12a
0458
(K12a
0458
)
A knot diagram
1
Linearized knot diagam
3 6 10 12 9 2 4 1 7 8 5 11
Solving Sequence
5,11
12
1,8
9 6 4 7 10 3 2
c
11
c
12
c
8
c
5
c
4
c
7
c
10
c
3
c
2
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.50272 × 10
508
u
183
+ 4.81379 × 10
508
u
182
+ ··· + 5.05629 × 10
507
b + 4.40651 × 10
508
,
4.37784 × 10
508
u
183
− 1.28883 × 10
509
u
182
+ ··· + 5.05629 × 10
507
a − 1.21040 × 10
509
, u
184
− u
183
+ ··· + 5u + 1i
I
u
2
= h4318092u
35
+ 4278394u
34
+ ··· + 627059b + 4485498,
− 2296428u
35
− 6821624u
34
+ ··· + 627059a − 828341, u
36
+ u
35
+ ··· − 2u + 1i
I
u
3
= h−u
2
+ b + u, −u
3
+ u
2
+ a, u
4
− u
3
+ u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 224 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−2.50 × 10
508
u
183
+ 4.81 × 10
508
u
182
+ · · · + 5.06 × 10
507
b + 4.41 ×
10
508
, 4.38 × 10
508
u
183
− 1.29 × 10
509
u
182
+ · · · + 5.06 × 10
507
a − 1.21 ×
10
509
, u
184
− u
183
+ · · · + 5u + 1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
8
=
−8.65822u
183
+ 25.4895u
182
+ ··· + 204.609u + 23.9386
4.94971u
183
− 9.52040u
182
+ ··· − 61.9664u − 8.71491
a
9
=
0.687710u
183
+ 11.7257u
182
+ ··· + 124.941u + 5.27965
−4.07758u
183
− 10.8828u
182
+ ··· − 110.199u − 14.6867
a
6
=
8.59308u
183
− 23.6383u
182
+ ··· − 180.726u − 46.3702
−6.10986u
183
− 4.33107u
182
+ ··· − 36.2462u − 4.36522
a
4
=
u
u
3
+ u
a
7
=
2.90959u
183
+ 7.18098u
182
+ ··· + 94.9978u + 2.60094
3.37583u
183
− 18.8275u
182
+ ··· − 149.441u − 23.3118
a
10
=
−10.5685u
183
+ 20.0248u
182
+ ··· + 118.185u + 26.8545
23.1516u
183
− 5.66655u
182
+ ··· + 10.6861u − 1.74697
a
3
=
−2.11007u
183
+ 24.7206u
182
+ ··· + 206.052u + 48.7688
19.4953u
183
+ 1.85177u
182
+ ··· + 82.3695u + 7.98087
a
2
=
17.3504u
183
+ 20.0924u
182
+ ··· + 166.223u + 39.3952
40.7180u
183
− 14.7779u
182
+ ··· + 14.5445u − 10.5460
(ii) Obstruction class = −1
(iii) Cusp Shapes = 40.5446u
183
− 51.3735u
182
+ ··· − 251.843u − 67.3318
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
184
+ 83u
183
+ ··· − 5u + 1
c
2
, c
6
u
184
− u
183
+ ··· + 5u + 1
c
3
u
184
+ 2u
183
+ ··· + 4095u + 691
c
4
, c
11
u
184
+ u
183
+ ··· − 5u + 1
c
5
u
184
+ 2u
183
+ ··· + 3708404u + 1584839
c
7
u
184
− 2u
183
+ ··· − 4095u + 691
c
8
u
184
− 2u
183
+ ··· − 3708404u + 1584839
c
9
u
184
− 11u
183
+ ··· + 8744u + 257
c
10
u
184
+ 11u
183
+ ··· − 8744u + 257
c
12
u
184
− 83u
183
+ ··· + 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
12
y
184
+ 47y
183
+ ··· − 2797y + 1
c
2
, c
4
, c
6
c
11
y
184
+ 83y
183
+ ··· − 5y + 1
c
3
, c
7
y
184
+ 2y
183
+ ··· − 20009815y + 477481
c
5
, c
8
y
184
− 18y
183
+ ··· − 530431543575720y + 2511714655921
c
9
, c
10
y
184
− 23y
183
+ ··· + 38603420y + 66049
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.894854 + 0.445183I
a = 1.130450 + 0.587646I
b = 0.870846 + 0.629086I
1.42713 − 4.91064I 0
u = −0.894854 − 0.445183I
a = 1.130450 − 0.587646I
b = 0.870846 − 0.629086I
1.42713 + 4.91064I 0
u = −0.505930 + 0.869761I
a = −1.11752 − 1.42800I
b = −0.943800 + 0.915800I
−2.46244 + 5.69178I 0
u = −0.505930 − 0.869761I
a = −1.11752 + 1.42800I
b = −0.943800 − 0.915800I
−2.46244 − 5.69178I 0
u = 0.711964 + 0.692118I
a = −0.94076 + 1.54269I
b = −1.42433 + 0.63907I
−4.26633 − 0.73149I 0
u = 0.711964 − 0.692118I
a = −0.94076 − 1.54269I
b = −1.42433 − 0.63907I
−4.26633 + 0.73149I 0
u = −0.911661 + 0.428389I
a = 1.24757 + 0.81419I
b = 1.21961 + 0.85454I
− 9.45857I 0
u = −0.911661 − 0.428389I
a = 1.24757 − 0.81419I
b = 1.21961 − 0.85454I
9.45857I 0
u = 0.912513 + 0.427584I
a = 1.34384 − 0.71854I
b = 1.259440 − 0.641346I
−6.16241 + 6.57875I 0
u = 0.912513 − 0.427584I
a = 1.34384 + 0.71854I
b = 1.259440 + 0.641346I
−6.16241 − 6.57875I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.913042 + 0.429711I
a = 1.27214 − 0.86579I
