12n
0823
(K12n
0823
)
A knot diagram
1
Linearized knot diagam
4 5 10 8 3 12 1 5 6 4 7 6
Solving Sequence
2,5
3
6,8
9 10 4 1 7 12 11
c
2
c
5
c
8
c
9
c
4
c
1
c
7
c
12
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h257u
24
− 3084u
23
+ ··· + 64b + 37824, −77u
24
+ 410u
23
+ ··· + 128a + 14912,
u
25
− 12u
24
+ ··· + 640u − 128i
I
u
2
= h−10a
5
u
2
+ 16a
4
u
2
+ ··· − 109a + 76,
a
6
− a
4
u
2
− 2a
4
u − 2a
3
u
2
− 2a
4
− 3a
3
u + a
2
u
2
− a
3
+ a
2
u + 4u
2
a − a
2
+ 7au − 3u
2
+ 4a − 4u − 2,
u
3
+ u
2
− 1i
I
u
3
= h2u
13
+ 7u
12
+ u
11
− 26u
10
− 32u
9
+ 24u
8
+ 74u
7
+ 23u
6
− 63u
5
− 51u
4
+ 16u
3
+ 26u
2
+ b − 5,
5u
14
+ 17u
13
+ ··· + a − 5,
u
15
+ 3u
14
− u
13
− 13u
12
− 11u
11
+ 18u
10
+ 34u
9
− u
8
− 39u
7
− 19u
6
+ 19u
5
+ 17u
4
− 4u
3
− 6u
2
+ 1i
I
u
4
= h−44a
7
u
2
− 73a
6
u
2
+ ··· − 213a + 245, −2a
6
u
2
− a
5
u
2
+ ··· + 7a + 13, u
3
+ u
2
− 1i
* 4 irreducible components of dim
C
= 0, with total 82 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
= h257u
24
− 3084u
23
+ · · · + 64b + 37824, −77u
24
+ 410u
23
+ · · · +
128a + 14912, u
25
− 12u
24
+ · · · + 640u − 128i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
−u
2
a
6
=
u
−u
3
+ u
a
8
=
77
128
u
24
−
205
64
u
23
+ ··· + 432u −
233
2
−
257
64
u
24
+
771
16
u
23
+ ··· +
4961
2
u − 591
a
9
=
77
128
u
24
−
205
64
u
23
+ ··· + 432u −
233
2
−
853
64
u
24
+
579
4
u
23
+ ··· +
9947
2
u − 1105
a
10
=
77
128
u
24
−
801
64
u
23
+ ··· − 1547u +
795
2
715
64
u
24
−
1849
16
u
23
+ ··· −
5931
2
u + 601
a
4
=
−
1
16
u
24
+
5
8
u
23
+ ··· + 4u +
1
2
−
1
8
u
23
+
5
4
u
22
+ ··· −
63
2
u + 8
a
1
=
−
15
16
u
24
+
167
16
u
23
+ ··· +
1391
4
u − 71
−
15
16
u
24
+
77
8
u
23
+ ··· + 128u − 16
a
7
=
65
8
u
24
−
1579
16
u
23
+ ··· − 5798u + 1396
333
16
u
24
−
3509
16
u
23
+ ··· − 5955u + 1208
a
12
=
−
41
16
u
24
+
455
16
u
23
+ ··· +
3727
4
u − 191
−
41
16
u
24
+
199
8
u
23
+ ··· − 40u + 56
a
11
=
−
421
64
u
24
+
4673
64
u
23
+ ··· +
11579
4
u − 663
−
423
64
u
24
+
1921
32
u
23
+ ··· + 110u + 70
(ii) Obstruction class = −1
(iii) Cusp Shapes =
553
16
u
24
−
3059
8
u
23
+ ··· − 15300u + 3482
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
25
− 3u
24
+ ··· + 2u + 1
c
2
, c
5
u
25
+ 12u
24
+ ··· + 640u + 128
c
3
, c
4
, c
8
c
10
u
25
− u
24
+ ··· + 2u − 1
c
6
