12a
1083
(K12a
1083
)
A knot diagram
1
Linearized knot diagam
4 7 10 12 1 9 3 11 2 8 6 5
Solving Sequence
1,6
5 12 4 2
8,11
9 7 10 3
c
5
c
12
c
4
c
1
c
11
c
8
c
6
c
10
c
3
c
2
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.11665 × 10
47
u
88
− 1.10564 × 10
47
u
87
+ ··· + 6.92682 × 10
46
b − 2.35140 × 10
47
,
3.99720 × 10
45
u
88
− 1.09937 × 10
45
u
87
+ ··· + 6.29711 × 10
45
a + 7.42531 × 10
45
, u
89
+ 2u
88
+ ··· − u + 1i
I
u
2
= h2u
4
− 12u
3
+ 7b + 9u + 6, −u
4
− u
3
+ 7a + 6u − 3, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 94 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
= h−2.12×10
47
u
88
−1.11×10
47
u
87
+· · ·+6.93×10
46
b−2.35×10
47
, 4.00×
10
45
u
88
−1.10×10
45
u
87
+· · ·+6.30×10
45
a+7.43×10
45
, u
89
+2u
88
+· · ·−u+1i
(i) Arc colorings
a
1
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
12
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
8
=
−0.634768u
88
+ 0.174583u
87
+ ··· + 7.02674u − 1.17916
3.05573u
88
+ 1.59617u
87
+ ··· − 5.89150u + 3.39464
a
11
=
−u
3
+ 2u
−u
3
+ u
a
9
=
−0.126780u
88
+ 0.404435u
87
+ ··· + 8.42304u − 0.381113
1.69946u
88
+ 0.554035u
87
+ ··· − 3.03296u + 2.56541
a
7
=
3.16567u
88
+ 2.81717u
87
+ ··· − 9.92028u + 0.927302
−1.96936u
88
− 2.61970u
87
+ ··· + 6.37800u − 2.57339
a
10
=
−0.388476u
88
+ 0.166599u
87
+ ··· + 8.37411u − 0.515987
1.83579u
88
+ 0.737421u
87
+ ··· − 2.95142u + 2.51815
a
3
=
−3.30265u
88
− 3.44449u
87
+ ··· − 0.682398u − 2.18348
2.41903u
88
+ 3.69517u
87
+ ··· + 1.98227u + 0.0416273
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6.44685u
88
− 7.91516u
87
+ ··· + 17.4108u + 0.723245
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
89
− 6u
88
+ ··· − 5907u + 847
c
2
, c
7
u
89
+ 2u
88
+ ··· − u + 1
c
3
7(7u
89
− 109u
88
+ ··· − 1197918u − 1021121)
c
4
, c
5
, c
12
u
89
+ 2u
88
+ ··· − u + 1
c
6
7(7u
89
+ 73u
88
+ ··· + 4.22849 × 10
7
u + 4324097)
c
8
, c
10
u
89
+ 6u
88
+ ··· + 1691u + 49
c
9
u
89
− 3u
88
+ ··· + 59096u
2
− 1568
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
89
+ 72y
88
+ ··· + 9580901y −717409
c
2
, c
7
y
89
− 60y
88
+ ··· − 11y −1
c
3
49
· (49y
89
− 7919y
88
+ ··· − 31244025855892y −1042688096641)
c
4
, c
5
, c
12
y
89
− 72y
88
+ ··· − 11y −1
c
6
49
· (49y
89
− 12749y
88
+ ··· + 178083980700794y −18697814865409)
c
8
, c
10
y
89
− 76y
88
+ ··· + 3133195y −2401
c
9
y
89
+ 33y
88
+ ··· + 185325056y −2458624
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.125382 + 0.878758I
a = −0.70658 + 2.95493I
b = −0.48390 + 2.47308I
12.57200 − 0.58676I 7.92936 + 0.I
u = 0.125382 − 0.878758I
a = −0.70658 − 2.95493I
b = −0.48390 − 2.47308I
12.57200 + 0.58676I 7.92936 + 0.I
u = −0.108009 + 0.878753I
a = 0.63992 + 3.41927I
b = 0.30080 + 2.77816I
8.44721 + 6.94338I 3.88118 − 5.23404I
u = −0.108009 − 0.878753I
a = 0.63992 − 3.41927I
b = 0.30080 − 2.77816I
8.44721 − 6.94338I 3.88118 + 5.23404I
u = 0.107640 + 0.869226I
a = −0.84277 + 3.64500I
