11a
209
(K11a
209
)
A knot diagram
1
Linearized knot diagam
7 1 11 8 10 2 5 3 6 4 9
Solving Sequence
2,6 7,9
10 1 3 5 8 4 11
c
6
c
9
c
1
c
2
c
5
c
8
c
4
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.30788 × 10
126
u
85
− 9.55625 × 10
125
u
84
+ ··· + 9.00015 × 10
126
b + 6.05580 × 10
127
,
− 2.03979 × 10
128
u
85
− 2.07030 × 10
128
u
84
+ ··· + 2.07003 × 10
128
a − 3.57647 × 10
129
,
u
86
+ u
85
+ ··· + 22u + 23i
I
u
2
= h−2u
14
− 7u
12
+ 2u
11
− 16u
10
+ 9u
9
− 23u
8
+ 15u
7
− 26u
6
+ 17u
5
− 22u
4
+ 10u
3
− 11u
2
+ b + 3u − 2,
u
14
+ u
13
+ 4u
12
+ 2u
11
+ 8u
10
+ u
9
+ 9u
8
− 2u
7
+ 9u
6
− 2u
5
+ 7u
4
+ 4u
2
+ a + u − 1,
u
16
+ 4u
14
− u
13
+ 10u
12
− 5u
11
+ 16u
10
− 10u
9
+ 20u
8
− 13u
7
+ 19u
6
− 10u
5
+ 13u
4
− 5u
3
+ 5u
2
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 102 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−6.31 × 10
126
u
85
− 9.56 × 10
125
u
84
+ · · · + 9.00 × 10
126
b + 6.06 ×
10
127
, −2.04 × 10
128
u
85
− 2.07 × 10
128
u
84
+ · · · + 2.07 × 10
128
a − 3.58 ×
10
129
, u
86
+ u
85
+ · · · + 22u + 23i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
9
=
0.985388u
85
+ 1.00013u
84
+ ··· + 21.7854u + 17.2774
0.700864u
85
+ 0.106179u
84
+ ··· + 14.6782u − 6.72856
a
10
=
1.68625u
85
+ 1.10631u
84
+ ··· + 36.4636u + 10.5488
0.700864u
85
+ 0.106179u
84
+ ··· + 14.6782u − 6.72856
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
5
=
0.179613u
85
+ 0.843358u
84
+ ··· − 1.56088u + 10.9518
0.440284u
85
+ 0.983845u
84
+ ··· + 15.9276u + 22.9163
a
8
=
1.68776u
85
+ 1.23127u
84
+ ··· + 40.7914u + 14.3817
0.860452u
85
+ 0.154872u
84
+ ··· + 20.0925u − 6.09132
a
4
=
1.13364u
85
+ 1.30317u
84
+ ··· + 25.1297u + 21.3228
0.585302u
85
+ 0.634965u
84
+ ··· + 18.0615u + 12.8964
a
11
=
−0.151976u
85
− 0.909808u
84
+ ··· − 7.21246u − 14.7505
0.0869857u
85
− 0.573926u
84
+ ··· − 0.0631483u − 8.62579
a
11
=
−0.151976u
85
− 0.909808u
84
+ ··· − 7.21246u − 14.7505
0.0869857u
85
− 0.573926u
84
+ ··· − 0.0631483u − 8.62579
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.93906u
85
− 1.80148u
84
+ ··· − 94.0864u − 29.1762
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
86
+ u
85
+ ··· + 22u + 23
c
2
u
86
+ 37u
85
+ ··· + 8624u + 529
c
3
, c
10
u
86
+ 5u
85
+ ··· + 228u + 34
c
4
, c
7
u
86
− 3u
85
+ ··· − 3u + 1
c
5
, c
9
u
86
− u
85
+ ··· + 977u + 253
c
8
u
86
+ u
85
+ ··· − 5u + 1
c
11
u
86
− 3u
85
+ ··· − 453u + 83
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
86
+ 37y
85
+ ··· + 8624y + 529
c
2
y
86
+ 33y
85
+ ··· + 1800508y + 279841
c
3
, c
10
y
86
+ 61y
85
+ ··· + 39068y + 1156
c
4
, c
7
y
86
+ 51y
85
+ ··· + 79y + 1
c
5
, c
9
y
86
+ 57y
85
+ ··· + 492125y + 64009
c
8
y
86
+ 7y
85
+ ··· + 89y + 1
c
11
y
86
− 15y
85
+ ··· − 330041y + 6889
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.440608 + 0.882453I
a = −1.41549 + 0.11610I
b = −0.14456 − 2.08024I
−6.69565 − 1.80753I 0
u = −0.440608 − 0.882453I
a = −1.41549 − 0.11610I
b = −0.14456 + 2.08024I
