11a
215
(K11a
215
)
A knot diagram
1
Linearized knot diagam
6 1 10 11 9 2 4 5 3 8 7
Solving Sequence
2,6
7 1
3,9
10 5 8 11 4
c
6
c
1
c
2
c
9
c
5
c
8
c
11
c
4
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−29u
26
+ 175u
25
+ ··· + 4b + 156, −41u
26
+ 209u
25
+ ··· + 8a + 92, u
27
− 7u
26
+ ··· − 48u + 8i
I
u
2
= h−4.28042 × 10
21
a
5
u
8
+ 3.83114 × 10
22
a
4
u
8
+ ··· − 6.06064 × 10
22
a + 4.42208 × 10
22
,
3u
8
a
3
+ 9u
8
a
2
+ ··· − 18a − 43, u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
I
u
3
= h−u
14
+ 3u
12
− 5u
10
+ 3u
8
+ u
7
− u
6
− 2u
5
− u
4
+ 2u
3
+ b − u − 1,
u
14
− 3u
13
− 3u
12
+ 10u
11
+ 4u
10
− 17u
9
− u
8
+ 11u
7
+ u
6
− u
5
− 6u
4
− 3u
3
+ 8u
2
+ a − u − 4,
u
15
− 4u
13
+ 8u
11
− 8u
9
− u
8
+ 4u
7
+ 3u
6
− 4u
4
+ 3u
2
− 1i
* 3 irreducible components of dim
C
= 0, with total 96 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−29u
26
+ 175u
25
+ · · · + 4b + 156, −41u
26
+ 209u
25
+ · · · + 8a +
92, u
27
− 7u
26
+ · · · − 48u + 8i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
9
=
5.12500u
26
− 26.1250u
25
+ ··· + 76.5000u − 11.5000
29
4
u
26
−
175
4
u
25
+ ··· +
447
2
u − 39
a
10
=
4.12500u
26
− 26.1250u
25
+ ··· + 212.500u − 43.5000
−
3
4
u
26
+
5
4
u
25
+ ··· +
101
2
u − 13
a
5
=
6u
26
−
67
2
u
25
+ ··· + 128u −
39
2
5
2
u
26
− 17u
25
+ ··· +
345
2
u − 36
a
8
=
19
4
u
26
−
53
2
u
25
+ ··· +
321
4
u − 11
17
4
u
26
−
101
4
u
25
+ ··· + 106u − 16
a
11
=
u
3
u
5
− u
3
+ u
a
4
=
−4u
26
+
45
2
u
25
+ ··· − 76u +
25
2
3
2
u
25
−
13
2
u
24
+ ··· −
71
2
u + 8
a
4
=
−4u
26
+
45
2
u
25
+ ··· − 76u +
25
2
3
2
u
25
−
13
2
u
24
+ ··· −
71
2
u + 8
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 7u
26
− 42u
25
+ 85u
24
+ 32u
23
− 464u
22
+ 782u
21
+ 58u
20
− 2162u
19
+ 3200u
18
−
304u
17
− 5341u
16
+ 7635u
15
− 2013u
14
− 7580u
13
+ 11422u
12
− 4923u
11
− 5645u
10
+
10277u
9
− 6041u
8
− 1288u
7
+ 4988u
6
− 3826u
5
+ 1037u
4
+ 557u
3
− 655u
2
+ 276u − 46
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
27
− 7u
26
+ ··· − 48u + 8
c
2
u
27
+ 13u
26
+ ··· + 224u + 64
c
3
, c
5
, c
8
c
9
u
27
+ u
26
+ ··· + 2u + 1
c
4
, c
7
u
27
+ 3u
25
+ ··· + 3u + 1
c
10
u
27
− 27u
26
+ ··· − 7424u + 512
c
11
u
27
− 21u
26
+ ··· − 19888u + 2664
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
27
− 13y
26
+ ··· + 224y −64
c
2
y
27
− y
26
+ ··· + 2560y −4096
c
3
, c
5
, c
8
c
9
y
27
− 25y
26
+ ··· − 10y −1
c
4
, c
7
y
27
+ 6y
26
+ ··· + 3y −1
c
10
y
27
− 5y
26
+ ··· + 2424832y −262144
c
11
y
27
+ 15y
26
+ ··· + 24224224y −7096896
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.250449 + 1.038140I
a = −0.444857 − 0.280509I
b = −1.222090 + 0.179844I
−5.84917 + 1.93910I −18.8822 − 3.3310I
u = 0.250449 − 1.038140I
a = −0.444857 + 0.280509I
b = −1.222090 − 0.179844I
−5.84917 − 1.93910I −18.8822 + 3.3310I
