12a
0893
(K12a
0893
)
A knot diagram
1
Linearized knot diagam
4 6 7 1 12 9 11 3 2 5 8 10
Solving Sequence
3,8 9,11
12 7 4 6 2 1 5 10
c
8
c
11
c
7
c
3
c
6
c
2
c
1
c
5
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.61103 × 10
2633
u
209
− 1.17812 × 10
2634
u
208
+ ··· + 2.36542 × 10
2634
b + 2.70080 × 10
2633
,
6.58387 × 10
2634
u
209
+ 1.29409 × 10
2635
u
208
+ ··· + 2.36542 × 10
2634
a − 3.74081 × 10
2635
,
3u
210
+ 6u
209
+ ··· − 26u + 1i
I
u
2
= h1.26412 × 10
171
u
55
− 3.51118 × 10
171
u
54
+ ··· + 2.84952 × 10
170
b − 1.69933 × 10
171
,
3.45571 × 10
170
u
55
− 9.11636 × 10
170
u
54
+ ··· + 2.84952 × 10
170
a + 1.97333 × 10
170
, 3u
56
− 9u
55
+ ··· − 7u + 1i
* 2 irreducible components of dim
C
= 0, with total 266 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−5.61 × 10
2633
u
209
− 1.18 × 10
2634
u
208
+ · · · + 2.37 × 10
2634
b +
2.70 × 10
2633
, 6.58 × 10
2634
u
209
+ 1.29 × 10
2635
u
208
+ · · · + 2.37 × 10
2634
a −
3.74 × 10
2635
, 3u
210
+ 6u
209
+ · · · − 26u + 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
11
=
−2.78338u
209
− 5.47088u
208
+ ··· − 408.910u + 15.8146
0.237211u
209
+ 0.498058u
208
+ ··· + 26.8040u − 0.114179
a
12
=
−3.02059u
209
− 5.96893u
208
+ ··· − 435.714u + 15.9288
0.237211u
209
+ 0.498058u
208
+ ··· + 26.8040u − 0.114179
a
7
=
1.17133u
209
+ 2.28236u
208
+ ··· + 251.317u − 19.4374
−0.336848u
209
− 0.679864u
208
+ ··· − 45.5636u + 1.65715
a
4
=
−0.0423068u
209
− 0.230676u
208
+ ··· + 68.9630u − 11.9556
−0.159705u
209
− 0.320978u
208
+ ··· − 26.1963u + 1.32984
a
6
=
1.48273u
209
+ 2.90344u
208
+ ··· + 295.968u − 21.0744
−0.336339u
209
− 0.680440u
208
+ ··· − 45.6823u + 1.65772
a
2
=
0.235422u
209
+ 0.325882u
208
+ ··· + 124.375u − 14.6092
−0.176154u
209
− 0.345408u
208
+ ··· − 29.8021u + 1.42071
a
1
=
2.43638u
209
+ 4.77805u
208
+ ··· + 340.373u − 14.4855
−0.238536u
209
− 0.486428u
208
+ ··· − 26.9801u + 0.410462
a
5
=
−0.272076u
209
− 0.664735u
208
+ ··· − 26.7015u + 0.929693
0.00207036u
209
+ 0.00307822u
208
+ ··· + 0.0551708u + 0.101753
a
10
=
−2.23770u
209
− 4.46873u
208
+ ··· − 371.192u + 13.8781
0.196187u
209
+ 0.405338u
208
+ ··· + 25.3540u − 0.160323
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.435971u
209
− 0.805405u
208
+ ··· + 121.187u − 8.89267
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
210
+ 10u
209
+ ··· − 27478849u + 12092767
c
2
u
210
− 6u
209
+ ··· + 49u + 1
c
3
u
210
+ 8u
208
+ ··· + 257055u + 4092
c
5
u
210
+ 7u
209
+ ··· + 1508984076u + 44022057
c
6
u
210
+ 12u
209
+ ··· + 4260u + 237
c
7
, c
11
u
210
+ 2u
209
+ ··· − 101779u + 358027
c
8
3(3u
210
+ 6u
209
+ ··· − 26u + 1)
c
9
3(3u
210
− 3u
209
+ ··· + 4592789u + 999482)
c
10
3(3u
210
+ 15u
209
+ ··· + 1.12391 × 10
8
u + 1.34206 × 10
7
)
c
12
u
210
+ 12u
209
+ ··· + 450u + 375
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
210
+ 148y
209
+ ··· + 7967626144440991y + 146235013716289
c
2
y
210
+ 22y
209
+ ··· + 49y + 1
c
3
y
210
+ 16y
209
+ ··· − 23452087521y + 16744464
c
5
y
210
+ 21y
209
+ ··· + 183177916340579052y + 1937941502511249
c
6
y
210
+ 8y
209
+ ··· + 4428546y + 56169
c
7
, c
11
y
210
− 102y
209
+ ··· − 7529227423575y + 128183332729
c
8
9(9y
210
+ 96y
209
+ ··· + 290y + 1)
c
9
9(9y
210
+ 537y
209
+ ··· − 2.72232 × 10
14
y + 9.98964 × 10
11
)
c
10
9
· (9y
210
− 525y
209
+ ··· − 18148003448693073y + 180112826454544)
c
12
y
210
− 34y
209
+ ··· − 9502500y + 140625
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.838294 + 0.540054I
a = 1.77803 − 0.11287I
b = 1.350600 + 0.028259I
−7.00637 − 2.65784I 0
u = 0.838294 − 0.540054I
a = 1.77803 + 0.11287I
b = 1.350600 − 0.028259I
−7.00637 + 2.65784I 0
u = −0.974110 + 0.329203I
a = 0.302974 + 0.036436I
b = 0.27482 − 1.51050I
3.01434 + 4.31771I 0
u = −0.974110 − 0.329203I
a = 0.302974 − 0.036436I
b = 0.27482 + 1.51050I
3.01434 − 4.31771I 0
u = −0.502020 + 0.818598I
a = 0.310752 − 1.345780I
b = −0.906972 + 0.145337I
−0.39504 + 4.95163I 0
u = −0.502020 − 0.818598I
a = 0.310752 + 1.345780I
b = −0.906972 − 0.145337I
−0.39504 − 4.95163I 0
u = −0.631212 + 0.704469I
a = 1.122220 + 0.782606I
b = −0.212816 − 0.811223I
4.13252 + 1.14382I 0
u = −0.631212 − 0.704469I
a = 1.122220 − 0.782606I
b = −0.212816 + 0.811223I
4.13252 − 1.14382I 0
u = 0.299721 + 0.889161I
a = 0.06887 + 1.80152I
b = −1.137400 − 0.557002I
1.50993 − 6.12543I 0
u = 0.299721 − 0.889161I
a = 0.06887 − 1.80152I
b = −1.137400 + 0.557002I
1.50993 + 6.12543I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.932725 + 0.048673I
