12n
0787
(K12n
0787
)
A knot diagram
1
Linearized knot diagam
4 5 11 8 3 12 5 12 1 4 6 9
Solving Sequence
8,12
9 1
5,10
4 2 7 6 11 3
c
8
c
12
c
9
c
4
c
1
c
7
c
6
c
11
c
3
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.86056 × 10
58
u
51
− 6.69927 × 10
58
u
50
+ ··· + 6.23296 × 10
59
b + 8.49108 × 10
59
,
− 6.68649 × 10
58
u
51
+ 2.75220 × 10
59
u
50
+ ··· + 4.79459 × 10
58
a + 8.71827 × 10
59
,
u
52
− 4u
51
+ ··· + 18u + 1i
I
u
2
= h−u
16
− u
15
+ ··· + b + 1, 2u
16
+ u
15
+ ··· + a − 6u, u
17
+ u
16
+ ··· − 2u − 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−4.86 × 10
58
u
51
− 6.70 × 10
58
u
50
+ · · · + 6.23 × 10
59
b + 8.49 ×
10
59
, −6.69 × 10
58
u
51
+ 2.75 × 10
59
u
50
+ · · · + 4.79 × 10
58
a + 8.72 ×
10
59
, u
52
− 4u
51
+ · · · + 18u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
−u
3
+ u
a
5
=
1.39459u
51
− 5.74023u
50
+ ··· + 155.294u − 18.1836
0.0779815u
51
+ 0.107481u
50
+ ··· − 22.1919u − 1.36229
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
1.47257u
51
− 5.63275u
50
+ ··· + 133.102u − 19.5459
0.0779815u
51
+ 0.107481u
50
+ ··· − 22.1919u − 1.36229
a
2
=
−4.28758u
51
+ 17.1080u
50
+ ··· − 1091.27u − 36.3160
0.0338379u
51
− 0.0711693u
50
+ ··· − 2.55862u + 1.27029
a
7
=
−1.21648u
51
+ 4.74618u
50
+ ··· − 367.518u − 25.5631
−0.0685253u
51
+ 0.296845u
50
+ ··· − 8.41934u + 0.118102
a
6
=
−1.21648u
51
+ 4.74618u
50
+ ··· − 367.518u − 25.5631
−0.194638u
51
+ 0.560317u
50
+ ··· − 5.04742u + 0.237849
a
11
=
1.55761u
51
− 6.02658u
50
+ ··· + 450.253u + 35.6977
0.0494698u
51
− 0.154809u
50
+ ··· + 12.1116u − 0.0549377
a
3
=
−1.21792u
51
+ 5.14238u
50
+ ··· − 481.653u − 35.7438
−0.124343u
51
+ 0.226786u
50
+ ··· − 5.42725u + 0.405315
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.948355u
51
− 2.66963u
50
+ ··· + 228.868u + 10.1763
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
52
− 9u
51
+ ··· + 27964u − 1601
c
2
, c
5
u
52
− 2u
51
+ ··· + 273u + 131
c
3
, c
10
u
52
− u
51
+ ··· + 455u + 47
c
4
, c
7
u
52
− 3u
51
+ ··· + 6u − 1
c
6
, c
11
u
52
− 14u
50
+ ··· − 1895u + 425
c
8
, c
9
, c
12
u
52
+ 4u
51
+ ··· − 18u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
52
− 69y
51
+ ··· + 3606192y + 2563201
c
2
, c
5
y
52
− 26y
51
+ ··· − 263693y + 17161
c
3
, c
10
y
52
+ 19y
51
+ ··· − 52301y + 2209
c
4
, c
7
y
52
+ 13y
51
+ ··· − 80y + 1
c
6
, c
11
y
52
− 28y
51
+ ··· − 3054675y + 180625
c
8
, c
9
, c
12
y
52
− 68y
51
+ ··· + 260y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.963102 + 0.345038I
a = 0.367913 + 0.884454I
b = −0.701674 − 0.540338I
1.19699 + 4.57480I 0
u = −0.963102 − 0.345038I
a = 0.367913 − 0.884454I
b = −0.701674 + 0.540338I
