12n
0351
(K12n
0351
)
A knot diagram
1
Linearized knot diagam
3 6 8 9 10 2 11 4 1 8 10 5
Solving Sequence
4,9 1,5
10 6 8 3 2 12 11 7
c
4
c
9
c
5
c
8
c
3
c
2
c
12
c
11
c
7
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.11138 × 10
47
u
32
+ 5.57581 × 10
46
u
31
+ ··· + 2.13390 × 10
50
b + 2.41977 × 10
50
,
− 2.54097 × 10
51
u
32
+ 4.05282 × 10
50
u
31
+ ··· + 3.69165 × 10
52
a + 5.61038 × 10
53
,
u
33
− u
32
+ ··· − 106u + 173i
I
u
2
= h−3u
17
+ 4u
16
+ ··· + 5b + 14, −19u
17
+ 2u
16
+ ··· + 5a + 57, u
18
− 9u
16
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 51 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−8.11 × 10
47
u
32
+ 5.58 × 10
46
u
31
+ · · · + 2.13 × 10
50
b + 2.42 ×
10
50
, −2.54 × 10
51
u
32
+ 4.05 × 10
50
u
31
+ · · · + 3.69 × 10
52
a + 5.61 ×
10
53
, u
33
− u
32
+ · · · − 106u + 173i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
1
=
0.0688301u
32
− 0.0109783u
31
+ ··· − 9.38616u − 15.1975
0.00380120u
32
− 0.000261296u
31
+ ··· − 0.303063u − 1.13396
a
5
=
1
u
2
a
10
=
0.0543141u
32
− 0.00150099u
31
+ ··· − 4.29999u − 10.4669
0.0221013u
32
− 0.00297101u
31
+ ··· − 2.07083u − 4.65333
a
6
=
0.0489761u
32
− 0.00899494u
31
+ ··· − 8.55348u − 10.6501
0.0256145u
32
− 0.00501638u
31
+ ··· − 3.35159u − 6.23090
a
8
=
u
u
a
3
=
−u
2
+ 1
−u
2
a
2
=
0.0537482u
32
− 0.00848860u
31
+ ··· − 7.70974u − 11.3277
0.0361202u
32
− 0.00667465u
31
+ ··· − 4.42265u − 7.79409
a
12
=
0.112795u
32
− 0.0212720u
31
+ ··· − 14.8584u − 24.0719
0.0284035u
32
− 0.00624395u
31
+ ··· − 4.33982u − 6.95902
a
11
=
0.0229993u
32
+ 0.000676223u
31
+ ··· − 2.29755u − 4.63975
−0.00921351u
32
− 0.000793791u
31
+ ··· − 0.0683872u + 1.17380
a
7
=
−0.0659945u
32
+ 0.0142976u
31
+ ··· + 11.0084u + 15.2187
−0.00761661u
32
− 0.0000982334u
31
+ ··· + 2.05310u + 2.41838
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.280111u
32
+ 0.0673788u
31
+ ··· + 28.5160u + 51.9527
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
33
+ 31u
32
+ ··· − 108u − 1
c
2
, c
6
u
33
− 3u
32
+ ··· + 10u + 1
c
3
, c
4
, c
8
u
33
− u
32
+ ··· − 106u + 173
c
5
u
33
+ u
32
+ ··· + 72271u + 18731
c
7
, c
10
u
33
+ u
32
+ ··· + 698u + 391
c
9
u
33
− 5u
32
+ ··· + 28u − 11
c
11
u
33
+ 55u
32
+ ··· − 781200u − 152881
c
12
u
33
− u
32
+ ··· − 428u + 187
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
33
− 45y
32
+ ··· − 3432y −1
c
2
, c
6
y
33
