12a
0712
(K12a
0712
)
A knot diagram
1
Linearized knot diagam
3 8 9 7 1 12 11 2 6 5 4 10
Solving Sequence
4,7 5,11
8 12 6 10 1 9 3 2
c
4
c
7
c
11
c
6
c
10
c
12
c
9
c
3
c
2
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
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).
1
I
u
1
= h1200u
27
− 22896u
26
+ ··· + b − 220937, −220937u
27
+ 3436077u
26
+ ··· + 1003a − 276943727,
u
28
− 21u
27
+ ··· − 8019u + 1003i
I
u
2
= h58u
21
− 1336u
20
+ ··· + b − 184389, −184389u
21
+ 4180402u
20
+ ··· + 4223a + 427232464,
u
22
− 24u
21
+ ··· − 46453u + 4223i
I
u
3
= ha
7
u + 2a
7
− 8a
5
u − 7a
5
− 4a
4
u − a
4
+ 13a
3
u + 8a
3
+ 4a
2
u − 2a
2
− 7au + b − 3a + 3,
a
8
− 3a
6
u − 5a
6
− 3a
5
u − 2a
5
+ 6a
4
u + 7a
4
+ 5a
3
u − 3a
2
u − 4a
2
− 2au + 2a + u + 1, u
2
+ u + 1i
I
u
4
= h466047239a
7
u
3
+ 39554105a
6
u
3
+ ··· + 1099016629a + 1191577537,
5a
6
u
3
− 6a
5
u
3
+ ··· + 8a + 151, u
4
+ u
3
− 2u + 1i
I
u
5
= h1.27748 × 10
33
u
41
+ 1.90856 × 10
34
u
40
+ ··· + 6.44565 × 10
32
b − 1.07355 × 10
33
,
1.07355 × 10
33
u
41
+ 1.73807 × 10
34
u
40
+ ··· + 6.44565 × 10
32
a − 5.56931 × 10
33
, u
42
+ 15u
41
+ ··· − u + 1i
I
u
6
= h32a
7
+ 2a
6
− 9a
5
− 140a
4
+ 168a
3
+ 111a
2
+ 61b + 49a + 13, a
8
− a
6
− 4a
5
+ 6a
4
+ 6a
3
− 5a
2
− a + 2,
u + 1i
I
u
7
= h1.76268 × 10
24
a
11
u
3
− 8.39105 × 10
22
a
10
u
3
+ ··· + 3.22438 × 10
23
a − 1.26409 × 10
24
,
− 4a
11
u
3
+ 14a
10
u
3
+ ··· − 616a − 69, u
4
+ u
3
− 2u + 1i
I
u
8
= h28032a
11
u + 4413a
10
u + ··· + 275661a − 56296, −a
11
u − 5a
10
u + ··· − 2a + 1, u
2
+ u + 1i
I
u
9
= h31947a
11
+ 53734b + ··· + 140465a − 40927,
a
12
+ a
11
− a
10
+ a
9
+ 4a
8
+ 6a
7
− 4a
6
− 21a
5
+ 7a
4
+ 10a
3
− 2a
2
− 2a + 1, u + 1i
I
u
10
= hb − 1, a + 1, u + 1i
I
v
1
= ha, b
4
+ b
2
− b + 1, v − 1i
I
v
2
= ha, b
6
+ b
5
+ 2b
4
+ 2b
3
+ 2b
2
+ 2b + 1, v − 1i
* 12 irreducible components of dim
C
= 0, with total 243 representations.
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I. I
u
1
= h1200u
27
− 22896u
26
+ · · · + b − 220937, −2.21 × 10
5
u
27
+ 3.44 ×
10
6
u
26
+ · · · + 1003a − 2.77 × 10
8
, u
28
− 21u
27
+ · · · − 8019u + 1003i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
5
=
1
−u
2
a
11
=
220.276u
27
− 3425.80u
26
+ ··· − 1.85179 × 10
6
u + 276115.
−1200u
27
+ 22896u
26
+ ··· − 2042510u + 220937
a
8
=
0.500499u
27
− 9.51047u
26
+ ··· + 267.069u − 4.49751
−u
27
+ 20u
26
+ ··· − 4008u + 502
a
12
=
−979.724u
27
+ 19470.2u
26
+ ··· − 3.89430 × 10
6
u + 497052.
−1200u
27
+ 22896u
26
+ ··· − 2042510u + 220937
a
6
=
−0.499501u
27
+ 9.48953u
26
+ ··· − 233.931u − 3.49751
−u
26
+ 19u
25
+ ··· + 3509u − 501
a
10
=
1324.28u
27
− 26401.8u
26
+ ··· + 5.50756 × 10
6
u − 706548.
1022u
27
− 17985u
26
+ ··· − 2603150u + 429561
a
1
=
428.276u
27
− 10015.8u
26
+ ··· + 6.01852 × 10
6
u − 831197.
2277u
27
− 44386u
26
+ ··· + 6582469u − 804129
a
9
=
−1331.36u
27
+ 25723.6u
26
+ ··· − 3.16627 × 10
6
u + 372898.
678u
27
− 14540u
26
+ ··· + 5772856u − 781700
a
3
=
−14.3749u
27
+ 325.872u
26
+ ··· − 186238.u + 25702.1
−48u
27
+ 972u
26
+ ··· − 243822u + 31720
a
2
=
−424.843u
27
+ 8504.71u
26
+ ··· − 1.87799 × 10
6
u + 241784.
134u
27
− 3113u
26
+ ··· + 1909522u − 264635
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1298u
27
− 23514u
26
+ ··· − 1450392u + 283234
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
28
+ 12u
27
+ ··· + 160u + 64
c
2
, c
8
u
28
+ 6u
27
+ ··· + 40u + 8
c
3
u
28
− 6u
27
+ ··· − 28744u + 3880
c
4
, c
12
u
28
+ 21u
27
+ ··· + 8019u + 1003
c
5
, c
7
, c
9
c
11
u
28
− u
27
+ ··· − u + 1
c
6
, c
10
u
28
− u
27
+ ··· − 2u + 10
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
+ 8y
27
+ ··· + 58880y + 4096
c
2
, c
8
y
28
+ 12y
27
+ ··· + 160y + 64
c
3
y
28
+ 4y
27
+ ··· − 22855776y + 15054400
c
4
, c
12
y
28
− 21y
27
+ ··· + 2369061y + 1006009
c
5
, c
7
, c
9
c
11
y
28
+ 9y
27
+ ··· + 35y + 1
c
6
, c
10
y
28
+ 19y
27
+ ··· + 1736y + 100
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.255884 + 0.893158I
a = −0.602738 − 0.627925I
b = −0.406606 + 0.699016I
−1.81341 − 7.68614I 0. + 8.22778I
u = 0.255884 − 0.893158I
a = −0.602738 + 0.627925I
b = −0.406606 − 0.699016I
−1.81341 + 7.68614I 0. − 8.22778I
u = 0.068858 + 0.795615I
a = 0.780549 + 0.451588I
b = 0.305543 − 0.652112I
0.21428 − 2.63147I 2.98987 + 4.53509I
u = 0.068858 − 0.795615I
a = 0.780549 − 0.451588I
b = 0.305543 + 0.652112I
0.21428 + 2.63147I 2.98987 − 4.53509I
u = 0.364425 + 0.513652I
a = −0.885699 − 1.065110I
b = −0.224323 + 0.843093I
−4.24210 − 0.23687I −3.97755 + 0.78715I
u = 0.364425 − 0.513652I
a = −0.885699 + 1.065110I
b = −0.224323 − 0.843093I
−4.24210 + 0.23687I −3.97755 − 0.78715I
u = −0.446227 + 0.363269I
a = 0.739248 − 0.644391I
b = 0.095785 − 0.556090I
0.57015 − 1.33238I 4.21018 + 5.70611I
u = −0.446227 − 0.363269I
a = 0.739248 + 0.644391I
b = 0.095785 + 0.556090I
0.57015 + 1.33238I 4.21018 − 5.70611I
u = 1.30381 + 0.63944I
a = 0.508862 + 0.586733I
b = −0.288283 − 1.090380I
−5.45715 + 1.59172I 0
u = 1.30381 − 0.63944I
a = 0.508862 − 0.586733I
b = −0.288283 + 1.090380I
−5.45715 − 1.59172I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.28320 + 0.83837I
a = 0.717468 + 0.432432I
b = −0.558117 − 1.156400I
−5.20632 + 10.84520I 0
u = 1.28320 − 0.83837I
a = 0.717468 − 0.432432I
b = −0.558117 + 1.156400I
−5.20632 − 10.84520I 0
u = 1.16856 + 1.02636I
a = −1.091200 − 0.031262I
b = 1.24305 + 1.15649I
0.9229 + 21.6752I 0
u = 1.16856 − 1.02636I
a = −1.091200 + 0.031262I
b = 1.24305 − 1.15649I
0.9229 − 21.6752I 0
u = 1.19278 + 1.00782I
a = −1.020190 − 0.114174I
b = 1.10179 + 1.16435I
−1.81840 + 13.23660I 0
u = 1.19278 − 1.00782I
a = −1.020190 + 0.114174I
b = 1.10179 − 1.16435I
−1.81840 − 13.23660I 0
u = 1.18001 + 1.03031I
a = 1.046090 + 0.029745I
b = −1.20375 − 1.11290I
3.3671 + 16.3184I 0
u = 1.18001 − 1.03031I
a = 1.046090 − 0.029745I
b = −1.20375 + 1.11290I
3.3671 − 16.3184I 0
u = 1.38335 + 0.78280I
a = −0.565439 − 0.415823I
b = 0.456694 + 1.017860I
−1.41308 + 6.14508I 0
u = 1.38335 − 0.78280I
a = −0.565439 + 0.415823I
b = 0.456694 − 1.017860I
−1.41308 − 6.14508I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.22841 + 1.05657I
a = 0.884436 + 0.007946I
b = −1.07806 − 0.94423I
5.4565 + 13.1132I 0
u = 1.22841 − 1.05657I
a = 0.884436 − 0.007946I
b = −1.07806 + 0.94423I
5.4565 − 13.1132I 0
u = 1.26956 + 1.06446I
a = −0.794082 − 0.027969I
b = 0.978364 + 0.880777I
4.78086 + 7.54326I 0
u = 1.26956 − 1.06446I
a = −0.794082 + 0.027969I
b = 0.978364 − 0.880777I
4.78086 − 7.54326I 0
u = −1.67808 + 0.17720I
a = 0.033642 − 0.204254I
b = 0.020260 − 0.348715I
5.76082 − 2.91752I 0
u = −1.67808 − 0.17720I
a = 0.033642 + 0.204254I
b = 0.020260 + 0.348715I
5.76082 + 2.91752I 0
u = 1.92546 + 0.15687I
a = −0.060515 − 0.375245I
b = 0.057653 + 0.732010I
4.63509 + 3.17553I 0
u = 1.92546 − 0.15687I
a = −0.060515 + 0.375245I
b = 0.057653 − 0.732010I
4.63509 − 3.17553I 0
