11a
135
(K11a
135
)
A knot diagram
1
Linearized knot diagam
6 1 11 10 2 5 4 3 7 8 9
Solving Sequence
1,6
2 3 5
7,9
8 11 4 10
c
1
c
2
c
5
c
6
c
8
c
11
c
3
c
10
c
4
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1271u
35
+ 7400u
34
+ ··· + 559b + 6593, 1511u
35
− 17846u
34
+ ··· + 2236a − 43197,
u
36
− 6u
35
+ ··· + u + 4i
I
u
2
= h−u
26
a + 317u
26
+ ··· + a + 1171, 4u
26
a − 3u
26
+ ··· − 6a + 9, u
27
+ 2u
26
+ ··· − 4u
2
− 1i
I
u
3
= h−2u
9
+ u
8
− 3u
7
+ u
6
− 6u
5
+ 4u
4
− 8u
3
+ 5u
2
+ b − 4u + 1, u
8
+ u
7
+ u
4
+ u
3
− u
2
+ a − 3,
u
10
− u
9
+ 2u
8
− u
7
+ 4u
6
− 3u
5
+ 6u
4
− 4u
3
+ 5u
2
− u + 1i
I
u
4
= hb + 1, a
2
− 2au − a − u − 2, u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 104 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
= h−1271u
35
+ 7400u
34
+ · · · + 559b + 6593, 1511u
35
− 17846u
34
+
· · · + 2236a − 43197, u
36
− 6u
35
+ · · · + u + 4i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
5
=
−u
u
3
+ u
a
7
=
−u
3
u
5
+ u
3
+ u
a
9
=
−0.675760u
35
+ 7.98122u
34
+ ··· + 27.4079u + 19.3189
2.27370u
35
− 13.2379u
34
+ ··· − 13.8336u − 11.7943
a
8
=
−5.13551u
35
+ 22.9168u
34
+ ··· − 13.4794u + 0.555009
11.4633u
35
− 59.1413u
34
+ ··· + 2.49732u − 22.1485
a
11
=
2.05322u
35
− 7.18515u
34
+ ··· + 17.4490u + 7.42889
−0.159213u
35
+ 0.654741u
34
+ ··· − 7.64580u − 1.40072
a
4
=
−4.34571u
35
+ 24.2531u
34
+ ··· + 1.93202u + 12.1552
1.29875u
35
− 5.67800u
34
+ ··· + 5.43649u + 1.81932
a
10
=
5.53712u
35
− 21.7594u
34
+ ··· + 26.2039u + 8.03444
−7.89624u
35
+ 42.0340u
34
+ ··· + 5.69052u + 20.5420
a
10
=
5.53712u
35
− 21.7594u
34
+ ··· + 26.2039u + 8.03444
−7.89624u
35
+ 42.0340u
34
+ ··· + 5.69052u + 20.5420
(ii) Obstruction class = −1
(iii) Cusp Shapes =
4133
559
u
35
−
18240
559
u
34
+ ··· +
10119
559
u −
3554
559
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
36
− 6u
35
+ ··· + u + 4
c
2
, c
6
u
36
+ 10u
35
+ ··· + 31u + 16
c
3
, c
7
u
36
+ 2u
35
+ ··· + 2u + 1
c
4
, c
8
u
36
+ 6u
34
+ ··· − 5u + 2
c
9
, c
11
u
36
+ 6u
35
+ ··· + 4u + 1
c
10
u
36
+ 19u
35
+ ··· + u + 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
36
+ 10y
35
+ ··· + 31y + 16
c
2
, c
6
y
36
+ 34y
35
+ ··· − 6849y + 256
c
3
, c
7
y
36
+ 24y
35
+ ··· + 44y + 1
c
4
, c
8
y
36
+ 12y
35
+ ··· + 27y + 4
c
9
, c
11
y
36
− 8y
35
+ ··· + 28y + 1
c
10
y
36
− y
35
+ ··· + 67y + 4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.276741 + 0.944175I
a = −1.25934 + 0.87235I
b = −1.18704 − 0.84945I
−3.77194 − 4.33449I −10.34773 + 8.70742I
u = −0.276741 − 0.944175I
a = −1.25934 − 0.87235I
b = −1.18704 + 0.84945I
