12n
0598
(K12n
0598
)
A knot diagram
1
Linearized knot diagam
3 7 12 11 8 2 6 4 3 8 9 10
Solving Sequence
3,7
2 1 6 8
5,10
9 12 4 11
c
2
c
1
c
6
c
7
c
5
c
9
c
12
c
3
c
11
c
4
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−7u
26
+ 30u
25
+ ··· + b + 25, −17u
26
+ 93u
25
+ ··· + 4a + 113, u
27
− 5u
26
+ ··· − 21u + 4i
I
u
2
= hu
17
+ 2u
16
+ ··· + b − u, −2u
18
− 2u
17
+ ··· − a + 1, u
19
+ 2u
18
+ ··· − 2u − 1i
I
u
3
= h−u
9
+ u
8
+ u
7
− 3u
6
− u
5
+ 3u
4
− u
3
− u
2
+ b − u,
− 3u
9
+ 3u
8
+ 4u
7
− 9u
6
− 4u
5
+ 11u
4
− 6u
2
+ a − 2u + 2,
u
10
− 2u
9
+ 4u
7
− 2u
6
− 4u
5
+ 4u
4
+ u
3
− u
2
− u + 1i
I
u
4
= hu
2
a + au − u
2
+ b − u − 1, −u
2
a + a
2
− 2au + 2u
2
− a + u + 1, u
3
+ u
2
− 1i
* 4 irreducible components of dim
C
= 0, with total 81 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−7u
26
+ 30u
25
+ · · · + b + 25, −17u
26
+ 93u
25
+ · · · + 4a +
113, u
27
− 5u
26
+ · · · − 21u + 4i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
6
=
u
−u
3
+ u
a
8
=
−u
3
u
5
− u
3
+ u
a
5
=
u
5
+ u
−u
7
+ u
5
− 2u
3
+ u
a
10
=
4.25000u
26
− 23.2500u
25
+ ··· + 127.250u − 28.2500
7u
26
− 30u
25
+ ··· + 120u − 25
a
9
=
−2.75000u
26
+ 6.75000u
25
+ ··· + 7.25000u − 3.25000
7u
26
− 30u
25
+ ··· + 120u − 25
a
12
=
−
1
4
u
26
−
7
4
u
25
+ ··· +
35
4
u +
1
4
4u
26
− 17u
25
+ ··· + 56u − 11
a
4
=
23
4
u
26
−
95
4
u
25
+ ··· +
295
4
u −
55
4
4u
26
− 14u
25
+ ··· + 23u − 3
a
11
=
−3.75000u
26
+ 11.7500u
25
+ ··· − 16.7500u + 3.75000
5u
26
− 24u
25
+ ··· + 109u − 25
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 19u
26
− 78u
25
+ 60u
24
+ 252u
23
− 548u
22
− 79u
21
+ 1369u
20
− 955u
19
− 1968u
18
+
3221u
17
+ 1042u
16
− 5938u
15
+ 2926u
14
+ 5761u
13
− 7754u
12
− 727u
11
+ 8181u
10
−
4909u
9
− 3262u
8
+ 5571u
7
− 1366u
6
− 2297u
5
+ 2086u
4
− 317u
3
− 482u
2
+ 330u − 70
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u
27
+ 11u
26
+ ··· + 113u + 16
c
2
, c
6
u
27
− 5u
26
+ ··· − 21u + 4
c
3
, c
8
u
27
− u
26
+ ··· + u + 1
c
4
, c
9
u
27
+ 11u
25
+ ··· + u + 2
c
10
, c
12
u
27
− 4u
26
+ ··· + 26u + 1
c
11
u
27
− 17u
26
+ ··· + 17u − 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
27
+ 13y
26
+ ··· − 1791y −256
c
2
, c
6
y
27
− 11y
26
+ ··· + 113y −16
c
3
, c
8
y
27
+ 17y
26
+ ··· − 25y −1
c
4
, c
9
y
27
