12a
0279
(K12a
0279
)
A knot diagram
1
Linearized knot diagam
3 6 8 9 2 12 10 5 4 1 7 11
Solving Sequence
4,9
5
1,10
11 8 3 2 7 12 6
c
4
c
9
c
10
c
8
c
3
c
1
c
7
c
12
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.21213 × 10
48
u
89
− 4.02565 × 10
48
u
88
+ ··· + 4.69496 × 10
48
b − 7.32492 × 10
48
,
1.52568 × 10
48
u
89
− 3.14305 × 10
48
u
88
+ ··· + 4.69496 × 10
48
a + 3.64549 × 10
48
, u
90
+ u
89
+ ··· − 8u + 4i
I
u
2
= hb − 2a − 1, 2a
2
+ au + 4a + u + 1, u
2
+ 2i
I
v
1
= ha, b + 1, v
2
+ v + 1i
* 3 irreducible components of dim
C
= 0, with total 96 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−1.21×10
48
u
89
−4.03×10
48
u
88
+· · ·+4.69×10
48
b−7.32×10
48
, 1.53×
10
48
u
89
−3.14×10
48
u
88
+· · ·+4.69×10
48
a+3.65×10
48
, u
90
+u
89
+· · ·−8u+4i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
1
=
−0.324961u
89
+ 0.669451u
88
+ ··· − 2.00627u − 0.776469
0.258177u
89
+ 0.857440u
88
+ ··· − 3.95149u + 1.56017
a
10
=
u
u
a
11
=
−0.0541425u
89
− 1.58665u
88
+ ··· + 14.2281u − 6.14640
0.819260u
89
− 1.18304u
88
+ ··· + 8.11565u − 3.84392
a
8
=
−u
u
3
+ u
a
3
=
−u
4
− u
2
+ 1
u
6
+ 2u
4
+ u
2
a
2
=
−0.342702u
89
+ 0.132880u
88
+ ··· + 2.50106u − 3.05984
0.245541u
89
+ 0.307126u
88
+ ··· − 3.58009u + 1.32787
a
7
=
−u
5
− 2u
3
− u
−u
5
− u
3
+ u
a
12
=
−0.121690u
89
− 1.29232u
88
+ ··· + 10.9200u − 5.18322
0.514237u
89
− 1.25759u
88
+ ··· + 6.90051u − 3.39690
a
6
=
0.645491u
89
− 0.0589180u
88
+ ··· + 0.373830u + 2.57549
1.13689u
89
+ 0.882237u
88
+ ··· + 3.67121u − 0.618462
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.39908u
89
− 4.87459u
88
+ ··· − 1.48366u + 5.99189
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
90
+ 49u
89
+ ··· + 64u + 9
c
2
, c
5
u
90
+ 3u
89
+ ··· + 8u + 3
c
3
u
90
+ u
89
+ ··· + 25496u + 8452
c
4
, c
8
, c
9
u
90
− u
89
+ ··· + 8u + 4
c
6
, c
11
u
90
− 2u
89
+ ··· + 5u + 3
c
7
u
90
+ 15u
89
+ ··· + 14592u + 2304
c
10
, c
12
u
90
+ 32u
89
+ ··· + 101u + 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
90
− 9y
89
+ ··· − 1180y + 81
c
2
, c
5
y
90
− 49y
89
+ ··· − 64y + 9
c
3
y
90
+ 25y
89
+ ··· + 1049955456y + 71436304
c
4
, c
8
, c
9
y
90
+ 85y
89
+ ··· − 192y + 16
c
6
, c
11
y
90
+ 32y
89
+ ··· + 101y + 9
c
7
y
90
+ 49y
89
+ ··· + 40402944y + 5308416
c
10
, c
12
y
90
+ 56y
89
+ ··· + 1517y + 81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.249552 + 1.084800I
a = −0.924355 + 0.774803I
b = 0.198066 + 0.911560I
2.16967 − 1.69067I 0
u = 0.249552 − 1.084800I
a = −0.924355 − 0.774803I
