12n
0393
(K12n
0393
)
A knot diagram
1
Linearized knot diagam
3 5 10 12 2 11 3 5 4 7 9 8
Solving Sequence
4,12 5,10
3 2 1 9 8 7 11 6
c
4
c
3
c
2
c
1
c
9
c
8
c
7
c
11
c
6
c
5
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.15453 × 10
112
u
51
+ 5.72428 × 10
112
u
50
+ ··· + 1.21115 × 10
113
b − 3.01826 × 10
112
,
− 2.72037 × 10
112
u
51
+ 1.17488 × 10
112
u
50
+ ··· + 3.63345 × 10
113
a + 5.57200 × 10
113
,
u
52
+ 3u
51
+ ··· − 24u + 3i
I
u
2
= h2.01791 × 10
18
u
27
− 2.77559 × 10
18
u
26
+ ··· + 3.98012 × 10
18
b − 1.63190 × 10
18
,
2.25156 × 10
18
u
27
− 4.18384 × 10
18
u
26
+ ··· + 3.98012 × 10
18
a − 1.75552 × 10
19
, u
28
− 2u
27
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 80 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
= h1.15 × 10
112
u
51
+ 5.72 × 10
112
u
50
+ · · · + 1.21 × 10
113
b − 3.02 ×
10
112
, −2.72 × 10
112
u
51
+ 1.17 × 10
112
u
50
+ · · · + 3.63 × 10
113
a + 5.57 ×
10
113
, u
52
+ 3u
51
+ · · · − 24u + 3i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
10
=
0.0748701u
51
− 0.0323350u
50
+ ··· − 79.8705u − 1.53353
−0.0953248u
51
− 0.472631u
50
+ ··· − 14.8071u + 0.249205
a
3
=
0.434214u
51
+ 1.30766u
50
+ ··· + 80.9069u − 0.00257423
0.125422u
51
+ 0.440759u
50
+ ··· + 12.0661u − 0.102321
a
2
=
0.449835u
51
+ 1.36244u
50
+ ··· + 67.6586u + 0.0846844
0.136943u
51
+ 0.472556u
50
+ ··· + 12.2091u − 0.126050
a
1
=
−0.210032u
51
− 0.352594u
50
+ ··· + 18.9538u − 4.39279
0.100422u
51
+ 0.347381u
50
+ ··· + 5.52097u − 0.778643
a
9
=
0.170195u
51
+ 0.440296u
50
+ ··· − 65.0634u − 1.78273
−0.0953248u
51
− 0.472631u
50
+ ··· − 14.8071u + 0.249205
a
8
=
0.0583544u
51
− 0.0330339u
50
+ ··· − 77.6730u − 1.74439
−0.148627u
51
− 0.687874u
50
+ ··· − 17.7790u + 0.662631
a
7
=
−0.413231u
51
− 1.41532u
50
+ ··· + 17.1606u − 7.46569
−0.137010u
51
− 0.426980u
50
+ ··· + 3.83576u − 1.09048
a
11
=
−0.520836u
51
− 1.12514u
50
+ ··· + 27.2715u − 4.83237
−0.0594728u
51
− 0.0801733u
50
+ ··· + 7.51076u − 0.926376
a
6
=
0.347122u
51
+ 0.924158u
50
+ ··· + 10.6820u − 4.29445
0.0547632u
51
+ 0.162363u
50
+ ··· + 2.60360u − 0.602166
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.254491u
51
− 0.628287u
50
+ ··· − 59.5014u − 3.23771
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
52
+ 81u
51
+ ··· − 3491600u + 40000
c
2
, c
5
u
52
+ u
51
+ ··· − 3900u + 200
c
3
, c
9
u
52
+ u
51
+ ··· + 343u + 41
c
4
u
52
+ 3u
51
+ ··· − 24u + 3
c
6
, c
10
u
52
− 3u
51
+ ··· + 1117u + 63
c
7
u
52
+ u
51
+ ··· + 47432u + 12463
c
8
u
52
+ 4u
51
+ ··· − 863539u + 134517
c
11
u
52
− 6u
51
+ ··· + 6257u + 2969
c
12
u
52
− u
51
+ ··· + 11094479u + 1097059
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
52
− 195y
51
+ ··· − 1710357280000y + 1600000000
c
2
, c
5
y
52
+ 81y
51
+ ··· − 3491600y + 40000
c
3
, c
9
y
52
+ 47y
51
+ ··· − 47539y + 1681
c
4
y
52
− 11y
51
+ ··· + 2274y + 9
c
6
, c
10
y
52
+ 53y
51
+ ··· − 286435y + 3969
c
7
y
52
+ 93y
51
+ ··· + 4931535532y + 155326369
c
8
y
