12a
0118
(K12a
0118
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 12 10 9 4 7 1 6 11
Solving Sequence
4,9
8
1,3
2 5 7 10 11 6 12
c
8
c
3
c
1
c
4
c
7
c
9
c
10
c
6
c
12
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h4.88767 × 10
39
u
69
− 2.05229 × 10
38
u
68
+ ··· + 4.39249 × 10
39
b − 2.55827 × 10
40
,
− 8.11974 × 10
39
u
69
+ 1.40212 × 10
39
u
68
+ ··· + 4.39249 × 10
39
a + 6.03714 × 10
40
, u
70
− u
69
+ ··· − 12u + 4i
I
v
1
= ha, b − v −1, v
2
+ v + 1i
* 2 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
= h4.89×10
39
u
69
−2.05×10
38
u
68
+· · ·+4.39×10
39
b−2.56×10
40
, −8.12×
10
39
u
69
+1.40×10
39
u
68
+· · ·+4.39×10
39
a+6.04×10
40
, u
70
−u
69
+· · ·−12u+4i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
1.84855u
69
− 0.319208u
68
+ ··· + 27.0154u − 13.7442
−1.11273u
69
+ 0.0467228u
68
+ ··· − 4.82981u + 5.82420
a
3
=
−u
−u
3
+ u
a
2
=
1.48418u
69
+ 0.111209u
68
+ ··· + 23.4623u − 12.2083
−0.723651u
69
+ 0.0742162u
68
+ ··· + 0.973362u + 4.02410
a
5
=
−0.263656u
69
− 0.120324u
68
+ ··· − 11.2277u + 1.80266
−1.58490u
69
+ 0.439531u
68
+ ··· − 15.7877u + 11.9416
a
7
=
−u
2
+ 1
u
2
a
10
=
u
4
− u
2
+ 1
−u
4
a
11
=
0.0566762u
69
+ 0.669845u
68
+ ··· + 13.0126u − 7.86292
−0.888567u
69
− 0.0370187u
68
+ ··· − 13.3944u + 7.93011
a
6
=
−u
6
+ u
4
− 2u
2
+ 1
u
6
+ u
2
a
12
=
0.233751u
69
+ 0.504289u
68
+ ··· + 14.1968u − 7.56914
−1.10374u
69
− 0.0225465u
68
+ ··· − 15.1789u + 8.49479
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.10416u
69
+ 0.201729u
68
+ ··· − 71.8492u + 42.8742
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
70
+ 41u
69
+ ··· + 8u + 1
c
2
, c
4
u
70
− 3u
69
+ ··· − 4u + 1
c
3
, c
8
u
70
+ u
69
+ ··· + 12u + 4
c
5
, c
11
u
70
+ 2u
69
+ ··· − u + 1
c
6
, c
7
, c
9
u
70
− 15u
69
+ ··· − 200u + 16
c
10
, c
12
u
70
+ 26u
69
+ ··· + 11u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
70
− 21y
69
+ ··· + 32y + 1
c
2
, c
4
y
70
− 41y
69
+ ··· − 8y + 1
c
3
, c
8
y
70
− 15y
69
+ ··· − 200y + 16
c
5
, c
11
y
70
+ 26y
69
+ ··· + 11y + 1
c
6
, c
7
, c
9
y
70
+ 77y
69
+ ··· + 2272y + 256
c
10
, c
12
y
70
+ 38y
69
+ ··· + 131y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.856012 + 0.547090I
a = −0.649388 + 0.664283I
b = 0.678669 − 1.019120I
−4.18862 − 5.65542I −4.40524 + 8.10333I
u = −0.856012 − 0.547090I
a = −0.649388 − 0.664283I
b = 0.678669 + 1.019120I
−4.18862 + 5.65542I −4.40524 − 8.10333I
u = −0.959078 + 0.338964I
a = 1.001140 − 0.104262I
b = −0.162521 − 0.081892I
3.53851 − 0.96635I 7.82026 + 0.I
u = −0.959078 − 0.338964I
a = 1.001140 + 0.104262I
b = −0.162521 + 0.081892I
3.53851 + 0.96635I 7.82026 + 0.I
u = −1.019040 + 0.052169I
a = 0.438523 − 0.219399I
b = −0.145309 − 0.850245I
4.86369 + 0.47978I 8.80207 + 0.I
u = −1.019040 − 0.052169I
a = 0.438523 + 0.219399I
b = −0.145309 + 0.850245I
4.86369 − 0.47978I 8.80207 + 0.I
