12n
0448
(K12n
0448
)
A knot diagram
1
Linearized knot diagam
3 6 9 7 12 2 12 1 4 8 6 10
Solving Sequence
3,9
4
6,10
2 1 8 12 5 7 11
c
3
c
9
c
2
c
1
c
8
c
12
c
5
c
7
c
11
c
4
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.53148 × 10
174
u
69
− 2.38859 × 10
175
u
68
+ ··· + 3.44094 × 10
175
b − 1.21041 × 10
177
,
2.30131 × 10
177
u
69
+ 1.00000 × 10
178
u
68
+ ··· + 6.43455 × 10
177
a + 4.92351 × 10
179
,
u
70
+ 5u
69
+ ··· + 133u + 187i
I
u
2
= h−1290033u
15
− 1131359u
14
+ ··· + 1197778b + 2926203,
953271u
15
+ 281899u
14
+ ··· + 1197778a − 2560769,
u
16
− 4u
14
+ 7u
13
+ 6u
12
− 35u
11
+ 5u
10
+ 78u
9
− 22u
8
− 81u
7
+ 26u
6
+ 40u
5
− 9u
4
− 8u
3
− u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 86 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−5.53 × 10
174
u
69
− 2.39 × 10
175
u
68
+ · · · + 3.44 × 10
175
b − 1.21 ×
10
177
, 2.30 × 10
177
u
69
+ 1.00 × 10
178
u
68
+ · · · + 6.43 × 10
177
a + 4.92 ×
10
179
, u
70
+ 5u
69
+ · · · + 133u + 187i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
6
=
−0.357648u
69
− 1.55411u
68
+ ··· + 58.4125u − 76.5167
0.160755u
69
+ 0.694167u
68
+ ··· − 18.3617u + 35.1769
a
10
=
u
−u
3
+ u
a
2
=
−0.604140u
69
− 2.42601u
68
+ ··· + 35.7773u − 123.764
0.131251u
69
+ 0.509409u
68
+ ··· − 7.76498u + 21.3345
a
1
=
−0.472890u
69
− 1.91660u
68
+ ··· + 28.0123u − 102.430
0.131251u
69
+ 0.509409u
68
+ ··· − 7.76498u + 21.3345
a
8
=
0.275335u
69
+ 1.10381u
68
+ ··· − 17.6228u + 17.7511
0.0632866u
69
+ 0.331110u
68
+ ··· − 27.9242u − 5.29801
a
12
=
−0.667462u
69
− 2.66521u
68
+ ··· + 34.6405u − 145.026
0.116091u
69
+ 0.444757u
68
+ ··· − 7.69700u + 20.6722
a
5
=
−0.951234u
69
− 3.74486u
68
+ ··· + 57.2709u − 233.605
0.227979u
69
+ 0.806971u
68
+ ··· − 7.92854u + 76.2656
a
7
=
−0.230826u
69
− 0.796506u
68
+ ··· + 7.27297u − 94.3983
−0.0228490u
69
− 0.253480u
68
+ ··· + 19.3716u + 36.8622
a
11
=
−0.131055u
69
− 0.396858u
68
+ ··· − 40.2047u − 27.6191
−0.0330884u
69
− 0.0924880u
68
+ ··· − 10.5368u − 26.3188
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.760434u
69
− 3.35415u
68
+ ··· + 44.1683u − 94.2290
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
4(4u
70
+ 131u
69
+ ··· + 48u + 1)
c
2
, c
6
2(2u
70
− 7u
69
+ ··· + 24u
2
+ 1)
c
3
, c
9
u
70
+ 5u
69
+ ··· + 133u + 187
c
4
u
70
− 5u
69
+ ··· − 149u − 23
c
5
, c
11
2(2u
70
− u
69
+ ··· + 4385u + 4757)
c
7
2(2u
70
− u
69
+ ··· + 5245u + 337)
c
8
u
70
− 3u
69
+ ··· − 1069u + 284
c
10
u
70
− 5u
69
+ ··· + 187129u − 210478
c
12
4(4u
70
+ 49u
69
+ ··· + 17u + 1)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
16(16y
70
− 209y
69
+ ··· + 68y + 1)
c
2
, c
6
4(4y
70
+ 131y
