12a
1172
(K12a
1172
)
A knot diagram
1
Linearized knot diagam
4 10 7 9 12 3 11 1 2 6 8 5
Solving Sequence
3,6
7
4,10
11 8 12 2 1 5 9
c
6
c
3
c
10
c
7
c
11
c
2
c
1
c
5
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.26512 × 10
751
u
149
+ 4.92723 × 10
751
u
148
+ ··· + 9.75259 × 10
750
b + 3.75083 × 10
754
,
1.46795 × 10
755
u
149
+ 6.05059 × 10
755
u
148
+ ··· + 3.54702 × 10
754
a + 5.97136 × 10
758
,
u
150
+ 5u
149
+ ··· + 25271u + 3637i
I
u
2
= h−5.55350 × 10
23
u
39
− 2.43477 × 10
24
u
38
+ ··· + 4.09608 × 10
22
b + 5.26413 × 10
23
,
− 3.66815 × 10
23
u
39
− 1.42903 × 10
24
u
38
+ ··· + 4.09608 × 10
22
a + 7.74087 × 10
23
,
u
40
+ 4u
39
+ ··· − 13u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 190 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
= h1.27 × 10
751
u
149
+ 4.93 × 10
751
u
148
+ · · · + 9.75 × 10
750
b + 3.75 ×
10
754
, 1.47 × 10
755
u
149
+ 6.05 × 10
755
u
148
+ · · · + 3.55 × 10
754
a + 5.97 ×
10
758
, u
150
+ 5u
149
+ · · · + 25271u + 3637i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
4
=
−u
−u
3
+ u
a
10
=
−4.13854u
149
− 17.0582u
148
+ ··· − 98334.7u − 16834.9
−1.29722u
149
− 5.05223u
148
+ ··· − 23607.2u − 3845.99
a
11
=
−5.43576u
149
− 22.1105u
148
+ ··· − 121942.u − 20680.9
−1.29722u
149
− 5.05223u
148
+ ··· − 23607.2u − 3845.99
a
8
=
7.01380u
149
+ 28.8224u
148
+ ··· + 162058.u + 27707.0
6.35386u
149
+ 26.1672u
148
+ ··· + 148191.u + 25334.3
a
12
=
3.94062u
149
+ 16.2785u
148
+ ··· + 89284.0u + 15295.2
0.141724u
149
+ 0.883339u
148
+ ··· + 7321.73u + 1509.73
a
2
=
−1.44983u
149
− 5.74168u
148
+ ··· − 31453.2u − 5285.38
−4.65175u
149
− 18.9905u
148
+ ··· − 109459.u − 18606.0
a
1
=
−5.14999u
149
− 20.9229u
148
+ ··· − 120587.u − 20507.9
−3.80366u
149
− 15.5738u
148
+ ··· − 90757.1u − 15456.8
a
5
=
3.43640u
149
+ 14.2416u
148
+ ··· + 76206.2u + 13142.3
2.56694u
149
+ 10.6431u
148
+ ··· + 62911.6u + 10837.4
a
9
=
1.70084u
149
+ 6.62008u
148
+ ··· + 29394.3u + 4671.47
1.88565u
149
+ 7.77565u
148
+ ··· + 42675.4u + 7307.30
(ii) Obstruction class = −1
(iii) Cusp Shapes = 11.7905u
149
+ 47.9073u
148
+ ··· + 263835.u + 44679.3
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
150
− 11u
149
+ ··· + 27517u − 277
c
2
, c
9
u
150
− 62u
148
+ ··· − 11776u + 448
c
3
, c
6
u
150
+ 5u
149
+ ··· + 25271u + 3637
c
4
u
150
+ 3u
149
+ ··· + 1401453u + 97263
c
5
, c
12
u
150
− 3u
149
+ ··· + 3773u + 227
c
7
, c
11
u
150
− 47u
148
+ ··· + 242552u + 55892
c
8
u
150
+ 3u
149
+ ··· + 117u + 27
c
10
u
150
+ u
149
+ ··· + 5517033568u + 726291007
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
150
− y
149
+ ··· − 661651313y + 76729
c
2
, c
9
y
150
− 124y
149
+ ··· − 58378240y + 200704
c
3
, c
6
y
150
− 93y
149
+ ··· + 1259345009y + 13227769
c
4
y
150
+ 49y
149
+ ··· − 447479481843y + 9460091169
c
5
, c
12
y
150
+ 109y
149
+ ··· + 1029767y + 51529
c
7
, c
11
y
150
− 94y
149
+ ··· − 105400910672y + 3123915664
c
8
y
150
− y
149
+ ··· + 27513y + 729
c
10
y
150
+ 49y
149
+ ··· + 2.26 × 10
19
y + 5.27 × 10
17
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.010160 + 0.001327I
a = −1.75230 − 0.22716I
b = 0.552597 − 0.775648I
−6.58473 − 0.02848I 0
u = 1.010160 − 0.001327I
a = −1.75230 + 0.22716I
b = 0.552597 + 0.775648I
−6.58473 + 0.02848I 0
u = −0.986489 + 0.066960I
a = −1.274150 + 0.028000I
b = 2.16405 − 0.90350I
0.12677 + 2.90266I 0
u = −0.986489 − 0.066960I
