12a
0819
(K12a
0819
)
A knot diagram
1
Linearized knot diagam
4 5 7 9 10 11 12 1 2 6 3 8
Solving Sequence
7,12
8
1,4
2 9 5 3 11 6 10
c
7
c
12
c
1
c
8
c
4
c
3
c
11
c
6
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h9.81389 × 10
215
u
101
− 1.43564 × 10
216
u
100
+ ··· + 8.44851 × 10
215
b + 1.19663 × 10
217
,
− 2.45404 × 10
217
u
101
+ 2.90155 × 10
217
u
100
+ ··· + 4.22426 × 10
216
a − 2.42146 × 10
218
,
u
102
− u
101
+ ··· + 18u + 1i
I
u
2
= hu
15
− 9u
13
+ u
12
+ 33u
11
− 6u
10
− 61u
9
+ 11u
8
+ 54u
7
− 2u
6
− 13u
5
− 11u
4
− 5u
3
+ 6u
2
+ b − u,
5u
15
− 340u
14
+ ··· + 361a − 237,
u
16
− u
15
− 9u
14
+ 9u
13
+ 33u
12
− 32u
11
− 62u
10
+ 53u
9
+ 61u
8
− 32u
7
− 28u
6
− 11u
5
+ 4u
4
+ 13u
3
+ u + 1i
I
u
3
= hb − 1, a + u + 2, u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 120 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
= h9.81 × 10
215
u
101
− 1.44 × 10
216
u
100
+ · · · + 8.45 × 10
215
b + 1.20 ×
10
217
, −2.45 × 10
217
u
101
+ 2.90 × 10
217
u
100
+ · · · + 4.22 × 10
216
a − 2.42 ×
10
218
, u
102
− u
101
+ · · · + 18u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
5.80939u
101
− 6.86878u
100
+ ··· + 523.205u + 57.3228
−1.16161u
101
+ 1.69928u
100
+ ··· − 146.794u − 14.1638
a
2
=
17.1128u
101
− 19.5202u
100
+ ··· + 1275.28u + 124.279
−2.65881u
101
+ 3.09872u
100
+ ··· − 216.087u − 19.4356
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
4.60503u
101
− 5.11479u
100
+ ··· + 386.505u + 44.5732
−1.25041u
101
+ 1.65858u
100
+ ··· − 144.962u − 13.8921
a
3
=
4.64778u
101
− 5.16950u
100
+ ··· + 376.411u + 43.1589
−1.16161u
101
+ 1.69928u
100
+ ··· − 146.794u − 14.1638
a
11
=
9.69143u
101
− 11.7940u
100
+ ··· + 697.904u + 71.4195
−2.46283u
101
+ 2.72548u
100
+ ··· − 193.856u − 17.8946
a
6
=
21.5584u
101
− 23.9838u
100
+ ··· + 1850.82u + 175.409
−1.80773u
101
+ 1.92185u
100
+ ··· − 143.234u − 14.0282
a
10
=
−25.0084u
101
+ 29.3750u
100
+ ··· − 1856.25u − 168.712
2.27979u
101
− 2.77364u
100
+ ··· + 167.806u + 16.0557
(ii) Obstruction class = −1
(iii) Cusp Shapes = −14.2614u
101
+ 16.1606u
100
+ ··· − 745.362u − 63.3257
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
102
+ 8u
101
+ ··· + 2562u − 279
c
2
u
102
− 8u
101
+ ··· − 2562u − 279
c
3
u
102
+ 3u
101
+ ··· + 27u − 1
c
4
u
102
− u
101
+ ··· + 1378u + 1357
c
5
, c
6
, c
10
u
102
− u
101
+ ··· + 18u + 1
c
7
, c
8
, c
12
u
102
+ u
101
+ ··· − 18u + 1
c
9
u
102
+ u
101
+ ··· − 1378u + 1357
c
11
u
102
− 3u
101
+ ··· − 27u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
y
102
+ 18y
101
+ ··· + 642168y + 77841
c
3
, c
11
y
102
− 5y
101
+ ··· − 1355y + 1
c
4
, c
9
y
102