−3.77194 + 4.33449I −10.34773 − 8.70742I
u = −0.304491 + 0.889790I
a = −0.062800 + 1.255710I
b = −1.142480 + 0.222558I
−3.69796 − 0.78585I −10.32257 + 1.08257I
u = −0.304491 − 0.889790I
a = −0.062800 − 1.255710I
b = −1.142480 − 0.222558I
−3.69796 + 0.78585I −10.32257 − 1.08257I
u = 0.700901 + 0.854931I
a = 0.21075 − 1.52850I
b = −0.322329 + 0.571982I
0.84484 + 3.07899I −2.36753 − 4.61435I
u = 0.700901 − 0.854931I
a = 0.21075 + 1.52850I
b = −0.322329 − 0.571982I
0.84484 − 3.07899I −2.36753 + 4.61435I
u = 0.670636 + 0.904481I
a = 0.853772 + 0.895928I
b = −0.023486 − 0.449791I
0.69868 + 2.21160I −2.61972 − 2.06632I
u = 0.670636 − 0.904481I
a = 0.853772 − 0.895928I
b = −0.023486 + 0.449791I
0.69868 − 2.21160I −2.61972 + 2.06632I
u = −0.848515 + 0.073137I
a = −0.708084 + 0.620130I
b = 0.741423 − 0.831359I
1.04891 + 7.93873I 2.26099 − 7.53856I
u = −0.848515 − 0.073137I
a = −0.708084 − 0.620130I
b = 0.741423 + 0.831359I
1.04891 − 7.93873I 2.26099 + 7.53856I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.335316 + 1.103160I
a = 0.986796 − 0.482008I
b = 1.076210 + 0.827984I
−2.43737 − 11.97940I −3.58846 + 9.69532I
u = −0.335316 − 1.103160I
a = 0.986796 + 0.482008I
b = 1.076210 − 0.827984I
−2.43737 + 11.97940I −3.58846 − 9.69532I
u = −0.754047 + 0.880053I
a = 0.256067 + 0.953865I
b = −1.57066 + 0.07535I
1.51994 − 2.85709I −2.33106 + 2.86602I
u = −0.754047 − 0.880053I
a = 0.256067 − 0.953865I
b = −1.57066 − 0.07535I
1.51994 + 2.85709I −2.33106 − 2.86602I
u = 0.836947 + 0.813811I
a = 1.45743 + 1.45510I
b = −0.90494 − 1.42986I
3.28088 − 2.39771I −4.49853 + 2.73594I
u = 0.836947 − 0.813811I
a = 1.45743 − 1.45510I
b = −0.90494 + 1.42986I
3.28088 + 2.39771I −4.49853 − 2.73594I
u = −0.185132 + 1.158740I
a = 0.116551 − 0.668626I
b = 0.655109 − 0.395481I
−3.33480 + 4.43993I −6.66340 − 7.47745I
u = −0.185132 − 1.158740I
a = 0.116551 + 0.668626I
b = 0.655109 + 0.395481I
−3.33480 − 4.43993I −6.66340 + 7.47745I
u = 0.911501 + 0.758905I
a = −1.10120 − 1.05489I
b = 1.12689 + 1.25578I
5.92417 − 11.34300I 2.20430 + 5.55458I
u = 0.911501 − 0.758905I
a = −1.10120 + 1.05489I
b = 1.12689 − 1.25578I
5.92417 + 11.34300I 2.20430 − 5.55458I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.824017 + 0.898169I
a = −0.177149 − 0.497820I
b = 0.921405 − 0.086126I
6.48061 − 3.07379I 6.45709 + 2.41299I
u = −0.824017 − 0.898169I
a = −0.177149 + 0.497820I
b = 0.921405 + 0.086126I
6.48061 + 3.07379I 6.45709 − 2.41299I
u = 0.021281 + 0.766965I
a = −1.40357 + 1.58774I
b = −1.045680 − 0.299865I
−2.80406 + 0.04358I −9.18489 + 0.34635I
u = 0.021281 − 0.766965I