u = 0.942577 + 0.503851I
a = −0.932522 + 0.762632I
b = −0.482241 − 0.629621I
1.12638 − 3.49850I −2.08740 + 6.42119I
u = 0.942577 − 0.503851I
a = −0.932522 − 0.762632I
b = −0.482241 + 0.629621I
1.12638 + 3.49850I −2.08740 − 6.42119I
u = 0.206067 + 0.899919I
a = 0.523648 + 0.537105I
b = 1.48683 − 0.50104I
−8.00804 + 11.41820I −8.36312 − 5.92536I
u = 0.206067 − 0.899919I
a = 0.523648 − 0.537105I
b = 1.48683 + 0.50104I
−8.00804 − 11.41820I −8.36312 + 5.92536I
u = −1.061350 + 0.298652I
a = −0.099401 + 0.688573I
b = −0.008660 + 0.493664I
−2.59299 + 0.52735I −7.52998 − 1.76243I
u = −1.061350 − 0.298652I
a = −0.099401 − 0.688573I
b = −0.008660 − 0.493664I
−2.59299 − 0.52735I −7.52998 + 1.76243I
u = 0.707332 + 0.846348I
a = −0.001548 + 0.443664I
b = −1.207210 + 0.175822I
−2.83672 + 3.13233I −8.60430 − 4.73932I
u = 0.707332 − 0.846348I
a = −0.001548 − 0.443664I
b = −1.207210 − 0.175822I
−2.83672 − 3.13233I −8.60430 + 4.73932I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.921192 + 0.733170I
a = 0.488034 − 0.960402I
b = 1.243300 + 0.306554I
−3.51361 − 8.92967I −8.84256 + 8.65936I
u = 0.921192 − 0.733170I
a = 0.488034 + 0.960402I
b = 1.243300 − 0.306554I
−3.51361 + 8.92967I −8.84256 − 8.65936I
u = 0.583614 + 0.540343I
a = −0.431550 + 0.437769I
b = 0.286435 − 0.643143I
2.16469 − 0.74717I 1.19667 + 1.31837I
u = 0.583614 − 0.540343I
a = −0.431550 − 0.437769I
b = 0.286435 + 0.643143I
2.16469 + 0.74717I 1.19667 − 1.31837I
u = 1.095640 + 0.533268I
a = 0.918975 + 0.305045I
b = 0.038720 + 0.614836I
−0.99910 − 6.61566I −2.67665 + 5.91111I
u = 1.095640 − 0.533268I
a = 0.918975 − 0.305045I
b = 0.038720 − 0.614836I
−0.99910 + 6.61566I −2.67665 − 5.91111I
u = 0.323531 + 0.655078I
a = −0.318838 − 0.202977I
b = 0.049362 + 0.615471I
1.20723 + 1.99852I 0.24096 − 2.02450I
u = 0.323531 − 0.655078I
a = −0.318838 + 0.202977I
b = 0.049362 − 0.615471I
1.20723 − 1.99852I 0.24096 + 2.02450I
u = −1.280650 + 0.313658I
a = −1.96356 − 0.72558I
b = −1.54139 − 0.41238I
−12.8060 − 7.3523I −13.07121 + 3.51912I
u = −1.280650 − 0.313658I
a = −1.96356 + 0.72558I
b = −1.54139 + 0.41238I
−12.8060 + 7.3523I −13.07121 − 3.51912I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.212520 + 0.560901I
a = −2.08232 + 1.39711I
b = −1.52806 − 0.55410I
−11.0486 − 16.7322I −11.0194 + 9.0355I
u = 1.212520 − 0.560901I
a = −2.08232 − 1.39711I
b = −1.52806 + 0.55410I
−11.0486 + 16.7322I −11.0194 − 9.0355I
u = −1.346150 + 0.244793I
a = 1.76713 + 0.21440I
b = 1.366950 + 0.073827I
−11.47790 + 2.36837I −17.5105 − 3.3278I
u = −1.346150 − 0.244793I
a = 1.76713 − 0.21440I
b = 1.366950 − 0.073827I
−11.47790 − 2.36837I −17.5105 + 3.3278I
u = −0.624607
a = −0.939222
b = −0.473047
−0.948941 −10.2360
u = 1.257530 + 0.592160I
a = 1.54642 − 1.10756I
b = 1.254580 + 0.299552I
−9.04410 − 7.78302I −15.7321 + 8.2671I
