12a
1059
(K12a
1059
)
A knot diagram
1
Linearized knot diagam
4 7 9 11 12 2 10 1 3 6 5 8
Solving Sequence
5,12 6,8
1 9 11 4 2 3 10 7
c
5
c
12
c
8
c
11
c
4
c
1
c
3
c
10
c
7
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.14828 × 10
28
u
37
+ 8.50493 × 10
28
u
36
+ ··· + 2.35548 × 10
29
b + 4.37452 × 10
29
,
− 9.04579 × 10
28
u
37
+ 6.37591 × 10
28
u
36
+ ··· + 1.17774 × 10
30
a − 2.01495 × 10
30
,
u
38
− 3u
37
+ ··· + 38u + 10i
I
u
2
= h2u
29
a − 3u
29
+ ··· + a − 9, u
29
+ 2u
28
+ ··· − a + 2, u
30
+ u
29
+ ··· − u + 1i
I
u
3
= hu
4
+ u
3
− u
2
+ 2b − u + 1, u
4
− 2u
2
+ a + 1, u
6
− 3u
4
+ 2u
2
+ 1i
I
v
1
= ha, b − 1, v + 1i
* 4 irreducible components of dim
C
= 0, with total 105 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−6.15 × 10
28
u
37
+ 8.50 × 10
28
u
36
+ · · · + 2.36 × 10
29
b + 4.37 ×
10
29
, −9.05 × 10
28
u
37
+ 6.38 × 10
28
u
36
+ · · · + 1.18 × 10
30
a − 2.01 ×
10
30
, u
38
− 3u
37
+ · · · + 38u + 10i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
u
2
a
8
=
0.0768064u
37
− 0.0541369u
36
+ ··· + 0.400423u + 1.71086
0.261020u
37
− 0.361070u
36
+ ··· − 9.03543u − 1.85717
a
1
=
0.0395912u
37
− 0.155029u
36
+ ··· + 2.31691u + 0.790017
0.0608242u
37
− 0.176995u
36
+ ··· + 0.234757u − 0.377871
a
9
=
0.140551u
37
− 0.0696244u
36
+ ··· − 1.72012u + 2.05575
0.615558u
37
− 0.922281u
36
+ ··· − 22.1653u − 4.52960
a
11
=
u
u
a
4
=
−u
2
+ 1
−u
2
a
2
=
−0.00943465u
37
− 0.0566721u
36
+ ··· + 2.16486u + 1.21012
−0.00165545u
37
− 0.0842333u
36
+ ··· + 2.11565u + 0.0816969
a
3
=
−0.100930u
37
+ 0.00413956u
36
+ ··· + 10.2335u + 3.54732
−0.209935u
37
+ 0.144189u
36
+ ··· + 9.07278u + 1.58098
a
10
=
−u
3
+ 2u
−u
5
+ u
3
+ u
a
7
=
0.0740422u
37
− 0.0468738u
36
+ ··· + 2.13281u + 2.06658
0.220414u
37
− 0.290916u
36
+ ··· − 6.68558u − 1.35661
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00842304u
37
+ 0.168232u
36
+ ··· − 43.3018u − 18.3994
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
64(64u
38
− 256u
37
+ ··· + 15u − 1)
c
2
, c
6
, c
8
c
12
u
38
− u
37
+ ··· + 17u − 5
c
3
, c
9
u
38
− 3u
37
+ ··· − 834u + 178
c
4
, c
5
, c
11
u
38
− 3u
37
+ ··· + 38u + 10
c
10
u
38
+ 9u
37
+ ··· − 58478u − 6110
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
4096(4096y
38
− 73728y
37
+ ··· − 391y + 1)
c
2
, c
6
, c
8
c
12
y
38
− 19y
37
