12n
0780
(K12n
0780
)
A knot diagram
1
Linearized knot diagam
4 7 9 12 8 2 11 2 1 7 5 10
Solving Sequence
1,4 2,10
9 3 8 12 5 6 11 7
c
1
c
9
c
3
c
8
c
12
c
4
c
5
c
11
c
7
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.42402 × 10
224
u
66
+ 2.00218 × 10
225
u
65
+ ··· + 1.65127 × 10
226
b − 1.54654 × 10
227
,
− 8.95512 × 10
225
u
66
− 7.50188 × 10
226
u
65
+ ··· + 9.90762 × 10
226
a + 5.44058 × 10
227
,
u
67
+ 8u
66
+ ··· − 598u − 48i
I
u
2
= h−2.15444 × 10
23
u
24
+ 2.41942 × 10
24
u
23
+ ··· + 2.49434 × 10
24
b + 2.77494 × 10
24
,
− 3.61629 × 10
24
u
24
+ 3.77069 × 10
25
u
23
+ ··· + 1.74604 × 10
25
a + 3.58327 × 10
24
,
u
25
− 11u
24
+ ··· + 51u − 7i
I
v
1
= ha, 2b − v + 1, v
2
− 3v + 4i
* 3 irreducible components of dim
C
= 0, with total 94 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
= h2.42 × 10
224
u
66
+ 2.00 × 10
225
u
65
+ · · · + 1.65 × 10
226
b − 1.55 ×
10
227
, −8.96 × 10
225
u
66
− 7.50 × 10
226
u
65
+ · · · + 9.91 × 10
226
a + 5.44 ×
10
227
, u
67
+ 8u
66
+ · · · − 598u − 48i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
10
=
0.0903862u
66
+ 0.757183u
65
+ ··· − 100.129u − 5.49131
−0.0146797u
66
− 0.121251u
65
+ ··· + 90.1351u + 9.36578
a
9
=
0.105066u
66
+ 0.878433u
65
+ ··· − 190.264u − 14.8571
−0.0146797u
66
− 0.121251u
65
+ ··· + 90.1351u + 9.36578
a
3
=
−0.316944u
66
− 2.33594u
65
+ ··· + 34.2884u − 1.14896
0.0203404u
66
+ 0.157212u
65
+ ··· − 22.0154u − 2.92085
a
8
=
0.138386u
66
+ 1.12730u
65
+ ··· − 127.840u − 7.31080
−0.0267518u
66
− 0.203790u
65
+ ··· + 81.1568u + 8.51674
a
12
=
−0.120970u
66
− 0.923504u
65
+ ··· + 155.057u + 11.2619
−0.0601185u
66
− 0.457036u
65
+ ··· + 28.2253u − 3.11159
a
5
=
0.0176294u
66
+ 0.156245u
65
+ ··· − 141.488u − 18.4618
0.131111u
66
+ 1.00844u
65
+ ··· − 242.412u − 24.2320
a
6
=
−0.0853676u
66
− 0.733079u
65
+ ··· + 209.833u + 19.9855
0.0109540u
66
+ 0.0742912u
65
+ ··· + 25.5932u + 2.90497
a
11
=
0.0720095u
66
+ 0.637377u
65
+ ··· − 191.893u − 18.0819
0.00236196u
66
+ 0.0159828u
65
+ ··· − 32.0071u − 3.14112
a
7
=
−0.0406592u
66
− 0.381310u
65
+ ··· + 150.160u + 14.6740
0.00155579u
66
+ 0.00725932u
65
+ ··· + 24.2117u + 2.62182
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.129023u
66
+ 1.04913u
65
+ ··· − 649.812u − 68.5329
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
67
− 8u
66
+ ··· − 598u + 48
c
2
, c
6
u
67
− 2u
66
+ ··· − 184950u + 8611
c
3
u
67
− 2u
66
+ ··· + 506387u + 120502
c
4
, c
11
u
67
+ 2u
66
+ ··· − 1717u + 199
c
5
2(2u
67
+ 3u
66
+ ··· + 3752u + 1330)
c
7
, c
10
u
67
− 2u
66
+ ··· + 1457u + 111
c
8
2(2u
67
+ u
66
+ ··· + 100416u + 88717)
c
9
, c
12
2(2u
