12n
0753
(K12n
0753
)
A knot diagram
1
Linearized knot diagam
4 6 8 9 2 12 3 11 4 1 7 9
Solving Sequence
3,7
8
4,12
6 2 1 5 11 9 10
c
7
c
3
c
6
c
2
c
1
c
5
c
11
c
8
c
9
c
4
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.36970 × 10
192
u
71
+ 1.13541 × 10
192
u
70
+ ··· + 8.77978 × 10
191
b − 2.52244 × 10
193
,
− 2.76575 × 10
194
u
71
+ 7.05669 × 10
194
u
70
+ ··· + 6.36534 × 10
194
a − 1.06301 × 10
196
,
2u
72
− 3u
71
+ ··· − 314u − 29i
I
u
2
= h1624226u
15
+ 189101u
14
+ ··· + 2048967b − 3069244,
1675780u
15
− 2140649u
14
+ ··· + 2048967a + 298066, u
16
− u
15
+ ··· − u + 1i
I
u
3
= hb + a + 2, a
2
+ 3a + 3, u + 1i
I
u
4
= hb − 1, a, u + 1i
I
u
5
= hb − 1, a − 3, 2u − 1i
* 5 irreducible components of dim
C
= 0, with total 92 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−1.37 × 10
192
u
71
+ 1.14 × 10
192
u
70
+ · · · + 8.78 × 10
191
b − 2.52 ×
10
193
, −2.77 × 10
194
u
71
+ 7.06 × 10
194
u
70
+ · · · + 6.37 × 10
194
a − 1.06 ×
10
196
, 2u
72
− 3u
71
+ · · · − 314u − 29i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
12
=
0.434501u
71
− 1.10861u
70
+ ··· + 347.297u + 16.7000
1.56006u
71
− 1.29321u
70
+ ··· + 356.879u + 28.7301
a
6
=
0.0355412u
71
+ 0.176136u
70
+ ··· − 11.6952u − 6.02177
3.01683u
71
− 1.28760u
70
+ ··· + 385.689u + 33.1010
a
2
=
1.01568u
71
− 0.393073u
70
+ ··· + 193.878u + 14.0114
−2.66963u
71
+ 1.21209u
70
+ ··· − 462.369u − 40.0424
a
1
=
−1.45544u
71
+ 1.03210u
70
+ ··· − 279.270u − 26.0870
−2.04836u
71
+ 1.02912u
70
+ ··· − 383.249u − 33.0258
a
5
=
1.33808u
71
− 0.482894u
70
+ ··· + 103.747u + 5.16521
0.454400u
71
+ 0.395730u
70
+ ··· − 29.3983u − 1.94875
a
11
=
1.99456u
71
− 2.40182u
70
+ ··· + 704.175u + 45.4301
1.56006u
71
− 1.29321u
70
+ ··· + 356.879u + 28.7301
a
9
=
−1.11558u
71
+ 1.08287u
70
+ ··· − 292.574u − 16.4833
0.445103u
71
− 0.585548u
70
+ ··· + 202.903u + 17.1718
a
10
=
−2.49602u
71
+ 1.67951u
70
+ ··· − 453.851u − 30.5168
0.204348u
71
− 0.282806u
70
+ ··· + 112.741u + 9.83185
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10.8009u
71
+ 8.28607u
70
+ ··· − 2650.54u − 220.978
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
2(2u
72
− 7u
71
+ ··· + 3152u + 248)
c
2
, c
5
u
72
+ 2u
71
+ ··· + 3215u + 491
c
3
, c
7
2(2u
72
− 3u
71
+ ··· − 314u − 29)
c
4
, c
9
2(2u
72
+ 3u
71
+ ··· − 3289u + 373)
c
6
, c
11
u
72
+ 2u
71
+ ··· − 32u − 13
c
8
u
72
− 9u
71
+ ··· − 34u − 16
c
10
u
72
− u
71
+ ··· − 868u + 172
c
12
4(4u
72
+ 7u
71
+ ··· + 3105391u − 546509)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
4(4y
72
+ 315y
71
+ ··· + 1.07828 × 10
7
y + 61504)
c
2
, c
5
y
72
− 34y
71
+ ··· − 7263547y + 241081