a = −1.274150 − 0.028000I
b = 2.16405 + 0.90350I
0.12677 − 2.90266I 0
u = −0.119280 + 0.963787I
a = 0.099277 + 1.380620I
b = −0.626734 − 0.783400I
−3.62768 + 4.13150I 0
u = −0.119280 − 0.963787I
a = 0.099277 − 1.380620I
b = −0.626734 + 0.783400I
−3.62768 − 4.13150I 0
u = −0.737777 + 0.719467I
a = 0.268764 + 0.035848I
b = −0.703268 + 0.646362I
3.69554 + 2.21429I 0
u = −0.737777 − 0.719467I
a = 0.268764 − 0.035848I
b = −0.703268 − 0.646362I
3.69554 − 2.21429I 0
u = 0.938985 + 0.427249I
a = −0.946853 − 0.614308I
b = 0.94381 − 1.59285I
−1.36518 + 1.23438I 0
u = 0.938985 − 0.427249I
a = −0.946853 + 0.614308I
b = 0.94381 + 1.59285I
−1.36518 − 1.23438I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.957385 + 0.105545I
a = −1.224200 − 0.152693I
b = 2.61460 − 0.05986I
−2.40883 − 8.55995I 0
u = 0.957385 − 0.105545I
a = −1.224200 + 0.152693I
b = 2.61460 + 0.05986I
−2.40883 + 8.55995I 0
u = 0.998838 + 0.292870I
a = −0.601572 − 0.901246I
b = 0.472808 − 0.556492I
−1.07866 − 3.62942I 0
u = 0.998838 − 0.292870I
a = −0.601572 + 0.901246I
b = 0.472808 + 0.556492I
−1.07866 + 3.62942I 0
u = 0.399736 + 0.866442I
a = −0.562313 − 0.384015I
b = 0.962382 + 0.449510I
5.61645 + 2.73061I 0
u = 0.399736 − 0.866442I
a = −0.562313 + 0.384015I
b = 0.962382 − 0.449510I
5.61645 − 2.73061I 0
u = −0.827895 + 0.470631I
a = −0.419188 − 0.213084I
b = −0.86315 + 1.61563I
3.23023 + 1.99379I 0
u = −0.827895 − 0.470631I
a = −0.419188 + 0.213084I
b = −0.86315 − 1.61563I
3.23023 − 1.99379I 0
u = −0.176065 + 0.932223I
a = −0.546997 − 1.119370I
b = 0.368260 + 0.700906I
−1.86777 + 4.08465I 0
u = −0.176065 − 0.932223I
a = −0.546997 + 1.119370I
b = 0.368260 − 0.700906I
−1.86777 − 4.08465I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.932265 + 0.169371I
a = 0.61464 + 1.75356I
b = 0.393835 + 0.238423I
−2.58412 + 4.82057I 0
u = −0.932265 − 0.169371I
a = 0.61464 − 1.75356I
b = 0.393835 − 0.238423I
−2.58412 − 4.82057I 0
u = −1.048040 + 0.169863I
a = −0.85088 + 1.38483I
b = 0.250228 + 0.748347I
−4.81324 + 5.56239I 0
u = −1.048040 − 0.169863I
a = −0.85088 − 1.38483I
b = 0.250228 − 0.748347I
−4.81324 − 5.56239I 0
u = −0.928918 + 0.085232I
a = −1.084560 − 0.650075I
b = −0.643149 − 1.167960I
0.26194 − 2.19269I 0
u = −0.928918 − 0.085232I
a = −1.084560 + 0.650075I
b = −0.643149 + 1.167960I
0.26194 + 2.19269I 0
u = −0.923812 + 0.115947I
a = 0.981095 + 0.202493I
b = −1.85969 + 0.55662I
−0.41992 + 2.90044I 0
u = −0.923812 − 0.115947I
a = 0.981095 − 0.202493I
b = −1.85969 − 0.55662I
−0.41992 − 2.90044I 0
u = 0.904769 + 0.195901I
a = 0.806718 − 1.097620I
b = 0.046242 − 0.544135I
1.64079 − 1.76353I 0
u = 0.904769 − 0.195901I
a = 0.806718 + 1.097620I
b = 0.046242 + 0.544135I
1.64079 + 1.76353I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.823699 + 0.694777I
a = 0.620668 + 0.478797I
b = 0.421267 − 1.238130I
−0.36032 + 2.64753I 0
u = −0.823699 − 0.694777I
a = 0.620668 − 0.478797I
b = 0.421267 + 1.238130I
−0.36032 − 2.64753I 0
u = −0.329008 + 1.028150I
a = −0.210408 − 0.188365I
b = 0.595601 + 0.084418I
1.52233 + 4.09710I 0
u = −0.329008 − 1.028150I
a = −0.210408 + 0.188365I
b = 0.595601 − 0.084418I
1.52233 − 4.09710I 0
u = 0.887346 + 0.227586I
a = −0.812711 + 0.964936I
b = −1.189660 + 0.551074I
−2.43795 + 7.14768I 0
u = 0.887346 − 0.227586I
a = −0.812711 − 0.964936I
b = −1.189660 − 0.551074I
−2.43795 − 7.14768I 0
u = 0.795254 + 0.737819I
