12n
0616
(K12n
0616
)
A knot diagram
1
Linearized knot diagam
3 7 12 11 3 10 2 5 4 7 9 6
Solving Sequence
6,10
7
3,11
2 8 1 5 4 9 12
c
6
c
10
c
2
c
7
c
1
c
5
c
4
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h3.55805 × 10
172
u
61
− 2.66340 × 10
172
u
60
+ ··· + 2.49043 × 10
174
b − 1.12400 × 10
175
,
1.21069 × 10
173
u
61
− 1.41526 × 10
173
u
60
+ ··· + 2.24139 × 10
175
a − 1.66162 × 10
174
,
u
62
− u
61
+ ··· − 540u + 108i
I
u
2
= h−4.69238 × 10
16
u
29
− 2.59707 × 10
16
u
28
+ ··· + 3.59633 × 10
16
b + 1.14239 × 10
17
,
2.84054 × 10
17
u
29
+ 2.41111 × 10
17
u
28
+ ··· + 3.59633 × 10
16
a − 3.99453 × 10
17
, u
30
− 8u
28
+ ··· + 2u + 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
= h3.56 × 10
172
u
61
− 2.66 × 10
172
u
60
+ · · · + 2.49 × 10
174
b − 1.12 ×
10
175
, 1.21 × 10
173
u
61
− 1.42 × 10
173
u
60
+ · · · + 2.24 × 10
175
a − 1.66 ×
10
174
, u
62
− u
61
+ · · · − 540u + 108i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
−0.00540152u
61
+ 0.00631420u
60
+ ··· − 10.9070u + 0.0741336
−0.0142869u
61
+ 0.0106945u
60
+ ··· − 11.8991u + 4.51328
a
11
=
−u
−u
3
+ u
a
2
=
0.00910760u
61
− 0.00500287u
60
+ ··· + 2.06831u − 4.53772
−0.0135155u
61
+ 0.00963239u
60
+ ··· − 11.7423u + 4.16854
a
8
=
−0.0102705u
61
+ 0.00570181u
60
+ ··· − 15.8947u + 5.04760
−0.00342408u
61
+ 0.00410364u
60
+ ··· − 0.919576u + 2.86804
a
1
=
0.00882729u
61
− 0.00418130u
60
+ ··· + 15.3641u − 4.48965
0.0182728u
61
− 0.0118352u
60
+ ··· + 11.4934u − 4.66813
a
5
=
0.0126898u
61
− 0.00781485u
60
+ ··· + 8.40923u − 4.07704
0.00409918u
61
− 0.00575768u
60
+ ··· + 1.40699u − 3.26558
a
4
=
0.0125680u
61
− 0.00647401u
60
+ ··· + 8.23390u − 3.71099
0.00486562u
61
− 0.00734645u
60
+ ··· + 2.25375u − 3.76329
a
9
=
−0.00661784u
61
+ 0.00354350u
60
+ ··· − 6.75785u + 4.98454
0.0172764u
61
− 0.00999165u
60
+ ··· + 14.4560u − 4.08059
a
12
=
−0.00944546u
61
+ 0.00765391u
60
+ ··· + 3.87066u + 0.178480
0.0182728u
61
− 0.0118352u
60
+ ··· + 11.4934u − 4.66813
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0529669u
61
− 0.0452256u
60
+ ··· + 42.2033u − 18.0098
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
62
+ 93u
61
+ ··· + 2327471u + 1442401
c
2
, c
7
u
62
− u
61
+ ··· − 7479u + 1201
c
3
u
62
− 5u
61
+ ··· − 351u + 81
c
4
u
62
+ u
61
+ ··· − 29453u + 24019
c
5
u
62
+ 45u
60
+ ··· − 7939816u + 1967081
c
6
, c
10
u
62
+ u
61
+ ··· + 540u + 108
c
8
u
62
+ 4u
61
+ ··· − 17319366u + 37837071
c
9
u
62
+ 2u
61