c
3
, c
7
4(4y
72
− 149y
71
+ ··· − 158162y + 841)
c
4
, c
9
4(4y
72
− 273y
71
+ ··· − 1.06512 × 10
7
y + 139129)
c
6
, c
11
y
72
+ 40y
71
+ ··· + 1758y + 169
c
8
y
72
+ 13y
71
+ ··· − 21636y + 256
c
10
y
72
+ 71y
71
+ ··· + 1106584y + 29584
c
12
16(16y
72
+ 383y
71
+ ··· − 2.25832 × 10
13
y + 2.98672 × 10
11
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.503006 + 0.831688I
a = −0.259579 + 1.246850I
b = 0.058808 − 1.112600I
3.45543 − 1.25801I 0
u = 0.503006 − 0.831688I
a = −0.259579 − 1.246850I
b = 0.058808 + 1.112600I
3.45543 + 1.25801I 0
u = −1.041580 + 0.024317I
a = 1.23868 − 0.87697I
b = 0.394506 + 1.005270I
−2.31888 + 0.24644I 0
u = −1.041580 − 0.024317I
a = 1.23868 + 0.87697I
b = 0.394506 − 1.005270I
−2.31888 − 0.24644I 0
u = −0.815728 + 0.487376I
a = −1.208560 − 0.387306I
b = 0.117552 + 0.652833I
−1.33286 − 0.50784I 0
u = −0.815728 − 0.487376I
a = −1.208560 + 0.387306I
b = 0.117552 − 0.652833I
−1.33286 + 0.50784I 0
u = −0.728632 + 0.606808I
a = 1.05815 + 1.44602I
b = 0.832891 − 1.079930I
6.64396 + 5.86161I 0
u = −0.728632 − 0.606808I
a = 1.05815 − 1.44602I
b = 0.832891 + 1.079930I
6.64396 − 5.86161I 0
u = 0.882988 + 0.321194I
a = 0.989354 − 0.026371I
b = 0.554950 + 1.267330I
7.66910 + 0.75809I 0
u = 0.882988 − 0.321194I
a = 0.989354 + 0.026371I
b = 0.554950 − 1.267330I
7.66910 − 0.75809I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.907468 + 0.164522I
a = 1.83157 − 1.23603I
b = 0.368044 + 0.713795I
−2.88359 − 0.80432I 0. + 8.12297I
u = 0.907468 − 0.164522I
a = 1.83157 + 1.23603I
b = 0.368044 − 0.713795I
−2.88359 + 0.80432I 0. − 8.12297I
u = 0.895691 + 0.175371I
a = −0.042597 − 1.012350I
b = −0.31696 + 1.83412I
7.94630 − 2.89493I −8.00000 + 0.I
u = 0.895691 − 0.175371I
a = −0.042597 + 1.012350I
b = −0.31696 − 1.83412I
7.94630 + 2.89493I −8.00000 + 0.I
u = 0.092924 + 1.093780I
a = −0.61636 − 1.43773I
b = 0.263182 + 1.078450I
0.22901 − 1.56376I 0
u = 0.092924 − 1.093780I
a = −0.61636 + 1.43773I
b = 0.263182 − 1.078450I
0.22901 + 1.56376I 0
u = −1.072600 + 0.291310I
a = 0.186386 − 0.014835I
b = 1.228110 + 0.658249I
−3.76116 + 2.21241I 0
u = −1.072600 − 0.291310I
a = 0.186386 + 0.014835I
b = 1.228110 − 0.658249I
−3.76116 − 2.21241I 0
u = −0.225907 + 0.857311I
a = 0.29618 − 1.73173I
b = 0.175849 + 1.362810I
11.23550 − 2.92648I 0
u = −0.225907 − 0.857311I
a = 0.29618 + 1.73173I
b = 0.175849 − 1.362810I
11.23550 + 2.92648I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.898595 + 0.693854I
a = 0.495800 + 0.631045I
b = −0.623277 − 1.241630I
6.17897 − 0.78005I 0
u = −0.898595 − 0.693854I
a = 0.495800 − 0.631045I
b = −0.623277 + 1.241630I
