12n
0849
(K12n
0849
)
A knot diagram
1
Linearized knot diagam
4 6 7 1 11 9 5 2 3 5 6 8
Solving Sequence
5,11
6
3,12
2 10 9 7 8 1 4
c
5
c
11
c
2
c
10
c
9
c
6
c
8
c
12
c
4
c
1
, c
3
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h14414381991662u
47
+ 292350624991207u
46
+ ··· + 165519047936b + 3699504946588160,
− 7225595598805u
47
− 223846226739163u
46
+ ··· + 662076191744a + 76742753642760704,
u
48
+ 23u
47
+ ··· − 16384u − 2048i
I
u
2
= h−1.88889 × 10
110
a
21
u
2
− 7.22697 × 10
109
a
20
u
2
+ ··· + 4.85317 × 10
111
a − 7.98335 × 10
111
,
− 3a
21
u
2
− a
20
u
2
+ ··· + 95954a + 14907, u
3
− u
2
+ 1i
I
u
3
= h−1731258u
33
− 1052843u
32
+ ··· + 59731b + 2238511,
− 2238511u
33
− 1731258u
32
+ ··· + 59731a + 4003959, u
34
− 13u
32
+ ··· − 4u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 148 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
= h1.44 × 10
13
u
47
+ 2.92 × 10
14
u
46
+ · · · + 1.66 × 10
11
b + 3.70 ×
10
15
, −7.23 × 10
12
u
47
− 2.24 × 10
14
u
46
+ · · · + 6.62 × 10
11
a + 7.67 ×
10
16
, u
48
+ 23u
47
+ · · · − 16384u − 2048i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
3
=
10.9135u
47
+ 338.097u
46
+ ··· − 795641.u − 115912.
−87.0859u
47
− 1766.27u
46
+ ··· − 62895.2u − 22350.9
a
12
=
−u
−u
3
+ u
a
2
=
−138.711u
47
− 2931.89u
46
+ ··· + 716421.u + 84790.7
−209.611u
47
− 4622.85u
46
+ ··· + 2.43872 × 10
6
u + 328655.
a
10
=
u
u
a
9
=
91.8720u
47
+ 2084.95u
46
+ ··· − 1.48673 × 10
6
u − 205474.
28.1022u
47
+ 751.561u
46
+ ··· − 1.29976 × 10
6
u − 188154.
a
7
=
−24.7817u
47
− 683.674u
46
+ ··· + 1.29959 × 10
6
u + 188722.
125.160u
47
+ 2650.22u
46
+ ··· − 622795.u − 72062.4
a
8
=
−149.941u
47
− 3333.90u
46
+ ··· + 1.92239 × 10
6
u + 260784.
125.160u
47
+ 2650.22u
46
+ ··· − 622795.u − 72062.4
a
1
=
89.8291u
47
+ 1976.87u
46
+ ··· − 998382.u − 133953.
−50.9494u
47
− 1049.69u
46
+ ··· + 60359.1u + 1292.65
a
4
=
113.889u
47
+ 2479.30u
46
+ ··· − 1.06684 × 10
6
u − 139256.
51.4138u
47
+ 1243.01u
46
+ ··· − 1.39957 × 10
6
u − 199576.
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
16683231602363
165519047936
u
47
+
389925962050557
165519047936
u
46
+ ··· −
1394447538636670
646558781
u −
196913051211846
646558781
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
48
− 12u
47
+ ··· − 352u + 64
c
2
, c
9
u
48
− 13u
46
+ ··· + 4u − 1
c
3
, c
8
u
48
+ u
47
+ ··· + 20u − 13
c
5
, c
10
, c
11
u
48
− 23u
47
+ ··· + 16384u − 2048
c
6
u
48
− 19u
47
+ ··· − 56u + 8
c
7
, c
12
u
48
− u
47
+ ··· + 11u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
48
+ 26y
47
+ ··· − 110080y + 4096
c
2
, c
9
y
48
− 26y
47
+ ··· + 10y + 1
c
3
, c
8
y
48
+ 7y
47
+ ··· + 2616y + 169
c
5
, c
10
, c
11
y
48
− 27y
47
+ ··· − 14680064y + 4194304
c
6
y
48
− 19y
47
+ ··· + 1056y + 64
c
7
, c
12
y
48
+ 33y
47
+ ··· − 59y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.485125 + 0.981047I
a = −1.089450 + 0.650919I
b = 0.110062 + 1.384580I
8.27627 − 1.52472I 0
u = −0.485125 − 0.981047I
a = −1.089450 − 0.650919I
b = 0.110062 − 1.384580I
8.27627 + 1.52472I 0
u = −0.530290 + 0.962673I
