12n
0785
(K12n
0785
)
A knot diagram
1
Linearized knot diagam
4 6 9 12 11 10 3 12 7 2 5 9
Solving Sequence
4,12 5,9
1 2 3 8 7 11 6 10
c
4
c
12
c
1
c
3
c
8
c
7
c
11
c
5
c
10
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−27u
23
− 304u
22
+ ··· + 32b − 800, −25u
23
− 246u
22
+ ··· + 64a + 5312,
u
24
+ 12u
23
+ ··· + 736u + 64i
I
u
2
= h1.86388 × 10
20
a
11
u
2
− 7.50093 × 10
19
a
10
u
2
+ ··· + 1.24248 × 10
20
a + 1.90879 × 10
20
,
− a
11
u
2
+ 13a
10
u
2
+ ··· + 2212a + 924, u
3
− u
2
+ 2u − 1i
I
u
3
= hu
13
+ u
12
+ 8u
11
+ 6u
10
+ 24u
9
+ 14u
8
+ 32u
7
+ 17u
6
+ 15u
5
+ 12u
4
− u
3
+ 4u
2
+ b + 2u,
u
12
+ u
11
+ 8u
10
+ 6u
9
+ 24u
8
+ 14u
7
+ 32u
6
+ 17u
5
+ 15u
4
+ 12u
3
− u
2
+ a + 4u + 2,
u
15
+ u
14
+ 10u
13
+ 8u
12
+ 40u
11
+ 26u
10
+ 80u
9
+ 44u
8
+ 78u
7
+ 40u
6
+ 25u
5
+ 16u
4
− 5u
3
+ 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 75 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−27u
23
− 304u
22
+ · · · + 32b − 800, −25u
23
− 246u
22
+ · · · + 64a +
5312, u
24
+ 12u
23
+ · · · + 736u + 64i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
25
64
u
23
+
123
32
u
22
+ ··· −
2843
4
u − 83
27
32
u
23
+
19
2
u
22
+ ··· +
741
2
u + 25
a
1
=
−u
23
−
47
4
u
22
+ ··· − 1008u −
191
2
−
1
4
u
23
−
7
2
u
22
+ ··· −
1279
2
u − 64
a
2
=
−0.750000u
23
− 8.25000u
22
+ ··· − 368.500u − 31.5000
−
1
4
u
23
−
7
2
u
22
+ ··· −
1279
2
u − 64
a
3
=
u
23
+
47
4
u
22
+ ··· + 1008u +
193
2
1
4
u
23
+
7
2
u
22
+ ··· +
1281
2
u + 64
a
8
=
25
64
u
23
+
123
32
u
22
+ ··· −
2843
4
u − 83
47
32
u
23
+
133
8
u
22
+ ··· +
1933
2
u + 79
a
7
=
−
1
2
u
23
−
111
16
u
22
+ ··· − 1654u − 165
15
8
u
23
+
337
16
u
22
+ ··· + 868u + 64
a
11
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
10
=
−
7
4
u
23
−
81
4
u
22
+ ··· −
6717
4
u − 160
5
4
u
23
+ 14u
22
+ ··· + 601u + 48
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1
2
u
23
−
23
4
u
22
+ ··· − 300u − 34
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
− 19u
23
+ ··· − 1308u + 680
c
2
, c
10
u
24
− u
23
+ ··· − 2u + 1
c
3
, c
8
, c
12
u
24
− u
23
+ ··· − u + 1
c
4
, c
5
, c
11
u
24
+ 12u
23
+ ··· + 736u + 64
c
6
, c
9
u
24
+ 11u
23
+ ··· + 116u + 8
c
7
u
24
+ u
23
+ ··· − 38u + 21
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 23y
23
+ ··· − 29904y + 462400
c
2
, c
10
y
24
+ y
23
+ ··· + 16y + 1
c
3
, c
8
, c
12
y
24
+ 31y
23
+ ··· + 23y + 1
c
4
, c
5
, c
11
y
24
+ 22y
23
+ ··· + 11264y + 4096
c
6
, c
9
y
24
+ 19y
23
+ ··· − 464y + 64
c
7
y
24
+ 15y
23
+ ··· + 3344y + 441
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.010640 + 0.471333I
a = 0.44326 − 1.53014I
b = −0.27323 − 1.75534I
−10.7115 + 10.0939I −0.04933 − 6.43639I
u = −1.010640 − 0.471333I
a = 0.44326 + 1.53014I
b = −0.27323 + 1.75534I
−10.7115 − 10.0939I −0.04933 + 6.43639I
u = −0.503255 + 0.574177I
a = 0.835381 + 0.150338I
