11a
256
(K11a
256
)
A knot diagram
1
Linearized knot diagam
10 8 1 2 9 3 11 6 5 4 7
Solving Sequence
5,9
6
2,10
1 4 11 8 3 7
c
5
c
9
c
1
c
4
c
10
c
8
c
2
c
7
c
3
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.45189 × 10
122
u
81
+ 2.24341 × 10
123
u
80
+ ··· + 2.70538 × 10
122
b + 1.42226 × 10
122
,
8.78383 × 10
122
u
81
− 2.33856 × 10
123
u
80
+ ··· + 2.70538 × 10
122
a + 1.70512 × 10
123
, u
82
− 3u
81
+ ··· − 15u + 1i
I
u
2
= h−u
14
− 2u
13
− 10u
12
− 17u
11
− 40u
10
− 55u
9
− 79u
8
− 82u
7
− 76u
6
− 51u
5
− 27u
4
− 4u
3
+ 2u
2
+ b + 4u,
u
15
+ u
14
+ 8u
13
+ 8u
12
+ 24u
11
+ 22u
10
+ 31u
9
+ 21u
8
+ 11u
7
− 4u
6
− 7u
5
− 11u
4
+ 2u
2
+ a + 3u + 1,
u
16
+ 2u
15
+ ··· − 4u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 98 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
= h−8.45 × 10
122
u
81
+ 2.24 × 10
123
u
80
+ · · · + 2.71 × 10
122
b + 1.42 ×
10
122
, 8.78 × 10
122
u
81
− 2.34 × 10
123
u
80
+ · · · + 2.71 × 10
122
a + 1.71 ×
10
123
, u
82
− 3u
81
+ · · · − 15u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
−u
2
a
2
=
−3.24680u
81
+ 8.64413u
80
+ ··· + 21.7051u − 6.30272
3.12411u
81
− 8.29242u
80
+ ··· + 33.1864u − 0.525715
a
10
=
u
u
a
1
=
−3.22493u
81
+ 8.55324u
80
+ ··· − 4.56661u − 4.12654
3.14598u
81
− 8.38332u
80
+ ··· + 6.91462u + 1.65046
a
4
=
1.33864u
81
− 5.77320u
80
+ ··· + 70.5182u − 3.70405
2.19651u
81
− 7.34656u
80
+ ··· + 138.368u − 9.13067
a
11
=
2.25185u
81
− 4.76796u
80
+ ··· − 96.2134u + 13.7071
0.445401u
81
− 1.81537u
80
+ ··· + 70.4997u − 5.88345
a
8
=
−u
u
3
+ u
a
3
=
−3.17256u
81
+ 8.52796u
80
+ ··· + 25.0463u − 6.52919
2.66750u
81
− 7.37850u
80
+ ··· + 28.3211u − 0.192700
a
7
=
0.358941u
81
− 1.54211u
80
+ ··· + 57.8850u − 6.06076
−0.465964u
81
+ 0.770839u
80
+ ··· + 50.0079u − 3.41294
a
7
=
0.358941u
81
− 1.54211u
80
+ ··· + 57.8850u − 6.06076
−0.465964u
81
+ 0.770839u
80
+ ··· + 50.0079u − 3.41294
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.26125u
81
− 15.9680u
80
+ ··· + 511.715u − 28.2831
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
82
+ 8u
81
+ ··· + 3960u + 472
c
2
u
82
− u
81
+ ··· − 4352u + 512
c
3
u
82
+ 6u
81
+ ··· + 1547u + 543
c
4
u
82
+ 9u
80
+ ··· + 1938u + 279
c
5
, c
8
, c
9
u
82
+ 3u
81
+ ··· + 15u + 1
c
6
u
82
+ u
81
+ ··· − 14536u + 9797
c
7
, c
11
u
82
+ 24u
80
+ ··· − 37u + 43
c
10
u
82
+ 4u
80
+ ··· − 30u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
82
+ 26y
81
+ ··· + 4280224y + 222784
c
2
y
82
− 25y
81
+ ··· − 18808832y + 262144
c
3
y
82
− 24y
81
+ ··· − 2823265y + 294849
c
4
y
82
+ 18y
81
+ ··· + 1070856y + 77841
c
5
, c
8
, c
9
y
82
+ 87y
81
+ ··· + 17y + 1
c
6
y
82
− 35y
81
+ ··· − 3758984936y + 95981209
c
7
, c
11
y
82
+ 48y
81
+ ··· + 40857y + 1849
c
10
y
82
+ 8y
81
+ ··· − 26y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.848421 + 0.520032I
a = −0.279218 + 0.153559I
b = 0.021124 + 0.940599I
−5.23833 + 3.58110I 0
