11n
182
(K11n
182
)
A knot diagram
1
Linearized knot diagam
9 7 1 10 11 3 5 3 4 7 8
Solving Sequence
5,7 8,10
11 1 4 3 2 6 9
c
7
c
10
c
11
c
4
c
3
c
2
c
6
c
9
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−20148888016u
22
− 749797203535u
21
+ ··· + 2663810305417b − 383665719756,
− 10534409632231u
22
+ 12986341631640u
21
+ ··· + 2663810305417a − 72898377806205,
u
23
− u
22
+ ··· + 5u + 1i
I
u
2
= h−4.69374 × 10
59
u
39
+ 1.06924 × 10
60
u
38
+ ··· + 3.76856 × 10
59
b + 1.45903 × 10
61
,
6.35380 × 10
61
u
39
− 1.40886 × 10
62
u
38
+ ··· + 5.46442 × 10
61
a − 2.06339 × 10
63
, u
40
− 3u
39
+ ··· − 25u + 29i
I
u
3
= h−45306u
13
− 181273u
12
+ ··· + 142097b + 321146,
803669u
13
+ 4740916u
12
+ ··· + 142097a + 1220228,
u
14
+ 6u
13
+ 12u
12
+ 6u
11
− 3u
10
+ 23u
9
+ 59u
8
+ 22u
7
− 43u
6
− 45u
5
− 7u
4
+ 16u
3
+ 14u
2
+ 5u + 1i
I
u
4
= hb + u + 1, a, u
3
+ u
2
− 1i
* 4 irreducible components of dim
C
= 0, with total 80 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−2.01×10
10
u
22
−7.50×10
11
u
21
+· · ·+2.66×10
12
b−3.84×10
11
, −1.05×
10
13
u
22
+1.30×10
13
u
21
+· · ·+2.66×10
12
a−7.29×10
13
, u
23
−u
22
+· · ·+5u+1i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
10
=
3.95464u
22
− 4.87510u
21
+ ··· − 45.3209u + 27.3662
0.00756394u
22
+ 0.281475u
21
+ ··· + 1.99017u + 0.144029
a
11
=
3.96220u
22
− 4.59362u
21
+ ··· − 43.3307u + 27.5102
0.00756394u
22
+ 0.281475u
21
+ ··· + 1.99017u + 0.144029
a
1
=
4.19771u
22
− 4.99533u
21
+ ··· − 46.1260u + 27.9976
−0.296345u
22
+ 0.358714u
21
+ ··· + 2.58565u + 0.310226
a
4
=
−22.8331u
22
+ 26.1180u
21
+ ··· + 253.774u − 151.915
0.0861032u
22
− 0.0646937u
21
+ ··· − 0.600147u + 0.912866
a
3
=
−22.0355u
22
+ 25.3812u
21
+ ··· + 246.765u − 147.718
0.0237345u
22
− 0.319401u
21
+ ··· − 2.39210u + 0.616521
a
2
=
−22.0593u
22
+ 25.7006u
21
+ ··· + 249.157u − 148.334
0.0237345u
22
− 0.319401u
21
+ ··· − 2.39210u + 0.616521
a
6
=
−22.6866u
22
+ 26.0341u
21
+ ··· + 251.311u − 149.997
0.0604215u
22
− 0.0191991u
21
+ ··· + 0.136923u + 1.00555
a
9
=
−122.419u
22
+ 140.753u
21
+ ··· + 1356.31u − 817.081
0.550132u
22
− 0.666197u
21
+ ··· − 5.81233u + 4.35302
a
9
=
−122.419u
22
+ 140.753u
21
+ ··· + 1356.31u − 817.081
0.550132u
22
− 0.666197u
21
+ ··· − 5.81233u + 4.35302
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
94310497538971
2663810305417
u
22
−
105799611203026
2663810305417
u
21
+ ··· −
1045853706856708
2663810305417
u +
633409804939426
2663810305417
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
23
− 6u
21
+ ··· − 40u − 4
c
2
, c
6
u
23
− 3u
22
+ ··· + 47u − 8
c
3
, c
7
u
23
− u
22
+ ··· + 5u + 1
c
4
, c
9
u
23
− 9u
22
+ ··· − 40u + 16
