11a
116
(K11a
116
)
A knot diagram
1
Linearized knot diagam
5 1 9 7 2 10 3 11 4 6 8
Solving Sequence
1,5
2 3
6,8
7 4 11 9 10
c
1
c
2
c
5
c
7
c
4
c
11
c
8
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h3.00006 × 10
116
u
83
− 6.80069 × 10
116
u
82
+ ··· + 1.41969 × 10
116
b − 5.82904 × 10
117
,
− 2.28133 × 10
118
u
83
+ 8.84656 × 10
118
u
82
+ ··· + 2.41347 × 10
117
a − 2.50578 × 10
119
,
u
84
− 5u
83
+ ··· + 84u − 17i
I
u
2
= h−u
15
+ 4u
13
− u
12
− 10u
11
+ 4u
10
+ 15u
9
− 10u
8
− 18u
7
+ 12u
6
+ 13u
5
− 11u
4
− 6u
3
+ 7u
2
+ b + 2u − 2,
− 4u
15
+ 2u
14
+ ··· + a − 3, u
16
− 4u
14
+ 10u
12
− 16u
10
+ u
9
+ 21u
8
− 19u
6
− 2u
5
+ 11u
4
+ u
3
− 4u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 100 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
= h3.00 × 10
116
u
83
− 6.80 × 10
116
u
82
+ · · · + 1.42 × 10
116
b − 5.83 ×
10
117
, −2.28 × 10
118
u
83
+ 8.85 × 10
118
u
82
+ · · · + 2.41 × 10
117
a − 2.51 ×
10
119
, u
84
− 5u
83
+ · · · + 84u − 17i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
8
=
9.45248u
83
− 36.6550u
82
+ ··· − 485.532u + 103.825
−2.11318u
83
+ 4.79027u
82
+ ··· − 94.7799u + 41.0586
a
7
=
7.48664u
83
− 30.4435u
82
+ ··· − 470.700u + 107.907
−3.18690u
83
+ 11.1199u
82
+ ··· + 76.7100u − 4.10517
a
4
=
2.35529u
83
− 10.5702u
82
+ ··· − 179.463u + 31.5654
−6.32184u
83
+ 25.6009u
82
+ ··· + 384.645u − 88.1719
a
11
=
−2.19228u
83
+ 8.56750u
82
+ ··· + 103.363u − 13.1483
2.18637u
83
− 10.0740u
82
+ ··· − 193.104u + 50.8633
a
9
=
−5.09729u
83
+ 19.6966u
82
+ ··· + 234.342u − 37.5811
1.58854u
83
− 2.48611u
82
+ ··· + 94.3251u − 33.4791
a
10
=
1.48871u
83
− 5.29073u
82
+ ··· − 48.2350u + 12.4535
2.48559u
83
− 14.1259u
82
+ ··· − 360.853u + 102.556
a
10
=
1.48871u
83
− 5.29073u
82
+ ··· − 48.2350u + 12.4535
2.48559u
83
− 14.1259u
82
+ ··· − 360.853u + 102.556
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8.42434u
83
+ 26.3174u
82
+ ··· + 49.5896u − 2.87092
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
84
+ 5u
83
+ ··· − 84u − 17
c
2
u
84
+ 35u
83
+ ··· + 4574u + 289
c
3
, c
9
u
84
− u
83
+ ··· − 344u − 313
c
4
u
84
− 3u
83
+ ··· − 36000u + 7373
c
6
, c
10
u
84
− 2u
83
+ ··· + 2657u + 1007
c
7
u
84
+ u
83
+ ··· + 1236u − 149
c
8
, c
11
u
84
− 4u
83
+ ··· + 943u + 169
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
84
− 35y
83
+ ··· − 4574y + 289
c
2
y
84
+ 37y
83
+ ··· + 1003798y + 83521
c
3
, c
9
y
84
− 63y
83
+ ··· − 575316y + 97969
c
4
y
84
− 23y
83
+ ··· − 1969346598y + 54361129
c
6
, c
10
y
84
+ 58y
83
+ ··· − 14592009y + 1014049
c
7
y
84
+ 9y
83
+ ··· − 735016y + 22201
c
8
, c
11
y
84
+ 54y
83
+ ··· − 133481y + 28561
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.924233 + 0.381001I
