12a
1245
(K12a
1245
)
A knot diagram
1
Linearized knot diagam
5 6 10 9 11 3 12 1 4 2 8 7
Solving Sequence
7,12
8 1
3,9
6 2 11 5 4 10
c
7
c
12
c
8
c
6
c
2
c
11
c
5
c
4
c
10
c
1
, c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.10423 × 10
148
u
106
− 7.11831 × 10
147
u
105
+ ··· + 4.99479 × 10
148
b − 4.54934 × 10
149
,
1.94237 × 10
149
u
106
+ 4.11737 × 10
149
u
105
+ ··· + 9.49010 × 10
149
a + 6.20020 × 10
150
,
u
107
+ 47u
105
+ ··· + 141u + 19i
I
u
2
= h−u
18
− u
17
+ ··· + b + 1, −u
20
− 3u
19
+ ··· + a + 2, u
21
+ u
20
+ ··· − 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 128 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−3.10 × 10
148
u
106
− 7.12 × 10
147
u
105
+ · · · + 4.99 × 10
148
b − 4.55 ×
10
149
, 1.94 × 10
149
u
106
+ 4.12 × 10
149
u
105
+ · · · + 9.49 × 10
149
a + 6.20 ×
10
150
, u
107
+ 47u
105
+ · · · + 141u + 19i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
u
a
3
=
−0.204673u
106
− 0.433859u
105
+ ··· − 46.4584u − 6.53333
0.621494u
106
+ 0.142515u
105
+ ··· + 61.8909u + 9.10817
a
9
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
6
=
−0.106621u
106
+ 1.50979u
105
+ ··· + 122.935u + 18.4439
−1.10574u
106
− 0.316137u
105
+ ··· − 140.594u − 23.7789
a
2
=
−0.700162u
106
+ 1.60344u
105
+ ··· + 21.6036u − 3.11076
−0.791948u
106
− 1.19829u
105
+ ··· − 211.859u − 36.8786
a
11
=
u
u
3
+ u
a
5
=
0.0653729u
106
+ 0.714844u
105
+ ··· + 58.6773u + 8.36870
−0.839895u
106
+ 0.179953u
105
+ ··· − 96.0311u − 18.7501
a
4
=
0.508771u
106
+ 1.70694u
105
+ ··· + 210.070u + 33.7699
−1.31324u
106
− 0.319179u
105
+ ··· − 135.759u − 21.9463
a
10
=
−0.451438u
106
+ 0.642648u
105
+ ··· − 59.0515u − 15.1553
−0.610494u
106
− 0.619999u
105
+ ··· − 144.993u − 26.1983
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.227553u
106
− 0.275413u
105
+ ··· − 161.851u − 42.6015
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
107
+ 7u
106
+ ··· − 3628491u − 687859
c
2
, c
6
u
107
+ 2u
106
+ ··· − 142u + 7
c
3
, c
4
, c
9
u
107
+ u
106
+ ··· + 43u + 1
c
5
u
107
+ u
106
+ ··· + 229u + 31
c
7
, c
11
, c
12
u
107
+ 47u
105
+ ··· + 141u + 19
c
8
u
107
− 21u
105
+ ··· + 516631u + 130055
c
10
u
107
− 7u
106
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
107
− 25y
106
+ ··· + 17280320516861y −473150003881
c
2
, c
6
y
107
− 62y
106
+ ··· + 4890y −49
c
3
, c
4
, c
9
y
107
+ 109y
106
+ ··· + 1159y −1
c
5
y
107
+ 15y
106
+ ··· − 27601y −961
c
7
, c
11
, c
12
y
107
+ 94y
106
+ ··· + 6619y −361
c
8
y
107
− 42y
106
+ ··· + 181397207991y −16914303025
c
10
y
107
+ y
106
+ ··· + 111y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.905238 + 0.411449I
a = −1.096800 − 0.625171I
b = 0.733290 − 0.222077I
−7.44404 − 2.71116I 0
u = 0.905238 − 0.411449I
a = −1.096800 + 0.625171I
b = 0.733290 + 0.222077I