, c
11
, c
12
u
25
+ 6u
24
+ ··· + 40u + 8
c
7
u
25
− 6u
24
+ ··· − 56u + 464
c
9
u
25
+ u
24
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
− 27y
24
+ ··· + 54y −1
c
2
, c
5
y
25
− 12y
24
+ ··· + 114688y −16384
c
3
, c
4
, c
8
c
10
y
25
− 5y
24
+ ··· + 18y −1
c
6
, c
11
, c
12
y
25
+ 22y
24
+ ··· + 416y −64
c
7
y
25
− 2y
24
+ ··· − 995392y −215296
c
9
y
25
− 23y
24
+ ··· + 66y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.439994 + 0.950507I
a = 0.449056 + 0.849462I
b = 0.905847 + 0.107899I
−3.00593 − 0.74051I 5.05508 + 0.18570I
u = 0.439994 − 0.950507I
a = 0.449056 − 0.849462I
b = 0.905847 − 0.107899I
−3.00593 + 0.74051I 5.05508 − 0.18570I
u = 0.617552 + 0.911770I
a = −0.520485 − 0.949952I
b = −1.202860 − 0.092876I
−9.79766 + 1.38415I 2.19427 − 0.69570I
u = 0.617552 − 0.911770I
a = −0.520485 + 0.949952I
b = −1.202860 + 0.092876I
−9.79766 − 1.38415I 2.19427 + 0.69570I
u = −0.155216 + 0.814496I
a = 0.569549 + 0.594113I
b = 0.482434 + 0.018405I
−2.49837 − 1.57308I 4.64082 + 4.61190I
u = −0.155216 − 0.814496I
a = 0.569549 − 0.594113I
b = 0.482434 − 0.018405I
−2.49837 + 1.57308I 4.64082 − 4.61190I
u = 0.473172 + 1.138930I
a = −0.327562 − 0.860505I
b = −0.840347 − 0.335702I
−1.79770 − 4.91771I 8.41927 + 6.28509I
u = 0.473172 − 1.138930I
a = −0.327562 + 0.860505I
b = −0.840347 + 0.335702I
−1.79770 + 4.91771I 8.41927 − 6.28509I
u = 1.097810 + 0.681530I
a = −0.926077 − 0.303192I
b = −1.55305 + 0.96565I
−8.25231 + 4.52896I 4.39857 − 4.77646I
u = 1.097810 − 0.681530I
a = −0.926077 + 0.303192I
b = −1.55305 − 0.96565I
−8.25231 − 4.52896I 4.39857 + 4.77646I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.569528 + 1.179720I
a = 0.270690 + 0.922850I
b = 0.887146 + 0.468456I
−7.44241 − 8.72137I 5.19162 + 6.35185I
u = 0.569528 − 1.179720I
a = 0.270690 − 0.922850I
b = 0.887146 − 0.468456I
−7.44241 + 8.72137I 5.19162 − 6.35185I
u = 1.32152
a = −0.469575
b = −1.93007
5.64216 30.1590
u = 1.306160 + 0.296832I
a = 0.548745 + 0.102029I
b = 1.63919 − 0.62194I
1.99285 + 5.34908I 13.9471 − 13.2059I
u = 1.306160 − 0.296832I
a = 0.548745 − 0.102029I
b = 1.63919 + 0.62194I
1.99285 − 5.34908I 13.9471 + 13.2059I
u = 1.214200 + 0.704239I
a = 0.907328 + 0.113165I
b = 1.41310 − 1.02138I
−0.61951 + 6.87942I 8.00000 − 4.38169I
