12n
0599
(K12n
0599
)
A knot diagram
1
Linearized knot diagam
3 7 12 7 10 2 11 4 3 5 8 9
Solving Sequence
4,8 9,12
1 3 11 7 5 2 6 10
c
8
c
12
c
3
c
11
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
= h2.08585 × 10
97
u
41
+ 7.14533 × 10
97
u
40
+ ··· + 2.87929 × 10
99
b + 1.73918 × 10
99
,
5.30575 × 10
95
u
41
+ 1.71743 × 10
97
u
40
+ ··· + 1.43964 × 10
99
a − 9.16089 × 10
98
, u
42
+ 3u
41
+ ··· + 64u + 32i
I
u
2
= h4075773832297u
14
− 2172521972436u
13
+ ··· + 11315912876891b − 9436584195071,
12204692706877u
14
− 2379455879777u
13
+ ··· + 11315912876891a − 25876335477767,
u
15
− 5u
13
− 10u
12
− 23u
11
− 49u
10
− 54u
9
− 6u
8
− 42u
7
− 27u
6
− 4u
5
+ 12u
4
+ 20u
3
+ 11u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 57 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
=
h2.09×10
97
u
41
+7.15×10
97
u
40
+· · ·+2.88×10
99
b+1.74×10
99
, 5.31×10
95
u
41
+
1.72 × 10
97
u
40
+ · · · + 1.44 × 10
99
a − 9.16 × 10
98
, u
42
+ 3u
41
+ · · · + 64u + 32i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
12
=
−0.000368546u
41
− 0.0119295u
40
+ ··· + 10.1776u + 0.636330
−0.00724434u
41
− 0.0248163u
40
+ ··· + 5.49278u − 0.604030
a
1
=
0.00215244u
41
+ 0.000734500u
40
+ ··· + 3.98031u + 0.893995
−0.00639184u
41
− 0.0228879u
40
+ ··· + 5.89992u − 0.440795
a
3
=
0.00520650u
41
+ 0.0133533u
40
+ ··· + 5.05203u + 1.97585
0.0108948u
41
+ 0.0265127u
40
+ ··· + 3.13035u + 0.813921
a
11
=
0.00687579u
41
+ 0.0128868u
40
+ ··· + 4.68483u + 1.24036
−0.00724434u
41
− 0.0248163u
40
+ ··· + 5.49278u − 0.604030
a
7
=
−0.0284111u
41
− 0.0802538u
40
+ ··· + 5.73043u + 0.660082
0.00297602u
41
+ 0.0148436u
40
+ ··· − 6.80600u + 0.842424
a
5
=
0.00358475u
41
+ 0.0184991u
40
+ ··· − 1.07592u + 1.21549
0.0129804u
41
+ 0.0337132u
40
+ ··· + 2.17091u + 1.68243
a
2
=
0.0241930u
41
+ 0.0654847u
40
+ ··· + 11.3542u + 2.32053
−0.00534000u
41
− 0.0268669u
40
+ ··· + 8.37009u − 1.59602
a
6
=
−0.0377424u
41
− 0.120931u
40
+ ··· + 1.19694u − 1.53872
−0.0110412u
41
− 0.0237259u
40
+ ··· − 0.776747u − 1.63777
a
10
=
0.0131333u
41
+ 0.0397783u
40
+ ··· + 8.14332u + 1.94601
−0.00917113u
41
− 0.0293322u
40
+ ··· + 2.00016u − 1.60632
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0471714u
41
− 0.112106u
40
+ ··· − 28.6268u − 3.86134
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
42
+ 64u
41
+ ··· − 161335u + 1849
c
2
, c
6
u
42
+ 2u
41
+ ··· − 601u + 43
c
3
u
42
− 6u
41
+ ··· + 16u − 1
c
4
u
42
+ 12u
41
+ ··· + 3596u + 676
c
5
, c
10
u
42
− u
41
+ ··· − 190u − 43
c
7
, c
11
u
42
− 3u
41
+ ··· − 11u − 1
