12a
1109
(K12a
1109
)
A knot diagram
1
Linearized knot diagam
4 7 11 1 12 2 10 5 6 3 8 9
Solving Sequence
3,11 4,7
2 1 6 10 8 12 5 9
c
3
c
2
c
1
c
6
c
10
c
7
c
11
c
5
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hb + u, −5.51351 × 10
20
u
32
− 1.00345 × 10
20
u
31
+ ··· + 4.96956 × 10
20
a − 2.61633 × 10
21
,
u
33
− 13u
31
+ ··· + 5u − 1i
I
u
2
= h−2.42889 × 10
666
u
125
+ 3.63484 × 10
665
u
124
+ ··· + 2.10762 × 10
666
b − 2.25797 × 10
671
,
− 4.35538 × 10
671
u
125
+ 2.72760 × 10
670
u
124
+ ··· + 1.67305 × 10
671
a − 3.95770 × 10
676
,
u
126
− u
125
+ ··· + 445179u − 79381i
I
u
3
= hb + u, 188u
17
− 64u
16
+ ··· + 75a − 796, u
18
− 7u
16
+ ··· − 3u − 1i
I
u
4
= h14246904u
17
− 7271564u
16
+ ··· + 21285647b − 49419894,
34578671u
17
+ 14037986u
16
+ ··· + 21285647a + 25444982, u
18
− 8u
16
+ ··· − u − 1i
* 4 irreducible components of dim
C
= 0, with total 195 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
= hb + u, −5.51 × 10
20
u
32
− 1.00 × 10
20
u
31
+ · · · + 4.97 × 10
20
a −
2.62 × 10
21
, u
33
− 13u
31
+ · · · + 5u − 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
7
=
1.10946u
32
+ 0.201920u
31
+ ··· − 4.37332u + 5.26470
−u
a
2
=
0.201920u
32
+ 0.164749u
31
+ ··· − 0.282581u + 2.10946
−u
2
a
1
=
0.255700u
32
+ 0.133298u
31
+ ··· + 0.339246u + 1.94471
0.114568u
32
+ 0.000982119u
31
+ ··· + 0.211036u − 0.0314510
a
6
=
0.944707u
32
+ 0.255700u
31
+ ··· − 5.47318u + 5.06278
u
3
− u
a
10
=
u
u
a
8
=
0.944707u
32
+ 0.255700u
31
+ ··· − 4.47318u + 5.06278
−0.164749u
32
+ 0.0537806u
31
+ ··· − 1.09986u − 0.201920
a
12
=
1.10599u
32
+ 0.285758u
31
+ ··· − 2.11902u + 5.03823
−0.0881370u
32
− 0.0855275u
31
+ ··· + 1.99609u − 0.626985
a
5
=
−0.185676u
32
+ 0.000949724u
31
+ ··· + 0.432526u + 0.710133
0.208808u
32
− 0.0230167u
31
+ ··· − 0.144418u + 0.0874475
a
9
=
−1.00512u
32
− 0.235683u
31
+ ··· + 2.95587u − 4.84331
0.100865u
32
+ 0.0500742u
31
+ ··· + 0.836846u + 0.194913
(ii) Obstruction class = −1
(iii) Cusp Shapes =
11742058737997963033618
4472604412221102382125
u
32
+
4842323161366125049279
4472604412221102382125
u
31
+ ··· −
89973330678246945712378
4472604412221102382125
u +
44302109184650100143056
4472604412221102382125
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
3(3u
33
− 68u
32
+ ··· + 6656u − 512)
c
2
, c
3
, c
6
c
10
u
33
− 13u
31
+ ··· + 5u − 1
c
5
3(3u
33
− 83u
32
+ ··· + 416u − 64)
c
7
3(3u
33
+ 83u
32
+ ··· + 19456u + 4096)
c
8
, c
12
u
33
+ u
32
+ ··· + 8u + 3
c
9
, c
11
u
33
+ u
32
+ ··· + 8u − 29
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
9(9y
33
+ 26y
32
+ ··· + 1.25829 × 10
7
y −262144)
c
2
, c
3
, c
6
c
10
y
33
− 26y
32
+ ··· + 7y −1
c
5
9(9y
33
− 181y
32
+ ··· − 89088y −4096)
c
7
9(9y
33
− 187y
32
+ ··· + 4.39353 × 10
8
y −1.67772 × 10
7
)
c
8
, c
12
y
33
+ 5y
32
+ ··· + 220y −9
c
9
, c
11
y
33
− 17y
32
+ ··· + 10620y −841
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.988042
a = 5.69224
b = 0.988042
0.389613 −30.4490
u = −0.738304 + 0.649893I
a = 0.098544 + 0.662865I
b = 0.738304 − 0.649893I
5.00094 − 3.09470I 0.408039 + 0.525523I
u = −0.738304 − 0.649893I
a = 0.098544 − 0.662865I
b = 0.738304 + 0.649893I
5.00094 + 3.09470I 0.408039 − 0.525523I
u = 1.002920 + 0.182034I
a = −3.32561 − 0.46867I
b = −1.002920 − 0.182034I
3.90996 − 10.24170I −4.98610 + 7.85593I
u = 1.002920 − 0.182034I
a = −3.32561 + 0.46867I
b = −1.002920 + 0.182034I
3.90996 + 10.24170I −4.98610 − 7.85593I
u = 0.354707 + 0.838712I
a = −0.949703 + 0.077776I
b = −0.354707 − 0.838712I
7.49019 + 0.59025I 6.83489 − 0.22860I
u = 0.354707 − 0.838712I
a = −0.949703 − 0.077776I
b = −0.354707 + 0.838712I
7.49019 − 0.59025I 6.83489 + 0.22860I
u = −0.305032 + 0.831776I
a = 1.269700 + 0.160717I
b = 0.305032 − 0.831776I
8.03993 − 9.04618I 2.12985 + 4.01485I
u = −0.305032 − 0.831776I
a = 1.269700 − 0.160717I
b = 0.305032 + 0.831776I