+ 22y
26
+ ··· − 51y −4
c
10
, c
12
y
27
+ 22y
26
+ ··· + 1168y −1
c
11
y
27
− 11y
26
+ ··· + 141y −4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.864243 + 0.479532I
a = −0.600429 + 0.483373I
b = 0.19687 − 1.45324I
1.57071 + 1.96220I −0.12576 − 3.74500I
u = −0.864243 − 0.479532I
a = −0.600429 − 0.483373I
b = 0.19687 + 1.45324I
1.57071 − 1.96220I −0.12576 + 3.74500I
u = 0.866868 + 0.574414I
a = 1.76716 − 0.03839I
b = 0.770838 − 0.761899I
1.97728 − 1.89599I 0.38293 + 1.93501I
u = 0.866868 − 0.574414I
a = 1.76716 + 0.03839I
b = 0.770838 + 0.761899I
1.97728 + 1.89599I 0.38293 − 1.93501I
u = 0.828720 + 0.632735I
a = −0.541336 − 1.188870I
b = −0.788115 − 0.419530I
2.08351 − 2.86910I 0.45455 + 4.55704I
u = 0.828720 − 0.632735I
a = −0.541336 + 1.188870I
b = −0.788115 + 0.419530I
2.08351 + 2.86910I 0.45455 − 4.55704I
u = 0.478338 + 0.945307I
a = −0.585812 − 1.214720I
b = −0.61991 − 1.41259I
−3.19592 + 10.10170I −2.96328 − 5.29527I
u = 0.478338 − 0.945307I
a = −0.585812 + 1.214720I
b = −0.61991 + 1.41259I
−3.19592 − 10.10170I −2.96328 + 5.29527I
u = −1.057110 + 0.305316I
a = 0.346302 − 0.328359I
b = −0.408568 + 1.012700I
−2.70927 + 0.54344I −7.65821 − 3.08033I
u = −1.057110 − 0.305316I
a = 0.346302 + 0.328359I
b = −0.408568 − 1.012700I
−2.70927 − 0.54344I −7.65821 + 3.08033I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.489865 + 0.986191I
a = −0.126436 + 0.961399I
b = −0.173783 + 1.172750I
−3.05897 − 4.78648I −4.88388 + 4.28001I
u = 0.489865 − 0.986191I
a = −0.126436 − 0.961399I
b = −0.173783 − 1.172750I
−3.05897 + 4.78648I −4.88388 − 4.28001I
u = 1.083610 + 0.532695I
a = −1.64599 − 0.83777I
b = −0.838842 + 0.861616I
−1.17518 − 6.47379I 0.54363 + 4.97870I
u = 1.083610 − 0.532695I
a = −1.64599 + 0.83777I
b = −0.838842 − 0.861616I
−1.17518 + 6.47379I 0.54363 − 4.97870I
u = −0.715640
a = 0.335339
b = −0.411723
−1.06047 −9.47740
u = −1.286490 + 0.001736I
a = −0.107348 − 0.508252I
b = 0.31892 + 1.49437I
−9.87702 + 7.48549I −8.34292 − 4.59339I
u = −1.286490 − 0.001736I
a = −0.107348 + 0.508252I
b = 0.31892 − 1.49437I
−9.87702 − 7.48549I −8.34292 + 4.59339I
u = −0.937750 + 0.894064I
a = −0.136167 + 0.040729I
b = 0.033877 − 0.391522I
8.81727 + 3.30718I 9.73232 − 0.26403I
u = −0.937750 − 0.894064I
a = −0.136167 − 0.040729I
