12a
1270
(K12a
1270
)
A knot diagram
1
Linearized knot diagam
5 7 11 9 12 10 4 1 2 3 6 8
Solving Sequence
1,5 2,8
9 10 4 7 12 6 11 3
c
1
c
8
c
9
c
4
c
7
c
12
c
5
c
11
c
3
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h7.74082 × 10
49
u
34
− 5.22423 × 10
49
u
33
+ ··· + 1.89535 × 10
51
b − 5.14492 × 10
51
,
− 9.06527 × 10
50
u
34
+ 2.64032 × 10
50
u
33
+ ··· + 1.13721 × 10
52
a + 6.01325 × 10
52
,
u
35
− u
34
+ ··· − 72u + 24i
I
u
2
= h2.37244 × 10
960
u
121
− 2.53157 × 10
961
u
120
+ ··· + 2.07793 × 10
963
b + 5.97659 × 10
962
,
6.58503 × 10
963
u
121
− 6.71449 × 10
964
u
120
+ ··· + 2.59741 × 10
965
a − 3.63631 × 10
966
,
u
122
− 10u
121
+ ··· − 1165u − 125i
I
u
3
= h−5.91071 × 10
45
u
25
+ 3.90400 × 10
46
u
24
+ ··· + 1.44135 × 10
48
b − 5.25354 × 10
46
,
− 7.34230 × 10
46
u
25
+ 5.10520 × 10
47
u
24
+ ··· + 2.59442 × 10
49
a − 7.68850 × 10
48
,
u
26
− 5u
25
+ ··· + 72u + 72i
I
u
4
= h−u
4
− 2u
3
− 2u
2
+ b + u + 2, u
4
+ u
3
+ 2u
2
+ a − u, u
5
+ u
4
+ u
3
− 2u
2
− u + 1i
I
v
1
= ha, b − 1, v −1i
* 5 irreducible components of dim
C
= 0, with total 189 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
= h7.74 × 10
49
u
34
− 5.22 × 10
49
u
33
+ · · · + 1.90 × 10
51
b − 5.14 ×
10
51
, −9.07 × 10
50
u
34
+ 2.64 × 10
50
u
33
+ · · · + 1.14 × 10
52
a + 6.01 ×
10
52
, u
35
− u
34
+ · · · − 72u + 24i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
8
=
0.0797150u
34
− 0.0232175u
33
+ ··· + 6.72639u − 5.28772
−0.0408411u
34
+ 0.0275634u
33
+ ··· + 1.10469u + 2.71450
a
9
=
0.120556u
34
− 0.0507809u
33
+ ··· + 5.62170u − 8.00222
−0.0408411u
34
+ 0.0275634u
33
+ ··· + 1.10469u + 2.71450
a
10
=
0.0824652u
34
− 0.0487772u
33
+ ··· + 4.59592u − 3.61311
−0.0251998u
34
+ 0.00644199u
33
+ ··· − 0.579405u + 3.58059
a
4
=
0.0655862u
34
− 0.0282322u
33
+ ··· + 6.52922u − 4.49058
−0.0520750u
34
+ 0.0187396u
33
+ ··· − 1.39210u + 3.75828
a
7
=
0.0172414u
34
+ 0.0160165u
33
+ ··· + 6.98453u − 2.51757
−0.0539820u
34
+ 0.0424703u
33
+ ··· + 1.30295u + 2.09516
a
12
=
−0.0922554u
34
+ 0.0569040u
33
+ ··· − 4.83296u + 4.75136
0.0643395u
34
− 0.0476159u
33
+ ··· + 2.75223u − 5.13137
a
6
=
−0.0164467u
34
+ 0.0368134u
33
+ ··· + 4.66015u − 0.538408
−0.0352242u
34
+ 0.0180585u
33
+ ··· − 0.463258u + 1.49036
a
11
=
−0.0102200u
34
− 0.0759094u
33
+ ··· − 6.62406u + 4.46752
0.102257u
34
− 0.0983097u
33
+ ··· − 0.249882u − 4.16563
a
3
=
−0.0421436u
34
+ 0.104920u
33
+ ··· + 3.60754u − 1.84121
0.00461815u
34
+ 0.0321789u
33
+ ··· + 5.76299u − 3.08071
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.126101u
34
+ 0.0195036u
33
+ ··· + 2.65610u − 11.8112
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
35
+ u
34
+ ··· − 72u − 24
c
2
, c
4
4(4u
35
− 16u
34
+ ··· + 6u − 1)
c
3
, c
8
, c
10
c
12
u
35
− u
34
+ ··· + 13u + 1
c
5
, c
11
4(4u
35
− 8u
34
+ ··· − 448u
2
− 128)
c
7
u
35
− 10u
34
+ ··· + 18240u − 2880
c
9
u
35
+ 5u
34
+ ··· + 1166u + 268
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
35
− 3y
34
+ ··· + 11136y −576
c
2
, c
4
16(16y
35
+ 160y
34
+ ··· − 20y −1)
c
3
, c
8
, c
10
c
12
y
35
− 23y
34
+ ··· + 217y −1
c
5
, c
11
16(16y
35
+ 384y
34
+ ··· − 114688y −16384)
c
7
y
35
+ 8y
34
+ ··· − 2390400y −8294400
c
9
y
35
− 9y
34
+ ··· + 179820y −71824
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.743105 + 0.625315I
a = 0.224684 + 0.309873I
b = −0.120177 − 0.806594I
2.81070 + 4.31847I 0.02638 − 5.66453I
u = −0.743105 − 0.625315I
a = 0.224684 − 0.309873I
b = −0.120177 + 0.806594I
2.81070 − 4.31847I 0.02638 + 5.66453I
u = −0.798409 + 0.548304I
a = −1.037460 − 0.810232I
b = −1.308290 + 0.467708I
−7.46752 + 7.34663I −12.52677 − 6.17572I
u = −0.798409 − 0.548304I
a = −1.037460 + 0.810232I
b = −1.308290 − 0.467708I
−7.46752 − 7.34663I −12.52677 + 6.17572I
u = 0.976925 + 0.344857I
a = −0.959722 + 0.124413I
b = −0.865289 + 0.985076I
−0.023653 + 1.127930I −10.10478 + 0.88302I
u = 0.976925 − 0.344857I
a = −0.959722 − 0.124413I
