11a
300
(K11a
300
)
1
Arc Sequences
5 10 1 8 2 9 4 11 3 6 7
Solving Sequence
4,7
8
5,11
9 1 2 3 6 10
c
7
c
4
c
8
c
11
c
1
c
3
c
6
c
10
c
2
, c
5
, c
9
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
20
2u
19
+ ··· + 4u 1, 83716u
19
+ 174490u
18
+ ··· + 26075b 78693,
427886u
19
+ 630440u
18
+ ··· + 26075a 534178i
I
u
2
= hu
96
u
95
+ ··· 60u 101,
1.15165 × 10
224
u
95
+ 2.85845 × 10
224
u
94
+ ··· + 6.61928 × 10
223
b + 4.00656 × 10
225
,
1.39175 × 10
226
u
95
+ 2.37648 × 10
226
u
94
+ ··· + 6.68548 × 10
225
a + 1.90811 × 10
228
i
There are 2 irreducible components with 116 representations.
1
The knot diagram image is adapter from “C. Livingston and A. H. Moore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I.
I
u
1
= hu
20
2u
19
+ · · · + 4u 1, 8.37 × 10
4
u
19
+ 1.74 × 10
5
u
18
+ · · · + 2.61 ×
10
4
b7.87×10
4
, 4.28×10
5
u
19
+6.30×10
5
u
18
+· · ·+2.61×10
4
a5.34×10
5
i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
8
=
u
u
a
5
=
u
2
+ 1
u
2
a
11
=
16.4098u
19
24.1779u
18
+ ··· 43.1378u + 20.4862
3.21058u
19
6.69185u
18
+ ··· 4.18919u + 3.01795
a
9
=
14.6256u
19
+ 19.3386u
18
+ ··· + 64.4739u 25.6434
24.1637u
19
33.4667u
18
+ ··· 83.8067u + 33.9123
a
1
=
16.4098u
19
24.1779u
18
+ ··· 43.1378u + 20.4862
4.94221u
19
+ 6.07747u
18
+ ··· + 13.9677u 5.62374
a
2
=
12.3386u
19
17.8878u
18
+ ··· 30.0888u + 15.6612
2.43973u
19
+ 1.22013u
18
+ ··· + 12.5420u 3.62389
a
3
=
30.6143u
19
+ 41.7586u
18
+ ··· + 119.116u 46.4503
25.8826u
19
33.7473u
18
+ ··· 97.4547u + 37.4879
a
6
=
14.8768u
19
14.2673u
18
+ ··· 94.1867u + 31.6433
0.251237u
19
+ 4.07133u
18
+ ··· 29.7129u + 9.99992
a
10
=
9.41515u
19
+ 11.1496u
18
+ ··· + 40.8150u 16.0518
51.8152u
19
+ 68.7753u
18
+ ··· + 201.898u 80.6084
a
10
=
9.41515u
19
+ 11.1496u
18
+ ··· + 40.8150u 16.0518
51.8152u
19
+ 68.7753u
18
+ ··· + 201.898u 80.6084
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.47088
a = 0.635196
b = 1.93439
5.30775 14.8430
u = 1.075040 0.521861I
a = 0.784241 0.459457I
b = 1.118013 0.528908I
2.09458 + 0.02571I 6.51387 + 0.81904I
u = 1.075040 + 0.521861I
a = 0.784241 + 0.459457I
b = 1.118013 + 0.528908I
2.09458 0.02571I 6.51387 0.81904I
u = 0.943250 0.349364I
a = 1.318129 0.221518I
b = 1.60990 + 0.18001I
1.69553 + 3.69576I 1.77162 1.96947I
u = 0.943250 + 0.349364I
a = 1.318129 + 0.221518I
b = 1.60990 0.18001I
1.69553 3.69576I 1.77162 + 1.96947I
u = 0.870518 0.079940I
a = 1.86271 + 3.21921I
b = 1.97718 + 2.02548I
1.90449 + 0.21781I 29.5538 14.4681I
