12a
1168
(K12a
1168
)
A knot diagram
1
Linearized knot diagam
4 10 7 9 11 3 12 1 2 5 6 8
Solving Sequence
5,10
11
3,6
7 12 2 9 4 1 8
c
10
c
5
c
6
c
11
c
2
c
9
c
4
c
1
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.02112 × 10
219
u
97
+ 2.42861 × 10
219
u
96
+ ··· + 1.88853 × 10
219
b + 4.15398 × 10
220
,
7.40552 × 10
221
u
97
− 1.66364 × 10
222
u
96
+ ··· + 8.12069 × 10
220
a − 2.62723 × 10
223
,
u
98
− u
97
+ ··· + 396u − 43i
I
u
2
= h−18u
20
+ 35u
19
+ ··· + 31b + 81, −29u
20
+ 3u
19
+ ··· + 31a + 84, u
21
− 12u
19
+ ··· − u − 1i
* 2 irreducible components of dim
C
= 0, with total 119 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−1.02 × 10
219
u
97
+ 2.43 × 10
219
u
96
+ · · · + 1.89 × 10
219
b + 4.15 ×
10
220
, 7.41 × 10
221
u
97
− 1.66 × 10
222
u
96
+ · · · + 8.12 × 10
220
a − 2.63 ×
10
223
, u
98
− u
97
+ · · · + 396u − 43i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
3
=
−9.11932u
97
+ 20.4864u
96
+ ··· − 3188.58u + 323.523
0.540697u
97
− 1.28598u
96
+ ··· + 214.779u − 21.9958
a
6
=
u
−u
3
+ u
a
7
=
−8.60049u
97
+ 19.0570u
96
+ ··· − 2814.24u + 268.683
−3.34750u
97
+ 7.42210u
96
+ ··· − 1148.85u + 116.947
a
12
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−8.57862u
97
+ 19.2004u
96
+ ··· − 2973.80u + 301.528
0.540697u
97
− 1.28598u
96
+ ··· + 214.779u − 21.9958
a
9
=
−6.09442u
97
+ 13.8926u
96
+ ··· − 2230.11u + 230.240
1.83837u
97
− 4.17749u
96
+ ··· + 651.713u − 66.9090
a
4
=
−2.31310u
97
+ 5.17198u
96
+ ··· − 655.200u + 50.8427
5.33139u
97
− 11.6945u
96
+ ··· + 1763.76u − 172.869
a
1
=
−1.29885u
97
+ 2.94361u
96
+ ··· − 318.314u + 17.2269
1.39998u
97
− 3.01976u
96
+ ··· + 427.622u − 39.1893
a
8
=
−6.34467u
97
+ 13.9931u
96
+ ··· − 2044.24u + 193.324
−0.534636u
97
+ 1.09416u
96
+ ··· − 173.613u + 19.4352
(ii) Obstruction class = −1
(iii) Cusp Shapes = 19.4904u
97
− 44.0633u
96
+ ··· + 7002.50u − 705.505
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
98
− u
97
+ ··· + 5u − 1
c
2
, c
9
u
98
− 33u
96
+ ··· − 1246u − 76
c
3
, c
6
u
98
− 2u
97
+ ··· − 6u + 1
c
4
u
98
+ 3u
97
+ ··· − 1183u − 187
c
5
, c
10
, c
11
u
98
− u
97
+ ··· + 396u − 43
c
7
, c
8
, c
12
u
98
+ 3u
97
+ ··· + 32u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
98
− 3y
97
+ ··· + 173y + 1
c
2
, c
9
y
98
− 66y
97
+ ··· − 1035260y + 5776
c
3
, c
6
y
98
− 54y
97
+ ··· + 132y + 1
c
4
y
98
− 25y
97
+ ··· − 1527771y + 34969
c
5
, c
10
, c
11
y
98
− 97y
97
+ ··· + 29288y + 1849
c
7
, c
8
, c
12
y
98
− 105y
97
