11a
26
(K11a
26
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 8 3 10 11 6 5 9
Solving Sequence
1,4
2
5,9
11 8 6 10 7 3
c
1
c
4
c
11
c
8
c
5
c
10
c
7
c
3
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h5.01473 × 10
70
u
83
+ 3.35718 × 10
71
u
82
+ ··· + 4.78692 × 10
70
b + 3.84233 × 10
70
,
3.48846 × 10
71
u
83
+ 2.03127 × 10
72
u
82
+ ··· + 4.78692 × 10
70
a + 1.50947 × 10
70
, u
84
+ 7u
83
+ ··· + 3u + 1i
I
u
2
= hb − a + 1, a
6
− 5a
5
+ 9a
4
− 8a
3
+ 5a
2
− 2a + 1, u − 1i
* 2 irreducible components of dim
C
= 0, with total 90 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
= h5.01 × 10
70
u
83
+ 3.36 × 10
71
u
82
+ · · · + 4.79 × 10
70
b + 3.84 × 10
70
, 3.49 ×
10
71
u
83
+2.03×10
72
u
82
+· · ·+4.79×10
70
a+1.51×10
70
, u
84
+7u
83
+· · ·+3u+1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
−7.28749u
83
− 42.4337u
82
+ ··· + 68.1358u − 0.315332
−1.04759u
83
− 7.01323u
82
+ ··· − 4.76652u − 0.802671
a
11
=
−5.90618u
83
− 34.5694u
82
+ ··· + 66.7237u + 3.09487
1.65285u
83
+ 10.0206u
82
+ ··· − 0.430299u + 2.21652
a
8
=
−3.26390u
83
− 19.2317u
82
+ ··· + 6.89193u − 6.39737
−2.92755u
83
− 18.7843u
82
+ ··· − 3.42332u − 3.43162
a
6
=
−2.95981u
83
− 19.0451u
82
+ ··· − 27.6514u − 5.08421
4.22596u
83
+ 24.4825u
82
+ ··· + 9.63893u + 3.12800
a
10
=
0.136122u
83
− 2.27013u
82
+ ··· + 75.7067u + 5.71691
9.00790u
83
+ 57.2317u
82
+ ··· + 14.5350u + 9.59135
a
7
=
0.297603u
83
+ 0.0843443u
82
+ ··· + 17.4398u + 1.52108
0.435133u
83
+ 4.60968u
82
+ ··· − 0.0556085u + 0.732737
a
3
=
−u
2
+ 1
u
2
a
3
=
−u
2
+ 1
u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −34.4571u
83
− 206.279u
82
+ ··· − 74.1253u − 20.5385
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
84
− 7u
83
+ ··· − 3u + 1
c
2
u
84
+ 41u
83
+ ··· − 157u + 1
c
3
, c
6
u
84
− u
83
+ ··· − 320u + 64
c
5
u
84
− 6u
83
+ ··· − 2u + 1
c
7
u
84
− 14u
83
+ ··· − 2u + 1
c
8
, c
11
u
84
+ 2u
83
+ ··· + 14u + 1
c
9
u
84
+ 2u
83
+ ··· − 418u + 367
c
10
u
84
+ 6u
83
+ ··· − 1166u − 101
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
84
− 41y
83
+ ··· + 157y + 1
c
2
y
84
+ 11y
83
+ ··· − 14895y + 1
c
3
, c
6
y
84
− 39y
83
+ ··· − 61440y + 4096
c
5
y
84
+ 14y
83
+ ··· + 6y + 1
c
7
y
84
− 6y
83
+ ··· − 14y + 1
c
8
, c
11
y
84
− 54y
83
+ ··· − 14y + 1
c
9
y
84
− 66y
83
+ ··· + 5678926y + 134689
c
10
y
84
− 82y
83
+ ··· − 878594y + 10201
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.332631 + 0.958315I
a = 1.67820 + 0.07513I
b = −1.37591 + 0.55145I
5.73608 − 12.12140I 0
u = −0.332631 − 0.958315I
a = 1.67820 − 0.07513I
b = −1.37591 − 0.55145I
5.73608 + 12.12140I 0
u = −0.951859 + 0.248441I
a = −0.218069 + 0.361485I
b = −1.120340 + 0.633983I
−1.61526 − 4.99229I 0
u = −0.951859 − 0.248441I
a = −0.218069 − 0.361485I
b = −1.120340 − 0.633983I
