12a
0086
(K12a
0086
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 9 11 12 4 1 7 6 10
Solving Sequence
6,12
11 7
4,8
9 3 5 2 10 1
c
11
c
6
c
7
c
8
c
3
c
5
c
2
c
10
c
12
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
90
+ u
89
+ ··· + 3u
2
+ b, −u
88
+ u
87
+ ··· + a − 3u, u
92
− 2u
91
+ ··· + 3u − 1i
I
u
2
= h−u
2
+ b − 1, −u
2
+ a − 2, u
3
+ 2u − 1i
I
u
3
= hu
3
+ u
2
+ b + u + 1, u
3
+ u
2
+ a + 2u + 2, u
4
+ u
3
+ 2u
2
+ 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 99 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−u
90
+u
89
+· · ·+3u
2
+b, −u
88
+u
87
+· · ·+a−3u, u
92
−2u
91
+· · ·+3u−1i
(i) Arc colorings
a
6
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
7
=
u
u
3
+ u
a
4
=
u
88
− u
87
+ ··· − 6u
2
+ 3u
u
90
− u
89
+ ··· + 6u
3
− 3u
2
a
8
=
u
3
+ 2u
u
3
+ u
a
9
=
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
u
12
+ 6u
10
+ 12u
8
+ 8u
6
+ u
4
+ 2u
2
a
3
=
2u
88
− u
87
+ ··· + 4u − 1
u
89
+ u
88
+ ··· − 2u
2
− u
a
5
=
−u
21
− 10u
19
+ ··· + 2u
3
− u
−u
23
− 11u
21
+ ··· − 2u
3
+ u
a
2
=
u
88
− u
87
+ ··· − 6u
2
+ 3u
u
88
− u
87
+ ··· + 5u
3
− 3u
2
a
10
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
−u
6
− 3u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
91
− 8u
90
+ ··· − 5u + 15
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
92
+ 44u
91
+ ··· + 78u + 1
c
2
, c
4
u
92
− 8u
91
+ ··· + 14u − 1
c
3
, c
8
u
92
+ u
91
+ ··· + 192u + 128
c
5
u
92
− 2u
91
+ ··· + 13397u − 11981
c
6
, c
10
, c
11
u
92
− 2u
91
+ ··· + 3u − 1
c
7
u
92
+ 2u
91
+ ··· + 19896u − 4360
c
9
, c
12
u
92
+ 14u
91
+ ··· + 3115u + 131
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
92
+ 16y
91
+ ··· − 5674y + 1
c
2
, c
4
y
92
− 44y
91
+ ··· − 78y + 1
c
3
, c
8
y
92
− 45y
91
+ ··· − 438272y + 16384
c
5
y
92
− 10y
91
+ ··· + 378763105y + 143544361
c
6
, c
10
, c
11
y
92
+ 86y
91
+ ··· + y + 1
c
7
y
92
+ 30y
91
+ ··· + 525356144y + 19009600
c
9
, c
12
y
92
+ 74y
91
+ ··· + 260373y + 17161
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.153909 + 1.134970I
a = 0.417347 + 1.214000I
b = 1.49588 − 1.44581I
1.12873 + 4.25478I 0
u = −0.153909 − 1.134970I
a = 0.417347 − 1.214000I
b = 1.49588 + 1.44581I
1.12873 − 4.25478I 0
u = −0.178162 + 1.177710I
a = −0.495039 − 1.310920I
b = −1.68518 + 1.60196I
2.58467 − 1.25382I 0
u = −0.178162 − 1.177710I
a = −0.495039 + 1.310920I
b = −1.68518 − 1.60196I
2.58467 + 1.25382I 0
u = 0.692151 + 0.390660I
a = −2.83083 + 0.45729I
b = −2.42917 + 0.16265I
−1.15801 + 12.77270I 5.19545 − 9.98793I
u = 0.692151 − 0.390660I
a = −2.83083 − 0.45729I
b = −2.42917 − 0.16265I
