12n
0548
(K12n
0548
)
A knot diagram
1
Linearized knot diagam
3 6 8 7 2 10 11 12 6 4 3 9
Solving Sequence
3,8 4,11
12 9 1 7 5 10 6 2
c
3
c
11
c
8
c
12
c
7
c
4
c
10
c
6
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h839541u
18
+ 414704u
17
+ ··· + 614275b + 334586,
− 1568119u
18
− 334586u
17
+ ··· + 614275a − 893399, u
19
+ 4u
17
+ ··· − 3u + 1i
I
u
2
= h−5.87295 × 10
66
u
41
− 1.75111 × 10
67
u
40
+ ··· + 2.94164 × 10
68
b − 3.67088 × 10
68
,
− 3.09411 × 10
67
u
41
− 7.74232 × 10
67
u
40
+ ··· + 2.94164 × 10
68
a − 4.17179 × 10
68
, u
42
+ 2u
41
+ ··· − u + 29i
I
u
3
= h−u
5
− 2u
4
− 3u
3
− u
2
+ b − u − 1, 2u
5
+ 3u
4
+ 4u
3
+ a + u + 1, u
6
+ u
5
+ 2u
4
+ 2u
2
+ 1i
I
u
4
= hb, −u
2
+ a − 4u − 4, u
3
+ 3u
2
+ 2u + 1i
I
u
5
= h−u
2
+ b + 2u − 3, a − u + 1, u
3
− u
2
+ 2u − 1i
I
u
6
= hb, −u
2
+ a + u − 2, u
3
− u
2
+ 2u − 1i
I
u
7
= h−u
3
+ 2u
2
+ 2b − 2u + 3, a, u
4
− u
3
− 3u − 1i
* 7 irreducible components of dim
C
= 0, with total 80 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
= h8.40 × 10
5
u
18
+ 4.15 × 10
5
u
17
+ · · · + 6.14 × 10
5
b + 3.35 × 10
5
, −1.57 ×
10
6
u
18
−3.35×10
5
u
17
+· · ·+6.14×10
5
a−8.93×10
5
, u
19
+4u
17
+· · · −3u +1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
2.55280u
18
+ 0.544684u
17
+ ··· + 6.35355u + 1.45440
−1.36672u
18
− 0.675111u
17
+ ··· + 0.0812568u − 0.544684
a
12
=
1.18608u
18
− 0.130427u
17
+ ··· + 6.43480u + 0.909711
−1.36672u
18
− 0.675111u
17
+ ··· + 0.0812568u − 0.544684
a
9
=
−1.87702u
18
− 1.06727u
17
+ ··· + 2.08800u − 0.313684
−0.605885u
18
+ 0.644166u
17
+ ··· − 4.44053u + 1.84186
a
1
=
2.29520u
18
− 2.10756u
17
+ ··· + 20.0462u − 4.88661
−2.87084u
18
− 0.364195u
17
+ ··· − 6.80711u + 0.344619
a
7
=
0.0815091u
18
− 1.84037u
17
+ ··· + 14.0499u − 3.45123
−1.35265u
18
+ 0.128936u
17
+ ··· − 5.52137u + 1.29569
a
5
=
4.14127u
18
− 5.59500u
17
+ ··· + 40.2826u − 11.9351
−2.76534u
18
+ 1.25245u
17
+ ··· − 13.5192u + 2.87564
a
10
=
2.55280u
18
+ 0.544684u
17
+ ··· + 7.35355u + 1.45440
−1.36672u
18
− 0.675111u
17
+ ··· + 0.0812568u − 0.544684
a
6
=
2.26892u
18
+ 0.0721110u
17
+ ··· + 8.09872u − 1.42611
−1.16048u
18
− 0.642082u
17
+ ··· − 0.393968u − 0.747222
a
2
=
5.16604u
18
− 1.74336u
17
+ ··· + 26.8533u − 5.23123
−2.87084u
18
− 0.364195u
17
+ ··· − 6.80711u + 0.344619
(ii) Obstruction class = −1
(iii) Cusp Shapes =
534153
614275
u
18
+
1331432
614275
u
17
+ ··· +
884838
614275
u +
5127063
614275
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
+ 16u
18
+ ··· + 7856u + 256
c
2
, c
5
u
19
+ 10u
18
+ ··· + 12u − 16
c
3
