12a
0565
(K12a
0565
)
A knot diagram
1
Linearized knot diagam
3 7 9 8 11 12 2 10 4 1 6 5
Solving Sequence
6,11
12
2,7
3 8 5 1 4 10 9
c
11
c
6
c
2
c
7
c
5
c
12
c
4
c
10
c
9
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h1.32158 × 10
56
u
107
+ 3.27224 × 10
55
u
106
+ ··· + 4.96026 × 10
55
b − 4.27420 × 10
55
,
− 1.26324 × 10
55
u
107
− 5.20004 × 10
54
u
106
+ ··· + 4.96026 × 10
55
a + 2.69630 × 10
55
, u
108
+ u
107
+ ··· + 4u − 1i
I
u
2
= h−u
4
+ u
2
a + 2u
2
+ b − a − 1, 4u
4
a + u
5
+ u
3
a − 2u
4
− 6u
2
a − 2u
3
+ a
2
− au + u
2
− 2a − u,
u
6
− 3u
4
+ 2u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 120 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
= h1.32 × 10
56
u
107
+ 3.27 × 10
55
u
106
+ · · · + 4.96 × 10
55
b − 4.27 ×
10
55
, −1.26 × 10
55
u
107
− 5.20 × 10
54
u
106
+ · · · + 4.96 × 10
55
a + 2.70 ×
10
55
, u
108
+ u
107
+ · · · + 4u − 1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
2
=
0.254671u
107
+ 0.104834u
106
+ ··· + 14.4074u − 0.543580
−2.66434u
107
− 0.659690u
106
+ ··· − 2.76765u + 0.861688
a
7
=
u
−u
3
+ u
a
3
=
−0.915359u
107
− 1.08630u
106
+ ··· + 14.1070u − 0.0176901
−1.60412u
107
− 0.998446u
106
+ ··· − 1.98244u + 1.40868
a
8
=
−1.55496u
107
− 1.18445u
106
+ ··· + 10.3009u − 2.64846
−0.0712391u
107
− 0.373281u
106
+ ··· + 10.1195u − 2.22072
a
5
=
−u
u
a
1
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
4
=
0.557394u
107
+ 0.518033u
106
+ ··· − 21.2085u + 4.62222
3.34901u
107
+ 0.543398u
106
+ ··· − 5.93596u + 1.29539
a
10
=
u
8
− 3u
6
+ u
4
+ 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
9
=
−1.38003u
107
+ 0.953232u
106
+ ··· + 9.29014u − 2.70352
−0.149367u
107
− 1.02014u
106
+ ··· + 12.1445u − 2.89736
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.876716u
107
+ 1.14842u
106
+ ··· − 33.0770u + 17.3306
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
108
+ 53u
107
+ ··· + 24u + 1
c
2
, c
7
u
108
+ u
107
+ ··· − 6u − 1
c
3
, c
9
u
108
+ u
107
+ ··· + 21u
2
− 5
c
4
u
108
+ 3u
107
+ ··· − 461530u − 25545
c
5
, c
6
, c
11
u
108
+ u
107
+ ··· + 4u − 1
c
8
u
108
− 53u
107
+ ··· − 210u + 25
c
10
u
108
− 23u
107
+ ··· − 841432u + 42793
c
12
u
108
− 3u
107
+ ··· − 334u + 99
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
108
+ 17y
107
+ ··· − 324y + 1
c
2
, c
7
y
108
+ 53y
107
+ ··· + 24y + 1
c
3
, c
9
y
108
− 53y
107
+ ··· − 210y + 25
c
4
y
108
+ 31y
107
+ ··· − 307924380910y + 652547025
c
5
, c
6
, c
11
y
108
− 99y
107
+ ··· + 4y + 1
c
8
y
108
+ 11y
107
+ ··· + 17950y + 625
c
10
y
108
+ 37y
107
+ ··· + 17887794312y + 1831240849