52
− 48y
51
+ ··· + 2165579994401y + 18094823289
c
11
y
52
− 22y
51
+ ··· + 15360791y + 8814961
c
12
y
52
+ 101y
51
+ ··· − 10565760499085y + 1203538449481
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.708724 + 0.680164I
a = −0.100097 + 0.191987I
b = −0.595963 + 0.249087I
0.03503 + 2.05162I 5.39897 − 4.92822I
u = −0.708724 − 0.680164I
a = −0.100097 − 0.191987I
b = −0.595963 − 0.249087I
0.03503 − 2.05162I 5.39897 + 4.92822I
u = 0.878775 + 0.357102I
a = −0.97636 − 1.27394I
b = 0.53011 − 1.39925I
−8.07817 − 5.41935I −4.45843 + 4.52929I
u = 0.878775 − 0.357102I
a = −0.97636 + 1.27394I
b = 0.53011 + 1.39925I
−8.07817 + 5.41935I −4.45843 − 4.52929I
u = −0.881457 + 0.277287I
a = 0.0599084 − 0.0718366I
b = 1.284870 + 0.271797I
−4.17741 + 1.20590I −2.75221 − 2.59899I
u = −0.881457 − 0.277287I
a = 0.0599084 + 0.0718366I
b = 1.284870 − 0.271797I
−4.17741 − 1.20590I −2.75221 + 2.59899I
u = −0.749902 + 0.508872I
a = −1.43683 − 0.65321I
b = −0.169969 + 0.090507I
−3.76658 + 1.68389I −2.84617 − 3.64063I
u = −0.749902 − 0.508872I
a = −1.43683 + 0.65321I
b = −0.169969 − 0.090507I
−3.76658 − 1.68389I −2.84617 + 3.64063I
u = −0.802192 + 0.772090I
a = 1.42692 − 0.99934I
b = −0.225361 − 1.345420I
−5.14249 + 5.73182I 0. − 6.15629I
u = −0.802192 − 0.772090I
a = 1.42692 + 0.99934I
b = −0.225361 + 1.345420I
−5.14249 − 5.73182I 0. + 6.15629I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.115030 + 0.173053I
a = 0.113863 + 1.162840I
b = −0.85985 + 1.58005I
−19.5669 − 0.5894I −4.05584 + 0.I
u = −1.115030 − 0.173053I
a = 0.113863 − 1.162840I
b = −0.85985 − 1.58005I
−19.5669 + 0.5894I −4.05584 + 0.I
u = −0.841443 + 0.214420I
a = −0.59150 − 2.64999I
b = 0.175662 − 1.294030I
−11.89730 + 0.93127I −4.76253 + 3.15286I
u = −0.841443 − 0.214420I
a = −0.59150 + 2.64999I
b = 0.175662 + 1.294030I
−11.89730 − 0.93127I −4.76253 − 3.15286I
u = 0.695977 + 0.910130I
a = 0.257161 − 1.365910I
b = 0.757695 + 0.250125I
−14.2666 + 1.4637I 0
u = 0.695977 − 0.910130I
a = 0.257161 + 1.365910I
b = 0.757695 − 0.250125I
−14.2666 − 1.4637I 0
u = 0.815804 + 0.187793I
a = 1.01232 + 1.74860I
b = −0.265590 + 1.277780I
−4.38589 − 0.71014I −1.35930 − 0.66728I
u = 0.815804 − 0.187793I
a = 1.01232 − 1.74860I
b = −0.265590 − 1.277780I
−4.38589 + 0.71014I −1.35930 + 0.66728I
u = 0.812522 + 0.190053I
a = −1.73658 − 2.02290I
b = −0.131544 − 1.319490I
−7.92837 + 3.04454I −7.11238 − 3.82066I
u = 0.812522 − 0.190053I
a = −1.73658 + 2.02290I
b = −0.131544 + 1.319490I
−7.92837 − 3.04454I −7.11238 + 3.82066I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.979985 + 0.697974I
a = −0.611258 + 1.164100I
b = 0.476167 + 1.030450I
−0.90089 + 3.29423I 0
u = −0.979985 − 0.697974I
a = −0.611258 − 1.164100I
b = 0.476167 − 1.030450I
−0.90089 − 3.29423I 0
u = 0.964261 + 0.735548I
a = −0.376689 + 0.280094I
b = 0.374982 − 0.351059I
−8.81601 − 2.96366I 0
u = 0.964261 − 0.735548I
a = −0.376689 − 0.280094I
b = 0.374982 + 0.351059I
−8.81601 + 2.96366I 0
u = −1.103090 + 0.621634I
