11a
76
(K11a
76
)
A knot diagram
1
Linearized knot diagam
6 1 10 8 2 3 4 11 5 7 9
Solving Sequence
1,6
2 3 7
5,9
10 11 8 4
c
1
c
2
c
6
c
5
c
9
c
11
c
8
c
4
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.57893 × 10
38
u
71
− 8.42472 × 10
38
u
70
+ ··· + 5.29862 × 10
37
b − 4.92590 × 10
38
,
− 2.62436 × 10
38
u
71
− 6.46971 × 10
38
u
70
+ ··· + 5.29862 × 10
37
a − 4.29443 × 10
38
, u
72
+ 3u
71
+ ··· + 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 72 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−3.58×10
38
u
71
−8.42×10
38
u
70
+· · ·+5.30×10
37
b−4.93×10
38
, −2.62×
10
38
u
71
−6.47×10
38
u
70
+· · ·+5.30×10
37
a−4.29×10
38
, u
72
+3u
71
+· · ·+2u+1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
7
=
−u
5
− 2u
3
− u
u
5
+ u
3
+ u
a
5
=
−u
u
3
+ u
a
9
=
4.95292u
71
+ 12.2102u
70
+ ··· + 8.11867u + 8.10480
6.75445u
71
+ 15.8998u
70
+ ··· + 4.44428u + 9.29657
a
10
=
8.15457u
71
+ 19.4489u
70
+ ··· + 9.45399u + 14.7692
0.407698u
71
+ 1.93942u
70
+ ··· + 1.57818u + 0.265920
a
11
=
−0.885669u
71
− 1.56905u
70
+ ··· + 4.09193u + 0.125580
8.06115u
71
+ 18.9971u
70
+ ··· + 5.31775u + 11.5270
a
8
=
11.8663u
71
+ 28.2113u
70
+ ··· + 8.42671u + 17.4400
−4.15633u
71
− 10.1011u
70
+ ··· − 2.88816u − 7.11562
a
4
=
6.08306u
71
+ 14.8577u
70
+ ··· + 4.98002u + 8.22859
1.62693u
71
+ 3.25246u
70
+ ··· + 0.558537u + 2.09582
a
4
=
6.08306u
71
+ 14.8577u
70
+ ··· + 4.98002u + 8.22859
1.62693u
71
+ 3.25246u
70
+ ··· + 0.558537u + 2.09582
(ii) Obstruction class = −1
(iii) Cusp Shapes = 39.6069u
71
+ 96.0017u
70
+ ··· + 38.2591u + 62.1849
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
72
− 3u
71
+ ··· − 2u + 1
c
2
u
72
+ 37u
71
+ ··· − 6u
2
+ 1
c
3
u
72
− 3u
71
+ ··· − 4u + 1
c
4
, c
7
u
72
− u
71
+ ··· − 6u
3
+ 1
c
6
u
72
+ 3u
71
+ ··· + 2514u + 1697
c
8
, c
11
u
72
− u
71
+ ··· − 4u + 1
c
9
u
72
+ 17u
71
+ ··· + 2668u + 521
c
10
u
72
− 11u
71
+ ··· − 54u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
72
+ 37y
71
+ ··· − 6y
2
+ 1
c
2
y
72
− 3y
71
+ ··· − 12y + 1
c
3
y
72
− 3y
71
+ ··· + 28y + 1
c
4
, c
7
y
72
− 43y
71
+ ··· + 22y
2
+ 1
c
6
y
72
− 43y
71
+ ··· + 43578392y + 2879809
c
8
, c
11
y
72
− 47y
71
+ ··· − 140y + 1
c
9
y
72
+ 77y
71
+ ··· + 10103952y + 271441
c
10
y
72
+ 73y
71
+ ··· − 1756y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.703184 + 0.720104I
a = −1.191830 − 0.212487I
b = 1.060910 + 0.489250I
2.94327 − 4.66277I 0
u = 0.703184 − 0.720104I
a = −1.191830 + 0.212487I
b = 1.060910 − 0.489250I
2.94327 + 4.66277I 0
u = 0.554410 + 0.823817I
a = 0.98373 + 1.65695I
b = 0.445673 − 0.783754I
4.88813 + 0.08217I 0
u = 0.554410 − 0.823817I
a = 0.98373 − 1.65695I
b = 0.445673 + 0.783754I
4.88813 − 0.08217I 0
