11a
314
(K11a
314
)
A knot diagram
1
Linearized knot diagam
9 6 1 10 11 2 5 3 4 7 8
Solving Sequence
2,7
6
3,11
5 8 10 4 9 1
c
6
c
2
c
5
c
7
c
10
c
4
c
9
c
1
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h8.61471 × 10
40
u
35
− 1.83411 × 10
41
u
34
+ ··· + 5.25231 × 10
41
b − 3.70395 × 10
41
,
2.23742 × 10
42
u
35
− 7.36115 × 10
42
u
34
+ ··· + 1.10299 × 10
43
a − 4.47196 × 10
43
, u
36
− 3u
35
+ ··· − 41u + 8i
I
u
2
= h−2.43055 × 10
20
au
32
+ 6.47281 × 10
20
u
32
+ ··· − 3.83637 × 10
20
a − 8.61406 × 10
20
,
4.95038 × 10
20
au
32
− 3.49948 × 10
20
u
32
+ ··· + 5.33454 × 10
20
a + 1.26914 × 10
21
, u
33
+ u
32
+ ··· − 2u − 1i
I
u
3
= hu
5
a − 3u
4
a − 4u
5
+ 4u
3
a + 3u
4
− 2u
2
a − 13u
3
+ 8u
2
+ 3b − a − 12u + 1,
21u
5
a + 19u
5
+ 63u
3
a − 23u
4
+ 14u
2
a + 72u
3
+ 7a
2
+ 42au − 67u
2
+ 56a + 80u − 20,
u
6
− u
5
+ 4u
4
− 3u
3
+ 5u
2
− u + 1i
I
u
4
= h−u
3
− 2u
2
+ b − 2u − 1, u
4
+ u
3
+ a − u − 2, u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 119 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
=
h8.61×10
40
u
35
−1.83×10
41
u
34
+· · ·+5.25×10
41
b−3.70×10
41
, 2.24×10
42
u
35
−
7.36 × 10
42
u
34
+ · · · + 1.10 × 10
43
a − 4.47 × 10
43
, u
36
− 3u
35
+ · · · − 41u + 8i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−u
2
a
3
=
−u
u
3
+ u
a
11
=
−0.202851u
35
+ 0.667384u
34
+ ··· − 15.2882u + 4.05441
−0.164017u
35
+ 0.349200u
34
+ ··· − 2.46540u + 0.705203
a
5
=
−0.105569u
35
+ 0.356434u
34
+ ··· − 12.7501u + 5.10427
−0.226388u
35
+ 0.544294u
34
+ ··· − 6.01564u + 1.25342
a
8
=
0.00692985u
35
− 0.108881u
34
+ ··· + 5.10249u + 0.776589
0.0935874u
35
− 0.140600u
34
+ ··· − 2.26813u + 1.29025
a
10
=
−0.0388338u
35
+ 0.318184u
34
+ ··· − 12.8228u + 3.34921
−0.164017u
35
+ 0.349200u
34
+ ··· − 2.46540u + 0.705203
a
4
=
−0.103938u
35
+ 0.595414u
34
+ ··· − 24.0552u + 7.44471
−0.283599u
35
+ 0.624540u
34
+ ··· − 3.18323u − 0.831508
a
9
=
−0.0881504u
35
+ 0.100434u
34
+ ··· + 3.42966u + 1.14876
0.201683u
35
− 0.426849u
34
+ ··· + 1.75702u + 0.310670
a
1
=
0.396588u
35
− 0.858030u
34
+ ··· + 4.64230u − 0.696871
−0.354176u
35
+ 0.932845u
34
+ ··· − 16.5994u + 2.94258
a
1
=
0.396588u
35
− 0.858030u
34
+ ··· + 4.64230u − 0.696871
−0.354176u
35
+ 0.932845u
34
+ ··· − 16.5994u + 2.94258
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.705642u
35
− 1.36959u
34
+ ··· − 2.37672u + 0.386803
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
36
+ 2u
35
+ ··· − 144u − 14
c
2
, c
6
u
36
+ 3u
35
+ ··· + 41u + 8
c
3
, c
7
u
36
− u
35
+ ··· + u − 7
c
4
, c
9
7(7u
36
− 27u
35
+ ··· − 32u − 64)
c
5
, c
8
7(7u
36
− 6u
35
+ ··· − 4u + 1)
c
11
u
36
+ 6u
35
+ ··· − 2641u − 394
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
36
+ 2y
35
+ ··· − 2592y + 196
c
2
, c
6
y
36
+ 13y
35
+ ··· − 641y + 64
c
3
, c
7
y
36
− 9y
35
+ ··· + 321y + 49
c
4
, c
9
49(49y
36
− 1289y
35
+ ··· − 31744y + 4096)
c
5
, c
8
49(49y
36
− 456y
35
+ ··· − 20y + 1)
c
11
y
36
+ 4y
35
+ ··· − 1886765y + 155236
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.664991 + 0.788504I
a = 0.206169 − 0.722289I
b = 0.096578 + 0.477168I
−1.34782 − 1.56519I 0.84439 + 2.92266I
u = 0.664991 − 0.788504I
a = 0.206169 + 0.722289I
b = 0.096578 − 0.477168I
−1.34782 + 1.56519I 0.84439 − 2.92266I
u = 0.309249 + 0.905547I
a = 1.79251 + 0.71331I
b = 0.751216 + 0.448888I
−1.22381 − 2.38943I −2.60962 + 0.88195I
u = 0.309249 − 0.905547I
a = 1.79251 − 0.71331I
b = 0.751216 − 0.448888I
−1.22381 + 2.38943I −2.60962 − 0.88195I
u = −0.888722 + 0.321374I
