12n
0635
(K12n
0635
)
A knot diagram
1
Linearized knot diagam
3 8 6 12 1 9 12 2 4 5 8 10
Solving Sequence
2,9
8 3
1,12
7 6 4 10 5 11
c
8
c
2
c
1
c
7
c
6
c
3
c
9
c
5
c
10
c
4
, c
11
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h7.72790 × 10
299
u
118
− 1.72629 × 10
299
u
117
+ ··· + 2.99648 × 10
300
b − 1.21626 × 10
302
,
− 5.20063 × 10
302
u
118
− 4.63209 × 10
302
u
117
+ ··· + 6.32257 × 10
302
a − 1.43930 × 10
305
,
u
119
+ u
118
+ ··· − 366u + 211i
I
u
2
= h−144442009874u
40
− 40660630315u
39
+ ··· + 55254454982b + 95137731796,
− 121324231307u
40
− 226756643017u
39
+ ··· + 55254454982a − 930709060133,
u
41
+ 11u
39
+ ··· + 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 160 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h7.73 × 10
299
u
118
− 1.73 × 10
299
u
117
+ · · · + 3.00 × 10
300
b − 1.22 ×
10
302
, −5.20 × 10
302
u
118
− 4.63 × 10
302
u
117
+ · · · + 6.32 × 10
302
a − 1.44 ×
10
305
, u
119
+ u
118
+ · · · − 366u + 211i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
0.822551u
118
+ 0.732629u
117
+ ··· − 379.214u + 227.644
−0.257900u
118
+ 0.0576106u
117
+ ··· − 222.436u + 40.5897
a
7
=
−0.401146u
118
+ 0.0348358u
117
+ ··· − 399.134u + 76.2959
−0.243493u
118
− 0.192213u
117
+ ··· + 48.6316u − 49.8415
a
6
=
−0.644639u
118
− 0.157377u
117
+ ··· − 350.502u + 26.4544
−0.243493u
118
− 0.192213u
117
+ ··· + 48.6316u − 49.8415
a
4
=
−0.598905u
118
− 0.744143u
117
+ ··· + 316.390u − 182.264
0.0505679u
118
− 0.0114233u
117
+ ··· + 37.3488u − 6.10829
a
10
=
−0.670832u
118
− 0.587891u
117
+ ··· + 246.350u − 149.706
0.0873593u
118
+ 0.00245992u
117
+ ··· + 49.1705u − 4.10884
a
5
=
−0.534374u
118
+ 0.0140889u
117
+ ··· − 449.449u + 76.2335
−0.158683u
118
− 0.273598u
117
+ ··· + 202.003u − 89.0966
a
11
=
−0.890241u
118
− 0.816127u
117
+ ··· + 395.180u − 249.260
0.267839u
118
+ 0.00116646u
117
+ ··· + 230.932u − 37.2540
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.432322u
118
− 2.26997u
117
+ ··· + 2494.32u − 733.077
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
119
+ 59u
118
+ ··· − 926108u − 44521
c
2
, c
8
u
119
+ u
118
+ ··· − 366u + 211
c
3
u
119
− 12u
118
+ ··· − 594u − 503
c
4
u
119
+ 3u
118
+ ··· + 95214u − 3293
c
5
u
119
+ u
118
+ ··· + 5201393u − 364301
c
6
u
119
− 4u
118
+ ··· − 2916191u − 324667
c
7
, c
11
u
119
+ u
118
+ ··· − 25u + 1
c
9
u
119
+ 2u
118
+ ··· + 3981u + 337
c
10
u
119
− 3u
117
+ ··· − 14155826u − 953372
c
12
u
119
+ 6u
118
+ ··· − 6u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
119
+ 19y
118
+ ··· − 89555795764y −1982119441
c
2
, c
8
y
119
+ 59y
118
+ ··· − 926108y −44521
c
3
y
119
− 44y
118
+ ··· − 2126954y −253009
c
4
y
119
− 11y
118
+ ··· + 2421268218y −10843849
c
5
y
119
+ y
118
+ ··· + 3889002396385y −132715218601
c
6
y
119
− 22y
118
+ ··· + 24438543848191y −105408660889
c
7
, c
11
y
119
− 81y
118
+ ··· − 153y −1
c
9
y
119
+ 14y
118
+ ··· − 16141701y −113569
c
10
y
119
− 6y
118
+ ··· + 61203268140316y −908918170384
c
12
y
119
− 26y
118
