12n
0557
(K12n
0557
)
A knot diagram
1
Linearized knot diagam
3 7 12 8 11 2 5 3 12 6 10 8
Solving Sequence
2,6
7 3
1,11
5 8 4 10 12 9
c
6
c
2
c
1
c
5
c
7
c
4
c
10
c
11
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.02105 × 10
101
u
67
− 4.63803 × 10
101
u
66
+ ··· + 1.96878 × 10
102
b − 8.88022 × 10
101
,
1.26302 × 10
102
u
67
+ 8.85176 × 10
101
u
66
+ ··· + 1.96878 × 10
102
a + 1.15700 × 10
102
, u
68
+ u
67
+ ··· + u − 1i
I
u
2
= h−5u
19
+ 33u
17
+ ··· + b + 11u, −11u
18
− 2u
17
+ ··· + a + 29, u
20
− 7u
18
+ ··· + u + 1i
* 2 irreducible components of dim
C
= 0, with total 88 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−1.02 × 10
101
u
67
− 4.64 × 10
101
u
66
+ · · · + 1.97 × 10
102
b − 8.88 ×
10
101
, 1.26 × 10
102
u
67
+ 8.85 × 10
101
u
66
+ · · · + 1.97 × 10
102
a + 1.16 ×
10
102
, u
68
+ u
67
+ · · · + u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
−0.641523u
67
− 0.449607u
66
+ ··· + 0.395110u − 0.587676
0.0518621u
67
+ 0.235579u
66
+ ··· − 1.81551u + 0.451053
a
5
=
−0.458253u
67
− 0.528500u
66
+ ··· + 2.40287u − 0.615703
0.243980u
67
+ 0.462555u
66
+ ··· − 2.28263u − 0.185736
a
8
=
0.141644u
67
− 0.134104u
66
+ ··· − 1.04997u + 2.16525
−0.308718u
67
− 0.377649u
66
+ ··· + 1.18451u − 1.47282
a
4
=
0.736347u
67
+ 0.739432u
66
+ ··· + 0.595559u − 0.749166
−0.210641u
67
− 0.118772u
66
+ ··· + 0.845338u + 0.371913
a
10
=
−0.693385u
67
− 0.685186u
66
+ ··· + 2.21062u − 1.03873
0.0518621u
67
+ 0.235579u
66
+ ··· − 1.81551u + 0.451053
a
12
=
−0.704846u
67
− 1.06386u
66
+ ··· + 4.02275u − 0.154197
0.263760u
67
+ 0.386209u
66
+ ··· − 1.73388u − 0.866876
a
9
=
0.147546u
67
− 0.0835648u
66
+ ··· − 1.04362u + 2.37990
−0.325349u
67
− 0.435020u
66
+ ··· + 1.13942u − 1.64284
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.626539u
67
− 1.34740u
66
+ ··· + 9.36366u − 10.4358
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
68
+ 37u
67
+ ··· − u + 1
c
2
, c
6
u
68
− u
67
+ ··· − u − 1
c
3
u
68
− 3u
67
+ ··· − 5590u − 1393
c
4
, c
7
u
68
− 2u
67
+ ··· + 682u + 107
c
5
, c
10
u
68
+ u
67
+ ··· − 5u + 1
c
8
u
68
+ u
67
+ ··· − 2029u − 1341
c
9
, c
11
u
68
+ 25u
67
+ ··· − 57u + 1
c
12
u
68
− 3u
67
+ ··· + 2287u + 121
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
68
+ 3y
67
+ ··· + 105y + 1
c
2
, c
6
y
68
− 37y
67
+ ··· + y + 1
c
3
y
68
− 69y
67
+ ··· − 13063878y + 1940449
c
4
, c
7
y
68
+ 28y
67
+ ··· − 23856y + 11449
c
5
, c
10
y
68
+ 25y
67
+ ··· − 57y + 1
c
8
y
68
− 67y
67
+ ··· + 17462531y + 1798281
c
9
, c
11
y
68
+ 45y
67
+ ··· − 977y + 1
c
12
y
68
− 75y
67
