12a
0730
(K12a
0730
)
A knot diagram
1
Linearized knot diagam
3 8 9 10 11 1 12 2 6 5 4 7
Solving Sequence
4,10
5 11 6
7,12
8 1 9 3 2
c
4
c
10
c
5
c
11
c
7
c
12
c
9
c
3
c
2
c
1
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
55
− 23u
53
+ ··· + 4b + 2u, u
53
− 22u
51
+ ··· + 4a − 4, u
58
+ 2u
57
+ ··· − u + 2i
I
u
2
= h2093u
7
a
2
− 394u
7
a + ··· + 1311a − 1282, 2u
7
a
2
− 4u
7
a + ··· + 6a − 1,
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
I
u
3
= h−u
5
+ u
4
+ 2u
3
− 2u
2
+ b − u, u
5
− 3u
3
+ a + 2u, u
6
− 3u
4
+ 2u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 88 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
= hu
55
−23u
53
+· · ·+4b+2u, u
53
−22u
51
+· · ·+4a−4, u
58
+2u
57
+· · ·−u+2i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
11
=
−u
−u
3
+ u
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
−
1
4
u
53
+
11
2
u
51
+ ··· +
1
4
u + 1
−
1
4
u
55
+
23
4
u
53
+ ··· +
5
2
u
2
−
1
2
u
a
12
=
u
3
− 2u
−u
3
+ u
a
8
=
1
2
u
57
+ u
56
+ ··· +
1
4
u + 1
−u
57
− u
56
+ ··· +
1
2
u − 1
a
1
=
1
4
u
54
−
23
4
u
52
+ ··· −
5
2
u +
1
2
−
1
4
u
54
+
11
2
u
52
+ ··· +
1
4
u
2
+ u
a
9
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
3
=
−u
12
+ 5u
10
− 9u
8
+ 6u
6
− u
2
+ 1
−u
14
+ 6u
12
− 13u
10
+ 10u
8
+ 2u
6
− 4u
4
− u
2
a
2
=
−
1
4
u
51
+
11
2
u
49
+ ··· −
9
4
u + 1
1
4
u
51
−
21
4
u
49
+ ··· −
1
2
u
2
+
1
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
57
+ 48u
55
+ ··· + 10u
2
− 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
58
+ 27u
57
+ ··· + 240u + 25
c
2
, c
8
u
58
− u
57
+ ··· − 10u + 5
c
3
u
58
− 2u
57
+ ··· − 18880u + 3200
c
4
, c
5
, c
10
u
58
+ 2u
57
+ ··· − u + 2
c
6
, c
7
, c
12
u
58
− u
57
+ ··· − 32u + 5
c
9
, c
11
u
58
− 6u
57
+ ··· − 608u + 128
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
58
+ 15y
57
+ ··· + 14700y + 625
c
2
, c
8
y
58
+ 27y
57
+ ··· + 240y + 25
c
3
y
58
− 18y
57
+ ··· − 108646400y + 10240000
c
4
, c
5
, c
10
y
58
− 48y
57
+ ··· + 19y + 4
c
6
, c
7
, c
12
y
58
+ 55y
57
+ ··· − 624y + 25
c
9
, c
11
y
58
+ 32y
57
+ ··· + 31744y + 16384
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.055470 + 0.361002I
a = 1.72697 − 1.44530I
b = −1.84334 − 1.14825I
2.13911 − 7.31160I 0
u = −1.055470 − 0.361002I
a = 1.72697 + 1.44530I
b = −1.84334 + 1.14825I
2.13911 + 7.31160I 0
u = 1.079220 + 0.287984I
a = −0.543736 − 0.144608I
b = 0.874982 − 0.215155I
−3.05587 + 3.30062I 0
u = 1.079220 − 0.287984I
a = −0.543736 + 0.144608I
b = 0.874982 + 0.215155I
−3.05587 − 3.30062I 0
u = 1.113240 + 0.346536I
a = 1.83136 + 1.57124I
b = −2.11612 + 1.33467I
4.49527 + 1.92718I 0
u = 1.113240 − 0.346536I
a = 1.83136 − 1.57124I
b = −2.11612 − 1.33467I
4.49527 − 1.92718I 0
u = −0.160239 + 0.809860I
a = −3.28036 + 1.61495I
b = 2.76593 − 0.91652I
4.87856 + 11.59130I −4.05373 − 7.92500I
u = −0.160239 − 0.809860I
a = −3.28036 − 1.61495I
b = 2.76593 + 0.91652I
4.87856 − 11.59130I −4.05373 + 7.92500I
u = 0.022956 + 0.824654I
a = −4.22626 − 0.30258I
b = 3.31540 + 0.17209I
10.56110 − 2.82315I 0.41076 + 3.01430I
u = 0.022956 − 0.824654I
a = −4.22626 + 0.30258I
b = 3.31540 − 0.17209I
