12a
0782
(K12a
0782
)
A knot diagram
1
Linearized knot diagam
3 8 10 1 12 11 2 5 4 7 6 9
Solving Sequence
1,4 5,9
10 3 2 8 7 12 6 11
c
4
c
9
c
3
c
1
c
8
c
7
c
12
c
5
c
11
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.11865 × 10
428
u
94
− 1.08212 × 10
429
u
93
+ ··· + 2.38307 × 10
427
b + 9.28828 × 10
427
,
3.77418 × 10
428
u
94
− 2.18208 × 10
429
u
93
+ ··· + 2.38307 × 10
427
a + 4.03773 × 10
428
, u
95
− 6u
94
+ ··· − 30u + 1i
I
u
2
= h−26712u
19
− 136095u
18
+ ··· + 41267b + 19242,
− 97076u
19
− 295395u
18
+ ··· + 41267a + 23990, u
20
+ 3u
19
+ ··· − 3u
3
+ 1i
* 2 irreducible components of dim
C
= 0, with total 115 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
= h2.12 × 10
428
u
94
− 1.08 × 10
429
u
93
+ · · · + 2.38 × 10
427
b + 9.29 ×
10
427
, 3.77 × 10
428
u
94
− 2.18 × 10
429
u
93
+ · · · + 2.38 × 10
427
a + 4.04 ×
10
428
, u
95
− 6u
94
+ · · · − 30u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
9
=
−15.8375u
94
+ 91.5658u
93
+ ··· + 24.0389u − 16.9434
−8.89041u
94
+ 45.4085u
93
+ ··· + 72.2169u − 3.89761
a
10
=
−24.7279u
94
+ 136.974u
93
+ ··· + 96.2557u − 20.8410
−8.89041u
94
+ 45.4085u
93
+ ··· + 72.2169u − 3.89761
a
3
=
6.52903u
94
− 30.9088u
93
+ ··· − 1287.55u + 60.5572
4.24134u
94
− 26.0490u
93
+ ··· + 899.845u − 36.4157
a
2
=
45.2454u
94
− 254.396u
93
+ ··· + 3003.20u − 103.906
20.5669u
94
− 115.764u
93
+ ··· + 1600.35u − 58.5354
a
8
=
−25.8044u
94
+ 142.203u
93
+ ··· + 184.186u − 24.2999
−14.1864u
94
+ 74.6594u
93
+ ··· − 192.744u + 5.26665
a
7
=
17.4039u
94
− 102.619u
93
+ ··· + 3770.93u − 153.901
35.8133u
94
− 200.858u
93
+ ··· + 2303.55u − 81.5877
a
12
=
61.6817u
94
− 355.931u
93
+ ··· + 5974.92u − 220.895
8.86630u
94
− 48.4230u
93
+ ··· + 165.604u − 2.28769
a
6
=
9.50913u
94
− 73.9815u
93
+ ··· + 6807.32u − 286.013
5.28830u
94
− 29.8106u
93
+ ··· + 261.607u − 7.96118
a
11
=
−135.721u
94
+ 772.386u
93
+ ··· − 9767.50u + 335.007
−17.0754u
94
+ 96.2722u
93
+ ··· − 790.075u + 25.1554
(ii) Obstruction class = −1
(iii) Cusp Shapes = 59.3924u
94
− 339.420u
93
+ ··· + 6474.19u − 259.078
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
95
+ 47u
94
+ ··· + 22027u + 1849
c
2
, c
7
u
95
+ u
94
+ ··· + 107u + 43
c
3
, c
9
u
95
+ u
94
+ ··· + 3057u + 677
c
4
u
95
− 6u
94
+ ··· − 30u + 1
c
5
, c
6
, c
10
c
11
u
95
− u
94
+ ··· + 378u + 43
c
8
u
95
+ 4u
94
+ ··· + 2534u + 649
c
12
u
95
+ 3u
94
+ ··· − 54430u − 10639
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
95
+ 13y
94
+ ··· − 54944849y −3418801
c
2
, c
7
y
95
− 47y
94
+ ··· + 22027y −1849
c
3
, c
9
y
95
+ 75y
94
+ ··· − 16234519y −458329
c
4
y
95
− 8y
94
+ ··· + 30y −1
c
5
, c
6
, c
10
c
11
y
95
