12n
0410
(K12n
0410
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 9 4 12 5 7 8 9
Solving Sequence
5,9 10,12
1 4 8 3 2 7 6 11
c
9
c
12
c
4
c
8
c
3
c
1
c
7
c
6
c
11
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.43647 × 10
106
u
70
+ 9.27917 × 10
106
u
69
+ ··· + 4.05492 × 10
107
b − 2.66090 × 10
107
,
− 2.33553 × 10
108
u
70
− 2.92909 × 10
108
u
69
+ ··· + 4.05492 × 10
107
a + 1.64345 × 10
109
,
u
71
+ u
70
+ ··· − 18u + 1i
I
u
2
= hu
2
+ b + 1, u
15
+ u
14
+ ··· + a − 4,
u
16
+ 10u
14
+ 40u
12
+ u
11
+ 82u
10
+ 7u
9
+ 92u
8
+ 18u
7
+ 58u
6
+ 21u
5
+ 25u
4
+ 11u
3
+ 10u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 87 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−3.44 × 10
106
u
70
+ 9.28 × 10
106
u
69
+ · · · + 4.05 × 10
107
b − 2.66 ×
10
107
, −2.34 × 10
108
u
70
− 2.93 × 10
108
u
69
+ · · · + 4.05 × 10
107
a + 1.64 ×
10
109
, u
71
+ u
70
+ · · · − 18u + 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
12
=
5.75975u
70
+ 7.22354u
69
+ ··· + 413.326u − 40.5299
0.0847481u
70
− 0.228837u
69
+ ··· − 1.63551u + 0.656214
a
1
=
5.84450u
70
+ 6.99470u
69
+ ··· + 411.690u − 39.8736
0.0847481u
70
− 0.228837u
69
+ ··· − 1.63551u + 0.656214
a
4
=
u
u
3
+ u
a
8
=
3.49699u
70
+ 4.19855u
69
+ ··· + 350.333u − 33.4246
0.239548u
70
+ 0.356147u
69
+ ··· + 3.79911u + 0.0294177
a
3
=
0.732278u
70
+ 1.28940u
69
+ ··· + 57.6526u − 22.5177
−0.0601700u
70
− 0.435875u
69
+ ··· + 18.4320u − 2.09649
a
2
=
−3.03287u
70
− 3.14673u
69
+ ··· − 288.328u + 33.4675
0.443733u
70
+ 0.847315u
69
+ ··· − 10.9879u + 0.729411
a
7
=
3.33586u
70
+ 3.74761u
69
+ ··· + 351.145u − 33.2572
0.284126u
70
+ 0.525249u
69
+ ··· − 0.443567u + 0.486594
a
6
=
3.61999u
70
+ 4.27286u
69
+ ··· + 350.702u − 32.7706
0.284126u
70
+ 0.525249u
69
+ ··· − 0.443567u + 0.486594
a
11
=
3.08919u
70
+ 3.79307u
69
+ ··· + 183.569u − 16.3818
−0.264976u
70
− 0.884934u
69
+ ··· − 4.44816u + 0.538795
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.714658u
70
+ 0.411160u
69
+ ··· − 172.611u + 3.21683
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
71
+ 37u
70
+ ··· + 39u + 1
c
2
, c
5
u
71
+ u
70
+ ··· − 5u + 1
c
3
, c
7
u
71
+ 2u
70
+ ··· + 938u + 419
c
4
, c
9
u
71
+ u
70
+ ··· − 18u + 1
c
6
u
71
− 11u
70
+ ··· + 45238u + 33013
c
8
, c
11
, c
12
u
71
− 3u
70
+ ··· + 182u + 73
c
10
u
71
+ 3u
70
+ ··· − 1366u + 113
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
71
+ 3y
70
+ ··· + 75y −1
c
2
, c
5
y
71
− 37y
70
+ ··· + 39y −1
c
3
, c
7
y
71
+ 32y
70
+ ··· − 3750944y −175561
c
4
, c