c
5
, c
8
u
23
− 6u
22
+ ··· + 22u − 5
c
11
u
23
+ 4u
22
+ ··· − 7u − 34
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
23
− 12y
22
+ ··· + 448y −16
c
2
, c
6
y
23
− 13y
22
+ ··· + 1233y −64
c
3
, c
7
y
23
− 5y
22
+ ··· + 41y −1
c
4
, c
9
y
23
− 43y
22
+ ··· − 1088y −256
c
5
, c
8
y
23
− 46y
22
+ ··· + 344y −25
c
11
y
23
+ 6y
22
+ ··· − 12055y −1156
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.555624 + 0.905584I
a = 0.910105 − 0.864749I
b = −1.40913 + 1.48491I
1.86354 − 5.26744I 5.28915 + 6.74191I
u = 0.555624 − 0.905584I
a = 0.910105 + 0.864749I
b = −1.40913 − 1.48491I
1.86354 + 5.26744I 5.28915 − 6.74191I
u = 1.08075
a = −0.674705
b = 2.01594
5.56139 −4.10580
u = 0.501300 + 0.715167I
a = −0.703633 − 0.411741I
b = 1.46848 − 0.46020I
6.01384 − 1.36939I 7.91646 + 4.62007I
u = 0.501300 − 0.715167I
a = −0.703633 + 0.411741I
b = 1.46848 + 0.46020I
6.01384 + 1.36939I 7.91646 − 4.62007I
u = 0.728418 + 0.872189I
a = −0.297023 + 0.916259I
b = −0.631160 − 0.422833I
3.37848 + 2.40469I 1.77991 − 2.36658I
u = 0.728418 − 0.872189I
a = −0.297023 − 0.916259I
b = −0.631160 + 0.422833I
3.37848 − 2.40469I 1.77991 + 2.36658I
u = −1.049550 + 0.569449I
a = 0.978794 + 0.476256I
b = −0.827795 − 0.239786I
−5.59031 + 2.93906I −3.96701 − 3.47635I
u = −1.049550 − 0.569449I
a = 0.978794 − 0.476256I
b = −0.827795 + 0.239786I
−5.59031 − 2.93906I −3.96701 + 3.47635I
u = −0.704512 + 0.984779I
a = 0.736671 + 0.559489I
b = −0.414106 − 1.231940I
−2.32908 + 5.49763I −4.79992 − 7.26042I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.704512 − 0.984779I
a = 0.736671 − 0.559489I
b = −0.414106 + 1.231940I
−2.32908 − 5.49763I −4.79992 + 7.26042I
u = 0.929406 + 0.853194I
a = 0.740478 + 0.793412I
b = −1.091640 + 0.630699I
5.11296 − 9.53315I 2.57549 + 7.49079I
u = 0.929406 − 0.853194I
a = 0.740478 − 0.793412I
b = −1.091640 − 0.630699I
5.11296 + 9.53315I 2.57549 − 7.49079I
u = 0.734602
a = 1.84769
b = −0.838790
−3.46093 0.434270
u = −1.000300 + 0.806208I
a = 0.146523 − 0.473900I
b = −0.602615 − 0.205653I
−0.46558 + 3.81570I 4.70967 − 3.05268I
u = −1.000300 − 0.806208I
a = 0.146523 + 0.473900I
b = −0.602615 + 0.205653I
−0.46558 − 3.81570I 4.70967 + 3.05268I
u = −0.188306 + 0.473727I
a = −1.261830 + 0.253849I
b = 0.271244 + 0.415630I
0.294559 + 1.131280I 2.80927 − 6.63257I
u = −0.188306 − 0.473727I
a = −1.261830 − 0.253849I
b = 0.271244 − 0.415630I
0.294559 − 1.131280I 2.80927 + 6.63257I
u = −1.33922 + 0.68743I
a = −0.831149 − 0.099202I
b = 1.41488 + 0.83581I
−3.36043 + 7.89416I −1.16388 − 6.61187I
u = −1.33922 − 0.68743I
a = −0.831149 + 0.099202I
b = 1.41488 − 0.83581I
