11a
284
(K11a
284
)
1
Arc Sequences
8 6 1 10 2 11 4 3 7 5 9
Solving Sequence
5,10
11
4,7
8 6 9 1 2 3
c
10
c
4
c
7
c
6
c
9
c
11
c
1
c
3
c
2
, c
5
, c
8
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= h4u
26
+ 5u
25
+ ··· 1415u 341,
3.58596 × 10
75
u
25
+ 5.19432 × 10
75
u
24
+ ··· + 3.47453 × 10
77
b 1.20299 × 10
78
,
3.81991 × 10
76
u
25
5.03538 × 10
76
u
24
+ ··· + 2.36963 × 10
79
a + 7.68072 × 10
78
i
I
u
2
= h4u
115
+ 81u
114
+ ··· 110808u 1701,
1.08587 × 10
1248
u
114
+ 2.18563 × 10
1249
u
113
+ ··· + 1.39651 × 10
1248
b 3.97881 × 10
1251
,
1.85880 × 10
1249
u
114
3.73499 × 10
1250
u
113
+ ··· + 9.77554 × 10
1248
a + 4.90772 × 10
1252
i
There are 2 irreducible components with 141 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
= h4u
26
+ 5u
25
+ · · · 1415u 341, 3.59 × 10
75
u
25
+ 5.19 × 10
75
u
24
+
· · · + 3.47 × 10
77
b 1.20 × 10
78
, 3.82 × 10
76
u
25
5.04 × 10
76
u
24
+ · · · +
2.37 × 10
79
a + 7.68 × 10
78
i
(i) Arc colorings
a
5
=
1
0
a
10
=
0.00161203u
25
+ 0.00212496u
24
+ ··· + 0.540474u 0.324131
0.0103207u
25
0.0149497u
24
+ ··· + 11.9514u + 3.46231
a
11
=
0.0119327u
25
+ 0.0170746u
24
+ ··· 11.4109u 3.78644
0.0103207u
25
0.0149497u
24
+ ··· + 11.9514u + 3.46231
a
4
=
0.0162273u
25
+ 0.0156143u
24
+ ··· 12.4362u 0.296971
0.00563449u
25
+ 0.00218548u
24
+ ··· 1.76458u + 2.84202
a
7
=
0
u
a
8
=
0.00582062u
25
0.00872647u
24
+ ··· + 7.77443u + 2.24943
0.0128004u
25
0.0161324u
24
+ ··· + 14.8585u + 2.99176
a
6
=
0.00925305u
25
0.0115922u
24
+ ··· + 7.25279u + 3.31087
0.000187764u
25
+ 0.000559625u
24
+ ··· + 1.39179u 0.903037
a
9
=
0.00161203u
25
+ 0.00212496u
24
+ ··· + 0.540474u 0.324131
0.00903229u
25
0.0139405u
24
+ ··· + 11.7751u + 3.45294
a
1
=
0.0225122u
25
+ 0.0291309u
24
+ ··· 24.4289u 7.06994
0.0133518u
25
+ 0.0174563u
24
+ ··· 17.9127u 3.28786
a
2
=
0.00722466u
25
+ 0.00938059u
24
+ ··· 7.19894u 2.86552
0.0121037u
25
0.0117444u
24
+ ··· + 8.42449u + 0.919092
a
3
=
0.00395233u
25
0.00653935u
24
+ ··· + 2.08201u + 0.964542
0.00179808u
25
+ 0.00232497u
24
+ ··· 1.51801u 1.96636
a
3
=
0.00395233u
25
0.00653935u
24
+ ··· + 2.08201u + 0.964542
0.00179808u
25
+ 0.00232497u
24
+ ··· 1.51801u 1.96636
(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 = 5.35208
a = 0.991864
b = 1.04378
3.13685 80.2547
u = 2.19762 0.93242I
a = 0.357553 0.084527I
b = 0.816237 + 0.239357I
0.28328 + 8.29218I 6.85575 7.14384I
u = 2.19762 + 0.93242I
a = 0.357553 + 0.084527I
b = 0.816237 0.239357I
0.28328 8.29218I 6.85575 + 7.14384I
u = 1.93482 0.62638I
a = 0.677749 + 0.224753I
b = 1.35649 + 0.51125I
3.19455 8.83044I 3.92140 + 6.56535I
u = 1.93482 + 0.62638I
