11n
146
(K11n
146
)
A knot diagram
1
Linearized knot diagam
7 1 9 8 3 9 2 11 7 4 5
Solving Sequence
1,7
2 3
5,8
4 11 9 6 10
c
1
c
2
c
7
c
4
c
11
c
8
c
6
c
10
c
3
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h9u
21
− 99u
20
+ ··· + 8b + 344, 63u
21
− 461u
20
+ ··· + 16a + 368, u
22
− 9u
21
+ ··· + 80u − 16i
I
u
2
= h−u
11
+ 4u
9
+ u
8
− 7u
7
− 2u
6
+ 8u
5
+ 4u
4
− 6u
3
− 5u
2
+ b + 2u + 3, u
14
+ 2u
13
+ ··· + 2a − 4,
u
15
− 5u
13
− u
12
+ 12u
11
+ 3u
10
− 19u
9
− 7u
8
+ 21u
7
+ 11u
6
− 16u
5
− 12u
4
+ 8u
3
+ 7u
2
− 2u − 2i
I
u
3
= h−34116957547a
7
u
2
+ 99566701011a
6
u
2
+ ··· + 1815673106251a + 882543035301,
3a
7
u
2
+ 7a
6
u
2
+ ··· − 56a + 65, u
3
+ u
2
− 1i
* 3 irreducible components of dim
C
= 0, with total 61 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
= h9u
21
− 99u
20
+ · · · + 8b + 344, 63u
21
− 461u
20
+ · · · + 16a +
368, u
22
− 9u
21
+ · · · + 80u − 16i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
5
=
−
63
16
u
21
+
461
16
u
20
+ ··· +
229
2
u − 23
−
9
8
u
21
+
99
8
u
20
+ ··· + 175u − 43
a
8
=
−u
−u
3
+ u
a
4
=
−
27
16
u
21
+
241
16
u
20
+ ··· +
323
2
u − 41
53
8
u
21
−
423
8
u
20
+ ··· − 356u + 79
a
11
=
9u
21
−
557
8
u
20
+ ··· −
1413
4
u +
135
2
−
7
8
u
21
+
31
8
u
20
+ ··· −
225
2
u + 38
a
9
=
−0.0625000u
21
+ 2.06250u
20
+ ··· + 41.2500u − 11.5000
19
4
u
21
−
79
2
u
20
+ ··· −
623
2
u + 75
a
6
=
27
16
u
21
−
241
16
u
20
+ ··· −
323
2
u + 40
−
53
8
u
21
+
423
8
u
20
+ ··· + 357u − 79
a
10
=
−0.0625000u
21
+ 2.06250u
20
+ ··· + 41.2500u − 11.5000
17
2
u
21
−
271
4
u
20
+ ··· −
865
2
u + 99
a
10
=
−0.0625000u
21
+ 2.06250u
20
+ ··· + 41.2500u − 11.5000
17
2
u
21
−
271
4
u
20
+ ··· −
865
2
u + 99
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
39
2
u
21
+
301
2
u
20
+ ··· + 914u − 202
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
22
− 9u
21
+ ··· + 80u − 16
c
2
u
22
+ 11u
21
+ ··· + 1408u + 256
c
3
, c
6
, c
9
u
22
+ 18u
20
+ ··· − 3u − 1
c
4
, c
11
u
22
− 6u
20
+ ··· + 4u − 1
c
5
u
22
+ 12u
21
+ ··· + 672u + 64
c
8
u
22
− 12u
21
+ ··· − 64u + 8
c
10
u
22
+ u
21
+ ··· − 2u
2
− 10
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
22
− 11y
21
+ ··· − 1408y + 256
c
2
y
22
+ y
21
+ ··· − 663552y + 65536
c
3
, c
6
, c
9
y
22
+ 36y
21
+ ··· + 9y + 1
c
4
, c
11
y
22
− 12y
21
+ ··· − 66y + 1
c
5
y
22
− 26y
21
+ ··· − 273920y + 4096
c
8
y
22
− 2y
21
+ ··· + 224y + 64
c
10
y
22
+ 19y
21
+ ··· + 40y + 100
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.066710 + 0.226222I
