12n
0628
(K12n
0628
)
A knot diagram
1
Linearized knot diagam
3 7 9 11 3 12 2 5 6 7 4 10
Solving Sequence
4,11
5
9,12
3 6 7 2 1 8 10
c
4
c
11
c
3
c
5
c
6
c
2
c
1
c
8
c
10
c
7
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h4.23039 × 10
40
u
36
+ 1.59605 × 10
41
u
35
+ ··· + 6.26742 × 10
42
b − 2.10116 × 10
42
,
7.35912 × 10
41
u
36
+ 3.34060 × 10
42
u
35
+ ··· + 5.64068 × 10
43
a + 1.24742 × 10
44
,
u
37
+ 5u
36
+ ··· + 135u + 216i
I
u
2
= h−287727135u
24
a − 4296024791u
24
+ ··· + 46372736648a − 5064132100,
203474647775u
24
a + 191008518002u
24
+ ··· + 1275756399988a + 9676139674612,
u
25
− 2u
24
+ ··· − 30u + 28i
I
u
3
= h−31u
15
a − 25u
15
+ ··· + 35a + 221, 344u
15
a + 659u
15
+ ··· + 206a + 177, u
16
+ u
15
+ ··· − 3u + 1i
I
u
4
= hu
4
− 2u
3
+ 2u
2
+ b − 2u, u
4
− u
3
+ a + u − 2, u
5
− 2u
4
+ 3u
3
− 3u
2
+ u − 1i
I
v
1
= ha, b
2
− b + 1, v + 1i
* 5 irreducible components of dim
C
= 0, with total 126 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
=
h4.23×10
40
u
36
+1.60×10
41
u
35
+· · ·+6.27×10
42
b−2.10×10
42
, 7.36×10
41
u
36
+
3.34 × 10
42
u
35
+ · · · + 5.64 × 10
43
a + 1.25 × 10
44
, u
37
+ 5u
36
+ · · · + 135u + 216i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
9
=
−0.0130465u
36
− 0.0592234u
35
+ ··· − 1.66509u − 2.21148
−0.00674980u
36
− 0.0254658u
35
+ ··· − 1.22229u + 0.335251
a
12
=
u
u
a
3
=
0.0169497u
36
+ 0.0766729u
35
+ ··· + 6.01317u + 1.90994
−0.00354995u
36
− 0.0254904u
35
+ ··· + 1.41026u − 3.00175
a
6
=
−0.00382624u
36
− 0.0152232u
35
+ ··· − 1.03783u − 0.0717343
−0.00227415u
36
− 0.000712979u
35
+ ··· − 1.69668u + 1.36009
a
7
=
0.00445702u
36
+ 0.0266027u
35
+ ··· + 0.208643u + 1.38622
0.00600911u
36
+ 0.0411129u
35
+ ··· − 0.450201u + 2.81805
a
2
=
0.00558813u
36
+ 0.0233426u
35
+ ··· + 2.98092u − 0.130169
0.00451436u
36
+ 0.0186563u
35
+ ··· + 1.47087u + 0.213858
a
1
=
0.00112681u
36
+ 0.000820182u
35
+ ··· − 0.872767u − 1.09599
0.00351553u
36
+ 0.0148665u
35
+ ··· − 0.874777u + 0.624270
a
8
=
−0.00872893u
36
− 0.0448289u
35
+ ··· − 0.880563u − 3.17420
−0.00335736u
36
− 0.0222397u
35
+ ··· − 1.26079u − 1.21851
a
10
=
−0.00135818u
36
− 0.00996207u
35
+ ··· − 0.442769u − 1.34439
0.00446321u
36
+ 0.0123465u
35
+ ··· + 1.74499u − 1.71917
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00136317u
36
− 0.00172311u
35
+ ··· + 2.61553u − 10.2082
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
37
+ 44u
36
+ ··· − 9216u − 4096
c
2
, c
7
u
37
− 4u
36
+ ··· + 288u − 64
c
3
, c
6
u
37
− u
36
+ ··· − 4u − 1
c
4
, c
11
u
37
− 5u
36
+ ··· + 135u − 216
c
5
, c
12
u
37
+ 2u
36
+ ··· + 55u − 13
c
8
, c
10
u
37
− 3u
36
+ ··· + 2158u − 419
c
9
u
37
− 9u
36
+ ··· + 352u + 128
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
37
− 92y
36
+ ··· + 5631901696y −16777216
c
2
, c
7
y
37
+ 44y
36
+ ··· − 9216y −4096
c
3
, c
6
y
37
− 3y
36
+ ··· + 26y −1
c
4
, c
11
y
37
+ 25y
36
+ ··· − 40095y −46656
c
5
, c
12
y
37
+ 30y
36
+ ··· − 4593y −169
c
8
, c
10
y
37
− 47y
36
+ ··· + 2060002y −175561
c
9
y
37
+ y
36
+ ··· − 232448y −16384
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.269152 + 0.903541I
a = −1.77650 − 0.73834I
b = −0.896333 + 0.889708I
−1.23041 + 6.04986I −1.10927 − 5.75372I
