12n
0870
(K12n
0870
)
A knot diagram
1
Linearized knot diagam
4 9 6 10 2 1 10 2 12 4 7 9
Solving Sequence
9,12 4,10
5 1 2 6 3 8 7 11
c
9
c
4
c
12
c
1
c
5
c
3
c
8
c
7
c
11
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.00164 × 10
56
u
36
− 3.79644 × 10
57
u
35
+ ··· + 2.25166 × 10
59
b − 2.70335 × 10
59
,
3.91048 × 10
57
u
36
+ 9.08535 × 10
57
u
35
+ ··· + 6.75498 × 10
59
a − 7.61995 × 10
59
, u
37
+ 3u
36
+ ··· + 27u + 27i
I
u
2
= h−1131323800u
24
+ 8093044710u
23
+ ··· + 3924483813b + 3811509091,
6486714421u
24
− 23913418584u
23
+ ··· + 3924483813a + 14656680362,
u
25
− 4u
24
+ ··· − 9u + 1i
* 2 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−9.00 × 10
56
u
36
− 3.80 × 10
57
u
35
+ · · · + 2.25 × 10
59
b − 2.70 ×
10
59
, 3.91 × 10
57
u
36
+ 9.09 × 10
57
u
35
+ · · · + 6.75 × 10
59
a − 7.62 ×
10
59
, u
37
+ 3u
36
+ · · · + 27u + 27i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
4
=
−0.00578904u
36
− 0.0134499u
35
+ ··· − 3.92304u + 1.12805
0.00399778u
36
+ 0.0168606u
35
+ ··· − 0.325413u + 1.20060
a
10
=
1
u
2
a
5
=
−0.000411239u
36
+ 0.00236692u
35
+ ··· − 4.29899u + 2.43442
0.00328021u
36
+ 0.0148958u
35
+ ··· − 0.462065u + 1.20915
a
1
=
−u
u
a
2
=
−0.0189562u
36
− 0.0588044u
35
+ ··· − 1.78606u − 1.25542
−0.00948539u
36
− 0.0280353u
35
+ ··· − 3.10510u − 0.162459
a
6
=
0.0309726u
36
+ 0.0803799u
35
+ ··· + 6.68023u − 0.585521
−0.00665213u
36
− 0.0225712u
35
+ ··· + 0.785980u − 1.34064
a
3
=
−0.00947083u
36
− 0.0307691u
35
+ ··· + 1.31904u − 1.09296
−0.00948539u
36
− 0.0280353u
35
+ ··· − 3.10510u − 0.162459
a
8
=
−0.0288137u
36
− 0.0681602u
35
+ ··· − 7.98371u + 2.22311
0.00233006u
36
+ 0.00798065u
35
+ ··· − 1.26663u + 1.55312
a
7
=
−0.0301650u
36
− 0.0794968u
35
+ ··· − 6.43270u + 0.176402
0.00584456u
36
+ 0.0216881u
35
+ ··· − 1.03351u + 1.74976
a
11
=
0.0207989u
36
+ 0.0467173u
35
+ ··· + 6.44147u − 1.65281
−0.0128462u
36
− 0.0354139u
35
+ ··· − 0.0326585u − 1.80165
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0119190u
36
+ 0.0677566u
35
+ ··· − 7.20128u − 2.71469
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
37
− 4u
36
+ ··· − 2323u + 371
c
2
, c
8
u
37
+ u
36
+ ··· − 73337u + 9059
c
3
u
37
− 3u
36
+ ··· − 924u + 436
c
4
, c
10
u
37
+ u
36
+ ··· + 57272u + 22021
c
5
u
37
− 2u
36
+ ··· + 26864u + 132947
c
6
u
37
+ 4u
36
+ ··· + 69u + 71
c
7
u
37
+ 5u
36
+ ··· − 90135u + 22247
c
9
, c
12
u
37
− 3u
36
+ ··· + 27u − 27
c
11
u
37
− 2u
36
+ ··· + 8266u + 347
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
37
+ 12y
36
+ ··· − 1418941y −137641
c
2
, c
8
y
37
+ 65y
36
+ ··· − 1244302617y −82065481
c
3
y
37
+ 15y
36
+ ··· − 3507096y −190096
c
4
, c
10
y
37
− 63y
36
+ ··· − 4284792146y −484924441
c
5
y
37
+ 84y
36
+ ··· − 186496418056y −17674904809
c
6
y
37
− 12y
36
