12n
0593
(K12n
0593
)
A knot diagram
1
Linearized knot diagam
3 7 11 7 10 2 4 12 3 5 9 8
Solving Sequence
9,11 4,12
3 8 1 7 5 2 6 10
c
11
c
3
c
8
c
12
c
7
c
4
c
2
c
6
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.56874 × 10
31
u
44
+ 1.26158 × 10
34
u
43
+ ··· + 1.98880 × 10
34
b − 6.49981 × 10
34
,
− 7.56930 × 10
33
u
44
− 2.14961 × 10
35
u
43
+ ··· + 1.39216 × 10
35
a + 1.06952 × 10
36
,
u
45
+ 18u
43
+ ··· + 19u − 7i
I
u
2
= hu
13
+ u
12
+ 6u
11
+ 5u
10
+ 12u
9
+ 8u
8
+ 6u
7
+ 3u
6
− 7u
5
− 2u
4
− 5u
3
− u
2
+ b + 2u,
− 2u
14
− 2u
13
− 14u
12
− 11u
11
− 36u
10
− 21u
9
− 37u
8
− 15u
7
− 4u
6
− 5u
5
+ 14u
4
− 7u
3
+ 4u
2
+ a − 4u,
u
15
+ u
14
+ 8u
13
+ 7u
12
+ 25u
11
+ 19u
10
+ 36u
9
+ 24u
8
+ 18u
7
+ 13u
6
− 8u
5
+ 2u
4
− 7u
3
+ u
2
+ 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−3.57 × 10
31
u
44
+ 1.26 × 10
34
u
43
+ · · · + 1.99 × 10
34
b − 6.50 ×
10
34
, −7.57 × 10
33
u
44
− 2.15 × 10
35
u
43
+ · · · + 1.39 × 10
35
a + 1.07 ×
10
36
, u
45
+ 18u
43
+ · · · + 19u − 7i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
4
=
0.0543710u
44
+ 1.54408u
43
+ ··· + 25.1156u − 7.68247
0.00179442u
44
− 0.634340u
43
+ ··· − 9.30054u + 3.26821
a
12
=
1
u
2
a
3
=
0.0561654u
44
+ 0.909740u
43
+ ··· + 15.8151u − 4.41426
0.00179442u
44
− 0.634340u
43
+ ··· − 9.30054u + 3.26821
a
8
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
7
=
0.358819u
44
− 0.964669u
43
+ ··· − 26.2905u + 8.77144
−0.420878u
44
+ 0.770220u
43
+ ··· + 18.2959u − 5.48848
a
5
=
0.0890726u
44
+ 2.49598u
43
+ ··· + 43.3584u − 17.2410
0.753177u
44
− 0.733270u
43
+ ··· − 18.9174u + 5.28417
a
2
=
−1.09866u
44
+ 3.02308u
43
+ ··· + 57.4402u − 18.2187
0.664157u
44
− 0.175210u
43
+ ··· − 7.32914u + 0.757240
a
6
=
−1.21775u
44
+ 2.63075u
43
+ ··· + 45.0187u − 14.3526
1.28859u
44
− 0.261761u
43
+ ··· − 11.5685u + 2.33427
a
10
=
−2.87696u
44
− 1.48285u
43
+ ··· − 5.99600u + 8.64539
0.352943u
44
+ 0.731911u
43
+ ··· + 12.7349u − 5.07045
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.911134u
44
+ 1.98306u
43
+ ··· + 48.6124u − 24.1982
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
45
+ 56u
44
+ ··· + 603838u + 78961
c
2
, c
6
u
45
− 28u
43
+ ··· + 1642u − 281
c
3
u
45
+ 3u
44
+ ··· + 25u + 5
c
4
, c
7
u
45
+ 5u
44
+ ··· + 23u + 1
c
5
, c
10
u
45
− u
44
+ ··· + 383u + 77
c
8
, c
11
, c
12
u
45
+ 18u
43
+ ··· + 19u − 7
c
9
u
45
+ 4u
44
+ ··· + 14063662u − 7404196
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
45
− 120y
44
+ ··· − 392839435230y −6234839521
c
2
, c
6
y
45
− 56y
44
+ ··· + 603838y −78961
c
3
y
45
− y
