12a
1042
(K12a
1042
)
A knot diagram
1
Linearized knot diagam
4 7 8 1 11 12 10 5 2 3 6 9
Solving Sequence
1,5
4
2,9
10 8 3 11 7 12 6
c
4
c
1
c
9
c
8
c
3
c
10
c
7
c
12
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.16283 × 10
40
u
55
+ 2.14434 × 10
41
u
54
+ ··· + 2.38481 × 10
39
b + 1.27043 × 10
43
,
2.48132 × 10
40
u
55
− 4.23380 × 10
41
u
54
+ ··· + 4.76963 × 10
39
a − 6.69755 × 10
42
,
u
56
− 18u
55
+ ··· − 19200u + 1024i
I
u
2
= h−3.81235 × 10
34
a
9
u
10
+ 3.02772 × 10
34
a
8
u
10
+ ··· − 9.29378 × 10
34
a − 1.45475 × 10
35
,
− u
10
a
9
− 5u
10
a
8
+ ··· − 295a − 110,
u
11
+ 3u
10
+ 8u
9
+ 13u
8
+ 18u
7
+ 20u
6
+ 18u
5
+ 15u
4
+ 9u
3
+ 5u
2
+ 2u + 1i
I
u
3
= h2.70992 × 10
15
u
39
+ 3.29546 × 10
16
u
38
+ ··· + 1.11311 × 10
15
b − 7.54465 × 10
15
,
7.54465 × 10
15
u
39
+ 1.00790 × 10
17
u
38
+ ··· + 1.11311 × 10
15
a + 2.52828 × 10
16
, u
40
+ 13u
39
+ ··· + 13u + 1i
* 3 irreducible components of dim
C
= 0, with total 206 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−1.16 × 10
40
u
55
+ 2.14 × 10
41
u
54
+ · · · + 2.38 × 10
39
b + 1.27 ×
10
43
, 2.48 × 10
40
u
55
− 4.23 × 10
41
u
54
+ · · · + 4.77 × 10
39
a − 6.70 ×
10
42
, u
56
− 18u
55
+ · · · − 19200u + 1024i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
−5.20233u
55
+ 88.7659u
54
+ ··· − 26720.5u + 1404.21
4.87600u
55
− 89.9163u
54
+ ··· + 98480.5u − 5327.19
a
10
=
−2.55698u
55
+ 46.0061u
54
+ ··· − 48621.2u + 2671.75
1.13506u
55
− 21.4817u
54
+ ··· + 29846.8u − 1621.76
a
8
=
−0.326331u
55
− 1.15037u
54
+ ··· + 71760.1u − 3922.98
4.87600u
55
− 89.9163u
54
+ ··· + 98480.5u − 5327.19
a
3
=
−0.799050u
55
+ 16.4891u
54
+ ··· − 50751.2u + 2785.10
−0.617890u
55
+ 12.6104u
54
+ ··· + 508.672u − 185.508
a
11
=
−1.84666u
55
+ 38.4053u
54
+ ··· − 114285.u + 6283.16
−2.63618u
55
+ 47.6390u
54
+ ··· − 48809.0u + 2622.80
a
7
=
−9.61807u
55
+ 164.399u
54
+ ··· − 63717.1u + 3382.01
6.38454u
55
− 121.688u
54
+ ··· + 211275.u − 11663.2
a
12
=
−1.22612u
55
+ 17.1359u
54
+ ··· + 17853.1u − 827.515
4.93425u
55
− 84.9272u
54
+ ··· + 24370.0u − 1255.54
a
6
=
1.26900u
55
− 29.2945u
54
+ ··· + 126784.u − 7023.07
3.92313u
55
− 71.4238u
54
+ ··· + 60639.9u − 3214.32
(ii) Obstruction class = −1
(iii) Cusp Shapes = −24.8470u
55
+ 419.627u
54
+ ··· − 95591.9u + 4633.30
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
56
− 18u
55
+ ··· − 19200u + 1024
c
2
, c
10
u
56
− 8u
54
+ ··· + 4u + 1
c
3
, c
9
u
56
− u
55
+ ··· + 8u + 1
c
5
, c
6
, c
11
u
56
+ 21u
55
+ ··· + 4096u + 2048
c
7
u
56
− 35u
55
+ ··· − 272u + 32
c
8
, c
12
u
56
− u
55
+ ··· + 12u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
56
+ 28y
55
+ ··· + 9502720y + 1048576
c
2
, c
10
y
56
− 16y
55
+ ··· − 34y + 1
c
3
, c
9
y
56
− 7y
55
+ ··· − 18y + 1
c
5
, c
6
, c
11
y
56
− 45y
55
+ ··· − 2097152y + 4194304
c
7
y
56
− 5y
55
+ ··· − 9984y + 1024
c
8
, c
12
y
56
+ 33y
55
+ ··· + 188y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.020630 + 0.993062I
a = 1.35474 − 0.80692I
b = −0.77337 − 1.36199I
7.50595 − 4.34710I 0
u = −0.020630 − 0.993062I
a = 1.35474 + 0.80692I
b = −0.77337 + 1.36199I
7.50595 + 4.34710I 0
u = −0.039442 + 0.978977I
a = −1.074070 + 0.779942I
b = 0.721182 + 1.082250I
1.92174 − 1.40595I 0
u = −0.039442 − 0.978977I
a = −1.074070 − 0.779942I
b = 0.721182 − 1.082250I
1.92174 + 1.40595I 0
u = −0.108043 + 1.022290I
a = 0.803024 − 0.451536I
b = −0.374842 − 0.869712I
2.27427 + 1.77133I 0
u = −0.108043 − 1.022290I
a = 0.803024 + 0.451536I
b = −0.374842 + 0.869712I
2.27427 − 1.77133I 0
u = 0.308226 + 0.983667I
a = −0.913578 − 0.497183I
b = −0.207475 + 1.051900I
7.64196 + 4.01513I 0
u = 0.308226 − 0.983667I
a = −0.913578 + 0.497183I
b = −0.207475 − 1.051900I
7.64196 − 4.01513I 0
u = 0.265198 + 1.021370I
a = 1.12081 − 0.94691I
b = −1.26438 − 0.89363I
4.37595 − 0.73115I 0
u = 0.265198 − 1.021370I
a = 1.12081 + 0.94691I
b = −1.26438 + 0.89363I
4.37595 + 0.73115I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.014072 + 1.086320I