67
+ 9u
66
+ ··· + 273u + 49)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
67
+ 2y
66
+ ··· − 58268y −2304
c
2
, c
6
y
67
+ 88y
66
+ ··· + 11021281668y −74149321
c
3
y
67
+ 30y
66
+ ··· − 216276728819y −14520732004
c
4
, c
11
y
67
+ 56y
66
+ ··· + 831923y −39601
c
5
4(4y
67
− 381y
66
+ ··· + 1.04728 × 10
8
y −1768900)
c
7
, c
10
y
67
− 56y
66
+ ··· + 1050589y −12321
c
8
4(4y
67
+ 383y
66
+ ··· − 1.06484 × 10
10
y −7.87071 × 10
9
)
c
9
, c
12
4(4y
67
+ 151y
66
+ ··· + 46305y −2401)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.724892 + 0.650339I
a = −0.45501 + 1.66338I
b = 0.708973 + 1.177730I
2.68181 + 8.64984I 0
u = −0.724892 − 0.650339I
a = −0.45501 − 1.66338I
b = 0.708973 − 1.177730I
2.68181 − 8.64984I 0
u = −0.925311 + 0.518203I
a = −0.236215 + 0.952903I
b = −0.45135 + 1.57905I
5.65075 − 2.56848I 0
u = −0.925311 − 0.518203I
a = −0.236215 − 0.952903I
b = −0.45135 − 1.57905I
5.65075 + 2.56848I 0
u = −0.567450 + 0.740677I
a = −0.227677 − 0.429310I
b = 0.476350 − 0.786922I
3.15388 + 0.99673I 0
u = −0.567450 − 0.740677I
a = −0.227677 + 0.429310I
b = 0.476350 + 0.786922I
3.15388 − 0.99673I 0
u = 0.748232 + 0.765006I
a = 0.557690 + 0.645886I
b = −0.600409 + 1.115360I
−1.01345 − 4.59612I 0
u = 0.748232 − 0.765006I
a = 0.557690 − 0.645886I
b = −0.600409 − 1.115360I
−1.01345 + 4.59612I 0
u = −0.669280 + 0.518896I
a = 0.27800 − 1.92075I
b = −0.504373 − 1.113640I
−0.16240 + 3.55156I −2.00000 − 2.68185I
u = −0.669280 − 0.518896I
a = 0.27800 + 1.92075I
b = −0.504373 + 1.113640I
−0.16240 − 3.55156I −2.00000 + 2.68185I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.094927 + 0.818059I
a = −0.199188 − 0.197329I
b = −0.914468 + 0.289293I
2.29919 − 1.44328I 0. + 4.87495I
u = 0.094927 − 0.818059I
a = −0.199188 + 0.197329I
b = −0.914468 − 0.289293I
2.29919 + 1.44328I 0. − 4.87495I
u = −0.835696 + 0.854025I
a = 0.340039 − 0.512207I
b = −1.027810 + 0.126765I
10.80940 + 3.04943I 0
u = −0.835696 − 0.854025I
a = 0.340039 + 0.512207I
b = −1.027810 − 0.126765I
10.80940 − 3.04943I 0
u = 0.426807 + 0.561222I
a = 2.47624 + 1.14400I
b = −0.368194 + 0.763988I
0.086574 − 0.675649I 0.57492 + 6.89256I
u = 0.426807 − 0.561222I
a = 2.47624 − 1.14400I
b = −0.368194 − 0.763988I
0.086574 + 0.675649I 0.57492 − 6.89256I
u = −0.211898 + 1.285080I
a = 0.324960 − 0.022923I
b = 0.412381 − 0.725580I
5.14094 − 4.36853I 0
u = −0.211898 − 1.285080I
a = 0.324960 + 0.022923I
b = 0.412381 + 0.725580I
5.14094 + 4.36853I 0
u = −0.148016 + 1.299050I
a = −0.487670 − 0.430571I
b = 0.476579 + 1.076290I
12.03620 + 0.40499I 0
u = −0.148016 − 1.299050I
a = −0.487670 + 0.430571I
b = 0.476579 − 1.076290I
