12n
0883
(K12n
0883
)
A knot diagram
1
Linearized knot diagam
4 11 10 8 2 3 12 4 1 6 7 8
Solving Sequence
4,8 2,5
6 9 1 10 3 12 7 11
c
4
c
5
c
8
c
1
c
9
c
3
c
12
c
7
c
11
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.59510 × 10
260
u
68
− 7.42718 × 10
260
u
67
+ ··· + 1.62945 × 10
263
b + 1.10045 × 10
264
,
2.38672 × 10
264
u
68
− 1.77424 × 10
264
u
67
+ ··· + 2.65600 × 10
265
a + 4.40019 × 10
267
,
u
69
− u
68
+ ··· + 5598u − 326i
I
u
2
= h4.71127 × 10
15
u
19
− 6.47791 × 10
15
u
18
+ ··· + 4.46458 × 10
16
b + 2.86340 × 10
16
,
2.26761 × 10
16
u
19
− 5.05266 × 10
16
u
18
+ ··· + 8.92916 × 10
16
a − 2.11962 × 10
17
, u
20
− 2u
19
+ ··· − 2u + 2i
* 2 irreducible components of dim
C
= 0, with total 89 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
= h1.60 × 10
260
u
68
− 7.43 × 10
260
u
67
+ · · · + 1.63 × 10
263
b + 1.10 ×
10
264
, 2.39 × 10
264
u
68
− 1.77 × 10
264
u
67
+ · · · + 2.66 × 10
265
a + 4.40 ×
10
267
, u
69
− u
68
+ · · · + 5598u − 326i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
2
=
−0.0898616u
68
+ 0.0668011u
67
+ ··· + 1857.03u − 165.670
−0.000978922u
68
+ 0.00455810u
67
+ ··· + 61.7443u − 6.75351
a
5
=
1
−u
2
a
6
=
0.119212u
68
− 0.0882484u
67
+ ··· − 2414.13u + 212.151
−0.0136947u
68
+ 0.00153908u
67
+ ··· + 13.6473u + 5.88030
a
9
=
u
u
a
1
=
−0.0908405u
68
+ 0.0713592u
67
+ ··· + 1918.77u − 172.423
−0.000978922u
68
+ 0.00455810u
67
+ ··· + 61.7443u − 6.75351
a
10
=
−0.0359205u
68
+ 0.0140602u
67
+ ··· + 385.225u − 23.0840
−0.0189792u
68
+ 0.0123122u
67
+ ··· + 377.671u − 33.9102
a
3
=
−0.0963752u
68
+ 0.0735527u
67
+ ··· + 1908.00u − 163.170
−0.00161754u
68
+ 0.00623717u
67
+ ··· + 185.450u − 20.1627
a
12
=
−0.0908405u
68
+ 0.0713592u
67
+ ··· + 1918.77u − 172.423
0.00621827u
68
+ 0.00190635u
67
+ ··· − 17.6980u − 0.402606
a
7
=
0.0373943u
68
− 0.0234926u
67
+ ··· − 647.218u + 50.3563
−0.00842474u
68
− 0.00858578u
67
+ ··· − 196.363u + 22.7404
a
11
=
−0.0936309u
68
+ 0.100845u
67
+ ··· + 2668.46u − 251.034
−0.00234625u
68
− 0.00660391u
67
+ ··· − 141.177u + 11.7322
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0737369u
68
− 0.0552753u
67
+ ··· − 1897.44u + 179.175
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
69
+ 3u
68
+ ··· − 7855u − 844
c
2
u
69
+ 4u
68
+ ··· − 447u − 94
c
3
u
69
+ 22u
67
+ ··· + 4528u + 2690
c
4
, c
8
u
69
+ u
68
+ ··· + 5598u + 326
c
5
u
69
+ 2u
67
+ ··· − 96u − 10
c
6
u
69
− 5u
68
+ ··· − 1042u − 242
c
7
, c
11
, c
12
u
69
− u
68
+ ··· + 8u + 2
c
9
u
69
+ 37u
67
+ ··· − 12439u + 1286
c
10
u
69
+ 2u
68
+ ··· + u + 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
69
+ 61y
68
+ ··· − 33395831y −712336
c
2
y
69
− 10y
68
+ ··· + 187213y −8836
c
3
y
69
+ 44y
68
+ ··· − 160249076y −7236100
c
4
, c