a = 0.864722 − 0.612025I
b = 0.41745 + 1.72341I
0.02417 − 2.76819I 0
u = 0.795254 − 0.737819I
a = 0.864722 + 0.612025I
b = 0.41745 − 1.72341I
0.02417 + 2.76819I 0
u = −0.133091 + 0.895417I
a = −0.17218 + 1.51826I
b = 0.808299 − 1.004490I
−4.47954 − 4.44672I 0
u = −0.133091 − 0.895417I
a = −0.17218 − 1.51826I
b = 0.808299 + 1.004490I
−4.47954 + 4.44672I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.185248 + 1.081780I
a = −0.465084 + 1.124470I
b = 0.128815 − 1.149810I
−6.66260 − 7.20467I 0
u = 0.185248 − 1.081780I
a = −0.465084 − 1.124470I
b = 0.128815 + 1.149810I
−6.66260 + 7.20467I 0
u = −1.003260 + 0.474064I
a = −0.426046 + 0.538649I
b = 0.315500 + 1.219820I
2.69954 + 2.37915I 0
u = −1.003260 − 0.474064I
a = −0.426046 − 0.538649I
b = 0.315500 − 1.219820I
2.69954 − 2.37915I 0
u = 0.865794 + 0.192350I
a = 0.819425 − 0.606169I
b = −0.79091 − 1.26456I
1.25757 − 0.97218I 0
u = 0.865794 − 0.192350I
a = 0.819425 + 0.606169I
b = −0.79091 + 1.26456I
1.25757 + 0.97218I 0
u = −0.943677 + 0.599804I
a = 0.717080 − 0.005338I
b = −0.155684 − 1.184590I
−0.58977 + 2.66247I 0
u = −0.943677 − 0.599804I
a = 0.717080 + 0.005338I
b = −0.155684 + 1.184590I
−0.58977 − 2.66247I 0
u = −1.056960 + 0.373139I
a = −0.0767874 − 0.0112237I
b = 0.149753 − 0.395142I
−1.83357 + 1.32917I 0
u = −1.056960 − 0.373139I
a = −0.0767874 + 0.0112237I
b = 0.149753 + 0.395142I
−1.83357 − 1.32917I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.051200 + 0.431460I
a = −0.129576 − 0.816108I
b = 1.068610 − 0.146172I
−2.27203 − 3.43715I 0
u = 1.051200 − 0.431460I
a = −0.129576 + 0.816108I
b = 1.068610 + 0.146172I
−2.27203 + 3.43715I 0
u = 0.704303 + 0.492491I
a = −0.116439 + 1.065210I
b = −1.62386 − 0.96825I
−0.60602 − 5.09602I 0
u = 0.704303 − 0.492491I
a = −0.116439 − 1.065210I
b = −1.62386 + 0.96825I
−0.60602 + 5.09602I 0
u = −1.118110 + 0.308233I
a = −0.277390 + 0.932094I
b = 0.979330 + 0.702422I
−3.24364 + 3.44616I 0
u = −1.118110 − 0.308233I
a = −0.277390 − 0.932094I
b = 0.979330 − 0.702422I
−3.24364 − 3.44616I 0
u = −0.328008 + 0.753116I
a = −0.902327 + 0.597892I
b = 1.165830 − 0.618355I
1.37688 − 8.62221I 0
u = −0.328008 − 0.753116I
a = −0.902327 − 0.597892I
b = 1.165830 + 0.618355I
1.37688 + 8.62221I 0
u = −0.810080 + 0.133797I
a = 0.661039 + 0.801510I
b = 0.433775 + 1.096310I
−0.24584 − 1.40229I 0
u = −0.810080 − 0.133797I
a = 0.661039 − 0.801510I
b = 0.433775 − 1.096310I
−0.24584 + 1.40229I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.125690 + 0.405810I
a = −0.212320 − 0.909509I
b = 0.465953 − 0.871792I
0.12094 − 6.12459I 0
u = 1.125690 − 0.405810I
a = −0.212320 + 0.909509I
b = 0.465953 + 0.871792I
0.12094 + 6.12459I 0
u = 1.200320 + 0.101588I
a = −0.130187 + 0.289602I
b = 0.305142 + 1.269170I
−6.75098 + 1.92609I 0
u = 1.200320 − 0.101588I
a = −0.130187 − 0.289602I
b = 0.305142 − 1.269170I
−6.75098 − 1.92609I 0
u = −0.080882 + 0.790242I
a = 0.10018 − 1.75276I
b = −0.029925 + 1.159940I
−7.75192 + 0.06941I 0
u = −0.080882 − 0.790242I
a = 0.10018 + 1.75276I
b = −0.029925 − 1.159940I
−7.75192 − 0.06941I 0
u = 0.790903
a = 1.65888
b = −1.23443
2.40030 0
u = −0.768103 + 0.145727I
a = 1.95529 − 0.92787I
b = −1.204540 − 0.151735I
−2.01380 − 3.01029I 0
u = −0.768103 − 0.145727I
a = 1.95529 + 0.92787I
b = −1.204540 + 0.151735I
−2.01380 + 3.01029I 0
u = −0.197554 + 1.205700I
a = 0.118695 − 1.167590I
b = −0.618277 + 1.032640I
