12a
0700
(K12a
0700
)
A knot diagram
1
Linearized knot diagam
3 8 6 10 1 11 2 5 12 7 4 9
Solving Sequence
2,7
8 3
1,11
6 4 12 5 10 9
c
7
c
2
c
1
c
6
c
3
c
11
c
5
c
10
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.67707 × 10
517
u
170
+ 2.41772 × 10
516
u
169
+ ··· + 4.22459 × 10
515
b + 4.07568 × 10
519
,
− 1.58770 × 10
520
u
170
+ 3.63892 × 10
519
u
169
+ ··· + 1.67716 × 10
518
a − 6.29761 × 10
522
,
u
171
− u
170
+ ··· + 586u − 397i
I
u
2
= h−205536567u
44
+ 2638046874u
43
+ ··· + 279594103b − 13616934025,
− 12067050844u
44
− 2918818158u
43
+ ··· + 838782309a − 5408626830,
u
45
− 14u
43
+ ··· − 9u + 3i
* 2 irreducible components of dim
C
= 0, with total 216 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
= h1.68 × 10
517
u
170
+ 2.42 × 10
516
u
169
+ · · · + 4.22 × 10
515
b + 4.08 ×
10
519
, −1.59 × 10
520
u
170
+ 3.64 × 10
519
u
169
+ · · · + 1.68 × 10
518
a − 6.30 ×
10
522
, u
171
− u
170
+ · · · + 586u − 397i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
94.6662u
170
− 21.6969u
169
+ ··· − 26585.7u + 37549.3
−39.6979u
170
− 5.72299u
169
+ ··· + 13115.3u − 9647.53
a
6
=
45.9599u
170
− 17.2381u
169
+ ··· − 12547.3u + 20732.1
−24.4709u
170
− 5.37117u
169
+ ··· + 8344.75u − 4907.67
a
4
=
11.3771u
170
− 0.208651u
169
+ ··· − 3186.44u + 3718.02
−3.07513u
170
− 1.79771u
169
+ ··· + 1127.40u − 259.968
a
12
=
29.4345u
170
− 32.1297u
169
+ ··· − 4225.62u + 22195.0
−32.0724u
170
− 1.34218u
169
+ ··· + 10101.1u − 9251.27
a
5
=
24.1839u
170
− 23.7891u
169
+ ··· − 4829.20u + 17221.1
−24.8459u
170
− 7.07327u
169
+ ··· + 8647.31u − 4301.28
a
10
=
54.9682u
170
− 27.4199u
169
+ ··· − 13470.4u + 27901.7
−39.6979u
170
− 5.72299u
169
+ ··· + 13115.3u − 9647.53
a
9
=
−10.9228u
170
− 8.36188u
169
+ ··· + 4785.16u − 94.6923
−19.2601u
170
+ 3.11046u
169
+ ··· + 5477.55u − 7237.79
(ii) Obstruction class = −1
(iii) Cusp Shapes = 61.8148u
170
+ 26.9336u
169
+ ··· − 21906.6u + 8391.20
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
171
+ 79u
170
+ ··· + 1899636u + 157609
c
2
, c
7
u
171
− u
170
+ ··· + 586u − 397
c
3
u
171
− 16u
170
+ ··· − 105850260074u + 6222620143
c
4
u
171
+ u
170
+ ··· + 6244268u + 1871863
c
5
u
171
− 24u
169
+ ··· − 319818841u − 22221569
c
6
, c
10
u
171
+ 2u
170
+ ··· − 92496u − 62927
c
8
u
171
− 5u
170
+ ··· + 7769088u + 837632
c
9
, c
12
u
171
− 6u
170
+ ··· − 48u + 1
c
11
u
171
− 3u
170
+ ··· − 5954691744u + 869790560
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
171
+ 41y
170
+ ··· + 2670305620588y −24840596881
c
2
, c
7
y
171
− 79y
170
+ ··· + 1899636y −157609
c
3
y
171
− 60y
170
+ ··· + 3.41 × 10
21
y −3.87 × 10
19
c
4
y
171
− 39y
170
+ ··· + 212094663334992y −3503871090769
c
5
y
171
− 48y
170
+ ··· + 23054962778381399y −493798128821761
c
6
, c
10
y
171
+ 100y
170
+ ··· − 122657730866y −3959807329
c
8
y
171
− 29y
170
+ ··· + 26226872811520y −701627367424
c
9
, c
12
y
171
+ 124y
170
+ ··· + 6y −1
c
11
y
171
− 61y
170
+ ··· + 5.18 × 10
19
y −7.57 × 10
17
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.956826 + 0.287603I
a = −0.214990 + 0.039118I
b = 0.617261 − 1.256480I
2.51554 + 4.66422I 0
u = 0.956826 − 0.287603I
a = −0.214990 − 0.039118I
b = 0.617261 + 1.256480I
2.51554 − 4.66422I 0
u = 0.878636 + 0.466670I
a = −1.81779 + 3.02433I
b = −0.127767 − 0.933514I
−2.23105 − 1.90040I 0
u = 0.878636 − 0.466670I
a = −1.81779 − 3.02433I
b = −0.127767 + 0.933514I
−2.23105 + 1.90040I 0
u = −0.797590 + 0.613927I
a = 0.36054 + 1.81675I
b = −0.495385 − 1.175970I
7.74690 + 0.58892I 0
u = −0.797590 − 0.613927I
a = 0.36054 − 1.81675I
b = −0.495385 + 1.175970I
7.74690 − 0.58892I 0
u = 0.897140 + 0.461300I
a = −0.222009 − 1.350370I
b = 1.236070 + 0.216738I
