12n
0178
(K12n
0178
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 10 9 12 3 6 1 7 11
Solving Sequence
5,10 3,6
2 1 11 4 9 7 12 8
c
5
c
2
c
1
c
10
c
4
c
9
c
6
c
12
c
7
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h9.57275 × 10
53
u
54
+ 1.47300 × 10
54
u
53
+ ··· + 8.10588 × 10
54
b + 5.80479 × 10
54
,
− 1.30447 × 10
55
u
54
− 2.66313 × 10
55
u
53
+ ··· + 8.10588 × 10
54
a − 2.06989 × 10
55
, u
55
+ 2u
54
+ ··· + 4u + 1i
I
u
2
= hb + 1, −u
3
− u
2
+ a − 3u − 2, u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 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
= h9.57×10
53
u
54
+1.47×10
54
u
53
+· · ·+8.11×10
54
b+5.80×10
54
, −1.30×
10
55
u
54
−2.66×10
55
u
53
+· · ·+8.11×10
54
a−2.07×10
55
, u
55
+2u
54
+· · ·+4u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
1.60929u
54
+ 3.28543u
53
+ ··· − 0.667235u + 2.55356
−0.118096u
54
− 0.181720u
53
+ ··· + 1.32185u − 0.716120
a
6
=
1
−u
2
a
2
=
1.49119u
54
+ 3.10371u
53
+ ··· + 0.654617u + 1.83744
−0.118096u
54
− 0.181720u
53
+ ··· + 1.32185u − 0.716120
a
1
=
0.0670214u
54
+ 0.408100u
53
+ ··· + 0.231214u − 0.865681
−0.119667u
54
− 0.280385u
53
+ ··· + 1.25999u + 0.229470
a
11
=
−0.0627514u
54
+ 0.225048u
53
+ ··· + 2.67144u + 0.447681
−0.115045u
54
− 0.310044u
53
+ ··· + 1.95308u + 0.125113
a
4
=
1.55763u
54
+ 3.14463u
53
+ ··· − 0.402533u + 2.59906
−0.0743860u
54
− 0.0787220u
53
+ ··· + 0.855578u − 0.799104
a
9
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
12
=
−0.451706u
54
− 0.711582u
53
+ ··· + 5.15586u + 0.621849
0.0254744u
54
− 0.291495u
53
+ ··· − 0.656683u − 0.382675
a
8
=
0.00353609u
54
− 0.0598773u
53
+ ··· − 2.34653u + 0.394759
0.0754811u
54
+ 0.239141u
53
+ ··· + 0.161367u − 0.119595
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.76753u
54
+ 0.155153u
53
+ ··· + 63.8827u + 5.20939
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
55
+ 24u
54
+ ··· − 40u + 1
c
2
, c
4
u
55
− 6u
54
+ ··· + 12u + 1
c
3
, c
8
u
55
+ u
54
+ ··· + 448u + 32
c
5
, c
6
, c
9
u
55
+ 2u
54
+ ··· + 4u + 1
c
7
, c
11
u
55
+ 2u
54
+ ··· + 4u + 1
c
10
, c
12
u
55
− 20u
54
+ ··· + 22u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
55
+ 20y
54
+ ··· − 40060y −1
c
2
, c
4
y
55
− 24y
54
+ ··· − 40y −1
c
3
, c
8
y
55
+ 33y
54
+ ··· + 27136y −1024
c
5
, c
6
, c
9
y
55
+ 44y
54
+ ··· + 22y −1
c
7
, c
11
y
55
− 20y
54
+ ··· + 22y −1
c
10
, c
12
y
55
+ 32y
54
+ ··· + 210y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.072313 + 0.999634I
a = 2.29927 − 6.60365I
b = −0.958174 − 0.009887I
−3.21384 − 2.03983I −44.2012 − 7.6598I
u = 0.072313 − 0.999634I
a = 2.29927 + 6.60365I
b = −0.958174 + 0.009887I
−3.21384 + 2.03983I −44.2012 + 7.6598I
u = 0.993934 + 0.162352I
a = −0.493168 + 1.055260I