u = 1.214200 − 0.704239I
a = 0.907328 − 0.113165I
b = 1.41310 + 1.02138I
−0.61951 − 6.87942I 8.00000 + 4.38169I
u = 1.22071 + 0.77249I
a = −0.990264 − 0.040589I
b = −1.37746 + 1.13069I
0.51235 + 11.71780I 8.00000 − 8.48371I
u = 1.22071 − 0.77249I
a = −0.990264 + 0.040589I
b = −1.37746 − 1.13069I
0.51235 − 11.71780I 8.00000 + 8.48371I
u = 1.20009 + 0.80742I
a = 1.066910 + 0.022071I
b = 1.40118 − 1.21648I
−5.4265 + 15.7509I 8.00000 − 8.57855I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.20009 − 0.80742I
a = 1.066910 − 0.022071I
b = 1.40118 + 1.21648I
−5.4265 − 15.7509I 8.00000 + 8.57855I
u = −0.338292
a = −1.19055
b = −0.300946
0.647725 15.2540
u = −1.66374
a = 0.444714
b = 0.277763
6.10335 20.9380
u = −1.64375 + 0.30866I
a = −0.440186 − 0.060519I
b = −0.278561 − 0.018758I
2.17466 − 4.23595I 0
u = −1.64375 − 0.30866I
a = −0.440186 + 0.060519I
b = −0.278561 + 0.018758I
2.17466 + 4.23595I 0
7
II. I
u
2
=
h−10a
5
u
2
+16a
4
u
2
+· · ·−109a +76, −a
4
u
2
−2a
3
u
2
+· · ·+4a −2, u
3
+u
2
−1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
−u
2
a
6
=
u
u
2
+ u − 1
a
8
=
a
0.169492a
5
u
2
− 0.271186a
4
u
2
+ ··· + 1.84746a − 1.28814
a
9
=
a
0.169492a
5
u
2
− 0.271186a
4
u
2
+ ··· + 1.84746a − 1.28814
a
10
=
−0.135593a
5
u
2
+ 0.0169492a
4
u
2
+ ··· − 0.677966a + 0.830508
−0.457627a
5
u
2
− 0.0677966a
4
u
2
+ ··· + 0.711864a − 1.32203
a
4
=
−a
2
u
0.0677966a
5
u
2
+ 0.491525a
4
u
2
+ ··· − 0.661017a + 1.08475
a
1
=
0.203390a
5
u
2
− 0.525424a
4
u
2
+ ··· + 1.01695a + 1.25424
0.610169a
5
u
2
+ 0.423729a
4
u
2
+ ··· + 1.05085a + 0.762712
a
7
=
−0.271186a
5
u
2
+ 1.03390a
4
u
2
+ ··· − 1.35593a + 0.661017
−a
5
u
2
− a
3
u
2
+ ··· − a
2
+ 1
a
12
=
0.0677966a
5
u
2
− 0.508475a
4
u
2
+ ··· + 0.338983a + 2.08475
−0.0169492a
5
u
2
+ 0.627119a
4
u
2
+ ··· + 0.915254a + 0.728814
a
11
=
0.237288a
5
u
2
+ 0.220339a
4
u
2
+ ··· + 1.18644a − 1.20339
1.67797a
5
u
2
− 0.0847458a
4
u
2
+ ··· + 0.389831a + 0.847458
(ii) Obstruction class = −1
(iii) Cusp Shapes =
152
59
a
5
u
2
+
40
59
a
4
u
2
+ ··· −
184
59
a +
1134
59
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 2u
17
+ ··· − 252u − 27
c
2
, c
5
(u
3
− u
2
+ 1)
6
c
3
, c
4
, c
8
c
10
u
18
− 3u
16
+ ··· + 6u − 11
c
6
, c
11
, c
12
(u
3
+ 2u + 1)
6
c
7
(u
3
+ 3u
2
+ 5u + 2)
6
c
9
u
18
+ u
