12n
0300
(K12n
0300
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 9 2 12 5 8 6 1 8
Solving Sequence
5,8
9 6
10,12
1 4 7 3 2 11
c
8
c
5
c
9
c
12
c
4
c
7
c
3
c
2
c
11
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.12945 × 10
24
u
51
− 1.35993 × 10
23
u
50
+ ··· + 4.17532 × 10
23
b + 3.14183 × 10
24
,
6.04213 × 10
24
u
51
− 1.00196 × 10
24
u
50
+ ··· + 8.35063 × 10
23
a − 2.70702 × 10
25
, u
52
− u
51
+ ··· − 4u + 4i
I
u
2
= hb − 1, u
3
a + 4u
2
a + 2u
3
+ 2a
2
+ 5u
2
− 2u − 6, u
4
− 2u
2
+ 2i
I
v
1
= ha, b + 1, v
2
− v + 1i
* 3 irreducible components of dim
C
= 0, with total 62 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−1.13×10
24
u
51
−1.36×10
23
u
50
+· · ·+4.18×10
23
b+3.14×10
24
, 6.04×
10
24
u
51
−1.00×10
24
u
50
+· · ·+8.35×10
23
a−2.71×10
25
, u
52
−u
51
+· · ·−4u+4i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
6
=
−u
−u
3
+ u
a
10
=
−u
2
+ 1
u
2
a
12
=
−7.23554u
51
+ 1.19986u
50
+ ··· + 2.91779u + 32.4170
2.70507u
51
+ 0.325706u
50
+ ··· + 4.65999u − 7.52477
a
1
=
−4.53046u
51
+ 1.52557u
50
+ ··· + 7.57778u + 24.8922
2.70507u
51
+ 0.325706u
50
+ ··· + 4.65999u − 7.52477
a
4
=
−u
5
+ 2u
3
− u
u
5
− u
3
+ u
a
7
=
−1.40746u
51
+ 1.66161u
50
+ ··· + 10.2665u + 13.5363
−2.60824u
51
+ 0.294345u
50
+ ··· + 0.650880u + 11.7241
a
3
=
−10.3091u
51
+ 0.907634u
50
+ ··· − 1.48074u + 45.2097
1.04491u
51
+ 0.213681u
50
+ ··· + 3.29442u − 2.54491
a
2
=
−8.56753u
51
+ 0.985809u
50
+ ··· − 0.320727u + 38.1282
0.924923u
51
+ 0.0989994u
50
+ ··· + 2.44711u − 2.74222
a
11
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
749517475400009275308222
208765812377423184830449
u
51
+
232040877417015531671918
208765812377423184830449
u
50
+ ··· −
192808974281683631616226
208765812377423184830449
u +
4448015067704942886567602
208765812377423184830449
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
52
+ 32u
51
+ ··· − 74u + 25
c
2
, c
6
u
52
− 2u
51
+ ··· − 8u + 5
c
3
u
52
+ 2u
51
+ ··· − 28u + 5
c
4
u
52
+ 3u
51
+ ··· + 460u + 76
c
5
, c
8
u
52
+ u
51
+ ··· + 4u + 4
c
7
, c
12
u
52
− 3u
51
+ ··· + 9u + 1
c
9
u
52
+ 31u
51
+ ··· + 80u + 16
c
10
u
52
− u
51
+ ··· + 1725404u + 2511892
c
11
u
52
− 13u
51
+ ··· − 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
52
− 16y
51
+ ··· − 48126y + 625
c
2
, c
6
y
52
+ 32y
51
+ ··· − 74y + 25
c
3
y
52
− 64y
51
+ ··· + 326y + 25
c
4
y
52
+ 61y
51
+ ··· − 8528y + 5776
c
5
, c
8
y
52
− 31y
51
+ ··· − 80y + 16
c
7
, c
12
y
52
− 13y
51
+ ··· − 3y + 1
c
9
y
52
− 15y
51
+ ··· − 3328y + 256
c
10
y
52
+ 121y
51
+ ··· − 158315434513616y + 6309601419664
c
11
y
52
+ 67y
51
+ ··· + 1413y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.005040 + 0.945584I
a = −1.120450 − 0.773586I
b = 0.86363 + 1.15342I
−10.20250 − 1.40325I −0.753210 + 0.700768I
u = −0.005040 − 0.945584I
a = −1.120450 + 0.773586I
b = 0.86363 − 1.15342I
−10.20250 + 1.40325I −0.753210 − 0.700768I
u = 0.107775 + 0.930905I
a = −1.78820 − 0.36766I
b = 1.15916 + 0.95665I
−9.20690 + 9.05102I 0.53002 − 4.91799I
u = 0.107775 − 0.930905I
