12a
0057
(K12a
0057
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 8 4 12 6 1 9 11
Solving Sequence
8,12 4,9
7 3 6 11 1 2 10 5
c
8
c
7
c
3
c
6
c
11
c
12
c
1
c
10
c
5
c
2
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h6.97582 × 10
34
u
103
+ 6.61069 × 10
35
u
102
+ ··· + 1.52431 × 10
34
b + 1.69169 × 10
35
,
1.01712 × 10
35
u
103
+ 8.18175 × 10
35
u
102
+ ··· + 2.17758 × 10
33
a + 1.06317 × 10
35
, u
104
+ 8u
103
+ ··· + 26u
2
+ 1i
I
u
2
= h3a
5
u + 9a
5
− 19a
4
u + 8a
4
− 32a
3
u + 47a
3
− 27a
2
u − 16a
2
− 64au + 13b + 29a − 15u + 7,
a
6
− a
5
u − 4a
4
u + 5a
4
− a
3
u − a
3
− 7a
2
u + 3a
2
− 3au + 2a − u + 1, u
2
− u + 1i
I
u
3
= hb, −u
3
− 2u
2
+ a − 2u, u
4
+ u
3
+ u
2
+ 1i
* 3 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
= h6.98 × 10
34
u
103
+ 6.61 × 10
35
u
102
+ · · · + 1.52 × 10
34
b + 1.69 ×
10
35
, 1.02 × 10
35
u
103
+ 8.18 × 10
35
u
102
+ · · · + 2.18 × 10
33
a + 1.06 ×
10
35
, u
104
+ 8u
103
+ · · · + 26u
2
+ 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
−46.7086u
103
− 375.726u
102
+ ··· + 7.43615u − 48.8233
−4.57639u
103
− 43.3685u
102
+ ··· + 5.03677u − 11.0981
a
9
=
1
u
2
a
7
=
6.85333u
103
+ 66.2746u
102
+ ··· − 8.70012u + 9.69003
−3.32389u
103
− 36.2817u
102
+ ··· + 12.7191u − 9.19042
a
3
=
−97.9649u
103
− 736.860u
102
+ ··· − 12.7281u − 70.4352
−47.5278u
103
− 414.116u
102
+ ··· + 50.0294u − 79.6418
a
6
=
10.1772u
103
+ 102.556u
102
+ ··· − 21.4192u + 18.8804
−3.32389u
103
− 36.2817u
102
+ ··· + 12.7191u − 9.19042
a
11
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
2
=
36.4714u
103
+ 295.722u
102
+ ··· − 1.60920u + 35.1731
5.67709u
103
+ 42.1133u
102
+ ··· + 5.76655u + 5.64315
a
10
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
5
=
−38.2688u
103
− 287.431u
102
+ ··· + 5.82490u − 35.2283
−16.9340u
103
− 158.639u
102
+ ··· + 30.8364u − 34.3757
(ii) Obstruction class = −1
(iii) Cusp Shapes = 68.6439u
103
+ 557.865u
102
+ ··· − 39.8300u + 80.6891
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
104
+ 57u
103
+ ··· − 38u + 1
c
2
, c
4
u
104
− 7u
103
+ ··· − 2u + 1
c
3
, c
7
u
104
− 3u
103
+ ··· + 56u + 16
c
5
, c
9
u
104
+ 2u
103
+ ··· + 8192u + 4096
c
6
u
104
− 33u
103
+ ··· − 3136u + 256
c
8
, c
11
u
104
− 8u
103
+ ··· + 26u
2
+ 1
c
10
, c
12
u
104
− 32u
103
+ ··· − 52u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
104
− 13y
103
+ ··· + 1086y + 1
c
2
, c
4
y
104
− 57y
103
+ ··· + 38y + 1
c
3
, c
7
y
104
− 33y
103
+ ··· − 3136y + 256
c
5
, c
9
y
104
+ 70y
103
+ ··· + 251658240y + 16777216
c
6
y
104
+ 71y
103
+ ··· + 4435968y + 65536
c
8
, c
11
y
104
+ 32y
103
+ ··· + 52y + 1
c
10
, c
12
y
104
+ 88y
103
+ ··· + 772y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.020101 + 0.968920I
