12a
1237
(K12a
1237
)
A knot diagram
1
Linearized knot diagam
5 6 9 12 10 11 4 1 3 2 7 8
Solving Sequence
1,8 4,9
3 10 7 12 5 2 11 6
c
8
c
3
c
9
c
7
c
12
c
4
c
1
c
11
c
6
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h4.20584 × 10
667
u
144
+ 3.01908 × 10
667
u
143
+ ··· + 8.60367 × 10
668
b − 7.21833 × 10
670
,
− 2.18124 × 10
668
u
144
+ 1.52575 × 10
670
u
143
+ ··· + 5.53216 × 10
671
a − 1.40274 × 10
673
,
u
145
− 43u
143
+ ··· + 14615u + 1286i
I
u
2
= h−8.26352 × 10
22
u
32
− 1.84889 × 10
23
u
31
+ ··· + 1.89990 × 10
22
b + 1.14959 × 10
24
,
− 5.63314 × 10
23
u
32
+ 8.09901 × 10
22
u
31
+ ··· + 1.32993 × 10
23
a − 2.25243 × 10
24
, u
33
+ u
32
+ ··· − 23u + 7i
* 2 irreducible components of dim
C
= 0, with total 178 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
= h4.21 × 10
667
u
144
+ 3.02 × 10
667
u
143
+ · · · + 8.60 × 10
668
b − 7.22 ×
10
670
, −2.18 × 10
668
u
144
+ 1.53 × 10
670
u
143
+ · · · + 5.53 × 10
671
a − 1.40 ×
10
673
, u
145
− 43u
143
+ · · · + 14615u + 1286i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
0.000394283u
144
− 0.0275797u
143
+ ··· + 45.5077u + 25.3561
−0.0488843u
144
− 0.0350906u
143
+ ··· + 1165.03u + 83.8983
a
9
=
1
−u
2
a
3
=
0.116495u
144
+ 0.0671820u
143
+ ··· − 1522.09u − 94.0097
−0.134528u
144
− 0.114336u
143
+ ··· + 2699.27u + 205.762
a
10
=
−0.109833u
144
− 0.104519u
143
+ ··· + 2368.10u + 190.837
0.650696u
144
+ 0.595136u
143
+ ··· − 13544.2u − 1087.67
a
7
=
−0.174719u
144
− 0.200942u
143
+ ··· + 581.947u + 54.6804
0.0514734u
144
+ 0.0874424u
143
+ ··· + 1450.89u + 111.392
a
12
=
−u
u
a
5
=
0.0662833u
144
+ 0.0400073u
143
+ ··· − 932.777u − 55.2379
−0.114773u
144
− 0.102678u
143
+ ··· + 2143.31u + 164.492
a
2
=
−0.0456777u
144
− 0.115858u
143
+ ··· − 172.059u − 13.9622
0.166438u
144
+ 0.194786u
143
+ ··· − 2125.71u − 181.588
a
11
=
−0.179609u
144
− 0.120283u
143
+ ··· + 5384.61u + 423.462
0.188114u
144
+ 0.126517u
143
+ ··· − 5191.59u − 407.693
a
6
=
0.151645u
144
+ 0.242592u
143
+ ··· − 1779.97u − 158.597
−0.0296550u
144
− 0.136351u
143
+ ··· + 97.9273u + 35.0310
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.312516u
144
− 1.83404u
143
+ ··· + 32956.9u + 2890.88
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
145
− 6u
144
+ ··· − 153422604074u + 82046221679
c
2
u
145
− u
144
+ ··· + 525670u + 55949
c
3
, c
9
u
145
− 5u
144
+ ··· + 12394259u + 542527
c
4
u
145
+ 10u
144
+ ··· − 32u − 1
c
5
u
145
+ 3u
144
+ ··· − 49936u + 13568
c
6
, c
11
u
145
− u
144
+ ··· − 134u + 1
c
7
u
145
− 3u
144
+ ··· + 1140u + 1117
c
8
, c
12
u
145
− 43u
143
+ ··· + 14615u − 1286
c
10
u
145
+ u
144
+ ··· − 27127u − 9606
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
145
− 84y
144
+ ··· + 3.96 × 10
23
y −6.73 × 10
21
c
2
y
145
+ 53y
144
+ ··· + 51147539762y −3130290601
c
3
, c
9
y
145
+ 73y
144
+ ··· + 4228767991095y −294335545729
c
4
y
145
− 74y
144
+ ··· + 198y −1
c
5
y
145
+ 37y
144
+ ··· + 1166626560y −184090624
c
6
, c
11
y
145
− 131y
144
+ ··· + 18524y −1
c
7
y
145
+ 21y
144
+ ··· + 52277246y −1247689
c
8
, c
12
y
145
− 86y
144
+ ··· + 66531265y −1653796
c
10
y
145
− 91y
144
+ ··· + 5892163597y −92275236
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.898633 + 0.433440I