8.03993 + 9.04618I 2.12985 − 4.01485I
u = −0.015597 + 0.759933I
a = −0.276956 + 0.620225I
b = 0.015597 − 0.759933I
3.45596 + 4.59127I 2.60162 − 5.91506I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.015597 − 0.759933I
a = −0.276956 − 0.620225I
b = 0.015597 + 0.759933I
3.45596 − 4.59127I 2.60162 + 5.91506I
u = 1.185980 + 0.380637I
a = −1.77450 + 1.34872I
b = −1.185980 − 0.380637I
−3.31674 − 2.54544I −5.71023 + 1.18268I
u = 1.185980 − 0.380637I
a = −1.77450 − 1.34872I
b = −1.185980 + 0.380637I
−3.31674 + 2.54544I −5.71023 − 1.18268I
u = −0.710776
a = 0.439454
b = 0.710776
−1.12251 −6.37110
u = 0.505026 + 0.474040I
a = 0.398174 − 0.651892I
b = −0.505026 − 0.474040I
3.18560 − 1.37010I −2.46667 + 3.82678I
u = 0.505026 − 0.474040I
a = 0.398174 + 0.651892I
b = −0.505026 + 0.474040I
3.18560 + 1.37010I −2.46667 − 3.82678I
u = −1.291930 + 0.311595I
a = 1.46041 + 0.85218I
b = 1.291930 − 0.311595I
−7.56174 − 0.61747I −11.13526 + 2.09611I
u = −1.291930 − 0.311595I
a = 1.46041 − 0.85218I
b = 1.291930 + 0.311595I
−7.56174 + 0.61747I −11.13526 − 2.09611I
u = 1.324490 + 0.182144I
a = −1.75789 + 0.39816I
b = −1.324490 − 0.182144I
−6.90993 − 0.81575I −13.00695 − 0.18547I
u = 1.324490 − 0.182144I
a = −1.75789 − 0.39816I
b = −1.324490 + 0.182144I
−6.90993 + 0.81575I −13.00695 + 0.18547I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.32813 + 0.48664I
a = 1.67278 + 0.89038I
b = 1.32813 − 0.48664I
−4.6785 + 13.5930I −6.98219 − 10.34778I
u = −1.32813 − 0.48664I
a = 1.67278 − 0.89038I
b = 1.32813 + 0.48664I
−4.6785 − 13.5930I −6.98219 + 10.34778I
u = 1.38591 + 0.41952I
a = −1.65623 + 0.48889I
b = −1.38591 − 0.41952I
−8.37796 − 5.05371I −12.03006 + 2.98505I
u = 1.38591 − 0.41952I
a = −1.65623 − 0.48889I
b = −1.38591 + 0.41952I
−8.37796 + 5.05371I −12.03006 − 2.98505I
u = −1.42702 + 0.32964I
a = 1.67206 + 0.08112I
b = 1.42702 − 0.32964I
−3.55978 + 5.14975I −8.65604 − 3.93341I
u = −1.42702 − 0.32964I
a = 1.67206 − 0.08112I
b = 1.42702 + 0.32964I
−3.55978 − 5.14975I −8.65604 + 3.93341I
u = −1.38771 + 0.56081I
a = 1.76185 + 0.49558I
b = 1.38771 − 0.56081I
0.76112 + 11.54690I 0. − 8.50232I
u = −1.38771 − 0.56081I
a = 1.76185 − 0.49558I
b = 1.38771 + 0.56081I
0.76112 − 11.54690I 0. + 8.50232I
u = 1.41446 + 0.61544I
a = −1.63169 + 0.52570I
b = −1.41446 − 0.61544I
0.9133 − 20.5211I 0. + 10.13871I
u = 1.41446 − 0.61544I
a = −1.63169 − 0.52570I
b = −1.41446 + 0.61544I
0.9133 + 20.5211I 0. − 10.13871I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.045978 + 0.364709I
a = 1.56117 − 0.41807I
b = −0.045978 − 0.364709I
−0.09428 + 1.57059I −1.17905 − 4.36541I
u = 0.045978 − 0.364709I
a = 1.56117 + 0.41807I
b = −0.045978 + 0.364709I
−0.09428 − 1.57059I −1.17905 + 4.36541I
u = 0.247344
a = 5.15743
b = −0.247344
2.57187 8.03110
8
II. I
u
2
= h−2.43 × 10
666
u
125
+ 3.63 × 10
665
u
124
+ · · · + 2.11 × 10
666
b − 2.26 ×
10
671
, −4.36 × 10
671
u
125
+ 2.73 × 10
670
u
124
+ · · · + 1.67 × 10
671
a − 3.96 ×
10
676
, u
126
− u
125
+ · · · + 445179u − 79381i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
7
=
2.60326u
125
− 0.163032u
124
+ ··· − 1.07321 × 10
6
u + 236556.
1.15243u
125
− 0.172462u
124
+ ··· − 476233.u + 107134.
a
2
=
3.60912u
125
− 0.273875u
124
+ ··· − 1.49893 × 10
6
u + 331671.
1.98933u
125
− 0.303058u
124
+ ··· − 845433.u + 190405.
a
1
=
2.75193u
125
− 0.382917u
124
+ ··· − 1.14608 × 10
6
u + 257320.
1.12658u
125
− 0.399171u
124
+ ··· − 483331.u + 113705.
a
6
=
−0.0908361u
125
+ 0.138689u
124
+ ··· + 91584.7u − 23023.8
0.960737u
125
+ 0.0952325u
124
+ ··· − 288454.u + 60008.7
a
10
=
u
u
a
8
=
1.32650u
125
− 0.178769u
124
+ ··· − 538299.u + 120639.
−0.124328u
125
− 0.188199u
124
+ ··· + 58675.8u − 8782.80
a
12
=
−2.02791u
125
+ 0.315409u
124
+ ··· + 824363.u − 185723.
−0.0189666u
125
+ 0.105342u
124
+ ··· + 105576.u − 26189.8
a
5
=
7.08729u
125
− 0.363708u
124
+ ··· − 2.76880 × 10
6
u + 608251.
