11a
268
(K11a
268
)
A knot diagram
1
Linearized knot diagam
9 8 1 10 2 3 11 6 4 5 7
Solving Sequence
7,11
8
1,3
4 2 6 9 5 10
c
7
c
11
c
3
c
2
c
6
c
8
c
5
c
10
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.49863 × 10
257
u
88
+ 5.28339 × 10
257
u
87
+ ··· + 2.06470 × 10
257
b + 1.62471 × 10
259
,
− 1.46587 × 10
259
u
88
+ 5.63526 × 10
259
u
87
+ ··· + 1.21817 × 10
259
a + 2.14864 × 10
261
,
u
89
− u
88
+ ··· + 48u + 59i
I
u
2
= hu
18
− 2u
17
+ ··· + b − 1, 2810u
19
− 4920u
18
+ ··· + 107a − 1193, u
20
− 2u
19
+ ··· + u − 1i
* 2 irreducible components of dim
C
= 0, with total 109 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−2.50 × 10
257
u
88
+ 5.28 × 10
257
u
87
+ · · · + 2.06 × 10
257
b + 1.62 ×
10
259
, −1.47 × 10
259
u
88
+ 5.64 × 10
259
u
87
+ · · · + 1.22 × 10
259
a + 2.15 ×
10
261
, u
89
− u
88
+ · · · + 48u + 59i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
1
=
u
u
a
3
=
1.20333u
88
− 4.62599u
87
+ ··· − 65.4798u − 176.382
1.21016u
88
− 2.55892u
87
+ ··· − 4.73499u − 78.6901
a
4
=
1.19352u
88
− 2.15965u
87
+ ··· + 34.4706u − 54.0216
1.20035u
88
− 0.0925750u
87
+ ··· + 95.2154u + 43.6703
a
2
=
0.866135u
88
− 1.82355u
87
+ ··· + 23.0760u − 53.1353
0.669502u
88
+ 0.854257u
87
+ ··· + 93.7021u + 66.7594
a
6
=
−1.85198u
88
+ 1.84275u
87
+ ··· − 99.2054u + 21.2049
−1.38144u
88
+ 0.574780u
87
+ ··· − 104.158u − 29.9703
a
9
=
−0.161350u
88
− 1.91766u
87
+ ··· − 107.928u − 102.769
1.27346u
88
− 2.34459u
87
+ ··· + 9.19607u − 60.8438
a
5
=
−1.27022u
88
+ 0.255281u
87
+ ··· − 89.4254u − 49.1154
−1.92719u
88
+ 0.959452u
87
+ ··· − 136.691u − 46.0116
a
10
=
−0.293092u
88
− 0.892600u
87
+ ··· − 95.2003u − 56.2570
0.191137u
88
+ 1.45973u
87
+ ··· + 91.9737u + 92.2085
a
10
=
−0.293092u
88
− 0.892600u
87
+ ··· − 95.2003u − 56.2570
0.191137u
88
+ 1.45973u
87
+ ··· + 91.9737u + 92.2085
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.667960u
88
+ 1.19445u
87
+ ··· + 98.6923u + 70.3629
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
89
− 4u
88
+ ··· − 121118u − 30299
c
2
u
89
− u
88
+ ··· + 74u − 3
c
3
u
89
+ 6u
88
+ ··· + 9173u − 3187
c
4
, c
9
, c
10
u
89
− 45u
87
+ ··· − 29u + 1
c
5
u
89
+ 5u
87
+ ··· − 1510u − 191
c
6
u
89
+ u
88
+ ··· + 84u − 2543
c
7
, c
11
u
89
+ u
88
+ ··· + 48u − 59
c
8
u
89
+ 8u
88
+ ··· + 21u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
89
+ 22y
88
+ ··· − 31326433006y −918029401
c
2
y
89
− 7y
88
+ ··· + 1222y −9
c
3
y
89
− 40y
88
+ ··· + 740124139y −10156969
c
4
, c
9
, c
