12a
1010
(K12a
1010
)
A knot diagram
1
Linearized knot diagam
4 6 12 1 9 10 11 3 2 8 7 5
Solving Sequence
1,4
2
5,9
6 10 7 12 3 8 11
c
1
c
4
c
5
c
9
c
6
c
12
c
3
c
8
c
11
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
11
− 2u
10
− 6u
9
− 9u
8
− 12u
7
− 13u
6
− 8u
5
− 5u
4
+ u
2
+ b,
u
11
+ 2u
10
+ 7u
9
+ 10u
8
+ 17u
7
+ 17u
6
+ 16u
5
+ 10u
4
+ 3u
3
+ a − 2u − 1,
u
13
+ 2u
12
+ 8u
11
+ 12u
10
+ 23u
9
+ 26u
8
+ 28u
7
+ 22u
6
+ 10u
5
+ 2u
4
− 4u
3
− 4u
2
− u − 1i
I
u
2
= h−1.77519 × 10
76
u
83
+ 3.36042 × 10
76
u
82
+ ··· + 4.02015 × 10
76
b − 3.79501 × 10
75
,
1.26819 × 10
76
u
83
− 1.95398 × 10
76
u
82
+ ··· + 4.02015 × 10
76
a − 7.98274 × 10
76
, u
84
− u
83
+ ··· − 8u + 1i
* 2 irreducible components of dim
C
= 0, with total 97 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−u
11
−2u
10
+· · ·+u
2
+b, u
11
+2u
10
+· · ·+a−1, u
13
+2u
12
+· · ·−u−1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
u
a
9
=
−u
11
− 2u
10
+ ··· + 2u + 1
u
11
+ 2u
10
+ 6u
9
+ 9u
8
+ 12u
7
+ 13u
6
+ 8u
5
+ 5u
4
− u
2
a
6
=
u
8
+ u
7
+ 4u
6
+ 3u
5
+ 5u
4
+ 2u
3
+ u
2
− u − 1
−u
8
− u
7
− 3u
6
− 3u
5
− 2u
4
− 2u
3
+ u
2
+ u
a
10
=
−u
11
− 2u
10
+ ··· − 2u
2
+ u
u
11
+ 2u
10
+ 6u
9
+ 8u
8
+ 11u
7
+ 10u
6
+ 6u
5
+ 3u
4
− u
3
− 2u
2
a
7
=
u
10
+ 2u
9
+ 7u
8
+ 10u
7
+ 16u
6
+ 16u
5
+ 13u
4
+ 8u
3
+ u
2
− 1
u
12
+ 2u
11
+ 6u
10
+ 8u
9
+ 10u
8
+ 8u
7
+ 2u
6
− 2u
5
− 5u
4
− 4u
3
a
12
=
u
2
+ 1
−u
2
a
3
=
u
5
+ 2u
3
+ u
−u
5
− u
3
+ u
a
8
=
−u
12
− 2u
11
+ ··· + u + 1
u
12
+ 2u
11
+ 7u
10
+ 10u
9
+ 16u
8
+ 16u
7
+ 13u
6
+ 8u
5
+ u
4
− u
3
− u
2
− u
a
11
=
−u
11
− 2u
10
+ ··· + u + 1
2u
11
+ 4u
10
+ ··· − u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
12
+ 4u
11
+ 24u
10
+ 20u
9
+ 52u
8
+ 36u
7
+ 48u
6
+ 32u
5
+ 24u
4
+ 24u
3
+ 16u
2
+ 12u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
, c
11
, c
12
u
13
− 2u
12
+ ··· − u + 1
c
2
, c
5
u
13
+ 2u
10
+ 7u
9
+ 10u
6
+ 12u
5
− 8u
4
+ 4u
3
+ 4u
2
+ u − 1
c
3
, c
6
u
13
+ 2u
12
+ ··· + 5u + 2
c
8
u
13
− 19u
12
+ ··· + 1856u − 256
c
9
u
13
− 19u
12
+ ··· + 1344u − 192
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
, c
11
, c
12
y
13
+ 12y
12
+ ··· − 7y −1
c
2
, c
5
y
13
+ 14y
11
+ ··· + 9y −1
c
3
, c
6
y
13
− 4y
12
+ ··· − 39y −4
c
8
y
13
− 35y
12
+ ··· + 135168y −65536
c
9
y
13
− 37y
12
+ ··· + 49152y −36864
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.345201 + 1.021440I
a = 0.383027 + 0.071451I
b = 0.786816 + 0.242416I
−0.092600 − 0.790634I −5.74730 − 0.20798I
u = −0.345201 − 1.021440I
a = 0.383027 − 0.071451I
b = 0.786816 − 0.242416I