b = −0.36192 + 3.00809I
13.1823 − 12.7067I 5.61691 + 6.76212I
u = 0.107640 − 0.869226I
a = −0.84277 − 3.64500I
b = −0.36192 − 3.00809I
13.1823 + 12.7067I 5.61691 − 6.76212I
u = −1.14112
a = −0.524359
b = −1.81639
3.04390 0
u = −0.018538 + 0.839308I
a = −0.04785 − 3.30693I
b = 0.26758 − 2.88148I
11.49580 + 2.45922I 9.88893 − 2.84321I
u = −0.018538 − 0.839308I
a = −0.04785 + 3.30693I
b = 0.26758 + 2.88148I
11.49580 − 2.45922I 9.88893 + 2.84321I
u = 0.061352 + 0.829162I
a = −0.545645 − 0.852361I
b = −0.955134 − 0.749592I
7.26203 − 6.26191I 5.35569 + 6.30354I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.061352 − 0.829162I
a = −0.545645 + 0.852361I
b = −0.955134 + 0.749592I
7.26203 + 6.26191I 5.35569 − 6.30354I
u = 0.014115 + 0.816635I
a = 1.52546 − 4.00461I
b = 0.82563 − 3.07082I
6.78894 − 1.20316I 1.70987 + 0.75534I
u = 0.014115 − 0.816635I
a = 1.52546 + 4.00461I
b = 0.82563 + 3.07082I
6.78894 + 1.20316I 1.70987 − 0.75534I
u = −0.061691 + 0.806346I
a = −0.245155 − 0.075307I
b = 0.214340 − 0.168825I
3.54962 + 2.89056I −0.65715 − 3.47288I
u = −0.061691 − 0.806346I
a = −0.245155 + 0.075307I
b = 0.214340 + 0.168825I
3.54962 − 2.89056I −0.65715 + 3.47288I
u = −0.517626 + 0.610535I
a = −1.32915 + 0.51384I
b = −0.251501 + 0.525803I
2.17162 + 2.14937I 6.30599 − 5.13356I
u = −0.517626 − 0.610535I
a = −1.32915 − 0.51384I
b = −0.251501 − 0.525803I
2.17162 − 2.14937I 6.30599 + 5.13356I
u = 0.034225 + 0.793430I
a = 2.62398 + 1.24253I
b = 1.60665 + 0.50390I
6.48290 − 0.18025I 6.74425 − 0.95194I
u = 0.034225 − 0.793430I
a = 2.62398 − 1.24253I
b = 1.60665 − 0.50390I
6.48290 + 0.18025I 6.74425 + 0.95194I
u = 1.22262
a = −0.570553
b = 2.43483
−1.22444 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.140140 + 0.447012I
a = 1.56190 − 1.40744I
b = −0.75301 − 1.95426I
9.46007 − 4.15016I 0
u = 1.140140 − 0.447012I
a = 1.56190 + 1.40744I
b = −0.75301 + 1.95426I
9.46007 + 4.15016I 0
u = 1.221650 + 0.117112I
a = 0.542321 − 1.049280I
b = 0.744477 − 0.262187I
1.49288 − 3.55667I 0
u = 1.221650 − 0.117112I
a = 0.542321 + 1.049280I
b = 0.744477 + 0.262187I
1.49288 + 3.55667I 0
u = 0.537235 + 0.543423I
a = 1.43198 + 0.25042I
b = −0.017291 + 0.227081I
6.94642 + 4.33545I 4.08323 − 1.64396I
u = 0.537235 − 0.543423I
a = 1.43198 − 0.25042I
b = −0.017291 − 0.227081I
6.94642 − 4.33545I 4.08323 + 1.64396I
u = 1.160450 + 0.432770I
a = 1.78321 − 1.56494I
b = −0.68857 − 2.55744I
9.95317 + 8.04672I 0
u = 1.160450 − 0.432770I
a = 1.78321 + 1.56494I
b = −0.68857 + 2.55744I
9.95317 − 8.04672I 0
u = −1.161820 + 0.445584I
a = −1.73625 − 1.46920I
b = 0.57367 − 2.32260I
5.21394 − 2.21357I 0
u = −1.161820 − 0.445584I
a = −1.73625 + 1.46920I
b = 0.57367 + 2.32260I
5.21394 + 2.21357I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.24503
a = −0.621366
b = 0.809575
−2.34521 0
u = −1.254420 + 0.066692I
a = −0.296221 − 1.087230I
b = −0.450958 + 0.738893I
−2.36817 + 1.69929I 0
u = −1.254420 − 0.066692I