+ ··· − 749y + 25
c
3
, c
9
y
38
+ 31y
37
+ ··· − 180424y + 31684
c
4
, c
5
, c
11
y
38
− 33y
37
+ ··· + 896y + 100
c
10
y
38
+ 3y
37
+ ··· − 52394384y + 37332100
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.832821 + 0.547125I
a = −0.86558 − 1.12589I
b = −0.800463 + 0.066461I
−9.55612 − 8.85033I −14.7980 + 4.0064I
u = −0.832821 − 0.547125I
a = −0.86558 + 1.12589I
b = −0.800463 − 0.066461I
−9.55612 + 8.85033I −14.7980 − 4.0064I
u = 0.758122 + 0.726911I
a = −0.598468 + 0.868086I
b = −0.909897 − 0.239586I
−3.21428 + 2.58317I −14.0149 − 7.3951I
u = 0.758122 − 0.726911I
a = −0.598468 − 0.868086I
b = −0.909897 + 0.239586I
−3.21428 − 2.58317I −14.0149 + 7.3951I
u = −0.254953 + 1.055630I
a = 0.191552 + 1.039430I
b = 0.408014 − 0.285100I
−5.53222 − 1.14690I −22.5523 + 4.7902I
u = −0.254953 − 1.055630I
a = 0.191552 − 1.039430I
b = 0.408014 + 0.285100I
−5.53222 + 1.14690I −22.5523 − 4.7902I
u = 0.377700 + 0.817120I
a = 0.930523 − 0.994516I
b = 1.103510 + 0.283151I
−2.13828 − 7.70452I −10.95675 + 8.64865I
u = 0.377700 − 0.817120I
a = 0.930523 + 0.994516I
b = 1.103510 − 0.283151I
−2.13828 + 7.70452I −10.95675 − 8.64865I
u = −0.304901 + 0.821700I
a = 1.12461 + 1.25299I
b = 1.316850 − 0.071626I
−7.8932 + 13.6180I −12.3598 − 8.2723I
u = −0.304901 − 0.821700I
a = 1.12461 − 1.25299I
b = 1.316850 + 0.071626I
−7.8932 − 13.6180I −12.3598 + 8.2723I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.191870 + 0.245310I
a = −0.597452 − 0.473091I
b = −1.368890 + 0.168011I
−0.40005 − 4.16689I −6.41890 + 7.16086I
u = 1.191870 − 0.245310I
a = −0.597452 + 0.473091I
b = −1.368890 − 0.168011I
−0.40005 + 4.16689I −6.41890 − 7.16086I
u = −1.096270 + 0.573423I
a = −0.932566 − 0.275848I
b = −1.361430 − 0.074950I
−8.26421 + 6.83120I −17.2078 − 8.7853I
u = −1.096270 − 0.573423I
a = −0.932566 + 0.275848I
b = −1.361430 + 0.074950I
−8.26421 − 6.83120I −17.2078 + 8.7853I
u = −1.244400 + 0.106432I
a = −0.500503 + 0.821730I
b = −1.86027 + 0.16899I
−2.57552 + 1.10250I −12.15322 + 1.49488I
u = −1.244400 − 0.106432I
a = −0.500503 − 0.821730I
b = −1.86027 − 0.16899I
−2.57552 − 1.10250I −12.15322 − 1.49488I
u = −0.737757
a = 0.738275
b = 0.681107
−1.10279 −8.36790
u = 1.288170 + 0.175763I
a = 0.202837 − 0.012188I
b = 0.693144 + 1.009580I
−4.92002 − 2.79762I −16.6701 + 3.7773I
u = 1.288170 − 0.175763I
