11a
49
(K11a
49
)
A knot diagram
1
Linearized knot diagam
5 1 7 2 4 10 3 11 6 8 9
Solving Sequence
8,11
9
1,3
2 7 4 10 6 5
c
8
c
11
c
2
c
7
c
3
c
10
c
6
c
5
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h9.01751 × 10
36
u
59
+ 5.15573 × 10
37
u
58
+ ··· + 2.98614 × 10
35
b − 6.79357 × 10
36
,
8.91336 × 10
36
u
59
+ 4.98175 × 10
37
u
58
+ ··· + 2.98614 × 10
35
a − 5.40121 × 10
36
, u
60
+ 7u
59
+ ··· − 6u − 1i
I
u
2
= h−a
2
+ b − 2a − 1, a
4
+ 3a
3
+ 4a
2
+ 3a + 2, u − 1i
I
u
3
= hb, a
2
+ au + 2a + 3u + 5, u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 68 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
= h9.02 × 10
36
u
59
+ 5.16 × 10
37
u
58
+ · · · + 2.99 × 10
35
b − 6.79 × 10
36
, 8.91 ×
10
36
u
59
+4.98×10
37
u
58
+· · ·+2.99×10
35
a−5.40×10
36
, u
60
+7u
59
+· · ·−6u−1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
u
2
a
1
=
−u
−u
3
+ u
a
3
=
−29.8491u
59
− 166.829u
58
+ ··· + 129.411u + 18.0876
−30.1979u
59
− 172.655u
58
+ ··· + 122.504u + 22.7504
a
2
=
−38.7260u
59
− 215.837u
58
+ ··· + 161.430u + 23.9641
−40.2858u
59
− 229.747u
58
+ ··· + 160.391u + 30.0045
a
7
=
−35.9915u
59
− 204.169u
58
+ ··· + 147.701u + 26.5908
−36.2977u
59
− 209.779u
58
+ ··· + 151.862u + 29.1133
a
4
=
−37.1833u
59
− 206.920u
58
+ ··· + 154.103u + 23.9174
−41.6797u
59
− 236.581u
58
+ ··· + 163.204u + 30.6805
a
10
=
u
u
a
6
=
−25.6472u
59
− 153.577u
58
+ ··· + 126.598u + 23.1246
−25.9534u
59
− 159.186u
58
+ ··· + 130.758u + 25.6472
a
5
=
−23.4754u
59
− 130.115u
58
+ ··· + 100.960u + 15.9285
−27.6129u
59
− 156.128u
58
+ ··· + 107.032u + 20.4621
a
5
=
−23.4754u
59
− 130.115u
58
+ ··· + 100.960u + 15.9285
−27.6129u
59
− 156.128u
58
+ ··· + 107.032u + 20.4621
(ii) Obstruction class = −1
(iii) Cusp Shapes = 50.7022u
59
+ 278.914u
58
+ ··· − 202.739u − 39.8944
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
60
+ 4u
59
+ ··· + 6u + 1
c
2
, c
5
u
60
+ 20u
59
+ ··· − 82u + 1
c
3
, c
7
u
60
− 2u
59
+ ··· − 16u + 16
c
6
, c
9
u
60
+ 3u
59
+ ··· − 24u − 16
c
8
, c
10
, c
11
u
60
− 7u
59
+ ··· + 6u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
60
+ 20y
59
+ ··· − 82y + 1
c
2
, c
5
y
60
+ 44y
59
+ ··· − 7010y + 1
c
3
, c
7
y
60
+ 30y
59
+ ··· + 1408y + 256
c
6
, c
9
y
60
− 33y
59
+ ··· − 576y + 256
c
8
, c
10
, c
11
y
60
− 57y
59
+ ··· − 48y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.318501 + 0.946527I
a = 0.673424 − 0.443134I
b = 0.628475 + 1.190740I
3.14485 − 10.38850I 0
u = 0.318501 − 0.946527I
a = 0.673424 + 0.443134I
b = 0.628475 − 1.190740I
3.14485 + 10.38850I 0
u = 0.260347 + 0.914658I
a = −0.502988 + 0.479081I
b = −0.548192 − 1.199390I
4.15844 − 4.56410I 0
u = 0.260347 − 0.914658I
a = −0.502988 − 0.479081I
b = −0.548192 + 1.199390I
4.15844 + 4.56410I 0
u = 1.050240 + 0.110830I
a = 2.93202 − 0.13396I
b = 0.514724 − 0.182101I
−1.44417 + 1.61127I 0
u = 1.050240 − 0.110830I
a = 2.93202 + 0.13396I
b = 0.514724 + 0.182101I
−1.44417 − 1.61127I 0
u = 0.636405 + 0.600822I
a = 0.0733025 − 0.0078478I
b = 0.618612 − 0.670882I
−3.26453 + 0.03248I −13.91224 + 0.I
