12n
0071
(K12n
0071
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 3 5 12 6 9 8 11
Solving Sequence
5,10 3,6
7 8 2 1 4 9 11 12
c
5
c
6
c
7
c
2
c
1
c
4
c
9
c
10
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.70615 × 10
34
u
39
+ 1.06745 × 10
33
u
38
+ ··· + 5.47651 × 10
34
b + 1.26128 × 10
35
,
− 1.54680 × 10
35
u
39
+ 2.39864 × 10
35
u
38
+ ··· + 1.09530 × 10
35
a − 4.53620 × 10
35
, u
40
− 2u
39
+ ··· + 4u − 4i
I
u
2
= hb + 1, −u
8
+ 2u
7
− 3u
6
+ 3u
5
− 4u
4
+ 4u
3
− 3u
2
+ a + 2u − 1, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
I
v
1
= ha, b + v −2, v
2
− 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 51 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−1.71×10
34
u
39
+1.07×10
33
u
38
+· · ·+5.48×10
34
b+1.26×10
35
, −1.55×
10
35
u
39
+2.40×10
35
u
38
+· · ·+1.10×10
35
a−4.54×10
35
, u
40
−2u
39
+· · ·+4u−4i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
1.41222u
39
− 2.18994u
38
+ ··· − 11.0073u + 4.14151
0.311540u
39
− 0.0194914u
38
+ ··· − 2.46184u − 2.30307
a
6
=
1
−u
2
a
7
=
1.29467u
39
− 2.32830u
38
+ ··· − 7.27281u + 5.25464
0.739952u
39
− 0.868974u
38
+ ··· − 6.01405u − 0.199281
a
8
=
0.554717u
39
− 1.45933u
38
+ ··· − 1.25876u + 5.45392
0.739952u
39
− 0.868974u
38
+ ··· − 6.01405u − 0.199281
a
2
=
1.72376u
39
− 2.20943u
38
+ ··· − 13.4692u + 1.83844
0.311540u
39
− 0.0194914u
38
+ ··· − 2.46184u − 2.30307
a
1
=
1.29467u
39
− 2.32830u
38
+ ··· − 7.27281u + 5.25464
−0.230688u
39
+ 0.321263u
38
+ ··· + 1.87952u − 0.844865
a
4
=
0.544195u
39
− 0.801448u
38
+ ··· − 5.22381u + 0.269369
−0.448480u
39
+ 0.683873u
38
+ ··· + 4.04346u − 1.80083
a
9
=
−u
u
3
+ u
a
11
=
−u
3
u
5
+ u
3
+ u
a
12
=
1.23672u
39
− 2.44708u
38
+ ··· − 6.97510u + 6.29059
−0.392051u
39
+ 0.485888u
38
+ ··· + 3.56359u − 0.624191
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.979451u
39
− 1.42354u
38
+ ··· + 1.47042u − 2.27161
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
40
+ 57u
39
+ ··· + 351u + 1
c
2
, c
4
u
40
− 11u
39
+ ··· + 9u + 1
c
3
, c
6
u
40
+ 2u
39
+ ··· + 512u − 512
c
5
, c
9
u
40
− 2u
39
+ ··· + 4u − 4
c
7
u
40
− 3u
39
+ ··· + u − 1
c
8
, c
11
u
40
+ 4u
39
+ ··· − 6u + 1
c
10
u
40
+ 18u
39
+ ··· − 104u + 16
c
12
u
40
− 20u
39
+ ··· − 94u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
40
− 137y
39
+ ··· − 102695y + 1
c
2
, c
4
y
40
− 57y
39
+ ··· − 351y + 1
c
3
, c
6
y
40
− 60y
39
+ ··· − 3407872y + 262144
c
5
, c
9
y
40
+ 18y
39
+ ··· − 104y + 16
c
7
y
40
− 85y
39
+ ··· − 31y + 1
c
8
, c
11
y
40
− 20y
39
+ ··· − 94y + 1
c
10
y
40
+ 6y
39
+ ··· − 26912y + 256
c
12
y
40
+ 4y
39
+ ··· − 7630y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.767555 + 0.682797I
a = 0.527466 − 0.374649I
b = 0.351491 + 0.041737I
3.81537 + 1.27262I 6.29824 − 0.66128I
u = −0.767555 − 0.682797I
a = 0.527466 + 0.374649I
b = 0.351491 − 0.041737I
3.81537 − 1.27262I 6.29824 + 0.66128I
u = 0.873000 + 0.401971I
a = 0.540073 + 0.763124I
b = −0.870382 − 0.585645I