+ ··· + 8y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.138327 + 0.990158I
a = −0.286934 − 0.313045I
b = 0.052155 + 0.442743I
−1.20206 + 2.35927I 0
u = 0.138327 − 0.990158I
a = −0.286934 + 0.313045I
b = 0.052155 − 0.442743I
−1.20206 − 2.35927I 0
u = −0.739519 + 0.687699I
a = −0.788897 − 0.116467I
b = −0.402628 + 0.797114I
1.71996 + 2.02950I 0
u = −0.739519 − 0.687699I
a = −0.788897 + 0.116467I
b = −0.402628 − 0.797114I
1.71996 − 2.02950I 0
u = −0.496588 + 0.840506I
a = −1.50275 − 0.07440I
b = 0.563776 − 0.214209I
6.09166 − 2.02663I 0
u = −0.496588 − 0.840506I
a = −1.50275 + 0.07440I
b = 0.563776 + 0.214209I
6.09166 + 2.02663I 0
u = 0.291882 + 0.991062I
a = 2.42800 + 1.33222I
b = −1.61394 − 0.21321I
−3.66465 − 1.30336I 0
u = 0.291882 − 0.991062I
a = 2.42800 − 1.33222I
b = −1.61394 + 0.21321I
−3.66465 + 1.30336I 0
u = −0.975681 + 0.408520I
a = −0.159640 − 0.390097I
b = −1.80212 + 0.55680I
−2.47917 + 5.10720I 0
u = −0.975681 − 0.408520I
a = −0.159640 + 0.390097I
b = −1.80212 − 0.55680I
−2.47917 − 5.10720I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.279448 + 1.020750I
a = 0.387550 − 0.487897I
b = −0.645036 − 0.220684I
−3.58440 + 3.05326I 0
u = 0.279448 − 1.020750I
a = 0.387550 + 0.487897I
b = −0.645036 + 0.220684I
−3.58440 − 3.05326I 0
u = −0.387905 + 0.848616I
a = 1.46565 + 0.71590I
b = −0.208033 + 0.268527I
5.46164 − 1.65387I 0
u = −0.387905 − 0.848616I
a = 1.46565 − 0.71590I
b = −0.208033 − 0.268527I
5.46164 + 1.65387I 0
u = −0.418303 + 0.986388I
a = −0.010321 + 0.195398I
b = −0.134150 + 0.933427I
1.81979 + 0.17648I 0
u = −0.418303 − 0.986388I
a = −0.010321 − 0.195398I
b = −0.134150 − 0.933427I
1.81979 − 0.17648I 0
u = −1.003850 + 0.388181I
a = 0.111883 + 0.228768I
b = 1.77448 − 0.55150I
−1.29566 + 13.00150I 0
u = −1.003850 − 0.388181I
a = 0.111883 − 0.228768I
b = 1.77448 + 0.55150I
−1.29566 − 13.00150I 0
u = 0.922762
a = 0.0853941
b = 1.16229
1.46894 0
u = 0.788579 + 0.740267I
a = 0.753124 − 0.313220I
b = −0.976181 + 0.934246I
0.16645 − 1.67645I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.788579 − 0.740267I
a = 0.753124 + 0.313220I
b = −0.976181 − 0.934246I
0.16645 + 1.67645I 0
u = −0.496136 + 0.970633I
a = −0.854963 + 0.799242I
b = 1.000490 − 0.787922I
2.31216 − 5.55103I 0
u = −0.496136 − 0.970633I
a = −0.854963 − 0.799242I
b = 1.000490 + 0.787922I
2.31216 + 5.55103I 0
u = −0.810179 + 0.738473I
a = −0.083773 + 0.261289I
b = 0.302850 + 0.201126I
5.24879 + 1.68195I 0
u = −0.810179 − 0.738473I
a = −0.083773 − 0.261289I
b = 0.302850 − 0.201126I
5.24879 − 1.68195I 0
u = 0.478133 + 0.988443I
a = 2.15726 + 1.87440I
b = −1.88840 + 0.42229I
−2.13295 + 2.85129I 0
u = 0.478133 − 0.988443I
a = 2.15726 − 1.87440I
b = −1.88840 − 0.42229I
−2.13295 − 2.85129I 0
u = 0.746227 + 0.505418I
a = −0.559951 − 0.280614I
b = −1.26175 − 0.66554I
0.32046 − 2.65425I 0
u = 0.746227 − 0.505418I
a = −0.559951 + 0.280614I
b = −1.26175 + 0.66554I
0.32046 + 2.65425I 0
u = −0.714016 + 0.849476I
a = 0.006926 + 0.808247I
b = 1.048330 − 0.037031I
