12n
0299
(K12n
0299
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 12 2 10 1 5 1 6 9
Solving Sequence
3,6
2 7
4,10
8 1 11 12 5 9
c
2
c
6
c
3
c
7
c
1
c
10
c
11
c
5
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−5u
28
− 22u
27
+ ··· + 2b + 4, −u
28
− u
27
+ ··· + 2a − 5, u
29
+ 6u
28
+ ··· − 10u − 4i
I
u
2
= h−123u
7
a
3
+ 644u
7
a
2
+ ··· − 2637a − 1781, −u
7
a
3
− u
7
a
2
+ ··· + 4a − 1,
u
8
− u
7
+ 3u
6
− 2u
5
+ 3u
4
− 2u
3
− 1i
I
u
3
= hu
18
− u
17
+ ··· + b + 1,
u
18
+ 5u
16
+ u
15
+ 12u
14
+ 3u
13
+ 15u
12
+ 4u
11
+ 8u
10
− 3u
8
− 4u
7
− 5u
6
− 4u
5
− u
4
+ u
2
+ a − u − 1,
u
19
− u
18
+ ··· + u − 1i
* 3 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−5u
28
−22u
27
+· · ·+2b+4, −u
28
−u
27
+· · ·+2a−5, u
29
+6u
28
+· · ·−10u−4i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
10
=
1
2
u
28
+
1
2
u
27
+ ··· + 2u +
5
2
5
2
u
28
+ 11u
27
+ ··· −
15
2
u − 2
a
8
=
−
3
4
u
28
− 5u
27
+ ··· +
71
4
u + 18
1
2
u
28
+ 6u
27
+ ··· −
19
2
u + 3
a
1
=
u
2
+ 1
u
2
a
11
=
−u
28
−
9
2
u
27
+ ··· +
21
2
u +
21
2
5
2
u
28
+ 15u
27
+ ··· −
27
2
u − 2
a
12
=
−u
28
−
9
2
u
27
+ ··· +
21
2
u +
21
2
−
5
2
u
28
− 8u
27
+ ··· −
5
2
u + 4
a
5
=
−
3
4
u
28
− 4u
27
+ ··· +
19
4
u + 3
−
1
2
u
28
− 3u
27
+ ··· +
11
2
u + 3
a
9
=
−
1
4
u
28
− u
27
+ ··· +
5
4
u + 1
−
5
2
u
28
− 11u
27
+ ··· +
9
2
u + 3
(ii) Obstruction class = −1
(iii) Cusp Shapes
= u
28
+ 6u
27
+ 26u
26
+ 78u
25
+ 195u
24
+ 404u
23
+ 742u
22
+ 1212u
21
+ 1814u
20
+ 2496u
19
+
3192u
18
+ 3810u
17
+ 4264u
16
+ 4505u
15
+ 4511u
14
+ 4302u
13
+ 3916u
12
+ 3391u
11
+
2793u
10
+ 2164u
9
+ 1573u
8
+ 1049u
7
+ 629u
6
+ 320u
5
+ 122u
4
+ 16u
3
−19u
2
−14u −10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
29
+ 16u
28
+ ··· + 108u − 16
c
2
, c
6
u
29
− 6u
28
+ ··· − 10u + 4
c
3
u
29
+ 6u
28
+ ··· + 102u + 52
c
4
, c
5
, c
9
c
11
u
29
+ 7u
27
+ ··· + 2u + 1
c
7
, c
10
u
29
− 3u
28
+ ··· − 21u + 1
c
8
, c
12
u
29
+ 19u
28
+ ··· + 2304u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
− 4y
28
+ ··· + 28400y −256
c
2
, c
6
y
29
+ 16y
28
+ ··· + 108y −16
c
3
y
29
− 24y
28
+ ··· + 12588y −2704
c
4
, c
5
, c
9
c
11
y
29
+ 14y
28
+ ··· − 10y −1
c
7
, c
10
y
29
− 49y
28
+ ··· + 83y −1
c
8
, c
12
y
29
+ 9y
28
+ ··· + 131072y −65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.529936 + 0.817458I
a = 0.234233 + 0.574816I
b = 0.345760 − 0.496091I
