11a
131
(K11a
131
)
A knot diagram
1
Linearized knot diagam
6 1 8 9 2 10 3 11 5 7 4
Solving Sequence
8,11 4,9
5 1 3 2 7 10 6
c
8
c
4
c
11
c
3
c
2
c
7
c
10
c
6
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.39241 × 10
297
u
76
+ 2.07034 × 10
298
u
75
+ ··· + 7.56609 × 10
293
b − 6.88514 × 10
297
,
1.90621 × 10
298
u
76
− 1.65962 × 10
299
u
75
+ ··· + 7.56609 × 10
293
a + 6.40142 × 10
298
, u
77
− 9u
76
+ ··· + 21u − 1i
I
u
2
= h265u
11
+ 395u
10
+ ··· + b + 529,
62u
11
+ 109u
10
+ 31u
9
− 12u
8
+ 252u
7
− 61u
6
− 934u
5
− 809u
4
+ 808u
3
+ 1745u
2
+ a + 992u + 184,
u
12
+ 2u
11
+ u
10
+ 4u
8
− 15u
6
− 17u
5
+ 9u
4
+ 31u
3
+ 24u
2
+ 8u + 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−2.39 × 10
297
u
76
+ 2.07 × 10
298
u
75
+ · · · + 7.57 × 10
293
b − 6.89 ×
10
297
, 1.91 × 10
298
u
76
− 1.66 × 10
299
u
75
+ · · · + 7.57 × 10
293
a + 6.40 ×
10
298
, u
77
− 9u
76
+ · · · + 21u − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
4
=
−25194.1u
76
+ 219350.u
75
+ ··· + 1.49608 × 10
6
u − 84606.7
3162.01u
76
− 27363.4u
75
+ ··· − 164906.u + 9100.00
a
9
=
1
−u
2
a
5
=
−24167.3u
76
+ 210600.u
75
+ ··· + 1.46132 × 10
6
u − 82903.8
2951.14u
76
− 25550.4u
75
+ ··· − 155615.u + 8608.65
a
1
=
36469.7u
76
− 317311.u
75
+ ··· − 2.14120 × 10
6
u + 120882.
2514.97u
76
− 21887.7u
75
+ ··· − 149547.u + 8482.64
a
3
=
−22032.1u
76
+ 191986.u
75
+ ··· + 1.33118 × 10
6
u − 75506.7
3162.01u
76
− 27363.4u
75
+ ··· − 164906.u + 9100.00
a
2
=
3328.29u
76
− 30427.5u
75
+ ··· − 404077.u + 25152.7
−7001.88u
76
+ 60698.7u
75
+ ··· + 377943.u − 20947.6
a
7
=
6514.01u
76
− 56697.7u
75
+ ··· − 387663.u + 21971.8
−1968.63u
76
+ 17131.1u
75
+ ··· + 116642.u − 6616.81
a
10
=
19882.8u
76
− 173045.u
75
+ ··· − 1.17852 × 10
6
u + 66715.8
−1263.34u
76
+ 10993.8u
75
+ ··· + 74786.7u − 4242.80
a
6
=
−37204.0u
76
+ 323703.u
75
+ ··· + 2.18430 × 10
6
u − 123307.
−2519.11u
76
+ 21922.8u
75
+ ··· + 149639.u − 8486.27
a
6
=
−37204.0u
76
+ 323703.u
75
+ ··· + 2.18430 × 10
6
u − 123307.
