12n
0587
(K12n
0587
)
A knot diagram
1
Linearized knot diagam
3 7 9 1 10 2 1 11 6 4 8 4
Solving Sequence
2,7 3,9
4 1 6 10 11 5 8 12
c
2
c
3
c
1
c
6
c
9
c
10
c
5
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−66u
31
− 537u
30
+ ··· + 4b − 972, −243u
31
− 1923u
30
+ ··· + 16a − 3048,
u
32
+ 9u
31
+ ··· + 128u + 16i
I
u
2
= h−1.75141 × 10
21
a
7
u
5
+ 4.76671 × 10
21
a
6
u
5
+ ··· + 1.01718 × 10
23
a − 3.39686 × 10
22
,
− a
7
u
5
+ 2a
6
u
5
+ ··· − 7a − 3, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
I
u
3
= h−5u
21
− 4u
20
+ ··· + b + 7, −7u
21
− 10u
20
+ ··· + 2a + 17, u
22
− 6u
20
+ ··· − u + 2i
* 3 irreducible components of dim
C
= 0, with total 102 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−66u
31
− 537u
30
+ · · · + 4b − 972, −243u
31
− 1923u
30
+ · · · + 16a −
3048, u
32
+ 9u
31
+ · · · + 128u + 16i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
9
=
15.1875u
31
+ 120.188u
30
+ ··· + 1410.75u + 190.500
33
2
u
31
+
537
4
u
30
+ ··· +
3507
2
u + 243
a
4
=
−
79
16
u
31
−
605
16
u
30
+ ··· −
619
2
u − 38
−
53
8
u
31
−
423
8
u
30
+ ··· − 593u − 79
a
1
=
−u
2
+ 1
−u
4
a
6
=
u
u
a
10
=
7.43750u
31
+ 64.9375u
30
+ ··· + 1101.75u + 154.500
35
4
u
31
+ 79u
30
+ ··· +
2889
2
u + 207
a
11
=
−3.87500u
31
− 41.7500u
30
+ ··· − 1002.75u − 142.500
121
8
u
31
+
865
8
u
30
+ ··· +
709
2
u + 30
a
5
=
43
16
u
31
+
369
16
u
30
+ ··· +
599
2
u + 41
35
8
u
31
+
305
8
u
30
+ ··· + 583u + 81
a
8
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
12
=
4.37500u
31
+ 25.7500u
30
+ ··· − 213.250u − 35.5000
75
8
u
31
+
527
8
u
30
+ ··· +
379
2
u + 16
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
19
2
u
31
−
149
2
u
30
+ ··· − 710u − 78
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
32
+ 15u
31
+ ··· + 1152u + 256
c
2
, c
6
u
32
− 9u
31
+ ··· − 128u + 16
c
3
, c
5
, c
9
u
32
+ 8u
30
+ ··· + 2u + 1
c
4
, c
12
u
32
+ 21u
30
+ ··· + u + 1
c
7
u
32
− 27u
31
+ ··· − 128512u + 13840
c
8
, c
11
u
32
+ 15u
31
+ ··· + 544u + 64
c
10
u
32
+ u
31
+ ··· − 24u + 10
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
+ 5y
31
+ ··· + 843776y + 65536
c
2
, c
6
y
32
− 15y
31
+ ··· − 1152y + 256
c
3
, c
5
, c
9
y
32
+ 16y
31
+ ··· + 4y + 1
c
4
, c
12
y
32
+ 42y
31
+ ··· − 21y + 1
c
7
y
32
+ 5y
31
+ ··· − 1955321984y + 191545600
c
8
, c
11
y
32
+ 15y
31
+ ··· + 23552y + 4096
c
10
y
32
− 29y
31
+ ··· − 2956y + 100
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.353223 + 0.914504I
a = 0.944290 − 0.963381I
b = −0.547471 − 1.203850I
1.14278 − 11.08640I 1.04376 + 6.11578I