10.56110 + 2.82315I 0.41076 − 3.01430I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.128868 + 0.804285I
a = −3.63497 − 1.53514I
b = 2.97126 + 0.87331I
7.48930 − 6.12555I −0.79979 + 4.12406I
u = 0.128868 − 0.804285I
a = −3.63497 + 1.53514I
b = 2.97126 − 0.87331I
7.48930 + 6.12555I −0.79979 − 4.12406I
u = 0.147502 + 0.778831I
a = 1.128860 + 0.689994I
b = −0.932523 − 0.020123I
−0.24972 − 7.28256I −7.79026 + 7.04615I
u = 0.147502 − 0.778831I
a = 1.128860 − 0.689994I
b = −0.932523 + 0.020123I
−0.24972 + 7.28256I −7.79026 − 7.04615I
u = −0.672408 + 0.378683I
a = 0.49133 + 1.34433I
b = −0.425204 + 0.224307I
1.18428 + 7.12571I −7.47098 − 7.52133I
u = −0.672408 − 0.378683I
a = 0.49133 − 1.34433I
b = −0.425204 − 0.224307I
1.18428 − 7.12571I −7.47098 + 7.52133I
u = 0.013221 + 0.738470I
a = 0.751533 − 0.518009I
b = −0.817557 + 0.051451I
3.40366 + 1.43308I −1.61750 − 4.02310I
u = 0.013221 − 0.738470I
a = 0.751533 + 0.518009I
b = −0.817557 − 0.051451I
3.40366 − 1.43308I −1.61750 + 4.02310I
u = −0.280682 + 0.663131I
a = 0.264754 + 0.958031I
b = −0.667970 − 0.059101I
2.50446 − 3.37914I −4.75082 + 2.18121I
u = −0.280682 − 0.663131I
a = 0.264754 − 0.958031I
b = −0.667970 + 0.059101I
2.50446 + 3.37914I −4.75082 − 2.18121I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.236100 + 0.370704I
a = 1.56436 + 2.14598I
b = −3.06777 + 0.90490I
6.81501 − 1.47559I 0
u = 1.236100 − 0.370704I
a = 1.56436 − 2.14598I
b = −3.06777 − 0.90490I
6.81501 + 1.47559I 0
u = 1.254450 + 0.308524I
a = 0.014085 − 0.736150I
b = 0.658157 − 0.385748I
−0.43433 − 5.22268I 0
u = 1.254450 − 0.308524I
a = 0.014085 + 0.736150I
b = 0.658157 + 0.385748I
−0.43433 + 5.22268I 0
u = 1.287890 + 0.180041I
a = −0.733143 − 0.305909I
b = 0.596300 − 0.730533I
−4.90932 − 2.79468I 0
u = 1.287890 − 0.180041I
a = −0.733143 + 0.305909I
b = 0.596300 + 0.730533I
−4.90932 + 2.79468I 0
u = 0.175184 + 0.669008I
a = 1.32336 + 0.54960I
b = −0.906192 + 0.070742I
−1.76183 + 0.33500I −10.67327 + 0.51437I
u = 0.175184 − 0.669008I
a = 1.32336 − 0.54960I
b = −0.906192 − 0.070742I
−1.76183 − 0.33500I −10.67327 − 0.51437I
u = 0.650108 + 0.232781I
a = −0.150677 − 0.390107I
b = 0.732516 + 0.177916I
−3.55630 − 3.54967I −13.4561 + 5.7470I
u = 0.650108 − 0.232781I
a = −0.150677 + 0.390107I
b = 0.732516 − 0.177916I
−3.55630 + 3.54967I −13.4561 − 5.7470I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.283030 + 0.296425I
a = −0.368173 + 0.033928I
b = 0.946623 + 0.546835I
−0.62219 + 2.29529I 0
u = −1.283030 − 0.296425I
a = −0.368173 − 0.033928I
b = 0.946623 − 0.546835I
−0.62219 − 2.29529I 0
u = −1.275740 + 0.370203I
a = 1.29830 − 2.30847I
b = −3.30928 − 0.54212I
6.52568 + 7.11793I 0
u = −1.275740 − 0.370203I
a = 1.29830 + 2.30847I
b = −3.30928 + 0.54212I
6.52568 − 7.11793I 0
u = 0.535752 + 0.365918I
a = 0.36495 − 1.47581I
b = −0.553992 − 0.181156I
3.29520 − 2.38278I −4.28188 + 3.63346I
u = 0.535752 − 0.365918I
a = 0.36495 + 1.47581I
b = −0.553992 + 0.181156I
3.29520 + 2.38278I −4.28188 − 3.63346I
u = 0.322023 + 0.539515I
a = 0.085417 − 1.114740I
b = −0.650618 − 0.010802I
4.03344 − 0.91043I −2.12378 + 4.36430I
u = 0.322023 − 0.539515I
a = 0.085417 + 1.114740I
b = −0.650618 + 0.010802I
