12a
1266
(K12a
1266
)
A knot diagram
1
Linearized knot diagam
5 7 10 9 12 2 11 1 4 3 6 8
Solving Sequence
2,6
7
3,11
8 12 5 1 9 4 10
c
6
c
2
c
7
c
11
c
5
c
1
c
8
c
4
c
10
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.12438 × 10
16
u
26
+ 3.39034 × 10
16
u
25
+ ··· + 3.51214 × 10
17
b − 1.86185 × 10
17
,
− 3.21225 × 10
16
u
26
+ 8.75841 × 10
17
u
25
+ ··· + 7.02429 × 10
18
a − 4.49004 × 10
18
, u
27
− u
26
+ ··· + 9u + 5i
I
u
2
= h2.28254 × 10
43
u
41
− 8.69949 × 10
42
u
40
+ ··· + 2.41192 × 10
44
b − 1.19984 × 10
44
,
− 7.56007 × 10
44
u
41
+ 5.11353 × 10
44
u
40
+ ··· + 1.20596 × 10
45
a + 2.17680 × 10
45
, u
42
− u
41
+ ··· + 2u − 1i
I
u
3
= hb + u, 4a
2
− 4au + 2a − u − 2, u
2
+ 1i
I
u
4
= hb, a + 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 74 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
= h2.12×10
16
u
26
+3.39×10
16
u
25
+· · ·+3.51×10
17
b−1.86×10
17
, −3.21×
10
16
u
26
+8.76×10
17
u
25
+· · ·+7.02×10
18
a−4.49×10
18
, u
27
−u
26
+· · ·+9u+5i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
0.00457306u
26
− 0.124688u
25
+ ··· + 3.79809u + 0.639216
−0.0604868u
26
− 0.0965321u
25
+ ··· + 1.90841u + 0.530119
a
8
=
−0.0206853u
26
+ 0.0614281u
25
+ ··· + 0.192050u + 0.879629
0.0369043u
26
+ 0.0238101u
25
+ ··· − 0.476441u − 0.325299
a
12
=
0.0650598u
26
− 0.0281555u
25
+ ··· + 1.88969u + 0.109097
−0.0604868u
26
− 0.0965321u
25
+ ··· + 1.90841u + 0.530119
a
5
=
0.0140907u
26
− 0.0116527u
25
+ ··· − 0.150722u + 0.977059
0.0259519u
26
− 0.0340007u
25
+ ··· + 0.326726u + 0.353353
a
1
=
0.0243171u
26
+ 0.00525786u
25
+ ··· + 0.823890u + 0.00567092
−0.121201u
26
− 0.108891u
25
+ ··· + 2.56585u + 0.714641
a
9
=
0.00888964u
26
+ 0.0799914u
25
+ ··· − 0.0211326u + 0.758044
−0.193188u
26
+ 0.0645916u
25
+ ··· + 1.32901u + 0.280707
a
4
=
0.0413949u
26
− 0.0691682u
25
+ ··· + 0.0713333u + 0.446077
0.0832991u
26
− 0.0769045u
25
+ ··· − 0.735872u − 0.238212
a
10
=
0.0565987u
26
− 0.0352749u
25
+ ··· + 3.17189u + 0.271852
0.0225032u
26
− 0.0446485u
25
+ ··· + 1.00153u + 0.190291
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
93486209329993615
351214301166382432
u
26
+
160253811475151391
175607150583191216
u
25
+ ··· −
1621899456495377937
87803575291595608
u −
3975960787929459125
351214301166382432
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
16(16u
27
+ 32u
26
+ ··· + 25u + 11)
c
2
, c
6
, c
8
c
12
u
27
− u
26
+ ··· + 9u + 5
c
3
, c
4
, c
9
c
10
u
27
+ 3u
26
+ ··· − 70u − 10
c
5
, c
11
u
27
− 3u
26