+ ··· − 4777829y + 14641
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.940907 + 0.259610I
a = 0.42197 − 2.48976I
b = −0.159587 − 1.033910I
−0.93999 − 1.07351I −13.16109 − 0.94732I
u = 0.940907 − 0.259610I
a = 0.42197 + 2.48976I
b = −0.159587 + 1.033910I
−0.93999 + 1.07351I −13.16109 + 0.94732I
u = −1.043650 + 0.145685I
a = −0.39955 + 2.55386I
b = 0.275203 + 0.962008I
−3.76897 + 2.72988I −8.00000 − 5.48520I
u = −1.043650 − 0.145685I
a = −0.39955 − 2.55386I
b = 0.275203 − 0.962008I
−3.76897 − 2.72988I −8.00000 + 5.48520I
u = 0.885464 + 0.597578I
a = 0.75942 + 1.75588I
b = 0.093114 + 0.992704I
−1.11071 − 2.33001I 0
u = 0.885464 − 0.597578I
a = 0.75942 − 1.75588I
b = 0.093114 − 0.992704I
−1.11071 + 2.33001I 0
u = −1.004080 + 0.415754I
a = 0.232891 − 0.695090I
b = −0.812580 + 0.667456I
−4.35054 + 1.56377I 0
u = −1.004080 − 0.415754I
a = 0.232891 + 0.695090I
b = −0.812580 − 0.667456I
−4.35054 − 1.56377I 0
u = −0.876146 + 0.645556I
a = 0.163390 + 0.383509I
b = −0.159247 − 0.049954I
2.13037 + 2.54033I 0
u = −0.876146 − 0.645556I
a = 0.163390 − 0.383509I
b = −0.159247 + 0.049954I
2.13037 − 2.54033I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.399517 + 1.015870I
a = 0.654911 + 0.379579I
b = −0.849945 + 0.659975I
0.65883 + 3.48006I 0
u = 0.399517 − 1.015870I
a = 0.654911 − 0.379579I
b = −0.849945 − 0.659975I
0.65883 − 3.48006I 0
u = −1.037540 + 0.398544I
a = −0.14880 + 1.55501I
b = −0.576579 + 1.193350I
−6.36651 − 0.81288I 0
u = −1.037540 − 0.398544I
a = −0.14880 − 1.55501I
b = −0.576579 − 1.193350I
−6.36651 + 0.81288I 0
u = 0.716409 + 0.891799I
a = 0.500992 − 0.440317I
b = −0.674233 − 0.922387I
3.29939 + 2.00709I 0
u = 0.716409 − 0.891799I
a = 0.500992 + 0.440317I
b = −0.674233 + 0.922387I
3.29939 − 2.00709I 0
u = −0.342929 + 1.097870I
a = 0.556771 + 0.538161I
b = −0.723860 + 1.040460I
−0.50810 − 9.35376I 0
u = −0.342929 − 1.097870I
a = 0.556771 − 0.538161I
b = −0.723860 − 1.040460I
−0.50810 + 9.35376I 0
u = −0.098391 + 0.835496I
a = 0.643296 − 0.760427I
b = 0.141512 − 1.090530I
−6.10032 − 3.11040I −10.83046 + 2.94729I
u = −0.098391 − 0.835496I
a = 0.643296 + 0.760427I
b = 0.141512 + 1.090530I
−6.10032 + 3.11040I −10.83046 − 2.94729I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.046410 + 0.508419I
a = −0.132346 + 0.527696I
b = −0.940830 + 0.317450I
−3.60038 − 4.71726I 0
u = 1.046410 − 0.508419I
a = −0.132346 − 0.527696I
b = −0.940830 − 0.317450I
−3.60038 + 4.71726I 0
u = −0.768060 + 0.318425I
a = −2.70476 + 2.59441I
b = 0.549168 + 0.792945I
−3.34454 + 1.57597I −9.61436 − 5.33785I
u = −0.768060 − 0.318425I