16
+ ··· − 52u − 43
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 6y
17
+ ··· − 81000y + 729
c
2
, c
5
(y
3
− y
2
+ 2y −1)
6
c
3
, c
4
, c
8
c
10
y
18
− 6y
17
+ ··· − 1136y + 121
c
6
, c
11
, c
12
(y
3
+ 4y
2
+ 4y −1)
6
c
7
(y
3
+ y
2
+ 13y −4)
6
c
9
y
18
+ 2y
17
+ ··· − 17840y + 1849
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = −0.927224 − 0.015489I
b = −0.407238 − 0.969235I
2.69787 − 2.82812I 17.1261 + 2.9794I
u = −0.877439 + 0.744862I
a = 1.104550 − 0.072177I
b = 1.63644 + 0.28753I
−7.53006 + 2.30982I 5.17231 − 0.22957I
u = −0.877439 + 0.744862I
a = 0.187603 + 1.191150I
b = −0.734633 + 0.080557I
−7.53006 + 2.30982I 5.17231 − 0.22957I
u = −0.877439 + 0.744862I
a = −1.241110 − 0.215785I
b = −1.66753 − 0.94699I
−7.53006 − 7.96606I 5.17231 + 6.18847I
u = −0.877439 + 0.744862I
a = 0.346778 − 1.240900I
b = 0.918807 + 0.323963I
−7.53006 − 7.96606I 5.17231 + 6.18847I
u = −0.877439 + 0.744862I
a = 0.529395 + 0.353208I
b = 0.254152 + 1.224170I
2.69787 − 2.82812I 17.1261 + 2.9794I
u = −0.877439 − 0.744862I
a = −0.927224 + 0.015489I
b = −0.407238 + 0.969235I
2.69787 + 2.82812I 17.1261 − 2.9794I
u = −0.877439 − 0.744862I
a = 1.104550 + 0.072177I
b = 1.63644 − 0.28753I
−7.53006 − 2.30982I 5.17231 + 0.22957I
u = −0.877439 − 0.744862I
a = 0.187603 − 1.191150I
b = −0.734633 − 0.080557I
−7.53006 − 2.30982I 5.17231 + 0.22957I
u = −0.877439 − 0.744862I
a = −1.241110 + 0.215785I
b = −1.66753 + 0.94699I
−7.53006 + 7.96606I 5.17231 − 6.18847I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 − 0.744862I
a = 0.346778 + 1.240900I
b = 0.918807 − 0.323963I
−7.53006 + 7.96606I 5.17231 − 6.18847I
u = −0.877439 − 0.744862I
a = 0.529395 − 0.353208I
b = 0.254152 − 1.224170I
2.69787 + 2.82812I 17.1261 − 2.9794I
u = 0.754878
a = 0.737750 + 0.212805I
b = 0.61766 + 2.03584I
−3.39248 + 5.13794I 11.70158 − 3.20902I
u = 0.754878
a = 0.737750 − 0.212805I
b = 0.61766 − 2.03584I
−3.39248 − 5.13794I 11.70158 + 3.20902I
u = 0.754878
a = −0.90888 + 1.32075I
b = −0.090652 − 1.376170I
−3.39248 − 5.13794I 11.70158 + 3.20902I
u = 0.754878
a = −0.90888 − 1.32075I
b = −0.090652 + 1.376170I
−3.39248 + 5.13794I 11.70158 − 3.20902I
u = 0.754878
a = −1.94302
b = −1.43643
6.83546 23.6550
u = 0.754878
a = 2.28528
b = 0.382411
6.83546 23.6550
12
III.
