12a
0418
(K12a
0418
)
A knot diagram
1
Linearized knot diagam
3 6 9 12 10 2 4 11 7 1 8 5
Solving Sequence
2,6
3 7
1,10
11 5 9 4 8 12
c
2
c
6
c
1
c
10
c
5
c
9
c
3
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.94917 × 10
418
u
163
+ 1.81536 × 10
418
u
162
+ ··· + 9.84278 × 10
417
b + 3.97689 × 10
418
,
6.96715 × 10
418
u
163
+ 2.22660 × 10
419
u
162
+ ··· + 9.84278 × 10
417
a − 9.30364 × 10
417
,
u
164
+ 3u
163
+ ··· + 12u − 1i
I
u
2
= h−6087254789723u
40
+ 551946361063u
39
+ ··· + 4003363922926b − 35131970365899,
− 25612286566117u
40
− 31874660592809u
39
+ ··· + 4003363922926a − 38454939383807,
u
41
+ 2u
40
+ ··· + 8u + 1i
* 2 irreducible components of dim
C
= 0, with total 205 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
= h1.95 × 10
418
u
163
+ 1.82 × 10
418
u
162
+ · · · + 9.84 × 10
417
b + 3.98 ×
10
418
, 6.97 × 10
418
u
163
+ 2.23 × 10
419
u
162
+ · · · + 9.84 × 10
417
a − 9.30 ×
10
417
, u
164
+ 3u
163
+ · · · + 12u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
1
=
u
2
+ 1
−u
4
a
10
=
−7.07843u
163
− 22.6216u
162
+ ··· − 81.9968u + 0.945225
−1.98031u
163
− 1.84436u
162
+ ··· + 52.9432u − 4.04041
a
11
=
−13.5263u
163
− 40.4393u
162
+ ··· − 121.786u + 4.44380
−6.32039u
163
− 15.8195u
162
+ ··· − 12.8020u + 1.46178
a
5
=
19.9472u
163
+ 65.1439u
162
+ ··· + 82.9225u + 2.33750
9.51618u
163
+ 39.6278u
162
+ ··· + 207.433u − 15.8542
a
9
=
−14.6689u
163
− 43.8271u
162
+ ··· − 142.694u + 6.42814
−9.57082u
163
− 23.0498u
162
+ ··· − 7.75367u + 1.44251
a
4
=
16.9894u
163
+ 45.6939u
162
+ ··· + 208.713u − 20.8237
8.02649u
163
+ 26.6253u
162
+ ··· + 100.474u − 9.14182
a
8
=
−15.1801u
163
− 46.9462u
162
+ ··· − 317.756u + 25.5664
−9.42833u
163
− 32.2679u
162
+ ··· − 155.021u + 13.1745
a
12
=
15.3039u
163
+ 26.9168u
162
+ ··· − 308.619u + 35.5341
11.1371u
163
+ 17.7015u
162
+ ··· − 102.845u + 8.62088
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.27418u
163
+ 4.99888u
162
+ ··· + 127.051u − 1.23676
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
164
+ 73u
163
+ ··· + 38u + 1
c
2
, c
6
u
164
− 3u
163
+ ··· − 12u − 1
c
3
u
164
+ u
163
+ ··· − 6629u + 661
c
4
, c
12
u
164
− 70u
162
+ ··· + 183149u − 105263
c
5
u
164
+ 2u
163
+ ··· + 7727742u − 383531
c
7
u
164
− 3u
163
+ ··· − 3133307254u + 688167281
c
8
, c
11
u
164
+ 10u
163
+ ··· + 815546u − 215404
c
9
u
164
− 16u
163
+ ··· + 4721792u − 344128
c
10
u
164
+ 17u
163
+ ··· + 79677738u + 6137707
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
164
+ 45y
163
+ ··· − 5694y + 1
c
2
, c
6
y
164
+ 73y
163
+ ··· + 38y + 1
c
3
y
164
+ 3y
163
+ ··· + 288317263y + 436921
c
4
, c
12
y
164
− 140y
163
+ ··· + 455834236047y + 11080299169
c
5
y
164
+ 36y
163
+ ··· − 17079481340522y + 147096027961
c
7
y
164
− 65y
163
+ ··· − 2.11 × 10
19
y + 4.74 × 10
17
c
8
, c
11
y
164
+ 108y
163
+ ··· − 1951599728220y + 46398883216
c
9
y
164
+ 22y
163
+ ··· − 2240828266496y + 118424080384
c
10
y
164
− 43y
163
+ ··· + 595530200008586y + 37671447217849
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.299392 + 0.960310I
a = 0.60880 + 1.60945I
b = −0.27189 + 2.44228I
3.17547 − 4.68771I 0
u = 0.299392 − 0.960310I
a = 0.60880 − 1.60945I
b = −0.27189 − 2.44228I
3.17547 + 4.68771I 0
u = 0.879399 + 0.502158I
a = 0.927321 + 0.740852I
b = 0.052034 + 0.404033I
3.92172 − 3.03974I 0
u = 0.879399 − 0.502158I
a = 0.927321 − 0.740852I
b = 0.052034 − 0.404033I
3.92172 + 3.03974I 0
u = 0.768904 + 0.661034I
a = −1.53865 − 0.65651I
b = −0.750438 − 0.087776I
10.44220 − 4.48135I 0
u = 0.768904 − 0.661034I
a = −1.53865 + 0.65651I
