11a
294
(K11a
294
)
A knot diagram
1
Linearized knot diagam
9 5 1 8 2 11 10 3 6 7 4
Solving Sequence
6,11 2,7
5 3 10 8 4 9 1
c
6
c
5
c
2
c
10
c
7
c
4
c
9
c
1
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−8634895226u
23
− 5433253456u
22
+ ··· + 735180934969b − 781237782063,
763967991611u
23
+ 23673073992u
22
+ ··· + 2940723739876a + 7856566749775,
u
24
+ 10u
22
+ ··· + 15u − 4i
I
u
2
= hu
19
a + 2u
19
+ ··· − 2a − 1, −2u
19
a − 4u
19
+ ··· + 6a + 15, u
20
− u
19
+ ··· − 2u − 1i
I
u
3
= hb + 1, −2u
2
+ 2a − 2u − 3, u
3
+ u
2
+ 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 67 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
=
h−8.63×10
9
u
23
−5.43×10
9
u
22
+· · ·+ 7.35×10
11
b−7.81×10
11
, 7.64×10
11
u
23
+
2.37 × 10
10
u
22
+ · · · + 2.94 × 10
12
a + 7.86 × 10
12
, u
24
+ 10u
22
+ · · · + 15u − 4i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
−0.259789u
23
− 0.00805008u
22
+ ··· + 6.57173u − 2.67164
0.0117453u
23
+ 0.00739036u
22
+ ··· − 0.781959u + 1.06265
a
7
=
1
−u
2
a
5
=
0.249773u
23
− 0.00306836u
22
+ ··· − 5.95799u + 2.87741
−0.0126772u
23
− 0.0249283u
22
+ ··· + 1.51797u − 1.05571
a
3
=
−0.517622u
23
− 0.0138817u
22
+ ··· + 12.5338u − 5.08757
0.0138817u
23
+ 0.00372967u
22
+ ··· − 2.67676u + 2.07049
a
10
=
−u
u
3
+ u
a
8
=
u
2
+ 1
−u
4
− 2u
2
a
4
=
0.265662u
23
+ 0.0117453u
22
+ ··· − 6.46270u + 3.20297
−0.00805008u
23
+ 0.0403920u
22
+ ··· + 1.22519u − 1.03916
a
9
=
−u
3
− 2u
u
3
+ u
a
1
=
−0.263929u
23
− 0.0126772u
22
+ ··· + 6.43357u − 2.44096
−0.00306836u
23
− 0.0138773u
22
+ ··· − 0.869183u + 0.999092
a
1
=
−0.263929u
23
− 0.0126772u
22
+ ··· + 6.43357u − 2.44096
−0.00306836u
23
− 0.0138773u
22
+ ··· − 0.869183u + 0.999092
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
818436095265
735180934969
u
23
+
92606395200
735180934969
u
22
+ ··· −
104556151676103
2940723739876
u +
5519991831807
735180934969
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
8(8u
24
− 12u
23
+ ··· − u + 1)
c
2
, c
3
, c
5
c
11
u
24
+ 3u
23
+ ··· + 6u − 1
c
6
, c
7
, c
10
u
24
+ 10u
22
+ ··· − 15u − 4
c
8
u
24
+ 3u
23
+ ··· + 224u + 128
c
9
u
24
− 6u
22
+ ··· − 1079u − 676
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
64(64y
24
− 656y
23
+ ··· − 7y + 1)
c
2
, c
3
, c
5
c
11
y
24
+ 13y
23
+ ··· − 38y + 1
c
6
, c
7
, c
10
y
24
+ 20y
23
+ ··· − 97y + 16
c
8
y
24
− 7y
23
+ ··· − 226304y + 16384
c
9
y
24
− 12y
23
+ ··· − 1380561y + 456976
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.021460 + 0.275515I
a = 0.39552 − 1.65501I
b = 0.047276 + 1.186360I
7.49230 − 1.49785I 16.5794 + 3.5131I
u = −1.021460 − 0.275515I
a = 0.39552 + 1.65501I
b = 0.047276 − 1.186360I
7.49230 + 1.49785I 16.5794 − 3.5131I
u = 0.870278 + 0.206907I
