12a
1217
(K12a
1217
)
A knot diagram
1
Linearized knot diagam
5 6 7 10 9 11 1 12 2 4 3 8
Solving Sequence
8,12
9 1
3,7
4 11 6 2 5 10
c
8
c
12
c
7
c
3
c
11
c
6
c
2
c
5
c
10
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.78483 × 10
62
u
51
− 9.23708 × 10
62
u
50
+ ··· + 3.66721 × 10
63
b − 9.19913 × 10
63
,
− 1.19194 × 10
64
u
51
− 3.36347 × 10
64
u
50
+ ··· + 1.02682 × 10
65
a − 4.62060 × 10
65
,
u
52
+ 3u
51
+ ··· + 155u + 28i
I
u
2
= h−6.32395 × 10
29
au
49
− 6.85959 × 10
30
u
49
+ ··· + 4.20919 × 10
31
a − 4.89805 × 10
31
,
5.23973 × 10
32
au
49
− 4.49244 × 10
32
u
49
+ ··· + 4.28747 × 10
33
a + 1.58434 × 10
33
,
u
50
− 2u
49
+ ··· − 60u + 19i
I
u
3
= hu
12
a + u
12
+ ··· − a + 11, 34u
12
a + 40u
12
+ ··· + 85a + 269,
u
13
− 2u
12
+ 9u
11
− 15u
10
+ 32u
9
− 45u
8
+ 58u
7
− 66u
6
+ 55u
5
− 44u
4
+ 24u
3
− 8u
2
+ 3u + 1i
I
u
4
= hu
7
+ 3u
6
+ 7u
5
+ 10u
4
+ 11u
3
+ 8u
2
+ b + 4u + 1, u
6
+ 2u
5
+ 5u
4
+ 6u
3
+ 7u
2
+ a + 4u + 3,
u
8
+ 2u
7
+ 6u
6
+ 8u
5
+ 11u
4
+ 9u
3
+ 7u
2
+ 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 186 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−3.78 × 10
62
u
51
− 9.24 × 10
62
u
50
+ · · · + 3.67 × 10
63
b − 9.20 ×
10
63
, −1.19 × 10
64
u
51
− 3.36 × 10
64
u
50
+ · · · + 1.03 × 10
65
a − 4.62 ×
10
65
, u
52
+ 3u
51
+ · · · + 155u + 28i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
3
=
0.116080u
51
+ 0.327562u
50
+ ··· + 24.4948u + 4.49991
0.103207u
51
+ 0.251883u
50
+ ··· + 11.1540u + 2.50848
a
7
=
u
2
+ 1
u
2
a
4
=
0.102816u
51
+ 0.276430u
50
+ ··· + 12.5832u + 1.52396
0.168183u
51
+ 0.455833u
50
+ ··· + 16.5012u + 3.07868
a
11
=
−0.0592969u
51
− 0.158117u
50
+ ··· − 23.0526u − 8.06748
−0.0168503u
51
− 0.0486054u
50
+ ··· − 3.42539u − 2.09057
a
6
=
−0.110268u
51
− 0.272050u
50
+ ··· − 30.8258u − 5.98247
0.0385349u
51
+ 0.0641253u
50
+ ··· − 7.47331u − 1.60516
a
2
=
−0.264232u
51
− 0.613333u
50
+ ··· − 41.2535u − 8.42966
0.0828615u
51
+ 0.241500u
50
+ ··· + 18.5521u + 3.43075
a
5
=
−0.0895885u
51
− 0.165558u
50
+ ··· − 17.3333u − 2.73222
0.0370596u
51
+ 0.136146u
50
+ ··· − 0.00391984u − 0.360451
a
10
=
−0.156030u
51
− 0.415662u
50
+ ··· − 41.1156u − 8.35564
0.0842371u
51
+ 0.0643931u
50
+ ··· − 1.68892u − 0.0133933
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.236976u
51
− 0.873090u
50
+ ··· − 17.6537u − 4.16045
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
52
− 3u
51
+ ··· − 1044u + 68
c
2
u
52
− 8u
51
+ ··· − 50175u + 6372
c
4
, c
10
17(17u
52
+ 9u
51
+ ··· − 1024u + 512)
c
5
, c
11
17(17u
52
+ 43u
51
+ ··· + 9u + 1)
c
6
, c
9
u
52
+ 6u
50
+ ··· + 94u + 17
c
7
, c
8
, c
12
u
52
− 3u
51
+ ··· − 155u + 28
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
52
+ y
51
+ ··· − 78640y + 4624
c
2
y
52
+ 8y
51
+ ··· − 699178473y + 40602384
c
4
, c
10
289(289y
52
+ 10289y
51
+ ··· − 393216y + 262144)
c
5
, c
11
289(289y
52
+ 3931y
51
+ ··· + 49y + 1)
c
6
, c
9
y
52
+ 12y
51
+ ··· − 3464y + 289
c
7
, c
8
, c
12
y
52
+ 45y
51
+ ··· − 6105y + 784
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.950344 + 0.322119I
a = 1.36230 − 0.69032I
b = 0.884105 + 0.214283I
6.7763 − 15.3902I 3.50991 + 9.23358I
u = −0.950344 − 0.322119I
a = 1.36230 + 0.69032I
b = 0.884105 − 0.214283I
6.7763 + 15.3902I 3.50991 − 9.23358I
u = 0.611986 + 0.823380I
a = 0.290031 + 0.143467I
b = −0.191685 + 0.783395I
5.64694 + 2.40410I 6.40463 − 1.49639I
u = 0.611986 − 0.823380I
a = 0.290031 − 0.143467I
b = −0.191685 − 0.783395I
5.64694 − 2.40410I 6.40463 + 1.49639I
u = −0.681639 + 0.820596I
a = −0.531183 + 0.353604I
b = −0.207357 + 0.308169I
0.58300 − 2.55616I 0. − 10.37772I
u = −0.681639 − 0.820596I
a = −0.531183 − 0.353604I
b = −0.207357 − 0.308169I
0.58300 + 2.55616I 0. + 10.37772I
u = 0.543343 + 0.739525I
a = −0.270104 − 1.316570I
b = −0.039019 − 0.651155I
−0.43165 − 5.19465I −2.45142 + 6.35490I
u = 0.543343 − 0.739525I
a = −0.270104 + 1.316570I