4.62344 − 2.72374I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.714016 − 0.849476I
a = 0.006926 − 0.808247I
b = 1.048330 + 0.037031I
4.62344 + 2.72374I 0
u = 1.062710 + 0.361334I
a = −0.399752 − 0.192692I
b = −1.49057 − 0.54867I
−1.67369 − 2.69642I 0
u = 1.062710 − 0.361334I
a = −0.399752 + 0.192692I
b = −1.49057 + 0.54867I
−1.67369 + 2.69642I 0
u = −0.296172 + 1.086400I
a = −1.69183 + 1.15499I
b = 0.892180 + 0.355930I
−7.27793 + 3.13200I 0
u = −0.296172 − 1.086400I
a = −1.69183 − 1.15499I
b = 0.892180 − 0.355930I
−7.27793 − 3.13200I 0
u = 0.447749 + 1.047640I
a = −2.55968 − 1.10443I
b = 1.76621 − 1.28570I
−5.80100 + 7.39063I 0
u = 0.447749 − 1.047640I
a = −2.55968 + 1.10443I
b = 1.76621 + 1.28570I
−5.80100 − 7.39063I 0
u = −0.459034 + 1.044890I
a = 1.56429 + 1.26948I
b = 0.34577 − 2.67909I
2.48039 − 7.32028I 0
u = −0.459034 − 1.044890I
a = 1.56429 − 1.26948I
b = 0.34577 + 2.67909I
2.48039 + 7.32028I 0
u = −0.483725 + 0.708066I
a = −1.92606 + 0.13905I
b = 0.836749 + 0.384169I
3.20043 + 1.50937I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.483725 − 0.708066I
a = −1.92606 − 0.13905I
b = 0.836749 − 0.384169I
3.20043 − 1.50937I 0
u = −0.856731
a = −0.524691
b = −1.63643
−2.28823 0
u = −0.099471 + 0.832500I
a = 0.496816 − 1.056410I
b = −1.123730 + 0.765445I
−2.95234 + 2.49175I 0
u = −0.099471 − 0.832500I
a = 0.496816 + 1.056410I
b = −1.123730 − 0.765445I
−2.95234 − 2.49175I 0
u = −0.517837 + 1.046110I
a = −1.51862 − 0.69786I
b = −0.03236 + 2.32711I
2.89267 + 0.64660I 0
u = −0.517837 − 1.046110I
a = −1.51862 + 0.69786I
b = −0.03236 − 2.32711I
2.89267 − 0.64660I 0
u = 0.465835 + 1.089250I
a = −1.54000 − 1.70807I
b = 1.92133 + 0.30785I
−5.60425 − 0.50345I 0
u = 0.465835 − 1.089250I
a = −1.54000 + 1.70807I
b = 1.92133 − 0.30785I
−5.60425 + 0.50345I 0
u = 0.432498 + 0.687899I
a = −0.162295 + 0.305230I
b = −1.353910 − 0.390504I
−1.09892 + 0.98947I 0
u = 0.432498 − 0.687899I
a = −0.162295 − 0.305230I
b = −1.353910 + 0.390504I
−1.09892 − 0.98947I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.318545 + 1.148260I
a = 1.75945 − 1.00275I
b = −1.169460 − 0.343271I
−7.28649 − 3.00967I 0
u = −0.318545 − 1.148260I
a = 1.75945 + 1.00275I
b = −1.169460 + 0.343271I
−7.28649 + 3.00967I 0
u = −0.665480 + 0.991083I
a = 0.663632 − 0.077340I
b = −0.386670 − 0.974153I
0.78034 − 7.39471I 0
u = −0.665480 − 0.991083I
a = 0.663632 + 0.077340I
b = −0.386670 + 0.974153I
0.78034 + 7.39471I 0
u = 0.600770 + 0.531768I
a = −0.510410 − 0.623358I
b = 0.011107 + 0.344970I
0.114771 + 1.133900I 0
u = 0.600770 − 0.531768I
a = −0.510410 + 0.623358I
b = 0.011107 − 0.344970I
0.114771 − 1.133900I 0
u = 0.709247 + 0.965823I
a = −0.37276 + 1.59051I
b = −0.688136 − 1.182700I
−0.53398 + 7.32591I 0
u = 0.709247 − 0.965823I
a = −0.37276 − 1.59051I
b = −0.688136 + 1.182700I
−0.53398 − 7.32591I 0
u = 0.762287 + 0.241211I
a = 0.57440 + 1.34529I
b = −0.002076 − 0.504846I
3.03967 − 5.60301I 0. + 5.55438I
u = 0.762287 − 0.241211I
a = 0.57440 − 1.34529I
b = −0.002076 + 0.504846I