u = −0.837136 + 0.439497I
a = −0.529813 − 0.200502I
b = 0.857480 + 0.147319I
1.09133 − 1.71913I 10.13735 + 8.67707I
u = −0.837136 − 0.439497I
a = −0.529813 + 0.200502I
b = 0.857480 − 0.147319I
1.09133 + 1.71913I 10.13735 − 8.67707I
u = 0.666082 + 0.842814I
a = −0.43355 + 1.75696I
b = 1.154260 − 0.555136I
2.58371 + 9.84905I 0
u = 0.666082 − 0.842814I
a = −0.43355 − 1.75696I
b = 1.154260 + 0.555136I
2.58371 − 9.84905I 0
u = 0.573630 + 0.724680I
a = −0.50836 − 1.44827I
b = 0.336237 + 0.963611I
5.17342 + 4.41975I 7.07565 − 5.46641I
u = 0.573630 − 0.724680I
a = −0.50836 + 1.44827I
b = 0.336237 − 0.963611I
5.17342 − 4.41975I 7.07565 + 5.46641I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.902993
a = 0.122962
b = 0.817766
1.62872 14.4780
u = 0.870170 + 0.219257I
a = −0.577040 − 0.897959I
b = 1.265190 + 0.363737I
−4.55958 − 5.79532I −1.85974 + 4.79370I
u = 0.870170 − 0.219257I
a = −0.577040 + 0.897959I
b = 1.265190 − 0.363737I
−4.55958 + 5.79532I −1.85974 − 4.79370I
u = −0.353333 + 0.805104I
a = 0.92846 + 1.60423I
b = −0.783546 − 0.692525I
−0.13917 − 3.83716I 1.00000 + 8.28494I
u = −0.353333 − 0.805104I
a = 0.92846 − 1.60423I
b = −0.783546 + 0.692525I
−0.13917 + 3.83716I 1.00000 − 8.28494I
u = −0.847791 + 0.226071I
a = −0.60759 + 1.31018I
b = 1.34762 − 0.58716I
−0.87898 + 11.82610I 1.72108 − 6.69260I
u = −0.847791 − 0.226071I
a = −0.60759 − 1.31018I
b = 1.34762 + 0.58716I
−0.87898 − 11.82610I 1.72108 + 6.69260I
u = −0.669002 + 0.948123I
a = −0.111095 − 1.006420I
b = 0.863289 + 0.208347I
−0.37569 − 3.68901I 0
u = −0.669002 − 0.948123I
a = −0.111095 + 1.006420I
b = 0.863289 − 0.208347I
−0.37569 + 3.68901I 0
u = −0.414747 + 1.088110I
a = 1.064490 − 0.308621I
b = −0.164245 − 0.000885I
−0.99398 − 3.59877I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.414747 − 1.088110I
a = 1.064490 + 0.308621I
b = −0.164245 + 0.000885I
−0.99398 + 3.59877I 0
u = 0.375559 + 1.113330I
a = 0.620105 + 0.228683I
b = −0.499431 − 0.701739I
−3.85692 + 1.17317I 0
u = 0.375559 − 1.113330I
a = 0.620105 − 0.228683I
b = −0.499431 + 0.701739I
−3.85692 − 1.17317I 0
u = −0.523901 + 1.061300I
a = 0.247478 − 0.212453I
b = 0.300963 − 0.117398I
−0.51681 − 3.31003I 0
u = −0.523901 − 1.061300I
a = 0.247478 + 0.212453I
b = 0.300963 + 0.117398I
−0.51681 + 3.31003I 0
u = 0.086705 + 0.810295I
a = 0.054377 − 0.634992I
b = −1.340240 + 0.233502I
−2.46132 + 1.37762I −4.75486 − 3.44131I
u = 0.086705 − 0.810295I
a = 0.054377 + 0.634992I
b = −1.340240 − 0.233502I
−2.46132 − 1.37762I −4.75486 + 3.44131I
u = −0.336341 + 1.136910I
a = 0.882111 − 0.095962I
b = −0.111214 + 1.175180I
−0.89681 + 2.33659I 0
u = −0.336341 − 1.136910I
a = 0.882111 + 0.095962I
b = −0.111214 − 1.175180I
