12n
0489
(K12n
0489
)
A knot diagram
1
Linearized knot diagam
3 6 10 12 2 11 12 1 4 1 5 8
Solving Sequence
2,5
6
3,11
7 12 8 1 4 10 9
c
5
c
2
c
6
c
11
c
7
c
1
c
4
c
10
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−17u
26
− 87u
25
+ ··· + 4b − 12, 47u
26
+ 291u
25
+ ··· + 8a + 260, u
27
+ 7u
26
+ ··· + 44u + 8i
I
u
2
= h58848u
7
a
5
+ 58468u
7
a
4
+ ··· + 79844a + 35715, 2u
7
a
5
+ 15u
7
a
4
+ ··· + 216a + 224,
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1i
I
u
3
= hu
15
− 2u
13
+ u
12
+ 6u
11
− u
10
− 8u
9
+ 4u
8
+ 11u
7
− 3u
6
− 8u
5
+ 4u
4
+ 6u
3
− 2u
2
+ b − u,
− 2u
15
+ 2u
14
+ ··· + a − 4,
u
16
− 3u
14
+ u
13
+ 8u
12
− 2u
11
− 13u
10
+ 5u
9
+ 17u
8
− 6u
7
− 15u
6
+ 6u
5
+ 10u
4
− 4u
3
− 4u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 91 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−17u
26
− 87u
25
+ · · · + 4b − 12, 47u
26
+ 291u
25
+ · · · + 8a +
260, u
27
+ 7u
26
+ · · · + 44u + 8i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
−5.87500u
26
− 36.3750u
25
+ ··· − 165.250u − 32.5000
17
4
u
26
+
87
4
u
25
+ ··· + 34u + 3
a
7
=
53
8
u
26
+
301
8
u
25
+ ··· +
475
4
u + 21
−
3
4
u
26
−
11
4
u
25
+ ··· +
47
2
u + 7
a
12
=
−10.1250u
26
− 58.1250u
25
+ ··· − 199.250u − 35.5000
17
4
u
26
+
87
4
u
25
+ ··· + 34u + 3
a
8
=
−
75
8
u
26
−
461
8
u
25
+ ··· −
535
2
u − 52
15
2
u
26
+ 40u
25
+ ··· +
165
2
u + 11
a
1
=
u
3
u
5
− u
3
+ u
a
4
=
19
8
u
26
+
107
8
u
25
+ ··· +
245
4
u + 13
1
4
u
26
+
13
4
u
25
+ ··· +
65
2
u + 7
a
10
=
13.1250u
26
+ 78.6250u
25
+ ··· + 338.750u + 63.5000
−
27
4
u
26
−
121
4
u
25
+ ··· + 68u + 25
a
9
=
115
8
u
26
+
749
8
u
25
+ ··· +
1047
2
u + 108
−17u
26
−
185
2
u
25
+ ··· −
455
2
u − 35
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −23u
26
−150u
25
−376u
24
−261u
23
+ 729u
22
+ 1734u
21
+ 538u
20
−2534u
19
−2547u
18
+
3058u
17
+ 6966u
16
+ 232u
15
− 11605u
14
− 12159u
13
+ 2392u
12
+ 15331u
11
+ 11486u
10
−
2810u
9
−10111u
8
−4910u
7
+ 3090u
6
+ 4696u
5
+ 1095u
4
−1912u
3
−2073u
2
−972u −214
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
+ 9u
26
+ ··· + 144u + 64
c
2
, c
5
u
27
+ 7u
26
+ ··· + 44u + 8
c
3
, c
4
, c
9
c
11
u
27
+ 4u
25
+ ··· + 3u + 1
c
6
, c
10
u
27
− 2u
26
+ ··· + 10u + 1
c
7
, c
8
, c
12
u
27
+ 15u
26
+ ··· + 2816u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
+ 19y
26
+ ··· − 11008y −4096
c
2
, c
5
y
27
− 9y
26
+ ··· + 144y −64
c
3
, c
4
, c
9
c
11
y
27
+ 8y
26
+ ··· − 5y −1
c
6
, c
10
y
27
− 18y
26
+ ··· + 116y −1
c
7
, c
8
, c
12
y
27
− 15y
26
+ ··· + 524288y −65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.685572 + 0.852680I