b = −0.865289 − 0.985076I
−0.023653 − 1.127930I −10.10478 − 0.88302I
u = 0.853048 + 0.649064I
a = 0.547797 − 1.026300I
b = 1.002960 − 0.262125I
−0.81004 + 3.41365I −10.43435 − 4.21994I
u = 0.853048 − 0.649064I
a = 0.547797 + 1.026300I
b = 1.002960 + 0.262125I
−0.81004 − 3.41365I −10.43435 + 4.21994I
u = −0.758809 + 0.450562I
a = −1.56781 − 2.38091I
b = −0.889682 − 0.120944I
0.926289 − 0.422645I −8.89997 − 5.86272I
u = −0.758809 − 0.450562I
a = −1.56781 + 2.38091I
b = −0.889682 + 0.120944I
0.926289 + 0.422645I −8.89997 + 5.86272I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.706010 + 1.013230I
a = 0.355151 + 0.130036I
b = 0.243640 + 1.121330I
8.09911 + 8.05470I 1.54795 − 6.13176I
u = −0.706010 − 1.013230I
a = 0.355151 − 0.130036I
b = 0.243640 − 1.121330I
8.09911 − 8.05470I 1.54795 + 6.13176I
u = 0.310600 + 1.210570I
a = 0.487959 − 0.160101I
b = −0.052662 − 0.627718I
5.68435 − 2.06312I 2.89452 + 3.67321I
u = 0.310600 − 1.210570I
a = 0.487959 + 0.160101I
b = −0.052662 + 0.627718I
5.68435 + 2.06312I 2.89452 − 3.67321I
u = 1.193170 + 0.377442I
a = −1.331010 + 0.363750I
b = −1.204850 − 0.074357I
−6.47571 − 0.47299I −13.45061 − 0.55355I
u = 1.193170 − 0.377442I
a = −1.331010 − 0.363750I
b = −1.204850 + 0.074357I
−6.47571 + 0.47299I −13.45061 + 0.55355I
u = −0.494027 + 0.506228I
a = −0.93006 − 1.12219I
b = −0.664830 − 0.648856I
2.66885 − 2.56110I 0.76974 + 3.55295I
u = −0.494027 − 0.506228I
a = −0.93006 + 1.12219I
b = −0.664830 + 0.648856I
2.66885 + 2.56110I 0.76974 − 3.55295I
u = 0.513237 + 0.402612I
a = −0.448803 − 0.445867I
b = −0.047772 + 0.461900I
−0.384148 − 1.201750I −4.76559 + 5.16723I
u = 0.513237 − 0.402612I
a = −0.448803 + 0.445867I
b = −0.047772 − 0.461900I
−0.384148 + 1.201750I −4.76559 − 5.16723I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.994202 + 0.939323I
a = 1.24343 − 0.91505I
b = 1.267270 + 0.429167I
−4.44986 − 13.42210I −7.33283 + 10.23246I
u = 0.994202 − 0.939323I
a = 1.24343 + 0.91505I
b = 1.267270 − 0.429167I
−4.44986 + 13.42210I −7.33283 − 10.23246I
u = −1.241200 + 0.597729I
a = 1.256640 + 0.157556I
b = 1.26207 − 0.73224I
−3.44745 + 12.16340I −7.50485 − 9.70091I
u = −1.241200 − 0.597729I
a = 1.256640 − 0.157556I
b = 1.26207 + 0.73224I
−3.44745 − 12.16340I −7.50485 + 9.70091I
u = −0.578602
a = −2.20779
b = 0.0669685
2.84525 6.43630
u = 1.32688 + 0.77751I
a = 1.280860 + 0.118894I
b = 1.305910 + 0.311259I
−3.10003 − 5.12933I −9.17022 + 3.26485I
u = 1.32688 − 0.77751I
a = 1.280860 − 0.118894I
b = 1.305910 − 0.311259I
−3.10003 + 5.12933I −9.17022 − 3.26485I
u = 0.401727 + 0.087884I
a = 0.419510 + 1.323910I
b = 1.081750 − 0.491933I
−2.03242 + 0.52401I −1.68884 + 3.20849I
u = 0.401727 − 0.087884I
a = 0.419510 − 1.323910I
b = 1.081750 + 0.491933I
−2.03242 − 0.52401I −1.68884 − 3.20849I
u = 1.21105 + 1.23455I
a = −1.260120 + 0.315341I
b = −1.33047 − 0.63221I
1.1748 − 20.6417I 0. + 10.47448I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21105 − 1.23455I
a = −1.260120 − 0.315341I
b = −1.33047 + 0.63221I
1.1748 + 20.6417I 0. − 10.47448I
u = −1.18457 + 1.29983I
a = 0.924235 + 0.510686I
b = 1.152670 − 0.132602I
−5.94053 + 5.22826I 0
u = −1.18457 − 1.29983I
a = 0.924235 − 0.510686I
b = 1.152670 + 0.132602I
−5.94053 − 5.22826I 0
u = −1.06541 + 1.88244I
a = −1.101420 − 0.116501I
b = −1.365740 + 0.283029I
−3.45972 + 8.84721I 0
u = −1.06541 − 1.88244I
a = −1.101420 + 0.116501I
b = −1.365740 − 0.283029I
−3.45972 − 8.84721I 0
8
II. I
u
2
= h2.37 × 10
960
u
121
− 2.53 × 10
961
u
120
+ · · · + 2.08 × 10
963
b + 5.98 ×
10
962
, 6.59 × 10
963
u
121
− 6.71 × 10
964
u
120
+ · · · + 2.60 × 10
965
a − 3.64 ×
10
966
, u
122
− 10u
121
+ · · · − 1165u − 125i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
8
=
−0.0253523u
121
+ 0.258507u
120
+ ··· + 85.9840u + 13.9997
−0.00114173u
121
+ 0.0121832u
120
+ ··· + 10.4661u − 0.287622
a
9
=
−0.0242106u
121
+ 0.246324u
120
+ ··· + 75.5179u + 14.2874
−0.00114173u
121
+ 0.0121832u