b = 0.033877 + 0.391522I
8.81727 − 3.30718I 9.73232 + 0.26403I
u = 0.329816 + 0.609577I
a = 1.36642 + 0.69246I
b = 0.666101 + 0.693872I
0.93369 + 1.94924I 2.26750 − 2.60215I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.329816 − 0.609577I
a = 1.36642 − 0.69246I
b = 0.666101 − 0.693872I
0.93369 − 1.94924I 2.26750 + 2.60215I
u = 0.608776 + 0.305198I
a = 1.34189 − 0.96968I
b = 0.380204 − 0.410363I
1.64937 − 1.34941I 2.63194 + 5.42860I
u = 0.608776 − 0.305198I
a = 1.34189 + 0.96968I
b = 0.380204 + 0.410363I
1.64937 + 1.34941I 2.63194 − 5.42860I
u = 1.143500 + 0.680077I
a = 1.81946 + 0.18199I
b = 0.70224 − 1.53818I
−5.2490 − 16.0451I −4.81305 + 8.97986I
u = 1.143500 − 0.680077I
a = 1.81946 − 0.18199I
b = 0.70224 + 1.53818I
−5.2490 + 16.0451I −4.81305 − 8.97986I
u = 1.173910 + 0.686395I
a = −1.190380 + 0.306818I
b = −0.033969 + 1.183180I
−5.21816 − 1.33994I −6.48707 + 0.52665I
u = 1.173910 − 0.686395I
a = −1.190380 − 0.306818I
b = −0.033969 − 1.183180I
−5.21816 + 1.33994I −6.48707 − 0.52665I
7
II.
I
u
2
= hu
17
+2u
16
+· · ·+b−u, −2u
18
−2u
17
+· · ·−a+1, u
19
+2u
18
+· · ·−2u−1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
6
=
u
−u
3
+ u
a
8
=
−u
3
u
5
− u
3
+ u
a
5
=
u
5
+ u
−u
7
+ u
5
− 2u
3
+ u
a
10
=
a
−u
17
− 2u
16
+ ··· − au + u
a
9
=
u
17
+ 2u
16
+ ··· + a − u
−u
17
− 2u
16
+ ··· − au + u
a
12
=
−u
18
a + u
18
+ ··· − au − 2u
2
u
18
a + 2u
17
a + ··· − u − 1
a
4
=
−u
18
a + u
18
+ ··· + au + 3u
2
u
16
+ u
15
+ ··· + au − u
a
11
=
−u
16
+ 4u
14
+ ··· + a − 1
u
18
− 5u
16
+ ··· − au + u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
18
− 6u
17
+ 5u
16
+ 26u
15
− 2u
14
− 63u
13
− 13u
12
+ 90u
11
+
53u
10
− 93u
9
− 89u
8
+ 50u
7
+ 98u
6
− 6u
5
− 48u
4
− 18u
3
+ 7u
2
+ u + 3
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
(u
19
+ 8u
18
+ ··· − 2u + 1)
2
c
2
, c
6
(u
19
+ 2u
18
+ ··· − 2u − 1)
2
c
3
, c
8
u
38
− 2u
37
+ ··· − u + 2
c
4
, c
9
u
38
+ 14u
36
+ ··· + 1099u + 139
c
10
, c
12
u
38
+ 7u
37
+ ··· + 513u + 108
c
11
(u
19
+ 9u
18
+ ··· − 36u − 8)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
(y
19
+ 8y
18
+ ··· + 18y −1)
2
c
2
, c
6
(y
19
− 8y
18
+ ··· − 2y −1)
2
c
3
, c
8
y
38
+ 14y
36
+ ··· + 79y + 4
c
4
, c
9
y
38
+ 28y
37
+ ··· + 386251y + 19321
c
10
, c
12
y
38
+ 33y
37
