11a
232
(K11a
232
)
A knot diagram
1
Linearized knot diagam
7 1 9 11 3 10 2 4 6 8 5
Solving Sequence
4,11
5
1,9
3 6 2 8 7 10
c
4
c
11
c
3
c
5
c
2
c
8
c
7
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.29642 × 10
17
u
27
− 9.84068 × 10
16
u
26
+ ··· + 1.77262 × 10
17
b − 9.04547 × 10
17
,
8.06637 × 10
17
u
27
+ 5.36595 × 10
17
u
26
+ ··· + 7.09049 × 10
17
a + 6.30715 × 10
17
, u
28
+ u
27
+ ··· + 14u + 1i
I
u
2
= h8.83675 × 10
38
u
39
− 8.11011 × 10
37
u
38
+ ··· + 1.46509 × 10
38
b − 1.09806 × 10
40
,
− 4.97706 × 10
40
u
39
+ 1.13228 × 10
40
u
38
+ ··· + 2.49066 × 10
39
a + 8.16831 × 10
41
,
u
40
+ u
39
+ ··· + 62u − 17i
I
u
3
= hb − u, 4a
2
+ 4au + 2a + u, u
2
+ 1i
I
u
4
= hb, a + 1, u − 1i
I
u
5
= h2b + 3a − 1, 9a
2
− 6a − 7, u + 1i
* 5 irreducible components of dim
C
= 0, with total 75 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−1.30×10
17
u
27
−9.84×10
16
u
26
+· · ·+1.77×10
17
b−9.05×10
17
, 8.07×
10
17
u
27
+5.37×10
17
u
26
+· · ·+7.09×10
17
a+6.31×10
17
, u
28
+u
27
+· · ·+14u+1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
1
=
u
−u
3
+ u
a
9
=
−1.13763u
27
− 0.756780u
26
+ ··· − 56.2473u − 0.889522
0.731356u
27
+ 0.555147u
26
+ ··· + 37.3554u + 5.10287
a
3
=
−4.73051u
27
− 4.00227u
26
+ ··· − 238.602u − 33.2692
0.00848632u
27
− 0.147004u
26
+ ··· − 4.43645u + 0.321958
a
6
=
3.99376u
27
+ 3.52913u
26
+ ··· + 207.156u + 31.6346
0.380852u
27
+ 0.222239u
26
+ ··· + 15.0373u + 1.13763
a
2
=
−4.57712u
27
− 3.99984u
26
+ ··· − 234.261u − 32.6359
−0.0116520u
27
− 0.0162144u
26
+ ··· − 2.05596u + 0.804312
a
8
=
−0.406276u
27
− 0.201633u
26
+ ··· − 18.8919u + 4.21335
0.731356u
27
+ 0.555147u
26
+ ··· + 37.3554u + 5.10287
a
7
=
3.64578u
27
+ 3.25367u
26
+ ··· + 189.608u + 30.0323
0.380288u
27
+ 0.344685u
26
+ ··· + 18.3337u + 1.71038
a
10
=
−1.60226u
27
− 1.25428u
26
+ ··· − 80.5253u − 4.88328
0.572743u
27
+ 0.573307u
26
+ ··· + 33.1611u + 4.72202
a
10
=
−1.60226u
27
− 1.25428u
26
+ ··· − 80.5253u − 4.88328
0.572743u
27
+ 0.573307u
26
+ ··· + 33.1611u + 4.72202
(ii) Obstruction class = −1
(iii) Cusp Shapes =
33965909975637527
11078896897135864
u
27
+
122607961560954003
44315587588543456
u
26
+···+
3170991077588347389
22157793794271728
u+
1229656491980719955
44315587588543456
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
28
− 3u
27
+ ··· + 14u − 10
c
2
u
28
+ 13u
27
+ ··· − 404u + 100
c
3
, c
8
u
28
− 3u
27
+ ··· + 170u − 26
c
4
, c
6
, c
9
c
11
u
28
− u
27
+ ··· − 14u + 1
c
5
, c
10
16(16u
28
+ 48u
27
+ ··· − 4u − 1)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
28
− 13y
27
+ ··· + 404y + 100
c
2
y
28
+ 7y
27
+ ··· − 672016y + 10000
c
3