+ ··· + 1506u + 313
c
11
u
62
+ 3u
61
+ ··· + 9u + 1
c
12
u
62
+ u
61
+ ··· + 40816u + 5087
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
62
− 227y
61
+ ··· + 374501199567555y + 2080520644801
c
2
, c
7
y
62
+ 93y
61
+ ··· + 2327471y + 1442401
c
3
y
62
+ 25y
61
+ ··· + 101331y + 6561
c
4
y
62
+ 27y
61
+ ··· + 214913007y + 576912361
c
5
y
62
+ 90y
61
+ ··· − 46218775789508y + 3869407660561
c
6
, c
10
y
62
− 51y
61
+ ··· − 56376y + 11664
c
8
y
62
− 60y
61
+ ··· + 40273910932902534y + 1431643941859041
c
9
y
62
+ 4y
61
+ ··· + 269768y + 97969
c
11
y
62
− 5y
61
+ ··· − 19y + 1
c
12
y
62
+ 101y
61
+ ··· − 990656780y + 25877569
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.928426 + 0.274577I
a = −0.141263 − 0.866305I
b = −0.918957 − 0.595441I
0.81276 + 2.95644I 8.56413 − 5.92863I
u = −0.928426 − 0.274577I
a = −0.141263 + 0.866305I
b = −0.918957 + 0.595441I
0.81276 − 2.95644I 8.56413 + 5.92863I
u = −0.883961 + 0.394719I
a = 0.59269 − 1.64149I
b = −0.500699 − 0.932554I
−0.87581 + 4.78527I 0.6309 − 14.5936I
u = −0.883961 − 0.394719I
a = 0.59269 + 1.64149I
b = −0.500699 + 0.932554I
−0.87581 − 4.78527I 0.6309 + 14.5936I
u = 0.798892 + 0.328131I
a = −1.46380 − 0.42820I
b = −0.640242 − 0.054068I
−0.95457 − 1.51938I 1.17952 + 4.85265I
u = 0.798892 − 0.328131I
a = −1.46380 + 0.42820I
b = −0.640242 + 0.054068I
−0.95457 + 1.51938I 1.17952 − 4.85265I
u = 1.064810 + 0.545706I
a = −0.0830119 + 0.0387708I
b = 0.386898 + 0.525528I
−1.79842 − 1.83762I 0
u = 1.064810 − 0.545706I
a = −0.0830119 − 0.0387708I
b = 0.386898 − 0.525528I
−1.79842 + 1.83762I 0
u = 1.232990 + 0.083982I
a = 0.103400 − 0.171742I
b = −0.704160 + 0.181168I
−0.911910 + 0.560071I 0
u = 1.232990 − 0.083982I
a = 0.103400 + 0.171742I
b = −0.704160 − 0.181168I
−0.911910 − 0.560071I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.162130 + 0.432774I
a = 0.781400 + 0.862594I
b = −0.656170 + 0.829181I
−2.56521 − 5.62136I 0
u = 1.162130 − 0.432774I
a = 0.781400 − 0.862594I
b = −0.656170 − 0.829181I
−2.56521 + 5.62136I 0
u = −0.053502 + 1.258700I
a = −0.993543 + 0.161721I
b = 1.224160 + 0.468794I
3.01979 − 1.86961I 0
u = −0.053502 − 1.258700I
a = −0.993543 − 0.161721I
b = 1.224160 − 0.468794I
3.01979 + 1.86961I 0
u = 0.555763 + 0.420314I
a = −0.688240 + 0.980201I
b = −0.413944 − 0.903869I
−0.49204 + 1.99531I −0.82675 − 4.20883I
u = 0.555763 − 0.420314I
a = −0.688240 − 0.980201I
b = −0.413944 + 0.903869I
−0.49204 − 1.99531I −0.82675 + 4.20883I