12.03620 − 0.40499I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.813988 + 1.032320I
a = 0.151949 − 0.237008I
b = 1.314940 − 0.427650I
15.7564 + 8.7654I 0
u = −0.813988 − 1.032320I
a = 0.151949 + 0.237008I
b = 1.314940 + 0.427650I
15.7564 − 8.7654I 0
u = −0.133283 + 0.663172I
a = 1.81112 − 0.09469I
b = −0.447751 − 0.987023I
−0.79766 + 2.78003I 0.63579 − 1.56020I
u = −0.133283 − 0.663172I
a = 1.81112 + 0.09469I
b = −0.447751 + 0.987023I
−0.79766 − 2.78003I 0.63579 + 1.56020I
u = 0.468554 + 0.460116I
a = 0.447575 + 0.766561I
b = 1.54432 + 0.45161I
5.57514 + 1.10673I 1.35083 + 4.91539I
u = 0.468554 − 0.460116I
a = 0.447575 − 0.766561I
b = 1.54432 − 0.45161I
5.57514 − 1.10673I 1.35083 − 4.91539I
u = −0.250308 + 1.328670I
a = 0.337131 + 0.456800I
b = −0.252963 − 0.418558I
8.44639 + 2.67875I 0
u = −0.250308 − 1.328670I
a = 0.337131 − 0.456800I
b = −0.252963 + 0.418558I
8.44639 − 2.67875I 0
u = 1.051200 + 0.850832I
a = −0.779289 − 0.897029I
b = 0.086402 − 1.119550I
−3.58384 − 0.97175I 0
u = 1.051200 − 0.850832I
a = −0.779289 + 0.897029I
b = 0.086402 + 1.119550I
−3.58384 + 0.97175I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.945508 + 0.971914I
a = −0.792434 + 0.981469I
b = 0.472404 + 0.891290I
2.86919 + 4.89934I 0
u = −0.945508 − 0.971914I
a = −0.792434 − 0.981469I
b = 0.472404 − 0.891290I
2.86919 − 4.89934I 0
u = 0.980558 + 0.951830I
a = −0.40866 − 1.80636I
b = 0.528089 − 0.965307I
4.86085 − 6.32955I 0
u = 0.980558 − 0.951830I
a = −0.40866 + 1.80636I
b = 0.528089 + 0.965307I
4.86085 + 6.32955I 0
u = −0.757255 + 1.144680I
a = 1.067290 − 0.843683I
b = −0.600703 − 1.255410I
7.43131 + 8.78239I 0
u = −0.757255 − 1.144680I
a = 1.067290 + 0.843683I
b = −0.600703 + 1.255410I
7.43131 − 8.78239I 0
u = −0.503451 + 0.296390I
a = −1.42130 + 1.77557I
b = 0.045681 + 1.055430I
−2.32732 − 1.50510I −3.62508 + 4.84160I
u = −0.503451 − 0.296390I
a = −1.42130 − 1.77557I
b = 0.045681 − 1.055430I
−2.32732 + 1.50510I −3.62508 − 4.84160I
u = −0.408007 + 0.388335I
a = 0.41552 + 2.37315I
b = 0.461414 + 1.065220I
4.05029 − 0.69376I −0.95573 + 1.56415I
u = −0.408007 − 0.388335I
a = 0.41552 − 2.37315I
b = 0.461414 − 1.065220I
4.05029 + 0.69376I −0.95573 − 1.56415I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.270314 + 0.480681I
a = −4.96634 − 0.63452I
b = 0.404961 − 0.576990I
13.7431 − 3.4268I 5.66546 + 7.15698I
u = −0.270314 − 0.480681I
a = −4.96634 + 0.63452I
b = 0.404961 + 0.576990I
13.7431 + 3.4268I 5.66546 − 7.15698I
u = 1.01283 + 1.06302I
a = 0.306569 + 1.174990I
b = −0.46399 + 1.41018I
−2.96983 − 6.50647I 0
u = 1.01283 − 1.06302I
a = 0.306569 − 1.174990I
b = −0.46399 − 1.41018I