a = 0.901020 − 0.101260I
b = 0.380322 − 0.921086I
3.99581 + 0.06032I 0
u = −0.530290 − 0.962673I
a = 0.901020 + 0.101260I
b = 0.380322 + 0.921086I
3.99581 − 0.06032I 0
u = −0.864674 + 0.731233I
a = 1.25224 − 0.88853I
b = 0.43306 − 1.68397I
4.75585 + 2.84058I 0
u = −0.864674 − 0.731233I
a = 1.25224 + 0.88853I
b = 0.43306 + 1.68397I
4.75585 − 2.84058I 0
u = −0.429460 + 1.063940I
a = −0.732211 + 0.055128I
b = −0.255802 + 0.802706I
7.68349 − 4.13518I 0
u = −0.429460 − 1.063940I
a = −0.732211 − 0.055128I
b = −0.255802 − 0.802706I
7.68349 + 4.13518I 0
u = −0.886566 + 0.742815I
a = −1.39850 + 0.79251I
b = −0.65118 + 1.74144I
4.69075 + 2.77591I 0
u = −0.886566 − 0.742815I
a = −1.39850 − 0.79251I
b = −0.65118 − 1.74144I
4.69075 − 2.77591I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.167430 + 0.129361I
a = −0.206635 + 0.246262I
b = 0.273089 − 0.260763I
1.58195 + 0.65248I 0
u = 1.167430 − 0.129361I
a = −0.206635 − 0.246262I
b = 0.273089 + 0.260763I
1.58195 − 0.65248I 0
u = −0.494005 + 1.099620I
a = 0.953875 − 0.604813I
b = −0.193845 − 1.347680I
3.09129 − 6.44202I 0
u = −0.494005 − 1.099620I
a = 0.953875 + 0.604813I
b = −0.193845 + 1.347680I
3.09129 + 6.44202I 0
u = −0.552382 + 1.105430I
a = −0.909474 + 0.662368I
b = 0.229824 + 1.371240I
6.60458 − 12.25780I 0
u = −0.552382 − 1.105430I
a = −0.909474 − 0.662368I
b = 0.229824 − 1.371240I
6.60458 + 12.25780I 0
u = 0.648175 + 0.341671I
a = 0.150106 − 0.372567I
b = −0.224590 + 0.190202I
−0.314464 − 0.268937I −8.00000 + 0.I
u = 0.648175 − 0.341671I
a = 0.150106 + 0.372567I
b = −0.224590 − 0.190202I
−0.314464 + 0.268937I −8.00000 + 0.I
u = −0.635682 + 1.098030I
a = −0.808152 + 0.282764I
b = −0.203245 + 1.067120I
7.01061 + 4.54766I 0
u = −0.635682 − 1.098030I
a = −0.808152 − 0.282764I
b = −0.203245 − 1.067120I
7.01061 − 4.54766I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.278030 + 0.264389I
a = 0.319676 + 0.937003I
b = 0.656290 + 1.113000I
−2.93683 + 5.48157I 0
u = −1.278030 − 0.264389I
a = 0.319676 − 0.937003I
b = 0.656290 − 1.113000I
−2.93683 − 5.48157I 0
u = 0.358024 + 0.582809I
a = 1.062550 + 0.446046I
b = −0.120460 − 0.778961I
−0.94188 − 1.73288I −5.17947 + 1.25821I
u = 0.358024 − 0.582809I
a = 1.062550 − 0.446046I
b = −0.120460 + 0.778961I
−0.94188 + 1.73288I −5.17947 − 1.25821I
u = −1.33184
a = −0.851126
b = −1.13356
−6.08512 0
u = −1.095600 + 0.816987I
a = 0.865533 − 0.655040I
b = 0.41312 − 1.42479I
5.53516 + 2.26996I 0
u = −1.095600 − 0.816987I
a = 0.865533 + 0.655040I
b = 0.41312 + 1.42479I
5.53516 − 2.26996I 0
u = −1.181650 + 0.698223I
a = −0.677817 + 0.708409I
b = −0.306317 + 1.310360I
1.93618 + 6.05436I 0
u = −1.181650 − 0.698223I
a = −0.677817 − 0.708409I
b = −0.306317 − 1.310360I
1.93618 − 6.05436I 0
u = −1.195270 + 0.698625I
a = 1.37256 − 0.94570I
b = 0.97988 − 2.08927I
6.06307 + 7.68979I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.195270 − 0.698625I
a = 1.37256 + 0.94570I
b = 0.97988 + 2.08927I
6.06307 − 7.68979I 0
u = −1.18735 + 0.78240I
a = 1.33912 − 0.77886I
b = 0.98063 − 1.97251I
4.6066 + 19.0224I 0