a = 2.30883 + 0.48865I
b = 1.072620 + 0.492248I
−4.49722 − 5.58626I 0
u = 0.932725 − 0.048673I
a = 2.30883 − 0.48865I
b = 1.072620 − 0.492248I
−4.49722 + 5.58626I 0
u = −0.975344 + 0.442624I
a = −1.11120 − 1.12254I
b = −0.959846 − 0.255558I
−3.94127 + 2.23313I 0
u = −0.975344 − 0.442624I
a = −1.11120 + 1.12254I
b = −0.959846 + 0.255558I
−3.94127 − 2.23313I 0
u = −0.561718 + 0.923956I
a = −0.574246 − 0.849632I
b = −0.899775 + 0.623859I
1.71023 + 4.27980I 0
u = −0.561718 − 0.923956I
a = −0.574246 + 0.849632I
b = −0.899775 − 0.623859I
1.71023 − 4.27980I 0
u = −0.910592 + 0.588984I
a = −2.11961 − 0.21354I
b = −1.114550 + 0.369861I
−3.23520 + 7.08529I 0
u = −0.910592 − 0.588984I
a = −2.11961 + 0.21354I
b = −1.114550 − 0.369861I
−3.23520 − 7.08529I 0
u = 0.602104 + 0.902630I
a = 0.352390 + 0.985041I
b = −0.676345 + 0.160093I
−1.28161 − 4.61716I 0
u = 0.602104 − 0.902630I
a = 0.352390 − 0.985041I
b = −0.676345 − 0.160093I
−1.28161 + 4.61716I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.794512 + 0.745220I
a = −0.0260919 − 0.1248450I
b = 0.098483 + 1.091630I
2.07212 − 7.26772I 0
u = 0.794512 − 0.745220I
a = −0.0260919 + 0.1248450I
b = 0.098483 − 1.091630I
2.07212 + 7.26772I 0
u = 0.882397 + 0.218865I
a = −2.41669 − 0.21438I
b = −1.076990 − 0.277729I
−4.24696 − 3.56604I 0
u = 0.882397 − 0.218865I
a = −2.41669 + 0.21438I
b = −1.076990 + 0.277729I
−4.24696 + 3.56604I 0
u = −1.077580 + 0.192610I
a = 1.063200 + 0.208572I
b = 1.51413 − 0.32222I
−2.95365 − 1.10457I 0
u = −1.077580 − 0.192610I
a = 1.063200 − 0.208572I
b = 1.51413 + 0.32222I
−2.95365 + 1.10457I 0
u = 0.883763 + 0.193908I
a = 0.915880 − 0.288558I
b = 1.289470 + 0.457581I
−2.85438 + 0.37294I 0
u = 0.883763 − 0.193908I
a = 0.915880 + 0.288558I
b = 1.289470 − 0.457581I
−2.85438 − 0.37294I 0
u = 0.291081 + 0.846442I
a = 0.881435 − 0.399940I
b = −0.622853 + 0.669170I
3.55993 − 0.33553I 0
u = 0.291081 − 0.846442I
a = 0.881435 + 0.399940I
b = −0.622853 − 0.669170I
3.55993 + 0.33553I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.038123 + 1.104440I
a = 1.131140 + 0.040930I
b = −1.328670 − 0.120397I
3.24826 − 0.03375I 0
u = −0.038123 − 1.104440I
a = 1.131140 − 0.040930I
b = −1.328670 + 0.120397I
3.24826 + 0.03375I 0
u = −0.268475 + 1.072690I
a = 0.043255 − 0.398396I
b = −0.785143 + 0.405357I
1.50142 + 3.76427I 0
u = −0.268475 − 1.072690I
a = 0.043255 + 0.398396I
b = −0.785143 − 0.405357I
1.50142 − 3.76427I 0
u = 0.142639 + 1.103720I
a = 0.306795 − 0.176767I
b = −0.526898 − 0.279012I
6.06903 + 0.32205I 0
u = 0.142639 − 1.103720I
a = 0.306795 + 0.176767I
b = −0.526898 + 0.279012I
6.06903 − 0.32205I 0
u = −0.806291 + 0.362257I
a = 1.224860 + 0.178142I
b = 1.27334 − 0.93876I
−0.52426 + 3.89742I 0
u = −0.806291 − 0.362257I
a = 1.224860 − 0.178142I
b = 1.27334 + 0.93876I
−0.52426 − 3.89742I 0
u = 0.352923 + 0.810416I
a = −0.665121 − 0.292336I
b = −0.881282 + 0.748614I
1.79631 + 0.92582I 0
u = 0.352923 − 0.810416I
a = −0.665121 + 0.292336I
b = −0.881282 − 0.748614I
1.79631 − 0.92582I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.861574 + 0.729370I
a = −2.19323 − 0.96284I
b = −0.565584 + 0.608098I
5.01219 + 8.07894I 0
u = −0.861574 − 0.729370I
a = −2.19323 + 0.96284I
b = −0.565584 − 0.608098I
5.01219 − 8.07894I 0
u = −1.129100 + 0.140684I
a = −1.23791 − 0.89091I
b = −0.810907 + 0.540868I
0.28583 + 6.27248I 0
u = −1.129100 − 0.140684I
a = −1.23791 + 0.89091I
b = −0.810907 − 0.540868I
0.28583 − 6.27248I 0
u = −0.206487 + 0.835219I
a = −1.60062 − 1.85574I
b = −0.576402 − 0.135329I
1.13788 − 6.73057I 0
u = −0.206487 − 0.835219I
a = −1.60062 + 1.85574I
b = −0.576402 + 0.135329I
1.13788 + 6.73057I 0
u = 0.956158 + 0.628238I
a = −1.83593 + 0.38440I
b = −1.234210 − 0.338031I
−4.47132 − 5.17456I 0
u = 0.956158 − 0.628238I
a = −1.83593 − 0.38440I
b = −1.234210 + 0.338031I
−4.47132 + 5.17456I 0
u = 0.761568 + 0.874361I
a = −0.185779 + 0.940016I
b = 0.281809 − 0.549412I
−1.99263 + 2.64285I 0
u = 0.761568 − 0.874361I
a = −0.185779 − 0.940016I
b = 0.281809 + 0.549412I
−1.99263 − 2.64285I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.665830 + 0.949582I
a = −0.216448 + 0.192004I
b = 0.925219 + 0.649865I
1.28817 + 1.13940I 0
u = −0.665830 − 0.949582I
a = −0.216448 − 0.192004I
b = 0.925219 − 0.649865I
1.28817 − 1.13940I 0
u = 0.282254 + 1.131240I
a = −1.10347 + 1.66886I
b = −0.761673 − 0.275295I
−2.76953 − 0.36673I 0
u = 0.282254 − 1.131240I
a = −1.10347 − 1.66886I
b = −0.761673 + 0.275295I
−2.76953 + 0.36673I 0
u = −0.513702 + 1.048320I