−1.24696 − 4.30194I 0
u = 0.897140 − 0.461300I
a = −0.222009 + 1.350370I
b = 1.236070 − 0.216738I
−1.24696 + 4.30194I 0
u = 0.868052 + 0.461448I
a = 0.76462 + 1.23283I
b = −1.314450 + 0.413646I
−1.156070 + 0.546217I 0
u = 0.868052 − 0.461448I
a = 0.76462 − 1.23283I
b = −1.314450 − 0.413646I
−1.156070 − 0.546217I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.975014 + 0.100724I
a = −0.197692 − 0.624980I
b = −0.324228 + 1.176300I
4.48921 + 2.47656I 0
u = 0.975014 − 0.100724I
a = −0.197692 + 0.624980I
b = −0.324228 − 1.176300I
4.48921 − 2.47656I 0
u = −0.546543 + 0.862927I
a = −0.257752 + 0.432459I
b = 1.257840 − 0.106489I
0.67913 − 2.32400I 0
u = −0.546543 − 0.862927I
a = −0.257752 − 0.432459I
b = 1.257840 + 0.106489I
0.67913 + 2.32400I 0
u = −0.491789 + 0.845790I
a = 0.401471 − 0.341501I
b = −1.148200 + 0.080607I
5.73401 − 8.33723I 0
u = −0.491789 − 0.845790I
a = 0.401471 + 0.341501I
b = −1.148200 − 0.080607I
5.73401 + 8.33723I 0
u = −0.608462 + 0.761738I
a = 0.47379 + 2.13450I
b = −0.297301 − 1.222780I
5.48470 − 3.12328I 0
u = −0.608462 − 0.761738I
a = 0.47379 − 2.13450I
b = −0.297301 + 1.222780I
5.48470 + 3.12328I 0
u = 0.934716 + 0.439830I
a = 2.64369 − 1.69700I
b = 0.224833 + 0.839728I
1.55184 − 5.66028I 0
u = 0.934716 − 0.439830I
a = 2.64369 + 1.69700I
b = 0.224833 − 0.839728I
1.55184 + 5.66028I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.026210 + 0.132140I
a = 0.94526 − 1.12379I
b = 0.682948 + 0.550960I
−2.33748 − 4.36060I 0
u = 1.026210 − 0.132140I
a = 0.94526 + 1.12379I
b = 0.682948 − 0.550960I
−2.33748 + 4.36060I 0
u = 0.853301 + 0.448186I
a = 0.83149 − 3.63508I
b = 0.078705 + 0.937908I
1.80141 + 2.02979I 0
u = 0.853301 − 0.448186I
a = 0.83149 + 3.63508I
b = 0.078705 − 0.937908I
1.80141 − 2.02979I 0
u = −0.459919 + 0.838834I
a = 0.003273 − 0.141996I
b = −1.007690 + 0.303161I
5.64380 + 4.62745I 0
u = −0.459919 − 0.838834I
a = 0.003273 + 0.141996I
b = −1.007690 − 0.303161I
5.64380 − 4.62745I 0
u = −0.921616 + 0.490534I
a = −0.735283 − 0.208805I
b = −0.550307 − 0.688727I
−1.89895 + 2.67491I 0
u = −0.921616 − 0.490534I
a = −0.735283 + 0.208805I
b = −0.550307 + 0.688727I
−1.89895 − 2.67491I 0
u = −0.907689 + 0.517824I
a = −0.92556 − 1.31095I
b = −1.165630 + 0.699508I
−0.69875 + 4.90531I 0
u = −0.907689 − 0.517824I
a = −0.92556 + 1.31095I
b = −1.165630 − 0.699508I
−0.69875 − 4.90531I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877483 + 0.376347I
a = 0.667543 + 0.222189I
b = 0.671106 − 0.312724I
−1.40660 + 0.95422I 0
u = −0.877483 − 0.376347I
a = 0.667543 − 0.222189I
b = 0.671106 + 0.312724I
−1.40660 − 0.95422I 0
u = −0.900009 + 0.536045I
a = 1.356680 − 0.146144I
b = 0.456857 + 0.768723I
2.43989 + 6.24179I 0
u = −0.900009 − 0.536045I
a = 1.356680 + 0.146144I
b = 0.456857 − 0.768723I
2.43989 − 6.24179I 0
u = −0.789179 + 0.530446I
a = −1.53402 + 0.29766I
b = −0.532062 + 0.537487I
2.78965 − 1.92572I 0
u = −0.789179 − 0.530446I
a = −1.53402 − 0.29766I
b = −0.532062 − 0.537487I
2.78965 + 1.92572I 0
u = 0.448529 + 0.949574I
a = −0.00572 − 1.62100I
b = −0.57346 + 1.34895I
9.7363 + 14.3889I 0
u = 0.448529 − 0.949574I
a = −0.00572 + 1.62100I
b = −0.57346 − 1.34895I
9.7363 − 14.3889I 0
u = 0.355744 + 0.993600I
a = −0.142783 − 1.263270I
b = −0.66863 + 1.35759I
8.71974 + 1.76736I 0
u = 0.355744 − 0.993600I
a = −0.142783 + 1.263270I
b = −0.66863 − 1.35759I
8.71974 − 1.76736I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.657732 + 0.829253I
a = −0.62813 + 1.85085I
b = −0.41368 − 1.49142I
10.95280 + 2.50693I 0
u = 0.657732 − 0.829253I
a = −0.62813 − 1.85085I
b = −0.41368 + 1.49142I
10.95280 − 2.50693I 0
u = −0.423891 + 0.974839I
a = 0.09072 − 1.71356I
b = 0.099083 + 1.055390I
3.39888 − 0.77235I 0
