11a
197
(K11a
197
)
1
Arc Sequences
6 1 11 7 10 2 4 3 5 9 8
Solving Sequence
2,6
7 1
3,10
5 4 9 11 8
c
6
c
1
c
2
c
5
c
4
c
9
c
10
c
8
c
3
, c
7
, c
11
Representation Ideals
I =
4
\
i=1
I
u
i
I
u
1
= hu
8
2u
6
u
5
+ 3u
4
+ u
3
2u
2
+ 1, u
6
2u
4
u
3
+ 3u
2
+ a + u 2,
u
7
u
6
2u
5
+ u
4
+ 4u
3
u
2
+ b 2u + 2i
I
u
2
= hu
68
+ u
67
+ ··· + 12u + 1, 5.39287 × 10
83
u
67
+ 1.27307 × 10
84
u
66
+ ··· + 3.20363 × 10
85
b 9.06375 × 10
84
,
8.57839 × 10
85
u
67
+ 7.60134 × 10
85
u
66
+ ··· + 3.20363 × 10
85
a + 6.51656 × 10
86
i
I
u
3
= hu
8
2u
6
+ 3u
4
+ u
3
2u
2
u + 1, a + 1, 2u
7
u
6
+ 3u
5
+ 2u
4
4u
3
5u
2
+ b + 1i
I
u
4
= hu
19
4u
17
+ ··· u 1, a + 1, 36u
18
13u
17
+ ··· + 29b 6i
There are 4 irreducible components with 103 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
8
2u
6
u
5
+ 3u
4
+ u
3
2u
2
+ 1, u
6
2u
4
u
3
+ 3u
2
+ a + u
2, u
7
u
6
2u
5
+ u
4
+ 4u
3
u
2
+ b 2u + 2i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
7
=
u
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
10
=
u
6
+ 2u
4
+ u
3
3u
2
u + 2
u
7
+ u
6
+ 2u
5
u
4
4u
3
+ u
2
+ 2u 2
a
5
=
2u
7
+ 3u
5
+ 2u
4
4u
3
u
2
+ u 1
2u
7
u
6
3u
5
+ 5u
3
2u
2
2u + 2
a
4
=
2u
7
+ 3u
5
+ 2u
4
4u
3
2u
2
+ u
2u
7
u
6
3u
5
+ 5u
3
u
2
2u + 1
a
9
=
u
7
+ u
6
+ 2u
5
4u
3
+ 2u + 1
u
7
u
6
u
5
+ 2u
3
2u
2
a
11
=
2u
7
3u
5
3u
4
+ 4u
3
+ 2u
2
u
7
+ u
6
+ u
5
3u
3
+ u
2
a
8
=
u
6
u
4
2u
3
+ u
2
+ u + 1
u
6
+ u
5
+ u
4
2u
2
+ u
a
8
=
u
6
u
4
2u
3
+ u
2
+ u + 1
u
6
+ u
5
+ u
4
2u
2
+ u
(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 = 0.940851 0.831065I
a = 0.078333 0.629717I
b = 0.070951 + 0.424335I
4.42801 2.37936I 2.50152 3.27706I
u = 0.940851 + 0.831065I
a = 0.078333 + 0.629717I
b = 0.070951 0.424335I
4.42801 + 2.37936I 2.50152 + 3.27706I
u = 0.794982 0.257086I
a = 1.16123 0.83877I
b = 2.07095 + 1.05537I
1.13814 + 3.38562I 9.49848 3.42631I
u = 0.794982 + 0.257086I
a = 1.16123 + 0.83877I
b = 2.07095 1.05537I
1.13814 3.38562I 9.49848 + 3.42631I
u = 0.597036 0.527369I
a = 0.19453 + 1.56382I
b = 0.070951 + 0.424335I
4.42801 2.37936I 2.50152 3.27706I
u = 0.597036 + 0.527369I
a = 0.19453 1.56382I
b = 0.070951 0.424335I
4.42801 + 2.37936I 2.50152 + 3.27706I
u = 1.138796 0.368271I
a = 0.565903 + 0.408758I
b = 2.07095 + 1.05537I
1.13814 + 3.38562I 9.49848 3.42631I
u = 1.138796 + 0.368271I
a = 0.565903 0.408758I
b = 2.07095 1.05537I
1.13814 3.38562I 9.49848 + 3.42631I
3
II. I
u
2
=
hu
68
+u
67
+· · ·+12u+1, 5.39×10
83
u
67
+1.27×10
84
u
66
+· · ·+3.20×10
85
b
9.06 × 10
84
, 8.58 × 10
85
u
67
+ 7.60 × 10
85
u
66
