12a
0638
(K12a
0638
)
A knot diagram
1
Linearized knot diagam
3 7 10 9 12 2 11 6 4 1 8 5
Solving Sequence
3,10 4,7
2 1 11 6 9 5 8 12
c
3
c
2
c
1
c
10
c
6
c
9
c
4
c
8
c
12
c
5
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.88047 × 10
205
u
89
+ 4.82669 × 10
205
u
88
+ ··· + 8.17391 × 10
204
b + 1.54211 × 10
206
,
2.69752 × 10
206
u
89
− 3.08673 × 10
206
u
88
+ ··· + 8.17391 × 10
204
a − 1.57877 × 10
207
, u
90
− u
89
+ ··· − 13u − 1i
* 1 irreducible components of dim
C
= 0, with total 90 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−3.88 × 10
205
u
89
+ 4.83 × 10
205
u
88
+ · · · + 8.17 × 10
204
b + 1.54 ×
10
206
, 2.70 × 10
206
u
89
− 3.09 × 10
206
u
88
+ · · · + 8.17 × 10
204
a − 1.58 ×
10
207
, u
90
− u
89
+ · · · − 13u − 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
7
=
−33.0016u
89
+ 37.7631u
88
+ ··· + 1468.09u + 193.147
4.74738u
89
− 5.90500u
88
+ ··· − 173.610u − 18.8662
a
2
=
−8.45664u
89
+ 11.0243u
88
+ ··· + 256.917u + 9.20347
−6.17248u
89
+ 7.40897u
88
+ ··· + 257.954u + 31.5861
a
1
=
−14.6291u
89
+ 18.4333u
88
+ ··· + 514.871u + 40.7896
−6.17248u
89
+ 7.40897u
88
+ ··· + 257.954u + 31.5861
a
11
=
17.7342u
89
− 28.6739u
88
+ ··· − 80.1654u + 48.2554
10.8888u
89
− 13.4259u
88
+ ··· − 401.828u − 45.1321
a
6
=
−23.5669u
89
+ 26.3603u
88
+ ··· + 1121.51u + 150.471
−0.908820u
89
+ 0.780287u
88
+ ··· + 61.0914u + 11.0352
a
9
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
−10.0388u
89
+ 4.07039u
88
+ ··· + 1067.53u + 183.313
9.64910u
89
− 12.1029u
88
+ ··· − 343.266u − 36.0497
a
12
=
−9.59366u
89
+ 12.3295u
88
+ ··· + 310.049u + 14.7507
−5.77007u
89
+ 6.89531u
88
+ ··· + 241.600u + 29.5670
(ii) Obstruction class = −1
(iii) Cusp Shapes = 31.5469u
89
− 41.0990u
88
+ ··· − 989.110u − 113.884
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
90
+ 35u
89
+ ··· + 223u + 9
c
2
, c
6
u
90
− 3u
89
+ ··· − 19u + 3
c
3
, c
4
, c
9
u
90
+ u
89
+ ··· + 13u − 1
c
5
, c
12
u
90
− 3u
89
+ ··· − 19u + 3
c
7
, c
11
u
90
+ u
89
+ ··· − 17u − 1
c
8
1089(1089u
90
+ 7095u
89
+ ··· + 166909u − 7597)
c
10
1089(1089u
90
+ 5709u
89
+ ··· + 497255u + 37873)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
90
+ 41y
89
+ ··· + 119237y + 81
c
2
, c
6
y
90
− 35y
89
+ ··· − 223y + 9
c
3
, c
4
, c
9
y
90
+ 89y
89
+ ··· − 83y + 1
c
5
, c
12
y
90
+ 57y
89
+ ··· + 65y + 9
c
7
, c
11
y
90
− 63y
89
+ ··· − 275y + 1
c
8
1185921
· (1185921y
90
− 32124411y
89
+ ··· − 5463038131y + 57714409)
c
10
1185921
· (1185921y
90
+ 31046301y
89
