12n
0530
(K12n
0530
)
A knot diagram
1
Linearized knot diagam
3 5 11 9 2 4 10 5 12 3 7 8
Solving Sequence
4,9 5,11
3 2 6 1 8 10 7 12
c
4
c
3
c
2
c
5
c
1
c
8
c
10
c
7
c
12
c
6
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.64573 × 10
258
u
71
+ 1.93369 × 10
258
u
70
+ ··· + 2.61570 × 10
260
b − 8.84362 × 10
260
,
1.94505 × 10
261
u
71
− 9.37390 × 10
260
u
70
+ ··· + 1.85715 × 10
262
a + 2.78533 × 10
263
,
u
72
+ 7u
70
+ ··· + 174u + 71i
I
u
2
= h2184459735u
30
+ 2467043153u
29
+ ··· + 148046503b + 1530935116,
− 5788205505u
30
− 2520329514u
29
+ ··· + 148046503a − 9787930487, u
31
+ u
30
+ ··· + u − 1i
* 2 irreducible components of dim
C
= 0, with total 103 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−3.65 × 10
258
u
71
+ 1.93 × 10
258
u
70
+ · · · + 2.62 × 10
260
b − 8.84 ×
10
260
, 1.95 × 10
261
u
71
− 9.37 × 10
260
u
70
+ · · · + 1.86 × 10
262
a + 2.79 ×
10
263
, u
72
+ 7u
70
+ · · · + 174u + 71i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
11
=
−0.104733u
71
+ 0.0504747u
70
+ ··· − 10.2744u − 14.9979
0.0139379u
71
− 0.00739262u
70
+ ··· + 0.899364u + 3.38097
a
3
=
−0.100244u
71
+ 0.0145687u
70
+ ··· − 6.20768u − 21.3805
0.0524115u
71
− 0.0459288u
70
+ ··· + 11.4091u + 1.78594
a
2
=
−0.127174u
71
+ 0.0337253u
70
+ ··· − 13.0344u − 24.2008
0.0395871u
71
− 0.0395261u
70
+ ··· + 9.98786u + 0.425816
a
6
=
0.156586u
71
− 0.111459u
70
+ ··· + 35.4012u + 9.44122
0.104480u
71
− 0.0235722u
70
+ ··· + 11.3081u + 19.1362
a
1
=
−0.163406u
71
+ 0.0989962u
70
+ ··· − 20.5083u − 13.3356
−0.252000u
71
+ 0.111375u
70
+ ··· − 34.9609u − 28.5427
a
8
=
u
u
3
+ u
a
10
=
0.0257924u
71
+ 0.00721650u
70
+ ··· − 4.53635u + 7.33620
0.101128u
71
− 0.0222456u
70
+ ··· + 15.6108u + 16.7202
a
7
=
0.261066u
71
− 0.135031u
70
+ ··· + 46.7093u + 28.5775
0.104480u
71
− 0.0235722u
70
+ ··· + 11.3081u + 19.1362
a
12
=
−0.173734u
71
+ 0.110746u
70
+ ··· − 23.3198u − 13.1488
−0.269089u
71
+ 0.124908u
70
+ ··· − 39.0835u − 29.1901
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.631363u
71
+ 0.329602u
70
+ ··· − 114.221u − 62.1901
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
72
+ 90u
71
+ ··· + 1404496977u + 27447121
c
2
, c
5
u
72
+ 4u
71
+ ··· − 28717u + 5239
c
3
, c
10
u
72
+ 2u
71
+ ··· + 1164u + 89
c
4
, c
8
u
72
+ 7u
70
+ ··· − 174u + 71
c
6
u
72
+ 12u
71
+ ··· + 183732u + 262579
c
7
u
72
− 11u
70
+ ··· − 251726u + 58649
c
9
u
72
+ 3u
71
+ ··· + 92u + 29
c
11
u
72
+ u
71
+ ··· − 2131u + 145
c
12
u
72
− u
71
+ ··· + 9071598635u + 6503913561
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
72
− 202y
71
+ ··· + 499387466684415153y + 753344451188641
c
2
, c
5
y
72
+ 90y
71
+ ··· + 1404496977y + 27447121
c
3
, c
10
y
72
− 56y
71
