11a
150
(K11a
150
)
A knot diagram
1
Linearized knot diagam
6 1 11 9 2 5 10 3 7 4 8
Solving Sequence
2,6
1 3 5
7,9
10 4 8 11
c
1
c
2
c
5
c
6
c
9
c
4
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h5.92448 × 10
33
u
61
− 1.02898 × 10
34
u
60
+ ··· + 1.17126 × 10
34
b − 5.31916 × 10
33
,
8.54907 × 10
32
u
61
+ 2.67122 × 10
33
u
60
+ ··· + 1.17126 × 10
34
a − 1.99667 × 10
34
, u
62
− 3u
61
+ ··· − 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 62 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
= h5.92 × 10
33
u
61
− 1.03 × 10
34
u
60
+ · · · + 1.17 × 10
34
b − 5.32 × 10
33
, 8.55 ×
10
32
u
61
+2.67×10
33
u
60
+· · ·+1.17×10
34
a−2.00×10
34
, u
62
−3u
61
+· · ·−3u+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
5
=
−u
u
a
7
=
−u
3
u
3
+ u
a
9
=
−0.0729904u
61
− 0.228063u
60
+ ··· − 3.85257u + 1.70472
−0.505821u
61
+ 0.878522u
60
+ ··· + 0.946087u + 0.454140
a
10
=
0.0556025u
61
− 0.656967u
60
+ ··· − 3.50832u + 1.53444
−0.800994u
61
+ 1.63689u
60
+ ··· − 0.390734u + 0.638367
a
4
=
0.955009u
61
− 3.66751u
60
+ ··· + 4.99704u − 2.34895
−0.104931u
61
+ 0.897107u
60
+ ··· + 0.756639u − 0.648091
a
8
=
−0.101533u
61
− 0.116613u
60
+ ··· − 5.40842u + 1.67042
−0.557807u
61
+ 1.02766u
60
+ ··· + 0.790291u + 0.499051
a
11
=
−0.212577u
61
+ 0.857984u
60
+ ··· − 5.64360u + 3.30260
−1.52544u
61
+ 4.42060u
60
+ ··· + 2.47746u − 0.957556
a
11
=
−0.212577u
61
+ 0.857984u
60
+ ··· − 5.64360u + 3.30260
−1.52544u
61
+ 4.42060u
60
+ ··· + 2.47746u − 0.957556
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.26821u
61
+ 7.95048u
60
+ ··· − 1.19620u + 11.3832
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
62
− 3u
61
+ ··· − 3u + 1
c
2
, c
6
u
62
+ 17u
61
+ ··· − u + 1
c
3
, c
10
u
62
+ 3u
61
+ ··· − u + 1
c
4
u
62
+ 15u
61
+ ··· + 14601u − 4393
c
7
, c
9
u
62
+ u
61
+ ··· + 3u − 1
c
8
u
62
+ u
61
+ ··· − 11u − 1
c
11
u
62
+ 27u
61
+ ··· − 73u − 43
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
62
+ 17y
61
+ ··· − y + 1
c
2
, c
6
y
62
+ 57y
61
+ ··· − 49y + 1
c
3
, c
10
y
62
+ 37y
61
+ ··· − y + 1
c
4
y
62
+ 345y
61
+ ··· − 184476553y + 19298449
c
7
, c
9
y
62
− 43y
61
+ ··· + 67y + 1
c
8
y
62
− 3y
61
+ ··· + 27y + 1
c
11
y
62
− 343y
61
+ ··· − 98037y + 1849
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.233941 + 0.974873I
a = −0.130745 + 1.231300I
b = 1.20344 − 0.93140I
−5.58386 − 5.07710I 0. + 6.39246I
u = −0.233941 − 0.974873I
a = −0.130745 − 1.231300I
b = 1.20344 + 0.93140I
−5.58386 + 5.07710I 0. − 6.39246I
u = −0.342652 + 0.944226I
a = −0.419993 − 0.060562I
b = −0.625287 + 0.596594I
−5.00545 − 0.49255I 0. + 3.20018I
u = −0.342652 − 0.944226I
a = −0.419993 + 0.060562I
b = −0.625287 − 0.596594I
−5.00545 + 0.49255I 0. − 3.20018I
u = 0.153290 + 0.920392I
a = 0.174303 + 0.695564I
b = −0.725323 − 0.206126I
−1.76466 + 1.66966I 2.52149 − 4.58368I
u = 0.153290 − 0.920392I
a = 0.174303 − 0.695564I
b = −0.725323 + 0.206126I
−1.76466 − 1.66966I 2.52149 + 4.58368I
u = 0.929527
a = −0.431713
b = −0.530504
4.73356 21.5180
u = 0.736100 + 0.839352I
a = 0.625972 − 1.122520I
b = 0.25553 + 1.54232I
1.37977 + 2.70121I 0
u = 0.736100 − 0.839352I
a = 0.625972 + 1.122520I
