12a
0898
(K12a
0898
)
A knot diagram
1
Linearized knot diagam
4 6 8 10 2 11 3 12 1 5 7 9
Solving Sequence
8,12
9 1
4,10
5 3 7 11 6 2
c
8
c
12
c
9
c
4
c
3
c
7
c
11
c
6
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.96183 × 10
229
u
98
− 1.54116 × 10
230
u
97
+ ··· + 5.52314 × 10
228
b + 3.65483 × 10
230
,
2.26754 × 10
231
u
98
+ 7.18353 × 10
231
u
97
+ ··· + 5.52314 × 10
228
a − 1.28816 × 10
232
, u
99
+ 3u
98
+ ··· − 20u + 1i
I
u
2
= h187u
15
− 333u
14
+ ··· + 71b − 316, 68u
15
− 205u
14
+ ··· + 71a − 457, u
16
− 2u
15
+ ··· − 6u − 1i
* 2 irreducible components of dim
C
= 0, with total 115 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−4.96 × 10
229
u
98
− 1.54 × 10
230
u
97
+ · · · + 5.52 × 10
228
b + 3.65 ×
10
230
, 2.27 × 10
231
u
98
+ 7.18 × 10
231
u
97
+ · · · + 5.52 × 10
228
a − 1.29 ×
10
232
, u
99
+ 3u
98
+ · · · − 20u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
−410.552u
98
− 1300.62u
97
+ ··· − 33247.6u + 2332.30
8.98371u
98
+ 27.9038u
97
+ ··· + 851.061u − 66.1730
a
10
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
−426.755u
98
− 1351.65u
97
+ ··· − 34375.4u + 2404.93
10.5930u
98
+ 32.6000u
97
+ ··· + 948.262u − 72.6394
a
3
=
−401.569u
98
− 1272.72u
97
+ ··· − 32396.5u + 2266.13
8.98371u
98
+ 27.9038u
97
+ ··· + 851.061u − 66.1730
a
7
=
−190.944u
98
− 604.011u
97
+ ··· − 15994.4u + 1130.44
38.9398u
98
+ 120.404u
97
+ ··· + 3169.91u − 230.155
a
11
=
−525.908u
98
− 1667.80u
97
+ ··· − 44094.0u + 3123.09
22.7841u
98
+ 74.5759u
97
+ ··· + 2125.65u − 154.013
a
6
=
847.939u
98
+ 2682.65u
97
+ ··· + 70075.5u − 4962.87
43.6317u
98
+ 137.298u
97
+ ··· + 3675.73u − 263.137
a
2
=
−839.291u
98
− 2655.52u
97
+ ··· − 69413.1u + 4916.87
−43.1587u
98
− 135.565u
97
+ ··· − 3615.21u + 258.560
(ii) Obstruction class = −1
(iii) Cusp Shapes = −84.5894u
98
− 274.529u
97
+ ··· − 7761.27u + 561.078
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
99
− u
98
+ ··· − 420367u − 86857
c
2
, c
5
u
99
− 30u
97
+ ··· + 7u − 1
c
3
, c
7
u
99
− 2u
98
+ ··· − 303u + 61
c
4
, c
10
u
99
− u
98
+ ··· − 39u + 937
c
6
, c
11
u
99
+ u
98
+ ··· − 5u + 1
c
8
, c
9
, c
12
u
99
− 3u
98
+ ··· − 20u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
99
+ 29y
98
+ ··· + 12950485171y −7544138449
c
2
, c
5
y
99
− 60y
98
+ ··· + 125y −1
c
3
, c
7
y
99
− 60y
98
+ ··· + 178673y −3721
c
4
, c
10
y
99
− 83y
98
+ ··· + 55082129y −877969
c
6
, c
11
y
99
− 67y
98
+ ··· + 147y −1
c
8
, c
9
, c
12
y
99
− 107y
98
+ ··· + 92y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.740716 + 0.660134I
a = −0.418260 − 0.619628I
b = 1.051910 − 0.341857I
−2.64189 + 2.94712I 0
u = −0.740716 − 0.660134I
a = −0.418260 + 0.619628I
b = 1.051910 + 0.341857I
−2.64189 − 2.94712I 0
u = 0.936978 + 0.373185I
a = 0.652429 − 0.083726I
b = 0.041110 + 0.447920I
6.51007 + 1.78657I 0