−3.51177 − 13.09830I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.197554 − 1.205700I
a = 0.118695 + 1.167590I
b = −0.618277 − 1.032640I
−3.51177 + 13.09830I 0
u = −1.137090 + 0.483728I
a = 0.705841 − 0.822951I
b = −0.902469 − 1.043400I
−1.11967 + 13.28180I 0
u = −1.137090 − 0.483728I
a = 0.705841 + 0.822951I
b = −0.902469 + 1.043400I
−1.11967 − 13.28180I 0
u = 0.353759 + 0.676643I
a = 0.891013 − 0.135254I
b = −0.974476 − 0.381969I
2.53456 + 1.99299I 0
u = 0.353759 − 0.676643I
a = 0.891013 + 0.135254I
b = −0.974476 + 0.381969I
2.53456 − 1.99299I 0
u = 1.012010 + 0.713114I
a = 1.139800 − 0.709059I
b = −0.16775 + 1.73082I
−9.93134 − 2.81764I 0
u = 1.012010 − 0.713114I
a = 1.139800 + 0.709059I
b = −0.16775 − 1.73082I
−9.93134 + 2.81764I 0
u = 1.119970 + 0.534044I
a = 0.612602 + 0.596707I
b = −0.731038 + 0.973587I
3.33083 − 7.86755I 0
u = 1.119970 − 0.534044I
a = 0.612602 − 0.596707I
b = −0.731038 − 0.973587I
3.33083 + 7.86755I 0
u = −1.206740 + 0.340769I
a = −0.079170 − 0.126321I
b = −0.151525 − 0.532132I
−1.82153 + 1.37745I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.206740 − 0.340769I
a = −0.079170 + 0.126321I
b = −0.151525 + 0.532132I
−1.82153 − 1.37745I 0
u = 1.260210 + 0.172455I
a = −0.135021 + 0.180414I
b = −0.677884 + 1.119710I
−4.38561 − 7.47780I 0
u = 1.260210 − 0.172455I
a = −0.135021 − 0.180414I
b = −0.677884 − 1.119710I
−4.38561 + 7.47780I 0
u = −1.199980 + 0.424503I
a = −1.387600 − 0.106421I
b = 0.70374 + 1.38992I
−11.12970 + 4.31255I 0
u = −1.199980 − 0.424503I
a = −1.387600 + 0.106421I
b = 0.70374 − 1.38992I
−11.12970 − 4.31255I 0
u = 1.249870 + 0.261258I
a = −1.189710 − 0.133220I
b = 0.745972 − 0.911972I
−5.59630 − 3.62180I 0
u = 1.249870 − 0.261258I
a = −1.189710 + 0.133220I
b = 0.745972 + 0.911972I
−5.59630 + 3.62180I 0
u = −1.289970 + 0.062116I
a = −1.264730 + 0.502231I
b = 0.324334 + 0.567660I
−7.03513 + 3.45364I 0
u = −1.289970 − 0.062116I
a = −1.264730 − 0.502231I
b = 0.324334 − 0.567660I
−7.03513 − 3.45364I 0
u = −0.554916 + 1.191230I
a = 0.279928 + 0.843523I
b = 0.242778 − 0.965248I
0.800417 + 0.658476I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.554916 − 1.191230I
a = 0.279928 − 0.843523I
b = 0.242778 + 0.965248I
0.800417 − 0.658476I 0
u = 1.277280 + 0.348366I
a = 1.052750 − 0.146962I
b = −0.64441 + 1.53491I
−11.96840 − 4.09990I 0
u = 1.277280 − 0.348366I
a = 1.052750 + 0.146962I
b = −0.64441 − 1.53491I
−11.96840 + 4.09990I 0
u = 0.126956 + 1.318390I
a = −0.067964 − 0.830117I
b = 0.399682 + 0.803392I
0.58179 + 4.95472I 0
u = 0.126956 − 1.318390I
a = −0.067964 + 0.830117I
b = 0.399682 − 0.803392I
0.58179 − 4.95472I 0
u = 1.258900 + 0.412713I
a = −1.070070 + 0.418378I
b = 0.331062 − 0.793301I
−8.75414 + 0.03880I 0
u = 1.258900 − 0.412713I
a = −1.070070 − 0.418378I
b = 0.331062 + 0.793301I
−8.75414 − 0.03880I 0
u = 1.262320 + 0.466159I
a = 1.075930 + 0.002867I
b = −1.27205 + 1.46493I
−6.09175 − 8.66685I 0
u = 1.262320 − 0.466159I
a = 1.075930 − 0.002867I
b = −1.27205 − 1.46493I
−6.09175 + 8.66685I 0
u = 0.295681 + 1.321680I
a = −0.033215 + 1.020050I
b = −0.426538 − 0.883202I
0.95791 + 5.99188I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.295681 − 1.321680I
a = −0.033215 − 1.020050I
b = −0.426538 + 0.883202I
0.95791 − 5.99188I 0
u = −1.244810 + 0.533642I
a = 1.146590 + 0.037037I
b = −1.08362 − 1.87446I
−7.84345 + 9.65025I 0
u = −1.244810 − 0.533642I