a = −1.40357 − 1.58774I
b = −1.045680 + 0.299865I
−2.80406 − 0.04358I −9.18489 − 0.34635I
u = 0.789000 + 0.963507I
a = −0.51131 − 2.47418I
b = −1.06736 + 1.45192I
2.81727 + 8.47181I −5.83967 − 8.29612I
u = 0.789000 − 0.963507I
a = −0.51131 + 2.47418I
b = −1.06736 − 1.45192I
2.81727 − 8.47181I −5.83967 + 8.29612I
u = 0.374008 + 0.626804I
a = 0.891587 − 0.075576I
b = 0.070132 + 0.290278I
0.10177 + 1.47413I 1.25501 − 4.83821I
u = 0.374008 − 0.626804I
a = 0.891587 + 0.075576I
b = 0.070132 − 0.290278I
0.10177 − 1.47413I 1.25501 + 4.83821I
u = 1.028740 + 0.773325I
a = 0.187909 + 0.308356I
b = −0.190982 − 0.521409I
4.99883 + 3.21347I 19.6525 + 3.8446I
u = 1.028740 − 0.773325I
a = 0.187909 − 0.308356I
b = −0.190982 + 0.521409I
4.99883 − 3.21347I 19.6525 − 3.8446I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.798120 + 1.025270I
a = 0.57651 + 2.10645I
b = 1.23838 − 1.24673I
5.0855 + 17.6564I 0.86604 − 10.01914I
u = 0.798120 − 1.025270I
a = 0.57651 − 2.10645I
b = 1.23838 + 1.24673I
5.0855 − 17.6564I 0.86604 + 10.01914I
u = 0.880565 + 1.020470I
a = 0.032721 − 0.717303I
b = −0.616024 + 0.418194I
4.23977 + 3.68667I 0. − 11.71183I
u = 0.880565 − 1.020470I
a = 0.032721 + 0.717303I
b = −0.616024 − 0.418194I
4.23977 − 3.68667I 0. + 11.71183I
u = −0.483436 + 0.080826I
a = 1.52835 − 0.78222I
b = −0.758556 + 0.609588I
−1.25585 + 1.57291I −2.37601 − 4.05394I
u = −0.483436 − 0.080826I
a = 1.52835 + 0.78222I
b = −0.758556 − 0.609588I
−1.25585 − 1.57291I −2.37601 + 4.05394I
8
II. I
u
2
= h−u
26
a + 317u
26
+ · · · + a + 1171, 4u
26
a − 3u
26
+ · · · − 6a +
9, u
27
+ 2u
26
+ · · · − 4u
2
− 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
5
=
−u
u
3
+ u
a
7
=
−u
3
u
5
+ u
3
+ u
a
9
=
a
0.00201613au
26
− 0.639113u
26
+ ··· − 0.00201613a − 2.36089
a
8
=
0.00806452au
26
− 1.55645u
26
+ ··· + 0.991935a + 0.556452
−0.00201613au
26
− 0.360887u
26
+ ··· + 0.00201613a − 3.63911
a
11
=
0.360887au
26
+ 2.59879u
26
+ ··· + 0.639113a + 0.401210
0.917339au
26
− 0.796371u
26
+ ··· − 0.917339a + 3.79637
a
4
=
1.08266au
26
− 3.20363u
26
+ ··· − 0.0826613a + 2.20363
−0.0524194au
26
− 0.383065u
26
+ ··· + 1.05242a + 1.38306
a
10
=
−0.00201613au
26
− 0.360887u
26
+ ··· + 1.00202a + 0.360887
0.00806452au
26
+ 0.443548u
26
+ ··· − 0.00806452a − 3.44355
a
10
=
−0.00201613au
26
− 0.360887u
26
+ ··· + 1.00202a + 0.360887
0.00806452au
26
+ 0.443548u
26
+ ··· − 0.00806452a − 3.44355
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 3u
26
+ 5u
24
−u
23
+ 18u
22
−8u
21
+ 17u
20
−8u
19
+ 27u
18
−30u
17
+ 9u
16
+ 2u
15
−8u
14
−
4u
13
−14u
12
+64u
11
−52u
10