u = −1.18735 − 0.78240I
a = 1.33912 + 0.77886I
b = 0.98063 + 1.97251I
4.6066 − 19.0224I 0
u = −1.20933 + 0.76456I
a = −1.30402 + 0.83062I
b = −0.94193 + 2.00149I
0.87016 + 13.12930I 0
u = −1.20933 − 0.76456I
a = −1.30402 − 0.83062I
b = −0.94193 − 2.00149I
0.87016 − 13.12930I 0
u = −1.23864 + 0.74371I
a = 0.661993 − 0.592040I
b = 0.379666 − 1.225650I
5.19931 + 10.67840I 0
u = −1.23864 − 0.74371I
a = 0.661993 + 0.592040I
b = 0.379666 + 1.225650I
5.19931 − 10.67840I 0
u = 0.093558 + 0.533903I
a = 0.324021 + 0.855715I
b = 0.426554 − 0.253055I
1.21279 − 2.43642I −4.24996 + 4.94851I
u = 0.093558 − 0.533903I
a = 0.324021 − 0.855715I
b = 0.426554 + 0.253055I
1.21279 + 2.43642I −4.24996 − 4.94851I
u = −1.44267 + 0.21746I
a = −0.68065 + 2.03149I
b = −0.54019 + 3.07879I
−6.76961 + 4.70527I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44267 − 0.21746I
a = −0.68065 − 2.03149I
b = −0.54019 − 3.07879I
−6.76961 − 4.70527I 0
u = 1.48960 + 0.13187I
a = 0.305557 + 0.139429I
b = −0.436770 − 0.247989I
−4.21849 + 2.31870I 0
u = 1.48960 − 0.13187I
a = 0.305557 − 0.139429I
b = −0.436770 + 0.247989I
−4.21849 − 2.31870I 0
u = 1.54460 + 0.00922I
a = −0.253984 + 0.118646I
b = 0.393396 − 0.180918I
−1.53991 − 8.40513I 0
u = 1.54460 − 0.00922I
a = −0.253984 − 0.118646I
b = 0.393396 + 0.180918I
−1.53991 + 8.40513I 0
u = 0.425779
a = 0.565774
b = −0.240895
−0.780920 −12.7940
u = −1.64161 + 0.03646I
a = −0.0546808 − 0.1253800I
b = −0.094336 − 0.203832I
−8.54644 + 1.50129I 0
u = −1.64161 − 0.03646I
a = −0.0546808 + 0.1253800I
b = −0.094336 + 0.203832I
−8.54644 − 1.50129I 0
9
II. I
u
2
= h−1.89 × 10
110
a
21
u
2
− 7.23 × 10
109
a
20
u
2
+ · · · + 4.85 × 10
111
a −
7.98 × 10
111
, −3a
21
u
2
− a
20
u
2
+ · · · + 95954a + 14907, u
3
− u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
3
=
a
0.297935a
21
u
2
+ 0.113991a
20
u
2
+ ··· − 7.65490a + 12.5921
a
12
=
−u
−u
2
+ u + 1
a
2
=
−0.297935a
21
u
2
− 0.113991a
20
u
2
+ ··· + 8.65490a − 12.5921
0.105230a
21
u
2
+ 0.223129a
20
u
2
+ ··· − 52.5944a + 28.7118
a
10
=
u
u
a
9
=
−0.444006a
21
u
2
+ 0.0389262a
20
u
2
+ ··· − 37.4768a − 1.11629
0.219343a
21
u
2
+ 0.183640a
20
u
2
+ ··· − 44.5258a + 31.9350
a
7
=
−0.129004a
21
u
2
+ 0.124229a
20
u
2
+ ··· − 52.7203a + 17.2976
0.313975a
21
u
2
+ 0.132304a
20
u
2
+ ··· − 3.59373a + 21.0298
a
8
=
−0.442978a
21
u
2
− 0.00807409a
20
u
2
+ ··· − 49.1266a − 3.73220
0.313975a
21
u
2
+ 0.132304a
20
u
2
+ ··· − 3.59373a + 21.0298
a
1
=
0.186169a
21
u
2
− 0.104298a
20
u
2
+ ··· + 39.4472a − 13.6705
−0.314462a
21
u
2
− 0.0891353a
20
u
2
+ ··· + 5.08668a − 13.7803
a
4
=
−0.180523a
21
u
2
− 0.0945800a
20
u
2
+ ··· + 2.88290a − 6.04935
0.255393a
21
u
2
+ 0.177825a
20
u
2
+ ··· − 31.5249a + 24.9875
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.26166a
21
u
2
− 0.476423a
20
u
2
+ ··· + 4.34057a − 83.6301
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
11
+ 3u
10
+ ··· + 2u + 1)
6
c
2
, c
9
u
66
− 3u
65
+ ··· + 7772u − 1789
c
3
, c
8
u
66
− u
65
+ ··· + 17622u − 13807
c
5
, c
10
, c
11
(u
3
+ u
2
− 1)
22
c
6
(u
11
+ 5u
10
