12n
0102
(K12n
0102
)
A knot diagram
1
Linearized knot diagam
3 5 6 2 10 4 11 5 12 8 6 9
Solving Sequence
7,11 4,8
6 12 3 10 5 2 1 9
c
7
c
6
c
11
c
3
c
10
c
5
c
2
c
1
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h8320485u
18
+ 10563177u
17
+ ··· + 38476288b − 13934311,
577476311u
18
+ 1351379411u
17
+ ··· + 615620608a − 4237296637, u
19
+ 2u
18
+ ··· − 7u + 1i
I
u
2
= h6839a
5
u + 100530a
4
u + ··· − 679911a + 101996,
a
6
+ 5a
5
u − 6a
5
− 20a
4
u + 2a
4
+ 16a
3
u + 22a
3
+ 6a
2
u − 29a
2
− 8au + 7a + u, u
2
+ 1i
I
u
3
= hb, 5u
2
+ 4a + 3u + 11, u
3
+ 2u − 1i
I
u
4
= h−4214u
9
− 17396u
8
+ ··· + 334809b − 381952,
− 40716u
9
+ 776951u
8
+ ··· + 5691753a − 2589163,
u
10
− u
8
+ 15u
6
− u
5
+ 57u
4
+ 7u
3
+ 56u
2
+ 12u + 17i
I
u
5
= hb, u
3
+ a + u, u
4
+ u
3
+ 2u
2
+ 2u + 1i
* 5 irreducible components of dim
C
= 0, with total 48 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
= h8.32 × 10
6
u
18
+ 1 .06 × 10
7
u
17
+ · · · + 3.85 × 10
7
b − 1.39 × 10
7
, 5.77 ×
10
8
u
18
+1.35×10
9
u
17
+· · ·+6.16×10
8
a−4.24×10
9
, u
19
+2u
18
+· · · −7u +1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
−0.938039u
18
− 2.19515u
17
+ ··· − 14.3029u + 6.88297
−0.216250u
18
− 0.274537u
17
+ ··· − 5.00433u + 0.362153
a
8
=
1
u
2
a
6
=
0.628575u
18
+ 1.63591u
17
+ ··· − 1.38123u − 0.584679
−0.299899u
18
− 0.718244u
17
+ ··· + 0.505642u − 0.218705
a
12
=
0.00390625u
18
+ 0.00390625u
17
+ ··· + 1.96875u − 0.996094
0.00781250u
18
+ 0.00781250u
17
+ ··· + 1.93750u + 0.00781250
a
3
=
−0.437270u
18
− 1.23881u
17
+ ··· − 4.63744u + 5.33139
0.000159761u
18
+ 0.202746u
17
+ ··· − 8.42258u + 0.956342
a
10
=
u
u
3
+ u
a
5
=
0.602641u
18
+ 1.62088u
17
+ ··· − 3.67950u − 0.116155
−0.324143u
18
− 0.736442u
17
+ ··· − 1.50878u + 0.212974
a
2
=
−1.35943u
18
− 3.14988u
17
+ ··· − 11.6390u + 6.93843
0.201483u
18
+ 0.509159u
17
+ ··· − 3.35421u + 0.130337
a
1
=
−0.00781250u
18
− 0.00781250u
17
+ ··· − 1.93750u + 0.992188
−0.0156250u
18
− 0.0156250u
17
+ ··· − 1.87500u − 0.0156250
a
9
=
0.00390625u
18
+ 0.00390625u
17
+ ··· + 1.96875u + 0.00390625
0.00781250u
18
+ 0.00781250u
17
+ ··· + 0.937500u + 0.00781250
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
9530088851
2462482432
u
18
−
22393935231
2462482432
u
17
+ ··· −
7325733887
615620608
u +
3696058001
2462482432
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
+ 18u
18
+ ··· + 45729u + 256
c
2
, c
4
u
19
− 4u
18
+ ··· + 225u − 16
c
3
, c
6
u
19
+ 3u
18
+ ··· + 688u + 128
c
5
u
19
− 6u
18
+ ··· + 12u − 4
c
7
, c
9
, c
10
c
12
u
19
− 2u
18
+ ··· − 7u − 1
c
8
, c
11
u
19
− 29u
17
+ ··· − 320u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
− 46y
18
