11a
143
(K11a
143
)
A knot diagram
1
Linearized knot diagam
6 1 10 9 2 5 11 3 4 7 8
Solving Sequence
7,10
11 8
1,4
3 2 9 5 6
c
10
c
7
c
11
c
3
c
2
c
9
c
4
c
6
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h3.31268 × 10
32
u
49
− 5.56961 × 10
32
u
48
+ ··· + 3.84136 × 10
32
b + 1.21137 × 10
33
,
− 1.01160 × 10
33
u
49
− 2.15416 × 10
33
u
48
+ ··· + 4.60963 × 10
33
a + 6.11980 × 10
33
,
u
50
− 3u
49
+ ··· − 14u − 3i
I
u
2
= h−2a
3
+ 3a
2
+ 5b − 15a + 7, a
4
− 2a
3
+ 7a
2
− 6a + 3, u + 1i
I
u
3
= hb, a
2
− a + 1, u − 1i
* 3 irreducible components of dim
C
= 0, with total 56 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
= h3.31 × 10
32
u
49
− 5.57 × 10
32
u
48
+ · · · + 3.84 × 10
32
b + 1.21 ×
10
33
, −1.01 × 10
33
u
49
− 2.15 × 10
33
u
48
+ · · · + 4.61 × 10
33
a + 6.12 ×
10
33
, u
50
− 3u
49
+ · · · − 14u − 3i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
8
=
u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
4
=
0.219454u
49
+ 0.467318u
48
+ ··· + 9.86130u − 1.32761
−0.862372u
49
+ 1.44991u
48
+ ··· − 16.7135u − 3.15351
a
3
=
1.08183u
49
− 0.982587u
48
+ ··· + 26.5748u + 1.82589
−0.862372u
49
+ 1.44991u
48
+ ··· − 16.7135u − 3.15351
a
2
=
0.247278u
49
+ 0.359922u
48
+ ··· + 11.7803u − 0.445043
−0.895841u
49
+ 1.30207u
48
+ ··· − 19.0363u − 3.62861
a
9
=
−0.694954u
49
+ 1.84791u
48
+ ··· + 28.4151u + 4.77905
0.141172u
49
− 0.0191976u
48
+ ··· + 5.14402u − 0.584566
a
5
=
−0.562523u
49
+ 0.817800u
48
+ ··· − 8.66416u + 1.58746
0.649198u
49
− 0.790264u
48
+ ··· + 15.0431u + 2.83582
a
6
=
−0.152066u
49
+ 0.970436u
48
+ ··· + 28.0155u + 3.66927
−0.384959u
49
+ 0.691554u
48
+ ··· − 5.39208u − 2.02124
a
6
=
−0.152066u
49
+ 0.970436u
48
+ ··· + 28.0155u + 3.66927
−0.384959u
49
+ 0.691554u
48
+ ··· − 5.39208u − 2.02124
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.874649u
49
+ 2.02419u
48
+ ··· + 4.43493u + 1.54316
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
50
− 2u
49
+ ··· − 3u + 3
c
2
, c
6
u
50
+ 16u
49
+ ··· − 39u + 9
c
3
, c
4
, c
9
u
50
− u
49
+ ··· + 16u − 4
c
7
, c
10
, c
11
u
50
− 3u
49
+ ··· − 14u − 3
c
8
u
50
+ u
49
+ ··· + 928u − 404
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
50
+ 16y
49
+ ··· − 39y + 9
c
2
, c
6
y
50
+ 40y
49
+ ··· − 11439y + 81
c
3
, c
4
, c
9
y
50
+ 45y
49
+ ··· − 480y
2
+ 16
c
7
, c
10
, c
11
y
50
− 49y
49
+ ··· + 68y + 9
c
8
y
50
− 15y
49
+ ··· + 470400y + 163216
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.768044 + 0.620254I
a = 0.51382 + 1.55754I
b = 0.223518 + 1.133800I
0.52020 − 1.74042I 8.32117 + 2.63326I
u = −0.768044 − 0.620254I
a = 0.51382 − 1.55754I
b = 0.223518 − 1.133800I
0.52020 + 1.74042I 8.32117 − 2.63326I