, c
8
y
28
+ 17y
27
+ ··· + 8332y + 676
c
4
, c
6
, c
9
c
11
y
28
− 19y
27
+ ··· − 94y + 1
c
5
, c
10
256(256y
28
− 5248y
27
+ ··· − 74y + 1)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.449964 + 0.955908I
a = 0.151228 − 0.563693I
b = −0.237420 + 1.011880I
−0.873376 − 0.763619I −0.834378 − 1.006413I
u = −0.449964 − 0.955908I
a = 0.151228 + 0.563693I
b = −0.237420 − 1.011880I
−0.873376 + 0.763619I −0.834378 + 1.006413I
u = 0.619030 + 0.625848I
a = −0.254904 − 0.940243I
b = −0.564972 + 0.419726I
−2.54273 + 3.94340I −3.92883 − 8.11948I
u = 0.619030 − 0.625848I
a = −0.254904 + 0.940243I
b = −0.564972 − 0.419726I
−2.54273 − 3.94340I −3.92883 + 8.11948I
u = 1.16749
a = 1.09598
b = −1.79695
−0.740696 13.3630
u = 0.197638 + 0.798678I
a = −0.160215 − 0.828722I
b = −0.165189 + 0.201586I
−1.59476 − 1.80480I −5.09710 + 1.86642I
u = 0.197638 − 0.798678I
a = −0.160215 + 0.828722I
b = −0.165189 − 0.201586I
−1.59476 + 1.80480I −5.09710 − 1.86642I
u = 0.737049
a = −0.944844
b = 1.11268
−2.48664 −6.62100
u = −1.279000 + 0.337291I
a = −0.47967 + 1.95384I
b = −0.47948 − 1.61552I
5.51780 − 7.86345I 5.31743 + 6.29867I
u = −1.279000 − 0.337291I
a = −0.47967 − 1.95384I
b = −0.47948 + 1.61552I
5.51780 + 7.86345I 5.31743 − 6.29867I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.343250 + 0.043119I
a = 0.13328 − 1.60960I
b = −0.76458 + 1.59693I
10.03540 − 2.66746I 10.12620 + 2.06407I
u = −1.343250 − 0.043119I
a = 0.13328 + 1.60960I
b = −0.76458 − 1.59693I
10.03540 + 2.66746I 10.12620 − 2.06407I
u = −1.326140 + 0.226084I
a = −0.460345 − 0.367905I
b = 1.374270 + 0.188673I
7.76911 − 3.65914I 8.46465 + 3.07912I
u = −1.326140 − 0.226084I
a = −0.460345 + 0.367905I
b = 1.374270 − 0.188673I
7.76911 + 3.65914I 8.46465 − 3.07912I
u = 1.320310 + 0.365382I
a = 0.305908 − 0.482073I
b = −1.262860 + 0.217604I
6.13143 + 10.28480I 5.46409 − 7.36805I
u = 1.320310 − 0.365382I
a = 0.305908 + 0.482073I
b = −1.262860 − 0.217604I
6.13143 − 10.28480I 5.46409 + 7.36805I
u = 1.399260 + 0.113511I
a = 0.13439 + 1.69651I
b = 0.64640 − 1.61358I
12.33890 + 4.05891I 10.87964 − 3.34376I
u = 1.399260 − 0.113511I
a = 0.13439 − 1.69651I
b = 0.64640 + 1.61358I
12.33890 − 4.05891I 10.87964 + 3.34376I
u = −0.351747 + 0.453003I
a = 0.576176 − 0.742859I
b = 0.246070 + 0.616533I
0.183505 − 1.179080I 2.03457 + 5.91305I
u = −0.351747 − 0.453003I
a = 0.576176 + 0.742859I
b = 0.246070 − 0.616533I
0.183505 + 1.179080I 2.03457 − 5.91305I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.47134 + 0.46584I
a = 0.62737 + 1.64310I
b = 0.52803 − 1.50973I
13.2391 + 10.1973I 8.61620 − 4.40012I
u = 1.47134 − 0.46584I
a = 0.62737 − 1.64310I
