12n
0395
(K12n
0395
)
A knot diagram
1
Linearized knot diagam
3 5 11 9 2 12 3 1 12 4 7 4
Solving Sequence
4,12 1,7
6 11 3 2 5 10 9 8
c
12
c
6
c
11
c
3
c
1
c
5
c
10
c
9
c
8
c
2
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h−377702541u
18
− 368786459u
17
+ ··· + 156030809b + 1065050773,
509610922u
18
+ 379813420u
17
+ ··· + 156030809a − 1049301116, u
19
+ u
18
+ ··· − 3u − 1i
I
u
2
= h1.29506 × 10
87
u
39
+ 1.53497 × 10
87
u
38
+ ··· + 2.69800 × 10
88
b − 3.45877 × 10
88
,
5.34951 × 10
86
u
39
+ 5.15111 × 10
86
u
38
+ ··· + 2.69800 × 10
88
a + 9.82066 × 10
88
, u
40
+ u
39
+ ··· − 15u + 1i
I
u
3
= h−u
10
+ 29u
9
+ 25u
8
− 45u
7
+ 31u
6
+ 58u
5
− 50u
4
+ 86u
3
+ 101u
2
+ 47b − 20u − 11,
31u
10
+ 41u
9
− 23u
8
− 15u
7
+ 26u
6
+ 35u
5
+ 93u
4
+ 60u
3
+ 65u
2
+ 47a − 38u − 129,
u
11
+ u
10
− 2u
9
+ 3u
7
− u
6
+ 2u
5
+ 4u
4
− 2u
3
− 2u
2
+ 1i
I
u
4
= h−2u
9
+ u
8
+ 8u
7
+ 2u
6
− 15u
5
− 7u
4
+ 10u
3
+ 6u
2
+ b − 6u − 3,
− u
9
− u
8
+ 6u
7
+ 5u
6
− 10u
5
− 11u
4
+ 8u
3
+ 8u
2
+ a − 5u − 6,
u
10
− 4u
8
− 3u
7
+ 6u
6
+ 7u
5
− 2u
4
− 5u
3
+ u
2
+ 3u + 1i
* 4 irreducible components of dim
C
= 0, with total 80 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−3.78 × 10
8
u
18
− 3.69 × 10
8
u
17
+ · · · + 1.56 × 10
8
b + 1.07 × 10
9
, 5.10 ×
10
8
u
18
+ 3.80 × 10
8
u
17
+ · · · + 1.56 × 10
8
a − 1.05 × 10
9
, u
19
+ u
18
+ · · · − 3u − 1i
(i) Arc colorings
a
4
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
7
=
−3.26609u
18
− 2.43422u
17
+ ··· + 14.6633u + 6.72496
2.42069u
18
+ 2.36355u
17
+ ··· − 9.38422u − 6.82590
a
6
=
−5.68678u
18
− 4.79777u
17
+ ··· + 24.0475u + 13.5509
2.42069u
18
+ 2.36355u
17
+ ··· − 9.38422u − 6.82590
a
11
=
8.21607u
18
+ 4.60275u
17
+ ··· − 30.9090u − 8.69525
−0.467933u
18
− 1.05048u
17
+ ··· + 3.62390u + 3.61332
a
3
=
2.94393u
18
+ 3.81230u
17
+ ··· − 11.6400u − 13.6846
0.852487u
18
− 0.589367u
17
+ ··· − 1.92514u + 2.74496
a
2
=
4.03573u
18
+ 2.94704u
17
+ ··· − 19.3471u − 5.85388
−1.97347u
18
− 0.834541u
17
+ ··· + 6.74227u + 1.47324
a
5
=
−3.87980u
18
− 5.91327u
17
+ ··· + 16.8878u + 20.9112
0.467933u
18
+ 1.05048u
17
+ ··· − 1.62390u − 3.61332
a
10
=
8.21607u
18
+ 4.60275u
17
+ ··· − 30.9090u − 8.69525
u
a
9
=
8.21607u
18
+ 4.60275u
17
+ ··· − 31.9090u − 8.69525
u
a
8
=
8.68401u
18
+ 5.65323u
17
+ ··· − 33.5329u − 12.3086
0.580147u
18
+ 0.361879u
17
+ ··· − 1.21559u − 0.582551
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
858705183
156030809
u
18
−
1012526591
156030809
u
17
+ ··· +
5471923598
156030809
u +
4145235745
156030809
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
+ 7u
18
+ ··· − 4u − 1
c
2
, c
5
, c
6
c
11
u
19
+ u
18
+ ··· + 2u − 1
c
3
, c
10
u
19
− 11u
18
