12n
0611
(K12n
0611
)
A knot diagram
1
Linearized knot diagam
3 7 9 7 10 2 12 11 3 5 8 4
Solving Sequence
8,11 3,9
4 12 7 5 2 1 6 10
c
8
c
3
c
11
c
7
c
4
c
2
c
1
c
6
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
21
+ 2u
20
+ ··· + 2b + 2, 3u
21
− 14u
20
+ ··· + 4a − 36, u
22
− 4u
21
+ ··· − 22u + 4i
I
u
2
= h2u
12
+ u
11
+ 10u
10
+ 3u
9
+ 15u
8
+ u
7
+ 3u
6
− 4u
5
− 3u
4
− 4u
3
+ 5u
2
+ b − 2u,
− 2u
10
− 2u
9
− 11u
8
− 9u
7
− 20u
6
− 13u
5
− 11u
4
− 4u
3
+ a + 3u − 3,
u
13
+ u
12
+ 7u
11
+ 6u
10
+ 18u
9
+ 13u
8
+ 19u
7
+ 10u
6
+ 5u
5
− 2u
4
− u
3
− 4u
2
+ 2u + 1i
I
u
3
= h−4a
3
u
2
− 19a
3
u + 8a
2
u
2
+ 9a
3
− 17a
2
u − 8u
2
a + 4a
2
+ 28au − 17u
2
+ 22b − 15a − u − 25,
a
3
u
2
+ a
4
+ 2a
2
u
2
+ 3a
3
+ 2a
2
u + 25u
2
a + 5a
2
+ 12au + 15u
2
+ 55a + 7u + 33, u
3
+ 2u − 1i
I
u
4
= h−6a
3
u
3
− 8u
3
a
2
+ ··· − 27a + 12,
2a
3
u
3
+ a
3
u
2
+ u
3
a
2
+ a
4
+ 4a
3
u + a
2
u
2
− 4u
3
a + a
3
+ a
2
u − 5u
2
a + 2u
3
+ 2a
2
− 4au + 2u
2
− 6a + 2u,
u
4
+ u
3
+ 2u
2
+ 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 63 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−u
21
+2u
20
+· · ·+2b+2, 3u
21
−14u
20
+· · ·+4a−36, u
22
−4u
21
+· · ·−22u+4i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
3
=
−
3
4
u
21
+
7
2
u
20
+ ··· −
151
4
u + 9
1
2
u
21
− u
20
+ ··· +
3
2
u − 1
a
9
=
1
−u
2
a
4
=
−
5
4
u
21
+
11
2
u
20
+ ··· −
213
4
u + 12
1
2
u
21
+ 2u
19
+ ··· −
1
2
u − 1
a
12
=
u
u
a
7
=
u
2
+ 1
u
2
a
5
=
−
3
4
u
21
+
5
2
u
20
+ ··· −
47
4
u + 1
−
1
2
u
21
+ 2u
20
+ ··· +
31
2
u − 5
a
2
=
−
17
4
u
21
+
29
2
u
20
+ ··· −
289
4
u + 14
−
5
2
u
21
+ 10u
20
+ ··· −
81
2
u + 7
a
1
=
3
2
u
21
−
11
2
u
20
+ ··· +
73
2
u −
15
2
1
2
u
21
− 3u
20
+ ··· +
27
2
u − 2
a
6
=
−
5
2
u
21
+
17
2
u
20
+ ··· −
83
2
u +
19
2
−
3
2
u
21
+ 6u
20
+ ··· −
91
2
u + 10
a
10
=
−
1
2
u
20
+ u
19
+ ··· + 7u −
3
2
1
2
u
21
− 2u
20
+ ··· +
19
2
u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −3u
21
+ 6u
20
−38u
19
+ 66u
18
−203u
17
+ 302u
16
−585u
15
+ 720u
14
−948u
13
+ 889u
12
−
769u
11
+ 404u
10
−114u
9
−165u
8
+ 169u
7
−85u
6
−97u
5
+ 171u
4
−190u
3
+ 104u
2
−36u −2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
+ 18u
21
+ ··· − 4096u + 16384
c
2
, c
6
u
22
− 12u
21
+ ··· − 576u + 128
c
3
, c
5
, c
9
c
10
u
22
− u
20
+ ··· + u + 1
c
4
, c
12
u
22
+ 4u
21
+ ··· + u + 1
c
7
, c
8
, c
11
u
22
+ 4u
21
+ ··· + 22u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
− 34y
21
+ ··· + 83886080y + 268435456
c
2
, c
6
y
22
− 18y
21
+ ··· + 4096y + 16384
c
3
, c
5
, c
9
c
10
y
22
− 2y
21
+ ··· + 5y + 1
c
4
, c
12
y
22
+ 26y
21
+ ··· + 53y + 1
c
7
, c
8
, c
11
y
22
+ 20y
21
