12a
0281
(K12a
0281
)
A knot diagram
1
Linearized knot diagam
3 6 8 9 2 12 11 10 5 4 1 7
Solving Sequence
2,5
6
3,9
10 1 4 11 12 8 7
c
5
c
2
c
9
c
1
c
4
c
10
c
11
c
8
c
7
c
3
, c
6
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h5u
42
+ 12u
41
+ ··· + 8b − 19, 11u
42
+ 29u
41
+ ··· + 8a − 44, u
43
+ u
42
+ ··· + 2u + 1i
I
u
2
= h2.26163 × 10
32
u
69
− 1.52330 × 10
31
u
68
+ ··· + 1.91814 × 10
32
b + 6.95419 × 10
32
,
− 2.76673 × 10
33
u
69
− 1.62384 × 10
33
u
68
+ ··· + 9.59072 × 10
32
a − 2.22275 × 10
34
, u
70
+ u
69
+ ··· + 14u + 5i
I
u
3
= h3a
3
+ 14a
2
+ 155b − 74a − 75, a
4
− 12a
2
+ 4a + 65, u − 1i
I
u
4
= h−a
2
+ b − 3a − 2, a
3
+ 3a
2
+ 3a + 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 120 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
=
h5u
42
+12u
41
+· · ·+8b−19, 11u
42
+29u
41
+· · ·+8a−44, u
43
+u
42
+· · ·+2u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−1.37500u
42
− 3.62500u
41
+ ··· + 10.8750u + 5.50000
−
5
8
u
42
−
3
2
u
41
+ ··· +
37
8
u +
19
8
a
10
=
−
3
4
u
42
−
17
8
u
41
+ ··· +
25
4
u +
25
8
−
5
8
u
42
−
3
2
u
41
+ ··· +
37
8
u +
19
8
a
1
=
u
3
u
5
− u
3
+ u
a
4
=
1
8
u
42
+
11
8
u
41
+ ··· −
25
8
u −
3
2
1
8
u
42
+
5
4
u
41
+ ··· −
15
8
u −
11
8
a
11
=
−
1
8
u
41
−
1
8
u
40
+ ··· −
3
4
u +
1
8
−
1
8
u
41
−
1
8
u
40
+ ··· −
3
4
u +
1
8
a
12
=
−
1
8
u
41
−
1
8
u
40
+ ··· −
3
4
u +
1
8
−
1
8
u
41
−
1
8
u
40
+ ··· −
3
4
u +
1
8
a
8
=
1
8
u
42
+
1
8
u
41
+ ··· −
1
8
u + 1
1
8
u
42
+
1
8
u
41
+ ··· +
3
4
u
2
−
1
8
u
a
7
=
1
8
u
42
+
1
8
u
41
+ ··· −
1
8
u + 1
1
8
u
42
+
1
8
u
41
+ ··· +
7
4
u
2
−
1
8
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
7
2
u
42
−
19
4
u
41
+ ··· −
1
2
u −
49
4
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
43
+ 21u
42
+ ··· + 10u + 1
c
2
, c
5
, c
6
c
12
u
43
+ u
42
+ ··· + 2u + 1
c
3
u
43
+ 3u
42
+ ··· + 238u + 194
c
4
, c
9
u
43
− 3u
42
+ ··· − 6u + 2
c
7
u
43
+ 3u
42
+ ··· + 256u + 256
c
8
u
43
+ 21u
42
+ ··· + 4u + 4
c
10
u
43
− 9u
42
+ ··· − 118u + 38
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
43
+ 11y
42
+ ··· + 18y −1
c
2
, c
5
, c
6
c
12
y
43
− 21y
42
+ ··· + 10y −1
c
3
y
43
+ 3y
42
+ ··· + 106308y −37636
c
4
, c
9
y
43
− 21y
42
+ ··· + 4y −4
c
7
y
43
+ 23y
42
+ ··· + 1441792y −65536
c
8
y
43
+ 3y
42
+ ··· + 80y −16
c
10
y
43
+ 15y
42
+ ··· − 31068y −1444
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.748644 + 0.637641I
a = 0.080537 − 0.526871I
b = 1.013350 + 0.562622I
1.89821 − 0.96458I −3.28074 − 0.62200I
u = −0.748644 − 0.637641I
