12a
0605
(K12a
0605
)
A knot diagram
1
Linearized knot diagam
3 7 9 12 10 2 6 11 1 8 4 5
Solving Sequence
2,6
7 3
8,10
11 1 5 9 12 4
c
6
c
2
c
7
c
10
c
1
c
5
c
9
c
12
c
4
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.87845 × 10
64
u
82
+ 1.27988 × 10
64
u
81
+ ··· + 2.92888 × 10
64
b − 1.21244 × 10
64
,
− 1.31389 × 10
63
u
82
− 1.25844 × 10
64
u
81
+ ··· + 2.92888 × 10
64
a − 7.49424 × 10
64
, u
83
− 2u
82
+ ··· + 2u − 1i
I
u
2
= h8u
5
+ 10u
4
− 20u
3
− 6u
2
+ 23b + 21u − 1, −5u
5
+ 11u
4
+ u
3
− 2u
2
+ 23a + 7u − 8,
u
6
− u
5
− u
4
+ 2u
3
− u + 1i
* 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
= h−1.88×10
64
u
82
+1.28×10
64
u
81
+· · ·+2.93×10
64
b−1.21×10
64
, −1.31×
10
63
u
82
−1.26×10
64
u
81
+· · ·+2.93×10
64
a−7.49×10
64
, u
83
−2u
82
+· · ·+2u−1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
10
=
0.0448598u
82
+ 0.429664u
81
+ ··· − 0.168626u + 2.55874
0.641352u
82
− 0.436985u
81
+ ··· − 2.72216u + 0.413960
a
11
=
0.0314267u
82
+ 0.354611u
81
+ ··· − 0.923848u + 1.65310
0.640827u
82
− 0.379524u
81
+ ··· − 2.64509u + 0.368450
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
1.40123u
82
− 2.52242u
81
+ ··· − 2.31312u + 0.870884
1.07497u
82
− 1.14368u
81
+ ··· + 2.45617u + 0.923234
a
9
=
−0.000305313u
82
+ 0.492328u
81
+ ··· − 0.144340u + 2.50567
0.594051u
82
− 0.368881u
81
+ ··· − 2.46994u + 0.309558
a
12
=
1.27948u
82
− 1.88951u
81
+ ··· − 2.58516u + 1.03474
1.29851u
82
− 1.69376u
81
+ ··· + 1.45034u + 1.55967
a
4
=
−1.24128u
82
+ 0.934848u
81
+ ··· − 0.924884u − 1.12049
−1.26658u
82
+ 1.49098u
81
+ ··· + 5.74887u − 2.52264
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.63470u
82
+ 9.65125u
81
+ ··· − 3.31630u − 0.497855
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
83
+ 24u
82
+ ··· + 8u + 1
c
2
, c
6
u
83
− 2u
82
+ ··· + 2u − 1
c
3
23(23u
83
− 133u
82
+ ··· + 1.50077 × 10
7
u − 1502291)
c
4
, c
11
, c
12
u
83
− 2u
82
+ ··· − 4u
2
+ 1
c
5
23(23u
83
+ 64u
82
+ ··· + 8416615u + 1304033)
c
8
, c
10
u
83
+ 7u
82
+ ··· − 1641u − 529
c
9
u
83
+ 7u
82
+ ··· − 69184u + 33856
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
83
+ 72y
82
+ ··· + 44y −1
c
2
, c
6
y
83
− 24y
82
+ ··· + 8y −1
c
3
529
· (529y
83
+ 28081y
82
+ ··· + 38188375604614y −2256878248681)
c
4
, c
11
, c
12
y
83
− 84y
82
+ ··· + 8y −1
c
5
529
· (529y
83
− 32708y
82
+ ··· + 39172776651029y −1700502065089)
c
8
, c
10
y
83
− 75y
82
+ ··· + 5875345y −279841
c
9
y
83
+ 39y
82
+ ··· − 8242446336y −1146228736
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.889482 + 0.456836I
