12n
0745
(K12n
0745
)
A knot diagram
1
Linearized knot diagam
4 12 8 9 12 2 11 1 2 8 7 5
Solving Sequence
5,9 1,4
2 10 8 3 12 6 7 11
c
4
c
1
c
9
c
8
c
3
c
12
c
5
c
6
c
11
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.72392 × 10
20
u
31
− 1.85563 × 10
20
u
30
+ ··· + 1.12162 × 10
21
b + 1.59649 × 10
21
, a − 1,
u
32
− u
30
+ ··· − 2u + 1i
I
u
2
= h−1.04878 × 10
64
u
47
− 4.13535 × 10
64
u
46
+ ··· + 4.36700 × 10
65
b + 2.54209 × 10
65
,
− 6.42157 × 10
113
u
47
− 2.04396 × 10
114
u
46
+ ··· + 2.06184 × 10
114
a − 4.26495 × 10
114
,
u
48
+ 3u
47
+ ··· − 8u + 4i
I
u
3
= h−4169u
17
− 110u
16
+ ··· + 1711b + 2133, a + 1, u
18
+ 4u
16
+ ··· − u + 1i
* 3 irreducible components of dim
C
= 0, with total 98 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−7.72 × 10
20
u
31
− 1.86 × 10
20
u
30
+ · · · + 1.12 × 10
21
b + 1.60 ×
10
21
, a − 1, u
32
− u
30
+ · · · − 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
1
0.688642u
31
+ 0.165443u
30
+ ··· + 2.18437u − 1.42339
a
4
=
1
u
2
a
2
=
−0.688642u
31
− 0.165443u
30
+ ··· − 2.18437u + 2.42339
0.608785u
31
+ 0.235945u
30
+ ··· + 2.54213u − 1.25794
a
10
=
0.678532u
31
+ 0.284449u
30
+ ··· + 1.99493u − 1.92526
−0.695736u
31
− 0.103896u
30
+ ··· − 2.15066u + 0.952167
a
8
=
−u
−0.165443u
31
− 0.0798571u
30
+ ··· + 1.04610u + 0.688642
a
3
=
−0.0798571u
31
+ 0.0705021u
30
+ ··· + 0.357757u + 1.16544
0.220463u
31
− 0.127057u
30
+ ··· − 0.347333u − 0.749034
a
12
=
−0.688642u
31
− 0.165443u
30
+ ··· − 2.18437u + 2.42339
0.688642u
31
+ 0.165443u
30
+ ··· + 2.18437u − 1.42339
a
6
=
−1.07690u
31
− 0.654094u
30
+ ··· − 8.58223u + 0.101317
0.388260u
31
+ 0.488651u
30
+ ··· + 6.39786u + 2.32207
a
7
=
−0.390513u
31
− 0.541351u
30
+ ··· − 6.51468u − 1.02957
0.00795809u
31
+ 0.188677u
30
+ ··· + 3.52208u + 2.59118
a
11
=
0.657110u
31
+ 0.487486u
30
+ ··· + 2.71903u − 2.58761
−1.04986u
31
− 0.281223u
30
+ ··· − 4.71166u + 1.64877
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
5229796107208695447003
1121615042862392489704
u
31
−
715184273316583329535
1121615042862392489704
u
30
+ ··· −
8046640764422946709729
1121615042862392489704
u +
1349461904188813944858
140201880357799061213
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
32
− 20u
31
+ ··· − 30u + 4
c
2
, c
6
u
32
+ 3u
31
+ ··· + 4u + 1
c
3
, c
9
u
32
− u
31
+ ··· − 4u + 1
c
4
, c
8
u
32
− u
30
+ ··· − 2u + 1
c
5
, c
12
u
32
− 22u
31
+ ··· − 65536u + 4096
c
7
, c
10
, c
11
u
32
+ 9u
31
+ ··· + 84u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
+ 6y
31
+ ··· + 52y + 16
c
2
, c
6
y
32
+ 31y
31
+ ··· + 16y + 1
c
3
, c
9
y
32
+ 3y
31
+ ··· + 28y + 1
c
4
, c
8
y
32
− 2y
31
+ ··· − 6y + 1
c
5
, c
12
y
32
+ 20y
31
+ ··· − 58720256y + 16777216
c
7
, c
10
, c