u = −0.353223 − 0.914504I
a = 0.944290 + 0.963381I
b = −0.547471 + 1.203850I
1.14278 + 11.08640I 1.04376 − 6.11578I
u = −0.695104 + 0.783443I
a = −1.016910 − 0.357438I
b = −0.986887 + 0.548231I
5.02104 + 1.18323I 4.63011 − 3.73174I
u = −0.695104 − 0.783443I
a = −1.016910 + 0.357438I
b = −0.986887 − 0.548231I
5.02104 − 1.18323I 4.63011 + 3.73174I
u = −0.971427 + 0.423273I
a = 1.30738 − 0.94887I
b = 0.86839 − 1.47514I
−0.29798 + 3.82056I 0.73357 − 6.52529I
u = −0.971427 − 0.423273I
a = 1.30738 + 0.94887I
b = 0.86839 + 1.47514I
−0.29798 − 3.82056I 0.73357 + 6.52529I
u = −0.319145 + 0.868644I
a = −1.069240 + 0.753126I
b = 0.312955 + 1.169150I
2.75461 − 4.44216I 3.37878 + 2.54361I
u = −0.319145 − 0.868644I
a = −1.069240 − 0.753126I
b = 0.312955 − 1.169150I
2.75461 + 4.44216I 3.37878 − 2.54361I
u = −0.041796 + 0.911678I
a = 0.708186 − 0.291456I
b = −0.236115 − 0.657820I
−4.79614 − 1.53152I 1.62395 + 4.66418I
u = −0.041796 − 0.911678I
a = 0.708186 + 0.291456I
b = −0.236115 + 0.657820I
−4.79614 + 1.53152I 1.62395 − 4.66418I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.720598 + 0.879414I
a = 0.761879 + 0.617760I
b = 1.092280 − 0.224850I
3.47851 + 6.82150I −0.20982 − 8.20349I
u = −0.720598 − 0.879414I
a = 0.761879 − 0.617760I
b = 1.092280 + 0.224850I
3.47851 − 6.82150I −0.20982 + 8.20349I
u = 0.802808 + 0.175070I
a = −0.250305 − 0.176055I
b = 0.170125 + 0.185160I
−1.38436 − 0.59539I −4.63872 + 0.87070I
u = 0.802808 − 0.175070I
a = −0.250305 + 0.176055I
b = 0.170125 − 0.185160I
−1.38436 + 0.59539I −4.63872 − 0.87070I
u = −0.967071 + 0.715806I
a = 0.056661 − 0.893739I
b = −0.584948 − 0.904868I
4.22303 + 4.44069I 3.22085 + 0.12023I
u = −0.967071 − 0.715806I
a = 0.056661 + 0.893739I
b = −0.584948 + 0.904868I
4.22303 − 4.44069I 3.22085 − 0.12023I
u = 1.229680 + 0.226268I
a = −0.293850 − 0.315256I
b = 0.290008 + 0.454153I
−2.37206 + 1.13232I −1.58887 − 1.12287I
u = 1.229680 − 0.226268I
a = −0.293850 + 0.315256I
b = 0.290008 − 0.454153I
−2.37206 − 1.13232I −1.58887 + 1.12287I
u = −0.994634 + 0.800004I
a = 0.411302 + 0.751543I
b = 1.010330 + 0.418467I
2.67500 − 0.65003I −3.51745 + 3.19613I
u = −0.994634 − 0.800004I
a = 0.411302 − 0.751543I
b = 1.010330 − 0.418467I
2.67500 + 0.65003I −3.51745 − 3.19613I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.283860 + 0.162995I
a = 0.258937 + 0.394634I
b = −0.268116 − 0.548861I
−4.52901 + 7.74803I −4.31211 − 4.99223I
u = 1.283860 − 0.162995I
a = 0.258937 − 0.394634I
b = −0.268116 + 0.548861I
−4.52901 − 7.74803I −4.31211 + 4.99223I