− 33y
101
+ ··· − 92622476y + 1841449
c
5
, c
6
, c
7
c
8
, c
10
, c
12
y
102
− 109y
101
+ ··· − 154y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.421881 + 0.913460I
a = −0.165545 − 0.490628I
b = 0.888810 − 0.537019I
−8.03164 + 7.68352I 0
u = −0.421881 − 0.913460I
a = −0.165545 + 0.490628I
b = 0.888810 + 0.537019I
−8.03164 − 7.68352I 0
u = 0.948769 + 0.365737I
a = 0.663232 + 0.274203I
b = 1.233530 − 0.266394I
−4.88209 − 0.50422I 0
u = 0.948769 − 0.365737I
a = 0.663232 − 0.274203I
b = 1.233530 + 0.266394I
−4.88209 + 0.50422I 0
u = −0.649076 + 0.789280I
a = 0.353140 − 0.770907I
b = 1.18870 + 0.83480I
−7.3328 − 13.2263I 0
u = −0.649076 − 0.789280I
a = 0.353140 + 0.770907I
b = 1.18870 − 0.83480I
−7.3328 + 13.2263I 0
u = 0.656934 + 0.801294I
a = −0.230937 − 0.577852I
b = −0.860693 + 0.757017I
9.25295I 0
u = 0.656934 − 0.801294I
a = −0.230937 + 0.577852I
b = −0.860693 − 0.757017I
− 9.25295I 0
u = −0.618166 + 0.738762I
a = −0.455893 + 0.460022I
b = −0.586392 − 0.519509I
1.45177 − 2.24448I 0
u = −0.618166 − 0.738762I
a = −0.455893 − 0.460022I
b = −0.586392 + 0.519509I
1.45177 + 2.24448I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.748254 + 0.536631I
a = 1.006120 − 0.725807I
b = −0.816259 − 0.391671I
−7.39412 − 1.87601I 0
u = 0.748254 − 0.536631I
a = 1.006120 + 0.725807I
b = −0.816259 + 0.391671I
−7.39412 + 1.87601I 0
u = 0.356069 + 1.033270I
a = 0.118651 − 0.235636I
b = −0.441341 − 0.229273I
−0.84908 − 3.47127I 0
u = 0.356069 − 1.033270I
a = 0.118651 + 0.235636I
b = −0.441341 + 0.229273I
−0.84908 + 3.47127I 0
u = −0.631769 + 0.896852I
a = 0.037064 − 0.290429I
b = 0.365478 + 0.498966I
0.84908 − 3.47127I 0
u = −0.631769 − 0.896852I
a = 0.037064 + 0.290429I
b = 0.365478 − 0.498966I
0.84908 + 3.47127I 0
u = −0.847496 + 0.274573I
a = −0.446501 + 0.051731I
b = −0.886146 − 0.010622I
0.652997 + 0.202759I 0
u = −0.847496 − 0.274573I
a = −0.446501 − 0.051731I
b = −0.886146 + 0.010622I
0.652997 − 0.202759I 0
u = 0.446889 + 0.764035I
a = 0.953721 + 0.634503I
b = 0.917901 − 0.731514I
−3.55803 + 4.98722I 0
u = 0.446889 − 0.764035I
a = 0.953721 − 0.634503I
b = 0.917901 + 0.731514I
−3.55803 − 4.98722I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.607479 + 0.536834I
a = −0.057997 + 0.146408I
b = 0.625451 + 0.753642I
−2.87163 − 0.43109I 0
u = 0.607479 − 0.536834I
a = −0.057997 − 0.146408I
b = 0.625451 − 0.753642I
−2.87163 + 0.43109I 0
u = 1.243250 + 0.067945I
a = 0.863393 − 0.902732I
b = −0.183056 − 0.072866I
−3.85916 + 1.48032I 0
u = 1.243250 − 0.067945I
a = 0.863393 + 0.902732I
b = −0.183056 + 0.072866I
−3.85916 − 1.48032I 0
u = −0.536711 + 0.504007I
