12a
0863
(K12a
0863
)
A knot diagram
1
Linearized knot diagam
4 5 10 9 3 12 11 1 2 8 7 6
Solving Sequence
7,12
6
1,3
5 2 11 8 9 4 10
c
6
c
12
c
5
c
2
c
11
c
7
c
8
c
4
c
10
c
1
, c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.21287 × 10
19
u
64
+ 1.88559 × 10
21
u
63
+ ··· + 2.29526 × 10
21
b − 1.81954 × 10
17
,
1.21260 × 10
19
u
64
− 1.88577 × 10
21
u
63
+ ··· + 2.29526 × 10
21
a − 4.20780 × 10
21
, u
65
− u
64
+ ··· + 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 65 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−1.21×10
19
u
64
+1.89×10
21
u
63
+· · ·+2.30×10
21
b−1.82×10
17
, 1.21×
10
19
u
64
−1.89×10
21
u
63
+· · ·+2.30×10
21
a−4.21×10
21
, u
65
−u
64
+· · ·+3u+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
6
=
1
u
2
a
1
=
u
u
3
+ u
a
3
=
−0.00528304u
64
+ 0.821593u
63
+ ··· − 3.85538u + 1.83325
0.00528425u
64
− 0.821515u
63
+ ··· − 3.16643u + 0.0000792739
a
5
=
0.00446144u
64
+ 0.730022u
63
+ ··· − 5.30127u + 2.48337
−0.00446223u
64
− 0.730061u
63
+ ··· − 3.31679u − 0.0000393275
a
2
=
0.00281825u
64
+ 0.833252u
63
+ ··· + 4.38543u + 0.116626
−0.00281820u
64
− 0.833212u
63
+ ··· + 0.716788u + 0.0000405652
a
11
=
−u
u
a
8
=
u
2
+ 1
−u
2
a
9
=
−u
6
− 3u
4
+ 1
−u
8
− 4u
6
− 4u
4
− 2u
2
a
4
=
0.000622185u
64
+ 0.0750748u
63
+ ··· − 3.85513u + 1.83334
−0.000622272u
64
− 0.0750774u
63
+ ··· − 3.16667u − 2.69978 × 10
−6
a
10
=
−u
3
− 2u
u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
7390754013604632808088
2295261755894092887829
u
64
+
5553779548253673895596
2295261755894092887829
u
63
+ ··· +
14535116494160491630104
2295261755894092887829
u +
12347743172761319269322
2295261755894092887829
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
65
− 11u
64
+ ··· − u + 1
c
2
, c
5
u
65
+ u
64
+ ··· + 11u − 1
c
3
u
65
+ u
64
+ ··· − 587u + 953
c
4
u
65
+ 3u
64
+ ··· + 963u + 251
c
6
, c
7
, c
10
c
11
, c
12
u
65
+ u
64
+ ··· + 3u − 1
c
8
u
65
+ u
64
+ ··· − 107u − 1
c
9
u
65
− 3u
64
+ ··· − u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
65
+ 3y
64
+ ··· − 11y −1
c
2
, c
5
y
65
− 45y
64
+ ··· − 11y −1
c
3
y
65
− 45y
64
+ ··· − 18627755y −908209
c
4
y
65
− 73y
64
+ ··· + 2575937y −63001
c
6
, c
7
, c
10
c
11
, c
12
y
65
+ 83y
64
+ ··· − 3y −1
c
8
y
65
− 21y
64
+ ··· + 6349y −1
c
9
y
65
+ 11y
64
+ ··· − 3y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.324128 + 0.936130I
a = −1.09302 + 1.30299I
b = 0.082181 − 0.503434I
−2.40034 + 7.24090I 0
u = 0.324128 − 0.936130I
