12a
0621
(K12a
0621
)
A knot diagram
1
Linearized knot diagam
3 7 10 8 11 2 5 12 1 6 4 9
Solving Sequence
2,6
7
3,10
4 11 1 5 8 9 12
c
6
c
2
c
3
c
10
c
1
c
5
c
7
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.20239 × 10
215
u
107
+ 1.87947 × 10
215
u
106
+ ··· + 1.06285 × 10
214
b − 3.23420 × 10
217
,
5.28723 × 10
217
u
107
− 8.28194 × 10
217
u
106
+ ··· + 1.28605 × 10
216
a + 1.46385 × 10
220
,
u
108
− 2u
107
+ ··· + 665u − 121i
I
u
2
= hu
20
+ 2u
19
+ ··· + b + 5, −12u
20
− 5u
19
+ ··· + a − 15, u
21
+ u
20
+ ··· + 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 129 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−1.20 × 10
215
u
107
+ 1.88 × 10
215
u
106
+ · · · + 1.06 × 10
214
b − 3.23 ×
10
217
, 5.29 × 10
217
u
107
− 8.28 × 10
217
u
106
+ · · · + 1.29 × 10
216
a + 1.46 ×
10
220
, u
108
− 2u
107
+ · · · + 665u − 121i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
−41.1122u
107
+ 64.3984u
106
+ ··· + 36653.3u − 11382.6
11.3129u
107
− 17.6833u
106
+ ··· − 9984.50u + 3042.95
a
4
=
0.827553u
107
− 2.28938u
106
+ ··· − 1509.86u + 617.568
−4.54597u
107
+ 6.83298u
106
+ ··· + 3815.14u − 1175.67
a
11
=
−29.7993u
107
+ 46.7151u
106
+ ··· + 26668.8u − 8339.62
11.3129u
107
− 17.6833u
106
+ ··· − 9984.50u + 3042.95
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
−16.4923u
107
+ 26.9884u
106
+ ··· + 15115.1u − 4723.79
22.4428u
107
− 33.7114u
106
+ ··· − 18998.4u + 5793.78
a
8
=
49.2264u
107
− 75.9538u
106
+ ··· − 42626.0u + 13138.8
3.39652u
107
− 6.09058u
106
+ ··· − 3073.51u + 962.163
a
9
=
−42.3987u
107
+ 66.3530u
106
+ ··· + 37791.9u − 11742.9
5.22265u
107
− 8.18612u
106
+ ··· − 4597.36u + 1378.17
a
12
=
−20.8291u
107
+ 33.7038u
106
+ ··· + 19474.8u − 6266.69
12.6839u
107
− 20.1507u
106
+ ··· − 11239.0u + 3449.01
(ii) Obstruction class = −1
(iii) Cusp Shapes = −44.1834u
107
+ 68.3158u
106
+ ··· + 39249.5u − 11362.2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
108
+ 42u
107
+ ··· + 640907u + 14641
c
2
, c
6
u
108
− 2u
107
+ ··· + 665u − 121
c
3
u
108
− 16u
106
+ ··· − 2048u + 4096
c
4
, c
7
u
108
− 3u
107
+ ··· + 3492u − 216
c
5
, c
10
u
108
+ u
107
+ ··· − 2u + 1
c
8
, c
9
, c
12
u
108
− 8u
107
+ ··· + 29u − 49
c
11
u
108
− 5u
107
+ ··· − 1003776u + 284645
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
108
+ 58y
107
+ ··· − 10226920779y + 214358881
c
2
, c
6
y
108
− 42y
107
+ ··· − 640907y + 14641
c
3
y
108
− 32y
107
+ ··· − 20971520y + 16777216
c
4
, c
7
y
108
+ 85y
107
+ ··· − 4952016y + 46656
c
5
, c
10
y
108
+ 67y
107
+ ··· + 34y + 1
c
8
, c
9
, c
12
y
108
− 122y
107
+ ··· − 168029y + 2401
c
11
y
108
− 41y
107
+ ··· − 1084936184916y + 81022776025
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.473060 + 0.875553I