a = 0.363466 − 0.084941I
b = 0.703627 − 0.796093I
−1.32711 − 7.08620I −4.38282 + 7.74538I
u = −0.888722 − 0.321374I
a = 0.363466 + 0.084941I
b = 0.703627 + 0.796093I
−1.32711 + 7.08620I −4.38282 − 7.74538I
u = −0.518925 + 1.036550I
a = −0.767941 + 0.827823I
b = −1.051610 + 0.091581I
3.19944 + 1.84265I 5.26933 − 1.44076I
u = −0.518925 − 1.036550I
a = −0.767941 − 0.827823I
b = −1.051610 − 0.091581I
3.19944 − 1.84265I 5.26933 + 1.44076I
u = −1.16822
a = −0.710710
b = 0.650117
−7.32636 −13.3830
u = 0.478238 + 1.066020I
a = 2.08338 + 0.02701I
b = 0.97824 − 1.76146I
−0.67631 − 8.62575I 0.85500 + 10.45337I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.478238 − 1.066020I
a = 2.08338 − 0.02701I
b = 0.97824 + 1.76146I
−0.67631 + 8.62575I 0.85500 − 10.45337I
u = 0.398028 + 1.136150I
a = 0.553917 + 0.951098I
b = 1.25000 + 0.81047I
−0.316044 + 1.377840I 0.40549 − 3.04607I
u = 0.398028 − 1.136150I
a = 0.553917 − 0.951098I
b = 1.25000 − 0.81047I
−0.316044 − 1.377840I 0.40549 + 3.04607I
u = −0.420762 + 1.153070I
a = −1.70439 + 0.18358I
b = −1.14723 − 1.04061I
3.76935 + 5.55914I 7.29930 − 8.75003I
u = −0.420762 − 1.153070I
a = −1.70439 − 0.18358I
b = −1.14723 + 1.04061I
3.76935 − 5.55914I 7.29930 + 8.75003I
u = 1.22770
a = 0.220807
b = 0.272974
−2.30591 −25.6820
u = 0.773847 + 1.014680I
a = 0.823733 + 0.526895I
b = 0.348098 − 0.539202I
−0.76840 − 4.07443I −2.61964 + 5.42418I
u = 0.773847 − 1.014680I
a = 0.823733 − 0.526895I
b = 0.348098 + 0.539202I
−0.76840 + 4.07443I −2.61964 − 5.42418I
u = 1.213610 + 0.471997I
a = 0.0522347 + 0.0634017I
b = −0.99435 − 1.13172I
−7.25713 + 12.05490I −6.87385 − 7.36867I
u = 1.213610 − 0.471997I
a = 0.0522347 − 0.0634017I
b = −0.99435 + 1.13172I
−7.25713 − 12.05490I −6.87385 + 7.36867I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.611418 + 1.156610I
a = 1.75019 − 0.34229I
b = 0.948743 + 0.849128I
1.15223 + 12.56020I −2.14661 − 10.43699I
u = −0.611418 − 1.156610I
a = 1.75019 + 0.34229I
b = 0.948743 − 0.849128I
1.15223 − 12.56020I −2.14661 + 10.43699I
u = −0.096544 + 1.309750I
a = 1.024940 − 0.533084I
b = 0.729584 − 0.253643I
4.46757 − 3.67706I 3.45782 + 3.48358I
u = −0.096544 − 1.309750I
a = 1.024940 + 0.533084I
b = 0.729584 + 0.253643I
4.46757 + 3.67706I 3.45782 − 3.48358I
u = 0.556045 + 0.380280I
a = 0.75859 + 1.37452I
b = 0.611800 − 1.101080I
−2.98357 − 5.46509I −4.40298 + 5.74809I
u = 0.556045 − 0.380280I
a = 0.75859 − 1.37452I
b = 0.611800 + 1.101080I
−2.98357 + 5.46509I −4.40298 − 5.74809I
u = 0.331294 + 0.549198I
a = −2.03245 + 0.47407I
b = 0.44966 + 1.55974I
−2.49638 + 4.90008I −3.79310 − 7.77480I
u = 0.331294 − 0.549198I
a = −2.03245 − 0.47407I
b = 0.44966 − 1.55974I
−2.49638 − 4.90008I −3.79310 + 7.77480I
u = −0.572685 + 0.080761I
a = 0.472008 − 0.470814I
b = −0.639767 + 0.652105I
0.74933 − 1.67412I 0.81111 + 4.63626I
u = −0.572685 − 0.080761I
a = 0.472008 + 0.470814I
b = −0.639767 − 0.652105I
0.74933 + 1.67412I 0.81111 − 4.63626I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.74631 + 1.24839I
a = −1.54739 − 0.38151I
b = −1.09203 + 1.33473I
−4.7264 − 18.9578I −4.99741 + 9.85636I
u = 0.74631 − 1.24839I
a = −1.54739 + 0.38151I
b = −1.09203 − 1.33473I
−4.7264 + 18.9578I −4.99741 − 9.85636I
u = −0.19922 + 1.64465I
a = −0.938395 − 0.165870I
b = −1.27867 − 0.61003I
1.57745 + 7.38932I 0
u = −0.19922 − 1.64465I
a = −0.938395 + 0.165870I
b = −1.27867 + 0.61003I
1.57745 − 7.38932I 0
u = 0.317864
a = 1.05754
b = 0.804397
−3.24067 −2.80810
u = −1.70401
a = 0.0619210
b = −1.05525
−5.25552 0
8
II.