+ · · · + 3.20 × 10
85
a + 6.52 × 10
86
i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
7
=
u
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
10
=
2.67771u
67
2.37273u
66
+ ··· 117.286u 20.3412
0.0168336u
67
0.0397382u
66
+ ··· + 4.55440u + 0.282921
a
5
=
3.42003u
67
2.92890u
66
+ ··· 149.114u 18.7300
0.0114041u
67
+ 0.0251783u
66
+ ··· + 2.20727u 0.439508
a
4
=
3.51021u
67
3.08328u
66
+ ··· 152.016u 19.2577
0.0787800u
67
+ 0.179560u
66
+ ··· + 5.10834u + 0.0882006
a
9
=
0.455399u
67
0.660796u
66
+ ··· 24.2276u 16.8165
0.00148963u
67
0.0439924u
66
+ ··· + 10.7179u + 1.83259
a
11
=
3.97350u
67
+ 3.69439u
66
+ ··· + 192.973u + 24.4426
0.532051u
67
0.0357733u
66
+ ··· + 1.27856u + 0.717878
a
8
=
0.802960u
67
1.00892u
66
+ ··· 32.7095u 18.4012
0.0380368u
67
0.0558636u
66
+ ··· + 9.00530u + 1.68707
a
8
=
0.802960u
67
1.00892u
66
+ ··· 32.7095u 18.4012
0.0380368u
67
0.0558636u
66
+ ··· + 9.00530u + 1.68707
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
4
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.317105 0.285126I
a = 0.385835 + 0.536317I
b = 1.58617 0.15836I
0.20559 3.65421I 2.89345 + 3.62280I
u = 1.317105 + 0.285126I
a = 0.385835 0.536317I
b = 1.58617 + 0.15836I
0.20559 + 3.65421I 2.89345 3.62280I
u = 1.11075 0.90512I
a = 0.064342 + 0.618842I
b = 0.152783 0.028868I
4.76682 3.09252I 3.99662 + 6.42171I
u = 1.11075 + 0.90512I
a = 0.064342 0.618842I
b = 0.152783 + 0.028868I
4.76682 + 3.09252I 3.99662 6.42171I
u = 1.055707 0.635834I
a = 0.826634 + 0.129610I
b = 1.89607 + 0.46828I
1.12918 5.12471I 3.84707 + 4.93018I
u = 1.055707 + 0.635834I
a = 0.826634 0.129610I
b = 1.89607 0.46828I
1.12918 + 5.12471I 3.84707 4.93018I
u = 1.051503 0.006134I
a = 1.026765 0.498051I
b = 2.23979 0.33085I
3.86295 + 4.69165I 11.49179 4.07331I
u = 1.051503 + 0.006134I
a = 1.026765 + 0.498051I
b = 2.23979 + 0.33085I
3.86295 4.69165I 11.49179 + 4.07331I
u = 1.009624 0.341294I
a = 0.108196 + 0.271755I
b = 0.349052 + 0.896231I
0.25133 4.16817I 3.64588 + 7.80948I
u = 1.009624 + 0.341294I
a = 0.108196 0.271755I
b = 0.349052 0.896231I
0.25133 + 4.16817I 3.64588 7.80948I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.002661 0.625345I
a = 1.255037 + 0.037371I
b = 2.71233 0.14330I
3.65105 8.06945I 2.24961 + 10.45643I
u = 1.002661 + 0.625345I
a = 1.255037 0.037371I
b = 2.71233 + 0.14330I
3.65105 + 8.06945I 2.24961 10.45643I
u = 0.996977 0.619808I
a = 1.068974 0.528149I
b = 2.43029 0.30695I
0.84333 8.53070I 5.83691 + 8.88541I
u = 0.996977 + 0.619808I
a = 1.068974 + 0.528149I
