11a
1
(K11a
1
)
A knot diagram
1
Linearized knot diagam
5 1 8 2 3 10 4 6 11 7 9
Solving Sequence
7,11
10
3,6
5 9 1 2 8 4
c
10
c
6
c
5
c
9
c
11
c
2
c
8
c
3
c
1
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h4u
68
+ 5u
67
+ ··· + 2b + 3u, 4u
68
+ 8u
67
+ ··· + a + 2, u
69
+ 3u
68
+ ··· + 2u + 1i
I
u
2
= h−u
2
b + b
2
+ bu − u + 1, a, u
3
− u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 75 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
= h4u
68
+5u
67
+· · ·+2b+3u, 4u
68
+8u
67
+· · ·+a+2, u
69
+3u
68
+· · ·+2u+1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
10
=
1
−u
2
a
3
=
−4u
68
− 8u
67
+ ··· − 6u − 2
−2u
68
−
5
2
u
67
+ ··· −
3
2
u
3
−
3
2
u
a
6
=
u
−u
3
+ u
a
5
=
u
18
− 3u
16
+ ··· + 4u + 1
−
1
2
u
67
− u
66
+ ··· − 3u
2
+
1
2
u
a
9
=
−u
2
+ 1
−u
2
a
1
=
u
4
− u
2
+ 1
u
4
a
2
=
−
3
2
u
68
− 3u
67
+ ··· − 3u −
1
2
−
3
2
u
68
− 5u
67
+ ··· − 3u − 3
a
8
=
−u
6
+ u
4
− 2u
2
+ 1
u
8
− 2u
6
+ 2u
4
− 2u
2
a
4
=
u
66
+ u
65
+ ··· + 12u
3
− 2u
−u
68
−
11
2
u
67
+ ··· −
7
2
u − 4
a
4
=
u
66
+ u
65
+ ··· + 12u
3
− 2u
−u
68
−
11
2
u
67
+ ··· −
7
2
u − 4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
15
2
u
68
− 16u
67
+ ··· − 12u −
17
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
69
+ 4u
68
+ ··· − 3u − 1
c
2
u
69
+ 34u
68
+ ··· − 3u − 1
c
3
, c
7
u
69
− u
68
+ ··· + 224u + 64
c
5
u
69
− 4u
68
+ ··· + 5265u − 1153
c
6
, c
10
u
69
+ 3u
68
+ ··· + 2u + 1
c
8
u
69
− 3u
68
+ ··· − 7540u + 937
c
9
, c
11
u
69
+ 23u
68
+ ··· − 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
69
+ 34y
68
+ ··· − 3y −1
c
2
y
69
+ 6y
68
+ ··· + 29y −1
c
3
, c
7
y
69
+ 35y
68
+ ··· − 44032y −4096
c
5
y
69
− 22y
68
+ ··· + 5956197y −1329409
c
6
, c
10
y
69
− 23y
68
+ ··· − 4y −1
c
8
y
69
− 11y
68
+ ··· + 10500084y −877969
c
9
, c
11
y
69
+ 49y
68
+ ··· − 4y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.620084 + 0.792709I
a = −0.74143 − 1.28998I
b = 0.57525 − 1.64676I
−3.30752 − 1.68121I 0
u = −0.620084 − 0.792709I
a = −0.74143 + 1.28998I
b = 0.57525 + 1.64676I
−3.30752 + 1.68121I 0
u = 0.684134 + 0.748318I
a = 0.36010 + 2.15851I
b = 2.88057 + 0.64719I
1.42174 + 3.69530I 0
u = 0.684134 − 0.748318I
a = 0.36010 − 2.15851I
b = 2.88057 − 0.64719I
1.42174 − 3.69530I 0
u = −1.018820 + 0.054091I
a = −2.12560 + 0.70969I
b = −1.080890 + 0.121563I
−4.13213 + 3.64791I −10.05983 + 0.I
u = −1.018820 − 0.054091I
a = −2.12560 − 0.70969I
b = −1.080890 − 0.121563I
−4.13213 − 3.64791I −10.05983 + 0.I
u = 0.757016 + 0.607386I
a = −0.61533 + 1.53607I
b = 1.55783 + 1.59883I
−0.06717 − 3.13357I −4.80388 + 4.92855I
u = 0.757016 − 0.607386I
a = −0.61533 − 1.53607I
b = 1.55783 − 1.59883I
−0.06717 + 3.13357I −4.80388 − 4.92855I
u = −0.753436 + 0.711663I
a = 0.189133 − 0.672774I
b = −0.509996 − 0.067709I
2.48833 + 3.11204I 0
u = −0.753436 − 0.711663I
a = 0.189133 + 0.672774I