a = 0.933452 + 0.478499I
b = 0.852363 − 0.218931I
−1.69340 + 1.74417I 0
u = −0.513702 − 1.048320I
a = 0.933452 − 0.478499I
b = 0.852363 + 0.218931I
−1.69340 − 1.74417I 0
u = −0.556498 + 0.618059I
a = −1.37127 − 0.60951I
b = −1.32437 + 0.77348I
0.86117 + 13.48710I 0
u = −0.556498 − 0.618059I
a = −1.37127 + 0.60951I
b = −1.32437 − 0.77348I
0.86117 − 13.48710I 0
u = 0.499885 + 0.663782I
a = −1.44798 + 0.85498I
b = −1.254670 − 0.634309I
−2.50988 − 8.05345I 0
u = 0.499885 − 0.663782I
a = −1.44798 − 0.85498I
b = −1.254670 + 0.634309I
−2.50988 + 8.05345I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.805967 + 0.177860I
a = 0.434459 + 0.646256I
b = −0.146359 − 0.254865I
0.95657 + 3.34017I 0
u = 0.805967 − 0.177860I
a = 0.434459 − 0.646256I
b = −0.146359 + 0.254865I
0.95657 − 3.34017I 0
u = −0.730148 + 0.325441I
a = 0.689403 + 0.803956I
b = 0.248934 + 0.487387I
−2.34065 + 1.51221I 0
u = −0.730148 − 0.325441I
a = 0.689403 − 0.803956I
b = 0.248934 − 0.487387I
−2.34065 − 1.51221I 0
u = 0.082067 + 0.789063I
a = −2.51671 − 0.30100I
b = 0.700472 − 0.136876I
4.67674 + 2.13623I 0
u = 0.082067 − 0.789063I
a = −2.51671 + 0.30100I
b = 0.700472 + 0.136876I
4.67674 − 2.13623I 0
u = −0.396844 + 0.672747I
a = 0.477507 − 0.394204I
b = 0.354193 − 0.256651I
−0.59462 + 1.63631I 0
u = −0.396844 − 0.672747I
a = 0.477507 + 0.394204I
b = 0.354193 + 0.256651I
−0.59462 − 1.63631I 0
u = 0.000149 + 0.779699I
a = −2.05632 − 0.40832I
b = 1.151910 + 0.441528I
1.73719 − 11.11930I 0
u = 0.000149 − 0.779699I
a = −2.05632 + 0.40832I
b = 1.151910 − 0.441528I
1.73719 + 11.11930I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.949273 + 0.771417I
a = 0.579696 − 0.324202I
b = 0.328331 + 1.185990I
1.57222 − 4.42354I 0
u = 0.949273 − 0.771417I
a = 0.579696 + 0.324202I
b = 0.328331 − 1.185990I
1.57222 + 4.42354I 0
u = 0.219917 + 1.206290I
a = −0.247126 + 0.003737I
b = −0.695623 − 0.473447I
4.41442 − 9.47905I 0
u = 0.219917 − 1.206290I
a = −0.247126 − 0.003737I
b = −0.695623 + 0.473447I
4.41442 + 9.47905I 0
u = −0.202107 + 0.740906I
a = −1.43945 + 0.88654I
b = 0.957278 − 0.420548I
−2.24052 + 6.62924I 0
u = −0.202107 − 0.740906I
a = −1.43945 − 0.88654I
b = 0.957278 + 0.420548I
−2.24052 − 6.62924I 0
u = −1.088940 + 0.577327I
a = 1.376260 + 0.191861I
b = 1.50735 + 0.08128I
−5.87042 − 1.91423I 0
u = −1.088940 − 0.577327I
a = 1.376260 − 0.191861I
b = 1.50735 − 0.08128I
−5.87042 + 1.91423I 0
u = −0.299101 + 0.694271I
a = 0.229867 − 0.239996I
b = 0.305748 − 0.639795I
−0.06110 + 1.78502I 0
u = −0.299101 − 0.694271I
a = 0.229867 + 0.239996I
b = 0.305748 + 0.639795I
−0.06110 − 1.78502I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.702449 + 0.275050I
a = 3.41512 + 0.46045I
b = 1.117660 − 0.549361I
−0.05361 + 11.89730I 0
u = −0.702449 − 0.275050I
a = 3.41512 − 0.46045I
b = 1.117660 + 0.549361I
−0.05361 − 11.89730I 0
u = −0.773109 + 0.976730I
a = −0.168386 − 0.112342I
b = −0.339086 − 0.627992I
−0.88491 + 4.23594I 0
u = −0.773109 − 0.976730I
a = −0.168386 + 0.112342I
b = −0.339086 + 0.627992I
−0.88491 − 4.23594I 0
u = −1.138080 + 0.558034I
a = −1.281100 − 0.010003I
b = −1.389430 − 0.120494I
−7.72543 + 5.67594I 0
u = −1.138080 − 0.558034I
a = −1.281100 + 0.010003I
b = −1.389430 + 0.120494I
−7.72543 − 5.67594I 0
u = −0.503915 + 0.527742I
a = 0.307213 + 0.874366I
b = 0.920430 − 0.907941I
−0.74677 + 6.77543I 0
u = −0.503915 − 0.527742I
a = 0.307213 − 0.874366I
b = 0.920430 + 0.907941I
−0.74677 − 6.77543I 0
u = 0.580935 + 1.145110I
a = 0.058772 − 0.156627I
b = −0.538663 + 0.798032I
5.18100 − 1.10780I 0
u = 0.580935 − 1.145110I
a = 0.058772 + 0.156627I
b = −0.538663 − 0.798032I
5.18100 + 1.10780I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.286489 + 0.647018I
a = −1.14375 − 2.69066I
b = −0.982337 + 0.550153I
2.47295 + 5.07532I 0
u = −0.286489 − 0.647018I
a = −1.14375 + 2.69066I
b = −0.982337 − 0.550153I
2.47295 − 5.07532I 0
u = 0.556103 + 0.432905I
a = −0.46178 − 1.70459I
b = 0.350612 − 0.679158I
2.20453 − 7.10994I 0
u = 0.556103 − 0.432905I
a = −0.46178 + 1.70459I
b = 0.350612 + 0.679158I
2.20453 + 7.10994I 0
u = 0.993146 + 0.878069I
a = 0.165270 − 0.243800I
b = −0.142644 + 1.176400I
1.53849 − 3.99678I 0
u = 0.993146 − 0.878069I
a = 0.165270 + 0.243800I
b = −0.142644 − 1.176400I
1.53849 + 3.99678I 0
u = 0.572408 + 1.196250I
a = −0.227683 + 0.056236I
b = 0.458780 − 0.414775I
4.38891 − 8.29891I 0
u = 0.572408 − 1.196250I
a = −0.227683 − 0.056236I
b = 0.458780 + 0.414775I
4.38891 + 8.29891I 0
u = 1.179300 + 0.610583I
