12n
0511
(K12n
0511
)
A knot diagram
1
Linearized knot diagam
3 6 10 8 2 9 12 5 1 4 1 8
Solving Sequence
2,5
6
3,8
9 1 10 4 12 7 11
c
5
c
2
c
8
c
1
c
9
c
4
c
12
c
7
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
24
+ 3u
23
+ ··· + 2b + u, 2u
24
+ u
23
+ ··· + 2a − 17, u
25
+ 5u
24
+ ··· + 18u + 4i
I
u
2
= h−u
14
+ 3u
12
− u
11
− 7u
10
+ 2u
9
+ 9u
8
− 5u
7
− 9u
6
+ 5u
5
+ 6u
4
− 5u
3
− 3u
2
+ b + 2u + 1,
u
11
− 3u
9
+ u
8
+ 6u
7
− 3u
6
− 7u
5
+ 5u
4
+ 5u
3
− 5u
2
+ a − 3u + 3,
u
15
− 3u
13
+ u
12
+ 7u
11
− 2u
10
− 10u
9
+ 5u
8
+ 11u
7
− 6u
6
− 9u
5
+ 6u
4
+ 5u
3
− 4u
2
− 2u + 1i
I
u
3
= h−3393922u
7
a
3
− 6147191u
7
a
2
+ ··· + 12439448a + 20529116, 2u
7
a
3
− 2u
7
a
2
+ ··· − 23a + 17,
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1i
* 3 irreducible components of dim
C
= 0, with total 72 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
= hu
24
+3u
23
+· · ·+2b+u, 2u
24
+u
23
+· · ·+2a−17, u
25
+5u
24
+· · ·+18u+4i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
24
−
1
2
u
23
+ ··· + 22u +
17
2
−
1
2
u
24
−
3
2
u
23
+ ··· − u
2
−
1
2
u
a
9
=
−
3
2
u
24
− 2u
23
+ ··· +
43
2
u +
17
2
−
1
2
u
24
−
3
2
u
23
+ ··· − u
2
−
1
2
u
a
1
=
u
3
u
5
− u
3
+ u
a
10
=
9
2
u
24
+ 16u
23
+ ··· +
55
2
u +
9
2
3
2
u
24
+
23
2
u
23
+ ··· +
145
2
u + 22
a
4
=
7
4
u
24
+
29
4
u
23
+ ··· +
99
4
u + 7
−
1
2
u
24
−
3
2
u
23
+ ··· −
9
2
u − 1
a
12
=
−
3
4
u
24
−
17
4
u
23
+ ··· −
79
4
u − 6
1
2
u
24
+
1
2
u
23
+ ··· −
17
2
u − 3
a
7
=
9
4
u
24
+
31
4
u
23
+ ··· +
45
4
u + 3
−
1
2
u
24
−
1
2
u
23
+ ··· +
17
2
u + 3
a
11
=
−
31
4
u
24
−
117
4
u
23
+ ··· −
255
4
u − 14
3
2
u
24
−
5
2
u
23
+ ··· −
129
2
u − 21
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
24
−9u
23
−18u
22
+ 8u
21
+ 66u
20
+ 40u
19
−108u
18
−139u
17
+
116u
16
+ 307u
15
+ 29u
14
−388u
13
−280u
12
+ 239u
11
+ 390u
10
−41u
9
−409u
8
−217u
7
+
209u
6
+ 339u
5
+ 137u
4
− 74u
3
− 126u
2
− 72u − 22
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
25
+ 9u
24
+ ··· − 36u + 16
c
2
, c
5
u
25
+ 5u
24
+ ··· + 18u + 4
c
3
, c
4
, c
8
c
10
u
25
− u
24
+ ··· + u + 1
c
6
, c
9
u
25
+ 5u
24
+ ··· + 19u − 1
c
7
, c
12
u
25
− 15u
24
+ ··· + 1280u − 256
c
11
u
25
+ 19u
24
+ ··· + 131072u + 65536
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
+ 15y
24
+ ··· + 2544y −256
c
2
, c
5
y
25
− 9y
24
+ ··· − 36y −16
c
3
, c
4
, c
8
c
10
y
25
− y
24
+ ··· + 7y −1
c
6
, c
9
y
25
+ 15y
24
+ ··· + 395y −1
c
7
, c
12
y
25
− 19y
24
+ ··· + 131072y −65536
c
11
y
25
− 39y
24
+ ··· + 31138512896y −4294967296
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.022010 + 0.128401I
a = −0.46250 − 1.36086I
b = 0.463679 − 0.734252I
−3.37093 − 3.23509I −5.61108 + 7.22985I
u = 1.022010 − 0.128401I
a = −0.46250 + 1.36086I
b = 0.463679 + 0.734252I
