11a
262
(K11a
262
)
A knot diagram
1
Linearized knot diagam
8 5 1 2 11 10 3 4 7 6 9
Solving Sequence
6,10 3,7
8 11 5 2 4 9 1
c
6
c
7
c
10
c
5
c
2
c
4
c
9
c
11
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.26359 × 10
15
u
52
− 1.96443 × 10
17
u
51
+ ··· + 2.39123 × 10
17
b − 1.89562 × 10
13
,
− 289619771524u
52
+ 18666048239996u
51
+ ··· + 239122974590735869a − 438392119644066415,
u
53
+ u
52
+ ··· + 3u − 1i
* 1 irreducible components of dim
C
= 0, with total 53 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−1.26×10
15
u
52
−1.96×10
17
u
51
+· · ·+2.39×10
17
b−1.90×10
13
, −2.90×
10
11
u
52
+1.87×10
13
u
51
+· · ·+2.39×10
17
a−4.38×10
17
, u
53
+u
52
+· · ·+3u−1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
1.21118 × 10
−6
u
52
− 0.0000780605u
51
+ ··· + 3.83847u + 1.83333
0.00528425u
52
+ 0.821515u
51
+ ··· + 3.16643u + 0.0000792739
a
7
=
1
−u
2
a
8
=
0.00254871u
52
− 0.00326419u
51
+ ··· − 4.41855u − 0.716687
0.00254880u
52
− 0.00324345u
51
+ ··· − 3.31660u − 0.0000206367
a
11
=
u
u
a
5
=
u
2
+ 1
u
2
a
2
=
−2.84090 × 10
−6
u
52
+ 0.000195650u
51
+ ··· + 3.13319u + 1.01667
−0.0113905u
52
+ 0.805395u
51
+ ··· + 3.18393u − 0.000198494
a
4
=
0.0000154157u
52
− 0.00105631u
51
+ ··· + 4.17250u + 1.75000
0.0622368u
52
+ 0.794538u
51
+ ··· + 3.24677u + 0.00107174
a
9
=
−u
u
3
+ u
a
1
=
−u
5
− 2u
3
+ u
u
7
+ 3u
5
+ 2u
3
+ u
a
1
=
−u
5
− 2u
3
+ u
u
7
+ 3u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
769977140804634968
239122974590735869
u
52
−
578599056246783756
239122974590735869
u
51
+ ··· −
1896881691414989920
239122974590735869
u +
1286401897025890394
239122974590735869
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
53
− 3u
52
+ ··· − u + 1
c
2
, c
4
u
53
+ u
52
+ ··· + 9u − 1
c
3
u
53
− 9u
52
+ ··· + u − 1
c
5
, c
6
, c
9
c
10
u
53
+ u
52
+ ··· + 3u − 1
c
7
u
53
+ u
52
+ ··· − 721u − 271
c
8
u
53
− u
52
+ ··· + 37u − 89
c
11
u
53
− 11u
52
+ ··· + 1317u − 163
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
53
− 9y
52
+ ··· + 3y −1
c
2
, c
4
y
53
− 37y
52
+ ··· − 9y −1
c
3
y
53
+ 3y
52
+ ··· − 9y −1
c
5
, c
6
, c
9
c
10
y
53
+ 59y
52
+ ··· + 3y −1
c
7
y
53
+ 35y
52
+ ··· + 1272679y −73441
c
8
y
53
+ 59y
52
+ ··· − 255841y −7921
c
11
y
53
+ 19y
52
+ ··· + 1976055y −26569
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.650984 + 0.674299I
a = 0.257151 − 0.877552I
b = −0.137847 + 0.272025I
3.29153 + 3.40743I 13.0359 − 10.0924I
u = 0.650984 − 0.674299I
a = 0.257151 + 0.877552I
b = −0.137847 − 0.272025I
3.29153 − 3.40743I 13.0359 + 10.0924I
u = 0.224761 + 1.071330I
a = −0.775347 − 0.428894I
b = −0.275336 + 0.269078I
0.20296 + 4.75561I 0
u = 0.224761 − 1.071330I
a = −0.775347 + 0.428894I
b = −0.275336 − 0.269078I
0.20296 − 4.75561I 0
u = −0.592128 + 0.654438I
a = 0.84258 + 1.72659I
b = 0.076882 − 0.228703I
4.38092 − 11.94560I 6.49757 + 9.10409I
u = −0.592128 − 0.654438I
a = 0.84258 − 1.72659I