b = 0.506730 − 0.403999I
−2.49625 + 3.04099I 1.32899 − 3.32840I
u = −0.503255 − 0.574177I
a = 0.835381 − 0.150338I
b = 0.506730 + 0.403999I
−2.49625 − 3.04099I 1.32899 + 3.32840I
u = −1.180380 + 0.399451I
a = −0.295273 + 1.321890I
b = 0.17950 + 1.67829I
−5.17987 + 4.24750I 3.02010 − 8.12803I
u = −1.180380 − 0.399451I
a = −0.295273 − 1.321890I
b = 0.17950 − 1.67829I
−5.17987 − 4.24750I 3.02010 + 8.12803I
u = −1.004630 + 0.835014I
a = 0.759653 − 1.021870I
b = −0.09010 − 1.66092I
−9.75365 − 3.54379I −0.99118 + 4.27014I
u = −1.004630 − 0.835014I
a = 0.759653 + 1.021870I
b = −0.09010 + 1.66092I
−9.75365 + 3.54379I −0.99118 − 4.27014I
u = −0.308009 + 0.555063I
a = −0.449528 + 0.382050I
b = 0.073603 + 0.367191I
0.196861 + 1.129420I 2.90140 − 6.41925I
u = −0.308009 − 0.555063I
a = −0.449528 − 0.382050I
b = 0.073603 − 0.367191I
0.196861 − 1.129420I 2.90140 + 6.41925I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.516904 + 0.317864I
a = −0.256314 − 1.078460I
b = −0.475294 − 0.475988I
−3.21746 + 0.49631I 0.08904 − 3.40641I
u = −0.516904 − 0.317864I
a = −0.256314 + 1.078460I
b = −0.475294 + 0.475988I
−3.21746 − 0.49631I 0.08904 + 3.40641I
u = 0.21488 + 1.45533I
a = −0.517010 + 0.329331I
b = 0.590380 + 0.681655I
1.83425 + 1.78702I 1.23481 − 2.86773I
u = 0.21488 − 1.45533I
a = −0.517010 − 0.329331I
b = 0.590380 − 0.681655I
1.83425 − 1.78702I 1.23481 + 2.86773I
u = −0.13976 + 1.54947I
a = −0.236789 − 0.330108I
b = −0.544586 + 0.320761I
4.59873 + 5.35349I 4.00000 + 0.I
u = −0.13976 − 1.54947I
a = −0.236789 + 0.330108I
b = −0.544586 − 0.320761I
4.59873 − 5.35349I 4.00000 + 0.I
u = −0.10640 + 1.57603I
a = 0.285679 + 0.026175I
b = 0.071649 − 0.447453I
7.58277 + 2.71010I 1.02540 − 3.86743I
u = −0.10640 − 1.57603I
a = 0.285679 − 0.026175I
b = 0.071649 + 0.447453I
7.58277 − 2.71010I 1.02540 + 3.86743I
u = −0.43383 + 1.51943I
a = 0.868418 − 0.623221I
b = −0.57020 − 1.58987I
0.89209 + 9.87509I 6.51442 − 6.39656I
u = −0.43383 − 1.51943I
a = 0.868418 + 0.623221I
b = −0.57020 + 1.58987I
0.89209 − 9.87509I 6.51442 + 6.39656I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.39076 + 1.53782I
a = −0.947929 + 0.618450I
b = 0.58065 + 1.69940I
−4.2980 + 15.1741I 4.00000 − 7.27803I
u = −0.39076 − 1.53782I
a = −0.947929 − 0.618450I
b = 0.58065 − 1.69940I
−4.2980 − 15.1741I 4.00000 + 7.27803I
u = −0.62030 + 1.53231I
a = −0.739547 + 0.593643I
b = 0.45090 + 1.50145I
−1.65465 + 3.46994I 7.08633 − 7.90223I
u = −0.62030 − 1.53231I
a = −0.739547 − 0.593643I
b = 0.45090 − 1.50145I
−1.65465 − 3.46994I 7.08633 + 7.90223I
7
II. I
u
2
= h1.86 × 10
20
a
11
u
2
− 7.50 × 10
19
a
10
u
2
+ · · · + 1.24 × 10
20
a + 1.91 ×
10
20
, −a
11
u
2
+ 13a
10
u
2
+ · · · + 2212a + 924, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
a
−3.24277a
11
u
2
+ 1.30501a
10
u
2
+ ··· − 2.16165a − 3.32090
