12a
0230
(K12a
0230
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 11 2 1 12 4 8 5 10
Solving Sequence
8,12 5,9
4 11 6 10 1 7 3 2
c
8
c
4
c
11
c
5
c
10
c
12
c
7
c
3
c
2
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−11158891u
48
− 471894272u
47
+ ··· + 4194304b + 6878327209984,
− 79952981u
48
− 3436338262u
47
+ ··· + 8388608a − 448987463155712,
u
49
+ 44u
48
+ ··· + 201326592u + 8388608i
I
u
2
= h−3.30457 × 10
120
a
45
u + 1.96555 × 10
120
a
44
u + ··· + 2.43626 × 10
123
a − 4.32752 × 10
122
,
− a
45
u − 12a
44
u + ··· + 633a − 110, u
2
− u + 1i
I
u
3
= h−22u
23
− 61u
22
+ ··· + b + 41, −38u
23
− 111u
22
+ ··· + a + 59, u
24
+ 3u
23
+ ··· − 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 165 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−1.12 × 10
7
u
48
− 4.72 × 10
8
u
47
+ · · · + 4.19 × 10
6
b + 6.88 ×
10
12
, −8.00 × 10
7
u
48
− 3.44 × 10
9
u
47
+ · · · + 8.39 × 10
6
a − 4.49 ×
10
14
, u
49
+ 44u
48
+ · · · + 201326592u + 8388608i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
5
=
9.53114u
48
+ 409.643u
47
+ ··· + 1.27596 × 10
9
u + 5.35235 × 10
7
2.66049u
48
+ 112.508u
47
+ ··· − 1.29286 × 10
7
u − 1639921
a
9
=
1
−u
2
a
4
=
−0.195494u
48
− 11.2622u
47
+ ··· − 5.89390 × 10
8
u − 2.64295 × 10
7
5.17357u
48
+ 225.387u
47
+ ··· + 1.32808 × 10
9
u + 5.76352 × 10
7
a
11
=
−0.000244141u
48
− 0.0107422u
47
+ ··· − 48128u − 2047.50
−0.000488281u
48
− 0.0209961u
47
+ ··· − 49151.5u − 2048
a
6
=
14.0885u
48
+ 603.980u
47
+ ··· + 1.57173 × 10
9
u + 6.49774 × 10
7
−4.13982u
48
− 186.093u
47
+ ··· − 2.19280 × 10
9
u − 9.69151 × 10
7
a
10
=
0.000244141u
48
+ 0.0102539u
47
+ ··· + 1023.50u + 0.500000
−0.000488281u
48
− 0.0209961u
47
+ ··· − 49151.5u − 2048
a
1
=
−0.00219727u
48
− 0.0959473u
47
+ ··· − 386048.u − 16384
0.000732422u
48
+ 0.0346680u
47
+ ··· + 425985u + 18432
a
7
=
−0.0363770u
48
− 1.54468u
47
+ ··· − 1803264u − 70655
0.0534668u
48
+ 2.30933u
47
+ ··· + 7382016u + 311296
a
3
=
34.9112u
48
+ 1497.44u
47
+ ··· + 4.47944 × 10
9
u + 1.88451 × 10
8
−14.8198u
48
− 653.719u
47
+ ··· − 5.04287 × 10
9
u − 2.20698 × 10
8
a
2
=
13.8492u
48
+ 591.479u
47
+ ··· + 1.33993 × 10
9
u + 5.53213 × 10
7
−13.8870u
48
− 602.707u
47
+ ··· − 2.88876 × 10
9
u − 1.24329 × 10
8
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1939025
262144
u
48
+
175746237
524288
u
47
+ ··· + 4242276468u + 187028462
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
49
+ 24u
48
+ ··· + 108u − 16
c
2
, c
6
u
49
− 6u
48
+ ··· + 38u − 4
c
3
u
49
+ 6u
48
+ ··· − 2874u − 612
c
4
, c
5
, c
9
c
11
u
49
+ 17u
47
+ ··· + 2u − 1
c
7
u
49
− 30u
48
+ ··· + 42842u − 3676
c
8
u
49
− 44u
48
+ ··· + 201326592u − 8388608
c
10
, c
12
u
49
− 2u
48
+ ··· − 6u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
49
+ 4y
48
+ ··· + 26352y −256
c
2
, c
6
y
49
+ 24y
48
+ ··· + 108y −16
c
3
y
49
− 10y
48
+ ··· + 7605036y −374544
c
4
, c
5
, c
9
c
11
y
49
+ 34y
48
+ ··· + 12y
2
− 1
c
7
y
49
+ 16y
48
+ ··· + 484690764y −13512976
c
8
y
49
+ 14y
47
+ ··· + 140737488355328y −70368744177664
c
10
, c
12
y
49
− 14y
48
+ ··· + 32y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.878929 + 0.494546I
a = 0.534524 + 0.601733I
b = −0.037915 + 0.411539I
3.54777 − 3.28188I 0
u = −0.878929 − 0.494546I
a = 0.534524 − 0.601733I
b = −0.037915 − 0.411539I