−2519.11u
76
+ 21922.8u
75
+ ··· + 149639.u − 8486.27
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2184.18u
76
− 18961.6u
75
+ ··· − 120593.u + 6664.56
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
77
− u
76
+ ··· + 15u − 1
c
2
u
77
+ 29u
76
+ ··· − 41u − 1
c
3
, c
7
u
77
− u
76
+ ··· − 165u − 29
c
4
, c
9
u
77
+ u
76
+ ··· − 1709u − 751
c
6
, c
10
u
77
− u
76
+ ··· + 2607u − 121
c
8
u
77
+ 9u
76
+ ··· + 21u + 1
c
11
u
77
− 2u
76
+ ··· − 11u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
77
+ 29y
76
+ ··· − 41y −1
c
2
y
77
+ 45y
76
+ ··· − 1989y −1
c
3
, c
7
y
77
− 39y
76
+ ··· + 32561y −841
c
4
, c
9
y
77
− 57y
76
+ ··· − 8745353y −564001
c
6
, c
10
y
77
− 61y
76
+ ··· + 895279y −14641
c
8
y
77
− 7y
76
+ ··· + 53y −1
c
11
y
77
+ 2y
76
+ ··· − 43y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772580 + 0.649599I
a = −0.427166 + 1.251420I
b = 1.273380 − 0.435053I
−4.61742 + 6.13658I 0
u = 0.772580 − 0.649599I
a = −0.427166 − 1.251420I
b = 1.273380 + 0.435053I
−4.61742 − 6.13658I 0
u = −0.831929 + 0.574661I
a = 0.241087 − 0.114363I
b = −1.265010 + 0.301142I
−0.23261 + 3.64167I 0
u = −0.831929 − 0.574661I
a = 0.241087 + 0.114363I
b = −1.265010 − 0.301142I
−0.23261 − 3.64167I 0
u = −0.458067 + 0.856288I
a = 1.293790 − 0.404733I
b = 0.896924 + 0.374361I
1.80693 − 4.42620I 0
u = −0.458067 − 0.856288I
a = 1.293790 + 0.404733I
b = 0.896924 − 0.374361I
1.80693 + 4.42620I 0
u = −0.758441 + 0.763394I
a = −0.535976 + 0.962822I
b = 0.110329 − 0.733577I
3.84970 − 0.08012I 0
u = −0.758441 − 0.763394I
a = −0.535976 − 0.962822I
b = 0.110329 + 0.733577I
3.84970 + 0.08012I 0
u = 1.094390 + 0.064995I
a = 1.58015 − 0.73304I
b = −0.775291 + 0.429157I
5.46593 − 3.52443I 0
u = 1.094390 − 0.064995I
a = 1.58015 + 0.73304I
b = −0.775291 − 0.429157I
5.46593 + 3.52443I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.584838 + 0.939434I
a = −0.146487 + 0.899216I
b = 1.211330 − 0.130649I
−5.89787 − 1.17472I 0
u = 0.584838 − 0.939434I
a = −0.146487 − 0.899216I
b = 1.211330 + 0.130649I
−5.89787 + 1.17472I 0
u = −0.716415 + 0.853385I
a = 0.502942 − 1.047360I
b = 0.104207 + 0.712436I
3.61473 − 5.50095I 0
u = −0.716415 − 0.853385I
a = 0.502942 + 1.047360I
b = 0.104207 − 0.712436I
3.61473 + 5.50095I 0
u = 1.124370 + 0.023892I
a = −1.76474 + 0.35679I
b = 0.851750 − 0.208072I
6.39464 + 1.13968I 0
u = 1.124370 − 0.023892I
a = −1.76474 − 0.35679I
b = 0.851750 + 0.208072I
6.39464 − 1.13968I 0
u = 0.566723 + 0.642863I
a = 0.135597 − 1.323930I
b = −1.097940 + 0.358861I
−2.05915 + 1.76225I 0
u = 0.566723 − 0.642863I
a = 0.135597 + 1.323930I
b = −1.097940 − 0.358861I
−2.05915 − 1.76225I 0
u = 1.102000 + 0.373121I
a = 0.532793 − 0.960517I
b = −0.191518 + 0.862539I
2.70359 + 3.26674I 0
u = 1.102000 − 0.373121I