a = 0.707490 + 0.870890I
b = −0.693599 − 1.206920I
2.70722 + 7.95600I 0
u = 0.473060 − 0.875553I
a = 0.707490 − 0.870890I
b = −0.693599 + 1.206920I
2.70722 − 7.95600I 0
u = −0.549471 + 0.842594I
a = 1.008210 − 0.819907I
b = −0.396404 + 1.083280I
5.18492 − 5.01087I 0
u = −0.549471 − 0.842594I
a = 1.008210 + 0.819907I
b = −0.396404 − 1.083280I
5.18492 + 5.01087I 0
u = −0.838043 + 0.573550I
a = −2.21721 + 1.72162I
b = 0.349372 + 1.102210I
8.48917 + 5.97444I 0
u = −0.838043 − 0.573550I
a = −2.21721 − 1.72162I
b = 0.349372 − 1.102210I
8.48917 − 5.97444I 0
u = 0.919844 + 0.431107I
a = −2.06859 − 0.63924I
b = 0.083628 − 0.715885I
0.333552 + 0.320050I 0
u = 0.919844 − 0.431107I
a = −2.06859 + 0.63924I
b = 0.083628 + 0.715885I
0.333552 − 0.320050I 0
u = 0.853517 + 0.591429I
a = −2.11840 − 0.23828I
b = 0.56054 − 1.87766I
6.82179 − 1.22996I 0
u = 0.853517 − 0.591429I
a = −2.11840 + 0.23828I
b = 0.56054 + 1.87766I
6.82179 + 1.22996I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.852765 + 0.594286I
a = −0.382859 + 1.083340I
b = −0.83303 − 1.78714I
6.82273 − 3.46268I 0
u = 0.852765 − 0.594286I
a = −0.382859 − 1.083340I
b = −0.83303 + 1.78714I
6.82273 + 3.46268I 0
u = −0.708277 + 0.646884I
a = 1.64335 − 0.76091I
b = −1.34848 − 0.50829I
5.12587 − 1.17539I 0
u = −0.708277 − 0.646884I
a = 1.64335 + 0.76091I
b = −1.34848 + 0.50829I
5.12587 + 1.17539I 0
u = 0.927702 + 0.218176I
a = 0.681705 − 0.897707I
b = −0.690327 + 0.454815I
6.57674 − 5.64279I 0
u = 0.927702 − 0.218176I
a = 0.681705 + 0.897707I
b = −0.690327 − 0.454815I
6.57674 + 5.64279I 0
u = 0.926121 + 0.504353I
a = 1.104810 + 0.665303I
b = −0.523582 − 0.110172I
0.09015 − 3.83905I 0
u = 0.926121 − 0.504353I
a = 1.104810 − 0.665303I
b = −0.523582 + 0.110172I
0.09015 + 3.83905I 0
u = −0.878524 + 0.584465I
a = 1.205720 − 0.130671I
b = −0.541178 + 1.046540I
8.35182 − 1.37489I 0
u = −0.878524 − 0.584465I
a = 1.205720 + 0.130671I
b = −0.541178 − 1.046540I
8.35182 + 1.37489I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.885925 + 0.270042I
a = 0.674994 + 0.890462I
b = 0.09003 + 1.54119I
−4.90763 − 1.11610I 0
u = 0.885925 − 0.270042I
a = 0.674994 − 0.890462I
b = 0.09003 − 1.54119I
−4.90763 + 1.11610I 0
u = −0.670529 + 0.843882I
a = −1.41684 + 0.60093I
b = 1.144080 + 0.271829I
13.4229 − 5.1024I 0
u = −0.670529 − 0.843882I
a = −1.41684 − 0.60093I
b = 1.144080 − 0.271829I
13.4229 + 5.1024I 0
u = −0.586082 + 0.699959I
a = 1.351240 + 0.417284I
b = −0.277289 − 1.121530I
5.00143 + 1.83882I 0
u = −0.586082 − 0.699959I
a = 1.351240 − 0.417284I
b = −0.277289 + 1.121530I
5.00143 − 1.83882I 0
u = 1.091640 + 0.073011I
a = 0.103738 − 0.992056I
b = −0.139220 − 1.307480I
−6.53240 + 1.23702I 0
u = 1.091640 − 0.073011I
a = 0.103738 + 0.992056I