u = 0.269152 − 0.903541I
a = −1.77650 + 0.73834I
b = −0.896333 − 0.889708I
−1.23041 − 6.04986I −1.10927 + 5.75372I
u = 0.872271 + 0.100098I
a = 0.030203 − 0.658754I
b = −0.818627 + 0.925714I
0.32389 + 6.56803I 2.05536 − 8.38131I
u = 0.872271 − 0.100098I
a = 0.030203 + 0.658754I
b = −0.818627 − 0.925714I
0.32389 − 6.56803I 2.05536 + 8.38131I
u = 0.492670 + 1.011790I
a = −0.724839 − 0.785958I
b = −0.425898 + 0.318622I
−3.00341 + 1.76524I −6.22185 − 1.31475I
u = 0.492670 − 1.011790I
a = −0.724839 + 0.785958I
b = −0.425898 − 0.318622I
−3.00341 − 1.76524I −6.22185 + 1.31475I
u = −0.420104 + 0.739731I
a = 1.169150 − 0.559343I
b = 0.508246 + 0.930731I
0.59435 − 2.34473I 4.94040 + 1.97464I
u = −0.420104 − 0.739731I
a = 1.169150 + 0.559343I
b = 0.508246 − 0.930731I
0.59435 + 2.34473I 4.94040 − 1.97464I
u = 0.917730 + 0.731301I
a = −0.009924 + 0.473838I
b = 0.809176 + 0.515910I
−1.04010 − 1.96201I −3.92093 + 3.59450I
u = 0.917730 − 0.731301I
a = −0.009924 − 0.473838I
b = 0.809176 − 0.515910I
−1.04010 + 1.96201I −3.92093 − 3.59450I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.416470 + 0.699073I
a = 0.604746 + 0.012396I
b = −0.071559 + 0.795337I
0.73020 − 1.39454I 3.96402 + 4.72107I
u = −0.416470 − 0.699073I
a = 0.604746 − 0.012396I
b = −0.071559 − 0.795337I
0.73020 + 1.39454I 3.96402 − 4.72107I
u = −0.805868 + 0.098826I
a = −1.063250 − 0.356749I
b = −0.788565 + 0.577403I
−8.40989 + 1.02946I −2.28755 − 3.65982I
u = −0.805868 − 0.098826I
a = −1.063250 + 0.356749I
b = −0.788565 − 0.577403I
−8.40989 − 1.02946I −2.28755 + 3.65982I
u = −1.22415
a = 0.225372
b = −0.602117
2.30908 24.7760
u = 0.410867 + 1.163200I
a = −1.63461 − 0.14310I
b = −1.007580 + 0.398227I
−3.67004 + 5.51506I −8.53570 − 9.26676I
u = 0.410867 − 1.163200I
a = −1.63461 + 0.14310I
b = −1.007580 − 0.398227I
−3.67004 − 5.51506I −8.53570 + 9.26676I
u = −0.650738 + 1.117350I
a = 0.898248 − 1.072900I
b = 0.312545 − 0.041809I
−11.29550 − 2.67171I −5.33997 + 0.05553I
u = −0.650738 − 1.117350I
a = 0.898248 + 1.072900I
b = 0.312545 + 0.041809I
−11.29550 + 2.67171I −5.33997 − 0.05553I
u = −0.466931 + 1.223260I
a = 2.04392 − 0.46693I
b = 0.883818 + 0.444424I
−11.81660 − 5.68244I −7.57615 + 8.42428I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.466931 − 1.223260I
a = 2.04392 + 0.46693I
b = 0.883818 − 0.444424I
−11.81660 + 5.68244I −7.57615 − 8.42428I
u = −0.248666 + 1.316480I
a = 1.212910 − 0.492241I
b = 0.772807 − 0.987892I
−12.83220 − 2.62224I −2.96286 + 0.29649I
u = −0.248666 − 1.316480I
a = 1.212910 + 0.492241I
b = 0.772807 + 0.987892I
−12.83220 + 2.62224I −2.96286 − 0.29649I
u = −0.161469 + 1.332340I
a = −1.50038 − 0.23483I
b = −0.83492 − 1.22643I
−4.52806 − 3.48372I −2.33948 + 2.63349I
u = −0.161469 − 1.332340I
a = −1.50038 + 0.23483I
b = −0.83492 + 1.22643I
−4.52806 + 3.48372I −2.33948 − 2.63349I
u = 0.614318 + 0.108865I
a = 0.175521 + 0.463933I
b = 0.484967 + 0.414617I
−0.52930 − 1.61126I −1.10989 + 5.35570I
u = 0.614318 − 0.108865I
a = 0.175521 − 0.463933I
b = 0.484967 − 0.414617I
−0.52930 + 1.61126I −1.10989 − 5.35570I
u = −0.076677 + 1.400490I
a = 1.080420 + 0.334648I
b = 1.118970 + 0.407322I
−4.39513 − 4.13503I −4.32540 + 3.40282I
u = −0.076677 − 1.400490I