a = −1.09302 − 1.30299I
b = 0.082181 + 0.503434I
−2.40034 − 7.24090I 0
u = 0.058124 + 1.021150I
a = 0.39135 − 1.54603I
b = −0.539037 + 0.901278I
−5.27537 − 0.99487I 0
u = 0.058124 − 1.021150I
a = 0.39135 + 1.54603I
b = −0.539037 − 0.901278I
−5.27537 + 0.99487I 0
u = −0.269057 + 0.937054I
a = 0.284515 − 0.610952I
b = −0.532484 + 0.070320I
−2.06253 − 2.90913I 0
u = −0.269057 − 0.937054I
a = 0.284515 + 0.610952I
b = −0.532484 − 0.070320I
−2.06253 + 2.90913I 0
u = 0.385420 + 0.961736I
a = 0.23634 − 2.24647I
b = 0.104185 + 1.382700I
2.02839 + 13.16090I 0
u = 0.385420 − 0.961736I
a = 0.23634 + 2.24647I
b = 0.104185 − 1.382700I
2.02839 − 13.16090I 0
u = −0.429847 + 0.964672I
a = 0.078850 + 1.312400I
b = −0.087710 − 0.887262I
0.89662 − 4.74808I 0
u = −0.429847 − 0.964672I
a = 0.078850 − 1.312400I
b = −0.087710 + 0.887262I
0.89662 + 4.74808I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.314439 + 0.872956I
a = −0.31327 + 2.44697I
b = 0.259549 − 1.127420I
2.14552 + 4.73651I 0
u = 0.314439 − 0.872956I
a = −0.31327 − 2.44697I
b = 0.259549 + 1.127420I
2.14552 − 4.73651I 0
u = −0.261979 + 0.871741I
a = −2.35233 − 2.92298I
b = 1.35421 + 3.02563I
0.12711 − 2.45591I 0
u = −0.261979 − 0.871741I
a = −2.35233 + 2.92298I
b = 1.35421 − 3.02563I
0.12711 + 2.45591I 0
u = 0.289053 + 0.805920I
a = 0.560101 + 0.910910I
b = 0.769764 − 0.657178I
2.61125 + 0.92001I 10.35838 − 1.61741I
u = 0.289053 − 0.805920I
a = 0.560101 − 0.910910I
b = 0.769764 + 0.657178I
2.61125 − 0.92001I 10.35838 + 1.61741I
u = −0.162835 + 0.838324I
a = 1.67399 + 0.87780I
b = −0.280248 − 1.013690I
−0.87255 − 1.60805I 6.00000 + 5.45317I
u = −0.162835 − 0.838324I
a = 1.67399 − 0.87780I
b = −0.280248 + 1.013690I
−0.87255 + 1.60805I 6.00000 − 5.45317I
u = −0.092628 + 1.180290I
a = −0.840978 + 0.802329I
b = 0.236084 − 0.580343I
−2.83299 − 5.08772I 0
u = −0.092628 − 1.180290I
a = −0.840978 − 0.802329I
b = 0.236084 + 0.580343I
−2.83299 + 5.08772I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.532472 + 0.581936I
a = 0.359653 + 0.752618I
b = −0.697410 − 0.164439I
3.09795 − 3.00575I 14.1045 + 10.0032I
u = −0.532472 − 0.581936I
a = 0.359653 − 0.752618I
b = −0.697410 + 0.164439I
3.09795 + 3.00575I 14.1045 − 10.0032I
u = 0.451917 + 0.639368I
a = −0.029660 − 0.522836I
b = −1.028710 + 0.520293I
3.91640 − 6.17027I 7.07971 + 2.30194I
u = 0.451917 − 0.639368I
a = −0.029660 + 0.522836I
b = −1.028710 − 0.520293I
3.91640 + 6.17027I 7.07971 − 2.30194I
u = −0.680129 + 0.170323I