+ ··· + 36y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.113355 + 1.047390I
a = −0.249378 + 0.867554I
b = −0.12451 + 1.46269I
−0.89584 − 1.46775I −2.56568 + 4.64859I
u = −0.113355 − 1.047390I
a = −0.249378 − 0.867554I
b = −0.12451 − 1.46269I
−0.89584 + 1.46775I −2.56568 − 4.64859I
u = 0.616202 + 0.646773I
a = −1.102880 − 0.376255I
b = −1.397390 − 0.117675I
−7.62299 − 5.54296I −4.40972 + 2.06977I
u = 0.616202 − 0.646773I
a = −1.102880 + 0.376255I
b = −1.397390 + 0.117675I
−7.62299 + 5.54296I −4.40972 − 2.06977I
u = 0.764482 + 0.400206I
a = 0.05821 − 2.20084I
b = −0.292901 − 0.229775I
−6.80118 + 10.22180I −2.84650 − 6.91774I
u = 0.764482 − 0.400206I
a = 0.05821 + 2.20084I
b = −0.292901 + 0.229775I
−6.80118 − 10.22180I −2.84650 + 6.91774I
u = −0.761299 + 0.247632I
a = −0.069067 + 1.023690I
b = −0.281528 + 0.013910I
1.16275 − 1.85731I 3.99806 − 0.12476I
u = −0.761299 − 0.247632I
a = −0.069067 − 1.023690I
b = −0.281528 − 0.013910I
1.16275 + 1.85731I 3.99806 + 0.12476I
u = 0.686555 + 0.284442I
a = 0.25180 + 1.77617I
b = −0.119863 − 0.209977I
0.31091 + 4.61412I −2.14647 − 8.90403I
u = 0.686555 − 0.284442I
a = 0.25180 − 1.77617I
b = −0.119863 + 0.209977I
0.31091 − 4.61412I −2.14647 + 8.90403I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.311371 + 0.544088I
a = −0.100430 + 0.264067I
b = 0.670256 + 0.493905I
−0.97447 − 1.03210I −5.19046 + 2.87964I
u = 0.311371 − 0.544088I
a = −0.100430 − 0.264067I
b = 0.670256 − 0.493905I
−0.97447 + 1.03210I −5.19046 − 2.87964I
u = −0.358815 + 1.338970I
a = 0.157826 − 0.737154I
b = 0.60731 − 1.77839I
−3.79504 − 5.99391I −0.31044 + 7.14857I
u = −0.358815 − 1.338970I
a = 0.157826 + 0.737154I
b = 0.60731 + 1.77839I
−3.79504 + 5.99391I −0.31044 − 7.14857I
u = 0.13972 + 1.42206I
a = 0.802494 + 0.162707I
b = 0.846933 − 0.294845I
−6.97755 + 0.69684I −7.99990 + 2.38959I
u = 0.13972 − 1.42206I
a = 0.802494 − 0.162707I
b = 0.846933 + 0.294845I
−6.97755 − 0.69684I −7.99990 − 2.38959I
u = 0.26914 + 1.41520I
a = −1.10275 − 1.22518I
b = −2.25955 − 2.13113I
−5.12121 + 8.09916I −6.73561 − 9.40400I
u = 0.26914 − 1.41520I
a = −1.10275 + 1.22518I
b = −2.25955 + 2.13113I
−5.12121 − 8.09916I −6.73561 + 9.40400I
u = 0.28842 + 1.47378I
a = 1.05609 + 1.33953I
b = 2.19735 + 3.10840I
−12.8364 + 14.0560I −6.34753 − 6.94319I
u = 0.28842 − 1.47378I
a = 1.05609 − 1.33953I
b = 2.19735 − 3.10840I
−12.8364 − 14.0560I −6.34753 + 6.94319I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.15759 + 1.53295I
a = 0.048081 − 0.334870I
b = 1.153890 + 0.023955I
−14.8442 − 2.8448I −8.44574 + 2.22597I
u = 0.15759 − 1.53295I
a = 0.048081 + 0.334870I
b = 1.153890 − 0.023955I
−14.8442 + 2.8448I −8.44574 − 2.22597I
7
II.