u = 0.936978 − 0.373185I
a = 0.652429 + 0.083726I
b = 0.041110 − 0.447920I
6.51007 − 1.78657I 0
u = −0.101390 + 0.907405I
a = −0.846291 + 0.518149I
b = −0.597672 + 0.210243I
1.37944 − 3.96642I 0
u = −0.101390 − 0.907405I
a = −0.846291 − 0.518149I
b = −0.597672 − 0.210243I
1.37944 + 3.96642I 0
u = 0.651492 + 0.873430I
a = −0.411850 − 0.833116I
b = −1.246290 + 0.572677I
0.38169 + 13.20470I 0
u = 0.651492 − 0.873430I
a = −0.411850 + 0.833116I
b = −1.246290 − 0.572677I
0.38169 − 13.20470I 0
u = 0.905341
a = 0.739427
b = −1.62008
−7.39496 0
u = −0.561511 + 0.671788I
a = 0.20921 − 1.46205I
b = 1.200880 + 0.244534I
−3.26168 − 6.50239I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.561511 − 0.671788I
a = 0.20921 + 1.46205I
b = 1.200880 − 0.244534I
−3.26168 + 6.50239I 0
u = −0.380686 + 0.733717I
a = 0.574255 − 0.663992I
b = 1.254820 + 0.607843I
−3.66994 − 7.66735I 0
u = −0.380686 − 0.733717I
a = 0.574255 + 0.663992I
b = 1.254820 − 0.607843I
−3.66994 + 7.66735I 0
u = −0.496979 + 0.655506I
a = 0.281407 − 0.243550I
b = 1.269220 − 0.043803I
−3.47162 + 1.98683I 0
u = −0.496979 − 0.655506I
a = 0.281407 + 0.243550I
b = 1.269220 + 0.043803I
−3.47162 − 1.98683I 0
u = 0.818206
a = 2.13556
b = −1.09275
4.08306 0
u = 0.662406 + 0.453421I
a = −0.235423 + 0.522548I
b = −0.064412 − 1.004580I
3.86389 + 7.67810I 0
u = 0.662406 − 0.453421I
a = −0.235423 − 0.522548I
b = −0.064412 + 1.004580I
3.86389 − 7.67810I 0
u = 0.523831 + 1.105700I
a = −0.105946 − 0.261595I
b = −1.031180 − 0.382990I
−0.13947 − 6.93665I 0
u = 0.523831 − 1.105700I
a = −0.105946 + 0.261595I
b = −1.031180 + 0.382990I
−0.13947 + 6.93665I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.450653 + 0.606011I
a = −0.110925 − 1.084860I
b = −1.283860 + 0.169700I
−7.12534 + 2.00701I 0
u = 0.450653 − 0.606011I
a = −0.110925 + 1.084860I
b = −1.283860 − 0.169700I
−7.12534 − 2.00701I 0
u = −0.365780 + 0.654899I
a = −0.639028 + 0.869862I
b = −0.365840 − 0.469149I
1.00378 − 3.95796I 0
u = −0.365780 − 0.654899I
a = −0.639028 − 0.869862I
b = −0.365840 + 0.469149I
1.00378 + 3.95796I 0
u = −0.656614 + 0.362229I
a = 0.0542687 + 0.0829791I
b = −0.631447 + 0.366281I
1.010570 + 0.037156I 0
u = −0.656614 − 0.362229I
a = 0.0542687 − 0.0829791I
b = −0.631447 − 0.366281I
1.010570 − 0.037156I 0
u = −0.347291 + 0.663112I
a = −1.069160 + 0.749279I
b = −0.979170 − 0.487234I
−0.08310 − 3.86265I 0
u = −0.347291 − 0.663112I
a = −1.069160 − 0.749279I
b = −0.979170 + 0.487234I
−0.08310 + 3.86265I 0
u = −0.391345 + 0.627891I
a = −1.11464 + 1.09083I
b = −0.966274 − 0.492186I
−0.05253 − 3.83284I 0
u = −0.391345 − 0.627891I
a = −1.11464 − 1.09083I
b = −0.966274 + 0.492186I
−0.05253 + 3.83284I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.271100 + 0.059881I
a = −0.26161 + 1.40515I
b = −0.440116 − 0.157984I
2.03091 + 1.52575I 0