a = 1.001600 + 0.629885I
b = −0.553761 + 0.076940I
4.35899 − 1.00540I 20.7008 + 5.0169I
u = −0.680129 − 0.170323I
a = 1.001600 − 0.629885I
b = −0.553761 − 0.076940I
4.35899 + 1.00540I 20.7008 − 5.0169I
u = 0.619172 + 0.144302I
a = 1.59691 − 0.92448I
b = −0.623408 − 0.537423I
5.42013 + 9.76545I 9.79000 − 7.37220I
u = 0.619172 − 0.144302I
a = 1.59691 + 0.92448I
b = −0.623408 + 0.537423I
5.42013 − 9.76545I 9.79000 + 7.37220I
u = 0.205923 + 0.598857I
a = 1.29669 − 0.57305I
b = −0.059987 − 0.280461I
−0.66580 − 1.57263I 3.10575 + 2.35415I
u = 0.205923 − 0.598857I
a = 1.29669 + 0.57305I
b = −0.059987 + 0.280461I
−0.66580 + 1.57263I 3.10575 − 2.35415I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.010335 + 0.617504I
a = 1.307680 − 0.534985I
b = −0.197340 − 0.348140I
−0.65799 − 1.53035I 2.49577 + 4.53431I
u = −0.010335 − 0.617504I
a = 1.307680 + 0.534985I
b = −0.197340 + 0.348140I
−0.65799 + 1.53035I 2.49577 − 4.53431I
u = 0.528313 + 0.122256I
a = −0.528984 − 0.299527I
b = 0.005243 + 0.913496I
0.83726 + 4.33484I 8.01107 − 7.64767I
u = 0.528313 − 0.122256I
a = −0.528984 + 0.299527I
b = 0.005243 − 0.913496I
0.83726 − 4.33484I 8.01107 + 7.64767I
u = 0.524320 + 0.036054I
a = −2.00699 + 0.30540I
b = 0.874865 + 0.548909I
4.90067 + 1.87571I 15.7861 − 4.1218I
u = 0.524320 − 0.036054I
a = −2.00699 − 0.30540I
b = 0.874865 − 0.548909I
4.90067 − 1.87571I 15.7861 + 4.1218I
u = −0.458267
a = −6.03074
b = −0.211824
2.77275 −28.7580
u = −0.445497 + 0.094527I
a = 0.637012 − 0.423531I
b = 0.226599 − 0.250291I
1.107960 − 0.463162I 9.21159 + 1.20629I
u = −0.445497 − 0.094527I
a = 0.637012 + 0.423531I
b = 0.226599 + 0.250291I
1.107960 + 0.463162I 9.21159 − 1.20629I
u = 0.02751 + 1.56537I
a = −0.432111 + 0.242266I
b = −0.285023 − 0.338181I
−3.27465 − 4.58250I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.02751 − 1.56537I
a = −0.432111 − 0.242266I
b = −0.285023 + 0.338181I
−3.27465 + 4.58250I 0
u = 0.03404 + 1.66686I
a = 1.11783 − 1.17422I
b = −2.37959 + 2.42684I
−9.12781 − 0.99471I 0
u = 0.03404 − 1.66686I
a = 1.11783 + 1.17422I
b = −2.37959 − 2.42684I
−9.12781 + 0.99471I 0
u = 0.06301 + 1.66986I
a = 1.005040 + 0.262704I
b = −1.22784 − 0.87146I
−6.11147 + 2.17232I 0
u = 0.06301 − 1.66986I
a = 1.005040 − 0.262704I
b = −1.22784 + 0.87146I
−6.11147 − 2.17232I 0
u = 0.07662 + 1.68231I
a = 0.45152 + 2.14712I
b = −0.42780 − 5.18456I
−6.84024 + 6.21304I 0
u = 0.07662 − 1.68231I
a = 0.45152 − 2.14712I
b = −0.42780 + 5.18456I
−6.84024 − 6.21304I 0
