11a
19
(K11a
19
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 11 3 10 5 6 8 9
Solving Sequence
7,10
8
4,11
3 6 5 9 1 2
c
7
c
10
c
3
c
6
c
5
c
9
c
11
c
2
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.87320 × 10
210
u
81
− 1.20023 × 10
211
u
80
+ ··· + 9.45125 × 10
210
b + 3.16425 × 10
211
,
− 3.92506 × 10
210
u
81
− 1.98955 × 10
211
u
80
+ ··· + 9.45125 × 10
210
a + 1.04962 × 10
212
,
u
82
+ 2u
81
+ ··· − 14u + 1i
I
u
2
= hb, u
4
+ 2u
3
− u
2
+ a − 2u + 1, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 87 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−4.87 × 10
210
u
81
− 1.20 × 10
211
u
80
+ · · · + 9.45 × 10
210
b + 3.16 ×
10
211
, −3.93 × 10
210
u
81
− 1.99 × 10
211
u
80
+ · · · + 9.45 × 10
210
a + 1.05 ×
10
212
, u
82
+ 2u
81
+ · · · − 14u + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
u
2
a
4
=
0.415295u
81
+ 2.10506u
80
+ ··· + 60.6066u − 11.1056
0.515615u
81
+ 1.26991u
80
+ ··· + 34.9413u − 3.34798
a
11
=
−u
−u
3
+ u
a
3
=
−0.100320u
81
+ 0.835147u
80
+ ··· + 25.6654u − 7.75762
0.515615u
81
+ 1.26991u
80
+ ··· + 34.9413u − 3.34798
a
6
=
−3.43660u
81
− 6.69037u
80
+ ··· − 178.963u + 19.1560
0.576262u
81
+ 1.37956u
80
+ ··· + 35.0206u − 4.11670
a
5
=
−3.52357u
81
− 6.81623u
80
+ ··· − 181.274u + 19.5081
0.650978u
81
+ 1.56146u
80
+ ··· + 38.0919u − 4.51689
a
9
=
3.00786u
81
+ 6.93064u
80
+ ··· + 127.142u − 16.1937
−0.830021u
81
− 1.31043u
80
+ ··· − 9.56980u + 1.53913
a
1
=
−0.391728u
81
− 0.569793u
80
+ ··· − 11.0911u + 0.107632
0.209315u
81
+ 0.531440u
80
+ ··· + 14.4741u − 1.32129
a
2
=
−1.27363u
81
− 1.06364u
80
+ ··· − 21.3993u − 3.22549
0.928834u
81
+ 2.25698u
80
+ ··· + 59.9874u − 6.00986
a
2
=
−1.27363u
81
− 1.06364u
80
+ ··· − 21.3993u − 3.22549
0.928834u
81
+ 2.25698u
80
+ ··· + 59.9874u − 6.00986
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.57351u
81
− 11.9801u
80
+ ··· − 75.2514u + 4.08934
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
82
− 6u
81
+ ··· + 8u − 1
c
2
u
82
+ 42u
81
+ ··· + 32u + 1
c
3
, c
6
u
82
− u
81
+ ··· + 160u + 32
c
5
u
82
− 6u
81
+ ··· + 2u − 1
c
7
, c
10
u
82
− 2u
81
+ ··· + 14u + 1
c
8
u
82
− 2u
81
+ ··· − 2362u − 484
c
9
u
82
+ 2u
81
+ ··· − 20520u − 1647
c
11
u
82
+ 14u
81
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
82
− 42y
81
+ ··· − 32y + 1
c
2
y
82
+ 2y
81
+ ··· − 484y + 1
c
3
, c
6
y
82
− 33y
81
+ ··· − 19968y + 1024
c
5
y
82
− 14y
81
+ ··· − 6y + 1
c
7
, c
10
y
82
− 58y
81
+ ··· + 14y + 1
c
8
y
82
+ 90y
81
+ ··· + 10862436y + 234256
c
9
y
82
+ 50y
81
+ ··· − 261288342y + 2712609
c
11
y
82
+ 6y
81
+ ··· + 14y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.372669 + 0.922938I
a = −0.285302 + 0.713657I
b = 1.210700 − 0.018520I
5.22827 − 3.35824I 0
u = −0.372669 − 0.922938I
a = −0.285302 − 0.713657I
b = 1.210700 + 0.018520I
