12n
0301
(K12n
0301
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 11 2 12 10 5 4 7 11
Solving Sequence
2,7
6 3 4
1,11
5 10 9 12 8
c
6
c
2
c
3
c
1
c
5
c
10
c
9
c
12
c
7
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.34577 × 10
36
u
46
+ 4.13410 × 10
36
u
45
+ ··· + 6.18526 × 10
36
b + 7.22944 × 10
36
,
− 4.63131 × 10
36
u
46
− 3.13332 × 10
37
u
45
+ ··· + 6.18526 × 10
37
a − 1.27145 × 10
38
, u
47
+ 2u
46
+ ··· − 7u
2
+ 5i
I
u
2
= hb + 1, a
4
+ 4a
3
u − 8a
2
u − 8a
2
+ 8a + 5u, u
2
+ u + 1i
I
u
3
= hb − 1, a
3
+ 3a
2
u + 3au − 3a − 1, u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 61 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
= h1.35 × 10
36
u
46
+ 4.13 × 10
36
u
45
+ · · · + 6.19 × 10
36
b + 7.23 ×
10
36
, −4.63 × 10
36
u
46
− 3.13 × 10
37
u
45
+ · · · + 6.19 × 10
37
a − 1.27 ×
10
38
, u
47
+ 2u
46
+ · · · − 7u
2
+ 5i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
11
=
0.0748766u
46
+ 0.506578u
45
+ ··· − 0.0189566u + 2.05560
−0.217577u
46
− 0.668379u
45
+ ··· + 0.153362u − 1.16882
a
5
=
0.371873u
46
+ 0.438846u
45
+ ··· + 1.29351u + 0.575382
−0.151221u
46
− 0.179133u
45
+ ··· − 1.44030u + 0.207091
a
10
=
0.234371u
46
+ 1.04621u
45
+ ··· + 0.637032u + 2.96733
−0.245873u
46
− 0.763265u
45
+ ··· − 0.314870u − 1.29989
a
9
=
−0.0256670u
46
− 0.692390u
45
+ ··· − 1.49667u − 3.70685
0.0370363u
46
+ 0.134133u
45
+ ··· + 1.12375u + 0.747882
a
12
=
0.292454u
46
+ 1.17496u
45
+ ··· − 0.172319u + 3.22442
−0.217577u
46
− 0.668379u
45
+ ··· + 0.153362u − 1.16882
a
8
=
−0.187891u
46
− 0.374761u
45
+ ··· + 0.526224u + 0.0784946
0.216050u
46
+ 0.341229u
45
+ ··· + 1.29950u + 0.242159
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.884631u
46
+ 2.37548u
45
+ ··· + 0.300832u + 0.344938
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
47
+ 30u
46
+ ··· + 70u − 25
c
2
, c
6
u
47
− 2u
46
+ ··· + 7u
2
− 5
c
3
u
47
+ 2u
46
+ ··· + 20u − 5
c
4
, c
9
u
47
+ u
46
+ ··· + 12u + 4
c
5
u
47
− u
46
+ ··· + 36u + 4
c
7
, c
11
u
47
+ 3u
46
+ ··· − 29u + 1
c
8
u
47
− 21u
46
+ ··· + 80u − 16
c
10
u
47
+ 3u
46
+ ··· − 1940u − 172
c
12
u
47
+ 63u
46
+ ··· + 175u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
47
− 18y
46
+ ··· + 2450y −625
c
2
, c
6
y
47
+ 30y
46
+ ··· + 70y −25
c
3
y
47
− 66y
46
+ ··· − 330y −25
c
4
, c
9
y
47
− 21y
46
+ ··· + 80y −16
c
5
y
47
− 69y
46
+ ··· − 112y −16
c
7
, c
11
y
47
− 63y
46
+ ··· + 175y −1
c
8
y
47
+ 15y
46
+ ··· + 256y −256
c
10
y
47
− 9y
46
+ ··· + 1462928y −29584
c
12
y
47
− 143y
46
+ ··· + 12319y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.520853 + 0.848466I
a = −1.084380 + 0.109048I
b = −0.0925902 + 0.0236889I
2.45436 + 5.70987I 4.10397 − 7.52673I
u = 0.520853 − 0.848466I
a = −1.084380 − 0.109048I
b = −0.0925902 − 0.0236889I
2.45436 − 5.70987I 4.10397 + 7.52673I
u = −0.954753
a = −0.462105
b = 1.61809
−4.77856 −0.0822940
u = −0.426277 + 0.843973I
a = 0.695944 + 0.007832I
b = −0.126186 + 0.180791I
−0.08833 − 1.82304I −0.21214 + 3.66824I
u = −0.426277 − 0.843973I