a
1
=
a
2
u
−0.581414a
11
u
2
+ 3.43653a
10
u
2
+ ··· − 7.52437a − 2.00296
a
2
=
0.581414a
11
u
2
− 3.43653a
10
u
2
+ ··· + 7.52437a + 2.00296
−0.581414a
11
u
2
+ 3.43653a
10
u
2
+ ··· − 7.52437a − 2.00296
a
3
=
3.13144a
11
u
2
+ 0.478770a
10
u
2
+ ··· − 1.90212a + 2.66819
−6.90860a
11
u
2
+ 7.51166a
10
u
2
+ ··· − 16.6685a − 8.90871
a
8
=
a
−3.24277a
11
u
2
+ 1.30501a
10
u
2
+ ··· − 2.16165a − 3.32090
a
7
=
−1.35924a
11
u
2
− 0.912568a
10
u
2
+ ··· + 2.14523a − 1.30624
0.862884a
11
u
2
− 3.85601a
10
u
2
+ ··· + 6.58457a + 2.47234
a
11
=
u
u
2
− u + 1
a
6
=
u
2
+ 1
u
2
− u + 1
a
10
=
1.44285a
11
u
2
− 0.692279a
10
u
2
+ ··· + 1.99663a + 1.48796
2.28994a
11
u
2
+ 0.187392a
10
u
2
+ ··· − 0.897794a + 2.62937
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
739013742275411059680
57478066342067795059
a
11
u
2
+
40574843941814876112
57478066342067795059
a
10
u
2
+ ··· +
328493151198246771284
57478066342067795059
a −
454117950256466456506
57478066342067795059
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 5u
5
+ 7u
4
− 2u
2
+ 3u − 1)
6
c
2
, c
10
u
36
− 5u
35
+ ··· + 8u − 1
c
3
, c
8
, c
12
u
36
− u
35
+ ··· − 7944u + 1231
c
4
, c
5
, c
11
(u
3
− u
2
+ 2u − 1)
12
c
6
, c
9
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
6
c
7
u
36
+ u
35
+ ··· + 4818u − 3979
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 11y
5
+ 45y
4
− 60y
3
− 10y
2
− 5y + 1)
6
c
2
, c
10
y
36
− 5y
35
+ ··· + 2420y
2
+ 1
c
3
, c
8
, c
12
y
36
+ 35y
35
+ ··· − 8165144y + 1515361
c
4
, c
5
, c
11
(y
3
+ 3y
2
+ 2y −1)
12
c
6
, c
9
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
6
c
7
y
36
+ 23y
35
+ ··· − 900566708y + 15832441
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.292445 − 0.976914I
b = −0.010553 − 0.974222I
5.74941 − 2.82812I 7.77925 + 2.97945I
u = 0.215080 + 1.307140I
a = 0.879256 + 0.628433I
b = −0.20795 + 1.64474I
−1.17182 − 2.82812I 8.92653 + 2.97945I
u = 0.215080 + 1.307140I
a = −0.835208 − 0.315914I
b = 0.22908 − 2.03181I
−4.87092 − 0.85571I 0.085479 − 0.705331I
u = 0.215080 + 1.307140I
a = −0.818019 − 0.239393I
b = 1.59293 − 0.13103I
1.78490 − 7.42025I 4.09089 + 6.18427I
u = 0.215080 + 1.307140I
a = 1.103510 + 0.320281I
b = −1.04255 + 1.64876I
−4.87092 − 4.80053I 0.08548 + 6.66423I
u = 0.215080 + 1.307140I
a = −0.097635 + 1.202570I
b = −0.136981 + 1.120760I
1.78490 − 7.42025I 4.09089 + 6.18427I
u = 0.215080 + 1.307140I
a = −1.199620 − 0.356474I
b = 0.63234 − 1.28448I
−1.17182 − 2.82812I 8.92653 + 2.97945I
u = 0.215080 + 1.307140I
a = −0.505561 + 0.535105I
b = 0.404790 + 0.730191I
1.78490 + 1.76400I 4.09089 − 0.22537I
u = 0.215080 + 1.307140I
a = 0.726954 + 0.111541I
b = −1.339860 − 0.172152I
5.74941 − 2.82812I 7.77925 + 2.97945I
u = 0.215080 + 1.307140I
a = −0.593503 + 0.212019I
b = 0.808193 + 0.545750I