+ 12u
9
+ 15u
8
+ 8u
7
− 4u
6
− 8u
5
− 3u
4
+ 3u
3
+ 3u
2
− 1)
6
c
7
, c
12
u
66
+ u
65
+ ··· + 509278u − 214703
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
11
+ 7y
10
+ ··· − 6y −1)
6
c
2
, c
9
y
66
+ 15y
65
+ ··· − 174341816y + 3200521
c
3
, c
8
y
66
+ 3y
65
+ ··· − 190413984y + 190633249
c
5
, c
10
, c
11
(y
3
− y
2
+ 2y −1)
22
c
6
(y
11
− y
10
+ ··· + 6y −1)
6
c
7
, c
12
y
66
− 9y
65
+ ··· − 545194749936y + 46097378209
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 0.902102 − 0.486271I
b = 0.320024 − 1.143140I
−0.99957 − 2.82812I −20.7516 + 2.9794I
u = 0.877439 + 0.744862I
a = 0.430794 + 0.937113I
b = −1.153740 − 0.245268I
−0.99957 − 2.82812I −20.7516 + 2.9794I
u = 0.877439 + 0.744862I
a = −0.552422 − 0.887606I
b = −0.098598 − 1.033000I
0.576298 − 0.123714I −11.95786 + 3.06277I
u = 0.877439 + 0.744862I
a = −0.463244 + 0.951207I
b = −0.19763 + 1.72019I
3.13943 − 8.75255I −11.6607 + 13.0030I
u = 0.877439 + 0.744862I
a = 0.646143 + 0.628778I
b = −0.176427 + 1.190300I
0.576298 − 0.123714I −11.95786 + 3.06277I
u = 0.877439 + 0.744862I
a = 0.543271 + 0.997448I
b = −0.247363 + 0.953185I
1.51685 + 2.38817I −8.92628 − 6.03333I
u = 0.877439 + 0.744862I
a = −0.372113 − 0.770438I
b = 0.266274 − 1.279860I
1.51685 + 2.38817I −8.92628 − 6.03333I
u = 0.877439 + 0.744862I
a = 0.332427 + 1.215800I
b = 0.01738 + 1.77304I
6.00992 + 2.17262I −0.64965 − 3.24807I
u = 0.877439 + 0.744862I
a = 1.129210 + 0.564488I
b = −0.03139 + 1.49377I
0.955193 − 0.580337I −12.12606 − 2.08415I
u = 0.877439 + 0.744862I
a = −0.819129 − 1.007060I
b = −0.57034 − 1.33641I
0.955193 − 0.580337I −12.12606 − 2.08415I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 1.333130 − 0.022190I
b = 1.29442 + 1.74631I
6.00992 − 7.82886I −0.64965 + 9.20696I
u = 0.877439 + 0.744862I
a = −1.370440 − 0.181563I
b = −1.36448 − 1.31693I
1.51685 − 8.04441I −8.9263 + 11.9922I
u = 0.877439 + 0.744862I
a = 1.40246 + 0.31556I
b = 1.26362 + 1.15269I
0.57630 − 5.53253I −11.95786 + 2.89612I
u = 0.877439 + 0.744862I
a = −1.43975 − 0.11169I
b = −0.75840 − 1.62760I
0.95519 − 5.07591I −12.1261 + 8.0430I
u = 0.877439 + 0.744862I
a = −1.45028 − 0.09496I
b = −0.546673 + 0.224501I
3.13943 + 3.09630I −11.66070 − 7.04410I
u = 0.877439 + 0.744862I
a = −1.48510 − 0.05299I
b = −0.99552 − 1.32153I
0.57630 − 5.53253I −11.95786 + 2.89612I
u = 0.877439 + 0.744862I
a = 0.235861 − 0.456083I
b = 1.20180 + 1.16358I
3.13943 + 3.09630I −11.66070 − 7.04410I
u = 0.877439 + 0.744862I
a = −0.83632 − 1.25050I
b = 1.114990 − 0.489573I
3.13943 − 8.75255I −11.6607 + 13.0030I
u = 0.877439 + 0.744862I
a = −1.00846 − 1.16462I
b = 0.61392 − 1.31441I
6.00992 + 2.17262I −0.64965 − 3.24807I
u = 0.877439 + 0.744862I
a = 1.41750 + 0.65162I
b = 1.18010 + 1.17042I
0.95519 − 5.07591I −12.1261 + 8.0430I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 1.64426 + 0.10506I
b = 1.06724 + 1.18010I
1.51685 − 8.04441I −8.9263 + 11.9922I
u = 0.877439 + 0.744862I
a = −1.83928 − 0.42886I
b = −1.18627 − 0.97353I
6.00992 − 7.82886I −0.64965 + 9.20696I
u = 0.877439 − 0.744862I