a = 0.677749 0.224753I
b = 1.35649 0.51125I
3.19455 + 8.83044I 3.92140 6.56535I
u = 0.962455 1.024584I
a = 0.526857 + 0.137069I
b = 0.206182 0.192031I
2.42427 0.67930I 4.38910 + 2.66937I
u = 0.962455 + 1.024584I
a = 0.526857 0.137069I
b = 0.206182 + 0.192031I
2.42427 + 0.67930I 4.38910 2.66937I
u = 0.690396 0.190219I
a = 1.02958 1.16070I
b = 0.227577 0.672977I
0.421435 + 1.186281I 4.72479 2.80501I
u = 0.690396 + 0.190219I
a = 1.02958 + 1.16070I
b = 0.227577 + 0.672977I
0.421435 1.186281I 4.72479 + 2.80501I
u = 0.253458 0.308127I
a = 0.01891 1.86651I
b = 0.087210 + 0.961580I
1.16980 + 3.77509I 2.33539 3.30863I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.253458 + 0.308127I
a = 0.01891 + 1.86651I
b = 0.087210 0.961580I
1.16980 3.77509I 2.33539 + 3.30863I
u = 0.146652 0.299251I
a = 0.448440 0.613353I
b = 0.11363 1.63639I
3.68864 + 1.45554I 15.4501 + 9.8201I
u = 0.146652 + 0.299251I
a = 0.448440 + 0.613353I
b = 0.11363 + 1.63639I
3.68864 1.45554I 15.4501 9.8201I
u = 0.087014 0.495453I
a = 2.00772 0.68452I
b = 0.144725 + 0.492800I
1.07549 + 4.08283I 0.16567 2.93988I
u = 0.087014 + 0.495453I
a = 2.00772 + 0.68452I
b = 0.144725 0.492800I
1.07549 4.08283I 0.16567 + 2.93988I
u = 0.806746 0.268347I
a = 0.161169 0.880882I
b = 1.356158 0.095896I
3.05153 7.14647I 5.02875 + 6.53250I
u = 0.806746 + 0.268347I
a = 0.161169 + 0.880882I
b = 1.356158 + 0.095896I
3.05153 + 7.14647I 5.02875 6.53250I
u = 1.044925 0.844418I
a = 0.322556 + 0.436209I
b = 1.254264 + 0.252501I
5.43384 + 2.60736I 6.61005 1.10855I
u = 1.044925 + 0.844418I
a = 0.322556 0.436209I
b = 1.254264 0.252501I
5.43384 2.60736I 6.61005 + 1.10855I
u = 1.15965 1.18566I
a = 0.063132 + 0.469152I
b = 1.070485 + 0.296067I
4.79002 5.38029I 5.23955 + 8.87254I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.15965 + 1.18566I
a = 0.063132 0.469152I
b = 1.070485 0.296067I
4.79002 + 5.38029I 5.23955 8.87254I
u = 2.01532 0.34937I
a = 0.671037 + 0.042467I
b = 1.281619 + 0.541938I
5.29738 + 2.79205I 3.89539 + 9.28399I
u = 2.01532 + 0.34937I
a = 0.671037 0.042467I
b = 1.281619 0.541938I
5.29738 2.79205I 3.89539 9.28399I
u = 2.04506 0.65132I
a = 0.741852 + 0.321555I
b = 1.47927 + 0.22060I
6.54530 + 4.65043I 9.47001 + 3.40221I
u = 2.04506 + 0.65132I
a = 0.741852 0.321555I
b = 1.47927 0.22060I
6.54530 4.65043I 9.47001 3.40221I
u = 2.15545
a = 0.425611
b = 1.47023
4.89292 14.4608
5
II. I
u
2
= h4u
115
+ 81u
114
+ · · · 110808u 1701, 1.09 × 10
1248
u
114
+ 2.19 ×
10
1249
u
113
+ · · · + 1.40 × 10
1248
b 3.98 × 10
1251
, 1.86 × 10
1249
u
114
3.73 ×
10
1250
u
113
+ · · · + 9.78 × 10
1248
a + 4.91 × 10
1252
i
(i) Arc colorings
