12a
1044
(K12a
1044
)
A knot diagram
1
Linearized knot diagam
4 7 8 1 12 11 10 6 2 3 9 5
Solving Sequence
7,10 3,8
4 11 2 1 6 9 12 5
c
7
c
3
c
10
c
2
c
1
c
6
c
9
c
11
c
5
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.07361 × 10
36
u
42
− 2.49991 × 10
38
u
41
+ ··· + 3.01538 × 10
35
b + 8.06957 × 10
37
,
− 4.03479 × 10
37
u
42
− 1.11159 × 10
39
u
41
+ ··· + 6.03076 × 10
35
a + 3.58061 × 10
38
,
u
43
+ 28u
42
+ ··· − 18u − 4i
I
u
2
= h−6967u
18
a
3
− 29606u
18
a
2
+ ··· − 20917a + 13395, u
18
a
3
+ 9u
18
a
2
+ ··· + 15a
2
+ 25,
u
19
− 9u
18
+ ··· − 5u
2
+ 1i
I
u
3
= h300258u
21
− 3737558u
20
+ ··· + 83731b − 586404,
586404u
21
− 7322994u
20
+ ··· + 83731a − 1066330, u
22
− 13u
21
+ ··· − 5u + 1i
* 3 irreducible components of dim
C
= 0, with total 141 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−9.07 × 10
36
u
42
− 2.50 × 10
38
u
41
+ · · · + 3.02 × 10
35
b + 8.07 ×
10
37
, −4.03 × 10
37
u
42
− 1.11 × 10
39
u
41
+ · · · + 6.03 × 10
35
a + 3.58 ×
10
38
, u
43
+ 28u
42
+ · · · − 18u − 4i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
3
=
66.9034u
42
+ 1843.21u
41
+ ··· − 1350.13u − 593.724
30.0911u
42
+ 829.054u
41
+ ··· − 610.538u − 267.614
a
8
=
1
u
2
a
4
=
50.3090u
42
+ 1386.73u
41
+ ··· − 1013.61u − 446.475
25.2456u
42
+ 696.395u
41
+ ··· − 529.788u − 234.919
a
11
=
−98.4362u
42
− 2711.47u
41
+ ··· + 2005.14u + 868.683
−44.7454u
42
− 1232.43u
41
+ ··· + 904.168u + 393.745
a
2
=
36.8123u
42
+ 1014.15u
41
+ ··· − 739.587u − 326.111
30.0911u
42
+ 829.054u
41
+ ··· − 610.538u − 267.614
a
1
=
73.3891u
42
+ 2021.12u
41
+ ··· − 1468.02u − 641.215
49.4695u
42
+ 1362.87u
41
+ ··· − 1004.50u − 437.492
a
6
=
68.7543u
42
+ 1894.58u
41
+ ··· − 1384.29u − 631.191
50.9823u
42
+ 1403.48u
41
+ ··· − 1017.06u − 453.999
a
9
=
−29.3850u
42
− 809.446u
41
+ ··· + 610.479u + 260.175
−24.3059u
42
− 669.592u
41
+ ··· + 492.496u + 214.763
a
12
=
−96.7826u
42
− 2666.41u
41
+ ··· + 1954.20u + 856.576
−58.6162u
42
− 1614.92u
41
+ ··· + 1190.66u + 525.323
a
5
=
65.9599u
42
+ 1818.07u
41
+ ··· − 1334.13u − 599.264
42.8407u
42
+ 1180.03u
41
+ ··· − 866.574u − 384.197
(ii) Obstruction class = −1
(iii) Cusp Shapes = −119.862u
42
− 3311.57u
41
+ ··· + 2522.42u + 1244.58
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
12
u
43
− 9u
42
+ ··· − 172u + 16
c
2
, c
10
u
43
− 2u
41
+ ··· − 2u + 1
c
3
, c
9
u
43
− u
42
+ ··· − 16u + 2
c
6
u
43
− 32u
42
+ ··· − 7864320u + 524288
c
7
u
43
− 28u
42
+ ··· − 18u + 4
c
8
, c
11
u
43
+ 3u
42
+ ··· + 20u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
12
y
43
+ 51y
42
+ ··· − 3536y −256
c
2
, c
10
y
43
− 4y
42
+ ··· + 8y −1
c
3
, c
9
y
43
− 9y
42
+ ··· + 96y −4
c
6
y
43
+ 18y
42
+ ··· − 137438953472y −274877906944
c
7
y
43
+ 2y
42
+ ··· + 668y −16
c
8
, c
11
y
43
+ 23y
42
+ ··· + 94y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.619281 + 0.736910I
a = 0.20054 − 1.52504I
b = −0.99963 − 1.09221I
9.96243 + 4.04675I 0
u = −0.619281 − 0.736910I
a = 0.20054 + 1.52504I
b = −0.99963 + 1.09221I
9.96243 − 4.04675I 0
u = −0.593747 + 0.928986I
