12a
0672
(K12a
0672
)
A knot diagram
1
Linearized knot diagam
3 7 11 9 10 2 6 12 1 8 4 5
Solving Sequence
2,6
7 3
8,10
11 1 5 9 4 12
c
6
c
2
c
7
c
10
c
1
c
5
c
9
c
4
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.12902 × 10
190
u
139
+ 9.34933 × 10
189
u
138
+ ··· + 1.58755 × 10
189
b − 1.09247 × 10
190
,
3.44317 × 10
189
u
139
− 4.78461 × 10
189
u
138
+ ··· + 1.58755 × 10
189
a + 2.42089 × 10
189
,
u
140
− 23u
138
+ ··· + 3u + 1i
I
u
2
= h2u
26
− 9u
24
+ ··· + b + 1, −7u
26
+ 2u
25
+ ··· + a − 5, u
27
− 5u
25
+ ··· + 2u + 1i
I
u
3
= h−u
2
+ b, a − 1, u
9
− u
7
+ u
5
− u − 1i
I
u
4
= hb − 1, a − 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 177 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−1.13 × 10
190
u
139
+ 9.35 × 10
189
u
138
+ · · · + 1.59 × 10
189
b − 1.09 ×
10
190
, 3.44 × 10
189
u
139
− 4.78 × 10
189
u
138
+ · · · + 1.59 × 10
189
a + 2.42 ×
10
189
, u
140
− 23u
138
+ · · · + 3u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
10
=
−2.16886u
139
+ 3.01383u
138
+ ··· + 8.23078u − 1.52492
7.11170u
139
− 5.88917u
138
+ ··· + 10.0353u + 6.88147
a
11
=
−2.44142u
139
+ 0.866654u
138
+ ··· + 5.48517u − 1.49467
10.2142u
139
− 7.71787u
138
+ ··· + 19.1330u + 10.8573
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
0.750500u
139
− 1.39779u
138
+ ··· − 3.01121u + 1.60235
−10.5023u
139
+ 8.41153u
138
+ ··· − 14.6571u − 11.6073
a
9
=
0.943249u
139
− 1.67414u
138
+ ··· + 18.2542u + 3.74345
12.1315u
139
− 8.89990u
138
+ ··· + 19.8046u + 11.8666
a
4
=
−0.673830u
139
+ 0.601372u
138
+ ··· − 14.0653u + 1.43963
−12.6642u
139
+ 10.6942u
138
+ ··· − 26.6036u − 15.5682
a
12
=
5.96244u
139
+ 1.79950u
138
+ ··· − 1.90249u − 2.91637
12.5060u
139
− 17.4576u
138
+ ··· + 33.8666u + 16.1824
(ii) Obstruction class = −1
(iii) Cusp Shapes = −24.6097u
139
+ 19.1757u
138
+ ··· − 68.5270u − 30.0952
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
140
+ 46u
139
+ ··· + 27u + 1
c
2
, c
6
u
140
− 23u
138
+ ··· + 3u + 1
c
3
, c
11
u
140
− 6u
139
+ ··· − 52600u − 21104
c
4
u
140
+ 5u
139
+ ··· + 35297u − 7759
c
5
u
140
+ u
139
+ ··· + 8346945u + 492823
c
8
u
140
+ u
139
+ ··· − 30u − 1
c
9
u
140
+ 4u
139
+ ··· − 49356u + 1718
c
10
u
140
− 6u
139
+ ··· + 378931u − 19471
c
12
u
140
− 5u
138
+ ··· − 39u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
140
+ 110y
139
+ ··· − 551y + 1
c
2
, c
6
y
140
− 46y
139
+ ··· − 27y + 1
c
3
, c
11
y
140
− 90y
139
+ ··· − 46338922560y + 445378816
c
4
y
140
− 27y
139
+ ··· − 3984913835y + 60202081
c
5
y
140
− 35y
139
+ ··· − 12584572781083y + 242874509329
c
8
y
140
+ 17y
139
+ ··· − 82y + 1
c
9
y
140
+ 4y
139
+ ··· − 573798944y + 2951524
c
10
y
140
− 10y
139
+ ··· − 105927544083y + 379119841
c
12
y
140
− 10y
139
+ ··· − 447y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.637272 + 0.774252I
a = 1.259990 − 0.002369I
b = −1.46338 + 0.19143I
4.03902 − 0.85594I 0
u = −0.637272 − 0.774252I
a = 1.259990 + 0.002369I
b = −1.46338 − 0.19143I
4.03902 + 0.85594I 0
u = 1.011350 + 0.012085I
a = −0.793113 + 0.223949I
b = 0.434213 + 0.174661I
−6.37978 + 0.00238I 0
u = 1.011350 − 0.012085I
a = −0.793113 − 0.223949I
b = 0.434213 − 0.174661I
−6.37978 − 0.00238I 0
u = 1.02392
a = −0.662890
b = 0.547273
−6.37988 0
u = 1.017280 + 0.184941I
a = −0.10014 − 1.71881I
b = 0.907707 − 1.026470I
−2.61394 − 5.50337I 0
u = 1.017280 − 0.184941I
a = −0.10014 + 1.71881I
b = 0.907707 + 1.026470I