−2.96983 + 6.50647I 0
u = 0.522826
a = −0.906766
b = 0.155835
−0.851902 −11.8250
u = −1.38220 + 0.58366I
a = −0.06273 + 1.82082I
b = 0.493648 + 0.588432I
14.0188 − 2.1719I 0
u = −1.38220 − 0.58366I
a = −0.06273 − 1.82082I
b = 0.493648 − 0.588432I
14.0188 + 2.1719I 0
u = 0.61363 + 1.42565I
a = 0.191494 + 0.172346I
b = 0.511973 + 0.704030I
5.71379 − 2.08750I 0
u = 0.61363 − 1.42565I
a = 0.191494 − 0.172346I
b = 0.511973 − 0.704030I
5.71379 + 2.08750I 0
u = 1.31384 + 0.87886I
a = −0.186926 − 1.174250I
b = 0.751276 − 1.187270I
3.15397 − 6.00794I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.31384 − 0.87886I
a = −0.186926 + 1.174250I
b = 0.751276 + 1.187270I
3.15397 + 6.00794I 0
u = 0.042146 + 0.364830I
a = 0.616885 − 1.221060I
b = −0.622839 − 0.246111I
1.50095 + 0.26981I 5.70736 − 1.09398I
u = 0.042146 − 0.364830I
a = 0.616885 + 1.221060I
b = −0.622839 + 0.246111I
1.50095 − 0.26981I 5.70736 + 1.09398I
u = 1.62809 + 0.28245I
a = −0.631173 − 1.101710I
b = −0.014280 − 0.901427I
−3.75621 + 0.09719I 0
u = 1.62809 − 0.28245I
a = −0.631173 + 1.101710I
b = −0.014280 + 0.901427I
−3.75621 − 0.09719I 0
u = −1.13711 + 1.26548I
a = −0.449814 + 1.224260I
b = 0.76542 + 1.28283I
12.9901 + 15.9614I 0
u = −1.13711 − 1.26548I
a = −0.449814 − 1.224260I
b = 0.76542 − 1.28283I
12.9901 − 15.9614I 0
u = −0.178247 + 0.217967I
a = 1.47892 + 1.81066I
b = −0.05878 + 1.95338I
4.44006 − 0.58389I 0.23132 − 12.75139I
u = −0.178247 − 0.217967I
a = 1.47892 − 1.81066I
b = −0.05878 − 1.95338I
4.44006 + 0.58389I 0.23132 + 12.75139I
u = −0.81250 + 1.51648I
a = −0.044626 + 0.509445I
b = −0.645926 + 0.509503I
9.29444 + 2.41886I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.81250 − 1.51648I
a = −0.044626 − 0.509445I
b = −0.645926 − 0.509503I
9.29444 − 2.41886I 0
u = 1.85972 + 0.09589I
a = −0.133611 − 1.239450I
b = −0.237674 − 0.886602I
−4.56426 + 0.98558I 0
u = 1.85972 − 0.09589I
a = −0.133611 + 1.239450I
b = −0.237674 + 0.886602I
−4.56426 − 0.98558I 0
u = −1.38760 + 1.28625I
a = 0.306616 − 1.314680I
b = −0.603081 − 1.058240I
7.65998 + 7.36772I 0
u = −1.38760 − 1.28625I
a = 0.306616 + 1.314680I
b = −0.603081 + 1.058240I
7.65998 − 7.36772I 0
u = −1.43963 + 1.35722I
a = 0.286381 − 0.678767I
b = 0.531858 − 1.051630I
12.50620 − 6.44912I 0
u = −1.43963 − 1.35722I
a = 0.286381 + 0.678767I
b = 0.531858 + 1.051630I
12.50620 + 6.44912I 0
11
II. I
u
2
= h−2.15 × 10
23
u
24
+ 2.42 × 10
24
u
23
+ · · · + 2.49 × 10
24
b + 2.77 ×
10
24
, −3.62 × 10
24
u
24
+ 3.77 × 10
25
u
23
+ · · · + 1.75 × 10
25
a + 3.58 ×
10
24
, u
25
− 11u
24
+ · · · + 51u − 7i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