8
II. I
u
2
= h58u
21
− 1336u
20
+ · · · + b − 184389, −1.84 × 10
5
u
21
+ 4.18 ×
10
6
u
20
+ · · · + 4223a + 4.27 × 10
8
, u
22
− 24u
21
+ · · · − 46453u + 4223i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
5
=
1
−u
2
a
11
=
43.6630u
21
− 989.913u
20
+ ··· + 1.08626 × 10
6
u − 101168
−58u
21
+ 1336u
20
+ ··· − 1927111u + 184389
a
8
=
0.499882u
21
− 10.9972u
20
+ ··· + 20030.3u − 2105
−u
21
+ 22u
20
+ ··· − 21115u + 2111
a
12
=
−14.3370u
21
+ 346.087u
20
+ ··· − 840852.u + 83221
−58u
21
+ 1336u
20
+ ··· − 1927111u + 184389
a
6
=
0.499882u
21
− 11.9972u
20
+ ··· + 22140.3u − 2106
u
21
− 23u
20
+ ··· + 23227u − 2112
a
10
=
41.6630u
21
− 970.913u
20
+ ··· + 1.66903 × 10
6
u − 161713
2u
21
− 22u
20
+ ··· − 588420u + 61922
a
1
=
72.6630u
21
− 1625.91u
20
+ ··· + 1.23544 × 10
6
u − 108237
−114u
21
+ 2650u
20
+ ··· − 4438373u + 429323
a
9
=
62.9946u
21
− 1471.87u
20
+ ··· + 2.59856 × 10
6
u − 251727
19u
21
− 393u
20
+ ··· − 557436u + 63322
a
3
=
−10.1253u
21
+ 229.006u
20
+ ··· − 152359.u + 12682
−u
21
+ 13u
20
+ ··· + 211150u − 21644
a
2
=
0.468387u
21
− 48.2413u
20
+ ··· + 1.09162 × 10
6
u − 112815
34u
21
− 771u
20
+ ··· + 696795u − 61367
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −166u
21
+ 3833u
20
− 43763u
19
+ 327218u
18
− 1793102u
17
+ 7643905u
16
−
26278137u
15
+ 74562324u
14
− 177325077u
13
+ 357053127u
12
− 612487772u
11
+
897797312u
10
− 1124753307u
9
+ 1201124031u
8
− 1087079978u
7
+ 825843900u
6
−
518873251u
5
+ 263618515u
4
− 104567593u
3
+ 30542893u
2
− 5878416u + 563603
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
11
+ 5u
10
+ ··· + 12u − 16)
2
c
2
, c
8
(u
11
+ 3u
10
+ ··· + 14u + 4)
2
c
3
(u
11
− 3u
10
+ ··· − 122u + 52)
2
c
4
, c
12
u
22
+ 24u
21
+ ··· + 46453u + 4223
c
5
, c
7
, c
9
c
11
u
22
+ 3u
20
+ ··· + 3u + 1
c
6
, c
10
(u
11
− u
9
− u
8
+ u
7
− 2u
5
+ u
3
+ u
2
+ 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
11
+ y
10
+ ··· + 880y −256)
2
c
2
, c
8
(y
11
+ 5y
10
+ ··· + 12y −16)
2
c
3
(y
11
+ 3y
10
+ ··· + 2508y −2704)
2
c
4
, c
12
y
22
− 6y
21
+ ··· − 6355615y + 17833729
c
5
, c
7
, c
9
c
11
y
22
+ 6y
21
+ ··· − 5y + 1
c
6
, c
10
(y
11
− 2y
10
+ 3y
9
− 7y
8
+ 7y
7
− 6y
6
+ 8y
5
− 2y
4
+ y
3
− y
2
− 2y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.569190 + 0.902443I
a = 1.002770 + 0.118181I
b = −0.464117 − 0.972214I
−3.98200 0
u = 0.569190 − 0.902443I
a = 1.002770 − 0.118181I
b = −0.464117 + 0.972214I
−3.98200 0
u = 0.665961 + 0.873592I
a = −1.119080 − 0.226419I
b = 0.547464 + 1.128400I
−7.32685 + 4.12958I 0
u = 0.665961 − 0.873592I
a = −1.119080 + 0.226419I
b = 0.547464 − 1.128400I
−7.32685 − 4.12958I 0
u = 0.965148 + 0.597000I
a = 1.37873 + 0.32939I
b = −1.13404 − 1.14101I
−3.07896 + 4.61958I 0
u = 0.965148 − 0.597000I
a = 1.37873 − 0.32939I
b = −1.13404 + 1.14101I
−3.07896 − 4.61958I 0
u = 0.618130 + 0.998682I
a = −0.898873 − 0.254107I
b = 0.301849 + 1.054760I
−7.32685 − 4.12958I 0
u = 0.618130 − 0.998682I
a = −0.898873 + 0.254107I
b = 0.301849 − 1.054760I
−7.32685 + 4.12958I 0
u = 1.075720 + 0.659234I
a = −1.250770 − 0.261696I
b = 1.17295 + 1.10606I
2.54096 + 7.62702I 0
u = 1.075720 − 0.659234I
a = −1.250770 + 0.261696I
b = 1.17295 − 1.10606I
2.54096 − 7.62702I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.056510 + 0.700607I
a = 1.289360 + 0.212601I
b = −1.21327 − 1.12795I
0.14523 + 13.14880I 0
u = 1.056510 − 0.700607I
a = 1.289360 − 0.212601I
b = −1.21327 + 1.12795I
0.14523 − 13.14880I 0
u = 1.364160 + 0.332809I
a = −0.656827 − 0.739936I
b = 0.649759 + 1.227990I
4.77583 + 3.28335I 0
u = 1.364160 − 0.332809I
a = −0.656827 + 0.739936I
b = 0.649759 − 1.227990I
4.77583 − 3.28335I 0
u = 1.11439 + 1.41811I
a = −0.035380 + 0.452400I
b = 0.680977 − 0.453977I
0.14523 − 13.14880I 0
u = 1.11439 − 1.41811I
a = −0.035380 − 0.452400I
b = 0.680977 + 0.453977I
0.14523 + 13.14880I 0
u = 0.90255 + 1.66935I
a = 0.120689 + 0.278102I
b = 0.355322 − 0.452472I
−3.07896 − 4.61958I 0
u = 0.90255 − 1.66935I
a = 0.120689 − 0.278102I
b = 0.355322 + 0.452472I
−3.07896 + 4.61958I 0
u = 1.17195 + 1.49716I
a = 0.050918 − 0.369879I
b = −0.613442 + 0.357248I
2.54096 − 7.62702I 0
u = 1.17195 − 1.49716I
a = 0.050918 + 0.369879I
b = −0.613442 − 0.357248I
2.54096 + 7.62702I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 2.49630 + 1.36748I
a = 0.1184540 + 0.0089508I
b = −0.283455 − 0.184327I
4.77583 − 3.28335I 0
u = 2.49630 − 1.36748I
a = 0.1184540 − 0.0089508I
b = −0.283455 + 0.184327I
4.77583 + 3.28335I 0
14
III. I
u
3
= ha
7
u − 8a
5
u + · · · − 3a + 3, −3a
6
u − 3a
5
u + · · · + 2a + 1, u
2
+ u + 1i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
5
=
1
u + 1
a
11
=
a
−a
7
u + 8a
5
u + ··· + 3a − 3
a
8
=
a
2
u
a
5
u + a
5
− 4a
3
u − a
3
− 2a
2
u + 3au − 2
a
12
=
−a
7
u + 8a
5
u + ··· + 4a − 3
−a
7
u + 8a
5
u + ··· + 3a − 3
a
6
=
a
5
u − a
3
u + 3a
3
+ a
2
u + a
2
− 3a − 2u
−a
5
+ 3a
3
u + 4a
3
+ 2a
2
u + a
2
− 3au − 3a + 2
a
10
=
−a
7
u + 8a
5
u + ··· + 3a − 3
−3a
7
u + 15a
5
u + ··· − a − 6
a
1
=
−2a
7
u + 7a
5
u + ··· − 2a − 3
−a
7
u − a
5
u + ··· + 4a
2
− 6a
a
9
=
a
3
u + a
3
− 2au − a
−a
7
u + 8a
5
u + ··· + 4a − 3
a
3
=
−a
7
u + 5a
5
u + ··· + 3a − 2
−a
7
u + 9a
5
u + ··· + 4a − 4
a
2
=
−a
7
u + 5a
5
u + ··· + 4a − 2
a
7
u + 2a
5
u + ··· + 6a − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −8a
7
u−4a
7
−4a
6
+24a
5
u−8a
5
+16a
4
u+ 4a
4
−4a
3
u+ 32a
3
+4a
2
u+ 12a
2
−8au −8a−4u+2
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
4
c
2
, c
8
(u
4
+ u
2
+ u + 1)
4
c
3
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
4
c
4
, c
12
(u
2
− u + 1)
8
c
5
, c
7
, c
9
c
11
u
16
− u
14
+ ··· + 6u + 1
c
6
, c
10
u
16
− 5u
14
+ ··· − 48u + 13
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
4
c
2
, c
8
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
4
c
3
(y
4
− y
3
+ 2y
2
+ 7y + 4)
4
c
4
, c
12
(y
2
+ y + 1)
8
c
5
, c
7
, c
9
c
11
y
16
− 2y
15
+ ··· − 8y + 1
c
6
, c
10
y
16
− 10y
15
+ ··· − 120y + 169
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 1.001440 + 0.170413I
b = −1.42920 + 0.60080I
0.98010 − 5.45685I 3.77019 + 10.79556I
u = −0.500000 + 0.866025I
a = 0.920317 + 0.321873I
b = −0.505431 − 0.130828I
0.98010 − 2.66268I 3.77019 + 3.06084I
u = −0.500000 + 0.866025I
a = −1.073320 + 0.161507I
b = 1.64121 − 1.09663I
−2.62503 − 11.70310I −1.77019 + 13.43907I
u = −0.500000 + 0.866025I
a = −1.294380 + 0.345375I
b = −0.348905 − 0.259137I
−2.62503 + 3.58361I −1.77019 + 0.41733I
u = −0.500000 + 0.866025I
a = −0.139416 − 0.503130I
b = 0.738909 − 0.636081I
0.98010 − 2.66268I 3.77019 + 3.06084I
u = −0.500000 + 0.866025I
a = −1.23491 − 0.93732I
b = 0.648300 − 0.782062I
0.98010 − 5.45685I 3.77019 + 10.79556I
u = −0.500000 + 0.866025I
a = 0.049967 − 0.431729I
b = −0.348088 + 1.293660I
−2.62503 + 3.58361I −1.77019 + 0.41733I
u = −0.500000 + 0.866025I
a = 1.77032 + 0.87301I
b = −0.396792 + 1.010280I
