12n
0180
(K12n
0180
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 9 12 4 6 5 1 6 11
Solving Sequence
6,12 4,7
8 9 3 5 2 11 1 10
c
6
c
7
c
8
c
3
c
5
c
2
c
11
c
12
c
10
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h8.59216 × 10
59
u
59
+ 7.11341 × 10
60
u
58
+ ··· + 2.71076 × 10
61
b + 6.33557 × 10
61
,
− 2.02586 × 10
62
u
59
− 3.30298 × 10
62
u
58
+ ··· + 4.60829 × 10
62
a − 1.81464 × 10
63
,
u
60
+ 3u
59
+ ··· + 12u + 17i
I
u
2
= h−51u
3
a
2
+ 106u
3
a + ··· − 80a − 21,
− 2u
3
a
2
− 2a
2
u
2
+ u
3
a + a
3
+ a
2
u + 2u
2
a + 6u
3
+ 2a
2
− 3au + 9u
2
− 2a + 2u − 2, u
4
− u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 72 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
= h8.59 × 10
59
u
59
+ 7.11 × 10
60
u
58
+ · · · + 2.71 × 10
61
b + 6.34 ×
10
61
, −2.03 × 10
62
u
59
− 3.30 × 10
62
u
58
+ · · · + 4.61 × 10
62
a − 1.81 ×
10
63
, u
60
+ 3u
59
+ · · · + 12u + 17i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
4
=
0.439611u
59
+ 0.716748u
58
+ ··· − 0.813297u + 3.93778
−0.0316965u
59
− 0.262414u
58
+ ··· + 4.37519u − 2.33720
a
7
=
1
−u
2
a
8
=
0.0820681u
59
+ 0.302588u
58
+ ··· − 10.8701u − 5.50752
−0.0713087u
59
− 0.287800u
58
+ ··· + 3.92724u + 1.83826
a
9
=
0.153377u
59
+ 0.590388u
58
+ ··· − 14.7973u − 7.34578
−0.0713087u
59
− 0.287800u
58
+ ··· + 3.92724u + 1.83826
a
3
=
0.106413u
59
+ 0.119118u
58
+ ··· − 4.94013u − 3.96049
0.0147849u
59
+ 0.000149588u
58
+ ··· + 3.53440u + 4.49621
a
5
=
−0.313827u
59
− 0.803067u
58
+ ··· + 2.00850u − 0.850375
−0.0119731u
59
− 0.0516958u
58
+ ··· + 2.55197u + 2.41305
a
2
=
0.111888u
59
+ 0.442512u
58
+ ··· − 5.49722u − 3.98640
0.0511739u
59
+ 0.197997u
58
+ ··· − 3.04177u + 1.75645
a
11
=
−u
u
a
1
=
u
3
−u
3
+ u
a
10
=
−u
5
− u
u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.359408u
59
+ 0.109275u
58
+ ··· + 23.9102u + 7.48289
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
60
+ 35u
59
+ ··· + 64u + 1
c
2
, c
4
u
60
− 5u
59
+ ··· − 16u + 1
c
3
, c
7
u
60
− u
59
+ ··· − 4u + 1
c
5
, c
8
, c
9
u
60
− 3u
59
+ ··· − 154u + 49
c
6
, c
11
u
60
− 3u
59
+ ··· − 12u + 17
c
10
, c
12
u
60
− 17u
59
+ ··· − 2558u + 289
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
60
− 15y
59
+ ··· + 2064y + 1
c
2
, c
4
y
60
− 35y
59
+ ··· − 64y + 1
c
3
, c
7
y
60
− 15y
59
+ ··· − 40y + 1
c
5
, c
8
, c
9
y
60
+ 21y
59
+ ··· + 34104y + 2401
c
6
, c
11
y
60
− 17y
59
+ ··· − 2558y + 289
c
10
, c
12
y
60
+ 59y
59
+ ··· − 725794y + 83521
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.929012 + 0.409111I
a = −3.04269 + 1.15379I
b = 2.59631 + 1.09970I
