11a
270
(K11a
270
)
A knot diagram
1
Linearized knot diagam
9 8 1 10 2 3 11 6 5 4 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
= h6.22010 × 10
178
u
84
− 1.04877 × 10
178
u
83
+ ··· + 1.33787 × 10
178
b − 2.94730 × 10
180
,
7.81629 × 10
180
u
84
− 4.66338 × 10
179
u
83
+ ··· + 1.19071 × 10
180
a − 4.40124 × 10
182
,
u
85
+ 22u
83
+ ··· + 295u − 89i
I
u
2
= h−u
16
+ u
15
+ ··· + b − 2u, 37u
16
− 30u
15
+ ··· + 3a + 35,
u
17
− u
16
+ 4u
15
− 4u
14
+ 6u
13
− 7u
12
− u
11
− 16u
9
+ 19u
8
− 27u
7
+ 33u
6
− 22u
5
+ 24u
4
− 8u
3
+ 8u
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
= h6.22 × 10
178
u
84
− 1.05 × 10
178
u
83
+ · · · + 1.34 × 10
178
b − 2.95 ×
10
180
, 7.82 × 10
180
u
84
− 4.66 × 10
179
u
83
+ · · · + 1.19 × 10
180
a − 4.40 ×
10
182
, u
85
+ 22u
83
+ · · · + 295u − 89i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
1
=
u
u
a
3
=
−6.56441u
84
+ 0.391648u
83
+ ··· − 695.862u + 369.633
−4.64925u
84
+ 0.783909u
83
+ ··· − 336.319u + 220.298
a
4
=
−4.93046u
84
− 0.281089u
83
+ ··· − 750.595u + 334.722
−3.01529u
84
+ 0.111172u
83
+ ··· − 391.051u + 185.387
a
2
=
−6.44414u
84
− 1.95066u
83
+ ··· − 1731.95u + 624.788
−5.82573u
84
− 0.575017u
83
+ ··· − 1038.01u + 428.764
a
6
=
18.3104u
84
− 3.35235u
83
+ ··· + 987.156u − 751.241
14.6628u
84
− 4.03186u
83
+ ··· + 189.488u − 456.528
a
9
=
14.7840u
84
+ 23.8120u
83
+ ··· + 11886.5u − 3407.30
13.1209u
84
+ 19.3511u
83
+ ··· + 9780.17u − 2819.79
a
5
=
26.1341u
84
− 10.8653u
83
+ ··· − 1474.91u − 346.013
17.7162u
84
− 10.4087u
83
+ ··· − 2202.90u + 77.1428
a
10
=
−1.61190u
84
+ 12.6221u
83
+ ··· + 5431.09u − 1319.21
0.891403u
84
+ 6.87910u
83
+ ··· + 3129.32u − 802.311
a
10
=
−1.61190u
84
+ 12.6221u
83
+ ··· + 5431.09u − 1319.21
0.891403u
84
+ 6.87910u
83
+ ··· + 3129.32u − 802.311
(ii) Obstruction class = −1
(iii) Cusp Shapes = 10.9888u
84
− 31.5549u
83
+ ··· − 12310.5u + 2763.36
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
85
− 4u
84
+ ··· + 405u − 83
c
2
u
85
− u
84
+ ··· − 171u − 89
c
3
u
85
+ u
84
+ ··· + 172u + 28
c
4
, c
9
, c
10
u
85
+ u
84
+ ··· + 28u − 1
c
5
u
85
− 2u
84
+ ··· + 2503u + 701
c
6
u
85
− 3u
84
+ ··· − 216u − 47
c
7
, c
11
u
85
+ 22u
83
+ ··· + 295u − 89
c
8
u
85
+ 6u
84
+ ··· − 18u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
85
− 22y
84
+ ··· + 57951y −6889
c
2
y
85
+ 5y
84
+ ··· − 428219y −7921
c
3
y
85
− y
84
+ ··· + 36528y −784
c
4
, c
9
, c
10
y
85
+ 91y
84
+ ··· + 108y −1
c
5
y
85
− 26y
84
+ ··· + 15305105y −491401
c
6
y
85
− 27y
84
+ ··· − 226978y −2209
c
7
, c
11
y
85
+ 44y
84
+ ··· − 152029y −7921
c
8
y
85
+ 14y
84
+ ··· − 46y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.990583 + 0.156780I
a = −0.010000 − 0.290185I
b = 0.910228 − 0.729936I
0.50703 + 7.20249I 0