1.19699 − 4.57480I 0
u = 1.010440 + 0.226511I
a = −0.195406 + 0.336697I
b = −0.565644 − 0.187214I
−1.74134 − 0.12755I 0
u = 1.010440 − 0.226511I
a = −0.195406 − 0.336697I
b = −0.565644 + 0.187214I
−1.74134 + 0.12755I 0
u = −0.284882 + 1.011440I
a = 0.769715 + 0.747090I
b = −0.604356 − 0.603378I
3.70336 − 4.26964I 0
u = −0.284882 − 1.011440I
a = 0.769715 − 0.747090I
b = −0.604356 + 0.603378I
3.70336 + 4.26964I 0
u = −0.654100 + 0.538210I
a = 0.26052 + 1.52753I
b = 0.855051 − 0.775108I
−1.64856 + 4.08097I −3.59358 − 7.53580I
u = −0.654100 − 0.538210I
a = 0.26052 − 1.52753I
b = 0.855051 + 0.775108I
−1.64856 − 4.08097I −3.59358 + 7.53580I
u = 1.109320 + 0.362480I
a = −0.49904 + 1.54272I
b = −0.519449 − 0.934936I
0.59353 − 3.33817I 0
u = 1.109320 − 0.362480I
a = −0.49904 − 1.54272I
b = −0.519449 + 0.934936I
0.59353 + 3.33817I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.822872 + 0.103062I
a = 0.257461 + 0.646673I
b = −0.242471 + 1.056410I
6.24954 − 0.94391I 0.647108 − 0.326933I
u = −0.822872 − 0.103062I
a = 0.257461 − 0.646673I
b = −0.242471 − 1.056410I
6.24954 + 0.94391I 0.647108 + 0.326933I
u = −0.862860 + 0.795004I
a = 0.01742 − 1.46293I
b = −0.818392 + 0.955221I
1.92110 + 10.19650I 0
u = −0.862860 − 0.795004I
a = 0.01742 + 1.46293I
b = −0.818392 − 0.955221I
1.92110 − 10.19650I 0
u = 0.940755 + 0.772008I
a = −0.376983 − 0.720478I
b = 0.668255 + 0.424349I
−0.98442 − 3.07513I 0
u = 0.940755 − 0.772008I
a = −0.376983 + 0.720478I
b = 0.668255 − 0.424349I
−0.98442 + 3.07513I 0
u = −0.038382 + 0.763918I
a = 0.34582 − 2.02691I
b = −0.418556 + 0.708156I
4.27045 − 0.69241I 2.11238 − 0.92531I
u = −0.038382 − 0.763918I
a = 0.34582 + 2.02691I
b = −0.418556 − 0.708156I
4.27045 + 0.69241I 2.11238 + 0.92531I
u = 1.251610 + 0.050476I
a = −0.50166 + 1.68503I
b = −0.371536 − 1.046800I
0.92724 − 3.35039I 0
u = 1.251610 − 0.050476I
a = −0.50166 − 1.68503I
b = −0.371536 + 1.046800I
0.92724 + 3.35039I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.272460 + 0.135660I
a = 0.48984 + 1.43474I
b = −0.144334 − 0.106513I
1.17738 + 4.15170I 0
u = −1.272460 − 0.135660I
a = 0.48984 − 1.43474I
b = −0.144334 + 0.106513I
1.17738 − 4.15170I 0
u = −0.687341 + 0.187968I
a = −0.167504 − 0.552195I
b = 0.675651 + 0.912887I
−1.04394 − 1.60688I −0.66527 − 4.34427I
u = −0.687341 − 0.187968I
a = −0.167504 + 0.552195I
b = 0.675651 − 0.912887I
−1.04394 + 1.60688I −0.66527 + 4.34427I
u = 0.647636 + 0.201060I
a = −0.00791 − 1.98697I
b = 0.806130 + 0.597381I
−1.174450 − 0.681589I −4.08137 − 1.34656I
u = 0.647636 − 0.201060I
a = −0.00791 + 1.98697I
b = 0.806130 − 0.597381I
−1.174450 + 0.681589I −4.08137 + 1.34656I