+ ··· − 127015229803y + 1434364129)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.884407 + 0.552119I
a = 0.67651 − 1.37576I
b = 1.101550 + 0.648053I
−5.7142 − 13.3590I 0
u = 0.884407 − 0.552119I
a = 0.67651 + 1.37576I
b = 1.101550 − 0.648053I
−5.7142 + 13.3590I 0
u = 0.601482 + 0.851986I
a = 0.21021 − 1.43020I
b = 1.058390 + 0.151927I
−8.19443 + 0.91794I 0
u = 0.601482 − 0.851986I
a = 0.21021 + 1.43020I
b = 1.058390 − 0.151927I
−8.19443 − 0.91794I 0
u = −0.814653 + 0.489377I
a = −0.491507 − 1.062780I
b = −0.465241 + 0.591482I
−3.95289 − 2.63059I 0
u = −0.814653 − 0.489377I
a = −0.491507 + 1.062780I
b = −0.465241 − 0.591482I
−3.95289 + 2.63059I 0
u = −0.771114 + 0.546663I
a = −0.422283 − 0.500726I
b = 0.466094 + 0.844275I
−3.81555 + 7.81863I 0
u = −0.771114 − 0.546663I
a = −0.422283 + 0.500726I
b = 0.466094 − 0.844275I
−3.81555 − 7.81863I 0
u = 0.900983 + 0.596501I
a = −0.093843 + 0.502442I
b = 0.675937 − 0.597711I
0.35978 − 1.93194I 0
u = 0.900983 − 0.596501I
a = −0.093843 − 0.502442I
b = 0.675937 + 0.597711I
0.35978 + 1.93194I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.098559 + 1.088140I
a = 0.503311 + 0.971372I
b = 0.794285 + 0.078555I
−0.372000 − 0.941624I 0
u = 0.098559 − 1.088140I
a = 0.503311 − 0.971372I
b = 0.794285 − 0.078555I
−0.372000 + 0.941624I 0
u = 0.552124 + 0.658398I
a = −0.58144 + 1.50903I
b = −0.934698 − 0.601704I
1.69508 − 3.63423I 0
u = 0.552124 − 0.658398I
a = −0.58144 − 1.50903I
b = −0.934698 + 0.601704I
1.69508 + 3.63423I 0
u = −0.302255 + 0.800949I
a = 0.372411 + 0.562512I
b = −0.686516 − 0.599127I
2.40975 − 1.13743I 0
u = −0.302255 − 0.800949I
a = 0.372411 − 0.562512I
b = −0.686516 + 0.599127I
2.40975 + 1.13743I 0
u = −1.076480 + 0.436655I
a = 0.595229 + 1.070310I
b = 0.954303 − 0.607541I
−0.46815 + 6.73608I 0
u = −1.076480 − 0.436655I
a = 0.595229 − 1.070310I
b = 0.954303 + 0.607541I
−0.46815 − 6.73608I 0
u = 0.960861 + 0.666348I
a = −0.021599 − 0.436431I
b = −1.029310 + 0.585367I
−5.49644 + 7.35262I 0
u = 0.960861 − 0.666348I
a = −0.021599 + 0.436431I
b = −1.029310 − 0.585367I
−5.49644 − 7.35262I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.761360 + 0.304996I
a = −0.866787 + 0.057866I
b = −1.213130 + 0.029847I
−9.78593 − 5.59963I 0
u = 0.761360 − 0.304996I
a = −0.866787 − 0.057866I
b = −1.213130 − 0.029847I
−9.78593 + 5.59963I 0
u = −0.609807 + 0.522517I
a = −0.83495 − 1.34108I
b = −1.111850 + 0.628955I
−1.34383 + 8.34560I 0
u = −0.609807 − 0.522517I
a = −0.83495 + 1.34108I
b = −1.111850 − 0.628955I
−1.34383 − 8.34560I 0
u = −0.023627 + 1.287760I
a = −0.321563 + 0.311867I
b = −0.825395 − 0.322297I