a = −0.985765 + 0.029422I
b = 0.018090 + 1.071270I
7.66190 + 4.32014I 0
u = −0.014072 − 1.086320I
a = −0.985765 − 0.029422I
b = 0.018090 − 1.071270I
7.66190 − 4.32014I 0
u = 0.865982 + 0.248427I
a = −0.324727 − 1.231120I
b = −0.024636 + 1.146800I
8.42861 + 2.90333I 0
u = 0.865982 − 0.248427I
a = −0.324727 + 1.231120I
b = −0.024636 − 1.146800I
8.42861 − 2.90333I 0
u = 1.120500 + 0.105543I
a = −0.772508 + 0.933095I
b = 0.964078 − 0.964000I
2.4180 + 14.4623I 0
u = 1.120500 − 0.105543I
a = −0.772508 − 0.933095I
b = 0.964078 + 0.964000I
2.4180 − 14.4623I 0
u = 0.636402 + 0.940838I
a = 0.832826 + 0.391168I
b = −0.161987 − 1.032490I
1.054820 + 0.344037I 0
u = 0.636402 − 0.940838I
a = 0.832826 − 0.391168I
b = −0.161987 + 1.032490I
1.054820 − 0.344037I 0
u = −0.707342 + 0.457791I
a = 0.250539 + 0.339848I
b = 0.332797 + 0.125694I
−1.73690 + 0.63011I 0
u = −0.707342 − 0.457791I
a = 0.250539 − 0.339848I
b = 0.332797 − 0.125694I
−1.73690 − 0.63011I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.163670 + 0.137451I
a = 0.603623 − 0.768644I
b = −0.808071 + 0.811482I
−3.35204 + 9.77983I 0
u = 1.163670 − 0.137451I
a = 0.603623 + 0.768644I
b = −0.808071 − 0.811482I
−3.35204 − 9.77983I 0
u = 0.786118 + 0.200802I
a = 0.79806 − 1.39804I
b = −0.908100 + 0.938770I
3.66238 + 7.09364I 0
u = 0.786118 − 0.200802I
a = 0.79806 + 1.39804I
b = −0.908100 − 0.938770I
3.66238 − 7.09364I 0
u = 0.508543 + 1.110890I
a = −1.41993 + 0.31079I
b = 1.06734 + 1.41934I
0.83845 − 6.82264I 0
u = 0.508543 − 1.110890I
a = −1.41993 − 0.31079I
b = 1.06734 − 1.41934I
0.83845 + 6.82264I 0
u = 1.197390 + 0.249700I
a = −0.296015 + 0.680603I
b = 0.524393 − 0.741036I
−1.42857 + 4.12269I 0
u = 1.197390 − 0.249700I
a = −0.296015 − 0.680603I
b = 0.524393 + 0.741036I
−1.42857 − 4.12269I 0
u = −0.731646 + 0.982650I
a = 0.071450 − 0.268151I
b = −0.211222 − 0.266402I
−0.20428 + 4.86627I 0
u = −0.731646 − 0.982650I
a = 0.071450 + 0.268151I
b = −0.211222 + 0.266402I
−0.20428 − 4.86627I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.669015 + 1.080040I
a = −0.911259 − 0.400202I
b = 0.177414 + 1.251930I
1.76632 − 5.80202I 0
u = 0.669015 − 1.080040I
a = −0.911259 + 0.400202I
b = 0.177414 − 1.251930I
1.76632 + 5.80202I 0
u = 0.625036 + 0.353244I
a = −0.54480 + 1.54547I
b = 0.886448 − 0.773523I
−1.39205 + 2.34242I 0
u = 0.625036 − 0.353244I
a = −0.54480 − 1.54547I
b = 0.886448 + 0.773523I
−1.39205 − 2.34242I 0
u = 0.505060 + 1.184110I
a = 1.35790 − 0.41395I
b = −1.17598 − 1.39883I
6.61152 − 11.89410I 0
u = 0.505060 − 1.184110I
a = 1.35790 + 0.41395I
b = −1.17598 + 1.39883I
6.61152 + 11.89410I 0
u = 0.182497 + 1.304990I
a = 0.644331 − 0.308225I
b = −0.519818 − 0.784595I
5.19823 − 0.38486I 0
u = 0.182497 − 1.304990I
a = 0.644331 + 0.308225I
b = −0.519818 + 0.784595I
5.19823 + 0.38486I 0
u = 0.355367 + 1.286890I
a = −1.096520 + 0.095012I
b = 0.51194 + 1.37734I
13.11000 − 1.19025I 0
u = 0.355367 − 1.286890I
a = −1.096520 − 0.095012I
b = 0.51194 − 1.37734I
13.11000 + 1.19025I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.598285 + 1.230550I
a = 1.107960 + 0.185777I
b = −0.43427 − 1.47455I
11.31360 − 8.41411I 0
u = 0.598285 − 1.230550I
a = 1.107960 − 0.185777I
b = −0.43427 + 1.47455I
11.31360 + 8.41411I 0
u = 0.58111 + 1.32533I
a = −1.200120 + 0.346172I
b = 1.15620 + 1.38939I
6.2353 − 20.4547I 0
u = 0.58111 − 1.32533I
a = −1.200120 − 0.346172I
b = 1.15620 − 1.38939I
6.2353 + 20.4547I 0
u = 0.62767 + 1.30970I
a = −0.994170 + 0.135205I
b = 0.80109 + 1.21720I
2.00380 − 10.50370I 0
u = 0.62767 − 1.30970I
a = −0.994170 − 0.135205I
b = 0.80109 − 1.21720I
2.00380 + 10.50370I 0
u = 0.59880 + 1.32640I
a = 1.086980 − 0.284336I
b = −1.02803 − 1.27151I
0.3961 − 15.9494I 0
u = 0.59880 − 1.32640I
a = 1.086980 + 0.284336I
b = −1.02803 + 1.27151I
0.3961 + 15.9494I 0
u = 0.22066 + 1.55593I
a = −0.375610 − 0.024297I
b = 0.045077 + 0.589783I
2.64603 + 4.04647I 0
u = 0.22066 − 1.55593I
a = −0.375610 + 0.024297I
b = 0.045077 − 0.589783I