a = 0.534958 − 0.131930I
b = 0.104167 − 0.719375I
−1.41772 + 1.74895I 0
u = −0.889482 − 0.456836I
a = 0.534958 + 0.131930I
b = 0.104167 + 0.719375I
−1.41772 − 1.74895I 0
u = −0.935965 + 0.259286I
a = −1.04483 + 1.50530I
b = 0.900121 + 0.852842I
3.42942 + 5.61464I 0. − 7.27404I
u = −0.935965 − 0.259286I
a = −1.04483 − 1.50530I
b = 0.900121 − 0.852842I
3.42942 − 5.61464I 0. + 7.27404I
u = 0.941175 + 0.204587I
a = −0.721363 − 0.988163I
b = 0.592450 − 0.675808I
−2.60762 − 3.23702I −5.49466 + 7.80005I
u = 0.941175 − 0.204587I
a = −0.721363 + 0.988163I
b = 0.592450 + 0.675808I
−2.60762 + 3.23702I −5.49466 − 7.80005I
u = −0.953043 + 0.078413I
a = −0.334788 + 0.276834I
b = 0.331892 + 0.225291I
−1.83683 + 0.10839I −5.40972 + 0.I
u = −0.953043 − 0.078413I
a = −0.334788 − 0.276834I
b = 0.331892 − 0.225291I
−1.83683 − 0.10839I −5.40972 + 0.I
u = 0.849141 + 0.242956I
a = 1.018340 − 0.060762I
b = 0.905830 + 0.798266I
3.46734 + 0.71154I −0.47127 + 2.15369I
u = 0.849141 − 0.242956I
a = 1.018340 + 0.060762I
b = 0.905830 − 0.798266I
3.46734 − 0.71154I −0.47127 − 2.15369I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.816703 + 0.768943I
a = 1.75089 + 0.20685I
b = −1.082510 + 0.403406I
3.52701 − 1.42228I 0
u = 0.816703 − 0.768943I
a = 1.75089 − 0.20685I
b = −1.082510 − 0.403406I
3.52701 + 1.42228I 0
u = −0.835455 + 0.753520I
a = 3.50927 + 0.93237I
b = −1.97135 − 2.14558I
9.03093 + 2.89498I 0
u = −0.835455 − 0.753520I
a = 3.50927 − 0.93237I
b = −1.97135 + 2.14558I
9.03093 − 2.89498I 0
u = −0.802716 + 0.802162I
a = 1.54959 − 0.71704I
b = −0.933558 + 0.245697I
3.74533 − 1.60662I 0
u = −0.802716 − 0.802162I
a = 1.54959 + 0.71704I
b = −0.933558 − 0.245697I
3.74533 + 1.60662I 0
u = 0.027665 + 0.862785I
a = −0.867205 − 0.219871I
b = 1.133800 + 0.169437I
4.74686 + 2.93300I 8.76121 − 3.91326I
u = 0.027665 − 0.862785I
a = −0.867205 + 0.219871I
b = 1.133800 − 0.169437I
4.74686 − 2.93300I 8.76121 + 3.91326I
u = −1.105370 + 0.315329I
a = 0.014499 − 1.098310I
b = −1.29278 − 0.74240I
8.45345 + 11.00130I 0
u = −1.105370 − 0.315329I
a = 0.014499 + 1.098310I
b = −1.29278 + 0.74240I
8.45345 − 11.00130I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.807856 + 0.824094I
a = 1.75320 + 0.96864I
b = −1.040670 − 0.534905I
10.24590 + 3.75990I 0
u = 0.807856 − 0.824094I
a = 1.75320 − 0.96864I
b = −1.040670 + 0.534905I
10.24590 − 3.75990I 0
u = 0.834963
a = 3.68259
b = 4.90505
5.65010 −26.1310
u = 0.515647 + 0.654524I
a = 0.414145 − 0.145965I
b = 0.261027 + 0.341321I
2.62411 + 0.87584I 0.235931 + 0.049304I
u = 0.515647 − 0.654524I