+ 31y
32
+ ··· − 108y −1
c
3
, c
4
, c
8
y
33
− 43y
32
+ ··· + 292880y −29929
c
5
y
33
+ 77y
32
+ ··· − 6878739425y −350850361
c
7
, c
10
y
33
+ 55y
32
+ ··· − 781200y −152881
c
9
y
33
− 7y
32
+ ··· − 778y −121
c
11
y
33
− 149y
32
+ ··· − 105634649180y −23372600161
c
12
y
33
+ 57y
32
+ ··· − 214378y −34969
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.881268 + 0.494274I
a = 1.028140 − 0.103856I
b = 0.744044 − 0.822426I
−7.71312 − 1.78537I −0.85266 + 4.65753I
u = 0.881268 − 0.494274I
a = 1.028140 + 0.103856I
b = 0.744044 + 0.822426I
−7.71312 + 1.78537I −0.85266 − 4.65753I
u = 0.806093 + 0.733762I
a = −0.048706 + 0.852350I
b = −0.516099 + 0.675037I
−0.34629 + 2.42589I −3.38432 − 3.33398I
u = 0.806093 − 0.733762I
a = −0.048706 − 0.852350I
b = −0.516099 − 0.675037I
−0.34629 − 2.42589I −3.38432 + 3.33398I
u = −0.798281 + 0.311266I
a = −0.571033 − 0.836849I
b = −0.50701 + 2.28619I
−12.33120 + 1.02478I −6.59141 + 2.03554I
u = −0.798281 − 0.311266I
a = −0.571033 + 0.836849I
b = −0.50701 − 2.28619I
−12.33120 − 1.02478I −6.59141 − 2.03554I
u = 0.811379 + 0.055840I
a = −0.54698 + 1.54986I
b = −0.429316 + 0.085080I
−0.52878 + 4.48782I −5.13520 − 5.73220I
u = 0.811379 − 0.055840I
a = −0.54698 − 1.54986I
b = −0.429316 − 0.085080I
−0.52878 − 4.48782I −5.13520 + 5.73220I
u = −0.461701 + 0.612571I
a = 0.658166 − 0.583233I
b = −0.093739 + 0.146770I
0.081645 + 1.028670I 0.74020 − 3.82977I
u = −0.461701 − 0.612571I
a = 0.658166 + 0.583233I
b = −0.093739 − 0.146770I
0.081645 − 1.028670I 0.74020 + 3.82977I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.520817 + 0.403957I
a = −0.656947 + 0.628673I
b = −0.343599 + 0.875931I
0.07174 + 2.09017I −0.84653 − 3.88061I
u = −0.520817 − 0.403957I
a = −0.656947 − 0.628673I
b = −0.343599 − 0.875931I
0.07174 − 2.09017I −0.84653 + 3.88061I
u = 0.541626 + 0.352089I
a = −1.57063 + 0.32219I
b = −0.995588 + 0.334486I
−3.54901 − 0.96370I −7.30947 + 1.19731I
u = 0.541626 − 0.352089I
a = −1.57063 − 0.32219I
b = −0.995588 − 0.334486I
−3.54901 + 0.96370I −7.30947 − 1.19731I
u = 1.367540 + 0.181430I
a = −0.883343 − 0.451036I
b = −1.89904 − 0.40011I
−5.14586 − 3.44515I −3.74377 + 8.43324I
u = 1.367540 − 0.181430I
a = −0.883343 + 0.451036I
b = −1.89904 + 0.40011I
−5.14586 + 3.44515I −3.74377 − 8.43324I
u = −0.263257 + 0.516809I
a = 0.905386 − 0.059376I
b = 0.061869 + 0.214108I
0.112234 + 1.091570I 1.51179 − 6.02970I