+ ··· + 1968323393y −65536
c
2
, c
4
y
19
− 18y
18
+ ··· + 45729y −256
c
3
, c
6
y
19
+ 9y
18
+ ··· + 214272y −16384
c
5
y
19
− 2y
18
+ ··· + 152y −16
c
7
, c
9
, c
10
c
12
y
19
+ 2y
18
+ ··· − y −1
c
8
, c
11
y
19
− 58y
18
+ ··· + 106496y −4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.065994 + 0.703453I
a = 1.146140 − 0.182747I
b = −1.168000 + 0.494902I
2.15420 − 5.93819I −10.00409 + 7.04982I
u = 0.065994 − 0.703453I
a = 1.146140 + 0.182747I
b = −1.168000 − 0.494902I
2.15420 + 5.93819I −10.00409 − 7.04982I
u = 1.308400 + 0.398474I
a = 0.207847 + 1.170010I
b = 0.312558 + 1.138020I
−3.47657 − 1.31737I −6.24812 − 2.66398I
u = 1.308400 − 0.398474I
a = 0.207847 − 1.170010I
b = 0.312558 − 1.138020I
−3.47657 + 1.31737I −6.24812 + 2.66398I
u = −0.072468 + 0.615756I
a = −1.048370 + 0.662466I
b = 1.211950 − 0.244182I
3.66948 − 0.63571I −5.45626 − 0.87908I
u = −0.072468 − 0.615756I
a = −1.048370 − 0.662466I
b = 1.211950 + 0.244182I
3.66948 + 0.63571I −5.45626 + 0.87908I
u = 0.531110
a = 0.510168
b = −0.274813
−0.869373 −11.1210
u = −0.27618 + 1.56855I
a = 0.0759776 + 0.1041410I
b = 0.191656 − 0.770544I
7.41380 + 4.96650I −10.42447 + 0.17242I
u = −0.27618 − 1.56855I
a = 0.0759776 − 0.1041410I
b = 0.191656 + 0.770544I
7.41380 − 4.96650I −10.42447 − 0.17242I
u = 0.087202 + 0.342519I
a = 1.53123 + 0.07499I
b = −0.140322 − 0.778902I
−0.99829 − 1.27054I −8.20061 + 4.97839I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.087202 − 0.342519I
a = 1.53123 − 0.07499I
b = −0.140322 + 0.778902I
−0.99829 + 1.27054I −8.20061 − 4.97839I
u = −1.54056 + 0.78681I
a = −0.421033 + 1.025860I
b = 0.73485 + 2.99107I
−5.13904 + 5.65628I −9.07225 − 4.94267I
u = −1.54056 − 0.78681I
a = −0.421033 − 1.025860I
b = 0.73485 − 2.99107I
−5.13904 − 5.65628I −9.07225 + 4.94267I
u = 0.234786
a = 6.08809
b = −0.438368
−2.17097 4.15310
u = −1.03991 + 1.54219I
a = 0.810661 − 0.834761I
b = −1.49692 − 1.76255I
−12.3003 + 14.4824I −6.92108 − 6.18391I
u = −1.03991 − 1.54219I
a = 0.810661 + 0.834761I
b = −1.49692 + 1.76255I
−12.3003 − 14.4824I −6.92108 + 6.18391I
u = −1.86882
a = −0.500182
b = −3.63345
−8.22250 −12.0580
u = 1.01897 + 1.61412I
a = −0.726491 − 0.564033I
b = 1.02754 − 1.79037I
−12.01080 − 6.53502I −7.12923 + 2.43738I
u = 1.01897 − 1.61412I
a = −0.726491 + 0.564033I
b = 1.02754 + 1.79037I
−12.01080 + 6.53502I −7.12923 − 2.43738I
6
II. I
u
2
= h6839a
5
u + 1.01 × 10
5
a
4
u + · · · − 6.80 × 10
5
a + 1.02 × 10
5
, 5a
5
u −
20a
4
u + · · · − 29a
2
+ 7a, u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
a
−0.163327a
5
u − 2.40083a
4
u + ··· + 16.2375a − 2.43584
a
8
=
1
−1
a
6
=
0.0197263a
5
u − 0.856399a
4
u + ··· + 3.63150a + 0.836673