+70u
9
−24u
8
+71u
7
−52u
6
+46u
5
−25u
4
+2u
3
−11u
2
+2u+3
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
27
+ 2u
26
+ ··· − 4u
2
− 1)
2
c
2
, c
6
(u
27
+ 8u
26
+ ··· − 8u − 1)
2
c
3
, c
7
u
54
+ 4u
53
+ ··· + 9u + 2
c
4
, c
8
u
54
+ 2u
53
+ ··· − 1697u + 407
c
9
, c
11
u
54
− 5u
53
+ ··· − 529u + 44
c
10
(u
27
− 13u
26
+ ··· − 10u + 4)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
27
+ 8y
26
+ ··· − 8y −1)
2
c
2
, c
6
(y
27
+ 24y
26
+ ··· − 12y −1)
2
c
3
, c
7
y
54
− 8y
53
+ ··· + 87y + 4
c
4
, c
8
y
54
+ 12y
53
+ ··· + 4226411y + 165649
c
9
, c
11
y
54
+ 23y
53
+ ··· + 25783y + 1936
c
10
(y
27
− 5y
26
+ ··· + 236y −16)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.144711 + 0.987236I
a = −1.044320 + 0.252570I
b = −1.10548 + 0.93118I
−3.43692 + 4.10370I −10.33067 − 7.76154I
u = 0.144711 + 0.987236I
a = 1.17591 + 1.35422I
b = 0.694713 − 0.161571I
−3.43692 + 4.10370I −10.33067 − 7.76154I
u = 0.144711 − 0.987236I
a = −1.044320 − 0.252570I
b = −1.10548 − 0.93118I
−3.43692 − 4.10370I −10.33067 + 7.76154I
u = 0.144711 − 0.987236I
a = 1.17591 − 1.35422I
b = 0.694713 + 0.161571I
−3.43692 − 4.10370I −10.33067 + 7.76154I
u = 0.504183 + 0.966350I
a = 0.867903 + 0.476539I
b = 0.929423 + 0.017439I
−1.43447 + 1.57559I −0.45968 + 6.99556I
u = 0.504183 + 0.966350I
a = 0.992670 − 0.899903I
b = −0.809221 − 0.348625I
−1.43447 + 1.57559I −0.45968 + 6.99556I
u = 0.504183 − 0.966350I
a = 0.867903 − 0.476539I
b = 0.929423 − 0.017439I
−1.43447 − 1.57559I −0.45968 − 6.99556I
u = 0.504183 − 0.966350I
a = 0.992670 + 0.899903I
b = −0.809221 + 0.348625I
−1.43447 − 1.57559I −0.45968 − 6.99556I
u = −0.770533 + 0.784290I
a = −0.44956 + 1.58387I
b = 0.151642 − 0.255883I
2.45928 + 3.09185I −2.04409 − 4.31047I
u = −0.770533 + 0.784290I
a = 1.53553 − 1.36774I
b = −1.00807 + 1.68610I
2.45928 + 3.09185I −2.04409 − 4.31047I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.770533 − 0.784290I
a = −0.44956 − 1.58387I
b = 0.151642 + 0.255883I
2.45928 − 3.09185I −2.04409 + 4.31047I
u = −0.770533 − 0.784290I
a = 1.53553 + 1.36774I
b = −1.00807 − 1.68610I
2.45928 − 3.09185I −2.04409 + 4.31047I
u = 0.291946 + 1.107070I
a = 0.931124 + 0.230119I
b = 0.646966 − 0.516614I
−0.60671 + 3.68820I 4.86231 − 6.92207I
u = 0.291946 + 1.107070I
a = −0.323787 + 0.014224I
b = −0.311394 + 0.647844I
−0.60671 + 3.68820I 4.86231 − 6.92207I
u = 0.291946 − 1.107070I
a = 0.931124 − 0.230119I
b = 0.646966 + 0.516614I
−0.60671 − 3.68820I 4.86231 + 6.92207I
u = 0.291946 − 1.107070I
a = −0.323787 − 0.014224I
b = −0.311394 − 0.647844I
−0.60671 − 3.68820I 4.86231 + 6.92207I
