11a
129
(K11a
129
)
A knot diagram
1
Linearized knot diagam
6 1 10 11 2 9 3 5 7 4 8
Solving Sequence
3,10
4 11
5,8
1 2 7 9 6
c
3
c
10
c
4
c
11
c
2
c
7
c
9
c
6
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h3.90365 × 10
58
u
58
+ 1.01441 × 10
59
u
57
+ ··· + 8.38498 × 10
58
b − 3.01985 × 10
57
,
7.15963 × 10
59
u
58
+ 1.21631 × 10
60
u
57
+ ··· + 9.22348 × 10
59
a − 2.03520 × 10
59
, u
59
+ 2u
58
+ ··· + 5u
2
− 1i
I
u
2
= h4u
2
+ 7b + 2u − 1, 3u
2
+ 7a + 5u + 1, u
3
+ u
2
− 1i
* 2 irreducible components of dim
C
= 0, with total 62 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
=
h3.90×10
58
u
58
+1.01×10
59
u
57
+· · ·+8.38×10
58
b−3.02×10
57
, 7.16×10
59
u
58
+
1.22 × 10
60
u
57
+ · · · + 9.22 × 10
59
a − 2.04 × 10
59
, u
59
+ 2u
58
+ · · · + 5u
2
− 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
11
=
u
−u
3
+ u
a
5
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
−0.776240u
58
− 1.31871u
57
+ ··· − 5.39605u + 0.220655
−0.465552u
58
− 1.20979u
57
+ ··· − 0.0812092u + 0.0360150
a
1
=
0.239979u
58
+ 0.405379u
57
+ ··· − 1.25169u − 0.147253
−0.137513u
58
− 0.253368u
57
+ ··· − 1.66158u + 0.0969722
a
2
=
0.166747u
58
+ 0.266603u
57
+ ··· + 0.146341u + 0.989129
−0.000963728u
58
− 0.0132996u
57
+ ··· + 0.189286u − 0.00637696
a
7
=
−1.24179u
58
− 2.52850u
57
+ ··· − 5.47726u + 0.256670
−0.465552u
58
− 1.20979u
57
+ ··· − 0.0812092u + 0.0360150
a
9
=
−1.16012u
58
− 2.33933u
57
+ ··· − 5.42935u + 0.193474
−0.485917u
58
− 1.19021u
57
+ ··· + 1.07906u + 0.0222353
a
6
=
−0.225910u
58
− 0.512221u
57
+ ··· − 0.169913u + 0.169646
0.0153499u
58
− 0.101739u
57
+ ··· − 1.19569u + 0.0827941
a
6
=
−0.225910u
58
− 0.512221u
57
+ ··· − 0.169913u + 0.169646
0.0153499u
58
− 0.101739u
57
+ ··· − 1.19569u + 0.0827941
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.22898u
58
− 6.33023u
57
+ ··· − 0.906990u + 1.85953
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
59
− 2u
58
+ ··· − 4u + 1
c
2
u
59
+ 24u
58
+ ··· + 10u − 1
c
3
, c
4
, c
10
u
59
− 2u
58
+ ··· − 5u
2
+ 1
c
6
, c
9
u
59
+ 4u
58
+ ··· − 257u + 49
c
7
7(7u
59
− 22u
58
+ ··· − 126239u + 81841)
c
8
7(7u
59
− 6u
58
+ ··· + 6234u + 1903)
c
11
u
59
+ 5u
58
+ ··· − 868u + 392
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
59
+ 24y
58
+ ··· + 10y − 1
c
2
y
59
+ 24y
58
+ ··· + 462y − 1
c
3
, c
4
, c
10
y
59
− 60y
58
+ ··· + 10y − 1
c
6
, c
9
y
59
− 50y
58
+ ··· + 74183y − 2401
c
7
49(49y
59
+ 3394y
58
+ ··· − 9.08304 × 10
10
y − 6.69795 × 10
9
)
c
8
49(49y
59
− 64y
58
+ ··· + 2.29562 × 10
8
y − 3621409)
c
11
y
59
+ 21y
58
+ ··· − 2147376y − 153664
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.622068 + 0.787958I
a = 0.481268 + 0.468907I
b = 0.71713 − 1.28444I
4.44674 + 11.62550I 0
u = 0.622068 − 0.787958I
a = 0.481268 − 0.468907I
