12a
0072
(K12a
0072
)
A knot diagram
1
Linearized knot diagam
3 5 7 9 2 10 1 12 11 6 4 8
Solving Sequence
1,7 4,8
3 2 12 9 5 11 10 6
c
7
c
3
c
1
c
12
c
8
c
4
c
11
c
9
c
6
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.32959 × 10
206
u
99
+ 1.69512 × 10
207
u
98
+ ··· + 6.75897 × 10
206
b + 1.91806 × 10
207
,
− 1.41888 × 10
207
u
99
+ 4.03733 × 10
207
u
98
+ ··· + 1.35179 × 10
207
a + 1.32866 × 10
207
,
u
100
− 3u
99
+ ··· − 3u + 1i
I
u
2
= hb − 2a, 9a
2
+ 3a + 1, u − 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
= h−6.33 × 10
206
u
99
+ 1.70 × 10
207
u
98
+ · · · + 6.76 × 10
206
b + 1.92 ×
10
207
, −1.42 × 10
207
u
99
+ 4.04 × 10
207
u
98
+ · · · + 1.35 × 10
207
a + 1.33 ×
10
207
, u
100
− 3u
99
+ · · · − 3u + 1i
(i) Arc colorings
a
1
=
0
u
a
7
=
1
0
a
4
=
1.04962u
99
− 2.98664u
98
+ ··· + 6.34730u − 0.982883
0.936471u
99
− 2.50796u
98
+ ··· + 6.62856u − 2.83779
a
8
=
1
u
2
a
3
=
1.98610u
99
− 5.49460u
98
+ ··· + 12.9759u − 3.82068
0.936471u
99
− 2.50796u
98
+ ··· + 6.62856u − 2.83779
a
2
=
1.70678u
99
− 4.41746u
98
+ ··· + 8.22720u − 1.90725
0.664511u
99
− 1.72941u
98
+ ··· + 7.22090u − 1.53859
a
12
=
u
u
3
+ u
a
9
=
u
2
+ 1
u
4
+ 2u
2
a
5
=
1.63960u
99
− 4.58407u
98
+ ··· + 11.4770u − 3.31402
0.842942u
99
− 2.32288u
98
+ ··· + 5.17857u − 2.87068
a
11
=
0.299070u
99
− 0.681394u
98
+ ··· − 0.0995288u + 0.179816
−0.174011u
99
+ 0.486273u
98
+ ··· − 1.84111u + 0.551369
a
10
=
0.113513u
99
− 0.283888u
98
+ ··· + 0.301011u + 1.22509
0.161016u
99
− 0.384450u
98
+ ··· + 1.82572u − 0.0369255
a
6
=
−0.564895u
99
+ 1.43061u
98
+ ··· − 2.08996u + 0.587368
−0.283434u
99
+ 0.817441u
98
+ ··· − 2.41682u + 1.03126
(ii) Obstruction class = −1
(iii) Cusp Shapes = 5.15454u
99
− 14.0100u
98
+ ··· + 24.9994u + 1.17271
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
100
+ 38u
99
+ ··· + 2486u + 81
c
2
, c
5
u
100
+ 2u
99
+ ··· + 14u + 9
c
3
9(9u
100
− 129u
99
+ ··· + 1927454u + 1683748)
c
4
9(9u
100
+ 156u
99
+ ··· + 48280u + 5821)
c
6
, c
10
u
100
+ 3u
99
+ ··· + 3u + 1
c
7
, c
8
, c
12
u
100
− 3u
99
+ ··· − 3u + 1
c
9
u
100
− 39u
99
+ ··· − 7u + 1
c
11
u
100
− 5u
99
+ ··· − 216u + 108
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
100
+ 50y
99
+ ··· + 2843042y + 6561
c
2
, c
5
y
100
+ 38y
99
+ ··· + 2486y + 81
c
3
81
· (81y
100
+ 5517y
99
+ ··· + 95872846757236y + 2835007327504)
c
4
81(81y
100
+ 1278y
99
+ ··· − 3.67849 × 10
8
y + 3.38840 × 10
7
)
c
6
, c
10
y
100
+ 39y
99
+ ··· + 7y + 1
c
7
, c
8
, c
12
y
100
+ 99y
99
+ ··· + 7y + 1
c
9
y
100
+ 31y