5.22827 + 3.35824I 0
u = 0.111866 + 0.982814I
a = 1.122340 + 0.776633I
b = −0.795431 + 0.455251I
−2.09067 − 2.95787I 0
u = 0.111866 − 0.982814I
a = 1.122340 − 0.776633I
b = −0.795431 − 0.455251I
−2.09067 + 2.95787I 0
u = −0.948714 + 0.407094I
a = −0.318376 − 0.441347I
b = −1.406120 − 0.046993I
3.48456 + 2.48996I 0
u = −0.948714 − 0.407094I
a = −0.318376 + 0.441347I
b = −1.406120 + 0.046993I
3.48456 − 2.48996I 0
u = 1.037470 + 0.112404I
a = −0.90746 + 3.49927I
b = −0.959272 + 0.364632I
−0.006489 − 1.319230I 0
u = 1.037470 − 0.112404I
a = −0.90746 − 3.49927I
b = −0.959272 − 0.364632I
−0.006489 + 1.319230I 0
u = 1.043930 + 0.027951I
a = 3.12377 + 3.75803I
b = 0.502899 + 0.690068I
−3.74856 − 1.03244I 0
u = 1.043930 − 0.027951I
a = 3.12377 − 3.75803I
b = 0.502899 − 0.690068I
−3.74856 + 1.03244I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.924124 + 0.155896I
a = −1.74666 + 0.78782I
b = 0.137431 + 0.591455I
−2.85067 − 0.96287I 0
u = 0.924124 − 0.155896I
a = −1.74666 − 0.78782I
b = 0.137431 − 0.591455I
−2.85067 + 0.96287I 0
u = −0.528336 + 0.760241I
a = 0.090830 − 1.282120I
b = −1.209490 − 0.228611I
4.80113 + 1.92406I 0
u = −0.528336 − 0.760241I
a = 0.090830 + 1.282120I
b = −1.209490 + 0.228611I
4.80113 − 1.92406I 0
u = −1.062450 + 0.212626I
a = −0.49224 − 1.74839I
b = −1.17978 − 0.78731I
0.01560 + 3.91593I 0
u = −1.062450 − 0.212626I
a = −0.49224 + 1.74839I
b = −1.17978 + 0.78731I
0.01560 − 3.91593I 0
u = 0.055196 + 1.089590I
a = 0.226034 − 0.928899I
b = −0.518282 − 0.941047I
−1.46560 − 5.42569I 0
u = 0.055196 − 1.089590I
a = 0.226034 + 0.928899I
b = −0.518282 + 0.941047I
−1.46560 + 5.42569I 0
u = 1.09577
a = −5.87610
b = 0.385176
−3.80714 0
u = −1.087480 + 0.153969I
a = −0.10618 − 1.58690I
b = −0.214732 − 1.243670I
−2.85407 + 3.43010I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.087480 − 0.153969I
a = −0.10618 + 1.58690I
b = −0.214732 + 1.243670I
−2.85407 − 3.43010I 0
u = −1.099320 + 0.078865I
a = 0.76703 − 1.64881I
b = 0.713526 − 1.219340I
−4.70519 + 2.39134I 0
u = −1.099320 − 0.078865I
a = 0.76703 + 1.64881I
b = 0.713526 + 1.219340I
−4.70519 − 2.39134I 0
u = −1.115110 + 0.022821I
a = 0.240080 − 1.062120I
b = 1.243650 − 0.511416I
−5.52870 + 0.86398I 0
u = −1.115110 − 0.022821I
a = 0.240080 + 1.062120I
b = 1.243650 + 0.511416I
−5.52870 − 0.86398I 0
u = 1.121470 + 0.103386I
a = 1.55262 − 3.24881I
b = 1.050130 − 0.595633I
−2.13971 − 6.01246I 0
u = 1.121470 − 0.103386I
a = 1.55262 + 3.24881I
b = 1.050130 + 0.595633I
−2.13971 + 6.01246I 0
u = 0.817286 + 0.838746I
a = −0.177044 − 0.087912I
b = 0.879104 + 0.018096I
−0.34685 − 2.85468I 0
u = 0.817286 − 0.838746I
a = −0.177044 + 0.087912I
b = 0.879104 − 0.018096I
−0.34685 + 2.85468I 0
u = −0.041190 + 1.176220I
a = −0.356813 − 0.500680I
b = 1.110290 − 0.524652I