3.54777 + 3.28188I 0
u = −0.865025 + 0.523898I
a = −0.562542 − 0.624626I
b = 0.018820 − 0.459526I
1.46395 − 8.18754I 0
u = −0.865025 − 0.523898I
a = −0.562542 + 0.624626I
b = 0.018820 + 0.459526I
1.46395 + 8.18754I 0
u = −0.955239 + 0.438408I
a = 0.432545 + 0.574512I
b = −0.127692 + 0.307642I
4.19521 − 1.27465I 0
u = −0.955239 − 0.438408I
a = 0.432545 − 0.574512I
b = −0.127692 − 0.307642I
4.19521 + 1.27465I 0
u = −0.791178 + 0.467861I
a = −0.606368 − 0.538508I
b = −0.086188 − 0.372058I
−0.734882 − 1.080480I 0
u = −0.791178 − 0.467861I
a = −0.606368 + 0.538508I
b = −0.086188 + 0.372058I
−0.734882 + 1.080480I 0
u = −1.014950 + 0.426931I
a = −0.366400 − 0.583109I
b = 0.195165 − 0.258541I
2.69787 + 3.43928I 0
u = −1.014950 − 0.426931I
a = −0.366400 + 0.583109I
b = 0.195165 + 0.258541I
2.69787 − 3.43928I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.086130 + 0.826479I
a = −0.707850 − 0.528651I
b = −0.900881 + 0.081531I
1.59244 − 0.95867I 0
u = −0.086130 − 0.826479I
a = −0.707850 + 0.528651I
b = −0.900881 − 0.081531I
1.59244 + 0.95867I 0
u = −1.195740 + 0.181382I
a = −0.121708 − 0.451777I
b = 0.138505 + 0.060157I
1.31700 − 1.83287I 0
u = −1.195740 − 0.181382I
a = −0.121708 + 0.451777I
b = 0.138505 − 0.060157I
1.31700 + 1.83287I 0
u = −0.280549 + 0.737409I
a = 0.792075 + 0.528472I
b = 0.761622 + 0.137681I
−0.08983 + 3.80204I 0
u = −0.280549 − 0.737409I
a = 0.792075 − 0.528472I
b = 0.761622 − 0.137681I
−0.08983 − 3.80204I 0
u = −0.499829 + 0.470865I
a = 0.806268 + 0.484022I
b = 0.380406 + 0.228190I
−1.56327 − 2.59162I 0
u = −0.499829 − 0.470865I
a = 0.806268 − 0.484022I
b = 0.380406 − 0.228190I
−1.56327 + 2.59162I 0
u = −0.112436 + 1.367480I
a = −0.632922 − 0.297654I
b = −1.56223 + 0.08456I
1.20898 − 3.44226I 0
u = −0.112436 − 1.367480I
a = −0.632922 + 0.297654I
b = −1.56223 − 0.08456I
1.20898 + 3.44226I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.566381
a = −0.802762
b = −0.197153
0.798103 0
u = −0.28939 + 1.46994I
a = 0.671650 + 0.215873I
b = 1.72303 + 0.09497I
−0.56151 − 8.64070I 0
u = −0.28939 − 1.46994I
a = 0.671650 − 0.215873I
b = 1.72303 − 0.09497I
−0.56151 + 8.64070I 0
u = −0.92906 + 1.39653I
a = 0.907569 − 0.198739I
b = 2.06801 + 0.68691I
−6.4260 − 19.1684I 0
u = −0.92906 − 1.39653I
a = 0.907569 + 0.198739I
b = 2.06801 − 0.68691I
−6.4260 + 19.1684I 0
u = −0.92101 + 1.40687I
a = −0.896980 + 0.187047I
b = −2.06222 − 0.67875I
−4.0767 − 13.9817I 0
u = −0.92101 − 1.40687I
a = −0.896980 − 0.187047I
b = −2.06222 + 0.67875I
−4.0767 + 13.9817I 0
u = −0.88294 + 1.43634I
a = −0.869308 + 0.141348I
b = −2.03878 − 0.65008I
−2.41043 − 11.37180I 0
u = −0.88294 − 1.43634I
a = −0.869308 − 0.141348I
b = −2.03878 + 0.65008I
−2.41043 + 11.37180I 0
u = −0.85826 + 1.46268I
a = 0.844125 − 0.115722I
b = 2.02991 + 0.62302I
−3.21746 − 6.27360I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.85826 − 1.46268I
a = 0.844125 + 0.115722I
b = 2.02991 − 0.62302I
−3.21746 + 6.27360I 0
u = −0.94044 + 1.42695I
a = 0.869943 − 0.204288I
b = 2.07688 + 0.66610I
−8.9618 − 11.1456I 0
u = −0.94044 − 1.42695I
a = 0.869943 + 0.204288I
b = 2.07688 − 0.66610I
−8.9618 + 11.1456I 0
u = −1.79760 + 0.18403I
a = −0.014886 + 0.527128I
b = −0.230920 − 0.745030I
1.27697 + 2.46560I 0
u = −1.79760 − 0.18403I
a = −0.014886 − 0.527128I
b = −0.230920 + 0.745030I
