12n
0660
(K12n
0660
)
A knot diagram
1
Linearized knot diagam
3 7 10 12 9 11 2 6 3 5 7 4
Solving Sequence
6,11 2,7
3 8 9 12 1 5 4 10
c
6
c
2
c
7
c
8
c
11
c
1
c
5
c
4
c
10
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−11564599u
15
− 9251046u
14
+ ··· + 53220158b + 13391876,
− 43861146u
15
− 59898749u
14
+ ··· + 53220158a − 99727540,
u
16
+ u
15
+ u
14
+ 2u
13
+ 9u
12
+ 9u
11
+ 16u
10
+ 9u
9
+ 8u
8
+ 19u
7
− 33u
6
− 6u
5
+ 3u
4
− 33u
3
+ 4u
2
+ 3u − 1i
I
u
2
= h−1.75232 × 10
59
u
33
+ 3.07107 × 10
59
u
32
+ ··· + 1.28337 × 10
61
b + 1.83553 × 10
61
,
1.93452 × 10
60
u
33
− 1.32279 × 10
60
u
32
+ ··· + 1.28337 × 10
61
a − 1.86396 × 10
62
, u
34
− u
33
+ ··· − 180u − 3i
I
u
3
= h1.97277 × 10
16
u
25
+ 6.79934 × 10
15
u
24
+ ··· + 1.89124 × 10
16
b + 5.92285 × 10
16
,
6.86300 × 10
15
u
25
− 1.50215 × 10
16
u
24
+ ··· + 1.89124 × 10
16
a − 1.96975 × 10
16
, u
26
− 8u
24
+ ··· + 4u − 1i
I
u
4
= h−u
2
+ b − 1, a − u + 1, u
3
+ u + 1i
I
u
5
= hb − 1, a + 1, u − 1i
* 5 irreducible components of dim
C
= 0, with total 80 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
= h−1.16 × 10
7
u
15
− 9.25 × 10
6
u
14
+ · · · + 5.32 × 10
7
b + 1.34 × 10
7
, −4.39 ×
10
7
u
15
− 5.99× 10
7
u
14
+ · · · + 5.32 × 10
7
a −9.97 × 10
7
, u
16
+ u
15
+ · · · + 3u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
0.824145u
15
+ 1.12549u
14
+ ··· − 7.08904u + 1.87387
0.217297u
15
+ 0.173826u
14
+ ··· − 2.02601u − 0.251632
a
7
=
1
−u
2
a
3
=
1.07004u
15
+ 1.41983u
14
+ ··· − 9.19494u + 1.92358
0.105243u
15
+ 0.195897u
14
+ ··· − 2.12657u − 0.300078
a
8
=
1.10638u
15
+ 1.15362u
14
+ ··· − 1.22536u + 4.57509
0.295873u
15
+ 0.428955u
14
+ ··· − 1.45986u + 0.643823
a
9
=
1.40226u
15
+ 1.58258u
14
+ ··· − 2.68521u + 5.21891
0.295873u
15
+ 0.428955u
14
+ ··· − 1.45986u + 0.643823
a
12
=
u
−u
3
+ u
a
1
=
1.32715u
15
+ 1.46973u
14
+ ··· − 2.19396u + 5.38564
0.376362u
15
+ 0.378182u
14
+ ··· − 2.77171u + 0.956452
a
5
=
0.615985u
15
+ 1.01147u
14
+ ··· − 9.98396u − 0.124338
−0.166727u
15
− 0.0916225u
14
+ ··· − 1.31231u − 0.991434
a
4
=
0.749067u
15
+ 1.13559u
14
+ ··· − 10.2278u + 0.171535
−0.0503356u
15
+ 0.0874600u
14
+ ··· − 1.71606u − 0.686604
a
10
=
1.75205u
15
+ 2.07302u
14
+ ··· − 3.97175u + 6.28895
0.386527u
15
+ 0.542106u
14
+ ··· − 2.07567u + 0.749067
(ii) Obstruction class = −1
(iii) Cusp Shapes =
40466911
53220158
u
15
+
23371529
26610079
u
14
+ ··· −
846110475