+ ··· − 143289y + 11664
c
11
(y
19
− 7y
18
+ ··· + 912y −64)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.495132 + 0.903993I
a = 0.326792 − 1.156850I
b = 0.084217 − 1.225400I
−4.57497 − 2.26653I −5.53703 + 1.30901I
u = −0.495132 + 0.903993I
a = −0.198007 + 1.367670I
b = −0.45362 + 1.47333I
−4.57497 − 2.26653I −5.53703 + 1.30901I
u = −0.495132 − 0.903993I
a = 0.326792 + 1.156850I
b = 0.084217 + 1.225400I
−4.57497 + 2.26653I −5.53703 − 1.30901I
u = −0.495132 − 0.903993I
a = −0.198007 − 1.367670I
b = −0.45362 − 1.47333I
−4.57497 + 2.26653I −5.53703 − 1.30901I
u = 0.865844 + 0.312367I
a = 0.330717 + 1.227550I
b = 1.29333 + 1.02623I
−2.00068 + 2.76328I −8.14585 − 3.98933I
u = 0.865844 + 0.312367I
a = 1.60295 + 1.73808I
b = −0.202234 − 0.834328I
−2.00068 + 2.76328I −8.14585 − 3.98933I
u = 0.865844 − 0.312367I
a = 0.330717 − 1.227550I
b = 1.29333 − 1.02623I
−2.00068 − 2.76328I −8.14585 + 3.98933I
u = 0.865844 − 0.312367I
a = 1.60295 − 1.73808I
b = −0.202234 + 0.834328I
−2.00068 − 2.76328I −8.14585 + 3.98933I
u = 1.008240 + 0.438547I
a = −1.46222 − 0.04840I
b = −0.203202 − 0.259413I
−2.91274 − 5.70416I −9.32023 + 6.32015I
u = 1.008240 + 0.438547I
a = −1.71663 − 0.83269I
b = −0.77453 + 1.51432I
−2.91274 − 5.70416I −9.32023 + 6.32015I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.008240 − 0.438547I
a = −1.46222 + 0.04840I
b = −0.203202 + 0.259413I
−2.91274 + 5.70416I −9.32023 − 6.32015I
u = 1.008240 − 0.438547I
a = −1.71663 + 0.83269I
b = −0.77453 − 1.51432I
−2.91274 + 5.70416I −9.32023 − 6.32015I
u = −1.038990 + 0.393441I
a = 1.154670 − 0.111351I
b = −0.171518 + 1.354850I
−3.09652 + 0.72162I −9.47856 − 1.89123I
u = −1.038990 + 0.393441I
a = −0.579638 − 0.515808I
b = −0.198180 + 0.573068I
−3.09652 + 0.72162I −9.47856 − 1.89123I
u = −1.038990 − 0.393441I
a = 1.154670 + 0.111351I
b = −0.171518 − 1.354850I
−3.09652 − 0.72162I −9.47856 + 1.89123I
u = −1.038990 − 0.393441I
a = −0.579638 + 0.515808I
b = −0.198180 − 0.573068I
−3.09652 − 0.72162I −9.47856 + 1.89123I
u = −0.632677 + 0.606994I
a = 1.25258 − 0.71231I
b = 0.591039 − 0.989300I
1.03071 − 3.14319I 2.24359 + 4.30108I
u = −0.632677 + 0.606994I
a = −1.62772 + 1.55849I
b = −1.50531 − 0.08884I
1.03071 − 3.14319I 2.24359 + 4.30108I
u = −0.632677 − 0.606994I
a = 1.25258 + 0.71231I