5.64107u
125
+ 0.170762u
124
+ ··· − 2.39045 × 10
6
u + 516688.
a
9
=
13.5383u
125
− 1.09910u
124
+ ··· − 5.28559 × 10
6
u + 1.16915 × 10
6
14.3116u
125
− 1.33426u
124
+ ··· − 5.61938 × 10
6
u + 1.24685 × 10
6
(ii) Obstruction class = −1
(iii) Cusp Shapes = 13.1438u
125
−2.17406u
124
+ ··· −4.54071 ×10
6
u + 1.02447 ×10
6
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
63
+ 11u
62
+ ··· + 159u − 1)
2
c
2
, c
3
, c
6
c
10
u
126
− u
125
+ ··· + 445179u − 79381
c
5
(u
63
+ 16u
62
+ ··· + 5u + 1)
2
c
7
(u
63
− 14u
62
+ ··· − 694u + 39)
2
c
8
, c
12
u
126
+ 8u
125
+ ··· − 23405u − 2473
c
9
, c
11
u
126
− 2u
125
+ ··· − 81829844u − 30650633
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
63
+ 35y
62
+ ··· + 29501y −1)
2
c
2
, c
3
, c
6
c
10
y
126
− 85y
125
+ ··· − 14924889155y + 6301343161
c
5
(y
63
− 26y
62
+ ··· + 47y −1)
2
c
7
(y
63
− 104y
61
+ ··· + 27910y −1521)
2
c
8
, c
12
y
126
+ 32y
125
+ ··· − 362675137y + 6115729
c
9
, c
11
y
126
− 58y
125
+ ··· − 22519621465061486y + 939461303300689
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.231017 + 0.974102I
a = −0.161333 + 0.201744I
b = −1.223380 + 0.555574I
2.80266 + 5.31618I 0
u = 0.231017 − 0.974102I
a = −0.161333 − 0.201744I
b = −1.223380 − 0.555574I
2.80266 − 5.31618I 0
u = −0.726101 + 0.685259I
a = −0.712122 + 0.711786I
b = 0.475020 + 0.495981I
4.00952 − 1.59909I 0
u = −0.726101 − 0.685259I
a = −0.712122 − 0.711786I
b = 0.475020 − 0.495981I
4.00952 + 1.59909I 0
u = −0.945676 + 0.299992I
a = −2.86713 − 0.06400I
b = −0.958414 + 0.093245I
2.80740 + 1.73216I 0
u = −0.945676 − 0.299992I
a = −2.86713 + 0.06400I
b = −0.958414 − 0.093245I
2.80740 − 1.73216I 0
u = −1.01420
a = 3.19187
b = −0.739216
0.282990 0
u = 0.186212 + 1.003630I
a = 1.198480 − 0.372593I
b = 0.560041 + 0.609185I
6.05015 − 0.21785I 0
u = 0.186212 − 1.003630I
a = 1.198480 + 0.372593I
b = 0.560041 − 0.609185I
6.05015 + 0.21785I 0
u = −0.968483 + 0.034921I
a = −2.52345 − 0.92440I
b = −1.382910 + 0.259862I
−1.14077 + 1.10990I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.968483 − 0.034921I
a = −2.52345 + 0.92440I
b = −1.382910 − 0.259862I
−1.14077 − 1.10990I 0
u = 0.933812 + 0.255135I
a = 0.515557 − 0.310399I
b = 0.022124 + 0.753927I
0.72649 − 2.79094I 0
u = 0.933812 − 0.255135I
a = 0.515557 + 0.310399I
b = 0.022124 − 0.753927I
0.72649 + 2.79094I 0
u = −0.383512 + 0.887504I
a = 0.0706374 + 0.0522425I
b = 1.153240 + 0.239311I
−0.93547 − 2.28826I 0
u = −0.383512 − 0.887504I
a = 0.0706374 − 0.0522425I
b = 1.153240 − 0.239311I
−0.93547 + 2.28826I 0
u = 0.958414 + 0.093245I
a = 2.90275 + 0.55187I
b = 0.945676 + 0.299992I
2.80740 − 1.73216I 0
u = 0.958414 − 0.093245I
a = 2.90275 − 0.55187I
b = 0.945676 − 0.299992I
2.80740 + 1.73216I 0
u = 1.048070 + 0.054620I
a = 2.44274 + 0.18348I
b = 2.02951 − 0.22269I
−0.91409 − 5.95546I 0
u = 1.048070 − 0.054620I
a = 2.44274 − 0.18348I
b = 2.02951 + 0.22269I
−0.91409 + 5.95546I 0
u = −1.056660 + 0.048917I
a = 1.47570 − 0.45195I
b = 1.228370 + 0.454325I
−1.71117 + 1.03772I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.056660 − 0.048917I
a = 1.47570 + 0.45195I
b = 1.228370 − 0.454325I
−1.71117 − 1.03772I 0
u = 0.092151 + 0.931553I
a = −0.434887 + 0.576532I
b = −1.222610 − 0.329948I
−0.38295 − 8.49628I 0
u = 0.092151 − 0.931553I
a = −0.434887 − 0.576532I
b = −1.222610 + 0.329948I
−0.38295 + 8.49628I 0
u = −0.990794 + 0.406870I
a = −0.565079 + 0.557528I
b = −0.23128 + 1.45237I
4.70571 + 3.83850I 0
u = −0.990794 − 0.406870I
a = −0.565079 − 0.557528I
b = −0.23128 − 1.45237I
4.70571 − 3.83850I 0
u = 0.926911 + 0.015610I
a = −2.55747 + 0.29813I
b = −1.95135 − 0.38954I
−0.31440 − 5.74271I 0
u = 0.926911 − 0.015610I
a = −2.55747 − 0.29813I
b = −1.95135 + 0.38954I
−0.31440 + 5.74271I 0
u = −0.969437 + 0.465037I
a = −0.589741 − 0.268638I
b = −0.700197 + 1.005260I
3.18701 + 6.15547I 0
u = −0.969437 − 0.465037I
a = −0.589741 + 0.268638I
b = −0.700197 − 1.005260I
3.18701 − 6.15547I 0
u = 0.960150 + 0.537279I
a = 0.527575 − 0.156061I
b = −0.036489 − 0.560410I
3.14161 − 1.66960I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.960150 − 0.537279I
a = 0.527575 + 0.156061I
b = −0.036489 + 0.560410I
3.14161 + 1.66960I 0
u = −0.873818 + 0.684520I
a = 0.524809 − 0.616571I
b = −0.721317 − 0.270053I
4.68388 + 8.26965I 0
u = −0.873818 − 0.684520I
a = 0.524809 + 0.616571I
b = −0.721317 + 0.270053I
4.68388 − 8.26965I 0