11
y
32
+ 29y
31
+ ··· + 976y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.854141 + 0.589787I
a = 1.00000
b = 1.61917 − 0.24070I
1.65554 + 9.31216I 1.84214 − 8.38213I
u = 0.854141 − 0.589787I
a = 1.00000
b = 1.61917 + 0.24070I
1.65554 − 9.31216I 1.84214 + 8.38213I
u = −0.681898 + 0.783221I
a = 1.00000
b = 1.05126 − 1.11867I
−2.14431 − 0.79389I −0.82722 + 2.16238I
u = −0.681898 − 0.783221I
a = 1.00000
b = 1.05126 + 1.11867I
−2.14431 + 0.79389I −0.82722 − 2.16238I
u = −0.890039 + 0.585697I
a = 1.00000
b = 1.43226 + 0.19100I
6.67694 − 4.51179I 6.15098 + 5.45447I
u = −0.890039 − 0.585697I
a = 1.00000
b = 1.43226 − 0.19100I
6.67694 + 4.51179I 6.15098 − 5.45447I
u = 0.916035 + 0.550973I
a = 1.00000
b = 1.219860 − 0.165666I
3.73962 − 0.48491I 4.20188 − 0.50541I
u = 0.916035 − 0.550973I
a = 1.00000
b = 1.219860 + 0.165666I
3.73962 + 0.48491I 4.20188 + 0.50541I
u = 0.431637 + 0.743730I
a = 1.00000
b = 0.92824 + 1.35316I
1.65395 + 4.46956I 0.48829 − 7.44725I
u = 0.431637 − 0.743730I
a = 1.00000
b = 0.92824 − 1.35316I
1.65395 − 4.46956I 0.48829 + 7.44725I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.024610 + 0.504956I
a = 1.00000
b = 0.533957 + 0.881464I
−1.70935 + 1.94531I −0.00275 − 3.34094I
u = 1.024610 − 0.504956I
a = 1.00000
b = 0.533957 − 0.881464I
−1.70935 − 1.94531I −0.00275 + 3.34094I
u = −0.777247 + 0.867459I
a = 1.00000
b = 0.179266 − 0.950489I
−1.94782 − 2.84531I −1.95741 + 3.32411I
u = −0.777247 − 0.867459I
a = 1.00000
b = 0.179266 + 0.950489I
−1.94782 + 2.84531I −1.95741 − 3.32411I
u = −0.283223 + 0.764433I
a = 1.00000
b = 1.02191 − 1.47989I
−2.68020 − 8.65463I −5.91760 + 9.44360I
u = −0.283223 − 0.764433I
a = 1.00000
b = 1.02191 + 1.47989I
−2.68020 + 8.65463I −5.91760 − 9.44360I
u = −0.809344 + 0.018130I
a = 1.00000
b = 0.415210 + 0.522569I
−1.03206 + 2.11233I 2.04339 − 4.47982I
u = −0.809344 − 0.018130I
a = 1.00000
b = 0.415210 − 0.522569I
−1.03206 − 2.11233I 2.04339 + 4.47982I
u = 0.659843 + 0.411748I
a = 1.00000
b = 0.448371 + 0.082927I
1.117840 + 0.605282I 7.12622 − 1.99848I
u = 0.659843 − 0.411748I
a = 1.00000
b = 0.448371 − 0.082927I
1.117840 − 0.605282I 7.12622 + 1.99848I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.561882 + 0.315219I
a = 1.00000
b = 0.234400 − 1.066140I
−1.17379 − 1.66385I −1.34708 + 4.23096I
u = −0.561882 − 0.315219I
a = 1.00000
b = 0.234400 + 1.066140I
−1.17379 + 1.66385I −1.34708 − 4.23096I
u = 0.92006 + 1.19321I
a = 1.00000
b = 0.11932 + 1.69118I
−11.89360 + 4.45420I 10.94466 + 4.53535I
u = 0.92006 − 1.19321I
a = 1.00000
b = 0.11932 − 1.69118I
−11.89360 − 4.45420I 10.94466 − 4.53535I
u = −1.06882 + 1.12604I
a = 1.00000
b = 0.64807 − 1.43272I
−0.30085 − 6.14505I 2.00000 + 4.65224I
u = −1.06882 − 1.12604I
