12n
0832
(K12n
0832
)
A knot diagram
1
Linearized knot diagam
4 5 11 8 3 10 1 5 7 6 4 7
Solving Sequence
6,10
7
3,11
4 12 5 2 1 9 8
c
6
c
10
c
3
c
11
c
5
c
2
c
1
c
9
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h755u
20
− 5418u
19
+ ··· + 1124b + 9500, 865u
20
− 6654u
19
+ ··· + 2248a − 4904,
u
21
− 8u
20
+ ··· + 84u − 8i
I
u
2
= hu
25
a + 113u
25
+ ··· − a − 113, −u
25
a + 59u
25
+ ··· + 35a − 380, u
26
+ 3u
25
+ ··· − 10u − 1i
I
u
3
= hu
10
− u
9
+ 6u
8
− 5u
7
+ 13u
6
− 8u
5
+ 13u
4
− 4u
3
+ 6u
2
+ b + 1,
u
9
+ 5u
7
+ 8u
5
+ u
4
+ 5u
3
+ 4u
2
+ a + 2u + 3,
u
11
− u
10
+ 7u
9
− 6u
8
+ 18u
7
− 13u
6
+ 22u
5
− 12u
4
+ 14u
3
− 4u
2
+ 4u − 1i
I
u
4
= h−u
4
a + u
3
a − u
4
− 4u
2
a + u
3
+ 4au − 4u
2
+ 5b − a + 4u − 6, u
4
a + 3u
2
a − u
3
+ a
2
+ 3a − u − 1,
u
5
+ 3u
3
+ 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 94 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
= h755u
20
− 5418u
19
+ · · · + 1124b + 9500, 865u
20
− 6654u
19
+ · · · +
2248a − 4904, u
21
− 8u
20
+ · · · + 84u − 8i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
−0.384786u
20
+ 2.95996u
19
+ ··· + 3.87811u + 2.18149
−0.671708u
20
+ 4.82028u
19
+ ··· + 82.4751u − 8.45196
a
11
=
−u
u
a
4
=
−0.938167u
20
+ 6.46886u
19
+ ··· + 51.8496u − 3.19217
−0.118327u
20
+ 1.31139u
19
+ ··· + 34.5036u − 3.07829
a
12
=
−1.46486u
20
+ 10.4733u
19
+ ··· + 114.085u − 10.8790
−0.601423u
20
+ 4.76690u
19
+ ··· + 65.6459u − 6.20996
a
5
=
−0.776246u
20
+ 5.60854u
19
+ ··· + 23.2527u + 0.441281
−1.29004u
20
+ 9.63167u
19
+ ··· + 156.479u − 16.5302
a
2
=
0.978203u
20
− 6.60053u
19
+ ··· − 67.8283u + 8.22242
0.298043u
20
− 2.75801u
19
+ ··· − 46.1744u + 4.83630
a
1
=
−1.14279u
20
+ 8.33630u
19
+ ··· + 86.8238u − 7.12456
−0.241993u
20
+ 1.87367u
19
+ ··· + 31.3043u − 2.69395
a
9
=
u
u
3
+ u
a
8
=
−0.424822u
20
+ 3.09164u
19
+ ··· + 19.8568u − 2.84875
1.07206u
20
− 7.63701u
19
+ ··· − 71.7616u + 7.75445
(ii) Obstruction class = −1
(iii) Cusp Shapes =
797
281
u
20
−
5987
281
u
19
+ ··· −
114148
281
u +
15414
281
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
− 20u
20
+ ··· + 1600u − 128
c
2
, c
3
, c
5
c
11
u
21
− 8u
19
+ ··· − 3u − 1
c
4
, c
7
, c
8
c
12
u
21
− 5u
19
+ ··· + 2u − 1
c
6
, c
9
, c
10
u
21
− 8u
20
+ ··· + 84u − 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
+ 6y
20
+ ··· − 692224y −16384
c
2
, c
3
, c
5
c
11
y
21
− 16y
20
+ ··· + 25y −1
c
4
, c
7
, c
8
c
12
y
21
− 10y
20
+ ··· + 12y −1
c
6
, c
9
, c
10
y
21
+ 20y
20
+ ··· + 528y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.430675 + 0.863692I
a = 0.474474 + 0.031759I
b = −0.241235 + 0.131245I