b = −0.750438 + 0.087776I
10.44220 + 4.48135I 0
u = −0.351296 + 0.951234I
a = 0.917235 + 0.672606I
b = 0.21016 + 2.41929I
3.93571 + 4.23402I 0
u = −0.351296 − 0.951234I
a = 0.917235 − 0.672606I
b = 0.21016 − 2.41929I
3.93571 − 4.23402I 0
u = 0.777796 + 0.590959I
a = 0.579012 + 1.072520I
b = −0.0728974 + 0.0331661I
6.35048 + 4.60400I 0
u = 0.777796 − 0.590959I
a = 0.579012 − 1.072520I
b = −0.0728974 − 0.0331661I
6.35048 − 4.60400I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.238763 + 0.945986I
a = −1.46789 + 0.78124I
b = −1.49860 + 0.16095I
−0.149224 − 0.169896I 0
u = 0.238763 − 0.945986I
a = −1.46789 − 0.78124I
b = −1.49860 − 0.16095I
−0.149224 + 0.169896I 0
u = 0.740212 + 0.635545I
a = 1.069500 + 0.363686I
b = −0.394024 − 0.029105I
5.62071 − 1.86385I 0
u = 0.740212 − 0.635545I
a = 1.069500 − 0.363686I
b = −0.394024 + 0.029105I
5.62071 + 1.86385I 0
u = −0.921997 + 0.455468I
a = −1.28542 + 0.85638I
b = 0.0495941 + 0.0144672I
9.9214 + 14.3056I 0
u = −0.921997 − 0.455468I
a = −1.28542 − 0.85638I
b = 0.0495941 − 0.0144672I
9.9214 − 14.3056I 0
u = −0.378982 + 0.894534I
a = −1.23129 + 0.97389I
b = −0.208485 + 1.361120I
0.347330 + 0.768195I 0
u = −0.378982 − 0.894534I
a = −1.23129 − 0.97389I
b = −0.208485 − 1.361120I
0.347330 − 0.768195I 0
u = −0.447189 + 0.928338I
a = −1.35708 − 1.01684I
b = −1.11220 − 1.73109I
−1.84221 − 1.36025I 0
u = −0.447189 − 0.928338I
a = −1.35708 + 1.01684I
b = −1.11220 + 1.73109I
−1.84221 + 1.36025I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.557374 + 0.791815I
a = −0.482399 − 0.768678I
b = −1.23517 − 2.06127I
7.39094 + 2.59798I 0
u = 0.557374 − 0.791815I
a = −0.482399 + 0.768678I
b = −1.23517 + 2.06127I
7.39094 − 2.59798I 0
u = 0.398604 + 0.956254I
a = −0.169125 − 0.522395I
b = 0.81974 − 1.63318I
−3.27085 + 1.40346I 0
u = 0.398604 − 0.956254I
a = −0.169125 + 0.522395I
b = 0.81974 + 1.63318I
−3.27085 − 1.40346I 0
u = −0.958668 + 0.415310I
a = 0.488932 − 0.758331I
b = −0.119181 − 0.169137I
3.09195 + 1.90052I 0
u = −0.958668 − 0.415310I
a = 0.488932 + 0.758331I
b = −0.119181 + 0.169137I
3.09195 − 1.90052I 0
u = 0.940805 + 0.458237I
a = 1.063080 + 0.628106I
b = 0.045194 − 0.137682I
4.07982 − 8.13142I 0
u = 0.940805 − 0.458237I
a = 1.063080 − 0.628106I
b = 0.045194 + 0.137682I
4.07982 + 8.13142I 0
u = −0.369144 + 0.878753I
a = 0.48718 + 1.32777I
b = 0.22971 + 1.48146I
−1.46546 − 2.01029I 0
u = −0.369144 − 0.878753I
a = 0.48718 − 1.32777I
b = 0.22971 − 1.48146I
−1.46546 + 2.01029I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.432136 + 0.847873I
a = 1.288150 + 0.341937I
b = −0.434002 − 0.225203I
6.21544 + 2.38522I 0
u = 0.432136 − 0.847873I
a = 1.288150 − 0.341937I
b = −0.434002 + 0.225203I
6.21544 − 2.38522I 0
u = −0.845231 + 0.429893I
a = 1.45361 − 0.98536I
b = −0.0101961 − 0.0485208I
5.40206 + 8.06177I 0
u = −0.845231 − 0.429893I
a = 1.45361 + 0.98536I
b = −0.0101961 + 0.0485208I
5.40206 − 8.06177I 0
u = 0.548834 + 0.904247I
a = −1.068760 − 0.332027I
b = 0.552373 + 0.118981I
7.03162 + 1.83421I 0
u = 0.548834 − 0.904247I
a = −1.068760 + 0.332027I
b = 0.552373 − 0.118981I
7.03162 − 1.83421I 0
u = −0.482212 + 0.942267I
a = 0.79432 − 1.40082I
b = 0.17581 − 2.31004I
−1.59798 − 3.73222I 0
u = −0.482212 − 0.942267I
a = 0.79432 + 1.40082I
b = 0.17581 + 2.31004I
−1.59798 + 3.73222I 0
u = 0.836392 + 0.430610I
a = −1.149630 − 0.650383I
b = 0.0605292 + 0.1066340I
0.92738 − 4.13160I 0
u = 0.836392 − 0.430610I
a = −1.149630 + 0.650383I
b = 0.0605292 − 0.1066340I
0.92738 + 4.13160I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.750798 + 0.748395I
