12n
0461
(K12n
0461
)
A knot diagram
1
Linearized knot diagam
3 5 11 12 2 9 4 3 5 8 7 10
Solving Sequence
3,5
2 6
1,10
9 8 11 12 4 7
c
2
c
5
c
1
c
9
c
8
c
10
c
12
c
4
c
7
c
3
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.96588 × 10
228
u
66
+ 2.60681 × 10
228
u
65
+ ··· + 5.14418 × 10
229
b − 5.03692 × 10
229
,
7.11870 × 10
230
u
66
+ 1.26348 × 10
231
u
65
+ ··· + 1.59470 × 10
231
a + 9.95544 × 10
232
,
u
67
+ 2u
66
+ ··· + 603u + 31i
I
u
2
= h995343950102u
24
+ 3663166642595u
23
+ ··· + 266559078319b + 2009076529451,
− 758722386667u
24
− 2572820961963u
23
+ ··· + 266559078319a + 2793047519965,
u
25
+ 3u
24
+ ··· + 12u + 1i
* 2 irreducible components of dim
C
= 0, with total 92 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
= h1.97 × 10
228
u
66
+ 2.61 × 10
228
u
65
+ · · · + 5.14 × 10
229
b − 5.04 ×
10
229
, 7.12 × 10
230
u
66
+ 1.26 × 10
231
u
65
+ · · · + 1.59 × 10
231
a + 9.96 ×
10
232
, u
67
+ 2u
66
+ · · · + 603u + 31i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
10
=
−0.446398u
66
− 0.792300u
65
+ ··· − 931.788u − 62.4284
−0.0382156u
66
− 0.0506750u
65
+ ··· + 6.93009u + 0.979148
a
9
=
−0.446398u
66
− 0.792300u
65
+ ··· − 931.788u − 62.4284
−0.0659120u
66
− 0.0964250u
65
+ ··· − 39.8309u − 2.13624
a
8
=
−0.512310u
66
− 0.888725u
65
+ ··· − 971.619u − 64.5646
−0.0659120u
66
− 0.0964250u
65
+ ··· − 39.8309u − 2.13624
a
11
=
0.665717u
66
+ 1.16106u
65
+ ··· + 1367.94u + 89.9273
0.0771011u
66
+ 0.126191u
65
+ ··· + 101.139u + 6.37264
a
12
=
−0.0814414u
66
− 0.0919983u
65
+ ··· + 172.852u + 18.2940
−0.105789u
66
− 0.173936u
65
+ ··· − 154.253u − 9.77732
a
4
=
−0.146834u
66
− 0.291150u
65
+ ··· − 526.345u − 36.6710
0.0133343u
66
+ 0.0148802u
65
+ ··· + 9.89412u + 0.806420
a
7
=
−0.782527u
66
− 1.35663u
65
+ ··· − 1584.69u − 109.331
−0.142531u
66
− 0.231198u
65
+ ··· − 195.994u − 11.1014
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6.00516u
66
+ 10.3283u
65
+ ··· + 10856.4u + 703.480
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
67
+ 96u
66
+ ··· − 6593u − 961
c
2
, c
5
u
67
− 2u
66
+ ··· + 603u − 31
c
3
u
67
− 2u
65
+ ··· + 12u + 1
c
4
u
67
+ u
66
+ ··· + 78u − 4
c
6
u
67
− 3u
66
+ ··· + 1112592u − 190913
c
7
u
67
− 4u
66
+ ··· − 152u − 19
c
8
u
67
− 21u
65
+ ··· + 3707522u − 708772
c
9
u
67
+ u
66
+ ··· − 7924808u − 913579
c
10
u
67
+ 10u
66
+ ··· − 24u − 1
c
11
u
67
+ u
66
+ ··· + 22u − 1
c
12
u
67
− 5u
66
+ ··· + 4917808u − 488737
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
67
− 248y
66
+ ··· + 1205710659y −923521
c
2
, c
5
y
67
+ 96y
66
+ ··· − 6593y −961
c
3
y
67
− 4y
66
+ ··· + 52y −1
c
4
y
67
− 15y
66
+ ··· + 2428y −16
c
6
y
67
+ 129y
66
+ ··· − 167561891380y −36447773569
c
7
y
67
+ 6y
66
+ ··· − 8740y −361
c
8
y
67
− 42y
66
+ ··· + 5030461829868y −502357747984
c
9
y