a = −0.50041 − 2.31304I
b = −0.49469 + 1.37599I
9.3482 + 11.6156I 9.04984 − 7.14425I
u = 0.870278 − 0.206907I
a = −0.50041 + 2.31304I
b = −0.49469 − 1.37599I
9.3482 − 11.6156I 9.04984 + 7.14425I
u = −0.711520 + 0.880248I
a = −0.496210 + 1.180490I
b = −0.138302 − 1.193200I
5.61526 − 4.36903I 11.9512 + 7.5869I
u = −0.711520 − 0.880248I
a = −0.496210 − 1.180490I
b = −0.138302 + 1.193200I
5.61526 + 4.36903I 11.9512 − 7.5869I
u = 0.507475 + 1.020800I
a = 0.471884 + 1.006850I
b = −0.411983 − 1.346680I
6.85359 − 6.74871I 7.12828 + 3.44529I
u = 0.507475 − 1.020800I
a = 0.471884 − 1.006850I
b = −0.411983 + 1.346680I
6.85359 + 6.74871I 7.12828 − 3.44529I
u = 0.263649 + 1.293920I
a = 0.137301 + 0.951214I
b = 1.347430 + 0.188650I
−4.17750 + 3.32302I 7.49326 − 7.01534I
u = 0.263649 − 1.293920I
a = 0.137301 − 0.951214I
b = 1.347430 − 0.188650I
−4.17750 − 3.32302I 7.49326 + 7.01534I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.102906 + 1.325920I
a = 0.978679 + 0.749632I
b = 0.912691 − 0.587846I
−5.99931 + 2.29383I −3.48033 − 0.30083I
u = 0.102906 − 1.325920I
a = 0.978679 − 0.749632I
b = 0.912691 + 0.587846I
−5.99931 − 2.29383I −3.48033 + 0.30083I
u = 0.656566
a = −1.48947
b = 1.29551
−0.112715 17.2960
u = −0.181673 + 1.332990I
a = −0.477910 + 0.021115I
b = −0.263704 + 0.229700I
−3.41691 − 2.41506I 4.35202 + 1.54076I
u = −0.181673 − 1.332990I
a = −0.477910 − 0.021115I
b = −0.263704 − 0.229700I
−3.41691 + 2.41506I 4.35202 − 1.54076I
u = 0.36901 + 1.39774I
a = −1.48756 − 1.23046I
b = −0.55509 + 1.37302I
4.2704 + 16.0735I 4.86533 − 8.67439I
u = 0.36901 − 1.39774I
a = −1.48756 + 1.23046I
b = −0.55509 − 1.37302I
4.2704 − 16.0735I 4.86533 + 8.67439I
u = −0.45316 + 1.40935I
a = 0.831561 − 1.018120I
b = 0.207861 + 1.159740I
2.26090 − 6.77325I 8.15326 + 8.68487I
u = −0.45316 − 1.40935I
a = 0.831561 + 1.018120I
b = 0.207861 − 1.159740I
2.26090 + 6.77325I 8.15326 − 8.68487I
u = −0.496850
a = −0.482259
b = −0.161437
0.853473 12.2560
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.11292 + 1.52095I
a = −0.621242 + 0.178604I
b = −0.381421 − 1.074640I
−2.48001 − 6.89114I 2.89593 + 8.03535I
u = −0.11292 − 1.52095I
a = −0.621242 − 0.178604I
b = −0.381421 + 1.074640I
−2.48001 + 6.89114I 2.89593 − 8.03535I
u = 0.287554 + 0.235788I
a = −0.37075 + 1.66780I
b = 0.662890 − 0.292141I
−1.22051 + 0.86188I −4.63925 − 4.32694I
u = 0.287554 − 0.235788I
a = −0.37075 − 1.66780I
b = 0.662890 + 0.292141I
−1.22051 − 0.86188I −4.63925 + 4.32694I
7
II. I
u
2
=
hu
19
a+2u
19
+· · ·−2a−1, −2u
19
a−4u
19
+· · ·+6a+15, u
20
−u
19
+· · ·−2u−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
a
−u
19
a − 2u
19
+ ··· + 2a + 1
a
7
=
1
−u
2
a
5
=
−2u
19
a − 4u
19
+ ··· + a + 7
u
