11a
151
(K11a
151
)
A knot diagram
1
Linearized knot diagam
6 1 10 11 2 9 5 3 7 4 8
Solving Sequence
1,6
2
3,9
7 10 5 8 11 4
c
1
c
2
c
6
c
9
c
5
c
8
c
11
c
4
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h5.94710 × 10
52
u
65
+ 1.17236 × 10
53
u
64
+ ··· + 8.35081 × 10
52
b + 2.54635 × 10
53
,
− 8.47686 × 10
52
u
65
− 1.39894 × 10
53
u
64
+ ··· + 1.19297 × 10
52
a − 2.19440 × 10
53
, u
66
+ 2u
65
+ ··· + 4u + 1i
I
u
2
= hu
2
+ 7b + 6u + 4, −u
2
+ a − u − 2, u
3
+ u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 69 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
= h5.95×10
52
u
65
+1.17×10
53
u
64
+· · ·+8.35×10
52
b+2.55×10
53
, −8.48×
10
52
u
65
−1.40×10
53
u
64
+· · ·+1.19×10
52
a−2.19×10
53
, u
66
+2u
65
+· · ·+4u+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
9
=
7.10566u
65
+ 11.7265u
64
+ ··· + 31.4641u + 18.3944
−0.712158u
65
− 1.40388u
64
+ ··· − 2.74081u − 3.04922
a
7
=
8.72726u
65
+ 14.2298u
64
+ ··· + 35.4678u + 22.1382
−2.15625u
65
− 3.59400u
64
+ ··· − 6.93271u − 6.34045
a
10
=
−5.31162u
65
− 8.22686u
64
+ ··· − 15.8436u − 12.2934
3.63832u
65
+ 5.58995u
64
+ ··· + 12.4635u + 8.35519
a
5
=
−u
u
3
+ u
a
8
=
7.66328u
65
+ 12.2341u
64
+ ··· + 30.8189u + 18.9851
−1.32415u
65
− 2.02616u
64
+ ··· − 2.81894u − 3.05516
a
11
=
−8.35519u
65
− 13.0721u
64
+ ··· − 33.0049u − 20.9573
2.39639u
65
+ 3.80632u
64
+ ··· + 8.95306u + 5.31162
a
4
=
9.70575u
65
+ 15.5979u
64
+ ··· + 36.1966u + 23.0110
−3.81358u
65
− 6.82103u
64
+ ··· − 15.8119u − 9.70575
a
4
=
9.70575u
65
+ 15.5979u
64
+ ··· + 36.1966u + 23.0110
−3.81358u
65
− 6.82103u
64
+ ··· − 15.8119u − 9.70575
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8.99978u
65
− 13.8805u
64
+ ··· − 26.7379u − 16.3346
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
66
− 2u
65
+ ··· − 4u + 1
c
2
u
66
+ 30u
65
+ ··· + 2u + 1
c
3
, c
4
, c
10
u
66
− 2u
65
+ ··· − u
2
− 1
c
6
, c
9
u
66
− 4u
65
+ ··· + 491u − 49
c
7
7(7u
66
− 18u
65
+ ··· + 13446u − 999)
c
8
7(7u
66
− 10u
65
+ ··· + 1391u + 241)
c
11
u
66
− 5u
65
+ ··· − 3108u + 392
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
66
+ 30y
65
+ ··· + 2y + 1
c
2
y
66
+ 14y
65
+ ··· + 14y + 1
c
3
, c
4
, c
10
y
66
− 62y
65
+ ··· + 2y + 1
c
6
, c
9
y
66
− 36y
65
+ ··· − 105155y + 2401
c
7
49(49y
66
+ 2434y
65
+ ··· − 8.20438 × 10
7
y + 998001)
c
8
49(49y
66
+ 880y
65
+ ··· − 442127y + 58081)
c
11
y
66
− 21y
65
+ ··· − 925904y + 153664
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.886940 + 0.437138I
a = −1.43804 + 0.06126I
b = 0.278206 − 1.239240I
6.34153 + 10.49840I 7.22778 − 5.33949I
u = −0.886940 − 0.437138I
a = −1.43804 − 0.06126I
b = 0.278206 + 1.239240I
6.34153 − 10.49840I 7.22778 + 5.33949I
u = 0.900019 + 0.409306I
a = 1.287910 + 0.018413I
b = −0.259301 − 0.971541I
0.06237 − 6.42817I 0. + 5.79651I
u = 0.900019 − 0.409306I
a = 1.287910 − 0.018413I
b = −0.259301 + 0.971541I
0.06237 + 6.42817I 0. − 5.79651I
u = −0.301350 + 0.971582I