b = −0.039019 + 0.651155I
−0.43165 + 5.19465I −2.45142 − 6.35490I
u = −0.120480 + 1.099310I
a = −0.218284 − 0.770739I
b = 1.12128 − 0.86767I
0.82652 − 6.20060I 0. + 7.06936I
u = −0.120480 − 1.099310I
a = −0.218284 + 0.770739I
b = 1.12128 + 0.86767I
0.82652 + 6.20060I 0. − 7.06936I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.766416 + 0.315534I
a = −1.80534 − 0.65677I
b = −0.925661 + 0.046111I
0.92463 + 9.67458I 0.95373 − 10.15291I
u = 0.766416 − 0.315534I
a = −1.80534 + 0.65677I
b = −0.925661 − 0.046111I
0.92463 − 9.67458I 0.95373 + 10.15291I
u = −0.784865 + 0.085590I
a = −0.781041 + 0.938598I
b = −0.373670 + 0.098029I
2.02396 − 1.07247I 0.35961 + 2.83019I
u = −0.784865 − 0.085590I
a = −0.781041 − 0.938598I
b = −0.373670 − 0.098029I
2.02396 + 1.07247I 0.35961 − 2.83019I
u = −0.089628 + 1.215000I
a = −0.506782 + 0.741949I
b = −1.62883 − 0.59977I
−0.06262 + 4.46410I 0
u = −0.089628 − 1.215000I
a = −0.506782 − 0.741949I
b = −1.62883 + 0.59977I
−0.06262 − 4.46410I 0
u = −0.727691 + 0.990444I
a = 0.248516 − 1.062610I
b = 0.408630 − 0.571110I
4.83035 + 9.64704I 0
u = −0.727691 − 0.990444I
a = 0.248516 + 1.062610I
b = 0.408630 + 0.571110I
4.83035 − 9.64704I 0
u = −0.248355 + 1.254680I
a = −0.424101 + 1.097270I
b = −0.12990 + 1.95024I
−1.52199 − 2.58358I 0
u = −0.248355 − 1.254680I
a = −0.424101 − 1.097270I
b = −0.12990 − 1.95024I
−1.52199 + 2.58358I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.596766 + 0.352197I
a = 0.061531 + 0.340342I
b = −0.775647 + 0.574721I
2.70277 + 3.52281I −0.87054 − 2.02677I
u = −0.596766 − 0.352197I
a = 0.061531 − 0.340342I
b = −0.775647 − 0.574721I
2.70277 − 3.52281I −0.87054 + 2.02677I
u = 1.037590 + 0.811762I
a = 0.531961 + 0.511091I
b = 0.475050 + 0.089805I
3.22572 + 3.55521I 0
u = 1.037590 − 0.811762I
a = 0.531961 − 0.511091I
b = 0.475050 − 0.089805I
3.22572 − 3.55521I 0
u = 0.558051 + 0.379501I
a = 1.164260 + 0.600486I
b = 0.547966 − 0.424737I
−1.36085 + 3.43390I −6.76914 − 8.21807I
u = 0.558051 − 0.379501I
a = 1.164260 − 0.600486I
b = 0.547966 + 0.424737I
−1.36085 − 3.43390I −6.76914 + 8.21807I
u = −0.122610 + 1.325890I
a = 0.708094 + 0.759028I
b = 2.33633 + 0.17751I
−1.84227 − 2.86744I 0
u = −0.122610 − 1.325890I
a = 0.708094 − 0.759028I
b = 2.33633 − 0.17751I
−1.84227 + 2.86744I 0
u = −0.549323 + 0.253198I
a = −1.21969 + 0.81806I
b = −0.465578 − 0.970504I
2.63275 − 6.47736I −1.14133 + 11.11228I
u = −0.549323 − 0.253198I
a = −1.21969 − 0.81806I
b = −0.465578 + 0.970504I
2.63275 + 6.47736I −1.14133 − 11.11228I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.377950 + 1.358930I
a = 0.699285 + 0.212035I
b = 1.70671 − 0.17659I
−2.52853 − 5.35110I 0
u = −0.377950 − 1.358930I
a = 0.699285 − 0.212035I
b = 1.70671 + 0.17659I
−2.52853 + 5.35110I 0
u = 0.252344 + 1.391100I
a = −0.430609 + 0.154231I
b = −1.58256 − 0.68085I
−6.51872 + 2.69482I 0
u = 0.252344 − 1.391100I
a = −0.430609 − 0.154231I
b = −1.58256 + 0.68085I
−6.51872 − 2.69482I 0
u = −0.22905 + 1.40159I
a = 0.720518 + 0.079628I
b = 2.99526 + 0.53269I
−2.67681 − 9.40242I 0
u = −0.22905 − 1.40159I
a = 0.720518 − 0.079628I
b = 2.99526 − 0.53269I
−2.67681 + 9.40242I 0
u = −0.19045 + 1.43223I
a = 0.257532 + 0.194949I
b = 1.25353 − 0.98903I
−3.13364 + 0.73826I 0
u = −0.19045 − 1.43223I
a = 0.257532 − 0.194949I
b = 1.25353 + 0.98903I
−3.13364 − 0.73826I 0
u = 0.472544 + 0.263306I
a = 0.087356 + 0.662820I
b = 0.584757 + 0.218301I
−1.380760 − 0.242567I −6.94484 − 0.12994I
u = 0.472544 − 0.263306I
a = 0.087356 − 0.662820I
b = 0.584757 − 0.218301I
−1.380760 + 0.242567I −6.94484 + 0.12994I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.20341 + 1.44904I
a = −0.755410 + 0.149534I
b = −2.69872 + 0.20686I
−7.26378 + 6.23517I 0
u = 0.20341 − 1.44904I
a = −0.755410 − 0.149534I
b = −2.69872 − 0.20686I
−7.26378 − 6.23517I 0
u = 0.30298 + 1.43159I
a = 1.052730 − 0.687104I
b = 3.01855 − 0.49877I
