12n
0789
(K12n
0789
)
A knot diagram
1
Linearized knot diagam
4 5 10 8 3 12 5 11 3 1 7 9
Solving Sequence
5,7 8,11
9 12 1 4 2 3 6 10
c
7
c
8
c
11
c
12
c
4
c
1
c
2
c
6
c
10
c
3
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.62341 × 10
256
u
81
+ 4.36659 × 10
257
u
80
+ ··· + 3.22941 × 10
256
b − 7.42547 × 10
256
,
4.79036 × 10
256
u
81
− 4.33578 × 10
257
u
80
+ ··· + 3.22941 × 10
256
a − 1.08341 × 10
258
, u
82
− 5u
81
+ ··· − 9u + 1i
I
u
2
= h−2.14857 × 10
33
u
37
− 1.68774 × 10
34
u
36
+ ··· + 4.97146 × 10
32
b − 1.06077 × 10
33
,
3.40194 × 10
33
u
37
+ 2.65994 × 10
34
u
36
+ ··· + 4.97146 × 10
32
a + 3.48145 × 10
33
, u
38
+ 8u
37
+ ··· + 7u + 1i
* 2 irreducible components of dim
C
= 0, with total 120 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−9.62 × 10
256
u
81
+ 4.37 × 10
257
u
80
+ · · · + 3.23 × 10
256
b − 7.43 ×
10
256
, 4.79 × 10
256
u
81
− 4.34 × 10
257
u
80
+ · · · + 3.23 × 10
256
a − 1.08 ×
10
258
, u
82
− 5u
81
+ · · · − 9u + 1i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
−1.48335u
81
+ 13.4259u
80
+ ··· − 314.049u + 33.5482
2.97993u
81
− 13.5213u
80
+ ··· + 0.624686u + 2.29933
a
9
=
−6.90787u
81
+ 34.0673u
80
+ ··· − 7.25907u − 12.3927
−3.93969u
81
+ 21.1683u
80
+ ··· − 134.630u + 16.2614
a
12
=
1.49657u
81
− 0.0953944u
80
+ ··· − 313.424u + 35.8475
2.97993u
81
− 13.5213u
80
+ ··· + 0.624686u + 2.29933
a
1
=
−6.98693u
81
+ 29.0151u
80
+ ··· + 266.633u − 50.5502
−5.97289u
81
+ 28.6846u
80
+ ··· − 19.3508u − 3.05047
a
4
=
u
u
3
+ u
a
2
=
−8.09243u
81
+ 34.6437u
80
+ ··· + 228.950u − 46.1752
−6.93732u
81
+ 33.6383u
80
+ ··· − 55.0188u + 1.22337
a
3
=
−8.09243u
81
+ 34.6437u
80
+ ··· + 228.950u − 46.1752
−6.40134u
81
+ 30.5632u
80
+ ··· − 10.7452u − 4.59507
a
6
=
18.4534u
81
− 92.4177u
80
+ ··· + 301.801u − 21.4321
2.22211u
81
− 13.2729u
80
+ ··· + 136.502u − 18.2729
a
10
=
−1.54299u
81
+ 11.0282u
80
+ ··· − 136.510u + 14.2742
2.49596u
81
− 11.4503u
80
+ ··· + 53.5123u − 3.37749
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.97826u
81
+ 10.7782u
80
+ ··· + 181.549u − 52.6251
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
82
− 2u
81
+ ··· − 144006814u + 92506631
c
2
, c
5
u
82
+ 8u
81
+ ··· + 285305320u + 28654393
c
3
, c
9
u
82
− 2u
81
+ ··· + 3176u + 3053
c
4
, c
7
u
82
− 5u
81
+ ··· − 9u + 1
c
6
, c
11
u
82
− 2u
81
+ ··· − 1903u + 193
c
8
u
82
+ 3u
81
+ ··· − 14399u + 1273
c
10
u
82
+ 4u
81
+ ··· + 1322u + 307
c
12
u
82
− 4u
81