a = 2.04578 − 0.71402I
b = 0.022491 + 0.409068I
−9.14402 − 10.24780I 0
u = −0.898633 − 0.433440I
a = 2.04578 + 0.71402I
b = 0.022491 − 0.409068I
−9.14402 + 10.24780I 0
u = −0.073050 + 0.994240I
a = 0.095870 + 0.255895I
b = −0.482995 + 0.354364I
−0.43751 − 3.83986I 0
u = −0.073050 − 0.994240I
a = 0.095870 − 0.255895I
b = −0.482995 − 0.354364I
−0.43751 + 3.83986I 0
u = −0.914397 + 0.386602I
a = −2.78356 + 0.34868I
b = 2.04338 − 1.02761I
−7.57636 − 3.28778I 0
u = −0.914397 − 0.386602I
a = −2.78356 − 0.34868I
b = 2.04338 + 1.02761I
−7.57636 + 3.28778I 0
u = 0.937361 + 0.386454I
a = −2.15080 − 0.47024I
b = 0.744495 + 0.535402I
−3.86981 + 6.90906I 0
u = 0.937361 − 0.386454I
a = −2.15080 + 0.47024I
b = 0.744495 − 0.535402I
−3.86981 − 6.90906I 0
u = −0.475893 + 0.849331I
a = −0.377473 + 0.252302I
b = −0.316276 + 1.206530I
−8.42083 − 4.77169I 0
u = −0.475893 − 0.849331I
a = −0.377473 − 0.252302I
b = −0.316276 − 1.206530I
−8.42083 + 4.77169I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.836276 + 0.480474I
a = 1.76801 − 0.15769I
b = −0.951024 − 0.248799I
−3.17451 + 2.02375I 0
u = 0.836276 − 0.480474I
a = 1.76801 + 0.15769I
b = −0.951024 + 0.248799I
−3.17451 − 2.02375I 0
u = −0.963301
a = 1.25592
b = −0.349566
1.75193 0
u = 0.848320 + 0.414953I
a = −1.86905 − 0.89346I
b = −0.009494 + 0.545050I
−8.25194 + 1.66327I 0
u = 0.848320 − 0.414953I
a = −1.86905 + 0.89346I
b = −0.009494 − 0.545050I
−8.25194 − 1.66327I 0
u = −1.034370 + 0.211409I
a = −1.36610 − 0.57021I
b = 0.887823 − 0.812845I
2.98997 − 0.80961I 0
u = −1.034370 − 0.211409I
a = −1.36610 + 0.57021I
b = 0.887823 + 0.812845I
2.98997 + 0.80961I 0
u = −1.003690 + 0.338682I
a = 2.79524 − 0.57397I
b = −1.93910 + 1.12849I
−7.39281 − 3.03542I 0
u = −1.003690 − 0.338682I
a = 2.79524 + 0.57397I
b = −1.93910 − 1.12849I
−7.39281 + 3.03542I 0
u = 0.906664 + 0.227126I
a = −2.01583 + 2.24650I
b = 2.21764 − 2.30679I
−7.91749 + 8.92787I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.906664 − 0.227126I
a = −2.01583 − 2.24650I
b = 2.21764 + 2.30679I
−7.91749 − 8.92787I 0
u = −0.960213 + 0.462729I
a = −0.696597 − 0.501211I
b = 0.772732 − 0.563054I
1.32240 − 2.06915I 0
u = −0.960213 − 0.462729I
a = −0.696597 + 0.501211I
b = 0.772732 + 0.563054I
1.32240 + 2.06915I 0
u = 0.876368 + 0.322529I
a = 0.005716 − 0.379310I
b = −0.576803 + 0.637195I
−2.98776 + 1.27870I 0
u = 0.876368 − 0.322529I
a = 0.005716 + 0.379310I
b = −0.576803 − 0.637195I
−2.98776 − 1.27870I 0
u = 0.933708
a = 6.36337
b = −0.420025
−5.10444 0
u = −0.821912 + 0.689402I
a = −1.388660 + 0.031507I
b = −0.129311 − 0.440745I
−7.46361 − 0.84977I 0
u = −0.821912 − 0.689402I
a = −1.388660 − 0.031507I
b = −0.129311 + 0.440745I
−7.46361 + 0.84977I 0
u = −0.897131 + 0.205839I
a = −1.50037 + 0.65516I
b = 0.711261 + 0.549688I
−0.872138 − 0.966382I 0
u = −0.897131 − 0.205839I
a = −1.50037 − 0.65516I
b = 0.711261 − 0.549688I
−0.872138 + 0.966382I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.839571 + 0.329804I
a = 2.38943 − 0.64658I
b = −1.085090 + 0.532412I
−3.69986 + 2.87607I 0
u = −0.839571 − 0.329804I
a = 2.38943 + 0.64658I
b = −1.085090 − 0.532412I
−3.69986 − 2.87607I 0
u = 1.015250 + 0.435576I
a = 1.080660 − 0.190779I
b = −0.990627 + 0.459760I
