11a
68
(K11a
68
)
A knot diagram
1
Linearized knot diagam
5 1 11 2 9 10 4 3 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
= h1.33754 × 10
33
u
52
− 3.23197 × 10
33
u
51
+ ··· + 3.06100 × 10
33
b − 5.79603 × 10
32
,
2.88344 × 10
33
u
52
− 6.19301 × 10
33
u
51
+ ··· + 1.53050 × 10
33
a + 5.13286 × 10
33
, u
53
− 3u
52
+ ··· − 2u − 1i
I
u
2
= h2b − a − 1, a
2
+ 3, u − 1i
* 2 irreducible components of dim
C
= 0, with total 55 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
= h1.34 × 10
33
u
52
− 3.23 × 10
33
u
51
+ · · · + 3.06 × 10
33
b − 5.80 × 10
32
, 2.88 ×
10
33
u
52
−6.19×10
33
u
51
+· · ·+1.53×10
33
a+5.13×10
33
, u
53
−3u
52
+· · ·−2u−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
=
−1.88398u
52
+ 4.04640u
51
+ ··· − 10.2306u − 3.35372
−0.436961u
52
+ 1.05586u
51
+ ··· + 2.97372u + 0.189351
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
−1.44702u
52
+ 2.99054u
51
+ ··· − 13.2043u − 3.54307
−0.436961u
52
+ 1.05586u
51
+ ··· + 2.97372u + 0.189351
a
3
=
7.03077u
52
− 17.2162u
51
+ ··· + 48.9314u + 11.3527
−0.134450u
52
+ 0.381432u
51
+ ··· + 3.81964u + 1.58483
a
4
=
−7.77919u
52
+ 19.0017u
51
+ ··· − 53.0234u − 12.7464
0.270228u
52
− 0.655751u
51
+ ··· − 3.43986u − 1.30077
a
8
=
−4.90683u
52
+ 11.3667u
51
+ ··· − 31.5879u − 8.19442
−0.449321u
52
+ 0.286138u
51
+ ··· + 3.58531u + 0.111845
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 = 44.2881u
52
− 103.441u
51
+ ··· + 256.874u + 76.5517
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
53
+ 2u
52
+ ··· − 11u − 1
c
2
u
53
+ 24u
52
+ ··· + 25u − 1
c
3
u
53
+ 5u
52
+ ··· + 4u − 4
c
5
, c
6
, c
9
c
10
u
53
+ 3u
52
+ ··· − 2u + 1
c
7
u
53
+ 2u
52
+ ··· − 127u − 29
c
8
u
53
− 20u
51
+ ··· + 127u + 59
c
11
u
53
− 3u
52
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
53
+ 24y
52
+ ··· + 25y −1
c
2
y
53
+ 12y
52
+ ··· + 425y −1
c
3
y
53
+ 15y
52
+ ··· + 8y −16
c
5
, c
6
, c
9
c
10
y
53
− 63y
52
+ ··· + 8y −1
c
7
y
53
− 60y
52
+ ··· + 14273y −841
c
8
y
53
− 40y
52
+ ··· − 44759y −3481
c
11
y
53
− 7y
52
+ ··· + 8y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.733711 + 0.645681I
a = −1.46416 − 1.02659I
b = 0.413624 − 1.013730I
−3.39428 − 3.43400I 0
u = 0.733711 − 0.645681I
a = −1.46416 + 1.02659I
b = 0.413624 + 1.013730I
−3.39428 + 3.43400I 0
u = −0.858540 + 0.570989I
a = −1.30456 + 1.52035I
b = 0.626693 + 1.121900I
−2.08339 + 11.83770I 0
u = −0.858540 − 0.570989I
a = −1.30456 − 1.52035I
b = 0.626693 − 1.121900I
−2.08339 − 11.83770I 0
u = −0.890477 + 0.316821I
a = 0.33516 − 1.62827I
b = 0.071350 − 1.206910I
−5.68960 + 3.88038I −9.36604 − 5.67169I
u = −0.890477 − 0.316821I
a = 0.33516 + 1.62827I
b = 0.071350 + 1.206910I
−5.68960 − 3.88038I −9.36604 + 5.67169I
u = −0.790831 + 0.511450I
a = 0.133210 + 0.424681I
b = 0.848973 − 0.421707I
0.02021 + 6.36572I 0. − 6.01738I
u = −0.790831 − 0.511450I
a = 0.133210 − 0.424681I
b = 0.848973 + 0.421707I
0.02021 − 6.36572I 0. + 6.01738I
u = 1.042420 + 0.526470I
a = 0.186261 + 0.817290I
b = 0.483358 + 1.013930I
−2.96394 + 2.74414I 0
u = 1.042420 − 0.526470I
a = 0.186261 − 0.817290I
b = 0.483358 − 1.013930I