120
+ ··· + 10.4661u − 0.287622
a
10
=
−0.0247253u
121
+ 0.252149u
120
+ ··· + 84.0962u + 13.4725
−0.00133947u
121
+ 0.0142212u
120
+ ··· + 11.1913u − 0.202908
a
4
=
0.00170178u
121
− 0.0158265u
120
+ ··· − 4.36369u − 3.55710
0.00514350u
121
− 0.0520866u
120
+ ··· − 15.0763u − 3.93614
a
7
=
−0.00960896u
121
+ 0.0992660u
120
+ ··· + 39.1663u + 3.85279
0.00362962u
121
− 0.0364387u
120
+ ··· − 7.65652u − 3.24338
a
12
=
−0.0331351u
121
+ 0.337007u
120
+ ··· + 93.2270u + 19.6629
−0.00164599u
121
+ 0.0169720u
120
+ ··· − 1.38532u − 1.94562
a
6
=
0.0118904u
121
− 0.118522u
120
+ ··· − 25.4450u − 15.0847
0.0150745u
121
− 0.153448u
120
+ ··· − 48.8293u − 10.4630
a
11
=
0.0118399u
121
− 0.120721u
120
+ ··· − 31.6689u − 4.06732
−0.000359836u
121
+ 0.00356077u
120
+ ··· − 2.45589u + 0.840103
a
3
=
0.00736804u
121
− 0.0742955u
120
+ ··· − 27.2932u − 8.74550
0.00884442u
121
− 0.0901755u
120
+ ··· − 25.3312u − 5.99966
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0191521u
121
− 0.194669u
120
+ ··· − 102.892u − 26.6829
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
122
+ 10u
121
+ ··· + 1165u − 125
c
2
, c
4
25(25u
122
+ 75u
121
+ ··· + 7u + 1)
c
3
, c
8
, c
10
c
12
u
122
− 36u
120
+ ··· + 929u + 103
c
5
, c
11
25(5u
61
+ u
60
+ ··· − 2062u + 569)
2
c
7
(u
61
+ 8u
60
+ ··· + 6810u + 724)
2
c
9
(u
61
− 18u
59
+ ··· − 10865u + 9784)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
122
+ 18y
121
+ ··· − 1184975y + 15625
c
2
, c
4
625(625y
122
− 5675y
121
+ ··· − 29y + 1)
c
3
, c
8
, c
10
c
12
y
122
− 72y
121
+ ··· − 412519y + 10609
c
5
, c
11
625(25y
61
+ 1199y
60
+ ··· − 3158812y −323761)
2
c
7
(y
61
− 28y
60
+ ··· − 1108164y −524176)
2
c
9
(y
61
− 36y
60
+ ··· + 2341110001y −95726656)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.344896 + 0.943013I
a = −0.599105 − 0.080280I
b = −1.039280 − 0.249283I
0.44283 − 2.75797I 0
u = −0.344896 − 0.943013I
a = −0.599105 + 0.080280I
b = −1.039280 + 0.249283I
0.44283 + 2.75797I 0
u = 0.735741 + 0.690425I
a = −1.58994 + 1.55980I
b = −1.142120 − 0.332656I
−3.20560 0
u = 0.735741 − 0.690425I
a = −1.58994 − 1.55980I
b = −1.142120 + 0.332656I
−3.20560 0
u = −0.496884 + 0.848888I
a = 2.07101 + 0.37586I
b = 0.855278 − 0.341384I
0.77506 − 2.15360I 0
u = −0.496884 − 0.848888I
a = 2.07101 − 0.37586I
b = 0.855278 + 0.341384I
0.77506 + 2.15360I 0
u = 0.313005 + 0.995145I
a = 0.296120 − 0.166755I
b = −0.138377 − 1.259260I
5.85317 − 3.26425I 0
u = 0.313005 − 0.995145I
a = 0.296120 + 0.166755I
b = −0.138377 + 1.259260I
5.85317 + 3.26425I 0
u = −0.744001 + 0.585851I
a = −0.212690 − 0.848290I
b = −0.899146 − 0.319862I
0.30534 − 1.56924I 0
u = −0.744001 − 0.585851I
a = −0.212690 + 0.848290I
b = −0.899146 + 0.319862I
0.30534 + 1.56924I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.350579 + 0.874543I
a = −0.329074 − 0.131092I
b = −0.130068 − 1.346020I
5.04372 + 0.96008I 0
u = −0.350579 − 0.874543I
a = −0.329074 + 0.131092I
b = −0.130068 + 1.346020I
5.04372 − 0.96008I 0
u = 0.907758 + 0.545285I
a = 0.98203 − 1.37002I
b = 0.786601 − 0.090659I
0.30534 − 1.56924I 0
u = 0.907758 − 0.545285I
a = 0.98203 + 1.37002I
b = 0.786601 + 0.090659I
0.30534 + 1.56924I 0
u = −0.879973 + 0.614710I
a = −0.887999 − 1.010960I
b = −1.222680 + 0.191124I
−7.72980 − 3.10750I 0
u = −0.879973 − 0.614710I
a = −0.887999 + 1.010960I
b = −1.222680 − 0.191124I
−7.72980 + 3.10750I 0
u = −0.706675 + 0.598682I
a = −1.378770 + 0.089695I
b = −1.45716 + 0.71442I
1.07069 + 4.78696I 0
u = −0.706675 − 0.598682I
a = −1.378770 − 0.089695I
b = −1.45716 − 0.71442I
1.07069 − 4.78696I 0
u = 0.940683 + 0.525430I
a = 0.821611 − 0.841974I
b = 1.097730 + 0.388331I
−3.17611 − 1.97793I 0
u = 0.940683 − 0.525430I
a = 0.821611 + 0.841974I
b = 1.097730 − 0.388331I
−3.17611 + 1.97793I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.790673 + 0.764744I
a = 0.663204 − 0.078125I
b = 0.016357 + 0.608342I
0.10617 + 3.36466I 0
u = 0.790673 − 0.764744I