a = −0.294505 + 0.463699I
b = −0.669615 − 0.882383I
1.08424 − 3.42475I −3.67335 + 3.91434I
u = −0.685572 − 0.852680I
a = −0.294505 − 0.463699I
b = −0.669615 + 0.882383I
1.08424 + 3.42475I −3.67335 − 3.91434I
u = −0.627323 + 0.898264I
a = 0.159682 − 0.346047I
b = 0.73050 + 1.24655I
3.67005 − 10.56210I −0.83521 + 5.59011I
u = −0.627323 − 0.898264I
a = 0.159682 + 0.346047I
b = 0.73050 − 1.24655I
3.67005 + 10.56210I −0.83521 − 5.59011I
u = −0.237310 + 0.870614I
a = 0.179034 + 0.342963I
b = 0.625069 − 0.943841I
1.43533 + 6.41550I −1.16841 − 7.33424I
u = −0.237310 − 0.870614I
a = 0.179034 − 0.342963I
b = 0.625069 + 0.943841I
1.43533 − 6.41550I −1.16841 + 7.33424I
u = 1.098600 + 0.138393I
a = 1.98959 + 0.36891I
b = 0.870859 + 0.704449I
−5.71910 − 3.18007I −10.81910 + 3.99905I
u = 1.098600 − 0.138393I
a = 1.98959 − 0.36891I
b = 0.870859 − 0.704449I
−5.71910 + 3.18007I −10.81910 − 3.99905I
u = 0.693539 + 0.484425I
a = −0.697012 + 0.794438I
b = −0.093480 − 0.606899I
1.37365 − 1.86319I −0.94665 + 4.18320I
u = 0.693539 − 0.484425I
a = −0.697012 − 0.794438I
b = −0.093480 + 0.606899I
1.37365 + 1.86319I −0.94665 − 4.18320I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.024830 + 0.541180I
a = 0.720475 + 1.113140I
b = 0.938303 + 0.355958I
−3.31479 + 3.49091I −9.36494 − 3.65965I
u = −1.024830 − 0.541180I
a = 0.720475 − 1.113140I
b = 0.938303 − 0.355958I
−3.31479 − 3.49091I −9.36494 + 3.65965I
u = 1.179100 + 0.151427I
a = −1.68814 − 0.80165I
b = −0.832047 − 1.051930I
−3.55373 − 9.54122I −7.19005 + 7.47977I
u = 1.179100 − 0.151427I
a = −1.68814 + 0.80165I
b = −0.832047 + 1.051930I
−3.55373 + 9.54122I −7.19005 − 7.47977I
u = −0.777167
a = −0.501723
b = −0.408121
−1.00831 −10.7050
u = −1.143530 + 0.466150I
a = −0.139215 − 0.916449I
b = −0.656924 − 0.691492I
−1.52298 − 1.56653I −6.91776 + 4.99160I
u = −1.143530 − 0.466150I
a = −0.139215 + 0.916449I
b = −0.656924 + 0.691492I
−1.52298 + 1.56653I −6.91776 − 4.99160I
u = −0.916430 + 0.866188I
a = −0.479520 − 1.066450I
b = −0.009586 + 0.768274I
9.08124 + 3.20872I 9.49976 − 1.13015I
u = −0.916430 − 0.866188I
a = −0.479520 + 1.066450I
b = −0.009586 − 0.768274I
9.08124 − 3.20872I 9.49976 + 1.13015I
u = −1.036230 + 0.737283I
a = 1.67104 + 0.91689I
b = 0.731439 − 0.942909I
0.00440 + 9.36453I −4.76974 − 8.14508I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.036230 − 0.737283I
a = 1.67104 − 0.91689I
b = 0.731439 + 0.942909I
0.00440 − 9.36453I −4.76974 + 8.14508I
u = −1.072090 + 0.729726I
a = −1.92994 − 0.65272I
b = −0.79138 + 1.29074I
2.2965 + 16.5821I −2.72249 − 9.74695I
u = −1.072090 − 0.729726I