a = −0.031042 − 0.926856I
b = −0.879468 − 0.521481I
5.16180 − 0.19404I 0
u = −0.593747 − 0.928986I
a = −0.031042 + 0.926856I
b = −0.879468 + 0.521481I
5.16180 + 0.19404I 0
u = −1.228530 + 0.119928I
a = −0.547925 − 0.708005I
b = −0.758052 − 0.804094I
7.54354 + 0.37611I 0
u = −1.228530 − 0.119928I
a = −0.547925 + 0.708005I
b = −0.758052 + 0.804094I
7.54354 − 0.37611I 0
u = −0.975794 + 0.782038I
a = 0.076356 + 1.241860I
b = 1.04569 + 1.15208I
−0.28345 + 6.38071I 0
u = −0.975794 − 0.782038I
a = 0.076356 − 1.241860I
b = 1.04569 − 1.15208I
−0.28345 − 6.38071I 0
u = −0.507092 + 1.162540I
a = −0.081421 + 0.837209I
b = 0.932000 + 0.519197I
13.99450 − 1.63545I 0
u = −0.507092 − 1.162540I
a = −0.081421 − 0.837209I
b = 0.932000 − 0.519197I
13.99450 + 1.63545I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.069420 + 0.710868I
a = 0.324200 + 0.759138I
b = 0.886353 + 0.581374I
1.42612 + 2.66485I 0
u = −1.069420 − 0.710868I
a = 0.324200 − 0.759138I
b = 0.886353 − 0.581374I
1.42612 − 2.66485I 0
u = 0.687050
a = 0.599117
b = −0.411623
−1.10828 −9.43920
u = 0.336275 + 0.564768I
a = 0.699167 − 1.217530I
b = −0.922733 + 0.014557I
9.44828 − 2.46853I 1.53023 + 3.59562I
u = 0.336275 − 0.564768I
a = 0.699167 + 1.217530I
b = −0.922733 − 0.014557I
9.44828 + 2.46853I 1.53023 − 3.59562I
u = −0.528719 + 0.200325I
a = 0.00069 + 2.22752I
b = 0.446594 + 1.177590I
−0.62097 + 2.44438I −15.0343 − 15.0278I
u = −0.528719 − 0.200325I
a = 0.00069 − 2.22752I
b = 0.446594 − 1.177590I
−0.62097 − 2.44438I −15.0343 + 15.0278I
u = −1.09557 + 0.93019I
a = −0.029411 − 1.088810I
b = −1.04502 − 1.16551I
−3.62136 + 10.95930I 0
u = −1.09557 − 0.93019I
a = −0.029411 + 1.088810I
b = −1.04502 + 1.16551I
−3.62136 − 10.95930I 0
u = 0.223350 + 0.508490I
a = −0.358014 + 1.243700I
b = 0.712370 − 0.095733I
1.36482 − 1.89009I 0.58099 + 5.23171I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.223350 − 0.508490I
a = −0.358014 − 1.243700I
b = 0.712370 + 0.095733I
1.36482 + 1.89009I 0.58099 − 5.23171I
u = −1.11997 + 1.04983I
a = −0.025975 + 1.031520I
b = 1.05383 + 1.18254I
−1.2574 + 15.5298I 0
u = −1.11997 − 1.04983I
a = −0.025975 − 1.031520I
b = 1.05383 − 1.18254I
−1.2574 − 15.5298I 0
u = −0.443394 + 0.008368I
a = 1.66096 − 1.26229I
b = 0.725895 − 0.573592I
0.83810 − 1.87876I 0.39664 + 2.99774I
u = −0.443394 − 0.008368I
a = 1.66096 + 1.26229I
b = 0.725895 + 0.573592I
0.83810 + 1.87876I 0.39664 − 2.99774I
u = 0.351842 + 0.194871I
a = −2.94605 + 0.20344I
b = 1.076190 + 0.502519I
8.75469 + 1.88268I −0.00595 − 3.28324I
u = 0.351842 − 0.194871I
a = −2.94605 − 0.20344I
b = 1.076190 − 0.502519I
8.75469 − 1.88268I −0.00595 + 3.28324I
u = −1.12504 + 1.14203I
a = 0.064944 − 0.996760I
b = −1.06527 − 1.19556I
7.3041 + 18.4273I 0
u = −1.12504 − 1.14203I
a = 0.064944 + 0.996760I
b = −1.06527 + 1.19556I
7.3041 − 18.4273I 0
u = −1.28079 + 0.98206I
a = −0.218083 − 0.599042I
b = −0.867616 − 0.553074I
2.84744 + 7.10779I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.28079 − 0.98206I
a = −0.218083 + 0.599042I
b = −0.867616 + 0.553074I
2.84744 − 7.10779I 0
