11a
323
(K11a
323
)
A knot diagram
1
Linearized knot diagam
9 6 1 11 8 2 10 3 7 5 4
Solving Sequence
5,11
4 1 3
7,10
8 6 2 9
c
4
c
11
c
3
c
10
c
7
c
5
c
2
c
9
c
1
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h2.31401 × 10
21
u
43
− 3.54437 × 10
21
u
42
+ ··· + 8.57234 × 10
19
b + 4.94843 × 10
21
,
− 5.89751 × 10
21
u
43
+ 9.06194 × 10
21
u
42
+ ··· + 8.57234 × 10
19
a − 1.26997 × 10
22
, u
44
− 2u
43
+ ··· + 5u − 1i
I
u
2
= hu
2
+ 5b + 7u + 4, −4u
2
+ 5a + 2u − 6, u
3
+ u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 47 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
= h2.31×10
21
u
43
−3.54×10
21
u
42
+· · ·+8.57×10
19
b+4.95×10
21
, −5.90×
10
21
u
43
+9.06×10
21
u
42
+· · ·+8.57×10
19
a−1.27×10
22
, u
44
−2u
43
+· · ·+5u−1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
68.7969u
43
− 105.711u
42
+ ··· − 427.419u + 148.148
−26.9939u
43
+ 41.3466u
42
+ ··· + 164.286u − 57.7256
a
10
=
u
u
a
8
=
48.3780u
43
− 74.2119u
42
+ ··· − 300.591u + 103.624
−47.4129u
43
+ 72.8461u
42
+ ··· + 291.114u − 102.249
a
6
=
−21.2354u
43
+ 32.3030u
42
+ ··· + 140.637u − 45.5104
64.6016u
43
− 99.5702u
42
+ ··· − 387.835u + 137.751
a
2
=
−6.60822u
43
+ 11.0300u
42
+ ··· + 33.2318u − 11.2429
−30.3756u
43
+ 47.4335u
42
+ ··· + 187.153u − 65.4032
a
9
=
7.06760u
43
− 10.5739u
42
+ ··· − 44.3693u + 13.4967
−31.4705u
43
+ 48.2831u
42
+ ··· + 193.366u − 67.6179
a
9
=
7.06760u
43
− 10.5739u
42
+ ··· − 44.3693u + 13.4967
−31.4705u
43
+ 48.2831u
42
+ ··· + 193.366u − 67.6179
(ii) Obstruction class = −1
(iii) Cusp Shapes =
98838962520190550252816
428617191062252656975
u
43
−
152658479968934161876903
428617191062252656975
u
42
+ ··· −
605374312863961326763079
428617191062252656975
u +
218640669764653807216074
428617191062252656975
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
5(5u
44
− 21u
43
+ ··· + 864u + 823)
c
2
, c
6
u
44
+ 2u
43
+ ··· + u − 1
c
3
, c
4
, c
10
c
11
u
44
− 2u
43
+ ··· + 5u − 1
c
5
5(5u
44
− 2u
43
+ ··· + 23513u + 5383)
c
7
, c
9
u
44
+ 4u
43
+ ··· + 16u − 25
c
8
u
44
+ u
43
+ ··· − 220u + 200
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
25(25y
44
− 671y
43
+ ··· − 2153826y + 677329)
c
2
, c
6
y
44
+ 30y
43
+ ··· − 23y + 1
c
3
, c
4
, c
10
c
11
y
44
+ 54y
43
+ ··· − 23y + 1
c
5
25(25y
44
− 914y
43
+ ··· − 1.98283 × 10
8
y + 2.89767 × 10
7
)
c
7
, c
9
y
44
− 40y
43
+ ··· − 9756y + 625
c
8
y
44
− 21y
43
+ ··· − 482000y + 40000
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.531615 + 0.932164I
a = 0.040863 + 0.471379I
b = −0.29401 + 1.86560I
9.4938 − 10.7466I 0
u = 0.531615 − 0.932164I
a = 0.040863 − 0.471379I
b = −0.29401 − 1.86560I
9.4938 + 10.7466I 0
u = 0.604409 + 0.897873I
a = 0.417373 + 0.331876I
b = −0.387595 + 1.341230I
9.03616 + 1.64979I 0
u = 0.604409 − 0.897873I
a = 0.417373 − 0.331876I
b = −0.387595 − 1.341230I
9.03616 − 1.64979I 0
u = −0.102848 + 0.888493I
a = −0.581285 + 0.418665I
b = −0.15348 − 1.41968I
7.69062 + 2.11031I 11.34242 − 3.52324I
u = −0.102848 − 0.888493I
a = −0.581285 − 0.418665I
b = −0.15348 + 1.41968I
7.69062 − 2.11031I 11.34242 + 3.52324I
u = −0.570126 + 0.967451I
a = −0.241178 + 0.550119I
