12n
0536
(K12n
0536
)
A knot diagram
1
Linearized knot diagam
3 5 10 12 2 9 5 4 6 4 9 8
Solving Sequence
4,12 5,9
8 1 7 6 11 10 3 2
c
4
c
8
c
12
c
7
c
6
c
11
c
10
c
3
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1.71591 × 10
136
u
61
+ 3.72192 × 10
136
u
60
+ ··· + 3.75605 × 10
136
b − 9.70874 × 10
136
,
− 7.27064 × 10
135
u
61
− 1.52290 × 10
136
u
60
+ ··· + 3.75605 × 10
136
a − 1.84906 × 10
137
,
u
62
+ 3u
61
+ ··· + 6u + 1i
I
u
2
= h163809549521227u
21
+ 58330736636863u
20
+ ··· + 384149611137554b + 205005886037235,
− 51253454018903u
21
+ 148522476867159u
20
+ ··· + 384149611137554a − 60479472657577,
u
22
− 5u
20
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 84 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
= h1.72 × 10
136
u
61
+ 3.72 × 10
136
u
60
+ · · · + 3.76 × 10
136
b − 9.71 ×
10
136
, −7.27 × 10
135
u
61
− 1.52 × 10
136
u
60
+ · · · + 3.76 × 10
136
a − 1.85 ×
10
137
, u
62
+ 3u
61
+ · · · + 6u + 1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
0.193572u
61
+ 0.405454u
60
+ ··· + 27.6970u + 4.92287
−0.456839u
61
− 0.990915u
60
+ ··· + 18.2428u + 2.58483
a
8
=
−0.263267u
61
− 0.585461u
60
+ ··· + 45.9398u + 7.50770
−0.456839u
61
− 0.990915u
60
+ ··· + 18.2428u + 2.58483
a
1
=
1.16917u
61
+ 3.24162u
60
+ ··· + 20.2903u + 1.35776
1.30286u
61
+ 4.60798u
60
+ ··· + 14.7698u + 0.862367
a
7
=
1.18336u
61
+ 3.73183u
60
+ ··· + 26.7343u + 4.71853
−1.32861u
61
− 4.00841u
60
+ ··· + 16.9317u + 2.60741
a
6
=
2.34621u
61
+ 7.59680u
60
+ ··· + 30.9047u + 3.59561
1.43721u
61
+ 4.71130u
60
+ ··· + 6.07767u − 0.182858
a
11
=
−0.0591481u
61
− 0.655677u
60
+ ··· + 9.74878u + 1.14092
−0.0745467u
61
− 0.710685u
60
+ ··· − 2.22824u − 0.645530
a
10
=
−0.133695u
61
− 1.36636u
60
+ ··· + 7.52055u + 0.495394
−0.0745467u
61
− 0.710685u
60
+ ··· − 2.22824u − 0.645530
a
3
=
3.14078u
61
+ 9.08276u
60
+ ··· − 3.04070u + 2.45575
0.541059u
61
+ 1.40800u
60
+ ··· − 0.406442u + 0.432472
a
2
=
1.87526u
61
+ 5.39621u
60
+ ··· − 3.73749u + 2.36287
0.865858u
61
+ 2.48532u
60
+ ··· + 0.198925u + 0.322445
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10.2334u
61
− 37.5928u
60
+ ··· − 136.983u − 17.5188
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
62
+ 22u
61
+ ··· + 620u + 4
c
2
, c
5
u
62
+ 11u
60
+ ··· − 10u + 2
c
3
, c
10
u
62
+ u
61
+ ··· + 170u + 289
c
4
u
62
+ 3u
61
+ ··· + 6u + 1
c
6
, c
9
u
62
+ 2u
61
+ ··· + 10u + 1
c
7
u
62
+ 8u
61
+ ··· − 12576553u + 1906367
c
8
u
62
+ 2u
61
+ ··· − 68u + 26
c
11
u
62
− u
61
+ ··· − 150u + 67
c
12
u
62
− u
61
+ ··· − 104469u + 9059
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
62
+ 46y
61
+ ··· − 67792y + 16
c
2
, c
5
y
62
+ 22y
61
+ ··· + 620y + 4
c
3
, c
10
y
62
− y
61
+ ··· + 2388874y + 83521
c
4
y
62
