12a
0087
(K12a
0087
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 9 11 1 4 7 12 6 10
Solving Sequence
1,7 4,8
9 10 3 2 5 12 11 6
c
7
c
8
c
9
c
3
c
1
c
4
c
12
c
10
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.26080 × 10
259
u
95
+ 6.13882 × 10
258
u
94
+ ··· + 2.17742 × 10
262
b + 1.97351 × 10
262
,
− 1.46854 × 10
260
u
95
+ 1.49274 × 10
260
u
94
+ ··· + 1.08871 × 10
263
a − 6.09536 × 10
263
,
u
96
− 2u
95
+ ··· − 460u − 200i
I
u
2
= hb − u, −u
8
+ u
7
+ 2u
6
− 3u
5
− u
4
+ 3u
3
− 2u
2
+ a + 1, u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 105 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
= h1.26 × 10
259
u
95
+ 6.14 × 10
258
u
94
+ · · · + 2.18 × 10
262
b + 1.97 ×
10
262
, −1.47 × 10
260
u
95
+ 1.49 × 10
260
u
94
+ · · · + 1.09 × 10
263
a − 6.10 ×
10
263
, u
96
− 2u
95
+ · · · − 460u − 200i
(i) Arc colorings
a
1
=
0
u
a
7
=
1
0
a
4
=
0.00134888u
95
− 0.00137111u
94
+ ··· − 23.9339u + 5.59870
−0.000579033u
95
− 0.000281931u
94
+ ··· + 1.99179u − 0.906349
a
8
=
1
−u
2
a
9
=
−0.00264479u
95
+ 0.00389553u
94
+ ··· − 21.5177u + 8.21684
−0.00108988u
95
+ 0.000477782u
94
+ ··· − 2.75847u − 1.78684
a
10
=
−0.00373468u
95
+ 0.00437331u
94
+ ··· − 24.2761u + 6.43000
−0.00108988u
95
+ 0.000477782u
94
+ ··· − 2.75847u − 1.78684
a
3
=
−0.000268801u
95
+ 0.000972032u
94
+ ··· − 26.8057u + 6.23972
0.000223594u
95
− 0.00110886u
94
+ ··· + 2.72574u − 0.727907
a
2
=
0.00893103u
95
− 0.0164647u
94
+ ··· − 30.2478u − 0.173459
−0.000308624u
95
+ 0.00120035u
94
+ ··· + 7.65580u − 0.365428
a
5
=
0.0103283u
95
− 0.0184415u
94
+ ··· − 30.8959u − 0.822307
−0.00139406u
95
+ 0.00166301u
94
+ ··· + 7.00023u − 0.528959
a
12
=
−0.00735718u
95
+ 0.0171983u
94
+ ··· + 35.3516u + 1.21405
−0.00106631u
95
− 0.000829870u
94
+ ··· − 8.00807u + 0.599583
a
11
=
0.00580303u
95
− 0.0104224u
94
+ ··· + 4.52281u − 6.13898
0.000466017u
95
+ 0.000741362u
94
+ ··· + 4.55819u + 0.807933
a
6
=
0.00893420u
95
− 0.0167785u
94
+ ··· − 23.8956u − 1.35127
−0.00309604u
95
+ 0.00328517u
94
+ ··· + 4.71205u − 0.746936
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00392468u
95
− 0.00398262u
94
+ ··· − 17.9482u + 11.0656
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
96
+ 42u
95
+ ··· + 29u + 1
c
2
, c
4
u
96
− 10u
95
+ ··· + 13u − 1
c
3
, c
8
u
96
+ u
95
+ ··· + 1536u + 512
c
5
, c
7
u
96
− 2u
95
+ ··· − 460u − 200
c
6
, c
11
u
96
− 2u
95
+ ··· + u − 1
c
9
u
96
+ 10u
95
+ ··· − 45760u − 5824
c
10
, c
12
u
96
+ 30u
95
+ ··· + 7u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
96
+ 34y
95
+ ··· − 261y + 1
c
2
, c
4
y