−2.96446 + 2.83003I 0
u = 1.015250 − 0.435576I
a = 1.080660 + 0.190779I
b = −0.990627 − 0.459760I
−2.96446 − 2.83003I 0
u = −0.331846 + 1.056180I
a = −0.227682 + 0.465537I
b = −0.685480 − 1.094000I
−10.73840 + 4.63721I 0
u = −0.331846 − 1.056180I
a = −0.227682 − 0.465537I
b = −0.685480 + 1.094000I
−10.73840 − 4.63721I 0
u = −0.848352 + 0.263430I
a = 0.698771 + 1.023240I
b = −0.78796 − 1.77851I
−3.78660 − 5.60011I 0
u = −0.848352 − 0.263430I
a = 0.698771 − 1.023240I
b = −0.78796 + 1.77851I
−3.78660 + 5.60011I 0
u = 0.491158 + 0.735989I
a = 0.367473 − 0.319825I
b = −0.021538 + 0.914830I
−3.89250 + 2.59486I 0
u = 0.491158 − 0.735989I
a = 0.367473 + 0.319825I
b = −0.021538 − 0.914830I
−3.89250 − 2.59486I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.836435 + 0.245410I
a = −3.46495 − 0.12438I
b = 2.42765 + 0.29999I
−8.09693 − 6.69957I 0
u = 0.836435 − 0.245410I
a = −3.46495 + 0.12438I
b = 2.42765 − 0.29999I
−8.09693 + 6.69957I 0
u = −0.144921 + 1.122370I
a = −0.004153 − 0.339743I
b = 0.613411 + 1.178640I
−11.26920 + 4.43339I 0
u = −0.144921 − 1.122370I
a = −0.004153 + 0.339743I
b = 0.613411 − 1.178640I
−11.26920 − 4.43339I 0
u = 0.868225
a = 5.44804
b = 0.110422
−5.23111 0
u = −1.115650 + 0.205892I
a = 1.59095 − 0.40657I
b = −1.10848 + 1.45346I
0.51133 − 5.86067I 0
u = −1.115650 − 0.205892I
a = 1.59095 + 0.40657I
b = −1.10848 − 1.45346I
0.51133 + 5.86067I 0
u = −0.863460
a = −3.98667
b = 0.266556
−0.389672 0
u = 0.384602 + 0.771833I
a = −0.524388 + 0.192221I
b = −0.624082 + 0.685763I
−5.27893 − 2.49198I 0
u = 0.384602 − 0.771833I
a = −0.524388 − 0.192221I
b = −0.624082 − 0.685763I
−5.27893 + 2.49198I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.117890 + 0.257186I
a = 1.182530 + 0.496514I
b = −0.433470 + 0.529528I
1.64618 − 0.93659I 0
u = −1.117890 − 0.257186I
a = 1.182530 − 0.496514I
b = −0.433470 − 0.529528I
1.64618 + 0.93659I 0
u = 1.138700 + 0.178079I
a = −1.46336 − 0.00916I
b = 1.117940 + 0.749491I
4.54964 + 2.34980I 0
u = 1.138700 − 0.178079I
a = −1.46336 + 0.00916I
b = 1.117940 − 0.749491I
4.54964 − 2.34980I 0
u = −1.113680 + 0.307956I
a = −0.475025 − 1.248050I
b = 0.72223 + 1.32017I
−2.67518 − 5.53153I 0
u = −1.113680 − 0.307956I
a = −0.475025 + 1.248050I
b = 0.72223 − 1.32017I
−2.67518 + 5.53153I 0
u = 1.039010 + 0.517552I
a = 1.307890 − 0.431307I
b = −0.877573 − 1.049230I
−3.36739 + 7.26851I 0
u = 1.039010 − 0.517552I
a = 1.307890 + 0.431307I
b = −0.877573 + 1.049230I
−3.36739 − 7.26851I 0
u = 0.782201 + 0.292217I
a = 0.185923 − 0.605067I
b = −0.151287 − 1.391030I
−8.61903 + 1.53554I 0
u = 0.782201 − 0.292217I
a = 0.185923 + 0.605067I
b = −0.151287 + 1.391030I
−8.61903 − 1.53554I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.062853 + 0.830271I
a = −0.277114 + 0.555346I
b = 0.869667 + 0.872090I
−6.08621 + 8.40067I 0
u = 0.062853 − 0.830271I
a = −0.277114 − 0.555346I
b = 0.869667 − 0.872090I
−6.08621 − 8.40067I 0
u = 1.120600 + 0.358973I
a = −1.71531 + 0.77940I
b = 0.733277 + 0.838598I
−2.41047 + 1.27904I 0
u = 1.120600 − 0.358973I
a = −1.71531 − 0.77940I
b = 0.733277 − 0.838598I
−2.41047 − 1.27904I 0
u = −0.645790 + 0.476309I
a = 0.466016 − 0.865417I
b = 0.072640 − 1.236160I
−9.88006 + 6.43655I 0
u = −0.645790 − 0.476309I