+ 119y
94
+ ··· − 54314y −1849
c
8
y
95
− 24y
94
+ ··· + 11018672y −421201
c
12
y
95
− 41y
94
+ ··· + 5892243774y −113188321
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.289117 + 0.959904I
a = 0.247983 − 0.890243I
b = −0.444716 + 0.246446I
−0.95680 + 2.64726I 0
u = −0.289117 − 0.959904I
a = 0.247983 + 0.890243I
b = −0.444716 − 0.246446I
−0.95680 − 2.64726I 0
u = 0.994310 + 0.055911I
a = 0.783766 − 0.213159I
b = −0.87312 + 1.52848I
−13.5623 − 6.1465I 0
u = 0.994310 − 0.055911I
a = 0.783766 + 0.213159I
b = −0.87312 − 1.52848I
−13.5623 + 6.1465I 0
u = −0.720342 + 0.734951I
a = 1.182430 + 0.140111I
b = −1.49757 − 0.03566I
−9.78510 + 9.45959I 0
u = −0.720342 − 0.734951I
a = 1.182430 − 0.140111I
b = −1.49757 + 0.03566I
−9.78510 − 9.45959I 0
u = −0.964676 + 0.376723I
a = 0.691405 + 0.116066I
b = −0.522740 − 1.139190I
−3.29940 + 0.97709I 0
u = −0.964676 − 0.376723I
a = 0.691405 − 0.116066I
b = −0.522740 + 1.139190I
−3.29940 − 0.97709I 0
u = −0.460088 + 0.936654I
a = −0.477266 + 1.215140I
b = 0.745588 − 0.483057I
−9.39170 + 3.08813I 0
u = −0.460088 − 0.936654I
a = −0.477266 − 1.215140I
b = 0.745588 + 0.483057I
−9.39170 − 3.08813I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.904927 + 0.274763I
a = 1.023640 + 0.473666I
b = −0.567159 + 1.166250I
−3.73367 − 3.88567I 0
u = 0.904927 − 0.274763I
a = 1.023640 − 0.473666I
b = −0.567159 − 1.166250I
−3.73367 + 3.88567I 0
u = −1.035510 + 0.231678I
a = 0.861175 + 1.081130I
b = 0.327085 + 0.335473I
−11.24410 − 5.06256I 0
u = −1.035510 − 0.231678I
a = 0.861175 − 1.081130I
b = 0.327085 − 0.335473I
−11.24410 + 5.06256I 0
u = −0.668864 + 0.829081I
a = −0.984513 − 0.209552I
b = 1.202030 + 0.080693I
−0.93766 + 7.51485I 0
u = −0.668864 − 0.829081I
a = −0.984513 + 0.209552I
b = 1.202030 − 0.080693I
−0.93766 − 7.51485I 0
u = 0.927854 + 0.110516I
a = −0.751235 − 0.065614I
b = 0.73470 − 1.39916I
−5.20284 − 5.28701I 0
u = 0.927854 − 0.110516I
a = −0.751235 + 0.065614I
b = 0.73470 + 1.39916I
−5.20284 + 5.28701I 0
u = −0.958848 + 0.490910I
a = −0.934638 + 0.178527I
b = 0.903421 + 0.646140I
−3.06403 + 1.76286I 0
u = −0.958848 − 0.490910I
a = −0.934638 − 0.178527I
b = 0.903421 − 0.646140I
−3.06403 − 1.76286I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.345722 + 0.851089I
a = −1.033130 − 0.722887I
b = 0.456443 + 0.763853I
0.13024 + 2.18300I 0
u = −0.345722 − 0.851089I
a = −1.033130 + 0.722887I
b = 0.456443 − 0.763853I
0.13024 − 2.18300I 0
u = −0.280938 + 1.045430I
a = 0.66353 + 1.42921I
b = −0.109739 − 0.905737I
−0.03198 + 3.42317I 0
u = −0.280938 − 1.045430I
a = 0.66353 − 1.42921I
b = −0.109739 + 0.905737I
−0.03198 − 3.42317I 0
u = 0.292505 + 0.842148I
