12n
0458
(K12n
0458
)
A knot diagram
1
Linearized knot diagam
3 6 11 10 2 1 4 3 7 8 9 7
Solving Sequence
3,11 4,9
12 8 7 1 6 2 5 10
c
3
c
11
c
8
c
7
c
12
c
6
c
2
c
5
c
10
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h5.47880 × 10
25
u
40
+ 7.88111 × 10
25
u
39
+ ··· + 1.50975 × 10
24
b + 6.96929 × 10
25
,
− 1.08127 × 10
26
u
40
− 1.53797 × 10
26
u
39
+ ··· + 1.50975 × 10
24
a − 1.21442 × 10
26
, u
41
+ u
40
+ ··· + 2u + 1i
I
u
2
= h−2.49556 × 10
86
u
43
− 8.35365 × 10
86
u
42
+ ··· + 3.43675 × 10
87
b + 3.73757 × 10
87
,
2.75946 × 10
87
u
43
+ 1.12653 × 10
88
u
42
+ ··· + 5.84247 × 10
88
a + 3.07830 × 10
89
, u
44
+ 4u
43
+ ··· + 77u + 17i
I
u
3
= h−u
18
+ u
17
+ ··· + b + 4u, −4u
18
+ 4u
17
+ ··· + a − 1, u
19
− u
18
+ ··· − 4u
2
+ 1i
I
u
4
= hb − u − 1, a − u − 1, u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 106 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
= h5.48×10
25
u
40
+7.88×10
25
u
39
+· · ·+1.51×10
24
b+6.97×10
25
, −1.08×
10
26
u
40
−1.54×10
26
u
39
+· · ·+1.51×10
24
a−1.21×10
26
, u
41
+u
40
+· · ·+2u+1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
9
=
71.6189u
40
+ 101.869u
39
+ ··· + 340.999u + 80.4384
−36.2894u
40
− 52.2014u
39
+ ··· − 199.232u − 46.1618
a
12
=
−64.2074u
40
− 87.5660u
39
+ ··· − 425.889u − 95.1075
−18.2487u
40
− 25.7511u
39
+ ··· − 53.4475u − 14.3937
a
8
=
107.908u
40
+ 154.070u
39
+ ··· + 540.231u + 126.600
−36.2894u
40
− 52.2014u
39
+ ··· − 199.232u − 46.1618
a
7
=
107.908u
40
+ 154.070u
39
+ ··· + 541.231u + 126.600
−36.2894u
40
− 52.2014u
39
+ ··· − 199.232u − 46.1618
a
1
=
−197.492u
40
− 281.182u
39
+ ··· − 1214.12u − 264.909
−0.0153376u
40
− 1.23868u
39
+ ··· + 111.193u + 23.1345
a
6
=
74.2253u
40
+ 243.405u
39
+ ··· + 1398.14u + 562.092
39.9044u
40
+ 24.6029u
39
+ ··· − 18.7145u − 94.6713
a
2
=
−197.477u
40
− 279.943u
39
+ ··· − 1325.31u − 288.043
−0.0153376u
40
− 1.23868u
39
+ ··· + 111.193u + 23.1345
a
5
=
−64.8577u
40
− 25.7158u
39
+ ··· + 90.6679u + 163.055
−22.8032u
40
− 1.56551u
39
+ ··· + 55.9091u + 43.7009
a
10
=
0.594704u
40
+ 4.62146u
39
+ ··· − 162.562u − 30.5253
−46.5535u
40
− 66.4364u
39
+ ··· − 207.880u − 50.1886
(ii) Obstruction class = −1
(iii) Cusp Shapes =
46609776655609602573804741
1509752124425304287631895
u
40
−
555844712353330908256438968
1509752124425304287631895
u
39
+
··· −
4270771601823530319752574608
1509752124425304287631895
u −
2076142798565092784971764701
1509752124425304287631895
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
41
+ 19u
40
+ ··· + 89u + 16
c
2
, c
5
u
41
+ 5u
40
+ ··· + 7u + 4
c
3
, c
7
u
41
+ u
40
+ ··· + 2u + 1
c
4
, c
8
u
41
− 9u
39
+ ··· − 69u + 17
c
6
, c
12