b = 0.591039 + 0.989300I
1.03071 + 3.14319I 2.24359 − 4.30108I
u = −0.632677 − 0.606994I
a = −1.62772 − 1.55849I
b = −1.50531 + 0.08884I
1.03071 + 3.14319I 2.24359 − 4.30108I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.988101 + 0.580996I
a = 1.46840 − 1.05539I
b = 1.81349 + 0.22469I
−0.04803 + 7.86790I −1.22775 − 10.06274I
u = −0.988101 + 0.580996I
a = −2.10220 + 0.92508I
b = −0.557031 − 1.108630I
−0.04803 + 7.86790I −1.22775 − 10.06274I
u = −0.988101 − 0.580996I
a = 1.46840 + 1.05539I
b = 1.81349 − 0.22469I
−0.04803 − 7.86790I −1.22775 + 10.06274I
u = −0.988101 − 0.580996I
a = −2.10220 − 0.92508I
b = −0.557031 + 1.108630I
−0.04803 − 7.86790I −1.22775 + 10.06274I
u = 0.875870 + 0.775879I
a = 0.541655 − 1.082210I
b = 0.060166 − 0.657829I
4.39114 − 2.91967I −13.8851 + 7.0340I
u = 0.875870 + 0.775879I
a = 0.979790 − 0.982545I
b = −0.18315 − 1.69701I
4.39114 − 2.91967I −13.8851 + 7.0340I
u = 0.875870 − 0.775879I
a = 0.541655 + 1.082210I
b = 0.060166 + 0.657829I
4.39114 + 2.91967I −13.8851 − 7.0340I
u = 0.875870 − 0.775879I
a = 0.979790 + 0.982545I
b = −0.18315 + 1.69701I
4.39114 + 2.91967I −13.8851 − 7.0340I
u = 1.23857
a = −0.257034 + 0.567682I
b = 0.07595 − 1.57396I
−11.0179 −9.97210
u = 1.23857
a = −0.257034 − 0.567682I
b = 0.07595 + 1.57396I
−11.0179 −9.97210
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.122560 + 0.674821I
a = −1.66618 − 0.22925I
b = −0.275014 − 1.270650I
−6.49446 + 8.08492I −6.96765 − 5.83653I
u = −1.122560 + 0.674821I
a = 1.70523 + 0.07261I
b = 0.54278 + 1.65806I
−6.49446 + 8.08492I −6.96765 − 5.83653I
u = −1.122560 − 0.674821I
a = −1.66618 + 0.22925I
b = −0.275014 + 1.270650I
−6.49446 − 8.08492I −6.96765 + 5.83653I
u = −1.122560 − 0.674821I
a = 1.70523 − 0.07261I
b = 0.54278 − 1.65806I
−6.49446 − 8.08492I −6.96765 + 5.83653I
u = −0.091769 + 0.494960I
a = 1.20013 − 0.93318I
b = −0.411060 + 0.279588I
−0.52471 + 2.63664I −2.19536 − 2.28037I
u = −0.091769 + 0.494960I
a = 1.04671 + 1.38130I
b = 0.473887 + 1.101510I
−0.52471 + 2.63664I −2.19536 − 2.28037I
u = −0.091769 − 0.494960I
a = 1.20013 + 0.93318I
b = −0.411060 − 0.279588I
−0.52471 − 2.63664I −2.19536 + 2.28037I
u = −0.091769 − 0.494960I
a = 1.04671 − 1.38130I
b = 0.473887 − 1.101510I
−0.52471 − 2.63664I −2.19536 + 2.28037I
14
III.