−2.61394 + 5.50337I 0
u = 0.960574 + 0.067275I
a = 0.031287 − 1.341240I
b = −0.77872 − 1.36857I
−6.79916 − 5.81167I 0
u = 0.960574 − 0.067275I
a = 0.031287 + 1.341240I
b = −0.77872 + 1.36857I
−6.79916 + 5.81167I 0
u = 0.935095 + 0.212379I
a = −0.99923 − 1.11674I
b = 0.609100 − 0.820049I
−2.75766 − 3.86610I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.935095 − 0.212379I
a = −0.99923 + 1.11674I
b = 0.609100 + 0.820049I
−2.75766 + 3.86610I 0
u = −0.745262 + 0.727310I
a = −1.32678 − 1.06529I
b = 0.29285 + 1.73891I
−1.53936 − 5.19280I 0
u = −0.745262 − 0.727310I
a = −1.32678 + 1.06529I
b = 0.29285 − 1.73891I
−1.53936 + 5.19280I 0
u = −0.879911 + 0.561119I
a = −1.44299 + 1.54598I
b = 0.932754 − 0.266761I
−3.48917 + 5.68868I 0
u = −0.879911 − 0.561119I
a = −1.44299 − 1.54598I
b = 0.932754 + 0.266761I
−3.48917 − 5.68868I 0
u = −0.942327 + 0.122868I
a = 0.449286 + 1.238000I
b = 1.21615 + 0.87500I
−0.41690 + 1.63156I 0
u = −0.942327 − 0.122868I
a = 0.449286 − 1.238000I
b = 1.21615 − 0.87500I
−0.41690 − 1.63156I 0
u = 0.779383 + 0.703759I
a = 0.594080 + 0.164147I
b = −0.284029 + 1.298440I
−1.17235 − 5.37475I 0
u = 0.779383 − 0.703759I
a = 0.594080 − 0.164147I
b = −0.284029 − 1.298440I
−1.17235 + 5.37475I 0
u = 1.028920 + 0.260799I
a = 0.202383 + 1.007000I
b = −1.027600 + 0.942415I
−0.71138 − 8.15105I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.028920 − 0.260799I
a = 0.202383 − 1.007000I
b = −1.027600 − 0.942415I
−0.71138 + 8.15105I 0
u = −0.698027 + 0.608519I
a = 1.240040 − 0.212448I
b = 0.202084 − 0.411980I
−1.78318 − 0.31648I 0
u = −0.698027 − 0.608519I
a = 1.240040 + 0.212448I
b = 0.202084 + 0.411980I
−1.78318 + 0.31648I 0
u = 0.814503 + 0.701975I
a = 2.26007 + 1.41025I
b = −0.482272 − 0.358926I
−1.59077 + 3.20105I 0
u = 0.814503 − 0.701975I
a = 2.26007 − 1.41025I
b = −0.482272 + 0.358926I
−1.59077 − 3.20105I 0
u = 0.753855 + 0.775047I
a = 1.95414 + 1.03664I
b = −1.76398 − 0.64520I
5.39914 + 0.65450I 0
u = 0.753855 − 0.775047I
a = 1.95414 − 1.03664I
b = −1.76398 + 0.64520I
5.39914 − 0.65450I 0
u = −1.056330 + 0.255019I
a = −0.736586 − 0.502673I
b = −0.521953 + 0.416676I
−0.81071 − 1.71202I 0
u = −1.056330 − 0.255019I
a = −0.736586 + 0.502673I
b = −0.521953 − 0.416676I
−0.81071 + 1.71202I 0
u = 0.867566 + 0.659942I
a = 0.92138 − 1.11949I
b = 0.201058 + 1.214890I
2.14246 − 2.56378I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.867566 − 0.659942I
a = 0.92138 + 1.11949I
b = 0.201058 − 1.214890I
2.14246 + 2.56378I 0
u = −0.842091 + 0.343705I
a = −0.82656 + 2.16593I
b = 0.502030 − 0.113865I
−3.58332 + 5.58428I 0
u = −0.842091 − 0.343705I
a = −0.82656 − 2.16593I
b = 0.502030 + 0.113865I
−3.58332 − 5.58428I 0
u = −0.723221 + 0.823322I
a = 1.37155 − 0.80169I
b = −1.24957 + 1.08257I
4.04950 − 4.96120I 0
u = −0.723221 − 0.823322I
a = 1.37155 + 0.80169I
b = −1.24957 − 1.08257I
4.04950 + 4.96120I 0
u = −0.903834 + 0.016154I
a = −1.16716 − 2.44769I
b = 0.474301 − 0.934610I
−5.80281 − 4.37403I 0
u = −0.903834 − 0.016154I
a = −1.16716 + 2.44769I
b = 0.474301 + 0.934610I
−5.80281 + 4.37403I 0
u = 0.825710 + 0.725196I
a = −2.37145 − 1.23965I
b = 1.49023 − 0.63141I
0.76253 − 1.70916I 0
u = 0.825710 − 0.725196I
a = −2.37145 + 1.23965I
b = 1.49023 + 0.63141I
0.76253 + 1.70916I 0
u = 0.755812 + 0.805461I
a = 1.51275 + 0.00873I
b = −1.239210 + 0.216436I
4.70506 − 1.57922I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.755812 − 0.805461I
