12a
0847
(K12a
0847
)
A knot diagram
1
Linearized knot diagam
4 5 9 2 11 1 12 3 7 6 8 10
Solving Sequence
5,11 2,6
4 1 7 10 9 3 12 8
c
5
c
4
c
1
c
6
c
10
c
9
c
3
c
12
c
7
c
2
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h3.31232 × 10
25
u
39
− 1.32076 × 10
25
u
38
+ ··· + 2.23057 × 10
24
b + 8.08236 × 10
25
,
6.20649 × 10
25
u
39
− 3.16207 × 10
25
u
38
+ ··· + 4.46114 × 10
24
a + 1.24112 × 10
26
, u
40
+ 16u
38
+ ··· + 7u + 1i
I
u
2
= h1.14706 × 10
193
u
65
+ 1.22942 × 10
193
u
64
+ ··· + 3.43598 × 10
195
b + 3.53438 × 10
197
,
2.71067 × 10
205
u
65
− 5.82931 × 10
205
u
64
+ ··· + 1.90669 × 10
207
a − 8.28943 × 10
207
,
u
66
− 2u
65
+ ··· + 34394u + 12919i
I
u
3
= h4u
19
− 2u
18
+ ··· + b − 11, 3u
19
+ u
18
+ ··· + a − 7, u
20
+ 10u
18
+ ··· − 3u + 1i
I
u
4
= hb + 1, −u
3
+ u
2
+ 2a − u + 1, u
4
+ u
2
+ u + 1i
I
u
5
= h−1211u
11
− 823u
10
+ ··· + 3595b − 1417, 41974u
11
+ 28420u
10
+ ··· + 17975a + 80569,
u
12
+ u
11
+ 6u
10
+ 8u
9
+ 18u
8
+ 22u
7
+ 33u
6
+ 32u
5
+ 40u
4
+ 28u
3
+ 25u
2
+ 8u + 1i
I
u
6
= h−u
5
+ u
4
+ u
2
+ b − 1, −u
5
+ u
4
− u
3
+ u
2
+ a − u, u
6
− u
5
+ u
4
− 2u
3
+ u
2
+ 1i
I
u
7
= hb + 1, u
5
+ 2u
3
+ a + u, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
* 7 irreducible components of dim
C
= 0, with total 154 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
=
h3.31×10
25
u
39
−1.32×10
25
u
38
+· · ·+2.23×10
24
b+8.08×10
25
, 6.21×10
25
u
39
−
3.16 × 10
25
u
38
+ · · · + 4.46 × 10
24
a + 1.24 × 10
26
, u
40
+ 16u
38
+ · · · + 7u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
−13.9124u
39
+ 7.08805u
38
+ ··· − 142.107u − 27.8207
−14.8497u
39
+ 5.92119u
38
+ ··· − 166.279u − 36.2345
a
6
=
1
−u
2
a
4
=
20.7647u
39
− 9.52093u
38
+ ··· + 216.317u + 47.3812
16.0965u
39
− 8.17260u
38
+ ··· + 162.898u + 33.3163
a
1
=
−2.26192u
39
+ 1.18742u
38
+ ··· − 21.6467u − 4.47265
11.7428u
39
− 6.33020u
38
+ ··· + 113.470u + 22.5394
a
7
=
u
2
+ 1
−21.3520u
39
+ 10.9238u
38
+ ··· − 212.920u − 43.0436
a
10
=
−u
u
3
+ u
a
9
=
14.0047u
39
− 7.51762u
38
+ ··· + 135.117u + 27.0121
24.7644u
39
− 11.3372u
38
+ ··· + 260.565u + 53.8552
a
3
=
0.937301u
39
+ 1.16685u
38
+ ··· + 24.1723u + 8.41388
−14.8497u
39
+ 5.92119u
38
+ ··· − 166.279u − 36.2345
a
12
=
u
8.66191u
39
− 4.47265u
38
+ ··· + 84.7737u + 16.8793
a
8
=
1
−16.8793u
39
+ 8.66191u
38
+ ··· − 169.166u − 34.3817
(ii) Obstruction class = −1
(iii) Cusp Shapes =
508719562560300388532815543
8922270227352332483078648
u
39
−
221418439641702281753489705
8922270227352332483078648
u
38
+
··· +
5435560502953002870748740305
8922270227352332483078648
u +
1044739494354333632689026635
8922270227352332483078648
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
40
− 3u
39
+ ··· + 304u − 64
c
3
, c
8
u
40
+ 7u
39
+ ··· − 6912u − 1024
c
5
, c
7
, c
10
c
11
u
40
+ 16u
38
+ ··· + 7u + 1
c
6
, c
9
u
40
− u
39
+ ··· − 6u
2
+ 1
c
12
u
40
− 41u
39
+ ··· − 458752u + 16384
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
40
− 37y
39
+ ··· − 54528y + 4096
c
3
, c
8
y
40
− 21y
39
+ ··· − 2424832y + 1048576
c
5
, c
7
, c
10
c
11
y
40
+ 32y
39
+ ··· − 25y + 1
c
6
, c
9
y
40
− y
39
+ ··· − 12y + 1
c
12
y
40
− 7y
39
+ ··· − 7516192768y + 268435456
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.899188 + 0.492178I
a = 0.304374 + 0.682153I
b = 1.333640 − 0.137059I
−1.89685 + 2.95688I −6.78245 − 3.87727I
u = 0.899188 − 0.492178I
a = 0.304374 − 0.682153I
b = 1.333640 + 0.137059I
−1.89685 − 2.95688I −6.78245 + 3.87727I
u = −0.505765 + 0.977883I
a = 0.749759 − 0.348939I
b = 1.157940 + 0.190104I
−4.44118 − 8.25953I −12.0108 + 13.6205I
u = −0.505765 − 0.977883I
a = 0.749759 + 0.348939I
b = 1.157940 − 0.190104I
−4.44118 + 8.25953I −12.0108 − 13.6205I
u = −0.153292 + 1.111650I
a = 0.349737 − 0.040990I
b = 0.240109 − 0.939576I
−2.05358 − 4.12454I −6.82065 + 6.66260I
u = −0.153292 − 1.111650I
a = 0.349737 + 0.040990I
b = 0.240109 + 0.939576I
−2.05358 + 4.12454I −6.82065 − 6.66260I
u = −0.245672 + 1.109570I
a = −0.933493 − 0.173368I
b = −0.507959 − 1.155590I
−4.98920 − 4.83447I −16.1832 + 16.3407I
u = −0.245672 − 1.109570I
a = −0.933493 + 0.173368I
b = −0.507959 + 1.155590I