a = −0.351562 + 1.204950I
b = −1.33435 − 1.00611I
−7.91386 − 3.73886I 0
u = −0.536711 − 0.504007I
a = −0.351562 − 1.204950I
b = −1.33435 + 1.00611I
−7.91386 + 3.73886I 0
u = 0.332736 + 0.635981I
a = −0.486881 − 0.278645I
b = −1.24108 + 0.82202I
−8.60735 + 5.94490I 0
u = 0.332736 − 0.635981I
a = −0.486881 + 0.278645I
b = −1.24108 − 0.82202I
−8.60735 − 5.94490I 0
u = −0.166338 + 0.666357I
a = 0.252426 − 0.088045I
b = 0.688253 + 0.733228I
−1.45177 − 2.24448I −7.42940 + 6.53557I
u = −0.166338 − 0.666357I
a = 0.252426 + 0.088045I
b = 0.688253 − 0.733228I
−1.45177 + 2.24448I −7.42940 − 6.53557I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.479515 + 0.488023I
a = 0.279138 + 1.179520I
b = 0.885725 − 0.779306I
−1.44911 + 3.19144I −7.35679 − 8.71973I
u = 0.479515 − 0.488023I
a = 0.279138 − 1.179520I
b = 0.885725 + 0.779306I
−1.44911 − 3.19144I −7.35679 + 8.71973I
u = −1.335720 + 0.108681I
a = −0.37231 + 1.37405I
b = −0.138461 − 0.851390I
2.87163 − 0.43109I 0
u = −1.335720 − 0.108681I
a = −0.37231 − 1.37405I
b = −0.138461 + 0.851390I
2.87163 + 0.43109I 0
u = 0.159323 + 0.633172I
a = 1.12688 + 1.85019I
b = 0.711101 + 0.356367I
−7.28113 + 4.19641I −7.17543 − 4.77818I
u = 0.159323 − 0.633172I
a = 1.12688 − 1.85019I
b = 0.711101 − 0.356367I
−7.28113 − 4.19641I −7.17543 + 4.77818I
u = −0.264474 + 0.551378I
a = −0.72511 + 1.64636I
b = −0.569908 − 0.161854I
−1.10064 − 3.42771I −7.99632 + 9.02699I
u = −0.264474 − 0.551378I
a = −0.72511 − 1.64636I
b = −0.569908 + 0.161854I
−1.10064 + 3.42771I −7.99632 − 9.02699I
u = −1.388920 + 0.144019I
a = −0.23998 − 1.64481I
b = 0.1004980 − 0.0409276I
−2.44020 − 6.79345I 0
u = −1.388920 − 0.144019I
a = −0.23998 + 1.64481I
b = 0.1004980 + 0.0409276I
−2.44020 + 6.79345I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.595566 + 0.056430I
a = −1.275670 + 0.429355I
b = −0.102020 − 0.301000I
1.42393 − 0.14814I 6.94586 − 0.46279I
u = −0.595566 − 0.056430I
a = −1.275670 − 0.429355I
b = −0.102020 + 0.301000I
1.42393 + 0.14814I 6.94586 + 0.46279I
u = −1.40670
a = −0.190717
b = −1.36954
−3.91844 0
u = 1.403230 + 0.157306I
a = −0.20679 + 1.82905I
b = 0.91053 − 1.38663I
3.55803 + 4.98722I 0
u = 1.403230 − 0.157306I
a = −0.20679 − 1.82905I
b = 0.91053 + 1.38663I
3.55803 − 4.98722I 0
u = −0.530263 + 0.189652I
a = 0.499941 + 0.711171I
b = 0.12126 − 1.59467I
−4.46231 − 5.76178I 1.80073 + 7.63380I
u = −0.530263 − 0.189652I
a = 0.499941 − 0.711171I
b = 0.12126 + 1.59467I
−4.46231 + 5.76178I 1.80073 − 7.63380I
u = −0.323849 + 0.452126I
a = 0.87936 + 1.56567I
b = −1.076990 + 0.414157I
−8.42239 + 0.35931I −8.15948 + 0.80270I
u = −0.323849 − 0.452126I