0.31209 + 1.75113I 3.06893 − 1.22304I
u = −0.430675 − 0.863692I
a = 0.474474 − 0.031759I
b = −0.241235 − 0.131245I
0.31209 − 1.75113I 3.06893 + 1.22304I
u = 0.941579 + 0.500830I
a = 0.468449 + 0.441296I
b = −1.230110 + 0.582897I
2.10752 − 11.16100I 8.47490 + 8.35858I
u = 0.941579 − 0.500830I
a = 0.468449 − 0.441296I
b = −1.230110 − 0.582897I
2.10752 + 11.16100I 8.47490 − 8.35858I
u = 0.864822 + 0.780507I
a = 0.228758 + 0.686980I
b = −1.034020 − 0.254427I
2.88881 + 5.10968I 10.51418 − 4.53183I
u = 0.864822 − 0.780507I
a = 0.228758 − 0.686980I
b = −1.034020 + 0.254427I
2.88881 − 5.10968I 10.51418 + 4.53183I
u = 0.784060 + 0.089570I
a = 0.148949 − 0.280369I
b = 0.899061 − 0.583293I
−0.161111 + 0.298509I 5.89200 − 0.80081I
u = 0.784060 − 0.089570I
a = 0.148949 + 0.280369I
b = 0.899061 + 0.583293I
−0.161111 − 0.298509I 5.89200 + 0.80081I
u = 0.337572 + 0.642009I
a = −1.027230 − 0.769285I
b = 0.807982 − 0.604519I
2.55000 − 2.18542I 13.17858 + 4.25561I
u = 0.337572 − 0.642009I
a = −1.027230 + 0.769285I
b = 0.807982 + 0.604519I
2.55000 + 2.18542I 13.17858 − 4.25561I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.445135 + 1.219610I
a = −0.175359 − 0.810246I
b = 0.671583 + 0.440706I
3.28725 − 4.77138I 12.62050 + 2.51819I
u = 0.445135 − 1.219610I
a = −0.175359 + 0.810246I
b = 0.671583 − 0.440706I
3.28725 + 4.77138I 12.62050 − 2.51819I
u = 0.274538 + 1.362470I
a = −1.61794 − 0.34738I
b = 1.32395 − 0.68359I
4.45013 − 3.41075I 7.62872 + 0.78780I
u = 0.274538 − 1.362470I
a = −1.61794 + 0.34738I
b = 1.32395 + 0.68359I
4.45013 + 3.41075I 7.62872 − 0.78780I
u = 0.09790 + 1.57918I
a = −1.59282 + 0.10699I
b = 1.107320 − 0.838285I
10.08840 − 3.80196I 14.3317 + 1.4217I
u = 0.09790 − 1.57918I
a = −1.59282 − 0.10699I
b = 1.107320 + 0.838285I
10.08840 + 3.80196I 14.3317 − 1.4217I
u = 0.34514 + 1.54955I
a = 1.75952 + 0.28354I
b = −1.50761 + 0.74551I
8.7389 − 15.8550I 11.09832 + 8.19798I
u = 0.34514 − 1.54955I
a = 1.75952 − 0.28354I
b = −1.50761 − 0.74551I
8.7389 + 15.8550I 11.09832 − 8.19798I
u = 0.19250 + 1.66330I
a = 1.163750 + 0.386362I
b = −1.076850 + 0.271112I
11.34600 + 1.18083I 12.33791 − 3.38306I
u = 0.19250 − 1.66330I
a = 1.163750 − 0.386362I
b = −1.076850 − 0.271112I
11.34600 − 1.18083I 12.33791 + 3.38306I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.294851
a = 1.33890
b = 0.559847
0.900446 10.7090
7
II. I
u
2
= hu
25
a + 113u
25
+ · · · − a − 113, −u
25
a + 59u
25
+ · · · + 35a −
380, u
26
+ 3u
25
+ · · · − 10u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
a
−0.00204918au
25
− 0.231557u
25
+ ··· + 0.00204918a + 0.231557
a
11
=
−u
u
a
4
=