b = 0.71713 + 1.28444I
4.44674 − 11.62550I 0
u = 0.506194 + 0.887762I
a = 0.672945 − 0.231781I
b = −0.249130 − 0.995558I
4.02435 − 6.11409I 0
u = 0.506194 − 0.887762I
a = 0.672945 + 0.231781I
b = −0.249130 + 0.995558I
4.02435 + 6.11409I 0
u = 0.857653 + 0.464032I
a = −0.033575 + 0.146733I
b = 0.707909 − 0.257892I
−1.83113 + 3.37489I 0. − 6.31964I
u = 0.857653 − 0.464032I
a = −0.033575 − 0.146733I
b = 0.707909 + 0.257892I
−1.83113 − 3.37489I 0. + 6.31964I
u = −0.627541 + 0.812622I
a = −0.518848 + 0.363833I
b = −0.548211 − 1.240870I
6.17346 − 5.56581I 0
u = −0.627541 − 0.812622I
a = −0.518848 − 0.363833I
b = −0.548211 + 1.240870I
6.17346 + 5.56581I 0
u = −0.970195
a = 0.167848
b = −0.593313
1.61678 5.00000
u = −0.555862 + 0.900899I
a = −0.619428 − 0.061218I
b = 0.036940 − 1.051180I
5.85876 − 0.11889I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.555862 − 0.900899I
a = −0.619428 + 0.061218I
b = 0.036940 + 1.051180I
5.85876 + 0.11889I 0
u = 0.741521 + 0.922413I
a = 0.318033 + 0.111847I
b = 0.354088 − 0.782867I
−1.23742 + 3.26694I 0
u = 0.741521 − 0.922413I
a = 0.318033 − 0.111847I
b = 0.354088 + 0.782867I
−1.23742 − 3.26694I 0
u = 0.444629 + 0.510368I
a = −0.46434 − 1.56907I
b = −0.808317 + 0.689154I
−0.33205 + 6.44214I 4.62600 − 9.28024I
u = 0.444629 − 0.510368I
a = −0.46434 + 1.56907I
b = −0.808317 − 0.689154I
−0.33205 − 6.44214I 4.62600 + 9.28024I
u = 0.313615 + 0.597705I
a = −0.041562 − 1.003380I
b = −0.545415 + 0.167871I
−3.28171 + 0.39501I −2.00061 − 1.54672I
u = 0.313615 − 0.597705I
a = −0.041562 + 1.003380I
b = −0.545415 − 0.167871I
−3.28171 − 0.39501I −2.00061 + 1.54672I
u = −0.418675 + 0.447852I
a = 0.77452 − 1.30125I
b = 0.552817 + 0.774161I
0.92823 − 1.58622I 7.27802 + 5.02607I
u = −0.418675 − 0.447852I
a = 0.77452 + 1.30125I
b = 0.552817 − 0.774161I
0.92823 + 1.58622I 7.27802 − 5.02607I
u = −0.556478 + 0.207218I
a = 2.56199 − 0.99726I
b = −0.135387 + 0.940443I
3.71804 − 4.17211I 12.3249 + 7.4178I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.556478 − 0.207218I
a = 2.56199 + 0.99726I
b = −0.135387 − 0.940443I
3.71804 + 4.17211I 12.3249 − 7.4178I
u = 0.559723 + 0.140117I
a = −2.77388 − 0.66591I
b = 0.244493 + 0.672850I
4.05953 − 0.76565I 13.67462 − 0.08522I
u = 0.559723 − 0.140117I
a = −2.77388 + 0.66591I
b = 0.244493 − 0.672850I
4.05953 + 0.76565I 13.67462 + 0.08522I
u = 0.423114 + 0.391843I
a = −0.472532 + 0.185081I
b = 0.957559 + 0.540672I
−0.25044 − 3.21979I 3.90025 + 0.90131I
u = 0.423114 − 0.391843I
a = −0.472532 − 0.185081I
b = 0.957559 − 0.540672I
−0.25044 + 3.21979I 3.90025 − 0.90131I
u = −1.42183 + 0.07250I
a = 1.57296 − 1.41800I
b = −1.32202 + 1.36648I
5.48223 + 1.81992I 0
u = −1.42183 − 0.07250I
a = 1.57296 + 1.41800I
b = −1.32202 − 1.36648I
5.48223 − 1.81992I 0