a = −0.839759 + 0.369119I
b = 0.760407 + 0.174654I
2.37641 + 0.47115I 0
u = 0.292505 − 0.842148I
a = −0.839759 − 0.369119I
b = 0.760407 − 0.174654I
2.37641 − 0.47115I 0
u = −1.065600 + 0.308081I
a = −0.679248 − 0.343845I
b = 0.59924 + 1.40120I
−11.60630 + 0.90409I 0
u = −1.065600 − 0.308081I
a = −0.679248 + 0.343845I
b = 0.59924 − 1.40120I
−11.60630 − 0.90409I 0
u = −0.883069
a = 0.647690
b = −0.352931
−1.80352 0
u = 0.671202 + 0.561115I
a = −1.45085 + 0.08625I
b = 1.116020 + 0.035605I
−7.48014 − 4.78255I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.671202 − 0.561115I
a = −1.45085 − 0.08625I
b = 1.116020 − 0.035605I
−7.48014 + 4.78255I 0
u = −0.259215 + 1.102920I
a = −0.67085 − 1.72442I
b = 0.078689 + 1.097050I
−7.87333 + 3.80259I 0
u = −0.259215 − 1.102920I
a = −0.67085 + 1.72442I
b = 0.078689 − 1.097050I
−7.87333 − 3.80259I 0
u = −0.586307 + 0.973561I
a = 0.695896 + 0.316974I
b = −0.745228 − 0.093350I
1.69308 + 4.33267I 0
u = −0.586307 − 0.973561I
a = 0.695896 − 0.316974I
b = −0.745228 + 0.093350I
1.69308 − 4.33267I 0
u = −0.983002 + 0.573098I
a = 1.138440 − 0.219507I
b = −1.173070 − 0.648972I
−11.15500 + 2.05012I 0
u = −0.983002 − 0.573098I
a = 1.138440 + 0.219507I
b = −1.173070 + 0.648972I
−11.15500 − 2.05012I 0
u = 1.110710 + 0.290968I
a = −1.135840 − 0.546865I
b = 0.390635 − 0.902935I
−9.35548 − 3.78734I 0
u = 1.110710 − 0.290968I
a = −1.135840 + 0.546865I
b = 0.390635 + 0.902935I
−9.35548 + 3.78734I 0
u = −1.152000 + 0.039647I
a = −0.722058 − 0.475056I
b = −0.076023 − 0.384783I
−3.37674 − 2.78375I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.152000 − 0.039647I
a = −0.722058 + 0.475056I
b = −0.076023 + 0.384783I
−3.37674 + 2.78375I 0
u = 0.501415 + 0.649342I
a = 1.240930 − 0.257663I
b = −0.968639 − 0.104841I
0.59827 − 2.85627I 0
u = 0.501415 − 0.649342I
a = 1.240930 + 0.257663I
b = −0.968639 + 0.104841I
0.59827 + 2.85627I 0
u = 0.971469 + 0.866417I
a = 1.43450 − 0.30255I
b = −0.28159 + 1.42485I
−18.0405 − 6.3079I 0
u = 0.971469 − 0.866417I
a = 1.43450 + 0.30255I
b = −0.28159 − 1.42485I
−18.0405 + 6.3079I 0
u = 1.076390 + 0.734224I
a = −1.213520 + 0.008244I
b = 0.246608 − 1.273080I
−8.70092 − 4.69865I 0
u = 1.076390 − 0.734224I
a = −1.213520 − 0.008244I
b = 0.246608 + 1.273080I
−8.70092 + 4.69865I 0
u = 0.005021 + 0.677987I
a = 2.14658 + 1.03569I
b = −0.504060 − 0.709244I
−6.31275 + 2.09871I 0.46926 − 2.25158I
u = 0.005021 − 0.677987I
a = 2.14658 − 1.03569I
b = −0.504060 + 0.709244I
−6.31275 − 2.09871I 0.46926 + 2.25158I
u = 0.426863 + 0.431697I
a = −2.28395 − 2.76519I
b = 0.469197 − 1.010660I
−10.94880 − 7.65283I −5.22797 + 11.06490I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.426863 − 0.431697I