a = −1.189090 − 0.186102I
b = −0.584907 + 0.883967I
−5.50829 + 1.23925I 0
u = 0.924233 − 0.381001I
a = −1.189090 + 0.186102I
b = −0.584907 − 0.883967I
−5.50829 − 1.23925I 0
u = 0.848735 + 0.552750I
a = 0.80963 − 1.88902I
b = 0.03682 + 1.54888I
1.67908 − 4.25752I 0
u = 0.848735 − 0.552750I
a = 0.80963 + 1.88902I
b = 0.03682 − 1.54888I
1.67908 + 4.25752I 0
u = 0.845759 + 0.569884I
a = −1.65496 + 1.53990I
b = −0.147553 − 1.309790I
1.66836 − 0.23942I 0
u = 0.845759 − 0.569884I
a = −1.65496 − 1.53990I
b = −0.147553 + 1.309790I
1.66836 + 0.23942I 0
u = 0.968420 + 0.136764I
a = −0.704553 − 0.369797I
b = 0.165468 − 0.727616I
−0.639069 − 0.016973I 0
u = 0.968420 − 0.136764I
a = −0.704553 + 0.369797I
b = 0.165468 + 0.727616I
−0.639069 + 0.016973I 0
u = −0.838743 + 0.586229I
a = −0.283784 − 0.310721I
b = −0.589308 − 0.180708I
1.63611 + 2.33220I 0
u = −0.838743 − 0.586229I
a = −0.283784 + 0.310721I
b = −0.589308 + 0.180708I
1.63611 − 2.33220I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.971423
a = 1.33586
b = 0.757439
−5.46066 0
u = −0.813349 + 0.501390I
a = −0.766920 − 1.077030I
b = 0.55474 + 1.54764I
1.29451 − 0.79166I 0
u = −0.813349 − 0.501390I
a = −0.766920 + 1.077030I
b = 0.55474 − 1.54764I
1.29451 + 0.79166I 0
u = −0.614279 + 0.844816I
a = 0.06379 + 1.49673I
b = −0.219292 − 1.201960I
5.79981 − 0.28419I 0
u = −0.614279 − 0.844816I
a = 0.06379 − 1.49673I
b = −0.219292 + 1.201960I
5.79981 + 0.28419I 0
u = 0.798838 + 0.677298I
a = −1.19317 + 1.38455I
b = 0.34954 − 1.41280I
2.12448 + 0.03164I 0
u = 0.798838 − 0.677298I
a = −1.19317 − 1.38455I
b = 0.34954 + 1.41280I
2.12448 − 0.03164I 0
u = −1.046440 + 0.103775I
a = 0.681099 + 0.610527I
b = 0.332202 + 1.081850I
−2.03076 − 3.48760I 0
u = −1.046440 − 0.103775I
a = 0.681099 − 0.610527I
b = 0.332202 − 1.081850I
−2.03076 + 3.48760I 0
u = −0.914999 + 0.533114I
a = 1.51015 + 1.36327I
b = 0.73110 − 1.33781I
0.92165 + 4.97911I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.914999 − 0.533114I
a = 1.51015 − 1.36327I
b = 0.73110 + 1.33781I
0.92165 − 4.97911I 0
u = −0.935408 + 0.527321I
a = −0.86462 − 2.90843I
b = −0.207875 + 1.010240I
−4.63959 + 6.23446I 0
u = −0.935408 − 0.527321I
a = −0.86462 + 2.90843I
b = −0.207875 − 1.010240I
−4.63959 − 6.23446I 0
u = −0.763420 + 0.761760I
a = 0.973936 + 0.865621I
b = −0.85674 − 1.29167I
1.14157 − 1.26918I 0
u = −0.763420 − 0.761760I
a = 0.973936 − 0.865621I
b = −0.85674 + 1.29167I
1.14157 + 1.26918I 0
u = 0.521170 + 0.758710I
a = 0.03417 + 1.68577I
b = 0.424961 − 1.276360I
3.02744 + 4.89516I 0
u = 0.521170 − 0.758710I
a = 0.03417 − 1.68577I
b = 0.424961 + 1.276360I
3.02744 − 4.89516I 0
u = −0.768826 + 0.492020I
a = 2.46598 + 2.55062I
b = −0.012025 − 0.813250I
−4.06248 − 2.06222I 0
