11a
212
(K11a
212
)
A knot diagram
1
Linearized knot diagam
6 1 8 7 10 2 11 3 5 9 4
Solving Sequence
3,8
4
9,11
1 2 7 5 6 10
c
3
c
8
c
11
c
2
c
7
c
4
c
6
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−10169u
18
− 100279u
17
+ ··· + 16444b + 115784,
− 15886u
18
− 173333u
17
+ ··· + 147996a − 951450, u
19
+ 11u
18
+ ··· − 408u − 72i
I
u
2
= h−75u
35
+ 383u
34
+ ··· + 8b + 212, 636u
35
a + 43u
35
+ ··· + 1470a − 238, u
36
− 5u
35
+ ··· − 16u + 3i
I
u
3
= h−2u
7
+ 5u
6
− 11u
5
+ 12u
4
− 11u
3
+ 6u
2
+ b − 5u + 1, −2u
7
+ 3u
6
− 7u
5
+ 3u
4
− 3u
3
− u
2
+ a − 2u − 2,
u
8
− 2u
7
+ 5u
6
− 5u
5
+ 6u
4
− 4u
3
+ 4u
2
− u + 1i
I
u
4
= hu
2
a − u
3
+ au − u
2
+ b − u + 1, −u
3
a − 2u
2
a + 2u
3
+ a
2
− 3au + 2u
2
− a + 3u − 1, u
4
+ u
3
+ 2u
2
+ 1i
I
v
1
= ha, b − 1, v −1i
* 5 irreducible components of dim
C
= 0, with total 108 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−1.02×10
4
u
18
−1.00×10
5
u
17
+· · ·+1.64×10
4
b+1.16×10
5
, −1.59×10
4
u
18
−
1.73 × 10
5
u
17
+ · · · + 1.48 × 10
5
a − 9.51 × 10
5
, u
19
+ 11u
18
+ · · · − 408u − 72i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
9
=
u
u
a
11
=
0.107341u
18
+ 1.17120u
17
+ ··· + 18.8285u + 6.42889
0.618402u
18
+ 6.09821u
17
+ ··· − 54.0570u − 7.04111
a
1
=
0.0977932u
18
+ 0.457323u
17
+ ··· + 69.0524u + 14.1574
−0.694661u
18
− 7.34791u
17
+ ··· + 195.043u + 36.7964
a
2
=
−0.222793u
18
− 2.08232u
17
+ ··· + 5.44757u − 0.157423
−0.0553393u
18
− 0.402092u
17
+ ··· + 28.9571u + 8.20360
a
7
=
−0.324472u
18
− 2.74858u
17
+ ··· − 8.23791u − 2.15037
0.157869u
18
+ 2.29762u
17
+ ··· − 175.909u − 35.7215
a
5
=
−0.480381u
18
− 5.30821u
17
+ ··· + 103.723u + 14.5621
−0.150389u
18
− 1.42623u
17
+ ··· − 84.6227u − 22.7665
a
6
=
−0.901210u
18
− 9.04017u
17
+ ··· + 115.314u + 16.7261
−0.348699u
18
− 2.61384u
17
+ ··· − 168.918u − 39.7808
a
10
=
0.400700u
18
+ 4.88295u
17
+ ··· − 227.797u − 43.5867
0.911761u
18
+ 9.80996u
17
+ ··· − 300.682u − 57.0567
a
10
=
0.400700u
18
+ 4.88295u
17
+ ··· − 227.797u − 43.5867
0.911761u
18
+ 9.80996u
17
+ ··· − 300.682u − 57.0567
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
4653
4111
u
18
−
45527
4111
u
17
+ ··· +
398988
4111
u +
53874
4111
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
9
u
19
+ u
18
+ ··· + 2u + 1
c
2
, c
10
u
19
+ 9u
18
+ ··· − 2u + 1
c
3
, c
8
u
19
− 11u
18
+ ··· − 408u + 72
c
4
u
19
− 17u
18
+ ··· − 1920u + 256
c
7
, c
11
u
19
− 2u
18
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
y
19
− 9y
18
+ ··· − 2y −1
c
2
, c
10
y
19
+ 7y
18
+ ··· + 26y −1
c
3
, c
8
y
19
+ 11y
18
+ ··· + 2016y −5184
c
4
y
19
− y
18
+ ··· + 245760y −65536
c
7
, c
11
y
19
− 6y
18
+ ··· + 27y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.358353 + 0.924986I
a = −0.311412 + 0.717346I
b = −0.150073 + 0.860307I
−0.58834 − 1.54269I −4.69839 + 4.51597I
u = −0.358353 − 0.924986I
a = −0.311412 − 0.717346I
b = −0.150073 − 0.860307I
−0.58834 + 1.54269I −4.69839 − 4.51597I
u = −0.966676 + 0.332222I