−1.15801 − 12.77270I 5.19545 + 9.98793I
u = −0.655533 + 0.444833I
a = −0.568758 + 0.309874I
b = −0.165875 + 0.683566I
−4.78712 − 0.77055I 4.27518 − 2.02219I
u = −0.655533 − 0.444833I
a = −0.568758 − 0.309874I
b = −0.165875 − 0.683566I
−4.78712 + 0.77055I 4.27518 + 2.02219I
u = −0.622505 + 0.481239I
a = 0.245787 − 0.637722I
b = −0.380467 − 0.619541I
−4.93263 − 3.45869I 3.45815 + 8.17533I
u = −0.622505 − 0.481239I
a = 0.245787 + 0.637722I
b = −0.380467 + 0.619541I
−4.93263 + 3.45869I 3.45815 − 8.17533I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.681826 + 0.378269I
a = 2.73645 − 0.17651I
b = 2.29636 − 0.07821I
1.22083 + 7.21067I 8.33989 − 6.35791I
u = 0.681826 − 0.378269I
a = 2.73645 + 0.17651I
b = 2.29636 + 0.07821I
1.22083 − 7.21067I 8.33989 + 6.35791I
u = 0.555518 + 0.540981I
a = −1.11207 + 2.49940I
b = −0.953299 + 0.378073I
−1.75174 − 8.58830I 3.72994 + 4.13812I
u = 0.555518 − 0.540981I
a = −1.11207 − 2.49940I
b = −0.953299 − 0.378073I
−1.75174 + 8.58830I 3.72994 − 4.13812I
u = −0.666620 + 0.388015I
a = −0.958765 − 0.000505I
b = −0.754029 + 0.679010I
−3.47583 − 6.55474I 3.56008 + 7.35236I
u = −0.666620 − 0.388015I
a = −0.958765 + 0.000505I
b = −0.754029 − 0.679010I
−3.47583 + 6.55474I 3.56008 − 7.35236I
u = 0.145987 + 1.225320I
a = 0.007933 + 0.249436I
b = 0.748621 − 0.760668I
−2.36582 + 0.77393I 0
u = 0.145987 − 1.225320I
a = 0.007933 − 0.249436I
b = 0.748621 + 0.760668I
−2.36582 − 0.77393I 0
u = 0.651996 + 0.392636I
a = −3.32272 − 0.41767I
b = −2.40704 − 0.36202I
−4.32011 + 3.99543I 4.12422 − 6.59810I
u = 0.651996 − 0.392636I
a = −3.32272 + 0.41767I
b = −2.40704 + 0.36202I
−4.32011 − 3.99543I 4.12422 + 6.59810I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.529646 + 0.527281I
a = 0.83363 − 2.44550I
b = 0.670451 − 0.398275I
0.59744 − 3.14929I 6.80686 + 0.31636I
u = 0.529646 − 0.527281I
a = 0.83363 + 2.44550I
b = 0.670451 + 0.398275I
0.59744 + 3.14929I 6.80686 − 0.31636I
u = −0.545896 + 0.498041I
a = −0.053053 − 0.997688I
b = −0.841966 − 0.459143I
−3.96124 + 2.53513I 1.92062 − 0.95185I
u = −0.545896 − 0.498041I
a = −0.053053 + 0.997688I
b = −0.841966 + 0.459143I
−3.96124 − 2.53513I 1.92062 + 0.95185I
u = −0.625833 + 0.381321I
a = 0.834785 + 0.303156I
b = 0.802569 − 0.344086I
−1.98725 − 2.24402I 5.47486 + 2.60472I
u = −0.625833 − 0.381321I
a = 0.834785 − 0.303156I
b = 0.802569 + 0.344086I
−1.98725 + 2.24402I 5.47486 − 2.60472I
u = 0.556284 + 0.474387I
a = −0.38833 + 3.14529I
b = −0.480167 + 1.085090I
−4.69977 − 0.02977I 2.52437 + 0.10755I
u = 0.556284 − 0.474387I
a = −0.38833 − 3.14529I
b = −0.480167 − 1.085090I
−4.69977 + 0.02977I 2.52437 − 0.10755I
