12n
0795
(K12n
0795
)
A knot diagram
1
Linearized knot diagam
4 6 10 8 2 11 12 4 1 3 8 7
Solving Sequence
8,11
12 7 1
3,6
2 5 10 4 9
c
11
c
7
c
12
c
6
c
2
c
5
c
10
c
3
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.02240 × 10
36
u
53
− 1.89768 × 10
37
u
52
+ ··· + 3.08931 × 10
37
b + 8.64765 × 10
37
,
− 3.79905 × 10
37
u
53
− 2.32864 × 10
37
u
52
+ ··· + 3.39824 × 10
38
a + 7.15973 × 10
38
,
u
54
+ 2u
53
+ ··· − 68u − 11i
I
u
2
= h−u
14
− 7u
12
− 18u
10
+ u
9
− 19u
8
+ 5u
7
− 4u
6
+ 7u
5
+ 3u
4
+ u
3
− u
2
+ b − 3u,
− u
14
+ 2u
13
− 9u
12
+ 15u
11
− 31u
10
+ 43u
9
− 50u
8
+ 56u
7
− 35u
6
+ 26u
5
− 3u
4
− 6u
3
+ 7u
2
+ a − 5u + 4,
u
15
− u
14
+ 9u
13
− 8u
12
+ 32u
11
− 25u
10
+ 55u
9
− 37u
8
+ 42u
7
− 22u
6
+ 4u
5
+ 3u
4
− 8u
3
+ 7u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 69 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−1.02 × 10
36
u
53
− 1.90 × 10
37
u
52
+ · · · + 3.09 × 10
37
b + 8.65 ×
10
37
, −3.80 × 10
37
u
53
− 2.33 × 10
37
u
52
+ · · · + 3.40 × 10
38
a + 7.16 ×
10
38
, u
54
+ 2u
53
+ · · · − 68u − 11i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
0.111794u
53
+ 0.0685248u
52
+ ··· − 6.32751u − 2.10689
0.0330947u
53
+ 0.614273u
52
+ ··· − 14.1115u − 2.79922
a
6
=
u
3
+ 2u
u
3
+ u
a
2
=
−0.0462518u
53
− 0.197231u
52
+ ··· + 18.3660u + 3.41252
−0.0768640u
53
+ 0.598332u
52
+ ··· − 7.25300u − 0.884533
a
5
=
0.598411u
53
+ 0.724886u
52
+ ··· − 4.83758u − 2.53344
0.644293u
53
+ 0.0999628u
52
+ ··· + 2.37484u − 0.981251
a
10
=
0.869370u
53
+ 1.10346u
52
+ ··· − 57.0809u − 12.2337
0.758825u
53
+ 2.10666u
52
+ ··· − 76.2371u − 14.3877
a
4
=
−0.598411u
53
− 0.724886u
52
+ ··· + 4.83758u + 2.53344
0.0503708u
53
+ 0.206592u
52
+ ··· + 23.1342u + 6.17254
a
9
=
1.21296u
53
+ 1.80879u
52
+ ··· − 76.8483u − 15.7970
0.882160u
53
+ 2.58325u
52
+ ··· − 91.2590u − 17.2428
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.660515u
53
− 1.00096u
52
+ ··· − 64.0934u − 26.6095
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
54
− u
53
+ ··· + 161u − 7
c
2
, c
5
u
54
+ 4u
53
+ ··· + 100u − 7
c
3
, c
10
u
54
+ u
53
+ ··· − 24u + 79
c
4
, c
8
u
54
− 3u
53
+ ··· − 1056u + 279
c
6
u
54
− 2u
53
+ ··· − 9058u − 3839
c
7
, c
11
, c
12
u
54
+ 2u
53
+ ··· − 68u − 11
c
9
u
54
+ u
53
+ ··· + 34u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
54
+ 53y
53
+ ··· − 8141y + 49
c
2
, c
5
y
54
− 22y
53
+ ··· − 10854y + 49
c
3
, c
10
y
54
+ 49y
53
+ ··· − 26804y + 6241
c
4
, c
8
y
54
− 59y
53
+ ··· − 3109428y + 77841
c
6
y
54
+ 4y
53
+ ··· + 184125862y + 14737921
c
7
, c
11
, c
12
y
54
+ 52y
53
+ ··· − 1082y + 121
c
9
y
54
+ 55y
53
+ ··· − 1762y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.881137 + 0.332755I
a = 0.54399 − 2.13485I
b = −0.39987 − 1.44588I
−1.46224 + 9.75579I −6.92865 − 6.33368I
u = −0.881137 − 0.332755I