a = 0.080537 + 0.526871I
b = 1.013350 − 0.562622I
1.89821 + 0.96458I −3.28074 + 0.62200I
u = 0.804750 + 0.623565I
a = 0.222175 − 1.018610I
b = 0.529140 + 0.662060I
3.32140 − 3.80226I −0.99469 + 6.39942I
u = 0.804750 − 0.623565I
a = 0.222175 + 1.018610I
b = 0.529140 − 0.662060I
3.32140 + 3.80226I −0.99469 − 6.39942I
u = −0.900705 + 0.522951I
a = −1.36239 − 0.90089I
b = −1.035780 − 0.144530I
−1.80687 + 4.07167I −9.95788 − 6.11472I
u = −0.900705 − 0.522951I
a = −1.36239 + 0.90089I
b = −1.035780 + 0.144530I
−1.80687 − 4.07167I −9.95788 + 6.11472I
u = 0.894694 + 0.620124I
a = −0.903919 − 0.027255I
b = 0.412108 − 0.716509I
2.75595 − 5.96538I −2.44764 + 6.68032I
u = 0.894694 − 0.620124I
a = −0.903919 + 0.027255I
b = 0.412108 + 0.716509I
2.75595 + 5.96538I −2.44764 − 6.68032I
u = −0.929214 + 0.629305I
a = 1.48748 + 2.03173I
b = 1.082430 − 0.572492I
0.79286 + 10.89690I −5.90232 − 10.97141I
u = −0.929214 − 0.629305I
a = 1.48748 − 2.03173I
b = 1.082430 + 0.572492I
0.79286 − 10.89690I −5.90232 + 10.97141I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.821297 + 0.283255I
a = −2.93341 + 0.45122I
b = −1.139100 − 0.422179I
−4.79407 − 5.18096I −10.28186 + 9.63354I
u = 0.821297 − 0.283255I
a = −2.93341 − 0.45122I
b = −1.139100 + 0.422179I
−4.79407 + 5.18096I −10.28186 − 9.63354I
u = −0.230146 + 0.788552I
a = −1.13253 + 1.42685I
b = −1.118980 − 0.552972I
−0.99153 − 7.44962I −4.80788 + 5.14749I
u = −0.230146 − 0.788552I
a = −1.13253 − 1.42685I
b = −1.118980 + 0.552972I
−0.99153 + 7.44962I −4.80788 − 5.14749I
u = −0.469810 + 0.644333I
a = −0.302237 − 1.339690I
b = −0.975090 + 0.534458I
1.37306 + 3.64200I −1.97274 − 6.09907I
u = −0.469810 − 0.644333I
a = −0.302237 + 1.339690I
b = −0.975090 − 0.534458I
1.37306 − 3.64200I −1.97274 + 6.09907I
u = 0.766243 + 0.202401I
a = 2.75313 − 0.25431I
b = 1.137770 − 0.456668I
−4.56135 + 2.74808I −8.63761 + 1.53004I
u = 0.766243 − 0.202401I
a = 2.75313 + 0.25431I
b = 1.137770 + 0.456668I
−4.56135 − 2.74808I −8.63761 − 1.53004I
u = −0.735504 + 0.278747I
a = 0.282174 − 0.733558I
b = 0.039236 − 0.647029I
−1.56483 + 1.33884I −5.91775 − 5.05918I
u = −0.735504 − 0.278747I
a = 0.282174 + 0.733558I
b = 0.039236 + 0.647029I
−1.56483 − 1.33884I −5.91775 + 5.05918I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.244913 + 0.744578I
a = 0.531179 + 0.238214I
b = −0.323354 − 0.721542I
1.32443 + 2.58910I −1.27516 − 1.34286I
u = 0.244913 − 0.744578I
a = 0.531179 − 0.238214I
b = −0.323354 + 0.721542I
1.32443 − 2.58910I −1.27516 + 1.34286I
