12a
0874
(K12a
0874
)
A knot diagram
1
Linearized knot diagam
4 6 7 9 12 10 11 1 2 3 8 5
Solving Sequence
5,12
6
1,9
4 2 3 10 8 11 7
c
5
c
12
c
4
c
1
c
2
c
9
c
8
c
11
c
7
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.84886 × 10
1402
u
190
+ 3.70297 × 10
1402
u
189
+ ··· + 1.63068 × 10
1404
b + 1.52642 × 10
1408
,
− 2.20329 × 10
1408
u
190
+ 6.86665 × 10
1407
u
189
+ ··· + 4.27740 × 10
1409
a + 4.99679 × 10
1413
,
u
191
+ 65u
189
+ ··· − 7345527u + 262307i
I
u
2
= h2.77823 × 10
73
u
49
+ 1.70736 × 10
73
u
48
+ ··· + 7.28128 × 10
73
b − 2.44122 × 10
74
,
1.03235 × 10
75
u
49
+ 1.05630 × 10
75
u
48
+ ··· + 7.28128 × 10
73
a + 2.83270 × 10
75
, u
50
+ u
49
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 241 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−1.85 × 10
1402
u
190
+ 3.70 × 10
1402
u
189
+ · · · + 1.63 × 10
1404
b +
1.53 × 10
1408
, −2.20 × 10
1408
u
190
+ 6.87 × 10
1407
u
189
+ · · · + 4.28 ×
10
1409
a + 5.00 × 10
1413
, u
191
+ 65u
189
+ · · · − 7345527u + 262307i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
u
u
a
9
=
0.0515100u
190
− 0.0160533u
189
+ ··· + 326321.u − 11681.9
0.0113379u
190
− 0.0227081u
189
+ ··· + 258745.u − 9360.63
a
4
=
0.0586402u
190
+ 0.144311u
189
+ ··· − 1.14998 × 10
6
u + 42130.4
0.0514121u
190
+ 0.0955835u
189
+ ··· − 729887.u + 26842.3
a
2
=
0.0935137u
190
+ 0.0724429u
189
+ ··· − 477887.u + 18316.9
0.0288888u
190
+ 0.0540440u
189
+ ··· − 432033.u + 15860.7
a
3
=
0.0640409u
190
+ 0.0599123u
189
+ ··· − 402318.u + 15175.3
0.00513012u
190
+ 0.0403217u
189
+ ··· − 347720.u + 12573.8
a
10
=
−0.0724069u
190
− 0.0906965u
189
+ ··· + 611737.u − 23521.2
−0.0645735u
190
− 0.0493419u
189
+ ··· + 237286.u − 9472.89
a
8
=
0.0235649u
190
− 0.0269071u
189
+ ··· + 364666.u − 13427.4
−0.0166072u
190
− 0.0335619u
189
+ ··· + 297090.u − 11106.2
a
11
=
−0.117562u
190
+ 0.0353139u
189
+ ··· − 638817.u + 21444.7
−0.0523487u
190
+ 0.0300864u
189
+ ··· − 450943.u + 15665.9
a
7
=
−0.161698u
190
− 0.0975729u
189
+ ··· + 566662.u − 23287.5
−0.107800u
190
− 0.0856358u
189
+ ··· + 547467.u − 21437.9
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0664855u
190
+ 0.106706u
189
+ ··· − 806183.u + 28495.4
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
191
+ 8u
190
+ ··· + 12090u − 521
c
2
u
191
+ 9u
189
+ ··· + 26856u − 3123
c
3
u
191
+ 8u
190
+ ··· − 40446u − 4563
c
4
u
191
+ 23u
189
+ ··· − 6088215u − 1128983
c
5
, c
12
u
191
+ 65u
189
+ ··· − 7345527u − 262307
c
6
u
191
+ 2u
190
+ ··· − 26u − 1
c
7
, c
11
u
191
− 4u
190
+ ··· − 644237242u − 33057935
c
8
u
191
+ 4u
190
+ ··· − 14u − 1
c
9
u
191
+ 3u
190
+ ··· + 2081393442u − 208449613
c
10
u
191
+ 4u
190
+ ··· − 517308u − 92933
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
191
+ 18y
190
+ ··· + 7672754y −271441
c
2
y
191
+ 18y
190
+ ··· − 1093867848y −9753129
c
3
y
191
+ 48y
190
+ ··· − 547954632y −20820969
c
4
y
191
+ 46y
190
+ ··· − 71896540462205y −1274602614289
c
5
, c
12
y
191
+ 130y
190
+ ··· + 5931925730613y −68804962249
c
6
y
191
− 14y
190
+ ··· + 150y −1
c
7
, c
11
y
191
− 140y
190
+ ··· + 148730603959730924y −1092827066464225
c
8
y
191
+ 16y
190
+ ··· − 1830y −1
c
9
y
191
− 55y
190
+ ··· + 2565423313669011206y −43451241159849769
c
10
y
191
− 24y
190
+ ··· + 682916036430y −8636542489
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.512846 + 0.859954I
a = −0.993688 + 0.949455I
b = −0.962967 + 0.962306I
1.62279 − 0.11399I 0
u = 0.512846 − 0.859954I
a = −0.993688 − 0.949455I
b = −0.962967 − 0.962306I
1.62279 + 0.11399I 0
u = 0.978114 + 0.183462I
a = −0.473054 + 0.830311I
b = 0.619112 + 1.108490I
3.58690 + 5.22077I 0
u = 0.978114 − 0.183462I
a = −0.473054 − 0.830311I
b = 0.619112 − 1.108490I
3.58690 − 5.22077I 0
u = −0.102811 + 1.007920I
a = −3.34076 − 0.79703I
b = 0.387767 + 0.166638I
−1.76777 − 0.26711I 0
u = −0.102811 − 1.007920I
a = −3.34076 + 0.79703I
b = 0.387767 − 0.166638I
−1.76777 + 0.26711I 0
u = 0.652465 + 0.737354I
a = 0.11217 + 2.09971I
b = 0.66513 + 1.32327I
4.43750 − 0.16046I 0
u = 0.652465 − 0.737354I