I
u
3
= h2u
13
+7u
12
+· · ·+b−5, 5u
14
+17u
13
+· · ·+a−5, u
15
+3u
14
+· · ·−6u
2
+1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
−u
2
a
6
=
u
−u
3
+ u
a
8
=
−5u
14
− 17u
13
+ ··· + 4u + 5
−2u
13
− 7u
12
+ ··· − 26u
2
+ 5
a
9
=
−5u
14
− 17u
13
+ ··· + 4u + 5
3u
14
+ 8u
13
+ ··· − 5u + 3
a
10
=
−7u
14
− 24u
13
+ ··· + 9u + 5
u
14
+ 2u
13
+ ··· − 2u + 2
a
4
=
u
14
+ 4u
13
+ ··· − 10u − 6
u
14
+ 3u
13
+ ··· − 4u
2
− 5u
a
1
=
5u
14
+ 16u
13
+ ··· − 17u − 8
u
13
+ 3u
12
+ ··· − 4u − 4
a
7
=
−9u
14
− 32u
13
+ ··· + 15u + 15
−4u
14
− 14u
13
+ ··· + 10u + 3
a
12
=
6u
14
+ 19u
13
+ ··· − 21u − 8
u
14
+ 4u
13
+ ··· − 7u − 4
a
11
=
3u
14
+ 13u
13
+ ··· − 3u − 4
3u
14
+ 9u
13
+ ··· − u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
14
+ 21u
13
− 11u
12
− 84u
11
− 54u
10
+ 113u
9
+ 166u
8
− 35u
7
−
173u
6
− 38u
5
+ 82u
4
+ 34u
3
− 32u
2
− 6u + 9
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
+ 3u
14
+ ··· + 4u
2
− 1
c
2
u
15
+ 3u
14
+ ··· − 6u
2
+ 1
c
3
, c
8
u
15
+ u
14
+ ··· + 6u
2
− 1
c
4
, c
10
u
15
− u
14
+ ··· − 6u
2
+ 1
c
5
u
15
− 3u
14
+ ··· + 6u
2
− 1
c
6
u
15
+ u
14
+ ··· − 3u
2
+ 1
c
7
u
15
− u
14
+ ··· − 2u + 1
c
9
u
15
+ u
14
+ ··· − 4u
2
+ 1
c
11
, c
12
u
15
− u
14
+ ··· + 3u
2
− 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
+ 7y
14
+ ··· + 8y −1
c
2
, c
5
y
15
− 11y
14
+ ··· + 12y −1
c
3
, c
4
, c
8
c
10
y
15
− 15y
14
+ ··· + 12y −1
c
6
, c
11
, c
12
y
15
+ 15y
14
+ ··· + 6y −1
c
7
y
15
− 5y
14
+ ··· + 2y −1
c
9
y
15
+ 3y
14
+ ··· + 8y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772963 + 0.597189I
a = −0.827811 − 0.016279I
b = −0.343553 − 1.218360I
1.77519 − 3.34740I 8.50075 + 8.05329I
u = −0.772963 − 0.597189I
a = −0.827811 + 0.016279I
b = −0.343553 + 1.218360I
1.77519 + 3.34740I 8.50075 − 8.05329I
u = 1.21630
a = −1.10982
b = −0.609066
8.60341 19.2250
u = 1.216020 + 0.268411I
a = 1.037430 − 0.282211I
b = 0.591253 − 0.100818I
4.59696 + 3.78442I 13.45506 − 3.52568I
u = 1.216020 − 0.268411I
a = 1.037430 + 0.282211I
b = 0.591253 + 0.100818I
4.59696 − 3.78442I 13.45506 + 3.52568I
u = −0.741693 + 1.001970I
a = 0.645240 + 0.343179I
b = 0.168411 + 0.864224I
−1.02527 − 2.06106I 10.76904 + 5.89866I
u = −0.741693 − 1.001970I
a = 0.645240 − 0.343179I
b = 0.168411 − 0.864224I
−1.02527 + 2.06106I 10.76904 − 5.89866I
u = −0.581097 + 0.353670I
a = 1.215450 − 0.514042I
b = 0.12631 + 1.63261I