+ ··· − 188640y + 7921
c
4
, c
8
y
72
+ 14y
71
+ ··· − 52712y + 5041
c
6
y
72
+ 70y
71
+ ··· + 2835486348132y + 68947731241
c
7
y
72
− 22y
71
+ ··· − 71347990678y + 3439705201
c
9
y
72
+ 9y
71
+ ··· + 38110y + 841
c
11
y
72
− 13y
71
+ ··· − 1039701y + 21025
c
12
y
72
+ 77y
71
+ ··· + 3.46 × 10
20
y + 4.23 × 10
19
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395735 + 0.962899I
a = 0.15710 − 1.90724I
b = 1.103020 + 0.378441I
−2.35206 − 4.90102I 0
u = 0.395735 − 0.962899I
a = 0.15710 + 1.90724I
b = 1.103020 − 0.378441I
−2.35206 + 4.90102I 0
u = 0.449062 + 0.795024I
a = −0.122453 − 0.304927I
b = −0.087555 + 0.465957I
0.05590 − 1.89763I −1.60993 + 3.15256I
u = 0.449062 − 0.795024I
a = −0.122453 + 0.304927I
b = −0.087555 − 0.465957I
0.05590 + 1.89763I −1.60993 − 3.15256I
u = 0.121973 + 1.102890I
a = −0.886065 − 0.527000I
b = −0.440152 + 0.475467I
3.69129 − 1.79239I 0
u = 0.121973 − 1.102890I
a = −0.886065 + 0.527000I
b = −0.440152 − 0.475467I
3.69129 + 1.79239I 0
u = 0.051307 + 0.865237I
a = −1.073040 − 0.163089I
b = 0.964573 + 0.239283I
−0.715343 − 0.560826I −2.22835 + 1.84045I
u = 0.051307 − 0.865237I
a = −1.073040 + 0.163089I
b = 0.964573 − 0.239283I
−0.715343 + 0.560826I −2.22835 − 1.84045I
u = 0.854276 + 0.144443I
a = 1.394460 + 0.022960I
b = 1.52014 − 0.19291I
−5.10447 + 1.24571I −11.85389 − 4.33977I
u = 0.854276 − 0.144443I
a = 1.394460 − 0.022960I
b = 1.52014 + 0.19291I
−5.10447 − 1.24571I −11.85389 + 4.33977I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.540643 + 1.035120I
a = −1.01016 + 1.22898I
b = −1.026380 − 0.257760I
−2.36515 − 4.35350I 0
u = 0.540643 − 1.035120I
a = −1.01016 − 1.22898I
b = −1.026380 + 0.257760I
−2.36515 + 4.35350I 0
u = −0.836968 + 0.820484I
a = 0.062748 + 0.354211I
b = −0.028412 + 0.257770I
−7.21762 + 1.57842I 0
u = −0.836968 − 0.820484I
a = 0.062748 − 0.354211I
b = −0.028412 − 0.257770I
−7.21762 − 1.57842I 0
u = −0.089104 + 1.169450I
a = 1.390420 + 0.100465I
b = 0.418314 − 0.347525I
2.56389 + 4.98234I 0
u = −0.089104 − 1.169450I
a = 1.390420 − 0.100465I
b = 0.418314 + 0.347525I
2.56389 − 4.98234I 0
u = 1.146330 + 0.264545I
a = −1.42952 + 0.07044I
b = −1.293780 + 0.058915I
−5.24347 − 1.12672I 0
u = 1.146330 − 0.264545I
a = −1.42952 − 0.07044I
b = −1.293780 − 0.058915I
−5.24347 + 1.12672I 0
u = 0.443052 + 0.675051I
a = −0.782382 + 0.844362I
b = 0.437835 − 0.368886I
−0.38463 − 1.62177I −3.30795 + 2.54804I
u = 0.443052 − 0.675051I
a = −0.782382 − 0.844362I
b = 0.437835 + 0.368886I
−0.38463 + 1.62177I −3.30795 − 2.54804I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.967859 + 0.698281I
a = −1.55826 − 0.52021I
b = −1.54355 + 0.43095I
−5.51623 + 9.76846I 0
u = −0.967859 − 0.698281I
a = −1.55826 + 0.52021I
