12n
0860
(K12n
0860
)
A knot diagram
1
Linearized knot diagam
4 6 9 8 11 3 5 1 2 5 6 7
Solving Sequence
3,6 7,11
12 1 2 5 8 4 10 9
c
6
c
11
c
12
c
2
c
5
c
7
c
4
c
10
c
9
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hb + u, −6573198u
24
− 7407745u
23
+ ··· + 830359a − 20171003, u
25
− 6u
23
+ ··· + 10u
2
− 1i
I
u
2
= h4.04286 × 10
177
u
71
− 1.22456 × 10
178
u
70
+ ··· + 1.03797 × 10
179
b + 1.12104 × 10
180
,
2.07451 × 10
180
u
71
− 5.60040 × 10
180
u
70
+ ··· + 6.92329 × 10
181
a + 4.53244 × 10
182
,
u
72
− 2u
71
+ ··· + 3115u + 667i
I
u
3
= hb + u, 3u
13
− u
12
− 10u
11
+ 7u
10
+ 16u
9
− 21u
8
− 13u
7
+ 31u
6
− 7u
5
− 19u
4
+ 17u
3
− 2u
2
+ a − 3u + 3,
u
14
− 4u
12
+ u
11
+ 8u
10
− 5u
9
− 10u
8
+ 10u
7
+ 5u
6
− 10u
5
+ 2u
4
+ 4u
3
− 2u
2
+ 1i
I
u
4
= hu
11
− u
10
− 4u
9
+ 5u
8
+ 5u
7
− 9u
6
− 3u
5
+ 9u
4
+ 5u
3
− 5u
2
+ b − 4u + 1,
− 8u
11
+ 3u
10
+ 34u
9
− 20u
8
− 51u
7
+ 43u
6
+ 45u
5
− 44u
4
− 61u
3
+ a + 28u + 8,
u
12
− u
11
− 4u
10
+ 5u
9
+ 5u
8
− 9u
7
− 3u
6
+ 9u
5
+ 5u
4
− 5u
3
− 4u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 123 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
= hb + u, −6.57 × 10
6
u
24
− 7.41 × 10
6
u
23
+ · · · + 8.30 × 10
5
a − 2.02 ×
10
7
, u
25
− 6u
23
+ · · · + 10u
2
− 1i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
11
=
7.91609u
24
+ 8.92114u
23
+ ··· + 10.3907u + 24.2919
−u
a
12
=
7.91609u
24
+ 8.92114u
23
+ ··· + 9.39074u + 24.2919
−u
a
1
=
3.56601u
24
+ 5.57186u
23
+ ··· + 2.47465u + 15.3708
1.95267u
24
+ 1.21283u
23
+ ··· + 3.35008u + 3.34927
a
2
=
−u
u
a
5
=
−8.92114u
24
− 4.35008u
23
+ ··· − 24.2919u − 6.91609
u
2
a
8
=
−3.94984u
24
− 1.36141u
23
+ ··· − 15.3813u − 3.39671
−1.21283u
24
− 0.779766u
23
+ ··· − 3.34927u − 1.95267
a
4
=
−0.533909u
24
+ 2.27446u
23
+ ··· − 10.2048u + 7.37157
1.04484u
24
+ 0.684652u
23
+ ··· + 1.56683u + 1.02792
a
10
=
3.56601u
24
+ 5.57186u
23
+ ··· + 3.47465u + 15.3708
u
3
− u
a
9
=
1.16861u
24
+ 3.43542u
23
+ ··· − 0.0913593u + 9.79891
2.39741u
24
+ 2.13644u
23
+ ··· + 2.56601u + 5.57186
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
22412
830359
u
24
+
3732748
830359
u
23
+ ··· −
3546046
830359
u +
19755477
830359
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
25
− u
24
+ ··· + 2u − 1
c
2
, c
5
, c
6
c
10
, c
11
u
25
− 6u
23
+ ··· + 10u
2
− 1
c
3
u
25
− 18u
24
+ ··· − 144u + 32
c
4
, c
7
u
25
− 15u
24
+ ··· + 864u − 64
c
9
u
25
− u
24
+ ··· + u − 1
c
12
u
25
+ u
24
+ ··· + 48u − 19
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
25
+ 3y
24
+ ··· − 18y −1
c
2
, c
5
, c
6
c
10
, c
11
y
25
− 12y
24
+ ··· + 20y −1
c
3
y
25
+ 8y
24
+ ··· + 28416y −1024
c
4
, c
7
y
25
+ 19y
24
+ ··· + 9216y −4096
c
9
y
25
+ 7y
24
+ ··· − 11y −1
c
12
y
25
+ 9y
24
+ ··· + 860y −361
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.04100
a = 1.37005
b = −1.04100
2.22466 3.28160
u = −0.988163 + 0.354424I
a = −0.606149 − 1.059700I
b = 0.988163 − 0.354424I
7.43769 + 2.03575I 10.09013 + 0.83711I
u = −0.988163 − 0.354424I
a = −0.606149 + 1.059700I
b = 0.988163 + 0.354424I
7.43769 − 2.03575I 10.09013 − 0.83711I
u = −1.064740 + 0.110709I
a = −2.02955 + 0.79466I