a = 0.202837 + 0.012188I
b = 0.693144 − 1.009580I
−4.92002 + 2.79762I −16.6701 − 3.7773I
u = 0.062119 + 0.674628I
a = −1.066350 − 0.720953I
b = −0.548733 − 0.123939I
3.02249 + 0.79229I −0.26606 − 2.46888I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.062119 − 0.674628I
a = −1.066350 + 0.720953I
b = −0.548733 + 0.123939I
3.02249 − 0.79229I −0.26606 + 2.46888I
u = −1.307770 + 0.250331I
a = 0.089765 + 0.665827I
b = −0.340750 + 0.653216I
−1.25101 + 2.53582I −5.26256 − 1.09268I
u = −1.307770 − 0.250331I
a = 0.089765 − 0.665827I
b = −0.340750 − 0.653216I
−1.25101 − 2.53582I −5.26256 + 1.09268I
u = 1.376180 + 0.215614I
a = −0.007963 − 1.118930I
b = −0.93586 − 1.62045I
−4.46084 − 3.77438I −17.8969 + 4.8599I
u = 1.376180 − 0.215614I
a = −0.007963 + 1.118930I
b = −0.93586 + 1.62045I
−4.46084 + 3.77438I −17.8969 − 4.8599I
u = −0.181936 + 0.531158I
a = −2.10293 + 1.17618I
b = −0.852184 + 0.229977I
0.533620 + 0.994797I −12.5887 − 7.1482I
u = −0.181936 − 0.531158I
a = −2.10293 − 1.17618I
b = −0.852184 − 0.229977I
0.533620 − 0.994797I −12.5887 + 7.1482I
u = 1.43812 + 0.32819I
a = 1.024740 + 0.167678I
b = 3.38065 − 0.99960I
−13.4573 − 17.7785I −15.9854 + 8.9050I
u = 1.43812 − 0.32819I
a = 1.024740 − 0.167678I
b = 3.38065 + 0.99960I
−13.4573 + 17.7785I −15.9854 − 8.9050I
u = −1.46219 + 0.31744I
a = 0.886952 − 0.098679I
b = 3.18286 + 0.68484I
−8.0205 + 11.8161I −14.4580 − 8.0646I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46219 − 0.31744I
a = 0.886952 + 0.098679I
b = 3.18286 − 0.68484I
−8.0205 − 11.8161I −14.4580 + 8.0646I
u = 1.53956 + 0.03471I
a = −0.926435 + 0.236128I
b = −3.32141 + 0.36741I
−17.7030 + 7.3147I −19.0498 − 4.2883I
u = 1.53956 − 0.03471I
a = −0.926435 − 0.236128I
b = −3.32141 − 0.36741I
−17.7030 − 7.3147I −19.0498 + 4.2883I
u = 1.51262 + 0.38346I
a = 0.770644 − 0.138564I
b = 2.50061 − 0.54552I
−11.37270 − 4.09288I −21.9706 + 0.I
u = 1.51262 − 0.38346I
a = 0.770644 + 0.138564I
b = 2.50061 + 0.54552I
−11.37270 + 4.09288I −21.9706 + 0.I
u = −1.61211
a = −0.778308
b = −3.05374
−12.1718 −21.8720
u = −0.184289 + 0.301680I
a = 1.096640 − 0.014738I
b = −0.099433 − 0.437896I
−0.612808 + 0.881258I −10.27041 − 7.59569I
u = −0.184289 − 0.301680I
a = 1.096640 + 0.014738I
b = −0.099433 + 0.437896I
−0.612808 − 0.881258I −10.27041 + 7.59569I
8
II.
