12a
0566
(K12a
0566
)
A knot diagram
1
Linearized knot diagam
3 7 9 8 12 11 2 10 4 1 6 5
Solving Sequence
6,12
5 1 11
2,7
3 8 4 10 9
c
5
c
12
c
11
c
6
c
2
c
7
c
4
c
10
c
9
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h1.48359 × 10
42
u
84
+ 1.49960 × 10
42
u
83
+ ··· + 3.29594 × 10
42
b − 1.20784 × 10
43
,
2.21165 × 10
41
u
84
+ 2.55434 × 10
41
u
83
+ ··· + 8.23985 × 10
41
a + 1.14680 × 10
42
, u
85
+ u
84
+ ··· + 5u + 1i
I
u
2
= h−u
2
a + u
3
+ b − a + 3u, −2u
3
a + u
3
+ a
2
− 8au − a + 4u − 4, u
4
+ 3u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 93 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
= h1.48 × 10
42
u
84
+ 1.50 × 10
42
u
83
+ · · · + 3.30 × 10
42
b − 1.21 × 10
43
, 2.21 ×
10
41
u
84
+2.55×10
41
u
83
+· · ·+8.24×10
41
a+1.15×10
42
, u
85
+u
84
+· · ·+5u+1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
1
=
u
u
3
+ u
a
11
=
−u
u
a
2
=
−0.268409u
84
− 0.309998u
83
+ ··· − 2.53477u − 1.39178
−0.450127u
84
− 0.454986u
83
+ ··· + 16.2601u + 3.66462
a
7
=
u
2
+ 1
−u
2
a
3
=
0.706834u
84
+ 0.799119u
83
+ ··· + 14.4948u + 2.69792
0.649070u
84
+ 0.131711u
83
+ ··· + 16.4414u + 3.28599
a
8
=
−4.29653u
84
− 2.10680u
83
+ ··· − 24.9777u + 0.363311
0.945075u
84
− 0.221620u
83
+ ··· + 0.773811u + 0.688980
a
4
=
3.13890u
84
+ 2.19012u
83
+ ··· + 23.1159u + 1.31435
1.00849u
84
− 0.279889u
83
+ ··· − 14.1954u − 4.54399
a
10
=
u
5
+ 2u
3
− u
u
7
+ 3u
5
+ 2u
3
+ u
a
9
=
−2.98788u
84
− 2.09995u
83
+ ··· − 26.9778u − 1.05953
−0.483470u
84
− 0.327238u
83
+ ··· + 1.60308u + 1.52630
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.44824u
84
+ 3.41811u
83
+ ··· + 56.6384u + 20.3411
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
85
+ 43u
84
+ ··· + 72u − 16
c
2
, c
7
u
85
+ u
84
+ ··· − 12u − 4
c
3
, c
9
u
85
+ u
84
+ ··· − u − 5
c
4
u
85
+ 3u
84
+ ··· − 6487u − 28835
c
5
, c
6
, c
11
c
12
u
85
− u
84
+ ··· + 5u − 1
c
8
u
85
− 41u
84
+ ··· + 131u − 25
c
10
u
85
− 23u
84
+ ··· + 41u − 283
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
85
+ 7y
84
+ ··· + 31264y −256
c
2
, c
7
y
85
+ 43y
84
+ ··· + 72y −16
c
3
, c
9
y
85
− 41y
84
+ ··· + 131y −25
c
4
y
85
+ 19y
84
+ ··· − 11204895241y −831457225
c
5
, c
6
, c
11
c
12
y
85
+ 99y
84
+ ··· − 9y −1
c
8
y
85
+ 11y
84
+ ··· − 6589y −625
c
10
y
85
− 9y
84
+ ··· + 1664023y −80089
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.269016 + 0.961532I
a = 1.34501 + 0.86076I
b = −0.677659 + 0.501079I
−1.44363 + 5.72996I 0
u = −0.269016 − 0.961532I
a = 1.34501 − 0.86076I
b = −0.677659 − 0.501079I
−1.44363 − 5.72996I 0
u = −0.015593 + 0.966863I
a = 0.574880 + 0.741720I
b = −0.201759 + 0.491321I
−0.320817 − 1.348260I 0
u = −0.015593 − 0.966863I
a = 0.574880 − 0.741720I
b = −0.201759 − 0.491321I
−0.320817 + 1.348260I 0
u = −0.547823 + 0.722739I
a = −1.92103 − 1.40701I
b = 0.484593 − 0.384674I
0.66837 − 12.95260I 0