3.03967 + 5.60301I 0. − 5.55438I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.573019 + 1.072380I
a = −0.755360 + 0.386094I
b = 0.382549 − 0.052592I
−1.59421 + 3.66056I 0
u = 0.573019 − 1.072380I
a = −0.755360 − 0.386094I
b = 0.382549 + 0.052592I
−1.59421 − 3.66056I 0
u = 0.759427 + 0.162887I
a = 0.223339 + 0.563571I
b = 1.177310 + 0.550276I
0.79937 − 3.58749I 6.97277 + 6.80076I
u = 0.759427 − 0.162887I
a = 0.223339 − 0.563571I
b = 1.177310 − 0.550276I
0.79937 + 3.58749I 6.97277 − 6.80076I
u = −0.377563 + 0.675853I
a = 2.07199 + 0.23800I
b = 0.073505 − 0.134839I
2.87635 − 3.63043I 4.92553 + 9.56207I
u = −0.377563 − 0.675853I
a = 2.07199 − 0.23800I
b = 0.073505 + 0.134839I
2.87635 + 3.63043I 4.92553 − 9.56207I
u = −0.553141 + 1.093970I
a = −1.68295 + 1.16746I
b = 1.55723 + 0.08891I
−5.52129 − 10.35290I 0
u = −0.553141 − 1.093970I
a = −1.68295 − 1.16746I
b = 1.55723 − 0.08891I
−5.52129 + 10.35290I 0
u = 0.590478 + 1.076160I
a = 1.67142 + 1.30633I
b = −1.47597 + 0.90883I
−1.43290 + 7.74922I 0
u = 0.590478 − 1.076160I
a = 1.67142 − 1.30633I
b = −1.47597 − 0.90883I
−1.43290 − 7.74922I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.742077 + 0.987462I
a = 0.069782 + 0.233284I
b = 0.365621 − 0.169693I
4.48972 − 7.51330I 0
u = −0.742077 − 0.987462I
a = 0.069782 − 0.233284I
b = 0.365621 + 0.169693I
4.48972 + 7.51330I 0
u = −0.496978 + 1.132190I
a = 1.75877 − 1.18182I
b = −1.77208 − 0.15738I
−6.12428 − 4.94727I 0
u = −0.496978 − 1.132190I
a = 1.75877 + 1.18182I
b = −1.77208 + 0.15738I
−6.12428 + 4.94727I 0
u = 0.279256 + 1.206360I
a = −0.723783 + 0.618528I
b = 0.721057 + 0.197708I
−1.38561 − 2.19285I 0
u = 0.279256 − 1.206360I
a = −0.723783 − 0.618528I
b = 0.721057 − 0.197708I
−1.38561 + 2.19285I 0
u = 0.355752 + 1.186210I
a = −1.61878 − 0.95739I
b = 1.65648 + 0.21388I
−3.19874 + 0.12797I 0
u = 0.355752 − 1.186210I
a = −1.61878 + 0.95739I
b = 1.65648 − 0.21388I
−3.19874 − 0.12797I 0
u = −0.734610 + 0.151583I
a = 0.143181 − 0.339367I
b = −1.396670 + 0.114089I
−3.32187 + 0.44404I −1.02888 + 1.07661I
u = −0.734610 − 0.151583I
a = 0.143181 + 0.339367I
b = −1.396670 − 0.114089I
−3.32187 − 0.44404I −1.02888 − 1.07661I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.646531 + 0.373993I
a = −0.633547 + 0.402501I
b = 1.272210 − 0.217794I
−3.44497 + 5.62860I 0.63930 − 5.04650I
u = −0.646531 − 0.373993I
a = −0.633547 − 0.402501I
b = 1.272210 + 0.217794I
−3.44497 − 5.62860I 0.63930 + 5.04650I
u = 0.278442 + 0.682046I
a = 1.97074 − 0.67525I
b = 0.91703 + 1.25412I
−4.25778 − 4.07230I 5.38922 + 7.64539I
u = 0.278442 − 0.682046I
a = 1.97074 + 0.67525I
b = 0.91703 − 1.25412I
−4.25778 + 4.07230I 5.38922 − 7.64539I
u = −0.431986 + 1.188660I
a = 1.90467 − 1.01789I
b = −1.98435 − 0.47209I
−5.96194 − 4.35894I 0
u = −0.431986 − 1.188660I
a = 1.90467 + 1.01789I
b = −1.98435 + 0.47209I
−5.96194 + 4.35894I 0
u = 0.999965 + 0.779570I
a = 0.119807 + 0.390665I
b = 0.701938 + 0.168142I
1.20381 + 7.07038I 0
u = 0.999965 − 0.779570I