a = −0.818238 + 0.627994I
b = −0.311396 − 0.164177I
4.64927 + 0.26455I −1.71990 + 1.02803I
u = −0.966676 − 0.332222I
a = −0.818238 − 0.627994I
b = −0.311396 + 0.164177I
4.64927 − 0.26455I −1.71990 − 1.02803I
u = −0.161360 + 1.222540I
a = 0.464053 − 1.047230I
b = −0.11073 − 2.09115I
−8.96802 − 0.88990I −16.2208 + 0.4171I
u = −0.161360 − 1.222540I
a = 0.464053 + 1.047230I
b = −0.11073 + 2.09115I
−8.96802 + 0.88990I −16.2208 − 0.4171I
u = −1.289970 + 0.199680I
a = 0.686320 − 0.541724I
b = −0.058453 + 0.397559I
1.64114 + 11.01570I −7.29016 − 9.56628I
u = −1.289970 − 0.199680I
a = 0.686320 + 0.541724I
b = −0.058453 − 0.397559I
1.64114 − 11.01570I −7.29016 + 9.56628I
u = −0.957767 + 0.906773I
a = 0.311369 + 0.803824I
b = −0.398706 + 0.951941I
−2.39512 + 0.38448I −10.41076 − 2.93354I
u = −0.957767 − 0.906773I
a = 0.311369 − 0.803824I
b = −0.398706 − 0.951941I
−2.39512 − 0.38448I −10.41076 + 2.93354I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.580441 + 1.193400I
a = −0.361294 + 1.095690I
b = −0.81291 + 1.75794I
1.92326 − 5.83662I −4.80851 + 2.86417I
u = −0.580441 − 1.193400I
a = −0.361294 − 1.095690I
b = −0.81291 − 1.75794I
1.92326 + 5.83662I −4.80851 − 2.86417I
u = 0.601065
a = −0.393184
b = 0.378379
−1.08922 −8.82220
u = −0.65100 + 1.34345I
a = 0.271854 − 1.066410I
b = 0.98510 − 2.05670I
−2.0202 − 17.7092I −9.44410 + 10.28902I
u = −0.65100 − 1.34345I
a = 0.271854 + 1.066410I
b = 0.98510 + 2.05670I
−2.0202 + 17.7092I −9.44410 − 10.28902I
u = −0.88646 + 1.29579I
a = −0.280005 − 0.575557I
b = 0.078111 − 1.304770I
−3.47013 − 7.94178I −12.2006 + 9.0681I
u = −0.88646 − 1.29579I
a = −0.280005 + 0.575557I
b = 0.078111 + 1.304770I
−3.47013 + 7.94178I −12.2006 − 9.0681I
u = 0.05150 + 1.63379I
a = 0.067278 − 0.325219I
b = −0.410127 − 0.971726I
−5.85414 + 4.86122I −16.7957 − 3.2884I
u = 0.05150 − 1.63379I
a = 0.067278 + 0.325219I
b = −0.410127 + 0.971726I
−5.85414 − 4.86122I −16.7957 + 3.2884I
6
II. I
u
2
= h−75u
35
+ 383u
34
+ · · · + 8b + 212, 636u
35
a + 43u
35
+ · · · + 1470a −
238, u
36
− 5u
35
+ · · · − 16u + 3i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
9
=
u
u
a
11
=
a
9.37500u
35
− 47.8750u
34
+ ··· + 161.750u − 26.5000
a
1
=
−
75
8
u
35
+
383
8
u
34
+ ··· + a +
53
2
9
4
u
35
−
125
8
u
34
+ ··· +
941
8
u −
47
2
a
2
=
−3.37500au
35
+ 1.54167u
35
+ ··· + 21.3750a − 3.66667
−0.250000au
35
− 4.75000u
35
+ ··· + 16.5000a + 13.5000
a
7
=
−9.37500au
35
− 3.66667u
35
+ ··· + 26.5000a + 1.79167
−
57
8
u
35
a −
47
8
u
35
+ ··· + 3a −
7
4
a
5
=
−4.87500au
35
+ 12.2917u
35
+ ··· + 26.7500a − 25.7917
−7.37500au
35
+ 13.5000u
35
+ ··· + 17.6250a − 23.3750
a
6
=
5.87500au
35
+ 13.7083u
35
+ ··· + 2.75000a − 6.33333
1.62500au
35
+ 4.87500u
35
+ ··· + 12.7500a − 26.7500
a
10
=
−
57
8
u
35
+
129
4
u
34
+ ··· + a + 3
9
4
u
35
−
125
8
u
34
+ ··· +
941
8
u −
47
2
a
10
=
−
57
8
u
35
+
129
4
u
34
+ ··· + a + 3
9
4
u
35
−
125
8
u
34
+ ··· +
941
8
u −
47
2
(ii) Obstruction class = −1