a = 0.414145 + 0.145965I
b = 0.261027 − 0.341321I
2.62411 − 0.87584I 0.235931 − 0.049304I
u = 1.140330 + 0.259412I
a = −0.706300 + 0.694710I
b = −1.008980 − 0.277275I
8.05514 + 3.48111I 0
u = 1.140330 − 0.259412I
a = −0.706300 − 0.694710I
b = −1.008980 + 0.277275I
8.05514 − 3.48111I 0
u = −0.033678 + 0.823507I
a = −1.127770 + 0.564262I
b = 1.337490 − 0.420345I
12.04910 − 7.13476I 9.25485 + 4.05212I
u = −0.033678 − 0.823507I
a = −1.127770 − 0.564262I
b = 1.337490 + 0.420345I
12.04910 + 7.13476I 9.25485 − 4.05212I
u = 0.884797 + 0.775848I
a = −1.77395 + 1.63904I
b = −0.07694 − 2.70204I
5.37866 − 2.92461I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.884797 − 0.775848I
a = −1.77395 − 1.63904I
b = −0.07694 + 2.70204I
5.37866 + 2.92461I 0
u = 1.127720 + 0.337758I
a = −0.044991 + 0.823378I
b = −0.960090 + 0.541916I
1.04660 − 7.01205I 0
u = 1.127720 − 0.337758I
a = −0.044991 − 0.823378I
b = −0.960090 − 0.541916I
1.04660 + 7.01205I 0
u = −0.732275 + 0.922468I
a = −1.009770 + 0.052035I
b = 1.227170 − 0.199103I
16.1676 + 3.4606I 0
u = −0.732275 − 0.922468I
a = −1.009770 − 0.052035I
b = 1.227170 + 0.199103I
16.1676 − 3.4606I 0
u = 0.754229 + 0.905051I
a = −1.52604 − 0.95557I
b = 1.72976 + 0.81123I
16.6561 + 10.4380I 0
u = 0.754229 − 0.905051I
a = −1.52604 + 0.95557I
b = 1.72976 − 0.81123I
16.6561 − 10.4380I 0
u = −0.867281 + 0.802103I
a = 0.810453 − 0.423035I
b = −1.014500 + 0.771217I
7.30880 + 1.13595I 0
u = −0.867281 − 0.802103I
a = 0.810453 + 0.423035I
b = −1.014500 − 0.771217I
7.30880 − 1.13595I 0
u = −0.917071 + 0.745377I
a = −0.69179 + 3.01817I
b = 2.07340 − 1.42336I
8.78061 + 2.79415I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.917071 − 0.745377I
a = −0.69179 − 3.01817I
b = 2.07340 + 1.42336I
8.78061 − 2.79415I 0
u = −0.731443 + 0.355891I
a = 0.99738 + 2.75342I
b = 0.486901 − 0.522296I
7.80848 + 3.23449I 6.54878 − 6.03977I
u = −0.731443 − 0.355891I
a = 0.99738 − 2.75342I
b = 0.486901 + 0.522296I
7.80848 − 3.23449I 6.54878 + 6.03977I
u = −0.757746 + 0.913416I
a = −1.21392 + 0.81604I
b = 1.48040 − 0.75317I
9.48311 − 6.48346I 0
u = −0.757746 − 0.913416I
a = −1.21392 − 0.81604I
b = 1.48040 + 0.75317I
9.48311 + 6.48346I 0
u = 1.034880 + 0.585496I
a = 0.099302 + 0.223114I
b = −0.135254 + 0.437889I
1.11865 − 5.75066I 0
u = 1.034880 − 0.585496I
a = 0.099302 − 0.223114I
b = −0.135254 − 0.437889I
1.11865 + 5.75066I 0
u = 0.750775 + 0.926710I
a = −0.987309 − 0.492800I
b = 1.262870 + 0.541456I
9.20226 + 0.93743I 0
u = 0.750775 − 0.926710I
a = −0.987309 + 0.492800I
b = 1.262870 − 0.541456I
9.20226 − 0.93743I 0
