11a
141
(K11a
141
)
A knot diagram
1
Linearized knot diagam
6 1 11 7 2 5 10 3 4 8 9
Solving Sequence
2,5
6 7 1 3
4,9
10 8 11
c
5
c
6
c
1
c
2
c
4
c
9
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h4.26487 × 10
16
u
52
− 5.40372 × 10
16
u
51
+ ··· + 1.36187 × 10
16
b + 1.03514 × 10
16
,
− 5.55636 × 10
16
u
52
− 1.64714 × 10
16
u
51
+ ··· + 4.08560 × 10
16
a + 3.29067 × 10
16
, u
53
− 2u
52
+ ··· + 5u − 1i
I
u
2
= hb − u, a + 1, u
2
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 55 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
= h4.26×10
16
u
52
−5.40×10
16
u
51
+· · ·+1.36×10
16
b+1.04×10
16
, −5.56×
10
16
u
52
−1.65×10
16
u
51
+· · ·+4.09×10
16
a+3.29×10
16
, u
53
−2u
52
+· · ·+5u−1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
7
=
u
2
+ 1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
4
=
u
4
+ u
2
+ 1
−u
4
a
9
=
1.35999u
52
+ 0.403157u
51
+ ··· + 12.2341u − 0.805431
−3.13164u
52
+ 3.96788u
51
+ ··· + 3.80587u − 0.760087
a
10
=
−0.239857u
52
+ 2.87394u
51
+ ··· + 17.1081u − 2.41707
−3.38916u
52
+ 5.76021u
51
+ ··· + 10.4571u − 2.36000
a
8
=
−0.240103u
52
+ 2.73675u
51
+ ··· + 17.6038u − 1.54783
−3.25991u
52
+ 5.55889u
51
+ ··· + 10.1878u − 2.35999
a
11
=
0.200023u
52
+ 0.0418941u
51
+ ··· + 1.97228u + 0.477613
−0.441941u
52
− 0.197074u
51
+ ··· + 0.522504u − 0.200023
a
11
=
0.200023u
52
+ 0.0418941u
51
+ ··· + 1.97228u + 0.477613
−0.441941u
52
− 0.197074u
51
+ ··· + 0.522504u − 0.200023
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
275359995103539017
13618658791677283
u
52
+
577412524426465435
13618658791677283
u
51
+ ··· +
1768558808672064537
13618658791677283
u −
316215934356851336
13618658791677283
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
53
− 2u
52
+ ··· + 5u − 1
c
2
, c
4
, c
6
u
53
+ 12u
52
+ ··· + u − 1
c
3
u
53
+ 4u
52
+ ··· + u + 1
c
7
, c
10
u
53
+ 3u
52
+ ··· + 8u − 1
c
8
u
53
+ 2u
52
+ ··· + 361u − 31
c
9
u
53
+ 10u
51
+ ··· − 4625u − 6737
c
11
u
53
− 9u
52
+ ··· − 4u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
53
+ 12y
52
+ ··· + y −1
c
2
, c
4
, c
6
y
53
+ 60y
52
+ ··· + 185y −1
c
3
y
53
− 8y
52
+ ··· + y −1
c
7
, c
10
y
53
− 43y
52
+ ··· − 84y −1
c
8
y
53
+ 68y
52
+ ··· + 28145y −961
c
9
y
53
+ 20y
52
+ ··· + 623516737y −45387169
c
11
y
53
+ 15y
52
+ ··· − 120y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.441064 + 0.891798I
a = −1.020870 − 0.571634I
b = 0.328536 + 0.775979I
−0.83694 − 5.74776I 0. + 9.66844I
u = −0.441064 − 0.891798I
a = −1.020870 + 0.571634I
b = 0.328536 − 0.775979I
−0.83694 + 5.74776I 0. − 9.66844I
u = 0.049379 + 1.054040I
a = −0.0434698 + 0.0967864I
b = −0.695181 − 0.606165I
0.26646 + 4.82522I 1.00000 − 6.65378I
u = 0.049379 − 1.054040I
a = −0.0434698 − 0.0967864I
b = −0.695181 + 0.606165I
0.26646 − 4.82522I 1.00000 + 6.65378I
u = 0.648943 + 0.852337I
a = 0.538490 + 0.498386I
b = −0.203229 − 0.464579I
0.64509 + 2.50411I −2.75636 − 4.40791I
u = 0.648943 − 0.852337I
a = 0.538490 − 0.498386I
b = −0.203229 + 0.464579I
0.64509 − 2.50411I −2.75636 + 4.40791I
u = −0.499123 + 0.779146I
a = −1.020240 − 0.640877I
b = −0.424147 − 0.588184I
3.37085 − 3.65736I 8.56973 + 8.26952I
u = −0.499123 − 0.779146I
a = −1.020240 + 0.640877I
b = −0.424147 + 0.588184I
3.37085 + 3.65736I 8.56973 − 8.26952I