u = 1.027600 + 0.119592I
a = −0.292337 − 0.225712I
b = 0.205304 − 0.936042I
4.71065 + 4.96261I 8.04821 − 7.02524I
u = 1.027600 − 0.119592I
a = −0.292337 + 0.225712I
b = 0.205304 + 0.936042I
4.71065 − 4.96261I 8.04821 + 7.02524I
u = −0.443664 + 0.844769I
a = −0.538375 + 0.337845I
b = −0.096708 − 0.471281I
−1.19762 + 5.98159I −0.92170 − 7.29563I
u = −0.443664 − 0.844769I
a = −0.538375 − 0.337845I
b = −0.096708 + 0.471281I
−1.19762 − 5.98159I −0.92170 + 7.29563I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.971885 + 0.410627I
a = −1.096340 − 0.187273I
b = 0.241292 − 0.293397I
2.85579 + 6.32679I 0
u = 0.971885 − 0.410627I
a = −1.096340 + 0.187273I
b = 0.241292 + 0.293397I
2.85579 − 6.32679I 0
u = 0.839415 + 0.383054I
a = 0.167368 + 0.464643I
b = 0.014763 − 1.203170I
−0.17528 + 3.69433I 3.69302 − 7.55665I
u = 0.839415 − 0.383054I
a = 0.167368 − 0.464643I
b = 0.014763 + 1.203170I
−0.17528 − 3.69433I 3.69302 + 7.55665I
u = −0.610913 + 0.667828I
a = −1.309430 + 0.512503I
b = 0.409626 + 0.116110I
−5.02013 + 1.13894I −7.42078 − 0.58795I
u = −0.610913 − 0.667828I
a = −1.309430 − 0.512503I
b = 0.409626 − 0.116110I
−5.02013 − 1.13894I −7.42078 + 0.58795I
u = 1.007960 + 0.482476I
a = 0.671035 + 0.116495I
b = −0.043821 − 0.531729I
1.70900 + 5.48430I 0
u = 1.007960 − 0.482476I
a = 0.671035 − 0.116495I
b = −0.043821 + 0.531729I
1.70900 − 5.48430I 0
u = 0.367833 + 0.798582I
a = 0.547260 + 0.067881I
b = 0.238259 − 0.220293I
−0.434483 − 0.891477I 0.84820 + 1.91068I
u = 0.367833 − 0.798582I
a = 0.547260 − 0.067881I
b = 0.238259 + 0.220293I
−0.434483 + 0.891477I 0.84820 − 1.91068I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.688189 + 0.495014I
a = −0.751143 − 0.485185I
b = 0.731991 + 0.183516I
−1.70612 + 1.90353I −1.29790 − 4.47310I
u = 0.688189 − 0.495014I
a = −0.751143 + 0.485185I
b = 0.731991 − 0.183516I
−1.70612 − 1.90353I −1.29790 + 4.47310I
u = −1.024030 + 0.531995I
a = −0.847273 + 0.128927I
b = 0.143783 − 0.298287I
0.79072 − 10.96610I 0
u = −1.024030 − 0.531995I
a = −0.847273 − 0.128927I
b = 0.143783 + 0.298287I
0.79072 + 10.96610I 0
u = −0.734851 + 0.407087I
a = −2.18354 + 0.39505I
b = −0.093179 + 0.722090I
−1.82583 − 3.75171I −0.39629 + 7.22205I
u = −0.734851 − 0.407087I
a = −2.18354 − 0.39505I
b = −0.093179 − 0.722090I
−1.82583 + 3.75171I −0.39629 − 7.22205I
u = −0.690889 + 0.415366I
a = −0.012282 + 0.905962I
b = −0.01931 − 1.84269I
−1.97137 + 0.49525I −1.21375 + 3.39141I
u = −0.690889 − 0.415366I
a = −0.012282 − 0.905962I
b = −0.01931 + 1.84269I
−1.97137 − 0.49525I −1.21375 − 3.39141I
u = 0.859252 + 0.847811I
a = −1.12334 − 1.09661I
b = 2.28142 − 0.13713I
−3.86556 + 1.55363I 0
u = 0.859252 − 0.847811I
a = −1.12334 + 1.09661I
b = 2.28142 + 0.13713I
−3.86556 − 1.55363I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.850893 + 0.884624I