2.64603 − 4.04647I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.38904 + 1.53423I
a = 0.396798 + 0.277446I
b = 0.271294 − 0.716716I
7.74841 + 8.71344I 0
u = 0.38904 − 1.53423I
a = 0.396798 − 0.277446I
b = 0.271294 + 0.716716I
7.74841 − 8.71344I 0
u = 0.257267 + 0.289166I
a = 1.44997 + 0.86456I
b = −0.123028 − 0.641707I
1.02800 + 1.00373I 4.20772 − 2.96757I
u = 0.257267 − 0.289166I
a = 1.44997 − 0.86456I
b = −0.123028 + 0.641707I
1.02800 − 1.00373I 4.20772 + 2.96757I
u = −1.84068 + 0.56528I
a = 0.0300490 − 0.0308640I
b = 0.0378637 − 0.0737969I
−3.96631 + 2.95414I 0
u = −1.84068 − 0.56528I
a = 0.0300490 + 0.0308640I
b = 0.0378637 + 0.0737969I
−3.96631 − 2.95414I 0
10
II. I
u
2
= h−3.81 × 10
34
a
9
u
10
+ 3.03 × 10
34
a
8
u
10
+ · · · − 9.29 × 10
34
a − 1.45 ×
10
35
, −u
10
a
9
− 5u
10
a
8
+ · · · − 295a − 110, u
11
+ 3u
10
+ · · · + 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
a
0.907182a
9
u
10
− 0.720474a
8
u
10
+ ··· + 2.21154a + 3.46170
a
10
=
−0.492257a
9
u
10
+ 0.00342511a
8
u
10
+ ··· + 1.48128a − 0.271791
−4.10347a
9
u
10
+ 2.09816a
8
u
10
+ ··· + 2.51299a + 1.85463
a
8
=
0.907182a
9
u
10
− 0.720474a
8
u
10
+ ··· + 3.21154a + 3.46170
0.907182a
9
u
10
− 0.720474a
8
u
10
+ ··· + 2.21154a + 3.46170
a
3
=
5.07518a
9
u
10
+ 1.03594a
8
u
10
+ ··· − 5.93466a + 1.08613
3.75966a
9
u
10
+ 0.538146a
8
u
10
+ ··· − 2.76372a − 0.0156369
a
11
=
1.84368a
9
u
10
− 0.176828a
8
u
10
+ ··· − 7.34564a − 5.54919
3.36159a
9
u
10
− 0.793945a
8
u
10
+ ··· − 1.68096a − 0.279916
a
7
=
1.78885a
9
u
10
− 1.21260a
8
u
10
+ ··· + 2.00706a + 4.05887
−0.457991a
9
u
10
+ 0.204668a
8
u
10
+ ··· − 2.09454a + 0.327920
a
12
=
a
2
u
1.80869a
9
u
10
+ 0.558889a
8
u
10
+ ··· + 0.709045a − 0.353266
a
6
=
2.93332a
9
u
10
− 1.13790a
8
u
10
+ ··· − 1.40440a + 2.91248
3.28932a
9
u
10
− 0.643942a
8
u
10
+ ··· + 0.763603a + 2.90564
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6.21162a
9
u
10
+ 5.41134a
8
u
10
+ ··· + 9.56003a − 2.29340
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
11
+ 3u
10
+ ··· + 2u + 1)
10
c
2
, c
10
u
110
+ 3u
109
+ ··· − 72u + 1
c
3
, c
9
u
110
+ u
109
+ ··· − 288500u − 72659
c
5
, c
6
, c
11
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
22
c
7
(u
11
+ 5u
10
+ 12u
9
+ 15u
8
+ 8u
7
− 4u
6
− 8u
5
− 3u
4
+ 3u
3
+ 3u
2
− 1)
10
c
8
, c
12
u
110
− u
109
+ ··· + 26520u − 547
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
11
+ 7y
10
+ ··· − 6y − 1)
10
c
2
, c
10
y
110
+ 35y
109
+ ··· − 7528y + 1
c
3
, c
9
y
110
− 25y
109
+ ··· + 621106657840y + 5279330281
c
5
, c
6
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
22
c
7
(y
11
− y
10
+ ··· + 6y − 1)
10
c
8
, c
12
y
110
− 21y
109
+ ··· − 39626548y + 299209
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.253759 + 0.946686I
a = −1.214280 + 0.254968I
b = 1.406490 − 0.038889I
−1.17818 − 3.68571I −3.92092 + 4.58213I
u = 0.253759 + 0.946686I
a = 1.00777 − 0.99699I
b = −1.66471 − 0.72815I
4.36528 − 0.81546I 0.30828 + 5.51419I
u = 0.253759 + 0.946686I
a = −0.33322 + 1.39637I
b = 0.549509 + 1.084840I
−1.17818 − 3.68571I −3.92092 + 4.58213I
u = 0.253759 + 0.946686I
a = −0.278887 + 0.480235I
b = 2.56562 − 0.97418I
4.36528 − 9.61712I 0.30828 + 12.51136I
u = 0.253759 + 0.946686I
a = 0.127850 − 0.489290I
b = 0.68642 − 1.90567I
0.89380 − 5.21629I −2.95489 + 9.01278I
u = 0.253759 + 0.946686I
a = 0.405552 − 0.162342I
b = −1.86813 + 0.97949I
−1.17818 − 6.74687I −3.92092 + 13.44342I
u = 0.253759 + 0.946686I
a = 1.15735 − 1.44823I
b = −1.199570 − 0.701047I
4.36528 − 0.81546I 0.30828 + 5.51419I
u = 0.253759 + 0.946686I
a = 1.69672 + 1.17989I
b = −0.495647 + 0.003128I
0.89380 − 5.21629I −2.95489 + 9.01278I
u = 0.253759 + 0.946686I
a = −0.47180 − 2.09980I
b = −0.256599 − 0.342734I
−1.17818 − 6.74687I −3.92092 + 13.44342I
u = 0.253759 + 0.946686I
a = 0.28232 + 2.78578I
b = 0.525402 + 0.142154I
4.36528 − 9.61712I 0.30828 + 12.51136I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.253759 − 0.946686I