a = 1.51275 − 0.00873I
b = −1.239210 − 0.216436I
4.70506 + 1.57922I 0
u = −0.909980 + 0.626719I
a = 2.59745 − 0.58433I
b = −1.086080 − 0.753826I
−3.72434 − 0.98515I 0
u = −0.909980 − 0.626719I
a = 2.59745 + 0.58433I
b = −1.086080 + 0.753826I
−3.72434 + 0.98515I 0
u = −0.682246 + 0.872598I
a = −0.819823 + 0.713190I
b = 0.988583 − 0.825638I
0.32816 − 5.72400I 0
u = −0.682246 − 0.872598I
a = −0.819823 − 0.713190I
b = 0.988583 + 0.825638I
0.32816 + 5.72400I 0
u = 0.688053 + 0.882581I
a = −1.51131 − 0.78456I
b = 1.41721 + 0.87490I
1.92917 + 13.82410I 0
u = 0.688053 − 0.882581I
a = −1.51131 + 0.78456I
b = 1.41721 − 0.87490I
1.92917 − 13.82410I 0
u = 0.869980 + 0.708482I
a = −2.43913 + 2.34344I
b = −0.01244 − 3.15134I
0.81893 − 2.71443I 0
u = 0.869980 − 0.708482I
a = −2.43913 − 2.34344I
b = −0.01244 + 3.15134I
0.81893 + 2.71443I 0
u = −0.743353 + 0.852323I
a = −1.53534 + 1.10594I
b = 1.52043 − 0.80465I
6.56077 − 7.34720I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.743353 − 0.852323I
a = −1.53534 − 1.10594I
b = 1.52043 + 0.80465I
6.56077 + 7.34720I 0
u = 0.808654 + 0.795047I
a = −0.84326 − 1.30185I
b = 1.14857 + 0.84874I
3.37292 − 1.72822I 0
u = 0.808654 − 0.795047I
a = −0.84326 + 1.30185I
b = 1.14857 − 0.84874I
3.37292 + 1.72822I 0
u = −0.778044 + 0.839237I
a = 1.48124 − 0.72700I
b = −0.995013 + 0.401193I
3.97627 − 2.35525I 0
u = −0.778044 − 0.839237I
a = 1.48124 + 0.72700I
b = −0.995013 − 0.401193I
3.97627 + 2.35525I 0
u = 0.755240 + 0.861550I
a = −0.744629 + 0.046044I
b = 0.857049 + 0.206186I
6.69538 − 2.46683I 0
u = 0.755240 − 0.861550I
a = −0.744629 − 0.046044I
b = 0.857049 − 0.206186I
6.69538 + 2.46683I 0
u = 0.681796 + 0.920876I
a = 1.37920 + 0.41022I
b = −1.135510 − 0.468563I
1.77849 + 4.30367I 0
u = 0.681796 − 0.920876I
a = 1.37920 − 0.41022I
b = −1.135510 + 0.468563I
1.77849 − 4.30367I 0
u = −0.826457 + 0.794325I
a = 1.202260 − 0.027016I
b = −0.984494 + 0.419369I
6.94462 + 0.32347I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.826457 − 0.794325I
a = 1.202260 + 0.027016I
b = −0.984494 − 0.419369I
6.94462 − 0.32347I 0
u = −0.852687
a = 0.457434
b = −1.66923
−3.61800 0
u = 0.917783 + 0.695410I
a = −2.86701 − 0.05432I
b = 0.606389 − 0.484552I
−1.91229 − 8.57330I 0
u = 0.917783 − 0.695410I
a = −2.86701 + 0.05432I
b = 0.606389 + 0.484552I
−1.91229 + 8.57330I 0
u = −1.134300 + 0.207590I
a = 0.096639 − 1.075190I
b = −1.14181 − 0.89648I
−5.4923 + 13.5525I 0
u = −1.134300 − 0.207590I
a = 0.096639 + 1.075190I
b = −1.14181 + 0.89648I
−5.4923 − 13.5525I 0
u = 0.780067 + 0.855177I
a = 1.169240 − 0.256613I
b = −0.748320 − 0.368537I
3.80136 + 3.65097I 0
u = 0.780067 − 0.855177I
a = 1.169240 + 0.256613I
b = −0.748320 + 0.368537I
3.80136 − 3.65097I 0
u = 0.911894 + 0.713790I
a = 1.56209 + 1.20005I
b = −1.66376 − 0.55939I
0.49607 − 3.78910I 0
u = 0.911894 − 0.713790I
a = 1.56209 − 1.20005I
b = −1.66376 + 0.55939I
0.49607 + 3.78910I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.142360 + 0.194064I
a = −0.021770 + 0.653476I
b = −0.548491 + 0.752756I
−6.96686 − 5.37463I 0
u = 1.142360 − 0.194064I
a = −0.021770 − 0.653476I
b = −0.548491 − 0.752756I
−6.96686 + 5.37463I 0
u = −0.961955 + 0.652383I
a = −0.720924 − 0.064504I
b = 0.122679 − 0.405902I
−2.55925 + 5.34694I 0
u = −0.961955 − 0.652383I
a = −0.720924 + 0.064504I
b = 0.122679 + 0.405902I
−2.55925 − 5.34694I 0
u = −0.821488 + 0.151520I