a = 0.902102 + 0.486271I
b = 0.320024 + 1.143140I
−0.99957 + 2.82812I −20.7516 − 2.9794I
u = 0.877439 − 0.744862I
a = 0.430794 − 0.937113I
b = −1.153740 + 0.245268I
−0.99957 + 2.82812I −20.7516 − 2.9794I
u = 0.877439 − 0.744862I
a = −0.552422 + 0.887606I
b = −0.098598 + 1.033000I
0.576298 + 0.123714I −11.95786 − 3.06277I
u = 0.877439 − 0.744862I
a = −0.463244 − 0.951207I
b = −0.19763 − 1.72019I
3.13943 + 8.75255I −11.6607 − 13.0030I
u = 0.877439 − 0.744862I
a = 0.646143 − 0.628778I
b = −0.176427 − 1.190300I
0.576298 + 0.123714I −11.95786 − 3.06277I
u = 0.877439 − 0.744862I
a = 0.543271 − 0.997448I
b = −0.247363 − 0.953185I
1.51685 − 2.38817I −8.92628 + 6.03333I
u = 0.877439 − 0.744862I
a = −0.372113 + 0.770438I
b = 0.266274 + 1.279860I
1.51685 − 2.38817I −8.92628 + 6.03333I
u = 0.877439 − 0.744862I
a = 0.332427 − 1.215800I
b = 0.01738 − 1.77304I
6.00992 − 2.17262I −0.64965 + 3.24807I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 − 0.744862I
a = 1.129210 − 0.564488I
b = −0.03139 − 1.49377I
0.955193 + 0.580337I −12.12606 + 2.08415I
u = 0.877439 − 0.744862I
a = −0.819129 + 1.007060I
b = −0.57034 + 1.33641I
0.955193 + 0.580337I −12.12606 + 2.08415I
u = 0.877439 − 0.744862I
a = 1.333130 + 0.022190I
b = 1.29442 − 1.74631I
6.00992 + 7.82886I −0.64965 − 9.20696I
u = 0.877439 − 0.744862I
a = −1.370440 + 0.181563I
b = −1.36448 + 1.31693I
1.51685 + 8.04441I −8.9263 − 11.9922I
u = 0.877439 − 0.744862I
a = 1.40246 − 0.31556I
b = 1.26362 − 1.15269I
0.57630 + 5.53253I −11.95786 − 2.89612I
u = 0.877439 − 0.744862I
a = −1.43975 + 0.11169I
b = −0.75840 + 1.62760I
0.95519 + 5.07591I −12.1261 − 8.0430I
u = 0.877439 − 0.744862I
a = −1.45028 + 0.09496I
b = −0.546673 − 0.224501I
3.13943 − 3.09630I −11.66070 + 7.04410I
u = 0.877439 − 0.744862I
a = −1.48510 + 0.05299I
b = −0.99552 + 1.32153I
0.57630 + 5.53253I −11.95786 − 2.89612I
u = 0.877439 − 0.744862I
a = 0.235861 + 0.456083I
b = 1.20180 − 1.16358I
3.13943 − 3.09630I −11.66070 + 7.04410I
u = 0.877439 − 0.744862I
a = −0.83632 + 1.25050I
b = 1.114990 + 0.489573I
3.13943 + 8.75255I −11.6607 − 13.0030I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 − 0.744862I
a = −1.00846 + 1.16462I
b = 0.61392 + 1.31441I
6.00992 − 2.17262I −0.64965 + 3.24807I
u = 0.877439 − 0.744862I
a = 1.41750 − 0.65162I
b = 1.18010 − 1.17042I
0.95519 + 5.07591I −12.1261 − 8.0430I
u = 0.877439 − 0.744862I
a = 1.64426 − 0.10506I
b = 1.06724 − 1.18010I
1.51685 + 8.04441I −8.9263 − 11.9922I
u = 0.877439 − 0.744862I
a = −1.83928 + 0.42886I
b = −1.18627 + 0.97353I
6.00992 + 7.82886I −0.64965 − 9.20696I
u = −0.754878
a = −0.533542 + 0.548275I
b = −0.21703 + 1.70176I
−3.18239 + 2.24779I −18.6553 − 5.0636I
u = −0.754878
a = −0.533542 − 0.548275I
b = −0.21703 − 1.70176I
−3.18239 − 2.24779I −18.6553 + 5.0636I
u = −0.754878
a = −0.279438 + 0.521422I
b = −0.747235 − 1.047170I
−2.62073 + 5.21629I −15.4555 − 9.0128I
u = −0.754878
a = −0.279438 − 0.521422I
b = −0.747235 + 1.047170I
−2.62073 − 5.21629I −15.4555 + 9.0128I
u = −0.754878
a = −0.275349 + 0.202814I
b = 0.183994 − 1.275850I