−3.37093 + 3.23509I −5.61108 − 7.22985I
u = −0.607816 + 0.864536I
a = −1.47268 + 0.78689I
b = 1.19042 − 1.00082I
−3.85370 − 9.16879I 1.40851 + 4.09106I
u = −0.607816 − 0.864536I
a = −1.47268 − 0.78689I
b = 1.19042 + 1.00082I
−3.85370 + 9.16879I 1.40851 − 4.09106I
u = −0.701915 + 0.801942I
a = 1.143080 − 0.216154I
b = −0.667380 + 0.687693I
2.88462 − 2.98752I 1.24178 + 4.92994I
u = −0.701915 − 0.801942I
a = 1.143080 + 0.216154I
b = −0.667380 − 0.687693I
2.88462 + 2.98752I 1.24178 − 4.92994I
u = −0.907357 + 0.568454I
a = 0.534312 − 0.354050I
b = 0.130379 − 0.742012I
−1.07299 + 2.19225I −2.62579 − 1.77817I
u = −0.907357 − 0.568454I
a = 0.534312 + 0.354050I
b = 0.130379 + 0.742012I
−1.07299 − 2.19225I −2.62579 + 1.77817I
u = −0.332071 + 0.816286I
a = −1.186400 − 0.698523I
b = 0.916099 + 0.927578I
−5.43513 + 5.46912I 0.78254 − 4.99205I
u = −0.332071 − 0.816286I
a = −1.186400 + 0.698523I
b = 0.916099 − 0.927578I
−5.43513 − 5.46912I 0.78254 + 4.99205I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.771350 + 0.820157I
a = 1.190320 + 0.400479I
b = −0.775875 + 0.036362I
3.94043 − 0.14935I 4.83254 + 1.63894I
u = 0.771350 − 0.820157I
a = 1.190320 − 0.400479I
b = −0.775875 − 0.036362I
3.94043 + 0.14935I 4.83254 − 1.63894I
u = −1.14488
a = −0.0580320
b = 0.402484
−2.58383 −9.25590
u = 1.164980 + 0.105711I
a = 0.110899 + 0.971898I
b = −1.02874 + 1.10276I
−10.62140 − 8.07096I −4.98343 + 5.16742I
u = 1.164980 − 0.105711I
a = 0.110899 − 0.971898I
b = −1.02874 − 1.10276I
−10.62140 + 8.07096I −4.98343 − 5.16742I
u = −1.003900 + 0.721068I
a = −1.77847 + 0.86765I
b = 0.663062 + 0.750145I
1.96585 + 8.72477I −0.55953 − 10.18504I
u = −1.003900 − 0.721068I
a = −1.77847 − 0.86765I
b = 0.663062 − 0.750145I
1.96585 − 8.72477I −0.55953 + 10.18504I
u = −1.108570 + 0.552402I
a = −0.613758 − 0.766814I
b = −0.745695 + 0.996770I
−7.80108 − 0.44100I −3.37024 + 0.98535I
u = −1.108570 − 0.552402I
a = −0.613758 + 0.766814I
b = −0.745695 − 0.996770I
−7.80108 + 0.44100I −3.37024 − 0.98535I
u = 0.970256 + 0.774295I
a = −1.083210 − 0.441322I
b = 0.817211 − 0.103305I
3.34163 − 5.81240I 4.36911 + 4.55947I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.970256 − 0.774295I
a = −1.083210 + 0.441322I
b = 0.817211 + 0.103305I
3.34163 + 5.81240I 4.36911 − 4.55947I
u = −1.065260 + 0.710865I
a = 2.12764 − 1.03485I
b = −1.23337 − 1.05815I
−5.2477 + 15.0268I −0.46984 − 8.38163I
u = −1.065260 − 0.710865I
a = 2.12764 + 1.03485I
b = −1.23337 + 1.05815I
−5.2477 − 15.0268I −0.46984 + 8.38163I
u = −0.129278 + 0.516797I
a = 1.019780 + 0.018690I
b = −0.431034 − 0.465642I
0.243380 + 1.219270I 2.61337 − 5.64120I
u = −0.129278 − 0.516797I
a = 1.019780 − 0.018690I
b = −0.431034 + 0.465642I
0.243380 − 1.219270I 2.61337 + 5.64120I
7
II.