b = −1.54355 − 0.43095I
−5.51623 − 9.76846I 0
u = −1.029520 + 0.617322I
a = 1.55254 + 0.54349I
b = 1.48143 − 0.48596I
−5.12009 + 3.07867I 0
u = −1.029520 − 0.617322I
a = 1.55254 − 0.54349I
b = 1.48143 + 0.48596I
−5.12009 − 3.07867I 0
u = −0.303232 + 1.174180I
a = 0.067205 − 1.186790I
b = −1.340260 + 0.045475I
−3.37394 − 4.41777I 0
u = −0.303232 − 1.174180I
a = 0.067205 + 1.186790I
b = −1.340260 − 0.045475I
−3.37394 + 4.41777I 0
u = −0.680975 + 0.228717I
a = −0.009465 + 0.667107I
b = 0.005071 + 0.860625I
−0.64872 − 2.42772I −5.12888 + 2.87093I
u = −0.680975 − 0.228717I
a = −0.009465 − 0.667107I
b = 0.005071 − 0.860625I
−0.64872 + 2.42772I −5.12888 − 2.87093I
u = −0.832013 + 0.984749I
a = 0.312085 − 0.103923I
b = 0.219473 − 0.028625I
−6.76288 + 4.64270I 0
u = −0.832013 − 0.984749I
a = 0.312085 + 0.103923I
b = 0.219473 + 0.028625I
−6.76288 − 4.64270I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.573176 + 0.388286I
a = 1.29722 + 1.23670I
b = 1.168720 − 0.573152I
−3.16144 + 2.19845I −6.25562 − 1.59959I
u = −0.573176 − 0.388286I
a = 1.29722 − 1.23670I
b = 1.168720 + 0.573152I
−3.16144 − 2.19845I −6.25562 + 1.59959I
u = 0.094458 + 1.330650I
a = −0.148020 + 0.447289I
b = −1.139030 − 0.357153I
1.31162 − 5.11847I 0
u = 0.094458 − 1.330650I
a = −0.148020 − 0.447289I
b = −1.139030 + 0.357153I
1.31162 + 5.11847I 0
u = −0.571365 + 0.268353I
a = −1.57384 − 2.30271I
b = −1.097390 + 0.512023I
−3.68144 + 7.02753I −8.48206 − 7.62204I
u = −0.571365 − 0.268353I
a = −1.57384 + 2.30271I
b = −1.097390 − 0.512023I
−3.68144 − 7.02753I −8.48206 + 7.62204I
u = −0.578086 + 0.219362I
a = 0.051134 − 0.479362I
b = 0.193593 − 1.265520I
0.42855 + 3.78859I −11.02576 − 5.40615I
u = −0.578086 − 0.219362I
a = 0.051134 + 0.479362I
b = 0.193593 + 1.265520I
0.42855 − 3.78859I −11.02576 + 5.40615I
u = −0.441835 + 0.400017I
a = 0.356531 + 0.389777I
b = 1.016320 − 0.905156I
−5.02849 + 3.73076I −5.1233 − 21.3943I
u = −0.441835 − 0.400017I
a = 0.356531 − 0.389777I
b = 1.016320 + 0.905156I
−5.02849 − 3.73076I −5.1233 + 21.3943I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.09417 + 0.94741I
a = −1.43865 − 0.61242I
b = −1.49559 + 0.20888I
−13.0216 + 6.2886I 0
u = −1.09417 − 0.94741I
a = −1.43865 + 0.61242I
b = −1.49559 − 0.20888I
−13.0216 − 6.2886I 0
u = −0.397869 + 0.372222I
a = 1.56775 − 0.76536I
b = −0.813659 + 0.553224I
−6.67154 + 2.30013I −7.54665 − 1.33223I
u = −0.397869 − 0.372222I
a = 1.56775 + 0.76536I
b = −0.813659 − 0.553224I
−6.67154 − 2.30013I −7.54665 + 1.33223I
u = 0.335065 + 0.350080I
a = −5.42556 + 0.37620I
b = −0.827281 + 0.133830I
−1.19027 − 4.32625I −9.73628 + 5.44169I
u = 0.335065 − 0.350080I
a = −5.42556 − 0.37620I
b = −0.827281 − 0.133830I
−1.19027 + 4.32625I −9.73628 − 5.44169I