u = 1.42899 + 0.06703I
a = −0.209013 − 0.868503I
b = −0.03651 + 1.49771I
1.98258 − 2.19587I 0
u = 1.42899 − 0.06703I
a = −0.209013 + 0.868503I
b = −0.03651 − 1.49771I
1.98258 + 2.19587I 0
u = 1.59652
a = 0.0339995
b = −0.841839
−2.31786 0
u = 1.61247 + 0.20315I
a = 0.576829 − 1.030930I
b = 1.00137 + 1.04577I
−9.32125 − 7.00176I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.61247 − 0.20315I
a = 0.576829 + 1.030930I
b = 1.00137 − 1.04577I
−9.32125 + 7.00176I 0
u = −1.64815 + 0.06439I
a = 0.225695 + 1.000060I
b = 1.06497 − 1.24440I
−9.35796 + 1.73629I 0
u = −1.64815 − 0.06439I
a = 0.225695 − 1.000060I
b = 1.06497 + 1.24440I
−9.35796 − 1.73629I 0
u = 0.025016 + 0.346811I
a = −1.56278 − 0.62107I
b = 0.478121 + 0.406062I
−0.212444 − 1.082960I −3.65080 + 5.73682I
u = 0.025016 − 0.346811I
a = −1.56278 + 0.62107I
b = 0.478121 − 0.406062I
−0.212444 + 1.082960I −3.65080 − 5.73682I
u = −0.324576 + 0.095938I
a = −1.45555 + 2.26639I
b = −0.12420 − 1.49308I
7.90529 + 1.59104I −6.15709 − 6.22190I
u = −0.324576 − 0.095938I
a = −1.45555 − 2.26639I
b = −0.12420 + 1.49308I
7.90529 − 1.59104I −6.15709 + 6.22190I
u = 1.67054 + 0.05789I
a = 0.072885 + 0.406252I
b = 1.08948 − 0.99449I
−9.55452 + 0.59565I 0
u = 1.67054 − 0.05789I
a = 0.072885 − 0.406252I
b = 1.08948 + 0.99449I
−9.55452 − 0.59565I 0
u = 1.69396 + 0.07384I
a = 0.019572 − 0.434345I
b = −1.29976 + 0.82350I
−8.09214 − 6.09898I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.69396 − 0.07384I
a = 0.019572 + 0.434345I
b = −1.29976 − 0.82350I
−8.09214 + 6.09898I 0
u = 1.69403 + 0.24798I
a = −0.417925 + 1.083500I
b = −0.99514 − 1.24001I
−6.6989 − 14.2733I 0
u = 1.69403 − 0.24798I
a = −0.417925 − 1.083500I
b = −0.99514 + 1.24001I
−6.6989 + 14.2733I 0
u = −1.72157 + 0.11548I
a = −0.252652 − 0.581934I
b = −1.024730 + 0.709607I
−11.31890 + 1.98764I 0
u = −1.72157 − 0.11548I
a = −0.252652 + 0.581934I
b = −1.024730 − 0.709607I
−11.31890 − 1.98764I 0
u = −1.73054 + 0.06720I
a = −0.366356 − 0.965910I
b = −0.79731 + 1.27731I
−9.45621 + 4.84743I 0
u = −1.73054 − 0.06720I
a = −0.366356 + 0.965910I
b = −0.79731 − 1.27731I
−9.45621 − 4.84743I 0
u = −1.72514 + 0.16764I
a = 0.047255 + 0.719370I
b = 1.21416 − 0.93670I
−10.30920 + 6.54217I 0
u = −1.72514 − 0.16764I
a = 0.047255 − 0.719370I
b = 1.21416 + 0.93670I
−10.30920 − 6.54217I 0
u = 1.76333
a = 0.283022
b = 0.127597
−3.04170 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.0287121 + 0.0617140I
a = −26.0966 + 4.5514I
b = −0.332012 − 0.710988I
5.14104 − 3.45107I 1.85198 + 12.31156I
u = −0.0287121 − 0.0617140I
a = −26.0966 − 4.5514I
b = −0.332012 + 0.710988I
5.14104 + 3.45107I 1.85198 − 12.31156I
10
II.