0.09726 − 2.75203I −2.88480 + 4.23304I
u = 0.873000 − 0.401971I
a = 0.540073 − 0.763124I
b = −0.870382 + 0.585645I
0.09726 + 2.75203I −2.88480 − 4.23304I
u = 0.552365 + 0.888486I
a = 0.518410 + 0.192533I
b = 0.342558 + 0.168348I
0.08572 + 2.19817I 0.38918 − 2.62021I
u = 0.552365 − 0.888486I
a = 0.518410 − 0.192533I
b = 0.342558 − 0.168348I
0.08572 − 2.19817I 0.38918 + 2.62021I
u = −0.027732 + 0.938035I
a = 0.600853 − 0.094307I
b = −0.017454 + 0.471847I
−1.55152 + 1.36538I −4.32744 − 4.03663I
u = −0.027732 − 0.938035I
a = 0.600853 + 0.094307I
b = −0.017454 − 0.471847I
−1.55152 − 1.36538I −4.32744 + 4.03663I
u = 0.431539 + 0.988175I
a = 0.546146 + 0.283746I
b = −0.284057 − 0.713228I
−0.42853 + 2.82368I −2.74140 − 3.00000I
u = 0.431539 − 0.988175I
a = 0.546146 − 0.283746I
b = −0.284057 + 0.713228I
−0.42853 − 2.82368I −2.74140 + 3.00000I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.079360 + 0.315602I
a = 0.188664 + 0.002235I
b = 1.79704 − 0.10786I
−11.27530 + 1.20929I −5.80586 + 0.92387I
u = −1.079360 − 0.315602I
a = 0.188664 − 0.002235I
b = 1.79704 + 0.10786I
−11.27530 − 1.20929I −5.80586 − 0.92387I
u = 0.216652 + 1.135450I
a = −1.66179 − 0.18633I
b = −1.318890 − 0.413598I
−5.01603 − 0.16820I −8.63543 + 0.05327I
u = 0.216652 − 1.135450I
a = −1.66179 + 0.18633I
b = −1.318890 + 0.413598I
−5.01603 + 0.16820I −8.63543 − 0.05327I
u = 0.481478 + 1.060550I
a = 2.09296 + 1.81237I
b = 1.77358 − 0.16425I
−8.56336 + 3.34791I −4.12753 − 2.29966I
u = 0.481478 − 1.060550I
a = 2.09296 − 1.81237I
b = 1.77358 + 0.16425I
−8.56336 − 3.34791I −4.12753 + 2.29966I
u = −0.389413 + 1.130570I
a = −1.39760 + 0.84641I
b = −1.016230 − 0.711563I
−4.30445 − 2.98930I −8.10205 + 2.51738I
u = −0.389413 − 1.130570I
a = −1.39760 − 0.84641I
b = −1.016230 + 0.711563I
−4.30445 + 2.98930I −8.10205 − 2.51738I
u = −0.697362 + 1.004410I
a = 0.423595 − 0.213085I
b = 0.479221 − 0.154409I
2.84493 − 6.83482I 4.23533 + 5.20206I
u = −0.697362 − 1.004410I
a = 0.423595 + 0.213085I
b = 0.479221 + 0.154409I
2.84493 + 6.83482I 4.23533 − 5.20206I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.496749 + 1.146130I
a = −1.36151 + 0.53213I
b = −1.45579 + 0.29115I
−3.51298 − 4.94394I −5.28672 + 5.25390I
u = −0.496749 − 1.146130I
a = −1.36151 − 0.53213I
b = −1.45579 − 0.29115I
−3.51298 + 4.94394I −5.28672 − 5.25390I
u = 1.125440 + 0.571611I
a = 0.189635 − 0.004384I
b = 1.78560 + 0.20613I
−9.38333 − 6.25287I −3.71429 + 3.55273I
u = 1.125440 − 0.571611I
a = 0.189635 + 0.004384I
b = 1.78560 − 0.20613I
−9.38333 + 6.25287I −3.71429 − 3.55273I
u = −0.711358 + 0.187576I
a = 0.28261 + 1.89131I
b = −1.119340 − 0.213535I
−0.733261 + 0.420305I −2.53134 − 5.06503I
u = −0.711358 − 0.187576I
a = 0.28261 − 1.89131I
b = −1.119340 + 0.213535I
−0.733261 − 0.420305I −2.53134 + 5.06503I
u = 0.452397 + 0.566444I
a = 0.191549 − 0.000487I
b = 1.59905 + 0.08829I
−6.90633 + 0.62272I −3.96477 − 7.65597I
u = 0.452397 − 0.566444I