c
8
u
42
− 3u
41
+ ··· − 64u + 32
c
9
u
42
− u
41
+ ··· − 2006840u + 356879
c
12
u
42
− 29u
40
+ ··· − 342u − 76
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
42
− 192y
41
+ ··· − 7743629545y + 3418801
c
2
, c
6
y
42
− 64y
41
+ ··· + 161335y + 1849
c
3
y
42
+ 6y
41
+ ··· − 180y + 1
c
4
y
42
+ 2y
41
+ ··· − 1564952y + 456976
c
5
, c
10
y
42
+ 3y
41
+ ··· − 31284y + 1849
c
7
, c
11
y
42
− 37y
41
+ ··· − 245y + 1
c
8
y
42
+ y
41
+ ··· − 27136y + 1024
c
9
y
42
− 109y
41
+ ··· − 1736409911214y + 127362620641
c
12
y
42
− 58y
41
+ ··· + 99636y + 5776
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.648045 + 0.762828I
a = −0.199463 − 1.026950I
b = 0.000607 − 0.888637I
−2.26225 + 2.79311I −8.37862 − 3.97835I
u = 0.648045 − 0.762828I
a = −0.199463 + 1.026950I
b = 0.000607 + 0.888637I
−2.26225 − 2.79311I −8.37862 + 3.97835I
u = 0.462736 + 0.870276I
a = 1.082390 + 0.631958I
b = 1.380710 − 0.068283I
7.99084 − 2.22911I 4.00956 + 3.14309I
u = 0.462736 − 0.870276I
a = 1.082390 − 0.631958I
b = 1.380710 + 0.068283I
7.99084 + 2.22911I 4.00956 − 3.14309I
u = −0.371673 + 0.796152I
a = 0.020113 + 0.557804I
b = −0.222389 + 0.704830I
−0.17172 − 1.89179I −2.28677 + 1.75619I
u = −0.371673 − 0.796152I
a = 0.020113 − 0.557804I
b = −0.222389 − 0.704830I
−0.17172 + 1.89179I −2.28677 − 1.75619I
u = −0.314772 + 0.773309I
a = −0.38000 + 1.41391I
b = 1.093270 + 0.667135I
−10.09930 − 2.74341I −5.66707 + 2.17488I
u = −0.314772 − 0.773309I
a = −0.38000 − 1.41391I
b = 1.093270 − 0.667135I
−10.09930 + 2.74341I −5.66707 − 2.17488I
u = −1.000680 + 0.665007I
a = −0.077148 + 0.584959I
b = −1.209930 + 0.230150I
2.61996 − 1.17635I −6 − 1.021926 + 0.10I
u = −1.000680 − 0.665007I
a = −0.077148 − 0.584959I
b = −1.209930 − 0.230150I
2.61996 + 1.17635I −6 − 1.021926 + 0.10I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.629318 + 0.386672I
a = −1.66190 − 0.25886I
b = 1.123620 − 0.203923I
−0.311934 − 0.851962I −4.13073 + 4.38646I
u = −0.629318 − 0.386672I
a = −1.66190 + 0.25886I
b = 1.123620 + 0.203923I
−0.311934 + 0.851962I −4.13073 − 4.38646I
u = −0.205200 + 1.287660I
a = 0.412852 − 0.718154I
b = 0.200970 − 0.672153I
−2.91171 − 2.40047I −9.33804 + 3.58482I
u = −0.205200 − 1.287660I
a = 0.412852 + 0.718154I
b = 0.200970 + 0.672153I
−2.91171 + 2.40047I −9.33804 − 3.58482I
u = −0.317104 + 1.341020I
a = −0.596540 + 0.932678I
b = 0.024355 + 0.846164I
−12.43750 + 0.62091I 0
u = −0.317104 − 1.341020I
a = −0.596540 − 0.932678I
b = 0.024355 − 0.846164I
−12.43750 − 0.62091I 0
u = −0.443573 + 0.327558I
a = 0.77751 − 1.87015I
