11a
271
(K11a
271
)
A knot diagram
1
Linearized knot diagam
10 9 1 7 2 3 11 5 6 8 4
Solving Sequence
4,11
1
3,8
7 5 6 10 2 9
c
11
c
3
c
7
c
4
c
6
c
10
c
1
c
9
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −1787419727u
22
+ 404361799u
21
+ ··· + 1141379489a − 6968741388,
u
23
+ 10u
21
+ ··· + 6u + 1i
I
u
2
= h−8.66938 × 10
235
u
81
− 4.61286 × 10
236
u
80
+ ··· + 7.40850 × 10
236
b − 6.46383 × 10
238
,
4.79729 × 10
238
u
81
+ 3.73078 × 10
239
u
80
+ ··· + 4.31916 × 10
239
a + 1.02668 × 10
242
,
u
82
+ 4u
81
+ ··· + 1581u + 583i
I
u
3
= hb + u, −2u
7
+ u
6
− 6u
5
+ u
4
− 6u
3
+ a, u
8
− u
7
+ 4u
6
− 3u
5
+ 6u
4
− 4u
3
+ 3u
2
− 2u + 1i
I
u
4
= h12u
9
− 27u
8
+ 100u
7
− 154u
6
+ 247u
5
− 252u
4
+ 225u
3
− 149u
2
+ b + 59u − 16,
− u
9
+ 3u
8
− 11u
7
+ 21u
6
− 37u
5
+ 45u
4
− 46u
3
+ 34u
2
+ a − 18u + 6,
u
10
− 3u
9
+ 10u
8
− 19u
7
+ 30u
6
− 36u
5
+ 34u
4
− 26u
3
+ 14u
2
− 5u + 1i
I
u
5
= hb + u, a − u + 1, u
2
− u + 1i
* 5 irreducible components of dim
C
= 0, with total 125 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, −1.79 × 10
9
u
22
+ 4.04 × 10
8
u
21
+ · · · + 1.14 × 10
9
a − 6.97 ×
10
9
, u
23
+ 10u
21
+ · · · + 6u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
3
=
u
u
3
+ u
a
8
=
1.56602u
22
− 0.354275u
21
+ ··· + 5.26162u + 6.10554
u
a
7
=
1.56602u
22
− 0.354275u
21
+ ··· + 6.26162u + 6.10554
u
a
5
=
−0.0100717u
22
− 0.0618659u
21
+ ··· + 9.45541u + 7.55747
0.474519u
22
+ 0.0483773u
21
+ ··· + 0.440369u − 0.354275
a
6
=
1.43020u
22
− 0.552730u
21
+ ··· + 4.93721u + 5.70289
−0.0398045u
22
+ 0.0200600u
21
+ ··· + 1.00214u − 0.204197
a
10
=
0.354275u
22
+ 0.474519u
21
+ ··· + 3.29056u + 2.56602
−u
2
a
2
=
−0.515155u
22
+ 1.53719u
21
+ ··· + 7.98960u + 2.53517
0.246833u
22
− 0.706353u
21
+ ··· − 3.61365u − 0.610339
a
9
=
−1.76578u
22
+ 0.872515u
21
+ ··· + 0.752076u − 1.55408
0.528715u
22
− 0.182288u
21
+ ··· + 0.732677u + 0.346273
a
9
=
−1.76578u
22
+ 0.872515u
21
+ ··· + 0.752076u − 1.55408
0.528715u
22
− 0.182288u
21
+ ··· + 0.732677u + 0.346273
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1113912392
1141379489
u
22
+
1733888615
1141379489
u
21
+ ··· +
15405030005
1141379489
u +
4456929967
1141379489
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
+ 22u
22
+ ··· + 7424u + 512
c
2
u
23
+ 19u
22
+ ··· − 96u − 16
c
3
, c
7
, c
10
c
11
u
23
+ 10u
21
+ ··· + 6u + 1
c
4
u
23
− 19u
22
+ ··· − 960u + 256
c
5
, c
9
u
23
− u
22
+ ··· − u + 1
c
6
, c
8
u
23
− u
22
+ ··· + 4u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
− 2y
22
+ ··· + 11599872y −262144
c
2
y
23
− 5y
22
+ ··· − 6016y −256
c
3
, c
7
, c
10
c
11
y
23
+ 20y
22
+ ··· + 20y −1
c
4
y
23
− 7y
22
+ ··· + 1011712y −65536
c
5
, c
9
y
23
− 3y
22
+ ··· − 3y −1
c
6
, c
8
y
23
− 9y
22
+ ··· + 80y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.097203 + 1.048750I
a = −0.88581 − 3.73190I
b = 0.097203 + 1.048750I
0.41923 − 7.68149I −2.73500 + 7.62634I
u = 0.097203 − 1.048750I
a = −0.88581 + 3.73190I
b = 0.097203 − 1.048750I
0.41923 + 7.68149I −2.73500 − 7.62634I
u = −0.878283 + 0.234924I
a = −0.069448 − 0.504553I
b = −0.878283 + 0.234924I
−4.00620 + 1.06800I −20.0904 − 5.7474I