a = 1.146590 − 0.037037I
b = −1.08362 + 1.87446I
−7.84345 − 9.65025I 0
u = 1.346190 + 0.154865I
a = −0.978217 − 0.404343I
b = 0.552647 − 0.913798I
−6.06255 − 3.50500I 0
u = 1.346190 − 0.154865I
a = −0.978217 + 0.404343I
b = 0.552647 + 0.913798I
−6.06255 + 3.50500I 0
u = −0.287406 + 1.324740I
a = −0.230390 − 0.842557I
b = −0.155678 + 0.649352I
−1.00538 + 3.93685I 0
u = −0.287406 − 1.324740I
a = −0.230390 + 0.842557I
b = −0.155678 − 0.649352I
−1.00538 − 3.93685I 0
u = −1.372310 + 0.181545I
a = 0.937634 + 0.109162I
b = −0.960941 − 0.931633I
−6.19633 − 1.10236I 0
u = −1.372310 − 0.181545I
a = 0.937634 − 0.109162I
b = −0.960941 + 0.931633I
−6.19633 + 1.10236I 0
u = −0.448553 + 0.408232I
a = 1.153760 + 0.202942I
b = −0.101711 − 0.735684I
−0.68571 + 1.61057I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.448553 − 0.408232I
a = 1.153760 − 0.202942I
b = −0.101711 + 0.735684I
−0.68571 − 1.61057I 0
u = 1.335230 + 0.414506I
a = 1.058170 − 0.038207I
b = −1.03786 + 1.05581I
−6.51133 − 8.68462I 0
u = 1.335230 − 0.414506I
a = 1.058170 + 0.038207I
b = −1.03786 − 1.05581I
−6.51133 + 8.68462I 0
u = 1.309990 + 0.492124I
a = −0.893429 + 0.195552I
b = 0.98673 − 1.88933I
−7.86878 − 9.22885I 0
u = 1.309990 − 0.492124I
a = −0.893429 − 0.195552I
b = 0.98673 + 1.88933I
−7.86878 + 9.22885I 0
u = 0.127023 + 0.582377I
a = 1.397510 − 0.052929I
b = −1.132450 + 0.273477I
0.215867 − 0.378588I 0
u = 0.127023 − 0.582377I
a = 1.397510 + 0.052929I
b = −1.132450 − 0.273477I
0.215867 + 0.378588I 0
u = 0.108367 + 0.572963I
a = −0.54085 − 2.01928I
b = 0.890209 + 0.199885I
−2.41089 + 4.44861I 0
u = 0.108367 − 0.572963I
a = −0.54085 + 2.01928I
b = 0.890209 − 0.199885I
−2.41089 − 4.44861I 0
u = −1.37752 + 0.43741I
a = 1.151110 + 0.008848I
b = −0.680649 − 1.239550I
−11.6290 + 12.4102I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.37752 − 0.43741I
a = 1.151110 − 0.008848I
b = −0.680649 + 1.239550I
−11.6290 − 12.4102I 0
u = −1.34386 + 0.62926I
a = −1.085810 − 0.132229I
b = 0.98164 + 1.65016I
−7.1775 + 19.5574I 0
u = −1.34386 − 0.62926I
a = −1.085810 + 0.132229I
b = 0.98164 − 1.65016I
−7.1775 − 19.5574I 0
u = −1.39878 + 0.50511I
a = −0.799514 − 0.231472I
b = 0.609749 + 0.848863I
−5.59908 + 1.81169I 0
u = −1.39878 − 0.50511I
a = −0.799514 + 0.231472I
b = 0.609749 − 0.848863I
−5.59908 − 1.81169I 0
u = −1.31210 + 0.70854I
a = 0.889883 + 0.225649I
b = −0.63596 − 1.39780I
−1.88379 + 6.31357I 0
u = −1.31210 − 0.70854I
a = 0.889883 − 0.225649I
b = −0.63596 + 1.39780I
−1.88379 − 6.31357I 0
u = −1.41740 + 0.52878I
a = −0.800456 − 0.198628I
b = 0.93773 + 1.25672I
−5.27062 + 2.76969I 0
u = −1.41740 − 0.52878I
a = −0.800456 + 0.198628I
b = 0.93773 − 1.25672I
−5.27062 − 2.76969I 0
u = 1.36382 + 0.65822I
a = −1.007980 + 0.193575I
b = 0.95654 − 1.47225I
−2.63430 − 12.90040I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.36382 − 0.65822I
a = −1.007980 − 0.193575I
b = 0.95654 + 1.47225I
−2.63430 + 12.90040I 0
u = 1.38996 + 0.60561I
a = 0.899065 − 0.050559I
b = −0.84422 + 1.40131I
−3.56779 − 11.58210I 0
u = 1.38996 − 0.60561I
a = 0.899065 + 0.050559I
b = −0.84422 − 1.40131I
−3.56779 + 11.58210I 0
u = 1.39630 + 0.62620I
a = −0.776360 + 0.315025I
b = 0.305289 − 1.349360I
−10.35040 + 0.86822I 0
u = 1.39630 − 0.62620I
a = −0.776360 − 0.315025I
b = 0.305289 + 1.349360I
−10.35040 − 0.86822I 0
u = 0.200900 + 0.416136I
a = 1.278000 + 0.123209I