+ ··· + 153577y −5041
c
7
y
37
− 79y
36
+ ··· − 621600391y −494929009
c
9
, c
12
y
37
+ 35y
36
+ ··· − 6075y −729
c
11
y
37
− 16y
36
+ ··· + 76266810y −120409
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.167576 + 1.059820I
a = −3.68479 + 0.47830I
b = 4.00168 − 0.78199I
−6.33270 + 0.58456I 4.48833 + 4.92922I
u = −0.167576 − 1.059820I
a = −3.68479 − 0.47830I
b = 4.00168 + 0.78199I
−6.33270 − 0.58456I 4.48833 − 4.92922I
u = −0.459153 + 1.191530I
a = 0.82442 − 1.37289I
b = −1.58984 + 0.88747I
4.34687 + 6.37531I 4.85551 − 8.12342I
u = −0.459153 − 1.191530I
a = 0.82442 + 1.37289I
b = −1.58984 − 0.88747I
4.34687 − 6.37531I 4.85551 + 8.12342I
u = −0.665909 + 0.256393I
a = 0.205806 − 1.100060I
b = −0.923196 − 0.122607I
1.54386 − 2.11310I 0.69649 + 4.84319I
u = −0.665909 − 0.256393I
a = 0.205806 + 1.100060I
b = −0.923196 + 0.122607I
1.54386 + 2.11310I 0.69649 − 4.84319I
u = 0.384563 + 1.236730I
a = 0.923969 + 0.381334I
b = −1.57334 − 0.01590I
1.13766 − 4.82922I −4.75413 + 6.35770I
u = 0.384563 − 1.236730I
a = 0.923969 − 0.381334I
b = −1.57334 + 0.01590I
1.13766 + 4.82922I −4.75413 − 6.35770I
u = −0.323724 + 1.264700I
a = 0.175356 − 0.423168I
b = 0.510942 − 0.182266I
6.26009 + 0.98488I 1.65796 − 0.75056I
u = −0.323724 − 1.264700I
a = 0.175356 + 0.423168I
b = 0.510942 + 0.182266I
6.26009 − 0.98488I 1.65796 + 0.75056I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.385093 + 0.545017I
a = −0.268434 − 1.007740I
b = 0.185188 + 0.521817I
−0.024291 − 1.165760I −0.80928 + 6.18459I
u = 0.385093 − 0.545017I
a = −0.268434 + 1.007740I
b = 0.185188 − 0.521817I
−0.024291 + 1.165760I −0.80928 − 6.18459I
u = −0.061867 + 1.394640I
a = −0.984047 + 0.296932I
b = 0.406963 − 0.361276I
13.74180 + 1.41481I 6.56734 − 5.56716I
u = −0.061867 − 1.394640I
a = −0.984047 − 0.296932I
b = 0.406963 + 0.361276I
13.74180 − 1.41481I 6.56734 + 5.56716I
u = 0.567279 + 0.193554I
a = −0.42064 + 2.13487I
b = 0.585496 + 0.181304I
0.41125 + 3.00174I −3.07390 − 3.64949I
u = 0.567279 − 0.193554I
a = −0.42064 − 2.13487I
b = 0.585496 − 0.181304I
0.41125 − 3.00174I −3.07390 + 3.64949I
u = 0.322097 + 1.363570I
a = −0.809804 + 0.171126I
b = 1.48039 + 0.37445I
3.14917 − 0.96903I 0
u = 0.322097 − 1.363570I
a = −0.809804 − 0.171126I
b = 1.48039 − 0.37445I
3.14917 + 0.96903I 0
u = 0.481521 + 0.299204I
a = −0.29262 + 2.32677I
b = −0.287518 − 0.472642I
−1.88357 + 1.37786I −9.19174 + 1.54938I
u = 0.481521 − 0.299204I
a = −0.29262 − 2.32677I
b = −0.287518 + 0.472642I
−1.88357 − 1.37786I −9.19174 − 1.54938I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.14297 + 1.43646I
a = −0.164059 + 0.136453I
b = −0.482858 + 0.065845I
4.94395 − 5.26244I 4.95493 + 7.25561I
u = 0.14297 − 1.43646I
a = −0.164059 − 0.136453I
b = −0.482858 − 0.065845I
4.94395 + 5.26244I 4.95493 − 7.25561I