2.93914 − 6.11947I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.041190 − 1.176220I
a = −0.356813 + 0.500680I
b = 1.110290 + 0.524652I
2.93914 + 6.11947I 0
u = 0.783636 + 0.165518I
a = 0.38779 + 2.04319I
b = −0.959378 − 0.173898I
0.603497 + 0.216471I −3.00000 − 5.07001I
u = 0.783636 − 0.165518I
a = 0.38779 − 2.04319I
b = −0.959378 + 0.173898I
0.603497 − 0.216471I −3.00000 + 5.07001I
u = −1.085630 + 0.509853I
a = 0.180279 + 0.797287I
b = 1.382850 + 0.228355I
2.97750 + 8.50086I 0
u = −1.085630 − 0.509853I
a = 0.180279 − 0.797287I
b = 1.382850 − 0.228355I
2.97750 − 8.50086I 0
u = −1.190570 + 0.263500I
a = 0.40339 + 1.85670I
b = 1.16152 + 0.83000I
−3.13741 + 9.59200I 0
u = −1.190570 − 0.263500I
a = 0.40339 − 1.85670I
b = 1.16152 − 0.83000I
−3.13741 − 9.59200I 0
u = 0.516137 + 1.108300I
a = −0.114506 − 0.399456I
b = −0.916579 − 0.485003I
−1.65757 + 0.93442I 0
u = 0.516137 − 1.108300I
a = −0.114506 + 0.399456I
b = −0.916579 + 0.485003I
−1.65757 − 0.93442I 0
u = −0.014957 + 0.768895I
a = −0.717422 + 0.722948I
b = 0.134543 + 0.766173I
0.28541 − 1.54658I −0.57343 + 2.06881I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.014957 − 0.768895I
a = −0.717422 − 0.722948I
b = 0.134543 − 0.766173I
0.28541 + 1.54658I −0.57343 − 2.06881I
u = 0.025777 + 1.279070I
a = 0.180112 + 0.766794I
b = −1.131140 + 0.685484I
0.45408 − 11.38860I 0
u = 0.025777 − 1.279070I
a = 0.180112 − 0.766794I
b = −1.131140 − 0.685484I
0.45408 + 11.38860I 0
u = 0.586949 + 0.306956I
a = −0.394714 − 1.242930I
b = 1.013700 + 0.500772I
−0.96667 + 4.63901I −3.87963 − 8.57640I
u = 0.586949 − 0.306956I
a = −0.394714 + 1.242930I
b = 1.013700 − 0.500772I
−0.96667 − 4.63901I −3.87963 + 8.57640I
u = 1.34181
a = 0.104308
b = 0.435201
−2.55123 0
u = −1.294620 + 0.433035I
a = 0.629514 − 1.164780I
b = 0.399119 − 1.045250I
−3.71598 + 6.06156I 0
u = −1.294620 − 0.433035I
a = 0.629514 + 1.164780I
b = 0.399119 + 1.045250I
−3.71598 − 6.06156I 0
u = −1.42187 + 0.12543I
a = 0.601248 + 0.581607I
b = 0.535579 + 0.443898I
−7.77694 + 4.95365I 0
u = −1.42187 − 0.12543I
a = 0.601248 − 0.581607I
b = 0.535579 − 0.443898I
−7.77694 − 4.95365I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.34855 + 0.46968I
a = 0.39620 − 1.58221I
b = −1.033970 − 0.543976I
−6.58899 + 8.11200I 0
u = −1.34855 − 0.46968I
a = 0.39620 + 1.58221I
b = −1.033970 + 0.543976I
−6.58899 − 8.11200I 0
u = −1.36225 + 0.50910I
a = −0.87526 + 1.16446I
b = −0.617126 + 1.091420I
−5.89382 + 11.02700I 0
u = −1.36225 − 0.50910I
a = −0.87526 − 1.16446I
b = −0.617126 − 1.091420I
−5.89382 − 11.02700I 0
u = −1.36047 + 0.56106I
a = −0.02227 + 1.66535I
b = 1.189870 + 0.667621I
−1.22744 + 12.16920I 0
u = −1.36047 − 0.56106I
a = −0.02227 − 1.66535I
b = 1.189870 − 0.667621I
−1.22744 − 12.16920I 0
u = −1.46239 + 0.32296I
a = −0.756015 + 0.523946I
b = −0.596900 + 0.506514I