a = 1.080420 − 0.334648I
b = 1.118970 − 0.407322I
−4.39513 + 4.13503I −4.32540 − 3.40282I
u = −1.46354 + 0.04533I
a = 0.232820 + 0.196289I
b = 0.974356 − 0.901856I
−7.90935 + 10.21460I −0.56188 − 6.56611I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46354 − 0.04533I
a = 0.232820 − 0.196289I
b = 0.974356 + 0.901856I
−7.90935 − 10.21460I −0.56188 + 6.56611I
u = 0.42524 + 1.40381I
a = 1.52208 + 0.03579I
b = 0.99008 − 1.24001I
−4.48931 + 11.38620I −0.95014 − 7.32093I
u = 0.42524 − 1.40381I
a = 1.52208 − 0.03579I
b = 0.99008 + 1.24001I
−4.48931 − 11.38620I −0.95014 + 7.32093I
u = −0.65785 + 1.48194I
a = −1.43080 + 0.21430I
b = −1.05752 − 1.16840I
−12.5004 − 17.5192I −1.31148 + 7.96520I
u = −0.65785 − 1.48194I
a = −1.43080 − 0.21430I
b = −1.05752 + 1.16840I
−12.5004 + 17.5192I −1.31148 − 7.96520I
u = −0.52186 + 1.81589I
a = −0.629899 + 0.337579I
b = −1.152920 + 0.434503I
−13.84930 + 2.33793I 0
u = −0.52186 − 1.81589I
a = −0.629899 − 0.337579I
b = −1.152920 − 0.434503I
−13.84930 − 2.33793I 0
8
II. I
u
2
= h−2.88 × 10
8
au
24
− 4.30 × 10
9
u
24
+ · · · + 4.64 × 10
10
a − 5.06 ×
10
9
, 2.03 × 10
11
au
24
+ 1.91 × 10
11
u
24
+ · · · + 1.28 × 10
12
a + 9.68 ×
10
12
, u
25
− 2u
24
+ · · · − 30u + 28i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
9
=
a
0.0888371au
24
+ 1.32642u
24
+ ··· − 14.3178a + 1.56357
a
12
=
u
u
a
3
=
1.14416au
24
+ 0.500026u
24
+ ··· + 5.09968a + 90.8069
0.371315au
24
+ 0.682157u
24
+ ··· − 1.83371a + 39.0764
a
6
=
−0.790302au
24
− 0.0000829280u
24
+ ··· − 18.4541a − 47.8678
−0.278952au
24
− 0.182215u
24
+ ··· − 2.48744a + 3.86283
a
7
=
−0.511350au
24
+ 0.219023u
24
+ ··· − 15.9667a − 15.8313
0.0368918u
24
+ 0.431609u
23
+ ··· − 46.5022u + 35.8993
a
2
=
0.548179au
24
− 0.887679u
24
+ ··· + 8.28779a + 12.4597
0.393575au
24
+ 0.443170u
24
+ ··· − 14.2099a + 11.1167
a
1
=
−0.227457au
24
+ 1.49200u
24
+ ··· − 50.7667a − 36.5596
−0.109588au
24
+ 0.713764u
24
+ ··· − 43.9560a − 29.8354
a
8
=
0.0888371au
24
+ 1.32642u
24
+ ··· − 13.3178a + 1.56357
−0.0290318au
24
+ 2.10466u
24
+ ··· − 22.1285a − 5.16064
a
10
=
−0.330051au
24
+ 2.09033u
24
+ ··· − 28.2218a + 68.6377
−0.176435au
24
+ 2.12604u
24
+ ··· − 17.8855a + 67.5663
(ii) Obstruction class = −1
(iii) Cusp Shapes =
919833563
809704132
u
24
−
3264468405
809704132
u
23
+ ··· +
98309380939
404852066
u −
28748753193
202426033
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
25
+ 30u
24
+ ··· + 180u − 81)
2
c
2
, c
7
(u
25
+ 15u
23
+ ··· + 60u − 9)
2
c
3
, c
6
u
50
− u
49
+ ··· − 3u + 1
c
4
, c
11
(u
25
+ 2u
24
+ ··· − 30u − 28)
2
c
5
, c
12
u
50
+ 10u
49
+ ··· − 20945u + 3023
c
8
, c
10
u
50
+ 2u
49
+ ··· − 14284u + 311
c
9
(u
25
+ 5u
24
+ ··· − 12u + 8)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
25
− 62y
24
+ ··· + 1407132y −6561)
2
c
2
, c
7
(y
25
+ 30y
24
+ ··· + 180y −81)
2
c
3
, c
6
y
50
+ 21y
49
+ ··· − 13y + 1
c
4
, c
11
(y
25
+ 24y
24
+ ··· − 12596y −784)
2
c
5
, c
12
y
50
− 8y
49
+ ··· − 156235997y + 9138529
c
8
, c
10
y
50
+ 12y
49
+ ··· − 46687804y + 96721
c
9
(y
25
+ 13y
24
+ ··· − 752y −64)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.449283 + 0.973936I
a = 0.217764 + 1.043870I
b = 0.244229 − 0.814938I