−7.44404 + 2.71116I 0
u = 0.968712 + 0.181097I
a = −0.0104473 + 0.1331340I
b = 0.937029 + 0.334740I
−6.63928 − 0.01925I 0
u = 0.968712 − 0.181097I
a = −0.0104473 − 0.1331340I
b = 0.937029 − 0.334740I
−6.63928 + 0.01925I 0
u = −0.364131 + 0.957400I
a = −1.067810 + 0.496371I
b = 0.302228 + 1.008320I
−7.21376 − 2.28542I 0
u = −0.364131 − 0.957400I
a = −1.067810 − 0.496371I
b = 0.302228 − 1.008320I
−7.21376 + 2.28542I 0
u = 0.345292 + 0.840140I
a = 1.007790 + 0.275821I
b = −1.130510 − 0.470696I
2.36893 + 4.77276I 0
u = 0.345292 − 0.840140I
a = 1.007790 − 0.275821I
b = −1.130510 + 0.470696I
2.36893 − 4.77276I 0
u = −0.867184 + 0.240558I
a = −0.47649 + 1.37668I
b = 1.27141 + 0.66969I
−6.4986 + 13.0493I 0
u = −0.867184 − 0.240558I
a = −0.47649 − 1.37668I
b = 1.27141 − 0.66969I
−6.4986 − 13.0493I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.536285 + 0.966933I
a = −0.548316 + 0.237729I
b = 1.236170 − 0.610065I
−4.26410 − 8.12654I 0
u = −0.536285 − 0.966933I
a = −0.548316 − 0.237729I
b = 1.236170 + 0.610065I
−4.26410 + 8.12654I 0
u = −0.857929
a = 0.114460
b = −0.723700
−1.60767 −15.4610
u = 0.206911 + 1.131310I
a = 0.695628 + 0.106558I
b = −0.329623 + 0.782791I
−0.025083 + 0.213579I 0
u = 0.206911 − 1.131310I
a = 0.695628 − 0.106558I
b = −0.329623 − 0.782791I
−0.025083 − 0.213579I 0
u = −0.345424 + 1.108080I
a = 0.985098 − 0.289554I
b = −0.849398 − 0.359510I
1.80844 + 4.40835I 0
u = −0.345424 − 1.108080I
a = 0.985098 + 0.289554I
b = −0.849398 + 0.359510I
1.80844 − 4.40835I 0
u = −0.792358 + 0.211587I
a = 0.490747 − 0.859656I
b = 0.329735 − 1.191950I
−9.52738 + 6.53629I −6.31446 − 5.70415I
u = −0.792358 − 0.211587I
a = 0.490747 + 0.859656I
b = 0.329735 + 1.191950I
−9.52738 − 6.53629I −6.31446 + 5.70415I
u = 0.637713 + 1.006310I
a = −0.868509 − 0.634692I
b = 1.080370 − 0.397617I
−4.09706 − 5.51234I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.637713 − 1.006310I
a = −0.868509 + 0.634692I
b = 1.080370 + 0.397617I
−4.09706 + 5.51234I 0
u = −0.084007 + 1.190680I
a = 1.380240 − 0.083337I
b = −0.977538 − 0.646999I
1.72016 + 4.71467I 0
u = −0.084007 − 1.190680I
a = 1.380240 + 0.083337I
b = −0.977538 + 0.646999I
1.72016 − 4.71467I 0
u = 0.800773 + 0.066671I
a = −0.873723 + 1.092160I
b = −0.904582 + 0.442790I
−7.42230 − 4.55808I −5.52745 + 6.03757I
u = 0.800773 − 0.066671I
a = −0.873723 − 1.092160I
b = −0.904582 − 0.442790I
−7.42230 + 4.55808I −5.52745 − 6.03757I
u = 0.767976 + 0.222888I
a = 0.70826 + 1.47282I
b = −1.214880 + 0.531219I
0.31440 − 8.85668I −0.78742 + 8.52974I
u = 0.767976 − 0.222888I
a = 0.70826 − 1.47282I
b = −1.214880 − 0.531219I
0.31440 + 8.85668I −0.78742 − 8.52974I
u = 0.367132 + 0.696445I
a = −0.959933 + 0.599740I
b = 0.128465 + 0.600907I
−6.67824 − 1.82046I −6.27188 + 3.23038I
u = 0.367132 − 0.696445I
