12n
0098
(K12n
0098
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 12 3 11 5 6 8 10 9
Solving Sequence
7,11 3,8
6 10 12 5 2 4 9 1
c
7
c
6
c
10
c
11
c
5
c
2
c
4
c
9
c
12
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h4.18552 × 10
72
u
61
+ 3.25275 × 10
72
u
60
+ ··· + 1.83626 × 10
74
b − 1.12303 × 10
74
,
− 1.03434 × 10
74
u
61
− 5.26235 × 10
74
u
60
+ ··· + 1.83626 × 10
74
a + 1.05888 × 10
76
,
u
62
+ 5u
61
+ ··· − 113u + 1i
I
u
2
= hb, −u
3
+ a + 2, u
4
+ u
2
− u + 1i
I
u
3
= h−120a
2
u + 44a
2
− 865au + 691b + 202a + 177u − 134, a
3
− a
2
u + 8a
2
− 4au + a − 5u − 7, u
2
− u + 1i
I
u
4
= hb, −u
3
− u
2
+ a − 2u − 1, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 78 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
= h4.19 × 10
72
u
61
+ 3.25 × 10
72
u
60
+ · · · + 1.84 × 10
74
b − 1.12 ×
10
74
, −1.03 × 10
74
u
61
− 5.26 × 10
74
u
60
+ · · · + 1.84 × 10
74
a + 1.06 ×
10
76
, u
62
+ 5u
61
+ · · · − 113u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
0.563286u
61
+ 2.86580u
60
+ ··· − 4.40887u − 57.6652
−0.0227937u
61
− 0.0177140u
60
+ ··· − 3.56182u + 0.611587
a
8
=
1
u
2
a
6
=
−0.398010u
61
− 2.06178u
60
+ ··· + 15.0559u + 34.3666
0.108322u
61
+ 0.265127u
60
+ ··· + 7.66296u − 0.403405
a
10
=
u
u
3
+ u
a
12
=
u
3
u
5
+ u
3
+ u
a
5
=
−0.364245u
61
− 1.69585u
60
+ ··· − 5.63070u + 34.5483
−0.0484629u
61
− 0.227602u
60
+ ··· + 6.86074u − 0.394692
a
2
=
0.351605u
61
+ 1.74250u
60
+ ··· − 1.36842u − 32.2841
0.0484629u
61
+ 0.227602u
60
+ ··· − 6.86074u + 0.394692
a
4
=
−0.586080u
61
− 2.88351u
60
+ ··· + 0.847056u + 58.2767
0.0227937u
61
+ 0.0177140u
60
+ ··· + 3.56182u − 0.611587
a
9
=
−0.0628689u
61
− 0.211226u
60
+ ··· + 1.30026u − 10.6392
−0.121039u
61
− 0.637166u
60
+ ··· + 18.6696u − 0.0518508
a
1
=
0.0216935u
61
− 0.0922332u
60
+ ··· + 16.0468u − 1.14018
0.115443u
61
+ 0.357638u
60
+ ··· + 2.47253u − 0.00153419
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.152156u
61
+ 1.18827u
60
+ ··· + 7.99782u − 8.81670
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
62
+ 71u
61
+ ··· + 267u + 1
c
2
, c
4
u
62
− 13u
61
+ ··· + 15u − 1
c
3
, c
6
u
62
+ 3u
61
+ ··· − 8192u − 1024
c
5
u
62
+ 4u
61
+ ··· − 10u
2
+ 1
c
7
, c
10
u
62
− 5u
61
+ ··· + 113u + 1
c
8
u
62
+ 4u
61
+ ··· − 3025807u + 537503
c
9
u
62
+ 44u
60
+ ··· + 9664u + 824
c
11
u
62
− 21u
61
+ ··· + 12769u + 1
c
12
u
62
− 6u
61
+ ··· − 1248u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
62
− 147y
61
+ ··· − 20183y + 1
c
2
, c
4
y
62
− 71y
61
+ ··· − 267y + 1
c
3
, c
6
y
62
− 57y
61
+ ··· + 9961472y + 1048576
c
5
y
62
− 4y
61
+ ··· − 20y + 1
c
7
, c
10
y
62
+ 21y
61
+ ··· − 12769y + 1
c
8
y
62
+ 16y
61
+ ··· − 11200434939731y + 288909475009
c
9
y
62
+ 88y
61
+ ··· + 13013520y + 678976
c
11
y
62
+ 45y
61
+ ··· − 163345321y + 1
