12n
0413
(K12n
0413
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 9 5 12 7 4 8 9
Solving Sequence
6,9
7
3,10
2 1 5 4 12 8 11
c
6
c
9
c
2
c
1
c
5
c
4
c
12
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.68083 × 10
106
u
48
+ 1.80477 × 10
107
u
47
+ ··· + 7.70077 × 10
108
b + 4.07046 × 10
109
,
6.39121 × 10
109
u
48
− 1.62145 × 10
110
u
47
+ ··· + 1.28603 × 10
111
a − 1.39682 × 10
112
,
u
49
− 2u
48
+ ··· − 1083u − 167i
I
u
2
= h−4356880u
16
+ 8072348u
15
+ ··· + 14725657b + 19826117,
15345062u
16
− 28541073u
15
+ ··· + 14725657a − 99165990, u
17
− u
16
+ ··· − 5u − 1i
I
u
3
= hb + 1, u
3
+ 2u
2
+ a − 1, u
4
+ 3u
3
+ 2u
2
+ 1i
I
u
4
= hb + 1, a + 2, u − 1i
* 4 irreducible components of dim
C
= 0, with total 71 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−9.68 × 10
106
u
48
+ 1.80 × 10
107
u
47
+ · · · + 7.70 × 10
108
b + 4.07 ×
10
109
, 6.39 × 10
109
u
48
− 1.62 × 10
110
u
47
+ · · · + 1.29 × 10
111
a − 1.40 ×
10
112
, u
49
− 2u
48
+ · · · − 1083u − 167i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
7
=
1
u
2
a
3
=
−0.0496973u
48
+ 0.126082u
47
+ ··· + 51.3655u + 10.8615
0.0125713u
48
− 0.0234362u
47
+ ··· − 23.9191u − 5.28578
a
10
=
−u
−u
3
+ u
a
2
=
−0.0371260u
48
+ 0.102646u
47
+ ··· + 27.4464u + 5.57574
0.0125713u
48
− 0.0234362u
47
+ ··· − 23.9191u − 5.28578
a
1
=
−0.0147332u
48
+ 0.0581855u
47
+ ··· − 5.41058u + 0.310122
0.0402524u
48
− 0.122863u
47
+ ··· − 26.9497u − 3.52830
a
5
=
−0.0182261u
48
+ 0.0716241u
47
+ ··· − 6.44692u − 6.24038
−0.152512u
48
+ 0.408573u
47
+ ··· + 193.403u + 40.3475
a
4
=
0.0676174u
48
− 0.168317u
47
+ ··· − 101.750u − 24.4584
−0.182706u
48
+ 0.491490u
47
+ ··· + 229.123u + 47.1670
a
12
=
−0.0147332u
48
+ 0.0581855u
47
+ ··· − 5.41058u + 0.310122
0.0101824u
48
− 0.0352370u
47
+ ··· + 1.69276u + 1.26781
a
8
=
0.0328901u
48
− 0.0927795u
47
+ ··· − 48.5742u − 1.25960
0.0758750u
48
− 0.205486u
47
+ ··· − 90.6780u − 20.9576
a
11
=
−0.0537472u
48
+ 0.151765u
47
+ ··· + 60.2707u + 8.53722
0.0318713u
48
− 0.0804240u
47
+ ··· − 41.2502u − 8.00996
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.462159u
48
− 1.17412u
47
+ ··· − 696.600u − 157.924
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
49
+ 29u
48
+ ··· + 3724u + 784
c
2
, c
5
u
49
− 3u
48
+ ··· − 70u + 28
c
3
u
49
+ 2u
48
+ ··· − 3520u + 227
c
4
, c
10
u
49
+ 3u
48
+ ··· − 60u + 29
c
6
, c
9
u
49
+ 2u
48
+ ··· − 1083u + 167
c
7
u
49
− 4u
48
+ ··· − 400u + 79
c
8
, c
11
, c
12
u
49
− 5u
48
+ ··· + 127u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
49
− 13y
48
+ ··· − 10750992y −614656
c
2
, c
5
y
49
− 29y
48
+ ··· + 3724y −784
c
3
y
49
− 86y
48
+ ··· + 4342796y −51529
c
4
, c