b = −0.139220 + 1.307480I
−6.53240 − 1.23702I 0
u = 0.451011 + 0.784212I
a = 1.273660 − 0.133702I
b = −0.568027 − 0.047119I
8.07381 + 1.59724I 0
u = 0.451011 − 0.784212I
a = 1.273660 + 0.133702I
b = −0.568027 + 0.047119I
8.07381 − 1.59724I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.083430 + 0.170919I
a = −0.698255 + 0.527280I
b = −0.378511 + 1.246240I
−2.92616 − 1.09003I 0
u = −1.083430 − 0.170919I
a = −0.698255 − 0.527280I
b = −0.378511 − 1.246240I
−2.92616 + 1.09003I 0
u = −1.09795
a = −0.368465
b = 0.666440
2.62003 0
u = −0.523837 + 0.733708I
a = −0.696556 + 0.981163I
b = 0.346320 − 1.044430I
−1.38558 − 2.70089I 0
u = −0.523837 − 0.733708I
a = −0.696556 − 0.981163I
b = 0.346320 + 1.044430I
−1.38558 + 2.70089I 0
u = −0.984732 + 0.540814I
a = 1.48087 − 1.27252I
b = −0.359632 − 1.138000I
1.10854 + 5.71480I 0
u = −0.984732 − 0.540814I
a = 1.48087 + 1.27252I
b = −0.359632 + 1.138000I
1.10854 − 5.71480I 0
u = −0.703662 + 0.518712I
a = −1.031900 − 0.031481I
b = 0.543441 − 1.001150I
2.03756 − 1.38231I 0
u = −0.703662 − 0.518712I
a = −1.031900 + 0.031481I
b = 0.543441 + 1.001150I
2.03756 + 1.38231I 0
u = 0.757168 + 0.434719I
a = 3.39105 + 0.12282I
b = −0.010875 + 0.740927I
7.60270 + 2.67213I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.757168 − 0.434719I
a = 3.39105 − 0.12282I
b = −0.010875 − 0.740927I
7.60270 − 2.67213I 0
u = −0.936532 + 0.633259I
a = −1.00052 + 1.11876I
b = 1.55972 − 0.17892I
4.45386 + 6.18095I 0
u = −0.936532 − 0.633259I
a = −1.00052 − 1.11876I
b = 1.55972 + 0.17892I
4.45386 − 6.18095I 0
u = −0.976297 + 0.585566I
a = −1.78809 + 0.08042I
b = 0.454982 + 1.235360I
−2.63040 + 3.86869I 0
u = −0.976297 − 0.585566I
a = −1.78809 − 0.08042I
b = 0.454982 − 1.235360I
−2.63040 − 3.86869I 0
u = −0.227089 + 0.828776I
a = 0.283807 + 0.030814I
b = −0.465423 + 0.863386I
3.05305 − 0.31048I 0
u = −0.227089 − 0.828776I
a = 0.283807 − 0.030814I
b = −0.465423 − 0.863386I
3.05305 + 0.31048I 0
u = 0.541017 + 1.005910I
a = −0.650168 − 0.745155I
b = 0.646450 + 1.252080I
10.3554 + 11.3655I 0
u = 0.541017 − 1.005910I
a = −0.650168 + 0.745155I
b = 0.646450 − 1.252080I
10.3554 − 11.3655I 0
u = 0.875093 + 0.734313I
a = −0.663314 + 0.334049I
b = 0.400839 − 0.319523I
3.72639 − 2.82265I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.875093 − 0.734313I
a = −0.663314 − 0.334049I
b = 0.400839 + 0.319523I
3.72639 + 2.82265I 0
u = −0.959651 + 0.645938I
a = −0.005851 + 0.347104I
b = 0.523713 − 0.959481I
4.00904 + 3.32493I 0
u = −0.959651 − 0.645938I
a = −0.005851 − 0.347104I
b = 0.523713 + 0.959481I
4.00904 − 3.32493I 0
u = 0.876860 + 0.761678I
a = −0.179546 + 0.607540I
b = −0.054879 − 0.291273I
3.75178 − 2.88559I 0
u = 0.876860 − 0.761678I