u = 0.360123 + 0.813464I
a = −0.143330 + 0.781657I
b = 0.328335 − 0.649856I
−0.31212 + 1.82370I −0.23465 − 3.74406I
u = 0.360123 − 0.813464I
a = −0.143330 − 0.781657I
b = 0.328335 + 0.649856I
−0.31212 − 1.82370I −0.23465 + 3.74406I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498548 + 1.006320I
a = 0.884968 + 0.778679I
b = −0.520382 − 0.426991I
3.53599 − 10.89690I 0. + 9.33368I
u = −0.498548 − 1.006320I
a = 0.884968 − 0.778679I
b = −0.520382 + 0.426991I
3.53599 + 10.89690I 0. − 9.33368I
u = −0.058697 + 0.871659I
a = −0.154861 + 0.218927I
b = 0.703232 + 0.859606I
−2.88229 + 1.21772I −6.65956 − 1.75393I
u = −0.058697 − 0.871659I
a = −0.154861 − 0.218927I
b = 0.703232 − 0.859606I
−2.88229 − 1.21772I −6.65956 + 1.75393I
u = −0.779580 + 0.384102I
a = −1.185820 − 0.265108I
b = 0.590861 + 0.432097I
5.58297 + 6.26331I 7.90346 − 4.21705I
u = −0.779580 − 0.384102I
a = −1.185820 + 0.265108I
b = 0.590861 − 0.432097I
5.58297 − 6.26331I 7.90346 + 4.21705I
u = 0.806775 + 0.311658I
a = −0.503384 − 0.515854I
b = 0.454004 − 0.075314I
5.20216 + 2.75088I 10.46106 − 4.15294I
u = 0.806775 − 0.311658I
a = −0.503384 + 0.515854I
b = 0.454004 + 0.075314I
5.20216 − 2.75088I 10.46106 + 4.15294I
u = 0.465334 + 1.071850I
a = 0.049065 − 0.485236I
b = 0.111361 + 0.133659I
2.69406 + 1.87334I 0
u = 0.465334 − 1.071850I
a = 0.049065 + 0.485236I
b = 0.111361 − 0.133659I
2.69406 − 1.87334I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.402299 + 0.726076I
a = −3.65272 − 1.29209I
b = 1.21879 + 3.14865I
1.60800 + 1.58917I −20.2435 + 28.7194I
u = 0.402299 − 0.726076I
a = −3.65272 + 1.29209I
b = 1.21879 − 3.14865I
1.60800 − 1.58917I −20.2435 − 28.7194I
u = −0.515749 + 0.636430I
a = 0.432284 − 0.168531I
b = −0.512700 − 1.266930I
3.82116 − 0.24618I 10.83777 + 0.95093I
u = −0.515749 − 0.636430I
a = 0.432284 + 0.168531I
b = −0.512700 + 1.266930I
3.82116 + 0.24618I 10.83777 − 0.95093I
u = −0.863056 + 0.887990I
a = −1.65478 − 0.77530I
b = 2.21161 − 1.53777I
7.17905 − 1.93629I 0
u = −0.863056 − 0.887990I
a = −1.65478 + 0.77530I
b = 2.21161 + 1.53777I
7.17905 + 1.93629I 0
u = 0.884612 + 0.880353I
a = −1.51477 + 2.13280I
b = 3.40212 − 0.12803I
7.52996 − 2.28269I 0
u = 0.884612 − 0.880353I
a = −1.51477 − 2.13280I
b = 3.40212 + 0.12803I
7.52996 + 2.28269I 0
u = −0.863542 + 0.916240I
a = 1.38248 − 1.19728I
b = 1.00868 + 3.62762I
9.03621 − 3.20134I 0
u = −0.863542 − 0.916240I
a = 1.38248 + 1.19728I
b = 1.00868 − 3.62762I
9.03621 + 3.20134I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.844326 + 0.935290I
a = 0.86102 + 1.47989I
b = −2.81617 − 0.43408I
7.02956 − 4.40333I 0
u = −0.844326 − 0.935290I
a = 0.86102 − 1.47989I
b = −2.81617 + 0.43408I
7.02956 + 4.40333I 0
u = 0.926910 + 0.856986I
a = 1.48020 − 1.69821I
b = −3.07089 − 0.21883I
13.0625 − 8.3599I 0
u = 0.926910 − 0.856986I
a = 1.48020 + 1.69821I
b = −3.07089 + 0.21883I
13.0625 + 8.3599I 0
u = −0.941108 + 0.850159I
a = 1.212510 + 0.718988I
b = −1.84382 + 0.61613I
12.44450 − 0.05461I 0
u = −0.941108 − 0.850159I
a = 1.212510 − 0.718988I
b = −1.84382 − 0.61613I
12.44450 + 0.05461I 0
u = 0.882408 + 0.910943I
a = −2.24359 + 0.19247I
b = 2.57676 + 1.79721I
11.69800 + 1.02561I 0
u = 0.882408 − 0.910943I
a = −2.24359 − 0.19247I
b = 2.57676 − 1.79721I
11.69800 − 1.02561I 0