−0.092600 + 0.790634I −5.74730 + 0.20798I
u = −0.816966 + 0.218516I
a = −1.090410 − 0.648020I
b = 0.316522 − 0.929361I
−4.93693 + 9.42698I −10.17355 − 7.65318I
u = −0.816966 − 0.218516I
a = −1.090410 + 0.648020I
b = 0.316522 + 0.929361I
−4.93693 − 9.42698I −10.17355 + 7.65318I
u = 0.242549 + 1.320770I
a = 2.31317 + 2.33263I
b = −2.01116 − 2.58449I
5.96169 − 6.15155I 2.5842 − 14.2195I
u = 0.242549 − 1.320770I
a = 2.31317 − 2.33263I
b = −2.01116 + 2.58449I
5.96169 + 6.15155I 2.5842 + 14.2195I
u = 0.609274
a = −2.87003
b = 2.28717
−2.44873 31.6660
u = −0.08989 + 1.44411I
a = 0.86609 + 1.34154I
b = −1.31236 − 2.11003I
13.07620 + 0.19322I 5.00344 + 0.65090I
u = −0.08989 − 1.44411I
a = 0.86609 − 1.34154I
b = −1.31236 + 2.11003I
13.07620 − 0.19322I 5.00344 − 0.65090I
u = −0.34207 + 1.41123I
a = −0.20187 − 2.15080I
b = −0.37276 + 3.06306I
5.4451 + 17.8321I −1.52643 − 9.77243I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.34207 − 1.41123I
a = −0.20187 + 2.15080I
b = −0.37276 − 3.06306I
5.4451 − 17.8321I −1.52643 + 9.77243I
u = 0.046940 + 0.495776I
a = 0.665010 + 1.116330I
b = 0.449357 + 0.078161I
0.68765 − 1.39515I −0.97323 + 4.26024I
u = 0.046940 − 0.495776I
a = 0.665010 − 1.116330I
b = 0.449357 − 0.078161I
0.68765 + 1.39515I −0.97323 − 4.26024I
6
II.
I
u
2
= h−1.78×10
76
u
83
+3.36×10
76
u
82
+· · ·+4.02×10
76
b−3.80×10
75
, 1.27×
10
76
u
83
−1.95×10
76
u
82
+· · ·+4.02×10
76
a−7.98×10
76
, u
84
−u
83
+· · ·−8u+1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
u
a
9
=
−0.315458u
83
+ 0.486047u
82
+ ··· + 5.80096u + 1.98568
0.441574u
83
− 0.835893u
82
+ ··· − 5.12507u + 0.0943996
a
6
=
0.789727u
83
− 0.878458u
82
+ ··· + 11.7409u − 0.991810
0.518038u
83
− 0.964879u
82
+ ··· − 4.65016u + 0.772193
a
10
=
−0.0980563u
83
+ 0.387555u
82
+ ··· + 12.6062u + 1.72069
0.0831270u
83
− 0.0730730u
82
+ ··· − 4.39119u − 0.0245108
a
7
=
0.0825732u
83
+ 0.185608u
82
+ ··· − 8.24132u − 0.987882
0.241456u
83
− 1.04811u
82
+ ··· + 5.35494u − 0.163213
a
12
=
u
2
+ 1
−u
2
a
3
=
u
5
+ 2u
3
+ u
−u
5
− u
3
+ u
a
8
=
−0.567135u
83
+ 0.694103u
82
+ ··· + 11.9492u + 1.30203
0.271257u
83
− 0.00854034u
82
+ ··· − 3.68237u − 0.132308
a
11
=
−0.934228u
83
+ 0.597004u
82
+ ··· + 6.80551u + 0.971587
−0.0459951u
83
+ 0.774208u
82
+ ··· − 3.42474u + 0.306200
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.70327u
83
+ 5.21911u
82
+ ··· + 16.9568u − 8.13028
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
, c
11
, c
12
u
84
+ u
83
+ ··· + 8u + 1
c
2
, c
5
u
84
− 7u
83
+ ··· + 8u
2
+ 1
c
3
, c
6
u
84
− u
83