a
5
=
1
0
a
10
=
1.90148u
114
+ 38.2075u
113
+ ··· 296642.u 5020.41
0.777562u
114
15.6507u
113
+ ··· + 160033.u + 2849.12
a
11
=
2.67904u
114
+ 53.8582u
113
+ ··· 456675.u 7869.53
0.777562u
114
15.6507u
113
+ ··· + 160033.u + 2849.12
a
4
=
3.44826u
114
+ 69.4415u
113
+ ··· 736137.u 13101.5
0.303018u
114
+ 6.11166u
113
+ ··· 73411.2u 1311.77
a
7
=
0
u
a
8
=
1.80468u
114
+ 36.3125u
113
+ ··· 341750.u 5939.78
0.955604u
114
19.2404u
113
+ ··· + 204055.u + 3647.61
a
6
=
0.935918u
114
18.8939u
113
+ ··· + 240162.u + 4313.93
0.361192u
114
+ 7.27284u
113
+ ··· 75337.7u 1337.51
a
9
=
1.90148u
114
+ 38.2075u
113
+ ··· 296642.u 5020.41
0.822412u
114
16.5526u
113
+ ··· + 167465.u + 2975.63
a
1
=
1.44471u
114
29.0824u
113
+ ··· + 283974.u + 4930.38
1.14514u
114
+ 23.0696u
113
+ ··· 259771.u 4675.55
a
2
=
1.04325u
114
+ 21.0543u
113
+ ··· 267092.u 4813.54
0.188146u
114
3.78865u
113
+ ··· + 39707.6u + 706.946
a
3
=
0.154167u
114
3.10419u
113
+ ··· + 43209.4u + 808.579
0.311992u
114
6.28097u
113
+ ··· + 62842.4u + 1108.34
a
3
=
0.154167u
114
3.10419u
113
+ ··· + 43209.4u + 808.579
0.311992u
114
6.28097u
113
+ ··· + 62842.4u + 1108.34
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
6
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 2.65694 0.59509I
a = 0.220787 + 0.176788I
b = 1.010130 + 0.380651I
0.30874 9.37379I 1.28089 + 12.81196I
u = 2.65694 + 0.59509I
a = 0.220787 0.176788I
b = 1.010130 0.380651I
0.30874 + 9.37379I 1.28089 12.81196I
u = 2.21887 0.65859I
a = 0.687143 0.252028I
b = 1.40743 0.58100I
4.4085 19.2643I 5.06792 + 10.08172I
u = 2.21887 + 0.65859I
a = 0.687143 + 0.252028I
b = 1.40743 + 0.58100I
4.4085 + 19.2643I 5.06792 10.08172I
u = 2.18850 2.29645I
a = 1.041791 + 0.014840I
b = 1.059197 0.052066I
3.06735 0.13431I 20.9462 + 10.0697I
u = 2.18850 + 2.29645I
a = 1.041791 0.014840I
b = 1.059197 + 0.052066I
3.06735 + 0.13431I 20.9462 10.0697I
u = 2.13022 0.41998I
a = 0.694251 + 0.382916I
b = 1.30808 + 0.59816I
4.13667 9.74502I 9.7338 + 11.2797I
u = 2.13022 + 0.41998I
a = 0.694251 0.382916I
b = 1.30808 0.59816I
4.13667 + 9.74502I 9.7338 11.2797I
u = 2.12165 0.40200I
a = 0.754619 0.090717I
b = 0.973927 0.511293I
1.97163 8.25765I 0.61706 + 8.92695I
u = 2.12165 + 0.40200I
a = 0.754619 + 0.090717I
b = 0.973927 + 0.511293I
1.97163 + 8.25765I 0.61706 8.92695I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 2.11983 1.23253I
a = 0.914658 + 0.318873I
b = 1.035289 + 0.037346I
2.68146 0.59329I 7.46676 2.53430I
u = 2.11983 + 1.23253I
a = 0.914658 0.318873I
b = 1.035289 0.037346I
2.68146 + 0.59329I 7.46676 + 2.53430I
u = 2.08683 0.49064I
a = 0.622819 0.148989I