a = −1.62773 + 0.60872I
b = 1.104780 + 0.011234I
4.85259 − 0.00883I 0
u = 0.020101 − 0.968920I
a = −1.62773 − 0.60872I
b = 1.104780 − 0.011234I
4.85259 + 0.00883I 0
u = 0.088929 + 1.032320I
a = 1.54140 − 0.10414I
b = −1.106510 + 0.209872I
4.42375 − 4.85437I 0
u = 0.088929 − 1.032320I
a = 1.54140 + 0.10414I
b = −1.106510 − 0.209872I
4.42375 + 4.85437I 0
u = 0.508673 + 0.806106I
a = −1.67780 − 3.42402I
b = 0.259513 − 0.337681I
−1.76705 − 1.65580I 0
u = 0.508673 − 0.806106I
a = −1.67780 + 3.42402I
b = 0.259513 + 0.337681I
−1.76705 + 1.65580I 0
u = −0.724250 + 0.757923I
a = −0.249685 + 0.014515I
b = −1.214800 + 0.436033I
−1.03612 − 4.58038I 0
u = −0.724250 − 0.757923I
a = −0.249685 − 0.014515I
b = −1.214800 − 0.436033I
−1.03612 + 4.58038I 0
u = 0.551150 + 0.900436I
a = 0.76590 + 2.14805I
b = 0.163285 + 0.546485I
−1.41743 − 2.62965I 0
u = 0.551150 − 0.900436I
a = 0.76590 − 2.14805I
b = 0.163285 − 0.546485I
−1.41743 + 2.62965I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.700965 + 0.624043I
a = 0.821618 + 0.490951I
b = 0.853960 + 0.159820I
0.063961 + 0.318270I 0
u = 0.700965 − 0.624043I
a = 0.821618 − 0.490951I
b = 0.853960 − 0.159820I
0.063961 − 0.318270I 0
u = −0.711021 + 0.819449I
a = −0.086162 + 0.367371I
b = 1.233520 − 0.260497I
0.360291 + 0.869699I 0
u = −0.711021 − 0.819449I
a = −0.086162 − 0.367371I
b = 1.233520 + 0.260497I
0.360291 − 0.869699I 0
u = 0.338448 + 0.821183I
a = 0.439609 − 0.068020I
b = −0.203409 − 0.340268I
0.32890 − 1.53001I 0
u = 0.338448 − 0.821183I
a = 0.439609 + 0.068020I
b = −0.203409 + 0.340268I
0.32890 + 1.53001I 0
u = 0.371975 + 1.056300I
a = 0.219181 + 0.313047I
b = −0.737120 − 0.575993I
0.284397 − 1.151140I 0
u = 0.371975 − 1.056300I
a = 0.219181 − 0.313047I
b = −0.737120 + 0.575993I
0.284397 + 1.151140I 0
u = 0.763473 + 0.833575I
a = 1.23213 + 1.16646I
b = 0.825340 + 0.691127I
−2.19732 − 0.20425I 0
u = 0.763473 − 0.833575I
a = 1.23213 − 1.16646I
b = 0.825340 − 0.691127I
−2.19732 + 0.20425I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.307670 + 1.089840I
a = −1.52467 − 1.13055I
b = 0.781449 − 0.708430I
−3.12443 − 2.29817I 0
u = 0.307670 − 1.089840I
a = −1.52467 + 1.13055I
b = 0.781449 + 0.708430I
−3.12443 + 2.29817I 0
u = 0.277505 + 1.104830I
a = −0.1271100 − 0.0362554I
b = 0.688170 + 0.874892I
−2.91862 − 4.97555I 0
u = 0.277505 − 1.104830I
a = −0.1271100 + 0.0362554I
b = 0.688170 − 0.874892I
−2.91862 + 4.97555I 0
u = −0.760110 + 0.849074I
a = 0.534218 − 1.195980I
b = −0.182890 − 1.029530I
−4.67900 + 0.62095I 0
u = −0.760110 − 0.849074I
a = 0.534218 + 1.195980I
b = −0.182890 + 1.029530I
−4.67900 − 0.62095I 0
u = 0.239231 + 1.116540I
a = 1.36880 + 0.80283I
b = −0.978221 + 0.642817I
1.11393 − 6.06429I 0