a = −0.959933 − 0.599740I
b = 0.128465 − 0.600907I
−6.67824 + 1.82046I −6.27188 − 3.23038I
u = −0.199384 + 1.216730I
a = −0.964810 − 0.781065I
b = 0.968682 − 0.447513I
3.29244 + 0.02020I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.199384 − 1.216730I
a = −0.964810 + 0.781065I
b = 0.968682 + 0.447513I
3.29244 − 0.02020I 0
u = −0.670392 + 0.370224I
a = 0.754651 − 0.747405I
b = −0.937967 − 0.200384I
−0.37452 + 2.01494I −5.67970 − 7.04796I
u = −0.670392 − 0.370224I
a = 0.754651 + 0.747405I
b = −0.937967 + 0.200384I
−0.37452 − 2.01494I −5.67970 + 7.04796I
u = 0.354215 + 1.193730I
a = −0.445993 + 0.201512I
b = −0.929440 − 0.357635I
−3.96766 + 0.38490I 0
u = 0.354215 − 1.193730I
a = −0.445993 − 0.201512I
b = −0.929440 + 0.357635I
−3.96766 − 0.38490I 0
u = 0.223063 + 1.253010I
a = 3.05099 + 2.52713I
b = −0.834320 + 0.218356I
−4.56973 − 2.16436I 0
u = 0.223063 − 1.253010I
a = 3.05099 − 2.52713I
b = −0.834320 − 0.218356I
−4.56973 + 2.16436I 0
u = 0.714097 + 0.136994I
a = −0.436764 − 0.715435I
b = −0.147954 − 0.920169I
−2.91868 − 3.67856I −4.86738 + 6.69635I
u = 0.714097 − 0.136994I
a = −0.436764 + 0.715435I
b = −0.147954 + 0.920169I
−2.91868 + 3.67856I −4.86738 − 6.69635I
u = −0.575944 + 0.442931I
a = 0.149085 − 1.097360I
b = −1.44419 − 0.17281I
−1.49802 + 1.95208I 1.14695 − 2.61988I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.575944 − 0.442931I
a = 0.149085 + 1.097360I
b = −1.44419 + 0.17281I
−1.49802 − 1.95208I 1.14695 + 2.61988I
u = −0.722586
a = 0.995155
b = 0.393582
−2.02123 −7.49440
u = −0.716054
a = 0.757130
b = 0.209876
−2.02575 −6.33530
u = −0.243672 + 1.267380I
a = −0.096938 − 0.702103I
b = −1.05045 + 0.96322I
0.565624 − 0.596893I 0
u = −0.243672 − 1.267380I
a = −0.096938 + 0.702103I
b = −1.05045 − 0.96322I
0.565624 + 0.596893I 0
u = −0.036370 + 1.293160I
a = 0.074088 − 0.754865I
b = 0.410950 + 0.208667I
4.91364 + 1.37867I 0
u = −0.036370 − 1.293160I
a = 0.074088 + 0.754865I
b = 0.410950 − 0.208667I
4.91364 − 1.37867I 0
u = 0.078685 + 1.297580I
a = 0.078391 − 0.672197I
b = 0.607084 + 0.770314I
4.79778 + 1.11673I 0
u = 0.078685 − 1.297580I
a = 0.078391 + 0.672197I
b = 0.607084 − 0.770314I
4.79778 − 1.11673I 0
u = −0.288101 + 1.269850I
a = 0.170344 + 0.588717I
b = 0.469201 + 0.289222I
1.91279 + 3.65319I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.288101 − 1.269850I
a = 0.170344 − 0.588717I
b = 0.469201 − 0.289222I
1.91279 − 3.65319I 0
u = −0.143161 + 1.305410I
a = 1.79846 − 1.26846I
b = −1.28537 + 0.74411I
2.38914 − 1.51143I 0
u = −0.143161 − 1.305410I
a = 1.79846 + 1.26846I
b = −1.28537 − 0.74411I
2.38914 + 1.51143I 0
u = −0.296280 + 1.282910I
a = 0.477597 + 0.281281I
b = 0.196285 − 0.041031I
1.97856 + 3.65328I 0
u = −0.296280 − 1.282910I
a = 0.477597 − 0.281281I
b = 0.196285 + 0.041031I