b = 1.064740 − 0.110709I
5.86298 − 2.94895I 8.99062 + 3.88971I
u = −1.064740 − 0.110709I
a = −2.02955 − 0.79466I
b = 1.064740 + 0.110709I
5.86298 + 2.94895I 8.99062 − 3.88971I
u = 0.773294 + 0.776856I
a = 0.399881 − 0.058553I
b = −0.773294 − 0.776856I
2.95958 + 3.45034I 20.3542 + 1.7595I
u = 0.773294 − 0.776856I
a = 0.399881 + 0.058553I
b = −0.773294 + 0.776856I
2.95958 − 3.45034I 20.3542 − 1.7595I
u = −0.701802 + 0.884948I
a = −1.189240 − 0.493880I
b = 0.701802 − 0.884948I
−1.69441 + 5.16318I 2.00598 − 2.40163I
u = −0.701802 − 0.884948I
a = −1.189240 + 0.493880I
b = 0.701802 + 0.884948I
−1.69441 − 5.16318I 2.00598 + 2.40163I
u = 0.926391 + 0.732700I
a = 1.176220 − 0.249303I
b = −0.926391 − 0.732700I
0.74727 + 1.79853I 6.90577 + 1.84258I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.926391 − 0.732700I
a = 1.176220 + 0.249303I
b = −0.926391 + 0.732700I
0.74727 − 1.79853I 6.90577 − 1.84258I
u = 0.968203 + 0.709190I
a = 1.83876 − 0.47348I
b = −0.968203 − 0.709190I
−3.63929 + 1.05448I 1.231686 − 0.208690I
u = 0.968203 − 0.709190I
a = 1.83876 + 0.47348I
b = −0.968203 + 0.709190I
−3.63929 − 1.05448I 1.231686 + 0.208690I
u = 0.661030 + 0.060128I
a = 1.12111 − 4.60091I
b = −0.661030 − 0.060128I
4.19613 − 4.91912I 7.66633 − 1.97464I
u = 0.661030 − 0.060128I
a = 1.12111 + 4.60091I
b = −0.661030 + 0.060128I
4.19613 + 4.91912I 7.66633 + 1.97464I
u = −1.102000 + 0.839497I
a = −1.332340 − 0.405431I
b = 1.102000 − 0.839497I
−2.91779 − 11.36900I 2.13618 + 9.01386I
u = −1.102000 − 0.839497I
a = −1.332340 + 0.405431I
b = 1.102000 + 0.839497I
−2.91779 + 11.36900I 2.13618 − 9.01386I
u = −1.205760 + 0.684622I
a = −1.78051 − 0.40770I
b = 1.205760 − 0.684622I
3.10788 − 9.77200I 8.73131 + 8.65125I
u = −1.205760 − 0.684622I
a = −1.78051 + 0.40770I
b = 1.205760 + 0.684622I
3.10788 + 9.77200I 8.73131 − 8.65125I
u = 0.440634 + 0.404637I
a = 0.806981 + 0.033453I
b = −0.440634 − 0.404637I
0.941070 + 0.845446I 6.47361 − 3.95819I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.440634 − 0.404637I
a = 0.806981 − 0.033453I
b = −0.440634 + 0.404637I
0.941070 − 0.845446I 6.47361 + 3.95819I
u = 1.21789 + 0.78084I
a = 1.65813 − 0.60616I
b = −1.21789 − 0.78084I
1.4999 + 18.1479I 5.42967 − 9.83817I
u = 1.21789 − 0.78084I
a = 1.65813 + 0.60616I
b = −1.21789 + 0.78084I
1.4999 − 18.1479I 5.42967 + 9.83817I
u = −0.445487 + 0.066130I
a = −0.74831 + 2.96157I
b = 0.445487 − 0.066130I
−0.69655 − 2.56141I 7.34373 + 3.13996I
u = −0.445487 − 0.066130I
a = −0.74831 − 2.96157I
b = 0.445487 + 0.066130I
−0.69655 + 2.56141I 7.34373 − 3.13996I
7
II. I
u
2
= h4.04 × 10
177
u
71
− 1.22 × 10
178
u
70
+ · · · + 1.04 × 10
179
b + 1.12 ×
10
180
, 2.07 × 10
180
u
71
− 5.60 × 10
180
u
70
+ · · · + 6.92 × 10
181
a + 4.53 ×
10
182
, u
72
− 2u
71
+ · · · + 3115u + 667i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
11
=
−0.0299642u
71
+ 0.0808921u
70
+ ··· − 54.0865u − 6.54665
−0.0389495u
71
+ 0.117976u
70
+ ··· − 102.322u − 10.8003
a
12
=
−0.0689137u
71
+ 0.198868u
70
+ ··· − 156.409u − 17.3469
−0.0389495u
71
+ 0.117976u
70
+ ··· − 102.322u − 10.8003
a
1
=
0.0188809u
71
− 0.0488389u
70
