12n
0122
(K12n
0122
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 12 3 11 6 5 8 10 9
Solving Sequence
7,11 3,8
6 10 12 5 2 1 4 9
c
7
c
6
c
10
c
11
c
5
c
2
c
1
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.51787 × 10
81
u
67
+ 2.11041 × 10
82
u
66
+ ··· + 3.86959 × 10
83
b + 2.32790 × 10
83
,
2.89477 × 10
83
u
67
− 1.45377 × 10
84
u
66
+ ··· + 3.86959 × 10
83
a + 1.55319 × 10
85
, u
68
− 5u
67
+ ··· + 61u + 1i
I
u
2
= hb, −u
8
+ 2u
7
− 3u
6
+ 2u
5
− 3u
4
+ 2u
3
− 2u
2
+ a − 1, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
I
u
3
= h−120a
2
u − 76a
2
− 865au + 691b − 663a + 177u + 43, a
3
− a
2
u + 7a
2
− 4au − 3a − 5u − 12,
u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 83 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−5.52 × 10
81
u
67
+ 2.11 × 10
82
u
66
+ · · · + 3.87 × 10
83
b + 2.33 ×
10
83
, 2.89 × 10
83
u
67
− 1.45 × 10
84
u
66
+ · · · + 3.87 × 10
83
a + 1.55 ×
10
85
, u
68
− 5u
67
+ · · · + 61u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
−0.748081u
67
+ 3.75690u
66
+ ··· + 210.979u − 40.1384
0.0142596u
67
− 0.0545384u
66
+ ··· − 3.15431u − 0.601589
a
8
=
1
−u
2
a
6
=
−0.341935u
67
+ 1.84496u
66
+ ··· + 122.527u − 21.0582
−0.0113435u
67
+ 0.205218u
66
+ ··· + 3.86731u − 0.239724
a
10
=
−u
u
3
+ u
a
12
=
−u
3
u
5
+ u
3
+ u
a
5
=
−0.338281u
67
+ 1.62581u
66
+ ··· + 112.042u − 21.2277
0.0236591u
67
− 0.0564694u
66
+ ··· + 3.36495u − 0.255517
a
2
=
−0.330587u
67
+ 1.67938u
66
+ ··· + 116.221u − 23.6818
0.0236591u
67
− 0.0564694u
66
+ ··· + 3.36495u − 0.255517
a
1
=
0.0416035u
67
− 0.370846u
66
+ ··· − 11.8634u + 0.807059
0.0469200u
67
− 0.282851u
66
+ ··· − 0.607431u + 0.0154252
a
4
=
−0.762341u
67
+ 3.81144u
66
+ ··· + 214.133u − 39.5368
0.0142596u
67
− 0.0545384u
66
+ ··· − 3.15431u − 0.601589
a
9
=
0.105467u
67
− 0.401649u
66
+ ··· − 40.5394u + 7.48605
−0.151780u
67
+ 0.736790u
66
+ ··· + 7.94430u + 0.222620
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.145860u
67
+ 0.285659u
66
+ ··· + 33.4674u − 8.97504
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
68
+ 72u
67
+ ··· − 116u + 1
c
2
, c
4
u
68
− 12u
67
+ ··· + 4u − 1
c
3
, c
6
u
68
+ 3u
67
+ ··· + 2048u + 512
c
5
u
68
+ 4u
67
+ ··· + 20u
2
− 1
c
7
, c
10
u
68
+ 5u
67
+ ··· − 61u + 1
c
8
u
68
− 8u
67
+ ··· − 679u + 1423
c
9
u
68
− 4u
67
+ ··· − 1569175u − 179693
c
11
u
68
+ 33u
67
+ ··· − 4365u + 1
c
12
u
68
+ 6u
67
+ ··· − 992u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
68
− 140y
67
+ ··· + 13088y + 1
c
2
, c
4
y
68
− 72y
67
+ ··· + 116y + 1
c
3
, c
6