a = 1.00000
b = 0.64807 + 1.43272I
−0.30085 + 6.14505I 2.00000 − 4.65224I
u = 1.08392 + 1.16200I
a = 1.00000
b = 0.74928 + 1.40670I
2.88862 + 11.98220I 2.00000 − 7.44446I
u = 1.08392 − 1.16200I
a = 1.00000
b = 0.74928 − 1.40670I
2.88862 − 11.98220I 2.00000 + 7.44446I
u = −1.07590 + 1.18845I
a = 1.00000
b = 0.80706 − 1.39926I
−1.9477 − 17.3570I 0. + 9.21229I
u = −1.07590 − 1.18845I
a = 1.00000
b = 0.80706 + 1.39926I
−1.9477 + 17.3570I 0. − 9.21229I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.258111 + 0.252796I
a = 1.00000
b = −0.40763 + 2.09525I
−7.70724 + 1.01308I 5.62144 − 11.03014I
u = 0.258111 − 0.252796I
a = 1.00000
b = −0.40763 − 2.09525I
−7.70724 − 1.01308I 5.62144 + 11.03014I
8
II. I
u
2
= h−1.05 × 10
64
u
47
− 4.14 × 10
64
u
46
+ · · · + 4.37 × 10
65
b + 2.54 ×
10
65
, −6.42 × 10
113
u
47
− 2.04 × 10
114
u
46
+ · · · + 2.06 × 10
114
a − 4.26 ×
10
114
, u
48
+ 3u
47
+ · · · − 8u + 4i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
0.311449u
47
+ 0.991329u
46
+ ··· + 0.847152u + 2.06852
0.0240161u
47
+ 0.0946955u
46
+ ··· − 0.639391u − 0.582113
a
4
=
1
u
2
a
2
=
0.278120u
47
+ 0.883581u
46
+ ··· + 0.696600u + 2.42270
0.0496330u
47
+ 0.175946u
46
+ ··· − 0.568159u − 0.551070
a
10
=
−0.735175u
47
− 1.98945u
46
+ ··· + 26.4077u − 1.01077
0.198693u
47
+ 0.565009u
46
+ ··· + 0.667493u − 0.561155
a
8
=
−0.516499u
47
− 1.38596u
46
+ ··· + 19.5082u − 1.01728
0.217962u
47
+ 0.585339u
46
+ ··· + 2.47664u − 0.963807
a
3
=
0.307444u
47
+ 1.10182u
46
+ ··· − 6.60757u − 0.540466
−0.0564039u
47
− 0.210594u
46
+ ··· + 1.90700u − 1.45060
a
12
=
0.287433u
47
+ 0.896634u
46
+ ··· + 1.48654u + 2.65063
0.0240161u
47
+ 0.0946955u
46
+ ··· − 0.639391u − 0.582113
a
6
=
0.216936u
47
+ 0.846122u
46
+ ··· − 10.5723u + 0.131137
0.0240161u
47
+ 0.0946955u
46
+ ··· − 0.639391u + 0.417887
a
7
=
0.374374u
47
+ 1.21541u
46
+ ··· − 3.68521u + 8.14264
−0.0673151u
47
− 0.193492u
46
+ ··· − 0.803336u − 0.737240
a
11
=
−0.0696329u
47
− 0.0589159u
46
+ ··· + 6.42131u − 3.80302
0.118786u
47
+ 0.364650u
46
+ ··· − 1.74055u + 0.186064
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.487275u
47
− 1.61319u
46
+ ··· + 30.2781u − 4.18524
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
12
+ 5u
11
+ ··· + 3u
2
+ 1)
4
c
2
, c
6
u
48
− u
47
+ ··· + 188u + 304
c
3
, c
9
u
48
+ u
47
+ ··· − 972u + 432
c
4
, c
8
u
48
+ 3u
47
+ ··· − 8u + 4
c
5
, c
12
(u
2
+ u + 1)
24
c
7
, c
10
, c
11
(u
12
− 3u
11
+ ··· + 2u + 1)
4
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
12
+ y
11
+ ··· + 6y + 1)
4
c
2
, c
6
y
48
+ 15y
47
+ ··· + 4909520y + 92416
c
3
, c
9
y
48
+ 3y
47
+ ··· + 2702160y + 186624
c
4
, c
8
y
48
+ 15y
47
+ ··· + 264y + 16
c
5
, c
12
(y
2
+ y + 1)
24
c
7
, c
10