b = 1.30328 − 0.90182I
−2.1765 + 15.2001I 0
u = 0.913042 − 0.429711I
a = 1.27214 + 0.86579I
b = 1.30328 + 0.90182I
−2.1765 − 15.2001I 0
u = −0.480224 + 0.863743I
a = −0.758550 − 0.515933I
b = −1.34440 − 0.80705I
−2.51303 − 1.69167I 0
u = −0.480224 − 0.863743I
a = −0.758550 + 0.515933I
b = −1.34440 + 0.80705I
−2.51303 + 1.69167I 0
u = −0.823126 + 0.594241I
a = −0.616204 − 1.118430I
b = −1.10371 − 0.91332I
−2.93943 − 1.39204I 0
u = −0.823126 − 0.594241I
a = −0.616204 + 1.118430I
b = −1.10371 + 0.91332I
−2.93943 + 1.39204I 0
u = 0.696281 + 0.684139I
a = 1.50341 + 0.43910I
b = 0.665119 − 0.261921I
−0.510482 + 0.490371I 0
u = 0.696281 − 0.684139I
a = 1.50341 − 0.43910I
b = 0.665119 + 0.261921I
−0.510482 − 0.490371I 0
u = 0.152840 + 0.963831I
a = 1.166230 − 0.182836I
b = −0.463762 + 0.579118I
−0.16328 − 1.51231I 0
u = 0.152840 − 0.963831I
a = 1.166230 + 0.182836I
b = −0.463762 − 0.579118I
−0.16328 + 1.51231I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.381338 + 0.953885I
a = 1.53715 − 0.34005I
b = 0.504853 + 0.770017I
0.16328 − 1.51231I 0
u = 0.381338 − 0.953885I
a = 1.53715 + 0.34005I
b = 0.504853 − 0.770017I
0.16328 + 1.51231I 0
u = 0.843737 + 0.481906I
a = 1.036830 − 0.436222I
b = 0.636621 − 0.450084I
0.606146 − 1.140740I 0
u = 0.843737 − 0.481906I
a = 1.036830 + 0.436222I
b = 0.636621 + 0.450084I
0.606146 + 1.140740I 0
u = 0.793686 + 0.656060I
a = −0.67850 + 1.38327I
b = −1.32553 + 0.93427I
−3.89040 + 5.00488I 0
u = 0.793686 − 0.656060I
a = −0.67850 − 1.38327I
b = −1.32553 − 0.93427I
−3.89040 − 5.00488I 0
u = 0.487021 + 0.908990I
a = −1.382000 − 0.167841I
b = −0.933256 + 0.346925I
0.67186 − 2.31975I 0
u = 0.487021 − 0.908990I
a = −1.382000 + 0.167841I
b = −0.933256 − 0.346925I
0.67186 + 2.31975I 0
u = −0.258634 + 1.001010I
a = 1.026540 + 0.626638I
b = −0.608734 − 1.144460I
1.179990 − 0.430240I 0
u = −0.258634 − 1.001010I
a = 1.026540 − 0.626638I
b = −0.608734 + 1.144460I
1.179990 + 0.430240I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.377689 + 0.965511I
a = 2.36112 − 0.96293I
b = 1.33765 + 1.31026I
2.95745 + 5.07220I 0
u = 0.377689 − 0.965511I
a = 2.36112 + 0.96293I
b = 1.33765 − 1.31026I
2.95745 − 5.07220I 0
u = 0.200530 + 1.018050I
a = 1.186000 − 0.505365I
b = −0.710658 + 0.984129I
0.36441 + 4.08864I 0
u = 0.200530 − 1.018050I
a = 1.186000 + 0.505365I
b = −0.710658 − 0.984129I
0.36441 − 4.08864I 0
u = −0.373627 + 0.969972I
a = 2.00297 + 1.12039I
b = 1.36042 − 0.96472I
4.76977 − 0.02280I 0
u = −0.373627 − 0.969972I
a = 2.00297 − 1.12039I
b = 1.36042 + 0.96472I
4.76977 + 0.02280I 0
u = −0.536403 + 0.906961I
a = −1.74681 − 0.53934I
b = −1.42395 + 0.11348I
−2.99007 + 5.88748I 0
u = −0.536403 − 0.906961I
a = −1.74681 + 0.53934I
b = −1.42395 − 0.11348I
−2.99007 − 5.88748I 0
u = −0.713873 + 0.612272I
a = 1.213510 − 0.492034I
b = 0.798352 + 0.374709I
−2.75046 − 6.50723I 0
u = −0.713873 − 0.612272I
a = 1.213510 + 0.492034I
b = 0.798352 − 0.374709I
−2.75046 + 6.50723I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.463990 + 0.816495I
a = −0.73359 + 1.81235I
b = −0.541609 − 0.530760I
0.33646 − 1.58880I 0
u = 0.463990 − 0.816495I
a = −0.73359 − 1.81235I
b = −0.541609 + 0.530760I
0.33646 + 1.58880I 0
u = −0.549717 + 0.760668I
a = −1.20472 − 1.75793I
b = −1.051140 + 0.039586I
−3.43015 − 1.51038I 0
u = −0.549717 − 0.760668I
a = −1.20472 + 1.75793I
b = −1.051140 − 0.039586I
−3.43015 + 1.51038I 0
u = −0.840506 + 0.652157I
a = 1.053580 − 0.135131I
b = 0.905372 + 0.023325I
−7.61513 + 2.24725I 0
u = −0.840506 − 0.652157I
a = 1.053580 + 0.135131I
b = 0.905372 − 0.023325I
−7.61513 − 2.24725I 0
u = −0.356964 + 1.003780I
a = 1.10995 + 1.34623I
b = 1.363320 − 0.196047I
4.71361 + 2.34843I 0
u = −0.356964 − 1.003780I
a = 1.10995 − 1.34623I
b = 1.363320 + 0.196047I
4.71361 − 2.34843I 0
u = 0.414228 + 0.981909I
