12n
0005
(K12n
0005
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 9 10 4 12 8 1 10
Solving Sequence
9,12
10
1,4
8 5 7 6 3 2 11
c
9
c
12
c
8
c
4
c
7
c
6
c
3
c
2
c
11
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.36971 × 10
37
u
58
− 2.98861 × 10
38
u
57
+ ··· + 7.91576 × 10
35
b − 5.88078 × 10
37
,
− 2.37843 × 10
37
u
58
+ 2.97918 × 10
38
u
57
+ ··· + 7.91576 × 10
35
a + 4.16646 × 10
37
,
u
59
− 13u
58
+ ··· − 10u + 1i
I
u
2
= ha
2
+ b + a − 1, a
4
+ a
3
− 2a
2
− a + 2, u + 1i
I
u
3
= hb, −u
2
a + a
2
+ 2au + 3u
2
− a − 5u + 4, u
3
− u
2
+ 1i
I
u
4
= ha
5
− 3a
4
+ 4a
2
+ b + a − 1, a
6
− 3a
5
+ 5a
3
− a
2
− 2a + 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 75 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
= h2.37 × 10
37
u
58
− 2.99 × 10
38
u
57
+ · · · + 7.92 × 10
35
b − 5.88 ×
10
37
, −2.38 × 10
37
u
58
+ 2.98 × 10
38
u
57
+ · · · + 7.92 × 10
35
a + 4.17 ×
10
37
, u
59
− 13u
58
+ · · · − 10u + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
30.0468u
58
− 376.361u
57
+ ··· + 458.241u − 52.6350
−29.9366u
58
+ 377.552u
57
+ ··· − 562.231u + 74.2920
a
8
=
−97.4057u
58
+ 1230.14u
57
+ ··· − 1933.17u + 261.759
43.2007u
58
− 546.214u
57
+ ··· + 862.007u − 117.674
a
5
=
81.4771u
58
− 1025.89u
57
+ ··· + 1495.08u − 200.409
−51.6915u
58
+ 650.519u
57
+ ··· − 976.689u + 133.016
a
7
=
−125.970u
58
+ 1593.18u
57
+ ··· − 2531.21u + 343.296
44.4332u
58
− 561.763u
57
+ ··· + 916.403u − 125.970
a
6
=
−81.5367u
58
+ 1031.41u
57
+ ··· − 1614.81u + 217.326
44.4332u
58
− 561.763u
57
+ ··· + 916.403u − 125.970
a
3
=
48.4210u
58
− 610.082u
57
+ ··· + 892.310u − 120.705
−39.1740u
58
+ 493.545u
57
+ ··· − 742.666u + 101.904
a
2
=
−39.3383u
58
+ 496.662u
57
+ ··· − 738.577u + 96.1780
0.368728u
58
− 5.81774u
57
+ ··· + 16.8281u + 0.227251
a
11
=
−u
3
u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −147.797u
58
+ 1865.74u
57
+ ··· − 2967.33u + 417.985
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
59
+ 31u
58
+ ··· + 42u − 1
c
2
, c
5
u
59
+ 5u
58
+ ··· + 2u − 1
c
3
u
59
− 5u
58
+ ··· + 4180u − 292
c
4
, c
8
u
59
− 2u
58
+ ··· + 160u − 64
c
6
u
59
− 4u
58
+ ··· − u − 1
c
7
, c
10
u
59
+ 3u
58
+ ··· − 1024u − 1024
c
9
, c
12
u
59
+ 13u
58
+ ··· − 10u − 1
c
11
u
59
− 13u
58
+ ··· + 36u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
59
− y
58
+ ··· + 2542y −1
c
2
, c
5
y
59
+ 31y
58
+ ··· + 42y −1
c
3
y
59
− 33y
58
+ ··· + 4654184y −85264
c
4
, c
8
y
59
+ 40y
58
+ ··· − 7168y −4096
c
6
y
59
− 74y
58
+ ··· + 5y −1
c
7
, c
10
y
59
+ 69y
58
+ ··· − 21495808y −1048576
c
9
, c
12
y
59
− 13y
58
+ ··· + 36y −1
c
11
y
59
+ 79y
58
+ ··· + 36y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.784682 + 0.615628I
a = −0.577187 − 0.016841I
b = 0.241820 + 0.743409I
−3.71513 + 1.17573I 0
u = 0.784682 − 0.615628I
a = −0.577187 + 0.016841I
b = 0.241820 − 0.743409I
−3.71513 − 1.17573I 0
u = −0.989776 + 0.099585I
a = 3.21578 + 0.56260I
b = −0.477754 − 0.051833I
1.37753 − 2.34293I 0
u = −0.989776 − 0.099585I
a = 3.21578 − 0.56260I
b = −0.477754 + 0.051833I