a = 0.532793 + 0.960517I
b = −0.191518 − 0.862539I
2.70359 − 3.26674I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.279776 + 0.784788I
a = −1.51840 − 0.35367I
b = −0.790743 − 0.263954I
1.46625 + 1.20974I 0
u = −0.279776 − 0.784788I
a = −1.51840 + 0.35367I
b = −0.790743 + 0.263954I
1.46625 − 1.20974I 0
u = 1.022290 + 0.632834I
a = 0.023347 − 1.053100I
b = 0.177886 + 1.221810I
8.28927 + 10.45150I 0
u = 1.022290 − 0.632834I
a = 0.023347 + 1.053100I
b = 0.177886 − 1.221810I
8.28927 − 10.45150I 0
u = −1.155300 + 0.454833I
a = −0.561575 + 0.200722I
b = 0.667917 − 0.411478I
2.46824 − 1.00702I 0
u = −1.155300 − 0.454833I
a = −0.561575 − 0.200722I
b = 0.667917 + 0.411478I
2.46824 + 1.00702I 0
u = −0.913499 + 0.854540I
a = 0.09410 − 1.50305I
b = 1.148930 + 0.468555I
0.86302 − 4.48046I 0
u = −0.913499 − 0.854540I
a = 0.09410 + 1.50305I
b = 1.148930 − 0.468555I
0.86302 + 4.48046I 0
u = −0.673445 + 0.327727I
a = −0.111958 + 0.526638I
b = 0.491929 − 0.543095I
1.227580 − 0.394060I 0
u = −0.673445 − 0.327727I
a = −0.111958 − 0.526638I
b = 0.491929 + 0.543095I
1.227580 + 0.394060I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.096450 + 0.632837I
a = −0.049964 + 0.927017I
b = −0.230006 − 1.090050I
9.74860 + 4.47979I 0
u = 1.096450 − 0.632837I
a = −0.049964 − 0.927017I
b = −0.230006 + 1.090050I
9.74860 − 4.47979I 0
u = −0.796961 + 0.996614I
a = 0.275085 − 1.055370I
b = 1.011980 + 0.499831I
−0.33626 − 4.72282I 0
u = −0.796961 − 0.996614I
a = 0.275085 + 1.055370I
b = 1.011980 − 0.499831I
−0.33626 + 4.72282I 0
u = −0.572914 + 0.422408I
a = −0.215285 + 0.421413I
b = 1.020670 − 0.758296I
1.164470 − 0.722959I 0
u = −0.572914 − 0.422408I
a = −0.215285 − 0.421413I
b = 1.020670 + 0.758296I
1.164470 + 0.722959I 0
u = −0.978567 + 0.845945I
a = 0.14374 + 1.52350I
b = −1.221000 − 0.424375I
−0.15779 − 9.61338I 0
u = −0.978567 − 0.845945I
a = 0.14374 − 1.52350I
b = −1.221000 + 0.424375I
−0.15779 + 9.61338I 0
u = −0.772842 + 1.043420I
a = 0.079148 − 0.986729I
b = 1.179490 + 0.706716I
0.48900 − 5.35296I 0
u = −0.772842 − 1.043420I
a = 0.079148 + 0.986729I
b = 1.179490 − 0.706716I
0.48900 + 5.35296I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.774013 + 1.051790I
a = 0.041612 + 0.969778I
b = −1.31184 − 0.73020I
−0.77093 − 10.59390I 0
u = −0.774013 − 1.051790I
a = 0.041612 − 0.969778I
b = −1.31184 + 0.73020I
−0.77093 + 10.59390I 0
u = −0.769505 + 1.080340I
a = −0.036932 + 0.616536I
b = −1.300530 − 0.421555I
−4.57880 − 4.18550I 0
u = −0.769505 − 1.080340I
a = −0.036932 − 0.616536I
b = −1.300530 + 0.421555I
−4.57880 + 4.18550I 0
u = −0.324035 + 0.552616I
a = −0.07864 − 1.43992I
b = −0.279592 + 0.135545I
−1.33936 − 1.90829I −3.28849 + 4.48822I
u = −0.324035 − 0.552616I
a = −0.07864 + 1.43992I
b = −0.279592 − 0.135545I
