11a
69
(K11a
69
)
A knot diagram
1
Linearized knot diagam
5 1 11 2 10 9 4 3 6 7 8
Solving Sequence
5,10 2,6
1 3 4 9 7 11 8
c
5
c
1
c
2
c
4
c
9
c
6
c
10
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.93466 × 10
44
u
69
+ 1.74032 × 10
45
u
68
+ ··· + 8.25681 × 10
45
b + 7.83469 × 10
45
,
5.13127 × 10
45
u
69
+ 8.43947 × 10
44
u
68
+ ··· + 8.25681 × 10
45
a − 4.71677 × 10
45
, u
70
+ u
69
+ ··· + 5u + 1i
* 1 irreducible components of dim
C
= 0, with total 70 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
= h1.93 × 10
44
u
69
+ 1.74 × 10
45
u
68
+ · · · + 8.26 × 10
45
b + 7.83 × 10
45
, 5.13 ×
10
45
u
69
+8.44×10
44
u
68
+· · ·+8.26×10
45
a−4.72×10
45
, u
70
+u
69
+· · ·+5u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
2
=
−0.621458u
69
− 0.102212u
68
+ ··· − 1.03500u + 0.571258
−0.0234310u
69
− 0.210773u
68
+ ··· − 5.77695u − 0.948876
a
6
=
1
u
2
a
1
=
−0.598027u
69
+ 0.108561u
68
+ ··· + 4.74196u + 1.52013
−0.0234310u
69
− 0.210773u
68
+ ··· − 5.77695u − 0.948876
a
3
=
−0.755347u
69
+ 0.563488u
68
+ ··· − 11.1749u − 1.14377
0.00374491u
69
− 0.220825u
68
+ ··· − 5.42897u − 1.96817
a
4
=
−0.586927u
69
+ 0.648245u
68
+ ··· − 11.4105u − 1.27713
−0.0206773u
69
− 0.191932u
68
+ ··· − 5.40917u − 1.81465
a
9
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
4
+ 2u
2
a
11
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
8
=
−0.196281u
69
+ 0.196656u
68
+ ··· − 2.97884u − 0.704438
−0.119642u
69
− 0.282284u
68
+ ··· + 2.93455u + 0.00852081
a
8
=
−0.196281u
69
+ 0.196656u
68
+ ··· − 2.97884u − 0.704438
−0.119642u
69
− 0.282284u
68
+ ··· + 2.93455u + 0.00852081
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.55662u
69
− 1.96540u
68
+ ··· + 29.0576u + 10.9549
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
70
+ u
69
+ ··· + 7u + 1
c
2
u
70
+ 29u
69
+ ··· + 7u + 1
c
3
u
70
+ 7u
69
+ ··· + u + 1
c
5
, c
6
, c
9
u
70
− u
69
+ ··· − 5u + 1
c
7
u
70
+ 3u
69
+ ··· − 23u + 1
c
8
u
70
+ u
69
+ ··· + 49u + 4
c
10
u
70
+ u
69
+ ··· − 1887u + 578
c
11
u
70
− 5u
69
+ ··· − u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
70
+ 29y
69
+ ··· + 7y + 1
c
2
y
70
+ 25y
69
+ ··· + 347y + 1
c
3
y
70
+ 5y
69
+ ··· + 7y + 1
c
5
, c
6
, c
9
y
70
+ 61y
69
+ ··· − 5y + 1
c
7
y
70
− 71y
69
+ ··· − 45y + 1
c
8
y
70
− 75y
69
+ ··· − 401y + 16
c
10
y
70
− 15y
69
+ ··· − 869601y + 334084
c
11
y
70
− 7y
69
+ ··· − 5y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.484335 + 0.875355I
a = −0.060674 + 0.946739I
b = −0.620167 + 1.091350I
0.05172 − 8.00134I 0
u = −0.484335 − 0.875355I
a = −0.060674 − 0.946739I
b = −0.620167 − 1.091350I
0.05172 + 8.00134I 0
u = 0.236828 + 1.056350I
a = 0.383136 − 0.264141I