u = −1.52010 + 0.15518I
a = 0.388678 + 0.524402I
b = −1.48572 + 0.39435I
13.2585 + 5.7889I 0
u = −1.52010 − 0.15518I
a = 0.388678 − 0.524402I
b = −1.48572 − 0.39435I
13.2585 − 5.7889I 0
u = −0.460772
a = 1.49046
b = 0.985143
−1.64677 −6.24120
u = 1.14789 + 1.07616I
a = 0.290213 + 0.775019I
b = −1.39903 − 0.23170I
−5.26058 − 4.15697I 20.8250 + 0.I
u = 1.14789 − 1.07616I
a = 0.290213 − 0.775019I
b = −1.39903 + 0.23170I
−5.26058 + 4.15697I 20.8250 + 0.I
u = −0.129945 + 0.296598I
a = 1.42426 − 2.10190I
b = 1.58369 + 0.22057I
9.68278 − 0.71257I −0.76102 − 2.68873I
u = −0.129945 − 0.296598I
a = 1.42426 + 2.10190I
b = 1.58369 − 0.22057I
9.68278 + 0.71257I −0.76102 + 2.68873I
u = −0.06893 + 1.69284I
a = −2.11977 − 0.00511I
b = 3.07286 − 0.11340I
17.2905 + 0.2066I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.06893 − 1.69284I
a = −2.11977 + 0.00511I
b = 3.07286 + 0.11340I
17.2905 − 0.2066I 0
u = −0.65528 + 1.58363I
a = 1.13446 − 1.07747I
b = −2.20101 + 0.73181I
18.6868 + 13.3663I 0
u = −0.65528 − 1.58363I
a = 1.13446 + 1.07747I
b = −2.20101 − 0.73181I
18.6868 − 13.3663I 0
u = 0.22500 + 1.73667I
a = −1.55015 + 0.10298I
b = 2.47070 + 0.29718I
7.62465 − 0.70239I 0
u = 0.22500 − 1.73667I
a = −1.55015 − 0.10298I
b = 2.47070 − 0.29718I
7.62465 + 0.70239I 0
u = −0.87353 + 1.60469I
a = 0.515257 − 0.731056I
b = −0.347949 − 0.452043I
17.5224 + 2.6853I 0
u = −0.87353 − 1.60469I
a = 0.515257 + 0.731056I
b = −0.347949 + 0.452043I
17.5224 − 2.6853I 0
8
II.
I
u
2
= h−1.13 × 10
9
u
24
+ 8.09 × 10
9
u
23
+ · · · + 3.92 × 10
9
b + 3.81 × 10
9
, 6.49 ×
10
9
u
24
−2.39×10
10
u
23
+· · ·+3.92×10
9
a+1.47×10
10
, u
25
−4u
24
+· · ·−9u+1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
4
=
−1.65288u
24
+ 6.09339u
23
+ ··· − 2.91819u − 3.73468
0.288273u
24
− 2.06219u
23
+ ··· + 11.6354u − 0.971213
a
10
=
1
u
2
a
5
=
−1.70636u
24
+ 5.59466u
23
+ ··· + 11.7276u − 5.22403
0.556721u
24
− 2.37317u
23
+ ··· + 5.27525u − 0.258587
a
1
=
−u
u
a
2
=
−2.56378u
24
+ 7.61504u
23
+ ··· − 28.4470u + 2.55259
0.486242u
24
− 1.35369u
23
+ ··· + 3.80240u − 0.384318
a
6
=
2.87677u
24
− 11.8498u
23
+ ··· + 78.7045u − 11.8129
−0.240444u
24
+ 1.16517u
23
+ ··· − 12.2022u + 1.62144
a
3
=
−3.05002u
24
+ 8.96873u
23
+ ··· − 32.2494u + 2.93691
0.486242u
24
− 1.35369u
23
+ ··· + 3.80240u − 0.384318
a
8
=
2.78473u
24
− 11.4190u
23
+ ··· + 69.1681u − 10.1842
−0.363384u
24
+ 1.54406u
23
+ ··· − 10.9514u + 1.76945
a
7
=
2.73126u
24
− 10.9178u
23
+ ··· + 74.8139u − 11.6736
−0.0949357u
24
+ 0.233088u
23
+ ··· − 8.31152u + 1.48207
a
11
=
3.25777u
24
− 11.9300u
23
+ ··· + 42.3975u − 3.58230
−0.233376u
24
+ 1.03096u
23
+ ··· − 10.7272u + 1.36206
(ii) Obstruction class = 1
(iii) Cusp Shapes =
16865762293
3924483813
u
24
−
26283566834
1308161271
u
23
+ ··· +