+ ··· + 124914u + 10897
c
8
(u
42
+ 9u
41
+ ··· − 19u − 1)
2
c
9
(u
42
+ 8u
41
+ ··· + 4u − 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
, c
11
, c
12
y
84
+ 71y
83
+ ··· + 392y
2
+ 1
c
2
, c
5
y
84
+ 7y
83
+ ··· + 16y + 1
c
3
, c
6
y
84
− 29y
83
+ ··· + 1118832658y + 118744609
c
8
(y
42
− 29y
41
+ ··· − 99y + 1)
2
c
9
(y
42
− 42y
41
+ ··· − 64y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.518175 + 0.869909I
a = −0.038515 − 0.361398I
b = −0.396322 − 0.279186I
−2.21491 − 3.65443I 0
u = 0.518175 − 0.869909I
a = −0.038515 + 0.361398I
b = −0.396322 + 0.279186I
−2.21491 + 3.65443I 0
u = −0.486616 + 0.918991I
a = 0.669010 − 0.149675I
b = 0.548977 + 0.391483I
2.27560 − 8.94034I 0
u = −0.486616 − 0.918991I
a = 0.669010 + 0.149675I
b = 0.548977 − 0.391483I
2.27560 + 8.94034I 0
u = −0.433633 + 0.954309I
a = −0.568715 + 0.074268I
b = −0.630900 − 0.351516I
−2.64853 − 4.93654I 0
u = −0.433633 − 0.954309I
a = −0.568715 − 0.074268I
b = −0.630900 + 0.351516I
−2.64853 + 4.93654I 0
u = 0.874722 + 0.339102I
a = 0.230055 − 0.515951I
b = −0.327717 − 0.197359I
−0.08162 − 4.63366I 0
u = 0.874722 − 0.339102I
a = 0.230055 + 0.515951I
b = −0.327717 + 0.197359I
−0.08162 + 4.63366I 0
u = 0.922673 + 0.158839I
a = 0.134609 − 0.475277I
b = −0.171410 − 0.216206I
−0.40808 + 2.05165I 0
u = 0.922673 − 0.158839I
a = 0.134609 + 0.475277I
b = −0.171410 + 0.216206I
−0.40808 − 2.05165I 0
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.875995 + 0.247622I
a = −0.202518 + 0.483595I
b = 0.264623 + 0.227684I
−4.19534 − 1.24503I −19.3254 + 4.7543I
u = 0.875995 − 0.247622I
a = −0.202518 − 0.483595I
b = 0.264623 − 0.227684I
−4.19534 + 1.24503I −19.3254 − 4.7543I
u = 0.589935 + 0.687179I
a = −0.092443 + 0.519015I
b = 0.441781 + 0.227681I
1.163260 − 0.381253I −6.00000 + 5.04367I
u = 0.589935 − 0.687179I
a = −0.092443 − 0.519015I
b = 0.441781 − 0.227681I
1.163260 + 0.381253I −6.00000 − 5.04367I
u = 0.542934 + 0.983292I
a = 0.024629 + 0.211855I
b = 0.392576 + 0.359601I
2.14428 − 7.17345I 0
u = 0.542934 − 0.983292I
a = 0.024629 − 0.211855I
b = 0.392576 − 0.359601I
2.14428 + 7.17345I 0
u = −0.829852 + 0.247067I
a = 1.064070 + 0.579575I
b = −0.354088 + 0.962644I
0.17793 + 13.60140I −5.67868 − 8.84142I
u = −0.829852 − 0.247067I
a = 1.064070 − 0.579575I
b = −0.354088 − 0.962644I
0.17793 − 13.60140I −5.67868 + 8.84142I
u = −0.782980 + 0.182023I
a = 1.108420 + 0.771590I
b = −0.240622 + 0.900055I
−2.64853 + 4.93654I −8.21045 − 3.85583I
u = −0.782980 − 0.182023I
a = 1.108420 − 0.771590I
b = −0.240622 − 0.900055I