u = −0.768826 − 0.492020I
a = 2.46598 − 2.55062I
b = −0.012025 + 0.813250I
−4.06248 + 2.06222I 0
u = 0.516212 + 0.960636I
a = 0.42670 − 1.54053I
b = −0.57898 + 1.31209I
−0.87258 + 11.01470I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.516212 − 0.960636I
a = 0.42670 + 1.54053I
b = −0.57898 − 1.31209I
−0.87258 − 11.01470I 0
u = 0.909276 + 0.647697I
a = 0.98702 − 1.94972I
b = 0.58065 + 1.37768I
1.77553 − 5.16233I 0
u = 0.909276 − 0.647697I
a = 0.98702 + 1.94972I
b = 0.58065 − 1.37768I
1.77553 + 5.16233I 0
u = −0.481764 + 1.013270I
a = −0.35439 − 1.57120I
b = 0.323971 + 1.259510I
3.90791 − 4.63787I 0
u = −0.481764 − 1.013270I
a = −0.35439 + 1.57120I
b = 0.323971 − 1.259510I
3.90791 + 4.63787I 0
u = 0.961253 + 0.594515I
a = 0.251395 − 0.984707I
b = 0.850842 − 0.051552I
−2.09802 − 5.16082I 0
u = 0.961253 − 0.594515I
a = 0.251395 + 0.984707I
b = 0.850842 + 0.051552I
−2.09802 + 5.16082I 0
u = −1.131210 + 0.112806I
a = −0.733591 − 0.853437I
b = −0.905943 + 0.572167I
−9.57353 − 3.10518I 0
u = −1.131210 − 0.112806I
a = −0.733591 + 0.853437I
b = −0.905943 − 0.572167I
−9.57353 + 3.10518I 0
u = 0.471917 + 0.702478I
a = 0.572616 + 1.060120I
b = −1.144530 − 0.094381I
−4.65745 + 5.03247I −9.49279 − 3.83658I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.471917 − 0.702478I
a = 0.572616 − 1.060120I
b = −1.144530 + 0.094381I
−4.65745 − 5.03247I −9.49279 + 3.83658I
u = 1.096910 + 0.382434I
a = −1.061400 − 0.276192I
b = −0.531659 − 0.788541I
−5.82688 − 3.28009I 0
u = 1.096910 − 0.382434I
a = −1.061400 + 0.276192I
b = −0.531659 + 0.788541I
−5.82688 + 3.28009I 0
u = −0.942860 + 0.714978I
a = −0.78435 − 1.79433I
b = −1.03147 + 1.21286I
0.59518 + 6.86334I 0
u = −0.942860 − 0.714978I
a = −0.78435 + 1.79433I
b = −1.03147 − 1.21286I
0.59518 − 6.86334I 0
u = 0.596089 + 0.557713I
a = −0.347197 − 0.090408I
b = 0.773058 − 0.097107I
−1.089040 + 0.486692I −7.73280 − 0.29333I
u = 0.596089 − 0.557713I
a = −0.347197 + 0.090408I
b = 0.773058 + 0.097107I
−1.089040 − 0.486692I −7.73280 + 0.29333I
u = −1.056950 + 0.545848I
a = 0.208689 + 0.551098I
b = 1.020060 − 0.148712I
−2.67134 + 5.68638I 0
u = −1.056950 − 0.545848I
a = 0.208689 − 0.551098I
b = 1.020060 + 0.148712I
−2.67134 − 5.68638I 0
u = −1.140200 + 0.448126I
a = 0.650913 − 0.755668I
b = −0.174963 − 0.798938I
−5.41622 + 4.47785I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.140200 − 0.448126I
a = 0.650913 + 0.755668I
b = −0.174963 + 0.798938I
−5.41622 − 4.47785I 0
u = 1.061020 + 0.614747I
a = 0.288056 + 0.710613I
b = −1.345650 + 0.262453I
−6.34457 − 10.11980I 0
u = 1.061020 − 0.614747I
a = 0.288056 − 0.710613I
b = −1.345650 − 0.262453I
−6.34457 + 10.11980I 0
u = 0.476265 + 1.137210I
a = 0.061878 + 1.260730I