u = −0.220636 + 1.250340I
a = −0.44070 − 1.47175I
b = −2.06377 + 1.59068I
1.98043 − 5.03762I 0
u = −0.220636 − 1.250340I
a = −0.44070 + 1.47175I
b = −2.06377 − 1.59068I
1.98043 + 5.03762I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.164083 + 1.261680I
a = 0.65175 + 1.65425I
b = 2.23983 − 2.06975I
−4.01978 − 2.64901I 0
u = −0.164083 − 1.261680I
a = 0.65175 − 1.65425I
b = 2.23983 + 2.06975I
−4.01978 + 2.64901I 0
u = 0.192419 + 1.262480I
a = 0.0551400 − 0.1149010I
b = −1.019200 + 0.512780I
−2.86556 + 4.87473I 0
u = 0.192419 − 1.262480I
a = 0.0551400 + 0.1149010I
b = −1.019200 − 0.512780I
−2.86556 − 4.87473I 0
u = 0.646126 + 0.313529I
a = 1.75378 + 0.37623I
b = 1.56532 − 0.11169I
3.18820 + 3.73788I 10.37835 − 6.18860I
u = 0.646126 − 0.313529I
a = 1.75378 − 0.37623I
b = 1.56532 + 0.11169I
3.18820 − 3.73788I 10.37835 + 6.18860I
u = −0.233887 + 1.270730I
a = 0.39170 + 1.45839I
b = 2.08527 − 1.50862I
0.05201 − 10.63290I 0
u = −0.233887 − 1.270730I
a = 0.39170 − 1.45839I
b = 2.08527 + 1.50862I
0.05201 + 10.63290I 0
u = −0.557320 + 0.428223I
a = 0.386482 + 0.794648I
b = 0.785288 + 0.179548I
−2.25038 − 1.52905I 4.54304 + 4.84070I
u = −0.557320 − 0.428223I
a = 0.386482 − 0.794648I
b = 0.785288 − 0.179548I
−2.25038 + 1.52905I 4.54304 − 4.84070I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.629600 + 0.259973I
a = −1.195540 − 0.301501I
b = −1.198360 + 0.315983I
2.36633 − 1.56857I 9.57501 − 0.35949I
u = 0.629600 − 0.259973I
a = −1.195540 + 0.301501I
b = −1.198360 − 0.315983I
2.36633 + 1.56857I 9.57501 + 0.35949I
u = 0.076396 + 1.320050I
a = 0.273441 − 0.089865I
b = −0.205489 − 0.776355I
−3.46868 + 1.61071I 0
u = 0.076396 − 1.320050I
a = 0.273441 + 0.089865I
b = −0.205489 + 0.776355I
−3.46868 − 1.61071I 0
u = −0.659928 + 0.077076I
a = 2.57388 + 0.32862I
b = 2.32497 − 0.07020I
4.21134 − 7.37974I 11.34871 + 6.94008I
u = −0.659928 − 0.077076I
a = 2.57388 − 0.32862I
b = 2.32497 + 0.07020I
4.21134 + 7.37974I 11.34871 − 6.94008I
u = −0.652326 + 0.044106I
a = −2.70896 − 0.22220I
b = −2.38718 + 0.02177I
5.94549 − 1.85105I 14.4520 + 1.6433I
u = −0.652326 − 0.044106I
a = −2.70896 + 0.22220I
b = −2.38718 − 0.02177I
5.94549 + 1.85105I 14.4520 − 1.6433I
u = −0.017316 + 1.356330I
a = −0.772933 + 0.352254I
b = 0.77425 + 1.27105I
−6.60923 − 1.10020I 0
u = −0.017316 − 1.356330I
a = −0.772933 − 0.352254I
b = 0.77425 − 1.27105I
−6.60923 + 1.10020I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.241955 + 0.580936I
a = −0.50859 + 1.49464I
b = 0.284696 − 0.316284I
0.97832 + 4.80181I 5.01410 − 5.93125I
u = 0.241955 − 0.580936I
a = −0.50859 − 1.49464I
b = 0.284696 + 0.316284I