u = 0.239231 − 1.116540I
a = 1.36880 − 0.80283I
b = −0.978221 − 0.642817I
1.11393 + 6.06429I 0
u = −0.888885 + 0.718904I
a = −0.531734 + 1.184580I
b = −1.048580 + 0.760099I
−6.53896 − 5.97441I 0
u = −0.888885 − 0.718904I
a = −0.531734 − 1.184580I
b = −1.048580 − 0.760099I
−6.53896 + 5.97441I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.849313 + 0.087081I
a = 0.56368 − 1.29841I
b = 0.969631 − 0.765873I
−6.10338 − 7.37044I 0
u = 0.849313 − 0.087081I
a = 0.56368 + 1.29841I
b = 0.969631 + 0.765873I
−6.10338 + 7.37044I 0
u = 0.146678 + 0.835966I
a = 0.508790 + 0.043311I
b = 0.025150 − 0.703991I
0.50382 − 1.71842I 0
u = 0.146678 − 0.835966I
a = 0.508790 − 0.043311I
b = 0.025150 + 0.703991I
0.50382 + 1.71842I 0
u = −0.914130 + 0.710133I
a = 0.66641 − 1.29667I
b = 1.065570 − 0.825694I
−9.8021 − 11.2187I 0
u = −0.914130 − 0.710133I
a = 0.66641 + 1.29667I
b = 1.065570 + 0.825694I
−9.8021 + 11.2187I 0
u = 0.765930 + 0.869765I
a = −0.02115 + 2.55065I
b = −0.791634 + 0.793650I
−5.87770 − 1.49881I 0
u = 0.765930 − 0.869765I
a = −0.02115 − 2.55065I
b = −0.791634 − 0.793650I
−5.87770 + 1.49881I 0
u = −0.892156 + 0.739909I
a = 0.30564 + 1.68316I
b = 0.759500 + 0.991887I
−10.79950 − 4.57831I 0
u = −0.892156 − 0.739909I
a = 0.30564 − 1.68316I
b = 0.759500 − 0.991887I
−10.79950 + 4.57831I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.549237 + 1.021450I
a = 0.277415 + 1.180080I
b = −0.913257 − 0.043795I
1.67910 − 1.36015I 0
u = 0.549237 − 1.021450I
a = 0.277415 − 1.180080I
b = −0.913257 + 0.043795I
1.67910 + 1.36015I 0
u = −0.704293 + 0.925402I
a = −0.520684 + 1.249690I
b = 1.256970 + 0.183413I
0.69382 + 4.56111I 0
u = −0.704293 − 0.925402I
a = −0.520684 − 1.249690I
b = 1.256970 − 0.183413I
0.69382 − 4.56111I 0
u = −0.888784 + 0.755463I
a = 0.292839 − 1.319880I
b = 0.949109 − 0.740773I
−11.11310 − 1.60376I 0
u = −0.888784 − 0.755463I
a = 0.292839 + 1.319880I
b = 0.949109 + 0.740773I
−11.11310 + 1.60376I 0
u = 0.812047 + 0.837491I
a = −1.39732 − 1.12186I
b = −0.953304 − 0.748451I
−5.37858 + 4.30990I 0
u = 0.812047 − 0.837491I
a = −1.39732 + 1.12186I
b = −0.953304 + 0.748451I
−5.37858 − 4.30990I 0
u = −0.872599 + 0.774567I
a = −0.21957 − 1.49195I
b = −0.674295 − 0.904933I
−7.68839 + 0.16391I 0
u = −0.872599 − 0.774567I
a = −0.21957 + 1.49195I
b = −0.674295 + 0.904933I
−7.68839 − 0.16391I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.768255 + 0.881229I
a = 1.090040 − 0.500963I
b = −0.955497 + 0.043580I
−6.17949 + 2.90009I 0
u = −0.768255 − 0.881229I
a = 1.090040 + 0.500963I
b = −0.955497 − 0.043580I
−6.17949 − 2.90009I 0
u = 0.761656 + 0.891292I
a = −1.30304 − 1.35327I
b = −0.757619 − 0.846783I
−5.81140 − 4.27423I 0
u = 0.761656 − 0.891292I