69
+ ··· + 48y + 1)
c
3
, c
9
y
70
− 43y
69
+ ··· − 380095y + 34969
c
4
y
70
− 91y
69
+ ··· − 5733y + 529
c
5
, c
11
4(4y
70
− 297y
69
+ ··· − 5.60955 × 10
8
y + 2.26290 × 10
7
)
c
7
4(4y
70
− 321y
69
+ ··· − 1.42558 × 10
7
y + 113569)
c
8
y
70
− 13y
69
+ ··· − 1442097y + 80656
c
10
y
70
− 105y
69
+ ··· − 745406611913y + 44300988484
c
12
16(16y
70
− 345y
69
+ ··· − 19y + 1)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.464599 + 0.883560I
a = 1.159180 + 0.080014I
b = −0.192943 + 1.274430I
−11.04220 + 1.60100I −6.10686 + 0.I
u = −0.464599 − 0.883560I
a = 1.159180 − 0.080014I
b = −0.192943 − 1.274430I
−11.04220 − 1.60100I −6.10686 + 0.I
u = −0.979753 + 0.210842I
a = 2.34254 − 0.46008I
b = −0.772034 + 0.883693I
1.58904 − 5.03788I 0. + 6.76160I
u = −0.979753 − 0.210842I
a = 2.34254 + 0.46008I
b = −0.772034 − 0.883693I
1.58904 + 5.03788I 0. − 6.76160I
u = −0.700302 + 0.719629I
a = −0.993946 − 0.751903I
b = 0.030140 − 0.832344I
−2.63354 − 1.54336I 0
u = −0.700302 − 0.719629I
a = −0.993946 + 0.751903I
b = 0.030140 + 0.832344I
−2.63354 + 1.54336I 0
u = −0.005359 + 1.009280I
a = 0.816422 − 0.387914I
b = −0.844609 − 0.315485I
−5.80873 − 4.94651I 0. + 3.47805I
u = −0.005359 − 1.009280I
a = 0.816422 + 0.387914I
b = −0.844609 + 0.315485I
−5.80873 + 4.94651I 0. − 3.47805I
u = 1.015010 + 0.071788I
a = 1.84250 + 0.88128I
b = −0.714598 − 1.034220I
1.19682 + 0.83148I 0
u = 1.015010 − 0.071788I
a = 1.84250 − 0.88128I
b = −0.714598 + 1.034220I
1.19682 − 0.83148I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.955337 + 0.359418I
a = −0.886703 − 0.633142I
b = 0.160983 − 1.036430I
−1.42067 − 2.70624I 0
u = −0.955337 − 0.359418I
a = −0.886703 + 0.633142I
b = 0.160983 + 1.036430I
−1.42067 + 2.70624I 0
u = 0.298324 + 0.928107I
a = −1.228530 + 0.434075I
b = 0.622819 + 0.942231I
−0.05346 + 2.92988I −3.13586 + 0.I
u = 0.298324 − 0.928107I
a = −1.228530 − 0.434075I
b = 0.622819 − 0.942231I
−0.05346 − 2.92988I −3.13586 + 0.I
u = −0.781018 + 0.554341I
a = −0.31978 − 1.78763I
b = 0.442194 − 0.572328I
−3.82658 − 3.59438I −3.04697 + 8.28909I
u = −0.781018 − 0.554341I
a = −0.31978 + 1.78763I
b = 0.442194 + 0.572328I
−3.82658 + 3.59438I −3.04697 − 8.28909I
u = 1.05918
a = −2.48414
b = 2.15607
−0.181143 59.2940
u = 0.915256 + 0.029276I
a = −0.099666 − 0.493144I
b = 0.17584 + 1.44219I
0.571914 + 0.371518I 2.08669 + 4.04564I
u = 0.915256 − 0.029276I
a = −0.099666 + 0.493144I
b = 0.17584 − 1.44219I
0.571914 − 0.371518I 2.08669 − 4.04564I
u = −0.906146 + 0.074934I
a = −3.73501 − 0.59930I
b = 0.431575 + 0.671244I
−4.02627 − 1.96972I −0.155162 − 1.208213I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.906146 − 0.074934I