−2.96394 − 2.74414I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.143820 + 0.277610I
a = −0.769630 − 1.108100I
b = 0.398755 − 0.662277I
−1.68806 − 1.03417I 0
u = 1.143820 − 0.277610I
a = −0.769630 + 1.108100I
b = 0.398755 + 0.662277I
−1.68806 + 1.03417I 0
u = −0.058774 + 0.801973I
a = −0.804431 − 0.186468I
b = 0.583629 − 1.059960I
0.34476 − 7.28943I −1.89770 + 7.29263I
u = −0.058774 − 0.801973I
a = −0.804431 + 0.186468I
b = 0.583629 + 1.059960I
0.34476 + 7.28943I −1.89770 − 7.29263I
u = 0.687960 + 0.265512I
a = −0.675163 − 0.410284I
b = 0.229892 + 0.048634I
−1.33343 − 0.48154I −6.01943 + 1.63910I
u = 0.687960 − 0.265512I
a = −0.675163 + 0.410284I
b = 0.229892 − 0.048634I
−1.33343 + 0.48154I −6.01943 − 1.63910I
u = −0.651505 + 0.261966I
a = 1.01458 − 2.10036I
b = −0.598899 − 1.150440I
−0.87805 + 4.69027I −3.22278 − 10.95263I
u = −0.651505 − 0.261966I
a = 1.01458 + 2.10036I
b = −0.598899 + 1.150440I
−0.87805 − 4.69027I −3.22278 + 10.95263I
u = −0.116335 + 0.680396I
a = −1.030080 + 0.147365I
b = 0.691596 + 0.477793I
2.06084 − 2.35698I 2.09384 + 2.25421I
u = −0.116335 − 0.680396I
a = −1.030080 − 0.147365I
b = 0.691596 − 0.477793I
2.06084 + 2.35698I 2.09384 − 2.25421I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.269726 + 0.624271I
a = −0.593135 − 0.023709I
b = 0.209100 + 0.945558I
−2.15945 − 0.98457I −6.47095 + 3.55570I
u = 0.269726 − 0.624271I
a = −0.593135 + 0.023709I
b = 0.209100 − 0.945558I
−2.15945 + 0.98457I −6.47095 − 3.55570I
u = 0.655763 + 0.086361I
a = 2.67182 + 5.33529I
b = −0.482724 + 0.895174I
−1.15754 − 2.23299I 20.7265 − 16.6825I
u = 0.655763 − 0.086361I
a = 2.67182 − 5.33529I
b = −0.482724 − 0.895174I
−1.15754 + 2.23299I 20.7265 + 16.6825I
u = −0.466397 + 0.273654I
a = 0.439898 − 0.865824I
b = −0.801200 − 0.670609I
1.29588 + 2.67274I 3.47265 − 8.90150I
u = −0.466397 − 0.273654I
a = 0.439898 + 0.865824I
b = −0.801200 + 0.670609I
1.29588 − 2.67274I 3.47265 + 8.90150I
u = 0.495853 + 0.132805I
a = −2.14393 + 2.54599I
b = −0.437475 − 0.833838I
−0.90053 + 1.58968I −1.24595 − 11.67218I
u = 0.495853 − 0.132805I
a = −2.14393 − 2.54599I
b = −0.437475 + 0.833838I
−0.90053 − 1.58968I −1.24595 + 11.67218I
u = −0.339540 + 0.303762I
a = −0.849048 − 0.809276I
b = −0.694807 + 0.319248I
1.60066 − 0.35812I 5.75025 − 1.86999I
u = −0.339540 − 0.303762I
a = −0.849048 + 0.809276I
b = −0.694807 − 0.319248I
1.60066 + 0.35812I 5.75025 + 1.86999I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.56006
a = −0.846407
b = −1.04242
−4.89339 0
u = 1.57394 + 0.03176I
a = −0.266076 + 0.952973I
b = −0.981473 + 0.829936I
−5.77422 − 3.45795I 0
u = 1.57394 − 0.03176I
a = −0.266076 − 0.952973I
b = −0.981473 − 0.829936I
−5.77422 + 3.45795I 0
u = −1.58085 + 0.00270I
a = −0.420614 + 0.517476I
b = −0.490850 − 0.618356I
−8.08310 + 1.37745I 0
u = −1.58085 − 0.00270I
a = −0.420614 − 0.517476I
b = −0.490850 + 0.618356I
−8.08310 − 1.37745I 0
u = 1.60794 + 0.05864I
a = 0.21792 + 2.23198I
b = −0.60448 + 1.28732I
−8.69900 − 5.79684I 0
u = 1.60794 − 0.05864I
a = 0.21792 − 2.23198I
b = −0.60448 − 1.28732I
−8.69900 + 5.79684I 0
u = −1.61440 + 0.12056I
a = 0.0040355 + 0.1222230I
b = 0.623522 − 0.278275I