+ ··· + 18u − 58
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
256(256y
27
− 3968y
26
+ ··· + 977y −121)
c
2
, c
6
, c
8
c
12
y
27
− 15y
26
+ ··· − 59y −25
c
3
, c
4
, c
9
c
10
y
27
+ 33y
26
+ ··· − 160y −100
c
5
, c
11
y
27
+ 15y
26
+ ··· − 67768y −3364
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.364874 + 0.825098I
a = −0.238313 + 0.397025I
b = 0.112921 − 1.126640I
3.64402 − 0.53435I 4.34399 + 2.80873I
u = 0.364874 − 0.825098I
a = −0.238313 − 0.397025I
b = 0.112921 + 1.126640I
3.64402 + 0.53435I 4.34399 − 2.80873I
u = −1.161210 + 0.177318I
a = −1.55299 + 0.71207I
b = −1.02417 + 1.45743I
−4.02024 + 2.79292I −13.1385 − 5.9846I
u = −1.161210 − 0.177318I
a = −1.55299 − 0.71207I
b = −1.02417 − 1.45743I
−4.02024 − 2.79292I −13.1385 + 5.9846I
u = −1.19546
a = 1.84775
b = 1.71581
−5.68324 −17.5310
u = −0.682757 + 0.364207I
a = 0.789005 − 0.357352I
b = 0.022604 − 1.395470I
−0.14501 + 1.44728I −5.76179 − 4.68277I
u = −0.682757 − 0.364207I
a = 0.789005 + 0.357352I
b = 0.022604 + 1.395470I
−0.14501 − 1.44728I −5.76179 + 4.68277I
u = 1.235400 + 0.089712I
a = 0.774713 − 0.907018I
b = 0.67807 − 1.77115I
−13.27050 − 1.98767I −16.4839 + 3.0792I
u = 1.235400 − 0.089712I
a = 0.774713 + 0.907018I
b = 0.67807 + 1.77115I
−13.27050 + 1.98767I −16.4839 − 3.0792I
u = 1.214930 + 0.391524I
a = 1.60058 + 0.31754I
b = 0.80643 + 1.29561I
−2.26047 − 8.25333I −7.35249 + 7.59279I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.214930 − 0.391524I
a = 1.60058 − 0.31754I
b = 0.80643 − 1.29561I
−2.26047 + 8.25333I −7.35249 − 7.59279I
u = 1.272470 + 0.241748I
a = −1.45426 + 0.39776I
b = −1.380070 + 0.244451I
−9.23965 − 5.78427I −13.7128 + 6.1785I
u = 1.272470 − 0.241748I
a = −1.45426 − 0.39776I
b = −1.380070 − 0.244451I
−9.23965 + 5.78427I −13.7128 − 6.1785I
u = −0.290377 + 1.268100I
a = −0.032432 + 0.388759I
b = −0.230064 − 0.925197I
1.90694 − 0.98903I −9.51739 + 7.74908I
u = −0.290377 − 1.268100I
a = −0.032432 − 0.388759I
b = −0.230064 + 0.925197I
1.90694 + 0.98903I −9.51739 − 7.74908I
u = −1.32694 + 0.50922I
a = −1.52492 + 0.11633I
b = −0.70253 + 1.32123I
−5.85291 + 12.82750I −9.51213 − 8.73383I
u = −1.32694 − 0.50922I
a = −1.52492 − 0.11633I
b = −0.70253 − 1.32123I
−5.85291 − 12.82750I −9.51213 + 8.73383I
u = 0.346727 + 0.443868I
a = 1.38523 + 1.47579I
b = 0.249094 + 0.559328I
−7.24892 − 1.17668I −9.05075 + 5.85143I
u = 0.346727 − 0.443868I
a = 1.38523 − 1.47579I
b = 0.249094 − 0.559328I
−7.24892 + 1.17668I −9.05075 − 5.85143I
u = −1.41709 + 0.38831I