a = −2.70476 − 2.59441I
b = 0.549168 − 0.792945I
−3.34454 − 1.57597I −9.61436 + 5.33785I
u = 1.047410 + 0.527364I
a = 1.61700 + 1.10646I
b = −0.706839 + 1.027240I
−5.45556 − 7.28309I 0
u = 1.047410 − 0.527364I
a = 1.61700 − 1.10646I
b = −0.706839 − 1.027240I
−5.45556 + 7.28309I 0
u = 1.083690 + 0.530024I
a = −0.553710 − 0.091586I
b = −0.851770 − 0.802509I
3.49437 − 0.97425I 0
u = 1.083690 − 0.530024I
a = −0.553710 + 0.091586I
b = −0.851770 + 0.802509I
3.49437 + 0.97425I 0
u = −0.934372 + 0.781624I
a = 0.053522 + 0.417489I
b = 0.680894 − 0.644957I
3.42338 + 2.92327I 0
u = −0.934372 − 0.781624I
a = 0.053522 − 0.417489I
b = 0.680894 + 0.644957I
3.42338 − 2.92327I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.841651 + 0.883672I
a = 0.868517 − 0.485589I
b = −0.677512 − 0.774206I
3.75199 + 3.22331I 0
u = −0.841651 − 0.883672I
a = 0.868517 + 0.485589I
b = −0.677512 + 0.774206I
3.75199 − 3.22331I 0
u = 0.548357 + 0.532260I
a = −0.28832 − 1.56425I
b = 0.576815 + 0.947312I
−3.88368 + 2.91929I −8.58150 − 1.60014I
u = 0.548357 − 0.532260I
a = −0.28832 + 1.56425I
b = 0.576815 − 0.947312I
−3.88368 − 2.91929I −8.58150 + 1.60014I
u = −1.24899
a = −1.01889
b = 0.341297
−6.77611 0
u = 0.750601
a = 0.454925
b = 0.481221
−1.11068 −8.83830
u = −1.157710 + 0.488774I
a = 0.89610 − 1.78056I
b = −0.790649 − 0.975806I
2.95487 + 7.09497I 0
u = −1.157710 − 0.488774I
a = 0.89610 + 1.78056I
b = −0.790649 + 0.975806I
2.95487 − 7.09497I 0
u = 1.019200 + 0.755143I
a = −1.43617 − 1.55373I
b = 0.644876 − 1.003110I
2.34696 − 8.08537I 0
u = 1.019200 − 0.755143I
a = −1.43617 + 1.55373I
b = 0.644876 + 1.003110I
2.34696 + 8.08537I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.137780 + 0.597361I
a = −0.680702 + 0.371018I
b = −0.611829 + 0.671402I
2.91478 + 2.04568I 0
u = −1.137780 − 0.597361I
a = −0.680702 − 0.371018I
b = −0.611829 − 0.671402I
2.91478 − 2.04568I 0
u = 1.210900 + 0.474728I
a = 0.58877 + 2.13386I
b = −0.619959 + 0.991046I
1.92170 − 6.94863I 0
u = 1.210900 − 0.474728I
a = 0.58877 − 2.13386I
b = −0.619959 − 0.991046I
1.92170 + 6.94863I 0
u = −1.188350 + 0.530219I
a = 0.57443 − 1.99425I
b = −0.133485 − 1.246610I
−9.23070 + 8.01469I 0
u = −1.188350 − 0.530219I
a = 0.57443 + 1.99425I
b = −0.133485 + 1.246610I
−9.23070 − 8.01469I 0
u = 0.444105 + 0.517971I
a = 0.608976 − 0.934274I
b = 0.732751 + 0.181612I
−1.85955 + 0.48121I −4.42539 + 0.48875I
u = 0.444105 − 0.517971I
a = 0.608976 + 0.934274I
b = 0.732751 − 0.181612I
−1.85955 − 0.48121I −4.42539 − 0.48875I
u = −0.172980 + 0.644207I
a = −0.086216 + 0.618638I