u = 0.870518 + 0.079940I
a = 1.86271 3.21921I
b = 1.97718 2.02548I
1.90449 0.21781I 29.5538 + 14.4681I
u = 0.18394 1.47398I
a = 0.010162 0.193943I
b = 0.265936 + 0.099639I
8.22954 + 1.82787I 11.49994 0.55574I
u = 0.18394 + 1.47398I
a = 0.010162 + 0.193943I
b = 0.265936 0.099639I
8.22954 1.82787I 11.49994 + 0.55574I
u = 0.257767 0.750032I
a = 0.63846 + 1.31360I
b = 0.114431 + 0.221367I
1.03432 + 2.65731I 0.50510 5.09226I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.257767 + 0.750032I
a = 0.63846 1.31360I
b = 0.114431 0.221367I
1.03432 2.65731I 0.50510 + 5.09226I
u = 0.327450 0.357934I
a = 1.324808 0.382640I
b = 1.071918 + 0.209283I
2.35457 2.06275I 0.52131 + 2.65726I
u = 0.327450 + 0.357934I
a = 1.324808 + 0.382640I
b = 1.071918 0.209283I
2.35457 + 2.06275I 0.52131 2.65726I
u = 0.665798 0.019209I
a = 0.454713 + 1.236375I
b = 2.27505 0.00824I
6.31669 6.08976I 1.60733 + 2.73564I
u = 0.665798 + 0.019209I
a = 0.454713 1.236375I
b = 2.27505 + 0.00824I
6.31669 + 6.08976I 1.60733 2.73564I
u = 1.139757 0.511268I
a = 1.311956 + 0.412109I
b = 2.22421 + 0.51632I
1.55717 7.34738I 4.09988 + 9.89194I
u = 1.139757 + 0.511268I
a = 1.311956 0.412109I
b = 2.22421 0.51632I
1.55717 + 7.34738I 4.09988 9.89194I
u = 1.283222 0.360701I
a = 0.459491 0.417035I
b = 1.62844 0.07437I
3.05795 7.46965I 3.02238 + 6.16209I
u = 1.283222 + 0.360701I
a = 0.459491 + 0.417035I
b = 1.62844 + 0.07437I
3.05795 + 7.46965I 3.02238 6.16209I
u = 1.53262
a = 0.398865
b = 2.51400
3.47385 31.1937
4
II. I
u
2
= hu
96
u
95
+ · · · 60u 101, 1.15 × 10
224
u
95
+ 2.86 × 10
224
u
94
+
· · · + 6.62 × 10
223
b + 4.01 × 10
225
, 1.39 × 10
226
u
95
+ 2.38 × 10
226
u
94
+ · · · +
6.69 × 10
225
a + 1.91 × 10
228
i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
8
=
u
u
a
5
=
u
2
+ 1
u
2
a
11
=
2.08176u
95
3.55469u
94
+ ··· + 197.968u 285.411
1.73985u
95
4.31837u
94
+ ··· 117.502u 60.5286
a
9
=
1.24799u
95
2.67874u
94
+ ··· 28.9106u 84.7160
4.35997u
95
+ 7.46261u
94
+ ··· 277.555u + 544.819
a
1
=
2.08176u
95
3.55469u
94
+ ··· + 197.968u 285.411
0.674710u
95
2.45760u
94
+ ··· 239.384u + 88.2378
a
2
=
3.03786u
95
5.50866u
94
+ ··· + 217.871u 372.359
0.857210u
95
3.31524u
94
+ ··· 298.155u + 120.832
a
3
=
0.716645u
95
1.23894u
94
+ ··· + 46.6136u 88.8107
7.19143u
95
13.3353u
94
+ ··· + 253.129u 765.315
a
6
=
6.99182u
95
+ 12.9299u
94
+ ··· 418.566u + 809.348
7.61234u
95
+ 15.3132u
94
+ ··· 158.318u + 705.173
a
10
=
0.140812u
95
0.0828640u
94
+ ··· + 44.4501u 43.1144
5.40993u
95