u = 1.44289 + 0.04366I
a = 0.12384 − 3.55457I
b = −0.75861 + 3.44954I
6.34398 + 2.28663I 0
u = 1.44289 − 0.04366I
a = 0.12384 + 3.55457I
b = −0.75861 − 3.44954I
6.34398 − 2.28663I 0
u = −1.44268 + 0.15844I
a = −0.095089 − 1.313110I
b = 0.121163 + 0.706508I
2.38922 − 3.00723I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44268 − 0.15844I
a = −0.095089 + 1.313110I
b = 0.121163 − 0.706508I
2.38922 + 3.00723I 0
u = 1.45554 + 0.08236I
a = −0.41802 − 2.00373I
b = −0.05710 + 1.65402I
6.50215 + 2.38989I 0
u = 1.45554 − 0.08236I
a = −0.41802 + 2.00373I
b = −0.05710 − 1.65402I
6.50215 − 2.38989I 0
u = −1.48770
a = −0.815446
b = 1.74556
8.30655 0
u = 1.49253 + 0.12922I
a = 0.04923 − 1.94060I
b = −0.422930 + 1.117500I
7.23997 + 3.63562I 0
u = 1.49253 − 0.12922I
a = 0.04923 + 1.94060I
b = −0.422930 − 1.117500I
7.23997 − 3.63562I 0
u = −1.49781 + 0.14706I
a = −0.27642 − 1.94523I
b = 0.530534 + 1.009310I
6.06759 − 8.77463I 0
u = −1.49781 − 0.14706I
a = −0.27642 + 1.94523I
b = 0.530534 − 1.009310I
6.06759 + 8.77463I 0
u = −1.52791 + 0.03503I
a = 0.720143 − 1.079900I
b = 0.482971 + 0.730580I
11.01860 + 0.16153I 0
u = −1.52791 − 0.03503I
a = 0.720143 + 1.079900I
b = 0.482971 − 0.730580I
11.01860 − 0.16153I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52787 + 0.04986I
a = −0.71061 − 1.45487I
b = −0.434084 + 0.962095I
10.66650 + 5.04841I 0
u = 1.52787 − 0.04986I
a = −0.71061 + 1.45487I
b = −0.434084 − 0.962095I
10.66650 − 5.04841I 0
u = −0.304004 + 0.352318I
a = 0.725827 + 0.031622I
b = −0.401580 + 1.001260I
0.818669 − 1.086870I 6.95263 + 5.92982I
u = −0.304004 − 0.352318I
a = 0.725827 − 0.031622I
b = −0.401580 − 1.001260I
0.818669 + 1.086870I 6.95263 − 5.92982I
u = −0.336012 + 0.317334I
a = 1.151780 − 0.392616I
b = 0.165774 + 0.934262I
0.674447 − 1.055540I 6.88917 + 6.16079I
u = −0.336012 − 0.317334I
a = 1.151780 + 0.392616I
b = 0.165774 − 0.934262I
0.674447 + 1.055540I 6.88917 − 6.16079I
u = −1.57375 + 0.26330I
a = −0.02665 + 1.87772I
b = −0.97014 − 1.69830I
11.6590 − 15.5089I 0
u = −1.57375 − 0.26330I
a = −0.02665 − 1.87772I
b = −0.97014 + 1.69830I
11.6590 + 15.5089I 0
u = 1.57863 + 0.26847I
a = 0.12971 + 1.73446I
b = 0.85618 − 1.61480I
13.4212 + 9.5497I 0
u = 1.57863 − 0.26847I
a = 0.12971 − 1.73446I
b = 0.85618 + 1.61480I
13.4212 − 9.5497I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59529 + 0.29735I
a = 0.350459 + 1.145760I
b = 0.534635 − 1.221130I
12.98450 + 4.58039I 0
u = 1.59529 − 0.29735I
a = 0.350459 − 1.145760I
b = 0.534635 + 1.221130I
12.98450 − 4.58039I 0
u = −1.60262 + 0.26158I
a = 0.106004 + 1.357480I
b = −0.94318 − 1.26607I
6.48770 − 7.42956I 0
u = −1.60262 − 0.26158I
a = 0.106004 − 1.357480I
b = −0.94318 + 1.26607I
6.48770 + 7.42956I 0
u = −1.59529 + 0.32218I
a = −0.428036 + 0.868477I
