12n
0337
(K12n
0337
)
A knot diagram
1
Linearized knot diagam
3 6 8 7 11 2 9 4 12 6 10 9
Solving Sequence
6,10
11
3,12
2 7 1 5 4 9 8
c
10
c
11
c
2
c
6
c
1
c
5
c
4
c
9
c
7
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h8.75045 × 10
28
u
62
+ 5.63839 × 10
29
u
61
+ ··· + 4.42036 × 10
29
b + 4.19132 × 10
29
,
− 8.61586 × 10
29
u
62
+ 6.95817 × 10
29
u
61
+ ··· + 2.21018 × 10
29
a + 3.02574 × 10
30
, u
63
− u
62
+ ··· − 10u + 1i
I
u
2
= hu
5
b + u
3
b + 2u
2
b + b
2
+ 2bu − u
2
− u − 2, −u
4
+ a − 1, u
6
+ u
4
+ 2u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 75 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
= h8.75×10
28
u
62
+5.64×10
29
u
61
+· · ·+4.42×10
29
b+4.19×10
29
, −8.62×
10
29
u
62
+6.96×10
29
u
61
+· · ·+2.21×10
29
a+3.03×10
30
, u
63
−u
62
+· · ·−10u+1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
3
=
3.89826u
62
− 3.14824u
61
+ ··· + 86.3365u − 13.6900
−0.197958u
62
− 1.27555u
61
+ ··· + 12.6503u − 0.948184
a
12
=
u
2
+ 1
u
2
a
2
=
3.89826u
62
− 3.14824u
61
+ ··· + 86.3365u − 13.6900
−0.929682u
62
− 1.65830u
61
+ ··· + 16.2523u − 1.69821
a
7
=
1.53828u
62
− 0.187645u
61
+ ··· + 14.1508u − 6.97201
2.72772u
62
− 1.67622u
61
+ ··· + 30.4294u − 4.29057
a
1
=
u
6
+ u
4
+ 2u
2
+ 1
u
6
+ u
2
a
5
=
u
u
3
+ u
a
4
=
0.471410u
62
− 0.471626u
61
+ ··· + 16.3283u + 1.49775
−2.28058u
62
− 0.384216u
61
+ ··· − 9.13957u + 2.00704
a
9
=
u
4
+ u
2
+ 1
u
4
a
8
=
1.43450u
62
− 0.861770u
61
+ ··· + 27.0832u − 9.69122
1.91211u
62
− 0.548333u
61
+ ··· + 17.6204u − 2.91399
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.06158u
62
− 4.22142u
61
+ ··· + 98.6123u − 19.1903
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
63
+ 23u
62
+ ··· − 11050u − 625
c
2
, c
6
u
63
− u
62
+ ··· + 40u − 25
c
3
, c
8
u
63
− u
62
+ ··· + 2u
2
− 1
c
4
u
63
− 3u
62
+ ··· + 736u − 53
c
5
, c
10
u
63
+ u
62
+ ··· − 10u − 1
c
7
u
63
− 35u
62
+ ··· + 4u − 1
c
9
, c
11
, c
12
u
63
− 23u
62
+ ··· + 38u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
63
+ 47y
62
+ ··· − 20571250y −390625
c
2
, c
6
y
63
+ 23y
62
+ ··· − 11050y −625
c
3
, c
8
y
63
− 35y
62
+ ··· + 4y −1
c
4
y
63
+ 49y
62
+ ··· + 209280y −2809
c
5
, c
10
y
63
+ 23y
62
+ ··· + 38y −1
c
7
y
63
− 7y
62
+ ··· + 4y −1
c
9
, c
11
, c
12
y
63
+ 39y
62
+ ··· + 682y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.615481 + 0.782024I
a = 0.924724 + 0.192341I
b = −0.085512 − 1.194750I
−2.81026 − 3.12410I 1.80668 + 2.74088I
u = 0.615481 − 0.782024I
a = 0.924724 − 0.192341I