a = 0.663204 + 0.078125I
b = 0.016357 − 0.608342I
0.10617 − 3.36466I 0
u = −0.258195 + 1.082180I
a = −0.296332 + 0.134497I
b = 0.671474 − 0.779981I
2.91739 + 5.62744I 0
u = −0.258195 − 1.082180I
a = −0.296332 − 0.134497I
b = 0.671474 + 0.779981I
2.91739 − 5.62744I 0
u = −0.619621 + 0.934025I
a = 0.695199 + 1.119970I
b = 1.120040 − 0.394013I
0.10617 + 3.36466I 0
u = −0.619621 − 0.934025I
a = 0.695199 − 1.119970I
b = 1.120040 + 0.394013I
0.10617 − 3.36466I 0
u = −0.591252 + 0.960898I
a = −0.106773 − 0.250520I
b = −0.161790 − 1.173080I
6.00057 + 5.23295I 0
u = −0.591252 − 0.960898I
a = −0.106773 + 0.250520I
b = −0.161790 + 1.173080I
6.00057 − 5.23295I 0
u = 0.896544 + 0.707064I
a = −0.489143 + 0.168933I
b = −0.156697 − 0.819636I
−0.26653 − 9.02592I 0
u = 0.896544 − 0.707064I
a = −0.489143 − 0.168933I
b = −0.156697 + 0.819636I
−0.26653 + 9.02592I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.369969 + 0.731942I
a = −0.213708 − 0.807599I
b = 0.045076 + 0.580892I
0.44283 − 2.75797I 0
u = 0.369969 − 0.731942I
a = −0.213708 + 0.807599I
b = 0.045076 − 0.580892I
0.44283 + 2.75797I 0
u = −0.817541 + 0.058779I
a = 1.003230 + 0.191642I
b = 0.829240 + 1.130720I
−1.37438 + 5.03809I 0
u = −0.817541 − 0.058779I
a = 1.003230 − 0.191642I
b = 0.829240 − 1.130720I
−1.37438 − 5.03809I 0
u = 0.524914 + 1.071220I
a = 0.279357 − 0.309824I
b = 0.201360 − 1.075790I
6.74364 − 1.82953I 0
u = 0.524914 − 1.071220I
a = 0.279357 + 0.309824I
b = 0.201360 + 1.075790I
6.74364 + 1.82953I 0
u = −0.660640 + 0.462872I
a = 0.942936 − 0.907949I
b = 0.234151 + 0.070924I
−3.17392 + 4.40270I 0
u = −0.660640 − 0.462872I
a = 0.942936 + 0.907949I
b = 0.234151 − 0.070924I
−3.17392 − 4.40270I 0
u = 0.611359 + 0.511877I
a = 1.218500 − 0.012171I
b = 1.34892 + 0.84641I
0.77506 − 2.15360I 0
u = 0.611359 − 0.511877I
a = 1.218500 + 0.012171I
b = 1.34892 − 0.84641I
0.77506 + 2.15360I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.676011 + 0.995074I
a = −0.262278 + 0.188808I
b = −0.160143 + 1.220980I
4.8547 − 14.2006I 0
u = 0.676011 − 0.995074I
a = −0.262278 − 0.188808I
b = −0.160143 − 1.220980I
4.8547 + 14.2006I 0
u = −0.049469 + 1.221170I
a = −0.537878 − 0.039817I
b = 0.585256 + 0.487855I
3.38091 + 7.67122I 0
u = −0.049469 − 1.221170I
a = −0.537878 + 0.039817I
b = 0.585256 − 0.487855I
3.38091 − 7.67122I 0
u = 0.589586 + 0.478408I
a = 1.59735 − 0.40331I
b = 1.31214 + 0.81529I
0.58899 − 6.83774I 0
u = 0.589586 − 0.478408I
a = 1.59735 + 0.40331I
b = 1.31214 − 0.81529I
0.58899 + 6.83774I 0
u = −0.633627 + 0.344067I
a = −1.76866 + 0.00062I
b = −1.22270 + 0.75356I
2.28409 + 3.58575I 0
u = −0.633627 − 0.344067I
a = −1.76866 − 0.00062I
b = −1.22270 − 0.75356I
2.28409 − 3.58575I 0
u = −0.017193 + 1.322030I
a = 0.352713 − 0.162984I
b = −0.657413 + 0.343441I
6.74364 − 1.82953I 0
u = −0.017193 − 1.322030I
a = 0.352713 + 0.162984I
b = −0.657413 − 0.343441I
6.74364 + 1.82953I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.600197 + 0.312067I
a = −0.338113 + 1.077580I
b = 0.503287 − 0.360908I
−1.60260 − 0.22148I −8.15196 + 3.06639I
u = 0.600197 − 0.312067I
a = −0.338113 − 1.077580I
b = 0.503287 + 0.360908I
−1.60260 + 0.22148I −8.15196 − 3.06639I
u = 0.529198 + 1.213910I
a = −0.438502 − 0.185971I
b = −0.142221 + 0.680779I
1.18305 − 3.04202I 0
u = 0.529198 − 1.213910I
a = −0.438502 + 0.185971I
b = −0.142221 − 0.680779I
1.18305 + 3.04202I 0
u = −0.581785 + 0.335169I
a = −1.40293 − 0.83160I
b = 0.040109 + 0.305612I
2.82130 4.70535 + 0.I
u = −0.581785 − 0.335169I
a = −1.40293 + 0.83160I
b = 0.040109 − 0.305612I
2.82130 4.70535 + 0.I
u = −0.639963 + 0.089726I
a = 1.52060 − 0.02924I
b = 1.311930 + 0.276930I
−1.60260 + 0.22148I −8.15196 − 3.06639I
u = −0.639963 − 0.089726I
a = 1.52060 + 0.02924I
b = 1.311930 − 0.276930I
−1.60260 − 0.22148I −8.15196 + 3.06639I
u = 0.566158 + 0.303999I
a = −1.330430 + 0.255756I
b = −1.33865 + 0.80106I
−3.00354 − 3.38830I −9.3034 + 15.7841I
u = 0.566158 − 0.303999I