10
y
89
− 90y
88
+ ··· + 123y −1
c
5
y
89
+ 10y
88
+ ··· − 1020380y −36481
c
6
y
89
− 17y
88
+ ··· + 242227806y −6466849
c
7
, c
11
y
89
+ 57y
88
+ ··· − 106492y −3481
c
8
y
89
+ 12y
88
+ ··· + 29y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.087265 + 0.982767I
a = −0.04086 − 1.58758I
b = −0.19737 − 2.33544I
−0.50502 + 3.23925I 0
u = 0.087265 − 0.982767I
a = −0.04086 + 1.58758I
b = −0.19737 + 2.33544I
−0.50502 − 3.23925I 0
u = 0.046780 + 1.013680I
a = 0.416851 − 0.354974I
b = −0.111187 + 1.159690I
−3.50317 + 2.78548I 0
u = 0.046780 − 1.013680I
a = 0.416851 + 0.354974I
b = −0.111187 − 1.159690I
−3.50317 − 2.78548I 0
u = −0.446021 + 0.914047I
a = −2.48559 + 0.54321I
b = −0.571797 − 0.795448I
−5.19564 − 7.48572I 0
u = −0.446021 − 0.914047I
a = −2.48559 − 0.54321I
b = −0.571797 + 0.795448I
−5.19564 + 7.48572I 0
u = 0.260416 + 1.013500I
a = 2.27900 − 0.32057I
b = 0.659896 − 0.535201I
−0.59074 + 5.03975I 0
u = 0.260416 − 1.013500I
a = 2.27900 + 0.32057I
b = 0.659896 + 0.535201I
−0.59074 − 5.03975I 0
u = 1.064020 + 0.063310I
a = 0.045029 − 0.215883I
b = −0.911465 − 0.659115I
−0.03232 − 7.23979I 0
u = 1.064020 − 0.063310I
a = 0.045029 + 0.215883I
b = −0.911465 + 0.659115I
−0.03232 + 7.23979I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.039185 + 1.073690I
a = −1.47979 − 1.15466I
b = −0.627270 − 0.234640I
−3.66917 − 2.24819I 0
u = 0.039185 − 1.073690I
a = −1.47979 + 1.15466I
b = −0.627270 + 0.234640I
−3.66917 + 2.24819I 0
u = 0.497647 + 0.954960I
a = 1.28701 + 0.60287I
b = 0.477386 + 0.066075I
−4.69329 + 4.27856I 0
u = 0.497647 − 0.954960I
a = 1.28701 − 0.60287I
b = 0.477386 − 0.066075I
−4.69329 − 4.27856I 0
u = 0.039765 + 1.076270I
a = 1.46166 + 0.75014I
b = 1.017060 − 0.460738I
−4.07004 + 0.47327I 0
u = 0.039765 − 1.076270I
a = 1.46166 − 0.75014I
b = 1.017060 + 0.460738I
−4.07004 − 0.47327I 0
u = −0.615419 + 0.671458I
a = 0.189017 − 0.505603I
b = −0.560076 + 1.171310I
−4.51518 + 3.24714I 0
u = −0.615419 − 0.671458I
a = 0.189017 + 0.505603I
b = −0.560076 − 1.171310I
−4.51518 − 3.24714I 0
u = −0.121420 + 1.106610I
a = 1.31626 + 0.66629I
b = 1.031160 + 0.909995I
−1.75568 − 2.78654I 0
u = −0.121420 − 1.106610I
a = 1.31626 − 0.66629I
b = 1.031160 − 0.909995I
−1.75568 + 2.78654I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.875117 + 0.034580I
a = −0.386985 − 0.034842I
b = −0.155945 − 0.596885I
2.36715 − 0.35769I 0
u = −0.875117 − 0.034580I
a = −0.386985 + 0.034842I
b = −0.155945 + 0.596885I
2.36715 + 0.35769I 0