u = −1.107760 + 0.086604I
a = 0.187691 − 0.538217I
b = 0.244907 − 1.237800I
−3.04963 − 0.18332I 0
u = −1.107760 − 0.086604I
a = 0.187691 + 0.538217I
b = 0.244907 + 1.237800I
−3.04963 + 0.18332I 0
u = 0.882048 + 0.019394I
a = −0.0941606 + 0.0415742I
b = −0.705452 + 1.009270I
3.20385 + 0.81417I 0
u = 0.882048 − 0.019394I
a = −0.0941606 − 0.0415742I
b = −0.705452 − 1.009270I
3.20385 − 0.81417I 0
u = 1.151890 + 0.193176I
a = −0.244501 − 0.415125I
b = −0.051266 + 0.545218I
−3.26702 − 3.89641I 0
u = 1.151890 − 0.193176I
a = −0.244501 + 0.415125I
b = −0.051266 − 0.545218I
−3.26702 + 3.89641I 0
u = 1.073500 + 0.469067I
a = −0.321729 − 0.595620I
b = −0.061776 − 1.241670I
5.25739 − 5.36322I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073500 − 0.469067I
a = −0.321729 + 0.595620I
b = −0.061776 + 1.241670I
5.25739 + 5.36322I 0
u = −0.560041 + 0.609185I
a = −1.49673 + 0.39580I
b = −0.186212 + 1.003630I
6.05015 + 0.21785I 0
u = −0.560041 − 0.609185I
a = −1.49673 − 0.39580I
b = −0.186212 − 1.003630I
6.05015 − 0.21785I 0
u = −1.172060 + 0.069673I
a = −1.81051 − 0.54262I
b = −1.53503 − 0.89173I
−3.42898 + 2.30117I 0
u = −1.172060 − 0.069673I
a = −1.81051 + 0.54262I
b = −1.53503 + 0.89173I
−3.42898 − 2.30117I 0
u = 1.161000 + 0.193168I
a = 2.20920 + 0.10935I
b = 1.50555 + 0.73851I
0.20473 − 6.15765I 0
u = 1.161000 − 0.193168I
a = 2.20920 − 0.10935I
b = 1.50555 − 0.73851I
0.20473 + 6.15765I 0
u = −1.153240 + 0.239311I
a = 0.0537071 + 0.0481322I
b = 0.383512 + 0.887504I
−0.93547 + 2.28826I 0
u = −1.153240 − 0.239311I
a = 0.0537071 − 0.0481322I
b = 0.383512 − 0.887504I
−0.93547 − 2.28826I 0
u = −1.146770 + 0.277757I
a = 0.697238 − 0.020965I
b = −0.058951 − 0.436078I
−0.131859 − 0.845720I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.146770 − 0.277757I
a = 0.697238 + 0.020965I
b = −0.058951 + 0.436078I
−0.131859 + 0.845720I 0
u = −1.160410 + 0.245312I
a = 2.07907 − 0.09023I
b = 1.69972 − 0.75102I
−0.24112 + 4.51482I 0
u = −1.160410 − 0.245312I
a = 2.07907 + 0.09023I
b = 1.69972 + 0.75102I
−0.24112 − 4.51482I 0
u = 0.700197 + 1.005260I
a = 0.334272 − 0.460166I
b = 0.969437 + 0.465037I
3.18701 − 6.15547I 0
u = 0.700197 − 1.005260I
a = 0.334272 + 0.460166I
b = 0.969437 − 0.465037I
3.18701 + 6.15547I 0
u = 0.721317 + 0.270053I
a = 0.364380 + 1.108540I
b = 0.873818 − 0.684520I
4.68388 + 8.26965I 0
u = 0.721317 − 0.270053I
a = 0.364380 − 1.108540I
b = 0.873818 + 0.684520I
4.68388 − 8.26965I 0
u = 0.705452 + 1.009270I
a = −0.0622091 + 0.0396078I
b = −0.882048 + 0.019394I
3.20385 − 0.81417I 0
u = 0.705452 − 1.009270I
a = −0.0622091 − 0.0396078I
b = −0.882048 − 0.019394I
3.20385 + 0.81417I 0
u = −0.759979
a = 0.415564
b = 0.631645
−1.12173 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.061776 + 1.241670I
a = −0.637555 + 0.021425I
b = −1.073500 − 0.469067I
5.25739 − 5.36322I 0
u = 0.061776 − 1.241670I
a = −0.637555 − 0.021425I
b = −1.073500 + 0.469067I
5.25739 + 5.36322I 0
u = −0.022124 + 0.753927I
a = 0.188008 − 0.749126I
b = −0.933812 + 0.255135I
0.72649 + 2.79094I 0
u = −0.022124 − 0.753927I
a = 0.188008 + 0.749126I
b = −0.933812 − 0.255135I
0.72649 − 2.79094I 0
u = −1.169410 + 0.466173I
a = 0.215838 − 0.511817I
b = −0.023556 − 1.346520I
5.3085 + 13.7961I 0
u = −1.169410 − 0.466173I
a = 0.215838 + 0.511817I
b = −0.023556 + 1.346520I
5.3085 − 13.7961I 0
u = 0.739216
a = −4.37922
b = 1.01420
0.282990 0
u = −0.244907 + 1.237800I
a = 0.500977 + 0.031194I
b = 1.107760 − 0.086604I
−3.04963 − 0.18332I 0
u = −0.244907 − 1.237800I
a = 0.500977 − 0.031194I
b = 1.107760 + 0.086604I
−3.04963 + 0.18332I 0
u = 1.222610 + 0.329948I
a = −0.512435 − 0.149610I
b = −0.092151 − 0.931553I
−0.38295 − 8.49628I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.222610 − 0.329948I
a = −0.512435 + 0.149610I
b = −0.092151 + 0.931553I
−0.38295 + 8.49628I 0
u = −1.151610 + 0.532353I
a = −1.39892 − 0.98201I
b = −1.315840 + 0.477195I
−3.35885 + 7.50906I 0
u = −1.151610 − 0.532353I
a = −1.39892 + 0.98201I
b = −1.315840 − 0.477195I
−3.35885 − 7.50906I 0
u = 1.017080 + 0.766078I
a = −0.223433 − 0.144013I
b = −0.203048 + 0.285531I
3.11818 − 4.10927I 0
u = 1.017080 − 0.766078I
a = −0.223433 + 0.144013I
b = −0.203048 − 0.285531I
3.11818 + 4.10927I 0
u = 1.260050 + 0.248723I
a = 1.68332 − 0.52135I
b = 1.39597 + 0.57738I
−7.11081 − 6.68152I 0
u = 1.260050 − 0.248723I
a = 1.68332 + 0.52135I
b = 1.39597 − 0.57738I