u = −0.990583 − 0.156780I
a = −0.010000 + 0.290185I
b = 0.910228 + 0.729936I
0.50703 − 7.20249I 0
u = 0.348189 + 0.949764I
a = −0.299627 − 0.451517I
b = 0.343573 + 1.260330I
5.97217 − 3.17989I 0
u = 0.348189 − 0.949764I
a = −0.299627 + 0.451517I
b = 0.343573 − 1.260330I
5.97217 + 3.17989I 0
u = −0.826847 + 0.527088I
a = −1.26230 + 0.66261I
b = −0.805769 − 0.073598I
7.26328 − 2.81966I 0
u = −0.826847 − 0.527088I
a = −1.26230 − 0.66261I
b = −0.805769 + 0.073598I
7.26328 + 2.81966I 0
u = −0.504249 + 0.900938I
a = −0.495942 − 0.147918I
b = −0.175068 + 0.862462I
6.60839 − 2.04669I 0
u = −0.504249 − 0.900938I
a = −0.495942 + 0.147918I
b = −0.175068 − 0.862462I
6.60839 + 2.04669I 0
u = 0.370751 + 0.964511I
a = 2.09678 + 0.74849I
b = 1.78001 − 0.38010I
−1.29284 + 1.77043I 0
u = 0.370751 − 0.964511I
a = 2.09678 − 0.74849I
b = 1.78001 + 0.38010I
−1.29284 − 1.77043I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.121508 + 1.029770I
a = −1.44704 + 0.90742I
b = −1.006470 − 0.378372I
−3.93614 − 0.79985I 0
u = −0.121508 − 1.029770I
a = −1.44704 − 0.90742I
b = −1.006470 + 0.378372I
−3.93614 + 0.79985I 0
u = −0.532279 + 0.762499I
a = −1.46595 − 0.28104I
b = −0.0316121 + 0.1122330I
7.05028 − 2.25316I 0
u = −0.532279 − 0.762499I
a = −1.46595 + 0.28104I
b = −0.0316121 − 0.1122330I
7.05028 + 2.25316I 0
u = −0.251015 + 1.055200I
a = −2.11732 − 0.34070I
b = −0.701200 − 0.509768I
−0.68905 − 4.95944I 0
u = −0.251015 − 1.055200I
a = −2.11732 + 0.34070I
b = −0.701200 + 0.509768I
−0.68905 + 4.95944I 0
u = −0.290713 + 0.867463I
a = 1.38286 − 0.59197I
b = 1.28028 − 1.10864I
5.29095 − 1.80419I 0
u = −0.290713 − 0.867463I
a = 1.38286 + 0.59197I
b = 1.28028 + 1.10864I
5.29095 + 1.80419I 0
u = −0.270696 + 0.871703I
a = 2.72325 + 0.14432I
b = 1.54169 + 0.09691I
5.31835 − 0.73098I 0
u = −0.270696 − 0.871703I
a = 2.72325 − 0.14432I
b = 1.54169 − 0.09691I
5.31835 + 0.73098I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.476405 + 0.979571I
a = 0.020053 − 0.849554I
b = −0.55978 − 1.60625I
6.89508 + 8.42993I 0
u = 0.476405 − 0.979571I
a = 0.020053 + 0.849554I
b = −0.55978 + 1.60625I
6.89508 − 8.42993I 0
u = −0.251627 + 0.867975I
a = 1.72706 + 0.60350I
b = 0.898499 + 0.920377I
0.47607 + 1.35841I 0
u = −0.251627 − 0.867975I
a = 1.72706 − 0.60350I
b = 0.898499 − 0.920377I
0.47607 − 1.35841I 0
u = 0.867924 + 0.117197I
a = 0.401814 − 0.078087I
b = 0.073704 − 0.631355I
2.45654 + 0.38545I 0
u = 0.867924 − 0.117197I
a = 0.401814 + 0.078087I
b = 0.073704 + 0.631355I
2.45654 − 0.38545I 0
u = −0.511179 + 1.033880I
a = −0.860377 + 0.932551I
b = −1.197380 − 0.080280I
−3.67030 − 1.93800I 0
u = −0.511179 − 1.033880I
a = −0.860377 − 0.932551I
b = −1.197380 + 0.080280I
−3.67030 + 1.93800I 0
u = 0.804514 + 0.199840I