I
u
3
= h−u
9
+ u
8
+ · · · + b − u, −3u
9
+ 3u
8
+ · · · + a + 2, u
10
− 2u
9
+ · · · − u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
6
=
u
−u
3
+ u
a
8
=
−u
3
u
5
− u
3
+ u
a
5
=
u
5
+ u
−u
7
+ u
5
− 2u
3
+ u
a
10
=
3u
9
− 3u
8
− 4u
7
+ 9u
6
+ 4u
5
− 11u
4
+ 6u
2
+ 2u − 2
u
9
− u
8
− u
7
+ 3u
6
+ u
5
− 3u
4
+ u
3
+ u
2
+ u
a
9
=
2u
9
− 2u
8
− 3u
7
+ 6u
6
+ 3u
5
− 8u
4
− u
3
+ 5u
2
+ u − 2
u
9
− u
8
− u
7
+ 3u
6
+ u
5
− 3u
4
+ u
3
+ u
2
+ u
a
12
=
u
9
− 2u
8
+ 5u
6
− 2u
5
− 5u
4
+ 5u
3
+ 2u
2
− u − 1
−u
8
+ u
7
+ u
6
− 2u
5
− u
4
+ 2u
3
− 1
a
4
=
−u
9
+ 2u
8
+ u
7
− 5u
6
+ u
5
+ 7u
4
− 3u
3
− 4u
2
+ u + 2
−u
9
+ 2u
8
− 4u
6
+ 2u
5
+ 4u
4
− 3u
3
− u
2
+ 1
a
11
=
2u
9
− 3u
8
− 2u
7
+ 7u
6
+ u
5
− 9u
4
+ u
3
+ 5u
2
+ u − 2
u
9
− u
8
− u
7
+ 3u
6
+ u
5
− 3u
4
+ u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7u
9
+ 14u
8
+ 3u
7
− 27u
6
+ 9u
5
+ 30u
4
− 13u
3
− 7u
2
− 3u + 5
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
10
− 4u
9
+ ··· − 3u + 1
c
2
u
10
− 2u
9
+ 4u
7
− 2u
6
− 4u
5
+ 4u
4
+ u
3
− u
2
− u + 1
c
3
, c
8
u
10
+ u
9
+ 3u
8
+ 2u
7
+ 3u
6
+ u
5
+ 3u
4
+ u
3
+ u
2
+ 1
c
4
, c
9
u
10
+ u
8
+ u
7
+ 3u
6
+ u
5
+ 3u
4
+ 2u
3
+ 3u
2
+ u + 1
c
6
u
10
+ 2u
9
− 4u
7
− 2u
6
+ 4u
5
+ 4u
4
− u
3
− u
2
+ u + 1
c
7
u
10
+ 4u
9
+ ··· + 3u + 1
c
10
, c
12
u
10
+ 2u
9
+ 7u
8
+ 11u
7
+ 19u
6
+ 21u
5
+ 23u
4
+ 18u
3
+ 11u
2
+ 5u + 1
c
11
u
10
+ 12u
9
+ ··· + 553u + 119
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
10
+ 8y
9
+ ··· + 13y + 1
c
2
, c
6
y
10
− 4y
9
+ ··· − 3y + 1
c
3
, c
8
y
10
+ 5y
9
+ 11y
8
+ 18y
7
+ 23y
6
+ 21y
5
+ 19y
4
+ 11y
3
+ 7y
2
+ 2y + 1
c
4
, c
9
y
10
+ 2y
9
+ 7y
8
+ 11y
7
+ 19y
6
+ 21y
5
+ 23y
4
+ 18y
3
+ 11y
2
+ 5y + 1
c
10
, c
12
y
10
+ 10y
9
+ ··· − 3y + 1
c
11
y
10
− 4y
9
+ ··· − 10213y + 14161
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.032960 + 0.512793I
a = −1.97942 − 0.87039I
b = −0.928863 + 0.882694I
−1.82490 − 7.04514I −7.00691 + 10.78410I
u = 1.032960 − 0.512793I
a = −1.97942 + 0.87039I
b = −0.928863 − 0.882694I
−1.82490 + 7.04514I −7.00691 − 10.78410I
u = −1.081750 + 0.414901I
a = 0.399098 − 0.224008I
b = −0.536015 + 0.989716I
−2.42349 − 0.47280I −4.11542 + 3.42753I
u = −1.081750 − 0.414901I
a = 0.399098 + 0.224008I
b = −0.536015 − 0.989716I
−2.42349 + 0.47280I −4.11542 − 3.42753I
u = 0.620721 + 0.483253I
a = 1.37337 + 1.79298I
b = 0.853256 + 0.680596I
−0.43993 + 2.89386I −3.51583 − 3.73185I
u = 0.620721 − 0.483253I
a = 1.37337 − 1.79298I
b = 0.853256 − 0.680596I
−0.43993 − 2.89386I −3.51583 + 3.73185I
u = −0.517593 + 0.494789I
a = 0.307549 − 0.733697I
b = 0.572538 + 0.706393I
−0.42431 + 4.26902I −1.71632 − 7.11667I
u = −0.517593 − 0.494789I
a = 0.307549 + 0.733697I
b = 0.572538 − 0.706393I
−0.42431 − 4.26902I −1.71632 + 7.11667I
u = 0.945660 + 0.933377I
a = 0.399398 − 0.395934I
b = 0.039085 − 0.697555I
8.40249 − 3.42159I −8.64553 + 4.94639I
u = 0.945660 − 0.933377I
a = 0.399398 + 0.395934I
b = 0.039085 + 0.697555I
8.40249 + 3.42159I −8.64553 − 4.94639I
18
IV.