a = −0.549187 + 0.521781I
b = 1.154500 + 0.228095I
9.04363 + 3.27761I 0
u = −0.750798 − 0.748395I
a = −0.549187 − 0.521781I
b = 1.154500 − 0.228095I
9.04363 − 3.27761I 0
u = −0.014646 + 0.934202I
a = 0.835336 + 0.862024I
b = 1.73920 + 1.44468I
5.30699 + 0.59712I 0
u = −0.014646 − 0.934202I
a = 0.835336 − 0.862024I
b = 1.73920 − 1.44468I
5.30699 − 0.59712I 0
u = −0.451807 + 0.969583I
a = −0.347414 − 1.097210I
b = −0.85650 − 3.31703I
−0.60140 − 2.79339I 0
u = −0.451807 − 0.969583I
a = −0.347414 + 1.097210I
b = −0.85650 + 3.31703I
−0.60140 + 2.79339I 0
u = 0.421276 + 0.984650I
a = 0.707714 + 0.767029I
b = 1.63573 + 1.64755I
5.81286 + 1.07075I 0
u = 0.421276 − 0.984650I
a = 0.707714 − 0.767029I
b = 1.63573 − 1.64755I
5.81286 − 1.07075I 0
u = 0.284246 + 0.884148I
a = −0.736505 + 0.773825I
b = 0.183588 + 1.283280I
−1.84261 − 1.12348I 0
u = 0.284246 − 0.884148I
a = −0.736505 − 0.773825I
b = 0.183588 − 1.283280I
−1.84261 + 1.12348I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.438175 + 0.991043I
a = 0.39167 − 2.14462I
b = 0.73933 − 3.19107I
−1.19869 + 2.96238I 0
u = 0.438175 − 0.991043I
a = 0.39167 + 2.14462I
b = 0.73933 + 3.19107I
−1.19869 − 2.96238I 0
u = 0.928409 + 0.561212I
a = −0.881006 − 0.537475I
b = 0.267249 − 0.407232I
5.32602 − 4.19072I 0
u = 0.928409 − 0.561212I
a = −0.881006 + 0.537475I
b = 0.267249 + 0.407232I
5.32602 + 4.19072I 0
u = −0.741730 + 0.535042I
a = −1.77120 + 0.68439I
b = −0.0960172 + 0.0442305I
10.40440 + 1.43479I 0
u = −0.741730 − 0.535042I
a = −1.77120 − 0.68439I
b = −0.0960172 − 0.0442305I
10.40440 − 1.43479I 0
u = 0.465130 + 0.981677I
a = 0.416192 − 0.861546I
b = −0.29798 − 2.04261I
−2.82509 + 4.30262I 0
u = 0.465130 − 0.981677I
a = 0.416192 + 0.861546I
b = −0.29798 + 2.04261I
−2.82509 − 4.30262I 0
u = −0.534504 + 0.947191I
a = 1.60616 + 0.59004I
b = 0.96702 + 1.16237I
1.37832 − 5.70791I 0
u = −0.534504 − 0.947191I
a = 1.60616 − 0.59004I
b = 0.96702 − 1.16237I
1.37832 + 5.70791I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.041954 + 1.087430I
a = −0.461914 + 0.776057I
b = −0.280749 + 1.304690I
−2.21523 − 1.50731I 0
u = 0.041954 − 1.087430I
a = −0.461914 − 0.776057I
b = −0.280749 − 1.304690I
−2.21523 + 1.50731I 0
u = −1.065720 + 0.263554I
a = −0.240281 + 0.642974I
b = 0.054112 − 0.432591I
7.55264 − 0.93341I 0
u = −1.065720 − 0.263554I
a = −0.240281 − 0.642974I
b = 0.054112 + 0.432591I
7.55264 + 0.93341I 0
u = −0.757902 + 0.488167I
a = 0.601889 − 0.713001I
b = −0.532600 + 0.366916I
4.74807 + 0.41354I 0
u = −0.757902 − 0.488167I
a = 0.601889 + 0.713001I
b = −0.532600 − 0.366916I
4.74807 − 0.41354I 0
u = −0.521044 + 0.971902I
a = −0.310263 + 0.800196I
b = 1.26445 + 2.47889I
4.98219 − 9.72797I 0
u = −0.521044 − 0.971902I
a = −0.310263 − 0.800196I
b = 1.26445 − 2.47889I
4.98219 + 9.72797I 0
u = 0.926508 + 0.613901I
a = −0.357281 − 0.921852I
b = −0.0254180 − 0.0761209I
10.8514 + 9.4860I 0
u = 0.926508 − 0.613901I
a = −0.357281 + 0.921852I
b = −0.0254180 + 0.0761209I
10.8514 − 9.4860I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.501121 + 0.730651I
a = −0.30445 − 1.76265I
b = 0.26676 − 2.11459I
2.09757 + 1.45815I 0
u = −0.501121 − 0.730651I
a = −0.30445 + 1.76265I
b = 0.26676 + 2.11459I
2.09757 − 1.45815I 0
u = −0.714764 + 0.517405I
a = −0.816943 + 0.755481I
b = −0.173082 + 0.127356I
1.69961 − 1.06857I 0
u = −0.714764 − 0.517405I
a = −0.816943 − 0.755481I
b = −0.173082 − 0.127356I
1.69961 + 1.06857I 0
u = −0.465464 + 1.021420I
a = −0.715803 + 0.902529I
b = −0.75375 + 1.64324I
−0.30359 − 3.66478I 0