a = −2.28395 + 2.76519I
b = 0.469197 + 1.010660I
−10.94880 + 7.65283I −5.22797 − 11.06490I
u = −0.57480 + 1.29543I
a = 0.450516 + 0.332022I
b = −0.416072 − 1.184950I
−4.33687 + 0.29946I 0
u = −0.57480 − 1.29543I
a = 0.450516 − 0.332022I
b = −0.416072 + 1.184950I
−4.33687 − 0.29946I 0
u = 0.481464 + 0.319780I
a = 0.89697 + 2.60290I
b = −0.359298 + 1.076130I
−3.23096 − 6.09113I −3.77113 + 12.10008I
u = 0.481464 − 0.319780I
a = 0.89697 − 2.60290I
b = −0.359298 − 1.076130I
−3.23096 + 6.09113I −3.77113 − 12.10008I
u = −0.16641 + 1.41807I
a = 0.098862 − 0.226912I
b = −0.161596 − 0.347833I
−1.34120 + 2.57391I 0
u = −0.16641 − 1.41807I
a = 0.098862 + 0.226912I
b = −0.161596 + 0.347833I
−1.34120 − 2.57391I 0
u = 0.63328 + 1.29448I
a = 0.237064 − 0.603765I
b = 0.07138 + 1.63295I
−16.8400 − 0.1881I 0
u = 0.63328 − 1.29448I
a = 0.237064 + 0.603765I
b = 0.07138 − 1.63295I
−16.8400 + 0.1881I 0
u = 0.470623 + 0.153489I
a = 0.84615 − 1.99787I
b = 0.161106 − 1.169670I
−2.10008 − 3.17693I −1.78235 + 1.84660I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.470623 − 0.153489I
a = 0.84615 + 1.99787I
b = 0.161106 + 1.169670I
−2.10008 + 3.17693I −1.78235 − 1.84660I
u = −1.22924 + 0.89403I
a = 0.498695 + 0.194874I
b = −0.162574 − 1.065220I
−3.52126 + 0.24217I 0
u = −1.22924 − 0.89403I
a = 0.498695 − 0.194874I
b = −0.162574 + 1.065220I
−3.52126 − 0.24217I 0
u = −1.08638 + 1.07371I
a = −0.743525 − 0.138471I
b = 0.413995 + 1.178270I
−0.71653 + 3.86741I 0
u = −1.08638 − 1.07371I
a = −0.743525 + 0.138471I
b = 0.413995 − 1.178270I
−0.71653 − 3.86741I 0
u = −1.10562 + 1.07856I
a = 0.925228 + 0.207336I
b = −0.482928 − 1.283410I
−3.13830 + 8.02376I 0
u = −1.10562 − 1.07856I
a = 0.925228 − 0.207336I
b = −0.482928 + 1.283410I
−3.13830 − 8.02376I 0
u = −1.10479 + 1.09357I
a = −1.048780 − 0.298417I
b = 0.53126 + 1.37393I
−11.7724 + 10.6064I 0
u = −1.10479 − 1.09357I
a = −1.048780 + 0.298417I
b = 0.53126 − 1.37393I
−11.7724 − 10.6064I 0
u = 0.427563 + 0.067044I
a = −1.72094 − 0.04130I
b = 0.19085 − 1.52986I
−6.20830 + 1.24493I −11.68136 − 0.65851I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.427563 − 0.067044I
a = −1.72094 + 0.04130I
b = 0.19085 + 1.52986I
−6.20830 − 1.24493I −11.68136 + 0.65851I
u = 0.355675 + 0.207652I
a = 1.56513 − 1.07893I
b = −0.32861 + 2.05152I
−16.2010 + 0.7832I −17.0479 + 0.5823I
u = 0.355675 − 0.207652I
a = 1.56513 + 1.07893I
b = −0.32861 − 2.05152I
−16.2010 − 0.7832I −17.0479 − 0.5823I
u = 1.21695 + 1.09079I
a = 0.995083 − 0.184335I
b = −0.62985 + 1.48106I
−14.6050 − 16.6598I 0
u = 1.21695 − 1.09079I
a = 0.995083 + 0.184335I
b = −0.62985 − 1.48106I