b = 2.43029 + 0.30695I
0.84333 + 8.53070I 5.83691 8.88541I
u = 0.947558 0.631277I
a = 0.109546 0.861259I
b = 0.745958 + 0.265682I
1.50330 5.20280I 3.13300 + 5.66125I
u = 0.947558 + 0.631277I
a = 0.109546 + 0.861259I
b = 0.745958 0.265682I
1.50330 + 5.20280I 3.13300 5.66125I
u = 0.945712 0.714178I
a = 0.135099 0.793465I
b = 0.056456 + 1.090178I
5.57461 2.65210I 3.99824 + 1.76358I
u = 0.945712 + 0.714178I
a = 0.135099 + 0.793465I
b = 0.056456 1.090178I
5.57461 + 2.65210I 3.99824 1.76358I
u = 0.942365 0.149982I
a = 0.626878 0.663127I
b = 2.53057 + 0.70778I
1.66267 + 2.38839I 3.74252 3.92268I
u = 0.942365 + 0.149982I
a = 0.626878 + 0.663127I
b = 2.53057 0.70778I
1.66267 2.38839I 3.74252 + 3.92268I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.880387 0.820730I
a = 0.0541795 + 0.1112342I
b = 0.342774 + 0.217708I
4.05974 3.04464I 8.15642 + 5.02705I
u = 0.880387 + 0.820730I
a = 0.0541795 0.1112342I
b = 0.342774 0.217708I
4.05974 + 3.04464I 8.15642 5.02705I
u = 0.661103 0.596374I
a = 0.88392 + 1.22866I
b = 1.58617 + 0.15836I
0.20559 + 3.65421I 2.89345 3.62280I
u = 0.661103 + 0.596374I
a = 0.88392 1.22866I
b = 1.58617 0.15836I
0.20559 3.65421I 2.89345 + 3.62280I
u = 0.631595 0.629139I
a = 0.16621 + 1.59864I
b = 0.152783 + 0.028868I
4.76682 + 3.09252I 3.99662 6.42171I
u = 0.631595 + 0.629139I
a = 0.16621 1.59864I
b = 0.152783 0.028868I
4.76682 3.09252I 3.99662 + 6.42171I
u = 0.565902 1.182342I
a = 0.738007 0.337275I
b = 0.938619 0.417174I
6.41329 4.23932I 5.89514 + 7.96165I
u = 0.565902 + 1.182342I
a = 0.738007 + 0.337275I
b = 0.938619 + 0.417174I
6.41329 + 4.23932I 5.89514 7.96165I
u = 0.564035 1.001080I
a = 0.106119 1.137353I
b = 0.046159 0.748421I
7.06234 + 11.08516I 1.13522 6.17412I
u = 0.564035 + 1.001080I
a = 0.106119 + 1.137353I
b = 0.046159 + 0.748421I
7.06234 11.08516I 1.13522 + 6.17412I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.561019 0.675410I
a = 0.183465 + 0.983026I
b = 0.618763
2.60763 0.509555
u = 0.561019 + 0.675410I
a = 0.183465 0.983026I
b = 0.618763
2.60763 0.509555
u = 0.138992 0.053462I
a = 3.53919 + 7.26619I
b = 0.342774 0.217708I
4.05974 + 3.04464I 8.15642 5.02705I
u = 0.138992 + 0.053462I
a = 3.53919 7.26619I
b = 0.342774 + 0.217708I
4.05974 3.04464I 8.15642 + 5.02705I
u = 0.016489 0.311297I
a = 1.26461 + 3.17630I
b = 0.349052 0.896231I
0.25133 + 4.16817I 3.64588 7.80948I
u = 0.016489 + 0.311297I
a = 1.26461 3.17630I
b = 0.349052 + 0.896231I
0.25133 4.16817I 3.64588 + 7.80948I
u = 0.290878 0.638310I
a = 0.660964 1.159325I
b = 0.233581 0.361656I