a = −1.262920 + 0.190665I
b = −1.61506 − 0.03720I
−4.92707 − 10.37180I 0
u = 1.179300 − 0.610583I
a = −1.262920 − 0.190665I
b = −1.61506 + 0.03720I
−4.92707 + 10.37180I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.077930 + 0.785964I
a = −0.236627 + 0.217969I
b = −0.378843 − 1.139770I
6.38657 + 5.55190I 0
u = −1.077930 − 0.785964I
a = −0.236627 − 0.217969I
b = −0.378843 + 1.139770I
6.38657 − 5.55190I 0
u = −0.370481 + 0.533275I
a = 1.083500 + 0.849965I
b = 1.224680 − 0.380525I
−2.17764 + 1.67158I 0
u = −0.370481 − 0.533275I
a = 1.083500 − 0.849965I
b = 1.224680 + 0.380525I
−2.17764 − 1.67158I 0
u = −0.844209 + 1.057240I
a = 1.62430 + 0.88862I
b = 1.106270 − 0.464937I
2.27330 + 12.13740I 0
u = −0.844209 − 1.057240I
a = 1.62430 − 0.88862I
b = 1.106270 + 0.464937I
2.27330 − 12.13740I 0
u = −0.751764 + 1.131800I
a = −1.23605 − 1.06569I
b = −1.016700 + 0.677033I
3.84639 + 6.58326I 0
u = −0.751764 − 1.131800I
a = −1.23605 + 1.06569I
b = −1.016700 − 0.677033I
3.84639 − 6.58326I 0
u = 0.083256 + 0.621860I
a = −1.089660 + 0.209851I
b = −0.967510 − 0.795769I
3.55279 + 4.63528I 0
u = 0.083256 − 0.621860I
a = −1.089660 − 0.209851I
b = −0.967510 + 0.795769I
3.55279 − 4.63528I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.544266 + 1.290110I
a = 0.134657 − 0.191636I
b = 0.628070 + 0.270831I
0.98489 + 1.78465I 0
u = −0.544266 − 1.290110I
a = 0.134657 + 0.191636I
b = 0.628070 − 0.270831I
0.98489 − 1.78465I 0
u = 0.429507 + 0.407611I
a = 1.29030 − 0.96089I
b = 1.31815 + 0.63665I
−2.12743 − 4.25100I 0
u = 0.429507 − 0.407611I
a = 1.29030 + 0.96089I
b = 1.31815 − 0.63665I
−2.12743 + 4.25100I 0
u = 0.571298 + 0.140121I
a = 1.75453 − 0.00376I
b = 1.39662 + 0.64840I
−1.15203 − 2.71654I 0
u = 0.571298 − 0.140121I
a = 1.75453 + 0.00376I
b = 1.39662 − 0.64840I
−1.15203 + 2.71654I 0
u = 0.75235 + 1.19938I
a = 0.268695 + 0.266373I
b = −1.11748 + 0.92510I
3.57512 − 2.37918I 0
u = 0.75235 − 1.19938I
a = 0.268695 − 0.266373I
b = −1.11748 − 0.92510I
3.57512 + 2.37918I 0
u = −1.07753 + 0.92119I
a = 1.75661 + 0.51364I
b = 0.787113 − 0.392648I
6.29350 + 0.71217I 0
u = −1.07753 − 0.92119I
a = 1.75661 − 0.51364I
b = 0.787113 + 0.392648I
6.29350 − 0.71217I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.95245 + 1.05842I
a = −0.0593108 + 0.0983097I
b = 0.358476 − 1.008920I
−1.38946 − 9.53042I 0
u = 0.95245 − 1.05842I
a = −0.0593108 − 0.0983097I
b = 0.358476 + 1.008920I
−1.38946 + 9.53042I 0
u = −1.01245 + 1.02934I
a = −0.1044490 + 0.0090545I
b = 0.419459 + 1.221530I
3.1418 + 15.2882I 0
u = −1.01245 − 1.02934I
a = −0.1044490 − 0.0090545I
b = 0.419459 − 1.221530I
3.1418 − 15.2882I 0
u = 0.392570 + 0.385220I
a = 1.59506 − 1.60422I
b = 1.178910 + 0.632393I
−1.69409 − 3.94908I 0
u = 0.392570 − 0.385220I
a = 1.59506 + 1.60422I
b = 1.178910 − 0.632393I
−1.69409 + 3.94908I 0
u = −0.91619 + 1.12719I
a = −0.627803 − 0.956862I
b = 0.036746 + 0.921669I
3.21822 − 7.78812I 0
u = −0.91619 − 1.12719I
a = −0.627803 + 0.956862I
b = 0.036746 − 0.921669I
3.21822 + 7.78812I 0
u = 1.43287 + 0.29295I
a = −1.62321 − 0.46309I
b = −0.736511 + 0.089319I
−2.89131 − 3.41550I 0
u = 1.43287 − 0.29295I
a = −1.62321 + 0.46309I
b = −0.736511 − 0.089319I
−2.89131 + 3.41550I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.014909 + 0.531363I
a = 0.453187 + 0.029063I
b = −0.107859 − 1.004670I
0.79385 + 2.10722I 8.15045 − 5.26873I
u = 0.014909 − 0.531363I
a = 0.453187 − 0.029063I
b = −0.107859 + 1.004670I
0.79385 − 2.10722I 8.15045 + 5.26873I
u = −1.13983 + 0.92777I
a = 0.318709 − 0.032039I
b = −0.29566 − 1.68166I
3.24679 + 4.68284I 0
u = −1.13983 − 0.92777I
a = 0.318709 + 0.032039I
b = −0.29566 + 1.68166I
3.24679 − 4.68284I 0
u = 0.149898 + 0.472455I
a = −0.341742 + 0.540391I
b = 0.581439 + 0.999013I
1.37894 − 4.54768I 6.26858 + 10.41405I
u = 0.149898 − 0.472455I
a = −0.341742 − 0.540391I
b = 0.581439 − 0.999013I
1.37894 + 4.54768I 6.26858 − 10.41405I
u = 0.448268 + 0.195955I
a = −2.52717 + 3.05511I
b = −1.024250 − 0.392230I
−5.23201 − 1.19230I −14.5106 + 0.I
u = 0.448268 − 0.195955I
a = −2.52717 − 3.05511I
b = −1.024250 + 0.392230I
−5.23201 + 1.19230I −14.5106 + 0.I
u = −0.347392 + 0.342546I
a = 4.09657 + 1.43461I
b = 1.077110 − 0.450997I
2.55963 + 0.63721I 3.86681 − 1.76840I
u = −0.347392 − 0.342546I
a = 4.09657 − 1.43461I
b = 1.077110 + 0.450997I
2.55963 − 0.63721I 3.86681 + 1.76840I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.95610 + 1.17232I
a = 1.46292 − 0.76538I
b = 1.033660 + 0.376306I
−0.44883 − 4.77662I 0