b = 0.52803 + 1.50973I
13.2391 − 10.1973I 8.61620 + 4.40012I
u = −1.45739 + 0.55230I
a = −0.73550 + 1.62993I
b = −0.51262 − 1.48286I
11.5116 − 16.4523I 6.49151 + 8.57137I
u = −1.45739 − 0.55230I
a = −0.73550 − 1.62993I
b = −0.51262 + 1.48286I
11.5116 + 16.4523I 6.49151 − 8.57137I
u = −0.11349 + 1.56139I
a = 0.012320 − 0.622298I
b = −0.039307 + 1.237680I
1.50736 + 2.52809I 9.13783 − 4.03367I
u = −0.11349 − 1.56139I
a = 0.012320 + 0.622298I
b = −0.039307 − 1.237680I
1.50736 − 2.52809I 9.13783 + 4.03367I
u = −0.138862 + 0.028897I
a = 6.57439 − 1.46045I
b = 0.073787 + 0.991855I
1.72032 − 2.04511I 7.95707 + 3.99629I
u = −0.138862 − 0.028897I
a = 6.57439 + 1.46045I
b = 0.073787 − 0.991855I
1.72032 + 2.04511I 7.95707 − 3.99629I
7
II. I
u
2
= h8.84 × 10
38
u
39
− 8.11 × 10
37
u
38
+ · · · + 1.47 × 10
38
b − 1.10 ×
10
40
, −4.98 × 10
40
u
39
+ 1.13 × 10
40
u
38
+ · · · + 2.49 × 10
39
a + 8.17 ×
10
41
, u
40
+ u
39
+ · · · + 62u − 17i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
1
=
u
−u
3
+ u
a
9
=
19.9829u
39
− 4.54610u
38
+ ··· + 1425.22u − 327.958
−6.03152u
39
+ 0.553556u
38
+ ··· − 361.279u + 74.9478
a
3
=
−2.14148u
39
+ 1.22331u
38
+ ··· − 238.675u + 70.6524
9.32536u
39
− 1.34018u
38
+ ··· + 615.450u − 133.266
a
6
=
42.0817u
39
− 10.6590u
38
+ ··· + 3089.04u − 737.735
−3.20706u
39
− 0.115380u
38
+ ··· − 141.669u + 19.2163
a
2
=
9.46024u
39
− 0.795742u
38
+ ··· + 543.626u − 105.550
5.22480u
39
− 0.852228u
38
+ ··· + 356.034u − 77.9153
a
8
=
13.9514u
39
− 3.99254u
38
+ ··· + 1063.94u − 253.010
−6.03152u
39
+ 0.553556u
38
+ ··· − 361.279u + 74.9478
a
7
=
21.9203u
39
− 3.79830u
38
+ ··· + 1464.70u − 321.059
1.20951u
39
− 0.423156u
38
+ ··· + 108.425u − 25.8667
a
10
=
46.8670u
39
− 4.18670u
38
+ ··· + 2852.32u − 583.520
−7.30074u
39
+ 1.70611u
38
+ ··· − 508.014u + 122.126
a
10
=
46.8670u
39
− 4.18670u
38
+ ··· + 2852.32u − 583.520
−7.30074u
39
+ 1.70611u
38
+ ··· − 508.014u + 122.126
(ii) Obstruction class = −1
(iii) Cusp Shapes = 41.4508u
39
− 6.22688u
38
+ ··· + 2767.85u − 602.998
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
20
+ u
19
+ ··· + 3u
2
− 1)
2
c
2
(u
20
+ 7u
19
+ ··· + 6u + 1)
2
c
3
, c
8
(u
20
+ u
19
+ ··· + 2u − 1)
2
c
4
, c
6
, c
9
c
11
u
40
− u
39
+ ··· − 62u − 17
c
5
, c
10
u
40
− 5u
39
+ ··· − 3518u + 8903
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
20
− 7y
19
+ ··· − 6y + 1)
2
c
2
(y
20
+ 13y
19
+ ··· − 6y + 1)
2
c
3
, c
8
(y
20
+ 17y
19
+ ··· − 6y + 1)
2
c
4
, c
6
, c
9
c
11
y
40
− 29y
39
+ ··· − 2824y + 289
c
5
, c
10
y
40
− 25y
39
+ ··· − 6761242056y + 79263409
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.044840 + 0.243936I
