12a
0313
(K12a
0313
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 2 5 10 12 4 7 1 9
Solving Sequence
8,12 4,9
10 1 3 2 7 11 5 6
c
8
c
9
c
12
c
3
c
1
c
7
c
11
c
4
c
6
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.70812 × 10
157
u
106
− 3.03141 × 10
158
u
105
+ ··· + 2.56694 × 10
158
b + 6.21022 × 10
158
,
1.09767 × 10
160
u
106
+ 6.85071 × 10
160
u
105
+ ··· + 7.18742 × 10
159
a − 1.03525 × 10
160
, u
107
+ 7u
106
+ ··· − 7u − 2i
I
u
2
= h−u
3
+ b + u + 1, u
3
+ u
2
+ a + u − 1, u
4
− u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 111 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−1.71 × 10
157
u
106
− 3.03 × 10
158
u
105
+ · · · + 2.57 × 10
158
b + 6.21 ×
10
158
, 1.10 × 10
160
u
106
+ 6.85 × 10
160
u
105
+ · · · + 7.19 × 10
159
a − 1.04 ×
10
160
, u
107
+ 7u
106
+ · · · − 7u − 2i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
−1.52721u
106
− 9.53153u
105
+ ··· + 11.6434u + 1.44036
0.0665430u
106
+ 1.18095u
105
+ ··· − 2.78415u − 2.41931
a
9
=
1
−u
2
a
10
=
−0.906926u
106
− 6.15088u
105
+ ··· + 12.2394u + 4.67446
−0.0941909u
106
− 0.564758u
105
+ ··· + 1.37335u + 0.115362
a
1
=
u
−u
3
+ u
a
3
=
−1.46067u
106
− 8.35058u
105
+ ··· + 8.85926u − 0.978951
0.0665430u
106
+ 1.18095u
105
+ ··· − 2.78415u − 2.41931
a
2
=
−1.38743u
106
− 8.09403u
105
+ ··· + 0.613109u + 0.639209
−0.318537u
106
− 1.68135u
105
+ ··· + 1.60195u + 0.444072
a
7
=
−1.07925u
106
− 6.86061u
105
+ ··· − 2.88963u + 1.87350
−0.628187u
106
− 3.75798u
105
+ ··· + 2.64801u + 1.32955
a
11
=
−u
3
u
5
− u
3
+ u
a
5
=
−1.07654u
106
− 6.14521u
105
+ ··· + 8.78359u − 0.113308
−0.188990u
106
− 0.943983u
105
+ ··· + 0.658999u − 0.957025
a
6
=
0.277869u
106
+ 1.24570u
105
+ ··· − 1.71526u + 1.88041
−0.108162u
106
− 0.980032u
105
+ ··· + 1.06338u + 0.961280
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.55581u
106
+ 12.7480u
105
+ ··· − 20.5992u − 13.0896
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
107
+ 33u
106
+ ··· + 16u + 1
c
2
, c
5
u
107
+ 5u
106
+ ··· + 6u + 1
c
3
u
107
− 9u
106
+ ··· + 51550u + 30431
c
4
u
107
− 29u
106
+ ··· − 71644122u + 19604249
c
7
, c
10
u
107
− 7u
106
+ ··· − 32u + 1
c
8
, c
12
u
107
− 7u
106
+ ··· − 7u + 2
c
9
u
107
− u
106
+ ··· − 18u + 1
c
11
u
107
− 47u
106
+ ··· + 37u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
107
+ 87y
106
+ ··· − 576y −1
c
2
, c
5
y
107
− 33y
106
+ ··· + 16y −1
c
3
y
107
+ 241y
106
+ ··· − 56603744314y −926045761
c
4
y
107
− 155y
106
+ ··· − 7615585881180646y −384326578854001
c
7
, c
10
y
107
+ 83y
106
+ ··· + 504y −1
c
8
, c
12
y
107
− 47y
106
+ ··· + 37y −4
c
9
y
107
+ 11y
106
+ ··· + 64y −1
c
11
y
107
+ 29y
106
+ ··· + 9921y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.538348 + 0.843458I