99
+ ··· − 145y + 1
c
11
y
100
− 15y
99
+ ··· − 266328y + 11664
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.806473 + 0.591389I
a = −0.534727 + 0.504038I
b = −0.94326 − 1.23691I
0.3575 − 14.2046I 0
u = 0.806473 − 0.591389I
a = −0.534727 − 0.504038I
b = −0.94326 + 1.23691I
0.3575 + 14.2046I 0
u = −0.546043 + 0.809650I
a = −0.134535 + 0.328605I
b = 1.080430 + 0.135935I
−3.71729 + 3.01524I 0
u = −0.546043 − 0.809650I
a = −0.134535 − 0.328605I
b = 1.080430 − 0.135935I
−3.71729 − 3.01524I 0
u = −0.819790 + 0.617909I
a = 0.443599 + 0.442074I
b = 0.913739 − 1.027520I
−1.74024 + 8.28061I 0
u = −0.819790 − 0.617909I
a = 0.443599 − 0.442074I
b = 0.913739 + 1.027520I
−1.74024 − 8.28061I 0
u = 0.885531 + 0.541350I
a = 0.577249 + 0.387777I
b = −0.476099 + 0.963566I
0.14133 + 8.65432I 0
u = 0.885531 − 0.541350I
a = 0.577249 − 0.387777I
b = −0.476099 − 0.963566I
0.14133 − 8.65432I 0
u = 0.768075 + 0.699611I
a = 0.405219 − 0.220532I
b = 0.219659 + 0.995918I
5.59331 − 0.24478I 0
u = 0.768075 − 0.699611I
a = 0.405219 + 0.220532I
b = 0.219659 − 0.995918I
5.59331 + 0.24478I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.894618 + 0.554353I
a = −0.541190 + 0.182357I
b = −0.413795 − 0.978910I
5.03594 − 5.50250I 0
u = 0.894618 − 0.554353I
a = −0.541190 − 0.182357I
b = −0.413795 + 0.978910I
5.03594 + 5.50250I 0
u = 0.689565 + 0.613665I
a = 0.257348 − 0.659662I
b = 0.754718 + 1.002490I
2.15199 − 8.54454I 0
u = 0.689565 − 0.613665I
a = 0.257348 + 0.659662I
b = 0.754718 − 1.002490I
2.15199 + 8.54454I 0
u = −0.649060 + 0.632624I
a = −0.124977 − 0.526204I
b = −0.646398 + 0.806683I
−0.00478 + 3.13265I 0
u = −0.649060 − 0.632624I
a = −0.124977 + 0.526204I
b = −0.646398 − 0.806683I
−0.00478 − 3.13265I 0
u = 0.809148 + 0.358489I
a = −0.579234 − 0.298804I
b = 0.309286 − 0.515151I
1.38927 + 3.67810I 0
u = 0.809148 − 0.358489I
a = −0.579234 + 0.298804I
b = 0.309286 + 0.515151I
1.38927 − 3.67810I 0
u = −1.008300 + 0.535583I
a = −0.303715 + 0.325379I
b = 0.342553 + 0.714358I
−2.13845 − 2.44995I 0
u = −1.008300 − 0.535583I
a = −0.303715 − 0.325379I
b = 0.342553 − 0.714358I
−2.13845 + 2.44995I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.123120 + 0.241416I
a = 0.293122 − 0.183192I
b = 0.193002 − 0.431935I
−1.60583 + 1.75045I 0
u = −1.123120 − 0.241416I
a = 0.293122 + 0.183192I
b = 0.193002 + 0.431935I
−1.60583 − 1.75045I 0
u = 0.451232 + 0.718097I
a = 0.307351 + 0.358342I
b = −1.189450 + 0.478819I
−2.96850 + 2.69519I 0
u = 0.451232 − 0.718097I
a = 0.307351 − 0.358342I