I
u
2
= h−u
14
+3u
12
+· · ·+b+1, u
11
−3u
9
+· · ·+a+3, u
15
−3u
13
+· · ·−2u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
11
+ 3u
9
− u
8
− 6u
7
+ 3u
6
+ 7u
5
− 5u
4
− 5u
3
+ 5u
2
+ 3u − 3
u
14
− 3u
12
+ ··· − 2u − 1
a
9
=
u
14
− 3u
12
+ 7u
10
+ u
9
− 10u
8
− u
7
+ 12u
6
+ 2u
5
− 11u
4
+ 8u
2
+ u − 4
u
14
− 3u
12
+ ··· − 2u − 1
a
1
=
u
3
u
5
− u
3
+ u
a
10
=
u
14
+ u
13
+ ··· + 2u − 4
u
14
− 4u
12
+ ··· − 2u − 1
a
4
=
−u
14
+ 2u
12
− 5u
10
− u
9
+ 7u
8
− 8u
6
− u
5
+ 9u
4
− u
3
− 5u
2
+ u + 3
−u
14
+ 3u
12
+ ··· + 2u + 1
a
12
=
−u
14
+ 2u
12
+ ··· + 5u − 1
−u
13
+ 2u
11
− u
10
− 4u
9
+ u
8
+ 4u
7
− 3u
6
− 3u
5
+ 2u
4
+ 2u
3
− 2u
2
+ 1
a
7
=
u
14
+ u
13
+ ··· + 2u
2
− 4u
u
13
− 2u
11
+ u
10
+ 4u
9
− u
8
− 4u
7
+ 3u
6
+ 3u
5
− 2u
4
− 2u
3
+ 2u
2
− 1
a
11
=
−u
14
+ u
13
+ ··· + 6u − 1
−u
13
− u
12
+ ··· − u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −11u
14
− 2u
13
+ 30u
12
− 6u
11
− 65u
10
+ 8u
9
+ 82u
8
− 35u
7
−
82u
6
+ 37u
5
+ 60u
4
− 36u
3
− 29u
2
+ 19u + 10
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 6u
14
+ ··· + 12u − 1
c
2
u
15
− 3u
13
+ ··· − 2u − 1
c
3
, c
8
u
15
+ u
14
+ ··· − 2u − 1
c
4
, c
10
u
15
− u
14
+ ··· − 2u + 1
c
5
u
15
− 3u
13
+ ··· − 2u + 1
c
6
, c
9
u
15
− u
14
+ ··· + 4u − 1
c
7
u
15
− 4u
14
+ ··· + u − 1
c
11
u
15
− 16u
14
+ ··· + 11u − 1
c
12
u
15
+ 4u
14
+ ··· + u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
+ 10y
14
+ ··· + 48y −1
c
2
, c
5
y
15
− 6y
14
+ ··· + 12y −1
c
3
, c
4
, c
8
c
10
y
15
− 11y
14
+ ··· + 4y −1
c
6
, c
9
y
15
− 15y
14
+ ··· + 84y −1
c
7
, c
12
y
15
− 16y
14
+ ··· + 11y −1
c
11
y
15
− 32y
14
+ ··· + 19y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.610459 + 0.818977I
a = 0.845782 + 0.040690I
b = −0.828532 − 0.288942I
4.08493 + 1.50545I 8.35754 − 2.89339I
u = 0.610459 − 0.818977I
a = 0.845782 − 0.040690I
b = −0.828532 + 0.288942I
4.08493 − 1.50545I 8.35754 + 2.89339I
u = −0.769013 + 0.725023I
a = 2.33071 − 0.73449I
b = −1.393460 − 0.182294I
6.41341 + 0.87585I 5.46284 + 0.51162I
u = −0.769013 − 0.725023I
a = 2.33071 + 0.73449I
b = −1.393460 + 0.182294I
6.41341 − 0.87585I 5.46284 − 0.51162I
u = 0.926602
a = 0.105302
b = 1.43340
1.68940 −5.69740
u = 0.865065 + 0.641915I
a = 0.325602 + 1.317420I
b = 0.034258 + 0.919510I
−2.70696 − 2.50359I −7.46265 + 2.73240I
u = 0.865065 − 0.641915I
a = 0.325602 − 1.317420I
b = 0.034258 − 0.919510I
−2.70696 + 2.50359I −7.46265 − 2.73240I
u = −0.841141 + 0.268178I
a = −2.21555 − 0.38844I
b = 0.099804 + 0.728419I
−4.83754 + 1.17574I −4.66883 − 5.44721I