−8.00907 + 3.75643I 0
u = −1.46239 − 0.32296I
a = −0.756015 − 0.523946I
b = −0.596900 − 0.506514I
−8.00907 − 3.75643I 0
u = 1.31960 + 0.71550I
a = −0.208693 − 1.217520I
b = 0.940672 − 0.500766I
−1.85423 − 3.78257I 0
u = 1.31960 − 0.71550I
a = −0.208693 + 1.217520I
b = 0.940672 + 0.500766I
−1.85423 + 3.78257I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43309 + 0.47733I
a = 0.54768 + 1.85069I
b = −0.676418 + 0.654214I
−5.91812 − 0.62603I 0
u = 1.43309 − 0.47733I
a = 0.54768 − 1.85069I
b = −0.676418 − 0.654214I
−5.91812 + 0.62603I 0
u = 1.39410 + 0.58186I
a = −0.362073 − 1.189890I
b = −0.603714 − 0.799274I
−5.73183 − 3.04738I 0
u = 1.39410 − 0.58186I
a = −0.362073 + 1.189890I
b = −0.603714 + 0.799274I
−5.73183 + 3.04738I 0
u = 1.49404 + 0.24932I
a = 0.416319 + 0.504070I
b = 0.717839 + 0.375621I
−2.65606 + 0.12519I 0
u = 1.49404 − 0.24932I
a = 0.416319 − 0.504070I
b = 0.717839 − 0.375621I
−2.65606 − 0.12519I 0
u = −1.41333 + 0.57602I
a = −0.03235 − 1.85061I
b = −1.169980 − 0.781904I
−4.0922 + 17.7863I 0
u = −1.41333 − 0.57602I
a = −0.03235 + 1.85061I
b = −1.169980 + 0.781904I
−4.0922 − 17.7863I 0
u = 0.017201 + 0.444698I
a = −0.421573 + 0.688439I
b = 1.140810 − 0.618738I
0.34729 − 6.79546I −2.04718 + 3.52041I
u = 0.017201 − 0.444698I
a = −0.421573 − 0.688439I
b = 1.140810 + 0.618738I
0.34729 + 6.79546I −2.04718 − 3.52041I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.047106 + 0.410466I
a = −1.47054 − 0.16933I
b = −0.217093 + 0.544112I
0.041508 − 1.376630I 0.16544 + 4.98668I
u = 0.047106 − 0.410466I
a = −1.47054 + 0.16933I
b = −0.217093 − 0.544112I
0.041508 + 1.376630I 0.16544 − 4.98668I
u = 1.46595 + 0.77759I
a = −0.08409 + 1.44082I
b = −1.043820 + 0.658784I
−4.37377 − 8.54127I 0
u = 1.46595 − 0.77759I
a = −0.08409 − 1.44082I
b = −1.043820 − 0.658784I
−4.37377 + 8.54127I 0
u = −0.116621 + 0.310795I
a = −0.295025 − 1.350840I
b = −1.130240 + 0.389337I
2.44851 − 1.57419I 1.58009 − 0.44639I
u = −0.116621 − 0.310795I
a = −0.295025 + 1.350840I
b = −1.130240 − 0.389337I
2.44851 + 1.57419I 1.58009 + 0.44639I
u = 1.67621 + 0.41894I
a = −0.801743 − 0.790902I
b = −0.973653 − 0.605011I
−5.00012 + 4.29669I 0
u = 1.67621 − 0.41894I
a = −0.801743 + 0.790902I
b = −0.973653 + 0.605011I
−5.00012 − 4.29669I 0
u = 0.182502 + 0.012960I
a = −5.67324 + 0.60050I
b = 0.570425 + 0.460109I
−2.36954 − 0.63816I −5.46759 − 1.52326I
u = 0.182502 − 0.012960I
a = −5.67324 − 0.60050I
b = 0.570425 − 0.460109I
−2.36954 + 0.63816I −5.46759 + 1.52326I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.054094 + 0.154978I
a = −4.35975 − 0.04873I
b = 0.408288 + 0.821403I
−1.87549 − 1.38403I −4.93593 + 0.98614I
u = 0.054094 − 0.154978I
a = −4.35975 + 0.04873I
b = 0.408288 − 0.821403I
−1.87549 + 1.38403I −4.93593 − 0.98614I
13
II. I
u
2
= hb, u
4
+ 2u
3
− u
2