0.34821 + 5.88006I 4.30099 − 9.81968I
u = 0.449283 + 0.973936I
a = −2.24809 − 0.13074I
b = −1.26226 + 0.93873I
0.34821 + 5.88006I 4.30099 − 9.81968I
u = 0.449283 − 0.973936I
a = 0.217764 − 1.043870I
b = 0.244229 + 0.814938I
0.34821 − 5.88006I 4.30099 + 9.81968I
u = 0.449283 − 0.973936I
a = −2.24809 + 0.13074I
b = −1.26226 − 0.93873I
0.34821 − 5.88006I 4.30099 + 9.81968I
u = −0.399469 + 0.829102I
a = 0.700444 + 0.414029I
b = 0.040945 + 0.712613I
0.78426 − 1.36586I 3.84923 + 4.03900I
u = −0.399469 + 0.829102I
a = 0.433443 − 0.136431I
b = −0.109234 + 1.113410I
0.78426 − 1.36586I 3.84923 + 4.03900I
u = −0.399469 − 0.829102I
a = 0.700444 − 0.414029I
b = 0.040945 − 0.712613I
0.78426 + 1.36586I 3.84923 − 4.03900I
u = −0.399469 − 0.829102I
a = 0.433443 + 0.136431I
b = −0.109234 − 1.113410I
0.78426 + 1.36586I 3.84923 − 4.03900I
u = 0.369340 + 0.770969I
a = 1.213080 − 0.407998I
b = −0.205521 − 0.180923I
0.95824 − 2.12068I 4.21040 + 2.51534I
u = 0.369340 + 0.770969I
a = 0.227728 + 0.451157I
b = 0.671745 + 1.189840I
0.95824 − 2.12068I 4.21040 + 2.51534I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.369340 − 0.770969I
a = 1.213080 + 0.407998I
b = −0.205521 + 0.180923I
0.95824 + 2.12068I 4.21040 − 2.51534I
u = 0.369340 − 0.770969I
a = 0.227728 − 0.451157I
b = 0.671745 − 1.189840I
0.95824 + 2.12068I 4.21040 − 2.51534I
u = 1.095450 + 0.502626I
a = 0.017947 − 1.161590I
b = 0.618295 + 1.048920I
−7.16565 + 3.70405I 2.35407 − 4.32771I
u = 1.095450 + 0.502626I
a = −0.470827 + 0.084074I
b = −0.488587 + 0.835280I
−7.16565 + 3.70405I 2.35407 − 4.32771I
u = 1.095450 − 0.502626I
a = 0.017947 + 1.161590I
b = 0.618295 − 1.048920I
−7.16565 − 3.70405I 2.35407 + 4.32771I
u = 1.095450 − 0.502626I
a = −0.470827 − 0.084074I
b = −0.488587 − 0.835280I
−7.16565 − 3.70405I 2.35407 + 4.32771I
u = −0.142250 + 0.744211I
a = 0.09725 + 1.93007I
b = 0.049028 − 0.916961I
3.43402 + 2.58613I 11.44299 + 4.06566I
u = −0.142250 + 0.744211I
a = −0.61783 + 2.45056I
b = −0.58927 + 1.78427I
3.43402 + 2.58613I 11.44299 + 4.06566I
u = −0.142250 − 0.744211I
a = 0.09725 − 1.93007I
b = 0.049028 + 0.916961I
3.43402 − 2.58613I 11.44299 − 4.06566I
u = −0.142250 − 0.744211I
a = −0.61783 − 2.45056I
b = −0.58927 − 1.78427I
3.43402 − 2.58613I 11.44299 − 4.06566I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.090470 + 1.253630I
a = −0.06412 + 1.46745I
b = −0.115968 − 0.899494I
−8.29442 − 4.34943I 0.89531 + 3.74757I
u = −0.090470 + 1.253630I
a = 1.74640 + 0.64289I
b = 1.18233 + 1.13631I
−8.29442 − 4.34943I 0.89531 + 3.74757I
u = −0.090470 − 1.253630I
a = −0.06412 − 1.46745I
b = −0.115968 + 0.899494I
−8.29442 + 4.34943I 0.89531 − 3.74757I
u = −0.090470 − 1.253630I
a = 1.74640 − 0.64289I
b = 1.18233 − 1.13631I
−8.29442 + 4.34943I 0.89531 − 3.74757I
u = −1.26849
a = 0.230653
b = −0.852852
2.30693 28.4360
u = −1.26849
a = 0.196338
b = −0.385079
2.30693 28.4360
u = −0.677112 + 1.125090I
a = −0.764175 + 0.376765I
b = −0.377246 − 0.617872I
−0.52839 − 6.36999I 1.14515 + 6.74051I
u = −0.677112 + 1.125090I
a = 1.60738 − 0.40721I
b = 1.21405 + 1.07055I
−0.52839 − 6.36999I 1.14515 + 6.74051I
u = −0.677112 − 1.125090I
a = −0.764175 − 0.376765I
b = −0.377246 + 0.617872I
−0.52839 + 6.36999I 1.14515 − 6.74051I