−6.69565 + 1.80753I 0
u = 0.435411 + 0.874421I
a = 2.18520 − 0.30062I
b = −0.236877 − 0.859775I
−0.020421 + 1.232540I 0
u = 0.435411 − 0.874421I
a = 2.18520 + 0.30062I
b = −0.236877 + 0.859775I
−0.020421 − 1.232540I 0
u = −0.254148 + 0.997671I
a = −0.0121662 − 0.0653344I
b = 0.658248 + 0.624038I
−3.68445 − 0.23182I 0
u = −0.254148 − 0.997671I
a = −0.0121662 + 0.0653344I
b = 0.658248 − 0.624038I
−3.68445 + 0.23182I 0
u = 0.472137 + 0.915188I
a = −0.650907 + 0.686202I
b = 0.557676 − 0.372423I
−0.27091 + 2.38443I 0
u = 0.472137 − 0.915188I
a = −0.650907 − 0.686202I
b = 0.557676 + 0.372423I
−0.27091 − 2.38443I 0
u = 0.819335 + 0.516743I
a = 0.735754 − 1.133700I
b = −0.303943 + 1.157700I
−4.27251 − 4.47107I 0
u = 0.819335 − 0.516743I
a = 0.735754 + 1.133700I
b = −0.303943 − 1.157700I
−4.27251 + 4.47107I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.799498 + 0.671496I
a = −1.082950 − 0.476132I
b = 0.862405 − 0.332801I
6.03113 − 0.23797I 0
u = −0.799498 − 0.671496I
a = −1.082950 + 0.476132I
b = 0.862405 + 0.332801I
6.03113 + 0.23797I 0
u = 0.519186 + 0.913358I
a = −1.30951 + 1.25452I
b = 0.235203 + 1.254150I
0.55328 + 3.31179I 0
u = 0.519186 − 0.913358I
a = −1.30951 − 1.25452I
b = 0.235203 − 1.254150I
0.55328 − 3.31179I 0
u = 0.498753 + 0.796047I
a = 0.520912 + 0.215764I
b = −0.477711 + 1.141280I
0.958565 + 0.837035I 0
u = 0.498753 − 0.796047I
a = 0.520912 − 0.215764I
b = −0.477711 − 1.141280I
0.958565 − 0.837035I 0
u = −0.957226 + 0.470426I
a = −0.694272 − 0.926525I
b = 0.65505 + 1.27900I
−0.73034 + 11.32340I 0
u = −0.957226 − 0.470426I
a = −0.694272 + 0.926525I
b = 0.65505 − 1.27900I
−0.73034 − 11.32340I 0
u = 0.718222 + 0.590569I
a = −1.66020 + 0.78424I
b = 1.230230 + 0.333871I
2.36607 − 4.79257I 0
u = 0.718222 − 0.590569I
a = −1.66020 − 0.78424I
b = 1.230230 − 0.333871I
2.36607 + 4.79257I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.363945 + 0.853778I
a = 2.39581 + 1.39052I
b = 0.058045 + 0.753718I
−1.69428 + 3.12126I 0
u = −0.363945 − 0.853778I
a = 2.39581 − 1.39052I
b = 0.058045 − 0.753718I
−1.69428 − 3.12126I 0
u = 0.678602 + 0.851107I
a = 1.348950 + 0.317447I
b = −0.704996 − 0.539942I
1.82473 + 1.72939I 0
u = 0.678602 − 0.851107I
a = 1.348950 − 0.317447I
b = −0.704996 + 0.539942I
1.82473 − 1.72939I 0
u = 1.002180 + 0.442960I
a = −0.459083 + 0.579423I
b = 0.526479 − 1.140670I
3.53168 − 4.85270I 0
u = 1.002180 − 0.442960I
a = −0.459083 − 0.579423I
b = 0.526479 + 1.140670I
3.53168 + 4.85270I 0
u = −0.574135 + 0.697745I
a = 1.295480 + 0.432521I
b = −0.593842 − 0.982625I
0.55800 + 3.23439I 0
u = −0.574135 − 0.697745I
a = 1.295480 − 0.432521I
b = −0.593842 + 0.982625I
0.55800 − 3.23439I 0
u = −0.301901 + 1.060790I
a = 0.243556 + 0.478235I
b = 0.333285 + 0.966852I
−3.68916 − 0.50545I 0
u = −0.301901 − 1.060790I
a = 0.243556 − 0.478235I
b = 0.333285 − 0.966852I
−3.68916 + 0.50545I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.566298 + 0.952248I
a = −2.01719 − 1.25230I