a = 0.396484 − 1.133500I
b = −0.14752 − 1.46554I
−6.17949 − 0.04065I 0
u = −1.103090 − 0.621634I
a = 0.396484 + 1.133500I
b = −0.14752 + 1.46554I
−6.17949 + 0.04065I 0
u = 0.633067 + 0.299009I
a = 0.975776 + 0.355361I
b = −0.595127 − 0.034941I
−0.80784 − 2.80941I 6.07107 − 0.12951I
u = 0.633067 − 0.299009I
a = 0.975776 − 0.355361I
b = −0.595127 + 0.034941I
−0.80784 + 2.80941I 6.07107 + 0.12951I
u = 1.105660 + 0.703039I
a = −0.139321 + 0.319582I
b = −1.392190 + 0.234949I
−15.6989 − 7.5261I 0
u = 1.105660 − 0.703039I
a = −0.139321 − 0.319582I
b = −1.392190 − 0.234949I
−15.6989 + 7.5261I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.256521 + 0.579369I
a = −0.381053 + 0.298557I
b = 0.504015 + 0.385095I
0.936572 + 0.614095I 8.99495 − 4.11967I
u = 0.256521 − 0.579369I
a = −0.381053 − 0.298557I
b = 0.504015 − 0.385095I
0.936572 − 0.614095I 8.99495 + 4.11967I
u = −0.594426 + 0.168375I
a = 1.21600 + 6.58426I
b = 0.282057 + 1.244100I
−17.3212 + 2.2018I −9.43793 − 5.50317I
u = −0.594426 − 0.168375I
a = 1.21600 − 6.58426I
b = 0.282057 − 1.244100I
−17.3212 − 2.2018I −9.43793 + 5.50317I
u = 1.23149 + 0.71950I
a = 0.53492 + 1.59800I
b = −0.421372 + 1.155520I
−2.55953 − 6.00845I 0
u = 1.23149 − 0.71950I
a = 0.53492 − 1.59800I
b = −0.421372 − 1.155520I
−2.55953 + 6.00845I 0
u = 0.74873 + 1.36600I
a = 0.157923 + 0.928465I
b = 0.294781 + 1.140120I
0.109056 − 1.147700I 0
u = 0.74873 − 1.36600I
a = 0.157923 − 0.928465I
b = 0.294781 − 1.140120I
0.109056 + 1.147700I 0
u = −0.50494 + 1.49032I
a = −0.151007 + 0.507289I
b = 0.074898 + 0.780251I
1.27937 + 2.65970I 0
u = −0.50494 − 1.49032I
a = −0.151007 − 0.507289I
b = 0.074898 − 0.780251I
1.27937 − 2.65970I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.32086 + 0.90728I
a = −0.377846 − 1.253450I
b = 0.41422 − 1.59450I
−10.50430 − 7.26761I 0
u = 1.32086 − 0.90728I
a = −0.377846 + 1.253450I
b = 0.41422 + 1.59450I
−10.50430 + 7.26761I 0
u = −1.29148 + 0.99643I
a = 0.66417 − 1.37600I
b = −0.55364 − 1.55688I
18.0895 + 14.3293I 0
u = −1.29148 − 0.99643I
a = 0.66417 + 1.37600I
b = −0.55364 + 1.55688I
18.0895 − 14.3293I 0
u = 1.05120 + 1.25196I
a = −0.803070 − 0.868324I
b = −0.01326 − 1.44826I
−9.16955 − 1.20799I 0
u = 1.05120 − 1.25196I
a = −0.803070 + 0.868324I
b = −0.01326 + 1.44826I
−9.16955 + 1.20799I 0
u = −1.04234 + 1.47547I
a = 0.399903 − 0.795864I
b = 0.31303 − 1.49004I
19.4826 − 5.4787I 0
u = −1.04234 − 1.47547I
a = 0.399903 + 0.795864I
b = 0.31303 + 1.49004I
19.4826 + 5.4787I 0
u = −1.42616 + 1.26843I
a = −0.476867 + 1.122810I
b = 0.15933 + 1.51184I
−15.2344 + 5.0637I 0
u = −1.42616 − 1.26843I
a = −0.476867 − 1.122810I
b = 0.15933 − 1.51184I
−15.2344 − 5.0637I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.0262988 + 0.0695915I
a = −4.55689 − 4.96984I
b = −0.770424 − 0.600625I
−1.83496 + 2.22975I −2.73852 − 6.11093I
u = 0.0262988 − 0.0695915I
a = −4.55689 + 4.96984I
b = −0.770424 + 0.600625I
−1.83496 − 2.22975I −2.73852 + 6.11093I
10
II.