−2.62503 − 11.70310I −1.77019 + 13.43907I
u = −0.500000 − 0.866025I
a = 1.001440 − 0.170413I
b = −1.42920 − 0.60080I
0.98010 + 5.45685I 3.77019 − 10.79556I
u = −0.500000 − 0.866025I
a = 0.920317 − 0.321873I
b = −0.505431 + 0.130828I
0.98010 + 2.66268I 3.77019 − 3.06084I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 − 0.866025I
a = −1.073320 − 0.161507I
b = 1.64121 + 1.09663I
−2.62503 + 11.70310I −1.77019 − 13.43907I
u = −0.500000 − 0.866025I
a = −1.294380 − 0.345375I
b = −0.348905 + 0.259137I
−2.62503 − 3.58361I −1.77019 − 0.41733I
u = −0.500000 − 0.866025I
a = −0.139416 + 0.503130I
b = 0.738909 + 0.636081I
0.98010 + 2.66268I 3.77019 − 3.06084I
u = −0.500000 − 0.866025I
a = −1.23491 + 0.93732I
b = 0.648300 + 0.782062I
0.98010 + 5.45685I 3.77019 − 10.79556I
u = −0.500000 − 0.866025I
a = 0.049967 + 0.431729I
b = −0.348088 − 1.293660I
−2.62503 − 3.58361I −1.77019 − 0.41733I
u = −0.500000 − 0.866025I
a = 1.77032 − 0.87301I
b = −0.396792 − 1.010280I
−2.62503 + 11.70310I −1.77019 − 13.43907I
19
IV. I
u
4
= h4.66 × 10
8
a
7
u
3
+ 3.96 × 10
7
a
6
u
3
+ · · · + 1.10 × 10
9
a + 1.19 ×
10
9
, 5a
6
u
3
− 6a
5
u
3
+ · · · + 8a + 151, u
4
+ u
3
− 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
5
=
1
−u
2
a
11
=
a
−1.19133a
7
u
3
− 0.101110a
6
u
3
+ ··· − 2.80935a − 3.04596
a
8
=
a
2
u
0.747094a
7
u
3
+ 1.26829a
6
u
3
+ ··· − 1.44020a − 0.455661
a
12
=
−1.19133a
7
u
3
− 0.101110a
6
u
3
+ ··· − 1.80935a − 3.04596
−1.19133a
7
u
3
− 0.101110a
6
u
3
+ ··· − 2.80935a − 3.04596
a
6
=
−1.64138a
7
u
3
− 1.21333a
6
u
3
+ ··· + 1.06681a − 0.725432
−2.38847a
7
u
3
− 2.48162a
6
u
3
+ ··· + 2.50700a − 0.269771
a
10
=
−1.19133a
7
u
3
− 0.101110a
6
u
3
+ ··· − 1.80935a − 3.04596
−0.189051a
7
u
3
+ 1.44010a
6
u
3
+ ··· − 2.87624a − 0.702324
a
1
=
−2.04568a
7
u
3
− 0.255362a
6
u
3
+ ··· − 3.42226a + 5.35118
−1.94824a
7
u
3
+ 0.693009a
6
u
3
+ ··· − 3.47520a + 2.00606
a
9
=
0.750635a
7
u
3
+ 0.917910a
6
u
3
+ ··· + 2.93356a − 3.60664
2.55051a
7
u
3
+ 1.09438a
6
u
3
+ ··· + 0.923181a + 1.14900
a
3
=
1.45888a
7
u
3
+ 1.41417a
6
u
3
+ ··· + 3.04678a + 1.31020
3.29760a
7
u
3
+ 2.36267a
6
u
3
+ ··· − 0.517014a + 1.69334
a
2
=
3.35619a
7
u
3
+ 2.53901a
6
u
3
+ ··· + 0.983459a + 2.72072
2.69534a
7
u
3
+ 0.575282a
6
u
3
+ ··· + 2.03500a − 1.46172
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
226626196
391199161
a
7
u
3
+
812287948
391199161
a
6
u
3
+ ··· −
1739775136
391199161
a +
15821222826
391199161
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
8
c
2
, c
8
(u
4
+ u
2
+ u + 1)
8
c
3
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
8
c
4
, c
12
(u
4
− u
3
+ 2u + 1)
8
c
5
, c
7
, c
9
c
11
u
32
− 7u
30
+ ··· − 62u + 19
c
6
, c
10
(u
16
+ 7u
14
+ ··· + 50u + 19)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
8
c
2
, c
8
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
8
c
3
(y
4
− y
3
+ 2y
2
+ 7y + 4)
8
c
4
, c
12
(y
4
− y
3
+ 6y
2
− 4y + 1)
8
c
5
, c
7
, c
9
c
11
y
32
− 14y
31
+ ··· − 13914y + 361
c
6
, c
10
(y
16
+ 14y
15
+ ··· + 1984y + 361)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621964 + 0.187730I
a = −0.977151 + 0.454354I
b = 0.77300 + 1.30665I
4.26996 + 2.66268I 15.7702 − 3.0608I
u = 0.621964 + 0.187730I
a = −1.210180 + 0.185764I
b = 1.78156 − 1.57240I
0.66484 + 11.70310I 10.2298 − 13.4391I
u = 0.621964 + 0.187730I
a = 0.673950 + 0.107343I
b = −0.90454 + 1.57461I
4.26996 + 5.45685I 15.7702 − 10.7956I
u = 0.621964 + 0.187730I
a = 1.81059 − 0.09585I
b = −1.58749 − 0.84779I
0.66484 − 3.58361I 10.22981 − 0.41733I
u = 0.621964 + 0.187730I
a = −1.72022 − 1.58162I
b = 0.693049 − 0.099151I
4.26996 + 2.66268I 15.7702 − 3.0608I
u = 0.621964 + 0.187730I
a = 2.71633 + 0.54320I
b = −1.144120 − 0.280285I
0.66484 − 3.58361I 10.22981 − 0.41733I
u = 0.621964 + 0.187730I
a = 0.63256 − 2.72260I
b = −0.399022 − 0.193284I
4.26996 + 5.45685I 15.7702 − 10.7956I
u = 0.621964 + 0.187730I
a = −1.92588 + 3.10942I
b = 0.787562 + 0.111649I
0.66484 + 11.70310I 10.2298 − 13.4391I
u = 0.621964 − 0.187730I
a = −0.977151 − 0.454354I
b = 0.77300 − 1.30665I
4.26996 − 2.66268I 15.7702 + 3.0608I
u = 0.621964 − 0.187730I
a = −1.210180 − 0.185764I
b = 1.78156 + 1.57240I
0.66484 − 11.70310I 10.2298 + 13.4391I
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621964 − 0.187730I
a = 0.673950 − 0.107343I
b = −0.90454 − 1.57461I
4.26996 − 5.45685I 15.7702 + 10.7956I
u = 0.621964 − 0.187730I
a = 1.81059 + 0.09585I
b = −1.58749 + 0.84779I
0.66484 + 3.58361I 10.22981 + 0.41733I
u = 0.621964 − 0.187730I
a = −1.72022 + 1.58162I
b = 0.693049 + 0.099151I
4.26996 − 2.66268I 15.7702 + 3.0608I
u = 0.621964 − 0.187730I
a = 2.71633 − 0.54320I
b = −1.144120 + 0.280285I
0.66484 + 3.58361I 10.22981 + 0.41733I
u = 0.621964 − 0.187730I
a = 0.63256 + 2.72260I
b = −0.399022 + 0.193284I
4.26996 − 5.45685I 15.7702 + 10.7956I
u = 0.621964 − 0.187730I
a = −1.92588 − 3.10942I
b = 0.787562 − 0.111649I
0.66484 − 11.70310I 10.2298 + 13.4391I
u = −1.12196 + 1.05376I
a = 0.979313 + 0.156439I
b = −1.207890 + 0.522688I
4.26996 − 5.45685I 15.7702 + 10.7956I
u = −1.12196 + 1.05376I
a = −1.077380 + 0.148392I
b = 1.121690 − 0.779857I
0.66484 − 11.70310I 10.2298 + 13.4391I
u = −1.12196 + 1.05376I
a = 0.878049 + 0.129588I
b = −1.05242 + 1.30179I
0.66484 − 11.70310I 10.2298 + 13.4391I
u = −1.12196 + 1.05376I
a = −0.804489 − 0.289712I
b = 1.26360 − 0.85644I
4.26996 − 5.45685I 15.7702 + 10.7956I
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.12196 + 1.05376I
a = 0.649337 + 0.477773I
b = −0.902753 + 0.226276I
4.26996 − 2.66268I 15.7702 + 3.0608I
u = −1.12196 + 1.05376I
a = −0.528150 − 0.294364I
b = 1.231990 − 0.148198I
4.26996 − 2.66268I 15.7702 + 3.0608I
u = −1.12196 + 1.05376I
a = −0.183232 − 0.497918I
b = 0.276041 + 0.099305I
0.66484 + 3.58361I 10.22981 + 0.41733I
u = −1.12196 + 1.05376I
a = 0.086554 + 0.169802I
b = −0.730263 − 0.365565I
0.66484 + 3.58361I 10.22981 + 0.41733I
u = −1.12196 − 1.05376I
a = 0.979313 − 0.156439I
b = −1.207890 − 0.522688I
4.26996 + 5.45685I 15.7702 − 10.7956I
u = −1.12196 − 1.05376I
a = −1.077380 − 0.148392I
b = 1.121690 + 0.779857I
0.66484 + 11.70310I 10.2298 − 13.4391I
u = −1.12196 − 1.05376I
a = 0.878049 − 0.129588I
b = −1.05242 − 1.30179I
0.66484 + 11.70310I 10.2298 − 13.4391I
u = −1.12196 − 1.05376I
a = −0.804489 + 0.289712I
b = 1.26360 + 0.85644I
4.26996 + 5.45685I 15.7702 − 10.7956I
u = −1.12196 − 1.05376I
a = 0.649337 − 0.477773I
b = −0.902753 − 0.226276I
4.26996 + 2.66268I 15.7702 − 3.0608I
u = −1.12196 − 1.05376I
a = −0.528150 + 0.294364I
b = 1.231990 + 0.148198I
4.26996 + 2.66268I 15.7702 − 3.0608I
25
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.12196 − 1.05376I
a = −0.183232 + 0.497918I
b = 0.276041 − 0.099305I
0.66484 − 3.58361I 10.22981 − 0.41733I
u = −1.12196 − 1.05376I
a = 0.086554 − 0.169802I
b = −0.730263 + 0.365565I
0.66484 − 3.58361I 10.22981 − 0.41733I
26
V.