−4.98920 + 4.83447I −16.1832 − 16.3407I
u = 0.115716 + 1.177370I
a = −2.09154 − 0.45683I
b = −1.69077 + 0.33258I
−8.23430 + 1.39458I −28.5152 + 0.I
u = 0.115716 − 1.177370I
a = −2.09154 + 0.45683I
b = −1.69077 − 0.33258I
−8.23430 − 1.39458I −28.5152 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.007905 + 1.204090I
a = −1.073410 + 0.114351I
b = −1.22367 + 0.82479I
−7.20523 + 2.58935I −15.5309 − 10.4789I
u = 0.007905 − 1.204090I
a = −1.073410 − 0.114351I
b = −1.22367 − 0.82479I
−7.20523 − 2.58935I −15.5309 + 10.4789I
u = 0.430105 + 0.650761I
a = 0.877780 + 0.331031I
b = 0.370394 − 0.064690I
0.45659 + 1.62282I 2.32756 − 4.56782I
u = 0.430105 − 0.650761I
a = 0.877780 − 0.331031I
b = 0.370394 + 0.064690I
0.45659 − 1.62282I 2.32756 + 4.56782I
u = 0.681372 + 0.282436I
a = 0.438187 − 0.627394I
b = −0.011016 + 0.544192I
2.28233 + 0.65151I 2.38168 − 2.37217I
u = 0.681372 − 0.282436I
a = 0.438187 + 0.627394I
b = −0.011016 − 0.544192I
2.28233 − 0.65151I 2.38168 + 2.37217I
u = −0.429621 + 1.202460I
a = 1.82094 − 1.08033I
b = 1.56402 + 0.39727I
−11.6215 − 10.3010I 0
u = −0.429621 − 1.202460I
a = 1.82094 + 1.08033I
b = 1.56402 − 0.39727I
−11.6215 + 10.3010I 0
u = −0.687805 + 0.123786I
a = 0.921252 − 0.941879I
b = 1.373420 + 0.283320I
−3.70989 − 7.46384I −3.38238 + 6.85585I
u = −0.687805 − 0.123786I
a = 0.921252 + 0.941879I
b = 1.373420 − 0.283320I
−3.70989 + 7.46384I −3.38238 − 6.85585I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.458954 + 1.247010I
a = 0.813390 − 0.191482I
b = 0.571932 + 0.480290I
−3.81688 − 8.54712I 0
u = −0.458954 − 1.247010I
a = 0.813390 + 0.191482I
b = 0.571932 − 0.480290I
−3.81688 + 8.54712I 0
u = −0.666505 + 0.035654I
a = −0.173423 − 0.645490I
b = −0.218557 + 0.730406I
1.33850 + 3.81150I 0.15740 − 5.31306I
u = −0.666505 − 0.035654I
a = −0.173423 + 0.645490I
b = −0.218557 − 0.730406I
1.33850 − 3.81150I 0.15740 + 5.31306I
u = 0.583105 + 0.067597I
a = −1.53898 + 1.40884I
b = −1.258620 − 0.201718I
−1.54538 − 2.08926I −2.89309 + 1.69264I
u = 0.583105 − 0.067597I
a = −1.53898 − 1.40884I
b = −1.258620 + 0.201718I
−1.54538 + 2.08926I −2.89309 − 1.69264I
u = −0.506401 + 0.183038I
a = −0.073289 + 0.989507I
b = −0.953484 − 0.298364I
−0.851728 − 0.087915I −4.80507 − 1.55596I
u = −0.506401 − 0.183038I
a = −0.073289 − 0.989507I
b = −0.953484 + 0.298364I
−0.851728 + 0.087915I −4.80507 + 1.55596I
u = 0.42754 + 1.43537I
a = −0.526841 − 0.127695I
b = −0.906742 − 0.781507I
−9.12833 + 7.99600I 0
u = 0.42754 − 1.43537I
a = −0.526841 + 0.127695I
b = −0.906742 + 0.781507I
−9.12833 − 7.99600I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.20214 + 1.52671I
a = 1.87657 + 0.05326I
b = 1.68617 + 0.05399I
−18.6019 + 4.9632I 0
u = 0.20214 − 1.52671I
a = 1.87657 − 0.05326I
b = 1.68617 − 0.05399I
−18.6019 − 4.9632I 0
u = −0.48648 + 1.46673I
a = −2.04704 + 0.84915I
b = −1.50882 − 0.19508I
−10.5590 − 11.1934I 0
u = −0.48648 − 1.46673I
a = −2.04704 − 0.84915I
b = −1.50882 + 0.19508I
−10.5590 + 11.1934I 0
u = −0.444154
a = 1.59262
b = 1.40375
−7.48349 −12.7110
u = 0.54569 + 1.45909I
a = −0.713456 − 0.217255I
b = −0.393775 + 0.967180I
−7.6190 + 13.9228I 0
u = 0.54569 − 1.45909I
a = −0.713456 + 0.217255I
b = −0.393775 − 0.967180I
−7.6190 − 13.9228I 0
u = 0.62636 + 1.51205I
a = 1.58254 + 1.10290I
b = 1.51152 − 0.37480I
−13.7344 + 18.7811I 0
u = 0.62636 − 1.51205I
a = 1.58254 − 1.10290I
b = 1.51152 + 0.37480I
−13.7344 − 18.7811I 0
u = −0.313111
a = 0.781264
b = −0.675226
−1.07586 −8.30510
8
II. I
u
2
= h1.15 × 10
193
u
65
+ 1.23 × 10
193
u
64
+ · · · + 3.44 × 10
195
b + 3.53 ×
10
197
, 2.71 × 10
205
u
65
− 5.83 × 10
205
u
64
+ · · · + 1.91 × 10
207
a − 8.29 ×
10
207
, u
66
− 2u
65
+ · · · + 34394u + 12919i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
−0.0142166u
65
+ 0.0305728u
64
+ ··· − 124.176u + 4.34754
−0.00333837u
65
− 0.00357808u
64
+ ··· − 293.492u − 102.864
a
6
=
1
−u
2
a
4
=
0.00674273u
65
− 0.0145348u
64
+ ··· + 31.5399u − 9.34998
0.00726997u
65
− 0.0175175u
64
+ ··· + 2.63735u − 25.0305
a
1
=
−0.0147760u
65
+ 0.0187754u
64
+ ··· − 487.354u − 129.290
−0.00486970u
65
− 0.00338081u
64
+ ··· − 411.583u − 140.339
a
7
=
0.0107903u
65