−0.0806247a
5
u + 0.463927a
4
u + ··· − 1.15007a + 0.616698
a
12
=
0.476488a
5
u − 1.95505a
4
u + ··· − 5.95668a + 1.47857
−1
a
3
=
0.0829652a
5
u + 3.40057a
4
u + ··· − 16.6394a + 2.51647
−0.546629a
5
u + 2.89361a
4
u + ··· + 3.20882a − 2.34698
a
10
=
u
0
a
5
=
0.100351a
5
u − 1.32033a
4
u + ··· + 4.78158a + 0.219975
−0.0806247a
5
u + 0.463927a
4
u + ··· − 1.15007a + 0.616698
a
2
=
0.121486a
5
u + 0.333532a
4
u + ··· − 4.75610a + 1.54498
−0.186540a
5
u + 2.61663a
4
u + ··· − 7.68727a + 0.569914
a
1
=
−1
0
a
9
=
0.113677a
5
u − 2.86738a
4
u + ··· + 7.36799a + 0.753708
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
6556
41873
a
5
u −
362488
41873
a
4
u + ··· +
1586112
41873
a −
146544
41873
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
2
, c
6
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
3
, c
4
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
5
u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1
c
7
, c
9
, c
10
c
12
(u
2
+ 1)
6
c
8
u
12
− 2u
11
+ ··· − 192u + 64
c
11
u
12
+ 2u
11
+ ··· + 192u + 64
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
2
, c
3
, c
4
c
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
5
(y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
c
7
, c
9
, c
10
c
12
(y + 1)
12
c
8
, c
11
y
12
− 12y
10
+ 736y
8
− 3584y
6
+ 9472y
4
− 9216y
2
+ 4096
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.217590 + 0.251449I
b = −1.073950 − 0.558752I
3.28987 + 5.69302I −2.00000 − 5.51057I
u = 1.000000I
a = −1.010760 − 0.965580I
b = 1.002190 + 0.295542I
5.18047 + 0.92430I 1.71672 − 0.79423I
u = 1.000000I
a = 0.318306 − 0.177934I
b = 1.002190 − 0.295542I
5.18047 − 0.92430I 1.71672 + 0.79423I
u = 1.000000I
a = 0.100084 − 0.103550I
b = −1.073950 + 0.558752I
3.28987 − 5.69302I −2.00000 + 5.51057I
u = 1.000000I
a = 2.39185 − 1.23447I
b = −0.428243 + 0.664531I
1.39926 + 0.92430I −5.71672 − 0.79423I
u = 1.000000I
a = 2.98293 − 2.76991I
b = −0.428243 − 0.664531I
1.39926 − 0.92430I −5.71672 + 0.79423I
u = − 1.000000I
a = 1.217590 − 0.251449I
b = −1.073950 + 0.558752I
3.28987 − 5.69302I −2.00000 + 5.51057I
u = − 1.000000I
a = −1.010760 + 0.965580I
b = 1.002190 − 0.295542I
5.18047 − 0.92430I 1.71672 + 0.79423I
u = − 1.000000I
a = 0.318306 + 0.177934I
b = 1.002190 + 0.295542I
5.18047 + 0.92430I 1.71672 − 0.79423I
u = − 1.000000I
a = 0.100084 + 0.103550I
b = −1.073950 − 0.558752I
3.28987 + 5.69302I −2.00000 − 5.51057I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = − 1.000000I
a = 2.39185 + 1.23447I
b = −0.428243 − 0.664531I
1.39926 − 0.92430I −5.71672 + 0.79423I
u = − 1.000000I
a = 2.98293 + 2.76991I
b = −0.428243 + 0.664531I