−0.89681 − 2.33659I 0
u = 0.461388 + 1.106090I
a = −3.24942 − 10.03350I
b = −0.988930 + 0.015219I
−2.44126 + 3.69610I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.461388 − 1.106090I
a = −3.24942 + 10.03350I
b = −0.988930 − 0.015219I
−2.44126 − 3.69610I 0
u = −0.534376 + 0.579633I
a = 0.158156 + 0.589487I
b = 0.203968 − 0.319447I
0.96165 − 1.08206I 5.49471 + 3.65986I
u = −0.534376 − 0.579633I
a = 0.158156 − 0.589487I
b = 0.203968 + 0.319447I
0.96165 + 1.08206I 5.49471 − 3.65986I
u = 0.410737 + 1.151630I
a = 0.008261 − 0.632747I
b = −1.42190 − 0.72250I
−5.42611 + 0.39495I 0
u = 0.410737 − 1.151630I
a = 0.008261 + 0.632747I
b = −1.42190 + 0.72250I
−5.42611 − 0.39495I 0
u = −0.734770 + 0.228880I
a = −0.13940 − 1.62166I
b = 0.099801 + 1.198770I
3.07611 + 5.61775I 4.77724 − 5.53521I
u = −0.734770 − 0.228880I
a = −0.13940 + 1.62166I
b = 0.099801 − 1.198770I
3.07611 − 5.61775I 4.77724 + 5.53521I
u = −0.437096 + 1.150220I
a = −0.761902 + 1.185660I
b = −1.58389 + 0.14802I
−6.25046 − 3.83055I 0
u = −0.437096 − 1.150220I
a = −0.761902 − 1.185660I
b = −1.58389 − 0.14802I
−6.25046 + 3.83055I 0
u = −0.457989 + 1.149910I
a = −1.06297 + 1.77278I
b = −1.49634 − 0.32588I
−6.10263 − 4.25285I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.457989 − 1.149910I
a = −1.06297 − 1.77278I
b = −1.49634 + 0.32588I
−6.10263 + 4.25285I 0
u = 0.510504 + 1.133840I
a = −0.655326 − 0.914374I
b = −0.208519 + 0.839334I
−2.88144 + 6.56829I 0
u = 0.510504 − 1.133840I
a = −0.655326 + 0.914374I
b = −0.208519 − 0.839334I
−2.88144 − 6.56829I 0
u = 0.213790 + 0.718682I
a = 0.31066 − 1.79444I
b = −0.981466 + 0.294623I
−2.07488 + 1.01631I −5.73873 − 0.14540I
u = 0.213790 − 0.718682I
a = 0.31066 + 1.79444I
b = −0.981466 − 0.294623I
−2.07488 − 1.01631I −5.73873 + 0.14540I
u = 0.478733 + 1.155820I
a = −1.07122 − 1.88937I
b = −1.30955 + 0.89704I
−4.94380 + 7.74825I 0
u = 0.478733 − 1.155820I
a = −1.07122 + 1.88937I
b = −1.30955 − 0.89704I
−4.94380 − 7.74825I 0
u = −0.524409 + 1.149510I
a = −1.282010 + 0.581428I
b = 0.089436 − 1.312110I
0.39914 − 10.36720I 0
u = −0.524409 − 1.149510I
a = −1.282010 − 0.581428I
b = 0.089436 + 1.312110I
0.39914 + 10.36720I 0
u = −0.301957 + 1.235170I
a = 0.695125 − 0.172739I
b = 1.37244 − 0.51422I
−5.50939 + 8.09445I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.301957 − 1.235170I
a = 0.695125 + 0.172739I
b = 1.37244 + 0.51422I
−5.50939 − 8.09445I 0
u = −0.218429 + 1.270380I
a = 0.739347 − 0.207359I
b = 1.140640 + 0.181011I
−4.51697 − 4.89443I 0
u = −0.218429 − 1.270380I
a = 0.739347 + 0.207359I
b = 1.140640 − 0.181011I
−4.51697 + 4.89443I 0
u = 0.299117 + 1.256120I
a = 0.707957 + 0.222610I
b = 1.312930 + 0.258586I
−9.29460 − 1.93916I 0