67
+ 99y
66
+ ··· + 1331996748366y −834626589241
c
10
y
67
+ 18y
66
+ ··· − 86y −1
c
11
y
67
+ 5y
66
+ ··· + 12y −1
c
12
y
67
− 111y
66
+ ··· + 2732023039434y −238863855169
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.457533 + 0.954014I
a = 0.589994 + 0.995559I
b = 0.778600 + 0.667694I
−2.30669 − 1.69781I 0
u = 0.457533 − 0.954014I
a = 0.589994 − 0.995559I
b = 0.778600 − 0.667694I
−2.30669 + 1.69781I 0
u = −0.115958 + 1.054650I
a = 0.263031 + 0.627824I
b = 0.21100 + 1.58802I
−0.557773 − 1.254050I 0
u = −0.115958 − 1.054650I
a = 0.263031 − 0.627824I
b = 0.21100 − 1.58802I
−0.557773 + 1.254050I 0
u = −0.193472 + 0.917062I
a = −0.773951 + 0.955297I
b = 0.193510 + 0.352286I
−4.33901 − 2.24983I 0
u = −0.193472 − 0.917062I
a = −0.773951 − 0.955297I
b = 0.193510 − 0.352286I
−4.33901 + 2.24983I 0
u = 0.893939 + 0.275897I
a = −0.407031 − 0.202432I
b = −0.623251 + 0.431858I
0.01989 − 3.98298I 0
u = 0.893939 − 0.275897I
a = −0.407031 + 0.202432I
b = −0.623251 − 0.431858I
0.01989 + 3.98298I 0
u = −0.697295 + 0.620282I
a = −0.364005 + 0.741958I
b = −0.087737 − 1.325970I
−0.80774 + 6.08975I 0
u = −0.697295 − 0.620282I
a = −0.364005 − 0.741958I
b = −0.087737 + 1.325970I
−0.80774 − 6.08975I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.187614 + 0.909547I
a = 0.751918 + 1.020130I
b = 0.512623 − 0.137739I
−2.66802 − 2.88160I 0
u = 0.187614 − 0.909547I
a = 0.751918 − 1.020130I
b = 0.512623 + 0.137739I
−2.66802 + 2.88160I 0
u = −0.516210 + 0.989811I
a = 0.103606 + 0.654257I
b = 0.409249 + 0.491498I
−0.24728 − 2.81998I 0
u = −0.516210 − 0.989811I
a = 0.103606 − 0.654257I
b = 0.409249 − 0.491498I
−0.24728 + 2.81998I 0
u = 0.400784 + 1.045870I
a = −0.43114 − 1.47222I
b = 0.155940 − 0.982519I
−3.41227 − 6.93248I 0
u = 0.400784 − 1.045870I
a = −0.43114 + 1.47222I
b = 0.155940 + 0.982519I
−3.41227 + 6.93248I 0
u = −0.538706 + 0.567850I
a = −0.955441 − 0.064037I
b = −0.564344 + 0.249827I
0.98191 − 1.38534I 0
u = −0.538706 − 0.567850I
a = −0.955441 + 0.064037I
b = −0.564344 − 0.249827I
0.98191 + 1.38534I 0
u = 0.784394 + 0.984178I
a = 0.420939 + 0.642128I
b = 0.255313 − 0.360077I
−4.27934 + 2.18416I 0
u = 0.784394 − 0.984178I
a = 0.420939 − 0.642128I
b = 0.255313 + 0.360077I
−4.27934 − 2.18416I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.501023 + 0.539600I
a = 1.45647 + 0.55036I
b = 0.180295 − 0.246221I
−1.49173 + 5.01883I 0
u = 0.501023 − 0.539600I
a = 1.45647 − 0.55036I
b = 0.180295 + 0.246221I
−1.49173 − 5.01883I 0
u = −0.674453 + 1.076020I
a = −0.390071 + 0.864497I
b = −0.094098 + 0.624906I
−0.39462 − 3.04715I 0
u = −0.674453 − 1.076020I
a = −0.390071 − 0.864497I
b = −0.094098 − 0.624906I
−0.39462 + 3.04715I 0
u = −0.893676 + 0.921028I
a = −0.090719 − 1.104600I
b = −0.280112 − 0.478115I
−0.24710 − 1.93291I 0
u = −0.893676 − 0.921028I