(iii) Cusp Shapes =
47
2
u
35
−
211
2
u
34
+ ··· + 73u +
3
2
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
9
u
72
− u
71
+ ··· − 26u + 43
c
2
, c
10
u
72
+ 29u
71
+ ··· + 25272u + 1849
c
3
, c
8
(u
36
+ 5u
35
+ ··· + 16u + 3)
2
c
4
(u
36
+ 7u
35
+ ··· + 10u + 1)
2
c
7
, c
11
u
72
− 2u
71
+ ··· − 22u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
y
72
− 29y
71
+ ··· − 25272y + 1849
c
2
, c
10
y
72
+ 31y
71
+ ··· − 7699036y + 3418801
c
3
, c
8
(y
36
+ 23y
35
+ ··· + 140y + 9)
2
c
4
(y
36
+ 7y
35
+ ··· − 4y + 1)
2
c
7
, c
11
y
72
− 4y
71
+ ··· − 18y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.323607 + 0.937654I
a = −0.175351 − 0.450939I
b = −1.42855 − 2.11019I
−0.65303 + 8.38929I −8.7813 − 13.2523I
u = 0.323607 + 0.937654I
a = 2.11473 − 0.35700I
b = 1.05507 − 1.24949I
−0.65303 + 8.38929I −8.7813 − 13.2523I
u = 0.323607 − 0.937654I
a = −0.175351 + 0.450939I
b = −1.42855 + 2.11019I
−0.65303 − 8.38929I −8.7813 + 13.2523I
u = 0.323607 − 0.937654I
a = 2.11473 + 0.35700I
b = 1.05507 + 1.24949I
−0.65303 − 8.38929I −8.7813 + 13.2523I
u = −0.407223 + 0.893066I
a = −0.791967 + 0.557123I
b = 0.506201 + 0.724691I
1.70318 − 0.95050I −2.58255 + 0.79026I
u = −0.407223 + 0.893066I
a = −0.28278 + 1.70972I
b = −1.24717 + 1.80857I
1.70318 − 0.95050I −2.58255 + 0.79026I
u = −0.407223 − 0.893066I
a = −0.791967 − 0.557123I
b = 0.506201 − 0.724691I
1.70318 + 0.95050I −2.58255 − 0.79026I
u = −0.407223 − 0.893066I
a = −0.28278 − 1.70972I
b = −1.24717 − 1.80857I
1.70318 + 0.95050I −2.58255 − 0.79026I
u = 0.285005 + 0.986264I
a = 0.906188 + 0.471916I
b = −0.680137 + 0.614572I
1.39070 + 5.45819I −4.75268 − 7.85090I
u = 0.285005 + 0.986264I
a = −0.18402 − 1.83089I
b = −0.98618 − 2.55701I
1.39070 + 5.45819I −4.75268 − 7.85090I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.285005 − 0.986264I
a = 0.906188 − 0.471916I
b = −0.680137 − 0.614572I
1.39070 − 5.45819I −4.75268 + 7.85090I
u = 0.285005 − 0.986264I
a = −0.18402 + 1.83089I
b = −0.98618 + 2.55701I
1.39070 − 5.45819I −4.75268 + 7.85090I
u = −0.204395 + 0.939901I
a = 0.159162 − 0.415191I
b = 1.60287 − 1.64255I
0.14515 − 3.09361I −8.82386 + 5.93072I
u = −0.204395 + 0.939901I
a = 1.66507 + 1.03102I
b = 0.64754 + 1.27304I
0.14515 − 3.09361I −8.82386 + 5.93072I
u = −0.204395 − 0.939901I
a = 0.159162 + 0.415191I
b = 1.60287 + 1.64255I
0.14515 + 3.09361I −8.82386 − 5.93072I
u = −0.204395 − 0.939901I
a = 1.66507 − 1.03102I
b = 0.64754 − 1.27304I
0.14515 + 3.09361I −8.82386 − 5.93072I
u = −0.988537 + 0.351198I
a = 0.225935 + 0.946460I
b = −0.0017989 − 0.1085760I
−1.77149 − 4.10144I −9.97996 + 6.24934I
u = −0.988537 + 0.351198I
a = 0.588772 + 0.758163I
b = −0.473418 + 0.617705I
−1.77149 − 4.10144I −9.97996 + 6.24934I
u = −0.988537 − 0.351198I
a = 0.225935 − 0.946460I
b = −0.0017989 + 0.1085760I
−1.77149 + 4.10144I −9.97996 − 6.24934I
u = −0.988537 − 0.351198I
a = 0.588772 − 0.758163I
b = −0.473418 − 0.617705I