a = 1.215140 + 0.373473I
b = 1.248380 + 0.154329I
−19.0366 + 8.9897I −13.6836 − 4.5362I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41709 − 0.38831I
a = 1.215140 − 0.373473I
b = 1.248380 − 0.154329I
−19.0366 − 8.9897I −13.6836 + 4.5362I
u = 0.31044 + 1.48273I
a = 0.120252 + 0.379616I
b = 0.355070 − 0.859580I
−6.71203 + 1.54503I −10.23539 − 4.25212I
u = 0.31044 − 1.48273I
a = 0.120252 − 0.379616I
b = 0.355070 + 0.859580I
−6.71203 − 1.54503I −10.23539 + 4.25212I
u = 1.41907 + 0.58513I
a = 1.45781 − 0.00636I
b = 0.65443 + 1.34532I
−15.3179 − 15.6052I −10.54586 + 7.38863I
u = 1.41907 − 0.58513I
a = 1.45781 + 0.00636I
b = 0.65443 − 1.34532I
−15.3179 + 15.6052I −10.54586 − 7.38863I
u = −0.187802 + 0.286116I
a = −0.563690 + 0.885446I
b = −0.148069 + 0.298333I
−0.206928 + 0.796519I −5.58390 − 8.64848I
u = −0.187802 − 0.286116I
a = −0.563690 − 0.885446I
b = −0.148069 − 0.298333I
−0.206928 − 0.796519I −5.58390 + 8.64848I
7
II.
I
u
2
= h2.28×10
43
u
41
−8.70×10
42
u
40
+· · ·+2.41×10
44
b−1.20×10
44
, −7.56×
10
44
u
41
+5.11×10
44
u
40
+· · ·+1.21×10
45
a+2.18×10
45
, u
42
−u
41
+· · ·+2u−1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
0.626892u
41
− 0.424021u
40
+ ··· + 17.7437u − 1.80503
−0.0946359u
41
+ 0.0360687u
40
+ ··· − 2.56626u + 0.497461
a
8
=
−0.957966u
41
+ 1.20380u
40
+ ··· − 2.43714u + 0.291897
0.108267u
41
+ 0.0256008u
40
+ ··· + 5.44460u − 0.834598
a
12
=
0.721528u
41
− 0.460090u
40
+ ··· + 20.3099u − 2.30250
−0.0946359u
41
+ 0.0360687u
40
+ ··· − 2.56626u + 0.497461
a
5
=
0.620643u
41
− 0.813885u
40
+ ··· + 2.26414u + 2.28794
−0.0198339u
41
− 0.0132637u
40
+ ··· − 4.39112u + 0.608259
a
1
=
2.25050u
41
− 2.34710u
40
+ ··· + 11.2525u − 5.46408
−0.340874u
41
+ 0.341757u
40
+ ··· − 1.40077u + 0.973676
a
9
=
0.353819u
41
− 0.400322u
40
+ ··· + 5.77072u − 4.35429
0.197477u
41
− 0.175445u
40
+ ··· − 3.35600u + 0.644767
a
4
=
−0.937637u
41
+ 1.14987u
40
+ ··· + 13.7232u + 0.948572
0.307741u
41
− 0.331030u
40
+ ··· − 1.73977u − 0.240444
a
10
=
0.583059u
41
− 0.427551u
40
+ ··· + 17.4925u − 1.91785
−0.121381u
41
+ 0.0565404u
40
+ ··· − 2.26417u + 0.562919
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.351958u
41
− 0.318899u
40
+ ··· + 1.24803u − 5.09170
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
25(25u
42
+ 85u
41
+ ··· + 83528u − 95309)
c
2
, c
6
, c
8
c
12
u
42
− u
41
+ ··· + 2u − 1
c
3
, c
4
, c
9
c
10
(u
21
− u
20
+ ··· + u + 1)
2
c
5
, c
11
(u
21
+ u
20
+ ··· + u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
