11a
99
(K11a
99
)
A knot diagram
1
Linearized knot diagam
6 1 10 8 2 3 11 5 7 4 9
Solving Sequence
2,6
1 3
7,9
10 5 8 4 11
c
1
c
2
c
6
c
9
c
5
c
8
c
4
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−3u
27
− 26u
26
+ ··· + 2b − 6, 9u
27
+ 72u
26
+ ··· + 4a + 84, u
28
+ 6u
27
+ ··· + 26u + 4i
I
u
2
= h5947395u
9
a
3
− 110563267u
9
a
2
+ ··· + 261341462a − 88347236, −u
9
a
3
− 5u
9
a
2
+ ··· − 8a − 7,
u
10
− u
9
+ 3u
8
− 3u
7
+ 5u
6
− 5u
5
+ 4u
4
− 4u
3
+ 3u
2
− 2u + 1i
I
u
3
= hu
11
− u
10
+ 4u
9
− 3u
8
+ 7u
7
− 4u
6
+ 4u
5
− u
3
+ 3u
2
+ b − 2u + 3,
− 2u
12
+ u
11
− 6u
10
+ u
9
− 8u
8
− u
7
− 2u
6
− 4u
5
+ u
4
− 2u
3
+ a − 2u − 2,
u
13
− u
12
+ 4u
11
− 3u
10
+ 7u
9
− 4u
8
+ 5u
7
− u
6
+ 2u
4
− 2u
3
+ 3u
2
− u + 1i
I
u
4
= ha
3
u − a
2
u
2
+ a
2
u + u
2
a − a
2
+ 4u
2
+ b + a − 2u + 5,
a
4
− 3a
2
u
2
+ a
3
+ 3a
2
u − 3u
2
a − 4a
2
+ 3au + 9u
2
− 4a − 6u + 13, u
3
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 93 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−3u
27
− 26u
26
+ · · · + 2b − 6, 9u
27
+ 72u
26
+ · · · + 4a + 84, u
28
+
6u
27
+ · · · + 26u + 4i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
7
=
−u
5
− 2u
3
− u
−u
7
− u
5
+ u
a
9
=
−
9
4
u
27
− 18u
26
+ ··· −
513
4
u − 21
3
2
u
27
+ 13u
26
+ ··· +
77
2
u + 3
a
10
=
11
4
u
27
+ 14u
26
+ ··· +
143
4
u + 5
−
5
2
u
27
− 15u
26
+ ··· −
127
2
u − 11
a
5
=
−u
u
a
8
=
−
21
4
u
27
− 29u
26
+ ··· −
449
4
u − 19
9
2
u
27
+ 24u
26
+ ··· +
45
2
u + 1
a
4
=
−
1
2
u
27
−
3
2
u
26
+ ··· −
41
2
u −
7
2
−
5
2
u
27
− 14u
26
+ ··· −
55
2
u − 4
a
11
=
1
2
u
27
+
9
2
u
26
+ ··· +
73
2
u +
13
2
−
1
2
u
27
− 3u
26
+ ··· +
7
2
u + 2
a
11
=
1
2
u
27
+
9
2
u
26
+ ··· +
73
2
u +
13
2
−
1
2
u
27
− 3u
26
+ ··· +
7
2
u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −13u
27
− 78u
26
− 316u
25
− 906u
24
− 2126u
23
− 4197u
22
−
7359u
21
− 11710u
20
− 17291u
19
− 23878u
18
− 30954u
17
− 37835u
16
− 43786u
15
−
48249u
14
− 50700u
13
− 50669u
12
− 48099u
11
− 43213u
10
− 36755u
9
− 29326u
8
−
21691u
7
− 14716u
6
− 9106u
5
− 5172u
4
− 2641u
3
− 1112u
2
− 342u − 54
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
28
− 6u
27
+ ··· − 26u + 4
c
2
u
28
+ 14u
27
+ ··· + 36u + 16
c
3
, c
4
, c
8
c
10
u
28
+ u
27
+ ··· + 3u + 1
c
6
u
28
+ 6u
27
+ ··· + 1800u + 712
c
7
u
28
− 29u
27
+ ··· − 118784u + 8192
c
9
, c
11
u
28
− 2u
27
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
28
+ 14y
27
+ ··· + 36y + 16
c
2
y
28
− 2y
27
+ ··· − 240y + 256
c
3
, c
4
, c
8
c
10
y
28
− 23y
27
+ ··· + 3y + 1
c
6
y
28
− 18y
27
+ ··· + 1943360y + 506944
