 10
20
a + 9.65 ×
10
20
, u
24
+ u
23
+ · · · − 44u + 11i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
9
=
0.0699593u
23
+ 0.0665395u
22
+ ··· + 9.63491u − 2.79229
0.0150225u
23
+ 0.115770u
22
+ ··· − 4.63853u + 2.37232
a
6
=
−0.0928494u
23
− 0.0868942u
22
+ ··· − 9.98371u + 2.96317
0.0522743u
23
+ 0.0351421u
22
+ ··· + 3.47830u − 1.17586
a
3
=
−0.0584261u
23
− 0.0726681u
22
+ ··· − 2.98534u + 2.06543
−0.0104009u
23
− 0.0174400u
22
+ ··· − 0.324061u − 0.146453
a
10
=
0.0922899u
23
+ 0.00485746u
22
+ ··· + 13.3534u − 5.12700
−0.0389206u
23
+ 0.0983243u
22
+ ··· − 8.58073u + 3.29646
a
4
=
−0.102004u
23
− 0.0433298u
22
+ ··· − 5.35548u + 3.32001
0.110443u
23
+ 0.133690u
22
+ ··· − 1.11943u + 0.108090
a
8
=
0.0549367u
23
− 0.0492302u
22
+ ··· + 14.2734u − 5.16462
0.0150225u
23
+ 0.115770u
22
+ ··· − 4.63853u + 2.37232
a
12
=
0.00642856u
23
+ 0.107106u
22
+ ··· − 3.16939u − 0.222412
0.100468u
23
+ 0.0520650u
22
+ ··· + 9.13311u − 1.00274
a
7
=
0.0894022u
23
+ 0.212775u
22
+ ··· + 3.14475u − 0.583318
0.0414184u
23
− 0.0679770u
22
+ ··· + 3.67274u − 0.718675
a
11
=
−0.0605590u
23
− 0.0764932u
22
+ ··· − 2.19170u − 3.18750
0.131334u
23
+ 0.186917u
22
+ ··· + 4.57549u + 0.711578
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
20232201390387827417
94289151679873337469
u
23
−
37327327826068007036
94289151679873337469
u
22
+ ··· −
2650972892552315053228
94289151679873337469
u +
529524306171287821257
31429717226624445823
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
24
+ u
23
+ ··· − 44u + 11
c
2
(u
12
− 6u
11
+ ··· − 8u
2
+ 1)
2
c
4
, c
10
11(11u
24
+ 178u
22
+ ··· + 9157u
2
+ 1787)
c
5
, c
11
11(11u
24
− 11u
23
+ ··· − 6u + 1)
c
6
, c
9
u
24
− 2u
23
+ ··· + 35u
2
+ 11
c
7
, c
8
(u
12
+ u
11
+ ··· + 5u + 1)
2
c
12
(u
12
− u
11
+ ··· − 5u + 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
24
+ 9y
23
+ ··· + 1188y + 121
c
2
(y
12
− 10y
11
+ ··· − 16y + 1)
2
c
4
, c
10
121(11y
12
+ 178y
11
+ ··· + 9157y + 1787)
2
c
5
, c
11
121(121y
24
− 1045y
23
+ ··· − 6y + 1)
c
6
, c
9
y
24
+ 2y
23
+ ··· + 770y + 121
c
7
, c
8
, c
12
(y
12
− 15y
11
+ ··· − 35y + 1)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.226624 + 0.959178I
a = 0.508092 + 0.684855I
b = −1.72631 − 0.04641I
12.28740 + 0.00594I 8.38698 + 0.17944I
u = 0.226624 − 0.959178I
a = 0.508092 − 0.684855I
b = −1.72631 + 0.04641I
12.28740 − 0.00594I 8.38698 − 0.17944I
u = 0.922925 + 0.061385I
a = −0.174769 + 0.419362I
b = −0.275795 − 0.765914I
6.00889 + 5.09812I 7.06856 − 4.43197I
u = 0.922925 − 0.061385I
a = −0.174769 − 0.419362I
b = −0.275795 + 0.765914I
6.00889 − 5.09812I 7.06856 + 4.43197I
u = 0.126570 + 0.914912I
a = 0.511884 + 0.830363I
b = −1.72631 + 0.04641I
12.28740 − 0.00594I 8.38698 − 0.17944I
u = 0.126570 − 0.914912I
a = 0.511884 − 0.830363I
b = −1.72631 − 0.04641I