a = −0.296221 + 1.087230I
b = −0.450958 − 0.738893I
−2.36817 − 1.69929I 0
u = 0.473696 + 0.568911I
a = 1.032500 + 0.374017I
b = 0.033167 + 0.777124I
7.13183 − 8.33264I 3.55448 + 7.75216I
u = 0.473696 − 0.568911I
a = 1.032500 − 0.374017I
b = 0.033167 − 0.777124I
7.13183 + 8.33264I 3.55448 − 7.75216I
u = −1.215220 + 0.345432I
a = −0.321172 + 0.016545I
b = 0.022056 + 0.329477I
0.013033 + 1.266560I 0
u = −1.215220 − 0.345432I
a = −0.321172 − 0.016545I
b = 0.022056 − 0.329477I
0.013033 − 1.266560I 0
u = 1.210740 + 0.372378I
a = −0.344730 − 0.246031I
b = −0.644449 + 1.070780I
3.72918 + 1.93529I 0
u = 1.210740 − 0.372378I
a = −0.344730 + 0.246031I
b = −0.644449 − 1.070780I
3.72918 − 1.93529I 0
u = 1.28089
a = 8.66646
b = −13.2618
−0.642402 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.276390 + 0.158096I
a = −0.699550 − 0.079722I
b = 0.948418 − 0.603694I
−2.68953 + 0.28084I 0
u = −1.276390 − 0.158096I
a = −0.699550 + 0.079722I
b = 0.948418 + 0.603694I
−2.68953 − 0.28084I 0
u = 1.244620 + 0.338635I
a = 1.97834 + 0.84588I
b = 1.92110 − 0.87909I
2.75165 − 3.89874I 0
u = 1.244620 − 0.338635I
a = 1.97834 − 0.84588I
b = 1.92110 + 0.87909I
2.75165 + 3.89874I 0
u = 1.257930 + 0.362564I
a = −1.49421 + 2.10833I
b = 1.46227 + 3.01516I
2.93653 − 3.03854I 0
u = 1.257930 − 0.362564I
a = −1.49421 − 2.10833I
b = 1.46227 − 3.01516I
2.93653 + 3.03854I 0
u = −1.253420 + 0.382637I
a = 1.69811 + 0.87469I
b = −0.39093 + 2.92458I
7.67284 + 1.92905I 0
u = −1.253420 − 0.382637I
a = 1.69811 − 0.87469I
b = −0.39093 − 2.92458I
7.67284 − 1.92905I 0
u = −1.280020 + 0.364382I
a = 2.70109 + 0.60013I
b = 0.23888 + 3.04951I
2.76333 + 5.45191I 0
u = −1.280020 − 0.364382I
a = 2.70109 − 0.60013I
b = 0.23888 − 3.04951I
2.76333 − 5.45191I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.330850 + 0.108907I
a = 0.295863 − 1.001570I
b = 0.320656 − 0.175813I
−3.20338 + 5.50473I 0
u = −1.330850 − 0.108907I
a = 0.295863 + 1.001570I
b = 0.320656 + 0.175813I
−3.20338 − 5.50473I 0
u = 1.283730 + 0.380785I
a = −1.98430 + 1.01020I
b = 0.85763 + 2.70580I
7.44375 − 6.84138I 0
u = 1.283730 − 0.380785I
a = −1.98430 − 1.01020I
b = 0.85763 − 2.70580I
7.44375 + 6.84138I 0
u = −1.293800 + 0.348698I
a = 0.47441 − 1.60670I
b = 1.41902 − 0.31806I
2.33908 + 4.29811I 0
u = −1.293800 − 0.348698I
a = 0.47441 + 1.60670I
b = 1.41902 + 0.31806I
2.33908 − 4.29811I 0
u = 1.347160 + 0.076029I
a = −0.278467 − 0.594511I
b = −0.511180 − 0.135896I
−6.28340 − 1.68453I 0
u = 1.347160 − 0.076029I
a = −0.278467 + 0.594511I
b = −0.511180 + 0.135896I
−6.28340 + 1.68453I 0
u = 1.311970 + 0.356969I
a = −0.344886 + 0.019411I
b = 0.331785 − 0.013612I
−0.74881 − 7.08396I 0
u = 1.311970 − 0.356969I
a = −0.344886 − 0.019411I
b = 0.331785 + 0.013612I
−0.74881 + 7.08396I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.312650 + 0.370540I
a = 0.534803 + 0.679320I
b = −1.136720 + 0.422168I
2.96518 + 10.57800I 0
u = −1.312650 − 0.370540I
a = 0.534803 − 0.679320I