u = −0.465464 − 1.021420I
a = −0.715803 − 0.902529I
b = −0.75375 − 1.64324I
−0.30359 + 3.66478I 0
u = −0.401285 + 0.773801I
a = 1.43942 − 0.22752I
b = 0.640016 − 1.131530I
−0.945604 − 0.017885I 0
u = −0.401285 − 0.773801I
a = 1.43942 + 0.22752I
b = 0.640016 + 1.131530I
−0.945604 + 0.017885I 0
u = 0.525055 + 1.001130I
a = 0.425312 + 0.520951I
b = −0.621904 + 1.250260I
−0.28254 + 6.78019I 0
u = 0.525055 − 1.001130I
a = 0.425312 − 0.520951I
b = −0.621904 − 1.250260I
−0.28254 − 6.78019I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.531748 + 0.997649I
a = −1.21483 + 1.57023I
b = −0.98013 + 2.45169I
4.62202 + 10.47530I 0
u = 0.531748 − 0.997649I
a = −1.21483 − 1.57023I
b = −0.98013 − 2.45169I
4.62202 − 10.47530I 0
u = −0.270943 + 0.818131I
a = 0.239998 + 0.917143I
b = −1.288110 − 0.410197I
0.290512 − 0.483114I 0
u = −0.270943 − 0.818131I
a = 0.239998 − 0.917143I
b = −1.288110 + 0.410197I
0.290512 + 0.483114I 0
u = −0.852393 + 0.058059I
a = −0.425356 + 0.869711I
b = 0.043667 + 0.320666I
2.54431 − 0.44312I 0
u = −0.852393 − 0.058059I
a = −0.425356 − 0.869711I
b = 0.043667 − 0.320666I
2.54431 + 0.44312I 0
u = −0.922500 + 0.689599I
a = 0.640833 − 0.410913I
b = 0.189476 + 0.228100I
5.38406 − 2.97330I 0
u = −0.922500 − 0.689599I
a = 0.640833 + 0.410913I
b = 0.189476 − 0.228100I
5.38406 + 2.97330I 0
u = −0.671021 + 0.942363I
a = −0.358673 + 0.356468I
b = −0.71479 + 2.16500I
8.43126 − 8.68485I 0
u = −0.671021 − 0.942363I
a = −0.358673 − 0.356468I
b = −0.71479 − 2.16500I
8.43126 + 8.68485I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.760797 + 0.357498I
a = −0.23185 − 1.57632I
b = 0.0203426 + 0.0797491I
9.59548 − 1.17327I 0
u = 0.760797 − 0.357498I
a = −0.23185 + 1.57632I
b = 0.0203426 − 0.0797491I
9.59548 + 1.17327I 0
u = −0.440537 + 0.706562I
a = −0.693077 − 0.196240I
b = 0.80705 + 2.06031I
5.91470 + 5.66066I 0
u = −0.440537 − 0.706562I
a = −0.693077 + 0.196240I
b = 0.80705 − 2.06031I
5.91470 − 5.66066I 0
u = −0.738876 + 0.365341I
a = 0.458731 + 0.805769I
b = 0.126492 + 0.651881I
3.83063 − 0.18506I 0
u = −0.738876 − 0.365341I
a = 0.458731 − 0.805769I
b = 0.126492 − 0.651881I
3.83063 + 0.18506I 0
u = 0.494363 + 1.070300I
a = 1.39081 + 0.64361I
b = 1.44093 + 1.10957I
1.52438 + 6.76882I 0
u = 0.494363 − 1.070300I
a = 1.39081 − 0.64361I
b = 1.44093 − 1.10957I
1.52438 − 6.76882I 0
u = 0.644086 + 0.988561I
a = 0.615047 + 0.507180I
b = 1.18887 + 1.14949I
5.15147 + 0.73865I 0
u = 0.644086 − 0.988561I
a = 0.615047 − 0.507180I
b = 1.18887 − 1.14949I
5.15147 − 0.73865I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.640621 + 1.001180I
a = 0.232834 + 0.906106I
b = 0.60213 + 2.28399I
4.50826 + 7.12902I 0
u = 0.640621 − 1.001180I
a = 0.232834 − 0.906106I
b = 0.60213 − 2.28399I
4.50826 − 7.12902I 0
u = 0.663496 + 0.991218I
a = −0.62906 − 1.52482I
b = −0.98281 − 2.09318I
9.43359 + 9.90023I 0
u = 0.663496 − 0.991218I
a = −0.62906 + 1.52482I
b = −0.98281 + 2.09318I
9.43359 − 9.90023I 0
u = −0.056239 + 1.196750I
a = 0.530645 − 0.630207I
b = 0.51561 − 1.48474I
−1.52756 − 2.48388I 0
u = −0.056239 − 1.196750I
a = 0.530645 + 0.630207I
b = 0.51561 + 1.48474I
−1.52756 + 2.48388I 0
u = −0.577117 + 1.054040I
a = −0.782117 − 0.364603I
b = −0.543377 − 0.707896I
1.90034 − 4.71281I 0
u = −0.577117 − 1.054040I
a = −0.782117 + 0.364603I
b = −0.543377 + 0.707896I
1.90034 + 4.71281I 0
u = −0.100366 + 1.204710I
a = −0.889302 − 0.610483I
b = −1.70613 − 1.21344I
−0.23525 + 5.56676I 0
u = −0.100366 − 1.204710I
a = −0.889302 + 0.610483I
b = −1.70613 + 1.21344I