+ ··· − 360727464u + 76941877
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
82
− 86y
81
+ ··· − 27578920347511596y + 8557476778970161
c
2
, c
5
y
82
+ 84y
81
+ ··· − 16527381541916668y + 821074238198449
c
3
, c
9
y
82
− 70y
81
+ ··· − 64668510y + 9320809
c
4
, c
7
y
82
+ 19y
81
+ ··· + 81y + 1
c
6
, c
11
y
82
+ 76y
81
+ ··· − 3045y + 37249
c
8
y
82
+ 19y
81
+ ··· + 35322967y + 1620529
c
10
y
82
+ 4y
81
+ ··· + 789978y + 94249
c
12
y
82
+ 38y
81
+ ··· + 86506044299292766y + 5920052436283129
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.056723 + 0.964872I
a = 1.37031 + 0.67536I
b = −0.289704 − 0.025564I
1.40440 + 4.15567I 0
u = 0.056723 − 0.964872I
a = 1.37031 − 0.67536I
b = −0.289704 + 0.025564I
1.40440 − 4.15567I 0
u = −0.178708 + 1.060670I
a = 0.672194 − 0.146847I
b = −0.14351 − 1.65591I
−4.60976 − 1.70624I 0
u = −0.178708 − 1.060670I
a = 0.672194 + 0.146847I
b = −0.14351 + 1.65591I
−4.60976 + 1.70624I 0
u = −0.462793 + 0.789203I
a = 1.94590 + 0.72997I
b = −0.383521 − 1.052400I
−0.66968 + 1.34659I 0
u = −0.462793 − 0.789203I
a = 1.94590 − 0.72997I
b = −0.383521 + 1.052400I
−0.66968 − 1.34659I 0
u = −0.100143 + 0.905993I
a = −2.03793 + 0.42379I
b = 0.613296 + 0.753156I
3.23144 − 0.92093I 0
u = −0.100143 − 0.905993I
a = −2.03793 − 0.42379I
b = 0.613296 − 0.753156I
3.23144 + 0.92093I 0
u = 0.819623 + 0.726122I
a = 0.365501 + 0.230418I
b = 0.20556 + 1.48772I
−7.23484 − 0.77529I 0
u = 0.819623 − 0.726122I
a = 0.365501 − 0.230418I
b = 0.20556 − 1.48772I
−7.23484 + 0.77529I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.303048 + 0.851736I
a = −1.88227 − 1.10824I
b = 1.226900 − 0.082101I
4.36049 − 2.15843I 0
u = 0.303048 − 0.851736I
a = −1.88227 + 1.10824I
b = 1.226900 + 0.082101I
4.36049 + 2.15843I 0
u = 0.096694 + 1.151330I
a = 1.317440 − 0.057645I
b = −0.898102 − 0.440443I
0.102335 − 0.805883I 0
u = 0.096694 − 1.151330I
a = 1.317440 + 0.057645I
b = −0.898102 + 0.440443I
0.102335 + 0.805883I 0
u = −0.699295 + 0.395601I
a = 3.21229 − 2.97384I
b = 0.10447 − 1.70528I
−7.31286 + 5.25289I −4.83806 − 7.69489I
u = −0.699295 − 0.395601I
a = 3.21229 + 2.97384I
b = 0.10447 + 1.70528I
−7.31286 − 5.25289I −4.83806 + 7.69489I
u = 0.578459 + 0.528250I
a = 1.13288 + 1.69205I
b = 0.089527 + 0.178860I
−0.57429 − 6.85107I 2.69108 − 1.63480I
u = 0.578459 − 0.528250I
a = 1.13288 − 1.69205I
b = 0.089527 − 0.178860I
−0.57429 + 6.85107I 2.69108 + 1.63480I
u = −0.726408 + 0.292025I
a = 0.290860 + 0.066462I