, c
10
u
19
+ 4u
17
+ ··· − 3u + 1
c
4
, c
11
u
19
+ 2u
18
+ ··· + 12u + 8
c
6
, c
8
, c
9
c
12
u
19
+ u
18
+ ··· + 3u + 1
c
7
u
19
+ 13u
18
+ ··· − 48u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
− 48y
18
+ ··· + 38868736y −65536
c
2
, c
5
y
19
− 16y
18
+ ··· + 7856y −256
c
3
, c
10
y
19
+ 8y
18
+ ··· + 5y −1
c
4
, c
11
y
19
− 2y
18
+ ··· + 592y −64
c
6
, c
8
, c
9
c
12
y
19
+ y
18
+ ··· + 21y −1
c
7
y
19
+ 5y
18
+ ··· + 328y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.554327 + 0.816296I
a = 0.449718 − 0.399149I
b = −1.077030 + 0.552624I
−2.67732 − 0.51592I 1.091807 − 0.810974I
u = −0.554327 − 0.816296I
a = 0.449718 + 0.399149I
b = −1.077030 − 0.552624I
−2.67732 + 0.51592I 1.091807 + 0.810974I
u = 1.07189
a = −0.191560
b = 0.851800
0.580619 13.0550
u = −0.762242 + 0.899191I
a = 1.206180 + 0.397943I
b = −0.491185 − 0.844790I
−2.15014 + 2.80593I −2.26586 − 2.17358I
u = −0.762242 − 0.899191I
a = 1.206180 − 0.397943I
b = −0.491185 + 0.844790I
−2.15014 − 2.80593I −2.26586 + 2.17358I
u = 0.235296 + 0.747067I
a = −2.32482 − 0.34119I
b = 1.52404 + 0.10128I
3.56934 − 0.90767I −0.55417 + 9.36864I
u = 0.235296 − 0.747067I
a = −2.32482 + 0.34119I
b = 1.52404 − 0.10128I
3.56934 + 0.90767I −0.55417 − 9.36864I
u = −0.037268 + 1.233190I
a = −0.275398 + 0.188667I
b = 0.398506 + 0.971850I
8.03976 + 1.79924I 7.69871 − 3.75838I
u = −0.037268 − 1.233190I
a = −0.275398 − 0.188667I
b = 0.398506 − 0.971850I
8.03976 − 1.79924I 7.69871 + 3.75838I
u = −0.752726
a = 0.641735
b = −0.389121
−1.23606 −8.48800
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.876387 + 0.962111I
a = −0.967056 + 0.743601I
b = −0.225183 − 0.785891I
−9.02909 + 1.94624I −2.17011 − 0.32172I
u = 0.876387 − 0.962111I
a = −0.967056 − 0.743601I
b = −0.225183 + 0.785891I
−9.02909 − 1.94624I −2.17011 + 0.32172I
u = 0.078541 + 0.678324I
a = 3.11733 + 0.71264I
b = −1.41252 + 0.68698I
−3.99480 − 5.52551I 3.44622 + 2.46689I
u = 0.078541 − 0.678324I
a = 3.11733 − 0.71264I
b = −1.41252 − 0.68698I
−3.99480 + 5.52551I 3.44622 − 2.46689I
u = 0.722855 + 1.170890I
a = −1.224490 + 0.542047I
b = 0.84423 − 1.36180I
−0.20840 − 9.16203I 0.05762 + 7.52328I
u = 0.722855 − 1.170890I
a = −1.224490 − 0.542047I
b = 0.84423 + 1.36180I
−0.20840 + 9.16203I 0.05762 − 7.52328I
u = −0.86076 + 1.25309I
a = 1.147680 + 0.364414I
b = −1.02645 − 1.52491I
−7.0282 + 15.9756I −0.06436 − 7.92433I
u = −0.86076 − 1.25309I
a = 1.147680 − 0.364414I
b = −1.02645 + 1.52491I
−7.0282 − 15.9756I −0.06436 + 7.92433I
u = 0.283860
a = 2.29154
b = 0.468504
1.29410 7.95340
6
II.