53220158
u +
684608261
53220158
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
+ 15u
15
+ ··· − 732u + 16
c
2
, c
7
u
16
+ 5u
15
+ ··· − 30u + 4
c
3
, c
6
, c
9
c
11
u
16
− u
15
+ ··· − 3u − 1
c
4
, c
5
, c
8
c
12
u
16
+ 2u
15
+ ··· + 2u + 3
c
10
u
16
− 6u
15
+ ··· + 32u − 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 25y
15
+ ··· − 540400y + 256
c
2
, c
7
y
16
+ 15y
15
+ ··· − 732y + 16
c
3
, c
6
, c
9
c
11
y
16
+ y
15
+ ··· − 17y + 1
c
4
, c
5
, c
8
c
12
y
16
+ 22y
15
+ ··· − 130y + 9
c
10
y
16
+ 2y
15
+ ··· − 12288y + 1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.304353 + 0.972075I
a = 0.50278 − 1.51617I
b = −0.285550 − 0.101448I
−4.22498 + 1.58731I 9.57126 − 4.28514I
u = 0.304353 − 0.972075I
a = 0.50278 + 1.51617I
b = −0.285550 + 0.101448I
−4.22498 − 1.58731I 9.57126 + 4.28514I
u = 0.963344
a = −1.08170
b = 1.15231
4.93639 18.2520
u = −1.113490 + 0.020930I
a = −1.059080 − 0.259286I
b = 0.93667 + 1.24298I
3.10928 − 2.74603I 11.38606 + 5.54848I
u = −1.113490 − 0.020930I
a = −1.059080 + 0.259286I
b = 0.93667 − 1.24298I
3.10928 + 2.74603I 11.38606 − 5.54848I
u = 0.431687 + 1.044540I
a = 1.081630 − 0.710533I
b = 0.548841 − 0.957392I
−5.91455 + 0.25172I 1.47661 + 0.31305I
u = 0.431687 − 1.044540I
a = 1.081630 + 0.710533I
b = 0.548841 + 0.957392I
−5.91455 − 0.25172I 1.47661 − 0.31305I
u = −0.50668 + 1.37706I
a = −0.002750 − 0.610446I
b = −1.002360 − 0.102183I
−8.11817 − 5.61695I 5.09400 + 3.95642I
u = −0.50668 − 1.37706I
a = −0.002750 + 0.610446I
b = −1.002360 + 0.102183I
−8.11817 + 5.61695I 5.09400 − 3.95642I
u = −0.361628
a = 0.476897
b = 0.311919
0.559694 17.7300
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.243172 + 0.156892I
a = −0.78094 − 3.46394I
b = −0.825200 − 0.606999I
−3.15093 + 2.24302I 8.63814 − 3.97383I
u = 0.243172 − 0.156892I
a = −0.78094 + 3.46394I
b = −0.825200 + 0.606999I
−3.15093 − 2.24302I 8.63814 + 3.97383I
u = 1.27026 + 1.20475I
a = −0.782583 + 0.974911I
b = 2.42805 + 0.34147I
−16.2016 + 14.8675I 7.45320 − 6.24128I
u = 1.27026 − 1.20475I
a = −0.782583 − 0.974911I
b = 2.42805 − 0.34147I
−16.2016 − 14.8675I 7.45320 + 6.24128I
u = −1.43016 + 1.05558I
a = 0.843348 + 0.695582I
b = −2.53256 + 0.01545I
−15.1277 − 3.7434I 6.88958 + 1.90259I
u = −1.43016 − 1.05558I
a = 0.843348 − 0.695582I
b = −2.53256 − 0.01545I
−15.1277 + 3.7434I 6.88958 − 1.90259I
6
II. I
u
2
= h−1.75 × 10
59
u
33
+ 3.07 × 10
59
u
32