4.03344 + 0.91043I −2.12378 − 4.36430I
u = −1.381860 + 0.067257I
a = 0.298361 − 0.582536I
b = 1.14365 + 1.03316I
−2.65450 + 3.62930I 0
u = −1.381860 − 0.067257I
a = 0.298361 + 0.582536I
b = 1.14365 − 1.03316I
−2.65450 − 3.62930I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.354170 + 0.284240I
a = −0.282971 + 0.964369I
b = 1.050160 + 0.253647I
−6.57455 + 3.16360I 0
u = −1.354170 − 0.284240I
a = −0.282971 − 0.964369I
b = 1.050160 − 0.253647I
−6.57455 − 3.16360I 0
u = −1.370230 + 0.194123I
a = −0.013281 − 0.259852I
b = 1.010250 + 0.806222I
−1.25158 + 3.51548I 0
u = −1.370230 − 0.194123I
a = −0.013281 + 0.259852I
b = 1.010250 − 0.806222I
−1.25158 − 3.51548I 0
u = −1.347860 + 0.346662I
a = 0.54429 − 2.41322I
b = −3.45164 + 0.39084I
2.84200 + 10.27730I 0
u = −1.347860 − 0.346662I
a = 0.54429 + 2.41322I
b = −3.45164 − 0.39084I
2.84200 − 10.27730I 0
u = −1.355220 + 0.332018I
a = −0.151021 + 0.986947I
b = 0.899192 + 0.120955I
−4.98693 + 11.30040I 0
u = −1.355220 − 0.332018I
a = −0.151021 − 0.986947I
b = 0.899192 − 0.120955I
−4.98693 − 11.30040I 0
u = −1.402640 + 0.030948I
a = −0.621414 − 0.054979I
b = −0.624989 + 0.196548I
−9.84382 + 4.17376I 0
u = −1.402640 − 0.030948I
a = −0.621414 + 0.054979I
b = −0.624989 − 0.196548I
−9.84382 − 4.17376I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.365450 + 0.346164I
a = 0.39863 + 2.28058I
b = −3.29230 − 0.55110I
0.0648 − 15.7631I 0
u = 1.365450 − 0.346164I
a = 0.39863 − 2.28058I
b = −3.29230 + 0.55110I
0.0648 + 15.7631I 0
u = 1.387300 + 0.259107I
a = −0.215334 + 0.244520I
b = 1.053360 − 0.706502I
−2.76639 + 0.04256I 0
u = 1.387300 − 0.259107I
a = −0.215334 − 0.244520I
b = 1.053360 + 0.706502I
−2.76639 − 0.04256I 0
u = 1.42580 + 0.05543I
a = 0.187121 + 0.701410I
b = 1.22349 − 0.96601I
−5.43020 − 8.23971I 0
u = 1.42580 − 0.05543I
a = 0.187121 − 0.701410I
b = 1.22349 + 0.96601I
−5.43020 + 8.23971I 0
u = −0.205515 + 0.291758I
a = 1.197660 + 0.567196I
b = −0.081785 − 0.431720I
−0.619748 + 0.918576I −10.20880 − 7.11535I
u = −0.205515 − 0.291758I
a = 1.197660 − 0.567196I
b = −0.081785 + 0.431720I
−0.619748 − 0.918576I −10.20880 + 7.11535I
10
II. I
u
2
= h2093u
7
a
2
− 394u
7
a + · · · + 1311a − 1282, 2u
7
a
2
− 4u
7
a + · · · +
6a − 1, u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
11
=
−u
−u
3
+ u
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
a
−0.699298a
2
u
7
+ 0.131640au
7
+ ··· − 0.438022a + 0.428333
a
12
=
u
3
− 2u
−u
3
+ u
a
8
=
−0.188774a
2
u
7
+ 0.106248au
7
+ ··· + 0.991647a − 1.14668
−0.358503a
2
u
7
+ 0.214166au
7
+ ··· − 0.334447a + 1.04711
a
1
=
0.193451a
2
u
7
+ 0.438022au
7
+ ··· − 0.911794a + 0.668894
au
a
9
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
3
=
u
3
− 2u
−u
3
+ u
a
2
=
0.374206a
2
u
7
− 0.458403au
7
+ ··· − 0.611761a − 0.222519
0.558637a
2
u
7
+ 0.715670au
7
+ ··· − 0.320414a + 0.653525
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
6
+ 12u
4
+ 4u
3
− 8u
2
− 8u − 14
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
+ 16u
23
+ ··· − 4u + 1
c
2
, c
6
, c
7
c
8
, c
12
u
24
+ 8u
22
+ ··· − 2u − 1
c
3
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
3
c
4