u = 1.156160 + 0.436646I
a = −2.27777 + 0.12084I
b = −1.157530 + 0.522173I
−8.54240 + 0.05443I −13.25807 + 1.27713I
u = 1.156160 − 0.436646I
a = −2.27777 − 0.12084I
b = −1.157530 − 0.522173I
−8.54240 − 0.05443I −13.25807 − 1.27713I
u = −1.151630 + 0.457340I
a = −0.353184 + 0.596905I
b = −0.199663 + 0.761913I
−5.75226 + 4.72408I −9.80399 − 4.71758I
u = −1.151630 − 0.457340I
a = −0.353184 − 0.596905I
b = −0.199663 − 0.761913I
−5.75226 − 4.72408I −9.80399 + 4.71758I
u = 0.368859 + 0.661669I
a = 0.306430 − 0.852800I
b = −0.587313 + 0.602075I
2.51319 + 0.87621I 0.614769 − 0.778636I
u = 0.368859 − 0.661669I
a = 0.306430 + 0.852800I
b = −0.587313 − 0.602075I
2.51319 − 0.87621I 0.614769 + 0.778636I
u = −1.139070 + 0.530786I
a = −0.355456 − 0.234216I
b = −0.851539 − 0.591728I
−2.78091 + 5.63282I −7.68461 − 3.26690I
u = −1.139070 − 0.530786I
a = −0.355456 + 0.234216I
b = −0.851539 + 0.591728I
−2.78091 − 5.63282I −7.68461 + 3.26690I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140641 + 0.728292I
a = 1.221290 − 0.180259I
b = 1.104910 − 0.276140I
−2.87123 + 0.12831I −7.71481 − 0.77840I
u = −0.140641 − 0.728292I
a = 1.221290 + 0.180259I
b = 1.104910 + 0.276140I
−2.87123 − 0.12831I −7.71481 + 0.77840I
u = 1.178850 + 0.464753I
a = 2.75499 − 0.42952I
b = 1.173340 + 0.326229I
−9.87566 − 8.22613I −14.9046 + 7.3441I
u = 1.178850 − 0.464753I
a = 2.75499 + 0.42952I
b = 1.173340 − 0.326229I
−9.87566 + 8.22613I −14.9046 − 7.3441I
u = 1.165570 + 0.544375I
a = −1.09575 + 0.95090I
b = −0.701705 − 0.646518I
−2.33002 − 10.45450I −6.00000 + 9.18893I
u = 1.165570 − 0.544375I
a = −1.09575 − 0.95090I
b = −0.701705 + 0.646518I
−2.33002 + 10.45450I −6.00000 − 9.18893I
u = −1.206960 + 0.526147I
a = 2.05937 + 1.28523I
b = 1.169220 + 0.252610I
−8.97242 + 9.46345I −14.0760 − 5.8340I
u = −1.206960 − 0.526147I
a = 2.05937 − 1.28523I
b = 1.169220 − 0.252610I
−8.97242 − 9.46345I −14.0760 + 5.8340I
u = 1.203670 + 0.545583I
a = 0.839018 + 0.724019I
b = −0.298947 + 0.789061I
−4.36938 − 12.53960I −6.00000 + 7.94110I
u = 1.203670 − 0.545583I
a = 0.839018 − 0.724019I
b = −0.298947 − 0.789061I
−4.36938 + 12.53960I −6.00000 − 7.94110I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.214000 + 0.548661I
a = −2.58304 − 1.74814I
b = −1.144850 + 0.564961I
−6.8639 + 17.6023I −6.00000 − 11.44619I
u = −1.214000 − 0.548661I
a = −2.58304 + 1.74814I
b = −1.144850 − 0.564961I
−6.8639 − 17.6023I −6.00000 + 11.44619I
u = −0.477384
a = 1.52383
b = 0.744709
−1.08036 −9.00420
9
II.