a = 0.87936 − 1.56567I
b = −1.076990 − 0.414157I
−8.42239 − 0.35931I −8.15948 − 0.80270I
u = 1.44559 + 0.13953I
a = 0.13946 − 1.68727I
b = −0.161842 + 0.586300I
4.46231 + 5.76178I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44559 − 0.13953I
a = 0.13946 + 1.68727I
b = −0.161842 − 0.586300I
4.46231 − 5.76178I 0
u = 0.466187 + 0.285491I
a = −0.684856 + 0.412840I
b = 0.813263 + 0.154187I
−1.42393 − 0.14814I −6.94586 − 0.46279I
u = 0.466187 − 0.285491I
a = −0.684856 − 0.412840I
b = 0.813263 − 0.154187I
−1.42393 + 0.14814I −6.94586 + 0.46279I
u = 1.45431 + 0.02048I
a = −0.951292 − 0.896201I
b = 1.79673 + 0.70112I
4.88209 + 0.50422I 0
u = 1.45431 − 0.02048I
a = −0.951292 + 0.896201I
b = 1.79673 − 0.70112I
4.88209 − 0.50422I 0
u = −1.44798 + 0.18036I
a = 0.72702 + 1.82534I
b = −1.57595 − 1.31600I
−2.86058 − 8.79148I 0
u = −1.44798 − 0.18036I
a = 0.72702 − 1.82534I
b = −1.57595 + 1.31600I
−2.86058 + 8.79148I 0
u = −1.48460 + 0.05083I
a = 0.63408 − 1.77146I
b = −1.10430 + 1.51531I
7.28113 − 4.19641I 0
u = −1.48460 − 0.05083I
a = 0.63408 + 1.77146I
b = −1.10430 − 1.51531I
7.28113 + 4.19641I 0
u = 1.48976 + 0.04878I
a = −0.05888 − 2.10123I
b = −0.93265 + 1.08671I
1.00808 + 6.07571I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48976 − 0.04878I
a = −0.05888 + 2.10123I
b = −0.93265 − 1.08671I
1.00808 − 6.07571I 0
u = −1.49523 + 0.07916I
a = −0.79260 + 1.22174I
b = 0.91211 − 1.16668I
3.85916 − 1.48032I 0
u = −1.49523 − 0.07916I
a = −0.79260 − 1.22174I
b = 0.91211 + 1.16668I
3.85916 + 1.48032I 0
u = −1.49922 + 0.03734I
a = 0.10155 − 1.60495I
b = 0.804629 + 0.956431I
7.91386 − 3.73886I 0
u = −1.49922 − 0.03734I
a = 0.10155 + 1.60495I
b = 0.804629 − 0.956431I
7.91386 + 3.73886I 0
u = 1.52152 + 0.00958I
a = 0.121602 − 0.998252I
b = −0.831129 + 0.730519I
8.42239 + 0.35931I 0
u = 1.52152 − 0.00958I
a = 0.121602 + 0.998252I
b = −0.831129 − 0.730519I
8.42239 − 0.35931I 0
u = 1.52779 + 0.07140I
a = −0.37212 − 2.35107I
b = 0.43650 + 2.32127I
2.44020 + 6.79345I 0
u = 1.52779 − 0.07140I
a = −0.37212 + 2.35107I
b = 0.43650 − 2.32127I
2.44020 − 6.79345I 0
u = −1.52325 + 0.14078I
a = −0.43026 − 2.00109I
b = 0.86769 + 1.39894I
5.22562 − 5.43260I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.52325 − 0.14078I
a = −0.43026 + 2.00109I
b = 0.86769 − 1.39894I
5.22562 + 5.43260I 0
u = −1.51654 + 0.27355I
a = 0.02065 − 1.54952I
b = 1.13737 + 0.89063I
2.86058 − 8.79148I 0
u = −1.51654 − 0.27355I
a = 0.02065 + 1.54952I
b = 1.13737 − 0.89063I
2.86058 + 8.79148I 0
u = 1.53675 + 0.14550I
a = 0.75979 − 2.20368I
b = −1.42765 + 1.55977I
−1.00808 + 6.07571I 0
u = 1.53675 − 0.14550I