u = −0.423891 − 0.974839I
a = 0.09072 + 1.71356I
b = 0.099083 − 1.055390I
3.39888 + 0.77235I 0
u = 0.444365 + 0.969023I
a = −0.02205 + 1.50059I
b = 0.57395 − 1.36722I
4.81458 + 8.62639I 0
u = 0.444365 − 0.969023I
a = −0.02205 − 1.50059I
b = 0.57395 + 1.36722I
4.81458 − 8.62639I 0
u = 0.863125 + 0.350401I
a = 0.238619 + 0.673714I
b = −0.722226 + 1.021860I
0.55593 + 1.81783I 0
u = 0.863125 − 0.350401I
a = 0.238619 − 0.673714I
b = −0.722226 − 1.021860I
0.55593 − 1.81783I 0
u = 0.419292 + 0.829504I
a = 0.083582 + 0.849301I
b = −0.212142 − 0.509063I
3.81399 + 2.47640I 0
u = 0.419292 − 0.829504I
a = 0.083582 − 0.849301I
b = −0.212142 + 0.509063I
3.81399 − 2.47640I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.893807 + 0.590700I
a = 1.98942 + 2.00045I
b = 0.599518 − 1.103710I
7.44851 + 4.15937I 0
u = −0.893807 − 0.590700I
a = 1.98942 − 2.00045I
b = 0.599518 + 1.103710I
7.44851 − 4.15937I 0
u = −0.731601 + 0.786359I
a = −0.60679 − 1.96764I
b = 0.402401 + 1.167230I
8.68265 − 3.67599I 0
u = −0.731601 − 0.786359I
a = −0.60679 + 1.96764I
b = 0.402401 − 1.167230I
8.68265 + 3.67599I 0
u = −0.997567 + 0.422352I
a = 0.318505 + 0.536245I
b = 0.916995 − 0.035295I
−1.11246 + 1.02477I 0
u = −0.997567 − 0.422352I
a = 0.318505 − 0.536245I
b = 0.916995 + 0.035295I
−1.11246 − 1.02477I 0
u = −0.715901 + 0.558446I
a = −0.96085 − 1.69301I
b = 0.53387 + 1.35453I
2.74819 − 2.02548I 0
u = −0.715901 − 0.558446I
a = −0.96085 + 1.69301I
b = 0.53387 − 1.35453I
2.74819 + 2.02548I 0
u = −0.769705 + 0.481037I
a = −0.205971 + 0.066204I
b = 0.928769 + 0.717151I
−0.257115 − 0.769190I 0
u = −0.769705 − 0.481037I
a = −0.205971 − 0.066204I
b = 0.928769 − 0.717151I
−0.257115 + 0.769190I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.629651 + 0.653076I
a = −0.684637 − 0.601316I
b = 0.515604 + 0.038534I
5.48230 − 0.00666I 0
u = 0.629651 − 0.653076I
a = −0.684637 + 0.601316I
b = 0.515604 − 0.038534I
5.48230 + 0.00666I 0
u = −1.055510 + 0.289408I
a = −0.156422 − 0.303114I
b = −0.783991 − 0.413477I
−0.154658 + 0.882825I 0
u = −1.055510 − 0.289408I
a = −0.156422 + 0.303114I
b = −0.783991 + 0.413477I
−0.154658 − 0.882825I 0
u = 1.099160 + 0.059660I
a = −1.24839 + 0.84415I
b = −0.704221 − 0.285989I
−5.17273 + 1.06158I 0
u = 1.099160 − 0.059660I
a = −1.24839 − 0.84415I
b = −0.704221 + 0.285989I
−5.17273 − 1.06158I 0
u = −0.947361 + 0.564417I
a = −1.60462 − 1.97667I
b = −0.68096 + 1.33596I
2.01829 + 6.54575I 0
u = −0.947361 − 0.564417I
a = −1.60462 + 1.97667I
b = −0.68096 − 1.33596I
2.01829 − 6.54575I 0
u = −0.499183 + 0.740716I
a = −0.31445 − 2.53620I
b = 0.190700 + 1.321380I
9.35134 − 3.73596I 0
u = −0.499183 − 0.740716I
a = −0.31445 + 2.53620I
b = 0.190700 − 1.321380I
9.35134 + 3.73596I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.052171 + 0.890147I
a = 0.328412 − 1.158230I
b = −0.038467 + 0.913102I
2.43343 + 0.40201I 0
u = 0.052171 − 0.890147I
a = 0.328412 + 1.158230I
b = −0.038467 − 0.913102I
2.43343 − 0.40201I 0
u = 0.950646 + 0.605652I
a = 0.429186 + 0.558810I
b = −0.715465 + 0.031647I
4.56106 − 4.88116I 0
u = 0.950646 − 0.605652I
a = 0.429186 − 0.558810I
b = −0.715465 − 0.031647I
4.56106 + 4.88116I 0
u = 0.780546 + 0.387785I
a = −0.44848 − 1.91492I
b = 0.475862 − 0.756033I
6.07407 + 0.41324I 0
u = 0.780546 − 0.387785I
a = −0.44848 + 1.91492I
b = 0.475862 + 0.756033I
6.07407 − 0.41324I 0
u = 1.023490 + 0.478232I
a = 0.332231 − 0.663588I
b = 0.645889 + 0.477697I
−0.43257 − 4.81082I 0
u = 1.023490 − 0.478232I
a = 0.332231 + 0.663588I
b = 0.645889 − 0.477697I
−0.43257 + 4.81082I 0
u = 1.057740 + 0.397018I
a = 0.655901 − 0.082297I
b = −0.095713 − 0.808191I
5.03945 − 3.57385I 0
u = 1.057740 − 0.397018I
a = 0.655901 + 0.082297I