I
u
2
= h−5.87×10
66
u
41
−1.75×10
67
u
40
+· · ·+2.94×10
68
b−3.67×10
68
, −3.09×
10
67
u
41
−7.74×10
67
u
40
+· · ·+2.94×10
68
a−4.17×10
68
, u
42
+2u
41
+· · ·−u+29i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
0.105183u
41
+ 0.263197u
40
+ ··· + 13.0930u + 1.41818
0.0199649u
41
+ 0.0595283u
40
+ ··· + 1.86016u + 1.24790
a
12
=
0.125148u
41
+ 0.322725u
40
+ ··· + 14.9532u + 2.66608
0.0199649u
41
+ 0.0595283u
40
+ ··· + 1.86016u + 1.24790
a
9
=
−0.227872u
41
− 0.440210u
40
+ ··· − 20.1740u + 8.13423
0.0339899u
41
+ 0.0632354u
40
+ ··· + 0.553957u − 1.62888
a
1
=
−0.243217u
41
− 0.412652u
40
+ ··· − 7.86097u + 18.2275
−0.0293195u
41
− 0.0612038u
40
+ ··· − 3.53683u − 0.800021
a
7
=
−0.284778u
41
− 0.544075u
40
+ ··· − 18.4556u + 10.5971
0.0229160u
41
+ 0.0406297u
40
+ ··· − 0.272377u − 0.834006
a
5
=
0.429098u
41
+ 1.08741u
40
+ ··· + 62.8716u + 11.7818
−0.0368126u
41
− 0.0787071u
40
+ ··· − 2.03432u + 1.99774
a
10
=
0.123438u
41
+ 0.337722u
40
+ ··· + 17.9506u + 4.19819
0.0205559u
41
+ 0.0509951u
40
+ ··· + 1.36876u + 0.145489
a
6
=
−0.380839u
41
− 0.803076u
40
+ ··· − 34.7432u + 7.26273
0.0150353u
41
+ 0.0151766u
40
+ ··· − 1.15105u − 2.01514
a
2
=
−0.213898u
41
− 0.351449u
40
+ ··· − 4.32414u + 19.0276
−0.0293195u
41
− 0.0612038u
40
+ ··· − 3.53683u − 0.800021
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.244611u
41
− 0.621694u
40
+ ··· − 40.9379u + 5.54966
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
21
+ 25u
20
+ ··· + 84u + 1)
2
c
2
, c
5
(u
21
− 5u
20
+ ··· − 14u + 1)
2
c
3
, c
10
u
42
+ 2u
41
+ ··· − u + 29
c
4
, c
11
u
42
+ 6u
41
+ ··· − 124u + 8
c
6
, c
8
, c
9
c
12
u
42
− 2u
41
+ ··· − 24u + 29
c
7
(u
21
− 6u
20
+ ··· + 12u + 4)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
21
− 53y
20
+ ··· − 180y −1)
2
c
2
, c
5
(y
21
− 25y
20
+ ··· + 84y −1)
2
c
3
, c
10
y
42
+ 4y
41
+ ··· + 10439y + 841
c
4
, c
11
y
42
+ 16y
41
+ ··· − 1424y + 64
c
6
, c
8
, c
9
c
12
y
42
− 8y
41
+ ··· − 2722y + 841
c
7
(y
21
− 12y
20
+ ··· + 504y −16)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.910809 + 0.492994I
a = 0.604245 − 0.480077I
b = −0.012249 + 1.136170I
−2.24713 + 3.07529I −2.94639 − 4.21084I
u = 0.910809 − 0.492994I
a = 0.604245 + 0.480077I
b = −0.012249 − 1.136170I
−2.24713 − 3.07529I −2.94639 + 4.21084I
u = 0.395865 + 0.853042I
a = 1.134820 − 0.230653I
b = −0.404156 + 0.264334I
2.28813 + 0.50504I 2.35502 − 2.42758I
u = 0.395865 − 0.853042I
a = 1.134820 + 0.230653I
b = −0.404156 − 0.264334I
2.28813 − 0.50504I 2.35502 + 2.42758I
u = −0.160574 + 0.922004I
a = 1.78763 + 0.41444I
b = −2.14163 − 0.02583I