+ a − 2u + 1, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
u
2
a
4
=
−u
4
− 2u
3
+ u
2
+ 2u − 1
0
a
11
=
−u
−u
3
+ u
a
3
=
−u
4
− 2u
3
+ u
2
+ 2u − 1
0
a
6
=
1
0
a
5
=
−u
4
+ u
2
+ 1
−u
4
+ u
3
+ u
2
− 2u + 1
a
9
=
u
u
a
1
=
u
4
− u
2
− 1
u
4
− u
3
− u
2
+ 2u − 1
a
2
=
−2u
3
+ 2u − 2
u
4
− u
3
− u
2
+ 2u − 1
a
2
=
−2u
3
+ 2u − 2
u
4
− u
3
− u
2
+ 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
4
− 7u
3
+ 2u
2
+ 6u − 7
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
5
c
2
, c
4
(u + 1)
5
c
3
, c
6
u
5
c
5
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
7
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
8
, c
11
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
9
, c
10
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
6
y
5
c
5
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
7
, c
9
, c
10
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
8
, c
11
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21774
a = −2.89210
b = 0
−4.04602 −15.9650
u = 0.309916 + 0.549911I
a = −0.01014 + 1.59703I
b = 0
−1.97403 − 1.53058I −3.57269 + 4.45807I
u = 0.309916 − 0.549911I
a = −0.01014 − 1.59703I
b = 0
−1.97403 + 1.53058I −3.57269 − 4.45807I
u = −1.41878 + 0.21917I
a = −0.043806 − 0.365575I
b = 0
−7.51750 + 4.40083I −3.44484 − 1.78781I
u = −1.41878 − 0.21917I
a = −0.043806 + 0.365575I
b = 0
−7.51750 − 4.40083I −3.44484 + 1.78781I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
82
− 6u
81
+ ··· + 8u − 1)
c
2
((u + 1)
5
)(u
82
+ 42u
81
+ ··· + 32u + 1)
c
3
, c
6
u
5
(u
82
− u
81
+ ··· + 160u + 32)
c
4
((u + 1)
5
)(u
82
− 6u
81
+ ··· + 8u − 1)
c
5
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)(u
82
− 6u
81
+ ··· + 2u − 1)
c
7
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
82
− 2u
81
+ ··· + 14u + 1)
c
8
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
82
− 2u
81
+ ··· − 2362u − 484)
c
9
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
82
+ 2u
81
+ ··· − 20520u − 1647)
c
10
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
82
− 2u
81
+ ··· + 14u + 1)
c
11
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
82
+ 14u
81
+ ··· + 2u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
5
)(y
82
− 42y
81
+ ··· − 32y + 1)
c
2
((y −1)
5
)(y
82
+ 2y
81
+ ··· − 484y + 1)
c
3
, c
6
y
5
(y
82
− 33y
81
+ ··· − 19968y + 1024)
c
5
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
82
− 14y
81
+ ··· − 6y + 1)
c
7
, c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
82
− 58y
81
+ ··· + 14y + 1)
c
8
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
· (y
82
+ 90y
81
+ ··· + 10862436y + 234256)
c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
· (y
82
+ 50y
81
+ ··· − 261288342y + 2712609)
c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
82
+ 6y
81
+ ··· + 14y + 1)
19