a = 0.11217 − 2.09971I
b = 0.66513 − 1.32327I
4.43750 + 0.16046I 0
u = −0.063400 + 0.979157I
a = 1.66806 − 1.73143I
b = −0.255460 − 0.917578I
−3.41286 − 0.27827I 0
u = −0.063400 − 0.979157I
a = 1.66806 + 1.73143I
b = −0.255460 + 0.917578I
−3.41286 + 0.27827I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.334797 + 0.964987I
a = 0.360107 − 0.486954I
b = 0.727671 − 0.923644I
4.04608 − 4.03130I 0
u = 0.334797 − 0.964987I
a = 0.360107 + 0.486954I
b = 0.727671 + 0.923644I
4.04608 + 4.03130I 0
u = −0.245261 + 0.991590I
a = 1.08011 + 1.00475I
b = 1.22574 + 1.23155I
3.24219 − 4.65971I 0
u = −0.245261 − 0.991590I
a = 1.08011 − 1.00475I
b = 1.22574 − 1.23155I
3.24219 + 4.65971I 0
u = −0.923435 + 0.314359I
a = −0.093251 − 0.285405I
b = 0.862564 − 0.892525I
−0.56099 − 10.00740I 0
u = −0.923435 − 0.314359I
a = −0.093251 + 0.285405I
b = 0.862564 + 0.892525I
−0.56099 + 10.00740I 0
u = 0.067457 + 0.965865I
a = 0.324948 − 0.329435I
b = 0.745054 + 0.046203I
−1.96101 − 1.49328I 0
u = 0.067457 − 0.965865I
a = 0.324948 + 0.329435I
b = 0.745054 − 0.046203I
−1.96101 + 1.49328I 0
u = 0.763160 + 0.575586I
a = −0.02349 − 1.82947I
b = −0.900127 − 1.006580I
4.29389 − 8.15564I 0
u = 0.763160 − 0.575586I
a = −0.02349 + 1.82947I
b = −0.900127 + 1.006580I
4.29389 + 8.15564I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351723 + 0.887873I
a = −0.176619 + 0.859935I
b = −0.802411 + 0.916053I
3.14538 + 1.39324I 0
u = 0.351723 − 0.887873I
a = −0.176619 − 0.859935I
b = −0.802411 − 0.916053I
3.14538 − 1.39324I 0
u = −0.420057 + 0.958849I
a = 0.961807 + 0.025499I
b = 1.38879 + 0.46497I
0.86595 − 4.74204I 0
u = −0.420057 − 0.958849I
a = 0.961807 − 0.025499I
b = 1.38879 − 0.46497I
0.86595 + 4.74204I 0
u = 0.196400 + 1.046200I
a = −1.57183 − 2.09208I
b = −0.046973 − 0.660831I
−0.23823 + 11.38630I 0
u = 0.196400 − 1.046200I
a = −1.57183 + 2.09208I
b = −0.046973 + 0.660831I
−0.23823 − 11.38630I 0
u = 1.053650 + 0.155311I
a = 0.007011 + 0.199597I
b = −0.767990 + 0.943186I
2.09784 − 6.73290I 0
u = 1.053650 − 0.155311I
a = 0.007011 − 0.199597I
b = −0.767990 − 0.943186I
2.09784 + 6.73290I 0
u = −0.636027 + 0.683004I
a = 0.423049 − 0.420854I
b = 0.670440 + 0.234980I
1.89166 − 2.30214I 0
u = −0.636027 − 0.683004I
a = 0.423049 + 0.420854I
b = 0.670440 − 0.234980I
1.89166 + 2.30214I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.203809 + 1.048740I
a = 1.19180 + 1.78538I
b = −0.145495 + 0.643514I
0.87699 + 3.92374I 0
u = 0.203809 − 1.048740I
a = 1.19180 − 1.78538I
b = −0.145495 − 0.643514I
0.87699 − 3.92374I 0
u = −0.149392 + 1.063000I
a = 1.03449 − 1.56066I
b = 0.068658 − 0.906663I
−1.78563 − 3.42046I 0
u = −0.149392 − 1.063000I
a = 1.03449 + 1.56066I
b = 0.068658 + 0.906663I
−1.78563 + 3.42046I 0
u = −0.125292 + 0.912031I
a = −1.01216 + 3.00472I
b = −0.208639 + 0.568525I
−0.797459 − 0.334339I 0
u = −0.125292 − 0.912031I
a = −1.01216 − 3.00472I
b = −0.208639 − 0.568525I
−0.797459 + 0.334339I 0
u = 0.537404 + 0.954621I
a = −1.153260 + 0.337003I
b = −1.55005 + 0.46691I
3.75061 + 4.90766I 0
u = 0.537404 − 0.954621I
a = −1.153260 − 0.337003I
b = −1.55005 − 0.46691I
3.75061 − 4.90766I 0
u = −0.004471 + 0.901983I
a = 0.42577 − 2.27412I
b = −0.73911 − 1.36029I
−0.81189 + 2.82019I 0
u = −0.004471 − 0.901983I
a = 0.42577 + 2.27412I
b = −0.73911 + 1.36029I
−0.81189 − 2.82019I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.094679 + 0.882420I
a = 0.08973 − 3.33527I
b = −0.16408 − 1.43641I
4.88992 + 5.75364I 0
u = 0.094679 − 0.882420I
a = 0.08973 + 3.33527I
b = −0.16408 + 1.43641I
4.88992 − 5.75364I 0
u = 0.140999 + 0.865493I
a = −1.97414 − 0.68224I
b = −2.04877 − 0.50684I
−1.33549 + 5.07868I 0
u = 0.140999 − 0.865493I
a = −1.97414 + 0.68224I
b = −2.04877 + 0.50684I
−1.33549 − 5.07868I 0
u = 0.245291 + 1.100020I
a = −0.154490 − 1.035660I
b = −1.25904 − 0.73250I
−0.74677 + 5.69470I 0
u = 0.245291 − 1.100020I
a = −0.154490 + 1.035660I
b = −1.25904 + 0.73250I
−0.74677 − 5.69470I 0
u = 0.538302 + 0.993486I
a = 1.122900 − 0.150927I
b = 1.60951 − 0.43310I
2.99242 + 13.07300I 0
u = 0.538302 − 0.993486I