u = −1.271100 − 0.059881I
a = −0.26161 − 1.40515I
b = −0.440116 + 0.157984I
2.03091 − 1.52575I 0
u = 0.722291 + 0.051213I
a = −1.62389 + 0.90390I
b = 0.804246 − 0.598002I
1.59199 − 1.46670I 0
u = 0.722291 − 0.051213I
a = −1.62389 − 0.90390I
b = 0.804246 + 0.598002I
1.59199 + 1.46670I 0
u = −0.485156 + 0.504923I
a = 0.377985 − 0.473286I
b = −0.316264 + 0.537966I
1.47556 + 0.10354I 0
u = −0.485156 − 0.504923I
a = 0.377985 + 0.473286I
b = −0.316264 − 0.537966I
1.47556 − 0.10354I 0
u = 0.652970 + 1.136450I
a = 0.431392 + 0.440530I
b = 1.072920 − 0.439287I
4.12271 + 5.39603I 0
u = 0.652970 − 1.136450I
a = 0.431392 − 0.440530I
b = 1.072920 + 0.439287I
4.12271 − 5.39603I 0
u = −0.685910
a = −0.246736
b = −0.433093
0.890789 0
u = 1.39035
a = 3.75335
b = −3.80795
5.21323 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.399680 + 0.087417I
a = −0.38568 − 1.67583I
b = 0.558612 + 0.259158I
5.78712 + 6.53835I 0
u = 1.399680 − 0.087417I
a = −0.38568 + 1.67583I
b = 0.558612 − 0.259158I
5.78712 − 6.53835I 0
u = −1.400530 + 0.115235I
a = −0.38152 − 1.52179I
b = 0.782265 + 0.573377I
3.64494 − 2.28231I 0
u = −1.400530 − 0.115235I
a = −0.38152 + 1.52179I
b = 0.782265 − 0.573377I
3.64494 + 2.28231I 0
u = −1.41818 + 0.01985I
a = −1.78789 − 3.09256I
b = 2.08833 + 2.72201I
4.68486 + 0.26157I 0
u = −1.41818 − 0.01985I
a = −1.78789 + 3.09256I
b = 2.08833 − 2.72201I
4.68486 − 0.26157I 0
u = 1.40357 + 0.23061I
a = −0.008833 + 0.931264I
b = 1.236100 − 0.413960I
3.29811 + 2.26423I 0
u = 1.40357 − 0.23061I
a = −0.008833 − 0.931264I
b = 1.236100 + 0.413960I
3.29811 − 2.26423I 0
u = 1.43957 + 0.02655I
a = −0.651757 − 0.245845I
b = 1.316080 + 0.146662I
3.35235 + 0.02455I 0
u = 1.43957 − 0.02655I
a = −0.651757 + 0.245845I
b = 1.316080 − 0.146662I
3.35235 − 0.02455I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43958 + 0.09510I
a = 0.62498 + 1.27990I
b = −0.599662 − 0.585723I
7.52065 + 1.93273I 0
u = 1.43958 − 0.09510I
a = 0.62498 − 1.27990I
b = −0.599662 + 0.585723I
7.52065 − 1.93273I 0
u = −1.45637 + 0.00770I
a = 0.039120 + 1.009860I
b = −1.359020 − 0.383649I
9.19651 − 0.99992I 0
u = −1.45637 − 0.00770I
a = 0.039120 − 1.009860I
b = −1.359020 + 0.383649I
9.19651 + 0.99992I 0
u = −1.46744 + 0.01290I
a = −0.05298 − 1.79361I
b = 1.117730 + 0.579902I
7.50489 − 5.71904I 0
u = −1.46744 − 0.01290I
a = −0.05298 + 1.79361I
b = 1.117730 − 0.579902I
7.50489 + 5.71904I 0
u = 1.45767 + 0.24111I
a = −0.47894 + 1.68889I
b = 1.36486 − 0.89980I
2.25200 + 11.14920I 0
u = 1.45767 − 0.24111I
a = −0.47894 − 1.68889I
b = 1.36486 + 0.89980I
2.25200 − 11.14920I 0
u = 1.46515 + 0.22421I
a = 0.16687 − 1.54702I
b = −1.166860 + 0.696988I
5.81806 + 7.08117I 0
u = 1.46515 − 0.22421I
a = 0.16687 + 1.54702I
b = −1.166860 − 0.696988I
5.81806 − 7.08117I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46946 + 0.19795I
