12n
0645
(K12n
0645
)
A knot diagram
1
Linearized knot diagam
3 8 10 8 12 11 2 4 1 7 6 4
Solving Sequence
2,7
8
3,10
4 5 11 1 6 9 12
c
7
c
2
c
3
c
4
c
10
c
1
c
6
c
9
c
12
c
5
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h8.90809 × 10
47
u
45
+ 8.84240 × 10
47
u
44
+ ··· + 2.05702 × 10
48
b − 2.45319 × 10
49
,
− 6.59670 × 10
48
u
45
+ 1.83893 × 10
49
u
44
+ ··· + 6.37677 × 10
49
a − 1.07007 × 10
51
,
u
46
− 10u
44
+ ··· + 11u + 31i
I
u
2
= h−2u
10
+ u
9
+ 6u
8
− 4u
7
− 16u
6
+ 6u
5
+ 19u
4
− 5u
3
− 15u
2
+ b + u + 4,
u
9
− 2u
8
− 2u
7
+ 6u
6
+ 4u
5
− 13u
4
− 3u
3
+ 12u
2
+ a + u − 6,
u
11
− u
10
− 3u
9
+ 4u
8
+ 7u
7
− 8u
6
− 8u
5
+ 9u
4
+ 5u
3
− 5u
2
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 57 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
= h8.91 × 10
47
u
45
+ 8.84 × 10
47
u
44
+ · · · + 2.06 × 10
48
b − 2.45 ×
10
49
, −6.60 × 10
48
u
45
+ 1.84 × 10
49
u
44
+ · · · + 6.38 × 10
49
a − 1.07 ×
10
51
, u
46
− 10u
44
+ · · · + 11u + 31i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
0.103449u
45
− 0.288379u
44
+ ··· − 0.284809u + 16.7807
−0.433057u
45
− 0.429864u
44
+ ··· + 15.8856u + 11.9259
a
4
=
−0.141416u
45
+ 0.395932u
44
+ ··· − 9.32244u − 28.9599
0.366395u
45
+ 0.483053u
44
+ ··· − 16.9943u − 16.7074
a
5
=
0.284534u
45
+ 0.603944u
44
+ ··· − 26.3454u − 33.3933
0.611972u
45
+ 0.566589u
44
+ ··· − 32.4869u − 23.1557
a
11
=
−0.329608u
45
− 0.718243u
44
+ ··· + 15.6007u + 28.7066
−0.433057u
45
− 0.429864u
44
+ ··· + 15.8856u + 11.9259
a
1
=
u
3
u
5
− u
3
+ u
a
6
=
1.30358u
45
+ 0.927847u
44
+ ··· − 65.6458u − 32.8545
0.264798u
45
+ 0.224989u
44
+ ··· − 12.0873u − 7.10220
a
9
=
0.365076u
45
− 0.0975018u
44
+ ··· − 13.4315u + 10.4704
−0.146690u
45
− 0.269810u
44
+ ··· + 2.05043u + 6.63521
a
12
=
1.08634u
45
+ 0.507925u
44
+ ··· − 43.7616u − 12.5340
1.02109u
45
+ 0.771426u
44
+ ··· − 46.8793u − 30.5007
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.400585u
45
− 0.275909u
44
+ ··· − 48.1051u − 42.5676
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
46
+ 20u
45
+ ··· + 14009u + 961
c
2
, c
7
u
46
− 10u
44
+ ··· − 11u + 31
c
3
u
46
+ u
45
+ ··· + 2u − 1
c
4
, c
8
u
46
− 3u
45
+ ··· − 2160u − 1621
c
5
, c
6
, c
10
c
11
u
46
− u
45
+ ··· − 10u − 1
c
9
u
46
− 24u
44
+ ··· + 183u + 43
c
12
u
46
+ 7u
45
+ ··· − 3420u − 343
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
46
+ 32y
45
+ ··· + 2013751y + 923521
c
2
, c
7
y
46
− 20y
45
+ ··· − 14009y + 961
c
3
y
46
+ 7y
45
+ ··· − 42y + 1
c
4
, c
8
y
46
− 41y
45
+ ··· − 68296334y + 2627641
c
5
, c
6
, c
10
c
11
y
46
+ 51y
45
+ ··· − 60y + 1
c
9
y
46
− 48y
45
+ ··· − 93001y + 1849
c
12
y
46
− 51y
45