− 0.0413034u
64
+ ··· − 381.121u − 187.126
0.00399074u
65
− 0.00892910u
64
+ ··· − 2.60791u − 13.3411
a
10
=
−u
u
3
+ u
a
9
=
−0.0164614u
65
+ 0.0450455u
64
+ ··· + 97.0027u + 96.4317
−0.00370284u
65
+ 0.00573036u
64
+ ··· − 68.3400u − 15.5754
a
3
=
−0.0108782u
65
+ 0.0341509u
64
+ ··· + 169.316u + 107.211
−0.00333837u
65
− 0.00357808u
64
+ ··· − 293.492u − 102.864
a
12
=
−0.0134444u
65
+ 0.0331534u
64
+ ··· − 34.2797u + 41.8605
−0.00234103u
65
− 0.00400860u
64
+ ··· − 261.336u − 91.3337
a
8
=
0.00944116u
65
− 0.0162681u
64
+ ··· + 186.076u + 38.7895
0.00153644u
65
− 0.0114564u
64
+ ··· − 197.120u − 79.6548
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00422084u
65
+ 0.0288638u
64
+ ··· + 374.236u + 158.979
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
(u
11
− 2u
10
− 4u
9
+ 8u
8
+ 6u
7
− 8u
6
− 7u
5
− 2u
4
+ 7u
3
+ 3u
2
− u + 1)
6
c
3
, c
8
(u
11
+ 2u
10
− u
9
− 3u
8
+ u
7
+ 2u
6
+ 4u
5
+ 11u
4
+ 9u
3
+ u
2
− 2u − 2)
6
c
5
, c
7
, c
10
c
11
u
66
− 2u
65
+ ··· + 34394u + 12919
c
6
, c
9
u
66
− 6u
65
+ ··· − 10740u + 839
c
12
(u
3
+ u
2
− 1)
22
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y
11
− 12y
10
+ ··· − 5y −1)
6
c
3
, c
8
(y
11
− 6y
10
+ ··· + 8y −4)
6
c
5
, c
7
, c
10
c
11
y
66
+ 54y
65
+ ··· − 70983068y + 166900561
c
6
, c
9
y
66
− 18y
65
+ ··· − 32088596y + 703921
c
12
(y
3
− y
2
+ 2y −1)
22
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.443676 + 0.885304I
a = 0.536240 + 0.053539I
b = 0.172742 + 0.362556I
−0.17973 + 2.08617I 0. − 1.86035I
u = 0.443676 − 0.885304I
a = 0.536240 − 0.053539I
b = 0.172742 − 0.362556I
−0.17973 − 2.08617I 0. + 1.86035I
u = −0.375020 + 0.888196I
a = −1.50514 + 1.64605I
b = −0.780044
−3.03685 − 2.82812I −13.9197 + 2.9794I
u = −0.375020 − 0.888196I
a = −1.50514 − 1.64605I
b = −0.780044
−3.03685 + 2.82812I −13.9197 − 2.9794I
u = −0.940224 + 0.094709I
a = 0.246658 + 0.185640I
b = 0.172742 − 0.362556I
−0.17973 + 3.57008I −0.95097 − 4.09854I
u = −0.940224 − 0.094709I
a = 0.246658 − 0.185640I
b = 0.172742 + 0.362556I
−0.17973 − 3.57008I −0.95097 + 4.09854I
u = −0.076827 + 1.134660I
a = 0.961916 + 0.477898I
b = 0.172742 − 0.362556I
−4.31731 + 0.74196I 0
u = −0.076827 − 1.134660I
a = 0.961916 − 0.477898I
b = 0.172742 + 0.362556I
−4.31731 − 0.74196I 0
u = −0.056692 + 1.151960I
a = −0.423038 + 0.195770I
b = −0.399448 + 0.789847I
−2.58191 + 1.86929I 0
u = −0.056692 − 1.151960I
a = −0.423038 − 0.195770I
b = −0.399448 − 0.789847I
−2.58191 − 1.86929I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.778393 + 0.258934I
a = 0.225557 − 0.154015I
b = 1.48612 − 0.29515I
−8.68019 + 5.82303I −10.27594 − 2.59947I
u = −0.778393 − 0.258934I
a = 0.225557 + 0.154015I
b = 1.48612 + 0.29515I
−8.68019 − 5.82303I −10.27594 + 2.59947I
u = 0.220570 + 1.161500I
a = −2.83450 − 0.03658I
b = −1.379210 − 0.103381I
−5.11629 + 0.40920I 0
u = 0.220570 − 1.161500I
a = −2.83450 + 0.03658I
b = −1.379210 + 0.103381I
−5.11629 − 0.40920I 0
u = 0.439380 + 1.101000I
a = 1.072290 + 0.114146I
b = 0.172742 − 0.362556I
−0.17973 + 3.57008I 0
u = 0.439380 − 1.101000I
a = 1.072290 − 0.114146I
b = 0.172742 + 0.362556I
−0.17973 − 3.57008I 0
u = −0.308061 + 1.174420I
a = 1.52228 − 1.82843I
b = 1.48612 + 0.29515I
−12.8178 − 8.6511I 0
u = −0.308061 − 1.174420I
a = 1.52228 + 1.82843I
b = 1.48612 − 0.29515I
−12.8178 + 8.6511I 0
u = −0.180416 + 1.202800I
a = −1.038560 + 0.679711I
b = −0.399448 − 0.789847I
−6.71949 − 4.69742I 0
u = −0.180416 − 1.202800I
a = −1.038560 − 0.679711I
b = −0.399448 + 0.789847I
−6.71949 + 4.69742I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.047433 + 1.219130I
a = 2.73614 + 0.94411I
b = 1.50982 − 0.17565I
−10.52640 − 0.24361I 0
u = 0.047433 − 1.219130I
a = 2.73614 − 0.94411I
b = 1.50982 + 0.17565I
−10.52640 + 0.24361I 0
u = 0.260163 + 1.235840I
a = −3.40983 − 0.79732I
b = −1.379210 + 0.103381I
−5.11629 + 5.24705I 0
u = 0.260163 − 1.235840I
a = −3.40983 + 0.79732I
b = −1.379210 − 0.103381I
−5.11629 − 5.24705I 0
u = −1.246790 + 0.256999I
a = −1.175530 + 0.234212I
b = −1.379210 − 0.103381I
−5.11629 − 5.24705I 0
u = −1.246790 − 0.256999I
a = −1.175530 − 0.234212I
b = −1.379210 + 0.103381I
−5.11629 + 5.24705I 0