−1.33936 + 1.90829I −3.28849 − 4.48822I
u = −1.06710 + 1.01825I
a = 0.195883 + 0.983581I
b = −1.087150 − 0.216785I
−3.63556 − 3.63723I 0
u = −1.06710 − 1.01825I
a = 0.195883 − 0.983581I
b = −1.087150 + 0.216785I
−3.63556 + 3.63723I 0
u = −1.37924 + 0.59849I
a = 0.610740 + 0.090379I
b = −0.896422 + 0.265763I
1.15451 + 3.72703I 0
u = −1.37924 − 0.59849I
a = 0.610740 − 0.090379I
b = −0.896422 − 0.265763I
1.15451 − 3.72703I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.113956 + 0.377311I
a = −0.081851 + 0.887678I
b = 1.24468 − 1.64088I
2.31339 + 2.06400I −22.0462 + 12.4650I
u = −0.113956 − 0.377311I
a = −0.081851 − 0.887678I
b = 1.24468 + 1.64088I
2.31339 − 2.06400I −22.0462 − 12.4650I
u = 0.335262 + 0.119310I
a = −1.09156 − 2.32545I
b = −1.073860 + 0.675324I
0.02842 + 2.19997I 4.77678 − 3.74049I
u = 0.335262 − 0.119310I
a = −1.09156 + 2.32545I
b = −1.073860 − 0.675324I
0.02842 − 2.19997I 4.77678 + 3.74049I
u = 0.048363 + 0.351944I
a = −0.110601 − 1.089750I
b = −1.32320 + 1.63039I
2.00559 − 2.59230I −21.8153 − 13.3624I
u = 0.048363 − 0.351944I
a = −0.110601 + 1.089750I
b = −1.32320 − 1.63039I
2.00559 + 2.59230I −21.8153 + 13.3624I
u = 0.335209 + 0.036264I
a = −2.55630 + 6.06495I
b = −0.820378 − 0.379925I
5.36519 − 7.03538I 8.75195 + 9.18938I
u = 0.335209 − 0.036264I
a = −2.55630 − 6.06495I
b = −0.820378 + 0.379925I
5.36519 + 7.03538I 8.75195 − 9.18938I
u = 1.23280 + 1.12711I
a = −0.049627 + 1.009430I
b = 1.32035 − 0.63988I
4.7027 + 16.9146I 0
u = 1.23280 − 1.12711I
a = −0.049627 − 1.009430I
b = 1.32035 + 0.63988I
4.7027 − 16.9146I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.285935 + 0.153568I
a = −0.31692 − 2.19667I
b = −0.366677 + 0.724507I
−0.05781 + 1.76242I 0.07414 − 5.41523I
u = 0.285935 − 0.153568I
a = −0.31692 + 2.19667I
b = −0.366677 − 0.724507I
−0.05781 − 1.76242I 0.07414 + 5.41523I
u = 0.312107 + 0.020941I
a = 4.10024 − 5.28583I
b = 0.865786 + 0.306816I
6.12753 − 1.30742I 8.16681 + 3.90506I
u = 0.312107 − 0.020941I
a = 4.10024 + 5.28583I
b = 0.865786 − 0.306816I
6.12753 + 1.30742I 8.16681 − 3.90506I
u = 1.25412 + 1.18786I
a = −0.018665 − 0.921057I
b = −1.262300 + 0.607915I
6.51212 + 10.46960I 0
u = 1.25412 − 1.18786I
a = −0.018665 + 0.921057I
b = −1.262300 − 0.607915I
6.51212 − 10.46960I 0
u = 0.255137
a = 3.04447
b = 1.33814
2.92476 1.67450
u = 1.90461 + 0.33298I
a = −0.204161 + 0.131039I
b = −0.442330 − 0.184001I
7.54983 + 0.02659I 0
u = 1.90461 − 0.33298I
a = −0.204161 − 0.131039I
b = −0.442330 + 0.184001I
7.54983 − 0.02659I 0
u = 0.14509 + 1.98112I
a = 0.515709 − 0.055700I
b = 0.763715 − 0.227475I
4.77190 − 4.51965I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.14509 − 1.98112I
a = 0.515709 + 0.055700I
b = 0.763715 + 0.227475I
4.77190 + 4.51965I 0