a = −0.179546 − 0.607540I
b = −0.054879 + 0.291273I
3.75178 + 2.88559I 0
u = 1.028930 + 0.587128I
a = 1.90164 + 0.62956I
b = −0.87739 + 1.40295I
−0.30441 − 7.63518I 0
u = 1.028930 − 0.587128I
a = 1.90164 − 0.62956I
b = −0.87739 − 1.40295I
−0.30441 + 7.63518I 0
u = 0.861830 + 0.816429I
a = 0.071175 − 1.214830I
b = 0.182839 + 0.432133I
10.65380 − 3.10774I 0
u = 0.861830 − 0.816429I
a = 0.071175 + 1.214830I
b = 0.182839 − 0.432133I
10.65380 + 3.10774I 0
u = −0.760443 + 0.271321I
a = −0.002660 − 0.265274I
b = −0.338167 + 0.464740I
−1.25535 + 0.69450I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.760443 − 0.271321I
a = −0.002660 + 0.265274I
b = −0.338167 − 0.464740I
−1.25535 − 0.69450I 0
u = 1.040690 + 0.589174I
a = −0.923884 − 0.806157I
b = 0.499188 + 0.215260I
6.23284 − 6.65466I 0
u = 1.040690 − 0.589174I
a = −0.923884 + 0.806157I
b = 0.499188 − 0.215260I
6.23284 + 6.65466I 0
u = 1.201340 + 0.015247I
a = −0.503046 − 0.959905I
b = 0.256160 − 1.198350I
−1.06906 − 3.31616I 0
u = 1.201340 − 0.015247I
a = −0.503046 + 0.959905I
b = 0.256160 + 1.198350I
−1.06906 + 3.31616I 0
u = −0.208754 + 1.187980I
a = −0.259697 + 0.052384I
b = 0.394602 − 0.862464I
9.93351 + 0.77910I 0
u = −0.208754 − 1.187980I
a = −0.259697 − 0.052384I
b = 0.394602 + 0.862464I
9.93351 − 0.77910I 0
u = 0.747978 + 0.953978I
a = 0.461708 − 0.162440I
b = −0.306209 + 0.634133I
3.85688 − 3.32718I 0
u = 0.747978 − 0.953978I
a = 0.461708 + 0.162440I
b = −0.306209 − 0.634133I
3.85688 + 3.32718I 0
u = 1.102530 + 0.504475I
a = 1.226100 + 0.569982I
b = −0.125324 + 0.660192I
−0.43748 − 3.66386I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.102530 − 0.504475I
a = 1.226100 − 0.569982I
b = −0.125324 − 0.660192I
−0.43748 + 3.66386I 0
u = −0.541468 + 0.567666I
a = −0.028249 − 1.023690I
b = −0.234324 + 0.946299I
−1.48923 + 0.77150I 0
u = −0.541468 − 0.567666I
a = −0.028249 + 1.023690I
b = −0.234324 − 0.946299I
−1.48923 − 0.77150I 0
u = −1.051390 + 0.633166I
a = 1.88360 − 0.20286I
b = −0.462804 − 1.171660I
−2.92953 + 7.93071I 0
u = −1.051390 − 0.633166I
a = 1.88360 + 0.20286I
b = −0.462804 + 1.171660I
−2.92953 − 7.93071I 0
u = 0.959577 + 0.788105I
a = 0.838671 − 0.381486I
b = −0.528764 + 0.258032I
10.36730 − 2.98702I 0
u = 0.959577 − 0.788105I
a = 0.838671 + 0.381486I
b = −0.528764 − 0.258032I
10.36730 + 2.98702I 0
u = −1.022620 + 0.716898I
a = 0.975752 − 0.785034I
b = −1.286650 + 0.123126I
12.3366 + 10.9198I 0
u = −1.022620 − 0.716898I
a = 0.975752 + 0.785034I
b = −1.286650 − 0.123126I
12.3366 − 10.9198I 0
u = −0.727701 + 0.161722I
a = 1.77728 − 0.36588I
b = −0.753976 − 1.046270I
4.92697 − 0.20226I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.727701 − 0.161722I
a = 1.77728 + 0.36588I
b = −0.753976 + 1.046270I