− 5y
61
+ ··· + 14y + 1
c
6
, c
9
y
62
+ 12y
61
+ ··· + 52y + 1
c
7
y
62
− 84y
61
+ ··· − 322575225344421y + 3634235138689
c
8
y
62
+ 56y
61
+ ··· − 22200y + 676
c
11
y
62
− 59y
61
+ ··· + 164028y + 4489
c
12
y
62
+ 67y
61
+ ··· + 488736985y + 82065481
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.165930 + 0.930592I
a = −0.10701 + 2.06026I
b = −0.057682 − 0.972148I
3.40685 − 2.08743I 8.13116 + 4.36654I
u = 0.165930 − 0.930592I
a = −0.10701 − 2.06026I
b = −0.057682 + 0.972148I
3.40685 + 2.08743I 8.13116 − 4.36654I
u = −0.997985 + 0.380629I
a = 0.433419 + 1.028500I
b = −0.13150 − 1.44905I
−1.18532 + 5.73345I 0. − 8.28149I
u = −0.997985 − 0.380629I
a = 0.433419 − 1.028500I
b = −0.13150 + 1.44905I
−1.18532 − 5.73345I 0. + 8.28149I
u = −0.002944 + 0.924364I
a = 0.211183 − 1.006820I
b = −0.16712 + 1.85863I
2.71444 + 3.86842I 6.79055 − 7.43016I
u = −0.002944 − 0.924364I
a = 0.211183 + 1.006820I
b = −0.16712 − 1.85863I
2.71444 − 3.86842I 6.79055 + 7.43016I
u = −0.812041 + 0.713431I
a = −0.915182 − 0.646168I
b = −0.609084 + 0.870903I
−0.67509 + 1.55554I 0
u = −0.812041 − 0.713431I
a = −0.915182 + 0.646168I
b = −0.609084 − 0.870903I
−0.67509 − 1.55554I 0
u = −1.063550 + 0.207154I
a = −0.420018 + 0.637174I
b = 0.467651 + 0.802572I
−5.03634 − 0.65577I 0
u = −1.063550 − 0.207154I
a = −0.420018 − 0.637174I
b = 0.467651 − 0.802572I
−5.03634 + 0.65577I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.465488 + 0.779154I
a = −0.092600 − 1.357340I
b = −0.97065 + 1.22533I
−2.61957 + 4.38386I 1.07305 − 7.42421I
u = −0.465488 − 0.779154I
a = −0.092600 + 1.357340I
b = −0.97065 − 1.22533I
−2.61957 − 4.38386I 1.07305 + 7.42421I
u = 0.750587 + 0.427782I
a = 1.65282 − 0.94218I
b = 0.736969 + 0.934309I
−0.11147 − 6.99469I −3.20173 + 9.81711I
u = 0.750587 − 0.427782I
a = 1.65282 + 0.94218I
b = 0.736969 − 0.934309I
−0.11147 + 6.99469I −3.20173 − 9.81711I
u = 1.221520 + 0.120806I
a = 0.339911 − 0.433001I
b = −0.558973 − 0.091877I
−7.45390 − 2.15136I 0
u = 1.221520 − 0.120806I
a = 0.339911 + 0.433001I
b = −0.558973 + 0.091877I
−7.45390 + 2.15136I 0
u = −0.517704 + 0.562485I
a = −0.668372 − 0.070624I
b = −0.476542 + 0.257017I
−1.05258 + 1.18693I −4.45668 − 4.18814I
u = −0.517704 − 0.562485I
a = −0.668372 + 0.070624I
b = −0.476542 − 0.257017I
−1.05258 − 1.18693I −4.45668 + 4.18814I
u = 0.523431 + 0.513052I
a = −0.535706 + 1.288960I
b = 0.266709 − 1.273450I
1.82519 − 1.36296I 1.54329 + 4.17454I
u = 0.523431 − 0.513052I
a = −0.535706 − 1.288960I
b = 0.266709 + 1.273450I
1.82519 + 1.36296I 1.54329 − 4.17454I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.321102 + 0.647348I
a = −0.022673 + 1.348950I
b = 0.501475 − 0.865448I
1.85599 − 1.13423I −0.309363 − 0.900307I
u = 0.321102 − 0.647348I