b = −0.095713 + 0.808191I
5.03945 + 3.57385I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.080720 + 0.333118I
a = 0.300920 − 0.879667I
b = −0.148834 − 0.810497I
−2.47482 + 0.35682I 0
u = −1.080720 − 0.333118I
a = 0.300920 + 0.879667I
b = −0.148834 + 0.810497I
−2.47482 − 0.35682I 0
u = −1.073620 + 0.371045I
a = −1.11411 + 1.47222I
b = 0.075761 + 0.967597I
1.88955 − 2.80465I 0
u = −1.073620 − 0.371045I
a = −1.11411 − 1.47222I
b = 0.075761 − 0.967597I
1.88955 + 2.80465I 0
u = −1.133280 + 0.097822I
a = 0.411402 − 0.098226I
b = 0.436494 − 0.750592I
−1.65161 − 0.28706I 0
u = −1.133280 − 0.097822I
a = 0.411402 + 0.098226I
b = 0.436494 + 0.750592I
−1.65161 + 0.28706I 0
u = −0.618815 + 0.956893I
a = 0.26610 + 1.73277I
b = −0.230480 − 1.025900I
5.27721 − 4.74019I 0
u = −0.618815 − 0.956893I
a = 0.26610 − 1.73277I
b = −0.230480 + 1.025900I
5.27721 + 4.74019I 0
u = −0.999315 + 0.557726I
a = 1.56045 + 1.97365I
b = 0.52231 − 1.47912I
4.25925 + 10.37730I 0
u = −0.999315 − 0.557726I
a = 1.56045 − 1.97365I
b = 0.52231 + 1.47912I
4.25925 − 10.37730I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.026620 + 0.515290I
a = 1.50980 − 1.23387I
b = 0.443325 + 0.968721I
1.66202 − 5.45117I 0
u = 1.026620 − 0.515290I
a = 1.50980 + 1.23387I
b = 0.443325 − 0.968721I
1.66202 + 5.45117I 0
u = 0.701585 + 0.909646I
a = 0.54255 − 1.65656I
b = 0.32908 + 1.44257I
6.51171 − 3.33192I 0
u = 0.701585 − 0.909646I
a = 0.54255 + 1.65656I
b = 0.32908 − 1.44257I
6.51171 + 3.33192I 0
u = 0.641433 + 0.954963I
a = −0.37001 + 1.68349I
b = −0.365328 − 1.355340I
10.9047 − 9.1848I 0
u = 0.641433 − 0.954963I
a = −0.37001 − 1.68349I
b = −0.365328 + 1.355340I
10.9047 + 9.1848I 0
u = −0.384231 + 0.752644I
a = −0.66156 + 2.15744I
b = 0.011068 − 1.169530I
8.86354 + 1.16409I 0
u = −0.384231 − 0.752644I
a = −0.66156 − 2.15744I
b = 0.011068 + 1.169530I
8.86354 − 1.16409I 0
u = 1.045440 + 0.500289I
a = 1.55631 + 0.79175I
b = 0.327276 + 0.894070I
2.70284 − 9.59229I 0
u = 1.045440 − 0.500289I
a = 1.55631 − 0.79175I
b = 0.327276 − 0.894070I
2.70284 + 9.59229I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.164600 + 0.035478I
a = 1.195810 − 0.452210I
b = 0.842116 + 0.153274I
−0.18274 + 6.37415I 0
u = 1.164600 − 0.035478I
a = 1.195810 + 0.452210I
b = 0.842116 − 0.153274I
−0.18274 − 6.37415I 0
u = 1.064200 + 0.493606I
a = −1.44542 + 0.00461I
b = −0.421817 − 0.851917I
−1.47247 − 6.67780I 0
u = 1.064200 − 0.493606I
a = −1.44542 − 0.00461I
b = −0.421817 + 0.851917I
−1.47247 + 6.67780I 0
u = −0.970071 + 0.691846I
a = −1.25517 − 2.24157I
b = −0.459137 + 1.200560I
7.92987 + 9.25535I 0
u = −0.970071 − 0.691846I
a = −1.25517 + 2.24157I
b = −0.459137 − 1.200560I
7.92987 − 9.25535I 0
u = 1.098540 + 0.464721I
a = −0.825490 + 0.965885I
b = −0.718239 − 0.822930I
0.98619 − 6.36772I 0
u = 1.098540 − 0.464721I
a = −0.825490 − 0.965885I
b = −0.718239 + 0.822930I
0.98619 + 6.36772I 0
u = −0.601887 + 0.524283I
a = 1.25899 + 2.22365I
b = −0.38381 − 1.43638I
5.47043 − 5.91272I 0
u = −0.601887 − 0.524283I
a = 1.25899 − 2.22365I
b = −0.38381 + 1.43638I
5.47043 + 5.91272I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.023600 + 0.643339I
a = 1.39465 + 1.97316I
b = 0.384228 − 1.268350I
4.21967 + 8.45540I 0
u = −1.023600 − 0.643339I
a = 1.39465 − 1.97316I
b = 0.384228 + 1.268350I
4.21967 − 8.45540I 0
u = 0.777227 + 0.129594I
a = 0.959945 + 0.223678I
b = 0.483962 − 1.070420I
0.68261 + 3.33658I 0
u = 0.777227 − 0.129594I
a = 0.959945 − 0.223678I
b = 0.483962 + 1.070420I
0.68261 − 3.33658I 0
u = 0.201653 + 0.748321I
a = −0.546846 + 1.052700I
b = 0.476959 − 0.637820I
3.73708 + 2.01591I 0
u = 0.201653 − 0.748321I
a = −0.546846 − 1.052700I
b = 0.476959 + 0.637820I