9
y
71
+ 63y
70
+ ··· + 108y −1
c
6
y
71
− 9y
70
+ ··· + 48618179848y −1089858169
c
8
, c
11
, c
12
y
71
− 29y
70
+ ··· + 317240y −5329
c
10
y
71
− y
70
+ ··· + 908846y −12769
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215895 + 0.983718I
a = 0.589334 − 0.165404I
b = −0.879742 − 0.511318I
1.75447 + 1.33869I 0
u = 0.215895 − 0.983718I
a = 0.589334 + 0.165404I
b = −0.879742 + 0.511318I
1.75447 − 1.33869I 0
u = −1.034460 + 0.273032I
a = −0.310181 + 1.214850I
b = 1.25991 + 0.78950I
−3.60320 + 10.88280I 0
u = −1.034460 − 0.273032I
a = −0.310181 − 1.214850I
b = 1.25991 − 0.78950I
−3.60320 − 10.88280I 0
u = 0.863903 + 0.285907I
a = 0.419083 + 0.810149I
b = 0.502982 + 1.144460I
−5.98210 − 3.93114I −10.12837 + 4.65462I
u = 0.863903 − 0.285907I
a = 0.419083 − 0.810149I
b = 0.502982 − 1.144460I
−5.98210 + 3.93114I −10.12837 − 4.65462I
u = −0.891768 + 0.070118I
a = 0.15503 − 1.61433I
b = 0.865255 − 0.883952I
−5.06777 − 1.72842I −9.03248 + 1.95766I
u = −0.891768 − 0.070118I
a = 0.15503 + 1.61433I
b = 0.865255 + 0.883952I
−5.06777 + 1.72842I −9.03248 − 1.95766I
u = 0.858375 + 0.211623I
a = −0.41891 − 1.51444I
b = 1.096520 − 0.693922I
−0.51051 − 5.75064I −3.89282 + 5.23747I
u = 0.858375 − 0.211623I
a = −0.41891 + 1.51444I
b = 1.096520 + 0.693922I
−0.51051 + 5.75064I −3.89282 − 5.23747I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.495327 + 1.001070I
a = 0.956532 + 0.720660I
b = −0.499506 + 0.873457I
−3.81338 − 0.91720I 0
u = 0.495327 − 1.001070I
a = 0.956532 − 0.720660I
b = −0.499506 − 0.873457I
−3.81338 + 0.91720I 0
u = 0.852063 + 0.003332I
a = 0.570898 − 0.952541I
b = 0.941084 − 0.848655I
−4.83336 − 4.67682I −8.91178 + 3.62804I
u = 0.852063 − 0.003332I
a = 0.570898 + 0.952541I
b = 0.941084 + 0.848655I
−4.83336 + 4.67682I −8.91178 − 3.62804I
u = 0.728501 + 0.383628I
a = 0.609475 + 0.530243I
b = −1.021450 − 0.201318I
1.66148 + 1.60219I −0.85852 − 4.44801I
u = 0.728501 − 0.383628I
a = 0.609475 − 0.530243I
b = −1.021450 + 0.201318I
1.66148 − 1.60219I −0.85852 + 4.44801I
u = −0.801396 + 0.186918I
a = 0.435494 + 0.875125I
b = −0.579792 + 0.108548I
−0.08587 − 1.45375I −4.06625 + 0.26026I
u = −0.801396 − 0.186918I
a = 0.435494 − 0.875125I
b = −0.579792 − 0.108548I
−0.08587 + 1.45375I −4.06625 − 0.26026I
u = −0.029612 + 1.179580I
a = −0.715627 + 0.669083I
b = 1.015610 − 0.624913I
4.02651 − 1.18106I 0
u = −0.029612 − 1.179580I
a = −0.715627 − 0.669083I
b = 1.015610 + 0.624913I
4.02651 + 1.18106I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.044105 + 1.211070I