c
12
y
108
− 7y
107
+ ··· − 323416y + 9801
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.078510 + 0.066384I
a = 0.74913 + 2.91711I
b = −0.159122 − 1.375640I
−1.75904 − 2.65358I 0
u = −1.078510 − 0.066384I
a = 0.74913 − 2.91711I
b = −0.159122 + 1.375640I
−1.75904 + 2.65358I 0
u = −1.091430 + 0.244782I
a = 0.49231 + 2.62431I
b = −0.860462 − 0.916898I
−0.96511 − 4.47596I 0
u = −1.091430 − 0.244782I
a = 0.49231 − 2.62431I
b = −0.860462 + 0.916898I
−0.96511 + 4.47596I 0
u = 1.133480 + 0.015855I
a = 1.05659 + 3.14794I
b = 0.06419 − 1.93882I
−0.45128 + 2.17405I 0
u = 1.133480 − 0.015855I
a = 1.05659 − 3.14794I
b = 0.06419 + 1.93882I
−0.45128 − 2.17405I 0
u = 1.099430 + 0.302544I
a = 0.38080 − 2.61193I
b = −1.083300 + 0.814934I
1.19055 + 9.20491I 0
u = 1.099430 − 0.302544I
a = 0.38080 + 2.61193I
b = −1.083300 − 0.814934I
1.19055 − 9.20491I 0
u = 1.164780 + 0.108311I
a = 0.637076 − 0.329305I
b = −0.785331 + 0.058134I
1.56546 + 0.67321I 0
u = 1.164780 − 0.108311I
a = 0.637076 + 0.329305I
b = −0.785331 − 0.058134I
1.56546 − 0.67321I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.691156 + 0.445702I
a = −0.57421 + 2.25405I
b = 0.881318 + 0.430710I
2.28872 − 9.22034I 8.40055 + 5.38134I
u = 0.691156 − 0.445702I
a = −0.57421 − 2.25405I
b = 0.881318 − 0.430710I
2.28872 + 9.22034I 8.40055 − 5.38134I
u = 0.312027 + 0.742416I
a = −0.599810 − 0.003658I
b = −2.50501 + 0.43469I
0.94501 + 13.40950I 5.88106 − 10.27839I
u = 0.312027 − 0.742416I
a = −0.599810 + 0.003658I
b = −2.50501 − 0.43469I
0.94501 − 13.40950I 5.88106 + 10.27839I
u = −0.304870 + 0.721074I
a = −0.533307 + 0.121712I
b = −2.43367 − 0.20539I
−1.48238 − 8.19805I 2.90543 + 6.87933I
u = −0.304870 − 0.721074I
a = −0.533307 − 0.121712I
b = −2.43367 + 0.20539I
−1.48238 + 8.19805I 2.90543 − 6.87933I
u = 0.345057 + 0.699162I
a = −0.286884 − 0.018001I
b = −1.97972 + 0.27664I
3.40555 + 5.22912I 9.21272 − 5.28491I
u = 0.345057 − 0.699162I
a = −0.286884 + 0.018001I
b = −1.97972 − 0.27664I
3.40555 − 5.22912I 9.21272 + 5.28491I
u = −0.338529 + 0.700114I
a = −0.176477 − 0.453278I
b = 0.044291 + 0.534112I
3.32780 − 7.81069I 9.09509 + 6.82204I
u = −0.338529 − 0.700114I
a = −0.176477 + 0.453278I
b = 0.044291 − 0.534112I
3.32780 + 7.81069I 9.09509 − 6.82204I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.651351 + 0.404173I
a = −0.34954 − 2.24628I
b = 0.828682 − 0.267745I
−0.17377 + 4.20459I 5.40595 − 1.84900I
u = −0.651351 − 0.404173I
a = −0.34954 + 2.24628I
b = 0.828682 + 0.267745I
−0.17377 − 4.20459I 5.40595 + 1.84900I
u = 0.098301 + 0.756192I