−3.36043 − 7.89416I −1.16388 + 6.61187I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.23451 + 0.89988I
a = −0.999661 + 0.218042I
b = 1.34140 − 1.32358I
0.6169 − 16.3897I −0.60357 + 8.49133I
u = 1.23451 − 0.89988I
a = −0.999661 − 0.218042I
b = 1.34140 + 1.32358I
0.6169 + 16.3897I −0.60357 − 8.49133I
u = −0.150085
a = 36.9885
b = −0.216243
−0.0107219 320.580
7
II. I
u
2
= h−4.69 × 10
59
u
39
+ 1.07 × 10
60
u
38
+ · · · + 3.77 × 10
59
b + 1.46 ×
10
61
, 6.35 × 10
61
u
39
− 1.41 × 10
62
u
38
+ · · · + 5.46 × 10
61
a − 2.06 ×
10
63
, u
40
− 3u
39
+ · · · − 25u + 29i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
10
=
−1.16276u
39
+ 2.57824u
38
+ ··· + 15.4232u + 37.7606
1.24550u
39
− 2.83726u
38
+ ··· − 21.4581u − 38.7159
a
11
=
0.0827388u
39
− 0.259017u
38
+ ··· − 6.03488u − 0.955344
1.24550u
39
− 2.83726u
38
+ ··· − 21.4581u − 38.7159
a
1
=
−1.18195u
39
+ 2.57423u
38
+ ··· + 12.7538u + 38.0738
0.434159u
39
− 1.02128u
38
+ ··· − 8.80280u − 10.8518
a
4
=
0.296393u
39
− 0.547600u
38
+ ··· + 8.50789u − 11.9654
0.237025u
39
− 0.603121u
38
+ ··· − 13.2225u − 4.41074
a
3
=
−1.03486u
39
+ 2.43611u
38
+ ··· + 28.2109u + 46.3778
0.440164u
39
− 0.996927u
38
+ ··· − 8.56472u − 15.8344
a
2
=
−1.47503u
39
+ 3.43303u
38
+ ··· + 36.7756u + 62.2122
0.440164u
39
− 0.996927u
38
+ ··· − 8.56472u − 15.8344
a
6
=
0.246893u
39
− 0.444760u
38
+ ··· + 0.0495641u − 2.02219
−0.286524u
39
+ 0.705961u
38
+ ··· + 6.76415u + 14.3540
a
9
=
1.94454u
39
− 4.32792u
38
+ ··· − 27.3144u − 65.7640
−0.600066u
39
+ 1.33935u
38
+ ··· + 6.52606u + 22.9357
a
9
=
1.94454u
39
− 4.32792u
38
+ ··· − 27.3144u − 65.7640
−0.600066u
39
+ 1.33935u
38
+ ··· + 6.52606u + 22.9357
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.41432u
39
− 4.79564u
38
+ ··· + 14.4984u − 64.7958
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
40
+ 9u
38
+ ··· + 244u − 44
c
2
, c
6
(u
20
+ 2u
19
+ ··· + 8u + 1)
2
c
3
, c
7
u
40
− 3u
39
+ ··· − 25u + 29
c
4
, c
9
(u
20
+ u
19
+ ··· − 25u − 11)
2
c
5
, c
8
u
40
+ u
39
+ ··· − 47u − 169
c
11
(u
20
− u
19
+ ··· + 7u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
40
+ 18y
39
+ ··· − 94208y + 1936
c
2
, c
6
(y
20
− 14y
19
+ ··· + 40y + 1)
2
c
3
, c
7
y
40
− 19y
39
+ ··· − 12747y + 841
c
4
, c
9
(y
20
− 13y
19
+ ··· − 1021y + 121)
2
c
5
, c
8
y
40
+ 7y
39
+ ··· − 530503y + 28561
c
11
(y
20
+ 3y
19
+ ··· − 35y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.843881 + 0.602804I
a = 0.232508 + 0.949215I
b = −1.042200 + 0.656943I
5.13837 − 3.10653I 2.77090 + 3.27458I
u = 0.843881 − 0.602804I
a = 0.232508 − 0.949215I
b = −1.042200 − 0.656943I
5.13837 + 3.10653I 2.77090 − 3.27458I
u = −0.724639 + 0.605856I
a = −0.421379 − 0.634087I