I
u
2
= h2.26×10
32
u
69
−1.52×10
31
u
68
+· · ·+1.92×10
32
b+6.95×10
32
, −2.77×
10
33
u
69
−1.62×10
33
u
68
+· · ·+9.59×10
32
a−2.22×10
34
, u
70
+u
69
+· · ·+14u+5i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
2.88480u
69
+ 1.69314u
68
+ ··· + 45.6456u + 23.1760
−1.17907u
69
+ 0.0794152u
68
+ ··· − 5.46180u − 3.62548
a
10
=
4.06388u
69
+ 1.61372u
68
+ ··· + 51.1074u + 26.8015
−1.17907u
69
+ 0.0794152u
68
+ ··· − 5.46180u − 3.62548
a
1
=
u
3
u
5
− u
3
+ u
a
4
=
−2.48460u
69
− 1.83539u
68
+ ··· − 42.8103u − 20.1308
0.313075u
69
− 0.0137492u
68
+ ··· + 0.361832u + 3.97119
a
11
=
1.01374u
69
+ 1.31338u
68
+ ··· + 16.8630u + 10.0091
−0.802260u
69
− 0.995297u
68
+ ··· − 18.0333u − 8.31468
a
12
=
1.07882u
69
+ 1.15734u
68
+ ··· + 21.7282u + 11.2174
−1.17518u
69
− 1.49537u
68
+ ··· − 26.6216u − 8.81004
a
8
=
−1.17026u
69
− 1.03708u
68
+ ··· − 17.8795u − 14.3278
−0.0599899u
69
+ 0.0501336u
68
+ ··· + 11.0870u + 8.41410
a
7
=
−1.60497u
69
− 1.02250u
68
+ ··· − 11.2062u − 7.83476
−0.241672u
69
− 0.176589u
68
+ ··· + 3.75637u + 2.48177
(ii) Obstruction class = −1
(iii) Cusp Shapes = −7.12152u
69
− 2.74694u
68
+ ··· − 113.643u − 66.9331
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
70
+ 41u
69
+ ··· + 116u + 25
c
2
, c
5
, c
6
c
12
u
70
+ u
69
+ ··· + 14u + 5
c
3
(u
35
− u
34
+ ··· − 8u + 1)
2
c
4
, c
9
(u
35
+ u
34
+ ··· + 2u + 1)
2
c
7
(u
35
+ 3u
34
+ ··· + 14u + 5)
2
c
8
(u
35
+ 17u
34
+ ··· + 2u + 1)
2
c
10
(u
35
+ 3u
34
+ ··· + 58u + 7)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
70
− 25y
69
+ ··· − 22056y + 625
c
2
, c
5
, c
6
c
12
y
70
− 41y
69
+ ··· − 116y + 25
c
3
(y
35
− y
34
+ ··· + 34y −1)
2
c
4
, c
9
(y
35
− 17y
34
+ ··· + 2y −1)
2
c
7
(y
35
+ 23y
34
+ ··· + 166y −25)
2
c
8
(y
35
+ 3y
34
+ ··· − 14y −1)
2
c
10
(y
35
+ 11y
34
+ ··· + 1446y −49)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.793674 + 0.627689I
a = −0.99722 − 1.98668I
b = −1.053770 + 0.564883I
1.77010 + 5.85664I −3.47437 − 5.76903I
u = −0.793674 − 0.627689I
a = −0.99722 + 1.98668I
b = −1.053770 − 0.564883I
1.77010 − 5.85664I −3.47437 + 5.76903I
u = −0.921362 + 0.317106I
a = 0.691410 − 1.228980I
b = −0.996188 − 0.423828I
−4.82753 − 1.71623I −11.26691 + 0.I
u = −0.921362 − 0.317106I
a = 0.691410 + 1.228980I
b = −0.996188 + 0.423828I
−4.82753 + 1.71623I −11.26691 + 0.I
u = 0.739547 + 0.624054I
a = 0.820919 − 0.310599I
b = −0.460984 + 0.678579I
3.50734 − 1.04155I − 60.10 + 0.572954I
u = 0.739547 − 0.624054I
a = 0.820919 + 0.310599I
b = −0.460984 − 0.678579I
3.50734 + 1.04155I − 60.10 − 0.572954I
u = 0.630984 + 0.657903I
a = 0.122104 + 0.833410I
b = −0.460984 − 0.678579I
3.50734 + 1.04155I −0.146267 − 0.572954I
u = 0.630984 − 0.657903I