a = 1.122900 + 0.150927I
b = 1.60951 + 0.43310I
2.99242 − 13.07300I 0
u = 0.857824 + 0.132948I
a = 0.475836 − 0.301211I
b = −0.781613 + 0.549576I
7.73115 − 7.16300I 0
u = 0.857824 − 0.132948I
a = 0.475836 + 0.301211I
b = −0.781613 − 0.549576I
7.73115 + 7.16300I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.216038 + 0.828045I
a = 0.056967 + 0.244949I
b = 1.194940 + 0.498301I
−0.82493 − 1.48368I 0
u = −0.216038 − 0.828045I
a = 0.056967 − 0.244949I
b = 1.194940 − 0.498301I
−0.82493 + 1.48368I 0
u = −0.765012 + 0.361285I
a = 0.382919 + 0.555963I
b = −0.601198 − 0.692072I
6.87864 − 2.95599I 0
u = −0.765012 − 0.361285I
a = 0.382919 − 0.555963I
b = −0.601198 + 0.692072I
6.87864 + 2.95599I 0
u = −1.154930 + 0.023766I
a = −0.048559 + 0.137207I
b = 0.773974 + 0.296975I
6.21670 + 0.18236I 0
u = −1.154930 − 0.023766I
a = −0.048559 − 0.137207I
b = 0.773974 − 0.296975I
6.21670 − 0.18236I 0
u = 0.270166 + 0.790707I
a = 1.12593 + 1.26255I
b = 1.67917 + 0.94477I
−1.41533 − 2.76220I 0
u = 0.270166 − 0.790707I
a = 1.12593 − 1.26255I
b = 1.67917 − 0.94477I
−1.41533 + 2.76220I 0
u = −0.307718 + 1.137970I
a = 0.130836 − 1.390020I
b = 0.918476 − 0.802985I
−2.07824 − 2.61344I 0
u = −0.307718 − 1.137970I
a = 0.130836 + 1.390020I
b = 0.918476 + 0.802985I
−2.07824 + 2.61344I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.759204 + 0.904304I
a = −0.870024 + 0.176525I
b = −1.354370 − 0.038262I
3.82808 − 3.36796I 0
u = −0.759204 − 0.904304I
a = −0.870024 − 0.176525I
b = −1.354370 + 0.038262I
3.82808 + 3.36796I 0
u = 0.215667 + 0.781332I
a = −0.09282 + 2.90289I
b = −0.065974 + 1.301720I
3.75123 + 1.22811I 0
u = 0.215667 − 0.781332I
a = −0.09282 − 2.90289I
b = −0.065974 − 1.301720I
3.75123 − 1.22811I 0
u = −0.070495 + 0.800619I
a = −0.18103 + 3.27892I
b = −0.37119 + 1.90392I
4.33921 + 3.00466I 0
u = −0.070495 − 0.800619I
a = −0.18103 − 3.27892I
b = −0.37119 − 1.90392I
4.33921 − 3.00466I 0
u = 0.379809 + 1.143710I
a = 0.12608 − 1.96227I
b = −0.93069 − 1.46292I
−4.58008 + 7.62774I 0
u = 0.379809 − 1.143710I
a = 0.12608 + 1.96227I
b = −0.93069 + 1.46292I
−4.58008 − 7.62774I 0
u = −1.204200 + 0.051631I
a = −0.134195 + 0.224731I
b = −0.509548 + 0.711296I
−1.43643 + 1.06724I 0
u = −1.204200 − 0.051631I
a = −0.134195 − 0.224731I
b = −0.509548 − 0.711296I
−1.43643 − 1.06724I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.130357 + 1.206490I
a = 0.52079 − 2.00918I
b = 1.25295 − 1.50619I
−3.50446 − 5.10385I 0
u = −0.130357 − 1.206490I
a = 0.52079 + 2.00918I
b = 1.25295 + 1.50619I
−3.50446 + 5.10385I 0
u = −0.978809 + 0.720736I
a = 0.22600 − 1.40774I
b = 0.938598 − 0.949593I
4.45374 − 2.93608I 0
u = −0.978809 − 0.720736I
a = 0.22600 + 1.40774I
b = 0.938598 + 0.949593I
4.45374 + 2.93608I 0
u = 0.430559 + 1.148940I
a = 0.06746 − 1.85481I
b = −0.74802 − 1.46882I
−5.14020 + 4.43600I 0
u = 0.430559 − 1.148940I
a = 0.06746 + 1.85481I
b = −0.74802 + 1.46882I
−5.14020 − 4.43600I 0
u = 0.231567 + 1.210320I
a = −1.07254 + 1.32991I
b = 0.225923 + 0.791440I
−6.04240 + 2.26440I 0
u = 0.231567 − 1.210320I
a = −1.07254 − 1.32991I
b = 0.225923 − 0.791440I
−6.04240 − 2.26440I 0
u = 0.748825 + 0.134176I
a = −1.029500 + 0.659070I
b = 0.483999 − 0.212481I
5.78898 − 0.92272I 0
u = 0.748825 − 0.134176I
a = −1.029500 − 0.659070I
b = 0.483999 + 0.212481I
5.78898 + 0.92272I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.318924 + 1.197870I
a = −0.52440 + 1.92588I
b = 0.66140 + 1.27385I
−5.42410 + 6.89918I 0
u = 0.318924 − 1.197870I
a = −0.52440 − 1.92588I
b = 0.66140 − 1.27385I
−5.42410 − 6.89918I 0
u = 0.502605 + 1.133200I
a = 1.218780 − 0.256912I
b = −0.090194 − 0.635435I
−2.19176 + 1.79090I 0
u = 0.502605 − 1.133200I
a = 1.218780 + 0.256912I
b = −0.090194 + 0.635435I
−2.19176 − 1.79090I 0
u = 0.020802 + 1.240620I
a = −0.58472 − 1.95104I
b = 0.200347 − 0.949379I
−5.28743 − 2.75029I 0
u = 0.020802 − 1.240620I
a = −0.58472 + 1.95104I
b = 0.200347 + 0.949379I
−5.28743 + 2.75029I 0
u = 0.672281 + 1.044110I
a = −0.733412 + 0.389703I
b = 0.248286 + 0.924151I
−4.06067 + 2.71323I 0