8.61300u
94
+ ··· + 626.190u 818.869
a
10
=
0.140812u
95
0.0828640u
94
+ ··· + 44.4501u 43.1144
5.40993u
95
8.61300u
94
+ ··· + 626.190u 818.869
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
5
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.49653
a = 0.431098
b = 2.70299
3.59541 35.1986
u = 1.34315 0.63648I
a = 0.758774 0.155327I
b = 1.87449 0.56731I
4.94765 + 5.11148I 4.23566 4.48140I
u = 1.34315 + 0.63648I
a = 0.758774 + 0.155327I
b = 1.87449 + 0.56731I
4.94765 5.11148I 4.23566 + 4.48140I
u = 1.334156 0.459106I
a = 0.447884 + 0.060286I
b = 0.723423 + 0.523916I
1.96286 1.30339I 3.03121 + 5.70430I
u = 1.334156 + 0.459106I
a = 0.447884 0.060286I
b = 0.723423 0.523916I
1.96286 + 1.30339I 3.03121 5.70430I
u = 1.291905 0.457802I
a = 0.542089 + 0.004792I
b = 1.259772 0.411822I
4.50509 + 2.67262I 7.25375 3.37476I
u = 1.291905 + 0.457802I
a = 0.542089 0.004792I
b = 1.259772 + 0.411822I
4.50509 2.67262I 7.25375 + 3.37476I
u = 1.29000 0.66251I
a = 1.031645 + 0.088942I
b = 2.14241 + 0.58657I
0.39090 + 11.66793I 0.87433 8.04211I
u = 1.29000 + 0.66251I
a = 1.031645 0.088942I
b = 2.14241 0.58657I
0.39090 11.66793I 0.87433 + 8.04211I
u = 1.28105 0.63592I
a = 1.146073 0.209540I
b = 2.25361 0.70063I
3.9614 + 17.9979I 0.82370 9.34783I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.28105 + 0.63592I
a = 1.146073 + 0.209540I
b = 2.25361 + 0.70063I
3.9614 17.9979I 0.82370 + 9.34783I
u = 1.239563 0.325165I
a = 0.532771 0.184694I
b = 2.03587 + 0.99913I
2.24244 + 7.86585I 5.52086 10.32768I
u = 1.239563 + 0.325165I
a = 0.532771 + 0.184694I
b = 2.03587 0.99913I
2.24244 7.86585I 5.52086 + 10.32768I
u = 1.138974 0.354041I
a = 1.065377 0.068325I
b = 1.60225 0.16597I
2.56439 + 1.51823I 3.61769 1.58173I
u = 1.138974 + 0.354041I
a = 1.065377 + 0.068325I
b = 1.60225 + 0.16597I
2.56439 1.51823I 3.61769 + 1.58173I
u = 1.117503 0.389905I
a = 1.348187 + 0.122688I
b = 2.01274 + 0.01928I
2.49221 + 1.38820I 5.62685 2.45875I
u = 1.117503 + 0.389905I
a = 1.348187 0.122688I
b = 2.01274 0.01928I
2.49221 1.38820I 5.62685 + 2.45875I
u = 1.098548 0.204380I
a = 1.17929 + 1.10757I
b = 1.39783 + 1.55797I
0.605747 + 0.447290I 3.63388 + 1.74254I
u = 1.098548 + 0.204380I
a = 1.17929 1.10757I
b = 1.39783 1.55797I
0.605747 0.447290I 3.63388 1.74254I
u = 1.098359 0.373633I
a = 0.655179 0.707878I
b = 1.19845 0.80685I
0.829229 + 0.160481I 0.241525 + 0.067951I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.098359 + 0.373633I
a = 0.655179 + 0.707878I