+ ··· + 60u − 8
c
4
u
19
+ 12u
18
+ ··· − 176u − 32
c
7
u
19
− u
18
+ ··· + 1133u − 517
c
8
u
19
+ 11u
17
+ ··· − 7u − 13
c
9
, c
12
u
19
+ u
18
+ ··· − 3u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
+ 23y
18
+ ··· + 28y −1
c
2
, c
5
, c
6
c
11
y
19
+ 7y
18
+ ··· − 4y −1
c
3
, c
10
y
19
+ 3y
18
+ ··· − 368y −64
c
4
y
19
+ 8y
18
+ ··· + 6912y −1024
c
7
y
19
− 7y
18
+ ··· + 566093y −267289
c
8
y
19
+ 22y
18
+ ··· − 2291y −169
c
9
, c
12
y
19
− 23y
18
+ ··· + 9y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.043320 + 0.605021I
a = −0.095431 − 1.196260I
b = −0.072994 − 1.051030I
−3.46673 − 2.11998I 0.23396 + 2.61296I
u = −1.043320 − 0.605021I
a = −0.095431 + 1.196260I
b = −0.072994 + 1.051030I
−3.46673 + 2.11998I 0.23396 − 2.61296I
u = 1.279840 + 0.395378I
a = 0.190387 − 0.406271I
b = 0.221252 − 0.463223I
1.07628 + 1.45118I 13.08253 + 0.58489I
u = 1.279840 − 0.395378I
a = 0.190387 + 0.406271I
b = 0.221252 + 0.463223I
1.07628 − 1.45118I 13.08253 − 0.58489I
u = −0.091308 + 0.542033I
a = −0.05772 − 3.40851I
b = −0.321625 − 0.991324I
−6.77802 + 4.24933I −2.37252 − 3.20470I
u = −0.091308 − 0.542033I
a = −0.05772 + 3.40851I
b = −0.321625 + 0.991324I
−6.77802 − 4.24933I −2.37252 + 3.20470I
u = −0.396664 + 0.369740I
a = 1.23276 + 1.31882I
b = 0.190738 + 0.915706I
−2.12350 + 1.85148I 4.32931 − 4.24457I
u = −0.396664 − 0.369740I
a = 1.23276 − 1.31882I
b = 0.190738 − 0.915706I
−2.12350 − 1.85148I 4.32931 + 4.24457I
u = 1.49967 + 0.06625I
a = −0.574936 − 0.248373I
b = 0.819301 + 1.051500I
8.33063 + 6.97397I 8.76530 − 4.76080I
u = 1.49967 − 0.06625I
a = −0.574936 + 0.248373I
b = 0.819301 − 1.051500I
8.33063 − 6.97397I 8.76530 + 4.76080I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.356851 + 0.335765I
a = 1.25082 + 2.28548I
b = −0.656301 − 0.536511I
−3.49379 + 2.71619I 7.39466 − 0.32501I
u = −0.356851 − 0.335765I
a = 1.25082 − 2.28548I
b = −0.656301 + 0.536511I
−3.49379 − 2.71619I 7.39466 + 0.32501I
u = −1.56268 + 0.05774I
a = −1.259550 − 0.485799I
b = 0.975642 − 0.970457I
9.19399 − 6.70093I 9.82122 + 4.48583I
u = −1.56268 − 0.05774I
a = −1.259550 + 0.485799I
b = 0.975642 + 0.970457I
9.19399 + 6.70093I 9.82122 − 4.48583I
u = 0.315741
a = 1.20666
b = 0.408538
0.727380 13.8820
u = 1.68314 + 0.54519I
a = 0.259507 − 0.084155I
b = −0.986094 + 0.888888I
9.98818 + 1.53259I 10.28519 + 0.05847I
u = 1.68314 − 0.54519I
a = 0.259507 + 0.084155I
b = −0.986094 − 0.888888I
9.98818 − 1.53259I 10.28519 − 0.05847I
u = −1.66969 + 0.71456I
a = 0.950831 + 0.876319I
b = −0.87419 + 1.14110I
8.2934 − 15.6503I 8.00000 + 8.25494I
u = −1.66969 − 0.71456I
a = 0.950831 − 0.876319I
b = −0.87419 − 1.14110I
8.2934 + 15.6503I 8.00000 − 8.25494I
6
II.