19
a − u
19
+ ··· + 2a + 3
a
3
=
−u
19
− 8u
17
− 26u
15
− 42u
13
− 31u
11
− 2u
9
+ 10u
7
+ 4u
5
− u
3
− 2u
u
19
− u
18
+ ··· + 2u + 1
a
10
=
−u
u
3
+ u
a
8
=
u
2
+ 1
−u
4
− 2u
2
a
4
=
−2u
19
a − u
19
+ ··· − 7u + 3
−2u
19
+ 2u
18
+ ··· − 2u + 2
a
9
=
−u
3
− 2u
u
3
+ u
a
1
=
−2u
19
a − u
19
+ ··· + 2a − 2
−u
18
a − 2u
19
+ ··· + 2a + 2
a
1
=
−2u
19
a − u
19
+ ··· + 2a − 2
−u
18
a − 2u
19
+ ··· + 2a + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
18
−4u
17
+ 32u
16
−28u
15
+ 104u
14
−76u
13
+ 164u
12
−92u
11
+
104u
10
− 32u
9
− 28u
8
+ 20u
7
− 60u
6
+ 4u
5
− 4u
4
− 8u
3
+ 16u
2
+ 4u + 10
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
40
− 3u
39
+ ··· − 60100u + 13049
c
2
, c
3
, c
5
c
11
u
40
− 7u
39
+ ··· − 2u + 1
c
6
, c
7
, c
10
(u
20
+ u
19
+ ··· + 2u − 1)
2
c
8
(u
20
− u
19
+ ··· + 3u
2
− 1)
2
c
9
(u
20
− u
19
+ ··· + 4u − 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
40
− 21y
39
+ ··· − 1779930400y + 170276401
c
2
, c
3
, c
5
c
11
y
40
+ 27y
39
+ ··· + 40y
2
+ 1
c
6
, c
7
, c
10
(y
20
+ 17y
19
+ ··· − 6y + 1)
2
c
8
(y
20
− 7y
19
+ ··· − 6y + 1)
2
c
9
(y
20
− 11y
19
+ ··· − 6y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.274747 + 1.069600I
a = −0.650977 − 1.009380I
b = 0.31766 + 1.39547I
2.02098 − 2.13456I 4.50898 + 2.16962I
u = 0.274747 + 1.069600I
a = −0.084213 − 0.753588I
b = −0.918130 − 0.259874I
2.02098 − 2.13456I 4.50898 + 2.16962I
u = 0.274747 − 1.069600I
a = −0.650977 + 1.009380I
b = 0.31766 − 1.39547I
2.02098 + 2.13456I 4.50898 − 2.16962I
u = 0.274747 − 1.069600I
a = −0.084213 + 0.753588I
b = −0.918130 + 0.259874I
2.02098 + 2.13456I 4.50898 − 2.16962I
u = 0.773104 + 0.153161I
a = 0.829907 − 0.370587I
b = −1.084140 + 0.080482I
4.77271 + 6.07240I 7.45285 − 5.87540I
u = 0.773104 + 0.153161I
a = 0.37153 + 2.57431I
b = 0.49433 − 1.41099I
4.77271 + 6.07240I 7.45285 − 5.87540I
u = 0.773104 − 0.153161I
a = 0.829907 + 0.370587I
b = −1.084140 − 0.080482I
4.77271 − 6.07240I 7.45285 + 5.87540I
u = 0.773104 − 0.153161I
a = 0.37153 − 2.57431I
b = 0.49433 + 1.41099I
4.77271 − 6.07240I 7.45285 + 5.87540I
u = 0.772326
a = 0.10498 + 2.42938I
b = −0.56866 − 1.40361I
8.84775 12.4400
u = 0.772326
a = 0.10498 − 2.42938I
b = −0.56866 + 1.40361I
8.84775 12.4400
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.198534 + 1.239650I
a = 1.83297 − 0.91329I
b = 0.199750 − 0.784968I
0.52569 − 2.16136I 0.73748 + 3.31855I
u = −0.198534 + 1.239650I
a = 0.01849 − 2.83921I
b = 0.053071 + 1.161370I
0.52569 − 2.16136I 0.73748 + 3.31855I
u = −0.198534 − 1.239650I
a = 1.83297 + 0.91329I
b = 0.199750 + 0.784968I
0.52569 + 2.16136I 0.73748 − 3.31855I
u = −0.198534 − 1.239650I
a = 0.01849 + 2.83921I
b = 0.053071 − 1.161370I