+ ··· + 90.0890u + 34.1673
−0.0889634u
71
+ 0.252754u
70
+ ··· − 268.409u − 58.9026
a
2
=
−u
u
a
5
=
−0.0651825u
71
+ 0.179180u
70
+ ··· − 242.727u − 67.7837
0.166790u
71
− 0.453094u
70
+ ··· + 527.156u + 147.002
a
8
=
−0.223937u
71
+ 0.596286u
70
+ ··· − 698.688u − 227.960
0.0455790u
71
− 0.143310u
70
+ ··· + 99.0482u + 32.3226
a
4
=
0.330004u
71
− 0.827582u
70
+ ··· + 1170.44u + 406.804
−0.379833u
71
+ 0.967703u
70
+ ··· − 1316.74u − 456.659
a
10
=
−0.251947u
71
+ 0.675384u
70
+ ··· − 830.082u − 256.511
0.222661u
71
− 0.588650u
70
+ ··· + 758.415u + 259.668
a
9
=
−0.238360u
71
+ 0.640195u
70
+ ··· − 761.894u − 237.727
0.209074u
71
− 0.553461u
70
+ ··· + 690.227u + 240.885
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.391897u
71
− 1.05190u
70
+ ··· + 1236.46u + 477.192
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
72
− 3u
71
+ ··· − 82u + 11
c
2
, c
5
, c
6
c
10
, c
11
u
72
− 2u
71
+ ··· + 3115u + 667
c
3
(u
36
+ 8u
35
+ ··· + 7u + 1)
2
c
4
, c
7
(u
36
+ 5u
35
+ ··· + 28u + 16)
2
c
9
u
72
− 3u
71
+ ··· + 88969u + 14521
c
12
u
72
− 3u
71
+ ··· − 2021932u + 128729
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
72
+ 13y
71
+ ··· + 1064y + 121
c
2
, c
5
, c
6
c
10
, c
11
y
72
− 26y
71
+ ··· − 11424085y + 444889
c
3
(y
36
+ 6y
35
+ ··· + 21y + 1)
2
c
4
, c
7
(y
36
+ 23y
35
+ ··· + 3856y + 256)
2
c
9
y
72
+ 17y
71
+ ··· − 2734709623y + 210859441
c
12
y
72
− 47y
71
+ ··· + 403916111712y + 16571155441
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.293202 + 0.951655I
a = 0.481565 + 0.249611I
b = −0.838778 − 0.744988I
0.48370 + 3.80390I 4.85781 − 6.80392I
u = −0.293202 − 0.951655I
a = 0.481565 − 0.249611I
b = −0.838778 + 0.744988I
0.48370 − 3.80390I 4.85781 + 6.80392I
u = 0.890259 + 0.409075I
a = −1.97398 + 0.49040I
b = 1.56186 − 0.03250I
7.34403 + 6.98740I 7.55942 − 8.82435I
u = 0.890259 − 0.409075I
a = −1.97398 − 0.49040I
b = 1.56186 + 0.03250I
7.34403 − 6.98740I 7.55942 + 8.82435I
u = 1.027250 + 0.164771I
a = −0.300916 + 1.323190I
b = 0.612382 + 0.594068I
5.85322 + 5.89280I 8.66037 − 8.10595I
u = 1.027250 − 0.164771I
a = −0.300916 − 1.323190I
b = 0.612382 − 0.594068I
5.85322 − 5.89280I 8.66037 + 8.10595I
u = −0.771348 + 0.704911I
a = 0.363589 + 0.021793I
b = 0.256284 + 1.024750I
−2.86714 − 2.24037I −6.49145 + 0.I
u = −0.771348 − 0.704911I
a = 0.363589 − 0.021793I
b = 0.256284 − 1.024750I
−2.86714 + 2.24037I −6.49145 + 0.I
u = 0.672916 + 0.810395I
a = 0.379223 − 0.353553I
b = −1.103690 + 0.782639I
−0.59000 − 3.03841I 0
u = 0.672916 − 0.810395I
a = 0.379223 + 0.353553I
b = −1.103690 − 0.782639I
−0.59000 + 3.03841I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.256284 + 1.024750I
a = −0.152002 + 0.326686I
b = 0.771348 + 0.704911I
−2.86714 + 2.24037I −6.49145 + 0.I
u = −0.256284 − 1.024750I
a = −0.152002 − 0.326686I
b = 0.771348 − 0.704911I
−2.86714 − 2.24037I −6.49145 + 0.I
u = 0.531576 + 0.763888I
a = −1.13923 + 1.17739I
b = 0.941625 + 0.640917I
−2.34237 + 2.97268I −3.52902 + 0.65034I
u = 0.531576 − 0.763888I
a = −1.13923 − 1.17739I
b = 0.941625 − 0.640917I
−2.34237 − 2.97268I −3.52902 − 0.65034I
u = −0.885695 + 0.609764I