a = 0.43981 + 1.65317I
b = −0.201509 + 0.663357I
4.95641 + 2.35832I 5.64775 − 4.49783I
u = −1.044840 − 0.243936I
a = 0.43981 − 1.65317I
b = −0.201509 − 0.663357I
4.95641 − 2.35832I 5.64775 + 4.49783I
u = 1.101170 + 0.208325I
a = −2.01145 + 0.48533I
b = −0.201509 + 0.663357I
4.95641 + 2.35832I 5.64775 − 4.49783I
u = 1.101170 − 0.208325I
a = −2.01145 − 0.48533I
b = −0.201509 − 0.663357I
4.95641 − 2.35832I 5.64775 + 4.49783I
u = −1.13898
a = 0.459946
b = −0.358818
2.60969 −2.76210
u = −1.156830 + 0.007308I
a = 1.56319 + 2.12053I
b = 0.274747 − 1.069600I
4.55875 − 2.13456I 3.49102 + 2.16962I
u = −1.156830 − 0.007308I
a = 1.56319 − 2.12053I
b = 0.274747 + 1.069600I
4.55875 + 2.13456I 3.49102 − 2.16962I
u = −0.598773 + 0.548760I
a = −1.130270 − 0.298739I
b = −0.198534 − 1.239650I
6.05405 − 2.16136I 7.26252 + 3.31855I
u = −0.598773 − 0.548760I
a = −1.130270 + 0.298739I
b = −0.198534 + 1.239650I
6.05405 + 2.16136I 7.26252 − 3.31855I
u = −0.059958 + 0.789733I
a = 0.671566 + 0.796017I
b = 0.773104 + 0.153161I
1.80703 − 6.07240I 0.54715 + 5.87540I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.059958 − 0.789733I
a = 0.671566 − 0.796017I
b = 0.773104 − 0.153161I
1.80703 + 6.07240I 0.54715 − 5.87540I
u = −1.151180 + 0.376978I
a = 0.78707 − 1.80536I
b = 0.327541 + 1.260030I
1.63329 − 3.96853I 0. + 3.79787I
u = −1.151180 − 0.376978I
a = 0.78707 + 1.80536I
b = 0.327541 − 1.260030I
1.63329 + 3.96853I 0. − 3.79787I
u = −0.265136 + 1.197750I
a = −0.299881 + 0.427278I
b = −0.295567 − 1.352050I
7.72048 − 4.43308I 7.31630 + 0.I
u = −0.265136 − 1.197750I
a = −0.299881 − 0.427278I
b = −0.295567 + 1.352050I
7.72048 + 4.43308I 7.31630 + 0.I
u = −1.219460 + 0.187157I
a = 0.0698643 − 0.0332146I
b = −0.692333 − 0.156175I
2.96536 − 0.81573I 0
u = −1.219460 − 0.187157I
a = 0.0698643 + 0.0332146I
b = −0.692333 + 0.156175I
2.96536 + 0.81573I 0
u = 0.733960
a = −1.52495
b = −0.358818
2.60969 −2.76210
u = 0.616504 + 0.374474I
a = −0.258415 + 0.450813I
b = 0.772326
−2.26801 −4.44026 + 0.I
u = 0.616504 − 0.374474I
a = −0.258415 − 0.450813I
b = 0.772326
−2.26801 −4.44026 + 0.I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.046221 + 0.711923I
a = −0.345881 + 0.305536I
b = 0.327541 − 1.260030I
1.63329 + 3.96853I 0.10651 − 3.79787I
u = −0.046221 − 0.711923I
a = −0.345881 − 0.305536I
b = 0.327541 + 1.260030I
1.63329 − 3.96853I 0.10651 + 3.79787I
u = 0.094315 + 1.289960I
a = 0.241791 + 0.504558I
b = 0.328206 − 1.357610I
6.57229 + 10.05770I 0
u = 0.094315 − 1.289960I
a = 0.241791 − 0.504558I
b = 0.328206 + 1.357610I
6.57229 − 10.05770I 0
u = 1.240730 + 0.365535I
a = 0.0134609 + 0.0435217I