, c
5
, c
10
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
3
c
9
, c
11
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
3
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 16y
23
+ ··· − 20y + 1
c
2
, c
6
, c
7
c
8
, c
12
y
24
+ 16y
23
+ ··· − 4y + 1
c
3
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
3
c
4
, c
5
, c
10
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
3
c
9
, c
11
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
3
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.180120 + 0.268597I
a = 0.283758 + 0.634812I
b = 0.459071 + 0.556325I
−1.04066 + 1.13123I −7.41522 − 0.51079I
u = −1.180120 + 0.268597I
a = −0.519143 + 0.133347I
b = 0.839838 + 0.369976I
−1.04066 + 1.13123I −7.41522 − 0.51079I
u = −1.180120 + 0.268597I
a = 2.48773 − 1.66933I
b = −2.44064 − 2.38764I
−1.04066 + 1.13123I −7.41522 − 0.51079I
u = −1.180120 − 0.268597I
a = 0.283758 − 0.634812I
b = 0.459071 − 0.556325I
−1.04066 − 1.13123I −7.41522 + 0.51079I
u = −1.180120 − 0.268597I
a = −0.519143 − 0.133347I
b = 0.839838 − 0.369976I
−1.04066 − 1.13123I −7.41522 + 0.51079I
u = −1.180120 − 0.268597I
a = 2.48773 + 1.66933I
b = −2.44064 + 2.38764I
−1.04066 − 1.13123I −7.41522 + 0.51079I
u = −0.108090 + 0.747508I
a = 0.536114 + 0.684251I
b = −0.769284 − 0.082442I
2.15941 + 2.57849I −4.27708 − 3.56796I
u = −0.108090 + 0.747508I
a = 1.086910 − 0.593279I
b = −0.893968 + 0.013597I
2.15941 + 2.57849I −4.27708 − 3.56796I
u = −0.108090 + 0.747508I
a = −4.33823 + 2.20659I
b = 3.37373 − 1.26294I
2.15941 + 2.57849I −4.27708 − 3.56796I
u = −0.108090 − 0.747508I
a = 0.536114 − 0.684251I
b = −0.769284 + 0.082442I
2.15941 − 2.57849I −4.27708 + 3.56796I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.108090 − 0.747508I
a = 1.086910 + 0.593279I
b = −0.893968 − 0.013597I
2.15941 − 2.57849I −4.27708 + 3.56796I
u = −0.108090 − 0.747508I
a = −4.33823 − 2.20659I
b = 3.37373 + 1.26294I
2.15941 − 2.57849I −4.27708 + 3.56796I
u = 1.37100
a = 0.478541 + 0.816744I
b = 1.31000 − 1.17794I
−6.50273 −13.8640
u = 1.37100
a = 0.478541 − 0.816744I
b = 1.31000 + 1.17794I
−6.50273 −13.8640
u = 1.37100
a = −0.656575
b = −0.423632
−6.50273 −13.8640
u = 1.334530 + 0.318930I
a = −0.162462 − 0.927232I
b = 0.882181 − 0.209095I
−2.37968 − 6.44354I −9.42845 + 5.29417I
u = 1.334530 + 0.318930I
a = −0.367019 + 0.108941I
b = 1.033880 − 0.589591I
−2.37968 − 6.44354I −9.42845 + 5.29417I
u = 1.334530 + 0.318930I
a = 0.47028 + 2.85958I
b = −3.97967 − 0.51225I
−2.37968 − 6.44354I −9.42845 + 5.29417I
u = 1.334530 − 0.318930I
a = −0.162462 + 0.927232I
b = 0.882181 + 0.209095I
−2.37968 + 6.44354I −9.42845 − 5.29417I
u = 1.334530 − 0.318930I
a = −0.367019 − 0.108941I
b = 1.033880 + 0.589591I
−2.37968 + 6.44354I −9.42845 − 5.29417I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.334530 − 0.318930I
a = 0.47028 − 2.85958I
b = −3.97967 + 0.51225I
−2.37968 + 6.44354I −9.42845 − 5.29417I
u = −0.463640
a = 0.308333
b = 0.453402
−0.845036 −11.8940
u = −0.463640
a = 1.21764 + 2.13829I
b = −0.830005 + 0.371154I
−0.845036 −11.8940
u = −0.463640
a = 1.21764 − 2.13829I
b = −0.830005 − 0.371154I
−0.845036 −11.8940
16
III.