a = 0.087958 − 0.863959I
b = 0.747538 + 0.983352I
−1.119130 + 0.584051I 0
u = −0.885695 − 0.609764I
a = 0.087958 + 0.863959I
b = 0.747538 − 0.983352I
−1.119130 − 0.584051I 0
u = 0.787960 + 0.744009I
a = −0.357461 + 0.311061I
b = 0.704662 − 1.077400I
−4.19566 + 4.49488I 0
u = 0.787960 − 0.744009I
a = −0.357461 − 0.311061I
b = 0.704662 + 1.077400I
−4.19566 − 4.49488I 0
u = −0.907072 + 0.627082I
a = 1.34405 + 0.65566I
b = −1.058510 + 0.908441I
−1.01674 − 5.40026I 0
u = −0.907072 − 0.627082I
a = 1.34405 − 0.65566I
b = −1.058510 − 0.908441I
−1.01674 + 5.40026I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.862186 + 0.187093I
a = −2.96882 + 0.09371I
b = 1.352310 − 0.151982I
6.63312 − 2.62155I 8.92614 + 3.90011I
u = −0.862186 − 0.187093I
a = −2.96882 − 0.09371I
b = 1.352310 + 0.151982I
6.63312 + 2.62155I 8.92614 − 3.90011I
u = 0.838778 + 0.744988I
a = −0.024461 + 0.480843I
b = 0.293202 − 0.951655I
0.48370 + 3.80390I 0
u = 0.838778 − 0.744988I
a = −0.024461 − 0.480843I
b = 0.293202 + 0.951655I
0.48370 − 3.80390I 0
u = 0.364630 + 1.071780I
a = −0.078780 + 0.321315I
b = 0.474680 + 0.069349I
−0.78509 + 3.12879I 0
u = 0.364630 − 1.071780I
a = −0.078780 − 0.321315I
b = 0.474680 − 0.069349I
−0.78509 − 3.12879I 0
u = 0.959342 + 0.613115I
a = −0.174877 + 1.288700I
b = 0.625453 − 0.136024I
3.84875 + 1.88710I 0
u = 0.959342 − 0.613115I
a = −0.174877 − 1.288700I
b = 0.625453 + 0.136024I
3.84875 − 1.88710I 0
u = −0.941625 + 0.640917I
a = 1.212970 + 0.566092I
b = −0.531576 + 0.763888I
−2.34237 − 2.97268I 0
u = −0.941625 − 0.640917I
a = 1.212970 − 0.566092I
b = −0.531576 − 0.763888I
−2.34237 + 2.97268I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.612382 + 0.594068I
a = −0.62536 + 1.53198I
b = −1.027250 + 0.164771I
5.85322 − 5.89280I 8.66037 + 8.10595I
u = −0.612382 − 0.594068I
a = −0.62536 − 1.53198I
b = −1.027250 − 0.164771I
5.85322 + 5.89280I 8.66037 − 8.10595I
u = 0.636856 + 0.544293I
a = −0.071506 − 0.131213I
b = −0.791953 + 1.119880I
−1.91320 − 1.84212I −3.44243 − 5.52826I
u = 0.636856 − 0.544293I
a = −0.071506 + 0.131213I
b = −0.791953 − 1.119880I
−1.91320 + 1.84212I −3.44243 + 5.52826I
u = 1.062770 + 0.507679I
a = −2.09378 + 0.51230I
b = 0.956860 + 0.881818I
−0.51407 + 6.14300I 0
u = 1.062770 − 0.507679I
a = −2.09378 − 0.51230I
b = 0.956860 − 0.881818I
−0.51407 − 6.14300I 0
u = 0.724136 + 0.357495I
a = 2.73817 − 1.26087I
b = −1.46519 + 0.13406I
6.72657 − 3.75562I 6.73637 + 0.95271I
u = 0.724136 − 0.357495I
a = 2.73817 + 1.26087I
b = −1.46519 − 0.13406I
6.72657 + 3.75562I 6.73637 − 0.95271I
u = −0.747538 + 0.983352I
a = −0.747664 + 0.111862I
b = 0.885695 + 0.609764I
−1.119130 − 0.584051I 0
u = −0.747538 − 0.983352I
a = −0.747664 − 0.111862I
b = 0.885695 − 0.609764I
−1.119130 + 0.584051I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.017220 + 0.717548I
a = −1.76664 + 0.88939I
b = 1.33238 + 0.73343I
0.44819 + 8.78228I 0
u = 1.017220 − 0.717548I
a = −1.76664 − 0.88939I
b = 1.33238 − 0.73343I
0.44819 − 8.78228I 0
u = 0.522514 + 1.148640I
a = −0.460106 + 0.085403I
b = 1.027380 − 0.764780I
−0.70110 − 11.26830I 0
u = 0.522514 − 1.148640I