b = 0.470639 − 1.102850I
−0.23044 − 7.80201I 0
u = −0.566298 − 0.952248I
a = −2.01719 + 1.25230I
b = 0.470639 + 1.102850I
−0.23044 + 7.80201I 0
u = −0.458991 + 1.014050I
a = −1.36992 − 0.61444I
b = 0.328045 + 0.090852I
−2.49113 − 6.25666I 0
u = −0.458991 − 1.014050I
a = −1.36992 + 0.61444I
b = 0.328045 − 0.090852I
−2.49113 + 6.25666I 0
u = −0.535541 + 0.976845I
a = 1.84339 − 0.12152I
b = −0.49099 + 1.53261I
−5.79066 − 2.94337I 0
u = −0.535541 − 0.976845I
a = 1.84339 + 0.12152I
b = −0.49099 − 1.53261I
−5.79066 + 2.94337I 0
u = 0.155910 + 0.854062I
a = 0.610198 − 1.248350I
b = −1.094600 + 0.553981I
−2.07684 − 4.50458I −4.60378 + 5.16323I
u = 0.155910 − 0.854062I
a = 0.610198 + 1.248350I
b = −1.094600 − 0.553981I
−2.07684 + 4.50458I −4.60378 − 5.16323I
u = 0.727983 + 0.866986I
a = −0.295618 + 1.161150I
b = 0.552356 − 0.433486I
1.80523 + 3.66895I 0
u = 0.727983 − 0.866986I
a = −0.295618 − 1.161150I
b = 0.552356 + 0.433486I
1.80523 − 3.66895I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.037161 + 1.155380I
a = −0.290467 − 0.823431I
b = 0.16766 − 1.42237I
−10.06360 − 2.70380I 0
u = 0.037161 − 1.155380I
a = −0.290467 + 0.823431I
b = 0.16766 + 1.42237I
−10.06360 + 2.70380I 0
u = 0.356735 + 1.106460I
a = 0.771475 + 0.196566I
b = 0.51455 − 1.45263I
−4.90859 − 0.03496I 0
u = 0.356735 − 1.106460I
a = 0.771475 − 0.196566I
b = 0.51455 + 1.45263I
−4.90859 + 0.03496I 0
u = −0.784201 + 0.874304I
a = 0.646233 − 1.252980I
b = −0.075808 + 0.802027I
3.13190 − 2.94290I 0
u = −0.784201 − 0.874304I
a = 0.646233 + 1.252980I
b = −0.075808 − 0.802027I
3.13190 + 2.94290I 0
u = 0.471061 + 1.075990I
a = −1.75793 + 0.83086I
b = 0.99776 + 1.30307I
−4.20557 + 7.31255I 0
u = 0.471061 − 1.075990I
a = −1.75793 − 0.83086I
b = 0.99776 − 1.30307I
−4.20557 − 7.31255I 0
u = −0.651807 + 0.489532I
a = 0.39844 − 1.41823I
b = 0.197920 + 1.236210I
−4.44910 − 1.59822I −3.44505 + 3.04430I
u = −0.651807 − 0.489532I
a = 0.39844 + 1.41823I
b = 0.197920 − 1.236210I
−4.44910 + 1.59822I −3.44505 − 3.04430I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.624334 + 1.022790I
a = 0.969124 − 0.965579I
b = −1.47236 + 0.18895I
1.06511 + 9.94951I 0
u = 0.624334 − 1.022790I
a = 0.969124 + 0.965579I
b = −1.47236 − 0.18895I
1.06511 − 9.94951I 0
u = −0.788393 + 0.093088I
a = 0.175436 + 0.306457I
b = 0.330111 + 0.644700I
0.40272 − 2.72268I 2.86940 + 3.16788I
u = −0.788393 − 0.093088I
a = 0.175436 − 0.306457I
b = 0.330111 − 0.644700I
0.40272 + 2.72268I 2.86940 − 3.16788I
u = −0.683162 + 0.995349I
a = 0.756961 + 0.517256I
b = −0.997716 − 0.121911I
5.03331 − 5.32903I 0
u = −0.683162 − 0.995349I
a = 0.756961 − 0.517256I
b = −0.997716 + 0.121911I
5.03331 + 5.32903I 0
u = −0.536132 + 1.087660I
a = −1.55660 − 0.83006I
b = 0.756634 − 0.727652I
−2.10386 − 6.56947I 0
u = −0.536132 − 1.087660I
a = −1.55660 + 0.83006I
b = 0.756634 + 0.727652I
−2.10386 + 6.56947I 0
u = −0.573481 + 1.085080I
a = −1.67333 − 0.55597I
b = 0.531502 − 0.970130I