u = −0.898179 + 0.746104I
a = −0.594838 + 0.861512I
b = 0.874324 − 0.984284I
7.41344 + 3.23384I 5.98510 − 2.95350I
u = −0.898179 + 0.746104I
a = 0.595344 − 1.207400I
b = −0.349108 + 1.259600I
7.41344 + 3.23384I 5.98510 − 2.95350I
u = −0.898179 − 0.746104I
a = −0.594838 − 0.861512I
b = 0.874324 + 0.984284I
7.41344 − 3.23384I 5.98510 + 2.95350I
u = −0.898179 − 0.746104I
a = 0.595344 + 1.207400I
b = −0.349108 − 1.259600I
7.41344 − 3.23384I 5.98510 + 2.95350I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.799598 + 0.863452I
a = 0.472052 + 1.331300I
b = −0.753138 − 1.063980I
5.90777 − 1.53174I 5.51904 + 2.02847I
u = 0.799598 + 0.863452I
a = 0.53604 + 2.57871I
b = 1.21139 − 1.71770I
5.90777 − 1.53174I 5.51904 + 2.02847I
u = 0.799598 − 0.863452I
a = 0.472052 − 1.331300I
b = −0.753138 + 1.063980I
5.90777 + 1.53174I 5.51904 − 2.02847I
u = 0.799598 − 0.863452I
a = 0.53604 − 2.57871I
b = 1.21139 + 1.71770I
5.90777 + 1.53174I 5.51904 − 2.02847I
u = 0.802525
a = 0.064178 + 0.713542I
b = 0.219481 − 0.777240I
3.09479 9.01780
u = 0.802525
a = 0.064178 − 0.713542I
b = 0.219481 + 0.777240I
3.09479 9.01780
u = 0.785462 + 0.911233I
a = −1.79873 − 1.10105I
b = 1.09759 + 1.87961I
5.75923 + 7.48234I 4.88411 − 7.87589I
u = 0.785462 + 0.911233I
a = −1.04193 − 2.09558I
b = −0.810627 + 0.965025I
5.75923 + 7.48234I 4.88411 − 7.87589I
u = 0.785462 − 0.911233I
a = −1.79873 + 1.10105I
b = 1.09759 − 1.87961I
5.75923 − 7.48234I 4.88411 + 7.87589I
u = 0.785462 − 0.911233I
a = −1.04193 + 2.09558I
b = −0.810627 − 0.965025I
5.75923 − 7.48234I 4.88411 + 7.87589I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.740227 + 0.958313I
a = 0.17325 − 1.77767I
b = 0.279114 + 0.386141I
1.92805 − 8.81809I −3.51760 + 9.35403I
u = −0.740227 + 0.958313I
a = −0.83078 + 2.42491I
b = −1.23050 − 1.60076I
1.92805 − 8.81809I −3.51760 + 9.35403I
u = −0.740227 − 0.958313I
a = 0.17325 + 1.77767I
b = 0.279114 − 0.386141I
1.92805 + 8.81809I −3.51760 − 9.35403I
u = −0.740227 − 0.958313I
a = −0.83078 − 2.42491I
b = −1.23050 + 1.60076I
1.92805 + 8.81809I −3.51760 − 9.35403I
u = −0.818350 + 0.893459I
a = 0.013291 − 1.076530I
b = 1.005790 + 0.379819I
6.46144 − 3.05379I 5.97423 + 2.71426I
u = −0.818350 + 0.893459I
a = −0.350459 + 0.093702I
b = 0.789809 − 0.525186I
6.46144 − 3.05379I 5.97423 + 2.71426I
u = −0.818350 − 0.893459I
a = 0.013291 + 1.076530I
b = 1.005790 − 0.379819I
6.46144 + 3.05379I 5.97423 − 2.71426I
u = −0.818350 − 0.893459I
a = −0.350459 − 0.093702I
b = 0.789809 + 0.525186I
6.46144 + 3.05379I 5.97423 − 2.71426I
u = −0.194164 + 0.737666I
a = −0.1051250 − 0.0794208I