10
y
49
+ 61y
48
+ ··· − 7014y −841
c
6
, c
9
y
49
− 48y
48
+ ··· + 633479y −27889
c
7
y
49
− 6y
48
+ ··· + 26648y −6241
c
8
, c
11
, c
12
y
49
− 3y
48
+ ··· + 7771y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.850931 + 0.053544I
a = 0.104499 − 0.401543I
b = −0.905932 + 0.857759I
−3.32807 + 3.38377I −7.75310 − 1.13902I
u = −0.850931 − 0.053544I
a = 0.104499 + 0.401543I
b = −0.905932 − 0.857759I
−3.32807 − 3.38377I −7.75310 + 1.13902I
u = −0.718657 + 0.427589I
a = −0.668880 + 0.170629I
b = −0.699751 − 0.643620I
−3.14393 − 2.25034I −3.25983 + 3.67150I
u = −0.718657 − 0.427589I
a = −0.668880 − 0.170629I
b = −0.699751 + 0.643620I
−3.14393 + 2.25034I −3.25983 − 3.67150I
u = 0.212773 + 1.173370I
a = −0.478582 − 0.559994I
b = 1.032280 + 0.304555I
−0.81823 − 3.68405I 0
u = 0.212773 − 1.173370I
a = −0.478582 + 0.559994I
b = 1.032280 − 0.304555I
−0.81823 + 3.68405I 0
u = 0.285077 + 1.160990I
a = −0.507725 − 1.069200I
b = −0.362811 + 0.450437I
−3.86581 − 3.46047I 0
u = 0.285077 − 1.160990I
a = −0.507725 + 1.069200I
b = −0.362811 − 0.450437I
−3.86581 + 3.46047I 0
u = −1.165410 + 0.313519I
a = −0.211471 − 0.778096I
b = −0.044659 + 1.016460I
−1.48591 + 4.14998I 0
u = −1.165410 − 0.313519I
a = −0.211471 + 0.778096I
b = −0.044659 − 1.016460I
−1.48591 − 4.14998I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.220420 + 0.103596I
a = −0.409963 − 0.768191I
b = −1.44014 + 0.49949I
−5.69136 + 1.78229I 0
u = −1.220420 − 0.103596I
a = −0.409963 + 0.768191I
b = −1.44014 − 0.49949I
−5.69136 − 1.78229I 0
u = 1.259170 + 0.059094I
a = 0.228657 + 0.856126I
b = −0.126950 − 0.770054I
−2.40638 − 0.33187I 0
u = 1.259170 − 0.059094I
a = 0.228657 − 0.856126I
b = −0.126950 + 0.770054I
−2.40638 + 0.33187I 0
u = −1.184680 + 0.442717I
a = 0.330399 + 0.355978I
b = 0.824658 + 0.266758I
2.29612 − 1.29906I 0
u = −1.184680 − 0.442717I
a = 0.330399 − 0.355978I
b = 0.824658 − 0.266758I
2.29612 + 1.29906I 0
u = −0.268177 + 0.569650I
a = 0.806426 + 0.964971I
b = 0.227906 − 0.424848I
1.32877 − 0.64027I 5.53279 + 1.79656I
u = −0.268177 − 0.569650I
a = 0.806426 − 0.964971I
b = 0.227906 + 0.424848I
1.32877 + 0.64027I 5.53279 − 1.79656I
u = 1.367990 + 0.149902I
a = 0.15755 − 1.41438I
b = 1.29944 + 0.59734I
−12.95210 − 5.26540I 0
u = 1.367990 − 0.149902I
a = 0.15755 + 1.41438I
b = 1.29944 − 0.59734I
−12.95210 + 5.26540I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.28015 + 0.61372I
a = 0.78597 − 1.20619I
b = 0.988679 + 0.244010I
−5.81191 − 4.96842I 0
u = 1.28015 − 0.61372I
a = 0.78597 + 1.20619I
b = 0.988679 − 0.244010I
−5.81191 + 4.96842I 0
u = 1.12078 + 0.91260I
a = −0.551284 + 0.887947I
b = 0.754353 − 0.445736I
−5.19854 − 2.05240I 0
