11n
109
(K11n
109
)
A knot diagram
1
Linearized knot diagam
6 1 7 9 2 10 1 4 5 7 4
Solving Sequence
2,5 6,10
7 1 8 9 4 3 11
c
5
c
6
c
1
c
7
c
9
c
4
c
3
c
11
c
2
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.53910 × 10
25
u
37
− 4.74008 × 10
25
u
36
+ ··· + 3.48267 × 10
25
b − 4.36228 × 10
24
,
2.88601 × 10
25
u
37
− 3.57200 × 10
25
u
36
+ ··· + 3.48267 × 10
25
a + 4.29759 × 10
24
, u
38
− 2u
37
+ ··· − 3u + 1i
I
u
2
= h−u
9
− 3u
7
+ u
6
− 4u
5
+ 2u
4
− 3u
3
+ u
2
+ b + 1,
u
9
+ 3u
8
+ 6u
7
+ 10u
6
+ 12u
5
+ 14u
4
+ 12u
3
+ 12u
2
+ a + 8u + 4,
u
10
+ u
9
+ 4u
8
+ 3u
7
+ 7u
6
+ 4u
5
+ 7u
4
+ 4u
3
+ 4u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 48 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
= h3.54 × 10
25
u
37
− 4.74 × 10
25
u
36
+ · · · + 3.48 × 10
25
b − 4.36 × 10
24
, 2.89 ×
10
25
u
37
−3.57×10
25
u
36
+· · ·+3.48×10
25
a+4.30×10
24
, u
38
−2u
37
+· · ·−3u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
10
=
−0.828678u
37
+ 1.02565u
36
+ ··· − 2.81126u − 0.123399
−1.01620u
37
+ 1.36105u
36
+ ··· − 0.588254u + 0.125257
a
7
=
0.631271u
37
+ 0.581742u
36
+ ··· − 2.12748u + 3.40130
−0.642147u
37
+ 1.04198u
36
+ ··· − 0.717938u + 0.0244084
a
1
=
−u
u
3
+ u
a
8
=
0.607524u
37
− 0.145250u
36
+ ··· + 0.310068u + 2.19514
−0.307663u
37
+ 0.666840u
36
+ ··· − 0.855780u + 0.456085
a
9
=
0.187524u
37
− 0.335397u
36
+ ··· − 2.22301u − 0.248656
−1.01620u
37
+ 1.36105u
36
+ ··· − 0.588254u + 0.125257
a
4
=
−1.27334u
37
+ 1.88196u
36
+ ··· + 0.0209510u − 0.151656
1.28508u
37
− 2.98814u
36
+ ··· + 3.97779u − 1.10711
a
3
=
−u
3
u
5
+ u
3
+ u
a
11
=
−0.0155744u
37
+ 0.751097u
36
+ ··· − 1.99782u + 0.341364
−1.31911u
37
+ 1.47526u
36
+ ··· − 3.17447u + 0.821375
a
11
=
−0.0155744u
37
+ 0.751097u
36
+ ··· − 1.99782u + 0.341364
−1.31911u
37
+ 1.47526u
36
+ ··· − 3.17447u + 0.821375
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
134839754017820031393971870
34826691050833540478655473
u
37
+
3307262072424404195903844
440844190516880259223487
u
36
+
··· −
433267787549488445549936384
34826691050833540478655473
u +
614901013376164862123029830
34826691050833540478655473
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
38
− 2u
37
+ ··· − 3u + 1
c
2
u
38
+ 20u
37
+ ··· − 7u + 1
c
3
u
38
− u
37
+ ··· − 130u − 29
c
4
, c
8
, c
9
u
38
+ u
37
+ ··· − 24u − 19
c
6
, c
10
u
38
− 3u
37
+ ··· + 94u − 11
c
7
u
38
+ u
37
+ ··· − 39u − 2
c
11
u
38
− 2u
37