u = 0.848421 − 0.520032I
a = −0.279218 − 0.153559I
b = 0.021124 − 0.940599I
−5.23833 − 3.58110I 0
u = 0.230054 + 0.982996I
a = 1.35831 + 0.40646I
b = 0.713068 − 0.162440I
−1.89873 + 0.22579I 0
u = 0.230054 − 0.982996I
a = 1.35831 − 0.40646I
b = 0.713068 + 0.162440I
−1.89873 − 0.22579I 0
u = 0.795746 + 0.648558I
a = 0.378936 − 0.665797I
b = −0.952509 − 0.992848I
−3.52948 + 12.80360I 0
u = 0.795746 − 0.648558I
a = 0.378936 + 0.665797I
b = −0.952509 + 0.992848I
−3.52948 − 12.80360I 0
u = 0.754635 + 0.607172I
a = 0.713871 − 0.481869I
b = −0.481239 − 0.864034I
−5.61608 + 1.76260I 0
u = 0.754635 − 0.607172I
a = 0.713871 + 0.481869I
b = −0.481239 + 0.864034I
−5.61608 − 1.76260I 0
u = −0.807999 + 0.646747I
a = 0.421301 + 0.522180I
b = −0.853184 + 0.818654I
0.03640 − 6.74939I 0
u = −0.807999 − 0.646747I
a = 0.421301 − 0.522180I
b = −0.853184 − 0.818654I
0.03640 + 6.74939I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.946706 + 0.464469I
a = −0.359761 − 0.292329I
b = −0.551014 + 0.678230I
−2.89935 − 7.15022I 0
u = 0.946706 − 0.464469I
a = −0.359761 + 0.292329I
b = −0.551014 − 0.678230I
−2.89935 + 7.15022I 0
u = −0.397863 + 0.833537I
a = 1.41819 + 0.02085I
b = 0.558559 + 0.571616I
−2.38163 + 0.76876I 0
u = −0.397863 − 0.833537I
a = 1.41819 − 0.02085I
b = 0.558559 − 0.571616I
−2.38163 − 0.76876I 0
u = −1.057730 + 0.537571I
a = −0.133063 + 0.144826I
b = −0.298352 − 0.505129I
0.627372 + 0.834212I 0
u = −1.057730 − 0.537571I
a = −0.133063 − 0.144826I
b = −0.298352 + 0.505129I
0.627372 − 0.834212I 0
u = −0.258041 + 1.236650I
a = 0.647994 + 0.587108I
b = −0.727125 + 0.295134I
−2.10746 − 3.48943I 0
u = −0.258041 − 1.236650I
a = 0.647994 − 0.587108I
b = −0.727125 − 0.295134I
−2.10746 + 3.48943I 0
u = −0.520829 + 0.502496I
a = 0.008481 − 0.838189I
b = 0.897801 − 0.647875I
0.82893 − 1.90450I 4.86742 + 1.67415I
u = −0.520829 − 0.502496I
a = 0.008481 + 0.838189I
b = 0.897801 + 0.647875I
0.82893 + 1.90450I 4.86742 − 1.67415I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.304388 + 0.650719I
a = 0.344531 + 0.177159I
b = −1.102020 + 0.249997I
−3.24142 − 2.49646I −3.48952 + 0.93958I
u = 0.304388 − 0.650719I
a = 0.344531 − 0.177159I
b = −1.102020 − 0.249997I
−3.24142 + 2.49646I −3.48952 − 0.93958I
u = −0.653697 + 0.269632I
a = −0.292759 − 0.182981I
b = 0.844074 − 1.113800I
−0.62966 − 4.63978I 1.72550 + 8.55711I
u = −0.653697 − 0.269632I
a = −0.292759 + 0.182981I
b = 0.844074 + 1.113800I
−0.62966 + 4.63978I 1.72550 − 8.55711I
u = 0.435259 + 0.520271I
a = −0.51925 + 1.44214I
b = 0.964368 + 1.021760I
0.01973 + 4.53345I 1.62927 − 10.52525I
u = 0.435259 − 0.520271I
a = −0.51925 − 1.44214I
b = 0.964368 − 1.021760I
0.01973 − 4.53345I 1.62927 + 10.52525I
u = −0.416371 + 0.520352I
a = 0.571637 − 0.611403I
b = 0.797691 − 0.137985I
0.79688 − 1.51228I 5.59497 + 5.28418I
u = −0.416371 − 0.520352I
a = 0.571637 + 0.611403I
b = 0.797691 + 0.137985I