a = 0.119807 − 0.390665I
b = 0.701938 − 0.168142I
1.20381 − 7.07038I 0
u = 0.549235 + 1.145670I
a = 0.903087 − 0.591506I
b = −0.470524 + 0.061033I
0.43501 + 10.51100I 0
u = 0.549235 − 1.145670I
a = 0.903087 + 0.591506I
b = −0.470524 − 0.061033I
0.43501 − 10.51100I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.514202 + 1.166920I
a = −1.77474 − 0.81946I
b = 1.35799 − 0.99070I
−2.10553 + 8.31464I 0
u = 0.514202 − 1.166920I
a = −1.77474 + 0.81946I
b = 1.35799 + 0.99070I
−2.10553 − 8.31464I 0
u = −0.898202 + 0.912485I
a = −0.83055 + 1.61811I
b = 2.58056 − 0.29119I
8.03104 − 3.29649I 0
u = −0.898202 − 0.912485I
a = −0.83055 − 1.61811I
b = 2.58056 + 0.29119I
8.03104 + 3.29649I 0
u = −0.469554 + 0.528231I
a = 3.06157 − 0.46503I
b = −0.04131 − 1.99226I
4.51736 − 4.80623I 3.84214 + 0.I
u = −0.469554 − 0.528231I
a = 3.06157 + 0.46503I
b = −0.04131 + 1.99226I
4.51736 + 4.80623I 3.84214 + 0.I
u = −0.347157 + 0.613481I
a = −4.27454 + 0.28412I
b = 0.74276 + 2.25657I
4.02701 + 3.72908I 2.01216 − 9.01288I
u = −0.347157 − 0.613481I
a = −4.27454 − 0.28412I
b = 0.74276 − 2.25657I
4.02701 − 3.72908I 2.01216 + 9.01288I
u = 0.924734 + 0.949976I
a = −0.228117 − 0.689922I
b = 0.056096 − 0.292394I
0.669566 − 0.225276I 0
u = 0.924734 − 0.949976I
a = −0.228117 + 0.689922I
b = 0.056096 + 0.292394I
0.669566 + 0.225276I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.668240 + 1.176870I
a = 1.71510 − 1.24404I
b = −2.12407 − 0.70620I
−4.83612 − 11.07470I 0
u = −0.668240 − 1.176870I
a = 1.71510 + 1.24404I
b = −2.12407 + 0.70620I
−4.83612 + 11.07470I 0
u = −0.666253 + 1.196630I
a = −1.69121 + 1.19661I
b = 2.01215 + 0.74008I
−3.7935 − 19.0385I 0
u = −0.666253 − 1.196630I
a = −1.69121 − 1.19661I
b = 2.01215 − 0.74008I
−3.7935 + 19.0385I 0
u = 0.520165 + 1.279600I
a = −1.45884 − 0.69260I
b = 1.52018 − 0.65498I
−2.35447 + 5.14712I 0
u = 0.520165 − 1.279600I
a = −1.45884 + 0.69260I
b = 1.52018 + 0.65498I
−2.35447 − 5.14712I 0
u = 0.664062 + 1.223270I
a = 1.31321 + 0.94759I
b = −1.51048 + 0.94889I
−4.37657 + 8.87869I 0
u = 0.664062 − 1.223270I
a = 1.31321 − 0.94759I
b = −1.51048 − 0.94889I
−4.37657 − 8.87869I 0
u = −0.076345 + 1.396290I
a = 1.69133 − 0.30740I
b = −1.89384 − 0.25249I
−8.98725 + 1.61360I 0
u = −0.076345 − 1.396290I
a = 1.69133 + 0.30740I
b = −1.89384 + 0.25249I
−8.98725 − 1.61360I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.113233 + 1.396810I
a = −1.72884 + 0.46399I
b = 1.86429 + 0.07896I
−7.75197 + 9.27410I 0
u = −0.113233 − 1.396810I
a = −1.72884 − 0.46399I
b = 1.86429 − 0.07896I
−7.75197 − 9.27410I 0
u = 0.496207 + 0.326893I
a = −0.595724 − 0.843965I
b = 1.37588 − 0.43903I
−3.36813 + 4.52330I −2.57588 − 7.39314I
u = 0.496207 − 0.326893I
a = −0.595724 + 0.843965I
b = 1.37588 + 0.43903I
−3.36813 − 4.52330I −2.57588 + 7.39314I
u = 0.586510
a = −0.335309
b = 0.244845
1.92513 4.80940
u = 0.366162 + 0.410778I
a = −0.683049 − 0.572761I
b = 0.041114 + 0.353554I
0.045091 + 1.133750I 0.66238 − 5.25472I
u = 0.366162 − 0.410778I
a = −0.683049 + 0.572761I