u = 0.636405 − 0.600822I
a = 0.0733025 + 0.0078478I
b = 0.618612 + 0.670882I
−3.26453 − 0.03248I −13.91224 + 0.I
u = 1.119040 + 0.184637I
a = 1.292300 − 0.042199I
b = 0.213622 + 0.675044I
−1.23369 − 0.89939I 0
u = 1.119040 − 0.184637I
a = 1.292300 + 0.042199I
b = 0.213622 − 0.675044I
−1.23369 + 0.89939I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.387799 + 0.734072I
a = 0.750801 − 1.082130I
b = 0.543968 + 0.934007I
−2.46678 − 4.55995I −10.63324 + 6.84099I
u = 0.387799 − 0.734072I
a = 0.750801 + 1.082130I
b = 0.543968 − 0.934007I
−2.46678 + 4.55995I −10.63324 − 6.84099I
u = −1.182510 + 0.025488I
a = −0.149815 + 0.792334I
b = −0.08319 + 1.71273I
4.58752 + 3.28588I 0
u = −1.182510 − 0.025488I
a = −0.149815 − 0.792334I
b = −0.08319 − 1.71273I
4.58752 − 3.28588I 0
u = 0.960690 + 0.700258I
a = −0.170467 − 0.529914I
b = 0.429578 − 1.064780I
1.22350 + 4.74489I 0
u = 0.960690 − 0.700258I
a = −0.170467 + 0.529914I
b = 0.429578 + 1.064780I
1.22350 − 4.74489I 0
u = 1.022220 + 0.626579I
a = 0.346636 + 0.523779I
b = −0.299489 + 1.056400I
1.87463 − 0.78688I 0
u = 1.022220 − 0.626579I
a = 0.346636 − 0.523779I
b = −0.299489 − 1.056400I
1.87463 + 0.78688I 0
u = 1.216360 + 0.116183I
a = −2.34185 + 0.37415I
b = −0.685889 + 0.406589I
−1.99576 − 3.02877I 0
u = 1.216360 − 0.116183I
a = −2.34185 − 0.37415I
b = −0.685889 − 0.406589I
−1.99576 + 3.02877I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.307636 + 0.644850I
a = 1.144270 + 0.031313I
b = 0.165753 − 1.304350I
6.42634 − 1.17254I −0.566200 + 1.294911I
u = −0.307636 − 0.644850I
a = 1.144270 − 0.031313I
b = 0.165753 + 1.304350I
6.42634 + 1.17254I −0.566200 − 1.294911I
u = 0.250540 + 0.658416I
a = 0.582040 + 0.468015I
b = 0.960204 − 0.362556I
0.56981 − 4.60985I −6.69053 + 5.91571I
u = 0.250540 − 0.658416I
a = 0.582040 − 0.468015I
b = 0.960204 + 0.362556I
0.56981 + 4.60985I −6.69053 − 5.91571I
u = −0.397265 + 0.581288I
a = −1.344430 + 0.129900I
b = −0.284219 + 1.305220I
6.05175 + 4.76483I −1.11123 − 4.56468I
u = −0.397265 − 0.581288I
a = −1.344430 − 0.129900I
b = −0.284219 − 1.305220I
6.05175 − 4.76483I −1.11123 + 4.56468I
u = 0.166593 + 0.624695I
a = 0.134377 + 1.238880I
b = −0.262438 − 0.985240I
1.53389 − 2.11161I −1.83843 + 4.55656I
u = 0.166593 − 0.624695I
a = 0.134377 − 1.238880I
b = −0.262438 + 0.985240I
1.53389 + 2.11161I −1.83843 − 4.55656I
u = 1.360300 + 0.086702I
a = −1.78259 − 0.56257I
b = −0.611650 − 0.809721I
−4.90942 − 2.39733I 0
u = 1.360300 − 0.086702I
a = −1.78259 + 0.56257I
b = −0.611650 + 0.809721I
−4.90942 + 2.39733I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.370480 + 0.211215I
a = −1.42173 − 0.57455I
b = −1.254690 − 0.485726I
−3.80109 + 2.07837I 0
u = −1.370480 − 0.211215I
a = −1.42173 + 0.57455I
b = −1.254690 + 0.485726I
−3.80109 − 2.07837I 0
u = −1.372610 + 0.240045I
a = −1.206450 + 0.088768I
b = −0.536814 + 1.263550I
−3.38098 + 5.24726I 0
u = −1.372610 − 0.240045I
a = −1.206450 − 0.088768I
b = −0.536814 − 1.263550I
−3.38098 − 5.24726I 0
u = −1.401420 + 0.163779I