6.17897 + 0.78005I 0
u = −0.851572 + 0.098574I
a = −0.44810 − 2.02667I
b = −0.307315 + 1.330400I
−0.33014 + 2.90561I −12.38642 − 2.35566I
u = −0.851572 − 0.098574I
a = −0.44810 + 2.02667I
b = −0.307315 − 1.330400I
−0.33014 − 2.90561I −12.38642 + 2.35566I
u = 0.425042 + 0.726403I
a = −0.375790 + 0.136052I
b = 0.749628 − 0.466090I
5.42275 − 0.09793I −5.98952 + 0.I
u = 0.425042 − 0.726403I
a = −0.375790 − 0.136052I
b = 0.749628 + 0.466090I
5.42275 + 0.09793I −5.98952 + 0.I
u = 1.146890 + 0.239896I
a = −1.34749 + 1.59261I
b = −0.446655 − 1.147350I
2.40983 − 6.94246I 0
u = 1.146890 − 0.239896I
a = −1.34749 − 1.59261I
b = −0.446655 + 1.147350I
2.40983 + 6.94246I 0
u = 0.169569 + 0.808248I
a = 0.473104 − 1.295420I
b = −0.444943 + 1.156660I
1.56234 + 4.15508I −3.60189 − 5.54738I
u = 0.169569 − 0.808248I
a = 0.473104 + 1.295420I
b = −0.444943 − 1.156660I
1.56234 − 4.15508I −3.60189 + 5.54738I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.071170 + 0.491622I
a = −0.926908 + 0.936678I
b = −0.454134 − 1.102540I
1.52629 − 3.66253I 0
u = 1.071170 − 0.491622I
a = −0.926908 − 0.936678I
b = −0.454134 + 1.102540I
1.52629 + 3.66253I 0
u = 1.002430 + 0.646161I
a = −0.621070 + 1.079490I
b = −0.772604 − 0.519623I
3.91147 − 4.95776I 0
u = 1.002430 − 0.646161I
a = −0.621070 − 1.079490I
b = −0.772604 + 0.519623I
3.91147 + 4.95776I 0
u = −0.798501
a = −0.785864
b = −0.447077
−1.17921 −8.47920
u = 1.202480 + 0.283076I
a = 0.138975 − 0.079543I
b = −1.153200 + 0.368484I
−6.45016 − 1.40130I 0
u = 1.202480 − 0.283076I
a = 0.138975 + 0.079543I
b = −1.153200 − 0.368484I
−6.45016 + 1.40130I 0
u = −1.235190 + 0.143374I
a = 0.617261 − 0.416546I
b = 0.447349 − 0.814159I
−2.50871 + 2.84294I 0
u = −1.235190 − 0.143374I
a = 0.617261 + 0.416546I
b = 0.447349 + 0.814159I
−2.50871 − 2.84294I 0
u = −1.244310 + 0.423740I
a = 0.0054853 − 0.0913034I
b = −1.309550 − 0.242884I
0.98123 + 9.65251I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.244310 − 0.423740I
a = 0.0054853 + 0.0913034I
b = −1.309550 + 0.242884I
0.98123 − 9.65251I 0
u = −1.233970 + 0.484514I
a = −1.36969 − 0.62929I
b = −0.365240 + 1.167500I
8.05277 + 7.84555I 0
u = −1.233970 − 0.484514I
a = −1.36969 + 0.62929I
b = −0.365240 − 1.167500I
8.05277 − 7.84555I 0
u = 1.314710 + 0.242671I
a = 1.134490 + 0.342556I
b = 0.114449 + 0.782911I
−3.79390 − 2.56082I 0
u = 1.314710 − 0.242671I
a = 1.134490 − 0.342556I
b = 0.114449 − 0.782911I
−3.79390 + 2.56082I 0
u = 0.154651 + 1.330290I
a = −0.363017 + 1.326710I
b = 0.447735 − 1.196460I
8.31993 + 9.72275I 0
u = 0.154651 − 1.330290I
a = −0.363017 − 1.326710I
b = 0.447735 + 1.196460I
8.31993 − 9.72275I 0