a = −2.72874 − 0.40673I
b = 0.734871 − 0.897217I
2.77599 − 4.56849I 0
u = 0.044105 − 1.211070I
a = −2.72874 + 0.40673I
b = 0.734871 + 0.897217I
2.77599 + 4.56849I 0
u = 0.373923 + 1.168140I
a = −0.735197 + 0.107279I
b = 0.917139 − 0.074511I
4.27301 − 5.82007I 0
u = 0.373923 − 1.168140I
a = −0.735197 − 0.107279I
b = 0.917139 + 0.074511I
4.27301 + 5.82007I 0
u = −0.310509 + 1.196830I
a = 0.839804 − 0.739127I
b = −0.785280 − 0.707355I
1.34885 + 3.63857I 0
u = −0.310509 − 1.196830I
a = 0.839804 + 0.739127I
b = −0.785280 + 0.707355I
1.34885 − 3.63857I 0
u = 0.075611 + 1.234620I
a = 5.12968 + 2.04707I
b = −0.673053 + 0.192726I
7.70644 − 3.86757I 0
u = 0.075611 − 1.234620I
a = 5.12968 − 2.04707I
b = −0.673053 − 0.192726I
7.70644 + 3.86757I 0
u = −0.410342 + 1.186330I
a = −1.72235 + 1.94541I
b = 0.608459 + 0.094132I
2.97939 + 5.92999I 0
u = −0.410342 − 1.186330I
a = −1.72235 − 1.94541I
b = 0.608459 − 0.094132I
2.97939 − 5.92999I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.729742 + 0.114637I
a = 0.618046 − 0.750040I
b = 0.630374 − 0.759705I
−1.95583 + 0.14817I −7.00132 − 0.69470I
u = −0.729742 − 0.114637I
a = 0.618046 + 0.750040I
b = 0.630374 + 0.759705I
−1.95583 − 0.14817I −7.00132 + 0.69470I
u = −0.021725 + 1.263670I
a = −0.677026 − 0.120394I
b = −0.752422 + 0.007514I
8.01619 + 2.99746I 0
u = −0.021725 − 1.263670I
a = −0.677026 + 0.120394I
b = −0.752422 − 0.007514I
8.01619 − 2.99746I 0
u = −0.413858 + 1.213910I
a = 1.27530 − 1.84827I
b = −0.805605 − 0.898461I
−1.55000 + 6.39536I 0
u = −0.413858 − 1.213910I
a = 1.27530 + 1.84827I
b = −0.805605 + 0.898461I
−1.55000 − 6.39536I 0
u = 0.158281 + 1.275040I
a = −2.74022 − 0.73963I
b = 0.811606 + 0.350669I
6.58304 − 0.58218I 0
u = 0.158281 − 1.275040I
a = −2.74022 + 0.73963I
b = 0.811606 − 0.350669I
6.58304 + 0.58218I 0
u = −0.790440 + 1.070780I
a = 0.367717 − 0.165936I
b = −1.28280 + 0.61070I
−1.27848 − 4.71003I 0
u = −0.790440 − 1.070780I
a = 0.367717 + 0.165936I
b = −1.28280 − 0.61070I
−1.27848 + 4.71003I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.384604 + 1.283090I
a = 0.905704 + 0.769999I
b = −0.892660 + 0.805268I
−0.82831 − 9.10842I 0
u = 0.384604 − 1.283090I
a = 0.905704 − 0.769999I
b = −0.892660 − 0.805268I
−0.82831 + 9.10842I 0
u = 0.411196 + 1.277040I
a = −0.287177 + 0.546454I
b = −1.036780 − 0.878537I
−0.870786 + 0.150985I 0
u = 0.411196 − 1.277040I
a = −0.287177 − 0.546454I
b = −1.036780 + 0.878537I
−0.870786 − 0.150985I 0
u = −0.062315 + 1.356300I
a = −0.536885 − 0.568354I
b = 0.622978 + 0.855958I