12.28740 + 0.00594I 8.38698 + 0.17944I
u = −0.212274 + 1.072130I
a = −0.172036 + 0.488889I
b = −0.851765 − 0.010312I
3.83086 + 5.34244I 7.49705 − 6.68257I
u = −0.212274 − 1.072130I
a = −0.172036 − 0.488889I
b = −0.851765 + 0.010312I
3.83086 − 5.34244I 7.49705 + 6.68257I
u = −0.505210 + 0.998540I
a = −0.602620 − 0.570906I
b = 0.178846
5.25401 7.03525 + 0.I
u = −0.505210 − 0.998540I
a = −0.602620 + 0.570906I
b = 0.178846
5.25401 7.03525 + 0.I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.446395 + 0.680430I
a = −0.27530 − 1.85841I
b = 0.973033 − 0.374713I
1.89515 − 1.45316I 12.20795 + 4.85996I
u = 0.446395 − 0.680430I
a = −0.27530 + 1.85841I
b = 0.973033 + 0.374713I
1.89515 + 1.45316I 12.20795 − 4.85996I
u = −0.640989 + 1.053800I
a = 0.006004 − 0.978688I
b = −0.275795 − 0.765914I
6.00889 + 5.09812I 7.06856 − 4.43197I
u = −0.640989 − 1.053800I
a = 0.006004 + 0.978688I
b = −0.275795 + 0.765914I
6.00889 − 5.09812I 7.06856 + 4.43197I
u = −1.19641 + 0.99995I
a = 0.480437 + 0.475873I
b = 1.43493
9.90643 12.16830 + 0.I
u = −1.19641 − 0.99995I
a = 0.480437 − 0.475873I
b = 1.43493
9.90643 12.16830 + 0.I
u = 0.246525 + 0.331360I
a = −1.04428 + 1.30839I
b = 0.973033 + 0.374713I
1.89515 + 1.45316I 12.20795 − 4.85996I
u = 0.246525 − 0.331360I
a = −1.04428 − 1.30839I
b = 0.973033 − 0.374713I
1.89515 − 1.45316I 12.20795 + 4.85996I
u = −0.77362 + 1.45062I
a = −0.204555 + 1.028440I
b = 1.57394 + 0.14834I
12.8107 + 7.9962I 3.73769 − 2.20153I
u = −0.77362 − 1.45062I
a = −0.204555 − 1.028440I
b = 1.57394 − 0.14834I
12.8107 − 7.9962I 3.73769 + 2.20153I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.75685 + 1.46605I
a = 0.100105 − 0.674178I
b = −0.851765 − 0.010312I
3.83086 + 5.34244I 7.49705 − 6.68257I
u = −0.75685 − 1.46605I
a = 0.100105 + 0.674178I
b = −0.851765 + 0.010312I
3.83086 − 5.34244I 7.49705 + 6.68257I
u = 1.61631 + 0.87256I
a = 0.139769 − 0.348919I
b = 1.57394 + 0.14834I
12.8107 + 7.9962I 3.73769 − 2.20153I
u = 1.61631 − 0.87256I
a = 0.139769 + 0.348919I
b = 1.57394 − 0.14834I
12.8107 − 7.9962I 3.73769 + 2.20153I
26
IV. I
u
4
= h−u
2
+ b + u − 1, u
3
− u
2
+ a + 2u, u
5
− u
4
+ 3u
3
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
9
=
−u
3
+ u
2
− 2u
u
2
− u + 1
a
6
=
−1
−u
2
+ u − 1
a
3
=
u
u
3
− u
2
+ 2u − 1
a
10
=
0
−u
3
+ u
2
− 2u
a
4
=
0
u
a
8
=
−u
3
− u − 1
u
2
− u + 1
a
12
=
u
3
+ u + 1
u
4
− 2u
3
+ 3u
2
− 2u + 1
a
7
=
−1
−u
4
+ u
3
− 4u
2
+ u − 2
a
11
=
0
−u
3
+ u
2
− 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
4
− 10u
3
+ 20u
2
− 4u + 9
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
5
− u
4
+ 3u
3
+ u + 1
c
2
u
5
+ 4u
4
+ 9u
3
+ 13u
2
+ 11u + 5
c
4
, c
10
u
5
c
5
, c
11
u
5
− u
4
+ u
3
+ u − 1
c
6
, c
9
u
5
+ u
4
+ u
2
+ u + 1
c
7
, c
8
u
5
− u
4
− 3u
3
+ 3u
2
+ 1
c
12
u
5
+ u
4
− 3u
3
− 3u
2
− 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