a = 0.582497 − 0.315067I
b = 2.05472 + 0.23854I
−1.85912 − 5.30654I 4.29467 + 5.82125I
u = 0.098301 − 0.756192I
a = 0.582497 + 0.315067I
b = 2.05472 − 0.23854I
−1.85912 + 5.30654I 4.29467 − 5.82125I
u = 1.209590 + 0.269103I
a = 0.44287 − 2.25971I
b = −1.16164 + 1.17315I
2.86997 + 2.24160I 0
u = 1.209590 − 0.269103I
a = 0.44287 + 2.25971I
b = −1.16164 − 1.17315I
2.86997 − 2.24160I 0
u = 0.583376 + 0.482300I
a = −0.37395 + 1.83053I
b = 0.557650 + 0.305960I
4.32970 − 1.18610I 11.36506 − 0.65831I
u = 0.583376 − 0.482300I
a = −0.37395 − 1.83053I
b = 0.557650 − 0.305960I
4.32970 + 1.18610I 11.36506 + 0.65831I
u = −0.584735 + 0.471879I
a = 0.824618 − 0.223152I
b = −0.381146 + 0.027264I
4.29184 + 3.79474I 11.40196 − 0.85477I
u = −0.584735 − 0.471879I
a = 0.824618 + 0.223152I
b = −0.381146 − 0.027264I
4.29184 − 3.79474I 11.40196 + 0.85477I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.635568I
a = −0.198792 − 0.793432I
b = 0.094136 + 0.219436I
4.88640 + 0.26560I 11.56392 + 0.30422I
u = −0.395123 − 0.635568I
a = −0.198792 + 0.793432I
b = 0.094136 − 0.219436I
4.88640 − 0.26560I 11.56392 − 0.30422I
u = −1.229210 + 0.242947I
a = 0.896086 + 1.028220I
b = −1.278550 − 0.286411I
3.00417 − 4.91856I 0
u = −1.229210 − 0.242947I
a = 0.896086 − 1.028220I
b = −1.278550 + 0.286411I
3.00417 + 4.91856I 0
u = −0.486434 + 0.557533I
a = 0.532437 − 0.172628I
b = −0.699156 − 0.094278I
5.23596 − 4.22319I 11.96155 + 6.69488I
u = −0.486434 − 0.557533I
a = 0.532437 + 0.172628I
b = −0.699156 + 0.094278I
5.23596 + 4.22319I 11.96155 − 6.69488I
u = 0.321740 + 0.658812I
a = −0.033716 + 0.539334I
b = 0.190501 − 0.454927I
0.71793 + 2.99181I 5.99049 − 3.37437I
u = 0.321740 − 0.658812I
a = −0.033716 − 0.539334I
b = 0.190501 + 0.454927I
0.71793 − 2.99181I 5.99049 + 3.37437I
u = −0.116202 + 0.710518I
a = 0.459041 + 0.428398I
b = 1.92755 − 0.02931I
−3.89427 + 0.88977I −0.482474 − 1.035537I
u = −0.116202 − 0.710518I
a = 0.459041 − 0.428398I
b = 1.92755 + 0.02931I
−3.89427 − 0.88977I −0.482474 + 1.035537I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.010129 + 0.719466I
a = 0.417716 − 0.122153I
b = 1.55361 + 0.38676I
−0.79600 + 1.37844I 6.81642 − 0.64656I
u = 0.010129 − 0.719466I
a = 0.417716 + 0.122153I
b = 1.55361 − 0.38676I
−0.79600 − 1.37844I 6.81642 + 0.64656I
u = −0.263626 + 0.654252I
a = −0.325800 + 0.611267I
b = −2.25097 + 0.64555I
−3.32605 − 5.48665I 1.87864 + 8.65808I
u = −0.263626 − 0.654252I
a = −0.325800 − 0.611267I
b = −2.25097 − 0.64555I
−3.32605 + 5.48665I 1.87864 − 8.65808I
u = −1.280520 + 0.227409I