u = −0.87810 + 1.42078I
a = −0.356045 + 0.017937I
b = −0.287159 + 0.521613I
−2.50543 − 3.29694I 0
u = −0.87810 − 1.42078I
a = −0.356045 − 0.017937I
b = −0.287159 − 0.521613I
−2.50543 + 3.29694I 0
u = 0.183954 + 0.099778I
a = 5.23413 − 0.12638I
b = −0.975449 − 0.499001I
0.95612 + 1.98935I 0.00401 − 3.39354I
u = 0.183954 − 0.099778I
a = 5.23413 + 0.12638I
b = −0.975449 + 0.499001I
0.95612 − 1.98935I 0.00401 + 3.39354I
u = −1.34458 + 1.19695I
a = 0.135418 + 0.548413I
b = 0.838502 + 0.575295I
10.9150 + 10.1097I 0
u = −1.34458 − 1.19695I
a = 0.135418 − 0.548413I
b = 0.838502 − 0.575295I
10.9150 − 10.1097I 0
u = −1.31475 + 1.27295I
a = 0.349842 − 0.161305I
b = 0.254620 − 0.657408I
−1.00239 − 7.03044I 0
u = −1.31475 − 1.27295I
a = 0.349842 + 0.161305I
b = 0.254620 + 0.657408I
−1.00239 + 7.03044I 0
u = 0.25305 + 1.89084I
a = 0.123915 + 0.158134I
b = 0.267649 − 0.274318I
2.16526 − 1.06347I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.25305 − 1.89084I
a = 0.123915 − 0.158134I
b = 0.267649 + 0.274318I
2.16526 + 1.06347I 0
u = −1.56723 + 1.17558I
a = −0.325755 + 0.235679I
b = −0.233475 + 0.752315I
6.94224 − 9.40178I 0
u = −1.56723 − 1.17558I
a = −0.325755 − 0.235679I
b = −0.233475 − 0.752315I
6.94224 + 9.40178I 0
9
II. I
u
2
= h−6967a
3
u
18
− 2.96 × 10
4
a
2
u
18
+ · · · − 2.09 × 10
4
a + 1.34 ×
10
4
, u
18
a
3
+ 9u
18
a
2
+ · · · + 15a
2
+ 25, u
19
− 9u
18
+ · · · − 5u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
3
=
a
0.333078a
3
u
18
+ 1.41540a
2
u
18
+ ··· + a − 0.640388
a
8
=
1
u
2
a
4
=
−0.333078a
3
u
18
− 1.41540a
2
u
18
+ ··· + 1.70770a
2
+ 0.640388
1.00076a
3
u
18
+ 1.75379a
2
u
18
+ ··· + a − 0.0788354
a
11
=
a
2
u
−0.584596a
3
u
18
− 0.333078a
2
u
18
+ ··· + a + 0.999952
a
2
=
−0.333078a
3
u
18
− 1.41540a
2
u
18
+ ··· + 1.70770a
2
+ 0.640388
0.333078a
3
u
18
+ 1.41540a
2
u
18
+ ··· + a − 0.640388
a
1
=
−0.668451a
3
u
18
− 1.09217a
2
u
18
+ ··· − a − 0.482717
0.326959a
3
u
18
+ 1.38509a
2
u
18
+ ··· + 3a − 0.00970502
a
6
=
0.292298a
3
u
18
− 0.333461a
2
u
18
+ ··· − 2a + 0.500024
−0.584596a
3
u
18
− 0.333078a
2
u
18
+ ··· + a − 0.0000478080
a
9
=
0.661615a
3
u
18
+ 0.667687a
2
u
18
+ ··· + 2a − 0.000191232
−0.0770187a
3
u
18
− 0.334608a
2
u
18
+ ··· − 3a − 0.999761
a
12
=
0.784721a
3
u
18
+ 0.668069a
2
u
18
+ ··· + a + 0.499737
−0.246211a
3
u
18
− 1.00076a
2
u
18
+ ··· − 4a + 0.000143424
a
5
=
0.0145336a
3
u
18
− 0.678013a
2
u
18
+ ··· − a + 0.502127
0.385093a
3
u
18
+ 0.673041a
2
u
18
+ ··· + a − 0.00119520
(ii) Obstruction class = −1
(iii) Cusp Shapes =
48912
20917
u
18
a
3
+
27868
20917
u
18
a
2
+ ··· − 4a −
711174
20917
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
12
(u
19
+ 3u
18
+ ··· + 2u + 1)
4
c
2
, c
10
u
76
+ 3u
75
+ ··· + 2u + 1
c
3
, c
9
u
76
+ u
75
+ ··· − 44450u + 29629
c
6
(u
2
+ u + 1)
38
c
7
(u
19
+ 9u
18
+ ··· + 5u
2
− 1)
4
c
8
, c
11
u
76
+ u
75
+ ··· − 12u + 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
12
(y
19
+ 23y
18
+ ··· − 10y −1)
4
c
2
, c
10
y
76
+ 27y
75
+ ··· + 120y + 1
c
3
, c
9
y
76
− 17y
75
+ ··· − 10612715258y + 877877641