2.72401 − 1.49869I 0
u = −0.023627 − 1.287760I
a = −0.321563 − 0.311867I
b = −0.825395 + 0.322297I
2.72401 + 1.49869I 0
u = −0.623609 + 0.336920I
a = 0.405546 + 0.480688I
b = 0.992798 + 0.546801I
−1.81658 − 4.27889I −8.84469 + 3.54931I
u = −0.623609 − 0.336920I
a = 0.405546 − 0.480688I
b = 0.992798 − 0.546801I
−1.81658 + 4.27889I −8.84469 − 3.54931I
u = −0.683352 + 0.035665I
a = −1.15998 − 1.27267I
b = −0.737342 − 0.023719I
−3.54008 − 2.29909I −15.6562 + 3.4828I
u = −0.683352 − 0.035665I
a = −1.15998 + 1.27267I
b = −0.737342 + 0.023719I
−3.54008 + 2.29909I −15.6562 − 3.4828I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.020939 + 1.317360I
a = 0.841938 − 0.798254I
b = −1.48993 + 0.39916I
−1.52334 + 1.49242I 0
u = −0.020939 − 1.317360I
a = 0.841938 + 0.798254I
b = −1.48993 − 0.39916I
−1.52334 − 1.49242I 0
u = 0.399308 + 0.534416I
a = 0.379511 − 0.330704I
b = −0.385031 + 0.822298I
0.75694 − 2.95526I −5.08894 + 6.31612I
u = 0.399308 − 0.534416I
a = 0.379511 + 0.330704I
b = −0.385031 − 0.822298I
0.75694 + 2.95526I −5.08894 − 6.31612I
u = −0.012917 + 1.352440I
a = −0.573501 + 0.807296I
b = −1.029960 − 0.423805I
2.50328 − 1.37457I 0
u = −0.012917 − 1.352440I
a = −0.573501 − 0.807296I
b = −1.029960 + 0.423805I
2.50328 + 1.37457I 0
u = 0.067251 + 1.357430I
a = 0.84277 + 1.88859I
b = −1.16317 − 0.98650I
−0.36011 − 4.01830I 0
u = 0.067251 − 1.357430I
a = 0.84277 − 1.88859I
b = −1.16317 + 0.98650I
−0.36011 + 4.01830I 0
u = −0.222723 + 1.348860I
a = 0.456670 + 0.372203I
b = 1.086160 − 0.137606I
0.79911 + 5.51509I 0
u = −0.222723 − 1.348860I
a = 0.456670 − 0.372203I
b = 1.086160 + 0.137606I
0.79911 − 5.51509I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.039927 + 1.392050I
a = 0.95543 − 2.34340I
b = −0.900060 + 0.718184I
2.99123 + 2.77285I 0
u = −0.039927 − 1.392050I
a = 0.95543 + 2.34340I
b = −0.900060 − 0.718184I
2.99123 − 2.77285I 0
u = −0.10475 + 1.41483I
a = 0.33002 − 1.70854I
b = −0.443610 + 1.191010I
2.41571 + 5.48154I 0
u = −0.10475 − 1.41483I
a = 0.33002 + 1.70854I
b = −0.443610 − 1.191010I
2.41571 − 5.48154I 0
u = 0.558853 + 0.067857I
a = 1.216400 − 0.107507I
b = 0.626395 + 0.443533I
−0.656767 − 0.000726I −8.13427 + 0.83328I
u = 0.558853 − 0.067857I
a = 1.216400 + 0.107507I
b = 0.626395 − 0.443533I
−0.656767 + 0.000726I −8.13427 − 0.83328I
u = 0.26542 + 1.41434I
a = −0.232973 − 0.565179I
b = 1.314000 + 0.089191I
−4.30452 − 9.26784I 0
u = 0.26542 − 1.41434I
a = −0.232973 + 0.565179I
b = 1.314000 − 0.089191I
−4.30452 + 9.26784I 0
u = 0.08745 + 1.44566I
a = 0.198476 + 0.968695I