a = 0.75979 + 2.20368I
b = −1.42765 − 1.55977I
−1.00808 − 6.07571I 0
u = −1.49251 + 0.43030I
a = −0.346839 + 0.639465I
b = 0.067986 − 0.620504I
2.28760 − 2.26927I 0
u = −1.49251 − 0.43030I
a = −0.346839 − 0.639465I
b = 0.067986 + 0.620504I
2.28760 + 2.26927I 0
u = 0.434805 + 0.097618I
a = 1.95914 + 2.03130I
b = 0.363256 − 0.760387I
1.44911 + 3.19144I 7.35679 − 8.71973I
u = 0.434805 − 0.097618I
a = 1.95914 − 2.03130I
b = 0.363256 + 0.760387I
1.44911 − 3.19144I 7.35679 + 8.71973I
u = 1.56268
a = 0.587667
b = −1.29423
8.57239 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.56445 + 0.25318I
a = 0.064615 − 1.305070I
b = −0.920531 + 0.918148I
8.60735 + 5.94490I 0
u = 1.56445 − 0.25318I
a = 0.064615 + 1.305070I
b = −0.920531 − 0.918148I
8.60735 − 5.94490I 0
u = 1.42824 + 0.69356I
a = −0.198797 + 0.184560I
b = 0.408032 + 0.148288I
−2.28760 − 2.26927I 0
u = 1.42824 − 0.69356I
a = −0.198797 − 0.184560I
b = 0.408032 − 0.148288I
−2.28760 + 2.26927I 0
u = 1.57263 + 0.28115I
a = −0.026754 + 1.327210I
b = 0.633582 − 1.094220I
8.03164 + 7.68352I 0
u = 1.57263 − 0.28115I
a = −0.026754 − 1.327210I
b = 0.633582 + 1.094220I
8.03164 − 7.68352I 0
u = −1.59918
a = −1.33841
b = 2.19481
3.91844 0
u = −1.58178 + 0.26953I
a = 0.23352 + 1.56390I
b = −1.05120 − 1.17547I
7.3328 − 13.2263I 0
u = −1.58178 − 0.26953I
a = 0.23352 − 1.56390I
b = −1.05120 + 1.17547I
7.3328 + 13.2263I 0
u = 1.58356 + 0.26771I
a = −0.40968 + 1.69637I
b = 1.36740 − 1.13901I
17.1602I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.58356 − 0.26771I
a = −0.40968 − 1.69637I
b = 1.36740 + 1.13901I
− 17.1602I 0
u = 0.356649 + 0.156360I
a = −1.03119 + 1.31362I
b = −0.476026 − 1.106660I
1.10064 + 3.42771I 7.99632 − 9.02699I
u = 0.356649 − 0.156360I
a = −1.03119 − 1.31362I
b = −0.476026 + 1.106660I
1.10064 − 3.42771I 7.99632 + 9.02699I
u = −0.350648 + 0.105043I
a = −2.78594 + 3.95960I
b = −0.581556 − 0.978801I
−5.22562 − 5.43260I 6.43384 + 6.15958I
u = −0.350648 − 0.105043I
a = −2.78594 − 3.95960I
b = −0.581556 + 0.978801I
−5.22562 + 5.43260I 6.43384 − 6.15958I
u = −1.64265
a = 0.643909
b = −0.0289151
1.46197 0
u = −1.64130 + 0.22779I
a = −0.221317 − 0.900678I
b = 0.741738 + 0.734271I
7.39412 − 1.87601I 0
u = −1.64130 − 0.22779I
a = −0.221317 + 0.900678I
b = 0.741738 − 0.734271I
7.39412 + 1.87601I 0
u = 1.67186
a = 0.992925
b = −1.01022
−1.46197 0
u = −0.147584 + 0.068672I
a = 3.79006 + 2.75652I
b = 1.118130 − 0.400748I
−0.652997 − 0.202759I −7.20656 + 6.25888I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.147584 − 0.068672I
a = 3.79006 − 2.75652I
b = 1.118130 + 0.400748I
−0.652997 + 0.202759I −7.20656 − 6.25888I