a = 0.74012 + 1.33954I
b = −1.167030 − 0.485918I
−0.91244 − 4.91882I 0
u = −1.46946 − 0.19795I
a = 0.74012 − 1.33954I
b = −1.167030 + 0.485918I
−0.91244 + 4.91882I 0
u = 1.39576 + 0.53376I
a = 0.189616 + 0.503312I
b = 0.520698 + 0.028555I
6.45396 + 2.02499I 0
u = 1.39576 − 0.53376I
a = 0.189616 − 0.503312I
b = 0.520698 − 0.028555I
6.45396 − 2.02499I 0
u = 1.48191 + 0.26155I
a = −0.08251 − 1.46403I
b = −0.680631 + 0.669773I
6.98172 + 7.44981I 0
u = 1.48191 − 0.26155I
a = −0.08251 + 1.46403I
b = −0.680631 − 0.669773I
6.98172 − 7.44981I 0
u = 1.51340 + 0.06368I
a = 0.519798 + 1.055950I
b = −0.410844 − 0.828111I
7.91657 + 1.31701I 0
u = 1.51340 − 0.06368I
a = 0.519798 − 1.055950I
b = −0.410844 + 0.828111I
7.91657 − 1.31701I 0
u = 1.50217 + 0.21346I
a = 0.18452 − 1.71021I
b = −1.048460 + 0.615613I
6.22115 + 6.89414I 0
u = 1.50217 − 0.21346I
a = 0.18452 + 1.71021I
b = −1.048460 − 0.615613I
6.22115 − 6.89414I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55288 + 0.15662I
a = 0.32381 − 1.59916I
b = −0.24255 + 1.46889I
11.1954 − 10.0068I 0
u = −1.55288 − 0.15662I
a = 0.32381 + 1.59916I
b = −0.24255 − 1.46889I
11.1954 + 10.0068I 0
u = −0.025265 + 0.430438I
a = 1.50952 + 1.48306I
b = 0.668301 + 0.118557I
−1.202850 + 0.483660I −4.55970 + 1.18319I
u = −0.025265 − 0.430438I
a = 1.50952 − 1.48306I
b = 0.668301 − 0.118557I
−1.202850 − 0.483660I −4.55970 − 1.18319I
u = 1.55291 + 0.22303I
a = −0.62785 + 1.55930I
b = 1.104160 − 0.431801I
3.73273 + 9.79679I 0
u = 1.55291 − 0.22303I
a = −0.62785 − 1.55930I
b = 1.104160 + 0.431801I
3.73273 − 9.79679I 0
u = −1.59493 + 0.15891I
a = −0.173089 + 1.219070I
b = 0.227269 − 1.134870I
14.7475 − 4.1486I 0
u = −1.59493 − 0.15891I
a = −0.173089 − 1.219070I
b = 0.227269 + 1.134870I
14.7475 + 4.1486I 0
u = −0.263578 + 0.291460I
a = −0.327340 + 0.152958I
b = −0.905011 + 1.083140I
0.448592 + 0.918224I 4.55809 + 12.61038I
u = −0.263578 − 0.291460I
a = −0.327340 − 0.152958I
b = −0.905011 − 1.083140I
0.448592 − 0.918224I 4.55809 − 12.61038I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.58652 + 0.29743I
a = 0.36085 + 1.51692I
b = −1.36467 − 0.75652I
7.6756 − 17.5314I 0
u = −1.58652 − 0.29743I
a = 0.36085 − 1.51692I
b = −1.36467 + 0.75652I
7.6756 + 17.5314I 0
u = −1.62548 + 0.07252I
a = −0.690393 − 0.963420I
b = 0.344934 + 0.690280I
9.73410 + 0.77955I 0
u = −1.62548 − 0.07252I
a = −0.690393 + 0.963420I
b = 0.344934 − 0.690280I
9.73410 − 0.77955I 0
u = −1.63242
a = 1.49914
b = −0.727141
12.5284 0
u = 0.060339 + 0.361917I
a = 1.09542 + 1.69316I
b = 0.652611 − 0.069393I
−1.221060 + 0.471555I −5.19431 − 0.44409I
u = 0.060339 − 0.361917I
a = 1.09542 − 1.69316I
b = 0.652611 + 0.069393I
−1.221060 − 0.471555I −5.19431 + 0.44409I
u = −1.60187 + 0.33615I
a = −0.212049 − 1.278830I
b = 1.29576 + 0.66671I
11.4391 − 10.5221I 0
u = −1.60187 − 0.33615I