u = 1.12078 − 0.91260I
a = −0.551284 − 0.887947I
b = 0.754353 + 0.445736I
−5.19854 + 2.05240I 0
u = 1.43653 + 0.16422I
a = −0.358028 − 0.892202I
b = 0.171432 + 1.020400I
−9.49455 − 0.58370I 0
u = 1.43653 − 0.16422I
a = −0.358028 + 0.892202I
b = 0.171432 − 1.020400I
−9.49455 + 0.58370I 0
u = 0.526163
a = 1.19463
b = −0.608001
−1.12208 −10.0430
u = −0.520256 + 0.072784I
a = −0.63731 + 1.59304I
b = 0.871886 − 0.778003I
4.54654 + 2.92338I −9.70360 − 6.96370I
u = −0.520256 − 0.072784I
a = −0.63731 − 1.59304I
b = 0.871886 + 0.778003I
4.54654 − 2.92338I −9.70360 + 6.96370I
u = −1.40029 + 0.51673I
a = 0.253189 + 1.133510I
b = 1.33405 − 0.50974I
−5.71203 + 9.55647I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40029 − 0.51673I
a = 0.253189 − 1.133510I
b = 1.33405 + 0.50974I
−5.71203 − 9.55647I 0
u = −1.50499 + 0.03703I
a = 0.135912 − 0.745098I
b = 1.44136 + 0.38763I
−15.0837 + 3.2894I 0
u = −1.50499 − 0.03703I
a = 0.135912 + 0.745098I
b = 1.44136 − 0.38763I
−15.0837 − 3.2894I 0
u = 1.47957 + 0.40480I
a = −0.074080 + 1.221990I
b = −1.202330 − 0.506289I
−5.53719 − 4.43702I 0
u = 1.47957 − 0.40480I
a = −0.074080 − 1.221990I
b = −1.202330 + 0.506289I
−5.53719 + 4.43702I 0
u = −1.50367 + 0.38165I
a = 0.139516 + 0.920366I
b = −0.161176 − 1.103200I
−9.77091 + 8.62339I 0
u = −1.50367 − 0.38165I
a = 0.139516 − 0.920366I
b = −0.161176 + 1.103200I
−9.77091 − 8.62339I 0
u = −0.249001 + 0.193937I
a = 3.79562 − 2.57743I
b = −0.883863 + 0.524484I
3.15492 + 2.13839I −0.12860 − 2.71183I
u = −0.249001 − 0.193937I
a = 3.79562 + 2.57743I
b = −0.883863 − 0.524484I
3.15492 − 2.13839I −0.12860 + 2.71183I
u = 0.197940 + 0.226170I
a = −4.74888 − 2.79183I
b = 1.246010 − 0.150153I
−8.82996 + 3.71591I −8.95298 − 2.19762I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.197940 − 0.226170I
a = −4.74888 + 2.79183I
b = 1.246010 + 0.150153I
−8.82996 − 3.71591I −8.95298 + 2.19762I
u = 1.67411 + 0.47879I
a = 0.207774 − 0.858058I
b = 1.189780 + 0.403248I
−6.21895 − 4.32179I 0
u = 1.67411 − 0.47879I
a = 0.207774 + 0.858058I
b = 1.189780 − 0.403248I
−6.21895 + 4.32179I 0
u = −1.68681 + 0.54892I
a = −0.116244 − 1.107380I
b = −1.32009 + 0.60354I
−13.3928 + 14.7009I 0
u = −1.68681 − 0.54892I
a = −0.116244 + 1.107380I
b = −1.32009 − 0.60354I
−13.3928 − 14.7009I 0
u = 1.80483 + 0.31448I
a = −0.085676 + 0.557680I
b = −1.35959 − 0.40465I
−14.4034 − 5.4986I 0
u = 1.80483 − 0.31448I
a = −0.085676 − 0.557680I
b = −1.35959 + 0.40465I
−14.4034 + 5.4986I 0
u = 0.89129 + 1.69936I
a = 0.290327 + 0.793046I
b = −1.070560 − 0.387674I
−5.92444 − 6.99855I 0
u = 0.89129 − 1.69936I
a = 0.290327 − 0.793046I
b = −1.070560 + 0.387674I
−5.92444 + 6.99855I 0
9
II.