a = −0.460106 − 0.085403I
b = 1.027380 + 0.764780I
−0.70110 + 11.26830I 0
u = −0.721923 + 0.108877I
a = 2.19903 + 0.06047I
b = −1.57929 − 0.32171I
6.09105 + 1.33098I 24.1529 + 1.8328I
u = −0.721923 − 0.108877I
a = 2.19903 − 0.06047I
b = −1.57929 + 0.32171I
6.09105 − 1.33098I 24.1529 − 1.8328I
u = −1.027380 + 0.764780I
a = −0.013580 + 0.460866I
b = −0.522514 − 1.148640I
−0.70110 − 11.26830I 0
u = −1.027380 − 0.764780I
a = −0.013580 − 0.460866I
b = −0.522514 + 1.148640I
−0.70110 + 11.26830I 0
u = −0.704662 + 1.077400I
a = 0.204603 + 0.342419I
b = −0.787960 − 0.744009I
−4.19566 + 4.49488I 0
u = −0.704662 − 1.077400I
a = 0.204603 − 0.342419I
b = −0.787960 + 0.744009I
−4.19566 − 4.49488I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.956860 + 0.881818I
a = 1.67455 + 1.00133I
b = −1.062770 + 0.507679I
−0.51407 − 6.14300I 0
u = −0.956860 − 0.881818I
a = 1.67455 − 1.00133I
b = −1.062770 − 0.507679I
−0.51407 + 6.14300I 0
u = 1.103690 + 0.782639I
a = 0.296915 − 0.273434I
b = −0.672916 + 0.810395I
−0.59000 + 3.03841I 0
u = 1.103690 − 0.782639I
a = 0.296915 + 0.273434I
b = −0.672916 − 0.810395I
−0.59000 − 3.03841I 0
u = −0.625453 + 0.136024I
a = 1.83722 − 1.40567I
b = −0.959342 − 0.613115I
3.84875 + 1.88710I 7.66826 − 3.81200I
u = −0.625453 − 0.136024I
a = 1.83722 + 1.40567I
b = −0.959342 + 0.613115I
3.84875 − 1.88710I 7.66826 + 3.81200I
u = −1.352310 + 0.151982I
a = −1.90862 + 0.25598I
b = 0.862186 − 0.187093I
6.63312 − 2.62155I 0
u = −1.352310 − 0.151982I
a = −1.90862 − 0.25598I
b = 0.862186 + 0.187093I
6.63312 + 2.62155I 0
u = 0.791953 + 1.119880I
a = 0.0838039 + 0.0361554I
b = −0.636856 + 0.544293I
−1.91320 + 1.84212I 0
u = 0.791953 − 1.119880I
a = 0.0838039 − 0.0361554I
b = −0.636856 − 0.544293I
−1.91320 − 1.84212I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.058510 + 0.908441I
a = −1.002760 + 0.626210I
b = 0.907072 + 0.627082I
−1.01674 + 5.40026I 0
u = 1.058510 − 0.908441I
a = −1.002760 − 0.626210I
b = 0.907072 − 0.627082I
−1.01674 − 5.40026I 0
u = 1.46519 + 0.13406I
a = 1.64306 − 0.19527I
b = −0.724136 + 0.357495I
6.72657 + 3.75562I 0
u = 1.46519 − 0.13406I
a = 1.64306 + 0.19527I
b = −0.724136 − 0.357495I
6.72657 − 3.75562I 0
u = −0.474680 + 0.069349I
a = 0.759723 + 0.179938I
b = −0.364630 + 1.071780I
−0.78509 − 3.12879I 11.00723 + 7.07943I
u = −0.474680 − 0.069349I
a = 0.759723 − 0.179938I
b = −0.364630 − 1.071780I
−0.78509 + 3.12879I 11.00723 − 7.07943I
u = −1.33238 + 0.73343I
a = 1.51778 + 0.56308I
b = −1.017220 + 0.717548I
0.44819 − 8.78228I 0
u = −1.33238 − 0.73343I
a = 1.51778 − 0.56308I
b = −1.017220 − 0.717548I
0.44819 + 8.78228I 0
u = −1.56186 + 0.03250I
a = 1.248130 + 0.263462I
b = −0.890259 − 0.409075I
7.34403 + 6.98740I 0
u = −1.56186 − 0.03250I
a = 1.248130 − 0.263462I
b = −0.890259 + 0.409075I
7.34403 − 6.98740I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.57929 + 0.32171I
a = −0.944923 + 0.316441I
b = 0.721923 − 0.108877I
6.09105 + 1.33098I 0
u = 1.57929 − 0.32171I
a = −0.944923 − 0.316441I
b = 0.721923 + 0.108877I
6.09105 − 1.33098I 0
18
III. I
u
3
= hb + u, 3u
13
− u
12
+ · · · + a + 3, u
14
− 4u
12
+ · · · − 2u
2