10
=
0.207114u
24
− 2.15957u
23
+ ··· + 0.893359u − 0.205222
0.0863732u
24
− 0.969963u
23
+ ··· + 0.963679u − 1.11249
a
9
=
0.120740u
24
− 1.18960u
23
+ ··· − 0.0703196u + 0.907269
0.0863732u
24
− 0.969963u
23
+ ··· + 0.963679u − 1.11249
a
3
=
−0.161700u
24
+ 1.67399u
23
+ ··· + 9.49049u − 1.34021
0.146730u
24
− 1.50806u
23
+ ··· − 8.85768u + 1.02341
a
8
=
0.165263u
24
− 1.62427u
23
+ ··· + 7.11373u − 1.17500
0.149537u
24
− 1.57324u
23
+ ··· − 1.53381u − 0.726923
a
12
=
0.389064u
24
− 4.16420u
23
+ ··· − 44.1399u + 6.12234
0.242863u
24
− 2.70271u
23
+ ··· − 49.7547u + 7.52376
a
5
=
−0.301472u
24
+ 3.18495u
23
+ ··· + 4.97739u + 0.806735
−0.261937u
24
+ 2.85038u
23
+ ··· + 15.6017u + 0.776526
a
6
=
−0.126122u
24
+ 1.41715u
23
+ ··· + 25.6831u − 4.32152
0.117110u
24
− 1.23278u
23
+ ··· − 3.36207u + 0.462233
a
11
=
0.207012u
24
− 2.14134u
23
+ ··· − 9.69981u + 2.11080
0.0785433u
24
− 0.874037u
23
+ ··· + 0.310348u − 0.875109
a
7
=
−0.196251u
24
+ 2.17415u
23
+ ··· + 26.6422u − 4.57511
0.142085u
24
− 1.49552u
23
+ ··· − 3.11722u + 0.361246
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
4632133958374614897414942
2494343012093848286566241
u
24
+
51382786867744495621657764
2494343012093848286566241
u
23
+
··· +
662500251813301072900532963
2494343012093848286566241
u −
78942529084008091571332926
2494343012093848286566241
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
25
− 11u
24
+ ··· + 51u − 7
c
2
u
25
+ u
24
+ ··· − 2u − 1
c
3
u
25
+ u
23
+ ··· + u
2
+ 1
c
4
u
25
− 3u
24
+ ··· − 11u + 11
c
5
u
25
+ 16u
24
+ ··· + 153u + 31
c
6
u
25
− u
24
+ ··· − 2u + 1
c
7
u
25
− 7u
24
+ ··· − 5u + 1
c
8
u
25
+ 5u
23
+ ··· + 33u + 11
c
9
u
25
+ 2u
24
+ ··· + 2u
2
+ 1
c
10
u
25
+ 7u
24
+ ··· − 5u − 1
c
11
u
25
+ 3u
24
+ ··· − 11u − 11
c
12
u
25
− 2u
24
+ ··· − 2u
2
− 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
− 7y
24
+ ··· − 535y −49
c
2
, c
6
y
25
+ 17y
24
+ ··· + 10y −1
c
3
y
25
+ 2y
24
+ ··· − 2y −1
c
4
, c
11
y
25
+ 21y
24
+ ··· − 1155y −121
c
5
y
25
− 32y
24
+ ··· + 5801y −961
c
7
, c
10
y
25
− 11y
24
+ ··· + 11y −1
c
8
y
25
+ 10y
24
+ ··· + 4851y −121
c
9
, c
12
y
25
+ 20y
24
+ ··· − 4y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.873017 + 0.521357I
a = −2.17789 + 2.09736I
b = −0.118295 + 0.555686I
13.21080 − 2.99397I −3.88960 + 0.65192I
u = −0.873017 − 0.521357I
a = −2.17789 − 2.09736I
b = −0.118295 − 0.555686I
13.21080 + 2.99397I −3.88960 − 0.65192I
u = 0.638842 + 0.658318I
a = −1.262000 − 0.515540I
b = 0.517828 − 1.026310I
−1.63015 − 3.73279I −3.58443 + 3.77316I
u = 0.638842 − 0.658318I
a = −1.262000 + 0.515540I
b = 0.517828 + 1.026310I
