11a
315
(K11a
315
)
1
Arc Sequences
9 6 1 10 8 2 11 3 4 7 5
Solving Sequence
7,10
11
5,8
1 4 3 9 2 6
c
10
c
7
c
11
c
4
c
3
c
9
c
1
c
6
c
2
, c
5
, c
8
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
18
+ 5u
17
+ ··· 245u + 57,
1.60306 × 10
31
u
17
8.41818 × 10
31
u
16
+ ··· + 4.56116 × 10
33
b 2.52373 × 10
33
,
2.81036 × 10
31
u
17
+ 3.06620 × 10
33
u
16
+ ··· + 7.79959 × 10
35
a 6.15769 × 10
36
i
I
u
2
= hu
96
+ 10u
95
+ ··· 1115312u + 120261,
3.33842 × 10
844
u
95
3.43831 × 10
845
u
94
+ ··· + 7.18610 × 10
849
b 1.20327 × 10
850
,
2.18020 × 10
850
u
95
2.14919 × 10
851
u
94
+ ··· + 2.59262 × 10
855
a + 1.21959 × 10
856
i
There are 2 irreducible components with 114 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
18
+5u
17
+· · ·245u+57, 1.60×10
31
u
17
8.42×10
31
u
16
+· · ·+4.56×10
33
b
2.52 × 10
33
, 2.81 × 10
31
u
17
+ 3.07 × 10
33
u
16
+ · · · + 7.80 × 10
35
a 6.16 × 10
36
i
(i) Arc colorings
a
7
=
0
u
a
10
=
0.0000360321u
17
0.00393123u
16
+ ··· + 32.0734u + 7.89490
0.00351458u
17
+ 0.0184562u
16
+ ··· 7.75082u + 0.553309
a
11
=
0.0000360321u
17
0.00393123u
16
+ ··· + 32.0734u + 7.89490
0.00504093u
17
+ 0.0249407u
16
+ ··· 6.83386u + 0.339498
a
5
=
1
0
a
8
=
0.0234771u
17
0.113158u
16
+ ··· + 43.6642u + 8.42856
0.00331131u
17
0.0165304u
16
+ ··· + 1.64586u 1.14273
a
1
=
0.00507697u
17
0.0288719u
16
+ ··· + 38.9073u + 7.55540
0.00504093u
17
+ 0.0249407u
16
+ ··· 6.83386u + 0.339498
a
4
=
0.0242758u
17
0.116883u
16
+ ··· + 27.4763u + 3.92768
0.00553113u
17
0.0294334u
16
+ ··· + 8.36730u 1.72680
a
3
=
0.0303467u
17
0.154044u
16
+ ··· + 82.0558u + 14.2748
0.00231349u
17
0.0106233u
16
+ ··· 0.995193u 1.36487
a
9
=
0.0126717u
17
0.0574738u
16
+ ··· + 15.1225u + 4.73493
0.00647947u
17
0.0346712u
16
+ ··· + 6.79539u 1.57633
a
2
=
0.0174589u
17
0.0889757u
16
+ ··· + 38.6930u + 5.52810
0.00669984u
17
0.0307108u
16
+ ··· + 2.56033u 1.21576
a
6
=
0.0129022u
17
0.0650112u
16
+ ··· + 37.1365u + 7.64317
0.00163303u
17
0.00928892u
16
+ ··· + 1.82239u 0.946120
a
6
=
0.0129022u
17
0.0650112u
16
+ ··· + 37.1365u + 7.64317
0.00163303u
17
0.00928892u
16
+ ··· + 1.82239u 0.946120
(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 = 1.25009 1.39391I
a = 0.294878 0.705475I
b = 0.940989 + 0.307748I
4.68551 7.79285I 0.53996 + 6.36550I
u = 1.25009 + 1.39391I
a = 0.294878 + 0.705475I
b = 0.940989 0.307748I
4.68551 + 7.79285I 0.53996 6.36550I
u = 1.20604 1.87608I
a = 0.196879 0.183552I
b = 1.167761 + 0.264907I
0.02231 + 6.50584I 1.20256 7.92471I
u = 1.20604 + 1.87608I
a = 0.196879 + 0.183552I