c
6
(y
2
+ y + 1)
38
c
7
(y
19
− y
18
+ ··· + 10y −1)
4
c
8
, c
11
y
76
− 9y
75
+ ··· − 56y + 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.224406 + 0.979990I
a = −0.079941 − 1.063040I
b = 0.75493 − 1.56939I
10.77910 − 7.75317I 2.36068 + 8.39109I
u = 0.224406 + 0.979990I
a = −0.531501 − 1.301450I
b = 0.205893 + 0.046196I
10.77910 − 3.69340I 2.36068 + 1.46289I
u = 0.224406 + 0.979990I
a = 1.35403 + 1.08041I
b = −1.023830 + 0.316893I
10.77910 − 7.75317I 2.36068 + 8.39109I
u = 0.224406 + 0.979990I
a = −0.090504 + 0.189372I
b = −1.156140 + 0.812919I
10.77910 − 3.69340I 2.36068 + 1.46289I
u = 0.224406 − 0.979990I
a = −0.079941 + 1.063040I
b = 0.75493 + 1.56939I
10.77910 + 7.75317I 2.36068 − 8.39109I
u = 0.224406 − 0.979990I
a = −0.531501 + 1.301450I
b = 0.205893 − 0.046196I
10.77910 + 3.69340I 2.36068 − 1.46289I
u = 0.224406 − 0.979990I
a = 1.35403 − 1.08041I
b = −1.023830 − 0.316893I
10.77910 + 7.75317I 2.36068 − 8.39109I
u = 0.224406 − 0.979990I
a = −0.090504 − 0.189372I
b = −1.156140 − 0.812919I
10.77910 + 3.69340I 2.36068 − 1.46289I
u = 0.411578 + 0.796293I
a = −0.017212 + 1.037780I
b = −0.87911 + 1.55841I
1.87060 − 6.27257I 0.97656 + 11.51556I
u = 0.411578 + 0.796293I
a = −0.100441 + 1.281310I
b = −0.0472227 − 0.0855841I
1.87060 − 2.21281I 0.97656 + 4.58736I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.411578 + 0.796293I
a = 0.1090080 − 0.0029603I
b = 1.061640 − 0.447379I
1.87060 − 2.21281I 0.97656 + 4.58736I
u = 0.411578 + 0.796293I
a = −1.09415 − 1.66953I
b = 0.833461 − 0.413422I
1.87060 − 6.27257I 0.97656 + 11.51556I
u = 0.411578 − 0.796293I
a = −0.017212 − 1.037780I
b = −0.87911 − 1.55841I
1.87060 + 6.27257I 0.97656 − 11.51556I
u = 0.411578 − 0.796293I
a = −0.100441 − 1.281310I
b = −0.0472227 + 0.0855841I
1.87060 + 2.21281I 0.97656 − 4.58736I
u = 0.411578 − 0.796293I
a = 0.1090080 + 0.0029603I
b = 1.061640 + 0.447379I
1.87060 + 2.21281I 0.97656 − 4.58736I
u = 0.411578 − 0.796293I
a = −1.09415 + 1.66953I
b = 0.833461 + 0.413422I
1.87060 + 6.27257I 0.97656 − 11.51556I
u = 0.738136 + 0.285129I
a = 0.220113 − 0.805434I
b = 1.18836 − 1.32414I
−1.93123 − 3.81353I −12.8478 + 10.3305I
u = 0.738136 + 0.285129I
a = −0.298557 − 0.491122I
b = −1.164680 − 0.741015I
−1.93123 + 0.24623I −12.84779 + 3.40225I
u = 0.738136 + 0.285129I
a = 1.71044 + 0.34319I
b = 0.080342 + 0.447642I
−1.93123 + 0.24623I −12.84779 + 3.40225I
u = 0.738136 + 0.285129I
a = −0.79794 + 2.10213I
b = −0.392126 + 0.531760I
−1.93123 − 3.81353I −12.8478 + 10.3305I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.738136 − 0.285129I
a = 0.220113 + 0.805434I
b = 1.18836 + 1.32414I
−1.93123 + 3.81353I −12.8478 − 10.3305I
u = 0.738136 − 0.285129I
a = −0.298557 + 0.491122I
b = −1.164680 + 0.741015I
−1.93123 − 0.24623I −12.84779 − 3.40225I
u = 0.738136 − 0.285129I
a = 1.71044 − 0.34319I
b = 0.080342 − 0.447642I
−1.93123 − 0.24623I −12.84779 − 3.40225I
u = 0.738136 − 0.285129I
a = −0.79794 − 2.10213I
b = −0.392126 − 0.531760I
−1.93123 + 3.81353I −12.8478 − 10.3305I
u = −0.578057 + 0.369314I