a = 0.88215 − 1.13546I
b = 0.01092 − 1.59339I
−2.39930 + 0.35910I 0
u = −0.821488 − 0.151520I
a = 0.88215 + 1.13546I
b = 0.01092 + 1.59339I
−2.39930 − 0.35910I 0
u = −0.956096 + 0.673027I
a = 0.253311 + 0.055704I
b = 0.150893 − 0.986242I
−2.29376 + 5.19888I 0
u = −0.956096 − 0.673027I
a = 0.253311 − 0.055704I
b = 0.150893 + 0.986242I
−2.29376 − 5.19888I 0
u = −0.220210 + 0.800606I
a = −0.382355 − 0.292702I
b = 0.598812 + 0.349617I
−2.39895 + 2.29733I 0
u = −0.220210 − 0.800606I
a = −0.382355 + 0.292702I
b = 0.598812 − 0.349617I
−2.39895 − 2.29733I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.822610
a = 0.318844
b = 0.502826
−1.19691 0
u = 0.152222 + 0.806909I
a = −1.214810 + 0.533344I
b = 1.119620 − 0.651030I
−1.13413 − 10.33050I 0
u = 0.152222 − 0.806909I
a = −1.214810 − 0.533344I
b = 1.119620 + 0.651030I
−1.13413 + 10.33050I 0
u = −0.960838 + 0.701466I
a = −1.20259 − 1.18921I
b = −0.47405 + 1.83054I
−2.19001 + 10.66420I 0
u = −0.960838 − 0.701466I
a = −1.20259 + 1.18921I
b = −0.47405 − 1.83054I
−2.19001 − 10.66420I 0
u = 1.118710 + 0.423282I
a = −0.540688 + 0.645565I
b = −0.875083 − 0.618712I
−4.20294 + 5.96067I 0
u = 1.118710 − 0.423282I
a = −0.540688 − 0.645565I
b = −0.875083 + 0.618712I
−4.20294 − 5.96067I 0
u = 0.762326 + 0.243629I
a = 0.54841 − 1.76335I
b = 0.458839 + 0.009570I
0.95809 − 2.33250I 0
u = 0.762326 − 0.243629I
a = 0.54841 + 1.76335I
b = 0.458839 − 0.009570I
0.95809 + 2.33250I 0
u = −0.930379 + 0.764329I
a = −1.47065 + 1.24556I
b = 0.878778 + 0.494336I
6.62280 + 5.53881I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.930379 − 0.764329I
a = −1.47065 − 1.24556I
b = 0.878778 − 0.494336I
6.62280 − 5.53881I 0
u = −0.275713 + 0.743369I
a = 1.71178 + 0.20982I
b = −0.824660 + 0.056725I
−1.54045 − 1.72177I 0
u = −0.275713 − 0.743369I
a = 1.71178 − 0.20982I
b = −0.824660 − 0.056725I
−1.54045 + 1.72177I 0
u = 0.944071 + 0.753450I
a = 2.06751 + 0.23061I
b = −1.16859 + 1.12275I
2.95088 − 4.10114I 0
u = 0.944071 − 0.753450I
a = 2.06751 − 0.23061I
b = −1.16859 − 1.12275I
2.95088 + 4.10114I 0
u = −1.184390 + 0.245273I
a = −0.262272 + 0.668229I
b = 0.784968 + 0.495560I
−6.17296 + 3.76247I 0
u = −1.184390 − 0.245273I
a = −0.262272 − 0.668229I
b = 0.784968 − 0.495560I
−6.17296 − 3.76247I 0
u = 0.969377 + 0.726084I
a = −2.37911 − 1.46880I
b = 1.77426 − 0.80381I
4.74137 − 6.33735I 0
u = 0.969377 − 0.726084I
a = −2.37911 + 1.46880I
b = 1.77426 + 0.80381I
4.74137 + 6.33735I 0
u = −0.861515 + 0.857109I
a = −1.240820 + 0.110008I
b = 1.031860 + 0.056520I
5.09717 + 8.21953I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.861515 − 0.857109I
a = −1.240820 − 0.110008I
b = 1.031860 − 0.056520I
5.09717 − 8.21953I 0
u = 0.977299 + 0.739925I
a = −0.97138 − 1.37098I
b = 1.194840 + 0.066259I
4.02323 − 4.23290I 0
u = 0.977299 − 0.739925I
a = −0.97138 + 1.37098I
b = 1.194840 − 0.066259I
4.02323 + 4.23290I 0
u = −0.919729 + 0.828173I
a = 1.11885 − 0.97074I
b = −0.920706 − 0.035146I
4.90974 − 1.98154I 0
u = −0.919729 − 0.828173I
a = 1.11885 + 0.97074I
b = −0.920706 + 0.035146I
4.90974 + 1.98154I 0
u = −1.033150 + 0.690623I
a = −0.89339 + 1.63972I
b = 1.379040 + 0.302725I
2.84875 + 6.42576I 0
u = −1.033150 − 0.690623I
a = −0.89339 − 1.63972I
b = 1.379040 − 0.302725I
2.84875 − 6.42576I 0
u = −0.980881 + 0.766272I
a = −1.89982 + 0.66124I
b = 1.042310 + 0.536585I
3.34146 + 8.35351I 0
u = −0.980881 − 0.766272I