u = 1.236540 + 0.527449I
a = 0.836971 − 1.017340I
b = 0.73985 + 1.21388I
−1.67018 − 9.17442I 0
u = 1.236540 − 0.527449I
a = 0.836971 + 1.017340I
b = 0.73985 − 1.21388I
−1.67018 + 9.17442I 0
u = 0.207226 + 0.606021I
a = −0.89244 + 1.68919I
b = 0.559166 + 0.057445I
4.92815 − 5.65520I −7.10674 + 3.77487I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.207226 − 0.606021I
a = −0.89244 − 1.68919I
b = 0.559166 − 0.057445I
4.92815 + 5.65520I −7.10674 − 3.77487I
u = 0.633327
a = 2.67730
b = 0.903177
−3.55339 −29.9400
u = 1.348140 + 0.296280I
a = 0.203425 + 0.158263I
b = 0.811304 − 0.216892I
−5.73500 − 3.48707I 0
u = 1.348140 − 0.296280I
a = 0.203425 − 0.158263I
b = 0.811304 + 0.216892I
−5.73500 + 3.48707I 0
u = −0.606261
a = −1.45762
b = −1.05497
−1.75883 −2.53260
u = −1.399550 + 0.110346I
a = −0.124373 − 0.433867I
b = −0.634981 − 0.141517I
−0.46262 + 2.79739I 0
u = −1.399550 − 0.110346I
a = −0.124373 + 0.433867I
b = −0.634981 + 0.141517I
−0.46262 − 2.79739I 0
u = 0.576573 + 0.148773I
a = −3.20227 + 0.71254I
b = 0.134280 + 0.503659I
4.97316 − 5.48093I −7.15436 + 1.78291I
u = 0.576573 − 0.148773I
a = −3.20227 − 0.71254I
b = 0.134280 − 0.503659I
4.97316 + 5.48093I −7.15436 − 1.78291I
u = −1.27477 + 0.62767I
a = −0.508037 − 1.269480I
b = −0.67450 + 1.28161I
−3.45946 + 7.92978I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.27477 − 0.62767I
a = −0.508037 + 1.269480I
b = −0.67450 − 1.28161I
−3.45946 − 7.92978I 0
u = 1.36637 + 0.66092I
a = −0.690847 + 1.216050I
b = −0.68777 − 1.34270I
4.4898 − 16.5640I 0
u = 1.36637 − 0.66092I
a = −0.690847 − 1.216050I
b = −0.68777 + 1.34270I
4.4898 + 16.5640I 0
u = −1.42815 + 0.61310I
a = 0.607526 + 1.114140I
b = 0.530368 − 1.219960I
−2.66048 + 8.50861I 0
u = −1.42815 − 0.61310I
a = 0.607526 − 1.114140I
b = 0.530368 + 1.219960I
−2.66048 − 8.50861I 0
u = −0.236862 + 0.337792I
a = −0.751492 + 0.941497I
b = −0.262698 + 0.288681I
−0.679533 + 0.910759I −9.46747 − 7.43737I
u = −0.236862 − 0.337792I
a = −0.751492 − 0.941497I
b = −0.262698 − 0.288681I
−0.679533 − 0.910759I −9.46747 + 7.43737I
u = 1.49094 + 0.88314I
a = −0.089296 + 1.196100I
b = −0.296159 − 1.050160I
2.84660 − 0.20549I 0
u = 1.49094 − 0.88314I
a = −0.089296 − 1.196100I
b = −0.296159 + 1.050160I
2.84660 + 0.20549I 0
u = −0.0772319
a = −9.75455
b = −0.694596
−1.59790 −5.22370
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.13305 + 2.22143I
a = 0.247002 + 1.038800I
b = −0.131303 − 0.926881I
1.94667 − 0.60383I 0
u = −1.13305 − 2.22143I
a = 0.247002 − 1.038800I
b = −0.131303 + 0.926881I
1.94667 + 0.60383I 0
12
II. I
u
2
= h1.62 × 10
6
u
15
+ 1.89 × 10
5
u
14
+ · · · + 2.05 × 10
6
