11a
28
(K11a
28
)
A knot diagram
1
Linearized knot diagam
5 1 10 2 9 3 11 4 6 7 8
Solving Sequence
7,11
8
1,3
2 6 10 4 9 5
c
7
c
11
c
2
c
6
c
10
c
3
c
9
c
5
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h2.01615 × 10
63
u
59
− 7.91768 × 10
63
u
58
+ ··· + 1.22570 × 10
63
b − 6.80954 × 10
62
,
4.32115 × 10
62
u
59
− 2.12406 × 10
63
u
58
+ ··· + 4.08568 × 10
62
a − 3.28832 × 10
62
, u
60
− 5u
59
+ ··· + 5u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 60 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
=
h2.02×10
63
u
59
−7.92×10
63
u
58
+· · ·+1.23×10
63
b−6.81×10
62
, 4.32×10
62
u
59
−
2.12 × 10
63
u
58
+ · · · + 4.09 × 10
62
a − 3.29 × 10
62
, u
60
− 5u
59
+ · · · + 5u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
1
=
−u
−u
3
+ u
a
3
=
−1.05763u
59
+ 5.19879u
58
+ ··· − 2.64467u + 0.804841
−1.64489u
59
+ 6.45970u
58
+ ··· − 0.851795u + 0.555561
a
2
=
−3.61502u
59
+ 14.3888u
58
+ ··· + 0.169951u + 2.62747
−3.69618u
59
+ 14.2840u
58
+ ··· − 1.10903u + 2.32983
a
6
=
0.370829u
59
− 0.610393u
58
+ ··· + 4.23462u + 0.393300
−1.17480u
59
+ 5.71906u
58
+ ··· + 2.79612u + 1.18421
a
10
=
u
u
a
4
=
−2.95589u
59
+ 12.2653u
58
+ ··· − 2.05741u + 2.48023
−3.54315u
59
+ 13.5262u
58
+ ··· − 0.264534u + 2.23095
a
9
=
3.21953u
59
− 12.4002u
58
+ ··· + 0.378631u − 1.25671
5.61791u
59
− 21.2160u
58
+ ··· + 0.447850u − 2.31429
a
5
=
3.31846u
59
− 11.7462u
58
+ ··· − 0.711385u − 2.30380
3.31846u
59
− 11.7462u
58
+ ··· − 2.71138u − 2.30380
a
5
=
3.31846u
59
− 11.7462u
58
+ ··· − 0.711385u − 2.30380
3.31846u
59
− 11.7462u
58
+ ··· − 2.71138u − 2.30380
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10.2583u
59
+ 32.5172u
58
+ ··· + 12.1083u + 12.4600
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
60
+ u
59
+ ··· − 2u + 1
c
2
u
60
+ 25u
59
+ ··· + 6u + 1
c
3
u
60
− 3u
59
+ ··· − 4u + 1
c
5
, c
9
u
60
− u
59
+ ··· + 5u
2
+ 1
c
6
u
60
− 13u
59
+ ··· − 46u − 1
c
7
, c
10
, c
11
u
60
+ 5u
59
+ ··· + 5u
2
+ 1
c
8
u
60
+ 17u
59
+ ··· + 288u + 79
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
60
+ 25y
59
+ ··· + 6y + 1
c
2
y
60
+ 21y
59
+ ··· + 62y + 1
c
3
y
60
+ 5y
59
+ ··· + 30y + 1
c
5
, c
9
y
60
− 43y
59
+ ··· + 10y + 1
c
6
y
60
+ 109y
59
+ ··· − 2526y + 1
c
7
, c
10
, c
11
y
60
− 59y
59
+ ··· + 10y + 1
c
8
y
60
+ 73y
59
+ ··· − 15478y + 6241
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.533782 + 0.834528I
a = −0.670577 − 0.244749I
b = −0.90360 + 1.11851I
3.66250 + 11.73970I 0. − 9.07508I
u = −0.533782 − 0.834528I
a = −0.670577 + 0.244749I
b = −0.90360 − 1.11851I
3.66250 − 11.73970I 0. + 9.07508I
u = 0.911823 + 0.442516I
a = 0.720916 − 0.600914I
b = 0.661282 + 0.144344I
−2.94476 − 0.12365I 0
u = 0.911823 − 0.442516I
a = 0.720916 + 0.600914I
b = 0.661282 − 0.144344I
−2.94476 + 0.12365I 0
u = −0.698160 + 0.696499I
a = −0.527979 + 0.494269I
b = 0.451910 + 0.688864I
4.58804 − 1.10123I 0
u = −0.698160 − 0.696499I
a = −0.527979 − 0.494269I
b = 0.451910 − 0.688864I
4.58804 + 1.10123I 0
u = 0.481557 + 0.943096I
a = 0.369140 − 0.171842I
b = 0.746469 + 0.482040I
−1.19130 − 5.66306I 0
u = 0.481557 − 0.943096I