a = 0.354458 − 1.062160I
b = −0.371091 + 1.052520I
4.26633 − 0.73149I 0
u = 0.414228 − 0.981909I
a = 0.354458 + 1.062160I
b = −0.371091 − 1.052520I
4.26633 + 0.73149I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.129488 + 0.915164I
a = 0.960675 + 0.426662I
b = −0.296636 − 0.987355I
1.82416 − 1.29895I 0
u = −0.129488 − 0.915164I
a = 0.960675 − 0.426662I
b = −0.296636 + 0.987355I
1.82416 + 1.29895I 0
u = −0.383178 + 1.005400I
a = 0.618638 + 1.012630I
b = −0.393790 − 1.184510I
3.42616 − 4.42719I 0
u = −0.383178 − 1.005400I
a = 0.618638 − 1.012630I
b = −0.393790 + 1.184510I
3.42616 + 4.42719I 0
u = 0.321449 + 1.031970I
a = 0.62025 − 1.47461I
b = 1.41421 − 0.14004I
2.71913 − 7.28797I 0
u = 0.321449 − 1.031970I
a = 0.62025 + 1.47461I
b = 1.41421 + 0.14004I
2.71913 + 7.28797I 0
u = 0.481357 + 0.968112I
a = −1.053720 − 0.021626I
b = 0.07893 − 1.73838I
−0.36441 − 4.08864I 0
u = 0.481357 − 0.968112I
a = −1.053720 + 0.021626I
b = 0.07893 + 1.73838I
−0.36441 + 4.08864I 0
u = 0.477961 + 0.978704I
a = −2.55928 + 0.63156I
b = −0.540892 − 0.552874I
3.89040 − 5.00488I 0
u = 0.477961 − 0.978704I
a = −2.55928 − 0.63156I
b = −0.540892 + 0.552874I
3.89040 + 5.00488I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.288183 + 1.051500I
a = 0.451947 + 0.568551I
b = −0.168159 − 0.824343I
3.43015 − 1.51038I 0
u = 0.288183 − 1.051500I
a = 0.451947 − 0.568551I
b = −0.168159 + 0.824343I
3.43015 + 1.51038I 0
u = 0.997685 + 0.442110I
a = −0.260668 + 0.432401I
b = −0.503103 + 0.532034I
0.510482 + 0.490371I 0
u = 0.997685 − 0.442110I
a = −0.260668 − 0.432401I
b = −0.503103 − 0.532034I
0.510482 − 0.490371I 0
u = −0.965634 + 0.515995I
a = −0.226054 − 0.635251I
b = −0.543836 − 0.760332I
−0.39103 − 5.61584I 0
u = −0.965634 − 0.515995I
a = −0.226054 + 0.635251I
b = −0.543836 + 0.760332I
−0.39103 + 5.61584I 0
u = −0.899610 + 0.655284I
a = 0.891423 − 0.168943I
b = 0.942689 − 0.215527I
−3.50746 + 10.61500I 0
u = −0.899610 − 0.655284I
a = 0.891423 + 0.168943I
b = 0.942689 + 0.215527I
−3.50746 − 10.61500I 0
u = 0.508993 + 0.990974I
a = −1.19790 − 0.86056I
b = 0.77945 − 2.15645I
2.08454 − 10.78560I 0
u = 0.508993 − 0.990974I
a = −1.19790 + 0.86056I
b = 0.77945 + 2.15645I
2.08454 + 10.78560I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.483626 + 1.004630I
a = −2.46022 − 0.80412I
b = −0.550966 + 0.771385I
2.80619 + 10.52050I 0
u = −0.483626 − 1.004630I
a = −2.46022 + 0.80412I
b = −0.550966 − 0.771385I
2.80619 − 10.52050I 0
u = 0.887503 + 0.675169I
a = 0.889093 + 0.104858I
b = 0.856581 + 0.175152I
−1.42713 − 4.91064I 0
u = 0.887503 − 0.675169I
a = 0.889093 − 0.104858I
b = 0.856581 − 0.175152I
−1.42713 + 4.91064I 0
u = −0.686763 + 0.553968I
a = −1.15225 − 1.14999I
b = −1.155710 − 0.749097I
−2.63356 − 2.12680I 0
u = −0.686763 − 0.553968I
a = −1.15225 + 1.14999I
b = −1.155710 + 0.749097I
−2.63356 + 2.12680I 0
u = −0.499533 + 1.001820I
a = −0.859826 + 0.800973I
b = 0.83318 + 1.81298I
3.92280 + 5.88359I 0
u = −0.499533 − 1.001820I
a = −0.859826 − 0.800973I
b = 0.83318 − 1.81298I
3.92280 − 5.88359I 0
u = 0.381904 + 0.774779I
a = 0.963184 + 0.422425I
b = −0.59196 + 1.67135I
−1.179990 + 0.430240I 0
u = 0.381904 − 0.774779I
a = 0.963184 − 0.422425I
b = −0.59196 − 1.67135I
−1.179990 − 0.430240I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.727245 + 0.460284I
a = −1.33174 + 0.72097I
b = −1.47714 + 0.71726I
−4.76977 + 0.02280I 0
u = 0.727245 − 0.460284I
a = −1.33174 − 0.72097I
b = −1.47714 − 0.71726I
−4.76977 − 0.02280I 0
u = −0.471708 + 1.045510I
a = −0.057598 + 0.754177I
b = 0.962909 + 0.998986I
3.94857 + 4.14341I 0
u = −0.471708 − 1.045510I
a = −0.057598 − 0.754177I
b = 0.962909 − 0.998986I
3.94857 − 4.14341I 0
u = −0.337591 + 1.098550I
a = 0.591677 − 0.468827I
b = −0.236721 + 0.673392I
2.99007 + 5.88748I 0
u = −0.337591 − 1.098550I