c
12
y
62
− 30y
61
+ ··· − 185344y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.197990 + 0.977965I
a = −0.817839 − 0.403463I
b = −0.181458 + 0.756746I
3.58947 − 0.62301I 3.36345 + 2.22600I
u = −0.197990 − 0.977965I
a = −0.817839 + 0.403463I
b = −0.181458 − 0.756746I
3.58947 + 0.62301I 3.36345 − 2.22600I
u = 0.504265 + 0.860405I
a = 8.46750 − 1.97416I
b = 0.596380 − 0.013951I
−1.08843 − 2.05155I 143.754 + 62.581I
u = 0.504265 − 0.860405I
a = 8.46750 + 1.97416I
b = 0.596380 + 0.013951I
−1.08843 + 2.05155I 143.754 − 62.581I
u = 0.315979 + 0.963839I
a = 1.63289 + 2.55056I
b = 0.261416 − 0.638531I
−0.90689 − 2.60619I −4.21909 + 1.98730I
u = 0.315979 − 0.963839I
a = 1.63289 − 2.55056I
b = 0.261416 + 0.638531I
−0.90689 + 2.60619I −4.21909 − 1.98730I
u = −0.399423 + 0.961282I
a = −0.895928 + 0.237941I
b = 0.251217 + 1.010200I
3.47148 − 0.76506I 5.05392 + 1.67806I
u = −0.399423 − 0.961282I
a = −0.895928 − 0.237941I
b = 0.251217 − 1.010200I
3.47148 + 0.76506I 5.05392 − 1.67806I
u = 0.725465 + 0.771295I
a = −1.45382 + 1.64302I
b = −0.430975 − 0.493018I
−2.91907 − 1.90864I −12.3927 + 9.8412I
u = 0.725465 − 0.771295I
a = −1.45382 − 1.64302I
b = −0.430975 + 0.493018I
−2.91907 + 1.90864I −12.3927 − 9.8412I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.136821 + 1.054380I
a = 1.362710 + 0.360651I
b = −1.45675 − 0.24203I
−6.85055 − 2.44704I −9.28052 + 0.I
u = 0.136821 − 1.054380I
a = 1.362710 − 0.360651I
b = −1.45675 + 0.24203I
−6.85055 + 2.44704I −9.28052 + 0.I
u = −0.517898 + 0.767660I
a = 1.41294 − 0.15513I
b = 0.36454 − 1.41210I
2.81830 + 4.57708I −11.91750 + 5.21602I
u = −0.517898 − 0.767660I
a = 1.41294 + 0.15513I
b = 0.36454 + 1.41210I
2.81830 − 4.57708I −11.91750 − 5.21602I
u = 0.665583 + 0.887668I
a = −2.37729 + 1.89006I
b = −1.71321 − 0.09060I
−9.63287 − 2.57588I 0
u = 0.665583 − 0.887668I
a = −2.37729 − 1.89006I
b = −1.71321 + 0.09060I
−9.63287 + 2.57588I 0
u = 0.526282 + 0.983879I
a = −0.264138 − 0.339596I
b = 0.036445 + 0.286407I
0.16449 − 2.80931I 0
u = 0.526282 − 0.983879I
a = −0.264138 + 0.339596I
b = 0.036445 − 0.286407I
0.16449 + 2.80931I 0
u = −0.864169 + 0.712568I
a = −1.19224 − 0.87800I
b = −1.86795 − 0.77559I
−13.75470 − 2.34725I 0
u = −0.864169 − 0.712568I
a = −1.19224 + 0.87800I
b = −1.86795 + 0.77559I
−13.75470 + 2.34725I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.490146 + 0.722105I
a = −0.672429 + 0.917928I
b = 0.441436 − 0.137299I
−0.75966 − 1.41499I −4.04897 + 4.67258I
u = 0.490146 − 0.722105I
a = −0.672429 − 0.917928I
b = 0.441436 + 0.137299I
−0.75966 + 1.41499I −4.04897 − 4.67258I
u = −0.899492 + 0.692074I
a = −1.65853 − 0.70275I
b = −1.66067 − 0.07116I
−6.43547 − 4.60616I 0
u = −0.899492 − 0.692074I
a = −1.65853 + 0.70275I
b = −1.66067 + 0.07116I
−6.43547 + 4.60616I 0