I
u
2
= h2.02 × 10
18
u
27
− 2.78 × 10
18
u
26
+ · · · + 3.98 × 10
18
b − 1.63 × 10
18
, 2.25 ×
10
18
u
27
−4.18×10
18
u
26
+· · ·+3.98×10
18
a−1.76×10
19
, u
28
−2u
27
+· · ·−2u+1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
10
=
−0.565702u
27
+ 1.05118u
26
+ ··· − 5.77226u + 4.41073
−0.506997u
27
+ 0.697363u
26
+ ··· − 3.04835u + 0.410013
a
3
=
−0.104193u
27
+ 0.658612u
26
+ ··· − 9.55638u + 0.700265
−0.0157737u
27
+ 0.222925u
26
+ ··· + 0.262195u − 0.371218
a
2
=
−0.321907u
27
+ 0.668581u
26
+ ··· − 8.81393u + 0.621257
−0.235371u
27
+ 0.587360u
26
+ ··· − 0.371007u + 0.0542399
a
1
=
0.407606u
27
− 3.01277u
26
+ ··· + 21.3963u − 3.81808
0.526919u
27
− 1.24495u
26
+ ··· − 0.0602728u + 0.118550
a
9
=
−0.0587047u
27
+ 0.353821u
26
+ ··· − 2.72391u + 4.00072
−0.506997u
27
+ 0.697363u
26
+ ··· − 3.04835u + 0.410013
a
8
=
−0.576417u
27
+ 0.920531u
26
+ ··· − 6.30379u + 4.64714
−0.673214u
27
+ 1.14674u
26
+ ··· − 3.46806u + 0.878726
a
7
=
−2.14853u
27
+ 4.24022u
26
+ ··· − 3.79489u − 1.02880
−0.223741u
27
+ 0.185180u
26
+ ··· + 1.93274u − 0.665710
a
11
=
−0.356798u
27
− 0.321712u
26
+ ··· + 16.0454u − 0.792188
0.258849u
27
− 0.928798u
26
+ ··· + 0.894645u + 0.0884191
a
6
=
2.72555u
27
− 4.80908u
26
+ ··· + 2.79742u + 2.38076
−0.348792u
27
+ 0.765969u
26
+ ··· − 3.86859u + 2.05108
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
736448018193272236
3980122070783762781
u
27
+
976636596843390286
3980122070783762781
u
26
+ ··· −
16460922416404249957
3980122070783762781
u +
2887584208684426207
3980122070783762781
11
(iv) u-Polynomials at the component
12
Crossings u-Polynomials at each crossing
c
1
u
28
− 32u
27
+ ··· − 278u + 9
c
2
u
28
+ 16u
26
+ ··· + 2u + 3
c
3
u
28
+ 11u
26
+ ··· − 3u + 9
c
4
u
28
− 2u
27
+ ··· − 2u + 1
c
5
u
28
+ 16u
26
+ ··· − 2u + 3
c
6
u
28
− 2u
27
+ ··· + 3u + 1
c
7
u
28
+ 18u
26
+ ··· + 118u + 27
c
8
u
28
− u
27
+ ··· + 3u + 1
c
9
u
28
+ 11u
26
+ ··· + 3u + 9
c
10
u
28
+ 2u
27
+ ··· − 3u + 1
c
11
u
28
+ 3u
27
+ ··· + 23u + 3
c
12
u
28
+ 8u
26
+ ··· − 3u + 9
13
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
− 48y
27
+ ··· − 5950y + 81
c
2
, c
5
y
28
+ 32y
27
+ ··· + 278y + 9
c
3
, c
9
y
28
+ 22y
27
+ ··· + 765y + 81
c
4
y
28
+ 4y
26
+ ··· + 2y + 1
c
6
, c
10
y
28
+ 16y
27
+ ··· + 17y + 1
c
7
y
28
+ 36y
27
+ ··· − 10468y + 729
c
8
y
28
− 5y
27
+ ··· + 9y + 1
c
11
y
28
+ y
27
+ ··· + 11y + 9
c
12
y
28
+ 16y
27
+ ··· − 801y + 81
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.802001 + 0.664072I
a = −0.308745 − 0.187754I
