12n
0225
(K12n
0225
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 11 9 3 10 7 12 5 10
Solving Sequence
3,7
4
5,8
2
1,10
9 12 11 6
c
3
c
7
c
2
c
1
c
9
c
12
c
11
c
5
c
4
, c
6
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−108733460839492u
15
+ 235633173020139u
14
+ ··· + 44568754122034192d − 655346094957840,
− 5.82443 × 10
14
u
15
+ 2.17023 × 10
15
u
14
+ ··· + 8.91375 × 10
16
c + 4.50759 × 10
16
,
− 2.11450 × 10
14
u
15
+ 6.65971 × 10
14
u
14
+ ··· + 4.45688 × 10
16
b − 9.31909 × 10
15
,
40959130934865u
15
− 340344314483579u
14
+ ··· + 89137508244068384a − 71636506057825568,
u
16
− 3u
15
+ ··· − 64u + 32i
I
u
2
= h−2059u
7
− 2277u
6
+ ··· + 6184d + 18886, 1033u
7
a − 1546u
7
+ ··· − 5850a + 12368,
− 109u
7
a + 121u
7
+ ··· + 2066a − 3882, 9443u
7
a − 4639u
7
+ ··· − 14966a + 1182,
u
8
+ u
7
− 7u
6
− 4u
5
+ 16u
4
− 3u
3
− 9u
2
− 8u − 4i
I
v
1
= ha, d, c − v, b − 1, v
2
− v + 1i
I
v
2
= hc, d + v − 1, b, a − 1, v
2
− v + 1i
I
v
3
= ha, d + 1, c + a, b − 1, v + 1i
I
v
4
= ha, a
2
d + c
2
v − 2ca − cv + a + v, dv − 1, c
2
v
2
− 2cav − v
2
c + a
2
+ av + v
2
, b − 1i
* 5 irreducible components of dim
C
= 0, with total 37 representations.
* 1 irreducible components of dim
C
= 1
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−1.09 × 10
14
u
15
+ 2.36 × 10
14
u
14
+ · · · + 4.46 × 10
16
d − 6.55 ×
10
14
, −5.82×10
14
u
15
+2.17×10
15
u
14
+· · ·+8.91×10
16
c+4.51×10
16
, −2.11×
10
14
u
15
+ 6.66 × 10
14
u
14
+ · · · + 4.46 × 10
16
b − 9.32 × 10
15
, 4.10 × 10
13
u
15
−
3.40 × 10
14
u
14
+ · · · + 8.91 × 10
16
a − 7.16 × 10
16
, u
16
− 3u
15
+ · · · − 64u + 32i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
5
=
−0.000459505u
15
+ 0.00381819u
14
+ ··· + 0.107302u + 0.803663
0.00474436u
15
− 0.0149425u
14
+ ··· + 0.0874996u + 0.209095
a
8
=
u
u
a
2
=
−0.000459505u
15
+ 0.00381819u
14
+ ··· + 0.107302u + 0.803663
−0.00677644u
15
+ 0.0186134u
14
+ ··· − 0.258343u − 0.131025
a
1
=
−0.00723595u
15
+ 0.0224316u
14
+ ··· − 0.151041u + 0.672638
−0.00677644u
15
+ 0.0186134u
14
+ ··· − 0.258343u − 0.131025
a
10
=
0.00653421u
15
− 0.0243470u
14
+ ··· + 2.83891u − 0.505689
0.00243968u
15
− 0.00528696u
14
+ ··· + 0.774255u + 0.0147042
a
9
=
0.00653421u
15
− 0.0243470u
14
+ ··· + 2.83891u − 0.505689
0.00173022u
15
− 0.00528404u
14
+ ··· + 1.28699u − 0.137115
a
12
=
−0.0137698u
15
+ 0.0405121u
14
+ ··· + 0.840506u − 0.270168
−0.00358475u
15
+ 0.0138882u
14
+ ··· + 0.0905304u − 0.518106
a
11
=
0.00162230u
15
+ 0.00210951u
14
+ ··· + 0.961532u − 0.579761
−0.00282285u
15
+ 0.0157954u
14
+ ··· − 0.870510u + 0.171332
a
6
=
0.00409453u
15
− 0.0190600u
14
+ ··· + 2.06466u − 0.520393
−0.000723742u
15
− 0.00139819u
14
+ ··· − 0.209537u − 0.231550
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
3870228309913117
22284377061017096
u
15
+
2739800330771103
5571094265254274
u
14
+ ···−
43609984858099500
2785547132627137
u −
900447030377212
2785547132627137
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
16
+ u
15
+ ··· − 9u + 1
c
2
, c
4
, c
6
c
9
u
16
− 5u
15
+ ··· − u + 1
c
3
, c
7
u
16
− 3u
15
+ ··· − 64u + 32
c
5
, c
11
u
16
− u
15
+ ··· + 8u + 4
c
10
, c
12
u
16
− 9u
15
+ ··· + 24u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