I
u
2
= h2u
29
a−3u
29
+· · · + a−9, u
29
+2u
28
+· · · − a+2, u
30
+u
29
+· · · − u+1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
u
2
a
8
=
a
−
2
5
u
29
a +
3
5
u
29
+ ··· −
1
5
a +
9
5
a
1
=
u
29
+ u
28
+ ··· + 3u − 1
6
5
u
29
a −
1
5
u
29
+ ··· +
3
5
a −
3
5
a
9
=
u
20
− 9u
18
+ 33u
16
− 60u
14
+ 48u
12
+ 3u
10
− 25u
8
+ 2u
6
+ 9u
4
− u
2
− 1
u
20
− 8u
18
+ 26u
16
− 42u
14
+ 31u
12
− 2u
10
− 8u
8
− 2u
6
+ 5u
4
a
11
=
u
u
a
4
=
−u
2
+ 1
−u
2
a
2
=
1
5
u
29
a +
9
5
u
29
+ ··· +
3
5
a +
2
5
4
5
u
29
a +
6
5
u
29
+ ··· +
2
5
a +
3
5
a
3
=
u
21
− 10u
19
+ ··· − 6u
3
− u
u
23
− 9u
21
+ ··· − 2u
3
− u
a
10
=
−u
3
+ 2u
−u
5
+ u
3
+ u
a
7
=
3
5
u
29
a +
3
5
u
29
+ ··· +
9
5
a −
1
5
7
5
u
29
a +
2
5
u
29
+ ··· +
6
5
a +
6
5
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
28
− 52u
26
+ 4u
25
+ 292u
24
− 48u
23
− 912u
22
+ 244u
21
+
1684u
20
−672u
19
−1752u
18
+ 1056u
17
+ 752u
16
−896u
15
+ 212u
14
+ 332u
13
−180u
12
−
64u
11
− 156u
10
+ 112u
9
+ 96u
8
− 64u
7
+ 20u
6
+ 8u
5
− 8u
4
− 20u
3
+ 12u − 14
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
25(25u
60
+ 175u
59
+ ··· − 6914990u + 533119)
c
2
, c
6
, c
8
c
12
u
60
− u
59
+ ··· + 2u
2
+ 1
c
3
, c
9
(u
30
+ u
29
+ ··· + u + 1)
2
c
4
, c
5
, c
11
(u
30
+ u
29
+ ··· − u + 1)
2
c
10
(u
30
− 3u
29
+ ··· − u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
625
· (625y
60
− 20625y
59
+ ··· − 3671828841416y + 284215868161)
c
2
, c
6
, c
8
c
12
y
60
− 41y
59
+ ··· + 4y + 1
c
3
, c
9
(y
30
+ 25y
29
+ ··· + 3y + 1)
2
c
4
, c
5
, c
11
(y
30
− 27y
29
+ ··· + 3y + 1)
2
c
10
(y
30
+ y
29
+ ··· − y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.006930 + 0.206480I
a = 1.106440 + 0.089649I
b = 0.700491 + 0.212708I
−4.85148 − 3.89629I −11.54228 + 4.15365I
u = 1.006930 + 0.206480I
a = −0.062835 − 0.576338I
b = 0.716396 + 0.426617I
−4.85148 − 3.89629I −11.54228 + 4.15365I
u = 1.006930 − 0.206480I
a = 1.106440 − 0.089649I
b = 0.700491 − 0.212708I
−4.85148 + 3.89629I −11.54228 − 4.15365I
u = 1.006930 − 0.206480I
a = −0.062835 + 0.576338I
b = 0.716396 − 0.426617I
−4.85148 + 3.89629I −11.54228 − 4.15365I
u = −0.832034 + 0.169903I
a = 0.837632 + 0.478792I
b = 0.728628 − 0.013221I
−1.081760 − 0.029483I −7.62798 − 0.47071I
u = −0.832034 + 0.169903I
a = 0.541539 − 0.269552I
b = 0.764830 − 0.085001I
−1.081760 − 0.029483I −7.62798 − 0.47071I
u = −0.832034 − 0.169903I
a = 0.837632 − 0.478792I
b = 0.728628 + 0.013221I
−1.081760 + 0.029483I −7.62798 + 0.47071I