1.78490 + 1.76400I 4.09089 − 0.22537I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −1.10032 − 0.97863I
b = 0.18131 − 1.51133I
−4.87092 − 4.80053I 0.08548 + 6.66423I
u = 0.215080 + 1.307140I
a = 1.48534 + 0.41966I
b = −0.233308 + 1.159680I
−4.87092 − 0.85571I 0.085479 − 0.705331I
u = 0.215080 − 1.307140I
a = 0.292445 + 0.976914I
b = −0.010553 + 0.974222I
5.74941 + 2.82812I 7.77925 − 2.97945I
u = 0.215080 − 1.307140I
a = 0.879256 − 0.628433I
b = −0.20795 − 1.64474I
−1.17182 + 2.82812I 8.92653 − 2.97945I
u = 0.215080 − 1.307140I
a = −0.835208 + 0.315914I
b = 0.22908 + 2.03181I
−4.87092 + 0.85571I 0.085479 + 0.705331I
u = 0.215080 − 1.307140I
a = −0.818019 + 0.239393I
b = 1.59293 + 0.13103I
1.78490 + 7.42025I 4.09089 − 6.18427I
u = 0.215080 − 1.307140I
a = 1.103510 − 0.320281I
b = −1.04255 − 1.64876I
−4.87092 + 4.80053I 0.08548 − 6.66423I
u = 0.215080 − 1.307140I
a = −0.097635 − 1.202570I
b = −0.136981 − 1.120760I
1.78490 + 7.42025I 4.09089 − 6.18427I
u = 0.215080 − 1.307140I
a = −1.199620 + 0.356474I
b = 0.63234 + 1.28448I
−1.17182 + 2.82812I 8.92653 − 2.97945I
u = 0.215080 − 1.307140I
a = −0.505561 − 0.535105I
b = 0.404790 − 0.730191I
1.78490 − 1.76400I 4.09089 + 0.22537I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 − 1.307140I
a = 0.726954 − 0.111541I
b = −1.339860 + 0.172152I
5.74941 + 2.82812I 7.77925 − 2.97945I
u = 0.215080 − 1.307140I
a = −0.593503 − 0.212019I
b = 0.808193 − 0.545750I
1.78490 − 1.76400I 4.09089 + 0.22537I
u = 0.215080 − 1.307140I
a = −1.10032 + 0.97863I
b = 0.18131 + 1.51133I
−4.87092 + 4.80053I 0.08548 − 6.66423I
u = 0.215080 − 1.307140I
a = 1.48534 − 0.41966I
b = −0.233308 − 1.159680I
−4.87092 + 0.85571I 0.085479 + 0.705331I
u = 0.569840
a = 0.037672 + 0.791957I
b = −1.126600 + 0.574406I
−2.35268 − 4.59213I −2.43837 + 3.20482I
u = 0.569840
a = 0.037672 − 0.791957I
b = −1.126600 − 0.574406I
−2.35268 + 4.59213I −2.43837 − 3.20482I
u = 0.569840
a = −0.371632
b = 0.950019
1.61183 1.25000
u = 0.569840
a = −1.66717
b = 0.211771
1.61183 1.25000
u = 0.569840
a = 1.97705 + 1.00801I
b = −0.021467 + 0.451289I
−2.35268 + 4.59213I −2.43837 − 3.20482I
u = 0.569840
a = 1.97705 − 1.00801I
b = −0.021467 − 0.451289I
−2.35268 − 4.59213I −2.43837 + 3.20482I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.569840
a = 0.01895 + 2.50724I
b = 0.38309 + 1.86300I
−9.00850 + 1.97241I −6.44379 − 3.68478I
u = 0.569840
a = 0.01895 − 2.50724I
b = 0.38309 − 1.86300I
−9.00850 − 1.97241I −6.44379 + 3.68478I
u = 0.569840
a = 0.32036 + 2.66289I
b = −0.18256 + 1.51742I
−5.30941 2.39727 + 0.I
u = 0.569840
a = 0.32036 − 2.66289I
b = −0.18256 − 1.51742I
−5.30941 2.39727 + 0.I
u = 0.569840
a = −0.67227 + 3.26933I
b = −0.01080 + 1.42872I
−9.00850 − 1.97241I −6.44379 + 3.68478I
u = 0.569840
a = −0.67227 − 3.26933I
b = −0.01080 − 1.42872I
−9.00850 + 1.97241I −6.44379 − 3.68478I
14
III.
