12n
0018
(K12n
0018
)
A knot diagram
1
Linearized knot diagam
3 5 6 7 2 10 5 12 7 1 9 11
Solving Sequence
2,5
3
6,10
7 1 11 4 9 12 8
c
2
c
5
c
6
c
1
c
10
c
4
c
9
c
12
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.62383 × 10
39
u
61
− 1.19751 × 10
40
u
60
+ ··· + 3.98732 × 10
38
b − 9.31049 × 10
39
,
− 3.15003 × 10
39
u
61
+ 1.51549 × 10
40
u
60
+ ··· + 1.99366 × 10
38
a + 1.87829 × 10
40
,
u
62
− 5u
61
+ ··· − 19u + 1i
I
u
2
= ha
3
u + a
3
− 2a
2
− 3au + b − a + u + 1, a
4
+ 2a
3
u − 3a
2
u − 3a
2
+ a + u, u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 70 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
= h2.62 × 10
39
u
61
− 1.20 × 10
40
u
60
+ · · · + 3.99 × 10
38
b − 9.31 ×
10
39
, −3.15 × 10
39
u
61
+ 1.52 × 10
40
u
60
+ · · · + 1.99 × 10
38
a + 1.88 ×
10
40
, u
62
− 5u
61
+ · · · − 19u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
−u
2
a
6
=
u
u
a
10
=
15.8002u
61
− 76.0156u
60
+ ··· + 1227.65u − 94.2130
−6.58044u
61
+ 30.0330u
60
+ ··· − 304.461u + 23.3502
a
7
=
−15.9053u
61
+ 77.9924u
60
+ ··· − 1333.00u + 105.025
8.30759u
61
− 33.2844u
60
+ ··· + 178.838u − 14.4250
a
1
=
u
2
+ 1
−u
4
a
11
=
19.2096u
61
− 92.8297u
60
+ ··· + 1541.75u − 118.551
−8.39084u
61
+ 37.4877u
60
+ ··· − 309.379u + 23.5628
a
4
=
u
4
+ u
2
+ 1
u
4
a
9
=
23.0925u
61
− 111.738u
60
+ ··· + 1863.68u − 145.752
−10.1051u
61
+ 43.0078u
60
+ ··· − 361.476u + 28.7800
a
12
=
15.5897u
61
− 75.0040u
60
+ ··· + 1258.28u − 100.587
−1.52637u
61
+ 10.2099u
60
+ ··· − 153.436u + 11.8910
a
8
=
15.9053u
61
− 77.9924u
60
+ ··· + 1333.00u − 105.025
−10.5447u
61
+ 39.2440u
60
+ ··· − 192.085u + 15.9594
(ii) Obstruction class = −1
(iii) Cusp Shapes = 32.0809u
61
− 157.631u
60
+ ··· + 2379.84u − 187.341
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
62
+ 33u
61
+ ··· − 77u + 1
c
2
, c
5
u
62
+ 5u
61
+ ··· + 19u + 1
c
3
u
62
− 5u
61
+ ··· + 28315u + 1921
c
4
, c
7
u
62
+ 5u
61
+ ··· − 1152u + 256
c
6
, c
9
u
62
− 3u
61
+ ··· − 3u + 1
c
8
, c
11
u
62
+ 3u
61
+ ··· − 5u + 1
c
10
, c
12
u
62
+ 23u
61
+ ··· + 11u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
62
− 3y
61
+ ··· − 3593y + 1
c
2
, c
5
y
62
+ 33y
61
+ ··· − 77y + 1
c
3
y
62
− 39y
61
+ ··· − 237987197y + 3690241
c
4
, c
7
y
62
+ 45y
61
+ ··· + 1261568y + 65536
c