b = −0.085512 + 1.194750I
−2.81026 + 3.12410I 1.80668 − 2.74088I
u = −0.817617 + 0.593503I
a = 1.176330 − 0.407742I
b = −0.666725 − 0.147698I
−0.28869 − 4.27274I 0. + 2.20858I
u = −0.817617 − 0.593503I
a = 1.176330 + 0.407742I
b = −0.666725 + 0.147698I
−0.28869 + 4.27274I 0. − 2.20858I
u = −0.822477 + 0.507948I
a = −0.501572 − 1.068710I
b = 0.080964 − 0.498715I
4.20996 − 3.12624I 4.99490 + 1.04203I
u = −0.822477 − 0.507948I
a = −0.501572 + 1.068710I
b = 0.080964 + 0.498715I
4.20996 + 3.12624I 4.99490 − 1.04203I
u = −0.654440 + 0.706606I
a = 1.004440 − 0.278481I
b = −0.521492 + 0.799483I
−3.29416 − 2.07147I −0.14477 + 3.47358I
u = −0.654440 − 0.706606I
a = 1.004440 + 0.278481I
b = −0.521492 − 0.799483I
−3.29416 + 2.07147I −0.14477 − 3.47358I
u = 0.822755 + 0.498425I
a = 1.246610 + 0.349007I
b = −0.388160 + 0.165493I
4.25689 + 0.43803I 5.01449 + 0.38960I
u = 0.822755 − 0.498425I
a = 1.246610 − 0.349007I
b = −0.388160 − 0.165493I
4.25689 − 0.43803I 5.01449 − 0.38960I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.358362 + 0.992150I
a = −0.074839 − 0.827034I
b = −0.15062 − 1.56941I
4.17413 + 3.04921I 11.13137 − 4.86659I
u = −0.358362 − 0.992150I
a = −0.074839 + 0.827034I
b = −0.15062 + 1.56941I
4.17413 − 3.04921I 11.13137 + 4.86659I
u = 0.581922 + 0.742342I
a = −0.988921 − 0.922896I
b = 0.40243 − 1.83245I
−2.47100 + 1.06449I 2.36761 − 0.85729I
u = 0.581922 − 0.742342I
a = −0.988921 + 0.922896I
b = 0.40243 + 1.83245I
−2.47100 − 1.06449I 2.36761 + 0.85729I
u = 0.867209 + 0.606173I
a = 1.202120 + 0.457899I
b = −0.693184 + 0.345225I
2.65432 + 9.47231I 4.00000 − 5.30483I
u = 0.867209 − 0.606173I
a = 1.202120 − 0.457899I
b = −0.693184 − 0.345225I
2.65432 − 9.47231I 4.00000 + 5.30483I
u = 0.142481 + 0.926913I
a = 1.282780 − 0.021406I
b = 0.772343 − 0.206200I
0.767985 + 0.824168I 9.41506 + 0.65151I
u = 0.142481 − 0.926913I
a = 1.282780 + 0.021406I
b = 0.772343 + 0.206200I
0.767985 − 0.824168I 9.41506 − 0.65151I
u = −0.700176 + 0.840660I
a = −0.765140 + 0.730947I
b = 0.23555 + 1.51474I
−4.60599 + 2.68345I 0
u = −0.700176 − 0.840660I
a = −0.765140 − 0.730947I
b = 0.23555 − 1.51474I
−4.60599 − 2.68345I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.628609 + 0.908068I
a = 0.219058 + 0.696182I
b = 1.37912 + 1.43255I
−2.41121 − 1.77391I 0
u = 0.628609 − 0.908068I
a = 0.219058 − 0.696182I
b = 1.37912 − 1.43255I
−2.41121 + 1.77391I 0
u = −0.026642 + 0.893006I
a = −0.482850 − 0.230070I
b = −1.76148 − 0.77429I
0.96850 − 2.33689I 10.51063 + 3.88561I