a = −0.351526 + 0.307053I
b = −0.539318 + 0.910382I
−2.44040 + 0.11720I −7.20404 − 1.75445I
u = −1.066710 − 0.226222I
a = −0.351526 − 0.307053I
b = −0.539318 − 0.910382I
−2.44040 − 0.11720I −7.20404 + 1.75445I
u = 1.039800 + 0.529986I
a = 0.729503 + 1.140060I
b = −0.827030 + 0.144364I
0.80566 − 4.34766I −4.70703 + 6.76579I
u = 1.039800 − 0.529986I
a = 0.729503 − 1.140060I
b = −0.827030 − 0.144364I
0.80566 + 4.34766I −4.70703 − 6.76579I
u = 0.392350 + 0.705715I
a = −1.47104 − 0.61591I
b = 0.989758 + 0.677091I
1.86600 + 2.08328I 1.28577 − 1.87912I
u = 0.392350 − 0.705715I
a = −1.47104 + 0.61591I
b = 0.989758 − 0.677091I
1.86600 − 2.08328I 1.28577 + 1.87912I
u = 0.583477 + 1.050930I
a = 0.954459 + 0.738545I
b = −1.41570 − 0.82771I
11.22610 + 7.92016I −1.17318 − 3.44504I
u = 0.583477 − 1.050930I
a = 0.954459 − 0.738545I
b = −1.41570 + 0.82771I
11.22610 − 7.92016I −1.17318 + 3.44504I
u = 0.498409 + 0.620816I
a = −1.379510 + 0.247291I
b = 0.877040 − 0.154406I
2.40742 − 0.20200I −0.358944 + 0.576250I
u = 0.498409 − 0.620816I
a = −1.379510 − 0.247291I
b = 0.877040 + 0.154406I
2.40742 + 0.20200I −0.358944 − 0.576250I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.091100 + 0.568772I
a = 1.66508 + 1.05767I
b = −1.084320 + 0.882593I
−0.17078 − 6.97976I −0.36212 + 5.29220I
u = 1.091100 − 0.568772I
a = 1.66508 − 1.05767I
b = −1.084320 − 0.882593I
−0.17078 + 6.97976I −0.36212 − 5.29220I
u = 0.520231 + 1.151080I
a = 0.694248 + 0.193737I
b = −1.102170 − 0.272719I
10.39030 − 0.61941I 1.005762 + 0.209971I
u = 0.520231 − 1.151080I
a = 0.694248 − 0.193737I
b = −1.102170 + 0.272719I
10.39030 + 0.61941I 1.005762 − 0.209971I
u = 1.154680 + 0.769733I
a = −1.41430 − 0.79322I
b = 1.38480 − 1.09712I
9.4240 − 14.4970I −3.20540 + 7.40924I
u = 1.154680 − 0.769733I
a = −1.41430 + 0.79322I
b = 1.38480 + 1.09712I
9.4240 + 14.4970I −3.20540 − 7.40924I
u = 1.21138 + 0.80873I
a = −0.770380 − 0.556560I
b = 0.946982 − 0.664925I
8.24676 − 6.35399I −2.34309 + 5.14871I
u = 1.21138 − 0.80873I
a = −0.770380 + 0.556560I
b = 0.946982 + 0.664925I
8.24676 + 6.35399I −2.34309 − 5.14871I
u = −1.46566 + 0.12857I
a = 0.213752 + 0.149488I
b = 0.844485 + 0.429706I
2.91041 + 4.96923I −3.04819 − 6.01952I
u = −1.46566 − 0.12857I
a = 0.213752 − 0.149488I
b = 0.844485 − 0.429706I
2.91041 − 4.96923I −3.04819 + 6.01952I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.492053
a = −0.403784
b = −0.296446
−0.825428 −11.7690
u = 1.57389
a = 0.163193
b = 0.147402
−7.90371 −59.0100
7
II.