−3.01993 + 5.87862I 3.16317 − 5.53402I
u = −0.160574 − 0.922004I
a = 1.78763 − 0.41444I
b = −2.14163 + 0.02583I
−3.01993 − 5.87862I 3.16317 + 5.53402I
u = 0.306219 + 0.860956I
a = 0.75794 − 1.62449I
b = 0.101490 + 0.115855I
2.86504 − 3.02547I 1.74153 + 5.07163I
u = 0.306219 − 0.860956I
a = 0.75794 + 1.62449I
b = 0.101490 − 0.115855I
2.86504 + 3.02547I 1.74153 − 5.07163I
u = −0.790784 + 0.845104I
a = 1.39288 − 0.51155I
b = −0.968075 − 0.894251I
−3.01993 + 5.87862I 3.16317 − 5.53402I
u = −0.790784 − 0.845104I
a = 1.39288 + 0.51155I
b = −0.968075 + 0.894251I
−3.01993 − 5.87862I 3.16317 + 5.53402I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.038600 + 0.523837I
a = −0.942154 + 0.475195I
b = −0.236220 − 1.166820I
−10.7460 −4.50742 + 0.I
u = 1.038600 − 0.523837I
a = −0.942154 − 0.475195I
b = −0.236220 + 1.166820I
−10.7460 −4.50742 + 0.I
u = −0.797787 + 0.875105I
a = −0.534733 − 0.411863I
b = 0.404891 + 1.292910I
−2.24713 + 3.07529I −2.94639 − 4.21084I
u = −0.797787 − 0.875105I
a = −0.534733 + 0.411863I
b = 0.404891 − 1.292910I
−2.24713 − 3.07529I −2.94639 + 4.21084I
u = −0.879615 + 0.797579I
a = −1.51117 − 0.36130I
b = −0.021383 + 0.843147I
−8.46800 + 6.35526I −2.09227 − 5.05576I
u = −0.879615 − 0.797579I
a = −1.51117 + 0.36130I
b = −0.021383 − 0.843147I
−8.46800 − 6.35526I −2.09227 + 5.05576I
u = 0.871026 + 0.898919I
a = 0.667226 − 0.327012I
b = −0.81971 + 1.63423I
−9.19963 − 8.42224I −2.59003 + 5.45173I
u = 0.871026 − 0.898919I
a = 0.667226 + 0.327012I
b = −0.81971 − 1.63423I
−9.19963 + 8.42224I −2.59003 − 5.45173I
u = 0.723315
a = −0.282353
b = 1.55958
0.602093 30.8920
u = 0.252564 + 1.269630I
a = −1.05577 + 1.07496I
b = 1.09518 − 1.86934I
4.79941 − 2.44365I 9.18422 − 5.36256I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.252564 − 1.269630I
a = −1.05577 − 1.07496I
b = 1.09518 + 1.86934I
4.79941 + 2.44365I 9.18422 + 5.36256I
u = −0.826857 + 1.036500I
a = 0.291224 + 0.365062I
b = −0.31488 − 1.67829I
−7.74435 −1.51944 + 0.I
u = −0.826857 − 1.036500I
a = 0.291224 − 0.365062I
b = −0.31488 + 1.67829I
−7.74435 −1.51944 + 0.I
u = 0.874570 + 1.009200I
a = 1.065470 − 0.129907I
b = −0.858651 + 0.720112I
1.31849 − 7.43334I −1.09731 + 4.98321I
u = 0.874570 − 1.009200I
a = 1.065470 + 0.129907I
b = −0.858651 − 0.720112I
1.31849 + 7.43334I −1.09731 − 4.98321I
u = 0.088014 + 0.633793I
a = −1.21829 − 1.18843I
b = 1.008390 − 0.520783I
2.28813 − 0.50504I 2.35502 + 2.42758I
u = 0.088014 − 0.633793I
a = −1.21829 + 1.18843I
b = 1.008390 + 0.520783I
2.28813 + 0.50504I 2.35502 − 2.42758I
u = −0.264329 + 1.335610I
a = −0.344279 − 1.152810I
b = 0.082329 + 1.358030I
2.86504 + 3.02547I 1.74153 − 5.07163I