b = 0.15696 + 1.84987I
0.78911 + 3.05252I 1.27188 − 4.35560I
u = −0.724639 − 0.605856I
a = −0.421379 + 0.634087I
b = 0.15696 − 1.84987I
0.78911 − 3.05252I 1.27188 + 4.35560I
u = −0.893885 + 0.284008I
a = −1.55376 + 0.35417I
b = 0.232385 + 1.342720I
−1.76779 + 6.66107I −3.08867 − 6.78923I
u = −0.893885 − 0.284008I
a = −1.55376 − 0.35417I
b = 0.232385 − 1.342720I
−1.76779 − 6.66107I −3.08867 + 6.78923I
u = 0.424536 + 0.808576I
a = −0.90087 − 1.19479I
b = 0.545954 + 0.038305I
0.703344 + 0.559674I 1.56320 − 4.51761I
u = 0.424536 − 0.808576I
a = −0.90087 + 1.19479I
b = 0.545954 − 0.038305I
0.703344 − 0.559674I 1.56320 + 4.51761I
u = −1.048820 + 0.339914I
a = 0.806845 + 0.261493I
b = −0.420413 − 1.165930I
−4.78547 −5.34389 + 0.I
u = −1.048820 − 0.339914I
a = 0.806845 − 0.261493I
b = −0.420413 + 1.165930I
−4.78547 −5.34389 + 0.I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.773777 + 0.786429I
a = −0.789062 − 0.060278I
b = 0.747156 + 0.918386I
0.28152 + 2.20542I 2.09891 − 2.63579I
u = −0.773777 − 0.786429I
a = −0.789062 + 0.060278I
b = 0.747156 − 0.918386I
0.28152 − 2.20542I 2.09891 + 2.63579I
u = 0.778748 + 0.245271I
a = −1.255710 + 0.087033I
b = 0.33399 − 1.89842I
−7.62987 − 1.01721I 5.24970 + 11.81252I
u = 0.778748 − 0.245271I
a = −1.255710 − 0.087033I
b = 0.33399 + 1.89842I
−7.62987 + 1.01721I 5.24970 − 11.81252I
u = 0.795151
a = 1.84930
b = −2.27654
−2.04716 −7.60150
u = 0.733508 + 0.115684I
a = −2.02000 + 0.04989I
b = 1.102660 − 0.124486I
−6.94055 − 4.65557I 9.06224 − 2.69200I
u = 0.733508 − 0.115684I
a = −2.02000 − 0.04989I
b = 1.102660 + 0.124486I
−6.94055 + 4.65557I 9.06224 + 2.69200I
u = 1.009230 + 0.784248I
a = −0.998258 + 0.225230I
b = 1.23888 − 1.42271I
2.54638 − 8.54122I 0. + 7.30579I
u = 1.009230 − 0.784248I
a = −0.998258 − 0.225230I
b = 1.23888 + 1.42271I
2.54638 + 8.54122I 0. − 7.30579I
u = 0.937408 + 0.876311I
a = −0.714914 − 0.335707I
b = 1.346930 + 0.090646I
5.13837 + 3.10653I 2.77090 − 3.27458I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.937408 − 0.876311I
a = −0.714914 + 0.335707I
b = 1.346930 − 0.090646I
5.13837 − 3.10653I 2.77090 + 3.27458I
u = 0.804574 + 1.002740I
a = 0.211768 − 0.517712I
b = 0.292544 − 0.313955I
0.78911 − 3.05252I 0. + 4.35560I
u = 0.804574 − 1.002740I
a = 0.211768 + 0.517712I
b = 0.292544 + 0.313955I
0.78911 + 3.05252I 0. − 4.35560I
u = 1.28977
a = 1.14010
b = 0.165534
−2.04716 −7.60150
u = −0.139241 + 0.695732I
a = 0.611135 − 1.068020I
b = −0.574331 − 0.269819I
0.28152 − 2.20542I 2.09891 + 2.63579I
u = −0.139241 − 0.695732I
a = 0.611135 + 1.068020I
b = −0.574331 + 0.269819I
0.28152 + 2.20542I 2.09891 − 2.63579I
u = −0.603347 + 0.367132I