u = −0.263257 − 0.516809I
a = 0.905386 + 0.059376I
b = 0.061869 − 0.214108I
0.112234 − 1.091570I 1.51179 + 6.02970I
u = −1.46377
a = −0.611776
b = −1.74803
−3.79571 −0.350320
u = −1.55168 + 0.23953I
a = 0.606082 − 0.442133I
b = 2.42916 + 0.21011I
−10.65780 + 3.51663I −5.96026 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55168 − 0.23953I
a = 0.606082 + 0.442133I
b = 2.42916 − 0.21011I
−10.65780 − 3.51663I −5.96026 + 0.I
u = 1.56741 + 0.23862I
a = 0.584803 − 0.034792I
b = 1.91823 + 0.02308I
−7.35813 − 4.59771I 0
u = 1.56741 − 0.23862I
a = 0.584803 + 0.034792I
b = 1.91823 − 0.02308I
−7.35813 + 4.59771I 0
u = −0.95012 + 1.51122I
a = −0.549793 − 0.409182I
b = −0.633085 + 0.187322I
−14.0224 + 4.9505I 0
u = −0.95012 − 1.51122I
a = −0.549793 + 0.409182I
b = −0.633085 − 0.187322I
−14.0224 − 4.9505I 0
u = 1.79395 + 0.15288I
a = 0.565816 − 0.803329I
b = 1.74296 − 0.32540I
17.5407 − 3.2542I 0
u = 1.79395 − 0.15288I
a = 0.565816 + 0.803329I
b = 1.74296 + 0.32540I
17.5407 + 3.2542I 0
u = −1.79808 + 0.17463I
a = −0.774547 + 0.627665I
b = −2.05265 + 0.43342I
−17.5402 + 4.7342I 0
u = −1.79808 − 0.17463I
a = −0.774547 − 0.627665I
b = −2.05265 − 0.43342I
−17.5402 − 4.7342I 0
u = 1.81040 + 0.47252I
a = 0.816894 + 0.399455I
b = 2.24901 + 0.45557I
16.7809 − 12.3351I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.81040 − 0.47252I
a = 0.816894 − 0.399455I
b = 2.24901 − 0.45557I
16.7809 + 12.3351I 0
u = −2.00385 + 0.04235I
a = 0.612520 − 0.356931I
b = 1.69886 − 0.37474I
−11.89190 + 2.84171I 0
u = −2.00385 − 0.04235I
a = 0.612520 + 0.356931I
b = 1.69886 + 0.37474I
−11.89190 − 2.84171I 0
8
II. I
u
2
= h−3u
17
+ 4u
16
+ · · · + 5b + 14, −19u
17
+ 2u
16
+ · · · + 5a + 57, u
18
−
9u
16
+ · · · − 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
1
=
19
5
u
17
−
2
5
u
16
+ ··· −
62
5
u −
57
5
3
5
u
17
−
4
5
u
16
+ ··· −
9
5
u −
14
5
a
5
=
1
u
2
a
10
=
9
5
u
17
−
2
5
u
16
+ ··· −
12
5
u −
47
5
−
9
5
u
17
−
18
5
u
16
+ ··· −
8
5
u +
2
5
a
6
=
−5.40000u
17
− 3.80000u
16
+ ··· + 4.20000u + 11.2000
−2.60000u
17
− 3.20000u
16
+ ··· − 2.20000u + 3.80000
a
8
=
u
u
a
3
=
−u
2
+ 1
−u
2
a
2
=
2u
17
− 3u
16
+ ··· − 13u − 6
−
4
5
u
17
−
28
5
u
16
+ ··· −
33
5
u −
3
5
a
12
=
12
5
u
17
−
16
5
u
16
+ ··· −
76
5
u −
41
5
−u
17
− 5u
16
+ ··· − 6u
2
− 6u
a
11
=
2
5
u
17
−
16
5
u
16
+ ··· −
26
5
u −
31
5
−3.20000u
17
− 6.40000u
16