a = 0.122104 − 0.833410I
b = −0.460984 + 0.678579I
3.50734 − 1.04155I −0.146267 + 0.572954I
u = −0.586712 + 0.693730I
a = −0.303058 + 0.936732I
b = −1.053770 − 0.564883I
1.77010 − 5.85664I −3.47437 + 5.76903I
u = −0.586712 − 0.693730I
a = −0.303058 − 0.936732I
b = −1.053770 + 0.564883I
1.77010 + 5.85664I −3.47437 − 5.76903I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.178332 + 0.886392I
a = 1.31932 − 1.25242I
b = 1.134940 + 0.561389I
−3.75035 − 12.38410I −8.15786 + 8.57579I
u = −0.178332 − 0.886392I
a = 1.31932 + 1.25242I
b = 1.134940 − 0.561389I
−3.75035 + 12.38410I −8.15786 − 8.57579I
u = 0.185862 + 0.864939I
a = −0.416310 − 0.083692I
b = 0.308085 + 0.766136I
−1.32397 + 7.38977I −4.98434 − 5.00078I
u = 0.185862 − 0.864939I
a = −0.416310 + 0.083692I
b = 0.308085 − 0.766136I
−1.32397 − 7.38977I −4.98434 + 5.00078I
u = −0.144791 + 0.848190I
a = −1.42439 + 0.13590I
b = −1.146120 + 0.254789I
−5.81015 − 4.45397I −11.15239 + 2.81525I
u = −0.144791 − 0.848190I
a = −1.42439 − 0.13590I
b = −1.146120 − 0.254789I
−5.81015 + 4.45397I −11.15239 − 2.81525I
u = −1.029850 + 0.501579I
a = 0.184614 + 0.230509I
b = 0.890522 + 0.542191I
−0.250501 + 0.838616I 0
u = −1.029850 − 0.501579I
a = 0.184614 − 0.230509I
b = 0.890522 − 0.542191I
−0.250501 − 0.838616I 0
u = 1.094160 + 0.367378I
a = −1.35264 + 1.51551I
b = −0.688085 − 0.531421I
−4.07070 − 2.01862I 0
u = 1.094160 − 0.367378I
a = −1.35264 − 1.51551I
b = −0.688085 + 0.531421I
−4.07070 + 2.01862I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.237931 + 0.803328I
a = −0.006775 + 0.772034I
b = 0.665614 − 0.623440I
0.41242 + 5.45820I −3.39004 − 5.96309I
u = 0.237931 − 0.803328I
a = −0.006775 − 0.772034I
b = 0.665614 + 0.623440I
0.41242 − 5.45820I −3.39004 + 5.96309I
u = −1.164710 + 0.016951I
a = 0.367943 − 0.438805I
b = 0.396163 − 0.521609I
−2.19805 − 0.44632I 0
u = −1.164710 − 0.016951I
a = 0.367943 + 0.438805I
b = 0.396163 + 0.521609I
−2.19805 + 0.44632I 0
u = −1.125860 + 0.332862I
a = 0.336942 − 0.575199I
b = 0.217277 − 0.699987I
−2.69753 + 0.59945I 0
u = −1.125860 − 0.332862I
a = 0.336942 + 0.575199I
b = 0.217277 + 0.699987I
−2.69753 − 0.59945I 0
u = 1.188300 + 0.142603I
a = −2.52952 + 0.58517I
b = −0.996188 − 0.423828I
−4.82753 − 1.71623I 0
u = 1.188300 − 0.142603I
a = −2.52952 − 0.58517I
b = −0.996188 + 0.423828I
−4.82753 + 1.71623I 0
u = 1.087540 + 0.520480I
a = 0.98039 − 1.12342I
b = 0.665614 + 0.623440I
0.41242 − 5.45820I 0
u = 1.087540 − 0.520480I
a = 0.98039 + 1.12342I
b = 0.665614 − 0.623440I
0.41242 + 5.45820I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.209060 + 0.033666I
a = 2.36745 + 0.25960I
b = 1.059800 − 0.502369I
−4.09889 + 4.67146I 0
u = 1.209060 − 0.033666I