I
u
2
= h2u
12
+u
11
+· · ·+b−2u, −2u
10
−2u
9
+· · ·+a−3, u
13
+u
12
+· · ·+2u+1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
3
=
2u
10
+ 2u
9
+ 11u
8
+ 9u
7
+ 20u
6
+ 13u
5
+ 11u
4
+ 4u
3
− 3u + 3
−2u
12
− u
11
+ ··· − 5u
2
+ 2u
a
9
=
1
−u
2
a
4
=
−u
11
+ u
10
+ ··· − 5u + 3
−2u
12
− 2u
11
+ ··· − u
2
− 1
a
12
=
u
u
a
7
=
u
2
+ 1
u
2
a
5
=
u
10
+ u
9
+ 6u
8
+ 5u
7
+ 12u
6
+ 8u
5
+ 8u
4
+ 3u
3
+ u
2
− 2u + 2
−u
12
+ u
11
+ ··· − 5u
2
+ 3u
a
2
=
u
10
+ u
9
+ 6u
8
+ 5u
7
+ 12u
6
+ 8u
5
+ 8u
4
+ 4u
3
+ u
2
+ 2
−u
12
− 5u
10
+ u
9
− 7u
8
+ 4u
7
+ 4u
5
+ 2u
4
+ 2u
3
− 4u
2
+ 3u
a
1
=
−u
12
− 8u
10
+ ··· + 9u − 6
2u
12
+ 2u
11
+ ··· − u
2
+ 2
a
6
=
u
12
+ u
11
+ 7u
10
+ 5u
9
+ 17u
8
+ 8u
7
+ 15u
6
+ 2u
5
− 6u
3
− 2u
2
− 5u + 3
2u
11
+ u
10
+ 9u
9
+ 3u
8
+ 12u
7
+ 2u
6
+ 2u
5
− 2u
4
− u
3
− 3u
2
+ 3u − 1
a
10
=
u
11
+ u
10
+ 6u
9
+ 5u
8
+ 13u
7
+ 9u
6
+ 11u
5
+ 5u
4
+ 2u
3
− 2u
2
− 2
u
12
+ 2u
11
+ ··· − 2u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −8u
12
−9u
11
−49u
10
−45u
9
−108u
8
−76u
7
−97u
6
−34u
5
−29u
4
+ 19u
3
−7u
2
+ 8u −9
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− 15u
12
+ ··· + 33u − 4
c
2
u
13
− 3u
12
+ ··· + u − 2
c
3
, c
10
u
13
+ 5u
11
+ u
10
+ 7u
9
+ 4u
8
+ 4u
6
− 4u
5
− u
4
− 2u
2
− 1
c
4
, c
12
u
13
− 2u
12
+ ··· − 4u − 1
c
5
, c
9
u
13
+ 5u
11
− u
10
+ 7u
9
− 4u
8
− 4u
6
− 4u
5
+ u
4
+ 2u
2
+ 1
c
6
u
13
+ 3u
12
+ ··· + u + 2
c
7
, c
8
u
13
+ u
12
+ ··· + 2u + 1
c
11
u
13
− u
12
+ ··· + 2u − 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
− 27y
12
+ ··· − 79y −16
c
2
, c
6
y
13
− 15y
12
+ ··· + 33y −4
c
3
, c
5
, c
9
c
10
y
13
+ 10y
12
+ ··· − 4y −1
c
4
, c
12
y
13
− 10y
12
+ ··· − 4y −1
c
7
, c
8
, c
11
y
13
+ 13y
12
+ ··· + 12y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.773550 + 0.446076I
a = −0.305684 + 0.776454I
b = −0.221370 + 0.094049I
1.27688 − 2.47819I 8.06933 + 11.56907I
u = −0.773550 − 0.446076I
a = −0.305684 − 0.776454I
b = −0.221370 − 0.094049I
1.27688 + 2.47819I 8.06933 − 11.56907I
u = 0.098733 + 1.212320I
a = 1.13507 + 1.02542I
b = 1.70497 + 2.47623I
1.58553 + 1.07079I 1.79491 + 0.89145I
u = 0.098733 − 1.212320I
a = 1.13507 − 1.02542I
b = 1.70497 − 2.47623I
1.58553 − 1.07079I 1.79491 − 0.89145I
u = −0.125906 + 1.364640I
a = −1.26556 − 0.79157I