I
u
5
= h1.28 × 10
33
u
41
+ 1.91 × 10
34
u
40
+ · · · + 6.45 × 10
32
b − 1.07 × 10
33
, 1.07 ×
10
33
u
41
+1.74×10
34
u
40
+· · ·+6.45×10
32
a−5.57×10
33
, u
42
+15u
41
+· · ·−u+1i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
5
=
1
−u
2
a
11
=
−1.66554u
41
− 26.9650u
40
+ ··· − 3.84330u + 8.64041
−1.98193u
41
− 29.6101u
40
+ ··· + 6.97487u + 1.66554
a
8
=
−8.53838u
41
− 121.963u
40
+ ··· + 37.4134u − 17.0826
6.11285u
41
+ 88.3892u
40
+ ··· − 24.6209u + 8.53838
a
12
=
−3.64747u
41
− 56.5751u
40
+ ··· + 3.13158u + 10.3059
−1.98193u
41
− 29.6101u
40
+ ··· + 6.97487u + 1.66554
a
6
=
0.383756u
41
+ 7.30611u
40
+ ··· + 0.822780u − 6.11865
2.80928u
41
+ 40.8797u
40
+ ··· − 9.96971u + 2.42553
a
10
=
−3.52865u
41
− 55.7576u
40
+ ··· + 2.81519u + 12.2879
−0.485887u
41
− 8.91958u
40
+ ··· + 5.95760u + 0.819692
a
1
=
−7.94641u
41
− 115.880u
40
+ ··· + 27.8228u − 12.5337
3.66038u
41
+ 52.3024u
40
+ ··· − 20.0368u + 8.68418
a
9
=
4.25719u
41
+ 64.1917u
40
+ ··· − 7.34303u − 0.456602
−1.01130u
41
− 14.1686u
40
+ ··· + 10.3749u − 6.00626
a
3
=
7.79160u
41
+ 111.524u
40
+ ··· − 42.9937u + 17.6407
−8.57486u
41
− 123.729u
40
+ ··· + 34.0005u − 10.9299
a
2
=
23.1394u
41
+ 328.560u
40
+ ··· − 94.7998u + 47.3295
−15.7355u
41
− 226.885u
40
+ ··· + 59.6762u − 19.9526
(ii) Obstruction class = 1
(iii) Cusp Shapes = 90.5206u
41
+ 1300.34u
40
+ ··· − 351.273u + 134.214
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
21
− 11u
20
+ ··· − 2u + 1)
2
c
2
, c
8
u
42
+ 11u
40
+ ··· − 2u
2
− 1
c
3
u
42
+ 5u
40
+ ··· + 14u
2
− 1
c
4
u
42
+ 15u
41
+ ··· − u + 1
c
5
, c
9
u
42
+ 3u
41
+ ··· + 5u + 1
c
6
, c
10
u
42
+ 12u
40
+ ··· + 29u
2
− 1
c
7
, c
11
u
42
− 3u
41
+ ··· − 5u + 1
c
12
u
42
− 15u
41
+ ··· + u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
21
+ 5y
20
+ ··· + 14y −1)
2
c
2
, c
8
(y
21
+ 11y
20
+ ··· − 2y −1)
2
c
3
(y
21
+ 5y
20
+ ··· + 14y −1)
2
c
4
, c
12
y
42
− 25y
41
+ ··· − 17y + 1
c
5
, c
7
, c
9
c
11
y
42
− 15y
41
+ ··· + 43y + 1
c
6
, c
10
(y
21
+ 12y
20
+ ··· + 29y −1)
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.843299
a = −1.41614
b = 1.19423
3.24670 13.8130
u = −1.23223
a = −0.653952
b = 0.805821
3.24670 0
u = −0.574753 + 0.504148I
a = 1.72067 + 0.51327I
b = −1.247720 + 0.572473I
−1.90716 − 4.43445I −1.93239 + 10.23598I
u = −0.574753 − 0.504148I
a = 1.72067 − 0.51327I
b = −1.247720 − 0.572473I
−1.90716 + 4.43445I −1.93239 − 10.23598I
u = −0.863744 + 0.908039I
a = 1.010870 − 0.008849I
b = −0.865097 + 0.925552I
−2.24999 − 3.58506I 0
u = −0.863744 − 0.908039I
a = 1.010870 + 0.008849I
b = −0.865097 − 0.925552I
−2.24999 + 3.58506I 0
u = 0.593725 + 0.363088I
a = 0.635051 + 0.944176I
b = 0.034226 + 0.791160I
3.40776 + 3.10864I 6.48262 − 8.04147I
u = 0.593725 − 0.363088I
a = 0.635051 − 0.944176I
b = 0.034226 − 0.791160I
3.40776 − 3.10864I 6.48262 + 8.04147I
u = −0.996147 + 0.881069I
a = −1.068970 + 0.009212I
b = 1.05673 − 0.95101I
2.09472 − 6.24827I 0
u = −0.996147 − 0.881069I
a = −1.068970 − 0.009212I
b = 1.05673 + 0.95101I
2.09472 + 6.24827I 0
30
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.664367 + 0.045163I
a = 2.13243 + 0.63238I
b = −1.44528 − 0.32383I
0.45068 − 4.20753I 6.6007 + 13.6446I
u = −0.664367 − 0.045163I
a = 2.13243 − 0.63238I
b = −1.44528 + 0.32383I
0.45068 + 4.20753I 6.6007 − 13.6446I
u = −0.978913 + 0.920650I
a = 1.107530 − 0.022551I
b = −1.06342 + 1.04173I
−0.25722 − 11.15780I 0
u = −0.978913 − 0.920650I
a = 1.107530 + 0.022551I
b = −1.06342 − 1.04173I
−0.25722 + 11.15780I 0
u = −0.017661 + 0.632268I
a = 0.00455 − 1.57428I
b = 0.995289 + 0.030682I
−2.24999 − 3.58506I −0.59837 + 3.73397I
u = −0.017661 − 0.632268I
a = 0.00455 + 1.57428I
b = 0.995289 − 0.030682I
−2.24999 + 3.58506I −0.59837 − 3.73397I
u = 0.334034 + 0.500387I
a = −1.27714 + 0.71003I
b = −0.781900 − 0.401892I
2.09472 − 6.24827I 5.90455 + 4.30327I
u = 0.334034 − 0.500387I
a = −1.27714 − 0.71003I
b = −0.781900 + 0.401892I
2.09472 + 6.24827I 5.90455 − 4.30327I
u = 0.557686 + 0.004861I
a = −0.58961 − 1.46487I
b = −0.321698 − 0.819806I
3.78104 − 4.89859I 6.74639 + 0.46418I
u = 0.557686 − 0.004861I
a = −0.58961 + 1.46487I
b = −0.321698 + 0.819806I
3.78104 + 4.89859I 6.74639 − 0.46418I
31
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42771 + 0.25315I
a = −0.444722 + 0.820962I
b = 0.427103 − 1.284680I
4.76533 − 3.36777I 0
u = −1.42771 − 0.25315I
a = −0.444722 − 0.820962I
b = 0.427103 + 1.284680I
4.76533 + 3.36777I 0
u = −0.60496 + 1.34098I
a = −0.420247 − 0.131204I
b = 0.430177 − 0.484171I
−1.90716 − 4.43445I 0
u = −0.60496 − 1.34098I
a = −0.420247 + 0.131204I
b = 0.430177 + 0.484171I
−1.90716 + 4.43445I 0
u = −1.06621 + 1.02009I
a = 0.917361 + 0.381399I
b = −1.36717 + 0.52914I
2.45161 − 0.89322I 0
u = −1.06621 − 1.02009I
a = 0.917361 − 0.381399I
b = −1.36717 − 0.52914I
2.45161 + 0.89322I 0
u = −1.09969 + 0.99358I
a = −0.894840 − 0.241819I
b = 1.224310 − 0.623167I
3.78104 − 4.89859I 0
u = −1.09969 − 0.99358I
a = −0.894840 + 0.241819I
b = 1.224310 + 0.623167I
3.78104 + 4.89859I 0
u = 0.436024 + 0.274043I
a = −1.02640 − 1.58737I
b = −0.012529 − 0.973412I
2.28921 + 6.86346I −0.50086 − 9.25967I
u = 0.436024 − 0.274043I
a = −1.02640 + 1.58737I
b = −0.012529 + 0.973412I
2.28921 − 6.86346I −0.50086 + 9.25967I
32
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.05789 + 1.07412I
a = 0.741922 + 0.468741I
b = −1.288360 + 0.301037I
2.28921 − 6.86346I 0
u = −1.05789 − 1.07412I
a = 0.741922 − 0.468741I
b = −1.288360 − 0.301037I
2.28921 + 6.86346I 0
u = 0.219100 + 0.415395I
a = 1.81651 − 1.35538I
b = 0.961016 + 0.457604I
−0.25722 − 11.15780I 2.12054 + 8.30958I
u = 0.219100 − 0.415395I
a = 1.81651 + 1.35538I
b = 0.961016 − 0.457604I
−0.25722 + 11.15780I 2.12054 − 8.30958I
u = 0.435293 + 0.085043I
a = 0.12294 − 2.34678I
b = 0.253094 − 1.011080I
2.45161 + 0.89322I 0.23604 + 3.59460I
u = 0.435293 − 0.085043I
a = 0.12294 + 2.34678I
b = 0.253094 + 1.011080I
2.45161 − 0.89322I 0.23604 − 3.59460I
u = −1.10590 + 1.11558I
a = −0.640202 − 0.361768I
b = 1.111580 − 0.314119I
3.40776 − 3.10864I 0
u = −1.10590 − 1.11558I
a = −0.640202 + 0.361768I
b = 1.111580 + 0.314119I
3.40776 + 3.10864I 0
u = −1.49469 + 0.63238I
a = 0.222955 + 0.313790I
b = −0.531685 − 0.328025I
0.45068 + 4.20753I 0
u = −1.49469 − 0.63238I
a = 0.222955 − 0.313790I
b = −0.531685 + 0.328025I
0.45068 − 4.20753I 0
33
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 2.91453 + 0.82313I
a = −0.0356095 − 0.0426239I
b = −0.068700 − 0.153540I
4.76533 − 3.36777I 0
u = 2.91453 − 0.82313I
a = −0.0356095 + 0.0426239I
b = −0.068700 + 0.153540I
4.76533 + 3.36777I 0
34
VI.