a = −0.090719 + 1.104600I
b = −0.280112 + 0.478115I
−0.24710 + 1.93291I 0
u = −0.730247 + 1.176420I
a = 0.046631 − 0.413439I
b = −0.209172 + 0.541131I
−2.91897 − 2.04519I 0
u = −0.730247 − 1.176420I
a = 0.046631 + 0.413439I
b = −0.209172 − 0.541131I
−2.91897 + 2.04519I 0
u = −0.196064 + 0.545051I
a = −1.288410 + 0.052000I
b = −0.114737 + 0.808653I
0.68348 − 1.57687I 3.99292 + 3.23694I
u = −0.196064 − 0.545051I
a = −1.288410 − 0.052000I
b = −0.114737 − 0.808653I
0.68348 + 1.57687I 3.99292 − 3.23694I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.95653 + 1.16937I
a = −0.368103 − 0.666516I
b = −0.272757 − 0.017375I
−2.56627 + 10.48270I 0
u = 0.95653 − 1.16937I
a = −0.368103 + 0.666516I
b = −0.272757 + 0.017375I
−2.56627 − 10.48270I 0
u = 0.388067 + 0.223024I
a = −0.727120 + 0.753413I
b = 0.737018 + 0.522103I
−1.43906 − 1.78237I −1.33211 + 2.71073I
u = 0.388067 − 0.223024I
a = −0.727120 − 0.753413I
b = 0.737018 − 0.522103I
−1.43906 + 1.78237I −1.33211 − 2.71073I
u = −0.325137 + 0.268142I
a = −0.13146 + 2.12340I
b = 0.505270 + 1.102930I
0.79855 − 2.50260I −1.01061 − 3.08759I
u = −0.325137 − 0.268142I
a = −0.13146 − 2.12340I
b = 0.505270 − 1.102930I
0.79855 + 2.50260I −1.01061 + 3.08759I
u = −0.380315 + 0.053193I
a = −1.40378 + 1.50656I
b = 0.358957 + 0.785864I
0.27383 − 2.13551I 6.80663 + 3.84102I
u = −0.380315 − 0.053193I
a = −1.40378 − 1.50656I
b = 0.358957 − 0.785864I
0.27383 + 2.13551I 6.80663 − 3.84102I
u = 0.05485 + 1.68623I
a = −1.242600 + 0.118981I
b = −2.63143 + 0.35846I
−9.40596 + 6.77180I 0
u = 0.05485 − 1.68623I
a = −1.242600 − 0.118981I
b = −2.63143 − 0.35846I
−9.40596 − 6.77180I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.281287
a = −4.51882
b = −0.486994
2.29735 23.7480
u = −0.258984 + 0.039539I
a = −4.31229 − 0.59288I
b = −0.302792 + 0.311893I
2.29249 + 0.02089I 16.8227 + 1.1436I
u = −0.258984 − 0.039539I
a = −4.31229 + 0.59288I
b = −0.302792 − 0.311893I
2.29249 − 0.02089I 16.8227 − 1.1436I
u = 0.07896 + 1.73800I
a = 1.039740 + 0.199144I
b = 2.21124 + 0.08008I
−7.10246 − 1.28623I 0
u = 0.07896 − 1.73800I
a = 1.039740 − 0.199144I
b = 2.21124 − 0.08008I
−7.10246 + 1.28623I 0
u = −0.19011 + 1.74929I
a = 1.325720 − 0.103891I
b = 2.54637 − 0.41828I
−13.6672 − 4.5083I 0
u = −0.19011 − 1.74929I
a = 1.325720 + 0.103891I
b = 2.54637 + 0.41828I
−13.6672 + 4.5083I 0
u = 0.17362 + 1.78193I
a = −0.970603 − 0.264089I
b = −2.23387 − 0.50105I
−12.23740 − 0.69980I 0
u = 0.17362 − 1.78193I
a = −0.970603 + 0.264089I
b = −2.23387 + 0.50105I
−12.23740 + 0.69980I 0
u = −0.046320 + 0.187995I
a = 0.07739 + 5.42360I
b = −0.956677 − 0.830313I
0.32362 − 8.28539I 2.11045 + 6.37695I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.046320 − 0.187995I
a = 0.07739 − 5.42360I
b = −0.956677 + 0.830313I