b = 0.25553 − 1.54232I
1.37977 − 2.70121I 0
u = −0.789702 + 0.810743I
a = 1.12489 − 1.57251I
b = −1.73762 + 0.87825I
4.18121 − 0.02705I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.789702 − 0.810743I
a = 1.12489 + 1.57251I
b = −1.73762 − 0.87825I
4.18121 + 0.02705I 0
u = 0.817053 + 0.788358I
a = −1.72604 − 1.05558I
b = 1.91057 + 0.30098I
1.14770 − 3.66515I 0
u = 0.817053 − 0.788358I
a = −1.72604 + 1.05558I
b = 1.91057 − 0.30098I
1.14770 + 3.66515I 0
u = −0.330897 + 1.086980I
a = 0.052301 − 0.533925I
b = −1.136400 − 0.072139I
−2.42165 − 10.69330I 0
u = −0.330897 − 1.086980I
a = 0.052301 + 0.533925I
b = −1.136400 + 0.072139I
−2.42165 + 10.69330I 0
u = −0.191245 + 1.125970I
a = 0.424086 + 0.452072I
b = −0.112808 − 0.950910I
−3.25243 + 3.43205I 0
u = −0.191245 − 1.125970I
a = 0.424086 − 0.452072I
b = −0.112808 + 0.950910I
−3.25243 − 3.43205I 0
u = 0.699940 + 0.915282I
a = 0.883343 + 0.109262I
b = −0.665362 + 0.493910I
1.15333 + 2.78689I 0
u = 0.699940 − 0.915282I
a = 0.883343 − 0.109262I
b = −0.665362 − 0.493910I
1.15333 − 2.78689I 0
u = 0.293896 + 0.791599I
a = 1.372560 − 0.140152I
b = −1.74453 + 0.97363I
−0.39022 + 3.86672I 5.90788 − 9.08899I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.293896 − 0.791599I
a = 1.372560 + 0.140152I
b = −1.74453 − 0.97363I
−0.39022 − 3.86672I 5.90788 + 9.08899I
u = −0.751244 + 0.881873I
a = 7.9454 + 16.0972I
b = 5.3873 − 20.3768I
3.03672 − 2.84894I −90.977 − 147.127I
u = −0.751244 − 0.881873I
a = 7.9454 − 16.0972I
b = 5.3873 + 20.3768I
3.03672 + 2.84894I −90.977 + 147.127I
u = 0.099206 + 0.819273I
a = −0.693059 + 0.958627I
b = −0.97879 + 1.67339I
−1.49291 − 0.30288I 6.68102 − 7.18270I
u = 0.099206 − 0.819273I
a = −0.693059 − 0.958627I
b = −0.97879 − 1.67339I
−1.49291 + 0.30288I 6.68102 + 7.18270I
u = −0.811325 + 0.855337I
a = 1.02748 − 1.98302I
b = −1.43041 + 0.97746I
5.99939 + 0.78225I 0
u = −0.811325 − 0.855337I
a = 1.02748 + 1.98302I
b = −1.43041 − 0.97746I
5.99939 − 0.78225I 0
u = −0.817162 + 0.076718I
a = 0.557951 + 0.249895I
b = 0.619554 + 0.545965I
0.96723 + 6.76946I 10.42875 − 6.10913I
u = −0.817162 − 0.076718I
a = 0.557951 − 0.249895I
b = 0.619554 − 0.545965I
0.96723 − 6.76946I 10.42875 + 6.10913I
u = 0.903335 + 0.763131I
a = 1.58371 + 1.40581I
b = −2.04345 + 0.10821I
5.82273 − 9.92532I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.903335 − 0.763131I
a = 1.58371 − 1.40581I
b = −2.04345 − 0.10821I
5.82273 + 9.92532I 0
u = 0.801297 + 0.878767I
a = −0.483885 − 0.937624I
b = 0.274288 + 0.065829I
6.91724 + 2.74492I 0
u = 0.801297 − 0.878767I
a = −0.483885 + 0.937624I
b = 0.274288 − 0.065829I
6.91724 − 2.74492I 0
u = −0.919899 + 0.762554I
a = −1.09122 + 1.22881I
b = 1.52740 − 0.02797I
9.64228 + 3.86851I 0
u = −0.919899 − 0.762554I
a = −1.09122 − 1.22881I
b = 1.52740 + 0.02797I
9.64228 − 3.86851I 0
u = 0.384411 + 1.134740I
a = −0.110043 − 0.199538I
b = 0.727530 − 0.187535I
0.94109 + 4.46712I 0
u = 0.384411 − 1.134740I
a = −0.110043 + 0.199538I
b = 0.727530 + 0.187535I
0.94109 − 4.46712I 0
u = 0.794631 + 0.900072I
a = 0.529387 + 0.334235I
b = −1.36232 − 0.59261I
6.85084 + 3.23980I 0
u = 0.794631 − 0.900072I
