12n
0525
(K12n
0525
)
A knot diagram
1
Linearized knot diagam
3 5 9 7 2 11 1 4 3 12 6 4
Solving Sequence
3,9
4
5,10
2 6 1 8 7 12 11
c
3
c
9
c
2
c
5
c
1
c
8
c
7
c
12
c
11
c
4
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h730697u
21
+ 8724191u
20
+ ··· + 1495432b + 38274232,
− 1973739u
21
− 26703501u
20
+ ··· + 5981728a − 159009976, u
22
+ 11u
21
+ ··· + 232u + 32i
I
u
2
= h−10u
29
+ 31u
28
+ ··· + 8b − 6, −54u
29
a + 37u
29
+ ··· + 104a − 100, u
30
− 5u
29
+ ··· − 2u + 1i
I
u
3
= hu
11
+ 2u
10
+ 7u
9
+ 10u
8
+ 18u
7
+ 15u
6
+ 19u
5
+ 5u
4
+ 7u
3
− 2u
2
+ b + 2u,
− u
11
− u
10
− 5u
9
− 3u
8
− 8u
7
+ 3u
6
− 4u
5
+ 14u
4
− 2u
3
+ 8u
2
+ a − 4u + 1,
u
12
+ 2u
11
+ 7u
10
+ 10u
9
+ 19u
8
+ 17u
7
+ 24u
6
+ 11u
5
+ 15u
4
+ 2u
3
+ 6u
2
+ 1i
I
u
4
= h−u
2
a + u
3
− u
2
+ b + u, u
5
a − 2u
4
a − 4u
5
+ 5u
3
a + 5u
4
− 6u
2
a − 11u
3
+ a
2
+ 5au + 9u
2
− 2a − 10u,
u
6
− u
5
+ 3u
4
− 2u
3
+ 3u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 106 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
=
h7.31×10
5
u
21
+8.72×10
6
u
20
+· · · +1.50×10
6
b+3.83×10
7
, −1.97×10
6
u
21
−
2.67 × 10
7
u
20
+ · · · + 5.98 × 10
6
a − 1.59 × 10
8
, u
22
+ 11u
21
+ · · · + 232u + 32i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
0.329961u
21
+ 4.46418u
20
+ ··· + 167.160u + 26.5826
−0.488619u
21
− 5.83389u
20
+ ··· − 164.041u − 25.5941
a
10
=
−u
u
a
2
=
−0.678659u
21
− 6.54536u
20
+ ··· − 66.3494u − 8.74650
0.549186u
21
+ 5.23031u
20
+ ··· + 73.2841u + 11.2249
a
6
=
−0.309352u
21
− 2.39786u
20
+ ··· + 59.0207u + 10.7541
−0.730680u
21
− 8.31181u
20
+ ··· − 218.761u − 33.2810
a
1
=
−0.129473u
21
− 1.31505u
20
+ ··· + 6.93466u + 2.47838
0.549186u
21
+ 5.23031u
20
+ ··· + 73.2841u + 11.2249
a
8
=
u
u
3
+ u
a
7
=
0.770630u
21
+ 8.00468u
20
+ ··· + 111.293u + 15.5266
0.580458u
21
+ 6.16373u
20
+ ··· + 148.964u + 22.7178
a
12
=
−0.459930u
21
− 4.72878u
20
+ ··· − 87.5298u − 12.2394
0.109153u
21
+ 1.41941u
20
+ ··· + 32.5161u + 4.14313
a
11
=
−0.709930u
21
− 7.22878u
20
+ ··· − 117.030u − 16.7394
0.359153u
21
+ 3.66941u
20
+ ··· + 37.0161u + 4.14313
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
297700
186929
u
21
−
2758587
186929
u
20
+ ··· −
6073132
186929
u −
1067206
186929
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
22
+ 13u
21
+ ··· + 6u + 1
c
2
, c
5
, c
6
c
11
u
22
+ u
21
+ ··· − 2u + 1
c
3
, c
8
, c
9
u
22
+ 11u
21
+ ··· + 232u + 32
c
4
u
22
− 15u
21
+ ··· − 480u + 64
c
7
, c
12
u
22
+ 13u
20
+ ··· − u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
22
+ y
21
+ ··· + 34y + 1
c
2
, c
5
, c
6
c
11
y
22
+ 13y
21
+ ··· + 6y + 1
c
3
, c
8
, c
9
y
22
+ 11y
21
+ ··· + 3264y + 1024
c
4
y
22
+ 7y
21
+ ··· + 39936y + 4096
c
7
, c
12
y
22
+ 26y
21
+ ··· + 17y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.767910 + 0.699836I
