11a
53
(K11a
53
)
A knot diagram
1
Linearized knot diagam
5 1 11 2 9 10 3 4 6 7 8
Solving Sequence
5,9
6 10
2,7
1 3 4 8 11
c
5
c
9
c
6
c
1
c
2
c
4
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.81606 × 10
31
u
49
+ 5.08261 × 10
31
u
48
+ ··· + 4.27879 × 10
31
b − 1.93634 × 10
30
,
− 4.15334 × 10
31
u
49
− 1.01081 × 10
32
u
48
+ ··· + 5.34849 × 10
30
a + 8.37501 × 10
31
, u
50
+ 3u
49
+ ··· − 8u − 1i
I
u
2
= hb
2
− b + 1, a + 1, u + 1i
* 2 irreducible components of dim
C
= 0, with total 52 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
= h2.82×10
31
u
49
+5.08×10
31
u
48
+· · ·+4.28×10
31
b−1.94×10
30
, −4.15×
10
31
u
49
−1.01×10
32
u
48
+· · ·+5.35×10
30
a+8.38×10
31
, u
50
+3u
49
+· · ·−8u−1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
−u
2
a
10
=
u
−u
3
+ u
a
2
=
7.76545u
49
+ 18.8989u
48
+ ··· − 81.3213u − 15.6586
−0.658144u
49
− 1.18786u
48
+ ··· + 4.71381u + 0.0452544
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
8.42359u
49
+ 20.0868u
48
+ ··· − 86.0351u − 15.7039
−0.658144u
49
− 1.18786u
48
+ ··· + 4.71381u + 0.0452544
a
3
=
16.5522u
49
+ 40.5819u
48
+ ··· − 183.821u − 29.5368
−0.186883u
49
− 0.0491952u
48
+ ··· − 0.958193u + 0.142958
a
4
=
−15.7480u
49
− 38.5171u
48
+ ··· + 171.517u + 27.4764
0.344150u
49
+ 0.520346u
48
+ ··· − 2.34513u − 0.685097
a
8
=
−13.2353u
49
− 30.8285u
48
+ ··· + 140.710u + 20.3271
3.76331u
49
+ 9.12279u
48
+ ··· − 33.9045u − 5.65366
a
11
=
−u
3
+ 2u
u
5
− 3u
3
+ u
a
11
=
−u
3
+ 2u
u
5
− 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 24.5612u
49
+ 62.4649u
48
+ ··· − 284.357u − 43.1928
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
50
+ 2u
49
+ ··· − 11u + 1
c
2
u
50
+ 18u
49
+ ··· − 71u + 1
c
3
u
50
+ 5u
49
+ ··· + 12u + 4
c
5
, c
6
, c
9
c
10
u
50
− 3u
49
+ ··· + 8u − 1
c
7
u
50
− 2u
49
+ ··· − 293u − 41
c
8
u
50
+ 13u
48
+ ··· + 3545u − 3881
c
11
u
50
+ 3u
49
+ ··· − 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
50
+ 18y
49
+ ··· − 71y + 1
c
2
y
50
+ 30y
49
+ ··· − 6727y + 1
c
3
y
50
− 15y
49
+ ··· + 24y + 16
c
5
, c
6
, c
9
c
10
y
50
− 61y
49
+ ··· + 2y + 1
c
7
y
50
+ 66y
49
+ ··· − 16723y + 1681
c
8
y
50
+ 26y
49
+ ··· − 134903907y + 15062161
c
11
y
50
+ 3y
49
+ ··· + 2y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.937098 + 0.462135I
a = 0.211512 + 0.192941I
b = 0.858299 − 0.573619I
4.82985 + 5.83927I 0
u = 0.937098 − 0.462135I
a = 0.211512 − 0.192941I
b = 0.858299 + 0.573619I
4.82985 − 5.83927I 0
u = −0.839672 + 0.647094I
a = −0.81593 − 1.41627I
b = 0.661316 − 0.821509I
3.56400 − 2.80079I 0
u = −0.839672 − 0.647094I
a = −0.81593 + 1.41627I
b = 0.661316 + 0.821509I
3.56400 + 2.80079I 0
u = 0.912689 + 0.553110I
a = −1.10695 + 1.60264I
b = 0.696189 + 1.071020I
3.32747 + 11.61540I 0
u = 0.912689 − 0.553110I
a = −1.10695 − 1.60264I
b = 0.696189 − 1.071020I
3.32747 − 11.61540I 0
u = −0.976441 + 0.595366I
a = 0.230649 + 0.449741I
b = 0.650338 + 0.887749I
3.35842 + 2.29493I 0
u = −0.976441 − 0.595366I
a = 0.230649 − 0.449741I
b = 0.650338 − 0.887749I
3.35842 − 2.29493I 0
u = 0.841656 + 0.047389I