a = −1.78820 + 0.36766I
b = 1.15916 − 0.95665I
−9.20690 − 9.05102I 0.53002 + 4.91799I
u = 1.037360 + 0.298010I
a = 0.005298 + 0.154343I
b = 0.189541 + 0.596804I
−1.89487 − 1.25455I −1.66552 + 0.64316I
u = 1.037360 − 0.298010I
a = 0.005298 − 0.154343I
b = 0.189541 − 0.596804I
−1.89487 + 1.25455I −1.66552 − 0.64316I
u = −0.860656 + 0.321405I
a = −1.10246 + 2.20010I
b = 0.964482 + 0.321134I
1.45283 + 3.79114I 3.95154 − 7.81429I
u = −0.860656 − 0.321405I
a = −1.10246 − 2.20010I
b = 0.964482 − 0.321134I
1.45283 − 3.79114I 3.95154 + 7.81429I
u = 0.890991 + 0.199303I
a = 2.09257 − 0.24712I
b = −1.210700 − 0.125141I
0.64653 − 3.09032I −0.45726 + 5.33318I
u = 0.890991 − 0.199303I
a = 2.09257 + 0.24712I
b = −1.210700 + 0.125141I
0.64653 + 3.09032I −0.45726 − 5.33318I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.056109 + 0.903857I
a = −1.370050 + 0.327066I
b = 0.983868 − 0.956085I
−5.60216 − 3.52882I 2.88518 + 2.10285I
u = −0.056109 − 0.903857I
a = −1.370050 − 0.327066I
b = 0.983868 + 0.956085I
−5.60216 + 3.52882I 2.88518 − 2.10285I
u = −0.993815 + 0.500766I
a = −1.65168 + 0.85430I
b = 0.815359 + 0.433581I
−0.20710 + 4.60134I 3.51877 − 6.93021I
u = −0.993815 − 0.500766I
a = −1.65168 − 0.85430I
b = 0.815359 − 0.433581I
−0.20710 − 4.60134I 3.51877 + 6.93021I
u = 0.824227 + 0.185520I
a = 0.19223 − 2.35056I
b = 0.870779 − 0.282220I
0.857181 + 1.058030I 0.02381 + 1.93865I
u = 0.824227 − 0.185520I
a = 0.19223 + 2.35056I
b = 0.870779 + 0.282220I
0.857181 − 1.058030I 0.02381 − 1.93865I
u = 0.448459 + 0.705408I
a = 1.35058 + 0.91047I
b = −0.593885 − 0.727712I
−1.53921 + 3.53715I 0.35654 − 4.05104I
u = 0.448459 − 0.705408I
a = 1.35058 − 0.91047I
b = −0.593885 + 0.727712I
−1.53921 − 3.53715I 0.35654 + 4.05104I
u = 1.017620 + 0.594178I
a = −1.99134 − 0.34195I
b = 0.772747 − 0.753613I
−3.15906 − 8.48239I 0. + 8.84514I
u = 1.017620 − 0.594178I
a = −1.99134 + 0.34195I
b = 0.772747 + 0.753613I
−3.15906 + 8.48239I 0. − 8.84514I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.092570 + 0.474230I
a = −1.086010 − 0.165719I
b = 0.133855 − 0.142339I
−2.46320 − 1.67636I 0
u = 1.092570 − 0.474230I
a = −1.086010 + 0.165719I
b = 0.133855 + 0.142339I
−2.46320 + 1.67636I 0
u = −1.202650 + 0.144960I
a = −0.033095 − 0.253143I
b = 0.422921 − 1.043410I
−6.67676 − 1.37465I 0
u = −1.202650 − 0.144960I
a = −0.033095 + 0.253143I
b = 0.422921 + 1.043410I
−6.67676 + 1.37465I 0
u = 0.602001 + 0.506117I
a = 1.058240 − 0.518986I
b = −0.213970 + 0.512677I
−0.76208 − 1.83218I −0.54081 + 5.00541I
u = 0.602001 − 0.506117I
a = 1.058240 + 0.518986I
b = −0.213970 − 0.512677I
−0.76208 + 1.83218I −0.54081 − 5.00541I
u = −1.154940 + 0.386919I
a = −0.205260 − 0.701723I
b = −0.272895 − 0.607754I
−3.12200 + 5.95808I 0
u = −1.154940 − 0.386919I
a = −0.205260 + 0.701723I
b = −0.272895 + 0.607754I
−3.12200 − 5.95808I 0
u = 1.177630 + 0.344211I
a = −1.000060 − 0.963724I
b = 1.300120 − 0.319188I
−3.30400 − 3.98463I 0
u = 1.177630 − 0.344211I
a = −1.000060 + 0.963724I
b = 1.300120 + 0.319188I