4.73209 + 4.54811I 0
u = −0.062315 − 1.356300I
a = −0.536885 + 0.568354I
b = 0.622978 − 0.855958I
4.73209 − 4.54811I 0
u = −0.271944 + 1.345690I
a = −0.490299 − 0.243669I
b = 0.495860 − 0.020177I
4.81607 + 2.25039I 0
u = −0.271944 − 1.345690I
a = −0.490299 + 0.243669I
b = 0.495860 + 0.020177I
4.81607 − 2.25039I 0
u = 0.182403 + 0.589273I
a = 0.996728 − 0.100964I
b = −0.991109 − 0.385570I
1.70326 + 1.36799I 0.40449 − 3.56103I
u = 0.182403 − 0.589273I
a = 0.996728 + 0.100964I
b = −0.991109 + 0.385570I
1.70326 − 1.36799I 0.40449 + 3.56103I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.431353 + 1.324400I
a = 0.293265 + 0.052341I
b = −0.943113 + 0.822147I
−0.70979 + 3.01801I 0
u = −0.431353 − 1.324400I
a = 0.293265 − 0.052341I
b = −0.943113 − 0.822147I
−0.70979 − 3.01801I 0
u = −0.297751 + 1.379490I
a = −0.354498 − 0.522063I
b = −0.529414 + 0.965808I
2.81600 + 3.85009I 0
u = −0.297751 − 1.379490I
a = −0.354498 + 0.522063I
b = −0.529414 − 0.965808I
2.81600 − 3.85009I 0
u = 0.072525 + 0.577336I
a = 1.009780 − 0.310556I
b = −1.024930 − 0.366527I
1.70099 + 1.36936I 0.45558 − 4.27250I
u = 0.072525 − 0.577336I
a = 1.009780 + 0.310556I
b = −1.024930 + 0.366527I
1.70099 − 1.36936I 0.45558 + 4.27250I
u = 0.38135 + 1.40084I
a = 1.72461 + 1.25646I
b = −1.136280 + 0.778925I
4.58064 − 10.24330I 0
u = 0.38135 − 1.40084I
a = 1.72461 − 1.25646I
b = −1.136280 − 0.778925I
4.58064 + 10.24330I 0
u = 0.35642 + 1.47308I
a = −0.357872 + 0.562711I
b = −0.58989 − 1.37575I
−0.32317 − 8.36888I 0
u = 0.35642 − 1.47308I
a = −0.357872 − 0.562711I
b = −0.58989 + 1.37575I
−0.32317 + 8.36888I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.44180 + 1.45915I
a = 1.55032 − 1.07079I
b = −1.26177 − 0.88192I
1.8628 + 16.1602I 0
u = −0.44180 − 1.45915I
a = 1.55032 + 1.07079I
b = −1.26177 + 0.88192I
1.8628 − 16.1602I 0
u = −0.384489
a = 0.931181
b = 0.216711
−0.795110 −12.9180
u = −0.01278 + 1.63519I
a = −1.81847 − 0.01243I
b = 1.95257 + 0.19361I
9.71665 + 1.57100I 0
u = −0.01278 − 1.63519I
a = −1.81847 + 0.01243I
b = 1.95257 − 0.19361I
9.71665 − 1.57100I 0
u = 0.07124 + 1.74068I
a = −1.55530 − 0.11713I
b = 1.62577 − 0.01058I
10.11340 − 1.78495I 0
u = 0.07124 − 1.74068I
a = −1.55530 + 0.11713I
b = 1.62577 + 0.01058I
10.11340 + 1.78495I 0
u = 0.018862 + 0.200440I
a = −3.71179 − 0.53258I
b = −0.727811 − 0.911451I
−0.32381 + 4.17151I −4.56463 − 9.46069I
u = 0.018862 − 0.200440I
a = −3.71179 + 0.53258I
b = −0.727811 + 0.911451I
−0.32381 − 4.17151I −4.56463 + 9.46069I
u = 0.0994581 + 0.0263391I