b = −0.087141 − 1.137640I
−2.39617 + 2.63265I 0. − 3.56398I
u = −0.726408 − 0.292025I
a = 0.290860 − 0.066462I
b = −0.087141 + 1.137640I
−2.39617 − 2.63265I 0. + 3.56398I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.389609 + 0.672619I
a = −0.312060 − 0.644701I
b = −0.10406 + 1.55102I
−5.28113 + 6.02668I −0.83509 − 9.93765I
u = −0.389609 − 0.672619I
a = −0.312060 + 0.644701I
b = −0.10406 − 1.55102I
−5.28113 − 6.02668I −0.83509 + 9.93765I
u = −1.227010 + 0.083228I
a = −0.228622 − 0.202291I
b = 0.125008 − 1.085830I
−6.76066 + 0.17831I 0
u = −1.227010 − 0.083228I
a = −0.228622 + 0.202291I
b = 0.125008 + 1.085830I
−6.76066 − 0.17831I 0
u = 0.213840 + 0.716879I
a = 2.94719 − 3.15470I
b = −0.10463 + 1.62106I
−4.77668 − 4.91554I 5.80425 + 7.31495I
u = 0.213840 − 0.716879I
a = 2.94719 + 3.15470I
b = −0.10463 − 1.62106I
−4.77668 + 4.91554I 5.80425 − 7.31495I
u = −0.845531 + 0.931008I
a = −0.790053 + 0.732156I
b = 0.887959 + 0.172806I
−2.10266 + 4.70360I 0
u = −0.845531 − 0.931008I
a = −0.790053 − 0.732156I
b = 0.887959 − 0.172806I
−2.10266 − 4.70360I 0
u = 0.749079 + 1.025990I
a = 1.47656 + 0.10493I
b = −0.27067 + 1.41969I
−6.33650 − 5.10935I 0
u = 0.749079 − 1.025990I
a = 1.47656 − 0.10493I
b = −0.27067 − 1.41969I
−6.33650 + 5.10935I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.646385 + 1.094070I
a = −1.088150 − 0.099223I
b = 0.582063 + 0.903467I
−3.13677 + 5.80187I 0
u = −0.646385 − 1.094070I
a = −1.088150 + 0.099223I
b = 0.582063 − 0.903467I
−3.13677 − 5.80187I 0
u = −0.862329 + 0.934321I
a = 0.528921 − 0.207487I
b = −0.651249 + 0.150043I
−2.11824 + 1.66557I 0
u = −0.862329 − 0.934321I
a = 0.528921 + 0.207487I
b = −0.651249 − 0.150043I
−2.11824 − 1.66557I 0
u = −0.366398 + 1.230750I
a = −1.44997 − 0.60149I
b = 0.645386 + 1.088180I
2.07065 + 5.92091I 0
u = −0.366398 − 1.230750I
a = −1.44997 + 0.60149I
b = 0.645386 − 1.088180I
2.07065 − 5.92091I 0
u = 0.542418 + 0.448908I
a = −0.808272 − 0.209146I
b = 0.410061 + 0.391443I
−2.49574 − 1.83560I 0.724028 + 0.349432I
u = 0.542418 − 0.448908I
a = −0.808272 + 0.209146I
b = 0.410061 − 0.391443I
−2.49574 + 1.83560I 0.724028 − 0.349432I
u = 0.962244 + 0.895870I
a = −1.59591 − 0.91749I
b = 0.86805 − 1.72981I
−13.1403 − 7.5526I 0
u = 0.962244 − 0.895870I
a = −1.59591 + 0.91749I
b = 0.86805 + 1.72981I
−13.1403 + 7.5526I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.069690 + 0.791365I
a = −0.263944 + 0.770014I
b = 1.58821 − 0.26194I