b = 1.167761 0.264907I
0.02231 6.50584I 1.20256 + 7.92471I
u = 0.98624 2.74450I
a = 0.112751 + 0.264532I
b = 0.76892 2.11639I
1.21414 + 2.10668I 22.6892 + 85.4035I
u = 0.98624 + 2.74450I
a = 0.112751 0.264532I
b = 0.76892 + 2.11639I
1.21414 2.10668I 22.6892 85.4035I
u = 0.75399 1.60653I
a = 0.411913 + 0.292815I
b = 0.212915 0.379437I
4.36134 + 2.18737I 8.80548 3.19554I
u = 0.75399 + 1.60653I
a = 0.411913 0.292815I
b = 0.212915 + 0.379437I
4.36134 2.18737I 8.80548 + 3.19554I
u = 0.450147 0.308085I
a = 0.903733 0.296006I
b = 1.45900 + 0.31070I
4.14491 3.52032I 8.96118 + 2.06912I
u = 0.450147 + 0.308085I
a = 0.903733 + 0.296006I
b = 1.45900 0.31070I
4.14491 + 3.52032I 8.96118 2.06912I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.268461 0.465096I
a = 1.43674 1.55841I
b = 1.122480 0.498735I
3.88886 + 2.12243I 8.14463 0.96498I
u = 0.268461 + 0.465096I
a = 1.43674 + 1.55841I
b = 1.122480 + 0.498735I
3.88886 2.12243I 8.14463 + 0.96498I
u = 0.102527
a = 12.0037
b = 0.609420
0.310540 5.19686
u = 0.323960 1.164587I
a = 0.635754 + 0.846649I
b = 0.157242 0.316666I
5.97627 1.80190I 7.12473 + 2.98531I
u = 0.323960 + 1.164587I
a = 0.635754 0.846649I
b = 0.157242 + 0.316666I
5.97627 + 1.80190I 7.12473 2.98531I
u = 0.95542 1.86127I
a = 0.012938 0.598280I
b = 1.36242 + 0.64729I
1.14935 + 7.43290I 0.39473 7.84303I
u = 0.95542 + 1.86127I
a = 0.012938 + 0.598280I
b = 1.36242 0.64729I
1.14935 7.43290I 0.39473 + 7.84303I
u = 2.16866
a = 0.333860
b = 1.27402
4.50458 17.2587
4
II. I
u
2
= hu
96
+ 10u
95
+ · · · 1115312u + 120261, 3.34 × 10
844
u
95
3.44 ×
10
845
u
94
+ · · · + 7.19 × 10
849
b 1.20 × 10
850
, 2.18 × 10
850
u
95
2.15 ×
10
851
u
94
+ · · · + 2.59 × 10
855
a + 1.22 × 10
856
i
(i) Arc colorings
a
7
=
0
u
a
10
=
8.40924 × 10
6
u
95
+ 0.0000828963u
94
+ ··· + 109.832u 4.70409
4.64567 × 10
6
u
95
+ 0.0000478467u
94
+ ··· + 1.50995u + 1.67444
a
11
=
8.40924 × 10
6
u
95
+ 0.0000828963u
94
+ ··· + 109.832u 4.70409
4.77602 × 10
6
u
95
+ 0.0000490355u
94
+ ··· + 3.85530u + 1.53060
a
5
=
1
0
a
8
=
0.0000116333u
95
0.000116847u
94
+ ··· 71.3857u 0.390596
2.78201 × 10
6
u
95
0.0000285659u
94
+ ··· + 15.9131u 2.73444
a
1
=
3.63322 × 10
6
u
95
+ 0.0000338608u
94
+ ··· + 105.976u 6.23468
4.77602 × 10
6
u
95
+ 0.0000490355u
94
+ ··· + 3.85530u + 1.53060
a
4
=
0.0000222239u
95
0.000219467u
94
+ ··· 192.056u + 10.0473
4.68429 × 10
7
u
95
5.77651 × 10
6
u
94
+ ··· + 16.8655u 3.98384
a
3
=
4.47034 × 10
7
u
95
+ 7.02143 × 10
6
u
94
+ ··· 51.8952u + 9.67011
3.63569 × 10
6
u
95
0.0000365437u
94
+ ··· 24.8055u + 1.15731