1.64111 0.20863I 8.20722 0.26692I
u = 0.290878 + 0.638310I
a = 0.660964 + 1.159325I
b = 0.233581 + 0.361656I
1.64111 + 0.20863I 8.20722 + 0.26692I
u = 0.386639 1.166929I
a = 0.299479 0.859826I
b = 0.209410 0.948715I
6.19582 1.01878I 4.58808 1.16723I
u = 0.386639 + 1.166929I
a = 0.299479 + 0.859826I
b = 0.209410 + 0.948715I
6.19582 + 1.01878I 4.58808 + 1.16723I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.647494 0.746939I
a = 0.145332 + 1.142606I
b = 0.745958 + 0.265682I
1.50330 5.20280I 3.13300 + 5.66125I
u = 0.647494 + 0.746939I
a = 0.145332 1.142606I
b = 0.745958 0.265682I
1.50330 + 5.20280I 3.13300 5.66125I
u = 0.690205 0.530887I
a = 0.752813 + 0.796344I
b = 2.53057 + 0.70778I
1.66267 + 2.38839I 3.74252 3.92268I
u = 0.690205 + 0.530887I
a = 0.752813 0.796344I
b = 2.53057 0.70778I
1.66267 2.38839I 3.74252 + 3.92268I
u = 0.694440 0.653905I
a = 0.208538 + 1.224788I
b = 0.056456 + 1.090178I
5.57461 2.65210I 3.99824 + 1.76358I
u = 0.694440 + 0.653905I
a = 0.208538 1.224788I
b = 0.056456 1.090178I
5.57461 + 2.65210I 3.99824 1.76358I
u = 0.790274 0.662432I
a = 1.180699 + 0.185124I
b = 1.89607 0.46828I
1.12918 + 5.12471I 3.84707 4.93018I
u = 0.790274 + 0.662432I
a = 1.180699 0.185124I
b = 1.89607 + 0.46828I
1.12918 5.12471I 3.84707 + 4.93018I
u = 0.816414 0.681712I
a = 1.120895 0.512258I
b = 0.938619 + 0.417174I
6.41329 + 4.23932I 5.89514 7.96165I
u = 0.816414 + 0.681712I
a = 1.120895 + 0.512258I
b = 0.938619 0.417174I
6.41329 4.23932I 5.89514 + 7.96165I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.887566 0.681913I
a = 0.361258 1.037199I
b = 0.209410 + 0.948715I
6.19582 + 1.01878I 4.58808 + 1.16723I
u = 0.887566 + 0.681913I
a = 0.361258 + 1.037199I
b = 0.209410 0.948715I
6.19582 1.01878I 4.58808 1.16723I
u = 0.888822 0.653363I
a = 0.298402 0.954440I
b = 0.0798253
0.823819 4.83529
u = 0.888822 + 0.653363I
a = 0.298402 + 0.954440I
b = 0.0798253
0.823819 4.83529
u = 0.932269 0.084679I
a = 0.371139 + 0.650974I
b = 0.233581 0.361656I
1.64111 0.20863I 8.20722 0.26692I
u = 0.932269 + 0.084679I
a = 0.371139 0.650974I
b = 0.233581 + 0.361656I
1.64111 + 0.20863I 8.20722 + 0.26692I
u = 1.020774 0.110450I
a = 0.936806 0.678425I
b = 1.89916 + 1.02700I
0.49208 2.14474I 4.47534 + 2.22851I
u = 1.020774 + 0.110450I
a = 0.936806 + 0.678425I
b = 1.89916 1.02700I
0.49208 + 2.14474I 4.47534 2.22851I
u = 1.031199 0.589049I
a = 0.700224 0.507095I
b = 1.89916 1.02700I
0.49208 + 2.14474I 4.47534 2.22851I
u = 1.031199 + 0.589049I
a = 0.700224 + 0.507095I
b = 1.89916 + 1.02700I