u = 0.297766 + 0.375697I
a = −0.900173 − 0.634319I
b = 0.455987 + 0.336230I
−0.352890 − 1.156840I −3.33626 + 6.27843I
u = 0.297766 − 0.375697I
a = −0.900173 + 0.634319I
b = 0.455987 − 0.336230I
−0.352890 + 1.156840I −3.33626 − 6.27843I
u = −0.98368 + 1.16684I
a = −1.152340 − 0.780833I
b = −1.44325 + 0.05558I
−12.32380 + 1.39774I 0
u = −0.98368 − 1.16684I
a = −1.152340 + 0.780833I
b = −1.44325 − 0.05558I
−12.32380 − 1.39774I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10388 + 1.52966I
a = −0.36680 − 1.40579I
b = 0.14248 + 1.43260I
5.86544 − 1.77991I 0
u = −0.10388 − 1.52966I
a = −0.36680 + 1.40579I
b = 0.14248 − 1.43260I
5.86544 + 1.77991I 0
u = 0.453819 + 0.080930I
a = 1.95367 + 2.95184I
b = 0.783084 − 0.260390I
−0.198226 + 0.836420I −5.38993 − 3.91161I
u = 0.453819 − 0.080930I
a = 1.95367 − 2.95184I
b = 0.783084 + 0.260390I
−0.198226 − 0.836420I −5.38993 + 3.91161I
u = 1.19227 + 1.02193I
a = −0.453256 + 0.116492I
b = −0.02029 − 1.48602I
−8.87243 − 8.99590I 0
u = 1.19227 − 1.02193I
a = −0.453256 − 0.116492I
b = −0.02029 + 1.48602I
−8.87243 + 8.99590I 0
u = −0.45141 + 1.52991I
a = 0.263474 + 0.588048I
b = 1.48307 + 0.04643I
−1.78537 + 3.12124I 0
u = −0.45141 − 1.52991I
a = 0.263474 − 0.588048I
b = 1.48307 − 0.04643I
−1.78537 − 3.12124I 0
u = −1.34640 + 0.95807I
a = 1.35297 + 0.43389I
b = 1.359800 − 0.221402I
−11.83750 + 3.84980I 0
u = −1.34640 − 0.95807I
a = 1.35297 − 0.43389I
b = 1.359800 + 0.221402I
−11.83750 − 3.84980I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.07100 + 1.27533I
a = 1.06920 − 0.95111I
b = 1.51696 + 0.65693I
−13.7424 − 16.3876I 0
u = 1.07100 − 1.27533I
a = 1.06920 + 0.95111I
b = 1.51696 − 0.65693I
−13.7424 + 16.3876I 0
u = 1.45912 + 0.82147I
a = −0.861847 + 0.180322I
b = −1.74894 + 0.62571I
−14.3075 − 0.9208I 0
u = 1.45912 − 0.82147I
a = −0.861847 − 0.180322I
b = −1.74894 − 0.62571I
−14.3075 + 0.9208I 0
u = 1.13934 + 1.24259I
a = 0.490867 − 0.170499I
b = −0.34581 + 1.55094I
−8.26186 + 0.50360I 0
u = 1.13934 − 1.24259I
a = 0.490867 + 0.170499I
b = −0.34581 − 1.55094I
−8.26186 − 0.50360I 0
u = 1.40221 + 0.96945I
a = 0.906396 − 0.225397I
b = 1.65571 − 0.47881I
−14.9087 + 7.5805I 0
u = 1.40221 − 0.96945I
a = 0.906396 + 0.225397I
b = 1.65571 + 0.47881I
−14.9087 − 7.5805I 0
u = 1.04699 + 1.39296I
a = −0.886462 + 0.974314I
b = −1.59579 − 0.76315I
−12.4101 − 8.0043I 0
u = 1.04699 − 1.39296I
a = −0.886462 − 0.974314I
b = −1.59579 + 0.76315I
−12.4101 + 8.0043I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21287 + 1.28487I
a = 1.128290 + 0.522196I
b = 1.361540 − 0.097914I
−10.89700 + 5.27373I 0
u = −1.21287 − 1.28487I
a = 1.128290 − 0.522196I
b = 1.361540 + 0.097914I
−10.89700 − 5.27373I 0
12
II.