−0.23119 + 1.94297I −2.05685 − 11.08290I
u = 0.929012 − 0.409111I
a = −3.04269 − 1.15379I
b = 2.59631 − 1.09970I
−0.23119 − 1.94297I −2.05685 + 11.08290I
u = −0.832822 + 0.587944I
a = −1.21567 − 1.08428I
b = 0.069828 − 1.012120I
3.25865 + 0.70404I −1.90677 + 0.77167I
u = −0.832822 − 0.587944I
a = −1.21567 + 1.08428I
b = 0.069828 + 1.012120I
3.25865 − 0.70404I −1.90677 − 0.77167I
u = 0.004950 + 1.024030I
a = 0.183534 − 0.050087I
b = 0.740563 − 0.693298I
−3.25466 − 4.08265I −4.68553 + 7.94094I
u = 0.004950 − 1.024030I
a = 0.183534 + 0.050087I
b = 0.740563 + 0.693298I
−3.25466 + 4.08265I −4.68553 − 7.94094I
u = −0.822970 + 0.630204I
a = 1.54004 + 1.13008I
b = −0.133459 + 1.061150I
3.19637 − 5.46860I −1.43660 + 7.42023I
u = −0.822970 − 0.630204I
a = 1.54004 − 1.13008I
b = −0.133459 − 1.061150I
3.19637 + 5.46860I −1.43660 − 7.42023I
u = 0.809567 + 0.501021I
a = −5.62494 − 3.66221I
b = −0.98200 + 6.14395I
−0.08137 + 2.05589I 27.6617 + 22.2084I
u = 0.809567 − 0.501021I
a = −5.62494 + 3.66221I
b = −0.98200 − 6.14395I
−0.08137 − 2.05589I 27.6617 − 22.2084I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.006930 + 0.332122I
a = −1.315940 − 0.433014I
b = 0.99469 − 1.18965I
0.04819 − 3.77072I 0.50249 + 5.64131I
u = −1.006930 − 0.332122I
a = −1.315940 + 0.433014I
b = 0.99469 + 1.18965I
0.04819 + 3.77072I 0.50249 − 5.64131I
u = −1.079450 + 0.120285I
a = −1.043550 − 0.134913I
b = 0.563555 − 0.123402I
1.73585 − 0.04165I 7.02929 − 1.55117I
u = −1.079450 − 0.120285I
a = −1.043550 + 0.134913I
b = 0.563555 + 0.123402I
1.73585 + 0.04165I 7.02929 + 1.55117I
u = −0.931671 + 0.569277I
a = 0.339977 + 1.097140I
b = −0.986373 − 0.325235I
1.83197 − 2.08769I 7.31144 + 2.76134I
u = −0.931671 − 0.569277I
a = 0.339977 − 1.097140I
b = −0.986373 + 0.325235I
1.83197 + 2.08769I 7.31144 − 2.76134I
u = 1.085650 + 0.220553I
a = 2.03983 + 0.42897I
b = −1.19988 − 0.96562I
3.75827 + 4.28418I 7.39769 − 5.27258I
u = 1.085650 − 0.220553I
a = 2.03983 − 0.42897I
b = −1.19988 + 0.96562I
3.75827 − 4.28418I 7.39769 + 5.27258I
u = −0.758636 + 0.887275I
a = −0.340815 − 0.278642I
b = −0.78502 − 1.49028I
−3.82130 + 3.76339I 0
u = −0.758636 − 0.887275I
a = −0.340815 + 0.278642I
b = −0.78502 + 1.49028I
−3.82130 − 3.76339I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.802241 + 0.075713I
a = 2.17404 − 1.63873I
b = −0.323287 + 0.783361I
6.00487 − 2.27473I 9.19193 + 3.71392I
u = 0.802241 − 0.075713I
a = 2.17404 + 1.63873I
b = −0.323287 − 0.783361I
6.00487 + 2.27473I 9.19193 − 3.71392I
u = 0.879342 + 0.837979I
a = −0.176337 − 0.434177I
b = 0.073200 − 0.870222I
−4.62872 + 2.55229I 0