a = 0.54399 + 2.13485I
b = −0.39987 + 1.44588I
−1.46224 − 9.75579I −6.92865 + 6.33368I
u = −0.661598 + 0.849697I
a = 0.701547 − 1.110120I
b = 0.308972 − 1.370990I
0.12696 − 4.49631I −5.88481 + 2.41612I
u = −0.661598 − 0.849697I
a = 0.701547 + 1.110120I
b = 0.308972 + 1.370990I
0.12696 + 4.49631I −5.88481 − 2.41612I
u = 0.862493 + 0.086515I
a = −0.43056 − 2.27902I
b = 0.194758 − 1.252480I
−5.81257 − 2.56927I −8.23844 + 3.31387I
u = 0.862493 − 0.086515I
a = −0.43056 + 2.27902I
b = 0.194758 + 1.252480I
−5.81257 + 2.56927I −8.23844 − 3.31387I
u = 0.034093 + 1.169890I
a = 0.694656 + 1.176320I
b = −0.07515 + 1.63362I
−5.56210 − 0.29699I 0
u = 0.034093 − 1.169890I
a = 0.694656 − 1.176320I
b = −0.07515 − 1.63362I
−5.56210 + 0.29699I 0
u = −0.061275 + 1.202860I
a = −1.171810 − 0.220502I
b = 0.682474 + 0.808517I
4.62735 + 2.61524I 0
u = −0.061275 − 1.202860I
a = −1.171810 + 0.220502I
b = 0.682474 − 0.808517I
4.62735 − 2.61524I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.703654 + 0.331302I
a = −0.449981 + 0.493740I
b = −0.953667 + 0.272713I
3.98978 − 4.89959I −3.74361 + 5.61016I
u = 0.703654 − 0.331302I
a = −0.449981 − 0.493740I
b = −0.953667 − 0.272713I
3.98978 + 4.89959I −3.74361 − 5.61016I
u = 0.517589 + 0.579128I
a = 0.432842 − 1.079910I
b = 0.686610 + 0.121861I
4.91286 + 0.83348I −0.991616 + 0.466967I
u = 0.517589 − 0.579128I
a = 0.432842 + 1.079910I
b = 0.686610 − 0.121861I
4.91286 − 0.83348I −0.991616 − 0.466967I
u = −0.660016 + 0.406956I
a = −1.06148 + 1.12929I
b = 0.127395 + 1.287570I
−6.55286 + 2.04235I −7.25331 − 3.50673I
u = −0.660016 − 0.406956I
a = −1.06148 − 1.12929I
b = 0.127395 − 1.287570I
−6.55286 − 2.04235I −7.25331 + 3.50673I
u = −0.152086 + 1.230400I
a = −2.21560 + 0.95171I
b = −0.022858 + 1.045750I
4.59893 − 0.06572I 0
u = −0.152086 − 1.230400I
a = −2.21560 − 0.95171I
b = −0.022858 − 1.045750I
4.59893 + 0.06572I 0
u = 0.464769 + 1.178440I
a = −0.444192 − 1.161940I
b = −0.045829 − 1.278020I
−2.46094 − 2.14351I 0
u = 0.464769 − 1.178440I
a = −0.444192 + 1.161940I
b = −0.045829 + 1.278020I
−2.46094 + 2.14351I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.718867
a = 0.234022
b = 0.516900
−2.00172 −2.11670
u = 0.618358 + 0.333206I
a = 1.21587 + 2.22737I
b = −0.07061 + 1.56445I
−7.42325 − 1.74416I −4.39978 + 3.82440I
u = 0.618358 − 0.333206I
a = 1.21587 − 2.22737I
b = −0.07061 − 1.56445I
−7.42325 + 1.74416I −4.39978 − 3.82440I
u = −0.300837 + 1.283390I
a = 0.334898 − 0.433885I
b = −0.533318 + 0.132363I
2.00821 + 3.67955I 0
u = −0.300837 − 1.283390I
a = 0.334898 + 0.433885I
b = −0.533318 − 0.132363I
2.00821 − 3.67955I 0
u = 0.154982 + 1.323550I
a = 0.726837 − 0.314235I
b = −0.614893 − 0.397811I
1.72966 − 2.23286I 0
u = 0.154982 − 1.323550I
a = 0.726837 + 0.314235I
b = −0.614893 + 0.397811I
1.72966 + 2.23286I 0