a = 0.1347570 − 0.0218999I
b = −0.920135 − 0.479166I
4.03403 + 1.68694I 17.7316 − 3.8537I
u = 0.841656 − 0.047389I
a = 0.1347570 + 0.0218999I
b = −0.920135 + 0.479166I
4.03403 − 1.68694I 17.7316 + 3.8537I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.013239 + 0.817870I
a = 0.14125 − 1.78357I
b = 0.652193 − 1.000830I
0.50489 − 7.07418I 6.05066 + 7.49946I
u = −0.013239 − 0.817870I
a = 0.14125 + 1.78357I
b = 0.652193 + 1.000830I
0.50489 + 7.07418I 6.05066 − 7.49946I
u = 0.777120 + 0.168669I
a = 1.10335 − 1.09992I
b = −0.722164 − 1.091670I
2.23469 + 4.31809I 12.5022 − 9.4172I
u = 0.777120 − 0.168669I
a = 1.10335 + 1.09992I
b = −0.722164 + 1.091670I
2.23469 − 4.31809I 12.5022 + 9.4172I
u = 0.682472 + 0.374309I
a = 0.57023 − 1.65391I
b = −0.099953 − 1.191010I
−1.85305 + 4.44722I 3.76604 − 8.28097I
u = 0.682472 − 0.374309I
a = 0.57023 + 1.65391I
b = −0.099953 + 1.191010I
−1.85305 − 4.44722I 3.76604 + 8.28097I
u = −1.221480 + 0.183402I
a = −1.080910 − 0.602437I
b = 0.279012 − 0.809479I
1.05793 − 1.23765I 0
u = −1.221480 − 0.183402I
a = −1.080910 + 0.602437I
b = 0.279012 + 0.809479I
1.05793 + 1.23765I 0
u = −0.757757
a = −0.709973
b = −0.110317
1.34192 6.63920
u = −0.131668 + 0.739765I
a = 0.376094 + 1.066140I
b = 0.687246 + 0.639785I
1.57561 − 1.87137I 8.35358 + 3.09221I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.131668 − 0.739765I
a = 0.376094 − 1.066140I
b = 0.687246 − 0.639785I
1.57561 + 1.87137I 8.35358 − 3.09221I
u = −0.685724 + 0.043728I
a = 4.76222 − 1.81115I
b = −0.527660 + 0.858592I
1.19764 − 2.12710I −32.7806 − 10.7013I
u = −0.685724 − 0.043728I
a = 4.76222 + 1.81115I
b = −0.527660 − 0.858592I
1.19764 + 2.12710I −32.7806 + 10.7013I
u = 0.199761 + 0.536069I
a = −1.28134 + 2.18752I
b = 0.039661 + 1.022140I
−3.29175 − 1.28959I −1.33459 + 1.03958I
u = 0.199761 − 0.536069I
a = −1.28134 − 2.18752I
b = 0.039661 − 1.022140I
−3.29175 + 1.28959I −1.33459 − 1.03958I
u = −0.333573 + 0.304189I
a = −1.30977 + 1.12638I
b = −0.233321 + 0.353112I
0.612959 − 1.077400I 6.64880 + 6.13369I
u = −0.333573 − 0.304189I
a = −1.30977 − 1.12638I
b = −0.233321 − 0.353112I
0.612959 + 1.077400I 6.64880 − 6.13369I
u = 1.57172 + 0.04490I
a = −0.40787 − 1.60676I
b = −0.155069 − 0.894721I
7.32051 + 1.86287I 0
u = 1.57172 − 0.04490I
a = −0.40787 + 1.60676I
b = −0.155069 + 0.894721I
7.32051 − 1.86287I 0
u = −1.62108 + 0.08215I
a = 0.341548 + 1.070770I
b = −0.158199 + 1.345830I
6.10353 − 6.02446I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.62108 − 0.08215I
a = 0.341548 − 1.070770I
b = −0.158199 − 1.345830I
6.10353 + 6.02446I 0
u = −0.345144 + 0.142770I
a = −3.26141 − 2.20278I
b = −0.487438 − 0.764766I
0.63823 + 1.46904I 4.89468 − 6.43467I
u = −0.345144 − 0.142770I
a = −3.26141 + 2.20278I
b = −0.487438 + 0.764766I
0.63823 − 1.46904I 4.89468 + 6.43467I
u = 1.63598 + 0.01535I
a = 2.27440 + 0.34670I
b = −0.602748 − 0.867884I
9.40555 + 2.37088I 0
u = 1.63598 − 0.01535I
a = 2.27440 − 0.34670I
b = −0.602748 + 0.867884I
9.40555 − 2.37088I 0
u = −1.65081 + 0.03847I
a = 0.853099 + 0.632218I
b = −0.82834 + 1.18201I