−14.6050 + 16.6598I 0
u = 1.46702 + 0.73223I
a = 0.683592 + 0.065915I
b = −0.040154 + 1.129080I
−4.43466 − 1.20428I 0
u = 1.46702 − 0.73223I
a = 0.683592 − 0.065915I
b = −0.040154 − 1.129080I
−4.43466 + 1.20428I 0
u = −0.136891 + 0.322702I
a = −2.60789 + 0.71307I
b = 0.269010 + 0.682992I
0.385020 + 1.267230I 3.97029 − 5.44435I
u = −0.136891 − 0.322702I
a = −2.60789 − 0.71307I
b = 0.269010 − 0.682992I
0.385020 − 1.267230I 3.97029 + 5.44435I
u = −1.25254 + 1.07390I
a = −0.362692 − 0.428942I
b = −0.028944 + 1.230660I
−11.96400 − 2.23884I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.25254 − 1.07390I
a = −0.362692 + 0.428942I
b = −0.028944 − 1.230660I
−11.96400 + 2.23884I 0
u = 1.25127 + 1.12817I
a = −0.849440 + 0.130050I
b = 0.52648 − 1.42248I
−5.7110 − 13.5269I 0
u = 1.25127 − 1.12817I
a = −0.849440 − 0.130050I
b = 0.52648 + 1.42248I
−5.7110 + 13.5269I 0
u = 0.221687 + 0.111443I
a = −6.26482 + 0.66732I
b = 0.199795 + 0.664032I
−6.58989 − 2.82612I −5.29343 + 0.17006I
u = 0.221687 − 0.111443I
a = −6.26482 − 0.66732I
b = 0.199795 − 0.664032I
−6.58989 + 2.82612I −5.29343 − 0.17006I
u = 1.30422 + 1.23689I
a = 0.641285 − 0.114442I
b = −0.37853 + 1.37706I
−3.00402 − 8.54591I 0
u = 1.30422 − 1.23689I
a = 0.641285 + 0.114442I
b = −0.37853 − 1.37706I
−3.00402 + 8.54591I 0
u = 0.0974839 + 0.1009380I
a = 6.53790 + 0.14587I
b = −0.280215 − 0.524506I
0.188702 − 1.373040I 1.57614 + 4.30040I
u = 0.0974839 − 0.1009380I
a = 6.53790 − 0.14587I
b = −0.280215 + 0.524506I
0.188702 + 1.373040I 1.57614 − 4.30040I
u = 1.32927 + 1.32418I
a = 0.297328 − 0.413174I
b = 0.251344 + 1.216280I
−14.1998 + 7.5723I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.32927 − 1.32418I
a = 0.297328 + 0.413174I
b = 0.251344 − 1.216280I
−14.1998 − 7.5723I 0
u = 1.15816 + 1.50493I
a = −0.404891 + 0.251702I
b = 0.17621 − 1.41765I
−6.30515 − 3.27171I 0
u = 1.15816 − 1.50493I
a = −0.404891 − 0.251702I
b = 0.17621 + 1.41765I
−6.30515 + 3.27171I 0
u = 1.57110 + 1.12346I
a = −0.428088 + 0.171106I
b = −0.112599 − 1.159780I
−5.81046 + 3.88421I 0
u = 1.57110 − 1.12346I
a = −0.428088 − 0.171106I
b = −0.112599 + 1.159780I
−5.81046 − 3.88421I 0
14
II.
I
u
2
= h−2.67 × 10
4
u
19
− 1.36 × 10
5
u
18
+ · · · + 4.13 × 10
4
b + 1.92 × 10
4
, −9.71 ×
10
4
u
19
−2.95×10
5
u
18
+· · ·+4.13×10
4
a+2.40×10
4
, u
20
+3u
19
+· · ·−3u
3
+1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
9
=
2.35239u
19
+ 7.15814u
18
+ ··· − 0.282647u − 0.581336
0.647297u
19
+ 3.29791u
18
+ ··· − 0.981438u − 0.466281
a
10
=
2.99968u
19
+ 10.4561u
18
+ ··· − 1.26409u − 1.04762
0.647297u
19
+ 3.29791u
18
+ ··· − 0.981438u − 0.466281
a
3
=
0.498340u
19
+ 2.01844u
18