u
41
+ 15u
40
+ ··· + 87u + 4
c
9
, c
11
u
41
− 4u
40
+ ··· + 27u + 1
c
10
u
41
− 26u
40
+ ··· + 23u − 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
41
+ 9y
40
+ ··· − 3311y −256
c
2
, c
5
y
41
− 19y
40
+ ··· + 89y −16
c
3
, c
7
y
41
+ 17y
40
+ ··· − 36y −1
c
4
, c
8
y
41
− 18y
40
+ ··· + 5577y −289
c
6
, c
12
y
41
+ y
40
+ ··· + 633y −16
c
9
, c
11
y
41
− 58y
40
+ ··· + 333y −1
c
10
y
41
+ 68y
39
+ ··· + 81y −4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.347021 + 1.021800I
a = 0.446471 + 0.717252I
b = 0.856068 + 0.901582I
2.01077 + 1.97128I 0
u = 0.347021 − 1.021800I
a = 0.446471 − 0.717252I
b = 0.856068 − 0.901582I
2.01077 − 1.97128I 0
u = −0.517326 + 0.952123I
a = −0.494773 + 0.392816I
b = −1.002680 + 0.556094I
2.33608 + 2.70211I 0
u = −0.517326 − 0.952123I
a = −0.494773 − 0.392816I
b = −1.002680 − 0.556094I
2.33608 − 2.70211I 0
u = −0.380066 + 0.811067I
a = 0.82614 + 1.79073I
b = 0.853726 − 0.187521I
4.94484 − 5.32421I 4.21074 + 0.90918I
u = −0.380066 − 0.811067I
a = 0.82614 − 1.79073I
b = 0.853726 + 0.187521I
4.94484 + 5.32421I 4.21074 − 0.90918I
u = 0.054668 + 1.145580I
a = 0.106091 + 1.208380I
b = 0.17829 + 1.44060I
1.57207 − 1.96637I 0
u = 0.054668 − 1.145580I
a = 0.106091 − 1.208380I
b = 0.17829 − 1.44060I
1.57207 + 1.96637I 0
u = 0.358415 + 0.770361I
a = −0.68843 + 2.01808I
b = −0.906548 − 0.088949I
6.85307 + 0.06384I 7.45973 + 4.03926I
u = 0.358415 − 0.770361I
a = −0.68843 − 2.01808I
b = −0.906548 + 0.088949I
6.85307 − 0.06384I 7.45973 − 4.03926I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.045169 + 0.822753I
a = −0.154528 + 1.094100I
b = 0.346455 + 0.374027I
1.46454 + 1.46331I 5.06919 − 4.70044I
u = −0.045169 − 0.822753I
a = −0.154528 − 1.094100I
b = 0.346455 − 0.374027I
1.46454 − 1.46331I 5.06919 + 4.70044I
u = −0.229168 + 0.751258I
a = −0.04740 + 1.82480I
b = 0.739876 + 0.180844I
1.64581 + 1.65716I 2.62674 − 4.29220I
u = −0.229168 − 0.751258I
a = −0.04740 − 1.82480I
b = 0.739876 − 0.180844I
1.64581 − 1.65716I 2.62674 + 4.29220I
u = 0.325313 + 0.680386I
a = −0.29563 + 2.60667I
b = −1.039970 + 0.122963I
7.08787 − 2.96529I 8.51449 + 5.47804I
u = 0.325313 − 0.680386I
a = −0.29563 − 2.60667I
b = −1.039970 − 0.122963I
7.08787 + 2.96529I 8.51449 − 5.47804I
u = −0.314460 + 0.648327I
a = 0.08581 + 2.85549I
b = 1.088460 + 0.205257I
5.38587 + 8.24752I 6.33209 − 10.48383I
u = −0.314460 − 0.648327I
a = 0.08581 − 2.85549I
b = 1.088460 − 0.205257I
5.38587 − 8.24752I 6.33209 + 10.48383I
u = 1.054420 + 0.767365I
a = 0.225727 − 0.075550I
b = 0.757531 − 0.087155I
−5.03812 + 0.55979I 0
u = 1.054420 − 0.767365I
a = 0.225727 + 0.075550I
b = 0.757531 + 0.087155I