−1.77149 + 4.10144I −9.97996 − 6.24934I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.080650 + 0.243992I
a = −0.856190 − 0.655908I
b = −0.047350 + 0.413085I
3.39022 − 5.68113I −3.92911 + 4.67272I
u = 1.080650 + 0.243992I
a = 0.724773 + 0.544582I
b = 0.249139 − 0.068035I
3.39022 − 5.68113I −3.92911 + 4.67272I
u = 1.080650 − 0.243992I
a = −0.856190 + 0.655908I
b = −0.047350 − 0.413085I
3.39022 + 5.68113I −3.92911 − 4.67272I
u = 1.080650 − 0.243992I
a = 0.724773 − 0.544582I
b = 0.249139 + 0.068035I
3.39022 + 5.68113I −3.92911 − 4.67272I
u = −0.118764 + 0.883260I
a = 1.240850 + 0.207363I
b = −0.794679 + 0.293981I
0.57130 + 1.50593I −8.88680 + 0.90138I
u = −0.118764 + 0.883260I
a = −0.11523 − 1.91114I
b = 0.64321 − 2.55956I
0.57130 + 1.50593I −8.88680 + 0.90138I
u = −0.118764 − 0.883260I
a = 1.240850 − 0.207363I
b = −0.794679 − 0.293981I
0.57130 − 1.50593I −8.88680 − 0.90138I
u = −0.118764 − 0.883260I
a = −0.11523 + 1.91114I
b = 0.64321 + 2.55956I
0.57130 − 1.50593I −8.88680 − 0.90138I
u = 0.375701 + 1.185220I
a = −0.185369 − 0.878085I
b = 0.06699 − 1.99722I
−4.64275 + 3.93521I −11.18615 − 4.33934I
u = 0.375701 + 1.185220I
a = 0.543890 + 1.086350I
b = 0.68365 + 1.43792I
−4.64275 + 3.93521I −11.18615 − 4.33934I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.375701 − 1.185220I
a = −0.185369 + 0.878085I
b = 0.06699 + 1.99722I
−4.64275 − 3.93521I −11.18615 + 4.33934I
u = 0.375701 − 1.185220I
a = 0.543890 − 1.086350I
b = 0.68365 − 1.43792I
−4.64275 − 3.93521I −11.18615 + 4.33934I
u = 0.366522 + 0.661253I
a = −1.43742 − 0.22873I
b = 0.789147 + 0.111369I
0.15412 − 5.32337I −7.89175 + 4.81078I
u = 0.366522 + 0.661253I
a = −0.25927 + 1.87585I
b = 1.20633 + 1.72823I
0.15412 − 5.32337I −7.89175 + 4.81078I
u = 0.366522 − 0.661253I
a = −1.43742 + 0.22873I
b = 0.789147 − 0.111369I
0.15412 + 5.32337I −7.89175 − 4.81078I
u = 0.366522 − 0.661253I
a = −0.25927 − 1.87585I
b = 1.20633 − 1.72823I
0.15412 + 5.32337I −7.89175 − 4.81078I
u = 0.733621 + 0.056495I
a = −0.712576 + 0.589887I
b = 0.390901 + 0.249697I
−1.027180 + 0.066620I −7.89585 − 0.16999I
u = 0.733621 + 0.056495I
a = 0.000334 − 0.690063I
b = 0.498708 − 0.023336I
−1.027180 + 0.066620I −7.89585 − 0.16999I
u = 0.733621 − 0.056495I
a = −0.712576 − 0.589887I
b = 0.390901 − 0.249697I
−1.027180 − 0.066620I −7.89585 + 0.16999I
u = 0.733621 − 0.056495I
a = 0.000334 + 0.690063I
b = 0.498708 + 0.023336I
−1.027180 − 0.066620I −7.89585 + 0.16999I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.461229 + 1.192960I
a = 0.735450 + 0.704350I
b = 0.941882 + 0.432336I
−4.33727 + 4.33344I 0. − 7.98095I
u = 0.461229 + 1.192960I
a = −0.079786 − 0.637262I
b = −0.29680 − 1.88578I
−4.33727 + 4.33344I 0. − 7.98095I
u = 0.461229 − 1.192960I
a = 0.735450 − 0.704350I
b = 0.941882 − 0.432336I
−4.33727 − 4.33344I 0. + 7.98095I
u = 0.461229 − 1.192960I
a = −0.079786 + 0.637262I
b = −0.29680 + 1.88578I
−4.33727 − 4.33344I 0. + 7.98095I
u = 0.261513 + 1.263160I
a = 0.008648 + 0.711153I
b = 0.111760 + 1.082130I