a = 0.591677 + 0.468827I
b = −0.236721 − 0.673392I
2.99007 − 5.88748I 0
u = 0.631075 + 0.965174I
a = −1.92745 + 0.64474I
b = −1.55707 − 1.01380I
−3.42616 − 4.42719I 0
u = 0.631075 − 0.965174I
a = −1.92745 − 0.64474I
b = −1.55707 + 1.01380I
−3.42616 + 4.42719I 0
u = 0.629650 + 0.976191I
a = 1.23250 − 1.48669I
b = 0.528126 + 0.382461I
0.39103 − 5.61584I 0
u = 0.629650 − 0.976191I
a = 1.23250 + 1.48669I
b = 0.528126 − 0.382461I
0.39103 + 5.61584I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.352055 + 0.754820I
a = −2.00994 + 2.12921I
b = −0.146379 + 0.209850I
2.93943 + 1.39204I 0
u = 0.352055 − 0.754820I
a = −2.00994 − 2.12921I
b = −0.146379 − 0.209850I
2.93943 − 1.39204I 0
u = −0.708371 + 0.431036I
a = −1.293870 − 0.230762I
b = −1.41656 − 0.14464I
−4.71361 − 2.34843I 0
u = −0.708371 − 0.431036I
a = −1.293870 + 0.230762I
b = −1.41656 + 0.14464I
−4.71361 + 2.34843I 0
u = 0.455227 + 1.089340I
a = 0.974536 − 0.050067I
b = 0.0693944 − 0.0112381I
2.46244 − 5.69178I 0
u = 0.455227 − 1.089340I
a = 0.974536 + 0.050067I
b = 0.0693944 + 0.0112381I
2.46244 + 5.69178I 0
u = 0.688567 + 0.441057I
a = −1.40211 + 0.89740I
b = −1.30493 + 1.02462I
−3.92280 + 5.88359I 0
u = 0.688567 − 0.441057I
a = −1.40211 − 0.89740I
b = −1.30493 − 1.02462I
−3.92280 − 5.88359I 0
u = −0.419510 + 1.107550I
a = 0.856484 − 0.171836I
b = −0.130336 + 0.242419I
2.51303 + 1.69167I 0
u = −0.419510 − 1.107550I
a = 0.856484 + 0.171836I
b = −0.130336 − 0.242419I
2.51303 − 1.69167I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.626190 + 1.006950I
a = 0.98225 + 1.52642I
b = 0.596201 − 0.476832I
−1.56303 + 11.65710I 0
u = −0.626190 − 1.006950I
a = 0.98225 − 1.52642I
b = 0.596201 + 0.476832I
−1.56303 − 11.65710I 0
u = −0.639333 + 0.496386I
a = −1.37503 − 1.08086I
b = −1.082360 − 0.869374I
−2.56168 − 2.03706I 0
u = −0.639333 − 0.496386I
a = −1.37503 + 1.08086I
b = −1.082360 + 0.869374I
−2.56168 + 2.03706I 0
u = 0.381601 + 0.713137I
a = 1.096170 − 0.184203I
b = 0.159797 + 0.195526I
− 1.68467I 0
u = 0.381601 − 0.713137I
a = 1.096170 + 0.184203I
b = 0.159797 − 0.195526I
1.68467I 0
u = −0.571186 + 1.051590I
a = −1.93792 − 1.06331I
b = −1.16702 + 1.19477I
−0.91389 + 6.81255I 0
u = −0.571186 − 1.051590I
a = −1.93792 + 1.06331I
b = −1.16702 − 1.19477I
−0.91389 − 6.81255I 0
u = −0.611075 + 1.029990I
a = −1.77487 − 0.80064I
b = −1.27397 + 1.09185I
−1.22565 + 7.16377I 0
u = −0.611075 − 1.029990I
a = −1.77487 + 0.80064I
b = −1.27397 − 1.09185I
−1.22565 − 7.16377I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.466709 + 1.107420I
a = 0.335162 − 0.964918I
b = 1.262510 − 0.540668I
1.71729 + 0.12884I 0
u = 0.466709 − 1.107420I
a = 0.335162 + 0.964918I
b = 1.262510 + 0.540668I
1.71729 − 0.12884I 0
u = 0.671010 + 1.006380I
a = −1.81191 + 0.52143I
b = −1.41030 − 1.30320I
−2.80619 − 10.52050I 0
u = 0.671010 − 1.006380I
a = −1.81191 − 0.52143I
b = −1.41030 + 1.30320I
−2.80619 + 10.52050I 0
u = 0.771291 + 0.937193I
a = 0.686302 − 0.575965I
b = 0.616297 + 0.140686I
−0.606146 − 1.140740I 0
u = 0.771291 − 0.937193I
a = 0.686302 + 0.575965I
b = 0.616297 − 0.140686I
−0.606146 + 1.140740I 0
u = −0.698063 + 0.995619I
a = 0.841382 + 1.013130I
b = 0.695453 − 0.262974I
−6.56925 + 3.46231I 0
u = −0.698063 − 0.995619I
a = 0.841382 − 1.013130I
b = 0.695453 + 0.262974I
−6.56925 − 3.46231I 0
u = 0.578191 + 1.071130I
a = −1.86866 + 1.25531I
b = −1.30169 − 1.31275I
−2.08454 − 10.78560I 0
u = 0.578191 − 1.071130I
a = −1.86866 − 1.25531I
b = −1.30169 + 1.31275I
−2.08454 + 10.78560I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.592842 + 1.073840I
a = −1.54460 + 1.30495I
b = −1.47667 − 1.10479I
−2.95745 − 5.07220I 0
u = 0.592842 − 1.073840I
a = −1.54460 − 1.30495I
b = −1.47667 + 1.10479I
−2.95745 + 5.07220I 0
u = −0.765303 + 0.050024I
a = 0.363568 + 0.066459I
b = −0.605791 + 0.141338I