3.73708 − 2.01591I 0
u = −1.062810 + 0.610540I
a = −1.53245 − 1.90484I
b = −0.252757 + 1.365120I
7.67677 + 8.88951I 0
u = −1.062810 − 0.610540I
a = −1.53245 + 1.90484I
b = −0.252757 − 1.365120I
7.67677 − 8.88951I 0
u = 1.006210 + 0.701570I
a = −1.01339 + 1.03657I
b = 0.31039 − 1.54528I
9.88701 − 8.21353I 0
u = 1.006210 − 0.701570I
a = −1.01339 − 1.03657I
b = 0.31039 + 1.54528I
9.88701 + 8.21353I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.353560 + 0.686344I
a = 0.237192 − 1.370010I
b = −0.342356 + 0.951239I
3.56741 + 0.97425I 0
u = 0.353560 − 0.686344I
a = 0.237192 + 1.370010I
b = −0.342356 − 0.951239I
3.56741 − 0.97425I 0
u = 0.982207 + 0.762492I
a = 0.87896 − 1.13557I
b = −0.20604 + 1.45475I
5.64166 − 2.77773I 0
u = 0.982207 − 0.762492I
a = 0.87896 + 1.13557I
b = −0.20604 − 1.45475I
5.64166 + 2.77773I 0
u = 1.129400 + 0.523555I
a = 0.149966 − 0.149458I
b = −0.026911 + 0.536085I
−0.68138 − 4.96666I 0
u = 1.129400 − 0.523555I
a = 0.149966 + 0.149458I
b = −0.026911 − 0.536085I
−0.68138 + 4.96666I 0
u = 1.107220 + 0.614084I
a = −0.357940 + 0.030959I
b = 0.371437 − 0.389310I
1.75486 − 7.82536I 0
u = 1.107220 − 0.614084I
a = −0.357940 − 0.030959I
b = 0.371437 + 0.389310I
1.75486 + 7.82536I 0
u = −1.133710 + 0.580785I
a = 1.73765 + 1.14915I
b = 0.113348 − 1.120830I
6.62756 + 3.91886I 0
u = −1.133710 − 0.580785I
a = 1.73765 − 1.14915I
b = 0.113348 + 1.120830I
6.62756 − 3.91886I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.084830 + 0.668997I
a = −0.016927 − 0.887342I
b = −1.251400 − 0.246759I
−0.97454 + 8.00469I 0
u = −1.084830 − 0.668997I
a = −0.016927 + 0.887342I
b = −1.251400 + 0.246759I
−0.97454 − 8.00469I 0
u = −1.100450 + 0.654244I
a = 0.000708 + 0.931750I
b = 1.192120 + 0.180677I
3.8981 + 13.9221I 0
u = −1.100450 − 0.654244I
a = 0.000708 − 0.931750I
b = 1.192120 − 0.180677I
3.8981 − 13.9221I 0
u = 0.395128 + 0.577795I
a = 0.662352 − 0.202823I
b = −0.258732 + 0.154000I
1.50624 + 0.63678I 0
u = 0.395128 − 0.577795I
a = 0.662352 + 0.202823I
b = −0.258732 − 0.154000I
1.50624 − 0.63678I 0
u = −1.275160 + 0.288536I
a = 0.556265 + 0.526628I
b = 0.573912 + 1.173870I
3.17167 + 2.22003I 0
u = −1.275160 − 0.288536I
a = 0.556265 − 0.526628I
b = 0.573912 − 1.173870I
3.17167 − 2.22003I 0
u = 0.625907 + 0.283235I
a = −1.81089 + 0.52243I
b = −0.436916 + 1.066190I
4.37183 + 5.81068I 0
u = 0.625907 − 0.283235I
a = −1.81089 − 0.52243I
b = −0.436916 − 1.066190I
4.37183 − 5.81068I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.146160 + 0.641935I
a = 0.197611 + 0.829437I
b = 1.041370 + 0.540878I
3.57226 + 0.90902I 0
u = −1.146160 − 0.641935I
a = 0.197611 − 0.829437I
b = 1.041370 − 0.540878I
3.57226 − 0.90902I 0
u = −1.094860 + 0.734129I
a = 0.97485 + 1.67816I
b = 0.333132 − 1.066640I
3.76767 + 10.92770I 0
u = −1.094860 − 0.734129I
a = 0.97485 − 1.67816I
b = 0.333132 + 1.066640I
3.76767 − 10.92770I 0
u = 1.056010 + 0.805725I
a = −0.757862 + 1.005940I
b = 0.262911 − 1.335100I
9.66032 + 2.80712I 0
u = 1.056010 − 0.805725I
a = −0.757862 − 1.005940I
b = 0.262911 + 1.335100I
9.66032 − 2.80712I 0
u = −1.329700 + 0.052146I
a = 0.579672 − 0.017659I
b = 0.506227 + 1.251760I
3.21395 − 11.38510I 0
u = −1.329700 − 0.052146I
a = 0.579672 + 0.017659I
b = 0.506227 − 1.251760I
3.21395 + 11.38510I 0
u = 1.154050 + 0.675178I
a = 1.57792 − 1.47486I
b = 0.62611 + 1.33918I
7.5740 − 20.3185I 0
u = 1.154050 − 0.675178I
a = 1.57792 + 1.47486I
b = 0.62611 − 1.33918I
7.5740 + 20.3185I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.156650 + 0.684773I
a = −1.13854 − 1.37593I
b = −0.226020 + 1.073220I
1.17660 + 6.77733I 0
u = −1.156650 − 0.684773I
a = −1.13854 + 1.37593I
b = −0.226020 − 1.073220I
1.17660 − 6.77733I 0