b = −0.489406 − 0.250651I
1.23691 − 2.50489I 0
u = 0.236828 − 1.056350I
a = 0.383136 + 0.264141I
b = −0.489406 + 0.250651I
1.23691 + 2.50489I 0
u = 0.829379 + 0.365662I
a = 0.94611 + 1.69775I
b = −0.469428 + 0.973496I
−2.85780 − 3.99529I −10.44720 + 9.33363I
u = 0.829379 − 0.365662I
a = 0.94611 − 1.69775I
b = −0.469428 − 0.973496I
−2.85780 + 3.99529I −10.44720 − 9.33363I
u = 0.899262 + 0.112004I
a = −0.09567 − 1.68409I
b = −0.406148 − 0.936613I
−3.33093 + 1.52607I −13.07472 − 1.31899I
u = 0.899262 − 0.112004I
a = −0.09567 + 1.68409I
b = −0.406148 + 0.936613I
−3.33093 − 1.52607I −13.07472 + 1.31899I
u = −0.289959 + 1.067950I
a = 1.02846 − 1.50899I
b = −0.140513 − 1.175150I
−3.16104 − 0.50300I 0
u = −0.289959 − 1.067950I
a = 1.02846 + 1.50899I
b = −0.140513 + 1.175150I
−3.16104 + 0.50300I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.403491 + 0.782625I
a = 0.390557 − 0.716194I
b = −0.768228 − 0.457281I
1.92693 − 2.73519I 2.12851 + 1.17713I
u = −0.403491 − 0.782625I
a = 0.390557 + 0.716194I
b = −0.768228 + 0.457281I
1.92693 + 2.73519I 2.12851 − 1.17713I
u = 0.499100 + 1.027490I
a = 0.80149 + 1.34174I
b = −0.507327 + 1.004450I
−0.50648 − 6.46270I 0
u = 0.499100 − 1.027490I
a = 0.80149 − 1.34174I
b = −0.507327 − 1.004450I
−0.50648 + 6.46270I 0
u = −0.814672 + 0.264193I
a = 0.73755 − 2.31927I
b = −0.652177 − 1.126720I
−1.87843 + 12.59620I −3.11036 − 9.02697I
u = −0.814672 − 0.264193I
a = 0.73755 + 2.31927I
b = −0.652177 + 1.126720I
−1.87843 − 12.59620I −3.11036 + 9.02697I
u = −0.764380 + 0.264018I
a = −0.812441 − 0.044328I
b = −0.884444 + 0.447119I
0.17592 + 6.93073I −0.67959 − 5.56176I
u = −0.764380 − 0.264018I
a = −0.812441 + 0.044328I
b = −0.884444 − 0.447119I
0.17592 − 6.93073I −0.67959 + 5.56176I
u = 0.562477 + 0.578232I
a = 0.208519 − 0.713965I
b = −0.297139 − 0.882531I
−1.94107 − 0.75277I −7.49106 + 4.95501I
u = 0.562477 − 0.578232I
a = 0.208519 + 0.713965I
b = −0.297139 + 0.882531I
−1.94107 + 0.75277I −7.49106 − 4.95501I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.745456 + 0.148738I
a = −0.36458 + 2.64857I
b = −0.050089 + 1.257290I
−5.92974 + 4.34707I −7.96325 − 5.56332I
u = −0.745456 − 0.148738I
a = −0.36458 − 2.64857I
b = −0.050089 − 1.257290I
−5.92974 − 4.34707I −7.96325 + 5.56332I
u = −0.107903 + 1.245720I
a = 0.523629 − 1.003470I
b = 0.416221 − 1.189180I
1.99705 − 2.44523I 0
u = −0.107903 − 1.245720I
a = 0.523629 + 1.003470I
b = 0.416221 + 1.189180I
1.99705 + 2.44523I 0
u = 0.200108 + 1.261720I
a = 0.32731 + 2.79217I
b = 0.401964 + 0.917807I
2.39518 − 0.54119I 0
u = 0.200108 − 1.261720I
a = 0.32731 − 2.79217I
b = 0.401964 − 0.917807I
2.39518 + 0.54119I 0
u = 0.368590 + 1.279980I