I
u
2
= h1.30 × 10
87
u
39
+ 1.53 × 10
87
u
38
+ · · · + 2.70 × 10
88
b − 3.46 × 10
88
, 5.35 ×
10
86
u
39
+5.15×10
86
u
38
+· · ·+2.70×10
88
a+9.82×10
88
, u
40
+u
39
+· · ·−15u+1i
(i) Arc colorings
a
4
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
7
=
−0.0198277u
39
− 0.0190923u
38
+ ··· − 44.7904u − 3.63997
−0.0480005u
39
− 0.0568927u
38
+ ··· + 0.311946u + 1.28197
a
6
=
0.0281728u
39
+ 0.0378004u
38
+ ··· − 45.1024u − 4.92194
−0.0480005u
39
− 0.0568927u
38
+ ··· + 0.311946u + 1.28197
a
11
=
0.536629u
39
+ 0.596877u
38
+ ··· − 25.4262u − 5.72637
−0.0756455u
39
− 0.0881317u
38
+ ··· + 1.50300u + 0.486117
a
3
=
0.458136u
39
+ 0.471790u
38
+ ··· + 63.8377u − 7.67485
−0.0990701u
39
− 0.0884537u
38
+ ··· − 17.1405u + 0.775723
a
2
=
0.0573134u
39
+ 0.0688277u
38
+ ··· + 43.4630u + 6.53740
0.0953537u
39
+ 0.101112u
38
+ ··· + 5.88241u − 2.22024
a
5
=
−0.638325u
39
− 0.657958u
38
+ ··· − 103.579u + 9.05298
0.0880767u
39
+ 0.0956592u
38
+ ··· + 22.3476u − 0.616054
a
10
=
0.536629u
39
+ 0.596877u
38
+ ··· − 25.4262u − 5.72637
−0.0734017u
39
− 0.0888770u
38
+ ··· + 1.87009u + 0.425868
a
9
=
0.610031u
39
+ 0.685754u
38
+ ··· − 27.2963u − 6.15224
−0.0734017u
39
− 0.0888770u
38
+ ··· + 1.87009u + 0.425868
a
8
=
0.542040u
39
+ 0.596575u
38
+ ··· − 24.9003u − 5.80209
−0.0788525u
39
− 0.0842106u
38
+ ··· + 2.11993u + 0.404680
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.442497u
39
+ 0.473863u
38
+ ··· + 3.13307u + 13.3769
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
40
+ 8u
39
+ ··· + 1381u + 121
c
2
, c
5
, c
6
c
11
u
40
− 2u
39
+ ··· + 29u + 11
c
3
, c
10
(u
20
+ 5u
19
+ ··· + 5u + 1)
2
c
4
(u
20
− 5u
19
+ ··· − 6u + 1)
2
c
7
u
40
− 18u
38
+ ··· + 26588u + 210103
c
8
u
40
− 2u
39
+ ··· − 350134u + 28487
c
9
, c
12
u
40
+ u
39
+ ··· − 15u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
40
+ 40y
39
+ ··· + 111361y + 14641
c
2
, c
5
, c
6
c
11
y
40
+ 8y
39
+ ··· + 1381y + 121
c
3
, c
10
(y
20
− y
19
+ ··· − 9y + 1)
2
c
4
(y
20
− y
19
+ ··· − 20y + 1)
2
c
7
y
40
− 36y
39
+ ··· + 252213388832y + 44143270609
c
8
y
40
+ 40y
39
+ ··· − 4553546458y + 811509169
c
9
, c
12
y
40
− 33y
39
+ ··· + 5y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.789817 + 0.551198I
a = −0.69551 + 1.55288I
b = 0.459315 + 1.209800I
−1.25686 + 2.87744I 8.53861 + 0.21509I
u = 0.789817 − 0.551198I
a = −0.69551 − 1.55288I
b = 0.459315 − 1.209800I
−1.25686 − 2.87744I 8.53861 − 0.21509I
u = −0.882283 + 0.194843I
a = −0.417404 − 0.174483I
b = 1.234230 + 0.246821I
3.22335 − 0.66671I 5.55879 + 11.26225I
u = −0.882283 − 0.194843I
a = −0.417404 + 0.174483I
b = 1.234230 − 0.246821I
3.22335 + 0.66671I 5.55879 − 11.26225I
u = 1.096700 + 0.080097I
a = −0.169582 − 0.382784I
b = 0.661294 + 0.316017I
1.73797 + 1.66833I 9.09788 − 4.11752I
u = 1.096700 − 0.080097I
a = −0.169582 + 0.382784I
b = 0.661294 − 0.316017I
1.73797 − 1.66833I 9.09788 + 4.11752I
u = −0.702136 + 0.452232I
a = 1.65697 + 0.89964I
b = −0.604929 + 1.075710I
−5.01038 − 2.16864I 2.33481 + 6.10094I
u = −0.702136 − 0.452232I
a = 1.65697 − 0.89964I
b = −0.604929 − 1.075710I
−5.01038 + 2.16864I 2.33481 − 6.10094I
u = −1.178690 + 0.159087I
a = 0.183886 + 0.503919I
b = −0.538174 + 0.434982I
−0.69886 − 4.77224I 8.00000 + 7.57794I
u = −1.178690 − 0.159087I
a = 0.183886 − 0.503919I
b = −0.538174 − 0.434982I