I
u
2
= h−4.36 × 10
6
u
16
+ 8.07 × 10
6
u
15
+ · · · + 1.47 × 10
7
b + 1.98 × 10
7
, 1.53 ×
10
7
u
16
− 2.85 × 10
7
u
15
+ · · · + 1.47 × 10
7
a − 9.92 × 10
7
, u
17
− u
16
+ · · · − 5u − 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
7
=
1
u
2
a
3
=
−1.04206u
16
+ 1.93819u
15
+ ··· + 21.4169u + 6.73423
0.295870u
16
− 0.548183u
15
+ ··· − 5.56821u − 1.34637
a
10
=
−u
−u
3
+ u
a
2
=
−0.746193u
16
+ 1.39000u
15
+ ··· + 15.8487u + 5.38787
0.295870u
16
− 0.548183u
15
+ ··· − 5.56821u − 1.34637
a
1
=
0.878435u
16
− 0.528983u
15
+ ··· + 7.77681u − 5.08941
−0.0718985u
16
+ 0.127527u
15
+ ··· − 0.371082u + 2.59084
a
5
=
2.09405u
16
− 2.55950u
15
+ ··· − 6.65219u − 5.86775
−1.19341u
16
+ 1.25712u
15
+ ··· + 3.60488u + 2.71050
a
4
=
2.43046u
16
− 2.74542u
15
+ ··· − 5.93479u − 5.57732
−1.03784u
16
+ 1.06714u
15
+ ··· + 3.97631u + 2.57055
a
12
=
0.878435u
16
− 0.528983u
15
+ ··· + 7.77681u − 5.08941
−0.231578u
16
+ 0.469827u
15
+ ··· + 2.25461u + 2.94030
a
8
=
−u
16
+ u
15
+ ··· − 6u + 6
0.910587u
16
− 1.03215u
15
+ ··· + 1.54869u − 2.77612
a
11
=
0.349452u
16
− 0.509132u
15
+ ··· − 0.697239u + 0.878435
0.0785691u
16
+ 0.224318u
15
+ ··· + 4.40810u + 0.117874
(ii) Obstruction class = 1
(iii) Cusp Shapes =
44098255
14725657
u
16
−
9781706
14725657
u
15
+ ··· +
81882286
14725657
u +
161815615
14725657
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 9u
16
+ ··· + 12u − 1
c
2
u
17
− u
16
+ ··· + 6u
2
− 1
c
3
u
17
+ u
16
+ ··· + 13u
2
− 1
c
4
u
17
+ 10u
15
+ ··· + 2u − 1
c
5
u
17
+ u
16
+ ··· − 6u
2
+ 1
c
6
u
17
− u
16
+ ··· − 5u − 1
c
7
u
17
+ 3u
16
+ ··· − u
2
+ 1
c
8
u
17
− 4u
16
+ ··· − 3u + 1
c
9
u
17
+ u
16
+ ··· − 5u + 1
c
10
u
17
+ 10u
15
+ ··· + 2u + 1
c
11
, c
12
u
17
+ 4u
16
+ ··· − 3u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 7y
16
+ ··· + 8y −1
c
2
, c
5
y
17
− 9y
16
+ ··· + 12y −1
c
3
y
17
− 11y
16
+ ··· + 26y −1
c
4
, c
10
y
17
+ 20y
16
+ ··· − 28y −1
c
6
, c
9
y
17
− 17y
16
+ ··· + 37y −1
c
7
y
17
+ 9y
16
+ ··· + 2y −1
c
8
, c
11
, c
12
y
17
− 16y
16
+ ··· + y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.957854 + 0.298951I
a = −0.334041 + 0.709299I
b = −0.650226 − 0.887312I
−2.95875 − 4.08497I −3.71386 + 10.03298I
u = 0.957854 − 0.298951I
a = −0.334041 − 0.709299I
b = −0.650226 + 0.887312I
−2.95875 + 4.08497I −3.71386 − 10.03298I
u = −0.963042 + 0.343353I
a = −0.229026 − 0.855460I
b = −0.904042 − 0.243298I
1.77275 − 1.07365I −7.71871 − 0.81835I
u = −0.963042 − 0.343353I
a = −0.229026 + 0.855460I
b = −0.904042 + 0.243298I