−1.63015 + 3.73279I −3.58443 − 3.77316I
u = 0.285038 + 1.141820I
a = −0.653935 + 0.058789I
b = −0.317460 − 0.222677I
5.23338 − 3.15853I −0.40044 + 3.09681I
u = 0.285038 − 1.141820I
a = −0.653935 − 0.058789I
b = −0.317460 + 0.222677I
5.23338 + 3.15853I −0.40044 − 3.09681I
u = 1.110010 + 0.556593I
a = 0.11010 + 1.42617I
b = −0.657406 + 1.201350I
1.60179 − 8.35296I −2.83402 + 5.66180I
u = 1.110010 − 0.556593I
a = 0.11010 − 1.42617I
b = −0.657406 − 1.201350I
1.60179 + 8.35296I −2.83402 − 5.66180I
u = 0.859581 + 0.916668I
a = 0.934455 + 0.778615I
b = −0.140802 + 1.213470I
−3.05368 − 0.24758I −0.95829 − 1.44670I
u = 0.859581 − 0.916668I
a = 0.934455 − 0.778615I
b = −0.140802 − 1.213470I
−3.05368 + 0.24758I −0.95829 + 1.44670I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.885359 + 0.961472I
a = −0.667102 + 1.139400I
b = 0.624827 + 0.961509I
3.43246 + 5.41653I 3.68615 − 6.97433I
u = −0.885359 − 0.961472I
a = −0.667102 − 1.139400I
b = 0.624827 − 0.961509I
3.43246 − 5.41653I 3.68615 + 6.97433I
u = −0.297921 + 0.582459I
a = 0.349297 − 0.385458I
b = 1.14999 − 0.96619I
3.78337 − 0.31702I 5.23660 − 3.93151I
u = −0.297921 − 0.582459I
a = 0.349297 + 0.385458I
b = 1.14999 + 0.96619I
3.78337 + 0.31702I 5.23660 + 3.93151I
u = 0.95238 + 1.05184I
a = −0.343147 − 1.153870I
b = 0.47644 − 1.45581I
−2.58834 − 6.55163I 6.70727 + 8.22356I
u = 0.95238 − 1.05184I
a = −0.343147 + 1.153870I
b = 0.47644 + 1.45581I
−2.58834 + 6.55163I 6.70727 − 8.22356I
u = 0.475102
a = 1.15437
b = 0.355743
0.389428 −2.67250
u = −0.26586 + 1.57538I
a = 0.303847 + 0.011380I
b = −0.180186 − 0.761078I
7.76670 + 2.88354I −2.00000 − 4.28447I
u = −0.26586 − 1.57538I
a = 0.303847 − 0.011380I
b = −0.180186 + 0.761078I
7.76670 − 2.88354I −2.00000 + 4.28447I
u = 0.115239 + 0.324580I
a = 0.30974 + 1.92571I
b = −0.96787 + 1.84409I
4.66627 + 0.68818I 22.6012 + 6.6797I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.115239 − 0.324580I
a = 0.30974 − 1.92571I
b = −0.96787 − 1.84409I
4.66627 − 0.68818I 22.6012 − 6.6797I
u = 1.77458 + 0.26650I
a = 0.404449 + 1.197080I
b = 0.036023 + 0.937294I
−4.90145 + 0.19049I −9.88934 + 0.I
u = 1.77458 − 0.26650I
a = 0.404449 − 1.197080I
b = 0.036023 − 0.937294I
−4.90145 − 0.19049I −9.88934 + 0.I
u = 1.84893 + 0.28181I
a = 0.186439 + 1.197460I
b = 0.399041 + 0.896974I
−3.04190 + 1.64191I 0
u = 1.84893 − 0.28181I
a = 0.186439 − 1.197460I
b = 0.399041 − 0.896974I
−3.04190 − 1.64191I 0
19
III. I
v
1
= ha, 2b − v + 1, v
2
− 3v + 4i
(i) Arc colorings
a
1
=
1
0
a
4
=
v
0
a
2
=
1
0
a
10
=
0
1
2
v −
1
2
a
9
=
−
1
2
v +
1
2
1
2
v −
1
2
a
3
=
v − 1
1
a
8
=
0
1
2
v −
1
2
a
12
=
1
1
4
v −
3
4
a
5