b = 0.19226 + 1.63923I
4.65109 + 4.83905I 0
u = −0.570126 − 0.967451I
a = −0.241178 − 0.550119I
b = 0.19226 − 1.63923I
4.65109 − 4.83905I 0
u = −0.872602
a = −1.52363
b = −0.0954626
1.65108 6.63730
u = 0.305076 + 0.810839I
a = 0.943477 + 0.286013I
b = −0.190221 − 0.529393I
3.79818 − 5.24105I 5.59410 + 7.80794I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.305076 − 0.810839I
a = 0.943477 − 0.286013I
b = −0.190221 + 0.529393I
3.79818 + 5.24105I 5.59410 − 7.80794I
u = 0.797364 + 0.047017I
a = 1.63358 − 0.22748I
b = −0.086123 + 0.241603I
6.50673 − 6.32792I 4.03492 + 4.79564I
u = 0.797364 − 0.047017I
a = 1.63358 + 0.22748I
b = −0.086123 − 0.241603I
6.50673 + 6.32792I 4.03492 − 4.79564I
u = 0.081349 + 0.763523I
a = 0.965343 − 0.286817I
b = 0.82836 − 1.74768I
3.38183 − 0.95789I 3.69098 − 0.13410I
u = 0.081349 − 0.763523I
a = 0.965343 + 0.286817I
b = 0.82836 + 1.74768I
3.38183 + 0.95789I 3.69098 + 0.13410I
u = −0.305152 + 0.698148I
a = −0.781840 + 0.333278I
b = −0.1039550 − 0.0572812I
0.43661 + 1.95503I −1.24229 − 4.92252I
u = −0.305152 − 0.698148I
a = −0.781840 − 0.333278I
b = −0.1039550 + 0.0572812I
0.43661 − 1.95503I −1.24229 + 4.92252I
u = 0.204088 + 0.682624I
a = 0.621470 + 1.202720I
b = 1.050420 + 0.714579I
3.43037 + 0.37049I 6.62918 + 1.94701I
u = 0.204088 − 0.682624I
a = 0.621470 − 1.202720I
b = 1.050420 − 0.714579I
3.43037 − 0.37049I 6.62918 − 1.94701I
u = −0.151472 + 1.375050I
a = 0.017281 + 1.065310I
b = 0.10520 + 1.54249I
4.06071 + 2.79744I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.151472 − 1.375050I
a = 0.017281 − 1.065310I
b = 0.10520 − 1.54249I
4.06071 − 2.79744I 0
u = −0.454810 + 0.226491I
a = −0.497393 − 0.333605I
b = −0.242173 + 0.388805I
−0.971761 + 0.735222I −7.08962 − 4.08922I
u = −0.454810 − 0.226491I
a = −0.497393 + 0.333605I
b = −0.242173 − 0.388805I
−0.971761 − 0.735222I −7.08962 + 4.08922I
u = 0.458929 + 0.000125I
a = 0.137414 + 1.167950I
b = 0.582805 − 0.448947I
1.39676 − 2.58910I −1.63153 + 3.81812I
u = 0.458929 − 0.000125I
a = 0.137414 − 1.167950I
b = 0.582805 + 0.448947I
1.39676 + 2.58910I −1.63153 − 3.81812I
u = 0.03581 + 1.62441I
a = 1.92074 + 0.53469I
b = 1.80303 + 0.20163I
11.45350 − 0.37506I 0
u = 0.03581 − 1.62441I
a = 1.92074 − 0.53469I
b = 1.80303 − 0.20163I
11.45350 + 0.37506I 0
u = −0.265508 + 0.254499I
a = 0.92439 + 3.14403I
b = −1.069800 + 0.487521I
4.32587 + 0.97456I −0.21065 − 1.62578I
u = −0.265508 − 0.254499I
a = 0.92439 − 3.14403I
b = −1.069800 − 0.487521I
4.32587 − 0.97456I −0.21065 + 1.62578I
u = −0.06818 + 1.63407I
a = −0.111899 − 0.172474I
b = 0.429905 − 0.322388I
8.58047 + 3.25505I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.06818 − 1.63407I
a = −0.111899 + 0.172474I
b = 0.429905 + 0.322388I
8.58047 − 3.25505I 0
u = 0.01583 + 1.65226I
a = 0.98946 − 2.95954I
b = 0.81579 − 3.72896I
11.90430 − 1.28750I 0
u = 0.01583 − 1.65226I
a = 0.98946 + 2.95954I
b = 0.81579 + 3.72896I
11.90430 + 1.28750I 0
u = 0.07456 + 1.65915I
a = −0.477531 − 0.715296I
b = −1.35641 − 0.97677I
12.42890 − 6.64650I 0
u = 0.07456 − 1.65915I
a = −0.477531 + 0.715296I
b = −1.35641 + 0.97677I
12.42890 + 6.64650I 0
u = −0.02340 + 1.67896I