−0.00204918au
25
+ 1.01844u
25
+ ··· + 1.00205a − 0.0184426
−
5
4
u
25
−
13
4
u
24
+ ··· −
25
4
u +
1
4
a
12
=
0.786885au
25
+ 3.41803u
25
+ ··· + 0.213115a − 17.9180
−1.01844au
25
− 0.334016u
25
+ ··· + 0.0184426a − 2.66598
a
5
=
−0.0184426au
25
− 2.08402u
25
+ ··· − 0.231557a + 17.8340
0.0184426au
25
− 1.66598u
25
+ ··· + 0.231557a + 3.41598
a
2
=
1.08607au
25
+ 3.60041u
25
+ ··· − 2.08607a − 18.8504
−0.573770au
25
+ 0.913934u
25
+ ··· − 1.17623a − 8.41393
a
1
=
0.231557au
25
+ 2.91598u
25
+ ··· + 0.768443a − 19.1660
−0.323770au
25
+ 1.16393u
25
+ ··· − 0.176230a − 3.66393
a
9
=
u
u
3
+ u
a
8
=
u
25
a −
1
4
u
25
+ ··· −
11
4
a +
35
4
−0.512295au
25
− 0.764344u
25
+ ··· + 1.26230a + 5.76434
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6u
25
−16u
24
−101u
23
−221u
22
−726u
21
−1318u
20
−2920u
19
−
4393u
18
− 7154u
17
− 8772u
16
− 10705u
15
− 10189u
14
− 8827u
13
− 5415u
12
− 2068u
11
+
1201u
10
+ 2439u
9
+ 3056u
8
+ 1615u
7
+ 1083u
6
−79u
5
−164u
4
−80u
3
−87u
2
+ 98u + 43
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
26
+ 4u
25
+ ··· − 14u − 1)
2
c
2
, c
3
, c
5
c
11
u
52
− 16u
50
+ ··· − 18950u − 3929
c
4
, c
7
, c
8
c
12
u
52
− u
51
+ ··· − 116u − 173
c
6
, c
9
, c
10
(u
26
+ 3u
25
+ ··· − 10u − 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
26
− 10y
25
+ ··· − 44y + 1)
2
c
2
, c
3
, c
5
c
11
y
52
− 32y
51
+ ··· − 267831830y + 15437041
c
4
, c
7
, c
8
c
12
y
52
− 25y
51
+ ··· − 356688y + 29929
c
6
, c
9
, c
10
(y
26
+ 27y
25
+ ··· − 64y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.936700 + 0.371884I
a = 0.462570 − 0.350885I
b = −1.195860 − 0.440014I
−0.05500 + 4.49672I 6.90644 − 6.32358I
u = −0.936700 + 0.371884I
a = −0.039258 + 0.375495I
b = 0.980992 + 0.468137I
−0.05500 + 4.49672I 6.90644 − 6.32358I
u = −0.936700 − 0.371884I
a = 0.462570 + 0.350885I
b = −1.195860 + 0.440014I
−0.05500 − 4.49672I 6.90644 + 6.32358I
u = −0.936700 − 0.371884I
a = −0.039258 − 0.375495I
b = 0.980992 − 0.468137I
−0.05500 − 4.49672I 6.90644 + 6.32358I
u = 0.161010 + 0.937138I
a = −0.372337 − 0.320316I
b = 0.594088 + 0.976193I
1.50012 + 2.81558I 10.54904 − 1.62602I
u = 0.161010 + 0.937138I
a = 1.69655 − 0.75534I
b = −0.578944 + 0.313413I
1.50012 + 2.81558I 10.54904 − 1.62602I
u = 0.161010 − 0.937138I
a = −0.372337 + 0.320316I
b = 0.594088 − 0.976193I
1.50012 − 2.81558I 10.54904 + 1.62602I
u = 0.161010 − 0.937138I
a = 1.69655 + 0.75534I
b = −0.578944 − 0.313413I
1.50012 − 2.81558I 10.54904 + 1.62602I
u = −0.708992 + 0.951444I
a = 0.651485 − 0.808528I
b = −1.011240 + 0.204754I
1.64103 + 1.22347I 13.51964 + 0.98097I
u = −0.708992 + 0.951444I