b = 1.39446 0.56738I
3.46118 10.66995I 6.80898 + 11.15712I
u = 2.08683 + 0.49064I
a = 0.622819 + 0.148989I
b = 1.39446 + 0.56738I
3.46118 + 10.66995I 6.80898 11.15712I
u = 2.07484 0.99188I
a = 0.710196 + 0.130334I
b = 1.38682 + 0.39595I
4.21702 8.99203I 12.6798 + 9.4717I
u = 2.07484 + 0.99188I
a = 0.710196 0.130334I
b = 1.38682 0.39595I
4.21702 + 8.99203I 12.6798 9.4717I
u = 2.03921 0.92776I
a = 0.364379 0.335432I
b = 1.146104 + 0.150850I
3.21433 4.24659I 10.12535 + 2.58383I
u = 2.03921 + 0.92776I
a = 0.364379 + 0.335432I
b = 1.146104 0.150850I
3.21433 + 4.24659I 10.12535 2.58383I
u = 1.85075 1.47814I
a = 0.344486 0.063181I
b = 0.780035 + 0.054648I
1.53749 0.92367I 5.04340 + 3.98601I
u = 1.85075 + 1.47814I
a = 0.344486 + 0.063181I
b = 0.780035 0.054648I
1.53749 + 0.92367I 5.04340 3.98601I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.65654 0.77193I
a = 0.537665 0.158098I
b = 0.982358 0.491043I
4.07307 1.94826I 1.83333 + 2.74729I
u = 1.65654 + 0.77193I
a = 0.537665 + 0.158098I
b = 0.982358 + 0.491043I
4.07307 + 1.94826I 1.83333 2.74729I
u = 1.40358 0.23697I
a = 0.903877 0.242663I
b = 1.32127 0.65726I
4.19786 + 5.91313I 9.94340 4.15613I
u = 1.40358 + 0.23697I
a = 0.903877 + 0.242663I
b = 1.32127 + 0.65726I
4.19786 5.91313I 9.94340 + 4.15613I
u = 1.28674 1.28880I
a = 0.221742 + 0.341912I
b = 1.122023 + 0.035704I
5.49191 3.64527I 9.06683 + 6.94235I
u = 1.28674 + 1.28880I
a = 0.221742 0.341912I
b = 1.122023 0.035704I
5.49191 + 3.64527I 9.06683 6.94235I
u = 1.260579 0.437210I
a = 0.494800 + 0.520798I
b = 1.172711 + 0.567648I
5.80540 + 6.12206I 10.35178 8.89051I
u = 1.260579 + 0.437210I
a = 0.494800 0.520798I
b = 1.172711 0.567648I
5.80540 6.12206I 10.35178 + 8.89051I
u = 1.25155 1.45628I
a = 0.026520 + 0.438876I
b = 1.034361 + 0.088071I
5.06782 + 4.62329I 8.69727 1.12985I
u = 1.25155 + 1.45628I
a = 0.026520 0.438876I
b = 1.034361 0.088071I
5.06782 4.62329I 8.69727 + 1.12985I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.209772 0.673691I
a = 0.811757 + 0.233000I
b = 1.53256 + 0.61309I
1.61279 9.53611I 0.65267 + 12.76163I
u = 1.209772 + 0.673691I
a = 0.811757 0.233000I
b = 1.53256 0.61309I
1.61279 + 9.53611I 0.65267 12.76163I
u = 1.14409 1.27338I
a = 1.264046 0.321879I
b = 1.163111 + 0.215218I
2.40903 + 9.64189I 7.25494 10.55727I
u = 1.14409 + 1.27338I
a = 1.264046 + 0.321879I
b = 1.163111 0.215218I
2.40903 9.64189I 7.25494 + 10.55727I
u = 1.10610 1.22650I
a = 0.611487 + 0.141027I
b = 0.133252 0.192188I
0.60271 + 7.63366I 1.06736 3.34725I
u = 1.10610 + 1.22650I
a = 0.611487 0.141027I
b = 0.133252 + 0.192188I
0.60271 7.63366I 1.06736 + 3.34725I