a = 0.888145 − 0.307129I
b = −0.688888 − 0.277789I
−0.286662 + 0.737446I 3.26178 − 2.36364I
u = −0.767910 − 0.699836I
a = 0.888145 + 0.307129I
b = −0.688888 + 0.277789I
−0.286662 − 0.737446I 3.26178 + 2.36364I
u = −0.350255 + 1.075900I
a = 0.81263 − 1.53152I
b = −0.240178 + 0.810554I
−2.88260 + 1.01233I −4.09792 + 3.96823I
u = −0.350255 − 1.075900I
a = 0.81263 + 1.53152I
b = −0.240178 − 0.810554I
−2.88260 − 1.01233I −4.09792 − 3.96823I
u = −1.033280 + 0.527627I
a = −0.721729 − 0.194727I
b = 0.417851 − 1.163520I
−8.25550 − 1.54810I −5.19018 + 2.03970I
u = −1.033280 − 0.527627I
a = −0.721729 + 0.194727I
b = 0.417851 + 1.163520I
−8.25550 + 1.54810I −5.19018 − 2.03970I
u = 0.755708 + 0.364616I
a = 0.685218 + 0.575896I
b = −0.063685 + 1.154200I
−4.85462 − 1.77876I −4.79807 + 3.91708I
u = 0.755708 − 0.364616I
a = 0.685218 − 0.575896I
b = −0.063685 − 1.154200I
−4.85462 + 1.77876I −4.79807 − 3.91708I
u = −0.774895 + 1.020220I
a = −0.766277 + 0.769605I
b = 0.885411 − 0.402143I
0.61034 + 5.16314I 3.96974 − 2.90756I
u = −0.774895 − 1.020220I
a = −0.766277 − 0.769605I
b = 0.885411 + 0.402143I
0.61034 − 5.16314I 3.96974 + 2.90756I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.221500 + 0.677927I
a = 0.567702 − 0.117730I
b = −0.558982 + 1.253320I
−6.12965 − 9.37239I −3.35170 + 5.78555I
u = −1.221500 − 0.677927I
a = 0.567702 + 0.117730I
b = −0.558982 − 1.253320I
−6.12965 + 9.37239I −3.35170 − 5.78555I
u = −0.127935 + 1.398640I
a = −1.71401 − 0.32772I
b = 0.565971 + 0.644936I
6.04024 + 2.92164I 4.28614 + 0.75325I
u = −0.127935 − 1.398640I
a = −1.71401 + 0.32772I
b = 0.565971 − 0.644936I
6.04024 − 2.92164I 4.28614 − 0.75325I
u = −0.304981 + 0.451421I
a = 0.960223 − 0.185150I
b = −0.310004 − 0.375864I
0.090652 + 0.977959I 1.72728 − 6.82657I
u = −0.304981 − 0.451421I
a = 0.960223 + 0.185150I
b = −0.310004 + 0.375864I
0.090652 − 0.977959I 1.72728 + 6.82657I
u = −0.76091 + 1.25738I
a = 1.92912 + 0.01305I
b = −0.557890 − 1.095380I
−5.97217 + 8.17735I −2.07600 − 6.92513I
u = −0.76091 − 1.25738I
a = 1.92912 − 0.01305I
b = −0.557890 + 1.095380I
−5.97217 − 8.17735I −2.07600 + 6.92513I
u = −0.89339 + 1.20903I
a = −1.79322 + 0.05043I
b = 0.663517 + 1.230310I
−4.4232 + 16.8853I −1.04656 − 9.40882I
u = −0.89339 − 1.20903I
a = −1.79322 − 0.05043I
b = 0.663517 − 1.230310I
−4.4232 − 16.8853I −1.04656 + 9.40882I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.02066 + 1.63363I
a = −0.972799 + 0.791268I
b = 0.386878 − 1.096150I
3.03407 − 4.86939I −4.68451 + 3.83035I
u = −0.02066 − 1.63363I
a = −0.972799 − 0.791268I
b = 0.386878 + 1.096150I
3.03407 + 4.86939I −4.68451 − 3.83035I
7
II. I
u
2
= h−10u
29
+ 31u
28
+ · · · + 8b − 6, −54u
29
a + 37u
29
+ · · · + 104a −
100, u
30
− 5u
29
+ · · · − 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