6
, c
9
y
62
+ 15y
61
+ ··· + 11y + 1
c
8
, c
11
y
62
+ 23y
61
+ ··· + 11y + 1
c
10
, c
12
y
62
+ 35y
61
+ ··· − 185y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.965704 + 0.297719I
a = −1.43043 − 0.52995I
b = −0.306577 + 0.174570I
−1.29157 − 10.33450I 0
u = 0.965704 − 0.297719I
a = −1.43043 + 0.52995I
b = −0.306577 − 0.174570I
−1.29157 + 10.33450I 0
u = −0.411885 + 0.945709I
a = −2.27569 + 1.18972I
b = −1.71285 + 1.28141I
−0.55472 − 4.37820I 0
u = −0.411885 − 0.945709I
a = −2.27569 − 1.18972I
b = −1.71285 − 1.28141I
−0.55472 + 4.37820I 0
u = −0.508605 + 0.906380I
a = 2.86917 − 1.37868I
b = 2.47102 − 1.51786I
−0.017864 − 0.355429I 0
u = −0.508605 − 0.906380I
a = 2.86917 + 1.37868I
b = 2.47102 + 1.51786I
−0.017864 + 0.355429I 0
u = 0.892742 + 0.303283I
a = 1.40786 + 0.50551I
b = 0.211520 − 0.223149I
0.27929 − 4.71522I 0
u = 0.892742 − 0.303283I
a = 1.40786 − 0.50551I
b = 0.211520 + 0.223149I
0.27929 + 4.71522I 0
u = −0.930590 + 0.096301I
a = 0.057491 − 0.985327I
b = −0.005994 − 0.189910I
3.48850 − 2.47160I 10.13177 + 3.68218I
u = −0.930590 − 0.096301I
a = 0.057491 + 0.985327I
b = −0.005994 + 0.189910I
3.48850 + 2.47160I 10.13177 − 3.68218I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.374481 + 0.850793I
a = −0.743628 + 0.575009I
b = 0.77387 + 1.47048I
6.46808 + 4.86140I 0
u = 0.374481 − 0.850793I
a = −0.743628 − 0.575009I
b = 0.77387 − 1.47048I
6.46808 − 4.86140I 0
u = 0.891739 + 0.124753I
a = −1.43390 − 0.46536I
b = −0.330798 + 0.437779I
−5.82429 − 3.24893I −2.83073 + 2.56223I
u = 0.891739 − 0.124753I
a = −1.43390 + 0.46536I
b = −0.330798 − 0.437779I
−5.82429 + 3.24893I −2.83073 − 2.56223I
u = −0.531933 + 0.965807I
a = 0.024523 − 1.037090I
b = 0.21487 − 1.50621I
−0.14262 − 2.78903I 0
u = −0.531933 − 0.965807I
a = 0.024523 + 1.037090I
b = 0.21487 + 1.50621I
−0.14262 + 2.78903I 0
u = 0.382543 + 0.801832I
a = 0.843253 − 0.451303I
b = −0.78761 − 1.22730I
6.61497 − 1.56581I 0. + 8.95092I
u = 0.382543 − 0.801832I
a = 0.843253 + 0.451303I
b = −0.78761 + 1.22730I
6.61497 + 1.56581I 0. − 8.95092I
u = −0.480114 + 0.743056I
a = 2.00911 − 1.21894I
b = 1.67487 − 1.75063I
0.46926 − 3.71058I −6.23280 + 11.34763I
u = −0.480114 − 0.743056I
a = 2.00911 + 1.21894I
b = 1.67487 + 1.75063I