a = 2.36745 − 0.25960I
b = 1.059800 + 0.502369I
−4.09889 − 4.67146I 0
u = −0.279476 + 0.738470I
a = 0.380082 + 1.009830I
b = 0.890522 − 0.542191I
−0.250501 − 0.838616I −4.53860 − 0.32367I
u = −0.279476 − 0.738470I
a = 0.380082 − 1.009830I
b = 0.890522 + 0.542191I
−0.250501 + 0.838616I −4.53860 + 0.32367I
u = 1.170540 + 0.309953I
a = 2.31769 − 0.03429I
b = 1.131430 − 0.520956I
−5.29071 + 4.02658I 0
u = 1.170540 − 0.309953I
a = 2.31769 + 0.03429I
b = 1.131430 + 0.520956I
−5.29071 − 4.02658I 0
u = −1.195020 + 0.281595I
a = −0.424932 − 0.412941I
b = −0.688085 − 0.531421I
−4.07070 − 2.01862I 0
u = −1.195020 − 0.281595I
a = −0.424932 + 0.412941I
b = −0.688085 + 0.531421I
−4.07070 + 2.01862I 0
u = 1.166680 + 0.383023I
a = −2.78317 + 0.44147I
b = −1.141570 − 0.325389I
−6.61464 − 3.85709I 0
u = 1.166680 − 0.383023I
a = −2.78317 − 0.44147I
b = −1.141570 + 0.325389I
−6.61464 + 3.85709I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.149290 + 0.441973I
a = 1.121900 + 0.806342I
b = −0.276974 + 0.740238I
−5.86442 − 3.36312I 0
u = 1.149290 − 0.441973I
a = 1.121900 − 0.806342I
b = −0.276974 − 0.740238I
−5.86442 + 3.36312I 0
u = −0.698993 + 0.306329I
a = −0.45204 + 3.09002I
b = 1.059800 − 0.502369I
−4.09889 + 4.67146I −8.51273 − 7.37463I
u = −0.698993 − 0.306329I
a = −0.45204 − 3.09002I
b = 1.059800 + 0.502369I
−4.09889 − 4.67146I −8.51273 + 7.37463I
u = −1.155970 + 0.462646I
a = −2.75547 − 2.20046I
b = −1.134810 + 0.545503I
−8.35620 + 8.22097I 0
u = −1.155970 − 0.462646I
a = −2.75547 + 2.20046I
b = −1.134810 − 0.545503I
−8.35620 − 8.22097I 0
u = −0.623001 + 0.405449I
a = 1.237280 + 0.532014I
b = 0.903342
−0.945432 −7.85887 + 0.I
u = −0.623001 − 0.405449I
a = 1.237280 − 0.532014I
b = 0.903342
−0.945432 −7.85887 + 0.I
u = −1.184780 + 0.432685I
a = 2.03697 + 1.61827I
b = 1.142990 + 0.287310I
−10.10360 + 0.30557I 0
u = −1.184780 − 0.432685I
a = 2.03697 − 1.61827I
b = 1.142990 − 0.287310I
−10.10360 − 0.30557I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.035280 + 0.733280I
a = −1.39985 + 0.49717I
b = −1.141570 + 0.325389I
−6.61464 + 3.85709I −12.01107 − 3.91391I
u = 0.035280 − 0.733280I
a = −1.39985 − 0.49717I
b = −1.141570 − 0.325389I
−6.61464 − 3.85709I −12.01107 + 3.91391I
u = 1.149890 + 0.529483I
a = −0.943407 − 0.655113I
b = 0.308085 − 0.766136I
−1.32397 − 7.38977I 0
u = 1.149890 − 0.529483I
a = −0.943407 + 0.655113I
b = 0.308085 + 0.766136I
−1.32397 + 7.38977I 0
u = −1.164290 + 0.498574I
a = −1.93672 − 1.37737I
b = −1.146120 − 0.254789I
−5.81015 + 4.45397I 0
u = −1.164290 − 0.498574I
a = −1.93672 + 1.37737I
b = −1.146120 + 0.254789I
−5.81015 − 4.45397I 0
u = −1.165560 + 0.537682I
a = 2.49847 + 1.93336I
b = 1.134940 − 0.561389I
−3.75035 + 12.38410I 0