+ ··· − 568y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.438752 + 0.891193I
a = 0.362502 + 0.686195I
b = 1.303190 − 0.450763I
−5.41570 + 8.09818I 0
u = 0.438752 − 0.891193I
a = 0.362502 − 0.686195I
b = 1.303190 + 0.450763I
−5.41570 − 8.09818I 0
u = 0.391864 + 0.898326I
a = 0.903543 − 0.068277I
b = 0.528510 − 0.233621I
4.41768 − 2.63930I 0
u = 0.391864 − 0.898326I
a = 0.903543 + 0.068277I
b = 0.528510 + 0.233621I
4.41768 + 2.63930I 0
u = 0.391411 + 0.898450I
a = 0.580518 − 0.049871I
b = 0.939209 + 0.499556I
2.92084 − 1.91064I 0
u = 0.391411 − 0.898450I
a = 0.580518 + 0.049871I
b = 0.939209 − 0.499556I
2.92084 + 1.91064I 0
u = 0.938750 + 0.254685I
a = 0.112409 + 0.225776I
b = 1.381750 − 0.029759I
1.79041 − 0.16871I 0
u = 0.938750 − 0.254685I
a = 0.112409 − 0.225776I
b = 1.381750 + 0.029759I
1.79041 + 0.16871I 0
u = −0.852144 + 0.390335I
a = 0.578814 − 0.432802I
b = −0.246807 + 0.692959I
6.86100 − 2.05030I 0
u = −0.852144 − 0.390335I
a = 0.578814 + 0.432802I
b = −0.246807 − 0.692959I
6.86100 + 2.05030I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.915479
a = −1.31935
b = 1.49906
−5.21283 0
u = −0.058479 + 0.894470I
a = 0.577736 − 0.337542I
b = 0.458079 + 0.502884I
4.16131 − 2.22766I 0
u = −0.058479 − 0.894470I
a = 0.577736 + 0.337542I
b = 0.458079 − 0.502884I
4.16131 + 2.22766I 0
u = −0.446241 + 1.029130I
a = −0.434185 + 0.599991I
b = −1.262990 − 0.482764I
1.37895 − 11.98030I 0
u = −0.446241 − 1.029130I
a = −0.434185 − 0.599991I
b = −1.262990 + 0.482764I
1.37895 + 11.98030I 0
u = 0.792923 + 0.793440I
a = 0.282718 − 0.510672I
b = −1.156990 − 0.219396I
−4.42238 − 2.43268I 0
u = 0.792923 − 0.793440I
a = 0.282718 + 0.510672I
b = −1.156990 + 0.219396I
−4.42238 + 2.43268I 0
u = 1.132050 + 0.247239I
a = −0.15095 − 2.01792I
b = −1.047450 + 0.584414I
4.99022 + 6.27593I 0
u = 1.132050 − 0.247239I
a = −0.15095 + 2.01792I
b = −1.047450 − 0.584414I
4.99022 − 6.27593I 0
u = −0.456258 + 0.670176I
a = −0.171983 + 0.785584I
b = −1.36966 − 0.40803I
−5.36300 − 2.92221I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.456258 − 0.670176I
a = −0.171983 − 0.785584I
b = −1.36966 + 0.40803I
−5.36300 + 2.92221I 0
u = −0.106869 + 0.787117I
a = −0.807532 − 0.213605I
b = −0.822220 + 0.300167I
−1.42261 + 1.54220I 0
u = −0.106869 − 0.787117I
a = −0.807532 + 0.213605I
b = −0.822220 − 0.300167I
−1.42261 − 1.54220I 0
u = 0.513550 + 0.603793I
a = −0.410518 + 0.368788I
b = 0.041349 − 0.849349I
5.22586 + 7.17879I 0
u = 0.513550 − 0.603793I
a = −0.410518 − 0.368788I
b = 0.041349 + 0.849349I