u = −0.133664
a = 10.7869
b = −1.10414
−8.57239 −11.9520
15
II. I
u
2
=
hu
15
−9u
13
+· · ·+b−u, 5u
15
−340u
14
+· · ·+361a−237, u
16
−u
15
+· · ·+u+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
−0.0138504u
15
+ 0.941828u
14
+ ··· + 3.97507u + 0.656510
−u
15
+ 9u
13
+ ··· − 6u
2
+ u
a
2
=
−0.714681u
15
+ 0.598338u
14
+ ··· − 1.88643u + 0.675900
−0.437673u
15
− 0.238227u
14
+ ··· − 0.387812u − 0.454294
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
−0.792244u
15
+ 0.872576u
14
+ ··· + 4.37396u + 0.152355
−0.620499u
15
+ 0.193906u
14
+ ··· + 0.0831025u − 0.188366
a
3
=
−1.01385u
15
+ 0.941828u
14
+ ··· + 4.97507u + 0.656510
−u
15
+ 9u
13
+ ··· − 6u
2
+ u
a
11
=
0.218837u
15
+ 0.119114u
14
+ ··· − 9.80609u − 0.772853
0.451524u
15
− 0.703601u
14
+ ··· − 1.58726u − 0.202216
a
6
=
−0.152355u
15
+ 0.360111u
14
+ ··· − 10.2742u − 2.77839
0.221607u
15
− 0.0692521u
14
+ ··· − 0.601108u − 1.50416
a
10
=
0.110803u
15
− 0.534626u
14
+ ··· + 8.19945u + 2.74792
−0.639889u
15
+ 0.512465u
14
+ ··· + 0.648199u + 0.930748
(ii) Obstruction class = 1
(iii) Cusp Shapes =
113
19
u
15
−
103
19
u
14
+ ··· −
473
19
u −
2
19
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 8u
15
+ ··· + 9u − 1
c
2
u
16
+ 8u
15
+ ··· − 9u − 1
c
3
u
16
− 2u
15
+ ··· − u − 1
c
4
u
16
+ 4u
15
+ ··· + 4u + 1
c
5
, c
6
, c
12
u
16
+ u
15
+ ··· − u + 1
c
7
, c
8
, c
10
u
16
− u
15
+ ··· + u + 1
c
9
u
16
− 4u
15
+ ··· − 4u + 1
c
11
u
16
+ 2u
15
+ ··· + u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
y
16
+ 12y
15
+ ··· − 23y + 1
c
3
, c
11
y
16
− 12y
14
+ ··· + 5y + 1
c
4
, c
9
y
16
− 8y
15
+ ··· − 8y + 1
c
5
, c
6
, c
7
c
8
, c
10
, c
12
y
16
− 19y
15
+ ··· − y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.926270
a = −0.556516
b = −0.945338
0.241885 −10.1920
u = 1.11003
a = 0.842232
b = 1.17328
−6.25072 −6.91940
u = −0.202630 + 0.630852I
a = −0.696258 + 0.477965I
b = −0.258907 − 0.581574I
− 3.18079I 0. + 8.04553I
u = −0.202630 − 0.630852I
a = −0.696258 − 0.477965I
b = −0.258907 + 0.581574I
3.18079I 0. − 8.04553I
u = 1.30517 + 0.59727I
a = 0.0225910 + 0.0898992I
b = 0.303011 + 0.279380I
−2.06431 − 2.21113I 11.41011 + 0.86465I
u = 1.30517 − 0.59727I
a = 0.0225910 − 0.0898992I
b = 0.303011 − 0.279380I
−2.06431 + 2.21113I 11.41011 − 0.86465I
u = −1.43222 + 0.33519I
a = 0.448272 − 0.814439I
b = −0.204408 + 0.676444I
2.06431 − 2.21113I −11.41011 + 0.86465I
u = −1.43222 − 0.33519I
a = 0.448272 + 0.814439I
b = −0.204408 − 0.676444I
2.06431 + 2.21113I −11.41011 − 0.86465I
u = −1.49037 + 0.10946I
a = −0.19936 − 2.49024I
b = 0.82300 + 1.51770I
− 7.14063I 0. + 7.57677I