−5.03812 − 0.55979I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.954640 + 0.895605I
a = −0.323203 − 0.114281I
b = −0.907475 − 0.104542I
−1.12434 + 3.55718I 0
u = −0.954640 − 0.895605I
a = −0.323203 + 0.114281I
b = −0.907475 + 0.104542I
−1.12434 − 3.55718I 0
u = −0.652653
a = −0.0877425
b = −0.483905
−1.46612 −7.06880
u = −0.001515 + 0.601854I
a = −0.852039 + 0.542047I
b = 0.481262 + 0.639634I
0.81408 + 1.37351I 2.99559 − 3.76838I
u = −0.001515 − 0.601854I
a = −0.852039 − 0.542047I
b = 0.481262 − 0.639634I
0.81408 − 1.37351I 2.99559 + 3.76838I
u = 1.03621 + 0.97465I
a = 0.272897 − 0.206391I
b = 0.879946 − 0.246548I
−4.42034 − 8.30464I 0
u = 1.03621 − 0.97465I
a = 0.272897 + 0.206391I
b = 0.879946 + 0.246548I
−4.42034 + 8.30464I 0
u = 0.051342 + 0.543114I
a = 1.57833 + 0.32834I
b = −0.542371 + 0.798966I
−1.14789 − 5.43637I −0.71682 + 6.54388I
u = 0.051342 − 0.543114I
a = 1.57833 − 0.32834I
b = −0.542371 − 0.798966I
−1.14789 + 5.43637I −0.71682 − 6.54388I
u = −0.005268 + 0.490051I
a = 0.720841 − 0.530154I
b = −0.243798 + 0.805884I
−2.19779 + 1.00862I −5.99392 − 1.40222I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.005268 − 0.490051I
a = 0.720841 + 0.530154I
b = −0.243798 − 0.805884I
−2.19779 − 1.00862I −5.99392 + 1.40222I
u = −0.92388 + 1.21329I
a = −0.693432 − 0.848976I
b = −1.60443 − 0.79675I
7.22406 + 2.19782I 0
u = −0.92388 − 1.21329I
a = −0.693432 + 0.848976I
b = −1.60443 + 0.79675I
7.22406 − 2.19782I 0
u = 0.93985 + 1.21945I
a = 0.624751 − 0.961319I
b = 1.57161 − 0.93510I
8.66754 − 7.90114I 0
u = 0.93985 − 1.21945I
a = 0.624751 + 0.961319I
b = 1.57161 + 0.93510I
8.66754 + 7.90114I 0
u = −0.96302 + 1.20795I
a = −0.367468 − 0.971278I
b = −1.31719 − 1.03611I
1.99155 + 9.34995I 0
u = −0.96302 − 1.20795I
a = −0.367468 + 0.971278I
b = −1.31719 + 1.03611I
1.99155 − 9.34995I 0
u = 0.96655 + 1.22224I
a = 0.421833 − 1.155040I
b = 1.43574 − 1.19661I
7.8645 − 11.8540I 0
u = 0.96655 − 1.22224I
a = 0.421833 + 1.155040I
b = 1.43574 + 1.19661I
7.8645 + 11.8540I 0
u = −0.97295 + 1.22134I
a = −0.348119 − 1.207570I
b = −1.38255 − 1.27245I
5.7918 + 17.4569I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.97295 − 1.22134I
a = −0.348119 + 1.207570I
b = −1.38255 + 1.27245I
5.7918 − 17.4569I 0
9
II. I
u
2
= h−2.50 × 10
86
u
43
− 8.35 × 10
86
u
42
+ · · · + 3.44 × 10
87
b + 3.74 ×
10
87
, 2.76 × 10
87
u
43
+ 1.13 × 10
88
u
42
+ · · · + 5.84 × 10
88
a + 3.08 ×
10
89
, u
44
+ 4u
43
+ · · · + 77u + 17i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
9
=
−0.0472311u
43
− 0.192817u
42
+ ··· − 14.3118u − 5.26884
0.0726141u
43
+ 0.243068u
42
+ ··· − 1.78608u − 1.08753
a
12
=
−0.0360992u
43
− 0.157605u