a = −1.61538 + 1.06505I
b = 0.082291 + 0.853240I
0.703344 + 0.559674I 1.56320 − 4.51761I
u = −0.603347 − 0.367132I
a = −1.61538 − 1.06505I
b = 0.082291 − 0.853240I
0.703344 − 0.559674I 1.56320 + 4.51761I
u = −0.570217 + 0.118702I
a = −1.71022 − 0.71186I
b = 1.03717 + 2.48340I
−0.39627 − 4.88151I −5.90664 + 1.87878I
u = −0.570217 − 0.118702I
a = −1.71022 + 0.71186I
b = 1.03717 − 2.48340I
−0.39627 + 4.88151I −5.90664 − 1.87878I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.23114 + 0.76536I
a = 1.030760 − 0.025210I
b = −1.28074 + 0.75129I
−1.76779 − 6.66107I 0
u = 1.23114 − 0.76536I
a = 1.030760 + 0.025210I
b = −1.28074 − 0.75129I
−1.76779 + 6.66107I 0
u = 0.65753 + 1.37826I
a = −0.005515 + 0.856499I
b = −0.615352 − 0.430269I
2.54638 + 8.54122I 0
u = 0.65753 − 1.37826I
a = −0.005515 − 0.856499I
b = −0.615352 + 0.430269I
2.54638 − 8.54122I 0
u = 1.29816 + 1.03823I
a = 0.574100 − 0.302843I
b = −1.04929 + 0.95851I
−0.39627 − 4.88151I 0
u = 1.29816 − 1.03823I
a = 0.574100 + 0.302843I
b = −1.04929 − 0.95851I
−0.39627 + 4.88151I 0
u = −1.31598 + 1.12343I
a = 0.727776 + 0.471526I
b = −0.461214 − 1.201270I
−6.94055 + 4.65557I 0
u = −1.31598 − 1.12343I
a = 0.727776 − 0.471526I
b = −0.461214 + 1.201270I
−6.94055 − 4.65557I 0
u = −2.19127 + 0.09123I
a = 0.450657 + 0.128384I
b = −0.617875 − 0.033077I
−7.62987 − 1.01721I 0
u = −2.19127 − 0.09123I
a = 0.450657 − 0.128384I
b = −0.617875 + 0.033077I
−7.62987 + 1.01721I 0
14
III.
I
u
3
= h−4.53 × 10
4
u
13
− 1.81 × 10
5
u
12
+ · · · + 1.42 × 10
5
b + 3.21 × 10
5
, 8.04 ×
10
5
u
13
+4.74×10
6
u
12
+· · · +1.42×10
5
a+1.22×10
6
, u
14
+6u
13
+· · · +5u +1i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
10
=
−5.65578u
13
− 33.3639u
12
+ ··· − 56.1552u − 8.58729
0.318839u
13
+ 1.27570u
12
+ ··· − 4.67346u − 2.26005
a
11
=
−5.33694u
13
− 32.0882u
12
+ ··· − 60.8286u − 10.8473
0.318839u
13
+ 1.27570u
12
+ ··· − 4.67346u − 2.26005
a
1
=
−4.51223u
13
− 27.0057u
12
+ ··· − 50.4852u − 8.52068
0.190356u
13
+ 0.431761u
12
+ ··· − 6.16986u − 2.39439
a
4
=
−5.25817u
13
− 25.6393u
12
+ ··· + 29.6480u + 19.5162
1.06661u
13
+ 5.25611u
12
+ ··· − 0.837358u − 0.336939
a
3
=
−5.69548u
13
− 27.1106u
12
+ ··· + 33.8647u + 23.0100
−1.82155u
13
− 10.4029u
12
+ ··· − 13.0398u − 1.99691
a
2
=
−3.87393u
13
− 16.7077u
12
+ ··· + 46.9046u + 25.0069
−1.82155u
13
− 10.4029u
12
+ ··· − 13.0398u − 1.99691
a
6
=
−3.82170u
13
− 18.0285u
12
+ ··· + 29.6178u + 20.3626
0.369860u
13
+ 2.35460u
12
+ ··· + 2.80717u + 1.18340
a
9
=
−34.2887u
13
− 201.354u
12
+ ··· − 347.739u − 55.6924
−1.64859u
13
− 10.2510u
12
+ ··· − 23.4938u − 6.08505
a
9
=
−34.2887u
13
− 201.354u
12
+ ··· − 347.739u − 55.6924