0.97832 − 4.80181I 5.01410 + 5.93125I
u = 0.351832 + 0.510395I
a = 0.46830 − 1.66268I
b = −0.0939873 + 0.0881433I
2.22250 − 0.24767I 7.73913 − 0.56298I
u = 0.351832 − 0.510395I
a = 0.46830 + 1.66268I
b = −0.0939873 − 0.0881433I
2.22250 + 0.24767I 7.73913 + 0.56298I
u = 0.116845 + 1.384250I
a = 0.041303 − 0.388215I
b = −0.633374 − 0.727871I
−3.55337 + 1.37478I 0
u = 0.116845 − 1.384250I
a = 0.041303 + 0.388215I
b = −0.633374 + 0.727871I
−3.55337 − 1.37478I 0
u = 0.604374 + 0.041012I
a = −0.127766 + 0.081512I
b = −0.185218 + 0.709651I
1.12451 + 1.96589I 10.80196 − 4.05866I
u = 0.604374 − 0.041012I
a = −0.127766 − 0.081512I
b = −0.185218 − 0.709651I
1.12451 − 1.96589I 10.80196 + 4.05866I
u = 0.05273 + 1.41471I
a = −0.364160 + 0.574122I
b = 0.622545 + 0.777866I
−5.11969 + 5.69600I 0
u = 0.05273 − 1.41471I
a = −0.364160 − 0.574122I
b = 0.622545 − 0.777866I
−5.11969 − 5.69600I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22845 + 1.40463I
a = −0.584878 + 0.164449I
b = −2.06966 − 0.85642I
−2.94894 + 1.53520I 0
u = 0.22845 − 1.40463I
a = −0.584878 − 0.164449I
b = −2.06966 + 0.85642I
−2.94894 − 1.53520I 0
u = −0.567594
a = 3.54330
b = 2.58102
−0.173277 14.7950
u = 0.24441 + 1.42516I
a = 0.811666 − 0.501528I
b = 2.72720 + 0.93818I
−2.38662 + 6.98651I 0
u = 0.24441 − 1.42516I
a = 0.811666 + 0.501528I
b = 2.72720 − 0.93818I
−2.38662 − 6.98651I 0
u = −0.23688 + 1.44898I
a = 0.157512 + 0.487133I
b = 0.614421 − 0.604235I
−7.87270 − 5.41534I 0
u = −0.23688 − 1.44898I
a = 0.157512 − 0.487133I
b = 0.614421 + 0.604235I
−7.87270 + 5.41534I 0
u = −0.20910 + 1.45390I
a = −0.200284 + 0.476133I
b = 0.839346 − 0.055335I
−8.29005 − 4.36445I 0
u = −0.20910 − 1.45390I
a = −0.200284 − 0.476133I
b = 0.839346 + 0.055335I
−8.29005 + 4.36445I 0
u = 0.24393 + 1.45525I
a = −1.39528 + 1.22066I
b = −4.12013 − 1.03876I
−10.26670 + 7.27552I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.24393 − 1.45525I
a = −1.39528 − 1.22066I
b = −4.12013 + 1.03876I
−10.26670 − 7.27552I 0
u = 0.25656 + 1.45349I
a = 0.92293 − 1.21619I
b = 3.66245 + 0.51819I
−4.67134 + 10.63770I 0
u = 0.25656 − 1.45349I
a = 0.92293 + 1.21619I
b = 3.66245 − 0.51819I
−4.67134 − 10.63770I 0
u = −0.24966 + 1.45541I
a = −0.324280 − 0.465634I
b = −0.455645 + 0.854292I
−9.40835 − 9.90508I 0
u = −0.24966 − 1.45541I
a = −0.324280 + 0.465634I
b = −0.455645 − 0.854292I
−9.40835 + 9.90508I 0
u = 0.20029 + 1.46346I
a = 1.06981 + 1.23843I
b = 0.30114 + 2.78559I
−10.91640 + 2.73847I 0
u = 0.20029 − 1.46346I
a = 1.06981 − 1.23843I
b = 0.30114 − 2.78559I
−10.91640 − 2.73847I 0
u = 0.18047 + 1.46741I
a = −0.570968 − 1.146810I