4.92697 + 0.20226I 0
u = 0.622029 + 0.398139I
a = −1.52293 − 0.22173I
b = 0.472209 + 0.032024I
1.073050 − 0.034370I 0
u = 0.622029 − 0.398139I
a = −1.52293 + 0.22173I
b = 0.472209 − 0.032024I
1.073050 + 0.034370I 0
u = −1.262390 + 0.001421I
a = 0.132361 + 0.701874I
b = 0.363612 + 1.190420I
−3.61718 + 5.59007I 0
u = −1.262390 − 0.001421I
a = 0.132361 − 0.701874I
b = 0.363612 − 1.190420I
−3.61718 − 5.59007I 0
u = 0.486653 + 0.553887I
a = −0.76014 − 1.31274I
b = 0.878383 + 1.068390I
1.19643 + 2.94178I 0
u = 0.486653 − 0.553887I
a = −0.76014 + 1.31274I
b = 0.878383 − 1.068390I
1.19643 − 2.94178I 0
u = −0.657418 + 0.310518I
a = 2.51515 + 0.43393I
b = 0.094082 − 1.281950I
5.31723 + 1.96329I 0
u = −0.657418 − 0.310518I
a = 2.51515 − 0.43393I
b = 0.094082 + 1.281950I
5.31723 − 1.96329I 0
u = −1.080210 + 0.682836I
a = −2.01230 + 0.23776I
b = 0.464349 + 1.137860I
3.58932 + 10.70600I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.080210 − 0.682836I
a = −2.01230 − 0.23776I
b = 0.464349 − 1.137860I
3.58932 − 10.70600I 0
u = 1.109350 + 0.662620I
a = −1.73834 − 0.48707I
b = 0.71822 − 1.35841I
0.79512 − 13.63080I 0
u = 1.109350 − 0.662620I
a = −1.73834 + 0.48707I
b = 0.71822 + 1.35841I
0.79512 + 13.63080I 0
u = 1.141290 + 0.730712I
a = 1.69619 + 0.39257I
b = −0.66089 + 1.36226I
8.4801 − 17.6568I 0
u = 1.141290 − 0.730712I
a = 1.69619 − 0.39257I
b = −0.66089 − 1.36226I
8.4801 + 17.6568I 0
u = −1.193680 + 0.662241I
a = −1.038890 + 0.558810I
b = 0.366469 + 1.171730I
0.27951 + 5.89405I 0
u = −1.193680 − 0.662241I
a = −1.038890 − 0.558810I
b = 0.366469 − 1.171730I
0.27951 − 5.89405I 0
u = 1.261090 + 0.636921I
a = −0.803064 − 0.444751I
b = 0.126758 − 0.654920I
5.57865 − 6.57980I 0
u = 1.261090 − 0.636921I
a = −0.803064 + 0.444751I
b = 0.126758 + 0.654920I
5.57865 + 6.57980I 0
u = −1.43120 + 0.14591I
a = 0.191855 − 0.602946I
b = −0.358116 − 1.174330I
2.45534 + 8.59444I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43120 − 0.14591I
a = 0.191855 + 0.602946I
b = −0.358116 + 1.174330I
2.45534 − 8.59444I 0
u = 0.76870 + 1.21907I
a = −0.400142 + 0.042707I
b = 0.274008 − 0.711337I
10.54990 − 3.98993I 0
u = 0.76870 − 1.21907I
a = −0.400142 − 0.042707I
b = 0.274008 + 0.711337I
10.54990 + 3.98993I 0
u = −1.30134 + 0.78639I
a = 0.908626 − 0.350281I
b = −0.363659 − 1.180110I
6.72804 + 6.21729I 0
u = −1.30134 − 0.78639I
a = 0.908626 + 0.350281I
b = −0.363659 + 1.180110I
6.72804 − 6.21729I 0
u = 0.440218 + 0.007816I
a = −0.24041 − 1.63056I
b = 0.758652 + 0.713064I
1.19054 + 2.71950I 0.99256 − 6.37992I
u = 0.440218 − 0.007816I
a = −0.24041 + 1.63056I
b = 0.758652 − 0.713064I
1.19054 − 2.71950I 0.99256 + 6.37992I
u = 0.419660
a = −1.87954
b = 0.381743
0.914841 13.1320
15
II.