a
5
4
u
29
−
31
8
u
28
+ ··· +
25
8
u +
3
4
a
10
=
−u
u
a
2
=
−
3
2
u
29
a +
5
4
u
29
+ ··· −
7
8
a +
3
8
7
8
u
29
a −
1
8
u
29
+ ··· −
3
4
a −
29
8
a
6
=
−0.500000au
29
+ 2.12500u
29
+ ··· − 1.62500a − 2.75000
−
3
2
u
29
a −
11
2
u
29
+ ··· + 2a +
69
8
a
1
=
−
5
8
u
29
a +
9
8
u
29
+ ··· −
13
8
a −
13
4
7
8
u
29
a −
1
8
u
29
+ ··· −
3
4
a −
29
8
a
8
=
u
u
3
+ u
a
7
=
−4u
29
a + 4u
29
+ ··· +
19
4
a −
19
4
u
29
a +
9
4
u
29
+ ··· +
3
4
a −
9
8
a
12
=
−2u
29
a −
5
8
u
29
+ ··· +
3
8
a +
15
8
5
4
u
29
a +
13
4
u
29
+ ··· −
5
8
a −
49
8
a
11
=
−3u
29
a +
15
8
u
29
+ ··· +
11
2
a −
5
2
3
4
u
29
a −
13
4
u
29
+ ··· −
5
4
a −
1
8
(ii) Obstruction class = −1
(iii) Cusp Shapes = 19u
29
−
169
2
u
28
+ ··· + 26u −
5
2
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
60
+ 30u
59
+ ··· + 31603u + 2209
c
2
, c
5
, c
6
c
11
u
60
− 2u
59
+ ··· + 81u + 47
c
3
, c
8
, c
9
(u
30
− 5u
29
+ ··· − 2u + 1)
2
c
4
(u
30
+ 6u
29
+ ··· + 9u + 1)
2
c
7
, c
12
u
60
+ 5u
59
+ ··· − 18u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
60
+ 6y
59
+ ··· − 90081877y + 4879681
c
2
, c
5
, c
6
c
11
y
60
+ 30y
59
+ ··· + 31603y + 2209
c
3
, c
8
, c
9
(y
30
+ 9y
29
+ ··· + 14y + 1)
2
c
4
(y
30
+ 10y
29
+ ··· − 9y + 1)
2
c
7
, c
12
y
60
+ 39y
59
+ ··· − 40y + 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.408738 + 0.809128I
a = 1.47348 + 0.03228I
b = −0.881093 − 0.652728I
1.95297 + 0.83755I 3.80919 − 0.73546I
u = −0.408738 + 0.809128I
a = 0.65867 + 1.49537I
b = 0.483976 − 0.827208I
1.95297 + 0.83755I 3.80919 − 0.73546I
u = −0.408738 − 0.809128I
a = 1.47348 − 0.03228I
b = −0.881093 + 0.652728I
1.95297 − 0.83755I 3.80919 + 0.73546I
u = −0.408738 − 0.809128I
a = 0.65867 − 1.49537I
b = 0.483976 + 0.827208I
1.95297 − 0.83755I 3.80919 + 0.73546I
u = 0.204797 + 0.865298I
a = 0.913167 + 0.827489I
b = −0.717809 − 1.010560I
0.86908 + 5.05707I 0.52377 − 4.80046I
u = 0.204797 + 0.865298I
a = 0.79610 − 2.03259I
b = 0.378609 + 0.969447I
0.86908 + 5.05707I 0.52377 − 4.80046I
u = 0.204797 − 0.865298I
a = 0.913167 − 0.827489I
b = −0.717809 + 1.010560I
0.86908 − 5.05707I 0.52377 + 4.80046I
u = 0.204797 − 0.865298I
a = 0.79610 + 2.03259I
b = 0.378609 − 0.969447I
0.86908 − 5.05707I 0.52377 + 4.80046I
u = 0.846145 + 0.766192I
a = −0.742838 + 0.117308I
b = 0.633812 − 0.058357I
−5.03543 − 2.48830I −2.08110 + 3.16963I
u = 0.846145 + 0.766192I
a = 0.161640 + 0.601130I
b = 0.123075 + 1.176780I
−5.03543 − 2.48830I −2.08110 + 3.16963I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.846145 − 0.766192I
a = −0.742838 − 0.117308I
b = 0.633812 + 0.058357I
−5.03543 + 2.48830I −2.08110 − 3.16963I
u = 0.846145 − 0.766192I
a = 0.161640 − 0.601130I
b = 0.123075 − 1.176780I
−5.03543 + 2.48830I −2.08110 − 3.16963I
u = 0.476164 + 0.624124I
a = 1.065700 + 0.769850I