a = −1.214280 − 0.254968I
b = 1.406490 + 0.038889I
−1.17818 + 3.68571I −3.92092 − 4.58213I
u = 0.253759 − 0.946686I
a = 1.00777 + 0.99699I
b = −1.66471 + 0.72815I
4.36528 + 0.81546I 0.30828 − 5.51419I
u = 0.253759 − 0.946686I
a = −0.33322 − 1.39637I
b = 0.549509 − 1.084840I
−1.17818 + 3.68571I −3.92092 − 4.58213I
u = 0.253759 − 0.946686I
a = −0.278887 − 0.480235I
b = 2.56562 + 0.97418I
4.36528 + 9.61712I 0.30828 − 12.51136I
u = 0.253759 − 0.946686I
a = 0.127850 + 0.489290I
b = 0.68642 + 1.90567I
0.89380 + 5.21629I −2.95489 − 9.01278I
u = 0.253759 − 0.946686I
a = 0.405552 + 0.162342I
b = −1.86813 − 0.97949I
−1.17818 + 6.74687I −3.92092 − 13.44342I
u = 0.253759 − 0.946686I
a = 1.15735 + 1.44823I
b = −1.199570 + 0.701047I
4.36528 + 0.81546I 0.30828 − 5.51419I
u = 0.253759 − 0.946686I
a = 1.69672 − 1.17989I
b = −0.495647 − 0.003128I
0.89380 + 5.21629I −2.95489 − 9.01278I
u = 0.253759 − 0.946686I
a = −0.47180 + 2.09980I
b = −0.256599 + 0.342734I
−1.17818 + 6.74687I −3.92092 − 13.44342I
u = 0.253759 − 0.946686I
a = 0.28232 − 2.78578I
b = 0.525402 − 0.142154I
4.36528 + 9.61712I 0.30828 − 12.51136I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.10821
a = 1.06944
b = −1.43122
−1.62261 −14.7800
u = −1.10821
a = 0.780503 + 0.437504I
b = −0.756153 − 0.220972I
−3.69459 − 1.53058I −15.7462 + 4.4306I
u = −1.10821
a = 0.780503 − 0.437504I
b = −0.756153 + 0.220972I
−3.69459 + 1.53058I −15.7462 − 4.4306I
u = −1.10821
a = −0.696511 + 0.898164I
b = 0.625664 − 0.610265I
1.84887 + 4.40083I −11.51702 − 3.49859I
u = −1.10821
a = −0.696511 − 0.898164I
b = 0.625664 + 0.610265I
1.84887 − 4.40083I −11.51702 + 3.49859I
u = −1.10821
a = 0.564570 + 0.550675I
b = −0.771883 − 0.995357I
1.84887 − 4.40083I −11.51702 + 3.49859I
u = −1.10821
a = 0.564570 − 0.550675I
b = −0.771883 + 0.995357I
1.84887 + 4.40083I −11.51702 − 3.49859I
u = −1.10821
a = −0.682318 + 0.199395I
b = 0.864963 − 0.484847I
−3.69459 + 1.53058I −15.7462 − 4.4306I
u = −1.10821
a = −0.682318 − 0.199395I
b = 0.864963 + 0.484847I
−3.69459 − 1.53058I −15.7462 + 4.4306I
u = −1.10821
a = −1.29147
b = 1.18517
−1.62261 −14.7800
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.572881 + 0.536287I
a = 0.516653 + 0.935169I
b = −0.0210317 − 0.0200933I
−1.73984 + 0.71721I −7.12070 − 0.63295I
u = −0.572881 + 0.536287I
a = 0.845678 + 0.745623I
b = −1.32964 + 0.56677I
0.33215 + 2.24779I −6.15467 − 5.06360I
u = −0.572881 + 0.536287I
a = −1.111270 − 0.406619I
b = 0.472061 − 1.079550I
−1.73984 + 3.77836I −7.12070 − 9.49424I
u = −0.572881 + 0.536287I
a = −0.588376 + 0.498556I
b = −1.04070 − 0.97694I
3.80363 − 2.15305I −2.89150 − 1.56501I
u = −0.572881 + 0.536287I
a = 1.348260 + 0.235231I
b = −0.31739 + 1.60636I
3.80363 + 6.64862I −2.89150 − 8.56218I
u = −0.572881 + 0.536287I
a = 1.37932 − 0.59320I
b = −0.854688 + 0.363014I
−1.73984 + 3.77836I −7.12070 − 9.49424I
u = −0.572881 + 0.536287I
a = −0.11737 − 1.81518I
b = −0.069700 + 0.601152I
3.80363 − 2.15305I −2.89150 − 1.56501I
u = −0.572881 + 0.536287I
a = −1.73057 − 0.63068I
b = 0.884341 − 0.026373I
0.33215 + 2.24779I −6.15467 − 5.06360I
u = −0.572881 + 0.536287I
a = −0.0020671 − 0.0370092I
b = 0.797500 + 0.258666I
−1.73984 + 0.71721I −7.12070 − 0.63295I
u = −0.572881 + 0.536287I
a = −1.69422 + 1.21800I
b = 0.898542 − 0.588293I
3.80363 + 6.64862I −2.89150 − 8.56218I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.572881 − 0.536287I
a = 0.516653 − 0.935169I
b = −0.0210317 + 0.0200933I
−1.73984 − 0.71721I −7.12070 + 0.63295I
u = −0.572881 − 0.536287I
a = 0.845678 − 0.745623I
b = −1.32964 − 0.56677I
0.33215 − 2.24779I −6.15467 + 5.06360I
u = −0.572881 − 0.536287I
a = −1.111270 + 0.406619I
b = 0.472061 + 1.079550I
−1.73984 − 3.77836I −7.12070 + 9.49424I
u = −0.572881 − 0.536287I
a = −0.588376 − 0.498556I
b = −1.04070 + 0.97694I
3.80363 + 2.15305I −2.89150 + 1.56501I
u = −0.572881 − 0.536287I
a = 1.348260 − 0.235231I
b = −0.31739 − 1.60636I
3.80363 − 6.64862I −2.89150 + 8.56218I