u = −0.357982 + 0.888739I
a = −0.66589 − 2.42275I
b = 0.310740 − 1.355660I
−1.38805 − 9.13876I 5.39526 + 7.47528I
u = −0.357982 − 0.888739I
a = −0.66589 + 2.42275I
b = 0.310740 + 1.355660I
−1.38805 + 9.13876I 5.39526 − 7.47528I
u = −0.419643 + 0.836664I
a = 0.70010 + 2.28634I
b = −0.299889 + 1.309250I
−0.58057 − 3.35428I 6.95050 + 2.72855I
u = −0.419643 − 0.836664I
a = 0.70010 − 2.28634I
b = −0.299889 − 1.309250I
−0.58057 + 3.35428I 6.95050 − 2.72855I
u = −0.875258 + 0.621898I
a = −0.48983 − 1.56500I
b = −0.261961 − 1.228410I
0.20741 + 3.87448I 7.86992 − 3.23394I
u = −0.875258 − 0.621898I
a = −0.48983 + 1.56500I
b = −0.261961 + 1.228410I
0.20741 − 3.87448I 7.86992 + 3.23394I
u = 0.600873 + 0.702881I
a = −0.263588 − 0.464164I
b = −0.718050 − 0.066541I
3.72925 − 0.33634I 12.06779 − 0.57902I
u = 0.600873 − 0.702881I
a = −0.263588 + 0.464164I
b = −0.718050 + 0.066541I
3.72925 + 0.33634I 12.06779 + 0.57902I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.494891 + 0.774626I
a = 0.302543 + 0.581565I
b = 0.737047 + 0.149487I
3.36565 + 5.33408I 10.62323 − 6.45202I
u = 0.494891 − 0.774626I
a = 0.302543 − 0.581565I
b = 0.737047 − 0.149487I
3.36565 − 5.33408I 10.62323 + 6.45202I
u = −1.065360 + 0.257655I
a = −0.23062 − 1.52209I
b = −0.10488 − 1.42170I
−4.48476 + 0.36744I 2.34065 + 0.74088I
u = −1.065360 − 0.257655I
a = −0.23062 + 1.52209I
b = −0.10488 + 1.42170I
−4.48476 − 0.36744I 2.34065 − 0.74088I
u = 1.100360 + 0.172393I
a = −0.0409123 + 0.0182444I
b = −0.313724 + 0.372597I
1.27025 + 1.19184I 7.00000 + 2.50368I
u = 1.100360 − 0.172393I
a = −0.0409123 − 0.0182444I
b = −0.313724 − 0.372597I
1.27025 − 1.19184I 7.00000 − 2.50368I
u = −0.207647 + 0.672129I
a = −1.26448 − 2.57161I
b = 0.182493 − 1.383300I
−6.96148 − 3.84491I −1.20333 + 4.74598I
u = −0.207647 − 0.672129I
a = −1.26448 + 2.57161I
b = 0.182493 + 1.383300I
−6.96148 + 3.84491I −1.20333 − 4.74598I
u = −1.349830 + 0.119644I
a = 0.951187 + 0.404966I
b = −0.680112 + 0.135570I
2.86347 − 3.60406I 0
u = −1.349830 − 0.119644I
a = 0.951187 − 0.404966I
b = −0.680112 − 0.135570I
2.86347 + 3.60406I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.419371 + 0.489432I
a = 1.23676 + 1.66984I
b = −0.103698 + 1.289300I
−3.33666 − 1.69681I 6.02735 + 3.86873I
u = −0.419371 − 0.489432I
a = 1.23676 − 1.66984I
b = −0.103698 − 1.289300I
−3.33666 + 1.69681I 6.02735 − 3.86873I
u = 1.352170 + 0.098819I
a = 1.161170 + 0.144436I
b = −0.211969 − 1.214280I
−0.313966 − 0.436878I 0
u = 1.352170 − 0.098819I
a = 1.161170 − 0.144436I
b = −0.211969 + 1.214280I
−0.313966 + 0.436878I 0
u = −1.356110 + 0.045936I
a = −0.03253 − 1.71582I
b = −0.02262 − 1.56889I
−0.83159 − 2.75739I 0