, c
11
(y
12
+ 9y
11
+ ··· − 6y + 1)
4
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.466251 + 0.940882I
a = −1.53047 + 0.34796I
b = −0.500000 − 0.866025I
−6.16619 + 4.56735I −8.43865 − 5.17685I
u = 0.466251 − 0.940882I
a = −1.53047 − 0.34796I
b = −0.500000 + 0.866025I
−6.16619 − 4.56735I −8.43865 + 5.17685I
u = −0.934419 + 0.170095I
a = −1.07506 + 1.58682I
b = −0.500000 + 0.866025I
0.55801 − 6.49071I 5.64801 + 8.19237I
u = −0.934419 − 0.170095I
a = −1.07506 − 1.58682I
b = −0.500000 − 0.866025I
0.55801 + 6.49071I 5.64801 − 8.19237I
u = 0.442095 + 0.991323I
a = −0.505636 − 0.363702I
b = −0.500000 − 0.866025I
−6.16619 − 0.50759I −8.43865 − 1.75135I
u = 0.442095 − 0.991323I
a = −0.505636 + 0.363702I
b = −0.500000 + 0.866025I
−6.16619 + 0.50759I −8.43865 + 1.75135I
u = −0.924979 + 0.574553I
a = 0.624586 − 1.242220I
b = −0.500000 − 0.866025I
−1.25303 − 4.19921I −2.04009 + 7.81755I
u = −0.924979 − 0.574553I
a = 0.624586 + 1.242220I
b = −0.500000 + 0.866025I
−1.25303 + 4.19921I −2.04009 − 7.81755I
u = 0.241577 + 1.064520I
a = −0.508209 + 0.077004I
b = −0.500000 + 0.866025I
−4.65197 + 3.37411I −4.52298 − 5.09926I
u = 0.241577 − 1.064520I
a = −0.508209 − 0.077004I
b = −0.500000 − 0.866025I
−4.65197 − 3.37411I −4.52298 + 5.09926I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.859240 + 0.201681I
a = −0.00624 + 2.08104I
b = −0.500000 + 0.866025I
3.58098 − 1.11020I 9.53074 − 3.71786I
u = 0.859240 − 0.201681I
a = −0.00624 − 2.08104I
b = −0.500000 − 0.866025I
3.58098 + 1.11020I 9.53074 + 3.71786I
u = −0.839585 + 0.875884I
a = −1.252350 + 0.217188I
b = −0.500000 + 0.866025I
−1.93740 − 5.36645I 0
u = −0.839585 − 0.875884I
a = −1.252350 − 0.217188I
b = −0.500000 − 0.866025I
−1.93740 + 5.36645I 0
u = −0.284359 + 0.711335I
a = −0.603734 + 0.347904I
b = −0.500000 − 0.866025I
−1.93740 − 1.30669I 3.82297 − 1.53987I
u = −0.284359 − 0.711335I
a = −0.603734 − 0.347904I
b = −0.500000 + 0.866025I
−1.93740 + 1.30669I 3.82297 + 1.53987I
u = 0.137007 + 0.662039I
a = −1.30336 − 0.93751I
b = −0.500000 + 0.866025I
−6.16619 + 0.50759I −8.43865 + 1.75135I
u = 0.137007 − 0.662039I
a = −1.30336 + 0.93751I
b = −0.500000 − 0.866025I
−6.16619 − 0.50759I −8.43865 − 1.75135I
u = −0.204744 + 0.522394I
a = −1.92353 + 0.29146I
b = −0.500000 − 0.866025I
−4.65197 − 3.37411I −4.52298 + 5.09926I
u = −0.204744 − 0.522394I
a = −1.92353 − 0.29146I
b = −0.500000 + 0.866025I
−4.65197 + 3.37411I −4.52298 − 5.09926I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.66481 + 1.27906I
a = −0.957832 − 0.374579I
b = −0.500000 + 0.866025I
−4.65197 − 7.43387I 0
u = −0.66481 − 1.27906I
a = −0.957832 + 0.374579I
b = −0.500000 − 0.866025I
−4.65197 + 7.43387I 0
u = −0.075799 + 0.528387I
a = −1.24345 + 0.71654I