u = 1.159470 + 0.682039I
a = −1.51417 + 1.37920I
b = −0.64031 − 1.34487I
2.6220 − 14.6271I 0
u = 1.159470 − 0.682039I
a = −1.51417 − 1.37920I
b = −0.64031 + 1.34487I
2.6220 + 14.6271I 0
u = −1.336180 + 0.318844I
a = −0.709587 − 0.177161I
b = −0.182692 + 0.997650I
−2.16590 + 4.01442I 0
u = −1.336180 − 0.318844I
a = −0.709587 + 0.177161I
b = −0.182692 − 0.997650I
−2.16590 − 4.01442I 0
u = 1.203850 + 0.686808I
a = 1.51283 − 1.12259I
b = 0.71844 + 1.34366I
6.15942 − 7.85351I 0
u = 1.203850 − 0.686808I
a = 1.51283 + 1.12259I
b = 0.71844 − 1.34366I
6.15942 + 7.85351I 0
u = −1.401290 + 0.064881I
a = −0.461300 − 0.060735I
b = −0.446894 − 1.275540I
−1.88291 − 5.32739I 0
u = −1.401290 − 0.064881I
a = −0.461300 + 0.060735I
b = −0.446894 + 1.275540I
−1.88291 + 5.32739I 0
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42131 + 0.16924I
a = −0.014903 − 0.702802I
b = −0.019227 + 0.865514I
−3.09989 − 2.97045I 0
u = 1.42131 − 0.16924I
a = −0.014903 + 0.702802I
b = −0.019227 − 0.865514I
−3.09989 + 2.97045I 0
u = 0.117927 + 0.534820I
a = 0.001465 + 0.307492I
b = 0.315676 − 1.013720I
0.81903 + 2.70073I −2.00000 − 5.11544I
u = 0.117927 − 0.534820I
a = 0.001465 − 0.307492I
b = 0.315676 + 1.013720I
0.81903 − 2.70073I −2.00000 + 5.11544I
u = −0.158677 + 0.456783I
a = 0.545024 − 1.146370I
b = −0.687236 + 0.017538I
0.93325 + 2.38158I −1.41377 − 3.83906I
u = −0.158677 − 0.456783I
a = 0.545024 + 1.146370I
b = −0.687236 − 0.017538I
0.93325 − 2.38158I −1.41377 + 3.83906I
u = −0.391840 + 0.251747I
a = 1.028240 − 0.267682I
b = 0.550906 − 0.430609I
−1.043840 + 0.852144I −5.50407 − 3.87194I
u = −0.391840 − 0.251747I
a = 1.028240 + 0.267682I
b = 0.550906 + 0.430609I
−1.043840 − 0.852144I −5.50407 + 3.87194I
u = 1.60607
a = −1.41368
b = −1.60425
−7.39818 0
u = −0.016009 + 0.338498I
a = 1.46867 + 1.31692I
b = −0.277602 + 1.151600I
4.63827 + 5.90569I 4.55439 − 6.54282I
21
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.016009 − 0.338498I
a = 1.46867 − 1.31692I
b = −0.277602 − 1.151600I
4.63827 − 5.90569I 4.55439 + 6.54282I
22
II.
I
u
2
= h−2.06 × 10
8
u
44
+ 2.64 × 10
9
u
43
+ · · · + 2.80× 10
8
b − 1.36 ×10
10
, −1.21 ×
10
10
u
44
−2.92×10
9
u
43
+· · ·+8.39×10
8
a−5.41×10
9
, u
45
−14u
43
+· · ·−9u+3i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
14.3864u
44
+ 3.47983u
43
+ ··· − 62.0208u + 6.44819
0.735125u
44
− 9.43527u
43
+ ··· − 113.429u + 48.7025
a
6
=
−21.3826u
44
+ 23.2195u
43
+ ··· + 248.158u − 57.7914
−9.90995u
44
+ 12.6579u
43
+ ··· + 112.152u − 26.8012
a
4
=
70.0347u
44
− 55.1840u
43
+ ··· − 770.387u + 194.200
9.35385u
44
− 7.39135u
43
+ ··· − 83.1329u + 32.3156
a
12
=
11.0692u
44
− 42.3151u
43
+ ··· − 241.690u + 88.9789
−3.23793u
44
− 14.4606u
43
+ ··· − 44.0576u + 20.6904
a
5
=
−21.3826u
44
+ 22.2195u
43
+ ··· + 248.158u − 57.7914
−9.90995u
44
+ 12.6579u
43
+ ··· + 113.152u − 26.8012
a
10
=
15.1215u
44
− 5.95545u
43
+ ··· − 175.449u + 55.1507
0.735125u
44
− 9.43527u
43
+ ··· − 113.429u + 48.7025
a
9
=
20.6422u
44
− 38.9962u
43
+ ··· − 106.634u + 40.7160
8.21791u
44
− 1.90426u
43
+ ··· + 16.7274u − 5.43927
(ii) Obstruction class = 1
(iii) Cusp Shapes =
11094634093
279594103
u
44
−
7438644211
279594103
u
43
+ ··· −
63794950288
279594103
u −
886923009
279594103
23
(iv) u-Polynomials at the component
24
Crossings u-Polynomials at each crossing
c
1
u
45
− 28u
44
+ ··· + 183u − 9
c
2
u
45
− 14u
43
+ ··· − 9u − 3
c
3
u
45
+ 21u
44
+ ··· + 5u + 1
c
4
u
45
− 6u
43
+ ··· + 15u + 3
c
5
u
45
+ 3u
44
+ ··· + 12u + 1
c
6
u
45
+ u
44
+ ··· + u + 1
c
7
u
45
− 14u
43
+ ··· − 9u + 3
c
8
u
45
− 3u
43
+ ··· + 12u + 1
c
9
u
45
− 7u
44
+ ··· + 13u − 1
c
10
u
45
− u
44
+ ··· + u − 1
c
11
u
45
− 2u
44
+ ··· + 2u − 1