a
9
=
0.0000216126u
95
0.000218111u
94
+ ··· 85.3481u 3.69303
3.94836 × 10
7
u
95
4.62579 × 10
6
u
94
+ ··· + 36.7831u 4.65971
a
2
=
0.0000172197u
95
0.000174672u
94
+ ··· 107.021u 3.45287
1.20493 × 10
6
u
95
+ 0.0000106317u
94
+ ··· + 35.5154u 5.31050
a
6
=
3.16251 × 10
7
u
95
3.91214 × 10
7
u
94
+ ··· + 104.553u 17.8687
7.75550 × 10
6
u
95
+ 0.0000778141u
94
+ ··· + 52.8541u 2.78259
a
6
=
3.16251 × 10
7
u
95
3.91214 × 10
7
u
94
+ ··· + 104.553u 17.8687
7.75550 × 10
6
u
95
+ 0.0000778141u
94
+ ··· + 52.8541u 2.78259
(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 = 1.87769 2.11082I
a = 0.131986 + 0.262880I
b = 0.958660 + 0.109699I
0.46559 + 5.39912I 1.01006 3.39870I
u = 1.87769 + 2.11082I
a = 0.131986 0.262880I
b = 0.958660 0.109699I
0.46559 5.39912I 1.01006 + 3.39870I
u = 1.52956 1.14500I
a = 0.308327 + 0.297876I
b = 1.65825 0.25745I
0.84537 + 1.76194I 12.62435 0.01898I
u = 1.52956 + 1.14500I
a = 0.308327 0.297876I
b = 1.65825 + 0.25745I
0.84537 1.76194I 12.62435 + 0.01898I
u = 1.42851 0.93155I
a = 0.541716 + 0.205401I
b = 1.297098 0.157095I
0.98928 + 7.38324I 1.82726 9.18355I
u = 1.42851 + 0.93155I
a = 0.541716 0.205401I
b = 1.297098 + 0.157095I
0.98928 7.38324I 1.82726 + 9.18355I
u = 1.40087 1.46289I
a = 0.251455 0.462568I
b = 1.266763 + 0.610244I
2.08843 5.19122I 0.85158 + 3.46677I
u = 1.40087 + 1.46289I
a = 0.251455 + 0.462568I
b = 1.266763 0.610244I
2.08843 + 5.19122I 0.85158 3.46677I
u = 1.36297 2.02478I
a = 0.122804 0.524719I
b = 0.946848 + 0.403711I
5.53218 8.19891I 7.61617 + 9.98808I
u = 1.36297 + 2.02478I
a = 0.122804 + 0.524719I
b = 0.946848 0.403711I
5.53218 + 8.19891I 7.61617 9.98808I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.14737 1.61054I
a = 0.259287 + 0.680771I
b = 1.132444 0.443855I
6.17066 5.58274I 4.12333 + 4.48207I
u = 1.14737 + 1.61054I
a = 0.259287 0.680771I
b = 1.132444 + 0.443855I
6.17066 + 5.58274I 4.12333 4.48207I
u = 1.037679 0.282168I
a = 0.156796 + 0.440217I
b = 0.275542 0.539171I
3.76234 + 0.68062I 5.82964 + 1.30237I
u = 1.037679 + 0.282168I
a = 0.156796 0.440217I
b = 0.275542 + 0.539171I
3.76234 0.68062I 5.82964 1.30237I
u = 0.91642 2.01081I
a = 0.025384 + 0.667738I
b = 1.41644 0.60207I
3.1429 18.2725I 0.95412 + 9.52905I
u = 0.91642 + 2.01081I
a = 0.025384 0.667738I
b = 1.41644 + 0.60207I
3.1429 + 18.2725I 0.95412 9.52905I
u = 0.72806 1.74145I
a = 0.032878 0.784741I
b = 1.40190 + 0.70932I
0.20764 9.18905I 0.36820 + 8.22179I
u = 0.72806 + 1.74145I
a = 0.032878 + 0.784741I
b = 1.40190 0.70932I
0.20764 + 9.18905I 0.36820 8.22179I
