12a
0568
(K12a
0568
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 8 12 2 5 4 1 6 11
Solving Sequence
4,10 1,5
11 9 3 2 8 6 7 12
c
4
c
10
c
9
c
3
c
1
c
8
c
5
c
7
c
12
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h6.14215 × 10
45
u
89
− 3.30510 × 10
45
u
88
+ ··· + 8.82311 × 10
45
b − 2.12797 × 10
46
,
− 3.98658 × 10
46
u
89
+ 5.02790 × 10
46
u
88
+ ··· + 8.82311 × 10
45
a + 2.64205 × 10
47
, u
90
− u
89
+ ··· − 11u − 1i
I
u
2
= hu
4
a + u
4
− 2u
2
a − 2u
2
+ b − a, −u
5
a + 3u
3
a − u
4
+ a
2
− 2au + 3u
2
− 2, u
6
− 3u
4
+ 2u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 102 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
= h6.14×10
45
u
89
−3.31×10
45
u
88
+· · ·+8.82×10
45
b−2.13×10
46
, −3.99×
10
46
u
89
+5.03×10
46
u
88
+· · ·+8.82×10
45
a+2.64×10
47
, u
90
−u
89
+· · ·−11u−1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
1
=
4.51834u
89
− 5.69856u
88
+ ··· − 157.416u − 29.9447
−0.696143u
89
+ 0.374596u
88
+ ··· + 4.22395u + 2.41181
a
5
=
1
u
2
a
11
=
5.71831u
89
− 7.17155u
88
+ ··· − 186.704u − 44.7259
−1.66422u
89
− 0.736261u
88
+ ··· − 37.5768u − 5.22880
a
9
=
u
u
a
3
=
−u
2
+ 1
−u
2
a
2
=
4.57115u
89
− 6.31172u
88
+ ··· − 163.112u − 31.9782
−1.06131u
89
− 0.301013u
88
+ ··· − 1.47856u + 1.93140
a
8
=
−u
3
+ 2u
−u
5
+ u
3
+ u
a
6
=
u
6
− 3u
4
+ 2u
2
+ 1
u
8
− 2u
6
+ 2u
2
a
7
=
3.67198u
89
− 3.85942u
88
+ ··· − 90.2360u − 27.2951
2.09638u
89
− 0.675864u
88
+ ··· − 16.6943u − 4.75859
a
12
=
5.32448u
89
− 6.50749u
88
+ ··· − 171.372u − 42.3482
−1.29912u
89
− 0.713830u
88
+ ··· − 34.4333u − 4.88931
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.10870u
89
− 2.12548u
88
+ ··· − 53.7193u − 31.3376
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
90
+ 41u
89
+ ··· − 69u + 1
c
2
, c
7
u
90
+ u
89
+ ··· + 13u − 1
c
3
, c
4
, c
9
u
90
+ u
89
+ ··· + 11u − 1
c
5
, c
8
u
90
− 3u
89
+ ··· − 10133u + 783
c
6
, c
11
u
90
+ u
89
+ ··· + 9u − 5
c
10
, c
12
u
90
+ 29u
89
+ ··· + 471u + 25
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
90
+ 29y
89
+ ··· − 1117y + 1
c
2
, c
7
y
90
+ 41y
89
+ ··· − 69y + 1
c
3
, c
4
, c
9
y
90
− 75y
89
+ ··· − 89y + 1
c
5
, c
8
y
90
+ 65y
89
+ ··· − 60583609y + 613089
c
6
, c
11
y
90
− 29y
89
+ ··· − 471y + 25
c
10
, c
12
y
90
+ 71y
89
+ ··· − 78091y + 625
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.063363 + 0.857170I
a = −1.60157 − 0.02571I
b = −0.981273 + 0.593879I
9.60013 − 0.30151I −1.10817 + 1.54965I
u = −0.063363 − 0.857170I
a = −1.60157 + 0.02571I
b = −0.981273 − 0.593879I
9.60013 + 0.30151I −1.10817 − 1.54965I