−4.6504 + 13.5551I 0
u = 0.30298 − 1.43159I
a = 1.052730 + 0.687104I
b = 3.01855 + 0.49877I
−4.6504 − 13.5551I 0
u = 0.04590 + 1.51101I
a = 0.842968 + 0.263947I
b = 2.09013 + 0.76931I
−8.16490 − 3.52694I 0
u = 0.04590 − 1.51101I
a = 0.842968 − 0.263947I
b = 2.09013 − 0.76931I
−8.16490 + 3.52694I 0
u = −0.37967 + 1.46684I
a = −0.971631 − 0.548746I
b = −2.85141 − 0.36099I
1.0712 − 20.1676I 0
u = −0.37967 − 1.46684I
a = −0.971631 + 0.548746I
b = −2.85141 + 0.36099I
1.0712 + 20.1676I 0
u = −0.358104 + 0.224691I
a = −2.05195 + 1.47795I
b = −0.730995 + 0.426246I
2.90602 − 1.02604I −2.45090 + 4.57830I
u = −0.358104 − 0.224691I
a = −2.05195 − 1.47795I
b = −0.730995 − 0.426246I
2.90602 + 1.02604I −2.45090 − 4.57830I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.11236 + 1.65989I
a = −0.746881 + 0.209388I
b = −2.02713 + 0.41841I
−5.77267 + 7.71312I 0
u = 0.11236 − 1.65989I
a = −0.746881 − 0.209388I
b = −2.02713 − 0.41841I
−5.77267 − 7.71312I 0
10
II. I
u
2
= h−6.32 × 10
29
au
49
− 6.86 × 10
30
u
49
+ · · · + 4.21 × 10
31
a − 4.90 ×
10
31
, 5.24 × 10
32
au
49
− 4.49 × 10
32
u
49
+ · · · + 4.29 × 10
33
a + 1.58 ×
10
33
, u
50
− 2u
49
+ · · · − 60u + 19i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
3
=
a
0.576750au
49
+ 6.25601u
49
+ ··· − 38.3882a + 44.6707
a
7
=
u
2
+ 1
u
2
a
4
=
−0.469262au
49
− 1.44273u
49
+ ··· + 9.18875a − 26.6023
−0.0309561au
49
+ 1.81285u
49
+ ··· + 3.21660a + 19.2108
a
11
=
−0.962384au
49
+ 0.264443u
49
+ ··· − 25.1510a + 21.5640
−1.42355au
49
− 1.05929u
49
+ ··· − 20.1266a + 10.7323
a
6
=
−2.02043au
49
+ 0.397524u
49
+ ··· + 4.02193a + 44.8952
−3.77917au
49
+ 0.173659u
49
+ ··· − 10.9582a + 29.0254
a
2
=
2.03999au
49
− 0.314324u
49
+ ··· + 117.548a + 22.1600
2.72020au
49
+ 0.169295u
49
+ ··· + 189.705a + 6.65237
a
5
=
−2.02043au
49
− 0.564860u
49
+ ··· + 4.02193a + 19.7442
−3.77917au
49
− 0.461168u
49
+ ··· − 10.9582a + 5.02442
a
10
=
0.388513au
49
− 1.01109u
49
+ ··· + 32.7453a + 20.5741
−0.509271au
49
+ 0.194193u
49
+ ··· + 51.2128a − 27.4119
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10.2250u
49
+ 10.1462u
48
+ ··· + 237.491u − 95.5175
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
100
+ 3u
99
+ ··· − 2324u + 5732
c
2
(u
50
+ 7u
49
+ ··· + 843u + 121)
2
c
4
, c
10
(u
50
+ u
49
+ ··· + 14u − 109)
2
c
5
, c
11
u
100
+ 2u
99
+ ··· + 44u + 1
c
6
, c
9
u
100
+ 2u
99
+ ··· − 23154u + 5887
c
7
, c
8
, c
12
(u
50
+ 2u
49
+ ··· + 60u + 19)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
100
+ 35y
99
+ ··· + 1531073088y + 32855824
c
2
(y
50
− 31y
49
+ ··· − 433801y + 14641)
2
c
4
, c
10
(y
50
+ 39y
49
+ ··· − 91756y + 11881)
2
c
5
, c
11
y
100
− 38y
99
+ ··· − 242y + 1
c
6
, c
9
y
100
+ 26y
99
+ ··· + 1584012916y + 34656769
c
7
, c
8
, c
12
(y
50
+ 48y
49
+ ··· − 4094y + 361)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.853092 + 0.375766I
a = 0.463582 + 0.017365I
b = 0.431688 + 0.229001I
1.39801 − 3.06602I 3.27179 + 10.84309I
u = −0.853092 + 0.375766I
a = −1.39240 + 0.72586I
b = −0.720065 + 0.095569I
1.39801 − 3.06602I 3.27179 + 10.84309I
u = −0.853092 − 0.375766I
a = 0.463582 − 0.017365I
b = 0.431688 − 0.229001I
1.39801 + 3.06602I 3.27179 − 10.84309I
u = −0.853092 − 0.375766I
a = −1.39240 − 0.72586I
b = −0.720065 − 0.095569I
1.39801 + 3.06602I 3.27179 − 10.84309I
u = 0.044252 + 1.114680I
a = 1.183460 − 0.165449I
b = 4.34484 + 0.02560I
5.20918 − 4.43480I 4.65491 + 2.25442I
u = 0.044252 + 1.114680I
a = −0.341028 − 1.172380I
b = −0.010640 − 0.375629I
5.20918 − 4.43480I 4.65491 + 2.25442I
u = 0.044252 − 1.114680I
a = 1.183460 + 0.165449I
b = 4.34484 − 0.02560I
5.20918 + 4.43480I 4.65491 − 2.25442I
u = 0.044252 − 1.114680I
a = −0.341028 + 1.172380I
b = −0.010640 + 0.375629I
5.20918 + 4.43480I 4.65491 − 2.25442I
u = 1.142970 + 0.129346I
a = 1.153980 + 0.810410I
b = 1.068290 − 0.191524I
4.30836 + 5.93955I 0. − 19.3318I
u = 1.142970 + 0.129346I