c
12
u
45
+ 7u
44
+ ··· + 13u + 1
25
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
45
− 8y
44
+ ··· − 1197y −81
c
2
, c
7
y
45
− 28y
44
+ ··· + 183y −9
c
3
y
45
− y
44
+ ··· − 17y −1
c
4
y
45
− 12y
44
+ ··· + 291y −9
c
5
y
45
− y
44
+ ··· + 46y −1
c
6
, c
10
y
45
+ 19y
44
+ ··· − 35y −1
c
8
y
45
− 6y
44
+ ··· + 116y −1
c
9
, c
12
y
45
+ 31y
44
+ ··· + 9y −1
c
11
y
45
− 6y
44
+ ··· + 36y −1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.947809 + 0.305574I
a = 1.85682 + 0.07236I
b = 0.436192 + 1.130770I
3.52768 − 7.44394I 2.08118 + 8.77686I
u = 0.947809 − 0.305574I
a = 1.85682 − 0.07236I
b = 0.436192 − 1.130770I
3.52768 + 7.44394I 2.08118 − 8.77686I
u = −0.951159 + 0.284825I
a = −1.14322 − 1.22982I
b = −0.057179 − 0.558033I
−3.16927 + 1.13946I −10.11592 − 1.44344I
u = −0.951159 − 0.284825I
a = −1.14322 + 1.22982I
b = −0.057179 + 0.558033I
−3.16927 − 1.13946I −10.11592 + 1.44344I
u = −0.968011 + 0.338728I
a = −0.27699 + 2.42754I
b = −0.099732 + 0.609870I
0.76831 − 2.21148I −6.70922 + 0.81167I
u = −0.968011 − 0.338728I
a = −0.27699 − 2.42754I
b = −0.099732 − 0.609870I
0.76831 + 2.21148I −6.70922 − 0.81167I
u = −0.945626 + 0.411263I
a = 0.462338 − 0.816959I
b = −1.156440 − 0.490738I
−1.82207 − 0.41947I −11.05625 + 0.63281I
u = −0.945626 − 0.411263I
a = 0.462338 + 0.816959I
b = −1.156440 + 0.490738I
−1.82207 + 0.41947I −11.05625 − 0.63281I
u = −0.696855 + 0.771438I
a = −0.85194 − 1.88650I
b = 0.256428 + 1.233250I
6.90755 − 4.20805I 5.47212 + 3.72388I
u = −0.696855 − 0.771438I
a = −0.85194 + 1.88650I
b = 0.256428 − 1.233250I
6.90755 + 4.20805I 5.47212 − 3.72388I
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.883323 + 0.332992I
a = −0.577896 − 0.899831I
b = −0.456747 + 1.219270I
3.71731 + 4.76539I 1.84468 − 3.19153I
u = 0.883323 − 0.332992I
a = −0.577896 + 0.899831I
b = −0.456747 − 1.219270I
3.71731 − 4.76539I 1.84468 + 3.19153I
u = 0.168187 + 0.919365I
a = −0.110980 + 1.250060I
b = 0.212712 − 0.861227I
2.04567 + 1.12246I −4.60064 − 4.94131I
u = 0.168187 − 0.919365I
a = −0.110980 − 1.250060I
b = 0.212712 + 0.861227I
2.04567 − 1.12246I −4.60064 + 4.94131I
u = 0.519147 + 0.775496I
a = −0.555425 − 0.961309I
b = −0.014988 + 0.724426I
4.43504 + 3.18421I 5.83087 − 4.61697I
u = 0.519147 − 0.775496I
a = −0.555425 + 0.961309I
b = −0.014988 − 0.724426I
4.43504 − 3.18421I 5.83087 + 4.61697I
u = −0.870562 + 0.255402I
a = 2.87733 + 0.42507I
b = 0.156480 + 0.655159I
1.26592 + 4.72462I −2.87660 − 1.12758I
u = −0.870562 − 0.255402I
a = 2.87733 − 0.42507I
b = 0.156480 − 0.655159I
1.26592 − 4.72462I −2.87660 + 1.12758I
u = −0.829031 + 0.351113I
a = 0.38762 + 1.64400I
b = 1.145070 − 0.427982I
−1.32778 + 3.62805I −3.30796 + 1.26679I
u = −0.829031 − 0.351113I
a = 0.38762 − 1.64400I
b = 1.145070 + 0.427982I
−1.32778 − 3.62805I −3.30796 − 1.26679I
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.480627 + 0.716840I
a = −0.29200 + 2.11798I
b = −0.428740 − 1.152210I
7.42627 − 1.74440I 4.97155 + 1.28868I
u = −0.480627 − 0.716840I
a = −0.29200 − 2.11798I
b = −0.428740 + 1.152210I
7.42627 + 1.74440I 4.97155 − 1.28868I
u = 0.557471 + 0.652043I
a = −0.448328 − 0.200747I
b = 0.958388 − 0.320247I
0.58987 + 1.40557I 1.73054 − 1.77076I
u = 0.557471 − 0.652043I
a = −0.448328 + 0.200747I
b = 0.958388 + 0.320247I
0.58987 − 1.40557I 1.73054 + 1.77076I
u = 1.019760 + 0.530315I
a = −0.668591 + 1.009670I
b = −0.924437 − 0.575905I
−0.83829 − 5.99730I 0. + 9.88344I
u = 1.019760 − 0.530315I
a = −0.668591 − 1.009670I
b = −0.924437 + 0.575905I
−0.83829 + 5.99730I 0. − 9.88344I
u = −0.991698 + 0.639087I
a = −1.09594 − 2.10199I
b = −0.313964 + 1.302860I
5.96272 + 9.54800I 0
u = −0.991698 − 0.639087I
a = −1.09594 + 2.10199I