+ ··· − 1.77614u + 0.556789
0.498340u
19
+ 1.01844u
18
+ ··· + 1.22386u − 0.443211
a
2
=
−1.05845u
19
− 3.15359u
18
+ ··· − 0.767175u − 1.21935
0.0217607u
19
− 0.964378u
18
+ ··· + 2.78065u + 0.0584486
a
8
=
2.71638u
19
+ 8.43551u
18
+ ··· + 1.08830u − 0.946640
0.951414u
19
+ 4.72225u
18
+ ··· − 1.34543u − 0.651659
a
7
=
−0.946640u
19
− 5.55630u
18
+ ··· + 4.42426u − 1.08830
0.704364u
19
+ 1.75881u
18
+ ··· + 0.935517u + 0.698137
a
12
=
−2.00928u
19
− 5.79470u
18
+ ··· − 3.01112u − 3.01825
u
19
+ 3u
18
+ ··· − 3u
2
+ u
a
6
=
−0.240265u
19
+ 2.98309u
18
+ ··· − 8.26183u + 2.76000
−1.05513u
19
− 3.19047u
18
+ ··· − 0.214893u − 1.33293
a
11
=
4.42492u
19
+ 12.7758u
18
+ ··· + 5.13325u + 3.68919
−1.43638u
19
− 3.87469u
18
+ ··· − 2.43420u + 0.732135
(ii) Obstruction class = 1
(iii) Cusp Shapes =
2093
1423
u
19
+
15200
1423
u
18
+ ··· −
14211
1423
u −
3810
1423
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− 10u
19
+ ··· − 13u + 1
c
2
u
20
− 5u
18
+ ··· + u + 1
c
3
u
20
+ 10u
18
+ ··· + u + 1
c
4
u
20
+ 3u
19
+ ··· − 3u
3
+ 1
c
5
, c
6
u
20
+ 14u
18
+ ··· + 2u + 1
c
7
u
20
− 5u
18
+ ··· − u + 1
c
8
u
20
− u
19
+ ··· − 2u + 1
c
9
u
20
+ 10u
18
+ ··· − u + 1
c
10
, c
11
u
20
+ 14u
18
+ ··· − 2u + 1
c
12
u
20
− 4u
19
+ ··· − 4u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
+ 10y
19
+ ··· + 7y + 1
c
2
, c
7
y
20
− 10y
19
+ ··· − 13y + 1
c
3
, c
9
y
20
+ 20y
19
+ ··· + 17y + 1
c
4
y
20
+ y
19
+ ··· − 6y
2
+ 1
c
5
, c
6
, c
10
c
11
y
20
+ 28y
19
+ ··· + 24y + 1
c
8
y
20
− 3y
19
+ ··· + 2y + 1
c
12
y
20
− 12y
19
+ ··· − 12y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.354216 + 0.910702I
a = −0.83992 − 1.29403I
b = 0.112283 + 0.669508I
0.55730 + 3.17204I 5.96809 − 4.30599I
u = −0.354216 − 0.910702I
a = −0.83992 + 1.29403I
b = 0.112283 − 0.669508I
0.55730 − 3.17204I 5.96809 + 4.30599I
u = 0.940886 + 0.013452I
a = 0.401603 + 0.846607I
b = −0.485223 + 1.103280I
−3.89387 − 5.07290I −6.24968 + 7.07745I
u = 0.940886 − 0.013452I
a = 0.401603 − 0.846607I
b = −0.485223 − 1.103280I
−3.89387 + 5.07290I −6.24968 − 7.07745I
u = −1.086910 + 0.143350I
a = 0.988461 − 0.625648I
b = −0.481788 − 0.523177I
−8.60982 + 3.31110I −3.02160 − 0.26217I
u = −1.086910 − 0.143350I
a = 0.988461 + 0.625648I
b = −0.481788 + 0.523177I
−8.60982 − 3.31110I −3.02160 + 0.26217I
u = 0.831705 + 0.757532I
a = −0.545903 + 0.048817I
b = 0.26159 − 1.41773I
−5.34600 − 2.40154I −6.23549 + 2.82365I
u = 0.831705 − 0.757532I
a = −0.545903 − 0.048817I
b = 0.26159 + 1.41773I
−5.34600 + 2.40154I −6.23549 − 2.82365I
u = −1.124410 + 0.373073I
a = −0.734596 + 0.227076I
b = 0.546149 + 0.748639I
−2.02296 + 1.85750I 0.15205 − 3.47247I
u = −1.124410 − 0.373073I