−0.69886 + 4.77224I 8.00000 − 7.57794I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.000670 + 0.723305I
a = −0.588918 − 1.139490I
b = 0.40494 − 1.37467I
−1.08479 − 6.65241I 8.00000 + 8.68586I
u = −1.000670 − 0.723305I
a = −0.588918 + 1.139490I
b = 0.40494 + 1.37467I
−1.08479 + 6.65241I 8.00000 − 8.68586I
u = 0.958749 + 0.984714I
a = −0.41472 + 1.38571I
b = 0.465289 + 0.991245I
−0.69886 + 4.77224I 0
u = 0.958749 − 0.984714I
a = −0.41472 − 1.38571I
b = 0.465289 − 0.991245I
−0.69886 − 4.77224I 0
u = −1.50241 + 0.07716I
a = −0.496444 − 0.235822I
b = 0.983741 + 0.983994I
9.17040 + 0.45837I 0
u = −1.50241 − 0.07716I
a = −0.496444 + 0.235822I
b = 0.983741 − 0.983994I
9.17040 − 0.45837I 0
u = 1.50669 + 0.14155I
a = −1.44000 − 0.34489I
b = 0.940968 − 0.791711I
9.17040 + 0.45837I 0
u = 1.50669 − 0.14155I
a = −1.44000 + 0.34489I
b = 0.940968 + 0.791711I
9.17040 − 0.45837I 0
u = −1.52444 + 0.02714I
a = 0.708019 + 0.222574I
b = −0.352756 + 0.830770I
−1.25686 + 2.87744I 0
u = −1.52444 − 0.02714I
a = 0.708019 − 0.222574I
b = −0.352756 − 0.830770I
−1.25686 − 2.87744I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.284736 + 0.328185I
a = −4.60209 − 1.08232I
b = −0.118953 + 0.502474I
−5.01038 + 2.16864I 2.33481 − 6.10094I
u = −0.284736 − 0.328185I
a = −4.60209 + 1.08232I
b = −0.118953 − 0.502474I
−5.01038 − 2.16864I 2.33481 + 6.10094I
u = 1.59822 + 0.22825I
a = 0.335646 − 0.321778I
b = −0.129954 − 0.886577I
1.73797 + 1.66833I 0
u = 1.59822 − 0.22825I
a = 0.335646 + 0.321778I
b = −0.129954 + 0.886577I
1.73797 − 1.66833I 0
u = −1.60666 + 0.21833I
a = 1.27939 + 0.87709I
b = −0.562169 + 0.793968I
−1.08479 − 6.65241I 0
u = −1.60666 − 0.21833I
a = 1.27939 − 0.87709I
b = −0.562169 − 0.793968I
−1.08479 + 6.65241I 0
u = −1.56979 + 0.64601I
a = 0.224170 + 0.117637I
b = −1.115240 − 0.763070I
9.55391 − 8.46488I 0
u = −1.56979 − 0.64601I
a = 0.224170 − 0.117637I
b = −1.115240 + 0.763070I
9.55391 + 8.46488I 0
u = 1.74383 + 0.19203I
a = 1.44796 + 1.25852I
b = −0.391026 + 0.507425I
3.22335 − 0.66671I 0
u = 1.74383 − 0.19203I
a = 1.44796 − 1.25852I
b = −0.391026 − 0.507425I
3.22335 + 0.66671I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.46290 + 1.79705I
a = 0.361971 + 0.723514I
b = −0.776259 + 0.727271I
3.67864 + 0.89894I 0
u = 0.46290 − 1.79705I
a = 0.361971 − 0.723514I
b = −0.776259 − 0.727271I
3.67864 − 0.89894I 0
u = 1.76739 + 0.61988I
a = 1.022920 − 0.802923I
b = −0.906801 − 1.018680I
9.55391 + 8.46488I 0
u = 1.76739 − 0.61988I
a = 1.022920 + 0.802923I
b = −0.906801 + 1.018680I
9.55391 − 8.46488I 0
u = −0.0113205 + 0.0913606I
a = −2.90917 − 4.34403I
b = 1.072060 + 0.812581I
3.67864 + 0.89894I 14.7379 − 6.8397I
u = −0.0113205 − 0.0913606I
a = −2.90917 + 4.34403I
b = 1.072060 − 0.812581I
3.67864 − 0.89894I 14.7379 + 6.8397I
u = 0.0698929 + 0.0329543I
a = −6.77015 − 1.38688I
b = 0.98494 − 1.07091I
2.89322 − 6.53100I 16.6269 + 9.9012I
u = 0.0698929 − 0.0329543I
a = −6.77015 + 1.38688I
b = 0.98494 + 1.07091I
2.89322 + 6.53100I 16.6269 − 9.9012I
u = −0.23102 + 2.12015I
a = 0.283053 − 0.859606I
b = −0.710501 − 0.983550I
2.89322 + 6.53100I 0
u = −0.23102 − 2.12015I
a = 0.283053 + 0.859606I
b = −0.710501 + 0.983550I
2.89322 − 6.53100I 0
13
III. I
u
3
= h−u
10
+ 29u
9
+ · · · + 47b − 11, 31u
10
+ 41u
9
+ · · · + 47a −
129, u
11
+ u
10
+ · · · − 2u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