u = −0.026642 − 0.893006I
a = −0.482850 + 0.230070I
b = −1.76148 + 0.77429I
0.96850 + 2.33689I 10.51063 − 3.88561I
u = 0.603817 + 0.944430I
a = −1.014530 − 0.651522I
b = −0.14337 − 1.71884I
−1.81973 − 5.79600I 0
u = 0.603817 − 0.944430I
a = −1.014530 + 0.651522I
b = −0.14337 + 1.71884I
−1.81973 + 5.79600I 0
u = 0.052552 + 1.129890I
a = −0.775773 − 0.796782I
b = −1.07864 − 2.15641I
5.89708 − 3.19125I 0
u = 0.052552 − 1.129890I
a = −0.775773 + 0.796782I
b = −1.07864 + 2.15641I
5.89708 + 3.19125I 0
u = −0.767293 + 0.838686I
a = −0.536133 + 0.727624I
b = 0.38652 + 1.38050I
−4.75625 + 2.66334I 0
u = −0.767293 − 0.838686I
a = −0.536133 − 0.727624I
b = 0.38652 − 1.38050I
−4.75625 − 2.66334I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.791545 + 0.338366I
a = −0.47232 − 1.36375I
b = 0.146940 − 0.685183I
4.21373 + 5.84305I 4.20006 − 5.43025I
u = −0.791545 − 0.338366I
a = −0.47232 + 1.36375I
b = 0.146940 + 0.685183I
4.21373 − 5.84305I 4.20006 + 5.43025I
u = −0.641851 + 0.958734I
a = 0.290568 − 0.785458I
b = 1.28323 − 2.11096I
−2.52965 + 7.13795I 0
u = −0.641851 − 0.958734I
a = 0.290568 + 0.785458I
b = 1.28323 + 2.11096I
−2.52965 − 7.13795I 0
u = 0.706658 + 0.446411I
a = −0.295145 + 1.196460I
b = 0.201963 + 0.567576I
0.70382 − 1.36878I 1.16247 + 2.76782I
u = 0.706658 − 0.446411I
a = −0.295145 − 1.196460I
b = 0.201963 − 0.567576I
0.70382 + 1.36878I 1.16247 − 2.76782I
u = −0.096687 + 1.163890I
a = −0.845889 + 0.838885I
b = −1.03193 + 2.21147I
9.39173 + 8.34057I 0
u = −0.096687 − 1.163890I
a = −0.845889 − 0.838885I
b = −1.03193 − 2.21147I
9.39173 − 8.34057I 0
u = 0.003658 + 1.168730I
a = −0.699048 + 0.871689I
b = −0.99139 + 2.10096I
10.19250 − 1.37204I 0
u = 0.003658 − 1.168730I
a = −0.699048 − 0.871689I
b = −0.99139 − 2.10096I
10.19250 + 1.37204I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.796964 + 0.882251I
a = −0.538356 − 0.100627I
b = 0.233347 − 0.784599I
−3.04388 − 0.13688I 0
u = 0.796964 − 0.882251I
a = −0.538356 + 0.100627I
b = 0.233347 + 0.784599I
−3.04388 + 0.13688I 0
u = −0.752341 + 0.920918I
a = −0.786716 + 0.409689I
b = 0.013060 + 1.198020I
−4.50104 + 3.08347I 0
u = −0.752341 − 0.920918I
a = −0.786716 − 0.409689I
b = 0.013060 − 1.198020I
−4.50104 − 3.08347I 0
u = 0.804318 + 0.888939I
a = −0.159292 − 0.605167I
b = 0.615657 − 1.226000I
−3.02941 − 5.85741I 0
u = 0.804318 − 0.888939I
a = −0.159292 + 0.605167I
b = 0.615657 + 1.226000I
−3.02941 + 5.85741I 0
u = 0.617710 + 1.047470I
a = 0.859697 − 0.364923I
b = 0.97715 − 1.06171I