−7.11081 + 6.68152I 0
u = 1.297650 + 0.036904I
a = −1.203950 + 0.622431I
b = −1.02574 + 1.28472I
−1.63041 − 2.72909I 0
u = 1.297650 − 0.036904I
a = −1.203950 − 0.622431I
b = −1.02574 − 1.28472I
−1.63041 + 2.72909I 0
u = −1.228370 + 0.454325I
a = 0.955228 + 0.800841I
b = 1.056660 + 0.048917I
−1.71117 − 1.03772I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.228370 − 0.454325I
a = 0.955228 − 0.800841I
b = 1.056660 − 0.048917I
−1.71117 + 1.03772I 0
u = −0.475020 + 0.495981I
a = 1.02715 − 1.04284I
b = 0.726101 + 0.685259I
4.00952 + 1.59909I 0
u = −0.475020 − 0.495981I
a = 1.02715 + 1.04284I
b = 0.726101 − 0.685259I
4.00952 − 1.59909I 0
u = 1.223380 + 0.555574I
a = −0.124408 + 0.146861I
b = −0.231017 + 0.974102I
2.80266 − 5.31618I 0
u = 1.223380 − 0.555574I
a = −0.124408 − 0.146861I
b = −0.231017 − 0.974102I
2.80266 + 5.31618I 0
u = 0.023556 + 1.346520I
a = 0.518883 + 0.019332I
b = 1.169410 − 0.466173I
5.3085 + 13.7961I 0
u = 0.023556 − 1.346520I
a = 0.518883 − 0.019332I
b = 1.169410 + 0.466173I
5.3085 − 13.7961I 0
u = −0.631645
a = 0.499996
b = 0.759979
−1.12173 0
u = 1.315840 + 0.477195I
a = 1.33907 − 0.77910I
b = 1.151610 + 0.532353I
−3.35885 − 7.50906I 0
u = 1.315840 − 0.477195I
a = 1.33907 + 0.77910I
b = 1.151610 − 0.532353I
−3.35885 + 7.50906I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.382910 + 0.259862I
a = 1.62357 − 0.88874I
b = 0.968483 + 0.034921I
−1.14077 − 1.10990I 0
u = 1.382910 − 0.259862I
a = 1.62357 + 0.88874I
b = 0.968483 − 0.034921I
−1.14077 + 1.10990I 0
u = 1.284620 + 0.580625I
a = 1.68564 − 0.57116I
b = 1.49430 + 0.65030I
−0.50826 − 11.03970I 0
u = 1.284620 − 0.580625I
a = 1.68564 + 0.57116I
b = 1.49430 − 0.65030I
−0.50826 + 11.03970I 0
u = 0.036489 + 0.560410I
a = 0.305719 − 1.033610I
b = −0.960150 − 0.537279I
3.14161 − 1.66960I 0
u = 0.036489 − 0.560410I
a = 0.305719 + 1.033610I
b = −0.960150 + 0.537279I
3.14161 + 1.66960I 0
u = 0.051266 + 0.545218I
a = 0.920783 + 0.456056I
b = −1.151890 + 0.193176I
−3.26702 + 3.89641I −9.04905 − 7.09358I
u = 0.051266 − 0.545218I
a = 0.920783 − 0.456056I
b = −1.151890 − 0.193176I
−3.26702 − 3.89641I −9.04905 + 7.09358I
u = 0.23128 + 1.45237I
a = 0.560935 − 0.139980I
b = 0.990794 + 0.406870I
4.70571 − 3.83850I 0
u = 0.23128 − 1.45237I
a = 0.560935 + 0.139980I
b = 0.990794 − 0.406870I
4.70571 + 3.83850I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.39597 + 0.57738I
a = −1.31651 − 0.71518I
b = −1.260050 + 0.248723I
−7.11081 + 6.68152I 0
u = −1.39597 − 0.57738I
a = −1.31651 + 0.71518I
b = −1.260050 − 0.248723I
−7.11081 − 6.68152I 0
u = −1.48355 + 0.31884I
a = −1.56840 − 0.12801I
b = −1.34212 + 0.75474I
−3.81852 + 10.56760I 0
u = −1.48355 − 0.31884I
a = −1.56840 + 0.12801I
b = −1.34212 − 0.75474I
−3.81852 − 10.56760I 0
u = 1.34212 + 0.75474I
a = 1.43898 − 0.57811I
b = 1.48355 + 0.31884I
−3.81852 − 10.56760I 0
u = 1.34212 − 0.75474I
a = 1.43898 + 0.57811I
b = 1.48355 − 0.31884I
−3.81852 + 10.56760I 0
u = 0.058951 + 0.436078I
a = 0.24863 + 1.85380I
b = 1.146770 − 0.277757I
−0.131859 − 0.845720I 0.54565 + 5.75487I
u = 0.058951 − 0.436078I
a = 0.24863 − 1.85380I
b = 1.146770 + 0.277757I
−0.131859 + 0.845720I 0.54565 − 5.75487I
u = 0.191208 + 0.342488I
a = 1.25723 − 2.25192I
b = −0.191208 + 0.342488I
2.50167 4.01178 + 0.I
u = 0.191208 − 0.342488I
a = 1.25723 + 2.25192I
b = −0.191208 − 0.342488I
2.50167 4.01178 + 0.I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.49430 + 0.65030I
a = −1.46495 − 0.47357I
b = −1.284620 + 0.580625I
−0.50826 + 11.03970I 0
u = −1.49430 − 0.65030I
a = −1.46495 + 0.47357I
b = −1.284620 − 0.580625I
−0.50826 − 11.03970I 0
u = 1.02574 + 1.28472I
a = −0.964484 + 0.463887I
b = −1.297650 + 0.036904I
−1.63041 + 2.72909I 0
u = 1.02574 − 1.28472I
a = −0.964484 − 0.463887I
b = −1.297650 − 0.036904I
−1.63041 − 2.72909I 0
u = 0.203048 + 0.285531I
a = 0.545431 + 0.797365I
b = −1.017080 + 0.766078I
3.11818 + 4.10927I −0.22340 + 4.80248I
u = 0.203048 − 0.285531I
a = 0.545431 − 0.797365I
b = −1.017080 − 0.766078I
3.11818 − 4.10927I −0.22340 − 4.80248I
u = −1.50555 + 0.73851I
a = −1.50731 − 0.37159I
b = −1.161000 + 0.193168I
0.20473 + 6.15765I 0
u = −1.50555 − 0.73851I
a = −1.50731 + 0.37159I
b = −1.161000 − 0.193168I
0.20473 − 6.15765I 0
u = 1.53503 + 0.89173I
a = 1.196270 − 0.362799I
b = 1.172060 − 0.069673I
−3.42898 + 2.30117I 0
u = 1.53503 − 0.89173I
a = 1.196270 + 0.362799I
b = 1.172060 + 0.069673I
