11a
15
(K11a
15
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 10 3 5 11 6 8 9
Solving Sequence
1,4
2 3
5,9
11 8 7 6 10
c
1
c
2
c
4
c
11
c
8
c
7
c
6
c
10
c
3
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.04308 × 10
20
u
63
− 7.59004 × 10
20
u
62
+ ··· + 3.96371 × 10
19
b + 2.83284 × 10
20
,
− 7.35239 × 10
20
u
63
− 3.87644 × 10
21
u
62
+ ··· + 7.92742 × 10
19
a + 5.92603 × 10
20
,
u
64
+ 7u
63
+ ··· − 13u − 1i
I
u
2
= hb − 1, u
4
+ u
3
+ a − u, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
u
3
= ha
3
+ b + 1, a
5
+ a
4
+ a
3
+ 2a
2
+ a + 1, u − 1i
* 3 irreducible components of dim
C
= 0, with total 75 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−1.04 × 10
20
u
63
− 7.59 × 10
20
u
62
+ · · · + 3.96 × 10
19
b + 2.83 ×
10
20
, −7.35 × 10
20
u
63
− 3.88 × 10
21
u
62
+ · · · + 7.93 × 10
19
a + 5.93 ×
10
20
, u
64
+ 7u
63
+ · · · − 13u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
9.27463u
63
+ 48.8992u
62
+ ··· − 37.0886u − 7.47536
2.63156u
63
+ 19.1488u
62
+ ··· − 70.8971u − 7.14695
a
11
=
−5.65805u
63
− 29.1771u
62
+ ··· + 32.6675u + 8.99552
2.08876u
63
+ 9.72032u
62
+ ··· + 23.9118u + 3.59970
a
8
=
4.89840u
63
+ 26.5797u
62
+ ··· + 14.3202u + 4.18773
4.18435u
63
+ 30.2617u
62
+ ··· − 83.2794u − 6.53051
a
7
=
2.16346u
63
+ 8.50706u
62
+ ··· + 60.6164u + 7.93271
7.04006u
63
+ 48.8776u
62
+ ··· − 118.375u − 9.20353
a
6
=
−1.17863u
63
− 5.74060u
62
+ ··· + 14.7171u + 3.28124
3.74498u
63
+ 23.4799u
62
+ ··· − 36.4181u − 2.38859
a
10
=
−18.2987u
63
− 107.518u
62
+ ··· + 156.183u + 15.9335
−6.10504u
63
− 50.2563u
62
+ ··· + 221.478u + 19.9762
a
10
=
−18.2987u
63
− 107.518u
62
+ ··· + 156.183u + 15.9335
−6.10504u
63
− 50.2563u
62
+ ··· + 221.478u + 19.9762
(ii) Obstruction class = −1
(iii) Cusp Shapes =
154506605926350535629
9909273683398550218
u
63
+
2873546855263844556609
39637094733594200872
u
62
+ ··· +
3763600436801685598541
39637094733594200872
u +
551008705357518405765
39637094733594200872
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
64
− 7u
63
+ ··· + 13u − 1
c
2
u
64
+ 29u
63
+ ··· + 37u + 1
c
3
, c
6
u
64
− 2u
63
+ ··· − 128u + 32
c
5
, c
9
u
64
+ 2u
63
+ ··· + 128u − 64
c
7
u
64
+ 3u
63
+ ··· − 2001u − 1609
c
8
, c
10
, c
11
u
64
+ 8u
63
+ ··· + 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
64
− 29y
63
+ ··· − 37y + 1
c
2
y
64
+ 19y
63
+ ··· − 3653y + 1
c
3
, c
6
y
64
− 36y
63
+ ··· − 20992y + 1024
c
5
, c
9
y
64
+ 42y
63
+ ··· + 24576y + 4096
c
7
y
64
− 37y
63
+ ··· + 70611765y + 2588881
c
8
, c
10
, c
11
y
64
− 64y
63
+ ··· + 20y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.851015 + 0.553122I
a = 3.09153 + 1.65651I
b = −1.403090 + 0.050018I
3.26372 − 2.22000I 0