−1.93850 − 6.65557I 0
u = −0.573481 − 1.085080I
a = −1.67333 + 0.55597I
b = 0.531502 + 0.970130I
−1.93850 + 6.65557I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.131390 + 0.532631I
a = −0.273567 − 0.463197I
b = 0.248035 + 0.937067I
−0.23931 + 5.38129I 0
u = 1.131390 − 0.532631I
a = −0.273567 + 0.463197I
b = 0.248035 − 0.937067I
−0.23931 − 5.38129I 0
u = 0.657555 + 1.085690I
a = −1.92694 + 0.01672I
b = 0.437325 + 1.219940I
−5.97898 + 10.01160I 0
u = 0.657555 − 1.085690I
a = −1.92694 − 0.01672I
b = 0.437325 − 1.219940I
−5.97898 − 10.01160I 0
u = −0.613434 + 0.381423I
a = 1.142460 + 0.688198I
b = −0.522004 − 0.772282I
0.03093 + 1.91449I 1.42093 − 2.93716I
u = −0.613434 − 0.381423I
a = 1.142460 − 0.688198I
b = −0.522004 + 0.772282I
0.03093 − 1.91449I 1.42093 + 2.93716I
u = −0.624780 + 0.343324I
a = 1.41145 + 0.48892I
b = −0.637437 − 0.540547I
0.00762 + 1.99264I 2.82106 − 2.47705I
u = −0.624780 − 0.343324I
a = 1.41145 − 0.48892I
b = −0.637437 + 0.540547I
0.00762 − 1.99264I 2.82106 + 2.47705I
u = 0.006838 + 1.320150I
a = −0.042358 − 0.568413I
b = −0.369980 − 1.292530I
−7.52252 + 8.52696I 0
u = 0.006838 − 1.320150I
a = −0.042358 + 0.568413I
b = −0.369980 + 1.292530I
−7.52252 − 8.52696I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.682783 + 1.148320I
a = 1.73833 + 0.37633I
b = −0.70195 + 1.39798I
−2.8205 − 17.3023I 0
u = −0.682783 − 1.148320I
a = 1.73833 − 0.37633I
b = −0.70195 − 1.39798I
−2.8205 + 17.3023I 0
u = 0.385965 + 0.524461I
a = 1.33463 + 0.54748I
b = −0.346668 − 0.264256I
0.610346 + 1.128090I 4.76161 − 5.52253I
u = 0.385965 − 0.524461I
a = 1.33463 − 0.54748I
b = −0.346668 + 0.264256I
0.610346 − 1.128090I 4.76161 + 5.52253I
u = 0.689193 + 1.161250I
a = 1.45571 − 0.42058I
b = −0.55690 − 1.30946I
1.32319 + 10.94470I 0
u = 0.689193 − 1.161250I
a = 1.45571 + 0.42058I
b = −0.55690 + 1.30946I
1.32319 − 10.94470I 0
u = −0.178929 + 1.357480I
a = 0.024553 + 0.644724I
b = −0.122682 + 1.122470I
−4.10884 − 1.64866I 0
u = −0.178929 − 1.357480I
a = 0.024553 − 0.644724I
b = −0.122682 − 1.122470I
−4.10884 + 1.64866I 0
u = 0.591175 + 0.049975I
a = 1.31039 − 1.38090I
b = −0.687577 + 1.119080I
−1.62551 − 3.43865I −0.96501 + 2.90877I
u = 0.591175 − 0.049975I
a = 1.31039 + 1.38090I
b = −0.687577 − 1.119080I
−1.62551 + 3.43865I −0.96501 − 2.90877I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.145997 + 0.558877I
a = 1.02027 + 1.15455I
b = −0.467675 − 0.564857I
0.40918 + 1.48015I 2.24000 − 5.97587I
u = 0.145997 − 0.558877I
a = 1.02027 − 1.15455I
b = −0.467675 + 0.564857I
0.40918 − 1.48015I 2.24000 + 5.97587I
u = 0.62384 + 1.28071I
a = −0.820261 + 0.152739I
b = −0.005790 + 0.909994I
−3.04048 + 1.33044I 0
u = 0.62384 − 1.28071I
a = −0.820261 − 0.152739I
b = −0.005790 − 0.909994I
−3.04048 − 1.33044I 0
u = −0.87956 + 1.15875I
a = 0.821875 − 0.111111I
b = −0.137121 + 1.346990I
−4.20851 − 3.78318I 0
u = −0.87956 − 1.15875I
a = 0.821875 + 0.111111I
b = −0.137121 − 1.346990I
−4.20851 + 3.78318I 0
13
II.