−1.24507 + 2.13242I −1.54126 − 5.97211I
u = 0.529936 − 0.817458I
a = 0.234233 − 0.574816I
b = 0.345760 + 0.496091I
−1.24507 − 2.13242I −1.54126 + 5.97211I
u = −0.333397 + 0.883512I
a = −0.369414 + 0.421127I
b = 0.248910 + 0.466784I
−0.53686 − 1.47819I −4.90590 + 3.46156I
u = −0.333397 − 0.883512I
a = −0.369414 − 0.421127I
b = 0.248910 − 0.466784I
−0.53686 + 1.47819I −4.90590 − 3.46156I
u = 0.230674 + 1.031600I
a = 0.622836 − 0.242190I
b = −0.393514 − 0.586648I
−3.27588 + 2.17781I −14.9005 − 2.5155I
u = 0.230674 − 1.031600I
a = 0.622836 + 0.242190I
b = −0.393514 + 0.586648I
−3.27588 − 2.17781I −14.9005 + 2.5155I
u = 0.752784 + 0.560145I
a = 0.141867 − 0.328248I
b = −0.290661 + 0.167634I
4.48557 − 3.54679I −5.06701 + 3.83669I
u = 0.752784 − 0.560145I
a = 0.141867 + 0.328248I
b = −0.290661 − 0.167634I
4.48557 + 3.54679I −5.06701 − 3.83669I
u = −0.929027 + 0.116767I
a = −2.22411 + 0.15082I
b = −2.04864 + 0.39982I
−2.62991 + 9.91881I −5.74423 − 5.24249I
u = −0.929027 − 0.116767I
a = −2.22411 − 0.15082I
b = −2.04864 − 0.39982I
−2.62991 − 9.91881I −5.74423 + 5.24249I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.755090 + 0.452937I
a = −0.606953 − 0.612743I
b = −0.735838 − 0.187764I
4.01496 − 0.67489I −6.09853 + 2.29351I
u = −0.755090 − 0.452937I
a = −0.606953 + 0.612743I
b = −0.735838 + 0.187764I
4.01496 + 0.67489I −6.09853 − 2.29351I
u = −0.864712 + 0.123739I
a = 2.27119 + 0.52125I
b = 2.02843 + 0.16969I
−4.98255 + 2.50011I −6.07998 − 2.74065I
u = −0.864712 − 0.123739I
a = 2.27119 − 0.52125I
b = 2.02843 − 0.16969I
−4.98255 − 2.50011I −6.07998 + 2.74065I
u = 0.018688 + 1.158270I
a = −0.390605 + 0.430620I
b = 0.506072 + 0.444376I
−1.41808 − 2.24811I −11.36469 + 3.43943I
u = 0.018688 − 1.158270I
a = −0.390605 − 0.430620I
b = 0.506072 − 0.444376I
−1.41808 + 2.24811I −11.36469 − 3.43943I
u = 0.643120 + 0.992128I
a = −0.240554 − 0.246860I
b = −0.090211 + 0.397421I
3.21603 + 8.80773I −6.26763 − 8.83895I
u = 0.643120 − 0.992128I
a = −0.240554 + 0.246860I
b = −0.090211 − 0.397421I
3.21603 − 8.80773I −6.26763 + 8.83895I
u = −0.593156 + 1.076560I
a = 0.559837 + 0.468168I
b = 0.836083 − 0.325004I
2.16507 − 4.43085I −9.17518 + 3.77414I
u = −0.593156 − 1.076560I
a = 0.559837 − 0.468168I
b = 0.836083 + 0.325004I
2.16507 + 4.43085I −9.17518 − 3.77414I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.396847 + 1.258520I
a = 0.13510 − 1.71384I