a = −1.330430 − 0.255756I
b = −1.33865 − 0.80106I
−3.00354 + 3.38830I −9.3034 − 15.7841I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.961679 + 0.967643I
a = −1.051890 − 0.777569I
b = −1.169780 + 0.493748I
−0.26653 + 9.02592I 0
u = −0.961679 − 0.967643I
a = −1.051890 + 0.777569I
b = −1.169780 − 0.493748I
−0.26653 − 9.02592I 0
u = −1.147810 + 0.756870I
a = 1.301440 + 0.352111I
b = 1.307180 − 0.434278I
−7.72980 + 3.10750I 0
u = −1.147810 − 0.756870I
a = 1.301440 − 0.352111I
b = 1.307180 + 0.434278I
−7.72980 − 3.10750I 0
u = 0.990199 + 0.985383I
a = 0.725232 − 0.945815I
b = 1.009300 + 0.355900I
−3.00354 − 3.38830I 0
u = 0.990199 − 0.985383I
a = 0.725232 + 0.945815I
b = 1.009300 − 0.355900I
−3.00354 + 3.38830I 0
u = 0.448641 + 1.334150I
a = 0.946793 − 0.143219I
b = 1.202480 − 0.257369I
−3.31101 + 6.60026I 0
u = 0.448641 − 1.334150I
a = 0.946793 + 0.143219I
b = 1.202480 + 0.257369I
−3.31101 − 6.60026I 0
u = 0.129462 + 0.552946I
a = −3.05058 + 1.94389I
b = −0.891064 − 0.407435I
6.00057 − 5.23295I 1.84873 + 7.74629I
u = 0.129462 − 0.552946I
a = −3.05058 − 1.94389I
b = −0.891064 + 0.407435I
6.00057 + 5.23295I 1.84873 − 7.74629I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.89995 + 1.13098I
a = −1.092970 − 0.358507I
b = −1.30794 + 0.71230I
1.45825 + 7.97801I 0
u = −0.89995 − 1.13098I
a = −1.092970 + 0.358507I
b = −1.30794 − 0.71230I
1.45825 − 7.97801I 0
u = 0.74020 + 1.24770I
a = −0.821261 + 0.541383I
b = −1.242840 − 0.407682I
−3.31101 − 6.60026I 0
u = 0.74020 − 1.24770I
a = −0.821261 − 0.541383I
b = −1.242840 + 0.407682I
−3.31101 + 6.60026I 0
u = −0.494355 + 0.204787I
a = 0.356530 + 0.195010I
b = −0.057146 + 1.136030I
−3.17611 − 1.97793I −14.9748 − 1.5830I
u = −0.494355 − 0.204787I
a = 0.356530 − 0.195010I
b = −0.057146 − 1.136030I
−3.17611 + 1.97793I −14.9748 + 1.5830I
u = 0.41895 + 1.45466I
a = −0.281617 − 0.119487I
b = −0.413054 + 0.357878I
2.28409 − 3.58575I 0
u = 0.41895 − 1.45466I
a = −0.281617 + 0.119487I
b = −0.413054 − 0.357878I
2.28409 + 3.58575I 0
u = 1.17563 + 0.96053I
a = −1.101820 + 0.441791I
b = −1.106580 − 0.348173I
−3.17392 − 4.40270I 0
u = 1.17563 − 0.96053I
a = −1.101820 − 0.441791I
b = −1.106580 + 0.348173I
−3.17392 + 4.40270I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.144405 + 0.450720I
a = 3.89399 + 2.43715I
b = 0.925254 − 0.418220I
2.40959 + 11.44890I −1.70053 − 10.31542I
u = −0.144405 − 0.450720I
a = 3.89399 − 2.43715I
b = 0.925254 + 0.418220I
2.40959 − 11.44890I −1.70053 + 10.31542I
u = 0.87831 + 1.25741I
a = 1.132530 − 0.284190I
b = 1.44157 + 0.65642I
1.05957 − 10.04140I 0
u = 0.87831 − 1.25741I
a = 1.132530 + 0.284190I
b = 1.44157 − 0.65642I
1.05957 + 10.04140I 0
u = 1.17486 + 0.98749I
a = −1.61460 + 0.21853I
b = −1.010390 − 0.366048I
0.58899 − 6.83774I 0
u = 1.17486 − 0.98749I
a = −1.61460 − 0.21853I
b = −1.010390 + 0.366048I
0.58899 + 6.83774I 0
u = −1.11980 + 1.07506I
a = −1.39892 − 0.38174I
b = −1.30716 + 0.61211I
2.40959 + 11.44890I 0
u = −1.11980 − 1.07506I
a = −1.39892 + 0.38174I
b = −1.30716 − 0.61211I
2.40959 − 11.44890I 0
u = 1.40089 + 0.76880I
a = −1.165290 + 0.216440I
b = −1.127600 − 0.656228I
−1.37438 − 5.03809I 0
u = 1.40089 − 0.76880I
a = −1.165290 − 0.216440I
b = −1.127600 + 0.656228I
−1.37438 + 5.03809I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.58037 + 0.26664I
a = −1.311870 + 0.166164I
b = −0.723762 + 0.302661I
3.17421 + 0.38606I 0
u = −1.58037 − 0.26664I
a = −1.311870 − 0.166164I
b = −0.723762 − 0.302661I
3.17421 − 0.38606I 0
u = 0.396540
a = −1.29887
b = 0.620446
−1.56136 −7.63810
u = −0.037201 + 0.332227I
a = 1.78667 − 3.78999I
b = 0.578478 + 0.585209I
3.17421 + 0.38606I 5.14225 − 2.45135I
u = −0.037201 − 0.332227I
a = 1.78667 + 3.78999I
b = 0.578478 − 0.585209I
3.17421 − 0.38606I 5.14225 + 2.45135I
u = −0.319659
a = 2.92467
b = 1.10789
−1.56136 −7.63810
u = 1.20015 + 1.18066I
a = 1.335850 − 0.225523I
b = 1.270010 + 0.582561I
3.38091 − 7.67122I 0