1.37753 + 2.34293I 0
u = −0.510073 + 0.880995I
a = −0.25877 − 1.72077I
b = 0.43412 − 1.37809I
−5.44078 − 7.86618I 0
u = −0.510073 − 0.880995I
a = −0.25877 + 1.72077I
b = 0.43412 + 1.37809I
−5.44078 + 7.86618I 0
u = −0.270574 + 0.893509I
a = 0.10250 − 1.64711I
b = 0.067786 − 1.398240I
−6.44229 + 0.85012I 0
u = −0.270574 − 0.893509I
a = 0.10250 + 1.64711I
b = 0.067786 + 1.398240I
−6.44229 − 0.85012I 0
u = −0.425431 + 0.780931I
a = 0.11679 + 1.89599I
b = −0.291336 + 1.236710I
−2.39339 − 3.03762I 3.87633 + 3.56282I
u = −0.425431 − 0.780931I
a = 0.11679 − 1.89599I
b = −0.291336 − 1.236710I
−2.39339 + 3.03762I 3.87633 − 3.56282I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.116770 + 0.010437I
a = −1.98632 + 0.23400I
b = 0.470430 + 0.432140I
2.06662 + 1.38182I 0
u = −1.116770 − 0.010437I
a = −1.98632 − 0.23400I
b = 0.470430 − 0.432140I
2.06662 − 1.38182I 0
u = 0.549864 + 0.598185I
a = −0.916575 + 0.380349I
b = 0.464850 + 0.860348I
−3.74978 + 1.11248I −1.95186 − 2.77586I
u = 0.549864 − 0.598185I
a = −0.916575 − 0.380349I
b = 0.464850 − 0.860348I
−3.74978 − 1.11248I −1.95186 + 2.77586I
u = 0.953228 + 0.719223I
a = 0.184839 + 0.296714I
b = 0.377691 − 0.510927I
−3.14792 + 4.18097I 0
u = 0.953228 − 0.719223I
a = 0.184839 − 0.296714I
b = 0.377691 + 0.510927I
−3.14792 − 4.18097I 0
u = −0.714347 + 0.335341I
a = −0.654918 − 0.346050I
b = −0.524386 − 0.448839I
0.703685 + 0.029466I 6.19093 + 0.45904I
u = −0.714347 − 0.335341I
a = −0.654918 + 0.346050I
b = −0.524386 + 0.448839I
0.703685 − 0.029466I 6.19093 − 0.45904I
u = −1.199090 + 0.275765I
a = −1.074520 − 0.161421I
b = 0.135658 − 1.049150I
0.491598 − 1.220580I 0
u = −1.199090 − 0.275765I
a = −1.074520 + 0.161421I
b = 0.135658 + 1.049150I
0.491598 + 1.220580I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.695422 + 0.239788I
a = −1.38241 − 0.41635I
b = 0.572360 + 1.047320I
−1.66131 + 8.15293I −0.65355 − 9.84045I
u = 0.695422 − 0.239788I
a = −1.38241 + 0.41635I
b = 0.572360 − 1.047320I
−1.66131 − 8.15293I −0.65355 + 9.84045I
u = −1.205170 + 0.432461I
a = 0.914841 + 0.101782I
b = 0.127563 + 1.275290I
−2.87819 + 2.67724I 0
u = −1.205170 − 0.432461I
a = 0.914841 − 0.101782I
b = 0.127563 − 1.275290I
−2.87819 − 2.67724I 0
u = −1.321580 + 0.290312I
a = 1.067150 + 0.011907I
b = −0.293061 + 1.285920I
−2.52983 − 5.56373I 0
u = −1.321580 − 0.290312I
a = 1.067150 − 0.011907I
b = −0.293061 − 1.285920I
−2.52983 + 5.56373I 0
u = 0.600679 + 0.233224I
a = 1.54602 + 0.26343I
b = −0.576951 − 0.942414I
0.49550 + 3.30615I 3.00875 − 4.91162I
u = 0.600679 − 0.233224I
a = 1.54602 − 0.26343I
b = −0.576951 + 0.942414I
0.49550 − 3.30615I 3.00875 + 4.91162I
u = 0.974533 + 0.944343I
a = −0.031805 + 0.507306I
b = 1.139410 − 0.115232I
−4.99278 + 3.48527I 0
u = 0.974533 − 0.944343I
a = −0.031805 − 0.507306I
b = 1.139410 + 0.115232I
−4.99278 − 3.48527I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.951583 + 0.976048I
a = 0.53629 − 1.61324I
b = −0.007849 − 1.197600I
−5.80099 + 0.66681I 0
u = 0.951583 − 0.976048I
a = 0.53629 + 1.61324I
b = −0.007849 + 1.197600I