−2.36014 − 1.61358I 0
u = 0.261513 + 1.263160I
a = 0.056995 − 0.282130I
b = 0.796685 − 0.665417I
−2.36014 − 1.61358I 0
u = 0.261513 − 1.263160I
a = 0.008648 − 0.711153I
b = 0.111760 − 1.082130I
−2.36014 + 1.61358I 0
u = 0.261513 − 1.263160I
a = 0.056995 + 0.282130I
b = 0.796685 + 0.665417I
−2.36014 + 1.61358I 0
u = −0.386093 + 1.315540I
a = 0.321924 − 0.776161I
b = −0.07289 − 2.11359I
−6.83745 − 8.51873I 0
u = −0.386093 + 1.315540I
a = 0.567468 − 1.208310I
b = 1.22818 − 2.05777I
−6.83745 − 8.51873I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.386093 − 1.315540I
a = 0.321924 + 0.776161I
b = −0.07289 + 2.11359I
−6.83745 + 8.51873I 0
u = −0.386093 − 1.315540I
a = 0.567468 + 1.208310I
b = 1.22818 + 2.05777I
−6.83745 + 8.51873I 0
u = 0.790023 + 1.128140I
a = −0.183542 + 0.797397I
b = 0.321793 + 1.049820I
−2.51334 + 3.34840I 0
u = 0.790023 + 1.128140I
a = 0.286168 − 0.668765I
b = 0.038092 − 1.366730I
−2.51334 + 3.34840I 0
u = 0.790023 − 1.128140I
a = −0.183542 − 0.797397I
b = 0.321793 − 1.049820I
−2.51334 − 3.34840I 0
u = 0.790023 − 1.128140I
a = 0.286168 + 0.668765I
b = 0.038092 + 1.366730I
−2.51334 − 3.34840I 0
u = −0.341744 + 0.520197I
a = −0.607007 + 0.115057I
b = −0.304801 + 1.331690I
2.67726 − 2.50734I 0.46124 + 4.14494I
u = −0.341744 + 0.520197I
a = −2.20469 + 1.12056I
b = −0.885119 − 0.256430I
2.67726 − 2.50734I 0.46124 + 4.14494I
u = −0.341744 − 0.520197I
a = −0.607007 − 0.115057I
b = −0.304801 − 1.331690I
2.67726 + 2.50734I 0.46124 − 4.14494I
u = −0.341744 − 0.520197I
a = −2.20469 − 1.12056I
b = −0.885119 + 0.256430I
2.67726 + 2.50734I 0.46124 − 4.14494I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.598145 + 1.270670I
a = 0.364362 + 1.030040I
b = 0.72567 + 1.78948I
0.12476 + 11.63330I 0
u = 0.598145 + 1.270670I
a = −0.282009 − 1.154280I
b = −1.01814 − 2.10114I
0.12476 + 11.63330I 0
u = 0.598145 − 1.270670I
a = 0.364362 − 1.030040I
b = 0.72567 − 1.78948I
0.12476 − 11.63330I 0
u = 0.598145 − 1.270670I
a = −0.282009 + 1.154280I
b = −1.01814 + 2.10114I
0.12476 − 11.63330I 0
u = 0.255236 + 0.508176I
a = 0.494661 − 0.107326I
b = 0.75887 + 1.28212I
2.67098 − 2.77341I −0.394325 + 0.708366I
u = 0.255236 + 0.508176I
a = −2.79447 − 0.04340I
b = −0.731661 + 0.492551I
2.67098 − 2.77341I −0.394325 + 0.708366I
u = 0.255236 − 0.508176I
a = 0.494661 + 0.107326I
b = 0.75887 − 1.28212I
2.67098 + 2.77341I −0.394325 − 0.708366I
u = 0.255236 − 0.508176I
a = −2.79447 + 0.04340I
b = −0.731661 − 0.492551I
2.67098 + 2.77341I −0.394325 − 0.708366I
u = −0.58449 + 1.51506I
a = −0.162437 − 0.495879I
b = 0.227921 − 1.342130I
−5.13435 − 2.75063I 0
u = −0.58449 + 1.51506I
a = −0.024617 − 0.210269I
b = −0.521920 − 0.498154I
−5.13435 − 2.75063I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.58449 − 1.51506I
a = −0.162437 + 0.495879I
b = 0.227921 + 1.342130I
−5.13435 + 2.75063I 0
u = −0.58449 − 1.51506I
a = −0.024617 + 0.210269I
b = −0.521920 + 0.498154I
−5.13435 + 2.75063I 0
17
III.