a = 1.01800 + 1.10633I
b = −0.559633 + 0.170616I
0.012797 + 0.793621I 0
u = −0.301350 − 0.971582I
a = 1.01800 − 1.10633I
b = −0.559633 − 0.170616I
0.012797 − 0.793621I 0
u = 0.372330 + 0.966152I
a = −0.71705 + 1.22172I
b = 0.635335 − 0.613059I
−4.16615 + 1.29044I 0
u = 0.372330 − 0.966152I
a = −0.71705 − 1.22172I
b = 0.635335 + 0.613059I
−4.16615 − 1.29044I 0
u = −0.789339 + 0.681407I
a = −0.170305 − 0.711151I
b = 0.612194 + 0.634929I
1.79345 − 2.44057I 0
u = −0.789339 − 0.681407I
a = −0.170305 + 0.711151I
b = 0.612194 − 0.634929I
1.79345 + 2.44057I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.893203 + 0.332658I
a = −1.067730 + 0.068534I
b = 0.060619 − 0.632472I
0.93680 + 1.27321I 6.69528 − 2.55768I
u = −0.893203 − 0.332658I
a = −1.067730 − 0.068534I
b = 0.060619 + 0.632472I
0.93680 − 1.27321I 6.69528 + 2.55768I
u = 0.010647 + 0.950386I
a = 0.878581 + 0.110969I
b = 0.018046 + 0.954751I
4.00663 + 3.04870I 3.98275 − 2.96326I
u = 0.010647 − 0.950386I
a = 0.878581 − 0.110969I
b = 0.018046 − 0.954751I
4.00663 − 3.04870I 3.98275 + 2.96326I
u = 0.861313 + 0.608674I
a = 0.420830 − 0.985449I
b = −1.035080 + 0.573403I
7.36680 + 6.32316I 0
u = 0.861313 − 0.608674I
a = 0.420830 + 0.985449I
b = −1.035080 − 0.573403I
7.36680 − 6.32316I 0
u = 0.538866 + 0.909098I
a = −0.472812 + 0.706075I
b = 5.56489 + 0.30058I
3.51441 + 1.89915I 0
u = 0.538866 − 0.909098I
a = −0.472812 − 0.706075I
b = 5.56489 − 0.30058I
3.51441 − 1.89915I 0
u = −0.477372 + 0.943179I
a = 0.324367 + 0.983761I
b = −1.73724 − 2.48467I
−2.01954 − 2.54235I 0
u = −0.477372 − 0.943179I
a = 0.324367 − 0.983761I
b = −1.73724 + 2.48467I
−2.01954 + 2.54235I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.706967 + 0.574992I
a = −0.344274 − 0.907805I
b = −0.497576 + 1.179170I
2.68558 − 1.37819I 7.68512 + 2.61183I
u = 0.706967 − 0.574992I
a = −0.344274 + 0.907805I
b = −0.497576 − 1.179170I
2.68558 + 1.37819I 7.68512 − 2.61183I
u = −0.742966 + 0.521978I
a = 0.391741 − 1.288390I
b = 0.73070 + 1.45249I
9.13813 + 4.00163I 10.02198 − 1.95783I
u = −0.742966 − 0.521978I
a = 0.391741 + 1.288390I
b = 0.73070 − 1.45249I
9.13813 − 4.00163I 10.02198 + 1.95783I
u = −0.422028 + 1.013150I
a = 0.42251 + 1.48918I
b = −1.47500 − 1.02933I
−0.83525 − 3.14253I 0
u = −0.422028 − 1.013150I
a = 0.42251 − 1.48918I
b = −1.47500 + 1.02933I
−0.83525 + 3.14253I 0
u = 0.490775 + 1.009750I
a = 0.050202 + 1.234540I
b = 1.73077 − 1.49983I
−3.33981 + 4.65284I 0
u = 0.490775 − 1.009750I
a = 0.050202 − 1.234540I
b = 1.73077 + 1.49983I
−3.33981 − 4.65284I 0
u = 0.496332 + 0.710814I
a = −0.254141 + 0.800937I
b = 0.81193 + 2.11193I
4.10544 + 2.40688I 5.61601 − 0.93346I
u = 0.496332 − 0.710814I
a = −0.254141 − 0.800937I
b = 0.81193 − 2.11193I
4.10544 − 2.40688I 5.61601 + 0.93346I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.386686 + 0.758034I
a = 0.593747 + 0.711855I
b = 0.586006 + 1.214530I
−1.32206 − 1.19867I −0.30232 + 8.95765I
u = −0.386686 − 0.758034I