0.32362 + 8.28539I 2.11045 − 6.37695I
u = 0.21524 + 1.85123I
a = −0.980754 + 0.224611I
b = −2.10786 − 0.14045I
−12.43710 + 1.73591I 0
u = 0.21524 − 1.85123I
a = −0.980754 − 0.224611I
b = −2.10786 + 0.14045I
−12.43710 − 1.73591I 0
u = 0.30001 + 1.84870I
a = −1.090890 − 0.053036I
b = −2.41255 − 0.02971I
−14.0664 + 7.1346I 0
u = 0.30001 − 1.84870I
a = −1.090890 + 0.053036I
b = −2.41255 + 0.02971I
−14.0664 − 7.1346I 0
u = −0.18623 + 1.88315I
a = 1.257640 + 0.276336I
b = 2.47525 + 0.24961I
−11.26560 − 7.17364I 0
u = −0.18623 − 1.88315I
a = 1.257640 − 0.276336I
b = 2.47525 − 0.24961I
−11.26560 + 7.17364I 0
u = 0.19090 + 1.89325I
a = 1.303960 − 0.063429I
b = 2.30945 + 0.20589I
−14.0589 − 3.4940I 0
u = 0.19090 − 1.89325I
a = 1.303960 + 0.063429I
b = 2.30945 − 0.20589I
−14.0589 + 3.4940I 0
u = −0.30043 + 1.89642I
a = −1.214520 − 0.110478I
b = −2.18382 − 0.02368I
−10.07770 − 7.36116I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.30043 − 1.89642I
a = −1.214520 + 0.110478I
b = −2.18382 + 0.02368I
−10.07770 + 7.36116I 0
u = 0.27848 + 1.90879I
a = 1.157270 − 0.138990I
b = 2.43580 − 0.18451I
−13.2103 + 16.0921I 0
u = 0.27848 − 1.90879I
a = 1.157270 + 0.138990I
b = 2.43580 + 0.18451I
−13.2103 − 16.0921I 0
u = −0.20073 + 1.94278I
a = −1.099780 + 0.041621I
b = −2.30294 − 0.15469I
−14.2801 − 6.8482I 0
u = −0.20073 − 1.94278I
a = −1.099780 − 0.041621I
b = −2.30294 + 0.15469I
−14.2801 + 6.8482I 0
u = −0.27697 + 2.20674I
a = 0.627123 − 0.091513I
b = 2.34576 + 0.16640I
−9.88597 − 0.66645I 0
u = −0.27697 − 2.20674I
a = 0.627123 + 0.091513I
b = 2.34576 − 0.16640I
−9.88597 + 0.66645I 0
11
II. I
u
2
= h9.95 × 10
11
u
24
+ 3.66 × 10
12
u
23
+ · · · + 2.67 × 10
11
b + 2.01 ×
10
12
, −7.59 × 10
11
u
24
− 2.57 × 10
12
u
23
+ · · · + 2.67 × 10
11
a + 2.79 ×
10
12
, u
25
+ 3u
24
+ · · · + 12u + 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
10
=
2.84636u
24
+ 9.65197u
23
+ ··· − 5.84398u − 10.4782
−3.73405u
24
− 13.7424u
23
+ ··· − 81.2939u − 7.53708
a
9
=
2.84636u
24
+ 9.65197u
23
+ ··· − 5.84398u − 10.4782
−7.11798u
24
− 22.8323u
23
+ ··· − 97.4951u − 8.64998
a
8
=
−4.27162u
24
− 13.1803u
23
+ ··· − 103.339u − 19.1281
−7.11798u
24
− 22.8323u
23
+ ··· − 97.4951u − 8.64998
a
11
=
6.10256u
24
+ 6.20196u
23
+ ··· − 33.3409u + 1.25824
7.72169u
24
+ 13.6388u
23
+ ··· − 68.6810u − 6.55312
a
12
=
1.49665u
24
− 1.36716u
23
+ ··· − 96.5452u − 12.2669
−3.81577u
24
− 10.6336u
23
+ ··· − 24.1541u − 2.01074
a
4
=
−9.70049u
24
− 40.5565u
23
+ ··· − 291.643u − 26.4926
−1.49368u
24
− 11.6689u
23
+ ··· − 116.715u − 10.2072
a
7
=
2.07898u
24
+ 14.0602u
23
+ ··· + 49.4637u − 8.08709
−12.2235u
24
− 35.3803u
23
+ ··· − 90.1398u − 7.84101
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
12025892582404
266559078319
u
24
+
41146040688402
266559078319
u
23
+ ··· +