−8.81768 − 1.56510I 0
u = −1.069690 − 0.791365I
a = −0.263944 − 0.770014I
b = 1.58821 + 0.26194I
−8.81768 + 1.56510I 0
u = 0.880487 + 1.028230I
a = −0.277301 + 0.180815I
b = −0.80666 − 1.79638I
−12.69480 + 0.72849I 0
u = 0.880487 − 1.028230I
a = −0.277301 − 0.180815I
b = −0.80666 + 1.79638I
−12.69480 − 0.72849I 0
u = −0.353207 + 0.522372I
a = 0.740973 − 0.001919I
b = −0.218396 − 0.458164I
0.013980 + 1.160290I 0.33727 − 6.21213I
u = −0.353207 − 0.522372I
a = 0.740973 + 0.001919I
b = −0.218396 + 0.458164I
0.013980 − 1.160290I 0.33727 + 6.21213I
u = 1.159320 + 0.750807I
a = 1.09132 + 1.27721I
b = 0.14334 + 1.62386I
−13.52490 − 0.33649I 0
u = 1.159320 − 0.750807I
a = 1.09132 − 1.27721I
b = 0.14334 − 1.62386I
−13.52490 + 0.33649I 0
u = 1.016470 + 0.943389I
a = −1.58614 − 0.92505I
b = 0.32907 − 1.59367I
−8.30955 − 9.31916I 0
u = 1.016470 − 0.943389I
a = −1.58614 + 0.92505I
b = 0.32907 + 1.59367I
−8.30955 + 9.31916I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.88767 + 1.12945I
a = 0.894183 − 0.834230I
b = −1.75669 − 0.19726I
−7.72019 + 8.70253I 0
u = −0.88767 − 1.12945I
a = 0.894183 + 0.834230I
b = −1.75669 + 0.19726I
−7.72019 − 8.70253I 0
u = −0.19030 + 1.43376I
a = −1.377440 + 0.014744I
b = 0.430237 + 0.966969I
5.90567 + 1.67066I 0
u = −0.19030 − 1.43376I
a = −1.377440 − 0.014744I
b = 0.430237 − 0.966969I
5.90567 − 1.67066I 0
u = 0.97104 + 1.08776I
a = 0.027310 − 0.524556I
b = −0.29576 − 1.54330I
−7.89118 + 2.00203I 0
u = 0.97104 − 1.08776I
a = 0.027310 + 0.524556I
b = −0.29576 + 1.54330I
−7.89118 − 2.00203I 0
u = 1.22860 + 0.80379I
a = −0.240704 − 0.351393I
b = 0.06321 − 1.44996I
−11.44520 − 3.42440I 0
u = 1.22860 − 0.80379I
a = −0.240704 + 0.351393I
b = 0.06321 + 1.44996I
−11.44520 + 3.42440I 0
u = −1.27855 + 0.76471I
a = 0.236161 − 0.267489I
b = 0.284369 − 0.193813I
−6.77295 + 2.33302I 0
u = −1.27855 − 0.76471I
a = 0.236161 + 0.267489I
b = 0.284369 + 0.193813I
−6.77295 − 2.33302I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.19349 + 0.89404I
a = 0.064960 + 0.216012I
b = 0.64253 + 1.62640I
−14.6713 + 9.2496I 0
u = 1.19349 − 0.89404I
a = 0.064960 − 0.216012I
b = 0.64253 − 1.62640I
−14.6713 − 9.2496I 0
u = 0.97522 + 1.14997I
a = 1.47478 + 0.52261I
b = −0.65420 + 1.69757I
−13.7557 − 17.0492I 0
u = 0.97522 − 1.14997I
a = 1.47478 − 0.52261I
b = −0.65420 − 1.69757I
−13.7557 + 17.0492I 0
u = 0.90961 + 1.20942I
a = 0.405035 + 0.724327I
b = −0.08439 + 1.59694I
−12.04370 − 7.15684I 0
u = 0.90961 − 1.20942I