a = 0.191549 + 0.000487I
b = 1.59905 − 0.08829I
−6.90633 − 0.62272I −3.96477 + 7.65597I
u = 0.344447 + 0.623097I
a = −2.15466 − 2.41727I
b = −0.764103 + 0.413686I
0.797208 + 0.661473I −4.69435 − 5.79725I
u = 0.344447 − 0.623097I
a = −2.15466 + 2.41727I
b = −0.764103 − 0.413686I
0.797208 − 0.661473I −4.69435 + 5.79725I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.608559 + 1.157670I
a = −1.08482 − 0.95472I
b = −0.923559 + 0.844828I
−2.24385 + 8.24833I −4.49922 − 6.95806I
u = 0.608559 − 1.157670I
a = −1.08482 + 0.95472I
b = −0.923559 − 0.844828I
−2.24385 − 8.24833I −4.49922 + 6.95806I
u = −0.640898 + 1.241650I
a = 1.47950 − 1.37909I
b = 1.82246 + 0.25034I
−14.2021 − 7.3246I −7.52732 + 3.21849I
u = −0.640898 − 1.241650I
a = 1.47950 + 1.37909I
b = 1.82246 − 0.25034I
−14.2021 + 7.3246I −7.52732 − 3.21849I
u = −0.11613 + 1.42102I
a = 2.07367 − 0.26407I
b = 1.93738 + 0.04804I
−17.7940 − 3.0498I −8.36562 + 2.61097I
u = −0.11613 − 1.42102I
a = 2.07367 + 0.26407I
b = 1.93738 − 0.04804I
−17.7940 + 3.0498I −8.36562 − 2.61097I
u = 0.77397 + 1.20805I
a = 1.18273 + 1.46175I
b = 1.78706 − 0.30179I
−11.4479 + 13.0879I 0. − 6.81590I
u = 0.77397 − 1.20805I
a = 1.18273 − 1.46175I
b = 1.78706 + 0.30179I
−11.4479 − 13.0879I 0. + 6.81590I
u = 0.458630
a = 1.38775
b = −0.0558807
1.26099 8.96990
u = −0.325204
a = 1.75723
b = −0.755372
−1.11358 −9.07280
8
II.
I
u
2
= hb +1, −u
8
+2u
7
+· · · +a−1, u
9
−u
8
+2u
7
−u
6
+3u
5
−u
4
+2u
3
+u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
u
8
− 2u
7
+ 3u
6
− 3u
5
+ 4u
4
− 4u
3
+ 3u
2
− 2u + 1
−1
a
6
=
1
−u
2
a
7
=
1
−u
2
a
8
=
u
2
+ 1
−u
2
a
2
=
u
8
− 2u
7
+ 3u
6
− 3u
5
+ 4u
4
− 4u
3
+ 3u
2
− 2u
−1
a
1
=
−1
0
a
4
=
u
8
− 2u
7
+ 3u
6
− 3u
5
+ 4u
4
− 4u
3
+ 3u
2
− 2u + 1
−1
a
9
=
−u
u
3
+ u
a
11
=
−u
3
u
5
+ u
3
+ u
a
12
=
u
8
+ u
6
+ u
4
− 1
−u
8
+ u
7
− u
6
+ 2u
5
− u
4
+ 2u
3
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
8
− 8u
7
+ 12u
6
− 11u
5
+ 18u
4
− 17u
3
+ 15u
2
− 6u + 4
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
6
u
9
c
4
(u + 1)
9
c
5
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
7
, c
10
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
8
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
9
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
11
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
12
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
6
y
9
c
5
, c
9
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
7
, c
10
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
8
, c
11
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
12
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140343 + 0.966856I
a = −1.004430 + 0.297869I
b = −1.00000
−3.42837 − 2.09337I −6.83106 + 4.06115I
u = −0.140343 − 0.966856I
a = −1.004430 − 0.297869I
b = −1.00000
−3.42837 + 2.09337I −6.83106 − 4.06115I
u = −0.628449 + 0.875112I
a = −0.275254 + 0.816341I
b = −1.00000
−1.02799 − 2.45442I −7.33502 + 3.27944I