u = 0.672281 − 1.044110I
a = −0.733412 − 0.389703I
b = 0.248286 − 0.924151I
−4.06067 − 2.71323I 0
u = 0.231618 + 1.220750I
a = −1.000350 + 0.801072I
b = 0.033968 + 0.735142I
−5.80675 − 1.12388I 0
u = 0.231618 − 1.220750I
a = −1.000350 − 0.801072I
b = 0.033968 − 0.735142I
−5.80675 + 1.12388I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.317189 + 1.204070I
a = 0.679256 − 1.103960I
b = −0.118615 − 1.053290I
−6.10196 − 0.31502I 0
u = 0.317189 − 1.204070I
a = 0.679256 + 1.103960I
b = −0.118615 + 1.053290I
−6.10196 + 0.31502I 0
u = −1.166340 + 0.471514I
a = 0.0734794 − 0.0496177I
b = 0.433930 + 0.651683I
5.48069 + 1.09842I 0
u = −1.166340 − 0.471514I
a = 0.0734794 + 0.0496177I
b = 0.433930 − 0.651683I
5.48069 − 1.09842I 0
u = −0.239978 + 1.235820I
a = 0.06085 + 2.17482I
b = −0.65613 + 1.57978I
−5.37230 + 2.31650I 0
u = −0.239978 − 1.235820I
a = 0.06085 − 2.17482I
b = −0.65613 − 1.57978I
−5.37230 − 2.31650I 0
u = −0.528628 + 0.516502I
a = 0.659172 + 0.622640I
b = −0.822489 + 0.761066I
2.08705 − 2.16220I 0
u = −0.528628 − 0.516502I
a = 0.659172 − 0.622640I
b = −0.822489 − 0.761066I
2.08705 + 2.16220I 0
u = −0.479429 + 1.167820I
a = −0.64119 − 1.40633I
b = 0.790701 − 0.847266I
4.29924 − 1.75183I 0
u = −0.479429 − 1.167820I
a = −0.64119 + 1.40633I
b = 0.790701 + 0.847266I
4.29924 + 1.75183I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.118950 + 0.720662I
a = −1.33090 − 1.40307I
b = 0.773448 − 0.834229I
0.95846 − 9.77269I 0
u = 0.118950 − 0.720662I
a = −1.33090 + 1.40307I
b = 0.773448 + 0.834229I
0.95846 + 9.77269I 0
u = −0.019304 + 1.281100I
a = 0.05764 − 2.36847I
b = 0.182088 − 0.538508I
−2.31866 − 0.62559I 0
u = −0.019304 − 1.281100I
a = 0.05764 + 2.36847I
b = 0.182088 + 0.538508I
−2.31866 + 0.62559I 0
u = −1.013200 + 0.788182I
a = 0.060747 − 0.364733I
b = 0.614701 − 0.812307I
0.68445 + 4.54297I 0
u = −1.013200 − 0.788182I
a = 0.060747 + 0.364733I
b = 0.614701 + 0.812307I
0.68445 − 4.54297I 0
u = 0.087917 + 1.296680I
a = 0.80335 + 1.70467I
b = 0.065222 + 0.592573I
−4.92652 + 6.63323I 0
u = 0.087917 − 1.296680I
a = 0.80335 − 1.70467I
b = 0.065222 − 0.592573I
−4.92652 − 6.63323I 0
u = 0.364530 + 1.248020I
a = 0.662740 − 0.933826I
b = −0.721146 − 0.416633I
2.25517 + 5.02163I 0
u = 0.364530 − 1.248020I
a = 0.662740 + 0.933826I
b = −0.721146 + 0.416633I
2.25517 − 5.02163I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.409295 + 1.244130I
a = −0.10947 + 2.20468I
b = 0.72412 + 1.50675I
−2.64457 + 7.81616I 0
u = 0.409295 − 1.244130I
a = −0.10947 − 2.20468I
b = 0.72412 − 1.50675I
−2.64457 − 7.81616I 0
u = −0.633763 + 1.174030I
a = 0.430698 + 1.130150I
b = −0.785327 + 0.927632I
3.03587 − 7.38409I 0
u = −0.633763 − 1.174030I
a = 0.430698 − 1.130150I
b = −0.785327 − 0.927632I
3.03587 + 7.38409I 0
u = −1.340970 + 0.074381I
a = −0.211866 − 0.405795I
b = −0.845852 − 0.905238I
4.4685 + 14.6020I 0
u = −1.340970 − 0.074381I
a = −0.211866 + 0.405795I
b = −0.845852 + 0.905238I
4.4685 − 14.6020I 0
u = 0.965373 + 0.935425I
a = −0.629096 − 0.730552I
b = −1.18811 − 0.79225I
2.14071 + 5.07875I 0
u = 0.965373 − 0.935425I
a = −0.629096 + 0.730552I
b = −1.18811 + 0.79225I
2.14071 − 5.07875I 0
u = −0.420650 + 1.277450I
a = −0.1063630 + 0.0301120I
b = −0.581738 − 0.209769I
1.89645 − 5.49281I 0
u = −0.420650 − 1.277450I
a = −0.1063630 − 0.0301120I
b = −0.581738 + 0.209769I
1.89645 + 5.49281I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.242811 + 1.323580I
a = 0.20041 − 1.82739I
b = 1.02392 − 1.30427I
−3.20993 − 4.88215I 0
u = −0.242811 − 1.323580I
a = 0.20041 + 1.82739I
b = 1.02392 + 1.30427I
−3.20993 + 4.88215I 0
u = 0.471792 + 1.262920I
a = −0.268649 + 1.359460I
b = 0.947384 + 0.805087I
4.19933 + 12.03280I 0
u = 0.471792 − 1.262920I
a = −0.268649 − 1.359460I
b = 0.947384 − 0.805087I
4.19933 − 12.03280I 0
u = −0.541056 + 0.337442I
a = 0.89469 + 1.65882I
b = −0.769951 + 0.776699I
2.52783 + 0.91774I 0
u = −0.541056 − 0.337442I
a = 0.89469 − 1.65882I
b = −0.769951 − 0.776699I
2.52783 − 0.91774I 0
u = 0.010062 + 1.362780I
a = −0.163586 − 1.138370I
b = 0.200935 − 0.495770I