u = −0.572881 − 0.536287I
a = 1.37932 + 0.59320I
b = −0.854688 − 0.363014I
−1.73984 − 3.77836I −7.12070 + 9.49424I
u = −0.572881 − 0.536287I
a = −0.11737 + 1.81518I
b = −0.069700 − 0.601152I
3.80363 + 2.15305I −2.89150 + 1.56501I
u = −0.572881 − 0.536287I
a = −1.73057 + 0.63068I
b = 0.884341 + 0.026373I
0.33215 − 2.24779I −6.15467 + 5.06360I
u = −0.572881 − 0.536287I
a = −0.0020671 + 0.0370092I
b = 0.797500 − 0.258666I
−1.73984 − 0.71721I −7.12070 + 0.63295I
u = −0.572881 − 0.536287I
a = −1.69422 − 1.21800I
b = 0.898542 + 0.588293I
3.80363 − 6.64862I −2.89150 + 8.56218I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.290349 + 1.272230I
a = 1.016900 + 0.255279I
b = −0.375763 + 0.413196I
3.31489 + 3.47016I 4.35571 − 1.79686I
u = −0.290349 + 1.272230I
a = 0.454399 + 0.971570I
b = −0.805599 + 0.755681I
5.38688 + 5.00074I 5.32173 − 6.22751I
u = −0.290349 + 1.272230I
a = −0.850343 − 0.184422I
b = 1.53517 − 1.63532I
8.85836 + 9.40157I 8.58490 − 9.72610I
u = −0.290349 + 1.272230I
a = −0.701934 − 0.473022I
b = 1.368000 − 0.296006I
5.38688 + 5.00074I 5.32173 − 6.22751I
u = −0.290349 + 1.272230I
a = 0.725998 + 0.291082I
b = −1.32280 + 1.23898I
3.31489 + 6.53132I 4.35571 − 10.65816I
u = −0.290349 + 1.272230I
a = −1.335750 + 0.013724I
b = −0.014845 − 0.550001I
8.85836 + 0.59990I 8.58490 − 2.72893I
u = −0.290349 + 1.272230I
a = −1.151200 − 0.777020I
b = 0.581117 − 0.839123I
3.31489 + 6.53132I 4.35571 − 10.65816I
u = −0.290349 + 1.272230I
a = −0.372772 − 0.210283I
b = 0.620030 − 1.219620I
3.31489 + 3.47016I 4.35571 − 1.79686I
u = −0.290349 + 1.272230I
a = 0.408379 − 0.104869I
b = −0.37038 + 1.70337I
8.85836 + 0.59990I 8.58490 − 2.72893I
u = −0.290349 + 1.272230I
a = 1.48352 + 0.86811I
b = −0.481525 + 1.028290I
8.85836 + 9.40157I 8.58490 − 9.72610I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.290349 − 1.272230I
a = 1.016900 − 0.255279I
b = −0.375763 − 0.413196I
3.31489 − 3.47016I 4.35571 + 1.79686I
u = −0.290349 − 1.272230I
a = 0.454399 − 0.971570I
b = −0.805599 − 0.755681I
5.38688 − 5.00074I 5.32173 + 6.22751I
u = −0.290349 − 1.272230I
a = −0.850343 + 0.184422I
b = 1.53517 + 1.63532I
8.85836 − 9.40157I 8.58490 + 9.72610I
u = −0.290349 − 1.272230I
a = −0.701934 + 0.473022I
b = 1.368000 + 0.296006I
5.38688 − 5.00074I 5.32173 + 6.22751I
u = −0.290349 − 1.272230I
a = 0.725998 − 0.291082I
b = −1.32280 − 1.23898I
3.31489 − 6.53132I 4.35571 + 10.65816I
u = −0.290349 − 1.272230I
a = −1.335750 − 0.013724I
b = −0.014845 + 0.550001I
8.85836 − 0.59990I 8.58490 + 2.72893I
u = −0.290349 − 1.272230I
a = −1.151200 + 0.777020I
b = 0.581117 + 0.839123I
3.31489 − 6.53132I 4.35571 + 10.65816I
u = −0.290349 − 1.272230I
a = −0.372772 + 0.210283I
b = 0.620030 + 1.219620I
3.31489 − 3.47016I 4.35571 + 1.79686I
u = −0.290349 − 1.272230I
a = 0.408379 + 0.104869I
b = −0.37038 − 1.70337I
8.85836 − 0.59990I 8.58490 + 2.72893I
u = −0.290349 − 1.272230I
a = 1.48352 − 0.86811I
b = −0.481525 − 1.028290I
8.85836 − 9.40157I 8.58490 + 9.72610I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.234018 + 0.605151I
a = −0.699171 + 0.624862I
b = 1.199470 − 0.525523I
−2.11873 + 1.17383I −6.95250 + 4.51398I
u = 0.234018 + 0.605151I
a = −0.252370 + 0.599876I
b = −0.79612 + 1.45703I
−0.04675 + 2.70441I −5.98648 + 0.08333I
u = 0.234018 + 0.605151I
a = 0.04344 − 1.46541I
b = −1.62502 − 0.02887I
3.42473 − 1.69642I −2.72331 + 3.58191I
u = 0.234018 + 0.605151I
a = 0.14061 − 1.54546I
b = −0.442259 − 1.327510I
−2.11873 + 4.23499I −6.95250 − 4.34732I
u = 0.234018 + 0.605151I
a = −0.29345 + 1.76062I
b = 0.94330 + 1.69305I
3.42473 + 7.10524I −2.72331 − 3.41526I
u = 0.234018 + 0.605151I
a = 0.08866 + 2.01639I
b = 0.541754 + 0.276875I
−2.11873 + 1.17383I −6.95250 + 4.51398I
u = 0.234018 + 0.605151I
a = 2.15416 + 0.10221I
b = −0.968141 + 0.276574I
−2.11873 + 4.23499I −6.95250 − 4.34732I
u = 0.234018 + 0.605151I
a = 0.94485 − 2.31993I
b = −0.896960 + 0.316647I
3.42473 − 1.69642I −2.72331 + 3.58191I