u = 1.007920 + 0.535449I
a = 0.336385 − 0.013362I
b = 0.531325 + 0.593484I
−2.70373 + 0.98079I 0
u = 1.007920 − 0.535449I
a = 0.336385 + 0.013362I
b = 0.531325 − 0.593484I
−2.70373 − 0.98079I 0
u = 0.506291 + 1.032270I
a = 0.866930 + 0.935334I
b = 1.191080 − 0.080568I
−3.66544 + 1.93275I 0
u = 0.506291 − 1.032270I
a = 0.866930 − 0.935334I
b = 1.191080 + 0.080568I
−3.66544 − 1.93275I 0
u = −0.236142 + 1.129110I
a = 0.330233 − 1.155500I
b = 0.70775 − 2.08057I
−7.96934 − 7.75557I 0
u = −0.236142 − 1.129110I
a = 0.330233 + 1.155500I
b = 0.70775 + 2.08057I
−7.96934 + 7.75557I 0
u = −0.328525 + 0.779440I
a = −0.807758 + 0.527555I
b = −0.410749 + 0.471628I
−0.12055 − 1.56154I 0
u = −0.328525 − 0.779440I
a = −0.807758 − 0.527555I
b = −0.410749 − 0.471628I
−0.12055 + 1.56154I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.788124 + 0.303926I
a = −0.387345 + 0.099692I
b = 0.619681 + 0.601987I
0.06582 − 2.81820I 0
u = −0.788124 − 0.303926I
a = −0.387345 − 0.099692I
b = 0.619681 − 0.601987I
0.06582 + 2.81820I 0
u = 0.445920 + 1.083550I
a = 1.87113 + 0.43186I
b = 1.44730 − 0.78897I
−3.75095 + 4.98969I 0
u = 0.445920 − 1.083550I
a = 1.87113 − 0.43186I
b = 1.44730 + 0.78897I
−3.75095 − 4.98969I 0
u = 0.678170 + 0.961510I
a = 1.51669 + 0.65840I
b = 1.117050 − 0.384555I
−4.26488 + 4.97917I 0
u = 0.678170 − 0.961510I
a = 1.51669 − 0.65840I
b = 1.117050 + 0.384555I
−4.26488 − 4.97917I 0
u = 0.126780 + 1.184510I
a = −1.284540 + 0.461804I
b = −1.001690 − 0.662057I
−9.69819 + 3.33662I 0
u = 0.126780 − 1.184510I
a = −1.284540 − 0.461804I
b = −1.001690 + 0.662057I
−9.69819 − 3.33662I 0
u = −1.24771
a = −0.301097
b = −0.418317
2.46420 0
u = −0.244543 + 1.228290I
a = −1.23179 + 0.86747I
b = −0.793130 − 0.382921I
−4.75803 − 4.24642I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.244543 − 1.228290I
a = −1.23179 − 0.86747I
b = −0.793130 + 0.382921I
−4.75803 + 4.24642I 0
u = −0.677969 + 0.254536I
a = 0.409907 + 1.157920I
b = −1.069570 − 0.571323I
−7.15487 − 2.90968I −8.77339 + 3.39857I
u = −0.677969 − 0.254536I
a = 0.409907 − 1.157920I
b = −1.069570 + 0.571323I
−7.15487 + 2.90968I −8.77339 − 3.39857I
u = −1.277250 + 0.127509I
a = 0.0389394 − 0.1322070I
b = 1.044920 − 0.622691I
−6.62392 + 10.71350I 0
u = −1.277250 − 0.127509I
a = 0.0389394 + 0.1322070I
b = 1.044920 + 0.622691I
−6.62392 − 10.71350I 0
u = 0.069180 + 0.695826I
a = −2.02727 + 1.35133I
b = −0.960722 + 0.879130I
0.09907 − 1.94759I 1.047268 − 0.082305I
u = 0.069180 − 0.695826I
a = −2.02727 − 1.35133I