−4.31889 − 5.65349I 3.28441 + 7.61935I
u = −0.581097 − 0.353670I
a = 1.215450 + 0.514042I
b = 0.12631 − 1.63261I
−4.31889 + 5.65349I 3.28441 − 7.61935I
u = 0.661672
a = 2.39502
b = 0.953687
6.37007 2.43460
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.577868 + 0.178736I
a = −2.47388 + 1.02720I
b = −0.998690 + 0.209089I
1.98344 − 1.67719I 4.13214 − 1.25424I
u = 0.577868 − 0.178736I
a = −2.47388 − 1.02720I
b = −0.998690 − 0.209089I
1.98344 + 1.67719I 4.13214 + 1.25424I
u = −1.41521
a = 0.382739
b = 1.30454
5.30168 4.34420
u = −1.42952 + 0.46018I
a = −0.430407 − 0.024659I
b = −0.868313 − 0.551235I
1.65539 − 4.71343I 7.35653 + 5.31534I
u = −1.42952 − 0.46018I
a = −0.430407 + 0.024659I
b = −0.868313 + 0.551235I
1.65539 + 4.71343I 7.35653 − 5.31534I
17
IV. I
u
4
=
h−44a
7
u
2
−73a
6
u
2
+· · ·−213a+245, −2a
6
u
2
−a
5
u
2
+· · ·+7a+13, u
3
+u
2
−1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
−u
2
a
6
=
u
u
2
+ u − 1
a
8
=
a
0.273292a
7
u
2
+ 0.453416a
6
u
2
+ ··· + 1.32298a − 1.52174
a
9
=
a
0.273292a
7
u
2
+ 0.453416a
6
u
2
+ ··· + 1.32298a − 1.52174
a
10
=
−0.677019a
7
u
2
− 0.645963a
6
u
2
+ ··· + 0.745342a + 1.56522
−0.658385a
7
u
2
− 0.683230a
6
u
2
+ ··· + 1.40373a − 0.652174
a
4
=
−a
2
u
1.36025a
7
u
2
+ 0.279503a
6
u
2
+ ··· + 0.0621118a − 0.869565
a
1
=
−1.02484a
7
u
2
− 1.95031a
6
u
2
+ ··· + 2.78882a + 0.956522
−1.16149a
7
u
2
− 0.677019a
6
u
2
+ ··· − 0.372671a + 1.21739
a
7
=
−1.72671a
7
u
2
− 2.54658a
6
u
2
+ ··· + 5.32298a + 2.47826
0.00621118a
7
u
2
− 2.01242a
6
u
2
+ ··· + 2.55280a − 1.73913
a
12
=
0.608696a
7
u
2
− 2.21739a
6
u
2
+ ··· + 3.17391a − 0.434783
−
15
7
a
7
u
2
−
5
7
a
6
u
2
+ ··· +
9
7
a + 1
a
11
=
−0.950311a
7
u
2
+ 1.90062a
6
u
2
+ ··· − 2.57764a − 2.91304
0.124224a
7
u
2
+ 3.75155a
6
u
2
+ ··· − 4.94410a − 0.782609
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
52
23
a
7
u
2
−
80
23
a
6
u
2
+ ··· +
248
23
a +
254
23
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
− 5u
23
+ ··· − 20u + 109
c
2
, c
5
(u
3
− u
2
+ 1)
8
c
3
, c
4
, c
8
c
10
u
24
+ u
23
+ ··· − 24u + 7
c
6
, c
11
, c
12
(u
4
− u
3
+ 2u
2
− 2u + 1)
6
c
7
(u
2
− u + 1)
12
c
9
u
24
+ 3u
23
+ ··· + 20u + 19
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ 9y
23
+ ··· + 27504y + 11881
c
2
, c
5
(y
3
− y
2
+ 2y −1)
8
c
3
, c
4
, c
8
c
10
y
24
− 15y
23
+ ··· − 716y + 49
c
6
, c
11
, c
12
(y
4
+ 3y
3
+ 2y
2
+ 1)
6
c
7
(y
2