44
+ ··· + 595y −25
c
4
, c
7
y
45
+ 45y
44
+ ··· + 173y −1
c
5
, c
10
y
45
+ 3y
44
+ ··· + 136371y −5929
c
8
, c
11
, c
12
y
45
+ 36y
44
+ ··· − 157y −49
c
9
y
45
− 28y
44
+ ··· + 252875184270700y −54822118406416
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.008740 + 0.105187I
a = −0.793375 + 0.421615I
b = −1.17957 − 1.05675I
−12.4412 − 8.8186I −11.24074 + 4.62166I
u = 1.008740 − 0.105187I
a = −0.793375 − 0.421615I
b = −1.17957 + 1.05675I
−12.4412 + 8.8186I −11.24074 − 4.62166I
u = −0.386406 + 0.901026I
a = 0.972143 − 0.261563I
b = −0.853990 − 0.224349I
−1.53875 + 2.61522I −10.52840 − 2.22098I
u = −0.386406 − 0.901026I
a = 0.972143 + 0.261563I
b = −0.853990 + 0.224349I
−1.53875 − 2.61522I −10.52840 + 2.22098I
u = −0.973608 + 0.085974I
a = −0.651872 + 0.166835I
b = −1.12732 − 1.18722I
−12.05690 + 0.39267I −11.73771 − 0.23193I
u = −0.973608 − 0.085974I
a = −0.651872 − 0.166835I
b = −1.12732 + 1.18722I
−12.05690 − 0.39267I −11.73771 + 0.23193I
u = 0.059330 + 1.065280I
a = 2.12098 − 2.58813I
b = 0.090245 + 1.168500I
4.60968 − 0.45678I −4.72300 − 1.28970I
u = 0.059330 − 1.065280I
a = 2.12098 + 2.58813I
b = 0.090245 − 1.168500I
4.60968 + 0.45678I −4.72300 + 1.28970I
u = 0.114676 + 1.068030I
a = 0.114025 + 0.194088I
b = 1.033700 + 0.324573I
0.63009 − 3.63899I −6.69888 + 4.56263I
u = 0.114676 − 1.068030I
a = 0.114025 − 0.194088I
b = 1.033700 − 0.324573I
0.63009 + 3.63899I −6.69888 − 4.56263I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.07704
a = −0.250717
b = −0.595129
−5.84338 −27.3640
u = −0.759699 + 0.408323I
a = 0.154012 + 0.433176I
b = 0.747946 − 0.618927I
−2.98722 + 1.75252I −12.73751 − 3.21228I
u = −0.759699 − 0.408323I
a = 0.154012 − 0.433176I
b = 0.747946 + 0.618927I
−2.98722 − 1.75252I −12.73751 + 3.21228I
u = 0.847403
a = −1.81130
b = −0.770728
−6.54062 −18.4620
u = −0.130385 + 1.145750I
a = −0.383923 − 0.931720I
b = −0.511829 + 0.522136I
2.58249 + 1.78836I −4.62276 − 3.94731I
u = −0.130385 − 1.145750I
a = −0.383923 + 0.931720I
b = −0.511829 − 0.522136I
2.58249 − 1.78836I −4.62276 + 3.94731I
u = 0.288094 + 1.183980I
a = −0.40323 + 3.10896I
b = −0.594143 − 0.715509I
0.14683 − 6.35148I −6.06536 + 8.65205I
u = 0.288094 − 1.183980I
a = −0.40323 − 3.10896I
b = −0.594143 + 0.715509I
0.14683 + 6.35148I −6.06536 − 8.65205I
u = −0.072450 + 1.292850I
a = −1.19970 + 1.90753I
b = 0.303712 − 0.219752I
3.92457 + 2.86801I 0. − 4.92967I
u = −0.072450 − 1.292850I
a = −1.19970 − 1.90753I
b = 0.303712 + 0.219752I
3.92457 − 2.86801I 0. + 4.92967I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.114422 + 1.323690I