8
y
69
− 71y
68
+ ··· + 10709628y −106276
c
5
y
69
+ 4y
68
+ ··· − 111724y −100
c
6
y
69
+ 29y
68
+ ··· − 1680780y −58564
c
7
, c
11
, c
12
y
69
− 69y
68
+ ··· − 1868y −4
c
9
y
69
+ 74y
68
+ ··· − 48598167y −1653796
c
10
y
69
+ 70y
67
+ ··· − 99y −4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.937388 + 0.169929I
a = 0.043478 − 0.742272I
b = −1.43395 + 0.18421I
−7.84748 − 8.49945I 0
u = −0.937388 − 0.169929I
a = 0.043478 + 0.742272I
b = −1.43395 − 0.18421I
−7.84748 + 8.49945I 0
u = −0.900734 + 0.543791I
a = −0.880354 + 0.906296I
b = −0.10421 − 1.57726I
−0.86538 + 2.81593I 0
u = −0.900734 − 0.543791I
a = −0.880354 − 0.906296I
b = −0.10421 + 1.57726I
−0.86538 − 2.81593I 0
u = 0.901600 + 0.002839I
a = −0.299924 − 1.023530I
b = −1.241240 + 0.577767I
−6.61914 + 0.01529I 0
u = 0.901600 − 0.002839I
a = −0.299924 + 1.023530I
b = −1.241240 − 0.577767I
−6.61914 − 0.01529I 0
u = −1.098090 + 0.089462I
a = −0.231231 + 0.492442I
b = 1.47104 − 0.43938I
−6.40650 + 1.70687I 0
u = −1.098090 − 0.089462I
a = −0.231231 − 0.492442I
b = 1.47104 + 0.43938I
−6.40650 − 1.70687I 0
u = 0.891922
a = −1.33838
b = −0.319994
−3.90346 0
u = 1.084820 + 0.583325I
a = 0.429051 + 0.576072I
b = 0.30747 − 1.40594I
−1.38126 + 4.86406I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.084820 − 0.583325I
a = 0.429051 − 0.576072I
b = 0.30747 + 1.40594I
−1.38126 − 4.86406I 0
u = 0.122701 + 0.739942I
a = −0.892972 + 0.209852I
b = 0.443092 + 0.333001I
−1.26816 − 1.18876I −2.82487 + 5.99212I
u = 0.122701 − 0.739942I
a = −0.892972 − 0.209852I
b = 0.443092 − 0.333001I
−1.26816 + 1.18876I −2.82487 − 5.99212I
u = −0.521137 + 0.477077I
a = 1.87070 + 2.12252I
b = −0.053829 − 0.734075I
−9.29987 + 6.46112I −3.09471 − 4.46072I
u = −0.521137 − 0.477077I
a = 1.87070 − 2.12252I
b = −0.053829 + 0.734075I
−9.29987 − 6.46112I −3.09471 + 4.46072I
u = 0.616847 + 0.305370I
a = 0.386621 − 0.542148I
b = 1.270370 − 0.229148I
−5.74954 + 1.06735I −12.5664 − 6.4993I
u = 0.616847 − 0.305370I
a = 0.386621 + 0.542148I
b = 1.270370 + 0.229148I
−5.74954 − 1.06735I −12.5664 + 6.4993I
u = 1.315000 + 0.102944I
a = −0.278028 + 1.229770I
b = 0.39050 − 1.53129I
2.43759 + 4.36021I 0
u = 1.315000 − 0.102944I
a = −0.278028 − 1.229770I
b = 0.39050 + 1.53129I
2.43759 − 4.36021I 0
u = 0.294280 + 0.543366I
a = 1.01357 − 1.53056I
b = 0.314876 − 0.875991I
−8.76029 + 1.21269I −5.57587 − 5.50908I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.294280 − 0.543366I
a = 1.01357 + 1.53056I
b = 0.314876 + 0.875991I
−8.76029 − 1.21269I −5.57587 + 5.50908I
u = −0.456789 + 0.317551I
a = −0.559476 + 0.192992I
b = −0.115002 + 0.434041I
0.98160 − 1.05730I 2.65855 + 2.72887I
u = −0.456789 − 0.317551I
a = −0.559476 − 0.192992I
b = −0.115002 − 0.434041I