u = 0.879342 − 0.837979I
a = −0.176337 + 0.434177I
b = 0.073200 + 0.870222I
−4.62872 − 2.55229I 0
u = −0.715460 + 0.984773I
a = 0.344792 + 0.130176I
b = 1.03109 + 1.53314I
−7.75605 + 9.32324I 0
u = −0.715460 − 0.984773I
a = 0.344792 − 0.130176I
b = 1.03109 − 1.53314I
−7.75605 − 9.32324I 0
u = 0.830973 + 0.892744I
a = 1.215320 − 0.601098I
b = 0.180459 − 0.790574I
−8.14977 − 1.83674I 0
u = 0.830973 − 0.892744I
a = 1.215320 + 0.601098I
b = 0.180459 + 0.790574I
−8.14977 + 1.83674I 0
u = −0.792660 + 0.936246I
a = −0.092647 − 0.224921I
b = −0.210710 + 0.159454I
0.10426 − 3.90855I 0
u = −0.792660 − 0.936246I
a = −0.092647 + 0.224921I
b = −0.210710 − 0.159454I
0.10426 + 3.90855I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.929150 + 0.821763I
a = −1.301880 + 0.509111I
b = 0.142826 + 0.827123I
−4.47334 + 3.63985I 0
u = 0.929150 − 0.821763I
a = −1.301880 − 0.509111I
b = 0.142826 − 0.827123I
−4.47334 − 3.63985I 0
u = −0.880329 + 0.874378I
a = 0.520777 + 0.321136I
b = 0.56993 + 1.71766I
−8.33406 − 1.51336I 0
u = −0.880329 − 0.874378I
a = 0.520777 − 0.321136I
b = 0.56993 − 1.71766I
−8.33406 + 1.51336I 0
u = −0.703326 + 0.228376I
a = 1.271670 + 0.570807I
b = −0.813961 + 0.932874I
1.22817 − 0.90691I 4.10313 − 1.08221I
u = −0.703326 − 0.228376I
a = 1.271670 − 0.570807I
b = −0.813961 − 0.932874I
1.22817 + 0.90691I 4.10313 + 1.08221I
u = 1.228280 + 0.305750I
a = −1.68849 − 0.21445I
b = 1.32261 + 0.91261I
1.11802 + 8.63012I 0
u = 1.228280 − 0.305750I
a = −1.68849 + 0.21445I
b = 1.32261 − 0.91261I
1.11802 − 8.63012I 0
u = −0.945860 + 0.847488I
a = −1.70802 − 0.90011I
b = 0.58276 − 1.79431I
−8.12673 − 4.86921I 0
u = −0.945860 − 0.847488I
a = −1.70802 + 0.90011I
b = 0.58276 + 1.79431I
−8.12673 + 4.86921I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.986055 + 0.828942I
a = 0.073132 + 0.599164I
b = 0.121967 + 0.888675I
−7.66022 + 8.21302I 0
u = 0.986055 − 0.828942I
a = 0.073132 − 0.599164I
b = 0.121967 − 0.888675I
−7.66022 − 8.21302I 0
u = −1.021020 + 0.788235I
a = 1.76694 + 0.84443I
b = −0.88862 + 1.59075I
−3.00183 − 9.98439I 0
u = −1.021020 − 0.788235I
a = 1.76694 − 0.84443I
b = −0.88862 − 1.59075I
−3.00183 + 9.98439I 0
u = 0.829095 + 0.994657I
a = 0.002787 + 0.308797I
b = −0.202360 + 1.091070I
−9.58964 − 1.76558I 0
u = 0.829095 − 0.994657I
a = 0.002787 − 0.308797I
b = −0.202360 − 1.091070I
−9.58964 + 1.76558I 0
u = 0.530933 + 0.444057I
a = −0.119018 + 0.649917I
b = 0.495359 − 0.792874I
−1.52903 + 1.30429I −5.12625 − 3.74177I
u = 0.530933 − 0.444057I
a = −0.119018 − 0.649917I
b = 0.495359 + 0.792874I
−1.52903 − 1.30429I −5.12625 + 3.74177I