0.46926 + 3.71058I −6.23280 − 11.34763I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.094130 + 0.841210I
a = −1.51231 + 1.09297I
b = −0.499665 + 1.237070I
−1.62196 + 1.23455I −2.69106 − 2.17099I
u = −0.094130 − 0.841210I
a = −1.51231 − 1.09297I
b = −0.499665 − 1.237070I
−1.62196 − 1.23455I −2.69106 + 2.17099I
u = −0.257077 + 1.145650I
a = −0.587485 + 0.772224I
b = −0.87373 + 1.43182I
−3.22451 − 2.34711I 0
u = −0.257077 − 1.145650I
a = −0.587485 − 0.772224I
b = −0.87373 − 1.43182I
−3.22451 + 2.34711I 0
u = −0.900002 + 0.754167I
a = 0.124095 − 0.287439I
b = −0.145127 + 0.264679I
2.84220 − 0.80883I 0
u = −0.900002 − 0.754167I
a = 0.124095 + 0.287439I
b = −0.145127 − 0.264679I
2.84220 + 0.80883I 0
u = −0.475785 + 0.628202I
a = 1.193400 − 0.639563I
b = 0.566847 − 0.143962I
0.84056 − 1.37461I 5.29052 + 4.27881I
u = −0.475785 − 0.628202I
a = 1.193400 + 0.639563I
b = 0.566847 + 0.143962I
0.84056 + 1.37461I 5.29052 − 4.27881I
u = 0.442572 + 1.154760I
a = 0.043171 + 0.738046I
b = −0.93124 + 1.40738I
−3.45908 + 2.42252I 0
u = 0.442572 − 1.154760I
a = 0.043171 − 0.738046I
b = −0.93124 − 1.40738I
−3.45908 − 2.42252I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.745927 + 0.110754I
a = −1.277990 + 0.457571I
b = −0.255752 − 0.786572I
−1.84493 − 3.74840I 0.35274 + 2.59409I
u = 0.745927 − 0.110754I
a = −1.277990 − 0.457571I
b = −0.255752 + 0.786572I
−1.84493 + 3.74840I 0.35274 − 2.59409I
u = 0.468807 + 1.155530I
a = −0.152066 + 1.342220I
b = 0.48466 + 2.34406I
−3.26706 + 5.72300I 0
u = 0.468807 − 1.155530I
a = −0.152066 − 1.342220I
b = 0.48466 − 2.34406I
−3.26706 − 5.72300I 0
u = 0.406251 + 1.185420I
a = 0.29707 − 1.44572I
b = −0.37469 − 2.34822I
−5.55349 + 0.20577I 0
u = 0.406251 − 1.185420I
a = 0.29707 + 1.44572I
b = −0.37469 + 2.34822I
−5.55349 − 0.20577I 0
u = −0.893686 + 0.884980I
a = 0.0151757 + 0.0943643I
b = 0.275198 − 0.425254I
2.47898 − 5.65478I 0
u = −0.893686 − 0.884980I
a = 0.0151757 − 0.0943643I
b = 0.275198 + 0.425254I
2.47898 + 5.65478I 0
u = 0.236000 + 1.238430I
a = −0.245273 + 0.777145I
b = −0.93517 + 1.48259I
−4.87637 − 1.25419I 0
u = 0.236000 − 1.238430I
a = −0.245273 − 0.777145I
b = −0.93517 − 1.48259I
−4.87637 + 1.25419I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.331100 + 0.640866I
a = −1.73450 + 0.49909I
b = −1.35558 + 1.35491I