b = −0.509996 + 0.067709I
2.48833 − 3.11204I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.721710 + 0.747525I
a = −0.163681 + 0.945744I
b = −0.148711 − 0.025106I
3.30960 − 2.06237I 0
u = −0.721710 − 0.747525I
a = −0.163681 − 0.945744I
b = −0.148711 + 0.025106I
3.30960 + 2.06237I 0
u = 0.957145 + 0.038173I
a = 0.164596 + 0.280788I
b = 0.40893 + 1.40875I
−2.00723 − 2.55767I −10.61202 + 4.63475I
u = 0.957145 − 0.038173I
a = 0.164596 − 0.280788I
b = 0.40893 − 1.40875I
−2.00723 + 2.55767I −10.61202 − 4.63475I
u = 0.739249 + 0.744320I
a = −0.36989 − 1.54589I
b = −2.02675 − 0.23487I
3.53880 − 0.84616I 0
u = 0.739249 − 0.744320I
a = −0.36989 + 1.54589I
b = −2.02675 + 0.23487I
3.53880 + 0.84616I 0
u = −0.669660 + 0.814511I
a = 0.21586 + 1.69058I
b = −1.55340 + 0.94507I
1.48274 − 4.64133I 0
u = −0.669660 − 0.814511I
a = 0.21586 − 1.69058I
b = −1.55340 − 0.94507I
1.48274 + 4.64133I 0
u = −0.663443 + 0.838478I
a = −0.32742 − 2.04165I
b = 2.14814 − 1.38487I
−0.95244 − 9.80543I 0
u = −0.663443 − 0.838478I
a = −0.32742 + 2.04165I
b = 2.14814 + 1.38487I
−0.95244 + 9.80543I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.069640 + 0.121587I
a = 1.383900 + 0.064655I
b = 1.011640 + 0.155727I
−4.92005 − 4.43213I 0
u = 1.069640 − 0.121587I
a = 1.383900 − 0.064655I
b = 1.011640 − 0.155727I
−4.92005 + 4.43213I 0
u = −0.910624
a = 1.15059
b = 0.724599
−1.54956 −5.79310
u = 1.096170 + 0.077778I
a = −1.187760 + 0.693218I
b = −0.508671 − 0.071320I
−9.42165 − 0.97729I 0
u = 1.096170 − 0.077778I
a = −1.187760 − 0.693218I
b = −0.508671 + 0.071320I
−9.42165 + 0.97729I 0
u = 1.096180 + 0.140788I
a = −1.90353 − 0.09913I
b = −1.124720 + 0.210315I
−7.64943 − 9.45868I 0
u = 1.096180 − 0.140788I
a = −1.90353 + 0.09913I
b = −1.124720 − 0.210315I
−7.64943 + 9.45868I 0
u = −0.970729 + 0.528704I
a = −0.639720 − 0.025923I
b = −0.97663 − 1.40719I
−2.57806 + 1.76748I 0
u = −0.970729 − 0.528704I
a = −0.639720 + 0.025923I
b = −0.97663 + 1.40719I
−2.57806 − 1.76748I 0
u = −1.012390 + 0.483692I
a = 1.203180 + 0.248675I
b = 0.94688 + 2.11622I
−5.59193 − 2.78605I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.012390 − 0.483692I
a = 1.203180 − 0.248675I
b = 0.94688 − 2.11622I
−5.59193 + 2.78605I 0
u = 0.817402 + 0.784634I
a = −0.522773 − 0.578493I
b = −0.589673 + 0.434002I
4.09856 − 2.01146I 0
u = 0.817402 − 0.784634I
a = −0.522773 + 0.578493I
b = −0.589673 − 0.434002I
4.09856 + 2.01146I 0
u = −0.835392 + 0.165049I
a = 0.471504 − 0.753519I
b = 0.448734 − 0.560979I
−1.57618 + 0.35138I −8.53058 − 0.76832I
u = −0.835392 − 0.165049I
a = 0.471504 + 0.753519I
b = 0.448734 + 0.560979I
−1.57618 − 0.35138I −8.53058 + 0.76832I
u = 0.958278 + 0.638119I
a = 1.79930 − 0.63520I
b = 0.60710 − 3.04859I
−0.73989 − 1.80119I 0
u = 0.958278 − 0.638119I
a = 1.79930 + 0.63520I
b = 0.60710 + 3.04859I
−0.73989 + 1.80119I 0
u = −1.021490 + 0.565890I