u = 1.257530 − 0.592160I
a = 1.54642 + 1.10756I
b = 1.254580 − 0.299552I
−9.04410 + 7.78302I −15.7321 − 8.2671I
7
II. I
u
2
= h−4.28 × 10
21
a
5
u
8
+ 3.83 × 10
22
a
4
u
8
+ · · · − 6.06 × 10
22
a + 4.42 ×
10
22
, 3u
8
a
3
+9u
8
a
2
+· · ·−18a−43, u
9
+u
8
−2u
7
−3u
6
+u
5
+3u
4
+2u
3
−u−1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
9
=
a
0.135799a
5
u
8
− 1.21545a
4
u
8
+ ··· + 1.92277a − 1.40293
a
10
=
−0.216342a
5
u
8
− 0.570413a
4
u
8
+ ··· + 2.96433a − 0.595647
−0.150805a
5
u
8
− 1.50492a
4
u
8
+ ··· + 3.12982a − 1.29739
a
5
=
0.159195a
5
u
8
+ 0.143153a
4
u
8
+ ··· − 0.569358a + 0.0173501
−0.0275012a
5
u
8
− 1.94896a
4
u
8
+ ··· + 1.64651a − 1.62293
a
8
=
−0.554759a
5
u
8
− 0.883326a
4
u
8
+ ··· + 3.07806a + 0.120655
0.185431a
5
u
8
+ 0.876552a
4
u
8
+ ··· + 2.54167a + 0.420697
a
11
=
u
3
u
5
− u
3
+ u
a
4
=
−0.143558a
5
u
8
− 0.394845a
4
u
8
+ ··· + 0.834495a − 0.484708
0.0732090a
5
u
8
− 1.50089a
4
u
8
+ ··· + 1.91001a − 1.77924
a
4
=
−0.143558a
5
u
8
− 0.394845a
4
u
8
+ ··· + 0.834495a − 0.484708
0.0732090a
5
u
8
− 1.50089a
4
u
8
+ ··· + 1.91001a − 1.77924
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
2195399251632745551288
4502908240731220953089
u
8
a
5
−
1658362058057093286068
4502908240731220953089
u
8
a
4
+ ··· −
3414044045562139416812
4502908240731220953089
a −
24919211764634738825954
4502908240731220953089
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
6
c
2
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
6
c
3
, c
5
, c
8
c
9
u
54
− u
53
+ ··· − 2672u − 1393
c
4
, c
7
u
54
− 3u
53
+ ··· + 946u − 229
c
10
(u
3
+ u
2
− 1)
18
c
11
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
6
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
6
c
2
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
6
c
3
, c
5
, c
8
c
9
y
54
− 45y
53
+ ··· + 8846484y + 1940449
c
4
, c
7
y
54
+ 15y
53
+ ··· + 1004868y + 52441
c
10
(y
3
− y
2
+ 2y −1)
18
c
11
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
6
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772920 + 0.510351I
a = 0.421767 − 0.926709I
b = −1.202420 + 0.401684I
−4.26482 + 2.09337I −10.50452 − 4.16283I
u = −0.772920 + 0.510351I
a = 0.358651 − 0.337314I
b = 0.168504 + 0.856224I
−0.12724 + 4.92150I −3.97525 − 7.14228I
u = −0.772920 + 0.510351I
a = −1.58358 − 0.28481I
b = −0.365320 + 0.500469I
−0.127239 − 0.734748I −3.97525 − 1.18338I
u = −0.772920 + 0.510351I
a = −0.213181 − 0.257169I
b = −0.928682 − 0.475966I
−0.127239 − 0.734748I −3.97525 − 1.18338I
u = −0.772920 + 0.510351I
a = −0.77730 + 1.65150I
b = 1.122440 + 0.149270I
−4.26482 + 2.09337I −10.50452 − 4.16283I
u = −0.772920 + 0.510351I
a = 1.16973 + 1.42641I
b = 1.065130 − 0.464824I
−0.12724 + 4.92150I −3.97525 − 7.14228I
u = −0.772920 − 0.510351I
a = 0.421767 + 0.926709I