b = −1.189450 − 0.478819I
−2.96850 − 2.69519I 0
u = 0.019026 + 1.254550I
a = −1.084100 − 0.131474I
b = 0.989260 + 0.438692I
4.17823 + 1.48003I 0
u = 0.019026 − 1.254550I
a = −1.084100 + 0.131474I
b = 0.989260 − 0.438692I
4.17823 − 1.48003I 0
u = −0.656590 + 0.303405I
a = 0.585961 + 1.279240I
b = 0.951241 − 0.257563I
−5.16257 + 1.14229I −8.90976 + 0.I
u = −0.656590 − 0.303405I
a = 0.585961 − 1.279240I
b = 0.951241 + 0.257563I
−5.16257 − 1.14229I −8.90976 + 0.I
u = 0.607078 + 0.333879I
a = −0.85250 + 1.51795I
b = −1.071550 − 0.481802I
−4.10701 − 6.45308I −6.41998 + 8.18062I
u = 0.607078 − 0.333879I
a = −0.85250 − 1.51795I
b = −1.071550 + 0.481802I
−4.10701 + 6.45308I −6.41998 − 8.18062I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.171606 + 1.299010I
a = 0.401831 + 0.840841I
b = −0.312547 − 0.178701I
1.77774 + 2.26138I 0
u = −0.171606 − 1.299010I
a = 0.401831 − 0.840841I
b = −0.312547 + 0.178701I
1.77774 − 2.26138I 0
u = −0.498222 + 0.336771I
a = 0.354034 − 0.361091I
b = −0.423586 + 0.190215I
−1.025080 + 0.904940I −5.26396 − 3.56513I
u = −0.498222 − 0.336771I
a = 0.354034 + 0.361091I
b = −0.423586 − 0.190215I
−1.025080 − 0.904940I −5.26396 + 3.56513I
u = 0.033414 + 1.403500I
a = −0.60353 + 5.96754I
b = −0.00932 − 5.56780I
4.81821 − 4.08298I 0
u = 0.033414 − 1.403500I
a = −0.60353 − 5.96754I
b = −0.00932 + 5.56780I
4.81821 + 4.08298I 0
u = 0.09550 + 1.42643I
a = −0.16996 + 2.14660I
b = −0.56310 − 1.42628I
5.06416 − 3.99388I 0
u = 0.09550 − 1.42643I
a = −0.16996 − 2.14660I
b = −0.56310 + 1.42628I
5.06416 + 3.99388I 0
u = −0.18451 + 1.42346I
a = −0.31012 + 1.66932I
b = 0.541640 − 0.505034I
0.35816 + 4.08264I 0
u = −0.18451 − 1.42346I
a = −0.31012 − 1.66932I
b = 0.541640 + 0.505034I
0.35816 − 4.08264I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.00319 + 1.43777I
a = −6.87530 − 4.92737I
b = 7.47001 + 5.24272I
4.99345 − 0.06600I 0
u = −0.00319 − 1.43777I
a = −6.87530 + 4.92737I
b = 7.47001 − 5.24272I
4.99345 + 0.06600I 0
u = 0.039633 + 0.553022I
a = −0.87889 − 1.95381I
b = 0.208141 + 0.832840I
3.05240 + 1.32386I 8.90398 − 1.32443I
u = 0.039633 − 0.553022I
a = −0.87889 + 1.95381I
b = 0.208141 − 0.832840I
3.05240 − 1.32386I 8.90398 + 1.32443I
u = 0.17302 + 1.44365I
a = 0.35297 + 1.97037I
b = −0.722497 − 0.658580I
1.62877 − 9.18771I 0
u = 0.17302 − 1.44365I
a = 0.35297 − 1.97037I
b = −0.722497 + 0.658580I
1.62877 + 9.18771I 0
u = 0.119986 + 0.523502I
a = −2.31040 − 1.46234I
b = 0.419804 + 0.403800I
2.69979 − 4.51496I 7.09912 + 8.71486I
u = 0.119986 − 0.523502I