I
u
2
= h−2.43×10
20
au
32
+6.47×10
20
u
32
+· · ·−3.84×10
20
a−8.61×10
20
, 4.95×
10
20
au
32
−3.50×10
20
u
32
+· · ·+5.33×10
20
a+1.27×10
21
, u
33
+u
32
+· · ·−2u−1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−u
2
a
3
=
−u
u
3
+ u
a
11
=
a
6.17561au
32
− 16.4463u
32
+ ··· + 9.74756a + 21.8868
a
5
=
15.4244au
32
+ 18.6669u
32
+ ··· − 21.4494a + 11.7346
−2.41747au
32
− 4.89104u
32
+ ··· + 4.36925a + 5.31631
a
8
=
−20.3325au
32
− 29.5888u
32
+ ··· + 30.2366a + 1.23756
−1.92091au
32
+ 11.7466u
32
+ ··· − 5.00243a − 20.0640
a
10
=
−6.17561au
32
+ 16.4463u
32
+ ··· − 8.74756a − 21.8868
6.17561au
32
− 16.4463u
32
+ ··· + 9.74756a + 21.8868
a
4
=
8.00399au
32
+ 35.7108u
32
+ ··· − 26.8856a − 24.1021
9.29658au
32
− 21.9349u
32
+ ··· + 8.00399a + 41.1530
a
9
=
−9.74756au
32
− 30.4209u
32
+ ··· + 24.0610a + 16.6620
−10.5850au
32
+ 5.09705u
32
+ ··· + 6.17561a − 27.2965
a
1
=
0.494744au
32
+ 24.1111u
32
+ ··· − 16.2512a − 28.9205
11.8477au
32
− 13.2154u
32
+ ··· + 5.90658a + 35.7744
a
1
=
0.494744au
32
+ 24.1111u
32
+ ··· − 16.2512a − 28.9205
11.8477au
32
− 13.2154u
32
+ ··· + 5.90658a + 35.7744
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
233960085812908682097
13119091879006586663
u
32
−
122838803537233845053
39357275637019759989
u
31
+ ··· −
1020433678799244188345
39357275637019759989
u −
1174252898466954031738
39357275637019759989
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
66
− u
65
+ ··· + 360u + 11
c
2
, c
6
(u
33
− u
32
+ ··· − 2u + 1)
2
c
3
, c
7
u
66
− 11u
65
+ ··· − 3027u + 484
c
4
, c
9
(u
33
− 13u
31
+ ··· + 60u + 9)
2
c
5
, c
8
u
66
+ 2u
65
+ ··· − 9u + 2
c
11
(u
33
− 5u
32
+ ··· + 88u − 47)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
66
+ 25y
65
+ ··· − 60564y + 121
c
2
, c
6
(y
33
+ 21y
32
+ ··· − 20y −1)
2
c
3
, c
7
y
66
− 29y
65
+ ··· − 9905185y + 234256
c
4
, c
9
(y
33
− 26y
32
+ ··· + 828y −81)
2
c
5
, c
8
y
66
+ 28y
65
+ ··· − 41y + 4
c
11
(y
33
− 23y
32
+ ··· + 24852y −2209)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.417392 + 0.929081I
a = 0.117806 − 1.017110I
b = 0.61426 − 1.45227I
−0.35121 + 5.74395I −4.00846 − 9.48122I
u = −0.417392 + 0.929081I
a = −2.40309 + 0.13570I
b = −0.476485 − 0.850411I
−0.35121 + 5.74395I −4.00846 − 9.48122I
u = −0.417392 − 0.929081I
a = 0.117806 + 1.017110I
b = 0.61426 + 1.45227I
−0.35121 − 5.74395I −4.00846 + 9.48122I
u = −0.417392 − 0.929081I
a = −2.40309 − 0.13570I
b = −0.476485 + 0.850411I
−0.35121 − 5.74395I −4.00846 + 9.48122I
u = 0.414454 + 0.869237I
a = −0.900638 + 0.750691I
b = −0.465090 − 0.778291I
−0.30625 − 1.73487I −2.88654 + 2.20347I
u = 0.414454 + 0.869237I
a = −2.65339 − 0.05663I
b = −0.671706 + 0.442842I
−0.30625 − 1.73487I −2.88654 + 2.20347I
u = 0.414454 − 0.869237I
a = −0.900638 − 0.750691I
b = −0.465090 + 0.778291I