−2.56970 − 1.27507I 0
u = 0.010062 − 1.362780I
a = −0.163586 + 1.138370I
b = 0.200935 + 0.495770I
−2.56970 + 1.27507I 0
u = 0.051317 + 0.627084I
a = 1.26642 + 1.61076I
b = −0.701203 + 0.785413I
2.34994 − 2.26170I 0
u = 0.051317 − 0.627084I
a = 1.26642 − 1.61076I
b = −0.701203 − 0.785413I
2.34994 + 2.26170I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.600889 + 0.145198I
a = 0.457882 + 0.551784I
b = 0.757713 − 0.833049I
−1.69106 − 3.91075I 0
u = 0.600889 − 0.145198I
a = 0.457882 − 0.551784I
b = 0.757713 + 0.833049I
−1.69106 + 3.91075I 0
u = 0.599172 + 0.108712I
a = 0.158480 − 0.435292I
b = −0.439765 + 0.937930I
−2.19679 − 3.54459I 0
u = 0.599172 − 0.108712I
a = 0.158480 + 0.435292I
b = −0.439765 − 0.937930I
−2.19679 + 3.54459I 0
u = 0.034939 + 1.391420I
a = 0.394732 − 1.214730I
b = 0.446270 − 1.084400I
−3.10295 − 2.45282I 0
u = 0.034939 − 1.391420I
a = 0.394732 + 1.214730I
b = 0.446270 + 1.084400I
−3.10295 + 2.45282I 0
u = 0.585017 + 0.130141I
a = 0.821773 + 0.201357I
b = 0.433511 − 0.668420I
−2.25750 − 0.47262I 0
u = 0.585017 − 0.130141I
a = 0.821773 − 0.201357I
b = 0.433511 + 0.668420I
−2.25750 + 0.47262I 0
u = −0.417811 + 1.337290I
a = −0.02501 + 1.87044I
b = −0.97168 + 1.40325I
−5.4826 − 14.5916I 0
u = −0.417811 − 1.337290I
a = −0.02501 − 1.87044I
b = −0.97168 − 1.40325I
−5.4826 + 14.5916I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.401640 + 0.025007I
a = 0.260519 + 0.358606I
b = 0.847934 + 0.744420I
5.88744 + 6.12768I 0
u = −1.401640 − 0.025007I
a = 0.260519 − 0.358606I
b = 0.847934 − 0.744420I
5.88744 − 6.12768I 0
u = 0.709023 + 1.210860I
a = −0.229361 + 1.316210I
b = 0.80780 + 1.22940I
−3.20320 + 8.67885I 0
u = 0.709023 − 1.210860I
a = −0.229361 − 1.316210I
b = 0.80780 − 1.22940I
−3.20320 − 8.67885I 0
u = −0.981375 + 1.006190I
a = −0.257461 + 0.736246I
b = −0.894192 + 0.764677I
2.97232 − 2.94893I 0
u = −0.981375 − 1.006190I
a = −0.257461 − 0.736246I
b = −0.894192 − 0.764677I
2.97232 + 2.94893I 0
u = 0.57461 + 1.29268I
a = −0.30786 + 1.69479I
b = 0.88552 + 1.25518I
−1.45971 + 12.53020I 0
u = 0.57461 − 1.29268I
a = −0.30786 − 1.69479I
b = 0.88552 − 1.25518I
−1.45971 − 12.53020I 0
u = 1.45070 + 0.05722I
a = 0.349185 + 0.629194I
b = 0.928339 + 0.874071I
4.66391 + 3.84603I 0
u = 1.45070 − 0.05722I
a = 0.349185 − 0.629194I
b = 0.928339 − 0.874071I
4.66391 − 3.84603I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.50383 + 1.37168I
a = −0.08920 − 1.62084I
b = 0.80347 − 1.25971I
−6.01699 − 4.72778I 0
u = −0.50383 − 1.37168I
a = −0.08920 + 1.62084I
b = 0.80347 + 1.25971I
−6.01699 + 4.72778I 0
u = −0.62267 + 1.34491I
a = −0.031335 + 1.142560I
b = −0.829767 + 0.776852I
2.16361 − 6.46245I 0
u = −0.62267 − 1.34491I
a = −0.031335 − 1.142560I
b = −0.829767 − 0.776852I
2.16361 + 6.46245I 0
u = 0.47760 + 1.40469I
a = 0.523642 − 0.737459I
b = 0.326855 − 0.684462I
−2.93539 − 1.76763I 0
u = 0.47760 − 1.40469I
a = 0.523642 + 0.737459I
b = 0.326855 + 0.684462I
−2.93539 + 1.76763I 0
u = 0.52697 + 1.39412I
a = 0.42958 − 1.84167I
b = −0.66193 − 1.25010I
−1.21726 + 10.72700I 0
u = 0.52697 − 1.39412I
a = 0.42958 + 1.84167I
b = −0.66193 + 1.25010I
−1.21726 − 10.72700I 0
u = −0.43429 + 1.43705I
a = 0.453948 + 1.026310I
b = −0.177050 + 0.917103I
−6.42064 − 7.10901I 0
u = −0.43429 − 1.43705I
a = 0.453948 − 1.026310I
b = −0.177050 − 0.917103I
−6.42064 + 7.10901I 0
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.471516 + 0.162372I
a = 0.09652 + 1.69270I
b = 0.683837 − 0.148416I
1.79757 − 2.90164I 0
u = 0.471516 − 0.162372I
a = 0.09652 − 1.69270I
b = 0.683837 + 0.148416I
1.79757 + 2.90164I 0
u = 0.493235 + 0.030430I
a = 0.057781 + 0.239450I
b = −0.875825 + 1.045790I
1.09136 − 4.08112I 0
u = 0.493235 − 0.030430I
a = 0.057781 − 0.239450I
b = −0.875825 − 1.045790I
1.09136 + 4.08112I 0
u = −0.76251 + 1.30293I
a = −0.668876 − 0.646738I
b = 0.133876 − 0.887021I
−1.23023 − 11.74560I 0
u = −0.76251 − 1.30293I
a = −0.668876 + 0.646738I
b = 0.133876 + 0.887021I
−1.23023 + 11.74560I 0
u = 1.16332 + 0.96986I
a = −0.510220 + 0.252414I