c
7
y
28
+ 3y
27
+ ··· + 486539264y + 67108864
c
9
, c
11
y
28
+ 6y
27
+ ··· + 40y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.007890 + 0.244456I
a = 0.648218 + 0.649776I
b = 0.484897 − 0.362346I
−5.75558 + 1.16478I −9.81484 − 5.25007I
u = −1.007890 − 0.244456I
a = 0.648218 − 0.649776I
b = 0.484897 + 0.362346I
−5.75558 − 1.16478I −9.81484 + 5.25007I
u = 0.450069 + 0.945327I
a = 0.97063 − 1.16479I
b = −0.92359 + 1.77022I
1.30775 + 2.44749I −4.69640 − 9.53101I
u = 0.450069 − 0.945327I
a = 0.97063 + 1.16479I
b = −0.92359 − 1.77022I
1.30775 − 2.44749I −4.69640 + 9.53101I
u = 0.823545 + 0.669603I
a = −0.244511 + 1.089610I
b = −0.807023 − 0.636285I
−2.90686 − 3.71581I −3.96472 + 7.21162I
u = 0.823545 − 0.669603I
a = −0.244511 − 1.089610I
b = −0.807023 + 0.636285I
−2.90686 + 3.71581I −3.96472 − 7.21162I
u = −0.877743 + 0.205256I
a = −1.36751 − 0.95489I
b = −0.332382 + 1.109600I
−7.91511 + 11.38140I −4.44423 − 5.90932I
u = −0.877743 − 0.205256I
a = −1.36751 + 0.95489I
b = −0.332382 − 1.109600I
−7.91511 − 11.38140I −4.44423 + 5.90932I
u = 0.693563 + 0.915180I
a = −1.289000 − 0.358838I
b = 1.64479 − 0.73716I
−3.67868 + 9.29135I −4.02619 − 9.42557I
u = 0.693563 − 0.915180I
a = −1.289000 + 0.358838I
b = 1.64479 + 0.73716I
−3.67868 − 9.29135I −4.02619 + 9.42557I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.417630 + 1.105260I
a = −0.990060 − 0.503261I
b = 0.343945 + 0.624215I
−2.12382 − 1.70105I −2.95787 + 0.05705I
u = −0.417630 − 1.105260I
a = −0.990060 + 0.503261I
b = 0.343945 − 0.624215I
−2.12382 + 1.70105I −2.95787 − 0.05705I
u = −0.483475 + 1.130610I
a = 1.03565 + 1.24896I
b = −0.38060 − 1.45896I
−1.61917 − 5.94948I −1.73292 + 6.08838I
u = −0.483475 − 1.130610I
a = 1.03565 − 1.24896I
b = −0.38060 + 1.45896I
−1.61917 + 5.94948I −1.73292 − 6.08838I
u = 0.433444 + 0.634083I
a = 1.80511 − 0.76581I
b = −1.031200 + 0.788265I
2.24308 + 1.31021I 4.48172 + 2.40271I
u = 0.433444 − 0.634083I
a = 1.80511 + 0.76581I
b = −1.031200 − 0.788265I
2.24308 − 1.31021I 4.48172 − 2.40271I
u = −0.305330 + 0.675911I
a = −0.630555 + 0.172210I
b = 0.360299 + 0.412592I
−0.257625 − 1.154960I −2.96071 + 5.77634I
u = −0.305330 − 0.675911I
a = −0.630555 − 0.172210I
b = 0.360299 − 0.412592I
−0.257625 + 1.154960I −2.96071 − 5.77634I
u = −0.315106 + 1.262770I
a = 0.488001 + 0.002907I
b = 0.100408 + 1.021430I
−12.6068 + 7.4137I −9.32623 − 3.45211I
u = −0.315106 − 1.262770I
a = 0.488001 − 0.002907I
b = 0.100408 − 1.021430I
−12.6068 − 7.4137I −9.32623 + 3.45211I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.554721 + 1.203480I