−9.21922 + 2.19279I 0
u = −1.61440 − 0.12056I
a = 0.0040355 − 0.1222230I
b = 0.623522 + 0.278275I
−9.21922 − 2.19279I 0
u = −1.61997 + 0.02761I
a = 1.27413 − 2.99101I
b = −0.490506 − 0.975564I
−9.14547 + 2.68229I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.61997 − 0.02761I
a = 1.27413 + 2.99101I
b = −0.490506 + 0.975564I
−9.14547 − 2.68229I 0
u = 1.64104 + 0.14587I
a = 0.552638 − 0.075300I
b = 0.956160 + 0.388075I
−8.29591 − 8.86132I 0
u = 1.64104 − 0.14587I
a = 0.552638 + 0.075300I
b = 0.956160 − 0.388075I
−8.29591 + 8.86132I 0
u = −1.64394 + 0.19308I
a = −0.87986 + 1.71349I
b = 0.514455 + 1.092180I
−11.49850 + 6.63397I 0
u = −1.64394 − 0.19308I
a = −0.87986 − 1.71349I
b = 0.514455 − 1.092180I
−11.49850 − 6.63397I 0
u = 1.66296 + 0.08851I
a = 0.24702 + 2.16359I
b = 0.098247 + 1.348150I
−14.5372 − 5.4639I 0
u = 1.66296 − 0.08851I
a = 0.24702 − 2.16359I
b = 0.098247 − 1.348150I
−14.5372 + 5.4639I 0
u = 1.66393 + 0.16732I
a = −0.72953 − 1.98988I
b = 0.650090 − 1.173960I
−10.7030 − 14.7003I 0
u = 1.66393 − 0.16732I
a = −0.72953 + 1.98988I
b = 0.650090 + 1.173960I
−10.7030 + 14.7003I 0
u = −0.111963 + 0.267344I
a = −0.771605 − 0.811778I
b = −0.612381 + 0.946401I
0.54222 − 2.63785I 2.19810 + 0.73658I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.111963 − 0.267344I
a = −0.771605 + 0.811778I
b = −0.612381 − 0.946401I
0.54222 + 2.63785I 2.19810 − 0.73658I
u = −1.71557 + 0.08761I
a = 0.04836 − 1.70377I
b = 0.316553 − 1.065110I
−12.82680 − 0.50129I 0
u = −1.71557 − 0.08761I
a = 0.04836 + 1.70377I
b = 0.316553 + 1.065110I
−12.82680 + 0.50129I 0
10
II. I
u
2
= h2b − a − 1, a
2
+ 3, u − 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
1
a
6
=
1
1
a
10
=
−1
0
a
2
=
a
1
2
a +
1
2
a
7
=
0
1
a
1
=
1
2
a −
1
2
1
2
a +
1
2
a
3
=
1
2
a −
1
2
1
2
a −
1
2
a
4
=
1
2
a −
1
2
1
2
a −
1
2
a
8
=
1
2
a +
1
2
1
2
a +
3
2
a
11
=
−1
−1
a
11
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2a − 3
11
(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
12
(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
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.73205I
b = 0.500000 + 0.866025I
−1.64493 + 2.02988I −3.00000 − 3.46410I
u = 1.00000
a = − 1.73205I
b = 0.500000 − 0.866025I
−1.64493 − 2.02988I −3.00000 + 3.46410I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)(u
53
+ 2u
52
+ ··· − 11u − 1)
c
2
(u
2
+ u + 1)(u
53
+ 24u
52
+ ··· + 25u − 1)
c
3
u
2
(u
53
+ 5u
52
+ ··· + 4u − 4)
c
4
(u
2
− u + 1)(u
53
+ 2u
52
+ ··· − 11u − 1)
c
5
, c
6
((u − 1)
2
)(u
53
+ 3u
52
+ ··· − 2u + 1)
c
7
(u
2
− u + 1)(u
53
+ 2u
52
+ ··· − 127u − 29)
c
8
(u
2
− u + 1)(u
53
− 20u
51
+ ··· + 127u + 59)
c
9
, c
10
((u + 1)
2
)(u
53
+ 3u
52
+ ··· − 2u + 1)
c
11
((u + 1)
2
)(u
53
− 3u
52
+ ··· − 2u + 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
2
+ y + 1)(y
53
+ 24y
52
+ ··· + 25y −1)
c
2
(y
2
+ y + 1)(y
53
+ 12y
52
+ ··· + 425y −1)
c
3
y
2
(y
53
+ 15y
52
+ ··· + 8y −16)
c
5
, c
6
, c
9
c
10
((y −1)
2
)(y
53
− 63y
52
+ ··· + 8y −1)
c
7
(y
2
+ y + 1)(y
53
− 60y
52
+ ··· + 14273y −841)
c
8
(y
2
+ y + 1)(y
53
− 40y
52
+ ··· − 44759y −3481)
c
11
((y −1)
2
)(y
53
− 7y
52
+ ··· + 8y −1)
16