a = −0.181917 + 0.494490I
b = 0.829524 + 0.085781I
1.64103 + 1.22347I 13.51964 + 0.98097I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.708992 − 0.951444I
a = 0.651485 + 0.808528I
b = −1.011240 − 0.204754I
1.64103 − 1.22347I 13.51964 − 0.98097I
u = −0.708992 − 0.951444I
a = −0.181917 − 0.494490I
b = 0.829524 − 0.085781I
1.64103 − 1.22347I 13.51964 − 0.98097I
u = −0.182776 + 1.209640I
a = −0.090918 − 0.481727I
b = 0.060610 + 1.140650I
0.96206 + 2.92695I 6.81519 − 4.13402I
u = −0.182776 + 1.209640I
a = 1.70603 − 0.03119I
b = −0.791516 − 0.157097I
0.96206 + 2.92695I 6.81519 − 4.13402I
u = −0.182776 − 1.209640I
a = −0.090918 + 0.481727I
b = 0.060610 − 1.140650I
0.96206 − 2.92695I 6.81519 + 4.13402I
u = −0.182776 − 1.209640I
a = 1.70603 + 0.03119I
b = −0.791516 + 0.157097I
0.96206 − 2.92695I 6.81519 + 4.13402I
u = 0.742160
a = −1.06248
b = −1.03522
8.17916 11.6390
u = 0.742160
a = 0.161952
b = −1.55683
8.17916 11.6390
u = −0.102954 + 1.349080I
a = −0.610876 + 0.469921I
b = 0.63694 − 1.34522I
3.48444 + 1.51475I 10.09301 − 0.89690I
u = −0.102954 + 1.349080I
a = −2.20534 − 0.51903I
b = 1.178160 + 0.125283I
3.48444 + 1.51475I 10.09301 − 0.89690I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.102954 − 1.349080I
a = −0.610876 − 0.469921I
b = 0.63694 + 1.34522I
3.48444 − 1.51475I 10.09301 + 0.89690I
u = −0.102954 − 1.349080I
a = −2.20534 + 0.51903I
b = 1.178160 − 0.125283I
3.48444 − 1.51475I 10.09301 + 0.89690I
u = −0.610623
a = 0.940549 + 0.478437I
b = −0.356583 + 0.750287I
−2.72154 0.113340
u = −0.610623
a = 0.940549 − 0.478437I
b = −0.356583 − 0.750287I
−2.72154 0.113340
u = −0.064094 + 1.398480I
a = 1.071330 − 0.853228I
b = −0.900991 − 0.546298I
12.03230 + 0.75720I 11.78661 + 1.87156I
u = −0.064094 + 1.398480I
a = −2.30664 + 0.33287I
b = 1.94629 + 0.32791I
12.03230 + 0.75720I 11.78661 + 1.87156I
u = −0.064094 − 1.398480I
a = 1.071330 + 0.853228I
b = −0.900991 + 0.546298I
12.03230 − 0.75720I 11.78661 − 1.87156I
u = −0.064094 − 1.398480I
a = −2.30664 − 0.33287I
b = 1.94629 − 0.32791I
12.03230 − 0.75720I 11.78661 − 1.87156I
u = 0.29359 + 1.38566I
a = 0.917664 + 0.651922I
b = −1.089370 + 0.544537I
12.72520 − 3.76756I 12.82417 + 5.83874I
u = 0.29359 + 1.38566I
a = 1.92497 + 0.71873I
b = −1.70830 + 0.11335I
12.72520 − 3.76756I 12.82417 + 5.83874I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.29359 − 1.38566I
a = 0.917664 − 0.651922I
b = −1.089370 − 0.544537I
12.72520 + 3.76756I 12.82417 − 5.83874I
u = 0.29359 − 1.38566I
a = 1.92497 − 0.71873I
b = −1.70830 − 0.11335I
12.72520 + 3.76756I 12.82417 − 5.83874I
u = 0.16283 + 1.41681I