+ ··· − 4.40000u + 3.60000
a
7
=
−6.60000u
17
− 6.20000u
16
+ ··· + 7.80000u + 15.8000
−3.40000u
17
− 5.80000u
16
+ ··· − 3.80000u + 7.20000
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
17
+ 5u
16
+ 27u
15
− 34u
14
− 125u
13
+ 95u
12
+ 270u
11
−
122u
10
− 239u
9
+ 41u
8
− 99u
7
+ 37u
6
+ 384u
5
+ 32u
4
− 257u
3
− 88u
2
+ 25u + 15
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 12u
17
+ ··· − 16u + 1
c
2
u
18
− 2u
17
+ ··· − 2u + 1
c
3
, c
4
u
18
− 9u
16
+ ··· − 2u + 1
c
5
u
18
+ 7u
16
+ ··· + u + 1
c
6
u
18
+ 2u
17
+ ··· + 2u + 1
c
7
u
18
+ 8u
16
+ ··· + 4u
2
+ 1
c
8
u
18
− 9u
16
+ ··· + 2u + 1
c
9
u
18
− 6u
17
+ ··· − 2u + 1
c
10
u
18
+ 8u
16
+ ··· + 4u
2
+ 1
c
11
u
18
+ 16u
17
+ ··· + 8u + 1
c
12
u
18
+ 11u
16
+ ··· − 2u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 20y
16
+ ··· − 24y + 1
c
2
, c
6
y
18
+ 12y
17
+ ··· + 16y + 1
c
3
, c
4
, c
8
y
18
− 18y
17
+ ··· − 20y + 1
c
5
y
18
+ 14y
17
+ ··· − 3y + 1
c
7
, c
10
y
18
+ 16y
17
+ ··· + 8y + 1
c
9
y
18
+ 2y
17
+ ··· − 10y + 1
c
11
y
18
− 24y
17
+ ··· + 4y + 1
c
12
y
18
+ 22y
17
+ ··· + 14y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.085759 + 1.011970I
a = 0.071482 + 0.659946I
b = −0.330517 + 0.071724I
−1.08613 − 0.96816I −6.34211 + 0.57071I
u = 0.085759 − 1.011970I
a = 0.071482 − 0.659946I
b = −0.330517 − 0.071724I
−1.08613 + 0.96816I −6.34211 − 0.57071I
u = −1.114560 + 0.293820I
a = −0.931989 + 0.046707I
b = −1.33734 − 0.90053I
−8.46698 + 1.31286I −9.83068 + 0.32018I
u = −1.114560 − 0.293820I
a = −0.931989 − 0.046707I
b = −1.33734 + 0.90053I
−8.46698 − 1.31286I −9.83068 − 0.32018I
u = 1.300570 + 0.029273I
a = −0.536713 − 1.019510I
b = −1.28702 − 0.60196I
−2.94807 − 4.42128I −4.69559 + 5.41775I
u = 1.300570 − 0.029273I
a = −0.536713 + 1.019510I
b = −1.28702 + 0.60196I
−2.94807 + 4.42128I −4.69559 − 5.41775I
u = −1.306820 + 0.073942I
a = 0.030062 + 0.945777I
b = 0.663121 + 0.218291I
−3.48940 + 1.60644I −4.34335 − 1.67805I
u = −1.306820 − 0.073942I
a = 0.030062 − 0.945777I
b = 0.663121 − 0.218291I
−3.48940 − 1.60644I −4.34335 + 1.67805I
u = 1.232400 + 0.491104I
a = 0.340655 − 0.011913I
b = 1.05787 − 1.88552I
−12.53040 − 2.23082I −8.19150 + 3.26212I
u = 1.232400 − 0.491104I
a = 0.340655 + 0.011913I
b = 1.05787 + 1.88552I
−12.53040 + 2.23082I −8.19150 − 3.26212I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.329640 + 0.238506I