a = −1.30304 + 1.35327I
b = −0.757619 + 0.846783I
−5.81140 + 4.27423I 0
u = −0.125362 + 0.816549I
a = −1.60573 + 1.61861I
b = 1.037850 + 0.456374I
3.10305 + 2.04932I 0
u = −0.125362 − 0.816549I
a = −1.60573 − 1.61861I
b = 1.037850 − 0.456374I
3.10305 − 2.04932I 0
u = −0.209971 + 0.797600I
a = 1.38225 − 1.86157I
b = −1.090740 − 0.631167I
0.79834 + 7.03577I 0
u = −0.209971 − 0.797600I
a = 1.38225 + 1.86157I
b = −1.090740 + 0.631167I
0.79834 − 7.03577I 0
u = −0.751265 + 0.907966I
a = −0.782532 + 0.938819I
b = −0.104033 + 1.028450I
−4.49816 + 5.10320I 0
u = −0.751265 − 0.907966I
a = −0.782532 − 0.938819I
b = −0.104033 − 1.028450I
−4.49816 − 5.10320I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.629659 + 0.996600I
a = −0.15233 − 1.68044I
b = 0.966172 − 0.232867I
1.19714 − 5.44523I 0
u = 0.629659 − 0.996600I
a = −0.15233 + 1.68044I
b = 0.966172 + 0.232867I
1.19714 + 5.44523I 0
u = 0.249058 + 1.157640I
a = −1.18468 − 0.88217I
b = 1.036260 − 0.748871I
−1.84605 − 11.00330I 0
u = 0.249058 − 1.157640I
a = −1.18468 + 0.88217I
b = 1.036260 + 0.748871I
−1.84605 + 11.00330I 0
u = 0.748713 + 0.918405I
a = 0.05162 − 2.36288I
b = 0.908277 − 0.688694I
−1.93769 − 5.52130I 0
u = 0.748713 − 0.918405I
a = 0.05162 + 2.36288I
b = 0.908277 + 0.688694I
−1.93769 + 5.52130I 0
u = 0.376983 + 1.135080I
a = 0.039090 − 0.287969I
b = 0.938525 + 0.697645I
−2.64255 + 3.10548I 0
u = 0.376983 − 1.135080I
a = 0.039090 + 0.287969I
b = 0.938525 − 0.697645I
−2.64255 − 3.10548I 0
u = −0.709617 + 0.965654I
a = 0.57312 − 1.56112I
b = −1.250540 − 0.367308I
−0.39950 + 10.08460I 0
u = −0.709617 − 0.965654I
a = 0.57312 + 1.56112I
b = −1.250540 + 0.367308I
−0.39950 − 10.08460I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.789470 + 0.019412I
a = 0.20756 + 1.53579I
b = 0.787797 + 0.828757I
−6.67050 − 1.40384I −5.97563 + 0.I
u = 0.789470 − 0.019412I
a = 0.20756 − 1.53579I
b = 0.787797 − 0.828757I
−6.67050 + 1.40384I −5.97563 + 0.I
u = 0.672399 + 0.413520I
a = −0.560928 + 0.078758I
b = −0.871864 + 0.212793I
−0.08856 − 3.26981I 0
u = 0.672399 − 0.413520I
a = −0.560928 − 0.078758I
b = −0.871864 − 0.212793I
−0.08856 + 3.26981I 0
u = −0.912970 + 0.802094I
a = 0.47515 + 1.36604I
b = 0.796629 + 0.772479I
−11.58130 + 4.12334I 0
u = −0.912970 − 0.802094I
a = 0.47515 − 1.36604I
b = 0.796629 − 0.772479I
−11.58130 − 4.12334I 0
u = 0.781050 + 0.934561I
a = −0.18844 + 2.38464I
b = −0.994076 + 0.763353I
−5.07610 − 10.28260I 0
u = 0.781050 − 0.934561I
a = −0.18844 − 2.38464I
b = −0.994076 − 0.763353I
−5.07610 + 10.28260I 0
u = 0.776301 + 0.076386I
a = −0.319455 + 1.211640I
b = −0.867979 + 0.710791I
−2.88166 − 2.72171I 0. + 3.00862I
u = 0.776301 − 0.076386I
a = −0.319455 − 1.211640I
b = −0.867979 − 0.710791I