a = 0.705105 − 0.650077I
b = 1.78899 + 1.10656I
−6.45549 + 5.60193I 0
u = −1.021490 − 0.565890I
a = 0.705105 + 0.650077I
b = 1.78899 − 1.10656I
−6.45549 − 5.60193I 0
u = −0.954179 + 0.682947I
a = 0.475159 − 0.057085I
b = 0.520320 − 0.735924I
1.87091 + 2.24800I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.954179 − 0.682947I
a = 0.475159 + 0.057085I
b = 0.520320 + 0.735924I
1.87091 − 2.24800I 0
u = 0.851035 + 0.816929I
a = 0.494489 + 0.078024I
b = −0.423380 − 0.437237I
2.44272 − 6.15643I 0
u = 0.851035 − 0.816929I
a = 0.494489 − 0.078024I
b = −0.423380 + 0.437237I
2.44272 + 6.15643I 0
u = 0.965906 + 0.700019I
a = −1.50890 − 0.31337I
b = −2.06844 + 1.83162I
2.84817 − 4.66103I 0
u = 0.965906 − 0.700019I
a = −1.50890 + 0.31337I
b = −2.06844 − 1.83162I
2.84817 + 4.66103I 0
u = 0.929274 + 0.754481I
a = −0.504463 − 0.456421I
b = −1.276140 − 0.176378I
3.75509 − 3.78687I 0
u = 0.929274 − 0.754481I
a = −0.504463 + 0.456421I
b = −1.276140 + 0.176378I
3.75509 + 3.78687I 0
u = −0.977343 + 0.698293I
a = −0.773277 + 0.042094I
b = −1.143270 + 0.001207I
2.53315 + 7.57441I 0
u = −0.977343 − 0.698293I
a = −0.773277 − 0.042094I
b = −1.143270 − 0.001207I
2.53315 − 7.57441I 0
u = 0.996040 + 0.691361I
a = 2.09972 + 0.48052I
b = 2.83797 − 2.81894I
0.48440 − 9.18841I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.996040 − 0.691361I
a = 2.09972 − 0.48052I
b = 2.83797 + 2.81894I
0.48440 + 9.18841I 0
u = 0.915358 + 0.795783I
a = 0.055765 + 0.369318I
b = 0.341328 + 1.097470I
2.24452 + 0.13399I 0
u = 0.915358 − 0.795783I
a = 0.055765 − 0.369318I
b = 0.341328 − 1.097470I
2.24452 − 0.13399I 0
u = −0.363800 + 0.683750I
a = 0.159725 − 0.902915I
b = 1.194090 − 0.050123I
−4.64351 − 0.95645I −6.95143 + 0.40009I
u = −0.363800 − 0.683750I
a = 0.159725 + 0.902915I
b = 1.194090 + 0.050123I
−4.64351 + 0.95645I −6.95143 − 0.40009I
u = −1.031700 + 0.690591I
a = 1.31406 + 0.73889I
b = 0.12386 + 2.26773I
−4.53517 + 7.27554I 0
u = −1.031700 − 0.690591I
a = 1.31406 − 0.73889I
b = 0.12386 − 2.26773I
−4.53517 − 7.27554I 0
u = −1.022320 + 0.715446I
a = −1.59446 − 0.20723I
b = −1.63571 − 2.33602I
0.41311 + 10.39030I 0
u = −1.022320 − 0.715446I
a = −1.59446 + 0.20723I
b = −1.63571 + 2.33602I
0.41311 − 10.39030I 0
u = −1.033670 + 0.722916I
a = 1.93233 + 0.24814I
b = 1.87661 + 3.18870I
−2.0811 + 15.6439I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.033670 − 0.722916I
a = 1.93233 − 0.24814I
b = 1.87661 − 3.18870I
−2.0811 − 15.6439I 0
u = −0.222610 + 0.700574I
a = −1.01534 − 1.68362I
b = 0.425358 − 1.228400I
−3.29307 + 6.95572I −4.27136 − 6.38165I
u = −0.222610 − 0.700574I
a = −1.01534 + 1.68362I
b = 0.425358 + 1.228400I
−3.29307 − 6.95572I −4.27136 + 6.38165I
u = −0.237379 + 0.619505I
a = 0.999266 + 0.903446I
b = −0.257184 + 0.499151I
−0.72685 + 2.26761I −0.99875 − 3.18261I
u = −0.237379 − 0.619505I