b = −0.960722 − 0.879130I
0.09907 + 1.94759I 1.047268 + 0.082305I
u = −0.398390 + 1.249610I
a = −1.70242 + 0.10142I
b = −1.44678 − 1.39596I
−11.29010 − 6.82846I 0
u = −0.398390 − 1.249610I
a = −1.70242 − 0.10142I
b = −1.44678 + 1.39596I
−11.29010 + 6.82846I 0
u = 0.683363
a = 0.835726
b = 0.596379
−2.43815 −4.51530
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.435092 + 0.490628I
a = −0.98737 + 1.36578I
b = −0.993481 + 0.278310I
−0.11272 − 1.93319I 1.42858 + 4.41047I
u = −0.435092 − 0.490628I
a = −0.98737 − 1.36578I
b = −0.993481 − 0.278310I
−0.11272 + 1.93319I 1.42858 − 4.41047I
u = 0.151916 + 0.595849I
a = −0.441550 − 0.656585I
b = 0.352124 + 1.046440I
0.84180 − 2.66745I 5.74905 − 1.98095I
u = 0.151916 − 0.595849I
a = −0.441550 + 0.656585I
b = 0.352124 − 1.046440I
0.84180 + 2.66745I 5.74905 + 1.98095I
u = −0.414299 + 1.325530I
a = 1.59253 + 0.08221I
b = 1.46438 + 0.92926I
−4.63913 − 7.16183I 0
u = −0.414299 − 1.325530I
a = 1.59253 − 0.08221I
b = 1.46438 − 0.92926I
−4.63913 + 7.16183I 0
u = −0.644934 + 1.230390I
a = −0.736732 + 0.726576I
b = −1.44148 + 0.01984I
−9.62472 − 2.50943I 0
u = −0.644934 − 1.230390I
a = −0.736732 − 0.726576I
b = −1.44148 − 0.01984I
−9.62472 + 2.50943I 0
u = 0.246352 + 1.373650I
a = 1.15659 + 0.88248I
b = 0.695662 − 0.461228I
−11.08240 + 7.06191I 0
u = 0.246352 − 1.373650I
a = 1.15659 − 0.88248I
b = 0.695662 + 0.461228I
−11.08240 − 7.06191I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.530049 + 1.305380I
a = −1.45314 + 0.19683I
b = −1.052980 − 0.528704I
−1.83963 − 5.67513I 0
u = −0.530049 − 1.305380I
a = −1.45314 − 0.19683I
b = −1.052980 + 0.528704I
−1.83963 + 5.67513I 0
u = 0.49937 + 1.32808I
a = −0.488895 − 0.527064I
b = −0.686607 + 0.222863I
−4.57148 − 1.94462I 0
u = 0.49937 − 1.32808I
a = −0.488895 + 0.527064I
b = −0.686607 − 0.222863I
−4.57148 + 1.94462I 0
u = −0.215639 + 0.534209I
a = −1.16518 + 2.62450I
b = −1.021100 − 0.309250I
−7.02333 − 2.79209I −10.65282 + 2.82685I
u = −0.215639 − 0.534209I
a = −1.16518 − 2.62450I
b = −1.021100 + 0.309250I
−7.02333 + 2.79209I −10.65282 − 2.82685I
u = 0.54058 + 1.33341I
a = −1.57123 − 0.12787I
b = −1.42757 + 0.93579I
−4.02189 + 12.94080I 0
u = 0.54058 − 1.33341I
a = −1.57123 + 0.12787I
b = −1.42757 − 0.93579I
−4.02189 − 12.94080I 0
u = 0.513373 + 0.147678I
a = −0.753590 + 0.248252I
b = 0.800692 + 0.560525I
−1.23216 − 1.17836I −4.88311 + 4.54684I
u = 0.513373 − 0.147678I
a = −0.753590 − 0.248252I
b = 0.800692 − 0.560525I