a = 0.257409 − 0.903828I
b = −1.119530 + 0.548161I
1.39290 + 0.75681I 0
u = 0.114422 − 1.323690I
a = 0.257409 + 0.903828I
b = −1.119530 − 0.548161I
1.39290 − 0.75681I 0
u = 0.386963 + 1.277220I
a = 1.013090 − 0.512275I
b = 0.784008 − 0.030215I
−2.57080 − 4.43171I 0
u = 0.386963 − 1.277220I
a = 1.013090 + 0.512275I
b = 0.784008 + 0.030215I
−2.57080 + 4.43171I 0
u = −0.516771 + 1.244220I
a = 0.81944 + 1.89768I
b = 1.07051 − 1.15978I
−8.49081 + 4.89195I 0
u = −0.516771 − 1.244220I
a = 0.81944 − 1.89768I
b = 1.07051 + 1.15978I
−8.49081 − 4.89195I 0
u = 0.569830 + 1.241570I
a = −0.734691 + 0.190323I
b = 1.15852 − 1.01628I
−8.96525 + 3.25529I 0
u = 0.569830 − 1.241570I
a = −0.734691 − 0.190323I
b = 1.15852 + 1.01628I
−8.96525 − 3.25529I 0
u = 0.205740 + 1.371440I
a = −0.63512 + 1.75657I
b = −0.338407 − 1.348220I
8.00276 − 3.83937I 0
u = 0.205740 − 1.371440I
a = −0.63512 − 1.75657I
b = −0.338407 + 1.348220I
8.00276 + 3.83937I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.550103 + 1.293590I
a = 0.059859 + 0.501110I
b = 0.624990 − 0.274138I
−1.88022 + 5.73606I 0
u = −0.550103 − 1.293590I
a = 0.059859 − 0.501110I
b = 0.624990 + 0.274138I
−1.88022 − 5.73606I 0
u = 0.582077 + 0.106172I
a = 1.27394 + 1.42446I
b = 0.829596 − 0.667678I
−3.07621 + 3.07145I −13.51053 − 3.59920I
u = 0.582077 − 0.106172I
a = 1.27394 − 1.42446I
b = 0.829596 + 0.667678I
−3.07621 − 3.07145I −13.51053 + 3.59920I
u = −0.45273 + 1.36982I
a = −1.002820 − 0.419354I
b = 1.17560 + 1.20040I
−7.48754 + 5.49061I 0
u = −0.45273 − 1.36982I
a = −1.002820 + 0.419354I
b = 1.17560 − 1.20040I
−7.48754 − 5.49061I 0
u = 0.471958 + 0.271253I
a = 0.837882 + 0.291023I
b = 0.128615 + 1.136710I
2.86451 − 1.30518I −1.84549 + 5.31752I
u = 0.471958 − 0.271253I
a = 0.837882 − 0.291023I
b = 0.128615 − 1.136710I
2.86451 + 1.30518I −1.84549 − 5.31752I
u = 0.46756 + 1.38448I
a = 0.47175 − 1.91674I
b = 1.18172 + 1.08384I
−7.7658 − 14.0813I 0
u = 0.46756 − 1.38448I
a = 0.47175 + 1.91674I
b = 1.18172 − 1.08384I
−7.7658 + 14.0813I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22570 + 1.49863I
a = 0.21030 − 1.42436I
b = −0.691548 + 0.992057I
3.35542 + 5.28363I 0
u = −0.22570 − 1.49863I
a = 0.21030 + 1.42436I
b = −0.691548 − 0.992057I
3.35542 − 5.28363I 0
u = 0.094137 + 0.391258I
a = 2.78827 − 0.14083I
b = −0.752412 + 0.154261I
−1.06912 + 2.39494I −7.24233 + 0.84783I
u = 0.094137 − 0.391258I
a = 2.78827 + 0.14083I
b = −0.752412 − 0.154261I
−1.06912 − 2.39494I −7.24233 − 0.84783I
u = −0.361714
a = 0.913846
b = 0.445021
−0.670926 −14.8180
9
II.