a = 0.466016 + 0.865417I
b = 0.072640 + 1.236160I
−9.88006 − 6.43655I 0
u = 0.774380 + 0.053858I
a = 2.95434 + 0.15321I
b = −1.258710 + 0.574099I
−4.72280 − 0.62776I 0
u = 0.774380 − 0.053858I
a = 2.95434 − 0.15321I
b = −1.258710 − 0.574099I
−4.72280 + 0.62776I 0
u = 0.158103 + 1.213980I
a = 0.081824 + 0.301611I
b = 0.624654 − 1.104520I
−12.3347 − 13.4249I 0
u = 0.158103 − 1.213980I
a = 0.081824 − 0.301611I
b = 0.624654 + 1.104520I
−12.3347 + 13.4249I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.237180 + 0.077493I
a = 0.846736 − 0.280248I
b = −0.698183 − 0.515999I
3.31935 − 4.02427I 0
u = 1.237180 − 0.077493I
a = 0.846736 + 0.280248I
b = −0.698183 + 0.515999I
3.31935 + 4.02427I 0
u = −1.175410 + 0.450966I
a = 1.152680 + 0.175544I
b = −0.708836 + 1.198700I
−2.44550 − 5.88329I 0
u = −1.175410 − 0.450966I
a = 1.152680 − 0.175544I
b = −0.708836 − 1.198700I
−2.44550 + 5.88329I 0
u = 1.204180 + 0.420425I
a = −1.49791 − 0.20124I
b = 1.11052 + 1.10939I
3.24137 + 5.64934I 0
u = 1.204180 − 0.420425I
a = −1.49791 + 0.20124I
b = 1.11052 − 1.10939I
3.24137 − 5.64934I 0
u = 1.223000 + 0.368504I
a = −0.570052 − 0.298849I
b = 0.358043 + 1.108290I
1.98338 + 4.93352I 0
u = 1.223000 − 0.368504I
a = −0.570052 + 0.298849I
b = 0.358043 − 1.108290I
1.98338 − 4.93352I 0
u = 1.285900 + 0.021169I
a = −0.188657 − 0.967948I
b = −0.154303 + 0.244970I
−4.00952 − 1.21936I 0
u = 1.285900 − 0.021169I
a = −0.188657 + 0.967948I
b = −0.154303 − 0.244970I
−4.00952 + 1.21936I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.607686 + 0.374263I
a = −0.256818 + 0.126683I
b = 0.378365 − 1.347710I
−4.85534 − 3.53482I 0
u = 0.607686 − 0.374263I
a = −0.256818 − 0.126683I
b = 0.378365 + 1.347710I
−4.85534 + 3.53482I 0
u = 0.006194 + 1.296310I
a = −0.194923 − 0.134528I
b = −0.405453 + 1.086060I
−10.03280 − 3.13108I 0
u = 0.006194 − 1.296310I
a = −0.194923 + 0.134528I
b = −0.405453 − 1.086060I
−10.03280 + 3.13108I 0
u = −1.29995
a = 0.998521
b = −1.05683
0.925547 0
u = 1.185940 + 0.534791I
a = 0.997722 − 0.001953I
b = −0.933561 + 0.035527I
−2.95837 + 2.92828I 0
u = 1.185940 − 0.534791I
a = 0.997722 + 0.001953I
b = −0.933561 − 0.035527I
−2.95837 − 2.92828I 0
u = −1.250980 + 0.457236I
a = −1.62475 − 0.23683I
b = 0.98700 − 1.03739I
−2.20657 − 12.99010I 0
u = −1.250980 − 0.457236I
a = −1.62475 + 0.23683I
b = 0.98700 + 1.03739I
−2.20657 + 12.99010I 0
u = 1.180260 + 0.645438I
a = −0.095049 + 0.660989I
b = 0.419081 − 0.686751I
−2.94867 − 3.33911I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.180260 − 0.645438I
a = −0.095049 − 0.660989I
b = 0.419081 + 0.686751I
−2.94867 + 3.33911I 0
u = −1.288430 + 0.393723I
a = 1.145800 + 0.062438I
b = −0.916583 + 0.507128I
4.10046 − 1.25400I 0
u = −1.288430 − 0.393723I
a = 1.145800 − 0.062438I
b = −0.916583 − 0.507128I
4.10046 + 1.25400I 0
u = −1.302400 + 0.377450I
a = −1.38469 + 0.64761I
b = 1.16529 − 1.16618I
1.30978 − 6.31424I 0
u = −1.302400 − 0.377450I
a = −1.38469 − 0.64761I
b = 1.16529 + 1.16618I
1.30978 + 6.31424I 0
u = 1.270290 + 0.475410I
a = 1.144090 − 0.252910I
b = −0.870719 − 0.767104I
3.61384 + 8.84204I 0
u = 1.270290 − 0.475410I
a = 1.144090 + 0.252910I
b = −0.870719 + 0.767104I
3.61384 − 8.84204I 0
u = −0.013019 + 0.638822I