u = 0.147409 + 1.275360I
a = −2.42548 − 1.73360I
b = −1.379210 + 0.103381I
−9.25387 + 2.41892I 0
u = 0.147409 − 1.275360I
a = −2.42548 + 1.73360I
b = −1.379210 − 0.103381I
−9.25387 − 2.41892I 0
u = −0.525325 + 0.474288I
a = −0.823277 − 0.894645I
b = 1.50982 − 0.17565I
−10.52640 + 5.41263I −12.68218 − 3.99605I
u = −0.525325 − 0.474288I
a = −0.823277 + 0.894645I
b = 1.50982 + 0.17565I
−10.52640 − 5.41263I −12.68218 + 3.99605I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.327359 + 1.280560I
a = −0.931884 − 0.077016I
b = −0.399448 − 0.789847I
−2.58191 − 7.52554I 0
u = −0.327359 − 1.280560I
a = −0.931884 + 0.077016I
b = −0.399448 + 0.789847I
−2.58191 + 7.52554I 0
u = 1.316550 + 0.129461I
a = 0.096039 − 0.664759I
b = −0.399448 + 0.789847I
−2.58191 + 7.52554I 0
u = 1.316550 − 0.129461I
a = 0.096039 + 0.664759I
b = −0.399448 − 0.789847I
−2.58191 − 7.52554I 0
u = −0.465671 + 1.263740I
a = 0.611659 − 0.355667I
b = 0.172742 + 0.362556I
−4.31731 − 0.74196I 0
u = −0.465671 − 1.263740I
a = 0.611659 + 0.355667I
b = 0.172742 − 0.362556I
−4.31731 + 0.74196I 0
u = 0.090743 + 1.365980I
a = 1.98628 + 0.52916I
b = 1.48612 − 0.29515I
−8.68019 + 5.82303I 0
u = 0.090743 − 1.365980I
a = 1.98628 − 0.52916I
b = 1.48612 + 0.29515I
−8.68019 − 5.82303I 0
u = 0.449718 + 0.434222I
a = 3.81144 + 3.91525I
b = −0.780044
−3.03685 + 2.82812I −13.9197 − 2.9794I
u = 0.449718 − 0.434222I
a = 3.81144 − 3.91525I
b = −0.780044
−3.03685 − 2.82812I −13.9197 + 2.9794I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.511528 + 0.255393I
a = 1.068800 − 0.261235I
b = −0.399448 + 0.789847I
−2.58191 + 1.86929I −7.40900 − 2.90378I
u = −0.511528 − 0.255393I
a = 1.068800 + 0.261235I
b = −0.399448 − 0.789847I
−2.58191 − 1.86929I −7.40900 + 2.90378I
u = −0.35301 + 1.40034I
a = 2.24536 − 1.00339I
b = 1.48612 + 0.29515I
−8.6802 − 11.4793I 0
u = −0.35301 − 1.40034I
a = 2.24536 + 1.00339I
b = 1.48612 − 0.29515I
−8.6802 + 11.4793I 0
u = −0.352352 + 0.407836I
a = 1.45368 + 0.28228I
b = 0.172742 + 0.362556I
−0.17973 + 2.08617I −0.95097 − 1.86035I
u = −0.352352 − 0.407836I
a = 1.45368 − 0.28228I
b = 0.172742 − 0.362556I
−0.17973 − 2.08617I −0.95097 + 1.86035I
u = 0.09895 + 1.48132I
a = 1.047790 + 0.860164I
b = −0.780044
−7.17443 0
u = 0.09895 − 1.48132I
a = 1.047790 − 0.860164I
b = −0.780044
−7.17443 0
u = −0.60128 + 1.36273I
a = 1.75565 − 1.07071I
b = 1.50982 + 0.17565I
−10.52640 − 5.41263I 0
u = −0.60128 − 1.36273I
a = 1.75565 + 1.07071I
b = 1.50982 − 0.17565I
−10.52640 + 5.41263I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.15601 + 1.48861I
a = 2.10336 − 0.53063I
b = 1.50982 − 0.17565I
−14.6640 + 2.5845I 0
u = −0.15601 − 1.48861I
a = 2.10336 + 0.53063I
b = 1.50982 + 0.17565I
−14.6640 − 2.5845I 0
u = 1.30444 + 0.73850I
a = 0.507558 − 0.152575I
b = 1.50982 + 0.17565I
−10.52640 + 0.24361I 0
u = 1.30444 − 0.73850I
a = 0.507558 + 0.152575I
b = 1.50982 − 0.17565I
−10.52640 − 0.24361I 0
u = 1.52504 + 0.08143I
a = 0.668002 + 0.574978I
b = 1.48612 − 0.29515I
−8.6802 + 11.4793I 0
u = 1.52504 − 0.08143I
a = 0.668002 − 0.574978I
b = 1.48612 + 0.29515I
−8.6802 − 11.4793I 0
u = 0.400408 + 0.081856I
a = 0.52657 − 2.12304I
b = −1.379210 − 0.103381I
−5.11629 + 0.40920I −9.41840 − 0.08998I
u = 0.400408 − 0.081856I
a = 0.52657 + 2.12304I
b = −1.379210 + 0.103381I
−5.11629 − 0.40920I −9.41840 + 0.08998I
u = 0.73809 + 1.54227I
a = −0.437236 − 0.561720I
b = −0.399448 + 0.789847I
−6.71949 + 4.69742I 0
u = 0.73809 − 1.54227I
a = −0.437236 + 0.561720I
b = −0.399448 − 0.789847I
−6.71949 − 4.69742I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.63179 + 1.62577I
a = −1.96213 + 0.83870I
b = −1.379210 − 0.103381I
−9.25387 − 2.41892I 0
u = −0.63179 − 1.62577I
a = −1.96213 − 0.83870I
b = −1.379210 + 0.103381I
−9.25387 + 2.41892I 0
u = 0.94973 + 1.57978I
a = 1.18882 + 1.01732I
b = 1.48612 − 0.29515I
−12.8178 + 8.6511I 0
u = 0.94973 − 1.57978I
a = 1.18882 − 1.01732I
b = 1.48612 + 0.29515I
−12.8178 − 8.6511I 0
u = 0.45443 + 2.02885I
a = 1.44690 − 0.11028I
b = 1.50982 + 0.17565I
−14.6640 − 2.5845I 0
u = 0.45443 − 2.02885I
a = 1.44690 + 0.11028I
b = 1.50982 − 0.17565I
−14.6640 + 2.5845I 0
18
III.