a = −0.093463 + 0.827692I
b = −1.61147 + 1.31105I
8.03276 + 9.35799I −5.9941 − 13.3695I
u = −0.578057 + 0.369314I
a = −0.59366 − 1.69489I
b = 0.069383 − 1.329150I
8.03276 + 5.29822I −5.99414 − 6.44128I
u = −0.578057 + 0.369314I
a = 1.12844 − 1.57839I
b = −0.969117 − 0.760498I
8.03276 + 5.29822I −5.99414 − 6.44128I
u = −0.578057 + 0.369314I
a = −3.00868 + 0.34582I
b = 0.251651 + 0.512970I
8.03276 + 9.35799I −5.9941 − 13.3695I
u = −0.578057 − 0.369314I
a = −0.093463 − 0.827692I
b = −1.61147 − 1.31105I
8.03276 − 9.35799I −5.9941 + 13.3695I
u = −0.578057 − 0.369314I
a = −0.59366 + 1.69489I
b = 0.069383 + 1.329150I
8.03276 − 5.29822I −5.99414 + 6.44128I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.578057 − 0.369314I
a = 1.12844 + 1.57839I
b = −0.969117 + 0.760498I
8.03276 − 5.29822I −5.99414 + 6.44128I
u = −0.578057 − 0.369314I
a = −3.00868 − 0.34582I
b = 0.251651 − 0.512970I
8.03276 − 9.35799I −5.9941 + 13.3695I
u = 1.07839 + 0.92133I
a = 0.020594 + 1.098290I
b = −0.650210 + 1.015400I
−2.60244 − 4.96452I −11.91453 + 1.46747I
u = 1.07839 + 0.92133I
a = −0.116481 − 0.842068I
b = 0.98968 − 1.20336I
−2.60244 − 4.96452I −11.91453 + 1.46747I
u = 1.07839 + 0.92133I
a = 0.470035 + 0.385689I
b = −0.180979 + 0.648976I
−2.60244 − 0.90475I −11.91453 − 5.46074I
u = 1.07839 + 0.92133I
a = −0.200198 − 0.430759I
b = −0.151536 − 0.848982I
−2.60244 − 0.90475I −11.91453 − 5.46074I
u = 1.07839 − 0.92133I
a = 0.020594 − 1.098290I
b = −0.650210 − 1.015400I
−2.60244 + 4.96452I −11.91453 − 1.46747I
u = 1.07839 − 0.92133I
a = −0.116481 + 0.842068I
b = 0.98968 + 1.20336I
−2.60244 + 4.96452I −11.91453 − 1.46747I
u = 1.07839 − 0.92133I
a = 0.470035 − 0.385689I
b = −0.180979 − 0.648976I
−2.60244 + 0.90475I −11.91453 + 5.46074I
u = 1.07839 − 0.92133I
a = −0.200198 + 0.430759I
b = −0.151536 + 0.848982I
−2.60244 + 0.90475I −11.91453 + 5.46074I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.515417 + 0.216459I
a = 0.136886 − 1.007060I
b = 1.56792 − 1.42933I
−0.60400 + 6.51999I −13.2217 − 15.7344I
u = −0.515417 + 0.216459I
a = −0.22464 + 1.91414I
b = 0.704217 + 1.183980I
−0.60400 + 2.46023I −13.2217 − 8.8062I
u = −0.515417 + 0.216459I
a = 0.34137 + 2.44050I
b = 0.298549 + 1.035200I
−0.60400 + 2.46023I −13.2217 − 8.8062I
u = −0.515417 + 0.216459I
a = 3.57597 − 1.27135I
b = −0.147434 − 0.548687I
−0.60400 + 6.51999I −13.2217 − 15.7344I
u = −0.515417 − 0.216459I
a = 0.136886 + 1.007060I
b = 1.56792 + 1.42933I
−0.60400 − 6.51999I −13.2217 + 15.7344I
u = −0.515417 − 0.216459I
a = −0.22464 − 1.91414I
b = 0.704217 − 1.183980I
−0.60400 − 2.46023I −13.2217 + 8.8062I
u = −0.515417 − 0.216459I
a = 0.34137 − 2.44050I
b = 0.298549 − 1.035200I
−0.60400 − 2.46023I −13.2217 + 8.8062I
u = −0.515417 − 0.216459I
a = 3.57597 + 1.27135I
b = −0.147434 + 0.548687I
−0.60400 − 6.51999I −13.2217 + 15.7344I
u = 1.28782 + 0.69169I
a = 0.217129 − 1.114740I
b = 0.426150 − 0.961228I
3.89129 − 4.57393I −8.47148 + 5.29372I
u = 1.28782 + 0.69169I
a = −0.621576 − 0.491356I
b = 0.132391 − 0.683945I