b = −1.202420 − 0.401684I
−4.26482 − 2.09337I −10.50452 + 4.16283I
u = −0.772920 − 0.510351I
a = 0.358651 + 0.337314I
b = 0.168504 − 0.856224I
−0.12724 − 4.92150I −3.97525 + 7.14228I
u = −0.772920 − 0.510351I
a = −1.58358 + 0.28481I
b = −0.365320 − 0.500469I
−0.127239 + 0.734748I −3.97525 + 1.18338I
u = −0.772920 − 0.510351I
a = −0.213181 + 0.257169I
b = −0.928682 + 0.475966I
−0.127239 + 0.734748I −3.97525 + 1.18338I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772920 − 0.510351I
a = −0.77730 − 1.65150I
b = 1.122440 − 0.149270I
−4.26482 − 2.09337I −10.50452 + 4.16283I
u = −0.772920 − 0.510351I
a = 1.16973 − 1.42641I
b = 1.065130 + 0.464824I
−0.12724 − 4.92150I −3.97525 + 7.14228I
u = 0.825933
a = −0.99489 + 1.36802I
b = −0.850633 − 0.711452I
−3.10912 − 2.82812I −13.14259 + 2.97945I
u = 0.825933
a = −0.99489 − 1.36802I
b = −0.850633 + 0.711452I
−3.10912 + 2.82812I −13.14259 − 2.97945I
u = 0.825933
a = −1.81663
b = −1.76108
−7.24670 −19.6720
u = 0.825933
a = 1.65119 + 2.62062I
b = 0.740435 + 0.041728I
−3.10912 − 2.82812I −13.14259 + 2.97945I
u = 0.825933
a = 1.65119 − 2.62062I
b = 0.740435 − 0.041728I
−3.10912 + 2.82812I −13.14259 − 2.97945I
u = 0.825933
a = 3.55546
b = 1.46912
−7.24670 −19.6720
u = 1.173910 + 0.391555I
a = −0.569282 − 1.077620I
b = 0.474901 − 1.323300I
−6.28202 + 1.49195I −11.77434 − 2.27770I
u = 1.173910 + 0.391555I
a = 0.516921 − 0.313844I
b = −0.185503 + 0.512258I
−6.28202 − 4.16429I −11.77434 + 3.68120I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.173910 + 0.391555I
a = −2.17850 + 0.12813I
b = −1.380310 + 0.183722I
−10.41960 − 1.33617I −18.3036 + 0.7017I
u = 1.173910 + 0.391555I
a = 1.92979 − 1.47306I
b = 1.83390 − 0.60150I
−10.41960 − 1.33617I −18.3036 + 0.7017I
u = 1.173910 + 0.391555I
a = 2.47431 − 0.76430I
b = 1.315040 + 0.370548I
−6.28202 − 4.16429I −11.77434 + 3.68120I
u = 1.173910 + 0.391555I
a = −2.60969 + 1.14050I
b = −1.262020 + 0.125124I
−6.28202 + 1.49195I −11.77434 − 2.27770I
u = 1.173910 − 0.391555I
a = −0.569282 + 1.077620I
b = 0.474901 + 1.323300I
−6.28202 − 1.49195I −11.77434 + 2.27770I
u = 1.173910 − 0.391555I
a = 0.516921 + 0.313844I
b = −0.185503 − 0.512258I
−6.28202 + 4.16429I −11.77434 − 3.68120I
u = 1.173910 − 0.391555I
a = −2.17850 − 0.12813I
b = −1.380310 − 0.183722I
−10.41960 + 1.33617I −18.3036 − 0.7017I
u = 1.173910 − 0.391555I
a = 1.92979 + 1.47306I
b = 1.83390 + 0.60150I
−10.41960 + 1.33617I −18.3036 − 0.7017I
u = 1.173910 − 0.391555I
a = 2.47431 + 0.76430I
b = 1.315040 − 0.370548I
−6.28202 + 4.16429I −11.77434 − 3.68120I
u = 1.173910 − 0.391555I
a = −2.60969 − 1.14050I
b = −1.262020 − 0.125124I
−6.28202 − 1.49195I −11.77434 + 2.27770I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.141484 + 0.739668I
a = −0.557068 − 0.760680I
b = −0.100409 + 0.439662I