7
=
−0.659574u
10
− 0.872340u
9
+ ··· + 0.808511u + 2.74468
0.0212766u
10
− 0.617021u
9
+ ··· + 0.425532u + 0.234043
a
6
=
−0.680851u
10
− 0.255319u
9
+ ··· + 0.382979u + 2.51064
0.0212766u
10
− 0.617021u
9
+ ··· + 0.425532u + 0.234043
a
11
=
−0.170213u
10
− 1.06383u
9
+ ··· + 0.595745u + 0.127660
0.191489u
10
+ 0.446809u
9
+ ··· − 1.17021u − 0.893617
a
3
=
−2.04255u
10
− 2.76596u
9
+ ··· + 4.14894u + 1.53191
0.106383u
10
− 0.0851064u
9
+ ··· − 0.872340u + 0.170213
a
2
=
−2.17021u
10
− 3.06383u
9
+ ··· + 0.595745u + 3.12766
0.744681u
10
+ 0.404255u
9
+ ··· − 1.10638u − 0.808511
a
5
=
1.65957u
10
+ 1.87234u
9
+ ··· − 3.80851u + 0.255319
0.191489u
10
+ 0.446809u
9
+ ··· + 0.829787u − 0.893617
a
10
=
−0.170213u
10
− 1.06383u
9
+ ··· + 0.595745u + 0.127660
−u
a
9
=
−0.170213u
10
− 1.06383u
9
+ ··· + 1.59574u + 0.127660
−u
a
8
=
−0.361702u
10
− 1.51064u
9
+ ··· + 0.765957u + 1.02128
0.340426u
10
+ 0.127660u
9
+ ··· − 1.19149u − 0.255319
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
69
47
u
10
−
168
47
u
9
−
315
47
u
8
+
379
47
u
7
+
117
47
u
6
−
524
47
u
5
+
254
47
u
4
−
388
47
u
3
−
906
47
u
2
+
111
47
u +
524
47
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
− 5u
10
+ ··· − 5u + 1
c
2
, c
6
u
11
+ u
10
+ 3u
9
+ 2u
8
+ 5u
7
+ 3u
6
+ 5u
5
+ 3u
4
+ 3u
3
+ 3u
2
+ u + 1
c
3
u
11
− 4u
10
+ ··· + u − 1
c
4
u
11
+ u
10
+ 5u
9
+ 4u
8
+ 7u
7
+ 4u
6
+ u
5
+ u
4
− 2u
3
+ 2u
2
+ 1
c
5
, c
11
u
11
− u
10
+ 3u
9
− 2u
8
+ 5u
7
− 3u
6
+ 5u
5
− 3u
4
+ 3u
3
− 3u
2
+ u − 1
c
7
u
11
+ u
10
+ 2u
9
+ 3u
7
+ 9u
6
+ 9u
5
+ 9u
4
+ 4u
3
+ 6u
2
+ 2u − 5
c
8
u
11
+ 2u
8
− 13u
6
− 6u
5
+ 10u
4
− 6u
3
+ 8u
2
+ 28u − 1
c
9
, c
12
u
11
+ u
10
− 2u
9
+ 3u
7
− u
6
+ 2u
5
+ 4u
4
− 2u
3
− 2u
2
+ 1
c
10
u
11
+ 4u
10
+ ··· + u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
+ 5y
10
+ ··· + 7y −1
c
2
, c
5
, c
6
c
11
y
11
+ 5y
10
+ ··· − 5y −1
c
3
, c
10
y
11
+ 4y
10
+ ··· + 9y −1
c
4
y
11
+ 9y
10
+ ··· − 4y −1
c
7
y
11
+ 3y
10
+ ··· + 64y −25
c
8
y
11
− 16y
8
+ ··· + 800y −1
c
9
, c
12
y
11
− 5y
10
+ ··· + 4y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.194813 + 1.083600I
a = −0.188300 − 0.835649I
b = 0.798763 − 1.016830I
2.21482 − 6.23543I 4.17349 + 4.51231I
u = 0.194813 − 1.083600I
a = −0.188300 + 0.835649I
b = 0.798763 + 1.016830I
2.21482 + 6.23543I 4.17349 − 4.51231I
u = −1.23629
a = −0.757555
b = 0.786378
3.42447 12.2680
u = 1.117710 + 0.686847I
a = −0.73823 + 1.39930I
b = 0.332169 + 1.072400I
−3.10454 + 5.87057I 1.19665 − 6.91999I
u = 1.117710 − 0.686847I
a = −0.73823 − 1.39930I
b = 0.332169 − 1.072400I
−3.10454 − 5.87057I 1.19665 + 6.91999I
u = 0.636137 + 0.234541I
a = 2.56547 − 1.10753I
b = −0.431158 − 1.012670I
−5.96203 + 4.88129I 4.96418 − 7.44610I
u = 0.636137 − 0.234541I
a = 2.56547 + 1.10753I
b = −0.431158 + 1.012670I
−5.96203 − 4.88129I 4.96418 + 7.44610I
u = −0.471226 + 0.455107I
a = 2.42243 + 0.72141I
b = −0.684227 + 0.713438I
−3.58964 − 3.66617I 5.73651 + 8.18144I
u = −0.471226 − 0.455107I
a = 2.42243 − 0.72141I
b = −0.684227 − 0.713438I
−3.58964 + 3.66617I 5.73651 − 8.18144I
u = −1.359290 + 0.343110I
a = 0.317420 + 0.120454I
b = 0.091264 + 0.708132I
0.50447 − 1.50110I −1.70486 + 0.65760I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.359290 − 0.343110I
a = 0.317420 − 0.120454I
b = 0.091264 − 0.708132I
0.50447 + 1.50110I −1.70486 − 0.65760I
18
IV.