u = −1.356110 − 0.045936I
a = −0.03253 + 1.71582I
b = −0.02262 + 1.56889I
−0.83159 + 2.75739I 0
u = 1.391060 + 0.243928I
a = 1.57875 − 0.80925I
b = −0.287890 − 1.351540I
−1.84682 + 7.14521I 0
u = 1.391060 − 0.243928I
a = 1.57875 + 0.80925I
b = −0.287890 + 1.351540I
−1.84682 − 7.14521I 0
u = −1.43839
a = −0.748101
b = 0.770058
6.46721 0
u = 1.43734 + 0.14823I
a = −1.093440 + 0.493494I
b = 0.323552 + 1.255700I
2.58460 + 3.94905I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43734 − 0.14823I
a = −1.093440 − 0.493494I
b = 0.323552 − 1.255700I
2.58460 − 3.94905I 0
u = −0.513376 + 0.156185I
a = 0.12350 + 1.97974I
b = 0.024574 + 0.485591I
0.74464 − 2.36364I 3.62478 + 4.11961I
u = −0.513376 − 0.156185I
a = 0.12350 − 1.97974I
b = 0.024574 − 0.485591I
0.74464 + 2.36364I 3.62478 − 4.11961I
u = 0.099189 + 0.524649I
a = −0.042705 + 1.015670I
b = 0.469409 + 0.309538I
−1.63114 + 1.42356I 2.31879 − 5.63109I
u = 0.099189 − 0.524649I
a = −0.042705 − 1.015670I
b = 0.469409 − 0.309538I
−1.63114 − 1.42356I 2.31879 + 5.63109I
u = 1.48543 + 0.34428I
a = 1.24716 − 1.34114I
b = −0.36507 − 1.42866I
4.5437 + 13.6084I 0
u = 1.48543 − 0.34428I
a = 1.24716 + 1.34114I
b = −0.36507 + 1.42866I
4.5437 − 13.6084I 0
u = 1.51636 + 0.16091I
a = 0.098166 + 0.420372I
b = −0.558023 + 0.923611I
7.88001 + 4.14120I 0
u = 1.51636 − 0.16091I
a = 0.098166 − 0.420372I
b = −0.558023 − 0.923611I
7.88001 − 4.14120I 0
u = 1.50169 + 0.30522I
a = −1.16719 + 1.21068I
b = 0.37957 + 1.39957I
5.64838 + 7.50037I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50169 − 0.30522I
a = −1.16719 − 1.21068I
b = 0.37957 − 1.39957I
5.64838 − 7.50037I 0
u = 1.53335 + 0.09779I
a = −0.209409 − 0.465882I
b = 0.526883 − 0.998341I
8.31731 − 1.99153I 0
u = 1.53335 − 0.09779I
a = −0.209409 + 0.465882I
b = 0.526883 + 0.998341I
8.31731 + 1.99153I 0
u = −1.51832 + 0.26912I
a = 0.407229 + 0.580854I
b = −0.874042 + 0.265626I
9.92580 − 9.13602I 0
u = −1.51832 − 0.26912I
a = 0.407229 − 0.580854I
b = −0.874042 − 0.265626I
9.92580 + 9.13602I 0
u = −1.53487 + 0.21619I
a = −0.418285 − 0.467881I
b = 0.882710 − 0.212600I
10.74210 − 2.95976I 0
u = −1.53487 − 0.21619I
a = −0.418285 + 0.467881I
b = 0.882710 + 0.212600I
10.74210 + 2.95976I 0
u = 0.377548
a = 0.538429
b = −0.387989
0.630546 15.8700
u = −0.096486 + 0.258092I
a = −4.46333 − 1.70481I
b = 0.050400 − 1.397800I
−5.03824 + 1.88230I −0.03756 − 2.83434I
u = −0.096486 − 0.258092I
a = −4.46333 + 1.70481I
b = 0.050400 + 1.397800I
−5.03824 − 1.88230I −0.03756 + 2.83434I
9
II. I
u
2
= h−2a
3
+ 3a
2
+ 5b − 15a + 7, a
4
− 2a
3
+ 7a
2
− 6a + 3, u + 1i
(i) Arc colorings
a
7
=
0
−1
a
10
=
1
0
a
11
=
1
−1
a
8
=
−1
0
a
1
=
0
−1
a
4
=
a
2
5
a
3
−
3
5
a