a = −0.212049 + 1.278830I
b = 1.29576 − 0.66671I
11.4391 + 10.5221I 0
u = 1.73495
a = −0.540652
b = 0.633937
6.52917 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.64465 + 0.57114I
a = −0.021397 + 0.670503I
b = −1.173420 − 0.398009I
5.87495 − 2.46826I 0
u = −1.64465 − 0.57114I
a = −0.021397 − 0.670503I
b = −1.173420 + 0.398009I
5.87495 + 2.46826I 0
u = 0.112870 + 0.195686I
a = 1.43436 + 0.89523I
b = 1.09114 − 1.27035I
−0.384516 − 0.802457I −4.4738 − 22.9416I
u = 0.112870 − 0.195686I
a = 1.43436 − 0.89523I
b = 1.09114 + 1.27035I
−0.384516 + 0.802457I −4.4738 + 22.9416I
u = 0.203707 + 0.028208I
a = 1.93686 − 8.64962I
b = 0.798444 + 0.440266I
1.72855 − 5.65485I 9.03689 + 7.91182I
u = 0.203707 − 0.028208I
a = 1.93686 + 8.64962I
b = 0.798444 − 0.440266I
1.72855 + 5.65485I 9.03689 − 7.91182I
u = 0.167144 + 0.003550I
a = −6.70304 − 5.00229I
b = −0.988849 + 0.291096I
3.59911 + 0.92364I 5.70852 − 0.99827I
u = 0.167144 − 0.003550I
a = −6.70304 + 5.00229I
b = −0.988849 − 0.291096I
3.59911 − 0.92364I 5.70852 + 0.99827I
u = −2.11117
a = 0.0909028
b = −0.618667
8.75658 0
14
II. I
u
2
= h187u
15
− 333u
14
+ · · · + 71b − 316, 68u
15
− 205u
14
+ · · · + 71a −
457, u
16
− 2u
15
+ · · · − 6u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
−0.957746u
15
+ 2.88732u
14
+ ··· + 10.4648u + 6.43662
−2.63380u
15
+ 4.69014u
14
+ ··· + 11.0282u + 4.45070
a
10
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
−2.57746u
15
+ 5.87324u
14
+ ··· + 18.6479u + 10.3662
−2.50704u
15
+ 4.35211u
14
+ ··· + 9.42254u + 3.76056
a
3
=
−3.59155u
15
+ 7.57746u
14
+ ··· + 21.4930u + 10.8873
−2.63380u
15
+ 4.69014u
14
+ ··· + 11.0282u + 4.45070
a
7
=
0.267606u
15
− 1.38028u
14
+ ··· − 8.05634u + 1.09859
0.676056u
15
+ 0.197183u
14
+ ··· + 12.4366u + 4.98592
a
11
=
1.46479u
15
− 3.23944u
14
+ ··· − 18.8873u − 3.19718
−2.84507u
15
+ 3.25352u
14
+ ··· − 1.29577u + 2.26761
a
6
=
−2.63380u
15
+ 4.69014u
14
+ ··· + 8.02817u + 6.45070
−0.760563u
15
+ 0.0281690u
14
+ ··· − 0.366197u + 1.14085
a
2
=
−2u
15
+ 3u
14
+ ··· − u + 2
−0.323944u
15
+ 0.197183u
14
+ ··· + 5.43662u + 1.98592
(ii) Obstruction class = 1
(iii) Cusp Shapes =
214
71
u
15
−
973
71
u
14
+ ··· −
3184
71
u −
250
71
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 6u
15
+ ··· − 11u + 1
c
2
u
16
+ 5u
15
+ ··· + 3u + 1
c
3
u
16
− u
15
+ ··· − u − 1
c
4
u
16
− 11u
14
+ ··· − 9u + 1
c
5
u
16
− 5u
15
+ ··· − 3u + 1
c
6
u
16
+ 2u
15
+ ··· + u − 1
c
7
u
16
+ u
15
+ ··· + u − 1
c
8
, c
9
u
16
− 2u
15
+ ··· − 6u − 1
c
10
u
16
− 11u
14
+ ··· + 9u + 1
c
11
u
16
− 2u
15
+ ··· − u − 1
c
12
u
16
+ 2u
15
+ ··· + 6u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 2y
15
+ ··· − 21y + 1
c
2
, c
5
y
16
− 15y
15
+ ··· − 27y + 1
c
3
, c
7
y
16
− 19y
15
+ ··· − 19y + 1
c
4
, c
10
y
16
− 22y
15
+ ··· − 39y + 1
c
6
, c
11
y
16