−1.64859u
13
− 10.2510u
12
+ ··· − 23.4938u − 6.08505
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
851937
142097
u
13
−
3765455
142097
u
12
+ ··· +
763404
142097
u −
615113
142097
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
14
+ 3u
13
+ ··· + 8u + 4
c
2
(u
7
− 2u
6
+ 2u
5
− 3u
4
+ 3u
2
− u + 1)
2
c
3
, c
7
u
14
+ 6u
13
+ ··· + 5u + 1
c
4
, c
9
u
14
− 3u
12
− 17u
10
+ 114u
8
− 277u
6
+ 352u
4
− 236u
2
+ 67
c
5
, c
8
u
14
+ 9u
12
+ ··· − 3u + 1
c
6
(u
7
+ 2u
6
+ 2u
5
+ 3u
4
− 3u
2
− u − 1)
2
c
11
(u
7
− 2u
6
+ 3u
5
− 3u
4
− 5u
3
+ 2u
2
+ 5u + 3)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
14
+ 15y
13
+ ··· + 96y + 16
c
2
, c
6
(y
7
− 8y
5
+ y
4
+ 18y
3
− 3y
2
− 5y −1)
2
c
3
, c
7
y
14
− 12y
13
+ ··· + 3y + 1
c
4
, c
9
(y
7
− 3y
6
− 17y
5
+ 114y
4
− 277y
3
+ 352y
2
− 236y + 67)
2
c
5
, c
8
y
14
+ 18y
13
+ ··· + 11y + 1
c
11
(y
7
+ 2y
6
− 13y
5
− 21y
4
+ 79y
3
− 36y
2
+ 13y −9)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.841811 + 0.182190I
a = 1.69734 + 0.14987I
b = −1.095480 − 0.201335I
−7.19586 + 4.79737I −15.3799 − 10.7291I
u = −0.841811 − 0.182190I
a = 1.69734 − 0.14987I
b = −1.095480 + 0.201335I
−7.19586 − 4.79737I −15.3799 + 10.7291I
u = 0.807415 + 0.203980I
a = −1.293990 + 0.103857I
b = 0.54475 − 1.78373I
−7.86115 − 0.79658I −13.7450 − 5.5444I
u = 0.807415 − 0.203980I
a = −1.293990 − 0.103857I
b = 0.54475 + 1.78373I
−7.86115 + 0.79658I −13.7450 + 5.5444I
u = −0.328860 + 0.493680I
a = −1.54515 − 1.23007I
b = 0.15112 + 2.21331I
0.20871 + 5.48705I 1.09915 − 7.96619I
u = −0.328860 − 0.493680I
a = −1.54515 + 1.23007I
b = 0.15112 − 2.21331I
0.20871 − 5.48705I 1.09915 + 7.96619I
u = 1.04271 + 1.08370I
a = −0.685924 + 0.369272I
b = 1.05349 − 1.00763I
0.20871 − 5.48705I 1.09915 + 7.96619I
u = 1.04271 − 1.08370I
a = −0.685924 − 0.369272I
b = 1.05349 + 1.00763I
0.20871 + 5.48705I 1.09915 − 7.96619I
u = −0.198097 + 0.363970I
a = 5.02166 − 2.73312I
b = −0.121264 − 0.413302I
0.0877733 −6.94848 + 0.I
u = −0.198097 − 0.363970I
a = 5.02166 + 2.73312I
b = −0.121264 + 0.413302I
0.0877733 −6.94848 + 0.I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.36446 + 1.14498I
a = −0.692299 − 0.446761I
b = 0.459655 + 1.110540I
−7.19586 + 4.79737I −15.3799 − 10.7291I
u = −1.36446 − 1.14498I
a = −0.692299 + 0.446761I
b = 0.459655 − 1.110540I
−7.19586 − 4.79737I −15.3799 + 10.7291I
u = −2.11690 + 0.04289I
a = −0.501625 − 0.095237I
b = 0.507720 + 0.269988I
−7.86115 − 0.79658I −13.7450 − 5.5444I
u = −2.11690 − 0.04289I
a = −0.501625 + 0.095237I
b = 0.507720 − 0.269988I
−7.86115 + 0.79658I −13.7450 + 5.5444I
19
IV. I
u
4
= hb + u + 1, a, u
3
+ u
2
− 1i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