−0.30625 + 1.73487I −2.88654 − 2.20347I
u = 0.414454 − 0.869237I
a = −2.65339 + 0.05663I
b = −0.671706 − 0.442842I
−0.30625 + 1.73487I −2.88654 − 2.20347I
u = −0.472417 + 1.010790I
a = −1.61213 + 0.10091I
b = −0.036980 − 0.568939I
−4.16587 + 3.01159I −11.51158 − 5.38736I
u = −0.472417 + 1.010790I
a = 2.01812 − 0.47306I
b = 1.80069 + 1.09379I
−4.16587 + 3.01159I −11.51158 − 5.38736I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.472417 − 1.010790I
a = −1.61213 − 0.10091I
b = −0.036980 + 0.568939I
−4.16587 − 3.01159I −11.51158 + 5.38736I
u = −0.472417 − 1.010790I
a = 2.01812 + 0.47306I
b = 1.80069 − 1.09379I
−4.16587 − 3.01159I −11.51158 + 5.38736I
u = 0.100593 + 1.216160I
a = 1.33835 + 0.55468I
b = 0.808856 + 0.245405I
4.81646 − 2.61267I 2.98003 + 2.49183I
u = 0.100593 + 1.216160I
a = −1.41971 + 0.56060I
b = −1.094700 + 0.741598I
4.81646 − 2.61267I 2.98003 + 2.49183I
u = 0.100593 − 1.216160I
a = 1.33835 − 0.55468I
b = 0.808856 − 0.245405I
4.81646 + 2.61267I 2.98003 − 2.49183I
u = 0.100593 − 1.216160I
a = −1.41971 − 0.56060I
b = −1.094700 − 0.741598I
4.81646 + 2.61267I 2.98003 − 2.49183I
u = −0.392936 + 0.664924I
a = 0.193117 − 0.538220I
b = −0.344357 + 1.111940I
−1.06351 − 2.23250I −4.94311 + 2.28132I
u = −0.392936 + 0.664924I
a = 1.58119 + 0.03868I
b = 0.675409 + 0.632548I
−1.06351 − 2.23250I −4.94311 + 2.28132I
u = −0.392936 − 0.664924I
a = 0.193117 + 0.538220I
b = −0.344357 − 1.111940I
−1.06351 + 2.23250I −4.94311 − 2.28132I
u = −0.392936 − 0.664924I
a = 1.58119 − 0.03868I
b = 0.675409 − 0.632548I
−1.06351 + 2.23250I −4.94311 − 2.28132I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.557709 + 1.097620I
a = −0.260077 + 0.915977I
b = −0.154095 − 1.041730I
−5.04427 + 9.67271I −8.11986 − 8.22619I
u = −0.557709 + 1.097620I
a = 1.93591 − 0.15684I
b = 1.09058 + 1.15805I
−5.04427 + 9.67271I −8.11986 − 8.22619I
u = −0.557709 − 1.097620I
a = −0.260077 − 0.915977I
b = −0.154095 + 1.041730I
−5.04427 − 9.67271I −8.11986 + 8.22619I
u = −0.557709 − 1.097620I
a = 1.93591 + 0.15684I
b = 1.09058 − 1.15805I
−5.04427 − 9.67271I −8.11986 + 8.22619I
u = −0.412549 + 0.632401I
a = 0.06708 − 1.54795I
b = 0.247885 + 0.969351I
−5.44291 + 0.78188I −12.85213 − 1.24354I
u = −0.412549 + 0.632401I
a = −0.41241 − 1.69473I
b = 0.85738 − 1.44035I
−5.44291 + 0.78188I −12.85213 − 1.24354I
u = −0.412549 − 0.632401I
a = 0.06708 + 1.54795I
b = 0.247885 − 0.969351I
−5.44291 − 0.78188I −12.85213 + 1.24354I
u = −0.412549 − 0.632401I
a = −0.41241 + 1.69473I
b = 0.85738 + 1.44035I
−5.44291 − 0.78188I −12.85213 + 1.24354I
u = 0.355820 + 0.662489I
a = 1.360960 − 0.272301I
b = 0.444016 − 0.015311I
−0.93123 − 1.60031I −4.00690 + 5.61012I
u = 0.355820 + 0.662489I
a = 0.518884 − 0.139240I
b = 0.020761 + 0.794705I