a = 4.2481 + 18.4423I
b = 0.724058 + 0.102943I
4.07198 + 3.05309I −15.3128 − 6.7632I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.0994581 − 0.0263391I
a = 4.2481 − 18.4423I
b = 0.724058 − 0.102943I
4.07198 − 3.05309I −15.3128 + 6.7632I
12
II. I
u
2
= hu
2
+ b + 1, u
15
+ u
14
+ · · · + a − 4, u
16
+ 10u
14
+ · · · + 2u + 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
12
=
−u
15
− u
14
+ ··· − 5u + 4
−u
2
− 1
a
1
=
−u
15
− u
14
+ ··· − 5u + 3
−u
2
− 1
a
4
=
u
u
3
+ u
a
8
=
u
15
− 2u
14
+ ··· + 2u − 4
u
4
+ 2u
2
+ 1
a
3
=
3u
15
+ 28u
13
+ ··· + 17u + 5
−u
13
− 8u
11
+ ··· − 3u − 1
a
2
=
2u
15
+ 19u
13
+ ··· + 12u
2
+ 10u
u
14
− u
13
+ ··· + 2u
2
− u
a
7
=
u
15
− u
14
+ ··· + 3u − 4
−u
14
− 8u
12
+ ··· − 3u
2
− u
a
6
=
u
15
− 2u
14
+ ··· + 2u − 4
−u
14
− 8u
12
+ ··· − 3u
2
− u
a
11
=
−u
14
− 8u
12
+ ··· − 2u
2
+ 2
u
6
+ 3u
4
+ 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
15
+ 4u
14
− 21u
13
+ 35u
12
− 88u
11
+ 121u
10
− 184u
9
+
211u
8
− 196u
7
+ 193u
6
− 95u
5
+ 87u
4
− 14u
3
+ 25u
2
− 2u + 10
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 8u
15
+ ··· − 11u + 1
c
2
u
16
− 4u
14
+ ··· + u + 1
c
3
u
16
+ u
15
+ ··· + 6u
2
+ 1
c
4
u
16
+ 10u
14
+ ··· − 2u + 1
c
5
u
16
− 4u
14
+ ··· − u + 1
c
6
u
16
+ 4u
15
+ ··· + 8u + 1
c
7
u
16
− u
15
+ ··· + 6u
2
+ 1
c
8
u
16
− 4u
15
+ ··· − 4u + 1
c
9
u
16
+ 10u
14
+ ··· + 2u + 1
c
10
u
16
+ 2u
14
+ ··· + 6u + 1
c
11
, c
12
u
16
+ 4u
15
+ ··· + 4u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ 8y
15
+ ··· + y + 1
c
2
, c
5
y
16
− 8y
15
+ ··· − 11y + 1
c
3
, c
7
y
16
+ 13y
15
+ ··· + 12y + 1
c
4
, c
9
y
16
+ 20y
15
+ ··· + 16y + 1
c
6
y
16
+ 8y
15
+ ··· − 20y + 1
c
8
, c
11
, c
12
y
16
− 16y
15
+ ··· − 12y + 1
c
10
y
16
+ 4y
15
+ ··· − 10y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.538323 + 0.609436I
a = 0.301986 − 0.587035I
b = −0.918380 − 0.656147I
−0.33171 + 3.10177I −4.27402 − 2.35012I
u = 0.538323 − 0.609436I
a = 0.301986 + 0.587035I
b = −0.918380 + 0.656147I
−0.33171 − 3.10177I −4.27402 + 2.35012I
u = −0.048339 + 1.222850I
a = 1.81741 − 1.11259I
b = 0.493024 + 0.118223I
7.19096 + 3.42244I −3.10678 − 2.43444I
u = −0.048339 − 1.222850I
a = 1.81741 + 1.11259I
b = 0.493024 − 0.118223I
7.19096 − 3.42244I −3.10678 + 2.43444I
u = 0.291351 + 1.201680I
a = −1.87567 − 0.05805I
b = 0.359153 − 0.700221I
1.84258 − 6.14957I −5.00852 + 7.34248I
u = 0.291351 − 1.201680I
a = −1.87567 + 0.05805I
b = 0.359153 + 0.700221I
1.84258 + 6.14957I −5.00852 − 7.34248I
u = −0.177579 + 1.300220I