−0.23525 − 5.56676I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.734445 + 0.280825I
a = 0.76609 + 1.50116I
b = 0.201745 + 0.747900I
3.90801 − 2.31367I 0
u = 0.734445 − 0.280825I
a = 0.76609 − 1.50116I
b = 0.201745 − 0.747900I
3.90801 + 2.31367I 0
u = −0.622617 + 1.045780I
a = −0.51612 + 1.46152I
b = −0.95413 + 2.80373I
8.88501 − 6.63527I 0
u = −0.622617 − 1.045780I
a = −0.51612 − 1.46152I
b = −0.95413 − 2.80373I
8.88501 + 6.63527I 0
u = −0.758008 + 0.968853I
a = 0.078152 − 0.866664I
b = 0.467844 − 1.307210I
4.52468 − 3.15181I 0
u = −0.758008 − 0.968853I
a = 0.078152 + 0.866664I
b = 0.467844 + 1.307210I
4.52468 + 3.15181I 0
u = 0.116118 + 1.225130I
a = 0.423933 − 0.475849I
b = 0.98332 − 1.06501I
−4.65639 − 1.57628I 0
u = 0.116118 − 1.225130I
a = 0.423933 + 0.475849I
b = 0.98332 + 1.06501I
−4.65639 + 1.57628I 0
u = −0.587947 + 1.089730I
a = −0.488979 + 0.823994I
b = −0.73857 + 1.54031I
−0.05297 − 3.92486I 0
u = −0.587947 − 1.089730I
a = −0.488979 − 0.823994I
b = −0.73857 − 1.54031I
−0.05297 + 3.92486I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.597767 + 1.098250I
a = 0.241632 − 0.476910I
b = 1.12063 − 1.39128I
2.91053 − 5.58907I 0
u = −0.597767 − 1.098250I
a = 0.241632 + 0.476910I
b = 1.12063 + 1.39128I
2.91053 + 5.58907I 0
u = 0.411445 + 0.602119I
a = 1.61840 − 1.89272I
b = 0.78147 − 1.42119I
5.88132 − 6.31602I 0
u = 0.411445 − 0.602119I
a = 1.61840 + 1.89272I
b = 0.78147 + 1.42119I
5.88132 + 6.31602I 0
u = 0.568053 + 1.147570I
a = −0.863970 − 0.313164I
b = −1.81928 − 0.62729I
7.23173 + 6.22543I 0
u = 0.568053 − 1.147570I
a = −0.863970 + 0.313164I
b = −1.81928 + 0.62729I
7.23173 − 6.22543I 0
u = −0.478985 + 1.187850I
a = 0.198688 − 0.480794I
b = 1.18990 − 0.96758I
3.00598 − 5.77364I 0
u = −0.478985 − 1.187850I
a = 0.198688 + 0.480794I
b = 1.18990 + 0.96758I
3.00598 + 5.77364I 0
u = 0.660383 + 1.100910I
a = 0.566795 + 0.948734I
b = 0.66189 + 1.85514I
2.09234 + 8.71613I 0
u = 0.660383 − 1.100910I
a = 0.566795 − 0.948734I
b = 0.66189 − 1.85514I
2.09234 − 8.71613I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.632796 + 1.117300I
a = −0.364264 − 1.054470I
b = −0.86021 − 2.16893I
−1.12213 + 9.60208I 0
u = 0.632796 − 1.117300I
a = −0.364264 + 1.054470I
b = −0.86021 + 2.16893I
−1.12213 − 9.60208I 0
u = −0.632340 + 1.120450I
a = 0.64477 − 1.26788I
b = 1.23150 − 2.55330I
3.33204 − 13.55160I 0
u = −0.632340 − 1.120450I
a = 0.64477 + 1.26788I
b = 1.23150 + 2.55330I
3.33204 + 13.55160I 0
u = −0.042404 + 1.293600I
a = 0.777671 + 0.567941I
b = 1.51752 + 1.19079I
3.53253 + 11.55200I 0
u = −0.042404 − 1.293600I
a = 0.777671 − 0.567941I
b = 1.51752 − 1.19079I
3.53253 − 11.55200I 0
u = 0.774048 + 1.056980I
a = −0.551602 − 0.389993I
b = −0.983474 − 0.734951I
9.52188 − 3.29261I 0
u = 0.774048 − 1.056980I
a = −0.551602 + 0.389993I
b = −0.983474 + 0.734951I
9.52188 + 3.29261I 0
u = 0.702770 + 1.112990I
a = −0.451366 − 0.854073I
b = −0.46492 − 2.01813I
3.60006 + 10.19360I 0
u = 0.702770 − 1.112990I
a = −0.451366 + 0.854073I
b = −0.46492 + 2.01813I
3.60006 − 10.19360I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.667913 + 1.140160I
a = −0.566023 + 1.178760I
b = −1.11865 + 2.41799I
7.8323 − 20.1341I 0
u = −0.667913 − 1.140160I
a = −0.566023 − 1.178760I
b = −1.11865 − 2.41799I
7.8323 + 20.1341I 0
u = 0.675516 + 1.143700I
a = 0.362254 + 1.059340I
b = 0.88101 + 2.05461I
1.9828 + 14.0339I 0
u = 0.675516 − 1.143700I
a = 0.362254 − 1.059340I
b = 0.88101 − 2.05461I
1.9828 − 14.0339I 0
u = −0.666766 + 1.161400I
a = 0.491921 − 0.629128I
b = 0.81799 − 1.38403I
0.81252 − 7.80419I 0