−3.56129 − 2.70441I −18.4871 − 0.0833I
u = −0.754878
a = −0.275349 − 0.202814I
b = 0.183994 + 1.275850I
−3.56129 + 2.70441I −18.4871 + 0.0833I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754878
a = −0.98988 + 1.38720I
b = −0.210941 − 0.393610I
−2.62073 − 5.21629I −15.4555 + 9.0128I
u = −0.754878
a = −0.98988 − 1.38720I
b = −0.210941 + 0.393610I
−2.62073 + 5.21629I −15.4555 − 9.0128I
u = −0.754878
a = 0.24374 + 1.69014I
b = −0.207855 − 0.153100I
−3.56129 + 2.70441I −18.4871 + 0.0833I
u = −0.754878
a = 0.24374 − 1.69014I
b = −0.207855 + 0.153100I
−3.56129 − 2.70441I −18.4871 − 0.0833I
u = −0.754878
a = 1.33232 + 1.38795I
b = 1.53989 + 0.03375I
1.87234 − 5.00074I −7.17892 + 6.22751I
u = −0.754878
a = 1.33232 − 1.38795I
b = 1.53989 − 0.03375I
1.87234 + 5.00074I −7.17892 − 6.22751I
u = −0.754878
a = 2.03992 + 0.04471I
b = 1.00574 + 1.04773I
1.87234 − 5.00074I −7.17892 + 6.22751I
u = −0.754878
a = 2.03992 − 0.04471I
b = 1.00574 − 1.04773I
1.87234 + 5.00074I −7.17892 − 6.22751I
u = −0.754878
a = −0.28750 + 2.25436I
b = −0.402759 + 0.413881I
−3.18239 + 2.24779I −18.6553 − 5.0636I
u = −0.754878
a = −0.28750 − 2.25436I
b = −0.402759 − 0.413881I
−3.18239 − 2.24779I −18.6553 + 5.0636I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754878
a = 2.95304 + 0.44701I
b = 3.18424 + 0.20464I
−0.99816 + 5.92443I 0
u = −0.754878
a = 2.95304 − 0.44701I
b = 3.18424 − 0.20464I
−0.99816 − 5.92443I 0
u = −0.754878
a = −3.15422
b = −3.35926
−5.13715 0
u = −0.754878
a = 4.21822 + 0.27109I
b = 2.22919 + 0.33744I
−0.99816 + 5.92443I 0
u = −0.754878
a = 4.21822 − 0.27109I
b = 2.22919 − 0.33744I
−0.99816 − 5.92443I 0
u = −0.754878
a = −4.45007
b = −2.38105
−5.13715 0
19
III.
I
u
3
= h−1.73 × 10
6
u
33
− 1.05 × 10
6
u
32
+ · · · + 5.97 × 10
4
b + 2.24 × 10
6
, −2.24 ×
10
6
u
33
−1.73×10
6
u
32
+· · ·+5.97×10
4
a+4.00×10
6
, u
34
−13u
32
+· · ·−4u
2
+1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
3
=
37.4765u
33
+ 28.9842u
32
+ ··· − 72.4005u − 67.0332
28.9842u
33
+ 17.6264u
32
+ ··· − 67.0332u − 37.4765
a
12
=
−u
−u
3
+ u
a
2
=
26.1187u
33
+ 23.6640u
32
+ ··· − 42.8439u − 58.5409
24.4307u
33
+ 15.0188u
32
+ ··· − 55.6753u − 32.1563
a
10
=
u
u
a
9
=
10.4182u
33
− 5.53038u
32
+ ··· − 32.7393u + 13.5756
−5.53038u
33
+ 2.99749u
32
+ ··· + 14.5756u − 10.4182
a
7
=
29.5853u
33
− 19.1478u
32
+ ··· − 80.7177u + 59.8427
−12.3570u
33
+ 6.32862u
32
+ ··· + 34.3663u − 16.4659
a
8
=
41.9423u
33
− 25.4764u
32
+ ··· − 115.084u + 76.3086
−12.3570u
33
+ 6.32862u
32
+ ··· + 34.3663u − 16.4659
a
1
=
−6.60429u
33
+ 10.0088u
32
+ ··· + 16.9741u − 26.1847
6.17162u
33
+ 0.380154u
32
+ ··· − 18.5804u − 3.40451
a
4
=
16.7796u
33
+ 11.6363u
32
+ ··· − 45.8180u − 28.3939
15.6963u
33
+ 8.48193u
32
+ ··· − 36.5974u − 21.8641
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
663479
59731
u
33
+
1468982
59731
u
32
+ ··· +
3288260
59731
u −
4500469
59731
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
34
− 11u
33
+ ··· − 153u + 25
c
2
, c
9
u
34
+ 8u
32
+ ··· + 4u − 1
c
3
, c
8
u
34
+ u
33
+ ··· + 4u − 1
c
4
u
34
+ 11u
33