b = 0.198066 − 0.911560I
2.16967 + 1.69067I 0
u = −0.568513 + 0.621394I
a = 1.30855 − 0.85772I
b = −0.363076 − 0.238702I
−1.48585 + 8.08974I 0. − 5.15061I
u = −0.568513 − 0.621394I
a = 1.30855 + 0.85772I
b = −0.363076 + 0.238702I
−1.48585 − 8.08974I 0. + 5.15061I
u = −0.738744 + 0.379283I
a = 0.748547 + 0.652206I
b = 0.90937 − 1.22327I
−0.63451 − 12.52790I 1.19702 + 10.10489I
u = −0.738744 − 0.379283I
a = 0.748547 − 0.652206I
b = 0.90937 + 1.22327I
−0.63451 + 12.52790I 1.19702 − 10.10489I
u = −0.262408 + 1.154250I
a = −1.108300 − 0.437411I
b = −0.065136 − 0.883635I
2.00112 − 3.95850I 0
u = −0.262408 − 1.154250I
a = −1.108300 + 0.437411I
b = −0.065136 + 0.883635I
2.00112 + 3.95850I 0
u = 0.519114 + 0.626640I
a = 0.995537 + 0.900909I
b = −0.058580 + 0.291151I
−0.36877 − 2.59359I 1.68494 + 0.36252I
u = 0.519114 − 0.626640I
a = 0.995537 − 0.900909I
b = −0.058580 − 0.291151I
−0.36877 + 2.59359I 1.68494 − 0.36252I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.096832 + 1.186310I
a = −0.033306 + 1.034330I
b = 0.058839 + 1.333360I
−1.98840 − 2.05606I 0
u = −0.096832 − 1.186310I
a = −0.033306 − 1.034330I
b = 0.058839 − 1.333360I
−1.98840 + 2.05606I 0
u = 0.727913 + 0.354357I
a = 0.684717 − 0.364269I
b = 0.934993 + 0.899990I
0.61238 + 6.86563I 3.32287 − 5.58195I
u = 0.727913 − 0.354357I
a = 0.684717 + 0.364269I
b = 0.934993 − 0.899990I
0.61238 − 6.86563I 3.32287 + 5.58195I
u = 0.704616 + 0.318801I
a = −0.594174 + 0.627580I
b = −0.71343 − 1.29610I
2.12059 + 7.40432I 4.77244 − 6.86130I
u = 0.704616 − 0.318801I
a = −0.594174 − 0.627580I
b = −0.71343 + 1.29610I
2.12059 − 7.40432I 4.77244 + 6.86130I
u = −0.662386 + 0.390781I
a = 1.46629 + 0.17474I
b = 0.227985 − 0.829505I
−5.62709 − 6.13908I −3.82787 + 6.97428I
u = −0.662386 − 0.390781I
a = 1.46629 − 0.17474I
b = 0.227985 + 0.829505I
−5.62709 + 6.13908I −3.82787 − 6.97428I
u = 0.033830 + 1.232490I
a = 2.87009 + 0.36125I
b = 1.95889 + 0.10621I
−4.18113 + 2.57306I 0
u = 0.033830 − 1.232490I
a = 2.87009 − 0.36125I
b = 1.95889 − 0.10621I
−4.18113 − 2.57306I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.302111 + 0.688104I
a = −1.182470 + 0.745000I
b = 0.0584853 + 0.1015010I
1.62034 − 1.81508I 4.15715 + 4.60801I
u = −0.302111 − 0.688104I
a = −1.182470 − 0.745000I
b = 0.0584853 − 0.1015010I
1.62034 + 1.81508I 4.15715 − 4.60801I
u = −0.559639 + 0.498551I
a = 1.040250 − 0.158770I
b = −0.161974 − 1.057690I
−6.07136 + 2.10121I −5.43931 − 0.33251I
u = −0.559639 − 0.498551I
a = 1.040250 + 0.158770I