b = −0.288801 + 0.766018I
−1.53306 − 1.74866I 0
u = 1.16332 − 0.96986I
a = −0.510220 − 0.252414I
b = −0.288801 − 0.766018I
−1.53306 + 1.74866I 0
u = −0.63886 + 1.38954I
a = −0.14475 − 1.70636I
b = 0.90619 − 1.31128I
0.3358 − 21.3830I 0
u = −0.63886 − 1.38954I
a = −0.14475 + 1.70636I
b = 0.90619 + 1.31128I
0.3358 + 21.3830I 0
21
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.63627 + 1.40843I
a = 0.05708 + 1.61775I
b = −0.91733 + 1.23690I
1.56115 − 13.02230I 0
u = −0.63627 − 1.40843I
a = 0.05708 − 1.61775I
b = −0.91733 − 1.23690I
1.56115 + 13.02230I 0
u = −0.10308 + 1.54733I
a = 0.17816 + 2.03259I
b = −0.130030 + 0.934174I
−3.93380 − 6.41017I 0
u = −0.10308 − 1.54733I
a = 0.17816 − 2.03259I
b = −0.130030 − 0.934174I
−3.93380 + 6.41017I 0
u = −0.430443
a = 0.729458
b = −0.587222
0.891162 11.3580
u = 0.67597 + 1.42812I
a = 0.05800 − 1.83179I
b = −0.83814 − 1.38166I
0.13213 + 11.03980I 0
u = 0.67597 − 1.42812I
a = 0.05800 + 1.83179I
b = −0.83814 + 1.38166I
0.13213 − 11.03980I 0
u = 0.60066 + 1.54835I
a = 0.492161 − 0.830434I
b = −0.094862 − 0.601382I
−0.36264 + 3.62125I 0
u = 0.60066 − 1.54835I
a = 0.492161 + 0.830434I
b = −0.094862 + 0.601382I
−0.36264 − 3.62125I 0
u = −0.69986 + 1.50828I
a = 0.311683 + 0.494677I
b = −0.195142 + 0.476333I
1.41700 − 5.68141I 0
22
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.69986 − 1.50828I
a = 0.311683 − 0.494677I
b = −0.195142 − 0.476333I
1.41700 + 5.68141I 0
u = 0.305378 + 0.141468I
a = −0.58697 − 3.19652I
b = −0.850298 − 0.538195I
−0.58924 + 5.03512I 4.75419 − 8.45098I
u = 0.305378 − 0.141468I
a = −0.58697 + 3.19652I
b = −0.850298 + 0.538195I
−0.58924 − 5.03512I 4.75419 + 8.45098I
u = −0.285913 + 0.176709I
a = 1.09796 + 1.97435I
b = −0.846664 + 0.081916I
0.619579 − 0.110739I 11.54104 + 2.72025I
u = −0.285913 − 0.176709I
a = 1.09796 − 1.97435I
b = −0.846664 − 0.081916I
0.619579 + 0.110739I 11.54104 − 2.72025I
u = 0.146492 + 0.002381I
a = −1.27865 + 4.48811I
b = 0.601020 + 1.183220I
−1.29385 − 3.59246I −0.92876 + 12.74754I
u = 0.146492 − 0.002381I
a = −1.27865 − 4.48811I
b = 0.601020 − 1.183220I
−1.29385 + 3.59246I −0.92876 − 12.74754I
u = −0.93942 + 1.64495I
a = −0.442953 − 0.361325I
b = −0.194015 − 0.515103I
−3.11311 + 2.95246I 0
u = −0.93942 − 1.64495I
a = −0.442953 + 0.361325I
b = −0.194015 + 0.515103I
−3.11311 − 2.95246I 0
u = −0.23786 + 2.42759I
a = 0.125212 + 0.533693I
b = 0.092313 + 0.524760I
−2.04730 + 6.29582I 0
23
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.23786 − 2.42759I
a = 0.125212 − 0.533693I
b = 0.092313 − 0.524760I
−2.04730 − 6.29582I 0
24
II.
I
u
2
= h2.78 × 10
73
u
49
+ 1.71 × 10
73
u
48
+ · · · + 7.28 × 10
73
b − 2.44 × 10
74
, 1.03 ×
10
75
u
49
+1.06×10
75
u
48
+· · ·+7.28×10
73
a+2.83×10
75
, u
50
+u
49
+· · ·+2u+1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
u
u
a
9
=
−14.1781u
49
− 14.5071u
48
+ ··· − 333.047u − 38.9039
−0.381558u
49
− 0.234486u
48
+ ··· − 36.6884u + 3.35273
a
4
=
5.44613u
49
− 0.720475u
48
+ ··· + 146.134u − 89.7317
−4.57949u
49
− 6.48764u
48
+ ··· − 43.0276u − 19.0639
a
2
=
−13.6635u
49
− 13.7424u
48
+ ··· − 325.119u − 62.7536
−5.13283u
49
− 3.63850u
48
+ ··· − 87.2480u − 11.3657
a
3
=
−17.3532u
49
− 17.8199u
48
+ ··· − 398.545u − 74.0403
−5.61853u
49
− 4.14179u
48
+ ··· − 91.7133u − 11.7535
a
10
=
2.55967u
49
− 1.84775u
48
+ ··· + 25.0574u − 42.6084
2.44359u
49
− 0.0586217u
48
+ ··· + 13.4012u − 13.3197
a
8
=
−12.6100u
49
− 13.3642u
48
+ ··· − 318.299u − 38.4279
1.18661u
49
+ 0.908347u
48
+ ··· − 21.9398u + 3.82873
a
11
=
19.3264u
49
+ 20.0355u
48
+ ··· + 404.021u + 87.5153
6.51464u
49
+ 3.67721u
48
+ ··· + 77.6126u + 1.47558
a
7
=
6.48982u
49
+ 13.1489u
48
+ ··· + 185.901u + 94.3675
5.23467u
49
+ 8.40995u
48
+ ··· + 93.4483u + 21.1482
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.398560u
49
+ 2.60237u
48
+ ··· + 206.783u + 112.904
25
(iv) u-Polynomials at the component
26
Crossings u-Polynomials at each crossing
c
1
u
50
− 15u
49
+ ··· + 5u + 1
c
2
u
50
− u
49
+ ··· + u + 1
c
3
u
50
− 5u
49
+ ··· + u + 1
c
4
u
50
+ u
49
+ ··· + 10u
2