a = 0.456205 − 0.130262I
b = 0.395363 − 0.697509I
−0.26999 − 1.63427I 0. + 5.25975I
u = −0.013019 − 0.638822I
a = 0.456205 + 0.130262I
b = 0.395363 + 0.697509I
−0.26999 + 1.63427I 0. − 5.25975I
u = 1.324790 + 0.345426I
a = 1.48774 + 1.13838I
b = −1.18572 − 1.94164I
−2.93740 + 8.61628I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.324790 − 0.345426I
a = 1.48774 − 1.13838I
b = −1.18572 + 1.94164I
−2.93740 − 8.61628I 0
u = −1.226150 + 0.625099I
a = 1.60290 − 0.18141I
b = −1.23535 + 1.29765I
−7.89645 − 10.62710I 0
u = −1.226150 − 0.625099I
a = 1.60290 + 0.18141I
b = −1.23535 − 1.29765I
−7.89645 + 10.62710I 0
u = −0.117272 + 0.603896I
a = −0.90517 − 1.13829I
b = −0.538411 − 0.718761I
−5.49473 + 1.74369I −5.85606 − 4.80060I
u = −0.117272 − 0.603896I
a = −0.90517 + 1.13829I
b = −0.538411 + 0.718761I
−5.49473 − 1.74369I −5.85606 + 4.80060I
u = 0.113489 + 1.387080I
a = 0.092029 − 0.253063I
b = −0.091131 + 0.767086I
−5.82799 − 0.68385I 0
u = 0.113489 − 1.387080I
a = 0.092029 + 0.253063I
b = −0.091131 − 0.767086I
−5.82799 + 0.68385I 0
u = −1.246240 + 0.646134I
a = −0.334713 − 0.260613I
b = 0.509481 − 0.280336I
1.97387 − 3.04466I 0
u = −1.246240 − 0.646134I
a = −0.334713 + 0.260613I
b = 0.509481 + 0.280336I
1.97387 + 3.04466I 0
u = 1.154430 + 0.807051I
a = −1.084390 + 0.241121I
b = 1.129930 + 0.604981I
−1.76551 + 2.91986I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.154430 − 0.807051I
a = −1.084390 − 0.241121I
b = 1.129930 − 0.604981I
−1.76551 − 2.91986I 0
u = −0.057357 + 0.586543I
a = −0.77673 − 1.35333I
b = 1.000910 − 0.724742I
−5.62610 + 2.08118I −5.84811 − 3.37812I
u = −0.057357 − 0.586543I
a = −0.77673 + 1.35333I
b = 1.000910 + 0.724742I
−5.62610 − 2.08118I −5.84811 + 3.37812I
u = −1.29883 + 0.59802I
a = −1.68501 + 0.26859I
b = 1.18761 − 1.25695I
−7.67746 − 10.47000I 0
u = −1.29883 − 0.59802I
a = −1.68501 − 0.26859I
b = 1.18761 + 1.25695I
−7.67746 + 10.47000I 0
u = 1.28284 + 0.67452I
a = 1.252440 + 0.041811I
b = −0.910566 − 0.810359I
−2.42139 + 7.59080I 0
u = 1.28284 − 0.67452I
a = 1.252440 − 0.041811I
b = −0.910566 + 0.810359I
−2.42139 − 7.59080I 0
u = −0.506710 + 0.172553I
a = −0.21425 + 2.51407I
b = −0.50236 − 2.06517I
−8.92961 + 0.23426I −9.16694 + 3.14387I
u = −0.506710 − 0.172553I
a = −0.21425 − 2.51407I
b = −0.50236 + 2.06517I
−8.92961 − 0.23426I −9.16694 − 3.14387I
u = −0.403234 + 0.350283I
a = 0.53928 − 2.21759I
b = 0.40326 + 1.75560I
−8.80263 − 0.13299I −8.04077 + 0.88602I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.403234 − 0.350283I
a = 0.53928 + 2.21759I
b = 0.40326 − 1.75560I
−8.80263 + 0.13299I −8.04077 − 0.88602I
u = 1.32675 + 0.63625I
a = −1.53051 − 0.23758I
b = 1.15204 + 1.31248I
−8.6793 + 19.8625I 0
u = 1.32675 − 0.63625I
a = −1.53051 + 0.23758I
b = 1.15204 − 1.31248I
−8.6793 − 19.8625I 0
u = −1.29731 + 0.71010I
a = 1.278090 + 0.023946I
b = −1.15402 + 0.88275I
−1.81745 − 13.82520I 0
u = −1.29731 − 0.71010I
a = 1.278090 − 0.023946I
b = −1.15402 − 0.88275I
−1.81745 + 13.82520I 0
u = 0.056774 + 0.498235I
a = 1.05776 − 1.07957I
b = −0.236580 − 0.572621I
−1.41654 − 1.54812I −3.80548 − 0.14559I
u = 0.056774 − 0.498235I
a = 1.05776 + 1.07957I
b = −0.236580 + 0.572621I
−1.41654 + 1.54812I −3.80548 + 0.14559I