b = −1.18557 − 2.02372I
−8.30588 − 1.59896I −12.80035 + 0.14504I
u = −0.125906 − 1.364640I
a = −1.26556 + 0.79157I
b = −1.18557 + 2.02372I
−8.30588 + 1.59896I −12.80035 − 0.14504I
u = 0.218616 + 1.386220I
a = −1.009230 − 0.765658I
b = −2.45521 − 2.30542I
−0.64678 + 3.91620I −4.73840 − 4.05034I
u = 0.218616 − 1.386220I
a = −1.009230 + 0.765658I
b = −2.45521 + 2.30542I
−0.64678 − 3.91620I −4.73840 + 4.05034I
u = 0.542233 + 0.204630I
a = 0.95589 + 2.90373I
b = 0.500761 + 0.448666I
4.46035 + 1.08841I 0.69467 − 6.25717I
u = 0.542233 − 0.204630I
a = 0.95589 − 2.90373I
b = 0.500761 − 0.448666I
4.46035 − 1.08841I 0.69467 + 6.25717I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.30546 + 1.45345I
a = 0.544780 − 0.691123I
b = 1.25789 − 1.48118I
−4.73020 − 6.43920I −5.54584 + 8.97180I
u = −0.30546 − 1.45345I
a = 0.544780 + 0.691123I
b = 1.25789 + 1.48118I
−4.73020 + 6.43920I −5.54584 − 8.97180I
u = −0.309328
a = 3.88946
b = −1.20295
−3.72913 −12.9490
12
III.
I
u
3
= h−4a
3
u
2
+8a
2
u
2
+· · ·−15a−25, a
3
u
2
+2a
2
u
2
+· · ·+55a+33, u
3
+2u−1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
3
=
a
0.181818a
3
u
2
− 0.363636a
2
u
2
+ ··· + 0.681818a + 1.13636
a
9
=
1
−u
2
a
4
=
−0.181818a
3
u
2
+ 0.363636a
2
u
2
+ ··· + 0.318182a − 1.13636
−0.590909a
3
u
2
+ 0.181818a
2
u
2
+ ··· − 0.590909a + 1.18182
a
12
=
u
u
a
7
=
u
2
+ 1
u
2
a
5
=
0.181818a
3
u
2
− 0.363636a
2
u
2
+ ··· + 0.681818a + 1.13636
−
1
2
a
3
u
2
−
3
2
a
2
u
2
+ ··· − a +
3
2
a
2
=
1.04545a
3
u
2
+ 0.409091a
2
u
2
+ ··· + 2.04545a + 1.90909
1.81818a
3
u
2
− 0.136364a
2
u
2
+ ··· + 2.31818a + 1.86364
a
1
=
0.727273a
3
u
2
+ 0.0454545a
2
u
2
+ ··· + 0.727273a + 2.54545
a
3
u
2
−
1
2
u
2
a + ··· + a − 1
a
6
=
−1.36364a
3
u
2
− 0.772727a
2
u
2
+ ··· − 1.36364a − 1.27273
−2.27273a
3
u
2
− 0.454545a
2
u
2
+ ··· − 2.27273a − 2.45455
a
10
=
−0.136364a
3
u
2
+ 0.272727a
2
u
2
+ ··· − 0.136364a + 0.272727
0.272727a
3
u
2
+ 1.45455a
2
u
2
+ ··· + 0.272727a + 1.45455
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
2
+ 4u + 2
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
+ 3u + 1)
6
c
2
, c
6
(u
2
+ u − 1)
6
c
3
, c
5
, c
9
c
10
u
12
+ u
10
+ u
9
+ 6u
8
+ 6u
7
+ 8u
6
+ 20u
5
+ 4u
4
+ 7u
3
+ 19u
2
+ 2u − 4
c
4
, c
12
u
12
+ 2u
11
+ ··· − 18u + 44
c
7
, c
8
, c
11
(u