b = −0.227503 − 0.997805I
−1.16692 − 5.02448I 0
u = 0.476265 − 1.137210I
a = 0.061878 − 1.260730I
b = −0.227503 + 0.997805I
−1.16692 + 5.02448I 0
u = 1.066260 + 0.631314I
a = 1.69408 − 1.38250I
b = 0.521263 + 1.244830I
1.40099 − 10.18500I 0
u = 1.066260 − 0.631314I
a = 1.69408 + 1.38250I
b = 0.521263 − 1.244830I
1.40099 + 10.18500I 0
u = −1.049430 + 0.693298I
a = −1.32203 − 1.27305I
b = −0.376111 + 1.147870I
4.46403 + 6.01634I 0
u = −1.049430 − 0.693298I
a = −1.32203 + 1.27305I
b = −0.376111 − 1.147870I
4.46403 − 6.01634I 0
u = 0.886751 + 0.914091I
a = 0.71937 − 1.38169I
b = −0.068110 + 0.784716I
−2.24639 − 3.36926I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.886751 − 0.914091I
a = 0.71937 + 1.38169I
b = −0.068110 − 0.784716I
−2.24639 + 3.36926I 0
u = 1.239180 + 0.296514I
a = 0.196626 − 0.608379I
b = 0.407542 + 0.459768I
−4.43546 − 1.79841I 0
u = 1.239180 − 0.296514I
a = 0.196626 + 0.608379I
b = 0.407542 − 0.459768I
−4.43546 + 1.79841I 0
u = −0.089516 + 0.711684I
a = 0.174468 − 0.352691I
b = −0.325409 + 0.982794I
−2.36639 − 0.26933I −7.90830 − 0.43010I
u = −0.089516 − 0.711684I
a = 0.174468 + 0.352691I
b = −0.325409 − 0.982794I
−2.36639 + 0.26933I −7.90830 + 0.43010I
u = −0.664677 + 0.252947I
a = 0.205579 + 0.749494I
b = 0.732836 + 0.736371I
−0.78313 − 1.64097I −1.66824 + 0.93836I
u = −0.664677 − 0.252947I
a = 0.205579 − 0.749494I
b = 0.732836 − 0.736371I
−0.78313 + 1.64097I −1.66824 − 0.93836I
u = 0.701904
a = −0.582122
b = 0.199043
−0.948107 −10.6510
u = −1.315360 + 0.063866I
a = −0.374103 − 0.149155I
b = −0.583906 + 1.040760I
−8.01674 + 8.52986I 0
u = −1.315360 − 0.063866I
a = −0.374103 + 0.149155I
b = −0.583906 − 1.040760I
−8.01674 − 8.52986I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.134840 + 0.703653I
a = −1.17173 + 1.58065I
b = −0.67909 − 1.35235I
−2.7877 − 17.0880I 0
u = 1.134840 − 0.703653I
a = −1.17173 − 1.58065I
b = −0.67909 + 1.35235I
−2.7877 + 17.0880I 0
u = −1.151250 + 0.708883I
a = 1.04101 + 1.44139I
b = 0.472819 − 1.330060I
1.84085 + 10.83500I 0
u = −1.151250 − 0.708883I
a = 1.04101 − 1.44139I
b = 0.472819 + 1.330060I
1.84085 − 10.83500I 0
u = 0.228391 + 0.589108I
a = −0.05996 − 1.99843I
b = 0.234801 + 1.210160I
2.17927 − 2.72756I −0.28263 + 2.49984I
u = 0.228391 − 0.589108I
a = −0.05996 + 1.99843I
b = 0.234801 − 1.210160I
2.17927 + 2.72756I −0.28263 − 2.49984I
u = 1.14069 + 0.84432I
a = −0.51171 + 1.44701I
b = −0.239373 − 1.032900I
−2.98338 − 3.56955I 0
u = 1.14069 − 0.84432I
a = −0.51171 − 1.44701I
b = −0.239373 + 1.032900I
−2.98338 + 3.56955I 0
u = 1.35887 + 0.47598I
a = 0.227188 − 0.474705I
b = 0.005261 + 0.633644I
−4.54385 − 1.75387I 0
u = 1.35887 − 0.47598I
a = 0.227188 + 0.474705I
b = 0.005261 − 0.633644I