3.89129 − 0.51417I −8.47148 − 1.63449I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.28782 + 0.69169I
a = 0.054314 + 0.717229I
b = −1.05067 + 1.28540I
3.89129 − 4.57393I −8.47148 + 5.29372I
u = 1.28782 + 0.69169I
a = 0.141597 + 0.455037I
b = 0.460612 + 1.062710I
3.89129 − 0.51417I −8.47148 − 1.63449I
u = 1.28782 − 0.69169I
a = 0.217129 + 1.114740I
b = 0.426150 + 0.961228I
3.89129 + 4.57393I −8.47148 − 5.29372I
u = 1.28782 − 0.69169I
a = −0.621576 + 0.491356I
b = 0.132391 + 0.683945I
3.89129 + 0.51417I −8.47148 + 1.63449I
u = 1.28782 − 0.69169I
a = 0.054314 − 0.717229I
b = −1.05067 − 1.28540I
3.89129 + 4.57393I −8.47148 − 5.29372I
u = 1.28782 − 0.69169I
a = 0.141597 − 0.455037I
b = 0.460612 − 1.062710I
3.89129 + 0.51417I −8.47148 + 1.63449I
u = −0.493766
a = −0.051780 + 1.334910I
b = −1.25352 + 1.55631I
−3.21610 + 2.02988I −23.6348 − 3.4641I
u = −0.493766
a = −0.051780 − 1.334910I
b = −1.25352 − 1.55631I
−3.21610 − 2.02988I −23.6348 + 3.4641I
u = −0.493766
a = −2.53869 + 3.15193I
b = −0.025567 + 0.659131I
−3.21610 + 2.02988I −23.6348 − 3.4641I
u = −0.493766
a = −2.53869 − 3.15193I
b = −0.025567 − 0.659131I
−3.21610 − 2.02988I −23.6348 + 3.4641I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.05045 + 1.11478I
a = −0.022759 − 0.967513I
b = 0.674813 − 1.211630I
−2.00492 − 6.85219I −7.9642 + 14.7411I
u = 1.05045 + 1.11478I
a = 0.273568 + 0.863111I
b = −1.05466 + 1.04170I
−2.00492 − 6.85219I −7.9642 + 14.7411I
u = 1.05045 + 1.11478I
a = −0.412467 − 0.506564I
b = 0.174195 − 0.578011I
−2.00492 − 2.79242I −7.96421 + 7.81289I
u = 1.05045 + 1.11478I
a = 0.196648 + 0.341558I
b = −0.131433 + 0.991934I
−2.00492 − 2.79242I −7.96421 + 7.81289I
u = 1.05045 − 1.11478I
a = −0.022759 + 0.967513I
b = 0.674813 + 1.211630I
−2.00492 + 6.85219I −7.9642 − 14.7411I
u = 1.05045 − 1.11478I
a = 0.273568 − 0.863111I
b = −1.05466 − 1.04170I
−2.00492 + 6.85219I −7.9642 − 14.7411I
u = 1.05045 − 1.11478I
a = −0.412467 + 0.506564I
b = 0.174195 + 0.578011I
−2.00492 + 2.79242I −7.96421 − 7.81289I
u = 1.05045 − 1.11478I
a = 0.196648 − 0.341558I
b = −0.131433 − 0.991934I
−2.00492 + 2.79242I −7.96421 − 7.81289I
u = 1.04957 + 1.25847I
a = 0.013720 + 0.933343I
b = −0.63265 + 1.28758I
5.56101 − 7.78064I −5.10596 + 10.77370I
u = 1.04957 + 1.25847I
a = −0.356143 − 0.799738I
b = 1.16018 − 0.99688I
5.56101 − 7.78064I −5.10596 + 10.77370I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.04957 + 1.25847I
a = 0.442870 + 0.549940I
b = −0.239273 + 0.532330I
5.56101 − 3.72087I −5.10596 + 3.84550I
u = 1.04957 + 1.25847I
a = −0.155952 − 0.320196I
b = 0.227258 − 1.134540I
5.56101 − 3.72087I −5.10596 + 3.84550I
u = 1.04957 − 1.25847I
a = 0.013720 − 0.933343I
b = −0.63265 − 1.28758I
5.56101 + 7.78064I −5.10596 − 10.77370I
u = 1.04957 − 1.25847I
a = −0.356143 + 0.799738I
b = 1.16018 + 0.99688I
5.56101 + 7.78064I −5.10596 − 10.77370I
u = 1.04957 − 1.25847I
a = 0.442870 − 0.549940I
b = −0.239273 − 0.532330I
5.56101 + 3.72087I −5.10596 − 3.84550I
u = 1.04957 − 1.25847I
a = −0.155952 + 0.320196I
b = 0.227258 + 1.134540I
5.56101 + 3.72087I −5.10596 − 3.84550I
20
III.