−0.93123 − 1.60031I −4.00690 + 5.61012I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.355820 − 0.662489I
a = 1.360960 + 0.272301I
b = 0.444016 + 0.015311I
−0.93123 + 1.60031I −4.00690 − 5.61012I
u = 0.355820 − 0.662489I
a = 0.518884 + 0.139240I
b = 0.020761 − 0.794705I
−0.93123 + 1.60031I −4.00690 − 5.61012I
u = 0.498996 + 1.149370I
a = −0.38658 − 1.38128I
b = −1.85663 − 1.80445I
−3.63632 − 8.62361I −12.3273 + 8.9713I
u = 0.498996 + 1.149370I
a = 1.90689 − 0.02871I
b = 0.79240 − 1.24669I
−3.63632 − 8.62361I −12.3273 + 8.9713I
u = 0.498996 − 1.149370I
a = −0.38658 + 1.38128I
b = −1.85663 + 1.80445I
−3.63632 + 8.62361I −12.3273 − 8.9713I
u = 0.498996 − 1.149370I
a = 1.90689 + 0.02871I
b = 0.79240 + 1.24669I
−3.63632 + 8.62361I −12.3273 − 8.9713I
u = 1.29498
a = 0.222091
b = 0.544464
−2.30187 −31.9940
u = 1.29498
a = 0.181714
b = 0.0439292
−2.30187 −31.9940
u = 0.691384 + 0.062495I
a = 0.254081 + 0.231283I
b = 0.467648 − 1.124340I
−6.68521 − 4.32166I −11.81943 + 6.69112I
u = 0.691384 + 0.062495I
a = 1.03700 + 2.83810I
b = −0.961413 − 0.876208I
−6.68521 − 4.32166I −11.81943 + 6.69112I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.691384 − 0.062495I
a = 0.254081 − 0.231283I
b = 0.467648 + 1.124340I
−6.68521 + 4.32166I −11.81943 − 6.69112I
u = 0.691384 − 0.062495I
a = 1.03700 − 2.83810I
b = −0.961413 + 0.876208I
−6.68521 + 4.32166I −11.81943 − 6.69112I
u = −0.601870 + 0.332174I
a = −0.145333 − 0.282143I
b = 0.676050 − 1.175820I
−7.19868 − 4.98844I −12.36402 + 2.27839I
u = −0.601870 + 0.332174I
a = 2.11833 − 2.52447I
b = −0.529191 + 0.664200I
−7.19868 − 4.98844I −12.36402 + 2.27839I
u = −0.601870 − 0.332174I
a = −0.145333 + 0.282143I
b = 0.676050 + 1.175820I
−7.19868 + 4.98844I −12.36402 − 2.27839I
u = −0.601870 − 0.332174I
a = 2.11833 + 2.52447I
b = −0.529191 − 0.664200I
−7.19868 + 4.98844I −12.36402 − 2.27839I
u = 0.626600 + 1.208130I
a = −0.891596 − 0.208892I
b = −0.885135 + 0.559574I
0.84876 − 6.19552I −3.00000 + 7.44126I
u = 0.626600 + 1.208130I
a = 1.51704 + 0.31423I
b = 0.819944 − 0.828069I
0.84876 − 6.19552I −3.00000 + 7.44126I
u = 0.626600 − 1.208130I
a = −0.891596 + 0.208892I
b = −0.885135 − 0.559574I
0.84876 + 6.19552I −3.00000 − 7.44126I
u = 0.626600 − 1.208130I
a = 1.51704 − 0.31423I
b = 0.819944 + 0.828069I
0.84876 + 6.19552I −3.00000 − 7.44126I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.60344 + 1.36253I
a = −0.300421 − 0.241381I
b = 0.183626 − 0.365150I
−3.20813 − 1.17398I −16.8881 + 0.I
u = −0.60344 + 1.36253I
a = −0.029011 + 0.370695I
b = −0.98290 + 1.89865I
−3.20813 − 1.17398I −16.8881 + 0.I
u = −0.60344 − 1.36253I
a = −0.300421 + 0.241381I
b = 0.183626 + 0.365150I
−3.20813 + 1.17398I −16.8881 + 0.I
u = −0.60344 − 1.36253I
a = −0.029011 − 0.370695I
b = −0.98290 − 1.89865I
−3.20813 + 1.17398I −16.8881 + 0.I