u = 0.870208 + 0.820915I
a = 1.250600 − 0.413944I
b = −0.905844 − 0.271334I
14.3924 − 0.4286I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.870208 − 0.820915I
a = 1.250600 + 0.413944I
b = −0.905844 + 0.271334I
14.3924 + 0.4286I 0
u = 0.937268 + 0.745740I
a = −1.19353 − 1.12183I
b = 1.122130 + 0.134120I
3.15571 − 4.31418I 0
u = 0.937268 − 0.745740I
a = −1.19353 + 1.12183I
b = 1.122130 − 0.134120I
3.15571 + 4.31418I 0
u = −0.909622 + 0.790683I
a = −1.56898 + 0.84569I
b = 0.853137 + 0.850342I
7.17818 + 4.83871I 0
u = −0.909622 − 0.790683I
a = −1.56898 − 0.84569I
b = 0.853137 − 0.850342I
7.17818 − 4.83871I 0
u = −1.178820 + 0.299322I
a = −0.340622 − 0.623463I
b = −0.844509 − 0.119752I
0.662850 + 1.033910I 0
u = −1.178820 − 0.299322I
a = −0.340622 + 0.623463I
b = −0.844509 + 0.119752I
0.662850 − 1.033910I 0
u = 0.916556 + 0.806377I
a = −1.28781 − 1.55467I
b = 0.779647 − 0.298397I
14.2487 − 5.6526I 0
u = 0.916556 − 0.806377I
a = −1.28781 + 1.55467I
b = 0.779647 + 0.298397I
14.2487 + 5.6526I 0
u = −0.955332 + 0.764210I
a = −1.80085 + 0.64179I
b = 1.017290 + 0.386028I
3.27752 + 7.49822I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.955332 − 0.764210I
a = −1.80085 − 0.64179I
b = 1.017290 − 0.386028I
3.27752 − 7.49822I 0
u = 0.731306 + 0.256638I
a = 0.78032 − 2.04828I
b = 0.327098 − 0.173264I
1.33574 − 2.24205I 4.43086 + 8.82898I
u = 0.731306 − 0.256638I
a = 0.78032 + 2.04828I
b = 0.327098 + 0.173264I
1.33574 + 2.24205I 4.43086 − 8.82898I
u = 0.960254 + 0.779064I
a = −2.28212 − 0.60862I
b = 1.118770 − 0.610843I
9.77627 − 9.76260I 0
u = 0.960254 − 0.779064I
a = −2.28212 + 0.60862I
b = 1.118770 + 0.610843I
9.77627 + 9.76260I 0
u = −0.730104 + 0.111818I
a = 0.68230 + 2.05904I
b = 0.07317 + 1.79240I
0.491768 + 0.412209I 3.6447 + 16.5037I
u = −0.730104 − 0.111818I
a = 0.68230 − 2.05904I
b = 0.07317 − 1.79240I
0.491768 − 0.412209I 3.6447 − 16.5037I
u = 1.024460 + 0.793490I
a = 2.08009 + 1.18604I
b = −1.72181 + 0.93118I
15.8084 − 16.7169I 0
u = 1.024460 − 0.793490I
a = 2.08009 − 1.18604I
b = −1.72181 − 0.93118I
15.8084 + 16.7169I 0
u = −1.026430 + 0.799370I
a = 1.78257 − 0.95986I
b = −1.44862 − 0.89101I
8.6384 + 12.8059I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.026430 − 0.799370I
a = 1.78257 + 0.95986I
b = −1.44862 + 0.89101I
8.6384 − 12.8059I 0
u = 1.035970 + 0.804028I
a = 1.33910 + 0.89568I
b = −1.187330 + 0.688916I
8.30656 − 7.31250I 0
u = 1.035970 − 0.804028I
a = 1.33910 − 0.89568I
b = −1.187330 − 0.688916I
8.30656 + 7.31250I 0
u = −1.046110 + 0.792804I
a = 0.87735 − 1.17014I