u = 1.007662 0.304689I
a = 0.043213 + 0.382930I
b = 1.024402 0.478941I
0.12708 5.59619I 1.11710 + 5.95871I
u = 1.007662 + 0.304689I
a = 0.043213 0.382930I
b = 1.024402 + 0.478941I
0.12708 + 5.59619I 1.11710 5.95871I
u = 0.971709 0.362614I
a = 0.777808 + 0.463035I
b = 1.31460 + 0.61425I
6.27820 1.86688I 10.45813 2.79746I
u = 0.971709 + 0.362614I
a = 0.777808 0.463035I
b = 1.31460 0.61425I
6.27820 + 1.86688I 10.45813 + 2.79746I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.793821 0.310188I
a = 1.286280 + 0.560939I
b = 0.954355 + 0.617889I
0.06859 2.68945I 0.59796 + 6.63077I
u = 0.793821 + 0.310188I
a = 1.286280 0.560939I
b = 0.954355 0.617889I
0.06859 + 2.68945I 0.59796 6.63077I
u = 0.702028 0.103139I
a = 0.825340 + 1.146117I
b = 0.134878 + 0.614359I
0.63327 1.84453I 0.14495 + 4.92506I
u = 0.702028 + 0.103139I
a = 0.825340 1.146117I
b = 0.134878 0.614359I
0.63327 + 1.84453I 0.14495 4.92506I
u = 0.681900 0.060345I
a = 1.47975 0.80880I
b = 0.510605 + 0.872391I
3.47321 3.16840I 2.22918 + 5.47455I
u = 0.681900 + 0.060345I
a = 1.47975 + 0.80880I
b = 0.510605 0.872391I
3.47321 + 3.16840I 2.22918 5.47455I
u = 0.510061 0.755807I
a = 0.532620 + 0.054980I
b = 0.319706 0.582678I
1.61019 + 1.66229I 0.046508 0.698637I
u = 0.510061 + 0.755807I
a = 0.532620 0.054980I
b = 0.319706 + 0.582678I
1.61019 1.66229I 0.046508 + 0.698637I
u = 0.478990 0.845201I
a = 0.043411 1.104521I
b = 0.367774 + 0.043771I
0.79505 + 2.96219I 9.07486 5.68579I
u = 0.478990 + 0.845201I
a = 0.043411 + 1.104521I
b = 0.367774 0.043771I
0.79505 2.96219I 9.07486 + 5.68579I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.453378 0.206050I
a = 1.52496 1.79039I
b = 0.286543 1.076000I
1.021757 + 0.432243I 10.98843 + 1.94424I
u = 0.453378 + 0.206050I
a = 1.52496 + 1.79039I
b = 0.286543 + 1.076000I
1.021757 0.432243I 10.98843 1.94424I
u = 0.396156 0.070745I
a = 0.48164 2.87150I
b = 0.959244 + 0.232094I
0.02959 + 5.02048I 3.58673 6.46546I
u = 0.396156 + 0.070745I
a = 0.48164 + 2.87150I
b = 0.959244 0.232094I
0.02959 5.02048I 3.58673 + 6.46546I
u = 0.312107 0.361125I
a = 0.678069 1.030679I
b = 0.011643 0.668932I
1.05915 + 1.57001I 1.42915 4.50979I
u = 0.312107 + 0.361125I
a = 0.678069 + 1.030679I
b = 0.011643 + 0.668932I
1.05915 1.57001I 1.42915 + 4.50979I
u = 0.264920 0.559813I
a = 0.916806 + 0.031721I
b = 0.530189 0.955205I
1.66491 + 3.01542I 0.38268 + 2.14618I
u = 0.264920 + 0.559813I
a = 0.916806 0.031721I
b = 0.530189 + 0.955205I
1.66491 3.01542I 0.38268 2.14618I
u = 0.251656 0.079464I
a = 1.13844 4.01446I
b = 0.225514 + 0.606525I
0.84959 + 4.92469I 2.11027 13.45244I
u = 0.251656 + 0.079464I
a = 1.13844 + 4.01446I