−2.52761 + 0.37370I −6.81817 − 0.06647I
u = −0.141484 + 0.739668I
a = −0.824663 + 0.004372I
b = −1.178650 + 0.193591I
−2.52761 + 0.37370I −6.81817 − 0.06647I
u = −0.141484 + 0.739668I
a = −0.305670 + 0.700140I
b = −1.62567 − 0.66037I
−6.66520 − 2.45442I −13.34743 + 2.91298I
u = −0.141484 + 0.739668I
a = 0.153194 + 0.618598I
b = −0.243877 − 1.275290I
−2.52761 − 5.28254I −6.81817 + 5.89242I
u = −0.141484 + 0.739668I
a = 1.39802 − 0.34488I
b = 1.252610 + 0.265598I
−2.52761 − 5.28254I −6.81817 + 5.89242I
u = −0.141484 + 0.739668I
a = 0.53019 − 1.33944I
b = 1.267560 + 0.161698I
−6.66520 − 2.45442I −13.34743 + 2.91298I
u = −0.141484 − 0.739668I
a = −0.557068 + 0.760680I
b = −0.100409 − 0.439662I
−2.52761 − 0.37370I −6.81817 + 0.06647I
u = −0.141484 − 0.739668I
a = −0.824663 − 0.004372I
b = −1.178650 − 0.193591I
−2.52761 − 0.37370I −6.81817 + 0.06647I
u = −0.141484 − 0.739668I
a = −0.305670 − 0.700140I
b = −1.62567 + 0.66037I
−6.66520 + 2.45442I −13.34743 − 2.91298I
u = −0.141484 − 0.739668I
a = 0.153194 − 0.618598I
b = −0.243877 + 1.275290I
−2.52761 + 5.28254I −6.81817 − 5.89242I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.141484 − 0.739668I
a = 1.39802 + 0.34488I
b = 1.252610 − 0.265598I
−2.52761 + 5.28254I −6.81817 − 5.89242I
u = −0.141484 − 0.739668I
a = 0.53019 + 1.33944I
b = 1.267560 − 0.161698I
−6.66520 + 2.45442I −13.34743 − 2.91298I
u = −1.172470 + 0.500383I
a = 1.35974 − 0.47536I
b = 0.21600 − 1.43941I
−5.50880 + 9.91305I −10.06705 − 8.89280I
u = −1.172470 + 0.500383I
a = −0.1039610 − 0.0108303I
b = 0.121537 + 0.653105I
−5.50880 + 4.25680I −10.06705 − 2.93390I
u = −1.172470 + 0.500383I
a = 1.80768 + 1.26186I
b = 1.324480 + 0.087624I
−5.50880 + 4.25680I −10.06705 − 2.93390I
u = −1.172470 + 0.500383I
a = −1.76757 − 1.99982I
b = −1.252120 + 0.251479I
−9.64638 + 7.08493I −16.5963 − 5.9133I
u = −1.172470 + 0.500383I
a = 2.41757 + 1.36405I
b = 1.66751 − 0.81351I
−9.64638 + 7.08493I −16.5963 − 5.9133I
u = −1.172470 + 0.500383I
a = −2.57279 − 1.25561I
b = −1.348440 + 0.274419I
−5.50880 + 9.91305I −10.06705 − 8.89280I
u = −1.172470 − 0.500383I
a = 1.35974 + 0.47536I
b = 0.21600 + 1.43941I
−5.50880 − 9.91305I −10.06705 + 8.89280I
u = −1.172470 − 0.500383I
a = −0.1039610 + 0.0108303I
b = 0.121537 − 0.653105I
−5.50880 − 4.25680I −10.06705 + 2.93390I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.172470 − 0.500383I
a = 1.80768 − 1.26186I
b = 1.324480 − 0.087624I
−5.50880 − 4.25680I −10.06705 + 2.93390I
u = −1.172470 − 0.500383I
a = −1.76757 + 1.99982I
b = −1.252120 − 0.251479I
−9.64638 − 7.08493I −16.5963 + 5.9133I
u = −1.172470 − 0.500383I
a = 2.41757 − 1.36405I
b = 1.66751 + 0.81351I
−9.64638 − 7.08493I −16.5963 + 5.9133I
u = −1.172470 − 0.500383I
a = −2.57279 + 1.25561I
b = −1.348440 − 0.274419I
−5.50880 − 9.91305I −10.06705 + 8.89280I
16
III.