a = 0.529387 − 0.334235I
b = −1.36232 + 0.59261I
6.85084 − 3.23980I 0
u = −0.758229 + 0.946770I
a = −1.32947 + 1.46124I
b = 2.03631 − 0.87059I
3.76313 − 5.80968I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.758229 − 0.946770I
a = −1.32947 − 1.46124I
b = 2.03631 + 0.87059I
3.76313 + 5.80968I 0
u = −0.792260 + 0.922878I
a = −1.64621 + 1.05149I
b = 2.57092 − 0.66498I
5.79100 − 6.78973I 0
u = −0.792260 − 0.922878I
a = −1.64621 − 1.05149I
b = 2.57092 + 0.66498I
5.79100 + 6.78973I 0
u = 0.989705 + 0.719878I
a = 0.244303 + 0.652654I
b = −0.528313 − 0.037104I
4.58484 + 2.57158I 0
u = 0.989705 − 0.719878I
a = 0.244303 − 0.652654I
b = −0.528313 + 0.037104I
4.58484 − 2.57158I 0
u = 0.767748 + 0.968583I
a = 0.93996 + 1.97333I
b = −1.74350 − 1.71204I
0.59571 + 9.61001I 0
u = 0.767748 − 0.968583I
a = 0.93996 − 1.97333I
b = −1.74350 + 1.71204I
0.59571 − 9.61001I 0
u = 0.796750 + 1.019410I
a = −1.09739 − 1.94527I
b = 2.54984 + 1.54483I
5.0175 + 16.2111I 0
u = 0.796750 − 1.019410I
a = −1.09739 + 1.94527I
b = 2.54984 − 1.54483I
5.0175 − 16.2111I 0
u = −0.208653 + 0.671289I
a = −0.50660 − 1.40640I
b = 0.966809 + 0.993102I
1.24146 − 0.98622I 9.68923 − 0.00108I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.208653 − 0.671289I
a = −0.50660 + 1.40640I
b = 0.966809 − 0.993102I
1.24146 + 0.98622I 9.68923 + 0.00108I
u = −0.804538 + 1.026660I
a = 0.95806 − 1.42226I
b = −2.12242 + 1.08518I
8.80960 − 10.22650I 0
u = −0.804538 − 1.026660I
a = 0.95806 + 1.42226I
b = −2.12242 − 1.08518I
8.80960 + 10.22650I 0
u = 0.852377 + 1.058720I
a = −0.240483 − 0.650672I
b = 0.924864 + 0.679823I
3.54226 + 4.13545I 0
u = 0.852377 − 1.058720I
a = −0.240483 + 0.650672I
b = 0.924864 − 0.679823I
3.54226 − 4.13545I 0
u = −0.267685 + 0.530806I
a = −1.06202 − 2.33490I
b = 0.263606 + 1.305770I
1.46923 − 1.18627I 9.25634 + 4.59290I
u = −0.267685 − 0.530806I
a = −1.06202 + 2.33490I
b = 0.263606 − 1.305770I
1.46923 + 1.18627I 9.25634 − 4.59290I
u = −0.535919 + 0.048687I
a = 0.045166 + 0.921741I
b = −0.559745 + 0.668972I
−2.56130 − 2.50988I 6.34359 + 3.13989I
u = −0.535919 − 0.048687I
a = 0.045166 − 0.921741I
b = −0.559745 − 0.668972I
−2.56130 + 2.50988I 6.34359 − 3.13989I
u = 0.335461 + 0.238621I
a = 1.34053 − 2.57954I
b = 0.814929 + 0.614489I
1.04914 − 1.31929I 11.02923 + 0.35157I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.335461 − 0.238621I
a = 1.34053 + 2.57954I
b = 0.814929 − 0.614489I
1.04914 + 1.31929I 11.02923 − 0.35157I
u = 0.330774
a = 0.847207
b = 0.497316
0.709445 14.3000
11
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
62
− 3u
61
+ ··· − 3u + 1
c
2
, c
6
u
62
+ 17u
61
+ ··· − u + 1
c
3
, c
10
u
62
+ 3u
61
+ ··· − u + 1
c
4
u
62
+ 15u
61
+ ··· + 14601u − 4393
c
7
, c
9
u
62
+ u
61
+ ··· + 3u − 1
c
8
u
62
+ u
61
+ ··· − 11u − 1
c
11
u
62
+ 27u
61
+ ··· − 73u − 43
12
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
62
+ 17y
61
+ ··· − y + 1
c
2
, c
6
y
62
+ 57y
61
+ ··· − 49y + 1
c
3
, c
10
y
62
+ 37y
61
+ ··· − y + 1
c
4
y
62
+ 345y
61
+ ··· − 184476553y + 19298449
c
7
, c
9
y
62
− 43y
61
+ ··· + 67y + 1
c
8
y
62
− 3y
61
+ ··· + 27y + 1
c
11
y
62
− 343y
61
+ ··· − 98037y + 1849
13