b = 0.225514 0.606525I
0.84959 4.92469I 2.11027 + 13.45244I
12
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.205233 0.326762I
a = 0.39801 + 2.18644I
b = 0.062709 1.257769I
0.87832 + 4.34613I 9.6939 14.1674I
u = 0.205233 + 0.326762I
a = 0.39801 2.18644I
b = 0.062709 + 1.257769I
0.87832 4.34613I 9.6939 + 14.1674I
u = 0.193910 0.866755I
a = 0.392212 0.346060I
b = 0.443788 0.795349I
1.83286 + 0.68624I 0.69950 1.32140I
u = 0.193910 + 0.866755I
a = 0.392212 + 0.346060I
b = 0.443788 + 0.795349I
1.83286 0.68624I 0.69950 + 1.32140I
u = 0.173813 0.030348I
a = 1.16377 + 5.48820I
b = 0.519165 0.876104I
5.59609 3.00304I 4.41820 + 3.71334I
u = 0.173813 + 0.030348I
a = 1.16377 5.48820I
b = 0.519165 + 0.876104I
5.59609 + 3.00304I 4.41820 3.71334I
u = 0.132064 0.415236I
a = 0.75535 1.84240I
b = 0.411316 0.582022I
0.82600 + 1.86825I 3.74526 4.03129I
u = 0.132064 + 0.415236I
a = 0.75535 + 1.84240I
b = 0.411316 + 0.582022I
0.82600 1.86825I 3.74526 + 4.03129I
u = 0.1063550 0.0066212I
a = 4.23374 + 0.50497I
b = 0.18102 1.75461I
3.53196 1.57888I 16.7748 + 14.5726I
u = 0.1063550 + 0.0066212I
a = 4.23374 0.50497I
b = 0.18102 + 1.75461I
3.53196 + 1.57888I 16.7748 14.5726I
13
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.073755 0.317572I
a = 1.32227 1.93052I
b = 0.345587 0.027787I
1.369570 0.113618I 10.02289 1.25200I
u = 0.073755 + 0.317572I
a = 1.32227 + 1.93052I
b = 0.345587 + 0.027787I
1.369570 + 0.113618I 10.02289 + 1.25200I
u = 0.0661340 0.0842306I
a = 0.67585 + 11.18295I
b = 0.004590 1.259353I
0.03533 + 12.87641I 2.94281 9.13821I
u = 0.0661340 + 0.0842306I
a = 0.67585 11.18295I
b = 0.004590 + 1.259353I
0.03533 12.87641I 2.94281 + 9.13821I
u = 0.000296 0.320036I
a = 3.75625 1.14675I
b = 1.026093 + 0.139218I
0.539034 0.195029I 1.72931 0.97162I
u = 0.000296 + 0.320036I
a = 3.75625 + 1.14675I
b = 1.026093 0.139218I
0.539034 + 0.195029I 1.72931 + 0.97162I
u = 0.106854 0.205249I
a = 4.54785 + 2.30411I
b = 0.012508 + 0.954942I
2.71019 + 7.23222I 5.48048 6.27911I
u = 0.106854 + 0.205249I
a = 4.54785 2.30411I
b = 0.012508 0.954942I
2.71019 7.23222I 5.48048 + 6.27911I
u = 0.130940 0.143133I
a = 0.92299 6.39383I
b = 0.234098 1.101474I
0.68914 3.66478I 9.85598 + 6.79125I
u = 0.130940 + 0.143133I
a = 0.92299 + 6.39383I
b = 0.234098 + 1.101474I
0.68914 + 3.66478I 9.85598 6.79125I
14
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.607237 0.519171I
a = 1.34755 + 0.61830I
b = 0.582607 + 0.698925I
1.62964 + 5.18438I 1.04465 9.63731I
u = 0.607237 + 0.519171I
a = 1.34755 0.61830I
b = 0.582607 0.698925I
1.62964 5.18438I 1.04465 + 9.63731I
u = 0.640894 0.375730I