u = −1.37810 + 0.69770I
a = −0.973448 + 0.212761I
b = 0.814170 − 0.929985I
−1.54230 − 6.50583I 0
u = −1.37810 − 0.69770I
a = −0.973448 − 0.212761I
b = 0.814170 + 0.929985I
−1.54230 + 6.50583I 0
u = 1.38713 + 0.68390I
a = 1.161990 + 0.260414I
b = −0.86430 − 1.33623I
−5.82548 + 10.01670I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38713 − 0.68390I
a = 1.161990 − 0.260414I
b = −0.86430 + 1.33623I
−5.82548 − 10.01670I 0
u = 1.16376 + 1.03937I
a = −0.633877 + 0.373111I
b = 0.936357 + 0.080902I
−2.42551 + 4.70764I 0
u = 1.16376 − 1.03937I
a = −0.633877 − 0.373111I
b = 0.936357 − 0.080902I
−2.42551 − 4.70764I 0
u = −0.46315 + 1.50664I
a = 0.096500 + 0.334106I
b = −0.474727 − 0.495902I
−4.81508 + 6.58039I 0
u = −0.46315 − 1.50664I
a = 0.096500 − 0.334106I
b = −0.474727 + 0.495902I
−4.81508 − 6.58039I 0
u = −1.45498 + 0.78984I
a = −0.598174 + 0.231653I
b = 0.129837 − 0.483813I
−5.65492 − 4.02160I 0
u = −1.45498 − 0.78984I
a = −0.598174 − 0.231653I
b = 0.129837 + 0.483813I
−5.65492 + 4.02160I 0
u = −0.324817 + 0.104466I
a = −1.25369 + 3.03046I
b = −0.474369 − 0.739669I
−1.86965 + 4.31631I 0.27220 − 10.11653I
u = −0.324817 − 0.104466I
a = −1.25369 − 3.03046I
b = −0.474369 + 0.739669I
−1.86965 − 4.31631I 0.27220 + 10.11653I
u = −0.174868 + 0.202967I
a = 1.66823 − 0.85991I
b = 0.561314 − 0.142823I
1.016650 − 0.880506I 6.93705 + 2.76149I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.174868 − 0.202967I
a = 1.66823 + 0.85991I
b = 0.561314 + 0.142823I
1.016650 + 0.880506I 6.93705 − 2.76149I
u = 1.63558 + 0.70218I
a = 0.394380 + 0.421054I
b = −0.200593 − 0.557267I
−5.76799 + 1.86737I 0
u = 1.63558 − 0.70218I
a = 0.394380 − 0.421054I
b = −0.200593 + 0.557267I
−5.76799 − 1.86737I 0
u = −1.97578 + 0.74683I
a = 0.200250 − 0.298376I
b = −0.010089 + 0.325948I
−6.36164 + 6.43248I 0
u = −1.97578 − 0.74683I
a = 0.200250 + 0.298376I
b = −0.010089 − 0.325948I
−6.36164 − 6.43248I 0
19
II.
I
u
2
= h−8.26×10
22
u
32
−1.85×10
23
u
31
+· · ·+1.90×10
22
b+1.15×10
24
, −5.63×
10
23
u
32
+8.10×10
22
u
31
+· · ·+1.33×10
23
a−2.25×10
24
, u
33
+u
32
+· · ·−23u+7i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
4.23567u
32
− 0.608981u
31
+ ··· − 136.033u + 16.9365
4.34946u
32
+ 9.73152u
31
+ ··· + 129.261u − 60.5083
a
9
=
1
−u
2
a
3
=
−2.59606u
32
− 8.51689u
31
+ ··· − 124.217u + 43.5321
7.71573u
32
+ 13.2448u
31
+ ··· + 106.190u − 68.0415
a
10
=
−4.22372u
32
− 10.1651u
31
+ ··· − 168.943u + 67.0929
−7.67922u
32
− 5.28030u
31
+ ··· + 189.987u − 50.9999
a
7
=
6.14716u
32
+ 10.3540u
31
+ ··· + 157.440u − 62.0963
−6.31206u
32
− 11.4819u
31
+ ··· − 200.613u + 88.5436
a
12
=
−u
u
a
5
=
0.0379203u
32
− 3.89155u
31
+ ··· − 88.2976u + 20.6983
8.54721u
32
+ 13.0141u
31
+ ··· + 81.5250u − 64.2701
a
2
=
5.36743u
32
+ 9.10918u
31
+ ··· + 43.2467u − 49.3129
−5.18141u
32
− 10.3485u
31
+ ··· − 83.2955u + 46.5137
a
11
=
−12.4019u
32
− 19.3748u
31
+ ··· − 107.650u + 101.766
9.38712u
32
+ 13.0652u
31
+ ··· + 21.5330u − 51.2101
a
6
=
0.945761u
32
− 3.85597u
31
+ ··· − 228.236u + 66.1110
−5.04118u
32
− 3.55639u
31
+ ··· + 135.430u − 31.7847
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
2591917967857514536584401
18998968333652458589737
u
32
+
702964844645848366569984