b = −2.10328 − 0.85015I
−9.21490 − 1.83630I −10.54114 + 0.46853I
u = −0.396847 − 1.258520I
a = 0.13510 + 1.71384I
b = −2.10328 + 0.85015I
−9.21490 + 1.83630I −10.54114 − 0.46853I
u = −0.525425 + 1.223980I
a = −0.68573 − 1.73877I
b = −2.48851 − 0.07427I
−8.26868 − 7.55554I −8.73863 + 5.55556I
u = −0.525425 − 1.223980I
a = −0.68573 + 1.73877I
b = −2.48851 + 0.07427I
−8.26868 + 7.55554I −8.73863 − 5.55556I
u = −0.398180 + 1.298960I
a = 0.28856 + 1.51336I
b = 2.08069 + 0.22776I
−7.09003 + 5.31029I −9.76890 − 2.61442I
u = −0.398180 − 1.298960I
a = 0.28856 − 1.51336I
b = 2.08069 − 0.22776I
−7.09003 − 5.31029I −9.76890 + 2.61442I
u = −0.533945 + 1.252430I
a = 0.25821 + 1.84759I
b = 2.45185 + 0.66312I
−6.0854 − 15.1894I −8.50713 + 8.09278I
u = −0.533945 − 1.252430I
a = 0.25821 − 1.84759I
b = 2.45185 − 0.66312I
−6.0854 + 15.1894I −8.50713 − 8.09278I
u = 0.309156
a = −0.988933
b = 0.305734
−0.776150 −12.5990
7
II. I
u
2
= h−123u
7
a
3
+ 644u
7
a
2
+ · · · − 2637a − 1781, −u
7
a
3
− u
7
a
2
+ · · · +
4a − 1, u
8
− u
7
+ 3u
6
− 2u
5
+ 3u
4
− 2u
3
− 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
10
=
a
0.0617160a
3
u
7
− 0.323131a
2
u
7
+ ··· + 1.32313a + 0.893628
a
8
=
−0.205218a
3
u
7
+ 0.497240a
2
u
7
+ ··· + 0.502760a − 2.00401
0.0145509a
3
u
7
+ 0.517311a
2
u
7
+ ··· − 1.51731a − 1.06573
a
1
=
u
2
+ 1
u
2
a
11
=
0.202208a
3
u
7
− 0.0180632a
2
u
7
+ ··· + 0.0180632a − 0.844456
0.255896a
3
u
7
− 0.730055a
2
u
7
+ ··· + 1.73006a + 0.119920
a
12
=
0.202208a
3
u
7
− 0.0180632a
2
u
7
+ ··· + 0.0180632a − 0.844456
0.0842950a
3
u
7
− 0.416959a
2
u
7
+ ··· + 1.41696a − 1.24285
a
5
=
−0.0496739a
3
u
7
+ 0.406422a
2
u
7
+ ··· − 0.406422a − 0.499749
0.308580a
3
u
7
+ 1.38435a
2
u
7
+ ··· + 0.615655a − 4.53186
a
9
=
−0.186653a
3
u
7
+ 0.708981a
2
u
7
+ ··· + 1.29102a − 2.60512
0.238334a
3
u
7
+ 0.231811a
2
u
7
+ ··· − 1.23181a − 1.66282
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1636
1993
u
7
a
3
+
3964
1993
u
7
a
2
+ ··· +
4008
1993
a −
11990
1993
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
8
+ 5u
7
+ 11u
6
+ 10u
5
− u
4
− 10u
3
− 6u
2
+ 1)
4
c
2
, c
6
(u
8
+ u
7
+ 3u
6
+ 2u
5
+ 3u
4
+ 2u
3
− 1)
4
c
3
(u
8
− u
7
− 5u
6
+ 4u
5
+ 7u
4
− 4u
3
− 2u
2
+ 2u − 1)
4
c
4
, c
5
, c
9
c
11
u
32
− u
31
+ ··· + 830u + 361
c
7
, c
10
u
32
− 5u
31
+ ··· − 27238u + 3169
c
8
, c
12
(u
2
− u + 1)
16