u = −0.677112 − 1.125090I
a = 1.60738 + 0.40721I
b = 1.21405 − 1.07055I
−0.52839 + 6.36999I 1.14515 − 6.74051I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.049518 + 0.613513I
a = −0.907524 + 0.658486I
b = −0.87857 + 1.19281I
−5.67553 + 3.93539I −9.4979 + 11.8109I
u = 0.049518 + 0.613513I
a = −1.64771 − 5.89429I
b = 0.227048 − 0.081503I
−5.67553 + 3.93539I −9.4979 + 11.8109I
u = 0.049518 − 0.613513I
a = −0.907524 − 0.658486I
b = −0.87857 − 1.19281I
−5.67553 − 3.93539I −9.4979 − 11.8109I
u = 0.049518 − 0.613513I
a = −1.64771 + 5.89429I
b = 0.227048 + 0.081503I
−5.67553 − 3.93539I −9.4979 − 11.8109I
u = −0.16128 + 1.41870I
a = 1.180970 − 0.553333I
b = 1.32141 − 0.71293I
−6.12566 − 3.25269I −3.16655 + 3.11297I
u = −0.16128 + 1.41870I
a = −1.37512 − 0.36081I
b = −0.971370 − 0.717911I
−6.12566 − 3.25269I −3.16655 + 3.11297I
u = −0.16128 − 1.41870I
a = 1.180970 + 0.553333I
b = 1.32141 + 0.71293I
−6.12566 + 3.25269I −3.16655 − 3.11297I
u = −0.16128 − 1.41870I
a = −1.37512 + 0.36081I
b = −0.971370 + 0.717911I
−6.12566 + 3.25269I −3.16655 − 3.11297I
u = 0.05510 + 1.46225I
a = 0.472581 + 0.499684I
b = 0.70443 + 2.04752I
1.07479 − 2.86382I −12.3628 + 23.0516I
u = 0.05510 + 1.46225I
a = −0.189090 − 0.602766I
b = −0.162985 − 0.304673I
1.07479 − 2.86382I −12.3628 + 23.0516I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.05510 − 1.46225I
a = 0.472581 − 0.499684I
b = 0.70443 − 2.04752I
1.07479 + 2.86382I −12.3628 − 23.0516I
u = 0.05510 − 1.46225I
a = −0.189090 + 0.602766I
b = −0.162985 + 0.304673I
1.07479 + 2.86382I −12.3628 − 23.0516I
u = 0.44488 + 1.48430I
a = −0.867276 − 0.593478I
b = −1.32121 − 1.02142I
−13.2038 + 9.0749I −2.66244 − 5.61588I
u = 0.44488 + 1.48430I
a = 1.43997 − 0.08489I
b = 0.924432 − 0.900718I
−13.2038 + 9.0749I −2.66244 − 5.61588I
u = 0.44488 − 1.48430I
a = −0.867276 + 0.593478I
b = −1.32121 + 1.02142I
−13.2038 − 9.0749I −2.66244 + 5.61588I
u = 0.44488 − 1.48430I
a = 1.43997 + 0.08489I
b = 0.924432 + 0.900718I
−13.2038 − 9.0749I −2.66244 + 5.61588I
u = 0.64125 + 1.73933I
a = −1.024150 − 0.259987I
b = −1.07899 + 1.46931I
−10.35020 + 5.69632I −2.22637 − 12.15089I
u = 0.64125 + 1.73933I
a = 0.571747 − 0.130860I
b = 0.482247 − 0.430599I
−10.35020 + 5.69632I −2.22637 − 12.15089I
u = 0.64125 − 1.73933I
a = −1.024150 + 0.259987I
b = −1.07899 − 1.46931I
−10.35020 − 5.69632I −2.22637 + 12.15089I
u = 0.64125 − 1.73933I
a = 0.571747 + 0.130860I
b = 0.482247 + 0.430599I
−10.35020 − 5.69632I −2.22637 + 12.15089I
16
III. I
u
3
= h−31u
15
a − 25u
15
+ · · · + 35a + 221, 344u
15
a + 659u
15
+ · · · +
206a + 177, u
16
+ u
15
+ · · · − 3u + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
9
=
a
0.373494au
15
+ 0.301205u
15
+ ··· − 0.421687a − 2.66265
a
12
=
u
u
a
3
=
1.07229au
15
+ 2.83133u
15
+ ··· + 0.240964a − 2.22892
0.385542au
15
+ 2.15663u
15
+ ··· + 0.951807a − 0.144578
a
6
=
−0.433735au
15
− 0.337349u
15
+ ··· + 0.554217a + 4.54217
−0.0120482au
15
− 0.578313u
15
+ ··· − 0.373494a + 3.07229
a
7
=
−0.421687au
15
− 0.915663u
15
+ ··· + 0.927711a + 5.61446
−1.15663u
15
+ 0.590361u
14
+ ··· − 14.9157u + 4.14458
a
2
=
0.590361au
15
− 2.83133u
15
+ ··· − 1.69880a − 1.77108
0.493976au
15
− 3.09639u
15
