12a
1171
(K12a
1171
)
A knot diagram
1
Linearized knot diagam
4 10 7 9 11 3 1 12 2 6 5 8
Solving Sequence
3,6
7
4,10
11 2 1 5 12 9 8
c
6
c
3
c
10
c
2
c
1
c
5
c
11
c
9
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.19554 × 10
254
u
79
− 4.06335 × 10
253
u
78
+ ··· + 6.78866 × 10
255
b − 1.22944 × 10
255
,
− 1.22177 × 10
256
u
79
+ 3.50873 × 10
254
u
78
+ ··· + 4.95572 × 10
257
a − 3.21558 × 10
258
,
u
80
− 42u
78
+ ··· + 695u + 73i
I
u
2
= h−8933u
22
+ 72416u
21
+ ··· + 26063b − 18756,
− 325452679u
22
+ 1996854611u
21
+ ··· + 187627537a − 428118748, u
23
− 5u
22
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 103 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
= h1.20 × 10
254
u
79
− 4.06 × 10
253
u
78
+ · · · + 6.79 × 10
255
b − 1.23 ×
10
255
, −1.22 × 10
256
u
79
+ 3.51 × 10
254
u
78
+ · · · + 4.96 × 10
257
a − 3.22 ×
10
258
, u
80
− 42u
78
+ · · · + 695u + 73i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
4
=
−u
−u
3
+ u
a
10
=
0.0246538u
79
− 0.000708015u
78
+ ··· + 10.2302u + 6.48862
−0.0176108u
79
+ 0.00598549u
78
+ ··· − 8.43907u + 0.181103
a
11
=
0.00704298u
79
+ 0.00527747u
78
+ ··· + 1.79116u + 6.66973
−0.0176108u
79
+ 0.00598549u
78
+ ··· − 8.43907u + 0.181103
a
2
=
−0.0318869u
79
+ 0.00250679u
78
+ ··· + 10.8269u − 5.17085
0.0182869u
79
− 0.00815417u
78
+ ··· + 21.5937u + 1.26735
a
1
=
−0.0126502u
79
− 0.0195104u
78
+ ··· + 18.8202u − 4.43663
0.0286845u
79
− 0.0261087u
78
+ ··· + 27.4980u + 2.14039
a
5
=
0.0000878937u
79
+ 0.000822250u
78
+ ··· + 46.4529u + 8.89458
0.0174489u
79
− 0.0174646u
78
+ ··· − 1.86747u − 0.633244
a
12
=
−0.0321181u
79
+ 0.0194870u
78
+ ··· + 11.6089u + 8.55274
−0.00592250u
79
+ 0.0298193u
78
+ ··· + 1.11590u − 0.766760
a
9
=
−0.00731128u
79
+ 0.00275510u
78
+ ··· + 52.6202u + 4.29409
0.00670229u
79
− 0.00572929u
78
+ ··· + 1.06723u + 0.396634
a
8
=
−0.00733362u
79
− 0.0104153u
78
+ ··· − 55.9268u − 4.94251
−0.00542082u
79
+ 0.00217554u
78
+ ··· + 32.0132u + 3.53866
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0629654u
79
− 0.0984874u
78
+ ··· − 37.1337u − 2.30507
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
80
− 11u
79
+ ··· − 1319100u + 193025
c
2
, c
9
u
80
− u
79
+ ··· + 37u + 1
c
3
, c
6
u
80
− 42u
78
+ ··· + 695u + 73
c
4
u
80
+ 3u
79
+ ··· + 9720133u + 1148717
c
5
, c
10
, c
11
u
80
+ u
79
+ ··· + 1161u + 173
c
7
, c
8
, c
12
u
80
− 2u
79
+ ··· + 27u + 19
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
80
− 45y
79