−4.54385 + 1.75387I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.488547 + 0.241932I
a = −1.66058 − 1.59540I
b = −0.692567 − 0.483700I
−4.39462 − 4.01027I −12.15712 + 6.29625I
u = 0.488547 − 0.241932I
a = −1.66058 + 1.59540I
b = −0.692567 + 0.483700I
−4.39462 + 4.01027I −12.15712 − 6.29625I
u = −0.186177 + 0.504914I
a = −0.700709 + 0.678816I
b = 0.526788 + 0.321365I
−0.67069 − 1.40506I −6.14953 + 4.21758I
u = −0.186177 − 0.504914I
a = −0.700709 − 0.678816I
b = 0.526788 − 0.321365I
−0.67069 + 1.40506I −6.14953 − 4.21758I
13
II. I
u
2
=
h−u
15
+4u
13
+· · · +b−2, −4u
15
+2u
14
+· · · +a−3, u
16
−4u
14
+· · · −4u
2
+1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
8
=
4u
15
− 2u
14
+ ··· − 8u + 3
u
15
− 4u
13
+ ··· − 2u + 2
a
7
=
3u
15
− 2u
14
+ ··· − 5u + 2
2u
15
− u
14
+ ··· − 2u + 3
a
4
=
−4u
15
+ 3u
14
+ ··· + 5u − 3
−u
11
+ u
10
+ 3u
9
− 4u
8
− 5u
7
+ 8u
6
+ 4u
5
− 10u
4
− 3u
3
+ 8u
2
+ u − 2
a
11
=
−4u
15
+ 2u
14
+ ··· + u − 2
u
14
− 3u
12
+ 6u
10
+ u
9
− 7u
8
− 2u
7
+ 9u
6
+ 6u
5
− 6u
4
− 6u
3
+ 2u
2
+ 2u
a
9
=
u
15
− u
14
+ ··· − 3u + 4
2u
15
− u
14
+ ··· + 4u
3
+ u
2
a
10
=
−2u
15
+ 7u
13
+ ··· − u
2
− u
−u
15
+ 2u
14
+ ··· + 4u
2
+ 2u
a
10
=
−2u
15
+ 7u
13
+ ··· − u
2
− u
−u
15
+ 2u
14
+ ··· + 4u
2
+ 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 11u
15
−12u
14
−31u
13
+ 38u
12
+ 61u
11
−78u
10
−68u
9
+ 106u
8
+
68u
7
− 95u
6
− 46u
5
+ 42u
4
+ 16u
3
− 17u
2
+ 2u − 9
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 4u
14
+ ··· − 4u
2
+ 1
c
2
u
16
+ 8u
15
+ ··· + 8u + 1
c
3
u
16
− 8u
14
+ ··· + 4u + 1
c
4
u
16
− 4u
15
+ ··· − 2u + 1
c
5
u
16
− 4u
14
+ ··· − 4u
2
+ 1
c
6
u
16
− u
15
+ ··· + 3u + 1
c
7
u
16
− 2u
14
+ ··· + 4u + 1
c
8
u
16
− 3u
15
+ ··· + u + 1
c
9
u
16
− 8u
14
+ ··· − 4u + 1
c
10
u
16
+ u
15
+ ··· − 3u + 1
c
11
u
16
+ 3u
15
+ ··· − u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
16
− 8y
15
+ ··· − 8y + 1
c
2
y
16
+ 8y
15
+ ··· + 12y + 1
c
3
, c
9
y
16
− 16y
15
+ ··· − 22y + 1
c
4
y
16
+ 8y
14
+ ··· + 18y
2
+ 1
c
6
, c
10
y
16
+ 13y
15
+ ··· + 13y + 1
c
7
y
16
− 4y
15
+ ··· − 6y + 1
c
8
, c
11
y
16
+ 13y
15
+ ··· + 13y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.743083 + 0.662007I
a = 1.10772 + 1.11669I
b = −0.68673 − 1.45406I
2.51186 − 1.38116I −1.59506 + 3.07074I
u = −0.743083 − 0.662007I
a = 1.10772 − 1.11669I
b = −0.68673 + 1.45406I
2.51186 + 1.38116I −1.59506 − 3.07074I
u = 0.885879 + 0.145084I
a = −0.298457 + 0.589537I
b = −0.592866 + 0.819454I
−1.41793 + 1.66100I −14.4564 − 2.0605I
u = 0.885879 − 0.145084I
a = −0.298457 − 0.589537I
b = −0.592866 − 0.819454I
−1.41793 − 1.66100I −14.4564 + 2.0605I
u = −1.043810 + 0.383036I
a = −0.141538 − 1.091570I
b = 0.247994 − 0.520970I
−6.09539 + 5.48551I −15.0605 − 7.1946I