u = −0.841141 − 0.268178I
a = −2.21555 + 0.38844I
b = 0.099804 − 0.728419I
−4.83754 − 1.17574I −4.66883 + 5.44721I
u = −0.948405 + 0.696988I
a = −1.67918 + 1.38536I
b = 1.44517 − 0.15870I
5.86123 + 4.56895I 3.18547 − 5.68185I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.948405 − 0.696988I
a = −1.67918 − 1.38536I
b = 1.44517 + 0.15870I
5.86123 − 4.56895I 3.18547 + 5.68185I
u = −1.23026
a = 0.155877
b = 0.554784
−2.29287 19.0230
u = 1.047680 + 0.712038I
a = −0.996406 − 0.863353I
b = 0.745668 − 0.399900I
2.79145 − 7.25376I 4.27394 + 8.38512I
u = 1.047680 − 0.712038I
a = −0.996406 + 0.863353I
b = 0.745668 + 0.399900I
2.79145 + 7.25376I 4.27394 − 8.38512I
u = 0.374372
a = −1.48310
b = −1.19401
3.70935 12.3780
12
III. I
u
3
= h−3.39 × 10
6
a
3
u
7
− 6.15 × 10
6
a
2
u
7
+ · · · + 1.24 × 10
7
a + 2.05 ×
10
7
, 2u
7
a
3
− 2u
7
a
2
+ · · · − 23a + 17, u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
a
0.283764a
3
u
7
+ 0.513963a
2
u
7
+ ··· − 1.04005a − 1.71643
a
9
=
0.283764a
3
u
7
+ 0.513963a
2
u
7
+ ··· − 0.0400540a − 1.71643
0.283764a
3
u
7
+ 0.513963a
2
u
7
+ ··· − 1.04005a − 1.71643
a
1
=
u
3
u
5
− u
3
+ u
a
10
=
0.440437a
3
u
7
+ 1.12437a
2
u
7
+ ··· + 0.166168a − 1.95484
−0.247023a
3
u
7
− 0.0629067a
2
u
7
+ ··· − 0.465339a − 0.571361
a
4
=
−0.324332a
3
u
7
+ 0.395429a
2
u
7
+ ··· + 3.89099a − 2.79578
−0.141400a
3
u
7
− 0.123061a
2
u
7
+ ··· − 0.426253a + 1.88661
a
12
=
−0.152786a
3
u
7
− 0.260932a
2
u
7
+ ··· − 0.651322a + 0.714680
−0.168076a
3
u
7
+ 0.726751a
2
u
7
+ ··· + 2.04153a − 2.64032
a
7
=
−0.229339a
3
u
7
− 0.0567257a
2
u
7
+ ··· − 0.549412a + 0.851419
−0.401302a
3
u
7
+ 0.320549a
2
u
7
+ ··· + 1.93722a − 2.26518
a
11
=
−0.0762339a
3
u
7
− 0.465138a
2
u
7
+ ··· − 0.753232a + 0.577941
0.0651496a
3
u
7
+ 1.13295a
2
u
7
+ ··· + 2.14585a − 3.01547
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
+ 8u
5
− 4u
4
− 8u
3
+ 4u
2
+ 4u − 6
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
4
c
2
, c
5
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
4
c
3
, c
4
, c
8
c
10
u
32
− u
31
+ ··· − 18u − 1
c
6
, c
9
u
32
+ 9u
31
+ ··· − 634u − 1
c
7
, c
12
(u
2
+ u − 1)
16
c
11
(u
2
+ 3u + 1)
16
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
4
c
2
, c
5
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
4
c
3
, c
4
, c
8
c
10
y
32
− 9y
31
+ ··· − 76y + 1
c
6
, c
9
y
32
− 9y
31
+ ··· − 398532y + 1
c
7
, c
12
(y
2
− 3y + 1)
16
c
11
(y
2
− 7y + 1)
16
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.570868 + 0.730671I