u = 0.851015 − 0.553122I
a = 3.09153 − 1.65651I
b = −1.403090 − 0.050018I
3.26372 + 2.22000I 0
u = −0.468773 + 0.906872I
a = 0.474383 − 0.050538I
b = −0.493081 + 0.851380I
5.97499 − 4.90532I 0
u = −0.468773 − 0.906872I
a = 0.474383 + 0.050538I
b = −0.493081 − 0.851380I
5.97499 + 4.90532I 0
u = 0.957619 + 0.369938I
a = −1.152950 − 0.390386I
b = 0.170773 − 0.218203I
−1.81999 − 1.29187I 0
u = 0.957619 − 0.369938I
a = −1.152950 + 0.390386I
b = 0.170773 + 0.218203I
−1.81999 + 1.29187I 0
u = −0.554715 + 0.872769I
a = 0.811122 − 0.142635I
b = −0.681254 − 0.756164I
6.56660 + 0.51971I 0
u = −0.554715 − 0.872769I
a = 0.811122 + 0.142635I
b = −0.681254 + 0.756164I
6.56660 − 0.51971I 0
u = −0.513391 + 0.900925I
a = 2.49041 + 0.02335I
b = −1.46519 + 0.07102I
8.42241 − 2.26761I 0
u = −0.513391 − 0.900925I
a = 2.49041 − 0.02335I
b = −1.46519 − 0.07102I
8.42241 + 2.26761I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.798906 + 0.537570I
a = 0.556103 + 0.446579I
b = −1.208400 + 0.288039I
2.82835 + 0.98333I 5.99923 − 3.36293I
u = −0.798906 − 0.537570I
a = 0.556103 − 0.446579I
b = −1.208400 − 0.288039I
2.82835 − 0.98333I 5.99923 + 3.36293I
u = 0.684326 + 0.663082I
a = −2.47318 − 0.47845I
b = 1.52333 + 0.22252I
8.25062 + 3.46517I 6.83292 + 0.I
u = 0.684326 − 0.663082I
a = −2.47318 + 0.47845I
b = 1.52333 − 0.22252I
8.25062 − 3.46517I 6.83292 + 0.I
u = −0.892560 + 0.567255I
a = 0.55087 − 1.60438I
b = −1.080850 − 0.394220I
2.50515 + 3.47504I 0
u = −0.892560 − 0.567255I
a = 0.55087 + 1.60438I
b = −1.080850 + 0.394220I
2.50515 − 3.47504I 0
u = −0.426816 + 0.971335I
a = −1.81629 − 0.41191I
b = 1.53562 − 0.30377I
12.5775 − 9.1285I 0
u = −0.426816 − 0.971335I
a = −1.81629 + 0.41191I
b = 1.53562 + 0.30377I
12.5775 + 9.1285I 0
u = 0.773933 + 0.525049I
a = 0.224362 + 0.775639I
b = −0.586485 − 0.667589I
1.392230 + 0.239734I 4.64422 + 0.I
u = 0.773933 − 0.525049I
a = 0.224362 − 0.775639I
b = −0.586485 + 0.667589I
1.392230 − 0.239734I 4.64422 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.926326 + 0.128275I
a = 0.70787 + 3.19878I
b = −0.967057 + 0.104240I
0.047902 − 0.498911I 2.1353 − 14.8724I
u = 0.926326 − 0.128275I
a = 0.70787 − 3.19878I
b = −0.967057 − 0.104240I
0.047902 + 0.498911I 2.1353 + 14.8724I
u = 0.912042 + 0.554130I
a = 1.43049 + 0.51144I
b = −0.469774 + 0.774809I
0.93426 − 4.62344I 0
u = 0.912042 − 0.554130I
a = 1.43049 − 0.51144I
b = −0.469774 − 0.774809I
0.93426 + 4.62344I 0
u = −0.965340 + 0.501059I
a = −0.068579 − 0.710395I
b = 0.040956 − 0.606385I
−1.01229 + 4.28688I 0
u = −0.965340 − 0.501059I
a = −0.068579 + 0.710395I
b = 0.040956 + 0.606385I
−1.01229 − 4.28688I 0
u = −0.796135 + 0.411444I
a = −0.560743 + 0.887793I
b = −0.166184 + 0.699479I