0.414871 + 0.997099I −2.34753 + 0.60698I
u = −0.331100 − 0.640866I
a = −1.73450 − 0.49909I
b = −1.35558 − 1.35491I
0.414871 − 0.997099I −2.34753 − 0.60698I
u = 0.493150 + 1.180330I
a = −0.100543 − 0.798998I
b = 0.89247 − 1.38242I
−4.93269 + 8.34798I 0
u = 0.493150 − 1.180330I
a = −0.100543 + 0.798998I
b = 0.89247 + 1.38242I
−4.93269 − 8.34798I 0
u = −0.576496 + 1.167110I
a = 0.393868 − 0.624631I
b = 0.650024 − 1.142500I
0.37776 − 2.87804I 0
u = −0.576496 − 1.167110I
a = 0.393868 + 0.624631I
b = 0.650024 + 1.142500I
0.37776 + 2.87804I 0
u = 0.594113 + 1.186310I
a = 0.175111 + 1.386080I
b = 0.62258 + 2.42837I
−2.39832 + 10.17330I 0
u = 0.594113 − 1.186310I
a = 0.175111 − 1.386080I
b = 0.62258 − 2.42837I
−2.39832 − 10.17330I 0
u = 0.376293 + 1.276620I
a = 0.095158 − 0.866722I
b = 0.90036 − 1.47315I
−10.22650 + 1.13523I 0
u = 0.376293 − 1.276620I
a = 0.095158 + 0.866722I
b = 0.90036 + 1.47315I
−10.22650 − 1.13523I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.524584 + 1.228200I
a = −0.01293 − 1.50624I
b = −0.52627 − 2.46501I
−9.15566 + 8.36279I 0
u = 0.524584 − 1.228200I
a = −0.01293 + 1.50624I
b = −0.52627 + 2.46501I
−9.15566 − 8.36279I 0
u = 0.217473 + 1.339040I
a = 0.291562 − 0.877888I
b = 0.94031 − 1.49949I
−6.91925 − 6.39307I 0
u = 0.217473 − 1.339040I
a = 0.291562 + 0.877888I
b = 0.94031 + 1.49949I
−6.91925 + 6.39307I 0
u = 0.616616 + 1.212360I
a = −0.23484 − 1.44633I
b = −0.64668 − 2.46160I
−4.0936 + 16.0686I 0
u = 0.616616 − 1.212360I
a = −0.23484 + 1.44633I
b = −0.64668 + 2.46160I
−4.0936 − 16.0686I 0
u = −0.506958 + 1.275800I
a = −0.538448 + 0.655638I
b = −0.82392 + 1.18632I
−0.59026 − 7.53314I 0
u = −0.506958 − 1.275800I
a = −0.538448 − 0.655638I
b = −0.82392 − 1.18632I
−0.59026 + 7.53314I 0
u = 0.616968 + 0.058257I
a = 1.42943 + 0.57487I
b = 0.066901 − 0.636161I
−0.28090 − 1.52056I 2.54136 + 2.72708I
u = 0.616968 − 0.058257I
a = 1.42943 − 0.57487I
b = 0.066901 + 0.636161I
−0.28090 + 1.52056I 2.54136 − 2.72708I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.152397 + 0.009114I
a = 3.01058 + 2.43110I
b = −0.233834 − 0.560896I
−0.056975 − 1.373480I −0.36734 + 4.59681I
u = 0.152397 − 0.009114I
a = 3.01058 − 2.43110I
b = −0.233834 + 0.560896I
−0.056975 + 1.373480I −0.36734 − 4.59681I
11
II.