−0.67186 + 2.31975I 0
u = −0.765303 − 0.050024I
a = 0.363568 − 0.066459I
b = −0.605791 − 0.141338I
−0.67186 − 2.31975I 0
u = −0.482768 + 1.135080I
a = 0.023930 − 1.119440I
b = −1.078560 − 0.200178I
−1.71729 + 0.12884I 0
u = −0.482768 − 1.135080I
a = 0.023930 + 1.119440I
b = −1.078560 + 0.200178I
−1.71729 − 0.12884I 0
u = −0.273788 + 0.715112I
a = −2.07465 − 1.93480I
b = −0.030393 − 0.433848I
1.51032 − 6.94428I 0
u = −0.273788 − 0.715112I
a = −2.07465 + 1.93480I
b = −0.030393 + 0.433848I
1.51032 + 6.94428I 0
u = 0.043452 + 1.233880I
a = 0.180099 + 0.343279I
b = 0.206814 − 0.906510I
6.56925 − 3.46231I 0
u = 0.043452 − 1.233880I
a = 0.180099 − 0.343279I
b = 0.206814 + 0.906510I
6.56925 + 3.46231I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.574543 + 1.100800I
a = −0.87193 − 1.23367I
b = −1.38106 + 0.55995I
−2.71913 + 7.28797I 0
u = −0.574543 − 1.100800I
a = −0.87193 + 1.23367I
b = −1.38106 − 0.55995I
−2.71913 − 7.28797I 0
u = −0.658091 + 1.053900I
a = −1.57184 − 0.57018I
b = −1.17515 + 1.21312I
−1.51032 + 6.94428I 0
u = −0.658091 − 1.053900I
a = −1.57184 + 0.57018I
b = −1.17515 − 1.21312I
−1.51032 − 6.94428I 0
u = 0.393787 + 0.643476I
a = 1.87357 + 0.29863I
b = 0.14001 + 1.89231I
0.91389 + 6.81255I 0
u = 0.393787 − 0.643476I
a = 1.87357 − 0.29863I
b = 0.14001 − 1.89231I
0.91389 − 6.81255I 0
u = 0.705100 + 0.214218I
a = 1.97229 − 0.17443I
b = 1.122970 + 0.284605I
−0.95485 − 4.47973I 0
u = 0.705100 − 0.214218I
a = 1.97229 + 0.17443I
b = 1.122970 − 0.284605I
−0.95485 + 4.47973I 0
u = −0.789536 + 0.995518I
a = 0.499761 + 0.691261I
b = 0.670421 − 0.086046I
−2.48531 − 4.47355I 0
u = −0.789536 − 0.995518I
a = 0.499761 − 0.691261I
b = 0.670421 + 0.086046I
−2.48531 + 4.47355I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.719646 + 0.108469I
a = 0.460682 − 0.104655I
b = −0.432315 − 0.228355I
−0.33646 + 1.58880I 0
u = 0.719646 − 0.108469I
a = 0.460682 + 0.104655I
b = −0.432315 + 0.228355I
−0.33646 − 1.58880I 0
u = −0.042466 + 1.272000I
a = 0.062952 − 0.240469I
b = 0.382049 + 0.836649I
7.61513 − 2.24725I 0
u = −0.042466 − 1.272000I
a = 0.062952 + 0.240469I
b = 0.382049 − 0.836649I
7.61513 + 2.24725I 0
u = 0.670465 + 0.278263I
a = −0.769817 − 0.284459I
b = −0.880367 − 0.143193I
−1.75718 − 0.31487I 0
u = 0.670465 − 0.278263I
a = −0.769817 + 0.284459I
b = −0.880367 + 0.143193I
−1.75718 + 0.31487I 0
u = −0.891440 + 0.913128I
a = 1.333200 + 0.349456I
b = 0.815105 − 0.053938I
−8.03800 + 3.27961I 0
u = −0.891440 − 0.913128I
a = 1.333200 − 0.349456I
b = 0.815105 + 0.053938I
−8.03800 − 3.27961I 0
u = 0.072964 + 1.286100I
a = −0.328203 + 0.088997I
b = 0.861394 − 0.890160I
3.98637 + 12.32940I 0
u = 0.072964 − 1.286100I
a = −0.328203 − 0.088997I
b = 0.861394 + 0.890160I
3.98637 − 12.32940I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.658651 + 1.109470I
a = 1.40526 − 0.61472I
b = 0.847148 + 0.649948I
2.48531 − 4.47355I 0
u = 0.658651 − 1.109470I
a = 1.40526 + 0.61472I
b = 0.847148 − 0.649948I
2.48531 + 4.47355I 0
u = −0.072007 + 1.289600I
a = −0.244543 − 0.105047I
b = 0.780553 + 0.864479I
6.16241 − 6.57875I 0
u = −0.072007 − 1.289600I
a = −0.244543 + 0.105047I
b = 0.780553 − 0.864479I
6.16241 + 6.57875I 0
u = −0.583473 + 0.398241I
a = −1.42999 + 0.51046I
b = −1.227490 + 0.489496I
−3.94857 + 4.14341I 0
u = −0.583473 − 0.398241I
a = −1.42999 − 0.51046I
b = −1.227490 − 0.489496I
−3.94857 − 4.14341I 0
u = 0.552376 + 1.183780I
a = −0.377343 + 0.758983I
b = −0.847109 − 0.240602I
0.95485 − 4.47973I 0
u = 0.552376 − 1.183780I
a = −0.377343 − 0.758983I
b = −0.847109 + 0.240602I
0.95485 + 4.47973I 0
u = −0.654889 + 1.131880I
a = 1.47794 + 0.71162I
b = 1.007870 − 0.807047I
3.50746 + 10.61500I 0
u = −0.654889 − 1.131880I
a = 1.47794 − 0.71162I
b = 1.007870 + 0.807047I
3.50746 − 10.61500I 0