y
68
− 51y
67
+ ··· − 1048576y + 262144
c
5
y
68
− 16y
67
+ ··· − 40y + 1
c
7
, c
10
y
68
+ 33y
67
+ ··· − 4365y + 1
c
8
y
68
− 68y
67
+ ··· + 88237y + 2024929
c
9
y
68
− 20y
67
+ ··· − 70781434415y + 32289574249
c
11
y
68
+ 9y
67
+ ··· − 19115909y + 1
c
12
y
68
+ 30y
67
+ ··· − 332800y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.424757 + 0.915138I
a = −1.40780 + 0.30590I
b = −0.22825 + 1.49715I
2.67134 + 4.86258I −14.4423 − 3.8383I
u = 0.424757 − 0.915138I
a = −1.40780 − 0.30590I
b = −0.22825 − 1.49715I
2.67134 − 4.86258I −14.4423 + 3.8383I
u = −0.485295 + 0.862009I
a = −6.44205 + 2.64222I
b = −0.604973 + 0.042933I
−1.10951 − 2.08005I 43.7323 + 52.4587I
u = −0.485295 − 0.862009I
a = −6.44205 − 2.64222I
b = −0.604973 − 0.042933I
−1.10951 + 2.08005I 43.7323 − 52.4587I
u = 0.731003 + 0.711801I
a = 0.461608 + 0.068557I
b = −0.061104 − 0.642060I
3.23957 − 1.57241I 8.29788 + 4.00370I
u = 0.731003 − 0.711801I
a = 0.461608 − 0.068557I
b = −0.061104 + 0.642060I
3.23957 + 1.57241I 8.29788 − 4.00370I
u = −0.532729 + 0.793838I
a = −4.58885 − 1.30458I
b = −0.430627 + 0.271631I
−1.11507 − 2.15821I −17.5757 + 1.3433I
u = −0.532729 − 0.793838I
a = −4.58885 + 1.30458I
b = −0.430627 − 0.271631I
−1.11507 + 2.15821I −17.5757 − 1.3433I
u = 0.005378 + 0.951686I
a = 0.387546 − 0.444818I
b = −0.238112 − 0.586278I
−1.99133 − 1.66625I −3.10323 + 3.30828I
u = 0.005378 − 0.951686I
a = 0.387546 + 0.444818I
b = −0.238112 + 0.586278I
−1.99133 + 1.66625I −3.10323 − 3.30828I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.408970 + 0.857975I
a = −0.45960 − 1.92882I
b = −0.637620 + 0.101517I
−1.07758 − 1.62874I 1.55460 + 6.14952I
u = −0.408970 − 0.857975I
a = −0.45960 + 1.92882I
b = −0.637620 − 0.101517I
−1.07758 + 1.62874I 1.55460 − 6.14952I
u = −0.766786 + 0.740371I
a = 0.651267 − 0.131314I
b = 0.615638 + 0.219403I
1.02080 − 2.73193I 0
u = −0.766786 − 0.740371I
a = 0.651267 + 0.131314I
b = 0.615638 − 0.219403I
1.02080 + 2.73193I 0
u = 0.864126 + 0.313585I
a = 0.309844 + 0.093672I
b = 1.37366 + 0.34187I
−1.42714 − 5.94125I −1.80038 + 5.00917I
u = 0.864126 − 0.313585I
a = 0.309844 − 0.093672I
b = 1.37366 − 0.34187I
−1.42714 + 5.94125I −1.80038 − 5.00917I
u = 1.039310 + 0.373209I
a = −0.065636 + 0.281257I
b = −1.54296 − 0.70662I
−8.36607 − 10.64720I 0
u = 1.039310 − 0.373209I
a = −0.065636 − 0.281257I
b = −1.54296 + 0.70662I
−8.36607 + 10.64720I 0
u = −0.626101 + 0.914760I
a = 0.325312 − 0.028892I
b = 0.152283 − 0.264499I
0.59153 − 2.55241I 0
u = −0.626101 − 0.914760I
a = 0.325312 + 0.028892I
