12n
0360
(K12n
0360
)
A knot diagram
1
Linearized knot diagam
3 5 7 11 2 9 1 4 6 5 9 4
Solving Sequence
2,6
5 3
1,11
4 10 9 7 8 12
c
5
c
2
c
1
c
4
c
10
c
9
c
6
c
7
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.17231 × 10
41
u
41
− 1.10310 × 10
41
u
40
+ ··· + 1.27534 × 10
41
b − 1.91700 × 10
42
,
− 3.79921 × 10
42
u
41
+ 1.16103 × 10
42
u
40
+ ··· + 1.27534 × 10
41
a − 5.15011 × 10
42
, u
42
+ 4u
40
+ ··· + 8u + 1i
I
u
2
= h−4867u
17
+ 14254u
16
+ ··· + 1012b + 2283, −6343u
17
+ 8982u
16
+ ··· + 1012a − 18113,
u
18
− 3u
17
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 60 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−3.17×10
41
u
41
−1.10×10
41
u
40
+· · ·+1.28×10
41
b−1.92×10
42
, −3.80×
10
42
u
41
+1.16×10
42
u
40
+· · ·+1.28×10
41
a−5.15×10
42
, u
42
+4u
40
+· · ·+8u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
11
=
29.7898u
41
− 9.10368u
40
+ ··· + 352.163u + 40.3823
2.48742u
41
+ 0.864947u
40
+ ··· + 84.3991u + 15.0313
a
4
=
−18.2967u
41
− 1.79519u
40
+ ··· − 427.707u − 64.5574
1.07748u
41
+ 0.260227u
40
+ ··· + 14.9654u − 0.377505
a
10
=
26.3588u
41
− 7.38711u
40
+ ··· + 310.803u + 34.4547
2.06799u
41
+ 0.593466u
40
+ ··· + 74.0976u + 13.3147
a
9
=
28.4268u
41
− 6.79364u
40
+ ··· + 384.901u + 47.7694
2.06799u
41
+ 0.593466u
40
+ ··· + 74.0976u + 13.3147
a
7
=
8.01480u
41
− 7.35645u
40
+ ··· − 49.3603u − 18.0733
5.08682u
41
+ 0.163226u
40
+ ··· + 86.5337u + 9.31672
a
8
=
7.63267u
41
− 7.14139u
40
+ ··· − 53.0896u − 18.3070
6.44055u
41
+ 0.639959u
40
+ ··· + 130.209u + 16.3404
a
12
=
19.0918u
41
+ 7.25817u
40
+ ··· + 568.854u + 93.4086
−1.69590u
41
+ 4.74779u
40
+ ··· + 94.9034u + 19.8886
(ii) Obstruction class = −1
(iii) Cusp Shapes = 29.4758u
41
− 5.89551u
40
+ ··· + 439.594u + 56.8690
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
42
+ 8u
41
+ ··· + 14u + 1
c
2
, c
5
u
42
+ 4u
40
+ ··· + 8u + 1
c
3
u
42
+ u
41
+ ··· + 15u + 1
c
4
, c
10
u
42
− 3u
40
+ ··· + 3884u + 653
c
6
, c
9
u
42
− 2u
41
+ ··· − 1450u + 2881
c
7
, c
11
u
42
− 2u
41
+ ··· + 102u + 116
c
8
u
42
+ 29u
40
+ ··· − 3172u + 968
c
12
u
42
+ u
41
+ ··· + 8821u + 713
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
42
+ 60y
41
+ ··· + 106y + 1
c
2
, c
5
y
42
+ 8y
41
+ ··· + 14y + 1
c
3
y
42
+ 7y
41
+ ··· + 461y + 1
c
4
, c
10
y
42
− 6y
41
+ ··· − 6058384y + 426409
c
6
, c
9
y
42
+ 54y
41
+ ··· + 123416908y + 8300161
c
7
, c
11
y
42
+ 50y
41
+ ··· + 280292y + 13456
c
8
y
42
+ 58y
41
+ ··· − 12741008y + 937024
c
12
y
42
− 59y
41
+ ··· − 9108213y + 508369
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.401386 + 0.907950I