+ ··· + 0.313253a − 0.987952
a
1
=
−0.108434au
15
− 4.97590u
15
+ ··· − 1.36145a − 0.253012
−0.0120482au
15
− 5.25301u
15
+ ··· − 0.373494a − 0.843373
a
8
=
0.373494au
15
+ 0.301205u
15
+ ··· + 0.578313a − 2.66265
0.469880au
15
+ 0.0240964u
15
+ ··· − 0.433735a − 3.25301
a
10
=
−0.771084au
15
+ 4.68675u
15
+ ··· + 1.09639a + 4.28916
−0.397590au
15
+ 4.10843u
15
+ ··· + 0.674699a + 6.36145
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1698
83
u
15
−
1338
83
u
14
+ ··· −
7092
83
u +
1810
83
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
16
− 18u
15
+ ··· − 1341u + 137)
2
c
2
, c
7
u
32
+ 18u
30
+ ··· + 1341u
2
+ 137
c
3
, c
6
u
32
+ 10u
30
+ ··· − 5u + 1
c
4
(u
16
+ u
15
+ ··· − 3u + 1)
2
c
5
, c
12
u
32
+ 3u
31
+ ··· − 5u + 1
c
8
, c
10
u
32
− u
31
+ ··· + 6u + 1
c
9
(u
16
+ 3u
15
+ ··· + 6u + 1)
2
c
11
(u
16
− u
15
+ ··· + 3u + 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
16
− 22y
15
+ ··· − 119209y + 18769)
2
c
2
, c
7
(y
16
+ 18y
15
+ ··· + 1341y + 137)
2
c
3
, c
6
y
32
+ 20y
31
+ ··· + 7y + 1
c
4
, c
11
(y
16
+ 13y
15
+ ··· + 3y + 1)
2
c
5
, c
12
y
32
− 15y
31
+ ··· − 7y + 1
c
8
, c
10
y
32
+ 23y
31
+ ··· + 88y + 1
c
9
(y
16
+ 3y
15
+ ··· − 34y + 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.556603 + 0.962832I
a = −0.921213 + 0.873113I
b = −0.556179 − 0.810448I
−0.34455 − 7.61065I 2.72263 + 12.25164I
u = −0.556603 + 0.962832I
a = 1.99886 − 0.42635I
b = 1.33582 + 0.99706I
−0.34455 − 7.61065I 2.72263 + 12.25164I
u = −0.556603 − 0.962832I
a = −0.921213 − 0.873113I
b = −0.556179 + 0.810448I
−0.34455 + 7.61065I 2.72263 − 12.25164I
u = −0.556603 − 0.962832I
a = 1.99886 + 0.42635I
b = 1.33582 − 0.99706I
−0.34455 + 7.61065I 2.72263 − 12.25164I
u = −0.032016 + 0.840954I
a = −0.23090 − 1.77242I
b = 0.027959 + 0.915232I
3.19292 − 2.96309I 1.98102 + 10.21006I
u = −0.032016 + 0.840954I
a = 0.92188 + 2.20234I
b = 0.56258 + 1.78858I
3.19292 − 2.96309I 1.98102 + 10.21006I
u = −0.032016 − 0.840954I
a = −0.23090 + 1.77242I
b = 0.027959 − 0.915232I
3.19292 + 2.96309I 1.98102 − 10.21006I
u = −0.032016 − 0.840954I
a = 0.92188 − 2.20234I
b = 0.56258 − 1.78858I
3.19292 + 2.96309I 1.98102 − 10.21006I
u = 0.544906 + 1.049820I
a = 0.287957 + 0.363174I
b = 0.006775 − 0.889582I
−0.05029 + 4.99288I 0.71952 − 1.67343I
u = 0.544906 + 1.049820I
a = −1.97600 − 0.24657I
b = −1.10287 + 1.01226I
−0.05029 + 4.99288I 0.71952 − 1.67343I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.544906 − 1.049820I
a = 0.287957 − 0.363174I
b = 0.006775 + 0.889582I
−0.05029 − 4.99288I 0.71952 + 1.67343I
u = 0.544906 − 1.049820I
a = −1.97600 + 0.24657I
b = −1.10287 − 1.01226I
−0.05029 − 4.99288I 0.71952 + 1.67343I
u = −0.738779 + 0.964356I
a = −0.161973 + 0.577107I
b = −1.07374 + 1.16087I
0.01374 + 2.63681I −0.70539 − 8.14668I
u = −0.738779 + 0.964356I
a = 0.023043 − 0.296668I
b = 0.534888 − 0.314296I
0.01374 + 2.63681I −0.70539 − 8.14668I
u = −0.738779 − 0.964356I
a = −0.161973 − 0.577107I
b = −1.07374 − 1.16087I
0.01374 − 2.63681I −0.70539 + 8.14668I
u = −0.738779 − 0.964356I
a = 0.023043 + 0.296668I
b = 0.534888 + 0.314296I
0.01374 − 2.63681I −0.70539 + 8.14668I
u = 0.722184
a = −0.487742 + 0.463178I
b = 0.449383 − 0.847051I
1.92817 3.78580
u = 0.722184