a = −0.317165 − 0.294089I
b = −0.197641 − 0.018529I
4.30836 + 5.93955I 0. − 19.3318I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.142970 − 0.129346I
a = 1.153980 − 0.810410I
b = 1.068290 + 0.191524I
4.30836 − 5.93955I 0. + 19.3318I
u = 1.142970 − 0.129346I
a = −0.317165 + 0.294089I
b = −0.197641 + 0.018529I
4.30836 − 5.93955I 0. + 19.3318I
u = −0.678868 + 0.459434I
a = 0.354346 + 0.922133I
b = −0.140136 + 0.662804I
5.87358 + 2.21185I 8.08574 − 3.74028I
u = −0.678868 + 0.459434I
a = −0.43873 − 1.46624I
b = −0.687287 + 0.630136I
5.87358 + 2.21185I 8.08574 − 3.74028I
u = −0.678868 − 0.459434I
a = 0.354346 − 0.922133I
b = −0.140136 − 0.662804I
5.87358 − 2.21185I 8.08574 + 3.74028I
u = −0.678868 − 0.459434I
a = −0.43873 + 1.46624I
b = −0.687287 − 0.630136I
5.87358 − 2.21185I 8.08574 + 3.74028I
u = −0.112980 + 0.786145I
a = 0.637797 + 0.810591I
b = 0.441663 + 0.645929I
−1.24215 − 2.05779I −5.13529 + 4.01837I
u = −0.112980 + 0.786145I
a = −0.861384 + 0.661693I
b = 0.108824 + 0.340962I
−1.24215 − 2.05779I −5.13529 + 4.01837I
u = −0.112980 − 0.786145I
a = 0.637797 − 0.810591I
b = 0.441663 − 0.645929I
−1.24215 + 2.05779I −5.13529 − 4.01837I
u = −0.112980 − 0.786145I
a = −0.861384 − 0.661693I
b = 0.108824 − 0.340962I
−1.24215 + 2.05779I −5.13529 − 4.01837I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.005335 + 1.206560I
a = −0.406736 + 1.318270I
b = −0.59428 + 1.36940I
4.38592 + 4.77177I 0
u = 0.005335 + 1.206560I
a = 0.0174261 + 0.0722519I
b = −4.73862 + 0.89005I
4.38592 + 4.77177I 0
u = 0.005335 − 1.206560I
a = −0.406736 − 1.318270I
b = −0.59428 − 1.36940I
4.38592 − 4.77177I 0
u = 0.005335 − 1.206560I
a = 0.0174261 − 0.0722519I
b = −4.73862 − 0.89005I
4.38592 − 4.77177I 0
u = 0.125803 + 1.220000I
a = −0.003607 − 0.764728I
b = 0.146091 + 1.147280I
2.80415 + 1.36558I 0
u = 0.125803 + 1.220000I
a = 0.222241 + 1.245950I
b = 0.74351 + 1.94444I
2.80415 + 1.36558I 0
u = 0.125803 − 1.220000I
a = −0.003607 + 0.764728I
b = 0.146091 − 1.147280I
2.80415 − 1.36558I 0
u = 0.125803 − 1.220000I
a = 0.222241 − 1.245950I
b = 0.74351 − 1.94444I
2.80415 − 1.36558I 0
u = 0.048382 + 1.268830I
a = 0.248925 + 1.072820I
b = 0.329224 + 0.922712I
−1.59254 − 1.81613I 0
u = 0.048382 + 1.268830I
a = 0.0448583 + 0.1175780I
b = 1.54639 + 0.12552I
−1.59254 − 1.81613I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.048382 − 1.268830I
a = 0.248925 − 1.072820I
b = 0.329224 − 0.922712I
−1.59254 + 1.81613I 0
u = 0.048382 − 1.268830I
a = 0.0448583 − 0.1175780I
b = 1.54639 − 0.12552I
−1.59254 + 1.81613I 0
u = 0.670397 + 0.276080I
a = −1.76420 − 0.28526I
b = −0.917938 + 0.521667I
7.01035 + 7.12560I 8.18906 − 7.44187I
u = 0.670397 + 0.276080I
a = −1.02274 + 2.04880I
b = −0.662347 − 0.212692I
7.01035 + 7.12560I 8.18906 − 7.44187I
u = 0.670397 − 0.276080I
a = −1.76420 + 0.28526I
b = −0.917938 − 0.521667I
7.01035 − 7.12560I 8.18906 + 7.44187I
u = 0.670397 − 0.276080I
a = −1.02274 − 2.04880I
b = −0.662347 + 0.212692I
7.01035 − 7.12560I 8.18906 + 7.44187I
u = −0.617921 + 0.375337I
a = 1.009360 + 0.092506I
b = 1.77235 − 0.76889I
5.94348 − 6.22168I 9.7112 + 10.3014I
u = −0.617921 + 0.375337I
a = −1.85217 + 0.38036I
b = −0.585915 − 0.406234I
5.94348 − 6.22168I 9.7112 + 10.3014I
u = −0.617921 − 0.375337I
a = 1.009360 − 0.092506I
b = 1.77235 + 0.76889I
5.94348 + 6.22168I 9.7112 − 10.3014I
u = −0.617921 − 0.375337I
a = −1.85217 − 0.38036I
b = −0.585915 + 0.406234I
5.94348 + 6.22168I 9.7112 − 10.3014I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.526791 + 0.459769I
a = 0.84206 − 1.22209I
b = −0.061240 − 0.451389I
6.14716 − 3.57703I 10.00737 + 1.70187I
u = 0.526791 + 0.459769I
a = 1.37409 − 0.61960I
b = 1.69522 + 0.95920I
6.14716 − 3.57703I 10.00737 + 1.70187I
u = 0.526791 − 0.459769I
a = 0.84206 + 1.22209I
b = −0.061240 + 0.451389I
6.14716 + 3.57703I 10.00737 − 1.70187I
u = 0.526791 − 0.459769I