1.39926 + 0.92430I −5.71672 − 0.79423I
11
III. I
u
3
= hb, 5u
2
+ 4a + 3u + 11, u
3
+ 2u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
−
5
4
u
2
−
3
4
u −
11
4
0
a
8
=
1
u
2
a
6
=
1
0
a
12
=
−u
u
a
3
=
−
5
4
u
2
−
3
4
u −
11
4
0
a
10
=
u
−u + 1
a
5
=
u
2
− u + 1
−u
2
+ 2u − 1
a
2
=
−
9
4
u
2
+
1
4
u −
15
4
u
2
− 2u + 1
a
1
=
−u
2
+ u − 1
u
2
− 2u + 1
a
9
=
u
2
+ u
−u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
197
16
u
2
−
175
16
u −
327
16
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
6
u
3
c
4
(u + 1)
3
c
5
u
3
− 3u
2
+ 5u − 2
c
7
, c
9
u
3
+ 2u − 1
c
8
, c
10
, c
11
c
12
u
3
+ 2u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
3
c
3
, c
6
y
3
c
5
y
3
+ y
2
+ 13y − 4
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y
3
+ 4y
2
+ 4y − 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22670 + 1.46771I
a = 0.048505 − 0.268962I
b = 0
7.79580 + 5.13794I 7.93256 − 7.85966I
u = −0.22670 − 1.46771I
a = 0.048505 + 0.268962I
b = 0
7.79580 − 5.13794I 7.93256 + 7.85966I
u = 0.453398
a = −3.34701
b = 0
−2.43213 −27.9280
15
IV. I
u
4
= h−4214u
9
− 17396u
8
+ · · · + 334809b − 381952, −4.07 × 10
4
u
9
+
7.77 × 10
5
u
8
+ · · · + 5.69 × 10
6
a − 2.59 × 10
6
, u
10
− u
8
+ · · · + 12u + 17i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
0.00715351u
9
− 0.136505u
8
+ ··· + 1.33232u + 0.454897
0.0125863u
9
+ 0.0519580u
8
+ ··· + 1.85250u + 1.14081
a
8
=
1
u
2
a
6
=
0.183014u
9
+ 0.127688u
8
+ ··· + 6.04964u + 1.97611
−0.00301366u
9
− 0.0874290u
8
+ ··· − 0.484378u − 1.18772
a
12
=
−0.0565798u
9
− 0.530953u
8
+ ··· − 5.14995u − 5.23480
−0.0776054u
9
+ 0.0934921u
8
+ ··· + 2.90428u + 1.74761
a
3
=
0.133636u
9
− 0.00226696u
8
+ ··· + 2.38641u + 1.94118
−0.00869750u
9
+ 0.0172516u
8
+ ··· + 0.862728u + 0.935922
a
10
=
u
u
3
+ u
a
5
=
0.284349u
9
+ 0.119606u
8
+ ··· + 7.81263u + 1.90279
0.00568384u
9
− 0.104681u
8
+ ··· − 0.347105u − 1.12365
a
2
=
−0.0989925u
9
− 0.173287u
8
+ ··· − 1.41442u − 0.0443807
0.0247395u
9
+ 0.0992805u
8
+ ··· + 2.43717u + 1.73927
a
1
=
−0.0853740u
9
− 0.0724174u
8
+ ··· + 0.169028u + 1.39848
0.0912341u
9
+ 0.0937609u
8
+ ··· + 2.48940u + 1.62958
a
9
=
−0.459120u
9
+ 0.0493266u
8
+ ··· + 1.16340u + 1.54656
0.137523u
9
+ 0.0788688u
8
+ ··· + 3.87382u − 0.231311
(ii) Obstruction class = −1
(iii) Cusp Shapes =
271
111603
u
9
+
61396
111603
u
8
−
14536
111603
u
7
−
39718
37201
u
6
+
31511
111603
u
5
+
350336
37201
u
4
−
88809
37201
u
3
+
2474827
111603
u
2
−
22387
37201
u +
443273
111603
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
+ 11u
4
+ 37u
3
+ 30u
2
− 12u + 1)
2
c
2
, c
4
(u
5
− 3u
4
− u
3
+ 6u
2
+ 1)
2
c
3
, c
6
(u
5
+ u
4
+ 8u
3
+ u
2
− 4u + 4)
2
c
5
(u
5
+ 2u