u = −0.094235 + 1.347490I
a = −0.883756 + 0.145148I
b = 0.620923 + 0.478168I
4.77656 + 2.05407I 0
u = −0.094235 − 1.347490I
a = −0.883756 − 0.145148I
b = 0.620923 − 0.478168I
4.77656 − 2.05407I 0
u = 0.376292 + 1.326680I
a = 1.34754 + 1.24800I
b = −0.310469 + 1.232490I
−1.38617 − 7.00293I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.376292 − 1.326680I
a = 1.34754 − 1.24800I
b = −0.310469 − 1.232490I
−1.38617 + 7.00293I 0
u = −0.229873 + 1.369020I
a = 1.07939 − 1.70290I
b = −0.34520 − 1.44114I
6.29624 + 5.50512I 0
u = −0.229873 − 1.369020I
a = 1.07939 + 1.70290I
b = −0.34520 + 1.44114I
6.29624 − 5.50512I 0
u = −0.201736 + 1.374670I
a = −0.069667 − 0.195301I
b = 0.77398 − 1.23082I
6.68190 + 1.90913I 0
u = −0.201736 − 1.374670I
a = −0.069667 + 0.195301I
b = 0.77398 + 1.23082I
6.68190 − 1.90913I 0
u = −0.569109 + 0.157556I
a = 0.21924 + 4.04070I
b = 0.271278 + 1.251950I
1.40834 + 2.55636I −7.88899 − 3.76167I
u = −0.569109 − 0.157556I
a = 0.21924 − 4.04070I
b = 0.271278 − 1.251950I
1.40834 − 2.55636I −7.88899 + 3.76167I
u = 0.26439 + 1.43158I
a = −1.176170 − 0.713113I
b = 0.20131 − 1.51219I
−1.76307 − 5.05086I 0
u = 0.26439 − 1.43158I
a = −1.176170 + 0.713113I
b = 0.20131 + 1.51219I
−1.76307 + 5.05086I 0
u = 0.27745 + 1.43289I
a = −0.482110 − 0.560176I
b = 1.128380 − 0.228809I
9.62901 − 8.48480I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.27745 − 1.43289I
a = −0.482110 + 0.560176I
b = 1.128380 + 0.228809I
9.62901 + 8.48480I 0
u = −0.501917 + 0.181939I
a = −0.02666 + 1.76555I
b = −0.658368 + 1.057790I
1.69160 − 0.71190I −8.63375 − 2.05858I
u = −0.501917 − 0.181939I
a = −0.02666 − 1.76555I
b = −0.658368 − 1.057790I
1.69160 + 0.71190I −8.63375 + 2.05858I
u = −0.27382 + 1.46493I
a = 1.043680 − 0.263678I
b = −0.267903 − 1.143590I
−0.53926 + 5.52355I 0
u = −0.27382 − 1.46493I
a = 1.043680 + 0.263678I
b = −0.267903 + 1.143590I
−0.53926 − 5.52355I 0
u = −0.35422 + 1.45911I
a = −1.24409 + 1.06931I
b = 0.48568 + 1.47325I
4.2552 + 14.2219I 0
u = −0.35422 − 1.45911I
a = −1.24409 − 1.06931I
b = 0.48568 − 1.47325I
4.2552 − 14.2219I 0
u = 0.14172 + 1.50342I
a = 0.239640 + 0.749072I
b = −0.722793 + 0.242786I
11.72290 − 1.51265I 0
u = 0.14172 − 1.50342I
a = 0.239640 − 0.749072I
b = −0.722793 − 0.242786I
11.72290 + 1.51265I 0
u = 0.475960
a = −1.20947
b = 0.452125
−2.46570 2.76380
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.254809 + 0.273319I
a = 0.778345 − 0.766727I
b = −0.196995 − 0.477015I
−0.216037 + 0.828510I −5.24914 − 8.37217I
u = −0.254809 − 0.273319I
a = 0.778345 + 0.766727I
b = −0.196995 + 0.477015I
−0.216037 − 0.828510I −5.24914 + 8.37217I
u = −0.09766 + 1.65580I
a = −0.169231 + 0.249301I
b = −0.248336 + 1.196290I
8.90251 − 1.85529I 0
u = −0.09766 − 1.65580I
a = −0.169231 − 0.249301I
b = −0.248336 − 1.196290I
8.90251 + 1.85529I 0
10
II.