−3.30400 + 3.98463I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.684305 + 0.345498I
a = 2.21655 − 0.15101I
b = −1.084480 + 0.183921I
1.94565 − 0.69515I 5.57940 − 2.37743I
u = −0.684305 − 0.345498I
a = 2.21655 + 0.15101I
b = −1.084480 − 0.183921I
1.94565 + 0.69515I 5.57940 + 2.37743I
u = −1.121360 + 0.516692I
a = −0.85701 + 1.13115I
b = 1.077300 − 0.327985I
−2.00208 + 3.98418I 0
u = −1.121360 − 0.516692I
a = −0.85701 − 1.13115I
b = 1.077300 + 0.327985I
−2.00208 − 3.98418I 0
u = −0.200571 + 0.677423I
a = 2.15588 + 0.29190I
b = −1.145000 − 0.260693I
0.568023 + 0.563021I 1.46294 − 0.43596I
u = −0.200571 − 0.677423I
a = 2.15588 − 0.29190I
b = −1.145000 + 0.260693I
0.568023 − 0.563021I 1.46294 + 0.43596I
u = −0.448987 + 0.506853I
a = 1.66812 − 0.26657I
b = −0.715266 + 0.202676I
1.316970 − 0.435931I 7.52137 + 1.21169I
u = −0.448987 − 0.506853I
a = 1.66812 + 0.26657I
b = −0.715266 − 0.202676I
1.316970 + 0.435931I 7.52137 − 1.21169I
u = 1.276530 + 0.439785I
a = −0.254365 + 0.161558I
b = −0.937038 − 1.050200I
−9.70077 − 1.19639I 0
u = 1.276530 − 0.439785I
a = −0.254365 − 0.161558I
b = −0.937038 + 1.050200I
−9.70077 + 1.19639I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.255740 + 0.501539I
a = 1.35852 − 1.19157I
b = −1.07227 − 0.96226I
−9.23940 + 8.57003I 0
u = −1.255740 − 0.501539I
a = 1.35852 + 1.19157I
b = −1.07227 + 0.96226I
−9.23940 − 8.57003I 0
u = 1.254730 + 0.531819I
a = 1.66106 + 1.24516I
b = −1.22933 + 0.93613I
−12.6957 − 14.3132I 0
u = 1.254730 − 0.531819I
a = 1.66106 − 1.24516I
b = −1.22933 − 0.93613I
−12.6957 + 14.3132I 0
u = −1.302310 + 0.406465I
a = 0.040415 − 0.203783I
b = −1.14144 + 1.05229I
−13.6366 − 4.3879I 0
u = −1.302310 − 0.406465I
a = 0.040415 + 0.203783I
b = −1.14144 − 1.05229I
−13.6366 + 4.3879I 0
u = −1.289050 + 0.482994I
a = −0.450643 − 0.411802I
b = −0.79762 + 1.24088I
−14.1610 + 6.4835I 0
u = −1.289050 − 0.482994I
a = −0.450643 + 0.411802I
b = −0.79762 − 1.24088I
−14.1610 − 6.4835I 0
u = 1.292070 + 0.476980I
a = 1.24277 + 0.80176I
b = −0.97197 + 1.17126I
−14.2080 − 3.6508I 0
u = 1.292070 − 0.476980I
a = 1.24277 − 0.80176I
b = −0.97197 − 1.17126I
−14.2080 + 3.6508I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.053574 + 0.599232I
a = 0.868407 − 0.120577I
b = 0.332102 − 0.211608I
0.20589 − 2.30089I −0.01971 + 3.72749I
u = 0.053574 − 0.599232I
a = 0.868407 + 0.120577I
b = 0.332102 + 0.211608I
0.20589 + 2.30089I −0.01971 − 3.72749I
10
II. I
u
2
= hb − 1, u
3
a + 4u
2
a + 2u
3
+ 2a
2
+ 5u
2
− 2u − 6, u
4
− 2u
2
+ 2i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
6
=
−u
−u
3
+ u
a
10
=
−u
2
+ 1
u
2
a
12
=
a
1
a
1
=
a + 1
1
a
4
=
u
u
3
− u
a
7
=
a + 1
1
a
3
=
3
2
u
3
+ au + u
2
+ a + u
u
3
a + 2u
3
− au − 3u
a
2
=
u
2
a +
3
2
u
3
+ au + u
2
− a − 2
u
3
a − u
2
a + u
3
− au − 2u
2
− 2u + 2
a
11
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
3
a + 4u
3
− 4au + 4u
2
− 8u − 4
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u
2
− u + 1)
4
c
3
, c
6
(u
2
+ u + 1)
4
c
4
, c
10
(u
4
+ 2u
2
+ 2)
2
c
5
, c
8
(u
4
− 2u
2
+ 2)
2
c
7
(u − 1)
8