+ ··· − 611400686100y + 37258650625
c
2
, c
9
y
80
− 69y
79
+ ··· + 21y + 1
c
3
, c
6
y
80
− 84y
79
+ ··· + 146819y + 5329
c
4
y
80
+ 51y
79
+ ··· + 26316054060919y + 1319550746089
c
5
, c
10
, c
11
y
80
+ 95y
79
+ ··· + 207349y + 29929
c
7
, c
8
, c
12
y
80
+ 90y
79
+ ··· + 11507y + 361
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.933025 + 0.257843I
a = 0.0297219 + 0.0412596I
b = 0.279840 − 0.440086I
−1.57667 + 1.00823I 0
u = −0.933025 − 0.257843I
a = 0.0297219 − 0.0412596I
b = 0.279840 + 0.440086I
−1.57667 − 1.00823I 0
u = −0.899699 + 0.132536I
a = −1.049370 + 0.742428I
b = −0.022659 + 1.203980I
−4.83425 + 2.94657I 0
u = −0.899699 − 0.132536I
a = −1.049370 − 0.742428I
b = −0.022659 − 1.203980I
−4.83425 − 2.94657I 0
u = 1.110620 + 0.130479I
a = −0.231583 − 0.901934I
b = 0.181838 − 0.539644I
−1.72864 − 2.75147I 0
u = 1.110620 − 0.130479I
a = −0.231583 + 0.901934I
b = 0.181838 + 0.539644I
−1.72864 + 2.75147I 0
u = 0.156021 + 0.835387I
a = 0.54574 − 1.58978I
b = 0.03618 + 1.58404I
−8.84658 − 0.73985I −4.45300 + 0.I
u = 0.156021 − 0.835387I
a = 0.54574 + 1.58978I
b = 0.03618 − 1.58404I
−8.84658 + 0.73985I −4.45300 + 0.I
u = −0.238929 + 0.796640I
a = −0.710211 − 1.099990I
b = 0.317628 + 0.536262I
−1.58821 + 3.69119I 0. − 9.71616I
u = −0.238929 − 0.796640I
a = −0.710211 + 1.099990I
b = 0.317628 − 0.536262I
−1.58821 − 3.69119I 0. + 9.71616I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.107313 + 0.798256I
a = −0.757440 + 0.103976I
b = 0.647442 + 0.471902I
−4.82509 + 2.15434I 0. − 3.25418I
u = −0.107313 − 0.798256I
a = −0.757440 − 0.103976I
b = 0.647442 − 0.471902I
−4.82509 − 2.15434I 0. + 3.25418I
u = −0.377538 + 1.138370I
a = 0.530912 + 0.824510I
b = −0.532890 − 0.584575I
−8.15329 + 5.47182I 0
u = −0.377538 − 1.138370I
a = 0.530912 − 0.824510I
b = −0.532890 + 0.584575I
−8.15329 − 5.47182I 0
u = 0.296833 + 0.728763I
a = −0.627261 − 0.274114I
b = 0.22622 − 1.47408I
−11.11080 − 5.32394I −1.60578 + 2.44564I
u = 0.296833 − 0.728763I
a = −0.627261 + 0.274114I
b = 0.22622 + 1.47408I
−11.11080 + 5.32394I −1.60578 − 2.44564I
u = −0.596798 + 0.368285I
a = −0.737061 − 1.015400I
b = 0.147050 + 1.051450I
−3.90294 − 0.95979I −6.90709 − 1.74186I
u = −0.596798 − 0.368285I
a = −0.737061 + 1.015400I
b = 0.147050 − 1.051450I
−3.90294 + 0.95979I −6.90709 + 1.74186I
u = −1.222420 + 0.458831I
a = 0.0443970 − 0.0548076I
b = −0.632083 + 0.462534I
−8.11023 + 2.43176I 0
u = −1.222420 − 0.458831I
a = 0.0443970 + 0.0548076I