−1.23216 + 1.17836I −4.88311 − 4.54684I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.25454 + 1.44381I
a = −1.336270 + 0.250303I
b = −1.46023 + 0.90075I
−12.93760 + 3.41499I 0
u = 0.25454 − 1.44381I
a = −1.336270 − 0.250303I
b = −1.46023 − 0.90075I
−12.93760 − 3.41499I 0
u = −0.62479 + 1.38493I
a = 1.47088 − 0.22892I
b = 1.40808 + 0.97394I
−10.6453 − 17.3382I 0
u = −0.62479 − 1.38493I
a = 1.47088 + 0.22892I
b = 1.40808 − 0.97394I
−10.6453 + 17.3382I 0
u = 1.52669
a = 0.294467
b = 0.782757
−2.00885 0
u = 1.41052 + 0.59034I
a = 0.0916655 − 0.0956405I
b = −0.641469 + 0.112408I
−5.83989 − 1.30562I 0
u = 1.41052 − 0.59034I
a = 0.0916655 + 0.0956405I
b = −0.641469 − 0.112408I
−5.83989 + 1.30562I 0
u = 0.67751 + 1.43400I
a = −0.795814 − 0.141330I
b = −0.920623 + 0.747247I
−9.42451 + 9.01167I 0
u = 0.67751 − 1.43400I
a = −0.795814 + 0.141330I
b = −0.920623 − 0.747247I
−9.42451 − 9.01167I 0
u = −0.55611 + 1.48766I
a = 0.601362 − 0.005171I
b = 0.692230 + 0.691299I
−2.70633 − 4.15001I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.55611 − 1.48766I
a = 0.601362 + 0.005171I
b = 0.692230 − 0.691299I
−2.70633 + 4.15001I 0
u = 0.54992 + 1.52692I
a = 1.225460 + 0.136232I
b = 1.130120 − 0.483941I
−7.35822 + 7.24063I 0
u = 0.54992 − 1.52692I
a = 1.225460 − 0.136232I
b = 1.130120 + 0.483941I
−7.35822 − 7.24063I 0
u = −0.180594 + 0.309779I
a = 5.14197 + 1.52978I
b = 0.775482 + 0.702564I
−5.46219 + 5.61812I −2.79757 − 0.10435I
u = −0.180594 − 0.309779I
a = 5.14197 − 1.52978I
b = 0.775482 − 0.702564I
−5.46219 − 5.61812I −2.79757 + 0.10435I
u = 0.252949 + 0.250663I
a = 1.47113 − 0.57500I
b = 0.288716 − 1.130940I
1.14260 + 3.25401I 3.95954 − 7.62313I
u = 0.252949 − 0.250663I
a = 1.47113 + 0.57500I
b = 0.288716 + 1.130940I
1.14260 − 3.25401I 3.95954 + 7.62313I
u = −0.33710 + 1.61859I
a = 0.795660 − 0.350100I
b = 1.030800 + 0.166941I
−12.68790 + 4.35097I 0
u = −0.33710 − 1.61859I
a = 0.795660 + 0.350100I
b = 1.030800 − 0.166941I
−12.68790 − 4.35097I 0
13
II. I
u
2
= hu
18
− 2u
17
+ · · · + b − 1, 2810u
19
− 4920u
18
+ · · · + 107a −
1193, u
20
− 2u
19
+ · · · + u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
1
=
u
u
a
3
=
−26.2617u
19
+ 45.9813u
18
+ ··· + 23.3364u + 11.1495
−u
18
+ 2u
17
+ ··· + 9u
2
+ 1
a
4
=
−11.8131u
19
+ 19.2991u
18
+ ··· + 2.61682u + 5.60748
14.4486u
19
− 27.6822u
18
+ ··· − 20.7196u − 4.54206
a
2
=
−11.8131u
19
+ 19.2991u
18
+ ··· + 3.61682u + 5.60748
6.62617u
19
− 13.5981u
18
+ ··· − 12.2336u − 1.21495
a
6
=
14.8411u
19
− 54.6542u
18