u = −0.264329 − 1.335610I
a = −0.344279 + 1.152810I
b = 0.082329 − 1.358030I
2.86504 − 3.02547I 1.74153 + 5.07163I
u = 0.693494 + 1.227500I
a = 1.112370 − 0.689204I
b = −0.84731 + 1.80325I
−8.46800 − 6.35526I −2.09227 + 5.05576I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.693494 − 1.227500I
a = 1.112370 + 0.689204I
b = −0.84731 − 1.80325I
−8.46800 + 6.35526I −2.09227 − 5.05576I
u = −1.29885 + 0.57323I
a = −0.474359 − 0.451833I
b = −0.446176 + 0.991503I
−9.19963 − 8.42224I −2.59003 + 5.45173I
u = −1.29885 − 0.57323I
a = −0.474359 + 0.451833I
b = −0.446176 − 0.991503I
−9.19963 + 8.42224I −2.59003 − 5.45173I
u = −0.81774 + 1.19364I
a = −0.963505 − 0.230411I
b = 1.15324 + 1.04594I
1.31849 + 7.43334I 0. − 4.98321I
u = −0.81774 − 1.19364I
a = −0.963505 + 0.230411I
b = 1.15324 − 1.04594I
1.31849 − 7.43334I 0. + 4.98321I
u = −0.412206 + 0.290564I
a = 0.837857 − 0.179649I
b = −1.51919 − 0.91903I
−0.776391 + 0.135824I 2.3494 − 19.5336I
u = −0.412206 − 0.290564I
a = 0.837857 + 0.179649I
b = −1.51919 + 0.91903I
−0.776391 − 0.135824I 2.3494 + 19.5336I
u = 0.150066 + 0.471958I
a = −3.05515 + 2.48532I
b = 0.512237 + 0.339241I
4.79941 − 2.44365I 9.18422 − 5.36256I
u = 0.150066 − 0.471958I
a = −3.05515 − 2.48532I
b = 0.512237 − 0.339241I
4.79941 + 2.44365I 9.18422 + 5.36256I
u = −1.54778 + 0.70297I
a = 0.079788 + 0.241372I
b = 0.264751 − 0.005228I
−0.776391 − 0.135824I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.54778 − 0.70297I
a = 0.079788 − 0.241372I
b = 0.264751 + 0.005228I
−0.776391 + 0.135824I 0
u = 1.70730
a = −0.119622
b = 0.374632
0.602093 0
14
III. I
u
3
=
h−u
5
−2u
4
−3u
3
−u
2
+b−u−1, 2u
5
+3u
4
+4u
3
+a+u+1, u
6
+u
5
+2u
4
+2u
2
+1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
−2u
5
− 3u
4
− 4u
3
− u − 1
u
5
+ 2u
4
+ 3u
3
+ u
2
+ u + 1
a
12
=
−u
5
− u
4
− u
3
+ u
2
u
5
+ 2u
4
+ 3u
3
+ u
2
+ u + 1
a
9
=
u
5
+ u
4
+ 2u
3
+ u − 1
−u
3
− u
2
− u
a
1
=
−u
5
+ u
3
+ 4u
2
+ u + 1
2u
5
+ 3u
4
+ 4u
3
+ u
a
7
=
u
5
+ 2u
3
+ u
2
+ 6u − 1
u
4
+ u
3
− 2u
a
5
=
4u
5
+ u
3
− 10u
2
+ 3u − 7
−3u
5
− 2u
4
− 4u
3
+ 3u
2
− 3u + 3
a
10
=
−2u
5
− 3u
4
− 4u
3
− 2u − 1
u
5
+ 2u
4
+ 2u
3
+ u
2
+ u + 1
a
6
=
u
5
+ u
3
+ 4u
u
4
+ u
3
+ u
2
− u
a
2
=
−3u
5
− 3u
4
− 3u
3
+ 4u
2
+ 1
2u
5
+ 3u
4
+ 4u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
5
+ 10u
4
+ 16u
3
+ 8u
2
+ 9u + 9
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 4u
5
− 4u
4
+ 17u
3
+ 20u
2
+ 1
c
2
u
6
+ 4u
5
+ 6u
4
+ 7u
3
+ 8u
2
+ 4u + 1
c
3
, c
10
u
6
+ u
5
+ 2u
4
+ 2u
2
+ 1
c
4
, c
11
u
6
+ 2u
5
− 2u
4
− 6u
3
+ 3u
2
+ 16u + 11
c
5
u
6
− 4u
5
+ 6u
4
− 7u
3
+ 8u
2