u = −0.90200 + 1.23014I
a = 0.567900 − 0.143956I
b = 0.233108 + 0.551448I
−2.85108 + 10.01350I 0
u = −0.90200 + 1.23014I
a = −1.36302 + 0.57989I
b = −1.16123 − 1.45442I
−2.85108 + 10.01350I 0
u = −0.90200 − 1.23014I
a = 0.567900 + 0.143956I
b = 0.233108 − 0.551448I
−2.85108 − 10.01350I 0
u = −0.90200 − 1.23014I
a = −1.36302 − 0.57989I
b = −1.16123 + 1.45442I
−2.85108 − 10.01350I 0
u = −0.050458 + 0.377504I
a = −0.729840 − 1.049950I
b = 0.396037 + 1.206410I
−6.81266 + 4.73250I −21.9711 − 14.2148I
u = −0.050458 + 0.377504I
a = −9.49427 − 0.72345I
b = −1.60778 − 0.29179I
−6.81266 + 4.73250I −21.9711 − 14.2148I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.050458 − 0.377504I
a = −0.729840 + 1.049950I
b = 0.396037 − 1.206410I
−6.81266 − 4.73250I −21.9711 + 14.2148I
u = −0.050458 − 0.377504I
a = −9.49427 + 0.72345I
b = −1.60778 + 0.29179I
−6.81266 − 4.73250I −21.9711 + 14.2148I
u = 0.57543 + 1.63125I
a = −0.238828 − 0.129721I
b = 0.07358 + 1.85946I
−2.87513 − 0.70475I 0
u = 0.57543 + 1.63125I
a = 0.005781 + 0.205594I
b = 0.231256 + 0.346251I
−2.87513 − 0.70475I 0
u = 0.57543 − 1.63125I
a = −0.238828 + 0.129721I
b = 0.07358 − 1.85946I
−2.87513 + 0.70475I 0
u = 0.57543 − 1.63125I
a = 0.005781 − 0.205594I
b = 0.231256 − 0.346251I
−2.87513 + 0.70475I 0
18
III. I
u
3
= hu
5
a − 4u
5
+ · · · − a + 1, 21u
5
a + 19u
5
+ · · · + 56a − 20, u
6
− u
5
+
4u
4
− 3u
3
+ 5u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−u
2
a
3
=
−u
u
3
+ u
a
11
=
a
−
1
3
u
5
a +
4
3
u
5
+ ··· +
1
3
a −
1
3
a
5
=
−0.333333au
5
+ 0.476190u
5
+ ··· + 1.33333a + 2.09524
2
3
u
5
a +
1
3
u
5
+ ··· +
1
3
a −
7
3
a
8
=
u
5
a + u
5
+ u
3
a − 2u
4
+ 2u
2
a + 5u
3
+ au − 7u
2
+ 6u − 3
4
3
u
5
a −
7
3
u
5
+ ··· +
2
3
a +
7
3
a
10
=
1
3
u
5
a −
4
3
u
5
+ ··· +
2
3
a +
1
3
−
1
3
u
5
a +
4
3
u
5
+ ··· +
1
3
a −
1
3
a
4
=
1
3
u
5
a −
7
3
u
5
+ ··· −
1
3
a +
7
3
−
1
3
u
5
a +
7
3
u
5
+ ··· +
1
3
a −
7
3
a
9
=
1
3
u
5
a +
5
3
u
5
+ ··· −
1
3
a −
8
3
2
3
u
5
a −
8
3
u
5
+ ··· +
1
3
a +
8
3
a
1
=
u
4
a + 2u
5
+ u
3
a − 4u
4
+ 8u
3
+ 2au − 11u
2
+ 10u − 5
−
7
3
u
5
a −
2
3
u
5
+ ··· +
4
3
a +
11
3
a
1
=
u
4
a + 2u
5
+ u
3
a − 4u
4
+ 8u
3
+ 2au − 11u
2
+ 10u − 5
−
7
3
u
5
a −
2
3
u
5
+ ··· +
4
3
a +
11
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
5
− 4u
4
+ 19u
3
+ 2u
2
+ 14u + 10
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
12
+ 5u
10
+ ··· + 42u + 14
c
2
(u
6
+ u
5
+ 4u
4
+ 3u
3
+ 5u
2
+ u + 1)
2
c
3
, c
7
u
12
− 2u
11
+ ··· + 28u + 7
c
4
, c
9
7(7u
12
− 66u
10
+ 264u
8
− 572u
6
+ 709u
4
− 477u
2
+ 137)
c
5
, c
8
7(7u
12
+ 7u
11
+ ··· − 3u + 1)
c
6
(u
6
− u
5
+ 4u
4
− 3u
3
+ 5u
2
− u + 1)
2
c
11
(u
6
− 5u
5
+ 10u
4
− 9u
3
+ u
2
+ u + 3)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
12
+ 10y
11
+ ··· − 280y + 196
c
2
, c
6
(y
6
+ 7y
