12n
0772
(K12n
0772
)
A knot diagram
1
Linearized knot diagam
4 6 9 12 2 12 10 3 1 7 4 8
Solving Sequence
3,8
9
1,4
10 7 12 5 6 2 11
c
8
c
3
c
9
c
7
c
12
c
4
c
6
c
2
c
11
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.73255 × 10
170
u
87
+ 3.77083 × 10
170
u
86
+ ··· + 1.71978 × 10
169
b + 4.69942 × 10
170
,
− 7.39052 × 10
170
u
87
+ 1.04203 × 10
171
u
86
+ ··· + 1.71978 × 10
169
a + 1.27642 × 10
171
,
u
88
− 2u
87
+ ··· − 7u
2
+ 1i
I
u
2
= h1869070191u
24
+ 1444290010u
23
+ ··· + 1044856181b + 1214090807,
7580555710u
24
+ 8345483601u
23
+ ··· + 1044856181a − 1136568902, u
25
+ u
24
+ ··· − 9u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 113 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−2.73 × 10
170
u
87
+ 3.77 × 10
170
u
86
+ · · · + 1.72 × 10
169
b + 4.70 ×
10
170
, −7.39 × 10
170
u
87
+ 1.04 × 10
171
u
86
+ · · · + 1.72 × 10
169
a + 1.28 ×
10
171
, u
88
− 2u
87
+ · · · − 7u
2
+ 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
1
=
42.9735u
87
− 60.5909u
86
+ ··· − 109.824u − 74.2200
15.8889u
87
− 21.9262u
86
+ ··· − 39.2450u − 27.3257
a
4
=
−u
−u
3
+ u
a
10
=
−29.6028u
87
+ 33.5360u
86
+ ··· + 25.1212u + 32.7939
7.55835u
87
− 9.72166u
86
+ ··· − 17.3864u − 11.9790
a
7
=
20.5958u
87
− 33.3831u
86
+ ··· − 72.8706u − 43.0649
5.79378u
87
− 7.20014u
86
+ ··· − 11.8431u − 9.92354
a
12
=
27.0846u
87
− 38.6647u
86
+ ··· − 70.5794u − 46.8944
15.8889u
87
− 21.9262u
86
+ ··· − 39.2450u − 27.3257
a
5
=
6.81156u
87
− 7.84254u
86
+ ··· − 10.9251u − 11.1767
−10.4758u
87
+ 9.82933u
86
+ ··· + 5.39362u + 10.8270
a
6
=
−20.5261u
87
+ 28.6221u
86
+ ··· + 55.1947u + 37.5188
−16.5192u
87
+ 24.9588u
86
+ ··· + 53.4694u + 32.4270
a
2
=
26.3861u
87
− 36.7076u
86
+ ··· − 64.1178u − 45.1799
27.6983u
87
− 38.1481u
86
+ ··· − 68.3642u − 47.0744
a
11
=
39.6126u
87
− 56.9442u
86
+ ··· − 105.928u − 69.0794
6.68892u
87
− 9.17729u
86
+ ··· − 16.4241u − 11.9172
(ii) Obstruction class = −1
(iii) Cusp Shapes = −19.2430u
87
+ 15.1487u
86
+ ··· − 24.6831u + 10.9472
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
88
+ 8u
86
+ ··· − 22991u − 4937
c
2
, c
5
u
88
+ 4u
87
+ ··· + 5u − 79
c
3
, c
8
u
88
+ 2u
87
+ ··· − 7u
2
+ 1
c
4
, c
11
u
88
+ u
87
+ ··· + 43878u − 1549
c
6
u
88
− 2u
87
+ ··· + 2779127u − 52466021
c
7
, c
10
u
88
+ 5u
87
+ ··· − 39868u − 4364
c
9
u
88
− 6u
87
+ ··· − 2747u − 199
c
12
u
88
+ 2u
87
+ ··· + 4454u − 497
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
88
+ 16y
87
+ ··· + 1139448487y + 24373969
c
2
, c
5
y
88
− 28y
87
+ ··· − 157709y + 6241
c
3
, c
8
y
88
− 50y
87
+ ··· − 14y + 1
c
4
, c
11
y
88
+ 73y
87
+ ··· − 414362598y + 2399401
c
6
y
88
− 54y
87
+ ··· − 104763397554533243y + 2752683359572441