b = 0.041114 − 0.353554I
0.045091 − 1.133750I 0.66238 + 5.25472I
u = 0.20323 + 1.56886I
a = 1.42605 + 0.26447I
b = −2.42826 − 0.10636I
−8.37781 + 1.82504I 0
u = 0.20323 − 1.56886I
a = 1.42605 − 0.26447I
b = −2.42826 + 0.10636I
−8.37781 − 1.82504I 0
16
II. I
u
2
= h−1.44 × 10
11
u
40
− 4.07 × 10
10
u
39
+ · · · + 5.53 × 10
10
b + 9.51 ×
10
10
, −1.21 × 10
11
u
40
− 2.27 × 10
11
u
39
+ · · · + 5.53 × 10
10
a − 9.31 ×
10
11
, u
41
+ 11u
39
+ · · · + 3u + 1i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
2.19574u
40
+ 4.10386u
39
+ ··· + 50.0980u + 16.8441
2.61412u
40
+ 0.735880u
39
+ ··· − 5.55037u − 1.72181
a
7
=
−3.98340u
40
+ 0.707726u
39
+ ··· − 23.5816u − 3.68457
0.481141u
40
+ 3.46547u
39
+ ··· + 20.9829u + 6.27553
a
6
=
−3.50226u
40
+ 4.17319u
39
+ ··· − 2.59869u + 2.59096
0.481141u
40
+ 3.46547u
39
+ ··· + 20.9829u + 6.27553
a
4
=
−7.25532u
40
+ 0.518686u
39
+ ··· − 22.8700u − 2.67551
2.79724u
40
+ 1.02933u
39
+ ··· + 17.8055u + 3.09345
a
10
=
0.611517u
40
+ 0.222422u
39
+ ··· + 25.1385u + 3.56748
3.14608u
40
− 0.689440u
39
+ ··· − 5.90365u − 4.68980
a
5
=
−2.22904u
40
+ 3.43438u
39
+ ··· + 1.95932u + 3.60657
−0.240301u
40
+ 3.16860u
39
+ ··· + 17.9338u + 4.57821
a
11
=
5.29089u
40
+ 3.51661u
39
+ ··· + 59.0550u + 19.2261
0.519711u
40
+ 1.92846u
39
+ ··· − 6.88375u − 1.13456
(ii) Obstruction class = 1
(iii) Cusp Shapes =
478810616922
27627227491
u
40
+
53035081567
55254454982
u
39
+ ···+
466506714074
27627227491
u −
80878950287
27627227491
17
(iv) u-Polynomials at the component
18
Crossings u-Polynomials at each crossing
c
1
u
41
− 22u
40
+ ··· − 5u + 1
c
2
u
41
+ 11u
39
+ ··· + 3u − 1
c
3
u
41
+ 21u
40
+ ··· + 17u + 1
c
4
u
41
+ 10u
39
+ ··· − u + 1
c
5
u
41
− 3u
38
+ ··· + 84u − 19
c
6
u
41
− 7u
40
+ ··· + 734u − 97
c
7
u
41
− 5u
39
+ ··· + 2u − 1
c
8
u
41
+ 11u
39
+ ··· + 3u + 1
c
9
u
41
+ u
40
+ ··· − 2u + 1
c
10
u
41
+ u
40
+ ··· + 34u + 4
c
11
u
41
− 5u
39
+ ··· + 2u + 1
c
12
u
41
− 13u
40
+ ··· − 11u + 1
19
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
41
+ 10y
40
+ ··· + 283y −1
c
2
, c
8
y
41
+ 22y
40
+ ··· − 5y −1
c
3
y
41
− 25y
40
+ ··· + 21y −1
c
4
y
41
+ 20y
40
+ ··· − 7y −1
c
5
y
41
− 24y
39
+ ··· + 17392y −361
c
6
y
41
+ 13y
40
+ ··· + 481138y −9409
c
7
, c
11
y
41
− 10y
40
+ ··· − 26y −1
c
9
y
41
+ y
40
+ ··· − 34y −1
c
10
y
41
+ 21y
40
+ ··· + 156y −16
c
12
y
41
− 15y
40
+ ··· + 3y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.598988 + 0.865344I
a = −1.022990 − 0.235083I
b = 0.231334 − 0.128745I
6.61505 − 2.36343I 13.1454 + 6.7907I
u = −0.598988 − 0.865344I
a = −1.022990 + 0.235083I
b = 0.231334 + 0.128745I
6.61505 + 2.36343I 13.1454 − 6.7907I
u = −0.376941 + 0.868744I
a = 1.57439 + 0.66804I
b = −0.380334 + 0.224394I
5.27220 − 1.59317I −16.2236 − 5.3973I
u = −0.376941 − 0.868744I
a = 1.57439 − 0.66804I
b = −0.380334 − 0.224394I
5.27220 + 1.59317I −16.2236 + 5.3973I
u = 0.577208 + 0.721237I
a = −2.64372 + 0.75658I
b = −0.31343 − 1.86635I
4.61404 + 5.56812I 5.78476 − 10.37610I