5
+ 5y
4
+ 11y
3
+ 8y
2
+ y −1
c
2
y
5
+ 2y
4
− y
3
− 11y
2
− 9y −25
c
4
, c
10
y
5
c
5
, c
11
y
5
+ y
4
+ 3y
3
+ y −1
c
6
, c
9
y
5
− y
4
− 3y
2
− y −1
c
7
, c
8
, c
12
y
5
− 7y
4
+ 15y
3
− 7y
2
− 6y −1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.210516 + 0.857202I
a = −0.656781 − 0.837593I
b = 0.099006 − 0.496292I
0.38751 − 3.74061I 0.97469 + 5.95799I
u = 0.210516 − 0.857202I
a = −0.656781 + 0.837593I
b = 0.099006 + 0.496292I
0.38751 + 3.74061I 0.97469 − 5.95799I
u = −0.507589
a = 1.40360
b = 1.76524
6.95916 17.8890
u = 0.54328 + 1.49449I
a = 0.454980 + 0.649504I
b = −1.48162 + 0.12936I
6.00251 − 5.77307I 9.58063 + 8.87442I
u = 0.54328 − 1.49449I
a = 0.454980 − 0.649504I
b = −1.48162 − 0.12936I
6.00251 + 5.77307I 9.58063 − 8.87442I
30
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
5
− u
4
+ 3u
3
+ u + 1)(u
24
+ u
23
+ ··· − 44u + 11)
· (u
36
− 3u
35
+ ··· − 31u + 11)(u
84
+ 6u
83
+ ··· − 75402u + 16109)
c
2
(u
5
+ 4u
4
+ 9u
3
+ 13u
2
+ 11u + 5)(u
12
− 6u
11
+ ··· − 8u
2
+ 1)
2
· (u
36
− 7u
35
+ ··· − 12071u + 1268)
· (u
42
+ 7u
41
+ ··· + 3649u + 1139)
2
c
4
, c
10
121u
5
(11u
24
+ 178u
22
+ ··· + 9157u
2
+ 1787)
· (11u
36
− 27u
35
+ ··· − 224u + 64)(u
42
+ u
41
+ ··· − 42u + 11)
2
c
5
, c
11
121(u
5
− u
4
+ u
3
+ u − 1)(11u
24
− 11u
23
+ ··· − 6u + 1)
· (11u
36
− 5u
35
+ ··· + 11u + 1)(u
84
− 21u
82
+ ··· − 44416u + 6119)
c
6
, c
9
(u
5
+ u
4
+ u
2
+ u + 1)(u
24
− 2u
23
+ ··· + 35u
2
+ 11)
· (u
36
+ u
35
+ ··· + 17u + 11)(u
84
− u
83
+ ··· − 2672u + 2143)
c
7
, c
8
(u
5
− u
4
− 3u
3
+ 3u
2
+ 1)(u
12
+ u
11
+ ··· + 5u + 1)
2
· (u
36
+ 4u
35
+ ··· − 71u + 28)(u
42
− 2u
41
+ ··· + 22u + 19)
2
c
12
(u
5
+ u
4
− 3u
3
− 3u
2
− 1)(u
12
− u
11
+ ··· − 5u + 1)
2
· (u
36
+ 4u
35
+ ··· − 71u + 28)(u
42
− 2u
41
+ ··· + 22u + 19)
2
31
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y
5
+ 5y
4
+ 11y
3
+ 8y
2
+ y −1)(y
24
+ 9y
23
+ ··· + 1188y + 121)
· (y
36
+ 17y
35
+ ··· + 1525y + 121)
· (y
84
+ 32y
83
+ ··· + 5914049372y + 259499881)
c
2
(y
5
+ 2y
4
− y
3
− 11y
2
− 9y −25)(y
12
− 10y
11
+ ··· − 16y + 1)
2
· (y
36
− 5y
35
+ ··· − 32055665y + 1607824)
· (y
42
− 41y
41
+ ··· + 6170811y + 1297321)
2
c
4
, c
10
14641y
5
(11y
12
+ 178y
11
+ ··· + 9157y + 1787)
2
· (121y
36
+ 4177y
35
+ ··· − 52224y + 4096)
· (y
42
+ 39y
41
+ ··· − 5570y + 121)
2
c
5
, c
11
14641(y
5
+ y
4
+ 3y
3
+ y −1)(121y
24
− 1045y
23
+ ··· − 6y + 1)
· (121y
36
− 179y
35
+ ··· − 15y + 1)
· (y
84
− 42y
83
+ ··· − 2518510190y + 37442161)
c
6
, c
9
(y
5
− y
4
− 3y
2
− y −1)(y
24
+ 2y
23
+ ··· + 770y + 121)
· (y
36
− 9y
35
+ ··· − 993y + 121)
· (y
84
+ 33y
83
+ ··· + 197735502y + 4592449)
c
7
, c
8
, c
12
(y
5
− 7y
4
+ 15y
3
− 7y
2
− 6y −1)(y
12
− 15y
11
+ ··· − 35y + 1)
2
· (y
36
− 42y
35
+ ··· − 10025y + 784)
· (y
42
− 50y
41
+ ··· − 7704y + 361)
2
32