a = 0.100131 + 0.909513I
b = −0.22302 − 1.66557I
4.47253 − 7.65205I 11.23629 + 6.29966I
u = 0.16283 + 1.41681I
a = −2.22930 + 0.31922I
b = 1.051180 − 0.297212I
4.47253 − 7.65205I 11.23629 + 6.29966I
u = 0.16283 − 1.41681I
a = 0.100131 − 0.909513I
b = −0.22302 + 1.66557I
4.47253 + 7.65205I 11.23629 − 6.29966I
u = 0.16283 − 1.41681I
a = −2.22930 − 0.31922I
b = 1.051180 + 0.297212I
4.47253 + 7.65205I 11.23629 − 6.29966I
u = 0.493206 + 0.200165I
a = 1.076770 − 0.731073I
b = −0.326392 − 1.066810I
−0.80371 − 5.33299I 4.24998 + 6.99887I
u = 0.493206 + 0.200165I
a = −2.05186 − 0.89000I
b = 0.729963 − 0.736528I
−0.80371 − 5.33299I 4.24998 + 6.99887I
u = 0.493206 − 0.200165I
a = 1.076770 + 0.731073I
b = −0.326392 + 1.066810I
−0.80371 + 5.33299I 4.24998 − 6.99887I
u = 0.493206 − 0.200165I
a = −2.05186 + 0.89000I
b = 0.729963 + 0.736528I
−0.80371 + 5.33299I 4.24998 − 6.99887I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.35604 + 1.48740I
a = −1.43298 + 0.24002I
b = 1.30868 + 0.78884I
5.91538 + 9.14466I 9.03397 − 5.78146I
u = −0.35604 + 1.48740I
a = 1.78847 − 0.40103I
b = −1.48606 − 0.55120I
5.91538 + 9.14466I 9.03397 − 5.78146I
u = −0.35604 − 1.48740I
a = −1.43298 − 0.24002I
b = 1.30868 − 0.78884I
5.91538 − 9.14466I 9.03397 + 5.78146I
u = −0.35604 − 1.48740I
a = 1.78847 + 0.40103I
b = −1.48606 + 0.55120I
5.91538 − 9.14466I 9.03397 + 5.78146I
u = −0.09423 + 1.62135I
a = −1.44999 − 0.23090I
b = 1.30588 + 0.80444I
10.65970 + 3.56149I 13.44467 − 2.96926I
u = −0.09423 + 1.62135I
a = 1.36417 − 0.54374I
b = −0.916341 − 0.287709I
10.65970 + 3.56149I 13.44467 − 2.96926I
u = −0.09423 − 1.62135I
a = −1.44999 + 0.23090I
b = 1.30588 − 0.80444I
10.65970 − 3.56149I 13.44467 + 2.96926I
u = −0.09423 − 1.62135I
a = 1.36417 + 0.54374I
b = −0.916341 + 0.287709I
10.65970 − 3.56149I 13.44467 + 2.96926I
u = −0.323487
a = −3.05669 + 1.44801I
b = 0.747118 + 0.692393I
−0.934190 4.31950
u = −0.323487
a = −3.05669 − 1.44801I
b = 0.747118 − 0.692393I
−0.934190 4.31950
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.137752
a = 4.04980
b = 1.83276
7.19870 28.0100
u = −0.137752
a = −12.4944
b = −0.810333
7.19870 28.0100
16
III. I
u
3
= hu
10
− u
9
+ · · · + b + 1, u
9
+ 5u
7
+ 8u
5
+ u
4
+ 5u
3
+ 4u
2
+ a + 2u +
3, u
11
− u
10
+ · · · + 4u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
−u
9
− 5u
7
− 8u
5
− u
4
− 5u
3
− 4u
2
− 2u − 3
−u
10
+ u
9
− 6u
8
+ 5u
7
− 13u
6
+ 8u
5
− 13u
4
+ 4u
3
− 6u
2
− 1
a
11
=
−u
u
a
4
=
−u
8
− 5u
6
+ u
5
− 9u
4
+ 3u
3
− 8u
2
+ u − 4
−u
10
− 5u
8
− 8u
6
− u
5
− 5u
4
− 4u
3
− 2u
2
− 3u
a
12
=
u
10
− u
9
+ 8u
8
− 6u
7
+ 22u
6
− 12u
5
+ 26u
4
− 9u
3