b = −0.560439 + 1.270490I
−0.16540 − 7.91184I −1.25799 + 13.37489I
u = 0.476164 + 0.624124I
a = −3.03202 − 0.17816I
b = 0.670131 − 1.010730I
−0.16540 − 7.91184I −1.25799 + 13.37489I
u = 0.476164 − 0.624124I
a = 1.065700 − 0.769850I
b = −0.560439 − 1.270490I
−0.16540 + 7.91184I −1.25799 − 13.37489I
u = 0.476164 − 0.624124I
a = −3.03202 + 0.17816I
b = 0.670131 + 1.010730I
−0.16540 + 7.91184I −1.25799 − 13.37489I
u = 0.843824 + 0.910765I
a = 0.922245 + 0.095668I
b = −0.146948 + 1.374310I
−5.24308 − 3.14036I 3.38309 + 6.95597I
u = 0.843824 + 0.910765I
a = 0.418535 + 0.014710I
b = 0.036650 + 0.609588I
−5.24308 − 3.14036I 3.38309 + 6.95597I
u = 0.843824 − 0.910765I
a = 0.922245 − 0.095668I
b = −0.146948 − 1.374310I
−5.24308 + 3.14036I 3.38309 − 6.95597I
u = 0.843824 − 0.910765I
a = 0.418535 − 0.014710I
b = 0.036650 − 0.609588I
−5.24308 + 3.14036I 3.38309 − 6.95597I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.535931 + 0.532997I
a = 1.74162 − 0.15387I
b = −0.945912 + 0.839676I
1.99448 − 4.75213I 1.25920 + 8.38226I
u = 0.535931 + 0.532997I
a = −1.15336 − 2.63260I
b = 0.461109 − 0.821998I
1.99448 − 4.75213I 1.25920 + 8.38226I
u = 0.535931 − 0.532997I
a = 1.74162 + 0.15387I
b = −0.945912 − 0.839676I
1.99448 + 4.75213I 1.25920 − 8.38226I
u = 0.535931 − 0.532997I
a = −1.15336 + 2.63260I
b = 0.461109 + 0.821998I
1.99448 + 4.75213I 1.25920 − 8.38226I
u = −0.009746 + 0.748854I
a = 0.263930 − 0.170722I
b = −0.891285 − 0.086936I
3.73099 + 2.66963I 10.94282 − 2.46654I
u = −0.009746 + 0.748854I
a = −2.60774 − 1.78017I
b = 0.695330 + 0.857378I
3.73099 + 2.66963I 10.94282 − 2.46654I
u = −0.009746 − 0.748854I
a = 0.263930 + 0.170722I
b = −0.891285 + 0.086936I
3.73099 − 2.66963I 10.94282 + 2.46654I
u = −0.009746 − 0.748854I
a = −2.60774 + 1.78017I
b = 0.695330 − 0.857378I
3.73099 − 2.66963I 10.94282 + 2.46654I
u = 1.008520 + 0.761169I
a = 1.152310 + 0.354766I
b = −0.976428 + 0.128566I
−2.70377 + 3.89986I −0.32016 − 2.93300I
u = 1.008520 + 0.761169I
a = 0.479203 − 0.132479I
b = −0.523001 − 1.118150I
−2.70377 + 3.89986I −0.32016 − 2.93300I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.008520 − 0.761169I
a = 1.152310 − 0.354766I
b = −0.976428 − 0.128566I
−2.70377 − 3.89986I −0.32016 + 2.93300I
u = 1.008520 − 0.761169I
a = 0.479203 + 0.132479I
b = −0.523001 + 1.118150I
−2.70377 − 3.89986I −0.32016 + 2.93300I
u = 0.716463 + 1.086870I
a = 0.985703 + 0.963170I
b = −0.637549 − 0.440747I
−4.00624 − 3.41764I −0.54348 + 2.60438I
u = 0.716463 + 1.086870I
a = 1.73164 + 0.46125I
b = −0.354117 + 1.056240I
−4.00624 − 3.41764I −0.54348 + 2.60438I
u = 0.716463 − 1.086870I
a = 0.985703 − 0.963170I
b = −0.637549 + 0.440747I
−4.00624 + 3.41764I −0.54348 − 2.60438I
u = 0.716463 − 1.086870I
a = 1.73164 − 0.46125I
b = −0.354117 − 1.056240I