u = −0.878283 − 0.234924I
a = −0.069448 + 0.504553I
b = −0.878283 − 0.234924I
−4.00620 − 1.06800I −20.0904 + 5.7474I
u = 0.832612 + 0.199739I
a = 0.269970 − 0.994841I
b = 0.832612 + 0.199739I
−4.74103 + 7.77621I −9.99957 − 4.77400I
u = 0.832612 − 0.199739I
a = 0.269970 + 0.994841I
b = 0.832612 − 0.199739I
−4.74103 − 7.77621I −9.99957 + 4.77400I
u = 0.086667 + 1.177120I
a = 0.91809 − 1.64121I
b = 0.086667 + 1.177120I
4.82355 + 1.72572I 1.86379 − 3.16589I
u = 0.086667 − 1.177120I
a = 0.91809 + 1.64121I
b = 0.086667 − 1.177120I
4.82355 − 1.72572I 1.86379 + 3.16589I
u = 0.485747 + 0.587883I
a = 0.867752 + 0.473235I
b = 0.485747 + 0.587883I
−1.41194 + 2.54862I −8.72632 − 1.31178I
u = 0.485747 − 0.587883I
a = 0.867752 − 0.473235I
b = 0.485747 − 0.587883I
−1.41194 − 2.54862I −8.72632 + 1.31178I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.332148 + 1.312160I
a = −1.15057 − 2.08899I
b = −0.332148 + 1.312160I
6.09809 + 8.12392I 3.40597 − 8.83423I
u = −0.332148 − 1.312160I
a = −1.15057 + 2.08899I
b = −0.332148 − 1.312160I
6.09809 − 8.12392I 3.40597 + 8.83423I
u = 0.33824 + 1.37393I
a = 0.69111 − 1.66289I
b = 0.33824 + 1.37393I
9.61085 − 2.02294I 3.47785 + 0.15643I
u = 0.33824 − 1.37393I
a = 0.69111 + 1.66289I
b = 0.33824 − 1.37393I
9.61085 + 2.02294I 3.47785 − 0.15643I
u = −0.25671 + 1.41656I
a = −0.16528 − 1.74879I
b = −0.25671 + 1.41656I
6.46756 + 3.72990I 2.37255 − 3.19850I
u = −0.25671 − 1.41656I
a = −0.16528 + 1.74879I
b = −0.25671 − 1.41656I
6.46756 − 3.72990I 2.37255 + 3.19850I
u = −0.50959 + 1.43123I
a = −0.44449 − 1.89615I
b = −0.50959 + 1.43123I
3.75645 + 9.55892I −6.8688 − 15.7902I
u = −0.50959 − 1.43123I
a = −0.44449 + 1.89615I
b = −0.50959 − 1.43123I
3.75645 − 9.55892I −6.8688 + 15.7902I
u = 0.56914 + 1.42280I
a = 0.59171 − 1.70238I
b = 0.56914 + 1.42280I
3.0635 − 18.7890I −2.94689 + 9.73353I
u = 0.56914 − 1.42280I
a = 0.59171 + 1.70238I
b = 0.56914 − 1.42280I
3.0635 + 18.7890I −2.94689 − 9.73353I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.329226 + 0.326454I
a = 1.012200 + 0.058405I
b = −0.329226 + 0.326454I
−0.744276 + 1.012620I −5.79242 − 5.25340I
u = −0.329226 − 0.326454I
a = 1.012200 − 0.058405I
b = −0.329226 − 0.326454I
−0.744276 − 1.012620I −5.79242 + 5.25340I
u = −0.207295
a = 5.72955
b = −0.207295
−2.25842 3.07840
7
II. I
u
2
= h−8.67 × 10
235
u
81
− 4.61 × 10
236
u
80
+ · · · + 7.41 × 10
236
b − 6.46 ×
10
238
, 4.80 × 10
238
u
81
+ 3.73 × 10
239
u
80
+ · · · + 4.32 × 10
239
a + 1.03 ×
10
242
, u
82
+ 4u
81
+ · · · + 1581u + 583i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
3
=
u
u
3
+ u
a
8
=
−0.111070u
81
− 0.863775u
80
+ ··· − 708.703u − 237.704
0.117019u
81
+ 0.622644u
80
+ ··· + 301.616u + 87.2488
a
7
=
0.00594924u
81
− 0.241131u
80
+ ··· − 407.086u − 150.455
0.117019u
81
+ 0.622644u
80
+ ··· + 301.616u + 87.2488
a
5
=
−0.219221u
81
− 1.23505u
80
+ ··· − 634.131u − 201.913
0.150861u
81
+ 0.982201u
80
+ ··· + 631.616u + 195.251
a
6
=
−0.133406u
81
− 0.938320u
80
+ ··· − 706.882u − 233.890
0.131216u
81
+ 0.674433u
80
+ ··· + 304.040u + 85.3005
a
10
=
−0.344459u
81
− 1.29164u
80
+ ··· − 52.0179u + 50.8287
0.00955082u