+ 1
c
5
u
50
+ u
49
+ ··· + 2u + 1
c
6
u
50
+ u
49
+ ··· − 5u + 1
c
7
u
50
+ 3u
49
+ ··· + 319u + 67
c
8
u
50
− 3u
49
+ ··· − 5u + 1
c
9
u
50
− 4u
49
+ ··· + 11u + 1
c
10
u
50
− 3u
49
+ ··· − u + 1
c
11
u
50
− 3u
49
+ ··· − 319u + 67
c
12
u
50
− u
49
+ ··· − 2u + 1
27
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
50
+ 7y
49
+ ··· − 11y + 1
c
2
y
50
+ 27y
49
+ ··· + 11y + 1
c
3
y
50
+ 33y
49
+ ··· + 43y + 1
c
4
y
50
+ 11y
49
+ ··· + 20y + 1
c
5
, c
12
y
50
+ 43y
49
+ ··· + 102y + 1
c
6
y
50
+ 3y
49
+ ··· − 27y + 1
c
7
, c
11
y
50
− 35y
49
+ ··· − 57541y + 4489
c
8
y
50
+ 13y
49
+ ··· − 31y + 1
c
9
y
50
− 10y
49
+ ··· − 39y + 1
c
10
y
50
+ 5y
49
+ ··· + y + 1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.175737 + 0.978826I
a = −0.89388 − 1.14763I
b = −1.69851 − 0.96426I
−1.89447 + 5.40487I −2.21458 − 11.17990I
u = 0.175737 − 0.978826I
a = −0.89388 + 1.14763I
b = −1.69851 + 0.96426I
−1.89447 − 5.40487I −2.21458 + 11.17990I
u = 0.108986 + 0.986743I
a = 2.79072 + 0.09309I
b = −0.428963 + 0.304140I
−1.74289 + 0.34031I 19.8563 − 25.9702I
u = 0.108986 − 0.986743I
a = 2.79072 − 0.09309I
b = −0.428963 − 0.304140I
−1.74289 − 0.34031I 19.8563 + 25.9702I
u = 0.962506 + 0.119363I
a = −0.572983 + 0.108865I
b = 0.356369 − 0.254342I
5.41808 − 0.09137I 7.57607 − 2.30673I
u = 0.962506 − 0.119363I
a = −0.572983 − 0.108865I
b = 0.356369 + 0.254342I
5.41808 + 0.09137I 7.57607 + 2.30673I
u = −0.166851 + 1.042870I
a = −1.06937 − 1.21207I
b = 0.247813 − 0.938110I
−5.46671 − 0.71937I −4.35638 + 1.65522I
u = −0.166851 − 1.042870I
a = −1.06937 + 1.21207I
b = 0.247813 + 0.938110I
−5.46671 + 0.71937I −4.35638 − 1.65522I
u = 0.477774 + 0.950628I
a = −0.455343 − 0.176831I
b = 0.793618 + 0.429913I
1.18633 + 11.73570I 4.00000 − 9.86856I
u = 0.477774 − 0.950628I
a = −0.455343 + 0.176831I
b = 0.793618 − 0.429913I
1.18633 − 11.73570I 4.00000 + 9.86856I
30
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.024119 + 0.821510I
a = 0.20511 + 3.20283I
b = 0.47639 + 1.77707I
4.21889 − 3.22105I 0.7320 + 16.6879I
u = 0.024119 − 0.821510I
a = 0.20511 − 3.20283I
b = 0.47639 − 1.77707I
4.21889 + 3.22105I 0.7320 − 16.6879I
u = 0.406557 + 1.109500I
a = −0.715786 + 0.328159I
b = −0.990557 + 0.560139I
2.20924 + 4.53761I 0
u = 0.406557 − 1.109500I
a = −0.715786 − 0.328159I
b = −0.990557 − 0.560139I
2.20924 − 4.53761I 0
u = 0.531480 + 0.606910I
a = −0.39707 + 2.27300I
b = 0.296037 + 1.262530I
4.56234 + 0.24521I 13.8127 − 5.2792I
u = 0.531480 − 0.606910I
a = −0.39707 − 2.27300I
b = 0.296037 − 1.262530I
4.56234 − 0.24521I 13.8127 + 5.2792I
u = −0.415231 + 1.126350I
a = −0.36728 − 1.77634I
b = 0.76736 − 1.31532I
−4.57790 − 6.44467I 0
u = −0.415231 − 1.126350I
a = −0.36728 + 1.77634I
b = 0.76736 + 1.31532I
−4.57790 + 6.44467I 0
u = −0.569596 + 1.072160I
a = 1.104740 + 0.288422I
b = −0.179330 + 0.800716I
−2.61505 − 2.29576I 0
u = −0.569596 − 1.072160I
a = 1.104740 − 0.288422I
b = −0.179330 − 0.800716I
−2.61505 + 2.29576I 0
31
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.063025 + 1.236740I
a = −1.06506 − 2.23569I
b = −0.040736 − 0.411376I
−2.33411 − 0.19277I 0
u = −0.063025 − 1.236740I
a = −1.06506 + 2.23569I
b = −0.040736 + 0.411376I
−2.33411 + 0.19277I 0
u = 0.290391 + 0.696624I
a = 0.920345 + 0.820110I
b = 1.34566 + 0.93386I
−1.65988 − 3.02171I −6.89482 + 8.29972I
u = 0.290391 − 0.696624I
a = 0.920345 − 0.820110I
b = 1.34566 − 0.93386I
−1.65988 + 3.02171I −6.89482 − 8.29972I
u = −1.250260 + 0.224519I
a = 0.066986 − 0.800490I
b = 0.835020 − 0.988481I
4.35201 − 4.83110I 0
u = −1.250260 − 0.224519I
a = 0.066986 + 0.800490I
b = 0.835020 + 0.988481I
4.35201 + 4.83110I 0
u = −0.995042 + 0.791707I
a = −0.493755 + 0.560747I
b = −1.119910 + 0.723627I
2.60132 − 3.78645I 0
u = −0.995042 − 0.791707I
a = −0.493755 − 0.560747I
b = −1.119910 − 0.723627I
2.60132 + 3.78645I 0
u = 0.402699 + 1.208040I
a = 0.622160 − 0.744990I
b = −0.704162 − 0.436292I
1.97452 + 5.01029I 0
u = 0.402699 − 1.208040I
a = 0.622160 + 0.744990I
b = −0.704162 + 0.436292I
1.97452 − 5.01029I 0
32