I
u
2
= hu
20
+2u
19
+· · ·+b+5, −12u
20
−5u
19
+· · ·+a−15, u
21
+u
20
+· · ·+3u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
12u
20
+ 5u
19
+ ··· + 36u + 15
−u
20
− 2u
19
+ ··· − 4u − 5
a
4
=
12u
20
+ 3u
19
+ ··· + 35u + 5
−2u
20
− u
19
+ ··· − 9u − 6
a
11
=
11u
20
+ 3u
19
+ ··· + 32u + 10
−u
20
− 2u
19
+ ··· − 4u − 5
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
7u
20
+ 5u
19
+ ··· + 16u + 12
−u
20
+ 4u
18
+ ··· − u − 1
a
8
=
−10u
20
− 3u
19
+ ··· − 33u − 12
−u
17
+ 4u
15
+ ··· − 2u + 1
a
9
=
12u
20
+ 5u
19
+ ··· + 37u + 16
u
20
− u
19
+ ··· + 3u − 1
a
12
=
−13u
20
− 6u
19
+ ··· − 40u − 14
−u
10
+ 3u
8
− u
7
− 6u
6
+ 3u
5
+ 6u
4
− 4u
3
− 5u
2
+ 2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −14u
20
−u
19
+ 63u
18
−25u
17
−196u
16
+ 132u
15
+ 375u
14
−360u
13
−534u
12
+ 648u
11
+
529u
10
− 804u
9
− 401u
8
+ 739u
7
+ 210u
6
− 461u
5
− 92u
4
+ 189u
3
+ 29u
2
− 41u − 6
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
− 9u
20
+ ··· + 11u − 1
c
2
u
21
− u
20
+ ··· + 3u − 1
c
3
u
21
+ u
20
+ ··· + 5u − 1
c
4
u
21
− 2u
20
+ ··· − 2u − 3
c
5
u
21
+ 10u
19
+ ··· + 6u + 1
c
6
u
21
+ u
20
+ ··· + 3u + 1
c
7
u
21
+ 2u
20
+ ··· − 2u + 3
c
8
, c
9
u
21
+ u
20
+ ··· + 5u + 1
c
10
u
21
+ 10u
19
+ ··· + 6u − 1
c
11
u
21
− 2u
19
+ ··· + 6u + 1
c
12
u
21
− u
20
+ ··· + 5u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
+ 15y
20
+ ··· − 17y −1
c
2
, c
6
y
21
− 9y
20
+ ··· + 11y −1
c
3
y
21
− 7y
20
+ ··· + 19y −1
c
4
, c
7
y
21
+ 22y
20
+ ··· − 104y −9
c
5
, c
10
y
21
+ 20y
20
+ ··· + 10y −1
c
8
, c
9
, c
12
y
21
− 29y
20
+ ··· + 9y −1
c
11
y
21
− 4y
20
+ ··· + 32y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.820423 + 0.631013I
a = 1.050250 + 0.253276I
b = 0.21601 − 1.68021I
6.89986 + 2.50759I 9.76319 − 2.39511I
u = −0.820423 − 0.631013I
a = 1.050250 − 0.253276I
b = 0.21601 + 1.68021I
6.89986 − 2.50759I 9.76319 + 2.39511I
u = 0.903321 + 0.133481I
a = 0.775922 + 0.968361I
b = 0.01390 + 1.46618I
−5.15941 − 0.56745I −1.92028 − 2.84114I
u = 0.903321 − 0.133481I
a = 0.775922 − 0.968361I
b = 0.01390 − 1.46618I
−5.15941 + 0.56745I −1.92028 + 2.84114I
u = 0.716086 + 0.505123I
a = −2.35062 + 0.26772I
b = 0.74430 − 1.29894I
6.07693 − 0.03732I 9.37966 − 0.12123I
u = 0.716086 − 0.505123I
a = −2.35062 − 0.26772I
b = 0.74430 + 1.29894I
6.07693 + 0.03732I 9.37966 + 0.12123I
u = 0.819984 + 0.838814I
a = 0.253614 − 0.504529I
b = −0.140516 + 0.590111I
3.42574 − 3.14778I −5.74962 + 6.21620I
u = 0.819984 − 0.838814I
a = 0.253614 + 0.504529I
b = −0.140516 − 0.590111I
3.42574 + 3.14778I −5.74962 − 6.21620I
u = 1.009200 + 0.606978I
a = −0.058815 + 0.756627I
b = −0.711331 − 0.858548I
5.00283 − 4.45517I 7.26864 + 4.48388I
u = 1.009200 − 0.606978I
a = −0.058815 − 0.756627I
b = −0.711331 + 0.858548I