b = −0.07249 − 1.84130I
−5.78797 − 0.59952I 0
u = 0.18047 − 1.46741I
a = −0.570968 + 1.146810I
b = −0.07249 + 1.84130I
−5.78797 + 0.59952I 0
u = −0.19235 + 1.46609I
a = 0.407594 − 0.477800I
b = −0.969850 − 0.229697I
−10.25700 − 0.14816I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.19235 − 1.46609I
a = 0.407594 + 0.477800I
b = −0.969850 + 0.229697I
−10.25700 + 0.14816I 0
u = 0.25926 + 1.45968I
a = −0.83788 + 1.37375I
b = −3.73811 − 0.29307I
−7.1149 + 16.2459I 0
u = 0.25926 − 1.45968I
a = −0.83788 − 1.37375I
b = −3.73811 + 0.29307I
−7.1149 − 16.2459I 0
u = 0.18213 + 1.47921I
a = 0.48220 + 1.33181I
b = −0.32791 + 1.78574I
−8.26083 − 5.95025I 0
u = 0.18213 − 1.47921I
a = 0.48220 − 1.33181I
b = −0.32791 − 1.78574I
−8.26083 + 5.95025I 0
u = −0.23642 + 1.47425I
a = −0.345417 − 0.152000I
b = 0.050317 + 0.631314I
−10.98450 − 4.02659I 0
u = −0.23642 − 1.47425I
a = −0.345417 + 0.152000I
b = 0.050317 − 0.631314I
−10.98450 + 4.02659I 0
u = −0.21737 + 1.47965I
a = 0.389128 − 0.167581I
b = −0.545415 − 0.427739I
−11.27020 − 6.51429I 0
u = −0.21737 − 1.47965I
a = 0.389128 + 0.167581I
b = −0.545415 + 0.427739I
−11.27020 + 6.51429I 0
u = 0.396015
a = 0.287101
b = −0.240748
0.637008 15.7460
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.139636 + 0.286971I
a = −0.22054 + 2.15421I
b = 0.621920 + 0.269076I
−1.64649 − 0.67439I −2.11777 + 2.06502I
u = −0.139636 − 0.286971I
a = −0.22054 − 2.15421I
b = 0.621920 − 0.269076I
−1.64649 + 0.67439I −2.11777 − 2.06502I
14
II. I
u
2
= h−u
2
+ b − 1, −u
2
+ a − 2, u
3
+ 2u − 1i
(i) Arc colorings
a
6
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
7
=
u
−u + 1
a
4
=
u
2
+ 2
u
2
+ 1
a
8
=
1
−u + 1
a
9
=
1
−u + 1
a
3
=
u
2
+ 2
u
2
+ 1
a
5
=
−u
u
2
a
2
=
u
2
+ u + 2
1
a
10
=
u
2
+ 1
u
a
1
=
u
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
2
+ 3u + 2
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
8
u
3
c
4
(u + 1)
3
c
5
, c
6
, c
9
u
3
+ 2u + 1
c
7
u
3
+ 3u
2
+ 5u + 2
c
10
, c
11
, c
12
u
3
+ 2u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
8
y
3
c
5
, c
6
, c
9
c
10
, c
11
, c
12
y
3
+ 4y
2
+ 4y −1
c
7
y
3
+ y
2
+ 13y −4
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22670 + 1.46771I
a = −0.102785 − 0.665457I
b = −1.102790 − 0.665457I
−11.08570 − 5.13794I −0.78288 + 3.73768I
u = −0.22670 − 1.46771I
a = −0.102785 + 0.665457I
b = −1.102790 + 0.665457I
−11.08570 + 5.13794I −0.78288 − 3.73768I
u = 0.453398
a = 2.20557
b = 1.20557
−0.857735 3.56580
18
III. I
u
3
= hu
3
+ u
2
+ b + u + 1, u
3
+ u
2
+ a + 2u + 2, u
4
+ u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
6