u = 0.577208 − 0.721237I
a = −2.64372 − 0.75658I
b = −0.31343 + 1.86635I
4.61404 − 5.56812I 5.78476 + 10.37610I
u = −0.775290 + 0.751998I
a = −0.346154 − 0.132107I
b = 0.0691839 − 0.0964018I
5.44963 + 1.93408I 11.9006 − 10.7077I
u = −0.775290 − 0.751998I
a = −0.346154 + 0.132107I
b = 0.0691839 + 0.0964018I
5.44963 − 1.93408I 11.9006 + 10.7077I
u = −0.046755 + 1.091780I
a = 0.491463 + 0.371920I
b = −0.635572 + 0.477388I
0.12252 + 2.09558I 2.43267 − 3.85110I
u = −0.046755 − 1.091780I
a = 0.491463 − 0.371920I
b = −0.635572 − 0.477388I
0.12252 − 2.09558I 2.43267 + 3.85110I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.290111 + 1.077500I
a = 2.57965 − 0.60292I
b = −1.59780 − 0.66936I
−5.84751 − 6.10867I −3.02706 + 6.27837I
u = −0.290111 − 1.077500I
a = 2.57965 + 0.60292I
b = −1.59780 + 0.66936I
−5.84751 + 6.10867I −3.02706 − 6.27837I
u = 0.506584 + 0.720753I
a = 3.36015 − 0.51820I
b = −0.56682 + 2.05616I
4.31465 − 3.15120I 7.36591 − 1.26606I
u = 0.506584 − 0.720753I
a = 3.36015 + 0.51820I
b = −0.56682 − 2.05616I
4.31465 + 3.15120I 7.36591 + 1.26606I
u = 0.779051 + 0.399880I
a = 0.611833 + 0.348189I
b = 1.25404 + 0.66207I
−0.38639 − 2.80737I −0.94338 + 4.60551I
u = 0.779051 − 0.399880I
a = 0.611833 − 0.348189I
b = 1.25404 − 0.66207I
−0.38639 + 2.80737I −0.94338 − 4.60551I
u = −0.878494 + 0.704132I
a = −0.179408 − 0.359328I
b = 0.787974 + 0.264368I
−0.341763 + 1.186910I −2.35865 + 0.I
u = −0.878494 − 0.704132I
a = −0.179408 + 0.359328I
b = 0.787974 − 0.264368I
−0.341763 − 1.186910I −2.35865 + 0.I
u = 0.539288 + 1.013210I
a = −0.737631 + 1.056580I
b = −0.57393 − 2.20425I
3.29984 + 7.40836I 7.25276 − 8.70343I
u = 0.539288 − 1.013210I
a = −0.737631 − 1.056580I
b = −0.57393 + 2.20425I
3.29984 − 7.40836I 7.25276 + 8.70343I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.371786 + 1.095820I
a = −1.81220 − 1.27616I
b = 1.70252 + 0.29490I
−4.14457 − 0.28130I −3.87917 + 0.I
u = 0.371786 − 1.095820I
a = −1.81220 + 1.27616I
b = 1.70252 − 0.29490I
−4.14457 + 0.28130I −3.87917 + 0.I
u = −0.239658 + 0.776070I
a = −1.080170 − 0.676686I
b = −0.97715 + 1.08447I
−4.65604 + 3.86182I −10.82806 − 0.38545I
u = −0.239658 − 0.776070I
a = −1.080170 + 0.676686I
b = −0.97715 − 1.08447I
−4.65604 − 3.86182I −10.82806 + 0.38545I
u = 0.612959 + 1.043170I
a = 0.962565 − 0.342794I
b = 0.05830 + 1.99293I
3.55512 − 0.83534I 9.81400 + 1.40438I
u = 0.612959 − 1.043170I
a = 0.962565 + 0.342794I
b = 0.05830 − 1.99293I
3.55512 + 0.83534I 9.81400 − 1.40438I
u = −0.723449 + 0.979663I
a = −0.365626 + 0.036912I
b = 0.1026420 + 0.0070731I
4.74599 − 7.61395I 16.0976 + 11.9157I
u = −0.723449 − 0.979663I
a = −0.365626 − 0.036912I
b = 0.1026420 − 0.0070731I
4.74599 + 7.61395I 16.0976 − 11.9157I
u = −0.742190 + 0.969717I
a = 0.198042 + 1.073040I
b = 0.240406 − 0.653920I
−1.12954 − 7.16316I −5.85834 + 6.29910I
u = −0.742190 − 0.969717I
a = 0.198042 − 1.073040I
b = 0.240406 + 0.653920I
−1.12954 + 7.16316I −5.85834 − 6.29910I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.553386 + 1.139860I