b = −0.218782 − 0.796710I
5.30144 − 2.85258I 0
u = 0.08745 − 1.44566I
a = 0.198476 − 0.968695I
b = −0.218782 + 0.796710I
5.30144 + 2.85258I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.327818 + 0.441969I
a = −0.099545 + 0.451228I
b = 0.301109 + 0.375256I
−0.66813 − 1.43680I −6.16617 + 3.83190I
u = 0.327818 − 0.441969I
a = −0.099545 − 0.451228I
b = 0.301109 − 0.375256I
−0.66813 + 1.43680I −6.16617 − 3.83190I
u = −0.11891 + 1.46792I
a = 0.057526 + 0.678177I
b = −0.137007 + 0.135778I
1.87058 + 0.46637I 0
u = −0.11891 − 1.46792I
a = 0.057526 − 0.678177I
b = −0.137007 − 0.135778I
1.87058 − 0.46637I 0
u = 0.13768 + 1.49636I
a = −0.74996 + 1.34987I
b = 0.498210 − 1.062710I
7.38590 − 4.95511I 0
u = 0.13768 − 1.49636I
a = −0.74996 − 1.34987I
b = 0.498210 + 1.062710I
7.38590 + 4.95511I 0
u = −0.100131 + 0.471351I
a = 2.11220 − 3.32866I
b = −0.964049 + 0.377227I
−3.14756 + 1.44573I −4.22503 − 4.02855I
u = −0.100131 − 0.471351I
a = 2.11220 + 3.32866I
b = −0.964049 − 0.377227I
−3.14756 − 1.44573I −4.22503 + 4.02855I
u = −0.20992 + 1.51115I
a = −0.21381 + 1.85989I
b = 1.164280 − 0.730065I
5.30348 + 11.36100I 0
u = −0.20992 − 1.51115I
a = −0.21381 − 1.85989I
b = 1.164280 + 0.730065I
5.30348 − 11.36100I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.362356 + 0.280081I
a = −0.184823 + 0.658930I
b = 0.618686 − 0.922375I
−3.02034 + 3.80722I −12.3901 − 12.2378I
u = −0.362356 − 0.280081I
a = −0.184823 − 0.658930I
b = 0.618686 + 0.922375I
−3.02034 − 3.80722I −12.3901 + 12.2378I
u = −0.455545
a = 0.918271
b = 1.29804
−5.21822 −21.4390
u = −0.12637 + 1.54084I
a = −0.84741 − 1.23122I
b = 0.664543 + 0.856677I
9.93804 + 0.62946I 0
u = −0.12637 − 1.54084I
a = −0.84741 + 1.23122I
b = 0.664543 − 0.856677I
9.93804 − 0.62946I 0
u = 0.19712 + 1.53432I
a = −0.17189 − 1.88654I
b = 1.026710 + 0.716217I
8.81454 − 6.47340I 0
u = 0.19712 − 1.53432I
a = −0.17189 + 1.88654I
b = 1.026710 − 0.716217I
8.81454 + 6.47340I 0
u = −0.27087 + 1.53581I
a = 0.91848 + 1.15081I
b = −0.528265 − 0.960828I
2.96732 + 11.64670I 0
u = −0.27087 − 1.53581I
a = 0.91848 − 1.15081I
b = −0.528265 + 0.960828I
2.96732 − 11.64670I 0
u = 0.28495 + 1.54061I
a = 0.816840 − 0.991181I
b = −0.614552 + 0.823078I
7.24264 − 6.09297I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.28495 − 1.54061I
a = 0.816840 + 0.991181I
b = −0.614552 − 0.823078I
7.24264 + 6.09297I 0
u = −0.35868 + 1.53724I
a = −0.07238 − 1.83005I
b = −1.041090 + 0.690643I
5.94783 + 11.76030I 0
u = −0.35868 − 1.53724I
a = −0.07238 + 1.83005I
b = −1.041090 − 0.690643I