−5.80099 − 0.66681I 0
u = −0.619938
a = −0.614103
b = −0.379392
0.987384 10.0830
u = 1.008230 + 0.949033I
a = −0.79603 + 1.60808I
b = 0.203594 + 1.201400I
−5.61803 + 6.41573I 0
u = 1.008230 − 0.949033I
a = −0.79603 − 1.60808I
b = 0.203594 − 1.201400I
−5.61803 − 6.41573I 0
u = 0.938768 + 1.039960I
a = 0.071965 − 0.567951I
b = −1.352110 − 0.109099I
−8.53769 − 0.57441I 0
u = 0.938768 − 1.039960I
a = 0.071965 + 0.567951I
b = −1.352110 + 0.109099I
−8.53769 + 0.57441I 0
u = 0.830681 + 1.132630I
a = 0.214753 − 1.117890I
b = 0.48779 − 1.44380I
−9.96117 − 2.30085I 0
u = 0.830681 − 1.132630I
a = 0.214753 + 1.117890I
b = 0.48779 + 1.44380I
−9.96117 + 2.30085I 0
u = 0.79029 + 1.17849I
a = −0.187003 + 1.000660I
b = −0.63460 + 1.49501I
−13.0111 − 7.6806I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.79029 − 1.17849I
a = −0.187003 − 1.000660I
b = −0.63460 − 1.49501I
−13.0111 + 7.6806I 0
u = 1.05544 + 0.97189I
a = −0.008379 − 0.550553I
b = −1.335610 + 0.298327I
−8.15213 + 7.92720I 0
u = 1.05544 − 0.97189I
a = −0.008379 + 0.550553I
b = −1.335610 − 0.298327I
−8.15213 − 7.92720I 0
u = 0.91193 + 1.16122I
a = −0.388353 + 1.105940I
b = −0.33596 + 1.61613I
−14.8409 + 1.7634I 0
u = 0.91193 − 1.16122I
a = −0.388353 − 1.105940I
b = −0.33596 − 1.61613I
−14.8409 − 1.7634I 0
u = 1.14928 + 0.92975I
a = −1.11279 + 1.27285I
b = 0.61505 + 1.37396I
−8.89854 + 9.77362I 0
u = 1.14928 − 0.92975I
a = −1.11279 − 1.27285I
b = 0.61505 − 1.37396I
−8.89854 − 9.77362I 0
u = −0.217989 + 0.462422I
a = 0.352972 + 0.713663I
b = 0.883278 + 0.005614I
−1.01117 − 2.91966I 2.05527 + 5.38795I
u = −0.217989 − 0.462422I
a = 0.352972 − 0.713663I
b = 0.883278 − 0.005614I
−1.01117 + 2.91966I 2.05527 − 5.38795I
u = 1.18659 + 0.91747I
a = 1.16646 − 1.19440I
b = −0.73190 − 1.40356I
−11.6847 + 15.2392I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.18659 − 0.91747I
a = 1.16646 + 1.19440I
b = −0.73190 + 1.40356I
−11.6847 − 15.2392I 0
u = 1.14461 + 0.99662I
a = 0.96601 − 1.21203I
b = −0.49507 − 1.54081I
−14.0505 + 6.0390I 0
u = 1.14461 − 0.99662I
a = 0.96601 + 1.21203I
b = −0.49507 + 1.54081I
−14.0505 − 6.0390I 0
u = −0.442581 + 0.164163I
a = 0.19222 + 4.19542I
b = −0.094147 + 0.587865I
0.76407 − 2.30945I −0.54330 + 7.28911I
u = −0.442581 − 0.164163I
a = 0.19222 − 4.19542I
b = −0.094147 − 0.587865I
0.76407 + 2.30945I −0.54330 − 7.28911I
u = 0.321626 + 0.198610I
a = −1.71356 + 1.09600I
b = 0.744198 − 0.485695I
−0.01800 + 3.14526I 2.49375 − 2.79979I
u = 0.321626 − 0.198610I
a = −1.71356 − 1.09600I
b = 0.744198 + 0.485695I
−0.01800 − 3.14526I 2.49375 + 2.79979I
u = 0.375910 + 0.027813I
a = 2.24708 + 0.57233I
b = −0.625146 − 0.663345I
1.37130 + 1.43610I 4.58545 − 3.40911I
u = 0.375910 − 0.027813I
a = 2.24708 − 0.57233I
b = −0.625146 + 0.663345I
1.37130 − 1.43610I 4.58545 + 3.40911I
10
II. I
u
2
= ha
2
+ b + a − 1, a
4
+ a
3
− 2a
2
− a + 2, u + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
−1
a
10
=
1
−1
a
1
=
−1
0
a
4
=
a
−a
2
− a + 1
a
8
=
−a
3
− a
2
+ a + 1
a
3
+ a
2
− a − 1
a
5
=
−1
−a
2
+ 2
a
7
=
−a
3