b = −0.500000 + 0.866025I
−1.93740 + 1.30669I 3.82297 + 1.53987I
u = −0.075799 − 0.528387I
a = −1.24345 − 0.71654I
b = −0.500000 − 0.866025I
−1.93740 − 1.30669I 3.82297 − 1.53987I
u = 1.11589 + 0.97610I
a = −0.905536 − 0.354128I
b = −0.500000 − 0.866025I
−4.65197 + 7.43387I 0
u = 1.11589 − 0.97610I
a = −0.905536 + 0.354128I
b = −0.500000 + 0.866025I
−4.65197 − 7.43387I 0
u = 0.254089 + 0.445251I
a = 0.55945 + 4.05431I
b = −0.500000 − 0.866025I
−1.25303 + 8.25898I −2.0401 − 14.7458I
u = 0.254089 − 0.445251I
a = 0.55945 − 4.05431I
b = −0.500000 + 0.866025I
−1.25303 − 8.25898I −2.0401 + 14.7458I
u = 0.13599 + 1.50788I
a = 0.323082 + 0.642567I
b = −0.500000 − 0.866025I
−1.25303 − 4.19921I 0
u = 0.13599 − 1.50788I
a = 0.323082 − 0.642567I
b = −0.500000 + 0.866025I
−1.25303 + 4.19921I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.86123 + 1.27926I
a = −0.775182 + 0.134435I
b = −0.500000 − 0.866025I
−1.93740 + 5.36645I 0
u = 0.86123 − 1.27926I
a = −0.775182 − 0.134435I
b = −0.500000 + 0.866025I
−1.93740 − 5.36645I 0
u = −1.40081 + 0.77138I
a = −0.067526 − 0.143827I
b = −0.500000 − 0.866025I
0.55801 − 2.43094I 0
u = −1.40081 − 0.77138I
a = −0.067526 + 0.143827I
b = −0.500000 + 0.866025I
0.55801 + 2.43094I 0
u = −0.231026 + 0.304516I
a = −0.52387 − 5.30363I
b = −0.500000 + 0.866025I
3.58098 − 2.94957I 9.5307 + 10.6461I
u = −0.231026 − 0.304516I
a = −0.52387 + 5.30363I
b = −0.500000 − 0.866025I
3.58098 + 2.94957I 9.5307 − 10.6461I
u = −1.04097 + 1.27776I
a = −0.621280 + 0.141250I
b = −0.500000 + 0.866025I
−6.16619 − 4.56735I 0
u = −1.04097 − 1.27776I
a = −0.621280 − 0.141250I
b = −0.500000 − 0.866025I
−6.16619 + 4.56735I 0
u = 0.205537 + 0.149385I
a = −2.67472 + 5.69702I
b = −0.500000 − 0.866025I
0.55801 − 2.43094I 5.64801 + 1.26417I
u = 0.205537 − 0.149385I
a = −2.67472 − 5.69702I
b = −0.500000 + 0.866025I
0.55801 + 2.43094I 5.64801 − 1.26417I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.73464 + 1.66561I
a = −0.292633 + 0.431936I
b = −0.500000 − 0.866025I
0.55801 + 6.49071I 0
u = 0.73464 − 1.66561I
a = −0.292633 − 0.431936I
b = −0.500000 + 0.866025I
0.55801 − 6.49071I 0
u = −0.42507 + 1.78686I
a = −0.001442 − 0.480524I
b = −0.500000 + 0.866025I
3.58098 − 1.11020I 0
u = −0.42507 − 1.78686I
a = −0.001442 + 0.480524I
b = −0.500000 − 0.866025I
3.58098 + 1.11020I 0
u = 1.73607 + 1.06575I
a = −0.018444 + 0.186728I
b = −0.500000 + 0.866025I
3.58098 − 2.94957I 0
u = 1.73607 − 1.06575I
a = −0.018444 − 0.186728I
b = −0.500000 − 0.866025I
3.58098 + 2.94957I 0
u = −1.66304 + 1.27925I
a = 0.033399 − 0.242042I
b = −0.500000 − 0.866025I
−1.25303 + 8.25898I 0
u = −1.66304 − 1.27925I
a = 0.033399 + 0.242042I
b = −0.500000 + 0.866025I
−1.25303 − 8.25898I 0
16
III.