− 4u + 1
c
6
, c
8
u
6
− 2u
5
+ 3u
4
− 2u
3
+ u
2
− u + 1
c
7
u
6
+ 5u
5
+ 18u
4
+ 38u
3
+ 59u
2
+ 55u + 31
c
9
, c
12
u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ u
2
+ u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
− 24y
5
+ 192y
4
− 447y
3
+ 392y
2
+ 40y + 1
c
2
, c
5
y
6
− 4y
5
− 4y
4
+ 17y
3
+ 20y
2
+ 1
c
3
, c
10
y
6
+ 3y
5
+ 8y
4
+ 10y
3
+ 8y
2
+ 4y + 1
c
4
, c
11
y
6
− 8y
5
+ 34y
4
− 90y
3
+ 157y
2
− 190y + 121
c
6
, c
8
, c
9
c
12
y
6
+ 2y
5
+ 3y
4
+ 3y
2
+ y + 1
c
7
y
6
+ 11y
5
+ 62y
4
+ 192y
3
+ 417y
2
+ 633y + 961
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.503078 + 0.706849I
a = 2.29094 + 0.59312I
b = −1.48973 + 0.77624I
−4.68092 − 6.37541I −2.75473 + 8.04371I
u = 0.503078 − 0.706849I
a = 2.29094 − 0.59312I
b = −1.48973 − 0.77624I
−4.68092 + 6.37541I −2.75473 − 8.04371I
u = −0.169825 + 0.786403I
a = −2.31049 − 0.38566I
b = 1.42906 + 0.05811I
3.85563 + 0.42199I 8.41818 + 2.54413I
u = −0.169825 − 0.786403I
a = −2.31049 + 0.38566I
b = 1.42906 − 0.05811I
3.85563 − 0.42199I 8.41818 − 2.54413I
u = −0.83325 + 1.16541I
a = −0.980450 − 0.218037I
b = 1.060680 + 0.883526I
2.47022 + 7.96446I 6.33654 − 7.96443I
u = −0.83325 − 1.16541I
a = −0.980450 + 0.218037I
b = 1.060680 − 0.883526I
2.47022 − 7.96446I 6.33654 + 7.96443I
18
IV. I
u
4
= hb, −u
2
+ a − 4u − 4, u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
u
2
+ 4u + 4
0
a
12
=
u
2
+ 4u + 4
0
a
9
=
−3u − 7
u
a
1
=
5u
2
+ 9u − 6
u
2
+ 3u + 1
a
7
=
−3u − 7
u
a
5
=
−11u
2
− 32u − 14
−u − 2
a
10
=
2u
2
+ 7u + 5
−u
2
− u
a
6
=
−2u
2
− 10u − 12
u
2
+ 2u
a
2
=
4u
2
+ 6u − 7
u
2
+ 3u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −32u
2
− 43u − 18
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
3
u
3
+ 3u
2
+ 2u + 1
c
4
u
3
+ 4u
2
+ 9u + 11
c
5
u
3
− u
2
+ 1
c
6
(u + 1)
3
c
7
, c
8
u
3
− 4u
2
+ 5u − 1
c
9
(u − 1)
3
c
11
u
3
c
12
u
3
+ 4u
2
+ 5u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
3
+ 3y
2
+ 2y −1
c
2
, c
5
y
3
− y
2
+ 2y −1
c
3
y
3
− 5y
2
− 2y −1
c
4
y
3
+ 2y
2
− 7y −121
c
6
, c
9
(y −1)
3
c
7
, c
8
, c
12
y
3
− 6y
2
+ 17y −1
c
11
y
3
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.337641 + 0.562280I
a = 2.44728 + 1.86942I
b = 0
4.66906 + 2.82812I 2.98758 − 12.02771I
u = −0.337641 − 0.562280I
a = 2.44728 − 1.86942I
b = 0
4.66906 − 2.82812I 2.98758 + 12.02771I
u = −2.32472
a = 0.105442
b = 0
0.531480 −90.9750
22
V. I
u
5
= h−u
2
+ b + 2u − 3, a − u + 1, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
u − 1
u
2
− 2u + 3
a
12
=
u
2
− u + 2
u
2
− 2u + 3
a
9
=
u
2
− u + 2
u
2
− u + 3
a
1
=
0
−u
a
7
=
−u
2
− u + 1
u
2
+ 3u − 2
a
5
=
1
u
2
a
10
=
u