−1.61526 + 4.99229I 0
u = 0.967113 + 0.342930I
a = −3.13088 − 5.37988I
b = 0.997274 − 0.064037I
−0.170119 − 1.192110I 0
u = 0.967113 − 0.342930I
a = −3.13088 + 5.37988I
b = 0.997274 + 0.064037I
−0.170119 + 1.192110I 0
u = 0.928263 + 0.443032I
a = −2.21795 − 1.93233I
b = 1.27275 − 0.62263I
1.46677 − 3.41872I 0
u = 0.928263 − 0.443032I
a = −2.21795 + 1.93233I
b = 1.27275 + 0.62263I
1.46677 + 3.41872I 0
u = −0.653182 + 0.674145I
a = −0.419780 + 0.077857I
b = 0.453075 + 0.998389I
3.23379 + 3.44018I 0
u = −0.653182 − 0.674145I
a = −0.419780 − 0.077857I
b = 0.453075 − 0.998389I
3.23379 − 3.44018I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.043360 + 0.207956I
a = 1.44638 + 2.71546I
b = 0.911327 + 0.012256I
−0.506438 − 0.641182I 0
u = 1.043360 − 0.207956I
a = 1.44638 − 2.71546I
b = 0.911327 − 0.012256I
−0.506438 + 0.641182I 0
u = −0.879247 + 0.308527I
a = 0.151761 + 0.454759I
b = −0.664606 + 0.732185I
−3.09506 + 1.90596I 0
u = −0.879247 − 0.308527I
a = 0.151761 − 0.454759I
b = −0.664606 − 0.732185I
−3.09506 − 1.90596I 0
u = −0.535364 + 0.758601I
a = −1.84796 + 0.45576I
b = 1.58214 + 0.40524I
6.53306 + 0.44104I 0
u = −0.535364 − 0.758601I
a = −1.84796 − 0.45576I
b = 1.58214 − 0.40524I
6.53306 − 0.44104I 0
u = −0.996208 + 0.396743I
a = 0.714153 − 0.928374I
b = −0.437239 − 1.006900I
−3.77732 + 0.83071I 0
u = −0.996208 − 0.396743I
a = 0.714153 + 0.928374I
b = −0.437239 + 1.006900I
−3.77732 − 0.83071I 0
u = −0.445418 + 0.802301I
a = −1.370510 + 0.178277I
b = 1.41107 − 0.70362I
5.99281 − 3.52843I 0
u = −0.445418 − 0.802301I
a = −1.370510 − 0.178277I
b = 1.41107 + 0.70362I
5.99281 + 3.52843I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.369678 + 1.018600I
a = 1.50883 + 0.01924I
b = −1.102510 + 0.205014I
4.58405 − 3.81524I 0
u = −0.369678 − 1.018600I
a = 1.50883 − 0.01924I
b = −1.102510 − 0.205014I
4.58405 + 3.81524I 0
u = −0.340933 + 0.839696I
a = 0.202650 + 0.452508I
b = 0.019790 − 1.184810I
1.35757 − 6.09736I 0
u = −0.340933 − 0.839696I
a = 0.202650 − 0.452508I
b = 0.019790 + 1.184810I
1.35757 + 6.09736I 0
u = 0.292041 + 0.834139I
a = 1.49488 − 0.31220I
b = −1.018820 + 0.211435I
1.52052 − 3.66155I 0
u = 0.292041 − 0.834139I
a = 1.49488 + 0.31220I
b = −1.018820 − 0.211435I
1.52052 + 3.66155I 0
u = −0.965351 + 0.572013I
a = 0.760441 + 0.115778I
b = 0.753131 − 0.965934I
2.30506 + 1.39249I 0
u = −0.965351 − 0.572013I
a = 0.760441 − 0.115778I
b = 0.753131 + 0.965934I
2.30506 − 1.39249I 0
u = 0.507684 + 0.708326I
a = 2.14880 + 0.41256I
b = −1.269980 − 0.456591I
2.49717 + 6.15202I 0
u = 0.507684 − 0.708326I
a = 2.14880 − 0.41256I
b = −1.269980 + 0.456591I
2.49717 − 6.15202I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.790504 + 0.363992I
a = −2.05684 − 1.83461I
b = 1.372270 + 0.321304I
2.02169 − 0.07920I 0
u = 0.790504 − 0.363992I