u = −0.787434 + 0.853716I
a = 1.68063 + 1.07219I
b = 1.66617 − 0.48213I
−5.71401 + 2.41800I 0
u = −0.787434 − 0.853716I
a = 1.68063 − 1.07219I
b = 1.66617 + 0.48213I
−5.71401 − 2.41800I 0
u = −0.864706 + 0.785575I
a = 0.763723 − 0.520590I
b = −0.21711 − 1.75503I
−8.50399 − 1.01711I 0
u = −0.864706 − 0.785575I
a = 0.763723 + 0.520590I
b = −0.21711 + 1.75503I
−8.50399 + 1.01711I 0
u = 0.208762 + 1.162770I
a = −0.185951 + 0.070134I
b = −0.940797 − 0.197290I
1.17723 − 4.19224I 0
u = 0.208762 − 1.162770I
a = −0.185951 − 0.070134I
b = −0.940797 + 0.197290I
1.17723 + 4.19224I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.696927 + 0.413786I
a = −0.366466 + 0.375684I
b = 0.021846 + 0.653169I
−0.54827 − 2.57263I −2.89722 + 1.94542I
u = −0.696927 − 0.413786I
a = −0.366466 − 0.375684I
b = 0.021846 − 0.653169I
−0.54827 + 2.57263I −2.89722 − 1.94542I
u = −0.771631 + 0.911436I
a = 1.32051 + 1.02522I
b = 1.79646 + 0.19203I
−5.53536 + 3.45054I 0
u = −0.771631 − 0.911436I
a = 1.32051 − 1.02522I
b = 1.79646 − 0.19203I
−5.53536 − 3.45054I 0
u = −1.058050 + 0.587721I
a = 1.303340 + 0.454049I
b = 1.78791 + 0.73226I
−14.6014 − 9.8690I 0
u = −1.058050 − 0.587721I
a = 1.303340 − 0.454049I
b = 1.78791 − 0.73226I
−14.6014 + 9.8690I 0
u = 0.755284 + 0.186760I
a = −1.27730 − 1.17981I
b = −0.681043 + 0.426546I
−3.40045 − 1.02073I −17.4297 + 0.1751I
u = 0.755284 − 0.186760I
a = −1.27730 + 1.17981I
b = −0.681043 − 0.426546I
−3.40045 + 1.02073I −17.4297 − 0.1751I
u = 0.742734 + 0.976694I
a = −1.43902 + 0.14537I
b = −0.817159 + 0.178444I
−2.25042 − 3.70807I 0
u = 0.742734 − 0.976694I
a = −1.43902 − 0.14537I
b = −0.817159 − 0.178444I
−2.25042 + 3.70807I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.567404 + 1.096720I
a = 0.444623 + 0.031736I
b = −0.044670 − 0.603802I
1.46847 + 7.47551I 0
u = −0.567404 − 1.096720I
a = 0.444623 − 0.031736I
b = −0.044670 + 0.603802I
1.46847 − 7.47551I 0
u = 0.134046 + 0.748921I
a = 0.876067 + 0.880958I
b = 0.832847 + 0.417130I
−0.271555 − 0.561550I −5.56822 + 2.77116I
u = 0.134046 − 0.748921I
a = 0.876067 − 0.880958I
b = 0.832847 − 0.417130I
−0.271555 + 0.561550I −5.56822 − 2.77116I
u = −0.788289 + 0.988568I
a = −1.070600 + 0.268073I
b = 0.07391 + 1.84459I
−7.87011 + 7.16358I 0
u = −0.788289 − 0.988568I
a = −1.070600 − 0.268073I
b = 0.07391 − 1.84459I
−7.87011 − 7.16358I 0
u = −0.755347 + 1.030700I
a = −1.53203 − 1.28053I
b = −1.67066 + 0.94430I
−12.7715 + 8.3839I 0
u = −0.755347 − 1.030700I
a = −1.53203 + 1.28053I
b = −1.67066 − 0.94430I
−12.7715 − 8.3839I 0
u = −0.762645 + 1.049950I
a = −1.42252 − 1.19441I
b = −1.71280 + 0.31828I
−5.32588 + 10.75820I 0
u = −0.762645 − 1.049950I
a = −1.42252 + 1.19441I
b = −1.71280 − 0.31828I
−5.32588 − 10.75820I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.264390 + 0.508789I