−4.00624 + 3.41764I −0.54348 − 2.60438I
u = −0.464563 + 0.517217I
a = 0.810151 − 0.727418I
b = −0.576786 − 1.098220I
0.97854 + 2.53138I −0.41612 − 5.99517I
u = −0.464563 + 0.517217I
a = −0.46286 + 1.86979I
b = 0.737137 − 0.620730I
0.97854 + 2.53138I −0.41612 − 5.99517I
u = −0.464563 − 0.517217I
a = 0.810151 + 0.727418I
b = −0.576786 + 1.098220I
0.97854 − 2.53138I −0.41612 + 5.99517I
u = −0.464563 − 0.517217I
a = −0.46286 − 1.86979I
b = 0.737137 + 0.620730I
0.97854 − 2.53138I −0.41612 + 5.99517I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.037400 + 0.901379I
a = −1.183640 + 0.552154I
b = 0.465103 + 1.121610I
−7.97522 + 6.40080I −3.44445 − 6.75759I
u = −1.037400 + 0.901379I
a = 0.145261 + 0.219918I
b = 0.19421 − 1.45130I
−7.97522 + 6.40080I −3.44445 − 6.75759I
u = −1.037400 − 0.901379I
a = −1.183640 − 0.552154I
b = 0.465103 − 1.121610I
−7.97522 − 6.40080I −3.44445 + 6.75759I
u = −1.037400 − 0.901379I
a = 0.145261 − 0.219918I
b = 0.19421 + 1.45130I
−7.97522 − 6.40080I −3.44445 + 6.75759I
u = 0.862751 + 1.092420I
a = −1.077000 − 0.739852I
b = 1.047710 + 0.340566I
−1.66664 − 10.74240I 0. + 6.67563I
u = 0.862751 + 1.092420I
a = −1.77506 − 0.35041I
b = 0.627078 − 1.150130I
−1.66664 − 10.74240I 0. + 6.67563I
u = 0.862751 − 1.092420I
a = −1.077000 + 0.739852I
b = 1.047710 − 0.340566I
−1.66664 + 10.74240I 0. − 6.67563I
u = 0.862751 − 1.092420I
a = −1.77506 + 0.35041I
b = 0.627078 + 1.150130I
−1.66664 + 10.74240I 0. − 6.67563I
u = 0.173166 + 1.400750I
a = −1.367910 − 0.170007I
b = 0.212711 − 0.577463I
4.99765 + 1.93280I 0. − 5.83991I
u = 0.173166 + 1.400750I
a = −1.38631 − 0.99061I
b = 0.646364 + 0.999117I
4.99765 + 1.93280I 0. − 5.83991I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.173166 − 1.400750I
a = −1.367910 + 0.170007I
b = 0.212711 + 0.577463I
4.99765 − 1.93280I 0. + 5.83991I
u = 0.173166 − 1.400750I
a = −1.38631 + 0.99061I
b = 0.646364 − 0.999117I
4.99765 − 1.93280I 0. + 5.83991I
u = −1.00992 + 1.06850I
a = 1.291960 + 0.152355I
b = −0.39965 − 1.37579I
−7.50048 + 1.00444I 0
u = −1.00992 + 1.06850I
a = 0.154134 + 0.113540I
b = −0.344881 + 1.084600I
−7.50048 + 1.00444I 0
u = −1.00992 − 1.06850I
a = 1.291960 − 0.152355I
b = −0.39965 + 1.37579I
−7.50048 − 1.00444I 0
u = −1.00992 − 1.06850I
a = 0.154134 − 0.113540I
b = −0.344881 − 1.084600I
−7.50048 − 1.00444I 0
u = −0.237396 + 0.363229I
a = 0.87244 − 1.36981I
b = −0.849393 + 0.936354I
1.67828 − 1.77422I −0.88602 − 3.46618I
u = −0.237396 + 0.363229I
a = −0.74915 + 5.11939I
b = 0.392284 + 0.725566I
1.67828 − 1.77422I −0.88602 − 3.46618I
u = −0.237396 − 0.363229I
a = 0.87244 + 1.36981I
b = −0.849393 − 0.936354I
1.67828 + 1.77422I −0.88602 + 3.46618I
u = −0.237396 − 0.363229I
a = −0.74915 − 5.11939I
b = 0.392284 − 0.725566I
1.67828 + 1.77422I −0.88602 + 3.46618I
16
III.