u = −1.170100 + 0.596807I
a = 1.63919 − 0.72952I
b = 1.48263 − 1.83190I
0.19538 + 9.84539I 0. − 6.14820I
u = −1.170100 − 0.596807I
a = 1.63919 + 0.72952I
b = 1.48263 + 1.83190I
0.19538 − 9.84539I 0. + 6.14820I
u = −1.172780 + 0.623036I
a = −1.77974 + 0.55524I
b = −1.74130 + 1.76001I
−1.3469 + 16.7119I −1.47549 − 9.48564I
u = −1.172780 − 0.623036I
a = −1.77974 − 0.55524I
b = −1.74130 − 1.76001I
−1.3469 − 16.7119I −1.47549 + 9.48564I
u = −1.251720 + 0.492171I
a = −1.122650 + 0.775593I
b = −1.02352 + 1.52336I
−8.47765 + 6.52307I 0. − 9.62472I
u = −1.251720 − 0.492171I
a = −1.122650 − 0.775593I
b = −1.02352 − 1.52336I
−8.47765 − 6.52307I 0. + 9.62472I
u = 1.286480 + 0.428514I
a = 0.229293 + 0.227589I
b = −0.197456 − 0.391044I
−8.94178 − 3.23445I 0
u = 1.286480 − 0.428514I
a = 0.229293 − 0.227589I
b = −0.197456 + 0.391044I
−8.94178 + 3.23445I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.445223 + 0.386227I
a = −1.53443 + 0.10941I
b = −0.640907 + 0.641353I
1.140960 − 0.214496I 8.54432 + 0.39190I
u = −0.445223 − 0.386227I
a = −1.53443 − 0.10941I
b = −0.640907 − 0.641353I
1.140960 + 0.214496I 8.54432 − 0.39190I
8
II. I
u
2
= h−1.75 × 10
21
a
7
u
5
+ 4.77 × 10
21
a
6
u
5
+ · · · + 1.02 × 10
23
a − 3.40 ×
10
22
, −a
7
u
5
+ 2a
6
u
5
+ · · · − 7a − 3, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
9
=
a
0.0448967a
7
u
5
− 0.122193a
6
u
5
+ ··· − 2.60750a + 0.870772
a
4
=
−0.0464052a
7
u
5
+ 0.165108a
6
u
5
+ ··· − 0.295632a + 2.29477
−0.0396494a
7
u
5
+ 0.0414630a
6
u
5
+ ··· − 1.01369a + 2.96480
a
1
=
−u
2
+ 1
−u
4
a
6
=
u
u
a
10
=
0.00659432a
7
u
5
− 0.0344612a
6
u
5
+ ··· − 1.43280a + 1.87590
0.0514910a
7
u
5
− 0.156654a
6
u
5
+ ··· − 5.04030a + 2.74667
a
11
=
0.0418578a
7
u
5
+ 0.290122a
6
u
5
+ ··· + 1.67460a + 2.21502
−0.0967619a
7
u
5
+ 0.233461a
6
u
5
+ ··· + 2.80716a + 0.179361
a
5
=
−0.0205988a
7
u
5
− 0.0387646a
6
u
5
+ ··· + 0.613393a + 0.382177
0.00837862a
7
u
5
− 0.0176083a
6
u
5
+ ··· + 0.996366a + 1.27350
a
8
=
u
5
− 2u
3
+ u
u
5
− u
4
− 2u
3
+ u
2
+ u − 1
a
12
=
−0.0555186a
7
u
5
− 0.206112a
6
u
5
+ ··· − 0.522508a − 1.82114
0.0445458a
7
u
5
− 0.178610a
6
u
5
+ ··· − 1.10562a − 0.819014
(ii) Obstruction class = −1
(iii) Cusp Shapes =
4218289331032938010964
39009694828428132113233
a
7
u
5
−
881458935488935727072
39009694828428132113233
a
6
u
5
+ ··· −
457197832689430921693344
39009694828428132113233
a +
213457719652228846802666
39009694828428132113233
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
8
c
2
, c
6