b = −0.632083 − 0.462534I
−8.11023 − 2.43176I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.279500 + 0.360515I
a = 0.291837 + 0.607605I
b = −0.474926 + 0.715944I
−9.11742 − 6.23645I 0
u = 1.279500 − 0.360515I
a = 0.291837 − 0.607605I
b = −0.474926 − 0.715944I
−9.11742 + 6.23645I 0
u = −0.538435 + 0.378124I
a = 1.121120 + 0.169264I
b = −0.098631 − 0.827664I
−0.95937 + 1.55975I 2.01700 − 4.77080I
u = −0.538435 − 0.378124I
a = 1.121120 − 0.169264I
b = −0.098631 + 0.827664I
−0.95937 − 1.55975I 2.01700 + 4.77080I
u = 0.389677 + 1.292350I
a = −0.431269 + 0.939915I
b = 0.07554 − 1.56927I
−8.80812 − 5.04260I 0
u = 0.389677 − 1.292350I
a = −0.431269 − 0.939915I
b = 0.07554 + 1.56927I
−8.80812 + 5.04260I 0
u = −1.360730 + 0.003685I
a = 0.981515 + 0.029454I
b = −1.030470 − 0.448078I
−5.79631 − 1.42222I 0
u = −1.360730 − 0.003685I
a = 0.981515 − 0.029454I
b = −1.030470 + 0.448078I
−5.79631 + 1.42222I 0
u = 1.380500 + 0.156477I
a = 0.028479 + 0.503486I
b = 0.07032 + 1.53121I
−8.24917 + 0.23612I 0
u = 1.380500 − 0.156477I
a = 0.028479 − 0.503486I
b = 0.07032 − 1.53121I
−8.24917 − 0.23612I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.387760 + 0.076721I
a = −1.053390 − 0.203653I
b = 0.491717 − 0.666089I
−6.41963 − 2.52717I 0
u = 1.387760 − 0.076721I
a = −1.053390 + 0.203653I
b = 0.491717 + 0.666089I
−6.41963 + 2.52717I 0
u = 1.389780 + 0.140595I
a = −1.021750 − 0.096001I
b = 0.44598 − 1.81464I
19.1249 − 4.0847I 0
u = 1.389780 − 0.140595I
a = −1.021750 + 0.096001I
b = 0.44598 + 1.81464I
19.1249 + 4.0847I 0
u = −1.395520 + 0.114360I
a = −0.974540 − 0.048957I
b = 1.35472 − 0.51672I
−12.74490 + 2.98456I 0
u = −1.395520 − 0.114360I
a = −0.974540 + 0.048957I
b = 1.35472 + 0.51672I
−12.74490 − 2.98456I 0
u = −1.42165 + 0.06964I
a = −0.156336 + 1.118770I
b = 0.04076 + 1.58926I
−9.17850 + 3.49089I 0
u = −1.42165 − 0.06964I
a = −0.156336 − 1.118770I
b = 0.04076 − 1.58926I
−9.17850 − 3.49089I 0
u = 0.568595 + 0.041815I
a = −1.24087 − 1.09976I
b = 0.251287 − 0.048586I
−0.93338 − 2.24071I 7.29920 + 5.10530I
u = 0.568595 − 0.041815I
a = −1.24087 + 1.09976I
b = 0.251287 + 0.048586I
−0.93338 + 2.24071I 7.29920 − 5.10530I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42349 + 0.25160I
a = 1.010970 + 0.049425I
b = −0.768916 + 0.774349I
−6.98740 − 7.32316I 0
u = 1.42349 − 0.25160I
a = 1.010970 − 0.049425I
b = −0.768916 − 0.774349I
−6.98740 + 7.32316I 0
u = 1.40704 + 0.36853I
a = 0.969961 − 0.058572I
b = −0.31592 + 1.66165I