+ 1i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
11
=
−3u
13
+ u
12
+ ··· + 3u − 3
−u
a
12
=
−3u
13
+ u
12
+ ··· + 2u − 3
−u
a
1
=
−u
13
+ u
12
+ ··· + 3u
2
− 2
−u
13
+ 4u
11
− u
10
− 8u
9
+ 4u
8
+ 9u
7
− 8u
6
− 4u
5
+ 7u
4
− 2u
3
− u
2
+ u
a
2
=
−u
u
a
5
=
−u
13
+ 2u
12
+ ··· + 3u − 2
u
2
a
8
=
−u
10
− u
9
+ 3u
8
+ 2u
7
− 5u
6
− u
5
+ 6u
4
− 2u
3
− 2u
2
+ 3u − 1
u
9
+ u
8
− 2u
7
− 2u
6
+ 3u
5
+ u
4
− 3u
3
− u
2
− 1
a
4
=
2u
13
− 8u
11
+ ··· + 3u
2
− 2u
−u
13
− u
12
+ ··· − 2u
2
+ 2
a
10
=
−u
13
+ u
12
+ ··· + u − 2
u
3
− u
a
9
=
u
12
− 4u
10
+ 7u
8
− 2u
7
− 7u
6
+ 5u
5
+ 2u
4
− 4u
3
+ 3u
2
− 1
−u
13
+ 3u
11
− u
10
− 4u
9
+ 5u
8
+ 3u
7
− 8u
6
+ 3u
5
+ 5u
4
− 5u
3
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
−u
13
−12u
12
+5u
11
+44u
10
−20u
9
−80u
8
+59u
7
+86u
6
−95u
5
−25u
4
+73u
3
−27u
2
−16u+16
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
14
− u
13
+ ··· + 2u + 1
c
2
, c
5
u
14
− 4u
12
+ ··· − 2u
2
+ 1
c
3
u
14
− 5u
13
+ ··· − u + 1
c
4
u
14
− 2u
13
+ ··· + 7u
2
+ 1
c
6
, c
10
, c
11
u
14
− 4u
12
+ ··· − 2u
2
+ 1
c
7
u
14
+ 2u
13
+ ··· + 7u
2
+ 1
c
9
u
14
− u
13
+ ··· − 7u + 11
c
12
u
14
− u
13
+ ··· + 8u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
14
+ 3y
13
+ ··· + 2y + 1
c
2
, c
5
, c
6
c
10
, c
11
y
14
− 8y
13
+ ··· − 4y + 1
c
3
y
14
+ 7y
13
+ ··· + 5y + 1
c
4
, c
7
y
14
+ 16y
13
+ ··· + 14y + 1
c
9
y
14
+ 7y
13
+ ··· − 49y + 121
c
12
y
14
+ 9y
13
+ ··· + 12y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.708277 + 0.722829I
a = 0.178329 − 0.109327I
b = −0.708277 − 0.722829I
2.72350 + 3.66484I 1.0131 − 14.4704I
u = 0.708277 − 0.722829I
a = 0.178329 + 0.109327I
b = −0.708277 + 0.722829I
2.72350 − 3.66484I 1.0131 + 14.4704I
u = 0.814344 + 0.673833I
a = 1.28756 − 0.95732I
b = −0.814344 − 0.673833I
−1.72140 + 3.73975I 2.94829 − 5.83540I
u = 0.814344 − 0.673833I
a = 1.28756 + 0.95732I
b = −0.814344 + 0.673833I
−1.72140 − 3.73975I 2.94829 + 5.83540I
u = 1.217880 + 0.073388I
a = 1.62471 − 0.75115I
b = −1.217880 − 0.073388I
9.36722 + 5.19181I 12.06860 − 4.05955I
u = 1.217880 − 0.073388I
a = 1.62471 + 0.75115I
b = −1.217880 + 0.073388I
9.36722 − 5.19181I 12.06860 + 4.05955I
u = −1.241600 + 0.157386I
a = −1.97682 + 0.18018I
b = 1.241600 − 0.157386I
8.18724 − 2.78178I 15.1987 + 3.1820I
u = −1.241600 − 0.157386I
a = −1.97682 − 0.18018I
b = 1.241600 + 0.157386I
8.18724 + 2.78178I 15.1987 − 3.1820I
u = 0.274211 + 0.619417I
a = −0.442465 − 0.523132I
b = −0.274211 − 0.619417I
−1.59972 + 3.03409I −2.76274 − 6.66173I
u = 0.274211 − 0.619417I
a = −0.442465 + 0.523132I
b = −0.274211 + 0.619417I
−1.59972 − 3.03409I −2.76274 + 6.66173I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.638514 + 0.206273I
a = 0.49153 − 4.07653I
b = 0.638514 − 0.206273I
4.02966 − 5.46995I 2.98891 + 10.63955I
u = −0.638514 − 0.206273I
a = 0.49153 + 4.07653I
b = 0.638514 + 0.206273I
4.02966 + 5.46995I 2.98891 − 10.63955I
u = −1.134600 + 0.725892I
a = −1.66284 − 0.72296I
b = 1.134600 − 0.725892I
0.39766 − 7.80430I 4.54523 + 4.46826I
u = −1.134600 − 0.725892I
a = −1.66284 + 0.72296I
b = 1.134600 + 0.725892I
0.39766 + 7.80430I 4.54523 − 4.46826I
23
IV.