u = 0.211720 + 1.290750I
a = 1.223300 − 0.047119I
b = −1.211470 − 0.325634I
4.32311 − 2.81936I 0
u = 0.211720 − 1.290750I
a = 1.223300 + 0.047119I
b = −1.211470 + 0.325634I
4.32311 + 2.81936I 0
u = −0.342685 + 1.277490I
a = −0.204814 + 0.198955I
b = 0.50743 − 1.99401I
−10.60230 + 1.13329I 0
u = −0.342685 − 1.277490I
a = −0.204814 − 0.198955I
b = 0.50743 + 1.99401I
−10.60230 − 1.13329I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.614267 + 0.283569I
a = −1.021740 − 0.249635I
b = −0.711770 + 0.261415I
1.381510 − 0.110117I 9.95847 − 1.16431I
u = −0.614267 − 0.283569I
a = −1.021740 + 0.249635I
b = −0.711770 − 0.261415I
1.381510 + 0.110117I 9.95847 + 1.16431I
u = 1.188520 + 0.601200I
a = −0.477089 − 0.246417I
b = 0.493192 + 0.235501I
−2.66613 − 1.84132I 0
u = 1.188520 − 0.601200I
a = −0.477089 + 0.246417I
b = 0.493192 − 0.235501I
−2.66613 + 1.84132I 0
u = −0.568370 + 0.290816I
a = −1.077140 + 0.714898I
b = 0.031563 − 1.189600I
−9.40415 + 0.96502I −3.47084 − 7.40489I
u = −0.568370 − 0.290816I
a = −1.077140 − 0.714898I
b = 0.031563 + 1.189600I
−9.40415 − 0.96502I −3.47084 + 7.40489I
u = 0.173116 + 0.612853I
a = −1.97761 + 1.41609I
b = 0.761201 − 0.088010I
3.33244 − 2.13366I 9.28813 + 3.63241I
u = 0.173116 − 0.612853I
a = −1.97761 − 1.41609I
b = 0.761201 + 0.088010I
3.33244 + 2.13366I 9.28813 − 3.63241I
u = −1.237450 + 0.584054I
a = 0.412477 + 0.156333I
b = 0.857350 − 0.607671I
−0.60518 + 7.63571I 0
u = −1.237450 − 0.584054I
a = 0.412477 − 0.156333I
b = 0.857350 + 0.607671I
−0.60518 − 7.63571I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.337770 + 0.289922I
a = −0.616546 − 1.234550I
b = −0.84829 − 1.37346I
−2.91445 − 1.23024I 0
u = 1.337770 − 0.289922I
a = −0.616546 + 1.234550I
b = −0.84829 + 1.37346I
−2.91445 + 1.23024I 0
u = 0.528204 + 0.322278I
a = −1.136860 + 0.092169I
b = −0.300012 + 0.378008I
−0.80326 − 1.53767I −1.79348 + 5.24850I
u = 0.528204 − 0.322278I
a = −1.136860 − 0.092169I
b = −0.300012 − 0.378008I
−0.80326 + 1.53767I −1.79348 − 5.24850I
u = 1.397880 + 0.097398I
a = 0.10957 + 2.12503I
b = −0.41120 + 2.32836I
−9.86019 − 4.97411I 0
u = 1.397880 − 0.097398I
a = 0.10957 − 2.12503I
b = −0.41120 − 2.32836I
−9.86019 + 4.97411I 0
u = −1.41670 + 0.03978I
a = 0.056166 + 1.051810I
b = 0.96710 + 1.03620I
−6.57035 − 1.95796I 0
u = −1.41670 − 0.03978I
a = 0.056166 − 1.051810I
b = 0.96710 − 1.03620I
−6.57035 + 1.95796I 0
u = −1.42483 + 0.05605I
a = −0.14962 + 1.95097I
b = −0.32405 + 1.90177I