u = 0.66052 3.06449I
a = 0.079087 + 0.265052I
b = 0.45199 2.41206I
1.23627 + 2.13659I 107.7851 78.1754I
u = 0.66052 + 3.06449I
a = 0.079087 0.265052I
b = 0.45199 + 2.41206I
1.23627 2.13659I 107.7851 + 78.1754I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.621037 0.786754I
a = 0.766470 + 0.642759I
b = 0.619183 0.535394I
1.73174 + 0.39177I 6.89516 0.64739I
u = 0.621037 + 0.786754I
a = 0.766470 0.642759I
b = 0.619183 + 0.535394I
1.73174 0.39177I 6.89516 + 0.64739I
u = 0.60988 1.34584I
a = 0.099023 + 1.065464I
b = 1.131462 0.269948I
3.06332 8.99488I 0.91543 + 9.21439I
u = 0.60988 + 1.34584I
a = 0.099023 1.065464I
b = 1.131462 + 0.269948I
3.06332 + 8.99488I 0.91543 9.21439I
u = 0.577890 0.692916I
a = 0.608021 0.204956I
b = 0.389822 0.587934I
0.95940 + 3.02963I 2.72169 3.74300I
u = 0.577890 + 0.692916I
a = 0.608021 + 0.204956I
b = 0.389822 + 0.587934I
0.95940 3.02963I 2.72169 + 3.74300I
u = 0.574894 0.063821I
a = 0.181009 1.398355I
b = 0.922119 + 0.223860I
1.88316 + 3.59766I 0.91532 5.54910I
u = 0.574894 + 0.063821I
a = 0.181009 + 1.398355I
b = 0.922119 0.223860I
1.88316 3.59766I 0.91532 + 5.54910I
u = 0.453027 0.576045I
a = 0.71033 1.79092I
b = 0.227166 + 0.225140I
5.73921 6.56546I 3.85853 + 3.89750I
u = 0.453027 + 0.576045I
a = 0.71033 + 1.79092I
b = 0.227166 0.225140I
5.73921 + 6.56546I 3.85853 3.89750I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.329354 1.180299I
a = 0.115837 0.683179I
b = 0.913672 0.081730I
1.51493 + 0.74030I 3.82288 + 0.32384I
u = 0.329354 + 1.180299I
a = 0.115837 + 0.683179I
b = 0.913672 + 0.081730I
1.51493 0.74030I 3.82288 0.32384I
u = 0.31884 1.52521I
a = 0.412833 + 0.595215I
b = 0.053630 0.729782I
3.11184 + 1.53766I 1.90388 0.40759I
u = 0.31884 + 1.52521I
a = 0.412833 0.595215I
b = 0.053630 + 0.729782I
3.11184 1.53766I 1.90388 + 0.40759I
u = 0.253119 0.460043I
a = 2.30078 0.66793I
b = 1.273064 + 0.499899I
0.21784 11.64566I 0.80372 + 7.60523I
u = 0.253119 + 0.460043I
a = 2.30078 + 0.66793I
b = 1.273064 0.499899I
0.21784 + 11.64566I 0.80372 7.60523I
u = 0.222801 0.345339I
a = 3.39507 3.46168I
b = 1.009724 + 0.045042I
0.0922815 0.0457562I 20.9509 + 4.2181I
u = 0.222801 + 0.345339I
a = 3.39507 + 3.46168I
b = 1.009724 0.045042I
0.0922815 + 0.0457562I 20.9509 4.2181I
u = 0.17056 1.77255I
a = 0.444132 0.418657I
b = 0.892547 + 0.020136I
3.09922 + 2.44564I 1.33220 3.38531I
u = 0.17056 + 1.77255I
a = 0.444132 + 0.418657I
b = 0.892547 0.020136I
3.09922 2.44564I 1.33220 + 3.38531I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.17031 1.74426I