a = 0.593747 − 0.711855I
b = 0.586006 − 1.214530I
−1.32206 + 1.19867I −0.30232 − 8.95765I
u = −0.516301 + 1.034960I
a = −0.396217 + 1.250800I
b = −1.66301 − 1.61916I
1.42288 − 7.01342I 0
u = −0.516301 − 1.034960I
a = −0.396217 − 1.250800I
b = −1.66301 + 1.61916I
1.42288 + 7.01342I 0
u = −0.640786 + 0.965266I
a = −0.478037 + 0.069398I
b = −0.261638 − 0.444397I
0.94099 − 2.93508I 0
u = −0.640786 − 0.965266I
a = −0.478037 − 0.069398I
b = −0.261638 + 0.444397I
0.94099 + 2.93508I 0
u = 0.747809 + 0.382078I
a = 0.982939 + 0.436312I
b = 0.605214 − 0.686874I
8.51869 + 1.38556I 10.68003 − 0.04077I
u = 0.747809 − 0.382078I
a = 0.982939 − 0.436312I
b = 0.605214 + 0.686874I
8.51869 − 1.38556I 10.68003 + 0.04077I
u = 0.612668 + 1.023980I
a = 0.794130 + 0.357693I
b = 0.395162 − 1.268380I
1.33847 + 6.45954I 0
u = 0.612668 − 1.023980I
a = 0.794130 − 0.357693I
b = 0.395162 + 1.268380I
1.33847 − 6.45954I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.127139 + 0.784024I
a = −0.776775 + 0.573919I
b = −0.042614 + 0.780889I
−1.72069 − 1.07315I −1.43813 + 5.39557I
u = 0.127139 − 0.784024I
a = −0.776775 − 0.573919I
b = −0.042614 − 0.780889I
−1.72069 + 1.07315I −1.43813 − 5.39557I
u = −0.618729 + 1.050950I
a = −1.057990 + 0.338143I
b = −0.12777 − 1.65559I
7.56649 − 9.18924I 0
u = −0.618729 − 1.050950I
a = −1.057990 − 0.338143I
b = −0.12777 + 1.65559I
7.56649 + 9.18924I 0
u = −0.073346 + 1.249270I
a = −0.459853 − 0.956008I
b = −0.043571 + 0.947032I
0.33897 + 7.84486I 0
u = −0.073346 − 1.249270I
a = −0.459853 + 0.956008I
b = −0.043571 − 0.947032I
0.33897 − 7.84486I 0
u = 0.721856 + 1.027070I
a = 0.704898 − 0.295214I
b = −0.614618 − 0.468031I
6.10958 − 0.48289I 0
u = 0.721856 − 1.027070I
a = 0.704898 + 0.295214I
b = −0.614618 + 0.468031I
6.10958 + 0.48289I 0
u = 0.564876 + 1.135130I
a = −0.073078 − 0.707525I
b = −0.58777 + 1.86360I
6.26544 + 3.61924I 0
u = 0.564876 − 1.135130I
a = −0.073078 + 0.707525I
b = −0.58777 − 1.86360I
6.26544 − 3.61924I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.104431 + 1.298250I
a = 0.292746 − 0.847286I
b = −0.003012 + 0.940640I
−5.91703 − 3.42293I 0
u = 0.104431 − 1.298250I
a = 0.292746 + 0.847286I
b = −0.003012 − 0.940640I
−5.91703 + 3.42293I 0
u = −0.648304 + 1.133230I
a = −0.040925 − 1.149180I
b = 1.78851 + 1.92707I
4.2340 − 16.1582I 0
u = −0.648304 − 1.133230I
a = −0.040925 + 1.149180I
b = 1.78851 − 1.92707I
4.2340 + 16.1582I 0
u = 0.644245 + 1.145510I
a = 0.094859 − 1.051470I
b = −1.59384 + 1.71257I
−2.16297 + 12.09950I 0
u = 0.644245 − 1.145510I
a = 0.094859 + 1.051470I
b = −1.59384 − 1.71257I
−2.16297 − 12.09950I 0
u = −0.627293 + 1.165180I
a = −0.102093 − 0.901979I
b = 1.22622 + 1.56395I
−1.53699 − 6.84958I 0
u = −0.627293 − 1.165180I
a = −0.102093 + 0.901979I
b = 1.22622 − 1.56395I
−1.53699 + 6.84958I 0
u = −0.503518 + 0.347045I
a = 1.95488 − 0.23615I
b = −0.551149 + 1.270420I
3.23237 + 2.81118I 6.49138 − 3.43190I
u = −0.503518 − 0.347045I