+ ··· − 4953020y + 117649
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.777171 + 0.612835I
a = 1.016300 − 0.099619I
b = −0.331933 + 0.632697I
−0.45486 − 2.22136I 5.56372 + 4.55995I
u = 0.777171 − 0.612835I
a = 1.016300 + 0.099619I
b = −0.331933 − 0.632697I
−0.45486 + 2.22136I 5.56372 − 4.55995I
u = −0.796260 + 0.581104I
a = 0.123978 − 0.214987I
b = −0.37211 + 1.50267I
−0.132688 − 0.463216I 4.30646 − 2.07954I
u = −0.796260 − 0.581104I
a = 0.123978 + 0.214987I
b = −0.37211 − 1.50267I
−0.132688 + 0.463216I 4.30646 + 2.07954I
u = 0.891195 + 0.365209I
a = 2.81275 + 0.31631I
b = 0.031259 + 1.382470I
−1.86336 + 0.58097I 3.38443 + 0.69263I
u = 0.891195 − 0.365209I
a = 2.81275 − 0.31631I
b = 0.031259 − 1.382470I
−1.86336 − 0.58097I 3.38443 − 0.69263I
u = 0.758477 + 0.770111I
a = −1.31515 − 0.65871I
b = 0.712311 − 0.622242I
6.85172 − 1.46852I 7.65009 + 3.31921I
u = 0.758477 − 0.770111I
a = −1.31515 + 0.65871I
b = 0.712311 + 0.622242I
6.85172 + 1.46852I 7.65009 − 3.31921I
u = −0.913123 + 0.579538I
a = −1.81688 + 0.86698I
b = 0.25012 + 1.59325I
−0.51224 + 5.07727I 3.91334 − 4.47739I
u = −0.913123 − 0.579538I
a = −1.81688 − 0.86698I
b = 0.25012 − 1.59325I
−0.51224 − 5.07727I 3.91334 + 4.47739I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.913895 + 0.666325I
a = −0.649069 + 0.227447I
b = 0.338025 − 0.053987I
−1.08476 − 2.74841I 8.58326 + 2.30981I
u = 0.913895 − 0.666325I
a = −0.649069 − 0.227447I
b = 0.338025 + 0.053987I
−1.08476 + 2.74841I 8.58326 − 2.30981I
u = 0.854412 + 0.074876I
a = −0.93971 − 1.27956I
b = 0.02815 − 1.72557I
−13.22450 − 0.32397I −0.99400 − 2.11493I
u = 0.854412 − 0.074876I
a = −0.93971 + 1.27956I
b = 0.02815 + 1.72557I
−13.22450 + 0.32397I −0.99400 + 2.11493I
u = 0.812024 + 0.266747I
a = 1.03314 − 1.16176I
b = −0.222226 + 1.219740I
−1.58775 − 3.40530I 2.42508 + 8.01994I
u = 0.812024 − 0.266747I
a = 1.03314 + 1.16176I
b = −0.222226 − 1.219740I
−1.58775 + 3.40530I 2.42508 − 8.01994I
u = −0.612129 + 0.975994I
a = −0.737727 + 0.580195I
b = 0.741768 − 0.448363I
7.36473 − 3.39333I 8.53065 + 3.23087I
u = −0.612129 − 0.975994I
a = −0.737727 − 0.580195I
b = 0.741768 + 0.448363I
7.36473 + 3.39333I 8.53065 − 3.23087I
u = 0.066989 + 0.834868I
a = 0.507773 + 0.449914I
b = −0.081495 − 1.363900I
−3.81447 + 2.16547I 3.03202 − 3.16202I
u = 0.066989 − 0.834868I
a = 0.507773 − 0.449914I
b = −0.081495 + 1.363900I
−3.81447 − 2.16547I 3.03202 + 3.16202I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.835340
a = 1.52762
b = −0.699978
2.08624 3.59250
u = 0.957184 + 0.700082I
a = 0.757512 + 0.366942I
b = −0.873917 − 0.486869I
6.22467 − 4.09819I 6.87161 + 2.72251I
u = 0.957184 − 0.700082I