81
+ 0.102874u
80
+ ··· + 152.659u + 51.2985
a
2
=
−0.605273u
81
− 2.16854u
80
+ ··· + 61.9906u + 135.141
0.382816u
81
+ 1.45114u
80
+ ··· + 16.4038u − 62.7682
a
9
=
−0.344825u
81
− 1.48129u
80
+ ··· − 184.980u − 9.26806
0.138777u
81
+ 0.708851u
80
+ ··· + 267.957u + 70.7972
a
9
=
−0.344825u
81
− 1.48129u
80
+ ··· − 184.980u − 9.26806
0.138777u
81
+ 0.708851u
80
+ ··· + 267.957u + 70.7972
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.557208u
81
+ 1.61916u
80
+ ··· − 644.455u − 351.850
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
41
− 7u
40
+ ··· − 13u + 1)
2
c
2
(u
41
− 8u
40
+ ··· + 2u − 1)
2
c
3
, c
7
, c
10
c
11
u
82
+ 4u
81
+ ··· + 1581u + 583
c
4
(u
41
+ 11u
40
+ ··· + 92u + 11)
2
c
5
, c
9
u
82
− 5u
81
+ ··· + 61u + 11
c
6
, c
8
u
82
+ u
81
+ ··· − 5311u + 961
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
41
+ 11y
40
+ ··· + 9y −1)
2
c
2
(y
41
− 8y
40
+ ··· + 30y −1)
2
c
3
, c
7
, c
10
c
11
y
82
+ 58y
81
+ ··· + 8444515y + 339889
c
4
(y
41
+ 13y
40
+ ··· − 1898y −121)
2
c
5
, c
9
y
82
+ 13y
81
+ ··· + 6949y + 121
c
6
, c
8
y
82
− 31y
81
+ ··· − 8782989y + 923521
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.201433 + 0.974457I
a = −0.24847 − 2.21630I
b = −0.50859 + 1.75201I
2.07268 + 5.10749I 0
u = −0.201433 − 0.974457I
a = −0.24847 + 2.21630I
b = −0.50859 − 1.75201I
2.07268 − 5.10749I 0
u = −0.766022 + 0.674504I
a = 0.802065 + 0.258031I
b = 0.411623 − 1.052910I
0.21627 + 5.92950I 0
u = −0.766022 − 0.674504I
a = 0.802065 − 0.258031I
b = 0.411623 + 1.052910I
0.21627 − 5.92950I 0
u = 0.046473 + 1.022060I
a = 0.0453885 − 0.0654803I
b = −0.908235 + 0.579105I
−0.195730 − 0.062095I 0
u = 0.046473 − 1.022060I
a = 0.0453885 + 0.0654803I
b = −0.908235 − 0.579105I
−0.195730 + 0.062095I 0
u = 0.481687 + 0.914453I
a = −0.952194 − 0.769085I
b = 0.104564 − 0.731487I
−0.53309 − 6.66067I 0
u = 0.481687 − 0.914453I
a = −0.952194 + 0.769085I
b = 0.104564 + 0.731487I
−0.53309 + 6.66067I 0
u = −0.084502 + 0.953123I
a = 0.27716 + 3.12610I
b = −0.084502 − 0.953123I
−1.00058 0
u = −0.084502 − 0.953123I
a = 0.27716 − 3.12610I
b = −0.084502 + 0.953123I
−1.00058 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.908053 + 0.267502I
a = 0.122614 − 0.116976I
b = −0.436052 + 1.232410I
0.05211 + 4.45406I 0
u = 0.908053 − 0.267502I
a = 0.122614 + 0.116976I
b = −0.436052 − 1.232410I
0.05211 − 4.45406I 0
u = 0.356623 + 0.993352I
a = 0.318656 + 0.614201I
b = −1.239790 − 0.228596I
−1.92162 − 3.53381I 0
u = 0.356623 − 0.993352I
a = 0.318656 − 0.614201I
b = −1.239790 + 0.228596I
−1.92162 + 3.53381I 0
u = −0.908235 + 0.579105I
a = −0.0324041 − 0.0683877I
b = 0.046473 + 1.022060I
−0.195730 − 0.062095I 0
u = −0.908235 − 0.579105I
a = −0.0324041 + 0.0683877I
b = 0.046473 − 1.022060I
−0.195730 + 0.062095I 0
u = 0.068284 + 1.081370I
a = −0.96185 + 2.05879I
b = −0.42203 − 1.39285I
5.03352 − 3.32205I 0
u = 0.068284 − 1.081370I
a = −0.96185 − 2.05879I
b = −0.42203 + 1.39285I
5.03352 + 3.32205I 0
u = −0.333019 + 1.053950I
a = 0.318558 + 0.572725I
b = −0.818658 − 0.168076I
0.116913 + 1.387900I 0
u = −0.333019 − 1.053950I
a = 0.318558 − 0.572725I
b = −0.818658 + 0.168076I