a = 1.324477 + 0.230132I
b = 0.078049 + 0.552303I
2.97182 2.03893I 6.42535 + 4.02525I
u = 0.640894 + 0.375730I
a = 1.324477 0.230132I
b = 0.078049 0.552303I
2.97182 + 2.03893I 6.42535 4.02525I
u = 1.082280 0.128292I
a = 0.315897 0.353733I
b = 0.985307 + 0.117780I
1.77940 0.62020I 4.19144 + 0.32596I
u = 1.082280 + 0.128292I
a = 0.315897 + 0.353733I
b = 0.985307 0.117780I
1.77940 + 0.62020I 4.19144 0.32596I
u = 1.249113 0.259794I
a = 0.721018 + 0.215438I
b = 1.63914 + 0.48297I
5.24071 + 6.02921I 8.25746 5.43708I
u = 1.249113 + 0.259794I
a = 0.721018 0.215438I
b = 1.63914 0.48297I
5.24071 6.02921I 8.25746 + 5.43708I
u = 1.33799 0.54309I
a = 0.715577 + 0.326248I
b = 1.44936 + 0.36569I
3.47686 + 5.05598I 4.55066 7.76927I
u = 1.33799 + 0.54309I
a = 0.715577 0.326248I
b = 1.44936 0.36569I
3.47686 5.05598I 4.55066 + 7.76927I
15
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.53656 0.19860I
a = 0.488935 + 0.512306I
b = 1.273063 + 0.287079I
2.97685 + 5.07858I 2.94848 5.55455I
u = 1.53656 + 0.19860I
a = 0.488935 0.512306I
b = 1.273063 0.287079I
2.97685 5.07858I 2.94848 + 5.55455I
u = 1.73290 0.39402I
a = 0.743083 0.209249I
b = 1.232710 0.278290I
6.29691 0.61776I 12.21282 0.03848I
u = 1.73290 + 0.39402I
a = 0.743083 + 0.209249I
b = 1.232710 + 0.278290I
6.29691 + 0.61776I 12.21282 + 0.03848I
u = 1.73460 0.11633I
a = 0.474195 + 0.205606I
b = 1.45521 + 0.41254I
4.55954 1.63755I 10.44330 1.59802I
u = 1.73460 + 0.11633I
a = 0.474195 0.205606I
b = 1.45521 0.41254I
4.55954 + 1.63755I 10.44330 + 1.59802I
u = 1.89305 0.56364I
a = 0.365708 + 0.106510I
b = 1.43105 0.02510I
4.35240 + 0.58562I 7.19541 3.39197I
u = 1.89305 + 0.56364I
a = 0.365708 0.106510I
b = 1.43105 + 0.02510I
4.35240 0.58562I 7.19541 + 3.39197I
u = 1.91796 0.41300I
a = 0.688419 0.320430I
b = 1.106935 0.106044I
6.14019 0.62684I 12.34553 + 0.36710I
u = 1.91796 + 0.41300I
a = 0.688419 + 0.320430I
b = 1.106935 + 0.106044I
6.14019 + 0.62684I 12.34553 0.36710I
16
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.97396 0.68748I
a = 0.395610 + 0.203590I
b = 1.111113 + 0.194979I
2.52539 + 4.84612I 5.51959 6.84426I
u = 1.97396 + 0.68748I
a = 0.395610 0.203590I
b = 1.111113 0.194979I
2.52539 4.84612I 5.51959 + 6.84426I
u = 1.99168 0.76527I
a = 0.798973 + 0.262908I
b = 1.42361 + 0.20245I
6.76597 + 4.72878I 14.6888 8.1121I
u = 1.99168 + 0.76527I
a = 0.798973 0.262908I
b = 1.42361 0.20245I
6.76597 4.72878I 14.6888 + 8.1121I
u = 2.00021 0.37754I
a = 0.650607 0.000259I
b = 1.30419 0.62684I
5.39735 + 2.89988I 34.2168 31.1324I
u = 2.00021 + 0.37754I
a = 0.650607 + 0.000259I
b = 1.30419 + 0.62684I
5.39735 2.89988I 34.2168 + 31.1324I