I
u
6
= h32a
7
+61b +· · ·+49a + 13, a
8
−a
6
−4a
5
+6a
4
+6a
3
−5a
2
−a +2, u+1i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
−1
a
5
=
1
−1
a
11
=
a
−0.524590a
7
− 0.0327869a
6
+ ··· − 0.803279a − 0.213115
a
8
=
−a
2
0.0327869a
7
+ 0.377049a
6
+ ··· + 0.737705a − 2.04918
a
12
=
−0.524590a
7
− 0.0327869a
6
+ ··· + 0.196721a − 0.213115
−0.524590a
7
− 0.0327869a
6
+ ··· − 0.803279a − 0.213115
a
6
=
−0.0327869a
7
− 0.377049a
6
+ ··· − 0.737705a + 2.04918
−0.0655738a
7
− 0.754098a
6
+ ··· − 1.47541a + 2.09836
a
10
=
−0.524590a
7
− 0.0327869a
6
+ ··· + 1.19672a − 0.213115
−a
a
1
=
−a
−0.524590a
7
− 0.0327869a
6
+ ··· + 0.196721a − 0.213115
a
9
=
−0.147541a
7
− 0.196721a
6
+ ··· − 0.819672a − 0.278689
0.754098a
7
− 0.327869a
6
+ ··· − 3.03279a − 0.131148
a
3
=
0.213115a
7
− 0.0491803a
6
+ ··· − 1.70492a + 0.180328
0.786885a
7
+ 0.0491803a
6
+ ··· − 2.29508a − 1.18033
a
2
=
0.590164a
7
− 0.213115a
6
+ ··· − 2.72131a + 0.114754
0.557377a
7
+ 0.409836a
6
+ ··· + 0.540984a − 0.836066
(ii) Obstruction class = −1
(iii) Cusp Shapes =
48
61
a
7
−
180
61
a
6
−
44
61
a
5
−
88
61
a
4
+
984
61
a
3
−
840
61
a
2
−
872
61
a +
1270
61
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
2
c
2
, c
8
(u
4
+ u
2
+ u + 1)
2
c
3
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
2
c
4
, c
12
(u − 1)
8
c
5
, c
7
, c
9
c
11
u
8
− u
6
− 4u
5
+ 6u
4
+ 6u
3
− 5u
2
− u + 2
c
6
, c
10
(u
4
+ u
2
− u + 1)
2
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
2
c
2
, c
6
, c
8
c
10
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
2
c
3
(y
4
− y
3
+ 2y
2
+ 7y + 4)
2
c
4
, c
12
(y −1)
8
c
5
, c
7
, c
9
c
11
y
8
− 2y
7
+ 13y
6
− 38y
5
+ 98y
4
− 108y
3
+ 61y
2
− 21y + 4
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.771666 + 0.090528I
b = 1.31909 − 0.67618I
4.26996 − 1.39709I 15.7702 + 3.8674I
u = −1.00000
a = −0.771666 − 0.090528I
b = 1.31909 + 0.67618I
4.26996 + 1.39709I 15.7702 − 3.8674I
u = −1.00000
a = 0.548048 + 0.372915I
b = −1.09547 − 1.49379I
0.66484 + 7.64338I 10.22981 − 6.51087I
u = −1.00000
a = 0.548048 − 0.372915I
b = −1.09547 + 1.49379I
0.66484 − 7.64338I 10.22981 + 6.51087I
u = −1.00000
a = 1.31909 + 0.67618I
b = −0.771666 − 0.090528I
4.26996 + 1.39709I 15.7702 − 3.8674I
u = −1.00000
a = 1.31909 − 0.67618I
b = −0.771666 + 0.090528I
4.26996 − 1.39709I 15.7702 + 3.8674I
u = −1.00000
a = −1.09547 + 1.49379I
b = 0.548048 − 0.372915I
0.66484 − 7.64338I 10.22981 + 6.51087I
u = −1.00000
a = −1.09547 − 1.49379I
b = 0.548048 + 0.372915I
0.66484 + 7.64338I 10.22981 − 6.51087I
38
VII. I
u
7
= h1.76 × 10
24
a
11
u
3
− 8.39 × 10
22
a
10
u
3
+ · · · + 3.22 × 10
23
a − 1.26 ×
10
24
, −4a
11
u
3
+ 14a
10
u
3
+ · · · − 616a − 69, u
4
+ u
3
− 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
5
=
1
−u
2
a
11
=
a
−5.34716a
11
u
3
+ 0.254545a
10
u
3
+ ··· − 0.978124a + 3.83467
a
8
=
a
2
u
−3.04118a
11
u
3
− 1.15528a
10
u
3
+ ··· + 3.04555a + 0.377772
a
12
=
−5.34716a
11
u
3
+ 0.254545a
10
u
3
+ ··· + 0.0218757a + 3.83467
−5.34716a
11
u
3
+ 0.254545a
10
u
3
+ ··· − 0.978124a + 3.83467
a
6
=
0.501622a
11
u
3
− 2.39878a
10
u
3
+ ··· − 1.19856a − 0.394662
3.54280a
11
u
3
− 1.24351a
10
u
3
+ ··· − 4.24411a − 0.772434
a
10
=
−5.34716a
11
u
3
+ 0.254545a
10
u
3
+ ··· + 0.0218757a + 3.83467
9.09783a
11
u
3
+ 1.26462a
10
u
3
+ ··· − 0.788236a + 1.54331
a
1
=
−9.75458a
11
u
3
+ 0.321737a
10
u
3
+ ··· − 2.83633a − 2.93560
−2.98430a
11
u
3
+ 1.07383a
10
u
3
+ ··· − 2.71867a − 1.07643
a
9
=
−10.4447a
11
u
3
+ 3.59920a
10
u
3
+ ··· + 4.39400a + 2.72104
−19.4996a
11
u
3
− 3.15835a
10
u
3
+ ··· + 3.17653a + 0.490005
a
3
=
13.6981a
11
u
3
+ 4.12977a
10
u
3
+ ··· − 11.3469a − 0.656610
5.98651a
11
u
3
+ 5.94550a
10
u
3
+ ··· − 5.99717a + 0.401935
a
2
=
7.00872a
11
u
3
+ 5.13524a
10
u
3
+ ··· − 10.9359a − 0.321431
9.33703a
11
u
3
+ 8.36219a
10
u
3
+ ··· − 6.36694a + 1.00508
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1444257646756578282612
18516478257642672247
a
11
u
3
−
233926054440874263756
18516478257642672247
a
10
u
3
+ ··· +
235272260902340315932
18516478257642672247
a +
443655158928766892178
18516478257642672247
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
8
c
2
, c
8
(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
8
c
3
(u
3
− u
2
+ 1)
16
c
4
, c
12
(u
4
− u
3
+ 2u + 1)
12
c
5
, c
7
, c
9
c
11
u
48
+ u
47
+ ··· − 38u + 19
c
6
, c
10
(u
24
+ u
23
+ ··· + 38u + 19)
2
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
8
c
2
, c
8
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
8
c
3
(y
3
− y
2
+ 2y −1)
16
c
4
, c
12
(y
4
− y
3
+ 6y
2
− 4y + 1)
12
c
5
, c
7
, c
9
c
11
y
48
− 21y
47
+ ··· − 28424y + 361
c
6
, c
10
(y
24
+ 21y
23
+ ··· + 6156y + 361)
2
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621964 + 0.187730I
a = 1.129810 − 0.076852I
b = −1.57648 + 1.49241I
3.02413 + 6.88789I 13.5098 − 9.9077I
u = 0.621964 + 0.187730I
a = −1.359640 − 0.038104I
b = 1.75603 − 1.11814I
−1.11345 + 4.05977I 6.98049 − 6.92820I
u = 0.621964 + 0.187730I
a = 0.552012 − 0.200535I
b = −0.44814 − 1.66379I
3.02413 + 6.88789I 13.5098 − 9.9077I
u = 0.621964 + 0.187730I
a = −0.263646 − 0.039356I
b = 0.46064 − 1.80744I
3.02413 + 1.23164I 13.50976 − 3.94876I
u = 0.621964 + 0.187730I
a = −1.71804 + 0.33117I
b = 1.31093 + 0.91437I
3.02413 + 1.23164I 13.50976 − 3.94876I
u = 0.621964 + 0.187730I
a = 1.90388 + 0.35114I
b = −1.56087 + 0.06760I
−1.11345 + 4.05977I 6.98049 − 6.92820I
u = 0.621964 + 0.187730I
a = 2.26997 − 0.79384I
b = −1.118230 − 0.575815I
−1.11345 + 4.05977I 6.98049 − 6.92820I
u = 0.621964 + 0.187730I
a = −2.33842 − 0.76431I
b = 1.130730 + 0.116552I
3.02413 + 1.23164I 13.50976 − 3.94876I
u = 0.621964 + 0.187730I
a = 1.40037 + 2.25238I
b = −0.380978 + 0.021096I
3.02413 + 6.88789I 13.5098 − 9.9077I
u = 0.621964 + 0.187730I
a = 0.12513 + 2.86825I
b = 0.156590 + 0.073972I
3.02413 + 1.23164I 13.50976 − 3.94876I
42
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621964 + 0.187730I
a = −2.09030 + 2.42869I
b = 0.838495 + 0.278945I
−1.11345 + 4.05977I 6.98049 − 6.92820I
u = 0.621964 + 0.187730I
a = 1.65925 − 2.90033I
b = −0.717127 − 0.164300I
3.02413 + 6.88789I 13.5098 − 9.9077I
u = 0.621964 − 0.187730I
a = 1.129810 + 0.076852I