a = −0.022673 − 1.348950I
b = 0.501475 + 0.865448I
1.85599 + 1.13423I −0.309363 + 0.900307I
u = −0.168667 + 0.660664I
a = −3.06985 + 0.38017I
b = 0.171594 + 0.004198I
2.65932 + 6.57779I 7.85703 − 7.89113I
u = −0.168667 − 0.660664I
a = −3.06985 − 0.38017I
b = 0.171594 − 0.004198I
2.65932 − 6.57779I 7.85703 + 7.89113I
u = −1.315760 + 0.177104I
a = −0.421905 + 0.140944I
b = −0.418914 + 0.165670I
−2.41902 + 0.19351I 0
u = −1.315760 − 0.177104I
a = −0.421905 − 0.140944I
b = −0.418914 − 0.165670I
−2.41902 − 0.19351I 0
u = 0.234273 + 0.612614I
a = 2.46365 + 1.67487I
b = −0.105327 − 0.177690I
3.58080 − 1.15954I 9.57507 + 5.43915I
u = 0.234273 − 0.612614I
a = 2.46365 − 1.67487I
b = −0.105327 + 0.177690I
3.58080 + 1.15954I 9.57507 − 5.43915I
u = −0.904086 + 1.045360I
a = −0.249561 − 0.737893I
b = −0.42512 + 1.73156I
−0.00214 + 4.68956I 0
u = −0.904086 − 1.045360I
a = −0.249561 + 0.737893I
b = −0.42512 − 1.73156I
−0.00214 − 4.68956I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.281954 + 0.542697I
a = 0.219911 + 0.087140I
b = −2.26522 − 0.10868I
2.06711 − 7.02714I 7.2802 + 14.8527I
u = 0.281954 − 0.542697I
a = 0.219911 − 0.087140I
b = −2.26522 + 0.10868I
2.06711 + 7.02714I 7.2802 − 14.8527I
u = −0.026975 + 0.606723I
a = −0.084880 + 0.310459I
b = 1.89438 + 0.04499I
3.66976 + 0.24782I 12.04590 + 2.79775I
u = −0.026975 − 0.606723I
a = −0.084880 − 0.310459I
b = 1.89438 − 0.04499I
3.66976 − 0.24782I 12.04590 − 2.79775I
u = 0.335377 + 0.481418I
a = −0.06783 − 2.73237I
b = 0.557255 + 1.037380I
−4.01107 − 3.42086I −8.07352 + 4.07528I
u = 0.335377 − 0.481418I
a = −0.06783 + 2.73237I
b = 0.557255 − 1.037380I
−4.01107 + 3.42086I −8.07352 − 4.07528I
u = 0.92096 + 1.12984I
a = −0.401949 + 1.176920I
b = −0.52928 − 1.72739I
9.40777 − 1.77606I 0
u = 0.92096 − 1.12984I
a = −0.401949 − 1.176920I
b = −0.52928 + 1.72739I
9.40777 + 1.77606I 0
u = −0.93058 + 1.15260I
a = 0.366572 + 1.172380I
b = 0.68767 − 1.60197I
9.16673 + 8.01243I 0
u = −0.93058 − 1.15260I
a = 0.366572 − 1.172380I
b = 0.68767 + 1.60197I
9.16673 − 8.01243I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.01454 + 1.08458I
a = −0.612869 + 1.143460I
b = −0.227460 − 1.383390I
4.02353 − 3.94644I 0
u = 1.01454 − 1.08458I
a = −0.612869 − 1.143460I
b = −0.227460 + 1.383390I
4.02353 + 3.94644I 0
u = 1.45278 + 0.32226I
a = 0.186002 + 0.283851I
b = 0.180304 − 0.249974I
−5.07079 − 5.71196I 0
u = 1.45278 − 0.32226I
a = 0.186002 − 0.283851I
b = 0.180304 + 0.249974I
−5.07079 + 5.71196I 0
u = −0.172079 + 0.459052I
a = −0.346327 + 1.016920I
b = 0.095770 + 0.617374I
−0.26698 + 2.11215I −2.44927 − 3.44810I
u = −0.172079 − 0.459052I
a = −0.346327 − 1.016920I
b = 0.095770 − 0.617374I
−0.26698 − 2.11215I −2.44927 + 3.44810I
u = 1.16422 + 0.97896I