5
+ 20y
4
+ 31y
3
+ 27y
2
+ 9y + 1)
2
c
3
, c
7
y
12
− 14y
11
+ ··· − 238y + 49
c
4
, c
9
49(7y
6
− 66y
5
+ 264y
4
− 572y
3
+ 709y
2
− 477y + 137)
2
c
5
, c
8
49(49y
12
+ 399y
11
+ ··· + 25y + 1)
c
11
(y
6
− 5y
5
+ 12y
4
− 45y
3
+ 79y
2
+ 5y + 9)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.594531 + 1.108530I
a = 0.194027 − 0.521903I
b = −0.63798 − 1.31450I
−2.75606 − 8.49886I −3.32790 + 6.69892I
u = 0.594531 + 1.108530I
a = 1.88170 + 0.26063I
b = 0.93018 − 1.33338I
−2.75606 − 8.49886I −3.32790 + 6.69892I
u = 0.594531 − 1.108530I
a = 0.194027 + 0.521903I
b = −0.63798 + 1.31450I
−2.75606 + 8.49886I −3.32790 − 6.69892I
u = 0.594531 − 1.108530I
a = 1.88170 − 0.26063I
b = 0.93018 + 1.33338I
−2.75606 + 8.49886I −3.32790 − 6.69892I
u = 0.048182 + 0.510085I
a = −0.061872 − 0.552955I
b = 0.418645 + 1.257000I
−6.62587 + 4.61385I 9.30218 + 5.10701I
u = 0.048182 + 0.510085I
a = −7.42207 − 1.53777I
b = −1.40319 − 0.25404I
−6.62587 + 4.61385I 9.30218 + 5.10701I
u = 0.048182 − 0.510085I
a = −0.061872 + 0.552955I
b = 0.418645 − 1.257000I
−6.62587 − 4.61385I 9.30218 − 5.10701I
u = 0.048182 − 0.510085I
a = −7.42207 + 1.53777I
b = −1.40319 + 0.25404I
−6.62587 − 4.61385I 9.30218 − 5.10701I
u = −0.14271 + 1.54503I
a = 0.331160 + 0.030135I
b = 0.33934 + 1.85328I
−2.95507 + 0.81827I −26.9743 + 0.5102I
u = −0.14271 + 1.54503I
a = 0.077057 − 0.242870I
b = 0.353013 − 0.266813I
−2.95507 + 0.81827I −26.9743 + 0.5102I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.14271 − 1.54503I
a = 0.331160 − 0.030135I
b = 0.33934 − 1.85328I
−2.95507 − 0.81827I −26.9743 − 0.5102I
u = −0.14271 − 1.54503I
a = 0.077057 + 0.242870I
b = 0.353013 + 0.266813I
−2.95507 − 0.81827I −26.9743 − 0.5102I
23
IV.
I
u
4
= h−u
3
− 2u
2
+ b −2u − 1, u
4
+ u
3
+ a − u −2, u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−u
2
a
3
=
−u
u
3
+ u
a
11
=
−u
4
− u
3
+ u + 2
u
3
+ 2u
2
+ 2u + 1
a
5
=
u
4
+ 2u
3
+ 3u
2
+ 2u
−u
2
− u − 1
a
8
=
−u
4
− u
3
− u
2
+ 2
u
4
+ 2u
3
+ 3u
2
+ 2u + 1
a
10
=
−u
4
− 2u
3
− 2u
2
− u + 1
u
3
+ 2u
2
+ 2u + 1
a
4
=
u
4
+ 2u
3
+ 3u
2
+ 2u
−u
2
− u − 1
a
9
=
−u
4
− 2u
3
− 2u
2
− u + 1
u
3
+ 2u
2
+ 2u + 1
a
1
=
−u
4
− 3u
3
− 4u
2
− 4u − 2
−u
4
− u
3
− u
2
+ 1
a
1
=
−u
4
− 3u
3
− 4u
2
− 4u − 2
−u
4
− u
3
− u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
4
+ 13u
3
+ 25u
2
+ 15u + 9
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
5
− 2u
4
+ 3u
3
− 3u
2
+ 3u − 1
c
2
u
5
− 2u
4
+ 3u
3
− 3u
2
+ u − 1
c
3
, c
7
u
5
+ u
4
− u
3
− u
2
+ 1
c
4
, c
9
u
5
c
5
, c
8
u
5
− u
3
− u
2
+ u + 1
c
6
u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ u + 1
c
11
u
5
+ 3u
4
+ 5u
3
+ 4u
2
+ 3u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
5
+ 2y
4
+ 3y
3
+ 5y
2
+ 3y − 1
c
2
, c
6
y
5
+ 2y
4
− y
3
− 7y
2
− 5y − 1
c
3
, c
7
y
5
− 3y