b = −0.326610 + 0.038977I
2.48884 − 1.59471I 3.72664 + 4.36571I
u = −0.443573 − 0.327558I
a = 0.77751 + 1.87015I
b = −0.326610 − 0.038977I
2.48884 + 1.59471I 3.72664 − 4.36571I
u = −0.049515 + 0.529296I
a = 2.04051 + 2.26722I
b = −1.299150 + 0.384278I
−8.30711 − 5.04057I −3.92081 + 3.17900I
u = −0.049515 − 0.529296I
a = 2.04051 − 2.26722I
b = −1.299150 − 0.384278I
−8.30711 + 5.04057I −3.92081 − 3.17900I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.23414 + 0.89196I
a = −0.182278 + 0.535254I
b = 1.38820 + 0.29236I
4.93779 + 5.55158I 0
u = 1.23414 − 0.89196I
a = −0.182278 − 0.535254I
b = 1.38820 − 0.29236I
4.93779 − 5.55158I 0
u = 0.74924 + 1.34147I
a = 0.230039 + 0.931808I
b = 0.230395 + 0.978898I
−12.6753 + 8.4287I 0
u = 0.74924 − 1.34147I
a = 0.230039 − 0.931808I
b = 0.230395 − 0.978898I
−12.6753 − 8.4287I 0
u = 0.384683 + 0.031619I
a = 1.34403 + 0.53921I
b = −1.109290 + 0.500907I
1.63611 − 2.57651I −5.00070 + 6.84199I
u = 0.384683 − 0.031619I
a = 1.34403 − 0.53921I
b = −1.109290 − 0.500907I
1.63611 + 2.57651I −5.00070 − 6.84199I
u = −1.28548 + 1.06224I
a = 0.087304 − 0.822069I
b = 1.298780 − 0.402243I
1.80773 − 7.39822I 0
u = −1.28548 − 1.06224I
a = 0.087304 + 0.822069I
b = 1.298780 + 0.402243I
1.80773 + 7.39822I 0
u = 0.81695 + 1.45625I
a = −0.614121 − 0.644235I
b = −1.177860 − 0.025942I
5.03473 + 1.74643I 0
u = 0.81695 − 1.45625I
a = −0.614121 + 0.644235I
b = −1.177860 + 0.025942I
5.03473 − 1.74643I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.270533 + 0.172470I
a = −1.27279 + 1.50644I
b = −1.50571 + 0.35734I
2.32167 − 2.06853I 2.16490 − 4.78895I
u = −0.270533 − 0.172470I
a = −1.27279 − 1.50644I
b = −1.50571 − 0.35734I
2.32167 + 2.06853I 2.16490 + 4.78895I
u = 0.253217
a = 2.52423
b = 0.315009
−0.948564 −10.7560
u = −1.33409 + 1.57582I
a = −0.115373 + 0.761660I
b = −1.43288 + 0.41746I
−7.4115 − 13.4268I 0
u = −1.33409 − 1.57582I
a = −0.115373 − 0.761660I
b = −1.43288 − 0.41746I
−7.4115 + 13.4268I 0
u = 1.13096 + 1.81862I
a = −0.140526 − 0.505969I
b = −1.38971 − 0.26319I
2.17544 + 5.80065I 0
u = 1.13096 − 1.81862I
a = −0.140526 + 0.505969I
b = −1.38971 + 0.26319I
2.17544 − 5.80065I 0
u = −2.19471
a = 0.570796
b = −1.33714
−3.13160 0
u = 0.90971 + 2.03841I
a = 0.349021 + 0.532377I
b = 1.261520 + 0.388603I
−8.60268 + 3.81146I 0
u = 0.90971 − 2.03841I
a = 0.349021 − 0.532377I
b = 1.261520 − 0.388603I
−8.60268 − 3.81146I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 2.24585
a = −0.323672
b = 0.0679481
−7.70072 0
u = −3.53341
a = 0.0214051
b = 1.29639
−3.75495 0
9
II.