I
u
2
= hu
13
+u
12
+· · ·+b+2u, −2u
14
−2u
13
+· · ·+a−4u, u
15
+u
14
+· · ·+2u+1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
4
=
2u
14
+ 2u
13
+ ··· − 4u
2
+ 4u
−u
13
− u
12
+ ··· + u
2
− 2u
a
12
=
1
u
2
a
3
=
2u
14
+ u
13
+ ··· − 3u
2
+ 2u
−u
13
− u
12
+ ··· + u
2
− 2u
a
8
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
7
=
u
14
+ 2u
13
+ ··· + 4u − 2
u
14
+ u
13
+ ··· + 2u + 1
a
5
=
3u
13
+ 2u
12
+ ··· + 2u − 1
u
10
+ u
9
+ 5u
8
+ 4u
7
+ 8u
6
+ 5u
5
+ 3u
4
+ 2u
3
− 2u
2
+ u
a
2
=
2u
14
+ 3u
13
+ ··· + u + 2
−u
14
− 2u
13
+ ··· − 3u − 1
a
6
=
−2u
14
− 3u
13
+ ··· − 2u − 2
u
14
+ 2u
13
+ ··· + 3u + 1
a
10
=
−2u
14
− u
13
+ ··· + 4u + 1
−u
13
− u
12
− 7u
11
− 6u
10
− 18u
9
− 13u
8
− 18u
7
− 11u
6
− 2u
4
+ 8u
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
14
+ u
13
− 10u
12
+ 4u
11
− 35u
10
+ 4u
9
− 50u
8
− 3u
7
− 11u
6
−
12u
5
+ 36u
4
− 19u
3
+ 18u
2
− 10u − 12
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 13u
14
+ ··· + 9u − 1
c
2
u
15
− u
14
+ ··· + 3u − 1
c
3
u
15
− 2u
14
+ ··· + 5u
2
− 1
c
4
u
15
+ 2u
14
+ ··· − 4u
2
− 1
c
5
u
15
+ 7u
13
+ ··· + 3u
2
+ 1
c
6
u
15
+ u
14
+ ··· + 3u + 1
c
7
u
15
− 2u
14
+ ··· + 4u
2
+ 1
c
8
u
15
− u
14
+ ··· + 2u − 1
c
9
u
15
+ 5u
14
+ ··· − 10u + 52
c
10
u
15
+ 7u
13
+ ··· − 3u
2
− 1
c
11
, c
12
u
15
+ u
14
+ ··· + 2u + 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
− 9y
14
+ ··· − 7y −1
c
2
, c
6
y
15
− 13y
14
+ ··· + 9y −1
c
3
y
15
+ 6y
14
+ ··· + 10y −1
c
4
, c
7
y
15
+ 8y
14
+ ··· − 8y −1
c
5
, c
10
y
15
+ 14y
14
+ ··· − 6y −1
c
8
, c
11
, c
12
y
15
+ 15y
14
+ ··· + 2y −1
c
9
y
15
+ 7y
14
+ ··· − 5828y −2704
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.957819
a = −0.661926
b = −0.464046
−5.43240 −5.96330
u = 0.170684 + 1.191940I
a = 1.99278 − 2.50947I
b = −0.224051 + 0.994213I
4.95411 − 1.54403I −1.95869 + 3.90888I
u = 0.170684 − 1.191940I
a = 1.99278 + 2.50947I
b = −0.224051 − 0.994213I
4.95411 + 1.54403I −1.95869 − 3.90888I
u = −0.065754 + 1.280360I
a = −0.214962 + 0.173404I
b = −1.132550 − 0.235968I
2.00576 − 2.03853I −5.38866 + 3.46155I
u = −0.065754 − 1.280360I
a = −0.214962 − 0.173404I
b = −1.132550 + 0.235968I
2.00576 + 2.03853I −5.38866 − 3.46155I
u = −0.438447 + 1.226120I
a = 0.397262 − 0.091676I
b = 0.546264 − 0.057068I
−1.69926 + 4.99019I −7.83136 − 3.68033I
u = −0.438447 − 1.226120I
a = 0.397262 + 0.091676I
b = 0.546264 + 0.057068I