18998968333652458589737
u
31
+ ··· +
127391841753934086515861149
18998968333652458589737
u −
31357834078709952637703678
18998968333652458589737
20
(iv) u-Polynomials at the component
21
Crossings u-Polynomials at each crossing
c
1
u
33
+ 7u
32
+ ··· + 342u − 43
c
2
u
33
+ 8u
31
+ ··· − 14u − 1
c
3
u
33
− 6u
32
+ ··· + 7u + 1
c
4
u
33
+ 11u
32
+ ··· + 4u + 1
c
5
u
33
+ 6u
31
+ ··· − 6u + 1
c
6
u
33
− 14u
31
+ ··· − 20u − 1
c
7
u
33
+ 4u
31
+ ··· + 4u − 1
c
8
u
33
+ u
32
+ ··· − 23u + 7
c
9
u
33
+ 6u
32
+ ··· + 7u − 1
c
10
u
33
+ 6u
32
+ ··· − 2u − 1
c
11
u
33
− 14u
31
+ ··· − 20u + 1
c
12
u
33
− u
32
+ ··· − 23u − 7
22
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
33
− 17y
32
+ ··· + 22794y −1849
c
2
y
33
+ 16y
32
+ ··· + 50y −1
c
3
, c
9
y
33
− 24y
32
+ ··· − 41y −1
c
4
y
33
− 67y
32
+ ··· + 14y −1
c
5
y
33
+ 12y
32
+ ··· + 30y −1
c
6
, c
11
y
33
− 28y
32
+ ··· + 164y −1
c
7
y
33
+ 8y
32
+ ··· + 26y −1
c
8
, c
12
y
33
− 23y
32
+ ··· + 1047y −49
c
10
y
33
− 64y
32
+ ··· − 20y −1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.946805
a = −8.17582
b = 0.315702
−5.07674 255.360
u = −0.693516 + 0.810811I
a = 0.055720 + 0.407901I
b = −0.341944 − 0.962300I
−5.03614 − 2.51169I −8.24495 + 3.62297I
u = −0.693516 − 0.810811I
a = 0.055720 − 0.407901I
b = −0.341944 + 0.962300I
−5.03614 + 2.51169I −8.24495 − 3.62297I
u = −0.062985 + 1.098490I
a = −0.271665 + 0.224776I
b = −0.479375 − 1.138730I
−9.41807 + 3.35371I −3.59871 − 3.28110I
u = −0.062985 − 1.098490I
a = −0.271665 − 0.224776I
b = −0.479375 + 1.138730I
−9.41807 − 3.35371I −3.59871 + 3.28110I
u = −1.051880 + 0.341102I
a = −1.125080 − 0.657444I
b = 0.707446 − 0.599907I
2.14379 − 1.41755I 3.83956 + 2.89345I
u = −1.051880 − 0.341102I
a = −1.125080 + 0.657444I
b = 0.707446 + 0.599907I
2.14379 + 1.41755I 3.83956 − 2.89345I
u = −0.815239 + 0.351684I
a = 2.64100 + 0.17245I
b = −1.45435 + 0.58310I
−5.15167 − 1.81235I −4.63148 + 4.56344I
u = −0.815239 − 0.351684I
a = 2.64100 − 0.17245I
b = −1.45435 − 0.58310I
−5.15167 + 1.81235I −4.63148 − 4.56344I
u = −0.859334 + 0.144842I
a = −2.89540 − 0.99986I
b = 1.95474 + 1.41751I
−7.96378 − 8.31349I −3.08890 + 2.01042I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.859334 − 0.144842I
a = −2.89540 + 0.99986I
b = 1.95474 − 1.41751I
−7.96378 + 8.31349I −3.08890 − 2.01042I
u = −0.853820
a = 3.82341
b = −0.253346
−0.401967 −279.060
u = 0.593439 + 0.595037I
a = −0.670807 − 0.854987I
b = −0.252821 + 0.674843I
−1.95494 − 3.38129I −0.07191 + 4.04804I
u = 0.593439 − 0.595037I
a = −0.670807 + 0.854987I
b = −0.252821 − 0.674843I
−1.95494 + 3.38129I −0.07191 − 4.04804I
u = 1.143230 + 0.326512I
a = 1.125410 + 0.477868I
b = −0.84512 − 1.54860I
−0.01318 + 6.55703I 0.55002 − 9.90375I
u = 1.143230 − 0.326512I
a = 1.125410 − 0.477868I
b = −0.84512 + 1.54860I
−0.01318 − 6.55703I 0.55002 + 9.90375I
u = 0.718914 + 0.036769I
a = 1.274430 + 0.261478I
b = −0.58794 − 1.70231I
−8.19744 + 0.73324I −1.375841 + 0.050905I
u = 0.718914 − 0.036769I
a = 1.274430 − 0.261478I
b = −0.58794 + 1.70231I
−8.19744 − 0.73324I −1.375841 − 0.050905I
u = −1.163360 + 0.575700I
a = −0.311531 − 0.182246I
b = 0.505945 − 0.427915I
1.73496 − 3.02609I −9.36302 + 4.88460I
u = −1.163360 − 0.575700I
a = −0.311531 + 0.182246I