a = −0.036929 − 0.922221I
b = −0.254902 − 0.847557I
0.95320 − 3.02207I 0
u = 0.368590 − 1.279980I
a = −0.036929 + 0.922221I
b = −0.254902 + 0.847557I
0.95320 + 3.02207I 0
u = 0.193666 + 1.332510I
a = −0.68225 − 2.26640I
b = 0.541955 + 0.776960I
3.56607 − 0.95896I 0
u = 0.193666 − 1.332510I
a = −0.68225 + 2.26640I
b = 0.541955 − 0.776960I
3.56607 + 0.95896I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.150263 + 1.338740I
a = −0.223687 + 0.346604I
b = 0.838536 − 0.993294I
5.26003 − 1.16982I 0
u = −0.150263 − 1.338740I
a = −0.223687 − 0.346604I
b = 0.838536 + 0.993294I
5.26003 + 1.16982I 0
u = 0.231094 + 1.328390I
a = −3.66836 − 1.80527I
b = 0.536274 − 0.919865I
3.11019 − 5.29914I 0
u = 0.231094 − 1.328390I
a = −3.66836 + 1.80527I
b = 0.536274 + 0.919865I
3.11019 + 5.29914I 0
u = 0.611770 + 0.194791I
a = 0.407403 + 0.167127I
b = −0.224664 − 0.169997I
−1.37636 − 0.69918I −5.13733 + 2.33652I
u = 0.611770 − 0.194791I
a = 0.407403 − 0.167127I
b = −0.224664 + 0.169997I
−1.37636 + 0.69918I −5.13733 − 2.33652I
u = −0.613468 + 0.166353I
a = −0.44642 + 2.95844I
b = 0.616639 + 1.172650I
−0.93135 + 4.88535I −2.28013 − 10.40687I
u = −0.613468 − 0.166353I
a = −0.44642 − 2.95844I
b = 0.616639 − 1.172650I
−0.93135 − 4.88535I −2.28013 + 10.40687I
u = 0.200597 + 1.358150I
a = 0.286571 + 0.255300I
b = 0.250675 − 0.338013I
3.63488 − 3.48634I 0
u = 0.200597 − 1.358150I
a = 0.286571 − 0.255300I
b = 0.250675 + 0.338013I
3.63488 + 3.48634I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.183760 + 1.364120I
a = −0.072592 + 0.787390I
b = 1.003970 − 0.281861I
6.67319 + 1.90375I 0
u = −0.183760 − 1.364120I
a = −0.072592 − 0.787390I
b = 1.003970 + 0.281861I
6.67319 − 1.90375I 0
u = −0.247821 + 1.358540I
a = −1.60160 + 1.37832I
b = 0.693479 + 1.215560I
3.90043 + 8.04691I 0
u = −0.247821 − 1.358540I
a = −1.60160 − 1.37832I
b = 0.693479 − 1.215560I
3.90043 − 8.04691I 0
u = −0.212109 + 1.366200I
a = −0.941802 + 0.648116I
b = 1.001640 + 0.651261I
6.29345 + 5.42481I 0
u = −0.212109 − 1.366200I
a = −0.941802 − 0.648116I
b = 1.001640 − 0.651261I
6.29345 − 5.42481I 0
u = −0.303558 + 1.351170I
a = −0.92726 + 1.21935I
b = 0.006202 + 1.312430I
−1.19896 + 8.13596I 0
u = −0.303558 − 1.351170I
a = −0.92726 − 1.21935I
b = 0.006202 − 1.312430I
−1.19896 − 8.13596I 0
u = 0.594534 + 0.061490I
a = −2.14747 − 5.13430I
b = 0.485312 − 0.908136I
−1.29895 − 2.30609I 11.5630 − 16.8929I
u = 0.594534 − 0.061490I
a = −2.14747 + 5.13430I
b = 0.485312 + 0.908136I
−1.29895 + 2.30609I 11.5630 + 16.8929I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.30882 + 1.41041I
a = −0.018285 − 0.748543I
b = −0.938125 + 0.475226I
5.50503 + 10.82290I 0