a = 1.216130 − 0.189520I
b = 1.84891 + 0.06365I
−13.40670 − 2.05335I 0
u = 1.264390 − 0.508789I
a = 1.216130 + 0.189520I
b = 1.84891 − 0.06365I
−13.40670 + 2.05335I 0
u = 0.614370
a = −0.586809
b = −1.79199
−10.3258 −5.46580
u = −0.770276 + 1.155790I
a = 1.38193 + 1.38913I
b = 1.69467 − 0.85916I
−12.7985 + 16.4675I 0
u = −0.770276 − 1.155790I
a = 1.38193 − 1.38913I
b = 1.69467 + 0.85916I
−12.7985 − 16.4675I 0
u = 0.353080 + 0.481050I
a = −1.065470 − 0.202264I
b = 0.445711 + 0.289474I
−0.76460 − 1.25688I −5.53847 + 5.17379I
u = 0.353080 − 0.481050I
a = −1.065470 + 0.202264I
b = 0.445711 − 0.289474I
−0.76460 + 1.25688I −5.53847 − 5.17379I
u = 0.17018 + 1.45712I
a = −0.282598 − 0.503076I
b = 1.60733 + 0.37972I
−6.11414 − 6.99153I 0
u = 0.17018 − 1.45712I
a = −0.282598 + 0.503076I
b = 1.60733 − 0.37972I
−6.11414 + 6.99153I 0
u = 0.89705 + 1.25294I
a = 0.769774 − 0.969200I
b = 1.77378 + 0.20130I
−11.14940 − 5.54057I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.89705 − 1.25294I
a = 0.769774 + 0.969200I
b = 1.77378 − 0.20130I
−11.14940 + 5.54057I 0
u = 0.00884552
a = −57.7304
b = 0.580536
−1.10354 −8.74860
11
II. I
u
2
= hb, −u
3
+ a + 2, u
4
+ u
2
− u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
u
3
− 2
0
a
8
=
1
u
2
a
6
=
1
0
a
10
=
u
u
3
+ u
a
12
=
u
3
u
2
a
5
=
−u
3
+ u
2
− u + 1
−u
2
+ u − 1
a
2
=
2u
3
− u
2
+ u − 3
u
2
− u + 1
a
4
=
u
3
− 2
0
a
9
=
−u
3
u
3
+ u
a
1
=
u
3
− u
2
+ u − 1
u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
3
+ 6u
2
− 2u − 5
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
6
u
4
c
4
(u + 1)
4
c
5
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
7
u
4
+ u
2
− u + 1
c
8
, c
10
, c
12
u
4
+ u
2
+ u + 1
c
9
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
11
u
4
− 2u
3
+ 3u
2
− u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
6
y
4
c
5
, c
11
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
7
, c
8
, c
10
c
12
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
9
y
4
− y
3
+ 2y
2
+ 7y + 4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547424 + 0.585652I
a = −2.39923 + 0.32564I
b = 0
−2.62503 − 1.39709I −5.95551 + 2.35025I
u = 0.547424 − 0.585652I
a = −2.39923 − 0.32564I
b = 0
−2.62503 + 1.39709I −5.95551 − 2.35025I
u = −0.547424 + 1.120870I
a = −0.100768 − 0.400532I
b = 0
0.98010 + 7.64338I −11.5445 − 9.2043I
u = −0.547424 − 1.120870I
a = −0.100768 + 0.400532I
b = 0
0.98010 − 7.64338I −11.5445 + 9.2043I
15
III. I
u
3
=
h−120a
2
u−865au+· · ·+202a−134, a
3
−a
2
u+8a
2
−4au+a−5u−7, u
2
−u+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
a
0.173661a
2
u + 1.25181au + ··· − 0.292330a + 0.193922
a
8
=
1
u − 1
a
6
=
0.0274964a
2
u − 0.0101302au + ··· + 0.437048a + 2.31404
0.0709117a
2
u + 0.552822au + ··· − 0.136035a + 1.86252
a
10
=