a = 1.37409 + 0.61960I
b = 1.69522 − 0.95920I
6.14716 + 3.57703I 10.00737 − 1.70187I
u = −0.174909 + 1.320300I
a = −0.907411 − 0.914447I
b = −3.37304 − 1.13903I
−2.73234 − 2.38787I 0
u = −0.174909 + 1.320300I
a = 0.10701 − 1.52004I
b = −0.65165 − 1.95690I
−2.73234 − 2.38787I 0
u = −0.174909 − 1.320300I
a = −0.907411 + 0.914447I
b = −3.37304 + 1.13903I
−2.73234 + 2.38787I 0
u = −0.174909 − 1.320300I
a = 0.10701 + 1.52004I
b = −0.65165 + 1.95690I
−2.73234 + 2.38787I 0
u = 0.181356 + 1.346230I
a = −1.116740 + 0.490263I
b = −3.37696 + 0.71430I
−2.78326 + 6.40427I 0
u = 0.181356 + 1.346230I
a = 0.276595 − 0.652660I
b = 0.551421 + 0.750472I
−2.78326 + 6.40427I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.181356 − 1.346230I
a = −1.116740 − 0.490263I
b = −3.37696 − 0.71430I
−2.78326 − 6.40427I 0
u = 0.181356 − 1.346230I
a = 0.276595 + 0.652660I
b = 0.551421 − 0.750472I
−2.78326 − 6.40427I 0
u = −0.483100 + 1.288460I
a = −0.461572 + 1.154570I
b = −0.318050 + 1.152110I
−0.94231 − 2.57657I 0
u = −0.483100 + 1.288460I
a = −0.0824832 + 0.0764807I
b = −0.382551 + 0.298574I
−0.94231 − 2.57657I 0
u = −0.483100 − 1.288460I
a = −0.461572 − 1.154570I
b = −0.318050 − 1.152110I
−0.94231 + 2.57657I 0
u = −0.483100 − 1.288460I
a = −0.0824832 − 0.0764807I
b = −0.382551 − 0.298574I
−0.94231 + 2.57657I 0
u = 0.219024 + 1.376470I
a = −1.163940 + 0.421303I
b = −2.69240 + 0.43625I
0.90247 + 3.77376I 0
u = 0.219024 + 1.376470I
a = 0.276091 − 0.249385I
b = 2.78869 + 0.01106I
0.90247 + 3.77376I 0
u = 0.219024 − 1.376470I
a = −1.163940 − 0.421303I
b = −2.69240 − 0.43625I
0.90247 − 3.77376I 0
u = 0.219024 − 1.376470I
a = 0.276091 + 0.249385I
b = 2.78869 − 0.01106I
0.90247 − 3.77376I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.545636 + 0.174349I
a = −1.033890 + 0.176796I
b = −1.11182 + 0.94368I
5.88007 + 0.94320I 11.80952 − 4.74435I
u = 0.545636 + 0.174349I
a = 2.09585 + 1.00488I
b = 0.131818 − 0.052740I
5.88007 + 0.94320I 11.80952 − 4.74435I
u = 0.545636 − 0.174349I
a = −1.033890 − 0.176796I
b = −1.11182 − 0.94368I
5.88007 − 0.94320I 11.80952 + 4.74435I
u = 0.545636 − 0.174349I
a = 2.09585 − 1.00488I
b = 0.131818 + 0.052740I
5.88007 − 0.94320I 11.80952 + 4.74435I
u = 0.27087 + 1.40747I
a = 0.742204 − 0.592227I
b = 2.91164 − 0.67398I
1.64321 + 10.58060I 0
u = 0.27087 + 1.40747I
a = −0.59359 − 1.29306I
b = −0.95440 − 1.80716I
1.64321 + 10.58060I 0
u = 0.27087 − 1.40747I
a = 0.742204 + 0.592227I
b = 2.91164 + 0.67398I
1.64321 − 10.58060I 0
u = 0.27087 − 1.40747I
a = −0.59359 + 1.29306I
b = −0.95440 + 1.80716I
1.64321 − 10.58060I 0
u = −0.24739 + 1.43867I
a = 0.988248 + 0.467520I
b = 3.00664 + 0.74404I
0.15005 − 9.43660I 0
u = −0.24739 + 1.43867I
a = −0.169282 − 0.539428I
b = −0.83416 + 1.37577I
0.15005 − 9.43660I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.24739 − 1.43867I
a = 0.988248 − 0.467520I
b = 3.00664 − 0.74404I
0.15005 + 9.43660I 0
u = −0.24739 − 1.43867I
a = −0.169282 + 0.539428I
b = −0.83416 − 1.37577I
0.15005 + 9.43660I 0
u = −0.05270 + 1.48053I
a = 0.943169 − 0.175611I
b = 2.41240 − 0.70289I
−8.39115 − 2.77998I 0
u = −0.05270 + 1.48053I
a = −0.650925 − 0.232981I
b = −2.29835 − 0.82686I
−8.39115 − 2.77998I 0
u = −0.05270 − 1.48053I
a = 0.943169 + 0.175611I
b = 2.41240 + 0.70289I
−8.39115 + 2.77998I 0
u = −0.05270 − 1.48053I
a = −0.650925 + 0.232981I
b = −2.29835 + 0.82686I
−8.39115 + 2.77998I 0
u = 0.509032 + 0.082967I
a = −1.241340 − 0.406845I
b = −0.733130 − 0.966411I
1.77592 + 3.92629I 5.93998 − 7.39122I
u = 0.509032 + 0.082967I
a = 2.23928 + 1.54842I
b = 0.606279 − 0.373631I
1.77592 + 3.92629I 5.93998 − 7.39122I
u = 0.509032 − 0.082967I
a = −1.241340 + 0.406845I
b = −0.733130 + 0.966411I
1.77592 − 3.92629I 5.93998 + 7.39122I
u = 0.509032 − 0.082967I
a = 2.23928 − 1.54842I
b = 0.606279 + 0.373631I
1.77592 − 3.92629I 5.93998 + 7.39122I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.31394 + 1.45260I