+ · · · + 1.28 × 10
61
b + 1.84 ×
10
61
, 1.93 × 10
60
u
33
− 1.32 × 10
60
u
32
+ · · · + 1.28 × 10
61
a − 1.86 ×
10
62
, u
34
− u
33
+ · · · − 180u − 3i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
−0.150738u
33
+ 0.103072u
32
+ ··· − 19.2920u + 14.5240
0.0136541u
33
− 0.0239298u
32
+ ··· + 7.15407u − 1.43025
a
7
=
1
−u
2
a
3
=
−0.127221u
33
+ 0.100766u
32
+ ··· − 21.1701u + 12.9508
0.0120176u
33
− 0.0123381u
32
+ ··· + 3.26564u − 1.49388
a
8
=
−0.125329u
33
+ 0.136598u
32
+ ··· − 33.1044u + 23.4044
0.0207171u
33
− 0.0109669u
32
+ ··· + 2.15308u − 2.35556
a
9
=
−0.104612u
33
+ 0.125631u
32
+ ··· − 30.9513u + 21.0489
0.0207171u
33
− 0.0109669u
32
+ ··· + 2.15308u − 2.35556
a
12
=
u
−u
3
+ u
a
1
=
−0.242112u
33
+ 0.244691u
32
+ ··· − 63.7284u + 45.5880
0.0310457u
33
− 0.0424811u
32
+ ··· + 11.6632u − 5.05191
a
5
=
0.275594u
33
− 0.305067u
32
+ ··· + 77.7390u − 49.3650
−0.0182410u
33
+ 0.0204396u
32
+ ··· − 5.00749u + 5.64922
a
4
=
0.258882u
33
− 0.285726u
32
+ ··· + 72.4607u − 49.4683
−0.0432859u
33
+ 0.0437686u
32
+ ··· − 10.7090u + 5.53801
a
10
=
−0.221972u
33
+ 0.217908u
32
+ ··· − 54.9480u + 40.9740
0.0269077u
33
− 0.0347803u
32
+ ··· + 11.5785u − 4.56490
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00939630u
33
+ 0.0336814u
32
+ ··· + 4.89386u − 28.6989
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
17
+ 24u
16
+ ··· − 9908u − 1296)
2
c
2
, c
7
(u
17
− 2u
16
+ ··· − 26u + 36)
2
c
3
, c
6
, c
9
c
11
u
34
+ u
33
+ ··· + 180u − 3
c
4
, c
5
, c
8
c
12
u
34
+ 2u
33
+ ··· + 220u − 23
c
10
(u
17
+ 2u
16
+ ··· + 16u + 31)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
17
− 76y
16
+ ··· − 10988432y −1679616)
2
c
2
, c
7
(y
17
+ 24y
16
+ ··· − 9908y −1296)
2
c
3
, c
6
, c
9
c
11
y
34
− y
33
+ ··· − 33762y + 9
c
4
, c
5
, c
8
c
12
y
34
+ 26y
33
+ ··· − 8794y + 529
c
10
(y
17
+ 8y
16
+ ··· − 4084y −961)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.090627 + 1.004540I
a = 0.471078 + 0.756650I
b = 1.016570 − 0.157313I
−0.10165 + 2.03616I 9.54232 − 0.44456I
u = −0.090627 − 1.004540I
a = 0.471078 − 0.756650I
b = 1.016570 + 0.157313I
−0.10165 − 2.03616I 9.54232 + 0.44456I
u = −0.795551 + 0.572843I
a = 0.712957 − 0.584252I
b = 0.560213 + 0.299882I
2.05813 − 5.15332I 19.0308 + 6.5118I
u = −0.795551 − 0.572843I
a = 0.712957 + 0.584252I
b = 0.560213 − 0.299882I
2.05813 + 5.15332I 19.0308 − 6.5118I
u = −0.401638 + 0.943328I
a = −0.003706 − 0.972356I