I
u
2
= h2.18 × 10
9
u
30
+ 2.47 × 10
9
u
29
+ · · · + 1.48 × 10
8
b + 1.53 × 10
9
, −5.79 ×
10
9
u
30
− 2.52 × 10
9
u
29
+ · · · + 1.48 × 10
8
a − 9.79 × 10
9
, u
31
+ u
30
+ · · · + u − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
11
=
39.0972u
30
+ 17.0239u
29
+ ··· − 99.1802u + 66.1139
−14.7552u
30
− 16.6640u
29
+ ··· + 31.0442u − 10.3409
a
3
=
−18.0162u
30
− 2.47624u
29
+ ··· + 56.7338u − 29.8879
9.28688u
30
+ 9.90889u
29
+ ··· − 23.3547u + 0.230898
a
2
=
−14.4870u
30
− 6.55365u
29
+ ··· + 46.5324u − 14.5789
4.49815u
30
+ 7.70859u
29
+ ··· − 12.2189u − 7.37571
a
6
=
−12.0556u
30
− 16.1150u
29
+ ··· + 18.9197u − 8.33258
3.92187u
30
+ 9.65956u
29
+ ··· + 2.00374u − 4.05938
a
1
=
−10.8188u
30
− 23.6255u
29
+ ··· + 6.21977u + 24.1388
−3.93581u
30
+ 3.47531u
29
+ ··· + 11.1257u − 21.4435
a
8
=
u
u
3
+ u
a
10
=
9.24223u
30
+ 5.40214u
29
+ ··· − 13.6874u + 13.6500
−3.91150u
30
− 7.55693u
29
+ ··· + 7.31831u − 1.58206
a
7
=
−8.13377u
30
− 6.45547u
29
+ ··· + 20.9234u − 12.3920
3.92187u
30
+ 9.65956u
29
+ ··· + 2.00374u − 4.05938
a
12
=
−12.0704u
30
− 20.0918u
29
+ ··· + 17.1696u + 10.0725
−4.50508u
30
+ 5.97409u
29
+ ··· + 16.0388u − 30.7245
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
62375183
13458773
u
30
+
565714406
13458773
u
29
+ ··· +
551787507
13458773
u −
1029337351
13458773
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
31
− 31u
30
+ ··· − 30u + 1
c
2
u
31
+ u
30
+ ··· − 4u − 1
c
3
u
31
+ u
30
+ ··· − u + 1
c
4
u
31
+ u
30
+ ··· + u − 1
c
5
u
31
− u
30
+ ··· − 4u + 1
c
6
u
31
+ u
30
+ ··· + 21u − 1
c
7
u
31
− u
30
+ ··· + 3u − 1
c
8
u
31
− u
30
+ ··· + u + 1
c
9
u
31
+ 6u
30
+ ··· + 5u − 1
c
10
u
31
− u
30
+ ··· − u − 1
c
11
u
31
+ 2u
29
+ ··· + 6u − 1
c
12
u
31
+ 7u
29
+ ··· − 82u − 173
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
− 49y
30
+ ··· − 38y −1
c
2
, c
5
y
31
+ 31y
30
+ ··· − 30y −1
c
3
, c
10
y
31
− 15y
30
+ ··· + 23y −1
c
4
, c
8
y
31
+ 23y
30
+ ··· − 21y −1
c
6
y
31
+ 19y
30
+ ··· + 111y −1
c
7
y
31
+ 7y
30
+ ··· + 17y −1
c
9
y
31
− 2y
30
+ ··· + 5y −1
c
11
y
31
+ 4y
30
+ ··· + 28y −1
c
12
y
31
+ 14y
30
+ ··· − 95346y −29929
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00320
a = −1.44536
b = −1.45021
−4.80480 −8.23200
u = 0.414761 + 0.893790I
a = 0.0188869 + 0.1373480I
b = −1.051220 + 0.535306I
−2.06404 + 0.04099I −7.61696 + 0.53823I
u = 0.414761 − 0.893790I
a = 0.0188869 − 0.1373480I
b = −1.051220 − 0.535306I
−2.06404 − 0.04099I −7.61696 − 0.53823I
u = 0.514757 + 0.936922I