4
+ 2u
3
+ u + 1)
2
c
7
, c
9
, c
10
c
12
u
10
− u
8
+ 15u
6
+ u
5
+ 57u
4
− 7u
3
+ 56u
2
− 12u + 17
c
8
, c
11
u
10
− 7u
8
+ ··· − 8036u + 5191
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
− 47y
4
+ 685y
3
− 1810y
2
+ 84y − 1)
2
c
2
, c
4
(y
5
− 11y
4
+ 37y
3
− 30y
2
− 12y − 1)
2
c
3
, c
6
(y
5
+ 15y
4
+ 54y
3
− 73y
2
+ 8y − 16)
2
c
5
(y
5
+ 6y
3
+ y − 1)
2
c
7
, c
9
, c
10
c
12
y
10
− 2y
9
+ ··· + 1760y + 289
c
8
, c
11
y
10
− 14y
9
+ ··· − 17796004y + 26946481
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.223424 + 1.072270I
a = 2.57903 + 2.09848I
b = −1.04912
0.737094 −8.34961 + 0.I
u = 0.223424 − 1.072270I
a = 2.57903 − 2.09848I
b = −1.04912
0.737094 −8.34961 + 0.I
u = −0.005641 + 1.186120I
a = 0.249711 + 0.592601I
b = 0.465884 − 0.485496I
3.34738 − 1.37362I −3.54626 + 4.59823I
u = −0.005641 − 1.186120I
a = 0.249711 − 0.592601I
b = 0.465884 + 0.485496I
3.34738 + 1.37362I −3.54626 − 4.59823I
u = −0.232935 + 0.614344I
a = 1.68101 + 1.49249I
b = 0.465884 + 0.485496I
3.34738 + 1.37362I −3.54626 − 4.59823I
u = −0.232935 − 0.614344I
a = 1.68101 − 1.49249I
b = 0.465884 − 0.485496I
3.34738 − 1.37362I −3.54626 + 4.59823I
u = 1.84404 + 1.19233I
a = 0.416371 + 0.684418I
b = −0.44133 + 2.86818I
−14.4080 − 4.0569I −8.27894 + 1.95729I
u = 1.84404 − 1.19233I
a = 0.416371 − 0.684418I
b = −0.44133 − 2.86818I
−14.4080 + 4.0569I −8.27894 − 1.95729I
u = −1.82889 + 1.22222I
a = −0.484947 + 0.533445I
b = −0.44133 + 2.86818I
−14.4080 − 4.0569I −8.27894 + 1.95729I
u = −1.82889 − 1.22222I
a = −0.484947 − 0.533445I
b = −0.44133 − 2.86818I
−14.4080 + 4.0569I −8.27894 − 1.95729I
19
V. I
u
5
= hb, u
3
+ a + u, u
4
+ u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
−u
3
− u
0
a
8
=
1
u
2
a
6
=
1
0
a
12
=
−u
u
a
3
=
−u
3
− u
0
a
10
=
u
u
3
+ u
a
5
=
u
3
+ u
2
+ 2u + 2
u
3
+ u + 1
a
2
=
−2u
3
− u
2
− 3u − 2
−u
3
− u − 1
a
1
=
−u
3
− u
2
− 2u − 2
−u
3
− u − 1
a
9
=
u
3
+ 2u + 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
3
− 4u − 9
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
6
u
4
c
4
(u + 1)
4
c
5
(u
2
+ u + 1)
2
c
7
, c
9
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
8
, c
10
, c
11
c
12
u
4
− u
3
+ 2u
2
− 2u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
4
c
3
, c
6
y
4
c
5
(y
2
+ y + 1)
2
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621744 + 0.440597I
a = 0.500000 − 0.866025I
b = 0
1.64493 + 2.02988I −7.00000 − 3.46410I
u = −0.621744 − 0.440597I
a = 0.500000 + 0.866025I
b = 0
1.64493 − 2.02988I −7.00000 + 3.46410I
u = 0.121744 + 1.306620I
a = 0.500000 + 0.866025I
b = 0
1.64493 − 2.02988I −7.00000 + 3.46410I
u = 0.121744 − 1.306620I
a = 0.500000 − 0.866025I
b = 0