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.084335 + 1.306830I
a = −0.1227610 − 0.0657099I
b = 0.786767 − 0.649293I
3.62376I 0
u = 0.084335 − 1.306830I
a = −0.1227610 + 0.0657099I
b = 0.786767 + 0.649293I
− 3.62376I 0
u = −0.653521 + 1.144520I
a = 1.60117 + 0.89022I
b = 1.29751 − 1.04509I
2.1765 + 15.2001I 0
u = −0.653521 − 1.144520I
a = 1.60117 − 0.89022I
b = 1.29751 + 1.04509I
2.1765 − 15.2001I 0
u = 0.654293 + 1.145280I
a = 1.63202 − 0.93496I
b = 1.37220 + 1.10031I
− 20.9496I 0
u = 0.654293 − 1.145280I
a = 1.63202 + 0.93496I
b = 1.37220 − 1.10031I
20.9496I 0
u = 0.655460 + 1.144730I
a = 1.47891 − 0.91836I
b = 1.35520 + 0.84393I
−3.98637 − 12.32940I 0
u = 0.655460 − 1.144730I
a = 1.47891 + 0.91836I
b = 1.35520 − 0.84393I
−3.98637 + 12.32940I 0
u = −0.691727 + 1.137220I
a = −1.072790 − 0.230467I
b = −0.611869 + 1.073120I
1.56303 + 11.65710I 0
u = −0.691727 − 1.137220I
a = −1.072790 + 0.230467I
b = −0.611869 − 1.073120I
1.56303 − 11.65710I 0
21
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.300160 + 0.589936I
a = 1.84979 + 0.16496I
b = 0.17460 − 1.47213I
2.56168 − 2.03706I 0
u = −0.300160 − 0.589936I
a = 1.84979 − 0.16496I
b = 0.17460 + 1.47213I
2.56168 + 2.03706I 0
u = 0.673480 + 1.160280I
a = −0.899680 + 0.305205I
b = −0.598617 − 0.873033I
2.75046 − 6.50723I 0
u = 0.673480 − 1.160280I
a = −0.899680 − 0.305205I
b = −0.598617 + 0.873033I
2.75046 + 6.50723I 0
u = −0.503663 + 0.164702I
a = 2.10891 − 0.10121I
b = 0.663909 − 0.473720I
1.75718 − 0.31487I 4.85874 + 0.69141I
u = −0.503663 − 0.164702I
a = 2.10891 + 0.10121I
b = 0.663909 + 0.473720I
1.75718 + 0.31487I 4.85874 − 0.69141I
u = 0.10156 + 1.61260I
a = 0.1043490 + 0.0324267I
b = 0.0071572 + 0.0438190I
8.03800 − 3.27961I 0
u = 0.10156 − 1.61260I
a = 0.1043490 − 0.0324267I
b = 0.0071572 − 0.0438190I
8.03800 + 3.27961I 0
u = 0.313148 + 0.174770I
a = −0.12867 − 2.44491I
b = −0.303311 − 0.750052I
−1.82416 − 1.29895I −6.39100 + 3.91546I
u = 0.313148 − 0.174770I
a = −0.12867 + 2.44491I
b = −0.303311 + 0.750052I
−1.82416 + 1.29895I −6.39100 − 3.91546I
22
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.045217 + 0.207422I
a = 2.59304 + 3.75458I
b = 0.120451 − 1.038080I
2.63356 − 2.12680I 3.26407 + 2.56553I
u = 0.045217 − 0.207422I
a = 2.59304 − 3.75458I
b = 0.120451 + 1.038080I
2.63356 + 2.12680I 3.26407 − 2.56553I
u = −0.169545 + 0.014842I
a = −3.88240 − 4.02767I
b = 0.011450 + 1.116910I
1.22565 + 7.16377I −0.18012 − 7.55527I
u = −0.169545 − 0.014842I
a = −3.88240 + 4.02767I
b = 0.011450 − 1.116910I
1.22565 − 7.16377I −0.18012 + 7.55527I
23
II.
I
u
2
= h4.32 × 10
6
u
35
+ 4.28 × 10
6
u
34
+ · · · + 6.27 × 10
5
b + 4.49 × 10
6
, −2.30 ×
10
6
u
35
− 6.82 × 10
6
u
34
+ · · · + 6.27 × 10
5
a − 8.28 × 10
5
, u
36
+ u
35
+ · · · − 2u + 1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
8
=
3.66222u
35
+ 10.8788u
34
+ ··· + 3.26928u + 1.32099
−6.88626u
35
− 6.82295u
34
+ ··· + 1.75798u − 7.15323
a
9
=
3.66222u
35
+ 9.87876u
34
+ ··· + 5.26928u + 1.32099
−6.88626u
35
− 7.82295u
34
+ ··· + 1.75798u − 7.15323
a
6
=
4.54050u
35
− 3.56480u
34
+ ··· + 15.1947u − 6.72077
4.89493u
35
− 0.428559u
34
+ ··· + 13.6672u − 1.27951
a
4
=
u
u
3
+ u
a
7
=
1.21474u
35
+ 9.38756u
34
+ ··· + 1.18940u − 0.750177
−9.61950u
35
− 12.3039u
34
+ ··· + 4.03814u − 10.1807
a
10
=
5.53474u
35
− 6.59347u
34
+ ··· + 32.4088u − 7.62500
4.61633u
35
+ 6.06683u
34
+ ··· − 9.66456u + 3.24553
a
3
=
1.35537u
35
+ 1.33182u
34
+ ··· − 22.5959u + 8.94503
0.144138u
35
+ 0.635297u
34
+ ··· + 9.83686u + 0.194845
a
2
=
13.8338u
35
+ 16.4789u
34
+ ··· − 19.8380u + 20.7300
3.31813u
35
+ 9.23511u
34
+ ··· − 0.315557u + 4.39888
(ii) Obstruction class = 1
(iii) Cusp Shapes =
27488728
627059
u
35
+
14925233
627059
u
34
+ ··· +
36240697
627059
u −
2539348
627059
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
36