a = 1.005320 + 0.195931I
b = 0.406771 − 1.172380I
−6.11056 + 0.33405I 0
u = −1.401420 − 0.163779I
a = 1.005320 − 0.195931I
b = 0.406771 + 1.172380I
−6.11056 − 0.33405I 0
u = −1.40212 + 0.25943I
a = 1.38067 + 0.69174I
b = 1.225810 + 0.584729I
−4.71228 + 7.96352I 0
u = −1.40212 − 0.25943I
a = 1.38067 − 0.69174I
b = 1.225810 − 0.584729I
−4.71228 − 7.96352I 0
u = 0.153691 + 0.545787I
a = −0.556917 − 0.791426I
b = −0.921325 + 0.199362I
1.086080 + 0.692045I −4.81030 + 0.29508I
u = 0.153691 − 0.545787I
a = −0.556917 + 0.791426I
b = −0.921325 − 0.199362I
1.086080 − 0.692045I −4.81030 − 0.29508I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.40946 + 0.27587I
a = 1.41078 + 0.77344I
b = 0.461649 + 1.079170I
0.95728 − 2.24717I 0
u = 1.40946 − 0.27587I
a = 1.41078 − 0.77344I
b = 0.461649 − 1.079170I
0.95728 + 2.24717I 0
u = −1.45673
a = −1.09429
b = −0.967879
−7.21613 0
u = −1.43351 + 0.37170I
a = −1.60294 + 0.24999I
b = −0.76178 + 1.26721I
−1.23187 + 9.17979I 0
u = −1.43351 − 0.37170I
a = −1.60294 − 0.24999I
b = −0.76178 − 1.26721I
−1.23187 − 9.17979I 0
u = 1.46184 + 0.24029I
a = −1.51788 − 0.84748I
b = −0.558703 − 1.096040I
0.04969 − 7.86068I 0
u = 1.46184 − 0.24029I
a = −1.51788 + 0.84748I
b = −0.558703 + 1.096040I
0.04969 + 7.86068I 0
u = −1.45691 + 0.27854I
a = 1.51683 + 0.01897I
b = 0.657430 − 1.153890I
−8.38340 + 8.24100I 0
u = −1.45691 − 0.27854I
a = 1.51683 − 0.01897I
b = 0.657430 + 1.153890I
−8.38340 − 8.24100I 0
u = 0.489956
a = 0.405505
b = −0.332522
−0.859418 −11.8180
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46811 + 0.38180I
a = 1.69029 − 0.23279I
b = 0.80501 − 1.23713I
−2.5536 + 15.1714I 0
u = −1.46811 − 0.38180I
a = 1.69029 + 0.23279I
b = 0.80501 + 1.23713I
−2.5536 − 15.1714I 0
u = −1.53424 + 0.14331I
a = 0.949094 + 0.550926I
b = 0.848905 + 0.481246I
−10.47490 + 2.55878I 0
u = −1.53424 − 0.14331I
a = 0.949094 − 0.550926I
b = 0.848905 − 0.481246I
−10.47490 − 2.55878I 0
u = 0.320933 + 0.297553I
a = 0.20023 − 3.24402I
b = 0.180899 + 0.609146I
−0.66653 + 1.65828I −3.28323 + 3.22527I
u = 0.320933 − 0.297553I
a = 0.20023 + 3.24402I
b = 0.180899 − 0.609146I
−0.66653 − 1.65828I −3.28323 − 3.22527I
u = −1.68096 + 0.03245I
a = 0.170430 + 0.699797I
b = 0.154472 + 0.628288I
−8.49817 − 2.35434I 0
u = −1.68096 − 0.03245I
a = 0.170430 − 0.699797I
b = 0.154472 − 0.628288I
−8.49817 + 2.35434I 0
u = −0.1037940 + 0.0707771I
a = −5.31036 + 0.40793I
b = −0.357301 + 0.551894I
−0.33181 + 1.48905I −3.19515 − 4.46795I
u = −0.1037940 − 0.0707771I
a = −5.31036 − 0.40793I
b = −0.357301 − 0.551894I
−0.33181 − 1.48905I −3.19515 + 4.46795I
10
II. I
u
2
= h−a
2
+ b − 2a − 1, a
4
+ 3a
3
+ 4a
2
+ 3a + 2, u − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
1
a
9
=
1
1
a
1
=
−1
0
a
3
=
a
a
2
+ 2a + 1
a
2
=
a
2
+ 3a + 1
a
2
+ 2a + 1
a
7
=
−a
3
− 2a
2
− a + 1
−a
3
− 2a
2
− a + 1
a
4
=
−a
3
− 4a
2
− 5a − 3
−a
3
− 3a
2
− 4a − 2
a
10
=
1
1
a
6
=
−a
3
− 2a
2
− a + 1
−a
3
− 2a
2
− a + 1
a
5
=
−a − 2
−a − 1
a
5
=
−a − 2
−a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3a