a = −2.05684 + 1.83461I
b = 1.372270 − 0.321304I
2.02169 + 0.07920I 0
u = −1.080770 + 0.356839I
a = 0.265945 − 0.700185I
b = −0.863087 − 0.537497I
−2.46714 + 6.77503I 0
u = −1.080770 − 0.356839I
a = 0.265945 + 0.700185I
b = −0.863087 + 0.537497I
−2.46714 − 6.77503I 0
u = 1.084120 + 0.362868I
a = 0.489829 + 0.030229I
b = −0.122932 − 0.103046I
−2.25525 − 1.15492I 0
u = 1.084120 − 0.362868I
a = 0.489829 − 0.030229I
b = −0.122932 + 0.103046I
−2.25525 + 1.15492I 0
u = 1.038050 + 0.485618I
a = −1.140930 + 0.116289I
b = −0.059119 − 1.083010I
−3.10217 − 5.44544I 0
u = 1.038050 − 0.485618I
a = −1.140930 − 0.116289I
b = −0.059119 + 1.083010I
−3.10217 + 5.44544I 0
u = −0.446596 + 0.719406I
a = −3.45070 − 1.11496I
b = 1.082570 − 0.076456I
3.90317 − 1.17062I −12.4798 − 11.4287I
u = −0.446596 − 0.719406I
a = −3.45070 + 1.11496I
b = 1.082570 + 0.076456I
3.90317 + 1.17062I −12.4798 + 11.4287I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.161770 + 0.086552I
a = 1.236190 + 0.634667I
b = 1.185150 + 0.478372I
0.55551 + 1.40163I 0
u = 1.161770 − 0.086552I
a = 1.236190 − 0.634667I
b = 1.185150 − 0.478372I
0.55551 − 1.40163I 0
u = −1.028210 + 0.552628I
a = 0.320805 − 0.994333I
b = 0.760656 − 0.267559I
1.30476 + 4.74367I 0
u = −1.028210 − 0.552628I
a = 0.320805 + 0.994333I
b = 0.760656 + 0.267559I
1.30476 − 4.74367I 0
u = −0.547458 + 0.616819I
a = 0.380436 + 1.281360I
b = 0.533566 + 0.191258I
2.75270 − 0.12135I 4.31662 + 2.02203I
u = −0.547458 − 0.616819I
a = 0.380436 − 1.281360I
b = 0.533566 − 0.191258I
2.75270 + 0.12135I 4.31662 − 2.02203I
u = −0.807220 + 0.862104I
a = 1.76520 − 0.56811I
b = −1.359920 − 0.328154I
8.89963 + 7.63957I 0
u = −0.807220 − 0.862104I
a = 1.76520 + 0.56811I
b = −1.359920 + 0.328154I
8.89963 − 7.63957I 0
u = 1.18173
a = 0.931526
b = −0.234317
−2.49567 0
u = −0.318606 + 0.734288I
a = 0.612231 − 0.184593I
b = 0.013745 − 0.300945I
1.66501 − 1.71486I − 61.361742 + 0.10I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.318606 − 0.734288I
a = 0.612231 + 0.184593I
b = 0.013745 + 0.300945I
1.66501 + 1.71486I − 61.361742 + 0.10I
u = 0.984748 + 0.690918I
a = 1.54329 + 0.82282I
b = −0.949424 + 0.157182I
−0.71473 − 2.85212I 0
u = 0.984748 − 0.690918I
a = 1.54329 − 0.82282I
b = −0.949424 − 0.157182I
−0.71473 + 2.85212I 0
u = 1.056260 + 0.592575I
a = 1.87255 + 1.59328I
b = −1.32371 + 0.54168I
0.85835 − 11.16100I 0
u = 1.056260 − 0.592575I
a = 1.87255 − 1.59328I
b = −1.32371 − 0.54168I
0.85835 + 11.16100I 0
u = −1.042270 + 0.620203I
a = −0.79199 + 1.22850I
b = 1.66970 − 0.27894I
5.01931 + 4.78307I 0
u = −1.042270 − 0.620203I
a = −0.79199 − 1.22850I
b = 1.66970 + 0.27894I
5.01931 − 4.78307I 0
u = −0.880373 + 0.849310I
a = 1.37328 − 0.77373I
b = −1.313920 + 0.221045I
8.69358 − 1.42500I 0
u = −0.880373 − 0.849310I