c
7
, c
10
y
88
+ 51y
87
+ ··· − 245921472y + 19044496
c
9
y
88
+ 20y
87
+ ··· − 3705309y + 39601
c
12
y
88
+ 24y
87
+ ··· − 9443858y + 247009
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.079542 + 0.994795I
a = 0.076577 − 0.430813I
b = −0.515107 − 0.686427I
−4.50892 + 1.89281I 0
u = −0.079542 − 0.994795I
a = 0.076577 + 0.430813I
b = −0.515107 + 0.686427I
−4.50892 − 1.89281I 0
u = 0.922550 + 0.325110I
a = −0.84248 − 1.14264I
b = 1.142310 + 0.043068I
1.02793 + 2.90134I 0
u = 0.922550 − 0.325110I
a = −0.84248 + 1.14264I
b = 1.142310 − 0.043068I
1.02793 − 2.90134I 0
u = 1.004800 + 0.289516I
a = −0.760460 − 1.187730I
b = −1.14403 − 1.33949I
1.71320 − 3.32513I 0
u = 1.004800 − 0.289516I
a = −0.760460 + 1.187730I
b = −1.14403 + 1.33949I
1.71320 + 3.32513I 0
u = −0.196060 + 1.030950I
a = 0.0575028 + 0.0662019I
b = −0.854869 + 0.920640I
3.33215 − 4.72457I 0
u = −0.196060 − 1.030950I
a = 0.0575028 − 0.0662019I
b = −0.854869 − 0.920640I
3.33215 + 4.72457I 0
u = −0.997536 + 0.350050I
a = 1.47049 + 0.22383I
b = 2.03460 − 0.54513I
0.91193 + 7.76722I 0
u = −0.997536 − 0.350050I
a = 1.47049 − 0.22383I
b = 2.03460 + 0.54513I
0.91193 − 7.76722I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.994491 + 0.396359I
a = 1.322160 + 0.220742I
b = 1.53176 + 0.87479I
1.17606 − 1.83937I 0
u = 0.994491 − 0.396359I
a = 1.322160 − 0.220742I
b = 1.53176 − 0.87479I
1.17606 + 1.83937I 0
u = −0.978685 + 0.444812I
a = −0.71631 + 1.39357I
b = −0.62924 + 1.49042I
0.77445 − 1.30684I 0
u = −0.978685 − 0.444812I
a = −0.71631 − 1.39357I
b = −0.62924 − 1.49042I
0.77445 + 1.30684I 0
u = 0.173886 + 0.907980I
a = 0.103309 + 0.375265I
b = 0.504192 − 0.852320I
−2.05446 − 3.92042I 0
u = 0.173886 − 0.907980I
a = 0.103309 − 0.375265I
b = 0.504192 + 0.852320I
−2.05446 + 3.92042I 0
u = −0.844374 + 0.350658I
a = 1.022080 + 0.529940I
b = −0.690326 − 0.018294I
2.79140 + 0.99134I 0
u = −0.844374 − 0.350658I
a = 1.022080 − 0.529940I
b = −0.690326 + 0.018294I
2.79140 − 0.99134I 0
u = 0.906116
a = −0.567609
b = −1.52977
−0.995869 −8.76900
u = −0.888863 + 0.163693I
a = −0.205909 + 0.589104I
b = 1.079710 + 0.707273I
−5.06797 + 3.76463I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.888863 − 0.163693I
a = −0.205909 − 0.589104I
b = 1.079710 − 0.707273I
−5.06797 − 3.76463I 0
u = 0.630575 + 0.642930I
a = 0.122548 + 0.416302I
b = 0.455188 − 0.491182I
−3.15892 − 2.36393I 0
u = 0.630575 − 0.642930I
a = 0.122548 − 0.416302I
b = 0.455188 + 0.491182I
−3.15892 + 2.36393I 0
u = 0.191280 + 1.084180I
a = −0.0578598 − 0.0150131I
b = −0.816117 − 1.074180I
1.81959 + 11.50800I 0
u = 0.191280 − 1.084180I
a = −0.0578598 + 0.0150131I
b = −0.816117 + 1.074180I
1.81959 − 11.50800I 0