−2.64853 − 4.93654I −8.21045 + 3.85583I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.181275 + 1.215690I
a = −0.97248 − 1.68480I
b = 0.82732 + 2.93963I
4.16290 − 2.67804I 0
u = −0.181275 − 1.215690I
a = −0.97248 + 1.68480I
b = 0.82732 − 2.93963I
4.16290 + 2.67804I 0
u = −0.213038 + 1.221080I
a = −0.273011 + 0.639939I
b = 1.57872 − 0.41599I
1.163260 − 0.381253I 0
u = −0.213038 − 1.221080I
a = −0.273011 − 0.639939I
b = 1.57872 + 0.41599I
1.163260 + 0.381253I 0
u = 0.223743 + 1.261850I
a = 1.64598 + 2.46908I
b = −1.44659 − 2.87840I
5.38892 0
u = 0.223743 − 1.261850I
a = 1.64598 − 2.46908I
b = −1.44659 + 2.87840I
5.38892 0
u = −0.243997 + 1.261430I
a = 0.79293 + 2.00931I
b = −0.39956 − 3.42872I
−0.40808 + 2.05165I 0
u = −0.243997 − 1.261430I
a = 0.79293 − 2.00931I
b = −0.39956 + 3.42872I
−0.40808 − 2.05165I 0
u = 0.191076 + 1.275400I
a = 1.83468 + 0.25198I
b = −1.397140 − 0.155462I
2.23419 − 2.19201I 0
u = 0.191076 − 1.275400I
a = 1.83468 − 0.25198I
b = −1.397140 + 0.155462I
2.23419 + 2.19201I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.654693 + 0.253029I
a = −0.661570 − 0.897779I
b = 0.126788 − 1.087400I
5.45130 + 4.89000I −2.04083 − 7.34150I
u = −0.654693 − 0.253029I
a = −0.661570 + 0.897779I
b = 0.126788 + 1.087400I
5.45130 − 4.89000I −2.04083 + 7.34150I
u = −0.097059 + 1.295830I
a = −0.31003 − 1.38850I
b = −0.73782 + 1.56661I
7.82402 − 3.09693I 0
u = −0.097059 − 1.295830I
a = −0.31003 + 1.38850I
b = −0.73782 − 1.56661I
7.82402 + 3.09693I 0
u = −0.689220 + 0.080903I
a = 1.30178 + 1.19981I
b = 0.002720 + 0.837825I
−2.21491 + 3.65443I −12.4846 − 8.5699I
u = −0.689220 − 0.080903I
a = 1.30178 − 1.19981I
b = 0.002720 − 0.837825I
−2.21491 − 3.65443I −12.4846 + 8.5699I
u = −0.396279 + 0.566081I
a = −1.262610 − 0.217005I
b = −0.358488 − 0.131013I
6.62858 − 1.39134I 1.290119 + 0.468519I
u = −0.396279 − 0.566081I
a = −1.262610 + 0.217005I
b = −0.358488 + 0.131013I
6.62858 + 1.39134I 1.290119 − 0.468519I
u = −0.264019 + 1.290660I
a = 0.906071 − 0.047046I
b = −2.26160 − 0.54402I
−0.08162 + 4.63366I 0
u = −0.264019 − 1.290660I
a = 0.906071 + 0.047046I
b = −2.26160 + 0.54402I
−0.08162 − 4.63366I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.232670 + 1.297620I
a = −2.13788 − 2.73733I
b = 1.91976 + 3.02429I
1.63132 − 3.03620I 0
u = 0.232670 − 1.297620I
a = −2.13788 + 2.73733I
b = 1.91976 − 3.02429I
1.63132 + 3.03620I 0
u = −0.665673 + 0.116795I
a = 1.98351 − 0.73015I
b = 0.186269 − 0.357589I
0.97628 + 5.72904I −8.53885 − 9.66512I
u = −0.665673 − 0.116795I
a = 1.98351 + 0.73015I
b = 0.186269 + 0.357589I