b = 1.69468 + 0.58619I
−4.13468 − 1.27893I 6.22904 + 2.48332I
u = −0.401638 − 0.943328I
a = −0.003706 + 0.972356I
b = 1.69468 − 0.58619I
−4.13468 + 1.27893I 6.22904 − 2.48332I
u = 0.533553 + 0.717890I
a = −0.499113 − 0.115452I
b = −0.771593 − 0.101693I
−2.45331 + 1.97624I 7.42079 − 4.65833I
u = 0.533553 − 0.717890I
a = −0.499113 + 0.115452I
b = −0.771593 + 0.101693I
−2.45331 − 1.97624I 7.42079 + 4.65833I
u = −0.242610 + 1.170970I
a = 0.124452 + 1.367930I
b = −0.287544 − 0.335267I
−10.67730 − 4.79187I 4.90904 + 2.81945I
u = −0.242610 − 1.170970I
a = 0.124452 − 1.367930I
b = −0.287544 + 0.335267I
−10.67730 + 4.79187I 4.90904 − 2.81945I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.141690 + 0.552201I
a = 0.072479 − 0.208338I
b = −0.197604 + 0.959423I
−3.00514 + 5.34809I 2.18569 − 7.96624I
u = 1.141690 − 0.552201I
a = 0.072479 + 0.208338I
b = −0.197604 − 0.959423I
−3.00514 − 5.34809I 2.18569 + 7.96624I
u = 0.247480 + 0.680723I
a = −1.71388 + 3.04980I
b = 0.113602 + 0.371521I
−8.37839 + 4.78927I −7.37609 − 10.15653I
u = 0.247480 − 0.680723I
a = −1.71388 − 3.04980I
b = 0.113602 − 0.371521I
−8.37839 − 4.78927I −7.37609 + 10.15653I
u = −1.175820 + 0.580411I
a = −0.201812 − 0.121644I
b = 1.059910 + 0.852148I
−0.10165 − 2.03616I 9.54232 + 0.44456I
u = −1.175820 − 0.580411I
a = −0.201812 + 0.121644I
b = 1.059910 − 0.852148I
−0.10165 + 2.03616I 9.54232 − 0.44456I
u = 1.301190 + 0.209618I
a = 0.661986 − 0.991511I
b = −1.38761 + 1.80203I
2.05813 + 5.15332I 19.0308 − 6.5118I
u = 1.301190 − 0.209618I
a = 0.661986 + 0.991511I
b = −1.38761 − 1.80203I
2.05813 − 5.15332I 19.0308 + 6.5118I
u = 0.339308 + 0.591459I
a = −0.59919 − 3.85196I
b = −1.54924 + 0.17925I
−3.00514 + 5.34809I 2.18569 − 7.96624I
u = 0.339308 − 0.591459I
a = −0.59919 + 3.85196I
b = −1.54924 − 0.17925I
−3.00514 − 5.34809I 2.18569 + 7.96624I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.075291 + 0.633370I
a = 0.42574 − 1.35352I
b = −0.270546 − 0.037284I
−2.45331 − 1.97624I 7.42079 + 4.65833I
u = −0.075291 − 0.633370I
a = 0.42574 + 1.35352I
b = −0.270546 + 0.037284I
−2.45331 + 1.97624I 7.42079 − 4.65833I
u = −1.328000 + 0.437105I
a = 0.238908 + 0.776924I
b = −0.317094 + 0.353042I
−4.13468 − 1.27893I 6.22904 + 2.48332I
u = −1.328000 − 0.437105I
a = 0.238908 − 0.776924I
b = −0.317094 − 0.353042I
−4.13468 + 1.27893I 6.22904 − 2.48332I
u = 1.52739
a = −1.56471
b = 2.10462
7.66275 −28.8150