I
u
2
= h−u
11
+4u
9
+· · ·+b+3, u
14
+2u
13
+· · ·+2a−4, u
15
−5u
13
+· · ·−2u−2i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
5
=
−
1
2
u
14
− u
13
+ ··· −
13
2
u + 2
u
11
− 4u
9
− u
8
+ 7u
7
+ 2u
6
− 8u
5
− 4u
4
+ 6u
3
+ 5u
2
− 2u − 3
a
8
=
−u
−u
3
+ u
a
4
=
−
1
2
u
14
− u
13
+ ··· −
7
2
u + 2
−u
14
+ 5u
12
+ ··· − 5u − 3
a
11
=
5
2
u
14
−
23
2
u
12
+ ··· +
9
2
u − 5
u
14
+ 2u
13
+ ··· + 4u + 5
a
9
=
−
3
2
u
14
+ u
13
+ ··· −
7
2
u + 2
4u
14
+ 3u
13
+ ··· + 12u + 5
a
6
=
−
1
2
u
14
− u
13
+ ··· −
7
2
u + 1
−u
14
+ 5u
12
+ ··· − 4u − 3
a
10
=
−
3
2
u
14
+ u
13
+ ··· −
7
2
u + 2
4u
14
+ 4u
13
+ ··· + 11u + 7
a
10
=
−
3
2
u
14
+ u
13
+ ··· −
7
2
u + 2
4u
14
+ 4u
13
+ ··· + 11u + 7
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
14
− 11u
13
+ 37u
12
+ 56u
11
− 69u
10
− 119u
9
+ 89u
8
+
182u
7
− 56u
6
− 195u
5
− 6u
4
+ 135u
3
+ 41u
2
− 48u − 22
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 5u
13
+ ··· − 2u − 2
c
2
u
15
+ 10u
14
+ ··· + 32u + 4
c
3
, c
9
u
15
+ 4u
13
+ ··· + u − 1
c
4
, c
11
u
15
+ 2u
13
+ ··· + 4u − 1
c
5
u
15
− 11u
14
+ ··· + 73u − 25
c
6
u
15
+ 4u
13
+ ··· + u + 1
c
7
u
15
− 5u
13
+ ··· − 2u + 2
c
8
u
15
− 7u
14
+ ··· + 3u
2
− 1
c
10
u
15
+ u
14
+ ··· + 2u + 2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
15
− 10y
14
+ ··· + 32y −4
c
2
y
15
− 2y
14
+ ··· − 8y −16
c
3
, c
6
, c
9
y
15
+ 8y
14
+ ··· + 11y −1
c
4
, c
11
y
15
+ 4y
14
+ ··· + 14y −1
c
5
y
15
− 19y
14
+ ··· + 4329y −625
c
8
y
15
− 3y
14
+ ··· + 6y −1
c
10
y
15
+ 7y
14
+ ··· + 39y
2
− 4
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.945062 + 0.354082I
a = 0.565133 + 0.388167I
b = 0.570749 + 1.243190I
−3.02280 + 1.54146I −6.80860 + 0.33073I
u = 0.945062 − 0.354082I
a = 0.565133 − 0.388167I
b = 0.570749 − 1.243190I
−3.02280 − 1.54146I −6.80860 − 0.33073I
u = −0.573037 + 0.772166I
a = 0.944181 − 0.805222I
b = −0.884792 + 0.570619I
0.37010 − 2.03676I −5.30954 + 3.27219I
u = −0.573037 − 0.772166I
a = 0.944181 + 0.805222I
b = −0.884792 − 0.570619I
0.37010 + 2.03676I −5.30954 − 3.27219I
u = 0.869875 + 0.302392I
a = 0.175063 + 0.651509I
b = −0.271019 + 1.145180I
−2.66889 − 4.30403I −6.64337 + 8.95164I
u = 0.869875 − 0.302392I
a = 0.175063 − 0.651509I
b = −0.271019 − 1.145180I
−2.66889 + 4.30403I −6.64337 − 8.95164I
u = 0.867167 + 0.769940I
a = −0.507277 − 0.120829I
b = −0.266261 − 1.191970I
7.81854 − 2.90716I −1.49116 + 2.36324I
u = 0.867167 − 0.769940I
a = −0.507277 + 0.120829I