I
u
2
= h−u
14
−7u
12
+· · ·+b−3u, −u
14
+2u
13
+· · ·+a+4, u
15
−u
14
+· · ·+7u
2
+1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
u
14
− 2u
13
+ ··· + 5u − 4
u
14
+ 7u
12
+ 18u
10
− u
9
+ 19u
8
− 5u
7
+ 4u
6
− 7u
5
− 3u
4
− u
3
+ u
2
+ 3u
a
6
=
u
3
+ 2u
u
3
+ u
a
2
=
−u
13
+ u
12
+ ··· + 4u − 4
u
14
+ 7u
12
+ 18u
10
− u
9
+ 19u
8
− 5u
7
+ 4u
6
− 7u
5
− 2u
4
− u
3
+ 3u
2
+ 3u
a
5
=
u
14
− 2u
13
+ ··· + 10u − 1
−2u
13
+ 2u
12
+ ··· + 2u − 1
a
10
=
−2u
14
+ 2u
13
+ ··· − 11u + 1
u
13
− u
12
+ ··· + 6u
2
− 2u
a
4
=
u
14
− 2u
13
+ ··· + 10u − 1
−u
13
+ u
12
+ ··· − 5u
2
+ u
a
9
=
−2u
14
+ 2u
13
+ ··· − 14u + 1
u
13
− u
12
+ ··· + 6u
2
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
14
+ 6u
13
−24u
12
+ 42u
11
−71u
10
+ 108u
9
−89u
8
+ 115u
7
−
33u
6
+ 25u
5
+ 9u
4
− 22u
3
− 4u
2
+ 2u − 3
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
+ 3u
13
+ ··· − 3u − 1
c
2
u
15
+ 3u
14
+ ··· − 3u
2
− 1
c
3
u
15
+ 9u
13
+ ··· − 4u
2
+ 1
c
4
u
15
− 2u
14
+ ··· + 10u
2
− 1
c
5
u
15
− 3u
14
+ ··· + 3u
2
+ 1
c
6
u
15
− u
14
+ ··· + 2u − 1
c
7
u
15
+ u
14
+ ··· − 7u
2
− 1
c
8
u
15
+ 2u
14
+ ··· − 10u
2
+ 1
c
9
u
15
+ 6u
13
+ ··· + 3u
2
− 1
c
10
u
15
+ 9u
13
+ ··· + 4u
2
− 1
c
11
, c
12
u
15
− u
14
+ ··· + 7u
2
+ 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
+ 6y
14
+ ··· + 9y −1
c
2
, c
5
y
15
− 9y
14
+ ··· − 6y −1
c
3
, c
10
y
15
+ 18y
14
+ ··· + 8y −1
c
4
, c
8
y
15
− 6y
14
+ ··· + 20y −1
c
6
y
15
+ 5y
14
+ ··· − 18y −1
c
7
, c
11
, c
12
y
15
+ 17y
14
+ ··· − 14y −1
c
9
y
15
+ 12y
14
+ ··· + 6y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.203897 + 1.182510I
a = −0.354319 − 1.221590I
b = −0.08173 − 1.61035I
−5.71687 − 1.52845I −6.08651 + 4.82612I
u = 0.203897 − 1.182510I
a = −0.354319 + 1.221590I
b = −0.08173 + 1.61035I
−5.71687 + 1.52845I −6.08651 − 4.82612I
u = −0.033799 + 1.247150I
a = −1.91300 + 0.07166I
b = 0.496329 + 0.968310I
5.47176 + 1.87806I 1.95765 − 1.95299I
u = −0.033799 − 1.247150I
a = −1.91300 − 0.07166I
b = 0.496329 − 0.968310I
5.47176 − 1.87806I 1.95765 + 1.95299I
u = 0.695741 + 0.257174I
a = −1.14939 − 2.10113I
b = 0.10467 − 1.48695I
−8.37469 − 1.56439I −13.79063 + 1.52850I
u = 0.695741 − 0.257174I
a = −1.14939 + 2.10113I
b = 0.10467 + 1.48695I
−8.37469 + 1.56439I −13.79063 − 1.52850I
u = −0.270202 + 1.313250I
a = 0.494443 + 0.091423I
b = −0.379327 + 0.243587I