+ ··· + 153u + 25
c
5
u
34
− 13u
32
+ ··· − 4u
2
+ 1
c
6
u
34
− 22u
33
+ ··· − 11u + 1
c
7
, c
12
u
34
+ u
33
+ ··· + 7u − 1
c
10
, c
11
u
34
− 13u
32
+ ··· − 4u
2
+ 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
34
+ 19y
33
+ ··· + 9841y + 625
c
2
, c
9
y
34
+ 16y
33
+ ··· + 6y + 1
c
3
, c
8
y
34
− 3y
33
+ ··· + 4y + 1
c
5
, c
10
, c
11
y
34
− 26y
33
+ ··· − 8y + 1
c
6
y
34
− 18y
33
+ ··· − 13y + 1
c
7
, c
12
y
34
− 17y
33
+ ··· − 23y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.845244 + 0.604160I
a = 1.91410 + 0.14388I
b = 1.53095 + 1.27804I
3.25368 − 6.85148I −4.85043 + 7.91334I
u = 0.845244 − 0.604160I
a = 1.91410 − 0.14388I
b = 1.53095 − 1.27804I
3.25368 + 6.85148I −4.85043 − 7.91334I
u = −0.895619 + 0.699368I
a = −0.590494 + 0.168532I
b = 0.410992 − 0.563913I
4.00733 − 2.65022I −2.94134 + 1.85323I
u = −0.895619 − 0.699368I
a = −0.590494 − 0.168532I
b = 0.410992 + 0.563913I
4.00733 + 2.65022I −2.94134 − 1.85323I
u = −0.853323 + 0.773155I
a = 0.589236 − 0.220815I
b = −0.332084 + 0.643997I
−0.36168 + 2.92655I −4.69868 − 5.16619I
u = −0.853323 − 0.773155I
a = 0.589236 + 0.220815I
b = −0.332084 − 0.643997I
−0.36168 − 2.92655I −4.69868 + 5.16619I
u = −0.898698 + 0.721304I
a = −0.471500 + 0.227103I
b = 0.259926 − 0.544192I
3.97518 + 8.07880I −4.76528 − 6.64300I
u = −0.898698 − 0.721304I
a = −0.471500 − 0.227103I
b = 0.259926 + 0.544192I
3.97518 − 8.07880I −4.76528 + 6.64300I
u = 0.857194 + 0.802437I
a = −1.350540 − 0.116108I
b = −1.06450 − 1.18325I
1.52615 − 6.51453I −5.61054 + 6.02417I
u = 0.857194 − 0.802437I
a = −1.350540 + 0.116108I
b = −1.06450 + 1.18325I
1.52615 + 6.51453I −5.61054 − 6.02417I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.187710 + 0.191526I
a = −0.041458 − 0.375482I
b = 0.121155 + 0.438023I
−4.19227 + 6.40599I −15.5049 − 8.8278I
u = −1.187710 − 0.191526I
a = −0.041458 + 0.375482I
b = 0.121155 − 0.438023I
−4.19227 − 6.40599I −15.5049 + 8.8278I
u = 1.027460 + 0.661768I
a = −0.303568 − 0.915936I
b = 0.294234 − 1.141980I
2.64248 + 1.96167I −1.53326 − 1.99100I
u = 1.027460 − 0.661768I
a = −0.303568 + 0.915936I
b = 0.294234 + 1.141980I
2.64248 − 1.96167I −1.53326 + 1.99100I
u = 1.22760
a = −1.93511
b = −2.37554
−6.94043 −24.4110
u = 0.905250 + 0.844336I
a = 0.550716 + 0.724589I
b = −0.113261 + 1.120920I
1.39644 + 0.41153I −2.71773 − 1.79950I
u = 0.905250 − 0.844336I
a = 0.550716 − 0.724589I
b = −0.113261 − 1.120920I
1.39644 − 0.41153I −2.71773 + 1.79950I
u = 1.232980 + 0.132443I
a = 1.43939 − 0.87127I
b = 1.89014 − 0.88362I
−2.81974 − 6.65969I −13.9389 + 9.7504I
u = 1.232980 − 0.132443I
a = 1.43939 + 0.87127I
b = 1.89014 + 0.88362I
−2.81974 + 6.65969I −13.9389 − 9.7504I
u = −1.249730 + 0.109070I
a = 0.268415 − 0.308268I
b = −0.301823 + 0.414527I
−5.53822 − 1.91820I −16.6362 + 1.6027I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.249730 − 0.109070I
a = 0.268415 + 0.308268I
b = −0.301823 − 0.414527I
−5.53822 + 1.91820I −16.6362 − 1.6027I
u = 0.665736
a = −4.03140
b = −2.68384
−4.67762 −5.42070
u = −0.648923 + 0.147922I
a = 0.761243 − 0.982468I