1.77275 + 1.07365I −7.71871 + 0.81835I
u = −1.042230 + 0.131331I
a = 0.46890 − 1.60505I
b = −0.876881 + 0.678116I
1.44921 + 2.62103I −4.44930 − 3.32170I
u = −1.042230 − 0.131331I
a = 0.46890 + 1.60505I
b = −0.876881 − 0.678116I
1.44921 − 2.62103I −4.44930 + 3.32170I
u = 0.764814 + 0.879583I
a = −0.14665 + 1.60242I
b = 0.601934 − 0.283302I
−4.94180 − 3.21948I −5.99068 + 3.01805I
u = 0.764814 − 0.879583I
a = −0.14665 − 1.60242I
b = 0.601934 + 0.283302I
−4.94180 + 3.21948I −5.99068 − 3.01805I
u = 1.300670 + 0.072680I
a = −0.279715 + 0.828722I
b = −1.283940 − 0.573989I
−5.30566 − 2.10327I −5.60859 + 5.91464I
u = 1.300670 − 0.072680I
a = −0.279715 − 0.828722I
b = −1.283940 + 0.573989I
−5.30566 + 2.10327I −5.60859 − 5.91464I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.520538
a = 2.67975
b = −0.547185
−0.370928 3.41290
u = 1.35710 + 1.09082I
a = −0.108411 − 1.235250I
b = 1.120510 + 0.397524I
−6.97220 − 6.27581I −9.68626 + 6.62498I
u = 1.35710 − 1.09082I
a = −0.108411 + 1.235250I
b = 1.120510 − 0.397524I
−6.97220 + 6.27581I −9.68626 − 6.62498I
u = −0.243492 + 0.067657I
a = −1.97435 + 2.90440I
b = 0.880570 − 0.722002I
4.91174 + 2.75823I 9.07218 + 0.56830I
u = −0.243492 − 0.067657I
a = −1.97435 − 2.90440I
b = 0.880570 + 0.722002I
4.91174 − 2.75823I 9.07218 − 0.56830I
u = −1.89195 + 0.35480I
a = 0.263422 − 0.162539I
b = 0.885671 + 0.299147I
−0.92930 − 1.29681I −0.11122 + 4.93024I
u = −1.89195 − 0.35480I
a = 0.263422 + 0.162539I
b = 0.885671 − 0.299147I
−0.92930 + 1.29681I −0.11122 − 4.93024I
14
III. I
u
3
= hb + 1, u
3
+ 2u
2
+ a − 1, u
4
+ 3u
3
+ 2u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
7
=
1
u
2
a
3
=
−u
3
− 2u
2
+ 1
−1
a
10
=
−u
−u
3
+ u
a
2
=
−u
3
− 2u
2
−1
a
1
=
−1
0
a
5
=
−u
3
− 2u
2
+ 1
−1
a
4
=
−3u
3
− 5u
2
−3u
3
− 4u
2
+ 2u − 3
a
12
=
−1
−u
2
a
8
=
−u
−u
3
+ u
a
11
=
u
2
− 1
−3u
3
− 4u
2
− 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u + 1)
4
c
3
, c
4
, c
7
c
10
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
6
, c
9
u
4
− 3u
3
+ 2u
2
+ 1
c
8
, c
11
, c
12
u
4
+ 3u
3
+ 2u
2
+ 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
, c
7
c
10
y
4
+ 3y
3
+ 2y
2
+ 1
c
6
, c
8
, c
9
c
11
, c
12
y
4
− 5y
3
+ 6y
2
+ 4y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.192440 + 0.547877I
a = 1.69244 − 0.31815I
b = −1.00000
−1.64493 −6.00000
u = 0.192440 − 0.547877I
a = 1.69244 + 0.31815I
b = −1.00000
−1.64493 −6.00000
u = −1.69244 + 0.31815I
a = −0.192440 − 0.547877I
b = −1.00000
−1.64493 −6.00000