b = 0.24714 − 1.64517I
0.15408 − 4.76928I −1.41513 + 11.31767I
u = −0.194164 + 0.737666I
a = −3.27600 − 0.27489I
b = −0.393595 − 0.629207I
0.15408 − 4.76928I −1.41513 + 11.31767I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.194164 − 0.737666I
a = −0.1051250 + 0.0794208I
b = 0.24714 + 1.64517I
0.15408 + 4.76928I −1.41513 − 11.31767I
u = −0.194164 − 0.737666I
a = −3.27600 + 0.27489I
b = −0.393595 + 0.629207I
0.15408 + 4.76928I −1.41513 − 11.31767I
u = −0.786810 + 1.024740I
a = −0.87495 + 1.40397I
b = −0.499560 − 1.264320I
6.54280 − 9.46925I 4.33045 + 8.20563I
u = −0.786810 + 1.024740I
a = 0.67436 − 1.65262I
b = 0.990241 + 0.929170I
6.54280 − 9.46925I 4.33045 + 8.20563I
u = −0.786810 − 1.024740I
a = −0.87495 − 1.40397I
b = −0.499560 + 1.264320I
6.54280 + 9.46925I 4.33045 − 8.20563I
u = −0.786810 − 1.024740I
a = 0.67436 + 1.65262I
b = 0.990241 − 0.929170I
6.54280 + 9.46925I 4.33045 − 8.20563I
u = 0.522984 + 0.315101I
a = 0.220722 + 1.030080I
b = 0.852048 + 0.137605I
0.23096 + 2.37565I 1.69627 − 5.05605I
u = 0.522984 + 0.315101I
a = 1.14627 − 0.90462I
b = −0.541670 + 0.765569I
0.23096 + 2.37565I 1.69627 − 5.05605I
u = 0.522984 − 0.315101I
a = 0.220722 − 1.030080I
b = 0.852048 − 0.137605I
0.23096 − 2.37565I 1.69627 + 5.05605I
u = 0.522984 − 0.315101I
a = 1.14627 + 0.90462I
b = −0.541670 − 0.765569I
0.23096 − 2.37565I 1.69627 + 5.05605I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.241884 + 0.503654I
a = 0.93986 − 1.89203I
b = −0.363999 + 1.059620I
0.79481 + 2.83207I 2.50674 + 1.28047I
u = −0.241884 + 0.503654I
a = 2.35199 + 0.56436I
b = 0.686698 + 0.816102I
0.79481 + 2.83207I 2.50674 + 1.28047I
u = −0.241884 − 0.503654I
a = 0.93986 + 1.89203I
b = −0.363999 − 1.059620I
0.79481 − 2.83207I 2.50674 − 1.28047I
u = −0.241884 − 0.503654I
a = 2.35199 − 0.56436I
b = 0.686698 − 0.816102I
0.79481 − 2.83207I 2.50674 − 1.28047I
17
III.
I
u
3
= h−2u
9
+u
8
+· · ·+b+1, u
8
+u
7
+u
4
+u
3
−u
2
+a−3, u
10
−u
9
+· · ·−u+1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
5
=
−u
u
3
+ u
a
7
=
−u
3
u
5
+ u
3
+ u
a
9
=
−u
8
− u
7
− u
4
− u
3
+ u
2
+ 3
2u
9
− u
8
+ 3u
7
− u
6
+ 6u
5
− 4u
4
+ 8u
3
− 5u
2
+ 4u − 1
a
8
=
u
9
− u
8
+ u
7
+ 3u
5
− 2u
4
+ 3u
3
− u
2
+ 2u + 2
u
9
− u
8
+ 2u
7
− u
6
+ 4u
5
− 3u
4
+ 6u
3
− 4u
2
+ 4u − 1
a
11
=
−2u
9
+ 2u
8
− 4u
7
+ 2u
6
− 7u
5
+ 7u
4
− 10u
3
+ 9u
2
− 8u + 3
u
9
+ u
7
+ 2u
5
− u
4
+ 2u
3
− u
2
+ 1
a
4
=
u
9
− 2u
8
+ 2u
7
− 3u
6
+ 3u
5
− 7u
4
+ 6u
3
− 9u
2
+ 4u − 4
−u
9
+ u
8
− u
7
+ u
6
− 3u
5
+ 3u
4
− 3u
3
+ 3u
2
− 2u
a
10
=
u
9
+ u
7
+ u
6
+ 3u
5
+ u
4
+ 3u
3
+ 2u
2
+ u + 3
−u