5.00283 + 4.45517I 7.26864 − 4.48388I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.800131
a = 1.38397
b = −0.198977
0.422571 −5.22070
u = −1.110220 + 0.558025I
a = −1.25135 + 0.83423I
b = 0.455417 + 1.127270I
−0.46752 + 5.65574I −1.10475 − 5.29317I
u = −1.110220 − 0.558025I
a = −1.25135 − 0.83423I
b = 0.455417 − 1.127270I
−0.46752 − 5.65574I −1.10475 + 5.29317I
u = −0.646187 + 0.388815I
a = 1.47122 − 0.35668I
b = −0.628007 + 0.810454I
1.34744 − 1.67206I 1.52827 + 2.27823I
u = −0.646187 − 0.388815I
a = 1.47122 + 0.35668I
b = −0.628007 − 0.810454I
1.34744 + 1.67206I 1.52827 − 2.27823I
u = 0.790181 + 0.999133I
a = −0.052855 + 0.670525I
b = 0.090745 − 0.772295I
9.80396 − 3.59314I 3.21150 + 2.92520I
u = 0.790181 − 0.999133I
a = −0.052855 − 0.670525I
b = 0.090745 + 0.772295I
9.80396 + 3.59314I 3.21150 − 2.92520I
u = −1.272280 + 0.582453I
a = 0.919745 − 0.861219I
b = −0.279270 − 1.015850I
4.60320 + 7.62970I 3.69155 − 7.59260I
u = −1.272280 − 0.582453I
a = 0.919745 + 0.861219I
b = −0.279270 + 1.015850I
4.60320 − 7.62970I 3.69155 + 7.59260I
u = −0.489595 + 0.320187I
a = −3.44909 − 0.90345I
b = 0.338245 − 0.804670I
7.73410 − 3.58608I 7.04221 + 5.92560I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.489595 − 0.320187I
a = −3.44909 + 0.90345I
b = 0.338245 + 0.804670I
7.73410 + 3.58608I 7.04221 − 5.92560I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
21
− 9u
20
+ ··· + 11u − 1)(u
108
+ 42u
107
+ ··· + 640907u + 14641)
c
2
(u
21
− u
20
+ ··· + 3u − 1)(u
108
− 2u
107
+ ··· + 665u − 121)
c
3
(u
21
+ u
20
+ ··· + 5u − 1)(u
108
− 16u
106
+ ··· − 2048u + 4096)
c
4
(u
21
− 2u
20
+ ··· − 2u − 3)(u
108
− 3u
107
+ ··· + 3492u − 216)
c
5
(u
21
+ 10u
19
+ ··· + 6u + 1)(u
108
+ u
107
+ ··· − 2u + 1)
c
6
(u
21
+ u
20
+ ··· + 3u + 1)(u
108
− 2u
107
+ ··· + 665u − 121)
c
7
(u
21
+ 2u
20
+ ··· − 2u + 3)(u
108
− 3u
107
+ ··· + 3492u − 216)
c
8
, c
9
(u
21
+ u
20
+ ··· + 5u + 1)(u
108
− 8u
107
+ ··· + 29u − 49)
c
10
(u
21
+ 10u
19
+ ··· + 6u − 1)(u
108
+ u
107
+ ··· − 2u + 1)
c
11
(u
21
− 2u
19
+ ··· + 6u + 1)(u
108
− 5u
107
+ ··· − 1003776u + 284645)
c
12
(u
21
− u
20
+ ··· + 5u − 1)(u
108
− 8u
107
+ ··· + 29u − 49)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
21
+ 15y
20
+ ··· − 17y −1)
· (y
108
+ 58y
107
+ ··· − 10226920779y + 214358881)
c
2
, c
6
(y
21
− 9y
20
+ ··· + 11y −1)(y
108
− 42y
107
+ ··· − 640907y + 14641)
c
3
(y
21
− 7y
20
+ ··· + 19y −1)
· (y
108
− 32y
107
+ ··· − 20971520y + 16777216)
c
4
, c
7
(y
21
+ 22y
20
+ ··· − 104y −9)
· (y
108
+ 85y
107
+ ··· − 4952016y + 46656)
c
5
, c
10
(y
21
+ 20y
20
+ ··· + 10y −1)(y
108
+ 67y
107
+ ··· + 34y + 1)
c
8
, c
9
, c
12
(y
21
− 29y
20
+ ··· + 9y −1)(y
108
− 122y
107
+ ··· − 168029y + 2401)
c
11
(y
21
− 4y
20
+ ··· + 32y −1)
· (y
108
− 41y
107
+ ··· − 1084936184916y + 81022776025)
23