a = 0.015013 0.730681I
b = 0.303727 + 0.826969I
8.74132 0.96087I 8.21239 + 0.01997I
u = 0.17031 + 1.74426I
a = 0.015013 + 0.730681I
b = 0.303727 0.826969I
8.74132 + 0.96087I 8.21239 0.01997I
u = 0.05539 1.52057I
a = 0.302259 + 0.937239I
b = 0.723215 0.913951I
7.43009 + 0.76858I 5.79264 1.97637I
u = 0.05539 + 1.52057I
a = 0.302259 0.937239I
b = 0.723215 + 0.913951I
7.43009 0.76858I 5.79264 + 1.97637I
u = 0.030560 0.490704I
a = 2.04276 + 0.05816I
b = 0.125344 + 0.881334I
3.36615 + 6.57501I 2.21442 6.52106I
u = 0.030560 + 0.490704I
a = 2.04276 0.05816I
b = 0.125344 0.881334I
3.36615 6.57501I 2.21442 + 6.52106I
u = 0.023037 1.082068I
a = 0.403555 + 0.770095I
b = 0.081476 0.967865I
2.34632 + 0.52578I 3.45198 + 1.46881I
u = 0.023037 + 1.082068I
a = 0.403555 0.770095I
b = 0.081476 + 0.967865I
2.34632 0.52578I 3.45198 1.46881I
u = 0.01052 1.81312I
a = 0.258116 0.723447I
b = 0.027467 + 1.315465I
7.65553 11.67952I 4.31716 + 8.63334I
u = 0.01052 + 1.81312I
a = 0.258116 + 0.723447I
b = 0.027467 1.315465I
7.65553 + 11.67952I 4.31716 8.63334I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.0300174 0.1349694I
a = 3.52976 5.53512I
b = 1.35052 + 0.45439I
2.17740 4.59275I 0.31813 + 3.34543I
u = 0.0300174 + 0.1349694I
a = 3.52976 + 5.53512I
b = 1.35052 0.45439I
2.17740 + 4.59275I 0.31813 3.34543I
u = 0.042103 0.460494I
a = 2.24909 0.95953I
b = 1.284319 0.385123I
3.47528 + 0.56323I 4.03017 + 1.19135I
u = 0.042103 + 0.460494I
a = 2.24909 + 0.95953I
b = 1.284319 + 0.385123I
3.47528 0.56323I 4.03017 1.19135I
u = 0.08251 1.85040I
a = 0.176512 0.658113I
b = 0.100944 + 1.031113I
4.01052 + 6.12296I 3.15639 6.32047I
u = 0.08251 + 1.85040I
a = 0.176512 + 0.658113I
b = 0.100944 1.031113I
4.01052 6.12296I 3.15639 + 6.32047I
u = 0.093771 0.529016I
a = 2.29573 1.08406I
b = 1.043396 0.583502I
3.32455 2.39582I 3.71725 + 5.83675I
u = 0.093771 + 0.529016I
a = 2.29573 + 1.08406I
b = 1.043396 + 0.583502I
3.32455 + 2.39582I 3.71725 5.83675I
u = 0.094665 0.341188I
a = 0.68572 2.13183I
b = 1.54012 + 0.27260I
3.57314 + 3.55716I 5.43467 2.98039I
u = 0.094665 + 0.341188I
a = 0.68572 + 2.13183I
b = 1.54012 0.27260I
3.57314 3.55716I 5.43467 + 2.98039I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.111843 0.132993I
a = 3.07660 2.34096I
b = 0.154795 + 0.715846I
0.38771 2.27012I 1.43970 + 3.97986I
u = 0.111843 + 0.132993I
a = 3.07660 + 2.34096I
b = 0.154795 0.715846I
0.38771 + 2.27012I 1.43970 3.97986I
u = 0.12472 1.67870I
a = 0.471264 0.617263I
b = 1.073050 + 0.225617I
3.99445 3.25658I 2.88379 + 2.55286I
u = 0.12472 + 1.67870I