a = −0.73973 + 1.51693I
b = −0.951675 − 0.357092I
−1.70969 − 3.70189I −1.88232 + 1.78013I
u = 0.514757 − 0.936922I
a = −0.73973 − 1.51693I
b = −0.951675 + 0.357092I
−1.70969 + 3.70189I −1.88232 − 1.78013I
u = 0.157872 + 0.742681I
a = −0.06796 − 2.93576I
b = 1.086440 + 0.417304I
−2.53106 − 7.07661I −1.89774 + 8.89193I
u = 0.157872 − 0.742681I
a = −0.06796 + 2.93576I
b = 1.086440 − 0.417304I
−2.53106 + 7.07661I −1.89774 − 8.89193I
u = 0.206713 + 1.227890I
a = −0.835315 − 0.743685I
b = −0.726976 + 0.045716I
2.77050 − 2.34424I −3.13614 + 3.15282I
u = 0.206713 − 1.227890I
a = −0.835315 + 0.743685I
b = −0.726976 − 0.045716I
2.77050 + 2.34424I −3.13614 − 3.15282I
u = −0.799098 + 0.958393I
a = 0.210652 + 0.276427I
b = 0.591143 − 0.280685I
−6.97387 + 5.05702I −11.0205 − 11.4486I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.799098 − 0.958393I
a = 0.210652 − 0.276427I
b = 0.591143 + 0.280685I
−6.97387 − 5.05702I −11.0205 + 11.4486I
u = −0.767016 + 1.013840I
a = −0.606380 + 0.010069I
b = 0.544901 + 0.698390I
−6.88066 + 0.75245I −4.79263 + 1.69482I
u = −0.767016 − 1.013840I
a = −0.606380 − 0.010069I
b = 0.544901 − 0.698390I
−6.88066 − 0.75245I −4.79263 − 1.69482I
u = −0.065070 + 1.273420I
a = 1.28964 + 0.58739I
b = 0.731464 + 0.113037I
1.94312 + 4.25275I −3.91634 − 1.69636I
u = −0.065070 − 1.273420I
a = 1.28964 − 0.58739I
b = 0.731464 − 0.113037I
1.94312 − 4.25275I −3.91634 + 1.69636I
u = 0.033858 + 1.309040I
a = 0.131726 − 0.097082I
b = 1.170920 − 0.347806I
−0.15060 + 6.18563I −3.72734 − 7.09079I
u = 0.033858 − 1.309040I
a = 0.131726 + 0.097082I
b = 1.170920 + 0.347806I
−0.15060 − 6.18563I −3.72734 + 7.09079I
u = 0.271080 + 0.614683I
a = 2.54685 + 0.92775I
b = −0.601081 + 0.067316I
0.407610 + 0.293898I 2.93790 + 1.44236I
u = 0.271080 − 0.614683I
a = 2.54685 − 0.92775I
b = −0.601081 − 0.067316I
0.407610 − 0.293898I 2.93790 − 1.44236I
u = 0.050242 + 0.666747I
a = −2.76384 + 3.05830I
b = 0.645198 − 0.202972I
−0.60697 − 4.13489I 3.15721 + 1.64275I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.050242 − 0.666747I
a = −2.76384 − 3.05830I
b = 0.645198 + 0.202972I
−0.60697 + 4.13489I 3.15721 − 1.64275I
u = 0.178470 + 1.354410I
a = −0.001365 + 0.938047I
b = −1.247660 − 0.346739I
0.16222 − 3.81499I −2.00000 + 3.53888I
u = 0.178470 − 1.354410I
a = −0.001365 − 0.938047I
b = −1.247660 + 0.346739I
0.16222 + 3.81499I −2.00000 − 3.53888I
u = 0.258726 + 0.456167I
a = −1.035170 − 0.319743I
b = −0.149548 − 0.975049I
0.99073 − 3.69106I 3.33675 + 4.02693I
u = 0.258726 − 0.456167I