u = −0.832034 − 0.169903I
a = 0.541539 + 0.269552I
b = 0.764830 + 0.085001I
−1.081760 + 0.029483I −7.62798 + 0.47071I
u = 0.266850 + 0.721202I
a = 1.39335 + 0.53326I
b = 0.755461 + 0.165673I
−3.58803 − 7.69168I −9.96957 + 6.90287I
u = 0.266850 + 0.721202I
a = −1.34228 + 1.44900I
b = −1.176110 + 0.077817I
−3.58803 − 7.69168I −9.96957 + 6.90287I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.266850 − 0.721202I
a = 1.39335 − 0.53326I
b = 0.755461 − 0.165673I
−3.58803 + 7.69168I −9.96957 − 6.90287I
u = 0.266850 − 0.721202I
a = −1.34228 − 1.44900I
b = −1.176110 − 0.077817I
−3.58803 + 7.69168I −9.96957 − 6.90287I
u = 0.703536 + 0.310326I
a = 0.375402 + 1.132660I
b = 0.726738 + 0.185162I
−5.20234 + 3.85600I −12.77500 − 2.05029I
u = 0.703536 + 0.310326I
a = 1.35245 − 1.17888I
b = 0.727398 − 0.288938I
−5.20234 + 3.85600I −12.77500 − 2.05029I
u = 0.703536 − 0.310326I
a = 0.375402 − 1.132660I
b = 0.726738 − 0.185162I
−5.20234 − 3.85600I −12.77500 + 2.05029I
u = 0.703536 − 0.310326I
a = 1.35245 + 1.17888I
b = 0.727398 + 0.288938I
−5.20234 − 3.85600I −12.77500 + 2.05029I
u = −0.228391 + 0.710789I
a = 0.824807 − 0.489046I
b = 0.348965 + 0.017513I
0.89469 + 3.64220I −4.89571 − 4.72167I
u = −0.228391 + 0.710789I
a = −0.98019 − 1.20859I
b = −1.058380 + 0.072042I
0.89469 + 3.64220I −4.89571 − 4.72167I
u = −0.228391 − 0.710789I
a = 0.824807 + 0.489046I
b = 0.348965 − 0.017513I
0.89469 − 3.64220I −4.89571 + 4.72167I
u = −0.228391 − 0.710789I
a = −0.98019 + 1.20859I
b = −1.058380 − 0.072042I
0.89469 − 3.64220I −4.89571 + 4.72167I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.169829 + 0.699155I
a = −0.27507 + 1.43355I
b = −0.982543 + 0.271641I
−2.35081 + 0.37332I −7.79326 + 0.53471I
u = 0.169829 + 0.699155I
a = −0.129943 − 0.165869I
b = −0.264670 − 0.891458I
−2.35081 + 0.37332I −7.79326 + 0.53471I
u = 0.169829 − 0.699155I
a = −0.27507 − 1.43355I
b = −0.982543 − 0.271641I
−2.35081 − 0.37332I −7.79326 − 0.53471I
u = 0.169829 − 0.699155I
a = −0.129943 + 0.165869I
b = −0.264670 + 0.891458I
−2.35081 − 0.37332I −7.79326 − 0.53471I
u = −0.379833 + 0.540597I
a = 1.91795 + 1.04697I
b = 1.285490 + 0.431592I
−8.44109 + 1.73295I −15.3118 − 4.0988I
u = −0.379833 + 0.540597I
a = −0.70200 − 2.19064I
b = −0.195589 − 0.222195I
−8.44109 + 1.73295I −15.3118 − 4.0988I
u = −0.379833 − 0.540597I
a = 1.91795 − 1.04697I
b = 1.285490 − 0.431592I
−8.44109 − 1.73295I −15.3118 + 4.0988I
u = −0.379833 − 0.540597I
a = −0.70200 + 2.19064I