10.75670 − 5.06095I 0
u = −1.65081 − 0.03847I
a = 0.853099 − 0.632218I
b = −0.82834 − 1.18201I
10.75670 + 5.06095I 0
u = 1.65329
a = −0.266847
b = −0.430236
9.89733 0
u = −1.66404 + 0.01144I
a = 0.376644 − 0.005262I
b = −1.132200 + 0.490348I
12.84420 − 1.90653I 0
u = −1.66404 − 0.01144I
a = 0.376644 + 0.005262I
b = −1.132200 − 0.490348I
12.84420 + 1.90653I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.68368 + 0.15912I
a = −1.17332 − 1.00102I
b = 0.738252 − 1.117030I
12.2572 − 14.4160I 0
u = −1.68368 − 0.15912I
a = −1.17332 + 1.00102I
b = 0.738252 + 1.117030I
12.2572 + 14.4160I 0
u = −1.68783 + 0.12889I
a = −0.224075 − 0.279217I
b = 0.973382 + 0.580176I
13.9293 − 8.1748I 0
u = −1.68783 − 0.12889I
a = −0.224075 + 0.279217I
b = 0.973382 − 0.580176I
13.9293 + 8.1748I 0
u = 1.68474 + 0.18629I
a = −1.027680 + 0.904887I
b = 0.706180 + 0.945723I
12.25070 + 6.06384I 0
u = 1.68474 − 0.18629I
a = −1.027680 − 0.904887I
b = 0.706180 − 0.945723I
12.25070 − 6.06384I 0
u = 1.71548 + 0.13705I
a = −0.311148 − 0.002274I
b = 0.740020 − 0.757612I
12.82000 + 0.55523I 0
u = 1.71548 − 0.13705I
a = −0.311148 + 0.002274I
b = 0.740020 + 0.757612I
12.82000 − 0.55523I 0
u = −0.052112 + 0.257497I
a = −2.38696 + 2.67757I
b = −0.544579 + 0.964237I
−0.08326 − 2.77748I 2.22169 + 1.37022I
u = −0.052112 − 0.257497I
a = −2.38696 − 2.67757I
b = −0.544579 − 0.964237I
−0.08326 + 2.77748I 2.22169 − 1.37022I
9
II. I
u
2
= hb
2
− b + 1, a + 1, u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
−1
a
6
=
1
−1
a
10
=
−1
0
a
2
=
−1
b
a
7
=
0
−1
a
1
=
−b − 1
b
a
3
=
−b + 1
b − 1
a
4
=
−b + 1
b − 1
a
8
=
−b
b − 1
a
11
=
−1
1
a
11
=
−1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4b + 11
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
2
+ u + 1
c
3
u
2
c
4
, c
7
, c
8
u
2
− u + 1
c
5
, c
6
(u + 1)
2
c
9
, c
10
, c
11
(u − 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
8
y
2
+ y + 1
c
3
y
2
c
5
, c
6
, c
9
c
10
, c
11
(y −1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0.500000 + 0.866025I
1.64493 + 2.02988I 9.00000 − 3.46410I
u = −1.00000
a = −1.00000
b = 0.500000 − 0.866025I
1.64493 − 2.02988I 9.00000 + 3.46410I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)(u
50
+ 2u
49
+ ··· − 11u + 1)
c
2
(u
2
+ u + 1)(u
50
+ 18u
49
+ ··· − 71u + 1)
c
3
u
2
(u
50
+ 5u
49
+ ··· + 12u + 4)
c
4
(u
2
− u + 1)(u
50
+ 2u
49
+ ··· − 11u + 1)
c
5
, c
6
((u + 1)
2
)(u
50
− 3u
49
+ ··· + 8u − 1)
c
7
(u
2
− u + 1)(u
50
− 2u
49
+ ··· − 293u − 41)
c
8
(u
2
− u + 1)(u
50
+ 13u
48
+ ··· + 3545u − 3881)
c
9
, c
10
((u − 1)
2
)(u
50
− 3u
49
+ ··· + 8u − 1)
c
11
((u − 1)
2
)(u
50
+ 3u
49
+ ··· − 2u − 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
2
+ y + 1)(y
50
+ 18y
49
+ ··· − 71y + 1)
c
2
(y
2
+ y + 1)(y
50
+ 30y
49
+ ··· − 6727y + 1)
c
3
y
2
(y
50
− 15y
49
+ ··· + 24y + 16)
c
5
, c
6
, c
9
c
10
((y −1)
2
)(y
50
− 61y
49
+ ··· + 2y + 1)
c
7
(y
2
+ y + 1)(y
50
+ 66y
49
+ ··· − 16723y + 1681)
c
8
(y
2
+ y + 1)(y
50
+ 26y
49
+ ··· − 1.34904 × 10
8
y + 1.50622 × 10
7
)
c
11
((y −1)
2
)(y
50
+ 3y
49
+ ··· + 2y + 1)
15