1.27697 − 2.46560I 0
u = −1.00973 + 1.55018I
a = −0.739072 + 0.225610I
b = −2.12531 − 0.62805I
−11.2775 − 10.1132I 0
u = −1.00973 − 1.55018I
a = −0.739072 − 0.225610I
b = −2.12531 + 0.62805I
−11.2775 + 10.1132I 0
u = −0.97218 + 1.61858I
a = 0.704321 − 0.180784I
b = 2.14055 + 0.59806I
−7.53111 − 6.12262I 0
u = −0.97218 − 1.61858I
a = 0.704321 + 0.180784I
b = 2.14055 − 0.59806I
−7.53111 + 6.12262I 0
u = 0.67061 + 1.79412I
a = 0.370631 + 0.274191I
b = 1.92950 − 0.98140I
−4.15134 − 1.35238I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.67061 − 1.79412I
a = 0.370631 − 0.274191I
b = 1.92950 + 0.98140I
−4.15134 + 1.35238I 0
u = −1.04810 + 1.66695I
a = −0.655969 + 0.211021I
b = −2.17530 − 0.62293I
−10.78670 − 1.62503I 0
u = −1.04810 − 1.66695I
a = −0.655969 − 0.211021I
b = −2.17530 + 0.62293I
−10.78670 + 1.62503I 0
u = −1.90209 + 0.73507I
a = 0.135328 − 0.540424I
b = 0.954871 + 0.914227I
−3.75897 + 9.93453I 0
u = −1.90209 − 0.73507I
a = 0.135328 + 0.540424I
b = 0.954871 − 0.914227I
−3.75897 − 9.93453I 0
u = −1.94845 + 0.63471I
a = −0.107654 + 0.527578I
b = −0.814471 − 0.960374I
−1.20397 + 4.73351I 0
u = −1.94845 − 0.63471I
a = −0.107654 − 0.527578I
b = −0.814471 + 0.960374I
−1.20397 − 4.73351I 0
u = −2.20817 + 0.68429I
a = 0.114062 − 0.468012I
b = 0.84321 + 1.29608I
−6.05300 + 1.44263I 0
u = −2.20817 − 0.68429I
a = 0.114062 + 0.468012I
b = 0.84321 − 1.29608I
−6.05300 − 1.44263I 0
9
II. I
u
2
= h−3.30 × 10
120
a
45
u + 1.97 × 10
120
a
44
u + · · · + 2.44 × 10
123
a − 4.33 ×
10
122
, −a
45
u − 12a
44
u + · · · + 633a − 110, u
2
− u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
5
=
a
0.458983a
45
u − 0.273001a
44
u + ··· − 338.380a + 60.1064
a
9
=
1
−u + 1
a
4
=
−0.458983a
45
u + 0.273001a
44
u + ··· + 340.380a − 60.1064
0.712699a
45
u + 0.366732a
44
u + ··· − 135.930a − 12.3220
a
11
=
−a
2
u
−0.620448a
45
u − 0.330821a
44
u + ··· + 18.9814a + 34.0960
a
6
=
a
3
u − a
3
+ a
0.376188a
45
u + 0.234574a
44
u + ··· − 92.5711a − 3.98563
a
10
=
0.620448a
45
u + 0.330821a
44
u + ··· − 18.9814a − 34.0960
−0.620448a
45
u − 0.330821a
44
u + ··· + 18.9814a + 34.0960
a
1
=
0.792605a
45
u + 0.0826922a
44
u + ··· − 289.525a + 17.7536
−0.214889a
45
u + 0.0650753a
44
u + ··· + 124.079a − 13.1906
a
7
=
−0.297470a
45
u + 0.0576235a
44
u + ··· + 148.169a − 20.2849
0.258693a
45
u + 0.0763352a
44
u + ··· − 105.105a + 11.5799
a
3
=
0.350355a
45
u − 0.0218100a
44
u + ··· − 300.160a + 54.1637
0.826487a
45
u + 0.517442a
44
u + ··· − 22.8980a − 65.2687
a
2
=
0.615915a
45
u + 0.0935804a
44
u + ··· − 302.385a + 39.1733
1.23323a
45
u + 0.201466a
44
u + ··· − 436.330a + 21.0896
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.476405a
45
u + 0.265059a
44
u + ··· − 443.753a + 31.6047
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
23
+ 11u
22
+ ··· − 2u
2
− 1)
4
c
2
, c
6
(u
23
+ u
22
+ ··· + 2u + 1)
4
c
3
(u
23
− u
22
+ ··· − 8u + 5)
4
c
4
, c
5
, c
9
c
11
u
92
+ u
91
+ ··· − 2040u + 10099
c
7
(u
23
+ 5u
22
+ ··· + 32u + 7)
4
c
8
(u
2
+ u + 1)
46
c
10
, c
12
u
92
+ 25u
91
+ ··· + 292u + 13
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
23
+ 3y
22
+ ··· − 4y − 1)
4
c
2
, c
6
(y
23
+ 11y
22
+ ··· − 2y
2
− 1)
4
c
3
(y
23
− 5y
22
+ ··· + 264y − 25)
4
c
4
, c
5
, c
9
c
11
y
92
+ 75y
91
+ ··· + 6818843988y + 101989801
c
7
(y
23
+ 7y
22