u = −0.547823 − 0.722739I
a = −1.92103 + 1.40701I
b = 0.484593 + 0.384674I
0.66837 + 12.95260I 0
u = 0.244367 + 0.865284I
a = −1.22863 + 1.21755I
b = 0.628112 + 0.266767I
−3.62434 − 1.21550I 0
u = 0.244367 − 0.865284I
a = −1.22863 − 1.21755I
b = 0.628112 − 0.266767I
−3.62434 + 1.21550I 0
u = 0.519121 + 0.704971I
a = 1.90749 − 1.30014I
b = −0.328379 − 0.431956I
−1.71613 + 7.78904I 0
u = 0.519121 − 0.704971I
a = 1.90749 + 1.30014I
b = −0.328379 + 0.431956I
−1.71613 − 7.78904I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.539376 + 0.649975I
a = 0.680041 + 0.389729I
b = −0.387247 + 0.236701I
3.03875 + 7.48933I 0
u = 0.539376 − 0.649975I
a = 0.680041 − 0.389729I
b = −0.387247 − 0.236701I
3.03875 − 7.48933I 0
u = −0.546508 + 0.643529I
a = −1.67110 − 1.27874I
b = 0.206900 − 0.158340I
3.10332 − 4.91778I 0
u = −0.546508 − 0.643529I
a = −1.67110 + 1.27874I
b = 0.206900 + 0.158340I
3.10332 + 4.91778I 0
u = −0.484151 + 0.617500I
a = −0.521809 + 0.347871I
b = 0.314853 + 0.334436I
0.50765 − 2.73435I 6.00000 + 0.I
u = −0.484151 − 0.617500I
a = −0.521809 − 0.347871I
b = 0.314853 − 0.334436I
0.50765 + 2.73435I 6.00000 + 0.I
u = 0.413512 + 0.660509I
a = 2.03352 − 0.95008I
b = 0.195673 − 0.590485I
−3.42447 + 5.19941I 0. − 9.00516I
u = 0.413512 − 0.660509I
a = 2.03352 + 0.95008I
b = 0.195673 + 0.590485I
−3.42447 − 5.19941I 0. + 9.00516I
u = 0.550405 + 0.534191I
a = 0.588864 + 0.053000I
b = −0.474416 + 0.464089I
4.58369 − 0.40025I 10.99009 + 0.I
u = 0.550405 − 0.534191I
a = 0.588864 − 0.053000I
b = −0.474416 − 0.464089I
4.58369 + 0.40025I 10.99009 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.314976 + 0.689605I
a = −1.43860 + 1.93529I
b = 0.735061 − 0.199480I
−4.05679 − 0.01022I −1.68650 − 2.48548I
u = 0.314976 − 0.689605I
a = −1.43860 − 1.93529I
b = 0.735061 + 0.199480I
−4.05679 + 0.01022I −1.68650 + 2.48548I
u = −0.392985 + 0.613133I
a = 1.69591 + 2.23311I
b = −0.860634 − 0.456543I
−2.34167 − 4.34614I 3.43008 + 7.94130I
u = −0.392985 − 0.613133I
a = 1.69591 − 2.23311I
b = −0.860634 + 0.456543I
−2.34167 + 4.34614I 3.43008 − 7.94130I
u = −0.359208 + 0.617818I
a = −2.14589 − 0.65890I
b = −0.535781 − 0.510936I
−2.56438 − 0.05394I 2.49319 + 4.38221I
u = −0.359208 − 0.617818I
a = −2.14589 + 0.65890I
b = −0.535781 + 0.510936I
−2.56438 + 0.05394I 2.49319 − 4.38221I
u = 0.585676 + 0.405184I
a = 0.718348 − 0.889416I
b = 0.283524 + 0.302554I
4.96277 + 4.28677I 11.39976 − 6.82883I
u = 0.585676 − 0.405184I
a = 0.718348 + 0.889416I
b = 0.283524 − 0.302554I
4.96277 − 4.28677I 11.39976 + 6.82883I
u = −0.196837 + 0.670232I
a = −0.193639 + 0.601805I
b = 0.042269 + 0.380832I
−1.24323 − 1.82365I 3.45996 + 5.43784I
u = −0.196837 − 0.670232I
a = −0.193639 − 0.601805I
b = 0.042269 − 0.380832I
−1.24323 + 1.82365I 3.45996 − 5.43784I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.659136 + 0.185202I