a = 0.695944 − 0.007832I
b = −0.126186 − 0.180791I
−0.08833 + 1.82304I −0.21214 − 3.66824I
u = 0.080676 + 1.062940I
a = 2.21302 − 0.62081I
b = −1.251550 − 0.323161I
−1.26187 + 4.11733I −5.79211 − 3.02419I
u = 0.080676 − 1.062940I
a = 2.21302 + 0.62081I
b = −1.251550 + 0.323161I
−1.26187 − 4.11733I −5.79211 + 3.02419I
u = −1.065870 + 0.151558I
a = −0.220607 − 0.235501I
b = 1.73800 − 0.19985I
−9.19783 + 7.78492I −3.11194 − 4.36379I
u = −1.065870 − 0.151558I
a = −0.220607 + 0.235501I
b = 1.73800 + 0.19985I
−9.19783 − 7.78492I −3.11194 + 4.36379I
u = 1.074670 + 0.087030I
a = 0.234458 − 0.134402I
b = −1.76123 − 0.11585I
−11.04170 − 2.07575I −5.37324 + 0.07581I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.074670 − 0.087030I
a = 0.234458 + 0.134402I
b = −1.76123 + 0.11585I
−11.04170 + 2.07575I −5.37324 − 0.07581I
u = −0.416939 + 1.002100I
a = 1.021110 − 0.519987I
b = −0.564053 − 0.373274I
−0.35308 − 2.84906I 0.14660 + 5.36409I
u = −0.416939 − 1.002100I
a = 1.021110 + 0.519987I
b = −0.564053 + 0.373274I
−0.35308 + 2.84906I 0.14660 − 5.36409I
u = 0.045591 + 1.099550I
a = −1.79233 − 0.59931I
b = 1.189770 − 0.444997I
−3.94139 + 0.69325I −8.93702 − 1.07384I
u = 0.045591 − 1.099550I
a = −1.79233 + 0.59931I
b = 1.189770 + 0.444997I
−3.94139 − 0.69325I −8.93702 + 1.07384I
u = 0.514947 + 0.719739I
a = −0.652546 + 0.529793I
b = −0.095652 + 0.345286I
2.80273 − 1.43971I 4.88073 + 0.31816I
u = 0.514947 − 0.719739I
a = −0.652546 − 0.529793I
b = −0.095652 − 0.345286I
2.80273 + 1.43971I 4.88073 − 0.31816I
u = 0.606629 + 0.637775I
a = −0.221188 − 1.122120I
b = 1.161630 − 0.221796I
−1.182870 + 0.647616I −3.09275 + 0.88493I
u = 0.606629 − 0.637775I
a = −0.221188 + 1.122120I
b = 1.161630 + 0.221796I
−1.182870 − 0.647616I −3.09275 − 0.88493I
u = −0.091353 + 1.151430I
a = 0.063117 − 0.348259I
b = −0.154148 + 0.895743I
−2.52743 − 2.40559I −6.04313 + 3.27210I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.091353 − 1.151430I
a = 0.063117 + 0.348259I
b = −0.154148 − 0.895743I
−2.52743 + 2.40559I −6.04313 − 3.27210I
u = −0.067124 + 0.804789I
a = 1.56336 − 1.49824I
b = −1.064520 − 0.261047I
−0.09852 − 3.64662I −4.05106 + 4.37055I
u = −0.067124 − 0.804789I
a = 1.56336 + 1.49824I
b = −1.064520 + 0.261047I
−0.09852 + 3.64662I −4.05106 − 4.37055I
u = 0.688119 + 0.988855I
a = −0.236313 − 0.766691I
b = 1.328370 + 0.259774I
−2.22622 + 4.49419I −5.40692 − 5.46385I
u = 0.688119 − 0.988855I
a = −0.236313 + 0.766691I
b = 1.328370 − 0.259774I
−2.22622 − 4.49419I −5.40692 + 5.46385I
u = −0.586580 + 1.068360I
a = 0.267571 − 0.668867I
b = −1.138940 + 0.454251I
−2.43118 − 0.00318I −6.09049 + 0.I
u = −0.586580 − 1.068360I
a = 0.267571 + 0.668867I
b = −1.138940 − 0.454251I
−2.43118 + 0.00318I −6.09049 + 0.I
u = 0.290782 + 1.240950I
a = −1.325260 − 0.374001I
b = 0.985287 − 0.825561I
−5.50399 + 3.13913I 0
u = 0.290782 − 1.240950I
a = −1.325260 + 0.374001I
b = 0.985287 + 0.825561I
−5.50399 − 3.13913I 0
u = −0.377179 + 1.257740I
a = 1.235730 − 0.352288I
b = −0.848401 − 0.946720I