I
u
4
= hu
11
−u
10
+· · · +b + 1, −8u
11
+3u
10
+· · · +a + 8, u
12
−u
11
+· · · +u + 1i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
11
=
8u
11
− 3u
10
+ ··· − 28u − 8
−u
11
+ u
10
+ 4u
9
− 5u
8
− 5u
7
+ 9u
6
+ 3u
5
− 9u
4
− 5u
3
+ 5u
2
+ 4u − 1
a
12
=
7u
11
− 2u
10
+ ··· − 24u − 9
−u
11
+ u
10
+ 4u
9
− 5u
8
− 5u
7
+ 9u
6
+ 3u
5
− 9u
4
− 5u
3
+ 5u
2
+ 4u − 1
a
1
=
5u
11
− 3u
10
+ ··· − 16u − 3
2u
10
− 2u
9
− 6u
8
+ 7u
7
+ 6u
6
− 10u
5
− 5u
4
+ 10u
3
+ 9u
2
− u − 4
a
2
=
−u
u
a
5
=
8u
11
− 35u
9
+ ··· − 32u − 19
u
11
− 2u
10
− 3u
9
+ 9u
8
− 14u
6
+ 6u
5
+ 12u
4
− 4u
3
− 10u
2
+ u + 5
a
8
=
−15u
11
+ 11u
10
+ ··· + 32u + 6
12u
11
− 9u
10
+ ··· − 27u − 5
a
4
=
−10u
11
+ 9u
10
+ ··· + 19u + 2
5u
11
− 6u
10
+ ··· − 7u + 2
a
10
=
−11u
11
+ 8u
10
+ ··· + 27u + 5
4u
11
− 5u
10
+ ··· − 6u + 3
a
9
=
−7u
11
+ 6u
10
+ ··· + 16u + 1
−3u
10
+ 2u
9
+ ··· + 5u + 7
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 17u
11
+ 2u
10
− 73u
9
+ 3u
8
+ 127u
7
− 31u
6
− 145u
5
+ 46u
4
+ 175u
3
+ 67u
2
− 59u − 37
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
12
+ 3u
10
+ ··· − 2u + 1
c
2
, c
5
u
12
+ u
11
+ ··· − u + 1
c
3
(u
6
+ 3u
5
+ 5u
4
+ 3u
3
+ u
2
+ 1)
2
c
4
(u
6
+ u
5
+ 3u
4
+ u
3
+ 3u
2
+ 2)
2
c
6
, c
10
, c
11
u
12
− u
11
+ ··· + u + 1
c
7
(u
6
− u
5
+ 3u
4
− u
3
+ 3u
2
+ 2)
2
c
9
u
12
+ 6u
11
+ ··· − u + 1
c
12
u
12
− u
10
+ ··· − 26u + 7
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
12
+ 6y
11
+ ··· + 12y + 1
c
2
, c
5
, c
6
c
10
, c
11
y
12
− 9y
11
+ ··· − 9y + 1
c
3
(y
6
+ y
5
+ 9y
4
+ 3y
3
+ 11y
2
+ 2y + 1)
2
c
4
, c
7
(y
6
+ 5y
5
+ 13y
4
+ 21y
3
+ 21y
2
+ 12y + 4)
2
c
9
y
12
+ 2y
11
+ ··· + 17y + 1
c
12
y
12
− 2y
11
+ ··· − 340y + 49
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.507030 + 0.603459I
a = −0.162698 + 0.225256I
b = −0.816155 − 0.971374I
−1.63995 + 2.38212I 2.11510 − 6.09550I
u = −0.507030 − 0.603459I
a = −0.162698 − 0.225256I
b = −0.816155 + 0.971374I
−1.63995 − 2.38212I 2.11510 + 6.09550I
u = 0.816155 + 0.971374I
a = −0.155267 − 0.075441I
b = 0.507030 − 0.603459I
−1.63995 + 2.38212I 2.11510 − 6.09550I
u = 0.816155 − 0.971374I
a = −0.155267 + 0.075441I
b = 0.507030 + 0.603459I
−1.63995 − 2.38212I 2.11510 + 6.09550I
u = 0.727681 + 0.027817I
a = −2.92386 + 1.92438I
b = 1.372220 − 0.052457I
7.35953 − 4.74338I 11.87983 + 6.62323I
u = 0.727681 − 0.027817I
a = −2.92386 − 1.92438I
b = 1.372220 + 0.052457I
7.35953 + 4.74338I 11.87983 − 6.62323I
u = −0.644125 + 0.143028I
a = 2.71167 + 0.13099I
b = −1.47954 − 0.32853I
5.79496 + 1.44331I 0.00507 − 5.15575I
u = −0.644125 − 0.143028I
a = 2.71167 − 0.13099I
b = −1.47954 + 0.32853I
5.79496 − 1.44331I 0.00507 + 5.15575I