16
+ 39y
15
+ ··· + 25y + 1
c
2
, c
4
, c
6
c
9
y
16
− y
15
+ ··· + 9y + 1
c
3
, c
7
y
16
− 15y
15
+ ··· + 5120y + 1024
c
5
, c
11
y
16
+ 9y
15
+ ··· − 24y + 16
c
10
, c
12
y
16
− 3y
15
+ ··· + 1248y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.289911 + 0.801405I
a = 0.654021 + 0.248004I
b = 0.336785 − 0.506907I
c = 0.424894 + 0.573951I
d = −0.009143 + 0.596034I
−0.321814 + 1.225450I −4.70206 − 4.90073I
u = 0.289911 − 0.801405I
a = 0.654021 − 0.248004I
b = 0.336785 + 0.506907I
c = 0.424894 − 0.573951I
d = −0.009143 − 0.596034I
−0.321814 − 1.225450I −4.70206 + 4.90073I
u = −1.139570 + 0.424244I
a = 0.589120 − 0.792720I
b = −0.396064 + 0.812657I
c = −0.538420 + 0.512682I
d = −0.335035 + 1.153290I
0.71555 + 3.67228I −1.72542 − 4.33532I
u = −1.139570 − 0.424244I
a = 0.589120 + 0.792720I
b = −0.396064 − 0.812657I
c = −0.538420 − 0.512682I
d = −0.335035 − 1.153290I
0.71555 − 3.67228I −1.72542 + 4.33532I
u = 0.575594 + 0.321074I
a = 1.017480 + 0.434986I
b = −0.169050 − 0.355242I
c = 0.486567 + 0.345761I
d = 0.445993 + 0.577062I
−0.11872 + 1.44911I 0.36516 − 2.80335I
u = 0.575594 − 0.321074I
a = 1.017480 − 0.434986I
b = −0.169050 + 0.355242I
c = 0.486567 − 0.345761I
d = 0.445993 − 0.577062I
−0.11872 − 1.44911I 0.36516 + 2.80335I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.067191 + 0.531573I
a = 0.547892 + 0.020957I
b = 0.822510 − 0.069711I
c = 0.32158 + 1.50666I
d = −0.047954 + 0.289837I
−2.85279 + 2.27613I −11.67196 − 3.94896I
u = −0.067191 − 0.531573I
a = 0.547892 − 0.020957I
b = 0.822510 + 0.069711I
c = 0.32158 − 1.50666I
d = −0.047954 − 0.289837I
−2.85279 − 2.27613I −11.67196 + 3.94896I
u = −0.33229 + 1.72297I
a = 0.412801 − 0.282825I
b = 0.648602 + 1.129520I
c = −0.562057 + 0.484841I
d = 0.350130 + 0.805225I
4.26031 − 4.58330I −1.71878 + 4.05752I
u = −0.33229 − 1.72297I
a = 0.412801 + 0.282825I
b = 0.648602 − 1.129520I
c = −0.562057 − 0.484841I
d = 0.350130 − 0.805225I
4.26031 + 4.58330I −1.71878 − 4.05752I
u = −1.81588 + 0.68377I
a = −0.227904 + 0.980118I
b = −1.22507 − 0.96795I
c = −0.415075 − 0.689342I
d = −0.25632 − 1.93561I
6.64229 − 8.00732I −6.00576 + 3.88395I
u = −1.81588 − 0.68377I
a = −0.227904 − 0.980118I
b = −1.22507 + 0.96795I
c = −0.415075 + 0.689342I
d = −0.25632 + 1.93561I
6.64229 + 8.00732I −6.00576 − 3.88395I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.72439 + 0.95526I
a = −0.389017 − 0.972862I
b = −1.35436 + 0.88620I
c = 0.383140 − 0.726169I
d = 0.25852 − 2.04920I
9.8252 + 14.1242I −4.39428 − 6.97100I
u = 1.72439 − 0.95526I
a = −0.389017 + 0.972862I
b = −1.35436 − 0.88620I
c = 0.383140 + 0.726169I
d = 0.25852 + 2.04920I
9.8252 − 14.1242I −4.39428 + 6.97100I
u = 2.26504 + 0.41669I
a = −0.104392 − 0.792584I
b = −1.16335 + 1.24018I
c = 0.399366 − 0.621003I
d = 0.09381 − 1.83873I
12.28130 + 3.00558I −2.14690 − 1.40998I
u = 2.26504 − 0.41669I
a = −0.104392 + 0.792584I
b = −1.16335 − 1.24018I
c = 0.399366 + 0.621003I
d = 0.09381 + 1.83873I
12.28130 − 3.00558I −2.14690 + 1.40998I
7
II. I
u
2
= h−2059u
7
− 2277u
6
+ · · · + 6184d + 1.89 × 10
4
, 1033au
7
− 1546u
7
+
· · · − 5850a + 1.24 × 10
4
, −109au
7
+ 121u
7
+ · · · + 2066a − 3882, 9443au
7
−
4639u
7
+ · · · − 1.50 × 10
4
a + 1182, u
8
+ u
7