u = −0.933564 + 0.606799I
a = −1.178320 + 0.078452I
b = −0.388800 + 0.833976I
−5.25403 − 0.40703I 0
u = −0.933564 − 0.606799I
a = −1.178320 − 0.078452I
b = −0.388800 − 0.833976I
−5.25403 + 0.40703I 0
u = 1.074210 + 0.315862I
a = 1.80177 + 0.35922I
b = −0.443621 + 0.400108I
−0.38461 − 7.33578I 0
u = 1.074210 − 0.315862I
a = 1.80177 − 0.35922I
b = −0.443621 − 0.400108I
−0.38461 + 7.33578I 0
u = −1.079740 + 0.342099I
a = −0.70372 + 1.50217I
b = 1.036080 + 0.425207I
0.51946 + 4.26200I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.079740 − 0.342099I
a = −0.70372 − 1.50217I
b = 1.036080 − 0.425207I
0.51946 − 4.26200I 0
u = −1.098610 + 0.357725I
a = −0.08521 + 1.61396I
b = 0.682577 + 0.717539I
−1.10713 + 4.06055I 0
u = −1.098610 − 0.357725I
a = −0.08521 − 1.61396I
b = 0.682577 − 0.717539I
−1.10713 − 4.06055I 0
u = 1.168960 + 0.060743I
a = 0.381332 − 1.242970I
b = 0.490184 − 0.886114I
−2.00609 − 0.18246I 0
u = 1.168960 − 0.060743I
a = 0.381332 + 1.242970I
b = 0.490184 + 0.886114I
−2.00609 + 0.18246I 0
u = 1.104330 + 0.416918I
a = 0.23128 + 2.23065I
b = −1.13731 + 1.37000I
−6.21224 − 6.88000I 0
u = 1.104330 − 0.416918I
a = 0.23128 − 2.23065I
b = −1.13731 − 1.37000I
−6.21224 + 6.88000I 0
u = −1.166520 + 0.258171I
a = −0.25604 − 2.07092I
b = −0.60959 − 1.37557I
−7.78844 + 4.33788I 0
u = −1.166520 − 0.258171I
a = −0.25604 + 2.07092I
b = −0.60959 + 1.37557I
−7.78844 − 4.33788I 0
u = 0.067425 + 0.771021I
a = 0.297099 − 0.514777I
b = 0.484580 + 1.038620I
−2.63862 + 0.46353I −5.02348 + 0.56989I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.067425 − 0.771021I
a = 0.297099 + 0.514777I
b = 0.484580 − 1.038620I
−2.63862 − 0.46353I −5.02348 − 0.56989I
u = −0.718354 + 0.217212I
a = 0.54573 + 2.84620I
b = −0.124289 − 0.082300I
3.34564 + 1.92359I 4.88480 − 3.25735I
u = −0.718354 − 0.217212I
a = 0.54573 − 2.84620I
b = −0.124289 + 0.082300I
3.34564 − 1.92359I 4.88480 + 3.25735I
u = −1.173260 + 0.441118I
a = −0.721783 + 1.086860I
b = 0.503216 + 1.301010I
−6.19196 + 3.65772I 0
u = −1.173260 − 0.441118I
a = −0.721783 − 1.086860I
b = 0.503216 − 1.301010I
−6.19196 − 3.65772I 0
u = 0.732812 + 0.117122I
a = 0.61762 + 3.81785I
b = −0.562911 − 0.000503I
2.00948 − 5.38607I 0.87648 + 9.21229I
u = 0.732812 − 0.117122I
a = 0.61762 − 3.81785I
b = −0.562911 + 0.000503I
2.00948 + 5.38607I 0.87648 − 9.21229I
u = 1.200790 + 0.468762I
a = 0.39439 + 1.82813I
b = −0.87218 + 1.73127I
−5.97730 − 5.00488I 0
u = 1.200790 − 0.468762I
a = 0.39439 − 1.82813I
b = −0.87218 − 1.73127I
−5.97730 + 5.00488I 0
u = −0.292462 + 1.287080I
a = 0.0359230 + 0.0289302I
b = 0.490682 − 0.544345I
5.70942 − 3.91863I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.292462 − 1.287080I