I
u
4
= hu
2
a + au− u
2
+b −u − 1, −u
2
a + a
2
−2au +2u
2
−a +u + 1, u
3
+u
2
−1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
6
=
u
u
2
+ u − 1
a
8
=
u
2
− 1
u
2
a
5
=
1
0
a
10
=
a
−u
2
a − au + u
2
+ u + 1
a
9
=
u
2
a + au − u
2
+ a − u − 1
−u
2
a − au + u
2
+ u + 1
a
12
=
−u
2
+ a + 1
−u
2
a − au + u + 1
a
4
=
−2u
2
a − au + u
2
− a + 4u + 2
au − 2
a
11
=
−u
2
+ a + 1
−u
2
a − au + u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
2
− 9u + 6
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
3
, c
4
, c
8
c
9
u
6
+ u
5
+ 5u
4
+ 3u
3
+ 5u
2
+ u + 1
c
6
(u
3
− u
2
+ 1)
2
c
7
(u
3
+ u
2
+ 2u + 1)
2
c
10
, c
12
(u − 1)
6
c
11
u
6
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
6
(y
3
− y
2
+ 2y −1)
2
c
3
, c
4
, c
8
c
9
y
6
+ 9y
5
+ 29y
4
+ 41y
3
+ 29y
2
+ 9y + 1
c
10
, c
12
(y −1)
6
c
11
y
6
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0.565646 + 1.180490I
b = 0.048539 + 0.537677I
4.66906 + 2.82812I 12.60647 + 1.13909I
u = −0.877439 + 0.744862I
a = −1.10544 − 0.99790I
b = 0.16654 − 1.84482I
4.66906 + 2.82812I 12.60647 + 1.13909I
u = −0.877439 − 0.744862I
a = 0.565646 − 1.180490I
b = 0.048539 − 0.537677I
4.66906 − 2.82812I 12.60647 − 1.13909I
u = −0.877439 − 0.744862I
a = −1.10544 + 0.99790I
b = 0.16654 + 1.84482I
4.66906 − 2.82812I 12.60647 − 1.13909I
u = 0.754878
a = 1.53980 + 0.72359I
b = 0.284920 − 0.958551I
0.531480 −4.21290
u = 0.754878
a = 1.53980 − 0.72359I
b = 0.284920 + 0.958551I
0.531480 −4.21290
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
((u
3
− u
2
+ 2u − 1)
2
)(u
10
− 4u
9
+ ··· − 3u + 1)
· ((u
19
+ 8u
18
+ ··· − 2u + 1)
2
)(u
27
+ 11u
26
+ ··· + 113u + 16)
c
2
(u
3
+ u
2
− 1)
2
(u
10
− 2u
9
+ 4u
7
− 2u
6
− 4u
5
+ 4u
4
+ u
3
− u
2
− u + 1)
· ((u
19
+ 2u
18
+ ··· − 2u − 1)
2
)(u
27
− 5u
26
+ ··· − 21u + 4)
c
3
, c
8
(u
6
+ u
5
+ 5u
4
+ 3u
3
+ 5u
2