a = 0.454469 + 1.305840I
b = −1.051990 − 0.686908I
2.98007 − 4.88539I 0
u = −1.280520 − 0.227409I
a = 0.454469 − 1.305840I
b = −1.051990 + 0.686908I
2.98007 + 4.88539I 0
u = 1.309160 + 0.119036I
a = 1.13476 − 2.30065I
b = −1.28347 + 2.10489I
2.32381 + 3.02952I 0
u = 1.309160 − 0.119036I
a = 1.13476 + 2.30065I
b = −1.28347 − 2.10489I
2.32381 − 3.02952I 0
u = 0.268902 + 0.619610I
a = 0.347657 − 1.143590I
b = 1.69801 − 0.61561I
−2.24602 + 4.56963I 4.51511 − 7.48692I
u = 0.268902 − 0.619610I
a = 0.347657 + 1.143590I
b = 1.69801 + 0.61561I
−2.24602 − 4.56963I 4.51511 + 7.48692I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.194915 + 0.638039I
a = 0.292126 + 0.821408I
b = 1.77808 + 0.35167I
−4.08493 − 0.24577I −0.63553 + 2.29038I
u = −0.194915 − 0.638039I
a = 0.292126 − 0.821408I
b = 1.77808 − 0.35167I
−4.08493 + 0.24577I −0.63553 − 2.29038I
u = −1.33579
a = −0.0187117
b = −0.474558
5.83646 0
u = −1.305020 + 0.308818I
a = 1.51515 + 1.58378I
b = −2.37848 − 0.48598I
2.51934 + 1.46324I 0
u = −1.305020 − 0.308818I
a = 1.51515 − 1.58378I
b = −2.37848 + 0.48598I
2.51934 − 1.46324I 0
u = 0.485149 + 0.445066I
a = 0.763623 + 0.056116I
b = −0.504700 − 0.143811I
1.53101 + 0.65365I 8.18643 − 3.61177I
u = 0.485149 − 0.445066I
a = 0.763623 − 0.056116I
b = −0.504700 + 0.143811I
1.53101 − 0.65365I 8.18643 + 3.61177I
u = 0.245646 + 0.610621I
a = −0.053515 − 0.881772I
b = −1.91700 − 1.11447I
−2.50666 + 0.26869I 3.56195 − 3.97481I
u = 0.245646 − 0.610621I
a = −0.053515 + 0.881772I
b = −1.91700 + 1.11447I
−2.50666 − 0.26869I 3.56195 + 3.97481I
u = 1.327250 + 0.276931I
a = 1.40522 − 1.82470I
b = −2.37206 + 0.99248I
0.62962 + 2.67287I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.327250 − 0.276931I
a = 1.40522 + 1.82470I
b = −2.37206 − 0.99248I
0.62962 − 2.67287I 0
u = 1.373750 + 0.243039I
a = 1.40305 − 2.13535I
b = −2.56082 + 1.71267I
0.89903 + 3.44486I 0
u = 1.373750 − 0.243039I
a = 1.40305 + 2.13535I
b = −2.56082 − 1.71267I
0.89903 − 3.44486I 0
u = −1.380940 + 0.198807I
a = 0.708088 + 0.977587I
b = −0.892045 − 0.010544I
3.39614 − 4.59399I 0
u = −1.380940 − 0.198807I
a = 0.708088 − 0.977587I
b = −0.892045 + 0.010544I
3.39614 + 4.59399I 0
u = 0.119251 + 0.591860I
a = 0.493502 + 0.220355I
b = 0.685302 − 0.330415I
−1.34471 + 1.97131I 4.36318 − 4.94300I
u = 0.119251 − 0.591860I
a = 0.493502 − 0.220355I
b = 0.685302 + 0.330415I
−1.34471 − 1.97131I 4.36318 + 4.94300I
u = 1.387350 + 0.167078I
a = 1.219680 − 0.388168I
b = −1.009460 − 0.799919I
3.31742 − 0.59461I 0
u = 1.387350 − 0.167078I
a = 1.219680 + 0.388168I