a = −0.254918 − 0.463753I
b = 0.861149 + 0.863904I
4.16809 − 3.00834I 0
u = 0.804514 − 0.199840I
a = −0.254918 + 0.463753I
b = 0.861149 − 0.863904I
4.16809 + 3.00834I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.224344 + 0.788625I
a = 3.65794 − 0.56435I
b = 0.411602 − 0.536484I
6.72774 + 5.81245I 0. − 10.65615I
u = 0.224344 − 0.788625I
a = 3.65794 + 0.56435I
b = 0.411602 + 0.536484I
6.72774 − 5.81245I 0. + 10.65615I
u = 1.151880 + 0.340683I
a = −0.125453 − 0.215082I
b = −1.039420 − 0.763839I
7.27474 − 10.59070I 0
u = 1.151880 − 0.340683I
a = −0.125453 + 0.215082I
b = −1.039420 + 0.763839I
7.27474 + 10.59070I 0
u = −0.451547 + 1.119340I
a = −1.83462 + 0.36797I
b = −1.37742 − 0.92532I
−3.81248 − 5.22210I 0
u = −0.451547 − 1.119340I
a = −1.83462 − 0.36797I
b = −1.37742 + 0.92532I
−3.81248 + 5.22210I 0
u = −0.261477 + 0.747690I
a = −0.432549 − 1.141910I
b = 0.03198 − 1.67566I
0.88272 − 4.07370I 0. + 10.38748I
u = −0.261477 − 0.747690I
a = −0.432549 + 1.141910I
b = 0.03198 + 1.67566I
0.88272 + 4.07370I 0. − 10.38748I
u = 0.282937 + 1.182750I
a = 1.022110 + 0.688758I
b = 1.125510 + 0.384277I
−0.241277 + 0.561006I 0
u = 0.282937 − 1.182750I
a = 1.022110 − 0.688758I
b = 1.125510 − 0.384277I
−0.241277 − 0.561006I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.289715 + 0.708348I
a = 0.642373 + 0.547818I
b = 0.358840 + 0.533193I
−0.10663 + 1.41201I 0. − 4.19142I
u = 0.289715 − 0.708348I
a = 0.642373 − 0.547818I
b = 0.358840 − 0.533193I
−0.10663 − 1.41201I 0. + 4.19142I
u = 0.772781 + 0.972939I
a = 0.563431 + 0.899223I
b = 1.392510 − 0.236188I
1.25410 + 3.01463I 0
u = 0.772781 − 0.972939I
a = 0.563431 − 0.899223I
b = 1.392510 + 0.236188I
1.25410 − 3.01463I 0
u = 0.405461 + 1.174790I
a = −1.92488 + 0.10074I
b = −1.51977 + 0.86693I
−3.19196 + 6.54059I 0
u = 0.405461 − 1.174790I
a = −1.92488 − 0.10074I
b = −1.51977 − 0.86693I
−3.19196 − 6.54059I 0
u = 0.283503 + 1.211850I
a = 1.23366 + 0.88279I
b = 0.781274 − 0.343663I
−4.50297 + 4.26915I 0
u = 0.283503 − 1.211850I
a = 1.23366 − 0.88279I
b = 0.781274 + 0.343663I
−4.50297 − 4.26915I 0
u = 1.24666
a = 0.301059
b = 0.416139
2.46366 0
u = 0.483671 + 0.546181I
a = −2.58654 − 0.36620I
b = −0.779143 + 0.909707I
8.18862 − 4.43585I 5.12877 + 0.I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.483671 − 0.546181I
a = −2.58654 + 0.36620I
b = −0.779143 − 0.909707I
8.18862 + 4.43585I 5.12877 + 0.I
u = 0.531255 + 1.172220I
a = 1.68589 + 0.40460I
b = 1.08577 − 1.17737I
1.30376 + 7.93201I 0
u = 0.531255 − 1.172220I
a = 1.68589 − 0.40460I
b = 1.08577 + 1.17737I
1.30376 − 7.93201I 0
u = 0.470292 + 1.198160I
a = −1.090840 + 0.207986I
b = −0.837680 + 0.961854I
−0.82206 + 4.30776I 0
u = 0.470292 − 1.198160I
a = −1.090840 − 0.207986I
b = −0.837680 − 0.961854I