−13.12830 + 0.25112I 0
u = −1.42483 − 0.05605I
a = −0.14962 − 1.95097I
b = −0.32405 − 1.90177I
−13.12830 − 0.25112I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.138714 + 0.382151I
a = −1.028670 − 0.003428I
b = −0.405698 + 0.592213I
0.56906 − 1.80805I 2.62914 + 3.42135I
u = −0.138714 − 0.382151I
a = −1.028670 + 0.003428I
b = −0.405698 − 0.592213I
0.56906 + 1.80805I 2.62914 − 3.42135I
u = −1.59777 + 0.24654I
a = −0.140434 + 0.972924I
b = −0.81650 + 1.30662I
−3.14029 + 8.05378I 0
u = −1.59777 − 0.24654I
a = −0.140434 − 0.972924I
b = −0.81650 − 1.30662I
−3.14029 − 8.05378I 0
u = 1.53281 + 0.53294I
a = 0.81860 + 1.41695I
b = −0.23778 + 2.39126I
−16.3568 − 7.4045I 0
u = 1.53281 − 0.53294I
a = 0.81860 − 1.41695I
b = −0.23778 − 2.39126I
−16.3568 + 7.4045I 0
u = 0.330694 + 0.108076I
a = −1.128190 − 0.118541I
b = −0.21404 − 1.58285I
−5.82473 + 4.09311I −7.36144 + 5.13793I
u = 0.330694 − 0.108076I
a = −1.128190 + 0.118541I
b = −0.21404 + 1.58285I
−5.82473 − 4.09311I −7.36144 − 5.13793I
u = −0.053813 + 0.324295I
a = −3.15267 − 5.18917I
b = 0.633235 − 0.211555I
3.29821 − 6.08310I 10.9240 + 9.4569I
u = −0.053813 − 0.324295I
a = −3.15267 + 5.18917I
b = 0.633235 + 0.211555I
3.29821 + 6.08310I 10.9240 − 9.4569I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.06429 + 1.70451I
a = −0.034729 − 0.171847I
b = 0.17523 + 2.51987I
−8.83971 + 7.11017I 0
u = 0.06429 − 1.70451I
a = −0.034729 + 0.171847I
b = 0.17523 − 2.51987I
−8.83971 − 7.11017I 0
u = −1.51413 + 0.82312I
a = −0.89512 + 1.12015I
b = 1.05248 + 2.06010I
−14.0247 + 6.7818I 0
u = −1.51413 − 0.82312I
a = −0.89512 − 1.12015I
b = 1.05248 − 2.06010I
−14.0247 − 6.7818I 0
u = 1.74221 + 0.14569I
a = 0.225196 − 0.756516I
b = 1.81283 − 1.03004I
−4.56049 − 4.34139I 0
u = 1.74221 − 0.14569I
a = 0.225196 + 0.756516I
b = 1.81283 + 1.03004I
−4.56049 + 4.34139I 0
u = 1.58884 + 0.74366I
a = −0.81842 − 1.19718I
b = 0.81340 − 2.28442I
−13.7046 − 15.4840I 0
u = 1.58884 − 0.74366I
a = −0.81842 + 1.19718I
b = 0.81340 + 2.28442I
−13.7046 + 15.4840I 0
u = −1.75665 + 0.11101I
a = 0.12382 − 1.45778I
b = 0.12632 − 2.39437I
−14.1931 + 4.3228I 0
u = −1.75665 − 0.11101I
a = 0.12382 + 1.45778I
b = 0.12632 + 2.39437I
−14.1931 − 4.3228I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.87938 + 0.62453I
a = 0.532884 − 1.112330I
b = −0.52742 − 2.72829I
−15.0495 + 1.7796I 0
u = −1.87938 − 0.62453I
a = 0.532884 + 1.112330I
b = −0.52742 + 2.72829I
−15.0495 − 1.7796I 0
11
II.