5.22586 − 7.17879I 0
u = 1.210380 + 0.055278I
a = −0.64806 − 1.90999I
b = 0.729911 + 0.089716I
6.09977 + 5.59032I 0
u = 1.210380 − 0.055278I
a = −0.64806 + 1.90999I
b = 0.729911 − 0.089716I
6.09977 − 5.59032I 0
u = −1.22310
a = −0.188603
b = −1.50392
−3.65106 0
u = 0.774695
a = 0.494111
b = 0.985875
2.30370 4.50380
u = −1.245610 + 0.001635I
a = 0.11423 + 1.54880I
b = −0.806424 − 0.186193I
1.05719 + 2.40310I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.245610 − 0.001635I
a = 0.11423 − 1.54880I
b = −0.806424 + 0.186193I
1.05719 − 2.40310I 0
u = −0.397002 + 0.606555I
a = −0.06672 − 1.47204I
b = 1.206540 − 0.037207I
−5.34711 − 1.16504I −5.89004 + 4.77110I
u = −0.397002 − 0.606555I
a = −0.06672 + 1.47204I
b = 1.206540 + 0.037207I
−5.34711 + 1.16504I −5.89004 − 4.77110I
u = 0.197358 + 0.695563I
a = −1.05863 − 1.44758I
b = −1.209490 + 0.094174I
−0.50881 + 3.77042I −1.22991 − 5.05475I
u = 0.197358 − 0.695563I
a = −1.05863 + 1.44758I
b = −1.209490 − 0.094174I
−0.50881 − 3.77042I −1.22991 + 5.05475I
u = −1.289390 + 0.036606I
a = −0.57450 − 1.79709I
b = 1.16868 + 0.84371I
1.64723 − 2.83590I 0
u = −1.289390 − 0.036606I
a = −0.57450 + 1.79709I
b = 1.16868 − 0.84371I
1.64723 + 2.83590I 0
u = 1.322300 + 0.134120I
a = 0.037004 + 1.012680I
b = 0.967591 − 0.296262I
2.99763 + 1.06282I 0
u = 1.322300 − 0.134120I
a = 0.037004 − 1.012680I
b = 0.967591 + 0.296262I
2.99763 − 1.06282I 0
u = −1.329790 + 0.051565I
a = 0.714474 − 1.092350I
b = −0.429983 + 0.762264I
6.66431 − 1.15467I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.329790 − 0.051565I
a = 0.714474 + 1.092350I
b = −0.429983 − 0.762264I
6.66431 + 1.15467I 0
u = 0.474672 + 0.455473I
a = −1.79909 − 1.37357I
b = −1.117410 + 0.415698I
4.31172 + 6.23668I 4.72015 − 6.34301I
u = 0.474672 − 0.455473I
a = −1.79909 + 1.37357I
b = −1.117410 − 0.415698I
4.31172 − 6.23668I 4.72015 + 6.34301I
u = 1.34546
a = 0.218883
b = 1.55069
1.09642 0
u = 1.370950 + 0.051265I
a = 1.02671 + 1.27373I
b = −1.64996 − 0.89336I
6.60733 + 2.66078I 0
u = 1.370950 − 0.051265I
a = 1.02671 − 1.27373I
b = −1.64996 + 0.89336I
6.60733 − 2.66078I 0
u = 1.384850 + 0.203389I
a = 0.14247 − 1.56229I
b = −1.252250 + 0.535982I
3.79747 + 6.54307I 0
u = 1.384850 − 0.203389I
a = 0.14247 + 1.56229I
b = −1.252250 − 0.535982I
3.79747 − 6.54307I 0
u = −1.378540 + 0.268996I
a = −0.36382 − 1.84575I
b = 1.103300 + 0.247597I
4.49819 − 7.25601I 0
u = −1.378540 − 0.268996I
a = −0.36382 + 1.84575I
b = 1.103300 − 0.247597I