+ ··· − 404y − 49)
4
c
8
(y
2
+ y + 1)
46
c
10
, c
12
y
92
+ 19y
91
+ ··· − 4248y + 169
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.937121 − 0.371501I
b = −1.09291 − 0.92973I
−3.92076 + 1.08316I 4.43633 + 0.86900I
u = 0.500000 + 0.866025I
a = 0.841297 − 0.557369I
b = 0.148475 + 0.278228I
−5.96017 + 5.63569I −0.88555 − 7.95268I
u = 0.500000 + 0.866025I
a = 0.691012 + 0.830724I
b = 1.146660 − 0.462212I
−3.97784 − 0.99488I − 60.10 − 1.248015I
u = 0.500000 + 0.866025I
a = 0.054927 + 0.916811I
b = 0.664482 − 0.377958I
0.70641 + 3.76624I 5.79313 − 5.93000I
u = 0.500000 + 0.866025I
a = −0.524642 − 0.956462I
b = −1.014530 + 0.390058I
0.70471 − 3.49418I 6.00000 + 0.I
u = 0.500000 + 0.866025I
a = −0.225600 − 0.879982I
b = −0.789052 + 0.434009I
1.84607 − 1.13246I 7.66460 + 0.I
u = 0.500000 + 0.866025I
a = −0.963827 − 0.529838I
b = −1.36762 − 1.09117I
−4.71439 − 0.26236I 1.82667 + 0.I
u = 0.500000 + 0.866025I
a = 0.954176 + 0.573352I
b = 1.42108 + 1.17214I
−6.93621 − 4.99789I −1.56401 + 3.87629I
u = 0.500000 + 0.866025I
a = 1.099180 + 0.232834I
b = 1.91571 − 0.94244I
0.706409 + 0.293527I 6.00000 − 0.99820I
u = 0.500000 + 0.866025I
a = 0.809757 + 0.239901I
b = 0.788283 + 0.949215I
−5.55475 + 5.29231I 1.19624 − 5.73225I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.489628 + 1.061940I
b = 0.326898 − 0.113339I
0.706409 + 0.293527I 6.00000 + 0.I
u = 0.500000 + 0.866025I
a = −1.145350 − 0.237558I
b = −2.00157 + 0.90740I
1.84607 + 5.19223I 6.00000 − 6.93099I
u = 0.500000 + 0.866025I
a = 0.581793 + 1.018500I
b = 1.050400 − 0.345844I
−1.50338 − 8.56596I 6.00000 + 4.01378I
u = 0.500000 + 0.866025I
a = 1.037010 + 0.569702I
b = 1.54639 + 1.02940I
−8.67728 + 2.33323I −5.41146 + 0.I
u = 0.500000 + 0.866025I
a = 0.761599 + 0.258463I
b = 1.37115 − 1.03631I
0.70641 + 3.76624I 5.79313 − 5.93000I
u = 0.500000 + 0.866025I
a = 1.108030 + 0.502169I
b = 1.68312 − 0.49391I
−2.98164 + 2.02988I 0
u = 0.500000 + 0.866025I
a = 0.581895 − 1.076430I
b = −0.274328 + 0.068526I
1.84607 + 5.19223I 0
u = 0.500000 + 0.866025I
a = −1.211140 − 0.245723I
b = −2.13231 + 0.85180I
0.70471 + 7.55395I 0
u = 0.500000 + 0.866025I
a = 1.213000 + 0.292997I
b = 2.10489 − 0.74808I
−3.97784 + 5.05464I 0
u = 0.500000 + 0.866025I
a = −0.757345 + 0.999939I
b = 0.1345460 − 0.0411339I
−3.97784 + 5.05464I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 1.232090 + 0.243441I
b = 2.17934 − 0.84456I
−1.50338 + 12.62570I 0
u = 0.500000 + 0.866025I
a = −0.532945 + 0.493913I
b = 0.042143 − 0.502169I
−2.98164 + 2.02988I 3.52609 − 3.46410I
u = 0.500000 + 0.866025I
a = 1.264720 − 0.188799I
b = 0.661174 + 0.184455I
−5.55475 − 1.23254I 0
u = 0.500000 + 0.866025I
a = −1.218540 − 0.460431I
b = −1.91136 + 0.37517I
−5.96017 + 5.63569I 0
u = 0.500000 + 0.866025I
a = −1.167740 − 0.590081I
b = −1.82054 − 0.80138I
−8.67728 + 1.72653I 0
u = 0.500000 + 0.866025I
a = −1.129410 − 0.665295I
b = −1.50665 + 0.35250I
−5.96017 − 1.57592I 0
u = 0.500000 + 0.866025I
a = −0.630623 − 0.264977I
b = −1.19408 + 1.04901I
1.84607 − 1.13246I 7.66460 + 0.00279I
u = 0.500000 + 0.866025I
a = 0.721244 − 1.100800I
b = −0.199931 − 0.003278I
0.70471 + 7.55395I 0
u = 0.500000 + 0.866025I
a = 1.219210 + 0.578914I
b = 1.90724 + 0.64794I
−4.71439 + 4.32213I 0
u = 0.500000 + 0.866025I
a = −0.763483 + 1.120900I