557421548465
3924483813
u −
84415101034
3924483813
9
(iv) u-Polynomials at the component
10
Crossings u-Polynomials at each crossing
c
1
u
25
− 7u
24
+ ··· + 3u − 1
c
2
u
25
+ 6u
23
+ ··· + u + 1
c
3
u
25
− 6u
24
+ ··· + 3u − 1
c
4
u
25
− 8u
23
+ ··· + 8u + 1
c
5
u
25
+ 3u
24
+ ··· − 1944u + 631
c
6
u
25
− u
24
+ ··· − 15u + 1
c
7
u
25
+ 8u
24
+ ··· − 2345u − 797
c
8
u
25
+ 6u
23
+ ··· + u − 1
c
9
u
25
− 4u
24
+ ··· − 9u + 1
c
10
u
25
− 8u
23
+ ··· + 8u − 1
c
11
u
25
+ u
24
+ ··· + 2u − 1
c
12
u
25
+ 4u
24
+ ··· − 9u − 1
11
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
− 5y
24
+ ··· + 13y −1
c
2
, c
8
y
25
+ 12y
24
+ ··· − 31y −1
c
3
y
25
− 10y
24
+ ··· + 15y −1
c
4
, c
10
y
25
− 16y
24
+ ··· + 24y −1
c
5
y
25
+ 7y
24
+ ··· + 2558782y −398161
c
6
y
25
− 5y
24
+ ··· − 125y −1
c
7
y
25
− 16y
24
+ ··· − 2982649y −635209
c
9
, c
12
y
25
+ 18y
24
+ ··· + 7y −1
c
11
y
25
+ 11y
24
+ ··· − 12y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.211608 + 0.978671I
a = 4.02880 − 1.31629I
b = −4.19783 + 0.93997I
−6.57774 + 0.83601I −12.6564 − 11.7355I
u = −0.211608 − 0.978671I
a = 4.02880 + 1.31629I
b = −4.19783 − 0.93997I
−6.57774 − 0.83601I −12.6564 + 11.7355I
u = −1.04938
a = −0.0313361
b = 1.39743
−0.108576 0.152620
u = 0.798599 + 0.744182I
a = −0.551742 − 1.128860I
b = 0.836085 − 0.082926I
2.01196 + 0.69255I 1.79790 − 0.00493I
u = 0.798599 − 0.744182I
a = −0.551742 + 1.128860I
b = 0.836085 + 0.082926I
2.01196 − 0.69255I 1.79790 + 0.00493I
u = 0.501731 + 0.720411I
a = −0.249121 + 1.158170I
b = −0.568048 − 0.400869I
−1.84833 − 2.11157I −3.19865 + 3.94763I
u = 0.501731 − 0.720411I
a = −0.249121 − 1.158170I
b = −0.568048 + 0.400869I
−1.84833 + 2.11157I −3.19865 − 3.94763I
u = 0.209489 + 1.126730I
a = 0.157093 − 0.519084I
b = −1.141540 + 0.622781I
3.06603 − 4.36373I 1.36746 + 3.83070I
u = 0.209489 − 1.126730I
a = 0.157093 + 0.519084I
b = −1.141540 − 0.622781I
3.06603 + 4.36373I 1.36746 − 3.83070I
u = 0.103688 + 0.826073I
a = 1.21034 + 1.47977I
b = 0.314331 − 0.723879I
1.76724 + 3.08166I 2.11503 − 3.41199I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.103688 − 0.826073I
a = 1.21034 − 1.47977I
b = 0.314331 + 0.723879I
1.76724 − 3.08166I 2.11503 + 3.41199I
u = 0.535937 + 1.071200I
a = −0.690754 − 1.148390I
b = 1.67707 + 0.86201I
3.25606 − 5.74154I −0.57302 + 3.73990I
u = 0.535937 − 1.071200I
a = −0.690754 + 1.148390I
b = 1.67707 − 0.86201I
3.25606 + 5.74154I −0.57302 − 3.73990I
u = −0.318864 + 0.683122I
a = −0.054095 + 0.536492I
b = −1.59233 − 0.00324I
9.97950 + 1.46375I 3.71841 − 5.95020I
u = −0.318864 − 0.683122I
a = −0.054095 − 0.536492I
b = −1.59233 + 0.00324I
9.97950 − 1.46375I 3.71841 + 5.95020I
u = −0.510417 + 1.288240I
a = −0.87810 + 1.16015I
b = 1.43360 − 0.55061I
4.00523 + 5.32915I 1.41990 − 1.29007I