u = 0.299117 − 1.256120I
a = 0.707957 − 0.222610I
b = 1.312930 − 0.258586I
−9.29460 + 1.93916I 0
u = 0.665303 + 0.230468I
a = 0.405637 + 1.271800I
b = −0.184479 − 0.659604I
−0.29904 − 2.02628I 0.96838 + 3.48048I
u = 0.665303 − 0.230468I
a = 0.405637 − 1.271800I
b = −0.184479 + 0.659604I
−0.29904 + 2.02628I 0.96838 − 3.48048I
u = 0.682233 + 0.103764I
a = 0.81123 + 1.49379I
b = −1.25537 − 0.77052I
−1.97878 − 3.38165I −1.14448 + 6.05551I
u = 0.682233 − 0.103764I
a = 0.81123 − 1.49379I
b = −1.25537 + 0.77052I
−1.97878 + 3.38165I −1.14448 − 6.05551I
u = −0.554919 + 1.186620I
a = 0.89680 − 2.06063I
b = 1.38635 + 0.61330I
−3.7459 − 16.9805I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.554919 − 1.186620I
a = 0.89680 + 2.06063I
b = 1.38635 − 0.61330I
−3.7459 + 16.9805I 0
u = −0.377915 + 0.573931I
a = 3.41986 + 1.55094I
b = −0.787722 + 0.202785I
0.567632 + 0.583415I 2.34352 + 4.20477I
u = −0.377915 − 0.573931I
a = 3.41986 − 1.55094I
b = −0.787722 − 0.202785I
0.567632 − 0.583415I 2.34352 − 4.20477I
u = 0.557731 + 1.195530I
a = 0.67641 + 1.77118I
b = 1.319850 − 0.408500I
−7.48840 + 11.01550I 0
u = 0.557731 − 1.195530I
a = 0.67641 − 1.77118I
b = 1.319850 + 0.408500I
−7.48840 − 11.01550I 0
u = −0.646200 + 0.031395I
a = 0.381468 − 0.548179I
b = −1.42993 + 0.18760I
−3.04821 + 0.12497I −2.91080 + 1.49101I
u = −0.646200 − 0.031395I
a = 0.381468 + 0.548179I
b = −1.42993 − 0.18760I
−3.04821 − 0.12497I −2.91080 − 1.49101I
u = −0.537999 + 1.246180I
a = 0.703002 − 0.969373I
b = 0.982981 + 0.166252I
−2.00352 − 5.15126I 0
u = −0.537999 − 1.246180I
a = 0.703002 + 0.969373I
b = 0.982981 − 0.166252I
−2.00352 + 5.15126I 0
u = −0.628396
a = 1.10871
b = 0.154509
1.97438 6.08460
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.464730 + 0.246535I
a = 5.87102 + 4.17531I
b = −0.979390 + 0.061610I
−0.018901 + 0.220260I −2.6373 + 28.8822I
u = 0.464730 − 0.246535I
a = 5.87102 − 4.17531I
b = −0.979390 − 0.061610I
−0.018901 − 0.220260I −2.6373 − 28.8822I
12
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
72
− 3u
71
+ ··· − 2u + 1
c
2
u
72
+ 37u
71
+ ··· − 6u
2
+ 1
c
3
u
72
− 3u
71
+ ··· − 4u + 1
c
4
, c
7
u
72
− u
71
+ ··· − 6u
3
+ 1
c
6
u
72
+ 3u
71
+ ··· + 2514u + 1697
c
8
, c
11
u
72
− u
71
+ ··· − 4u + 1
c
9
u
72
+ 17u
71
+ ··· + 2668u + 521
c
10
u
72
− 11u
71
+ ··· − 54u + 1
13
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
72
+ 37y
71
+ ··· − 6y
2
+ 1
c
2
y
72
− 3y
71
+ ··· − 12y + 1
c
3
y
72
− 3y
71
+ ··· + 28y + 1
c
4
, c
7
y
72
− 43y
71
+ ··· + 22y
2
+ 1
c
6
y
72
− 43y
71
+ ··· + 43578392y + 2879809
c
8
, c
11
y
72
− 47y
71
+ ··· − 140y + 1
c
9
y
72
+ 77y
71
+ ··· + 10103952y + 271441
c
10
y
72
+ 73y
71
+ ··· − 1756y + 1
14