96
− 42y
95
+ ··· − 29y + 1
c
3
, c
8
y
96
− 57y
95
+ ··· − 7602176y + 262144
c
5
, c
7
y
96
− 82y
95
+ ··· + 739600y + 40000
c
6
, c
11
y
96
+ 30y
95
+ ··· + 7y + 1
c
9
y
96
− 26y
95
+ ··· + 1172319616y + 33918976
c
10
, c
12
y
96
+ 74y
95
+ ··· + 79y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.827779 + 0.624593I
a = 0.766054 − 0.164191I
b = 0.493580 − 0.463043I
3.48652 + 0.96941I 0
u = 0.827779 − 0.624593I
a = 0.766054 + 0.164191I
b = 0.493580 + 0.463043I
3.48652 − 0.96941I 0
u = −0.776180 + 0.705899I
a = −0.791059 − 0.015213I
b = −0.729017 − 0.490853I
2.73740 − 6.45315I 0
u = −0.776180 − 0.705899I
a = −0.791059 + 0.015213I
b = −0.729017 + 0.490853I
2.73740 + 6.45315I 0
u = 0.464918 + 0.808617I
a = 0.742252 + 0.500605I
b = 1.20591 − 1.12994I
−1.02113 + 6.02463I 0. − 6.77260I
u = 0.464918 − 0.808617I
a = 0.742252 − 0.500605I
b = 1.20591 + 1.12994I
−1.02113 − 6.02463I 0. + 6.77260I
u = −0.378156 + 1.002420I
a = −0.0671290 − 0.0699448I
b = −0.934967 − 0.347321I
−0.05564 + 4.08075I 0
u = −0.378156 − 1.002420I
a = −0.0671290 + 0.0699448I
b = −0.934967 + 0.347321I
−0.05564 − 4.08075I 0
u = −1.100440 + 0.034710I
a = 0.158113 + 0.235477I
b = −0.364706 + 0.755399I
−0.475309 − 0.554742I 0
u = −1.100440 − 0.034710I
a = 0.158113 − 0.235477I
b = −0.364706 − 0.755399I
−0.475309 + 0.554742I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.198330 + 0.838237I
a = −0.004574 + 0.568131I
b = −0.892057 + 0.019153I
0.69375 + 4.11299I 4.80660 − 6.49721I
u = 0.198330 − 0.838237I
a = −0.004574 − 0.568131I
b = −0.892057 − 0.019153I
0.69375 − 4.11299I 4.80660 + 6.49721I
u = 0.566068 + 0.648047I
a = 0.125153 − 0.466570I
b = 0.658996 − 0.216976I
1.40639 − 0.40707I 7.71113 + 0.I
u = 0.566068 − 0.648047I
a = 0.125153 + 0.466570I
b = 0.658996 + 0.216976I
1.40639 + 0.40707I 7.71113 + 0.I
u = 1.123300 + 0.256960I
a = −2.35906 + 0.10801I
b = 1.95563 + 1.12656I
−2.14141 + 2.71496I 0
u = 1.123300 − 0.256960I
a = −2.35906 − 0.10801I
b = 1.95563 − 1.12656I
−2.14141 − 2.71496I 0
u = −0.536243 + 0.654347I
a = −0.505424 + 0.534295I
b = −0.879070 − 1.082410I
−0.382139 − 0.796657I 1.13878 + 1.64523I
u = −0.536243 − 0.654347I
a = −0.505424 − 0.534295I
b = −0.879070 + 1.082410I
−0.382139 + 0.796657I 1.13878 − 1.64523I
u = −0.026316 + 1.166270I
a = 0.175568 + 0.203349I
b = 1.195080 − 0.079544I
−0.448862 + 0.214466I 0
u = −0.026316 − 1.166270I
a = 0.175568 − 0.203349I
b = 1.195080 + 0.079544I
−0.448862 − 0.214466I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.274505 + 0.786774I
a = 1.76746 + 0.75543I
b = 1.30709 + 0.68152I