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
8
c
3
, c
5
, c
9
u
48
− u
47
+ ··· + 1188u + 891
c
4
, c
12
u
48
− 3u
47
+ ··· + 2288u + 457
c
8
, c
11
(u
4
− u
3
+ u
2
+ 1)
12
c
10
u
48
− u
47
+ ··· − 56112u + 5549
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
8
c
2
, c
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
8
c
3
, c
5
, c
9
y
48
+ 27y
47
+ ··· + 36823248y + 793881
c
4
, c
12
y
48
+ 15y
47
+ ··· − 4710308y + 208849
c
8
, c
11
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
12
c
10
y
48
+ 3y
47
+ ··· − 1819227006y + 30791401
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = 0.507592 + 0.582683I
b = 0.937656 − 1.013070I
−7.03641 + 2.33941I −7.54346 − 5.70297I
u = −1.002190 + 0.295542I
a = 1.135000 − 0.676144I
b = 0.680912 + 0.433947I
−7.03641 + 2.33941I −7.54346 − 5.70297I
u = −1.002190 + 0.295542I
a = −0.59164 + 1.37928I
b = 0.352015 + 0.153786I
−7.03641 − 0.49080I −7.54346 + 4.11452I
u = −1.002190 + 0.295542I
a = 0.281512 + 0.236466I
b = −0.18530 + 1.55716I
−7.03641 − 0.49080I −7.54346 + 4.11452I
u = −1.002190 + 0.295542I
a = −1.02156 + 1.37764I
b = −1.36997 + 1.97493I
−0.03467 − 2.23966I −3.88998 + 1.77057I
u = −1.002190 + 0.295542I
a = 1.38666 − 1.35941I
b = 1.47255 − 1.58489I
−0.03467 + 4.08827I −3.88998 − 3.35903I
u = −1.002190 + 0.295542I
a = 1.78082 − 1.05627I
b = 0.98793 − 1.77221I
−0.03467 + 4.08827I −3.88998 − 3.35903I
u = −1.002190 + 0.295542I
a = −1.79224 + 1.44209I
b = −0.61665 + 1.68258I
−0.03467 − 2.23966I −3.88998 + 1.77057I
u = −1.002190 − 0.295542I
a = 0.507592 − 0.582683I
b = 0.937656 + 1.013070I
−7.03641 − 2.33941I −7.54346 + 5.70297I
u = −1.002190 − 0.295542I
a = 1.135000 + 0.676144I
b = 0.680912 − 0.433947I
−7.03641 − 2.33941I −7.54346 + 5.70297I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 − 0.295542I
a = −0.59164 − 1.37928I
b = 0.352015 − 0.153786I
−7.03641 + 0.49080I −7.54346 − 4.11452I
u = −1.002190 − 0.295542I
a = 0.281512 − 0.236466I
b = −0.18530 − 1.55716I
−7.03641 + 0.49080I −7.54346 − 4.11452I
u = −1.002190 − 0.295542I
a = −1.02156 − 1.37764I
b = −1.36997 − 1.97493I
−0.03467 + 2.23966I −3.88998 − 1.77057I
u = −1.002190 − 0.295542I
a = 1.38666 + 1.35941I
b = 1.47255 + 1.58489I
−0.03467 − 4.08827I −3.88998 + 3.35903I
u = −1.002190 − 0.295542I
a = 1.78082 + 1.05627I
b = 0.98793 + 1.77221I
−0.03467 − 4.08827I −3.88998 + 3.35903I
u = −1.002190 − 0.295542I
a = −1.79224 − 1.44209I
b = −0.61665 − 1.68258I
−0.03467 + 2.23966I −3.88998 − 1.77057I
u = 0.428243 + 0.664531I
a = −0.818193 + 0.122997I
b = −0.51591 − 1.51973I