a = 0.471264 + 0.617263I
b = 1.073050 0.225617I
3.99445 + 3.25658I 2.88379 2.55286I
u = 0.19792 1.65694I
a = 0.298101 + 0.644188I
b = 0.695441 0.685522I
6.30161 3.91490I 7.54972 + 4.78419I
u = 0.19792 + 1.65694I
a = 0.298101 0.644188I
b = 0.695441 + 0.685522I
6.30161 + 3.91490I 7.54972 4.78419I
u = 0.21819 1.50703I
a = 0.253254 + 0.813935I
b = 0.50519 1.36680I
3.57896 1.66051I 1.82059 + 0.30661I
u = 0.21819 + 1.50703I
a = 0.253254 0.813935I
b = 0.50519 + 1.36680I
3.57896 + 1.66051I 1.82059 0.30661I
u = 0.23311 1.65704I
a = 0.221589 0.557052I
b = 1.226227 + 0.283662I
1.24057 + 4.70878I 3.52453 5.73760I
u = 0.23311 + 1.65704I
a = 0.221589 + 0.557052I
b = 1.226227 0.283662I
1.24057 4.70878I 3.52453 + 5.73760I
12
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.293560 0.570273I
a = 0.020791 0.604433I
b = 0.338815 0.249348I
1.14552 + 0.85529I 6.99439 3.24657I
u = 0.293560 + 0.570273I
a = 0.020791 + 0.604433I
b = 0.338815 + 0.249348I
1.14552 0.85529I 6.99439 + 3.24657I
u = 0.298732 0.477488I
a = 1.54342 0.75875I
b = 1.307515 + 0.337320I
4.14708 + 6.10322I 5.06013 6.11695I
u = 0.298732 + 0.477488I
a = 1.54342 + 0.75875I
b = 1.307515 0.337320I
4.14708 6.10322I 5.06013 + 6.11695I
u = 0.359587 0.265627I
a = 1.27777 1.15288I
b = 1.245899 0.180263I
5.56839 2.63653I 11.15668 + 2.59785I
u = 0.359587 + 0.265627I
a = 1.27777 + 1.15288I
b = 1.245899 + 0.180263I
5.56839 + 2.63653I 11.15668 2.59785I
u = 0.379405 0.818194I
a = 0.81320 1.50433I
b = 0.845658 + 0.595779I
6.82851 + 6.31553I 5.16184 5.64666I
u = 0.379405 + 0.818194I
a = 0.81320 + 1.50433I
b = 0.845658 0.595779I
6.82851 6.31553I 5.16184 + 5.64666I
u = 0.51674 2.08872I
a = 0.111566 0.465570I
b = 1.197993 + 0.173924I
1.35126 + 4.74042I 3.61344 7.11766I
u = 0.51674 + 2.08872I
a = 0.111566 + 0.465570I
b = 1.197993 0.173924I
1.35126 4.74042I 3.61344 + 7.11766I
13
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.526932 0.666100I
a = 0.881469 0.091815I
b = 1.202908 0.107418I
2.40376 + 0.61006I 4.29849 0.46758I
u = 0.526932 + 0.666100I
a = 0.881469 + 0.091815I
b = 1.202908 + 0.107418I
2.40376 0.61006I 4.29849 + 0.46758I
u = 0.595387
a = 2.13525
b = 0.368940
0.742678 14.0666
u = 0.680728 0.650788I
a = 1.31481 + 0.55382I
b = 0.617575 0.245152I
5.48115 1.16165I 0.81975 4.51358I
u = 0.680728 + 0.650788I
a = 1.31481 0.55382I
b = 0.617575 + 0.245152I
5.48115 + 1.16165I 0.81975 + 4.51358I
u = 0.87681 1.92091I
a = 0.049494 0.614492I
b = 1.34921 + 0.52876I
1.43906 + 6.43123I 1.82992 0.87535I
u = 0.87681 + 1.92091I
a = 0.049494 + 0.614492I