0.49208 2.14474I 4.47534 + 2.22851I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.078727 0.747741I
a = 0.081328 + 0.871646I
b = 0.046159 0.748421I
7.06234 + 11.08516I 1.13522 6.17412I
u = 1.078727 + 0.747741I
a = 0.081328 0.871646I
b = 0.046159 + 0.748421I
7.06234 11.08516I 1.13522 + 6.17412I
u = 1.082702 0.517404I
a = 0.788423 + 0.382439I
b = 2.23979 0.33085I
3.86295 + 4.69165I 11.49179 4.07331I
u = 1.082702 + 0.517404I
a = 0.788423 0.382439I
b = 2.23979 + 0.33085I
3.86295 4.69165I 11.49179 + 4.07331I
u = 1.23501 0.82230I
a = 0.796083 + 0.023705I
b = 2.71233 + 0.14330I
3.65105 + 8.06945I 2.24961 10.45643I
u = 1.23501 + 0.82230I
a = 0.796083 0.023705I
b = 2.71233 0.14330I
3.65105 8.06945I 2.24961 + 10.45643I
u = 1.393094 0.136006I
a = 0.751927 0.371505I
b = 2.43029 + 0.30695I
0.84333 + 8.53070I 5.83691 8.88541I
u = 1.393094 + 0.136006I
a = 0.751927 + 0.371505I
b = 2.43029 0.30695I
0.84333 8.53070I 5.83691 + 8.88541I
11
III. I
u
3
=
hu
8
2u
6
+3u
4
+u
3
2u
2
u+1, a+1, 2u
7
u
6
+3u
5
+2u
4
4u
3
5u
2
+b+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
7
=
u
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
10
=
1
2u
7
+ u
6
3u
5
2u
4
+ 4u
3
+ 5u
2
1
a
5
=
u
u
7
u
6
+ 2u
5
+ 2u
4
3u
3
4u
2
+ 2
a
4
=
u
2
+ u + 1
u
7
u
6
+ 2u
5
+ 2u
4
3u
3
3u
2
+ 1
a
9
=
u
2
1
u
7
+ u
6
u
5
2u
4
+ u
3
+ 3u
2
+ u
a
11
=
u
4
+ u
2
1
u
7
+ u
6
u
5
u
4
+ 2u
3
+ 2u
2
a
8
=
u
7
2u
5
+ 2u
3
+ 2u
2
u 2
u
6
+ u
5
2u
4
u
3
+ 2u
2
+ 2u
a
8
=
u
7
2u
5
+ 2u
3
+ 2u
2
u 2
u
6
+ u
5
2u
4
u
3
+ 2u
2
+ 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
12
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.055796 0.329293I
a = 1.00000
b = 1.59228 0.31305I
2.20407 5.83988I 6.87391 + 7.08087I
u = 1.055796 + 0.329293I
a = 1.00000
b = 1.59228 + 0.31305I
2.20407 + 5.83988I 6.87391 7.08087I
u = 0.683279 0.753423I
a = 1.00000
b = 0.576687 + 0.161454I
5.20723 3.67399I 1.42456 + 6.52580I
u = 0.683279 + 0.753423I
a = 1.00000
b = 0.576687 0.161454I
5.20723 + 3.67399I 1.42456 6.52580I
u = 0.675066 0.209810I
a = 1.00000
b = 1.60016 1.80453I
0.794315 0.862931I 6.95751 + 0.59355I
u = 0.675066 + 0.209810I
a = 1.00000
b = 1.60016 + 1.80453I
0.794315 + 0.862931I 6.95751 0.59355I
u = 1.064009 0.670303I
a = 1.00000
b = 2.73088 0.07561I
2.78226 + 7.31144I 4.74402 5.01155I
u = 1.064009 + 0.670303I
a = 1.00000
b = 2.73088 + 0.07561I
2.78226 7.31144I 4.74402 + 5.01155I
13
IV. I
u
4
= hu
19
4u
17
+ · · · u 1, a + 1, 36u
18
13u
17
+ · · · + 29b 6i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
7
=
u