a = −0.845511 + 0.676945I
b = −0.00205 − 1.54662I
8.59237 − 5.95049I 0
u = 1.16422 − 0.97896I
a = −0.845511 − 0.676945I
b = −0.00205 + 1.54662I
8.59237 + 5.95049I 0
u = 1.09741 + 1.08495I
a = 0.471415 − 1.019370I
b = 0.60017 + 1.72962I
9.91197 − 8.88268I 0
u = 1.09741 − 1.08495I
a = 0.471415 + 1.019370I
b = 0.60017 − 1.72962I
9.91197 + 8.88268I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.10944 + 1.08719I
a = −0.451584 − 1.116400I
b = −0.68155 + 1.68234I
8.0311 + 16.0146I 0
u = −1.10944 − 1.08719I
a = −0.451584 + 1.116400I
b = −0.68155 − 1.68234I
8.0311 − 16.0146I 0
u = 1.04855 + 1.15112I
a = 0.698585 − 0.718469I
b = 0.06404 + 1.56751I
10.11830 + 0.77137I 0
u = 1.04855 − 1.15112I
a = 0.698585 + 0.718469I
b = 0.06404 − 1.56751I
10.11830 − 0.77137I 0
u = −1.20685 + 0.99490I
a = 0.725567 + 0.568353I
b = −0.13679 − 1.45257I
8.26868 − 0.11939I 0
u = −1.20685 − 0.99490I
a = 0.725567 − 0.568353I
b = −0.13679 + 1.45257I
8.26868 + 0.11939I 0
u = −1.05420 + 1.18099I
a = −0.710445 − 0.706964I
b = 0.12015 + 1.50569I
8.28897 − 7.80965I 0
u = −1.05420 − 1.18099I
a = −0.710445 + 0.706964I
b = 0.12015 − 1.50569I
8.28897 + 7.80965I 0
u = −1.08118 + 1.18882I
a = 0.421669 + 0.935093I
b = 0.258643 − 1.207240I
3.27959 + 4.26299I 0
u = −1.08118 − 1.18882I
a = 0.421669 − 0.935093I
b = 0.258643 + 1.207240I
3.27959 − 4.26299I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.203127 + 0.142996I
a = 1.83356 + 2.81105I
b = 0.160472 + 0.965429I
−0.23208 + 2.09229I −2.77990 − 2.89354I
u = −0.203127 − 0.142996I
a = 1.83356 − 2.81105I
b = 0.160472 − 0.965429I
−0.23208 − 2.09229I −2.77990 + 2.89354I
11
II.
I
u
2
= h1.64×10
14
u
21
+5.83×10
13
u
20
+· · ·+3.84×10
14
b+2.05×10
14
, −5.13×
10
13
u
21
+1.49×10
14
u
20
+· · ·+3.84×10
14
a−6.05×10
13
, u
22
−5u
20
+· · ·+2u+1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
0.133421u
21
− 0.386627u
20
+ ··· + 2.14873u + 0.157437
−0.426421u
21
− 0.151844u
20
+ ··· − 0.826693u − 0.533662
a
8
=
−0.293001u
21
− 0.538470u
20
+ ··· + 1.32204u − 0.376224
−0.426421u
21
− 0.151844u
20
+ ··· − 0.826693u − 0.533662
a
1
=
−0.647220u
21
− 0.166162u
20
+ ··· − 12.1300u − 4.73495
−0.353043u
21
+ 0.155220u
20
+ ··· − 3.80337u − 0.927868
a
7
=
0.353956u
21
− 0.383250u
20
+ ··· + 3.51867u + 0.695908
−0.552635u
21
− 0.137768u
20
+ ··· − 1.78409u − 0.688882
a
6
=
0.342136u
21
+ 0.492525u
20
+ ··· + 7.17325u + 3.00994
0.162285u
21
− 0.0994937u
20
+ ··· + 2.68471u + 0.397069
a
11
=
−0.00909788u
21
− 0.359656u
20
+ ··· − 3.79539u − 2.89303
−0.285080u
21
+ 0.0382739u
20
+ ··· − 2.53120u − 0.914050
a
10
=
−0.294178u
21
− 0.321382u
20
+ ··· − 6.32659u − 3.80708
−0.285080u
21
+ 0.0382739u
20
+ ··· − 2.53120u − 0.914050
a
3
=
−1.37389u
21
+ 0.229452u
20
+ ··· − 7.40788u − 0.433030