b = −0.348659 + 0.750150I
−2.03261 − 4.84635I −3.32627 + 1.12061I
u = −0.648923 − 0.147922I
a = 0.761243 + 0.982468I
b = −0.348659 − 0.750150I
−2.03261 + 4.84635I −3.32627 − 1.12061I
u = 0.659269 + 0.077443I
a = 4.04500 − 0.28467I
b = 2.68879 + 0.12558I
−0.48875 + 5.72099I −1.66381 − 3.21415I
u = 0.659269 − 0.077443I
a = 4.04500 + 0.28467I
b = 2.68879 − 0.12558I
−0.48875 − 5.72099I −1.66381 + 3.21415I
u = −0.595318 + 0.097089I
a = −0.052986 − 1.365210I
b = 0.164091 + 0.807592I
−2.91383 + 2.92551I −4.46735 − 4.14484I
u = −0.595318 − 0.097089I
a = −0.052986 + 1.365210I
b = 0.164091 − 0.807592I
−2.91383 − 2.92551I −4.46735 + 4.14484I
u = 1.42516 + 0.21887I
a = −0.74184 − 2.07454I
b = −0.60318 − 3.11893I
−6.84248 − 4.69187I −65.0121 + 0.I
u = 1.42516 − 0.21887I
a = −0.74184 + 2.07454I
b = −0.60318 + 3.11893I
−6.84248 + 4.69187I −65.0121 + 0.I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.62951 + 0.02230I
a = 0.0272909 + 0.0596106I
b = −0.0458005 − 0.0965277I
−8.58478 + 1.54555I 0
u = −1.62951 − 0.02230I
a = 0.0272909 − 0.0596106I
b = −0.0458005 + 0.0965277I
−8.58478 − 1.54555I 0
u = 0.059608 + 0.333902I
a = 2.94025 + 0.58858I
b = −0.021265 + 1.016840I
−1.89189 + 2.22619I −11.47365 − 4.34728I
u = 0.059608 − 0.333902I
a = 2.94025 − 0.58858I
b = −0.021265 − 1.016840I
−1.89189 − 2.22619I −11.47365 + 4.34728I
26
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
11
+ 3u
10
+ ··· + 2u + 1)
6
)(u
34
− 11u
33
+ ··· − 153u + 25)
· (u
48
− 12u
47
+ ··· − 352u + 64)
c
2
, c
9
(u
34
+ 8u
32
+ ··· + 4u − 1)(u
48
− 13u
46
+ ··· + 4u − 1)
· (u
66
− 3u
65
+ ··· + 7772u − 1789)
c
3
, c
8
(u
34
+ u
33
+ ··· + 4u − 1)(u
48
+ u
47
+ ··· + 20u − 13)
· (u
66
− u
65
+ ··· + 17622u − 13807)
c
4
((u
11
+ 3u
10
+ ··· + 2u + 1)
6
)(u
34
+ 11u
33
+ ··· + 153u + 25)
· (u
48
− 12u
47
+ ··· − 352u + 64)
c
5
((u
3
+ u
2
− 1)
22
)(u
34
− 13u
32
+ ··· − 4u
2
+ 1)
· (u
48
− 23u
47
+ ··· + 16384u − 2048)
c
6
(u
11
+ 5u
10
+ 12u
9
+ 15u
8
+ 8u
7
− 4u
6
− 8u
5
− 3u
4
+ 3u
3
+ 3u
2
− 1)
6
· (u
34
− 22u
33
+ ··· − 11u + 1)(u
48
− 19u
47
+ ··· − 56u + 8)
c
7
, c
12
(u
34
+ u
33
+ ··· + 7u − 1)(u
48
− u
47
+ ··· + 11u − 1)
· (u
66
+ u
65
+ ··· + 509278u − 214703)
c
10
, c
11
((u
3
+ u
2
− 1)
22
)(u
34
− 13u
32
+ ··· − 4u
2
+ 1)
· (u
48
− 23u
47
+ ··· + 16384u − 2048)
27
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
11
+ 7y
10
+ ··· − 6y −1)
6
)(y
34
+ 19y
33
+ ··· + 9841y + 625)
· (y
48
+ 26y
47
+ ··· − 110080y + 4096)
c
2
, c
9
(y
34
+ 16y
33
+ ··· + 6y + 1)(y
48
− 26y
47
+ ··· + 10y + 1)
· (y
66
+ 15y
65
+ ··· − 174341816y + 3200521)
c
3
, c
8
(y
34
− 3y
33
+ ··· + 4y + 1)(y
48
+ 7y
47
+ ··· + 2616y + 169)
· (y
66
+ 3y
65
+ ··· − 190413984y + 190633249)
c
5
, c
10
, c
11
((y
3
− y
2
+ 2y −1)
22
)(y
34
− 26y
33
+ ··· − 8y + 1)
· (y
48
− 27y
47
+ ··· − 14680064y + 4194304)
c
6
((y
11
− y
10
+ ··· + 6y −1)
6
)(y
34
− 18y
33
+ ··· − 13y + 1)
· (y
48
− 19y
47
+ ··· + 1056y + 64)
c
7
, c
12
(y
34
− 17y
33
+ ··· − 23y + 1)(y
48
+ 33y
47
+ ··· − 59y + 1)
· (y
66
− 9y
65
+ ··· − 545194749936y + 46097378209)
28