c
9
(u
2
+ 2u + 2)
4
c
11
, c
12
(u + 1)
8
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
(y
2
+ y + 1)
4
c
4
, c
10
(y
2
+ 2y + 2)
4
c
5
, c
8
(y
2
− 2y + 2)
4
c
7
, c
11
, c
12
(y −1)
8
c
9
(y
2
+ 4)
4
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.098680 + 0.455090I
a = −0.48809 − 1.66713I
b = 1.00000
−0.82247 − 5.69375I 2.00000 + 7.46410I
u = 1.098680 + 0.455090I
a = −1.83370 − 1.10976I
b = 1.00000
−0.82247 − 1.63398I 2.00000 + 0.53590I
u = 1.098680 − 0.455090I
a = −0.48809 + 1.66713I
b = 1.00000
−0.82247 + 5.69375I 2.00000 − 7.46410I
u = 1.098680 − 0.455090I
a = −1.83370 + 1.10976I
b = 1.00000
−0.82247 + 1.63398I 2.00000 − 0.53590I
u = −1.098680 + 0.455090I
a = −0.166298 + 0.890241I
b = 1.00000
−0.82247 + 1.63398I 2.00000 − 0.53590I
u = −1.098680 + 0.455090I
a = −1.51191 + 0.33287I
b = 1.00000
−0.82247 + 5.69375I 2.00000 − 7.46410I
u = −1.098680 − 0.455090I
a = −0.166298 − 0.890241I
b = 1.00000
−0.82247 − 1.63398I 2.00000 + 0.53590I
u = −1.098680 − 0.455090I
a = −1.51191 − 0.33287I
b = 1.00000
−0.82247 − 5.69375I 2.00000 + 7.46410I
14
III. I
v
1
= ha, b + 1, v
2
− v + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
9
=
1
0
a
6
=
v
0
a
10
=
1
0
a
12
=
0
−1
a
1
=
−1
−1
a
4
=
v
0
a
7
=
1
1
a
3
=
0
−v
a
2
=
−1
−v
a
11
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 4
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
5
, c
8
c
9
, c
10
u
2
c
7
, c
11
(u + 1)
2
c
12
(u − 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
y
2
+ y + 1
c
4
, c
5
, c
8
c
9
, c
10
y
2
c
7
, c
11
, c
12
(y − 1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −1.00000
1.64493 − 2.02988I 6.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = −1.00000
1.64493 + 2.02988I 6.00000 − 3.46410I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
5
)(u
52
+ 32u
51
+ ··· − 74u + 25)
c
2
((u
2
− u + 1)
4
)(u
2
+ u + 1)(u
52
− 2u
51
+ ··· − 8u + 5)
c
3
(u
2
− u + 1)(u
2
+ u + 1)
4
(u
52
+ 2u
51
+ ··· − 28u + 5)
c
4
u
2
(u
4
+ 2u
2
+ 2)
2
(u
52
+ 3u
51
+ ··· + 460u + 76)
c
5
, c
8
u
2
(u
4
− 2u
2
+ 2)
2
(u
52
+ u
51
+ ··· + 4u + 4)
c
6
(u
2
− u + 1)(u
2
+ u + 1)
4
(u
52
− 2u
51
+ ··· − 8u + 5)
c
7
((u − 1)
8
)(u + 1)
2
(u
52
− 3u
51
+ ··· + 9u + 1)
c
9
u
2
(u
2
+ 2u + 2)
4
(u
52
+ 31u
51
+ ··· + 80u + 16)
c
10
u
2
(u
4
+ 2u
2
+ 2)
2
(u
52
− u
51
+ ··· + 1725404u + 2511892)
c
11
((u + 1)
10
)(u
52
− 13u
51
+ ··· − 3u + 1)
c
12
((u − 1)
2
)(u + 1)
8
(u
52
− 3u
51
+ ··· + 9u + 1)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
5
)(y
52
− 16y
51
+ ··· − 48126y + 625)
c
2
, c
6
((y
2
+ y + 1)
5
)(y
52
+ 32y
51
+ ··· − 74y + 25)
c
3
((y
2
+ y + 1)
5
)(y
52
− 64y
51
+ ··· + 326y + 25)
c
4
y
2
(y
2
+ 2y + 2)
4
(y
52
+ 61y
51
+ ··· − 8528y + 5776)
c
5
, c
8
y
2
(y
2
− 2y + 2)
4
(y
52
− 31y
51
+ ··· − 80y + 16)
c
7
, c
12
((y − 1)
10
)(y
52
− 13y
51
+ ··· − 3y + 1)
c
9
y
2
(y
2
+ 4)
4
(y
52
− 15y
51
+ ··· − 3328y + 256)
c
10
y
2
(y
2
+ 2y + 2)
4
· (y
52
+ 121y
51
+ ··· − 158315434513616y + 6309601419664)
c
11
((y − 1)
10
)(y
52
+ 67y
51
+ ··· + 1413y + 1)
20