b − 3.07 × 10
6
, 1.68 ×
10
6
u
15
− 2.14 × 10
6
u
14
+ · · · + 2.05 × 10
6
a + 2.98 × 10
5
, u
16
− u
15
+ · · · − u + 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
12
=
−0.817866u
15
+ 1.04475u
14
+ ··· + 2.00021u − 0.145471
−0.792705u
15
− 0.0922909u
14
+ ··· + 0.278948u + 1.49795
a
6
=
0.729637u
15
− 0.967738u
14
+ ··· − 2.98482u + 0.0399850
0.196193u
15
+ 0.378990u
14
+ ··· + 2.20563u + 0.831459
a
2
=
−0.192246u
15
+ 0.746718u
14
+ ··· + 2.69815u − 0.322782
0.958092u
15
− 0.390810u
14
+ ··· − 0.0247515u − 1.89818
a
1
=
0.686458u
15
+ 0.569194u
14
+ ··· + 3.16943u − 1.78296
0.404897u
15
− 0.320210u
14
+ ··· − 0.673557u − 1.13918
a
5
=
0.358525u
15
− 0.111506u
14
+ ··· + 0.107810u + 1.23687
−0.816934u
15
+ 0.884996u
14
+ ··· + 2.49795u + 1.60964
a
11
=
−1.61057u
15
+ 0.952455u
14
+ ··· + 2.27916u + 1.35248
−0.792705u
15
− 0.0922909u
14
+ ··· + 0.278948u + 1.49795
a
9
=
−0.0112340u
15
− 0.628733u
14
+ ··· − 0.0790242u + 0.753342
0.196193u
15
− 0.621010u
14
+ ··· − 2.79437u − 1.16854
a
10
=
0.226867u
15
− 0.858932u
14
+ ··· − 0.848647u + 0.482979
0.0412032u
15
− 0.257966u
14
+ ··· − 2.25495u − 0.906080
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
305674
682989
u
15
+
1878059
682989
u
14
+ ··· +
12968633
682989
u −
6937978
682989
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
16
+ 4u
15
+ ··· + 6u + 9
c
2
u
16
+ 6u
15
+ ··· − 8u + 1
c
3
u
16
+ u
15
+ ··· + u + 1
c
4
u
16
− u
15
+ ··· + 3u − 1
c
5
u
16
− 6u
15
+ ··· + 8u + 1
c
6
u
16
+ 2u
15
+ ··· − u − 1
c
7
u
16
− u
15
+ ··· − u + 1
c
8
u
16
− 5u
15
+ ··· − 24u + 3
c
9
u
16
+ u
15
+ ··· − 3u − 1
c
10
u
16
+ 2u
15
+ ··· + 3u + 1
c
11
u
16
− 2u
15
+ ··· + u − 1
c
12
u
16
− 4u
15
+ ··· − 84u + 19
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 24y
14
+ ··· − 342y + 81
c
2
, c
5
y
16
− 14y
15
+ ··· − 92y + 1
c
3
, c
7
y
16
− 3y
15
+ ··· − 9y + 1
c
4
, c
9
y
16
+ 3y
15
+ ··· − 57y + 1
c
6
, c
11
y
16
+ 12y
15
+ ··· − 7y + 1
c
8
y
16
+ 7y
15
+ ··· + 30y + 9
c
10
y
16
+ 10y
15
+ ··· − 7y + 1
c
12
y
16
+ 42y
15
+ ··· − 1470y + 361
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.783327 + 0.431259I
a = 1.98472 + 1.73130I
b = 0.506320 − 0.759510I
4.95066 + 6.44197I −7.47929 − 9.49903I
u = −0.783327 − 0.431259I
a = 1.98472 − 1.73130I
b = 0.506320 + 0.759510I
4.95066 − 6.44197I −7.47929 + 9.49903I
u = −0.769550
a = −2.06724
b = −0.416003
−2.77589 −9.30260
u = 1.317990 + 0.153219I
a = −0.959345 − 0.606084I
b = −0.254210 − 0.816200I
−3.89973 − 3.06301I −14.8110 + 10.7308I
u = 1.317990 − 0.153219I
a = −0.959345 + 0.606084I
b = −0.254210 + 0.816200I
−3.89973 + 3.06301I −14.8110 − 10.7308I