a = −2.31040 + 1.46234I
b = 0.419804 − 0.403800I
2.69979 + 4.51496I 7.09912 − 8.71486I
u = 0.08012 + 1.46212I
a = −0.15853 + 1.60878I
b = −0.920375 − 1.029570I
5.28720 − 4.03509I 0
u = 0.08012 − 1.46212I
a = −0.15853 − 1.60878I
b = −0.920375 + 1.029570I
5.28720 + 4.03509I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.327534 + 0.422907I
a = 3.02963 + 0.59585I
b = 0.203105 − 0.967372I
0.55061 + 6.78066I 0.71844 − 12.16639I
u = −0.327534 − 0.422907I
a = 3.02963 − 0.59585I
b = 0.203105 + 0.967372I
0.55061 − 6.78066I 0.71844 + 12.16639I
u = −0.01975 + 1.47692I
a = 0.19520 − 1.62972I
b = −0.16784 + 1.64542I
4.98587 + 2.32048I 0
u = −0.01975 − 1.47692I
a = 0.19520 + 1.62972I
b = −0.16784 − 1.64542I
4.98587 − 2.32048I 0
u = −0.08443 + 1.48407I
a = 0.81270 + 1.47878I
b = 0.612753 − 0.888020I
6.82785 + 8.20158I 0
u = −0.08443 − 1.48407I
a = 0.81270 − 1.47878I
b = 0.612753 + 0.888020I
6.82785 − 8.20158I 0
u = −0.05536 + 1.48957I
a = 0.614448 + 0.218579I
b = 0.671449 − 0.182815I
8.32673 + 2.34943I 0
u = −0.05536 − 1.48957I
a = 0.614448 − 0.218579I
b = 0.671449 + 0.182815I
8.32673 − 2.34943I 0
u = −0.01932 + 1.49247I
a = 0.04141 − 1.45901I
b = 0.561884 + 1.107640I
7.27858 + 1.64673I 0
u = −0.01932 − 1.49247I
a = 0.04141 + 1.45901I
b = 0.561884 − 1.107640I
7.27858 − 1.64673I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.355798 + 0.346776I
a = −2.41660 + 0.66213I
b = −0.528640 − 0.898385I
−0.61317 − 2.59078I −2.75725 + 6.50369I
u = 0.355798 − 0.346776I
a = −2.41660 − 0.66213I
b = −0.528640 + 0.898385I
−0.61317 + 2.59078I −2.75725 − 6.50369I
u = −0.203929 + 0.451228I
a = 2.87535 − 0.41860I
b = −0.101648 − 0.254594I
1.93480 + 1.43759I 5.05470 − 4.70720I
u = −0.203929 − 0.451228I
a = 2.87535 + 0.41860I
b = −0.101648 + 0.254594I
1.93480 − 1.43759I 5.05470 + 4.70720I
u = 0.03128 + 1.50599I
a = −0.79227 − 1.27582I
b = −0.227575 + 0.639490I
9.38796 − 5.04495I 0
u = 0.03128 − 1.50599I
a = −0.79227 + 1.27582I
b = −0.227575 − 0.639490I
9.38796 + 5.04495I 0
u = 0.01153 + 1.50911I
a = −0.32993 − 1.96421I
b = −0.085234 + 1.070560I
9.82439 + 1.13815I 0
u = 0.01153 − 1.50911I
a = −0.32993 + 1.96421I
b = −0.085234 − 1.070560I
9.82439 − 1.13815I 0
u = −0.029724 + 0.477256I
a = 1.37517 − 0.57850I
b = −0.051368 + 0.680823I
0.81594 + 1.38660I 1.38598 − 4.17847I
u = −0.029724 − 0.477256I
a = 1.37517 + 0.57850I
b = −0.051368 − 0.680823I
0.81594 − 1.38660I 1.38598 + 4.17847I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.461839 + 0.022500I
a = −0.597939 − 0.071742I