u = −0.666766 − 1.161400I
a = 0.491921 + 0.629128I
b = 0.81799 + 1.38403I
0.81252 + 7.80419I 0
u = 0.016408 + 1.348930I
a = −0.349964 + 0.409208I
b = −0.885840 + 0.807709I
−2.56947 − 5.22751I 0
u = 0.016408 − 1.348930I
a = −0.349964 − 0.409208I
b = −0.885840 − 0.807709I
−2.56947 + 5.22751I 0
u = −0.167388 + 1.362480I
a = −0.332729 + 0.079366I
b = −0.518566 − 0.036861I
−3.18278 − 1.53386I 0
u = −0.167388 − 1.362480I
a = −0.332729 − 0.079366I
b = −0.518566 + 0.036861I
−3.18278 + 1.53386I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.244701 + 0.566261I
a = 0.076776 − 0.181732I
b = −0.73028 + 1.29401I
1.13389 − 2.73035I 2.00000 + 6.79549I
u = 0.244701 − 0.566261I
a = 0.076776 + 0.181732I
b = −0.73028 − 1.29401I
1.13389 + 2.73035I 2.00000 − 6.79549I
u = −0.289221 + 1.358550I
a = 0.314757 + 0.170460I
b = 0.374907 + 0.399764I
−2.17506 − 4.66653I 0
u = −0.289221 − 1.358550I
a = 0.314757 − 0.170460I
b = 0.374907 − 0.399764I
−2.17506 + 4.66653I 0
u = −0.73047 + 1.21971I
a = −0.142462 + 0.561515I
b = −0.790045 + 1.131310I
4.74108 − 5.50151I 0
u = −0.73047 − 1.21971I
a = −0.142462 − 0.561515I
b = −0.790045 − 1.131310I
4.74108 + 5.50151I 0
u = −0.459644
a = −0.736700
b = −0.346815
0.946440 11.8490
u = 0.266811 + 0.360332I
a = 0.491547 − 0.576665I
b = −0.623860 + 0.971366I
1.14558 − 2.72858I 2.11016 + 5.78056I
u = 0.266811 − 0.360332I
a = 0.491547 + 0.576665I
b = −0.623860 − 0.971366I
1.14558 + 2.72858I 2.11016 − 5.78056I
u = 0.228737 + 0.089878I
a = −2.98748 − 0.18037I
b = 0.115631 + 0.591309I
−1.22014 − 1.07257I −2.57454 + 4.07800I
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.228737 − 0.089878I
a = −2.98748 + 0.18037I
b = 0.115631 − 0.591309I
−1.22014 + 1.07257I −2.57454 − 4.07800I
u = −0.008869 + 0.159476I
a = 0.81014 − 7.41046I
b = 1.083760 − 0.592768I
5.69146 − 6.45095I 6.63966 + 5.51048I
u = −0.008869 − 0.159476I
a = 0.81014 + 7.41046I
b = 1.083760 + 0.592768I
5.69146 + 6.45095I 6.63966 − 5.51048I
u = 0.138622
a = −10.2464
b = −0.698276
0.573200 10.2980
21
II.
I
u
2
= h−6.09×10
12
u
40
+5.52×10
11
u
39
+· · ·+4.00×10
12
b−3.51×10
13
, −2.56×
10
13
u
40
−3.19×10
13
u
39
+· · ·+4.00×10
12
a−3.85×10
13
, u
41
+2u
40
+· · ·+8u+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
1
=
u
2
+ 1
−u
4
a
10
=
6.39769u
40
+ 7.96197u
39
+ ··· + 57.5210u + 9.60566
1.52053u
40
− 0.137871u
39
+ ··· + 45.6217u + 8.77561
a
11
=
9.89050u
40
+ 14.0150u
39
+ ··· + 132.554u + 22.6007
1.54527u
40
+ 0.320373u
39
+ ··· + 56.3245u + 9.92702
a
5
=
−17.9506u
40
− 30.0895u
39
+ ··· − 216.262u − 34.6837
3.14318u
40
+ 3.67726u
39
+ ··· − 21.5143u − 3.69934
a
9
=
5.01803u
40
+ 6.86196u
39
+ ··· + 49.1623u + 7.95118
0.140878u
40
− 1.23788u
39
+ ··· + 37.2630u + 7.12114
a
4
=
−1.61911u
40
− 5.32409u
39
+ ··· − 21.2126u − 2.44427
−8.53257u
40
− 17.1792u
39
+ ··· − 97.1531u − 12.9477
a
8
=
−3.52930u
40
− 7.77099u
39
+ ··· − 57.2363u − 10.3891
0.317794u
40
+ 0.583513u
39
+ ··· − 3.39487u + 1.66939
a
12
=
21.0938u
40
+ 33.7667u
39
+ ··· + 193.747u + 31.9844
0.0404309u
40
+ 3.02209u
39
+ ··· − 35.1775u − 5.24922
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
86468953253005
2001681961463
u
40
−
145958075951024
2001681961463
u
39
+ ··· −
823927223442766
2001681961463
u −
123141726376632
2001681961463
22
(iv) u-Polynomials at the component
23
Crossings u-Polynomials at each crossing
c
1
u
41
− 22u
40
+ ··· − 16u
2
+ 1
c
2
u
41
+ 2u
40
+ ··· + 8u + 1
c
3
u
41
+ 6u
39
+ ··· + 3u − 1
c
4
u
41
+ 3u
40
+ ··· + 5u − 1
c
5
u
41
+ u
40
+ ··· − 4u − 1
c
6
u
41
− 2u
40
+ ··· + 8u − 1
c
7
u
41