3.74655 + 4.08827I 3.54346 − 3.35903I
u = 0.428243 + 0.664531I
a = 0.597673 − 0.407666I
b = 0.74823 + 1.23067I
3.74655 − 2.23966I 3.54346 + 1.77057I
u = 0.428243 + 0.664531I
a = −0.682635 − 1.191630I
b = 0.70891 − 1.33525I
−3.25520 + 2.33941I −0.11002 − 5.70297I
u = 0.428243 + 0.664531I
a = 0.12918 + 1.52416I
b = −0.648527 + 1.032200I
−3.25520 − 0.49080I −0.11002 + 4.11452I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.428243 + 0.664531I
a = −0.65313 − 1.39681I
b = 0.957528 − 0.738558I
−3.25520 − 0.49080I −0.11002 + 4.11452I
u = 0.428243 + 0.664531I
a = −1.82121 − 0.04768I
b = −0.526856 − 0.222592I
3.74655 − 2.23966I 3.54346 + 1.77057I
u = 0.428243 + 0.664531I
a = 0.93397 + 1.66866I
b = −0.499539 + 0.963939I
−3.25520 + 2.33941I −0.11002 − 5.70297I
u = 0.428243 + 0.664531I
a = 1.96937 + 0.49277I
b = 0.432121 + 0.491042I
3.74655 + 4.08827I 3.54346 − 3.35903I
u = 0.428243 − 0.664531I
a = −0.818193 − 0.122997I
b = −0.51591 + 1.51973I
3.74655 − 4.08827I 3.54346 + 3.35903I
u = 0.428243 − 0.664531I
a = 0.597673 + 0.407666I
b = 0.74823 − 1.23067I
3.74655 + 2.23966I 3.54346 − 1.77057I
u = 0.428243 − 0.664531I
a = −0.682635 + 1.191630I
b = 0.70891 + 1.33525I
−3.25520 − 2.33941I −0.11002 + 5.70297I
u = 0.428243 − 0.664531I
a = 0.12918 − 1.52416I
b = −0.648527 − 1.032200I
−3.25520 + 0.49080I −0.11002 − 4.11452I
u = 0.428243 − 0.664531I
a = −0.65313 + 1.39681I
b = 0.957528 + 0.738558I
−3.25520 + 0.49080I −0.11002 − 4.11452I
u = 0.428243 − 0.664531I
a = −1.82121 + 0.04768I
b = −0.526856 + 0.222592I
3.74655 + 2.23966I 3.54346 − 1.77057I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.428243 − 0.664531I
a = 0.93397 − 1.66866I
b = −0.499539 − 0.963939I
−3.25520 − 2.33941I −0.11002 + 5.70297I
u = 0.428243 − 0.664531I
a = 1.96937 − 0.49277I
b = 0.432121 − 0.491042I
3.74655 − 4.08827I 3.54346 + 3.35903I
u = 1.073950 + 0.558752I
a = 0.263523 + 0.901679I
b = 0.32755 + 1.80005I
1.85594 − 2.52906I −0.17326 + 2.94577I
u = 1.073950 + 0.558752I
a = −0.660126 − 1.071870I
b = −0.74546 − 2.12446I
1.85594 − 8.85698I −0.17326 + 8.07537I
u = 1.073950 + 0.558752I
a = −0.92630 − 1.19417I
b = 0.220804 − 1.115600I
1.85594 − 2.52906I −0.17326 + 2.94577I
u = 1.073950 + 0.558752I
a = 1.69735 − 0.19586I
b = 1.96152 + 1.09909I
−5.14581 − 4.27792I −3.82674 + 0.60183I
u = 1.073950 + 0.558752I
a = −1.78478 − 0.33884I
b = −2.08469 − 1.42090I
−5.14581 − 7.10813I −3.82674 + 10.41931I
u = 1.073950 + 0.558752I
a = −1.85640 − 0.05757I
b = −1.93230 − 0.73805I
−5.14581 − 4.27792I −3.82674 + 0.60183I