b = 0.582563 + 0.589739I
0.74581 + 2.82348I −4.53636 − 4.83171I
u = 0.461839 − 0.022500I
a = −0.597939 + 0.071742I
b = 0.582563 − 0.589739I
0.74581 − 2.82348I −4.53636 + 4.83171I
u = 0.22904 + 1.55802I
a = −0.14484 − 1.83803I
b = 0.87787 + 1.48851I
9.3010 − 11.9435I 0
u = 0.22904 − 1.55802I
a = −0.14484 + 1.83803I
b = 0.87787 − 1.48851I
9.3010 + 11.9435I 0
u = −0.22129 + 1.56137I
a = 0.16999 − 1.66534I
b = −0.82156 + 1.38958I
7.22649 + 6.39687I 0
u = −0.22129 − 1.56137I
a = 0.16999 + 1.66534I
b = −0.82156 − 1.38958I
7.22649 − 6.39687I 0
u = 0.27624 + 1.56195I
a = 0.09685 + 1.90101I
b = −1.21047 − 1.59852I
7.3991 − 18.1926I 0
u = 0.27624 − 1.56195I
a = 0.09685 − 1.90101I
b = −1.21047 + 1.59852I
7.3991 + 18.1926I 0
u = 0.29885 + 1.56500I
a = −0.19914 + 1.43204I
b = −0.80085 − 1.28979I
11.9803 − 9.8409I 0
u = 0.29885 − 1.56500I
a = −0.19914 − 1.43204I
b = −0.80085 + 1.28979I
11.9803 + 9.8409I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.27816 + 1.56968I
a = −0.17140 + 1.70664I
b = 1.21269 − 1.40668I
5.40752 + 12.32690I 0
u = −0.27816 − 1.56968I
a = −0.17140 − 1.70664I
b = 1.21269 + 1.40668I
5.40752 − 12.32690I 0
u = 0.23215 + 1.57892I
a = 0.15758 − 1.52468I
b = 0.60684 + 1.43631I
13.08780 − 3.85885I 0
u = 0.23215 − 1.57892I
a = 0.15758 + 1.52468I
b = 0.60684 − 1.43631I
13.08780 + 3.85885I 0
u = 0.248024 + 0.314394I
a = 0.760188 + 0.656839I
b = −0.21625 + 2.01249I
−0.535608 + 0.453177I 4.48452 + 9.14316I
u = 0.248024 − 0.314394I
a = 0.760188 − 0.656839I
b = −0.21625 − 2.01249I
−0.535608 − 0.453177I 4.48452 − 9.14316I
u = 0.38199 + 1.55907I
a = −0.254235 + 0.592400I
b = −0.460504 − 0.568839I
7.37607 − 0.99312I 0
u = 0.38199 − 1.55907I
a = −0.254235 − 0.592400I
b = −0.460504 + 0.568839I
7.37607 + 0.99312I 0
u = 0.321418 + 0.223961I
a = −1.97865 + 0.14679I
b = −0.733646 − 0.883833I
−0.35523 − 2.56098I 1.68467 + 6.23098I
u = 0.321418 − 0.223961I
a = −1.97865 − 0.14679I
b = −0.733646 + 0.883833I
−0.35523 + 2.56098I 1.68467 − 6.23098I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.373148 + 0.039107I
a = 0.625428 + 0.426014I
b = −0.14835 + 1.85095I
0.650874 + 0.228088I −12.35292 + 1.32556I
u = −0.373148 − 0.039107I
a = 0.625428 − 0.426014I
b = −0.14835 − 1.85095I
0.650874 − 0.228088I −12.35292 − 1.32556I
u = −0.305575 + 0.209808I
a = −0.338043 + 0.740708I
b = 0.09441 + 2.44525I
0.05200 − 4.62844I −4.93644 − 10.66132I
u = −0.305575 − 0.209808I
a = −0.338043 − 0.740708I
b = 0.09441 − 2.44525I
0.05200 + 4.62844I −4.93644 + 10.66132I
u = −0.32708 + 1.60854I