0.116913 − 1.387900I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.044484 + 1.105450I
a = −0.10256 + 2.32484I
b = 0.46839 − 1.96413I
3.54374 − 4.65960I 0
u = 0.044484 − 1.105450I
a = −0.10256 − 2.32484I
b = 0.46839 + 1.96413I
3.54374 + 4.65960I 0
u = 0.133627 + 1.121670I
a = −0.10313 + 2.45385I
b = −0.49419 − 1.57359I
2.42232 − 4.46231I 0
u = 0.133627 − 1.121670I
a = −0.10313 − 2.45385I
b = −0.49419 + 1.57359I
2.42232 + 4.46231I 0
u = 0.411623 + 1.052910I
a = −0.536788 + 0.538970I
b = −0.766022 − 0.674504I
0.21627 − 5.92950I 0
u = 0.411623 − 1.052910I
a = −0.536788 − 0.538970I
b = −0.766022 + 0.674504I
0.21627 + 5.92950I 0
u = −1.124920 + 0.275824I
a = −0.110405 − 0.794266I
b = −0.461170 + 1.076770I
−1.45360 + 3.78207I 0
u = −1.124920 − 0.275824I
a = −0.110405 + 0.794266I
b = −0.461170 − 1.076770I
−1.45360 − 3.78207I 0
u = −0.818658 + 0.168076I
a = 0.796957 + 0.340759I
b = −0.333019 − 1.053950I
0.116913 − 1.387900I −6.84622 + 0.I
u = −0.818658 − 0.168076I
a = 0.796957 − 0.340759I
b = −0.333019 + 1.053950I
0.116913 + 1.387900I −6.84622 + 0.I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.538479 + 0.638550I
a = 1.065560 − 0.578549I
b = −0.039429 + 1.208320I
3.80604 + 1.84265I 2.21456 − 1.42669I
u = 0.538479 − 0.638550I
a = 1.065560 + 0.578549I
b = −0.039429 − 1.208320I
3.80604 − 1.84265I 2.21456 + 1.42669I
u = −0.461170 + 1.076770I
a = 0.561893 − 0.559451I
b = −1.124920 + 0.275824I
−1.45360 + 3.78207I 0
u = −0.461170 − 1.076770I
a = 0.561893 + 0.559451I
b = −1.124920 − 0.275824I
−1.45360 − 3.78207I 0
u = −0.807717 + 0.141453I
a = 0.769334 + 1.182630I
b = 0.510395 − 0.521903I
−3.37975 + 0.08879I −21.5224 − 1.1280I
u = −0.807717 − 0.141453I
a = 0.769334 − 1.182630I
b = 0.510395 + 0.521903I
−3.37975 − 0.08879I −21.5224 + 1.1280I
u = −0.569473 + 1.050610I
a = 0.135587 − 0.282589I
b = 0.193727 + 0.290248I
0.05619 + 2.96133I 0
u = −0.569473 − 1.050610I
a = 0.135587 + 0.282589I
b = 0.193727 − 0.290248I
0.05619 − 2.96133I 0
u = −0.039429 + 1.208320I
a = 0.279515 − 0.789725I
b = 0.538479 + 0.638550I
3.80604 + 1.84265I 0
u = −0.039429 − 1.208320I
a = 0.279515 + 0.789725I
b = 0.538479 − 0.638550I
3.80604 − 1.84265I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.000352 + 1.222750I
a = −0.431347 − 0.869500I
b = 1.142370 + 0.747319I
3.71714 + 2.02101I 0
u = −0.000352 − 1.222750I
a = −0.431347 + 0.869500I
b = 1.142370 − 0.747319I
3.71714 − 2.02101I 0
u = 0.543339 + 0.521380I
a = 0.469132 + 0.978730I
b = −0.290957 + 0.592426I
−1.39039 + 1.97007I −9.76462 − 4.48787I
u = 0.543339 − 0.521380I
a = 0.469132 − 0.978730I
b = −0.290957 − 0.592426I
−1.39039 − 1.97007I −9.76462 + 4.48787I
u = −1.239790 + 0.228596I
a = 0.310254 + 0.489196I
b = 0.356623 − 0.993352I
−1.92162 + 3.53381I 0
u = −1.239790 − 0.228596I
a = 0.310254 − 0.489196I
b = 0.356623 + 0.993352I
−1.92162 − 3.53381I 0
u = 0.104564 + 0.731487I
a = 1.70968 − 0.09004I
b = 0.481687 − 0.914453I
−0.53309 + 6.66067I −5.50818 − 4.99627I
u = 0.104564 − 0.731487I
a = 1.70968 + 0.09004I
b = 0.481687 + 0.914453I
−0.53309 − 6.66067I −5.50818 + 4.99627I
u = 0.510395 + 0.521903I
a = 0.07356 + 1.58312I