a = −1.89982 − 0.66124I
b = 1.042310 − 0.536585I
3.34146 − 8.35351I 0
u = −1.001250 + 0.740017I
a = −2.32041 + 1.05029I
b = 1.21937 + 1.18146I
3.19831 + 10.82260I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.001250 − 0.740017I
a = −2.32041 − 1.05029I
b = 1.21937 − 1.18146I
3.19831 − 10.82260I 0
u = −1.142940 + 0.505496I
a = −0.380757 − 0.326254I
b = −0.302817 + 0.260530I
−5.17244 + 2.46080I 0
u = −1.142940 − 0.505496I
a = −0.380757 + 0.326254I
b = −0.302817 − 0.260530I
−5.17244 − 2.46080I 0
u = 0.983424 + 0.777778I
a = −1.35741 − 1.22628I
b = 0.671774 − 0.420681I
3.16545 − 9.73007I 0
u = 0.983424 − 0.777778I
a = −1.35741 + 1.22628I
b = 0.671774 + 0.420681I
3.16545 + 9.73007I 0
u = −1.002890 + 0.762770I
a = 2.20240 − 0.95778I
b = −1.55274 − 0.93729I
5.7588 + 13.3676I 0
u = −1.002890 − 0.762770I
a = 2.20240 + 0.95778I
b = −1.55274 + 0.93729I
5.7588 − 13.3676I 0
u = 1.000110 + 0.776193I
a = 0.775668 + 0.871906I
b = −0.711578 + 0.341181I
5.93962 − 3.62411I 0
u = 1.000110 − 0.776193I
a = 0.775668 − 0.871906I
b = −0.711578 − 0.341181I
5.93962 + 3.62411I 0
u = 1.190310 + 0.445821I
a = −0.037022 − 0.244141I
b = 0.589124 + 0.107887I
−5.07547 − 4.72475I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.190310 − 0.445821I
a = −0.037022 + 0.244141I
b = 0.589124 − 0.107887I
−5.07547 + 4.72475I 0
u = −1.039600 + 0.747334I
a = 1.55290 − 0.63818I
b = −0.969162 − 0.967994I
−0.76957 + 11.74280I 0
u = −1.039600 − 0.747334I
a = 1.55290 + 0.63818I
b = −0.969162 + 0.967994I
−0.76957 − 11.74280I 0
u = 1.041780 + 0.752591I
a = 2.08262 + 1.13547I
b = −1.43012 + 0.96234I
0.8366 − 19.8900I 0
u = 1.041780 − 0.752591I
a = 2.08262 − 1.13547I
b = −1.43012 − 0.96234I
0.8366 + 19.8900I 0
u = 0.001353 + 0.709077I
a = −0.910847 − 0.845959I
b = 0.984833 + 0.520825I
2.63021 + 4.94426I 1.18827 − 5.95348I
u = 0.001353 − 0.709077I
a = −0.910847 + 0.845959I
b = 0.984833 − 0.520825I
2.63021 − 4.94426I 1.18827 + 5.95348I
u = 1.058860 + 0.764070I
a = −1.59765 − 0.98872I
b = 1.167610 − 0.572615I
0.60155 − 10.51070I 0
u = 1.058860 − 0.764070I
a = −1.59765 + 0.98872I
b = 1.167610 + 0.572615I
0.60155 + 10.51070I 0
u = −0.070124 + 0.609912I
a = 1.204140 + 0.383720I
b = −1.009010 − 0.725980I
0.84048 + 2.95141I 1.19411 − 6.24218I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.070124 − 0.609912I
a = 1.204140 − 0.383720I
b = −1.009010 + 0.725980I
0.84048 − 2.95141I 1.19411 + 6.24218I
u = −0.433846 + 0.045603I
a = 3.03223 + 0.18076I
b = 0.954581 − 0.287577I
−2.35372 + 0.01785I −13.3158 + 9.1548I
u = −0.433846 − 0.045603I
a = 3.03223 − 0.18076I
b = 0.954581 + 0.287577I
−2.35372 − 0.01785I −13.3158 − 9.1548I
u = 0.036970 + 0.417867I
a = 1.13295 + 1.25352I
b = −0.178046 − 0.646891I
−0.21087 + 1.54585I −2.00440 − 3.59904I
u = 0.036970 − 0.417867I
a = 1.13295 − 1.25352I
b = −0.178046 + 0.646891I
−0.21087 − 1.54585I −2.00440 + 3.59904I
u = 0.127912 + 0.323579I
a = 1.72370 − 1.12135I
b = −1.147850 + 0.179884I
2.49814 − 0.01830I 6.50419 − 0.26055I
u = 0.127912 − 0.323579I
a = 1.72370 + 1.12135I
b = −1.147850 − 0.179884I
2.49814 + 0.01830I 6.50419 + 0.26055I
u = −0.139509 + 0.207086I
a = −4.19951 − 0.76672I
b = 0.168910 − 1.002310I
−3.61362 + 4.87141I −5.76056 − 5.46607I
u = −0.139509 − 0.207086I
a = −4.19951 + 0.76672I
b = 0.168910 + 1.002310I
−3.61362 − 4.87141I −5.76056 + 5.46607I
u = 0.188479
a = 3.79660
b = −1.20821
2.54627 11.7520
18
II.