u = −1.01230 + 1.40773I
a = 0.490922 + 1.011800I
b = −2.20050 + 0.26772I
−16.6175 − 5.4104I 6.46581 + 2.30080I
u = −1.01230 − 1.40773I
a = 0.490922 − 1.011800I
b = −2.20050 − 0.26772I
−16.6175 + 5.4104I 6.46581 − 2.30080I
u = −1.18361 + 1.34447I
a = −0.495729 − 1.106020I
b = 3.09372 − 0.59515I
−8.37839 − 4.78927I −7.37609 + 10.15653I
u = −1.18361 − 1.34447I
a = −0.495729 + 1.106020I
b = 3.09372 + 0.59515I
−8.37839 + 4.78927I −7.37609 − 10.15653I
u = 1.26353 + 1.30740I
a = 0.682130 − 0.832341I
b = −2.34665 − 0.14641I
−10.67730 + 4.79187I 4.90904 − 2.81945I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.26353 − 1.30740I
a = 0.682130 + 0.832341I
b = −2.34665 + 0.14641I
−10.67730 − 4.79187I 4.90904 + 2.81945I
u = 1.22316 + 1.39721I
a = −0.519796 + 0.741917I
b = 2.51223 + 0.01536I
−16.6175 − 5.4104I 6.46581 + 0.I
u = 1.22316 − 1.39721I
a = −0.519796 − 0.741917I
b = 2.51223 − 0.01536I
−16.6175 + 5.4104I 6.46581 + 0.I
u = −0.0163031
a = 14.8699
b = −1.54968
7.66275 −28.8150
13
III.
I
u
3
= h1.97 × 10
16
u
25
+ 6.80 × 10
15
u
24
+ · · · + 1.89 × 10
16
b + 5.92 × 10
16
, 6.86 ×
10
15
u
25
−1.50×10
16
u
24
+· · ·+1.89×10
16
a−1.97×10
16
, u
26
−8u
24
+· · ·+4u−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
−0.362882u
25
+ 0.794263u
24
+ ··· − 6.49598u + 1.04151
−1.04311u
25
− 0.359516u
24
+ ··· + 5.85758u − 3.13172
a
7
=
1
−u
2
a
3
=
−1.24891u
25
+ 0.555400u
24
+ ··· − 4.17834u − 1.29595
−0.933911u
25
− 0.362622u
24
+ ··· + 5.78816u − 2.89286
a
8
=
−0.644866u
25
− 0.525042u
24
+ ··· − 0.433835u + 2.06673
−0.669601u
25
− 0.198230u
24
+ ··· − 0.570903u − 2.02388
a
9
=
−1.31447u
25
− 0.723272u
24
+ ··· − 1.00474u + 0.0428499
−0.669601u
25
− 0.198230u
24
+ ··· − 0.570903u − 2.02388
a
12
=
u
−u
3
+ u
a
1
=
−0.512169u
25
+ 0.425261u
24
+ ··· − 7.59602u − 1.32012
−2.68663u
25
− 0.699913u
24
+ ··· + 10.0675u − 7.75382
a
5
=
1.72730u
25
+ 0.723476u
24
+ ··· − 9.50521u + 5.71869
2.84479u
25
+ 1.04945u
24
+ ··· − 4.48272u + 6.55202
a
4
=
1.26940u
25
+ 0.646311u
24
+ ··· − 9.21808u + 5.37962
2.47802u
25
+ 0.981294u
24
+ ··· − 4.04635u + 6.29011
a
10
=
−0.680670u
25
− 0.925311u
24
+ ··· + 6.55118u − 2.78413
−0.946125u
25
− 0.246566u
24
+ ··· − 1.76142u − 4.29658
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
93950281467493955
4728112264090751
u
25
+
32248120106658880
4728112264090751
u
24
+···−
275322822416113371
4728112264090751
u+
349499963017582750