u
u − 1
a
12
=
−1
0
a
5
=
−0.0434153a
2
u − 0.562952au + ··· + 0.573082a + 0.451520
0.0709117a
2
u + 0.552822au + ··· − 0.136035a + 1.86252
a
2
=
0.0274964a
2
u − 0.0101302au + ··· + 0.437048a + 0.314038
0.0709117a
2
u + 0.552822au + ··· − 0.136035a + 1.86252
a
4
=
−0.173661a
2
u − 1.25181au + ··· + 1.29233a − 0.193922
0.173661a
2
u + 1.25181au + ··· − 0.292330a + 0.193922
a
9
=
−0.169320a
2
u − 0.0955137au + ··· − 0.164978a − 0.0390738
0
a
1
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1796
691
a
2
u −
401
691
a
2
−
3157
691
au −
4762
691
a +
8799
691
u −
8547
691
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
(u
3
− 3u
2
+ 2u + 1)
2
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
, c
11
(u
2
− u + 1)
3
c
8
, c
9
u
6
+ 2u
5
+ 7u
4
− 8u
3
+ 7u
2
− 3u + 1
c
10
(u
2
+ u + 1)
3
c
12
u
6
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
(y
3
− 5y
2
+ 10y −1)
2
c
7
, c
10
, c
11
(y
2
+ y + 1)
3
c
8
, c
9
y
6
+ 10y
5
+ 95y
4
+ 48y
3
+ 15y
2
+ 5y + 1
c
12
y
6
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.159960 − 0.102142I
b = −0.215080 − 1.307140I
3.02413 − 4.85801I 2.26089 + 13.10391I
u = 0.500000 + 0.866025I
a = 1.104070 + 0.474671I
b = −0.215080 + 1.307140I
3.02413 + 0.79824I −13.76355 − 1.90324I
u = 0.500000 + 0.866025I
a = −7.44411 + 0.49350I
b = −0.569840
−1.11345 − 2.02988I −55.9973 − 74.4205I
u = 0.500000 − 0.866025I
a = −1.159960 + 0.102142I
b = −0.215080 + 1.307140I
3.02413 + 4.85801I 2.26089 − 13.10391I
u = 0.500000 − 0.866025I
a = 1.104070 − 0.474671I
b = −0.215080 − 1.307140I
3.02413 − 0.79824I −13.76355 + 1.90324I
u = 0.500000 − 0.866025I
a = −7.44411 − 0.49350I
b = −0.569840
−1.11345 + 2.02988I −55.9973 + 74.4205I
19
IV. I
u
4
= hb, −u
3
− u
2
+ a − 2u − 1, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
u
3
+ u
2
+ 2u + 1
0
a
8
=
1
u
2
a
6
=
1
0
a
10
=
u
u
3
+ u
a
12
=
u
3
u
5
+ u
3
+ u
a
5
=
u
4
+ u
2
+ u + 1
−2u
5
− u
4
− 3u
3
− 2u
2
− 3u − 2
a
2
=
−u
4
+ u
3
+ u
2u
5
+ u
4
+ 3u
3
+ 2u
2
+ 3u + 2
a
4
=
u
3
+ u
2
+ 2u + 1
0
a
9
=
−u
3
u
3
+ u
a
1
=
−u
4
− u
2
− u − 1
2u
5
+ u
4
+ 3u
3
+ 2u
2
+ 3u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
5
+ u
4
+ 8u
3
+ 2u
2
+ 5u − 8
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
6
u
6
c
4
(u + 1)
6
c
5
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
7
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
8
, c
10
, c
12
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
9
(u
3
− u
2
+ 1)
2
c
11
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
6
y
6
c
5
, c
11
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
7
, c
8
, c
10
c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
9
(y
3
− y
2
+ 2y −1)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498832 + 1.001300I
a = −0.13238 + 2.74513I
b = 0