u = 0.95610 − 1.17232I
a = 1.46292 + 0.76538I
b = 1.033660 − 0.376306I
−0.44883 + 4.77662I 0
u = −0.048639 + 0.470469I
a = −2.31406 + 0.03989I
b = −1.323320 − 0.145327I
3.69101 − 2.39345I 23.9009 − 0.4945I
u = −0.048639 − 0.470469I
a = −2.31406 − 0.03989I
b = −1.323320 + 0.145327I
3.69101 + 2.39345I 23.9009 + 0.4945I
u = 1.16823 + 0.98512I
a = 0.910920 − 0.247874I
b = 1.228870 − 0.123085I
−1.31176 + 2.02917I 0
u = 1.16823 − 0.98512I
a = 0.910920 + 0.247874I
b = 1.228870 + 0.123085I
−1.31176 − 2.02917I 0
u = 0.66314 + 1.37761I
a = 0.190377 − 0.106451I
b = 0.851449 − 0.383190I
6.10659 + 2.68645I 0
u = 0.66314 − 1.37761I
a = 0.190377 + 0.106451I
b = 0.851449 + 0.383190I
6.10659 − 2.68645I 0
u = 1.02328 + 1.16149I
a = −1.23924 + 0.86395I
b = −1.32072 − 0.78390I
0.09478 − 12.58360I 0
u = 1.02328 − 1.16149I
a = −1.23924 − 0.86395I
b = −1.32072 + 0.78390I
0.09478 + 12.58360I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51398 + 0.34490I
a = −1.021860 − 0.415543I
b = −0.928023 + 0.383734I
−0.00403 − 2.60292I 0
u = 1.51398 − 0.34490I
a = −1.021860 + 0.415543I
b = −0.928023 − 0.383734I
−0.00403 + 2.60292I 0
u = 0.244829 + 0.374177I
a = 0.19981 − 2.56392I
b = −0.584939 + 0.369600I
1.90872 − 0.23293I 6.01992 − 1.16442I
u = 0.244829 − 0.374177I
a = 0.19981 + 2.56392I
b = −0.584939 − 0.369600I
1.90872 + 0.23293I 6.01992 + 1.16442I
u = 1.20586 + 1.02284I
a = −1.41319 + 0.52758I
b = −1.126070 − 0.471524I
−3.28929 − 8.48325I 0
u = 1.20586 − 1.02284I
a = −1.41319 − 0.52758I
b = −1.126070 + 0.471524I
−3.28929 + 8.48325I 0
u = 0.99834 + 1.24020I
a = 1.04576 − 1.01600I
b = 0.931144 + 0.816490I
1.56539 − 6.90162I 0
u = 0.99834 − 1.24020I
a = 1.04576 + 1.01600I
b = 0.931144 − 0.816490I
1.56539 + 6.90162I 0
u = 0.32917 + 1.59781I
a = −0.492373 + 0.905188I
b = −1.018380 − 0.352125I
−3.81269 − 2.36039I 0
u = 0.32917 − 1.59781I
a = −0.492373 − 0.905188I
b = −1.018380 + 0.352125I
−3.81269 + 2.36039I 0
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41581 + 0.82459I
a = 0.797505 − 0.038116I
b = 1.25655 − 0.69317I
−0.95765 + 4.25343I 0
u = 1.41581 − 0.82459I
a = 0.797505 + 0.038116I
b = 1.25655 + 0.69317I
−0.95765 − 4.25343I 0
u = 0.338788 + 0.110659I
a = 0.268919 − 0.782315I
b = 0.474984 + 1.174310I
0.60921 − 2.57123I −7.2904 − 14.6569I
u = 0.338788 − 0.110659I
a = 0.268919 + 0.782315I
b = 0.474984 − 1.174310I
0.60921 + 2.57123I −7.2904 + 14.6569I
u = −0.343467 + 0.089486I
a = −4.96228 − 2.87456I
b = −1.130510 + 0.321346I
−1.63552 − 4.25699I −3.97244 + 9.03897I
u = −0.343467 − 0.089486I
a = −4.96228 + 2.87456I
b = −1.130510 − 0.321346I
−1.63552 + 4.25699I −3.97244 − 9.03897I
u = −1.20762 + 1.11861I
a = −1.254210 − 0.536194I
b = −1.296090 + 0.500575I
−2.19139 + 12.57100I 0
u = −1.20762 − 1.11861I
a = −1.254210 + 0.536194I
b = −1.296090 − 0.500575I
−2.19139 − 12.57100I 0
u = 1.11410 + 1.21391I
a = 1.20748 − 0.77194I
b = 1.27619 + 0.72796I
0.3662 − 22.1609I 0
u = 1.11410 − 1.21391I
a = 1.20748 + 0.77194I
b = 1.27619 − 0.72796I
0.3662 + 22.1609I 0
21
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.10085 + 1.22725I
a = −1.133590 − 0.740167I
b = −1.32744 + 0.62068I
−2.19552 + 10.32140I 0
u = −1.10085 − 1.22725I
a = −1.133590 + 0.740167I
b = −1.32744 − 0.62068I
−2.19552 − 10.32140I 0
u = −1.07502 + 1.25069I
a = 0.303047 − 0.089067I
b = 0.748325 + 0.682495I
2.67896 + 2.42662I 0
u = −1.07502 − 1.25069I
a = 0.303047 + 0.089067I
b = 0.748325 − 0.682495I
2.67896 − 2.42662I 0
u = −0.36230 + 1.61183I
a = 0.804188 + 0.432479I
b = 0.788923 + 0.042075I
−0.156729 − 1.239850I 0
u = −0.36230 − 1.61183I
a = 0.804188 − 0.432479I
b = 0.788923 − 0.042075I
−0.156729 + 1.239850I 0
u = −1.12678 + 1.24570I
a = 1.20035 + 0.76809I
b = 1.208310 − 0.653298I
−4.0173 + 15.5282I 0
u = −1.12678 − 1.24570I
a = 1.20035 − 0.76809I
b = 1.208310 + 0.653298I
−4.0173 − 15.5282I 0
u = −0.089737 + 0.304445I
a = −2.50533 − 0.04589I
b = 0.316230 − 1.017040I
5.45847 + 4.02150I 8.76172 − 4.01523I
u = −0.089737 − 0.304445I
a = −2.50533 + 0.04589I
b = 0.316230 + 1.017040I
5.45847 − 4.02150I 8.76172 + 4.01523I
22
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.276028 + 0.152427I
a = −6.54022 − 8.80862I
b = 0.397416 + 0.226342I
4.38259 + 7.68124I 17.9968 + 1.1950I
u = −0.276028 − 0.152427I
a = −6.54022 + 8.80862I
b = 0.397416 − 0.226342I
4.38259 − 7.68124I 17.9968 − 1.1950I
u = −0.061119 + 0.303600I
a = −5.72825 + 7.50563I
b = −0.615006 − 0.171648I
5.56140 − 1.46096I 2.54516 + 10.47328I
u = −0.061119 − 0.303600I
a = −5.72825 − 7.50563I