139630789190729
266559078319
u +
4844913451607
266559078319
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
25
− 27u
24
+ ··· + 36u + 1
c
2
u
25
+ 3u
24
+ ··· + 12u + 1
c
3
u
25
+ 3u
24
+ ··· + u − 1
c
4
u
25
+ u
22
+ ··· − u + 3
c
5
u
25
− 3u
24
+ ··· + 12u − 1
c
6
u
25
+ 4u
24
+ ··· + 9u + 1
c
7
u
25
+ u
24
+ ··· − u − 1
c
8
u
25
− u
24
+ ··· − 10u − 7
c
9
u
25
+ 5u
23
+ ··· + 3u − 1
c
10
u
25
− 11u
24
+ ··· + 3u − 1
c
11
u
25
− 4u
24
+ ··· − 3u − 1
c
12
u
25
− 4u
24
+ ··· + 11u + 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
− 57y
24
+ ··· + 2256y −1
c
2
, c
5
y
25
+ 27y
24
+ ··· + 36y −1
c
3
y
25
− 5y
24
+ ··· + 17y −1
c
4
y
25
+ 10y
23
+ ··· + 115y −9
c
6
y
25
+ 28y
24
+ ··· + y −1
c
7
y
25
− 3y
24
+ ··· − 7y −1
c
8
y
25
− 7y
24
+ ··· − 278y −49
c
9
y
25
+ 10y
24
+ ··· + 11y −1
c
10
y
25
− 3y
24
+ ··· + 7y −1
c
11
y
25
+ 4y
24
+ ··· − 7y −1
c
12
y
25
− 52y
24
+ ··· − 21y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.267306 + 0.876530I
a = −0.913085 − 0.679632I
b = −0.556024 − 0.412117I
−1.42946 − 3.52997I 1.13574 + 8.28885I
u = −0.267306 − 0.876530I
a = −0.913085 + 0.679632I
b = −0.556024 + 0.412117I
−1.42946 + 3.52997I 1.13574 − 8.28885I
u = 0.441185 + 1.005030I
a = 0.085809 − 0.383901I
b = 0.319285 − 1.249550I
−0.40658 + 10.09140I 1.36280 − 8.09975I
u = 0.441185 − 1.005030I
a = 0.085809 + 0.383901I
b = 0.319285 + 1.249550I
−0.40658 − 10.09140I 1.36280 + 8.09975I
u = −0.444912 + 1.016980I
a = −0.610344 + 0.490309I
b = −0.290779 + 0.988294I
0.41239 − 2.64509I 5.51677 + 7.98470I
u = −0.444912 − 1.016980I
a = −0.610344 − 0.490309I
b = −0.290779 − 0.988294I
0.41239 + 2.64509I 5.51677 − 7.98470I
u = 0.794978 + 0.776068I
a = −0.119021 + 0.660012I
b = 0.018996 − 0.616325I
0.25264 − 5.73058I 2.96305 + 5.24684I
u = 0.794978 − 0.776068I
a = −0.119021 − 0.660012I
b = 0.018996 + 0.616325I
0.25264 + 5.73058I 2.96305 − 5.24684I
u = −0.241445 + 0.845709I
a = −0.568515 − 0.872633I
b = −0.716529 + 0.368656I
1.40705 − 0.40083I 3.99614 + 0.12172I
u = −0.241445 − 0.845709I
a = −0.568515 + 0.872633I
b = −0.716529 − 0.368656I
1.40705 + 0.40083I 3.99614 − 0.12172I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.065197 + 0.866585I
a = −0.810886 + 0.704566I
b = −0.66613 + 1.36652I
−1.11023 + 1.87220I −0.39546 − 6.82787I
u = −0.065197 − 0.866585I
a = −0.810886 − 0.704566I
b = −0.66613 − 1.36652I
−1.11023 − 1.87220I −0.39546 + 6.82787I
u = 0.160583 + 1.137230I
a = −0.031176 + 0.726781I
b = 0.39419 + 1.70553I
−0.742657 + 0.498514I 1.66823 + 3.77577I
u = 0.160583 − 1.137230I
a = −0.031176 − 0.726781I
b = 0.39419 − 1.70553I
−0.742657 − 0.498514I 1.66823 − 3.77577I
u = −0.603268 + 0.469736I
a = −0.103125 − 1.328870I
b = −0.463666 − 1.010800I
1.07581 − 2.76759I 15.7072 + 11.5636I
u = −0.603268 − 0.469736I
a = −0.103125 + 1.328870I