a = 0.0359230 − 0.0289302I
b = 0.490682 + 0.544345I
5.70942 + 3.91863I 0
u = 1.321070 + 0.205270I
a = 0.518107 + 0.965534I
b = 0.299075 + 0.939881I
−2.22242 + 0.26262I 0
u = 1.321070 − 0.205270I
a = 0.518107 − 0.965534I
b = 0.299075 − 0.939881I
−2.22242 − 0.26262I 0
u = 0.653096 + 0.066511I
a = −0.12139 − 3.51471I
b = −0.23429 − 1.62481I
3.15315 + 1.04728I 0.79658 + 2.16290I
u = 0.653096 − 0.066511I
a = −0.12139 + 3.51471I
b = −0.23429 + 1.62481I
3.15315 − 1.04728I 0.79658 − 2.16290I
u = 0.432935 + 1.283790I
a = −0.0001777 + 0.0483511I
b = 0.408222 + 0.427912I
5.48099 − 2.85596I 0
u = 0.432935 − 1.283790I
a = −0.0001777 − 0.0483511I
b = 0.408222 − 0.427912I
5.48099 + 2.85596I 0
u = −1.288010 + 0.429164I
a = 0.08759 − 1.66290I
b = −0.86600 − 1.60130I
−6.44473 + 8.52384I 0
u = −1.288010 − 0.429164I
a = 0.08759 + 1.66290I
b = −0.86600 + 1.60130I
−6.44473 − 8.52384I 0
u = 1.308160 + 0.451778I
a = −0.23493 − 1.66336I
b = 0.674764 − 0.977248I
−8.84452 − 6.89816I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.308160 − 0.451778I
a = −0.23493 + 1.66336I
b = 0.674764 + 0.977248I
−8.84452 + 6.89816I 0
u = −1.265070 + 0.578212I
a = −0.29802 + 1.68627I
b = 1.02271 + 1.20191I
−0.00629 + 10.46180I 0
u = −1.265070 − 0.578212I
a = −0.29802 − 1.68627I
b = 1.02271 − 1.20191I
−0.00629 − 10.46180I 0
u = 1.145180 + 0.810913I
a = −0.537461 − 0.250754I
b = 0.206115 − 0.610312I
−4.12923 − 3.49768I 0
u = 1.145180 − 0.810913I
a = −0.537461 + 0.250754I
b = 0.206115 + 0.610312I
−4.12923 + 3.49768I 0
u = −1.32759 + 0.49541I
a = 0.471694 − 0.971427I
b = 0.049646 − 0.822741I
−8.48967 + 3.58712I 0
u = −1.32759 − 0.49541I
a = 0.471694 + 0.971427I
b = 0.049646 + 0.822741I
−8.48967 − 3.58712I 0
u = 1.28750 + 0.59866I
a = −0.32528 − 1.68556I
b = 1.04022 − 1.38210I
−1.6142 − 17.4772I 0
u = 1.28750 − 0.59866I
a = −0.32528 + 1.68556I
b = 1.04022 + 1.38210I
−1.6142 + 17.4772I 0
u = 1.26826 + 0.66463I
a = 0.192837 + 1.075850I
b = −0.725906 + 0.774174I
2.53546 − 3.85500I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.26826 − 0.66463I
a = 0.192837 − 1.075850I
b = −0.725906 − 0.774174I
2.53546 + 3.85500I 0
u = −1.31123 + 0.64609I
a = 0.141360 − 1.157090I
b = −0.900210 − 0.930002I
2.31383 + 10.55020I 0
u = −1.31123 − 0.64609I
a = 0.141360 + 1.157090I
b = −0.900210 + 0.930002I
2.31383 − 10.55020I 0
u = −1.44827 + 0.26724I
a = 0.569007 − 0.898870I
b = 0.173628 − 1.081180I
−3.88688 − 6.49441I 0
u = −1.44827 − 0.26724I
a = 0.569007 + 0.898870I
b = 0.173628 + 1.081180I
−3.88688 + 6.49441I 0
u = −0.226617 + 0.468851I
a = 0.532408 + 0.145971I
b = −0.770904 + 0.234672I
1.33771 − 0.68942I 4.64648 + 2.14547I
u = −0.226617 − 0.468851I