b = −1.009460 + 0.799919I
3.31742 + 0.59461I 0
u = −1.400760 + 0.187653I
a = 1.26496 + 2.30774I
b = −2.25958 − 2.39901I
3.93453 − 0.63802I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.400760 − 0.187653I
a = 1.26496 − 2.30774I
b = −2.25958 + 2.39901I
3.93453 + 0.63802I 0
u = −1.39769 + 0.23851I
a = −2.84149 − 0.84830I
b = 2.65758 − 0.54537I
2.74784 − 3.38218I 0
u = −1.39769 − 0.23851I
a = −2.84149 + 0.84830I
b = 2.65758 + 0.54537I
2.74784 + 3.38218I 0
u = −1.40662 + 0.24260I
a = 1.46311 + 2.26771I
b = −2.85804 − 2.03183I
3.11491 − 7.73415I 0
u = −1.40662 − 0.24260I
a = 1.46311 − 2.26771I
b = −2.85804 + 2.03183I
3.11491 + 7.73415I 0
u = 1.40477 + 0.25503I
a = −2.81208 + 1.44750I
b = 3.09899 + 0.06696I
2.00366 + 8.80571I 0
u = 1.40477 − 0.25503I
a = −2.81208 − 1.44750I
b = 3.09899 − 0.06696I
2.00366 − 8.80571I 0
u = −1.42740 + 0.25561I
a = −0.265370 + 0.774547I
b = 0.230532 − 0.576712I
6.31895 − 6.33913I 0
u = −1.42740 − 0.25561I
a = −0.265370 − 0.774547I
b = 0.230532 + 0.576712I
6.31895 + 6.33913I 0
u = −1.44137 + 0.16472I
a = −0.917777 − 0.491847I
b = 0.614103 + 0.432152I
7.63096 − 2.89779I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44137 − 0.16472I
a = −0.917777 + 0.491847I
b = 0.614103 − 0.432152I
7.63096 + 2.89779I 0
u = 1.44903 + 0.11745I
a = 0.605643 + 0.825539I
b = 0.01844 − 1.83441I
6.39373 − 2.52928I 0
u = 1.44903 − 0.11745I
a = 0.605643 − 0.825539I
b = 0.01844 + 1.83441I
6.39373 + 2.52928I 0
u = 1.42656 + 0.28196I
a = −2.35252 + 2.19395I
b = 3.43850 − 0.89248I
4.05548 + 11.84760I 0
u = 1.42656 − 0.28196I
a = −2.35252 − 2.19395I
b = 3.43850 + 0.89248I
4.05548 − 11.84760I 0
u = −1.43204 + 0.29068I
a = −2.24646 − 2.37108I
b = 3.54962 + 1.12717I
6.5247 − 17.1645I 0
u = −1.43204 − 0.29068I
a = −2.24646 + 2.37108I
b = 3.54962 − 1.12717I
6.5247 + 17.1645I 0
u = 1.43777 + 0.26929I
a = −0.443434 − 0.787351I
b = 0.425283 + 0.761627I
9.0213 + 11.3443I 0
u = 1.43777 − 0.26929I
a = −0.443434 + 0.787351I
b = 0.425283 − 0.761627I
9.0213 − 11.3443I 0
u = −1.44010 + 0.26769I
a = −2.03984 − 1.94093I
b = 2.94110 + 1.01445I
9.12994 − 8.75266I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44010 − 0.26769I
a = −2.03984 + 1.94093I
b = 2.94110 − 1.01445I
9.12994 + 8.75266I 0
u = 1.44751 + 0.23678I
a = −0.258180 − 0.468103I
b = 0.490091 + 0.204809I
10.79720 + 2.91953I 0
u = 1.44751 − 0.23678I
a = −0.258180 + 0.468103I
b = 0.490091 − 0.204809I
10.79720 − 2.91953I 0
u = 1.46243 + 0.14469I
a = −0.587301 + 0.574641I
b = 0.255699 − 0.699484I
10.81440 − 1.67028I 0
u = 1.46243 − 0.14469I