a = 0.757512 − 0.366942I
b = −0.873917 + 0.486869I
6.22467 + 4.09819I 6.87161 − 2.72251I
u = −1.077260 + 0.505176I
a = −1.068580 + 0.594060I
b = 0.485546 + 0.365826I
−1.04957 + 4.66742I 5.56090 − 9.70253I
u = −1.077260 − 0.505176I
a = −1.068580 − 0.594060I
b = 0.485546 − 0.365826I
−1.04957 − 4.66742I 5.56090 + 9.70253I
u = 1.152890 + 0.432401I
a = −0.0608762 − 0.0298599I
b = 0.057001 + 0.488154I
−1.61761 − 2.37559I 0.879006 + 0.401607I
u = 1.152890 − 0.432401I
a = −0.0608762 + 0.0298599I
b = 0.057001 − 0.488154I
−1.61761 + 2.37559I 0.879006 − 0.401607I
u = −0.708951 + 0.204573I
a = −0.837428 − 0.839652I
b = 0.231335 − 0.896256I
−3.73770 + 0.61521I −1.20649 + 1.42032I
u = −0.708951 − 0.204573I
a = −0.837428 + 0.839652I
b = 0.231335 + 0.896256I
−3.73770 − 0.61521I −1.20649 − 1.42032I
u = 0.474202 + 1.186570I
a = −0.207177 − 0.587661I
b = 0.25018 + 1.48994I
1.08764 + 6.97219I 4.72387 − 4.64542I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.474202 − 1.186570I
a = −0.207177 + 0.587661I
b = 0.25018 − 1.48994I
1.08764 − 6.97219I 4.72387 + 4.64542I
u = −0.713380
a = 3.04004
b = 0.136531
2.80045 −4.62300
u = 1.195490 + 0.523779I
a = −1.69838 − 0.65171I
b = 0.16723 − 1.46549I
−7.05077 − 7.05212I 1.18080 + 6.79998I
u = 1.195490 − 0.523779I
a = −1.69838 + 0.65171I
b = 0.16723 + 1.46549I
−7.05077 + 7.05212I 1.18080 − 6.79998I
u = −1.097350 + 0.743718I
a = 1.174780 − 0.336310I
b = −0.817170 − 0.613699I
5.83564 + 9.64943I 6.00000 − 7.00268I
u = −1.097350 − 0.743718I
a = 1.174780 + 0.336310I
b = −0.817170 + 0.613699I
5.83564 − 9.64943I 6.00000 + 7.00268I
u = −0.378903 + 0.518753I
a = 1.067570 − 0.111522I
b = −0.441328 + 0.176398I
0.963425 − 0.418051I 9.96672 + 3.30631I
u = −0.378903 − 0.518753I
a = 1.067570 + 0.111522I
b = −0.441328 − 0.176398I
0.963425 + 0.418051I 9.96672 − 3.30631I
u = −1.130590 + 0.839549I
a = 0.972367 + 0.073701I
b = −0.09034 − 1.57331I
−7.92848 + 3.74029I 0
u = −1.130590 − 0.839549I
a = 0.972367 − 0.073701I
b = −0.09034 + 1.57331I
−7.92848 − 3.74029I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.22337 + 0.74620I
a = 1.47635 + 0.22540I
b = −0.28946 + 1.57516I
−1.32243 − 13.76490I 0
u = 1.22337 − 0.74620I
a = 1.47635 − 0.22540I
b = −0.28946 − 1.57516I
−1.32243 + 13.76490I 0
u = −1.12014 + 0.96904I
a = −0.842997 − 0.382179I
b = 0.060969 + 1.402580I
−5.91695 + 3.87147I 0
u = −1.12014 − 0.96904I
a = −0.842997 + 0.382179I
b = 0.060969 − 1.402580I
−5.91695 − 3.87147I 0
u = −1.46824 + 0.34467I
a = 0.350849 − 0.635636I
b = −0.05218 − 1.50558I
−8.25938 + 2.77632I 0
u = −1.46824 − 0.34467I
a = 0.350849 + 0.635636I
b = −0.05218 + 1.50558I
−8.25938 − 2.77632I 0
9
II.