0.52569 + 2.16136I 0.73748 − 3.31855I
u = −0.692333 + 0.156175I
a = 0.333781 + 0.644615I
b = 0.162072 + 0.252940I
3.61438 − 0.81573I 5.67172 + 1.07888I
u = −0.692333 + 0.156175I
a = −1.37017 + 2.40156I
b = −0.049861 − 1.112720I
3.61438 − 0.81573I 5.67172 + 1.07888I
u = −0.692333 − 0.156175I
a = 0.333781 − 0.644615I
b = 0.162072 − 0.252940I
3.61438 + 0.81573I 5.67172 − 1.07888I
u = −0.692333 − 0.156175I
a = −1.37017 − 2.40156I
b = −0.049861 + 1.112720I
3.61438 + 0.81573I 5.67172 − 1.07888I
u = 0.327541 + 1.260030I
a = 0.653810 + 0.673934I
b = −0.46464 − 1.49110I
4.94645 + 3.96853I 7.89349 − 3.79787I
u = 0.327541 + 1.260030I
a = −1.51060 − 1.23935I
b = −0.67909 + 1.31567I
4.94645 + 3.96853I 7.89349 − 3.79787I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.327541 − 1.260030I
a = 0.653810 − 0.673934I
b = −0.46464 + 1.49110I
4.94645 − 3.96853I 7.89349 + 3.79787I
u = 0.327541 − 1.260030I
a = −1.51060 + 1.23935I
b = −0.67909 − 1.31567I
4.94645 − 3.96853I 7.89349 + 3.79787I
u = −0.201509 + 0.663357I
a = −0.408683 − 0.835639I
b = −0.502025 − 0.160176I
1.62333 − 2.35832I 2.35225 + 4.49783I
u = −0.201509 + 0.663357I
a = 0.005727 − 0.731461I
b = 0.195325 + 1.163080I
1.62333 − 2.35832I 2.35225 + 4.49783I
u = −0.201509 − 0.663357I
a = −0.408683 + 0.835639I
b = −0.502025 + 0.160176I
1.62333 + 2.35832I 2.35225 − 4.49783I
u = −0.201509 − 0.663357I
a = 0.005727 + 0.731461I
b = 0.195325 − 1.163080I
1.62333 + 2.35832I 2.35225 − 4.49783I
u = −0.295567 + 1.352050I
a = 0.356054 + 0.330760I
b = 0.392505 + 0.067994I
−1.14075 − 4.43308I 0.68370 + 2.52728I
u = −0.295567 + 1.352050I
a = −1.53457 + 1.07334I
b = −0.177275 − 1.088720I
−1.14075 − 4.43308I 0.68370 + 2.52728I
u = −0.295567 − 1.352050I
a = 0.356054 − 0.330760I
b = 0.392505 − 0.067994I
−1.14075 + 4.43308I 0.68370 − 2.52728I
u = −0.295567 − 1.352050I
a = −1.53457 − 1.07334I
b = −0.177275 + 1.088720I
−1.14075 + 4.43308I 0.68370 − 2.52728I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.328206 + 1.357610I
a = −0.283063 − 0.801762I
b = −1.159930 − 0.023595I
0.00745 + 10.05770I 2.70834 − 7.26612I
u = 0.328206 + 1.357610I
a = 1.50051 + 1.23763I
b = 0.59445 − 1.40555I
0.00745 + 10.05770I 2.70834 − 7.26612I
u = 0.328206 − 1.357610I
a = −0.283063 + 0.801762I
b = −1.159930 + 0.023595I
0.00745 − 10.05770I 2.70834 + 7.26612I
u = 0.328206 − 1.357610I
a = 1.50051 − 1.23763I
b = 0.59445 + 1.40555I
0.00745 − 10.05770I 2.70834 + 7.26612I
u = −0.022410 + 1.403750I
a = −0.788895 − 0.405125I
b = −0.676901 + 0.349305I
−4.68486 − 2.84648I −1.60998 + 2.97861I
u = −0.022410 + 1.403750I
a = 0.387309 + 0.213744I
b = 0.495392 + 0.955288I
−4.68486 − 2.84648I −1.60998 + 2.97861I
u = −0.022410 − 1.403750I
a = −0.788895 + 0.405125I
b = −0.676901 − 0.349305I