2
+ u + 1
2u
2
− 3u + 4
a
6
=
u
u
2
− u + 1
a
2
=
u
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −53u
2
+ 32u − 92
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
u
3
c
5
u
3
− u
2
+ 1
c
6
, c
7
u
3
− 4u
2
+ 5u − 1
c
8
(u + 1)
3
c
9
u
3
+ 4u
2
+ 5u + 1
c
10
u
3
+ 3u
2
+ 2u + 1
c
11
u
3
+ 4u
2
+ 9u + 11
c
12
(u − 1)
3
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
3
+ 3y
2
+ 2y −1
c
2
, c
5
y
3
− y
2
+ 2y −1
c
4
y
3
c
6
, c
7
, c
9
y
3
− 6y
2
+ 17y −1
c
8
, c
12
(y −1)
3
c
10
y
3
− 5y
2
− 2y −1
c
11
y
3
+ 2y
2
− 7y −121
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.78492 + 1.30714I
b = 0.90748 − 2.05200I
4.66906 − 2.82812I 2.98758 + 12.02771I
u = 0.215080 − 1.307140I
a = −0.78492 − 1.30714I
b = 0.90748 + 2.05200I
4.66906 + 2.82812I 2.98758 − 12.02771I
u = 0.569840
a = −0.430160
b = 2.18504
0.531480 −90.9750
26
VI. I
u
6
= hb, −u
2
+ a + u − 2, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
u
2
− u + 2
0
a
12
=
u
2
− u + 2
0
a
9
=
u
2
− u + 2
u
a
1
=
0
−u
a
7
=
u
2
− u + 2
u
a
5
=
1
u
2
a
10
=
u
2
− 2u + 2
−u
2
+ 2u − 1
a
6
=
u
u
2
− u + 1
a
2
=
u
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7u
2
+ 5u − 5
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
10
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
, c
11
u
3
c
5
u
3
− u
2
+ 1
c
6
, c
7
, c
8
(u + 1)
3
c
9
, c
12
(u − 1)
3
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
10
y
3
+ 3y
2
+ 2y −1
c
2
, c
5
y
3
− y
2
+ 2y −1
c
4
, c
11
y
3
c
6
, c
7
, c
8
c
9
, c
12
(y −1)
3
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.122561 − 0.744862I
b = 0
4.66906 − 2.82812I 7.71191 + 2.59975I
u = 0.215080 − 1.307140I
a = 0.122561 + 0.744862I
b = 0
4.66906 + 2.82812I 7.71191 − 2.59975I
u = 0.569840
a = 1.75488
b = 0
0.531480 −4.42380
30
VII. I
u
7
= h−u
3
+ 2u
2
+ 2b − 2u + 3, a, u
4
− u
3
− 3u − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
0
1
2
u
3
− u
2
+ u −
3
2
a
12
=
1
2
u
3
− u
2
+ u −
3
2
1
2
u
3
− u
2
+ u −
3
2
a
9
=
1
2
u
3
− u −
3
2
1
2
u
3
−
3
2
a
1
=
1
2
u
3
− u −
3
2
−1
a
7
=
0
u
a
5
=
1
0
a
10
=
1
2
u
3
− u
2
+ u −
3
2
u
3
− u
2
− 2
a
6
=
−
1
2
u
3
+ u +
3
2
1
a
2
=
1
2
u
3
− u −
1
2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
3
+ 16u
2
+ 37
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
4
, c
10
c
11
u
4
− u
3
− 3u − 1
c
5
(u + 1)
4
c
6
, c
8
(u
2
− u − 1)
2
c
7
u
4
c
9
, c
12
(u
2
+ u − 1)
2
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
, c
10
c
11
y
4
− y
3
− 8y
2
− 9y + 1
c
6
, c
8
, c
9
c
12
(y
2
− 3y + 1)
2
c
7
y
4
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −0.309017 + 1.233910I
a = 0