b = 1.19845 + 0.80685I
0.829229 0.160481I 0.241525 0.067951I
u = 1.012860 0.386691I
a = 1.70841 + 0.29183I
b = 2.43790 + 0.52929I
1.89831 + 4.86756I 3.25012 8.87629I
u = 1.012860 + 0.386691I
a = 1.70841 0.29183I
b = 2.43790 0.52929I
1.89831 4.86756I 3.25012 + 8.87629I
u = 0.920510 0.063243I
a = 2.80396 + 3.68950I
b = 2.91244 + 2.54911I
1.83794 + 0.18273I 75.5057 + 43.5795I
u = 0.920510 + 0.063243I
a = 2.80396 3.68950I
b = 2.91244 2.54911I
1.83794 0.18273I 75.5057 43.5795I
u = 0.906398 0.330398I
a = 0.225881 1.242691I
b = 0.687111 + 0.490206I
5.75032 4.28762I 3.34541 + 1.61445I
u = 0.906398 + 0.330398I
a = 0.225881 + 1.242691I
b = 0.687111 0.490206I
5.75032 + 4.28762I 3.34541 1.61445I
u = 0.903876 0.214263I
a = 1.025043 0.009649I
b = 2.21555 + 1.20717I
1.17974 + 2.82902I 5.61860 4.60262I
u = 0.903876 + 0.214263I
a = 1.025043 + 0.009649I
b = 2.21555 1.20717I
1.17974 2.82902I 5.61860 + 4.60262I
u = 0.854277 0.227234I
a = 0.47347 + 1.42707I
b = 0.512405 0.166876I
1.28698 0.73115I 4.34059 + 0.04582I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.854277 + 0.227234I
a = 0.47347 1.42707I
b = 0.512405 + 0.166876I
1.28698 + 0.73115I 4.34059 0.04582I
u = 0.806144 0.214912I
a = 0.479634 0.510777I
b = 2.74269 1.13146I
6.28639 + 6.86236I 2.29076 11.45834I
u = 0.806144 + 0.214912I
a = 0.479634 + 0.510777I
b = 2.74269 + 1.13146I
6.28639 6.86236I 2.29076 + 11.45834I
u = 0.484663 0.344993I
a = 0.15641 + 2.03650I
b = 0.272220 + 0.665820I
0.39402 1.56177I 2.46525 + 2.62036I
u = 0.484663 + 0.344993I
a = 0.15641 2.03650I
b = 0.272220 0.665820I
0.39402 + 1.56177I 2.46525 2.62036I
u = 0.482036 0.315937I
a = 0.787837 0.903836I
b = 0.112088 0.507228I
0.406346 + 1.198921I 3.01437 6.03071I
u = 0.482036 + 0.315937I
a = 0.787837 + 0.903836I
b = 0.112088 + 0.507228I
0.406346 1.198921I 3.01437 + 6.03071I
u = 0.311941 1.209741I
a = 0.286940 + 0.820047I
b = 0.291640 0.190934I
2.77482 5.11934I 2.01941 + 6.39373I
u = 0.311941 + 1.209741I
a = 0.286940 0.820047I
b = 0.291640 + 0.190934I
2.77482 + 5.11934I 2.01941 6.39373I
u = 0.259269 1.131543I
a = 0.493881 0.981727I
b = 0.227318 + 0.035334I
7.19197 11.75554I 3.30340 + 7.13362I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.259269 + 1.131543I
a = 0.493881 + 0.981727I
b = 0.227318 0.035334I
7.19197 + 11.75554I 3.30340 7.13362I
u = 0.196440 1.339830I
a = 0.291523 0.379531I
b = 0.055324 + 0.273333I
8.68039 + 1.55353I 6.49878 + 5.32572I
u = 0.196440 + 1.339830I
a = 0.291523 + 0.379531I
b = 0.055324 0.273333I