u = −0.510417 − 1.288240I
a = −0.87810 − 1.16015I
b = 1.43360 + 0.55061I
4.00523 − 5.32915I 1.41990 + 1.29007I
u = −0.16459 + 1.42006I
a = 1.178580 − 0.185673I
b = −0.815305 − 0.153731I
13.10510 + 0.67738I −0.354087 + 0.858492I
u = −0.16459 − 1.42006I
a = 1.178580 + 0.185673I
b = −0.815305 + 0.153731I
13.10510 − 0.67738I −0.354087 − 0.858492I
u = 0.20160 + 1.49559I
a = 0.529194 − 0.551861I
b = −0.710252 + 0.710457I
4.43285 − 4.32284I 0.666667 + 0.650947I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.20160 − 1.49559I
a = 0.529194 + 0.551861I
b = −0.710252 − 0.710457I
4.43285 + 4.32284I 0.666667 − 0.650947I
u = 1.15413 + 1.05672I
a = 0.254363 + 0.770568I
b = −1.372110 − 0.235434I
−5.39972 − 4.16553I −36.8997 + 7.0211I
u = 1.15413 − 1.05672I
a = 0.254363 − 0.770568I
b = −1.372110 + 0.235434I
−5.39972 + 4.16553I −36.8997 − 7.0211I
u = 0.224993 + 0.114423I
a = −4.41889 − 1.18595I
b = 0.437604 + 0.274587I
−1.42493 − 1.96110I −1.97977 + 5.53360I
u = 0.224993 − 0.114423I
a = −4.41889 + 1.18595I
b = 0.437604 − 0.274587I
−1.42493 + 1.96110I −1.97977 − 5.53360I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
25
− 7u
24
+ ··· + 3u − 1)(u
37
− 4u
36
+ ··· − 2323u + 371)
c
2
(u
25
+ 6u
23
+ ··· + u + 1)(u
37
+ u
36
+ ··· − 73337u + 9059)
c
3
(u
25
− 6u
24
+ ··· + 3u − 1)(u
37
− 3u
36
+ ··· − 924u + 436)
c
4
(u
25
− 8u
23
+ ··· + 8u + 1)(u
37
+ u
36
+ ··· + 57272u + 22021)
c
5
(u
25
+ 3u
24
+ ··· − 1944u + 631)
· (u
37
− 2u
36
+ ··· + 26864u + 132947)
c
6
(u
25
− u
24
+ ··· − 15u + 1)(u
37
+ 4u
36
+ ··· + 69u + 71)
c
7
(u
25
+ 8u
24
+ ··· − 2345u − 797)(u
37
+ 5u
36
+ ··· − 90135u + 22247)
c
8
(u
25
+ 6u
23
+ ··· + u − 1)(u
37
+ u
36
+ ··· − 73337u + 9059)
c
9
(u
25
− 4u
24
+ ··· − 9u + 1)(u
37
− 3u
36
+ ··· + 27u − 27)
c
10
(u
25
− 8u
23
+ ··· + 8u − 1)(u
37
+ u
36
+ ··· + 57272u + 22021)
c
11
(u
25
+ u
24
+ ··· + 2u − 1)(u
37
− 2u
36
+ ··· + 8266u + 347)
c
12
(u
25
+ 4u
24
+ ··· − 9u − 1)(u
37
− 3u
36
+ ··· + 27u − 27)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
25
− 5y
24
+ ··· + 13y −1)(y
37
+ 12y
36
+ ··· − 1418941y −137641)
c
2
, c
8
(y
25
+ 12y
24
+ ··· − 31y −1)
· (y
37
+ 65y
36
+ ··· − 1244302617y −82065481)
c
3
(y
25
− 10y
24
+ ··· + 15y −1)
· (y
37
+ 15y
36
+ ··· − 3507096y −190096)
c
4
, c
10
(y
25
− 16y
24
+ ··· + 24y −1)
· (y
37
− 63y
36
+ ··· − 4284792146y −484924441)
c
5
(y
25
+ 7y
24
+ ··· + 2558782y −398161)
· (y
37
+ 84y
36
+ ··· − 186496418056y −17674904809)
c
6
(y
25
− 5y
24
+ ··· − 125y −1)(y
37
− 12y
36
+ ··· + 153577y −5041)
c
7
(y
25
− 16y
24
+ ··· − 2982649y −635209)
· (y
37
− 79y
36
+ ··· − 621600391y −494929009)
c
9
, c
12
(y
25
+ 18y
24
+ ··· + 7y −1)(y
37
+ 35y
36
+ ··· − 6075y −729)
c
11
(y
25
+ 11y
24
+ ··· − 12y −1)
· (y
37
− 16y
36
+ ··· + 76266810y −120409)
18