a = −1.83799 − 0.92930I
b = 1.96223 + 2.11484I
−10.9151 − 16.6086I −7.19926 + 9.00617I
u = −0.554721 − 1.203480I
a = −1.83799 + 0.92930I
b = 1.96223 − 2.11484I
−10.9151 + 16.6086I −7.19926 − 9.00617I
u = −0.243939 + 1.326510I
a = −0.0674133 + 0.0418679I
b = −0.033141 − 1.007620I
−11.26130 − 3.02152I −13.62827 + 2.14467I
u = −0.243939 − 1.326510I
a = −0.0674133 − 0.0418679I
b = −0.033141 + 1.007620I
−11.26130 + 3.02152I −13.62827 − 2.14467I
u = −0.608424 + 0.177740I
a = 0.665110 − 0.192137I
b = −0.474963 − 0.907755I
1.04620 + 1.66789I 3.14449 − 2.66380I
u = −0.608424 − 0.177740I
a = 0.665110 + 0.192137I
b = −0.474963 + 0.907755I
1.04620 − 1.66789I 3.14449 + 2.66380I
u = −0.586363 + 1.242360I
a = 1.064320 + 0.381059I
b = −1.41368 − 1.21973I
−8.88695 − 6.88314I −9.37455 + 6.80974I
u = −0.586363 − 1.242360I
a = 1.064320 − 0.381059I
b = −1.41368 + 1.21973I
−8.88695 + 6.88314I −9.37455 − 6.80974I
7
II. I
u
2
= h5.95 × 10
6
a
3
u
9
− 1.11 × 10
8
a
2
u
9
+ · · · + 2.61 × 10
8
a − 8.83 ×
10
7
, −u
9
a
3
− 5u
9
a
2
+ · · · − 8a − 7, u
10
− u
9
+ · · · − 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
7
=
−u
5
− 2u
3
− u
−u
7
− u
5
+ u
a
9
=
a
−0.0456620a
3
u
9
+ 0.848865a
2
u
9
+ ··· − 2.00649a + 0.678298
a
10
=
2.14382a
3
u
9
+ 1.09367a
2
u
9
+ ··· − 1.51933a + 0.196840
−0.260987a
3
u
9
+ 0.338504a
2
u
9
+ ··· + 0.870243a + 2.69447
a
5
=
−u
u
a
8
=
0.0644237a
3
u
9
+ 0.101106a
2
u
9
+ ··· − 1.19004a − 1.96492
−0.110086a
3
u
9
+ 0.747759a
2
u
9
+ ··· + 0.183553a + 2.64322
a
4
=
−0.770676a
3
u
9
− 0.285432a
2
u
9
+ ··· − 0.188169a − 1.85717
−0.0386232a
3
u
9
+ 0.223455a
2
u
9
+ ··· + 1.74875a + 3.11581
a
11
=
−0.277440a
3
u
9
− 0.327129a
2
u
9
+ ··· − 0.0644294a + 0.411808
−0.285316a
3
u
9
+ 0.175678a
2
u
9
+ ··· + 0.268957a − 0.519132
a
11
=
−0.277440a
3
u
9
− 0.327129a
2
u
9
+ ··· − 0.0644294a + 0.411808
−0.285316a
3
u
9
+ 0.175678a
2
u
9
+ ··· + 0.268957a − 0.519132
(ii) Obstruction class = −1
(iii) Cusp Shapes =
6098888
7661669
u
9
a
3
−
21091308
7661669
u
9
a
2
+ ··· +
116819364
7661669
a +
59639590
7661669
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
10
+ u
9
+ 3u
8
+ 3u
7
+ 5u
6
+ 5u
5
+ 4u
4
+ 4u
3
+ 3u
2
+ 2u + 1)
4
c
2
(u
10
+ 5u
9
+ 13u
8
+ 19u
7
+ 17u
6
+ 7u
5
− 2u
3
+ u
2
+ 2u + 1)
4
c
3
, c
4
, c
8
c
10
u
40
− u
39
+ ··· − 18u
2
+ 1
c
6
(u
10
+ 2u
9
− u
8
− 5u
7
− 3u
6
+ 4u
5
+ 12u
4
+ 13u
3
+ 5u
2
+ u + 2)
4
c
7
(u
2
+ u + 1)
20
c
9
, c
11
u
40
+ 11u
39
+ ··· + 644u + 61
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
10
+ 5y
9
+ 13y
8
+ 19y
7