I
u
3
= h−u
5
+ u
4
+ 2u
3
− 2u
2
+ b − u, u
5
− 3u
3
+ a + 2u, u
6
− 3u
4
+ 2u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
11
=
−u
−u
3
+ u
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
−u
5
+ 3u
3
− 2u
u
5
− u
4
− 2u
3
+ 2u
2
+ u
a
12
=
u
3
− 2u
−u
3
+ u
a
8
=
−u
5
+ 3u
3
+ u
2
− 2u − 1
u
5
− 2u
3
+ u
a
1
=
u
4
+ u
3
− 2u
2
− 2u + 1
−1
a
9
=
u
5
− 2u
3
+ u
0
a
3
=
1
0
a
2
=
u
4
+ u
3
− 2u
2
− 2u + 2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
4
− 8u
2
− 8
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
c
2
, c
6
, c
7
c
8
, c
12
(u
2
+ 1)
3
c
3
u
6
c
4
, c
5
, c
10
u
6
− 3u
4
+ 2u
2
+ 1
c
9
, c
11
u
6
+ u
4
+ 2u
2
+ 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
6
c
2
, c
6
, c
7
c
8
, c
12
(y + 1)
6
c
3
y
6
c
4
, c
5
, c
10
(y
3
− 3y
2
+ 2y + 1)
2
c
9
, c
11
(y
3
+ y
2
+ 2y + 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.307140 + 0.215080I
a = 0.744862 − 0.122561I
b = 0.877439 + 0.255138I
−3.02413 − 2.82812I −11.50976 + 2.97945I
u = 1.307140 − 0.215080I
a = 0.744862 + 0.122561I
b = 0.877439 − 0.255138I
−3.02413 + 2.82812I −11.50976 − 2.97945I
u = −1.307140 + 0.215080I
a = −0.744862 − 0.122561I
b = 0.87744 + 1.74486I
−3.02413 + 2.82812I −11.50976 − 2.97945I
u = −1.307140 − 0.215080I
a = −0.744862 + 0.122561I
b = 0.87744 − 1.74486I
−3.02413 − 2.82812I −11.50976 + 2.97945I
u = 0.569840I
a = − 1.75488I
b = −0.754878 + 1.000000I
1.11345 −4.98050
u = − 0.569840I
a = 1.75488I
b = −0.754878 − 1.000000I
1.11345 −4.98050
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
24
+ 16u
23
+ ··· − 4u + 1)(u
58
+ 27u
57
+ ··· + 240u + 25)
c
2
, c
8
((u
2
+ 1)
3
)(u
24
+ 8u
22
+ ··· − 2u − 1)(u
58
− u
57
+ ··· − 10u + 5)
c
3
u
6
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
3
· (u
58
− 2u
57
+ ··· − 18880u + 3200)
c
4
, c
5
, c
10
(u
6
− 3u
4
+ 2u
2
+ 1)(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
3
· (u
58
+ 2u
57
+ ··· − u + 2)
c
6
, c
7
, c
12
((u
2
+ 1)
3
)(u
24
+ 8u
22
+ ··· − 2u − 1)(u
58
− u
57
+ ··· − 32u + 5)
c
9
, c
11
(u
6
+ u
4
+ 2u
2
+ 1)
· (u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
3
· (u
58
− 6u
57
+ ··· − 608u + 128)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
6
)(y
24
− 16y
23
+ ··· − 20y + 1)
· (y
58
+ 15y
57
+ ··· + 14700y + 625)
c
2
, c
8
((y + 1)
6
)(y
24
+ 16y
23
+ ··· − 4y + 1)(y
58
+ 27y
57
+ ··· + 240y + 25)
c
3
y
6
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
3
· (y
58
− 18y
57
+ ··· − 108646400y + 10240000)
c
4
, c
5
, c
10
(y
3
− 3y
2
+ 2y + 1)
2
· (y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
3
· (y
58
− 48y
57
+ ··· + 19y + 4)
c
6
, c
7
, c
12
((y + 1)
6
)(y
24
+ 16y
23
+ ··· − 4y + 1)(y
58
+ 55y
57
+ ··· − 624y + 25)
c
9
, c
11
(y
3
+ y
2
+ 2y + 1)
2
· (y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
3
· (y
58
+ 32y
57
+ ··· + 31744y + 16384)
22