−1.37919 − 2.82812I −17.1597 + 2.2654I
u = 0.498832 − 1.001300I
a = −0.13238 − 2.74513I
b = 0
−1.37919 + 2.82812I −17.1597 − 2.2654I
u = −0.284920 + 1.115140I
a = 0.307599 + 0.479689I
b = 0
2.75839 −4.40089 − 2.50363I
u = −0.284920 − 1.115140I
a = 0.307599 − 0.479689I
b = 0
2.75839 −4.40089 + 2.50363I
u = −0.713912 + 0.305839I
a = −0.175218 + 0.614017I
b = 0
−1.37919 − 2.82812I −11.93937 + 4.05868I
u = −0.713912 − 0.305839I
a = −0.175218 − 0.614017I
b = 0
−1.37919 + 2.82812I −11.93937 − 4.05868I
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
3
− u
2
+ 2u − 1)
2
(u
62
+ 71u
61
+ ··· + 267u + 1)
c
2
((u − 1)
10
)(u
3
+ u
2
− 1)
2
(u
62
− 13u
61
+ ··· + 15u − 1)
c
3
u
10
(u
3
− u
2
+ 2u − 1)
2
(u
62
+ 3u
61
+ ··· − 8192u − 1024)
c
4
((u + 1)
10
)(u
3
− u
2
+ 1)
2
(u
62
− 13u
61
+ ··· + 15u − 1)
c
5
((u
3
− 3u
2
+ 2u + 1)
2
)(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ ··· + 2u
3
+ 1)
· (u
62
+ 4u
61
+ ··· − 10u
2
+ 1)
c
6
u
10
(u
3
+ u
2
+ 2u + 1)
2
(u
62
+ 3u
61
+ ··· − 8192u − 1024)
c
7
(u
2
− u + 1)
3
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
62
− 5u
61
+ ··· + 113u + 1)
c
8
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
6
+ 2u
5
+ 7u
4
− 8u
3
+ 7u
2
− 3u + 1)
· (u
62
+ 4u
61
+ ··· − 3025807u + 537503)
c
9
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
6
+ 2u
5
+ ··· − 3u + 1)(u
62
+ 44u
60
+ ··· + 9664u + 824)
c
10
(u
2
+ u + 1)
3
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
62
− 5u
61
+ ··· + 113u + 1)
c
11
(u
2
− u + 1)
3
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
62
− 21u
61
+ ··· + 12769u + 1)
c
12
u
6
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
62
− 6u
61
+ ··· − 1248u + 64)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
10
)(y
3
+ 3y
2
+ 2y −1)
2
(y
62
− 147y
61
+ ··· − 20183y + 1)
c
2
, c
4
((y −1)
10
)(y
3
− y
2
+ 2y −1)
2
(y
62
− 71y
61
+ ··· − 267y + 1)
c
3
, c
6
y
10
(y
3
+ 3y
2
+ 2y −1)
2
(y
62
− 57y
61
+ ··· + 9961472y + 1048576)
c
5
(y
3
− 5y
2
+ 10y −1)
2
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
· (y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)(y
62
− 4y
61
+ ··· − 20y + 1)
c
7
, c
10
(y
2
+ y + 1)
3
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
62
+ 21y
61
+ ··· − 12769y + 1)
c
8
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
6
+ 10y
5
+ 95y
4
+ 48y
3
+ 15y
2
+ 5y + 1)
· (y
62
+ 16y
61
+ ··· − 11200434939731y + 288909475009)
c
9
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
6
+ 10y
5
+ 95y
4
+ 48y
3
+ 15y
2
+ 5y + 1)
· (y
62
+ 88y
61
+ ··· + 13013520y + 678976)
c
11
((y
2
+ y + 1)
3
)(y
4
+ 2y
3
+ ··· + 5y + 1)(y
6
− y
5
+ ··· + 8y
2
+ 1)
· (y
62
+ 45y
61
+ ··· − 163345321y + 1)
c
12
y
6
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
62
− 30y
61
+ ··· − 185344y + 4096)
25