+ 17y
6
+ 7y
5
− 2y
3
+ y
2
+ 2y + 1)
4
c
2
(y
10
+ y
9
+ 13y
8
+ 11y
7
+ 45y
6
+ 35y
5
+ 12y
4
+ 2y
3
+ 9y
2
− 2y + 1)
4
c
3
, c
4
, c
8
c
10
y
40
− 33y
39
+ ··· − 36y + 1
c
6
(y
10
− 6y
9
+ ··· + 19y + 4)
4
c
7
(y
2
+ y + 1)
20
c
9
, c
11
y
40
+ 11y
39
+ ··· + 62528y + 3721
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.584958 + 0.771492I
a = −0.811252 − 0.684607I
b = 0.326566 + 1.346250I
0.002387 − 0.280172I −1.136314 + 0.057227I
u = −0.584958 + 0.771492I
a = −0.13825 + 1.48131I
b = 0.856552 − 0.765235I
0.002387 − 0.280172I −1.136314 + 0.057227I
u = −0.584958 + 0.771492I
a = 1.41803 − 0.77086I
b = −1.87810 − 0.26325I
0.00239 − 4.33994I −1.13631 + 6.98543I
u = −0.584958 + 0.771492I
a = −1.63324 − 0.44978I
b = 0.783367 + 0.997354I
0.00239 − 4.33994I −1.13631 + 6.98543I
u = −0.584958 − 0.771492I
a = −0.811252 + 0.684607I
b = 0.326566 − 1.346250I
0.002387 + 0.280172I −1.136314 − 0.057227I
u = −0.584958 − 0.771492I
a = −0.13825 − 1.48131I
b = 0.856552 + 0.765235I
0.002387 + 0.280172I −1.136314 − 0.057227I
u = −0.584958 − 0.771492I
a = 1.41803 + 0.77086I
b = −1.87810 + 0.26325I
0.00239 + 4.33994I −1.13631 − 6.98543I
u = −0.584958 − 0.771492I
a = −1.63324 + 0.44978I
b = 0.783367 − 0.997354I
0.00239 + 4.33994I −1.13631 − 6.98543I
u = 0.248527 + 0.782547I
a = −0.528657 + 0.220233I
b = 0.80276 − 1.85708I
−5.38286 + 3.26157I −6.90177 − 8.91318I
u = 0.248527 + 0.782547I
a = −0.77879 + 1.65055I
b = −0.1103870 − 0.0163537I
−5.38286 − 0.79819I −6.90177 − 1.98497I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.248527 + 0.782547I
a = −2.16490 − 1.33388I
b = 2.78977 + 0.25266I
−5.38286 − 0.79819I −6.90177 − 1.98497I
u = 0.248527 + 0.782547I
a = 2.27476 + 2.17074I
b = −1.93781 − 0.58149I
−5.38286 + 3.26157I −6.90177 − 8.91318I
u = 0.248527 − 0.782547I
a = −0.528657 − 0.220233I
b = 0.80276 + 1.85708I
−5.38286 − 3.26157I −6.90177 + 8.91318I
u = 0.248527 − 0.782547I
a = −0.77879 − 1.65055I
b = −0.1103870 + 0.0163537I
−5.38286 + 0.79819I −6.90177 + 1.98497I
u = 0.248527 − 0.782547I
a = −2.16490 + 1.33388I
b = 2.78977 − 0.25266I
−5.38286 + 0.79819I −6.90177 + 1.98497I
u = 0.248527 − 0.782547I
a = 2.27476 − 2.17074I
b = −1.93781 + 0.58149I
−5.38286 − 3.26157I −6.90177 + 8.91318I
u = 0.761643 + 0.208049I
a = −0.888121 − 0.198095I
b = 0.169145 − 1.209710I
−2.52120 − 5.50828I −2.80497 + 6.25925I
u = 0.761643 + 0.208049I
a = −1.109160 + 0.691872I
b = −0.405801 − 0.684900I
−2.52120 − 1.44851I −2.80497 − 0.66896I
u = 0.761643 + 0.208049I
a = −0.465789 − 0.420142I
b = 0.307020 + 0.341147I