4728112264090751
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
13
− 8u
12
+ ··· − 8u + 1)
2
c
2
(u
13
+ 4u
11
− 2u
10
+ 3u
9
− 7u
8
− 5u
7
− 10u
6
− 8u
5
− 9u
4
− 3u
3
− 4u
2
− 1)
2
c
3
, c
11
u
26
− 8u
24
+ ··· − 4u − 1
c
4
, c
8
u
26
− 3u
25
+ ··· − 5u
2
− 1
c
5
, c
12
u
26
+ 3u
25
+ ··· − 5u
2
− 1
c
6
, c
9
u
26
− 8u
24
+ ··· + 4u − 1
c
7
(u
13
+ 4u
11
+ 2u
10
+ 3u
9
+ 7u
8
− 5u
7
+ 10u
6
− 8u
5
+ 9u
4
− 3u
3
+ 4u
2
+ 1)
2
c
10
u
26
− 4u
24
+ ··· + 104u
2
− 131
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
13
− 20y
12
+ ··· − 4y −1)
2
c
2
, c
7
(y
13
+ 8y
12
+ ··· − 8y −1)
2
c
3
, c
6
, c
9
c
11
y
26
− 16y
25
+ ··· − 18y + 1
c
4
, c
5
, c
8
c
12
y
26
+ 11y
25
+ ··· + 10y + 1
c
10
(y
13
− 4y
12
+ ··· + 104y −131)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.817662 + 0.590599I
a = 0.935994 − 0.330693I
b = 0.220839 + 0.255226I
1.53627 − 5.17150I 2.98626 + 6.74281I
u = −0.817662 − 0.590599I
a = 0.935994 + 0.330693I
b = 0.220839 − 0.255226I
1.53627 + 5.17150I 2.98626 − 6.74281I
u = 0.805477 + 0.668712I
a = −0.470790 − 0.667412I
b = 0.160580 + 0.216270I
−3.28216 − 0.30187I 7.77799 + 0.28167I
u = 0.805477 − 0.668712I
a = −0.470790 + 0.667412I
b = 0.160580 − 0.216270I
−3.28216 + 0.30187I 7.77799 − 0.28167I
u = 0.400623 + 1.016220I
a = 0.10247 + 1.52610I
b = 1.406120 − 0.098892I
−0.92618 + 3.81353I 7.67664 − 4.03174I
u = 0.400623 − 1.016220I
a = 0.10247 − 1.52610I
b = 1.406120 + 0.098892I
−0.92618 − 3.81353I 7.67664 + 4.03174I
u = 1.039890 + 0.594363I
a = 0.150026 + 0.478822I
b = 0.217298 − 1.035160I
−2.42131 + 5.00871I 12.71310 − 2.53999I
u = 1.039890 − 0.594363I
a = 0.150026 − 0.478822I
b = 0.217298 + 1.035160I
−2.42131 − 5.00871I 12.71310 + 2.53999I
u = −1.155230 + 0.359006I
a = −0.511606 + 0.072561I
b = 0.24434 − 1.47710I
2.70797 + 1.25553I 8.00586 + 0.55931I
u = −1.155230 − 0.359006I
a = −0.511606 − 0.072561I
b = 0.24434 + 1.47710I
2.70797 − 1.25553I 8.00586 − 0.55931I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.297240 + 0.340645I
a = −1.197780 + 0.407415I
b = 1.92443 − 0.54500I
2.70797 + 1.25553I 8.00586 + 0.55931I
u = 1.297240 − 0.340645I
a = −1.197780 − 0.407415I
b = 1.92443 + 0.54500I
2.70797 − 1.25553I 8.00586 − 0.55931I
u = 0.252278 + 0.568954I
a = 1.74988 − 2.98359I
b = −0.143222 + 0.220123I
−8.07284 + 4.62322I 13.66718 + 0.84986I
u = 0.252278 − 0.568954I
a = 1.74988 + 2.98359I
b = −0.143222 − 0.220123I