a = 0.0012803 − 0.0415117I
b = 0.858143 + 0.471158I
−5.08424 − 2.07788I 0
u = 0.538348 − 0.843458I
a = 0.0012803 + 0.0415117I
b = 0.858143 − 0.471158I
−5.08424 + 2.07788I 0
u = 0.724167 + 0.687487I
a = 0.016726 − 0.450061I
b = 0.681883 + 0.359257I
−3.29442 + 3.53782I 0
u = 0.724167 − 0.687487I
a = 0.016726 + 0.450061I
b = 0.681883 − 0.359257I
−3.29442 − 3.53782I 0
u = 0.930019 + 0.372686I
a = 2.20548 + 1.35417I
b = −0.135750 − 0.340140I
1.32736 + 1.45194I 0
u = 0.930019 − 0.372686I
a = 2.20548 − 1.35417I
b = −0.135750 + 0.340140I
1.32736 − 1.45194I 0
u = 0.929735 + 0.381523I
a = 1.63048 + 1.15126I
b = −1.03346 − 1.83765I
4.37135 − 1.42306I 0
u = 0.929735 − 0.381523I
a = 1.63048 − 1.15126I
b = −1.03346 + 1.83765I
4.37135 + 1.42306I 0
u = 0.277946 + 0.953038I
a = −0.012755 − 0.142510I
b = −0.828557 − 0.641521I
0.791520 − 1.170380I 0
u = 0.277946 − 0.953038I
a = −0.012755 + 0.142510I
b = −0.828557 + 0.641521I
0.791520 + 1.170380I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.407587 + 0.923605I
a = −0.176569 − 0.045157I
b = 0.94846 − 1.19023I
6.42867 + 6.58412I 0
u = −0.407587 − 0.923605I
a = −0.176569 + 0.045157I
b = 0.94846 + 1.19023I
6.42867 − 6.58412I 0
u = 0.876007 + 0.506474I
a = −13.05690 − 2.84832I
b = 4.28571 + 13.04720I
0.55325 + 2.03087I 0
u = 0.876007 − 0.506474I
a = −13.05690 + 2.84832I
b = 4.28571 − 13.04720I
0.55325 − 2.03087I 0
u = −0.848217 + 0.495354I
a = −0.71565 + 1.26004I
b = −0.928805 − 0.227021I
−1.67631 − 2.03582I 0
u = −0.848217 − 0.495354I
a = −0.71565 − 1.26004I
b = −0.928805 + 0.227021I
−1.67631 + 2.03582I 0
u = 0.945165 + 0.410952I
a = −1.74898 − 1.55104I
b = 0.68112 + 2.28185I
4.48357 + 4.46503I 0
u = 0.945165 − 0.410952I
a = −1.74898 + 1.55104I
b = 0.68112 − 2.28185I
4.48357 − 4.46503I 0
u = −0.440601 + 0.945642I
a = 0.135398 + 0.088825I
b = −1.01143 + 1.20630I
5.56018 + 12.75520I 0
u = −0.440601 − 0.945642I
a = 0.135398 − 0.088825I
b = −1.01143 − 1.20630I
5.56018 − 12.75520I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.798317 + 0.518803I
a = −3.90926 + 4.77070I
b = 5.53872 + 1.77677I
4.57359 − 0.72532I 0
u = 0.798317 − 0.518803I
a = −3.90926 − 4.77070I
b = 5.53872 − 1.77677I
4.57359 + 0.72532I 0
u = −0.508044 + 0.802603I
a = −0.0667446 − 0.1074040I
b = −1.004010 + 0.955439I
−1.36856 + 7.06093I 0
u = −0.508044 − 0.802603I
a = −0.0667446 + 0.1074040I
b = −1.004010 − 0.955439I
−1.36856 − 7.06093I 0
u = 1.058620 + 0.030481I
a = 0.94489 − 1.88233I
b = −0.759151 + 0.928288I
4.30867 + 5.70483I 0
u = 1.058620 − 0.030481I
a = 0.94489 + 1.88233I
b = −0.759151 − 0.928288I
4.30867 − 5.70483I 0
u = 0.356848 + 0.998715I
a = 0.0357519 + 0.1146120I
b = 0.887175 + 0.629795I