625(625y
42
− 15625y
41
+ ··· − 1.44298 × 10
11
y + 9.08381 × 10
9
)
c
2
, c
6
, c
8
c
12
y
42
− 29y
41
+ ··· − 4y + 1
c
3
, c
4
, c
9
c
10
(y
21
+ 27y
20
+ ··· − y −1)
2
c
5
, c
11
(y
21
+ 11y
20
+ ··· − y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000750 + 0.247732I
a = 2.15592 − 0.26450I
b = 0.199725 + 0.739431I
−2.81557 − 1.02651I −5.11271 + 6.49406I
u = 1.000750 − 0.247732I
a = 2.15592 + 0.26450I
b = 0.199725 − 0.739431I
−2.81557 + 1.02651I −5.11271 − 6.49406I
u = −1.021330 + 0.145152I
a = 1.56374 − 0.38857I
b = 0.375476 − 1.140930I
−0.903078 + 0.771539I −5.08724 + 0.81413I
u = −1.021330 − 0.145152I
a = 1.56374 + 0.38857I
b = 0.375476 + 1.140930I
−0.903078 − 0.771539I −5.08724 − 0.81413I
u = 0.310624 + 1.009640I
a = −0.212763 − 0.473655I
b = −0.794642 + 0.241148I
−13.5849 − 4.1364I −11.71281 + 2.17514I
u = 0.310624 − 1.009640I
a = −0.212763 + 0.473655I
b = −0.794642 − 0.241148I
−13.5849 + 4.1364I −11.71281 − 2.17514I
u = −0.049213 + 1.055370I
a = 0.152235 − 0.405571I
b = 0.504141 + 1.153180I
−1.81098 − 7.30035I −6.83891 + 7.23595I
u = −0.049213 − 1.055370I
a = 0.152235 + 0.405571I
b = 0.504141 − 1.153180I
−1.81098 + 7.30035I −6.83891 − 7.23595I
u = −1.07621
a = −1.11344
b = −0.639263
−1.97351 −3.86210
u = 1.100220 + 0.092693I
a = −1.63403 + 0.13889I
b = −0.297476 + 1.182770I
−9.18536 − 0.72644I −6.52695 − 0.34896I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.100220 − 0.092693I
a = −1.63403 − 0.13889I
b = −0.297476 − 1.182770I
−9.18536 + 0.72644I −6.52695 + 0.34896I
u = −1.120660 + 0.175896I
a = −0.46285 + 1.49950I
b = 0.199725 + 0.739431I
−2.81557 − 1.02651I −5.11271 + 6.49406I
u = −1.120660 − 0.175896I
a = −0.46285 − 1.49950I
b = 0.199725 − 0.739431I
−2.81557 + 1.02651I −5.11271 − 6.49406I
u = 1.135500 + 0.423437I
a = −1.41111 − 0.14840I
b = −0.448707 − 1.150100I
1.14110 − 4.04104I −1.23432 + 4.27407I
u = 1.135500 − 0.423437I
a = −1.41111 + 0.14840I
b = −0.448707 + 1.150100I
1.14110 + 4.04104I −1.23432 − 4.27407I
u = 0.105993 + 0.746952I
a = 0.184562 − 0.232611I
b = −0.448707 + 1.150100I
1.14110 + 4.04104I −1.23432 − 4.27407I
u = 0.105993 − 0.746952I
a = 0.184562 + 0.232611I
b = −0.448707 − 1.150100I
1.14110 − 4.04104I −1.23432 + 4.27407I
u = 0.026147 + 1.279880I
a = −0.282427 − 0.429919I
b = −0.544516 + 1.163610I
−10.8630 + 9.1159I −8.57432 − 5.67037I
u = 0.026147 − 1.279880I
a = −0.282427 + 0.429919I
b = −0.544516 − 1.163610I
−10.8630 − 9.1159I −8.57432 + 5.67037I
u = −0.272541 + 0.659489I
a = −0.013376 − 0.755133I