I
u
3
= h3.00 × 10
5
u
21
− 3.74 × 10
6
u
20
+ · · · + 8.37 × 10
4
b − 5.86 × 10
5
, 5.86 ×
10
5
u
21
−7.32×10
6
u
20
+· · ·+8.37×10
4
a−1.07×10
6
, u
22
−13u
21
+· · ·−5u+1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
3
=
−7.00343u
21
+ 87.4586u
20
+ ··· − 44.3530u + 12.7352
−3.58598u
21
+ 44.6377u
20
+ ··· − 22.2820u + 7.00343
a
8
=
1
u
2
a
4
=
−5.39755u
21
+ 67.0370u
20
+ ··· − 32.9975u + 9.31774
−3.51768u
21
+ 44.3290u
20
+ ··· − 21.6136u + 6.54859
a
11
=
−2.61019u
21
+ 33.0158u
20
+ ··· − 16.3744u + 1.22024
−0.916650u
21
+ 11.9220u
20
+ ··· − 10.8307u + 2.61019
a
2
=
−3.41744u
21
+ 42.8209u
20
+ ··· − 22.0710u + 5.73176
−3.58598u
21
+ 44.6377u
20
+ ··· − 22.2820u + 7.00343
a
1
=
1.55273u
21
− 19.9663u
20
+ ··· + 12.4988u − 5.43283
−1.89051u
21
+ 22.0306u
20
+ ··· − 5.14530u + 0.758883
a
6
=
9.89821u
21
− 122.389u
20
+ ··· + 57.7470u − 15.1185
6.29352u
21
− 77.1234u
20
+ ··· + 31.3995u − 8.98156
a
9
=
−0.771387u
21
+ 8.42141u
20
+ ··· + 5.31399u − 3.08349
−0.922155u
21
+ 12.6725u
20
+ ··· − 8.85766u + 1.69354
a
12
=
−4.10925u
21
+ 51.3382u
20
+ ··· − 23.0531u + 3.38501
−2.70867u
21
+ 33.4842u
20
+ ··· − 17.1752u + 4.29466
a
5
=
0.817009u
21
− 8.99200u
20
+ ··· − 1.20787u + 2.56636
2.56637u
21
− 31.4113u
20
+ ··· + 10.3704u − 2.01674
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
3961003
83731
u
21
+
49875561
83731
u
20
+ ··· −
26977727
83731
u +
8950063
83731
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
22
− 4u
21
+ ··· − 8u + 1
c
2
, c
10
u
22
+ 6u
20
+ ··· − u + 1
c
3
, c
9
u
22
− u
21
+ ··· − 2u + 2
c
4
, c
5
u
22
+ 4u
21
+ ··· + 8u + 1
c
6
u
22
− u
21
+ ··· − 8u + 2
c
7
u
22
− 13u
21
+ ··· − 5u + 1
c
8
, c
11
u
22
+ 5u
21
+ ··· + 3u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
12
y
22
+ 28y
21
+ ··· + 16y + 1
c
2
, c
10
y
22
+ 12y
21
+ ··· + 21y + 1
c
3
, c
9
y
22
− 5y
21
+ ··· − 24y + 4
c
6
y
22
+ 17y
21
+ ··· + 20y + 4
c
7
y
22
+ 3y
21
+ ··· − 9y + 1
c
8
, c
11
y
22
− 5y
21
+ ··· + 3y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.438202 + 0.672246I
a = 0.61789 + 1.58697I
b = −0.796076 + 1.110790I
9.41063 − 5.22030I 0.06768 + 7.65102I
u = 0.438202 − 0.672246I
a = 0.61789 − 1.58697I
b = −0.796076 − 1.110790I
9.41063 + 5.22030I 0.06768 − 7.65102I
u = 0.928863 + 0.813564I
a = −0.047964 − 1.144700I
b = 0.88673 − 1.10229I
−0.78236 − 5.04646I −5.15506 + 3.89150I
u = 0.928863 − 0.813564I
a = −0.047964 + 1.144700I
b = 0.88673 + 1.10229I
−0.78236 + 5.04646I −5.15506 − 3.89150I
u = 1.024400 + 0.790762I
a = −0.325907 − 0.530025I
b = 0.085266 − 0.800669I
−2.42816 − 1.79273I −10.82224 + 3.56301I
u = 1.024400 − 0.790762I
a = −0.325907 + 0.530025I
b = 0.085266 + 0.800669I
−2.42816 + 1.79273I −10.82224 − 3.56301I
u = −0.608120 + 0.044532I
a = 0.92099 + 1.09142I
b = −0.608676 − 0.622702I
8.44045 − 8.43585I −1.95973 + 4.08065I
u = −0.608120 − 0.044532I
a = 0.92099 − 1.09142I
b = −0.608676 + 0.622702I
8.44045 + 8.43585I −1.95973 − 4.08065I
u = 0.192459 + 0.537307I
a = −1.411040 − 0.031910I
b = −0.254422 − 0.764305I