a = −1.92994 + 0.65272I
b = −0.79138 − 1.29074I
2.2965 − 16.5821I −2.72249 + 9.74695I
u = 0.931659 + 0.932655I
a = 0.416195 − 0.265879I
b = 0.053666 + 0.840001I
9.39926 − 3.40339I 4.88512 + 3.93618I
u = 0.931659 − 0.932655I
a = 0.416195 + 0.265879I
b = 0.053666 − 0.840001I
9.39926 + 3.40339I 4.88512 − 3.93618I
u = −0.271005 + 0.622370I
a = −0.406824 − 0.384016I
b = −0.692744 + 0.470458I
−1.39292 + 0.87413I −6.12461 − 2.84895I
u = −0.271005 − 0.622370I
a = −0.406824 + 0.384016I
b = −0.692744 − 0.470458I
−1.39292 − 0.87413I −6.12461 + 2.84895I
7
II. I
u
2
= h58848u
7
a
5
+ 58468u
7
a
4
+ · · · + 79844a + 35715, 2u
7
a
5
+ 15u
7
a
4
+
· · · + 216a + 224, 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
11
=
a
−4.54670a
5
u
7
− 4.51735a
4
u
7
+ ··· − 6.16889a − 2.75941
a
7
=
2.18697a
5
u
7
+ 4.03230a
4
u
7
+ ··· + 11.1542a + 13.0883
1.02326a
2
u
7
− 0.511628u
7
+ ··· + 0.139535a
2
− 1.06977
a
12
=
4.54670a
5
u
7
+ 4.51735a
4
u
7
+ ··· + 7.16889a + 2.75941
−4.54670a
5
u
7
− 4.51735a
4
u
7
+ ··· − 6.16889a − 2.75941
a
8
=
1.36213a
4
u
7
+ 1.69103a
3
u
7
+ ··· + 4.92691a + 9.32890
1.10871a
4
u
7
− 0.372093a
3
u
7
+ ··· + 1.68771a + 2.68964
a
1
=
u
3
u
5
− u
3
+ u
a
4
=
−1.81264a
5
u
7
− 4.09101a
4
u
7
+ ··· − 8.42162a − 8.29267
−0.374334a
5
u
7
+ 0.0587190a
4
u
7
+ ··· − 2.73260a − 2.79564
a
10
=
0.0878467a
5
u
7
− 0.620335a
4
u
7
+ ··· − 0.431353a − 0.271035
−3.49648a
5
u
7
− 2.67535a
4
u
7
+ ··· − 4.68160a − 2.52963
a
9
=
−2.58379a
4
u
7
− 2.84385a
3
u
7
+ ··· − 5.32558a − 9.18798
1.22166a
4
u
7
+ 2.10631a
3
u
7
+ ··· + 0.538206a − 0.140926
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
113224
12943
u
7
a
4
−
1880
301
u
7
a
3
+ ··· −
2960
301
a −
312682
12943
8
(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)
6
c
2
, c
5
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
6
c
3
, c
4
, c
9
c
11
u
48
+ u
47
+ ··· − 164u + 229
c
6
, c
10
u
48
− 9u
47
+ ··· + 666u + 661
c
7
, c
8
, c
12
(u
3
− u
2
+ 1)
16
9
(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)
6
c
2
, c
5
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
6
c
3
, c
4
, c
9
c
11
y
48
+ 27y
47
+ ··· + 832312y + 52441
c
6
, c
10
y
48
+ 15y
47
+ ··· − 734396y + 436921
c
7
, c
8
, c
12
(y
3
− y
2
+ 2y −1)
16
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.570868 + 0.730671I
a = 0.434653 − 0.839070I
b = 1.149610 + 0.301433I
0.87002 + 3.95936I −2.92498 − 3.49024I
u = 0.570868 + 0.730671I
a = −0.535134 + 0.647465I
b = −0.636009 − 0.805422I
0.87002 − 1.69689I −2.92498 + 2.46866I
u = 0.570868 + 0.730671I
a = −0.120842 + 0.801190I
b = 0.538735 − 0.794929I