b = −0.195589 + 0.222195I
−8.44109 − 1.73295I −15.3118 + 4.0988I
u = 1.351750 + 0.104838I
a = 0.918606 − 0.092731I
b = 3.58585 − 0.17980I
−6.82103 − 0.39832I −11.93478 − 1.62643I
u = 1.351750 + 0.104838I
a = −0.387734 + 0.353048I
b = 0.384313 − 0.303024I
−6.82103 − 0.39832I −11.93478 − 1.62643I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.351750 − 0.104838I
a = 0.918606 + 0.092731I
b = 3.58585 + 0.17980I
−6.82103 + 0.39832I −11.93478 + 1.62643I
u = 1.351750 − 0.104838I
a = −0.387734 − 0.353048I
b = 0.384313 + 0.303024I
−6.82103 + 0.39832I −11.93478 + 1.62643I
u = −1.363600 + 0.194579I
a = −0.776181 − 0.304313I
b = −3.24492 + 0.96961I
−8.06303 + 3.51597I −14.7951 − 5.1228I
u = −1.363600 + 0.194579I
a = 0.815095 − 0.090094I
b = 3.99423 + 2.25543I
−8.06303 + 3.51597I −14.7951 − 5.1228I
u = −1.363600 − 0.194579I
a = −0.776181 + 0.304313I
b = −3.24492 − 0.96961I
−8.06303 − 3.51597I −14.7951 + 5.1228I
u = −1.363600 − 0.194579I
a = 0.815095 + 0.090094I
b = 3.99423 − 2.25543I
−8.06303 − 3.51597I −14.7951 + 5.1228I
u = −1.360050 + 0.270550I
a = −0.801459 − 0.128170I
b = −3.02150 − 2.03985I
−7.18585 + 3.12979I −12.91872 − 1.86186I
u = −1.360050 + 0.270550I
a = 0.231493 − 0.068682I
b = −0.845504 + 1.046880I
−7.18585 + 3.12979I −12.91872 − 1.86186I
u = −1.360050 − 0.270550I
a = −0.801459 + 0.128170I
b = −3.02150 + 2.03985I
−7.18585 − 3.12979I −12.91872 + 1.86186I
u = −1.360050 − 0.270550I
a = 0.231493 + 0.068682I
b = −0.845504 − 1.046880I
−7.18585 − 3.12979I −12.91872 + 1.86186I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.39028 + 0.28253I
a = −0.893925 − 0.133521I
b = −3.12549 + 0.97945I
−4.25247 − 7.24749I −9.92864 + 5.63452I
u = 1.39028 + 0.28253I
a = 0.082294 + 0.578132I
b = 0.382082 + 0.552723I
−4.25247 − 7.24749I −9.92864 + 5.63452I
u = 1.39028 − 0.28253I
a = −0.893925 + 0.133521I
b = −3.12549 − 0.97945I
−4.25247 + 7.24749I −9.92864 − 5.63452I
u = 1.39028 − 0.28253I
a = 0.082294 − 0.578132I
b = 0.382082 − 0.552723I
−4.25247 + 7.24749I −9.92864 − 5.63452I
u = −1.42059 + 0.09196I
a = 1.085040 + 0.253869I
b = 3.38504 + 0.97196I
−11.61500 − 2.69486I −17.4134 + 2.4278I
u = −1.42059 + 0.09196I
a = −0.272288 − 0.773726I
b = 0.134709 − 1.163670I
−11.61500 − 2.69486I −17.4134 + 2.4278I
u = −1.42059 − 0.09196I
a = 1.085040 − 0.253869I
b = 3.38504 − 0.97196I
−11.61500 + 2.69486I −17.4134 − 2.4278I
u = −1.42059 − 0.09196I
a = −0.272288 + 0.773726I
b = 0.134709 + 1.163670I
−11.61500 + 2.69486I −17.4134 − 2.4278I