−4.68486 + 2.84648I −1.60998 − 2.97861I
u = −0.022410 − 1.403750I
a = 0.387309 − 0.213744I
b = 0.495392 − 0.955288I
−4.68486 + 2.84648I −1.60998 − 2.97861I
u = −0.358818
a = −4.26389 + 1.88679I
b = −0.123906 + 1.022770I
3.97005 10.7620
u = −0.358818
a = −4.26389 − 1.88679I
b = −0.123906 − 1.022770I
3.97005 10.7620
14
III. I
u
3
= hb + 1, −2u
2
+ 2a − 2u − 3, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
u
2
+ u +
3
2
−1
a
7
=
1
−u
2
a
5
=
u
2
+ u +
5
2
−1
a
3
=
2u
2
+ 2u + 4
−2
a
10
=
−u
−u
2
− u − 1
a
8
=
u
2
+ 1
−u
2
− u − 1
a
4
=
u
2
+ u + 2
−
1
2
u − 1
a
9
=
u
2
+ 1
−u
2
− u − 1
a
1
=
u
2
+ u + 2
1
2
u − 1
a
1
=
u
2
+ u + 2
1
2
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1
4
u − 2
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
8(8u
3
+ 4u
2
− 1)
c
2
, c
11
(u − 1)
3
c
3
, c
5
(u + 1)
3
c
4
8(8u
3
− 4u
2
+ 1)
c
6
, c
7
u
3
+ u
2
+ 2u + 1
c
8
u
3
c
9
u
3
+ u
2
− 1
c
10
u
3
− u
2
+ 2u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
64(64y
3
− 16y
2
+ 8y −1)
c
2
, c
3
, c
5
c
11
(y −1)
3
c
6
, c
7
, c
10
y
3
+ 3y
2
+ 2y −1
c
8
y
3
c
9
y
3
− y
2
+ 2y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −0.377439 + 0.744862I
b = −1.00000
−4.66906 − 2.82812I −2.05377 + 0.32679I
u = −0.215080 − 1.307140I
a = −0.377439 − 0.744862I
b = −1.00000
−4.66906 + 2.82812I −2.05377 − 0.32679I
u = −0.569840
a = 1.25488
b = −1.00000
−0.531480 −2.14250
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
64(8u
3
+ 4u
2
− 1)(8u
24
− 12u
23
+ ··· − u + 1)
· (u
40
− 3u
39
+ ··· − 60100u + 13049)
c
2
, c
11
((u − 1)
3
)(u
24
+ 3u
23
+ ··· + 6u − 1)(u
40
− 7u
39
+ ··· − 2u + 1)
c
3
, c
5
((u + 1)
3
)(u
24
+ 3u
23
+ ··· + 6u − 1)(u
40
− 7u
39
+ ··· − 2u + 1)
c
4
64(8u
3
− 4u
2
+ 1)(8u
24
− 12u
23
+ ··· − u + 1)
· (u
40
− 3u
39
+ ··· − 60100u + 13049)
c
6
, c
7
(u
3
+ u
2
+ 2u + 1)(u
20
+ u
19
+ ··· + 2u − 1)
2
· (u
24
+ 10u
22
+ ··· − 15u − 4)
c
8
u
3
(u
20
− u
19
+ ··· + 3u
2
− 1)
2
(u
24
+ 3u
23
+ ··· + 224u + 128)
c
9
(u
3
+ u
2
− 1)(u
20
− u
19
+ ··· + 4u − 1)
2
· (u
24
− 6u
22
+ ··· − 1079u − 676)
c
10
(u
3
− u
2
+ 2u − 1)(u
20
+ u
19
+ ··· + 2u − 1)
2
· (u
24
+ 10u
22
+ ··· − 15u − 4)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
4096(64y
3
− 16y
2
+ 8y −1)(64y
24
− 656y
23
+ ··· − 7y + 1)
· (y
40
− 21y
39
+ ··· − 1779930400y + 170276401)
c
2
, c
3
, c
5
c
11
((y −1)
3
)(y
24
+ 13y
23
+ ··· − 38y + 1)(y
40
+ 27y
39
+ ··· + 40y
2
+ 1)
c
6
, c
7
, c
10
(y
3
+ 3y
2
+ 2y −1)(y
20
+ 17y
19
+ ··· − 6y + 1)
2
· (y
24
+ 20y
23
+ ··· − 97y + 16)
c
8
y
3
(y
20
− 7y
19
+ ··· − 6y + 1)
2
(y
24
− 7y
23
+ ··· − 226304y + 16384)
c
9
(y
3
− y
2
+ 2y −1)(y
20
− 11y
19
+ ··· − 6y + 1)
2
· (y
24
− 12y
23
+ ··· − 1380561y + 456976)
20