b = −0.266261 + 1.191970I
7.81854 + 2.90716I −1.49116 − 2.36324I
u = −1.042710 + 0.599702I
a = −1.70977 + 0.73314I
b = 1.015990 + 0.881908I
−1.08562 + 7.20573I −9.25026 − 7.69565I
u = −1.042710 − 0.599702I
a = −1.70977 − 0.73314I
b = 1.015990 − 0.881908I
−1.08562 − 7.20573I −9.25026 + 7.69565I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.173890 + 0.354715I
a = 0.415207 + 1.215040I
b = 0.613391 − 0.103361I
2.75922 + 3.34728I −2.20513 − 3.30365I
u = −1.173890 − 0.354715I
a = 0.415207 − 1.215040I
b = 0.613391 + 0.103361I
2.75922 − 3.34728I −2.20513 + 3.30365I
u = −0.691226 + 0.240625I
a = 3.57976 + 0.40015I
b = −0.934484 − 0.438009I
4.67692 − 0.80845I 3.56798 − 2.11727I
u = −0.691226 − 0.240625I
a = 3.57976 − 0.40015I
b = −0.934484 + 0.438009I
4.67692 + 0.80845I 3.56798 + 2.11727I
u = 1.59751
a = 0.0753958
b = 0.312857
−7.82532 43.2800
12
III. I
u
3
= h−3.41 × 10
10
a
7
u
2
+ 9.96 × 10
10
a
6
u
2
+ · · · + 1.82 × 10
12
a + 8.83 ×
10
11
, 3a
7
u
2
+ 7a
6
u
2
+ · · · − 56a + 65, u
3
+ u
2
− 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
5
=
a
0.00955622a
7
u
2
− 0.0278888a
6
u
2
+ ··· − 0.508573a − 0.247202
a
8
=
−u
u
2
+ u − 1
a
4
=
−0.0206730a
7
u
2
+ 0.00671494a
6
u
2
+ ··· − 0.167214a + 0.361442
0.0365923a
7
u
2
− 0.106197a
6
u
2
+ ··· + 0.254915a − 0.349774
a
11
=
−0.0136970a
7
u
2
+ 0.167653a
6
u
2
+ ··· − 0.128713a + 0.671444
0.0545800a
7
u
2
− 0.0709107a
6
u
2
+ ··· − 0.318374a − 0.618795
a
9
=
−0.0337296a
7
u
2
− 0.0293879a
6
u
2
+ ··· + 0.243004a + 1.20707
−0.0280221a
7
u
2
+ 0.0695256a
6
u
2
+ ··· + 0.701359a − 0.906712
a
6
=
−0.0381529a
7
u
2
+ 0.0571347a
6
u
2
+ ··· + 0.560725a + 0.216812
0.0365923a
7
u
2
− 0.106197a
6
u
2
+ ··· − 0.745085a − 0.349774
a
10
=
−0.0337296a
7
u
2
− 0.0293879a
6
u
2
+ ··· + 0.243004a + 1.20707
−0.0419144a
7
u
2
+ 0.0898677a
6
u
2
+ ··· + 1.22012a − 0.592528
a
10
=
−0.0337296a
7
u
2
− 0.0293879a
6
u
2
+ ··· + 0.243004a + 1.20707
−0.0419144a
7
u
2
+ 0.0898677a
6
u
2
+ ··· + 1.22012a − 0.592528
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
1164454014992
3570132856135
a
7
u
2
+
1180088464472
3570132856135
a
6
u
2
+ ··· −
4943997575288
3570132856135
a −
7861314901686
3570132856135
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
3
+ u
2
− 1)
8
c
2
(u
3
+ u
2
+ 2u + 1)
8
c
3
, c
6
, c
9
u
24
− u
23
+ ··· − 276u + 1133
c
4
, c
11
u
24
− 3u
23
+ ··· − 54u + 59
c
5
(u
4
− 3u
3
+ u
2
+ 2u + 1)
6
c
8
(u
4
+ u
3
+ u
2
+ 1)
6
c
10
u
24