b = −0.807717 − 0.141453I
−3.37975 − 0.08879I −21.5224 + 1.1280I
u = 0.510395 − 0.521903I
a = 0.07356 − 1.58312I
b = −0.807717 + 0.141453I
−3.37975 + 0.08879I −21.5224 − 1.1280I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.277090 + 0.069235I
a = 0.128263 − 0.568984I
b = 0.442168 + 1.200420I
−1.61991 − 12.41910I 0
u = 1.277090 − 0.069235I
a = 0.128263 + 0.568984I
b = 0.442168 − 1.200420I
−1.61991 + 12.41910I 0
u = 0.442168 + 1.200420I
a = −0.471592 − 0.342980I
b = 1.277090 + 0.069235I
−1.61991 − 12.41910I 0
u = 0.442168 − 1.200420I
a = −0.471592 + 0.342980I
b = 1.277090 − 0.069235I
−1.61991 + 12.41910I 0
u = −0.436052 + 1.232410I
a = −0.0893396 − 0.0841235I
b = 0.908053 + 0.267502I
0.05211 + 4.45406I 0
u = −0.436052 − 1.232410I
a = −0.0893396 + 0.0841235I
b = 0.908053 − 0.267502I
0.05211 − 4.45406I 0
u = −0.290957 + 0.592426I
a = 1.226410 − 0.171231I
b = 0.543339 + 0.521380I
−1.39039 + 1.97007I −9.76462 − 4.48787I
u = −0.290957 − 0.592426I
a = 1.226410 + 0.171231I
b = 0.543339 − 0.521380I
−1.39039 − 1.97007I −9.76462 + 4.48787I
u = 1.142370 + 0.747319I
a = 0.440460 − 0.749568I
b = −0.000352 + 1.222750I
3.71714 + 2.02101I 0
u = 1.142370 − 0.747319I
a = 0.440460 + 0.749568I
b = −0.000352 − 1.222750I
3.71714 − 2.02101I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.156685 + 1.358810I
a = −0.101736 − 0.810141I
b = −0.402062 + 0.251568I
1.45241 + 4.98872I 0
u = −0.156685 − 1.358810I
a = −0.101736 + 0.810141I
b = −0.402062 − 0.251568I
1.45241 − 4.98872I 0
u = 0.542295 + 1.256440I
a = −0.73459 + 1.65323I
b = −0.56332 − 1.44907I
3.20535 − 9.84080I 0
u = 0.542295 − 1.256440I
a = −0.73459 − 1.65323I
b = −0.56332 + 1.44907I
3.20535 + 9.84080I 0
u = −0.27459 + 1.42022I
a = 0.24594 + 1.64727I
b = 0.68951 − 1.38477I
6.68388 + 9.32368I 0
u = −0.27459 − 1.42022I
a = 0.24594 − 1.64727I
b = 0.68951 + 1.38477I
6.68388 − 9.32368I 0
u = −0.42203 + 1.39285I
a = 1.04819 + 1.32794I
b = 0.068284 − 1.081370I
5.03352 + 3.32205I 0
u = −0.42203 − 1.39285I
a = 1.04819 − 1.32794I
b = 0.068284 + 1.081370I
5.03352 − 3.32205I 0
u = −0.402062 + 0.251568I
a = −2.00877 − 1.22876I
b = −0.156685 + 1.358810I
1.45241 + 4.98872I −4.83358 − 8.14945I
u = −0.402062 − 0.251568I
a = −2.00877 + 1.22876I
b = −0.156685 − 1.358810I
1.45241 − 4.98872I −4.83358 + 8.14945I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.68951 + 1.38477I
a = −0.63393 + 1.42256I
b = −0.27459 − 1.42022I
6.68388 − 9.32368I 0
u = 0.68951 − 1.38477I
a = −0.63393 − 1.42256I
b = −0.27459 + 1.42022I
6.68388 + 9.32368I 0
u = −0.56332 + 1.44907I
a = 0.59277 + 1.47793I
b = 0.542295 − 1.256440I
3.20535 + 9.84080I 0
u = −0.56332 − 1.44907I
a = 0.59277 − 1.47793I
b = 0.542295 + 1.256440I
3.20535 − 9.84080I 0
u = −0.49419 + 1.57359I
a = 0.37975 + 1.63862I
b = 0.133627 − 1.121670I
2.42232 + 4.46231I 0
u = −0.49419 − 1.57359I
a = 0.37975 − 1.63862I
b = 0.133627 + 1.121670I
2.42232 − 4.46231I 0
u = 0.193727 + 0.290248I
a = 1.072570 − 0.040966I
b = −0.569473 + 1.050610I
0.05619 + 2.96133I −4.67276 + 2.55942I
u = 0.193727 − 0.290248I
a = 1.072570 + 0.040966I
b = −0.569473 − 1.050610I
0.05619 − 2.96133I −4.67276 − 2.55942I
u = −0.50859 + 1.75201I