−8.07284 − 4.62322I 13.66718 − 0.84986I
u = −1.373330 + 0.156774I
a = 0.905553 + 0.967197I
b = −1.90137 − 2.16497I
1.53627 − 5.17150I 2.98626 + 6.74281I
u = −1.373330 − 0.156774I
a = 0.905553 − 0.967197I
b = −1.90137 + 2.16497I
1.53627 + 5.17150I 2.98626 − 6.74281I
u = −0.532362 + 0.136318I
a = 2.51322 + 3.41291I
b = −1.42628 − 0.03798I
−2.42131 − 5.00871I 12.71310 + 2.53999I
u = −0.532362 − 0.136318I
a = 2.51322 − 3.41291I
b = −1.42628 + 0.03798I
−2.42131 + 5.00871I 12.71310 − 2.53999I
u = 0.392695 + 0.368909I
a = −1.043130 + 0.923864I
b = 1.071210 + 0.710954I
−3.28216 + 0.30187I 7.77799 − 0.28167I
u = 0.392695 − 0.368909I
a = −1.043130 − 0.923864I
b = 1.071210 − 0.710954I
−3.28216 − 0.30187I 7.77799 + 0.28167I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45772 + 0.27763I
a = −0.0889095 + 0.0267155I
b = 0.277827 − 1.329280I
−0.92618 + 3.81353I 7.67664 − 4.03174I
u = 1.45772 − 0.27763I
a = −0.0889095 − 0.0267155I
b = 0.277827 + 1.329280I
−0.92618 − 3.81353I 7.67664 + 4.03174I
u = −1.49925
a = −1.61075
b = 2.14047
7.75703 56.3460
u = 0.309408
a = 0.394141
b = −1.51783
7.75703 56.3460
u = −1.17243 + 1.27604I
a = 0.563370 + 1.090940I
b = −2.86310 + 0.46404I
−8.07284 − 4.62322I 10.00000 + 0.I
u = −1.17243 − 1.27604I
a = 0.563370 − 1.090940I
b = −2.86310 − 0.46404I
−8.07284 + 4.62322I 10.00000 + 0.I
19
IV. I
u
4
= h−u
2
+ b − 1, a − u + 1, u
3
+ u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
u − 1
u
2
+ 1
a
7
=
1
−u
2
a
3
=
−1
u
2
− u
a
8
=
u
2
− u + 1
−u
2
− 1
a
9
=
−u
−u
2
− 1
a
12
=
u
2u + 1
a
1
=
−u
2
+ u − 1
2
a
5
=
0
u
2
− u + 1
a
4
=
−1
2u
2
− u
a
10
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
2
− 2u + 1
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
− 2u
2
+ u + 1
c
2
, c
6
, c
9
u
3
+ u + 1
c
3
, c
7
, c
11
u
3
+ u − 1
c
4
, c
8
u
3
− u
2
− 1
c
5
, c
12
u
3
+ u
2
+ 1
c
10
u
3
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
3
− 2y
2
+ 5y −1
c
2
, c
3
, c
6
c
7
, c
9
, c
11
y
3
+ 2y
2
+ y −1
c
4
, c
5
, c
8
c
12
y
3
− y
2
− 2y −1
c
10
y
3
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.341164 + 1.161540I
a = −0.658836 + 1.161540I
b = −0.232786 + 0.792552I
−5.50124 + 1.58317I 2.78324 − 3.90819I
u = 0.341164 − 1.161540I
a = −0.658836 − 1.161540I
b = −0.232786 − 0.792552I
−5.50124 − 1.58317I 2.78324 + 3.90819I
u = −0.682328
a = −1.68233
b = 1.46557
4.42273 1.43350
23
V. I
u
5
= hb − 1, a + 1, u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