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.171298 + 1.285580I
a = 0.32399 − 1.87950I
b = 1.12071 − 1.35619I
−3.17536 − 5.17301I 0
u = −0.171298 − 1.285580I
a = 0.32399 + 1.87950I
b = 1.12071 + 1.35619I
−3.17536 + 5.17301I 0
u = 0.762062 + 1.050190I
a = −0.578620 − 0.487556I
b = −1.172650 − 0.454079I
2.75994 + 5.15340I 0
u = 0.762062 − 1.050190I
a = −0.578620 + 0.487556I
b = −1.172650 + 0.454079I
2.75994 − 5.15340I 0
u = 0.16304 + 1.41124I
a = −0.12655 + 1.81902I
b = 0.002005 + 1.024370I
−5.37637 + 5.32887I 0
u = 0.16304 − 1.41124I
a = −0.12655 − 1.81902I
b = 0.002005 − 1.024370I
−5.37637 − 5.32887I 0
u = −0.89404 + 1.21003I
a = −0.557881 − 0.374025I
b = −0.241545 − 0.666236I
−3.54696 + 1.59294I 0
u = −0.89404 − 1.21003I
a = −0.557881 + 0.374025I
b = −0.241545 + 0.666236I
−3.54696 − 1.59294I 0
u = −0.58393 + 1.39791I
a = 0.23196 + 1.83674I
b = −0.77434 + 1.30822I
−0.53509 − 11.05320I 0
u = −0.58393 − 1.39791I
a = 0.23196 − 1.83674I
b = −0.77434 − 1.30822I
−0.53509 + 11.05320I 0
33
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.37698 + 1.47846I
a = 0.545028 − 0.729281I
b = 0.540239 − 0.589042I
−2.52583 − 3.06203I 0
u = 0.37698 − 1.47846I
a = 0.545028 + 0.729281I
b = 0.540239 + 0.589042I
−2.52583 + 3.06203I 0
u = −0.113848 + 0.451309I
a = 0.40620 + 2.43150I
b = 0.679433 − 0.072502I
−0.065225 + 0.242878I 0.89688 − 5.51398I
u = −0.113848 − 0.451309I
a = 0.40620 − 2.43150I
b = 0.679433 + 0.072502I
−0.065225 − 0.242878I 0.89688 + 5.51398I
u = −0.055408 + 0.221738I
a = −2.77675 + 0.79467I
b = −0.741522 − 0.825969I
0.50329 + 3.74601I 2.65104 − 4.84551I
u = −0.055408 − 0.221738I
a = −2.77675 − 0.79467I
b = −0.741522 + 0.825969I
0.50329 − 3.74601I 2.65104 + 4.84551I
u = −0.034909 + 0.210918I
a = −1.52241 − 7.20450I
b = 0.219587 − 1.195520I
5.93553 − 5.39947I 10.71798 + 5.04274I
u = −0.034909 − 0.210918I
a = −1.52241 + 7.20450I
b = 0.219587 + 1.195520I
5.93553 + 5.39947I 10.71798 − 5.04274I
u = 0.13110 + 2.23560I
a = −0.124499 + 0.643416I
b = −0.088031 + 0.420848I
−1.85059 − 6.24758I 0
u = 0.13110 − 2.23560I
a = −0.124499 − 0.643416I
b = −0.088031 − 0.420848I
−1.85059 + 6.24758I 0
34
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
50
− 15u
49
+ ··· + 5u + 1)(u
191
+ 8u
190
+ ··· + 12090u − 521)
c
2
(u
50
− u
49
+ ··· + u + 1)(u
191
+ 9u
189
+ ··· + 26856u − 3123)
c
3
(u
50
− 5u
49
+ ··· + u + 1)(u
191
+ 8u
190
+ ··· − 40446u − 4563)
c
4
(u
50
+ u
49
+ ··· + 10u
2
+ 1)
· (u
191
+ 23u
189
+ ··· − 6088215u − 1128983)
c
5
(u
50
+ u
49
+ ··· + 2u + 1)(u
191
+ 65u
189
+ ··· − 7345527u − 262307)
c
6
(u
50
+ u
49
+ ··· − 5u + 1)(u
191
+ 2u
190
+ ··· − 26u − 1)
c
7
(u
50
+ 3u
49
+ ··· + 319u + 67)
· (u
191
− 4u
190
+ ··· − 644237242u − 33057935)
c
8
(u
50
− 3u
49
+ ··· − 5u + 1)(u
191
+ 4u
190
+ ··· − 14u − 1)
c
9
(u
50
− 4u
49
+ ··· + 11u + 1)
· (u
191
+ 3u
190
+ ··· + 2081393442u − 208449613)
c
10
(u
50
− 3u
49
+ ··· − u + 1)(u
191
+ 4u
190
+ ··· − 517308u − 92933)
c
11
(u
50
− 3u
49
+ ··· − 319u + 67)
· (u
191
− 4u
190
+ ··· − 644237242u − 33057935)
c
12
(u
50
− u
49
+ ··· − 2u + 1)(u
191
+ 65u
189
+ ··· − 7345527u − 262307)
35
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
50
+ 7y
49
+ ··· − 11y + 1)
· (y
191
+ 18y
190
+ ··· + 7672754y −271441)
c
2
(y
50
+ 27y
49
+ ··· + 11y + 1)
· (y
191
+ 18y
190
+ ··· − 1093867848y −9753129)
c
3
(y
50
+ 33y
49
+ ··· + 43y + 1)
· (y
191
+ 48y
190
+ ··· − 547954632y −20820969)
c
4
(y
50
+ 11y
49
+ ··· + 20y + 1)
· (y
191
+ 46y
190
+ ··· − 71896540462205y −1274602614289)
c
5
, c
12
(y
50
+ 43y
49
+ ··· + 102y + 1)
· (y
191
+ 130y
190
+ ··· + 5931925730613y −68804962249)
c
6
(y
50
+ 3y
49
+ ··· − 27y + 1)(y
191
− 14y
190
+ ··· + 150y −1)
c
7
, c
11
(y
50
− 35y
49
+ ··· − 57541y + 4489)
· (y
191
− 140y
190
+ ··· + 148730603959730924y −1092827066464225)
c
8
(y
50
+ 13y
49
+ ··· − 31y + 1)(y
191
+ 16y
190
+ ··· − 1830y −1)
c
9
(y
50
− 10y
49
+ ··· − 39y + 1)
· (y
191
− 55y
190
+ ··· + 2565423313669011206y −43451241159849769)
c
10
(y
50
+ 5y
49
+ ··· + y + 1)
· (y
191
− 24y
190
+ ··· + 682916036430y −8636542489)
36