b = −0.397894 − 1.029760I
10.90240 + 1.52833I 0
u = −1.59529 − 0.32218I
a = −0.428036 − 0.868477I
b = −0.397894 + 1.029760I
10.90240 − 1.52833I 0
u = −0.046856 + 0.362935I
a = 0.240879 + 0.681944I
b = −0.04832 + 2.41526I
2.15381 + 2.27881I −7.94357 + 3.32360I
u = −0.046856 − 0.362935I
a = 0.240879 − 0.681944I
b = −0.04832 − 2.41526I
2.15381 − 2.27881I −7.94357 − 3.32360I
u = 0.349995
a = −2.41073
b = −0.734856
2.11871 0.678540
10
II. I
u
2
= h4u
2
+ 7b + 2u − 1, 3u
2
+ 7a + 5u + 1, u
3
+ u
2
− 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
11
=
u
u
2
+ u − 1
a
5
=
−u
2
+ 1
−u
2
+ u − 1
a
8
=
−
3
7
u
2
−
5
7
u −
1
7
−
4
7
u
2
−
2
7
u +
1
7
a
1
=
u
u
2
+ u − 1
a
2
=
u
2u
2
+ u − 2
a
7
=
−u
2
− u
−
4
7
u
2
−
2
7
u +
1
7
a
9
=
−u
2
− u
−
4
7
u
2
+
5
7
u +
1
7
a
6
=
0
−u
a
6
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
313
49
u
2
+
188
49
u +
424
49
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ u
2
+ 2u + 1
c
2
u
3
+ 3u
2
+ 2u − 1
c
3
, c
4
u
3
+ u
2
− 1
c
5
u
3
− u
2
+ 2u − 1
c
6
(u + 1)
3
c
7
7(7u
3
+ u
2
+ u − 1)
c
8
7(7u
3
− u
2
− 4u − 1)
c
9
(u − 1)
3
c
10
u
3
− u
2
+ 1
c
11
u
3
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
3
+ 3y
2
+ 2y − 1
c
2
y
3
− 5y
2
+ 10y − 1
c
3
, c
4
, c
10
y
3
− y
2
+ 2y − 1
c
6
, c
9
(y − 1)
3
c
7
49(49y
3
+ 13y
2
+ 3y − 1)
c
8
49(49y
3
− 57y
2
+ 14y − 1)
c
11
y
3
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0.391708 + 0.028159I
b = 0.270651 + 0.534120I
−1.37919 − 2.82812I 6.66044 − 5.49186I
u = −0.877439 − 0.744862I
a = 0.391708 − 0.028159I
b = 0.270651 − 0.534120I
−1.37919 + 2.82812I 6.66044 + 5.49186I
u = 0.754878
a = −0.926273
b = −0.398445
2.75839 15.1890
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
+ 2u + 1)(u
59
− 2u
58
+ ··· − 4u + 1)
c
2
(u
3
+ 3u
2
+ 2u − 1)(u
59
+ 24u
58
+ ··· + 10u − 1)
c
3
, c
4
(u
3
+ u
2
− 1)(u
59
− 2u
58
+ ··· − 5u
2
+ 1)
c
5
(u
3
− u
2
+ 2u − 1)(u
59
− 2u
58
+ ··· − 4u + 1)
c
6
((u + 1)
3
)(u
59
+ 4u
58
+ ··· − 257u + 49)
c
7
49(7u
3
+ u
2
+ u − 1)(7u
59
− 22u
58
+ ··· − 126239u + 81841)
c
8
49(7u
3
− u
2
− 4u − 1)(7u
59
− 6u
58
+ ··· + 6234u + 1903)
c
9
((u − 1)
3
)(u
59
+ 4u
58
+ ··· − 257u + 49)
c
10
(u
3
− u
2
+ 1)(u
59
− 2u
58
+ ··· − 5u
2
+ 1)
c
11
u
3
(u
59
+ 5u
58
+ ··· − 868u + 392)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
3
+ 3y
2
+ 2y − 1)(y
59
+ 24y
58
+ ··· + 10y − 1)
c
2
(y
3
− 5y
2
+ 10y − 1)(y
59
+ 24y
58
+ ··· + 462y − 1)
c
3
, c
4
, c
10
(y
3
− y
2
+ 2y − 1)(y
59
− 60y
58
+ ··· + 10y − 1)
c
6
, c
9
((y − 1)
3
)(y
59
− 50y
58
+ ··· + 74183y − 2401)
c
7
2401(49y
3
+ 13y
2
+ 3y − 1)
· (49y
59
+ 3394y
58
+ ··· − 90830373521y − 6697949281)
c
8
2401(49y
3
− 57y
2
+ 14y − 1)
· (49y
59
− 64y
58
+ ··· + 229562386y − 3621409)
c
11
y
3
(y
59
+ 21y
58
+ ··· − 2147376y − 153664)
16