b = 1.033280 − 0.648823I
0.91067 + 4.40051I 0.64951 − 3.45726I
u = 0.993934 − 0.162352I
a = −0.493168 − 1.055260I
b = 1.033280 + 0.648823I
0.91067 − 4.40051I 0.64951 + 3.45726I
u = −1.001870 + 0.130107I
a = −0.620284 − 1.134160I
b = 1.114800 + 0.710314I
2.39213 − 10.23010I 2.28495 + 7.44906I
u = −1.001870 − 0.130107I
a = −0.620284 + 1.134160I
b = 1.114800 − 0.710314I
2.39213 + 10.23010I 2.28495 − 7.44906I
u = 0.137708 + 0.978085I
a = 0.876327 − 0.305252I
b = −0.0541745 + 0.0630040I
−1.78463 + 2.08708I −0.67506 − 3.94082I
u = 0.137708 − 0.978085I
a = 0.876327 + 0.305252I
b = −0.0541745 − 0.0630040I
−1.78463 − 2.08708I −0.67506 + 3.94082I
u = −0.920019 + 0.123504I
a = −0.295321 − 1.372000I
b = 0.879379 + 0.854012I
7.49655 − 3.13489I 7.28291 + 3.22695I
u = −0.920019 − 0.123504I
a = −0.295321 + 1.372000I
b = 0.879379 − 0.854012I
7.49655 + 3.13489I 7.28291 − 3.22695I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.210457 + 1.111180I
a = 0.166418 − 1.112530I
b = −0.533647 + 0.528199I
−1.62268 + 2.42881I 0
u = 0.210457 − 1.111180I
a = 0.166418 + 1.112530I
b = −0.533647 − 0.528199I
−1.62268 − 2.42881I 0
u = −0.085057 + 1.147710I
a = −0.91778 + 1.25610I
b = −1.132530 − 0.298762I
−4.28823 − 1.16800I 0
u = −0.085057 − 1.147710I
a = −0.91778 − 1.25610I
b = −1.132530 + 0.298762I
−4.28823 + 1.16800I 0
u = 0.828480 + 0.174420I
a = 0.110067 + 1.220490I
b = 0.608202 − 0.730301I
2.20429 + 0.89304I 2.75128 − 2.60461I
u = 0.828480 − 0.174420I
a = 0.110067 − 1.220490I
b = 0.608202 + 0.730301I
2.20429 − 0.89304I 2.75128 + 2.60461I
u = −0.819216 + 0.097633I
a = 0.17500 − 1.53413I
b = 0.550668 + 0.941243I
4.13978 + 4.18210I 5.23081 − 2.78874I
u = −0.819216 − 0.097633I
a = 0.17500 + 1.53413I
b = 0.550668 − 0.941243I
4.13978 − 4.18210I 5.23081 + 2.78874I
u = −0.146957 + 1.227320I
a = −0.250773 + 0.958708I
b = −1.25230 − 0.85045I
−5.99858 − 1.47280I 0
u = −0.146957 − 1.227320I
a = −0.250773 − 0.958708I
b = −1.25230 + 0.85045I
−5.99858 + 1.47280I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.381441 + 1.177740I
a = −0.265339 − 0.556912I
b = 0.209231 + 1.073740I
−0.86862 + 3.44583I 0
u = 0.381441 − 1.177740I
a = −0.265339 + 0.556912I
b = 0.209231 − 1.073740I
−0.86862 − 3.44583I 0
u = 0.177845 + 1.232580I
a = −0.197287 − 0.999523I
b = −1.11540 + 1.02762I
−5.34328 + 6.53526I 0
u = 0.177845 − 1.232580I
a = −0.197287 + 0.999523I
b = −1.11540 − 1.02762I
−5.34328 − 6.53526I 0
u = −0.014389 + 1.247610I
a = −0.396154 + 0.123893I
b = −1.75259 − 0.09946I
−7.40193 − 2.54973I 0
u = −0.014389 − 1.247610I
a = −0.396154 − 0.123893I
b = −1.75259 + 0.09946I
−7.40193 + 2.54973I 0
u = 0.614835 + 1.102710I
a = −0.145574 + 0.034160I
b = 0.742661 + 0.465384I
−1.99257 + 1.17321I 0
u = 0.614835 − 1.102710I