a = −3.73501 + 0.59930I
b = 0.431575 − 0.671244I
−4.02627 + 1.96972I −0.155162 + 1.208213I
u = 1.09514
a = −0.943160
b = 0.676322
2.04249 0
u = −1.016640 + 0.503840I
a = 0.445291 − 0.380585I
b = −0.04953 + 1.48446I
−9.31077 − 6.63658I 0
u = −1.016640 − 0.503840I
a = 0.445291 + 0.380585I
b = −0.04953 − 1.48446I
−9.31077 + 6.63658I 0
u = 1.149990 + 0.209744I
a = −2.22769 − 1.61595I
b = 0.482390 + 1.005790I
−5.19048 + 5.83129I 0
u = 1.149990 − 0.209744I
a = −2.22769 + 1.61595I
b = 0.482390 − 1.005790I
−5.19048 − 5.83129I 0
u = 1.034100 + 0.567938I
a = 0.681424 + 0.467191I
b = 0.462907 − 1.023170I
−5.28639 − 0.22576I 0
u = 1.034100 − 0.567938I
a = 0.681424 − 0.467191I
b = 0.462907 + 1.023170I
−5.28639 + 0.22576I 0
u = −0.391578 + 0.720386I
a = −0.642454 − 0.037102I
b = 0.605943 + 0.816528I
0.38215 + 1.91370I −0.15986 − 5.17626I
u = −0.391578 − 0.720386I
a = −0.642454 + 0.037102I
b = 0.605943 − 0.816528I
0.38215 − 1.91370I −0.15986 + 5.17626I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.223040 + 0.318759I
a = −1.68312 + 0.43802I
b = 0.77584 − 1.27813I
−3.16283 − 7.92717I 0
u = −1.223040 − 0.318759I
a = −1.68312 − 0.43802I
b = 0.77584 + 1.27813I
−3.16283 + 7.92717I 0
u = 1.188100 + 0.449897I
a = −1.57614 + 0.48371I
b = 0.527707 + 1.135380I
2.16637 + 8.43711I 0
u = 1.188100 − 0.449897I
a = −1.57614 − 0.48371I
b = 0.527707 − 1.135380I
2.16637 − 8.43711I 0
u = −0.033746 + 1.275580I
a = 0.637310 − 0.236491I
b = −0.597078 − 1.151310I
−8.27588 + 10.26740I 0
u = −0.033746 − 1.275580I
a = 0.637310 + 0.236491I
b = −0.597078 + 1.151310I
−8.27588 − 10.26740I 0
u = −1.266110 + 0.223855I
a = −0.552498 − 0.286672I
b = 0.653293 + 0.084722I
4.87564 − 3.90309I 0
u = −1.266110 − 0.223855I
a = −0.552498 + 0.286672I
b = 0.653293 − 0.084722I
4.87564 + 3.90309I 0
u = 0.253601 + 0.655257I
a = −0.523537 + 1.271420I
b = −0.392653 + 0.946500I
−0.72586 − 4.14260I −5.59399 + 3.21010I
u = 0.253601 − 0.655257I
a = −0.523537 − 1.271420I
b = −0.392653 − 0.946500I
−0.72586 + 4.14260I −5.59399 − 3.21010I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.589808 + 0.186046I
a = −0.431512 − 0.260037I
b = −0.781861 − 0.026540I
−3.87088 + 0.03004I −1.022144 + 0.715959I
u = −0.589808 − 0.186046I
a = −0.431512 + 0.260037I
b = −0.781861 + 0.026540I
−3.87088 − 0.03004I −1.022144 − 0.715959I
u = 0.233481 + 0.564982I
a = −0.158219 − 0.884725I
b = −0.516928 − 1.202080I
−7.20734 + 4.68280I −4.29878 − 2.45438I
u = 0.233481 − 0.564982I
a = −0.158219 + 0.884725I
b = −0.516928 + 1.202080I
−7.20734 − 4.68280I −4.29878 + 2.45438I
u = 1.328310 + 0.413029I
a = 0.900655 − 0.938285I
b = −0.832474 + 0.700137I