b = −0.313964 − 1.302860I
5.96272 − 9.54800I 0
u = 1.097380 + 0.518347I
a = −0.887514 + 0.579345I
b = −0.442280 − 0.680263I
−0.85244 − 5.82908I 0
u = 1.097380 − 0.518347I
a = −0.887514 − 0.579345I
b = −0.442280 + 0.680263I
−0.85244 + 5.82908I 0
30
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.065530 + 0.584995I
a = 1.396940 + 0.095118I
b = 0.028170 + 0.637799I
2.73477 − 8.29362I 0
u = 1.065530 − 0.584995I
a = 1.396940 − 0.095118I
b = 0.028170 − 0.637799I
2.73477 + 8.29362I 0
u = 0.737026 + 0.256133I
a = −0.202223 − 0.024856I
b = 0.611294 − 1.091710I
1.04932 + 2.58085I −0.29998 − 1.67276I
u = 0.737026 − 0.256133I
a = −0.202223 + 0.024856I
b = 0.611294 + 1.091710I
1.04932 − 2.58085I −0.29998 + 1.67276I
u = −1.091430 + 0.645767I
a = 1.61926 + 1.52935I
b = 0.509078 − 1.270280I
5.59449 + 7.03942I 0
u = −1.091430 − 0.645767I
a = 1.61926 − 1.52935I
b = 0.509078 + 1.270280I
5.59449 − 7.03942I 0
u = 1.204020 + 0.488233I
a = 0.387300 − 0.777569I
b = 0.750937 − 0.894572I
3.68000 − 1.64209I 0
u = 1.204020 − 0.488233I
a = 0.387300 + 0.777569I
b = 0.750937 + 0.894572I
3.68000 + 1.64209I 0
u = 1.334470 + 0.143106I
a = −0.640922 + 0.104359I
b = −0.337684 − 1.142560I
−1.61470 − 4.60214I 0
u = 1.334470 − 0.143106I
a = −0.640922 − 0.104359I
b = −0.337684 + 1.142560I
−1.61470 + 4.60214I 0
31
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.372060 + 0.215211I
a = 0.014569 + 0.615610I
b = −0.114960 − 0.783314I
−3.35910 + 2.77030I 0
u = −1.372060 − 0.215211I
a = 0.014569 − 0.615610I
b = −0.114960 + 0.783314I
−3.35910 − 2.77030I 0
u = 0.463195 + 0.252618I
a = −0.04059 − 1.77064I
b = −0.421227 − 0.880509I
6.46206 − 1.94074I 5.94293 + 2.99498I
u = 0.463195 − 0.252618I
a = −0.04059 + 1.77064I
b = −0.421227 + 0.880509I
6.46206 + 1.94074I 5.94293 − 2.99498I
u = −1.60052
a = −1.41929
b = −1.59274
−7.40983 0
32
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
45
− 28u
44
+ ··· + 183u − 9)
· (u
171
+ 79u
170
+ ··· + 1899636u + 157609)
c
2
(u
45
− 14u
43
+ ··· − 9u − 3)(u
171
− u
170
+ ··· + 586u − 397)
c
3
(u
45
+ 21u
44
+ ··· + 5u + 1)
· (u
171
− 16u
170
+ ··· − 105850260074u + 6222620143)
c
4
(u
45
− 6u
43
+ ··· + 15u + 3)(u
171
+ u
170
+ ··· + 6244268u + 1871863)
c
5
(u
45
+ 3u
44
+ ··· + 12u + 1)
· (u
171
− 24u
169
+ ··· − 319818841u − 22221569)
c
6
(u
45
+ u
44
+ ··· + u + 1)(u
171
+ 2u
170
+ ··· − 92496u − 62927)
c
7
(u
45
− 14u
43
+ ··· − 9u + 3)(u
171
− u
170
+ ··· + 586u − 397)
c
8
(u
45
− 3u
43
+ ··· + 12u + 1)(u
171
− 5u
170
+ ··· + 7769088u + 837632)
c
9
(u
45
− 7u
44
+ ··· + 13u − 1)(u
171
− 6u
170
+ ··· − 48u + 1)
c
10
(u
45
− u
44
+ ··· + u − 1)(u
171
+ 2u
170
+ ··· − 92496u − 62927)
c
11
(u
45
− 2u
44
+ ··· + 2u − 1)
· (u
171
− 3u
170
+ ··· − 5954691744u + 869790560)
c
12
(u
45
+ 7u
44
+ ··· + 13u + 1)(u
171
− 6u
170
+ ··· − 48u + 1)
33
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
45
− 8y
44
+ ··· − 1197y −81)
· (y
171
+ 41y
170
+ ··· + 2670305620588y −24840596881)
c
2
, c
7
(y
45
− 28y
44
+ ··· + 183y −9)
· (y
171
− 79y
170
+ ··· + 1899636y −157609)
c
3
(y
45
− y
44
+ ··· − 17y −1)(y
171
− 60y
170
+ ··· + 3.40966 × 10
21
y −3.87210 × 10
19
)
c
4
(y
45
− 12y
44
+ ··· + 291y −9)
· (y
171
− 39y
170
+ ··· + 212094663334992y −3503871090769)
c
5
(y
45
− y
44
+ ··· + 46y −1)
· (y
171
− 48y
170
+ ··· + 23054962778381399y −493798128821761)
c
6
, c
10
(y
45
+ 19y
44
+ ··· − 35y −1)
· (y
171
+ 100y
170
+ ··· − 122657730866y −3959807329)
c
8
(y
45
− 6y
44
+ ··· + 116y −1)
· (y
171
− 29y
170
+ ··· + 26226872811520y −701627367424)
c
9
, c
12
(y
45
+ 31y
44
+ ··· + 9y −1)(y
171
+ 124y
170
+ ··· + 6y −1)
c
11
(y
45
− 6y
44
+ ··· + 36y −1)
· (y
171
− 61y
170
+ ··· + 5.18 × 10
19
y −7.57 × 10
17
)
34