0.98160 + 1.05730I 2.65855 − 2.72887I
u = 0.27792 + 1.43387I
a = 0.184504 − 0.104863I
b = 0.169303 − 0.837058I
−8.67747 + 0.45721I 0
u = 0.27792 − 1.43387I
a = 0.184504 + 0.104863I
b = 0.169303 + 0.837058I
−8.67747 − 0.45721I 0
u = −0.14990 + 1.48458I
a = 0.315672 + 0.178950I
b = 0.085797 − 0.238221I
−3.99806 − 3.95956I 0
u = −0.14990 − 1.48458I
a = 0.315672 − 0.178950I
b = 0.085797 + 0.238221I
−3.99806 + 3.95956I 0
u = 0.349929 + 0.366099I
a = −1.39394 + 0.39447I
b = 0.190178 + 0.220324I
−1.21862 − 0.72825I −4.93688 + 0.50068I
u = 0.349929 − 0.366099I
a = −1.39394 − 0.39447I
b = 0.190178 − 0.220324I
−1.21862 + 0.72825I −4.93688 − 0.50068I
u = 0.402832 + 0.287203I
a = −0.958411 − 0.330421I
b = 1.015600 + 0.448453I
−1.86231 − 1.13742I 2.46556 − 4.13256I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.402832 − 0.287203I
a = −0.958411 + 0.330421I
b = 1.015600 − 0.448453I
−1.86231 + 1.13742I 2.46556 + 4.13256I
u = −1.37941 + 0.63523I
a = 0.495306 − 1.088720I
b = 0.31114 + 1.68003I
1.20843 − 8.06995I 0
u = −1.37941 − 0.63523I
a = 0.495306 + 1.088720I
b = 0.31114 − 1.68003I
1.20843 + 8.06995I 0
u = −1.54862 + 0.18920I
a = 0.531241 − 0.765048I
b = −0.02146 + 1.56991I
2.62752 + 3.54439I 0
u = −1.54862 − 0.18920I
a = 0.531241 + 0.765048I
b = −0.02146 − 1.56991I
2.62752 − 3.54439I 0
u = 0.426848 + 0.055916I
a = 1.94065 − 0.16496I
b = 0.013936 + 0.901571I
−1.20775 − 4.21129I −4.14353 + 6.76110I
u = 0.426848 − 0.055916I
a = 1.94065 + 0.16496I
b = 0.013936 − 0.901571I
−1.20775 + 4.21129I −4.14353 − 6.76110I
u = −1.58578 + 0.06116I
a = 0.216735 + 0.784957I
b = −0.28573 − 1.56489I
2.33854 − 1.02618I 0
u = −1.58578 − 0.06116I
a = 0.216735 − 0.784957I
b = −0.28573 + 1.56489I
2.33854 + 1.02618I 0
u = −0.316446 + 0.256770I
a = −3.53853 − 1.87963I
b = 0.422485 − 0.553073I
−9.07448 + 1.51500I 2.38611 + 3.76927I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.316446 − 0.256770I
a = −3.53853 + 1.87963I
b = 0.422485 + 0.553073I
−9.07448 − 1.51500I 2.38611 − 3.76927I
u = −1.53034 + 0.45332I
a = 0.051803 − 1.168240I
b = 0.76970 + 1.51354I
−2.82820 − 6.39077I 0
u = −1.53034 − 0.45332I
a = 0.051803 + 1.168240I
b = 0.76970 − 1.51354I
−2.82820 + 6.39077I 0
u = 1.59807 + 0.28399I
a = 0.144623 + 1.087600I
b = 0.00268 − 1.61595I
7.27344 + 4.05568I 0
u = 1.59807 − 0.28399I
a = 0.144623 − 1.087600I
b = 0.00268 + 1.61595I
7.27344 − 4.05568I 0
u = 1.59921 + 0.31569I
a = −0.589281 − 0.847626I
b = −0.121264 + 1.185740I
0.519660 + 0.341918I 0
u = 1.59921 − 0.31569I
a = −0.589281 + 0.847626I
b = −0.121264 − 1.185740I
0.519660 − 0.341918I 0
u = −1.66807 + 0.10006I
a = −0.148154 + 0.990473I
b = −0.35286 − 1.39288I
5.90864 − 0.86319I 0
u = −1.66807 − 0.10006I
a = −0.148154 − 0.990473I
b = −0.35286 + 1.39288I
5.90864 + 0.86319I 0