u = 1.073950 + 0.558752I
a = 1.35622 + 1.27256I
b = 0.11003 + 1.51998I
1.85594 − 8.85698I −0.17326 + 8.07537I
u = 1.073950 + 0.558752I
a = 2.06935 + 0.24643I
b = 1.72743 + 1.36115I
−5.14581 − 7.10813I −3.82674 + 10.41931I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073950 − 0.558752I
a = 0.263523 − 0.901679I
b = 0.32755 − 1.80005I
1.85594 + 2.52906I −0.17326 − 2.94577I
u = 1.073950 − 0.558752I
a = −0.660126 + 1.071870I
b = −0.74546 + 2.12446I
1.85594 + 8.85698I −0.17326 − 8.07537I
u = 1.073950 − 0.558752I
a = −0.92630 + 1.19417I
b = 0.220804 + 1.115600I
1.85594 + 2.52906I −0.17326 − 2.94577I
u = 1.073950 − 0.558752I
a = 1.69735 + 0.19586I
b = 1.96152 − 1.09909I
−5.14581 + 4.27792I −3.82674 − 0.60183I
u = 1.073950 − 0.558752I
a = −1.78478 + 0.33884I
b = −2.08469 + 1.42090I
−5.14581 + 7.10813I −3.82674 − 10.41931I
u = 1.073950 − 0.558752I
a = −1.85640 + 0.05757I
b = −1.93230 + 0.73805I
−5.14581 + 4.27792I −3.82674 − 0.60183I
u = 1.073950 − 0.558752I
a = 1.35622 − 1.27256I
b = 0.11003 − 1.51998I
1.85594 + 8.85698I −0.17326 − 8.07537I
u = 1.073950 − 0.558752I
a = 2.06935 − 0.24643I
b = 1.72743 − 1.36115I
−5.14581 + 7.10813I −3.82674 − 10.41931I
16
III. I
u
3
=
h−5u
21
−4u
20
+· · ·+b+7, −7u
21
−10u
20
+· · ·+2a+17, u
22
−6u
20
+· · ·−u+2i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
9
=
7
2
u
21
+ 5u
20
+ ··· + 2u −
17
2
5u
21
+ 4u
20
+ ··· − 5u − 7
a
4
=
−
3
2
u
21
− u
20
+ ··· + 5u +
7
2
−u
21
+ 6u
19
+ ··· + u + 3
a
1
=
−u
2
+ 1
−u
4
a
6
=
u
u
a
10
=
7
2
u
21
+ 4u
20
+ ··· − 2u −
13
2
5u
21
+ 3u
20
+ ··· − 9u − 5
a
11
=
5
2
u
21
+ 2u
20
+ ··· − 2u +
3
2
3u
21
+ 3u
20
+ ··· + u − 5
a
5
=
−
3
2
u
21
+ 9u
19
+ ··· + 6u +
1
2
−u
21
+ u
20
+ ··· + 2u + 1
a
8
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
12
=
5
2
u
21
+ 2u
20
+ ··· − 2u −
1
2
2u
21
+ 2u
20
+ ··· + 4u − 5
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −12u
21
−5u
20
+ 65u
19
+ 29u
18
−189u
17
−87u
16
+ 341u
15
+ 140u
14
−435u
13
−105u
12
+
395u
11
−41u
10
−271u
9
+ 192u
8
+ 121u
7
−220u
6
−4u
5
+ 158u
4
−42u
3
−66u
2
+ 23u + 18
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
− 12u
21
+ ··· − 33u + 4
c
2
u
22
− 6u
20
+ ··· − u + 2
c
3
, c
9
u
22
+ 9u
20
+ ··· − u + 1
c
4
u
22
+ 2u
20
+ ··· − 2u + 1
c
5
u
22
+ 9u
20
+ ··· + u + 1
c
6
u
22
− 6u
20
+ ··· + u + 2
c
7
u
22
+ 2u
20
+ ··· + u + 2
c
8
u
22
+ 4u
21
+ ··· + 9u
2
+ 1
c
10
u
22
+ u
21
+ ··· + 161u + 208
c
11
u
22
− 4u
21
+ ··· + 9u
2
+ 1
c
12
u
22
+ 2u
20
+ ··· + 2u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
+ 4y
21