−12.91650 − 3.79429I 0
u = 1.40704 − 0.36853I
a = 0.969961 + 0.058572I
b = −0.31592 − 1.66165I
−12.91650 + 3.79429I 0
u = −1.45273 + 0.14202I
a = 1.122970 − 0.440056I
b = −0.04410 − 1.63069I
18.3007 − 0.5410I 0
u = −1.45273 − 0.14202I
a = 1.122970 + 0.440056I
b = −0.04410 + 1.63069I
18.3007 + 0.5410I 0
u = −1.46987 + 0.27140I
a = −0.851510 − 0.167573I
b = 0.509179 + 0.438607I
−5.64665 + 1.00939I 0
u = −1.46987 − 0.27140I
a = −0.851510 + 0.167573I
b = 0.509179 − 0.438607I
−5.64665 − 1.00939I 0
u = −1.46286 + 0.30961I
a = −1.193090 + 0.207085I
b = 0.14007 + 1.61352I
−14.2338 + 4.8692I 0
u = −1.46286 − 0.30961I
a = −1.193090 − 0.207085I
b = 0.14007 − 1.61352I
−14.2338 − 4.8692I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49177 + 0.17819I
a = 0.880021 − 0.391812I
b = −0.145201 − 0.700742I
−12.98350 − 1.27674I 0
u = 1.49177 − 0.17819I
a = 0.880021 + 0.391812I
b = −0.145201 + 0.700742I
−12.98350 + 1.27674I 0
u = −1.49301 + 0.20563I
a = 0.271872 − 0.890511I
b = −0.12925 − 1.62695I
−17.1793 + 8.4656I 0
u = −1.49301 − 0.20563I
a = 0.271872 + 0.890511I
b = −0.12925 + 1.62695I
−17.1793 − 8.4656I 0
u = 1.50221 + 0.34705I
a = −0.941368 + 0.004617I
b = 0.960337 − 0.913714I
−14.2323 − 10.4782I 0
u = 1.50221 − 0.34705I
a = −0.941368 − 0.004617I
b = 0.960337 + 0.913714I
−14.2323 + 10.4782I 0
u = 0.155519 + 0.409623I
a = 1.175290 − 0.037639I
b = −0.427697 − 0.189345I
0.861772 + 0.593079I 8.14040 − 3.49994I
u = 0.155519 − 0.409623I
a = 1.175290 + 0.037639I
b = −0.427697 + 0.189345I
0.861772 − 0.593079I 8.14040 + 3.49994I
u = 1.53473 + 0.32845I
a = −0.040041 − 0.446319I
b = −0.15983 − 1.61623I
−15.4607 + 0.5021I 0
u = 1.53473 − 0.32845I
a = −0.040041 + 0.446319I
b = −0.15983 + 1.61623I
−15.4607 − 0.5021I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.018150 + 0.396081I
a = 1.04718 − 2.72969I
b = −0.711168 − 0.566289I
−7.94238 − 1.27246I −5.21046 − 0.09579I
u = 0.018150 − 0.396081I
a = 1.04718 + 2.72969I
b = −0.711168 + 0.566289I
−7.94238 + 1.27246I −5.21046 + 0.09579I
u = −1.56074 + 0.43665I
a = 1.059430 − 0.062610I
b = −0.22521 − 1.64176I
−15.0846 + 11.0453I 0
u = −1.56074 − 0.43665I
a = 1.059430 + 0.062610I
b = −0.22521 + 1.64176I
−15.0846 − 11.0453I 0
u = 0.080693 + 0.331904I
a = −1.63830 + 3.85989I
b = −0.19093 − 1.67778I
−15.8360 + 2.3469I −8.33417 − 0.26186I
u = 0.080693 − 0.331904I
a = −1.63830 − 3.85989I
b = −0.19093 + 1.67778I
−15.8360 − 2.3469I −8.33417 + 0.26186I
u = 0.095857 + 0.299058I
a = 1.85934 + 0.46152I