1
a
2
=
−1
1
a
7
=
1
−1
a
3
=
−1
1
a
8
=
1
−1
a
9
=
0
−1
a
12
=
1
0
a
1
=
−1
1
a
5
=
1
1
a
4
=
0
1
a
10
=
−1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = 18
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
c
3
, c
6
, c
9
c
10
, c
11
u + 1
c
4
, c
5
, c
8
c
12
u − 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
c
3
, c
4
, c
5
c
6
, c
8
, c
9
c
10
, c
11
, c
12
y −1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = 1.00000
4.93480 18.0000
27
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
3
− 2u
2
+ u + 1)(u
13
− 8u
12
+ ··· − 8u + 1)
2
· (u
16
+ 15u
15
+ ··· − 732u + 16)(u
17
+ 24u
16
+ ··· − 9908u − 1296)
2
c
2
u(u
3
+ u + 1)
· (u
13
+ 4u
11
− 2u
10
+ 3u
9
− 7u
8
− 5u
7
− 10u
6
− 8u
5
− 9u
4
− 3u
3
− 4u
2
− 1)
2
· (u
16
+ 5u
15
+ ··· − 30u + 4)(u
17
− 2u
16
+ ··· − 26u + 36)
2
c
3
, c
11
(u + 1)(u
3
+ u − 1)(u
16
− u
15
+ ··· − 3u − 1)(u
26
− 8u
24
+ ··· − 4u − 1)
· (u
34
+ u
33
+ ··· + 180u − 3)
c
4
, c
8
(u − 1)(u
3
− u
2
− 1)(u
16
+ 2u
15
+ ··· + 2u + 3)(u
26
− 3u
25
+ ··· − 5u
2
− 1)
· (u
34
+ 2u
33
+ ··· + 220u − 23)
c
5
, c
12
(u − 1)(u
3
+ u
2
+ 1)(u
16
+ 2u
15
+ ··· + 2u + 3)(u
26
+ 3u
25
+ ··· − 5u
2
− 1)
· (u
34
+ 2u
33
+ ··· + 220u − 23)
c
6
, c
9
(u + 1)(u
3
+ u + 1)(u
16
− u
15
+ ··· − 3u − 1)(u
26
− 8u
24
+ ··· + 4u − 1)
· (u
34
+ u
33
+ ··· + 180u − 3)
c
7
u(u
3
+ u − 1)
· (u
13
+ 4u
11
+ 2u
10
+ 3u
9
+ 7u
8
− 5u
7
+ 10u
6
− 8u
5
+ 9u
4
− 3u
3
+ 4u
2
+ 1)
2
· (u
16
+ 5u
15
+ ··· − 30u + 4)(u
17
− 2u
16
+ ··· − 26u + 36)
2
c
10
u
3
(u + 1)(u
16
− 6u
15
+ ··· + 32u − 32)(u
17
+ 2u
16
+ ··· + 16u + 31)
2
· (u
26
− 4u
24
+ ··· + 104u
2
− 131)
28
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
3
− 2y
2
+ 5y −1)(y
13
− 20y
12
+ ··· − 4y −1)
2
· (y
16
− 25y
15
+ ··· − 540400y + 256)
· (y
17
− 76y
16
+ ··· − 10988432y −1679616)
2
c
2
, c
7
y(y
3
+ 2y
2
+ y −1)(y
13
+ 8y
12
+ ··· − 8y −1)
2
· (y
16
+ 15y
15
+ ··· − 732y + 16)(y
17
+ 24y
16
+ ··· − 9908y −1296)
2
c
3
, c
6
, c
9
c
11
(y −1)(y
3
+ 2y
2
+ y −1)(y
16
+ y
15
+ ··· − 17y + 1)
· (y
26
− 16y
25
+ ··· − 18y + 1)(y
34
− y
33
+ ··· − 33762y + 9)
c
4
, c
5
, c
8
c
12
(y −1)(y
3
− y
2
− 2y −1)(y
16
+ 22y
15
+ ··· − 130y + 9)
· (y
26
+ 11y
25
+ ··· + 10y + 1)(y
34
+ 26y
33
+ ··· − 8794y + 529)
c
10
y
3
(y −1)(y
13
− 4y
12
+ ··· + 104y −131)
2
· (y
16
+ 2y
15
+ ··· − 12288y + 1024)
· (y
17
+ 8y
16
+ ··· − 4084y −961)
2
29