b = −1.099350 − 0.306452I
15.1856 + 2.8676I 0
u = −1.046110 − 0.792804I
a = 0.87735 + 1.17014I
b = −1.099350 + 0.306452I
15.1856 − 2.8676I 0
u = −0.387829 + 0.383433I
a = 2.84274 + 0.86881I
b = −1.325450 − 0.237969I
8.75382 − 0.29598I 9.26455 − 1.68799I
u = −0.387829 − 0.383433I
a = 2.84274 − 0.86881I
b = −1.325450 + 0.237969I
8.75382 + 0.29598I 9.26455 + 1.68799I
u = −0.056323 + 0.493607I
a = 1.90426 − 1.11553I
b = −0.725500 + 0.857677I
5.99111 − 2.95551I 7.65900 + 2.93684I
u = −0.056323 − 0.493607I
a = 1.90426 + 1.11553I
b = −0.725500 − 0.857677I
5.99111 + 2.95551I 7.65900 − 2.93684I
u = −0.047810 + 0.406306I
a = 1.37577 + 0.54247I
b = −0.346996 − 0.440258I
0.164287 + 1.105020I 2.26614 − 6.04116I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.047810 − 0.406306I
a = 1.37577 − 0.54247I
b = −0.346996 + 0.440258I
0.164287 − 1.105020I 2.26614 + 6.04116I
u = 0.355483 + 0.185180I
a = 1.94592 − 0.44264I
b = −1.057690 + 0.002867I
2.29106 + 0.03654I 6.03784 + 2.48416I
u = 0.355483 − 0.185180I
a = 1.94592 + 0.44264I
b = −1.057690 − 0.002867I
2.29106 − 0.03654I 6.03784 − 2.48416I
13
II. I
u
2
= h8u
5
+ 10u
4
− 20u
3
− 6u
2
+ 23b + 21u − 1, −5u
5
+ 11u
4
+ u
3
−
2u
2
+ 23a + 7u − 8, u
6
− u
5
− u
4
+ 2u
3
− 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
8
=
−u
2
+ 1
u
2
a
10
=
0.217391u
5
− 0.478261u
4
+ ··· − 0.304348u + 0.347826
−0.347826u
5
− 0.434783u
4
+ ··· − 0.913043u + 0.0434783
a
11
=
0.217391u
5
− 0.478261u
4
+ ··· − 0.304348u − 0.652174
−0.347826u
5
− 0.434783u
4
+ ··· − 0.913043u + 0.0434783
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
0.0472590u
5
− 0.364839u
4
+ ··· − 0.283554u + 0.858223
0.272212u
5
− 0.181474u
4
+ ··· + 0.366730u + 0.183365
a
9
=
0.217391u
5
− 0.478261u
4
+ ··· − 0.304348u + 0.347826
−0.347826u
5
− 0.434783u
4
+ ··· − 0.913043u + 0.0434783
a
12
=
−0.676749u
5
− 0.215501u
4
+ ··· − 0.939509u + 0.0302457
0.621928u
5
− 0.0812854u
4
+ ··· + 0.268431u + 0.134216
a
4
=
−0.00378072u
5
− 0.330813u
4
+ ··· − 0.977316u + 0.0113422
−0.141777u
5
+ 0.0945180u
4
+ ··· + 0.850662u + 0.425331
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1101
529
u
5
+
2321
529
u
4
+
993
529
u
3
−
3458
529
u
2
+
2903
529
u +
4361
529
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
, c
4
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
3
23(23u
6
− 18u
5
+ 25u
4
− 8u
3
+ 7u
2
− u + 1)
c
5
23(23u
6
− 5u
5
− 17u
4
+ 10u
3
+ 3u
2
− 4u + 1)
c
6
, c
11
, c
12
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
7
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
8
(u + 1)
6
c
9