0.97628 − 5.72904I −8.53885 + 9.66512I
u = −0.671665 + 0.028872I
a = −1.86929 + 1.10308I
b = −0.181551 + 0.595117I
−4.19534 + 1.24503I −19.3254 − 4.7543I
u = −0.671665 − 0.028872I
a = −1.86929 − 1.10308I
b = −0.181551 − 0.595117I
−4.19534 − 1.24503I −19.3254 + 4.7543I
u = −0.279831 + 1.311700I
a = −0.44458 − 2.14417I
b = −0.20861 + 3.37194I
2.14428 + 7.17345I 0
u = −0.279831 − 1.311700I
a = −0.44458 + 2.14417I
b = −0.20861 − 3.37194I
2.14428 − 7.17345I 0
u = 0.169101 + 1.333000I
a = −1.96189 − 1.30999I
b = 1.49632 + 1.40578I
6.83951 0
u = 0.169101 − 1.333000I
a = −1.96189 + 1.30999I
b = 1.49632 − 1.40578I
6.83951 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.271899 + 1.335600I
a = −0.976790 − 0.436319I
b = 2.12600 + 1.18794I
5.55420 + 9.14579I 0
u = −0.271899 − 1.335600I
a = −0.976790 + 0.436319I
b = 2.12600 − 1.18794I
5.55420 − 9.14579I 0
u = 0.253751 + 1.345840I
a = −0.46166 + 1.46887I
b = 0.20067 − 1.82877I
3.26207 − 3.66273I 0
u = 0.253751 − 1.345840I
a = −0.46166 − 1.46887I
b = 0.20067 + 1.82877I
3.26207 + 3.66273I 0
u = 0.400341 + 1.315590I
a = −0.151092 + 0.581745I
b = −0.210879 − 0.996363I
4.16290 − 2.67804I 0
u = 0.400341 − 1.315590I
a = −0.151092 − 0.581745I
b = −0.210879 + 0.996363I
4.16290 + 2.67804I 0
u = 0.618543 + 0.047649I
a = 2.80528 + 0.04414I
b = −2.15290 + 0.03638I
1.63132 − 3.03620I 16.2002 − 11.9033I
u = 0.618543 − 0.047649I
a = 2.80528 − 0.04414I
b = −2.15290 − 0.03638I
1.63132 + 3.03620I 16.2002 + 11.9033I
u = 0.601189 + 0.103705I
a = 0.620455 − 0.101552I
b = −0.499415 − 0.638711I
−1.35422 − 0.52269I −7.55055 − 0.33202I
u = 0.601189 − 0.103705I
a = 0.620455 + 0.101552I
b = −0.499415 + 0.638711I
−1.35422 + 0.52269I −7.55055 + 0.33202I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.012027 + 1.402540I
a = −0.83750 − 1.49408I
b = 1.12949 + 2.23412I
6.62858 − 1.39134I 0
u = −0.012027 − 1.402540I
a = −0.83750 + 1.49408I
b = 1.12949 − 2.23412I
6.62858 + 1.39134I 0
u = −0.325385 + 1.374120I
a = −0.25382 − 2.11881I
b = −0.35289 + 3.10453I
2.27560 + 8.94034I 0
u = −0.325385 − 1.374120I
a = −0.25382 + 2.11881I
b = −0.35289 − 3.10453I
2.27560 − 8.94034I 0
u = −0.26872 + 1.38872I
a = 0.27275 + 2.17820I
b = 0.48372 − 3.10703I
10.65060 + 8.27956I 0
u = −0.26872 − 1.38872I
a = 0.27275 − 2.17820I
b = 0.48372 + 3.10703I
10.65060 − 8.27956I 0
u = −0.33963 + 1.39512I
a = 0.21657 + 2.13132I
b = 0.36363 − 3.07248I
0.17793 + 13.60140I 0
u = −0.33963 − 1.39512I
a = 0.21657 − 2.13132I
b = 0.36363 + 3.07248I
0.17793 − 13.60140I 0
u = 0.36831 + 1.39668I
a = −0.009205 − 0.851401I
b = 0.340567 + 1.271450I