8
+ u
7
− u
6
+ u
5
− 3u
4
+ 3u
3
− 3u
2
+ 3u − 1
a
10
=
u
9
+ u
7
+ u
6
+ 3u
5
+ u
4
+ 3u
3
+ 2u
2
+ u + 3
−u
8
+ u
7
− u
6
+ u
5
− 3u
4
+ 3u
3
− 3u
2
+ 3u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −10u
9
+ 6u
8
−18u
7
+ 6u
6
−31u
5
+ 20u
4
−46u
3
+ 26u
2
−23u + 4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
− u
9
+ 2u
8
− u
7
+ 4u
6
− 3u
5
+ 6u
4
− 4u
3
+ 5u
2
− u + 1
c
2
, c
6
u
10
+ 3u
9
+ ··· + 9u + 1
c
3
, c
7
u
10
+ u
8
+ 2u
7
− u
5
+ 3u
4
+ u
3
− u
2
+ 1
c
4
, c
8
u
10
− u
8
+ u
7
+ 3u
6
− u
5
+ 2u
3
+ u
2
+ 1
c
5
u
10
+ u
9
+ 2u
8
+ u
7
+ 4u
6
+ 3u
5
+ 6u
4
+ 4u
3
+ 5u
2
+ u + 1
c
9
, c
11
u
10
+ 2u
9
+ 7u
8
+ 7u
7
+ 13u
6
+ 5u
5
+ 8u
4
− 2u
3
+ u
2
− 2u + 1
c
10
u
10
− 8u
9
+ ··· − 94u + 21
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
10
+ 3y
9
+ ··· + 9y + 1
c
2
, c
6
y
10
+ 11y
9
+ ··· − 23y + 1
c
3
, c
7
y
10
+ 2y
9
+ y
8
+ 2y
7
+ 8y
6
− 5y
5
+ 13y
4
− 7y
3
+ 7y
2
− 2y + 1
c
4
, c
8
y
10
− 2y
9
+ 7y
8
− 7y
7
+ 13y
6
− 5y
5
+ 8y
4
+ 2y
3
+ y
2
+ 2y + 1
c
9
, c
11
y
10
+ 10y
9
+ ··· − 2y + 1
c
10
y
10
+ 4y
9
+ ··· + 488y + 441
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.127642 + 1.018330I
a = −0.976414 − 0.047787I
b = −0.463656 − 0.708869I
−1.78029 − 4.07054I −3.97032 + 7.89370I
u = −0.127642 − 1.018330I
a = −0.976414 + 0.047787I
b = −0.463656 + 0.708869I
−1.78029 + 4.07054I −3.97032 − 7.89370I
u = 0.802978 + 0.812239I
a = 1.00162 + 1.89487I
b = −0.43569 − 1.47399I
4.26091 − 2.70997I 3.89717 + 4.51185I
u = 0.802978 − 0.812239I
a = 1.00162 − 1.89487I
b = −0.43569 + 1.47399I
4.26091 + 2.70997I 3.89717 − 4.51185I
u = 0.766035 + 0.955271I
a = −1.00445 − 2.19705I
b = −0.61139 + 1.42806I
3.81810 + 8.61429I 2.88207 − 9.27981I
u = 0.766035 − 0.955271I
a = −1.00445 + 2.19705I
b = −0.61139 − 1.42806I
3.81810 − 8.61429I 2.88207 + 9.27981I
u = −0.959043 + 0.878682I
a = −0.164415 − 0.151502I
b = 0.403043 − 0.198949I
4.80462 − 3.47437I 3.99287 + 12.44497I
u = −0.959043 − 0.878682I
a = −0.164415 + 0.151502I
b = 0.403043 + 0.198949I
4.80462 + 3.47437I 3.99287 − 12.44497I
u = 0.017671 + 0.535344I
a = 2.64366 + 0.19676I
b = 0.107691 + 1.094780I
0.41119 + 3.68242I −1.80179 − 6.14716I
u = 0.017671 − 0.535344I
a = 2.64366 − 0.19676I
b = 0.107691 − 1.094780I
0.41119 − 3.68242I −1.80179 + 6.14716I
21
IV. I
u
4
= hb + 1, a
2
− 2au − a − u − 2, u
2
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u + 1
a
3
=
−u
u + 1
a
5
=
−u
u + 1
a
7
=
−1
0
a
9
=
a
−1
a
8
=
u + 1
−au − 2
a
11
=
a + 1
−1
a
4
=
2au + a + u + 2
−au − a + u
a
10
=
a + 1
−1
a
10
=
a + 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 9u − 3