b = 0.709616 + 0.181075I
−4.60791 + 2.71325I −10.44742 − 3.99913I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.272541 − 0.659489I
a = −0.013376 + 0.755133I
b = 0.709616 − 0.181075I
−4.60791 − 2.71325I −10.44742 + 3.99913I
u = 1.269690 + 0.210809I
a = 1.009430 − 0.033264I
b = 0.709616 − 0.181075I
−4.60791 − 2.71325I −10.44742 + 3.99913I
u = 1.269690 − 0.210809I
a = 1.009430 + 0.033264I
b = 0.709616 + 0.181075I
−4.60791 + 2.71325I −10.44742 − 3.99913I
u = −1.153270 + 0.592702I
a = −1.054360 − 0.605877I
b = −0.515219 + 0.758542I
−6.73763 + 2.10610I −12.68965 − 4.22092I
u = −1.153270 − 0.592702I
a = −1.054360 + 0.605877I
b = −0.515219 − 0.758542I
−6.73763 − 2.10610I −12.68965 + 4.22092I
u = 1.39064 + 0.33345I
a = −0.323551 + 0.496463I
b = −0.515219 + 0.758542I
−6.73763 + 2.10610I −12.68965 + 0.I
u = 1.39064 − 0.33345I
a = −0.323551 − 0.496463I
b = −0.515219 − 0.758542I
−6.73763 − 2.10610I −12.68965 + 0.I
u = −1.32978 + 0.55644I
a = 1.224510 − 0.037112I
b = 0.504141 − 1.153180I
−1.81098 + 7.30035I 0
u = −1.32978 − 0.55644I
a = 1.224510 + 0.037112I
b = 0.504141 + 1.153180I
−1.81098 − 7.30035I 0
u = −1.46842 + 0.32569I
a = −0.922519 − 0.020055I
b = −0.794642 − 0.241148I
−13.5849 + 4.1364I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46842 − 0.32569I
a = −0.922519 + 0.020055I
b = −0.794642 + 0.241148I
−13.5849 − 4.1364I 0
u = 1.32647 + 0.78499I
a = 0.867930 − 0.509797I
b = 0.631235 + 0.777388I
−16.2658 − 2.4434I 0
u = 1.32647 − 0.78499I
a = 0.867930 + 0.509797I
b = 0.631235 − 0.777388I
−16.2658 + 2.4434I 0
u = 1.47969 + 0.65675I
a = −1.114420 + 0.034710I
b = −0.544516 − 1.163610I
−10.8630 − 9.1159I 0
u = 1.47969 − 0.65675I
a = −1.114420 − 0.034710I
b = −0.544516 + 1.163610I
−10.8630 + 9.1159I 0
u = −1.58814 + 0.45186I
a = 0.400910 + 0.274750I
b = 0.631235 + 0.777388I
−16.2658 − 2.4434I 0
u = −1.58814 − 0.45186I
a = 0.400910 − 0.274750I
b = 0.631235 − 0.777388I
−16.2658 + 2.4434I 0
u = −0.175560 + 0.250558I
a = −3.45078 + 4.61056I
b = −0.297476 − 1.182770I
−9.18536 + 0.72644I −6.52695 + 0.34896I
u = −0.175560 − 0.250558I
a = −3.45078 − 4.61056I
b = −0.297476 + 1.182770I
−9.18536 − 0.72644I −6.52695 − 0.34896I
u = −0.016547 + 0.283471I
a = −2.71355 + 0.31034I
b = 0.375476 + 1.140930I
−0.903078 − 0.771539I −5.08724 − 0.81413I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.016547 − 0.283471I
a = −2.71355 − 0.31034I
b = 0.375476 − 1.140930I
−0.903078 + 0.771539I −5.08724 + 0.81413I
u = 0.175706
a = 3.58645
b = −0.639263