− 21u
35
+ ··· − 22u + 1
c
2
, c
4
u
36
− u
35
+ ··· + 2u + 1
c
3
u
36
+ 6u
34
+ ··· + 6u
2
+ 1
c
5
u
36
− 2u
35
+ ··· − 7u + 1
c
6
, c
11
u
36
+ u
35
+ ··· − 2u + 1
c
7
u
36
+ 6u
34
+ ··· + 6u
2
+ 1
c
8
u
36
+ 2u
35
+ ··· + 7u + 1
c
9
u
36
− 18u
35
+ ··· − 21u + 1
c
10
u
36
+ 18u
35
+ ··· + 21u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
12
y
36
+ y
35
+ ··· − 38y + 1
c
2
, c
4
, c
6
c
11
y
36
+ 21y
35
+ ··· + 22y + 1
c
3
, c
7
y
36
+ 12y
35
+ ··· + 12y + 1
c
5
, c
8
y
36
+ 8y
35
+ ··· − 5y + 1
c
9
, c
10
y
36
+ 4y
35
+ ··· − 31y + 1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.356759 + 0.951607I
a = 0.914331 − 0.965264I
b = 0.479126 − 0.692848I
3.79170 − 3.65299I 5.12688 + 4.63537I
u = 0.356759 − 0.951607I
a = 0.914331 + 0.965264I
b = 0.479126 + 0.692848I
3.79170 + 3.65299I 5.12688 − 4.63537I
u = −0.168805 + 0.968564I
a = −0.190175 + 0.324188I
b = −0.231683 + 0.977267I
−0.27034 + 2.03072I −1.37413 − 3.54155I
u = −0.168805 − 0.968564I
a = −0.190175 − 0.324188I
b = −0.231683 − 0.977267I
−0.27034 − 2.03072I −1.37413 + 3.54155I
u = −0.328701 + 0.921262I
a = 0.41300 + 1.42504I
b = 0.576857 + 1.040110I
2.17546 + 8.59712I 1.74361 − 10.55765I
u = −0.328701 − 0.921262I
a = 0.41300 − 1.42504I
b = 0.576857 − 1.040110I
2.17546 − 8.59712I 1.74361 + 10.55765I
u = −0.814995 + 0.636107I
a = −0.363443 − 0.522456I
b = −0.493974 − 0.752653I
−1.18883 − 5.41822I −3.24773 + 6.10728I
u = −0.814995 − 0.636107I
a = −0.363443 + 0.522456I
b = −0.493974 + 0.752653I
−1.18883 + 5.41822I −3.24773 − 6.10728I
u = −0.349182 + 0.897849I
a = 2.30551 + 1.09645I
b = 0.32685 − 1.41797I
2.12597 − 5.76800I 2.04602 + 5.29647I
u = −0.349182 − 0.897849I
a = 2.30551 − 1.09645I
b = 0.32685 + 1.41797I
2.12597 + 5.76800I 2.04602 − 5.29647I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.200589 + 1.038470I
a = 0.506535 + 0.199478I
b = −0.768317 + 0.977267I
0.27034 + 2.03072I 1.37413 − 3.54155I
u = 0.200589 − 1.038470I
a = 0.506535 − 0.199478I
b = −0.768317 − 0.977267I
0.27034 − 2.03072I 1.37413 + 3.54155I
u = 0.346855 + 0.870417I
a = 1.88560 − 1.51011I
b = 0.227687 + 1.020110I
3.49419 + 0.74030I 6.39310 + 1.20566I
u = 0.346855 − 0.870417I
a = 1.88560 + 1.51011I
b = 0.227687 − 1.020110I
3.49419 − 0.74030I 6.39310 − 1.20566I
u = −0.706790 + 0.591629I
a = −0.79057 − 1.32948I
b = −1.22769 − 1.02011I
−3.49419 − 0.74030I −6.39310 − 1.20566I
u = −0.706790 − 0.591629I
a = −0.79057 + 1.32948I
b = −1.22769 + 1.02011I
−3.49419 + 0.74030I −6.39310 + 1.20566I
u = 0.675614 + 0.524353I
a = −1.28892 + 1.33374I
b = −1.47913 + 0.69285I
−3.79170 + 3.65299I −5.12688 − 4.63537I
u = 0.675614 − 0.524353I
a = −1.28892 − 1.33374I
b = −1.47913 − 0.69285I
−3.79170 − 3.65299I −5.12688 + 4.63537I
u = 0.442727 + 1.088630I
a = 0.381092 + 0.198242I
b = 0.103714 − 0.465023I
2.48966 − 3.63792I 3.42962 + 4.01261I
u = 0.442727 − 1.088630I
a = 0.381092 − 0.198242I
b = 0.103714 + 0.465023I
2.48966 + 3.63792I 3.42962 − 4.01261I
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.626367 + 1.013070I
a = −1.54592 − 0.41097I
b = −0.500000 + 1.211640I
10.7799I 0. − 10.33735I
u = −0.626367 − 1.013070I
a = −1.54592 + 0.41097I
b = −0.500000 − 1.211640I
− 10.7799I 0. + 10.33735I
u = 0.643817 + 1.004750I
a = −1.38327 + 0.63511I
b = −0.506026 − 0.752653I
1.18883 − 5.41822I 3.24773 + 6.10728I
u = 0.643817 − 1.004750I
a = −1.38327 − 0.63511I
b = −0.506026 + 0.752653I
1.18883 + 5.41822I 3.24773 − 6.10728I
u = −0.597688 + 1.033090I
a = −1.92399 − 0.85913I
b = −1.32685 + 1.41797I
−2.12597 + 5.76800I −2.04602 − 5.29647I
u = −0.597688 − 1.033090I
a = −1.92399 + 0.85913I
b = −1.32685 − 1.41797I
−2.12597 − 5.76800I −2.04602 + 5.29647I
u = 0.589877 + 1.057630I
a = −1.69470 + 1.11132I
b = −1.57686 − 1.04011I
−2.17546 − 8.59712I −1.74361 + 10.55765I
u = 0.589877 − 1.057630I
a = −1.69470 − 1.11132I