b = 0.309017 + 1.233910I
7.23771 3.11146 + 0.I
u = −0.309017 − 1.233910I
a = 0
b = 0.309017 − 1.233910I
7.23771 3.11146 + 0.I
u = −0.319053
a = 0
b = −1.93709
−0.657974 38.8890
u = 1.93709
a = 0
b = 0.319053
−0.657974 38.8890
34
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
(u
3
− u
2
+ 2u − 1)
3
(u
6
− 4u
5
− 4u
4
+ 17u
3
+ 20u
2
+ 1)
· (u
19
+ 16u
18
+ ··· + 7856u + 256)(u
21
+ 25u
20
+ ··· + 84u + 1)
2
c
2
(u − 1)
4
(u
3
+ u
2
− 1)
3
(u
6
+ 4u
5
+ 6u
4
+ 7u
3
+ 8u
2
+ 4u + 1)
· (u
19
+ 10u
18
+ ··· + 12u − 16)(u
21
− 5u
20
+ ··· − 14u + 1)
2
c
3
, c
10
(u
3
− u
2
+ 2u − 1)
2
(u
3
+ 3u
2
+ 2u + 1)(u
4
− u
3
− 3u − 1)
· (u
6
+ u
5
+ 2u
4
+ 2u
2
+ 1)(u
19
+ 4u
17
+ ··· − 3u + 1)
· (u
42
+ 2u
41
+ ··· − u + 29)
c
4
, c
11
u
6
(u
3
+ 4u
2
+ 9u + 11)(u
4
− u
3
− 3u − 1)
· (u
6
+ 2u
5
+ ··· + 16u + 11)(u
19
+ 2u
18
+ ··· + 12u + 8)
· (u
42
+ 6u
41
+ ··· − 124u + 8)
c
5
(u + 1)
4
(u
3
− u
2
+ 1)
3
(u
6
− 4u
5
+ 6u
4
− 7u
3
+ 8u
2
− 4u + 1)
· (u
19
+ 10u
18
+ ··· + 12u − 16)(u
21
− 5u
20
+ ··· − 14u + 1)
2
c
6
, c
8
(u + 1)
6
(u
2
− u − 1)
2
(u
3
− 4u
2
+ 5u − 1)
· (u
6
− 2u
5
+ 3u
4
− 2u
3
+ u
2
− u + 1)(u
19
+ u
18
+ ··· + 3u + 1)
· (u
42
− 2u
41
+ ··· − 24u + 29)
c
7
u
4
(u + 1)
3
(u
3
− 4u
2
+ 5u − 1)
2
· (u
6
+ 5u
5
+ 18u
4
+ 38u
3
+ 59u
2
+ 55u + 31)
· (u
19
+ 13u
18
+ ··· − 48u − 4)(u
21
− 6u
20
+ ··· + 12u + 4)
2
c
9
, c
12
(u − 1)
6
(u
2
+ u − 1)
2
(u
3
+ 4u
2
+ 5u + 1)
· (u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ u
2
+ u + 1)(u
19
+ u
18
+ ··· + 3u + 1)
· (u
42
− 2u
41
+ ··· − 24u + 29)
35
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
4
(y
3
+ 3y
2
+ 2y −1)
3
· (y
6
− 24y
5
+ 192y
4
− 447y
3
+ 392y
2
+ 40y + 1)
· (y
19
− 48y
18
+ ··· + 38868736y −65536)
· (y
21
− 53y
20
+ ··· − 180y −1)
2
c
2
, c
5
(y −1)
4
(y
3
− y
2
+ 2y −1)
3
(y
6
− 4y
5
− 4y
4
+ 17y
3
+ 20y
2
+ 1)
· (y
19
− 16y
18
+ ··· + 7856y −256)(y
21
− 25y
20
+ ··· + 84y −1)
2
c
3
, c
10
(y
3
− 5y
2
− 2y −1)(y
3
+ 3y
2
+ 2y −1)
2
(y
4
− y
3
− 8y
2
− 9y + 1)
· (y
6
+ 3y
5
+ ··· + 4y + 1)(y
19
+ 8y
18
+ ··· + 5y −1)
· (y
42
+ 4y
41
+ ··· + 10439y + 841)
c
4
, c
11
y
6
(y
3
+ 2y
2
− 7y −121)(y
4
− y
3
− 8y
2
− 9y + 1)
· (y
6
− 8y
5
+ 34y
4
− 90y
3
+ 157y
2
− 190y + 121)
· (y
19
− 2y
18
+ ··· + 592y −64)(y
42
+ 16y
41
+ ··· − 1424y + 64)
c
6
, c
8
, c
9
c
12
(y −1)
6
(y
2
− 3y + 1)
2
(y
3
− 6y
2
+ 17y −1)
· (y
6
+ 2y
5
+ 3y
4
+ 3y
2
+ y + 1)(y
19
+ y
18
+ ··· + 21y −1)
· (y
42
− 8y
41
+ ··· − 2722y + 841)
c
7
y
4
(y −1)
3
(y
3
− 6y
2
+ 17y −1)
2
· (y
6
+ 11y
5
+ 62y
4
+ 192y
3
+ 417y
2
+ 633y + 961)
· (y
19
+ 5y
18
+ ··· + 328y −16)(y
21
− 12y
20
+ ··· + 504y −16)
2
36