a = 0.369140 + 0.171842I
b = 0.746469 − 0.482040I
−1.19130 + 5.66306I 0
u = −0.617210 + 0.869107I
a = 0.378949 − 0.544669I
b = −0.494270 − 0.791701I
3.47399 − 6.14744I 0
u = −0.617210 − 0.869107I
a = 0.378949 + 0.544669I
b = −0.494270 + 0.791701I
3.47399 + 6.14744I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.435894 + 0.774361I
a = 0.472416 + 0.478267I
b = 0.804781 − 1.056000I
5.33401 + 6.06206I 5.25486 − 4.79805I
u = −0.435894 − 0.774361I
a = 0.472416 − 0.478267I
b = 0.804781 + 1.056000I
5.33401 − 6.06206I 5.25486 + 4.79805I
u = 1.201330 + 0.191717I
a = 1.064620 − 0.375117I
b = 0.790732 + 0.105612I
−2.92701 − 0.02185I 0
u = 1.201330 − 0.191717I
a = 1.064620 + 0.375117I
b = 0.790732 − 0.105612I
−2.92701 + 0.02185I 0
u = 0.240498 + 0.711477I
a = −0.001003 + 0.236197I
b = −0.565357 − 0.577780I
0.18899 − 1.45187I 1.34936 + 5.34755I
u = 0.240498 − 0.711477I
a = −0.001003 − 0.236197I
b = −0.565357 + 0.577780I
0.18899 + 1.45187I 1.34936 − 5.34755I
u = −1.27084
a = −1.71198
b = −0.0201988
1.61104 0
u = −0.529233 + 0.441086I
a = −1.45011 − 1.15685I
b = −0.949462 + 0.711668I
−1.15016 + 4.52322I −1.58408 − 7.91740I
u = −0.529233 − 0.441086I
a = −1.45011 + 1.15685I
b = −0.949462 − 0.711668I
−1.15016 − 4.52322I −1.58408 + 7.91740I
u = 1.310500 + 0.080285I
a = 0.683386 − 0.575495I
b = 0.315013 + 1.084750I
0.72651 − 3.69060I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.310500 − 0.080285I
a = 0.683386 + 0.575495I
b = 0.315013 − 1.084750I
0.72651 + 3.69060I 0
u = 1.325720 + 0.012392I
a = 1.57480 − 0.05757I
b = 1.151530 + 0.076666I
−3.09648 − 0.01865I 0
u = 1.325720 − 0.012392I
a = 1.57480 + 0.05757I
b = 1.151530 − 0.076666I
−3.09648 + 0.01865I 0
u = −1.349120 + 0.039607I
a = −0.773783 + 1.050430I
b = −0.63332 + 1.71678I
−3.47046 + 2.59110I 0
u = −1.349120 − 0.039607I
a = −0.773783 − 1.050430I
b = −0.63332 − 1.71678I
−3.47046 − 2.59110I 0
u = −1.389380 + 0.126415I
a = 1.57913 − 0.80479I
b = 0.163124 − 0.074758I
−2.17172 + 6.43280I 0
u = −1.389380 − 0.126415I
a = 1.57913 + 0.80479I
b = 0.163124 + 0.074758I
−2.17172 − 6.43280I 0
u = −0.019258 + 0.599596I
a = 0.340438 + 0.021539I
b = −0.531337 − 0.774461I
0.288784 − 1.376440I 1.36514 + 4.13021I
u = −0.019258 − 0.599596I
a = 0.340438 − 0.021539I
b = −0.531337 + 0.774461I
0.288784 + 1.376440I 1.36514 − 4.13021I
u = −1.407840 + 0.014691I
a = 7.96415 + 10.48020I
b = 7.88865 + 10.58440I
−3.27672 + 2.05815I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.407840 − 0.014691I
a = 7.96415 − 10.48020I
b = 7.88865 − 10.58440I
−3.27672 − 2.05815I 0
u = 1.41880 + 0.09036I
a = −2.04902 − 0.26241I
b = −1.238870 − 0.042642I
−5.60317 − 3.97257I 0
u = 1.41880 − 0.09036I
a = −2.04902 + 0.26241I
b = −1.238870 + 0.042642I
−5.60317 + 3.97257I 0
u = −1.46251 + 0.26342I
a = −1.42804 + 0.02348I
b = −1.117840 + 0.804567I
−5.51717 + 5.00817I 0
u = −1.46251 − 0.26342I
a = −1.42804 − 0.02348I
b = −1.117840 − 0.804567I
−5.51717 − 5.00817I 0
u = −0.511763
a = −0.617467
b = 0.872896
2.63603 0.0801050
u = 0.224433 + 0.448869I
a = 3.03949 + 0.10848I
b = −0.050575 + 0.698984I
2.95363 − 4.39756I 7.00202 + 8.96362I