u = −1.49037 − 0.10946I
a = −0.19936 + 2.49024I
b = 0.82300 − 1.51770I
7.14063I 0. − 7.57677I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49011 + 0.13813I
a = 0.08568 − 2.00191I
b = −0.51703 + 1.36347I
5.83452 + 5.49826I 7.64316 − 7.42748I
u = 1.49011 − 0.13813I
a = 0.08568 + 2.00191I
b = −0.51703 − 1.36347I
5.83452 − 5.49826I 7.64316 + 7.42748I
u = 1.51494
a = 1.46282
b = −2.23729
6.25072 6.91940
u = 0.174995 + 0.371597I
a = 2.98493 + 1.28639I
b = 0.554575 − 1.010920I
−5.83452 + 5.49826I −7.64316 − 7.42748I
u = 0.174995 − 0.371597I
a = 2.98493 − 1.28639I
b = 0.554575 + 1.010920I
−5.83452 − 5.49826I −7.64316 + 7.42748I
u = −0.388811
a = −1.04023
b = −1.39112
−0.241885 10.1920
20
III. I
u
3
= hb − 1, a + u + 2, u
2
+ u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u − 1
a
1
=
u
−u + 1
a
4
=
−u − 2
1
a
2
=
−u − 3
2
a
9
=
u
−u
a
5
=
−2u − 2
u + 1
a
3
=
−u − 1
1
a
11
=
−u − 1
u + 1
a
6
=
u + 3
−u − 2
a
10
=
2u + 3
−u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
12
u
2
− u − 1
c
2
, c
7
, c
8
c
10
u
2
+ u − 1
c
3
, c
9
(u + 1)
2
c
4
, c
11
(u − 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
8
c
10
, c
12
y
2
− 3y + 1
c
3
, c
4
, c
9
c
11
(y −1)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −2.61803
b = 1.00000
−7.89568 0
u = −1.61803
a = −0.381966
b = 1.00000
7.89568 0
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u − 1)(u
16
− 8u
15
+ ··· + 9u − 1)(u
102
+ 8u
101
+ ··· + 2562u − 279)
c
2
(u
2
+ u − 1)(u
16
+ 8u
15
+ ··· − 9u − 1)(u
102
− 8u
101
+ ··· − 2562u − 279)
c
3
((u + 1)
2
)(u
16
− 2u
15
+ ··· − u − 1)(u
102
+ 3u
101
+ ··· + 27u − 1)
c
4
((u − 1)
2
)(u
16
+ 4u
15
+ ··· + 4u + 1)(u
102
− u
101
+ ··· + 1378u + 1357)
c
5
, c
6
(u
2
− u − 1)(u
16
+ u
15
+ ··· − u + 1)(u
102
− u
101
+ ··· + 18u + 1)
c
7
, c
8
(u
2
+ u − 1)(u
16
− u
15
+ ··· + u + 1)(u
102
+ u
101
+ ··· − 18u + 1)
c
9
((u + 1)
2
)(u
16
− 4u
15
+ ··· − 4u + 1)(u
102
+ u
101
+ ··· − 1378u + 1357)
c
10
(u
2
+ u − 1)(u
16
− u
15
+ ··· + u + 1)(u
102
− u
101
+ ··· + 18u + 1)
c
11
((u − 1)
2
)(u
16
+ 2u
15
+ ··· + u − 1)(u
102
− 3u
101
+ ··· − 27u − 1)
c
12
(u
2
− u − 1)(u
16
+ u
15
+ ··· − u + 1)(u
102
+ u
101
+ ··· − 18u + 1)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
(y
2
− 3y + 1)(y
16
+ 12y
15
+ ··· − 23y + 1)
· (y
102
+ 18y
101
+ ··· + 642168y + 77841)
c
3
, c
11
((y −1)
2
)(y
16
− 12y
14
+ ··· + 5y + 1)(y
102
− 5y
101
+ ··· − 1355y + 1)
c
4
, c
9
((y −1)
2
)(y
16
− 8y
15
+ ··· − 8y + 1)
· (y
102
− 33y
101
+ ··· − 92622476y + 1841449)
c
5
, c
6
, c
7
c
8
, c
10
, c
12
(y
2
− 3y + 1)(y
16
− 19y
15
+ ··· − y + 1)(y
102
− 109y
101
+ ··· − 154y + 1)
26