−1.42380 − 3.79251I 0. + 7.12596I
u = −0.274505 − 0.786774I
a = 1.76746 − 0.75543I
b = 1.30709 − 0.68152I
−1.42380 + 3.79251I 0. − 7.12596I
u = 0.711183 + 0.933780I
a = −0.664766 + 0.629968I
b = −0.525651 + 0.615669I
1.83320 + 5.67791I 0
u = 0.711183 − 0.933780I
a = −0.664766 − 0.629968I
b = −0.525651 − 0.615669I
1.83320 − 5.67791I 0
u = −0.813850 + 0.858127I
a = −0.267229 − 0.194580I
b = −0.572924 − 0.483599I
−2.36574 − 1.38104I 0
u = −0.813850 − 0.858127I
a = −0.267229 + 0.194580I
b = −0.572924 + 0.483599I
−2.36574 + 1.38104I 0
u = 0.113824 + 0.777555I
a = 1.15581 + 0.83439I
b = 1.38543 − 0.35114I
−5.10467 + 1.06897I −7.34001 − 0.30204I
u = 0.113824 − 0.777555I
a = 1.15581 − 0.83439I
b = 1.38543 + 0.35114I
−5.10467 − 1.06897I −7.34001 + 0.30204I
u = −1.21618
a = 2.35855
b = −2.53045
0.969248 0
u = 1.093860 + 0.533224I
a = 0.368064 − 0.089389I
b = 0.248387 − 0.349717I
3.61901 + 1.02354I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.093860 − 0.533224I
a = 0.368064 + 0.089389I
b = 0.248387 + 0.349717I
3.61901 − 1.02354I 0
u = −0.423602 + 1.151240I
a = 0.408811 + 0.403769I
b = 1.106640 + 0.403349I
−3.57664 − 5.39810I 0
u = −0.423602 − 1.151240I
a = 0.408811 − 0.403769I
b = 1.106640 − 0.403349I
−3.57664 + 5.39810I 0
u = 0.400539 + 0.627675I
a = −2.07511 + 0.80787I
b = −0.747446 + 0.842065I
−0.95421 − 1.31729I 2.18400 − 2.06346I
u = 0.400539 − 0.627675I
a = −2.07511 − 0.80787I
b = −0.747446 − 0.842065I
−0.95421 + 1.31729I 2.18400 + 2.06346I
u = −0.445856 + 0.557895I
a = −0.544443 + 0.185637I
b = −0.673309 + 0.120518I
−2.01713 − 1.57713I 0.42883 + 4.65454I
u = −0.445856 − 0.557895I
a = −0.544443 − 0.185637I
b = −0.673309 − 0.120518I
−2.01713 + 1.57713I 0.42883 − 4.65454I
u = 1.286230 + 0.076999I
a = −1.80122 + 0.72733I
b = 1.74533 − 1.39516I
9.63218 + 0.67885I 0
u = 1.286230 − 0.076999I
a = −1.80122 − 0.72733I
b = 1.74533 + 1.39516I
9.63218 − 0.67885I 0
u = 1.234880 + 0.379536I
a = −1.48139 + 0.72164I
b = 1.42509 − 0.17205I
3.11379 + 5.16324I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.234880 − 0.379536I
a = −1.48139 − 0.72164I
b = 1.42509 + 0.17205I
3.11379 − 5.16324I 0
u = 1.289470 + 0.129396I
a = 0.014621 − 0.284789I
b = 0.103192 − 0.622026I
2.48955 + 2.34627I 0
u = 1.289470 − 0.129396I
a = 0.014621 + 0.284789I
b = 0.103192 + 0.622026I
2.48955 − 2.34627I 0
u = −1.274750 + 0.328982I
a = −0.139931 − 0.224618I
b = 0.111267 − 0.851993I
−0.81320 − 5.10776I 0
u = −1.274750 − 0.328982I
a = −0.139931 + 0.224618I
b = 0.111267 + 0.851993I
−0.81320 + 5.10776I 0
u = 1.310800 + 0.170091I
a = 1.62551 − 0.47736I
b = −1.61937 + 0.38777I