2.35789 − 3.68565I 0
u = 0.617710 − 1.047470I
a = 0.859697 + 0.364923I
b = 0.97715 + 1.06171I
2.35789 + 3.68565I 0
u = −0.567021 + 1.085240I
a = 0.986354 + 0.368127I
b = 1.018770 + 0.967931I
6.42352 − 0.87285I 0
u = −0.567021 − 1.085240I
a = 0.986354 − 0.368127I
b = 1.018770 − 0.967931I
6.42352 + 0.87285I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.688188 + 1.054390I
a = 0.386516 − 0.981629I
b = 0.54971 − 2.74649I
1.09750 + 9.92639I 0
u = −0.688188 − 1.054390I
a = 0.386516 + 0.981629I
b = 0.54971 + 2.74649I
1.09750 − 9.92639I 0
u = 0.650788 + 1.081400I
a = 0.309480 + 1.022320I
b = 0.43116 + 2.53815I
5.99769 − 5.93570I 0
u = 0.650788 − 1.081400I
a = 0.309480 − 1.022320I
b = 0.43116 − 2.53815I
5.99769 + 5.93570I 0
u = −0.655982 + 1.078790I
a = 0.836188 + 0.475018I
b = 1.03372 + 1.10446I
5.91225 + 8.64566I 0
u = −0.655982 − 1.078790I
a = 0.836188 − 0.475018I
b = 1.03372 − 1.10446I
5.91225 − 8.64566I 0
u = 0.314549 + 0.662120I
a = 0.218311 + 0.670532I
b = −0.011835 + 0.612906I
0.267822 − 1.158260I 3.61517 + 5.66198I
u = 0.314549 − 0.662120I
a = 0.218311 − 0.670532I
b = −0.011835 − 0.612906I
0.267822 + 1.158260I 3.61517 − 5.66198I
u = 0.710541 + 1.068660I
a = 0.425206 + 1.016740I
b = 0.42500 + 2.83258I
4.0664 − 15.3392I 0
u = 0.710541 − 1.068660I
a = 0.425206 − 1.016740I
b = 0.42500 − 2.83258I
4.0664 + 15.3392I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.516415
a = 1.18250
b = −0.0216347
1.52695 6.20940
u = 0.178816 + 0.052588I
a = 0.97689 + 5.20866I
b = 0.848518 + 0.314174I
−1.74489 − 2.05954I −4.07565 + 4.15680I
u = 0.178816 − 0.052588I
a = 0.97689 − 5.20866I
b = 0.848518 − 0.314174I
−1.74489 + 2.05954I −4.07565 − 4.15680I
11
II.
I
u
2
= hu
5
b +u
3
b +2u
2
b +b
2
+ 2bu − u
2
− u − 2, −u
4
+ a − 1, u
6
+ u
4
+ 2u
2
+ 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
3
=
u
4
+ 1
b
a
12
=
u
2
+ 1
u
2
a
2
=
u
4
+ 1
−u
4
− u
2
+ b − 1
a
7
=
u
5
+ u
3
+ 2u
u
5
b + bu
a
1
=
0
−u
4
− u
2
− 1
a
5
=
u
u
3
+ u
a
4
=
u
5
b − u
5
− u
3
+ bu
−u
3
b + 2u
3
+ u
2
+ b + 3u
a
9
=
u
4
+ u
2
+ 1
u
4
a
8
=
u
5
b + u
5
+ u
3
b + bu + u
2u
5
b − u
5
− 2u
3
+ bu − u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
4
− 4u
3
− 4bu + 4u
2
+ 8
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
12
c
2
, c
6
(u
2
+ 1)
6
c
3
, c
4
, c
8
(u
4
− u
2
+ 1)
3
c
5
, c
10
(u
6
+ u
4
+ 2u
2
+ 1)
2
c
7
(u
2
+ u + 1)
6
c
9
(u
3
+ u
2
+ 2u + 1)
4
c
11
, c
12
(u
3
− u
2
+ 2u − 1)
4
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
12
c
2
, c
6