4
+ 3y
3
− 3y
2
+ 2y − 1
c
4
, c
9
y
5
c
5
, c
8
y
5
− 2y
4
+ 3y
3
− 3y
2
+ 3y − 1
c
11
y
5
+ y
4
+ 7y
3
+ 8y
2
+ y − 1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.372466 + 1.263920I
a = −1.347300 + 0.010044I
b = −0.929085 − 0.848284I
3.01018 + 5.17259I −1.83188 − 4.76077I
u = −0.372466 − 1.263920I
a = −1.347300 − 0.010044I
b = −0.929085 + 0.848284I
3.01018 − 5.17259I −1.83188 + 4.76077I
u = −1.33263
a = −0.119827
b = −0.480071
−2.14584 24.7190
u = 0.038780 + 0.656277I
a = 1.90721 + 0.97967I
b = 0.169121 + 1.134660I
−0.29233 − 3.70382I −0.52749 + 7.17476I
u = 0.038780 − 0.656277I
a = 1.90721 − 0.97967I
b = 0.169121 − 1.134660I
−0.29233 + 3.70382I −0.52749 − 7.17476I
27
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
5
− 2u
4
+ 3u
3
− 3u
2
+ 3u − 1)(u
12
+ 5u
10
+ ··· + 42u + 14)
· (u
36
+ 2u
35
+ ··· − 144u − 14)(u
66
− u
65
+ ··· + 360u + 11)
c
2
(u
5
− 2u
4
+ 3u
3
− 3u
2
+ u − 1)(u
6
+ u
5
+ 4u
4
+ 3u
3
+ 5u
2
+ u + 1)
2
· ((u
33
− u
32
+ ··· − 2u + 1)
2
)(u
36
+ 3u
35
+ ··· + 41u + 8)
c
3
, c
7
(u
5
+ u
4
− u
3
− u
2
+ 1)(u
12
− 2u
11
+ ··· + 28u + 7)(u
36
− u
35
+ ··· + u − 7)
· (u
66
− 11u
65
+ ··· − 3027u + 484)
c
4
, c
9
49u
5
(7u
12
− 66u
10
+ 264u
8
− 572u
6
+ 709u
4
− 477u
2
+ 137)
· ((u
33
− 13u
31
+ ··· + 60u + 9)
2
)(7u
36
− 27u
35
+ ··· − 32u − 64)
c
5
, c
8
49(u
5
− u
3
− u
2
+ u + 1)(7u
12
+ 7u
11
+ ··· − 3u + 1)
· (7u
36
− 6u
35
+ ··· − 4u + 1)(u
66
+ 2u
65
+ ··· − 9u + 2)
c
6
(u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ u + 1)(u
6
− u
5
+ 4u
4
− 3u
3
+ 5u
2
− u + 1)
2
· ((u
33
− u
32
+ ··· − 2u + 1)
2
)(u
36
+ 3u
35
+ ··· + 41u + 8)
c
11
(u
5
+ 3u
4
+ 5u
3
+ 4u
2
+ 3u + 1)(u
6
− 5u
5
+ 10u
4
− 9u
3
+ u
2
+ u + 3)
2
· ((u
33
− 5u
32
+ ··· + 88u − 47)
2
)(u
36
+ 6u
35
+ ··· − 2641u − 394)
28
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
5
+ 2y
4
+ 3y
3
+ 5y
2
+ 3y − 1)(y
12
+ 10y
11
+ ··· − 280y + 196)
· (y
36
+ 2y
35
+ ··· − 2592y + 196)(y
66
+ 25y
65
+ ··· − 60564y + 121)
c
2
, c
6
(y
5
+ 2y
4
− y
3
− 7y
2
− 5y − 1)
· (y
6
+ 7y
5
+ 20y
4
+ 31y
3
+ 27y
2
+ 9y + 1)
2
· ((y
33
+ 21y
32
+ ··· − 20y − 1)
2
)(y
36
+ 13y
35
+ ··· − 641y + 64)
c
3
, c
7
(y
5
− 3y
4
+ 3y
3
− 3y
2
+ 2y − 1)(y
12
− 14y
11
+ ··· − 238y + 49)
· (y
36
− 9y
35
+ ··· + 321y + 49)
· (y
66
− 29y
65
+ ··· − 9905185y + 234256)
c
4
, c
9
2401y
5
(7y
6
− 66y
5
+ 264y
4
− 572y
3
+ 709y
2
− 477y + 137)
2
· (y
33
− 26y
32
+ ··· + 828y − 81)
2
· (49y
36
− 1289y
35
+ ··· − 31744y + 4096)
c
5
, c
8
2401(y
5
− 2y
4
+ ··· + 3y − 1)(49y
12
+ 399y
11
+ ··· + 25y + 1)
· (49y
36
− 456y
35
+ ··· − 20y + 1)(y
66
+ 28y
65
+ ··· − 41y + 4)
c
11
(y
5
+ y
4
+ 7y
3
+ 8y
2
+ y − 1)
· (y
6
− 5y
5
+ 12y
4
− 45y
3
+ 79y
2
+ 5y + 9)
2
· (y
33
− 23y
32
+ ··· + 24852y − 2209)
2
· (y
36
+ 4y
35
+ ··· − 1886765y + 155236)
29