a = 0.532408 − 0.145971I
b = −0.770904 − 0.234672I
1.33771 + 0.68942I 4.64648 − 2.14547I
u = 1.38519 + 0.52829I
a = −0.284381 − 0.699179I
b = 0.536502 − 0.899083I
−5.58988 − 1.94882I 0
u = 1.38519 − 0.52829I
a = −0.284381 + 0.699179I
b = 0.536502 + 0.899083I
−5.58988 + 1.94882I 0
u = 0.266065 + 0.425883I
a = −0.107061 − 0.684637I
b = 0.994346 + 0.897178I
−3.79640 + 3.24219I 1.33253 − 6.90690I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.266065 − 0.425883I
a = −0.107061 + 0.684637I
b = 0.994346 − 0.897178I
−3.79640 − 3.24219I 1.33253 + 6.90690I
u = −0.461999 + 0.137703I
a = −0.55449 − 4.06412I
b = −0.95206 − 1.17692I
2.52847 − 4.86988I 0.68932 + 3.57290I
u = −0.461999 − 0.137703I
a = −0.55449 + 4.06412I
b = −0.95206 + 1.17692I
2.52847 + 4.86988I 0.68932 − 3.57290I
u = 0.444794
a = 1.20457
b = 0.334194
−0.893023 −11.8990
u = −0.281808 + 0.282040I
a = −3.25034 + 2.48063I
b = −0.383383 + 1.128520I
2.45411 + 4.85708I −1.43472 − 4.65944I
u = −0.281808 − 0.282040I
a = −3.25034 − 2.48063I
b = −0.383383 − 1.128520I
2.45411 − 4.85708I −1.43472 + 4.65944I
u = 0.049162 + 0.316034I
a = 3.93033 + 1.03578I
b = −0.621384 + 0.825063I
3.21443 − 1.34550I −0.662189 + 0.967949I
u = 0.049162 − 0.316034I
a = 3.93033 − 1.03578I
b = −0.621384 − 0.825063I
3.21443 + 1.34550I −0.662189 − 0.967949I
13
II. I
u
2
= h1.87 × 10
9
u
24
+ 1.44 × 10
9
u
23
+ · · · + 1.04 × 10
9
b + 1.21 × 10
9
, 7.58 ×
10
9
u
24
+8.35×10
9
u
23
+· · · +1.04×10
9
a−1.14×10
9
, u
25
+u
24
+· · · −9u
2
+1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
1
=
−7.25512u
24
− 7.98721u
23
+ ··· + 15.1067u + 1.08778
−1.78883u
24
− 1.38229u
23
+ ··· + 5.47091u − 1.16197
a
4
=
−u
−u
3
+ u
a
10
=
−2.57414u
24
− 1.92385u
23
+ ··· + 1.53371u − 1.13863
−2.04043u
24
− 2.52877u
23
+ ··· + 4.16946u + 1.11111
a
7
=
7.70126u
24
+ 9.77263u
23
+ ··· − 12.3665u − 2.45011
1.70277u
24
+ 1.73655u
23
+ ··· − 5.81111u − 0.867342
a
12
=
−5.46629u
24
− 6.60492u
23
+ ··· + 9.63575u + 2.24974
−1.78883u
24
− 1.38229u
23
+ ··· + 5.47091u − 1.16197
a
5
=
1.98092u
24
+ 1.77523u
23
+ ··· − 5.14453u + 2.08948
2.29891u
24
+ 3.07612u
23
+ ··· − 4.27983u + 0.428471
a
6
=
−0.848337u
24
− 2.13582u
23
+ ··· − 4.50417u + 3.03862
−1.46461u
24
− 1.79225u
23
+ ··· − 1.45519u + 2.81087
a
2
=
−4.57233u
24
− 5.28203u
23
+ ··· + 10.4764u + 1.24609
−2.91957u
24
− 2.51470u
23
+ ··· + 7.41840u − 1.34267
a
11
=
−7.59277u
24
− 8.77943u
23
+ ··· + 13.4650u + 2.33155
−0.905181u
24
− 0.451007u
23
+ ··· + 3.76813u − 1.19574
(ii) Obstruction class = 1
(iii) Cusp Shapes =
4028605052
1044856181
u
24
−
822387329
1044856181
u
23
+ ··· −
24905195484
1044856181
u +
3560291843
1044856181
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