b = −0.615006 + 0.171648I
5.56140 + 1.46096I 2.54516 − 10.47328I
u = 0.127682 + 0.241811I
a = 0.161881 + 0.596823I
b = −0.47670 + 1.57705I
3.80174 − 5.75146I 30.6157 + 36.4217I
u = 0.127682 − 0.241811I
a = 0.161881 − 0.596823I
b = −0.47670 − 1.57705I
3.80174 + 5.75146I 30.6157 − 36.4217I
u = 0.197842 + 0.105573I
a = −5.12098 + 5.46266I
b = 0.613635 − 0.414129I
−1.25154 − 2.95764I −0.30838 + 4.31551I
u = 0.197842 − 0.105573I
a = −5.12098 − 5.46266I
b = 0.613635 + 0.414129I
−1.25154 + 2.95764I −0.30838 − 4.31551I
u = −1.74537 + 0.44125I
a = 1.005500 − 0.056770I
b = 1.286470 + 0.298762I
−3.81826 − 0.86511I 0
u = −1.74537 − 0.44125I
a = 1.005500 + 0.056770I
b = 1.286470 − 0.298762I
−3.81826 + 0.86511I 0
23
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.94830 + 1.53248I
a = −0.871026 − 0.770294I
b = −1.235300 + 0.451902I
−2.96204 + 9.17723I 0
u = −0.94830 − 1.53248I
a = −0.871026 + 0.770294I
b = −1.235300 − 0.451902I
−2.96204 − 9.17723I 0
u = 1.33431 + 1.22026I
a = 1.194430 − 0.727727I
b = 0.969503 + 0.645506I
1.98954 − 7.58030I 0
u = 1.33431 − 1.22026I
a = 1.194430 + 0.727727I
b = 0.969503 − 0.645506I
1.98954 + 7.58030I 0
u = 1.38847 + 1.23917I
a = −1.020000 + 0.527609I
b = −1.241240 − 0.668372I
3.59647 − 11.93150I 0
u = 1.38847 − 1.23917I
a = −1.020000 − 0.527609I
b = −1.241240 + 0.668372I
3.59647 + 11.93150I 0
u = 0.0302633 + 0.0469418I
a = 1.90747 − 12.21410I
b = 0.783836 + 0.847861I
−0.01410 − 2.10099I −4.92474 + 5.03538I
u = 0.0302633 − 0.0469418I
a = 1.90747 + 12.21410I
b = 0.783836 − 0.847861I
−0.01410 + 2.10099I −4.92474 − 5.03538I
u = −1.90181 + 0.80601I
a = −0.970400 + 0.143811I
b = −1.126050 − 0.405336I
−5.32594 − 5.87879I 0
u = −1.90181 − 0.80601I
a = −0.970400 − 0.143811I
b = −1.126050 + 0.405336I
−5.32594 + 5.87879I 0
24
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.74086 + 1.20243I
a = −0.798269 − 0.020907I
b = −1.230410 + 0.516904I
−0.40068 + 12.77810I 0
u = 1.74086 − 1.20243I
a = −0.798269 + 0.020907I
b = −1.230410 − 0.516904I
−0.40068 − 12.77810I 0
u = 1.00866 + 1.89556I
a = 0.600196 − 0.430672I
b = 1.42509 + 0.18301I
−1.83726 + 2.39249I 0
u = 1.00866 − 1.89556I
a = 0.600196 + 0.430672I
b = 1.42509 − 0.18301I
−1.83726 − 2.39249I 0
u = 1.07420 + 1.90121I
a = 1.044720 − 0.329621I
b = 0.956987 + 0.049219I
−1.41111 − 1.62240I 0
u = 1.07420 − 1.90121I
a = 1.044720 + 0.329621I
b = 0.956987 − 0.049219I
−1.41111 + 1.62240I 0
u = −2.12783 + 0.56589I
a = 1.203670 + 0.053587I
b = 0.919266 + 0.112181I
−1.74764 + 1.95710I 0
u = −2.12783 − 0.56589I
a = 1.203670 − 0.053587I
b = 0.919266 − 0.112181I
−1.74764 − 1.95710I 0
u = −1.26382 + 1.80434I
a = 0.779221 + 0.602948I
b = 1.217150 − 0.527300I
−4.39505 + 2.23361I 0
u = −1.26382 − 1.80434I
a = 0.779221 − 0.602948I
b = 1.217150 + 0.527300I
−4.39505 − 2.23361I 0
25
II. I
u
2
= h1.26 × 10
171
u
55
− 3.51 × 10
171
u
54
+ · · · + 2.85 × 10
170
b − 1.70 ×
10
171
, 3.46 × 10
170
u
55
− 9.12 × 10
170
u
54
+ · · · + 2.85 × 10
170
a + 1.97 ×
10
170
, 3u
56
− 9u
55
+ · · · − 7u + 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
11
=
−1.21274u
55
+ 3.19926u
54
+ ··· − 3.05746u − 0.692515
−4.43627u
55
+ 12.3220u
54
+ ··· − 17.4745u + 5.96358
a
12
=
3.22353u
55
− 9.12274u
54
+ ··· + 14.4171u − 6.65610
−4.43627u
55
+ 12.3220u
54
+ ··· − 17.4745u + 5.96358
a
7
=
−7.58365u
55
+ 21.2071u
54
+ ··· − 27.1304u + 10.7748
−3.49544u
55
+ 9.92547u
54
+ ··· − 10.5357u + 6.00055
a
4
=
2.51008u
55
− 6.65444u
54
+ ··· + 6.95020u − 2.51414
3.58195u
55
− 9.95403u
54
+ ··· + 13.1115u − 4.88832
a
6
=
−4.40440u
55
+ 12.1696u
54
+ ··· − 17.6691u + 5.28884
−3.48854u
55
+ 9.91005u
54
+ ··· − 10.4283u + 5.83380
a
2
=
−2.26339u
55
+ 6.34545u
54
+ ··· − 8.13821u + 3.29395
1.10881u
55
− 2.93841u
54
+ ··· + 4.90056u − 1.06345
a
1
=
0.289817u
55
− 0.913245u
54
+ ··· + 2.36959u − 2.10817
0.924596u
55
− 2.66988u
54
+ ··· + 2.24190u − 1.88706
a
5
=
−1.05912u
55
+ 3.03960u
54
+ ··· − 5.28455u + 3.69035
1.26749u
55
− 3.54767u
54
+ ··· + 5.18685u − 1.57222
a
10
=
1.43960u
55
− 4.12835u
54
+ ··· + 5.40083u − 1.64207
−2.43889u
55
+ 6.65258u
54
+ ··· − 10.9087u + 3.38330
(ii) Obstruction class = 1
(iii) Cusp Shapes = 11.0111u
55
− 32.0262u
54
+ ··· + 23.8543u − 22.5533
26
(iv) u-Polynomials at the component
27
Crossings u-Polynomials at each crossing
c
1
u
56
− 11u
55
+ ··· − 14u + 1
c
2
u
56
+ u
55
+ ··· + 16u
2
+ 1
c
3
u
56
+ u
55
+ ··· − 102u + 21
c
4
u
56
+ 11u
55
+ ··· + 14u + 1
c
5
u
56
+ 2u
55
+ ··· − 195u + 21
c
6
u
56
+ 7u
55
+ ··· − 9u + 3
c
7
u
56
− u