+ · · · − 8u − 4i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
5
=
a
0.0352523au
7
− 0.0391332u
7
+ ··· − 0.668176a + 1.25550
a
8
=
u
u
a
2
=
a
−0.0352523au
7
+ 0.0391332u
7
+ ··· + 0.668176a − 1.25550
a
1
=
−0.0352523au
7
+ 0.0391332u
7
+ ··· + 1.66818a − 1.25550
−0.0352523au
7
+ 0.0391332u
7
+ ··· + 0.668176a − 1.25550
a
10
=
−
1033
6184
u
7
a +
1
4
u
7
+ ··· +
2925
3092
a − 2
0.332956u
7
+ 0.368208u
6
+ ··· − 4.89796u − 3.05401
a
9
=
−
1033
6184
u
7
a +
1
4
u
7
+ ··· +
2925
3092
a − 2
0.150712au
7
+ 0.332956u
7
+ ··· − 0.141009a − 3.05401
a
12
=
−0.0391332au
7
+ 0.0133409u
7
+ ··· + 1.25550a − 2.01892
−0.0187581au
7
− 0.0163325u
7
+ ··· + 0.172057a − 3.19502
a
11
=
−0.0163325au
7
+ 0.0133409u
7
+ ··· + 0.804981a − 2.01892
−0.00226391au
7
− 0.0593467u
7
+ ··· − 0.324062a − 3.35220
a
6
=
−0.167044au
7
− 0.0829560u
7
+ ··· + 0.945990a + 1.05401
0.150712au
7
− 0.483668u
7
+ ··· − 0.141009a + 3.19502
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
933
1546
u
7
−
561
1546
u
6
+
7043
1546
u
5
+
278
773
u
4
−
8922
773
u
3
+
11743
1546
u
2
+
10913
1546
u −
2838
773
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
16
+ 3u
15
+ ··· + 2336u + 256
c
2
, c
4
, c
6
c
9
u
16
− 3u
15
+ ··· + 40u − 16
c
3
, c
7
(u
8
+ u
7
− 7u
6
− 4u
5
+ 16u
4
− 3u
3
− 9u
2
− 8u − 4)
2
c
5
, c
11
(u
8
− 2u
7
+ 5u
6
− 6u
5
+ 7u
4
− 7u
3
+ 4u
2
− 4u + 1)
2
c
10
, c
12
(u
8
− 6u
7
+ 15u
6
− 14u
5
− 9u
4
+ 31u
3
− 26u
2
+ 8u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
16
+ 17y
15
+ ··· − 2843136y + 65536
c
2
, c
4
, c
6
c
9
y
16
− 3y
15
+ ··· − 2336y + 256
c
3
, c
7
(y
8
− 15y
7
+ 89y
6
− 252y
5
+ 366y
4
− 305y
3
− 95y
2
+ 8y + 16)
2
c
5
, c
11
(y
8
+ 6y
7
+ 15y
6
+ 14y
5
− 9y
4
− 31y
3
− 26y
2
− 8y + 1)
2
c
10
, c
12
(y
8
− 6y
7
+ 39y
6
− 146y
5
+ 267y
4
− 239y
3
+ 162y
2
− 116y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.170290 + 0.725937I
a = 0.508470 + 0.631641I
b = −0.226676 − 0.960653I
c = −1.002720 + 0.319564I
d = 0.519668 + 0.225325I
1.14222 − 1.62541I −1.41499 + 1.42555I
u = 1.170290 + 0.725937I
a = 0.406912 − 0.059872I
b = 1.40546 + 0.35393I
c = 0.507576 + 0.506015I
d = 0.136526 + 1.108320I
1.14222 − 1.62541I −1.41499 + 1.42555I
u = 1.170290 − 0.725937I
a = 0.508470 − 0.631641I
b = −0.226676 + 0.960653I
c = −1.002720 − 0.319564I
d = 0.519668 − 0.225325I
1.14222 + 1.62541I −1.41499 − 1.42555I
u = 1.170290 − 0.725937I
a = 0.406912 + 0.059872I
b = 1.40546 − 0.35393I
c = 0.507576 − 0.506015I
d = 0.136526 − 1.108320I
1.14222 + 1.62541I −1.41499 − 1.42555I
u = −0.195492 + 0.552709I
a = 0.527146 + 0.046214I
b = 0.882537 − 0.165040I
c = −0.51191 − 1.84722I
d = −0.94136 − 3.95806I
−2.92647 − 1.66195I −9.38368 + 3.48117I
u = −0.195492 + 0.552709I
a = −5.82950 + 3.76506I
b = −1.121050 − 0.078180I
c = 0.76737 + 1.32533I
d = −0.128596 + 0.282324I
−2.92647 − 1.66195I −9.38368 + 3.48117I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.195492 − 0.552709I
a = 0.527146 − 0.046214I
b = 0.882537 + 0.165040I
c = −0.51191 + 1.84722I
d = −0.94136 + 3.95806I
−2.92647 + 1.66195I −9.38368 − 3.48117I
u = −0.195492 − 0.552709I
a = −5.82950 − 3.76506I
b = −1.121050 + 0.078180I
c = 0.76737 − 1.32533I
d = −0.128596 − 0.282324I
−2.92647 + 1.66195I −9.38368 − 3.48117I