+ y + 1)
12
c
9
y
24
+ 5y
23
+ ··· + 1424y + 361
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = −0.040773 − 0.997477I
b = 0.617792 + 0.097671I
−1.37919 − 0.79824I 8.49024 − 0.48465I
u = −0.877439 + 0.744862I
a = 0.964624 − 0.327636I
b = 0.525863 + 0.945972I
−1.37919 − 4.85801I 8.49024 + 6.44355I
u = −0.877439 + 0.744862I
a = −1.039300 − 0.058321I
b = −1.39358 − 0.47039I
−1.37919 − 0.79824I 8.49024 − 0.48465I
u = −0.877439 + 0.744862I
a = 1.033460 + 0.263154I
b = 0.303126 + 0.916009I
−1.37919 − 0.79824I 8.49024 − 0.48465I
u = −0.877439 + 0.744862I
a = −0.254667 + 1.040960I
b = −0.745244 − 0.312818I
−1.37919 − 4.85801I 8.49024 + 6.44355I
u = −0.877439 + 0.744862I
a = −0.747266 − 0.522075I
b = −0.56367 − 1.44433I
−1.37919 − 4.85801I 8.49024 + 6.44355I
u = −0.877439 + 0.744862I
a = 1.121100 + 0.196208I
b = 1.43883 + 0.82244I
−1.37919 − 4.85801I 8.49024 + 6.44355I
u = −0.877439 + 0.744862I
a = −0.159736 − 0.339671I
b = 0.154539 − 1.116840I
−1.37919 − 0.79824I 8.49024 − 0.48465I
u = −0.877439 − 0.744862I
a = −0.040773 + 0.997477I
b = 0.617792 − 0.097671I
−1.37919 + 0.79824I 8.49024 + 0.48465I
u = −0.877439 − 0.744862I
a = 0.964624 + 0.327636I
b = 0.525863 − 0.945972I
−1.37919 + 4.85801I 8.49024 − 6.44355I
21
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 − 0.744862I
a = −1.039300 + 0.058321I
b = −1.39358 + 0.47039I
−1.37919 + 0.79824I 8.49024 + 0.48465I
u = −0.877439 − 0.744862I
a = 1.033460 − 0.263154I
b = 0.303126 − 0.916009I
−1.37919 + 0.79824I 8.49024 + 0.48465I
u = −0.877439 − 0.744862I
a = −0.254667 − 1.040960I
b = −0.745244 + 0.312818I
−1.37919 + 4.85801I 8.49024 − 6.44355I
u = −0.877439 − 0.744862I
a = −0.747266 + 0.522075I
b = −0.56367 + 1.44433I
−1.37919 + 4.85801I 8.49024 − 6.44355I
u = −0.877439 − 0.744862I
a = 1.121100 − 0.196208I
b = 1.43883 − 0.82244I
−1.37919 + 4.85801I 8.49024 − 6.44355I
u = −0.877439 − 0.744862I
a = −0.159736 + 0.339671I
b = 0.154539 + 1.116840I
−1.37919 + 0.79824I 8.49024 + 0.48465I
u = 0.754878
a = −0.935402 + 0.185618I
b = −0.56365 − 1.65106I
2.75839 + 2.02988I 15.0195 − 3.4641I
u = 0.754878
a = −0.935402 − 0.185618I
b = −0.56365 + 1.65106I
2.75839 − 2.02988I 15.0195 + 3.4641I
u = 0.754878
a = 1.027300 + 0.800722I
b = 0.28063 − 1.38647I
2.75839 + 2.02988I 15.0195 − 3.4641I
u = 0.754878
a = 1.027300 − 0.800722I
b = 0.28063 + 1.38647I
2.75839 − 2.02988I 15.0195 + 3.4641I
22