55
+ ··· + 2u + 1
c
8
3(3u
56
− 9u
55
+ ··· − 7u + 1)
c
9
3(3u
56
− 12u
55
+ ··· + 83u + 77)
c
10
3(3u
56
− 6u
55
+ ··· − 16u + 11)
c
11
u
56
+ u
55
+ ··· − 2u + 1
c
12
u
56
− 9u
55
+ ··· − 33u + 3
28
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
56
+ 47y
55
+ ··· + 126y + 1
c
2
y
56
+ 21y
55
+ ··· + 32y + 1
c
3
y
56
+ 31y
55
+ ··· − 534y + 441
c
5
y
56
− 4y
55
+ ··· + 2211y + 441
c
6
y
56
− 5y
55
+ ··· + 33y + 9
c
7
, c
11
y
56
− 23y
55
+ ··· − 52y + 1
c
8
9(9y
56
− 57y
55
+ ··· − 31y + 1)
c
9
9(9y
56
+ 132y
55
+ ··· + 78735y + 5929)
c
10
9(9y
56
− 66y
55
+ ··· − 2918y + 121)
c
12
y
56
− 23y
55
+ ··· + 51y + 9
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.170897 + 0.998779I
a = 1.160330 − 0.520147I
b = −1.189160 − 0.240228I
3.26605 + 1.02078I 5.19449 − 4.97831I
u = −0.170897 − 0.998779I
a = 1.160330 + 0.520147I
b = −1.189160 + 0.240228I
3.26605 − 1.02078I 5.19449 + 4.97831I
u = −0.627290 + 0.857461I
a = 0.153413 − 1.116260I
b = −0.688813 − 0.019138I
−2.56004 + 4.59795I −7.52704 − 5.02532I
u = −0.627290 − 0.857461I
a = 0.153413 + 1.116260I
b = −0.688813 + 0.019138I
−2.56004 − 4.59795I −7.52704 + 5.02532I
u = 1.071150 + 0.063233I
a = −1.52127 + 0.49577I
b = −1.075720 + 0.432191I
−4.00603 + 5.89030I −2.57521 − 10.35602I
u = 1.071150 − 0.063233I
a = −1.52127 − 0.49577I
b = −1.075720 − 0.432191I
−4.00603 − 5.89030I −2.57521 + 10.35602I
u = 0.362789 + 1.021530I
a = −0.262181 − 0.659306I
b = 0.434776 − 0.172084I
5.99639 + 1.17062I 5.60765 − 1.93661I
u = 0.362789 − 1.021530I
a = −0.262181 + 0.659306I
b = 0.434776 + 0.172084I
5.99639 − 1.17062I 5.60765 + 1.93661I
u = −0.716031 + 0.570272I
a = 0.46025 + 1.38032I
b = 0.734859 − 0.566812I
1.00674 + 5.33283I 2.18074 − 8.13944I
u = −0.716031 − 0.570272I
a = 0.46025 − 1.38032I
b = 0.734859 + 0.566812I
1.00674 − 5.33283I 2.18074 + 8.13944I
31
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.497736 + 0.983757I
a = 0.265549 + 0.392024I
b = 0.293576 − 0.534201I
1.36177 + 2.69579I 2.60422 − 3.73324I
u = −0.497736 − 0.983757I
a = 0.265549 − 0.392024I
b = 0.293576 + 0.534201I
1.36177 − 2.69579I 2.60422 + 3.73324I
u = −0.870299 + 0.166124I
a = 1.090980 + 0.312471I
b = 1.47913 − 0.31680I
−3.34180 − 0.67011I −16.1559 − 0.6381I
u = −0.870299 − 0.166124I
a = 1.090980 − 0.312471I
b = 1.47913 + 0.31680I
−3.34180 + 0.67011I −16.1559 + 0.6381I
u = −1.133300 + 0.144061I
a = −1.90853 − 0.39672I
b = −0.694078 − 0.312933I
−2.46627 + 2.69611I −6.79677 − 4.59448I
u = −1.133300 − 0.144061I
a = −1.90853 + 0.39672I
b = −0.694078 + 0.312933I
−2.46627 − 2.69611I −6.79677 + 4.59448I
u = 1.023780 + 0.565079I
a = −1.79343 + 0.13037I
b = −1.180000 − 0.280061I
−4.93911 − 6.04446I −6.86155 + 7.43666I
u = 1.023780 − 0.565079I
a = −1.79343 − 0.13037I
b = −1.180000 + 0.280061I
−4.93911 + 6.04446I −6.86155 − 7.43666I
u = −0.786028 + 0.236510I
a = 0.988465 + 0.458147I
b = 0.901347 − 0.956098I
0.36514 + 4.38434I −1.67435 − 10.00145I
u = −0.786028 − 0.236510I
a = 0.988465 − 0.458147I
b = 0.901347 + 0.956098I
0.36514 − 4.38434I −1.67435 + 10.00145I
32
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.299291 + 1.222440I
a = 0.61558 + 1.81623I
b = 0.646836 − 0.745244I
2.18151 + 7.47293I 0
u = −0.299291 − 1.222440I
a = 0.61558 − 1.81623I
b = 0.646836 + 0.745244I
2.18151 − 7.47293I 0
u = −0.722983 + 0.117569I
a = −1.81435 − 1.07383I
b = −1.178670 − 0.547086I
0.56050 − 11.50840I 1.28421 + 8.02826I
u = −0.722983 − 0.117569I
a = −1.81435 + 1.07383I
b = −1.178670 + 0.547086I
0.56050 + 11.50840I 1.28421 − 8.02826I
u = 0.336501 + 0.639735I
a = −0.571523 − 0.696790I
b = 0.830850 + 0.714772I
−0.28581 − 6.42749I 3.61440 + 6.02119I
u = 0.336501 − 0.639735I
a = −0.571523 + 0.696790I
b = 0.830850 − 0.714772I
−0.28581 + 6.42749I 3.61440 − 6.02119I
u = 0.446567 + 1.199170I
a = −0.039681 − 0.357375I
b = −0.382007 − 0.024552I
3.92498 − 8.71684I 0
u = 0.446567 − 1.199170I
a = −0.039681 + 0.357375I
b = −0.382007 + 0.024552I
3.92498 + 8.71684I 0
u = 0.237318 + 0.657069I
a = −1.87240 − 2.69636I
b = 0.514776 − 0.058134I
5.70986 + 1.03372I 9.24362 + 5.37789I
u = 0.237318 − 0.657069I
a = −1.87240 + 2.69636I
b = 0.514776 + 0.058134I
5.70986 − 1.03372I 9.24362 − 5.37789I
33
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.461092 + 1.255620I
a = 1.08572 − 1.24350I
b = 0.809748 + 0.229582I
−2.90856 − 1.27899I 0
u = 0.461092 − 1.255620I
a = 1.08572 + 1.24350I
b = 0.809748 − 0.229582I
−2.90856 + 1.27899I 0
u = 0.562504 + 0.226016I
a = −4.38690 + 4.16856I
b = −0.462747 + 0.085516I