−0.82206 − 4.30776I 0
u = −1.184660 + 0.505149I
a = −0.169952 − 0.204856I
b = 0.530026 − 0.504262I
8.34857 + 2.37496I 0
u = −1.184660 − 0.505149I
a = −0.169952 + 0.204856I
b = 0.530026 + 0.504262I
8.34857 − 2.37496I 0
u = 0.573453 + 1.187210I
a = −0.255978 − 0.616026I
b = −0.567825 + 0.210292I
−2.13717 + 1.86843I 0
u = 0.573453 − 1.187210I
a = −0.255978 + 0.616026I
b = −0.567825 − 0.210292I
−2.13717 − 1.86843I 0
u = −0.281772 + 1.330610I
a = 0.791575 − 0.657737I
b = 0.774412 + 0.043237I
−4.64818 + 2.67744I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.281772 − 1.330610I
a = 0.791575 + 0.657737I
b = 0.774412 − 0.043237I
−4.64818 − 2.67744I 0
u = −0.553567 + 1.250070I
a = 1.70321 − 0.18110I
b = 1.41016 + 0.89938I
−2.87315 − 12.69490I 0
u = −0.553567 − 1.250070I
a = 1.70321 + 0.18110I
b = 1.41016 − 0.89938I
−2.87315 + 12.69490I 0
u = −0.399494 + 1.309870I
a = −1.22949 + 0.92957I
b = −0.642917 − 0.341349I
1.87995 − 6.80929I 0
u = −0.399494 − 1.309870I
a = −1.22949 − 0.92957I
b = −0.642917 + 0.341349I
1.87995 + 6.80929I 0
u = 0.595445 + 0.174267I
a = 0.575031 + 0.318263I
b = −0.597052 + 0.752886I
0.34617 + 2.88115I 1.43324 − 4.17633I
u = 0.595445 − 0.174267I
a = 0.575031 − 0.318263I
b = −0.597052 − 0.752886I
0.34617 − 2.88115I 1.43324 + 4.17633I
u = −0.154501 + 0.596781I
a = 0.438606 − 0.655981I
b = −0.352733 + 1.047410I
0.84143 + 2.66817I 5.48084 + 2.01191I
u = −0.154501 − 0.596781I
a = 0.438606 + 0.655981I
b = −0.352733 − 1.047410I
0.84143 − 2.66817I 5.48084 − 2.01191I
u = 0.461171 + 0.387458I
a = 0.585527 + 1.214750I
b = 0.869382 + 0.309042I
−0.10975 + 1.69726I 1.00781 − 4.89719I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.461171 − 0.387458I
a = 0.585527 − 1.214750I
b = 0.869382 − 0.309042I
−0.10975 − 1.69726I 1.00781 + 4.89719I
u = 0.537044 + 1.295450I
a = 1.46046 + 0.21109I
b = 1.054190 − 0.533366I
−1.81524 + 5.66138I 0
u = 0.537044 − 1.295450I
a = 1.46046 − 0.21109I
b = 1.054190 + 0.533366I
−1.81524 − 5.66138I 0
u = −0.694195 + 1.229040I
a = 1.023410 − 0.120682I
b = 0.911760 + 0.906877I
5.84291 − 9.00773I 0
u = −0.694195 − 1.229040I
a = 1.023410 + 0.120682I
b = 0.911760 − 0.906877I
5.84291 + 9.00773I 0
u = −0.546200 + 0.154942I
a = 0.615539 + 0.119715I
b = −0.786001 + 0.587111I
−1.15598 + 1.24391I −4.65832 − 4.55750I
u = −0.546200 − 0.154942I
a = 0.615539 − 0.119715I
b = −0.786001 − 0.587111I
−1.15598 − 1.24391I −4.65832 + 4.55750I
u = 0.67035 + 1.26586I
a = −1.60680 − 0.35437I
b = −1.35253 + 0.93606I
4.3164 + 17.0324I 0
u = 0.67035 − 1.26586I
a = −1.60680 + 0.35437I
b = −1.35253 − 0.93606I
4.3164 − 17.0324I 0
u = −1.40601 + 0.30370I
a = −0.302783 − 0.013160I
b = −0.716976 + 0.312930I
7.71128 − 0.46262I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40601 − 0.30370I