−2.88166 + 2.72171I 0. − 3.00862I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.871773 + 0.916358I
a = −0.487194 − 0.299904I
b = −0.476647 − 0.027311I
−8.08278 + 3.22388I 0
u = −0.871773 − 0.916358I
a = −0.487194 + 0.299904I
b = −0.476647 + 0.027311I
−8.08278 − 3.22388I 0
u = −0.787166 + 0.996674I
a = −1.114630 + 0.530099I
b = −0.615591 + 0.925197I
−6.99502 + 5.99921I 0
u = −0.787166 − 0.996674I
a = −1.114630 − 0.530099I
b = −0.615591 − 0.925197I
−6.99502 − 5.99921I 0
u = −0.085683 + 0.721766I
a = −0.864203 − 0.162417I
b = −0.488075 + 0.845371I
−1.05235 + 1.55920I 2.00000 − 0.56987I
u = −0.085683 − 0.721766I
a = −0.864203 + 0.162417I
b = −0.488075 − 0.845371I
−1.05235 − 1.55920I 2.00000 + 0.56987I
u = −0.787073 + 1.014950I
a = −0.83389 + 2.18640I
b = 0.966571 + 0.702533I
−10.30340 + 7.81272I 0
u = −0.787073 − 1.014950I
a = −0.83389 − 2.18640I
b = 0.966571 − 0.702533I
−10.30340 − 7.81272I 0
u = −0.769663 + 1.032780I
a = 0.66899 − 2.14570I
b = −1.081960 − 0.741798I
−5.56416 + 12.12230I 0
u = −0.769663 − 1.032780I
a = 0.66899 + 2.14570I
b = −1.081960 + 0.741798I
−5.56416 − 12.12230I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.781137 + 1.024430I
a = 1.246290 − 0.543561I
b = 0.731376 − 1.014790I
−9.9128 + 10.7762I 0
u = −0.781137 − 1.024430I
a = 1.246290 + 0.543561I
b = 0.731376 + 1.014790I
−9.9128 − 10.7762I 0
u = −0.827217 + 1.003730I
a = 1.145160 − 0.311699I
b = 0.758216 − 0.743338I
−10.94860 + 2.29220I 0
u = −0.827217 − 1.003730I
a = 1.145160 + 0.311699I
b = 0.758216 + 0.743338I
−10.94860 − 2.29220I 0
u = −0.776209 + 1.048340I
a = −0.61023 + 2.22461I
b = 1.090020 + 0.819468I
−8.7457 + 17.4597I 0
u = −0.776209 − 1.048340I
a = −0.61023 − 2.22461I
b = 1.090020 − 0.819468I
−8.7457 − 17.4597I 0
u = 0.020183 + 0.632941I
a = 2.46837 − 2.16377I
b = −0.635810 − 0.436420I
−1.55529 − 0.64924I 2.02149 − 1.49466I
u = 0.020183 − 0.632941I
a = 2.46837 + 2.16377I
b = −0.635810 + 0.436420I
−1.55529 + 0.64924I 2.02149 + 1.49466I
u = −0.377275 + 0.426971I
a = −1.41493 − 0.32178I
b = −0.992506 + 0.513905I
−0.28186 − 4.76677I 1.57538 + 7.46851I
u = −0.377275 − 0.426971I
a = −1.41493 + 0.32178I
b = −0.992506 − 0.513905I
−0.28186 + 4.76677I 1.57538 − 7.46851I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.286490 + 0.181246I
a = 1.97003 + 0.54068I
b = 0.873438 − 0.227558I
1.48560 − 0.51100I 6.06395 + 1.23488I
u = −0.286490 − 0.181246I
a = 1.97003 − 0.54068I
b = 0.873438 + 0.227558I
1.48560 + 0.51100I 6.06395 − 1.23488I
u = 0.086556 + 0.161978I
a = 4.05051 − 2.38193I
b = −0.340109 − 0.515693I
−1.75512 − 0.68895I −4.16314 − 0.31578I
u = 0.086556 − 0.161978I
a = 4.05051 + 2.38193I
b = −0.340109 + 0.515693I
−1.75512 + 0.68895I −4.16314 + 0.31578I
15
II.