I
u
2
= h−2u
14
−7u
12
+· · ·+b−2, u
14
+u
13
+· · ·+a−1, u
16
+4u
14
+· · ·−u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
9
=
−u
14
− u
13
+ ··· − u + 1
2u
14
+ 7u
12
+ ··· − 3u + 2
a
10
=
u
14
− u
13
+ ··· − 4u + 3
2u
14
+ 7u
12
+ ··· − 3u + 2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
5
=
2u
14
− u
13
+ ··· − 5u + 4
u
15
− u
14
+ ··· + u − 1
a
8
=
−u
13
− u
12
+ ··· − u + 1
2u
14
+ 7u
12
+ ··· − 3u + 2
a
4
=
u
15
+ u
14
+ ··· + 4u − 2
u
15
− u
14
+ ··· + 2u − 1
a
11
=
u
15
+ 4u
13
+ ··· + 3u + 3
u
15
+ 4u
13
+ ··· − u
2
+ u
a
11
=
u
15
+ 4u
13
+ ··· + 3u + 3
u
15
+ 4u
13
+ ··· − u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= u
15
−u
14
+4u
13
+2u
12
+12u
11
+7u
10
+16u
9
+17u
8
+5u
7
+17u
6
−u
5
+20u
4
−6u
3
+18u
2
+5
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
+ 4u
14
+ ··· + u + 1
c
2
u
16
+ 8u
15
+ ··· + 9u + 1
c
3
u
16
+ 8u
14
+ ··· + u + 2
c
4
u
16
− 2u
15
+ ··· + 8u
2
+ 1
c
5
u
16
+ 8u
14
+ ··· + 2u + 1
c
6
u
16
+ 4u
14
+ ··· − u + 1
c
7
u
16
+ 2u
15
+ ··· + 8u
2
+ 1
c
8
u
16
+ 3u
14
+ ··· − 4u + 1
c
9
u
16
+ 8u
14
+ ··· − 2u + 1
c
10
u
16
+ 8u
14
+ ··· − u + 2
c
11
u
16
+ 6u
15
+ ··· + 5u
3
+ 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
16
+ 8y
15
+ ··· + 9y + 1
c
2
y
16
+ 8y
15
+ ··· + y + 1
c
3
, c
10
y
16
+ 16y
15
+ ··· + 39y + 4
c
4
, c
7
y
16
+ 14y
15
+ ··· + 16y + 1
c
5
, c
9
y
16
+ 16y
15
+ ··· + 14y + 1
c
8
y
16
+ 6y
15
+ ··· − 2y + 1
c
11
y
16
− 4y
15
+ ··· + 30y
2
+ 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.343340 + 0.903837I
a = 1.56676 − 0.12174I
b = 0.11176 + 1.95777I
−7.14694 − 1.43565I −10.40664 − 2.32978I
u = −0.343340 − 0.903837I
a = 1.56676 + 0.12174I
b = 0.11176 − 1.95777I
−7.14694 + 1.43565I −10.40664 + 2.32978I
u = 0.798443 + 0.511463I
a = −0.0414475 + 0.0829013I
b = −0.318907 − 0.710933I
0.31683 + 4.82313I 2.45674 − 4.45720I
u = 0.798443 − 0.511463I
a = −0.0414475 − 0.0829013I
b = −0.318907 + 0.710933I
0.31683 − 4.82313I 2.45674 + 4.45720I
u = −0.738361 + 0.873406I
a = 0.552854 − 1.253860I
b = −0.051627 + 0.529275I
3.66939 − 2.80776I 10.64447 + 1.16069I
u = −0.738361 − 0.873406I
a = 0.552854 + 1.253860I
b = −0.051627 − 0.529275I
3.66939 + 2.80776I 10.64447 − 1.16069I
u = 0.487072 + 1.055760I
a = −1.83617 + 1.15350I
b = 0.700331 + 0.823488I
−2.30232 + 7.54648I −2.14299 − 11.74045I
u = 0.487072 − 1.055760I
a = −1.83617 − 1.15350I