u = −1.160010 + 0.608816I
a = 0.545323 + 0.459676I
b = −0.612716 + 0.220527I
1.59454 − 2.41033I 0
u = −1.160010 − 0.608816I
a = 0.545323 − 0.459676I
b = −0.612716 − 0.220527I
1.59454 + 2.41033I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.643557 + 0.178198I
a = −2.12674 + 2.04600I
b = −0.025888 − 0.650354I
5.29698 + 3.34950I 6.77983 − 1.21808I
u = 0.643557 − 0.178198I
a = −2.12674 − 2.04600I
b = −0.025888 + 0.650354I
5.29698 − 3.34950I 6.77983 + 1.21808I
u = −1.083150 + 0.804487I
a = −1.74237 − 0.78537I
b = 1.12860 − 1.67159I
−6.5812 − 15.8690I 0
u = −1.083150 − 0.804487I
a = −1.74237 + 0.78537I
b = 1.12860 + 1.67159I
−6.5812 + 15.8690I 0
u = 1.039460 + 0.875271I
a = 1.252010 − 0.411170I
b = −0.250076 − 1.144770I
−8.90185 + 8.59101I 0
u = 1.039460 − 0.875271I
a = 1.252010 + 0.411170I
b = −0.250076 + 1.144770I
−8.90185 − 8.59101I 0
u = −0.069054 + 0.554266I
a = −0.493891 + 0.277556I
b = −0.601970 + 0.652027I
0.13598 − 1.52625I 0.94008 + 4.56682I
u = −0.069054 − 0.554266I
a = −0.493891 − 0.277556I
b = −0.601970 − 0.652027I
0.13598 + 1.52625I 0.94008 − 4.56682I
u = −0.224940 + 0.509809I
a = 2.05694 + 0.80981I
b = 0.902556 + 0.301696I
−2.40873 + 0.49788I −3.19283 + 1.76670I
u = −0.224940 − 0.509809I
a = 2.05694 − 0.80981I
b = 0.902556 − 0.301696I
−2.40873 − 0.49788I −3.19283 − 1.76670I
10
II.
I
u
2
= h−51u
3
a
2
+106u
3
a+· · ·−80a−21, −2u
3
a
2
+u
3
a+· · ·−2a−2, u
4
−u
2
+1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
4
=
a
0.111597a
2
u
3
− 0.231947au
3
+ ··· + 0.175055a + 0.0459519
a
7
=
1
−u
2
a
8
=
0.391685a
2
u
3
+ 0.166302au
3
+ ··· + 0.00656455a − 0.485777
u
3
a
9
=
0.391685a
2
u
3
+ 0.166302au
3
+ ··· + 0.00656455a − 0.485777
u
3
a
3
=
−0.111597a
2
u
3
+ 0.231947au
3
+ ··· + 0.824945a − 0.0459519
0.0656455a
2
u
3
− 0.312910au
3
+ ··· − 0.367615a + 0.203501
a
5
=
0.306346a
2
u
3
− 0.126915au
3
+ ··· + 0.284464a − 1.05033
1
a
2
=
0.256018a
2
u
3
− 0.120350au
3
+ ··· + 0.166302a − 0.306346
−0.256018a
2
u
3
+ 0.120350au
3
+ ··· − 0.166302a + 0.306346
a
11
=
−u
u
a
1
=
u
3
−u
3
+ u
a
10
=
−u
3
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
588
457
u
3
a
2
+
272
457
a
2
u
2
+
792
457
u
3
a +
400
457
a
2
u +
44
457
u
2
a −
112
457
u
3
−
384
457
a
2
−
688
457
au −
1428
457
u
2
+
368
457
a +
1556
457
u +
2016
457
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
− u
2
+ 2u − 1)
4
c
2
(u
3
+ u
2
− 1)
4
c
3
, c
7
(u
6
− 3u
4
+ 2u
2
+ 1)
2
c
4
(u
3
− u
2
+ 1)
4
c
5
, c
8
, c
9
(u
2
+ 1)
6
c
6
, c
11
(u
4
− u
2
+ 1)
3
c
10
(u
2
+ u + 1)
6
c
12
(u
2
− u + 1)
6
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