−0.527423u
21
+ 0.262335u
20
+ ··· − 1.88437u − 0.163479
a
2
=
−1.07248u
21
+ 0.185019u
20
+ ··· − 4.60852u − 0.499002
−0.522187u
21
+ 0.314870u
20
+ ··· − 2.09691u − 0.119046
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
44792649864550
192074805568777
u
21
+
164302245595680
192074805568777
u
20
+ ··· +
1491146875316471
192074805568777
u +
304827721883127
192074805568777
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
22
− 13u
21
+ ··· − 56u + 4
c
2
u
22
+ u
21
+ ··· + 2u + 2
c
3
u
22
+ 2u
21
+ ··· + 8u + 1
c
4
u
22
− 5u
20
+ ··· + 2u + 1
c
5
u
22
− u
21
+ ··· − 2u + 2
c
6
u
22
+ 9u
21
+ ··· + 4u + 1
c
7
u
22
+ u
21
+ ··· + u + 1
c
8
u
22
+ u
21
+ ··· + 9u
2
+ 2
c
9
u
22
− 9u
21
+ ··· − 4u + 1
c
10
u
22
− 2u
21
+ ··· − 8u + 1
c
11
u
22
− 2u
21
+ ··· − 4u + 1
c
12
u
22
+ 7u
20
+ ··· − 3u + 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
+ y
21
+ ··· − 120y + 16
c
2
, c
5
y
22
+ 13y
21
+ ··· + 56y + 4
c
3
, c
10
y
22
− 18y
21
+ ··· − 22y + 1
c
4
y
22
− 10y
21
+ ··· + 10y + 1
c
6
, c
9
y
22
+ 11y
21
+ ··· + 12y + 1
c
7
y
22
− 13y
21
+ ··· + 3y + 1
c
8
y
22
+ 11y
21
+ ··· + 36y + 4
c
11
y
22
− 12y
21
+ ··· − 8y + 1
c
12
y
22
+ 14y
21
+ ··· + 17y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.730385 + 0.664526I
a = −0.119371 − 1.335790I
b = −0.70021 + 1.27249I
−4.10993 + 5.20936I −6.16659 − 7.45799I
u = −0.730385 − 0.664526I
a = −0.119371 + 1.335790I
b = −0.70021 − 1.27249I
−4.10993 − 5.20936I −6.16659 + 7.45799I
u = −0.300453 + 0.938759I
a = 0.045977 + 1.064400I
b = −0.219417 − 0.860659I
1.93175 + 2.02632I 0.71587 − 5.34540I
u = −0.300453 − 0.938759I
a = 0.045977 − 1.064400I
b = −0.219417 + 0.860659I
1.93175 − 2.02632I 0.71587 + 5.34540I
u = −0.996020 + 0.273419I
a = −0.863515 + 0.618721I
b = 0.400853 + 0.697068I
−5.06317 − 1.44297I −5.03337 + 5.98899I
u = −0.996020 − 0.273419I
a = −0.863515 − 0.618721I
b = 0.400853 − 0.697068I
−5.06317 + 1.44297I −5.03337 − 5.98899I
u = 0.386934 + 0.803717I
a = 0.08802 − 1.72278I
b = 0.735248 + 1.035770I
−3.02316 − 3.32393I −0.67724 + 2.00395I
u = 0.386934 − 0.803717I
a = 0.08802 + 1.72278I
b = 0.735248 − 1.035770I
−3.02316 + 3.32393I −0.67724 − 2.00395I
u = −0.891638 + 0.917052I
a = 0.276614 + 0.800805I
b = 0.23326 − 1.72029I
0.27203 + 4.50446I 7.83463 − 1.95574I
u = −0.891638 − 0.917052I
a = 0.276614 − 0.800805I
b = 0.23326 + 1.72029I
0.27203 − 4.50446I 7.83463 + 1.95574I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.340900 + 0.190202I
a = 0.441956 − 0.071410I
b = 0.533210 − 0.500891I
−2.35927 + 0.54072I −3.88580 − 11.75057I
u = −1.340900 − 0.190202I
a = 0.441956 + 0.071410I
b = 0.533210 + 0.500891I
−2.35927 − 0.54072I −3.88580 + 11.75057I
u = 1.37204 + 0.36207I
a = 0.479530 − 0.058198I