4.49819 + 7.25601I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.996538 + 0.995942I
a = −0.147207 − 0.267647I
b = 1.054030 − 0.308627I
2.76808 + 5.25836I 0
u = −0.996538 − 0.995942I
a = −0.147207 + 0.267647I
b = 1.054030 + 0.308627I
2.76808 − 5.25836I 0
u = −1.412160 + 0.029118I
a = 0.57366 + 1.41669I
b = −0.398717 − 1.040950I
6.77476 + 1.07902I 0
u = −1.412160 − 0.029118I
a = 0.57366 − 1.41669I
b = −0.398717 + 1.040950I
6.77476 − 1.07902I 0
u = 1.40716 + 0.19956I
a = −0.442205 − 0.849721I
b = 0.591377 + 0.673716I
3.94160 + 1.46877I 0
u = 1.40716 − 0.19956I
a = −0.442205 + 0.849721I
b = 0.591377 − 0.673716I
3.94160 − 1.46877I 0
u = −0.251196 + 0.515381I
a = 1.77432 − 0.77605I
b = 1.081420 + 0.350458I
−1.42079 − 3.86409I 0.73110 + 8.65417I
u = −0.251196 − 0.515381I
a = 1.77432 + 0.77605I
b = 1.081420 − 0.350458I
−1.42079 + 3.86409I 0.73110 − 8.65417I
u = −1.37807 + 0.38773I
a = 0.048832 − 1.378100I
b = 0.969732 + 0.514999I
2.80879 − 6.07718I 0
u = −1.37807 − 0.38773I
a = 0.048832 + 1.378100I
b = 0.969732 − 0.514999I
2.80879 + 6.07718I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.192714 + 0.527897I
a = −0.968831 + 0.219684I
b = −0.933289 + 0.345314I
−1.44128 + 1.38418I 1.09886 + 2.24692I
u = −0.192714 − 0.527897I
a = −0.968831 − 0.219684I
b = −0.933289 − 0.345314I
−1.44128 − 1.38418I 1.09886 − 2.24692I
u = 1.43811 + 0.15125I
a = 0.11771 + 1.79107I
b = −0.04379 − 1.48336I
4.84521 + 5.36107I 0
u = 1.43811 − 0.15125I
a = 0.11771 − 1.79107I
b = −0.04379 + 1.48336I
4.84521 − 5.36107I 0
u = 1.43863 + 0.23949I
a = 0.69528 − 1.36386I
b = −0.966754 + 0.214159I
0.49710 + 4.31155I 0
u = 1.43863 − 0.23949I
a = 0.69528 + 1.36386I
b = −0.966754 − 0.214159I
0.49710 − 4.31155I 0
u = 0.537595
a = 3.07677
b = −0.133007
1.02611 14.3890
u = −0.212695 + 0.474080I
a = −1.25749 − 0.94890I
b = −0.144110 − 0.004155I
−1.49762 + 0.96898I −3.07162 + 1.33299I
u = −0.212695 − 0.474080I
a = −1.25749 + 0.94890I
b = −0.144110 + 0.004155I
−1.49762 − 0.96898I −3.07162 − 1.33299I
u = −1.47303 + 0.19946I
a = −0.086307 − 1.387760I
b = 1.37450 + 0.50369I
10.59140 − 8.83976I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.47303 − 0.19946I
a = −0.086307 + 1.387760I
b = 1.37450 − 0.50369I
10.59140 + 8.83976I 0
u = −0.328199 + 0.393122I
a = 0.615651 + 0.634354I
b = −0.242216 − 0.946347I
−0.88687 − 3.29713I 2.45536 + 10.56224I
u = −0.328199 − 0.393122I
a = 0.615651 − 0.634354I
b = −0.242216 + 0.946347I
−0.88687 + 3.29713I 2.45536 − 10.56224I
u = 0.455525 + 0.197947I
a = −0.521523 − 0.188750I
b = 0.262790 + 0.470646I