5.32908 + 2.46914I 0
u = 1.328310 − 0.413029I
a = 0.900655 + 0.938285I
b = −0.832474 − 0.700137I
5.32908 − 2.46914I 0
u = 0.599039 + 0.030720I
a = 0.56751 − 1.97937I
b = −0.453454 − 1.205370I
−7.42388 + 4.44358I −6.05332 + 3.21543I
u = 0.599039 − 0.030720I
a = 0.56751 + 1.97937I
b = −0.453454 + 1.205370I
−7.42388 − 4.44358I −6.05332 − 3.21543I
u = −1.382840 + 0.227853I
a = 0.473367 − 0.341147I
b = −0.092314 + 0.202393I
5.13577 − 3.94328I 0
u = −1.382840 − 0.227853I
a = 0.473367 + 0.341147I
b = −0.092314 − 0.202393I
5.13577 + 3.94328I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.31486 + 0.52213I
a = 1.93164 + 0.21624I
b = −0.735129 + 1.011560I
4.37815 − 8.33071I 0
u = −1.31486 − 0.52213I
a = 1.93164 − 0.21624I
b = −0.735129 − 1.011560I
4.37815 + 8.33071I 0
u = 1.32537 + 0.51263I
a = −1.157920 + 0.713920I
b = 1.074040 − 0.464067I
−1.69439 + 10.36170I 0
u = 1.32537 − 0.51263I
a = −1.157920 − 0.713920I
b = 1.074040 + 0.464067I
−1.69439 − 10.36170I 0
u = 0.252788 + 0.506991I
a = −0.532657 − 0.407831I
b = −0.153191 + 0.710555I
0.147499 + 1.102550I 0.28735 − 3.57953I
u = 0.252788 − 0.506991I
a = −0.532657 + 0.407831I
b = −0.153191 − 0.710555I
0.147499 − 1.102550I 0.28735 + 3.57953I
u = −1.41135 + 0.30987I
a = 0.828279 + 0.264347I
b = −0.549869 − 0.290535I
5.28134 − 4.06482I 0
u = −1.41135 − 0.30987I
a = 0.828279 − 0.264347I
b = −0.549869 + 0.290535I
5.28134 + 4.06482I 0
u = 0.194477 + 0.473241I
a = −0.656035 − 0.310197I
b = 0.089223 + 0.416326I
0.130111 + 1.160000I 1.63322 − 5.18662I
u = 0.194477 − 0.473241I
a = −0.656035 + 0.310197I
b = 0.089223 − 0.416326I
0.130111 − 1.160000I 1.63322 + 5.18662I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.39235 + 0.60772I
a = −1.73389 + 0.01315I
b = 0.715593 − 1.199470I
−4.0124 − 16.7820I 0
u = −1.39235 − 0.60772I
a = −1.73389 − 0.01315I
b = 0.715593 + 1.199470I
−4.0124 + 16.7820I 0
u = 1.42511 + 0.56986I
a = 1.42144 − 0.06516I
b = −0.546297 − 1.095260I
3.08348 + 8.62198I 0
u = 1.42511 − 0.56986I
a = 1.42144 + 0.06516I
b = −0.546297 + 1.095260I
3.08348 − 8.62198I 0
u = −1.65338 + 0.27922I
a = −1.48835 − 0.26253I
b = 0.440671 − 0.719090I
−1.64855 − 1.14131I 0
u = −1.65338 − 0.27922I
a = −1.48835 + 0.26253I
b = 0.440671 + 0.719090I
−1.64855 + 1.14131I 0
u = 1.99926 + 0.23997I
a = −0.880769 + 0.552125I
b = 0.480145 − 0.968668I
−2.50789 − 2.71379I 0
u = 1.99926 − 0.23997I
a = −0.880769 − 0.552125I
b = 0.480145 + 0.968668I
−2.50789 + 2.71379I 0
u = −0.32117 + 2.20502I
a = −0.784033 − 0.270740I
b = 0.387453 − 0.868439I
−1.99674 − 1.66389I 0
u = −0.32117 − 2.20502I
a = −0.784033 + 0.270740I
b = 0.387453 + 0.868439I
−1.99674 + 1.66389I 0
11
II.