I
u
3
= h4u
19
−2u
18
+· · ·+b−11, 3u
19
+u
18
+· · ·+a−7, u
20
+10u
18
+· · ·−3u+1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
−3u
19
− u
18
+ ··· − 18u + 7
−4u
19
+ 2u
18
+ ··· − 29u + 11
a
6
=
1
−u
2
a
4
=
7u
19
− 5u
18
+ ··· + 53u − 18
4u
19
− 4u
18
+ ··· + 39u − 15
a
1
=
−u
18
− 9u
16
+ ··· + 5u − 1
u
19
− u
18
+ ··· + 14u − 4
a
7
=
−u
2
− 1
−3u
19
− u
18
+ ··· − 14u − 1
a
10
=
−u
u
3
+ u
a
9
=
u
19
+ 10u
17
+ ··· + 9u − 3
−3u
18
− u
17
+ ··· + 19u − 14
a
3
=
u
19
− 3u
18
+ ··· + 11u − 4
−4u
19
+ 2u
18
+ ··· − 29u + 11
a
12
=
u
u
19
− u
18
+ ··· + 15u − 4
a
8
=
−1
−4u
19
− u
18
+ ··· − 15u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 16u
19
−19u
18
+ 143u
17
−240u
16
+ 582u
15
−1165u
14
+ 1560u
13
−3036u
12
+ 3081u
11
−
4937u
10
+4305u
9
−5388u
8
+3995u
7
−3982u
6
+2381u
5
−1876u
4
+847u
3
−535u
2
+140u−68
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
20
+ 4u
19
+ ··· − 5u + 1
c
3
u
20
− 6u
18
+ ··· − 3u + 1
c
4
u
20
− 4u
19
+ ··· + 5u + 1
c
5
, c
11
u
20
+ 10u
18
+ ··· − 3u + 1
c
6
, c
9
u
20
+ 3u
19
+ ··· − 5u
3
+ 1
c
7
, c
10
u
20
+ 10u
18
+ ··· + 3u + 1
c
8
u
20
− 6u
18
+ ··· + 3u + 1
c
12
u
20
+ 5u
19
+ ··· − 4u
2
+ 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
20
− 20y
19
+ ··· − y + 1
c
3
, c
8
y
20
− 12y
19
+ ··· − 9y + 1
c
5
, c
7
, c
10
c
11
y
20
+ 20y
19
+ ··· + 15y + 1
c
6
, c
9
y
20
− 5y
19
+ ··· + 6y
2
+ 1
c
12
y
20
− 5y
19
+ ··· − 8y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.329203 + 1.094160I
a = −0.962601 + 0.304522I
b = −0.501873 − 0.929654I
−4.82771 − 4.32358I −9.79873 + 1.76880I
u = −0.329203 − 1.094160I
a = −0.962601 − 0.304522I
b = −0.501873 + 0.929654I
−4.82771 + 4.32358I −9.79873 − 1.76880I
u = 0.457051 + 0.680670I
a = 1.33201 + 1.28366I
b = −0.215636 − 0.242909I
−2.12509 + 2.39395I −2.67442 − 1.16946I
u = 0.457051 − 0.680670I
a = 1.33201 − 1.28366I
b = −0.215636 + 0.242909I
−2.12509 − 2.39395I −2.67442 + 1.16946I
u = 0.574386 + 0.534332I
a = −0.016887 − 0.670126I
b = 1.366330 + 0.095115I
−7.13263 + 1.04802I −10.45930 − 4.67117I
u = 0.574386 − 0.534332I
a = −0.016887 + 0.670126I
b = 1.366330 − 0.095115I
−7.13263 − 1.04802I −10.45930 + 4.67117I
u = −0.371455 + 0.685308I
a = −6.01012 − 2.87138I
b = −1.027230 − 0.081684I
−3.59078 − 3.00431I −13.5133 − 14.5755I
u = −0.371455 − 0.685308I
a = −6.01012 + 2.87138I
b = −1.027230 + 0.081684I
−3.59078 + 3.00431I −13.5133 + 14.5755I
u = 0.163354 + 1.255280I
a = −1.81612 − 0.82484I
b = −1.44756 + 0.28033I
−7.76209 + 1.54255I −9.78950 − 1.62203I
u = 0.163354 − 1.255280I
a = −1.81612 + 0.82484I
b = −1.44756 − 0.28033I
−7.76209 − 1.54255I −9.78950 + 1.62203I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.211407 + 0.674773I
a = 0.560798 + 0.564369I
b = 0.071739 + 0.688234I
−0.55610 + 3.43447I −4.09896 − 6.99841I
u = 0.211407 − 0.674773I
a = 0.560798 − 0.564369I
b = 0.071739 − 0.688234I
−0.55610 − 3.43447I −4.09896 + 6.99841I
u = −0.591819 + 1.167140I
a = 1.39061 − 1.42254I
b = 1.50968 + 0.30012I
−11.3036 − 8.5873I −10.47244 + 4.94316I
u = −0.591819 − 1.167140I
a = 1.39061 + 1.42254I
b = 1.50968 − 0.30012I
−11.3036 + 8.5873I −10.47244 − 4.94316I
u = 0.220491 + 0.519453I
a = 1.49804 − 0.31407I
b = 1.295880 − 0.302541I
−4.50572 + 7.07402I −11.85478 − 3.67806I
u = 0.220491 − 0.519453I
a = 1.49804 + 0.31407I
b = 1.295880 + 0.302541I
−4.50572 − 7.07402I −11.85478 + 3.67806I
u = −0.09236 + 1.53921I
a = 0.332500 − 0.055199I
b = −0.549802 + 0.356787I
−7.01159 + 0.64910I −8.38884 − 9.90345I
u = −0.09236 − 1.53921I
a = 0.332500 + 0.055199I
b = −0.549802 − 0.356787I
−7.01159 − 0.64910I −8.38884 + 9.90345I
u = −0.24185 + 1.69545I
a = 1.69176 − 0.16532I
b = 1.49847 − 0.16427I
−13.69210 + 2.81932I −9.44972 − 3.43141I
u = −0.24185 − 1.69545I
a = 1.69176 + 0.16532I
b = 1.49847 + 0.16427I
−13.69210 − 2.81932I −9.44972 + 3.43141I
23
IV. I
u
4
= hb + 1, −u
3
+ u
2
+ 2a − u + 1, u
4
+ u
2
+ u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
1
2
u
3
−
1
2
u
2
+
1
2
u −
1
2
−1
a
6
=
1
−u
2
a
4
=
1
2
u
3
−
1
2
u
2
+
1
2
u +
1
2
−1
a
1
=
−1
0
a
7
=
u
2
+ 1
−u
2
a
10
=
−u
u
3
+ u
a
9
=
1
u
3
− u
2
− 1
a
3
=
1
2
u
3
−
1
2
u
2
+
1
2
u +
1
2
−1
a
12
=
u
−u
3
− u
2
− u − 1
a
8
=
1
u
3