a = −1.035170 + 0.319743I
b = −0.149548 + 0.975049I
0.99073 + 3.69106I 3.33675 − 4.02693I
u = −0.322722 + 0.307676I
a = −0.038832 − 1.039290I
b = −1.090450 + 0.785922I
−5.09942 + 3.47271I −12.7570 + 6.6208I
u = −0.322722 − 0.307676I
a = −0.038832 + 1.039290I
b = −1.090450 − 0.785922I
−5.09942 − 3.47271I −12.7570 − 6.6208I
u = 0.13208 + 1.57427I
a = 0.370056 − 1.343350I
b = −0.15120 + 1.53870I
5.70515 + 1.78957I −26.6318 + 0.I
u = 0.13208 − 1.57427I
a = 0.370056 + 1.343350I
b = −0.15120 − 1.53870I
5.70515 − 1.78957I −26.6318 + 0.I
u = −1.26626 + 1.08833I
a = 1.243460 + 0.514827I
b = 1.42486 − 0.17270I
−11.52450 + 4.48140I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.26626 − 1.08833I
a = 1.243460 − 0.514827I
b = 1.42486 + 0.17270I
−11.52450 − 4.48140I 0
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
31
− 31u
30
+ ··· − 30u + 1)
· (u
72
+ 90u
71
+ ··· + 1404496977u + 27447121)
c
2
(u
31
+ u
30
+ ··· − 4u − 1)(u
72
+ 4u
71
+ ··· − 28717u + 5239)
c
3
(u
31
+ u
30
+ ··· − u + 1)(u
72
+ 2u
71
+ ··· + 1164u + 89)
c
4
(u
31
+ u
30
+ ··· + u − 1)(u
72
+ 7u
70
+ ··· − 174u + 71)
c
5
(u
31
− u
30
+ ··· − 4u + 1)(u
72
+ 4u
71
+ ··· − 28717u + 5239)
c
6
(u
31
+ u
30
+ ··· + 21u − 1)(u
72
+ 12u
71
+ ··· + 183732u + 262579)
c
7
(u
31
− u
30
+ ··· + 3u − 1)(u
72
− 11u
70
+ ··· − 251726u + 58649)
c
8
(u
31
− u
30
+ ··· + u + 1)(u
72
+ 7u
70
+ ··· − 174u + 71)
c
9
(u
31
+ 6u
30
+ ··· + 5u − 1)(u
72
+ 3u
71
+ ··· + 92u + 29)
c
10
(u
31
− u
30
+ ··· − u − 1)(u
72
+ 2u
71
+ ··· + 1164u + 89)
c
11
(u
31
+ 2u
29
+ ··· + 6u − 1)(u
72
+ u
71
+ ··· − 2131u + 145)
c
12
(u
31
+ 7u
29
+ ··· − 82u − 173)
· (u
72
− u
71
+ ··· + 9071598635u + 6503913561)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
31
− 49y
30
+ ··· − 38y −1)
· (y
72
− 202y
71
+ ··· + 499387466684415153y + 753344451188641)
c
2
, c
5
(y
31
+ 31y
30
+ ··· − 30y −1)
· (y
72
+ 90y
71
+ ··· + 1404496977y + 27447121)
c
3
, c
10
(y
31
− 15y
30
+ ··· + 23y −1)(y
72
− 56y
71
+ ··· − 188640y + 7921)
c
4
, c
8
(y
31
+ 23y
30
+ ··· − 21y −1)(y
72
+ 14y
71
+ ··· − 52712y + 5041)
c
6
(y
31
+ 19y
30
+ ··· + 111y −1)
· (y
72
+ 70y
71
+ ··· + 2835486348132y + 68947731241)
c
7
(y
31
+ 7y
30
+ ··· + 17y −1)
· (y
72
− 22y
71
+ ··· − 71347990678y + 3439705201)
c
9
(y
31
− 2y
30
+ ··· + 5y −1)(y
72
+ 9y
71
+ ··· + 38110y + 841)
c
11
(y
31
+ 4y
30
+ ··· + 28y −1)(y
72
− 13y
71
+ ··· − 1039701y + 21025)
c
12
(y
31
+ 14y
30
+ ··· − 95346y −29929)
· (y
72
+ 77y
71
+ ··· + 3.46 × 10
20
y + 4.23 × 10
19
)
23