u = −0.04521 + 1.68391I
a = 1.25462 + 1.36266I
b = −2.68362 − 3.82166I
−9.85939 − 2.43463I 0
u = −0.04521 − 1.68391I
a = 1.25462 − 1.36266I
b = −2.68362 + 3.82166I
−9.85939 + 2.43463I 0
u = −0.06445 + 1.68600I
a = −1.21200 − 2.26617I
b = 4.03468 + 6.58326I
−8.91650 − 3.69377I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.06445 − 1.68600I
a = −1.21200 + 2.26617I
b = 4.03468 − 6.58326I
−8.91650 + 3.69377I 0
u = 0.08391 + 1.69898I
a = −0.73541 + 1.68409I
b = 1.62720 − 3.82199I
−11.6884 + 8.8421I 0
u = 0.08391 − 1.69898I
a = −0.73541 − 1.68409I
b = 1.62720 + 3.82199I
−11.6884 − 8.8421I 0
u = −0.07063 + 1.70293I
a = 0.154544 − 0.773326I
b = −0.67957 + 1.80754I
−11.41960 − 4.25212I 0
u = −0.07063 − 1.70293I
a = 0.154544 + 0.773326I
b = −0.67957 − 1.80754I
−11.41960 + 4.25212I 0
u = −0.11448 + 1.70115I
a = −0.284828 + 1.185120I
b = 0.15081 − 3.05011I
−8.41150 − 6.90652I 0
u = −0.11448 − 1.70115I
a = −0.284828 − 1.185120I
b = 0.15081 + 3.05011I
−8.41150 + 6.90652I 0
u = 0.10323 + 1.70470I
a = −0.40089 − 2.00987I
b = 0.48020 + 5.10501I
−7.3366 + 15.1066I 0
u = 0.10323 − 1.70470I
a = −0.40089 + 2.00987I
b = 0.48020 − 5.10501I
−7.3366 − 15.1066I 0
u = 0.01436 + 1.71792I
a = 0.02953 − 1.66944I
b = −0.45613 + 4.08328I
−15.0478 − 0.7036I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.01436 − 1.71792I
a = 0.02953 + 1.66944I
b = −0.45613 − 4.08328I
−15.0478 + 0.7036I 0
u = −0.01921 + 1.74361I
a = −1.01827 + 1.00574I
b = 2.14452 − 2.51876I
−13.2560 − 5.5225I 0
u = −0.01921 − 1.74361I
a = −1.01827 − 1.00574I
b = 2.14452 + 2.51876I
−13.2560 + 5.5225I 0
u = −0.175614 + 0.182608I
a = 2.82636 − 0.76498I
b = 0.995509 − 0.313938I
1.92909 − 0.63355I 4.68520 − 2.34882I
u = −0.175614 − 0.182608I
a = 2.82636 + 0.76498I
b = 0.995509 + 0.313938I
1.92909 + 0.63355I 4.68520 + 2.34882I
11
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
65
− 11u
64
+ ··· − u + 1
c
2
, c
5
u
65
+ u
64
+ ··· + 11u − 1
c
3
u
65
+ u
64
+ ··· − 587u + 953
c
4
u
65
+ 3u
64
+ ··· + 963u + 251
c
6
, c
7
, c
10
c
11
, c
12
u
65
+ u
64
+ ··· + 3u − 1
c
8
u
65
+ u
64
+ ··· − 107u − 1
c
9
u
65
− 3u
64
+ ··· − u + 1
12
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
65
+ 3y
64
+ ··· − 11y −1
c
2
, c
5
y
65
− 45y
64
+ ··· − 11y −1
c
3
y
65
− 45y
64
+ ··· − 18627755y −908209
c
4
y
65
− 73y
64
+ ··· + 2575937y −63001
c
6
, c
7
, c
10
c
11
, c
12
y
65
+ 83y
64
+ ··· − 3y −1
c
8
y
65
− 21y
64
+ ··· + 6349y −1
c
9
y
65
+ 11y
64
+ ··· − 3y −1
13