a = −1.026160 − 0.341518I
b = −2.02234 − 0.39359I
−5.47647 − 2.87572I −10.17496 − 1.27830I
u = 1.329640 − 0.238506I
a = −1.026160 + 0.341518I
b = −2.02234 + 0.39359I
−5.47647 + 2.87572I −10.17496 + 1.27830I
u = −0.375312 + 0.293384I
a = 1.52275 − 1.15299I
b = −0.663240 − 0.618071I
−0.093430 − 0.496699I −2.79813 + 0.04829I
u = −0.375312 − 0.293384I
a = 1.52275 + 1.15299I
b = −0.663240 + 0.618071I
−0.093430 + 0.496699I −2.79813 − 0.04829I
u = −1.52906 + 0.23255I
a = 0.647405 − 0.190244I
b = 2.05285 − 0.17653I
−7.41546 + 5.53534I −5.08064 − 8.15204I
u = −1.52906 − 0.23255I
a = 0.647405 + 0.190244I
b = 2.05285 + 0.17653I
−7.41546 − 5.53534I −5.08064 + 8.15204I
u = 0.377398 + 0.043983I
a = −1.11749 + 2.90937I
b = −0.133373 + 0.724783I
0.38303 + 4.11760I 1.95695 − 4.69583I
u = 0.377398 − 0.043983I
a = −1.11749 − 2.90937I
b = −0.133373 − 0.724783I
0.38303 − 4.11760I 1.95695 + 4.69583I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
18
− 12u
17
+ ··· − 16u + 1)(u
33
+ 31u
32
+ ··· − 108u − 1)
c
2
(u
18
− 2u
17
+ ··· − 2u + 1)(u
33
− 3u
32
+ ··· + 10u + 1)
c
3
, c
4
(u
18
− 9u
16
+ ··· − 2u + 1)(u
33
− u
32
+ ··· − 106u + 173)
c
5
(u
18
+ 7u
16
+ ··· + u + 1)(u
33
+ u
32
+ ··· + 72271u + 18731)
c
6
(u
18
+ 2u
17
+ ··· + 2u + 1)(u
33
− 3u
32
+ ··· + 10u + 1)
c
7
(u
18
+ 8u
16
+ ··· + 4u
2
+ 1)(u
33
+ u
32
+ ··· + 698u + 391)
c
8
(u
18
− 9u
16
+ ··· + 2u + 1)(u
33
− u
32
+ ··· − 106u + 173)
c
9
(u
18
− 6u
17
+ ··· − 2u + 1)(u
33
− 5u
32
+ ··· + 28u − 11)
c
10
(u
18
+ 8u
16
+ ··· + 4u
2
+ 1)(u
33
+ u
32
+ ··· + 698u + 391)
c
11
(u
18
+ 16u
17
+ ··· + 8u + 1)(u
33
+ 55u
32
+ ··· − 781200u − 152881)
c
12
(u
18
+ 11u
16
+ ··· − 2u + 1)(u
33
− u
32
+ ··· − 428u + 187)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
18
− 20y
16
+ ··· − 24y + 1)(y
33
− 45y
32
+ ··· − 3432y − 1)
c
2
, c
6
(y
18
+ 12y
17
+ ··· + 16y + 1)(y
33
+ 31y
32
+ ··· − 108y − 1)
c
3
, c
4
, c
8
(y
18
− 18y
17
+ ··· − 20y + 1)(y
33
− 43y
32
+ ··· + 292880y − 29929)
c
5
(y
18
+ 14y
17
+ ··· − 3y + 1)
· (y
33
+ 77y
32
+ ··· − 6878739425y − 350850361)
c
7
, c
10
(y
18
+ 16y
17
+ ··· + 8y + 1)(y
33
+ 55y
32
+ ··· − 781200y − 152881)
c
9
(y
18
+ 2y
17
+ ··· − 10y + 1)(y
33
− 7y
32
+ ··· − 778y − 121)
c
11
(y
18
− 24y
17
+ ··· + 4y + 1)
· (y
33
− 149y
32
+ ··· − 105634649180y − 23372600161)
c
12
(y
18
+ 22y
17
+ ··· + 14y + 1)(y
33
+ 57y
32
+ ··· − 214378y − 34969)
15