b = −0.161974 + 1.057690I
−6.07136 − 2.10121I −5.43931 + 0.33251I
u = 0.417371 + 0.622025I
a = −1.50102 − 0.47657I
b = 0.274564 − 0.052875I
0.95853 − 3.45680I 2.88557 + 1.23651I
u = 0.417371 − 0.622025I
a = −1.50102 + 0.47657I
b = 0.274564 + 0.052875I
0.95853 + 3.45680I 2.88557 − 1.23651I
u = −0.285589 + 1.221790I
a = 0.486068 + 1.304470I
b = −0.45701 + 1.52445I
1.54230 − 3.38846I 0
u = −0.285589 − 1.221790I
a = 0.486068 − 1.304470I
b = −0.45701 − 1.52445I
1.54230 + 3.38846I 0
u = −0.688837 + 0.276035I
a = −0.506158 − 0.412144I
b = −0.854238 + 0.944647I
3.12192 − 1.86091I 7.00300 + 1.72099I
u = −0.688837 − 0.276035I
a = −0.506158 + 0.412144I
b = −0.854238 − 0.944647I
3.12192 + 1.86091I 7.00300 − 1.72099I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.734669 + 0.080132I
a = −0.109774 + 0.752695I
b = 0.023197 − 1.081640I
5.21426 + 5.38493I 7.39429 − 6.48796I
u = 0.734669 − 0.080132I
a = −0.109774 − 0.752695I
b = 0.023197 + 1.081640I
5.21426 − 5.38493I 7.39429 + 6.48796I
u = −0.728864 + 0.033649I
a = −0.115841 − 0.702183I
b = −0.356277 + 1.021340I
5.40415 + 0.30307I 8.16735 + 0.42217I
u = −0.728864 − 0.033649I
a = −0.115841 + 0.702183I
b = −0.356277 − 1.021340I
5.40415 − 0.30307I 8.16735 − 0.42217I
u = 0.017786 + 1.274390I
a = 0.413923 − 0.857403I
b = 1.07386 − 1.49736I
−4.55744 − 1.40153I 0
u = 0.017786 − 1.274390I
a = 0.413923 + 0.857403I
b = 1.07386 + 1.49736I
−4.55744 + 1.40153I 0
u = 0.143394 + 1.287310I
a = −0.112381 − 1.079760I
b = −0.48289 − 1.86659I
−5.23372 + 4.97287I 0
u = 0.143394 − 1.287310I
a = −0.112381 + 1.079760I
b = −0.48289 + 1.86659I
−5.23372 − 4.97287I 0
u = 0.296460 + 1.261120I
a = 0.734857 − 1.082500I
b = −0.25481 − 1.57882I
1.05884 + 9.12126I 0
u = 0.296460 − 1.261120I
a = 0.734857 + 1.082500I
b = −0.25481 + 1.57882I
1.05884 − 9.12126I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621270 + 0.307573I
a = 1.061940 + 0.678358I
b = 0.319832 + 0.256604I
−0.83928 + 4.15309I 3.22592 − 6.96871I
u = 0.621270 − 0.307573I
a = 1.061940 − 0.678358I
b = 0.319832 − 0.256604I
−0.83928 − 4.15309I 3.22592 + 6.96871I
u = 0.567253 + 0.383310I
a = −1.116020 + 0.261961I
b = 0.028335 − 0.725819I
−2.58630 + 1.78860I −0.88529 − 3.97131I
u = 0.567253 − 0.383310I
a = −1.116020 − 0.261961I
b = 0.028335 + 0.725819I
−2.58630 − 1.78860I −0.88529 + 3.97131I
u = −0.572421 + 0.342007I
a = 0.541223 + 0.369016I
b = 0.75665 − 1.69733I
−2.53779 − 3.86488I −0.38418 + 6.24317I
u = −0.572421 − 0.342007I
a = 0.541223 − 0.369016I
b = 0.75665 + 1.69733I