I
u
4
= h−2u
9
+ u
8
+ · · · + b − 3, −u
9
− u
8
+ · · · + a − 6, u
10
− 4u
8
+ · · · + 3u + 1i
(i) Arc colorings
a
4
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
7
=
u
9
+ u
8
− 6u
7
− 5u
6
+ 10u
5
+ 11u
4
− 8u
3
− 8u
2
+ 5u + 6
2u
9
− u
8
− 8u
7
− 2u
6
+ 15u
5
+ 7u
4
− 10u
3
− 6u
2
+ 6u + 3
a
6
=
−u
9
+ 2u
8
+ 2u
7
− 3u
6
− 5u
5
+ 4u
4
+ 2u
3
− 2u
2
− u + 3
2u
9
− u
8
− 8u
7
− 2u
6
+ 15u
5
+ 7u
4
− 10u
3
− 6u
2
+ 6u + 3
a
11
=
3u
9
− 2u
8
− 11u
7
− 2u
6
+ 21u
5
+ 9u
4
− 14u
3
− 9u
2
+ 9u + 4
−3u
9
+ 2u
8
+ 11u
7
+ u
6
− 19u
5
− 8u
4
+ 12u
3
+ 7u
2
− 7u − 5
a
3
=
−4u
9
+ u
8
+ 16u
7
+ 8u
6
− 27u
5
− 22u
4
+ 15u
3
+ 17u
2
− 9u − 9
−u
9
+ u
8
+ 3u
7
− 6u
5
− u
4
+ 4u
3
+ u
2
− 3u
a
2
=
u
9
− u
8
− 3u
7
+ u
6
+ 5u
5
− 2u
4
− 3u
3
+ 3u
2
+ 4u
−u
9
+ 4u
7
+ 3u
6
− 7u
5
− 6u
4
+ 4u
3
+ 4u
2
− 3u − 2
a
5
=
u
9
+ u
8
− 5u
7
− 6u
6
+ 6u
5
+ 13u
4
− u
3
− 8u
2
+ 5
2u
9
− u
8
− 8u
7
− 2u
6
+ 15u
5
+ 7u
4
− 10u
3
− 6u
2
+ 7u + 3
a
10
=
3u
9
− 2u
8
− 11u
7
− 2u
6
+ 21u
5
+ 9u
4
− 14u
3
− 9u
2
+ 9u + 4
−2u
9
+ u
8
+ 8u
7
+ u
6
− 13u
5
− 6u
4
+ 8u
3
+ 4u
2
− 4u − 3
a
9
=
5u
9
− 3u
8
− 19u
7
− 3u
6
+ 34u
5
+ 15u
4
− 22u
3
− 13u
2
+ 13u + 7
−2u
9
+ u
8
+ 8u
7
+ u
6
− 13u
5
− 6u
4
+ 8u
3
+ 4u
2
− 4u − 3
a
8
=
4u
9
− 2u
8
− 16u
7
− 4u
6
+ 30u
5
+ 15u
4
− 21u
3
− 14u
2
+ 13u + 7
−u
9
+ u
8
+ 3u
7
− 5u
5
− 2u
4
+ 2u
3
+ 2u
2
− 2u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −10u
9
+ 2u
8
+ 44u
7
+ 12u
6
− 72u
5
− 40u
4
+ 48u
3
+ 24u
2
− 28u − 11
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
− 5u
9
+ ··· − 5u + 1
c
2
, c
6
u
10
+ u
9
+ 3u
8
+ 3u
7
+ 5u
6
+ 5u
5
+ 5u
4
+ 3u
3
+ 3u
2
+ u + 1
c
3
(u
5
+ 2u
4
+ 3u
3
+ 2u
2
− 1)
2
c
4
(u
5
+ 2u
3
+ u
2
+ 1)
2
c
5
, c
11
u
10
− u
9
+ 3u
8
− 3u
7
+ 5u
6
− 5u
5
+ 5u
4
− 3u
3
+ 3u
2
− u + 1
c
7
u
10
− 3u
9
+ ··· − 10u + 5
c
8
u
10
− u
9
− u
8
− 5u
7
+ 8u
6
+ 2u
5
+ 14u
4
+ u
3
+ u
2
− 2u + 1
c
9
, c
12
u
10
− 4u
8
− 3u
7
+ 6u
6
+ 7u
5
− 2u
4
− 5u
3
+ u
2
+ 3u + 1
c
10
(u
5
− 2u
4
+ 3u
3
− 2u
2
+ 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
10
+ y
9
+ 9y
8
+ 9y
7
+ 41y
6
+ 33y
5
+ 41y