I
u
2
= h2u
26
−9u
24
+· · ·+b+1, −7u
26
+2u
25
+· · ·+a−5, u
27
−5u
25
+· · ·+2u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
10
=
7u
26
− 2u
25
+ ··· − 13u + 5
−2u
26
+ 9u
24
+ ··· + 3u − 1
a
11
=
3u
26
− 3u
25
+ ··· − 7u + 2
4u
26
+ u
25
+ ··· + u − 1
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
u
26
+ 7u
25
+ ··· − 16u − 11
4u
26
− 2u
25
+ ··· − 27u
2
+ 5
a
9
=
8u
26
− 40u
24
+ ··· − 20u + 1
−u
26
+ u
25
+ ··· + 3u − 2
a
4
=
u
26
− 3u
25
+ ··· − u − 3
u
26
− 7u
24
+ ··· − u + 2
a
12
=
4u
26
− 5u
25
+ ··· + 14u + 8
5u
26
− 3u
25
+ ··· + 3u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 56u
26
− 16u
25
− 242u
24
+ 28u
23
+ 790u
22
− 93u
21
− 1678u
20
+
109u
19
+ 2944u
18
−243u
17
−3835u
16
+ 292u
15
+ 4218u
14
−591u
13
−3238u
12
+ 654u
11
+
1888u
10
− 840u
9
− 211u
8
+ 580u
7
− 532u
6
− 349u
5
+ 648u
4
+ 98u
3
− 334u
2
+ 39u + 44
19
(iv) u-Polynomials at the component
20
Crossings u-Polynomials at each crossing
c
1
u
27
− 10u
26
+ ··· + 14u − 1
c
2
u
27
− 5u
25
+ ··· + 2u − 1
c
3
u
27
+ 2u
26
+ ··· + 24u + 10
c
4
u
27
+ u
26
+ ··· − 2u + 1
c
5
u
27
+ 3u
26
+ ··· − 4u + 1
c
6
u
27
− 5u
25
+ ··· + 2u + 1
c
7
u
27
+ 10u
26
+ ··· + 14u + 1
c
8
u
27
− 5u
26
+ ··· + 9u + 1
c
9
u
27
+ 3u
26
+ ··· − 4u + 10
c
10
u
27
− 10u
26
+ ··· + 10u − 1
c
11
u
27
− 2u
26
+ ··· + 24u − 10
c
12
u
27
− 2u
26
+ ··· − u
2
+ 1
21
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
27
+ 18y
26
+ ··· + 34y −1
c
2
, c
6
y
27
− 10y
26
+ ··· + 14y −1
c
3
, c
11
y
27
− 18y
26
+ ··· + 676y −100
c
4
y
27
− 7y
26
+ ··· + 14y −1
c
5
y
27
+ 9y
26
+ ··· + 6y −1
c
8
y
27
+ 17y
26
+ ··· + 29y −1
c
9
y
27
+ 11y
26
+ ··· − 844y −100
c
10
y
27
+ 14y
26
+ ··· − 2y −1
c
12
y
27
+ 6y
26
+ ··· + 2y −1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.853029 + 0.648068I
a = 2.49844 − 0.29745I
b = −0.147943 − 0.989455I
−2.32180 − 2.25561I −6.46584 + 2.09687I
u = −0.853029 − 0.648068I
a = 2.49844 + 0.29745I
b = −0.147943 + 0.989455I
−2.32180 + 2.25561I −6.46584 − 2.09687I
u = 0.756012 + 0.769419I
a = 1.48984 + 0.28062I
b = −1.380350 − 0.265692I
5.33051 − 0.54518I 2.00562 + 2.64295I
u = 0.756012 − 0.769419I
a = 1.48984 − 0.28062I
b = −1.380350 + 0.265692I
5.33051 + 0.54518I 2.00562 − 2.64295I
u = −0.879271 + 0.641510I
a = −1.108550 + 0.722103I
b = 0.229177 − 0.886007I
−2.40619 + 7.28180I −5.66490 − 8.21445I
u = −0.879271 − 0.641510I
a = −1.108550 − 0.722103I
b = 0.229177 + 0.886007I
−2.40619 − 7.28180I −5.66490 + 8.21445I
u = 0.839517 + 0.301720I
a = 0.13559 + 1.54167I
b = 0.039699 − 0.613575I
−4.45291 + 3.45973I −8.14134 − 1.51472I
u = 0.839517 − 0.301720I
a = 0.13559 − 1.54167I
b = 0.039699 + 0.613575I
−4.45291 − 3.45973I −8.14134 + 1.51472I
u = 0.867000 + 0.699939I
a = 2.15472 − 1.89128I
b = −0.05702 + 2.67443I
0.75937 − 2.68723I −35.1129 − 15.8301I
u = 0.867000 − 0.699939I
a = 2.15472 + 1.89128I
b = −0.05702 − 2.67443I
0.75937 + 2.68723I −35.1129 + 15.8301I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.847137 + 0.232071I
a = −1.54632 − 2.15152I
b = 0.208901 − 0.852654I
−4.57630 − 5.82037I −11.5622 + 9.4372I
u = 0.847137 − 0.232071I
a = −1.54632 + 2.15152I
b = 0.208901 + 0.852654I
−4.57630 + 5.82037I −11.5622 − 9.4372I
u = −0.745527 + 0.869999I
a = 1.216160 − 0.404750I
b = −0.923191 + 0.651151I
2.88007 − 4.19210I −3.10818 + 5.17926I
u = −0.745527 − 0.869999I