u = −0.580387
a = 0.467644
b = 1.13838
c = −0.692019
d = −0.969961
−2.18625 −3.21290
u = −0.580387
a = 1.67123
b = −0.401639
c = 1.96141
d = −0.271415
−2.18625 −3.21290
u = 2.05532
a = 0.059530 + 0.815129I
b = −0.91088 − 1.22029I
c = 0.443183 − 0.593724I
d = 0.12235 − 1.67535I
7.78143 −4.64060
u = 2.05532
a = 0.059530 − 0.815129I
b = −0.91088 + 1.22029I
c = 0.443183 + 0.593724I
d = 0.12235 + 1.67535I
7.78143 −4.64060
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −2.21226 + 0.50002I
a = −0.131998 + 0.812425I
b = −1.19484 − 1.19923I
c = −0.440910 + 0.544962I
d = 0.02631 + 1.55679I
12.14610 − 5.90409I −2.27459 + 2.82977I
u = −2.21226 + 0.50002I
a = 0.140006 − 0.672065I
b = −0.70292 + 1.42606I
c = −0.397283 − 0.631875I
d = −0.11421 − 1.86330I
12.14610 − 5.90409I −2.27459 + 2.82977I
u = −2.21226 − 0.50002I
a = −0.131998 − 0.812425I
b = −1.19484 + 1.19923I
c = −0.440910 − 0.544962I
d = 0.02631 − 1.55679I
12.14610 + 5.90409I −2.27459 − 2.82977I
u = −2.21226 − 0.50002I
a = 0.140006 + 0.672065I
b = −0.70292 − 1.42606I
c = −0.397283 + 0.631875I
d = −0.11421 + 1.86330I
12.14610 + 5.90409I −2.27459 − 2.82977I
13
III. I
v
1
= ha, d, c − v, b − 1, v
2
− v + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
v
0
a
4
=
1
0
a
5
=
0
1
a
8
=
v
0
a
2
=
1
−1
a
1
=
0
−1
a
10
=
v
0
a
9
=
v
0
a
12
=
v − 1
−1
a
11
=
v − 1
−v
a
6
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 1
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
6
, c
7
c
8
, c
9
u
2
c
4
(u + 1)
2
c
5
, c
12
u
2
− u + 1
c
10
, c
11
u
2
+ u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
6
, c
7
c
8
, c
9
y
2
c
5
, c
10
, c
11
c
12
y
2
+ y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = 1.00000
c = 0.500000 + 0.866025I
d = 0
−1.64493 + 2.02988I −3.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = 1.00000
c = 0.500000 − 0.866025I
d = 0
−1.64493 − 2.02988I −3.00000 + 3.46410I
17
IV. I
v
2
= hc, d + v − 1, b, a − 1, v
2
− v + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
v
0
a
4
=
1
0
a
5
=
1
0
a
8
=
v
0
a
2
=
1
0
a
1
=
1
0
a
10
=
0
−v + 1
a
9
=
v
−v + 1
a
12
=
1
−v
a
11
=
−v + 1
−v
a
6
=
0
v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v − 5
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
u
2
c
5
, c
10
u
2
+ u + 1
c
6
, c
8
(u − 1)
2
c
9
(u + 1)
2
c
11
, c
12
u
2
− u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
y
2
c
5
, c
10
, c
11
c
12
y
2
+ y + 1
c
6
, c
8
, c
9
(y − 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 1.00000
b = 0
c = 0
d = 0.500000 − 0.866025I
−1.64493 − 2.02988I −3.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 1.00000
b = 0
c = 0
d = 0.500000 + 0.866025I
−1.64493 + 2.02988I −3.00000 − 3.46410I
21
V. I
v
3
= ha, d + 1, c + a, b − 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
−1
0
a
4
=
1
0
a
5
=
0
1
a
8
=
−1
0
a
2
=
1
−1
a
1
=
0
−1
a
10
=
0
−1
a
9
=
−1
−1
a
12
=
0
−1
a
11
=
0
−1
a
6
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u − 1
c
3
, c
5
, c
7
c
10
, c
11
, c
12
u
c
4
, c
9
u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
8
, c
9
y − 1
c
3
, c
5
, c
7
c
10
, c
11
, c
12
y
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
c = 0
d = −1.00000
−3.28987 −12.0000
25
VI.