b = 0.152283 + 0.264499I
0.59153 + 2.55241I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.400472 + 1.043800I
a = 0.03414 − 1.47370I
b = 0.099037 + 0.659391I
−2.78363 − 2.76140I 0
u = −0.400472 − 1.043800I
a = 0.03414 + 1.47370I
b = 0.099037 − 0.659391I
−2.78363 + 2.76140I 0
u = 0.476376 + 0.736339I
a = 1.265560 − 0.103489I
b = 0.004351 − 1.233950I
3.20421 − 1.15270I 2.54366 + 10.12386I
u = 0.476376 − 0.736339I
a = 1.265560 + 0.103489I
b = 0.004351 + 1.233950I
3.20421 + 1.15270I 2.54366 − 10.12386I
u = 0.811711 + 0.324295I
a = −0.395948 − 0.346003I
b = 1.49081 + 0.62148I
−9.06891 − 3.72651I −4.60990 + 1.47067I
u = 0.811711 − 0.324295I
a = −0.395948 + 0.346003I
b = 1.49081 − 0.62148I
−9.06891 + 3.72651I −4.60990 − 1.47067I
u = −0.512874 + 1.037760I
a = 1.84313 − 2.43983I
b = 1.60245 + 0.14929I
−9.13954 − 3.03771I 0
u = −0.512874 − 1.037760I
a = 1.84313 + 2.43983I
b = 1.60245 − 0.14929I
−9.13954 + 3.03771I 0
u = −0.625197 + 0.558754I
a = −0.748140 + 0.492702I
b = 1.46358 + 0.03079I
−7.66872 − 1.43842I −12.36030 + 1.63046I
u = −0.625197 − 0.558754I
a = −0.748140 − 0.492702I
b = 1.46358 − 0.03079I
−7.66872 + 1.43842I −12.36030 − 1.63046I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.788749 + 0.201384I
a = −0.513368 − 1.264270I
b = −0.132527 + 1.397610I
−3.90942 − 3.06813I −3.25697 + 2.62072I
u = 0.788749 − 0.201384I
a = −0.513368 + 1.264270I
b = −0.132527 − 1.397610I
−3.90942 + 3.06813I −3.25697 − 2.62072I
u = 0.255427 + 1.176880I
a = 1.79250 + 1.07133I
b = 1.90837 + 0.50499I
−13.78770 − 0.65730I 0
u = 0.255427 − 1.176880I
a = 1.79250 − 1.07133I
b = 1.90837 − 0.50499I
−13.78770 + 0.65730I 0
u = 0.416558 + 1.131590I
a = −1.83787 − 1.06821I
b = −1.42336 + 0.58360I
−5.18749 + 3.49319I 0
u = 0.416558 − 1.131590I
a = −1.83787 + 1.06821I
b = −1.42336 − 0.58360I
−5.18749 − 3.49319I 0
u = 0.698400 + 0.990081I
a = −0.386699 + 0.027385I
b = 0.004017 + 0.573210I
2.39963 + 7.06465I 0
u = 0.698400 − 0.990081I
a = −0.386699 − 0.027385I
b = 0.004017 − 0.573210I
2.39963 − 7.06465I 0
u = −1.22213
a = −0.185084
b = −1.38307
−4.25382 0
u = 0.473990 + 1.133450I
a = −1.74243 − 1.06594I
b = −1.70619 + 0.02634I
−4.78405 + 4.34186I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.473990 − 1.133450I
a = −1.74243 + 1.06594I
b = −1.70619 − 0.02634I
−4.78405 − 4.34186I 0
u = 0.330229 + 1.197830I
a = −0.598268 + 0.608886I
b = 0.36448 + 1.47439I
−8.15277 + 0.56922I 0
u = 0.330229 − 1.197830I
a = −0.598268 − 0.608886I
b = 0.36448 − 1.47439I
−8.15277 − 0.56922I 0
u = 0.219337 + 1.224320I
a = 1.99373 + 0.73372I