a = −0.302783 + 0.013160I
b = −0.716976 − 0.312930I
7.71128 + 0.46262I 0
u = −0.00121 + 1.51049I
a = −1.084020 − 0.360717I
b = −0.997531 − 0.147584I
−0.00345 − 5.98667I 0
u = −0.00121 − 1.51049I
a = −1.084020 + 0.360717I
b = −0.997531 + 0.147584I
−0.00345 + 5.98667I 0
u = −0.73908 + 1.37329I
a = −1.272940 + 0.343655I
b = −1.090350 − 0.558936I
4.16408 − 6.92555I 0
u = −0.73908 − 1.37329I
a = −1.272940 − 0.343655I
b = −1.090350 + 0.558936I
4.16408 + 6.92555I 0
13
II. I
u
2
=
h−u
16
+u
15
+· · ·+b −2u, 37u
16
−30u
15
+· · ·+3a +35, u
17
−u
16
+· · ·−u +1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
1
=
u
u
a
3
=
−
37
3
u
16
+ 10u
15
+ ··· − 27u −
35
3
u
16
− u
15
+ ··· − u
2
+ 2u
a
4
=
−
23
3
u
16
+ 5u
15
+ ··· − 16u −
28
3
17
3
u
16
− 6u
15
+ ··· + 13u +
7
3
a
2
=
−
23
3
u
16
+ 5u
15
+ ··· − 15u −
28
3
10
3
u
16
− 4u
15
+ ··· + 7u −
1
3
a
6
=
2
3
u
16
− 6u
15
+ ··· + 30u −
50
3
−2u
16
+ 6u
15
+ ··· − 7u + 5
a
9
=
16
3
u
16
− 3u
15
+ ··· − u −
10
3
26
3
u
16
− 10u
15
+ ··· + 24u −
32
3
a
5
=
3u
16
+ 9u
15
+ ··· − 11u + 29
−4u
16
+ 15u
15
+ ··· − 29u + 20
a
10
=
14
3
u
16
− 14u
15
+ ··· + 46u −
56
3
−
7
3
u
16
+ 3u
15
+ ··· − 8u +
31
3
a
10
=
14
3
u
16
− 14u
15
+ ··· + 46u −
56
3
−
7
3
u
16
+ 3u
15
+ ··· − 8u +
31
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 42u
16
− 60u
15
+ 163u
14
− 217u
13
+ 242u
12
− 312u
11
− 22u
10
+
163u
9
− 619u
8
+ 1042u
7
− 1162u
6
+ 1414u
5
− 1028u
4
+ 759u
3
− 380u
2
+ 131u − 50
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
+ u
16
+ ··· − 3u − 1
c
2
u
17
− 2u
15
+ ··· − u − 1
c
3
u
17
+ 6u
16
+ ··· + 24u + 4
c
4
u
17
+ 11u
15
+ ··· + 2u + 1
c
5
u
17
+ u
16
+ ··· − 5u − 1
c
6
u
17
− 4u
16
+ ··· − 2u + 1
c
7
u
17
− u
16
+ ··· − u + 1
c
8
u
17
− 3u
16
+ ··· − 2u
2
− 1
c
9
, c
10
u
17
+ 11u
15
+ ··· + 2u − 1
c
11
u
17
+ u
16
+ ··· − u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 11y
16
+ ··· − 3y −1
c
2
y
17
− 4y
16
+ ··· + 23y −1
c
3
y
17
+ 6y
16
+ ··· + 96y −16
c
4
, c
9
, c
10
y
17
+ 22y
16
+ ··· + 14y −1
c
5
y
17
− 7y
16
+ ··· + 11y −1
c
6
y
17
− 8y
16
+ ··· + 12y −1
c
7
, c
11
y
17
+ 7y
16
+ ··· − 15y −1
c
8
y
17
+ 5y
16
+ ··· − 4y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.296158 + 0.962340I
a = 1.74880 + 1.17015I
b = 1.69902 − 0.03786I
−1.66547 + 1.22003I −7.34562 + 1.66081I
u = 0.296158 − 0.962340I
a = 1.74880 − 1.17015I
b = 1.69902 + 0.03786I
−1.66547 − 1.22003I −7.34562 − 1.66081I
u = 0.266286 + 0.834120I
a = 2.23710 + 0.20745I
b = 1.39150 + 0.57569I
5.58457 + 1.36975I 7.85861 − 1.02572I
u = 0.266286 − 0.834120I
a = 2.23710 − 0.20745I
b = 1.39150 − 0.57569I
5.58457 − 1.36975I 7.85861 + 1.02572I
u = 1.197910 + 0.041998I
a = 0.213861 − 0.495187I
b = 0.492186 − 0.003093I