a = 1.95488 + 0.23615I
b = −0.551149 − 1.270420I
3.23237 − 2.81118I 6.49138 + 3.43190I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.263360 + 1.365470I
a = −0.207188 − 0.642987I
b = 0.127253 + 0.960247I
−4.52691 − 2.53329I 0
u = −0.263360 − 1.365470I
a = −0.207188 + 0.642987I
b = 0.127253 − 0.960247I
−4.52691 + 2.53329I 0
u = −0.427074
a = −0.433828
b = −0.336075
0.801791 12.7100
u = 0.308392 + 0.295184I
a = −2.16318 + 0.94286I
b = 0.436188 + 0.731540I
−1.70503 − 0.88678I −1.07228 + 2.74548I
u = 0.308392 − 0.295184I
a = −2.16318 − 0.94286I
b = 0.436188 − 0.731540I
−1.70503 + 0.88678I −1.07228 − 2.74548I
u = −0.407213
a = 3.44853
b = −1.05852
1.47039 6.43280
11
II. I
u
2
= hu
2
+ 7b + 6u + 4, −u
2
+ a − u − 2, u
3
+ u
2
+ 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
9
=
u
2
+ u + 2
−
1
7
u
2
−
6
7
u −
4
7
a
7
=
u
2
+ u + 2
−
1
7
u
2
+
1
7
u −
4
7
a
10
=
0
−u
a
5
=
−u
−u
2
− u − 1
a
8
=
4
7
u
2
+
3
7
u +
9
7
0
a
11
=
1
0
a
4
=
u
2
+ 1
−u
2
− u − 1
a
4
=
u
2
+ 1
−u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
204
49
u
2
+
517
49
u +
368
49
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ u
2
+ 2u + 1
c
2
u
3
+ 3u
2
+ 2u − 1
c
3
, c
4
u
3
+ u
2
− 1
c
5
u
3
− u
2
+ 2u − 1
c
6
(u − 1)
3
c
7
7(7u
3
+ u
2
− 4u + 1)
c
8
7(7u
3
− u
2
+ u + 1)
c
9
(u + 1)
3
c
10
u
3
− u
2
+ 1
c
11
u
3
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
3
+ 3y
2
+ 2y −1
c
2
y
3
− 5y
2
+ 10y −1
c
3
, c
4
, c
10
y
3
− y
2
+ 2y −1
c
6
, c
9
(y −1)
3
c
7
49(49y
3
− 57y
2
+ 14y −1)
c
8
49(49y
3
+ 13y
2
+ 3y −1)
c
11
y
3
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.122561 + 0.744862I
b = −0.149595 − 1.040080I
−4.66906 − 2.82812I −1.67995 + 11.45076I
u = −0.215080 − 1.307140I
a = 0.122561 − 0.744862I
b = −0.149595 + 1.040080I
−4.66906 + 2.82812I −1.67995 − 11.45076I
u = −0.569840
a = 1.75488
b = −0.129382
−0.531480 2.84970
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
+ 2u + 1)(u
66
− 2u
65
+ ··· − 4u + 1)
c
2
(u
3
+ 3u
2
+ 2u − 1)(u
66
+ 30u
65
+ ··· + 2u + 1)
c
3
, c
4
(u
3
+ u
2
− 1)(u
66
− 2u
65
+ ··· − u
2
− 1)
c
5
(u
3
− u
2
+ 2u − 1)(u
66
− 2u
65
+ ··· − 4u + 1)
c
6
((u − 1)
3
)(u
66
− 4u
65
+ ··· + 491u − 49)
c
7
49(7u
3
+ u
2
− 4u + 1)(7u
66
− 18u
65
+ ··· + 13446u − 999)
c
8
49(7u
3
− u
2
+ u + 1)(7u
66
− 10u
65
+ ··· + 1391u + 241)
c
9
((u + 1)
3
)(u
66
− 4u
65
+ ··· + 491u − 49)
c
10
(u
3
− u
2
+ 1)(u
66
− 2u
65
+ ··· − u
2
− 1)
c
11
u
3
(u
66
− 5u
65
+ ··· − 3108u + 392)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
3
+ 3y
2
+ 2y −1)(y
66
+ 30y
65
+ ··· + 2y + 1)
c
2
(y
3
− 5y
2
+ 10y −1)(y
66
+ 14y
65
+ ··· + 14y + 1)
c
3
, c
4
, c
10
(y
3
− y
2
+ 2y −1)(y
66
− 62y
65
+ ··· + 2y + 1)
c
6
, c
9
((y −1)
3
)(y
66
− 36y
65
+ ··· − 105155y + 2401)
c
7
2401(49y
3
− 57y
2
+ 14y −1)
· (49y
66
+ 2434y
65
+ ··· − 82043766y + 998001)
c
8
2401(49y
3
+ 13y
2
+ 3y −1)
· (49y
66
+ 880y
65
+ ··· − 442127y + 58081)
c
11
y
3
(y
66
− 21y
65
+ ··· − 925904y + 153664)
17