1.97856 − 3.65328I 0
u = −0.666478 + 0.124519I
a = −0.99150 + 1.99487I
b = 1.064320 + 0.389913I
0.07969 + 3.06984I −3.80104 − 5.63443I
u = −0.666478 − 0.124519I
a = −0.99150 − 1.99487I
b = 1.064320 − 0.389913I
0.07969 − 3.06984I −3.80104 + 5.63443I
u = −0.258550 + 1.307000I
a = 2.14969 − 1.17419I
b = −1.21296 − 0.94768I
0.97250 + 7.10853I 0
u = −0.258550 − 1.307000I
a = 2.14969 + 1.17419I
b = −1.21296 + 0.94768I
0.97250 − 7.10853I 0
u = 0.660120 + 0.091737I
a = −0.00874 − 2.54586I
b = −0.697407 − 0.390238I
−8.10990 − 0.94352I −6.26053 − 1.76573I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.660120 − 0.091737I
a = −0.00874 + 2.54586I
b = −0.697407 + 0.390238I
−8.10990 + 0.94352I −6.26053 + 1.76573I
u = −0.651207 + 0.035721I
a = −0.47420 − 1.85434I
b = −1.13728 − 0.93902I
−3.24839 + 3.81524I −3.39684 − 4.40039I
u = −0.651207 − 0.035721I
a = −0.47420 + 1.85434I
b = −1.13728 + 0.93902I
−3.24839 − 3.81524I −3.39684 + 4.40039I
u = 0.345619 + 1.308420I
a = 0.533771 + 1.175410I
b = −0.890795 + 0.506629I
−3.12323 − 8.68533I 0
u = 0.345619 − 1.308420I
a = 0.533771 − 1.175410I
b = −0.890795 − 0.506629I
−3.12323 + 8.68533I 0
u = 0.280938 + 1.324890I
a = 0.299470 − 0.684292I
b = −0.722655 − 0.561524I
−3.63976 − 4.39403I 0
u = 0.280938 − 1.324890I
a = 0.299470 + 0.684292I
b = −0.722655 + 0.561524I
−3.63976 + 4.39403I 0
u = −0.276724 + 1.344210I
a = −2.59997 + 1.55783I
b = 1.135090 + 0.374256I
4.72511 + 6.51457I 0
u = −0.276724 − 1.344210I
a = −2.59997 − 1.55783I
b = 1.135090 − 0.374256I
4.72511 − 6.51457I 0
u = 0.197941 + 1.358640I
a = −1.97103 − 1.00726I
b = 1.41982 + 0.25244I
7.03503 − 2.12409I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.197941 − 1.358640I
a = −1.97103 + 1.00726I
b = 1.41982 − 0.25244I
7.03503 + 2.12409I 0
u = 0.294414 + 1.345570I
a = −0.774690 + 0.483534I
b = −0.066343 − 1.022600I
1.75619 − 7.33781I 0
u = 0.294414 − 1.345570I
a = −0.774690 − 0.483534I
b = −0.066343 + 1.022600I
1.75619 + 7.33781I 0
u = −0.097815 + 1.376750I
a = −2.89041 + 0.92625I
b = 1.083180 − 0.131860I
7.07610 + 0.37862I 0
u = −0.097815 − 1.376750I
a = −2.89041 − 0.92625I
b = 1.083180 + 0.131860I
7.07610 − 0.37862I 0
u = 0.208123 + 1.386110I
a = −2.22237 − 0.82857I
b = 1.33473 − 0.67094I
6.95556 − 5.37743I 0
u = 0.208123 − 1.386110I
a = −2.22237 + 0.82857I
b = 1.33473 + 0.67094I
6.95556 + 5.37743I 0
u = −0.00838 + 1.42378I
a = −0.086807 − 0.587384I
b = −0.223732 + 1.105900I
−0.00133 − 2.31664I 0
u = −0.00838 − 1.42378I
a = −0.086807 + 0.587384I
b = −0.223732 − 1.105900I
−0.00133 + 2.31664I 0
u = 0.31803 + 1.39028I
a = 2.21075 + 1.25584I
b = −1.267560 + 0.539509I
5.42749 − 12.79330I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.31803 − 1.39028I
a = 2.21075 − 1.25584I
b = −1.267560 − 0.539509I
5.42749 + 12.79330I 0