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
7
=
u
u
3
+ u
a
4
=
−u
3
− u
2
− 2u − 2
−u
3
− u
2
− u − 1
a
8
=
u
3
+ 2u
u
3
+ u
a
9
=
u
3
+ 2u
u
3
+ u
a
3
=
−u
3
− u
2
− 2u − 2
−u
3
− u
2
− u − 1
a
5
=
−2u
3
− u
2
− 3u − 3
−u
3
− u
2
− u − 2
a
2
=
u
3
+ u + 1
1
a
10
=
u
2
+ 1
−u
3
− 2u − 1
a
1
=
2u
3
+ u
2
+ 3u + 3
u
3
+ u
2
+ u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
3
+ 2u
2
+ 6u + 5
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
8
u
4
c
4
(u + 1)
4
c
5
, c
6
, c
9
u
4
− u
3
+ 2u
2
− 2u + 1
c
7
(u
2
− u + 1)
2
c
10
, c
11
, c
12
u
4
+ u
3
+ 2u
2
+ 2u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
8
y
4
c
5
, c
6
, c
9
c
10
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
c
7
(y
2
+ y + 1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621744 + 0.440597I
a = −1.070700 − 0.758745I
b = −0.692440 − 0.318148I
−4.93480 − 2.02988I 2.26314 + 3.67497I
u = −0.621744 − 0.440597I
a = −1.070700 + 0.758745I
b = −0.692440 + 0.318148I
−4.93480 + 2.02988I 2.26314 − 3.67497I
u = 0.121744 + 1.306620I
a = 0.070696 − 0.758745I
b = 1.192440 + 0.547877I
−4.93480 + 2.02988I −0.76314 − 2.38721I
u = 0.121744 − 1.306620I
a = 0.070696 + 0.758745I
b = 1.192440 − 0.547877I
−4.93480 − 2.02988I −0.76314 + 2.38721I
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
7
)(u
92
+ 44u
91
+ ··· + 78u + 1)
c
2
((u − 1)
7
)(u
92
− 8u
91
+ ··· + 14u − 1)
c
3
, c
8
u
7
(u
92
+ u
91
+ ··· + 192u + 128)
c
4
((u + 1)
7
)(u
92
− 8u
91
+ ··· + 14u − 1)
c
5
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
92
− 2u
91
+ ··· + 13397u − 11981)
c
6
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
92
− 2u
91
+ ··· + 3u − 1)
c
7
((u
2
− u + 1)
2
)(u
3
+ 3u
2
+ 5u + 2)(u
92
+ 2u
91
+ ··· + 19896u − 4360)
c
9
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
92
+ 14u
91
+ ··· + 3115u + 131)
c
10
, c
11
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
92
− 2u
91
+ ··· + 3u − 1)
c
12
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
92
+ 14u
91
+ ··· + 3115u + 131)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
7
)(y
92
+ 16y
91
+ ··· − 5674y + 1)
c
2
, c
4
((y −1)
7
)(y
92
− 44y
91
+ ··· − 78y + 1)
c
3
, c
8
y
7
(y
92
− 45y
91
+ ··· − 438272y + 16384)
c
5
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
92
− 10y
91
+ ··· + 378763105y + 143544361)
c
6
, c
10
, c
11
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
92
+ 86y
91
+ ··· + y + 1)
c
7
(y
2
+ y + 1)
2
(y
3
+ y
2
+ 13y −4)
· (y
92
+ 30y
91
+ ··· + 525356144y + 19009600)
c
9
, c
12
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
92
+ 74y
91
+ ··· + 260373y + 17161)
24