a = −0.693391 − 0.115475I
b = 0.659034 + 0.461783I
4.53158 + 3.04680I −2.03030 − 5.70697I
u = −0.177579 − 1.300220I
a = −0.693391 + 0.115475I
b = 0.659034 − 0.461783I
4.53158 − 3.04680I −2.03030 + 5.70697I
u = −0.470847 + 0.357752I
a = 0.315886 − 0.653261I
b = −1.093710 + 0.336893I
1.130760 − 0.806623I −6.80428 − 2.97898I
u = −0.470847 − 0.357752I
a = 0.315886 + 0.653261I
b = −1.093710 − 0.336893I
1.130760 + 0.806623I −6.80428 + 2.97898I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.01876 + 1.58439I
a = −1.99295 + 0.09965I
b = 1.50993 + 0.05944I
11.46500 − 2.59376I 3.82711 + 3.90143I
u = −0.01876 − 1.58439I
a = −1.99295 − 0.09965I
b = 1.50993 − 0.05944I
11.46500 + 2.59376I 3.82711 − 3.90143I
u = −0.076930 + 0.383712I
a = 4.77737 − 0.98552I
b = −0.858683 + 0.059038I
4.38379 − 2.94039I 7.82295 − 1.05341I
u = −0.076930 − 0.383712I
a = 4.77737 + 0.98552I
b = −0.858683 − 0.059038I
4.38379 + 2.94039I 7.82295 + 1.05341I
u = −0.03722 + 1.68849I
a = −1.65065 + 0.07468I
b = 1.84963 + 0.12569I
9.26542 + 1.37057I −9.92616 + 2.04030I
u = −0.03722 − 1.68849I
a = −1.65065 − 0.07468I
b = 1.84963 − 0.12569I
9.26542 − 1.37057I −9.92616 − 2.04030I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
16
− 8u
15
+ ··· − 11u + 1)(u
71
+ 37u
70
+ ··· + 39u + 1)
c
2
(u
16
− 4u
14
+ ··· + u + 1)(u
71
+ u
70
+ ··· − 5u + 1)
c
3
(u
16
+ u
15
+ ··· + 6u
2
+ 1)(u
71
+ 2u
70
+ ··· + 938u + 419)
c
4
(u
16
+ 10u
14
+ ··· − 2u + 1)(u
71
+ u
70
+ ··· − 18u + 1)
c
5
(u
16
− 4u
14
+ ··· − u + 1)(u
71
+ u
70
+ ··· − 5u + 1)
c
6
(u
16
+ 4u
15
+ ··· + 8u + 1)(u
71
− 11u
70
+ ··· + 45238u + 33013)
c
7
(u
16
− u
15
+ ··· + 6u
2
+ 1)(u
71
+ 2u
70
+ ··· + 938u + 419)
c
8
(u
16
− 4u
15
+ ··· − 4u + 1)(u
71
− 3u
70
+ ··· + 182u + 73)
c
9
(u
16
+ 10u
14
+ ··· + 2u + 1)(u
71
+ u
70
+ ··· − 18u + 1)
c
10
(u
16
+ 2u
14
+ ··· + 6u + 1)(u
71
+ 3u
70
+ ··· − 1366u + 113)
c
11
, c
12
(u
16
+ 4u
15
+ ··· + 4u + 1)(u
71
− 3u
70
+ ··· + 182u + 73)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
16
+ 8y
15
+ ··· + y + 1)(y
71
+ 3y
70
+ ··· + 75y −1)
c
2
, c
5
(y
16
− 8y
15
+ ··· − 11y + 1)(y
71
− 37y
70
+ ··· + 39y −1)
c
3
, c
7
(y
16
+ 13y
15
+ ··· + 12y + 1)
· (y
71
+ 32y
70
+ ··· − 3750944y −175561)
c
4
, c
9
(y
16
+ 20y
15
+ ··· + 16y + 1)(y
71
+ 63y
70
+ ··· + 108y −1)
c
6
(y
16
+ 8y
15
+ ··· − 20y + 1)
· (y
71
− 9y
70
+ ··· + 48618179848y −1089858169)
c
8
, c
11
, c
12
(y
16
− 16y
15
+ ··· − 12y + 1)(y
71
− 29y
70
+ ··· + 317240y −5329)
c
10
(y
16
+ 4y
15
+ ··· − 10y + 1)(y
71
− y
70
+ ··· + 908846y −12769)
19