−3.42898 − 2.30117I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.69972 + 0.75102I
a = 1.310350 + 0.217312I
b = 1.160410 − 0.245312I
−0.24112 + 4.51482I 0
u = −1.69972 − 0.75102I
a = 1.310350 − 0.217312I
b = 1.160410 + 0.245312I
−0.24112 − 4.51482I 0
u = 1.95135 + 0.38954I
a = −1.147300 + 0.350190I
b = −0.926911 − 0.015610I
−0.31440 − 5.74271I 0
u = 1.95135 − 0.38954I
a = −1.147300 − 0.350190I
b = −0.926911 + 0.015610I
−0.31440 + 5.74271I 0
u = −2.02951 + 0.22269I
a = −1.224180 − 0.294816I
b = −1.048070 − 0.054620I
−0.91409 − 5.95546I 0
u = −2.02951 − 0.22269I
a = −1.224180 + 0.294816I
b = −1.048070 + 0.054620I
−0.91409 + 5.95546I 0
24
III. I
u
3
= hb + u, 188u
17
− 64u
16
+ · · · + 75a − 796, u
18
− 7u
16
+ · · · − 3u − 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
7
=
−2.50667u
17
+ 0.853333u
16
+ ··· + 7.41333u + 10.6133
−u
a
2
=
0.853333u
17
+ 0.773333u
16
+ ··· + 3.09333u − 1.50667
−u
2
a
1
=
0.840000u
17
+ 0.480000u
16
+ ··· − 0.0800000u − 2.28000
−0.453333u
17
+ 0.0266667u
16
+ ··· − 0.893333u − 0.293333
a
6
=
−3.28000u
17
+ 0.840000u
16
+ ··· + 6.36000u + 9.76000
u
3
− u
a
10
=
u
u
a
8
=
−3.28000u
17
+ 0.840000u
16
+ ··· + 7.36000u + 9.76000
−0.773333u
17
− 0.0133333u
16
+ ··· − 1.05333u − 0.853333
a
12
=
3u
17
−
9
5
u
16
+ ··· −
1
5
u −
34
5
−3.97333u
17
+ 2.18667u
16
+ ··· + 6.74667u + 3.14667
a
5
=
3.14667u
17
− 2.57333u
16
+ ··· − 12.2933u − 3.29333
2.76444u
17
− 0.448889u
16
+ ··· + 1.20444u − 0.262222
a
9
=
−2.84000u
17
+ 1.32000u
16
+ ··· + 1.28000u + 8.08000
0.160000u
17
− 0.480000u
16
+ ··· + 1.08000u + 1.28000
(ii) Obstruction class = 1
(iii) Cusp Shapes =
251
675
u
17
−
88
675
u
16
+ ··· +
11798
675
u −
13702
675
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
3(3u
18
− 19u
17
+ ··· − 12u + 1)
c
2
, c
10
u
18
− 7u
16
+ ··· + 3u − 1
c
3
, c
6
u
18
− 7u
16
+ ··· − 3u − 1
c
4
3(3u
18
+ 19u
17
+ ··· + 12u + 1)
c
5
3(3u
18
+ 34u
17
+ ··· + u − 1)
c
7
3(3u
18
+ 8u
17
+ ··· − u − 1)
c
8
, c
12
u
18
− u
17
+ ··· − 4u + 3
c
9
, c
11
u
18
− u
17
+ ··· + 5u
2
− 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
9(9y
18
+ 53y
17
+ ··· − 118y + 1)
c
2
, c
3
, c
6
c
10
y
18
− 14y
17
+ ··· − 13y + 1
c
5
9(9y
18
− 100y
17
+ ··· − 17y + 1)
c
7
9(9y
18
− 142y
17
+ ··· + 77y + 1)
c
8
, c
12
y
18
+ 5y
17
+ ··· − 10y + 9
c
9
, c
11
y
18
− 9y
17
+ ··· − 10y + 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.728348 + 0.635280I
a = −0.458923 + 0.337603I
b = −0.728348 − 0.635280I
3.10656 − 4.89008I −2.17362 + 6.61154I
u = 0.728348 − 0.635280I
a = −0.458923 − 0.337603I
b = −0.728348 + 0.635280I
3.10656 + 4.89008I −2.17362 − 6.61154I
u = 0.391387 + 0.741183I
a = −1.378030 + 0.054435I
b = −0.391387 − 0.741183I
5.27368 − 0.38885I 0.08674 + 2.66009I
u = 0.391387 − 0.741183I
a = −1.378030 − 0.054435I
b = −0.391387 + 0.741183I
5.27368 + 0.38885I 0.08674 − 2.66009I
u = −0.731290 + 0.259234I
a = 0.714498 − 0.425143I
b = 0.731290 − 0.259234I
−1.42988 − 0.78385I −8.25164 + 5.40521I
u = −0.731290 − 0.259234I
a = 0.714498 + 0.425143I
b = 0.731290 + 0.259234I
−1.42988 + 0.78385I −8.25164 − 5.40521I
u = 0.761751
a = 4.26767
b = −0.761751
1.11001 −4.48450
u = −0.620488 + 0.372051I
a = −1.61392 − 0.54454I
b = 0.620488 − 0.372051I
5.22937 + 9.86143I 0.47076 − 8.25956I
u = −0.620488 − 0.372051I
a = −1.61392 + 0.54454I
b = 0.620488 + 0.372051I
5.22937 − 9.86143I 0.47076 + 8.25956I
u = −1.219200 + 0.389635I
a = 1.77496 + 0.18361I
b = 1.219200 − 0.389635I
0.24188 + 3.16622I −1.12756 − 2.19385I
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.219200 − 0.389635I
a = 1.77496 − 0.18361I
b = 1.219200 + 0.389635I
0.24188 − 3.16622I −1.12756 + 2.19385I
u = 1.275660 + 0.472215I
a = −1.30229 + 0.62626I
b = −1.275660 − 0.472215I
−5.56191 − 7.26369I −7.00294 + 7.25514I
u = 1.275660 − 0.472215I
a = −1.30229 − 0.62626I
b = −1.275660 + 0.472215I
−5.56191 + 7.26369I −7.00294 − 7.25514I
u = 1.40083 + 0.30786I
a = −1.53871 − 0.02393I
b = −1.40083 − 0.30786I
−0.77540 + 4.13237I −5.30365 − 2.69060I
u = 1.40083 − 0.30786I
a = −1.53871 + 0.02393I
b = −1.40083 + 0.30786I
−0.77540 − 4.13237I −5.30365 + 2.69060I
u = −1.38025 + 0.59051I
a = 1.59019 + 0.50498I
b = 1.38025 − 0.59051I
−1.18687 + 10.35570I −5.47784 − 5.07503I
u = −1.38025 − 0.59051I
a = 1.59019 − 0.50498I
b = 1.38025 + 0.59051I
−1.18687 − 10.35570I −5.47784 + 5.07503I
u = −0.451749
a = 3.49012
b = 0.451749
2.25458 −18.2150
29
IV.