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.754878
a = 1.88775 + 0.07859I
b = 1.63567 + 0.61747I
2.75839 + 2.02988I 15.0195 − 3.4641I
u = 0.754878
a = 1.88775 − 0.07859I
b = 1.63567 − 0.61747I
2.75839 − 2.02988I 15.0195 + 3.4641I
u = 0.754878
a = −2.35710 + 0.41119I
b = −0.190292 − 0.406791I
2.75839 − 2.02988I 15.0195 + 3.4641I
u = 0.754878
a = −2.35710 − 0.41119I
b = −0.190292 + 0.406791I
2.75839 + 2.02988I 15.0195 − 3.4641I
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
15
+ 3u
14
+ ··· + 4u
2
− 1)(u
18
− 2u
17
+ ··· − 252u − 27)
· (u
24
− 5u
23
+ ··· − 20u + 109)(u
25
− 3u
24
+ ··· + 2u + 1)
c
2
((u
3
− u
2
+ 1)
14
)(u
15
+ 3u
14
+ ··· − 6u
2
+ 1)
· (u
25
+ 12u
24
+ ··· + 640u + 128)
c
3
, c
8
(u
15
+ u
14
+ ··· + 6u
2
− 1)(u
18
− 3u
16
+ ··· + 6u − 11)
· (u
24
+ u
23
+ ··· − 24u + 7)(u
25
− u
24
+ ··· + 2u − 1)
c
4
, c
10
(u
15
− u
14
+ ··· − 6u
2
+ 1)(u
18
− 3u
16
+ ··· + 6u − 11)
· (u
24
+ u
23
+ ··· − 24u + 7)(u
25
− u
24
+ ··· + 2u − 1)
c
5
((u
3
− u
2
+ 1)
14
)(u
15
− 3u
14
+ ··· + 6u
2
− 1)
· (u
25
+ 12u
24
+ ··· + 640u + 128)
c
6
((u
3
+ 2u + 1)
6
)(u
4
− u
3
+ 2u
2
− 2u + 1)
6
(u
15
+ u
14
+ ··· − 3u
2
+ 1)
· (u
25
+ 6u
24
+ ··· + 40u + 8)
c
7
((u
2
− u + 1)
12
)(u
3
+ 3u
2
+ 5u + 2)
6
(u
15
− u
14
+ ··· − 2u + 1)
· (u
25
− 6u
24
+ ··· − 56u + 464)
c
9
(u
15
+ u
14
+ ··· − 4u
2
+ 1)(u
18
+ u
16
+ ··· − 52u − 43)
· (u
24
+ 3u
23
+ ··· + 20u + 19)(u
25
+ u
24
+ ··· − 2u + 1)
c
11
, c
12
((u
3
+ 2u + 1)
6
)(u
4
− u
3
+ 2u
2
− 2u + 1)
6
(u
15
− u
14
+ ··· + 3u
2
− 1)
· (u
25
+ 6u
24
+ ··· + 40u + 8)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
15
+ 7y
14
+ ··· + 8y −1)(y
18
− 6y
17
+ ··· − 81000y + 729)
· (y
24
+ 9y
23
+ ··· + 27504y + 11881)(y
25
− 27y
24
+ ··· + 54y −1)
c
2
, c
5
((y
3
− y
2
+ 2y −1)
14
)(y
15
− 11y
14
+ ··· + 12y −1)
· (y
25
− 12y
24
+ ··· + 114688y −16384)
c
3
, c
4
, c
8
c
10
(y
15
− 15y
14
+ ··· + 12y −1)(y
18
− 6y
17
+ ··· − 1136y + 121)
· (y
24
− 15y
23
+ ··· − 716y + 49)(y
25
− 5y
24
+ ··· + 18y −1)
c
6
, c
11
, c
12
((y
3
+ 4y
2
+ 4y −1)
6
)(y
4
+ 3y
3
+ 2y
2
+ 1)
6
(y
15
+ 15y
14
+ ··· + 6y −1)
· (y
25
+ 22y
24
+ ··· + 416y −64)
c
7
((y
2
+ y + 1)
12
)(y
3
+ y
2
+ 13y −4)
6
(y
15
− 5y
14
+ ··· + 2y −1)
· (y
25
− 2y
24
+ ··· − 995392y −215296)
c
9
(y
15
+ 3y
14
+ ··· + 8y −1)(y
18
+ 2y
17
+ ··· − 17840y + 1849)
· (y
24
+ 5y
23
+ ··· + 1424y + 361)(y
25
− 23y
24
+ ··· + 66y −1)
25