a = 0.405035 − 0.724327I
b = −0.08439 − 1.59694I
−12.04370 + 7.15684I 0
u = 0.292039 + 0.374863I
a = 2.29251 + 4.43476I
b = −1.352360 + 0.155525I
2.85372 − 0.29029I −2.55127 − 11.86076I
u = 0.292039 − 0.374863I
a = 2.29251 − 4.43476I
b = −1.352360 − 0.155525I
2.85372 + 0.29029I −2.55127 + 11.86076I
u = 1.04570 + 1.18848I
a = −0.845910 − 0.168170I
b = −0.09756 − 1.49247I
−10.29390 − 4.70406I 0
u = 1.04570 − 1.18848I
a = −0.845910 + 0.168170I
b = −0.09756 + 1.49247I
−10.29390 + 4.70406I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.51769 + 1.53041I
a = 1.010180 + 0.184391I
b = −0.685735 − 1.129040I
−1.96971 + 6.53864I 0
u = −0.51769 − 1.53041I
a = 1.010180 − 0.184391I
b = −0.685735 + 1.129040I
−1.96971 − 6.53864I 0
u = −1.07949 + 1.23119I
a = −0.150197 − 0.200956I
b = −0.218385 − 0.170130I
−5.35295 + 6.03316I 0
u = −1.07949 − 1.23119I
a = −0.150197 + 0.200956I
b = −0.218385 + 0.170130I
−5.35295 − 6.03316I 0
u = 0.063591 + 0.355845I
a = −3.07917 − 2.53685I
b = −0.453391 − 0.046277I
2.07593 + 0.66087I 1.35169 − 2.61583I
u = 0.063591 − 0.355845I
a = −3.07917 + 2.53685I
b = −0.453391 + 0.046277I
2.07593 − 0.66087I 1.35169 + 2.61583I
u = 0.120818 + 0.330295I
a = 3.33005 + 0.04070I
b = −0.13948 + 1.54899I
−6.96880 − 2.54329I −2.34300 + 2.14779I
u = 0.120818 − 0.330295I
a = 3.33005 − 0.04070I
b = −0.13948 − 1.54899I
−6.96880 + 2.54329I −2.34300 − 2.14779I
u = 0.196647 + 0.242071I
a = −0.20585 − 6.91105I
b = −0.319550 + 0.356310I
1.89096 − 1.13098I 11.56539 + 0.21415I
u = 0.196647 − 0.242071I
a = −0.20585 + 6.91105I
b = −0.319550 − 0.356310I
1.89096 + 1.13098I 11.56539 − 0.21415I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.006054 + 0.240892I
a = −1.60761 + 1.00420I
b = −0.224096 + 1.245980I
−1.89830 − 3.55331I −1.6638 + 14.9075I
u = 0.006054 − 0.240892I
a = −1.60761 − 1.00420I
b = −0.224096 − 1.245980I
−1.89830 + 3.55331I −1.6638 − 14.9075I
13
II.
I
u
2
= h−2.15×10
33
u
37
−1.69×10
34
u
36
+· · ·+4.97×10
32
b−1.06×10
33
, 3.40×
10
33
u
37
+2.66×10
34
u
36
+· · ·+4.97×10
32
a+3.48×10
33
, u
38
+8u
37
+· · ·+7u+1i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
−6.84294u
37
− 53.5042u
36
+ ··· − 68.5747u − 7.00288
4.32182u
37
+ 33.9487u
36
+ ··· + 32.5932u + 2.13372
a
9
=
−3.65625u
37
− 24.2459u
36
+ ··· + 65.6553u + 9.21327
−0.343247u
37
− 0.716353u
36
+ ··· + 18.4677u + 4.74862
a
12
=
−2.52112u
37
− 19.5555u
36
+ ··· − 35.9815u − 4.86916
4.32182u
37
+ 33.9487u
36