0.79688 + 1.51228I 5.59497 − 5.28418I
u = −0.650179 + 0.021954I
a = 1.044090 + 0.474203I
b = −0.457863 − 0.103655I
1.67625 + 0.10307I 10.54193 + 3.13566I
u = −0.650179 − 0.021954I
a = 1.044090 − 0.474203I
b = −0.457863 + 0.103655I
1.67625 − 0.10307I 10.54193 − 3.13566I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.128547 + 1.365150I
a = 0.289436 + 1.362680I
b = −0.094192 + 0.392027I
−2.64053 − 2.49367I 0
u = −0.128547 − 1.365150I
a = 0.289436 − 1.362680I
b = −0.094192 − 0.392027I
−2.64053 + 2.49367I 0
u = 0.001717 + 1.377580I
a = 0.60777 − 1.42357I
b = 0.136132 − 0.849643I
−4.87547 − 2.11824I 0
u = 0.001717 − 1.377580I
a = 0.60777 + 1.42357I
b = 0.136132 + 0.849643I
−4.87547 + 2.11824I 0
u = 0.507423 + 0.282090I
a = 0.85273 − 2.27652I
b = −0.631159 − 0.157718I
−1.99505 + 5.47458I 4.98884 − 10.22721I
u = 0.507423 − 0.282090I
a = 0.85273 + 2.27652I
b = −0.631159 + 0.157718I
−1.99505 − 5.47458I 4.98884 + 10.22721I
u = −0.18012 + 1.42912I
a = 0.24496 − 2.12810I
b = 1.00818 − 1.76354I
−6.08165 − 7.53590I 0
u = −0.18012 − 1.42912I
a = 0.24496 + 2.12810I
b = 1.00818 + 1.76354I
−6.08165 + 7.53590I 0
u = 0.02220 + 1.44292I
a = 0.196096 + 0.753555I
b = 1.37471 + 0.48801I
−4.92663 + 2.65020I 0
u = 0.02220 − 1.44292I
a = 0.196096 − 0.753555I
b = 1.37471 − 0.48801I
−4.92663 − 2.65020I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.10846 + 1.44200I
a = 0.43873 + 1.89782I
b = 1.25310 + 1.46090I
−4.82607 + 4.19978I 0
u = 0.10846 − 1.44200I
a = 0.43873 − 1.89782I
b = 1.25310 − 1.46090I
−4.82607 − 4.19978I 0
u = 0.13089 + 1.44676I
a = −0.30134 − 1.87375I
b = −0.195164 − 0.403584I
−7.61606 + 7.63883I 0
u = 0.13089 − 1.44676I
a = −0.30134 + 1.87375I
b = −0.195164 + 0.403584I
−7.61606 − 7.63883I 0
u = 0.05018 + 1.50060I
a = −1.04358 + 2.00260I
b = −1.47718 + 1.91057I
−10.50140 + 6.17930I 0
u = 0.05018 − 1.50060I
a = −1.04358 − 2.00260I
b = −1.47718 − 1.91057I
−10.50140 − 6.17930I 0
u = −0.02775 + 1.50247I
a = −0.48028 − 1.52733I
b = −0.99957 − 1.36175I
−7.57075 − 1.91522I 0
u = −0.02775 − 1.50247I
a = −0.48028 + 1.52733I
b = −0.99957 + 1.36175I
−7.57075 + 1.91522I 0
u = −0.059419 + 0.483891I
a = 1.085630 − 0.472882I
b = −0.266045 − 0.814352I
−0.99676 − 1.52566I −2.22095 + 4.83726I
u = −0.059419 − 0.483891I
a = 1.085630 + 0.472882I
b = −0.266045 + 0.814352I
−0.99676 + 1.52566I −2.22095 − 4.83726I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.02962 + 1.51246I
a = −0.39952 − 1.90255I
b = 0.629294 − 1.019480I
−10.94790 − 5.28525I 0
u = −0.02962 − 1.51246I
a = −0.39952 + 1.90255I
b = 0.629294 + 1.019480I
−10.94790 + 5.28525I 0
u = 0.430412 + 0.182241I
a = −1.009350 − 0.375067I
b = 0.925819 + 0.818610I
0.58505 + 2.42533I 4.66741 + 0.55099I
u = 0.430412 − 0.182241I
a = −1.009350 + 0.375067I
b = 0.925819 − 0.818610I
0.58505 − 2.42533I 4.66741 − 0.55099I
u = −0.15326 + 1.53297I
a = 0.57245 − 1.84376I
b = 1.00812 − 1.41371I