a = −0.230119 − 1.194450I
b = −0.201433 + 0.974457I
2.07268 + 5.10749I 0
u = −0.50859 − 1.75201I
a = −0.230119 + 1.194450I
b = −0.201433 − 0.974457I
2.07268 − 5.10749I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.46839 + 1.96413I
a = −0.290971 + 1.241400I
b = 0.044484 − 1.105450I
3.54374 + 4.65960I 0
u = 0.46839 − 1.96413I
a = −0.290971 − 1.241400I
b = 0.044484 + 1.105450I
3.54374 − 4.65960I 0
19
III. I
u
3
= hb + u, −2u
7
+ u
6
− 6u
5
+ u
4
− 6u
3
+ a, u
8
− u
7
+ · · · − 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
3
=
u
u
3
+ u
a
8
=
2u
7
− u
6
+ 6u
5
− u
4
+ 6u
3
−u
a
7
=
2u
7
− u
6
+ 6u
5
− u
4
+ 6u
3
− u
−u
a
5
=
−2u
7
+ 3u
6
− 7u
5
+ 7u
4
− 6u
3
+ 5u
2
+ 2u − 3
−u
7
+ u
6
− 3u
5
+ 2u
4
− 3u
3
+ u
2
+ u − 1
a
6
=
2u
7
− u
6
+ 6u
5
+ 5u
3
+ 2u
2
− 2u + 1
u
6
− u
5
+ 3u
4
− 2u
3
+ 3u
2
− 2u + 1
a
10
=
u
7
− 2u
6
+ 5u
5
− 6u
4
+ 8u
3
− 6u
2
+ 4u − 1
−u
2
a
2
=
u
7
+ u
6
+ 6u
4
− 5u
3
+ 9u
2
− 8u + 4
u
4
− u
3
+ 3u
2
− 2u + 1
a
9
=
−2u
7
+ u
6
− 6u
5
+ u
4
− 5u
3
− u
2
+ 3u − 2
−u
7
+ u
6
− 3u
5
+ u
4
− 2u
3
− u
2
+ u − 1
a
9
=
−2u
7
+ u
6
− 6u
5
+ u
4
− 5u
3
− u
2
+ 3u − 2
−u
7
+ u
6
− 3u
5
+ u
4
− 2u
3
− u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
7
+ 2u
6
+ 13u
5
+ 14u
4
+ 6u
3
+ 18u
2
− 11u − 3
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− 2u
7
+ 4u
6
+ 2u
5
+ 6u
4
− 10u
3
+ 6u
2
− 3u + 1
c
2
u
8
− 2u
7
+ u
6
+ 2u
5
− 3u
3
+ u
2
+ 3u + 1
c
3
, c
10
u
8
+ u
7
+ 4u
6
+ 3u
5
+ 6u
4
+ 4u
3
+ 3u
2
+ 2u + 1
c
4
u
8
− u
7
− u
6
+ 18u
4
− 43u
3
+ 40u
2
− 18u + 5
c
5
, c
9
u
8
+ 2u
7
+ 2u
6
+ u
5
+ 4u
4
+ 4u
3
+ u
2
+ u + 1
c
6
, c
8
u
8
+ u
7
− 2u
6
− u
5
+ 5u
4
+ 2u
3
− 5u
2
+ 4
c
7
, c
11
u
8
− u
7
+ 4u
6
− 3u
5
+ 6u
4
− 4u
3
+ 3u
2
− 2u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
+ 4y
7
+ 36y
6
+ 16y
5
+ 114y
4
− 8y
3
− 12y
2
+ 3y + 1
c
2
y
8
− 2y
7
+ 9y
6
− 14y
5
+ 28y
4
− 19y
3
+ 19y
2
− 7y + 1
c
3
, c
7
, c
10
c
11
y
8
+ 7y
7
+ 22y
6
+ 37y
5
+ 34y
4
+ 16y
3
+ 5y
2
+ 2y + 1
c
4
y
8
− 3y
7
+ 37y
6
− 42y
5
+ 218y
4
− 419y
3
+ 232y
2
+ 76y + 25
c
5
, c
9
y
8
+ 8y
6
+ y
5
+ 10y
4
− 6y
3
+ y
2
+ y + 1
c
6
, c
8
y
8
− 5y
7
+ 16y
6
− 35y
5
+ 57y
4
− 70y
3
+ 65y
2
− 40y + 16
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.269479 + 0.786257I
a = 0.66386 − 1.86952I
b = 0.269479 − 0.786257I
−0.83890 + 7.80261I −8.9851 − 11.5999I
u = −0.269479 − 0.786257I
a = 0.66386 + 1.86952I
b = 0.269479 + 0.786257I
−0.83890 − 7.80261I −8.9851 + 11.5999I
u = −0.277017 + 1.255050I
a = 0.108092 + 1.358300I
b = 0.277017 − 1.255050I
2.76768 − 3.32852I −2.54114 + 3.52732I
u = −0.277017 − 1.255050I
a = 0.108092 − 1.358300I
b = 0.277017 + 1.255050I
2.76768 + 3.32852I −2.54114 − 3.52732I
u = 0.540306 + 0.341888I
a = −0.68710 + 1.58291I
b = −0.540306 − 0.341888I
−2.72625 − 0.35304I −9.09708 + 6.47245I
u = 0.540306 − 0.341888I
a = −0.68710 − 1.58291I
b = −0.540306 + 0.341888I
−2.72625 + 0.35304I −9.09708 − 6.47245I
u = 0.50619 + 1.37378I
a = −0.58486 + 1.70906I
b = −0.50619 − 1.37378I
4.08734 − 8.79857I −1.87665 + 4.90674I
u = 0.50619 − 1.37378I
a = −0.58486 − 1.70906I
b = −0.50619 + 1.37378I
4.08734 + 8.79857I −1.87665 − 4.90674I
23
IV.