4.79007 − 0.70146I 0
u = 1.310800 − 0.170091I
a = 1.62551 + 0.47736I
b = −1.61937 − 0.38777I
4.79007 + 0.70146I 0
u = −0.745639 + 1.091740I
a = 0.674140 + 0.477527I
b = 0.737945 + 0.876759I
0.85649 − 10.99580I 0
u = −0.745639 − 1.091740I
a = 0.674140 − 0.477527I
b = 0.737945 − 0.876759I
0.85649 + 10.99580I 0
u = −1.140160 + 0.671129I
a = −0.338273 − 0.104862I
b = −0.253242 − 0.467981I
2.79217 − 6.69642I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.140160 − 0.671129I
a = −0.338273 + 0.104862I
b = −0.253242 + 0.467981I
2.79217 + 6.69642I 0
u = −1.342110 + 0.110731I
a = 1.76836 + 0.67077I
b = −1.99856 − 1.24201I
10.26590 − 6.65314I 0
u = −1.342110 − 0.110731I
a = 1.76836 − 0.67077I
b = −1.99856 + 1.24201I
10.26590 + 6.65314I 0
u = −1.346640 + 0.193829I
a = 0.133789 + 0.425172I
b = −0.577467 + 0.438500I
5.59084 − 5.35666I 0
u = −1.346640 − 0.193829I
a = 0.133789 − 0.425172I
b = −0.577467 − 0.438500I
5.59084 + 5.35666I 0
u = 1.370410 + 0.134173I
a = −0.098663 + 0.414795I
b = 0.475158 + 0.391928I
6.31687 − 0.55010I 0
u = 1.370410 − 0.134173I
a = −0.098663 − 0.414795I
b = 0.475158 − 0.391928I
6.31687 + 0.55010I 0
u = 1.403460 + 0.020491I
a = 1.82408 + 0.48228I
b = −2.14446 − 1.34593I
11.20810 + 5.45907I 0
u = 1.403460 − 0.020491I
a = 1.82408 − 0.48228I
b = −2.14446 + 1.34593I
11.20810 − 5.45907I 0
u = 0.596086
a = 0.378856
b = 0.339787
0.826795 12.3850
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.39415 + 0.24042I
a = 2.29080 + 0.05093I
b = −3.32398 + 1.35225I
4.56353 − 1.83741I 0
u = −1.39415 − 0.24042I
a = 2.29080 − 0.05093I
b = −3.32398 − 1.35225I
4.56353 + 1.83741I 0
u = 0.064541 + 0.574239I
a = −0.546201 + 0.542337I
b = −0.368226 + 0.853562I
1.09357 + 2.72804I 4.37287 − 1.66251I
u = 0.064541 − 0.574239I
a = −0.546201 − 0.542337I
b = −0.368226 − 0.853562I
1.09357 − 2.72804I 4.37287 + 1.66251I
u = 1.38970 + 0.30493I
a = −2.28182 + 0.06308I
b = 3.21670 + 1.70719I
3.79038 + 7.72330I 0
u = 1.38970 − 0.30493I
a = −2.28182 − 0.06308I
b = 3.21670 − 1.70719I
3.79038 − 7.72330I 0
u = −1.43873 + 0.01362I
a = −1.80826 − 0.44328I
b = 2.34251 + 1.15556I
11.90280 − 0.51570I 0
u = −1.43873 − 0.01362I
a = −1.80826 + 0.44328I
b = 2.34251 − 1.15556I
11.90280 + 0.51570I 0
u = −1.45282 + 0.21004I
a = −1.67134 − 0.35027I
b = 2.30394 + 0.06403I
7.80775 − 2.46616I 0
u = −1.45282 − 0.21004I
a = −1.67134 + 0.35027I
b = 2.30394 − 0.06403I
7.80775 + 2.46616I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42836 + 0.35491I
a = 1.56214 + 0.55704I
b = −2.23729 − 0.08696I
5.97343 − 8.45094I 0
u = −1.42836 − 0.35491I