− u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
13
4
u
3
−
3
2
u
2
+
5
2
u −
21
4
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
8
u
4
c
4
(u + 1)
4
c
5
, c
7
u
4
+ u
2
+ u + 1
c
6
u
4
− 2u
3
+ 3u
2
− u + 1
c
9
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
10
, c
11
u
4
+ u
2
− u + 1
c
12
u
4
− 3u
3
+ 4u
2
− 3u + 2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
8
y
4
c
5
, c
7
, c
10
c
11
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
6
, c
9
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
12
y
4
− y
3
+ 2y
2
+ 7y + 4
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547424 + 0.585652I
a = −0.552438 + 0.776246I
b = −1.00000
−0.66484 − 1.39709I −5.25608 + 3.48426I
u = −0.547424 − 0.585652I
a = −0.552438 − 0.776246I
b = −1.00000
−0.66484 + 1.39709I −5.25608 − 3.48426I
u = 0.547424 + 1.120870I
a = −0.697562 − 0.253422I
b = −1.00000
−4.26996 + 7.64338I −8.61892 − 0.34032I
u = 0.547424 − 1.120870I
a = −0.697562 + 0.253422I
b = −1.00000
−4.26996 − 7.64338I −8.61892 + 0.34032I
27
V. I
u
5
= h−1211u
11
− 823u
10
+ · · · + 3595b − 1417, 41974u
11
+ 28420u
10
+
· · · + 17975a + 80569, u
12
+ u
11
+ · · · + 8u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
−2.33513u
11
− 1.58108u
10
+ ··· − 44.0883u − 4.48228
0.336857u
11
+ 0.228929u
10
+ ··· + 5.82253u + 0.394159
a
6
=
1
−u
2
a
4
=
−2.56534u
11
− 1.99332u
10
+ ··· − 52.2194u − 8.42904
0.431711u
11
+ 0.260362u
10
+ ··· + 8.20278u + 1.34743
a
1
=
−0.440779u
11
+ 0.100974u
10
+ ··· − 1.99866u + 5.07076
−1
a
7
=
−0.555271u
11
− 0.855911u
10
+ ··· − 16.6424u − 6.84679
0.118943u
11
+ 0.151321u
10
+ ··· + 3.89324u + 1.54175
a
10
=
−u
u
3
+ u
a
9
=
0.106648u
11
− 0.183310u
10
+ ··· − 2.30854u − 3.55260
0.0948540u
11
+ 0.0314325u
10
+ ··· + 2.38025u + 0.953268
a
3
=
−2.67199u
11
− 1.81001u
10
+ ··· − 49.9109u − 4.87644
0.336857u
11
+ 0.228929u
10
+ ··· + 5.82253u + 0.394159
a
12
=
−0.586871u
11
− 0.216412u
10
+ ··· − 5.51394u + 4.56139
0.0106815u
11
− 0.0133519u
10
+ ··· + 1.99883u − 0.661919
a
8
=
2.56534u
11
+ 1.99332u
10
+ ··· + 52.2194u + 8.42904
−0.431711u
11
− 0.260362u
10
+ ··· − 8.20278u − 1.34743
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
36624
17975
u
11
−
5224
3595
u
10
−
196924
17975
u
9
−
227388
17975
u
8
−
525084
17975
u
7
−
576964
17975
u
6
−
899048
17975
u
5
−
153372
3595
u
4
−
42068
719
u
3
−
582472
17975
u
2
−
575688
17975
u −
291894
17975
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
(u
3
− u − 1)
4
c
3
, c
8
(u − 1)
12
c
5
, c
7
, c
10
c
11
u
12
+ u
11
+ ··· + 8u + 1
c
6
, c
9
u
12
− 2u
11
+ ··· − 4u + 1
c
12
(u
3
+ u
2
− 1)
4
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y
3
− 2y
2
+ y −1)
4
c
3
, c
8
(y −1)
12
c
5
, c
7
, c
10
c
11
y
12
+ 11y
11
+ ··· − 14y + 1
c
6
, c
9
y
12
+ 4y
11
+ ··· − 4y + 1
c
12
(y
3
− y
2
+ 2y −1)
4
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.385431 + 1.108730I
a = −0.991675 + 0.538727I
b = −0.662359 − 0.562280I
−3.55561 − 2.82812I −10.49024 + 2.97945I
u = −0.385431 − 1.108730I
a = −0.991675 − 0.538727I
b = −0.662359 + 0.562280I
−3.55561 + 2.82812I −10.49024 − 2.97945I
u = −0.992399 + 0.680138I
a = 0.761675 − 0.795141I
b = 1.32472
−3.55561 + 2.82812I −10.49024 − 2.97945I
u = −0.992399 − 0.680138I
a = 0.761675 + 0.795141I
b = 1.32472
−3.55561 − 2.82812I −10.49024 + 2.97945I
u = 0.707479 + 1.051460I
a = 0.761004 + 0.716601I
b = 1.32472
−3.55561 + 2.82812I −10.49024 − 2.97945I
u = 0.707479 − 1.051460I
a = 0.761004 − 0.716601I
b = 1.32472
−3.55561 − 2.82812I −10.49024 + 2.97945I
u = −0.078903 + 1.344400I
a = 0.024791 + 0.422408I
b = −0.662359 + 0.562280I
−7.69319 −17.0195 + 0.I
u = −0.078903 − 1.344400I
a = 0.024791 − 0.422408I
b = −0.662359 − 0.562280I
−7.69319 −17.0195 + 0.I
u = 0.45634 + 1.66481I
a = −0.087267 + 0.318365I
b = −0.662359 − 0.562280I
−7.69319 −17.0195 + 0.I
u = 0.45634 − 1.66481I
a = −0.087267 − 0.318365I
b = −0.662359 + 0.562280I
−7.69319 −17.0195 + 0.I
31
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.207087 + 0.121997I
a = 3.53147 − 4.23160I
b = −0.662359 + 0.562280I
−3.55561 + 2.82812I −10.49024 − 2.97945I
u = −0.207087 − 0.121997I
a = 3.53147 + 4.23160I
b = −0.662359 − 0.562280I
−3.55561 − 2.82812I −10.49024 + 2.97945I
32
VI.