25
− 3u
24
+ ··· − 57u − 19
c
2
u
25
+ 3u
24
+ ··· − 3u − 1
c
3
u
25
− u
24
+ ··· + 9u
2
− 1
c
4
u
25
+ 7u
23
+ ··· + 6u + 1
c
5
u
25
− 3u
24
+ ··· − 3u + 1
c
6
u
25
− u
24
+ ··· + 4499u + 1921
c
7
u
25
+ 2u
24
+ ··· + 30u
2
+ 4
c
8
u
25
+ u
24
+ ··· − 9u
2
+ 1
c
9
u
25
+ u
24
+ ··· + 5u + 1
c
10
u
25
− 2u
24
+ ··· − 30u
2
− 4
c
11
u
25
+ 7u
23
+ ··· + 6u − 1
c
12
u
25
− u
24
+ ··· − 8u − 1
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
+ 9y
24
+ ··· + 7125y −361
c
2
, c
5
y
25
− 15y
24
+ ··· + 21y −1
c
3
, c
8
y
25
− 13y
24
+ ··· + 18y −1
c
4
, c
11
y
25
+ 14y
24
+ ··· + 22y −1
c
6
y
25
− 9y
24
+ ··· + 20698199y −3690241
c
7
, c
10
y
25
+ 20y
24
+ ··· − 240y −16
c
9
y
25
+ 9y
24
+ ··· + 13y −1
c
12
y
25
+ 9y
24
+ ··· + 14y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.234832 + 0.980599I
a = 0.113084 − 0.195544I
b = 0.430137 − 0.760335I
−5.36225 − 1.81528I −11.14207 + 2.80882I
u = 0.234832 − 0.980599I
a = 0.113084 + 0.195544I
b = 0.430137 + 0.760335I
−5.36225 + 1.81528I −11.14207 − 2.80882I
u = −0.971284 + 0.355184I
a = −0.182478 + 0.721195I
b = −0.710278 + 0.867919I
1.56502 + 0.38477I −3.98629 − 1.14117I
u = −0.971284 − 0.355184I
a = −0.182478 − 0.721195I
b = −0.710278 − 0.867919I
1.56502 − 0.38477I −3.98629 + 1.14117I
u = −0.791573 + 0.708579I
a = −0.379901 − 0.027315I
b = 0.550284 + 0.588220I
−3.41650 + 3.83634I −4.32298 − 9.06491I
u = −0.791573 − 0.708579I
a = −0.379901 + 0.027315I
b = 0.550284 − 0.588220I
−3.41650 − 3.83634I −4.32298 + 9.06491I
u = 1.084830 + 0.246557I
a = 0.272997 + 0.669177I
b = −1.038920 − 0.202667I
0.11138 − 6.19506I −5.87106 + 5.03614I
u = 1.084830 − 0.246557I
a = 0.272997 − 0.669177I
b = −1.038920 + 0.202667I
0.11138 + 6.19506I −5.87106 − 5.03614I
u = −0.820492 + 0.144059I
a = 0.16494 + 3.06417I
b = −0.090017 + 1.131300I
2.57334 + 1.82110I −6.56024 − 2.56455I
u = −0.820492 − 0.144059I
a = 0.16494 − 3.06417I
b = −0.090017 − 1.131300I
2.57334 − 1.82110I −6.56024 + 2.56455I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.797817 + 0.072151I
a = 0.71030 − 3.54945I
b = 0.753099 − 0.738416I
1.54244 + 4.77194I −8.04443 − 1.46713I
u = 0.797817 − 0.072151I
a = 0.71030 + 3.54945I
b = 0.753099 + 0.738416I
1.54244 − 4.77194I −8.04443 + 1.46713I
u = 1.140090 + 0.409847I
a = 0.21762 + 2.14661I
b = −1.05786 + 1.67671I
−6.77141 − 6.17736I −11.72137 + 5.36754I
u = 1.140090 − 0.409847I
a = 0.21762 − 2.14661I
b = −1.05786 − 1.67671I
−6.77141 + 6.17736I −11.72137 − 5.36754I
u = −0.132201 + 1.229250I
a = −0.348167 + 0.063763I
b = 0.224473 + 0.113667I
5.30565 + 3.34682I −6.70479 − 5.10326I
u = −0.132201 − 1.229250I
a = −0.348167 − 0.063763I
b = 0.224473 − 0.113667I