0.912741 + 0.481311I 9.01303 − 2.84195I
u = 0.455525 − 0.197947I
a = −0.521523 + 0.188750I
b = 0.262790 − 0.470646I
0.912741 − 0.481311I 9.01303 + 2.84195I
u = −1.49369 + 0.22603I
a = −0.24576 + 1.48020I
b = 0.086302 − 1.305070I
11.7083 − 10.2755I 0
u = −1.49369 − 0.22603I
a = −0.24576 − 1.48020I
b = 0.086302 + 1.305070I
11.7083 + 10.2755I 0
u = 1.50061 + 0.25185I
a = −0.75687 + 1.44958I
b = 1.42098 − 0.76085I
1.01132 + 6.33366I 0
u = 1.50061 − 0.25185I
a = −0.75687 − 1.44958I
b = 1.42098 + 0.76085I
1.01132 − 6.33366I 0
u = 1.45419 + 0.47323I
a = −0.169611 − 1.187990I
b = −0.880839 + 0.622003I
8.89047 + 7.50896I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45419 − 0.47323I
a = −0.169611 + 1.187990I
b = −0.880839 − 0.622003I
8.89047 − 7.50896I 0
u = −1.50465 + 0.33444I
a = 0.46537 + 1.50163I
b = −1.37280 − 0.67976I
0.83454 − 12.54040I 0
u = −1.50465 − 0.33444I
a = 0.46537 − 1.50163I
b = −1.37280 + 0.67976I
0.83454 + 12.54040I 0
u = −1.52625 + 0.25451I
a = 0.348897 − 0.782798I
b = −0.685228 + 0.790126I
9.49483 − 2.22841I 0
u = −1.52625 − 0.25451I
a = 0.348897 + 0.782798I
b = −0.685228 − 0.790126I
9.49483 + 2.22841I 0
u = −1.54653 + 0.16048I
a = −0.906041 − 0.650789I
b = 0.876050 + 0.099100I
3.84707 − 0.63312I 0
u = −1.54653 − 0.16048I
a = −0.906041 + 0.650789I
b = 0.876050 − 0.099100I
3.84707 + 0.63312I 0
u = 1.57420 + 0.05203I
a = −0.234381 − 1.161370I
b = −0.034751 + 0.993551I
14.9919 + 3.4450I 0
u = 1.57420 − 0.05203I
a = −0.234381 + 1.161370I
b = −0.034751 − 0.993551I
14.9919 − 3.4450I 0
u = 1.52801 + 0.38258I
a = −0.30158 + 1.46885I
b = 1.37760 − 0.65580I
7.6986 + 17.0468I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52801 − 0.38258I
a = −0.30158 − 1.46885I
b = 1.37760 + 0.65580I
7.6986 − 17.0468I 0
u = −1.56430 + 0.22600I
a = 0.190500 + 0.832144I
b = −1.157610 − 0.482699I
11.37440 − 1.57267I 0
u = −1.56430 − 0.22600I
a = 0.190500 − 0.832144I
b = −1.157610 + 0.482699I
11.37440 + 1.57267I 0
u = −1.62892
a = 1.44958
b = −2.05605
10.4262 0
u = 0.205747
a = 8.19845
b = −1.30217
−2.91352 −6.84150
u = 0.038209 + 0.193422I
a = −1.13932 + 3.29511I
b = 1.181660 − 0.747103I
2.10943 − 1.86396I 6.2079 + 13.3345I
u = 0.038209 − 0.193422I
a = −1.13932 − 3.29511I
b = 1.181660 + 0.747103I
2.10943 + 1.86396I 6.2079 − 13.3345I
u = 1.99579
a = 0.358034
b = −0.786064
14.2146 0
14
II. I
u
2
= h−18u
20
+ 35u
19
+ · · · + 31b + 81, −29u
20
+ 3u
19
+ · · · + 31a +
84, u
21
− 12u
19
+ · · · − u − 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