a = −0.145574 − 0.034160I
b = 0.742661 − 0.465384I
−1.99257 − 1.17321I 0
u = −0.468976 + 1.184810I
a = −0.356235 + 0.277549I
b = 0.611745 − 0.951185I
4.23996 − 1.81305I 0
u = −0.468976 − 1.184810I
a = −0.356235 − 0.277549I
b = 0.611745 + 0.951185I
4.23996 + 1.81305I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.394816 + 1.214720I
a = −0.407055 + 0.558974I
b = 0.327121 − 1.259930I
0.69756 − 8.56499I 0
u = −0.394816 − 1.214720I
a = −0.407055 − 0.558974I
b = 0.327121 + 1.259930I
0.69756 + 8.56499I 0
u = −0.601783 + 1.184100I
a = −0.280221 − 0.060494I
b = 0.893170 − 0.577080I
−0.82436 + 4.63316I 0
u = −0.601783 − 1.184100I
a = −0.280221 + 0.060494I
b = 0.893170 + 0.577080I
−0.82436 − 4.63316I 0
u = −0.33663 + 1.38775I
a = 0.970187 − 0.767712I
b = 0.813537 + 0.578538I
−0.568084 + 0.034758I 0
u = −0.33663 − 1.38775I
a = 0.970187 + 0.767712I
b = 0.813537 − 0.578538I
−0.568084 − 0.034758I 0
u = −0.42146 + 1.38024I
a = 0.787185 − 1.119040I
b = 1.083980 + 0.732016I
2.75927 − 7.95467I 0
u = −0.42146 − 1.38024I
a = 0.787185 + 1.119040I
b = 1.083980 − 0.732016I
2.75927 + 7.95467I 0
u = −0.46185 + 1.38681I
a = 0.562764 − 1.256260I
b = 1.29657 + 0.72034I
−2.3616 − 15.4470I 0
u = −0.46185 − 1.38681I
a = 0.562764 + 1.256260I
b = 1.29657 − 0.72034I
−2.3616 + 15.4470I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.45518 + 1.39872I
a = 0.558722 + 1.163830I
b = 1.25544 − 0.65692I
−3.98197 + 9.57742I 0
u = 0.45518 − 1.39872I
a = 0.558722 − 1.163830I
b = 1.25544 + 0.65692I
−3.98197 − 9.57742I 0
u = 0.38456 + 1.42439I
a = 0.750991 + 0.847131I
b = 0.988852 − 0.539464I
−2.92074 + 5.31715I 0
u = 0.38456 − 1.42439I
a = 0.750991 − 0.847131I
b = 0.988852 + 0.539464I
−2.92074 − 5.31715I 0
u = 0.443695 + 0.152031I
a = 2.39257 − 1.10066I
b = −0.785702 + 0.556656I
−1.28934 + 4.28381I 2.06004 − 6.33313I
u = 0.443695 − 0.152031I
a = 2.39257 + 1.10066I
b = −0.785702 − 0.556656I
−1.28934 − 4.28381I 2.06004 + 6.33313I
u = 0.458210 + 0.088205I
a = 1.25519 + 0.67781I
b = −0.128180 − 0.374679I
1.217180 + 0.208314I 8.43782 − 0.43348I
u = 0.458210 − 0.088205I
a = 1.25519 − 0.67781I
b = −0.128180 + 0.374679I
1.217180 − 0.208314I 8.43782 + 0.43348I
u = −0.359115 + 0.183471I
a = 2.71826 + 0.82408I
b = −0.926073 − 0.380961I
−1.94814 + 0.37120I −0.242965 − 0.911940I
u = −0.359115 − 0.183471I
a = 2.71826 − 0.82408I
b = −0.926073 + 0.380961I
−1.94814 − 0.37120I −0.242965 + 0.911940I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.069012 + 0.377349I
a = 3.57577 + 0.18002I
b = −1.196500 − 0.044788I
−2.88229 − 2.31843I 4.89435 + 2.66761I
u = −0.069012 − 0.377349I
a = 3.57577 − 0.18002I
b = −1.196500 + 0.044788I
−2.88229 + 2.31843I 4.89435 − 2.66761I
u = 0.05440 + 1.73056I
a = 0.565358 + 0.054624I