u = 1.42486 + 0.88427I
a = −0.543349 − 0.812666I
b = −0.073113 + 1.322830I
0.34448 + 1.46095I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42486 − 0.88427I
a = −0.543349 + 0.812666I
b = −0.073113 − 1.322830I
0.34448 − 1.46095I 0
u = −1.65530 + 0.35198I
a = −0.228611 − 1.013180I
b = 0.14810 + 1.42442I
4.34530 − 3.39833I 0
u = −1.65530 − 0.35198I
a = −0.228611 + 1.013180I
b = 0.14810 − 1.42442I
4.34530 + 3.39833I 0
u = 1.67896 + 0.56416I
a = −0.062341 − 0.915295I
b = −0.69881 + 1.44153I
−3.54897 + 7.24525I 0
u = 1.67896 − 0.56416I
a = −0.062341 + 0.915295I
b = −0.69881 − 1.44153I
−3.54897 − 7.24525I 0
u = 1.74673 + 0.30476I
a = 0.194566 − 0.972442I
b = −0.38911 + 1.61323I
3.46954 + 10.71400I 0
u = 1.74673 − 0.30476I
a = 0.194566 + 0.972442I
b = −0.38911 − 1.61323I
3.46954 − 10.71400I 0
u = 1.48603 + 0.98544I
a = 0.129346 + 1.000480I
b = 0.39902 − 1.52526I
0.25276 + 6.84890I 0
u = 1.48603 − 0.98544I
a = 0.129346 − 1.000480I
b = 0.39902 + 1.52526I
0.25276 − 6.84890I 0
u = −1.79984 + 0.31515I
a = −0.209297 + 1.015280I
b = 0.213560 − 1.208730I
4.92575 + 0.66345I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.79984 − 0.31515I
a = −0.209297 − 1.015280I
b = 0.213560 + 1.208730I
4.92575 − 0.66345I 0
u = 0.166218 + 0.017157I
a = 0.82946 + 4.69831I
b = −1.264600 + 0.167920I
−2.81269 + 4.67156I −3.12185 − 6.15405I
u = 0.166218 − 0.017157I
a = 0.82946 − 4.69831I
b = −1.264600 − 0.167920I
−2.81269 − 4.67156I −3.12185 + 6.15405I
u = −1.74104 + 0.69909I
a = −0.054215 + 1.043500I
b = −0.64425 − 1.54738I
−3.2595 − 15.9571I 0
u = −1.74104 − 0.69909I
a = −0.054215 − 1.043500I
b = −0.64425 + 1.54738I
−3.2595 + 15.9571I 0
u = −0.26113 + 1.90968I
a = 0.237425 − 0.276892I
b = −0.036362 + 0.960242I
−8.52014 + 6.77449I 0
u = −0.26113 − 1.90968I
a = 0.237425 + 0.276892I
b = −0.036362 − 0.960242I
−8.52014 − 6.77449I 0
u = 2.11120 + 0.09785I
a = 0.086951 + 0.988989I
b = 0.556942 − 1.075320I
0.48418 + 2.25326I 0
u = 2.11120 − 0.09785I
a = 0.086951 − 0.988989I
b = 0.556942 + 1.075320I
0.48418 − 2.25326I 0
11
II.
I
u
2
= h4.71 × 10
15
u
19
− 6.48 × 10
15
u
18
+ · · · + 4.46 × 10
16
b + 2.86 × 10
16
, 2.27 ×
10
16
u
19
−5.05×10
16
u
18
+· · ·+8.93×10
16
a−2.12×10
17
, u
20
−2u
19
+· · ·−2u+2i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
2
=
−0.253955u
19
+ 0.565861u
18
+ ··· − 4.57373u + 2.37382
−0.105525u
19
+ 0.145096u
18
+ ··· − 0.367388u − 0.641359
a
5
=
1
−u
2
a
6
=
0.0104055u
19
− 0.126171u
18
+ ··· + 3.06894u − 0.296781
0.0899192u
19
− 0.130317u
18
+ ··· − 0.138878u + 0.437370
a
9
=
u
u
a
1
=
−0.359480u
19
+ 0.710956u
18
+ ··· − 4.94112u + 1.73246
−0.105525u
19
+ 0.145096u
18
+ ··· − 0.367388u − 0.641359
a
10
=
0.903364u
19
− 1.70724u
18
+ ··· + 6.10414u − 3.55956
0.179321u