b = −0.353709 + 0.696590I
−6.65312 − 1.35752I −1.88118 + 0.54540I
u = 1.37204 − 0.36207I
a = 0.479530 + 0.058198I
b = −0.353709 − 0.696590I
−6.65312 + 1.35752I −1.88118 − 0.54540I
u = −0.244633 + 0.400597I
a = −1.10874 + 1.94332I
b = −0.946752 − 0.384915I
3.01849 + 0.66056I 0.692989 + 0.616171I
u = −0.244633 − 0.400597I
a = −1.10874 − 1.94332I
b = −0.946752 + 0.384915I
3.01849 − 0.66056I 0.692989 − 0.616171I
u = 1.51864 + 0.20543I
a = −0.157685 + 0.260638I
b = −0.261556 − 0.551871I
−4.90812 − 6.25806I −2.21179 + 10.98437I
u = 1.51864 − 0.20543I
a = −0.157685 − 0.260638I
b = −0.261556 + 0.551871I
−4.90812 + 6.25806I −2.21179 − 10.98437I
u = 1.04003 + 1.15736I
a = −0.559668 + 1.100690I
b = −0.202417 − 1.320470I
4.36949 − 4.17007I 10.88438 + 8.79804I
u = 1.04003 − 1.15736I
a = −0.559668 − 1.100690I
b = −0.202417 + 1.320470I
4.36949 + 4.17007I 10.88438 − 8.79804I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.186384 + 0.359934I
a = 2.47689 − 0.01169I
b = 1.281490 + 0.202287I
1.72060 − 6.53470I −2.27189 + 3.95440I
u = 0.186384 − 0.359934I
a = 2.47689 + 0.01169I
b = 1.281490 − 0.202287I
1.72060 + 6.53470I −2.27189 − 3.95440I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
22
− 13u
21
+ ··· − 56u + 4)(u
62
+ 22u
61
+ ··· + 620u + 4)
c
2
(u
22
+ u
21
+ ··· + 2u + 2)(u
62
+ 11u
60
+ ··· − 10u + 2)
c
3
(u
22
+ 2u
21
+ ··· + 8u + 1)(u
62
+ u
61
+ ··· + 170u + 289)
c
4
(u
22
− 5u
20
+ ··· + 2u + 1)(u
62
+ 3u
61
+ ··· + 6u + 1)
c
5
(u
22
− u
21
+ ··· − 2u + 2)(u
62
+ 11u
60
+ ··· − 10u + 2)
c
6
(u
22
+ 9u
21
+ ··· + 4u + 1)(u
62
+ 2u
61
+ ··· + 10u + 1)
c
7
(u
22
+ u
21
+ ··· + u + 1)(u
62
+ 8u
61
+ ··· − 1.25766 × 10
7
u + 1906367)
c
8
(u
22
+ u
21
+ ··· + 9u
2
+ 2)(u
62
+ 2u
61
+ ··· − 68u + 26)
c
9
(u
22
− 9u
21
+ ··· − 4u + 1)(u
62
+ 2u
61
+ ··· + 10u + 1)
c
10
(u
22
− 2u
21
+ ··· − 8u + 1)(u
62
+ u
61
+ ··· + 170u + 289)
c
11
(u
22
− 2u
21
+ ··· − 4u + 1)(u
62
− u
61
+ ··· − 150u + 67)
c
12
(u
22
+ 7u
20
+ ··· − 3u + 1)(u
62
− u
61
+ ··· − 104469u + 9059)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
22
+ y
21
+ ··· − 120y + 16)(y
62
+ 46y
61
+ ··· − 67792y + 16)
c
2
, c
5
(y
22
+ 13y
21
+ ··· + 56y + 4)(y
62
+ 22y
61
+ ··· + 620y + 4)
c
3
, c
10
(y
22
− 18y
21
+ ··· − 22y + 1)(y
62
− y
61
+ ··· + 2388874y + 83521)
c
4
(y
22
− 10y
21
+ ··· + 10y + 1)(y
62
− 5y
61
+ ··· + 14y + 1)
c
6
, c
9
(y
22
+ 11y
21
+ ··· + 12y + 1)(y
62
+ 12y
61
+ ··· + 52y + 1)
c
7
(y
22
− 13y
21
+ ··· + 3y + 1)
· (y
62
− 84y
61
+ ··· − 322575225344421y + 3634235138689)
c
8
(y
22
+ 11y
21
+ ··· + 36y + 4)(y
62
+ 56y
61
+ ··· − 22200y + 676)
c
11
(y
22
− 12y
21
+ ··· − 8y + 1)(y
62
− 59y
61
+ ··· + 164028y + 4489)
c
12
(y
22
+ 14y
21
+ ··· + 17y + 1)
· (y
62
+ 67y
61
+ ··· + 488736985y + 82065481)
21