u = 0.118441 + 0.851139I
a = 1.49393 − 0.11981I
b = 0.898638 + 0.842251I
7.97578 − 5.92214I −2.87748 + 3.29056I
u = 0.118441 − 0.851139I
a = 1.49393 + 0.11981I
b = 0.898638 − 0.842251I
7.97578 + 5.92214I −2.87748 − 3.29056I
u = −0.138419 + 0.847253I
a = 1.90893 + 0.26202I
b = 1.129030 − 0.755146I
6.97122 + 12.03910I −4.54855 − 8.02805I
u = −0.138419 − 0.847253I
a = 1.90893 − 0.26202I
b = 1.129030 + 0.755146I
6.97122 − 12.03910I −4.54855 + 8.02805I
u = 0.089333 + 0.853199I
a = −1.84826 + 0.20136I
b = −1.141640 − 0.418693I
9.00366 − 5.86140I −1.98243 + 3.66515I
u = 0.089333 − 0.853199I
a = −1.84826 − 0.20136I
b = −1.141640 + 0.418693I
9.00366 + 5.86140I −1.98243 − 3.66515I
u = −1.109560 + 0.413438I
a = −0.120973 + 1.369430I
b = 0.098202 + 0.474134I
3.99789 − 7.50254I 0
u = −1.109560 − 0.413438I
a = −0.120973 − 1.369430I
b = 0.098202 − 0.474134I
3.99789 + 7.50254I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.182370 + 0.122207I
a = 0.100406 + 0.432195I
b = 1.193500 + 0.510369I
−1.82140 − 0.65010I 0
u = 1.182370 − 0.122207I
a = 0.100406 − 0.432195I
b = 1.193500 − 0.510369I
−1.82140 + 0.65010I 0
u = 0.041756 + 0.807032I
a = −0.159012 − 0.738937I
b = 0.036451 + 0.424290I
4.52384 − 2.64817I −1.47152 + 3.33157I
u = 0.041756 − 0.807032I
a = −0.159012 + 0.738937I
b = 0.036451 − 0.424290I
4.52384 + 2.64817I −1.47152 − 3.33157I
u = −0.097470 + 0.785464I
a = 0.82289 + 1.43240I
b = 0.563552 − 0.155489I
0.42228 + 5.90745I −7.85230 − 6.60506I
u = −0.097470 − 0.785464I
a = 0.82289 − 1.43240I
b = 0.563552 + 0.155489I
0.42228 − 5.90745I −7.85230 + 6.60506I
u = 1.138980 + 0.412263I
a = −0.194847 − 1.067110I
b = 0.271357 − 0.244873I
4.84987 + 1.38168I 0
u = 1.138980 − 0.412263I
a = −0.194847 + 1.067110I
b = 0.271357 + 0.244873I
4.84987 − 1.38168I 0
u = −1.174040 + 0.310051I
a = 0.760441 + 0.711639I
b = 1.23530 + 0.88131I
−2.83425 − 1.91319I 0
u = −1.174040 − 0.310051I
a = 0.760441 − 0.711639I
b = 1.23530 − 0.88131I
−2.83425 + 1.91319I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.021656 + 0.777387I
a = 1.64509 + 0.25611I
b = 1.77954 + 0.17094I
2.06022 + 2.77574I −4.04299 − 3.19683I
u = −0.021656 − 0.777387I
a = 1.64509 − 0.25611I
b = 1.77954 − 0.17094I
2.06022 − 2.77574I −4.04299 + 3.19683I
u = −0.582202 + 0.482242I
a = 1.56154 − 1.15042I
b = 0.641273 − 0.707070I
2.15933 + 7.36357I −6.87028 − 8.54868I
u = −0.582202 − 0.482242I
a = 1.56154 + 1.15042I
b = 0.641273 + 0.707070I
2.15933 − 7.36357I −6.87028 + 8.54868I
u = 1.176580 + 0.408870I
a = 0.202086 + 1.238210I
b = 0.535480 + 0.478102I
5.66669 + 1.33161I 0