− u
23
+ ··· − 3286u + 2677
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
3
− y
2
+ 2y −1)
8
c
2
(y
3
+ 3y
2
+ 2y −1)
8
c
3
, c
6
, c
9
y
24
+ 27y
23
+ ··· + 64316y + 1283689
c
4
, c
11
y
24
+ 3y
23
+ ··· − 3152y + 3481
c
5
(y
4
− 7y
3
+ 15y
2
− 2y + 1)
6
c
8
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
6
c
10
y
24
+ 15y
23
+ ··· + 16368400y + 7166329
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = −0.921360 − 0.219493I
b = 0.902902 − 0.539690I
8.16994 + 1.41302I 1.33649 + 1.92930I
u = −0.877439 + 0.744862I
a = 0.504527 − 0.969052I
b = −1.196950 + 0.472705I
1.168190 − 0.335841I −2.31698 − 0.41465I
u = −0.877439 + 0.744862I
a = −0.779487 + 0.866165I
b = 0.685429 − 0.020892I
1.168190 − 0.335841I −2.31698 − 0.41465I
u = −0.877439 + 0.744862I
a = 0.051447 + 1.254950I
b = 1.53802 − 1.79281I
8.16994 + 4.24323I 1.33649 − 7.88819I
u = −0.877439 + 0.744862I
a = 1.42701 − 0.08967I
b = −0.947309 − 0.408550I
1.16819 + 5.99209I −2.31698 − 5.54425I
u = −0.877439 + 0.744862I
a = −1.58305 + 0.33835I
b = 1.28710 + 1.00044I
1.16819 + 5.99209I −2.31698 − 5.54425I
u = −0.877439 + 0.744862I
a = 1.04688 − 1.38550I
b = −0.605985 − 0.603603I
8.16994 + 4.24323I 1.33649 − 7.88819I
u = −0.877439 + 0.744862I
a = 1.87343 − 0.34348I
b = −1.01797 − 2.02902I
8.16994 + 1.41302I 1.33649 + 1.92930I
u = −0.877439 − 0.744862I
a = −0.921360 + 0.219493I
b = 0.902902 + 0.539690I
8.16994 − 1.41302I 1.33649 − 1.92930I
u = −0.877439 − 0.744862I
a = 0.504527 + 0.969052I
b = −1.196950 − 0.472705I
1.168190 + 0.335841I −2.31698 + 0.41465I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 − 0.744862I
a = −0.779487 − 0.866165I
b = 0.685429 + 0.020892I
1.168190 + 0.335841I −2.31698 + 0.41465I
u = −0.877439 − 0.744862I
a = 0.051447 − 1.254950I
b = 1.53802 + 1.79281I
8.16994 − 4.24323I 1.33649 + 7.88819I
u = −0.877439 − 0.744862I
a = 1.42701 + 0.08967I
b = −0.947309 + 0.408550I
1.16819 − 5.99209I −2.31698 + 5.54425I
u = −0.877439 − 0.744862I
a = −1.58305 − 0.33835I
b = 1.28710 − 1.00044I
1.16819 − 5.99209I −2.31698 + 5.54425I
u = −0.877439 − 0.744862I
a = 1.04688 + 1.38550I
b = −0.605985 + 0.603603I
8.16994 − 4.24323I 1.33649 + 7.88819I
u = −0.877439 − 0.744862I
a = 1.87343 + 0.34348I
b = −1.01797 + 2.02902I
8.16994 − 1.41302I 1.33649 − 1.92930I
u = 0.754878
a = 0.906952 + 0.366540I
b = 0.273354 + 1.242580I
−2.96939 + 3.16396I −8.84625 − 2.56480I
u = 0.754878
a = 0.906952 − 0.366540I
b = 0.273354 − 1.242580I