42
+ ··· − 15.0581u − 5.83261
0.0702088u
43
+ 0.234463u
42
+ ··· − 1.55171u − 1.42798
a
8
=
−0.119845u
43
− 0.435885u
42
+ ··· − 12.5257u − 4.18131
0.0726141u
43
+ 0.243068u
42
+ ··· − 1.78608u − 1.08753
a
7
=
−0.0588235u
43
− 0.235294u
42
+ ··· − 13u − 4.52941
0.0610217u
43
+ 0.200591u
42
+ ··· + 0.525708u − 0.348105
a
1
=
−0.101101u
43
− 0.408588u
42
+ ··· − 18.6194u − 7.52962
0.00441605u
43
− 0.0127382u
42
+ ··· − 3.21768u − 1.61521
a
6
=
−0.0490639u
43
− 0.254746u
42
+ ··· − 9.79483u − 5.26468
0.0362894u
43
+ 0.127630u
42
+ ··· − 0.376828u − 1.15074
a
2
=
−0.105517u
43
− 0.395849u
42
+ ··· − 15.4017u − 5.91441
0.00441605u
43
− 0.0127382u
42
+ ··· − 3.21768u − 1.61521
a
5
=
0.142243u
43
+ 0.513366u
42
+ ··· + 14.5329u + 3.09094
−0.00902369u
43
− 0.0430917u
42
+ ··· − 3.30811u − 1.10503
a
10
=
−0.0606353u
43
− 0.229405u
42
+ ··· − 7.19891u − 3.39724
−0.0456727u
43
− 0.162664u
42
+ ··· − 4.30750u − 1.00739
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.861289u
43
− 3.44599u
42
+ ··· − 97.7115u − 26.0425
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
22
+ 10u
21
+ ··· + 6u
2
+ 1)
2
c
2
, c
5
(u
22
− 2u
21
+ ··· − 5u
3
+ 1)
2
c
3
, c
7
u
44
+ 4u
43
+ ··· + 77u + 17
c
4
, c
8
u
44
+ 2u
43
+ ··· − 7681u + 1663
c
6
, c
12
(u
22
− 9u
21
+ ··· − 27u + 8)
2
c
9
, c
11
u
44
− 3u
43
+ ··· − 5634u + 459
c
10
(u
22
+ 9u
21
+ ··· + u + 2)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
22
+ 6y
21
+ ··· + 12y + 1)
2
c
2
, c
5
(y
22
− 10y
21
+ ··· + 6y
2
+ 1)
2
c
3
, c
7
y
44
− 8y
43
+ ··· + 1585y + 289
c
4
, c
8
y
44
− 20y
43
+ ··· + 60881257y + 2765569
c
6
, c
12
(y
22
− 5y
21
+ ··· − 137y + 64)
2
c
9
, c
11
y
44
− 23y
43
+ ··· + 46259586y + 210681
c
10
(y
22
+ 3y
21
+ ··· + 43y + 4)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.466106 + 0.845310I
a = 0.120142 + 0.417834I
b = 1.67800 + 0.61371I
−0.49172 + 7.76222I 0.81633 − 10.97056I
u = −0.466106 − 0.845310I
a = 0.120142 − 0.417834I
b = 1.67800 − 0.61371I
−0.49172 − 7.76222I 0.81633 + 10.97056I
u = −0.612747 + 0.847167I
a = −0.309849 + 0.822684I
b = 1.14999 + 1.06245I
−2.01009 + 2.56491I −5.72976 − 4.00419I
u = −0.612747 − 0.847167I
a = −0.309849 − 0.822684I
b = 1.14999 − 1.06245I
−2.01009 − 2.56491I −5.72976 + 4.00419I
u = 0.899310 + 0.535213I
a = 1.22496 + 1.07887I
b = −0.208918 + 0.720383I
−2.01009 − 2.56491I −5.72976 + 4.00419I
u = 0.899310 − 0.535213I
a = 1.22496 − 1.07887I
b = −0.208918 − 0.720383I
−2.01009 + 2.56491I −5.72976 − 4.00419I
u = 0.667133 + 0.876190I
a = 0.565670 + 0.915397I
b = −0.73275 + 1.28707I
−2.61181 − 5.56778I −6.67774 + 6.14625I
u = 0.667133 − 0.876190I
a = 0.565670 − 0.915397I
b = −0.73275 − 1.28707I