u = −1.165560 − 0.537682I
a = 2.49847 − 1.93336I
b = 1.134940 + 0.561389I
−3.75035 − 12.38410I 0
u = −1.257860 + 0.336624I
a = −0.370212 + 0.569226I
b = −0.276974 + 0.740238I
−5.86442 − 3.36312I 0
u = −1.257860 − 0.336624I
a = −0.370212 − 0.569226I
b = −0.276974 − 0.740238I
−5.86442 + 3.36312I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.248730 + 0.369448I
a = 2.80639 − 0.41145I
b = 1.142990 + 0.287310I
−10.10360 + 0.30557I 0
u = 1.248730 − 0.369448I
a = 2.80639 + 0.41145I
b = 1.142990 − 0.287310I
−10.10360 − 0.30557I 0
u = 0.674686 + 0.151897I
a = −1.80142 + 1.47569I
b = 0.396163 − 0.521609I
−2.19805 − 0.44632I −3.26109 + 2.08073I
u = 0.674686 − 0.151897I
a = −1.80142 − 1.47569I
b = 0.396163 + 0.521609I
−2.19805 + 0.44632I −3.26109 − 2.08073I
u = 1.276560 + 0.342849I
a = −2.23310 + 0.02681I
b = −1.134810 + 0.545503I
−8.35620 + 8.22097I 0
u = 1.276560 − 0.342849I
a = −2.23310 − 0.02681I
b = −1.134810 − 0.545503I
−8.35620 − 8.22097I 0
u = −0.041921 + 0.655776I
a = 1.62553 − 1.90135I
b = 1.131430 + 0.520956I
−5.29071 − 4.02658I −10.01018 + 2.90516I
u = −0.041921 − 0.655776I
a = 1.62553 + 1.90135I
b = 1.131430 − 0.520956I
−5.29071 + 4.02658I −10.01018 − 2.90516I
u = −0.032872 + 0.638178I
a = −0.785149 + 0.173061I
b = 0.217277 + 0.699987I
−2.69753 − 0.59945I −6.70115 + 0.74081I
u = −0.032872 − 0.638178I
a = −0.785149 − 0.173061I
b = 0.217277 − 0.699987I
−2.69753 + 0.59945I −6.70115 − 0.74081I
19
III. I
u
3
= h3a
3
+ 14a
2
+ 155b − 74a − 75, a
4
− 12a
2
+ 4a + 65, u − 1i
(i) Arc colorings
a
2
=
0
1
a
5
=
1
0
a
6
=
1
1
a
3
=
−1
0
a
9
=
a
−0.0193548a
3
− 0.0903226a
2
+ 0.477419a + 0.483871
a
10
=
0.0193548a
3
+ 0.0903226a
2
+ 0.522581a − 0.483871
−0.0193548a
3
− 0.0903226a
2
+ 0.477419a + 0.483871
a
1
=
1
1
a
4
=
0.0903226a
3
− 0.245161a
2
− 0.561290a − 0.258065
0.0645161a
3
− 0.0322581a
2
− 0.258065a − 0.612903
a
11
=
0.0258065a
3
− 0.212903a
2
− 0.303226a + 2.35484
0.0258065a
3
− 0.212903a
2
− 0.303226a + 1.35484
a
12
=
0.0258065a
3
− 0.212903a
2
− 0.303226a + 3.35484
0.0258065a
3
− 0.212903a
2
− 0.303226a + 2.35484
a
8
=
−0.0258065a
3
+ 0.212903a
2
+ 0.303226a − 2.35484
−0.0258065a
3
+ 0.212903a
2
+ 0.303226a − 1.35484
a
7
=
−0.0258065a
3
+ 0.212903a
2
+ 0.303226a − 2.35484
−0.0258065a
3
+ 0.212903a
2
+ 0.303226a − 1.35484
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
8
31
a
3
+
4
31
a
2
+
32
31
a −
544
31
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
11
c
12
(u − 1)
4
c
2
, c
6
(u + 1)
4
c
3
, c
10
u
4
+ 2u
2
+ 2
c
4
, c
9
u
4
− 2u
2
+ 2
c
7
u
4
c
8
(u
2
− 2u + 2)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y −1)
4
c
3
, c
10
(y
2
+ 2y + 2)
2
c
4
, c
9
(y
2
− 2y + 2)
2
c
7
y
4
c
8
(y
2