I
u
3
= hu
13
+ u
12
+ · · · + b + 2u, u
12
+ u
11
+ · · · + a + 2, u
15
+ u
14
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
−u
12
− u
11
+ ··· − 4u − 2
−u
13
− u
12
+ ··· − 4u
2
− 2u
a
1
=
u
13
+ u
12
+ ··· − 2u − 1
u
14
+ u
13
+ ··· + 8u
3
− 2u
2
a
2
=
−u
14
− 8u
12
+ ··· − 2u − 1
u
14
+ u
13
+ ··· + 8u
3
− 2u
2
a
3
=
u
13
+ u
12
+ ··· + 8u
2
− 2u
u
14
+ u
13
+ ··· − 2u
2
− u
a
8
=
−u
12
− u
11
+ ··· − 4u − 2
−u
14
− 2u
13
+ ··· − 6u
2
− 2u
a
7
=
−u
14
− 10u
12
+ ··· + 4u − 1
−u
10
− u
9
− 6u
8
− 4u
7
− 12u
6
− 5u
5
− 7u
4
− u
3
+ 4u
2
+ 2u + 1
a
11
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
10
=
u
12
+ 8u
10
+ 26u
8
+ u
7
+ 40u
6
+ 6u
5
+ 24u
4
+ 12u
3
− u
2
+ 6u
u
11
+ u
10
+ 7u
9
+ 5u
8
+ 18u
7
+ 10u
6
+ 20u
5
+ 10u
4
+ 7u
3
+ 4u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
14
− 4u
13
− 18u
12
− 27u
11
− 62u
10
− 71u
9
− 103u
8
− 86u
7
−
78u
6
− 42u
5
− 9u
4
− 10u
3
+ 17u
2
− 12u + 3
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 12u
14
+ ··· + 106u − 7
c
2
, c
10
u
15
− u
14
+ ··· − 3u + 1
c
3
, c
8
u
15
+ u
14
+ ··· − 5u
2
+ 1
c
4
, c
5
u
15
+ u
14
+ ··· + 2u + 1
c
6
u
15
+ 4u
14
+ ··· + 16u + 5
c
7
u
15
− u
14
+ ··· + 19u − 13
c
9
u
15
− 4u
14
+ ··· + 16u − 5
c
11
u
15
− u
14
+ ··· + 2u − 1
c
12
u
15
− u
14
+ ··· + 5u
2
− 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
− 12y
14
+ ··· + 5160y −49
c
2
, c
10
y
15
− 3y
14
+ ··· + 13y −1
c
3
, c
8
, c
12
y
15
+ 11y
14
+ ··· + 10y −1
c
4
, c
5
, c
11
y
15
+ 19y
14
+ ··· + 4y −1
c
6
, c
9
y
15
+ 14y
14
+ ··· − 84y −25
c
7
y
15
+ 11y
14
+ ··· + 517y −169
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.323844 + 1.269380I
a = 1.029620 + 0.553032I
b = −0.36857 + 1.48607I
−2.53804 − 2.24615I 2.16387 + 0.54553I
u = 0.323844 − 1.269380I
a = 1.029620 − 0.553032I
b = −0.36857 − 1.48607I
−2.53804 + 2.24615I 2.16387 − 0.54553I
u = 0.144598 + 1.313360I
a = −1.174410 − 0.519311I
b = 0.51223 − 1.61751I
−4.36159 − 3.39759I 2.91969 + 0.94976I
u = 0.144598 − 1.313360I
a = −1.174410 + 0.519311I
b = 0.51223 + 1.61751I
−4.36159 + 3.39759I 2.91969 − 0.94976I
u = −0.648777
a = 1.14669
b = −0.743944
2.16310 19.7840
u = −0.09083 + 1.51451I
a = −0.115298 + 0.423871I
b = −0.631485 − 0.213121I
4.83768 + 6.28589I 6.55684 − 7.16786I
u = −0.09083 − 1.51451I
a = −0.115298 − 0.423871I
b = −0.631485 + 0.213121I
4.83768 − 6.28589I 6.55684 + 7.16786I
u = 0.403094 + 0.263692I
a = −1.89519 − 2.58749I
b = −0.08164 − 1.54275I
−8.01131 + 1.56669I 2.47871 − 0.14188I
u = 0.403094 − 0.263692I
a = −1.89519 + 2.58749I
b = −0.08164 + 1.54275I