b = 0.742213 + 0.849423I
5.46513 + 2.81095I −4.67462 − 2.60873I
u = −0.172980 − 0.644207I
a = −0.086216 − 0.618638I
b = 0.742213 − 0.849423I
5.46513 − 2.81095I −4.67462 + 2.60873I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.312170 + 0.378943I
a = −0.96232 − 1.62440I
b = 0.069729 − 1.052040I
−10.44160 − 1.32359I 0
u = 1.312170 − 0.378943I
a = −0.96232 + 1.62440I
b = 0.069729 + 1.052040I
−10.44160 + 1.32359I 0
u = −0.587051 + 0.229586I
a = −0.76768 + 3.66509I
b = 0.455736 + 1.134590I
−4.71625 + 3.83876I −6.01425 − 8.08352I
u = −0.587051 − 0.229586I
a = −0.76768 − 3.66509I
b = 0.455736 − 1.134590I
−4.71625 − 3.83876I −6.01425 + 8.08352I
u = 1.192260 + 0.675113I
a = 0.403435 − 0.199397I
b = 0.934236 + 0.605763I
−1.79071 − 9.57598I 0
u = 1.192260 − 0.675113I
a = 0.403435 + 0.199397I
b = 0.934236 − 0.605763I
−1.79071 + 9.57598I 0
u = −1.24627 + 0.68565I
a = −1.04436 + 1.71892I
b = 0.735262 + 1.096550I
−3.3132 + 15.7131I 0
u = −1.24627 − 0.68565I
a = −1.04436 − 1.71892I
b = 0.735262 − 1.096550I
−3.3132 − 15.7131I 0
u = −1.49863 + 0.14703I
a = −0.238266 + 1.256530I
b = 0.643640 + 0.677255I
−6.04640 + 0.52618I 0
u = −1.49863 − 0.14703I
a = −0.238266 − 1.256530I
b = 0.643640 − 0.677255I
−6.04640 − 0.52618I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52986 + 0.24219I
a = 0.175494 + 1.248290I
b = 0.639173 + 0.989620I
−7.00901 + 4.52551I 0
u = 1.52986 − 0.24219I
a = 0.175494 − 1.248290I
b = 0.639173 − 0.989620I
−7.00901 − 4.52551I 0
u = 0.337839 + 0.292985I
a = −1.63156 − 0.79539I
b = 0.841620 − 0.916425I
5.70133 − 3.16227I −8.17605 + 1.97963I
u = 0.337839 − 0.292985I
a = −1.63156 + 0.79539I
b = 0.841620 + 0.916425I
5.70133 + 3.16227I −8.17605 − 1.97963I
u = 0.147872 + 0.344296I
a = 0.999072 + 0.433594I
b = −0.214633 + 0.698481I
−0.427609 − 1.011650I −6.71477 + 6.54763I
u = 0.147872 − 0.344296I
a = 0.999072 − 0.433594I
b = −0.214633 − 0.698481I
−0.427609 + 1.011650I −6.71477 − 6.54763I
u = −0.177594 + 0.322240I
a = −0.862215 + 0.770131I
b = 0.836335 − 0.904083I
5.73139 − 3.08529I −6.85812 + 5.06126I
u = −0.177594 − 0.322240I
a = −0.862215 − 0.770131I
b = 0.836335 + 0.904083I
5.73139 + 3.08529I −6.85812 − 5.06126I
11
II. I
u
2
=
h−5u
19
+33u
17
+· · ·+b+11u, −11u
18
−2u
17
+· · ·+a+29, u
20
−7u
18
+· · ·+u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
11u
18
+ 2u
17
+ ··· − 16u − 29
5u
19
− 33u
17
+ ··· − 11u
2
− 11u
a
5
=
−3u
19
+ 18u
17
+ ··· − 3u + 1
−4u
19
+ 26u
17
+ ··· + 9u − 1
a
8
=
−u
19
+ 7u
17
+ ··· + 2u − 6
u
19
− 2u
18
+ ··· − 32u
2
+ 6
a
4
=
3u
19
− u
18
+ ··· − 20u + 8
−8u
19