a = 1.37328 + 0.77373I
b = −1.313920 − 0.221045I
8.69358 + 1.42500I 0
u = −1.079070 + 0.586402I
a = −2.04909 + 2.47569I
b = 1.079110 + 0.152121I
2.03656 + 6.17754I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.079070 − 0.586402I
a = −2.04909 − 2.47569I
b = 1.079110 − 0.152121I
2.03656 − 6.17754I 0
u = 1.231670 + 0.215746I
a = 0.764987 + 0.972003I
b = −0.102288 + 0.984625I
−3.75795 + 2.95090I 0
u = 1.231670 − 0.215746I
a = 0.764987 − 0.972003I
b = −0.102288 − 0.984625I
−3.75795 − 2.95090I 0
u = −1.097490 + 0.619257I
a = −1.33392 + 1.58874I
b = 1.36356 + 0.82563I
4.05037 + 8.85752I 0
u = −1.097490 − 0.619257I
a = −1.33392 − 1.58874I
b = 1.36356 − 0.82563I
4.05037 − 8.85752I 0
u = −1.135860 + 0.560749I
a = 0.022478 + 0.205110I
b = −0.133149 + 0.453460I
−0.73011 + 6.65250I 0
u = −1.135860 − 0.560749I
a = 0.022478 − 0.205110I
b = −0.133149 − 0.453460I
−0.73011 − 6.65250I 0
u = −1.149120 + 0.600939I
a = −0.994556 + 0.196558I
b = −0.068869 + 1.265220I
−1.04730 + 11.43990I 0
u = −1.149120 − 0.600939I
a = −0.994556 − 0.196558I
b = −0.068869 − 1.265220I
−1.04730 − 11.43990I 0
u = 0.599364 + 0.250259I
a = 0.926149 + 0.825816I
b = 0.049986 − 0.360419I
−0.95967 − 1.37657I −3.31883 + 4.67522I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.599364 − 0.250259I
a = 0.926149 − 0.825816I
b = 0.049986 + 0.360419I
−0.95967 + 1.37657I −3.31883 − 4.67522I
u = −1.195940 + 0.633491I
a = 1.37020 − 1.59964I
b = −1.37982 − 0.60344I
3.1034 + 17.9006I 0
u = −1.195940 − 0.633491I
a = 1.37020 + 1.59964I
b = −1.37982 + 0.60344I
3.1034 − 17.9006I 0
u = 1.347240 + 0.200389I
a = 0.024274 − 0.287891I
b = −1.287330 − 0.518358I
−0.05021 + 8.32055I 0
u = 1.347240 − 0.200389I
a = 0.024274 + 0.287891I
b = −1.287330 + 0.518358I
−0.05021 − 8.32055I 0
u = −1.198560 + 0.662000I
a = 1.20928 − 1.12409I
b = −1.116610 − 0.326840I
2.02563 + 9.85203I 0
u = −1.198560 − 0.662000I
a = 1.20928 + 1.12409I
b = −1.116610 + 0.326840I
2.02563 − 9.85203I 0
u = 1.317000 + 0.412094I
a = 0.419058 + 0.540978I
b = −0.869525 + 0.090739I
−1.87887 − 1.58264I 0
u = 1.317000 − 0.412094I
a = 0.419058 − 0.540978I
b = −0.869525 − 0.090739I
−1.87887 + 1.58264I 0
u = 1.40291
a = 0.520882
b = −0.825783
−2.21927 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.332881 + 0.406496I
a = 0.404933 − 1.218440I
b = −0.058016 + 0.768540I
−1.24805 + 1.52698I −2.33035 − 1.80956I
u = 0.332881 − 0.406496I
a = 0.404933 + 1.218440I
b = −0.058016 − 0.768540I
−1.24805 − 1.52698I −2.33035 + 1.80956I
u = 0.0030157 + 0.1073640I
a = 2.68974 + 9.40123I
b = 1.016320 − 0.211690I
1.89935 − 0.79593I 4.72564 − 0.80285I
u = 0.0030157 − 0.1073640I
a = 2.68974 − 9.40123I
b = 1.016320 + 0.211690I
1.89935 + 0.79593I 4.72564 + 0.80285I
13
II. I
u
2
= hb − a + 1, a
6
− 5a
5
+ 9a
4
− 8a
3
+ 5a
2
− 2a + 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