I
u
2
= ha
3
u+a
3
−2a
2
−3au+b−a+u+1, a
4
+2a
3
u−3a
2
u−3a
2
+a+u, u
2
+u+1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u + 1
a
6
=
u
u
a
10
=
a
−a
3
u − a
3
+ 2a
2
+ 3au + a − u − 1
a
7
=
0
−a
3
u − a
3
+ a
2
+ au + 2u + 2
a
1
=
−u
−u
a
11
=
−a
3
u + 2a
2
u + 2a
2
− 2a − u
−2a
3
u − a
3
+ 2a
2
u + 4a
2
+ 3au − 2a − 2u − 1
a
4
=
0
u
a
9
=
a
a
3
u + a
3
− 3a
2
− 4au + a + 2u + 2
a
12
=
−a
3
u + a
2
u + a
2
− a
−2a
3
u − a
3
+ a
2
u + 2a
2
+ au − a + 2u + 2
a
8
=
0
−a
3
u − a
3
+ a
2
+ au + 2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −a
3
u − 3a
3
− 3a
2
u + a
2
− 3a + 9u + 10
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
4
c
2
(u
2
+ u + 1)
4
c
4
, c
7
u
8
c
6
, c
10
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
c
8
(u
4
− u
3
+ u
2
+ 1)
2
c
9
, c
12
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
c
11
(u
4
+ u
3
+ u
2
+ 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
4
c
4
, c
7
y
8
c
6
, c
9
, c
10
c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
c
8
, c
11
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.576953 + 0.283088I
b = −0.819983 + 0.968508I
6.79074 − 5.19385I 8.12668 + 10.02124I
u = −0.500000 + 0.866025I
a = −0.533637 − 0.358112I
b = 0.75842 − 1.22518I
6.79074 + 1.13408I 5.34148 + 6.40875I
u = −0.500000 + 0.866025I
a = −0.58443 − 1.44211I
b = −0.34305 − 2.03771I
−0.21101 − 3.44499I −0.01166 + 14.06194I
u = −0.500000 + 0.866025I
a = 1.54112 − 0.21492I
b = 0.904615 − 0.303685I
−0.211005 − 0.614778I −4.95650 + 1.55100I
u = −0.500000 − 0.866025I
a = 0.576953 − 0.283088I
b = −0.819983 − 0.968508I
6.79074 + 5.19385I 8.12668 − 10.02124I
u = −0.500000 − 0.866025I
a = −0.533637 + 0.358112I
b = 0.75842 + 1.22518I
6.79074 − 1.13408I 5.34148 − 6.40875I
u = −0.500000 − 0.866025I
a = −0.58443 + 1.44211I
b = −0.34305 + 2.03771I
−0.21101 + 3.44499I −0.01166 − 14.06194I
u = −0.500000 − 0.866025I
a = 1.54112 + 0.21492I
b = 0.904615 + 0.303685I
−0.211005 + 0.614778I −4.95650 − 1.55100I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
4
)(u
62
+ 33u
61
+ ··· − 77u + 1)
c
2
((u
2
+ u + 1)
4
)(u
62
+ 5u
61
+ ··· + 19u + 1)
c
3
((u
2
− u + 1)
4
)(u
62
− 5u
61
+ ··· + 28315u + 1921)
c
4
, c
7
u
8
(u
62
+ 5u
61
+ ··· − 1152u + 256)
c
5
((u
2
− u + 1)
4
)(u
62
+ 5u
61
+ ··· + 19u + 1)
c
6
((u
4
− u
3
+ 3u
2
− 2u + 1)
2
)(u
62
− 3u
61
+ ··· − 3u + 1)
c
8
((u
4
− u
3
+ u
2
+ 1)
2
)(u
62
+ 3u
61
+ ··· − 5u + 1)
c
9
((u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
)(u
62
− 3u
61
+ ··· − 3u + 1)
c
10
((u
4
− u
3
+ 3u
2
− 2u + 1)
2
)(u
62
+ 23u
61
+ ··· + 11u + 1)
c
11
((u
4
+ u
3
+ u
2
+ 1)
2
)(u
62
+ 3u
61
+ ··· − 5u + 1)
c
12
((u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
)(u
62
+ 23u
61
+ ··· + 11u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
4
)(y
62
− 3y
61
+ ··· − 3593y + 1)
c
2
, c
5
((y
2
+ y + 1)
4
)(y
62
+ 33y
61
+ ··· − 77y + 1)
c
3
((y
2
+ y + 1)
4
)(y
62
− 39y
61
+ ··· − 2.37987 × 10
8
y + 3690241)
c
4
, c
7
y
8
(y
62
+ 45y
61
+ ··· + 1261568y + 65536)
c
6
, c
9
((y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
)(y
62
+ 15y
61
+ ··· + 11y + 1)
c
8
, c
11
((y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
)(y
62
+ 23y
61
+ ··· + 11y + 1)
c
10
, c
12
((y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
)(y
62
+ 35y
61
+ ··· − 185y + 1)
17