I
u
2
= h−2u
10
+ u
9
+ · · · + b + 4, u
9
− 2u
8
+ · · · + a − 6, u
11
− u
10
+ · · · − u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
−u
9
+ 2u
8
+ 2u
7
− 6u
6
− 4u
5
+ 13u
4
+ 3u
3
− 12u
2
− u + 6
2u
10
− u
9
− 6u
8
+ 4u
7
+ 16u
6
− 6u
5
− 19u
4
+ 5u
3
+ 15u
2
− u − 4
a
4
=
−u
10
+ 4u
9
− 11u
7
+ 3u
6
+ 24u
5
− 9u
4
− 22u
3
+ 10u
2
+ 9u − 3
u
10
+ u
9
− 5u
8
− u
7
+ 14u
6
+ 3u
5
− 20u
4
− 2u
3
+ 16u
2
− 4
a
5
=
3u
9
− 3u
8
− 7u
7
+ 10u
6
+ 16u
5
− 17u
4
− 13u
3
+ 15u
2
+ 5u − 4
u
10
+ u
9
− 5u
8
− u
7
+ 14u
6
+ 3u
5
− 20u
4
− u
3
+ 16u
2
− u − 4
a
11
=
2u
10
− 2u
9
− 4u
8
+ 6u
7
+ 10u
6
− 10u
5
− 6u
4
+ 8u
3
+ 3u
2
− 2u + 2
2u
10
− u
9
− 6u
8
+ 4u
7
+ 16u
6
− 6u
5
− 19u
4
+ 5u
3
+ 15u
2
− u − 4
a
1
=
u
3
u
5
− u
3
+ u
a
6
=
7u
10
− 5u
9
+ ··· − 7u − 8
−2u
9
+ 2u
8
+ 5u
7
− 7u
6
− 11u
5
+ 12u
4
+ 10u
3
− 11u
2
− 4u + 2
a
9
=
−u
9
+ 2u
8
+ 2u
7
− 6u
6
− 4u
5
+ 13u
4
+ 3u
3
− 11u
2
− u + 6
2u
10
− u
9
− 6u
8
+ 4u
7
+ 16u
6
− 6u
5
− 18u
4
+ 5u
3
+ 14u
2
− u − 3
a
12
=
−2u
9
+ u
8
+ 7u
7
− 6u
6
− 16u
5
+ 10u
4
+ 19u
3
− 12u
2
− 9u + 4
−2u
10
+ 2u
9
+ ··· + 3u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 8u
10
− 13u
9
− 14u
8
+ 40u
7
+ 26u
6
− 77u
5
− 2u
4
+ 70u
3
− 13u
2
− 28u + 15
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
− 7u
10
+ ··· + 11u − 1
c
2
u
11
+ u
10
− 3u
9
− 4u
8
+ 7u
7
+ 8u
6
− 8u
5
− 9u
4
+ 5u
3
+ 5u
2
− u − 1
c
3
u
11
+ 4u
9
+ u
8
+ 3u
7
− u
5
− 3u
4
− u
3
− 2u
2
− 1
c
4
u
11
+ 2u
9
− u
8
+ 3u
7
− u
6
+ 3u
4
− u
3
+ 4u
2
+ 1
c
5
, c
6
u
11
+ 8u
9
+ 23u
7
+ 28u
5
+ u
4
+ 12u
3
+ 3u
2
+ 1
c
7
u
11
− u
10
− 3u
9
+ 4u
8
+ 7u
7
− 8u
6
− 8u
5
+ 9u
4
+ 5u
3
− 5u
2
− u + 1
c
8
u
11
+ 2u
9
+ u
8
+ 3u
7
+ u
6
− 3u
4
− u
3
− 4u
2
− 1
c
9
u
11
− u
10
− 5u
9
+ 5u
8
+ 9u
7
− 8u
6
− 8u
5
+ 7u
4
+ 4u
3
− 3u
2
− u + 1
c
10
, c
11
u
11
+ 8u
9
+ 23u
7
+ 28u
5
− u
4
+ 12u
3
− 3u
2
− 1
c
12
u
11
+ 3u
9
+ 8u
8
+ 3u
7
+ 10u
6
+ 12u
5
+ u
4
+ 9u
3
+ 5u
2
− 4u + 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
+ 13y
10
+ ··· + 15y −1
c
2
, c
7
y
11
− 7y
10
+ ··· + 11y −1
c
3
y
11
+ 8y
10
+ ··· − 4y −1
c
4
, c
8
y
11
+ 4y
10
+ ··· − 8y −1
c
5
, c
6
, c
10
c
11
y
11
+ 16y
10
+ ··· − 6y −1
c
9
y
11
− 11y
10
+ ··· + 7y −1
c
12
y
11
+ 6y
10
+ ··· + 6y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.926350 + 0.275446I
a = 0.604065 − 1.072750I
b = 0.02836 − 1.73242I
−13.09290 + 1.15540I 1.12930 − 6.75991I
u = −0.926350 − 0.275446I
a = 0.604065 + 1.072750I
b = 0.02836 + 1.73242I
−13.09290 − 1.15540I 1.12930 + 6.75991I
u = 0.931716 + 0.451527I
a = −0.012829 + 0.293025I
b = 0.166908 + 0.916041I