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
8
− 3y
7
+ 19y
6
− 34y
5
+ 71y
4
− 66y
3
+ 34y
2
− 12y + 1)
4
c
2
, c
6
(y
8
+ 5y
7
+ 11y
6
+ 10y
5
− y
4
− 10y
3
− 6y
2
+ 1)
4
c
3
(y
8
− 11y
7
+ 47y
6
− 98y
5
+ 103y
4
− 50y
3
+ 6y
2
+ 1)
4
c
4
, c
5
, c
9
c
11
y
32
+ 15y
31
+ ··· + 1378908y + 130321
c
7
, c
10
y
32
− 21y
31
+ ··· + 68151136y + 10042561
c
8
, c
12
(y
2
+ y + 1)
16
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.914675
a = 1.89629 + 0.39729I
b = 1.88389 + 0.10461I
−5.24109 − 2.02988I −5.82210 + 3.46410I
u = 0.914675
a = 1.89629 − 0.39729I
b = 1.88389 − 0.10461I
−5.24109 + 2.02988I −5.82210 − 3.46410I
u = 0.914675
a = −2.05963 + 0.11437I
b = −1.73449 + 0.36339I
−5.24109 + 2.02988I −5.82210 − 3.46410I
u = 0.914675
a = −2.05963 − 0.11437I
b = −1.73449 − 0.36339I
−5.24109 − 2.02988I −5.82210 + 3.46410I
u = 0.252896 + 0.819281I
a = 0.839815 + 0.637967I
b = 0.38233 + 2.21666I
4.44352 − 0.75456I −3.18053 − 1.62107I
u = 0.252896 + 0.819281I
a = 1.61466 + 0.45267I
b = −1.49292 + 1.35353I
4.44352 + 3.30520I −3.18053 − 8.54928I
u = 0.252896 + 0.819281I
a = −0.99481 − 2.12932I
b = −0.03748 − 1.43734I
4.44352 + 3.30520I −3.18053 − 8.54928I
u = 0.252896 + 0.819281I
a = −2.60176 − 0.33644I
b = 0.310288 − 0.849384I
4.44352 − 0.75456I −3.18053 − 1.62107I
u = 0.252896 − 0.819281I
a = 0.839815 − 0.637967I
b = 0.38233 − 2.21666I
4.44352 + 0.75456I −3.18053 + 1.62107I
u = 0.252896 − 0.819281I
a = 1.61466 − 0.45267I
b = −1.49292 − 1.35353I
4.44352 − 3.30520I −3.18053 + 8.54928I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.252896 − 0.819281I
a = −0.99481 + 2.12932I
b = −0.03748 + 1.43734I
4.44352 − 3.30520I −3.18053 + 8.54928I
u = 0.252896 − 0.819281I
a = −2.60176 + 0.33644I
b = 0.310288 + 0.849384I
4.44352 + 0.75456I −3.18053 + 1.62107I
u = −0.394459 + 1.112500I
a = −0.559029 + 1.096920I
b = 0.095737 + 0.849097I
0.58960 − 1.60295I −8.42240 + 1.05392I
u = −0.394459 + 1.112500I
a = −0.650891 + 0.316842I
b = 0.99981 + 1.05461I
0.58960 − 1.60295I −8.42240 + 1.05392I
u = −0.394459 + 1.112500I
a = 1.265140 + 0.509213I
b = 0.035342 − 0.694019I
0.58960 − 5.66272I −8.42240 + 7.98213I
u = −0.394459 + 1.112500I
a = 0.564174 − 0.168272I
b = 1.06554 − 1.20660I
0.58960 − 5.66272I −8.42240 + 7.98213I
u = −0.394459 − 1.112500I
a = −0.559029 − 1.096920I
b = 0.095737 − 0.849097I
0.58960 + 1.60295I −8.42240 − 1.05392I