5.30565 − 3.34682I −6.70479 + 5.10326I
u = −1.284280 + 0.415187I
a = 0.17270 − 1.76672I
b = −0.655780 − 1.209230I
−9.94901 + 6.32105I −12.06541 − 4.15926I
u = −1.284280 − 0.415187I
a = 0.17270 + 1.76672I
b = −0.655780 + 1.209230I
−9.94901 − 6.32105I −12.06541 + 4.15926I
u = −1.276560 + 0.580001I
a = −0.452352 + 0.697964I
b = 0.438961 + 1.015770I
−5.32473 + 2.19017I −4.47181 − 7.90728I
u = −1.276560 − 0.580001I
a = −0.452352 − 0.697964I
b = 0.438961 − 1.015770I
−5.32473 − 2.19017I −4.47181 + 7.90728I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.34269 + 0.53848I
a = −0.560270 − 0.911725I
b = 0.117614 − 0.935082I
−8.97451 − 4.05370I −13.5055 + 5.5208I
u = 1.34269 − 0.53848I
a = −0.560270 + 0.911725I
b = 0.117614 + 0.935082I
−8.97451 + 4.05370I −13.5055 − 5.5208I
u = 0.376239 + 0.279462I
a = 1.132080 − 0.479549I
b = 1.046320 + 0.909785I
−4.21298 + 2.86749I −8.99392 + 1.95922I
u = 0.376239 − 0.279462I
a = 1.132080 + 0.479549I
b = 1.046320 − 0.909785I
−4.21298 − 2.86749I −8.99392 − 1.95922I
u = −0.400199
a = −1.72110
b = −1.01605
0.0297575 0.779720
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
25
− 3u
24
+ ··· − 57u − 19)(u
88
+ 8u
86
+ ··· − 22991u − 4937)
c
2
(u
25
+ 3u
24
+ ··· − 3u − 1)(u
88
+ 4u
87
+ ··· + 5u − 79)
c
3
(u
25
− u
24
+ ··· + 9u
2
− 1)(u
88
+ 2u
87
+ ··· − 7u
2
+ 1)
c
4
(u
25
+ 7u
23
+ ··· + 6u + 1)(u
88
+ u
87
+ ··· + 43878u − 1549)
c
5
(u
25
− 3u
24
+ ··· − 3u + 1)(u
88
+ 4u
87
+ ··· + 5u − 79)
c
6
(u
25
− u
24
+ ··· + 4499u + 1921)
· (u
88
− 2u
87
+ ··· + 2779127u − 52466021)
c
7
(u
25
+ 2u
24
+ ··· + 30u
2
+ 4)(u
88
+ 5u
87
+ ··· − 39868u − 4364)
c
8
(u
25
+ u
24
+ ··· − 9u
2
+ 1)(u
88
+ 2u
87
+ ··· − 7u
2
+ 1)
c
9
(u
25
+ u
24
+ ··· + 5u + 1)(u
88
− 6u
87
+ ··· − 2747u − 199)
c
10
(u
25
− 2u
24
+ ··· − 30u
2
− 4)(u
88
+ 5u
87
+ ··· − 39868u − 4364)
c
11
(u
25
+ 7u
23
+ ··· + 6u − 1)(u
88
+ u
87
+ ··· + 43878u − 1549)
c
12
(u
25
− u
24
+ ··· − 8u − 1)(u
88
+ 2u
87
+ ··· + 4454u − 497)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
25
+ 9y
24
+ ··· + 7125y −361)
· (y
88
+ 16y
87
+ ··· + 1139448487y + 24373969)
c
2
, c
5
(y
25
− 15y
24
+ ··· + 21y −1)(y
88
− 28y
87
+ ··· − 157709y + 6241)
c
3
, c
8
(y
25
− 13y
24
+ ··· + 18y −1)(y
88
− 50y
87
+ ··· − 14y + 1)
c
4
, c
11
(y
25
+ 14y
24
+ ··· + 22y −1)
· (y
88
+ 73y
87
+ ··· − 414362598y + 2399401)
c
6
(y
25
− 9y
24
+ ··· + 20698199y −3690241)
· (y
88
− 54y
87
+ ··· − 104763397554533243y + 2752683359572441)
c
7
, c
10
(y
25
+ 20y
24
+ ··· − 240y −16)
· (y
88
+ 51y
87
+ ··· − 245921472y + 19044496)
c
9
(y
25
+ 9y
24
+ ··· + 13y −1)(y
88
+ 20y
87
+ ··· − 3705309y + 39601)
c
12
(y
25
+ 9y
24
+ ··· + 14y −1)(y
88
+ 24y
87
+ ··· − 9443858y + 247009)
23