b = −0.092790 + 1.367820I
−4.02985 − 2.33762I 2.59507 + 2.31518I
u = 0.095857 − 0.299058I
a = 1.85934 − 0.46152I
b = −0.092790 − 1.367820I
−4.02985 + 2.33762I 2.59507 − 2.31518I
u = −1.68949 + 0.48697I
a = −0.937193 + 0.047303I
b = 0.28129 + 1.70007I
16.5778 + 15.2060I 0
u = −1.68949 − 0.48697I
a = −0.937193 − 0.047303I
b = 0.28129 − 1.70007I
16.5778 − 15.2060I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.63666 + 1.69281I
a = 0.360260 − 0.664641I
b = −0.14249 + 1.58434I
−15.5302 − 7.8644I 0
u = 0.63666 − 1.69281I
a = 0.360260 + 0.664641I
b = −0.14249 − 1.58434I
−15.5302 + 7.8644I 0
u = −1.75601 + 0.59770I
a = 0.662793 + 0.226410I
b = −0.139860 − 0.490757I
−12.23370 + 2.28182I 0
u = −1.75601 − 0.59770I
a = 0.662793 − 0.226410I
b = −0.139860 + 0.490757I
−12.23370 − 2.28182I 0
u = 1.71422 + 0.74113I
a = −0.718767 + 0.152487I
b = 0.13592 − 1.55702I
−12.48250 − 3.26508I 0
u = 1.71422 − 0.74113I
a = −0.718767 − 0.152487I
b = 0.13592 + 1.55702I
−12.48250 + 3.26508I 0
u = −0.0918845 + 0.0886132I
a = 7.50598 + 2.95587I
b = 0.236793 − 0.529885I
−1.43444 + 1.51364I 0.75693 + 3.72542I
u = −0.0918845 − 0.0886132I
a = 7.50598 − 2.95587I
b = 0.236793 + 0.529885I
−1.43444 − 1.51364I 0.75693 − 3.72542I
u = 2.04902 + 0.91722I
a = 0.585507 − 0.130441I
b = −0.04510 + 1.57018I
−19.4247 − 2.9683I 0
u = 2.04902 − 0.91722I
a = 0.585507 + 0.130441I
b = −0.04510 − 1.57018I
−19.4247 + 2.9683I 0
12
II. I
u
2
= h−8933u
22
+ 72416u
21
+ · · · + 26063b − 18756, −3.25 × 10
8
u
22
+
2.00 × 10
9
u
21
+ · · · + 1.88 × 10
8
a − 4.28 × 10
8
, u
23
− 5u
22
+ · · · − 2u + 1i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
4
=
−u
−u
3
+ u
a
10
=
1.73457u
22
− 10.6427u
21
+ ··· + 15.7223u + 2.28175
0.342746u
22
− 2.77850u
21
+ ··· − 6.43487u + 0.719641
a
11
=
2.07731u
22
− 13.4212u
21
+ ··· + 9.28739u + 3.00139
0.342746u
22
− 2.77850u
21
+ ··· − 6.43487u + 0.719641
a
2
=
1.56835u
22
− 8.77970u
21
+ ··· − 21.4092u − 1.02035
0.844437u
22
− 3.99394u
21
+ ··· + 4.08247u + 0.437912
a
1
=
2.32346u
22
− 12.7898u
21
+ ··· − 22.9240u − 0.404159
0.773141u
22
− 3.43217u
21
+ ··· + 4.37302u + 0.0562597
a
5
=
−0.437912u
22
+ 3.03400u
21
+ ··· − 4.03499u + 3.95829
−u − 1
a
12
=
3.37733u
22
− 17.7045u
21
+ ··· − 13.5909u + 2.79696
1.06477u
22
− 4.72597u
21
+ ··· − 1.40513u + 0.342746
a
9
=
0.757435u
22
− 5.67549u
21
+ ··· + 11.9765u − 2.55321
−0.344110u
22
+ 1.85506u
21
+ ··· + 1.66476u − 0.242129
a
8
=
0.904547u
22
− 5.79853u
21
+ ··· + 16.1850u − 1.78107