+ 2u
40
+ ··· + 6u − 1
c
8
u
41
− 17u
40
+ ··· + 74u − 4
c
9
u
41
+ 3u
40
+ ··· + u + 1
c
10
u
41
+ 4u
40
+ ··· + 6u + 1
c
11
u
41
+ 17u
40
+ ··· + 74u + 4
c
12
u
41
− 3u
40
+ ··· + 5u + 1
24
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
41
+ 2y
40
+ ··· + 32y −1
c
2
, c
6
y
41
+ 22y
40
+ ··· + 16y
2
− 1
c
3
y
41
+ 12y
40
+ ··· + 23y −1
c
4
, c
12
y
41
− 39y
40
+ ··· + 27y −1
c
5
y
41
− 7y
40
+ ··· − 20y −1
c
7
y
41
− 4y
40
+ ··· + 24y −1
c
8
, c
11
y
41
+ 21y
40
+ ··· + 268y −16
c
9
y
41
− 17y
40
+ ··· + 7y −1
c
10
y
41
− 18y
40
+ ··· + 4y −1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.359332 + 0.954220I
a = 0.382234 − 0.780561I
b = −0.362851 + 0.215006I
4.67955 + 8.01277I 4.35208 − 7.49932I
u = 0.359332 − 0.954220I
a = 0.382234 + 0.780561I
b = −0.362851 − 0.215006I
4.67955 − 8.01277I 4.35208 + 7.49932I
u = 0.734475 + 0.750527I
a = 0.933361 + 0.012886I
b = −0.227858 + 0.303958I
7.45980 − 4.10919I 8.44521 + 3.61916I
u = 0.734475 − 0.750527I
a = 0.933361 − 0.012886I
b = −0.227858 − 0.303958I
7.45980 + 4.10919I 8.44521 − 3.61916I
u = −0.343196 + 0.873757I
a = 1.50419 + 0.50926I
b = 0.854173 + 0.102791I
−1.86107 − 0.15099I −5.41361 − 0.87603I
u = −0.343196 − 0.873757I
a = 1.50419 − 0.50926I
b = 0.854173 − 0.102791I
−1.86107 + 0.15099I −5.41361 + 0.87603I
u = −0.429417 + 0.973737I
a = −0.12259 − 1.61010I
b = −0.29477 − 2.60345I
−2.42579 − 2.92088I −7.06001 + 4.29578I
u = −0.429417 − 0.973737I
a = −0.12259 + 1.61010I
b = −0.29477 + 2.60345I
−2.42579 + 2.92088I −7.06001 − 4.29578I
u = 0.468499 + 0.957879I
a = 0.42414 − 1.47466I
b = 0.91887 − 3.28990I
−0.11865 + 2.66752I 11.06553 − 2.13389I
u = 0.468499 − 0.957879I
a = 0.42414 + 1.47466I
b = 0.91887 + 3.28990I
−0.11865 − 2.66752I 11.06553 + 2.13389I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.369263 + 0.854986I
a = −0.619409 + 1.134990I
b = −1.16194 + 2.81751I
5.01655 − 4.97589I 4.19587 + 2.13861I
u = 0.369263 − 0.854986I
a = −0.619409 − 1.134990I
b = −1.16194 − 2.81751I
5.01655 + 4.97589I 4.19587 − 2.13861I
u = 0.949373 + 0.514498I
a = −0.827303 − 0.679345I
b = 0.115602 − 0.326407I
3.80067 − 3.76175I 4.04687 + 8.60808I
u = 0.949373 − 0.514498I
a = −0.827303 + 0.679345I
b = 0.115602 + 0.326407I
3.80067 + 3.76175I 4.04687 − 8.60808I
u = −0.053293 + 1.107340I
a = 0.383401 − 0.688407I
b = 0.37077 − 1.43255I
−3.14304 − 1.96905I −5.47544 + 4.23016I
u = −0.053293 − 1.107340I
a = 0.383401 + 0.688407I
b = 0.37077 + 1.43255I
−3.14304 + 1.96905I −5.47544 − 4.23016I
u = −0.842946 + 0.184688I
a = −0.063766 + 0.943914I
b = 0.088811 + 0.528603I
2.22526 + 1.26142I 0.55804 − 3.51091I
u = −0.842946 − 0.184688I
a = −0.063766 − 0.943914I
b = 0.088811 − 0.528603I
2.22526 − 1.26142I 0.55804 + 3.51091I
u = 0.627069 + 0.950079I
a = 0.035353 + 1.094250I
b = −0.23352 + 2.49795I
6.81502 + 9.30322I 7.15508 − 8.78170I
u = 0.627069 − 0.950079I
a = 0.035353 − 1.094250I
b = −0.23352 − 2.49795I
6.81502 − 9.30322I 7.15508 + 8.78170I
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.515078 + 1.019620I
a = −1.174700 + 0.250763I
b = −0.878460 + 0.495854I
−0.15606 − 5.46645I 0. + 6.29888I
u = −0.515078 − 1.019620I
a = −1.174700 − 0.250763I
b = −0.878460 − 0.495854I
−0.15606 + 5.46645I 0. − 6.29888I
u = 0.384568 + 0.731819I
a = −1.05608 + 1.11737I
b = 0.281134 − 0.176060I
0.694797 + 1.001360I 9.13676 − 7.10067I
u = 0.384568 − 0.731819I
a = −1.05608 − 1.11737I
b = 0.281134 + 0.176060I
0.694797 − 1.001360I 9.13676 + 7.10067I
u = −0.348151 + 0.719690I
a = −0.47780 + 1.40512I
b = 0.24995 + 2.03906I
1.17599 + 1.75541I 1.77038 − 1.38585I