+ u
18
+ ··· + 14u − 6
a
10
=
−5u
19
+ 11u
18
+ ··· − 5u − 29
5u
19
− 33u
17
+ ··· − 11u
2
− 11u
a
12
=
−5u
19
+ u
18
+ ··· + 17u − 7
5u
19
− u
18
+ ··· − 6u + 5
a
9
=
−u
19
+ u
18
+ ··· + u − 7
u
19
− 2u
18
+ ··· − 33u
2
+ 6
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −2u
19
+ 4u
18
+ 12u
17
− 29u
16
− 32u
15
+ 101u
14
+ 46u
13
− 224u
12
− 25u
11
+ 343u
10
−
29u
9
− 382u
8
+ 73u
7
+ 319u
6
− 76u
5
− 197u
4
+ 45u
3
+ 92u
2
− 18u − 33
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
20
− 14u
19
+ ··· − 15u + 1
c
2
u
20
− 7u
18
+ ··· − u + 1
c
3
u
20
+ 6u
19
+ ··· + 6u + 1
c
4
u
20
− u
19
+ ··· − 4u
2
+ 1
c
5
u
20
+ 4u
18
+ ··· + u + 1
c
6
u
20
− 7u
18
+ ··· + u + 1
c
7
u
20
+ u
19
+ ··· − 4u
2
+ 1
c
8
u
20
− 4u
18
+ ··· − u + 1
c
9
u
20
− 8u
19
+ ··· − 11u + 1
c
10
u
20
+ 4u
18
+ ··· − u + 1
c
11
u
20
+ 8u
19
+ ··· + 11u + 1
c
12
u
20
+ 4u
19
+ ··· + 3u + 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
− 2y
19
+ ··· − 15y + 1
c
2
, c
6
y
20
− 14y
19
+ ··· − 15y + 1
c
3
y
20
− 14y
19
+ ··· + 6y + 1
c
4
, c
7
y
20
+ 11y
19
+ ··· − 8y + 1
c
5
, c
10
y
20
+ 8y
19
+ ··· + 11y + 1
c
8
y
20
− 8y
19
+ ··· + 11y + 1
c
9
, c
11
y
20
+ 16y
19
+ ··· − y + 1
c
12
y
20
− 12y
19
+ ··· + 63y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.916596 + 0.501656I
a = −0.23575 + 2.17377I
b = −0.084408 + 0.989106I
−0.08561 + 2.00156I −7.02876 − 3.01759I
u = −0.916596 − 0.501656I
a = −0.23575 − 2.17377I
b = −0.084408 − 0.989106I
−0.08561 − 2.00156I −7.02876 + 3.01759I
u = 0.619099 + 0.623336I
a = −0.745100 − 0.435517I
b = 0.837623 − 0.852995I
6.36763 − 3.79706I −1.32350 + 7.18577I
u = 0.619099 − 0.623336I
a = −0.745100 + 0.435517I
b = 0.837623 + 0.852995I
6.36763 + 3.79706I −1.32350 − 7.18577I
u = 0.893965 + 0.712196I
a = 0.533393 + 0.189780I
b = −0.077110 + 0.595222I
1.54640 − 2.72061I −12.89369 + 5.24622I
u = 0.893965 − 0.712196I
a = 0.533393 − 0.189780I
b = −0.077110 − 0.595222I
1.54640 + 2.72061I −12.89369 − 5.24622I
u = −0.592080 + 0.540578I
a = −0.450432 − 0.379257I
b = 0.815442 − 0.949836I
6.07415 − 2.37360I −2.82617 − 3.06916I
u = −0.592080 − 0.540578I
a = −0.450432 + 0.379257I
b = 0.815442 + 0.949836I
6.07415 + 2.37360I −2.82617 + 3.06916I
u = −1.139700 + 0.603954I
a = 0.97885 − 1.81385I
b = −0.733487 − 0.971689I
4.22590 + 7.07154I −3.35111 − 5.96009I
u = −1.139700 − 0.603954I
a = 0.97885 + 1.81385I
b = −0.733487 + 0.971689I
4.22590 − 7.07154I −3.35111 + 5.96009I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.104760 + 0.669023I
a = −0.476179 − 0.045276I
b = −0.774786 − 0.785443I