u = −0.30882 − 1.41041I
a = −0.018285 + 0.748543I
b = −0.938125 − 0.475226I
5.50503 − 10.82290I 0
u = −0.33175 + 1.41736I
a = 1.66811 − 1.38164I
b = −0.680160 − 1.138340I
3.4715 + 16.7403I 0
u = −0.33175 − 1.41736I
a = 1.66811 + 1.38164I
b = −0.680160 + 1.138340I
3.4715 − 16.7403I 0
u = 0.26824 + 1.43648I
a = 0.320427 + 0.345844I
b = −0.519294 − 0.588568I
4.08495 − 3.81337I 0
u = 0.26824 − 1.43648I
a = 0.320427 − 0.345844I
b = −0.519294 + 0.588568I
4.08495 + 3.81337I 0
u = −0.487601 + 0.208801I
a = 0.30455 + 1.43000I
b = 0.833768 + 0.669179I
1.32084 + 2.75218I 4.00267 − 8.42337I
u = −0.487601 − 0.208801I
a = 0.30455 − 1.43000I
b = 0.833768 − 0.669179I
1.32084 − 2.75218I 4.00267 + 8.42337I
u = −0.04696 + 1.47919I
a = 1.013550 − 0.079452I
b = −0.776577 − 0.650017I
9.19605 − 1.61168I 0
u = −0.04696 − 1.47919I
a = 1.013550 + 0.079452I
b = −0.776577 + 0.650017I
9.19605 + 1.61168I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.34186 + 1.45082I
a = 1.47158 + 1.05054I
b = −0.558838 + 0.987517I
2.91206 − 8.27553I 0
u = 0.34186 − 1.45082I
a = 1.47158 − 1.05054I
b = −0.558838 − 0.987517I
2.91206 + 8.27553I 0
u = −0.00295 + 1.51219I
a = 0.927152 + 0.098522I
b = −0.667838 + 0.997816I
8.13804 − 7.06461I 0
u = −0.00295 − 1.51219I
a = 0.927152 − 0.098522I
b = −0.667838 − 0.997816I
8.13804 + 7.06461I 0
u = 0.473311 + 0.093934I
a = 2.06318 − 1.63899I
b = 0.437497 + 0.816872I
−0.93813 + 1.54075I −3.94589 − 11.49495I
u = 0.473311 − 0.093934I
a = 2.06318 + 1.63899I
b = 0.437497 − 0.816872I
−0.93813 − 1.54075I −3.94589 + 11.49495I
u = −0.380898 + 0.262790I
a = 1.44857 + 0.52153I
b = 0.728444 − 0.317658I
1.64058 − 0.33786I 6.07692 − 1.73353I
u = −0.380898 − 0.262790I
a = 1.44857 − 0.52153I
b = 0.728444 + 0.317658I
1.64058 + 0.33786I 6.07692 + 1.73353I
u = −0.130656 + 0.280023I
a = 1.342180 − 0.108395I
b = 0.612892 − 0.951335I
0.54295 − 2.64582I 2.44579 + 0.83594I
u = −0.130656 − 0.280023I
a = 1.342180 + 0.108395I
b = 0.612892 + 0.951335I
0.54295 + 2.64582I 2.44579 − 0.83594I
11
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u
70
+ u
69
+ ··· + 7u + 1
c
2
u
70
+ 29u
69
+ ··· + 7u + 1
c
3
u
70
+ 7u
69
+ ··· + u + 1
c
5
, c
6
, c
9
u
70
− u
69
+ ··· − 5u + 1
c
7
u
70
+ 3u
69
+ ··· − 23u + 1
c
8
u
70
+ u
69
+ ··· + 49u + 4
c
10
u
70
+ u
69
+ ··· − 1887u + 578
c
11
u
70
− 5u
69
+ ··· − u + 1
12
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
70
+ 29y
69
+ ··· + 7y + 1
c
2
y
70
+ 25y
69
+ ··· + 347y + 1
c
3
y
70
+ 5y
69
+ ··· + 7y + 1
c
5
, c
6
, c
9
y
70
+ 61y
69
+ ··· − 5y + 1
c
7
y
70
− 71y
69
+ ··· − 45y + 1
c
8
y
70
− 75y
69
+ ··· − 401y + 16
c
10
y
70
− 15y
69
+ ··· − 869601y + 334084
c
11
y
70
− 7y
69
+ ··· − 5y + 1
13