−0.262566 − 0.498963I 2.74689 − 0.51399I
u = −0.796135 − 0.411444I
a = −0.560743 − 0.887793I
b = −0.166184 − 0.699479I
−0.262566 + 0.498963I 2.74689 + 0.51399I
u = 1.090500 + 0.201214I
a = −0.486035 + 0.573321I
b = −0.004735 + 0.287127I
−2.28356 − 0.63564I 0
u = 1.090500 − 0.201214I
a = −0.486035 − 0.573321I
b = −0.004735 − 0.287127I
−2.28356 + 0.63564I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.457914 + 0.741659I
a = −0.755401 + 0.029158I
b = 0.358616 − 0.179646I
2.38826 − 1.27360I 1.00000 + 1.24138I
u = −0.457914 − 0.741659I
a = −0.755401 − 0.029158I
b = 0.358616 + 0.179646I
2.38826 + 1.27360I 1.00000 − 1.24138I
u = −0.656679 + 0.923424I
a = −2.02373 + 0.73995I
b = 1.58190 + 0.20504I
14.1398 + 3.9767I 0
u = −0.656679 − 0.923424I
a = −2.02373 − 0.73995I
b = 1.58190 − 0.20504I
14.1398 − 3.9767I 0
u = 0.968165 + 0.622296I
a = −2.05377 − 2.02763I
b = 1.51383 − 0.27793I
7.38800 − 8.47452I 0
u = 0.968165 − 0.622296I
a = −2.05377 + 2.02763I
b = 1.51383 + 0.27793I
7.38800 + 8.47452I 0
u = −0.814156 + 0.225854I
a = 0.488791 − 0.388735I
b = 1.388550 − 0.248297I
4.72329 − 3.85111I 9.95444 − 1.38614I
u = −0.814156 − 0.225854I
a = 0.488791 + 0.388735I
b = 1.388550 + 0.248297I
4.72329 + 3.85111I 9.95444 + 1.38614I
u = −1.102490 + 0.469558I
a = 0.183729 + 1.038150I
b = 1.304930 + 0.108429I
2.70253 + 6.62281I 0
u = −1.102490 − 0.469558I
a = 0.183729 − 1.038150I
b = 1.304930 − 0.108429I
2.70253 − 6.62281I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.078950 + 0.604214I
a = −0.829008 + 0.571399I
b = 0.382661 + 0.323178I
0.55603 + 6.40064I 0
u = −1.078950 − 0.604214I
a = −0.829008 − 0.571399I
b = 0.382661 − 0.323178I
0.55603 − 6.40064I 0
u = 1.190520 + 0.380856I
a = 0.168620 − 1.294890I
b = 1.380510 − 0.021197I
2.11698 − 1.35062I 0
u = 1.190520 − 0.380856I
a = 0.168620 + 1.294890I
b = 1.380510 + 0.021197I
2.11698 + 1.35062I 0
u = 1.27051
a = 0.853993
b = −1.36931
1.81885 0
u = 1.269650 + 0.066401I
a = −0.275750 − 1.025770I
b = −0.479663 − 0.698680I
−0.29295 + 2.27028I 0
u = 1.269650 − 0.066401I
a = −0.275750 + 1.025770I
b = −0.479663 + 0.698680I
−0.29295 − 2.27028I 0
u = −1.078140 + 0.686845I
a = −0.219031 − 0.278038I
b = −0.763986 + 0.723012I
4.97472 + 5.25194I 0
u = −1.078140 − 0.686845I
a = −0.219031 + 0.278038I
b = −0.763986 − 0.723012I
4.97472 − 5.25194I 0
u = −1.037310 + 0.770242I
a = −1.42167 + 0.83458I
b = 1.59003 − 0.15683I
12.97910 + 2.20987I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.037310 − 0.770242I
a = −1.42167 − 0.83458I
b = 1.59003 + 0.15683I
12.97910 − 2.20987I 0
u = 0.016268 + 0.696606I
a = −1.34669 + 0.52337I
b = 1.41254 − 0.07728I
5.65313 − 2.65309I 8.42225 + 3.34216I
u = 0.016268 − 0.696606I
a = −1.34669 − 0.52337I