−2.53779 + 3.86488I −0.38418 − 6.24317I
u = −0.543916 + 0.354697I
a = 1.90366 − 1.12968I
b = −0.024846 − 0.225999I
−2.64298 + 0.52206I −0.94527 + 2.58356I
u = −0.543916 − 0.354697I
a = 1.90366 + 1.12968I
b = −0.024846 + 0.225999I
−2.64298 − 0.52206I −0.94527 − 2.58356I
u = −0.183085 + 1.378170I
a = 0.237488 + 1.059600I
b = 0.587711 + 1.225330I
−3.76130 − 2.80716I 0
u = −0.183085 − 1.378170I
a = 0.237488 − 1.059600I
b = 0.587711 − 1.225330I
−3.76130 + 2.80716I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.07605 + 1.41611I
a = 0.762154 + 0.634266I
b = 0.705448 + 0.428340I
−7.30151 + 0.27459I 0
u = 0.07605 − 1.41611I
a = 0.762154 − 0.634266I
b = 0.705448 − 0.428340I
−7.30151 − 0.27459I 0
u = 0.20024 + 1.41544I
a = 0.14556 + 2.59827I
b = 0.73592 + 2.79536I
−6.99603 + 1.49071I 0
u = 0.20024 − 1.41544I
a = 0.14556 − 2.59827I
b = 0.73592 − 2.79536I
−6.99603 − 1.49071I 0
u = 0.13079 + 1.42986I
a = 1.011740 − 0.821862I
b = 1.85147 − 1.21489I
−5.43906 − 1.71948I 0
u = 0.13079 − 1.42986I
a = 1.011740 + 0.821862I
b = 1.85147 + 1.21489I
−5.43906 + 1.71948I 0
u = −0.26501 + 1.41163I
a = −0.26366 + 2.21891I
b = −0.92081 + 2.51508I
−2.27071 − 5.32530I 0
u = −0.26501 − 1.41163I
a = −0.26366 − 2.21891I
b = −0.92081 − 2.51508I
−2.27071 + 5.32530I 0
u = 0.23928 + 1.42161I
a = −0.399489 + 1.246210I
b = −0.85015 + 1.46895I
−6.38310 + 7.30916I 0
u = 0.23928 − 1.42161I
a = −0.399489 − 1.246210I
b = −0.85015 − 1.46895I
−6.38310 − 7.30916I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.21404 + 1.43002I
a = −1.09694 − 1.14316I
b = −2.03628 − 1.56218I
−8.35807 − 2.30611I 0
u = −0.21404 − 1.43002I
a = −1.09694 + 1.14316I
b = −2.03628 + 1.56218I
−8.35807 + 2.30611I 0
u = −0.22373 + 1.42909I
a = −0.24193 − 3.07557I
b = 0.61653 − 3.63118I
−8.21464 − 6.81864I 0
u = −0.22373 − 1.42909I
a = −0.24193 + 3.07557I
b = 0.61653 + 3.63118I
−8.21464 + 6.81864I 0
u = 0.21733 + 1.43797I
a = 0.61351 − 1.92799I
b = 0.61832 − 2.74986I
−8.41519 + 4.68873I 0
u = 0.21733 − 1.43797I
a = 0.61351 + 1.92799I
b = 0.61832 + 2.74986I
−8.41519 − 4.68873I 0
u = 0.27151 + 1.43086I
a = −0.12555 − 2.56714I
b = −1.01892 − 3.14486I
−3.48348 + 10.95720I 0
u = 0.27151 − 1.43086I
a = −0.12555 + 2.56714I
b = −1.01892 + 3.14486I
−3.48348 − 10.95720I 0
u = 0.465562 + 0.275834I
a = 0.243457 − 0.134771I
b = 1.11439 + 1.01681I
−1.51017 − 1.07614I 1.98895 − 2.17758I
u = 0.465562 − 0.275834I
a = 0.243457 + 0.134771I
b = 1.11439 − 1.01681I
−1.51017 + 1.07614I 1.98895 + 2.17758I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.524772 + 0.121904I