+ 3y
2
+ 2y −1)
4
c
2
, c
4
(y
3
− y
2
+ 2y −1)
4
c
3
, c
7
(y
3
− 3y
2
+ 2y + 1)
4
c
5
, c
8
, c
9
(y + 1)
12
c
6
, c
11
(y
2
− y + 1)
6
c
10
, c
12
(y
2
+ y + 1)
6
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 1.79596 − 0.63842I
b = −0.14373 − 1.45121I
4.66906 − 0.79824I 5.50976 − 0.48465I
u = 0.866025 + 0.500000I
a = −2.29105 + 0.88075I
b = 0.60113 + 1.32865I
4.66906 + 4.85801I 5.50976 − 6.44355I
u = 0.866025 + 0.500000I
a = −1.37094 + 2.98973I
b = 3.27465 − 0.87744I
0.53148 + 2.02988I −1.01951 − 3.46410I
u = 0.866025 − 0.500000I
a = 1.79596 + 0.63842I
b = −0.14373 + 1.45121I
4.66906 + 0.79824I 5.50976 + 0.48465I
u = 0.866025 − 0.500000I
a = −2.29105 − 0.88075I
b = 0.60113 − 1.32865I
4.66906 − 4.85801I 5.50976 + 6.44355I
u = 0.866025 − 0.500000I
a = −1.37094 − 2.98973I
b = 3.27465 + 0.87744I
0.53148 − 2.02988I −1.01951 + 3.46410I
u = −0.866025 + 0.500000I
a = −0.383943 − 0.049811I
b = 0.235109 − 0.877439I
0.53148 − 2.02988I −1.01951 + 3.46410I
u = −0.866025 + 0.500000I
a = 0.87835 + 1.41333I
b = −0.356011 − 0.161073I
4.66906 − 4.85801I 5.50976 + 6.44355I
u = −0.866025 + 0.500000I
a = −0.62838 − 1.59557I
b = 0.388851 + 0.038512I
4.66906 + 0.79824I 5.50976 + 0.48465I
u = −0.866025 − 0.500000I
a = −0.383943 + 0.049811I
b = 0.235109 + 0.877439I
0.53148 + 2.02988I −1.01951 − 3.46410I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.866025 − 0.500000I
a = 0.87835 − 1.41333I
b = −0.356011 + 0.161073I
4.66906 + 4.85801I 5.50976 − 6.44355I
u = −0.866025 − 0.500000I
a = −0.62838 + 1.59557I
b = 0.388851 − 0.038512I
4.66906 − 0.79824I 5.50976 − 0.48465I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
− u
2
+ 2u − 1)
4
)(u
60
+ 35u
59
+ ··· + 64u + 1)
c
2
((u
3
+ u
2
− 1)
4
)(u
60
− 5u
59
+ ··· − 16u + 1)
c
3
, c
7
((u
6
− 3u
4
+ 2u
2
+ 1)
2
)(u
60
− u
59
+ ··· − 4u + 1)
c
4
((u
3
− u
2
+ 1)
4
)(u
60
− 5u
59
+ ··· − 16u + 1)
c
5
, c
8
, c
9
((u
2
+ 1)
6
)(u
60
− 3u
59
+ ··· − 154u + 49)
c
6
, c
11
((u
4
− u
2
+ 1)
3
)(u
60
− 3u
59
+ ··· − 12u + 17)
c
10
((u
2
+ u + 1)
6
)(u
60
− 17u
59
+ ··· − 2558u + 289)
c
12
((u
2
− u + 1)
6
)(u
60
− 17u
59
+ ··· − 2558u + 289)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
3
+ 3y
2
+ 2y −1)
4
)(y
60
− 15y
59
+ ··· + 2064y + 1)
c
2
, c
4
((y
3
− y
2
+ 2y −1)
4
)(y
60
− 35y
59
+ ··· − 64y + 1)
c
3
, c
7
((y
3
− 3y
2
+ 2y + 1)
4
)(y
60
− 15y
59
+ ··· − 40y + 1)
c
5
, c
8
, c
9
((y + 1)
12
)(y
60
+ 21y
59
+ ··· + 34104y + 2401)
c
6
, c
11
((y
2
− y + 1)
6
)(y
60
− 17y
59
+ ··· − 2558y + 289)
c
10
, c
12
((y
2
+ y + 1)
6
)(y
60
+ 59y
59
+ ··· − 725794y + 83521)
17