u
6
c
10
(u − 1)
6
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
4
, c
6
c
11
, c
12
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
3
529(529y
6
+ 826y
5
+ 659y
4
+ 296y
3
+ 83y
2
+ 13y + 1)
c
5
529(529y
6
− 807y
5
+ 527y
4
− 196y
3
+ 55y
2
− 10y + 1)
c
8
, c
10
(y −1)
6
c
9
y
6
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = 0.493592 + 0.608759I
b = 0.396884 + 0.370811I
−0.245672 + 0.924305I −2.14301 − 0.21731I
u = −1.002190 − 0.295542I
a = 0.493592 − 0.608759I
b = 0.396884 − 0.370811I
−0.245672 − 0.924305I −2.14301 + 0.21731I
u = 0.428243 + 0.664531I
a = 0.357844 − 0.079850I
b = −0.757689 − 0.164486I
3.53554 + 0.92430I 10.05826 − 0.61014I
u = 0.428243 − 0.664531I
a = 0.357844 + 0.079850I
b = −0.757689 + 0.164486I
3.53554 − 0.92430I 10.05826 + 0.61014I
u = 1.073950 + 0.558752I
a = 0.018129 − 0.725425I
b = 0.469501 − 0.157241I
1.64493 − 5.69302I 9.84656 + 3.72057I
u = 1.073950 − 0.558752I
a = 0.018129 + 0.725425I
b = 0.469501 + 0.157241I
1.64493 + 5.69302I 9.84656 − 3.72057I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)(u
83
+ 24u
82
+ ··· + 8u + 1)
c
2
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
83
− 2u
82
+ ··· + 2u − 1)
c
3
529(23u
6
− 18u
5
+ 25u
4
− 8u
3
+ 7u
2
− u + 1)
· (23u
83
− 133u
82
+ ··· + 15007694u − 1502291)
c
4
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
83
− 2u
82
+ ··· − 4u
2
+ 1)
c
5
529(23u
6
− 5u
5
− 17u
4
+ 10u
3
+ 3u
2
− 4u + 1)
· (23u
83
+ 64u
82
+ ··· + 8416615u + 1304033)
c
6
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
83
− 2u
82
+ ··· + 2u − 1)
c
7
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)(u
83
+ 24u
82
+ ··· + 8u + 1)
c
8
((u + 1)
6
)(u
83
+ 7u
82
+ ··· − 1641u − 529)
c
9
u
6
(u
83
+ 7u
82
+ ··· − 69184u + 33856)
c
10
((u − 1)
6
)(u
83
+ 7u
82
+ ··· − 1641u − 529)
c
11
, c
12
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
83
− 2u
82
+ ··· − 4u
2
+ 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
83
+ 72y
82
+ ··· + 44y −1)
c
2
, c
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
83
− 24y
82
+ ··· + 8y −1)
c
3
279841(529y
6
+ 826y
5
+ 659y
4
+ 296y
3
+ 83y
2
+ 13y + 1)
· (529y
83
+ 28081y
82
+ ··· + 38188375604614y −2256878248681)
c
4
, c
11
, c
12
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
83
− 84y
82
+ ··· + 8y −1)
c
5
279841(529y
6
− 807y
5
+ 527y
4
− 196y
3
+ 55y
2
− 10y + 1)
· (529y
83
− 32708y
82
+ ··· + 39172776651029y −1700502065089)
c
8
, c
10
((y −1)
6
)(y
83
− 75y
82
+ ··· + 5875345y −279841)
c
9
y
6
(y
83
+ 39y
82
+ ··· − 8.24245 × 10
9
y −1.14623 × 10
9
)
19