b = −0.486952 − 0.178301I
0.958164 + 0.683201I 7.40457 − 2.87603I
u = 0.200900 − 0.416136I
a = 1.278000 − 0.123209I
b = −0.486952 + 0.178301I
0.958164 − 0.683201I 7.40457 + 2.87603I
u = 1.51354 + 0.27782I
a = 0.863523 − 0.198890I
b = −0.440305 + 0.728766I
−9.64210 + 7.52770I 0
u = 1.51354 − 0.27782I
a = 0.863523 + 0.198890I
b = −0.440305 − 0.728766I
−9.64210 − 7.52770I 0
u = −1.48043 + 0.48903I
a = 0.928515 + 0.239641I
b = −0.664712 − 0.463216I
−7.66583 + 2.01094I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48043 − 0.48903I
a = 0.928515 − 0.239641I
b = −0.664712 + 0.463216I
−7.66583 − 2.01094I 0
u = −1.53548 + 0.32595I
a = −0.735885 − 0.015759I
b = 0.596023 + 0.808869I
−5.58878 + 1.16454I 0
u = −1.53548 − 0.32595I
a = −0.735885 + 0.015759I
b = 0.596023 − 0.808869I
−5.58878 − 1.16454I 0
u = −0.167293 + 0.348208I
a = 1.83787 − 0.67700I
b = −0.191489 + 0.714593I
−2.69119 − 3.50863I 1.23563 + 2.74710I
u = −0.167293 − 0.348208I
a = 1.83787 + 0.67700I
b = −0.191489 − 0.714593I
−2.69119 + 3.50863I 1.23563 − 2.74710I
u = 0.382127
a = 2.48249
b = −1.11213
2.55754 3.74130
u = −1.33777 + 0.99053I
a = −0.788204 − 0.513289I
b = 0.482787 + 1.122250I
−7.95606 + 4.32238I 0
u = −1.33777 − 0.99053I
a = −0.788204 + 0.513289I
b = 0.482787 − 1.122250I
−7.95606 − 4.32238I 0
u = −0.0344350 + 0.1134110I
a = 5.85783 + 7.20433I
b = 0.275772 − 0.538238I
−1.55837 + 1.70950I 0.72911 + 3.25859I
u = −0.0344350 − 0.1134110I
a = 5.85783 − 7.20433I
b = 0.275772 + 0.538238I
−1.55837 − 1.70950I 0.72911 − 3.25859I
19
II. I
u
2
= h−5.55 × 10
23
u
39
− 2.43 × 10
24
u
38
+ · · · + 4.10 × 10
22
b + 5.26 ×
10
23
, −3.67 × 10
23
u
39
− 1.43 × 10
24
u
38
+ · · · + 4.10 × 10
22
a + 7.74 ×
10
23
, u
40
+ 4u
39
+ · · · − 13u
2
+ 1i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
4
=
−u
−u
3
+ u
a
10
=
8.95528u
39
+ 34.8878u
38
+ ··· − 40.8076u − 18.8983
13.5581u
39
+ 59.4414u
38
+ ··· − 15.3877u − 12.8516
a
11
=
22.5134u
39
+ 94.3292u
38
+ ··· − 56.1953u − 31.7499
13.5581u
39
+ 59.4414u
38
+ ··· − 15.3877u − 12.8516
a
8
=
6.11501u
39
+ 28.8254u
38
+ ··· − 14.8372u + 0.685148
9.62786u
39
+ 46.7043u
38
+ ··· − 42.7936u − 21.3780
a
12
=
11.7260u
39
+ 45.6720u
38
+ ··· − 109.251u − 40.7737
22.4688u
39
+ 100.225u
38
+ ··· − 93.7170u − 38.4217
a
2
=
33.5636u
39
+ 154.032u
38
+ ··· − 115.281u − 58.1994
23.7593u
39
+ 104.919u
38
+ ··· − 77.3861u − 33.1720
a
1
=
47.5039u
39
+ 216.072u
38
+ ··· − 160.509u − 78.4307
14.6255u
39
+ 64.4696u
38
+ ··· − 46.0983u − 19.2195
a
5
=
−46.5007u
39
− 206.399u
38
+ ··· + 176.687u + 83.6972
−13.8529u
39
− 61.1999u
38
+ ··· + 83.3795u + 36.0321
a
9
=
−48.3382u
39
− 226.147u
38
+ ··· + 118.490u + 69.8401
−8.42535u
39
− 31.3321u
38
+ ··· + 86.7859u + 29.3183
(ii) Obstruction class = 1
(iii) Cusp Shapes =
3243539632135736316585250
40960772555460737449619
u
39
+
13701408707039706486241154
40960772555460737449619
u
38
+ ··· −
17779643118128027734669843
40960772555460737449619
u −
9132260379857267362032457
40960772555460737449619
20
(iv) u-Polynomials at the component
21
Crossings u-Polynomials at each crossing
c
1
u
40
− 6u
39
+ ··· + 4u + 1
c
2
u
40
+ u
39
+ ··· + u + 1
c
3
u
40
− 4u
39
+ ··· − 13u
2
+ 1
c
4
u
40
+ 6u
38
+ ··· + 17u
2
+ 1
c
5
u
40
+ 18u
38
+ ··· + 4u
2
+ 1
c
6
u
40
+ 4u
39
+ ··· − 13u
2
+ 1
c
7
u
40
− u
39
+ ··· + 22u
2
+ 4
c
8
u
40
− 3u
38
+ ··· − 8u + 1
c
9
u
40
− u
39
+ ··· − u + 1