−5.96597 − 4.32362I 0
u = −0.15326 − 1.53297I
a = 0.57245 + 1.84376I
b = 1.00812 + 1.41371I
−5.96597 + 4.32362I 0
u = 0.12868 + 1.53593I
a = 0.41675 + 2.20491I
b = 0.94615 + 1.52086I
−6.86700 + 6.57360I 0
u = 0.12868 − 1.53593I
a = 0.41675 − 2.20491I
b = 0.94615 − 1.52086I
−6.86700 − 6.57360I 0
u = −0.042565 + 0.452034I
a = −2.24799 − 3.08194I
b = 0.193511 − 0.934402I
−4.32269 − 4.92458I −8.27138 + 6.34141I
u = −0.042565 − 0.452034I
a = −2.24799 + 3.08194I
b = 0.193511 + 0.934402I
−4.32269 + 4.92458I −8.27138 − 6.34141I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.04315 + 1.55403I
a = −1.094390 + 0.581684I
b = −1.70027 + 0.57610I
−10.64210 − 1.47490I 0
u = 0.04315 − 1.55403I
a = −1.094390 − 0.581684I
b = −1.70027 − 0.57610I
−10.64210 + 1.47490I 0
u = 0.159107 + 0.397170I
a = 0.795971 + 1.104450I
b = −0.77358 + 1.39138I
−4.10333 + 5.41336I −8.23702 − 9.54805I
u = 0.159107 − 0.397170I
a = 0.795971 − 1.104450I
b = −0.77358 − 1.39138I
−4.10333 − 5.41336I −8.23702 + 9.54805I
u = −0.03478 + 1.57499I
a = 0.556673 + 0.515788I
b = −0.333490 + 0.387147I
−10.49290 − 0.25231I 0
u = −0.03478 − 1.57499I
a = 0.556673 − 0.515788I
b = −0.333490 − 0.387147I
−10.49290 + 0.25231I 0
u = 0.25279 + 1.55852I
a = 0.16688 − 1.45380I
b = −0.838801 − 1.072450I
−12.71050 + 5.46717I 0
u = 0.25279 − 1.55852I
a = 0.16688 + 1.45380I
b = −0.838801 + 1.072450I
−12.71050 − 5.46717I 0
u = 0.29458 + 1.55732I
a = −0.341317 + 1.352360I
b = 0.309405 + 1.319020I
−12.0528 + 7.7881I 0
u = 0.29458 − 1.55732I
a = −0.341317 − 1.352360I
b = 0.309405 − 1.319020I
−12.0528 − 7.7881I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.26917 + 1.57829I
a = −0.16937 + 1.54689I
b = −1.12498 + 1.16651I
−7.24965 − 10.72690I 0
u = −0.26917 − 1.57829I
a = −0.16937 − 1.54689I
b = −1.12498 − 1.16651I
−7.24965 + 10.72690I 0
u = 0.26626 + 1.58328I
a = −0.21215 − 1.75650I
b = −1.15684 − 1.34314I
−10.8601 + 16.7429I 0
u = 0.26626 − 1.58328I
a = −0.21215 + 1.75650I
b = −1.15684 + 1.34314I
−10.8601 − 16.7429I 0
u = 0.183942 + 0.338117I
a = 1.65770 + 0.71465I
b = 0.829211 − 0.571125I
0.45443 − 1.92720I 4.74257 + 2.64364I
u = 0.183942 − 0.338117I
a = 1.65770 − 0.71465I
b = 0.829211 + 0.571125I
0.45443 + 1.92720I 4.74257 − 2.64364I
u = −0.23386 + 1.62107I
a = 0.137921 − 1.034210I
b = 0.599466 − 0.974710I
−7.32228 − 3.91026I 0
u = −0.23386 − 1.62107I
a = 0.137921 + 1.034210I
b = 0.599466 + 0.974710I
−7.32228 + 3.91026I 0
u = 0.35096 + 1.68569I
a = −0.212323 + 0.518642I
b = 0.204650 + 0.653748I
−9.84458 − 1.89156I 0
u = 0.35096 − 1.68569I
a = −0.212323 − 0.518642I
b = 0.204650 − 0.653748I
−9.84458 + 1.89156I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.175841 + 0.112202I
a = −3.83138 − 2.52525I
b = 0.800141 + 0.471355I
0.40683 + 2.17965I 5.55317 − 5.50998I
u = 0.175841 − 0.112202I
a = −3.83138 + 2.52525I
b = 0.800141 − 0.471355I
0.40683 − 2.17965I 5.55317 + 5.50998I
13
II.