1.19519 + 3.29133I −5.91213 − 2.50289I
u = −0.270202 − 1.313250I
a = 0.494443 − 0.091423I
b = −0.379327 − 0.243587I
1.19519 − 3.29133I −5.91213 + 2.50289I
u = −0.641026
a = −0.683428
b = 0.308804
−2.98177 −14.5200
u = 0.33142 + 1.43193I
a = 1.189210 + 0.727838I
b = −0.179540 + 1.396510I
−2.94306 − 5.41071I −8.48695 + 4.16478I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.33142 − 1.43193I
a = 1.189210 − 0.727838I
b = −0.179540 − 1.396510I
−2.94306 + 5.41071I −8.48695 − 4.16478I
u = −0.02900 + 1.58206I
a = 0.355078 − 0.312207I
b = 0.266182 − 0.998489I
9.41454 − 1.04650I −0.68107 − 1.40813I
u = −0.02900 − 1.58206I
a = 0.355078 + 0.312207I
b = 0.266182 + 0.998489I
9.41454 + 1.04650I −0.68107 + 1.40813I
u = −0.077540 + 0.352277I
a = −3.28030 + 1.82680I
b = −0.380983 + 0.977431I
2.44402 − 1.47765I −3.24037 + 1.97101I
u = −0.077540 − 0.352277I
a = −3.28030 − 1.82680I
b = −0.380983 − 0.977431I
2.44402 + 1.47765I −3.24037 − 1.97101I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
15
+ 3u
13
+ ··· − 3u − 1)(u
54
− u
53
+ ··· + 161u − 7)
c
2
(u
15
+ 3u
14
+ ··· − 3u
2
− 1)(u
54
+ 4u
53
+ ··· + 100u − 7)
c
3
(u
15
+ 9u
13
+ ··· − 4u
2
+ 1)(u
54
+ u
53
+ ··· − 24u + 79)
c
4
(u
15
− 2u
14
+ ··· + 10u
2
− 1)(u
54
− 3u
53
+ ··· − 1056u + 279)
c
5
(u
15
− 3u
14
+ ··· + 3u
2
+ 1)(u
54
+ 4u
53
+ ··· + 100u − 7)
c
6
(u
15
− u
14
+ ··· + 2u − 1)(u
54
− 2u
53
+ ··· − 9058u − 3839)
c
7
(u
15
+ u
14
+ ··· − 7u
2
− 1)(u
54
+ 2u
53
+ ··· − 68u − 11)
c
8
(u
15
+ 2u
14
+ ··· − 10u
2
+ 1)(u
54
− 3u
53
+ ··· − 1056u + 279)
c
9
(u
15
+ 6u
13
+ ··· + 3u
2
− 1)(u
54
+ u
53
+ ··· + 34u − 1)
c
10
(u
15
+ 9u
13
+ ··· + 4u
2
− 1)(u
54
+ u
53
+ ··· − 24u + 79)
c
11
, c
12
(u
15
− u
14
+ ··· + 7u
2
+ 1)(u
54
+ 2u
53
+ ··· − 68u − 11)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
15
+ 6y
14
+ ··· + 9y −1)(y
54
+ 53y
53
+ ··· − 8141y + 49)
c
2
, c
5
(y
15
− 9y
14
+ ··· − 6y −1)(y
54
− 22y
53
+ ··· − 10854y + 49)
c
3
, c
10
(y
15
+ 18y
14
+ ··· + 8y −1)(y
54
+ 49y
53
+ ··· − 26804y + 6241)
c
4
, c
8
(y
15
− 6y
14
+ ··· + 20y −1)(y
54
− 59y
53
+ ··· − 3109428y + 77841)
c
6
(y
15
+ 5y
14
+ ··· − 18y −1)
· (y
54
+ 4y
53
+ ··· + 184125862y + 14737921)
c
7
, c
11
, c
12
(y
15
+ 17y
14
+ ··· − 14y −1)(y
54
+ 52y
53
+ ··· − 1082y + 121)
c
9
(y
15
+ 12y
14
+ ··· + 6y −1)(y
54
+ 55y
53
+ ··· − 1762y + 1)
17