a = −1.30994 + 2.33702I
b = 1.61047 − 0.43509I
5.91077 + 1.27313I 0.461828 + 0.968619I
u = −0.401386 − 0.907950I
a = −1.30994 − 2.33702I
b = 1.61047 + 0.43509I
5.91077 − 1.27313I 0.461828 − 0.968619I
u = −0.482655 + 0.905869I
a = 1.53119 + 1.57511I
b = 0.357628 − 1.155570I
−3.09049 − 4.22260I −5.14689 + 7.39649I
u = −0.482655 − 0.905869I
a = 1.53119 − 1.57511I
b = 0.357628 + 1.155570I
−3.09049 + 4.22260I −5.14689 − 7.39649I
u = −0.703951 + 0.646413I
a = 0.097005 − 0.274142I
b = 1.35281 − 0.45723I
7.00024 − 5.59064I 1.86038 + 6.99102I
u = −0.703951 − 0.646413I
a = 0.097005 + 0.274142I
b = 1.35281 + 0.45723I
7.00024 + 5.59064I 1.86038 − 6.99102I
u = 0.284092 + 1.017050I
a = −0.211153 − 0.796137I
b = 0.270228 + 0.532970I
−0.93324 + 2.30287I 0.55695 − 5.43151I
u = 0.284092 − 1.017050I
a = −0.211153 + 0.796137I
b = 0.270228 − 0.532970I
−0.93324 − 2.30287I 0.55695 + 5.43151I
u = −0.344707 + 1.010570I
a = −0.70988 − 2.54288I
b = −1.04250 + 1.60858I
−3.88818 − 1.43090I −6.13404 − 0.44141I
u = −0.344707 − 1.010570I
a = −0.70988 + 2.54288I
b = −1.04250 − 1.60858I
−3.88818 + 1.43090I −6.13404 + 0.44141I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.334236 + 0.869539I
a = 0.19107 + 1.40502I
b = −0.253907 + 0.343667I
2.57400 + 3.84916I −2.94638 − 4.40988I
u = 0.334236 − 0.869539I
a = 0.19107 − 1.40502I
b = −0.253907 − 0.343667I
2.57400 − 3.84916I −2.94638 + 4.40988I
u = 1.081170 + 0.341257I
a = −0.0779258 − 0.1028190I
b = −1.014370 − 0.665967I
6.88916 + 0.77238I 3.82875 + 0.50165I
u = 1.081170 − 0.341257I
a = −0.0779258 + 0.1028190I
b = −1.014370 + 0.665967I
6.88916 − 0.77238I 3.82875 − 0.50165I
u = 0.593161 + 0.466185I
a = −0.477779 + 0.366692I
b = 0.331918 + 0.155382I
0.97092 + 1.12729I 3.41044 − 3.72299I
u = 0.593161 − 0.466185I
a = −0.477779 − 0.366692I
b = 0.331918 − 0.155382I
0.97092 − 1.12729I 3.41044 + 3.72299I
u = −0.960756 + 0.862418I
a = 0.263391 − 0.247533I
b = 0.906451 − 0.144108I
8.16534 + 0.62011I 0
u = −0.960756 − 0.862418I
a = 0.263391 + 0.247533I
b = 0.906451 + 0.144108I
8.16534 − 0.62011I 0
u = 1.030270 + 0.851389I
a = 1.050060 − 0.637282I
b = 3.02403 + 0.18691I
15.8428 + 3.0373I 0
u = 1.030270 − 0.851389I
a = 1.050060 + 0.637282I
b = 3.02403 − 0.18691I
15.8428 − 3.0373I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.881885 + 1.024300I
a = 0.065443 + 1.314000I
b = 1.116300 + 0.121744I
7.64407 − 7.40138I 0
u = −0.881885 − 1.024300I
a = 0.065443 − 1.314000I
b = 1.116300 − 0.121744I
7.64407 + 7.40138I 0
u = −0.258984 + 0.576790I
a = 0.28812 − 1.63058I
b = −1.042850 − 0.283492I