u = −0.394459 − 1.112500I
a = −0.650891 − 0.316842I
b = 0.99981 − 1.05461I
0.58960 + 1.60295I −8.42240 − 1.05392I
u = −0.394459 − 1.112500I
a = 1.265140 − 0.509213I
b = 0.035342 + 0.694019I
0.58960 + 5.66272I −8.42240 − 7.98213I
u = −0.394459 − 1.112500I
a = 0.564174 + 0.168272I
b = 1.06554 + 1.20660I
0.58960 + 5.66272I −8.42240 − 7.98213I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.473514 + 1.273020I
a = −0.278598 + 1.324080I
b = −2.19588 + 0.14617I
−9.13765 + 2.90536I −8.98443 + 0.46988I
u = 0.473514 + 1.273020I
a = 0.15293 − 1.46513I
b = 2.23599 − 0.76370I
−9.13765 + 6.96513I −8.98443 − 6.45832I
u = 0.473514 + 1.273020I
a = 0.46276 − 1.55281I
b = 1.81750 − 0.27231I
−9.13765 + 2.90536I −8.98443 + 0.46988I
u = 0.473514 + 1.273020I
a = −0.04692 + 1.73899I
b = −1.93756 + 0.49908I
−9.13765 + 6.96513I −8.98443 − 6.45832I
u = 0.473514 − 1.273020I
a = −0.278598 − 1.324080I
b = −2.19588 − 0.14617I
−9.13765 − 2.90536I −8.98443 − 0.46988I
u = 0.473514 − 1.273020I
a = 0.15293 + 1.46513I
b = 2.23599 + 0.76370I
−9.13765 − 6.96513I −8.98443 + 6.45832I
u = 0.473514 − 1.273020I
a = 0.46276 + 1.55281I
b = 1.81750 + 0.27231I
−9.13765 − 2.90536I −8.98443 − 0.46988I
u = 0.473514 − 1.273020I
a = −0.04692 − 1.73899I
b = −1.93756 − 0.49908I
−9.13765 − 6.96513I −8.98443 + 6.45832I
u = −0.578577
a = −1.046970 + 0.657077I
b = −0.322351 + 1.227360I
3.58052 − 2.02988I −5.00319 + 3.46410I
u = −0.578577
a = −1.046970 − 0.657077I
b = −0.322351 − 1.227360I
3.58052 + 2.02988I −5.00319 − 3.46410I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.578577
a = −0.55714 + 2.12134I
b = −0.605755 + 0.380170I
3.58052 − 2.02988I −5.00319 + 3.46410I
u = −0.578577
a = −0.55714 − 2.12134I
b = −0.605755 − 0.380170I
3.58052 + 2.02988I −5.00319 − 3.46410I
14
III.
I
u
3
= hu
18
− u
17
+ · · · + b + 1, u
18
+ 5u
16
+ · · · + a − 1, u
19
− u
18
+ · · · + u − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
10
=
−u
18
− 5u
16
+ ··· + u + 1
−u
18
+ u
17
+ ··· + 2u − 1
a
8
=
2u
18
− 3u
17
+ ··· − 4u + 2
−u
18
− 4u
16
+ ··· + u + 2
a
1
=
u
2
+ 1
u
2
a
11
=
−u
18
− 5u
16
+ ··· + u + 1
−2u
18
+ 2u
17
+ ··· + 3u − 1
a
12
=
−u
18
− 5u
16
+ ··· + u + 1
−2u
18
+ 2u
17
+ ··· + 3u − 2
a
5
=
−u
18
+ 2u
17
+ ··· + 4u − 2
u
18
− u
17
+ ··· − 2u − 1
a
9
=
2u
18
− 2u
17
+ ··· − 4u + 1
−u
17
+ u
16
+ ··· − u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
17
+ 3u
16
−11u