a = 1.56214 − 0.55704I
b = −2.23729 + 0.08696I
5.97343 + 8.45094I 0
u = −0.227545 + 0.469775I
a = 0.669485 + 0.611296I
b = 0.109400 + 0.953333I
1.25988 + 2.50075I 4.93074 − 4.35385I
u = −0.227545 − 0.469775I
a = 0.669485 − 0.611296I
b = 0.109400 − 0.953333I
1.25988 − 2.50075I 4.93074 + 4.35385I
u = 1.47830 + 0.28430I
a = 0.150661 − 0.359583I
b = −0.340358 − 0.512654I
6.00203 + 4.38225I 0
u = 1.47830 − 0.28430I
a = 0.150661 + 0.359583I
b = −0.340358 + 0.512654I
6.00203 − 4.38225I 0
u = 1.46841 + 0.33425I
a = 1.60248 − 0.27369I
b = −2.21204 − 0.61429I
4.35724 + 5.37503I 0
u = 1.46841 − 0.33425I
a = 1.60248 + 0.27369I
b = −2.21204 + 0.61429I
4.35724 − 5.37503I 0
u = −1.48449 + 0.33794I
a = −0.182448 − 0.354150I
b = 0.440507 − 0.586608I
5.19049 − 10.28900I 0
u = −1.48449 − 0.33794I
a = −0.182448 + 0.354150I
b = 0.440507 + 0.586608I
5.19049 + 10.28900I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49767 + 0.48896I
a = −1.47863 + 0.46783I
b = 2.35341 + 0.59797I
2.38378 + 11.28690I 0
u = 1.49767 − 0.48896I
a = −1.47863 − 0.46783I
b = 2.35341 − 0.59797I
2.38378 − 11.28690I 0
u = −1.60171 + 0.28748I
a = −1.69683 − 0.22396I
b = 3.03634 − 0.58541I
11.35890 − 4.75367I 0
u = −1.60171 − 0.28748I
a = −1.69683 + 0.22396I
b = 3.03634 + 0.58541I
11.35890 + 4.75367I 0
u = 1.61272 + 0.32466I
a = 1.68260 − 0.20082I
b = −3.03258 − 0.82668I
10.5170 + 10.7052I 0
u = 1.61272 − 0.32466I
a = 1.68260 + 0.20082I
b = −3.03258 + 0.82668I
10.5170 − 10.7052I 0
u = −1.62641 + 0.39035I
a = 1.57855 + 0.40202I
b = −3.11954 + 0.35306I
9.3431 − 10.8284I 0
u = −1.62641 − 0.39035I
a = 1.57855 − 0.40202I
b = −3.11954 − 0.35306I
9.3431 + 10.8284I 0
u = −0.109583 + 0.281441I
a = −0.28901 + 2.49262I
b = −0.446133 − 0.376732I
−1.66371 − 0.62726I −3.34444 + 1.32021I
u = −0.109583 − 0.281441I
a = −0.28901 − 2.49262I
b = −0.446133 + 0.376732I
−1.66371 + 0.62726I −3.34444 − 1.32021I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.65178 + 0.42833I
a = −1.55828 + 0.37748I
b = 3.17967 + 0.58690I
8.4581 + 16.7665I 0
u = 1.65178 − 0.42833I
a = −1.55828 − 0.37748I
b = 3.17967 − 0.58690I
8.4581 − 16.7665I 0
u = 0.236161 + 0.122429I
a = −1.29570 − 3.83873I
b = 1.085450 + 0.089161I
6.12820 + 0.12816I 9.44901 + 0.18719I
u = 0.236161 − 0.122429I
a = −1.29570 + 3.83873I
b = 1.085450 − 0.089161I
6.12820 − 0.12816I 9.44901 − 0.18719I
u = −0.096047 + 0.122605I
a = 5.78359 − 3.98742I
b = −1.134920 − 0.077601I
6.02935 + 5.60945I 9.08052 − 5.99594I
u = −0.096047 − 0.122605I
a = 5.78359 + 3.98742I
b = −1.134920 + 0.077601I
6.02935 − 5.60945I 9.08052 + 5.99594I
14
II.