u = 0.234018 + 0.605151I
a = −1.65193 − 1.95440I
b = 0.422074 + 0.012340I
−0.04675 + 2.70441I −5.98648 + 0.08333I
u = 0.234018 + 0.605151I
a = −2.95816 + 0.41484I
b = 1.134110 − 0.234436I
3.42473 + 7.10524I −2.72331 − 3.41526I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.234018 − 0.605151I
a = −0.699171 − 0.624862I
b = 1.199470 + 0.525523I
−2.11873 − 1.17383I −6.95250 − 4.51398I
u = 0.234018 − 0.605151I
a = −0.252370 − 0.599876I
b = −0.79612 − 1.45703I
−0.04675 − 2.70441I −5.98648 − 0.08333I
u = 0.234018 − 0.605151I
a = 0.04344 + 1.46541I
b = −1.62502 + 0.02887I
3.42473 + 1.69642I −2.72331 − 3.58191I
u = 0.234018 − 0.605151I
a = 0.14061 + 1.54546I
b = −0.442259 + 1.327510I
−2.11873 − 4.23499I −6.95250 + 4.34732I
u = 0.234018 − 0.605151I
a = −0.29345 − 1.76062I
b = 0.94330 − 1.69305I
3.42473 − 7.10524I −2.72331 + 3.41526I
u = 0.234018 − 0.605151I
a = 0.08866 − 2.01639I
b = 0.541754 − 0.276875I
−2.11873 − 1.17383I −6.95250 − 4.51398I
u = 0.234018 − 0.605151I
a = 2.15416 − 0.10221I
b = −0.968141 − 0.276574I
−2.11873 − 4.23499I −6.95250 + 4.34732I
u = 0.234018 − 0.605151I
a = 0.94485 + 2.31993I
b = −0.896960 − 0.316647I
3.42473 + 1.69642I −2.72331 − 3.58191I
u = 0.234018 − 0.605151I
a = −1.65193 + 1.95440I
b = 0.422074 − 0.012340I
−0.04675 − 2.70441I −5.98648 − 0.08333I
u = 0.234018 − 0.605151I
a = −2.95816 − 0.41484I
b = 1.134110 + 0.234436I
3.42473 − 7.10524I −2.72331 + 3.41526I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.57044 + 1.34258I
a = −0.785939 − 0.641440I
b = 1.115300 − 0.438195I
2.51638 + 5.92443I −5.68931 − 10.02355I
u = −0.57044 + 1.34258I
a = 0.946446 + 0.248467I
b = −1.056870 + 0.809620I
0.44440 + 7.45501I −6.6553 − 14.4542I
u = −0.57044 + 1.34258I
a = 0.941032 + 0.405944I
b = −0.80426 + 1.48503I
5.98786 + 10.32530I −2.42614 − 13.52213I
u = −0.57044 + 1.34258I
a = −0.794135 − 0.449777I
b = 0.87348 − 1.12895I
0.44440 + 7.45501I −6.6553 − 14.4542I
u = −0.57044 + 1.34258I
a = −1.152550 − 0.109335I
b = 1.08182 − 1.03185I
5.98786 + 10.32530I −2.42614 − 13.52213I
u = −0.57044 + 1.34258I
a = 0.575454 + 0.586211I
b = −1.30952 + 0.68928I
2.51638 + 5.92443I −5.68931 − 10.02355I
u = −0.57044 + 1.34258I
a = 0.568427 + 0.363833I
b = −0.457563 + 0.652864I
0.44440 + 4.39385I −6.65534 − 5.59290I
u = −0.57044 + 1.34258I
a = 0.513603 − 0.308604I
b = −0.387048 + 0.710839I
5.98786 + 1.52359I −2.42614 − 6.52496I
u = −0.57044 + 1.34258I
a = −0.552249 − 0.053645I
b = −0.121346 − 0.865594I
5.98786 + 1.52359I −2.42614 − 6.52496I
u = −0.57044 + 1.34258I
a = −0.534574 − 0.113677I
b = 0.812729 − 0.555614I
0.44440 + 4.39385I −6.65534 − 5.59290I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.57044 − 1.34258I
a = −0.785939 + 0.641440I
b = 1.115300 + 0.438195I
2.51638 − 5.92443I −5.68931 + 10.02355I
u = −0.57044 − 1.34258I
a = 0.946446 − 0.248467I
b = −1.056870 − 0.809620I
0.44440 − 7.45501I −6.6553 + 14.4542I
u = −0.57044 − 1.34258I
a = 0.941032 − 0.405944I
b = −0.80426 − 1.48503I
5.98786 − 10.32530I −2.42614 + 13.52213I
u = −0.57044 − 1.34258I
a = −0.794135 + 0.449777I
b = 0.87348 + 1.12895I
0.44440 − 7.45501I −6.6553 + 14.4542I
u = −0.57044 − 1.34258I
a = −1.152550 + 0.109335I
b = 1.08182 + 1.03185I
5.98786 − 10.32530I −2.42614 + 13.52213I
u = −0.57044 − 1.34258I
a = 0.575454 − 0.586211I
b = −1.30952 − 0.68928I
2.51638 − 5.92443I −5.68931 + 10.02355I
u = −0.57044 − 1.34258I
a = 0.568427 − 0.363833I
b = −0.457563 − 0.652864I
0.44440 − 4.39385I −6.65534 + 5.59290I
u = −0.57044 − 1.34258I
a = 0.513603 + 0.308604I
b = −0.387048 − 0.710839I
5.98786 − 1.52359I −2.42614 + 6.52496I
u = −0.57044 − 1.34258I
a = −0.552249 + 0.053645I
b = −0.121346 + 0.865594I
5.98786 − 1.52359I −2.42614 + 6.52496I
u = −0.57044 − 1.34258I
a = −0.534574 + 0.113677I
b = 0.812729 + 0.555614I
0.44440 − 4.39385I −6.65534 + 5.59290I
24
III. I
u
3
=
h2.71×10
15
u
39
+3.30×10
16
u
38
+· · ·+1.11×10
15
b−7.54×10
15
, 7.54×10
15
u
39
+
1.01 × 10
17
u
38
+ · · · + 1.11 × 10
15