a = −0.734596 − 0.227076I
b = 0.546149 − 0.748639I
−2.02296 − 1.85750I 0.15205 + 3.47247I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.335386 + 0.673441I
a = 1.89916 + 2.10509I
b = −0.117754 − 0.611933I
−6.16437 + 3.50843I 1.04098 − 7.63550I
u = −0.335386 − 0.673441I
a = 1.89916 − 2.10509I
b = −0.117754 + 0.611933I
−6.16437 − 3.50843I 1.04098 + 7.63550I
u = 0.075229 + 0.691605I
a = 0.314256 − 1.001560I
b = 0.17170 + 1.96088I
−15.7703 − 1.0203I −1.42896 + 8.09833I
u = 0.075229 − 0.691605I
a = 0.314256 + 1.001560I
b = 0.17170 − 1.96088I
−15.7703 + 1.0203I −1.42896 − 8.09833I
u = −0.840408 + 1.000340I
a = 0.391400 + 0.249495I
b = −0.484708 − 1.165360I
−4.50713 − 0.43448I −8.00022 + 4.48441I
u = −0.840408 − 1.000340I
a = 0.391400 − 0.249495I
b = −0.484708 + 1.165360I
−4.50713 + 0.43448I −8.00022 − 4.48441I
u = 0.657334 + 0.200921I
a = 0.02446 + 1.99194I
b = 0.583165 + 0.888157I
−11.41920 + 6.77394I −8.69980 − 4.47672I
u = 0.657334 − 0.200921I
a = 0.02446 − 1.99194I
b = 0.583165 − 0.888157I
−11.41920 − 6.77394I −8.69980 + 4.47672I
u = −0.26383 + 1.56148I
a = 0.101075 + 0.499810I
b = −0.105421 − 0.774841I
−2.04126 + 2.70464I −9.52536 − 4.18246I
u = −0.26383 − 1.56148I
a = 0.101075 − 0.499810I
b = −0.105421 + 0.774841I
−2.04126 − 2.70464I −9.52536 + 4.18246I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
20
− 10u
19
+ ··· − 13u + 1)(u
95
+ 47u
94
+ ··· + 22027u + 1849)
c
2
(u
20
− 5u
18
+ ··· + u + 1)(u
95
+ u
94
+ ··· + 107u + 43)
c
3
(u
20
+ 10u
18
+ ··· + u + 1)(u
95
+ u
94
+ ··· + 3057u + 677)
c
4
(u
20
+ 3u
19
+ ··· − 3u
3
+ 1)(u
95
− 6u
94
+ ··· − 30u + 1)
c
5
, c
6
(u
20
+ 14u
18
+ ··· + 2u + 1)(u
95
− u
94
+ ··· + 378u + 43)
c
7
(u
20
− 5u
18
+ ··· − u + 1)(u
95
+ u
94
+ ··· + 107u + 43)
c
8
(u
20
− u
19
+ ··· − 2u + 1)(u
95
+ 4u
94
+ ··· + 2534u + 649)
c
9
(u
20
+ 10u
18
+ ··· − u + 1)(u
95
+ u
94
+ ··· + 3057u + 677)
c
10
, c
11
(u
20
+ 14u
18
+ ··· − 2u + 1)(u
95
− u
94
+ ··· + 378u + 43)
c
12
(u
20
− 4u
19
+ ··· − 4u + 1)(u
95
+ 3u
94
+ ··· − 54430u − 10639)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
20
+ 10y
19
+ ··· + 7y + 1)
· (y
95
+ 13y
94
+ ··· − 54944849y −3418801)
c
2
, c
7
(y
20
− 10y
19
+ ··· − 13y + 1)(y
95
− 47y
94
+ ··· + 22027y −1849)
c
3
, c
9
(y
20
+ 20y
19
+ ··· + 17y + 1)
· (y
95
+ 75y
94
+ ··· − 16234519y −458329)
c
4
(y
20
+ y
19
+ ··· − 6y
2
+ 1)(y
95
− 8y
94
+ ··· + 30y −1)
c
5
, c
6
, c
10
c
11
(y
20
+ 28y
19
+ ··· + 24y + 1)(y
95
+ 119y
94
+ ··· − 54314y −1849)
c
8
(y
20
− 3y
19
+ ··· + 2y + 1)(y
95
− 24y
94
+ ··· + 1.10187 × 10
7
y −421201)
c
12
(y
20
− 12y
19
+ ··· − 12y + 1)
· (y
95
− 41y
94
+ ··· + 5892243774y −113188321)
21