4.16769 − 7.77852I −13.0591 + 12.1864I
u = 0.562504 − 0.226016I
a = −4.38690 − 4.16856I
b = −0.462747 − 0.085516I
4.16769 + 7.77852I −13.0591 − 12.1864I
u = 0.528262 + 0.265271I
a = 1.52687 − 0.27136I
b = 1.38314 + 0.75889I
−1.23332 − 3.00153I −8.9128 + 16.9863I
u = 0.528262 − 0.265271I
a = 1.52687 + 0.27136I
b = 1.38314 − 0.75889I
−1.23332 + 3.00153I −8.9128 − 16.9863I
u = 0.999026 + 0.998171I
a = 1.121210 − 0.777371I
b = 1.154090 + 0.414442I
−4.09826 − 1.97477I 0
u = 0.999026 − 0.998171I
a = 1.121210 + 0.777371I
b = 1.154090 − 0.414442I
−4.09826 + 1.97477I 0
u = 1.22734 + 0.79348I
a = 0.319350 − 0.015958I
b = −0.08084 + 1.73935I
3.09274 − 4.81796I 0
u = 1.22734 − 0.79348I
a = 0.319350 + 0.015958I
b = −0.08084 − 1.73935I
3.09274 + 4.81796I 0
34
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.99183 + 1.16683I
a = −0.192222 + 0.000121I
b = −0.752753 − 0.743486I
2.42277 + 2.35883I 0
u = −0.99183 − 1.16683I
a = −0.192222 − 0.000121I
b = −0.752753 + 0.743486I
2.42277 − 2.35883I 0
u = −0.288760 + 0.336710I
a = −0.0291315 + 0.0250115I
b = 0.447932 − 1.207910I
0.68174 + 2.76182I 8.2057 − 22.8621I
u = −0.288760 − 0.336710I
a = −0.0291315 − 0.0250115I
b = 0.447932 + 1.207910I
0.68174 − 2.76182I 8.2057 + 22.8621I
u = −1.10440 + 1.14317I
a = −1.230600 − 0.665540I
b = −1.34834 + 0.55166I
−1.42124 + 11.76190I 0
u = −1.10440 − 1.14317I
a = −1.230600 + 0.665540I
b = −1.34834 − 0.55166I
−1.42124 − 11.76190I 0
u = −0.028287 + 0.367435I
a = −3.66048 + 0.08158I
b = −1.168440 − 0.141467I
3.43455 − 2.42547I −8.93107 + 4.39818I
u = −0.028287 − 0.367435I
a = −3.66048 − 0.08158I
b = −1.168440 + 0.141467I
3.43455 + 2.42547I −8.93107 − 4.39818I
u = 1.31540 + 1.12599I
a = −1.23056 + 0.72950I
b = −0.959385 − 0.673239I
1.79881 − 7.72829I 0
u = 1.31540 − 1.12599I
a = −1.23056 − 0.72950I
b = −0.959385 + 0.673239I
1.79881 + 7.72829I 0
35
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.220065 + 0.028927I
a = −1.60149 − 0.20182I
b = −0.35371 − 1.42919I
3.69697 + 5.65263I −10.81596 + 3.11923I
u = 0.220065 − 0.028927I
a = −1.60149 + 0.20182I
b = −0.35371 + 1.42919I
3.69697 − 5.65263I −10.81596 − 3.11923I
u = −1.41211 + 1.49055I
a = 0.834236 + 0.421453I
b = 1.301130 − 0.127620I
−1.59072 − 2.57928I 0
u = −1.41211 − 1.49055I
a = 0.834236 − 0.421453I
b = 1.301130 + 0.127620I
−1.59072 + 2.57928I 0
u = 2.35744 + 0.94848I
a = 0.992799 − 0.129856I
b = 1.082470 + 0.059488I
−1.65760 + 2.13230I 0
u = 2.35744 − 0.94848I
a = 0.992799 + 0.129856I
b = 1.082470 − 0.059488I
−1.65760 − 2.13230I 0
36
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
56
− 11u
55
+ ··· − 14u + 1)
· (u
210
+ 10u
209
+ ··· − 27478849u + 12092767)
c
2
(u
56
+ u
55
+ ··· + 16u
2
+ 1)(u
210
− 6u
209
+ ··· + 49u + 1)
c
3
(u
56
+ u
55
+ ··· − 102u + 21)(u
210
+ 8u
208
+ ··· + 257055u + 4092)
c
4
(u
56
+ 11u
55
+ ··· + 14u + 1)
· (u
210
+ 10u
209
+ ··· − 27478849u + 12092767)
c
5
(u
56
+ 2u
55
+ ··· − 195u + 21)
· (u
210
+ 7u
209
+ ··· + 1508984076u + 44022057)
c
6
(u
56
+ 7u
55
+ ··· − 9u + 3)(u
210
+ 12u
209
+ ··· + 4260u + 237)
c
7
(u
56
− u
55
+ ··· + 2u + 1)(u
210
+ 2u
209
+ ··· − 101779u + 358027)
c
8
9(3u
56
− 9u
55
+ ··· − 7u + 1)(3u
210
+ 6u
209
+ ··· − 26u + 1)
c
9
9(3u
56
− 12u
55
+ ··· + 83u + 77)
· (3u
210
− 3u
209
+ ··· + 4592789u + 999482)
c
10
9(3u
56
− 6u
55
+ ··· − 16u + 11)
· (3u
210
+ 15u
209
+ ··· + 112390753u + 13420612)
c
11
(u
56
+ u
55
+ ··· − 2u + 1)(u
210
+ 2u
209
+ ··· − 101779u + 358027)
c
12
(u
56
− 9u
55
+ ··· − 33u + 3)(u
210
+ 12u
209
+ ··· + 450u + 375)
37
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
56
+ 47y
55
+ ··· + 126y + 1)
· (y
210
+ 148y
209
+ ··· + 7967626144440991y + 146235013716289)
c
2
(y
56
+ 21y
55
+ ··· + 32y + 1)(y
210
+ 22y
209
+ ··· + 49y + 1)
c
3
(y
56
+ 31y
55
+ ··· − 534y + 441)
· (y
210
+ 16y
209
+ ··· − 23452087521y + 16744464)
c
5
(y
56
− 4y
55
+ ··· + 2211y + 441)
· (y
210
+ 21y
209
+ ··· + 183177916340579052y + 1937941502511249)
c
6
(y
56
− 5y
55
+ ··· + 33y + 9)(y
210
+ 8y
209
+ ··· + 4428546y + 56169)
c
7
, c
11
(y
56
− 23y
55
+ ··· − 52y + 1)
· (y
210
− 102y
209
+ ··· − 7529227423575y + 128183332729)
c
8
81(9y
56
− 57y
55
+ ··· − 31y + 1)(9y
210
+ 96y
209
+ ··· + 290y + 1)
c
9
81(9y
56
+ 132y
55
+ ··· + 78735y + 5929)
· (9y
210
+ 537y
209
+ ··· − 272232207635749y + 998964268324)
c
10
81(9y
56
− 66y
55
+ ··· − 2918y + 121)
· (9y
210
− 525y
209
+ ··· − 18148003448693073y + 180112826454544)
c
12
(y
56
− 23y
55
+ ··· + 51y + 9)
· (y
210
− 34y
209
+ ··· − 9502500y + 140625)
38