I
u
2
= h−u
16
−u
15
+· · ·+b+1, 2u
16
+u
15
+· · ·+a−6u, u
17
+u
16
+· · ·−2u−1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
−u
3
+ u
a
5
=
−2u
16
− u
15
+ ··· + 6u
2
+ 6u
u
16
+ u
15
+ ··· − 3u − 1
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
−u
16
+ 11u
14
+ ··· + 3u − 1
u
16
+ u
15
+ ··· − 3u − 1
a
2
=
7u
16
− u
15
+ ··· − 12u − 5
−u
16
+ u
15
+ ··· + 4u + 2
a
7
=
−2u
16
+ u
15
+ ··· − 4u − 1
−u
16
+ u
15
+ ··· + 2u + 3
a
6
=
−2u
16
+ u
15
+ ··· − 4u − 1
−5u
16
+ 2u
15
+ ··· + 6u + 6
a
11
=
−u
16
− u
15
+ ··· + 7u + 4
−3u
16
+ u
15
+ ··· + 5u + 1
a
3
=
2u
16
+ u
15
+ ··· − 15u − 2
u
14
− 9u
12
+ ··· + 6u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 10u
16
− 6u
15
− 110u
14
+ 70u
13
+ 488u
12
− 325u
11
− 1118u
10
+
745u
9
+ 1405u
8
− 837u
7
− 967u
6
+ 345u
5
+ 383u
4
+ 54u
3
− 104u
2
− 30u − 7
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 2u
16
+ ··· − 6u − 1
c
2
u
17
+ 3u
16
+ ··· + 3u + 1
c
3
u
17
+ 6u
15
+ ··· + 5u + 1
c
4
u
17
− 2u
16
+ ··· + 3u
2
+ 1
c
5
u
17
− 3u
16
+ ··· + 3u − 1
c
6
u
17
− u
16
+ ··· + u − 1
c
7
u
17
+ 2u
16
+ ··· − 3u
2
− 1
c
8
, c
9
u
17
+ u
16
+ ··· − 2u − 1
c
10
u
17
+ 6u
15
+ ··· + 5u − 1
c
11
u
17
+ u
16
+ ··· + u + 1
c
12
u
17
− u
16
+ ··· − 2u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 4y
16
+ ··· − 26y −1
c
2
, c
5
y
17
− 9y
16
+ ··· − y −1
c
3
, c
10
y
17
+ 12y
16
+ ··· − y −1
c
4
, c
7
y
17
+ 14y
16
+ ··· − 6y −1
c
6
, c
11
y
17
− 15y
16
+ ··· − 11y −1
c
8
, c
9
, c
12
y
17
− 23y
16
+ ··· − 10y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.814883 + 0.146214I
a = −0.160618 + 1.013790I
b = −0.571946 − 0.823470I
−1.33985 − 2.24720I −5.95506 + 5.95440I
u = 0.814883 − 0.146214I
a = −0.160618 − 1.013790I
b = −0.571946 + 0.823470I
−1.33985 + 2.24720I −5.95506 − 5.95440I
u = 1.095140 + 0.425247I
a = 0.092570 + 1.009470I
b = −0.455837 − 0.491181I
−1.08205 − 2.27893I −6.70496 + 1.73929I
u = 1.095140 − 0.425247I
a = 0.092570 − 1.009470I
b = −0.455837 + 0.491181I
−1.08205 + 2.27893I −6.70496 − 1.73929I
u = −1.275130 + 0.141662I
a = 0.37799 + 2.40221I
b = 0.219893 − 0.781229I
1.94744 + 4.76023I 2.64985 − 7.50749I
u = −1.275130 − 0.141662I
a = 0.37799 − 2.40221I
b = 0.219893 + 0.781229I
1.94744 − 4.76023I 2.64985 + 7.50749I
u = −1.360960 + 0.148840I
a = −0.176402 − 0.162239I
b = 0.183220 + 1.287410I
3.94456 + 3.04243I −0.60355 − 3.01266I
u = −1.360960 − 0.148840I