u = 1.20015 − 1.18066I
a = 1.335850 + 0.225523I
b = 1.270010 − 0.582561I
3.38091 + 7.67122I 0
u = −0.92322 + 1.40919I
a = −0.760983 − 0.333462I
b = −0.755945 − 0.396817I
3.01460 − 2.93673I 0
u = −0.92322 − 1.40919I
a = −0.760983 + 0.333462I
b = −0.755945 + 0.396817I
3.01460 + 2.93673I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.175473 + 0.216791I
a = −4.72010 − 0.88886I
b = −0.982810 + 0.647353I
3.01460 + 2.93673I 2.71064 − 4.31841I
u = −0.175473 − 0.216791I
a = −4.72010 + 0.88886I
b = −0.982810 − 0.647353I
3.01460 − 2.93673I 2.71064 + 4.31841I
u = −1.26065 + 1.24332I
a = 1.227040 + 0.294446I
b = 1.27312 − 0.62375I
4.8547 + 14.2006I 0
u = −1.26065 − 1.24332I
a = 1.227040 − 0.294446I
b = 1.27312 + 0.62375I
4.8547 − 14.2006I 0
u = −0.183442 + 0.050314I
a = −2.15551 + 3.44438I
b = −1.56584 + 0.08837I
1.18305 + 3.04202I −7.30430 − 3.73323I
u = −0.183442 − 0.050314I
a = −2.15551 − 3.44438I
b = −1.56584 − 0.08837I
1.18305 − 3.04202I −7.30430 + 3.73323I
u = 0.157988 + 0.083431I
a = 2.49309 + 2.31984I
b = 2.01787 − 0.14443I
−1.73688 − 7.47793I −21.7278 + 13.8856I
u = 0.157988 − 0.083431I
a = 2.49309 − 2.31984I
b = 2.01787 + 0.14443I
−1.73688 + 7.47793I −21.7278 − 13.8856I
u = −0.04459 + 1.87707I
a = 0.317304 − 0.063687I
b = 0.834718 + 0.221281I
1.07069 − 4.78696I 0
u = −0.04459 − 1.87707I
a = 0.317304 + 0.063687I
b = 0.834718 − 0.221281I
1.07069 + 4.78696I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.37917 + 1.51463I
a = −1.157720 + 0.289268I
b = −1.162460 − 0.485021I
−1.73688 − 7.47793I 0
u = 1.37917 − 1.51463I
a = −1.157720 − 0.289268I
b = −1.162460 + 0.485021I
−1.73688 + 7.47793I 0
u = 2.08788 + 0.25972I
a = −1.243040 − 0.304914I
b = −0.805807 − 0.214546I
1.45825 + 7.97801I 0
u = 2.08788 − 0.25972I
a = −1.243040 + 0.304914I
b = −0.805807 + 0.214546I
1.45825 − 7.97801I 0
u = 1.85592 + 1.19470I
a = 1.231730 + 0.024229I
b = 1.051450 + 0.384190I
2.91739 − 5.62744I 0
u = 1.85592 − 1.19470I
a = 1.231730 − 0.024229I
b = 1.051450 − 0.384190I
2.91739 + 5.62744I 0
u = −1.97170 + 0.99606I
a = 1.339360 − 0.085014I
b = 0.941989 − 0.287213I
5.04372 − 0.96008I 0
u = −1.97170 − 0.99606I
a = 1.339360 + 0.085014I
b = 0.941989 + 0.287213I
5.04372 + 0.96008I 0
u = −0.86426 + 2.62514I
a = 0.723391 + 0.070268I
b = 0.761110 + 0.158550I
5.85317 − 3.26425I 0
u = −0.86426 − 2.62514I
a = 0.723391 − 0.070268I
b = 0.761110 − 0.158550I
5.85317 + 3.26425I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 2.07272 + 2.12436I
a = −0.849224 + 0.216330I
b = −0.939027 + 0.212548I
1.05957 + 10.04140I 0
u = 2.07272 − 2.12436I
a = −0.849224 − 0.216330I
b = −0.939027 − 0.212548I
1.05957 − 10.04140I 0
24
III. I
u
3
= h−5.91 × 10
45
u
25
+ 3.90 × 10
46
u
24
+ · · · + 1.44 × 10
48
b − 5.25 ×
10
46
, −7.34 × 10
46
u
25
+ 5.11 × 10
47
u
24
+ · · · + 2.59 × 10
49
a − 7.69 ×
10
48
, u
26
− 5u
25
+ · · · + 72u + 72i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
8
=
0.00283003u
25
− 0.0196776u
24
+ ··· − 0.171032u + 0.296347
0.00410083u
25
− 0.0270858u
24
+ ··· + 0.896673u + 0.0364488
a
9
=
−0.00127080u
25
+ 0.00740817u
24
+ ··· − 1.06770u + 0.259898
0.00410083u
25
− 0.0270858u
24
+ ··· + 0.896673u + 0.0364488
a
10
=
0.00337665u
25
− 0.0228206u
24
+ ··· − 0.186628u + 0.372249
0.00463676u
25
− 0.0276966u
24
+ ··· + 1.06545u + 0.539840
a
4
=
−0.00198736u
25
+ 0.00969786u
24
+ ··· − 0.111126u − 0.0881769
0.00279986u
25
− 0.0117111u
24
+ ··· + 1.00084u + 0.467511
a
7
=
0.00548912u
25
− 0.0331545u
24
+ ··· − 0.217562u + 0.496326
0.000480416u
25
− 0.00619053u
24
+ ··· − 0.164514u + 0.204863
a
12
=
0.000332728u
25
− 0.00314793u
24
+ ··· − 1.49622u − 1.24392
0.00682593u
25
− 0.0384138u
24
+ ··· − 1.54824u − 1.77725
a
6
=
−0.00820086u
25
+ 0.0379672u
24
+ ··· − 1.13406u − 0.153281
−0.0166543u
25
+ 0.0765172u
24
+ ··· − 1.61999u − 0.637907
a
11
=
−0.00112518u
25
+ 0.00798859u
24
+ ··· + 0.175461u + 0.455177
0.00312682u
25
− 0.0138912u
24
+ ··· + 1.05302u + 1.03415