b = 1.34921 0.52876I
1.43906 6.43123I 1.82992 + 0.87535I
u = 1.021339 0.810167I
a = 0.529764 + 0.588866I
b = 1.94470 0.12581I
1.66864 + 3.14014I 4.43696 + 6.77075I
u = 1.021339 + 0.810167I
a = 0.529764 0.588866I
b = 1.94470 + 0.12581I
1.66864 3.14014I 4.43696 6.77075I
u = 1.06441 1.98140I
a = 0.055101 + 0.617102I
b = 1.36818 0.49974I
0.53270 + 11.56489I 0.46896 7.90184I
14
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.06441 + 1.98140I
a = 0.055101 0.617102I
b = 1.36818 + 0.49974I
0.53270 11.56489I 0.46896 + 7.90184I
u = 1.28390 1.95780I
a = 0.034903 0.463004I
b = 1.27437 + 0.65713I
1.23108 + 9.17111I 0.22282 11.35640I
u = 1.28390 + 1.95780I
a = 0.034903 + 0.463004I
b = 1.27437 0.65713I
1.23108 9.17111I 0.22282 + 11.35640I
u = 1.65001 1.55965I
a = 0.257669 + 0.427033I
b = 1.039182 0.060714I
2.34256 + 1.03453I 4.80502 + 0.38432I
u = 1.65001 + 1.55965I
a = 0.257669 0.427033I
b = 1.039182 + 0.060714I
2.34256 1.03453I 4.80502 0.38432I
u = 2.06432
a = 0.412717
b = 1.30404
4.16838 7.45265
15
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
18
+ 2u
16
+ ··· + 73u 9)(u
96
+ 5u
95
+ ··· + 21760u 2097)
c
2
(3u
18
+ 2u
17
+ ··· + 2u 1)(3u
96
+ 7u
95
+ ··· + 3339u 297)
c
3
(9u
18
+ 43u
17
+ ··· + 2u + 1)(504u
96
+ 7504u
95
+ ··· + 840u + 56)
c
4
(u
18
u
17
+ ··· + u 1)(u
96
+ 6u
95
+ ··· 6966u 1849)
c
5
(u
18
+ 5u
17
+ ··· + 5u 1)(u
96
+ 6u
95
+ ··· + 1962842u + 272431)
c
6
(3u
18
2u
17
+ ··· 2u 1)(3u
96
+ 7u
95
+ ··· + 3339u 297)
c
7
(3u
18
5u
17
+ ··· + 5u 1)(3u
96
+ 4u
95
+ ··· 590u 1097)
c
8
(u
18
2u
17
+ ··· 16u + 3)(u
96
+ u
95
+ ··· 56419u 24573)
c
9
(u
18
+ u
17
+ ··· u 1)(u
96
+ 6u
95
+ ··· 6966u 1849)
c
10
(3u
18
+ 5u
17
+ ··· 5u 1)(3u
96
+ 4u
95
+ ··· 590u 1097)
c
11
(u
18
+ u
17
+ ··· + u 3)(u
96
+ 2u
95
+ ··· + 89272u 13803)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
18
+ 4y
17
+ ··· 1963y + 81)
(y
96
+ 13y
95
+ ··· + 33993176y + 4397409)
c
2
, c
6
(9y
18
+ 92y
17
+ ··· + 20y + 1)
(9y
96
+ 593y
95
+ ··· + 7914915y + 88209)
c
3
(81y
18
337y
17
+ ··· + 68y + 1)
(204930y
96
4989160y
95
+ ··· + 139150y + 2530)
c
4
(y
18
7y
17
+ ··· + 7y + 1)
(y
96
58y
95
+ ··· 92290986y + 3418801)
c
5
(y
18
+ 5y
17
+ ··· 53y + 1)
(y
96
30y
95
+ ··· 473184951454y + 74218649761)
c
7
, c
10
(9y
18
97y
17
+ ··· 19y + 1)
(9y
96
460y
95
+ ··· 30941236y + 1203409)
c
8
(y
18
+ 10y
17
+ ··· 124y + 9)
(y
96
17y
95
+ ··· 17758136197y + 603832329)
c
9
(y
18
7y
17
+ ··· + 7y + 1)
(y
96
58y
95
+ ··· 92290986y + 3418801)
c
11
(y
18
11y
17
+ ··· + 221y + 9)
(y
96
+ 6y
95
+ ··· + 6944044184y + 190522809)
17