+ 15u
2
− u + 5
u
10
+ 5u
8
+ 9u
6
− u
5
+ 9u
4
− u
3
+ 6u
2
+ u + 1
a
5
=
u
10
+ 7u
8
− u
7
+ 18u
6
− 4u
5
+ 21u
4
− 3u
3
+ 13u
2
+ 2u + 5
u
10
− u
9
+ 6u
8
− 5u
7
+ 13u
6
− 9u
5
+ 14u
4
− 7u
3
+ 8u
2
− 2u + 2
a
2
=
2u
10
− 3u
9
+ ··· − 5u + 5
u
9
− u
8
+ 5u
7
− 4u
6
+ 8u
5
− 4u
4
+ 5u
3
+ u + 1
a
1
=
u
10
− u
9
+ 9u
8
− 7u
7
+ 27u
6
− 16u
5
+ 34u
4
− 13u
3
+ 20u
2
− u + 6
2u
10
− u
9
+ 10u
8
− 4u
7
+ 17u
6
− 5u
5
+ 14u
4
− u
3
+ 7u
2
+ u + 1
a
9
=
u
u
3
+ u
a
8
=
−2u
10
+ 2u
9
+ ··· + 6u − 8
−u
8
− 4u
6
− 5u
4
+ u
3
− 4u
2
− 2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 5u
10
− 6u
9
+ 31u
8
− 31u
7
+ 68u
6
− 50u
5
+ 66u
4
− 24u
3
+ 29u
2
+ 2u + 14
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
− 5u
10
+ ··· + 14u − 4
c
2
, c
11
u
11
− 3u
9
− 3u
8
+ 3u
7
+ 6u
6
+ 4u
5
− u
4
− 5u
3
− 5u
2
− 3u − 1
c
3
, c
5
u
11
− 3u
9
+ 3u
8
+ 3u
7
− 6u
6
+ 4u
5
+ u
4
− 5u
3
+ 5u
2
− 3u + 1
c
4
, c
7
u
11
− 4u
9
+ 7u
7
+ u
6
− 7u
5
− 2u
4
+ 3u
3
+ u
2
− 1
c
6
u
11
− u
10
+ ··· + 4u − 1
c
8
, c
12
u
11
− 4u
9
+ 7u
7
− u
6
− 7u
5
+ 2u
4
+ 3u
3
− u
2
+ 1
c
9
, c
10
u
11
+ u
10
+ ··· + 4u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
+ 7y
10
+ ··· + 28y −16
c
2
, c
3
, c
5
c
11
y
11
− 6y
10
+ ··· − y −1
c
4
, c
7
, c
8
c
12
y
11
− 8y
10
+ ··· + 2y −1
c
6
, c
9
, c
10
y
11
+ 13y
10
+ ··· + 8y −1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.634650 + 0.752345I
a = −0.414999 − 0.526959I
b = 0.765011 − 0.194619I
0.93793 − 2.36076I 9.00561 + 6.24789I
u = 0.634650 − 0.752345I
a = −0.414999 + 0.526959I
b = 0.765011 + 0.194619I
0.93793 + 2.36076I 9.00561 − 6.24789I
u = −0.223462 + 1.156870I
a = 0.598154 − 0.899354I
b = 0.026934 + 0.755329I
2.36275 + 5.98555I 8.86300 − 5.80132I
u = −0.223462 − 1.156870I
a = 0.598154 + 0.899354I
b = 0.026934 − 0.755329I
2.36275 − 5.98555I 8.86300 + 5.80132I
u = −0.243172 + 0.670452I
a = −1.41482 + 0.55978I
b = 0.345053 − 0.686432I
0.64563 − 4.10616I 7.55706 + 5.69313I
u = −0.243172 − 0.670452I
a = −1.41482 − 0.55978I
b = 0.345053 + 0.686432I
0.64563 + 4.10616I 7.55706 − 5.69313I
u = 0.11829 + 1.45395I
a = 1.61152 + 0.63237I
b = −1.43809 + 0.37083I
14.7672 − 1.4480I 15.9428 + 0.5637I
u = 0.11829 − 1.45395I
a = 1.61152 − 0.63237I
b = −1.43809 − 0.37083I
14.7672 + 1.4480I 15.9428 − 0.5637I
u = 0.08190 + 1.61228I
a = −1.42381 + 0.09154I
b = 1.001200 − 0.733988I
9.37084 − 4.46108I 6.94249 + 7.37115I
u = 0.08190 − 1.61228I
a = −1.42381 − 0.09154I
b = 1.001200 + 0.733988I
9.37084 + 4.46108I 6.94249 − 7.37115I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.263581
a = −3.91208
b = −1.40022
9.62873 16.3780
21
IV.