3
+ 2u + 1)
4
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
− 7y + 1)
6
c
2
, c
6
(y
2
− 3y + 1)
6
c
3
, c
5
, c
9
c
10
y
12
+ 2y
11
+ ··· − 156y + 16
c
4
, c
12
y
12
+ 6y
11
+ ··· + 820y + 1936
c
7
, c
8
, c
11
(y
3
+ 4y
2
+ 4y −1)
4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22670 + 1.46771I
a = 0.854692 − 0.614486I
b = 1.58719 − 1.61371I
−5.49289 − 5.13794I −7.31793 + 3.20902I
u = −0.22670 + 1.46771I
a = −0.263183 − 0.362701I
b = −1.65920 + 0.15080I
−13.3886 − 5.1379I −7.31793 + 3.20902I
u = −0.22670 + 1.46771I
a = −0.300182 + 0.203211I
b = −0.007380 + 0.210795I
−5.49289 − 5.13794I −7.31793 + 3.20902I
u = −0.22670 + 1.46771I
a = −1.18854 + 1.43943I
b = −2.47679 + 3.52208I
−13.3886 − 5.1379I −7.31793 + 3.20902I
u = −0.22670 − 1.46771I
a = 0.854692 + 0.614486I
b = 1.58719 + 1.61371I
−5.49289 + 5.13794I −7.31793 − 3.20902I
u = −0.22670 − 1.46771I
a = −0.263183 + 0.362701I
b = −1.65920 − 0.15080I
−13.3886 + 5.1379I −7.31793 − 3.20902I
u = −0.22670 − 1.46771I
a = −0.300182 − 0.203211I
b = −0.007380 − 0.210795I
−5.49289 + 5.13794I −7.31793 − 3.20902I
u = −0.22670 − 1.46771I
a = −1.18854 − 1.43943I
b = −2.47679 − 3.52208I
−13.3886 + 5.1379I −7.31793 − 3.20902I
u = 0.453398
a = −0.626782
b = 1.23526
−3.16064 4.63590
u = 0.453398
a = 0.99058 + 3.57131I
b = −0.343740 + 0.608968I
4.73504 4.63590
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.453398
a = 0.99058 − 3.57131I
b = −0.343740 − 0.608968I
4.73504 4.63590
u = 0.453398
a = −4.55994
b = 0.564588
−3.16064 4.63590
17
IV. I
u
4
= h−6a
3
u
3
− 8u
3
a
2
+ · · · − 27a + 12, 2a
3
u
3
+ u
3
a
2
+ · · · + 2a
2
−
6a, u
4
+ u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
3
=
a
0.176471a
3
u
3
+ 0.235294a
2
u
3
+ ··· + 0.794118a − 0.352941
a
9
=
1
−u
2
a
4
=
−0.176471a
3
u
3
− 0.235294a
2
u
3
+ ··· + 0.205882a + 0.352941
0.264706a
2
u
3
− 0.264706au
3
+ ··· + 0.441176a − 0.764706
a
12
=
u
u
a
7
=
u
2
+ 1
u
2
a
5
=
−0.558824a
3
u
3
+ 0.676471a
2
u
3
+ ··· − 0.117647a + 0.529412
−0.0882353a
3
u
3
+ 0.500000a
2
u
3
+ ··· − 0.117647a + 0.0588235
a
2
=
−0.117647a
3
u
3
+ 0.647059a
2
u
3
+ ··· + 2.58824a − 0.235294
0.0588235a
3
u
3
+ 0.617647a
2
u
3
+ ··· + 0.941176a + 0.176471
a
1
=
0.0294118a
3
u
3
+ 0.0882353a
2
u
3
+ ··· + 0.852941a + 0.0588235
−0.147059a