u = 1.176580 − 0.408870I
a = 0.202086 − 1.238210I
b = 0.535480 − 0.478102I
5.66669 − 1.33161I 0
u = −0.005141 + 0.749243I
a = −1.11720 + 1.29527I
b = −0.296478 + 0.005780I
1.47758 − 1.34536I −4.73272 + 0.56742I
u = −0.005141 − 0.749243I
a = −1.11720 − 1.29527I
b = −0.296478 − 0.005780I
1.47758 + 1.34536I −4.73272 − 0.56742I
u = −1.260060 + 0.057506I
a = −0.008082 − 0.481249I
b = −1.90367 − 0.70076I
−4.87070 + 2.52144I 0
u = −1.260060 − 0.057506I
a = −0.008082 + 0.481249I
b = −1.90367 + 0.70076I
−4.87070 − 2.52144I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.205890 + 0.409098I
a = 0.314677 − 1.064430I
b = 0.378068 − 0.298950I
6.08340 + 4.84091I 0
u = −1.205890 − 0.409098I
a = 0.314677 + 1.064430I
b = 0.378068 + 0.298950I
6.08340 − 4.84091I 0
u = 0.520473 + 0.500551I
a = 1.17156 + 1.23439I
b = 0.524177 + 0.800626I
2.66978 − 1.59618I −5.41754 + 3.51950I
u = 0.520473 − 0.500551I
a = 1.17156 − 1.23439I
b = 0.524177 − 0.800626I
2.66978 + 1.59618I −5.41754 − 3.51950I
u = 1.230560 + 0.352038I
a = 0.445034 − 0.089140I
b = 1.54264 − 0.03383I
0.86290 − 1.52902I 0
u = 1.230560 − 0.352038I
a = 0.445034 + 0.089140I
b = 1.54264 + 0.03383I
0.86290 + 1.52902I 0
u = −0.386151 + 0.600663I
a = −1.37669 + 1.32407I
b = −0.260073 + 0.690515I
2.78195 − 3.49276I −4.88676 + 2.39495I
u = −0.386151 − 0.600663I
a = −1.37669 − 1.32407I
b = −0.260073 − 0.690515I
2.78195 + 3.49276I −4.88676 − 2.39495I
u = −1.285160 + 0.169868I
a = 0.1170600 − 0.0114062I
b = −1.096790 − 0.353976I
−4.98736 + 2.80353I 0
u = −1.285160 − 0.169868I
a = 0.1170600 + 0.0114062I
b = −1.096790 + 0.353976I
−4.98736 − 2.80353I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.297550 + 0.009629I
a = −0.505550 − 0.905163I
b = −3.00177 − 1.14994I
−6.16458 − 2.17147I 0
u = 1.297550 − 0.009629I
a = −0.505550 + 0.905163I
b = −3.00177 + 1.14994I
−6.16458 + 2.17147I 0
u = −1.255600 + 0.330283I
a = −0.133760 + 0.939798I
b = −1.95449 − 0.44736I
−1.75554 + 1.21643I 0
u = −1.255600 − 0.330283I
a = −0.133760 − 0.939798I
b = −1.95449 + 0.44736I
−1.75554 − 1.21643I 0
u = −1.286820 + 0.199890I
a = 0.543186 − 0.643193I
b = 1.58806 − 0.78450I
−2.98447 + 4.84215I 0
u = −1.286820 − 0.199890I
a = 0.543186 + 0.643193I
b = 1.58806 + 0.78450I
−2.98447 − 4.84215I 0
u = 0.431408 + 0.548012I
a = −1.57826 − 0.95667I
b = −0.355469 − 0.430801I
2.94450 − 2.17437I −4.51675 + 3.49335I
u = 0.431408 − 0.548012I
a = −1.57826 + 0.95667I
b = −0.355469 + 0.430801I
2.94450 + 2.17437I −4.51675 − 3.49335I
u = −1.279690 + 0.313561I
a = 0.872641 − 0.321924I
b = 2.23380 − 0.02437I
−2.48888 + 5.16894I 0