3
=
0.935484u
20
− 0.0967742u
19
+ ··· + 9.48387u − 2.70968
0.580645u
20
− 1.12903u
19
+ ··· − 1.35484u − 2.61290
a
6
=
u
−u
3
+ u
a
7
=
−2.45161u
20
− 1.67742u
19
+ ··· − 12.6129u + 1.03226
0.0645161u
20
− 0.903226u
19
+ ··· + 1.51613u + 1.70968
a
12
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
1.51613u
20
− 1.22581u
19
+ ··· + 8.12903u − 5.32258
0.580645u
20
− 1.12903u
19
+ ··· − 1.35484u − 2.61290
a
9
=
2.41935u
20
+ 0.129032u
19
+ ··· + 6.35484u − 1.38710
−0.0645161u
20
− 0.0967742u
19
+ ··· − 2.51613u − 0.709677
a
4
=
0.0967742u
20
+ 1.64516u
19
+ ··· − 2.22581u + 0.0645161
0.129032u
20
+ 3.19355u
19
+ ··· + 4.03226u + 3.41935
a
1
=
1.58065u
20
− 0.129032u
19
+ ··· + 7.64516u − 7.61290
1.41935u
20
+ 2.12903u
19
+ ··· + 2.35484u + 1.61290
a
8
=
−2.38710u
20
− 1.58065u
19
+ ··· − 13.0968u + 2.74194
0.935484u
20
− 0.0967742u
19
+ ··· + 3.48387u + 2.29032
(ii) Obstruction class = 1
(iii) Cusp Shapes =
20
31
u
20
+
216
31
u
19
+ ··· +
780
31
u +
220
31
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
− 6u
20
+ ··· − 2u
2
+ 1
c
2
u
21
+ u
20
+ ··· + 3u − 1
c
3
u
21
+ 3u
20
+ ··· − 3u − 1
c
4
u
21
− 6u
19
+ ··· + 2u + 1
c
5
u
21
− 12u
19
+ ··· − u + 1
c
6
u
21
− 3u
20
+ ··· − 3u + 1
c
7
, c
8
u
21
− 14u
19
+ ··· − u − 1
c
9
u
21
− u
20
+ ··· + 3u + 1
c
10
, c
11
u
21
− 12u
19
+ ··· − u − 1
c
12
u
21
− 14u
19
+ ··· − u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
− 6y
20
+ ··· + 4y −1
c
2
, c
9
y
21
− 21y
20
+ ··· + 11y −1
c
3
, c
6
y
21
− 21y
20
+ ··· + 21y −1
c
4
y
21
− 12y
20
+ ··· + 16y −1
c
5
, c
10
, c
11
y
21
− 24y
20
+ ··· + 17y −1
c
7
, c
8
, c
12
y
21
− 28y
20
+ ··· + 13y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.674615 + 0.691211I
a = −0.741284 + 0.872608I
b = −0.825088 + 0.244562I
3.65927 + 4.03818I 3.47178 − 3.14396I
u = −0.674615 − 0.691211I
a = −0.741284 − 0.872608I
b = −0.825088 − 0.244562I
3.65927 − 4.03818I 3.47178 + 3.14396I
u = 1.20770
a = 0.862653
b = 1.41027
−0.227032 −1.33690
u = −1.23747
a = 0.0698864
b = −1.55801
−3.36420 15.3300
u = −1.255340 + 0.270736I
a = 0.24302 − 2.14553I
b = 0.957058 + 0.403999I
5.95829 − 7.42742I 8.04674 + 8.80531I
u = −1.255340 − 0.270736I
a = 0.24302 + 2.14553I
b = 0.957058 − 0.403999I
5.95829 + 7.42742I 8.04674 − 8.80531I
u = 0.300005 + 0.615985I
a = 1.184700 − 0.024718I
b = 0.790924 + 0.339359I
−1.87137 − 1.86348I −6.45473 + 8.21734I
u = 0.300005 − 0.615985I
a = 1.184700 + 0.024718I
b = 0.790924 − 0.339359I
−1.87137 + 1.86348I −6.45473 − 8.21734I