b = −1.136720 − 0.422168I
2.96518 − 10.57800I 0
u = 1.357590 + 0.223656I
a = 0.330273 − 0.203402I
b = −0.775634 − 1.129410I
−4.54409 − 4.94988I 0
u = 1.357590 − 0.223656I
a = 0.330273 + 0.203402I
b = −0.775634 + 1.129410I
−4.54409 + 4.94988I 0
u = −0.186642 + 0.594881I
a = −0.295138 + 0.951089I
b = −0.158997 + 0.865207I
0.35216 + 1.94903I −4.32842 − 5.49561I
u = −0.186642 − 0.594881I
a = −0.295138 − 0.951089I
b = −0.158997 − 0.865207I
0.35216 − 1.94903I −4.32842 + 5.49561I
u = −1.345940 + 0.387551I
a = −2.27394 − 0.90136I
b = −0.00868 − 3.24488I
8.6182 + 17.2188I 0
u = −1.345940 − 0.387551I
a = −2.27394 + 0.90136I
b = −0.00868 + 3.24488I
8.6182 − 17.2188I 0
u = 1.347310 + 0.393319I
a = 2.03377 − 0.95300I
b = −0.02306 − 3.02165I
3.87884 − 11.50730I 0
u = 1.347310 − 0.393319I
a = 2.03377 + 0.95300I
b = −0.02306 + 3.02165I
3.87884 + 11.50730I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.405720 + 0.154129I
a = 0.251570 + 0.203801I
b = 0.89571 − 1.25156I
1.13145 + 10.72670I 0
u = −1.405720 − 0.154129I
a = 0.251570 − 0.203801I
b = 0.89571 + 1.25156I
1.13145 − 10.72670I 0
u = −1.35901 + 0.39173I
a = −1.72454 − 0.72153I
b = −0.16351 − 2.75815I
7.90464 + 5.14950I 0
u = −1.35901 − 0.39173I
a = −1.72454 + 0.72153I
b = −0.16351 + 2.75815I
7.90464 − 5.14950I 0
u = −1.43311 + 0.11920I
a = 0.661784 − 0.160501I
b = 0.860338 − 0.810277I
0.57536 − 2.22101I 0
u = −1.43311 − 0.11920I
a = 0.661784 + 0.160501I
b = 0.860338 + 0.810277I
0.57536 + 2.22101I 0
u = 1.44205 + 0.17876I
a = −0.285437 − 0.246969I
b = −1.03613 − 1.20108I
−4.15123 − 4.81054I 0
u = 1.44205 − 0.17876I
a = −0.285437 + 0.246969I
b = −1.03613 + 1.20108I
−4.15123 + 4.81054I 0
u = 0.339746 + 0.376517I
a = 1.33791 + 0.97783I
b = 0.341605 − 0.405834I
1.91765 − 3.87309I 0.55666 + 8.72458I
u = 0.339746 − 0.376517I
a = 1.33791 − 0.97783I
b = 0.341605 + 0.405834I
1.91765 + 3.87309I 0.55666 − 8.72458I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.408647 + 0.240058I
a = −1.027240 + 0.453445I
b = −0.221980 − 0.162291I
−0.921165 + 0.597911I −8.15892 − 3.51104I
u = −0.408647 − 0.240058I
a = −1.027240 − 0.453445I
b = −0.221980 + 0.162291I
−0.921165 − 0.597911I −8.15892 + 3.51104I
u = 0.302175 + 0.323229I
a = 0.239200 + 0.620710I
b = 0.740732 + 0.559642I
1.88095 + 1.39164I 0.13565 + 1.94806I
u = 0.302175 − 0.323229I
a = 0.239200 − 0.620710I
b = 0.740732 − 0.559642I
1.88095 − 1.39164I 0.13565 − 1.94806I
u = −0.120036 + 0.422476I
a = −0.68149 + 2.35518I
b = −0.466667 − 0.230513I
5.40434 + 1.61762I 8.06305 − 4.45368I
u = −0.120036 − 0.422476I
a = −0.68149 − 2.35518I
b = −0.466667 + 0.230513I
5.40434 − 1.61762I 8.06305 + 4.45368I
u = −0.335863
a = 0.323498
b = −1.74395
3.97864 −10.7630
u = 0.131901 + 0.259616I
a = 0.04663 + 1.73551I
b = 0.648286 − 0.639044I
1.69944 − 0.54221I 5.59861 − 1.83592I
u = 0.131901 − 0.259616I
a = 0.04663 − 1.73551I
b = 0.648286 + 0.639044I
1.69944 + 0.54221I 5.59861 + 1.83592I
13
II.