I
u
3
= hu
11
+2u
10
+· · ·+b+2u, −u
11
−u
10
+· · ·+a+1, u
12
+2u
11
+· · ·+6u
2
+1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
u
11
+ u
10
+ 5u
9
+ 3u
8
+ 8u
7
− 3u
6
+ 4u
5
− 14u
4
+ 2u
3
− 8u
2
+ 4u − 1
−u
11
− 2u
10
+ ··· + 2u
2
− 2u
a
10
=
−u
u
a
2
=
−2u
11
− 2u
10
+ ··· − u + 6
2u
11
+ 4u
10
+ ··· + 4u − 1
a
6
=
u
11
+ 3u
9
− 4u
8
− 2u
7
− 22u
6
− 13u
5
− 38u
4
− 10u
3
− 24u
2
+ u − 7
−2u
11
− 4u
10
+ ··· − 6u + 1
a
1
=
2u
10
+ 5u
9
+ ··· + 3u + 5
2u
11
+ 4u
10
+ ··· + 4u − 1
a
8
=
u
u
3
+ u
a
7
=
−u
11
− 3u
10
+ ··· − 2u − 3
u
10
+ 2u
9
+ 6u
8
+ 8u
7
+ 13u
6
+ 9u
5
+ 11u
4
+ 2u
3
+ 3u
2
− u + 1
a
12
=
−u
11
− u
10
+ ··· − u + 4
2u
11
+ 5u
10
+ ··· + 3u
2
+ 5u
a
11
=
−u
11
− 2u
10
+ ··· − 4u − 2
u
11
+ 3u
10
+ 8u
9
+ 14u
8
+ 21u
7
+ 22u
6
+ 20u
5
+ 12u
4
+ 4u
3
+ u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −7u
11
− 13u
10
− 41u
9
− 49u
8
− 86u
7
− 47u
6
− 71u
5
+ 13u
4
− 26u
3
+ 32u
2
− 13u + 14
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
12
− 7u
11
+ ··· − 9u + 1
c
2
, c
6
u
12
+ u
11
+ ··· + u + 1
c
3
u
12
+ 2u
11
+ ··· + 6u
2
+ 1
c
4
u
12
− 2u
11
+ ··· − 2u + 1
c
5
, c
11
u
12
− u
11
+ ··· − u + 1
c
7
, c
12
u
12
+ 2u
10
− u
9
+ u
8
− 2u
7
+ u
6
+ 4u
4
+ 3u
3
− 2u
2
+ 1
c
8
, c
9
u
12
− 2u
11
+ ··· + 6u
2
+ 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
12
+ 3y
11
+ ··· − 11y + 1
c
2
, c
5
, c
6
c
11
y
12
+ 7y
11
+ ··· + 9y + 1
c
3
, c
8
, c
9
y
12
+ 10y
11
+ ··· + 12y + 1
c
4
y
12
+ 6y
11
+ ··· − 2y + 1
c
7
, c
12
y
12
+ 4y
11
+ ··· − 4y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.398201 + 0.944382I
a = 0.90750 − 1.42868I
b = −0.101632 + 0.556849I
−2.45692 + 1.58415I 2.68356 − 4.01575I
u = −0.398201 − 0.944382I
a = 0.90750 + 1.42868I
b = −0.101632 − 0.556849I
−2.45692 − 1.58415I 2.68356 + 4.01575I
u = 0.009554 + 1.336590I
a = −1.96403 + 0.31123I
b = 0.618206 − 0.752212I
6.04841 − 3.70923I 4.35790 + 9.04746I
u = 0.009554 − 1.336590I
a = −1.96403 − 0.31123I
b = 0.618206 + 0.752212I
6.04841 + 3.70923I 4.35790 − 9.04746I
u = 0.321162 + 0.526918I
a = 2.45149 + 1.05480I
b = −0.642424 + 1.102360I
0.26042 − 7.07580I 3.22594 + 4.98075I
u = 0.321162 − 0.526918I
a = 2.45149 − 1.05480I
b = −0.642424 − 1.102360I
0.26042 + 7.07580I 3.22594 − 4.98075I
u = −0.008480 + 0.565991I
a = 0.23065 + 2.01576I
b = −0.746714 − 0.688145I
2.91227 + 3.67114I 6.22425 − 5.54178I
u = −0.008480 − 0.565991I
a = 0.23065 − 2.01576I
b = −0.746714 + 0.688145I
2.91227 − 3.67114I 6.22425 + 5.54178I
u = −1.04086 + 1.00123I
a = 0.678256 − 0.226364I
b = −0.116334 − 1.202190I
−7.51749 + 3.74982I −4.74315 − 3.41984I
u = −1.04086 − 1.00123I
a = 0.678256 + 0.226364I
b = −0.116334 + 1.202190I