5.94783 − 11.76030I 0
u = 0.419234
a = 1.19049
b = 0.448220
−0.837454 −11.3960
u = 0.31347 + 1.55118I
a = 0.04378 + 1.98364I
b = −1.129830 − 0.708605I
1.1030 − 17.7385I 0
u = 0.31347 − 1.55118I
a = 0.04378 − 1.98364I
b = −1.129830 + 0.708605I
1.1030 + 17.7385I 0
u = −0.07791 + 1.59074I
a = −0.60632 + 1.82194I
b = 0.858650 − 0.560842I
3.81494 + 2.23955I 0
u = −0.07791 − 1.59074I
a = −0.60632 − 1.82194I
b = 0.858650 + 0.560842I
3.81494 − 2.23955I 0
u = 0.396844 + 0.087718I
a = 0.682314 − 0.970412I
b = 1.179620 + 0.687311I
−4.83227 − 2.51063I −22.5849 + 6.6629I
u = 0.396844 − 0.087718I
a = 0.682314 + 0.970412I
b = 1.179620 − 0.687311I
−4.83227 + 2.51063I −22.5849 − 6.6629I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.59605 + 1.47867I
a = −0.16897 + 1.46056I
b = −0.905517 − 0.603390I
2.62833 − 4.59705I 0
u = 0.59605 − 1.47867I
a = −0.16897 − 1.46056I
b = −0.905517 + 0.603390I
2.62833 + 4.59705I 0
u = −0.44828 + 1.59412I
a = 0.455290 + 0.803082I
b = −0.769954 − 0.583754I
3.05678 − 0.13018I 0
u = −0.44828 − 1.59412I
a = 0.455290 − 0.803082I
b = −0.769954 + 0.583754I
3.05678 + 0.13018I 0
u = −0.248734 + 0.077419I
a = −1.68658 − 13.39090I
b = −0.778966 − 0.491080I
−3.15248 − 2.07759I −32.3205 − 12.9726I
u = −0.248734 − 0.077419I
a = −1.68658 + 13.39090I
b = −0.778966 + 0.491080I
−3.15248 + 2.07759I −32.3205 + 12.9726I
u = −0.05012 + 1.79536I
a = −0.41783 + 1.36347I
b = 0.843814 − 0.588669I
3.71537 + 2.33713I 0
u = −0.05012 − 1.79536I
a = −0.41783 − 1.36347I
b = 0.843814 + 0.588669I
3.71537 − 2.33713I 0
u = −0.195407 + 0.024903I
a = 3.63408 + 5.14416I
b = 0.904589 − 0.529555I
−1.74724 + 2.04591I −12.42551 − 2.83945I
u = −0.195407 − 0.024903I
a = 3.63408 − 5.14416I
b = 0.904589 + 0.529555I
−1.74724 − 2.04591I −12.42551 + 2.83945I
13
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
90
+ 35u
89
+ ··· + 223u + 9
c
2
, c
6
u
90
− 3u
89
+ ··· − 19u + 3
c
3
, c
4
, c
9
u
90
+ u
89
+ ··· + 13u − 1
c
5
, c
12
u
90
− 3u
89
+ ··· − 19u + 3
c
7
, c
11
u
90
+ u
89
+ ··· − 17u − 1
c
8
1089(1089u
90
+ 7095u
89
+ ··· + 166909u − 7597)
c
10
1089(1089u
90
+ 5709u
89
+ ··· + 497255u + 37873)
14
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
90
+ 41y
89
+ ··· + 119237y + 81
c
2
, c
6
y
90
− 35y
89
+ ··· − 223y + 9
c
3
, c
4
, c
9
y
90
+ 89y
89
+ ··· − 83y + 1
c
5
, c
12
y
90
+ 57y
89
+ ··· + 65y + 9
c
7
, c
11
y
90
− 63y
89
+ ··· − 275y + 1
c
8
1185921
· (1185921y
90
− 32124411y
89
+ ··· − 5463038131y + 57714409)
c
10
1185921
· (1185921y
90
+ 31046301y
89
+ ··· − 127015229803y + 1434364129)
15