a = 1.258650 + 0.162631I
b = −1.118500 − 0.297335I
2.90719 + 1.13123I 0.584775 − 0.510791I
u = 0.570868 + 0.730671I
a = 0.187278 − 0.136386I
b = 0.389150 + 0.463337I
2.90719 + 1.13123I 0.584775 − 0.510791I
u = 0.570868 + 0.730671I
a = −1.69178 + 0.62542I
b = 0.84962 − 1.25909I
−4.98850 + 1.13123I 0.584775 − 0.510791I
u = 0.570868 + 0.730671I
a = −2.09371 − 0.69413I
b = 1.059860 + 0.824486I
−4.98850 + 1.13123I 0.584775 − 0.510791I
u = 0.570868 − 0.730671I
a = 1.258650 − 0.162631I
b = −1.118500 + 0.297335I
2.90719 − 1.13123I 0.584775 + 0.510791I
u = 0.570868 − 0.730671I
a = 0.187278 + 0.136386I
b = 0.389150 − 0.463337I
2.90719 − 1.13123I 0.584775 + 0.510791I
u = 0.570868 − 0.730671I
a = −1.69178 − 0.62542I
b = 0.84962 + 1.25909I
−4.98850 − 1.13123I 0.584775 + 0.510791I
u = 0.570868 − 0.730671I
a = −2.09371 + 0.69413I
b = 1.059860 − 0.824486I
−4.98850 − 1.13123I 0.584775 + 0.510791I
u = −0.855237 + 0.665892I
a = 0.754057 − 0.275844I
b = 0.044917 − 1.261120I
−1.78843 + 2.57849I 3.72292 − 3.56796I
u = −0.855237 + 0.665892I
a = −0.53860 − 2.07817I
b = 0.1299760 + 0.0516291I
−1.78843 + 2.57849I 3.72292 − 3.56796I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.855237 + 0.665892I
a = 2.08459 − 0.77588I
b = −1.48784 + 0.18074I
6.10726 + 2.57849I 3.72292 − 3.56796I
u = −0.855237 + 0.665892I
a = −2.16688 + 1.67503I
b = 1.42104 + 0.28124I
6.10726 + 2.57849I 3.72292 − 3.56796I
u = −0.855237 − 0.665892I
a = 0.754057 + 0.275844I
b = 0.044917 + 1.261120I
−1.78843 − 2.57849I 3.72292 + 3.56796I
u = −0.855237 − 0.665892I
a = −0.53860 + 2.07817I
b = 0.1299760 − 0.0516291I
−1.78843 − 2.57849I 3.72292 + 3.56796I
u = −0.855237 − 0.665892I
a = 2.08459 + 0.77588I
b = −1.48784 − 0.18074I
6.10726 − 2.57849I 3.72292 + 3.56796I
u = −0.855237 − 0.665892I
a = −2.16688 − 1.67503I
b = 1.42104 − 0.28124I
6.10726 − 2.57849I 3.72292 + 3.56796I
u = −1.09818
a = 0.108721 + 1.087540I
b = −1.10916 + 1.12580I
−10.4506 −5.86400
u = −1.09818
a = 0.108721 − 1.087540I
b = −1.10916 − 1.12580I
−10.4506 −5.86400
u = −1.09818
a = −0.041528 + 0.276829I
b = 0.423663 + 0.286570I
−2.55489 −5.86400
u = −1.09818
a = −0.041528 − 0.276829I
b = 0.423663 − 0.286570I
−2.55489 −5.86400
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.031810 + 0.655470I
a = −0.518841 + 1.172810I
b = −0.94630 − 1.36074I
−6.32752 − 6.44354I −1.42845 + 5.29417I
u = 1.031810 + 0.655470I
a = 0.498106 + 0.337320I
b = −0.249218 + 0.680436I
1.56816 − 6.44354I −1.42845 + 5.29417I
u = 1.031810 + 0.655470I
a = −1.23125 − 1.24773I
b = 1.074000 − 0.483326I