u = −0.348151 − 0.719690I
a = −0.47780 − 1.40512I
b = 0.24995 − 2.03906I
1.17599 − 1.75541I 1.77038 + 1.38585I
u = −0.666585 + 0.289368I
a = −0.769093 + 0.899300I
b = 0.041726 − 0.797647I
6.92177 − 0.69506I 8.24781 − 0.01319I
u = −0.666585 − 0.289368I
a = −0.769093 − 0.899300I
b = 0.041726 + 0.797647I
6.92177 + 0.69506I 8.24781 + 0.01319I
u = −0.709130 + 1.085470I
a = 0.031648 + 0.615539I
b = −0.58552 + 1.35606I
4.78480 − 4.89513I 0
u = −0.709130 − 1.085470I
a = 0.031648 − 0.615539I
b = −0.58552 − 1.35606I
4.78480 + 4.89513I 0
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.683871 + 1.128830I
a = −0.530714 − 0.869240I
b = −0.72080 − 1.85587I
1.87314 + 9.72586I 0
u = 0.683871 − 1.128830I
a = −0.530714 + 0.869240I
b = −0.72080 + 1.85587I
1.87314 − 9.72586I 0
u = −0.120430 + 1.319130I
a = 0.316599 − 0.217879I
b = 0.396791 − 0.560081I
−3.36099 − 1.75947I 0
u = −0.120430 − 1.319130I
a = 0.316599 + 0.217879I
b = 0.396791 + 0.560081I
−3.36099 + 1.75947I 0
u = −0.633061 + 1.230740I
a = 0.283268 − 0.419781I
b = 0.99610 − 1.01805I
3.61944 − 5.83436I 0
u = −0.633061 − 1.230740I
a = 0.283268 + 0.419781I
b = 0.99610 + 1.01805I
3.61944 + 5.83436I 0
u = −0.218617 + 1.378300I
a = −0.251015 − 0.030734I
b = −0.488752 + 0.205065I
−1.95628 − 4.86397I 0
u = −0.218617 − 1.378300I
a = −0.251015 + 0.030734I
b = −0.488752 − 0.205065I
−1.95628 + 4.86397I 0
u = −0.475752 + 0.158610I
a = 0.42257 − 1.75445I
b = −0.473322 + 0.842930I
6.83488 + 0.66437I 9.06576 − 0.01946I
u = −0.475752 − 0.158610I
a = 0.42257 + 1.75445I
b = −0.473322 − 0.842930I
6.83488 − 0.66437I 9.06576 + 0.01946I
30
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.441592
a = 2.35141
b = 0.227744
−0.223040 0.0879850
31
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
41
− 22u
40
+ ··· − 16u
2
+ 1)(u
164
+ 73u
163
+ ··· + 38u + 1)
c
2
(u
41
+ 2u
40
+ ··· + 8u + 1)(u
164
− 3u
163
+ ··· − 12u − 1)
c
3
(u
41
+ 6u
39
+ ··· + 3u − 1)(u
164
+ u
163
+ ··· − 6629u + 661)
c
4
(u
41
+ 3u
40
+ ··· + 5u − 1)(u
164
− 70u
162
+ ··· + 183149u − 105263)
c
5
(u
41
+ u
40
+ ··· − 4u − 1)(u
164
+ 2u
163
+ ··· + 7727742u − 383531)
c
6
(u
41
− 2u
40
+ ··· + 8u − 1)(u
164
− 3u
163
+ ··· − 12u − 1)
c
7
(u
41
+ 2u
40
+ ··· + 6u − 1)
· (u
164
− 3u
163
+ ··· − 3133307254u + 688167281)
c
8
(u
41
− 17u
40
+ ··· + 74u − 4)
· (u
164
+ 10u
163
+ ··· + 815546u − 215404)
c
9
(u
41
+ 3u
40
+ ··· + u + 1)(u
164
− 16u
163
+ ··· + 4721792u − 344128)
c
10
(u
41
+ 4u
40
+ ··· + 6u + 1)
· (u
164
+ 17u
163
+ ··· + 79677738u + 6137707)
c
11
(u
41
+ 17u
40
+ ··· + 74u + 4)
· (u
164
+ 10u
163
+ ··· + 815546u − 215404)
c
12
(u
41
− 3u
40
+ ··· + 5u + 1)(u
164
− 70u
162
+ ··· + 183149u − 105263)
32
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
41
+ 2y
40
+ ··· + 32y −1)(y
164
+ 45y
163
+ ··· − 5694y + 1)
c
2
, c
6
(y
41
+ 22y
40
+ ··· + 16y
2
− 1)(y
164
+ 73y
163
+ ··· + 38y + 1)
c
3
(y
41
+ 12y
40
+ ··· + 23y −1)
· (y
164
+ 3y
163
+ ··· + 288317263y + 436921)
c
4
, c
12
(y
41
− 39y
40
+ ··· + 27y −1)
· (y
164
− 140y
163
+ ··· + 455834236047y + 11080299169)
c
5
(y
41
− 7y
40
+ ··· − 20y −1)
· (y
164
+ 36y
163
+ ··· − 17079481340522y + 147096027961)
c
7
(y
41
− 4y
40
+ ··· + 24y −1)
· (y
164
− 65y
163
+ ··· − 2.11 × 10
19
y + 4.74 × 10
17
)
c
8
, c
11
(y
41
+ 21y
40
+ ··· + 268y −16)
· (y
164
+ 108y
163
+ ··· − 1951599728220y + 46398883216)
c
9
(y
41
− 17y
40
+ ··· + 7y −1)
· (y
164
+ 22y
163
+ ··· − 2240828266496y + 118424080384)
c
10
(y
41
− 18y
40
+ ··· + 4y −1)
· (y
164
− 43y
163
+ ··· + 595530200008586y + 37671447217849)
33