3
− 12a
2
− 7a − 10
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− u
3
+ u
2
+ 1
c
2
, c
5
, c
7
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
3
u
4
− u
3
+ 3u
2
− 2u + 1
c
4
u
4
+ u
3
+ u
2
+ 1
c
6
, c
9
u
4
c
8
(u − 1)
4
c
10
, c
11
(u + 1)
4
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
2
, c
3
, c
5
c
7
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
6
, c
9
y
4
c
8
, c
10
, c
11
(y −1)
4
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.148192 + 0.911292I
b = −0.10488 + 1.55249I
5.14581 + 3.16396I −0.358581 − 1.047693I
u = 1.00000
a = −0.148192 − 0.911292I
b = −0.10488 − 1.55249I
5.14581 − 3.16396I −0.358581 + 1.047693I
u = 1.00000
a = −1.35181 + 0.72034I
b = −0.395123 − 0.506844I
−1.85594 − 1.41510I −15.1414 + 7.6022I
u = 1.00000
a = −1.35181 − 0.72034I
b = −0.395123 + 0.506844I
−1.85594 + 1.41510I −15.1414 − 7.6022I
14
III. I
u
3
= hb, a
2
+ au + 2a + 3u + 5, u
2
+ u − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u + 1
a
1
=
−u
−u + 1
a
3
=
a
0
a
2
=
2au
3au − 2a
a
7
=
1
0
a
4
=
a
0
a
10
=
u
u
a
6
=
u
u − 1
a
5
=
a + 2u + 2
u − 1
a
5
=
a + 2u + 2
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5au − a − 3u − 19
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u
2
+ u + 1)
2
c
3
, c
7
u
4
c
4
(u
2
− u + 1)
2
c
6
, c
8
(u
2
+ u − 1)
2
c
9
, c
10
, c
11
(u
2
− u − 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
2
c
3
, c
7
y
4
c
6
, c
8
, c
9
c
10
, c
11
(y
2
− 3y + 1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −1.30902 + 2.26728I
b = 0
−0.98696 + 2.02988I −15.5000 − 9.2736I
u = 0.618034
a = −1.30902 − 2.26728I
b = 0
−0.98696 − 2.02988I −15.5000 + 9.2736I
u = −1.61803
a = −0.190983 + 0.330792I
b = 0
−8.88264 + 2.02988I −15.5000 + 2.3454I
u = −1.61803
a = −0.190983 − 0.330792I
b = 0
−8.88264 − 2.02988I −15.5000 − 2.3454I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
2
)(u
4
− u
3
+ u
2
+ 1)(u
60
+ 4u
59
+ ··· + 6u + 1)
c
2
, c
5
((u
2
+ u + 1)
2
)(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
60
+ 20u
59
+ ··· − 82u + 1)
c
3
u
4
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
60
− 2u
59
+ ··· − 16u + 16)
c
4
((u
2
− u + 1)
2
)(u
4
+ u
3
+ u
2
+ 1)(u
60
+ 4u
59
+ ··· + 6u + 1)
c
6
u
4
(u
2
+ u − 1)
2
(u
60
+ 3u
59
+ ··· − 24u − 16)
c
7
u
4
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
60
− 2u
59
+ ··· − 16u + 16)
c
8
((u − 1)
4
)(u
2
+ u − 1)
2
(u
60
− 7u
59
+ ··· + 6u − 1)
c
9
u
4
(u
2
− u − 1)
2
(u
60
+ 3u
59
+ ··· − 24u − 16)
c
10
, c
11
((u + 1)
4
)(u
2
− u − 1)
2
(u
60
− 7u
59
+ ··· + 6u − 1)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
2
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
60
+ 20y
59
+ ··· − 82y + 1)
c
2
, c
5
((y
2
+ y + 1)
2
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
60
+ 44y
59
+ ··· − 7010y + 1)
c
3
, c
7
y
4
(y
4
+ 5y
3
+ ··· + 2y + 1)(y
60
+ 30y
59
+ ··· + 1408y + 256)
c
6
, c
9
y
4
(y
2
− 3y + 1)
2
(y
60
− 33y
59
+ ··· − 576y + 256)
c
8
, c
10
, c
11
((y −1)
4
)(y
2
− 3y + 1)
2
(y
60
− 57y
59
+ ··· − 48y + 1)
20