−2.42611 − 2.12413I −9.83324 + 4.10839I
u = 0.192459 − 0.537307I
a = −1.411040 + 0.031910I
b = −0.254422 + 0.764305I
−2.42611 + 2.12413I −9.83324 − 4.10839I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.507414 + 0.170111I
a = 0.10803 − 2.51060I
b = 0.481898 − 1.255540I
−0.47711 − 2.32001I 17.0909 − 12.5042I
u = 0.507414 − 0.170111I
a = 0.10803 + 2.51060I
b = 0.481898 + 1.255540I
−0.47711 + 2.32001I 17.0909 + 12.5042I
u = 1.05623 + 1.06802I
a = 0.138131 + 0.911593I
b = −0.827700 + 1.110380I
−1.89257 − 6.00486I −6.00000 + 3.86001I
u = 1.05623 − 1.06802I
a = 0.138131 − 0.911593I
b = −0.827700 − 1.110380I
−1.89257 + 6.00486I −6.00000 − 3.86001I
u = −0.401084 + 0.262695I
a = −0.11004 − 1.70706I
b = 0.492569 + 0.655767I
−0.03830 − 5.91440I −3.99077 + 5.88417I
u = −0.401084 − 0.262695I
a = −0.11004 + 1.70706I
b = 0.492569 − 0.655767I
−0.03830 + 5.91440I −3.99077 − 5.88417I
u = 1.44802 + 0.65854I
a = 0.119183 + 0.619386I
b = −0.235311 + 0.975369I
4.14174 − 2.33203I 0
u = 1.44802 − 0.65854I
a = 0.119183 − 0.619386I
b = −0.235311 − 0.975369I
4.14174 + 2.33203I 0
u = 1.10164 + 1.20126I
a = −0.179933 − 0.841039I
b = 0.812088 − 1.142670I
5.53268 − 6.52999I 0
u = 1.10164 − 1.20126I
a = −0.179933 + 0.841039I
b = 0.812088 + 1.142670I
5.53268 + 6.52999I 0
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.81198 + 2.09035I
a = 0.170657 + 0.083688I
b = −0.036369 + 0.424686I
1.90327 − 0.91976I 0
u = 0.81198 − 2.09035I
a = 0.170657 − 0.083688I
b = −0.036369 − 0.424686I
1.90327 + 0.91976I 0
26
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
((u
19
+ 3u
18
+ ··· + 2u + 1)
4
)(u
22
− 4u
21
+ ··· − 8u + 1)
· (u
43
− 9u
42
+ ··· − 172u + 16)
c
2
, c
10
(u
22
+ 6u
20
+ ··· − u + 1)(u
43
− 2u
41
+ ··· − 2u + 1)
· (u
76
+ 3u
75
+ ··· + 2u + 1)
c
3
, c
9
(u
22
− u
21
+ ··· − 2u + 2)(u
43
− u
42
+ ··· − 16u + 2)
· (u
76
+ u
75
+ ··· − 44450u + 29629)
c
4
, c
5
((u
19
+ 3u
18
+ ··· + 2u + 1)
4
)(u
22
+ 4u
21
+ ··· + 8u + 1)
· (u
43
− 9u
42
+ ··· − 172u + 16)
c
6
((u
2
+ u + 1)
38
)(u
22
− u
21
+ ··· − 8u + 2)
· (u
43
− 32u
42
+ ··· − 7864320u + 524288)
c
7
((u
19
+ 9u
18
+ ··· + 5u
2
− 1)
4
)(u
22
− 13u
21
+ ··· − 5u + 1)
· (u
43
− 28u
42
+ ··· − 18u + 4)
c
8
, c
11
(u
22
+ 5u
21
+ ··· + 3u + 1)(u
43
+ 3u
42
+ ··· + 20u + 1)
· (u
76
+ u
75
+ ··· − 12u + 1)
27
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
12
((y
19
+ 23y
18
+ ··· − 10y −1)
4
)(y
22
+ 28y
21
+ ··· + 16y + 1)
· (y
43
+ 51y
42
+ ··· − 3536y −256)
c
2
, c
10
(y
22
+ 12y
21
+ ··· + 21y + 1)(y
43
− 4y
42
+ ··· + 8y −1)
· (y
76
+ 27y
75
+ ··· + 120y + 1)
c
3
, c
9
(y
22
− 5y
21
+ ··· − 24y + 4)(y
43
− 9y
42
+ ··· + 96y −4)
· (y
76
− 17y
75
+ ··· − 10612715258y + 877877641)
c
6
((y
2
+ y + 1)
38
)(y
22
+ 17y
21
+ ··· + 20y + 4)
· (y
43
+ 18y
42
+ ··· − 137438953472y −274877906944)
c
7
((y
19
− y
18
+ ··· + 10y −1)
4
)(y
22
+ 3y
21
+ ··· − 9y + 1)
· (y
43
+ 2y
42
+ ··· + 668y −16)
c
8
, c
11
(y
22
− 5y
21
+ ··· + 3y + 1)(y
43
+ 23y
42
+ ··· + 94y −1)
· (y
76
− 9y
75
+ ··· − 56y + 1)
28