I
u
2
= h−4.69×10
16
u
29
−2.60×10
16
u
28
+· · ·+3.60×10
16
b+1.14×10
17
, 2.84×
10
17
u
29
+2.41×10
17
u
28
+· · ·+3.60×10
16
a−3.99×10
17
, u
30
−8u
28
+· · ·+2u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
−7.89844u
29
− 6.70438u
28
+ ··· + 46.1262u + 11.1073
1.30477u
29
+ 0.722144u
28
+ ··· − 12.6546u − 3.17653
a
11
=
−u
−u
3
+ u
a
2
=
−11.9788u
29
− 10.9744u
28
+ ··· + 80.0880u + 20.9882
0.00854127u
29
− 0.937725u
28
+ ··· − 0.0341923u + 1.09346
a
8
=
19.2699u
29
+ 21.0285u
28
+ ··· − 171.610u − 55.6470
0.986098u
29
+ 3.09570u
28
+ ··· − 23.0758u − 8.58984
a
1
=
−19.6132u
29
− 21.5167u
28
+ ··· + 176.130u + 56.8875
−3.35827u
29
− 3.80005u
28
+ ··· + 28.1757u + 8.57614
a
5
=
−4.33768u
29
− 1.92583u
28
+ ··· + 27.6131u + 8.41369
−1.40261u
29
− 1.92358u
28
+ ··· + 17.1060u + 5.96332
a
4
=
−2.40167u
29
− 1.05482u
28
+ ··· + 17.1659u + 5.23135
−2.77770u
29
− 2.46020u
28
+ ··· + 23.8751u + 8.27464
a
9
=
4.79433u
29
+ 4.95182u
28
+ ··· − 45.5614u − 11.8368
4.33349u
29
+ 4.31110u
28
+ ··· − 35.8661u − 9.73763
a
12
=
−16.2549u
29
− 17.7167u
28
+ ··· + 147.955u + 48.3114
−3.35827u
29
− 3.80005u
28
+ ··· + 28.1757u + 8.57614
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
5213218321058946
35963279984144951
u
29
−
204199795425121514
35963279984144951
u
28
+···+
553381217539182497
35963279984144951
u+
8083989187387400
35963279984144951
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
30
− 32u
29
+ ··· − 27u + 1
c
2
u
30
+ 16u
28
+ ··· − 3u + 1
c
3
u
30
+ 8u
29
+ ··· + 23u + 11
c
4
u
30
+ 4u
29
+ ··· + 3u + 1
c
5
u
30
− 5u
29
+ ··· − 6u
2
+ 1
c
6
u
30
− 8u
28
+ ··· + 2u + 1
c
7
u
30
+ 16u
28
+ ··· + 3u + 1
c
8
u
30
+ u
29
+ ··· + 12u + 1
c
9
u
30
+ u
29
+ ··· + 6u
2
+ 1
c
10
u
30
− 8u
28
+ ··· − 2u + 1
c
11
u
30
− 6u
29
+ ··· − 3u + 1
c
12
u
30
+ 16u
28
+ ··· + 148u + 73
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
− 48y
29
+ ··· + 267y + 1
c
2
, c
7
y
30
+ 32y
29
+ ··· + 27y + 1
c
3
y
30
+ 16y
29
+ ··· + 2199y + 121
c
4
y
30
− 2y
29
+ ··· + 15y + 1
c
5
y
30
+ 9y
29
+ ··· − 12y + 1
c
6
, c
10
y
30
− 16y
29
+ ··· − 18y + 1
c
8
y
30
− 9y
29
+ ··· + 154y + 1
c
9
y
30
− 5y
29
+ ··· + 12y + 1
c
11
y
30
− 6y
29
+ ··· − 11y + 1
c
12
y
30
+ 32y
29
+ ··· − 588y + 5329
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.875224 + 0.412321I
a = 1.69841 − 0.60554I
b = 0.760440 − 0.576623I
−0.932767 + 0.879726I 3.02133 + 5.92289I
u = −0.875224 − 0.412321I
a = 1.69841 + 0.60554I
b = 0.760440 + 0.576623I
−0.932767 − 0.879726I 3.02133 − 5.92289I
u = −0.942420 + 0.425846I