8.68039 1.55353I 6.49878 5.32572I
u = 0.062314 0.872583I
a = 0.697958 + 0.722073I
b = 0.218603 0.035908I
0.67930 + 2.39127I 4.44117 2.67981I
u = 0.062314 + 0.872583I
a = 0.697958 0.722073I
b = 0.218603 + 0.035908I
0.67930 2.39127I 4.44117 + 2.67981I
u = 0.022589 0.476147I
a = 0.15988 1.75066I
b = 0.389940 0.426704I
0.40537 + 1.96180I 0.24306 3.42560I
u = 0.022589 + 0.476147I
a = 0.15988 + 1.75066I
b = 0.389940 + 0.426704I
0.40537 1.96180I 0.24306 + 3.42560I
u = 0.008073 0.918618I
a = 0.845657 0.866145I
b = 0.213671 0.217741I
2.07883 + 6.40543I 2.26835 7.03904I
u = 0.008073 + 0.918618I
a = 0.845657 + 0.866145I
b = 0.213671 + 0.217741I
2.07883 6.40543I 2.26835 + 7.03904I
u = 0.174730 0.720527I
a = 0.92719 + 1.47258I
b = 0.445127 + 0.106295I
2.85619 + 3.24531I 3.84884 3.66553I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.174730 + 0.720527I
a = 0.92719 1.47258I
b = 0.445127 0.106295I
2.85619 3.24531I 3.84884 + 3.66553I
u = 0.190796 0.503974I
a = 1.62713 1.21932I
b = 0.278154 + 0.391785I
3.96883 + 1.64207I 6.44304 1.04943I
u = 0.190796 + 0.503974I
a = 1.62713 + 1.21932I
b = 0.278154 0.391785I
3.96883 1.64207I 6.44304 + 1.04943I
u = 0.242468 0.772214I
a = 0.478051 1.047873I
b = 0.182437 0.334275I
1.43609 + 1.70978I 3.75375 + 0.93348I
u = 0.242468 + 0.772214I
a = 0.478051 + 1.047873I
b = 0.182437 + 0.334275I
1.43609 1.70978I 3.75375 0.93348I
u = 0.36725 1.37766I
a = 0.219632 + 0.242538I
b = 0.114121 + 0.239144I
8.49441 + 1.95871I 13.5926 11.4066I
u = 0.36725 + 1.37766I
a = 0.219632 0.242538I
b = 0.114121 0.239144I
8.49441 1.95871I 13.5926 + 11.4066I
u = 0.370926 0.648701I
a = 0.814789 1.056203I
b = 1.303848 + 0.413511I
6.72567 4.75540I 4.17528 + 5.46441I
u = 0.370926 + 0.648701I
a = 0.814789 + 1.056203I
b = 1.303848 0.413511I
6.72567 + 4.75540I 4.17528 5.46441I
u = 0.551904 0.378935I
a = 1.98161 + 0.25175I
b = 1.69107 + 1.02951I
7.44389 + 5.44199I 5.81540 0.88794I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.551904 + 0.378935I
a = 1.98161 0.25175I
b = 1.69107 1.02951I
7.44389 5.44199I 5.81540 + 0.88794I
u = 0.572749 0.484328I
a = 1.077036 0.000422I
b = 1.30179 0.83734I
3.40821 + 0.60971I 2.59694 + 1.66037I
u = 0.572749 + 0.484328I
a = 1.077036 + 0.000422I
b = 1.30179 + 0.83734I
3.40821 0.60971I 2.59694 1.66037I
u = 0.740637 0.481266I
a = 0.663803 + 0.527341I
b = 0.251382 0.818211I
5.35019 1.42280I 5.31734 + 3.30567I
u = 0.740637 + 0.481266I
a = 0.663803 0.527341I
b = 0.251382 + 0.818211I
5.35019 + 1.42280I 5.31734 3.30567I