u = −0.628449 − 0.875112I
a = −0.275254 − 0.816341I
b = −1.00000
−1.02799 + 2.45442I −7.33502 − 3.27944I
u = 0.796005 + 0.733148I
a = 0.070080 − 0.850995I
b = −1.00000
2.72642 − 1.33617I −2.78826 + 0.80685I
u = 0.796005 − 0.733148I
a = 0.070080 + 0.850995I
b = −1.00000
2.72642 + 1.33617I −2.78826 − 0.80685I
u = 0.728966 + 0.986295I
a = −0.195086 − 0.635552I
b = −1.00000
1.95319 + 7.08493I −4.66194 − 6.93476I
u = 0.728966 − 0.986295I
a = −0.195086 + 0.635552I
b = −1.00000
1.95319 − 7.08493I −4.66194 + 6.93476I
u = −0.512358
a = 3.80937
b = −1.00000
−0.446489 15.2330
12
III. I
v
1
= ha, b + v − 2, v
2
− 3v + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
v
0
a
3
=
0
−v + 2
a
6
=
1
0
a
7
=
1
−v + 3
a
8
=
v − 2
−v + 3
a
2
=
−v + 2
−v + 2
a
1
=
−v + 2
v − 3
a
4
=
v − 2
v − 3
a
9
=
v
0
a
11
=
v
0
a
12
=
2
v − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
− 3u + 1
c
2
, c
3
u
2
+ u − 1
c
4
, c
6
u
2
− u − 1
c
5
, c
9
, c
10
u
2
c
7
u
2
+ 3u + 1
c
8
(u + 1)
2
c
11
, c
12
(u − 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
2
− 7y + 1
c
2
, c
3
, c
4
c
6
y
2
− 3y + 1
c
5
, c
9
, c
10
y
2
c
8
, c
11
, c
12
(y − 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.381966
a = 0
b = 1.61803
−7.23771 −9.00000
v = 2.61803
a = 0
b = −0.618034
0.657974 −9.00000
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
2
− 3u + 1)(u
40
+ 57u
39
+ ··· + 351u + 1)
c
2
((u − 1)
9
)(u
2
+ u − 1)(u
40
− 11u
39
+ ··· + 9u + 1)
c
3
u
9
(u
2
+ u − 1)(u
40
+ 2u
39
+ ··· + 512u − 512)
c
4
((u + 1)
9
)(u
2
− u − 1)(u
40
− 11u
39
+ ··· + 9u + 1)
c
5
u
2
(u
9
− u
8
+ ··· + u + 1)(u
40
− 2u
39
+ ··· + 4u − 4)
c
6
u
9
(u
2
− u − 1)(u
40
+ 2u
39
+ ··· + 512u − 512)
c
7
(u
2
+ 3u + 1)(u
9
+ 3u
8
+ ··· + u − 1)
· (u
40
− 3u
39
+ ··· + u − 1)
c
8
(u + 1)
2
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
40
+ 4u
39
+ ··· − 6u + 1)
c
9
u
2
(u
9
+ u
8
+ ··· + u − 1)(u
40
− 2u
39
+ ··· + 4u − 4)
c
10
u
2
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
40
+ 18u
39
+ ··· − 104u + 16)
c
11
(u − 1)
2
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
40
+ 4u
39
+ ··· − 6u + 1)
c
12
(u − 1)
2
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
40
− 20u
39
+ ··· − 94u + 1)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
9
)(y
2
− 7y + 1)(y
40
− 137y
39
+ ··· − 102695y + 1)
c
2
, c
4
((y − 1)
9
)(y
2
− 3y + 1)(y
40
− 57y
39
+ ··· − 351y + 1)
c
3
, c
6
y
9
(y
2
− 3y + 1)(y
40
− 60y
39
+ ··· − 3407872y + 262144)
c
5
, c
9
y
2
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
40
+ 18y
39
+ ··· − 104y + 16)
c
7
(y
2
− 7y + 1)(y
9
+ 7y
8
+ ··· + 13y − 1)
· (y
40
− 85y
39
+ ··· − 31y + 1)
c
8
, c
11
(y − 1)
2
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
40
− 20y
39
+ ··· − 94y + 1)
c
10
y
2
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
· (y
40
+ 6y
39
+ ··· − 26912y + 256)
c
12
(y − 1)
2
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
40
+ 4y
39
+ ··· − 7630y + 1)
18