−2.96939 − 3.16396I −8.84625 + 2.56480I
u = 0.754878
a = 0.322520 + 1.369380I
b = −0.500853 + 1.057020I
−2.96939 − 3.16396I −8.84625 + 2.56480I
u = 0.754878
a = 0.322520 − 1.369380I
b = −0.500853 − 1.057020I
−2.96939 + 3.16396I −8.84625 − 2.56480I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.754878
a = −2.39656 + 0.93888I
b = 1.240420 + 0.312627I
4.03235 − 1.41510I −5.19277 + 4.90874I
u = 0.754878
a = −2.39656 − 0.93888I
b = 1.240420 − 0.312627I
4.03235 + 1.41510I −5.19277 − 4.90874I
u = 0.754878
a = −3.45231 + 0.29460I
b = −0.158156 − 0.540866I
4.03235 − 1.41510I −5.19277 + 4.90874I
u = 0.754878
a = −3.45231 − 0.29460I
b = −0.158156 + 0.540866I
4.03235 + 1.41510I −5.19277 − 4.90874I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
+ u
2
− 1)
8
)(u
15
− 5u
13
+ ··· − 2u − 2)(u
22
− 9u
21
+ ··· + 80u − 16)
c
2
((u
3
+ u
2
+ 2u + 1)
8
)(u
15
+ 10u
14
+ ··· + 32u + 4)
· (u
22
+ 11u
21
+ ··· + 1408u + 256)
c
3
, c
9
(u
15
+ 4u
13
+ ··· + u − 1)(u
22
+ 18u
20
+ ··· − 3u − 1)
· (u
24
− u
23
+ ··· − 276u + 1133)
c
4
, c
11
(u
15
+ 2u
13
+ ··· + 4u − 1)(u
22
− 6u
20
+ ··· + 4u − 1)
· (u
24
− 3u
23
+ ··· − 54u + 59)
c
5
((u
4
− 3u
3
+ u
2
+ 2u + 1)
6
)(u
15
− 11u
14
+ ··· + 73u − 25)
· (u
22
+ 12u
21
+ ··· + 672u + 64)
c
6
(u
15
+ 4u
13
+ ··· + u + 1)(u
22
+ 18u
20
+ ··· − 3u − 1)
· (u
24
− u
23
+ ··· − 276u + 1133)
c
7
((u
3
+ u
2
− 1)
8
)(u
15
− 5u
13
+ ··· − 2u + 2)(u
22
− 9u
21
+ ··· + 80u − 16)
c
8
((u
4
+ u
3
+ u
2
+ 1)
6
)(u
15
− 7u
14
+ ··· + 3u
2
− 1)
· (u
22
− 12u
21
+ ··· − 64u + 8)
c
10
(u
15
+ u
14
+ ··· + 2u + 2)(u
22
+ u
21
+ ··· − 2u
2
− 10)
· (u
24
− u
23
+ ··· − 3286u + 2677)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
((y
3
− y
2
+ 2y −1)
8
)(y
15
− 10y
14
+ ··· + 32y −4)
· (y
22
− 11y
21
+ ··· − 1408y + 256)
c
2
((y
3
+ 3y
2
+ 2y −1)
8
)(y
15
− 2y
14
+ ··· − 8y −16)
· (y
22
+ y
21
+ ··· − 663552y + 65536)
c
3
, c
6
, c
9
(y
15
+ 8y
14
+ ··· + 11y −1)(y
22
+ 36y
21
+ ··· + 9y + 1)
· (y
24
+ 27y
23
+ ··· + 64316y + 1283689)
c
4
, c
11
(y
15
+ 4y
14
+ ··· + 14y −1)(y
22
− 12y
21
+ ··· − 66y + 1)
· (y
24
+ 3y
23
+ ··· − 3152y + 3481)
c
5
((y
4
− 7y
3
+ 15y
2
− 2y + 1)
6
)(y
15
− 19y
14
+ ··· + 4329y −625)
· (y
22
− 26y
21
+ ··· − 273920y + 4096)
c
8
((y
4
+ y
3
+ 3y
2
+ 2y + 1)
6
)(y
15
− 3y
14
+ ··· + 6y −1)
· (y
22
− 2y
21
+ ··· + 224y + 64)
c
10
(y
15
+ 7y
14
+ ··· + 39y
2
− 4)(y
22
+ 19y
21
+ ··· + 40y + 100)
· (y
24
+ 15y
23
+ ··· + 16368400y + 7166329)
20