u = −1.279690 − 0.313561I
a = 0.872641 + 0.321924I
b = 2.23380 + 0.02437I
−2.48888 − 5.16894I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.279580 + 0.320443I
a = −0.535442 + 0.891919I
b = −1.03388 + 1.66321I
−2.52541 − 2.51929I 0
u = 1.279580 − 0.320443I
a = −0.535442 − 0.891919I
b = −1.03388 − 1.66321I
−2.52541 + 2.51929I 0
u = −1.32526
a = 0.698690
b = 2.15962
−6.06566 0
u = 1.286350 + 0.336602I
a = −0.476581 − 0.906569I
b = −2.19673 + 0.73627I
−2.01618 − 6.79326I 0
u = 1.286350 − 0.336602I
a = −0.476581 + 0.906569I
b = −2.19673 − 0.73627I
−2.01618 + 6.79326I 0
u = −0.147786 + 0.640241I
a = 0.110299 + 0.934916I
b = 0.760246 + 0.559116I
−1.72468 − 0.26912I −10.83738 − 0.89034I
u = −0.147786 − 0.640241I
a = 0.110299 − 0.934916I
b = 0.760246 − 0.559116I
−1.72468 + 0.26912I −10.83738 + 0.89034I
u = −1.297240 + 0.356564I
a = −0.378686 − 0.299994I
b = −1.50255 − 0.46141I
0.34536 + 6.83857I 0
u = −1.297240 − 0.356564I
a = −0.378686 + 0.299994I
b = −1.50255 + 0.46141I
0.34536 − 6.83857I 0
u = 1.343110 + 0.269514I
a = −0.524843 + 0.057528I
b = −1.27472 + 1.65070I
−6.42041 − 3.07803I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.343110 − 0.269514I
a = −0.524843 − 0.057528I
b = −1.27472 − 1.65070I
−6.42041 + 3.07803I 0
u = 1.314120 + 0.387182I
a = 0.396415 + 0.891589I
b = 2.26148 + 0.88058I
5.29539 − 4.16366I 0
u = 1.314120 − 0.387182I
a = 0.396415 − 0.891589I
b = 2.26148 − 0.88058I
5.29539 + 4.16366I 0
u = 1.330400 + 0.341932I
a = −0.971871 − 0.087810I
b = −2.83341 + 0.46508I
−4.06109 − 9.98132I 0
u = 1.330400 − 0.341932I
a = −0.971871 + 0.087810I
b = −2.83341 − 0.46508I
−4.06109 + 9.98132I 0
u = 1.373430 + 0.048365I
a = −0.767535 − 0.097752I
b = −2.97432 − 0.89635I
−9.16535 − 3.75736I 0
u = 1.373430 − 0.048365I
a = −0.767535 + 0.097752I
b = −2.97432 + 0.89635I
−9.16535 + 3.75736I 0
u = −1.331210 + 0.380889I
a = 0.583489 − 1.007120I
b = 2.53189 − 0.84297I
4.55165 + 10.29420I 0
u = −1.331210 − 0.380889I
a = 0.583489 + 1.007120I
b = 2.53189 + 0.84297I
4.55165 − 10.29420I 0
u = −1.384510 + 0.175464I
a = 0.313458 − 0.798286I
b = 1.16677 − 1.84566I
−2.77389 + 4.61364I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.384510 − 0.175464I
a = 0.313458 + 0.798286I
b = 1.16677 + 1.84566I
−2.77389 − 4.61364I 0
u = 0.088847 + 0.593570I
a = −1.267680 + 0.443062I
b = −0.355861 + 0.190586I
1.26113 − 1.94724I −1.26470 + 4.88857I
u = 0.088847 − 0.593570I
a = −1.267680 − 0.443062I
b = −0.355861 − 0.190586I
1.26113 + 1.94724I −1.26470 − 4.88857I
u = −1.348930 + 0.375417I
a = −0.450729 + 0.777779I