−1.89277 − 0.93054I −0.64123 − 5.03409I
u = −0.258984 − 0.576790I
a = 0.28812 + 1.63058I
b = −1.042850 + 0.283492I
−1.89277 + 0.93054I −0.64123 + 5.03409I
u = 0.889913 + 1.082940I
a = 0.32129 − 2.34661I
b = 3.16294 − 0.04261I
15.0651 + 4.0075I 0
u = 0.889913 − 1.082940I
a = 0.32129 + 2.34661I
b = 3.16294 + 0.04261I
15.0651 − 4.0075I 0
u = −1.10926 + 0.89934I
a = −0.999768 − 0.372325I
b = −2.69091 + 0.68963I
16.3728 + 6.2095I 0
u = −1.10926 − 0.89934I
a = −0.999768 + 0.372325I
b = −2.69091 − 0.68963I
16.3728 − 6.2095I 0
u = 1.08343 + 0.95036I
a = −0.278099 − 0.106243I
b = −0.808505 − 0.423181I
6.49243 + 3.66353I 0
u = 1.08343 − 0.95036I
a = −0.278099 + 0.106243I
b = −0.808505 + 0.423181I
6.49243 − 3.66353I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.59894 + 1.32646I
a = 0.840675 + 0.936960I
b = −1.74794 + 0.20763I
3.56306 + 5.56643I 0
u = 0.59894 − 1.32646I
a = 0.840675 − 0.936960I
b = −1.74794 − 0.20763I
3.56306 − 5.56643I 0
u = −0.95393 + 1.10294I
a = −0.08765 − 1.98339I
b = −2.77311 − 0.59101I
15.6580 − 13.6964I 0
u = −0.95393 − 1.10294I
a = −0.08765 + 1.98339I
b = −2.77311 + 0.59101I
15.6580 + 13.6964I 0
u = 1.03091 + 1.03246I
a = −0.171963 + 0.984513I
b = −1.270640 + 0.340074I
6.22484 + 3.97881I 0
u = 1.03091 − 1.03246I
a = −0.171963 − 0.984513I
b = −1.270640 − 0.340074I
6.22484 − 3.97881I 0
u = −0.373093 + 0.258025I
a = −1.14452 − 1.54216I
b = −0.465004 − 1.176860I
−1.61522 − 1.51020I −1.99512 + 5.26674I
u = −0.373093 − 0.258025I
a = −1.14452 + 1.54216I
b = −0.465004 + 1.176860I
−1.61522 + 1.51020I −1.99512 − 5.26674I
u = −0.179315 + 0.403078I
a = 0.716711 − 0.420282I
b = −0.586881 + 0.899608I
−1.85309 + 1.18150I 0.81194 + 1.42321I
u = −0.179315 − 0.403078I
a = 0.716711 + 0.420282I
b = −0.586881 − 0.899608I
−1.85309 − 1.18150I 0.81194 − 1.42321I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.276210 + 0.334239I
a = −0.89628 + 5.44219I
b = 0.563842 + 0.807265I
5.10998 − 3.43817I 2.08715 + 8.85459I
u = −0.276210 − 0.334239I
a = −0.89628 − 5.44219I
b = 0.563842 − 0.807265I
5.10998 + 3.43817I 2.08715 − 8.85459I
9
II. I
u
2
= h−4867u
17
+ 14254u
16
+ · · · + 1012b + 2283, −6343u
17
+ 8982u
16
+
· · · + 1012a − 18113, u
18
− 3u
17
+ · · · − 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
11
=
6.26779u
17
− 8.87549u
16
+ ··· − 5.28162u + 17.8982
4.80929u
17
− 14.0850u
16
+ ··· + 12.3113u − 2.25593
a
4
=
−0.265810u
17
− 6.61067u
16
+ ··· + 16.6670u − 18.5484
−3.83103u
17
+ 13.4328u
16
+ ··· − 22.5504u + 8.40810
a
10
=
2.98715u
17
− 2.83992u
16
+ ··· − 4.00494u + 10.2263
4.74605u