0.87002 − 1.69689I −2.92498 + 2.46866I
u = 0.570868 + 0.730671I
a = −0.277424 − 0.743391I
b = −0.544694 + 1.183380I
0.87002 + 3.95936I −2.92498 − 3.49024I
u = 0.570868 + 0.730671I
a = −0.579346 + 0.223976I
b = −0.004274 + 0.929917I
5.00760 + 1.13123I 3.60429 − 0.51079I
u = 0.570868 + 0.730671I
a = −0.081353 − 0.401232I
b = 0.676753 − 1.082970I
5.00760 + 1.13123I 3.60429 − 0.51079I
u = 0.570868 − 0.730671I
a = 0.434653 + 0.839070I
b = 1.149610 − 0.301433I
0.87002 − 3.95936I −2.92498 + 3.49024I
u = 0.570868 − 0.730671I
a = −0.535134 − 0.647465I
b = −0.636009 + 0.805422I
0.87002 + 1.69689I −2.92498 − 2.46866I
u = 0.570868 − 0.730671I
a = −0.120842 − 0.801190I
b = 0.538735 + 0.794929I
0.87002 + 1.69689I −2.92498 − 2.46866I
u = 0.570868 − 0.730671I
a = −0.277424 + 0.743391I
b = −0.544694 − 1.183380I
0.87002 − 3.95936I −2.92498 + 3.49024I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.570868 − 0.730671I
a = −0.579346 − 0.223976I
b = −0.004274 − 0.929917I
5.00760 − 1.13123I 3.60429 + 0.51079I
u = 0.570868 − 0.730671I
a = −0.081353 + 0.401232I
b = 0.676753 + 1.082970I
5.00760 − 1.13123I 3.60429 + 0.51079I
u = −0.855237 + 0.665892I
a = 0.842747 − 0.830266I
b = 0.090666 + 0.885994I
4.07009 + 5.40662I 0.21317 − 6.54740I
u = −0.855237 + 0.665892I
a = −0.494638 − 0.291001I
b = −0.786177 − 1.031780I
4.07009 − 0.24963I 0.213168 − 0.588510I
u = −0.855237 + 0.665892I
a = 1.57064 + 0.15400I
b = 0.08193 − 1.92144I
8.20767 + 2.57849I 6.74243 − 3.56796I
u = −0.855237 + 0.665892I
a = −1.43317 − 1.40899I
b = −0.02034 + 1.49548I
8.20767 + 2.57849I 6.74243 − 3.56796I
u = −0.855237 + 0.665892I
a = 2.08795 + 0.67193I
b = 0.909681 − 0.905479I
4.07009 + 5.40662I 0.21317 − 6.54740I
u = −0.855237 + 0.665892I
a = −2.33228 − 0.49803I
b = −0.167674 + 0.729716I
4.07009 − 0.24963I 0.213168 − 0.588510I
u = −0.855237 − 0.665892I
a = 0.842747 + 0.830266I
b = 0.090666 − 0.885994I
4.07009 − 5.40662I 0.21317 + 6.54740I
u = −0.855237 − 0.665892I
a = −0.494638 + 0.291001I
b = −0.786177 + 1.031780I
4.07009 + 0.24963I 0.213168 + 0.588510I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.855237 − 0.665892I
a = 1.57064 − 0.15400I
b = 0.08193 + 1.92144I
8.20767 − 2.57849I 6.74243 + 3.56796I
u = −0.855237 − 0.665892I
a = −1.43317 + 1.40899I
b = −0.02034 − 1.49548I
8.20767 − 2.57849I 6.74243 + 3.56796I
u = −0.855237 − 0.665892I
a = 2.08795 − 0.67193I
b = 0.909681 + 0.905479I
4.07009 − 5.40662I 0.21317 + 6.54740I
u = −0.855237 − 0.665892I
a = −2.33228 + 0.49803I
b = −0.167674 − 0.729716I
4.07009 + 0.24963I 0.213168 + 0.588510I
u = −1.09818
a = −0.352337 + 1.063250I
b = −0.390626 + 0.540817I