b = 1.41254 + 0.07728I
5.65313 + 2.65309I 8.42225 − 3.34216I
u = −1.109430 + 0.686273I
a = 1.83349 − 1.64073I
b = −1.46331 − 0.12160I
6.60913 + 8.11292I 0
u = −1.109430 − 0.686273I
a = 1.83349 + 1.64073I
b = −1.46331 + 0.12160I
6.60913 − 8.11292I 0
u = −1.131050 + 0.671760I
a = 1.043840 − 0.815468I
b = −0.438312 − 0.882770I
3.96365 + 10.71220I 0
u = −1.131050 − 0.671760I
a = 1.043840 + 0.815468I
b = −0.438312 + 0.882770I
3.96365 − 10.71220I 0
u = −1.172420 + 0.678120I
a = −1.26144 + 1.95035I
b = 1.51825 + 0.32917I
10.2926 + 15.1288I 0
u = −1.172420 − 0.678120I
a = −1.26144 − 1.95035I
b = 1.51825 − 0.32917I
10.2926 − 15.1288I 0
u = 1.350730 + 0.109045I
a = −0.034825 + 0.580788I
b = 1.50631 + 0.25249I
6.16621 + 5.77451I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.350730 − 0.109045I
a = −0.034825 − 0.580788I
b = 1.50631 − 0.25249I
6.16621 − 5.77451I 0
u = −0.004404 + 0.249946I
a = −1.65033 − 0.59592I
b = −0.278953 + 0.383140I
0.309124 − 1.130770I 3.85993 + 6.08046I
u = −0.004404 − 0.249946I
a = −1.65033 + 0.59592I
b = −0.278953 − 0.383140I
0.309124 + 1.130770I 3.85993 − 6.08046I
u = −0.133522
a = −5.10635
b = −1.14767
2.19568 3.71440
11
II. I
u
2
= hb − 1, u
4
+ u
3
+ a − u, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
−u
4
− u
3
+ u
1
a
11
=
−u
4
− u
3
+ u + 1
1
a
8
=
−1
0
a
7
=
−u
4
+ u
2
− 1
u
5
+ u
4
− 2u
3
− u
2
+ u + 1
a
6
=
−u
−u
3
+ u
a
10
=
−u
4
− u
3
+ u
1
a
10
=
−u
4
− u
3
+ u
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
4
+ 2u
3
− 5u
2
− 6u + 5
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
2
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
3
, c
4
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
5
, c
9
u
6
c
7
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
8
(u + 1)
6
c
10
, c
11
(u − 1)
6
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
2
, c
7
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
5
, c
9
y
6
c
8
, c
10
, c
11
(y −1)
6
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −0.23185 − 1.65564I
b = 1.00000
−0.245672 − 0.924305I −1.66012 + 2.42665I
u = 1.002190 − 0.295542I
a = −0.23185 + 1.65564I
b = 1.00000
−0.245672 + 0.924305I −1.66012 − 2.42665I
u = −0.428243 + 0.664531I
a = −0.659772 + 0.298454I
b = 1.00000
3.53554 − 0.92430I 8.55174 + 0.47256I
u = −0.428243 − 0.664531I
a = −0.659772 − 0.298454I
b = 1.00000
3.53554 + 0.92430I 8.55174 − 0.47256I
u = −1.073950 + 0.558752I
a = −0.108378 + 0.818891I
b = 1.00000
1.64493 + 5.69302I 3.10838 − 3.92918I
u = −1.073950 − 0.558752I
a = −0.108378 − 0.818891I
b = 1.00000
1.64493 − 5.69302I 3.10838 + 3.92918I
15
III. I
u
3
= ha
3
+ b + 1, a
5
+ a
4
+ a
3
+ 2a
2
+ a + 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