I
u
3
= h−u
14
+3u
12
+· · ·+b−1, u
14
−3u
13
+· · ·+a−4, u
15
−4u
13
+· · ·+3u
2
−1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
9
=
−u
14
+ 3u
13
+ ··· + u + 4
u
14
− 3u
12
+ 5u
10
− 3u
8
− u
7
+ u
6
+ 2u
5
+ u
4
− 2u
3
+ u + 1
a
10
=
−u
14
+ 2u
13
+ ··· + u + 3
u
14
− 3u
12
+ 5u
10
− 3u
8
− u
7
+ u
6
+ 3u
5
+ u
4
− 3u
3
+ 2u + 1
a
5
=
−u
14
− 2u
13
+ ··· − 2u − 4
−2u
14
+ 7u
12
− 12u
10
+ 9u
8
+ 2u
7
− 2u
6
− 5u
5
− 2u
4
+ 5u
3
− 3u − 1
a
8
=
−2u
14
+ 7u
12
+ ··· − 2u − 1
−u
14
− u
13
+ ··· − 3u − 1
a
11
=
u
3
u
5
− u
3
+ u
a
4
=
−u
14
− 2u
13
+ ··· − 2u − 4
−2u
14
− u
13
+ ··· − 3u − 2
a
4
=
−u
14
− 2u
13
+ ··· − 2u − 4
−2u
14
− u
13
+ ··· − 3u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 11u
14
− 5u
13
− 37u
12
+ 19u
11
+ 64u
10
− 33u
9
− 47u
8
+ 13u
7
+
19u
6
+ 24u
5
− 4u
4
− 32u
3
+ 17u
2
+ 13u − 12
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 4u
13
+ 8u
11
− 8u
9
+ u
8
+ 4u
7
− 3u
6
+ 4u
4
− 3u
2
+ 1
c
2
u
15
+ 8u
14
+ ··· + 6u + 1
c
3
, c
8
u
15
− u
14
+ ··· − u + 1
c
4
, c
7
u
15
+ 2u
13
− u
12
+ 3u
11
− u
10
+ 2u
9
+ u
7
+ 2u
6
− 3u
5
+ 4u
4
+ 1
c
5
, c
9
u
15
+ u
14
+ ··· − u − 1
c
6
u
15
− 4u
13
+ 8u
11
− 8u
9
− u
8
+ 4u
7
+ 3u
6
− 4u
4
+ 3u
2
− 1
c
10
u
15
+ 4u
14
+ ··· + 2u
2
− 1
c
11
u
15
+ 4u
13
+ ··· − 6u
2
+ 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
15
− 8y
14
+ ··· + 6y −1
c
2
y
15
+ 16y
13
+ ··· + 2y −1
c
3
, c
5
, c
8
c
9
y
15
− 15y
14
+ ··· + 11y −1
c
4
, c
7
y
15
+ 4y
14
+ ··· − 8y
2
− 1
c
10
y
15
− 4y
14
+ ··· + 4y −1
c
11
y
15
+ 8y
14
+ ··· + 12y −1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.997247 + 0.392970I
a = 0.90416 − 1.35022I
b = −0.590150 − 0.441101I
−3.33424 − 0.63342I −10.18580 + 1.00493I
u = −0.997247 − 0.392970I
a = 0.90416 + 1.35022I
b = −0.590150 + 0.441101I
−3.33424 + 0.63342I −10.18580 − 1.00493I
u = −0.221545 + 0.858385I
a = 0.287931 − 0.531907I
b = 1.251610 + 0.253271I
−5.11182 − 1.76571I −6.58449 + 0.22254I
u = −0.221545 − 0.858385I
a = 0.287931 + 0.531907I
b = 1.251610 − 0.253271I
−5.11182 + 1.76571I −6.58449 − 0.22254I
u = 0.589578 + 0.609250I
a = 0.697295 − 0.761609I
b = 0.678123 − 0.259013I
−0.80356 + 2.07411I −6.98577 − 3.75045I
u = 0.589578 − 0.609250I
a = 0.697295 + 0.761609I
b = 0.678123 + 0.259013I
−0.80356 − 2.07411I −6.98577 + 3.75045I
u = 1.030730 + 0.548115I
a = −0.835539 − 0.204114I
b = −0.583449 − 0.282497I
−2.19303 − 6.66891I −10.29248 + 6.91128I
u = 1.030730 − 0.548115I
a = −0.835539 + 0.204114I
b = −0.583449 + 0.282497I
−2.19303 + 6.66891I −10.29248 − 6.91128I
u = −0.734119 + 0.278311I