u = 1.280500 + 0.351953I
a = 0.077547 − 0.163165I
b = −1.028010 + 0.495475I
−6.99938 − 2.30685I −14.4564 + 3.2518I
u = 1.280500 − 0.351953I
a = 0.077547 + 0.163165I
b = −1.028010 − 0.495475I
−6.99938 + 2.30685I −14.4564 − 3.2518I
u = 0.633765 + 0.175934I
a = 0.413970 + 0.029249I
b = 0.27230 − 1.64247I
8.56738 − 2.49160I −1.63187 + 0.22782I
u = 0.633765 − 0.175934I
a = 0.413970 − 0.029249I
b = 0.27230 + 1.64247I
8.56738 + 2.49160I −1.63187 − 0.22782I
u = −1.36049 + 0.59822I
a = −0.543626 − 1.179430I
b = −0.660633 + 1.247720I
−4.42847 + 8.52038I −13.6558 − 6.9155I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.36049 − 0.59822I
a = −0.543626 + 1.179430I
b = −0.660633 − 1.247720I
−4.42847 − 8.52038I −13.6558 + 6.9155I
u = 0.231185 + 0.455324I
a = −1.15238 − 2.20524I
b = 0.325781 + 1.209720I
0.70911 − 2.87401I −4.30985 + 2.68066I
u = 0.231185 − 0.455324I
a = −1.15238 + 2.20524I
b = 0.325781 − 1.209720I
0.70911 + 2.87401I −4.30985 − 2.68066I
u = −0.482422
a = −2.04540
b = 0.358793
−2.53212 −15.5700
u = −0.19364 + 2.07771I
a = 0.235435 + 1.139290I
b = −0.132938 − 0.978059I
2.10949 − 0.54207I 0.7802 − 14.5628I
u = −0.19364 − 2.07771I
a = 0.235435 − 1.139290I
b = −0.132938 + 0.978059I
2.10949 + 0.54207I 0.7802 + 14.5628I
19
III. I
u
3
= hb + a + 2, a
2
+ 3a + 3, u + 1i
(i) Arc colorings
a
3
=
0
−1
a
7
=
1
0
a
8
=
1
1
a
4
=
1
0
a
12
=
a
−a − 2
a
6
=
−a − 2
−a − 1
a
2
=
−a − 1
0
a
1
=
−a − 1
0
a
5
=
−a − 3
−a − 1
a
11
=
−2
−a − 2
a
9
=
2a + 1
−a − 2
a
10
=
a − 1
−a − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −15
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
c
2
, c
4
, c
6
u
2
+ u + 1
c
3
, c
10
(u − 1)
2
c
5
, c
9
, c
11
u
2
− u + 1
c
7
, c
12
(u + 1)
2
c
8
u
2
− 3u + 3
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
2
c
2
, c
4
, c
5
c
6
, c
9
, c
11
y
2
+ y + 1
c
3
, c
7
, c
10
c
12
(y −1)
2
c
8
y
2
− 3y + 9
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.50000 + 0.86603I
b = −0.500000 − 0.866025I
−3.28987 −15.0000
u = −1.00000
a = −1.50000 − 0.86603I
b = −0.500000 + 0.866025I
−3.28987 −15.0000
23
IV. I
u
4
= hb − 1, a, u + 1i
(i) Arc colorings
a
3
=
0
−1
a
7
=
1
0
a
8
=
1
1
a
4
=
1
0
a
12
=
0
1
a
6
=
1
−1
a
2
=
−1
0
a
1
=
−1
0
a
5
=
0
−1
a
11
=
1
1
a
9
=
1
1
a
10
=
2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
c
2
, c
3
, c
4
c
6
, c
10
u − 1
c
5
, c
7
, c
9
c
11
, c
12
u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
10
, c
11
c
12
y −1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0
b = 1.00000
−3.28987 −12.0000
27
V. I
u
5
= hb − 1, a − 3, 2u − 1i
(i) Arc colorings
a
3
=
0
0.5
a
7
=
1
0
a
8
=
1
0.25
a
4
=
−0.5
0.375
a