u = 0.783146 0.511862I
a = 0.290897 + 0.060665I
b = 0.823598 + 1.035293I
5.22833 2.70073I 5.08810 + 3.53024I
u = 0.783146 + 0.511862I
a = 0.290897 0.060665I
b = 0.823598 1.035293I
5.22833 + 2.70073I 5.08810 3.53024I
u = 0.902669 0.787073I
a = 0.648694 0.664216I
b = 0.861874 0.578130I
0.0489695 0.0733989I 2.02771 0.16681I
u = 0.902669 + 0.787073I
a = 0.648694 + 0.664216I
b = 0.861874 + 0.578130I
0.0489695 + 0.0733989I 2.02771 + 0.16681I
u = 0.916587 0.428791I
a = 0.259816 1.314752I
b = 0.293836 0.416638I
2.44931 4.41382I 0.26841 + 6.59895I
12
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.916587 + 0.428791I
a = 0.259816 + 1.314752I
b = 0.293836 + 0.416638I
2.44931 + 4.41382I 0.26841 6.59895I
u = 0.961050 0.411937I
a = 0.08184 + 1.77255I
b = 0.528220 + 1.050803I
6.22408 8.95276I 3.24646 + 8.95795I
u = 0.961050 + 0.411937I
a = 0.08184 1.77255I
b = 0.528220 1.050803I
6.22408 + 8.95276I 3.24646 8.95795I
u = 0.966071 0.600501I
a = 0.400487 + 0.858100I
b = 1.253814 0.098472I
5.14389 0.01776I 5.29391 0.13930I
u = 0.966071 + 0.600501I
a = 0.400487 0.858100I
b = 1.253814 + 0.098472I
5.14389 + 0.01776I 5.29391 + 0.13930I
u = 1.086654 0.227251I
a = 0.815535 0.372245I
b = 1.51093 + 0.67769I
2.50058 4.48584I 8.03748 + 8.13430I
u = 1.086654 + 0.227251I
a = 0.815535 + 0.372245I
b = 1.51093 0.67769I
2.50058 + 4.48584I 8.03748 8.13430I
u = 1.091271 0.675322I
a = 1.018456 + 0.114459I
b = 1.380440 + 0.036127I
0.74726 5.71599I 1.75808 + 5.73314I
u = 1.091271 + 0.675322I
a = 1.018456 0.114459I
b = 1.380440 0.036127I
0.74726 + 5.71599I 1.75808 5.73314I
u = 1.137249 0.354539I
a = 0.688823 0.326882I
b = 1.97294 0.72250I
1.31348 5.11994I 0.88249 + 6.81553I
13
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.137249 + 0.354539I
a = 0.688823 + 0.326882I
b = 1.97294 + 0.72250I
1.31348 + 5.11994I 0.88249 6.81553I
u = 1.159410 0.498809I
a = 1.198746 + 0.524361I
b = 2.30687 + 0.48646I
0.00337 7.83254I 0.00246 + 7.65524I
u = 1.159410 + 0.498809I
a = 1.198746 0.524361I
b = 2.30687 0.48646I
0.00337 + 7.83254I 0.00246 7.65524I
u = 1.161283 0.524991I
a = 1.201881 0.326272I
b = 1.97611 0.33761I
1.29886 6.55523I 0.36651 + 1.41241I
u = 1.161283 + 0.524991I
a = 1.201881 + 0.326272I
b = 1.97611 + 0.33761I
1.29886 + 6.55523I 0.36651 1.41241I
u = 1.217488 0.082560I
a = 0.661628 + 0.057949I
b = 1.73589 0.75121I
5.03978 + 1.15243I 11.16857 5.29229I
u = 1.217488 + 0.082560I
a = 0.661628 0.057949I
b = 1.73589 + 0.75121I
5.03978 1.15243I 11.16857 + 5.29229I