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
10
=
1
1.24138u
18
+ 0.448276u
17
+ ··· + 1.17241u + 0.206897
a
5
=
u
0.448276u
18
+ 0.689655u
17
+ ··· + 2.03448u + 1.24138
a
4
=
0.137931u
18
0.172414u
17
+ ··· + 1.24138u + 0.689655
0.310345u
18
+ 0.862069u
17
+ ··· + 1.79310u + 0.551724
a
9
=
u
2
1
0.551724u
18
+ 0.310345u
17
+ ··· + 1.96552u 0.241379
a
11
=
u
4
+ u
2
1
0.379310u
18
+ 0.275862u
17
+ ··· + 1.41379u 0.103448
a
8
=
1.13793u
18
0.172414u
17
+ ··· 1.75862u 0.310345
0.241379u
18
+ 0.551724u
17
+ ··· + 2.82759u 0.206897
a
8
=
1.13793u
18
0.172414u
17
+ ··· 1.75862u 0.310345
0.241379u
18
+ 0.551724u
17
+ ··· + 2.82759u 0.206897
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
14
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.134642 0.741228I
a = 1.00000
b = 2.85973 + 0.02786I
5.2789 17.4106I 3.33834 + 9.88959I
u = 1.134642 + 0.741228I
a = 1.00000
b = 2.85973 0.02786I
5.2789 + 17.4106I 3.33834 9.88959I
u = 1.081474 0.236993I
a = 1.00000
b = 2.69425 + 0.08404I
5.58807 2.35049I 13.53566 + 3.60952I
u = 1.081474 + 0.236993I
a = 1.00000
b = 2.69425 0.08404I
5.58807 + 2.35049I 13.53566 3.60952I
u = 0.760847 0.732308I
a = 1.00000
b = 0.433531 0.406113I
6.12689 2.86646I 4.56371 + 2.58319I
u = 0.760847 + 0.732308I
a = 1.00000
b = 0.433531 + 0.406113I
6.12689 + 2.86646I 4.56371 2.58319I
u = 0.748605 0.616047I
a = 1.00000
b = 1.61197 1.28179I
2.13851 + 0.27818I 1.57258 + 0.84514I
u = 0.748605 + 0.616047I
a = 1.00000
b = 1.61197 + 1.28179I
2.13851 0.27818I 1.57258 0.84514I
u = 0.284118 0.394323I
a = 1.00000
b = 0.558556 0.663861I
1.76273 + 1.04354I 2.78842 1.15879I
u = 0.284118 + 0.394323I
a = 1.00000
b = 0.558556 + 0.663861I
1.76273 1.04354I 2.78842 + 1.15879I
15
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.563485
a = 1.00000
b = 0.386289
0.903842 11.0548
u = 0.635682 0.938951I
a = 1.00000
b = 0.853225 0.163346I
8.44383 4.90113I 0.70738 + 1.64116I
u = 0.635682 + 0.938951I
a = 1.00000
b = 0.853225 + 0.163346I
8.44383 + 4.90113I 0.70738 1.64116I
u = 0.978761 0.636195I
a = 1.00000
b = 3.27169 + 0.10559I
4.69963 + 7.70569I 1.03497 7.90507I
u = 0.978761 + 0.636195I
a = 1.00000
b = 3.27169 0.10559I
4.69963 7.70569I 1.03497 + 7.90507I
u = 1.014159 0.676349I
a = 1.00000
b = 2.40095 + 0.84612I
0.40114 + 10.64021I 4.95980 10.11213I
u = 1.014159 + 0.676349I
a = 1.00000
b = 2.40095 0.84612I
0.40114 10.64021I 4.95980 + 10.11213I
u = 1.099341 0.119273I
a = 1.00000
b = 2.24008 + 0.90234I
3.89495 2.33301I 11.16071 + 2.50399I
u = 1.099341 + 0.119273I
a = 1.00000