−0.454474 −2.84453 + 0.I
u = −1.09818
a = −0.352337 − 1.063250I
b = −0.390626 − 0.540817I
−0.454474 −2.84453 + 0.I
u = −1.09818
a = −1.87930 + 0.47836I
b = −1.035690 + 0.728269I
−4.59206 − 2.82812I −9.37379 + 2.97945I
u = −1.09818
a = −1.87930 − 0.47836I
b = −1.035690 − 0.728269I
−4.59206 + 2.82812I −9.37379 − 2.97945I
u = −1.09818
a = 1.61333 + 1.13807I
b = 0.740815 + 1.063820I
−4.59206 − 2.82812I −9.37379 + 2.97945I
u = −1.09818
a = 1.61333 − 1.13807I
b = 0.740815 − 1.063820I
−4.59206 + 2.82812I −9.37379 − 2.97945I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.031810 + 0.655470I
a = 0.012794 − 0.843235I
b = 0.798211 − 0.789739I
−0.46900 − 3.61542I −4.93820 + 2.31472I
u = 1.031810 + 0.655470I
a = −0.655325 + 1.142960I
b = −1.323150 + 0.413843I
−0.46900 − 9.27166I −4.93820 + 8.27362I
u = 1.031810 + 0.655470I
a = 1.57349 + 0.39663I
b = 0.140651 + 0.792574I
3.66858 − 6.44354I 1.59106 + 5.29417I
u = 1.031810 + 0.655470I
a = −1.65798 + 0.26104I
b = −0.901119 − 0.974313I
3.66858 − 6.44354I 1.59106 + 5.29417I
u = 1.031810 + 0.655470I
a = −1.55331 + 0.89766I
b = −0.668354 − 1.023270I
−0.46900 − 3.61542I −4.93820 + 2.31472I
u = 1.031810 + 0.655470I
a = 2.13206 − 0.70093I
b = 0.619236 + 1.261980I
−0.46900 − 9.27166I −4.93820 + 8.27362I
u = 1.031810 − 0.655470I
a = 0.012794 + 0.843235I
b = 0.798211 + 0.789739I
−0.46900 + 3.61542I −4.93820 − 2.31472I
u = 1.031810 − 0.655470I
a = −0.655325 − 1.142960I
b = −1.323150 − 0.413843I
−0.46900 + 9.27166I −4.93820 − 8.27362I
u = 1.031810 − 0.655470I
a = 1.57349 − 0.39663I
b = 0.140651 − 0.792574I
3.66858 + 6.44354I 1.59106 − 5.29417I
u = 1.031810 − 0.655470I
a = −1.65798 − 0.26104I
b = −0.901119 + 0.974313I
3.66858 + 6.44354I 1.59106 − 5.29417I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.031810 − 0.655470I
a = −1.55331 − 0.89766I
b = −0.668354 + 1.023270I
−0.46900 + 3.61542I −4.93820 − 2.31472I
u = 1.031810 − 0.655470I
a = 2.13206 + 0.70093I
b = 0.619236 − 1.261980I
−0.46900 + 9.27166I −4.93820 − 8.27362I
u = 0.603304
a = −1.01626 + 1.44968I
b = −0.374836 − 0.929425I
1.06564 − 2.82812I −7.40422 + 2.97945I
u = 0.603304
a = −1.01626 − 1.44968I
b = −0.374836 + 0.929425I
1.06564 + 2.82812I −7.40422 − 2.97945I
u = 0.603304
a = −1.03439 + 2.13156I
b = 0.13210 + 1.44648I
5.20322 −6 − 0.874953 + 0.10I
u = 0.603304
a = −1.03439 − 2.13156I
b = 0.13210 − 1.44648I
5.20322 −6 − 0.874953 + 0.10I
u = 0.603304
a = 0.23542 + 3.29584I
b = 0.474556 + 0.323382I
1.06564 − 2.82812I −7.40422 + 2.97945I
u = 0.603304
a = 0.23542 − 3.29584I
b = 0.474556 − 0.323382I
1.06564 + 2.82812I −7.40422 − 2.97945I
15
III.