u = 1.59985 + 1.21883I
a = −0.126330 + 0.598225I
b = 1.272530 − 0.403885I
−1.70122 + 7.58589I 0
u = 1.59985 − 1.21883I
a = −0.126330 − 0.598225I
b = 1.272530 + 0.403885I
−1.70122 − 7.58589I 0
u = 1.09059 + 2.01824I
a = −0.300796 − 0.315309I
b = −0.970357 + 0.344452I
6.12754 + 2.96766I 0
u = 1.09059 − 2.01824I
a = −0.300796 + 0.315309I
b = −0.970357 − 0.344452I
6.12754 − 2.96766I 0
u = 1.80088 + 1.78506I
a = −0.0842697 − 0.0436608I
b = 0.923298 + 0.276341I
4.20118 − 6.97147I 0
u = 1.80088 − 1.78506I
a = −0.0842697 + 0.0436608I
b = 0.923298 − 0.276341I
4.20118 + 6.97147I 0
12
II. I
u
2
= h265u
11
+ 395u
10
+ · · · + b + 529, 62u
11
+ 109u
10
+ · · · + a +
184, u
12
+ 2u
11
+ · · · + 8u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
4
=
−62u
11
− 109u
10
+ ··· − 992u − 184
−265u
11
− 395u
10
+ ··· − 3159u − 529
a
9
=
1
−u
2
a
5
=
−326u
11
− 507u
10
+ ··· − 4209u − 728
−200u
11
− 298u
10
+ ··· − 2383u − 399
a
1
=
−47u
11
− 78u
10
+ ··· − 679u − 122
−2u
11
− 3u
10
+ ··· − 31u − 8
a
3
=
−327u
11
− 504u
10
+ ··· − 4151u − 713
−265u
11
− 395u
10
+ ··· − 3159u − 529
a
2
=
−327u
11
− 504u
10
+ ··· − 4150u − 713
−89u
11
− 123u
10
+ ··· − 919u − 145
a
7
=
7u
11
+ 13u
10
+ ··· + 137u + 32
−u
11
− u
10
− 4u
7
+ 4u
6
+ 11u
5
+ 6u
4
− 15u
3
− 16u
2
− 8u − 1
a
10
=
25u
11
+ 44u
10
+ ··· + 423u + 87
u + 1
a
6
=
−55u
11
− 92u
10
+ ··· − 824u − 154
−2u
11
− 3u
10
+ ··· − 31u − 7
a
6
=
−55u
11
− 92u
10
+ ··· − 824u − 154
−2u
11
− 3u
10
+ ··· − 31u − 7
(ii) Obstruction class = 1
(iii) Cusp Shapes = 343u
11
+ 435u
10
+ 7u
9
− 22u
8
+ 1393u
7
− 1020u
6
− 4470u
5
−
2485u
4
+ 5112u
3
+ 6955u
2
+ 2864u + 383
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
− 2u
11
+ ··· − 2u + 1
c
2
u
12
+ 6u
11
+ ··· + 6u + 1
c
3
u
12
− u
10
+ u
9
− u
8
− u
7
+ 4u
6
− u
5
− u
4
+ u
3
− 2u
2
+ 1
c
4
u
12
− 2u
10
− u
9
− u
8
+ u
7
+ 4u
6
+ u
5
− u
4
− u
3
− u
2
+ 1
c
5
u
12
+ 2u
11
+ ··· + 2u + 1
c
6
u
12
− 4u
11
+ ··· − 2u + 1
c
7
u
12
− u
10
− u
9
− u
8
+ u
7
+ 4u
6
+ u
5
− u
4
− u
3
− 2u
2
+ 1
c
8
u
12
+ 2u
11
+ u
10
+ 4u
8
− 15u
6
− 17u
5
+ 9u
4
+ 31u
3
+ 24u
2
+ 8u + 1
c
9
u
12
− 2u
10
+ u
9
− u
8
− u
7
+ 4u
6
− u
5
− u
4
+ u
3
− u
2
+ 1
c
10
u
12
+ 4u
11
+ ··· + 2u + 1
c
11
u
12
− 3u
11
+ ··· − 4u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
12
+ 6y
11
+ ··· + 6y + 1
c
2
y
12
+ 6y
11
+ ··· − 2y + 1
c
3
, c
7
y
12
− 2y
11
+ ··· − 4y + 1
c
4
, c
9
y
12
− 4y
11
+ ··· − 2y + 1
c
6
, c
10
y
12
− 12y
11
+ ··· − 6y + 1
c
8
y
12
− 2y
11
+ ··· − 16y + 1
c
11
y
12
− y
11
+ ··· + 8y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.741008 + 0.843928I
a = −0.272841 + 1.370800I
b = −0.984853 − 0.549799I
−0.94624 − 4.30351I −2.15264 + 4.03867I
u = −0.741008 − 0.843928I
a = −0.272841 − 1.370800I
b = −0.984853 + 0.549799I