+ ··· + 31u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
38
+ 20y
37
+ ··· − 7y + 1
c
2
y
38
+ 4y
37
+ ··· − 95y + 1
c
3
y
38
+ 41y
37
+ ··· + 1138y + 841
c
4
, c
8
, c
9
y
38
− 35y
37
+ ··· − 6y + 361
c
6
, c
10
y
38
− 17y
37
+ ··· − 1686y + 121
c
7
y
38
+ 37y
37
+ ··· − 325y + 4
c
11
y
38
− 38y
37
+ ··· − 415y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.198690 + 0.927706I
a = −0.29365 − 1.42984I
b = −0.507231 − 0.501686I
−1.65932 + 1.72508I 3.99615 − 5.00557I
u = 0.198690 − 0.927706I
a = −0.29365 + 1.42984I
b = −0.507231 + 0.501686I
−1.65932 − 1.72508I 3.99615 + 5.00557I
u = −0.379743 + 0.859856I
a = −0.035838 + 1.400050I
b = 0.285476 + 0.554000I
1.30138 − 1.64549I 4.54049 − 1.93386I
u = −0.379743 − 0.859856I
a = −0.035838 − 1.400050I
b = 0.285476 − 0.554000I
1.30138 + 1.64549I 4.54049 + 1.93386I
u = 0.437061 + 1.002290I
a = 0.802004 − 0.659495I
b = 1.178350 − 0.751371I
−3.43318 + 1.20443I 6.92259 − 2.66519I
u = 0.437061 − 1.002290I
a = 0.802004 + 0.659495I
b = 1.178350 + 0.751371I
−3.43318 − 1.20443I 6.92259 + 2.66519I
u = 0.668607 + 0.872893I
a = −0.468782 + 0.686829I
b = −0.086247 + 0.537690I
1.01360 + 2.58424I 2.68887 − 3.99949I
u = 0.668607 − 0.872893I
a = −0.468782 − 0.686829I
b = −0.086247 − 0.537690I
1.01360 − 2.58424I 2.68887 + 3.99949I
u = 0.496586 + 1.000340I
a = −0.81802 + 1.31551I
b = 1.39385 + 0.31403I
−3.05076 + 4.70281I 7.22690 − 4.71362I
u = 0.496586 − 1.000340I
a = −0.81802 − 1.31551I
b = 1.39385 − 0.31403I
−3.05076 − 4.70281I 7.22690 + 4.71362I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.081330 + 0.386328I
a = −0.216812 − 0.071474I
b = 1.43091 − 0.33793I
1.95602 − 6.72677I 10.60803 + 3.77299I
u = 1.081330 − 0.386328I
a = −0.216812 + 0.071474I
b = 1.43091 + 0.33793I
1.95602 + 6.72677I 10.60803 − 3.77299I
u = −0.775393 + 0.236076I
a = −0.744379 − 0.266250I
b = −0.299152 − 0.795595I
−3.53482 + 2.58667I 7.16756 − 2.58418I
u = −0.775393 − 0.236076I
a = −0.744379 + 0.266250I
b = −0.299152 + 0.795595I
−3.53482 − 2.58667I 7.16756 + 2.58418I
u = −0.913408 + 0.776527I
a = −0.296533 − 0.156951I
b = 1.287170 + 0.114756I
5.31271 − 0.53174I 10.57597 + 0.24868I
u = −0.913408 − 0.776527I
a = −0.296533 + 0.156951I
b = 1.287170 − 0.114756I
5.31271 + 0.53174I 10.57597 − 0.24868I
u = 0.447680 + 0.663750I
a = 0.97208 − 2.47509I
b = −1.110300 + 0.132355I
−1.90577 − 0.72497I 8.59505 − 1.33995I
u = 0.447680 − 0.663750I
a = 0.97208 + 2.47509I
b = −1.110300 − 0.132355I