b = 1.390620 − 0.107878I
−6.53057 − 2.65488I 0
u = 0.219337 − 1.224320I
a = 1.99373 − 0.73372I
b = 1.390620 + 0.107878I
−6.53057 + 2.65488I 0
u = −0.523934 + 1.144670I
a = 1.74807 − 0.40921I
b = 0.856476 + 0.079544I
−1.26231 − 4.39904I 0
u = −0.523934 − 1.144670I
a = 1.74807 + 0.40921I
b = 0.856476 − 0.079544I
−1.26231 + 4.39904I 0
u = 0.532228 + 1.170640I
a = 0.919867 − 0.607693I
b = −0.24571 − 1.71682I
−6.75213 + 7.96693I 0
u = 0.532228 − 1.170640I
a = 0.919867 + 0.607693I
b = −0.24571 + 1.71682I
−6.75213 − 7.96693I 0
u = 0.580858 + 1.155040I
a = 1.64375 + 1.15261I
b = 1.50003 − 0.88828I
−11.5445 + 8.9372I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.580858 − 1.155040I
a = 1.64375 − 1.15261I
b = 1.50003 + 0.88828I
−11.5445 − 8.9372I 0
u = 0.590895 + 1.169050I
a = 1.76142 + 1.12256I
b = 1.59367 − 0.43143I
−4.00028 + 11.30660I 0
u = 0.590895 − 1.169050I
a = 1.76142 − 1.12256I
b = 1.59367 + 0.43143I
−4.00028 − 11.30660I 0
u = −0.637144 + 0.213090I
a = 0.983394 − 0.020692I
b = 0.436473 − 0.303668I
1.45198 − 0.17538I 6.99722 − 1.18140I
u = −0.637144 − 0.213090I
a = 0.983394 + 0.020692I
b = 0.436473 + 0.303668I
1.45198 + 0.17538I 6.99722 + 1.18140I
u = −0.272566 + 0.576168I
a = −2.41405 − 1.00736I
b = −0.635817 − 0.458472I
−1.175210 − 0.433161I −4.73090 + 4.14534I
u = −0.272566 − 0.576168I
a = −2.41405 + 1.00736I
b = −0.635817 + 0.458472I
−1.175210 + 0.433161I −4.73090 − 4.14534I
u = 0.670259 + 1.215250I
a = −1.67768 − 1.18901I
b = −1.58802 + 0.84313I
−10.9823 + 16.7933I 0
u = 0.670259 − 1.215250I
a = −1.67768 + 1.18901I
b = −1.58802 − 0.84313I
−10.9823 − 16.7933I 0
u = 0.603559 + 0.095740I
a = 0.085973 − 0.820052I
b = −1.250030 + 0.072344I
−1.98118 − 0.16998I −3.50308 + 0.05920I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.603559 − 0.095740I
a = 0.085973 + 0.820052I
b = −1.250030 − 0.072344I
−1.98118 + 0.16998I −3.50308 − 0.05920I
u = −1.095700 + 0.886640I
a = −0.177881 + 0.508174I
b = −1.41985 − 0.12337I
−5.26056 − 3.80306I 0
u = −1.095700 − 0.886640I
a = −0.177881 − 0.508174I
b = −1.41985 + 0.12337I
−5.26056 + 3.80306I 0
u = 0.11898 + 1.44090I
a = −1.66657 − 0.44374I
b = −1.71694 − 0.48047I
−14.9486 − 6.6050I 0
u = 0.11898 − 1.44090I
a = −1.66657 + 0.44374I
b = −1.71694 + 0.48047I
−14.9486 + 6.6050I 0
u = −0.62573 + 1.38215I
a = −1.24381 + 0.74714I
b = −1.52635 − 0.26330I
−8.52431 − 6.48393I 0
u = −0.62573 − 1.38215I
a = −1.24381 − 0.74714I
b = −1.52635 + 0.26330I
−8.52431 + 6.48393I 0
u = −0.0151235
a = −43.4959
b = −0.551958
−1.12640 −9.50710
11
II.