u = −0.32815 + 1.39091I
a = 0.678986 + 0.619610I
b = 0.324336 − 1.298330I
−4.44471 + 10.58770I 0
u = −0.32815 − 1.39091I
a = 0.678986 − 0.619610I
b = 0.324336 + 1.298330I
−4.44471 − 10.58770I 0
u = 0.519502 + 0.232304I
a = −0.33135 − 1.92210I
b = 1.133900 − 0.594006I
1.79284 − 2.65666I 4.50273 + 10.14622I
u = 0.519502 − 0.232304I
a = −0.33135 + 1.92210I
b = 1.133900 + 0.594006I
1.79284 + 2.65666I 4.50273 − 10.14622I
u = 0.42827 + 1.36797I
a = −0.529601 − 0.345886I
b = 0.836218 + 0.286440I
−1.81153 − 4.99186I 0
u = 0.42827 − 1.36797I
a = −0.529601 + 0.345886I
b = 0.836218 − 0.286440I
−1.81153 + 4.99186I 0
u = −0.28179 + 1.42821I
a = 1.84850 − 0.78017I
b = −1.163190 − 0.192867I
5.33469 + 5.55188I 0
u = −0.28179 − 1.42821I
a = 1.84850 + 0.78017I
b = −1.163190 + 0.192867I
5.33469 − 5.55188I 0
u = −0.20981 + 1.44344I
a = 2.08106 − 0.75214I
b = −1.70160 − 0.37611I
4.50767 + 4.78839I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.20981 − 1.44344I
a = 2.08106 + 0.75214I
b = −1.70160 + 0.37611I
4.50767 − 4.78839I 0
u = −0.36192 + 1.41375I
a = −1.95276 + 1.17852I
b = 1.30791 + 0.69666I
−1.2508 + 17.4764I 0
u = −0.36192 − 1.41375I
a = −1.95276 − 1.17852I
b = 1.30791 − 0.69666I
−1.2508 − 17.4764I 0
u = 0.00947 + 1.46699I
a = 2.37259 + 0.24262I
b = −1.239550 − 0.308975I
9.69671 + 4.17530I 0
u = 0.00947 − 1.46699I
a = 2.37259 − 0.24262I
b = −1.239550 + 0.308975I
9.69671 − 4.17530I 0
u = 0.39552 + 1.45562I
a = −1.68206 − 0.82245I
b = 0.907327 − 0.271019I
−1.60211 − 7.49643I 0
u = 0.39552 − 1.45562I
a = −1.68206 + 0.82245I
b = 0.907327 + 0.271019I
−1.60211 + 7.49643I 0
u = 0.393208 + 0.230128I
a = 0.094167 − 0.695236I
b = 1.166280 + 0.228328I
2.10704 + 0.24912I 5.11122 + 2.00536I
u = 0.393208 − 0.230128I
a = 0.094167 + 0.695236I
b = 1.166280 − 0.228328I
2.10704 − 0.24912I 5.11122 − 2.00536I
u = −0.150834 + 0.411324I
a = 0.614979 − 0.389209I
b = −0.088919 + 0.383206I
−0.018230 + 1.014060I −0.41757 − 6.37169I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.150834 − 0.411324I
a = 0.614979 + 0.389209I
b = −0.088919 − 0.383206I
−0.018230 − 1.014060I −0.41757 + 6.37169I
u = 0.06304 + 1.56420I
a = −1.94911 − 0.00828I
b = 1.337920 − 0.437620I
4.90196 − 7.43262I 0
u = 0.06304 − 1.56420I
a = −1.94911 + 0.00828I
b = 1.337920 + 0.437620I
4.90196 + 7.43262I 0
u = −0.263778 + 0.275422I
a = −2.48263 + 2.41700I
b = 0.934644 − 0.228588I
1.78989 − 1.01286I 2.41726 − 2.03464I
u = −0.263778 − 0.275422I
a = −2.48263 − 2.41700I
b = 0.934644 + 0.228588I
1.78989 + 1.01286I 2.41726 + 2.03464I
u = −0.337588 + 0.032266I
a = −0.739693 − 0.011776I
b = −1.148220 + 0.707709I
−1.80899 − 3.33482I −7.29428 − 2.25974I
u = −0.337588 − 0.032266I
a = −0.739693 + 0.011776I
b = −1.148220 − 0.707709I
−1.80899 + 3.33482I −7.29428 + 2.25974I
15
II.