b = 0.076882 + 0.228703I
4.38092 + 11.94560I 6.49757 − 9.10409I
u = −0.509097 + 0.611824I
a = −1.38091 − 1.15029I
b = −0.296709 − 0.366738I
−0.15260 − 6.19554I 4.01481 + 9.36178I
u = −0.509097 − 0.611824I
a = −1.38091 + 1.15029I
b = −0.296709 + 0.366738I
−0.15260 + 6.19554I 4.01481 − 9.36178I
u = 0.746383 + 0.258308I
a = 0.0258294 − 0.0088866I
b = −0.721551 + 0.170222I
4.51390 + 1.24711I 18.3925 − 3.9738I
u = 0.746383 − 0.258308I
a = 0.0258294 + 0.0088866I
b = −0.721551 − 0.170222I
4.51390 − 1.24711I 18.3925 + 3.9738I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.089202 + 0.749619I
a = 0.275857 + 1.205170I
b = −0.410304 − 0.149385I
−2.80915 + 1.17690I −3.10474 − 1.38405I
u = −0.089202 − 0.749619I
a = 0.275857 − 1.205170I
b = −0.410304 + 0.149385I
−2.80915 − 1.17690I −3.10474 + 1.38405I
u = −0.668726 + 0.300592I
a = −0.191315 − 0.567088I
b = −1.006360 − 0.726730I
5.42859 + 7.69645I 8.91950 − 3.87764I
u = −0.668726 − 0.300592I
a = −0.191315 + 0.567088I
b = −1.006360 + 0.726730I
5.42859 − 7.69645I 8.91950 + 3.87764I
u = −0.511815 + 0.524420I
a = −0.75753 − 2.01504I
b = 0.349101 + 0.003826I
4.20057 − 3.68117I 11.59505 + 7.70576I
u = −0.511815 − 0.524420I
a = −0.75753 + 2.01504I
b = 0.349101 − 0.003826I
4.20057 + 3.68117I 11.59505 − 7.70576I
u = 0.429766 + 0.592859I
a = 0.124286 + 0.894053I
b = −0.288153 + 0.342472I
0.14967 + 2.03204I 3.41312 − 3.39800I
u = 0.429766 − 0.592859I
a = 0.124286 − 0.894053I
b = −0.288153 − 0.342472I
0.14967 − 2.03204I 3.41312 + 3.39800I
u = −0.132734 + 1.284260I
a = −1.032290 − 0.063941I
b = −0.517989 + 0.093329I
0.47934 + 4.72102I 0
u = −0.132734 − 1.284260I
a = −1.032290 + 0.063941I
b = −0.517989 − 0.093329I
0.47934 − 4.72102I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.508709 + 0.437255I
a = 0.568345 − 0.326462I
b = 1.029690 + 0.612477I
4.45759 + 0.11922I 13.02951 + 0.69964I
u = −0.508709 − 0.437255I
a = 0.568345 + 0.326462I
b = 1.029690 − 0.612477I
4.45759 − 0.11922I 13.02951 − 0.69964I
u = 0.440292 + 0.499184I
a = −3.68961 + 0.83011I
b = 0.12450 − 1.78122I
2.13564 + 1.55948I −19.8548 + 10.4353I
u = 0.440292 − 0.499184I
a = −3.68961 − 0.83011I
b = 0.12450 + 1.78122I
2.13564 − 1.55948I −19.8548 − 10.4353I
u = −0.517939 + 0.301061I
a = 1.028670 + 0.666314I
b = 0.280251 + 0.735240I
0.73495 + 2.61446I 6.80748 − 3.27296I
u = −0.517939 − 0.301061I
a = 1.028670 − 0.666314I
b = 0.280251 − 0.735240I
0.73495 − 2.61446I 6.80748 + 3.27296I
u = 0.392523 + 0.351980I
a = 1.42826 − 0.06907I
b = 0.413573 + 0.275375I
0.839103 + 0.963368I 7.10556 − 5.20772I
u = 0.392523 − 0.351980I
a = 1.42826 + 0.06907I
b = 0.413573 − 0.275375I
0.839103 − 0.963368I 7.10556 + 5.20772I
u = −0.06198 + 1.50181I
a = −0.653059 − 0.670228I
b = −1.79399 − 1.78019I
−5.03695 + 1.09402I 0
u = −0.06198 − 1.50181I
a = −0.653059 + 0.670228I
b = −1.79399 + 1.78019I
−5.03695 − 1.09402I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.11826 + 1.51394I