a = 1.10267 − 1.18353I
b = −2.50998 + 0.01246I
−5.50548 + 3.78563I 0
u = −0.850893 − 0.884624I
a = 1.10267 + 1.18353I
b = −2.50998 − 0.01246I
−5.50548 − 3.78563I 0
u = −0.892645 + 0.859249I
a = −1.30636 + 1.71490I
b = 2.43773 + 0.22609I
−7.66688 − 0.08605I 0
u = −0.892645 − 0.859249I
a = −1.30636 − 1.71490I
b = 2.43773 − 0.22609I
−7.66688 + 0.08605I 0
u = −0.748791 + 0.124504I
a = 0.658521 − 0.117735I
b = −0.490170 + 0.349419I
1.174050 − 0.188994I 9.05728 + 0.63012I
u = −0.748791 − 0.124504I
a = 0.658521 + 0.117735I
b = −0.490170 − 0.349419I
1.174050 + 0.188994I 9.05728 − 0.63012I
u = −0.847834 + 0.919383I
a = −1.01430 + 1.70268I
b = 2.41082 − 0.49572I
−7.59275 + 3.10194I 0
u = −0.847834 − 0.919383I
a = −1.01430 − 1.70268I
b = 2.41082 + 0.49572I
−7.59275 − 3.10194I 0
u = 0.947471 + 0.820362I
a = −1.33084 − 1.01743I
b = 2.20960 − 0.80470I
−3.59203 + 4.66330I 0
u = 0.947471 − 0.820362I
a = −1.33084 + 1.01743I
b = 2.20960 + 0.80470I
−3.59203 − 4.66330I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.910528 + 0.864183I
a = 1.73727 + 1.07847I
b = −3.13501 + 0.34918I
−9.32357 + 0.88762I 0
u = 0.910528 − 0.864183I
a = 1.73727 − 1.07847I
b = −3.13501 − 0.34918I
−9.32357 − 0.88762I 0
u = −0.930113 + 0.845405I
a = −1.71742 + 0.97375I
b = 2.83461 + 0.49195I
−7.54935 − 6.24533I 0
u = −0.930113 − 0.845405I
a = −1.71742 − 0.97375I
b = 2.83461 − 0.49195I
−7.54935 + 6.24533I 0
u = 0.920205 + 0.860055I
a = 1.36723 + 1.80376I
b = −2.64509 + 0.40060I
−9.29275 + 5.50542I 0
u = 0.920205 − 0.860055I
a = 1.36723 − 1.80376I
b = −2.64509 − 0.40060I
−9.29275 − 5.50542I 0
u = −0.918074 + 0.869398I
a = 1.26727 − 1.14504I
b = −2.55438 − 0.51995I
−9.50690 − 3.21924I 0
u = −0.918074 − 0.869398I
a = 1.26727 + 1.14504I
b = −2.55438 + 0.51995I
−9.50690 + 3.21924I 0
u = 0.855164 + 0.943687I
a = 0.94923 + 1.77875I
b = −2.59048 − 0.67761I
−9.18918 − 8.56419I 0
u = 0.855164 − 0.943687I
a = 0.94923 − 1.77875I
b = −2.59048 + 0.67761I
−9.18918 + 8.56419I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.895190 + 0.908857I
a = 1.15254 + 1.83519I
b = −2.76109 − 0.15164I
−13.44380 − 1.53868I 0
u = 0.895190 − 0.908857I
a = 1.15254 − 1.83519I
b = −2.76109 + 0.15164I
−13.44380 + 1.53868I 0
u = −0.969783 + 0.836843I
a = 1.39145 − 1.05225I
b = −2.35136 − 0.97184I
−5.13123 − 10.16380I 0
u = −0.969783 − 0.836843I
a = 1.39145 + 1.05225I
b = −2.35136 + 0.97184I
−5.13123 + 10.16380I 0
u = 0.659724 + 0.283358I
a = 2.35512 + 0.08593I
b = 0.315252 + 0.457091I
−1.17058 − 1.08332I 2.65386 − 2.01895I
u = 0.659724 − 0.283358I
a = 2.35512 − 0.08593I
b = 0.315252 − 0.457091I
−1.17058 + 1.08332I 2.65386 + 2.01895I
u = −0.050359 + 0.716046I
a = 0.121117 − 0.635002I
b = 0.171445 + 0.650196I
0.76923 − 2.33777I 2.89499 + 4.69130I
u = −0.050359 − 0.716046I
a = 0.121117 + 0.635002I
b = 0.171445 − 0.650196I
0.76923 + 2.33777I 2.89499 − 4.69130I