0.97628 − 5.72904I 0
u = 0.36831 − 1.39668I
a = −0.009205 + 0.851401I
b = 0.340567 − 1.271450I
0.97628 + 5.72904I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21161 + 1.45666I
a = −0.30774 − 1.38801I
b = 0.58867 + 1.86348I
7.82402 − 3.09693I 0
u = 0.21161 − 1.45666I
a = −0.30774 + 1.38801I
b = 0.58867 − 1.86348I
7.82402 + 3.09693I 0
u = 0.04309 + 1.47202I
a = 0.69091 + 1.44752I
b = −1.01399 − 2.06695I
5.45130 − 4.89000I 0
u = 0.04309 − 1.47202I
a = 0.69091 − 1.44752I
b = −1.01399 + 2.06695I
5.45130 + 4.89000I 0
u = 0.36652 + 1.44263I
a = 0.150102 + 0.905438I
b = −0.47705 − 1.33644I
5.55420 − 9.14579I 0
u = 0.36652 − 1.44263I
a = 0.150102 − 0.905438I
b = −0.47705 + 1.33644I
5.55420 + 9.14579I 0
u = 0.02486 + 1.51626I
a = −0.69442 − 1.38331I
b = 1.06466 + 1.98709I
10.65060 − 8.27956I 0
u = 0.02486 − 1.51626I
a = −0.69442 + 1.38331I
b = 1.06466 − 1.98709I
10.65060 + 8.27956I 0
u = 0.411613 + 0.144017I
a = −2.50177 − 0.61683I
b = 1.344230 + 0.260671I
2.23419 + 2.19201I −3.74038 − 7.88851I
u = 0.411613 − 0.144017I
a = −2.50177 + 0.61683I
b = 1.344230 − 0.260671I
2.23419 − 2.19201I −3.74038 + 7.88851I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.014444 + 0.316245I
a = −2.50337 + 0.43646I
b = 0.643308 + 0.986079I
3.26207 − 3.66273I −0.562666 + 0.820436I
u = 0.014444 − 0.316245I
a = −2.50337 − 0.43646I
b = 0.643308 − 0.986079I
3.26207 + 3.66273I −0.562666 − 0.820436I
u = 0.152196 + 0.142659I
a = 3.54109 + 0.72739I
b = −0.751283 − 0.524651I
−1.35422 − 0.52269I −7.55055 − 0.33202I
u = 0.152196 − 0.142659I
a = 3.54109 − 0.72739I
b = −0.751283 + 0.524651I
−1.35422 + 0.52269I −7.55055 + 0.33202I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
, c
11
, c
12
(u
13
− 2u
12
+ ··· − u + 1)(u
84
+ u
83
+ ··· + 8u + 1)
c
2
, c
5
(u
13
+ 2u
10
+ 7u
9
+ 10u
6
+ 12u
5
− 8u
4
+ 4u
3
+ 4u
2
+ u − 1)
· (u
84
− 7u
83
+ ··· + 8u
2
+ 1)
c
3
, c
6
(u
13
+ 2u
12
+ ··· + 5u + 2)(u
84
− u
83
+ ··· + 124914u + 10897)
c
8
(u
13
− 19u
12
+ ··· + 1856u − 256)(u
42
+ 9u
41
+ ··· − 19u − 1)
2
c
9
(u
13
− 19u
12
+ ··· + 1344u − 192)(u
42
+ 8u
41
+ ··· + 4u − 1)
2
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
, c
11
, c
12
(y
13
+ 12y
12
+ ··· − 7y −1)(y
84
+ 71y
83
+ ··· + 392y
2
+ 1)
c
2
, c
5
(y
13
+ 14y
11
+ ··· + 9y −1)(y
84
+ 7y
83
+ ··· + 16y + 1)
c
3
, c
6
(y
13
− 4y
12
+ ··· − 39y −4)
· (y
84
− 29y
83
+ ··· + 1118832658y + 118744609)
c
8
(y
13
− 35y
12
+ ··· + 135168y −65536)
· (y
42
− 29y
41
+ ··· − 99y + 1)
2
c
9
(y
13
− 37y
12
+ ··· + 49152y −36864)(y
42
− 42y
41
+ ··· − 64y + 1)
2
20