−2.61181 + 5.56778I −6.67774 − 6.14625I
u = 0.420458 + 0.759517I
a = 0.0506571 + 0.0690852I
b = −1.51754 + 0.25724I
0.63374 − 3.32247I 4.93738 + 4.78079I
u = 0.420458 − 0.759517I
a = 0.0506571 − 0.0690852I
b = −1.51754 − 0.25724I
0.63374 + 3.32247I 4.93738 − 4.78079I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.592653 + 0.967467I
a = 0.548691 + 0.593530I
b = −0.351079 + 1.129330I
−2.49866 + 0.61650I −5.58678 − 1.76375I
u = 0.592653 − 0.967467I
a = 0.548691 − 0.593530I
b = −0.351079 − 1.129330I
−2.49866 − 0.61650I −5.58678 + 1.76375I
u = −0.510707 + 0.679843I
a = −0.82932 − 1.56718I
b = −1.70942 − 1.64533I
4.38951 + 8.87036I 2.10374 − 11.14588I
u = −0.510707 − 0.679843I
a = −0.82932 + 1.56718I
b = −1.70942 + 1.64533I
4.38951 − 8.87036I 2.10374 + 11.14588I
u = −0.748334 + 0.350797I
a = −1.67537 + 0.57034I
b = 0.087323 + 0.207716I
−2.61181 + 5.56778I −6.67774 − 6.14625I
u = −0.748334 − 0.350797I
a = −1.67537 − 0.57034I
b = 0.087323 − 0.207716I
−2.61181 − 5.56778I −6.67774 + 6.14625I
u = 0.438421 + 0.674226I
a = 0.90058 − 1.59216I
b = 1.81717 − 1.62217I
6.45761 − 3.23482I 6.36482 + 6.95069I
u = 0.438421 − 0.674226I
a = 0.90058 + 1.59216I
b = 1.81717 + 1.62217I
6.45761 + 3.23482I 6.36482 − 6.95069I
u = −0.784806 + 0.951389I
a = −0.431263 + 0.864629I
b = 0.541102 + 0.996237I
−0.29493 + 2.91734I 2.41857 − 2.23849I
u = −0.784806 − 0.951389I
a = −0.431263 − 0.864629I
b = 0.541102 − 0.996237I
−0.29493 − 2.91734I 2.41857 + 2.23849I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.149975 + 0.738011I
a = −0.89919 − 1.49365I
b = −2.06203 − 1.36914I
5.86334 − 6.33920I 7.62789 + 3.75640I
u = −0.149975 − 0.738011I
a = −0.89919 + 1.49365I
b = −2.06203 + 1.36914I
5.86334 + 6.33920I 7.62789 − 3.75640I
u = 0.229621 + 0.711467I
a = 0.93052 − 1.58410I
b = 2.01034 − 1.49221I
7.29150 + 0.70655I 9.80660 + 2.74214I
u = 0.229621 − 0.711467I
a = 0.93052 + 1.58410I
b = 2.01034 + 1.49221I
7.29150 − 0.70655I 9.80660 − 2.74214I
u = 1.057640 + 0.711303I
a = 0.72238 + 1.49263I
b = −0.394766 + 1.085170I
−0.49172 − 7.76222I 0. + 10.97056I
u = 1.057640 − 0.711303I
a = 0.72238 − 1.49263I
b = −0.394766 − 1.085170I
−0.49172 + 7.76222I 0. − 10.97056I
u = −1.010300 + 0.819633I
a = −0.496055 + 1.296710I
b = 0.521329 + 1.021470I
0.63374 + 3.32247I 4.93738 − 4.78079I
u = −1.010300 − 0.819633I
a = −0.496055 − 1.296710I
b = 0.521329 − 1.021470I
0.63374 − 3.32247I 4.93738 + 4.78079I
u = 0.456405 + 0.493869I
a = 1.008840 − 0.278321I
b = −0.785235 − 0.137592I
−0.29493 − 2.91734I 2.41857 + 2.23849I
u = 0.456405 − 0.493869I
a = 1.008840 + 0.278321I
b = −0.785235 + 0.137592I