b = −0.463666 + 1.010800I
1.07581 + 2.76759I 15.7072 − 11.5636I
u = −0.748501 + 1.162150I
a = 0.082048 + 0.976953I
b = 0.369357 + 0.442332I
−1.08945 − 2.35190I −3.94323 + 3.34279I
u = −0.748501 − 1.162150I
a = 0.082048 − 0.976953I
b = 0.369357 − 0.442332I
−1.08945 + 2.35190I −3.94323 − 3.34279I
u = −0.387563 + 0.431758I
a = −1.37723 + 0.64214I
b = 0.221518 − 0.847447I
−2.29200 − 4.06726I −3.68809 + 5.22736I
u = −0.387563 − 0.431758I
a = −1.37723 − 0.64214I
b = 0.221518 + 0.847447I
−2.29200 + 4.06726I −3.68809 − 5.22736I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.144825
a = −9.43737
b = −0.612024
2.12293 −23.1650
u = −0.18505 + 1.85309I
a = 1.261960 + 0.050324I
b = 2.45835 + 0.07175I
−12.15400 − 6.39485I 0
u = −0.18505 − 1.85309I
a = 1.261960 − 0.050324I
b = 2.45835 − 0.07175I
−12.15400 + 6.39485I 0
u = 0.11891 + 2.10989I
a = −0.677747 − 0.029496I
b = −2.28255 − 0.09598I
−9.65893 + 0.18915I 0
u = 0.11891 − 2.10989I
a = −0.677747 + 0.029496I
b = −2.28255 + 0.09598I
−9.65893 − 0.18915I 0
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
25
− 27u
24
+ ··· + 36u + 1)(u
67
+ 96u
66
+ ··· − 6593u − 961)
c
2
(u
25
+ 3u
24
+ ··· + 12u + 1)(u
67
− 2u
66
+ ··· + 603u − 31)
c
3
(u
25
+ 3u
24
+ ··· + u − 1)(u
67
− 2u
65
+ ··· + 12u + 1)
c
4
(u
25
+ u
22
+ ··· − u + 3)(u
67
+ u
66
+ ··· + 78u − 4)
c
5
(u
25
− 3u
24
+ ··· + 12u − 1)(u
67
− 2u
66
+ ··· + 603u − 31)
c
6
(u
25
+ 4u
24
+ ··· + 9u + 1)(u
67
− 3u
66
+ ··· + 1112592u − 190913)
c
7
(u
25
+ u
24
+ ··· − u − 1)(u
67
− 4u
66
+ ··· − 152u − 19)
c
8
(u
25
− u
24
+ ··· − 10u − 7)(u
67
− 21u
65
+ ··· + 3707522u − 708772)
c
9
(u
25
+ 5u
23
+ ··· + 3u − 1)(u
67
+ u
66
+ ··· − 7924808u − 913579)
c
10
(u
25
− 11u
24
+ ··· + 3u − 1)(u
67
+ 10u
66
+ ··· − 24u − 1)
c
11
(u
25
− 4u
24
+ ··· − 3u − 1)(u
67
+ u
66
+ ··· + 22u − 1)
c
12
(u
25
− 4u
24
+ ··· + 11u + 1)(u
67
− 5u
66
+ ··· + 4917808u − 488737)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
25
− 57y
24
+ ··· + 2256y −1)
· (y
67
− 248y
66
+ ··· + 1205710659y −923521)
c
2
, c
5
(y
25
+ 27y
24
+ ··· + 36y −1)(y
67
+ 96y
66
+ ··· − 6593y −961)
c
3
(y
25
− 5y
24
+ ··· + 17y −1)(y
67
− 4y
66
+ ··· + 52y −1)
c
4
(y
25
+ 10y
23
+ ··· + 115y −9)(y
67
− 15y
66
+ ··· + 2428y −16)
c
6
(y
25
+ 28y
24
+ ··· + y −1)
· (y
67
+ 129y
66
+ ··· − 167561891380y −36447773569)
c
7
(y
25
− 3y
24
+ ··· − 7y −1)(y
67
+ 6y
66
+ ··· − 8740y −361)
c
8
(y
25
− 7y
24
+ ··· − 278y −49)
· (y
67
− 42y
66
+ ··· + 5030461829868y −502357747984)
c
9
(y
25
+ 10y
24
+ ··· + 11y −1)
· (y
67
+ 99y
66
+ ··· + 1331996748366y −834626589241)
c
10
(y
25
− 3y
24
+ ··· + 7y −1)(y
67
+ 18y
66
+ ··· − 86y −1)
c
11
(y
25
+ 4y
24
+ ··· − 7y −1)(y
67
+ 5y
66
+ ··· + 12y −1)
c
12
(y
25
− 52y
24
+ ··· − 21y −1)
· (y
67
− 111y
66
+ ··· + 2732023039434y −238863855169)
21