I
u
4
= h12u
9
−27u
8
+· · ·+b−16, −u
9
+3u
8
+· · ·+a+6, u
10
−3u
9
+· · ·−5u+1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
3
=
u
u
3
+ u
a
8
=
u
9
− 3u
8
+ 11u
7
− 21u
6
+ 37u
5
− 45u
4
+ 46u
3
− 34u
2
+ 18u − 6
−12u
9
+ 27u
8
+ ··· − 59u + 16
a
7
=
−11u
9
+ 24u
8
+ ··· − 41u + 10
−12u
9
+ 27u
8
+ ··· − 59u + 16
a
5
=
−15u
9
+ 33u
8
+ ··· − 57u + 14
−12u
9
+ 27u
8
+ ··· − 54u + 15
a
6
=
−9u
9
+ 19u
8
+ ··· − 26u + 6
−9u
9
+ 20u
8
+ ··· − 41u + 11
a
10
=
−3u
9
+ 5u
8
− 21u
7
+ 25u
6
− 42u
5
+ 36u
4
− 34u
3
+ 23u
2
− 8u + 4
−12u
9
+ 28u
8
+ ··· − 61u + 17
a
2
=
8u
9
− 18u
8
+ ··· + 37u − 10
17u
9
− 38u
8
+ ··· + 82u − 23
a
9
=
−13u
9
+ 31u
8
+ ··· − 74u + 20
−22u
9
+ 51u
8
+ ··· − 117u + 32
a
9
=
−13u
9
+ 31u
8
+ ··· − 74u + 20
−22u
9
+ 51u
8
+ ··· − 117u + 32
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 54u
9
− 118u
8
+ 444u
7
− 672u
6
+ 1090u
5
− 1110u
4
+ 1006u
3
− 674u
2
+ 274u − 89
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
− u
3
+ u
2
+ u − 1)
2
c
2
(u
5
+ 2u
4
− 3u
2
+ 1)
2
c
3
, c
10
u
10
+ 3u
9
+ ··· + 5u + 1
c
4
(u
5
− u
4
− u
3
+ u
2
− 1)
2
c
5
, c
9
u
10
− 2u
9
+ 3u
8
− 3u
7
+ 5u
6
− 6u
5
+ 3u
4
− 3u
3
+ 3u
2
− u + 1
c
6
, c
8
u
10
− 2u
9
− 3u
8
+ 4u
7
+ 7u
6
− u
5
− 7u
4
− 4u
3
+ 2u
2
+ 3u + 1
c
7
, c
11
u
10
− 3u
9
+ ··· − 5u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
− 2y
4
+ 3y
3
− 3y
2
+ 3y −1)
2
c
2
(y
5
− 4y
4
+ 12y
3
− 13y
2
+ 6y −1)
2
c
3
, c
7
, c
10
c
11
y
10
+ 11y
9
+ 46y
8
+ 91y
7
+ 84y
6
+ 8y
5
− 46y
4
− 24y
3
+ 4y
2
+ 3y + 1
c
4
(y
5
− 3y
4
+ 3y
3
− 3y
2
+ 2y −1)
2
c
5
, c
9
y
10
+ 2y
9
+ 7y
8
+ 3y
7
+ y
6
− 8y
5
+ 3y
4
+ 7y
3
+ 9y
2
+ 5y + 1
c
6
, c
8
y
10
− 10y
9
+ ··· − 5y + 1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.109909 + 1.074360I
a = −0.19447 − 2.65794I
b = −0.18082 + 1.92265I
3.01018 + 5.17259I 0.22749 − 12.15389I
u = −0.109909 − 1.074360I
a = −0.19447 + 2.65794I
b = −0.18082 − 1.92265I
3.01018 − 5.17259I 0.22749 + 12.15389I
u = 0.449269 + 1.114270I
a = −0.015790 + 0.270852I
b = −0.719851 − 0.020388I
−0.29233 − 3.70382I −8.25691 + 5.45417I
u = 0.449269 − 1.114270I
a = −0.015790 − 0.270852I
b = −0.719851 + 0.020388I
−0.29233 + 3.70382I −8.25691 − 5.45417I
u = 0.719851 + 0.020388I
a = −0.424674 + 0.156629I
b = −0.449269 − 1.114270I
−0.29233 − 3.70382I −8.25691 + 5.45417I
u = 0.719851 − 0.020388I
a = −0.424674 − 0.156629I
b = −0.449269 + 1.114270I
−0.29233 + 3.70382I −8.25691 − 5.45417I
u = 0.259964 + 0.489435I
a = −0.96167 + 1.81054I
b = −0.259964 + 0.489435I
−2.14584 −12.94116 + 0.I
u = 0.259964 − 0.489435I
a = −0.96167 − 1.81054I
b = −0.259964 − 0.489435I
−2.14584 −12.94116 + 0.I
u = 0.18082 + 1.92265I
a = 0.09660 − 1.48727I
b = 0.109909 + 1.074360I
3.01018 − 5.17259I 0.22749 + 12.15389I
u = 0.18082 − 1.92265I
a = 0.09660 + 1.48727I
b = 0.109909 − 1.074360I
3.01018 + 5.17259I 0.22749 − 12.15389I
27
V. I
u
5
= hb + u, a − u + 1, u
2
− u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u − 1
a
3
=
u
u − 1
a
8
=
u − 1
−u
a
7
=
−1
−u
a
5
=
−u
1
a
6
=
−1
−u
a
10
=
0
−u + 1
a
2
=
1
2u − 1
a
9
=
u − 1
−u
a
9
=
u − 1