I
u
2
= h−u
18
−u
17
+· · ·+b+1, −u
20
−3u
19
+· · ·+a+2, u
21
+u
20
+· · ·−2u−1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
u
a
3
=
u
20
+ 3u
19
+ ··· − 7u − 2
u
18
+ u
17
+ ··· + u − 1
a
9
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
6
=
−2u
19
− 2u
18
+ ··· + 5u + 1
3u
19
+ 2u
18
+ ··· − 7u
2
− u
a
2
=
4u
20
+ 3u
19
+ ··· + u − 2
−3u
20
− 26u
18
+ ··· + 3u − 2
a
11
=
u
u
3
+ u
a
5
=
−4u
19
− 4u
18
+ ··· + 7u + 2
4u
19
+ 3u
18
+ ··· − 3u − 1
a
4
=
−u
20
− 4u
19
+ ··· + 5u + 1
u
20
+ 3u
19
+ ··· − 7u
2
− u
a
10
=
u
20
+ 7u
18
+ ··· + u + 3
−2u
20
− 17u
18
+ ··· + 7u
2
− 4u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 3u
20
− 3u
19
+ 26u
18
− 27u
17
+ 92u
16
− 99u
15
+ 161u
14
− 180u
13
+ 119u
12
− 148u
11
−
23u
10
− 14u
9
− 61u
8
+ 26u
7
+ 46u
6
− 41u
5
+ 92u
4
− 51u
3
+ 34u
2
− 12u + 1
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
+ 3u
19
+ ··· + 4u
3
− 1
c
2
u
21
− 3u
20
+ ··· − 3u + 1
c
3
, c
4
u
21
+ 12u
19
+ ··· − 3u
2
− 1
c
5
u
21
+ 3u
19
+ ··· − 3u
2
− 1
c
6
u
21
+ 3u
20
+ ··· − 3u − 1
c
7
u
21
+ u
20
+ ··· − 2u − 1
c
8
u
21
− u
20
+ ··· + 3u
2
− 1
c
9
u
21
+ 12u
19
+ ··· + 3u
2
+ 1
c
10
u
21
+ 4u
18
+ ··· + 2u − 1
c
11
, c
12
u
21
− u
20
+ ··· − 2u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
+ 6y
20
+ ··· + 4y
2
− 1
c
2
, c
6
y
21
− 15y
20
+ ··· + 21y −1
c
3
, c
4
, c
9
y
21
+ 24y
20
+ ··· − 6y −1
c
5
y
21
+ 6y
20
+ ··· − 6y −1
c
7
, c
11
, c
12
y
21
+ 21y
20
+ ··· + 6y −1
c
8
y
21
− 7y
20
+ ··· + 6y −1
c
10
y
21
+ 8y
19
+ ··· + 6y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.850535 + 0.270683I
a = 0.772663 − 1.107970I
b = −0.698181 − 0.147373I
−7.25334 + 2.25396I −2.51904 + 1.51124I
u = −0.850535 − 0.270683I
a = 0.772663 + 1.107970I
b = −0.698181 + 0.147373I
−7.25334 − 2.25396I −2.51904 − 1.51124I
u = −0.208319 + 1.151210I
a = −0.54251 + 2.07788I
b = −0.546624 + 0.066738I
−5.00712 + 1.29880I −2.18413 + 0.91161I
u = −0.208319 − 1.151210I
a = −0.54251 − 2.07788I
b = −0.546624 − 0.066738I
−5.00712 − 1.29880I −2.18413 − 0.91161I
u = 0.795925
a = 0.393034
b = 0.779315
−1.18509 6.11500
u = 0.123270 + 1.255540I
a = 0.103398 + 0.140021I
b = 0.806334 + 0.494666I
4.61981 + 0.10053I 4.67568 + 0.72372I
u = 0.123270 − 1.255540I
a = 0.103398 − 0.140021I
b = 0.806334 − 0.494666I
4.61981 − 0.10053I 4.67568 − 0.72372I
u = 0.316220 + 1.248030I
a = −0.236664 − 0.243629I
b = 0.725880 − 0.143499I
2.61302 − 4.01014I 8.65050 + 4.98325I
u = 0.316220 − 1.248030I
a = −0.236664 + 0.243629I
b = 0.725880 + 0.143499I
2.61302 + 4.01014I 8.65050 − 4.98325I
u = −0.077211 + 1.297150I
a = 0.786355 − 1.165330I
b = −1.00703 + 1.01195I
2.14044 − 2.54928I 3.26865 + 5.24031I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.077211 − 1.297150I