I
u
3
= h−2u
7
+ 5u
6
+ · · · +b + 1, −2u
7
+ 3u
6
+ · · · +a − 2, u
8
− 2u
7
+ · · · −u + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
9
=
u
u
a
11
=
2u
7
− 3u
6
+ 7u
5
− 3u
4
+ 3u
3
+ u
2
+ 2u + 2
2u
7
− 5u
6
+ 11u
5
− 12u
4
+ 11u
3
− 6u
2
+ 5u − 1
a
1
=
u
7
+ 6u
4
− 6u
3
+ 7u
2
− 2u + 4
2u
7
− 4u
6
+ 9u
5
− 8u
4
+ 7u
3
− 3u
2
+ 3u
a
2
=
−u
7
+ 3u
6
− 7u
5
+ 10u
4
− 11u
3
+ 10u
2
− 7u + 4
u
7
− 2u
6
+ 5u
5
− 5u
4
+ 5u
3
− 2u
2
+ u + 1
a
7
=
−u
7
+ u
6
− 3u
5
− u
3
− 2u
2
− 3
−u
7
+ 2u
6
− 5u
5
+ 5u
4
− 6u
3
+ 4u
2
− 3u
a
5
=
2u
7
− 5u
6
+ 11u
5
− 13u
4
+ 12u
3
− 9u
2
+ 6u − 1
−u
6
+ 2u
5
− 5u
4
+ 5u
3
− 6u
2
+ 3u − 2
a
6
=
3u
7
− 8u
6
+ 17u
5
− 20u
4
+ 17u
3
− 11u
2
+ 8u − 3
−2u
6
+ 4u
5
− 9u
4
+ 8u
3
− 7u
2
+ 3u − 3
a
10
=
2u
7
− 2u
6
+ 5u
5
+ 2u
4
− 2u
3
+ 6u
2
+ 4
2u
7
− 4u
6
+ 9u
5
− 7u
4
+ 6u
3
− u
2
+ 3u + 1
a
10
=
2u
7
− 2u
6
+ 5u
5
+ 2u
4
− 2u
3
+ 6u
2
+ 4
2u
7
− 4u
6
+ 9u
5
− 7u
4
+ 6u
3
− u
2
+ 3u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
7
+ 15u
6
− 33u
5
+ 42u
4
− 36u
3
+ 22u
2
− 18u − 3
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
8
− 2u
6
+ 3u
4
+ u
3
− 2u
2
− u + 1
c
2
, c
10
u
8
+ 4u
7
+ 10u
6
+ 16u
5
+ 19u
4
+ 17u
3
+ 12u
2
+ 5u + 1
c
3
u
8
− 2u
7
+ 5u
6
− 5u
5
+ 6u
4
− 4u
3
+ 4u
2
− u + 1
c
4
u
8
− 3u
7
+ 3u
6
− u
5
− u
4
+ u
3
+ 1
c
6
, c
9
u
8
− 2u
6
+ 3u
4
− u
3
− 2u
2
+ u + 1
c
7
, c
11
u
8
− u
7
+ 2u
4
− u
3
− u
2
+ 1
c
8
u
8
+ 2u
7
+ 5u
6
+ 5u
5
+ 6u
4
+ 4u
3
+ 4u
2
+ u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
y
8
− 4y
7
+ 10y
6
− 16y
5
+ 19y
4
− 17y
3
+ 12y
2
− 5y + 1
c
2
, c
10
y
8
+ 4y
7
+ 10y
6
+ 12y
5
+ 19y
4
+ 27y
3
+ 12y
2
− y + 1
c
3
, c
8
y
8
+ 6y
7
+ 17y
6
+ 27y
5
+ 34y
4
+ 32y
3
+ 20y
2
+ 7y + 1
c
4
y
8
− 3y
7
+ y
6
− y
5
+ 5y
4
+ 5y
3
− 2y
2
+ 1
c
7
, c
11
y
8
− y
7
+ 4y
6
− 4y
5
+ 6y
4
− 5y
3
+ 5y
2
− 2y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.792109 + 0.738037I
a = −0.382665 + 0.800987I
b = 0.073913 + 0.733193I
−2.49555 + 0.86293I −13.14261 − 3.03469I
u = 0.792109 − 0.738037I
a = −0.382665 − 0.800987I
b = 0.073913 − 0.733193I
−2.49555 − 0.86293I −13.14261 + 3.03469I
u = −0.289722 + 0.810357I
a = −1.207080 − 0.334530I
b = 0.08655 − 1.63964I
−0.50761 − 7.31144I −8.44025 + 5.07969I
u = −0.289722 − 0.810357I
a = −1.207080 + 0.334530I
b = 0.08655 + 1.63964I
−0.50761 + 7.31144I −8.44025 − 5.07969I
u = 0.010381 + 0.674737I
a = 1.24580 + 1.30467I
b = −0.28206 + 1.43052I
1.91736 + 3.67399I −5.72808 − 5.47869I
u = 0.010381 − 0.674737I
a = 1.24580 − 1.30467I
b = −0.28206 − 1.43052I
1.91736 − 3.67399I −5.72808 + 5.47869I
u = 0.48723 + 1.51401I
a = −0.156057 − 0.473494I
b = −0.378403 − 1.209690I
−5.49394 + 5.83988I −13.6891 − 9.4941I
u = 0.48723 − 1.51401I
a = −0.156057 + 0.473494I
b = −0.378403 + 1.209690I
−5.49394 − 5.83988I −13.6891 + 9.4941I
21
IV.