b = 2.24008 0.90234I
3.89495 + 2.33301I 11.16071 2.50399I
16
V. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
5
(u
8
2u
6
+ ··· u + 1)(u
8
2u
6
+ ··· 2u
2
+ 1)
(u
19
4u
17
+ ··· u 1)(u
68
+ u
67
+ ··· + 12u + 1)
c
2
(u
8
+ 4u
7
+ 10u
6
+ 16u
5
+ 19u
4
+ 17u
3
+ 12u
2
+ 5u + 1)
(u
8
+ 4u
7
+ 10u
6
+ 17u
5
+ 21u
4
+ 17u
3
+ 10u
2
+ 4u + 1)
(u
19
+ 8u
18
+ ··· + 5u + 1)(u
68
+ 25u
67
+ ··· + 60u + 1)
c
3
(u
8
u
6
u
5
+ 2u
4
u + 1)(u
8
u
6
+ 2u
5
u
4
u
3
+ 3u
2
3u + 1)
(u
19
3u
17
+ ··· + 5u + 1)(u
68
+ 7u
67
+ ··· + 375u + 257)
c
4
(u
4
+ 2u
2
+ u + 1)
2
(u
8
u
7
+ 4u
6
4u
5
+ 6u
4
5u
3
+ 5u
2
2u + 1)
(u
19
+ 12u
18
+ ··· 224u 32)
(5 34u + 55u
2
84u
3
+ 131u
4
249u
5
+ 657u
6
1321u
7
+ 2323u
8
3286u
9
+ 3981u
10
4225u
11
+ 4407u
12
4911u
13
+ 7195u
14
1.07 × 10
4
u
15
+ 1.67 × 10
4
u
16
2.27 × 10
4
u
17
+ 2.88 × 10
4
u
18
3.23 × 10
4
u
19
+ 3.33 × 10
4
u
20
3.11 × 10
4
u
21
+ 2.66 × 10
4
u
22
2.09 × 10
4
u
23
+ 1.50 × 10
4
u
24
9906u
25
+ 5972u
26
3245u
27
+ 1621u
28
700u
29
+ 281u
30
89u
31
+ 27u
32
5u
33
+ u
34
)
2
c
6
(u
8
2u
6
+ ··· + u + 1)(u
8
2u
6
+ ··· 2u
2
+ 1)
(u
19
4u
17
+ ··· u 1)(u
68
+ u
67
+ ··· + 12u + 1)
c
7
(u
4
+ 2u
2
u + 1)
2
(u
8
+ u
7
+ 4u
6
+ 4u
5
+ 6u
4
+ 5u
3
+ 5u
2
+ 2u + 1)
(u
19
+ 12u
18
+ ··· 224u 32)
(5 34u + 55u
2
84u
3
+ 131u
4
249u
5
+ 657u
6
1321u
7
+ 2323u
8
3286u
9
+ 3981u
10
4225u
11
+ 4407u
12
4911u
13
+ 7195u
14
1.07 × 10
4
u
15
+ 1.67 × 10
4
u
16
2.27 × 10
4
u
17
+ 2.88 × 10
4
u
18
3.23 × 10
4
u
19
+ 3.33 × 10
4
u
20
3.11 × 10
4
u
21
+ 2.66 × 10
4
u
22
2.09 × 10
4
u
23
+ 1.50 × 10
4
u
24
9906u
25
+ 5972u
26
3245u
27
+ 1621u
28
700u
29
+ 281u
30
89u
31
+ 27u
32
5u
33
+ u
34
)
2
c
8
(u
4
u
3
+ 1)
2
(u
8
+ 3u
7
+ 3u
6
+ u
5
u
4
u
3
+ 1)
(u
19
+ 18u
18
+ ··· 1184u 192)
(1 4u 3u
2
+ 39u
3
47u
4
117u
5
+ 370u
6
154u
7
897u
8
+ 1823u
9
809u
10
2157u
11
+ 3923u
12
1650u
13
2563u
14
+ 3752u
15
1216u
16
683u
17
171u
18
+ 752u
19
+ 1040u
20
2798u
21
+ 2185u
22
492u
23
220u
24
+ 57u
25
18u
26
+ 196u
27
201u
28
+ 29u
29
+ 88u
30
83u
31
+ 37u
32
9u
33
+ u
34
)
2
c
9
(u
8
2u
6
+ ··· + u + 1)(u
8
2u
6
+ ··· 2u
2
+ 1)
(u
19
4u
17
+ ··· u 1)(u
68
+ u
67
+ ··· + 12u + 1)
c
10
(u
8
+ 4u
7
+ 10u
6
+ 16u
5
+ 19u
4
+ 17u
3
+ 12u
2
+ 5u + 1)
(u
8
+ 4u
7
+ 10u
6
+ 17u
5
+ 21u
4
+ 17u
3
+ 10u
2
+ 4u + 1)
(u
19
+ 8u
18
+ ··· + 5u + 1)(u
68
+ 25u
67
+ ··· + 60u + 1)
c
11
(u
8
u
6
u
5
+ 2u
4
u + 1)(u
8
u
6
+ 2u
5
u
4
u
3
+ 3u
2
3u + 1)
(u
19
3u
17
+ ··· + 5u + 1)(u
68
+ 7u
67
+ ··· + 375u + 257)
17
VI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