u = −1.69244 − 0.31815I
a = −0.192440 + 0.547877I
b = −1.00000
−1.64493 −6.00000
18
IV. I
u
4
= hb + 1, a + 2, u − 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
1
a
7
=
1
1
a
3
=
−2
−1
a
10
=
−1
0
a
2
=
−3
−1
a
1
=
−1
0
a
5
=
−2
−1
a
4
=
−1
−1
a
12
=
−1
−1
a
8
=
−1
0
a
11
=
0
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
9
u + 1
c
3
, c
4
, c
7
c
8
, c
10
, c
11
c
12
u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −2.00000
b = −1.00000
−1.64493 −6.00000
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u + 1)
5
)(u
17
− 9u
16
+ ··· + 12u − 1)(u
49
+ 29u
48
+ ··· + 3724u + 784)
c
2
((u + 1)
5
)(u
17
− u
16
+ ··· + 6u
2
− 1)(u
49
− 3u
48
+ ··· − 70u + 28)
c
3
(u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
17
+ u
16
+ ··· + 13u
2
− 1)
· (u
49
+ 2u
48
+ ··· − 3520u + 227)
c
4
(u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
17
+ 10u
15
+ ··· + 2u − 1)
· (u
49
+ 3u
48
+ ··· − 60u + 29)
c
5
((u + 1)
5
)(u
17
+ u
16
+ ··· − 6u
2
+ 1)(u
49
− 3u
48
+ ··· − 70u + 28)
c
6
(u + 1)(u
4
− 3u
3
+ 2u
2
+ 1)(u
17
− u
16
+ ··· − 5u − 1)
· (u
49
+ 2u
48
+ ··· − 1083u + 167)
c
7
(u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
17
+ 3u
16
+ ··· − u
2
+ 1)
· (u
49
− 4u
48
+ ··· − 400u + 79)
c
8
(u − 1)(u
4
+ 3u
3
+ 2u
2
+ 1)(u
17
− 4u
16
+ ··· − 3u + 1)
· (u
49
− 5u
48
+ ··· + 127u + 7)
c
9
(u + 1)(u
4
− 3u
3
+ 2u
2
+ 1)(u
17
+ u
16
+ ··· − 5u + 1)
· (u
49
+ 2u
48
+ ··· − 1083u + 167)
c
10
(u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
17
+ 10u
15
+ ··· + 2u + 1)
· (u
49
+ 3u
48
+ ··· − 60u + 29)
c
11
, c
12
(u − 1)(u
4
+ 3u
3
+ 2u
2
+ 1)(u
17
+ 4u
16
+ ··· − 3u − 1)
· (u
49
− 5u
48
+ ··· + 127u + 7)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
5
)(y
17
+ 7y
16
+ ··· + 8y −1)
· (y
49
− 13y
48
+ ··· − 10750992y −614656)
c
2
, c
5
((y −1)
5
)(y
17
− 9y
16
+ ··· + 12y −1)(y
49
− 29y
48
+ ··· + 3724y −784)
c
3
(y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
17
− 11y
16
+ ··· + 26y −1)
· (y
49
− 86y
48
+ ··· + 4342796y −51529)
c
4
, c
10
(y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
17
+ 20y
16
+ ··· − 28y −1)
· (y
49
+ 61y
48
+ ··· − 7014y −841)
c
6
, c
9
(y −1)(y
4
− 5y
3
+ ··· + 4y + 1)(y
17
− 17y
16
+ ··· + 37y −1)
· (y
49
− 48y
48
+ ··· + 633479y −27889)
c
7
(y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
17
+ 9y
16
+ ··· + 2y −1)
· (y
49
− 6y
48
+ ··· + 26648y −6241)
c
8
, c
11
, c
12
(y −1)(y
4
− 5y
3
+ ··· + 4y + 1)(y
17
− 16y
16
+ ··· + y −1)
· (y
49
− 3y
48
+ ··· + 7771y −49)
24