− a
2
+ a + 1
a
3
+ a
2
− a − 1
a
6
=
0
a
3
+ a
2
− a − 1
a
3
=
a
a
3
+ a
2
− a − 1
a
2
=
−a
2
+ 1
a
3
+ 2a
2
− 1
a
11
=
1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3a
3
− 2a
2
− a + 10
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
4
− 2u
3
+ 3u
2
− u + 1
c
2
, c
4
u
4
+ u
2
+ u + 1
c
3
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
5
, c
8
u
4
+ u
2
− u + 1
c
7
, c
10
u
4
c
9
, c
11
(u + 1)
4
c
12
(u − 1)
4
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
2
, c
4
, c
5
c
8
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
3
y
4
− y
3
+ 2y
2
+ 7y + 4
c
7
, c
10
y
4
c
9
, c
11
, c
12
(y −1)
4
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.899232 + 0.400532I
b = −0.547424 − 1.120870I
−0.98010 + 7.64338I 6.92132 − 4.56334I
u = −1.00000
a = 0.899232 − 0.400532I
b = −0.547424 + 1.120870I
−0.98010 − 7.64338I 6.92132 + 4.56334I
u = −1.00000
a = −1.39923 + 0.32564I
b = 0.547424 + 0.585652I
2.62503 + 1.39709I 14.5787 − 4.1375I
u = −1.00000
a = −1.39923 − 0.32564I
b = 0.547424 − 0.585652I
2.62503 − 1.39709I 14.5787 + 4.1375I
14
III. I
u
3
= hb, −u
2
a + a
2
+ 2au + 3u
2
− a − 5u + 4, u
3
− u
2
+ 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
−u
2
a
1
=
u
−u
2
+ u + 1
a
4
=
a
0
a
8
=
1
0
a
5
=
a
0
a
7
=
−u
2
+ 1
u
2
− u − 1
a
6
=
−u
u
2
− u − 1
a
3
=
−au
2u
2
a − au − 2a
a
2
=
−au − u
2
+ 2u − 1
2u
2
a − au − 2a
a
11
=
−u
2
+ 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
2
a − 3au + 3u
2
− 8a − 9u + 10
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
3
c
2
(u
2
+ u + 1)
3
c
4
, c
8
u
6
c
6
(u
3
− 3u
2
+ 2u + 1)
2
c
7
, c
11
(u
3
+ u
2
+ 2u + 1)
2
c
9
(u
3
− u
2
+ 1)
2
c
10
(u
3
− u
2
+ 2u − 1)
2
c
12
(u
3
+ u
2
− 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
3
c
4
, c
8
y
6
c
6
(y
3
− 5y
2
+ 10y −1)
2
c
7
, c
10
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
c
9
, c
12
(y
3
− y
2
+ 2y −1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.111778 − 0.558770I
b = 0
−3.02413 + 4.85801I 4.05323 − 9.17563I
u = 0.877439 + 0.744862I
a = −0.428020 + 0.376187I
b = 0
−3.02413 + 0.79824I 7.63258 + 1.54443I
u = 0.877439 − 0.744862I
a = −0.111778 + 0.558770I
b = 0
−3.02413 − 4.85801I 4.05323 + 9.17563I
u = 0.877439 − 0.744862I
a = −0.428020 − 0.376187I
b = 0
−3.02413 − 0.79824I 7.63258 − 1.54443I
u = −0.754878
a = 1.53980 + 2.66701I
b = 0
1.11345 − 2.02988I 15.8142 − 4.6579I
u = −0.754878
a = 1.53980 − 2.66701I
b = 0
1.11345 + 2.02988I 15.8142 + 4.6579I
18
IV. I
u
4
= ha
5
− 3a
4
+ 4a
2
+ b + a − 1, a
6
− 3a
5
+ 5a
3
− a
2
− 2a + 1, u + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
−1
a
10
=
1
−1
a
1
=
−1
0
a
4
=
a
−a
5
+ 3a
4
− 4a
2
− a + 1
a
8
=
a
3
− 2a
2
− a + 2
−a
3
+ 2a
2
+ a − 2
a
5
=
−a
5
+ 2a
4
+ 2a
3
− 3a
2
− 2a + 1
a
4
− 2a
3
− a
2
+ 2a
a
7
=
a
3
− 2a
2
− a + 2
−a
3
+ 2a
2
+ a − 2
a
6
=
0
−a
3
+ 2a
2
+ a − 2
a
3
=
a
a
3
− a
2
− 2a
a
2
=
−a
4
+ a
3
+ 2a
2
− 1
−a
5
+ 3a
4
+ a
3
− 5a
2
− 2a + 1
a
11
=
1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5a
4
+ 8a
3
+ 8a
2