− 18y
15
+ ··· − 49y + 1
c
8
, c
9
, c
12
y
16
− 22y
15
+ ··· − 30y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.931033
a = −0.129306
b = −0.761120
0.460564 −7.23990
u = −0.839750
a = −0.822764
b = 1.58692
−7.52932 −28.4780
u = 0.733239
a = −2.27208
b = 0.856867
4.77255 12.8330
u = 0.011134 + 0.698922I
a = −1.86477 − 0.24882I
b = −0.825449 − 0.338768I
0.86280 − 5.46754I 0.81609 + 6.50543I
u = 0.011134 − 0.698922I
a = −1.86477 + 0.24882I
b = −0.825449 + 0.338768I
0.86280 + 5.46754I 0.81609 − 6.50543I
u = 1.34394
a = −1.84817
b = 1.92615
5.40039 13.3440
u = −1.45687
a = 2.22379
b = −2.80462
4.55552 18.0260
u = 1.44376 + 0.20567I
a = −0.07182 − 1.90856I
b = −0.857594 + 0.563765I
5.91039 + 8.42936I 4.57561 − 9.78666I
u = 1.44376 − 0.20567I
a = −0.07182 + 1.90856I
b = −0.857594 − 0.563765I
5.91039 − 8.42936I 4.57561 + 9.78666I
u = 1.36399 + 0.52591I
a = 0.343669 + 0.775057I
b = 1.085140 − 0.318825I
5.06570 + 3.53944I 6.10083 − 5.41679I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.36399 − 0.52591I
a = 0.343669 − 0.775057I
b = 1.085140 + 0.318825I
5.06570 − 3.53944I 6.10083 + 5.41679I
u = −1.61553
a = −1.47646
b = 0.578270
12.8265 21.8930
u = 1.68524
a = −0.0522246
b = 0.362196
6.88195 13.3710
u = −0.266288 + 0.043343I
a = 1.58642 + 1.04311I
b = −0.412260 + 0.963905I
−0.138512 − 1.003180I 6.34798 − 0.39102I
u = −0.266288 − 0.043343I
a = 1.58642 − 1.04311I
b = −0.412260 − 0.963905I
−0.138512 + 1.003180I 6.34798 + 0.39102I
u = −2.02444
a = 0.390217
b = −0.724345
8.44870 −3.42940
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
16
− 6u
15
+ ··· − 11u + 1)(u
99
− u
98
+ ··· − 420367u − 86857)
c
2
(u
16
+ 5u
15
+ ··· + 3u + 1)(u
99
− 30u
97
+ ··· + 7u − 1)
c
3
(u
16
− u
15
+ ··· − u − 1)(u
99
− 2u
98
+ ··· − 303u + 61)
c
4
(u
16
− 11u
14
+ ··· − 9u + 1)(u
99
− u
98
+ ··· − 39u + 937)
c
5
(u
16
− 5u
15
+ ··· − 3u + 1)(u
99
− 30u
97
+ ··· + 7u − 1)
c
6
(u
16
+ 2u
15
+ ··· + u − 1)(u
99
+ u
98
+ ··· − 5u + 1)
c
7
(u
16
+ u
15
+ ··· + u − 1)(u
99
− 2u
98
+ ··· − 303u + 61)
c
8
, c
9
(u
16
− 2u
15
+ ··· − 6u − 1)(u
99
− 3u
98
+ ··· − 20u − 1)
c
10
(u
16
− 11u
14
+ ··· + 9u + 1)(u
99
− u
98
+ ··· − 39u + 937)
c
11
(u
16
− 2u
15
+ ··· − u − 1)(u
99
+ u
98
+ ··· − 5u + 1)
c
12
(u
16
+ 2u
15
+ ··· + 6u − 1)(u
99
− 3u
98
+ ··· − 20u − 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
16
− 2y
15
+ ··· − 21y + 1)
· (y
99
+ 29y
98
+ ··· + 12950485171y −7544138449)
c
2
, c
5
(y
16
− 15y
15
+ ··· − 27y + 1)(y
99
− 60y
98
+ ··· + 125y −1)
c
3
, c
7
(y
16
− 19y
15
+ ··· − 19y + 1)(y
99
− 60y
98
+ ··· + 178673y −3721)
c
4
, c
10
(y
16
− 22y
15
+ ··· − 39y + 1)
· (y
99
− 83y
98
+ ··· + 55082129y −877969)
c
6
, c
11
(y
16
− 18y
15
+ ··· − 49y + 1)(y
99
− 67y
98
+ ··· + 147y −1)
c
8
, c
9
, c
12
(y
16
− 22y
15
+ ··· − 30y + 1)(y
99
− 107y
98
+ ··· + 92y −1)
21