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u − 10
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
7
, c
9
, c
11
u
2
− u + 1
c
2
(u − 1)
2
c
3
, c
10
u
2
+ u + 1
c
6
, c
8
u
2
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
7
, c
9
c
10
, c
11
y
2
+ y + 1
c
2
(y −1)
2
c
6
, c
8
y
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.500000 + 0.866025I
b = −0.500000 − 0.866025I
− 4.05977I −6.00000 + 6.92820I
u = 0.500000 − 0.866025I
a = −0.500000 − 0.866025I
b = −0.500000 + 0.866025I
4.05977I −6.00000 − 6.92820I
31
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
5
− u
3
+ u
2
+ u − 1)
2
· (u
8
− 2u
7
+ 4u
6
+ 2u
5
+ 6u
4
− 10u
3
+ 6u
2
− 3u + 1)
· (u
23
+ 22u
22
+ ··· + 7424u + 512)(u
41
− 7u
40
+ ··· − 13u + 1)
2
c
2
((u − 1)
2
)(u
5
+ 2u
4
− 3u
2
+ 1)
2
(u
8
− 2u
7
+ ··· + 3u + 1)
· (u
23
+ 19u
22
+ ··· − 96u − 16)(u
41
− 8u
40
+ ··· + 2u − 1)
2
c
3
, c
10
(u
2
+ u + 1)(u
8
+ u
7
+ 4u
6
+ 3u
5
+ 6u
4
+ 4u
3
+ 3u
2
+ 2u + 1)
· (u
10
+ 3u
9
+ ··· + 5u + 1)(u
23
+ 10u
21
+ ··· + 6u + 1)
· (u
82
+ 4u
81
+ ··· + 1581u + 583)
c
4
(u
2
− u + 1)(u
5
− u
4
− u
3
+ u
2
− 1)
2
· (u
8
− u
7
− u
6
+ 18u
4
− 43u
3
+ 40u
2
− 18u + 5)
· (u
23
− 19u
22
+ ··· − 960u + 256)(u
41
+ 11u
40
+ ··· + 92u + 11)
2
c
5
, c
9
(u
2
− u + 1)(u
8
+ 2u
7
+ 2u
6
+ u
5
+ 4u
4
+ 4u
3
+ u
2
+ u + 1)
· (u
10
− 2u
9
+ 3u
8
− 3u
7
+ 5u
6
− 6u
5
+ 3u
4
− 3u
3
+ 3u
2
− u + 1)
· (u
23
− u
22
+ ··· − u + 1)(u
82
− 5u
81
+ ··· + 61u + 11)
c
6
, c
8
u
2
(u
8
+ u
7
− 2u
6
− u
5
+ 5u
4
+ 2u
3
− 5u
2
+ 4)
· (u
10
− 2u
9
− 3u
8
+ 4u
7
+ 7u
6
− u
5
− 7u
4
− 4u
3
+ 2u
2
+ 3u + 1)
· (u
23
− u
22
+ ··· + 4u + 4)(u
82
+ u
81
+ ··· − 5311u + 961)
c
7
, c
11
(u
2
− u + 1)(u
8
− u
7
+ 4u
6
− 3u
5
+ 6u
4
− 4u
3
+ 3u
2
− 2u + 1)
· (u
10
− 3u
9
+ ··· − 5u + 1)(u
23
+ 10u
21
+ ··· + 6u + 1)
· (u
82
+ 4u
81
+ ··· + 1581u + 583)
32
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
5
− 2y
4
+ 3y
3
− 3y
2
+ 3y −1)
2
· (y
8
+ 4y
7
+ 36y
6
+ 16y
5
+ 114y
4
− 8y
3
− 12y
2
+ 3y + 1)
· (y
23
− 2y
22
+ ··· + 11599872y −262144)
· (y
41
+ 11y
40
+ ··· + 9y −1)
2
c
2
(y −1)
2
(y
5
− 4y
4
+ 12y
3
− 13y
2
+ 6y −1)
2
· (y
8
− 2y
7
+ 9y
6
− 14y
5
+ 28y
4
− 19y
3
+ 19y
2
− 7y + 1)
· (y
23
− 5y
22
+ ··· − 6016y −256)(y
41
− 8y
40
+ ··· + 30y −1)
2
c
3
, c
7
, c
10
c
11
(y
2
+ y + 1)(y
8
+ 7y
7
+ 22y
6
+ 37y
5
+ 34y
4
+ 16y
3
+ 5y
2
+ 2y + 1)
· (y
10
+ 11y
9
+ 46y
8
+ 91y
7
+ 84y
6
+ 8y
5
− 46y
4
− 24y
3
+ 4y
2
+ 3y + 1)
· (y
23
+ 20y
22
+ ··· + 20y −1)
· (y
82
+ 58y
81
+ ··· + 8444515y + 339889)
c
4
(y
2
+ y + 1)(y
5
− 3y
4
+ 3y
3
− 3y
2
+ 2y −1)
2
· (y
8
− 3y
7
+ 37y
6
− 42y
5
+ 218y
4
− 419y
3
+ 232y
2
+ 76y + 25)
· (y
23
− 7y
22
+ ··· + 1011712y −65536)
· (y
41
+ 13y
40
+ ··· − 1898y −121)
2
c
5
, c
9
(y
2
+ y + 1)(y
8
+ 8y
6
+ y
5
+ 10y
4
− 6y
3
+ y
2
+ y + 1)
· (y
10
+ 2y
9
+ 7y
8
+ 3y
7
+ y
6
− 8y
5
+ 3y
4
+ 7y
3
+ 9y
2
+ 5y + 1)
· (y
23
− 3y
22
+ ··· − 3y −1)(y
82
+ 13y
81
+ ··· + 6949y + 121)
c
6
, c
8
y
2
(y
8
− 5y
7
+ 16y
6
− 35y
5
+ 57y
4
− 70y
3
+ 65y
2
− 40y + 16)
· (y
10
− 10y
9
+ ··· − 5y + 1)(y
23
− 9y
22
+ ··· + 80y −16)
· (y
82
− 31y
81
+ ··· − 8782989y + 923521)
33