b = −1.57648 − 1.49241I
3.02413 − 6.88789I 13.5098 + 9.9077I
u = 0.621964 − 0.187730I
a = −1.359640 + 0.038104I
b = 1.75603 + 1.11814I
−1.11345 − 4.05977I 6.98049 + 6.92820I
u = 0.621964 − 0.187730I
a = 0.552012 + 0.200535I
b = −0.44814 + 1.66379I
3.02413 − 6.88789I 13.5098 + 9.9077I
u = 0.621964 − 0.187730I
a = −0.263646 + 0.039356I
b = 0.46064 + 1.80744I
3.02413 − 1.23164I 13.50976 + 3.94876I
u = 0.621964 − 0.187730I
a = −1.71804 − 0.33117I
b = 1.31093 − 0.91437I
3.02413 − 1.23164I 13.50976 + 3.94876I
u = 0.621964 − 0.187730I
a = 1.90388 − 0.35114I
b = −1.56087 − 0.06760I
−1.11345 − 4.05977I 6.98049 + 6.92820I
u = 0.621964 − 0.187730I
a = 2.26997 + 0.79384I
b = −1.118230 + 0.575815I
−1.11345 − 4.05977I 6.98049 + 6.92820I
u = 0.621964 − 0.187730I
a = −2.33842 + 0.76431I
b = 1.130730 − 0.116552I
3.02413 − 1.23164I 13.50976 + 3.94876I
43
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621964 − 0.187730I
a = 1.40037 − 2.25238I
b = −0.380978 − 0.021096I
3.02413 − 6.88789I 13.5098 + 9.9077I
u = 0.621964 − 0.187730I
a = 0.12513 − 2.86825I
b = 0.156590 − 0.073972I
3.02413 − 1.23164I 13.50976 + 3.94876I
u = 0.621964 − 0.187730I
a = −2.09030 − 2.42869I
b = 0.838495 − 0.278945I
−1.11345 − 4.05977I 6.98049 + 6.92820I
u = 0.621964 − 0.187730I
a = 1.65925 + 2.90033I
b = −0.717127 + 0.164300I
3.02413 − 6.88789I 13.5098 + 9.9077I
u = −1.12196 + 1.05376I
a = 1.022580 − 0.081870I
b = −1.119460 + 0.700856I
3.02413 − 6.88789I 13.5098 + 9.9077I
u = −1.12196 + 1.05376I
a = −0.994199 − 0.313700I
b = 1.266430 − 0.421436I
3.02413 − 1.23164I 13.50976 + 3.94876I
u = −1.12196 + 1.05376I
a = −0.802294 − 0.507994I
b = 1.113020 − 0.216287I
3.02413 − 6.88789I 13.5098 + 9.9077I
u = −1.12196 + 1.05376I
a = −0.898391 + 0.192258I
b = 0.965603 − 0.703775I
−1.11345 − 4.05977I 6.98049 + 6.92820I
u = −1.12196 + 1.05376I
a = 0.787176 + 0.363697I
b = −1.44602 + 0.69568I
3.02413 − 1.23164I 13.50976 + 3.94876I
u = −1.12196 + 1.05376I
a = −0.841854 − 0.166006I
b = 1.06102 − 1.16940I
3.02413 − 6.88789I 13.5098 + 9.9077I
44
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −1.12196 + 1.05376I
a = 0.770292 + 0.096192I
b = −0.805369 + 1.162390I
−1.11345 − 4.05977I 6.98049 + 6.92820I
u = −1.12196 + 1.05376I
a = 0.623281 + 0.392613I
b = −1.43545 + 0.27547I
3.02413 − 6.88789I 13.5098 + 9.9077I
u = −1.12196 + 1.05376I
a = 0.344921 + 0.424263I
b = −0.424844 + 0.123021I
3.02413 − 1.23164I 13.50976 + 3.94876I
u = −1.12196 + 1.05376I
a = −0.402249 − 0.126456I
b = 0.223975 − 0.607538I
−1.11345 − 4.05977I 6.98049 + 6.92820I
u = −1.12196 + 1.05376I
a = 0.376282 − 0.188089I
b = −0.584563 + 0.281994I
−1.11345 − 4.05977I 6.98049 + 6.92820I
u = −1.12196 + 1.05376I
a = −0.255906 − 0.130701I
b = 0.834059 + 0.112545I
3.02413 − 1.23164I 13.50976 + 3.94876I
u = −1.12196 − 1.05376I
a = 1.022580 + 0.081870I
b = −1.119460 − 0.700856I
3.02413 + 6.88789I 13.5098 − 9.9077I
u = −1.12196 − 1.05376I
a = −0.994199 + 0.313700I
b = 1.266430 + 0.421436I
3.02413 + 1.23164I 13.50976 − 3.94876I
u = −1.12196 − 1.05376I
a = −0.802294 + 0.507994I
b = 1.113020 + 0.216287I
3.02413 + 6.88789I 13.5098 − 9.9077I
u = −1.12196 − 1.05376I
a = −0.898391 − 0.192258I
b = 0.965603 + 0.703775I
−1.11345 + 4.05977I 6.98049 − 6.92820I
45
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −1.12196 − 1.05376I
a = 0.787176 − 0.363697I
b = −1.44602 − 0.69568I
3.02413 + 1.23164I 13.50976 − 3.94876I
u = −1.12196 − 1.05376I
a = −0.841854 + 0.166006I
b = 1.06102 + 1.16940I
3.02413 + 6.88789I 13.5098 − 9.9077I
u = −1.12196 − 1.05376I
a = 0.770292 − 0.096192I
b = −0.805369 − 1.162390I
−1.11345 + 4.05977I 6.98049 − 6.92820I
u = −1.12196 − 1.05376I
a = 0.623281 − 0.392613I
b = −1.43545 − 0.27547I
3.02413 + 6.88789I 13.5098 − 9.9077I
u = −1.12196 − 1.05376I
a = 0.344921 − 0.424263I
b = −0.424844 − 0.123021I
3.02413 + 1.23164I 13.50976 − 3.94876I
u = −1.12196 − 1.05376I
a = −0.402249 + 0.126456I
b = 0.223975 + 0.607538I
−1.11345 + 4.05977I 6.98049 − 6.92820I
u = −1.12196 − 1.05376I
a = 0.376282 + 0.188089I
b = −0.584563 − 0.281994I
−1.11345 + 4.05977I 6.98049 − 6.92820I
u = −1.12196 − 1.05376I
a = −0.255906 + 0.130701I
b = 0.834059 − 0.112545I
3.02413 + 1.23164I 13.50976 − 3.94876I
46
VIII. I
u
8
= h28032a
11
u + 4413a
10
u + · · · + 275661a − 56296, −a
11
u −
5a
10
u + · · · − 2a + 1, u
2
+ u + 1i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
5
=
1
u + 1
a
11
=
a
−0.189604a
11
u − 0.0298488a
10
u + ··· − 1.86453a + 0.380777
a
8
=
a
2
u
−0.0528865a
11
u − 0.146917a
10
u + ··· + 0.486882a − 0.351267
a
12
=
−0.189604a
11
u − 0.0298488a
10
u + ··· − 0.864527a + 0.380777
−0.189604a
11
u − 0.0298488a
10
u + ··· − 1.86453a + 0.380777
a
6
=
0.191511a
11
u + 0.0471440a
10
u + ··· + 0.700964a + 0.838337
0.244398a
11
u + 0.194061a
10
u + ··· + 0.214082a + 1.18960
a
10
=
−0.189604a
11
u − 0.0298488a
10
u + ··· − 1.86453a + 0.380777
−0.540871a
11
u − 0.463851a
10
u + ··· − 5.67046a + 1.19255
a
1
=
−0.351267a
11
u − 0.434002a
10
u + ··· − 1.80593a + 0.811776
−0.161663a
11
u − 0.404153a
10
u + ··· − 0.941405a + 0.430999
a
9
=
a
3
u + a
3
− 2au − a
−0.187054a
11
u + 0.385471a
10
u + ··· − 1.08035a + 0.572289
a
3
=
−0.139842a
11
u − 0.307011a
10
u + ··· − 0.994082a + 0.428388
0.623558a
11
u − 0.558727a
10
u + ··· − 1.93933a − 0.134127
a
2
=
−0.830275a
11
u + 0.444635a
10
u + ··· + 1.69826a + 0.471074
0.865880a
11
u − 0.655125a
10
u + ··· − 4.68477a − 0.514268
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
22124
29569
a
11
u +
45592
29569
a
10
u + ··· −
127780
29569
a +
126826
29569
47
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
4
c
2
, c
8
(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
4
c
3
(u
3
− u
2
+ 1)
8
c
4
, c
12
(u
2
− u + 1)
12
c
5
, c
7
, c
9
c
11
u
24
− u
23
+ ··· − 6u + 1
c
6
, c
10
u
24
− 3u
23
+ ··· + 228u + 37
48
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
4
c
2
, c
8
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
4
c
3
(y
3
− y
2
+ 2y −1)
8
c
4
, c
12
(y
2
+ y + 1)
12
c
5
, c
7
, c
9
c
11
y
24
− 3y
23
+ ··· + 4y + 1
c
6
, c
10
y
24
− 15y
23
+ ··· − 12764y + 1369
49
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 1.018560 − 0.089361I
b = −1.54846 + 0.99543I