b = 0.183770 + 0.032906I
−1.50338 + 12.62570I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.219790 − 0.603575I
b = −1.97180 − 0.70853I
−6.93621 + 9.05765I 0
u = 0.500000 + 0.866025I
a = 1.257640 + 0.526452I
b = 1.81897 + 0.38225I
−3.92076 + 2.97661I 0
u = 0.500000 + 0.866025I
a = −1.286200 − 0.520515I
b = −1.88974 − 0.14726I
−5.55475 − 1.23254I 0
u = 0.500000 + 0.866025I
a = −1.413420 + 0.031776I
b = −0.852089 − 0.112425I
−3.92076 + 2.97661I 0
u = 0.500000 + 0.866025I
a = 0.436590 − 0.170302I
b = 0.059353 + 0.847498I
−5.96017 − 1.57592I −0.885548 + 1.024476I
u = 0.500000 + 0.866025I
a = −1.41330 − 0.61316I
b = −1.43478 + 0.09616I
−5.55475 + 5.29231I 0
u = 0.500000 + 0.866025I
a = −0.396532 − 0.141057I
b = −0.88642 + 1.20546I
0.70471 − 3.49418I 6.27222 + 0.05746I
u = 0.500000 + 0.866025I
a = 1.49845 + 0.51570I
b = 1.342670 − 0.042527I
−3.92076 + 1.08316I 0
u = 0.500000 + 0.866025I
a = −1.62301 − 0.01758I
b = −0.934980 + 0.051452I
−4.71439 + 4.32213I 0
u = 0.500000 + 0.866025I
a = 0.365459 + 0.069498I
b = 0.83407 − 1.29484I
−1.50338 − 8.56596I 3.03092 + 4.01378I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 1.67713 + 0.13038I
b = 1.024320 − 0.080912I
−8.67728 + 1.72653I 0
u = 0.500000 + 0.866025I
a = 1.68669 + 0.00479I
b = 0.934674 − 0.100170I
−6.93621 + 9.05765I 0
u = 0.500000 + 0.866025I
a = 0.200879 + 0.210349I
b = 0.656529 − 1.082590I
−3.97784 − 0.99488I −0.122131 − 1.248015I
u = 0.500000 + 0.866025I
a = 1.65186 + 0.46081I
b = 1.248060 − 0.100528I
−4.71439 − 0.26236I 0
u = 0.500000 + 0.866025I
a = −1.68981 − 0.35841I
b = −1.180420 + 0.101292I
−8.67728 + 2.33323I 0
u = 0.500000 + 0.866025I
a = −1.70619 − 0.46839I
b = −1.239290 + 0.130393I
−6.93621 − 4.99789I 0
u = 0.500000 − 0.866025I
a = −0.937121 + 0.371501I
b = −1.09291 + 0.92973I
−3.92076 − 1.08316I 4.43633 − 0.86900I
u = 0.500000 − 0.866025I
a = 0.841297 + 0.557369I
b = 0.148475 − 0.278228I
−5.96017 − 5.63569I −0.88555 + 7.95268I
u = 0.500000 − 0.866025I
a = 0.691012 − 0.830724I
b = 1.146660 + 0.462212I
−3.97784 + 0.99488I − 60.10 + 1.248015I
u = 0.500000 − 0.866025I
a = 0.054927 − 0.916811I
b = 0.664482 + 0.377958I
0.70641 − 3.76624I 5.79313 + 5.93000I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 − 0.866025I
a = −0.524642 + 0.956462I
b = −1.014530 − 0.390058I
0.70471 + 3.49418I 6.00000 + 0.I
u = 0.500000 − 0.866025I
a = −0.225600 + 0.879982I
b = −0.789052 − 0.434009I
1.84607 + 1.13246I 7.66460 + 0.I
u = 0.500000 − 0.866025I
a = −0.963827 + 0.529838I
b = −1.36762 + 1.09117I
−4.71439 + 0.26236I 1.82667 + 0.I
u = 0.500000 − 0.866025I
a = 0.954176 − 0.573352I
b = 1.42108 − 1.17214I
−6.93621 + 4.99789I −1.56401 − 3.87629I
u = 0.500000 − 0.866025I
a = 1.099180 − 0.232834I
b = 1.91571 + 0.94244I
0.706409 − 0.293527I 6.00000 + 0.99820I
u = 0.500000 − 0.866025I
a = 0.809757 − 0.239901I
b = 0.788283 − 0.949215I
−5.55475 − 5.29231I 1.19624 + 5.73225I
u = 0.500000 − 0.866025I
a = −0.489628 − 1.061940I
b = 0.326898 + 0.113339I
0.706409 − 0.293527I 6.00000 + 0.I
u = 0.500000 − 0.866025I
a = −1.145350 + 0.237558I
b = −2.00157 − 0.90740I
1.84607 − 5.19223I 6.00000 + 6.93099I
u = 0.500000 − 0.866025I
a = 0.581793 − 1.018500I
b = 1.050400 + 0.345844I
−1.50338 + 8.56596I 6.00000 − 4.01378I
u = 0.500000 − 0.866025I
a = 1.037010 − 0.569702I
b = 1.54639 − 1.02940I