17
− 12.5277u
16
+ ··· + 7.97925u + 1.55040
a
9
=
7.73320u
17
− 15.3676u
16
+ ··· + 3.97431u + 11.7767
4.74605u
17
− 12.5277u
16
+ ··· + 7.97925u + 1.55040
a
7
=
−11.2737u
17
+ 34.3340u
16
+ ··· − 42.8745u + 11.0524
−0.487154u
17
+ 5.83992u
16
+ ··· − 20.4951u + 12.2737
a
8
=
−12.6947u
17
+ 37.8874u
16
+ ··· − 45.9595u + 10.5445
2.59783u
17
− 3.06522u
16
+ ··· − 9.92391u + 10.3152
a
12
=
−3.87253u
17
+ 24.6423u
16
+ ··· − 46.6433u + 37.0623
5.80929u
17
− 17.0850u
16
+ ··· + 20.3113u − 4.25593
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
9044
253
u
17
+
28784
253
u
16
+ ··· −
39132
253
u +
7280
253
10
(iv) u-Polynomials at the component
11
Crossings u-Polynomials at each crossing
c
1
u
18
− 7u
17
+ ··· − 14u + 1
c
2
u
18
+ 3u
17
+ ··· + 2u + 1
c
3
u
18
− 3u
16
+ ··· − 3u + 1
c
4
u
18
− u
17
+ ··· − 2u + 1
c
5
u
18
− 3u
17
+ ··· − 2u + 1
c
6
u
18
− u
17
+ ··· + 4u
2
+ 1
c
7
u
18
− 3u
17
+ ··· − 10u + 4
c
8
u
18
+ u
17
+ ··· + 76u + 57
c
9
u
18
+ u
17
+ ··· + 4u
2
+ 1
c
10
u
18
+ u
17
+ ··· + 2u + 1
c
11
u
18
+ 3u
17
+ ··· + 10u + 4
c
12
u
18
− 6u
16
+ ··· − 11u + 1
12
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 15y
17
+ ··· − 18y + 1
c
2
, c
5
y
18
+ 7y
17
+ ··· + 14y + 1
c
3
y
18
− 6y
17
+ ··· + 5y + 1
c
4
, c
10
y
18
+ 13y
17
+ ··· + 8y + 1
c
6
, c
9
y
18
+ 13y
17
+ ··· + 8y + 1
c
7
, c
11
y
18
+ 17y
17
+ ··· + 132y + 16
c
8
y
18
+ 9y
17
+ ··· + 9386y + 3249
c
12
y
18
− 12y
17
+ ··· − 81y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.240870 + 0.978943I
a = −1.25541 − 2.83197I
b = −0.21177 + 1.92601I
−3.86342 − 2.53444I −6.00075 + 4.97918I
u = −0.240870 − 0.978943I
a = −1.25541 + 2.83197I
b = −0.21177 − 1.92601I
−3.86342 + 2.53444I −6.00075 − 4.97918I
u = −0.765621 + 0.606358I
a = 0.278651 + 1.280040I
b = 1.24023 + 1.62359I
0.23703 − 1.69228I 0.83242 + 2.86969I
u = −0.765621 − 0.606358I
a = 0.278651 − 1.280040I
b = 1.24023 − 1.62359I
0.23703 + 1.69228I 0.83242 − 2.86969I
u = 0.337566 + 0.846099I
a = −0.091147 − 1.262980I
b = 0.939589 + 0.176841I
−2.00038 + 1.54339I −3.04611 − 5.94174I
u = 0.337566 − 0.846099I
a = −0.091147 + 1.262980I
b = 0.939589 − 0.176841I
−2.00038 − 1.54339I −3.04611 + 5.94174I
u = −0.620903 + 1.061930I
a = 1.55504 + 1.96968I
b = 1.56919 − 2.08170I
−1.22831 − 3.61122I −0.22198 + 3.20516I
u = −0.620903 − 1.061930I
a = 1.55504 − 1.96968I
b = 1.56919 + 2.08170I
−1.22831 + 3.61122I −0.22198 − 3.20516I
u = 0.467804 + 1.187440I
a = 0.623317 + 0.856528I
b = −1.323390 + 0.290602I
2.26110 + 5.81595I −4.03162 − 6.52282I
u = 0.467804 − 1.187440I
a = 0.623317 − 0.856528I