1.64493 + 2.02988I −7.00000 − 3.46410I
23
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
7
(u
5
+ 11u
4
+ 37u
3
+ 30u
2
− 12u + 1)
2
· (u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
19
+ 18u
18
+ ··· + 45729u + 256)
c
2
(u − 1)
7
(u
5
− 3u
4
− u
3
+ 6u
2
+ 1)
2
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
· (u
19
− 4u
18
+ ··· + 225u − 16)
c
3
u
7
(u
5
+ u
4
+ 8u
3
+ u
2
− 4u + 4)
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
· (u
19
+ 3u
18
+ ··· + 688u + 128)
c
4
(u + 1)
7
(u
5
− 3u
4
− u
3
+ 6u
2
+ 1)
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
· (u
19
− 4u
18
+ ··· + 225u − 16)
c
5
(u
2
+ u + 1)
2
(u
3
− 3u
2
+ 5u − 2)(u
5
+ 2u
4
+ 2u
3
+ u + 1)
2
· (u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1)(u
19
− 6u
18
+ ··· + 12u − 4)
c
6
u
7
(u
5
+ u
4
+ 8u
3
+ u
2
− 4u + 4)
2
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
· (u
19
+ 3u
18
+ ··· + 688u + 128)
c
7
, c
9
(u
2
+ 1)
6
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (u
10
− u
8
+ 15u
6
+ u
5
+ 57u
4
− 7u
3
+ 56u
2
− 12u + 17)
· (u
19
− 2u
18
+ ··· − 7u − 1)
c
8
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
10
− 7u
8
+ ··· − 8036u + 5191)
· (u
12
− 2u
11
+ ··· − 192u + 64)(u
19
− 29u
17
+ ··· − 320u + 64)
c
10
, c
12
(u
2
+ 1)
6
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
10
− u
8
+ 15u
6
+ u
5
+ 57u
4
− 7u
3
+ 56u
2
− 12u + 17)
· (u
19
− 2u
18
+ ··· − 7u − 1)
c
11
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
10
− 7u
8
+ ··· − 8036u + 5191)
· (u
12
+ 2u
11
+ ··· + 192u + 64)(u
19
− 29u
17
+ ··· − 320u + 64)
24
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
7
(y
5
− 47y
4
+ 685y
3
− 1810y
2
+ 84y − 1)
2
· (y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
19
− 46y
18
+ ··· + 1968323393y − 65536)
c
2
, c
4
(y − 1)
7
(y
5
− 11y
4
+ 37y
3
− 30y
2
− 12y − 1)
2
· (y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
19
− 18y
18
+ ··· + 45729y − 256)
c
3
, c
6
y
7
(y
5
+ 15y
4
+ 54y
3
− 73y
2
+ 8y − 16)
2
· (y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
19
+ 9y
18
+ ··· + 214272y − 16384)
c
5
(y
2
+ y + 1)
2
(y
3
+ y
2
+ 13y − 4)(y
5
+ 6y
3
+ y − 1)
2
· ((y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
)(y
19
− 2y
18
+ ··· + 152y − 16)
c
7
, c
9
, c
10
c
12
(y + 1)
12
(y
3
+ 4y
2
+ 4y − 1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
10
− 2y
9
+ ··· + 1760y + 289)(y
19
+ 2y
18
+ ··· − y − 1)
c
8
, c
11
(y
3
+ 4y
2
+ 4y − 1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
10
− 14y
9
+ ··· − 17796004y + 26946481)
· (y
12
− 12y
10
+ 736y
8
− 3584y
6
+ 9472y
4
− 9216y
2
+ 4096)
· (y
19
− 58y
18
+ ··· + 106496y − 4096)
25