+ ··· + 32.5932u + 2.13372
a
1
=
4.41538u
37
+ 35.3801u
36
+ ··· + 6.32562u − 1.24235
1.08405u
37
+ 10.1404u
36
+ ··· + 69.0262u + 11.2632
a
4
=
u
u
3
+ u
a
2
=
4.79819u
37
+ 37.9855u
36
+ ··· + 17.5569u + 0.749907
1.58195u
37
+ 13.8929u
36
+ ··· + 83.0743u + 13.7126
a
3
=
4.79819u
37
+ 37.9855u
36
+ ··· + 17.5569u + 0.749907
2.08366u
37
+ 18.2615u
36
+ ··· + 85.0723u + 13.3125
a
6
=
−1.04766u
37
− 10.7229u
36
+ ··· − 149.836u − 22.5274
−1.19355u
37
− 10.7078u
36
+ ··· − 10.3382u − 3.56641
a
10
=
2.65630u
37
+ 25.1708u
36
+ ··· + 62.8045u + 8.32877
1.77577u
37
+ 18.1344u
36
+ ··· + 102.376u + 16.9761
(ii) Obstruction class = 1
(iii) Cusp Shapes = −18.4365u
37
− 139.394u
36
+ ··· + 32.3432u + 20.9166
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
38
− 17u
37
+ ··· − 622u + 113
c
2
u
38
− u
37
+ ··· + 2u + 1
c
3
u
38
− u
37
+ ··· − 8u + 3
c
4
u
38
− 8u
37
+ ··· − 7u + 1
c
5
u
38
+ u
37
+ ··· − 2u + 1
c
6
u
38
− u
37
+ ··· − u + 3
c
7
u
38
+ 8u
37
+ ··· + 7u + 1
c
8
u
38
+ 6u
37
+ ··· − u + 1
c
9
u
38
+ u
37
+ ··· + 8u + 3
c
10
u
38
+ 7u
37
+ ··· − 2u + 1
c
11
u
38
+ u
37
+ ··· + u + 3
c
12
u
38
+ u
37
+ ··· + 110u + 89
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
− 31y
37
+ ··· − 367222y + 12769
c
2
, c
5
y
38
+ 3y
37
+ ··· − 14y + 1
c
3
, c
9
y
38
− 23y
37
+ ··· − 244y + 9
c
4
, c
7
y
38
+ 18y
37
+ ··· + 31y + 1
c
6
, c
11
y
38
+ 23y
37
+ ··· + 221y + 9
c
8
y
38
− 6y
37
+ ··· + 9y + 1
c
10
y
38
− 13y
37
+ ··· + 32y + 1
c
12
y
38
− 7y
37
+ ··· − 169808y + 7921
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.352789 + 0.866549I
a = 1.74784 + 0.95527I
b = −1.45792 + 0.06474I
3.95057 − 2.14775I −4.78032 + 3.77933I
u = 0.352789 − 0.866549I
a = 1.74784 − 0.95527I
b = −1.45792 − 0.06474I
3.95057 + 2.14775I −4.78032 − 3.77933I
u = −0.629027 + 0.687461I
a = 1.29753 − 1.46383I
b = −0.346037 − 0.507884I
−0.61277 + 7.33934I 1.7844 − 14.3872I
u = −0.629027 − 0.687461I
a = 1.29753 + 1.46383I
b = −0.346037 + 0.507884I
−0.61277 − 7.33934I 1.7844 + 14.3872I
u = −0.101139 + 0.897836I
a = −2.09405 + 0.51061I
b = 0.831878 + 0.573687I
2.79247 − 0.02816I 4.78465 − 3.03175I
u = −0.101139 − 0.897836I
a = −2.09405 − 0.51061I
b = 0.831878 − 0.573687I
2.79247 + 0.02816I 4.78465 + 3.03175I
u = 0.632844 + 0.917160I
a = −0.021342 − 0.196794I
b = −0.24191 − 1.52062I
−7.01708 + 0.55312I 0
u = 0.632844 − 0.917160I
a = −0.021342 + 0.196794I
b = −0.24191 + 1.52062I
−7.01708 − 0.55312I 0
u = −0.877524 + 0.699983I