−0.29493 + 2.91734I 2.41857 − 2.23849I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.352482 + 0.507121I
a = −1.07753 − 1.61193I
b = −1.91155 − 1.49298I
0.543309 + 0.646462I 7.41895 − 11.49115I
u = −0.352482 − 0.507121I
a = −1.07753 + 1.61193I
b = −1.91155 + 1.49298I
0.543309 − 0.646462I 7.41895 + 11.49115I
u = −0.439360 + 0.215788I
a = −2.17643 − 0.43074I
b = 0.249933 − 0.497594I
−2.49866 − 0.61650I −5.58678 + 1.76375I
u = −0.439360 − 0.215788I
a = −2.17643 + 0.43074I
b = 0.249933 + 0.497594I
−2.49866 + 0.61650I −5.58678 − 1.76375I
u = −1.42727 + 1.17674I
a = 0.732491 + 0.810544I
b = 0.999624 + 0.416425I
5.86334 + 6.33920I 0
u = −1.42727 − 1.17674I
a = 0.732491 − 0.810544I
b = 0.999624 − 0.416425I
5.86334 − 6.33920I 0
u = −1.58647 + 1.01845I
a = 0.919715 + 0.087483I
b = 0.855383 − 0.305806I
4.38951 − 8.87036I 0
u = −1.58647 − 1.01845I
a = 0.919715 − 0.087483I
b = 0.855383 + 0.305806I
4.38951 + 8.87036I 0
u = 1.49066 + 1.18106I
a = −0.792313 + 0.634501I
b = −0.974820 + 0.249567I
7.29150 − 0.70655I 0
u = 1.49066 − 1.18106I
a = −0.792313 − 0.634501I
b = −0.974820 − 0.249567I
7.29150 + 0.70655I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59443 + 1.07242I
a = −0.889783 + 0.221269I
b = −0.883190 − 0.162509I
6.45761 + 3.23482I 0
u = 1.59443 − 1.07242I
a = −0.889783 − 0.221269I
b = −0.883190 + 0.162509I
6.45761 − 3.23482I 0
u = −1.75816 + 1.21062I
a = 0.587756 + 0.268789I
b = 0.621112 + 0.027345I
0.543309 − 0.646462I 0
u = −1.75816 − 1.21062I
a = 0.587756 − 0.268789I
b = 0.621112 − 0.027345I
0.543309 + 0.646462I 0
17
III.
I
u
3
= h−u
18
+u
17
+· · ·+b+4u, −4u
18
+4u
17
+· · ·+a−1, u
19
−u
18
+· · ·−4u
2
+1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
9
=
4u
18
− 4u
17
+ ··· − 8u + 1
u
18
− u
17
+ ··· + u
2
− 4u
a
12
=
−8u
18
+ 9u
17
+ ··· + 14u − 4
−4u
18
+ 4u
17
+ ··· + 9u − 1
a
8
=
3u
18
− 3u
17
+ ··· − 4u + 1
u
18
− u
17
+ ··· + u
2
− 4u
a
7
=
3u
18
− 3u
17
+ ··· − 5u + 1
u
18
− u
17
+ ··· + u
2
− 4u
a
1
=
−u
18
+ 2u
16
+ ··· + 5u
2
− 2
2u
18
− 3u
17
+ ··· − 3u + 2
a
6
=
−4u
18
+ 5u
17
+ ··· − 6u
2
+ 8u
3u
18
− 3u
17
+ ··· + 9u
3
− 3u
a
2
=
−3u
18
+ 3u
17
+ ··· + 3u − 4
2u
18
− 3u
17
+ ··· − 3u + 2
a
5
=
−2u
18
+ 3u
17
+ ··· − 3u
3
− 1
−u
18
+ 4u
17
+ ··· + 3u − 5
a
10
=
−u
18
+ 2u
17
+ ··· + 2u − 2
−3u
18
+ 3u
17
+ ··· + 5u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7u
18
+ 12u
17
+ u
16
− 22u
15
− 16u
14
+ 59u
13
− 18u
12
− 76u
11
+
20u
10
+ 87u
9
− 54u
8
− 93u
7
+ 68u
6
+ 56u
5
− 50u
4
− 29u
3
+ 45u
2
+ 11u − 15
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
− 10u
18
+ ··· + 4u − 1
c
2
u
19
+ 2u
18
+ ··· − 2u − 1
c
3
, c
7
u
19
− u
18
+ ··· − 4u
2
+ 1
c
4
, c
8
u
19
− 4u
17
+ ··· − u + 1
c
5
u
19