a = −0.587301 − 0.574641I
b = 0.255699 + 0.699484I
10.81440 + 1.67028I 0
u = −1.46406 + 0.14706I
a = 0.276285 − 0.558000I
b = 0.37933 + 1.43135I
10.86460 − 0.98163I 0
u = −1.46406 − 0.14706I
a = 0.276285 + 0.558000I
b = 0.37933 − 1.43135I
10.86460 + 0.98163I 0
u = −1.46834 + 0.10526I
a = 0.438230 − 1.041400I
b = 0.24048 + 2.09534I
9.17034 + 7.53278I 0
u = −1.46834 − 0.10526I
a = 0.438230 + 1.041400I
b = 0.24048 − 2.09534I
9.17034 − 7.53278I 0
u = 1.46153 + 0.18829I
a = −1.008240 + 0.914479I
b = 0.978642 − 0.870160I
11.49880 + 6.90459I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46153 − 0.18829I
a = −1.008240 − 0.914479I
b = 0.978642 + 0.870160I
11.49880 − 6.90459I 0
u = −0.447001 + 0.170577I
a = 0.60361 − 2.65934I
b = 0.763007 + 0.045905I
−1.99045 + 2.33467I 4.94783 − 3.24934I
u = −0.447001 − 0.170577I
a = 0.60361 + 2.65934I
b = 0.763007 − 0.045905I
−1.99045 − 2.33467I 4.94783 + 3.24934I
u = 0.271412 + 0.385217I
a = −0.55786 − 1.78537I
b = 1.127460 − 0.377063I
−1.42196 − 1.69809I 8.03714 − 0.07727I
u = 0.271412 − 0.385217I
a = −0.55786 + 1.78537I
b = 1.127460 + 0.377063I
−1.42196 + 1.69809I 8.03714 + 0.07727I
u = 0.378359
a = 0.988497
b = −0.211165
0.761657 13.7450
u = 0.158976 + 0.327036I
a = 2.49132 + 0.81649I
b = 0.941699 − 0.463379I
−1.56493 + 2.24938I 7.49091 − 5.30893I
u = 0.158976 − 0.327036I
a = 2.49132 − 0.81649I
b = 0.941699 + 0.463379I
−1.56493 − 2.24938I 7.49091 + 5.30893I
15
II.
I
u
2
= h−u
4
+u
2
a+2u
2
+b−a−1, 4u
4
a+u
5
+· · ·+a
2
−2a, u
6
−3u
4
+2u
2
+1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
2
=
a
u
4
− u
2
a − 2u
2
+ a + 1
a
7
=
u
−u
3
+ u
a
3
=
u
4
− u
2
+ a − 1
−u
2
a + a + 1
a
8
=
−u
5
a + 2u
3
a − au + u
−u
5
+ u
3
a + 2u
3
− 2au − u
a
5
=
−u
u
a
1
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
4
=
u
5
a − 2u
3
a + 2u
4
+ au − 3u
2
+ a − 2u − 1
−u
5
a − u
5
+ 2u
3
a − u
4
− u
2
a + 3u
3
− au + 2u
2
+ a + 1
a
10
=
−u
4
+ u
2
+ 1
u
4
− u
2
− 1
a
9
=
−u
5
a + u
5
+ 3u
3
a − 2u
3
− 2au
−2u
5
+ 4u
3
− au
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
5
− 4u
3
a − 4u
4
− 4u
3
+ 8au + 8u
2
+ 4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
12
c
2
, c
7
(u
2
+ 1)
6
c
3
, c
4
, c
9
(u
4
− u
2
+ 1)
3
c
5
, c
6
, c
11
(u
6
− 3u
4
+ 2u
2
+ 1)
2
c
8
(u
2
+ u + 1)
6
c
10
(u
3
+ u
2
− 1)
4
c
12
(u
6
+ u
4
+ 2u
2
+ 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
12
c
2
, c
7
(y + 1)
12
c
3
, c
4
, c
9
(y
2
− y + 1)
6
c
5
, c
6
, c
11
(y
3
− 3y
2
+ 2y + 1)
4
c
8
(y
2
+ y + 1)
6
c
10
(y
3
− y
2
+ 2y −1)
4
c
12
(y
3
+ y
2
+ 2y + 1)
4