u = −1.043810 − 0.383036I
a = −0.141538 + 1.091570I
b = 0.247994 + 0.520970I
−6.09539 − 5.48551I −15.0605 + 7.1946I
u = −0.956828 + 0.652363I
a = −1.05291 − 1.74822I
b = −0.85612 + 1.30516I
1.84373 + 6.50590I −4.33080 − 8.06359I
u = −0.956828 − 0.652363I
a = −1.05291 + 1.74822I
b = −0.85612 − 1.30516I
1.84373 − 6.50590I −4.33080 + 8.06359I
u = −0.731255 + 0.295921I
a = 2.09759 + 1.66067I
b = 0.399130 + 0.560216I
−4.84776 − 2.55983I −14.7658 + 4.1285I
u = −0.731255 − 0.295921I
a = 2.09759 − 1.66067I
b = 0.399130 − 0.560216I
−4.84776 + 2.55983I −14.7658 − 4.1285I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.807009 + 0.916229I
a = 0.14430 − 1.70974I
b = 0.240373 + 0.893634I
−2.15077 − 4.46693I −9.53645 + 8.11349I
u = 0.807009 − 0.916229I
a = 0.14430 + 1.70974I
b = 0.240373 − 0.893634I
−2.15077 + 4.46693I −9.53645 − 8.11349I
u = 0.489877 + 0.414849I
a = −1.23723 + 2.02758I
b = −0.214471 − 1.388330I
1.19758 − 2.88706I −9.08478 + 2.57984I
u = 0.489877 − 0.414849I
a = −1.23723 − 2.02758I
b = −0.214471 + 1.388330I
1.19758 + 2.88706I −9.08478 − 2.57984I
u = 1.292210 + 0.554134I
a = −0.619476 + 0.381495I
b = −0.037307 − 0.762535I
−4.20079 − 2.10743I −7.17016 + 5.74785I
u = 1.292210 − 0.554134I
a = −0.619476 − 0.381495I
b = −0.037307 + 0.762535I
−4.20079 + 2.10743I −7.17016 − 5.74785I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
16
− 4u
14
+ ··· − 4u
2
+ 1)(u
84
+ 5u
83
+ ··· − 84u − 17)
c
2
(u
16
+ 8u
15
+ ··· + 8u + 1)(u
84
+ 35u
83
+ ··· + 4574u + 289)
c
3
(u
16
− 8u
14
+ ··· + 4u + 1)(u
84
− u
83
+ ··· − 344u − 313)
c
4
(u
16
− 4u
15
+ ··· − 2u + 1)(u
84
− 3u
83
+ ··· − 36000u + 7373)
c
5
(u
16
− 4u
14
+ ··· − 4u
2
+ 1)(u
84
+ 5u
83
+ ··· − 84u − 17)
c
6
(u
16
− u
15
+ ··· + 3u + 1)(u
84
− 2u
83
+ ··· + 2657u + 1007)
c
7
(u
16
− 2u
14
+ ··· + 4u + 1)(u
84
+ u
83
+ ··· + 1236u − 149)
c
8
(u
16
− 3u
15
+ ··· + u + 1)(u
84
− 4u
83
+ ··· + 943u + 169)
c
9
(u
16
− 8u
14
+ ··· − 4u + 1)(u
84
− u
83
+ ··· − 344u − 313)
c
10
(u
16
+ u
15
+ ··· − 3u + 1)(u
84
− 2u
83
+ ··· + 2657u + 1007)
c
11
(u
16
+ 3u
15
+ ··· − u + 1)(u
84
− 4u
83
+ ··· + 943u + 169)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
16
− 8y
15
+ ··· − 8y + 1)(y
84
− 35y
83
+ ··· − 4574y + 289)
c
2
(y
16
+ 8y
15
+ ··· + 12y + 1)(y
84
+ 37y
83
+ ··· + 1003798y + 83521)
c
3
, c
9
(y
16
− 16y
15
+ ··· − 22y + 1)(y
84
− 63y
83
+ ··· − 575316y + 97969)
c
4
(y
16
+ 8y
14
+ ··· + 18y
2
+ 1)
· (y
84
− 23y
83
+ ··· − 1969346598y + 54361129)
c
6
, c
10
(y
16
+ 13y
15
+ ··· + 13y + 1)
· (y
84
+ 58y
83
+ ··· − 14592009y + 1014049)
c
7
(y
16
− 4y
15
+ ··· − 6y + 1)(y
84
+ 9y
83
+ ··· − 735016y + 22201)
c
8
, c
11
(y
16
+ 13y
15
+ ··· + 13y + 1)(y
84
+ 54y
83
+ ··· − 133481y + 28561)
20