−3.41093 − 1.89765I 0.48715 + 3.11270I
u = 0.931716 − 0.451527I
a = −0.012829 − 0.293025I
b = 0.166908 − 0.916041I
−3.41093 + 1.89765I 0.48715 − 3.11270I
u = −1.092600 + 0.709214I
a = −0.636248 − 0.082249I
b = 0.193075 + 0.390923I
−1.63003 + 3.19570I −1.52279 − 9.85073I
u = −1.092600 − 0.709214I
a = −0.636248 + 0.082249I
b = 0.193075 − 0.390923I
−1.63003 − 3.19570I −1.52279 + 9.85073I
u = 0.605049 + 0.142384I
a = 2.74610 − 0.77777I
b = −0.233007 + 1.358440I
−1.39419 − 2.51034I 3.76451 + 0.24190I
u = 0.605049 − 0.142384I
a = 2.74610 + 0.77777I
b = −0.233007 − 1.358440I
−1.39419 + 2.51034I 3.76451 − 0.24190I
u = −0.612040
a = 3.26852
b = −0.445195
3.18891 17.5710
u = 1.28821 + 0.91096I
a = −0.835352 + 0.045091I
b = 0.06726 − 1.54442I
−8.38532 − 4.16451I −4.14359 + 8.28004I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.28821 − 0.91096I
a = −0.835352 − 0.045091I
b = 0.06726 + 1.54442I
−8.38532 + 4.16451I −4.14359 − 8.28004I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
11
− 7u
10
+ ··· + 11u − 1)(u
46
+ 20u
45
+ ··· + 14009u + 961)
c
2
(u
11
+ u
10
− 3u
9
− 4u
8
+ 7u
7
+ 8u
6
− 8u
5
− 9u
4
+ 5u
3
+ 5u
2
− u − 1)
· (u
46
− 10u
44
+ ··· − 11u + 31)
c
3
(u
11
+ 4u
9
+ ··· − 2u
2
− 1)(u
46
+ u
45
+ ··· + 2u − 1)
c
4
(u
11
+ 2u
9
− u
8
+ 3u
7
− u
6
+ 3u
4
− u
3
+ 4u
2
+ 1)
· (u
46
− 3u
45
+ ··· − 2160u − 1621)
c
5
, c
6
(u
11
+ 8u
9
+ 23u
7
+ 28u
5
+ u
4
+ 12u
3
+ 3u
2
+ 1)
· (u
46
− u
45
+ ··· − 10u − 1)
c
7
(u
11
− u
10
− 3u
9
+ 4u
8
+ 7u
7
− 8u
6
− 8u
5
+ 9u
4
+ 5u
3
− 5u
2
− u + 1)
· (u
46
− 10u
44
+ ··· − 11u + 31)
c
8
(u
11
+ 2u
9
+ u
8
+ 3u
7
+ u
6
− 3u
4
− u
3
− 4u
2
− 1)
· (u
46
− 3u
45
+ ··· − 2160u − 1621)
c
9
(u
11
− u
10
− 5u
9
+ 5u
8
+ 9u
7
− 8u
6
− 8u
5
+ 7u
4
+ 4u
3
− 3u
2
− u + 1)
· (u
46
− 24u
44
+ ··· + 183u + 43)
c
10
, c
11
(u
11
+ 8u
9
+ 23u
7
+ 28u
5
− u
4
+ 12u
3
− 3u
2
− 1)
· (u
46
− u
45
+ ··· − 10u − 1)
c
12
(u
11
+ 3u
9
+ 8u
8
+ 3u
7
+ 10u
6
+ 12u
5
+ u
4
+ 9u
3
+ 5u
2
− 4u + 1)
· (u
46
+ 7u
45
+ ··· − 3420u − 343)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
11
+ 13y
10
+ ··· + 15y −1)
· (y
46
+ 32y
45
+ ··· + 2013751y + 923521)
c
2
, c
7
(y
11
− 7y
10
+ ··· + 11y −1)(y
46
− 20y
45
+ ··· − 14009y + 961)
c
3
(y
11
+ 8y
10
+ ··· − 4y −1)(y
46
+ 7y
45
+ ··· − 42y + 1)
c
4
, c
8
(y
11
+ 4y
10
+ ··· − 8y −1)
· (y
46
− 41y
45
+ ··· − 68296334y + 2627641)
c
5
, c
6
, c
10
c
11
(y
11
+ 16y
10
+ ··· − 6y −1)(y
46
+ 51y
45
+ ··· − 60y + 1)
c
9
(y
11
− 11y
10
+ ··· + 7y −1)(y
46
− 48y
45
+ ··· − 93001y + 1849)
c
12
(y
11
+ 6y
10
+ ··· + 6y −1)(y
46
− 51y
45
+ ··· − 4953020y + 117649)
16