+ ··· − 77.2243u + 52.2336
6u
19
− 12u
18
+ ··· + 6u
2
− 7u
a
9
=
−13.8972u
19
+ 38.3645u
18
+ ··· + 25.4393u − 13.9159
−9.35514u
19
+ 13.8318u
18
+ ··· − 10.9720u + 20.3458
a
5
=
−3.65421u
19
+ 7.95327u
18
+ ··· + 31.8411u + 1.37383
−0.635514u
19
+ 19.3832u
18
+ ··· + 57.1028u − 49.0654
a
10
=
−4.98131u
19
+ 25.4299u
18
+ ··· + 45.2617u − 39.4393
0.644860u
19
− 8.16822u
18
+ ··· − 26.9720u + 29.3458
a
10
=
−4.98131u
19
+ 25.4299u
18
+ ··· + 45.2617u − 39.4393
0.644860u
19
− 8.16822u
18
+ ··· − 26.9720u + 29.3458
(ii) Obstruction class = 1
(iii) Cusp Shapes =
11858
107
u
19
−
34035
107
u
18
+ ··· −
56013
107
u +
24789
107
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
+ u
19
+ ··· − u − 1
c
2
u
20
− u
18
+ ··· − u − 1
c
3
u
20
+ 7u
19
+ ··· + 26u
2
− 1
c
4
u
20
− u
19
+ ··· + 2u + 1
c
5
u
20
+ 3u
19
+ ··· − u − 1
c
6
u
20
+ 4u
18
+ ··· + 3u − 1
c
7
u
20
− 2u
19
+ ··· + u − 1
c
8
u
20
− 3u
19
+ ··· − 3u
2
+ 1
c
9
, c
10
u
20
+ u
19
+ ··· − 2u + 1
c
11
u
20
+ 2u
19
+ ··· − u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
− 9y
19
+ ··· + y + 1
c
2
y
20
− 2y
19
+ ··· + y + 1
c
3
y
20
− 3y
19
+ ··· − 52y + 1
c
4
, c
9
, c
10
y
20
− 21y
19
+ ··· − 28y + 1
c
5
y
20
+ 3y
19
+ ··· + 11y + 1
c
6
y
20
+ 8y
19
+ ··· − 11y + 1
c
7
, c
11
y
20
+ 10y
19
+ ··· + 19y + 1
c
8
y
20
+ y
19
+ ··· − 6y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.023098 + 0.755612I
a = 0.77533 + 1.84505I
b = 0.19540 + 1.74306I
0.16874 + 2.77142I 2.49688 − 6.12151I
u = 0.023098 − 0.755612I
a = 0.77533 − 1.84505I
b = 0.19540 − 1.74306I
0.16874 − 2.77142I 2.49688 + 6.12151I
u = 0.541044 + 1.141770I
a = 1.81236 + 0.36763I
b = 0.920204 − 0.446036I
−5.23739 + 5.55861I −8.63842 − 8.06052I
u = 0.541044 − 1.141770I
a = 1.81236 − 0.36763I
b = 0.920204 + 0.446036I
−5.23739 − 5.55861I −8.63842 + 8.06052I
u = −0.416386 + 1.198530I
a = −1.62703 + 0.06947I
b = −1.019980 − 0.686033I
−2.35880 − 5.00950I −4.53218 + 5.02781I
u = −0.416386 − 1.198530I
a = −1.62703 − 0.06947I
b = −1.019980 + 0.686033I
−2.35880 + 5.00950I −4.53218 − 5.02781I
u = 1.27522
a = 0.595699
b = 0.485579
−1.31038 6.20020
u = 1.057510 + 0.728926I
a = −0.295893 + 0.357385I
b = 0.572386 − 0.096735I
−5.62801 − 1.51138I −5.02190 + 9.76370I
u = 1.057510 − 0.728926I
a = −0.295893 − 0.357385I
b = 0.572386 + 0.096735I
−5.62801 + 1.51138I −5.02190 − 9.76370I
u = −1.29712
a = −0.226506
b = −0.483546
2.35090 −37.5790
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.053636 + 0.686332I
a = 0.477848 + 0.259027I