− 2u
18
+ ··· − 2u + 1
c
6
u
19
− 6u
18
+ ··· + 14u − 3
c
9
, c
11
u
19
− 8u
18
+ ··· + 5u − 1
c
10
u
19
+ 11u
18
+ ··· + u − 3
c
12
u
19
+ 6u
18
+ ··· + 14u + 3
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
+ 2y
18
+ ··· + 74y
3
− 1
c
2
, c
5
y
19
− 10y
18
+ ··· + 4y −1
c
3
, c
7
y
19
− 5y
18
+ ··· + 8y −1
c
4
, c
8
y
19
− 8y
18
+ ··· + 5y −1
c
6
, c
12
y
19
+ 6y
18
+ ··· + 88y −9
c
9
, c
11
y
19
− 16y
17
+ ··· − 19y −1
c
10
y
19
− 3y
18
+ ··· + 217y −9
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.571670 + 0.772339I
a = 1.062330 + 0.376696I
b = −0.619150 + 0.836486I
−1.93329 − 0.79135I −1.90450 + 1.96423I
u = 0.571670 − 0.772339I
a = 1.062330 − 0.376696I
b = −0.619150 − 0.836486I
−1.93329 + 0.79135I −1.90450 − 1.96423I
u = −0.691700 + 0.817412I
a = −0.700220 + 0.415999I
b = 0.603256 + 0.712894I
−0.67906 + 4.36107I 0.50991 − 7.74806I
u = −0.691700 − 0.817412I
a = −0.700220 − 0.415999I
b = 0.603256 − 0.712894I
−0.67906 − 4.36107I 0.50991 + 7.74806I
u = −0.694686 + 0.594925I
a = −0.687377 + 1.111670I
b = 0.830443 + 0.711186I
−0.66120 + 2.86463I −0.58084 − 3.68051I
u = −0.694686 − 0.594925I
a = −0.687377 − 1.111670I
b = 0.830443 − 0.711186I
−0.66120 − 2.86463I −0.58084 + 3.68051I
u = −0.901419
a = 1.36528
b = 1.10936
0.308220 −0.909270
u = 0.590402 + 0.625214I
a = 1.20330 + 1.01252I
b = −0.798416 + 0.845493I
−1.76829 − 6.62156I −2.87860 + 10.87292I
u = 0.590402 − 0.625214I
a = 1.20330 − 1.01252I
b = −0.798416 − 0.845493I
−1.76829 + 6.62156I −2.87860 − 10.87292I
u = 0.769919 + 0.066620I
a = −2.09450 + 0.55481I
b = −1.289190 + 0.111552I
6.31789 − 1.80381I 3.64499 + 0.37370I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.769919 − 0.066620I
a = −2.09450 − 0.55481I
b = −1.289190 − 0.111552I
6.31789 + 1.80381I 3.64499 − 0.37370I
u = −0.756714 + 0.118401I
a = 1.98867 + 0.99926I
b = 1.289920 + 0.201830I
4.58239 + 7.30195I 0.96040 − 5.11591I
u = −0.756714 − 0.118401I
a = 1.98867 − 0.99926I
b = 1.289920 − 0.201830I
4.58239 − 7.30195I 0.96040 + 5.11591I
u = −0.966965 + 0.774347I
a = −0.231110 + 0.472518I
b = 0.630095 + 0.504581I
−2.00054 + 3.89777I −3.98253 − 5.34580I
u = −0.966965 − 0.774347I
a = −0.231110 − 0.472518I
b = 0.630095 − 0.504581I
−2.00054 − 3.89777I −3.98253 + 5.34580I
u = 1.100580 + 0.706359I
a = 0.062826 + 0.442679I
b = −0.643531 + 0.413021I
−5.47313 + 0.16274I −9.10286 + 4.27042I
u = 1.100580 − 0.706359I
a = 0.062826 − 0.442679I
b = −0.643531 − 0.413021I
−5.47313 − 0.16274I −9.10286 − 4.27042I
u = 1.028200 + 0.886045I
a = 0.213453 + 0.338188I
b = −0.558115 + 0.480952I
−5.11861 − 8.27352I −8.71133 + 6.81608I
u = 1.028200 − 0.886045I
a = 0.213453 − 0.338188I