a = 1.216160 + 0.404750I
b = −0.923191 − 0.651151I
2.88007 + 4.19210I −3.10818 − 5.17926I
u = 0.974203 + 0.722004I
a = −1.39689 − 1.42777I
b = 1.312570 − 0.400113I
4.65883 − 5.11360I 1.06462 + 3.67687I
u = 0.974203 − 0.722004I
a = −1.39689 + 1.42777I
b = 1.312570 + 0.400113I
4.65883 + 5.11360I 1.06462 − 3.67687I
u = 1.154600 + 0.381083I
a = −0.367093 − 0.551552I
b = 0.418495 − 0.218542I
−5.35960 − 5.22603I −10.8017 + 11.2233I
u = 1.154600 − 0.381083I
a = −0.367093 + 0.551552I
b = 0.418495 + 0.218542I
−5.35960 + 5.22603I −10.8017 − 11.2233I
u = 0.053816 + 0.780844I
a = 1.055010 − 0.476552I
b = −0.703324 − 0.024699I
−1.77605 + 1.14317I −6.18909 − 0.95442I
u = 0.053816 − 0.780844I
a = 1.055010 + 0.476552I
b = −0.703324 + 0.024699I
−1.77605 − 1.14317I −6.18909 + 0.95442I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.131580 + 0.451556I
a = −0.0015284 + 0.0613624I
b = 0.409195 + 0.207235I
−5.02699 + 2.84358I −4.52991 − 7.89589I
u = −1.131580 − 0.451556I
a = −0.0015284 − 0.0613624I
b = 0.409195 − 0.207235I
−5.02699 − 2.84358I −4.52991 + 7.89589I
u = −1.003860 + 0.768171I
a = −1.83200 + 0.81291I
b = 0.888987 + 0.798269I
2.07420 + 10.27290I −5.14062 − 9.39418I
u = −1.003860 − 0.768171I
a = −1.83200 − 0.81291I
b = 0.888987 − 0.798269I
2.07420 − 10.27290I −5.14062 + 9.39418I
u = −0.661803 + 0.149727I
a = −2.17325 + 0.60427I
b = −1.14518 + 1.21822I
−2.44308 + 0.15086I −62.6896 − 0.0416I
u = −0.661803 − 0.149727I
a = −2.17325 − 0.60427I
b = −1.14518 − 1.21822I
−2.44308 − 0.15086I −62.6896 + 0.0416I
u = −0.434431
a = 1.75175
b = −1.30003
2.29084 −20.3280
26
III. I
u
3
= h−u
2
+ b, a − 1, u
9
− u
7
+ u
5
− u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
10
=
1
u
2
a
11
=
u
6
− u
4
+ 1
−u
6
+ u
2
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
u
2
+ 1
u
4
a
9
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
4
=
u
6
− u
4
− u + 1
−u
6
− u
3
+ u
2
+ u
a
12
=
−u
−u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u
9
+ 2u
8
+ 3u
7
+ 2u
6
− u
5
− 2u
4
− 2u
3
+ u + 1
c
2
, c
6
, c
12
u
9
− u
7
+ u
5
− u − 1
c
3
, c
11
(u + 1)
9
c
4
u
9
− 2u
8
− u
7
+ 6u
6
− u
5
− 2u
4
− 2u
3
+ u + 1
c
8
u
9
+ 3u
7
+ 4u
6
+ 3u
5
− 8u
4
− 14u
3
− 12u
2
− 5u − 1
c
9
u
9
− u
7
+ 3u
6
− u
5
− 2u
4
+ 12u
3
+ 15u
2
+ 7u + 1
c
10
u
9
+ 2u
8
− u
7
− 6u
6
− u
5
+ 2u
4
− 2u
3
+ u − 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
9
+ 2y
8
− y
7
− 6y
6
− y
5
+ 2y
4
− 2y
3
+ y −1
c
2
, c
6
, c
12
y
9
− 2y
8
+ 3y
7
− 2y
6
− y
5
+ 2y
4
− 2y
3
+ y −1
c
3
, c
11
(y −1)
9
c
4
, c
10
y
9
− 6y
8
+ 23y
7
− 46y
6
+ 31y
5
+ 2y
4
− 10y
3
+ y −1
c
8
y
9
+ 6y
8
+ 15y
7
− 26y
6
− 21y
5
− 82y
4
− 18y
3
− 20y
2
+ y −1
c
9
y
9
− 2y
8
− y
7
+ 17y
6
+ 3y
5
− 132y
4
+ 184y
3
− 53y
2
+ 19y −1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.745920 + 0.654548I
a = 1.00000
b = 0.127964 − 0.976481I
−1.64493 −6.00000
u = −0.745920 − 0.654548I
a = 1.00000
b = 0.127964 + 0.976481I
−1.64493 −6.00000
u = −0.861832 + 0.303378I
a = 1.00000
b = 0.650717 − 0.522922I
−1.64493 −6.00000
u = −0.861832 − 0.303378I
a = 1.00000
b = 0.650717 + 0.522922I
−1.64493 −6.00000
u = 0.119990 + 0.892898I
a = 1.00000
b = −0.782869 + 0.214277I
−1.64493 −6.00000
u = 0.119990 − 0.892898I
a = 1.00000
b = −0.782869 − 0.214277I
−1.64493 −6.00000
u = 1.10594
a = 1.00000
b = 1.22310
−1.64493 −6.00000
u = 0.934793 + 0.693687I
a = 1.00000