a = 0.05845 − 1.55472I
b = 0.465484 + 1.313900I
2.25667 + 8.88522I 8.20811 − 6.10278I
u = −0.659136 − 0.185202I
a = 0.05845 + 1.55472I
b = 0.465484 − 1.313900I
2.25667 − 8.88522I 8.20811 + 6.10278I
u = −0.612889 + 0.281201I
a = −0.110132 − 0.982663I
b = 0.503598 + 1.053240I
4.16578 + 0.97431I 11.07134 + 0.36032I
u = −0.612889 − 0.281201I
a = −0.110132 + 0.982663I
b = 0.503598 − 1.053240I
4.16578 − 0.97431I 11.07134 − 0.36032I
u = 0.606559 + 0.273838I
a = 0.271560 − 0.649215I
b = 0.466788 + 0.311382I
4.14256 − 3.58567I 11.15367 + 1.13968I
u = 0.606559 − 0.273838I
a = 0.271560 + 0.649215I
b = 0.466788 − 0.311382I
4.14256 + 3.58567I 11.15367 − 1.13968I
u = 0.607167 + 0.185675I
a = −0.276334 − 1.351560I
b = −0.370556 + 1.231270I
−0.19692 − 3.95880I 5.21329 + 2.44859I
u = 0.607167 − 0.185675I
a = −0.276334 + 1.351560I
b = −0.370556 − 1.231270I
−0.19692 + 3.95880I 5.21329 − 2.44859I
u = −0.001468 + 1.366940I
a = 0.627049 + 0.005195I
b = −0.494432 + 0.813879I
−0.61240 − 1.33236I 0
u = −0.001468 − 1.366940I
a = 0.627049 − 0.005195I
b = −0.494432 − 0.813879I
−0.61240 + 1.33236I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.512315 + 0.314416I
a = −0.569207 − 0.470742I
b = −0.399479 + 0.238539I
1.39834 − 0.73943I 7.87386 + 3.67792I
u = −0.512315 − 0.314416I
a = −0.569207 + 0.470742I
b = −0.399479 − 0.238539I
1.39834 + 0.73943I 7.87386 − 3.67792I
u = 0.12437 + 1.43299I
a = 0.519499 − 0.493581I
b = −0.72793 + 1.70428I
−0.91192 + 6.79397I 0
u = 0.12437 − 1.43299I
a = 0.519499 + 0.493581I
b = −0.72793 − 1.70428I
−0.91192 − 6.79397I 0
u = −0.05687 + 1.44642I
a = −0.824931 − 0.226256I
b = 1.09810 + 1.10205I
−4.16478 − 2.54315I 0
u = −0.05687 − 1.44642I
a = −0.824931 + 0.226256I
b = 1.09810 − 1.10205I
−4.16478 + 2.54315I 0
u = 0.14350 + 1.53538I
a = −0.078894 + 0.187179I
b = −0.493019 − 0.204507I
−2.27580 + 2.04834I 0
u = 0.14350 − 1.53538I
a = −0.078894 − 0.187179I
b = −0.493019 + 0.204507I
−2.27580 − 2.04834I 0
u = −0.05600 + 1.54395I
a = −0.23000 + 2.11531I
b = 0.01046 − 4.55197I
−8.09582 + 0.73214I 0
u = −0.05600 − 1.54395I
a = −0.23000 − 2.11531I
b = 0.01046 + 4.55197I
−8.09582 − 0.73214I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.285398 + 0.344531I
a = 1.67817 + 3.05294I
b = −0.372607 − 0.839231I
−1.46071 + 1.72003I 7.87919 + 0.32865I
u = −0.285398 − 0.344531I
a = 1.67817 − 3.05294I
b = −0.372607 + 0.839231I
−1.46071 − 1.72003I 7.87919 − 0.32865I
u = 0.02780 + 1.55968I
a = −0.700925 + 1.104050I
b = 0.91776 − 1.54426I
−8.33632 − 2.21865I 0
u = 0.02780 − 1.55968I
a = −0.700925 − 1.104050I
b = 0.91776 + 1.54426I
−8.33632 + 2.21865I 0
u = −0.06585 + 1.57880I
a = 0.154107 + 0.916089I
b = 0.062457 − 1.376080I
−8.83591 − 2.80563I 0
u = −0.06585 − 1.57880I
a = 0.154107 − 0.916089I
b = 0.062457 + 1.376080I
−8.83591 + 2.80563I 0
u = −0.13776 + 1.57821I
a = −0.182103 + 0.360437I
b = 0.816779 − 0.596735I