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.307140 + 0.215080I
a = −0.03980 − 1.84565I
b = −0.88885 + 1.98972I
1.37919 + 0.79824I 5.50976 + 0.48465I
u = 1.307140 + 0.215080I
a = 1.47997 − 3.13579I
b = −2.62090 + 1.98972I
1.37919 + 4.85801I 5.50976 − 6.44355I
u = 1.307140 − 0.215080I
a = −0.03980 + 1.84565I
b = −0.88885 − 1.98972I
1.37919 − 0.79824I 5.50976 − 0.48465I
u = 1.307140 − 0.215080I
a = 1.47997 + 3.13579I
b = −2.62090 − 1.98972I
1.37919 − 4.85801I 5.50976 + 6.44355I
u = −1.307140 + 0.215080I
a = 0.705065 + 0.968214I
b = −0.888852 − 0.989724I
1.37919 − 4.85801I 5.50976 + 6.44355I
u = −1.307140 + 0.215080I
a = 2.22483 + 2.25835I
b = −2.62090 − 0.98972I
1.37919 − 0.79824I 5.50976 − 0.48465I
u = −1.307140 − 0.215080I
a = 0.705065 − 0.968214I
b = −0.888852 + 0.989724I
1.37919 + 4.85801I 5.50976 − 6.44355I
u = −1.307140 − 0.215080I
a = 2.22483 − 2.25835I
b = −2.62090 + 0.98972I
1.37919 + 0.79824I 5.50976 + 0.48465I
u = 0.569840I
a = −0.838781 + 0.377439I
b = 0.643730 + 0.500000I
−2.75839 + 2.02988I −1.01951 − 3.46410I
u = 0.569840I
a = 0.468706 + 0.377439I
b = 2.37578 + 0.50000I
−2.75839 − 2.02988I −1.01951 + 3.46410I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = − 0.569840I
a = −0.838781 − 0.377439I
b = 0.643730 − 0.500000I
−2.75839 − 2.02988I −1.01951 + 3.46410I
u = − 0.569840I
a = 0.468706 − 0.377439I
b = 2.37578 − 0.50000I
−2.75839 + 2.02988I −1.01951 − 3.46410I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
12
)(u
108
+ 53u
107
+ ··· + 24u + 1)
c
2
, c
7
((u
2
+ 1)
6
)(u
108
+ u
107
+ ··· − 6u − 1)
c
3
, c
9
((u
4
− u
2
+ 1)
3
)(u
108
+ u
107
+ ··· + 21u
2
− 5)
c
4
((u
4
− u
2
+ 1)
3
)(u
108
+ 3u
107
+ ··· − 461530u − 25545)
c
5
, c
6
, c
11
((u
6
− 3u
4
+ 2u
2
+ 1)
2
)(u
108
+ u
107
+ ··· + 4u − 1)
c
8
((u
2
+ u + 1)
6
)(u
108
− 53u
107
+ ··· − 210u + 25)
c
10
((u
3
+ u
2
− 1)
4
)(u
108
− 23u
107
+ ··· − 841432u + 42793)
c
12
((u
6
+ u
4
+ 2u
2
+ 1)
2
)(u
108
− 3u
107
+ ··· − 334u + 99)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
12
)(y
108
+ 17y
107
+ ··· − 324y + 1)
c
2
, c
7
((y + 1)
12
)(y
108
+ 53y
107
+ ··· + 24y + 1)
c
3
, c
9
((y
2
− y + 1)
6
)(y
108
− 53y
107
+ ··· − 210y + 25)
c
4
((y
2
− y + 1)
6
)(y
108
+ 31y
107
+ ··· − 3.07924 × 10
11
y + 6.52547 × 10
8
)
c
5
, c
6
, c
11
((y
3
− 3y
2
+ 2y + 1)
4
)(y
108
− 99y
107
+ ··· + 4y + 1)
c
8
((y
2
+ y + 1)
6
)(y
108
+ 11y
107
+ ··· + 17950y + 625)
c
10
(y
3
− y
2
+ 2y −1)
4
· (y
108
+ 37y
107
+ ··· + 17887794312y + 1831240849)
c
12
((y
3
+ y
2
+ 2y + 1)
4
)(y
108
− 7y
107
+ ··· − 323416y + 9801)
22