0.22354 − 6.83766I 0
u = 0.356848 − 0.998715I
a = 0.0357519 − 0.1146120I
b = 0.887175 − 0.629795I
0.22354 + 6.83766I 0
u = −0.387087 + 0.855084I
a = −0.0751594 − 0.0449728I
b = −0.534749 − 0.556902I
−0.84328 − 3.63714I 0
u = −0.387087 − 0.855084I
a = −0.0751594 + 0.0449728I
b = −0.534749 + 0.556902I
−0.84328 + 3.63714I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.055210 + 0.192329I
a = −1.36667 − 1.48800I
b = 0.363322 + 0.724291I
6.68383 − 1.43597I 0
u = 1.055210 − 0.192329I
a = −1.36667 + 1.48800I
b = 0.363322 − 0.724291I
6.68383 + 1.43597I 0
u = −1.041880 + 0.278409I
a = 0.339830 − 1.038090I
b = 0.292361 + 0.591597I
1.84494 − 1.26782I 0
u = −1.041880 − 0.278409I
a = 0.339830 + 1.038090I
b = 0.292361 − 0.591597I
1.84494 + 1.26782I 0
u = −1.038020 + 0.307188I
a = 0.17641 + 2.03180I
b = 0.174520 − 1.241290I
9.21752 + 2.67157I 0
u = −1.038020 − 0.307188I
a = 0.17641 − 2.03180I
b = 0.174520 + 1.241290I
9.21752 − 2.67157I 0
u = 0.770203 + 0.465799I
a = 2.32672 − 4.66591I
b = −4.31042 − 0.31373I
4.51594 + 4.86267I 0
u = 0.770203 − 0.465799I
a = 2.32672 + 4.66591I
b = −4.31042 + 0.31373I
4.51594 − 4.86267I 0
u = 0.926764 + 0.611947I
a = 0.48250 + 1.45921I
b = 0.333322 − 0.643480I
−2.67373 + 1.48301I 0
u = 0.926764 − 0.611947I
a = 0.48250 − 1.45921I
b = 0.333322 + 0.643480I
−2.67373 − 1.48301I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.011350 + 0.474049I
a = 0.502600 − 1.155450I
b = 1.29093 + 0.65238I
3.92698 − 1.33646I 0
u = −1.011350 − 0.474049I
a = 0.502600 + 1.155450I
b = 1.29093 − 0.65238I
3.92698 + 1.33646I 0
u = −1.062040 + 0.370218I
a = −0.01049 − 2.11857I
b = 0.018458 + 1.258440I
9.76950 − 3.99814I 0
u = −1.062040 − 0.370218I
a = −0.01049 + 2.11857I
b = 0.018458 − 1.258440I
9.76950 + 3.99814I 0
u = −0.704313 + 0.513659I
a = −0.101839 − 0.850106I
b = 1.070720 + 0.331936I
1.41677 − 2.15371I 0
u = −0.704313 − 0.513659I
a = −0.101839 + 0.850106I
b = 1.070720 − 0.331936I
1.41677 + 2.15371I 0
u = −1.004700 + 0.518463I
a = −0.522066 + 1.095000I
b = −1.34650 − 0.51458I
3.30694 − 7.04306I 0
u = −1.004700 − 0.518463I
a = −0.522066 − 1.095000I
b = −1.34650 + 0.51458I
3.30694 + 7.04306I 0
u = −1.000950 + 0.537908I
a = −0.68059 + 2.40648I
b = −0.562724 − 0.877889I
0.09255 − 4.08508I 0
u = −1.000950 − 0.537908I
a = −0.68059 − 2.40648I
b = −0.562724 + 0.877889I
0.09255 + 4.08508I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.771693 + 0.317836I
a = 0.409006 − 1.299830I
b = 1.073410 + 0.818738I
1.34536 − 2.21121I 0. + 4.32313I
u = −0.771693 − 0.317836I
a = 0.409006 + 1.299830I
b = 1.073410 − 0.818738I
1.34536 + 2.21121I 0. − 4.32313I
u = −1.081350 + 0.445727I
a = 0.533683 − 0.825481I
b = 0.282314 + 0.748640I