I
u
4
= h1.42 × 10
7
u
17
− 7.27 × 10
6
u
16
+ · · · + 2.13 × 10
7
b − 4.94 × 10
7
, 3.46 ×
10
7
u
17
+ 1.40 × 10
7
u
16
+ · · · + 2.13 × 10
7
a + 2.54 × 10
7
, u
18
− 8u
16
+ · · · − u − 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
7
=
−1.62451u
17
− 0.659505u
16
+ ··· − 10.2030u − 1.19541
−0.669320u
17
+ 0.341618u
16
+ ··· − 0.874644u + 2.32175
a
2
=
3.47945u
17
+ 0.610442u
16
+ ··· + 13.9590u − 0.732836
−1.03771u
17
+ 0.655256u
16
+ ··· − 5.58323u + 2.45600
a
1
=
1.51328u
17
+ 0.408393u
16
+ ··· + 4.28593u + 1.11273
−1.34697u
17
+ 0.347103u
16
+ ··· − 7.75144u + 2.25396
a
6
=
−2.31940u
17
+ 2.11153u
16
+ ··· − 12.8858u + 11.0839
0.297554u
17
+ 0.575634u
16
+ ··· + 1.86495u + 0.500963
a
10
=
u
u
a
8
=
−1.23022u
17
− 0.381531u
16
+ ··· − 8.24665u − 0.194283
−0.275035u
17
+ 0.619592u
16
+ ··· + 1.08167u + 3.32287
a
12
=
0.452704u
17
+ 0.0354049u
16
+ ··· + 6.46512u + 0.473319
−0.0855289u
17
− 1.03728u
16
+ ··· − 1.40122u − 3.55101
a
5
=
−4.76085u
17
+ 0.392469u
16
+ ··· − 22.3844u + 6.71242
1.36783u
17
+ 1.06022u
16
+ ··· + 11.1635u + 2.16201
a
9
=
−5.73432u
17
+ 3.28049u
16
+ ··· − 26.7164u + 16.5093
2.00084u
17
+ 0.840379u
16
+ ··· + 9.24226u − 2.13805
(ii) Obstruction class = 1
(iii) Cusp Shapes =
90205414
21285647
u
17
+
104305397
21285647
u
16
+ ··· +
376506031
21285647
u +
218259211
21285647
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
9
− 2u
8
+ 3u
7
− 7u
6
+ u
5
− 10u
4
− 4u
3
− 6u
2
− 4u − 1)
2
c
2
, c
10
u
18
− 8u
16
+ ··· + u − 1
c
3
, c
6
u
18
− 8u
16
+ ··· − u − 1
c
4
(u
9
+ 2u
8
+ 3u
7
+ 7u
6
+ u
5
+ 10u
4
− 4u
3
+ 6u
2
− 4u + 1)
2
c
5
(u
9
− 2u
8
− 2u
7
+ 13u
6
− 18u
5
+ 7u
4
+ 8u
3
− 6u
2
− u + 1)
2
c
7
(u
9
+ 4u
8
+ 5u
7
+ 3u
6
+ 2u
5
+ 2u
4
+ u
3
+ 1)
2
c
8
, c
12
u
18
+ 3u
17
+ ··· + u − 1
c
9
, c
11
u
18
+ 3u
17
+ ··· + 10u − 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
9
+ 2y
8
− 17y
7
− 91y
6
− 195y
5
− 220y
4
− 126y
3
− 24y
2
+ 4y −1)
2
c
2
, c
3
, c
6
c
10
y
18
− 16y
17
+ ··· − 19y + 1
c
5
(y
9
− 8y
8
+ 20y
7
− 53y
6
+ 84y
5
− 173y
4
+ 158y
3
− 66y
2
+ 13y −1)
2
c
7
(y
9
− 6y
8
+ 5y
7
− 3y
6
+ 2y
5
− 8y
4
− 5y
3
− 4y
2
− 1)
2
c
8
, c
12
y
18
+ 5y
17
+ ··· − 29y + 1
c
9
, c
11
y
18
− 13y
17
+ ··· − 22y + 1
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.05453
a = 1.61973
b = −0.529976
0.416370 13.0170
u = 0.619437 + 0.660413I
a = −0.793143 + 0.656703I
b = 0.374606 + 0.033571I
4.15988 − 1.15529I 8.56223 + 1.24581I
u = 0.619437 − 0.660413I
a = −0.793143 − 0.656703I
b = 0.374606 − 0.033571I
4.15988 + 1.15529I 8.56223 − 1.24581I
u = 1.082530 + 0.167606I
a = 2.56840 + 0.03078I
b = 2.12316 + 0.45346I
−0.72688 − 6.70635I −7.6717 + 15.3934I
u = 1.082530 − 0.167606I
a = 2.56840 − 0.03078I
b = 2.12316 − 0.45346I
−0.72688 + 6.70635I −7.6717 − 15.3934I
u = −1.178130 + 0.065422I
a = −1.39731 − 0.34024I
b = −1.12254 − 1.00565I
−3.57395 + 1.78451I −13.26411 + 1.60529I
u = −1.178130 − 0.065422I
a = −1.39731 + 0.34024I
b = −1.12254 + 1.00565I
−3.57395 − 1.78451I −13.26411 − 1.60529I
u = 1.046470 + 0.617812I
a = −0.137310 + 0.033916I
b = −0.067200 − 0.761301I
3.22264 − 4.71392I 2.36527 + 6.84291I
u = 1.046470 − 0.617812I
a = −0.137310 − 0.033916I
b = −0.067200 + 0.761301I
3.22264 + 4.71392I 2.36527 − 6.84291I
u = 0.067200 + 0.761301I
a = −0.083252 + 0.208919I
b = −1.046470 − 0.617812I
3.22264 − 4.71392I 2.36527 + 6.84291I
33