I
u
2
= h3a
5
u − 19a
4
u + · · · + 29a + 7, −a
5
u − 4a
4
u + · · · + 2a + 1, u
2
− u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
a
−0.230769a
5
u + 1.46154a
4
u + ··· − 2.23077a − 0.538462
a
9
=
1
u − 1
a
7
=
0.538462a
5
u − 0.0769231a
4
u + ··· + 1.53846a + 1.92308
0.153846a
5
u + 0.692308a
4
u + ··· + 1.15385a + 0.692308
a
3
=
−0.0769231a
5
u − 0.846154a
4
u + ··· + 1.92308a + 0.153846
0.461538a
5
u + 0.0769231a
4
u + ··· + 2.46154a + 0.0769231
a
6
=
0.384615a
5
u − 0.769231a
4
u + ··· + 0.384615a + 1.23077
0.153846a
5
u + 0.692308a
4
u + ··· + 1.15385a + 0.692308
a
11
=
u
u − 1
a
1
=
−1
0
a
2
=
0.0769231a
5
u − 0.153846a
4
u + ··· + 0.0769231a + 0.846154
−0.0769231a
5
u + 0.153846a
4
u + ··· + 1.92308a + 0.153846
a
10
=
1
u − 1
a
5
=
0.384615a
5
u − 0.769231a
4
u + ··· + 0.384615a + 1.23077
0.153846a
5
u + 0.692308a
4
u + ··· + 1.15385a + 0.692308
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
3
13
a
5
u−
43
13
a
5
+
98
13
a
4
u−
5
13
a
4
+
137
13
a
3
u−
135
13
a
3
+
64
13
a
2
u+
218
13
a
2
+
170
13
au−
23
13
a+
63
13
u+
72
13
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
2
, c
7
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
3
, c
4
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
5
, c
9
u
12
c
6
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
c
8
, c
12
(u
2
− u + 1)
6
c
10
, c
11
(u
2
+ u + 1)
6
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
2
, c
3
, c
4
c
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
5
, c
9
y
12
c
8
, c
10
, c
11
c
12
(y
2
+ y + 1)
6
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.104427 − 1.024660I
b = −0.428243 − 0.664531I
−1.89061 − 2.95419I −4.61123 + 3.83711I
u = 0.500000 + 0.866025I
a = −0.67283 − 1.28640I
b = 1.002190 − 0.295542I
1.89061 − 2.95419I 4.53097 + 3.97184I
u = 0.500000 + 0.866025I
a = −0.160939 − 0.449445I
b = 1.002190 + 0.295542I
1.89061 − 1.10558I 7.73749 + 2.70506I
u = 0.500000 + 0.866025I
a = −0.288082 + 0.269440I
b = −1.073950 − 0.558752I
3.66314I 3.68173 − 0.75872I
u = 0.500000 + 0.866025I
a = 0.67970 + 1.59070I
b = −1.073950 + 0.558752I
− 7.72290I −0.57335 + 8.68103I
u = 0.500000 + 0.866025I
a = 1.04658 + 1.76640I
b = −0.428243 + 0.664531I
−1.89061 − 1.10558I −0.765607 + 0.616236I
u = 0.500000 − 0.866025I
a = −0.104427 + 1.024660I
b = −0.428243 + 0.664531I
−1.89061 + 2.95419I −4.61123 − 3.83711I
u = 0.500000 − 0.866025I
a = −0.67283 + 1.28640I
b = 1.002190 + 0.295542I
1.89061 + 2.95419I 4.53097 − 3.97184I
u = 0.500000 − 0.866025I
a = −0.160939 + 0.449445I
b = 1.002190 − 0.295542I
1.89061 + 1.10558I 7.73749 − 2.70506I
u = 0.500000 − 0.866025I
a = −0.288082 − 0.269440I
b = −1.073950 + 0.558752I
− 3.66314I 3.68173 + 0.75872I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 − 0.866025I
a = 0.67970 − 1.59070I
b = −1.073950 − 0.558752I
7.72290I −0.57335 − 8.68103I
u = 0.500000 − 0.866025I
a = 1.04658 − 1.76640I
b = −0.428243 − 0.664531I
−1.89061 + 1.10558I −0.765607 − 0.616236I
20
III. I
u
3
= hb, −u
3
− 2u
2
+ a − 2u, u