+ 4)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −2.65246 + 0.81150I
b = −1.098680 + 0.455090I
−5.75727 + 3.66386I −16.0000 − 4.0000I
u = 1.00000
a = −2.65246 − 0.81150I
b = −1.098680 − 0.455090I
−5.75727 − 3.66386I −16.0000 + 4.0000I
u = 1.00000
a = 2.65246 + 1.18850I
b = 1.098680 − 0.455090I
−5.75727 + 3.66386I −16.0000 − 4.0000I
u = 1.00000
a = 2.65246 − 1.18850I
b = 1.098680 + 0.455090I
−5.75727 − 3.66386I −16.0000 + 4.0000I
23
IV. I
u
4
= h−a
2
+ b − 3a − 2, a
3
+ 3a
2
+ 3a + 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
3
=
1
0
a
9
=
a
a
2
+ 3a + 2
a
10
=
−a
2
− 2a − 2
a
2
+ 3a + 2
a
1
=
−1
−1
a
4
=
a + 2
−a
2
− 2a − 1
a
11
=
a
2
+ 3a + 1
a
2
+ 3a + 2
a
12
=
a
2
+ 3a
a
2
+ 3a + 1
a
8
=
a
2
+ 3a + 1
a
2
+ 3a + 2
a
7
=
a
2
+ 3a + 1
a
2
+ 3a + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a
2
+ 8a − 8
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
11
(u − 1)
3
c
3
, c
4
, c
7
c
8
, c
9
, c
10
u
3
c
5
, c
12
(u + 1)
3
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y −1)
3
c
3
, c
4
, c
7
c
8
, c
9
, c
10
y
3
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0
−3.28987 −12.0000
u = −1.00000
a = −1.00000
b = 0
−3.28987 −12.0000
u = −1.00000
a = −1.00000
b = 0
−3.28987 −12.0000
27
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
((u − 1)
7
)(u
43
+ 21u
42
+ ··· + 10u + 1)(u
70
+ 41u
69
+ ··· + 116u + 25)
c
2
, c
6
((u − 1)
3
)(u + 1)
4
(u
43
+ u
42
+ ··· + 2u + 1)(u
70
+ u
69
+ ··· + 14u + 5)
c
3
u
3
(u
4
+ 2u
2
+ 2)(u
35
− u
34
+ ··· − 8u + 1)
2
· (u
43
+ 3u
42
+ ··· + 238u + 194)
c
4
, c
9
u
3
(u
4
− 2u
2
+ 2)(u
35
+ u
34
+ ··· + 2u + 1)
2
(u
43
− 3u
42
+ ··· − 6u + 2)
c
5
, c
12
((u − 1)
4
)(u + 1)
3
(u
43
+ u
42
+ ··· + 2u + 1)(u
70
+ u
69
+ ··· + 14u + 5)
c
7
u
7
(u
35
+ 3u
34
+ ··· + 14u + 5)
2
(u
43
+ 3u
42
+ ··· + 256u + 256)
c
8
u
3
(u
2
− 2u + 2)
2
(u
35
+ 17u
34
+ ··· + 2u + 1)
2
· (u
43
+ 21u
42
+ ··· + 4u + 4)
c
10
u
3
(u
4
+ 2u
2
+ 2)(u
35
+ 3u
34
+ ··· + 58u + 7)
2
· (u
43
− 9u
42
+ ··· − 118u + 38)
28
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
((y −1)
7
)(y
43
+ 11y
42
+ ··· + 18y −1)
· (y
70
− 25y
69
+ ··· − 22056y + 625)
c
2
, c
5
, c
6
c
12
((y −1)
7
)(y
43
− 21y
42
+ ··· + 10y −1)(y
70
− 41y
69
+ ··· − 116y + 25)
c
3
y
3
(y
2
+ 2y + 2)
2
(y
35
− y
34
+ ··· + 34y −1)
2
· (y
43
+ 3y
42
+ ··· + 106308y −37636)
c
4
, c
9
y
3
(y
2
− 2y + 2)
2
(y
35
− 17y
34
+ ··· + 2y −1)
2
· (y
43
− 21y
42
+ ··· + 4y −4)
c
7
y
7
(y
35
+ 23y
34
+ ··· + 166y −25)
2
· (y
43
+ 23y
42
+ ··· + 1441792y −65536)
c
8
y
3
(y
2
+ 4)
2
(y
35
+ 3y
34
+ ··· − 14y −1)
2
(y
43
+ 3y
42
+ ··· + 80y −16)
c
10
y
3
(y
2
+ 2y + 2)
2
(y
35
+ 11y
34
+ ··· + 1446y −49)
2
· (y
43
+ 15y
42
+ ··· − 31068y −1444)
29