u = −1.40881 + 0.28598I
a = 0.178934 − 0.868467I
b = 1.10783 − 1.01091I
−8.9306 + 11.3520I −14.5534 − 7.3132I
u = −1.40881 + 0.28598I
a = −1.104570 + 0.226478I
b = −3.42336 − 0.88023I
−8.9306 + 11.3520I −14.5534 − 7.3132I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40881 − 0.28598I
a = 0.178934 + 0.868467I
b = 1.10783 + 1.01091I
−8.9306 − 11.3520I −14.5534 + 7.3132I
u = −1.40881 − 0.28598I
a = −1.104570 − 0.226478I
b = −3.42336 + 0.88023I
−8.9306 − 11.3520I −14.5534 + 7.3132I
u = 1.42434 + 0.20546I
a = 1.029910 + 0.423098I
b = 3.20762 − 0.64618I
−14.1830 − 4.4767I −19.0263 + 3.5734I
u = 1.42434 + 0.20546I
a = −1.070140 + 0.500011I
b = −2.72487 + 1.14691I
−14.1830 − 4.4767I −19.0263 + 3.5734I
u = 1.42434 − 0.20546I
a = 1.029910 − 0.423098I
b = 3.20762 + 0.64618I
−14.1830 + 4.4767I −19.0263 − 3.5734I
u = 1.42434 − 0.20546I
a = −1.070140 − 0.500011I
b = −2.72487 − 1.14691I
−14.1830 + 4.4767I −19.0263 − 3.5734I
u = 0.179795 + 0.471439I
a = 1.11876 − 1.63717I
b = 1.72380 − 0.44845I
−3.15470 − 0.99510I −9.51394 + 6.82295I
u = 0.179795 + 0.471439I
a = −0.51110 + 2.18288I
b = −0.096933 − 0.875944I
−3.15470 − 0.99510I −9.51394 + 6.82295I
u = 0.179795 − 0.471439I
a = 1.11876 + 1.63717I
b = 1.72380 + 0.44845I
−3.15470 + 0.99510I −9.51394 − 6.82295I
u = 0.179795 − 0.471439I
a = −0.51110 − 2.18288I
b = −0.096933 + 0.875944I
−3.15470 + 0.99510I −9.51394 − 6.82295I
17
III. I
u
3
= hu
4
+ u
3
− u
2
+ 2b − u + 1, u
4
− 2u
2
+ a + 1, u
6
− 3u
4
+ 2u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
u
2
a
8
=
−u
4
+ 2u
2
− 1
−
1
2
u
4
−
1
2
u
3
+ ··· +
1
2
u −
1
2
a
1
=
−u
5
+ 3u
3
− 2u
−u
5
−
1
2
u
4
+ 2u
3
+ u
2
+
1
2
u
a
9
=
−2u
4
+ 4u
2
− 2
−2u
4
− u
3
+ 2u
2
+ u
a
11
=
u
u
a
4
=
−u
2
+ 1
−u
2
a
2
=
−
3
2
u
5
+ 4u
3
+ ··· −
5
2
u +
1
2
−
3
2
u
5
−
1
2
u
4
+ ··· +
1
2
u
2
+
1
2
u
a
3
=
−2u
5
+ 6u
3
− u
2
− 4u + 1
−2u
5
− u
4
+ 4u
3
+ u
2
a
10
=
−u
3
+ 2u
−u
5
+ u
3
+ u
a
7
=
−u
4
+
1
2
u
3
+ 2u
2
− u −
1
2
1
2
u
5
− u
4
− u
3
+
3
2
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
4
− 8u
2
− 8
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
64(64u
6
− 192u
5
+ 256u
4
− 192u
3
+ 92u
2
− 28u + 5)
c
2
, c
3
, c
6
c
8
, c
9
, c
12
(u
2
+ 1)
3
c
4
, c
5
, c
11
u
6
− 3u
4
+ 2u
2
+ 1
c
10
u
6
+ u
4
+ 2u
2
+ 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
4096(4096y
6
− 4096y
5
+ 3584y
4
+ 128y
3
+ 272y
2
+ 136y + 25)
c
2
, c
3
, c
6
c
8
, c
9
, c
12
(y + 1)
6
c
4
, c
5
, c
11
(y
3
− 3y
2