4
+ u
3
+ u
2
+ 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
u
3
+ 2u
2
+ 2u
0
a
9
=
1
u
2
a
7
=
1
0
a
3
=
u
3
+ 2u
2
+ 2u
0
a
6
=
1
0
a
11
=
u
u
3
+ u
a
1
=
u
3
u
3
+ u
2
+ 1
a
2
=
2u
3
+ 2u
2
+ 2u
u
3
+ u
2
+ 1
a
10
=
u
2
+ 1
u
2
a
5
=
−u
3
−u
3
− u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
3
+ 3u
2
+ 8u
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
6
, c
7
u
4
c
4
(u + 1)
4
c
5
, c
10
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
8
u
4
+ u
3
+ u
2
+ 1
c
9
, c
12
u
4
− u
3
+ 3u
2
− 2u + 1
c
11
u
4
− u
3
+ u
2
+ 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
6
, c
7
y
4
c
5
, c
9
, c
10
c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
8
, c
11
y
4
+ y
3
+ 3y
2
+ 2y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351808 + 0.720342I
a = −0.59074 + 2.34806I
b = 0
−1.43393 − 1.41510I 3.14142 + 7.60220I
u = 0.351808 − 0.720342I
a = −0.59074 − 2.34806I
b = 0
−1.43393 + 1.41510I 3.14142 − 7.60220I
u = −0.851808 + 0.911292I
a = −0.409261 − 0.055548I
b = 0
−8.43568 + 3.16396I −11.64142 − 1.04769I
u = −0.851808 − 0.911292I
a = −0.409261 + 0.055548I
b = 0
−8.43568 − 3.16396I −11.64142 + 1.04769I
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
104
+ 57u
103
+ ··· − 38u + 1)
c
2
((u − 1)
4
)(u
6
+ u
5
+ ··· + u + 1)
2
(u
104
− 7u
103
+ ··· − 2u + 1)
c
3
u
4
(u
6
− u
5
+ ··· − u + 1)
2
(u
104
− 3u
103
+ ··· + 56u + 16)
c
4
((u + 1)
4
)(u
6
− u
5
+ ··· − u + 1)
2
(u
104
− 7u
103
+ ··· − 2u + 1)
c
5
u
12
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
104
+ 2u
103
+ ··· + 8192u + 4096)
c
6
u
4
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
· (u
104
− 33u
103
+ ··· − 3136u + 256)
c
7
u
4
(u
6
+ u
5
+ ··· + u + 1)
2
(u
104
− 3u
103
+ ··· + 56u + 16)
c
8
((u
2
− u + 1)
6
)(u
4
+ u
3
+ u
2
+ 1)(u
104
− 8u
103
+ ··· + 26u
2
+ 1)
c
9
u
12
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
104
+ 2u
103
+ ··· + 8192u + 4096)
c
10
((u
2
+ u + 1)
6
)(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
104
− 32u
103
+ ··· − 52u + 1)
c
11
((u
2
+ u + 1)
6
)(u
4
− u
3
+ u
2
+ 1)(u
104
− 8u
103
+ ··· + 26u
2
+ 1)
c
12
((u
2
− u + 1)
6
)(u
4
− u
3
+ 3u
2
− 2u + 1)(u
104
− 32u
103
+ ··· − 52u + 1)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
4
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
104
− 13y
103
+ ··· + 1086y + 1)
c
2
, c
4
(y −1)
4
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
104
− 57y
103
+ ··· + 38y + 1)
c
3
, c
7
y
4
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
104
− 33y
103
+ ··· − 3136y + 256)
c
5
, c
9
y
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
· (y
104
+ 70y
103
+ ··· + 251658240y + 16777216)
c
6
y
4
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
104
+ 71y
103
+ ··· + 4435968y + 65536)
c
8
, c
11
((y
2
+ y + 1)
6
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
104
+ 32y
103
+ ··· + 52y + 1)
c
10
, c
12
((y
2
+ y + 1)
6
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
104
+ 88y
103
+ ··· + 772y + 1)
26