−2.52120 − 1.44851I −2.80497 − 0.66896I
u = 0.761643 + 0.208049I
a = 1.44027 − 1.30172I
b = 0.177943 + 1.296040I
−2.52120 − 5.50828I −2.80497 + 6.25925I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.761643 − 0.208049I
a = −0.888121 + 0.198095I
b = 0.169145 + 1.209710I
−2.52120 + 5.50828I −2.80497 − 6.25925I
u = 0.761643 − 0.208049I
a = −1.109160 − 0.691872I
b = −0.405801 + 0.684900I
−2.52120 + 1.44851I −2.80497 + 0.66896I
u = 0.761643 − 0.208049I
a = −0.465789 + 0.420142I
b = 0.307020 − 0.341147I
−2.52120 + 1.44851I −2.80497 + 0.66896I
u = 0.761643 − 0.208049I
a = 1.44027 + 1.30172I
b = 0.177943 − 1.296040I
−2.52120 + 5.50828I −2.80497 − 6.25925I
u = −0.449566 + 1.164790I
a = 0.79423 − 1.18245I
b = −0.42710 + 2.17011I
−9.81146 − 6.17573I −10.98134 + 7.44010I
u = −0.449566 + 1.164790I
a = 0.152868 − 0.428323I
b = −1.107140 − 0.677603I
−9.81146 − 2.11597I −10.98134 + 0.51190I
u = −0.449566 + 1.164790I
a = 1.92707 + 0.90418I
b = −1.82941 − 2.34062I
−9.81146 − 6.17573I −10.98134 + 7.44010I
u = −0.449566 + 1.164790I
a = −1.75450 − 1.78926I
b = 2.08774 + 2.71705I
−9.81146 − 2.11597I −10.98134 + 0.51190I
u = −0.449566 − 1.164790I
a = 0.79423 + 1.18245I
b = −0.42710 − 2.17011I
−9.81146 + 6.17573I −10.98134 − 7.44010I
u = −0.449566 − 1.164790I
a = 0.152868 + 0.428323I
b = −1.107140 + 0.677603I
−9.81146 + 2.11597I −10.98134 − 0.51190I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.449566 − 1.164790I
a = 1.92707 − 0.90418I
b = −1.82941 + 2.34062I
−9.81146 + 6.17573I −10.98134 − 7.44010I
u = −0.449566 − 1.164790I
a = −1.75450 + 1.78926I
b = 2.08774 − 2.71705I
−9.81146 + 2.11597I −10.98134 − 0.51190I
u = 0.524355 + 1.163410I
a = 0.740427 + 0.151085I
b = −0.650836 − 0.191721I
−5.31595 + 6.25643I −6.17560 − 2.68471I
u = 0.524355 + 1.163410I
a = −1.43496 + 0.55642I
b = 1.51204 − 1.58158I
−5.31595 + 6.25643I −6.17560 − 2.68471I
u = 0.524355 + 1.163410I
a = −1.20657 + 1.25082I
b = 0.33739 − 1.88156I
−5.31595 + 10.31620I −6.17560 − 9.61291I
u = 0.524355 + 1.163410I
a = 2.16655 − 1.00309I
b = −2.30372 + 2.02238I
−5.31595 + 10.31620I −6.17560 − 9.61291I
u = 0.524355 − 1.163410I
a = 0.740427 − 0.151085I
b = −0.650836 + 0.191721I
−5.31595 − 6.25643I −6.17560 + 2.68471I
u = 0.524355 − 1.163410I
a = −1.43496 − 0.55642I
b = 1.51204 + 1.58158I
−5.31595 − 6.25643I −6.17560 + 2.68471I
u = 0.524355 − 1.163410I
a = −1.20657 − 1.25082I
b = 0.33739 + 1.88156I
−5.31595 − 10.31620I −6.17560 + 9.61291I
u = 0.524355 − 1.163410I
a = 2.16655 + 1.00309I
b = −2.30372 − 2.02238I
−5.31595 − 10.31620I −6.17560 + 9.61291I
14
III.