a = −0.73074 + 1.98729I
b = 0.716956 − 0.485550I
−2.27700 + 3.62441I −5.96892 − 8.49008I
u = −0.734119 − 0.278311I
a = −0.73074 − 1.98729I
b = 0.716956 + 0.485550I
−2.27700 − 3.62441I −5.96892 + 8.49008I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.162560 + 0.361615I
a = −1.97304 + 0.61805I
b = −1.51291 + 0.27185I
−9.32095 − 1.76748I −10.54757 + 3.86534I
u = 1.162560 − 0.361615I
a = −1.97304 − 0.61805I
b = −1.51291 − 0.27185I
−9.32095 + 1.76748I −10.54757 − 3.86534I
u = 0.729970
a = 2.88100
b = 1.60781
−6.71059 −0.932190
u = −1.194930 + 0.516966I
a = −1.79056 − 1.34493I
b = −1.264080 + 0.439528I
−8.14772 + 6.78722I −9.96888 − 3.95233I
u = −1.194930 − 0.516966I
a = −1.79056 + 1.34493I
b = −1.264080 − 0.439528I
−8.14772 − 6.78722I −9.96888 + 3.95233I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
6
· (u
15
− 4u
13
+ 8u
11
− 8u
9
+ u
8
+ 4u
7
− 3u
6
+ 4u
4
− 3u
2
+ 1)
· (u
27
− 7u
26
+ ··· − 48u + 8)
c
2
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
6
· (u
15
+ 8u
14
+ ··· + 6u + 1)(u
27
+ 13u
26
+ ··· + 224u + 64)
c
3
, c
8
(u
15
− u
14
+ ··· − u + 1)(u
27
+ u
26
+ ··· + 2u + 1)
· (u
54
− u
53
+ ··· − 2672u − 1393)
c
4
, c
7
(u
15
+ 2u
13
− u
12
+ 3u
11
− u
10
+ 2u
9
+ u
7
+ 2u
6
− 3u
5
+ 4u
4
+ 1)
· (u
27
+ 3u
25
+ ··· + 3u + 1)(u
54
− 3u
53
+ ··· + 946u − 229)
c
5
, c
9
(u
15
+ u
14
+ ··· − u − 1)(u
27
+ u
26
+ ··· + 2u + 1)
· (u
54
− u
53
+ ··· − 2672u − 1393)
c
6
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
6
· (u
15
− 4u
13
+ 8u
11
− 8u
9
− u
8
+ 4u
7
+ 3u
6
− 4u
4
+ 3u
2
− 1)
· (u
27
− 7u
26
+ ··· − 48u + 8)
c
10
((u
3
+ u
2
− 1)
18
)(u
15
+ 4u
14
+ ··· + 2u
2
− 1)
· (u
27
− 27u
26
+ ··· − 7424u + 512)
c
11
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
6
· (u
15
+ 4u
13
+ ··· − 6u
2
+ 1)(u
27
− 21u
26
+ ··· − 19888u + 2664)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
6
· (y
15
− 8y
14
+ ··· + 6y −1)(y
27
− 13y
26
+ ··· + 224y −64)
c
2
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
6
· (y
15
+ 16y
13
+ ··· + 2y −1)(y
27
− y
26
+ ··· + 2560y −4096)
c
3
, c
5
, c
8
c
9
(y
15
− 15y
14
+ ··· + 11y −1)(y
27
− 25y
26
+ ··· − 10y −1)
· (y
54
− 45y
53
+ ··· + 8846484y + 1940449)
c
4
, c
7
(y
15
+ 4y
14
+ ··· − 8y
2
− 1)(y
27
+ 6y
26
+ ··· + 3y −1)
· (y
54
+ 15y
53
+ ··· + 1004868y + 52441)
c
10
((y
3
− y
2
+ 2y −1)
18
)(y
15
− 4y
14
+ ··· + 4y −1)
· (y
27
− 5y
26
+ ··· + 2424832y −262144)
c
11
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
6
· (y
15
+ 8y
14
+ ··· + 12y −1)
· (y
27
+ 15y
26
+ ··· + 24224224y −7096896)
23