a = 0.260990 + 0.435541I
b = −0.700219 + 0.765497I
−2.00563 − 1.98586I 0
u = −0.11826 − 1.51394I
a = 0.260990 − 0.435541I
b = −0.700219 − 0.765497I
−2.00563 + 1.98586I 0
u = 0.147327 + 0.456963I
a = 2.93201 + 0.62412I
b = 0.304651 + 0.556917I
0.94420 + 1.17734I 5.61906 − 3.35640I
u = 0.147327 − 0.456963I
a = 2.93201 − 0.62412I
b = 0.304651 − 0.556917I
0.94420 − 1.17734I 5.61906 + 3.35640I
u = 0.08159 + 1.53711I
a = −0.78166 + 1.90967I
b = −2.08548 + 3.23108I
−5.71528 + 2.30391I 0
u = 0.08159 − 1.53711I
a = −0.78166 − 1.90967I
b = −2.08548 − 3.23108I
−5.71528 − 2.30391I 0
u = −0.13998 + 1.54014I
a = −0.04025 + 2.04781I
b = −0.40909 + 4.23233I
−2.69459 − 5.99005I 0
u = −0.13998 − 1.54014I
a = −0.04025 − 2.04781I
b = −0.40909 − 4.23233I
−2.69459 + 5.99005I 0
u = 0.11703 + 1.54415I
a = 2.07571 − 3.59104I
b = 3.41746 − 5.93402I
−4.76295 + 3.50697I 0
u = 0.11703 − 1.54415I
a = 2.07571 + 3.59104I
b = 3.41746 + 5.93402I
−4.76295 − 3.50697I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.14909 + 1.57118I
a = 0.35071 + 1.51086I
b = 1.12655 + 3.15217I
−7.49343 − 8.60231I 0
u = −0.14909 − 1.57118I
a = 0.35071 − 1.51086I
b = 1.12655 − 3.15217I
−7.49343 + 8.60231I 0
u = 0.12468 + 1.57523I
a = −0.587299 − 0.654804I
b = −0.76132 − 1.40539I
−7.21649 + 4.05118I 0
u = 0.12468 − 1.57523I
a = −0.587299 + 0.654804I
b = −0.76132 + 1.40539I
−7.21649 − 4.05118I 0
u = 0.20197 + 1.58241I
a = −0.010726 + 1.358400I
b = 0.23211 + 2.55470I
−4.20208 + 6.58081I 0
u = 0.20197 − 1.58241I
a = −0.010726 − 1.358400I
b = 0.23211 − 2.55470I
−4.20208 − 6.58081I 0
u = −0.18129 + 1.58506I
a = 0.26732 − 2.26211I
b = 0.59368 − 4.30095I
−3.1210 − 14.8139I 0
u = −0.18129 − 1.58506I
a = 0.26732 + 2.26211I
b = 0.59368 + 4.30095I
−3.1210 + 14.8139I 0
u = −0.02508 + 1.59817I
a = −0.41143 − 1.74917I
b = −0.48200 − 3.40640I
−10.80680 + 0.74411I 0
u = −0.02508 − 1.59817I
a = −0.41143 + 1.74917I
b = −0.48200 + 3.40640I
−10.80680 − 0.74411I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.03260 + 1.64453I
a = 0.806611 + 1.109860I
b = 1.82175 + 2.09258I
−8.94151 + 5.46940I 0
u = 0.03260 − 1.64453I
a = 0.806611 − 1.109860I
b = 1.82175 − 2.09258I
−8.94151 − 5.46940I 0
u = 0.232267
a = 3.13420
b = 1.23226
2.24636 1.69410
10
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
53
− 3u
52
+ ··· − u + 1
c
2
, c
4
u
53
+ u
52
+ ··· + 9u − 1
c
3
u
53
− 9u
52
+ ··· + u − 1
c
5
, c
6
, c
9
c
10
u
53
+ u
52
+ ··· + 3u − 1
c
7
u
53
+ u
52
+ ··· − 721u − 271
c
8
u
53
− u
52
+ ··· + 37u − 89
c
11
u
53
− 11u
52
+ ··· + 1317u − 163
11
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
53
− 9y
52
+ ··· + 3y −1
c
2
, c
4
y
53
− 37y
52
+ ··· − 9y −1
c
3
y
53
+ 3y
52
+ ··· − 9y −1
c
5
, c
6
, c
9
c
10
y
53
+ 59y
52
+ ··· + 3y −1
c
7
y
53
+ 35y
52
+ ··· + 1272679y −73441
c
8
y
53
+ 59y
52
+ ··· − 255841y −7921
c
11
y
53
+ 19y
52
+ ··· + 1976055y −26569
12