b = −2.66287 + 1.04047I
3.36379 + 10.33230I 0
u = −1.348930 − 0.375417I
a = −0.450729 − 0.777779I
b = −2.66287 − 1.04047I
3.36379 − 10.33230I 0
u = 1.359890 + 0.369867I
a = −0.653151 − 0.982400I
b = −3.12308 − 1.16988I
2.2530 − 16.4188I 0
u = 1.359890 − 0.369867I
a = −0.653151 + 0.982400I
b = −3.12308 + 1.16988I
2.2530 + 16.4188I 0
u = 1.396870 + 0.210945I
a = −0.084795 + 0.884790I
b = 0.41641 + 2.40101I
−2.84556 + 0.64989I 0
u = 1.396870 − 0.210945I
a = −0.084795 − 0.884790I
b = 0.41641 − 2.40101I
−2.84556 − 0.64989I 0
u = −1.41175 + 0.12137I
a = −0.095134 + 0.753585I
b = −1.32255 + 2.15631I
−3.48836 + 3.57809I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41175 − 0.12137I
a = −0.095134 − 0.753585I
b = −1.32255 − 2.15631I
−3.48836 − 3.57809I 0
u = 1.42791 + 0.09976I
a = −0.392155 − 0.947090I
b = −1.96208 − 2.58798I
−4.28279 − 9.13323I 0
u = 1.42791 − 0.09976I
a = −0.392155 + 0.947090I
b = −1.96208 + 2.58798I
−4.28279 + 9.13323I 0
u = −0.509221 + 0.204867I
a = 1.69198 + 0.01287I
b = 0.496630 − 0.602823I
−3.40120 + 2.98415I −15.2193 − 6.2457I
u = −0.509221 − 0.204867I
a = 1.69198 − 0.01287I
b = 0.496630 + 0.602823I
−3.40120 − 2.98415I −15.2193 + 6.2457I
u = 0.261176 + 0.331858I
a = 0.078211 − 0.357078I
b = 0.376699 + 0.343421I
−0.487076 − 1.059670I −6.96958 + 6.21248I
u = 0.261176 − 0.331858I
a = 0.078211 + 0.357078I
b = 0.376699 − 0.343421I
−0.487076 + 1.059670I −6.96958 − 6.21248I
u = 0.406442
a = −1.12943
b = 0.00215565
−0.922985 −11.2910
u = −0.147866 + 0.018730I
a = 4.32486 − 5.82803I
b = 0.993627 + 0.299114I
−1.72348 + 2.04115I −15.6502 − 3.1222I
u = −0.147866 − 0.018730I
a = 4.32486 + 5.82803I
b = 0.993627 − 0.299114I
−1.72348 − 2.04115I −15.6502 + 3.1222I
13
II. I
u
2
= hu
4
a + u
4
− 2u
2
a − 2u
2
+ b − a, −u
5
a + 3u
3
a − u
4
+ a
2
− 2au +
3u
2
− 2, u
6
− 3u
4
+ 2u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
1
=
a
−u
4
a − u
4
+ 2u
2
a + 2u
2
+ a
a
5
=
1
u
2
a
11
=
−u
5
+ 3u
3
+ a − 2u
u
5
a − u
4
a − u
5
− 2u
3
a + 2u
2
a + 2u
3
+ a + u
a
9
=
u
u
a
3
=
−u
2
+ 1
−u
2
a
2
=
−u
2
+ a + 1
−u
4
a − u
4
+ 2u
2
a + u
2
+ a
a
8
=
−u
3
+ 2u
−u
5
+ u
3
+ u
a
6
=
0
u
4
− u
2
− 1
a
7
=
−u
5
a + 2u
3
a − au
−u
5
a + u
3
a − u
3
+ u
a
12
=
−u
5
+ 3u
3
+ a − 2u
u
5
a − u
4
a − u
5
− 2u
3
a + u
2
a + 2u
3
+ a
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
4
− 4au − 8u
2
− 12
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
12
c
2
, c
7
(u
2
+ 1)
6
c
3
, c
4
, c
9
(u
6
− 3u
4
+ 2u
2
+ 1)
2
c
5
, c
8
(u
6
+ u
4
+ 2u
2
+ 1)
2
c
6
, c
11
(u
4
− u
2
+ 1)
3
c
10
(u
2
− u + 1)
6
c
12
(u
2
+ u + 1)