3
u
3
+ 0.294118a
2
u
3
+ ··· − 0.705882a + 0.470588
a
6
=
0.264706a
3
u
3
− 1.20588a
2
u
3
+ ··· − 2.32353a + 0.529412
3
34
a
3
u
3
−
8
17
u
3
a
2
+ ··· − a −
10
17
a
10
=
−0.294118a
2
u
3
+ 0.294118au
3
+ ··· + 0.676471a + 1.29412
−0.117647a
3
u
3
− 0.176471a
2
u
3
+ ··· + 0.882353a + 0.588235
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 4u − 2
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
+ 3u + 1)
8
c
2
, c
6
(u
2
+ u − 1)
8
c
3
, c
5
, c
9
c
10
u
16
− u
15
+ ··· − 4u + 1
c
4
, c
12
u
16
+ 5u
15
+ ··· + 50u + 19
c
7
, c
8
, c
11
(u
4
− u
3
+ 2u
2
− 2u + 1)
4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
− 7y + 1)
8
c
2
, c
6
(y
2
− 3y + 1)
8
c
3
, c
5
, c
9
c
10
y
16
+ 5y
15
+ ··· − 8y + 1
c
4
, c
12
y
16
− 7y
15
+ ··· − 752y + 361
c
7
, c
8
, c
11
(y
4
+ 3y
3
+ 2y
2
+ 1)
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621744 + 0.440597I
a = −0.542830 + 1.141380I
b = −0.231778 + 0.327115I
0.65797 − 2.02988I −4.00000 + 3.46410I
u = −0.621744 + 0.440597I
a = 1.35588 − 0.69513I
b = 1.316260 − 0.130390I
−7.23771 − 2.02988I −4.00000 + 3.46410I
u = −0.621744 + 0.440597I
a = −0.106754 + 0.135093I
b = −0.417805 − 0.121114I
0.65797 − 2.02988I −4.00000 + 3.46410I
u = −0.621744 + 0.440597I
a = 0.34475 − 2.64671I
b = 0.384377 − 0.408927I
−7.23771 − 2.02988I −4.00000 + 3.46410I
u = −0.621744 − 0.440597I
a = −0.542830 − 1.141380I
b = −0.231778 − 0.327115I
0.65797 + 2.02988I −4.00000 − 3.46410I
u = −0.621744 − 0.440597I
a = 1.35588 + 0.69513I
b = 1.316260 + 0.130390I
−7.23771 + 2.02988I −4.00000 − 3.46410I
u = −0.621744 − 0.440597I
a = −0.106754 − 0.135093I
b = −0.417805 + 0.121114I
0.65797 + 2.02988I −4.00000 − 3.46410I
u = −0.621744 − 0.440597I
a = 0.34475 + 2.64671I
b = 0.384377 + 0.408927I
−7.23771 + 2.02988I −4.00000 − 3.46410I
u = 0.121744 + 1.306620I
a = 0.904436 − 0.255157I
b = 0.193308 − 0.950380I
−7.23771 + 2.02988I −4.00000 − 3.46410I
u = 0.121744 + 1.306620I
a = 0.630729 + 1.205030I
b = 1.45960 + 3.32611I
0.65797 + 2.02988I −4.00000 − 3.46410I
21
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.121744 + 1.306620I
a = −1.52623 − 0.46379I
b = −2.35510 − 1.51441I
0.65797 + 2.02988I −4.00000 − 3.46410I
u = 0.121744 + 1.306620I
a = 1.44002 − 1.68542I
b = 2.15115 − 3.79271I