a = 0.999266 − 0.903446I
b = −0.257184 − 0.499151I
−0.72685 − 2.26761I −0.99875 + 3.18261I
u = 0.262483 + 0.300390I
a = −2.06293 + 0.91307I
b = 0.607715 + 1.007860I
−0.30141 − 2.59969I 1.01042 + 4.25911I
u = 0.262483 − 0.300390I
a = −2.06293 − 0.91307I
b = 0.607715 − 1.007860I
−0.30141 + 2.59969I 1.01042 − 4.25911I
u = −0.009849 + 0.393003I
a = 1.95800 − 0.60378I
b = 0.159962 − 0.526209I
0.74701 + 1.37700I 2.48134 − 4.28508I
u = −0.009849 − 0.393003I
a = 1.95800 + 0.60378I
b = 0.159962 + 0.526209I
0.74701 − 1.37700I 2.48134 + 4.28508I
11
II. I
u
2
= h−u
2
b + b
2
+ bu − u + 1, a, u
3
− u
2
+ 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
10
=
1
−u
2
a
3
=
0
b
a
6
=
u
−u
2
+ u + 1
a
5
=
u
−2u
2
+ b + 2u + 1
a
9
=
−u
2
+ 1
−u
2
a
1
=
−u
u
2
− u − 1
a
2
=
u
2
b
bu + 2b
a
8
=
0
u
a
4
=
0
b
a
4
=
0
b
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
2
b − 2bu + u
2
+ 2u − 5
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u
2
+ u + 1)
3
c
3
, c
7
u
6
c
4
(u
2
− u + 1)
3
c
6
(u
3
+ u
2
− 1)
2
c
8
, c
11
(u
3
+ u
2
+ 2u + 1)
2
c
9
(u
3
− u
2
+ 2u − 1)
2
c
10
(u
3
− u
2
+ 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
3
c
3
, c
7
y
6
c
6
, c
10
(y
3
− y
2
+ 2y −1)
2
c
8
, c
9
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 0
b = −0.818128 − 0.292480I
3.02413 − 4.85801I −2.23639 + 5.66123I
u = 0.877439 + 0.744862I
a = 0
b = 0.155769 + 0.854759I
3.02413 − 0.79824I −0.946254 + 0.677361I
u = 0.877439 − 0.744862I
a = 0
b = −0.818128 + 0.292480I
3.02413 + 4.85801I −2.23639 − 5.66123I
u = 0.877439 − 0.744862I
a = 0
b = 0.155769 − 0.854759I
3.02413 + 0.79824I −0.946254 − 0.677361I
u = −0.754878
a = 0
b = 0.662359 + 1.147240I
−1.11345 − 2.02988I −5.31735 + 1.07831I
u = −0.754878
a = 0
b = 0.662359 − 1.147240I
−1.11345 + 2.02988I −5.31735 − 1.07831I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
3
)(u
69
+ 4u
68
+ ··· − 3u − 1)
c
2
((u
2
+ u + 1)
3
)(u
69
+ 34u
68
+ ··· − 3u − 1)
c
3
, c
7
u
6
(u
69
− u
68
+ ··· + 224u + 64)
c
4
((u
2
− u + 1)
3
)(u
69
+ 4u
68
+ ··· − 3u − 1)
c
5
((u
2
+ u + 1)
3
)(u
69
− 4u
68
+ ··· + 5265u − 1153)
c
6
((u
3
+ u
2
− 1)
2
)(u
69
+ 3u
68
+ ··· + 2u + 1)
c
8
((u
3
+ u
2
+ 2u + 1)
2
)(u
69
− 3u
68
+ ··· − 7540u + 937)
c
9
((u
3
− u
2
+ 2u − 1)
2
)(u
69
+ 23u
68
+ ··· − 4u + 1)
c
10
((u
3
− u
2
+ 1)
2
)(u
69
+ 3u
68
+ ··· + 2u + 1)
c
11
((u
3
+ u
2
+ 2u + 1)
2
)(u
69
+ 23u
68
+ ··· − 4u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
3
)(y
69
+ 34y
68
+ ··· − 3y −1)
c
2
((y
2
+ y + 1)
3
)(y
69
+ 6y
68
+ ··· + 29y −1)
c
3
, c
7
y
6
(y
69
+ 35y
68
+ ··· − 44032y −4096)
c
5
((y
2
+ y + 1)
3
)(y
69
− 22y
68
+ ··· + 5956197y −1329409)
c
6
, c
10
((y
3
− y
2
+ 2y −1)
2
)(y
69
− 23y
68
+ ··· − 4y −1)
c
8
((y
3
+ 3y
2
+ 2y −1)
2
)(y
69
− 11y
68
+ ··· + 1.05001 × 10
7
y −877969)
c
9
, c
11
((y
3
+ 3y
2
+ 2y −1)
2
)(y
69
+ 49y
68
+ ··· − 4y −1)
17