I
u
4
= hu
2
a−u
3
+au−u
2
+b−u+1, −u
3
a+2u
3
+· · ·−a−1, u
4
+u
3
+2u
2
+1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
9
=
u
u
a
11
=
a
−u
2
a + u
3
− au + u
2
+ u − 1
a
1
=
−u
3
+ au − u
2
+ a − u + 1
−u
3
a − u
2
a − au − 1
a
2
=
−u
2
a + u
3
+ 2u
2
− a + 3u + 2
−u
3
a − u
2
a − au + u
2
− a + u + 1
a
7
=
u
3
a + u
2
a + au + u
2
− a + u + 2
u
3
a + u
2
a − u
3
+ au − u
2
− u + 1
a
5
=
u
3
a + u
2
a − u
3
+ 2au − u
2
− u + 2
−u
3
+ au − 2u
2
− 2u
a
6
=
u
3
a + 2u
2
a + 2au + u
2
+ u + 1
u
2
a − u
3
+ au − u
2
+ a − 2u
a
10
=
u
2
a − u
3
− u
2
+ 2a − u
−au + a − 1
a
10
=
u
2
a − u
3
− u
2
+ 2a − u
−au + a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
3
− 6u
2
− 7u − 7
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
8
− 2u
6
− u
5
+ 3u
4
+ u
3
− 2u
2
+ 1
c
2
, c
10
u
8
+ 4u
7
+ 10u
6
+ 17u
5
+ 21u
4
+ 17u
3
+ 10u
2
+ 4u + 1
c
3
(u
4
+ u
3
+ 2u
2
+ 1)
2
c
4
(u
4
+ u
3
+ 1)
2
c
6
, c
9
u
8
− 2u
6
+ u
5
+ 3u
4
− u
3
− 2u
2
+ 1
c
7
, c
11
u
8
− 3u
7
+ 3u
6
− u
5
− u
4
+ 2u
3
− u
2
+ 1
c
8
(u
4
− u
3
+ 2u
2
+ 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
y
8
− 4y
7
+ 10y
6
− 17y
5
+ 21y
4
− 17y
3
+ 10y
2
− 4y + 1
c
2
, c
10
y
8
+ 4y
7
+ 6y
6
+ 15y
5
+ 33y
4
+ 15y
3
+ 6y
2
+ 4y + 1
c
3
, c
8
(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
2
c
4
(y
4
− y
3
+ 2y
2
+ 1)
2
c
7
, c
11
y
8
− 3y
7
+ y
6
+ 3y
5
+ y
4
+ 4y
3
− y
2
− 2y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.175098 + 0.691825I
a = 1.258400 + 0.403038I
b = −0.799065 − 0.398882I
1.13814 + 2.37936I −4.06162 − 4.69148I
u = 0.175098 + 0.691825I
a = −0.87507 + 1.88950I
b = 0.00729 + 1.99959I
1.13814 + 2.37936I −4.06162 − 4.69148I
u = 0.175098 − 0.691825I
a = 1.258400 − 0.403038I
b = −0.799065 + 0.398882I
1.13814 − 2.37936I −4.06162 + 4.69148I
u = 0.175098 − 0.691825I
a = −0.87507 − 1.88950I
b = 0.00729 − 1.99959I
1.13814 − 2.37936I −4.06162 + 4.69148I
u = −0.675098 + 1.227920I
a = −0.243445 + 0.679234I
b = −0.693631 + 0.465880I
−4.42801 − 3.38562I −12.43838 + 2.38747I
u = −0.675098 + 1.227920I
a = −0.139876 − 0.483891I
b = −0.01459 − 1.49846I
−4.42801 − 3.38562I −12.43838 + 2.38747I
u = −0.675098 − 1.227920I
a = −0.243445 − 0.679234I
b = −0.693631 − 0.465880I
−4.42801 + 3.38562I −12.43838 − 2.38747I
u = −0.675098 − 1.227920I
a = −0.139876 + 0.483891I
b = −0.01459 + 1.49846I
−4.42801 + 3.38562I −12.43838 − 2.38747I
25
V. I
v
1
= ha, b − 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
1
0
a
4
=
1
0
a
9
=
1
0
a