−4.21139 − 8.46222I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.377179 − 1.257740I
a = 1.235730 + 0.352288I
b = −0.848401 + 0.946720I
−4.21139 + 8.46222I 0
u = −0.672082 + 0.139197I
a = −0.260444 − 1.022400I
b = −0.842370 − 0.552537I
−0.14779 − 4.58136I −1.59423 + 6.34344I
u = −0.672082 − 0.139197I
a = −0.260444 + 1.022400I
b = −0.842370 + 0.552537I
−0.14779 + 4.58136I −1.59423 − 6.34344I
u = −0.498424 + 1.300460I
a = −1.83978 + 1.10496I
b = 1.71077 + 0.16414I
−8.75756 − 5.17554I 0
u = −0.498424 − 1.300460I
a = −1.83978 − 1.10496I
b = 1.71077 − 0.16414I
−8.75756 + 5.17554I 0
u = −0.505508 + 0.300306I
a = −0.075783 + 0.611800I
b = −0.255894 + 0.505093I
1.57367 − 0.84058I 3.87048 + 1.10428I
u = −0.505508 − 0.300306I
a = −0.075783 − 0.611800I
b = −0.255894 − 0.505093I
1.57367 + 0.84058I 3.87048 − 1.10428I
u = −0.59657 + 1.30838I
a = −1.57480 + 1.26494I
b = 1.74692 + 0.35404I
−12.7785 − 13.7242I 0
u = −0.59657 − 1.30838I
a = −1.57480 − 1.26494I
b = 1.74692 − 0.35404I
−12.7785 + 13.7242I 0
u = 0.56882 + 1.33488I
a = 1.60835 + 1.16120I
b = −1.79435 + 0.29240I
−14.9238 + 7.9344I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.56882 − 1.33488I
a = 1.60835 − 1.16120I
b = −1.79435 − 0.29240I
−14.9238 − 7.9344I 0
u = −0.40822 + 1.40970I
a = −1.72088 + 0.73531I
b = 1.88085 − 0.04240I
−14.2777 + 2.5683I 0
u = −0.40822 − 1.40970I
a = −1.72088 − 0.73531I
b = 1.88085 + 0.04240I
−14.2777 − 2.5683I 0
u = 0.46183 + 1.39829I
a = 1.68707 + 0.85628I
b = −1.88332 + 0.06316I
−15.7940 + 3.3870I 0
u = 0.46183 − 1.39829I
a = 1.68707 − 0.85628I
b = −1.88332 − 0.06316I
−15.7940 − 3.3870I 0
u = 0.336586 + 0.137208I
a = 1.14561 − 1.39055I
b = 0.822565 − 0.188238I
−1.43951 + 0.37029I −6.25580 − 0.44865I
u = 0.336586 − 0.137208I
a = 1.14561 + 1.39055I
b = 0.822565 + 0.188238I
−1.43951 − 0.37029I −6.25580 + 0.44865I
9
II. I
u
2
= hb + 1, a
4
+ 4a
3
u − 8a
2
u − 8a
2
+ 8a + 5u, u
2
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−u − 1
a
3
=
u
u + 1
a
4
=
−1
u + 1
a
1
=
1
0
a
11
=
a
−1
a
5
=
−a
2
u − a
2
+ a + 1
au + a − u − 2
a
10
=
au + 2a − 1
−au + u
a
9
=
−a
3
u + a
3
+ 5a
2
u + 2a
2
− 3au − 5a + 1
−a
3
u − a
3
+ a
2
u + 3a
2
+ au − 2a − u + 1
a
12
=
a + 1
−1
a
8
=
−a
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a
2
u − 8au − 8a + 4u + 8
10
(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
9
(u
4
− 2u
2
+ 2)
2
c
5
, c
10
(u
4
+ 2u
2
+ 2)
2
c
7
, c
12
(u + 1)
8
c
8
(u
2
+ 2u + 2)
4
c
11
(u − 1)
8
11
(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
9
(y
2
− 2y + 2)
4
c
5
, c
10
(y
2
+ 2y + 2)
4
c
7
, c
11
, c
12
(y −1)
8
c
8
(y
2
+ 4)
4
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.679033 − 1.021250I
b = −1.00000
0.82247 − 5.69375I −2.00000 + 7.46410I
u = −0.500000 + 0.866025I
a = 1.223940 + 0.077436I
b = −1.00000
0.82247 + 1.63398I −2.00000 − 0.53590I
u = −0.500000 + 0.866025I
a = 1.67903 − 0.71080I
b = −1.00000
0.82247 − 5.69375I −2.00000 + 7.46410I
u = −0.500000 + 0.866025I
a = −0.22394 − 1.80949I
b = −1.00000
0.82247 + 1.63398I −2.00000 − 0.53590I