I
u
3
= hu
15
−2u
13
+· · ·+b−u, −2u
15
+2u
14
+· · ·+a−4, u
16
−3u
14
+· · ·+u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
2u
15
− 2u
14
+ ··· − 17u
2
+ 4
−u
15
+ 2u
13
+ ··· + 2u
2
+ u
a
7
=
−u
15
+ 2u
14
+ ··· − 5u + 1
u
13
− 2u
11
+ u
10
+ 5u
9
− u
8
− 6u
7
+ 3u
6
+ 6u
5
− 2u
4
− 3u
3
+ 2u
2
+ u − 1
a
12
=
3u
15
− 2u
14
+ ··· − u + 4
−u
15
+ 2u
13
+ ··· + 2u
2
+ u
a
8
=
2u
15
− 6u
13
+ ··· − 2u + 4
u
14
+ u
13
+ ··· − u − 2
a
1
=
u
3
u
5
− u
3
+ u
a
4
=
−2u
15
+ 6u
13
+ ··· + 4u − 2
−u
14
+ 3u
12
+ ··· + 2u + 2
a
10
=
2u
15
− 2u
14
+ ··· + u + 4
−u
15
+ 2u
13
+ ··· + u − 1
a
9
=
2u
15
− 6u
13
+ ··· − 2u + 4
u
14
+ u
13
+ ··· − u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
15
+ 11u
14
+ 12u
13
−34u
12
−20u
11
+ 84u
10
+ 32u
9
−132u
8
−
18u
7
+ 158u
6
+ 10u
5
− 120u
4
+ 9u
3
+ 70u
2
− 11u − 17
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 6u
15
+ ··· − 9u + 1
c
2
u
16
− 3u
14
+ ··· − u + 1
c
3
, c
11
u
16
+ 8u
14
+ ··· − u + 1
c
4
, c
9
u
16
+ 8u
14
+ ··· + u + 1
c
5
u
16
− 3u
14
+ ··· + u + 1
c
6
, c
10
u
16
+ 4u
15
+ ··· + 8u + 3
c
7
, c
8
u
16
+ 4u
15
+ ··· − 6u
2
+ 1
c
12
u
16
− 4u
15
+ ··· − 6u
2
+ 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ 14y
15
+ ··· + 7y + 1
c
2
, c
5
y
16
− 6y
15
+ ··· − 9y + 1
c
3
, c
4
, c
9
c
11
y
16
+ 16y
15
+ ··· + 11y + 1
c
6
, c
10
y
16
+ 6y
15
+ ··· + 14y + 9
c
7
, c
8
, c
12
y
16
− 14y
15
+ ··· − 12y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.697088 + 0.669632I
a = 0.872141 − 0.419345I
b = 0.555602 − 0.792024I
3.31760 + 1.95723I −1.91125 − 3.50456I
u = 0.697088 − 0.669632I
a = 0.872141 + 0.419345I
b = 0.555602 + 0.792024I
3.31760 − 1.95723I −1.91125 + 3.50456I
u = −0.858913 + 0.641497I
a = 1.57955 + 0.75916I
b = 0.04461 − 1.68746I
7.46435 + 2.50164I −6.64418 − 2.34827I
u = −0.858913 − 0.641497I
a = 1.57955 − 0.75916I
b = 0.04461 + 1.68746I
7.46435 − 2.50164I −6.64418 + 2.34827I
u = −1.083430 + 0.218721I
a = 0.063889 − 1.037280I
b = −0.397891 − 0.465672I
−0.441697 − 1.082400I −2.31411 + 4.80071I
u = −1.083430 − 0.218721I
a = 0.063889 + 1.037280I
b = −0.397891 + 0.465672I
−0.441697 + 1.082400I −2.31411 − 4.80071I
u = 0.993253 + 0.639630I
a = −1.76311 + 0.05393I
b = −0.670393 − 0.715848I
2.38716 − 7.06415I −5.02024 + 8.84090I
u = 0.993253 − 0.639630I
a = −1.76311 − 0.05393I
b = −0.670393 + 0.715848I
2.38716 + 7.06415I −5.02024 − 8.84090I
u = 0.764991 + 0.200725I