−8.01131 − 1.56669I 2.47871 + 0.14188I
u = −0.13670 + 1.53364I
a = −0.169899 − 0.313484I
b = 0.503998 − 0.217711I
8.19478 + 2.55021I 14.3952 − 0.7069I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.13670 − 1.53364I
a = −0.169899 + 0.313484I
b = 0.503998 + 0.217711I
8.19478 − 2.55021I 14.3952 + 0.7069I
u = −0.50718 + 1.50516I
a = 0.561674 + 0.312900I
b = −0.755832 + 0.686711I
2.15433 − 1.91136I 25.0958 + 12.5131I
u = −0.50718 − 1.50516I
a = 0.561674 − 0.312900I
b = −0.755832 − 0.686711I
2.15433 + 1.91136I 25.0958 − 12.5131I
u = −0.312435 + 0.251857I
a = −0.80984 − 1.74801I
b = 0.693274 + 0.342176I
−1.35739 + 4.89958I 6.99805 − 6.23368I
u = −0.312435 − 0.251857I
a = −0.80984 + 1.74801I
b = 0.693274 − 0.342176I
−1.35739 − 4.89958I 6.99805 + 6.23368I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
6
+ 5u
5
+ 7u
4
− 2u
2
+ 3u − 1)
6
)(u
15
− 12u
14
+ ··· + 106u − 7)
· (u
24
− 19u
23
+ ··· − 1308u + 680)
c
2
, c
10
(u
15
− u
14
+ ··· − 3u + 1)(u
24
− u
23
+ ··· − 2u + 1)
· (u
36
− 5u
35
+ ··· + 8u − 1)
c
3
, c
8
(u
15
+ u
14
+ ··· − 5u
2
+ 1)(u
24
− u
23
+ ··· − u + 1)
· (u
36
− u
35
+ ··· − 7944u + 1231)
c
4
, c
5
((u
3
− u
2
+ 2u − 1)
12
)(u
15
+ u
14
+ ··· + 2u + 1)
· (u
24
+ 12u
23
+ ··· + 736u + 64)
c
6
((u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
6
)(u
15
+ 4u
14
+ ··· + 16u + 5)
· (u
24
+ 11u
23
+ ··· + 116u + 8)
c
7
(u
15
− u
14
+ ··· + 19u − 13)(u
24
+ u
23
+ ··· − 38u + 21)
· (u
36
+ u
35
+ ··· + 4818u − 3979)
c
9
((u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
6
)(u
15
− 4u
14
+ ··· + 16u − 5)
· (u
24
+ 11u
23
+ ··· + 116u + 8)
c
11
((u
3
− u
2
+ 2u − 1)
12
)(u
15
− u
14
+ ··· + 2u − 1)
· (u
24
+ 12u
23
+ ··· + 736u + 64)
c
12
(u
15
− u
14
+ ··· + 5u
2
− 1)(u
24
− u
23
+ ··· − u + 1)
· (u
36
− u
35
+ ··· − 7944u + 1231)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 11y
5
+ 45y
4
− 60y
3
− 10y
2
− 5y + 1)
6
· (y
15
− 12y
14
+ ··· + 5160y −49)
· (y
24
− 23y
23
+ ··· − 29904y + 462400)
c
2
, c
10
(y
15
− 3y
14
+ ··· + 13y −1)(y
24
+ y
23
+ ··· + 16y + 1)
· (y
36
− 5y
35
+ ··· + 2420y
2
+ 1)
c
3
, c
8
, c
12
(y
15
+ 11y
14
+ ··· + 10y −1)(y
24
+ 31y
23
+ ··· + 23y + 1)
· (y
36
+ 35y
35
+ ··· − 8165144y + 1515361)
c
4
, c
5
, c
11
((y
3
+ 3y
2
+ 2y −1)
12
)(y
15
+ 19y
14
+ ··· + 4y −1)
· (y
24
+ 22y
23
+ ··· + 11264y + 4096)
c
6
, c
9
((y
6
+ 5y
5
+ ··· − 5y + 1)
6
)(y
15
+ 14y
14
+ ··· − 84y −25)
· (y
24
+ 19y
23
+ ··· − 464y + 64)
c
7
(y
15
+ 11y
14
+ ··· + 517y −169)(y
24
+ 15y
23
+ ··· + 3344y + 441)
· (y
36
+ 23y
35
+ ··· − 900566708y + 15832441)
21