u = −0.500000 − 0.866025I
a = −0.679033 + 1.021250I
b = −1.00000
0.82247 + 5.69375I −2.00000 − 7.46410I
u = −0.500000 − 0.866025I
a = 1.223940 − 0.077436I
b = −1.00000
0.82247 − 1.63398I −2.00000 + 0.53590I
u = −0.500000 − 0.866025I
a = 1.67903 + 0.71080I
b = −1.00000
0.82247 + 5.69375I −2.00000 − 7.46410I
u = −0.500000 − 0.866025I
a = −0.22394 + 1.80949I
b = −1.00000
0.82247 − 1.63398I −2.00000 + 0.53590I
13
III. I
u
3
= hb − 1, a
3
+ 3a
2
u + 3au − 3a − 1, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u − 1
a
3
=
u
u − 1
a
4
=
1
u − 1
a
1
=
−1
0
a
11
=
a
1
a
5
=
a
2
u − a
2
− a + 1
au − a + u − 2
a
10
=
−au + 2a + 1
au + u
a
9
=
a
2
u − a
2
− a − u
−a
2
u − 2au + 2a + 2
a
12
=
a − 1
1
a
8
=
a
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2a
2
u − 4au + 4a − 4u − 2
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
(u
2
− u + 1)
3
c
2
(u
2
+ u + 1)
3
c
4
, c
5
, c
8
c
9
, c
10
u
6
c
7
(u − 1)
6
c
11
, c
12
(u + 1)
6
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
(y
2
+ y + 1)
3
c
4
, c
5
, c
8
c
9
, c
10
y
6
c
7
, c
11
, c
12
(y −1)
6
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.500000 − 0.866025I
b = 1.00000
−1.64493 + 2.02988I −6.00000 − 3.46410I
u = 0.500000 + 0.866025I
a = −0.500000 − 0.866025I
b = 1.00000
−1.64493 + 2.02988I −6.00000 − 3.46410I
u = 0.500000 + 0.866025I
a = −0.500000 − 0.866025I
b = 1.00000
−1.64493 + 2.02988I −6.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = −0.500000 + 0.866025I
b = 1.00000
−1.64493 − 2.02988I −6.00000 + 3.46410I
u = 0.500000 − 0.866025I
a = −0.500000 + 0.866025I
b = 1.00000
−1.64493 − 2.02988I −6.00000 + 3.46410I
u = 0.500000 − 0.866025I
a = −0.500000 + 0.866025I
b = 1.00000
−1.64493 − 2.02988I −6.00000 + 3.46410I
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
7
)(u
47
+ 30u
46
+ ··· + 70u − 25)
c
2
((u
2
− u + 1)
4
)(u
2
+ u + 1)
3
(u
47
− 2u
46
+ ··· + 7u
2
− 5)
c
3
((u
2
− u + 1)
3
)(u
2
+ u + 1)
4
(u
47
+ 2u
46
+ ··· + 20u − 5)
c
4
, c
9
u
6
(u
4
− 2u
2
+ 2)
2
(u
47
+ u
46
+ ··· + 12u + 4)
c
5
u
6
(u
4
+ 2u
2
+ 2)
2
(u
47
− u
46
+ ··· + 36u + 4)
c
6
((u
2
− u + 1)
3
)(u
2
+ u + 1)
4
(u
47
− 2u
46
+ ··· + 7u
2
− 5)
c
7
((u − 1)
6
)(u + 1)
8
(u
47
+ 3u
46
+ ··· − 29u + 1)
c
8
u
6
(u
2
+ 2u + 2)
4
(u
47
− 21u
46
+ ··· + 80u − 16)
c
10
u
6
(u
4
+ 2u
2
+ 2)
2
(u
47
+ 3u
46
+ ··· − 1940u − 172)
c
11
((u − 1)
8
)(u + 1)
6
(u
47
+ 3u
46
+ ··· − 29u + 1)
c
12
((u + 1)
14
)(u
47
+ 63u
46
+ ··· + 175u + 1)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
7
)(y
47
− 18y
46
+ ··· + 2450y −625)
c
2
, c
6
((y
2
+ y + 1)
7
)(y
47
+ 30y
46
+ ··· + 70y −25)
c
3
((y
2
+ y + 1)
7
)(y
47
− 66y
46
+ ··· − 330y −25)
c
4
, c
9
y
6
(y
2
− 2y + 2)
4
(y
47
− 21y
46
+ ··· + 80y −16)
c
5
y
6
(y
2
+ 2y + 2)
4
(y
47
− 69y
46
+ ··· − 112y −16)
c
7
, c
11
((y −1)
14
)(y
47
− 63y
46
+ ··· + 175y −1)
c
8
y
6
(y
2
+ 4)
4
(y
47
+ 15y
46
+ ··· + 256y −256)
c
10
y
6
(y
2
+ 2y + 2)
4
(y
47
− 9y
46
+ ··· + 1462928y −29584)
c
12
((y −1)
14
)(y
47
− 143y
46
+ ··· + 12319y −1)
19