a = −0.176402 + 0.162239I
b = 0.183220 − 1.287410I
3.94456 − 3.04243I −0.60355 + 3.01266I
u = 1.42974 + 0.17726I
a = 0.068411 − 1.219830I
b = −0.04806 + 1.42695I
3.20138 − 0.56588I −0.308792 − 0.292572I
u = 1.42974 − 0.17726I
a = 0.068411 + 1.219830I
b = −0.04806 − 1.42695I
3.20138 + 0.56588I −0.308792 + 0.292572I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.361683 + 0.406042I
a = −2.74838 + 0.48990I
b = 0.271380 + 0.625613I
5.13097 − 2.92831I 1.67399 − 2.10848I
u = −0.361683 − 0.406042I
a = −2.74838 − 0.48990I
b = 0.271380 − 0.625613I
5.13097 + 2.92831I 1.67399 + 2.10848I
u = −0.067162 + 0.319437I
a = −2.12846 + 2.03319I
b = 0.101807 − 1.385190I
8.35935 − 1.32853I 8.08277 − 1.45889I
u = −0.067162 − 0.319437I
a = −2.12846 − 2.03319I
b = 0.101807 + 1.385190I
8.35935 + 1.32853I 8.08277 + 1.45889I
u = −1.68979 + 0.08907I
a = −0.307853 − 0.828725I
b = −0.95599 + 1.10192I
−10.26660 + 3.59650I −5.48002 − 1.90134I
u = −1.68979 − 0.08907I
a = −0.307853 + 0.828725I
b = −0.95599 − 1.10192I
−10.26660 − 3.59650I −5.48002 + 1.90134I
u = 1.82991
a = −0.0345207
b = 0.511063
−3.34108 −21.7080
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
17
− 2u
16
+ ··· − 6u − 1)(u
52
− 9u
51
+ ··· + 27964u − 1601)
c
2
(u
17
+ 3u
16
+ ··· + 3u + 1)(u
52
− 2u
51
+ ··· + 273u + 131)
c
3
(u
17
+ 6u
15
+ ··· + 5u + 1)(u
52
− u
51
+ ··· + 455u + 47)
c
4
(u
17
− 2u
16
+ ··· + 3u
2
+ 1)(u
52
− 3u
51
+ ··· + 6u − 1)
c
5
(u
17
− 3u
16
+ ··· + 3u − 1)(u
52
− 2u
51
+ ··· + 273u + 131)
c
6
(u
17
− u
16
+ ··· + u − 1)(u
52
− 14u
50
+ ··· − 1895u + 425)
c
7
(u
17
+ 2u
16
+ ··· − 3u
2
− 1)(u
52
− 3u
51
+ ··· + 6u − 1)
c
8
, c
9
(u
17
+ u
16
+ ··· − 2u − 1)(u
52
+ 4u
51
+ ··· − 18u + 1)
c
10
(u
17
+ 6u
15
+ ··· + 5u − 1)(u
52
− u
51
+ ··· + 455u + 47)
c
11
(u
17
+ u
16
+ ··· + u + 1)(u
52
− 14u
50
+ ··· − 1895u + 425)
c
12
(u
17
− u
16
+ ··· − 2u + 1)(u
52
+ 4u
51
+ ··· − 18u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
17
+ 4y
16
+ ··· − 26y −1)
· (y
52
− 69y
51
+ ··· + 3606192y + 2563201)
c
2
, c
5
(y
17
− 9y
16
+ ··· − y −1)(y
52
− 26y
51
+ ··· − 263693y + 17161)
c
3
, c
10
(y
17
+ 12y
16
+ ··· − y −1)(y
52
+ 19y
51
+ ··· − 52301y + 2209)
c
4
, c
7
(y
17
+ 14y
16
+ ··· − 6y −1)(y
52
+ 13y
51
+ ··· − 80y + 1)
c
6
, c
11
(y
17
− 15y
16
+ ··· − 11y −1)
· (y
52
− 28y
51
+ ··· − 3054675y + 180625)
c
8
, c
9
, c
12
(y
17
− 23y
16
+ ··· − 10y −1)(y
52
− 68y
51
+ ··· + 260y + 1)
17