a = 1.060920 + 0.562240I
b = 2.80199 + 0.37238I
−4.42525 − 7.21278I 0
u = −0.31394 + 1.45260I
a = −0.391186 − 0.309239I
b = −1.57316 − 0.08193I
−4.42525 − 7.21278I 0
u = −0.31394 − 1.45260I
a = 1.060920 − 0.562240I
b = 2.80199 − 0.37238I
−4.42525 + 7.21278I 0
u = −0.31394 − 1.45260I
a = −0.391186 + 0.309239I
b = −1.57316 + 0.08193I
−4.42525 + 7.21278I 0
u = 0.35794 + 1.44478I
a = 0.166068 + 0.890628I
b = 0.317764 − 0.036538I
−0.499183 − 0.060271I 0
u = 0.35794 + 1.44478I
a = −0.463721 + 0.167701I
b = −0.922676 + 0.152184I
−0.499183 − 0.060271I 0
u = 0.35794 − 1.44478I
a = 0.166068 − 0.890628I
b = 0.317764 + 0.036538I
−0.499183 + 0.060271I 0
u = 0.35794 − 1.44478I
a = −0.463721 − 0.167701I
b = −0.922676 − 0.152184I
−0.499183 + 0.060271I 0
u = 0.44541 + 1.43777I
a = −0.924400 + 0.519011I
b = −2.74553 + 0.12658I
−0.77358 + 11.45920I 0
u = 0.44541 + 1.43777I
a = 0.504235 − 0.292630I
b = 1.259920 − 0.160589I
−0.77358 + 11.45920I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.44541 − 1.43777I
a = −0.924400 − 0.519011I
b = −2.74553 − 0.12658I
−0.77358 − 11.45920I 0
u = 0.44541 − 1.43777I
a = 0.504235 + 0.292630I
b = 1.259920 + 0.160589I
−0.77358 − 11.45920I 0
u = −0.490689
a = 3.23420 + 1.30418I
b = 1.038740 − 0.216776I
1.48420 3.80140
u = −0.490689
a = 3.23420 − 1.30418I
b = 1.038740 + 0.216776I
1.48420 3.80140
u = −0.484703
a = −2.08878 + 0.14937I
b = −0.585405 + 0.408865I
1.82789 6.46830
u = −0.484703
a = −2.08878 − 0.14937I
b = −0.585405 − 0.408865I
1.82789 6.46830
u = −0.07060 + 1.57371I
a = −0.163936 + 0.993992I
b = −0.537368 + 0.431012I
−1.27490 − 1.07364I 0
u = −0.07060 + 1.57371I
a = 0.298943 + 0.086182I
b = 0.951356 − 0.070277I
−1.27490 − 1.07364I 0
u = −0.07060 − 1.57371I
a = −0.163936 − 0.993992I
b = −0.537368 − 0.431012I
−1.27490 + 1.07364I 0
u = −0.07060 − 1.57371I
a = 0.298943 − 0.086182I
b = 0.951356 + 0.070277I
−1.27490 + 1.07364I 0
23
III. I
u
3
=
hu
12
a+u
12
+· · ·−a+11, 34u
12
a+40u
12
+· · ·+85a+269, u
13
−2u
12
+· · ·+3u+1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
3
=
a
−
1
3
u
12
a −
1
3
u
12
+ ··· +
1
3
a −
11
3
a
7
=
u
2
+ 1
u
2
a
4
=
1
3
u
12
a +
1
3
u
12
+ ··· +
2
3
a +
5
3
1
3
u
12
a −
2
3
u
12
+ ··· −
1
3
a −
10
3
a
11
=
−u
11
a −
5
17
u
12
+ ··· − 2a −
40
17
2
3
u
12
a +
73
51
u
12
+ ··· −
2
3
a +
74
51
a
6
=
1
3
u
12
a −
5
3
u
12
+ ··· −
7
3
a −
22
3
2
3
u
12
a −
1
3
u
12
+ ··· +
1
3
a +
7
3
a
2
=
2
3
u
12
a +
2
3
u
12
+ ··· +
4
3
a +
16
3
2u
11
a − u
12
+ ··· + a − 3
a
5
=
1
3
u
12
a −
5
3
u
12
+ ··· −
7
3
a −
28
3
2
3
u
12
a +
2
3
u
12
+ ··· +
1
3
a +
4
3
a
10
=
−u
11
a + 2u
12
+ ··· + a + 8
u
12
a − 2u
12
+ ··· − a − 3u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
12
+ 10u
11
− 32u
10
+ 71u
9
− 126u
8
+ 194u
7
− 240u
6
+
249u
5
− 217u
4
+ 134u
3
− 59u
2
+ 11u + 12
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
26
+ 2u
25
+ ··· + 352u
2
+ 68
c
2
(u
13
− 8u
12
+ ··· + 11u + 7)
2
c
4
, c
10
17(17u
26
+ 317u
24
+ ··· + 75887u
2
+ 11131)
c
5
, c
11
17(17u
26
− 51u
25
+ ··· − 4u + 1)
c
6
, c
9
u
26
− 3u
25
+ ··· + 113u
2
+ 17
c
7
, c
8
(u
13
− 2u
12
+ ··· + 3u + 1)
2
c
12
(u
13
+ 2u
12
+ ··· + 3u − 1)
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
26
+ 16y
25
+ ··· + 47872y + 4624
c
2
(y
13
− 8y
12
+ ··· + 303y −49)
2
c
4
, c
10
289(17y
13
+ 317y
12
+ ··· + 75887y + 11131)
2
c
5
, c
11
289(289y
26
− 3383y
25
+ ··· − 12y + 1)
c
6
, c
9
y
26
+ 5y
25
+ ··· + 3842y + 289
c
7
, c
8
, c
12
(y
13
+ 14y
12
+ ··· + 25y −1)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.908624 + 0.142085I
a = 1.27668 + 0.78464I
b = 0.956911 − 0.389604I
4.49130 + 5.51584I 6.31451 − 2.47719I
u = 0.908624 + 0.142085I
a = −0.381290 + 0.003958I
b = −0.330401 − 0.431738I
4.49130 + 5.51584I 6.31451 − 2.47719I
u = 0.908624 − 0.142085I
a = 1.27668 − 0.78464I
b = 0.956911 + 0.389604I
4.49130 − 5.51584I 6.31451 + 2.47719I