−1.97351 −3.86210
15
III. I
u
3
= hb + u, 4a
2
− 4au + 2a − u − 2, u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−1
a
3
=
−u
2u
a
11
=
a
−u
a
8
=
−
1
2
a +
1
4
u +
3
2
−au − 2
a
12
=
a + u
−u
a
5
=
au
1
a
1
=
1
2
au + a −
1
2
u +
1
4
−a + u
a
9
=
au − a +
1
2
u + 2
−2au − 3
a
4
=
−3au − a + u −
3
2
4au + 2a − u + 2
a
10
=
3a − u
−4a + u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
16(16u
4
+ 16u
3
+ 4u
2
+ 5)
c
2
, c
5
, c
6
c
8
, c
11
, c
12
(u
2
+ 1)
2
c
3
, c
4
, c
9
c
10
u
4
+ 3u
2
+ 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
256(256y
4
− 128y
3
+ 176y
2
+ 40y + 25)
c
2
, c
5
, c
6
c
8
, c
11
, c
12
(y + 1)
4
c
3
, c
4
, c
9
c
10
(y
2
+ 3y + 1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.809017 + 0.500000I
b = − 1.000000I
−5.59278 −4.00000
u = 1.000000I
a = 0.309017 + 0.500000I
b = − 1.000000I
2.30291 −4.00000
u = − 1.000000I
a = −0.809017 − 0.500000I
b = 1.000000I
−5.59278 −4.00000
u = − 1.000000I
a = 0.309017 − 0.500000I
b = 1.000000I
2.30291 −4.00000
19
IV. I
u
4
= hb, a + 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
6
=
1
0
a
7
=
1
1
a
3
=
1
0
a
11
=
−1
0
a
8
=
0
1
a
12
=
−1
0
a
5
=
1
0
a
1
=
−1
−1
a
9
=
−1
0
a
4
=
1
0
a
10
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u − 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
c
6
, c
12
u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
y −1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0
−3.28987 −12.0000
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
6400(u − 1)(16u
4
+ 16u
3
+ 4u
2
+ 5)(16u
27
+ 32u
26
+ ··· + 25u + 11)
· (25u
42
+ 85u
41
+ ··· + 83528u − 95309)
c
2
, c
8
(u − 1)(u
2
+ 1)
2
(u
27
− u
26
+ ··· + 9u + 5)(u
42
− u
41
+ ··· + 2u − 1)
c
3
, c
4
, c
9
c
10
u(u
4
+ 3u
2
+ 1)(u
21
− u
20
+ ··· + u + 1)
2
(u
27
+ 3u
26
+ ··· − 70u − 10)
c
5
, c
11
u(u
2
+ 1)
2
(u
21
+ u
20
+ ··· + u + 1)
2
(u
27
− 3u
26
+ ··· + 18u − 58)
c
6
, c
12
(u + 1)(u
2
+ 1)
2
(u
27
− u
26
+ ··· + 9u + 5)(u
42
− u
41
+ ··· + 2u − 1)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
40960000(y −1)(256y
4
− 128y
3
+ 176y
2
+ 40y + 25)
· (256y
27
− 3968y
26
+ ··· + 977y −121)
· (625y
42
− 15625y
41
+ ··· − 144297752748y + 9083805481)
c
2
, c
6
, c
8
c
12
(y −1)(y + 1)
4
(y
27
− 15y
26
+ ··· − 59y −25)
· (y
42
− 29y
41
+ ··· − 4y + 1)
c
3
, c
4
, c
9
c
10
y(y
2
+ 3y + 1)
2
(y
21
+ 27y
20
+ ··· − y −1)
2
· (y
27
+ 33y
26
+ ··· − 160y −100)
c
5
, c
11
y(y + 1)
4
(y
21
+ 11y
20
+ ··· − y −1)
2
· (y
27
+ 15y
26
+ ··· − 67768y −3364)
25