I
u
2
= hb, −u
8
+ 2u
7
+ · · · + a − 1, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1 i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
u
8
− 2u
7
+ 3u
6
− 2u
5
+ 3u
4
− 2u
3
+ 2u
2
+ 1
0
a
8
=
1
−u
2
a
6
=
1
0
a
10
=
−u
u
3
+ u
a
12
=
−u
3
u
5
+ u
3
+ u
a
5
=
−u
8
− u
6
− u
4
+ 1
u
8
− u
7
+ u
6
− 2u
5
+ u
4
− 2u
3
− 2u − 1
a
2
=
2u
8
− 2u
7
+ 4u
6
− 2u
5
+ 4u
4
− 2u
3
+ 2u
2
−u
8
+ u
7
− u
6
+ 2u
5
− u
4
+ 2u
3
+ 2u + 1
a
1
=
u
8
+ u
6
+ u
4
− 1
−u
8
+ u
7
− u
6
+ 2u
5
− u
4
+ 2u
3
+ 2u + 1
a
4
=
u
8
− 2u
7
+ 3u
6
− 2u
5
+ 3u
4
− 2u
3
+ 2u
2
+ 1
0
a
9
=
u
2
+ 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
8
− 9u
7
+ 12u
6
− 13u
5
+ 15u
4
− 15u
3
+ 8u
2
− 5u − 3
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
6
u
9
c
4
(u + 1)
9
c
5
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
7
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
8
, c
11
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
9
, c
12
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
10
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
6
y
9
c
5
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
7
, c
10
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
8
, c
11
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
9
, c
12
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140343 + 0.966856I
a = −0.939568 + 0.981640I
b = 0
−3.42837 − 2.09337I −8.61953 + 2.85927I
u = −0.140343 − 0.966856I
a = −0.939568 − 0.981640I
b = 0
−3.42837 + 2.09337I −8.61953 − 2.85927I
u = −0.628449 + 0.875112I
a = 2.26219 + 2.13290I
b = 0
−1.02799 − 2.45442I −5.09778 + 12.45976I
u = −0.628449 − 0.875112I
a = 2.26219 − 2.13290I
b = 0
−1.02799 + 2.45442I −5.09778 − 12.45976I
u = 0.796005 + 0.733148I
a = 0.119081 + 0.409451I
b = 0
2.72642 − 1.33617I −5.51122 − 2.15019I
u = 0.796005 − 0.733148I
a = 0.119081 − 0.409451I
b = 0
2.72642 + 1.33617I −5.51122 + 2.15019I
u = 0.728966 + 0.986295I
a = −0.016164 − 0.378317I
b = 0
1.95319 + 7.08493I −9.51486 − 6.49599I
u = 0.728966 − 0.986295I
a = −0.016164 + 0.378317I
b = 0
1.95319 − 7.08493I −9.51486 + 6.49599I
u = −0.512358
a = 2.14893
b = 0
−0.446489 5.48680
15
III. I
u
3
=
h−120a
2
u−865au+· · ·−663a+43, a
3
−a
2
u+7a
2
−4au−3a−5u−12, u
2
+u+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
a
0.173661a
2
u + 1.25181au + ··· + 0.959479a − 0.0622287
a
8
=
1
u + 1
a
6
=
0.0274964a
2
u − 0.0101302au + ··· + 0.426918a + 0.548480
0.0709117a
2
u + 0.552822au + ··· + 0.416787a + 1.78292
a
10
=
−u
u + 1
a
12
=
−1
0
a
5
=
−0.0434153a
2
u − 0.562952au + ··· + 0.0101302a − 1.23444
0.0709117a
2
u + 0.552822au + ··· + 0.416787a + 1.78292
a
2
=
0.0274964a
2
u − 0.0101302au + ··· + 0.426918a − 1.45152
0.0709117a
2
u + 0.552822au + ··· + 0.416787a + 1.78292
a
1
=
−1
0
a
4
=
−0.173661a
2
u − 1.25181au + ··· + 0.0405210a + 0.0622287
0.173661a
2
u + 1.25181au + ··· + 0.959479a − 0.0622287
a
9
=
−0.162084a
2
u + 0.164978au + ··· − 0.0955137a − 0.0752533
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
837
691
a
2
u −
461
691
a
2
+
2345
691
au −
3467
691
a +
6538
691
u +
3634
691
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
(u
3
− 3u
2
+ 2u + 1)
2