b = 0.773104 − 0.153161I
1.80703 + 6.07240I 0
u = 1.240730 − 0.365535I
a = 0.0134609 − 0.0435217I
b = 0.773104 + 0.153161I
1.80703 − 6.07240I 0
u = 1.307700 + 0.029974I
a = −0.28588 − 2.24493I
b = −0.198534 + 1.239650I
6.05405 + 2.16136I 0
u = 1.307700 − 0.029974I
a = −0.28588 + 2.24493I
b = −0.198534 − 1.239650I
6.05405 − 2.16136I 0
u = 0.245936 + 0.564099I
a = −1.06678 + 0.97261I
b = −0.692333 + 0.156175I
2.96536 + 0.81573I 2.32828 − 1.07888I
u = 0.245936 − 0.564099I
a = −1.06678 − 0.97261I
b = −0.692333 − 0.156175I
2.96536 − 0.81573I 2.32828 + 1.07888I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.509345 + 0.095450I
a = 2.70967 + 2.44353I
b = 0.274747 + 1.069600I
4.55875 + 2.13456I 3.49102 − 2.16962I
u = 0.509345 − 0.095450I
a = 2.70967 − 2.44353I
b = 0.274747 − 1.069600I
4.55875 − 2.13456I 3.49102 + 2.16962I
u = 1.56466 + 0.43256I
a = −0.46583 − 1.54438I
b = −0.295567 + 1.352050I
7.72048 + 4.43308I 0
u = 1.56466 − 0.43256I
a = −0.46583 + 1.54438I
b = −0.295567 − 1.352050I
7.72048 − 4.43308I 0
u = −1.54550 + 0.58408I
a = 0.55643 − 1.46280I
b = 0.328206 + 1.357610I
6.57229 − 10.05770I 0
u = −1.54550 − 0.58408I
a = 0.55643 + 1.46280I
b = 0.328206 − 1.357610I
6.57229 + 10.05770I 0
u = −1.48897 + 0.75285I
a = −0.601546 + 1.129320I
b = −0.022410 − 1.403750I
11.26460 − 2.84648I 0
u = −1.48897 − 0.75285I
a = −0.601546 − 1.129320I
b = −0.022410 + 1.403750I
11.26460 + 2.84648I 0
u = 1.59903 + 0.60741I
a = 0.504411 + 1.265840I
b = −0.022410 − 1.403750I
11.26460 − 2.84648I 0
u = 1.59903 − 0.60741I
a = 0.504411 − 1.265840I
b = −0.022410 + 1.403750I
11.26460 + 2.84648I 0
14
III. I
u
3
= hb − u, 4a
2
+ 4au + 2a + u, u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
1
a
1
=
u
2u
a
9
=
a
u
a
3
=
−au + 1
1
a
6
=
1
2
a +
1
4
u + 1
−au + 1
a
2
=
−3au + 2
−4au + 3
a
8
=
a + u
u
a
7
=
−au + a +
1
2
u + 2
−2au + 3
a
10
=
1
2
au + a + u −
1
4
a + 2u
a
10
=
1
2
au + a + u −
1
4
a + 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8a − 4u
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
4
− u
2
+ 1
c
2
(u
2
+ u + 1)
2
c
3
, c
4
, c
6
c
8
, c
9
, c
11
(u
2
+ 1)
2
c
5
, c
10
16(16u
4
− 32u
3
+ 20u
2
− 4u + 1)
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
2
− y + 1)
2
c
2
(y
2
+ y + 1)
2
c
3
, c
4
, c
6
c
8
, c
9
, c
11
(y + 1)
4
c
5
, c
10
256(256y
4
− 384y
3
+ 176y
2
+ 24y + 1)
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.250000 − 0.933013I
b = 1.000000I
− 2.02988I 2.00000 + 3.46410I
u = 1.000000I
a = −0.250000 − 0.066987I
b = 1.000000I
2.02988I 2.00000 − 3.46410I
u = − 1.000000I
a = −0.250000 + 0.933013I
b = − 1.000000I
2.02988I 2.00000 − 3.46410I
u = − 1.000000I