u = 0.908624 − 0.142085I
a = −0.381290 − 0.003958I
b = −0.330401 + 0.431738I
4.49130 − 5.51584I 6.31451 + 2.47719I
u = 0.011602 + 1.218530I
a = 0.346263 + 1.261500I
b = 0.302325 + 1.122330I
4.08814 − 4.55288I −6.51388 − 1.38146I
u = 0.011602 + 1.218530I
a = 0.533525 − 0.196381I
b = 4.85984 + 0.38998I
4.08814 − 4.55288I −6.51388 − 1.38146I
u = 0.011602 − 1.218530I
a = 0.346263 − 1.261500I
b = 0.302325 − 1.122330I
4.08814 + 4.55288I −6.51388 + 1.38146I
u = 0.011602 − 1.218530I
a = 0.533525 + 0.196381I
b = 4.85984 − 0.38998I
4.08814 + 4.55288I −6.51388 + 1.38146I
u = 0.087631 + 0.681880I
a = 0.648174 + 0.318711I
b = −2.42238 + 0.66316I
6.21876 + 4.83799I 10.45135 − 6.26851I
u = 0.087631 + 0.681880I
a = 0.91097 − 1.54991I
b = 0.360359 − 0.591792I
6.21876 + 4.83799I 10.45135 − 6.26851I
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.087631 − 0.681880I
a = 0.648174 − 0.318711I
b = −2.42238 − 0.66316I
6.21876 − 4.83799I 10.45135 + 6.26851I
u = 0.087631 − 0.681880I
a = 0.91097 + 1.54991I
b = 0.360359 + 0.591792I
6.21876 − 4.83799I 10.45135 + 6.26851I
u = −0.366787 + 1.313730I
a = −0.600079 + 1.161840I
b = −0.64225 + 1.51319I
−0.87585 − 2.29682I 2.24764 − 6.91415I
u = −0.366787 + 1.313730I
a = 0.295205 − 0.422005I
b = 0.483790 − 0.782453I
−0.87585 − 2.29682I 2.24764 − 6.91415I
u = −0.366787 − 1.313730I
a = −0.600079 − 1.161840I
b = −0.64225 − 1.51319I
−0.87585 + 2.29682I 2.24764 + 6.91415I
u = −0.366787 − 1.313730I
a = 0.295205 + 0.422005I
b = 0.483790 + 0.782453I
−0.87585 + 2.29682I 2.24764 + 6.91415I
u = 0.27490 + 1.40809I
a = −0.894460 + 0.429020I
b = −3.03409 + 0.54029I
−0.65452 + 9.44192I −2.27737 − 7.35211I
u = 0.27490 + 1.40809I
a = 0.001485 − 0.491007I
b = −0.164012 + 0.562372I
−0.65452 + 9.44192I −2.27737 − 7.35211I
u = 0.27490 − 1.40809I
a = −0.894460 − 0.429020I
b = −3.03409 − 0.54029I
−0.65452 − 9.44192I −2.27737 + 7.35211I
u = 0.27490 − 1.40809I
a = 0.001485 + 0.491007I
b = −0.164012 − 0.562372I
−0.65452 − 9.44192I −2.27737 + 7.35211I
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.17411 + 1.55291I
a = −0.059473 + 0.931053I
b = −0.361402 + 0.069098I
−1.090940 − 0.479706I −4.73923 − 1.66529I
u = 0.17411 + 1.55291I
a = −0.227461 + 0.160748I
b = −0.842787 − 0.023903I
−1.090940 − 0.479706I −4.73923 − 1.66529I
u = 0.17411 − 1.55291I
a = −0.059473 − 0.931053I
b = −0.361402 − 0.069098I
−1.090940 + 0.479706I −4.73923 + 1.66529I
u = 0.17411 − 1.55291I
a = −0.227461 − 0.160748I
b = −0.842787 + 0.023903I
−1.090940 + 0.479706I −4.73923 + 1.66529I
u = −0.180166
a = −4.84954 + 1.75128I
b = 0.334095 − 0.912061I
5.25505 7.03400
u = −0.180166
a = −4.84954 − 1.75128I
b = 0.334095 + 0.912061I
5.25505 7.03400
29
IV. I
u
4
=
hu
7
+3u
6
+· · ·+b+1, u
6
+2u
5
+5u
4
+6u
3
+7u
2
+a+4u+3, u
8
+2u
7
+· · ·+2u+1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
3
=
−u
6
− 2u
5
− 5u
4
− 6u
3
− 7u
2
− 4u − 3
−u
7
− 3u
6
− 7u
5
− 10u
4
− 11u
3
− 8u
2
− 4u − 1
a
7
=
u
2
+ 1
u
2
a
4
=
u
7
+ u
6
+ 3u
5
+ u
4
+ u
3
− 2u
2
− u − 2
−u
6
− 3u
5
− 6u
4
− 8u
3
− 7u
2
− 4u − 1
a
11
=
−u
7
− 2u
6
− 6u
5
− 7u
4
− 9u
3
− 5u
2
− 3u + 1
u
4
+ 2u
3
+ 3u
2
+ 3u + 1
a
6
=
−u
6
− 2u
5
− 5u
4
− 6u
3
− 6u
2
− 4u − 2
−u
7
− 3u
6
− 7u
5
− 11u
4
− 12u
3
− 9u
2
− 5u − 1
a
2
=
−u
5
− 2u
4
− 4u
3
− 5u
2
− 3u − 1
u
7
+ 2u
6
+ 4u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ 2u + 1
a
5
=
u
7
+ u
6
+ 3u
5
+ u
4
+ u
3
− 2u
2
− u − 2
−u
6
− 3u
5
− 6u
4
− 8u
3
− 7u
2
− 4u − 1
a
10
=
−u
7
− 2u
6
− 6u
5
− 7u
4
− 9u
3
− 5u
2
− 3u + 1
u
4
+ 2u
3
+ 3u
2
+ 3u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
7
− 5u
6
− 14u
5
− 6u
4
+ 2u
3
+ 7u
2
+ 13u + 2
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
8
− 3u
7
+ 6u
6
− 9u
5
+ 12u
4
− 11u
3
+ 8u
2
− 4u + 1
c
2
u
8
+ 5u
7
+ 13u
6
+ 20u
5
+ 22u
4
+ 18u
3
+ 12u
2
+ 5u + 1
c
4
, c
10
u
8
c
5
, c
11
u
8
− u
7
+ 2u
6
− u
5
+ 2u
4
− u
3
+ 2u
2
+ 1
c
6
, c
9
u
8