1.89720 − 1.36648I 0
u = −1.081350 − 0.445727I
a = 0.533683 + 0.825481I
b = 0.282314 − 0.748640I
1.89720 + 1.36648I 0
u = 1.079870 + 0.458369I
a = −1.57845 − 0.59593I
b = −0.169046 + 0.554260I
9.17947 + 3.04501I 0
u = 1.079870 − 0.458369I
a = −1.57845 + 0.59593I
b = −0.169046 − 0.554260I
9.17947 − 3.04501I 0
u = 1.030840 + 0.565624I
a = −0.41501 − 1.56335I
b = −0.624364 + 0.978591I
−0.03788 + 4.90136I 0
u = 1.030840 − 0.565624I
a = −0.41501 + 1.56335I
b = −0.624364 − 0.978591I
−0.03788 − 4.90136I 0
u = 1.067030 + 0.512174I
a = 1.54443 + 0.34211I
b = 0.269873 − 0.483227I
7.87495 + 9.47071I 0
u = 1.067030 − 0.512174I
a = 1.54443 − 0.34211I
b = 0.269873 + 0.483227I
7.87495 − 9.47071I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.540373 + 0.597872I
a = 0.334757 + 0.154880I
b = −0.754203 − 0.490202I
−1.50744 − 0.24032I −8.09424 + 0.I
u = 0.540373 − 0.597872I
a = 0.334757 − 0.154880I
b = −0.754203 + 0.490202I
−1.50744 + 0.24032I −8.09424 + 0.I
u = −0.592919 + 0.524868I
a = −0.648786 − 0.821024I
b = −0.770101 + 0.683514I
−1.154640 − 0.287146I −7.71590 − 1.92694I
u = −0.592919 − 0.524868I
a = −0.648786 + 0.821024I
b = −0.770101 − 0.683514I
−1.154640 + 0.287146I −7.71590 + 1.92694I
u = −0.395589 + 0.684115I
a = −0.121440 + 0.459086I
b = 0.805810 − 0.913854I
2.34224 + 3.53764I −2.52473 − 3.13102I
u = −0.395589 − 0.684115I
a = −0.121440 − 0.459086I
b = 0.805810 + 0.913854I
2.34224 − 3.53764I −2.52473 + 3.13102I
u = −1.078460 + 0.569184I
a = 0.58716 − 2.08700I
b = 0.735789 + 1.175650I
4.30196 − 8.37888I 0
u = −1.078460 − 0.569184I
a = 0.58716 + 2.08700I
b = 0.735789 − 1.175650I
4.30196 + 8.37888I 0
u = −0.622531 + 1.069870I
a = 0.090402 − 0.118099I
b = −0.206516 − 0.526777I
4.45498 − 7.19870I 0
u = −0.622531 − 1.069870I
a = 0.090402 + 0.118099I
b = −0.206516 + 0.526777I
4.45498 + 7.19870I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.985487 + 0.754984I
a = −0.485905 + 0.229999I
b = 0.066046 − 0.316527I
1.33956 − 3.05501I 0
u = −0.985487 − 0.754984I
a = −0.485905 − 0.229999I
b = 0.066046 + 0.316527I
1.33956 + 3.05501I 0
u = −0.689969 + 1.042930I
a = −0.127837 + 0.115782I
b = 0.161060 + 0.439270I
4.72011 − 1.41790I 0
u = −0.689969 − 1.042930I
a = −0.127837 − 0.115782I
b = 0.161060 − 0.439270I
4.72011 + 1.41790I 0
u = −1.076560 + 0.636852I
a = −0.70293 + 1.96926I
b = −1.00415 − 1.14381I
0.34151 − 12.46680I 0
u = −1.076560 − 0.636852I
a = −0.70293 − 1.96926I
b = −1.00415 + 1.14381I
0.34151 + 12.46680I 0
u = 1.068190 + 0.660431I
a = 0.36213 + 1.44370I
b = 0.837852 − 0.757760I
−3.47800 + 7.66429I 0
u = 1.068190 − 0.660431I
a = 0.36213 − 1.44370I
b = 0.837852 + 0.757760I
−3.47800 − 7.66429I 0
u = 1.296900 + 0.075750I
a = −0.79521 − 1.34498I