I
u
2
= h4.08 × 10
12
u
14
− 2.17 × 10
12
u
13
+ · · · + 1.13 × 10
13
b − 9.44 × 10
12
, 1.22 ×
10
13
u
14
−2.38×10
12
u
13
+· · ·+1.13×10
13
a−2.59×10
13
, u
15
−5u
13
+· · ·+2u+1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
12
=
−1.07854u
14
+ 0.210275u
13
+ ··· − 6.56711u + 2.28672
−0.360181u
14
+ 0.191988u
13
+ ··· + 0.0721482u + 0.833922
a
1
=
−0.806967u
14
+ 0.0658041u
13
+ ··· − 7.29725u + 1.66307
−0.308908u
14
+ 0.126579u
13
+ ··· + 0.0547816u + 0.689450
a
3
=
0.426151u
14
+ 0.510477u
13
+ ··· + 15.5167u + 6.16385
0.467779u
14
+ 0.114972u
13
+ ··· + 7.73906u + 1.62977
a
11
=
−0.718362u
14
+ 0.0182870u
13
+ ··· − 6.63926u + 1.45280
−0.360181u
14
+ 0.191988u
13
+ ··· + 0.0721482u + 0.833922
a
7
=
−1.47573u
14
+ 0.316511u
13
+ ··· − 8.51856u + 2.54844
−0.154046u
14
+ 0.151268u
13
+ ··· + 0.936513u + 1.93108
a
5
=
0.420096u
14
+ 0.903948u
13
+ ··· + 23.2129u + 9.22115
0.610929u
14
+ 0.339885u
13
+ ··· + 12.1399u + 2.27431
a
2
=
−1.10086u
14
+ 0.660424u
13
+ ··· + 4.24610u + 8.58306
−0.103998u
14
+ 0.391996u
13
+ ··· + 7.60146u + 2.75811
a
6
=
0.394864u
14
− 0.515063u
13
+ ··· − 7.27332u − 5.30627
−0.411913u
14
− 0.0161825u
13
+ ··· − 6.23025u − 2.14792
a
10
=
3.56778u
14
− 0.0378933u
13
+ ··· + 31.8302u − 0.00774955
0.910294u
14
− 0.145683u
13
+ ··· + 4.90300u − 2.39025
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
9101535523664
11315912876891
u
14
−
12950974574918
11315912876891
u
13
+ ··· −
21645969002451
11315912876891
u +
1008303706222
11315912876891
10
(iv) u-Polynomials at the component
11
Crossings u-Polynomials at each crossing
c
1
u
15
− 15u
14
+ ··· + 7u − 1
c
2
u
15
− 3u
14
+ ··· + 3u − 1
c
3
u
15
+ 5u
14
+ ··· + 2u + 1
c
4
u
15
+ u
14
+ ··· − 4u − 1
c
5
u
15
+ 6u
13
+ ··· − 2u − 1
c
6
u
15
+ 3u
14
+ ··· + 3u + 1
c
7
u
15
− 8u
13
+ ··· − u + 1
c
8
u
15
− 5u
13
+ ··· + 2u + 1
c
9
u
15
− 14u
13
+ ··· − 4u + 1
c
10
u
15
+ 6u
13
+ ··· − 2u + 1
c
11
u
15
− 8u
13
+ ··· − u − 1
c
12
u
15
− u
14
+ ··· − 3u + 1
12
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
− 51y
14
+ ··· − 5y −1
c
2
, c
6
y
15
− 15y
14
+ ··· + 7y −1
c
3
y
15
+ 7y
14
+ ··· − 6y −1
c
4
y
15
− 13y
14
+ ··· − 24y −1
c
5
, c
10
y
15
+ 12y
14
+ ··· + 2y −1
c
7
, c
11
y
15
− 16y
14
+ ··· − 5y −1
c
8
y
15
− 10y
14
+ ··· − 18y −1
c
9
y
15
− 28y
14
+ ··· − 16y −1
c
12
y
15
− 13y
14
+ ··· + 19y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.596659 + 0.827825I
a = −0.045120 − 0.883234I
b = −0.238789 − 0.780455I
−0.66784 + 2.86329I −4.86388 − 6.69106I
u = 0.596659 − 0.827825I
a = −0.045120 + 0.883234I
b = −0.238789 + 0.780455I
−0.66784 − 2.86329I −4.86388 + 6.69106I
u = 0.755283
a = 1.45281
b = −1.12652
0.321895 0.516880
u = −0.184311 + 0.678178I
a = 1.60231 − 0.96713I
b = −0.042454 − 0.389554I
1.84141 − 1.47317I −9.34491 + 1.31525I