I
u
6
= h−u
5
+u
4
+u
2
+b−1, −u
5
+u
4
−u
3
+u
2
+a−u, u
6
−u
5
+u
4
−2u
3
+u
2
+1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
u
5
− u
4
+ u
3
− u
2
+ u
u
5
− u
4
− u
2
+ 1
a
6
=
1
−u
2
a
4
=
u
4
− u
3
+ u
2
− u + 1
−u
5
+ u
4
− u
3
+ u
2
− 1
a
1
=
u
5
− u
4
+ 1
−1
a
7
=
−u
4
+ u
3
+ u − 1
u
5
− 2u
4
+ u
3
− 2u
2
+ u + 1
a
10
=
−u
u
3
+ u
a
9
=
u
4
− 2u
3
+ u
2
− 2u + 2
−2u
5
+ 2u
4
− u
3
+ 2u
2
− 2
a
3
=
u
3
+ u − 1
u
5
− u
4
− u
2
+ 1
a
12
=
u
5
− u
4
+ u
3
− u
2
−u
5
+ u
4
− u
3
+ 2u
2
a
8
=
−u
4
+ u
3
− u
2
+ u − 1
u
5
− u
4
+ u
3
− u
2
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
5
+ 4u
4
− 4u
3
+ 4u
2
− 14
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
(u
3
− u − 1)
2
c
3
, c
8
(u − 1)
6
c
5
, c
7
, c
10
c
11
u
6
− u
5
+ u
4
− 2u
3
+ u
2
+ 1
c
6
, c
9
u
6
+ 2u
5
− 2u
4
− 5u
3
+ 4u
2
+ 12u + 7
c
12
(u
3
+ u
2
− 1)
2
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y
3
− 2y
2
+ y −1)
2
c
3
, c
8
(y −1)
6
c
5
, c
7
, c
10
c
11
y
6
+ y
5
− y
4
+ 3y
2
+ 2y + 1
c
6
, c
9
y
6
− 8y
5
+ 32y
4
− 75y
3
+ 108y
2
− 88y + 49
c
12
(y
3
− y
2
+ 2y −1)
2
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.206350 + 1.132320I
a = −1.083790 + 0.387453I
b = −0.662359 + 0.562280I
−3.55561 − 2.82812I −10.49024 + 2.97945I
u = −0.206350 − 1.132320I
a = −1.083790 − 0.387453I
b = −0.662359 − 0.562280I
−3.55561 + 2.82812I −10.49024 − 2.97945I
u = 1.083790 + 0.387453I
a = 0.206350 + 1.132320I
b = −0.662359 − 0.562280I
−3.55561 + 2.82812I −10.49024 − 2.97945I
u = 1.083790 − 0.387453I
a = 0.206350 − 1.132320I
b = −0.662359 + 0.562280I
−3.55561 − 2.82812I −10.49024 + 2.97945I
u = −0.377439 + 0.653743I
a = 0.377439 + 0.653743I
b = 1.32472
−7.69319 −17.0195 + 0.I
u = −0.377439 − 0.653743I
a = 0.377439 − 0.653743I
b = 1.32472
−7.69319 −17.0195 + 0.I
36
VII. I
u
7
= hb + 1, u
5
+ 2u
3
+ a + u, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
−u
5
− 2u
3
− u
−1
a
6
=
1
−u
2
a
4
=
−u
5
− 2u
3
− u + 1
−1
a
1
=
−1
0
a
7
=
u
2
+ 1
−u
2
a
10
=
−u
u
3
+ u
a
9
=
u
5
+ 2u
3
+ u − 1
1
a
3
=
−u
5
− 2u
3
− u + 1
−1
a
12
=
−u
4
− u
2
− 1
u
5
+ 2u
3
− u
2
+ 2u − 1
a
8
=
u
5
+ 2u
3
+ u − 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
3
+ 4u − 8
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
8
u
6
c
4
(u + 1)
6
c
5
, c
7
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
6
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
9
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
10
, c
11
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
12
(u
3
+ u
2
− 1)
2
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
8
y
6
c
5
, c
7
, c
10
c
11
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
6
, c
9
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
12
(y
3
− y
2
+ 2y −1)
2
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498832 + 1.001300I
a = −0.960138 + 0.693124I
b = −1.00000
−1.91067 − 2.82812I −4.49024 + 2.97945I
u = −0.498832 − 1.001300I
a = −0.960138 − 0.693124I
b = −1.00000
−1.91067 + 2.82812I −4.49024 − 2.97945I
u = 0.284920 + 1.115140I
a = −0.122561 + 0.479689I
b = −1.00000
−6.04826 −11.01951 + 0.I
u = 0.284920 − 1.115140I
a = −0.122561 − 0.479689I
b = −1.00000
−6.04826 −11.01951 + 0.I
u = 0.713912 + 0.305839I
a = −0.91730 − 1.43799I
b = −1.00000
−1.91067 − 2.82812I −4.49024 + 2.97945I
u = 0.713912 − 0.305839I
a = −0.91730 + 1.43799I
b = −1.00000
−1.91067 + 2.82812I −4.49024 − 2.97945I
40
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