a = −0.250000 + 0.066987I
b = − 1.000000I
− 2.02988I 2.00000 + 3.46410I
18
IV. I
u
4
= hb, a + 1, u − 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
1
a
5
=
1
−1
a
1
=
1
0
a
9
=
−1
0
a
3
=
1
0
a
6
=
0
−1
a
2
=
1
0
a
8
=
−1
0
a
7
=
−1
0
a
10
=
−1
1
a
10
=
−1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
u
c
4
, c
5
, c
9
c
10
u − 1
c
6
, c
11
u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
y
c
4
, c
5
, c
6
c
9
, c
10
, c
11
y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = 0
3.28987 12.0000
22
V. I
u
5
= h2b + 3a − 1, 9a
2
− 6a − 7, u + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
−1
a
5
=
1
−1
a
1
=
−1
0
a
9
=
a
−
3
2
a +
1
2
a
3
=
1
2
a +
13
6
−2
a
6
=
−
4
3
a +
4
9
a −
2
3
a
2
=
1
2
a +
1
6
−2
a
8
=
−
1
2
a +
1
2
−
3
2
a +
1
2
a
7
=
−a
3
2
a −
1
2
a
10
=
−
1
3
a +
4
9
−
1
2
a −
1
6
a
10
=
−
1
3
a +
4
9
−
1
2
a −
1
6
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
8
u
2
− 2
c
2
(u + 2)
2
c
4
, c
9
(u + 1)
2
c
5
, c
10
9(9u
2
− 6u − 1)
c
6
, c
11
(u − 1)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
c
8
(y −2)
2
c
2
(y −4)
2
c
4
, c
6
, c
9
c
11
(y −1)
2
c
5
, c
10
81(81y
2
− 54y + 1)
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.27614
b = −1.41421
−1.64493 4.00000
u = −1.00000
a = −0.609476
b = 1.41421
−1.64493 4.00000
26
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u(u
2
− 2)(u
4
− u
2
+ 1)(u
20
+ u
19
+ ··· + 3u
2
− 1)
2
· (u
28
− 3u
27
+ ··· + 14u − 10)
c
2
u(u + 2)
2
(u
2
+ u + 1)
2
(u
20
+ 7u
19
+ ··· + 6u + 1)
2
· (u
28
+ 13u
27
+ ··· − 404u + 100)
c
3
, c
8
u(u
2
− 2)(u
2
+ 1)
2
(u
20
+ u
19
+ ··· + 2u − 1)
2
· (u
28
− 3u
27
+ ··· + 170u − 26)
c
4
, c
9
(u − 1)(u + 1)
2
(u
2
+ 1)
2
(u
28
− u
27
+ ··· − 14u + 1)
· (u
40
− u
39
+ ··· − 62u − 17)
c
5
, c
10
2304(u − 1)(9u
2
− 6u − 1)(16u
4
− 32u
3
+ 20u
2
− 4u + 1)
· (16u
28
+ 48u
27
+ ··· − 4u − 1)(u
40
− 5u
39
+ ··· − 3518u + 8903)
c
6
, c
11
((u − 1)
2
)(u + 1)(u
2
+ 1)
2
(u
28
− u
27
+ ··· − 14u + 1)
· (u
40
− u
39
+ ··· − 62u − 17)
27
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y(y −2)
2
(y
2
− y + 1)
2
(y
20
− 7y
19
+ ··· − 6y + 1)
2
· (y
28
− 13y
27
+ ··· + 404y + 100)
c
2
y(y −4)
2
(y
2
+ y + 1)
2
(y
20
+ 13y
19
+ ··· − 6y + 1)
2
· (y
28
+ 7y
27
+ ··· − 672016y + 10000)
c
3
, c
8
y(y −2)
2
(y + 1)
4
(y
20
+ 17y
19
+ ··· − 6y + 1)
2
· (y
28
+ 17y
27
+ ··· + 8332y + 676)
c
4
, c
6
, c
9
c
11
((y −1)
3
)(y + 1)
4
(y
28
− 19y
27
+ ··· − 94y + 1)
· (y
40
− 29y
39
+ ··· − 2824y + 289)
c
5
, c
10
5308416(y −1)(81y
2
− 54y + 1)(256y
4
− 384y
3
+ ··· + 24y + 1)
· (256y
28
− 5248y
27
+ ··· − 74y + 1)
· (y
40
− 25y
39
+ ··· − 6761242056y + 79263409)
28