−8.67728 − 2.33323I −5.41146 + 0.I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 − 0.866025I
a = 0.761599 − 0.258463I
b = 1.37115 + 1.03631I
0.70641 − 3.76624I 5.79313 + 5.93000I
u = 0.500000 − 0.866025I
a = 1.108030 − 0.502169I
b = 1.68312 + 0.49391I
−2.98164 − 2.02988I 0
u = 0.500000 − 0.866025I
a = 0.581895 + 1.076430I
b = −0.274328 − 0.068526I
1.84607 − 5.19223I 0
u = 0.500000 − 0.866025I
a = −1.211140 + 0.245723I
b = −2.13231 − 0.85180I
0.70471 − 7.55395I 0
u = 0.500000 − 0.866025I
a = 1.213000 − 0.292997I
b = 2.10489 + 0.74808I
−3.97784 − 5.05464I 0
u = 0.500000 − 0.866025I
a = −0.757345 − 0.999939I
b = 0.1345460 + 0.0411339I
−3.97784 − 5.05464I 0
u = 0.500000 − 0.866025I
a = 1.232090 − 0.243441I
b = 2.17934 + 0.84456I
−1.50338 − 12.62570I 0
u = 0.500000 − 0.866025I
a = −0.532945 − 0.493913I
b = 0.042143 + 0.502169I
−2.98164 − 2.02988I 3.52609 + 3.46410I
u = 0.500000 − 0.866025I
a = 1.264720 + 0.188799I
b = 0.661174 − 0.184455I
−5.55475 + 1.23254I 0
u = 0.500000 − 0.866025I
a = −1.218540 + 0.460431I
b = −1.91136 − 0.37517I
−5.96017 − 5.63569I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 − 0.866025I
a = −1.167740 + 0.590081I
b = −1.82054 + 0.80138I
−8.67728 − 1.72653I 0
u = 0.500000 − 0.866025I
a = −1.129410 + 0.665295I
b = −1.50665 − 0.35250I
−5.96017 + 1.57592I 0
u = 0.500000 − 0.866025I
a = −0.630623 + 0.264977I
b = −1.19408 − 1.04901I
1.84607 + 1.13246I 7.66460 − 0.00279I
u = 0.500000 − 0.866025I
a = 0.721244 + 1.100800I
b = −0.199931 + 0.003278I
0.70471 − 7.55395I 0
u = 0.500000 − 0.866025I
a = 1.219210 − 0.578914I
b = 1.90724 − 0.64794I
−4.71439 − 4.32213I 0
u = 0.500000 − 0.866025I
a = −0.763483 − 1.120900I
b = 0.183770 − 0.032906I
−1.50338 − 12.62570I 0
u = 0.500000 − 0.866025I
a = −1.219790 + 0.603575I
b = −1.97180 + 0.70853I
−6.93621 − 9.05765I 0
u = 0.500000 − 0.866025I
a = 1.257640 − 0.526452I
b = 1.81897 − 0.38225I
−3.92076 − 2.97661I 0
u = 0.500000 − 0.866025I
a = −1.286200 + 0.520515I
b = −1.88974 + 0.14726I
−5.55475 + 1.23254I 0
u = 0.500000 − 0.866025I
a = −1.413420 − 0.031776I
b = −0.852089 + 0.112425I
−3.92076 − 2.97661I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 − 0.866025I
a = 0.436590 + 0.170302I
b = 0.059353 − 0.847498I
−5.96017 + 1.57592I −0.885548 − 1.024476I
u = 0.500000 − 0.866025I
a = −1.41330 + 0.61316I
b = −1.43478 − 0.09616I
−5.55475 − 5.29231I 0
u = 0.500000 − 0.866025I
a = −0.396532 + 0.141057I
b = −0.88642 − 1.20546I
0.70471 + 3.49418I 6.27222 − 0.05746I
u = 0.500000 − 0.866025I
a = 1.49845 − 0.51570I
b = 1.342670 + 0.042527I
−3.92076 − 1.08316I 0
u = 0.500000 − 0.866025I
a = −1.62301 + 0.01758I
b = −0.934980 − 0.051452I
−4.71439 − 4.32213I 0
u = 0.500000 − 0.866025I
a = 0.365459 − 0.069498I
b = 0.83407 + 1.29484I
−1.50338 + 8.56596I 3.03092 − 4.01378I
u = 0.500000 − 0.866025I
a = 1.67713 − 0.13038I
b = 1.024320 + 0.080912I
−8.67728 − 1.72653I 0
u = 0.500000 − 0.866025I
a = 1.68669 − 0.00479I
b = 0.934674 + 0.100170I
−6.93621 − 9.05765I 0
u = 0.500000 − 0.866025I
a = 0.200879 − 0.210349I
b = 0.656529 + 1.082590I
−3.97784 + 0.99488I −0.122131 + 1.248015I
u = 0.500000 − 0.866025I
a = 1.65186 − 0.46081I
b = 1.248060 + 0.100528I
−4.71439 + 0.26236I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 − 0.866025I
a = −1.68981 + 0.35841I
b = −1.180420 − 0.101292I