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.067200 − 0.761301I
a = −0.083252 − 0.208919I
b = −1.046470 + 0.617812I
3.22264 + 4.71392I 2.36527 − 6.84291I
u = 0.529976
a = −3.22290
b = 1.05453
0.416370 13.0170
u = 1.12254 + 1.00565I
a = 0.961556 − 0.585777I
b = 1.178130 − 0.065422I
−3.57395 + 1.78451I −13.26411 + 1.60529I
u = 1.12254 − 1.00565I
a = 0.961556 + 0.585777I
b = 1.178130 + 0.065422I
−3.57395 − 1.78451I −13.26411 − 1.60529I
u = −0.374606 + 0.033571I
a = 2.47735 − 0.09036I
b = −0.619437 + 0.660413I
4.15988 + 1.15529I 8.56223 − 1.24581I
u = −0.374606 − 0.033571I
a = 2.47735 + 0.09036I
b = −0.619437 − 0.660413I
4.15988 − 1.15529I 8.56223 + 1.24581I
u = −2.12316 + 0.45346I
a = −1.294700 − 0.058072I
b = −1.082530 + 0.167606I
−0.72688 + 6.70635I −7.6717 − 15.3934I
u = −2.12316 − 0.45346I
a = −1.294700 + 0.058072I
b = −1.082530 − 0.167606I
−0.72688 − 6.70635I −7.6717 + 15.3934I
34
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
9(u
9
− 2u
8
+ 3u
7
− 7u
6
+ u
5
− 10u
4
− 4u
3
− 6u
2
− 4u − 1)
2
· (3u
18
− 19u
17
+ ··· − 12u + 1)(3u
33
− 68u
32
+ ··· + 6656u − 512)
· (u
63
+ 11u
62
+ ··· + 159u − 1)
2
c
2
, c
10
(u
18
− 8u
16
+ ··· + u − 1)(u
18
− 7u
16
+ ··· + 3u − 1)
· (u
33
− 13u
31
+ ··· + 5u − 1)(u
126
− u
125
+ ··· + 445179u − 79381)
c
3
, c
6
(u
18
− 8u
16
+ ··· − u − 1)(u
18
− 7u
16
+ ··· − 3u − 1)
· (u
33
− 13u
31
+ ··· + 5u − 1)(u
126
− u
125
+ ··· + 445179u − 79381)
c
4
9(u
9
+ 2u
8
+ 3u
7
+ 7u
6
+ u
5
+ 10u
4
− 4u
3
+ 6u
2
− 4u + 1)
2
· (3u
18
+ 19u
17
+ ··· + 12u + 1)(3u
33
− 68u
32
+ ··· + 6656u − 512)
· (u
63
+ 11u
62
+ ··· + 159u − 1)
2
c
5
9(u
9
− 2u
8
− 2u
7
+ 13u
6
− 18u
5
+ 7u
4
+ 8u
3
− 6u
2
− u + 1)
2
· (3u
18
+ 34u
17
+ ··· + u − 1)(3u
33
− 83u
32
+ ··· + 416u − 64)
· (u
63
+ 16u
62
+ ··· + 5u + 1)
2
c
7
9(u
9
+ 4u
8
+ 5u
7
+ 3u
6
+ 2u
5
+ 2u
4
+ u
3
+ 1)
2
· (3u
18
+ 8u
17
+ ··· − u − 1)(3u
33
+ 83u
32
+ ··· + 19456u + 4096)
· (u
63
− 14u
62
+ ··· − 694u + 39)
2
c
8
, c
12
(u
18
− u
17
+ ··· − 4u + 3)(u
18
+ 3u
17
+ ··· + u − 1)
· (u
33
+ u
32
+ ··· + 8u + 3)(u
126
+ 8u
125
+ ··· − 23405u − 2473)
c
9
, c
11
(u
18
− u
17
+ ··· + 5u
2
− 1)(u
18
+ 3u
17
+ ··· + 10u − 1)
· (u
33
+ u
32
+ ··· + 8u − 29)
· (u
126
− 2u
125
+ ··· − 81829844u − 30650633)
35
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
81
· (y
9
+ 2y
8
− 17y
7
− 91y
6
− 195y
5
− 220y
4
− 126y
3
− 24y
2
+ 4y −1)
2
· (9y
18
+ 53y
17
+ ··· − 118y + 1)
· (9y
33
+ 26y
32
+ ··· + 12582912y −262144)
· (y
63
+ 35y
62
+ ··· + 29501y −1)
2
c
2
, c
3
, c
6
c
10
(y
18
− 16y
17
+ ··· − 19y + 1)(y
18
− 14y
17
+ ··· − 13y + 1)
· (y
33
− 26y
32
+ ··· + 7y −1)
· (y
126
− 85y
125
+ ··· − 14924889155y + 6301343161)
c
5
81
· (y
9
− 8y
8
+ 20y
7
− 53y
6
+ 84y
5
− 173y
4
+ 158y
3
− 66y
2
+ 13y −1)
2
· (9y
18
− 100y
17
+ ··· − 17y + 1)
· (9y
33
− 181y
32
+ ··· − 89088y −4096)
· (y
63
− 26y
62
+ ··· + 47y −1)
2
c
7
81(y
9
− 6y
8
+ 5y
7
− 3y
6
+ 2y
5
− 8y
4
− 5y
3
− 4y
2
− 1)
2
· (9y
18
− 142y
17
+ ··· + 77y + 1)
· (9y
33
− 187y
32
+ ··· + 439353344y −16777216)
· (y
63
− 104y
61
+ ··· + 27910y −1521)
2
c
8
, c
12
(y
18
+ 5y
17
+ ··· − 10y + 9)(y
18
+ 5y
17
+ ··· − 29y + 1)
· (y
33
+ 5y
32
+ ··· + 220y −9)
· (y
126
+ 32y
125
+ ··· − 362675137y + 6115729)
c
9
, c
11
(y
18
− 13y
17
+ ··· − 22y + 1)(y
18
− 9y
17
+ ··· − 10y + 1)
· (y
33
− 17y
32
+ ··· + 10620y −841)
· (y
126
− 58y
125
+ ··· − 22519621465061486y + 939461303300689)
36