+ u + 1)
· (u
10
+ u
9
+ 3u
8
+ 2u
7
+ 3u
6
+ u
5
+ 3u
4
+ u
3
+ u
2
+ 1)
· (u
27
− u
26
+ ··· + u + 1)(u
38
− 2u
37
+ ··· − u + 2)
c
4
, c
9
(u
6
+ u
5
+ 5u
4
+ 3u
3
+ 5u
2
+ u + 1)
· (u
10
+ u
8
+ u
7
+ 3u
6
+ u
5
+ 3u
4
+ 2u
3
+ 3u
2
+ u + 1)
· (u
27
+ 11u
25
+ ··· + u + 2)(u
38
+ 14u
36
+ ··· + 1099u + 139)
c
6
(u
3
− u
2
+ 1)
2
(u
10
+ 2u
9
− 4u
7
− 2u
6
+ 4u
5
+ 4u
4
− u
3
− u
2
+ u + 1)
· ((u
19
+ 2u
18
+ ··· − 2u − 1)
2
)(u
27
− 5u
26
+ ··· − 21u + 4)
c
7
((u
3
+ u
2
+ 2u + 1)
2
)(u
10
+ 4u
9
+ ··· + 3u + 1)
· ((u
19
+ 8u
18
+ ··· − 2u + 1)
2
)(u
27
+ 11u
26
+ ··· + 113u + 16)
c
10
, c
12
(u − 1)
6
· (u
10
+ 2u
9
+ 7u
8
+ 11u
7
+ 19u
6
+ 21u
5
+ 23u
4
+ 18u
3
+ 11u
2
+ 5u + 1)
· (u
27
− 4u
26
+ ··· + 26u + 1)(u
38
+ 7u
37
+ ··· + 513u + 108)
c
11
u
6
(u
10
+ 12u
9
+ ··· + 553u + 119)(u
19
+ 9u
18
+ ··· − 36u − 8)
2
· (u
27
− 17u
26
+ ··· + 17u − 2)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
((y
3
+ 3y
2
+ 2y −1)
2
)(y
10
+ 8y
9
+ ··· + 13y + 1)
· ((y
19
+ 8y
18
+ ··· + 18y −1)
2
)(y
27
+ 13y
26
+ ··· − 1791y −256)
c
2
, c
6
((y
3
− y
2
+ 2y −1)
2
)(y
10
− 4y
9
+ ··· − 3y + 1)
· ((y
19
− 8y
18
+ ··· − 2y −1)
2
)(y
27
− 11y
26
+ ··· + 113y −16)
c
3
, c
8
(y
6
+ 9y
5
+ 29y
4
+ 41y
3
+ 29y
2
+ 9y + 1)
· (y
10
+ 5y
9
+ 11y
8
+ 18y
7
+ 23y
6
+ 21y
5
+ 19y
4
+ 11y
3
+ 7y
2
+ 2y + 1)
· (y
27
+ 17y
26
+ ··· − 25y −1)(y
38
+ 14y
36
+ ··· + 79y + 4)
c
4
, c
9
(y
6
+ 9y
5
+ 29y
4
+ 41y
3
+ 29y
2
+ 9y + 1)
· (y
10
+ 2y
9
+ 7y
8
+ 11y
7
+ 19y
6
+ 21y
5
+ 23y
4
+ 18y
3
+ 11y
2
+ 5y + 1)
· (y
27
+ 22y
26
+ ··· − 51y −4)(y
38
+ 28y
37
+ ··· + 386251y + 19321)
c
10
, c
12
((y −1)
6
)(y
10
+ 10y
9
+ ··· − 3y + 1)(y
27
+ 22y
26
+ ··· + 1168y −1)
· (y
38
+ 33y
37
+ ··· − 143289y + 11664)
c
11
y
6
(y
10
− 4y
9
+ ··· − 10213y + 14161)
· ((y
19
− 7y
18
+ ··· + 912y −64)
2
)(y
27
− 11y
26
+ ··· + 141y −4)
24