−8.67728 − 2.33323I 0
u = 0.500000 − 0.866025I
a = −1.70619 + 0.46839I
b = −1.239290 − 0.130393I
−6.93621 + 4.99789I 0
22
III. I
u
3
= h−22u
23
− 61u
22
+ · · · + b + 41, −38u
23
− 111u
22
+ · · · + a +
59, u
24
+ 3u
23
+ · · · − 2u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
5
=
38u
23
+ 111u
22
+ ··· + 96u − 59
22u
23
+ 61u
22
+ ··· + 61u − 41
a
9
=
1
−u
2
a
4
=
41u
23
+ 145u
22
+ ··· + 79u − 21
2u
23
− 2u
22
+ ··· + 14u − 16
a
11
=
−3u
23
− 10u
22
+ ··· − 12u + 3
−u
23
− 3u
22
+ ··· − 3u + 2
a
6
=
−59u
23
− 215u
22
+ ··· − 106u + 22
−16u
23
− 50u
22
+ ··· − 35u + 18
a
10
=
−2u
23
− 7u
22
+ ··· − 9u + 1
−u
23
− 3u
22
+ ··· − 3u + 2
a
1
=
−u
23
− 5u
22
+ ··· − 3u − 7
−2u
23
− 7u
22
+ ··· − 8u + 1
a
7
=
−15u
23
− 51u
22
+ ··· − 42u + 13
−5u
23
− 14u
22
+ ··· − 15u + 13
a
3
=
48u
23
+ 168u
22
+ ··· + 92u − 10
13u
23
+ 38u
22
+ ··· + 40u − 13
a
2
=
40u
23
+ 123u
22
+ ··· + 100u − 38
7u
23
+ 13u
22
+ ··· + 33u − 17
(ii) Obstruction class = 1
(iii) Cusp Shapes = −61u
23
− 222u
22
− 346u
21
− 257u
20
− 411u
19
− 911u
18
−
749u
17
− 254u
16
− 973u
15
− 1592u
14
− 390u
13
− 74u
12
− 1416u
11
− 908u
10
+ 367u
9
−
377u
8
− 897u
7
+ 168u
6
+ 175u
5
− 448u
4
+ 21u
3
+ 105u
2
− 105u + 15
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
− 13u
23
+ ··· − 5u + 1
c
2
u
24
− u
23
+ ··· − u + 1
c
3
u
24
+ u
23
+ ··· + 3u + 1
c
4
, c
11
u
24
+ 13u
22
+ ··· − 3u + 1
c
5
, c
9
u
24
+ 13u
22
+ ··· + 3u + 1
c
6
u
24
+ u
23
+ ··· + u + 1
c
7
u
24
+ 5u
23
+ ··· + 3u + 1
c
8
u
24
+ 3u
23
+ ··· − 2u + 1
c
10
, c
12
u
24
+ 2u
23
+ ··· − 3u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ y
23
+ ··· + 9y + 1
c
2
, c
6
y
24
+ 13y
23
+ ··· + 5y + 1
c
3
y
24
− 5y
23
+ ··· + 9y + 1
c
4
, c
5
, c
9
c
11
y
24
+ 26y
23
+ ··· + 11y + 1
c
7
y
24
+ 9y
23
+ ··· + 19y + 1
c
8
y
24
− y
23
+ ··· + 2y + 1
c
10
, c
12
y
24
+ 2y
23
+ ··· − y + 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.816409 + 0.593474I
a = 0.963539 + 0.964379I
b = 0.845972 + 0.122344I
−8.03434 + 0.26941I −2.72076 + 0.97413I
u = 0.816409 − 0.593474I
a = 0.963539 − 0.964379I
b = 0.845972 − 0.122344I
−8.03434 − 0.26941I −2.72076 − 0.97413I
u = −0.949778 + 0.110011I
a = 0.273616 + 0.251971I
b = −0.583760 − 0.376285I
1.68243 − 2.41741I 8.43017 + 4.58087I
u = −0.949778 − 0.110011I
a = 0.273616 − 0.251971I
b = −0.583760 + 0.376285I
1.68243 + 2.41741I 8.43017 − 4.58087I
u = −0.760955 + 0.802756I
a = −0.223515 + 0.754303I
b = −1.37159 − 0.97719I
−1.61317 + 9.75044I 2.97430 − 11.20361I
u = −0.760955 − 0.802756I
a = −0.223515 − 0.754303I
b = −1.37159 + 0.97719I
−1.61317 − 9.75044I 2.97430 + 11.20361I
u = −1.085960 + 0.275502I
a = −0.117117 − 0.437613I
b = 0.638829 + 0.855751I
2.48107 + 2.14641I 12.43873 − 4.94998I
u = −1.085960 − 0.275502I
a = −0.117117 + 0.437613I
b = 0.638829 − 0.855751I
2.48107 − 2.14641I 12.43873 + 4.94998I
u = 0.420960 + 1.075700I
a = −1.070130 − 0.105332I
b = −1.48122 − 0.32953I
−5.61923 + 1.68735I −1.85148 − 1.98716I
u = 0.420960 − 1.075700I
a = −1.070130 + 0.105332I
b = −1.48122 + 0.32953I
−5.61923 − 1.68735I −1.85148 + 1.98716I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.281555 + 0.794809I
a = 1.58599 + 0.00451I
b = 1.32116 + 0.55449I
−7.00231 + 4.11367I −3.84808 − 4.14953I
u = 0.281555 − 0.794809I
a = 1.58599 − 0.00451I
b = 1.32116 − 0.55449I