c
10
u
40
+ 2u
38
+ ··· − 15u + 11
c
11
u
40
+ u
39
+ ··· + 22u
2
+ 4
c
12
u
40
+ 18u
38
+ ··· + 4u
2
+ 1
22
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
40
+ 10y
39
+ ··· + 24y + 1
c
2
, c
9
y
40
− 33y
39
+ ··· − 43y + 1
c
3
, c
6
y
40
− 22y
39
+ ··· − 26y + 1
c
4
y
40
+ 12y
39
+ ··· + 34y + 1
c
5
, c
12
y
40
+ 36y
39
+ ··· + 8y + 1
c
7
, c
11
y
40
− 31y
39
+ ··· + 176y + 16
c
8
y
40
− 6y
39
+ ··· − 26y + 1
c
10
y
40
+ 4y
39
+ ··· + 237y + 121
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.875550 + 0.472394I
a = −0.304334 + 0.063112I
b = −0.67850 − 1.70009I
2.08196 − 1.93157I 0.80761 + 3.55094I
u = 0.875550 − 0.472394I
a = −0.304334 − 0.063112I
b = −0.67850 + 1.70009I
2.08196 + 1.93157I 0.80761 − 3.55094I
u = −0.327790 + 0.919101I
a = −0.004312 − 0.724884I
b = −0.653889 + 0.387897I
1.12827 + 3.26253I 3.48799 − 2.61711I
u = −0.327790 − 0.919101I
a = −0.004312 + 0.724884I
b = −0.653889 − 0.387897I
1.12827 − 3.26253I 3.48799 + 2.61711I
u = 1.021970 + 0.240997I
a = 0.113817 − 1.268010I
b = 0.680352 − 0.154851I
−3.31425 − 4.94593I −5.82504 + 8.14606I
u = 1.021970 − 0.240997I
a = 0.113817 + 1.268010I
b = 0.680352 + 0.154851I
−3.31425 + 4.94593I −5.82504 − 8.14606I
u = −0.679908 + 0.814453I
a = 0.745749 + 0.692743I
b = 0.456859 − 1.306430I
1.68604 + 2.84031I 3.99275 − 3.95849I
u = −0.679908 − 0.814453I
a = 0.745749 − 0.692743I
b = 0.456859 + 1.306430I
1.68604 − 2.84031I 3.99275 + 3.95849I
u = −0.862166 + 0.133171I
a = 1.117500 + 0.619558I
b = −0.940368 + 0.878274I
1.99515 + 0.92442I 6.54916 − 0.54255I
u = −0.862166 − 0.133171I
a = 1.117500 − 0.619558I
b = −0.940368 − 0.878274I
1.99515 − 0.92442I 6.54916 + 0.54255I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.517393 + 0.641006I
a = 0.405272 + 0.881956I
b = −0.599237 + 0.090657I
2.73191 + 1.42296I 3.25505 − 3.03695I
u = −0.517393 − 0.641006I
a = 0.405272 − 0.881956I
b = −0.599237 − 0.090657I
2.73191 − 1.42296I 3.25505 + 3.03695I
u = −0.767119 + 0.289596I
a = −1.162540 + 0.124836I
b = −0.214441 + 0.748149I
−2.10702 + 2.31909I −7.30905 − 5.14053I
u = −0.767119 − 0.289596I
a = −1.162540 − 0.124836I
b = −0.214441 − 0.748149I
−2.10702 − 2.31909I −7.30905 + 5.14053I
u = 1.049010 + 0.558495I
a = −1.236740 + 0.515380I
b = 0.32342 − 1.54392I
−10.78120 − 2.33664I −8.07162 + 0.I
u = 1.049010 − 0.558495I
a = −1.236740 − 0.515380I
b = 0.32342 + 1.54392I
−10.78120 + 2.33664I −8.07162 + 0.I
u = 0.799198 + 0.087360I
a = 1.63740 + 1.21224I
b = −1.232190 + 0.471459I
−2.17410 + 3.36496I −4.41823 − 10.45035I
u = 0.799198 − 0.087360I
a = 1.63740 − 1.21224I
b = −1.232190 − 0.471459I
−2.17410 − 3.36496I −4.41823 + 10.45035I
u = −0.637771 + 0.465424I
a = −0.417965 − 0.196444I
b = −1.084680 + 0.745495I
0.80088 + 2.95314I 4.52574 − 4.72996I
u = −0.637771 − 0.465424I
a = −0.417965 + 0.196444I
b = −1.084680 − 0.745495I
0.80088 − 2.95314I 4.52574 + 4.72996I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.142360 + 0.458664I
a = −0.244402 + 0.348346I
b = 0.593603 + 0.571634I
−1.43073 + 1.72143I 0
u = −1.142360 − 0.458664I
a = −0.244402 − 0.348346I
b = 0.593603 − 0.571634I
−1.43073 − 1.72143I 0
u = 0.717137 + 0.178077I
a = −1.055540 − 0.763233I
b = −0.194278 + 0.327211I
−3.90732 − 4.60277I −4.49440 + 4.27254I
u = 0.717137 − 0.178077I
a = −1.055540 + 0.763233I
b = −0.194278 − 0.327211I
−3.90732 + 4.60277I −4.49440 − 4.27254I
u = −1.248860 + 0.319926I