b = 0.505945 + 0.427915I
1.73496 + 3.02609I −9.36302 − 4.88460I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.522326 + 0.408282I
a = 1.24876 − 1.37885I
b = −0.523967 + 0.983874I
−4.36558 + 4.86150I −3.13374 − 4.77236I
u = 0.522326 − 0.408282I
a = 1.24876 + 1.37885I
b = −0.523967 − 0.983874I
−4.36558 − 4.86150I −3.13374 + 4.77236I
u = 1.245390 + 0.557689I
a = −0.736046 − 0.577027I
b = 0.275016 + 0.448065I
−5.37755 + 1.52394I 0
u = 1.245390 − 0.557689I
a = −0.736046 + 0.577027I
b = 0.275016 − 0.448065I
−5.37755 − 1.52394I 0
u = 1.315730 + 0.408171I
a = −1.231240 − 0.655992I
b = 0.89145 + 1.26068I
0.73487 + 6.60167I 0
u = 1.315730 − 0.408171I
a = −1.231240 + 0.655992I
b = 0.89145 − 1.26068I
0.73487 − 6.60167I 0
u = −1.32155 + 0.64647I
a = 1.324680 − 0.229236I
b = −0.97301 + 1.29761I
−5.56808 − 9.61229I 0
u = −1.32155 − 0.64647I
a = 1.324680 + 0.229236I
b = −0.97301 − 1.29761I
−5.56808 + 9.61229I 0
u = 0.427200
a = −3.80557
b = −0.514697
−5.67457 −8.21000
u = 1.23852 + 0.97311I
a = −0.724844 + 0.238834I
b = 0.869214 + 0.282172I
−2.39110 + 4.14031I 0
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.23852 − 0.97311I
a = −0.724844 − 0.238834I
b = 0.869214 − 0.282172I
−2.39110 − 4.14031I 0
u = −1.56979 + 0.54746I
a = −0.410107 + 0.377566I
b = 0.480893 − 0.260672I
−6.10695 + 6.28977I 0
u = −1.56979 − 0.54746I
a = −0.410107 − 0.377566I
b = 0.480893 + 0.260672I
−6.10695 − 6.28977I 0
28
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
33
+ 7u
32
+ ··· + 342u − 43)
· (u
145
− 6u
144
+ ··· − 153422604074u + 82046221679)
c
2
(u
33
+ 8u
31
+ ··· − 14u − 1)(u
145
− u
144
+ ··· + 525670u + 55949)
c
3
(u
33
− 6u
32
+ ··· + 7u + 1)(u
145
− 5u
144
+ ··· + 1.23943 × 10
7
u + 542527)
c
4
(u
33
+ 11u
32
+ ··· + 4u + 1)(u
145
+ 10u
144
+ ··· − 32u − 1)
c
5
(u
33
+ 6u
31
+ ··· − 6u + 1)(u
145
+ 3u
144
+ ··· − 49936u + 13568)
c
6
(u
33
− 14u
31
+ ··· − 20u − 1)(u
145
− u
144
+ ··· − 134u + 1)
c
7
(u
33
+ 4u
31
+ ··· + 4u − 1)(u
145
− 3u
144
+ ··· + 1140u + 1117)
c
8
(u
33
+ u
32
+ ··· − 23u + 7)(u
145
− 43u
143
+ ··· + 14615u − 1286)
c
9
(u
33
+ 6u
32
+ ··· + 7u − 1)(u
145
− 5u
144
+ ··· + 1.23943 × 10
7
u + 542527)
c
10
(u
33
+ 6u
32
+ ··· − 2u − 1)(u
145
+ u
144
+ ··· − 27127u − 9606)
c
11
(u
33
− 14u
31
+ ··· − 20u + 1)(u
145
− u
144
+ ··· − 134u + 1)
c
12
(u
33
− u
32
+ ··· − 23u − 7)(u
145
− 43u
143
+ ··· + 14615u − 1286)
29
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
33
− 17y
32
+ ··· + 22794y −1849)
· (y
145
− 84y
144
+ ··· + 3.96 × 10
23
y −6.73 × 10
21
)
c
2
(y
33
+ 16y
32
+ ··· + 50y −1)
· (y
145
+ 53y
144
+ ··· + 51147539762y −3130290601)
c
3
, c
9
(y
33
− 24y
32
+ ··· − 41y −1)
· (y
145
+ 73y
144
+ ··· + 4228767991095y −294335545729)
c
4
(y
33
− 67y
32
+ ··· + 14y −1)(y
145
− 74y
144
+ ··· + 198y −1)
c
5
(y
33
+ 12y
32
+ ··· + 30y −1)
· (y
145
+ 37y
144
+ ··· + 1166626560y −184090624)
c
6
, c
11
(y
33
− 28y
32
+ ··· + 164y −1)(y
145
− 131y
144
+ ··· + 18524y −1)
c
7
(y
33
+ 8y
32
+ ··· + 26y −1)
· (y
145
+ 21y
144
+ ··· + 52277246y −1247689)
c
8
, c
12
(y
33
− 23y
32
+ ··· + 1047y −49)
· (y
145
− 86y
144
+ ··· + 66531265y −1653796)
c
10
(y
33
− 64y
32
+ ··· − 20y −1)
· (y
145
− 91y
144
+ ··· + 5892163597y −92275236)
30