+ 2y + 1)
2
c
10
(y
3
+ y
2
+ 2y + 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.307140 + 0.215080I
a = −0.122561 − 0.744862I
b = −1.26489 − 1.09229I
−3.02413 − 2.82812I −11.50976 + 2.97945I
u = 1.307140 − 0.215080I
a = −0.122561 + 0.744862I
b = −1.26489 + 1.09229I
−3.02413 + 2.82812I −11.50976 − 2.97945I
u = −1.307140 + 0.215080I
a = −0.122561 + 0.744862I
b = −0.520029 + 0.214851I
−3.02413 + 2.82812I −11.50976 − 2.97945I
u = −1.307140 − 0.215080I
a = −0.122561 − 0.744862I
b = −0.520029 − 0.214851I
−3.02413 − 2.82812I −11.50976 + 2.97945I
u = 0.569840I
a = −1.75488
b = −0.715080 + 0.377439I
1.11345 −4.98050
u = − 0.569840I
a = −1.75488
b = −0.715080 − 0.377439I
1.11345 −4.98050
21
IV. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
−1
0
a
6
=
1
0
a
8
=
0
1
a
1
=
−1
−1
a
9
=
−1
0
a
11
=
−1
0
a
4
=
1
0
a
2
=
0
−1
a
3
=
1
0
a
10
=
−1
0
a
7
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u − 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
c
6
, c
12
u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
y −1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−3.28987 −12.0000
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
102400(u − 1)(64u
6
− 192u
5
+ 256u
4
− 192u
3
+ 92u
2
− 28u + 5)
· (64u
38
− 256u
37
+ ··· + 15u − 1)
· (25u
60
+ 175u
59
+ ··· − 6914990u + 533119)
c
2
, c
8
(u − 1)(u
2
+ 1)
3
(u
38
− u
37
+ ··· + 17u − 5)(u
60
− u
59
+ ··· + 2u
2
+ 1)
c
3
, c
9
u(u
2
+ 1)
3
(u
30
+ u
29
+ ··· + u + 1)
2
(u
38
− 3u
37
+ ··· − 834u + 178)
c
4
, c
5
, c
11
u(u
6
− 3u
4
+ 2u
2
+ 1)(u
30
+ u
29
+ ··· − u + 1)
2
· (u
38
− 3u
37
+ ··· + 38u + 10)
c
6
, c
12
(u + 1)(u
2
+ 1)
3
(u
38
− u
37
+ ··· + 17u − 5)(u
60
− u
59
+ ··· + 2u
2
+ 1)
c
10
u(u
6
+ u
4
+ 2u
2
+ 1)(u
30
− 3u
29
+ ··· − u + 1)
2
· (u
38
+ 9u
37
+ ··· − 58478u − 6110)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
10485760000(y −1)
· (4096y
6
− 4096y
5
+ 3584y
4
+ 128y
3
+ 272y
2
+ 136y + 25)
· (4096y
38
− 73728y
37
+ ··· − 391y + 1)
· (625y
60
− 20625y
59
+ ··· − 3671828841416y + 284215868161)
c
2
, c
6
, c
8
c
12
(y −1)(y + 1)
6
(y
38
− 19y
37
+ ··· − 749y + 25)
· (y
60
− 41y
59
+ ··· + 4y + 1)
c
3
, c
9
y(y + 1)
6
(y
30
+ 25y
29
+ ··· + 3y + 1)
2
· (y
38
+ 31y
37
+ ··· − 180424y + 31684)
c
4
, c
5
, c
11
y(y
3
− 3y
2
+ 2y + 1)
2
(y
30
− 27y
29
+ ··· + 3y + 1)
2
· (y
38
− 33y
37
+ ··· + 896y + 100)
c
10
y(y
3
+ y
2
+ 2y + 1)
2
(y
30
+ y
29
+ ··· − y + 1)
2
· (y
38
+ 3y
37
+ ··· − 52394384y + 37332100)
27