b = −0.836807 + 0.306501I
−0.978219 + 0.992558I 0.438824 − 0.555457I
u = −0.802001 − 0.664072I
a = −0.308745 + 0.187754I
b = −0.836807 − 0.306501I
−0.978219 − 0.992558I 0.438824 + 0.555457I
u = −0.416978 + 0.849082I
a = 0.692013 + 0.012965I
b = −0.313501 − 1.303070I
−6.11964 + 4.39239I −1.68626 − 2.90655I
u = −0.416978 − 0.849082I
a = 0.692013 − 0.012965I
b = −0.313501 + 1.303070I
−6.11964 − 4.39239I −1.68626 + 2.90655I
u = 1.002310 + 0.361222I
a = −0.66314 − 1.73655I
b = −0.14938 − 1.41596I
−7.03266 + 2.28630I −1.74706 − 0.37676I
u = 1.002310 − 0.361222I
a = −0.66314 + 1.73655I
b = −0.14938 + 1.41596I
−7.03266 − 2.28630I −1.74706 + 0.37676I
u = −1.031490 + 0.268798I
a = 0.34522 + 2.22542I
b = −0.053226 + 1.300840I
−11.84170 + 1.80297I −4.19824 − 5.34890I
u = −1.031490 − 0.268798I
a = 0.34522 − 2.22542I
b = −0.053226 − 1.300840I
−11.84170 − 1.80297I −4.19824 + 5.34890I
u = −0.713533 + 0.497827I
a = −0.424380 + 0.234003I
b = 0.735148 + 0.137416I
−1.14749 + 3.45704I 0.35787 − 9.54916I
u = −0.713533 − 0.497827I
a = −0.424380 − 0.234003I
b = 0.735148 − 0.137416I
−1.14749 − 3.45704I 0.35787 + 9.54916I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.964407 + 0.669877I
a = 0.930850 + 0.043791I
b = −0.161243 + 0.771524I
−9.59714 − 2.80983I −5.67144 + 1.85970I
u = 0.964407 − 0.669877I
a = 0.930850 − 0.043791I
b = −0.161243 − 0.771524I
−9.59714 + 2.80983I −5.67144 − 1.85970I
u = −1.015050 + 0.642162I
a = −0.663021 + 1.059570I
b = 0.506351 + 0.822892I
−1.59932 + 3.89227I −1.52620 − 5.73593I
u = −1.015050 − 0.642162I
a = −0.663021 − 1.059570I
b = 0.506351 − 0.822892I
−1.59932 − 3.89227I −1.52620 + 5.73593I
u = 0.935710 + 0.760631I
a = −0.92714 − 1.55124I
b = 0.31481 − 1.43449I
−6.48639 − 7.46692I −1.34669 + 7.26562I
u = 0.935710 − 0.760631I
a = −0.92714 + 1.55124I
b = 0.31481 + 1.43449I
−6.48639 + 7.46692I −1.34669 − 7.26562I
u = 0.608556 + 0.500617I
a = 0.067655 + 0.537076I
b = 0.883004 + 0.833993I
−1.58392 + 1.43412I −0.76558 + 2.52420I
u = 0.608556 − 0.500617I
a = 0.067655 − 0.537076I
b = 0.883004 − 0.833993I
−1.58392 − 1.43412I −0.76558 − 2.52420I
u = 1.150320 + 0.612536I
a = 0.52209 + 1.86608I
b = −0.532530 + 1.150530I
−3.53200 − 5.98304I −4.48162 + 6.36220I
u = 1.150320 − 0.612536I
a = 0.52209 − 1.86608I
b = −0.532530 − 1.150530I
−3.53200 + 5.98304I −4.48162 − 6.36220I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.397838 + 0.304983I
a = 1.13622 − 2.12301I
b = −0.779294 − 0.640146I
−3.32810 − 0.27983I −0.952303 + 0.046698I
u = 0.397838 − 0.304983I