u = 0.872759 + 0.932792I
a = 0.47392 − 2.27764I
b = −2.51263 + 1.11829I
11.62840 + 5.46563I 0
u = 0.872759 − 0.932792I
a = 0.47392 + 2.27764I
b = −2.51263 − 1.11829I
11.62840 − 5.46563I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.853770 + 0.953263I
a = 2.23742 − 1.27474I
b = −3.56854 − 1.17457I
7.29873 + 8.71850I 0
u = 0.853770 − 0.953263I
a = 2.23742 + 1.27474I
b = −3.56854 + 1.17457I
7.29873 − 8.71850I 0
u = 0.860730 + 0.991421I
a = −1.80670 + 1.31853I
b = 3.40314 + 0.83193I
12.6289 + 14.9456I 0
u = 0.860730 − 0.991421I
a = −1.80670 − 1.31853I
b = 3.40314 − 0.83193I
12.6289 − 14.9456I 0
u = −0.864734 + 1.003780I
a = −0.882254 − 1.058650I
b = 2.07633 − 0.04773I
11.94950 − 6.58665I 0
u = −0.864734 − 1.003780I
a = −0.882254 + 1.058650I
b = 2.07633 + 0.04773I
11.94950 + 6.58665I 0
u = 0.169777 + 0.640051I
a = 2.09836 + 1.02675I
b = −0.152332 − 1.028930I
0.76782 + 1.19453I 4.26499 − 2.46898I
u = 0.169777 − 0.640051I
a = 2.09836 − 1.02675I
b = −0.152332 + 1.028930I
0.76782 − 1.19453I 4.26499 + 2.46898I
u = −0.518208 + 0.404309I
a = 1.50731 + 0.28565I
b = −0.094912 − 0.386134I
0.61609 + 2.03745I 4.84113 − 3.90583I
u = −0.518208 − 0.404309I
a = 1.50731 − 0.28565I
b = −0.094912 + 0.386134I
0.61609 − 2.03745I 4.84113 + 3.90583I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.373944 + 0.452314I
a = 1.42702 + 0.88137I
b = −0.383829 − 0.488009I
0.630433 + 1.227030I 4.67740 − 4.85116I
u = 0.373944 − 0.452314I
a = 1.42702 − 0.88137I
b = −0.383829 + 0.488009I
0.630433 − 1.227030I 4.67740 + 4.85116I
u = 0.259947
a = 3.48349
b = −1.23002
2.31399 2.87430
10
II. I
u
2
= hb − u, a + 1, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u + 1
a
7
=
u
−u + 1
a
1
=
−u
u − 1
a
3
=
1
0
a
4
=
0
u
a
9
=
−1
u
a
10
=
−1
2u − 1
a
8
=
u − 1
u
a
11
=
−u
u − 1
a
11
=
−u
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u + 5
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
8
, c
9
u
2
+ u + 1
c
4
, c
5
u
2
− u + 1
c
7
(u + 1)
2
c
10
(u − 1)
2
c
11
u
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
8
, c
9
y
2
+ y + 1
c
7
, c
10
(y −1)
2
c
11
y
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.00000
b = 0.500000 + 0.866025I
1.64493 + 2.02988I 3.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = −1.00000
b = 0.500000 − 0.866025I
1.64493 − 2.02988I 3.00000 + 3.46410I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)(u
53
− 2u
52
+ ··· + 5u − 1)
c
2
, c
6
(u
2
+ u + 1)(u
53
+ 12u
52
+ ··· + u − 1)
c
3
(u
2
+ u + 1)(u
53
+ 4u
52
+ ··· + u + 1)
c
4
(u
2
− u + 1)(u
53
+ 12u
52
+ ··· + u − 1)
c
5
(u
2
− u + 1)(u
53
− 2u
52
+ ··· + 5u − 1)
c
7
((u + 1)
2
)(u
53
+ 3u
52
+ ··· + 8u − 1)
c
8
(u
2
+ u + 1)(u
53
+ 2u
52
+ ··· + 361u − 31)
c
9
(u
2
+ u + 1)(u
53
+ 10u
51
+ ··· − 4625u − 6737)
c
10
((u − 1)
2
)(u
53
+ 3u
52
+ ··· + 8u − 1)
c
11
u
2
(u
53
− 9u
52
+ ··· − 4u − 4)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
2
+ y + 1)(y
53
+ 12y
52
+ ··· + y −1)
c
2
, c
4
, c
6
(y
2
+ y + 1)(y
53
+ 60y
52
+ ··· + 185y −1)
c
3
(y
2
+ y + 1)(y
53
− 8y
52
+ ··· + y −1)
c
7
, c
10
((y −1)
2
)(y
53
− 43y
52
+ ··· − 84y −1)
c
8
(y
2
+ y + 1)(y
53
+ 68y
52
+ ··· + 28145y −961)
c
9
(y
2
+ y + 1)(y
53
+ 20y
52
+ ··· + 6.23517 × 10
8
y −4.53872 × 10
7
)
c
11
y
2
(y
53
+ 15y
52
+ ··· − 120y −16)
16