u = −0.184311 − 0.678178I
a = 1.60231 + 0.96713I
b = −0.042454 + 0.389554I
1.84141 + 1.47317I −9.34491 − 1.31525I
u = −0.604205 + 0.216942I
a = −0.229198 + 0.703203I
b = −1.41923 + 0.52118I
2.36544 − 2.52653I 5.67594 + 10.87302I
u = −0.604205 − 0.216942I
a = −0.229198 − 0.703203I
b = −1.41923 − 0.52118I
2.36544 + 2.52653I 5.67594 − 10.87302I
u = 0.004697 + 0.321783I
a = 4.20961 − 1.65523I
b = 1.356600 + 0.159175I
6.44360 + 0.56743I −0.903335 − 0.669018I
u = 0.004697 − 0.321783I
a = 4.20961 + 1.65523I
b = 1.356600 − 0.159175I
6.44360 − 0.56743I −0.903335 + 0.669018I
u = −1.32947 + 1.11212I
a = −0.095911 − 0.699773I
b = 1.38775 − 0.28744I
4.46896 − 6.63905I −0.81267 + 7.15016I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.32947 − 1.11212I
a = −0.095911 + 0.699773I
b = 1.38775 + 0.28744I
4.46896 + 6.63905I −0.81267 − 7.15016I
u = 0.37677 + 1.72909I
a = −0.714436 − 0.247634I
b = −1.335870 − 0.137594I
6.08786 + 3.33489I 0.87409 − 4.16417I
u = 0.37677 − 1.72909I
a = −0.714436 + 0.247634I
b = −1.335870 + 0.137594I
6.08786 − 3.33489I 0.87409 + 4.16417I
u = −1.88197
a = 0.330680
b = 0.443370
−7.37862 3.59810
u = 3.40639
a = −0.237996
b = 1.26711
−4.41331 −11.3650
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
15
− 15u
14
+ ··· + 7u − 1)(u
42
+ 64u
41
+ ··· − 161335u + 1849)
c
2
(u
15
− 3u
14
+ ··· + 3u − 1)(u
42
+ 2u
41
+ ··· − 601u + 43)
c
3
(u
15
+ 5u
14
+ ··· + 2u + 1)(u
42
− 6u
41
+ ··· + 16u − 1)
c
4
(u
15
+ u
14
+ ··· − 4u − 1)(u
42
+ 12u
41
+ ··· + 3596u + 676)
c
5
(u
15
+ 6u
13
+ ··· − 2u − 1)(u
42
− u
41
+ ··· − 190u − 43)
c
6
(u
15
+ 3u
14
+ ··· + 3u + 1)(u
42
+ 2u
41
+ ··· − 601u + 43)
c
7
(u
15
− 8u
13
+ ··· − u + 1)(u
42
− 3u
41
+ ··· − 11u − 1)
c
8
(u
15
− 5u
13
+ ··· + 2u + 1)(u
42
− 3u
41
+ ··· − 64u + 32)
c
9
(u
15
− 14u
13
+ ··· − 4u + 1)(u
42
− u
41
+ ··· − 2006840u + 356879)
c
10
(u
15
+ 6u
13
+ ··· − 2u + 1)(u
42
− u
41
+ ··· − 190u − 43)
c
11
(u
15
− 8u
13
+ ··· − u − 1)(u
42
− 3u
41
+ ··· − 11u − 1)
c
12
(u
15
− u
14
+ ··· − 3u + 1)(u
42
− 29u
40
+ ··· − 342u − 76)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
15
− 51y
14
+ ··· − 5y −1)
· (y
42
− 192y
41
+ ··· − 7743629545y + 3418801)
c
2
, c
6
(y
15
− 15y
14
+ ··· + 7y −1)(y
42
− 64y
41
+ ··· + 161335y + 1849)
c
3
(y
15
+ 7y
14
+ ··· − 6y −1)(y
42
+ 6y
41
+ ··· − 180y + 1)
c
4
(y
15
− 13y
14
+ ··· − 24y −1)(y
42
+ 2y
41
+ ··· − 1564952y + 456976)
c
5
, c
10
(y
15
+ 12y
14
+ ··· + 2y −1)(y
42
+ 3y
41
+ ··· − 31284y + 1849)
c
7
, c
11
(y
15
− 16y
14
+ ··· − 5y −1)(y
42
− 37y
41
+ ··· − 245y + 1)
c
8
(y
15
− 10y
14
+ ··· − 18y −1)(y
42
+ y
41
+ ··· − 27136y + 1024)
c
9
(y
15
− 28y
14
+ ··· − 16y −1)
· (y
42
− 109y
41
+ ··· − 1736409911214y + 127362620641)
c
12
(y
15
− 13y
14
+ ··· + 19y −1)(y
42
− 58y
41
+ ··· + 99636y + 5776)
18