a = 1.13622 + 2.12301I
b = −0.779294 + 0.640146I
−3.32810 + 0.27983I −0.952303 − 0.046698I
u = −0.136188 + 0.418915I
a = 5.84836 − 1.23036I
b = 0.394968 − 1.162260I
−16.7744 − 1.7460I −0.101965 − 1.402576I
u = −0.136188 − 0.418915I
a = 5.84836 + 1.23036I
b = 0.394968 + 1.162260I
−16.7744 + 1.7460I −0.101965 + 1.402576I
u = −0.51542 + 1.49486I
a = 0.054047 + 0.586058I
b = −0.000501 + 0.703360I
1.46784 + 2.27349I 8.23182 + 4.49154I
u = −0.51542 − 1.49486I
a = 0.054047 − 0.586058I
b = −0.000501 − 0.703360I
1.46784 − 2.27349I 8.23182 − 4.49154I
u = 0.57152 + 1.58504I
a = 0.389974 + 0.825194I
b = −0.007796 + 1.208110I
−0.53410 − 2.32818I −1.55116 + 3.88201I
u = 0.57152 − 1.58504I
a = 0.389974 − 0.825194I
b = −0.007796 − 1.208110I
−0.53410 + 2.32818I −1.55116 − 3.88201I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
28
− 32u
27
+ ··· − 278u + 9)
· (u
52
+ 81u
51
+ ··· − 3491600u + 40000)
c
2
(u
28
+ 16u
26
+ ··· + 2u + 3)(u
52
+ u
51
+ ··· − 3900u + 200)
c
3
(u
28
+ 11u
26
+ ··· − 3u + 9)(u
52
+ u
51
+ ··· + 343u + 41)
c
4
(u
28
− 2u
27
+ ··· − 2u + 1)(u
52
+ 3u
51
+ ··· − 24u + 3)
c
5
(u
28
+ 16u
26
+ ··· − 2u + 3)(u
52
+ u
51
+ ··· − 3900u + 200)
c
6
(u
28
− 2u
27
+ ··· + 3u + 1)(u
52
− 3u
51
+ ··· + 1117u + 63)
c
7
(u
28
+ 18u
26
+ ··· + 118u + 27)(u
52
+ u
51
+ ··· + 47432u + 12463)
c
8
(u
28
− u
27
+ ··· + 3u + 1)(u
52
+ 4u
51
+ ··· − 863539u + 134517)
c
9
(u
28
+ 11u
26
+ ··· + 3u + 9)(u
52
+ u
51
+ ··· + 343u + 41)
c
10
(u
28
+ 2u
27
+ ··· − 3u + 1)(u
52
− 3u
51
+ ··· + 1117u + 63)
c
11
(u
28
+ 3u
27
+ ··· + 23u + 3)(u
52
− 6u
51
+ ··· + 6257u + 2969)
c
12
(u
28
+ 8u
26
+ ··· − 3u + 9)(u
52
− u
51
+ ··· + 1.10945 × 10
7
u + 1097059)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
28
− 48y
27
+ ··· − 5950y + 81)
· (y
52
− 195y
51
+ ··· − 1710357280000y + 1600000000)
c
2
, c
5
(y
28
+ 32y
27
+ ··· + 278y + 9)
· (y
52
+ 81y
51
+ ··· − 3491600y + 40000)
c
3
, c
9
(y
28
+ 22y
27
+ ··· + 765y + 81)(y
52
+ 47y
51
+ ··· − 47539y + 1681)
c
4
(y
28
+ 4y
26
+ ··· + 2y + 1)(y
52
− 11y
51
+ ··· + 2274y + 9)
c
6
, c
10
(y
28
+ 16y
27
+ ··· + 17y + 1)(y
52
+ 53y
51
+ ··· − 286435y + 3969)
c
7
(y
28
+ 36y
27
+ ··· − 10468y + 729)
· (y
52
+ 93y
51
+ ··· + 4931535532y + 155326369)
c
8
(y
28
− 5y
27
+ ··· + 9y + 1)
· (y
52
− 48y
51
+ ··· + 2165579994401y + 18094823289)
c
11
(y
28
+ y
27
+ ··· + 11y + 9)
· (y
52
− 22y
51
+ ··· + 15360791y + 8814961)
c
12
(y
28
+ 16y
27
+ ··· − 801y + 81)
· (y
52
+ 101y
51
+ ··· − 10565760499085y + 1203538449481)
20