b = −1.323390 − 0.290602I
2.26110 − 5.81595I −4.03162 + 6.52282I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.096150 + 0.673790I
a = 0.0129986 − 0.0113203I
b = −0.857327 − 0.140205I
7.53035 + 2.31013I 6.08544 − 2.15566I
u = 1.096150 − 0.673790I
a = 0.0129986 + 0.0113203I
b = −0.857327 + 0.140205I
7.53035 − 2.31013I 6.08544 + 2.15566I
u = 0.199181 + 0.600312I
a = −2.57923 + 3.26705I
b = −0.522876 − 0.873088I
4.82909 − 2.78799I −2.22398 − 0.71537I
u = 0.199181 − 0.600312I
a = −2.57923 − 3.26705I
b = −0.522876 + 0.873088I
4.82909 + 2.78799I −2.22398 + 0.71537I
u = 0.056256 + 0.577327I
a = −0.541472 − 1.074660I
b = 0.797007 − 0.718327I
−2.39405 + 1.36812I −15.0403 − 4.3531I
u = 0.056256 − 0.577327I
a = −0.541472 + 1.074660I
b = 0.797007 + 0.718327I
−2.39405 − 1.36812I −15.0403 + 4.3531I
u = 0.97044 + 1.14952I
a = −0.002747 + 0.847842I
b = −1.130650 + 0.094155I
6.14313 + 5.16446I 2.14687 − 7.70212I
u = 0.97044 − 1.14952I
a = −0.002747 − 0.847842I
b = −1.130650 − 0.094155I
6.14313 − 5.16446I 2.14687 + 7.70212I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
18
− 7u
17
+ ··· − 14u + 1)(u
42
+ 8u
41
+ ··· + 14u + 1)
c
2
(u
18
+ 3u
17
+ ··· + 2u + 1)(u
42
+ 4u
40
+ ··· + 8u + 1)
c
3
(u
18
− 3u
16
+ ··· − 3u + 1)(u
42
+ u
41
+ ··· + 15u + 1)
c
4
(u
18
− u
17
+ ··· − 2u + 1)(u
42
− 3u
40
+ ··· + 3884u + 653)
c
5
(u
18
− 3u
17
+ ··· − 2u + 1)(u
42
+ 4u
40
+ ··· + 8u + 1)
c
6
(u
18
− u
17
+ ··· + 4u
2
+ 1)(u
42
− 2u
41
+ ··· − 1450u + 2881)
c
7
(u
18
− 3u
17
+ ··· − 10u + 4)(u
42
− 2u
41
+ ··· + 102u + 116)
c
8
(u
18
+ u
17
+ ··· + 76u + 57)(u
42
+ 29u
40
+ ··· − 3172u + 968)
c
9
(u
18
+ u
17
+ ··· + 4u
2
+ 1)(u
42
− 2u
41
+ ··· − 1450u + 2881)
c
10
(u
18
+ u
17
+ ··· + 2u + 1)(u
42
− 3u
40
+ ··· + 3884u + 653)
c
11
(u
18
+ 3u
17
+ ··· + 10u + 4)(u
42
− 2u
41
+ ··· + 102u + 116)
c
12
(u
18
− 6u
16
+ ··· − 11u + 1)(u
42
+ u
41
+ ··· + 8821u + 713)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
18
+ 15y
17
+ ··· − 18y + 1)(y
42
+ 60y
41
+ ··· + 106y + 1)
c
2
, c
5
(y
18
+ 7y
17
+ ··· + 14y + 1)(y
42
+ 8y
41
+ ··· + 14y + 1)
c
3
(y
18
− 6y
17
+ ··· + 5y + 1)(y
42
+ 7y
41
+ ··· + 461y + 1)
c
4
, c
10
(y
18
+ 13y
17
+ ··· + 8y + 1)(y
42
− 6y
41
+ ··· − 6058384y + 426409)
c
6
, c
9
(y
18
+ 13y
17
+ ··· + 8y + 1)
· (y
42
+ 54y
41
+ ··· + 123416908y + 8300161)
c
7
, c
11
(y
18
+ 17y
17
+ ··· + 132y + 16)
· (y
42
+ 50y
41
+ ··· + 280292y + 13456)
c
8
(y
18
+ 9y
17
+ ··· + 9386y + 3249)
· (y
42
+ 58y
41
+ ··· − 12741008y + 937024)
c
12
(y
18
− 12y
17
+ ··· − 81y + 1)
· (y
42
− 59y
41
+ ··· − 9108213y + 508369)
18