b = −1.57686 + 1.04011I
−2.17546 + 8.59712I −1.74361 − 10.55765I
u = −0.900597 + 0.911872I
a = −1.323740 − 0.331610I
b = −0.801899 + 0.061698I
−8.00014 + 3.30429I 75.1029 − 50.7555I
u = −0.900597 − 0.911872I
a = −1.323740 + 0.331610I
b = −0.801899 − 0.061698I
−8.00014 − 3.30429I 75.1029 + 50.7555I
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.556811 + 0.339720I
a = 0.179003 − 0.837618I
b = −0.500000 + 0.202005I
− 0.232158I − 60.10 + 0.405410I
u = 0.556811 − 0.339720I
a = 0.179003 + 0.837618I
b = −0.500000 − 0.202005I
0.232158I − 60.10 − 0.405410I
u = 0.085789 + 0.390964I
a = −1.56881 + 2.35602I
b = −1.103710 − 0.465023I
−2.48966 − 3.63792I −3.42962 + 4.01261I
u = 0.085789 − 0.390964I
a = −1.56881 − 2.35602I
b = −1.103710 + 0.465023I
−2.48966 + 3.63792I −3.42962 − 4.01261I
u = 0.09429 + 1.62517I
a = −0.0115273 − 0.0094239I
b = −0.198101 − 0.061698I
8.00014 − 3.30429I 0
u = 0.09429 − 1.62517I
a = −0.0115273 + 0.0094239I
b = −0.198101 + 0.061698I
8.00014 + 3.30429I 0
30
III. I
u
3
= h−u
2
+ b + u, −u
3
+ u
2
+ a, u
4
− u
3
+ u
2
− u + 1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
8
=
u
3
− u
2
u
2
− u
a
9
=
1
u
2
a
6
=
u
u
3
+ u
a
4
=
u
u
3
+ u
a
7
=
−u + 1
−u
3
+ 2u
2
− u + 1
a
10
=
u
3
− 2u
2
+ 2u
u
3
− u + 1
a
3
=
2u
2
− u + 1
u
2
+ u − 1
a
2
=
2u
2
− u
u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
8
, c
11
, c
12
u
4
− u
3
+ u
2
− u + 1
c
2
, c
4
, c
5
c
7
u
4
+ u
3
+ u
2
+ u + 1
c
9
u
4
− 2u
3
+ 4u
2
− 3u + 1
c
10
u
4
+ 2u
3
+ 4u
2
+ 3u + 1
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
11
c
12
y
4
+ y
3
+ y
2
+ y + 1
c
9
, c
10
y
4
+ 4y
3
+ 6y
2
− y + 1
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.309017 + 0.951057I
a = 1.61803
b = −0.50000 − 1.53884I
0 0
u = −0.309017 − 0.951057I
a = 1.61803
b = −0.50000 + 1.53884I
0 0
u = 0.809017 + 0.587785I
a = −0.618034
b = −0.500000 + 0.363271I
0 0
u = 0.809017 − 0.587785I
a = −0.618034
b = −0.500000 − 0.363271I
0 0
34
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
− u
3
+ u
2
− u + 1)(u
36
− 21u
35
+ ··· − 22u + 1)
· (u
184
+ 83u
183
+ ··· − 5u + 1)
c
2
(u
4
+ u
3
+ u
2
+ u + 1)(u
36
− u
35
+ ··· + 2u + 1)(u
184
− u
183
+ ··· + 5u + 1)
c
3
(u
4
− u
3
+ u
2
− u + 1)(u
36
+ 6u
34
+ ··· + 6u
2
+ 1)
· (u
184
+ 2u
183
+ ··· + 4095u + 691)
c
4
(u
4
+ u
3
+ u
2
+ u + 1)(u
36
− u
35
+ ··· + 2u + 1)(u
184
+ u
183
+ ··· − 5u + 1)
c
5
(u
4
+ u
3
+ u
2
+ u + 1)(u
36
− 2u
35
+ ··· − 7u + 1)
· (u
184
+ 2u
183
+ ··· + 3708404u + 1584839)
c
6
(u
4
− u
3
+ u
2
− u + 1)(u
36
+ u
35
+ ··· − 2u + 1)(u
184
− u
183
+ ··· + 5u + 1)
c
7
(u
4
+ u
3
+ u
2
+ u + 1)(u
36
+ 6u
34
+ ··· + 6u
2
+ 1)
· (u
184
− 2u
183
+ ··· − 4095u + 691)
c
8
(u
4
− u
3
+ u
2
− u + 1)(u
36
+ 2u
35
+ ··· + 7u + 1)
· (u
184
− 2u
183
+ ··· − 3708404u + 1584839)
c
9
(u
4
− 2u
3
+ 4u
2
− 3u + 1)(u
36
− 18u
35
+ ··· − 21u + 1)
· (u
184
− 11u
183
+ ··· + 8744u + 257)
c
10
(u
4
+ 2u
3
+ 4u
2
+ 3u + 1)(u
36
+ 18u
35
+ ··· + 21u + 1)
· (u
184
+ 11u
183
+ ··· − 8744u + 257)
c
11
(u
4
− u
3
+ u
2
− u + 1)(u
36
+ u
35
+ ··· − 2u + 1)(u
184
+ u
183
+ ··· − 5u + 1)
c
12
(u
4
− u
3
+ u
2
− u + 1)(u
36
− 21u
35
+ ··· − 22u + 1)
· (u
184
− 83u
183
+ ··· + 5u + 1)
35
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
12
(y
4
+ y
3
+ y
2
+ y + 1)(y
36
+ y
35
+ ··· − 38y + 1)
· (y
184
+ 47y
183
+ ··· − 2797y + 1)
c
2
, c
4
, c
6
c
11
(y
4
+ y
3
+ y
2
+ y + 1)(y
36
+ 21y
35
+ ··· + 22y + 1)
· (y
184
+ 83y
183
+ ··· − 5y + 1)
c
3
, c
7
(y
4
+ y
3
+ y
2
+ y + 1)(y
36
+ 12y
35
+ ··· + 12y + 1)
· (y
184
+ 2y
183
+ ··· − 20009815y + 477481)
c
5
, c
8
(y
4
+ y
3
+ y
2
+ y + 1)(y
36
+ 8y
35
+ ··· − 5y + 1)
· (y
184
− 18y
183
+ ··· − 530431543575720y + 2511714655921)
c
9
, c
10
(y
4
+ 4y
3
+ 6y
2
− y + 1)(y
36
+ 4y
35
+ ··· − 31y + 1)
· (y
184
− 23y
183
+ ··· + 38603420y + 66049)
36