5
=
−1
0
a
9
=
a
a − 1
a
11
=
a
2
− a + 1
a
2
− 2a + 1
a
8
=
−a
3
+ 2a
2
− a + 1
−a
3
+ 3a
2
− 2a
a
6
=
0
a
5
− 4a
4
+ 4a
3
+ a
2
− 2a + 1
a
10
=
a
a
2
− 2a + 1
a
7
=
0
a
5
− 4a
4
+ 4a
3
+ a
2
− 2a + 1
a
3
=
0
1
a
3
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3a
5
− 16a
4
+ 35a
3
− 37a
2
+ 21a − 11
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
c
2
, c
4
(u + 1)
6
c
3
, c
6
u
6
c
5
, c
10
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
7
, c
11
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
8
, c
9
u
6
− u
5
− u
4
+ 2u
3
− u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
6
y
6
c
5
, c
10
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
7
, c
8
, c
9
c
11
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.571757 + 0.664531I
b = −0.428243 + 0.664531I
−3.53554 + 0.92430I −6.31051 − 0.25702I
u = 1.00000
a = 0.571757 − 0.664531I
b = −0.428243 − 0.664531I
−3.53554 − 0.92430I −6.31051 + 0.25702I
u = 1.00000
a = −0.073950 + 0.558752I
b = −1.073950 + 0.558752I
−1.64493 − 5.69302I −0.29418 + 8.33058I
u = 1.00000
a = −0.073950 − 0.558752I
b = −1.073950 − 0.558752I
−1.64493 + 5.69302I −0.29418 − 8.33058I
u = 1.00000
a = 2.00219 + 0.29554I
b = 1.002190 + 0.295542I
0.245672 + 0.924305I 0.60470 + 5.55069I
u = 1.00000
a = 2.00219 − 0.29554I
b = 1.002190 − 0.295542I
0.245672 − 0.924305I 0.60470 − 5.55069I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
84
− 7u
83
+ ··· − 3u + 1)
c
2
((u + 1)
6
)(u
84
+ 41u
83
+ ··· − 157u + 1)
c
3
, c
6
u
6
(u
84
− u
83
+ ··· − 320u + 64)
c
4
((u + 1)
6
)(u
84
− 7u
83
+ ··· − 3u + 1)
c
5
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)(u
84
− 6u
83
+ ··· − 2u + 1)
c
7
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
84
− 14u
83
+ ··· − 2u + 1)
c
8
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
84
+ 2u
83
+ ··· + 14u + 1)
c
9
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
84
+ 2u
83
+ ··· − 418u + 367)
c
10
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)(u
84
+ 6u
83
+ ··· − 1166u − 101)
c
11
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
84
+ 2u
83
+ ··· + 14u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
6
)(y
84
− 41y
83
+ ··· + 157y + 1)
c
2
((y −1)
6
)(y
84
+ 11y
83
+ ··· − 14895y + 1)
c
3
, c
6
y
6
(y
84
− 39y
83
+ ··· − 61440y + 4096)
c
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
84
+ 14y
83
+ ··· + 6y + 1)
c
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
84
− 6y
83
+ ··· − 14y + 1)
c
8
, c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
84
− 54y
83
+ ··· − 14y + 1)
c
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
84
− 66y
83
+ ··· + 5678926y + 134689)
c
10
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
84
− 82y
83
+ ··· − 878594y + 10201)
19