−0.595303u
22
+ 3.54364u
21
+ ··· + 1.40322u − 0.225478
(ii) Obstruction class = 1
(iii) Cusp Shapes =
516876394
187627537
u
22
−
2115207184
187627537
u
21
+ ··· −
1488236262
187627537
u −
1412792583
187627537
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
− 4u
22
+ ··· − 7u + 1
c
2
u
23
− 8u
21
+ ··· − 5u
2
+ 1
c
3
u
23
+ 5u
22
+ ··· − 2u − 1
c
4
u
23
+ 4u
21
+ ··· − 6u − 1
c
5
u
23
+ 14u
21
+ ··· − 13u
2
− 1
c
6
u
23
− 5u
22
+ ··· − 2u + 1
c
7
, c
8
u
23
− u
22
+ ··· + 2u
2
− 1
c
9
u
23
− 8u
21
+ ··· + 5u
2
− 1
c
10
, c
11
u
23
+ 14u
21
+ ··· + 13u
2
+ 1
c
12
u
23
+ u
22
+ ··· − 2u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
− 8y
22
+ ··· + 11y −1
c
2
, c
9
y
23
− 16y
22
+ ··· + 10y −1
c
3
, c
6
y
23
− 27y
22
+ ··· − 36y −1
c
4
y
23
+ 8y
22
+ ··· − 32y −1
c
5
, c
10
, c
11
y
23
+ 28y
22
+ ··· − 26y −1
c
7
, c
8
, c
12
y
23
+ 27y
22
+ ··· + 4y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.757600 + 0.580515I
a = 0.593505 − 0.234801I
b = 0.216088 − 1.343240I
−12.22340 − 5.69838I −9.25274 + 4.18072I
u = 0.757600 − 0.580515I
a = 0.593505 + 0.234801I
b = 0.216088 + 1.343240I
−12.22340 + 5.69838I −9.25274 − 4.18072I
u = −0.901939 + 0.010790I
a = −0.578634 + 0.851146I
b = −0.017203 + 0.313619I
−1.46016 + 2.03887I −5.32019 + 0.28073I
u = −0.901939 − 0.010790I
a = −0.578634 − 0.851146I
b = −0.017203 − 0.313619I
−1.46016 − 2.03887I −5.32019 − 0.28073I
u = −1.037860 + 0.492778I
a = 0.707359 + 0.115829I
b = 0.515794 − 0.477688I
−8.90749 + 3.00064I −9.05512 − 3.71283I
u = −1.037860 − 0.492778I
a = 0.707359 − 0.115829I
b = 0.515794 + 0.477688I
−8.90749 − 3.00064I −9.05512 + 3.71283I
u = 0.691752 + 0.160792I
a = −0.536177 − 0.443693I
b = −0.061742 + 1.302140I
−4.78747 − 2.56115I −8.34774 + 4.70612I
u = 0.691752 − 0.160792I
a = −0.536177 + 0.443693I
b = −0.061742 − 1.302140I
−4.78747 + 2.56115I −8.34774 − 4.70612I
u = −0.655673 + 0.212810I
a = −1.321680 + 0.225264I
b = −0.173862 + 0.612009I
−1.83707 + 1.99638I −8.40872 − 6.71639I
u = −0.655673 − 0.212810I
a = −1.321680 − 0.225264I
b = −0.173862 − 0.612009I
−1.83707 − 1.99638I −8.40872 + 6.71639I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.344240 + 0.025801I
a = −0.361149 − 0.831706I
b = 0.00843 − 1.53111I
−7.95471 − 2.08579I −5.56064 + 2.41042I
u = 1.344240 − 0.025801I
a = −0.361149 + 0.831706I
b = 0.00843 + 1.53111I
−7.95471 + 2.08579I −5.56064 − 2.41042I
u = −1.45736
a = −0.923005
b = 0.676281
−5.64416 −6.21070
u = −1.50060 + 0.27712I