I
u
3
= hu
11
− u
10
+ · · · + b + 3, −2u
12
+ u
11
+ · · · + a − 2, u
13
− u
12
+ · · · − u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
7
=
−u
5
− 2u
3
− u
−u
7
− u
5
+ u
a
9
=
2u
12
− u
11
+ 6u
10
− u
9
+ 8u
8
+ u
7
+ 2u
6
+ 4u
5
− u
4
+ 2u
3
+ 2u + 2
−u
11
+ u
10
− 4u
9
+ 3u
8
− 7u
7
+ 4u
6
− 4u
5
+ u
3
− 3u
2
+ 2u − 3
a
10
=
2u
12
− u
11
+ 6u
10
− 2u
9
+ 8u
8
− u
7
+ 2u
6
+ 2u
5
− u
4
+ 2u
3
+ 2u + 2
−u
11
+ u
10
− 3u
9
+ 3u
8
− 5u
7
+ 4u
6
− 2u
5
+ u
3
− 2u
2
+ 2u − 2
a
5
=
−u
u
a
8
=
u
12
+ 3u
10
+ u
9
+ 4u
8
+ 3u
7
+ u
6
+ 3u
5
+ u
2
+ 2
u
12
− 2u
11
+ ··· + 4u − 3
a
4
=
−u
12
− u
11
− 2u
10
− 4u
9
− 2u
8
− 6u
7
− 3u
5
− u
4
+ u
3
− 2u
2
− 3
−2u
12
+ 3u
11
+ ··· − 5u + 3
a
11
=
u
12
− 2u
11
+ ··· + 3u − 2
−2u
12
+ 2u
11
+ ··· − 4u + 1
a
11
=
u
12
− 2u
11
+ ··· + 3u − 2
−2u
12
+ 2u
11
+ ··· − 4u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
10
− 4u
9
+ 6u
8
− 8u
7
+ 7u
6
− 5u
5
+ u
4
+ 6u
3
− 3u
2
+ 3u − 9
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− u
12
+ ··· − u + 1
c
2
u
13
+ 7u
12
+ ··· − 5u − 1
c
3
, c
8
u
13
− u
12
+ ··· + 3u + 1
c
4
, c
10
u
13
+ u
12
+ ··· + 3u − 1
c
5
u
13
+ u
12
+ ··· − u − 1
c
6
u
13
− u
12
+ ··· + u − 1
c
7
u
13
− 2u
12
+ ··· + 2u − 1
c
9
, c
11
u
13
+ 2u
12
+ ··· + 2u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
13
+ 7y
12
+ ··· − 5y −1
c
2
y
13
− y
12
+ ··· + 7y −1
c
3
, c
4
, c
8
c
10
y
13
− 15y
12
+ ··· − 9y −1
c
6
y
13
− 9y
12
+ ··· − 11y −1
c
7
y
13
+ 2y
12
+ ··· − 2y −1
c
9
, c
11
y
13
+ 2y
12
+ ··· − 2y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.429348 + 0.836369I
a = −1.06443 − 0.95489I
b = 0.90233 + 1.19418I
1.50284 − 1.80144I −0.975171 + 0.624326I
u = −0.429348 − 0.836369I
a = −1.06443 + 0.95489I
b = 0.90233 − 1.19418I
1.50284 + 1.80144I −0.975171 − 0.624326I
u = 0.777700 + 0.380482I
a = −0.544452 + 0.841459I
b = −0.722544 − 0.675961I
−3.52105 − 2.68668I −6.71015 + 2.69355I
u = 0.777700 − 0.380482I
a = −0.544452 − 0.841459I
b = −0.722544 + 0.675961I
−3.52105 + 2.68668I −6.71015 − 2.69355I
u = −0.851574
a = 1.29542
b = 0.236834
−5.58548 −6.40050
u = 0.354755 + 1.099910I
a = 0.261043 − 1.280070I
b = 0.463549 + 0.404379I
−7.44002 − 0.06234I −10.48891 − 0.49082I
u = 0.354755 − 1.099910I
a = 0.261043 + 1.280070I
b = 0.463549 − 0.404379I
−7.44002 + 0.06234I −10.48891 + 0.49082I
u = −0.432945 + 1.190570I
a = 0.574206 + 0.848947I
b = −0.88235 − 1.94320I
−9.24726 − 4.36417I −9.35230 + 3.32302I
u = −0.432945 − 1.190570I
a = 0.574206 − 0.848947I
b = −0.88235 + 1.94320I
−9.24726 + 4.36417I −9.35230 − 3.32302I
u = 0.555159 + 1.145130I
a = −1.45591 + 0.17932I
b = 1.45752 − 1.05620I
−5.89830 + 7.73676I −8.25887 − 7.75024I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.555159 − 1.145130I
a = −1.45591 − 0.17932I
b = 1.45752 + 1.05620I
−5.89830 − 7.73676I −8.25887 + 7.75024I
u = 0.100465 + 0.707437I
a = 2.08183 + 1.26835I
b = −1.83693 + 0.64675I
−5.50214 + 2.30256I −8.51436 − 0.38924I
u = 0.100465 − 0.707437I
a = 2.08183 − 1.26835I
b = −1.83693 − 0.64675I
−5.50214 − 2.30256I −8.51436 + 0.38924I
19
IV.