8
4y
7
+ 10y
6
17y
5
+ 21y
4
17y
3
+ 10y
2
4y + 1)
(y
8
4y
7
+ 10y
6
16y
5
+ 19y
4
17y
3
+ 12y
2
5y + 1)
(y
19
8y
18
+ ··· + 5y 1)(y
68
25y
67
+ ··· 60y + 1)
c
2
(y
8
+ 4y
7
+ 6y
6
+ 15y
5
+ 33y
4
+ 15y
3
+ 6y
2
+ 4y + 1)
(y
8
+ 4y
7
+ 10y
6
+ 12y
5
+ 19y
4
+ 27y
3
+ 12y
2
y + 1)
(y
19
+ 12y
18
+ ··· 23y 1)(y
68
+ 39y
67
+ ··· 600y + 1)
c
3
(y
8
2y
7
y
6
+ 4y
5
+ y
4
+ 3y
3
+ y
2
3y + 1)
(y
8
2y
7
+ 5y
6
5y
5
+ 6y
4
4y
3
+ 4y
2
y + 1)
(y
19
6y
18
+ ··· + 29y 1)(y
68
15y
67
+ ··· 2055275y + 66049)
c
4
, c
7
(y
4
+ 4y
3
+ 6y
2
+ 3y + 1)
2
(y
8
+ 7y
7
+ 20y
6
+ 32y
5
+ 34y
4
+ 27y
3
+ 17y
2
+ 6y + 1)
(y
19
+ 12y
18
+ ··· + 1536y 1024)
(25 606y 1377y
2
3008y
3
1.90 × 10
4
y
4
3.99 × 10
4
y
5
+ 2.50 × 10
4
y
6
+ 2.27 × 10
5
y
7
+ 4.02 × 10
5
y
8
+ 5.55 × 10
5
y
9
+ 1.59 × 10
6
y
10
+ 4.75 × 10
6
y
11
+ 9.63 × 10
6
y
12
+ 1.43 × 10
7
y
13
+ 1.91 × 10
7
y
14
+ 2.90 × 10
7
y
15
+ 4.66 × 10
7
y
16
+ 6.46 × 10
7
y
17
+ 6.98 × 10
7
y
18
+ 5.68 × 10
7
y
19
+ 3.38 × 10
7
y
20
+ 1.40 × 10
7
y
21
+ 4.19 × 10
6
y
22
+ 2.10 × 10
6
y
23
+ 2.56 × 10
6
y
24
+ 2.53 × 10
6
y
25
+ 1.74 × 10
6
y
26
+ 8.76 × 10
5
y
27
+ 3.33 × 10
5
y
28
+ 9.69 × 10
4
y
29
+ 2.14 × 10
4
y
30
+ 3495y
31
+ 401y
32
+ 29y
33
+ y
34
)
2
c
5
(y
8
4y
7
+ 10y
6
17y
5
+ 21y
4
17y
3
+ 10y
2
4y + 1)
(y
8
4y
7
+ 10y
6
16y
5
+ 19y
4
17y
3
+ 12y
2
5y + 1)
(y
19
8y
18
+ ··· + 5y 1)(y
68
25y
67
+ ··· 60y + 1)
c
8
(y
4
y
3
+ 2y
2
+ 1)
2
(y
8
3y
7
+ y
6
y
5
+ 5y
4
+ 5y
3
2y
2
+ 1)
(y
19
4y
18
+ ··· + 50176y 36864)
(1 22y + 227y
2
1435y
3
+ 6089y
4
1.81 × 10
4
y
5
+ 3.84 × 10
4
y
6
5.85 × 10
4
y
7
+ 6.56 × 10
4
y
8
6.97 × 10
4
y
9
+ 1.31 × 10
5
y
10
3.57 × 10
5
y
11
+ 8.63 × 10
5
y
12
1.70 × 10
6
y
13
+ 2.79 × 10
6
y
14
3.91 × 10
6
y
15
+ 4.77 × 10
6
y
16
5.14 × 10
6
y
17
+ 4.95 × 10
6
y
18
4.28 × 10
6
y
19
+ 3.36 × 10
6
y
20
2.39 × 10
6
y
21
+ 1.55 × 10
6
y
22
9.11 × 10
5
y
23
+ 4.90 × 10
5
y
24
2.38 × 10
5
y
25
+ 1.05 × 10
5
y
26
4.15 × 10
4
y
27
+ 1.46 × 10
4
y
28
4427y
29
+ 1176y
30
257y
31
+ 51y
32
7y
33
+ y
34
)
2
c
9
(y
8
4y
7
+ 10y
6
17y
5
+ 21y
4
17y
3
+ 10y
2
4y + 1)
(y
8
4y
7
+ 10y
6
16y
5
+ 19y
4
17y
3
+ 12y
2
5y + 1)
(y
19
8y
18
+ ··· + 5y 1)(y
68
25y
67
+ ··· 60y + 1)
c
10
(y
8
+ 4y
7
+ 6y
6
+ 15y
5
+ 33y
4
+ 15y
3
+ 6y
2
+ 4y + 1)
(y
8
+ 4y
7
+ 10y
6
+ 12y
5
+ 19y
4
+ 27y
3
+ 12y
2
y + 1)
(y
19
+ 12y
18
+ ··· 23y 1)(y
68
+ 39y
67
+ ··· 600y + 1)
c
11
(y
8
2y
7
y
6
+ 4y
5
+ y
4
+ 3y
3
+ y
2
3y + 1)
(y
8
2y
7
+ 5y
6
5y
5
+ 6y
4
4y
3
+ 4y
2
y + 1)
(y
19
6y
18
+ ··· + 29y 1)(y
68
15y
67
+ ··· 2055275y + 66049)
18