12
=
3
1
a
6
=
−2
−1
a
2
=
2
1.5
a
1
=
2.75
0.9375
a
5
=
0
0.5
a
11
=
4
1
a
9
=
1
0.25
a
10
=
1.25
0.0625
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2.0625
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
2(2u − 3)
c
2
, c
6
, c
10
u − 1
c
3
, c
4
2(2u + 1)
c
5
, c
11
u + 1
c
7
, c
9
2(2u − 1)
c
8
u
c
12
4(4u + 1)
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
4(4y −9)
c
2
, c
5
, c
6
c
10
, c
11
y −1
c
3
, c
4
, c
7
c
9
4(4y −1)
c
8
y
c
12
16(16y −1)
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000
a = 3.00000
b = 1.00000
−3.28987 2.06250
31
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
4u
3
(2u − 3)(u
16
+ 4u
15
+ ··· + 6u + 9)(2u
72
− 7u
71
+ ··· + 3152u + 248)
c
2
((u − 1)
2
)(u
2
+ u + 1)(u
16
+ 6u
15
+ ··· − 8u + 1)
· (u
72
+ 2u
71
+ ··· + 3215u + 491)
c
3
4(u − 1)
3
(2u + 1)(u
16
+ u
15
+ ··· + u + 1)
· (2u
72
− 3u
71
+ ··· − 314u − 29)
c
4
4(u − 1)(2u + 1)(u
2
+ u + 1)(u
16
− u
15
+ ··· + 3u − 1)
· (2u
72
+ 3u
71
+ ··· − 3289u + 373)
c
5
((u + 1)
2
)(u
2
− u + 1)(u
16
− 6u
15
+ ··· + 8u + 1)
· (u
72
+ 2u
71
+ ··· + 3215u + 491)
c
6
((u − 1)
2
)(u
2
+ u + 1)(u
16
+ 2u
15
+ ··· − u − 1)
· (u
72
+ 2u
71
+ ··· − 32u − 13)
c
7
4(u + 1)
3
(2u − 1)(u
16
− u
15
+ ··· − u + 1)
· (2u
72
− 3u
71
+ ··· − 314u − 29)
c
8
u
2
(u
2
− 3u + 3)(u
16
− 5u
15
+ ··· − 24u + 3)(u
72
− 9u
71
+ ··· − 34u − 16)
c
9
4(u + 1)(2u − 1)(u
2
− u + 1)(u
16
+ u
15
+ ··· − 3u − 1)
· (2u
72
+ 3u
71
+ ··· − 3289u + 373)
c
10
((u − 1)
4
)(u
16
+ 2u
15
+ ··· + 3u + 1)(u
72
− u
71
+ ··· − 868u + 172)
c
11
((u + 1)
2
)(u
2
− u + 1)(u
16
− 2u
15
+ ··· + u − 1)
· (u
72
+ 2u
71
+ ··· − 32u − 13)
c
12
16(u + 1)
3
(4u + 1)(u
16
− 4u
15
+ ··· − 84u + 19)
· (4u
72
+ 7u
71
+ ··· + 3105391u − 546509)
32
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
16y
3
(4y −9)(y
16
− 24y
14
+ ··· − 342y + 81)
· (4y
72
+ 315y
71
+ ··· + 10782816y + 61504)
c
2
, c
5
((y −1)
2
)(y
2
+ y + 1)(y
16
− 14y
15
+ ··· − 92y + 1)
· (y
72
− 34y
71
+ ··· − 7263547y + 241081)
c
3
, c
7
16(y −1)
3
(4y −1)(y
16
− 3y
15
+ ··· − 9y + 1)
· (4y
72
− 149y
71
+ ··· − 158162y + 841)
c
4
, c
9
16(y −1)(4y −1)(y
2
+ y + 1)(y
16
+ 3y
15
+ ··· − 57y + 1)
· (4y
72
− 273y
71
+ ··· − 10651163y + 139129)
c
6
, c
11
((y −1)
2
)(y
2
+ y + 1)(y
16
+ 12y
15
+ ··· − 7y + 1)
· (y
72
+ 40y
71
+ ··· + 1758y + 169)
c
8
y
2
(y
2
− 3y + 9)(y
16
+ 7y
15
+ ··· + 30y + 9)
· (y
72
+ 13y
71
+ ··· − 21636y + 256)
c
10
((y −1)
4
)(y
16
+ 10y
15
+ ··· − 7y + 1)
· (y
72
+ 71y
71
+ ··· + 1106584y + 29584)
c
12
256(y −1)
3
(16y −1)(y
16
+ 42y
15
+ ··· − 1470y + 361)
· (16y
72
+ 383y
71
+ ··· − 22583235390339y + 298672087081)
33