a = −0.189971 + 0.127566I
b = 0.173812 − 0.815821I
−3.98950 + 3.38487I 0
u = −0.877524 − 0.699983I
a = −0.189971 − 0.127566I
b = 0.173812 + 0.815821I
−3.98950 − 3.38487I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.353345 + 1.083630I
a = 1.089930 − 0.598891I
b = −0.363056 − 0.740660I
0.86108 − 3.29316I 0
u = −0.353345 − 1.083630I
a = 1.089930 + 0.598891I
b = −0.363056 + 0.740660I
0.86108 + 3.29316I 0
u = −0.313695 + 0.770845I
a = −1.87038 + 0.30882I
b = −0.021223 + 0.432106I
2.46341 + 2.12648I 2.90240 − 5.27421I
u = −0.313695 − 0.770845I
a = −1.87038 − 0.30882I
b = −0.021223 − 0.432106I
2.46341 − 2.12648I 2.90240 + 5.27421I
u = 0.691018 + 1.038320I
a = −1.55280 + 0.11680I
b = 0.227951 − 1.392460I
−6.47040 − 5.59268I 0
u = 0.691018 − 1.038320I
a = −1.55280 − 0.11680I
b = 0.227951 + 1.392460I
−6.47040 + 5.59268I 0
u = −0.785751 + 1.079380I
a = 1.013560 − 0.146565I
b = −0.504573 − 0.542120I
−2.87110 + 2.81960I 0
u = −0.785751 − 1.079380I
a = 1.013560 + 0.146565I
b = −0.504573 + 0.542120I
−2.87110 − 2.81960I 0
u = −0.388723 + 1.277330I
a = −1.38052 − 0.50044I
b = 0.781808 + 1.052230I
1.43213 + 6.12968I 0
u = −0.388723 − 1.277330I
a = −1.38052 + 0.50044I
b = 0.781808 − 1.052230I
1.43213 − 6.12968I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.475743 + 0.330989I
a = −0.65399 + 4.68543I
b = 0.315408 + 0.726183I
1.52090 + 1.37055I −3.68681 − 9.43784I
u = −0.475743 − 0.330989I
a = −0.65399 − 4.68543I
b = 0.315408 − 0.726183I
1.52090 − 1.37055I −3.68681 + 9.43784I
u = −1.32070 + 0.55561I
a = −0.322060 − 0.082392I
b = −0.301072 + 0.813070I
−7.34031 + 1.79730I 0
u = −1.32070 − 0.55561I
a = −0.322060 + 0.082392I
b = −0.301072 − 0.813070I
−7.34031 − 1.79730I 0
u = −0.37905 + 1.38204I
a = 1.081510 + 0.406701I
b = −0.518632 − 1.152720I
−0.88392 + 6.83150I 0
u = −0.37905 − 1.38204I
a = 1.081510 − 0.406701I
b = −0.518632 + 1.152720I
−0.88392 − 6.83150I 0
u = 0.226714 + 0.484618I
a = −4.54772 − 4.12122I
b = 1.288630 − 0.043223I
2.95519 − 0.51266I 13.2029 + 16.8835I
u = 0.226714 − 0.484618I
a = −4.54772 + 4.12122I
b = 1.288630 + 0.043223I
2.95519 + 0.51266I 13.2029 − 16.8835I
u = −0.223592 + 0.482018I
a = −0.166910 + 0.346503I
b = −0.260798 + 1.336940I
−1.80869 − 3.25226I 5.74296 − 8.83230I
u = −0.223592 − 0.482018I
a = −0.166910 − 0.346503I
b = −0.260798 − 1.336940I
−1.80869 + 3.25226I 5.74296 + 8.83230I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22202 + 1.47524I
a = −1.326600 + 0.059140I