a = −0.082890 + 0.881250I
b = 0.863080 − 0.709104I
5.16223 + 7.23356I 0
u = −0.32708 − 1.60854I
a = −0.082890 − 0.881250I
b = 0.863080 + 0.709104I
5.16223 − 7.23356I 0
u = −0.19350 + 1.63913I
a = 0.098376 − 0.982820I
b = −0.603961 + 1.102340I
5.97742 + 2.31934I 0
u = −0.19350 − 1.63913I
a = 0.098376 + 0.982820I
b = −0.603961 − 1.102340I
5.97742 − 2.31934I 0
u = 0.27866 + 1.65228I
a = 0.269982 − 0.752919I
b = 0.336410 + 1.033640I
7.41573 + 4.03195I 0
u = 0.27866 − 1.65228I
a = 0.269982 + 0.752919I
b = 0.336410 − 1.033640I
7.41573 − 4.03195I 0
14
II. I
u
2
= hb − 2a, 9a
2
+ 3a + 1, u − 1i
(i) Arc colorings
a
1
=
0
1
a
7
=
1
0
a
4
=
a
2a
a
8
=
1
1
a
3
=
3a
2a
a
2
=
3a + 1
2a +
5
3
a
12
=
1
2
a
9
=
2
3
a
5
=
3a
5a
a
11
=
1
2
a
10
=
1
1
a
6
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
116
3
a −
53
9
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
9(9u
2
− 6u + 4)
c
4
9(9u
2
− 3u + 1)
c
6
, c
7
, c
8
c
9
(u − 1)
2
c
10
, c
12
(u + 1)
2
c
11
u
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
2
+ y + 1
c
3
81(81y
2
+ 36y + 16)
c
4
81(81y
2
+ 9y + 1)
c
6
, c
7
, c
8
c
9
, c
10
, c
12
(y −1)
2
c
11
y
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.166667 + 0.288675I
b = −0.333333 + 0.577350I
−1.64493 + 2.02988I 0.55556 − 11.16211I
u = 1.00000
a = −0.166667 − 0.288675I
b = −0.333333 − 0.577350I
−1.64493 − 2.02988I 0.55556 + 11.16211I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
100
+ 38u
99
+ ··· + 2486u + 81)
c
2
(u
2
+ u + 1)(u
100
+ 2u
99
+ ··· + 14u + 9)
c
3
81(9u
2
− 6u + 4)(9u
100
− 129u
99
+ ··· + 1927454u + 1683748)
c
4
81(9u
2
− 3u + 1)(9u
100
+ 156u
99
+ ··· + 48280u + 5821)
c
5
(u
2
− u + 1)(u
100
+ 2u
99
+ ··· + 14u + 9)
c
6
((u − 1)
2
)(u
100
+ 3u
99
+ ··· + 3u + 1)
c
7
, c
8
((u − 1)
2
)(u
100
− 3u
99
+ ··· − 3u + 1)
c
9
((u − 1)
2
)(u
100
− 39u
99
+ ··· − 7u + 1)
c
10
((u + 1)
2
)(u
100
+ 3u
99
+ ··· + 3u + 1)
c
11
u
2
(u
100
− 5u
99
+ ··· − 216u + 108)
c
12
((u + 1)
2
)(u
100
− 3u
99
+ ··· − 3u + 1)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
100
+ 50y
99
+ ··· + 2843042y + 6561)
c
2
, c
5
(y
2
+ y + 1)(y
100
+ 38y
99
+ ··· + 2486y + 81)
c
3
6561(81y
2
+ 36y + 16)
· (81y
100
+ 5517y
99
+ ··· + 95872846757236y + 2835007327504)
c
4
6561(81y
2
+ 9y + 1)
· (81y
100
+ 1278y
99
+ ··· − 367849434y + 33884041)
c
6
, c
10
((y −1)
2
)(y
100
+ 39y
99
+ ··· + 7y + 1)
c
7
, c
8
, c
12
((y −1)
2
)(y
100
+ 99y
99
+ ··· + 7y + 1)
c
9
((y −1)
2
)(y
100
+ 31y
99
+ ··· − 145y + 1)
c
11
y
2
(y
100
− 15y
99
+ ··· − 266328y + 11664)
20