I
u
2
= h−u
14
−2u
13
+· · ·+b+4u, u
15
+u
14
+· · ·+a+1, u
16
+2u
15
+· · ·−4u
2
+1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
−u
2
a
2
=
−u
15
− u
14
+ ··· − 3u − 1
u
14
+ 2u
13
+ ··· − 2u
2
− 4u
a
10
=
u
u
a
1
=
−u
5
− u
4
− 3u
3
− 3u
2
− 2u − 1
u
15
+ 2u
14
+ ··· − 3u
2
− 3u
a
4
=
−2u
15
− 4u
14
+ ··· + 5u + 2
−u
15
− u
14
+ ··· + 3u
2
− 2u
a
11
=
−u
14
− 6u
12
+ ··· − 5u − 4
−u
15
− 2u
14
+ ··· − u + 1
a
8
=
−u
u
3
+ u
a
3
=
−u
15
− 2u
14
+ ··· − 3u − 1
u
12
+ 2u
11
+ ··· − 4u − 1
a
7
=
u
15
+ u
14
+ ··· + 7u + 2
−u
14
− 3u
13
+ ··· + 7u
2
+ 4u
a
7
=
u
15
+ u
14
+ ··· + 7u + 2
−u
14
− 3u
13
+ ··· + 7u
2
+ 4u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
15
−5u
14
+ 15u
13
−56u
12
−48u
11
−251u
10
−328u
9
−544u
8
−
576u
7
− 549u
6
− 338u
5
− 185u
4
+ 6u
3
+ 13u
2
+ 21u + 1
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− u
15
+ ··· − u + 1
c
2
u
16
− 3u
14
+ ··· − 3u + 1
c
3
u
16
+ 9u
15
+ ··· + 8u + 1
c
4
u
16
− 7u
15
+ ··· − 5u + 1
c
5
u
16
+ 2u
15
+ ··· − 4u
2
+ 1
c
6
u
16
− 2u
14
+ ··· − u + 1
c
7
u
16
− u
15
+ ··· + 6u
2
+ 1
c
8
, c
9
u
16
− 2u
15
+ ··· − 4u
2
+ 1
c
10
u
16
− u
15
+ ··· − u + 1
c
11
u
16
+ u
15
+ ··· + 6u
2
+ 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ 5y
15
+ ··· + 7y + 1
c
2
y
16
− 6y
15
+ ··· + y + 1
c
3
y
16
+ 3y
15
+ ··· + 14y + 1
c
4
y
16
+ 5y
15
+ ··· − y + 1
c
5
, c
8
, c
9
y
16
+ 18y
15
+ ··· − 8y + 1
c
6
y
16
− 4y
15
+ ··· − 13y + 1
c
7
, c
11
y
16
+ 7y
15
+ ··· + 12y + 1
c
10
y
16
+ 7y
15
+ ··· + 5y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.125215 + 1.052150I
a = 1.52779 + 0.31343I
b = 0.997454 + 0.473846I
−1.44116 + 1.20136I 3.05969 − 5.58313I
u = −0.125215 − 1.052150I
a = 1.52779 − 0.31343I
b = 0.997454 − 0.473846I
−1.44116 − 1.20136I 3.05969 + 5.58313I
u = −0.794716 + 0.429068I
a = −0.020840 − 0.565606I
b = 0.269183 + 0.344796I
0.845853 + 0.501839I 4.49186 + 3.61839I
u = −0.794716 − 0.429068I
a = −0.020840 + 0.565606I
b = 0.269183 − 0.344796I
0.845853 − 0.501839I 4.49186 − 3.61839I
u = −0.192301 + 1.231470I
a = −0.777776 − 0.687447I
b = 0.784660 − 0.317944I
−1.88854 − 3.66694I 12.3158 + 12.6160I
u = −0.192301 − 1.231470I
a = −0.777776 + 0.687447I
b = 0.784660 + 0.317944I
−1.88854 + 3.66694I 12.3158 − 12.6160I
u = −0.409152 + 0.389086I
a = −0.598837 − 0.699315I
b = 0.99426 − 1.00837I
0.28915 − 3.18191I 1.33628 + 8.27653I
u = −0.409152 − 0.389086I
a = −0.598837 + 0.699315I