−7.51749 − 3.74982I −4.74315 + 3.41984I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.11683 + 1.44227I
a = −0.803868 − 0.992511I
b = 0.488896 + 1.051410I
4.04318 + 5.16032I 4.25149 − 6.22222I
u = 0.11683 − 1.44227I
a = −0.803868 + 0.992511I
b = 0.488896 − 1.051410I
4.04318 − 5.16032I 4.25149 + 6.22222I
21
IV. I
u
4
=
h−u
2
a+u
3
−u
2
+b+u, u
5
a−4u
5
+· · ·+a
2
−2a, u
6
−u
5
+3 u
4
−2u
3
+3 u
2
+1 i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
a
u
2
a − u
3
+ u
2
− u
a
10
=
−u
u
a
2
=
−u
5
a + u
4
a − 2u
5
− u
3
a + 2u
4
− 4u
3
+ 3u
2
− a − 4u + 2
u
5
a − u
4
a + u
5
+ 2u
3
a − u
4
− u
2
a + 2u
3
+ au − u
2
+ 2u − 1
a
6
=
u
3
a − 2u
4
+ 3u
3
− 5u
2
+ a + 3u − 3
u
5
− u
3
a + u
2
a − au + 2u
2
− u + 2
a
1
=
−u
5
+ u
3
a + u
4
− u
2
a − 2u
3
+ au + 2u
2
− a − 2u + 1
u
5
a − u
4
a + u
5
+ 2u
3
a − u
4
− u
2
a + 2u
3
+ au − u
2
+ 2u − 1
a
8
=
u
u
3
+ u
a
7
=
u
5
a − u
4
a − u
5
+ 3u
3
a + u
4
− 2u
2
a − 3u
3
+ 2au + 2u
2
− 2u
−u
3
a + u
4
− au + 2u
2
+ 1
a
12
=
−u
5
+ 2u
4
− u
2
a − 3u
3
+ 4u
2
− a − 3u + 2
−u
4
a + u
5
+ u
3
a − 2u
4
− u
2
a + 3u
3
+ au − 3u
2
+ 2u − 2
a
11
=
u
5
a − u
4
a − u
5
+ 2u
3
a + 2u
4
− 2u
2
a − 3u
3
+ au + 4u
2
− 3u + 1
−u
5
a − u
3
a − u
4
+ u
3
− 2u
2
− 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
5
+ 5u
4
− u
3
+ 11u
2
− 9u + 9
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
12
− 7u
11
+ ··· − 7u + 1
c
2
, c
6
u
12
+ u
11
+ ··· + u + 1
c
3
(u
6
− u
5
+ 3u
4
− 2u
3
+ 3u
2
+ 1)
2
c
4
(u
6
+ 2u
4
+ 2u
3
+ u + 1)
2
c
5
, c
11
u
12
− u
11
+ ··· − u + 1
c
7
, c
12
u
12
+ 4u
10
+ 5u
9
+ 6u
8
+ 11u
7
+ 9u
6
+ 6u
5
+ 2u
4
− 2u
3
− 2u
2
+ 1
c
8
, c
9
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 3u
2
+ 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
12
+ 3y
11
+ ··· + 3y + 1
c
2
, c
5
, c
6
c
11
y
12
+ 7y
11
+ ··· + 7y + 1
c
3
, c
8
, c
9
(y
6
+ 5y
5
+ 11y
4
+ 16y
3
+ 15y
2
+ 6y + 1)
2
c
4
(y
6
+ 4y
5
+ 4y
4
− 2y
3
− y + 1)
2
c
7
, c
12
y
12
+ 8y
11
+ ··· − 4y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.751720 + 0.952459I
a = 1.161910 + 0.208933I
b = −0.169435 + 1.321240I
−5.66414 − 2.84527I −10.09526 − 1.04786I
u = 0.751720 + 0.952459I
a = −0.214542 + 0.486127I
b = −0.095489 − 0.744618I
−5.66414 − 2.84527I −10.09526 − 1.04786I
u = 0.751720 − 0.952459I
a = 1.161910 − 0.208933I
b = −0.169435 − 1.321240I
−5.66414 + 2.84527I −10.09526 + 1.04786I
u = 0.751720 − 0.952459I
a = −0.214542 − 0.486127I
b = −0.095489 + 0.744618I
−5.66414 + 2.84527I −10.09526 + 1.04786I
u = −0.081708 + 1.363140I
a = −1.41421 + 0.28398I
b = 0.456929 + 0.708982I
5.25930 − 1.24964I 4.40551 − 3.55084I
u = −0.081708 + 1.363140I
a = −1.40363 + 1.20387I
b = 0.642260 − 0.996545I