10
(u
3
− u − 1)
6
· (u
11
− 2u
10
− 4u
9
+ 8u
8
+ 6u
7
− 8u
6
− 7u
5
− 2u
4
+ 7u
3
+ 3u
2
− u + 1)
6
· (u
20
+ 4u
19
+ ··· − 5u + 1)(u
40
− 3u
39
+ ··· + 304u − 64)
c
3
u
10
(u − 1)
18
· (u
11
+ 2u
10
− u
9
− 3u
8
+ u
7
+ 2u
6
+ 4u
5
+ 11u
4
+ 9u
3
+ u
2
− 2u − 2)
6
· (u
20
− 6u
18
+ ··· − 3u + 1)(u
40
+ 7u
39
+ ··· − 6912u − 1024)
c
4
(u + 1)
10
(u
3
− u − 1)
6
· (u
11
− 2u
10
− 4u
9
+ 8u
8
+ 6u
7
− 8u
6
− 7u
5
− 2u
4
+ 7u
3
+ 3u
2
− u + 1)
6
· (u
20
− 4u
19
+ ··· + 5u + 1)(u
40
− 3u
39
+ ··· + 304u − 64)
c
5
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ u
4
− 2u
3
+ u
2
+ 1)
· (u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)(u
12
+ u
11
+ ··· + 8u + 1)
· (u
20
+ 10u
18
+ ··· − 3u + 1)(u
40
+ 16u
38
+ ··· + 7u + 1)
· (u
66
− 2u
65
+ ··· + 34394u + 12919)
c
6
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
6
+ 2u
5
+ ··· + 12u + 7)(u
12
− 2u
11
+ ··· − 4u + 1)
· (u
20
+ 3u
19
+ ··· − 5u
3
+ 1)(u
40
− u
39
+ ··· − 6u
2
+ 1)
· (u
66
− 6u
65
+ ··· − 10740u + 839)
c
7
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ u
4
− 2u
3
+ u
2
+ 1)
· (u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)(u
12
+ u
11
+ ··· + 8u + 1)
· (u
20
+ 10u
18
+ ··· + 3u + 1)(u
40
+ 16u
38
+ ··· + 7u + 1)
· (u
66
− 2u
65
+ ··· + 34394u + 12919)
c
8
u
10
(u − 1)
18
· (u
11
+ 2u
10
− u
9
− 3u
8
+ u
7
+ 2u
6
+ 4u
5
+ 11u
4
+ 9u
3
+ u
2
− 2u − 2)
6
· (u
20
− 6u
18
+ ··· + 3u + 1)(u
40
+ 7u
39
+ ··· − 6912u − 1024)
c
9
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 2u
5
− 2u
4
− 5u
3
+ 4u
2
+ 12u + 7)
· (u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)(u
12
− 2u
11
+ ··· − 4u + 1)
· (u
20
+ 3u
19
+ ··· − 5u
3
+ 1)(u
40
− u
39
+ ··· − 6u
2
+ 1)
· (u
66
− 6u
65
+ ··· − 10740u + 839)
c
10
(u
4
+ u
2
− u + 1)(u
6
− u
5
+ u
4
− 2u
3
+ u
2
+ 1)
· (u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)(u
12
+ u
11
+ ··· + 8u + 1)
· (u
20
+ 10u
18
+ ··· + 3u + 1)(u
40
+ 16u
38
+ ··· + 7u + 1)
· (u
66
− 2u
65
+ ··· + 34394u + 12919)
c
11
(u
4
+ u
2
− u + 1)(u
6
− u
5
+ u
4
− 2u
3
+ u
2
+ 1)
· (u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)(u
12
+ u
11
+ ··· + 8u + 1)
· (u
20
+ 10u
18
+ ··· − 3u + 1)(u
40
+ 16u
38
+ ··· + 7u + 1)
· (u
66
− 2u
65
+ ··· + 34394u + 12919)
c
12
((u
3
+ u
2
− 1)
30
)(u
4
− 3u
3
+ ··· − 3u + 2)(u
20
+ 5u
19
+ ··· − 4u
2
+ 1)
· (u
40
− 41u
39
+ ··· − 458752u + 16384)
41
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
((y −1)
10
)(y
3
− 2y
2
+ y −1)
6
(y
11
− 12y
10
+ ··· − 5y −1)
6
· (y
20
− 20y
19
+ ··· − y + 1)(y
40
− 37y
39
+ ··· − 54528y + 4096)
c
3
, c
8
y
10
(y −1)
18
(y
11
− 6y
10
+ ··· + 8y −4)
6
(y
20
− 12y
19
+ ··· − 9y + 1)
· (y
40
− 21y
39
+ ··· − 2424832y + 1048576)
c
5
, c
7
, c
10
c
11
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ y
5
− y
4
+ 3y
2
+ 2y + 1)
· (y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)(y
12
+ 11y
11
+ ··· − 14y + 1)
· (y
20
+ 20y
19
+ ··· + 15y + 1)(y
40
+ 32y
39
+ ··· − 25y + 1)
· (y
66
+ 54y
65
+ ··· − 70983068y + 166900561)
c
6
, c
9
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− 8y
5
+ ··· − 88y + 49)
· (y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)(y
12
+ 4y
11
+ ··· − 4y + 1)
· (y
20
− 5y
19
+ ··· + 6y
2
+ 1)(y
40
− y
39
+ ··· − 12y + 1)
· (y
66
− 18y
65
+ ··· − 32088596y + 703921)
c
12
((y
3
− y
2
+ 2y −1)
30
)(y
4
− y
3
+ 2y
2
+ 7y + 4)(y
20
− 5y
19
+ ··· − 8y + 1)
· (y
40
− 7y
39
+ ··· − 7516192768y + 268435456)
42