a = 0.786355 + 1.165330I
b = −1.00703 − 1.01195I
2.14044 + 2.54928I 3.26865 − 5.24031I
u = −0.40075 + 1.35681I
a = 1.097720 − 0.843631I
b = −0.724177 − 0.339747I
−2.22720 + 6.87921I −2.11837 − 4.50343I
u = −0.40075 − 1.35681I
a = 1.097720 + 0.843631I
b = −0.724177 + 0.339747I
−2.22720 − 6.87921I −2.11837 + 4.50343I
u = 0.20322 + 1.41023I
a = −2.23359 − 0.86234I
b = 1.286100 − 0.411263I
6.67021 − 4.48387I 6.16458 + 1.58623I
u = 0.20322 − 1.41023I
a = −2.23359 + 0.86234I
b = 1.286100 + 0.411263I
6.67021 + 4.48387I 6.16458 − 1.58623I
u = −0.16274 + 1.44102I
a = 2.20325 − 0.36604I
b = −1.53931 − 0.67627I
4.13324 + 5.57019I 2.10575 − 7.26334I
u = −0.16274 − 1.44102I
a = 2.20325 + 0.36604I
b = −1.53931 + 0.67627I
4.13324 − 5.57019I 2.10575 + 7.26334I
u = 0.443564 + 0.214151I
a = −1.10819 − 2.26934I
b = 1.020830 − 0.400990I
1.32745 − 1.97147I −1.58797 + 2.75206I
u = 0.443564 − 0.214151I
a = −1.10819 + 2.26934I
b = 1.020830 + 0.400990I
1.32745 + 1.97147I −1.58797 − 2.75206I
u = −0.284687 + 0.209100I
a = 0.46104 − 2.21836I
b = −1.21347 − 0.79087I
−1.48915 + 3.72263I 3.48687 − 9.47280I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.284687 − 0.209100I
a = 0.46104 + 2.21836I
b = −1.21347 + 0.79087I
−1.48915 − 3.72263I 3.48687 + 9.47280I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
21
+ 3u
19
+ ··· + 4u
3
− 1)(u
107
+ 7u
106
+ ··· − 3628491u − 687859)
c
2
(u
21
− 3u
20
+ ··· − 3u + 1)(u
107
+ 2u
106
+ ··· − 142u + 7)
c
3
, c
4
(u
21
+ 12u
19
+ ··· − 3u
2
− 1)(u
107
+ u
106
+ ··· + 43u + 1)
c
5
(u
21
+ 3u
19
+ ··· − 3u
2
− 1)(u
107
+ u
106
+ ··· + 229u + 31)
c
6
(u
21
+ 3u
20
+ ··· − 3u − 1)(u
107
+ 2u
106
+ ··· − 142u + 7)
c
7
(u
21
+ u
20
+ ··· − 2u − 1)(u
107
+ 47u
105
+ ··· + 141u + 19)
c
8
(u
21
− u
20
+ ··· + 3u
2
− 1)(u
107
− 21u
105
+ ··· + 516631u + 130055)
c
9
(u
21
+ 12u
19
+ ··· + 3u
2
+ 1)(u
107
+ u
106
+ ··· + 43u + 1)
c
10
(u
21
+ 4u
18
+ ··· + 2u − 1)(u
107
− 7u
106
+ ··· + u + 1)
c
11
, c
12
(u
21
− u
20
+ ··· − 2u + 1)(u
107
+ 47u
105
+ ··· + 141u + 19)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
21
+ 6y
20
+ ··· + 4y
2
− 1)
· (y
107
− 25y
106
+ ··· + 17280320516861y −473150003881)
c
2
, c
6
(y
21
− 15y
20
+ ··· + 21y −1)(y
107
− 62y
106
+ ··· + 4890y −49)
c
3
, c
4
, c
9
(y
21
+ 24y
20
+ ··· − 6y −1)(y
107
+ 109y
106
+ ··· + 1159y −1)
c
5
(y
21
+ 6y
20
+ ··· − 6y −1)(y
107
+ 15y
106
+ ··· − 27601y −961)
c
7
, c
11
, c
12
(y
21
+ 21y
20
+ ··· + 6y −1)(y
107
+ 94y
106
+ ··· + 6619y −361)
c
8
(y
21
− 7y
20
+ ··· + 6y −1)
· (y
107
− 42y
106
+ ··· + 181397207991y −16914303025)
c
10
(y
21
+ 8y
19
+ ··· + 6y −1)(y
107
+ y
106
+ ··· + 111y −1)
23