b = 0.398450 + 1.240250I
12.58130 − 3.55728I 0
u = 1.296900 − 0.075750I
a = −0.79521 + 1.34498I
b = 0.398450 − 1.240250I
12.58130 + 3.55728I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.524388 + 0.459382I
a = −0.67805 + 1.75349I
b = −0.610123 + 0.359489I
1.91784 + 2.87133I −5.87328 − 1.05370I
u = −0.524388 − 0.459382I
a = −0.67805 − 1.75349I
b = −0.610123 − 0.359489I
1.91784 − 2.87133I −5.87328 + 1.05370I
u = 1.312490 + 0.036726I
a = 0.73066 + 1.37105I
b = −0.456515 − 1.288520I
12.0506 − 9.8166I 0
u = 1.312490 − 0.036726I
a = 0.73066 − 1.37105I
b = −0.456515 + 1.288520I
12.0506 + 9.8166I 0
u = −1.154450 + 0.646362I
a = 0.60774 − 1.86569I
b = 1.06229 + 1.44855I
8.7059 − 12.3236I 0
u = −1.154450 − 0.646362I
a = 0.60774 + 1.86569I
b = 1.06229 − 1.44855I
8.7059 + 12.3236I 0
u = −1.153990 + 0.666795I
a = −0.63005 + 1.84504I
b = −1.14235 − 1.44215I
7.7503 − 18.6395I 0
u = −1.153990 − 0.666795I
a = −0.63005 − 1.84504I
b = −1.14235 + 1.44215I
7.7503 + 18.6395I 0
u = 1.181870 + 0.620491I
a = −0.22535 − 1.45208I
b = −1.03468 + 0.97837I
3.47889 + 6.81457I 0
u = 1.181870 − 0.620491I
a = −0.22535 + 1.45208I
b = −1.03468 − 0.97837I
3.47889 − 6.81457I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.185460 + 0.655184I
a = 0.23810 + 1.41547I
b = 1.08106 − 0.91821I
2.75105 + 12.77430I 0
u = 1.185460 − 0.655184I
a = 0.23810 − 1.41547I
b = 1.08106 + 0.91821I
2.75105 − 12.77430I 0
u = 0.283592 + 0.568153I
a = 1.75474 + 0.61289I
b = −0.298494 + 0.647514I
5.76290 − 5.17672I −2.91656 + 3.83160I
u = 0.283592 − 0.568153I
a = 1.75474 − 0.61289I
b = −0.298494 − 0.647514I
5.76290 + 5.17672I −2.91656 − 3.83160I
u = 0.132946 + 0.574365I
a = −1.66518 − 0.07867I
b = 0.401104 − 0.770797I
6.64032 + 0.88970I −1.43854 − 1.57989I
u = 0.132946 − 0.574365I
a = −1.66518 + 0.07867I
b = 0.401104 + 0.770797I
6.64032 − 0.88970I −1.43854 + 1.57989I
u = −1.43121 + 0.03367I
a = 0.019543 − 0.759133I
b = 0.029487 + 0.867765I
7.10252 − 2.95976I 0
u = −1.43121 − 0.03367I
a = 0.019543 + 0.759133I
b = 0.029487 − 0.867765I
7.10252 + 2.95976I 0
u = −1.28047 + 0.71465I
a = 0.324680 − 0.485114I
b = 0.379430 + 0.520971I
6.64532 + 0.24779I 0
u = −1.28047 − 0.71465I
a = 0.324680 + 0.485114I
b = 0.379430 − 0.520971I
6.64532 − 0.24779I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.25373 + 0.76253I
a = −0.326061 + 0.448028I
b = −0.373077 − 0.451606I
6.55030 − 5.62035I 0
u = −1.25373 − 0.76253I
a = −0.326061 − 0.448028I
b = −0.373077 + 0.451606I
6.55030 + 5.62035I 0
u = −0.355726 + 0.387785I
a = 0.64017 − 1.96532I
b = 0.329582 − 0.543050I
2.22896 − 2.43828I −4.48588 + 4.98806I
u = −0.355726 − 0.387785I
a = 0.64017 + 1.96532I
b = 0.329582 + 0.543050I
2.22896 + 2.43828I −4.48588 − 4.98806I