3
=
0
1
a
5
=
−1
0
a
9
=
a
−a
3
− 1
a
11
=
−a
4
− a + 1
a
3
+ a
2
+ 2
a
8
=
−a
4
− a + 1
−a
4
− a + 1
a
7
=
0
−a
4
− a + 1
a
6
=
0
−a
4
− a + 1
a
10
=
a
a
4
+ a
3
+ a
2
+ 2a + 1
a
10
=
a
a
4
+ a
3
+ a
2
+ 2a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5a
4
+ 5a
3
+ 7a + 2
16
(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
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
7
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
8
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
9
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
10
, c
11
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
17
(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
, c
9
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
7
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
8
, c
10
, c
11
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.428550 + 1.039280I
b = 0.309916 + 0.549911I
−1.31583 + 1.53058I −1.49901 − 3.45976I
u = 1.00000
a = 0.428550 − 1.039280I
b = 0.309916 − 0.549911I
−1.31583 − 1.53058I −1.49901 + 3.45976I
u = 1.00000
a = −0.276511 + 0.728237I
b = −1.41878 + 0.21917I
4.22763 − 4.40083I 2.37737 + 5.82971I
u = 1.00000
a = −0.276511 − 0.728237I
b = −1.41878 − 0.21917I
4.22763 + 4.40083I 2.37737 − 5.82971I
u = 1.00000
a = −1.30408
b = 1.21774
0.756147 −3.75670
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
6
+ u
5
+ ··· + u + 1)(u
64
− 7u
63
+ ··· + 13u − 1)
c
2
(u + 1)
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
64
+ 29u
63
+ ··· + 37u + 1)
c
3
u
5
(u
6
− u
5
+ ··· − u + 1)(u
64
− 2u
63
+ ··· − 128u + 32)
c
4
((u + 1)
5
)(u
6
− u
5
+ ··· − u + 1)(u
64
− 7u
63
+ ··· + 13u − 1)
c
5
u
6
(u
5
+ u
4
+ ··· + u + 1)(u
64
+ 2u
63
+ ··· + 128u − 64)
c
6
u
5
(u
6
+ u
5
+ ··· + u + 1)(u
64
− 2u
63
+ ··· − 128u + 32)
c
7
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
64
+ 3u
63
+ ··· − 2001u − 1609)
c
8
((u + 1)
6
)(u
5
− u
4
+ ··· + u + 1)(u
64
+ 8u
63
+ ··· + 4u + 1)
c
9
u
6
(u
5
− u
4
+ ··· + u − 1)(u
64
+ 2u
63
+ ··· + 128u − 64)
c
10
, c
11
((u − 1)
6
)(u
5
+ u
4
+ ··· + u − 1)(u
64
+ 8u
63
+ ··· + 4u + 1)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y −1)
5
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
64
− 29y
63
+ ··· − 37y + 1)
c
2
((y −1)
5
)(y
6
+ y
5
+ ··· + 3y + 1)(y
64
+ 19y
63
+ ··· − 3653y + 1)
c
3
, c
6
y
5
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
64
− 36y
63
+ ··· − 20992y + 1024)
c
5
, c
9
y
6
(y
5
+ 3y
4
+ ··· − y −1)(y
64
+ 42y
63
+ ··· + 24576y + 4096)
c
7
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
64
− 37y
63
+ ··· + 70611765y + 2588881)
c
8
, c
10
, c
11
((y −1)
6
)(y
5
− 5y
4
+ ··· − y −1)(y
64
− 64y
63
+ ··· + 20y + 1)
21