−0.94624 + 4.30351I −2.15264 − 4.03867I
u = 1.262580 + 0.345242I
a = −1.032950 + 0.632710I
b = 0.754976 + 0.043647I
6.38132 + 0.21376I 6.25984 + 0.75137I
u = 1.262580 − 0.345242I
a = −1.032950 − 0.632710I
b = 0.754976 − 0.043647I
6.38132 − 0.21376I 6.25984 − 0.75137I
u = −0.578234 + 0.042931I
a = 0.384529 + 0.999319I
b = −0.102518 − 1.164980I
0.61422 − 1.43941I 10.88514 + 4.78461I
u = −0.578234 − 0.042931I
a = 0.384529 − 0.999319I
b = −0.102518 + 1.164980I
0.61422 + 1.43941I 10.88514 − 4.78461I
u = −1.24859 + 0.90135I
a = −0.191342 − 0.800979I
b = 1.210650 + 0.425814I
−2.97178 − 6.11551I 1.52678 + 5.55521I
u = −1.24859 − 0.90135I
a = −0.191342 + 0.800979I
b = 1.210650 − 0.425814I
−2.97178 + 6.11551I 1.52678 − 5.55521I
u = −0.457639 + 0.024191I
a = 0.547649 − 0.753294I
b = −0.044719 − 0.917677I
2.40807 + 2.46975I 4.62403 − 2.63831I
u = −0.457639 − 0.024191I
a = 0.547649 + 0.753294I
b = −0.044719 + 0.917677I
2.40807 − 2.46975I 4.62403 + 2.63831I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.76289 + 1.47705I
a = −0.435041 − 0.572739I
b = −0.833532 − 0.167507I
4.38401 − 5.97653I 5.35684 + 3.69125I
u = 0.76289 − 1.47705I
a = −0.435041 + 0.572739I
b = −0.833532 + 0.167507I
4.38401 + 5.97653I 5.35684 − 3.69125I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
12
− 2u
11
+ ··· − 2u + 1)(u
77
− u
76
+ ··· + 15u − 1)
c
2
(u
12
+ 6u
11
+ ··· + 6u + 1)(u
77
+ 29u
76
+ ··· − 41u − 1)
c
3
(u
12
− u
10
+ u
9
− u
8
− u
7
+ 4u
6
− u
5
− u
4
+ u
3
− 2u
2
+ 1)
· (u
77
− u
76
+ ··· − 165u − 29)
c
4
(u
12
− 2u
10
− u
9
− u
8
+ u
7
+ 4u
6
+ u
5
− u
4
− u
3
− u
2
+ 1)
· (u
77
+ u
76
+ ··· − 1709u − 751)
c
5
(u
12
+ 2u
11
+ ··· + 2u + 1)(u
77
− u
76
+ ··· + 15u − 1)
c
6
(u
12
− 4u
11
+ ··· − 2u + 1)(u
77
− u
76
+ ··· + 2607u − 121)
c
7
(u
12
− u
10
− u
9
− u
8
+ u
7
+ 4u
6
+ u
5
− u
4
− u
3
− 2u
2
+ 1)
· (u
77
− u
76
+ ··· − 165u − 29)
c
8
(u
12
+ 2u
11
+ u
10
+ 4u
8
− 15u
6
− 17u
5
+ 9u
4
+ 31u
3
+ 24u
2
+ 8u + 1)
· (u
77
+ 9u
76
+ ··· + 21u + 1)
c
9
(u
12
− 2u
10
+ u
9
− u
8
− u
7
+ 4u
6
− u
5
− u
4
+ u
3
− u
2
+ 1)
· (u
77
+ u
76
+ ··· − 1709u − 751)
c
10
(u
12
+ 4u
11
+ ··· + 2u + 1)(u
77
− u
76
+ ··· + 2607u − 121)
c
11
(u
12
− 3u
11
+ ··· − 4u + 1)(u
77
− 2u
76
+ ··· − 11u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
12
+ 6y
11
+ ··· + 6y + 1)(y
77
+ 29y
76
+ ··· − 41y −1)
c
2
(y
12
+ 6y
11
+ ··· − 2y + 1)(y
77
+ 45y
76
+ ··· − 1989y −1)
c
3
, c
7
(y
12
− 2y
11
+ ··· − 4y + 1)(y
77
− 39y
76
+ ··· + 32561y −841)
c
4
, c
9
(y
12
− 4y
11
+ ··· − 2y + 1)(y
77
− 57y
76
+ ··· − 8745353y −564001)
c
6
, c
10
(y
12
− 12y
11
+ ··· − 6y + 1)(y
77
− 61y
76
+ ··· + 895279y −14641)
c
8
(y
12
− 2y
11
+ ··· − 16y + 1)(y
77
− 7y
76
+ ··· + 53y −1)
c
11
(y
12
− y
11
+ ··· + 8y + 1)(y
77
+ 2y
76
+ ··· − 43y −1)
19