6
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
12
c
2
, c
7
(y + 1)
12
c
3
, c
4
, c
9
(y
3
− 3y
2
+ 2y + 1)
4
c
5
, c
8
(y
3
+ y
2
+ 2y + 1)
4
c
6
, c
11
(y
2
− y + 1)
6
c
10
, c
12
(y
2
+ y + 1)
6
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.307140 + 0.215080I
a = −0.478572 − 0.583789I
b = −0.45589 − 1.48442I
−4.66906 − 0.79824I −13.50976 − 0.48465I
u = 1.307140 + 0.215080I
a = −0.266290 + 0.706350I
b = 0.903629 + 0.779616I
−4.66906 − 4.85801I −13.5098 + 6.4435I
u = 1.307140 − 0.215080I
a = −0.478572 + 0.583789I
b = −0.45589 + 1.48442I
−4.66906 + 0.79824I −13.50976 + 0.48465I
u = 1.307140 − 0.215080I
a = −0.266290 − 0.706350I
b = 0.903629 − 0.779616I
−4.66906 + 4.85801I −13.5098 − 6.4435I
u = −1.307140 + 0.215080I
a = 0.478572 − 0.583789I
b = 2.21077 + 0.00530I
−4.66906 + 4.85801I −13.5098 − 6.4435I
u = −1.307140 + 0.215080I
a = 0.266290 + 0.706350I
b = 0.85125 + 2.26934I
−4.66906 + 0.79824I −13.50976 + 0.48465I
u = −1.307140 − 0.215080I
a = 0.478572 + 0.583789I
b = 2.21077 − 0.00530I
−4.66906 − 4.85801I −13.5098 + 6.4435I
u = −1.307140 − 0.215080I
a = 0.266290 − 0.706350I
b = 0.85125 − 2.26934I
−4.66906 − 0.79824I −13.50976 − 0.48465I
u = 0.569840I
a = −1.51977 + 0.87744I
b = −1.127410 + 0.215080I
−0.53148 + 2.02988I −6.98049 − 3.46410I
u = 0.569840I
a = 1.51977 + 0.87744I
b = −0.382348 + 0.215080I
−0.53148 − 2.02988I −6.98049 + 3.46410I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = − 0.569840I
a = −1.51977 − 0.87744I
b = −1.127410 − 0.215080I
−0.53148 − 2.02988I −6.98049 + 3.46410I
u = − 0.569840I
a = 1.51977 − 0.87744I
b = −0.382348 − 0.215080I
−0.53148 + 2.02988I −6.98049 − 3.46410I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
12
)(u
90
+ 41u
89
+ ··· − 69u + 1)
c
2
, c
7
((u
2
+ 1)
6
)(u
90
+ u
89
+ ··· + 13u − 1)
c
3
, c
4
, c
9
((u
6
− 3u
4
+ 2u
2
+ 1)
2
)(u
90
+ u
89
+ ··· + 11u − 1)
c
5
, c
8
((u
6
+ u
4
+ 2u
2
+ 1)
2
)(u
90
− 3u
89
+ ··· − 10133u + 783)
c
6
, c
11
((u
4
− u
2
+ 1)
3
)(u
90
+ u
89
+ ··· + 9u − 5)
c
10
((u
2
− u + 1)
6
)(u
90
+ 29u
89
+ ··· + 471u + 25)
c
12
((u
2
+ u + 1)
6
)(u
90
+ 29u
89
+ ··· + 471u + 25)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
12
)(y
90
+ 29y
89
+ ··· − 1117y + 1)
c
2
, c
7
((y + 1)
12
)(y
90
+ 41y
89
+ ··· − 69y + 1)
c
3
, c
4
, c
9
((y
3
− 3y
2
+ 2y + 1)
4
)(y
90
− 75y
89
+ ··· − 89y + 1)
c
5
, c
8
((y
3
+ y
2
+ 2y + 1)
4
)(y
90
+ 65y
89
+ ··· − 6.05836 × 10
7
y + 613089)
c
6
, c
11
((y
2
− y + 1)
6
)(y
90
− 29y
89
+ ··· − 471y + 25)
c
10
, c
12
((y
2
+ y + 1)
6
)(y
90
+ 71y
89
+ ··· − 78091y + 625)
20