+ ··· − 17y + 16
c
2
, c
6
y
22
− 12y
21
+ ··· − 33y + 4
c
3
, c
5
, c
9
y
22
+ 18y
21
+ ··· − 5y + 1
c
4
, c
12
y
22
+ 4y
21
+ ··· − 10y + 1
c
7
y
22
+ 4y
21
+ ··· − 33y + 4
c
8
, c
11
y
22
+ 14y
21
+ ··· + 18y + 1
c
10
y
22
+ y
21
+ ··· − 79169y + 43264
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.961848 + 0.296339I
a = −2.00016 − 1.79386I
b = −1.39226 − 2.31814I
0.56453 − 4.62883I 5.59956 + 11.73591I
u = 0.961848 − 0.296339I
a = −2.00016 + 1.79386I
b = −1.39226 + 2.31814I
0.56453 + 4.62883I 5.59956 − 11.73591I
u = −1.002840 + 0.352792I
a = 0.468251 − 0.558052I
b = −0.272706 + 0.724834I
−6.83956 + 0.45717I −4.57919 − 4.81225I
u = −1.002840 − 0.352792I
a = 0.468251 + 0.558052I
b = −0.272706 − 0.724834I
−6.83956 − 0.45717I −4.57919 + 4.81225I
u = −0.843470 + 0.703506I
a = −0.034848 − 0.250819I
b = 0.205846 + 0.187042I
3.60508 + 5.33056I −0.09464 − 5.51436I
u = −0.843470 − 0.703506I
a = −0.034848 + 0.250819I
b = 0.205846 − 0.187042I
3.60508 − 5.33056I −0.09464 + 5.51436I
u = 0.173815 + 0.853261I
a = −0.694604 − 0.751121I
b = 0.520170 − 0.723235I
−5.80927 + 0.76774I −5.23209 + 0.08222I
u = 0.173815 − 0.853261I
a = −0.694604 + 0.751121I
b = 0.520170 + 0.723235I
−5.80927 − 0.76774I −5.23209 − 0.08222I
u = 0.817172 + 0.275112I
a = 1.64987 + 2.09307I
b = 0.77240 + 2.16430I
1.11933 + 2.14001I 6.11579 − 0.86458I
u = 0.817172 − 0.275112I
a = 1.64987 − 2.09307I
b = 0.77240 − 2.16430I
1.11933 − 2.14001I 6.11579 + 0.86458I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.918631 + 0.703076I
a = 0.215399 + 0.106652I
b = −0.272856 + 0.053468I
3.37208 + 0.07368I 2.57677 − 1.78560I
u = −0.918631 − 0.703076I
a = 0.215399 − 0.106652I
b = −0.272856 − 0.053468I
3.37208 − 0.07368I 2.57677 + 1.78560I
u = 0.544682 + 0.641471I
a = 0.35849 + 1.75353I
b = −0.92958 + 1.18508I
−3.74937 + 1.02775I −3.94340 − 0.09185I
u = 0.544682 − 0.641471I
a = 0.35849 − 1.75353I
b = −0.92958 − 1.18508I
−3.74937 − 1.02775I −3.94340 + 0.09185I
u = 1.047900 + 0.563172I
a = −2.02559 + 0.01283I
b = −2.12984 − 1.12732I
−5.29588 − 5.77472I −4.89114 + 4.98759I
u = 1.047900 − 0.563172I
a = −2.02559 − 0.01283I
b = −2.12984 + 1.12732I
−5.29588 + 5.77472I −4.89114 − 4.98759I
u = −0.782222 + 0.186398I
a = 0.296177 − 0.982955I
b = −0.048455 + 0.824096I
−5.78836 + 2.01747I 0.74667 − 4.58846I
u = −0.782222 − 0.186398I
a = 0.296177 + 0.982955I
b = −0.048455 − 0.824096I
−5.78836 − 2.01747I 0.74667 + 4.58846I
u = −1.226180 + 0.389290I
a = −0.269525 + 0.335576I
b = 0.199850 − 0.516400I
−10.01640 + 3.30562I −9.26157 − 2.61451I