u = 1.320720 + 0.131954I
a = −0.95135 − 1.34628I
b = 1.020660 + 0.824318I
5.69652 + 3.26176I 5.56127 − 4.00526I
u = 1.320720 − 0.131954I
a = −0.95135 + 1.34628I
b = 1.020660 − 0.824318I
5.69652 − 3.26176I 5.56127 + 4.00526I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.671580
a = 2.57615
b = −1.29809
−2.29162 7.08010
u = 1.374880 + 0.258894I
a = 0.33045 − 1.63311I
b = −1.025960 + 0.595179I
2.06818 + 5.09061I 2.23390 − 4.25924I
u = 1.374880 − 0.258894I
a = 0.33045 + 1.63311I
b = −1.025960 − 0.595179I
2.06818 − 5.09061I 2.23390 + 4.25924I
u = −0.591959
a = −1.86907
b = 1.38648
−5.81449 −9.97790
u = 0.371508 + 0.405795I
a = 0.296302 − 0.282231I
b = −1.234530 + 0.499833I
2.16927 − 1.42059I 6.69492 − 3.05445I
u = 0.371508 − 0.405795I
a = 0.296302 + 0.282231I
b = −1.234530 − 0.499833I
2.16927 + 1.42059I 6.69492 + 3.05445I
u = −1.44756 + 0.09102I
a = −0.215464 − 0.503314I
b = −0.221826 + 0.307903I
5.06058 − 0.15354I 7.92430 − 1.48170I
u = −1.44756 − 0.09102I
a = −0.215464 + 0.503314I
b = −0.221826 − 0.307903I
5.06058 + 0.15354I 7.92430 + 1.48170I
u = −1.64477
a = −1.36791
b = 1.97611
10.3482 −42.6970
u = −0.331409
a = −4.38784
b = −0.516198
0.635448 −6.89680
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.94714
a = −0.176603
b = 0.676947
14.4498 23.5420
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
21
− 6u
20
+ ··· − 2u
2
+ 1)(u
98
− u
97
+ ··· + 5u − 1)
c
2
(u
21
+ u
20
+ ··· + 3u − 1)(u
98
− 33u
96
+ ··· − 1246u − 76)
c
3
(u
21
+ 3u
20
+ ··· − 3u − 1)(u
98
− 2u
97
+ ··· − 6u + 1)
c
4
(u
21
− 6u
19
+ ··· + 2u + 1)(u
98
+ 3u
97
+ ··· − 1183u − 187)
c
5
(u
21
− 12u
19
+ ··· − u + 1)(u
98
− u
97
+ ··· + 396u − 43)
c
6
(u
21
− 3u
20
+ ··· − 3u + 1)(u
98
− 2u
97
+ ··· − 6u + 1)
c
7
, c
8
(u
21
− 14u
19
+ ··· − u − 1)(u
98
+ 3u
97
+ ··· + 32u + 1)
c
9
(u
21
− u
20
+ ··· + 3u + 1)(u
98
− 33u
96
+ ··· − 1246u − 76)
c
10
, c
11
(u
21
− 12u
19
+ ··· − u − 1)(u
98
− u
97
+ ··· + 396u − 43)
c
12
(u
21
− 14u
19
+ ··· − u + 1)(u
98
+ 3u
97
+ ··· + 32u + 1)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
21
− 6y
20
+ ··· + 4y −1)(y
98
− 3y
97
+ ··· + 173y + 1)
c
2
, c
9
(y
21
− 21y
20
+ ··· + 11y −1)(y
98
− 66y
97
+ ··· − 1035260y + 5776)
c
3
, c
6
(y
21
− 21y
20
+ ··· + 21y −1)(y
98
− 54y
97
+ ··· + 132y + 1)
c
4
(y
21
− 12y
20
+ ··· + 16y −1)(y
98
− 25y
97
+ ··· − 1527771y + 34969)
c
5
, c
10
, c
11
(y
21
− 24y
20
+ ··· + 17y −1)(y
98
− 97y
97
+ ··· + 29288y + 1849)
c
7
, c
8
, c
12
(y
21
− 28y
20
+ ··· + 13y −1)(y
98
− 105y
97
+ ··· − 568y + 1)
22