a
3
=
−0.0106336u
25
+ 0.0551673u
24
+ ··· − 2.17842u − 0.748964
−0.00673065u
25
+ 0.0369688u
24
+ ··· − 2.28784u − 0.162962
(ii) Obstruction class = 1
(iii) Cusp Shapes = −0.0538162u
25
+ 0.297083u
24
+ ··· − 1.49417u − 5.56503
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
26
− 5u
25
+ ··· + 72u + 72
c
2
, c
4
36(36u
26
− 64u
24
+ ··· + 3u + 1)
c
3
, c
12
u
26
+ u
25
+ ··· − u + 1
c
5
, c
11
36(36u
26
+ 512u
24
+ ··· + 1550u
2
+ 113)
c
7
(u
13
+ 6u
12
+ ··· + 3u − 1)
2
c
8
, c
10
u
26
− u
25
+ ··· + u + 1
c
9
(u
13
+ 2u
12
+ ··· + 11u + 2)
2
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
26
+ 11y
25
+ ··· + 10944y + 5184
c
2
, c
4
1296(1296y
26
− 4608y
25
+ ··· − y + 1)
c
3
, c
8
, c
10
c
12
y
26
− 19y
25
+ ··· − 19y + 1
c
5
, c
11
1296(36y
13
+ 512y
12
+ ··· + 1550y + 113)
2
c
7
(y
13
− 4y
12
+ ··· + 3y −1)
2
c
9
(y
13
− 8y
12
+ ··· + 21y −4)
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.818792 + 0.588791I
a = 1.54607 − 0.01755I
b = 1.105830 + 0.603431I
2.07800 − 4.16695I −0.78590 + 6.73016I
u = 0.818792 − 0.588791I
a = 1.54607 + 0.01755I
b = 1.105830 − 0.603431I
2.07800 + 4.16695I −0.78590 − 6.73016I
u = −0.346674 + 0.961533I
a = −0.258359 − 0.241943I
b = 0.024817 − 1.263200I
5.63220 + 2.75504I −0.857086 − 0.087467I
u = −0.346674 − 0.961533I
a = −0.258359 + 0.241943I
b = 0.024817 + 1.263200I
5.63220 − 2.75504I −0.857086 + 0.087467I
u = −0.843567 + 0.120573I
a = −2.01435 + 0.02026I
b = −0.525765 + 0.186753I
2.25263 −4.75779 + 0.I
u = −0.843567 − 0.120573I
a = −2.01435 − 0.02026I
b = −0.525765 − 0.186753I
2.25263 −4.75779 + 0.I
u = 0.643283 + 0.443438I
a = 1.47082 + 0.06023I
b = 1.43845 + 0.73280I
1.75210 − 3.87661I −5.92175 + 8.27031I
u = 0.643283 − 0.443438I
a = 1.47082 − 0.06023I
b = 1.43845 − 0.73280I
1.75210 + 3.87661I −5.92175 − 8.27031I
u = 0.082526 + 1.304870I
a = −0.0965806 + 0.1024740I
b = −0.588688 − 0.448640I
2.07800 − 4.16695I −0.78590 + 6.73016I
u = 0.082526 − 1.304870I
a = −0.0965806 − 0.1024740I
b = −0.588688 + 0.448640I
2.07800 + 4.16695I −0.78590 − 6.73016I
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.060880 + 0.855857I
a = −0.872778 + 0.818917I
b = −1.012320 − 0.339179I
−3.10825 − 2.94174I −11.87764 − 0.77447I
u = 1.060880 − 0.855857I
a = −0.872778 − 0.818917I
b = −1.012320 + 0.339179I
−3.10825 + 2.94174I −11.87764 + 0.77447I
u = −0.055307 + 0.619318I
a = −1.51632 − 0.26589I
b = −1.79863 + 0.08354I
−1.43134 + 7.41780I 3.89732 − 7.81880I
u = −0.055307 − 0.619318I
a = −1.51632 + 0.26589I
b = −1.79863 − 0.08354I
−1.43134 − 7.41780I 3.89732 + 7.81880I
u = −0.90196 + 1.14405I
a = −1.189760 − 0.345469I
b = −1.38118 + 0.68005I
1.35320 + 9.54720I −0.35383 − 4.72435I
u = −0.90196 − 1.14405I
a = −1.189760 + 0.345469I
b = −1.38118 − 0.68005I
1.35320 − 9.54720I −0.35383 + 4.72435I
u = −0.432859 + 0.312166I
a = 1.67415 + 0.04406I
b = 0.907337 + 0.774765I
−3.10825 + 2.94174I −11.87764 + 0.77447I
u = −0.432859 − 0.312166I
a = 1.67415 − 0.04406I
b = 0.907337 − 0.774765I
−3.10825 − 2.94174I −11.87764 − 0.77447I
u = 0.21989 + 1.48866I
a = 0.446786 + 0.350595I
b = 0.241470 − 0.201081I
1.75210 − 3.87661I −5.92175 + 8.27031I
u = 0.21989 − 1.48866I
a = 0.446786 − 0.350595I
b = 0.241470 + 0.201081I
1.75210 + 3.87661I −5.92175 − 8.27031I
29
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.27926 + 1.55184I
a = 1.162720 − 0.260867I
b = 1.194910 + 0.453756I
−1.43134 − 7.41780I 3.89732 + 7.81880I
u = 1.27926 − 1.55184I
a = 1.162720 + 0.260867I
b = 1.194910 − 0.453756I
−1.43134 + 7.41780I 3.89732 − 7.81880I
u = −0.89322 + 1.95341I
a = 0.617507 + 0.397322I
b = 0.753866 + 0.045956I
5.63220 − 2.75504I 0
u = −0.89322 − 1.95341I
a = 0.617507 − 0.397322I
b = 0.753866 − 0.045956I
5.63220 + 2.75504I 0
u = 1.86895 + 1.17491I
a = −1.081020 + 0.464007I
b = −0.860091 + 0.185425I
1.35320 + 9.54720I 0
u = 1.86895 − 1.17491I
a = −1.081020 − 0.464007I
b = −0.860091 − 0.185425I
1.35320 − 9.54720I 0
30
IV.