(y + 1)
12
c
3
, c
4
, c
8
(y
2
− y + 1)
6
c
5
, c
10
(y
3
+ y
2
+ 2y + 1)
4
c
7
(y
2
+ y + 1)
6
c
9
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.744862 + 0.877439I
a = −0.662359 − 0.562280I
b = 1.06984 − 1.15137I
−4.66906 − 0.79824I −1.50976 − 0.48465I
u = 0.744862 + 0.877439I
a = −0.662359 − 0.562280I
b = −0.07740 − 2.12527I
−4.66906 − 4.85801I −1.50976 + 6.44355I
u = 0.744862 − 0.877439I
a = −0.662359 + 0.562280I
b = 1.06984 + 1.15137I
−4.66906 + 0.79824I −1.50976 + 0.48465I
u = 0.744862 − 0.877439I
a = −0.662359 + 0.562280I
b = −0.07740 + 2.12527I
−4.66906 + 4.85801I −1.50976 − 6.44355I
u = −0.744862 + 0.877439I
a = −0.662359 + 0.562280I
b = 0.507560 + 0.489013I
−4.66906 + 4.85801I −1.50976 − 6.44355I
u = −0.744862 + 0.877439I
a = −0.662359 + 0.562280I
b = −0.63968 + 1.46291I
−4.66906 + 0.79824I −1.50976 + 0.48465I
u = −0.744862 − 0.877439I
a = −0.662359 − 0.562280I
b = 0.507560 − 0.489013I
−4.66906 − 4.85801I −1.50976 + 6.44355I
u = −0.744862 − 0.877439I
a = −0.662359 − 0.562280I
b = −0.63968 − 1.46291I
−4.66906 − 0.79824I −1.50976 − 0.48465I
u = 0.754878I
a = 1.32472
b = −0.577399 − 0.662359I
−0.53148 − 2.02988I 5.01951 + 3.46410I
u = 0.754878I
a = 1.32472
b = 1.71708 − 0.66236I
−0.53148 + 2.02988I 5.01951 − 3.46410I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = − 0.754878I
a = 1.32472
b = −0.577399 + 0.662359I
−0.53148 + 2.02988I 5.01951 − 3.46410I
u = − 0.754878I
a = 1.32472
b = 1.71708 + 0.66236I
−0.53148 − 2.02988I 5.01951 + 3.46410I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
12
)(u
63
+ 23u
62
+ ··· − 11050u − 625)
c
2
, c
6
((u
2
+ 1)
6
)(u
63
− u
62
+ ··· + 40u − 25)
c
3
, c
8
((u
4
− u
2
+ 1)
3
)(u
63
− u
62
+ ··· + 2u
2
− 1)
c
4
((u
4
− u
2
+ 1)
3
)(u
63
− 3u
62
+ ··· + 736u − 53)
c
5
, c
10
((u
6
+ u
4
+ 2u
2
+ 1)
2
)(u
63
+ u
62
+ ··· − 10u − 1)
c
7
((u
2
+ u + 1)
6
)(u
63
− 35u
62
+ ··· + 4u − 1)
c
9
((u
3
+ u
2
+ 2u + 1)
4
)(u
63
− 23u
62
+ ··· + 38u + 1)
c
11
, c
12
((u
3
− u
2
+ 2u − 1)
4
)(u
63
− 23u
62
+ ··· + 38u + 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
12
)(y
63
+ 47y
62
+ ··· − 2.05713 × 10
7
y −390625)
c
2
, c
6
((y + 1)
12
)(y
63
+ 23y
62
+ ··· − 11050y −625)
c
3
, c
8
((y
2
− y + 1)
6
)(y
63
− 35y
62
+ ··· + 4y −1)
c
4
((y
2
− y + 1)
6
)(y
63
+ 49y
62
+ ··· + 209280y −2809)
c
5
, c
10
((y
3
+ y
2
+ 2y + 1)
4
)(y
63
+ 23y
62
+ ··· + 38y −1)
c
7
((y
2
+ y + 1)
6
)(y
63
− 7y
62
+ ··· + 4y −1)
c
9
, c
11
, c
12
((y
3
+ 3y
2
+ 2y −1)
4
)(y
63
+ 39y
62
+ ··· + 682y −1)
18