a + 2.53 × 10
16
, u
40
+ 13u
39
+ · · · + 13u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
−6.77798u
39
− 90.5483u
38
+ ··· − 212.235u − 22.7137
−2.43455u
39
− 29.6058u
38
+ ··· + 65.4001u + 6.77798
a
10
=
−10.2563u
39
− 134.947u
38
+ ··· − 192.304u − 20.6290
−1.84869u
39
− 22.1837u
38
+ ··· + 52.6431u + 5.51276
a
8
=
−9.21253u
39
− 120.154u
38
+ ··· − 146.835u − 15.9357
−2.43455u
39
− 29.6058u
38
+ ··· + 65.4001u + 6.77798
a
3
=
3.74877u
39
+ 42.7879u
38
+ ··· + 38.4646u + 7.38528
−3.49534u
39
− 47.8903u
38
+ ··· − 80.5441u − 7.24412
a
11
=
−0.531367u
39
− 10.4633u
38
+ ··· − 324.781u − 29.9644
0.254134u
39
− 0.214753u
38
+ ··· − 26.7084u − 0.649031
a
7
=
8.31931u
39
+ 104.042u
38
+ ··· + 177.914u + 13.1129
−4.40001u
39
− 59.1809u
38
+ ··· − 87.4335u − 6.88478
a
12
=
−7.95615u
39
− 103.494u
38
+ ··· − 209.573u − 21.6492
−0.0636530u
39
− 0.0518015u
38
+ ··· + 82.7808u + 7.95615
a
6
=
3.73312u
39
+ 51.5946u
38
+ ··· + 156.225u + 11.4603
−0.745671u
39
− 9.45596u
38
+ ··· − 33.4183u − 2.55272
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
49209887514998933
1113111866454425
u
39
+
663479598064214632
1113111866454425
u
38
+···+
1082356982452410238
1113111866454425
u+
83103687073235062
1113111866454425
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
40
− 13u
39
+ ··· − 13u + 1
c
2
, c
10
u
40
+ 11u
38
+ ··· − 5u − 1
c
3
, c
9
u
40
− u
39
+ ··· + 13u − 7
c
4
u
40
+ 13u
39
+ ··· + 13u + 1
c
5
, c
6
u
40
+ 2u
39
+ ··· − 3u + 1
c
7
u
40
− 22u
39
+ ··· − 7u + 1
c
8
, c
12
u
40
− 3u
39
+ ··· − 7u − 1
c
11
u
40
− 2u
39
+ ··· + 3u + 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
40
+ 21y
39
+ ··· + y + 1
c
2
, c
10
y
40
+ 22y
39
+ ··· − 5y + 1
c
3
, c
9
y
40
− 13y
39
+ ··· + 223y + 49
c
5
, c
6
, c
11
y
40
− 40y
39
+ ··· + y + 1
c
7
y
40
− 4y
39
+ ··· − 17y + 1
c
8
, c
12
y
40
− 13y
39
+ ··· + 5y + 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.302193 + 0.961756I
a = 1.36527 + 1.24156I
b = −1.60665 + 0.93787I
4.66350 + 0.68253I 0
u = −0.302193 − 0.961756I
a = 1.36527 − 1.24156I
b = −1.60665 − 0.93787I
4.66350 − 0.68253I 0
u = 0.179612 + 1.004620I
a = −0.962397 − 0.715529I
b = 0.545979 − 1.095360I
1.59926 − 4.62320I 0
u = 0.179612 − 1.004620I
a = −0.962397 + 0.715529I
b = 0.545979 + 1.095360I
1.59926 + 4.62320I 0
u = −0.958542 + 0.081933I
a = 0.753873 − 0.799079I
b = −0.657149 + 0.827718I
2.62062 + 4.54167I 0
u = −0.958542 − 0.081933I
a = 0.753873 + 0.799079I
b = −0.657149 − 0.827718I
2.62062 − 4.54167I 0
u = 0.475218 + 0.832257I
a = 0.105588 + 0.652587I
b = −0.492943 + 0.397997I
−1.07028 − 6.02780I 0
u = 0.475218 − 0.832257I
a = 0.105588 − 0.652587I
b = −0.492943 − 0.397997I
−1.07028 + 6.02780I 0
u = −1.04794
a = 1.25425
b = −1.31438
−1.05586 0
u = 0.198993 + 0.857079I
a = 0.529987 + 1.135620I
b = −0.867850 + 0.680220I
−1.29856 − 5.76607I −4.50377 + 5.05173I
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.198993 − 0.857079I
a = 0.529987 − 1.135620I
b = −0.867850 − 0.680220I
−1.29856 + 5.76607I −4.50377 − 5.05173I
u = 0.074658 + 0.859654I
a = −0.68878 − 1.60477I
b = 1.32812 − 0.71192I
4.46569 − 8.28143I 3.21081 + 5.41950I
u = 0.074658 − 0.859654I
a = −0.68878 + 1.60477I
b = 1.32812 + 0.71192I
4.46569 + 8.28143I 3.21081 − 5.41950I
u = −0.283043 + 0.807141I
a = 0.52662 + 1.64564I
b = −1.47732 − 0.04073I
4.14697 + 1.84028I 11.6326 − 8.8001I
u = −0.283043 − 0.807141I
a = 0.52662 − 1.64564I
b = −1.47732 + 0.04073I
4.14697 − 1.84028I 11.6326 + 8.8001I
u = −1.17611
a = −0.765486
b = 0.900298
−3.35566 0
u = 0.129149 + 0.793883I
a = 1.202550 + 0.737313I
b = −0.430032 + 1.049900I
0.81760 + 3.07351I 4.23417 − 3.39461I
u = 0.129149 − 0.793883I
a = 1.202550 − 0.737313I
b = −0.430032 − 1.049900I
0.81760 − 3.07351I 4.23417 + 3.39461I
u = −0.058694 + 1.270490I
a = −0.112190 − 0.771707I
b = 0.987030 − 0.097241I
6.17011 + 7.94112I 0
u = −0.058694 − 1.270490I
a = −0.112190 + 0.771707I
b = 0.987030 + 0.097241I
6.17011 − 7.94112I 0
29