u = −1.226180 − 0.389290I
a = −0.269525 − 0.335576I
b = 0.199850 + 0.516400I
−10.01640 − 3.30562I −9.26157 + 2.61451I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.227930 + 0.530969I
a = 1.286540 + 0.437612I
b = 1.34742 + 1.22047I
−8.99565 − 5.89312I −7.53678 + 2.20155I
u = 1.227930 − 0.530969I
a = 1.286540 − 0.437612I
b = 1.34742 − 1.22047I
−8.99565 + 5.89312I −7.53678 − 2.20155I
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
8
)(u
22
− 12u
21
+ ··· − 33u + 4)
· (u
32
+ 15u
31
+ ··· + 1152u + 256)
c
2
((u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
8
)(u
22
− 6u
20
+ ··· − u + 2)
· (u
32
− 9u
31
+ ··· − 128u + 16)
c
3
, c
9
(u
22
+ 9u
20
+ ··· − u + 1)(u
32
+ 8u
30
+ ··· + 2u + 1)
· (u
48
− u
47
+ ··· + 1188u + 891)
c
4
(u
22
+ 2u
20
+ ··· − 2u + 1)(u
32
+ 21u
30
+ ··· + u + 1)
· (u
48
− 3u
47
+ ··· + 2288u + 457)
c
5
(u
22
+ 9u
20
+ ··· + u + 1)(u
32
+ 8u
30
+ ··· + 2u + 1)
· (u
48
− u
47
+ ··· + 1188u + 891)
c
6
((u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
8
)(u
22
− 6u
20
+ ··· + u + 2)
· (u
32
− 9u
31
+ ··· − 128u + 16)
c
7
((u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
8
)(u
22
+ 2u
20
+ ··· + u + 2)
· (u
32
− 27u
31
+ ··· − 128512u + 13840)
c
8
((u
4
− u
3
+ u
2
+ 1)
12
)(u
22
+ 4u
21
+ ··· + 9u
2
+ 1)
· (u
32
+ 15u
31
+ ··· + 544u + 64)
c
10
(u
22
+ u
21
+ ··· + 161u + 208)(u
32
+ u
31
+ ··· − 24u + 10)
· (u
48
− u
47
+ ··· − 56112u + 5549)
c
11
((u
4
− u
3
+ u
2
+ 1)
12
)(u
22
− 4u
21
+ ··· + 9u
2
+ 1)
· (u
32
+ 15u
31
+ ··· + 544u + 64)
c
12
(u
22
+ 2u
20
+ ··· + 2u + 1)(u
32
+ 21u
30
+ ··· + u + 1)
· (u
48
− 3u
47
+ ··· + 2288u + 457)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
8
)(y
22
+ 4y
21
+ ··· − 17y + 16)
· (y
32
+ 5y
31
+ ··· + 843776y + 65536)
c
2
, c
6
((y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
8
)(y
22
− 12y
21
+ ··· − 33y + 4)
· (y
32
− 15y
31
+ ··· − 1152y + 256)
c
3
, c
5
, c
9
(y
22
+ 18y
21
+ ··· − 5y + 1)(y
32
+ 16y
31
+ ··· + 4y + 1)
· (y
48
+ 27y
47
+ ··· + 36823248y + 793881)
c
4
, c
12
(y
22
+ 4y
21
+ ··· − 10y + 1)(y
32
+ 42y
31
+ ··· − 21y + 1)
· (y
48
+ 15y
47
+ ··· − 4710308y + 208849)
c
7
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
8
)(y
22
+ 4y
21
+ ··· − 33y + 4)
· (y
32
+ 5y
31
+ ··· − 1955321984y + 191545600)
c
8
, c
11
((y
4
+ y
3
+ 3y
2
+ 2y + 1)
12
)(y
22
+ 14y
21
+ ··· + 18y + 1)
· (y
32
+ 15y
31
+ ··· + 23552y + 4096)
c
10
(y
22
+ y
21
+ ··· − 79169y + 43264)(y
32
− 29y
31
+ ··· − 2956y + 100)
· (y
48
+ 3y
47
+ ··· − 1819227006y + 30791401)
24