I
u
4
= h−u
4
a−u
4
+· · ·−a−6, u
4
a+3u
2
a−u
3
+a
2
+3a−u−1, u
5
+3u
3
+2u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
a
1
5
u
4
a +
1
5
u
4
+ ··· +
1
5
a +
6
5
a
11
=
−u
u
a
4
=
1
5
u
4
a +
1
5
u
4
+ ··· +
6
5
a +
1
5
−au − u + 1
a
12
=
2
5
u
4
a +
2
5
u
4
+ ··· +
7
5
a −
3
5
−
1
5
u
4
a −
6
5
u
4
+ ··· −
1
5
a −
1
5
a
5
=
−
1
5
u
4
a −
1
5
u
4
+ ··· −
1
5
a +
4
5
1
5
u
4
a +
6
5
u
4
+ ··· +
1
5
a +
11
5
a
2
=
−u
4
a − 2u
2
a + u
3
− u
2
+ 2u − 1
1
5
u
4
a −
9
5
u
4
+ ··· −
4
5
a −
14
5
a
1
=
−
1
5
u
4
a −
1
5
u
4
+ ··· +
4
5
a −
6
5
1
5
u
4
a −
4
5
u
4
+ ··· +
1
5
a −
4
5
a
9
=
u
u
3
+ u
a
8
=
−
3
5
u
4
a −
3
5
u
4
+ ··· −
8
5
a −
3
5
−
2
5
u
4
a −
2
5
u
4
+ ··· −
2
5
a −
7
5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
4
+ 4u
3
− 10u
2
+ 7u − 1
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
+ 3u
4
+ 3u
3
− u
2
− 2u + 1)
2
c
2
, c
11
u
10
+ 5u
9
+ 7u
8
− 2u
7
− 10u
6
− 2u
5
+ 7u
4
+ 5u
3
− u
2
− 2u − 1
c
3
, c
5
u
10
− 5u
9
+ 7u
8
+ 2u
7
− 10u
6
+ 2u
5
+ 7u
4
− 5u
3
− u
2
+ 2u − 1
c
4
, c
7
u
10
− 4u
8
− u
7
+ 6u
6
+ 3u
5
− 6u
4
− u
3
+ 4u
2
− 1
c
6
(u
5
+ 3u
3
+ 2u + 1)
2
c
8
, c
12
u
10
− 4u
8
+ u
7
+ 6u
6
− 3u
5
− 6u
4
+ u
3
+ 4u
2
− 1
c
9
, c
10
(u
5
+ 3u
3
+ 2u − 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
− 3y
4
+ 11y
3
− 19y
2
+ 6y −1)
2
c
2
, c
3
, c
5
c
11
y
10
− 11y
9
+ ··· − 2y + 1
c
4
, c
7
, c
8
c
12
y
10
− 8y
9
+ ··· − 8y + 1
c
6
, c
9
, c
10
(y
5
+ 6y
4
+ 13y
3
+ 12y
2
+ 4y −1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351694 + 0.989493I
a = −1.055910 − 0.933285I
b = 0.699891 + 0.503450I
0.60622 − 1.36579I 5.56321 − 0.05864I
u = 0.351694 + 0.989493I
a = 0.374825 + 0.036018I
b = 0.300109 − 0.503450I
0.60622 − 1.36579I 5.56321 − 0.05864I
u = 0.351694 − 0.989493I
a = −1.055910 + 0.933285I
b = 0.699891 − 0.503450I
0.60622 + 1.36579I 5.56321 + 0.05864I
u = 0.351694 − 0.989493I
a = 0.374825 − 0.036018I
b = 0.300109 + 0.503450I
0.60622 + 1.36579I 5.56321 + 0.05864I
u = −0.15201 + 1.49915I
a = 0.971714 − 0.799823I
b = −0.812288 − 0.425220I
12.36630 + 2.10101I 14.7849 − 2.0648I
u = −0.15201 + 1.49915I
a = −2.03866 + 0.13957I
b = 1.81229 + 0.42522I
12.36630 + 2.10101I 14.7849 − 2.0648I
u = −0.15201 − 1.49915I
a = 0.971714 + 0.799823I