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.528320 + 1.195220I
a = −1.074290 − 0.258592I
b = 0.87664 − 1.14739I
1.00109 + 6.32670I 0
u = −0.528320 − 1.195220I
a = −1.074290 + 0.258592I
b = 0.87664 + 1.14739I
1.00109 − 6.32670I 0
u = −0.489235 + 1.291200I
a = 1.114280 + 0.317822I
b = −0.95552 + 1.28328I
6.72770 + 9.59494I 0
u = −0.489235 − 1.291200I
a = 1.114280 − 0.317822I
b = −0.95552 − 1.28328I
6.72770 − 9.59494I 0
u = 0.477512 + 0.363096I
a = 0.170665 − 0.915354I
b = 0.413856 − 0.375125I
−2.02197 + 2.31681I −7.44581 − 1.97781I
u = 0.477512 − 0.363096I
a = 0.170665 + 0.915354I
b = 0.413856 + 0.375125I
−2.02197 − 2.31681I −7.44581 + 1.97781I
u = −0.372659 + 0.418740I
a = −1.60084 − 0.62809I
b = 0.859573 − 0.436271I
−2.23378 + 2.17048I −9.45805 − 4.37787I
u = −0.372659 − 0.418740I
a = −1.60084 + 0.62809I
b = 0.859573 + 0.436271I
−2.23378 − 2.17048I −9.45805 + 4.37787I
u = −0.53269 + 1.34734I
a = 0.688381 + 0.653576I
b = −1.247280 + 0.579327I
3.13515 + 5.60962I 0
u = −0.53269 − 1.34734I
a = 0.688381 − 0.653576I
b = −1.247280 − 0.579327I
3.13515 − 5.60962I 0
30
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.61009 + 1.31777I
a = −0.717459 − 0.307067I
b = 0.842360 − 0.758103I
0.65588 + 6.25816I 0
u = −0.61009 − 1.31777I
a = −0.717459 + 0.307067I
b = 0.842360 + 0.758103I
0.65588 − 6.25816I 0
u = −0.23388 + 1.45246I
a = 0.352930 + 0.326684I
b = −0.557037 + 0.436210I
1.84795 + 4.70321I 0
u = −0.23388 − 1.45246I
a = 0.352930 − 0.326684I
b = −0.557037 − 0.436210I
1.84795 − 4.70321I 0
u = −0.48225 + 1.43734I
a = −0.524798 + 0.095595I
b = 0.115679 − 0.800413I
6.71763 + 1.26141I 0
u = −0.48225 − 1.43734I
a = −0.524798 − 0.095595I
b = 0.115679 + 0.800413I
6.71763 − 1.26141I 0
u = −0.224887 + 0.132284I
a = −2.28821 − 2.94764I
b = 0.904514 + 0.360191I
−2.16831 − 2.11754I −8.35280 + 6.32544I
u = −0.224887 − 0.132284I
a = −2.28821 + 2.94764I
b = 0.904514 − 0.360191I
−2.16831 + 2.11754I −8.35280 − 6.32544I
u = −1.84663 + 0.54098I
a = −0.0855638 + 0.0608668I
b = 0.125077 − 0.158687I
−3.96169 + 2.98863I 0
u = −1.84663 − 0.54098I
a = −0.0855638 − 0.0608668I
b = 0.125077 + 0.158687I
−3.96169 − 2.98863I 0
31
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
11
+ 3u
10
+ ··· + 2u + 1)
10
)(u
40
− 13u
39
+ ··· − 13u + 1)
· (u
56
− 18u
55
+ ··· − 19200u + 1024)
c
2
, c
10
(u
40
+ 11u
38
+ ··· − 5u − 1)(u
56
− 8u
54
+ ··· + 4u + 1)
· (u
110
+ 3u
109
+ ··· − 72u + 1)
c
3
, c
9
(u
40
− u
39
+ ··· + 13u − 7)(u
56
− u
55
+ ··· + 8u + 1)
· (u
110
+ u
109
+ ··· − 288500u − 72659)
c
4
((u
11
+ 3u
10
+ ··· + 2u + 1)
10
)(u
40
+ 13u
39
+ ··· + 13u + 1)
· (u
56
− 18u
55
+ ··· − 19200u + 1024)
c
5
, c
6
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
22
)(u
40
+ 2u
39
+ ··· − 3u + 1)
· (u
56
+ 21u
55
+ ··· + 4096u + 2048)
c
7
(u
11
+ 5u
10
+ 12u
9
+ 15u
8
+ 8u
7
− 4u
6
− 8u
5
− 3u
4
+ 3u
3
+ 3u
2
− 1)
10
· (u
40
− 22u
39
+ ··· − 7u + 1)(u
56
− 35u
55
+ ··· − 272u + 32)
c
8
, c
12
(u
40
− 3u
39
+ ··· − 7u − 1)(u
56
− u
55
+ ··· + 12u + 1)
· (u
110
− u
109
+ ··· + 26520u − 547)
c
11
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
22
)(u
40
− 2u
39
+ ··· + 3u + 1)
· (u
56
+ 21u
55
+ ··· + 4096u + 2048)
32
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
11
+ 7y
10
+ ··· − 6y − 1)
10
)(y
40
+ 21y
39
+ ··· + y + 1)
· (y
56
+ 28y
55
+ ··· + 9502720y + 1048576)
c
2
, c
10
(y
40
+ 22y
39
+ ··· − 5y + 1)(y
56
− 16y
55
+ ··· − 34y + 1)
· (y
110
+ 35y
109
+ ··· − 7528y + 1)
c
3
, c
9
(y
40
− 13y
39
+ ··· + 223y + 49)(y
56
− 7y
55
+ ··· − 18y + 1)
· (y
110
− 25y
109
+ ··· + 621106657840y + 5279330281)
c
5
, c
6
, c
11
((y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
22
)(y
40
− 40y
39
+ ··· + y + 1)
· (y
56
− 45y
55
+ ··· − 2097152y + 4194304)
c
7
((y
11
− y
10
+ ··· + 6y − 1)
10
)(y
40
− 4y
39
+ ··· − 17y + 1)
· (y
56
− 5y
55
+ ··· − 9984y + 1024)
c
8
, c
12
(y
40
− 13y
39
+ ··· + 5y + 1)(y
56
+ 33y
55
+ ··· + 188y + 1)
· (y
110
− 21y
109
+ ··· − 39626548y + 299209)
33