−1.90577 + 0.72497I 8.59505 + 1.33995I
u = −0.526939 + 1.137220I
a = 0.54259 − 1.42286I
b = 1.53921 − 0.16530I
5.23331 − 4.18634I 5.68349 + 3.29449I
u = −0.526939 − 1.137220I
a = 0.54259 + 1.42286I
b = 1.53921 + 0.16530I
5.23331 + 4.18634I 5.68349 − 3.29449I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.784887 + 0.992111I
a = 0.32772 + 1.44641I
b = −1.252110 + 0.274462I
4.61276 − 5.70694I 9.04865 + 6.07255I
u = −0.784887 − 0.992111I
a = 0.32772 − 1.44641I
b = −1.252110 − 0.274462I
4.61276 + 5.70694I 9.04865 − 6.07255I
u = −0.561660 + 1.148650I
a = −0.34487 − 1.38992I
b = 0.258106 − 1.087690I
−6.14363 − 7.57123I 4.89087 + 5.76194I
u = −0.561660 − 1.148650I
a = −0.34487 + 1.38992I
b = 0.258106 + 1.087690I
−6.14363 + 7.57123I 4.89087 − 5.76194I
u = −0.297248 + 1.257890I
a = 0.693796 + 0.789863I
b = −0.164859 + 0.672738I
−8.06788 − 1.04561I 1.73854 + 0.76531I
u = −0.297248 − 1.257890I
a = 0.693796 − 0.789863I
b = −0.164859 − 0.672738I
−8.06788 + 1.04561I 1.73854 − 0.76531I
u = 0.693371
a = −0.324535
b = −1.38702
7.32047 11.7760
u = 0.534109 + 1.201300I
a = 0.76686 + 1.35110I
b = 1.196420 + 0.245037I
4.11680 + 4.64818I 7.00000 − 4.11714I
u = 0.534109 − 1.201300I
a = 0.76686 − 1.35110I
b = 1.196420 − 0.245037I
4.11680 − 4.64818I 7.00000 + 4.11714I
u = 0.326007 + 0.583311I
a = −0.52323 − 2.59696I
b = −0.878482 − 0.628167I
−2.08165 + 2.22554I 9.62442 − 6.36612I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.326007 − 0.583311I
a = −0.52323 + 2.59696I
b = −0.878482 + 0.628167I
−2.08165 − 2.22554I 9.62442 + 6.36612I
u = 0.698047 + 1.223380I
a = −0.14107 − 1.57898I
b = −1.47736 − 0.45823I
−0.64182 + 13.08690I 0
u = 0.698047 − 1.223380I
a = −0.14107 + 1.57898I
b = −1.47736 + 0.45823I
−0.64182 − 13.08690I 0
u = 0.19948 + 1.53203I
a = −0.874606 + 0.019930I
b = −1.233390 + 0.241654I
−4.80130 − 2.15880I 0
u = 0.19948 − 1.53203I
a = −0.874606 − 0.019930I
b = −1.233390 − 0.241654I
−4.80130 + 2.15880I 0
u = −0.337441 + 0.249883I
a = 1.16350 + 0.97340I
b = −1.59455 + 0.00504I
7.79085 − 0.03851I 8.05729 − 1.80582I
u = −0.337441 − 0.249883I
a = 1.16350 − 0.97340I
b = −1.59455 − 0.00504I
7.79085 + 0.03851I 8.05729 + 1.80582I
u = 0.284870
a = −0.696967
b = 0.455407
0.644934 15.5790
8
II.
I
u
2
= h−u
9
− 3u
7
+ · · · + b + 1, u
9
+ 3u
8
+ · · · + a + 4, u
10
+ u
9
+ · · · + u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
10
=
−u
9
− 3u
8
− 6u
7
− 10u
6
− 12u
5
− 14u
4
− 12u
3
− 12u