u = 0.206898 + 0.671469I
a = −0.186235 − 0.643840I
b = 0.128642 + 0.779464I
0.55234 − 2.49681I 1.97976 + 2.11018I
u = 0.206898 − 0.671469I
a = −0.186235 + 0.643840I
b = 0.128642 − 0.779464I
0.55234 + 2.49681I 1.97976 − 2.11018I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.959789 + 0.876252I
a = 1.88469 + 0.94024I
b = −3.04179 + 0.99068I
−13.2339 + 8.1232I 0
u = 0.959789 − 0.876252I
a = 1.88469 − 0.94024I
b = −3.04179 − 0.99068I
−13.2339 − 8.1232I 0
u = −0.990634 + 0.851943I
a = −1.86694 + 0.78225I
b = 2.57901 + 1.20339I
−7.13528 − 9.63342I 0
u = −0.990634 − 0.851943I
a = −1.86694 − 0.78225I
b = 2.57901 − 1.20339I
−7.13528 + 9.63342I 0
u = 1.002140 + 0.866479I
a = 1.94196 + 0.77269I
b = −2.66868 + 1.42802I
−8.7104 + 15.2194I 0
u = 1.002140 − 0.866479I
a = 1.94196 − 0.77269I
b = −2.66868 − 1.42802I
−8.7104 − 15.2194I 0
u = 0.635965 + 0.105400I
a = −0.744808 + 0.354776I
b = 1.18138 − 0.88640I
−0.93204 + 2.71089I 3.68951 − 7.69678I
u = 0.635965 − 0.105400I
a = −0.744808 − 0.354776I
b = 1.18138 + 0.88640I
−0.93204 − 2.71089I 3.68951 + 7.69678I
u = 0.282390 + 0.481929I
a = 1.21593 − 0.82030I
b = 0.095269 + 0.174525I
−1.68308 − 0.59288I −4.15264 + 0.08163I
u = 0.282390 − 0.481929I
a = 1.21593 + 0.82030I
b = 0.095269 − 0.174525I
−1.68308 + 0.59288I −4.15264 − 0.08163I
11
II. I
v
1
= ha, b − v − 1, v
2
+ v + 1i
(i) Arc colorings
a
4
=
v
0
a
9
=
1
0
a
8
=
1
0
a
1
=
0
v + 1
a
3
=
v
0
a
2
=
v
v + 1
a
5
=
0
−v − 1
a
7
=
1
0
a
10
=
1
0
a
11
=
1
v
a
6
=
1
0
a
12
=
v + 1
v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v − 1
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
6
, c
7
c
8
, c
9
u
2
c
4
(u + 1)
2
c
5
, c
12
u
2
+ u + 1
c
10
, c
11
u
2
− u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
6
, c
7
c
8
, c
9
y
2
c
5
, c
10
, c
11
c
12
y
2
+ y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = 0.500000 + 0.866025I
−1.64493 − 2.02988I −3.00000 + 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
−1.64493 + 2.02988I −3.00000 − 3.46410I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
70
+ 41u
69
+ ··· + 8u + 1)
c
2
((u − 1)
2
)(u
70
− 3u
69
+ ··· − 4u + 1)
c
3
, c
8
u
2
(u
70
+ u
69
+ ··· + 12u + 4)
c
4
((u + 1)
2
)(u
70
− 3u
69
+ ··· − 4u + 1)
c
5
(u
2
+ u + 1)(u
70
+ 2u
69
+ ··· − u + 1)
c
6
, c
7
, c
9
u
2
(u
70
− 15u
69
+ ··· − 200u + 16)
c
10
(u
2
− u + 1)(u
70
+ 26u
69
+ ··· + 11u + 1)
c
11
(u
2
− u + 1)(u
70
+ 2u
69
+ ··· − u + 1)
c
12
(u
2
+ u + 1)(u
70
+ 26u
69
+ ··· + 11u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
2
)(y
70
− 21y
69
+ ··· + 32y + 1)
c
2
, c
4
((y − 1)
2
)(y
70
− 41y
69
+ ··· − 8y + 1)
c
3
, c
8
y
2
(y
70
− 15y
69
+ ··· − 200y + 16)
c
5
, c
11
(y
2
+ y + 1)(y
70
+ 26y
69
+ ··· + 11y + 1)
c
6
, c
7
, c
9
y
2
(y
70
+ 77y
69
+ ··· + 2272y + 256)
c
10
, c
12
(y
2
+ y + 1)(y
70
+ 38y
69
+ ··· + 131y + 1)
17