I
u
3
= h−4169u
17
− 110u
16
+ · · · + 1711b + 2133, a + 1, u
18
+ 4u
16
+ · · · − u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
−1
2.43659u
17
+ 0.0642899u
16
+ ··· + 11.6990u − 1.24664
a
4
=
1
u
2
a
2
=
−2.43659u
17
− 0.0642899u
16
+ ··· − 11.6990u + 0.246639
2.96259u
17
+ 0.0333139u
16
+ ··· + 14.0713u − 1.18235
a
10
=
0.904734u
17
+ 0.506721u
16
+ ··· + 7.40035u + 0.910579
−0.842198u
17
− 0.109293u
16
+ ··· − 8.98831u + 1.01929
a
8
=
−u
0.0642899u
17
− 0.526008u
16
+ ··· + 2.18995u − 2.43659
a
3
=
−0.526008u
17
+ 0.0309760u
16
+ ··· − 2.37230u + 0.935710
0.526008u
17
− 0.0309760u
16
+ ··· + 2.37230u − 0.935710
a
12
=
−2.43659u
17
− 0.0642899u
16
+ ··· − 11.6990u + 0.246639
2.43659u
17
+ 0.0642899u
16
+ ··· + 11.6990u − 1.24664
a
6
=
−0.473992u
17
− 1.03098u
16
+ ··· − 0.627703u − 6.93571
2.91058u
17
+ 1.09527u
16
+ ··· + 12.3267u + 6.68907
a
7
=
1.45587u
17
− 1.09351u
16
+ ··· + 9.25599u − 6.27762
0.0572764u
17
+ 1.16774u
16
+ ··· − 1.92168u + 7.02922
a
11
=
0.830508u
17
+ 0.932203u
16
+ ··· + 6.13559u + 2.42373
−1.92577u
17
− 0.425482u
16
+ ··· − 14.7352u + 0.486850
(ii) Obstruction class = 1
(iii) Cusp Shapes =
420
1711
u
17
−
3903
1711
u
16
+ ··· +
16951
1711
u −
58693
1711
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 11u
17
+ ··· + 2u
2
+ 1
c
2
, c
6
u
18
+ 3u
17
+ ··· − 3u + 1
c
3
, c
9
u
18
− u
17
+ ··· + 3u + 5
c
4
, c
8
u
18
+ 4u
16
+ ··· − u + 1
c
5
u
18
+ 3u
17
+ ··· + 16u + 5
c
7
u
18
+ 4u
17
+ ··· + 8u + 1
c
10
, c
11
u
18
− 4u
17
+ ··· − 8u + 1
c
12
u
18
− 3u
17
+ ··· − 16u + 5
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 5y
17
+ ··· + 4y + 1
c
2
, c
6
y
18
+ y
17
+ ··· − 15y + 1
c
3
, c
9
y
18
+ y
17
+ ··· − 139y + 25
c
4
, c
8
y
18
+ 8y
17
+ ··· + 19y + 1
c
5
, c
12
y
18
+ 19y
17
+ ··· + 104y + 25
c
7
, c
10
, c
11
y
18
+ 20y
17
+ ··· + 16y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.227222 + 0.933002I
a = −1.00000
b = −0.570402 + 0.267582I
−5.91735 + 2.24114I −9.01697 − 3.26604I
u = 0.227222 − 0.933002I
a = −1.00000
b = −0.570402 − 0.267582I
−5.91735 − 2.24114I −9.01697 + 3.26604I
u = 0.636335 + 0.689593I
a = −1.00000
b = 0.563137 − 0.791150I
−1.04432 − 7.37218I −0.40617 + 4.21110I
u = 0.636335 − 0.689593I
a = −1.00000
b = 0.563137 + 0.791150I
−1.04432 + 7.37218I −0.40617 − 4.21110I
u = −0.664732 + 0.842154I
a = −1.00000
b = 0.462994 + 0.821976I
3.31445 + 2.16551I 4.00255 − 1.37120I
u = −0.664732 − 0.842154I
a = −1.00000
b = 0.462994 − 0.821976I
3.31445 − 2.16551I 4.00255 + 1.37120I
u = 0.718055 + 1.007170I
a = −1.00000
b = 0.358244 − 0.932951I
−0.42782 + 3.41794I 3.16879 − 3.77825I
u = 0.718055 − 1.007170I
a = −1.00000
b = 0.358244 + 0.932951I
−0.42782 − 3.41794I 3.16879 + 3.77825I