I
u
4
= h−u
4
−2u
3
−2u
2
+b+u+2, u
4
+u
3
+2u
2
+a−u, u
5
+u
4
+u
3
−2u
2
−u+1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
8
=
−u
4
− u
3
− 2u
2
+ u
u
4
+ 2u
3
+ 2u
2
− u − 2
a
9
=
−2u
4
− 3u
3
− 4u
2
+ 2u + 2
u
4
+ 2u
3
+ 2u
2
− u − 2
a
10
=
−1
2u
4
+ 3u
3
+ 3u
2
− 2u − 3
a
4
=
u
4
+ u
3
+ 2u
2
− u
−u
4
− 2u
3
− 3u
2
+ u + 2
a
7
=
−u
u
4
+ u
3
+ 2u
2
− 2
a
12
=
0
2u
4
+ 3u
3
+ 4u
2
− u − 3
a
6
=
0
u
a
11
=
0
2u
4
+ 3u
3
+ 4u
2
− u − 3
a
3
=
u
4
+ u
3
+ 2u
2
− u
u
4
+ 2u
3
+ 2u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
4
+ 2u
3
+ 3u
2
− 9u − 15
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
5
+ u
4
+ u
3
− 2u
2
− u + 1
c
2
, c
4
u
5
+ u
4
+ u
3
+ 2u
2
+ u + 1
c
3
, c
12
u
5
− 2u
3
− u
2
+ 2u + 1
c
5
, c
11
u
5
c
7
u
5
− 3u
4
+ 7u
3
− 9u
2
+ 4u − 1
c
8
, c
10
u
5
− 2u
3
+ u
2
+ 2u − 1
c
9
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
5
+ y
4
+ 3y
3
− 8y
2
+ 5y −1
c
2
, c
4
y
5
+ y
4
− y
3
− 4y
2
− 3y −1
c
3
, c
8
, c
10
c
12
y
5
− 4y
4
+ 8y
3
− 9y
2
+ 6y −1
c
5
, c
11
y
5
c
7
y
5
+ 5y
4
+ 3y
3
− 31y
2
− 2y −1
c
9
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.821196
a = −2.07090
b = −0.482881
2.24708 −5.78420
u = 0.688402 + 0.106340I
a = −0.732208 − 0.471915I
b = −0.964913 + 0.621896I
−2.50012 + 0.60716I −18.8170 + 0.0530I
u = 0.688402 − 0.106340I
a = −0.732208 + 0.471915I
b = −0.964913 − 0.621896I
−2.50012 − 0.60716I −18.8170 − 0.0530I
u = −0.77780 + 1.38013I
a = 0.767660 + 0.216900I
b = 1.206350 − 0.340852I
−5.20316 + 6.77491I −9.79092 − 7.94775I
u = −0.77780 − 1.38013I
a = 0.767660 − 0.216900I
b = 1.206350 + 0.340852I
−5.20316 − 6.77491I −9.79092 + 7.94775I
34
V. I
v
1
= ha, b − 1, v − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
1
0
a
2
=
1
0
a
8
=
0
1
a
9
=
−1
1
a
10
=
0
1
a
4
=
0
1
a
7
=
0
1
a
12
=
1
−1
a
6
=
0
1
a
11
=
1
−2
a
3
=
1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
u
c
2
, c
3
, c
4
c
5
, c
8
, c
9
c
10
, c
11
, c
12
u + 1
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
7
y
c
2
, c
3
, c
4
c
5
, c
8
, c
9
c
10
, c
11
, c
12
y −1
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
−1.64493 −6.00000
38
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u(u
5
+ u
4
+ ··· − u + 1)(u
26
− 5u
25
+ ··· + 72u + 72)
· (u
35
+ u
34
+ ··· − 72u − 24)(u
122
+ 10u
121
+ ··· + 1165u − 125)
c
2
, c
4
3600(u + 1)(u
5
+ u
4
+ ··· + u + 1)(36u
26
− 64u
24
+ ··· + 3u + 1)
· (4u
35
− 16u
34
+ ··· + 6u − 1)(25u
122
+ 75u
121
+ ··· + 7u + 1)
c
3
, c
12
(u + 1)(u
5
− 2u
3
− u
2
+ 2u + 1)(u
26
+ u
25
+ ··· − u + 1)
· (u
35
− u
34
+ ··· + 13u + 1)(u
122
− 36u
120
+ ··· + 929u + 103)
c
5
, c
11
3600u
5
(u + 1)(36u
26
+ 512u
24
+ ··· + 1550u
2
+ 113)
· (4u
35
− 8u
34
+ ··· − 448u
2
− 128)(5u
61
+ u
60
+ ··· − 2062u + 569)
2
c
7
u(u
5
− 3u
4
+ ··· + 4u − 1)(u
13
+ 6u
12
+ ··· + 3u − 1)
2
· (u
35
− 10u
34
+ ··· + 18240u − 2880)
· (u
61
+ 8u
60
+ ··· + 6810u + 724)
2
c
8
, c
10
(u + 1)(u
5
− 2u
3
+ u
2
+ 2u − 1)(u
26
− u
25
+ ··· + u + 1)
· (u
35
− u
34
+ ··· + 13u + 1)(u
122
− 36u
120
+ ··· + 929u + 103)
c
9
(u + 1)(u
5
− 3u
4
+ ··· − u + 1)(u
13
+ 2u
12
+ ··· + 11u + 2)
2
· (u
35
+ 5u
34
+ ··· + 1166u + 268)
· (u
61
− 18u
59
+ ··· − 10865u + 9784)
2
39
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y(y
5
+ y
4
+ ··· + 5y −1)(y
26
+ 11y
25
+ ··· + 10944y + 5184)
· (y
35
− 3y
34
+ ··· + 11136y −576)
· (y
122
+ 18y
121
+ ··· − 1184975y + 15625)
c
2
, c
4
12960000(y −1)(y
5
+ y
4
− y
3
− 4y
2
− 3y −1)
· (1296y
26
− 4608y
25
+ ··· − y + 1)(16y
35
+ 160y
34
+ ··· − 20y −1)
· (625y
122
− 5675y
121
+ ··· − 29y + 1)
c
3
, c
8
, c
10
c
12
(y −1)(y
5
− 4y
4
+ ··· + 6y −1)(y
26
− 19y
25
+ ··· − 19y + 1)
· (y
35
− 23y
34
+ ··· + 217y −1)
· (y
122
− 72y
121
+ ··· − 412519y + 10609)
c
5
, c
11
12960000y
5
(y −1)(36y
13
+ 512y
12
+ ··· + 1550y + 113)
2
· (16y
35
+ 384y
34
+ ··· − 114688y −16384)
· (25y
61
+ 1199y
60
+ ··· − 3158812y −323761)
2
c
7
y(y
5
+ 5y
4
+ ··· − 2y −1)(y
13
− 4y
12
+ ··· + 3y −1)
2
· (y
35
+ 8y
34
+ ··· − 2390400y −8294400)
· (y
61
− 28y
60
+ ··· − 1108164y −524176)
2
c
9
(y −1)(y
5
− y
4
+ ··· + 3y −1)(y
13
− 8y
12
+ ··· + 21y −4)
2
· (y
35
− 9y
34
+ ··· + 179820y −71824)
· (y
61
− 36y
60
+ ··· + 2341110001y −95726656)
2
40