a = −0.487742 − 0.463178I
b = 0.449383 + 0.847051I
1.92817 3.78580
u = 0.136011 + 0.607857I
a = −1.36599 + 0.53681I
b = −0.93420 + 1.21513I
−5.56489 + 4.12492I 9.2470 − 19.2793I
u = 0.136011 + 0.607857I
a = −1.06074 − 6.14319I
b = −0.257378 + 0.378958I
−5.56489 + 4.12492I 9.2470 − 19.2793I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.136011 − 0.607857I
a = −1.36599 − 0.53681I
b = −0.93420 − 1.21513I
−5.56489 − 4.12492I 9.2470 + 19.2793I
u = 0.136011 − 0.607857I
a = −1.06074 + 6.14319I
b = −0.257378 − 0.378958I
−5.56489 − 4.12492I 9.2470 + 19.2793I
u = 0.05735 + 1.46100I
a = −0.545524 + 0.413626I
b = −0.58434 + 2.07725I
1.19502 + 2.75460I 23.2685 + 8.6216I
u = 0.05735 + 1.46100I
a = −0.291458 + 0.552110I
b = −0.069545 + 0.362058I
1.19502 + 2.75460I 23.2685 + 8.6216I
u = 0.05735 − 1.46100I
a = −0.545524 − 0.413626I
b = −0.58434 − 2.07725I
1.19502 − 2.75460I 23.2685 − 8.6216I
u = 0.05735 − 1.46100I
a = −0.291458 − 0.552110I
b = −0.069545 − 0.362058I
1.19502 − 2.75460I 23.2685 − 8.6216I
u = −0.47311 + 1.43893I
a = 0.915192 + 0.209522I
b = 0.341050 + 0.024825I
−10.24790 − 4.86155I −1.48108 + 2.42981I
u = −0.47311 + 1.43893I
a = 1.43526 − 0.27129I
b = 1.00180 + 1.04133I
−10.24790 − 4.86155I −1.48108 + 2.42981I
u = −0.47311 − 1.43893I
a = 0.915192 − 0.209522I
b = 0.341050 − 0.024825I
−10.24790 + 4.86155I −1.48108 − 2.42981I
u = −0.47311 − 1.43893I
a = 1.43526 + 0.27129I
b = 1.00180 − 1.04133I
−10.24790 + 4.86155I −1.48108 − 2.42981I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.402310
a = −1.54065 + 1.12231I
b = 0.318004 − 0.977732I
1.94453 5.70980
u = 0.402310
a = −1.54065 − 1.12231I
b = 0.318004 + 0.977732I
1.94453 5.70980
23
IV.
I
u
4
= hu
4
−2u
3
+2u
2
+b −2u, u
4
−u
3
+a +u − 2, u
5
−2u
4
+3u
3
−3u
2
+u −1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
9
=
−u
4
+ u
3
− u + 2
−u
4
+ 2u
3
− 2u
2
+ 2u
a
12
=
u
u
a
3
=
u
4
− 2u
3
+ 3u
2
− 2u
−u
3
+ 2u
2
− 2u + 1
a
6
=
−u
4
+ u
3
− u
2
+ 2
−u
4
+ 2u
3
− 3u
2
+ 2u
a
7
=
−u
4
+ 2u
3
− 2u
2
+ u + 1
−u
4
+ 3u
3
− 4u
2
+ 3u − 1
a
2
=
u
4
− 2u
3
+ 3u
2
− 2u
−u
3
+ 2u
2
− 2u + 1
a
1
=
u
4
− 2u
3
+ 3u
2
− 2u
−u
3
+ 2u
2
− 2u + 1
a
8
=
−u
4
+ 2u
3
− 2u
2
+ u + 1
−u
4
+ 3u
3
− 4u
2
+ 3u − 1
a
10
=
−u
4
+ 3u
3
− 4u
2
+ 4u − 2
u
3
− u
2
+ 2u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7u
4
+ 13u
3
− 25u
2
+ 15u − 9
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
5
c
3
, c
6
u
5
− u
3
+ u
2
+ u − 1
c
4
u
5
− 2u
4
+ 3u
3
− 3u
2
+ u − 1
c
5
, c
12
u
5
− u
4
− u
3
+ u
2
− 1
c
8
, c
10
u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ 3u + 1
c
9
u
5
− 3u
4
+ 5u
3
− 4u
2
+ 3u − 1
c
11
u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
5
c
3
, c
6
y
5
− 2y
4
+ 3y
3
− 3y
2
+ 3y −1
c
4
, c
11
y
5
+ 2y
4
− y
3
− 7y
2
− 5y −1
c
5
, c
12
y
5
− 3y
4
+ 3y
3
− 3y
2
+ 2y −1
c
8
, c
10
y
5
+ 2y
4
+ 3y
3
+ 5y
2
+ 3y −1
c
9
y
5
+ y
4
+ 7y
3
+ 8y
2
+ y −1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.372466 + 1.263920I
a = −1.347300 − 0.010044I
b = −1.045750 + 0.405588I
−3.01018 + 5.17259I 1.83188 − 4.76077I
u = 0.372466 − 1.263920I
a = −1.347300 + 0.010044I
b = −1.045750 − 0.405588I
−3.01018 − 5.17259I 1.83188 + 4.76077I
u = 1.33263
a = −0.119827
b = 0.692872