u = 2.00455 1.44037I
a = 0.110241 + 0.283406I
b = 1.273154 + 0.109754I
3.69644 8.07570I 9.7356 + 11.4954I
u = 2.00455 + 1.44037I
a = 0.110241 0.283406I
b = 1.273154 0.109754I
3.69644 + 8.07570I 9.7356 11.4954I
u = 2.06095 0.71154I
a = 0.756836 + 0.294907I
b = 1.44383 + 0.21091I
6.77311 + 4.75588I 19.9085 9.7356I
u = 2.06095 + 0.71154I
a = 0.756836 0.294907I
b = 1.44383 0.21091I
6.77311 4.75588I 19.9085 + 9.7356I
17
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 2.11416 0.55047I
a = 0.739747 + 0.359743I
b = 1.362677 + 0.322519I
6.65120 + 5.03845I 13.3143 5.2572I
u = 2.11416 + 0.55047I
a = 0.739747 0.359743I
b = 1.362677 0.322519I
6.65120 5.03845I 13.3143 + 5.2572I
u = 2.22508 0.66318I
a = 0.734774 0.238041I
b = 1.324594 0.489779I
6.8504 + 12.4320I 7.07417 7.53683I
u = 2.22508 + 0.66318I
a = 0.734774 + 0.238041I
b = 1.324594 + 0.489779I
6.8504 12.4320I 7.07417 + 7.53683I
u = 2.23313
a = 0.525777
b = 1.31890
6.33944 15.0267
18
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(2u
26
3u
25
+ ··· + 5u + 1)(2u
115
+ 9u
114
+ ··· + 2406u 767)
c
2
(2u
26
5u
25
+ ··· 2u + 1)(2u
115
+ 3u
114
+ ··· + 3u 1)
c
3
(u
26
+ 2u
25
+ ··· 5u 1)(u
115
+ 9u
114
+ ··· 4u 1)
c
4
(u
26
+ 3u
25
+ ··· 5u 1)(u
115
+ 2u
114
+ ··· 3876u + 1201)
c
5
(2u
26
+ 5u
25
+ ··· + 2u + 1)(2u
115
+ 3u
114
+ ··· + 3u 1)
c
6
(u
26
+ u
25
+ ··· + 57u + 28)(u
115
13u
113
+ ··· + 85279u + 38788)
c
7
(u
26
u
25
+ ··· + 21u + 2)(u
115
+ 4u
114
+ ··· + 1.15703 × 10
7
u 823526)
c
8
(2u
26
+ u
25
+ ··· 7u 1)(2u
115
+ u
114
+ ··· + 114u + 7)
c
9
(4u
26
+ 61u
25
+ ··· + 12u + 1)
(12u
115
+ 171u
114
+ ··· + 45915u + 31917)
c
10
(u
26
3u
25
+ ··· + 5u 1)(u
115
+ 2u
114
+ ··· 3876u + 1201)
c
11
(u
26
4u
25
+ ··· 17u 2)(u
115
+ 9u
114
+ ··· 183323u 19982)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(4y
26
69y
25
+ ··· 7y + 1)
(4y
115
105y
114
+ ··· + 35082100y 588289)
c
2
(4y
26
73y
25
+ ··· 30y + 1)(12y
115
711y
114
+ ··· + 81y 3)
c
3
(y
26
+ 2y
25
+ ··· 3y + 1)(y
115
11y
114
+ ··· + 180y 1)
c
4
(y
26
15y
25
+ ··· + y + 1)
(y
115
76y
114
+ ··· + 36617356y 1442401)
c
5
(4y
26
73y
25
+ ··· 30y + 1)(12y
115
711y
114
+ ··· + 81y 3)
c
6
(y
26
9y
25
+ ··· 9857y + 784)
(y
115
26y
114
+ ··· + 89633162793y 1504508944)
c
7
(y
26
+ 15y
25
+ ··· 53y + 4)
(y
115
+ 54y
114
+ ··· 20235629660845y 678195072676)
c
8
(4y
26
41y
25
+ ··· 17y + 1)(4y
115
61y
114
+ ··· + 886y 49)
c
9
(16y
26
553y
25
+ ··· 32y + 1)
(240y
115
8055y
114
+ ··· + 33060488955y 1697824815)
c
10
(y
26
15y
25
+ ··· + y + 1)
(y
115
76y
114
+ ··· + 36617356y 1442401)
c
11
(y
26
4y
25
+ ··· 429y + 4)
(y
115
+ 23y
114
+ ··· 4932760351y 399280324)
20