u = −0.112765 + 0.658981I
a = −1.00000
b = −0.617520 − 0.993221I
−2.48715 − 1.52476I −12.11698 + 4.46390I
u = −0.112765 − 0.658981I
a = −1.00000
b = −0.617520 + 0.993221I
−2.48715 + 1.52476I −12.11698 − 4.46390I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.821490 + 1.131200I
a = −1.00000
b = −0.460000 + 0.702000I
−4.72724 − 6.31712I −4.50945 + 3.68152I
u = −0.821490 − 1.131200I
a = −1.00000
b = −0.460000 − 0.702000I
−4.72724 + 6.31712I −4.50945 − 3.68152I
u = 0.868208 + 1.108810I
a = −1.00000
b = −0.415489 − 1.012400I
−3.17492 + 5.22960I −4.69895 − 4.30954I
u = 0.868208 − 1.108810I
a = −1.00000
b = −0.415489 + 1.012400I
−3.17492 − 5.22960I −4.69895 + 4.30954I
u = −0.89808 + 1.21515I
a = −1.00000
b = −0.11100 + 1.63460I
−12.12290 − 4.59015I −15.2185 + 10.6507I
u = −0.89808 − 1.21515I
a = −1.00000
b = −0.11100 − 1.63460I
−12.12290 + 4.59015I −15.2185 − 10.6507I
u = 0.047242 + 0.417816I
a = −1.00000
b = −0.70996 + 2.08504I
−7.95638 + 0.90560I −22.2043 + 0.5995I
u = 0.047242 − 0.417816I
a = −1.00000
b = −0.70996 − 2.08504I
−7.95638 − 0.90560I −22.2043 − 0.5995I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
12
+ 5u
11
+ ··· + 3u
2
+ 1)
4
)(u
18
− 11u
17
+ ··· + 2u
2
+ 1)
· (u
32
− 20u
31
+ ··· − 30u + 4)
c
2
, c
6
(u
18
+ 3u
17
+ ··· − 3u + 1)(u
32
+ 3u
31
+ ··· + 4u + 1)
· (u
48
− u
47
+ ··· + 188u + 304)
c
3
, c
9
(u
18
− u
17
+ ··· + 3u + 5)(u
32
− u
31
+ ··· − 4u + 1)
· (u
48
+ u
47
+ ··· − 972u + 432)
c
4
, c
8
(u
18
+ 4u
16
+ ··· − u + 1)(u
32
− u
30
+ ··· − 2u + 1)
· (u
48
+ 3u
47
+ ··· − 8u + 4)
c
5
((u
2
+ u + 1)
24
)(u
18
+ 3u
17
+ ··· + 16u + 5)
· (u
32
− 22u
31
+ ··· − 65536u + 4096)
c
7
((u
12
− 3u
11
+ ··· + 2u + 1)
4
)(u
18
+ 4u
17
+ ··· + 8u + 1)
· (u
32
+ 9u
31
+ ··· + 84u + 16)
c
10
, c
11
((u
12
− 3u
11
+ ··· + 2u + 1)
4
)(u
18
− 4u
17
+ ··· − 8u + 1)
· (u
32
+ 9u
31
+ ··· + 84u + 16)
c
12
((u
2
+ u + 1)
24
)(u
18
− 3u
17
+ ··· − 16u + 5)
· (u
32
− 22u
31
+ ··· − 65536u + 4096)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
12
+ y
11
+ ··· + 6y + 1)
4
)(y
18
+ 5y
17
+ ··· + 4y + 1)
· (y
32
+ 6y
31
+ ··· + 52y + 16)
c
2
, c
6
(y
18
+ y
17
+ ··· − 15y + 1)(y
32
+ 31y
31
+ ··· + 16y + 1)
· (y
48
+ 15y
47
+ ··· + 4909520y + 92416)
c
3
, c
9
(y
18
+ y
17
+ ··· − 139y + 25)(y
32
+ 3y
31
+ ··· + 28y + 1)
· (y
48
+ 3y
47
+ ··· + 2702160y + 186624)
c
4
, c
8
(y
18
+ 8y
17
+ ··· + 19y + 1)(y
32
− 2y
31
+ ··· − 6y + 1)
· (y
48
+ 15y
47
+ ··· + 264y + 16)
c
5
, c
12
((y
2
+ y + 1)
24
)(y
18
+ 19y
17
+ ··· + 104y + 25)
· (y
32
+ 20y
31
+ ··· − 58720256y + 16777216)
c
7
, c
10
, c
11
((y
12
+ 9y
11
+ ··· − 6y + 1)
4
)(y
18
+ 20y
17
+ ··· + 16y + 1)
· (y
32
+ 29y
31
+ ··· + 976y + 256)
23