1.56816 − 6.44354I −1.42845 + 5.29417I
u = 1.031810 + 0.655470I
a = 2.43825 + 1.21067I
b = −1.21301 + 0.84470I
−6.32752 − 6.44354I −1.42845 + 5.29417I
u = 1.031810 − 0.655470I
a = −0.518841 − 1.172810I
b = −0.94630 + 1.36074I
−6.32752 + 6.44354I −1.42845 − 5.29417I
u = 1.031810 − 0.655470I
a = 0.498106 − 0.337320I
b = −0.249218 − 0.680436I
1.56816 + 6.44354I −1.42845 − 5.29417I
u = 1.031810 − 0.655470I
a = −1.23125 + 1.24773I
b = 1.074000 + 0.483326I
1.56816 + 6.44354I −1.42845 − 5.29417I
u = 1.031810 − 0.655470I
a = 2.43825 − 1.21067I
b = −1.21301 − 0.84470I
−6.32752 + 6.44354I −1.42845 − 5.29417I
u = 0.603304
a = 0.700053
b = −1.33642
3.10281 −3.89450
u = 0.603304
a = 1.83024
b = 1.04987
3.10281 −3.89450
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.603304
a = −3.31220 + 0.39407I
b = 0.375093 + 0.832047I
−4.79288 −3.89450
u = 0.603304
a = −3.31220 − 0.39407I
b = 0.375093 − 0.832047I
−4.79288 −3.89450
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
4
· (u
15
− 6u
14
+ ··· + 12u − 1)(u
25
+ 9u
24
+ ··· − 36u + 16)
c
2
((u
8
− u
7
+ ··· + 2u − 1)
4
)(u
15
− 3u
13
+ ··· − 2u − 1)
· (u
25
+ 5u
24
+ ··· + 18u + 4)
c
3
, c
8
(u
15
+ u
14
+ ··· − 2u − 1)(u
25
− u
24
+ ··· + u + 1)
· (u
32
− u
31
+ ··· − 18u − 1)
c
4
, c
10
(u
15
− u
14
+ ··· − 2u + 1)(u
25
− u
24
+ ··· + u + 1)
· (u
32
− u
31
+ ··· − 18u − 1)
c
5
((u
8
− u
7
+ ··· + 2u − 1)
4
)(u
15
− 3u
13
+ ··· − 2u + 1)
· (u
25
+ 5u
24
+ ··· + 18u + 4)
c
6
, c
9
(u
15
− u
14
+ ··· + 4u − 1)(u
25
+ 5u
24
+ ··· + 19u − 1)
· (u
32
+ 9u
31
+ ··· − 634u − 1)
c
7
((u
2
+ u − 1)
16
)(u
15
− 4u
14
+ ··· + u − 1)
· (u
25
− 15u
24
+ ··· + 1280u − 256)
c
11
((u
2
+ 3u + 1)
16
)(u
15
− 16u
14
+ ··· + 11u − 1)
· (u
25
+ 19u
24
+ ··· + 131072u + 65536)
c
12
((u
2
+ u − 1)
16
)(u
15
+ 4u
14
+ ··· + u + 1)
· (u
25
− 15u
24
+ ··· + 1280u − 256)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
4
· (y
15
+ 10y
14
+ ··· + 48y −1)(y
25
+ 15y
24
+ ··· + 2544y −256)
c
2
, c
5
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
4
· (y
15
− 6y
14
+ ··· + 12y −1)(y
25
− 9y
24
+ ··· − 36y −16)
c
3
, c
4
, c
8
c
10
(y
15
− 11y
14
+ ··· + 4y −1)(y
25
− y
24
+ ··· + 7y −1)
· (y
32
− 9y
31
+ ··· − 76y + 1)
c
6
, c
9
(y
15
− 15y
14
+ ··· + 84y −1)(y
25
+ 15y
24
+ ··· + 395y −1)
· (y
32
− 9y
31
+ ··· − 398532y + 1)
c
7
, c
12
((y
2
− 3y + 1)
16
)(y
15
− 16y
14
+ ··· + 11y −1)
· (y
25
− 19y
24
+ ··· + 131072y −65536)
c
11
((y
2
− 7y + 1)
16
)(y
15
− 32y
14
+ ··· + 19y −1)
· (y
25
− 39y
24
+ ··· + 31138512896y −4294967296)
21