11
=
0
1
a
1
=
−1
1
a
2
=
2
−1
a
7
=
1
−1
a
5
=
0
1
a
6
=
−1
0
a
10
=
1
1
a
10
=
1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
9
u − 1
c
2
, c
7
, c
10
c
11
u + 1
c
3
, c
8
u
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
9
, c
10
, c
11
y −1
c
3
, c
8
y
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
−4.93480 −18.0000
29
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)(u
8
− 2u
6
+ 3u
4
+ u
3
− 2u
2
− u + 1)
· (u
8
− 2u
6
− u
5
+ 3u
4
+ u
3
− 2u
2
+ 1)(u
19
+ u
18
+ ··· + 2u + 1)
· (u
72
− u
71
+ ··· − 26u + 43)
c
2
, c
10
(u + 1)(u
8
+ 4u
7
+ 10u
6
+ 16u
5
+ 19u
4
+ 17u
3
+ 12u
2
+ 5u + 1)
· (u
8
+ 4u
7
+ 10u
6
+ 17u
5
+ 21u
4
+ 17u
3
+ 10u
2
+ 4u + 1)
· (u
19
+ 9u
18
+ ··· − 2u + 1)(u
72
+ 29u
71
+ ··· + 25272u + 1849)
c
3
u(u
4
+ u
3
+ 2u
2
+ 1)
2
(u
8
− 2u
7
+ ··· − u + 1)
· (u
19
− 11u
18
+ ··· − 408u + 72)(u
36
+ 5u
35
+ ··· + 16u + 3)
2
c
4
(u − 1)(u
4
+ u
3
+ 1)
2
(u
8
− 3u
7
+ 3u
6
− u
5
− u
4
+ u
3
+ 1)
· (u
19
− 17u
18
+ ··· − 1920u + 256)(u
36
+ 7u
35
+ ··· + 10u + 1)
2
c
6
, c
9
(u − 1)(u
8
− 2u
6
+ 3u
4
− u
3
− 2u
2
+ u + 1)
· (u
8
− 2u
6
+ u
5
+ 3u
4
− u
3
− 2u
2
+ 1)(u
19
+ u
18
+ ··· + 2u + 1)
· (u
72
− u
71
+ ··· − 26u + 43)
c
7
, c
11
(u + 1)(u
8
− 3u
7
+ ··· − u
2
+ 1)(u
8
− u
7
+ ··· − u
2
+ 1)
· (u
19
− 2u
18
+ ··· + u + 1)(u
72
− 2u
71
+ ··· − 22u + 1)
c
8
u(u
4
− u
3
+ 2u
2
+ 1)
2
(u
8
+ 2u
7
+ ··· + u + 1)
· (u
19
− 11u
18
+ ··· − 408u + 72)(u
36
+ 5u
35
+ ··· + 16u + 3)
2
30
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
(y −1)(y
8
− 4y
7
+ 10y
6
− 17y
5
+ 21y
4
− 17y
3
+ 10y
2
− 4y + 1)
· (y
8
− 4y
7
+ 10y
6
− 16y
5
+ 19y
4
− 17y
3
+ 12y
2
− 5y + 1)
· (y
19
− 9y
18
+ ··· − 2y −1)(y
72
− 29y
71
+ ··· − 25272y + 1849)
c
2
, c
10
(y −1)(y
8
+ 4y
7
+ 6y
6
+ 15y
5
+ 33y
4
+ 15y
3
+ 6y
2
+ 4y + 1)
· (y
8
+ 4y
7
+ 10y
6
+ 12y
5
+ 19y
4
+ 27y
3
+ 12y
2
− y + 1)
· (y
19
+ 7y
18
+ ··· + 26y −1)
· (y
72
+ 31y
71
+ ··· − 7699036y + 3418801)
c
3
, c
8
y(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
2
· (y
8
+ 6y
7
+ 17y
6
+ 27y
5
+ 34y
4
+ 32y
3
+ 20y
2
+ 7y + 1)
· (y
19
+ 11y
18
+ ··· + 2016y −5184)(y
36
+ 23y
35
+ ··· + 140y + 9)
2
c
4
(y −1)(y
4
− y
3
+ 2y
2
+ 1)
2
(y
8
− 3y
7
+ ··· − 2y
2
+ 1)
· (y
19
− y
18
+ ··· + 245760y −65536)(y
36
+ 7y
35
+ ··· − 4y + 1)
2
c
7
, c
11
(y −1)(y
8
− 3y
7
+ y
6
+ 3y
5
+ y
4
+ 4y
3
− y
2
− 2y + 1)
· (y
8
− y
7
+ 4y
6
− 4y
5
+ 6y
4
− 5y
3
+ 5y
2
− 2y + 1)
· (y
19
− 6y
18
+ ··· + 27y −1)(y
72
− 4y
71
+ ··· − 18y + 1)
31