b = −0.558115 − 0.480952I
−5.11861 + 8.27352I −8.71133 − 6.81608I
22
IV. I
u
4
= hb − u − 1, a − u − 1, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u − 1
a
9
=
u + 1
u + 1
a
12
=
−u − 1
−1
a
8
=
0
u + 1
a
7
=
u + 1
1
a
1
=
−u − 1
−1
a
6
=
u + 1
1
a
2
=
−u
−1
a
5
=
1
0
a
10
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
9
c
11
(u − 1)
2
c
3
, c
4
, c
7
c
8
u
2
+ u + 1
c
5
(u + 1)
2
c
6
, c
10
, c
12
u
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
9
, c
11
(y −1)
2
c
3
, c
4
, c
7
c
8
y
2
+ y + 1
c
6
, c
10
, c
12
y
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = 0.500000 + 0.866025I
0 −3.00000
u = −0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = 0.500000 − 0.866025I
0 −3.00000
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
19
− 10u
18
+ ··· + 4u − 1)(u
22
+ 10u
21
+ ··· + 6u
2
+ 1)
2
· (u
41
+ 19u
40
+ ··· + 89u + 16)
c
2
((u − 1)
2
)(u
19
+ 2u
18
+ ··· − 2u − 1)(u
22
− 2u
21
+ ··· − 5u
3
+ 1)
2
· (u
41
+ 5u
40
+ ··· + 7u + 4)
c
3
, c
7
(u
2
+ u + 1)(u
19
− u
18
+ ··· − 4u
2
+ 1)(u
41
+ u
40
+ ··· + 2u + 1)
· (u
44
+ 4u
43
+ ··· + 77u + 17)
c
4
, c
8
(u
2
+ u + 1)(u
19
− 4u
17
+ ··· − u + 1)(u
41
− 9u
39
+ ··· − 69u + 17)
· (u
44
+ 2u
43
+ ··· − 7681u + 1663)
c
5
((u + 1)
2
)(u
19
− 2u
18
+ ··· − 2u + 1)(u
22
− 2u
21
+ ··· − 5u
3
+ 1)
2
· (u
41
+ 5u
40
+ ··· + 7u + 4)
c
6
u
2
(u
19
− 6u
18
+ ··· + 14u − 3)(u
22
− 9u
21
+ ··· − 27u + 8)
2
· (u
41
+ 15u
40
+ ··· + 87u + 4)
c
9
, c
11
((u − 1)
2
)(u
19
− 8u
18
+ ··· + 5u − 1)(u
41
− 4u
40
+ ··· + 27u + 1)
· (u
44
− 3u
43
+ ··· − 5634u + 459)
c
10
u
2
(u
19
+ 11u
18
+ ··· + u − 3)(u
22
+ 9u
21
+ ··· + u + 2)
2
· (u
41
− 26u
40
+ ··· + 23u − 2)
c
12
u
2
(u
19
+ 6u
18
+ ··· + 14u + 3)(u
22
− 9u
21
+ ··· − 27u + 8)
2
· (u
41
+ 15u
40
+ ··· + 87u + 4)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
2
)(y
19
+ 2y
18
+ ··· + 74y
3
− 1)(y
22
+ 6y
21
+ ··· + 12y + 1)
2
· (y
41
+ 9y
40
+ ··· − 3311y −256)
c
2
, c
5
((y −1)
2
)(y
19
− 10y
18
+ ··· + 4y −1)(y
22
− 10y
21
+ ··· + 6y
2
+ 1)
2
· (y
41
− 19y
40
+ ··· + 89y −16)
c
3
, c
7
(y
2
+ y + 1)(y
19
− 5y
18
+ ··· + 8y −1)(y
41
+ 17y
40
+ ··· − 36y −1)
· (y
44
− 8y
43
+ ··· + 1585y + 289)
c
4
, c
8
(y
2
+ y + 1)(y
19
− 8y
18
+ ··· + 5y −1)(y
41
− 18y
40
+ ··· + 5577y −289)
· (y
44
− 20y
43
+ ··· + 60881257y + 2765569)
c
6
, c
12
y
2
(y
19
+ 6y
18
+ ··· + 88y −9)(y
22
− 5y
21
+ ··· − 137y + 64)
2
· (y
41
+ y
40
+ ··· + 633y −16)
c
9
, c
11
((y −1)
2
)(y
19
− 16y
17
+ ··· − 19y −1)(y
41
− 58y
40
+ ··· + 333y −1)
· (y
44
− 23y
43
+ ··· + 46259586y + 210681)
c
10
y
2
(y
19
− 3y
18
+ ··· + 217y −9)(y
22
+ 3y
21
+ ··· + 43y + 4)
2
· (y
41
+ 68y
39
+ ··· + 81y −4)
28