−6.91236 − 4.99845I 0
u = −0.13776 − 1.57821I
a = −0.182103 − 0.360437I
b = 0.816779 + 0.596735I
−6.91236 + 4.99845I 0
u = −0.11131 + 1.58060I
a = −0.41436 + 2.41339I
b = −0.04646 − 4.81480I
−9.81048 − 6.18706I 0
u = −0.11131 − 1.58060I
a = −0.41436 − 2.41339I
b = −0.04646 + 4.81480I
−9.81048 + 6.18706I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10182 + 1.58235I
a = −2.00225 − 2.08990I
b = 3.40561 + 3.88332I
−10.07080 − 1.74204I 0
u = −0.10182 − 1.58235I
a = −2.00225 + 2.08990I
b = 3.40561 − 3.88332I
−10.07080 + 1.74204I 0
u = −0.16062 + 1.58065I
a = −0.68149 − 2.27240I
b = 1.42297 + 4.31766I
−4.36694 − 7.51892I 0
u = −0.16062 − 1.58065I
a = −0.68149 + 2.27240I
b = 1.42297 − 4.31766I
−4.36694 + 7.51892I 0
u = 0.15852 + 1.58458I
a = 0.290858 + 0.225954I
b = −1.037120 − 0.437350I
−4.47968 + 10.06050I 0
u = 0.15852 − 1.58458I
a = 0.290858 − 0.225954I
b = −1.037120 + 0.437350I
−4.47968 − 10.06050I 0
u = 0.11852 + 1.59189I
a = 1.60651 − 2.45671I
b = −2.83027 + 4.48704I
−11.08450 + 7.16481I 0
u = 0.11852 − 1.59189I
a = 1.60651 + 2.45671I
b = −2.83027 − 4.48704I
−11.08450 − 7.16481I 0
u = 0.387648 + 0.109053I
a = −1.68466 − 0.73928I
b = −0.018758 + 1.083720I
−1.97907 − 2.29985I 4.88318 + 3.39856I
u = 0.387648 − 0.109053I
a = −1.68466 + 0.73928I
b = −0.018758 − 1.083720I
−1.97907 + 2.29985I 4.88318 − 3.39856I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.08984 + 1.59739I
a = 0.25529 + 2.42981I
b = 0.17555 − 4.73211I
−11.86500 + 1.49631I 0
u = 0.08984 − 1.59739I
a = 0.25529 − 2.42981I
b = 0.17555 + 4.73211I
−11.86500 − 1.49631I 0
u = 0.15414 + 1.60617I
a = 0.77240 − 2.77579I
b = −1.61416 + 5.04413I
−9.54162 + 10.30850I 0
u = 0.15414 − 1.60617I
a = 0.77240 + 2.77579I
b = −1.61416 − 5.04413I
−9.54162 − 10.30850I 0
u = −0.16479 + 1.61251I
a = −0.53819 − 2.86452I
b = 1.28223 + 5.19500I
−7.2310 − 15.6340I 0
u = −0.16479 − 1.61251I
a = −0.53819 + 2.86452I
b = 1.28223 − 5.19500I
−7.2310 + 15.6340I 0
u = 0.06386 + 1.64218I
a = −0.03654 + 2.49786I
b = 0.51461 − 4.55707I
−12.24450 − 0.05155I 0
u = 0.06386 − 1.64218I
a = −0.03654 − 2.49786I
b = 0.51461 + 4.55707I
−12.24450 + 0.05155I 0
u = −0.172519 + 0.303305I
a = 0.38817 + 1.99634I
b = −0.252299 + 0.998625I
−1.57085 − 2.23434I 7.54133 + 5.61184I
u = −0.172519 − 0.303305I
a = 0.38817 − 1.99634I
b = −0.252299 − 0.998625I
−1.57085 + 2.23434I 7.54133 − 5.61184I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.346155
a = −0.231708
b = −0.339336
0.778740 13.6440
u = −0.00938 + 1.65482I
a = 0.19486 + 2.13079I
b = −0.47416 − 3.77161I
−9.25904 − 1.48114I 0
u = −0.00938 − 1.65482I
a = 0.19486 − 2.13079I
b = −0.47416 + 3.77161I
−9.25904 + 1.48114I 0
u = −0.05603 + 1.66550I
a = 0.20557 + 2.52921I
b = −0.76659 − 4.47074I
−10.52730 + 4.57594I 0
u = −0.05603 − 1.66550I
a = 0.20557 − 2.52921I
b = −0.76659 + 4.47074I
−10.52730 − 4.57594I 0
13
II.