u = −1.372220 + 0.052457I
a = 1.62389 − 0.89914I
b = −0.727681 − 0.027817I
7.35953 − 4.74338I 11.87983 + 6.62323I
u = −1.372220 − 0.052457I
a = 1.62389 + 0.89914I
b = −0.727681 + 0.027817I
7.35953 + 4.74338I 11.87983 − 6.62323I
27
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.47954 + 0.32853I
a = −1.093730 + 0.447972I
b = 0.644125 − 0.143028I
5.79496 + 1.44331I 0.00507 − 5.15575I
u = 1.47954 − 0.32853I
a = −1.093730 − 0.447972I
b = 0.644125 + 0.143028I
5.79496 − 1.44331I 0.00507 + 5.15575I
28
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
12
+ 3u
10
+ ··· − 2u + 1)(u
14
− u
13
+ ··· + 2u + 1)
· (u
25
− u
24
+ ··· + 2u − 1)(u
72
− 3u
71
+ ··· − 82u + 11)
c
2
, c
5
(u
12
+ u
11
+ ··· − u + 1)(u
14
− 4u
12
+ ··· − 2u
2
+ 1)
· (u
25
− 6u
23
+ ··· + 10u
2
− 1)(u
72
− 2u
71
+ ··· + 3115u + 667)
c
3
((u
6
+ 3u
5
+ 5u
4
+ 3u
3
+ u
2
+ 1)
2
)(u
14
− 5u
13
+ ··· − u + 1)
· (u
25
− 18u
24
+ ··· − 144u + 32)(u
36
+ 8u
35
+ ··· + 7u + 1)
2
c
4
((u
6
+ u
5
+ 3u
4
+ u
3
+ 3u
2
+ 2)
2
)(u
14
− 2u
13
+ ··· + 7u
2
+ 1)
· (u
25
− 15u
24
+ ··· + 864u − 64)(u
36
+ 5u
35
+ ··· + 28u + 16)
2
c
6
, c
10
, c
11
(u
12
− u
11
+ ··· + u + 1)(u
14
− 4u
12
+ ··· − 2u
2
+ 1)
· (u
25
− 6u
23
+ ··· + 10u
2
− 1)(u
72
− 2u
71
+ ··· + 3115u + 667)
c
7
((u
6
− u
5
+ 3u
4
− u
3
+ 3u
2
+ 2)
2
)(u
14
+ 2u
13
+ ··· + 7u
2
+ 1)
· (u
25
− 15u
24
+ ··· + 864u − 64)(u
36
+ 5u
35
+ ··· + 28u + 16)
2
c
9
(u
12
+ 6u
11
+ ··· − u + 1)(u
14
− u
13
+ ··· − 7u + 11)
· (u
25
− u
24
+ ··· + u − 1)(u
72
− 3u
71
+ ··· + 88969u + 14521)
c
12
(u
12
− u
10
+ ··· − 26u + 7)(u
14
− u
13
+ ··· + 8u + 1)
· (u
25
+ u
24
+ ··· + 48u − 19)(u
72
− 3u
71
+ ··· − 2021932u + 128729)
29
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
12
+ 6y
11
+ ··· + 12y + 1)(y
14
+ 3y
13
+ ··· + 2y + 1)
· (y
25
+ 3y
24
+ ··· − 18y −1)(y
72
+ 13y
71
+ ··· + 1064y + 121)
c
2
, c
5
, c
6
c
10
, c
11
(y
12
− 9y
11
+ ··· − 9y + 1)(y
14
− 8y
13
+ ··· − 4y + 1)
· (y
25
− 12y
24
+ ··· + 20y −1)
· (y
72
− 26y
71
+ ··· − 11424085y + 444889)
c
3
((y
6
+ y
5
+ ··· + 2y + 1)
2
)(y
14
+ 7y
13
+ ··· + 5y + 1)
· (y
25
+ 8y
24
+ ··· + 28416y −1024)(y
36
+ 6y
35
+ ··· + 21y + 1)
2
c
4
, c
7
(y
6
+ 5y
5
+ 13y
4
+ 21y
3
+ 21y
2
+ 12y + 4)
2
· (y
14
+ 16y
13
+ ··· + 14y + 1)(y
25
+ 19y
24
+ ··· + 9216y −4096)
· (y
36
+ 23y
35
+ ··· + 3856y + 256)
2
c
9
(y
12
+ 2y
11
+ ··· + 17y + 1)(y
14
+ 7y
13
+ ··· − 49y + 121)
· (y
25
+ 7y
24
+ ··· − 11y −1)
· (y
72
+ 17y
71
+ ··· − 2734709623y + 210859441)
c
12
(y
12
− 2y
11
+ ··· − 340y + 49)(y
14
+ 9y
13
+ ··· + 12y + 1)
· (y
25
+ 9y
24
+ ··· + 860y −361)
· (y
72
− 47y
71
+ ··· + 403916111712y + 16571155441)
30