I
u
2
= h−1.29 × 10
6
u
15
− 1.13 × 10
6
u
14
+ · · · + 1.20 × 10
6
b + 2.93 × 10
6
, 9.53 ×
10
5
u
15
+2.82×10
5
u
14
+· · · +1.20×10
6
a−2.56×10
6
, u
16
−4u
14
+· · · −u
2
+1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
6
=
−0.795866u
15
− 0.235352u
14
+ ··· + 4.26342u + 2.13793
1.07702u
15
+ 0.944548u
14
+ ··· − 1.60547u − 2.44303
a
10
=
u
−u
3
+ u
a
2
=
1.84022u
15
+ 1.64231u
14
+ ··· − 1.35878u − 3.85692
−1.74639u
15
− 0.653460u
14
+ ··· + 2.11509u + 0.759845
a
1
=
0.0938287u
15
+ 0.988846u
14
+ ··· + 0.756304u − 3.09708
−1.74639u
15
− 0.653460u
14
+ ··· + 2.11509u + 0.759845
a
8
=
0.382772u
15
− 1.57347u
14
+ ··· − 3.52755u + 3.36873
1.82910u
15
− 0.0135134u
14
+ ··· − 2.94809u + 0.179244
a
12
=
1.00004u
15
+ 1.75825u
14
+ ··· − 0.705337u − 4.34914
−1.24080u
15
− 0.124557u
14
+ ··· + 1.55966u + 0.277191
a
5
=
0.810195u
15
− 1.07195u
14
+ ··· + 1.39686u + 3.07255
1.92689u
15
+ 0.984967u
14
+ ··· − 2.74097u − 1.72000
a
7
=
−0.551846u
15
+ 0.0325922u
14
+ ··· − 0.915515u + 0.502171
1.10607u
15
+ 0.836355u
14
+ ··· + 0.354325u − 0.956254
a
11
=
−1.27414u
15
+ 1.26991u
14
+ ··· + 3.19297u − 2.72388
−0.979430u
15
+ 0.753485u
14
+ ··· + 0.0728900u − 1.30945
(ii) Obstruction class = 1
(iii) Cusp Shapes =
83543923
19164448
u
15
−
52495481
19164448
u
14
+ ··· −
23352059
19164448
u +
87198417
19164448
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
4(4u
16
− 31u
15
+ ··· − 9u + 1)
c
2
2(2u
16
− 3u
15
+ ··· − 3u + 1)
c
3
u
16
− 4u
14
+ ··· − u
2
+ 1
c
4
u
16
− 6u
15
+ ··· − 90u + 11
c
5
2(2u
16
− 7u
15
+ ··· + 2u + 1)
c
6
2(2u
16
+ 3u
15
+ ··· + 3u + 1)
c
7
2(2u
16
+ 5u
15
+ ··· − 2u + 1)
c
8
u
16
− 2u
15
+ ··· − 13u + 4
c
9
u
16
− 4u
14
+ ··· − u
2
+ 1
c
10
u
16
+ 6u
15
+ ··· + 29u + 26
c
11
2(2u
16
+ 7u
15
+ ··· − 2u + 1)
c
12
4(4u
16
− 27u
15
+ ··· − 10u + 1)
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
16(16y
16
+ 127y
15
+ ··· + 9y + 1)
c
2
, c
6
4(4y
16
+ 31y
15
+ ··· + 9y + 1)
c
3
, c
9
y
16
− 8y
15
+ ··· − 2y + 1
c
4
y
16
− 8y
15
+ ··· − 752y + 121
c
5
, c
11
4(4y
16
+ 3y
15
+ ··· − 8y + 1)
c
7
4(4y
16
− 37y
15
+ ··· + 14y + 1)
c
8
y
16
− 6y
15
+ ··· + 135y + 16
c
10
y
16
+ 2y
15
+ ··· − 269y + 676
c
12
16(16y
16
+ 55y
15
+ ··· − 10y + 1)
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.797657 + 0.343857I
a = 2.62392 − 1.53560I
b = 0.148206 − 0.607000I
−4.61528 + 2.55936I −8.49339 − 5.18844I
u = 0.797657 − 0.343857I
a = 2.62392 + 1.53560I
b = 0.148206 + 0.607000I
−4.61528 − 2.55936I −8.49339 + 5.18844I
u = −0.707983 + 0.173652I
a = 0.483804 − 1.222550I
b = 0.378031 − 1.204200I
−7.26365 − 4.94000I −1.72505 + 10.21759I
u = −0.707983 − 0.173652I
a = 0.483804 + 1.222550I
b = 0.378031 + 1.204200I
−7.26365 + 4.94000I −1.72505 − 10.21759I
u = 0.644670 + 0.122026I
a = 1.26759 − 1.06765I
b = −0.639556 + 1.085420I
−0.125269 − 0.619604I −4.11600 − 1.34409I
u = 0.644670 − 0.122026I
a = 1.26759 + 1.06765I
b = −0.639556 − 1.085420I