I
u
4
= h−a
2
u
2
+ u
2
a + · · · + a + 5, −3a
2
u
2
− 3u
2
a + · · · − 4a + 13, u
3
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
−u
2
− u
a
7
=
u
2
+ 1
−u
2
a
9
=
a
−a
3
u + a
2
u
2
− a
2
u − u
2
a + a
2
− 4u
2
− a + 2u − 5
a
10
=
a
3
u
2
+ 2a
2
u
2
+ a
3
− a
2
u − u
2
a + 3a
2
− 7u
2
− a + 5u − 11
−a
3
u
2
− a
3
u − a
2
u + au − 2u
2
+ u − 1
a
5
=
−u
u
a
8
=
a
3
u + a
3
+ u
2
a + a
2
+ au − u
2
+ a + 2u − 2
−2a
3
u + a
2
u
2
− a
3
− a
2
u − 2u
2
a − au − 3u
2
− a − 3
a
4
=
−a
3
u
2
− 3a
2
u
2
+ ··· + 3a + 14
−a
3
u − a
3
− 2a
2
u − 2a
2
− au − 2u + 2
a
11
=
a
3
u
2
+ a
2
u
2
+ a
3
− a
2
u − u
2
a + 2a
2
+ au − 6u
2
− 2a + 4u − 8
a
2
u
2
− 2
a
11
=
a
3
u
2
+ a
2
u
2
+ a
3
− a
2
u − u
2
a + 2a
2
+ au − 6u
2
− 2a + 4u − 8
a
2
u
2
− 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4a
3
u + 4a
2
u
2
− 4a
2
u − 4u
2
a + 4a
2
− 16u
2
− 4a + 8u − 30
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
3
+ u − 1)
4
c
2
(u
3
+ 2u
2
+ u − 1)
4
c
3
, c
4
, c
8
c
10
u
12
− 6u
10
+ ··· + 8u + 1
c
6
(u − 1)
12
c
7
(u
2
+ u + 1)
6
c
9
, c
11
u
12
+ 4u
11
+ ··· + 32u + 13
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
3
+ 2y
2
+ y −1)
4
c
2
(y
3
− 2y
2
+ 5y −1)
4
c
3
, c
4
, c
8
c
10
y
12
− 12y
11
+ ··· − 36y + 1
c
6
(y −1)
12
c
7
(y
2
+ y + 1)
6
c
9
, c
11
y
12
+ 8y
11
+ ··· + 848y + 169
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.341164 + 1.161540I
a = −1.034830 + 0.098333I
b = 0.500000 + 0.866025I
−6.57974 − 2.02988I −8.00000 + 3.46410I
u = 0.341164 + 1.161540I
a = 0.534830 − 0.964359I
b = 0.500000 + 0.866025I
−6.57974 − 2.02988I −8.00000 + 3.46410I
u = 0.341164 + 1.161540I
a = −0.478220 + 1.030980I
b = 0.500000 − 0.866025I
−6.57974 + 2.02988I −8.00000 − 3.46410I
u = 0.341164 + 1.161540I
a = −0.021780 − 0.164953I
b = 0.500000 − 0.866025I
−6.57974 + 2.02988I −8.00000 − 3.46410I
u = 0.341164 − 1.161540I
a = −1.034830 − 0.098333I
b = 0.500000 − 0.866025I
−6.57974 + 2.02988I −8.00000 − 3.46410I
u = 0.341164 − 1.161540I
a = 0.534830 + 0.964359I
b = 0.500000 − 0.866025I
−6.57974 + 2.02988I −8.00000 − 3.46410I
u = 0.341164 − 1.161540I
a = −0.478220 − 1.030980I
b = 0.500000 + 0.866025I
−6.57974 − 2.02988I −8.00000 + 3.46410I
u = 0.341164 − 1.161540I
a = −0.021780 + 0.164953I
b = 0.500000 + 0.866025I
−6.57974 − 2.02988I −8.00000 + 3.46410I
u = −0.682328
a = 1.83446 + 0.06511I
b = 0.500000 + 0.866025I
−6.57974 − 2.02988I −8.00000 + 3.46410I