19
− 0.253116u
18
+ ··· + 3.73612u + 0.00874632
a
3
=
0.315050u
19
− 1.00867u
18
+ ··· − 5.55543u − 6.78367
0.355127u
19
− 0.608260u
18
+ ··· + 3.13098u − 1.15233
a
12
=
−0.359480u
19
+ 0.710956u
18
+ ··· − 4.94112u + 1.73246
−0.206683u
19
+ 0.300685u
18
+ ··· − 1.07034u − 0.657368
a
7
=
−0.967208u
19
+ 1.77827u
18
+ ··· − 7.37065u + 3.15992
−0.0747343u
19
+ 0.110510u
18
+ ··· − 2.88862u − 0.711932
a
11
=
0.678448u
19
− 1.42392u
18
+ ··· + 7.26152u − 2.34715
0.0557314u
19
− 0.0278410u
18
+ ··· + 3.34451u + 0.244000
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
21125193779764826
44645823690514751
u
19
−
46994070852762617
44645823690514751
u
18
+···+
128450800382224996
44645823690514751
u−
896563895668882454
44645823690514751
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− 4u
19
+ ··· + 3u + 1
c
2
u
20
− 3u
19
+ ··· − 5u + 1
c
3
u
20
− u
19
+ ··· − 5u + 4
c
4
u
20
− 2u
19
+ ··· − 2u + 2
c
5
u
20
− 3u
19
+ ··· − 45u + 26
c
6
u
20
+ 7u
18
+ ··· − 2u + 2
c
7
u
20
− 12u
18
+ ··· − 5u + 2
c
8
u
20
+ 2u
19
+ ··· + 2u + 2
c
9
u
20
+ u
19
+ ··· + 14u + 7
c
10
u
20
− u
19
+ ··· + u + 1
c
11
, c
12
u
20
− 12u
18
+ ··· + 5u + 2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
+ 10y
19
+ ··· − 11y + 1
c
2
y
20
− y
19
+ ··· − 5y + 1
c
3
y
20
+ 17y
19
+ ··· + 215y + 16
c
4
, c
8
y
20
− 14y
19
+ ··· + 24y + 4
c
5
y
20
+ 13y
19
+ ··· − 10865y + 676
c
6
y
20
+ 14y
19
+ ··· + 32y + 4
c
7
, c
11
, c
12
y
20
− 24y
19
+ ··· − 41y + 4
c
9
y
20
+ 11y
19
+ ··· − 378y + 49
c
10
y
20
− 3y
19
+ ··· + 11y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.445341 + 1.006900I
a = 0.378996 − 0.609489I
b = 0.475822 − 0.653916I
−9.54640 + 0.43274I −14.2472 + 0.4571I
u = 0.445341 − 1.006900I
a = 0.378996 + 0.609489I
b = 0.475822 + 0.653916I
−9.54640 − 0.43274I −14.2472 − 0.4571I
u = −0.305160 + 1.095290I
a = 0.017343 + 1.275150I
b = 0.472191 − 0.019528I
−10.53160 + 6.61475I −10.62909 − 4.57987I
u = −0.305160 − 1.095290I
a = 0.017343 − 1.275150I
b = 0.472191 + 0.019528I
−10.53160 − 6.61475I −10.62909 + 4.57987I
u = 0.819504 + 0.038714I
a = −0.461140 + 0.552148I
b = −1.156310 − 0.340346I
−5.16397 − 0.27439I −4.64612 + 0.00082I
u = 0.819504 − 0.038714I
a = −0.461140 − 0.552148I
b = −1.156310 + 0.340346I
−5.16397 + 0.27439I −4.64612 − 0.00082I
u = 0.054278 + 1.230410I
a = −0.163473 − 0.310256I
b = 0.599474 + 0.188835I
−4.48083 − 4.26522I −11.29736 + 6.83205I
u = 0.054278 − 1.230410I
a = −0.163473 + 0.310256I
b = 0.599474 − 0.188835I
−4.48083 + 4.26522I −11.29736 − 6.83205I
u = −1.396840 + 0.098244I
a = 0.477139 − 0.906250I
b = −0.11675 + 1.53608I
2.63581 + 2.60541I −3.56183 − 0.71884I
u = −1.396840 − 0.098244I
a = 0.477139 + 0.906250I
b = −0.11675 − 1.53608I