−0.26574 − 6.88789I 1.50976 + 9.90765I
u = −0.500000 + 0.866025I
a = 0.329704 + 0.906545I
b = −0.857852 + 0.603445I
−0.26574 − 6.88789I 1.50976 + 9.90765I
u = −0.500000 + 0.866025I
a = −0.951524 − 0.441199I
b = 0.949943 + 0.167740I
−0.26574 − 6.88789I 1.50976 + 9.90765I
u = −0.500000 + 0.866025I
a = −0.883620 + 0.205979I
b = 1.37163 − 1.17905I
−4.40332 − 4.05977I −5.01951 + 6.92820I
u = −0.500000 + 0.866025I
a = −1.052750 − 0.314335I
b = 1.42042 − 0.28919I
−0.265740 − 1.231640I 1.50976 + 3.94876I
u = −0.500000 + 0.866025I
a = 1.161960 − 0.171014I
b = 0.184858 + 0.159144I
−0.265740 − 1.231640I 1.50976 + 3.94876I
u = −0.500000 + 0.866025I
a = 0.96066 + 1.08552I
b = −0.798597 + 0.754539I
−0.265740 − 1.231640I 1.50976 + 3.94876I
u = −0.500000 + 0.866025I
a = −1.46961 + 0.00084I
b = −0.089208 − 0.468821I
−4.40332 − 4.05977I −5.01951 + 6.92820I
u = −0.500000 + 0.866025I
a = 0.361406 − 0.311667I
b = −0.73407 + 1.27314I
−4.40332 − 4.05977I −5.01951 + 6.92820I
u = −0.500000 + 0.866025I
a = −0.045393 + 0.239664I
b = 0.432879 − 1.091800I
−0.265740 − 1.231640I 1.50976 + 3.94876I
50
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 1.70690 + 0.59834I
b = −0.263427 + 0.868227I
−4.40332 − 4.05977I −5.01951 + 6.92820I
u = −0.500000 + 0.866025I
a = −1.63629 − 0.84329I
b = 0.431890 − 0.926776I
−0.26574 − 6.88789I 1.50976 + 9.90765I
u = −0.500000 − 0.866025I
a = 1.018560 + 0.089361I
b = −1.54846 − 0.99543I
−0.26574 + 6.88789I 1.50976 − 9.90765I
u = −0.500000 − 0.866025I
a = 0.329704 − 0.906545I
b = −0.857852 − 0.603445I
−0.26574 + 6.88789I 1.50976 − 9.90765I
u = −0.500000 − 0.866025I
a = −0.951524 + 0.441199I
b = 0.949943 − 0.167740I
−0.26574 + 6.88789I 1.50976 − 9.90765I
u = −0.500000 − 0.866025I
a = −0.883620 − 0.205979I
b = 1.37163 + 1.17905I
−4.40332 + 4.05977I −5.01951 − 6.92820I
u = −0.500000 − 0.866025I
a = −1.052750 + 0.314335I
b = 1.42042 + 0.28919I
−0.265740 + 1.231640I 1.50976 − 3.94876I
u = −0.500000 − 0.866025I
a = 1.161960 + 0.171014I
b = 0.184858 − 0.159144I
−0.265740 + 1.231640I 1.50976 − 3.94876I
u = −0.500000 − 0.866025I
a = 0.96066 − 1.08552I
b = −0.798597 − 0.754539I
−0.265740 + 1.231640I 1.50976 − 3.94876I
u = −0.500000 − 0.866025I
a = −1.46961 − 0.00084I
b = −0.089208 + 0.468821I
−4.40332 + 4.05977I −5.01951 − 6.92820I
51
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 − 0.866025I
a = 0.361406 + 0.311667I
b = −0.73407 − 1.27314I
−4.40332 + 4.05977I −5.01951 − 6.92820I
u = −0.500000 − 0.866025I
a = −0.045393 − 0.239664I
b = 0.432879 + 1.091800I
−0.265740 + 1.231640I 1.50976 − 3.94876I
u = −0.500000 − 0.866025I
a = 1.70690 − 0.59834I
b = −0.263427 − 0.868227I
−4.40332 + 4.05977I −5.01951 − 6.92820I
u = −0.500000 − 0.866025I
a = −1.63629 + 0.84329I
b = 0.431890 + 0.926776I
−0.26574 + 6.88789I 1.50976 − 9.90765I
52
IX.
I
u
9
= h31947a
11
+53734b+· · ·+140465a−40927, a
12
+a
11
+· · ·−2a+1, u+1i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
−1
a
5
=
1
−1
a
11
=
a
−0.594540a
11
− 0.715469a
10
+ ··· − 2.61408a + 0.761659
a
8
=
−a
2
0.120929a
11
+ 0.286243a
10
+ ··· + 0.427420a − 1.59454
a
12
=
−0.594540a
11
− 0.715469a
10
+ ··· − 1.61408a + 0.761659
−0.594540a
11
− 0.715469a
10
+ ··· − 2.61408a + 0.761659
a
6
=
−0.120929a
11
− 0.286243a
10
+ ··· − 0.427420a + 1.59454
−0.241858a
11
− 0.572487a
10
+ ··· − 0.854841a + 1.18908
a
10
=
−0.594540a
11
− 0.715469a
10
+ ··· − 0.614080a + 0.761659
−a
a
1
=
−a
−0.594540a
11
− 0.715469a
10
+ ··· − 1.61408a + 0.761659
a
9
=
−0.429225a
11
− 0.567239a
10
+ ··· − 1.96676a + 0.640730
0.330629a
11
+ 0.296460a
10
+ ··· − 1.70536a − 0.241858
a
3
=
−0.582220a
11
− 0.859437a
10
+ ··· − 0.451576a + 1.32205
−0.697063a
11
− 1.06272a
10
+ ··· − 0.541929a − 0.0392303
a
2
=
−0.219972a
11
− 0.127331a
10
+ ··· − 0.0646518a + 1.07733
−1.35661a
11
− 2.21945a
10
+ ··· − 3.01496a + 1.37282
(ii) Obstruction class = −1
(iii) Cusp Shapes =
35532
26867
a
11
+
31860
26867
a
10
−
22492
26867
a
9
+
72808
26867
a
8
+
156816
26867
a
7
+
239124
26867
a
6
−
57412
26867
a
5
−
528896
26867
a
4
+
450048
26867
a
3
+
143852
26867
a
2
−
183272
26867
a +
242678
26867
53
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
2
c
2
, c
8
(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
2
c
3
(u
3
− u
2
+ 1)
4
c
4
, c
12
(u − 1)
12
c
5
, c
7
, c
9
c
11
u
12
+ u
11
+ ··· − 2u + 1
c
6
, c
10
(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
2
54
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
2
c
2
, c
6
, c
8
c
10
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
2
c
3
(y
3
− y
2
+ 2y −1)
4
c
4
, c
12
(y −1)
12
c
5
, c
7
, c
9
c
11
y
12
− 3y
11
+ ··· − 8y + 1
55
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.895115 + 0.065061I
b = −1.60903 − 0.37090I
3.02413 − 2.82812I 13.50976 + 2.97945I
u = −1.00000
a = 0.895115 − 0.065061I
b = −1.60903 + 0.37090I
3.02413 + 2.82812I 13.50976 − 2.97945I
u = −1.00000
a = −0.559232 + 0.271442I
b = 1.05806 − 1.27274I
3.02413 − 2.82812I 13.50976 + 2.97945I
u = −1.00000
a = −0.559232 − 0.271442I
b = 1.05806 + 1.27274I
3.02413 + 2.82812I 13.50976 − 2.97945I
u = −1.00000
a = −0.62279 + 1.38441I
b = 0.337871 − 0.269271I
−1.11345 6.98049 + 0.I
u = −1.00000
a = −0.62279 − 1.38441I
b = 0.337871 + 0.269271I
−1.11345 6.98049 + 0.I
u = −1.00000
a = 0.337871 + 0.269271I
b = −0.62279 − 1.38441I
−1.11345 6.98049 + 0.I
u = −1.00000
a = 0.337871 − 0.269271I
b = −0.62279 + 1.38441I
−1.11345 6.98049 + 0.I
u = −1.00000
a = −1.60903 + 0.37090I
b = 0.895115 − 0.065061I
3.02413 + 2.82812I 13.50976 − 2.97945I
u = −1.00000
a = −1.60903 − 0.37090I
b = 0.895115 + 0.065061I
3.02413 − 2.82812I 13.50976 + 2.97945I
56
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.05806 + 1.27274I
b = −0.559232 − 0.271442I
3.02413 + 2.82812I 13.50976 − 2.97945I
u = −1.00000
a = 1.05806 − 1.27274I
b = −0.559232 + 0.271442I
3.02413 − 2.82812I 13.50976 + 2.97945I
57
X. I
u
10
= hb − 1, a + 1, u + 1i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
−1
a
5
=
1
−1
a
11
=
−1
1
a
8
=
−1
0
a
12
=
0
1
a
6
=
0
−1
a
10
=
−1
1
a
1
=
1
0
a
9
=
−1
0
a
3
=
1
0
a
2
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
58
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
8
, c
10
u
c
4
, c
7
, c
11
u + 1
c
5
, c
9
, c