u = 1.247107 0.461576I
a = 1.131769 + 0.187384I
b = 2.14155 + 0.67845I
4.54881 7.06507I 6.29646 + 4.83795I
u = 1.247107 + 0.461576I
a = 1.131769 0.187384I
b = 2.14155 0.67845I
4.54881 + 7.06507I 6.29646 4.83795I
u = 1.261936 0.481638I
a = 1.265621 0.319174I
b = 2.14434 0.85116I
1.76805 11.34404I 1.36910 + 9.29137I
14
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.261936 + 0.481638I
a = 1.265621 + 0.319174I
b = 2.14434 + 0.85116I
1.76805 + 11.34404I 1.36910 9.29137I
u = 1.29382 0.66144I
a = 0.754481 + 0.329603I
b = 1.139359 + 0.676931I
5.25019 8.77138I 4.46840 + 7.75224I
u = 1.29382 + 0.66144I
a = 0.754481 0.329603I
b = 1.139359 0.676931I
5.25019 + 8.77138I 4.46840 7.75224I
u = 1.50709 0.12241I
a = 0.578362 + 0.132329I
b = 1.37970 + 0.54580I
0.64154 + 6.80371I 2.89098 5.94229I
u = 1.50709 + 0.12241I
a = 0.578362 0.132329I
b = 1.37970 0.54580I
0.64154 6.80371I 2.89098 + 5.94229I
u = 1.61712
a = 0.565490
b = 1.80695
4.87233 3.69304
15
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
20
2u
19
+ ··· 2u + 1)(u
96
+ u
95
+ ··· 44434u + 5239)
c
2
(u
20
+ u
19
+ ··· + 2u 1)(u
96
+ 32u
94
+ ··· + 1260u 193)
c
3
(u
20
+ 2u
19
+ ··· 6u 1)(u
96
+ 9u
95
+ ··· 371u 46)
c
4
(u
20
2u
19
+ ··· + 4u 1)(u
96
+ u
95
+ ··· + 60u 101)
c
5
(u
20
+ 2u
19
+ ··· + 2u + 1)(u
96
+ u
95
+ ··· 44434u + 5239)
c
6
(u
20
7u
19
+ ··· + 5u + 1)(u
96
+ 4u
95
+ ··· + 45u + 1)
c
7
(u
20
+ 2u
19
+ ··· 4u 1)(u
96
+ u
95
+ ··· + 60u 101)
c
8
(u
20
+ 3u
19
+ ··· + u + 1)(u
96
+ 10u
95
+ ··· + 3240u + 368)
c
9
(u
20
u
19
+ ··· 2u 1)(u
96
+ 32u
94
+ ··· + 1260u 193)
c
10
(u
20
u
19
+ ··· 3u 1)(u
96
+ 2u
95
+ ··· 159407u 226723)
c
11
(u
20
3u
19
+ ··· + 6u + 1)(u
96
+ 6u
95
+ ··· + 14458u + 1789)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
20
14y
19
+ ··· + 40y
2
+ 1)
(y
96
73y
95
+ ··· + 553636226y + 27447121)
c
2
(y
20
+ 11y
19
+ ··· + 8y + 1)(y
96
+ 64y
95
+ ··· + 1764038y + 37249)
c
3
(y
20
10y
19
+ ··· 2y + 1)(y
96
y
95
+ ··· + 405435y + 2116)
c
4
, c
7
(y
20
10y
19
+ ··· 8y + 1)(y
96
53y
95
+ ··· 127426y + 10201)
c
5
(y
20
14y
19
+ ··· + 40y
2
+ 1)
(y
96
73y
95
+ ··· + 553636226y + 27447121)
c
6
(y
20
5y
19
+ ··· 9y + 1)(y
96
4y
95
+ ··· 559y + 1)
c
8
(y
20
19y
19
+ ··· 15y + 1)
(y
96
10y
95
+ ··· + 3636544y + 135424)
c
9
(y
20
+ 11y
19
+ ··· + 8y + 1)(y
96
+ 64y
95
+ ··· + 1764038y + 37249)
c
10
(y
20
y
19
+ ··· 19y + 1)
(y
96
36y
95
+ ··· 374201254849y + 51403318729)
c
11
(y
20
+ 3y
19
+ ··· 24y + 1)
(y
96
16y
95
+ ··· 110849866y + 3200521)
17