−0.125269 + 0.619604I −4.11600 + 1.34409I
u = −1.377210 + 0.155372I
a = −0.648145 + 0.541114I
b = 0.447066 − 0.459032I
5.30998 − 4.36295I 7.4979 + 13.3422I
u = −1.377210 − 0.155372I
a = −0.648145 − 0.541114I
b = 0.447066 + 0.459032I
5.30998 + 4.36295I 7.4979 − 13.3422I
u = 1.35263 + 0.51219I
a = −1.79117 + 0.24331I
b = 0.682041 + 1.016320I
5.25074 + 8.71932I 6.03301 − 7.80268I
u = 1.35263 − 0.51219I
a = −1.79117 − 0.24331I
b = 0.682041 − 1.016320I
5.25074 − 8.71932I 6.03301 + 7.80268I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41542 + 0.38827I
a = −0.745369 − 0.818937I
b = 0.698052 + 0.669887I
6.31275 − 3.35729I 6.36373 + 1.01374I
u = −1.41542 − 0.38827I
a = −0.745369 + 0.818937I
b = 0.698052 − 0.669887I
6.31275 + 3.35729I 6.36373 − 1.01374I
u = −0.121039 + 0.395800I
a = 1.70352 + 2.40451I
b = −0.596112 + 0.848095I
0.37584 − 4.14012I 1.56359 + 5.26099I
u = −0.121039 − 0.395800I
a = 1.70352 − 2.40451I
b = −0.596112 − 0.848095I
0.37584 + 4.14012I 1.56359 − 5.26099I
u = 0.82670 + 1.79548I
a = 0.855849 − 0.349758I
b = −0.367727 − 0.826736I
−1.95525 + 1.59611I 37.6731 + 11.4660I
u = 0.82670 − 1.79548I
a = 0.855849 + 0.349758I
b = −0.367727 + 0.826736I
−1.95525 − 1.59611I 37.6731 − 11.4660I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
16(4u
16
− 31u
15
+ ··· − 9u + 1)(4u
70
+ 131u
69
+ ··· + 48u + 1)
c
2
4(2u
16
− 3u
15
+ ··· − 3u + 1)(2u
70
− 7u
69
+ ··· + 24u
2
+ 1)
c
3
(u
16
− 4u
14
+ ··· − u
2
+ 1)(u
70
+ 5u
69
+ ··· + 133u + 187)
c
4
(u
16
− 6u
15
+ ··· − 90u + 11)(u
70
− 5u
69
+ ··· − 149u − 23)
c
5
4(2u
16
− 7u
15
+ ··· + 2u + 1)(2u
70
− u
69
+ ··· + 4385u + 4757)
c
6
4(2u
16
+ 3u
15
+ ··· + 3u + 1)(2u
70
− 7u
69
+ ··· + 24u
2
+ 1)
c
7
4(2u
16
+ 5u
15
+ ··· − 2u + 1)(2u
70
− u
69
+ ··· + 5245u + 337)
c
8
(u
16
− 2u
15
+ ··· − 13u + 4)(u
70
− 3u
69
+ ··· − 1069u + 284)
c
9
(u
16
− 4u
14
+ ··· − u
2
+ 1)(u
70
+ 5u
69
+ ··· + 133u + 187)
c
10
(u
16
+ 6u
15
+ ··· + 29u + 26)(u
70
− 5u
69
+ ··· + 187129u − 210478)
c
11
4(2u
16
+ 7u
15
+ ··· − 2u + 1)(2u
70
− u
69
+ ··· + 4385u + 4757)
c
12
16(4u
16
− 27u
15
+ ··· − 10u + 1)(4u
70
+ 49u
69
+ ··· + 17u + 1)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
256(16y
16
+ 127y
15
+ ··· + 9y + 1)(16y
70
− 209y
69
+ ··· + 68y + 1)
c
2
, c
6
16(4y
16
+ 31y
15
+ ··· + 9y + 1)(4y
70
+ 131y
69
+ ··· + 48y + 1)
c
3
, c
9
(y
16
− 8y
15
+ ··· − 2y + 1)(y
70
− 43y
69
+ ··· − 380095y + 34969)
c
4
(y
16
− 8y
15
+ ··· − 752y + 121)(y
70
− 91y
69
+ ··· − 5733y + 529)
c
5
, c
11
16(4y
16
+ 3y
15
+ ··· − 8y + 1)
· (4y
70
− 297y
69
+ ··· − 560955385y + 22629049)
c
7
16(4y
16
− 37y
15
+ ··· + 14y + 1)
· (4y
70
− 321y
69
+ ··· − 14255815y + 113569)
c
8
(y
16
− 6y
15
+ ··· + 135y + 16)
· (y
70
− 13y
69
+ ··· − 1442097y + 80656)
c
10
(y
16
+ 2y
15
+ ··· − 269y + 676)
· (y
70
− 105y
69
+ ··· − 745406611913y + 44300988484)
c
12
256(16y
16
+ 55y
15
+ ··· − 10y + 1)(16y
70
− 345y
69
+ ··· − 19y + 1)
20