=
v − 1
−
1
4
v +
3
4
a
6
=
v − 1
1
a
11
=
−v + 2
1
2
v −
3
2
a
7
=
v − 2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
45
16
v −
91
16
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
c
2
, c
10
, c
11
(u − 1)
2
c
3
u
2
+ u + 2
c
4
, c
6
, c
7
(u + 1)
2
c
5
2(2u
2
+ 3u + 2)
c
8
, c
9
2(2u
2
+ u + 1)
c
12
2(2u
2
− u + 1)
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
2
c
2
, c
4
, c
6
c
7
, c
10
, c
11
(y − 1)
2
c
3
y
2
+ 3y + 4
c
5
4(4y
2
− y + 4)
c
8
, c
9
, c
12
4(4y
2
+ 3y + 1)
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.50000 + 1.32288I
a = 0
b = 0.250000 + 0.661438I
0 −1.46875 + 3.72059I
v = 1.50000 − 1.32288I
a = 0
b = 0.250000 − 0.661438I
0 −1.46875 − 3.72059I
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u
25
− 11u
24
+ ··· + 51u − 7)(u
67
− 8u
66
+ ··· − 598u + 48)
c
2
((u − 1)
2
)(u
25
+ u
24
+ ··· − 2u − 1)(u
67
− 2u
66
+ ··· − 184950u + 8611)
c
3
(u
2
+ u + 2)(u
25
+ u
23
+ ··· + u
2
+ 1)
· (u
67
− 2u
66
+ ··· + 506387u + 120502)
c
4
((u + 1)
2
)(u
25
− 3u
24
+ ··· − 11u + 11)(u
67
+ 2u
66
+ ··· − 1717u + 199)
c
5
4(2u
2
+ 3u + 2)(u
25
+ 16u
24
+ ··· + 153u + 31)
· (2u
67
+ 3u
66
+ ··· + 3752u + 1330)
c
6
((u + 1)
2
)(u
25
− u
24
+ ··· − 2u + 1)(u
67
− 2u
66
+ ··· − 184950u + 8611)
c
7
((u + 1)
2
)(u
25
− 7u
24
+ ··· − 5u + 1)(u
67
− 2u
66
+ ··· + 1457u + 111)
c
8
4(2u
2
+ u + 1)(u
25
+ 5u
23
+ ··· + 33u + 11)
· (2u
67
+ u
66
+ ··· + 100416u + 88717)
c
9
4(2u
2
+ u + 1)(u
25
+ 2u
24
+ ··· + 2u
2
+ 1)
· (2u
67
+ 9u
66
+ ··· + 273u + 49)
c
10
((u − 1)
2
)(u
25
+ 7u
24
+ ··· − 5u − 1)(u
67
− 2u
66
+ ··· + 1457u + 111)
c
11
((u − 1)
2
)(u
25
+ 3u
24
+ ··· − 11u − 11)(u
67
+ 2u
66
+ ··· − 1717u + 199)
c
12
4(2u
2
− u + 1)(u
25
− 2u
24
+ ··· − 2u
2
− 1)
· (2u
67
+ 9u
66
+ ··· + 273u + 49)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
2
(y
25
− 7y
24
+ ··· − 535y − 49)(y
67
+ 2y
66
+ ··· − 58268y − 2304)
c
2
, c
6
((y − 1)
2
)(y
25
+ 17y
24
+ ··· + 10y − 1)
· (y
67
+ 88y
66
+ ··· + 11021281668y − 74149321)
c
3
(y
2
+ 3y + 4)(y
25
+ 2y
24
+ ··· − 2y − 1)
· (y
67
+ 30y
66
+ ··· − 216276728819y − 14520732004)
c
4
, c
11
((y − 1)
2
)(y
25
+ 21y
24
+ ··· − 1155y − 121)
· (y
67
+ 56y
66
+ ··· + 831923y − 39601)
c
5
16(4y
2
− y + 4)(y
25
− 32y
24
+ ··· + 5801y − 961)
· (4y
67
− 381y
66
+ ··· + 104727644y − 1768900)
c
7
, c
10
((y − 1)
2
)(y
25
− 11y
24
+ ··· + 11y − 1)
· (y
67
− 56y
66
+ ··· + 1050589y − 12321)
c
8
16(4y
2
+ 3y + 1)(y
25
+ 10y
24
+ ··· + 4851y − 121)
· (4y
67
+ 383y
66
+ ··· − 10648370372y − 7870706089)
c
9
, c
12
16(4y
2
+ 3y + 1)(y
25
+ 20y
24
+ ··· − 4y − 1)
· (4y
67
+ 151y
66
+ ··· + 46305y − 2401)
25