b = 0.416637 + 0.999305I
5.77418 + 1.60449I 0
u = −0.22202 − 1.47524I
a = −1.326600 − 0.059140I
b = 0.416637 − 0.999305I
5.77418 − 1.60449I 0
u = 1.14464 + 0.99621I
a = 0.562780 + 0.396717I
b = −0.04204 + 1.52291I
−11.12780 − 4.08584I 0
u = 1.14464 − 0.99621I
a = 0.562780 − 0.396717I
b = −0.04204 − 1.52291I
−11.12780 + 4.08584I 0
u = 0.042712 + 0.378769I
a = 1.19454 + 4.71439I
b = −0.04195 − 1.66698I
−5.69981 − 4.89986I −3.76261 + 4.32816I
u = 0.042712 − 0.378769I
a = 1.19454 − 4.71439I
b = −0.04195 + 1.66698I
−5.69981 + 4.89986I −3.76261 − 4.32816I
u = −1.02039 + 1.29488I
a = −0.361341 + 0.091755I
b = 0.563084 + 0.458672I
−5.18233 + 6.46286I 0
u = −1.02039 − 1.29488I
a = −0.361341 − 0.091755I
b = 0.563084 − 0.458672I
−5.18233 − 6.46286I 0
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
38
− 17u
37
+ ··· − 622u + 113)
· (u
82
− 2u
81
+ ··· − 144006814u + 92506631)
c
2
(u
38
− u
37
+ ··· + 2u + 1)
· (u
82
+ 8u
81
+ ··· + 285305320u + 28654393)
c
3
(u
38
− u
37
+ ··· − 8u + 3)(u
82
− 2u
81
+ ··· + 3176u + 3053)
c
4
(u
38
− 8u
37
+ ··· − 7u + 1)(u
82
− 5u
81
+ ··· − 9u + 1)
c
5
(u
38
+ u
37
+ ··· − 2u + 1)
· (u
82
+ 8u
81
+ ··· + 285305320u + 28654393)
c
6
(u
38
− u
37
+ ··· − u + 3)(u
82
− 2u
81
+ ··· − 1903u + 193)
c
7
(u
38
+ 8u
37
+ ··· + 7u + 1)(u
82
− 5u
81
+ ··· − 9u + 1)
c
8
(u
38
+ 6u
37
+ ··· − u + 1)(u
82
+ 3u
81
+ ··· − 14399u + 1273)
c
9
(u
38
+ u
37
+ ··· + 8u + 3)(u
82
− 2u
81
+ ··· + 3176u + 3053)
c
10
(u
38
+ 7u
37
+ ··· − 2u + 1)(u
82
+ 4u
81
+ ··· + 1322u + 307)
c
11
(u
38
+ u
37
+ ··· + u + 3)(u
82
− 2u
81
+ ··· − 1903u + 193)
c
12
(u
38
+ u
37
+ ··· + 110u + 89)
· (u
82
− 4u
81
+ ··· − 360727464u + 76941877)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
38
− 31y
37
+ ··· − 367222y + 12769)
· (y
82
− 86y
81
+ ··· − 27578920347511596y + 8557476778970161)
c
2
, c
5
(y
38
+ 3y
37
+ ··· − 14y + 1)
· (y
82
+ 84y
81
+ ··· − 16527381541916668y + 821074238198449)
c
3
, c
9
(y
38
− 23y
37
+ ··· − 244y + 9)
· (y
82
− 70y
81
+ ··· − 64668510y + 9320809)
c
4
, c
7
(y
38
+ 18y
37
+ ··· + 31y + 1)(y
82
+ 19y
81
+ ··· + 81y + 1)
c
6
, c
11
(y
38
+ 23y
37
+ ··· + 221y + 9)(y
82
+ 76y
81
+ ··· − 3045y + 37249)
c
8
(y
38
− 6y
37
+ ··· + 9y + 1)
· (y
82
+ 19y
81
+ ··· + 35322967y + 1620529)
c
10
(y
38
− 13y
37
+ ··· + 32y + 1)(y
82
+ 4y
81
+ ··· + 789978y + 94249)
c
12
(y
38
− 7y
37
+ ··· − 169808y + 7921)
· (y
82
+ 38y
81
+ ··· + 86506044299292766y + 5920052436283129)
24