I
v
4
= ha, c
2
v − cv + · · · − 2ca + a, dv − 1, c
2
v
2
− v
2
c + · · · + a
2
+ av, b − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
v
0
a
4
=
1
0
a
5
=
0
1
a
8
=
v
0
a
2
=
1
−1
a
1
=
0
−1
a
10
=
c
d
a
9
=
c + v
d
a
12
=
c − 1
dc − 1
a
11
=
c − 1
dc − c
a
6
=
c
d
(ii) Obstruction class = −1
(iii) Cusp Shapes = −d
2
− v
2
− 4c − 8
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
26
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
−3.28987 + 2.02988I −8.06967 − 3.55149I
27
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
u
2
(u − 1)
3
(u
16
+ u
15
+ ··· − 9u + 1)(u
16
+ 3u
15
+ ··· + 2336u + 256)
c
2
, c
6
u
2
(u − 1)
3
(u
16
− 5u
15
+ ··· − u + 1)(u
16
− 3u
15
+ ··· + 40u − 16)
c
3
, c
7
u
5
(u
8
+ u
7
− 7u
6
− 4u
5
+ 16u
4
− 3u
3
− 9u
2
− 8u − 4)
2
· (u
16
− 3u
15
+ ··· − 64u + 32)
c
4
, c
9
u
2
(u + 1)
3
(u
16
− 5u
15
+ ··· − u + 1)(u
16
− 3u
15
+ ··· + 40u − 16)
c
5
, c
11
u(u
2
− u + 1)(u
2
+ u + 1)
· (u
8
− 2u
7
+ 5u
6
− 6u
5
+ 7u
4
− 7u
3
+ 4u
2
− 4u + 1)
2
· (u
16
− u
15
+ ··· + 8u + 4)
c
10
u(u
2
+ u + 1)
2
· (u
8
− 6u
7
+ 15u
6
− 14u
5
− 9u
4
+ 31u
3
− 26u
2
+ 8u + 1)
2
· (u
16
− 9u
15
+ ··· + 24u + 16)
c
12
u(u
2
− u + 1)
2
· (u
8
− 6u
7
+ 15u
6
− 14u
5
− 9u
4
+ 31u
3
− 26u
2
+ 8u + 1)
2
· (u
16
− 9u
15
+ ··· + 24u + 16)
28
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
2
(y − 1)
3
(y
16
+ 17y
15
+ ··· − 2843136y + 65536)
· (y
16
+ 39y
15
+ ··· + 25y + 1)
c
2
, c
4
, c
6
c
9
y
2
(y − 1)
3
(y
16
− 3y
15
+ ··· − 2336y + 256)(y
16
− y
15
+ ··· + 9y + 1)
c
3
, c
7
y
5
(y
8
− 15y
7
+ 89y
6
− 252y
5
+ 366y
4
− 305y
3
− 95y
2
+ 8y + 16)
2
· (y
16
− 15y
15
+ ··· + 5120y + 1024)
c
5
, c
11
y(y
2
+ y + 1)
2
· (y
8
+ 6y
7
+ 15y
6
+ 14y
5
− 9y
4
− 31y
3
− 26y
2
− 8y + 1)
2
· (y
16
+ 9y
15
+ ··· − 24y + 16)
c
10
, c
12
y(y
2
+ y + 1)
2
· (y
8
− 6y
7
+ 39y
6
− 146y
5
+ 267y
4
− 239y
3
+ 162y
2
− 116y + 1)
2
· (y
16
− 3y
15
+ ··· + 1248y + 256)
29