b = 0.867697 − 0.027497I
−12.32020 + 3.39229I 0
u = 0.05440 − 1.73056I
a = 0.565358 − 0.054624I
b = 0.867697 + 0.027497I
−12.32020 − 3.39229I 0
u = −0.223807
a = 2.72223
b = −0.882156
−1.26969 −9.83510
10
II. I
u
2
= hb + 1, −u
3
− u
2
+ a − 3u − 2, u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
u
3
+ u
2
+ 3u + 2
−1
a
6
=
1
−u
2
a
2
=
u
3
+ u
2
+ 3u + 1
−1
a
1
=
−1
0
a
11
=
u
u
a
4
=
u
3
+ u
2
+ 3u + 2
−1
a
9
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
12
=
−u
2
− 1
−u
2
a
8
=
−u
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
4
+ 3u
3
+ 20u
2
+ 8u + 8
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
8
u
5
c
4
(u + 1)
5
c
5
, c
6
, c
10
u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1
c
7
u
5
+ u
4
− u
2
+ u + 1
c
9
, c
12
u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1
c
11
u
5
− u
4
+ u
2
+ u − 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
8
y
5
c
5
, c
6
, c
9
c
10
, c
12
y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1
c
7
, c
11
y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.233677 + 0.885557I
a = 1.10636 + 1.69341I
b = −1.00000
−3.46474 − 2.21397I −5.40639 − 0.42541I
u = −0.233677 − 0.885557I
a = 1.10636 − 1.69341I
b = −1.00000
−3.46474 + 2.21397I −5.40639 + 0.42541I
u = −0.416284
a = 0.852303
b = −1.00000
−0.762751 8.03930
u = −0.05818 + 1.69128I
a = −0.532511 + 0.056433I
b = −1.00000
−12.60320 − 3.33174I −15.6132 − 0.3694I
u = −0.05818 − 1.69128I
a = −0.532511 − 0.056433I
b = −1.00000
−12.60320 + 3.33174I −15.6132 + 0.3694I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
55
+ 24u
54
+ ··· − 40u + 1)
c
2
((u − 1)
5
)(u
55
− 6u
54
+ ··· + 12u + 1)
c
3
, c
8
u
5
(u
55
+ u
54
+ ··· + 448u + 32)
c
4
((u + 1)
5
)(u
55
− 6u
54
+ ··· + 12u + 1)
c
5
, c
6
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)(u
55
+ 2u
54
+ ··· + 4u + 1)
c
7
(u
5
+ u
4
− u
2
+ u + 1)(u
55
+ 2u
54
+ ··· + 4u + 1)
c
9
(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)(u
55
+ 2u
54
+ ··· + 4u + 1)
c
10
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)(u
55
− 20u
54
+ ··· + 22u − 1)
c
11
(u
5
− u
4
+ u
2
+ u − 1)(u
55
+ 2u
54
+ ··· + 4u + 1)
c
12
(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)(u
55
− 20u
54
+ ··· + 22u − 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
5
)(y
55
+ 20y
54
+ ··· − 40060y −1)
c
2
, c
4
((y −1)
5
)(y
55
− 24y
54
+ ··· − 40y −1)
c
3
, c
8
y
5
(y
55
+ 33y
54
+ ··· + 27136y −1024)
c
5
, c
6
, c
9
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)(y
55
+ 44y
54
+ ··· + 22y −1)
c
7
, c
11
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)(y
55
− 20y
54
+ ··· + 22y −1)
c
10
, c
12
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)(y
55
+ 32y
54
+ ··· + 210y −1)
16