4.80560 − 1.34863I −2.53819 + 0.59167I
u = 1.104760 − 0.669023I
a = −0.476179 + 0.045276I
b = −0.774786 + 0.785443I
4.80560 + 1.34863I −2.53819 − 0.59167I
u = 1.303610 + 0.049480I
a = 0.089962 + 1.123820I
b = 0.496270 + 1.018040I
−7.77106 + 3.02337I −12.40469 − 2.49345I
u = 1.303610 − 0.049480I
a = 0.089962 − 1.123820I
b = 0.496270 − 1.018040I
−7.77106 − 3.02337I −12.40469 + 2.49345I
u = 0.678501 + 0.066867I
a = 0.90337 + 4.20276I
b = −0.482156 + 1.088980I
−5.21524 − 3.52525I −18.2464 + 1.7590I
u = 0.678501 − 0.066867I
a = 0.90337 − 4.20276I
b = −0.482156 − 1.088980I
−5.21524 + 3.52525I −18.2464 − 1.7590I
u = −1.368110 + 0.049620I
a = −0.68949 + 1.67187I
b = 0.501119 + 0.678815I
−6.60360 + 1.07496I −13.9720 − 6.3109I
u = −1.368110 − 0.049620I
a = −0.68949 − 1.67187I
b = 0.501119 − 0.678815I
−6.60360 − 1.07496I −13.9720 + 6.3109I
u = −0.583436 + 0.055335I
a = −2.40862 − 1.94316I
b = −0.498506 + 0.538267I
−3.34415 − 0.58323I −10.41549 − 1.69535I
u = −0.583436 − 0.055335I
a = −2.40862 + 1.94316I
b = −0.498506 − 0.538267I
−3.34415 + 0.58323I −10.41549 + 1.69535I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
20
− 14u
19
+ ··· − 15u + 1)(u
68
+ 37u
67
+ ··· − u + 1)
c
2
(u
20
− 7u
18
+ ··· − u + 1)(u
68
− u
67
+ ··· − u − 1)
c
3
(u
20
+ 6u
19
+ ··· + 6u + 1)(u
68
− 3u
67
+ ··· − 5590u − 1393)
c
4
(u
20
− u
19
+ ··· − 4u
2
+ 1)(u
68
− 2u
67
+ ··· + 682u + 107)
c
5
(u
20
+ 4u
18
+ ··· + u + 1)(u
68
+ u
67
+ ··· − 5u + 1)
c
6
(u
20
− 7u
18
+ ··· + u + 1)(u
68
− u
67
+ ··· − u − 1)
c
7
(u
20
+ u
19
+ ··· − 4u
2
+ 1)(u
68
− 2u
67
+ ··· + 682u + 107)
c
8
(u
20
− 4u
18
+ ··· − u + 1)(u
68
+ u
67
+ ··· − 2029u − 1341)
c
9
(u
20
− 8u
19
+ ··· − 11u + 1)(u
68
+ 25u
67
+ ··· − 57u + 1)
c
10
(u
20
+ 4u
18
+ ··· − u + 1)(u
68
+ u
67
+ ··· − 5u + 1)
c
11
(u
20
+ 8u
19
+ ··· + 11u + 1)(u
68
+ 25u
67
+ ··· − 57u + 1)
c
12
(u
20
+ 4u
19
+ ··· + 3u + 1)(u
68
− 3u
67
+ ··· + 2287u + 121)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
20
− 2y
19
+ ··· − 15y + 1)(y
68
+ 3y
67
+ ··· + 105y + 1)
c
2
, c
6
(y
20
− 14y
19
+ ··· − 15y + 1)(y
68
− 37y
67
+ ··· + y + 1)
c
3
(y
20
− 14y
19
+ ··· + 6y + 1)
· (y
68
− 69y
67
+ ··· − 13063878y + 1940449)
c
4
, c
7
(y
20
+ 11y
19
+ ··· − 8y + 1)(y
68
+ 28y
67
+ ··· − 23856y + 11449)
c
5
, c
10
(y
20
+ 8y
19
+ ··· + 11y + 1)(y
68
+ 25y
67
+ ··· − 57y + 1)
c
8
(y
20
− 8y
19
+ ··· + 11y + 1)
· (y
68
− 67y
67
+ ··· + 17462531y + 1798281)
c
9
, c
11
(y
20
+ 16y
19
+ ··· − y + 1)(y
68
+ 45y
67
+ ··· − 977y + 1)
c
12
(y
20
− 12y
19
+ ··· + 63y + 1)(y
68
− 75y
67
+ ··· − 4777829y + 14641)
20