b = 0.99426 + 1.00837I
0.28915 + 3.18191I 1.33628 − 8.27653I
u = 0.11544 + 1.46961I
a = −0.29937 + 2.22090I
b = 0.10144 + 1.44141I
−8.75819 + 6.76339I −4.52294 − 6.18611I
u = 0.11544 − 1.46961I
a = −0.29937 − 2.22090I
b = 0.10144 − 1.44141I
−8.75819 − 6.76339I −4.52294 + 6.18611I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.12811 + 1.51638I
a = 0.58938 − 2.08769I
b = 1.16770 − 1.64492I
−6.15992 − 5.12499I −2.54608 + 6.52368I
u = −0.12811 − 1.51638I
a = 0.58938 + 2.08769I
b = 1.16770 + 1.64492I
−6.15992 + 5.12499I −2.54608 − 6.52368I
u = 0.403245 + 0.047429I
a = −2.21447 − 0.06862I
b = −0.151854 + 0.863960I
−3.33071 + 5.01746I 1.44271 − 5.49455I
u = 0.403245 − 0.047429I
a = −2.21447 + 0.06862I
b = −0.151854 − 0.863960I
−3.33071 − 5.01746I 1.44271 + 5.49455I
u = 0.13081 + 1.62501I
a = −0.205878 + 0.077876I
b = −0.662841 − 0.129176I
−9.16530 − 2.37958I −1.57735 + 5.43766I
u = 0.13081 − 1.62501I
a = −0.205878 − 0.077876I
b = −0.662841 + 0.129176I
−9.16530 + 2.37958I −1.57735 − 5.43766I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
16
− u
15
+ ··· − u + 1)(u
82
+ 8u
81
+ ··· + 3960u + 472)
c
2
(u
16
− 3u
14
+ ··· − 3u + 1)(u
82
− u
81
+ ··· − 4352u + 512)
c
3
(u
16
+ 9u
15
+ ··· + 8u + 1)(u
82
+ 6u
81
+ ··· + 1547u + 543)
c
4
(u
16
− 7u
15
+ ··· − 5u + 1)(u
82
+ 9u
80
+ ··· + 1938u + 279)
c
5
(u
16
+ 2u
15
+ ··· − 4u
2
+ 1)(u
82
+ 3u
81
+ ··· + 15u + 1)
c
6
(u
16
− 2u
14
+ ··· − u + 1)(u
82
+ u
81
+ ··· − 14536u + 9797)
c
7
(u
16
− u
15
+ ··· + 6u
2
+ 1)(u
82
+ 24u
80
+ ··· − 37u + 43)
c
8
, c
9
(u
16
− 2u
15
+ ··· − 4u
2
+ 1)(u
82
+ 3u
81
+ ··· + 15u + 1)
c
10
(u
16
− u
15
+ ··· − u + 1)(u
82
+ 4u
80
+ ··· − 30u + 1)
c
11
(u
16
+ u
15
+ ··· + 6u
2
+ 1)(u
82
+ 24u
80
+ ··· − 37u + 43)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
16
+ 5y
15
+ ··· + 7y + 1)(y
82
+ 26y
81
+ ··· + 4280224y + 222784)
c
2
(y
16
− 6y
15
+ ··· + y + 1)(y
82
− 25y
81
+ ··· − 1.88088 × 10
7
y + 262144)
c
3
(y
16
+ 3y
15
+ ··· + 14y + 1)(y
82
− 24y
81
+ ··· − 2823265y + 294849)
c
4
(y
16
+ 5y
15
+ ··· − y + 1)(y
82
+ 18y
81
+ ··· + 1070856y + 77841)
c
5
, c
8
, c
9
(y
16
+ 18y
15
+ ··· − 8y + 1)(y
82
+ 87y
81
+ ··· + 17y + 1)
c
6
(y
16
− 4y
15
+ ··· − 13y + 1)
· (y
82
− 35y
81
+ ··· − 3758984936y + 95981209)
c
7
, c
11
(y
16
+ 7y
15
+ ··· + 12y + 1)(y
82
+ 48y
81
+ ··· + 40857y + 1849)
c
10
(y
16
+ 7y
15
+ ··· + 5y + 1)(y
82
+ 8y
81
+ ··· − 26y + 1)
20