12
u − 1
59
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
8
, c
10
y
c
4
, c
5
, c
7
c
9
, c
11
, c
12
y −1
60
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 1.00000
3.28987 12.0000
61
XI. I
v
1
= ha, b
4
+ b
2
− b + 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
7
=
1
0
a
5
=
1
0
a
11
=
0
b
a
8
=
1
−b
2
a
12
=
b
b
a
6
=
−b
2
+ 1
−b
2
a
10
=
b
b
a
1
=
b
b
a
9
=
b
3
b
3
+ b
a
3
=
−b
3
+ b
2
+ 1
−b
3
+ b
2
− b + 1
a
2
=
−b
3
+ b
2
− b + 1
b
2
− b + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4b
3
− 4b
2
+ 2
62
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
2
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
u
4
+ u
2
− u + 1
c
3
u
4
− 3u
3
+ 4u
2
− 3u + 2
c
4
, c
12
u
4
63
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
2
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
3
y
4
− y
3
+ 2y
2
+ 7y + 4
c
4
, c
12
y
4
64
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 0.547424 + 0.585652I
0.98010 + 1.39709I 3.77019 − 3.86736I
v = 1.00000
a = 0
b = 0.547424 − 0.585652I
0.98010 − 1.39709I 3.77019 + 3.86736I
v = 1.00000
a = 0
b = −0.547424 + 1.120870I
−2.62503 − 7.64338I −1.77019 + 6.51087I
v = 1.00000
a = 0
b = −0.547424 − 1.120870I
−2.62503 + 7.64338I −1.77019 − 6.51087I
65
XII. I
v
2
= ha, b
6
+ b
5
+ 2b
4
+ 2b
3
+ 2b
2
+ 2b + 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
7
=
1
0
a
5
=
1
0
a
11
=
0
b
a
8
=
1
−b
2
a
12
=
b
b
a
6
=
−b
2
+ 1
−b
2
a
10
=
b
b
a
1
=
b
b
a
9
=
b
3
b
3
+ b
a
3
=
b
5
+ b
4
+ 2b
3
+ 2b
2
+ 2b + 2
b
5
+ 2b
3
+ b
2
+ 2b + 1
a
2
=
b
4
+ b
2
+ b + 1
2b
5
+ b
4
+ 3b
3
+ 2b
2
+ 3b + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4b
3
− 4b − 2
66
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
2
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
3
(u
3
+ u
2
− 1)
2
c
4
, c
12
u
6
67
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
3
(y
3
− y
2
+ 2y −1)
2
c
4
, c
12
y
6
68
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 0.498832 + 1.001300I
−0.26574 + 2.82812I 1.50976 − 2.97945I
v = 1.00000
a = 0
b = 0.498832 − 1.001300I
−0.26574 − 2.82812I 1.50976 + 2.97945I
v = 1.00000
a = 0
b = −0.284920 + 1.115140I
−4.40332 −5.01951 + 0.I
v = 1.00000
a = 0
b = −0.284920 − 1.115140I
−4.40332 −5.01951 + 0.I
v = 1.00000
a = 0
b = −0.713912 + 0.305839I
−0.26574 + 2.82812I 1.50976 − 2.97945I
v = 1.00000
a = 0
b = −0.713912 − 0.305839I
−0.26574 − 2.82812I 1.50976 + 2.97945I
69
XIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
4
+ 2u
3
+ 3u
2
+ u + 1)
15
(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
15
· ((u
11
+ 5u
10
+ ··· + 12u − 16)
2
)(u
21
− 11u
20
+ ··· − 2u + 1)
2
· (u
28
+ 12u
27
+ ··· + 160u + 64)
c
2
, c
8
u(u
4
+ u
2
− u + 1)(u
4
+ u
2
+ u + 1)
14
· (u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
14
· (u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)(u
11
+ 3u
10
+ ··· + 14u + 4)
2
· (u
28
+ 6u
27
+ ··· + 40u + 8)(u
42
+ 11u
40
+ ··· − 2u
2
− 1)
c
3
u(u
3
− u
2
+ 1)
28
(u
3
+ u
2
− 1)
2
(u
4
− 3u
3
+ 4u
2
− 3u + 2)
· ((u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
14
)(u
11
− 3u
10
+ ··· − 122u + 52)
2
· (u
28
− 6u
27
+ ··· − 28744u + 3880)(u
42
+ 5u
40
+ ··· + 14u
2
− 1)
c
4
u
10
(u − 1)
20
(u + 1)(u
2
− u + 1)
20
(u
4
− u
3
+ 2u + 1)
20
· (u
22
+ 24u
21
+ ··· + 46453u + 4223)
· (u
28
+ 21u
27
+ ··· + 8019u + 1003)(u
42
+ 15u
41
+ ··· − u + 1)
c
5
, c
9
(u − 1)(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
8
− u
6
+ ··· − u + 2)(u
12
+ u
11
+ ··· − 2u + 1)
· (u
16
− u
14
+ ··· + 6u + 1)(u
22
+ 3u
20
+ ··· + 3u + 1)
· (u
24
− u
23
+ ··· − 6u + 1)(u
28
− u
27
+ ··· − u + 1)
· (u
32
− 7u
30
+ ··· − 62u + 19)(u
42
+ 3u
41
+ ··· + 5u + 1)
· (u
48
+ u
47
+ ··· − 38u + 19)
c
6
, c
10
u(u
4
+ u
2
− u + 1)
3
(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
· ((u
11
− u
9
+ ··· + u
2
+ 1)
2
)(u
16
− 5u
14
+ ··· − 48u + 13)
· ((u
16
+ 7u
14
+ ··· + 50u + 19)
2
)(u
24
− 3u
23
+ ··· + 228u + 37)
· ((u
24
+ u
23
+ ··· + 38u + 19)
2
)(u
28
− u
27
+ ··· − 2u + 10)
· (u
42
+ 12u
40
+ ··· + 29u
2
− 1)
c
7
, c
11
(u + 1)(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
8
− u
6
+ ··· − u + 2)(u
12
+ u
11
+ ··· − 2u + 1)
· (u
16
− u
14
+ ··· + 6u + 1)(u
22
+ 3u
20
+ ··· + 3u + 1)
· (u
24
− u
23
+ ··· − 6u + 1)(u
28
− u
27
+ ··· − u + 1)
· (u
32
− 7u
30
+ ··· − 62u + 19)(u
42
− 3u
41
+ ··· − 5u + 1)
· (u
48
+ u
47
+ ··· − 38u + 19)
c
12
u
10
(u − 1)
21
(u
2
− u + 1)
20
(u
4
− u
3
+ 2u + 1)
20
· (u
22
+ 24u
21
+ ··· + 46453u + 4223)
· (u
28
+ 21u
27
+ ··· + 8019u + 1003)(u
42
− 15u
41
+ ··· + u + 1)
70
XIV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
15
(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
15
· ((y
11
+ y
10
+ ··· + 880y −256)
2
)(y
21
+ 5y
20
+ ··· + 14y −1)
2
· (y
28
+ 8y
27
+ ··· + 58880y + 4096)
c
2
, c
8
y(y
4
+ 2y
3
+ 3y
2
+ y + 1)
15
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
15
· ((y
11
+ 5y
10
+ ··· + 12y −16)
2
)(y
21
+ 11y
20
+ ··· − 2y −1)
2
· (y
28
+ 12y
27
+ ··· + 160y + 64)
c
3
y(y
3
− y
2
+ 2y −1)
30
(y
4
− y
3
+ 2y
2
+ 7y + 4)
15
· ((y
11
+ 3y
10
+ ··· + 2508y −2704)
2
)(y
21
+ 5y
20
+ ··· + 14y −1)
2
· (y
28
+ 4y
27
+ ··· − 22855776y + 15054400)
c
4
, c
12
y
10
(y −1)
21
(y
2
+ y + 1)
20
(y
4
− y
3
+ 6y
2
− 4y + 1)
20
· (y
22
− 6y
21
+ ··· − 6355615y + 17833729)
· (y
28
− 21y
27
+ ··· + 2369061y + 1006009)
· (y
42
− 25y
41
+ ··· − 17y + 1)
c
5
, c
7
, c
9
c
11
(y −1)(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
8
− 2y
7
+ 13y
6
− 38y
5
+ 98y
4
− 108y
3
+ 61y
2
− 21y + 4)
· (y
12
− 3y
11
+ ··· − 8y + 1)(y
16
− 2y
15
+ ··· − 8y + 1)
· (y
22
+ 6y
21
+ ··· − 5y + 1)(y
24
− 3y
23
+ ··· + 4y + 1)
· (y
28
+ 9y
27
+ ··· + 35y + 1)(y
32
− 14y
31
+ ··· − 13914y + 361)
· (y
42
− 15y
41
+ ··· + 43y + 1)(y
48
− 21y
47
+ ··· − 28424y + 361)
c
6
, c
10
y(y
4
+ 2y
3
+ 3y
2
+ y + 1)
3
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
3
· (y
11
− 2y
10
+ 3y
9
− 7y
8
+ 7y
7
− 6y
6
+ 8y
5
− 2y
4
+ y
3
− y
2
− 2y −1)
2
· (y
16
− 10y
15
+ ··· − 120y + 169)(y
16
+ 14y
15
+ ··· + 1984y + 361)
2
· ((y
21
+ 12y
20
+ ··· + 29y −1)
2
)(y
24
− 15y
23
+ ··· − 12764y + 1369)
· (y
24
+ 21y
23
+ ··· + 6156y + 361)
2
· (y
28
+ 19y
27
+ ··· + 1736y + 100)
71