2
− 8u − 4
u
9
+ 3u
7
− u
6
+ 4u
5
− 2u
4
+ 3u
3
− u
2
− 1
a
7
=
2u
9
+ u
8
+ 6u
7
+ u
6
+ 8u
5
− u
4
+ 6u
3
+ u − 2
u
8
+ 3u
6
+ 4u
4
+ 2u
2
+ u
a
1
=
−u
u
3
+ u
a
8
=
u
9
+ 3u
7
− u
6
+ 4u
5
− 3u
4
+ 3u
3
− 2u
2
− 2
u
8
+ 3u
6
+ 4u
4
+ 3u
2
+ u
a
9
=
−2u
9
− 3u
8
− 9u
7
− 9u
6
− 16u
5
− 12u
4
− 15u
3
− 11u
2
− 8u − 3
u
9
+ 3u
7
− u
6
+ 4u
5
− 2u
4
+ 3u
3
− u
2
− 1
a
4
=
u
9
+ 3u
8
+ 5u
7
+ 9u
6
+ 9u
5
+ 12u
4
+ 8u
3
+ 10u
2
+ 6u + 2
u
9
+ u
8
+ 4u
7
+ 3u
6
+ 7u
5
+ 4u
4
+ 7u
3
+ 4u
2
+ 3u + 2
a
3
=
−u
3
u
5
+ u
3
+ u
a
11
=
−2u
9
− 5u
8
− 10u
7
− 16u
6
− 18u
5
− 22u
4
− 17u
3
− 19u
2
− 12u − 5
−u
7
− u
6
− 3u
5
− 2u
4
− 3u
3
− 2u
2
− 2u − 2
a
11
=
−2u
9
− 5u
8
− 10u
7
− 16u
6
− 18u
5
− 22u
4
− 17u
3
− 19u
2
− 12u − 5
−u
7
− u
6
− 3u
5
− 2u
4
− 3u
3
− 2u
2
− 2u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
9
+ u
8
+ 19u
7
− u
6
+ 26u
5
− 10u
4
+ 20u
3
− 9u
2
+ 2u
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
− u
9
+ 4u
8
− 3u
7
+ 7u
6
− 4u
5
+ 7u
4
− 4u
3
+ 4u
2
− u + 1
c
2
u
10
+ 7u
9
+ ··· + 7u + 1
c
3
u
10
+ 2u
8
+ u
7
− 4u
6
− 2u
5
− 2u
4
− 2u
3
+ 8u
2
− 2u + 1
c
4
u
10
− 6u
8
− u
7
+ 13u
6
+ 4u
5
− 12u
4
− 5u
3
+ 4u
2
+ 2u + 1
c
5
u
10
+ u
9
+ 4u
8
+ 3u
7
+ 7u
6
+ 4u
5
+ 7u
4
+ 4u
3
+ 4u
2
+ u + 1
c
6
u
10
− 2u
9
− u
8
+ 3u
7
+ u
5
− 2u
4
− 2u
3
+ 2u
2
+ 1
c
7
u
10
+ 2u
8
− 2u
7
− 2u
6
+ u
5
+ 3u
3
− u
2
− 2u + 1
c
8
, c
9
u
10
− 6u
8
+ u
7
+ 13u
6
− 4u
5
− 12u
4
+ 5u
3
+ 4u
2
− 2u + 1
c
10
u
10
+ 2u
9
− u
8
− 3u
7
− u
5
− 2u
4
+ 2u
3
+ 2u
2
+ 1
c
11
u
10
− 3u
9
+ u
8
+ 5u
7
− 7u
6
+ 3u
5
+ 4u
4
− 7u
3
+ 6u
2
− 3u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
10
+ 7y
9
+ ··· + 7y + 1
c
2
y
10
− y
9
+ ··· − 5y + 1
c
3
y
10
+ 4y
9
+ ··· + 12y + 1
c
4
, c
8
, c
9
y
10
− 12y
9
+ ··· + 4y + 1
c
6
, c
10
y
10
− 6y
9
+ 13y
8
− 9y
7
− 6y
6
+ 9y
5
+ 6y
4
− 12y
3
+ 4y + 1
c
7
y
10
+ 4y
9
− 12y
7
+ 6y
6
+ 9y
5
− 6y
4
− 9y
3
+ 13y
2
− 6y + 1
c
11
y
10
− 7y
9
+ 17y
8
− 13y
7
− 3y
6
+ y
5
+ 6y
4
+ 3y
3
+ 2y
2
+ 3y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.591573 + 0.895458I
a = −0.062941 + 0.916484I
b = −0.162645 + 0.362811I
1.88316 + 2.32533I 12.32535 − 3.44072I
u = 0.591573 − 0.895458I
a = −0.062941 − 0.916484I
b = −0.162645 − 0.362811I
1.88316 − 2.32533I 12.32535 + 3.44072I
u = −0.587969 + 0.580983I
a = −0.270490 − 0.170382I
b = 1.56713 + 0.08593I
8.26505 − 0.63915I 14.5970 + 5.3987I
u = −0.587969 − 0.580983I
a = −0.270490 + 0.170382I