2
+ 3a −
7
5
a
3
=
−
2
5
a
3
+
3
5
a
2
− 2a +
7
5
2
5
a
3
−
3
5
a
2
+ 3a −
7
5
a
2
=
−
2
5
a
3
+
3
5
a
2
− 2a +
7
5
4
5
a
3
−
6
5
a
2
+ 5a −
14
5
a
9
=
1
5
a
3
+
1
5
a
2
+ a −
1
5
−2
a
5
=
2
5
a
3
−
3
5
a
2
+ 2a −
7
5
−
2
5
a
3
+
3
5
a
2
− 3a +
7
5
a
6
=
2
5
a
3
−
3
5
a
2
+ 2a −
2
5
−
1
5
a
3
−
1
5
a
2
− a −
9
5
a
6
=
2
5
a
3
−
3
5
a
2
+ 2a −
2
5
−
1
5
a
3
−
1
5
a
2
− a −
9
5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
8
5
a
3
+
12
5
a
2
− 8a +
48
5
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
2
c
2
, c
5
, c
6
(u
2
+ u + 1)
2
c
3
, c
4
, c
8
c
9
(u
2
+ 2)
2
c
7
(u − 1)
4
c
10
, c
11
(u + 1)
4
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
(y
2
+ y + 1)
2
c
3
, c
4
, c
8
c
9
(y + 2)
4
c
7
, c
10
, c
11
(y −1)
4
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.500000 + 0.548188I
b = 1.414210I
−3.28987 + 2.02988I 6.00000 − 3.46410I
u = −1.00000
a = 0.500000 − 0.548188I
b = − 1.414210I
−3.28987 − 2.02988I 6.00000 + 3.46410I
u = −1.00000
a = 0.50000 + 2.28024I
b = 1.414210I
−3.28987 − 2.02988I 6.00000 + 3.46410I
u = −1.00000
a = 0.50000 − 2.28024I
b = − 1.414210I
−3.28987 + 2.02988I 6.00000 − 3.46410I
13
III. I
u
3
= hb, a
2
− a + 1, u − 1i
(i) Arc colorings
a
7
=
0
1
a
10
=
1
0
a
11
=
1
−1
a
8
=
1
0
a
1
=
0
−1
a
4
=
a
0
a
3
=
a
0
a
2
=
a
−a
a
9
=
1
0
a
5
=
a
0
a
6
=
a − 1
1
a
6
=
a − 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a + 10
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
2
+ u + 1
c
3
, c
4
, c
8
c
9
u
2
c
5
u
2
− u + 1
c
7
(u + 1)
2
c
10
, c
11
(u − 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
y
2
+ y + 1
c
3
, c
4
, c
8
c
9
y
2
c
7
, c
10
, c
11
(y −1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.500000 + 0.866025I
b = 0
1.64493 − 2.02988I 12.00000 + 3.46410I
u = 1.00000
a = 0.500000 − 0.866025I
b = 0
1.64493 + 2.02988I 12.00000 − 3.46410I
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
50
− 2u
49
+ ··· − 3u + 3)
c
2
, c
6
((u
2
+ u + 1)
3
)(u
50
+ 16u
49
+ ··· − 39u + 9)
c
3
, c
4
, c
9
u
2
(u
2
+ 2)
2
(u
50
− u
49
+ ··· + 16u − 4)
c
5
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
50
− 2u
49
+ ··· − 3u + 3)
c
7
((u − 1)
4
)(u + 1)
2
(u
50
− 3u
49
+ ··· − 14u − 3)
c
8
u
2
(u
2
+ 2)
2
(u
50
+ u
49
+ ··· + 928u − 404)
c
10
, c
11
((u − 1)
2
)(u + 1)
4
(u
50
− 3u
49
+ ··· − 14u − 3)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
2
+ y + 1)
3
)(y
50
+ 16y
49
+ ··· − 39y + 9)
c
2
, c
6
((y
2
+ y + 1)
3
)(y
50
+ 40y
49
+ ··· − 11439y + 81)
c
3
, c
4
, c
9
y
2
(y + 2)
4
(y
50
+ 45y
49
+ ··· − 480y
2
+ 16)
c
7
, c
10
, c
11
((y −1)
6
)(y
50
− 49y
49
+ ··· + 68y + 9)
c
8
y
2
(y + 2)
4
(y
50
− 15y
49
+ ··· + 470400y + 163216)
19