a = −1.271870 − 0.131954I
b = 0.544788 + 0.518239I
−6.57664 + 1.95208I 0
u = −1.248860 − 0.319926I
a = −1.271870 + 0.131954I
b = 0.544788 − 0.518239I
−6.57664 − 1.95208I 0
u = 1.291280 + 0.050770I
a = −0.995032 − 0.569847I
b = 0.584491 − 0.808147I
−6.48135 − 4.08929I 0
u = 1.291280 − 0.050770I
a = −0.995032 + 0.569847I
b = 0.584491 + 0.808147I
−6.48135 + 4.08929I 0
u = −0.083655 + 1.317110I
a = −0.191121 − 0.878922I
b = 0.413567 + 0.660370I
−0.71645 + 4.92833I 0
u = −0.083655 − 1.317110I
a = −0.191121 + 0.878922I
b = 0.413567 − 0.660370I
−0.71645 − 4.92833I 0
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.441638 + 0.473881I
a = 1.36401 + 0.95654I
b = 1.16961 − 1.06404I
1.78283 + 2.95963I 4.33254 − 4.07138I
u = −0.441638 − 0.473881I
a = 1.36401 − 0.95654I
b = 1.16961 + 1.06404I
1.78283 − 2.95963I 4.33254 + 4.07138I
u = 1.325690 + 0.449579I
a = 0.944504 + 0.023650I
b = −1.26971 + 1.56551I
−5.73472 − 10.46300I 0
u = 1.325690 − 0.449579I
a = 0.944504 − 0.023650I
b = −1.26971 − 1.56551I
−5.73472 + 10.46300I 0
u = 0.456244 + 0.019907I
a = 1.98624 + 0.75595I
b = 2.03048 − 0.02995I
−1.25415 − 8.06760I 3.02844 + 6.59328I
u = 0.456244 − 0.019907I
a = 1.98624 − 0.75595I
b = 2.03048 + 0.02995I
−1.25415 + 8.06760I 3.02844 − 6.59328I
u = −1.51094 + 0.40221I
a = −0.773594 − 0.112926I
b = 0.611013 + 0.730234I
−5.90782 + 1.45247I 0
u = −1.51094 − 0.40221I
a = −0.773594 + 0.112926I
b = 0.611013 − 0.730234I
−5.90782 − 1.45247I 0
u = −1.31648 + 0.92061I
a = 0.842952 + 0.500067I
b = −0.540893 − 1.198140I
−7.87941 + 4.14991I 0
u = −1.31648 − 0.92061I
a = 0.842952 − 0.500067I
b = −0.540893 + 1.198140I
−7.87941 − 4.14991I 0
28
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
40
− 6u
39
+ ··· + 4u + 1)(u
150
− 11u
149
+ ··· + 27517u − 277)
c
2
(u
40
+ u
39
+ ··· + u + 1)(u
150
− 62u
148
+ ··· − 11776u + 448)
c
3
(u
40
− 4u
39
+ ··· − 13u
2
+ 1)(u
150
+ 5u
149
+ ··· + 25271u + 3637)
c
4
(u
40
+ 6u
38
+ ··· + 17u
2
+ 1)(u
150
+ 3u
149
+ ··· + 1401453u + 97263)
c
5
(u
40
+ 18u
38
+ ··· + 4u
2
+ 1)(u
150
− 3u
149
+ ··· + 3773u + 227)
c
6
(u
40
+ 4u
39
+ ··· − 13u
2
+ 1)(u
150
+ 5u
149
+ ··· + 25271u + 3637)
c
7
(u
40
− u
39
+ ··· + 22u
2
+ 4)(u
150
− 47u
148
+ ··· + 242552u + 55892)
c
8
(u
40
− 3u
38
+ ··· − 8u + 1)(u
150
+ 3u
149
+ ··· + 117u + 27)
c
9
(u
40
− u
39
+ ··· − u + 1)(u
150
− 62u
148
+ ··· − 11776u + 448)
c
10
(u
40
+ 2u
38
+ ··· − 15u + 11)
· (u
150
+ u
149
+ ··· + 5517033568u + 726291007)
c
11
(u
40
+ u
39
+ ··· + 22u
2
+ 4)(u
150
− 47u
148
+ ··· + 242552u + 55892)
c
12
(u
40
+ 18u
38
+ ··· + 4u
2
+ 1)(u
150
− 3u
149
+ ··· + 3773u + 227)
29
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
40
+ 10y
39
+ ··· + 24y + 1)
· (y
150
− y
149
+ ··· − 661651313y + 76729)
c
2
, c
9
(y
40
− 33y
39
+ ··· − 43y + 1)
· (y
150
− 124y
149
+ ··· − 58378240y + 200704)
c
3
, c
6
(y
40
− 22y
39
+ ··· − 26y + 1)
· (y
150
− 93y
149
+ ··· + 1259345009y + 13227769)
c
4
(y
40
+ 12y
39
+ ··· + 34y + 1)
· (y
150
+ 49y
149
+ ··· − 447479481843y + 9460091169)
c
5
, c
12
(y
40
+ 36y
39
+ ··· + 8y + 1)
· (y
150
+ 109y
149
+ ··· + 1029767y + 51529)
c
7
, c
11
(y
40
− 31y
39
+ ··· + 176y + 16)
· (y
150
− 94y
149
+ ··· − 105400910672y + 3123915664)
c
8
(y
40
− 6y
39
+ ··· − 26y + 1)(y
150
− y
149
+ ··· + 27513y + 729)
c
10
(y
40
+ 4y
39
+ ··· + 237y + 121)
· (y
150
+ 49y
149
+ ··· + 2.26 × 10
19
y + 5.27 × 10
17
)
30