a = −1.70072 − 0.96778I
b = 1.42008 − 1.01478I
−2.71117 + 7.84427I 0. − 5.76093I
u = 0.553386 − 1.139860I
a = −1.70072 + 0.96778I
b = 1.42008 + 1.01478I
−2.71117 − 7.84427I 0. + 5.76093I
u = 0.887815 + 0.911680I
a = 0.83701 + 1.66221I
b = −2.61727 − 0.28447I
8.09689 + 3.26807I 53.3811 + 19.4020I
u = 0.887815 − 0.911680I
a = 0.83701 − 1.66221I
b = −2.61727 + 0.28447I
8.09689 − 3.26807I 53.3811 − 19.4020I
u = 0.207425 + 0.637090I
a = −1.30575 + 0.57486I
b = 1.147320 − 0.323866I
−2.21902 + 2.96944I 3.33270 − 6.32139I
u = 0.207425 − 0.637090I
a = −1.30575 − 0.57486I
b = 1.147320 + 0.323866I
−2.21902 − 2.96944I 3.33270 + 6.32139I
u = −0.089778 + 0.568406I
a = 3.10698 − 0.29000I
b = −0.469094 + 0.710383I
2.38066 − 2.85884I −1.45474 + 2.26695I
u = −0.089778 − 0.568406I
a = 3.10698 + 0.29000I
b = −0.469094 − 0.710383I
2.38066 + 2.85884I −1.45474 − 2.26695I
u = −0.15100 + 1.58017I
a = −1.42744 + 0.17298I
b = 2.40956 − 0.16208I
−8.30527 − 1.95740I 0
u = −0.15100 − 1.58017I
a = −1.42744 − 0.17298I
b = 2.40956 + 0.16208I
−8.30527 + 1.95740I 0
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.245695
a = 2.79945
b = 1.41605
−1.26204 2.91860
26
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
41
− 22u
40
+ ··· − 5u + 1)(u
119
+ 59u
118
+ ··· − 926108u − 44521)
c
2
(u
41
+ 11u
39
+ ··· + 3u − 1)(u
119
+ u
118
+ ··· − 366u + 211)
c
3
(u
41
+ 21u
40
+ ··· + 17u + 1)(u
119
− 12u
118
+ ··· − 594u − 503)
c
4
(u
41
+ 10u
39
+ ··· − u + 1)(u
119
+ 3u
118
+ ··· + 95214u − 3293)
c
5
(u
41
− 3u
38
+ ··· + 84u − 19)(u
119
+ u
118
+ ··· + 5201393u − 364301)
c
6
(u
41
− 7u
40
+ ··· + 734u − 97)
· (u
119
− 4u
118
+ ··· − 2916191u − 324667)
c
7
(u
41
− 5u
39
+ ··· + 2u − 1)(u
119
+ u
118
+ ··· − 25u + 1)
c
8
(u
41
+ 11u
39
+ ··· + 3u + 1)(u
119
+ u
118
+ ··· − 366u + 211)
c
9
(u
41
+ u
40
+ ··· − 2u + 1)(u
119
+ 2u
118
+ ··· + 3981u + 337)
c
10
(u
41
+ u
40
+ ··· + 34u + 4)(u
119
− 3u
117
+ ··· − 1.41558 × 10
7
u − 953372)
c
11
(u
41
− 5u
39
+ ··· + 2u + 1)(u
119
+ u
118
+ ··· − 25u + 1)
c
12
(u
41
− 13u
40
+ ··· − 11u + 1)(u
119
+ 6u
118
+ ··· − 6u − 1)
27
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
41
+ 10y
40
+ ··· + 283y −1)
· (y
119
+ 19y
118
+ ··· − 89555795764y −1982119441)
c
2
, c
8
(y
41
+ 22y
40
+ ··· − 5y −1)(y
119
+ 59y
118
+ ··· − 926108y −44521)
c
3
(y
41
− 25y
40
+ ··· + 21y −1)
· (y
119
− 44y
118
+ ··· − 2126954y −253009)
c
4
(y
41
+ 20y
40
+ ··· − 7y −1)
· (y
119
− 11y
118
+ ··· + 2421268218y −10843849)
c
5
(y
41
− 24y
39
+ ··· + 17392y −361)
· (y
119
+ y
118
+ ··· + 3889002396385y −132715218601)
c
6
(y
41
+ 13y
40
+ ··· + 481138y −9409)
· (y
119
− 22y
118
+ ··· + 24438543848191y −105408660889)
c
7
, c
11
(y
41
− 10y
40
+ ··· − 26y −1)(y
119
− 81y
118
+ ··· − 153y −1)
c
9
(y
41
+ y
40
+ ··· − 34y −1)
· (y
119
+ 14y
118
+ ··· − 16141701y −113569)
c
10
(y
41
+ 21y
40
+ ··· + 156y −16)
· (y
119
− 6y
118
+ ··· + 61203268140316y −908918170384)
c
12
(y
41
− 15y
40
+ ··· + 3y −1)(y
119
− 26y
118
+ ··· + 8y −1)
28