a = 0.990477 + 0.135569I
b = 0.667510 + 0.309330I
−1.20958 + 2.51761I 3.24397 − 8.62261I
u = −0.942420 − 0.425846I
a = 0.990477 − 0.135569I
b = 0.667510 − 0.309330I
−1.20958 − 2.51761I 3.24397 + 8.62261I
u = 0.918962 + 0.185501I
a = 0.772753 − 0.368979I
b = 0.980426 + 0.543348I
0.449422 + 0.992006I 4.91900 − 1.24662I
u = 0.918962 − 0.185501I
a = 0.772753 + 0.368979I
b = 0.980426 − 0.543348I
0.449422 − 0.992006I 4.91900 + 1.24662I
u = 0.805987 + 0.473388I
a = −1.14949 − 1.16426I
b = 0.472421 − 0.931467I
−1.04141 − 4.12353I −1.85641 + 2.83850I
u = 0.805987 − 0.473388I
a = −1.14949 + 1.16426I
b = 0.472421 + 0.931467I
−1.04141 + 4.12353I −1.85641 − 2.83850I
u = 1.030030 + 0.445576I
a = −0.224858 − 1.133130I
b = 0.752856 − 0.363100I
−0.50274 − 3.54177I 2.42929 + 4.86648I
u = 1.030030 − 0.445576I
a = −0.224858 + 1.133130I
b = 0.752856 + 0.363100I
−0.50274 + 3.54177I 2.42929 − 4.86648I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.101300 + 0.335368I
a = 0.718236 + 0.312049I
b = 0.365568 + 0.668549I
−2.43063 + 0.67941I −4.10126 − 2.36820I
u = 1.101300 − 0.335368I
a = 0.718236 − 0.312049I
b = 0.365568 − 0.668549I
−2.43063 − 0.67941I −4.10126 + 2.36820I
u = −0.637051 + 0.475657I
a = −0.641785 + 0.810694I
b = 0.371089 − 1.189360I
−9.15677 + 0.14682I 1.19258 + 1.36386I
u = −0.637051 − 0.475657I
a = −0.641785 − 0.810694I
b = 0.371089 + 1.189360I
−9.15677 − 0.14682I 1.19258 − 1.36386I
u = −1.198170 + 0.492756I
a = −0.389462 + 0.514253I
b = −0.429522 + 0.342584I
−0.28781 + 8.86990I 2.50133 − 9.25007I
u = −1.198170 − 0.492756I
a = −0.389462 − 0.514253I
b = −0.429522 − 0.342584I
−0.28781 − 8.86990I 2.50133 + 9.25007I
u = 0.347894 + 1.261540I
a = −1.145370 − 0.093955I
b = 1.46537 + 0.16374I
2.87728 − 1.15731I −0.12131 − 4.65886I
u = 0.347894 − 1.261540I
a = −1.145370 + 0.093955I
b = 1.46537 − 0.16374I
2.87728 + 1.15731I −0.12131 + 4.65886I
u = −0.582042 + 0.114441I
a = −3.71699 + 1.44960I
b = −0.518015 + 0.023656I
2.80413 − 5.94257I −4.38802 + 4.41854I
u = −0.582042 − 0.114441I
a = −3.71699 − 1.44960I
b = −0.518015 − 0.023656I
2.80413 + 5.94257I −4.38802 − 4.41854I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.592085 + 0.032840I
a = −3.11419 − 1.27073I
b = −0.431358 + 0.454461I
2.54811 − 1.76721I −0.0133359 − 0.0791266I
u = 0.592085 − 0.032840I
a = −3.11419 + 1.27073I
b = −0.431358 − 0.454461I
2.54811 + 1.76721I −0.0133359 + 0.0791266I
u = −0.03393 + 1.43301I
a = 0.954956 − 0.213579I
b = −1.060600 − 0.576962I
4.04859 − 3.36586I 2.59994 + 9.05520I
u = −0.03393 − 1.43301I