2.63581 − 2.60541I −3.56183 + 0.71884I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.33652 + 0.71442I
a = −0.185580 − 1.012890I
b = −0.48691 + 1.58830I
−0.48906 + 6.44073I −7.25375 − 5.52907I
u = 1.33652 − 0.71442I
a = −0.185580 + 1.012890I
b = −0.48691 − 1.58830I
−0.48906 − 6.44073I −7.25375 + 5.52907I
u = −0.291685 + 0.269932I
a = 1.83960 + 0.09965I
b = −0.920486 + 0.439782I
−2.17821 + 1.32113I −17.8526 − 7.1209I
u = −0.291685 − 0.269932I
a = 1.83960 − 0.09965I
b = −0.920486 − 0.439782I
−2.17821 − 1.32113I −17.8526 + 7.1209I
u = 0.164640 + 0.335831I
a = 2.58852 − 3.21941I
b = −0.684610 − 0.572192I
−9.34616 − 1.63192I −23.0792 + 7.1433I
u = 0.164640 − 0.335831I
a = 2.58852 + 3.21941I
b = −0.684610 + 0.572192I
−9.34616 + 1.63192I −23.0792 − 7.1433I
u = −1.76638 + 0.00494I
a = 0.060210 − 0.998278I
b = −0.323533 + 1.236200I
4.58999 + 1.40746I −3.39132 − 5.03852I
u = −1.76638 − 0.00494I
a = 0.060210 + 0.998278I
b = −0.323533 − 1.236200I
4.58999 − 1.40746I −3.39132 + 5.03852I
u = 1.93978 + 0.51365I
a = 0.448387 + 0.904270I
b = 0.141119 − 1.151680I
1.61171 + 0.65918I 1.95852 + 0.33886I
u = 1.93978 − 0.51365I
a = 0.448387 − 0.904270I
b = 0.141119 + 1.151680I
1.61171 − 0.65918I 1.95852 − 0.33886I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
20
− 4u
19
+ ··· + 3u + 1)(u
69
+ 3u
68
+ ··· − 7855u − 844)
c
2
(u
20
− 3u
19
+ ··· − 5u + 1)(u
69
+ 4u
68
+ ··· − 447u − 94)
c
3
(u
20
− u
19
+ ··· − 5u + 4)(u
69
+ 22u
67
+ ··· + 4528u + 2690)
c
4
(u
20
− 2u
19
+ ··· − 2u + 2)(u
69
+ u
68
+ ··· + 5598u + 326)
c
5
(u
20
− 3u
19
+ ··· − 45u + 26)(u
69
+ 2u
67
+ ··· − 96u − 10)
c
6
(u
20
+ 7u
18
+ ··· − 2u + 2)(u
69
− 5u
68
+ ··· − 1042u − 242)
c
7
(u
20
− 12u
18
+ ··· − 5u + 2)(u
69
− u
68
+ ··· + 8u + 2)
c
8
(u
20
+ 2u
19
+ ··· + 2u + 2)(u
69
+ u
68
+ ··· + 5598u + 326)
c
9
(u
20
+ u
19
+ ··· + 14u + 7)(u
69
+ 37u
67
+ ··· − 12439u + 1286)
c
10
(u
20
− u
19
+ ··· + u + 1)(u
69
+ 2u
68
+ ··· + u + 2)
c
11
, c
12
(u
20
− 12u
18
+ ··· + 5u + 2)(u
69
− u
68
+ ··· + 8u + 2)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
20
+ 10y
19
+ ··· − 11y + 1)
· (y
69
+ 61y
68
+ ··· − 33395831y −712336)
c
2
(y
20
− y
19
+ ··· − 5y + 1)(y
69
− 10y
68
+ ··· + 187213y −8836)
c
3
(y
20
+ 17y
19
+ ··· + 215y + 16)
· (y
69
+ 44y
68
+ ··· − 160249076y −7236100)
c
4
, c
8
(y
20
− 14y
19
+ ··· + 24y + 4)
· (y
69
− 71y
68
+ ··· + 10709628y −106276)
c
5
(y
20
+ 13y
19
+ ··· − 10865y + 676)
· (y
69
+ 4y
68
+ ··· − 111724y −100)
c
6
(y
20
+ 14y
19
+ ··· + 32y + 4)(y
69
+ 29y
68
+ ··· − 1680780y −58564)
c
7
, c
11
, c
12
(y
20
− 24y
19
+ ··· − 41y + 4)(y
69
− 69y
68
+ ··· − 1868y −4)
c
9
(y
20
+ 11y
19
+ ··· − 378y + 49)
· (y
69
+ 74y
68
+ ··· − 48598167y −1653796)
c
10
(y
20
− 3y
19
+ ··· + 11y + 1)(y
69
+ 70y
67
+ ··· − 99y −4)
18