7.65655 − 1.53651I 3.05438 + 1.89060I
u = 1.197910 − 0.041998I
a = 0.213861 + 0.495187I
b = 0.492186 + 0.003093I
7.65655 + 1.53651I 3.05438 − 1.89060I
u = −0.632711 + 1.066170I
a = −0.491801 + 0.633446I
b = −0.849453 − 0.302995I
−2.32528 − 2.66972I −3.07111 + 6.02917I
u = −0.632711 − 1.066170I
a = −0.491801 − 0.633446I
b = −0.849453 + 0.302995I
−2.32528 + 2.66972I −3.07111 − 6.02917I
u = −0.399374 + 1.204610I
a = −1.59525 + 0.01774I
b = −1.031450 − 0.727650I
−2.43226 − 4.98909I −3.85930 + 5.31412I
u = −0.399374 − 1.204610I
a = −1.59525 − 0.01774I
b = −1.031450 + 0.727650I
−2.43226 + 4.98909I −3.85930 − 5.31412I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.29892
a = −0.218895
b = −0.483375
2.34345 −34.4900
u = −0.024098 + 0.674226I
a = 0.994603 + 0.408289I
b = −0.117213 + 1.227870I
0.44571 + 3.07804I −4.36238 − 7.29027I
u = −0.024098 − 0.674226I
a = 0.994603 − 0.408289I
b = −0.117213 − 1.227870I
0.44571 − 3.07804I −4.36238 + 7.29027I
u = 0.481433 + 1.326120I
a = 1.38140 + 0.37383I
b = 0.754556 − 0.688360I
2.71154 + 7.20938I 2.03223 − 7.85052I
u = 0.481433 − 1.326120I
a = 1.38140 − 0.37383I
b = 0.754556 + 0.688360I
2.71154 − 7.20938I 2.03223 + 7.85052I
u = −0.036151 + 0.553257I
a = −3.87927 − 0.00814I
b = −0.097466 + 0.790200I
6.94718 − 5.08907I 1.93807 + 2.07497I
u = −0.036151 − 0.553257I
a = −3.87927 + 0.00814I
b = −0.097466 − 0.790200I
6.94718 + 5.08907I 1.93807 − 2.07497I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
17
+ u
16
+ ··· − 3u − 1)(u
85
− 4u
84
+ ··· + 405u − 83)
c
2
(u
17
− 2u
15
+ ··· − u − 1)(u
85
− u
84
+ ··· − 171u − 89)
c
3
(u
17
+ 6u
16
+ ··· + 24u + 4)(u
85
+ u
84
+ ··· + 172u + 28)
c
4
(u
17
+ 11u
15
+ ··· + 2u + 1)(u
85
+ u
84
+ ··· + 28u − 1)
c
5
(u
17
+ u
16
+ ··· − 5u − 1)(u
85
− 2u
84
+ ··· + 2503u + 701)
c
6
(u
17
− 4u
16
+ ··· − 2u + 1)(u
85
− 3u
84
+ ··· − 216u − 47)
c
7
(u
17
− u
16
+ ··· − u + 1)(u
85
+ 22u
83
+ ··· + 295u − 89)
c
8
(u
17
− 3u
16
+ ··· − 2u
2
− 1)(u
85
+ 6u
84
+ ··· − 18u − 1)
c
9
, c
10
(u
17
+ 11u
15
+ ··· + 2u − 1)(u
85
+ u
84
+ ··· + 28u − 1)
c
11
(u
17
+ u
16
+ ··· − u − 1)(u
85
+ 22u
83
+ ··· + 295u − 89)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
17
− 11y
16
+ ··· − 3y −1)(y
85
− 22y
84
+ ··· + 57951y −6889)
c
2
(y
17
− 4y
16
+ ··· + 23y −1)(y
85
+ 5y
84
+ ··· − 428219y −7921)
c
3
(y
17
+ 6y
16
+ ··· + 96y −16)(y
85
− y
84
+ ··· + 36528y −784)
c
4
, c
9
, c
10
(y
17
+ 22y
16
+ ··· + 14y −1)(y
85
+ 91y
84
+ ··· + 108y −1)
c
5
(y
17
− 7y
16
+ ··· + 11y −1)
· (y
85
− 26y
84
+ ··· + 15305105y −491401)
c
6
(y
17
− 8y
16
+ ··· + 12y −1)(y
85
− 27y
84
+ ··· − 226978y −2209)
c
7
, c
11
(y
17
+ 7y
16
+ ··· − 15y −1)(y
85
+ 44y
84
+ ··· − 152029y −7921)
c
8
(y
17
+ 5y
16
+ ··· − 4y −1)(y
85
+ 14y
84
+ ··· − 46y −1)
20