15
+ 15u
14
−28u
13
+ 35u
12
−39u
11
+ 41u
10
−
30u
9
+ 20u
8
− 10u
7
− 4u
6
− 3u
5
− 5u
3
+ 8u
2
− 3u − 2
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
− 11u
18
+ ··· − 5u + 1
c
2
u
19
− u
18
+ ··· + u − 1
c
3
u
19
+ u
18
+ ··· − u − 1
c
4
, c
11
u
19
+ 8u
17
+ ··· + 3u − 1
c
5
, c
9
u
19
+ 8u
17
+ ··· + 3u + 1
c
6
u
19
+ u
18
+ ··· + u + 1
c
7
, c
10
u
19
− 3u
18
+ ··· − 2u − 1
c
8
u
19
+ 2u
18
+ ··· + 3u − 1
c
12
u
19
− 2u
18
+ ··· + 3u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
− y
18
+ ··· − y −1
c
2
, c
6
y
19
+ 11y
18
+ ··· − 5y −1
c
3
y
19
− 13y
18
+ ··· − 11y −1
c
4
, c
5
, c
9
c
11
y
19
+ 16y
18
+ ··· − 21y −1
c
7
, c
10
y
19
− 3y
18
+ ··· − 8y −1
c
8
, c
12
y
19
+ 8y
18
+ ··· + 3y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.432409 + 0.844316I
a = −0.329441 + 0.448815I
b = −0.236489 − 0.472224I
−1.79244 − 1.81593I −13.41650 + 0.65086I
u = −0.432409 − 0.844316I
a = −0.329441 − 0.448815I
b = −0.236489 + 0.472224I
−1.79244 + 1.81593I −13.41650 − 0.65086I
u = 0.355611 + 1.040830I
a = 1.62344 + 0.58218I
b = −0.02864 + 1.89676I
2.78146 − 0.05347I −7.84525 − 1.09777I
u = 0.355611 − 1.040830I
a = 1.62344 − 0.58218I
b = −0.02864 − 1.89676I
2.78146 + 0.05347I −7.84525 + 1.09777I
u = 0.890704
a = −2.06630
b = −1.84047
−5.60220 −6.95090
u = −0.326702 + 1.147210I
a = −0.125098 − 0.538940I
b = 0.659149 + 0.032559I
1.46823 − 3.78813I −6.32142 + 3.96435I
u = −0.326702 − 1.147210I
a = −0.125098 + 0.538940I
b = 0.659149 − 0.032559I
1.46823 + 3.78813I −6.32142 − 3.96435I
u = 0.536152 + 1.067450I
a = −1.382960 − 0.137280I
b = −0.59494 − 1.54985I
4.08792 + 6.74742I −5.06014 − 6.00387I
u = 0.536152 − 1.067450I
a = −1.382960 + 0.137280I
b = −0.59494 + 1.54985I
4.08792 − 6.74742I −5.06014 + 6.00387I
u = 0.101153 + 0.760282I
a = 1.81914 + 1.18798I
b = −0.71919 + 1.50323I
4.29021 + 2.32381I −5.29787 − 0.37944I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.101153 − 0.760282I
a = 1.81914 − 1.18798I
b = −0.71919 − 1.50323I
4.29021 − 2.32381I −5.29787 + 0.37944I
u = −0.682478 + 0.327459I
a = −0.427115 + 0.321033I
b = 0.186371 − 0.358960I
5.43330 − 0.84474I 0.382477 + 1.325719I
u = −0.682478 − 0.327459I
a = −0.427115 − 0.321033I
b = 0.186371 + 0.358960I
5.43330 + 0.84474I 0.382477 − 1.325719I
u = −0.557218 + 1.113290I
a = 0.172420 + 0.230688I
b = −0.352897 + 0.063409I
3.17508 − 3.96127I −2.77988 + 1.70184I