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
, c
11
(u
2
+ u + 1)
3
c
8
, c
9
u
6
− 2u
5
+ 7u
4
+ 8u
3
+ 7u
2
+ 3u + 1
c
10
(u
2
− u + 1)
3
c
12
u
6
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
(y
3
− 5y
2
+ 10y −1)
2
c
7
, c
10
, c
11
(y
2
+ y + 1)
3
c
8
, c
9
y
6
+ 10y
5
+ 95y
4
+ 48y
3
+ 15y
2
+ 5y + 1
c
12
y
6
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.159960 − 0.102142I
b = −0.215080 − 1.307140I
3.02413 − 4.85801I 8.78307 + 4.05565I
u = −0.500000 + 0.866025I
a = 1.104070 + 0.474671I
b = −0.215080 + 1.307140I
3.02413 + 0.79824I −7.24138 + 7.14502I
u = −0.500000 + 0.866025I
a = −7.44411 + 0.49350I
b = −0.569840
−1.11345 − 2.02988I 37.9583 − 74.4205I
u = −0.500000 − 0.866025I
a = −1.159960 + 0.102142I
b = −0.215080 + 1.307140I
3.02413 + 4.85801I 8.78307 − 4.05565I
u = −0.500000 − 0.866025I
a = 1.104070 − 0.474671I
b = −0.215080 − 1.307140I
3.02413 − 0.79824I −7.24138 − 7.14502I
u = −0.500000 − 0.866025I
a = −7.44411 − 0.49350I
b = −0.569840
−1.11345 + 2.02988I 37.9583 + 74.4205I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
3
− u
2
+ 2u − 1)
2
(u
68
+ 72u
67
+ ··· − 116u + 1)
c
2
((u − 1)
9
)(u
3
+ u
2
− 1)
2
(u
68
− 12u
67
+ ··· + 4u − 1)
c
3
u
9
(u
3
− u
2
+ 2u − 1)
2
(u
68
+ 3u
67
+ ··· + 2048u + 512)
c
4
((u + 1)
9
)(u
3
− u
2
+ 1)
2
(u
68
− 12u
67
+ ··· + 4u − 1)
c
5
(u
3
− 3u
2
+ 2u + 1)
2
· (u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
68
+ 4u
67
+ ··· + 20u
2
− 1)
c
6
u
9
(u
3
+ u
2
+ 2u + 1)
2
(u
68
+ 3u
67
+ ··· + 2048u + 512)
c
7
(u
2
+ u + 1)
3
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
68
+ 5u
67
+ ··· − 61u + 1)
c
8
(u
6
− 2u
5
+ 7u
4
+ 8u
3
+ 7u
2
+ 3u + 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
68
− 8u
67
+ ··· − 679u + 1423)
c
9
(u
6
− 2u
5
+ 7u
4
+ 8u
3
+ 7u
2
+ 3u + 1)
· (u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
68
− 4u
67
+ ··· − 1569175u − 179693)
c
10
(u
2
− u + 1)
3
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
68
+ 5u
67
+ ··· − 61u + 1)
c
11
(u
2
+ u + 1)
3
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
68
+ 33u
67
+ ··· − 4365u + 1)
c
12
u
6
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
68
+ 6u
67
+ ··· − 992u + 64)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
3
+ 3y
2
+ 2y −1)
2
(y
68
− 140y
67
+ ··· + 13088y + 1)
c
2
, c
4
((y −1)
9
)(y
3
− y
2
+ 2y −1)
2
(y
68
− 72y
67
+ ··· + 116y + 1)
c
3
, c
6
y
9
(y
3
+ 3y
2
+ 2y −1)
2
(y
68
− 51y
67
+ ··· − 1048576y + 262144)
c
5
(y
3
− 5y
2
+ 10y −1)
2
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
68
− 16y
67
+ ··· − 40y + 1)
c
7
, c
10
(y
2
+ y + 1)
3
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
68
+ 33y
67
+ ··· − 4365y + 1)
c
8
(y
6
+ 10y
5
+ 95y
4
+ 48y
3
+ 15y
2
+ 5y + 1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
68
− 68y
67
+ ··· + 88237y + 2024929)
c
9
(y
6
+ 10y
5
+ 95y
4
+ 48y
3
+ 15y
2
+ 5y + 1)
· (y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
68
− 20y
67
+ ··· − 70781434415y + 32289574249)
c
11
((y
2
+ y + 1)
3
)(y
9
+ 7y
8
+ ··· + 13y −1)
· (y
68
+ 9y
67
+ ··· − 19115909y + 1)
c
12
y
6
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
68
+ 30y
67
+ ··· − 332800y + 4096)
21