−7.23771 + 2.02988I −4.00000 − 3.46410I
u = 0.121744 − 1.306620I
a = 0.904436 + 0.255157I
b = 0.193308 + 0.950380I
−7.23771 − 2.02988I −4.00000 + 3.46410I
u = 0.121744 − 1.306620I
a = 0.630729 − 1.205030I
b = 1.45960 − 3.32611I
0.65797 − 2.02988I −4.00000 + 3.46410I
u = 0.121744 − 1.306620I
a = −1.52623 + 0.46379I
b = −2.35510 + 1.51441I
0.65797 − 2.02988I −4.00000 + 3.46410I
u = 0.121744 − 1.306620I
a = 1.44002 + 1.68542I
b = 2.15115 + 3.79271I
−7.23771 − 2.02988I −4.00000 + 3.46410I
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ 3u + 1)
14
)(u
13
− 15u
12
+ ··· + 33u − 4)
· (u
22
+ 18u
21
+ ··· − 4096u + 16384)
c
2
((u
2
+ u − 1)
14
)(u
13
− 3u
12
+ ··· + u − 2)
· (u
22
− 12u
21
+ ··· − 576u + 128)
c
3
, c
10
(u
12
+ u
10
+ u
9
+ 6u
8
+ 6u
7
+ 8u
6
+ 20u
5
+ 4u
4
+ 7u
3
+ 19u
2
+ 2u − 4)
· (u
13
+ 5u
11
+ u
10
+ 7u
9
+ 4u
8
+ 4u
6
− 4u
5
− u
4
− 2u
2
− 1)
· (u
16
− u
15
+ ··· − 4u + 1)(u
22
− u
20
+ ··· + u + 1)
c
4
, c
12
(u
12
+ 2u
11
+ ··· − 18u + 44)(u
13
− 2u
12
+ ··· − 4u − 1)
· (u
16
+ 5u
15
+ ··· + 50u + 19)(u
22
+ 4u
21
+ ··· + u + 1)
c
5
, c
9
(u
12
+ u
10
+ u
9
+ 6u
8
+ 6u
7
+ 8u
6
+ 20u
5
+ 4u
4
+ 7u
3
+ 19u
2
+ 2u − 4)
· (u
13
+ 5u
11
− u
10
+ 7u
9
− 4u
8
− 4u
6
− 4u
5
+ u
4
+ 2u
2
+ 1)
· (u
16
− u
15
+ ··· − 4u + 1)(u
22
− u
20
+ ··· + u + 1)
c
6
((u
2
+ u − 1)
14
)(u
13
+ 3u
12
+ ··· + u + 2)
· (u
22
− 12u
21
+ ··· − 576u + 128)
c
7
, c
8
((u
3
+ 2u + 1)
4
)(u
4
− u
3
+ 2u
2
− 2u + 1)
4
(u
13
+ u
12
+ ··· + 2u + 1)
· (u
22
+ 4u
21
+ ··· + 22u + 4)
c
11
((u
3
+ 2u + 1)
4
)(u
4
− u
3
+ 2u
2
− 2u + 1)
4
(u
13
− u
12
+ ··· + 2u − 1)
· (u
22
+ 4u
21
+ ··· + 22u + 4)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
− 7y + 1)
14
)(y
13
− 27y
12
+ ··· − 79y −16)
· (y
22
− 34y
21
+ ··· + 83886080y + 268435456)
c
2
, c
6
((y
2
− 3y + 1)
14
)(y
13
− 15y
12
+ ··· + 33y −4)
· (y
22
− 18y
21
+ ··· + 4096y + 16384)
c
3
, c
5
, c
9
c
10
(y
12
+ 2y
11
+ ··· − 156y + 16)(y
13
+ 10y
12
+ ··· − 4y −1)
· (y
16
+ 5y
15
+ ··· − 8y + 1)(y
22
− 2y
21
+ ··· + 5y + 1)
c
4
, c
12
(y
12
+ 6y
11
+ ··· + 820y + 1936)(y
13
− 10y
12
+ ··· − 4y −1)
· (y
16
− 7y
15
+ ··· − 752y + 361)(y
22
+ 26y
21
+ ··· + 53y + 1)
c
7
, c
8
, c
11
(y
3
+ 4y
2
+ 4y −1)
4
(y
4
+ 3y
3
+ 2y
2
+ 1)
4
· (y
13
+ 13y
12
+ ··· + 12y −1)(y
22
+ 20y
21
+ ··· + 36y + 16)
24