a = −0.819856 + 0.283386I
b = −0.358442 + 0.076918I
1.068300 − 0.310599I 9.28567 + 1.52761I
u = −0.524772 − 0.121904I
a = −0.819856 − 0.283386I
b = −0.358442 − 0.076918I
1.068300 + 0.310599I 9.28567 − 1.52761I
u = 0.27891 + 1.44816I
a = 0.47047 + 2.25310I
b = 1.08998 + 2.60186I
−5.17217 + 10.53120I 0
u = 0.27891 − 1.44816I
a = 0.47047 − 2.25310I
b = 1.08998 − 2.60186I
−5.17217 − 10.53120I 0
u = −0.24865 + 1.45425I
a = −0.47436 − 2.20620I
b = −0.50744 − 3.09141I
−11.5596 − 9.4710I 0
u = −0.24865 − 1.45425I
a = −0.47436 + 2.20620I
b = −0.50744 + 3.09141I
−11.5596 + 9.4710I 0
u = 0.00071 + 1.48100I
a = 0.951292 − 0.124874I
b = 1.63370 − 0.35173I
−5.16458 − 2.36926I 0
u = 0.00071 − 1.48100I
a = 0.951292 + 0.124874I
b = 1.63370 + 0.35173I
−5.16458 + 2.36926I 0
u = −0.19182 + 1.47187I
a = −1.03740 − 2.05339I
b = −1.12384 − 2.83007I
−12.41680 − 0.62429I 0
u = −0.19182 − 1.47187I
a = −1.03740 + 2.05339I
b = −1.12384 + 2.83007I
−12.41680 + 0.62429I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.28097 + 1.46057I
a = 0.47100 − 2.64901I
b = 1.36018 − 3.25151I
−6.5496 − 16.2427I 0
u = −0.28097 − 1.46057I
a = 0.47100 + 2.64901I
b = 1.36018 + 3.25151I
−6.5496 + 16.2427I 0
u = 0.296147 + 0.411712I
a = 0.160974 + 0.241335I
b = 0.641515 + 0.525167I
−1.64633 − 0.98026I −1.55717 − 0.73161I
u = 0.296147 − 0.411712I
a = 0.160974 − 0.241335I
b = 0.641515 − 0.525167I
−1.64633 + 0.98026I −1.55717 + 0.73161I
u = 0.13717 + 1.48921I
a = −0.748243 + 0.772439I
b = −1.29711 + 0.80485I
−7.22968 − 0.37107I 0
u = 0.13717 − 1.48921I
a = −0.748243 − 0.772439I
b = −1.29711 − 0.80485I
−7.22968 + 0.37107I 0
u = −0.15630 + 1.50911I
a = −1.38321 − 0.82818I
b = −2.29005 − 1.13736I
−8.45219 + 5.57122I 0
u = −0.15630 − 1.50911I
a = −1.38321 + 0.82818I
b = −2.29005 + 1.13736I
−8.45219 − 5.57122I 0
u = 0.451714 + 0.073123I
a = −1.42887 + 1.70325I
b = −0.0829225 − 0.0834728I
−1.05321 + 2.73929I 4.57325 − 7.80754I
u = 0.451714 − 0.073123I
a = −1.42887 − 1.70325I
b = −0.0829225 + 0.0834728I
−1.05321 − 2.73929I 4.57325 + 7.80754I
13
II. I
u
2
= hb − 2a − 1, 2a
2
+ au + 4a + u + 1, u
2
+ 2i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
2
a
1
=
a
2a + 1
a
10
=
u
u
a
11
=
−au + a +
1
2
u + 1
−au + 2a + u + 2
a
8
=
−u
−u
a
3
=
−1
−2
a
2
=
a − 1
2a − 1
a
7
=
−u
−u
a
12
=
−au − a −
1
2
u − 1
−au
a
6
=
a
2a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4au + 4u − 8
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
4
c
2