I
u
2
= hb −u, −u
8
+u
7
+· · ·+a +1, u
9
−u
8
−2u
7
+3u
6
+u
5
−3u
4
+2u
3
−u+1i
(i) Arc colorings
a
1
=
0
u
a
7
=
1
0
a
4
=
u
8
− u
7
− 2u
6
+ 3u
5
+ u
4
− 3u
3
+ 2u
2
− 1
u
a
8
=
1
−u
2
a
9
=
1
−u
2
a
10
=
−u
2
+ 1
−u
2
a
3
=
u
8
− u
7
− 2u
6
+ 3u
5
+ u
4
− 3u
3
+ 2u
2
− 1
u
a
2
=
u
8
− u
7
− 2u
6
+ 3u
5
+ u
4
− 3u
3
+ 2u
2
− 1
2u
a
5
=
0
−u
a
12
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
11
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
6
=
−u
u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
8
− 4u
7
− 3u
6
+ 9u
5
− 10u
3
+ 2u
2
− 2u − 3
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
8
u
9
c
4
(u + 1)
9
c
5
, c
7
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
6
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
9
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
10
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
11
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
12
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
8
y
9
c
5
, c
7
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
6
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
9
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
10
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 + 0.510351I
a = −0.900982 + 0.594909I
b = 0.772920 + 0.510351I
−3.42837 + 2.09337I −5.30979 − 3.87975I
u = 0.772920 − 0.510351I
a = −0.900982 − 0.594909I
b = 0.772920 − 0.510351I
−3.42837 − 2.09337I −5.30979 + 3.87975I
u = −0.825933
a = 1.21075
b = −0.825933
−0.446489 2.50430
u = −1.173910 + 0.391555I
a = 0.766570 + 0.255687I
b = −1.173910 + 0.391555I
2.72642 − 1.33617I 1.53709 + 1.22905I
u = −1.173910 − 0.391555I
a = 0.766570 − 0.255687I
b = −1.173910 − 0.391555I
2.72642 + 1.33617I 1.53709 − 1.22905I
u = 0.141484 + 0.739668I
a = −0.249476 + 1.304240I
b = 0.141484 + 0.739668I
−1.02799 − 2.45442I 0.49381 + 3.35442I
u = 0.141484 − 0.739668I
a = −0.249476 − 1.304240I
b = 0.141484 − 0.739668I
−1.02799 + 2.45442I 0.49381 − 3.35442I
u = 1.172470 + 0.500383I
a = −0.721488 + 0.307914I
b = 1.172470 + 0.500383I
1.95319 + 7.08493I 0.02676 − 6.64241I
u = 1.172470 − 0.500383I
a = −0.721488 − 0.307914I
b = 1.172470 − 0.500383I
1.95319 − 7.08493I 0.02676 + 6.64241I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
96
+ 42u
95
+ ··· + 29u + 1)
c
2
((u − 1)
9
)(u
96
− 10u
95
+ ··· + 13u − 1)
c
3
, c
8
u
9
(u
96
+ u
95
+ ··· + 1536u + 512)
c
4
((u + 1)
9
)(u
96
− 10u
95
+ ··· + 13u − 1)
c
5
, c
7
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
96
− 2u
95
+ ··· − 460u − 200)
c
6
(u
9
− u
8
+ ··· + u + 1)(u
96
− 2u
95
+ ··· + u − 1)
c
9
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
96
+ 10u
95
+ ··· − 45760u − 5824)
c
10
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
96
+ 30u
95
+ ··· + 7u + 1)
c
11
(u
9
+ u
8
+ ··· + u − 1)(u
96
− 2u
95
+ ··· + u − 1)
c
12
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
96
+ 30u
95
+ ··· + 7u + 1)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
96
+ 34y
95
+ ··· − 261y + 1)
c
2
, c
4
((y −1)
9
)(y
96
− 42y
95
+ ··· − 29y + 1)
c
3
, c
8
y
9
(y
96
− 57y
95
+ ··· − 7602176y + 262144)
c
5
, c
7
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
96
− 82y
95
+ ··· + 739600y + 40000)
c
6
, c
11
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
96
+ 30y
95
+ ··· + 7y + 1)
c
9
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
96
− 26y
95
+ ··· + 1172319616y + 33918976)
c
10
, c
12
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
96
+ 74y
95
+ ··· + 79y + 1)
20