4
+ 9y
3
+ 9y
2
+ y + 1
c
2
, c
5
, c
6
c
11
y
10
+ 5y
9
+ ··· + 5y + 1
c
3
, c
10
(y
5
+ 2y
4
+ y
3
+ 4y −1)
2
c
4
(y
5
+ 4y
4
+ 4y
3
− y
2
− 2y −1)
2
c
7
y
10
+ 5y
9
+ ··· + 60y + 25
c
8
y
10
− 3y
9
+ ··· − 2y + 1
c
9
, c
12
y
10
− 8y
9
+ ··· − 7y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.804770 + 0.681218I
a = −0.35218 − 1.55295I
b = 0.364273 − 1.189650I
−1.84330 − 3.45949I 1.65571 + 6.38968I
u = −0.804770 − 0.681218I
a = −0.35218 + 1.55295I
b = 0.364273 + 1.189650I
−1.84330 + 3.45949I 1.65571 − 6.38968I
u = 0.723111 + 0.479695I
a = 2.48698 − 0.74114I
b = −0.386380 − 0.716912I
−4.86920 − 1.42206I 4.77727 − 3.18139I
u = 0.723111 − 0.479695I
a = 2.48698 + 0.74114I
b = −0.386380 + 0.716912I
−4.86920 + 1.42206I 4.77727 + 3.18139I
u = −1.011490 + 0.575037I
a = −0.444488 + 0.494221I
b = 0.869336 + 0.494221I
3.55538 14.13404 + 0.I
u = −1.011490 − 0.575037I
a = −0.444488 − 0.494221I
b = 0.869336 − 0.494221I
3.55538 14.13404 + 0.I
u = −0.529451 + 0.225672I
a = 2.29081 + 1.05667I
b = −0.582553 + 1.080900I
−4.86920 − 1.42206I 4.77727 − 3.18139I
u = −0.529451 − 0.225672I
a = 2.29081 − 1.05667I
b = −0.582553 − 1.080900I
−4.86920 + 1.42206I 4.77727 + 3.18139I
u = 1.62260 + 0.17621I
a = −0.481126 − 0.405232I
b = 0.235324 − 0.768526I
−1.84330 + 3.45949I 1.65571 − 6.38968I
u = 1.62260 − 0.17621I
a = −0.481126 + 0.405232I
b = 0.235324 + 0.768526I
−1.84330 − 3.45949I 1.65571 + 6.38968I
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
10
− 5u
9
+ ··· − 5u + 1)(u
11
− 5u
10
+ ··· − 5u + 1)
· (u
19
+ 7u
18
+ ··· − 4u − 1)(u
40
+ 8u
39
+ ··· + 1381u + 121)
c
2
, c
6
(u
10
+ u
9
+ 3u
8
+ 3u
7
+ 5u
6
+ 5u
5
+ 5u
4
+ 3u
3
+ 3u
2
+ u + 1)
· (u
11
+ u
10
+ 3u
9
+ 2u
8
+ 5u
7
+ 3u
6
+ 5u
5
+ 3u
4
+ 3u
3
+ 3u
2
+ u + 1)
· (u
19
+ u
18
+ ··· + 2u − 1)(u
40
− 2u
39
+ ··· + 29u + 11)
c
3
((u
5
+ 2u
4
+ 3u
3
+ 2u
2
− 1)
2
)(u
11
− 4u
10
+ ··· + u − 1)
· (u
19
− 11u
18
+ ··· + 60u − 8)(u
20
+ 5u
19
+ ··· + 5u + 1)
2
c
4
(u
5
+ 2u
3
+ u
2
+ 1)
2
· (u
11
+ u
10
+ 5u
9
+ 4u
8
+ 7u
7
+ 4u
6
+ u
5
+ u
4
− 2u
3
+ 2u
2
+ 1)
· (u
19
+ 12u
18
+ ··· − 176u − 32)(u