a = −0.19627 − 1.80468I
b = 0.08665 − 1.47695I
5.12690 − 0.82457I −2.88269 + 8.96873I
u = 0.764991 − 0.200725I
a = −0.19627 + 1.80468I
b = 0.08665 + 1.47695I
5.12690 + 0.82457I −2.88269 − 8.96873I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.904876 + 0.830651I
a = −0.816305 − 0.414345I
b = 0.015954 + 1.301360I
11.24100 + 3.09873I 4.47651 − 2.43200I
u = −0.904876 − 0.830651I
a = −0.816305 + 0.414345I
b = 0.015954 − 1.301360I
11.24100 − 3.09873I 4.47651 + 2.43200I
u = 0.921176 + 0.893488I
a = 0.327921 − 0.754564I
b = 0.029313 + 0.666177I
8.63862 − 3.28911I −10.02068 + 3.66308I
u = 0.921176 − 0.893488I
a = 0.327921 + 0.754564I
b = 0.029313 − 0.666177I
8.63862 + 3.28911I −10.02068 − 3.66308I
u = −0.529286 + 0.266978I
a = −0.06782 + 2.71225I
b = 0.336156 − 0.719208I
1.74451 + 3.30158I 2.81664 − 9.31541I
u = −0.529286 − 0.266978I
a = −0.06782 − 2.71225I
b = 0.336156 + 0.719208I
1.74451 − 3.30158I 2.81664 + 9.31541I
20
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)
6
· (u
16
− 6u
15
+ ··· − 9u + 1)(u
27
+ 9u
26
+ ··· + 144u + 64)
c
2
((u
8
− u
7
+ ··· + 2u − 1)
6
)(u
16
− 3u
14
+ ··· − u + 1)
· (u
27
+ 7u
26
+ ··· + 44u + 8)
c
3
, c
11
(u
16
+ 8u
14
+ ··· − u + 1)(u
27
+ 4u
25
+ ··· + 3u + 1)
· (u
48
+ u
47
+ ··· − 164u + 229)
c
4
, c
9
(u
16
+ 8u
14
+ ··· + u + 1)(u
27
+ 4u
25
+ ··· + 3u + 1)
· (u
48
+ u
47
+ ··· − 164u + 229)
c
5
((u
8
− u
7
+ ··· + 2u − 1)
6
)(u
16
− 3u
14
+ ··· + u + 1)
· (u
27
+ 7u
26
+ ··· + 44u + 8)
c
6
, c
10
(u
16
+ 4u
15
+ ··· + 8u + 3)(u
27
− 2u
26
+ ··· + 10u + 1)
· (u
48
− 9u
47
+ ··· + 666u + 661)
c
7
, c
8
((u
3
− u
2
+ 1)
16
)(u
16
+ 4u
15
+ ··· − 6u
2
+ 1)
· (u
27
+ 15u
26
+ ··· + 2816u + 256)
c
12
((u
3
− u
2
+ 1)
16
)(u
16
− 4u
15
+ ··· − 6u
2
+ 1)
· (u
27
+ 15u
26
+ ··· + 2816u + 256)
21
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)
6
· (y
16
+ 14y
15
+ ··· + 7y + 1)(y
27
+ 19y
26
+ ··· − 11008y −4096)
c
2
, c
5
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
6
· (y
16
− 6y
15
+ ··· − 9y + 1)(y
27
− 9y
26
+ ··· + 144y −64)
c
3
, c
4
, c
9
c
11
(y
16
+ 16y
15
+ ··· + 11y + 1)(y
27
+ 8y
26
+ ··· − 5y −1)
· (y
48
+ 27y
47
+ ··· + 832312y + 52441)
c
6
, c
10
(y
16
+ 6y
15
+ ··· + 14y + 9)(y
27
− 18y
26
+ ··· + 116y −1)
· (y
48
+ 15y
47
+ ··· − 734396y + 436921)
c
7
, c
8
, c
12
((y
3
− y
2
+ 2y −1)
16
)(y
16
− 14y
15
+ ··· − 12y + 1)
· (y
27
− 15y
26
+ ··· + 524288y −65536)
22