u = 0.224433 − 0.448869I
a = 3.03949 − 0.10848I
b = −0.050575 − 0.698984I
2.95363 + 4.39756I 7.00202 − 8.96362I
u = 1.49614 + 0.15819I
a = −1.86240 + 0.11159I
b = −1.065680 − 0.882622I
−7.75326 − 6.77334I 0
u = 1.49614 − 0.15819I
a = −1.86240 − 0.11159I
b = −1.065680 + 0.882622I
−7.75326 + 6.77334I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.058164 + 0.491656I
a = −1.57145 + 1.91980I
b = 0.377145 − 0.730232I
4.80170 + 1.71569I 12.12772 − 3.69255I
u = −0.058164 − 0.491656I
a = −1.57145 − 1.91980I
b = 0.377145 + 0.730232I
4.80170 − 1.71569I 12.12772 + 3.69255I
u = 1.49031 + 0.27633I
a = 1.71435 + 0.26114I
b = 1.16235 + 1.22739I
−0.89788 − 9.86974I 0
u = 1.49031 − 0.27633I
a = 1.71435 − 0.26114I
b = 1.16235 − 1.22739I
−0.89788 + 9.86974I 0
u = −1.54271 + 0.14787I
a = 1.228230 + 0.200344I
b = 0.883110 − 0.618293I
−10.59540 + 2.29159I 0
u = −1.54271 − 0.14787I
a = 1.228230 − 0.200344I
b = 0.883110 + 0.618293I
−10.59540 − 2.29159I 0
u = −1.52921 + 0.32206I
a = 1.51542 + 0.06338I
b = 1.204880 − 0.703616I
−7.70682 + 10.17220I 0
u = −1.52921 − 0.32206I
a = 1.51542 − 0.06338I
b = 1.204880 + 0.703616I
−7.70682 − 10.17220I 0
u = 1.53838 + 0.29681I
a = −1.84096 − 0.34579I
b = −1.29978 − 1.23886I
−3.0641 − 15.8799I 0
u = 1.53838 − 0.29681I
a = −1.84096 + 0.34579I
b = −1.29978 + 1.23886I
−3.0641 + 15.8799I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52138 + 0.44760I
a = −0.660099 + 0.354611I
b = −0.626261 − 0.056205I
−4.06241 − 3.68110I 0
u = 1.52138 − 0.44760I
a = −0.660099 − 0.354611I
b = −0.626261 + 0.056205I
−4.06241 + 3.68110I 0
u = −0.026377 + 0.398328I
a = 1.213060 + 0.011016I
b = 0.114689 − 1.009800I
0.55804 − 1.39773I 4.97891 + 5.04482I
u = −0.026377 − 0.398328I
a = 1.213060 − 0.011016I
b = 0.114689 + 1.009800I
0.55804 + 1.39773I 4.97891 − 5.04482I
u = 0.350200 + 0.158260I
a = 0.126066 − 0.674384I
b = −0.17853 − 2.29857I
2.11725 + 2.35876I −9.10328 + 7.61988I
u = 0.350200 − 0.158260I
a = 0.126066 + 0.674384I
b = −0.17853 + 2.29857I
2.11725 − 2.35876I −9.10328 − 7.61988I
u = −0.246546 + 0.282002I
a = −2.25461 + 0.06127I
b = −0.772232 + 0.632114I
−0.19554 + 2.59737I 1.80279 − 1.62726I
u = −0.246546 − 0.282002I
a = −2.25461 − 0.06127I
b = −0.772232 − 0.632114I
−0.19554 − 2.59737I 1.80279 + 1.62726I
u = 1.72565 + 0.13500I
a = −0.229827 + 0.251060I
b = −0.214921 − 0.081832I
−4.67108 + 1.62217I 0
u = 1.72565 − 0.13500I
a = −0.229827 − 0.251060I
b = −0.214921 + 0.081832I
−4.67108 − 1.62217I 0
10
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u
60
+ u
59
+ ··· − 2u + 1
c
2
u
60
+ 25u
59
+ ··· + 6u + 1
c
3
u
60
− 3u
59
+ ··· − 4u + 1
c
5
, c
9
u
60
− u
59
+ ··· + 5u
2
+ 1
c
6
u
60
− 13u
59
+ ··· − 46u − 1
c
7
, c
10
, c
11
u
60
+ 5u
59
+ ··· + 5u
2
+ 1
c
8
u
60
+ 17u
59
+ ··· + 288u + 79
11
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
60
+ 25y
59
+ ··· + 6y + 1
c
2
y
60
+ 21y
59
+ ··· + 62y + 1
c
3
y
60
+ 5y
59
+ ··· + 30y + 1
c
5
, c
9
y
60
− 43y
59
+ ··· + 10y + 1
c
6
y
60
+ 109y
59
+ ··· − 2526y + 1
c
7
, c
10
, c
11
y
60
− 59y
59
+ ··· + 10y + 1
c
8
y
60
+ 73y
59
+ ··· − 15478y + 6241
12