a = 0.954956 + 0.213579I
b = −1.060600 + 0.576962I
4.04859 + 3.36586I 2.59994 − 9.05520I
u = −0.289164 + 0.364349I
a = −0.762478 + 0.282994I
b = 0.13710 + 1.64032I
−5.61406 + 4.42294I 3.80460 − 11.65991I
u = −0.289164 − 0.364349I
a = −0.762478 − 0.282994I
b = 0.13710 − 1.64032I
−5.61406 − 4.42294I 3.80460 + 11.65991I
u = 1.50756 + 0.48121I
a = 0.300988 + 0.564457I
b = −1.175620 + 0.291973I
−2.12714 − 3.25888I 0.91150 + 4.03136I
u = 1.50756 − 0.48121I
a = 0.300988 − 0.564457I
b = −1.175620 − 0.291973I
−2.12714 + 3.25888I 0.91150 − 4.03136I
u = −1.74582 + 0.25668I
a = −0.29120 + 1.43523I
b = 0.14233 + 2.41540I
−14.0986 + 3.6495I 0
u = −1.74582 − 0.25668I
a = −0.29120 − 1.43523I
b = 0.14233 − 2.41540I
−14.0986 − 3.6495I 0
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
30
− 32u
29
+ ··· − 27u + 1)
· (u
62
+ 93u
61
+ ··· + 2327471u + 1442401)
c
2
(u
30
+ 16u
28
+ ··· − 3u + 1)(u
62
− u
61
+ ··· − 7479u + 1201)
c
3
(u
30
+ 8u
29
+ ··· + 23u + 11)(u
62
− 5u
61
+ ··· − 351u + 81)
c
4
(u
30
+ 4u
29
+ ··· + 3u + 1)(u
62
+ u
61
+ ··· − 29453u + 24019)
c
5
(u
30
− 5u
29
+ ··· − 6u
2
+ 1)(u
62
+ 45u
60
+ ··· − 7939816u + 1967081)
c
6
(u
30
− 8u
28
+ ··· + 2u + 1)(u
62
+ u
61
+ ··· + 540u + 108)
c
7
(u
30
+ 16u
28
+ ··· + 3u + 1)(u
62
− u
61
+ ··· − 7479u + 1201)
c
8
(u
30
+ u
29
+ ··· + 12u + 1)
· (u
62
+ 4u
61
+ ··· − 17319366u + 37837071)
c
9
(u
30
+ u
29
+ ··· + 6u
2
+ 1)(u
62
+ 2u
61
+ ··· + 1506u + 313)
c
10
(u
30
− 8u
28
+ ··· − 2u + 1)(u
62
+ u
61
+ ··· + 540u + 108)
c
11
(u
30
− 6u
29
+ ··· − 3u + 1)(u
62
+ 3u
61
+ ··· + 9u + 1)
c
12
(u
30
+ 16u
28
+ ··· + 148u + 73)(u
62
+ u
61
+ ··· + 40816u + 5087)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
30
− 48y
29
+ ··· + 267y + 1)
· (y
62
− 227y
61
+ ··· + 374501199567555y + 2080520644801)
c
2
, c
7
(y
30
+ 32y
29
+ ··· + 27y + 1)
· (y
62
+ 93y
61
+ ··· + 2327471y + 1442401)
c
3
(y
30
+ 16y
29
+ ··· + 2199y + 121)
· (y
62
+ 25y
61
+ ··· + 101331y + 6561)
c
4
(y
30
− 2y
29
+ ··· + 15y + 1)
· (y
62
+ 27y
61
+ ··· + 214913007y + 576912361)
c
5
(y
30
+ 9y
29
+ ··· − 12y + 1)
· (y
62
+ 90y
61
+ ··· − 46218775789508y + 3869407660561)
c
6
, c
10
(y
30
− 16y
29
+ ··· − 18y + 1)(y
62
− 51y
61
+ ··· − 56376y + 11664)
c
8
(y
30
− 9y
29
+ ··· + 154y + 1)
· (y
62
− 60y
61
+ ··· + 40273910932902534y + 1431643941859041)
c
9
(y
30
− 5y
29
+ ··· + 12y + 1)(y
62
+ 4y
61
+ ··· + 269768y + 97969)
c
11
(y
30
− 6y
29
+ ··· − 11y + 1)(y
62
− 5y
61
+ ··· − 19y + 1)
c
12
(y
30
+ 32y
29
+ ··· − 588y + 5329)
· (y
62
+ 101y
61
+ ··· − 990656780y + 25877569)
21