5.25930 − 1.24964I 4.40551 − 3.55084I
u = −0.081708 − 1.363140I
a = −1.41421 − 0.28398I
b = 0.456929 − 0.708982I
5.25930 + 1.24964I 4.40551 + 3.55084I
u = −0.081708 − 1.363140I
a = −1.40363 − 1.20387I
b = 0.642260 + 0.996545I
5.25930 + 1.24964I 4.40551 + 3.55084I
u = −0.170012 + 0.579072I
a = 1.72240 + 0.01156I
b = −0.828025 − 0.974687I
2.04978 + 2.32699I 7.18975 − 6.61882I
u = −0.170012 + 0.579072I
a = −1.35194 − 3.13856I
b = −0.506239 + 0.595906I
2.04978 + 2.32699I 7.18975 − 6.61882I
25
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.170012 − 0.579072I
a = 1.72240 − 0.01156I
b = −0.828025 + 0.974687I
2.04978 − 2.32699I 7.18975 + 6.61882I
u = −0.170012 − 0.579072I
a = −1.35194 + 3.13856I
b = −0.506239 − 0.595906I
2.04978 − 2.32699I 7.18975 + 6.61882I
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
12
− 7u
11
+ ··· − 7u + 1)(u
12
− 7u
11
+ ··· − 9u + 1)
· (u
22
+ 13u
21
+ ··· + 6u + 1)(u
60
+ 30u
59
+ ··· + 31603u + 2209)
c
2
, c
6
(u
12
+ u
11
+ ··· + u + 1)(u
12
+ u
11
+ ··· + u + 1)(u
22
+ u
21
+ ··· − 2u + 1)
· (u
60
− 2u
59
+ ··· + 81u + 47)
c
3
((u
6
− u
5
+ 3u
4
− 2u
3
+ 3u
2
+ 1)
2
)(u
12
+ 2u
11
+ ··· + 6u
2
+ 1)
· (u
22
+ 11u
21
+ ··· + 232u + 32)(u
30
− 5u
29
+ ··· − 2u + 1)
2
c
4
((u
6
+ 2u
4
+ 2u
3
+ u + 1)
2
)(u
12
− 2u
11
+ ··· − 2u + 1)
· (u
22
− 15u
21
+ ··· − 480u + 64)(u
30
+ 6u
29
+ ··· + 9u + 1)
2
c
5
, c
11
(u
12
− u
11
+ ··· − u + 1)(u
12
− u
11
+ ··· − u + 1)(u
22
+ u
21
+ ··· − 2u + 1)
· (u
60
− 2u
59
+ ··· + 81u + 47)
c
7
, c
12
(u
12
+ 2u
10
− u
9
+ u
8
− 2u
7
+ u
6
+ 4u
4
+ 3u
3
− 2u
2
+ 1)
· (u
12
+ 4u
10
+ 5u
9
+ 6u
8
+ 11u
7
+ 9u
6
+ 6u
5
+ 2u
4
− 2u
3
− 2u
2
+ 1)
· (u
22
+ 13u
20
+ ··· − u + 1)(u
60
+ 5u
59
+ ··· − 18u + 1)
c
8
, c
9
((u
6
+ u
5
+ 3u
4
+ 2u
3
+ 3u
2
+ 1)
2
)(u
12
− 2u
11
+ ··· + 6u
2
+ 1)
· (u
22
+ 11u
21
+ ··· + 232u + 32)(u
30
− 5u
29
+ ··· − 2u + 1)
2
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
12
+ 3y
11
+ ··· + 3y + 1)(y
12
+ 3y
11
+ ··· − 11y + 1)
· (y
22
+ y
21
+ ··· + 34y + 1)(y
60
+ 6y
59
+ ··· − 9.00819 × 10
7
y + 4879681)
c
2
, c
5
, c
6
c
11
(y
12
+ 7y
11
+ ··· + 9y + 1)(y
12
+ 7y
11
+ ··· + 7y + 1)
· (y
22
+ 13y
21
+ ··· + 6y + 1)(y
60
+ 30y
59
+ ··· + 31603y + 2209)
c
3
, c
8
, c
9
(y
6
+ 5y
5
+ 11y
4
+ 16y
3
+ 15y
2
+ 6y + 1)
2
· (y
12
+ 10y
11
+ ··· + 12y + 1)(y
22
+ 11y
21
+ ··· + 3264y + 1024)
· (y
30
+ 9y
29
+ ··· + 14y + 1)
2
c
4
((y
6
+ 4y
5
+ 4y
4
− 2y
3
− y + 1)
2
)(y
12
+ 6y
11
+ ··· − 2y + 1)
· (y
22
+ 7y
21
+ ··· + 39936y + 4096)(y
30
+ 10y
29
+ ··· − 9y + 1)
2
c
7
, c
12
(y
12
+ 4y
11
+ ··· − 4y + 1)(y
12
+ 8y
11
+ ··· − 4y + 1)
· (y
22
+ 26y
21
+ ··· + 17y + 1)(y
60
+ 39y
59
+ ··· − 40y + 1)
28