b = −0.274254 + 1.252550I
0.41433 + 2.93710I −8.44025 − 5.37355I
u = −0.053636 − 0.686332I
a = 0.477848 − 0.259027I
b = −0.274254 − 1.252550I
0.41433 − 2.93710I −8.44025 + 5.37355I
u = −0.172612 + 0.633647I
a = −2.39427 + 2.55984I
b = −0.558207 + 0.814180I
−5.94321 − 6.14570I −10.52858 + 8.02706I
u = −0.172612 − 0.633647I
a = −2.39427 − 2.55984I
b = −0.558207 − 0.814180I
−5.94321 + 6.14570I −10.52858 − 8.02706I
u = −0.391244 + 1.285840I
a = −0.905832 − 0.019168I
b = −0.869606 − 0.821260I
−2.62899 − 3.66788I −5.57286 + 1.70794I
u = −0.391244 − 1.285840I
a = −0.905832 + 0.019168I
b = −0.869606 + 0.821260I
−2.62899 + 3.66788I −5.57286 − 1.70794I
u = 0.319597 + 1.353040I
a = 1.048790 + 0.126841I
b = 0.732984 − 0.987021I
−9.99863 + 6.70009I −6.33266 − 4.76825I
u = 0.319597 − 1.353040I
a = 1.048790 − 0.126841I
b = 0.732984 + 0.987021I
−9.99863 − 6.70009I −6.33266 + 4.76825I
u = 0.103581 + 0.582151I
a = −0.57589 − 2.05632I
b = 0.300055 + 0.812653I
−2.20697 − 2.35727I 0.75955 + 2.29179I
u = 0.103581 − 0.582151I
a = −0.57589 + 2.05632I
b = 0.300055 − 0.812653I
−2.20697 + 2.35727I 0.75955 − 2.29179I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
20
+ u
19
+ ··· − u − 1)(u
89
− 4u
88
+ ··· − 121118u − 30299)
c
2
(u
20
− u
18
+ ··· − u − 1)(u
89
− u
88
+ ··· + 74u − 3)
c
3
(u
20
+ 7u
19
+ ··· + 26u
2
− 1)(u
89
+ 6u
88
+ ··· + 9173u − 3187)
c
4
(u
20
− u
19
+ ··· + 2u + 1)(u
89
− 45u
87
+ ··· − 29u + 1)
c
5
(u
20
+ 3u
19
+ ··· − u − 1)(u
89
+ 5u
87
+ ··· − 1510u − 191)
c
6
(u
20
+ 4u
18
+ ··· + 3u − 1)(u
89
+ u
88
+ ··· + 84u − 2543)
c
7
(u
20
− 2u
19
+ ··· + u − 1)(u
89
+ u
88
+ ··· + 48u − 59)
c
8
(u
20
− 3u
19
+ ··· − 3u
2
+ 1)(u
89
+ 8u
88
+ ··· + 21u + 1)
c
9
, c
10
(u
20
+ u
19
+ ··· − 2u + 1)(u
89
− 45u
87
+ ··· − 29u + 1)
c
11
(u
20
+ 2u
19
+ ··· − u − 1)(u
89
+ u
88
+ ··· + 48u − 59)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
20
− 9y
19
+ ··· + y + 1)
· (y
89
+ 22y
88
+ ··· − 31326433006y −918029401)
c
2
(y
20
− 2y
19
+ ··· + y + 1)(y
89
− 7y
88
+ ··· + 1222y −9)
c
3
(y
20
− 3y
19
+ ··· − 52y + 1)
· (y
89
− 40y
88
+ ··· + 740124139y −10156969)
c
4
, c
9
, c
10
(y
20
− 21y
19
+ ··· − 28y + 1)(y
89
− 90y
88
+ ··· + 123y −1)
c
5
(y
20
+ 3y
19
+ ··· + 11y + 1)(y
89
+ 10y
88
+ ··· − 1020380y −36481)
c
6
(y
20
+ 8y
19
+ ··· − 11y + 1)
· (y
89
− 17y
88
+ ··· + 242227806y −6466849)
c
7
, c
11
(y
20
+ 10y
19
+ ··· + 19y + 1)(y
89
+ 57y
88
+ ··· − 106492y −3481)
c
8
(y
20
+ y
19
+ ··· − 6y + 1)(y
89
+ 12y
88
+ ··· + 29y −1)
20