+ 2u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ u + 1
c
7
, c
8
u
8
+ 2u
7
+ 6u
6
+ 8u
5
+ 11u
4
+ 9u
3
+ 7u
2
+ 2u + 1
c
12
u
8
− 2u
7
+ 6u
6
− 8u
5
+ 11u
4
− 9u
3
+ 7u
2
− 2u + 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
8
+ 3y
7
+ 6y
6
+ 13y
5
+ 20y
4
+ 11y
3
+ 1
c
2
y
8
+ y
7
+ 13y
6
+ 16y
5
+ 28y
4
+ 30y
3
+ 8y
2
− y + 1
c
4
, c
10
y
8
c
5
, c
11
y
8
+ 3y
7
+ 6y
6
+ 9y
5
+ 12y
4
+ 11y
3
+ 8y
2
+ 4y + 1
c
6
, c
9
y
8
+ 4y
7
+ 8y
6
+ 11y
5
+ 12y
4
+ 9y
3
+ 6y
2
+ 3y + 1
c
7
, c
8
, c
12
y
8
+ 8y
7
+ 26y
6
+ 46y
5
+ 55y
4
+ 53y
3
+ 35y
2
+ 10y + 1
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.768546 + 0.720795I
a = −0.619652 + 0.420583I
b = −0.273444 + 0.137229I
0.48271 − 2.83701I −8.2706 + 14.3943I
u = −0.768546 − 0.720795I
a = −0.619652 − 0.420583I
b = −0.273444 − 0.137229I
0.48271 + 2.83701I −8.2706 − 14.3943I
u = 0.024235 + 1.274500I
a = −0.562390 + 0.690938I
b = −1.85858 − 0.33685I
−2.47121 + 3.78237I −4.61511 − 8.17766I
u = 0.024235 − 1.274500I
a = −0.562390 − 0.690938I
b = −1.85858 + 0.33685I
−2.47121 − 3.78237I −4.61511 + 8.17766I
u = −0.057100 + 0.488588I
a = −1.58676 − 1.06304I
b = 0.279299 − 0.676679I
0.43885 − 3.70343I −0.37256 + 5.31223I
u = −0.057100 − 0.488588I
a = −1.58676 + 1.06304I
b = 0.279299 + 0.676679I
0.43885 + 3.70343I −0.37256 − 5.31223I
u = −0.19859 + 1.50044I
a = 0.768803 + 0.157397I
b = 2.35273 + 0.22857I
−6.67501 − 5.79166I −2.74175 + 2.84036I
u = −0.19859 − 1.50044I
a = 0.768803 − 0.157397I
b = 2.35273 − 0.22857I
−6.67501 + 5.79166I −2.74175 − 2.84036I
33
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
8
− 3u
7
+ 6u
6
− 9u
5
+ 12u
4
− 11u
3
+ 8u
2
− 4u + 1)
· (u
26
+ 2u
25
+ ··· + 352u
2
+ 68)(u
52
− 3u
51
+ ··· − 1044u + 68)
· (u
100
+ 3u
99
+ ··· − 2324u + 5732)
c
2
(u
8
+ 5u
7
+ 13u
6
+ 20u
5
+ 22u
4
+ 18u
3
+ 12u
2
+ 5u + 1)
· ((u
13
− 8u
12
+ ··· + 11u + 7)
2
)(u
50
+ 7u
49
+ ··· + 843u + 121)
2
· (u
52
− 8u
51
+ ··· − 50175u + 6372)
c
4
, c
10
289u
8
(17u
26
+ 317u
24
+ ··· + 75887u
2
+ 11131)
· ((u
50
+ u
49
+ ··· + 14u − 109)
2
)(17u
52
+ 9u
51
+ ··· − 1024u + 512)
c
5
, c
11
289(u
8
− u
7
+ 2u
6
− u
5
+ 2u
4
− u
3
+ 2u
2
+ 1)
· (17u
26
− 51u
25
+ ··· − 4u + 1)(17u
52
+ 43u
51
+ ··· + 9u + 1)
· (u
100
+ 2u
99
+ ··· + 44u + 1)
c
6
, c
9
(u
8
+ 2u
6
+ ··· + u + 1)(u
26
− 3u
25
+ ··· + 113u
2
+ 17)
· (u
52
+ 6u
50
+ ··· + 94u + 17)(u
100
+ 2u
99
+ ··· − 23154u + 5887)
c
7
, c
8
(u
8
+ 2u
7
+ 6u
6
+ 8u
5
+ 11u
4
+ 9u
3
+ 7u
2
+ 2u + 1)
· ((u
13
− 2u
12
+ ··· + 3u + 1)
2
)(u
50
+ 2u
49
+ ··· + 60u + 19)
2
· (u
52
− 3u
51
+ ··· − 155u + 28)
c
12
(u
8
− 2u
7
+ 6u
6
− 8u
5
+ 11u
4
− 9u
3
+ 7u
2
− 2u + 1)
· ((u
13
+ 2u
12
+ ··· + 3u − 1)
2
)(u
50
+ 2u
49
+ ··· + 60u + 19)
2
· (u
52
− 3u
51
+ ··· − 155u + 28)
34
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y
8
+ 3y
7
+ 6y
6
+ 13y
5
+ 20y
4
+ 11y
3
+ 1)
· (y
26
+ 16y
25
+ ··· + 47872y + 4624)
· (y
52
+ y
51
+ ··· − 78640y + 4624)
· (y
100
+ 35y
99
+ ··· + 1531073088y + 32855824)
c
2
(y
8
+ y
7
+ 13y
6
+ 16y
5
+ 28y
4
+ 30y
3
+ 8y
2
− y + 1)
· (y
13
− 8y
12
+ ··· + 303y −49)
2
· (y
50
− 31y
49
+ ··· − 433801y + 14641)
2
· (y
52
+ 8y
51
+ ··· − 699178473y + 40602384)
c
4
, c
10
83521y
8
(17y
13
+ 317y
12
+ ··· + 75887y + 11131)
2
· (y
50
+ 39y
49
+ ··· − 91756y + 11881)
2
· (289y
52
+ 10289y
51
+ ··· − 393216y + 262144)
c
5
, c
11
83521(y
8
+ 3y
7
+ 6y
6
+ 9y
5
+ 12y
4
+ 11y
3
+ 8y
2
+ 4y + 1)
· (289y
26
− 3383y
25
+ ··· − 12y + 1)
· (289y
52
+ 3931y
51
+ ··· + 49y + 1)(y
100
− 38y
99
+ ··· − 242y + 1)
c
6
, c
9
(y
8
+ 4y
7
+ 8y
6
+ 11y
5
+ 12y
4
+ 9y
3
+ 6y
2
+ 3y + 1)
· (y
26
+ 5y
25
+ ··· + 3842y + 289)(y
52
+ 12y
51
+ ··· − 3464y + 289)
· (y
100
+ 26y
99
+ ··· + 1584012916y + 34656769)
c
7
, c
8
, c
12
(y
8
+ 8y
7
+ 26y
6
+ 46y
5
+ 55y
4
+ 53y
3
+ 35y
2
+ 10y + 1)
· ((y
13
+ 14y
12
+ ··· + 25y −1)
2
)(y
50
+ 48y
49
+ ··· − 4094y + 361)
2
· (y
52
+ 45y
51
+ ··· − 6105y + 784)
35