−1.69926 − 4.99019I −7.83136 + 3.68033I
u = 0.574249 + 0.201778I
a = −0.090007 + 0.468927I
b = 0.257595 + 1.314620I
2.04734 − 1.06098I −12.25326 + 1.45022I
u = 0.574249 − 0.201778I
a = −0.090007 − 0.468927I
b = 0.257595 − 1.314620I
2.04734 + 1.06098I −12.25326 − 1.45022I
u = 0.227689 + 1.394080I
a = −0.46823 + 1.79191I
b = −0.35742 − 1.57983I
7.19370 − 4.01988I −7.47475 + 4.21701I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.227689 − 1.394080I
a = −0.46823 − 1.79191I
b = −0.35742 + 1.57983I
7.19370 + 4.01988I −7.47475 − 4.21701I
u = −0.17862 + 1.44151I
a = 0.40873 − 1.60438I
b = −0.707302 + 0.825528I
4.37895 + 5.24684I −1.49909 − 5.49903I
u = −0.17862 − 1.44151I
a = 0.40873 + 1.60438I
b = −0.707302 − 0.825528I
4.37895 − 5.24684I −1.49909 + 5.49903I
u = −0.310890 + 0.262705I
a = −0.69461 + 2.22045I
b = 0.849487 − 0.449404I
−1.36000 + 3.17848I −10.11254 − 7.00555I
u = −0.310890 − 0.262705I
a = −0.69461 − 2.22045I
b = 0.849487 + 0.449404I
−1.36000 − 3.17848I −10.11254 + 7.00555I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
15
− 13u
14
+ ··· + 9u − 1)(u
45
+ 56u
44
+ ··· + 603838u + 78961)
c
2
(u
15
− u
14
+ ··· + 3u − 1)(u
45
− 28u
43
+ ··· + 1642u − 281)
c
3
(u
15
− 2u
14
+ ··· + 5u
2
− 1)(u
45
+ 3u
44
+ ··· + 25u + 5)
c
4
(u
15
+ 2u
14
+ ··· − 4u
2
− 1)(u
45
+ 5u
44
+ ··· + 23u + 1)
c
5
(u
15
+ 7u
13
+ ··· + 3u
2
+ 1)(u
45
− u
44
+ ··· + 383u + 77)
c
6
(u
15
+ u
14
+ ··· + 3u + 1)(u
45
− 28u
43
+ ··· + 1642u − 281)
c
7
(u
15
− 2u
14
+ ··· + 4u
2
+ 1)(u
45
+ 5u
44
+ ··· + 23u + 1)
c
8
(u
15
− u
14
+ ··· + 2u − 1)(u
45
+ 18u
43
+ ··· + 19u − 7)
c
9
(u
15
+ 5u
14
+ ··· − 10u + 52)
· (u
45
+ 4u
44
+ ··· + 14063662u − 7404196)
c
10
(u
15
+ 7u
13
+ ··· − 3u
2
− 1)(u
45
− u
44
+ ··· + 383u + 77)
c
11
, c
12
(u
15
+ u
14
+ ··· + 2u + 1)(u
45
+ 18u
43
+ ··· + 19u − 7)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
15
− 9y
14
+ ··· − 7y −1)
· (y
45
− 120y
44
+ ··· − 392839435230y −6234839521)
c
2
, c
6
(y
15
− 13y
14
+ ··· + 9y −1)(y
45
− 56y
44
+ ··· + 603838y −78961)
c
3
(y
15
+ 6y
14
+ ··· + 10y −1)(y
45
− y
44
+ ··· + 595y −25)
c
4
, c
7
(y
15
+ 8y
14
+ ··· − 8y −1)(y
45
+ 45y
44
+ ··· + 173y −1)
c
5
, c
10
(y
15
+ 14y
14
+ ··· − 6y −1)(y
45
+ 3y
44
+ ··· + 136371y −5929)
c
8
, c
11
, c
12
(y
15
+ 15y
14
+ ··· + 2y −1)(y
45
+ 36y
44
+ ··· − 157y −49)
c
9
(y
15
+ 7y
14
+ ··· − 5828y −2704)
· (y
45
− 28y
44
+ ··· + 252875184270700y −54822118406416)
16