b = 0.392636 + 1.296910I
−1.64493 −6.00000
u = 0.934793 − 0.693687I
a = 1.00000
b = 0.392636 − 1.296910I
−1.64493 −6.00000
30
IV. I
u
4
= hb − 1, a − 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
6
=
1
0
a
7
=
1
1
a
3
=
1
0
a
8
=
0
1
a
10
=
1
1
a
11
=
1
0
a
1
=
−1
−1
a
5
=
2
1
a
9
=
1
1
a
4
=
1
0
a
12
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
10
, c
12
u − 1
c
3
, c
9
, c
11
u
c
6
, c
7
, c
8
u + 1
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
y −1
c
3
, c
9
, c
11
y
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = 1.00000
0 0
34
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
9
+ 2u
8
+ 3u
7
+ 2u
6
− u
5
− 2u
4
− 2u
3
+ u + 1)
· (u
27
− 10u
26
+ ··· + 14u − 1)(u
140
+ 46u
139
+ ··· + 27u + 1)
c
2
(u − 1)(u
9
− u
7
+ u
5
− u − 1)(u
27
− 5u
25
+ ··· + 2u − 1)
· (u
140
− 23u
138
+ ··· + 3u + 1)
c
3
u(u + 1)
9
(u
27
+ 2u
26
+ ··· + 24u + 10)
· (u
140
− 6u
139
+ ··· − 52600u − 21104)
c
4
(u − 1)(u
9
− 2u
8
− u
7
+ 6u
6
− u
5
− 2u
4
− 2u
3
+ u + 1)
· (u
27
+ u
26
+ ··· − 2u + 1)(u
140
+ 5u
139
+ ··· + 35297u − 7759)
c
5
(u − 1)(u
9
+ 2u
8
+ 3u
7
+ 2u
6
− u
5
− 2u
4
− 2u
3
+ u + 1)
· (u
27
+ 3u
26
+ ··· − 4u + 1)(u
140
+ u
139
+ ··· + 8346945u + 492823)
c
6
(u + 1)(u
9
− u
7
+ u
5
− u − 1)(u
27
− 5u
25
+ ··· + 2u + 1)
· (u
140
− 23u
138
+ ··· + 3u + 1)
c
7
(u + 1)(u
9
+ 2u
8
+ 3u
7
+ 2u
6
− u
5
− 2u
4
− 2u
3
+ u + 1)
· (u
27
+ 10u
26
+ ··· + 14u + 1)(u
140
+ 46u
139
+ ··· + 27u + 1)
c
8
(u + 1)(u
9
+ 3u
7
+ 4u
6
+ 3u
5
− 8u
4
− 14u
3
− 12u
2
− 5u − 1)
· (u
27
− 5u
26
+ ··· + 9u + 1)(u
140
+ u
139
+ ··· − 30u − 1)
c
9
u(u
9
− u
7
+ 3u
6
− u
5
− 2u
4
+ 12u
3
+ 15u
2
+ 7u + 1)
· (u
27
+ 3u
26
+ ··· − 4u + 10)(u
140
+ 4u
139
+ ··· − 49356u + 1718)
c
10
(u − 1)(u
9
+ 2u
8
− u
7
− 6u
6
− u
5
+ 2u
4
− 2u
3
+ u − 1)
· (u
27
− 10u
26
+ ··· + 10u − 1)(u
140
− 6u
139
+ ··· + 378931u − 19471)
c
11
u(u + 1)
9
(u
27
− 2u
26
+ ··· + 24u − 10)
· (u
140
− 6u
139
+ ··· − 52600u − 21104)
c
12
(u − 1)(u
9
− u
7
+ u
5
− u − 1)(u
27
− 2u
26
+ ··· − u
2
+ 1)
· (u
140
− 5u
138
+ ··· − 39u + 1)
35
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y −1)(y
9
+ 2y
8
− y
7
− 6y
6
− y
5
+ 2y
4
− 2y
3
+ y −1)
· (y
27
+ 18y
26
+ ··· + 34y −1)(y
140
+ 110y
139
+ ··· − 551y + 1)
c
2
, c
6
(y −1)(y
9
− 2y
8
+ 3y
7
− 2y
6
− y
5
+ 2y
4
− 2y
3
+ y −1)
· (y
27
− 10y
26
+ ··· + 14y −1)(y
140
− 46y
139
+ ··· − 27y + 1)
c
3
, c
11
y(y −1)
9
(y
27
− 18y
26
+ ··· + 676y −100)
· (y
140
− 90y
139
+ ··· − 46338922560y + 445378816)
c
4
(y −1)(y
9
− 6y
8
+ 23y
7
− 46y
6
+ 31y
5
+ 2y
4
− 10y
3
+ y −1)
· (y
27
− 7y
26
+ ··· + 14y −1)
· (y
140
− 27y
139
+ ··· − 3984913835y + 60202081)
c
5
(y −1)(y
9
+ 2y
8
− y
7
− 6y
6
− y
5
+ 2y
4
− 2y
3
+ y −1)
· (y
27
+ 9y
26
+ ··· + 6y −1)
· (y
140
− 35y
139
+ ··· − 12584572781083y + 242874509329)
c
8
(y −1)(y
9
+ 6y
8
+ ··· + y −1)
· (y
27
+ 17y
26
+ ··· + 29y −1)(y
140
+ 17y
139
+ ··· − 82y + 1)
c
9
y(y
9
− 2y
8
− y
7
+ 17y
6
+ 3y
5
− 132y
4
+ 184y
3
− 53y
2
+ 19y −1)
· (y
27
+ 11y
26
+ ··· − 844y −100)
· (y
140
+ 4y
139
+ ··· − 573798944y + 2951524)
c
10
(y −1)(y
9
− 6y
8
+ 23y
7
− 46y
6
+ 31y
5
+ 2y
4
− 10y
3
+ y −1)
· (y
27
+ 14y
26
+ ··· − 2y −1)
· (y
140
− 10y
139
+ ··· − 105927544083y + 379119841)
c
12
(y −1)(y
9
− 2y
8
+ 3y
7
− 2y
6
− y
5
+ 2y
4
− 2y
3
+ y −1)
· (y
27
+ 6y
26
+ ··· + 2y −1)(y
140
− 10y
139
+ ··· − 447y + 1)
36