−7.00231 − 4.11367I −3.84808 + 4.14953I
u = 0.586299 + 0.605904I
a = −1.43457 − 0.88046I
b = −0.966693 − 0.386767I
−4.41697 + 2.99372I 3.50329 − 1.67317I
u = 0.586299 − 0.605904I
a = −1.43457 + 0.88046I
b = −0.966693 + 0.386767I
−4.41697 − 2.99372I 3.50329 + 1.67317I
u = 0.422755 + 0.679873I
a = −1.68856 − 0.47087I
b = −1.143110 − 0.509910I
−4.04330 + 1.84908I 3.56105 − 0.03419I
u = 0.422755 − 0.679873I
a = −1.68856 + 0.47087I
b = −1.143110 + 0.509910I
−4.04330 − 1.84908I 3.56105 + 0.03419I
u = 0.609175 + 0.518283I
a = 1.42573 + 1.12759I
b = 0.850019 + 0.410000I
−6.62215 + 7.58106I −0.32877 − 5.75311I
u = 0.609175 − 0.518283I
a = 1.42573 − 1.12759I
b = 0.850019 − 0.410000I
−6.62215 − 7.58106I −0.32877 + 5.75311I
u = −0.923032 + 0.769486I
a = 0.137292 − 0.653280I
b = 1.26828 + 1.07344I
0.69791 + 4.54840I 7.17943 − 8.20372I
u = −0.923032 − 0.769486I
a = 0.137292 + 0.653280I
b = 1.26828 − 1.07344I
0.69791 − 4.54840I 7.17943 + 8.20372I
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.345437 + 0.662676I
a = 1.87018 + 0.30991I
b = 1.180650 + 0.589271I
−5.92912 − 2.54338I −0.68969 + 4.27463I
u = 0.345437 − 0.662676I
a = 1.87018 − 0.30991I
b = 1.180650 − 0.589271I
−5.92912 + 2.54338I −0.68969 − 4.27463I
u = −1.26286 + 1.24115I
a = −0.222464 + 0.423128I
b = −1.55855 − 1.53086I
−4.34911 + 1.66239I 0. − 13.97070I
u = −1.26286 − 1.24115I
a = −0.222464 − 0.423128I
b = −1.55855 + 1.53086I
−4.34911 − 1.66239I 0. + 13.97070I
28
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
23
+ 11u
22
+ ··· − 2u
2
− 1)
4
)(u
24
− 13u
23
+ ··· − 5u + 1)
· (u
49
+ 24u
48
+ ··· + 108u − 16)
c
2
((u
23
+ u
22
+ ··· + 2u + 1)
4
)(u
24
− u
23
+ ··· − u + 1)
· (u
49
− 6u
48
+ ··· + 38u − 4)
c
3
((u
23
− u
22
+ ··· − 8u + 5)
4
)(u
24
+ u
23
+ ··· + 3u + 1)
· (u
49
+ 6u
48
+ ··· − 2874u − 612)
c
4
, c
11
(u
24
+ 13u
22
+ ··· − 3u + 1)(u
49
+ 17u
47
+ ··· + 2u − 1)
· (u
92
+ u
91
+ ··· − 2040u + 10099)
c
5
, c
9
(u
24
+ 13u
22
+ ··· + 3u + 1)(u
49
+ 17u
47
+ ··· + 2u − 1)
· (u
92
+ u
91
+ ··· − 2040u + 10099)
c
6
((u
23
+ u
22
+ ··· + 2u + 1)
4
)(u
24
+ u
23
+ ··· + u + 1)
· (u
49
− 6u
48
+ ··· + 38u − 4)
c
7
((u
23
+ 5u
22
+ ··· + 32u + 7)
4
)(u
24
+ 5u
23
+ ··· + 3u + 1)
· (u
49
− 30u
48
+ ··· + 42842u − 3676)
c
8
((u
2
+ u + 1)
46
)(u
24
+ 3u
23
+ ··· − 2u + 1)
· (u
49
− 44u
48
+ ··· + 201326592u − 8388608)
c
10
, c
12
(u
24
+ 2u
23
+ ··· − 3u + 1)(u
49
− 2u
48
+ ··· − 6u − 1)
· (u
92
+ 25u
91
+ ··· + 292u + 13)
29
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
23
+ 3y
22
+ ··· − 4y − 1)
4
)(y
24
+ y
23
+ ··· + 9y + 1)
· (y
49
+ 4y
48
+ ··· + 26352y − 256)
c
2
, c
6
((y
23
+ 11y
22
+ ··· − 2y
2
− 1)
4
)(y
24
+ 13y
23
+ ··· + 5y + 1)
· (y
49
+ 24y
48
+ ··· + 108y − 16)
c
3
((y
23
− 5y
22
+ ··· + 264y − 25)
4
)(y
24
− 5y
23
+ ··· + 9y + 1)
· (y
49
− 10y
48
+ ··· + 7605036y − 374544)
c
4
, c
5
, c
9
c
11
(y
24
+ 26y
23
+ ··· + 11y + 1)(y
49
+ 34y
48
+ ··· + 12y
2
− 1)
· (y
92
+ 75y
91
+ ··· + 6818843988y + 101989801)
c
7
((y
23
+ 7y
22
+ ··· − 404y − 49)
4
)(y
24
+ 9y
23
+ ··· + 19y + 1)
· (y
49
+ 16y
48
+ ··· + 484690764y − 13512976)
c
8
((y
2
+ y + 1)
46
)(y
24
− y
23
+ ··· + 2y + 1)
· (y
49
+ 14y
47
+ ··· + 140737488355328y − 70368744177664)
c
10
, c
12
(y
24
+ 2y
23
+ ··· − y + 1)(y
49
− 14y
48
+ ··· + 32y − 1)
· (y
92
+ 19y
91
+ ··· − 4248y + 169)
30