b = 1.56713 − 0.08593I
8.26505 + 0.63915I 14.5970 − 5.3987I
u = −0.642090 + 1.139230I
a = −0.42175 + 1.41771I
b = −1.43000 + 0.16541I
6.43677 − 4.34705I 13.62063 + 3.59101I
u = −0.642090 − 1.139230I
a = −0.42175 − 1.41771I
b = −1.43000 − 0.16541I
6.43677 + 4.34705I 13.62063 − 3.59101I
u = 0.059179 + 1.329340I
a = 0.597845 + 0.216685I
b = 0.995882 − 0.290486I
−5.58838 − 1.13850I 4.94587 − 0.33361I
u = 0.059179 − 1.329340I
a = 0.597845 − 0.216685I
b = 0.995882 + 0.290486I
−5.58838 + 1.13850I 4.94587 + 0.33361I
u = 0.079307 + 0.642927I
a = −0.84267 − 3.52089I
b = −0.970365 − 0.458151I
−2.77192 + 1.74853I 1.51113 − 2.06464I
u = 0.079307 − 0.642927I
a = −0.84267 + 3.52089I
b = −0.970365 + 0.458151I
−2.77192 − 1.74853I 1.51113 + 2.06464I
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
10
− u
9
+ 4u
8
− 3u
7
+ 7u
6
− 4u
5
+ 7u
4
− 4u
3
+ 4u
2
− u + 1)
· (u
38
− 2u
37
+ ··· − 3u + 1)
c
2
(u
10
+ 7u
9
+ ··· + 7u + 1)(u
38
+ 20u
37
+ ··· − 7u + 1)
c
3
(u
10
+ 2u
8
+ u
7
− 4u
6
− 2u
5
− 2u
4
− 2u
3
+ 8u
2
− 2u + 1)
· (u
38
− u
37
+ ··· − 130u − 29)
c
4
(u
10
− 6u
8
− u
7
+ 13u
6
+ 4u
5
− 12u
4
− 5u
3
+ 4u
2
+ 2u + 1)
· (u
38
+ u
37
+ ··· − 24u − 19)
c
5
(u
10
+ u
9
+ 4u
8
+ 3u
7
+ 7u
6
+ 4u
5
+ 7u
4
+ 4u
3
+ 4u
2
+ u + 1)
· (u
38
− 2u
37
+ ··· − 3u + 1)
c
6
(u
10
− 2u
9
− u
8
+ 3u
7
+ u
5
− 2u
4
− 2u
3
+ 2u
2
+ 1)
· (u
38
− 3u
37
+ ··· + 94u − 11)
c
7
(u
10
+ 2u
8
− 2u
7
− 2u
6
+ u
5
+ 3u
3
− u
2
− 2u + 1)
· (u
38
+ u
37
+ ··· − 39u − 2)
c
8
, c
9
(u
10
− 6u
8
+ u
7
+ 13u
6
− 4u
5
− 12u
4
+ 5u
3
+ 4u
2
− 2u + 1)
· (u
38
+ u
37
+ ··· − 24u − 19)
c
10
(u
10
+ 2u
9
− u
8
− 3u
7
− u
5
− 2u
4
+ 2u
3
+ 2u
2
+ 1)
· (u
38
− 3u
37
+ ··· + 94u − 11)
c
11
(u
10
− 3u
9
+ u
8
+ 5u
7
− 7u
6
+ 3u
5
+ 4u
4
− 7u
3
+ 6u
2
− 3u + 1)
· (u
38
− 2u
37
+ ··· + 31u + 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
10
+ 7y
9
+ ··· + 7y + 1)(y
38
+ 20y
37
+ ··· − 7y + 1)
c
2
(y
10
− y
9
+ ··· − 5y + 1)(y
38
+ 4y
37
+ ··· − 95y + 1)
c
3
(y
10
+ 4y
9
+ ··· + 12y + 1)(y
38
+ 41y
37
+ ··· + 1138y + 841)
c
4
, c
8
, c
9
(y
10
− 12y
9
+ ··· + 4y + 1)(y
38
− 35y
37
+ ··· − 6y + 361)
c
6
, c
10
(y
10
− 6y
9
+ 13y
8
− 9y
7
− 6y
6
+ 9y
5
+ 6y
4
− 12y
3
+ 4y + 1)
· (y
38
− 17y
37
+ ··· − 1686y + 121)
c
7
(y
10
+ 4y
9
− 12y
7
+ 6y
6
+ 9y
5
− 6y
4
− 9y
3
+ 13y
2
− 6y + 1)
· (y
38
+ 37y
37
+ ··· − 325y + 4)
c
11
(y
10
− 7y
9
+ 17y
8
− 13y
7
− 3y
6
+ y
5
+ 6y
4
+ 3y
3
+ 2y
2
+ 3y + 1)
· (y
38
− 38y
37
+ ··· − 415y + 1)
14