b = 0.700331 − 0.823488I
−2.30232 − 7.54648I −2.14299 + 11.74045I
u = 0.327557 + 1.160530I
a = 0.563947 − 0.360432I
b = 0.311651 − 1.038780I
−2.86838 − 0.11828I −0.88069 + 2.46501I
u = 0.327557 − 1.160530I
a = 0.563947 + 0.360432I
b = 0.311651 + 1.038780I
−2.86838 + 0.11828I −0.88069 − 2.46501I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.394909 + 0.626627I
a = 2.17510 − 1.35355I
b = −0.606467 + 0.609910I
−0.74107 − 3.74159I 1.01930 + 5.15973I
u = 0.394909 − 0.626627I
a = 2.17510 + 1.35355I
b = −0.606467 − 0.609910I
−0.74107 + 3.74159I 1.01930 − 5.15973I
u = −0.158611 + 0.649341I
a = 1.97289 − 0.31397I
b = −0.371932 − 0.795508I
0.080629 + 0.400598I −1.246602 − 0.185548I
u = −0.158611 − 0.649341I
a = 1.97289 + 0.31397I
b = −0.371932 + 0.795508I
0.080629 − 0.400598I −1.246602 + 0.185548I
u = −0.767670 + 1.139480I
a = −0.953934 + 0.004192I
b = 0.225194 − 1.371430I
−4.16761 − 3.51464I −0.94360 − 6.61638I
u = −0.767670 − 1.139480I
a = −0.953934 − 0.004192I
b = 0.225194 + 1.371430I
−4.16761 + 3.51464I −0.94360 + 6.61638I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
16
+ 4u
14
+ ··· + u + 1)(u
86
+ u
85
+ ··· + 22u + 23)
c
2
(u
16
+ 8u
15
+ ··· + 9u + 1)(u
86
+ 37u
85
+ ··· + 8624u + 529)
c
3
(u
16
+ 8u
14
+ ··· + u + 2)(u
86
+ 5u
85
+ ··· + 228u + 34)
c
4
(u
16
− 2u
15
+ ··· + 8u
2
+ 1)(u
86
− 3u
85
+ ··· − 3u + 1)
c
5
(u
16
+ 8u
14
+ ··· + 2u + 1)(u
86
− u
85
+ ··· + 977u + 253)
c
6
(u
16
+ 4u
14
+ ··· − u + 1)(u
86
+ u
85
+ ··· + 22u + 23)
c
7
(u
16
+ 2u
15
+ ··· + 8u
2
+ 1)(u
86
− 3u
85
+ ··· − 3u + 1)
c
8
(u
16
+ 3u
14
+ ··· − 4u + 1)(u
86
+ u
85
+ ··· − 5u + 1)
c
9
(u
16
+ 8u
14
+ ··· − 2u + 1)(u
86
− u
85
+ ··· + 977u + 253)
c
10
(u
16
+ 8u
14
+ ··· − u + 2)(u
86
+ 5u
85
+ ··· + 228u + 34)
c
11
(u
16
+ 6u
15
+ ··· + 5u
3
+ 1)(u
86
− 3u
85
+ ··· − 453u + 83)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
16
+ 8y
15
+ ··· + 9y + 1)(y
86
+ 37y
85
+ ··· + 8624y + 529)
c
2
(y
16
+ 8y
15
+ ··· + y + 1)(y
86
+ 33y
85
+ ··· + 1800508y + 279841)
c
3
, c
10
(y
16
+ 16y
15
+ ··· + 39y + 4)(y
86
+ 61y
85
+ ··· + 39068y + 1156)
c
4
, c
7
(y
16
+ 14y
15
+ ··· + 16y + 1)(y
86
+ 51y
85
+ ··· + 79y + 1)
c
5
, c
9
(y
16
+ 16y
15
+ ··· + 14y + 1)(y
86
+ 57y
85
+ ··· + 492125y + 64009)
c
8
(y
16
+ 6y
15
+ ··· − 2y + 1)(y
86
+ 7y
85
+ ··· + 89y + 1)
c
11
(y
16
− 4y
15
+ ··· + 30y
2
+ 1)(y
86
− 15y
85
+ ··· − 330041y + 6889)
20