(u + 1)
4
c
3
, c
4
, c
8
c
9
(u
2
+ 2)
2
c
6
, c
10
(u
2
− u + 1)
2
c
7
u
4
c
11
, c
12
(u
2
+ u + 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
, c
8
c
9
(y + 2)
4
c
6
, c
10
, c
11
c
12
(y
2
+ y + 1)
2
c
7
y
4
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = −0.387628 − 0.353553I
b = 0.224745 − 0.707107I
−6.57974 − 2.02988I −6.00000 + 3.46410I
u = 1.414210I
a = −1.61237 − 0.35355I
b = −2.22474 − 0.70711I
−6.57974 + 2.02988I −6.00000 − 3.46410I
u = − 1.414210I
a = −0.387628 + 0.353553I
b = 0.224745 + 0.707107I
−6.57974 + 2.02988I −6.00000 − 3.46410I
u = − 1.414210I
a = −1.61237 + 0.35355I
b = −2.22474 + 0.70711I
−6.57974 − 2.02988I −6.00000 + 3.46410I
17
III. I
v
1
= ha, b + 1, v
2
+ v + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
v
0
a
5
=
1
0
a
1
=
0
−1
a
10
=
v
0
a
11
=
v
v
a
8
=
v
0
a
3
=
1
0
a
2
=
1
−1
a
7
=
v
0
a
12
=
v + 1
v
a
6
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 2
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
4
, c
7
c
8
, c
9
u
2
c
5
(u + 1)
2
c
6
, c
12
u
2
+ u + 1
c
10
, c
11
u
2
− u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y − 1)
2
c
3
, c
4
, c
7
c
8
, c
9
y
2
c
6
, c
10
, c
11
c
12
y
2
+ y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = −1.00000
−1.64493 + 2.02988I 0. − 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = −1.00000
−1.64493 − 2.02988I 0. + 3.46410I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
90
+ 49u
89
+ ··· + 64u + 9)
c
2
((u − 1)
2
)(u + 1)
4
(u
90
+ 3u
89
+ ··· + 8u + 3)
c
3
u
2
(u
2
+ 2)
2
(u
90
+ u
89
+ ··· + 25496u + 8452)
c
4
, c
8
, c
9
u
2
(u
2
+ 2)
2
(u
90
− u
89
+ ··· + 8u + 4)
c
5
((u − 1)
4
)(u + 1)
2
(u
90
+ 3u
89
+ ··· + 8u + 3)
c
6
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
90
− 2u
89
+ ··· + 5u + 3)
c
7
u
6
(u
90
+ 15u
89
+ ··· + 14592u + 2304)
c
10
((u
2
− u + 1)
3
)(u
90
+ 32u
89
+ ··· + 101u + 9)
c
11
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
90
− 2u
89
+ ··· + 5u + 3)
c
12
((u
2
+ u + 1)
3
)(u
90
+ 32u
89
+ ··· + 101u + 9)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
6
)(y
90
− 9y
89
+ ··· − 1180y + 81)
c
2
, c
5
((y − 1)
6
)(y
90
− 49y
89
+ ··· − 64y + 9)
c
3
y
2
(y + 2)
4
(y
90
+ 25y
89
+ ··· + 1.04996 × 10
9
y + 7.14363 × 10
7
)
c
4
, c
8
, c
9
y
2
(y + 2)
4
(y
90
+ 85y
89
+ ··· − 192y + 16)
c
6
, c
11
((y
2
+ y + 1)
3
)(y
90
+ 32y
89
+ ··· + 101y + 9)
c
7
y
6
(y
90
+ 49y
89
+ ··· + 4.04029 × 10
7
y + 5308416)
c
10
, c
12
((y
2
+ y + 1)
3
)(y
90
+ 56y
89
+ ··· + 1517y + 81)
23