b = −0.812288 + 0.425220I
12.36630 − 2.10101I 14.7849 + 2.0648I
u = −0.15201 − 1.49915I
a = −2.03866 − 0.13957I
b = 1.81229 − 0.42522I
12.36630 − 2.10101I 14.7849 + 2.0648I
u = −0.399372
a = 0.147064
b = 1.76271
6.95362 −5.69630
u = −0.399372
a = −3.65100
b = −0.762709
6.95362 −5.69630
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
5
+ 3u
4
+ 3u
3
− u
2
− 2u + 1)
2
)(u
11
− 5u
10
+ ··· + 14u − 4)
· (u
21
− 20u
20
+ ··· + 1600u − 128)(u
26
+ 4u
25
+ ··· − 14u − 1)
2
c
2
, c
11
(u
10
+ 5u
9
+ 7u
8
− 2u
7
− 10u
6
− 2u
5
+ 7u
4
+ 5u
3
− u
2
− 2u − 1)
· (u
11
− 3u
9
− 3u
8
+ 3u
7
+ 6u
6
+ 4u
5
− u
4
− 5u
3
− 5u
2
− 3u − 1)
· (u
21
− 8u
19
+ ··· − 3u − 1)(u
52
− 16u
50
+ ··· − 18950u − 3929)
c
3
, c
5
(u
10
− 5u
9
+ 7u
8
+ 2u
7
− 10u
6
+ 2u
5
+ 7u
4
− 5u
3
− u
2
+ 2u − 1)
· (u
11
− 3u
9
+ 3u
8
+ 3u
7
− 6u
6
+ 4u
5
+ u
4
− 5u
3
+ 5u
2
− 3u + 1)
· (u
21
− 8u
19
+ ··· − 3u − 1)(u
52
− 16u
50
+ ··· − 18950u − 3929)
c
4
, c
7
(u
10
− 4u
8
− u
7
+ 6u
6
+ 3u
5
− 6u
4
− u
3
+ 4u
2
− 1)
· (u
11
− 4u
9
+ 7u
7
+ u
6
− 7u
5
− 2u
4
+ 3u
3
+ u
2
− 1)
· (u
21
− 5u
19
+ ··· + 2u − 1)(u
52
− u
51
+ ··· − 116u − 173)
c
6
((u
5
+ 3u
3
+ 2u + 1)
2
)(u
11
− u
10
+ ··· + 4u − 1)
· (u
21
− 8u
20
+ ··· + 84u − 8)(u
26
+ 3u
25
+ ··· − 10u − 1)
2
c
8
, c
12
(u
10
− 4u
8
+ u
7
+ 6u
6
− 3u
5
− 6u
4
+ u
3
+ 4u
2
− 1)
· (u
11
− 4u
9
+ 7u
7
− u
6
− 7u
5
+ 2u
4
+ 3u
3
− u
2
+ 1)
· (u
21
− 5u
19
+ ··· + 2u − 1)(u
52
− u
51
+ ··· − 116u − 173)
c
9
, c
10
((u
5
+ 3u
3
+ 2u − 1)
2
)(u
11
+ u
10
+ ··· + 4u + 1)
· (u
21
− 8u
20
+ ··· + 84u − 8)(u
26
+ 3u
25
+ ··· − 10u − 1)
2
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
5
− 3y
4
+ 11y
3
− 19y
2
+ 6y −1)
2
)(y
11
+ 7y
10
+ ··· + 28y −16)
· (y
21
+ 6y
20
+ ··· − 692224y −16384)(y
26
− 10y
25
+ ··· − 44y + 1)
2
c
2
, c
3
, c
5
c
11
(y
10
− 11y
9
+ ··· − 2y + 1)(y
11
− 6y
10
+ ··· − y −1)
· (y
21
− 16y
20
+ ··· + 25y −1)
· (y
52
− 32y
51
+ ··· − 267831830y + 15437041)
c
4
, c
7
, c
8
c
12
(y
10
− 8y
9
+ ··· − 8y + 1)(y
11
− 8y
10
+ ··· + 2y −1)
· (y
21
− 10y
20
+ ··· + 12y −1)(y
52
− 25y
51
+ ··· − 356688y + 29929)
c
6
, c
9
, c
10
((y
5
+ 6y
4
+ 13y
3
+ 12y
2
+ 4y −1)
2
)(y
11
+ 13y
10
+ ··· + 8y −1)
· (y
21
+ 20y
20
+ ··· + 528y −64)(y
26
+ 27y
25
+ ··· − 64y + 1)
2
27