2.14584 −24.7190
u = −0.038780 + 0.656277I
a = 1.90721 − 0.97967I
b = 0.699311 + 0.811268I
0.29233 − 3.70382I 0.52749 + 7.17476I
u = −0.038780 − 0.656277I
a = 1.90721 + 0.97967I
b = 0.699311 − 0.811268I
0.29233 + 3.70382I 0.52749 − 7.17476I
27
V. I
v
1
= ha, b
2
− b + 1, v + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
−1
0
a
5
=
1
0
a
9
=
0
b
a
12
=
−1
0
a
3
=
1
−b + 1
a
6
=
b
b
a
7
=
0
b
a
2
=
1
0
a
1
=
b
b
a
8
=
b
b
a
10
=
−1
b − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4b − 2
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
c
10
u
2
+ u + 1
c
4
, c
11
u
2
c
5
, c
9
, c
12
u
2
− u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
12
y
2
+ y + 1
c
4
, c
11
y
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 0.500000 + 0.866025I
− 2.02988I 0. + 3.46410I
v = −1.00000
a = 0
b = 0.500000 − 0.866025I
2.02988I 0. − 3.46410I
31
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
5
(u
2
+ u + 1)(u
16
− 18u
15
+ ··· − 1341u + 137)
2
· ((u
25
+ 30u
24
+ ··· + 180u − 81)
2
)(u
37
+ 44u
36
+ ··· − 9216u − 4096)
c
2
, c
7
u
5
(u
2
+ u + 1)(u
25
+ 15u
23
+ ··· + 60u − 9)
2
· (u
32
+ 18u
30
+ ··· + 1341u
2
+ 137)(u
37
− 4u
36
+ ··· + 288u − 64)
c
3
, c
6
(u
2
+ u + 1)(u
5
− u
3
+ u
2
+ u − 1)(u
32
+ 10u
30
+ ··· − 5u + 1)
· (u
37
− u
36
+ ··· − 4u − 1)(u
50
− u
49
+ ··· − 3u + 1)
c
4
u
2
(u
5
− 2u
4
+ ··· + u − 1)(u
16
+ u
15
+ ··· − 3u + 1)
2
· ((u
25
+ 2u
24
+ ··· − 30u − 28)
2
)(u
37
− 5u
36
+ ··· + 135u − 216)
c
5
, c
12
(u
2
− u + 1)(u
5
− u
4
− u
3
+ u
2
− 1)(u
32
+ 3u
31
+ ··· − 5u + 1)
· (u
37
+ 2u
36
+ ··· + 55u − 13)(u
50
+ 10u
49
+ ··· − 20945u + 3023)
c
8
, c
10
(u
2
+ u + 1)(u
5
+ 2u
4
+ ··· + 3u + 1)(u
32
− u
31
+ ··· + 6u + 1)
· (u
37
− 3u
36
+ ··· + 2158u − 419)(u
50
+ 2u
49
+ ··· − 14284u + 311)
c
9
(u
2
− u + 1)(u
5
− 3u
4
+ ··· + 3u − 1)(u
16
+ 3u
15
+ ··· + 6u + 1)
2
· ((u
25
+ 5u
24
+ ··· − 12u + 8)
2
)(u
37
− 9u
36
+ ··· + 352u + 128)
c
11
u
2
(u
5
+ 2u
4
+ ··· + u + 1)(u
16
− u
15
+ ··· + 3u + 1)
2
· ((u
25
+ 2u
24
+ ··· − 30u − 28)
2
)(u
37
− 5u
36
+ ··· + 135u − 216)
32
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
5
(y
2
+ y + 1)(y
16
− 22y
15
+ ··· − 119209y + 18769)
2
· (y
25
− 62y
24
+ ··· + 1407132y −6561)
2
· (y
37
− 92y
36
+ ··· + 5631901696y −16777216)
c
2
, c
7
y
5
(y
2
+ y + 1)(y
16
+ 18y
15
+ ··· + 1341y + 137)
2
· ((y
25
+ 30y
24
+ ··· + 180y −81)
2
)(y
37
+ 44y
36
+ ··· − 9216y −4096)
c
3
, c
6
(y
2
+ y + 1)(y
5
− 2y
4
+ ··· + 3y −1)(y
32
+ 20y
31
+ ··· + 7y + 1)
· (y
37
− 3y
36
+ ··· + 26y −1)(y
50
+ 21y
49
+ ··· − 13y + 1)
c
4
, c
11
y
2
(y
5
+ 2y
4
+ ··· − 5y −1)(y
16
+ 13y
15
+ ··· + 3y + 1)
2
· (y
25
+ 24y
24
+ ··· − 12596y −784)
2
· (y
37
+ 25y
36
+ ··· − 40095y −46656)
c
5
, c
12
(y
2
+ y + 1)(y
5
− 3y
4
+ ··· + 2y −1)(y
32
− 15y
31
+ ··· − 7y + 1)
· (y
37
+ 30y
36
+ ··· − 4593y −169)
· (y
50
− 8y
49
+ ··· − 156235997y + 9138529)
c
8
, c
10
(y
2
+ y + 1)(y
5
+ 2y
4
+ ··· + 3y −1)(y
32
+ 23y
31
+ ··· + 88y + 1)
· (y
37
− 47y
36
+ ··· + 2060002y −175561)
· (y
50
+ 12y
49
+ ··· − 46687804y + 96721)
c
9
(y
2
+ y + 1)(y
5
+ y
4
+ ··· + y −1)(y
16
+ 3y
15
+ ··· − 34y + 1)
2
· (y
25
+ 13y
24
+ ··· − 752y −64)
2
· (y
37
+ y
36
+ ··· − 232448y −16384)
33