− 8a + 4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
2
, c
4
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
3
(u
3
− u
2
+ 1)
2
c
5
, c
8
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
7
, c
10
u
6
c
9
, c
11
(u + 1)
6
c
12
(u − 1)
6
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
4
, c
5
c
8
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
3
(y
3
− y
2
+ 2y −1)
2
c
7
, c
10
y
6
c
9
, c
11
, c
12
(y −1)
6
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.897438 + 0.201182I
b = 0.498832 − 1.001300I
1.37919 − 2.82812I 10.11473 + 2.08748I
u = −1.00000
a = −0.897438 − 0.201182I
b = 0.498832 + 1.001300I
1.37919 + 2.82812I 10.11473 − 2.08748I
u = −1.00000
a = 0.500000 + 0.273346I
b = −0.284920 − 1.115140I
−2.75839 1.72561 + 0.99756I
u = −1.00000
a = 0.500000 − 0.273346I
b = −0.284920 + 1.115140I
−2.75839 1.72561 − 0.99756I
u = −1.00000
a = 1.89744 + 0.20118I
b = −0.713912 + 0.305839I
1.37919 + 2.82812I 9.65966 − 5.36114I
u = −1.00000
a = 1.89744 − 0.20118I
b = −0.713912 − 0.305839I
1.37919 − 2.82812I 9.65966 + 5.36114I
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
3
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
59
+ 31u
58
+ ··· + 42u − 1)
c
2
(u
2
+ u + 1)
3
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
59
+ 5u
58
+ ··· + 2u − 1)
c
3
(u
2
− u + 1)
3
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
59
− 5u
58
+ ··· + 4180u − 292)
c
4
u
6
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
59
− 2u
58
+ ··· + 160u − 64)
c
5
(u
2
− u + 1)
3
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
59
+ 5u
58
+ ··· + 2u − 1)
c
6
((u
3
− 3u
2
+ 2u + 1)
2
)(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ ··· − 2u
3
+ 1)
· (u
59
− 4u
58
+ ··· − u − 1)
c
7
u
10
(u
3
+ u
2
+ 2u + 1)
2
(u
59
+ 3u
58
+ ··· − 1024u − 1024)
c
8
u
6
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
59
− 2u
58
+ ··· + 160u − 64)
c
9
((u + 1)
10
)(u
3
− u
2
+ 1)
2
(u
59
+ 13u
58
+ ··· − 10u − 1)
c
10
u
10
(u
3
− u
2
+ 2u − 1)
2
(u
59
+ 3u
58
+ ··· − 1024u − 1024)
c
11
((u + 1)
10
)(u
3
+ u
2
+ 2u + 1)
2
(u
59
− 13u
58
+ ··· + 36u − 1)
c
12
((u − 1)
10
)(u
3
+ u
2
− 1)
2
(u
59
+ 13u
58
+ ··· − 10u − 1)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
3
)(y
4
+ 2y
3
+ ··· + 5y + 1)(y
6
− y
5
+ ··· + 8y
2
+ 1)
· (y
59
− y
58
+ ··· + 2542y −1)
c
2
, c
5
(y
2
+ y + 1)
3
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
59
+ 31y
58
+ ··· + 42y −1)
c
3
(y
2
+ y + 1)
3
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
59
− 33y
58
+ ··· + 4654184y −85264)
c
4
, c
8
y
6
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
59
+ 40y
58
+ ··· − 7168y −4096)
c
6
(y
3
− 5y
2
+ 10y −1)
2
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
· (y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)(y
59
− 74y
58
+ ··· + 5y −1)
c
7
, c
10
y
10
(y
3
+ 3y
2
+ 2y −1)
2
(y
59
+ 69y
58
+ ··· − 2.14958 × 10
7
y −1048576)
c
9
, c
12
((y −1)
10
)(y
3
− y
2
+ 2y −1)
2
(y
59
− 13y
58
+ ··· + 36y −1)
c
11
((y −1)
10
)(y
3
+ 3y
2
+ 2y −1)
2
(y
59
+ 79y
58
+ ··· + 36y −1)
24