a = 0.805496 + 0.225842I
b = −0.732389 + 0.189191I
−10.92140 + 1.50372I −5.21005 + 0.05843I
u = −1.50060 − 0.27712I
a = 0.805496 − 0.225842I
b = −0.732389 − 0.189191I
−10.92140 − 1.50372I −5.21005 − 0.05843I
u = 1.31555 + 0.81648I
a = 0.810501 − 0.429665I
b = −0.26432 + 1.54448I
−16.0466 − 5.3224I −9.22028 + 3.35316I
u = 1.31555 − 0.81648I
a = 0.810501 + 0.429665I
b = −0.26432 − 1.54448I
−16.0466 + 5.3224I −9.22028 − 3.35316I
u = 1.46966 + 0.55634I
a = −0.904069 + 0.122289I
b = 0.17591 − 1.58133I
−11.72400 − 3.23681I −1.85835 + 0.78114I
u = 1.46966 − 0.55634I
a = −0.904069 − 0.122289I
b = 0.17591 + 1.58133I
−11.72400 + 3.23681I −1.85835 − 0.78114I
u = 1.72260 + 0.33154I
a = 0.681003 + 0.099571I
b = −0.10028 + 1.65308I
−18.2680 − 1.7097I −8.26819 + 0.20200I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.72260 − 0.33154I
a = 0.681003 − 0.099571I
b = −0.10028 − 1.65308I
−18.2680 + 1.7097I −8.26819 − 0.20200I
u = 0.023342 + 0.193953I
a = 2.06534 + 5.01376I
b = 0.095440 − 1.016100I
−3.38863 + 2.01739I −3.39262 − 3.26924I
u = 0.023342 − 0.193953I
a = 2.06534 − 5.01376I
b = 0.095440 + 1.016100I
−3.38863 − 2.01739I −3.39262 + 3.26924I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
23
− 4u
22
+ ··· − 7u + 1)(u
80
− 11u
79
+ ··· − 1319100u + 193025)
c
2
(u
23
− 8u
21
+ ··· − 5u
2
+ 1)(u
80
− u
79
+ ··· + 37u + 1)
c
3
(u
23
+ 5u
22
+ ··· − 2u − 1)(u
80
− 42u
78
+ ··· + 695u + 73)
c
4
(u
23
+ 4u
21
+ ··· − 6u − 1)(u
80
+ 3u
79
+ ··· + 9720133u + 1148717)
c
5
(u
23
+ 14u
21
+ ··· − 13u
2
− 1)(u
80
+ u
79
+ ··· + 1161u + 173)
c
6
(u
23
− 5u
22
+ ··· − 2u + 1)(u
80
− 42u
78
+ ··· + 695u + 73)
c
7
, c
8
(u
23
− u
22
+ ··· + 2u
2
− 1)(u
80
− 2u
79
+ ··· + 27u + 19)
c
9
(u
23
− 8u
21
+ ··· + 5u
2
− 1)(u
80
− u
79
+ ··· + 37u + 1)
c
10
, c
11
(u
23
+ 14u
21
+ ··· + 13u
2
+ 1)(u
80
+ u
79
+ ··· + 1161u + 173)
c
12
(u
23
+ u
22
+ ··· − 2u
2
+ 1)(u
80
− 2u
79
+ ··· + 27u + 19)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
23
− 8y
22
+ ··· + 11y −1)
· (y
80
− 45y
79
+ ··· − 611400686100y + 37258650625)
c
2
, c
9
(y
23
− 16y
22
+ ··· + 10y −1)(y
80
− 69y
79
+ ··· + 21y + 1)
c
3
, c
6
(y
23
− 27y
22
+ ··· − 36y −1)(y
80
− 84y
79
+ ··· + 146819y + 5329)
c
4
(y
23
+ 8y
22
+ ··· − 32y −1)
· (y
80
+ 51y
79
+ ··· + 26316054060919y + 1319550746089)
c
5
, c
10
, c
11
(y
23
+ 28y
22
+ ··· − 26y −1)(y
80
+ 95y
79
+ ··· + 207349y + 29929)
c
7
, c
8
, c
12
(y
23
+ 27y
22
+ ··· + 4y −1)(y
80
+ 90y
79
+ ··· + 11507y + 361)
20