I
u
2
= h−u
2
a+u
3
+b −a + 3u, −2u
3
a+u
3
+a
2
−8au −a + 4u−4, u
4
+3u
2
+1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
1
=
u
u
3
+ u
a
11
=
−u
u
a
2
=
a
u
2
a − u
3
+ a − 3u
a
7
=
u
2
+ 1
−u
2
a
3
=
a − u
u
2
a − 2u
3
+ a − 4u
a
8
=
u
3
a + 2au + u
2
+ 1
au + 2
a
4
=
u
3
a − u
3
+ 3au + u
2
+ a − 4u + 4
u
2
a − 2u
3
− au + u
2
+ a − 3u − 2
a
10
=
−u
3
− 2u
u
3
+ u
a
9
=
−u
2
− 2
u
3
a + 2au + 3u
2
+ 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
3
− 4a + 16u
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
8
c
2
, c
7
(u
2
+ 1)
4
c
3
, c
4
, c
9
(u
4
− u
2
+ 1)
2
c
5
, c
6
, c
11
c
12
(u
4
+ 3u
2
+ 1)
2
c
8
(u
2
+ u + 1)
4
c
10
(u
2
+ u − 1)
4
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
8
c
2
, c
7
(y + 1)
8
c
3
, c
4
, c
9
(y
2
− y + 1)
4
c
5
, c
6
, c
11
c
12
(y
2
+ 3y + 1)
4
c
8
(y
2
+ y + 1)
4
c
10
(y
2
− 3y + 1)
4
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034I
a = 0.50000 + 1.37004I
b = 0.309017 − 0.771301I
−2.63189 − 2.02988I −2.00000 + 3.46410I
u = 0.618034I
a = 0.50000 + 3.10209I
b = 0.309017 + 0.299165I
−2.63189 + 2.02988I −2.00000 − 3.46410I
u = − 0.618034I
a = 0.50000 − 1.37004I
b = 0.309017 + 0.771301I
−2.63189 + 2.02988I −2.00000 − 3.46410I
u = − 0.618034I
a = 0.50000 − 3.10209I
b = 0.309017 − 0.299165I
−2.63189 − 2.02988I −2.00000 + 3.46410I
u = 1.61803I
a = 0.50000 + 1.37004I
b = −0.80902 − 2.83481I
−10.52760 − 2.02988I −2.00000 + 3.46410I
u = 1.61803I
a = 0.50000 + 3.10209I
b = −0.80902 − 5.63733I
−10.52760 + 2.02988I −2.00000 − 3.46410I
u = − 1.61803I
a = 0.50000 − 1.37004I
b = −0.80902 + 2.83481I
−10.52760 + 2.02988I −2.00000 − 3.46410I
u = − 1.61803I
a = 0.50000 − 3.10209I
b = −0.80902 + 5.63733I
−10.52760 − 2.02988I −2.00000 + 3.46410I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
85
+ 43u
84
+ ··· + 72u − 16)
c
2
, c
7
((u
2
+ 1)
4
)(u
85
+ u
84
+ ··· − 12u − 4)
c
3
, c
9
((u
4
− u
2
+ 1)
2
)(u
85
+ u
84
+ ··· − u − 5)
c
4
((u
4
− u
2
+ 1)
2
)(u
85
+ 3u
84
+ ··· − 6487u − 28835)
c
5
, c
6
, c
11
c
12
((u
4
+ 3u
2
+ 1)
2
)(u
85
− u
84
+ ··· + 5u − 1)
c
8
((u
2
+ u + 1)
4
)(u
85
− 41u
84
+ ··· + 131u − 25)
c
10
((u
2
+ u − 1)
4
)(u
85
− 23u
84
+ ··· + 41u − 283)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
8
)(y
85
+ 7y
84
+ ··· + 31264y −256)
c
2
, c
7
((y + 1)
8
)(y
85
+ 43y
84
+ ··· + 72y −16)
c
3
, c
9
((y
2
− y + 1)
4
)(y
85
− 41y
84
+ ··· + 131y −25)
c
4
((y
2
− y + 1)
4
)(y
85
+ 19y
84
+ ··· − 1.12049 × 10
10
y −8.31457 × 10
8
)
c
5
, c
6
, c
11
c
12
((y
2
+ 3y + 1)
4
)(y
85
+ 99y
84
+ ··· − 9y −1)
c
8
((y
2
+ y + 1)
4
)(y
85
+ 11y
84
+ ··· − 6589y −625)
c
10
((y
2
− 3y + 1)
4
)(y
85
− 9y
84
+ ··· + 1664023y −80089)
19