10
=
0
−u − 1
a
11
=
−u − 1
−u − 1
a
1
=
−1
−u
2
− u
a
4
=
0
u
a
3
=
u
u + 1
a
2
=
−1
u + 1
a
6
=
u
2
+ u + 1
u
2
+ 2u + 1
a
9
=
0
−u − 1
a
9
=
0
−u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
2
+ 7u
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
10
u
3
− 2u
2
+ u − 1
c
2
u
3
+ 2u
2
+ u + 1
c
3
, c
7
, c
11
u
3
+ u
2
− 1
c
4
, c
9
u
3
c
5
, c
8
u
3
− u − 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
10
y
3
− 2y
2
− 3y −1
c
3
, c
7
, c
11
y
3
− y
2
+ 2y −1
c
4
, c
9
y
3
c
5
, c
8
y
3
− 2y
2
+ y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0
b = −0.122561 − 0.744862I
−1.45094 + 3.77083I −4.63651 − 3.93596I
u = −0.877439 − 0.744862I
a = 0
b = −0.122561 + 0.744862I
−1.45094 − 3.77083I −4.63651 + 3.93596I
u = 0.754878
a = 0
b = −1.75488
6.19175 9.27300
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
3
− 2u
2
+ u − 1)(u
14
+ 3u
13
+ ··· + 8u + 4)(u
23
− 6u
21
+ ··· − 40u − 4)
· (u
40
+ 9u
38
+ ··· + 244u − 44)
c
2
(u
3
+ 2u
2
+ u + 1)(u
7
− 2u
6
+ 2u
5
− 3u
4
+ 3u
2
− u + 1)
2
· ((u
20
+ 2u
19
+ ··· + 8u + 1)
2
)(u
23
− 3u
22
+ ··· + 47u − 8)
c
3
, c
7
(u
3
+ u
2
− 1)(u
14
+ 6u
13
+ ··· + 5u + 1)(u
23
− u
22
+ ··· + 5u + 1)
· (u
40
− 3u
39
+ ··· − 25u + 29)
c
4
, c
9
u
3
(u
14
− 3u
12
− 17u
10
+ 114u
8
− 277u
6
+ 352u
4
− 236u
2
+ 67)
· ((u
20
+ u
19
+ ··· − 25u − 11)
2
)(u
23
− 9u
22
+ ··· − 40u + 16)
c
5
, c
8
(u
3
− u − 1)(u
14
+ 9u
12
+ ··· − 3u + 1)(u
23
− 6u
22
+ ··· + 22u − 5)
· (u
40
+ u
39
+ ··· − 47u − 169)
c
6
(u
3
− 2u
2
+ u − 1)(u
7
+ 2u
6
+ 2u
5
+ 3u
4
− 3u
2
− u − 1)
2
· ((u
20
+ 2u
19
+ ··· + 8u + 1)
2
)(u
23
− 3u
22
+ ··· + 47u − 8)
c
11
(u
3
+ u
2
− 1)(u
7
− 2u
6
+ 3u
5
− 3u
4
− 5u
3
+ 2u
2
+ 5u + 3)
2
· ((u
20
− u
19
+ ··· + 7u + 1)
2
)(u
23
+ 4u
22
+ ··· − 7u − 34)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
3
− 2y
2
− 3y −1)(y
14
+ 15y
13
+ ··· + 96y + 16)
· (y
23
− 12y
22
+ ··· + 448y −16)(y
40
+ 18y
39
+ ··· − 94208y + 1936)
c
2
, c
6
(y
3
− 2y
2
− 3y −1)(y
7
− 8y
5
+ y
4
+ 18y
3
− 3y
2
− 5y −1)
2
· ((y
20
− 14y
19
+ ··· + 40y + 1)
2
)(y
23
− 13y
22
+ ··· + 1233y −64)
c
3
, c
7
(y
3
− y
2
+ 2y −1)(y
14
− 12y
13
+ ··· + 3y + 1)
· (y
23
− 5y
22
+ ··· + 41y −1)(y
40
− 19y
39
+ ··· − 12747y + 841)
c
4
, c
9
y
3
(y
7
− 3y
6
− 17y
5
+ 114y
4
− 277y
3
+ 352y
2
− 236y + 67)
2
· (y
20
− 13y
19
+ ··· − 1021y + 121)
2
· (y
23
− 43y
22
+ ··· − 1088y −256)
c
5
, c
8
(y
3
− 2y
2
+ y −1)(y
14
+ 18y
13
+ ··· + 11y + 1)
· (y
23
− 46y
22
+ ··· + 344y −25)(y
40
+ 7y
39
+ ··· − 530503y + 28561)
c
11
(y
3
− y
2
+ 2y −1)(y
7
+ 2y
6
+ ··· + 13y −9)
2
· ((y
20
+ 3y
19
+ ··· − 35y + 1)
2
)(y
23
+ 6y
22
+ ··· − 12055y −1156)
25