u = −0.557218 − 1.113290I
a = 0.172420 − 0.230688I
b = −0.352897 − 0.063409I
3.17508 + 3.96127I −2.77988 − 1.70184I
u = 0.587141 + 0.436351I
a = −0.56266 − 1.67318I
b = 0.399733 − 1.227910I
5.94319 − 2.22864I −0.25827 + 1.68244I
u = 0.587141 − 0.436351I
a = −0.56266 + 1.67318I
b = 0.399733 + 1.227910I
5.94319 + 2.22864I −0.25827 − 1.68244I
u = 0.473398 + 1.262070I
a = 0.24543 − 1.57752I
b = 2.10713 − 0.43705I
−9.42638 + 4.85839I −9.92768 − 3.28951I
u = 0.473398 − 1.262070I
a = 0.24543 + 1.57752I
b = 2.10713 + 0.43705I
−9.42638 − 4.85839I −9.92768 + 3.28951I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
8
+ 5u
7
+ 11u
6
+ 10u
5
− u
4
− 10u
3
− 6u
2
+ 1)
4
· (u
19
− 11u
18
+ ··· − 5u + 1)(u
29
+ 16u
28
+ ··· + 108u − 16)
c
2
((u
8
+ u
7
+ ··· + 2u
3
− 1)
4
)(u
19
− u
18
+ ··· + u − 1)
· (u
29
− 6u
28
+ ··· − 10u + 4)
c
3
(u
8
− u
7
− 5u
6
+ 4u
5
+ 7u
4
− 4u
3
− 2u
2
+ 2u − 1)
4
· (u
19
+ u
18
+ ··· − u − 1)(u
29
+ 6u
28
+ ··· + 102u + 52)
c
4
, c
11
(u
19
+ 8u
17
+ ··· + 3u − 1)(u
29
+ 7u
27
+ ··· + 2u + 1)
· (u
32
− u
31
+ ··· + 830u + 361)
c
5
, c
9
(u
19
+ 8u
17
+ ··· + 3u + 1)(u
29
+ 7u
27
+ ··· + 2u + 1)
· (u
32
− u
31
+ ··· + 830u + 361)
c
6
((u
8
+ u
7
+ ··· + 2u
3
− 1)
4
)(u
19
+ u
18
+ ··· + u + 1)
· (u
29
− 6u
28
+ ··· − 10u + 4)
c
7
, c
10
(u
19
− 3u
18
+ ··· − 2u − 1)(u
29
− 3u
28
+ ··· − 21u + 1)
· (u
32
− 5u
31
+ ··· − 27238u + 3169)
c
8
((u
2
− u + 1)
16
)(u
19
+ 2u
18
+ ··· + 3u − 1)
· (u
29
+ 19u
28
+ ··· + 2304u + 256)
c
12
((u
2
− u + 1)
16
)(u
19
− 2u
18
+ ··· + 3u + 1)
· (u
29
+ 19u
28
+ ··· + 2304u + 256)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
8
− 3y
7
+ 19y
6
− 34y
5
+ 71y
4
− 66y
3
+ 34y
2
− 12y + 1)
4
· (y
19
− y
18
+ ··· − y −1)(y
29
− 4y
28
+ ··· + 28400y −256)
c
2
, c
6
(y
8
+ 5y
7
+ 11y
6
+ 10y
5
− y
4
− 10y
3
− 6y
2
+ 1)
4
· (y
19
+ 11y
18
+ ··· − 5y −1)(y
29
+ 16y
28
+ ··· + 108y −16)
c
3
(y
8
− 11y
7
+ 47y
6
− 98y
5
+ 103y
4
− 50y
3
+ 6y
2
+ 1)
4
· (y
19
− 13y
18
+ ··· − 11y −1)(y
29
− 24y
28
+ ··· + 12588y −2704)
c
4
, c
5
, c
9
c
11
(y
19
+ 16y
18
+ ··· − 21y −1)(y
29
+ 14y
28
+ ··· − 10y −1)
· (y
32
+ 15y
31
+ ··· + 1378908y + 130321)
c
7
, c
10
(y
19
− 3y
18
+ ··· − 8y −1)(y
29
− 49y
28
+ ··· + 83y −1)
· (y
32
− 21y
31
+ ··· + 68151136y + 10042561)
c
8
, c
12
((y
2
+ y + 1)
16
)(y
19
+ 8y
18
+ ··· + 3y −1)
· (y
29
+ 9y
28
+ ··· + 131072y −65536)
21