u = −0.682328
a = 1.83446 − 0.06511I
b = 0.500000 − 0.866025I
−6.57974 + 2.02988I −8.00000 − 3.46410I
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.682328
a = −2.33446 + 0.93114I
b = 0.500000 − 0.866025I
−6.57974 + 2.02988I −8.00000 − 3.46410I
u = −0.682328
a = −2.33446 − 0.93114I
b = 0.500000 + 0.866025I
−6.57974 − 2.02988I −8.00000 + 3.46410I
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u − 1)
4
· (u
10
+ u
9
+ 3u
8
+ 3u
7
+ 5u
6
+ 5u
5
+ 4u
4
+ 4u
3
+ 3u
2
+ 2u + 1)
4
· (u
13
− u
12
+ ··· − u + 1)(u
28
− 6u
27
+ ··· − 26u + 4)
c
2
(u
3
+ 2u
2
+ u − 1)
4
· (u
10
+ 5u
9
+ 13u
8
+ 19u
7
+ 17u
6
+ 7u
5
− 2u
3
+ u
2
+ 2u + 1)
4
· (u
13
+ 7u
12
+ ··· − 5u − 1)(u
28
+ 14u
27
+ ··· + 36u + 16)
c
3
, c
8
(u
12
− 6u
10
+ ··· + 8u + 1)(u
13
− u
12
+ ··· + 3u + 1)
· (u
28
+ u
27
+ ··· + 3u + 1)(u
40
− u
39
+ ··· − 18u
2
+ 1)
c
4
, c
10
(u
12
− 6u
10
+ ··· + 8u + 1)(u
13
+ u
12
+ ··· + 3u − 1)
· (u
28
+ u
27
+ ··· + 3u + 1)(u
40
− u
39
+ ··· − 18u
2
+ 1)
c
5
(u
3
+ u − 1)
4
· (u
10
+ u
9
+ 3u
8
+ 3u
7
+ 5u
6
+ 5u
5
+ 4u
4
+ 4u
3
+ 3u
2
+ 2u + 1)
4
· (u
13
+ u
12
+ ··· − u − 1)(u
28
− 6u
27
+ ··· − 26u + 4)
c
6
(u − 1)
12
· (u
10
+ 2u
9
− u
8
− 5u
7
− 3u
6
+ 4u
5
+ 12u
4
+ 13u
3
+ 5u
2
+ u + 2)
4
· (u
13
− u
12
+ ··· + u − 1)(u
28
+ 6u
27
+ ··· + 1800u + 712)
c
7
((u
2
+ u + 1)
26
)(u
13
− 2u
12
+ ··· + 2u − 1)
· (u
28
− 29u
27
+ ··· − 118784u + 8192)
c
9
, c
11
(u
12
+ 4u
11
+ ··· + 32u + 13)(u
13
+ 2u
12
+ ··· + 2u + 1)
· (u
28
− 2u
27
+ ··· − 2u + 1)(u
40
+ 11u
39
+ ··· + 644u + 61)
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
3
+ 2y
2
+ y −1)
4
· (y
10
+ 5y
9
+ 13y
8
+ 19y
7
+ 17y
6
+ 7y
5
− 2y
3
+ y
2
+ 2y + 1)
4
· (y
13
+ 7y
12
+ ··· − 5y −1)(y
28
+ 14y
27
+ ··· + 36y + 16)
c
2
(y
3
− 2y
2
+ 5y −1)
4
· (y
10
+ y
9
+ 13y
8
+ 11y
7
+ 45y
6
+ 35y
5
+ 12y
4
+ 2y
3
+ 9y
2
− 2y + 1)
4
· (y
13
− y
12
+ ··· + 7y −1)(y
28
− 2y
27
+ ··· − 240y + 256)
c
3
, c
4
, c
8
c
10
(y
12
− 12y
11
+ ··· − 36y + 1)(y
13
− 15y
12
+ ··· − 9y −1)
· (y
28
− 23y
27
+ ··· + 3y + 1)(y
40
− 33y
39
+ ··· − 36y + 1)
c
6
((y −1)
12
)(y
10
− 6y
9
+ ··· + 19y + 4)
4
(y
13
− 9y
12
+ ··· − 11y −1)
· (y
28
− 18y
27
+ ··· + 1943360y + 506944)
c
7
((y
2
+ y + 1)
26
)(y
13
+ 2y
12
+ ··· − 2y −1)
· (y
28
+ 3y
27
+ ··· + 486539264y + 67108864)
c
9
, c
11
(y
12
+ 8y
11
+ ··· + 848y + 169)(y
13
+ 2y
12
+ ··· − 2y −1)
· (y
28
+ 6y
27
+ ··· + 40y + 1)(y
40
+ 11y
39
+ ··· + 62528y + 3721)
26