u = −0.071310 + 0.236959I
a = −2.28255 − 2.03397I
b = −0.670210 − 0.726755I
−0.276755 + 0.306121I −6.99836 − 1.27809I
u = −0.071310 − 0.236959I
a = −2.28255 + 2.03397I
b = −0.670210 + 0.726755I
−0.276755 − 0.306121I −6.99836 + 1.27809I
u = 0.215388
a = 1.80238
b = −0.538020
−0.848981 −12.1680
15
II. I
u
2
= h−u
3
+ b + u + 1, u
3
+ u
2
+ a + u − 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
−u
3
− u
2
− u + 1
u
3
− u − 1
a
9
=
1
−u
2
a
10
=
u
2
− u − 1
u
3
a
1
=
u
−u
3
+ u
a
3
=
−u
2
− 2u
u
3
− u − 1
a
2
=
−u
2
− u
−1
a
7
=
u
2
+ u
1
a
11
=
−u
3
0
a
5
=
−u
2
− 2u
u
3
− u − 1
a
6
=
−u
u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
− 4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
u
4
− 4u
3
+ 5u
2
− 2u + 1
c
4
u
4
+ 2u
3
+ 5u
2
+ 4u + 1
c
5
, c
6
(u + 1)
4
c
7
, c
9
, c
10
(u
2
+ 1)
2
c
8
, c
12
u
4
− u
2
+ 1
c
11
(u
2
+ u + 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
(y −1)
4
c
3
y
4
− 6y
3
+ 11y
2
+ 6y + 1
c
4
y
4
+ 6y
3
+ 11y
2
− 6y + 1
c
7
, c
9
, c
10
(y + 1)
4
c
8
, c
12
(y
2
− y + 1)
2
c
11
(y
2
+ y + 1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −0.36603 − 2.36603I
b = −1.86603 + 0.50000I
2.02988I −6.00000 − 3.46410I
u = 0.866025 − 0.500000I
a = −0.36603 + 2.36603I
b = −1.86603 − 0.50000I
− 2.02988I −6.00000 + 3.46410I
u = −0.866025 + 0.500000I
a = 1.36603 − 0.63397I
b = −0.133975 + 0.500000I
− 2.02988I −6.00000 + 3.46410I
u = −0.866025 − 0.500000I
a = 1.36603 + 0.63397I
b = −0.133975 − 0.500000I
2.02988I −6.00000 − 3.46410I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
107
+ 33u
106
+ ··· + 16u + 1)
c
2
((u − 1)
4
)(u
107
+ 5u
106
+ ··· + 6u + 1)
c
3
(u
4
− 4u
3
+ 5u
2
− 2u + 1)(u
107
− 9u
106
+ ··· + 51550u + 30431)
c
4
(u
4
+ 2u
3
+ 5u
2
+ 4u + 1)
· (u
107
− 29u
106
+ ··· − 71644122u + 19604249)
c
5
((u + 1)
4
)(u
107
+ 5u
106
+ ··· + 6u + 1)
c
6
((u + 1)
4
)(u
107
+ 33u
106
+ ··· + 16u + 1)
c
7
, c
10
((u
2
+ 1)
2
)(u
107
− 7u
106
+ ··· − 32u + 1)
c
8
, c
12
(u
4
− u
2
+ 1)(u
107
− 7u
106
+ ··· − 7u + 2)
c
9
((u
2
+ 1)
2
)(u
107
− u
106
+ ··· − 18u + 1)
c
11
((u
2
+ u + 1)
2
)(u
107
− 47u
106
+ ··· + 37u − 4)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
((y −1)
4
)(y
107
+ 87y
106
+ ··· − 576y −1)
c
2
, c
5
((y −1)
4
)(y
107
− 33y
106
+ ··· + 16y −1)
c
3
(y
4
− 6y
3
+ 11y
2
+ 6y + 1)
· (y
107
+ 241y
106
+ ··· − 56603744314y −926045761)
c
4
(y
4
+ 6y
3
+ 11y
2
− 6y + 1)
· (y
107
− 155y
106
+ ··· − 7615585881180646y −384326578854001)
c
7
, c
10
((y + 1)
4
)(y
107
+ 83y
106
+ ··· + 504y −1)
c
8
, c
12
((y
2
− y + 1)
2
)(y
107
− 47y
106
+ ··· + 37y −4)
c
9
((y + 1)
4
)(y
107
+ 11y
106
+ ··· + 64y −1)
c
11
((y
2
+ y + 1)
2
)(y
107
+ 29y
106
+ ··· + 9921y −16)
21