a = −0.00277 − 2.47208I
b = 0.42738 − 3.58832I
16.7506 + 2.5780I 0
u = −0.02340 − 1.67896I
a = −0.00277 + 2.47208I
b = 0.42738 + 3.58832I
16.7506 − 2.5780I 0
u = 0.15119 + 1.69109I
a = −0.86535 + 2.55294I
b = −0.64062 + 3.50161I
18.5526 − 13.4473I 0
u = 0.15119 − 1.69109I
a = −0.86535 − 2.55294I
b = −0.64062 − 3.50161I
18.5526 + 13.4473I 0
u = 0.17519 + 1.69800I
a = −0.77442 + 2.09319I
b = −0.82209 + 2.95091I
17.9861 − 1.4504I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.17519 − 1.69800I
a = −0.77442 − 2.09319I
b = −0.82209 − 2.95091I
17.9861 + 1.4504I 0
u = −0.15533 + 1.70224I
a = 0.72708 + 2.39173I
b = 0.60080 + 3.24290I
13.8777 + 7.6987I 0
u = −0.15533 − 1.70224I
a = 0.72708 − 2.39173I
b = 0.60080 − 3.24290I
13.8777 − 7.6987I 0
u = 0.195443
a = −4.08600
b = 0.516511
1.30800 9.71570
9
II. I
u
2
= hu
2
+ 5b + 7u + 4, −4u
2
+ 5a + 2u − 6, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
1
=
−u
−u
2
− u − 1
a
3
=
u
2
+ 1
−u
2
− u − 1
a
7
=
4
5
u
2
−
2
5
u +
6
5
−
1
5
u
2
−
7
5
u −
4
5
a
10
=
u
u
a
8
=
4
5
u
2
+
3
5
u +
6
5
−
1
5
u
2
−
2
5
u −
4
5
a
6
=
13
25
u
2
+
6
25
u +
42
25
−
7
25
u
2
−
9
25
u −
13
25
a
2
=
−
4
25
u
2
−
23
25
u −
11
25
−
19
25
u
2
−
28
25
u −
21
25
a
9
=
4
5
u
2
+
3
5
u +
6
5
−
1
5
u
2
−
2
5
u −
4
5
a
9
=
4
5
u
2
+
3
5
u +
6
5
−
1
5
u
2
−
2
5
u −
4
5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
188
25
u
2
−
131
25
u −
92
25
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
5(5u
3
+ 4u
2
− u − 1)
c
2
u
3
+ u
2
− 1
c
3
, c
4
u
3
+ u
2
+ 2u + 1
c
5
5(5u
3
+ 7u
2
+ 4u + 1)
c
6
u
3
− u
2
+ 1
c
7
(u + 1)
3
c
8
u
3
c
9
(u − 1)
3
c
10
, c
11
u
3
− u
2
+ 2u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
25(25y
3
− 26y
2
+ 9y −1)
c
2
, c
6
y
3
− y
2
+ 2y −1
c
3
, c
4
, c
10
c
11
y
3
+ 3y
2
+ 2y −1
c
5
25(25y
3
− 9y
2
+ 2y −1)
c
7
, c
9
(y −1)
3
c
8
y
3
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −0.043855 − 0.972680I
b = −0.16642 − 1.71754I
4.66906 + 2.82812I 9.94796 − 2.62108I
u = −0.215080 − 1.307140I
a = −0.043855 + 0.972680I
b = −0.16642 + 1.71754I
4.66906 − 2.82812I 9.94796 + 2.62108I
u = −0.569840
a = 1.68771
b = −0.0671672
0.531480 −3.13590
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
25(5u
3
+ 4u
2
− u − 1)(5u
44
− 21u
43
+ ··· + 864u + 823)
c
2
(u
3
+ u
2
− 1)(u
44
+ 2u
43
+ ··· + u − 1)
c
3
, c
4
(u
3
+ u
2
+ 2u + 1)(u
44
− 2u
43
+ ··· + 5u − 1)
c
5
25(5u
3
+ 7u
2
+ 4u + 1)(5u
44
− 2u
43
+ ··· + 23513u + 5383)
c
6
(u
3
− u
2
+ 1)(u
44
+ 2u
43
+ ··· + u − 1)
c
7
((u + 1)
3
)(u
44
+ 4u
43
+ ··· + 16u − 25)
c
8
u
3
(u
44
+ u
43
+ ··· − 220u + 200)
c
9
((u − 1)
3
)(u
44
+ 4u
43
+ ··· + 16u − 25)
c
10
, c
11
(u
3
− u
2
+ 2u − 1)(u
44
− 2u
43
+ ··· + 5u − 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
625(25y
3
− 26y
2
+ 9y −1)
· (25y
44
− 671y
43
+ ··· − 2153826y + 677329)
c
2
, c
6
(y
3
− y
2
+ 2y −1)(y
44
+ 30y
43
+ ··· − 23y + 1)
c
3
, c
4
, c
10
c
11
(y
3
+ 3y
2
+ 2y −1)(y
44
+ 54y
43
+ ··· − 23y + 1)
c
5
625(25y
3
− 9y
2
+ 2y −1)
· (25y
44
− 914y
43
+ ··· − 198282959y + 28976689)
c
7
, c
9
((y −1)
3
)(y
44
− 40y
43
+ ··· − 9756y + 625)
c
8
y
3
(y
44
− 21y
43
+ ··· − 482000y + 40000)
15