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
(u
2
+ u + 1)
2
c
3
, c
4
, c
7
c
8
u
4
+ u
3
+ 3u
2
+ u + 1
c
5
(u
2
− u + 1)
2
c
9
, c
11
(u + 1)
4
c
10
u
4
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
(y
2
+ y + 1)
2
c
3
, c
4
, c
7
c
8
y
4
+ 5y
3
+ 9y
2
+ 5y + 1
c
9
, c
11
(y −1)
4
c
10
y
4
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.973561 + 0.421254I
b = −1.00000
−1.64493 − 2.02988I −7.50000 + 7.79423I
u = −0.500000 + 0.866025I
a = 0.97356 + 1.31080I
b = −1.00000
−1.64493 − 2.02988I −7.50000 + 7.79423I
u = −0.500000 − 0.866025I
a = −0.973561 − 0.421254I
b = −1.00000
−1.64493 + 2.02988I −7.50000 − 7.79423I
u = −0.500000 − 0.866025I
a = 0.97356 − 1.31080I
b = −1.00000
−1.64493 + 2.02988I −7.50000 − 7.79423I
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
2
)(u
10
− u
9
+ ··· − u + 1)
· ((u
27
+ 2u
26
+ ··· − 4u
2
− 1)
2
)(u
36
− 6u
35
+ ··· + u + 4)
c
2
, c
6
((u
2
+ u + 1)
2
)(u
10
+ 3u
9
+ ··· + 9u + 1)(u
27
+ 8u
26
+ ··· − 8u − 1)
2
· (u
36
+ 10u
35
+ ··· + 31u + 16)
c
3
, c
7
(u
4
+ u
3
+ 3u
2
+ u + 1)(u
10
+ u
8
+ 2u
7
− u
5
+ 3u
4
+ u
3
− u
2
+ 1)
· (u
36
+ 2u
35
+ ··· + 2u + 1)(u
54
+ 4u
53
+ ··· + 9u + 2)
c
4
, c
8
(u
4
+ u
3
+ 3u
2
+ u + 1)(u
10
− u
8
+ u
7
+ 3u
6
− u
5
+ 2u
3
+ u
2
+ 1)
· (u
36
+ 6u
34
+ ··· − 5u + 2)(u
54
+ 2u
53
+ ··· − 1697u + 407)
c
5
((u
2
− u + 1)
2
)(u
10
+ u
9
+ ··· + u + 1)
· ((u
27
+ 2u
26
+ ··· − 4u
2
− 1)
2
)(u
36
− 6u
35
+ ··· + u + 4)
c
9
, c
11
((u + 1)
4
)(u
10
+ 2u
9
+ ··· − 2u + 1)
· (u
36
+ 6u
35
+ ··· + 4u + 1)(u
54
− 5u
53
+ ··· − 529u + 44)
c
10
u
4
(u
10
− 8u
9
+ ··· − 94u + 21)(u
27
− 13u
26
+ ··· − 10u + 4)
2
· (u
36
+ 19u
35
+ ··· + u + 2)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
2
+ y + 1)
2
)(y
10
+ 3y
9
+ ··· + 9y + 1)(y
27
+ 8y
26
+ ··· − 8y −1)
2
· (y
36
+ 10y
35
+ ··· + 31y + 16)
c
2
, c
6
((y
2
+ y + 1)
2
)(y
10
+ 11y
9
+ ··· − 23y + 1)
· ((y
27
+ 24y
26
+ ··· − 12y −1)
2
)(y
36
+ 34y
35
+ ··· − 6849y + 256)
c
3
, c
7
(y
4
+ 5y
3
+ 9y
2
+ 5y + 1)
· (y
10
+ 2y
9
+ y
8
+ 2y
7
+ 8y
6
− 5y
5
+ 13y
4
− 7y
3
+ 7y
2
− 2y + 1)
· (y
36
+ 24y
35
+ ··· + 44y + 1)(y
54
− 8y
53
+ ··· + 87y + 4)
c
4
, c
8
(y
4
+ 5y
3
+ 9y
2
+ 5y + 1)
· (y
10
− 2y
9
+ 7y
8
− 7y
7
+ 13y
6
− 5y
5
+ 8y
4
+ 2y
3
+ y
2
+ 2y + 1)
· (y
36
+ 12y
35
+ ··· + 27y + 4)
· (y
54
+ 12y
53
+ ··· + 4226411y + 165649)
c
9
, c
11
((y −1)
4
)(y
10
+ 10y
9
+ ··· − 2y + 1)(y
36
− 8y
35
+ ··· + 28y + 1)
· (y
54
+ 23y
53
+ ··· + 25783y + 1936)
c
10
y
4
(y
10
+ 4y
9
+ ··· + 488y + 441)(y
27
− 5y
26
+ ··· + 236y −16)
2
· (y
36
− y
35
+ ··· + 67y + 4)
27