I
u
2
= h2u
4
−12u
3
+7b+9u+6, −u
4
−u
3
+7a+6u−3, u
5
−u
4
−2u
3
+u
2
+u+1i
(i) Arc colorings
a
1
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
12
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
8
=
1
7
u
4
+
1
7
u
3
−
6
7
u +
3
7
−
2
7
u
4
+
12
7
u
3
−
9
7
u −
6
7
a
11
=
−u
3
+ 2u
−u
3
+ u
a
9
=
1
7
u
4
−
6
7
u
3
+
8
7
u +
3
7
−
2
7
u
4
+
5
7
u
3
−
2
7
u −
6
7
a
7
=
0.326531u
4
− 0.959184u
3
+ ··· + 0.612245u + 1.26531
−0.795918u
4
+ 1.77551u
3
+ ··· − 0.367347u − 0.959184
a
10
=
1
7
u
4
−
6
7
u
3
+
8
7
u +
3
7
−
2
7
u
4
+
5
7
u
3
−
2
7
u −
6
7
a
3
=
−0.244898u
4
+ 0.469388u
3
+ ··· + 0.0408163u + 0.551020
1.34694u
4
− 1.08163u
3
+ ··· − 0.224490u + 0.469388
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
143
49
u
4
−
122
49
u
3
+
44
7
u
2
−
17
49
u +
138
49
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
2
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
3
7(7u
5
− 12u
4
+ 2u
3
− 7u
2
− 1)
c
4
, c
5
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
6
7(7u
5
+ 30u
4
+ 41u
3
+ 26u
2
+ 8u + 1)
c
7
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
8
(u + 1)
5
c
9
u
5
c
10
(u − 1)
5
c
12
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
2
, c
7
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
3
49(49y
5
− 116y
4
− 164y
3
− 73y
2
− 14y −1)
c
4
, c
5
, c
12
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
6
49(49y
5
− 326y
4
+ 233y
3
− 80y
2
+ 12y −1)
c
8
, c
10
(y −1)
5
c
9
y
5
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = 1.52851
b = −3.01533
−0.756147 10.6380
u = −0.309916 + 0.549911I
a = 0.719612 − 0.452376I
b = −0.006697 − 0.760662I
1.31583 + 1.53058I 1.21564 − 2.72429I
u = −0.309916 − 0.549911I
a = 0.719612 + 0.452376I
b = −0.006697 + 0.760662I
1.31583 − 1.53058I 1.21564 + 2.72429I
u = 1.41878 + 0.21917I
a = 0.087560 + 0.348847I
b = 0.87151 + 1.27076I
−4.22763 − 4.40083I −2.06547 − 6.56835I
u = 1.41878 − 0.21917I
a = 0.087560 − 0.348847I
b = 0.87151 − 1.27076I
−4.22763 + 4.40083I −2.06547 + 6.56835I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)(u
89
− 6u
88
+ ··· − 5907u + 847)
c
2
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
89
+ 2u
88
+ ··· − u + 1)
c
3
49(7u
5
− 12u
4
+ 2u
3
− 7u
2
− 1)
· (7u
89
− 109u
88
+ ··· − 1197918u − 1021121)
c
4
, c
5
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
89
+ 2u
88
+ ··· − u + 1)
c
6
49(7u
5
+ 30u
4
+ 41u
3
+ 26u
2
+ 8u + 1)
· (7u
89
+ 73u
88
+ ··· + 42284896u + 4324097)
c
7
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
89
+ 2u
88
+ ··· − u + 1)
c
8
((u + 1)
5
)(u
89
+ 6u
88
+ ··· + 1691u + 49)
c
9
u
5
(u
89
− 3u
88
+ ··· + 59096u
2
− 1568)
c
10
((u − 1)
5
)(u
89
+ 6u
88
+ ··· + 1691u + 49)
c
12
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
89
+ 2u
88
+ ··· − u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
· (y
89
+ 72y
88
+ ··· + 9580901y −717409)
c
2
, c
7
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
89
− 60y
88
+ ··· − 11y −1)
c
3
2401(49y
5
− 116y
4
− 164y
3
− 73y
2
− 14y −1)
· (49y
89
− 7919y
88
+ ··· − 31244025855892y −1042688096641)
c
4
, c
5
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
89
− 72y
88
+ ··· − 11y −1)
c
6
2401(49y
5
− 326y
4
+ 233y
3
− 80y
2
+ 12y −1)
· (49y
89
− 12749y
88
+ ··· + 178083980700794y −18697814865409)
c
8
, c
10
((y −1)
5
)(y
89
− 76y
88
+ ··· + 3133195y −2401)
c
9
y
5
(y
89
+ 33y
88
+ ··· + 1.85325 × 10
8
y −2458624)
19