20
− 5u
19
+ ··· − 6u + 1)
2
c
5
, c
11
(u
10
− u
9
+ 3u
8
− 3u
7
+ 5u
6
− 5u
5
+ 5u
4
− 3u
3
+ 3u
2
− u + 1)
· (u
11
− u
10
+ 3u
9
− 2u
8
+ 5u
7
− 3u
6
+ 5u
5
− 3u
4
+ 3u
3
− 3u
2
+ u − 1)
· (u
19
+ u
18
+ ··· + 2u − 1)(u
40
− 2u
39
+ ··· + 29u + 11)
c
7
(u
10
− 3u
9
+ ··· − 10u + 5)
· (u
11
+ u
10
+ 2u
9
+ 3u
7
+ 9u
6
+ 9u
5
+ 9u
4
+ 4u
3
+ 6u
2
+ 2u − 5)
· (u
19
− u
18
+ ··· + 1133u − 517)
· (u
40
− 18u
38
+ ··· + 26588u + 210103)
c
8
(u
10
− u
9
− u
8
− 5u
7
+ 8u
6
+ 2u
5
+ 14u
4
+ u
3
+ u
2
− 2u + 1)
· (u
11
+ 2u
8
− 13u
6
− 6u
5
+ 10u
4
− 6u
3
+ 8u
2
+ 28u − 1)
· (u
19
+ 11u
17
+ ··· − 7u − 13)(u
40
− 2u
39
+ ··· − 350134u + 28487)
c
9
, c
12
(u
10
− 4u
8
− 3u
7
+ 6u
6
+ 7u
5
− 2u
4
− 5u
3
+ u
2
+ 3u + 1)
· (u
11
+ u
10
− 2u
9
+ 3u
7
− u
6
+ 2u
5
+ 4u
4
− 2u
3
− 2u
2
+ 1)
· (u
19
+ u
18
+ ··· − 3u − 1)(u
40
+ u
39
+ ··· − 15u + 1)
c
10
((u
5
− 2u
4
+ 3u
3
− 2u
2
+ 1)
2
)(u
11
+ 4u
10
+ ··· + u + 1)
· (u
19
− 11u
18
+ ··· + 60u − 8)(u
20
+ 5u
19
+ ··· + 5u + 1)
2
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
10
+ y
9
+ 9y
8
+ 9y
7
+ 41y
6
+ 33y
5
+ 41y
4
+ 9y
3
+ 9y
2
+ y + 1)
· (y
11
+ 5y
10
+ ··· + 7y −1)(y
19
+ 23y
18
+ ··· + 28y −1)
· (y
40
+ 40y
39
+ ··· + 111361y + 14641)
c
2
, c
5
, c
6
c
11
(y
10
+ 5y
9
+ ··· + 5y + 1)(y
11
+ 5y
10
+ ··· − 5y −1)
· (y
19
+ 7y
18
+ ··· − 4y −1)(y
40
+ 8y
39
+ ··· + 1381y + 121)
c
3
, c
10
((y
5
+ 2y
4
+ y
3
+ 4y −1)
2
)(y
11
+ 4y
10
+ ··· + 9y −1)
· (y
19
+ 3y
18
+ ··· − 368y −64)(y
20
− y
19
+ ··· − 9y + 1)
2
c
4
((y
5
+ 4y
4
+ 4y
3
− y
2
− 2y −1)
2
)(y
11
+ 9y
10
+ ··· − 4y −1)
· (y
19
+ 8y
18
+ ··· + 6912y −1024)(y
20
− y
19
+ ··· − 20y + 1)
2
c
7
(y
10
+ 5y
9
+ ··· + 60y + 25)(y
11
+ 3y
10
+ ··· + 64y −25)
· (y
19
− 7y
18
+ ··· + 566093y −267289)
· (y
40
− 36y
39
+ ··· + 252213388832y + 44143270609)
c
8
(y
10
− 3y
9
+ ··· − 2y + 1)(y
11
− 16y
8
+ ··· + 800y −1)
· (y
19
+ 22y
18
+ ··· − 2291y −169)
· (y
40
+ 40y
39
+ ··· − 4553546458y + 811509169)
c
9
, c
12
(y
10
− 8y
9
+ ··· − 7y + 1)(y
11
− 5y
10
+ ··· + 4y −1)
· (y
19
− 23y
18
+ ··· + 9y −1)(y
40
− 33y
39
+ ··· + 5y + 1)
24
