Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [40,3,Mod(13,40)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(40, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("40.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 40.i (of order , degree , minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Coefficient field: | |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 13.2 | ||
Root | of defining polynomial | ||
Character | 40.13 | ||
Dual form | 40.3.i.a.37.2 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
−1.60823 | − | 1.18894i | −0.804116 | − | 0.594472i | |||||
−2.52630 | + | 2.52630i | −0.842100 | + | 0.842100i | −0.989132 | − | 0.147032i | ||
0.147032 | + | 0.989132i | ||||||||
1.17282 | + | 3.82420i | 0.293205 | + | 0.956049i | |||||
3.09141 | + | 3.92978i | 0.618282 | + | 0.785957i | |||||
7.06650 | − | 1.05925i | 1.17775 | − | 0.176541i | |||||
−5.20520 | + | 5.20520i | −0.743600 | + | 0.743600i | −0.973269 | − | 0.229669i | ||
0.229669 | + | 0.973269i | ||||||||
2.66059 | − | 7.54462i | 0.332574 | − | 0.943077i | |||||
− | 3.76437i | − | 0.418263i | |||||||
−0.299408 | − | 9.99552i | −0.0299408 | − | 0.999552i | |||||
− | 2.49236i | − | 0.226579i | −0.993562 | − | 0.113289i | ||||
0.993562 | − | 0.113289i | ||||||||
−12.6240 | − | 6.69817i | −1.05200 | − | 0.558181i | |||||
−6.65988 | + | 6.65988i | −0.512298 | + | 0.512298i | −0.915230 | − | 0.402932i | ||
0.402932 | + | 0.915230i | ||||||||
14.5599 | − | 2.18248i | 1.03999 | − | 0.155891i | |||||
−17.7376 | − | 2.11798i | −1.18251 | − | 0.141199i | |||||
−13.2490 | + | 8.97020i | −0.828061 | + | 0.560638i | |||||
21.9428 | − | 21.9428i | 1.29075 | − | 1.29075i | 0.356434 | − | 0.934320i | ||
0.934320 | − | 0.356434i | ||||||||
−4.47563 | + | 6.05398i | −0.248646 | + | 0.336332i | |||||
17.5567 | 0.924039 | 0.462020 | − | 0.886870i | ||||||
0.462020 | + | 0.886870i | ||||||||
−11.4026 | + | 16.4311i | −0.570130 | + | 0.821555i | |||||
− | 26.2998i | − | 1.25237i | |||||||
−2.96328 | + | 4.00830i | −0.134695 | + | 0.182195i | |||||
20.1791 | + | 20.1791i | 0.877354 | + | 0.877354i | 0.993260 | − | 0.115906i | ||
−0.115906 | + | 0.993260i | ||||||||
12.3385 | + | 25.7814i | 0.514105 | + | 1.07423i | |||||
−5.88639 | + | 24.2971i | −0.235455 | + | 0.971885i | |||||
18.6289 | − | 2.79240i | 0.716495 | − | 0.107400i | |||||
−13.2268 | − | 13.2268i | −0.489880 | − | 0.489880i | |||||
−26.0105 | − | 13.8010i | −0.928946 | − | 0.492891i | |||||
1.04754 | 0.0361220 | 0.0180610 | − | 0.999837i | ||||||
0.0180610 | + | 0.999837i | ||||||||
26.0081 | + | 24.4953i | 0.866935 | + | 0.816509i | |||||
−2.47263 | −0.0797623 | −0.0398812 | − | 0.999204i | ||||||
−0.0398812 | + | 0.999204i | ||||||||
31.9725 | + | 1.32614i | 0.999141 | + | 0.0414418i | |||||
6.29646 | + | 6.29646i | 0.190802 | + | 0.190802i | |||||
−61.3780 | + | 9.20035i | −1.80523 | + | 0.270599i | |||||
−36.5467 | − | 4.36391i | −1.04419 | − | 0.124683i | |||||
14.3957 | − | 4.41493i | 0.399880 | − | 0.122637i | |||||
19.2786 | + | 19.2786i | 0.521043 | + | 0.521043i | 0.917886 | − | 0.396843i | ||
−0.396843 | + | 0.917886i | ||||||||
−28.2353 | − | 20.8740i | −0.743035 | − | 0.549316i | |||||
− | 33.6497i | − | 0.862813i | |||||||
37.8737 | − | 12.8680i | 0.946842 | − | 0.321699i | |||||
−43.9414 | −1.07174 | −0.535871 | − | 0.844300i | ||||||
−0.535871 | + | 0.844300i | ||||||||
−31.2690 | + | 42.2962i | −0.744500 | + | 1.00705i | |||||
32.9394 | − | 32.9394i | 0.766032 | − | 0.766032i | −0.211373 | − | 0.977405i | ||
0.977405 | + | 0.211373i | ||||||||
9.53129 | − | 2.92310i | 0.216620 | − | 0.0664340i | |||||
14.7932 | − | 11.6372i | 0.328737 | − | 0.258604i | |||||
−8.46086 | − | 56.4446i | −0.183932 | − | 1.22706i | |||||
33.7079 | − | 33.7079i | 0.717189 | − | 0.717189i | −0.250840 | − | 0.968029i | ||
0.968029 | + | 0.250840i | ||||||||
10.8095 | − | 56.1323i | 0.225197 | − | 1.16942i | |||||
− | 5.18827i | − | 0.105883i | |||||||
38.3546 | − | 32.0768i | 0.767092 | − | 0.641537i | |||||
110.868i | 2.17389i | |||||||||
−33.2795 | − | 17.6578i | −0.639991 | − | 0.339574i | |||||
−36.4034 | + | 36.4034i | −0.686856 | + | 0.686856i | −0.961536 | − | 0.274679i | ||
0.274679 | + | 0.961536i | ||||||||
5.54582 | + | 36.9976i | 0.102700 | + | 0.685141i | |||||
9.79445 | − | 7.70491i | 0.178081 | − | 0.140089i | |||||
25.4224 | + | 53.1202i | 0.453971 | + | 0.948575i | |||||
−44.3536 | + | 44.3536i | −0.778133 | + | 0.778133i | |||||
−1.68469 | − | 1.24547i | −0.0290463 | − | 0.0214736i | |||||
30.5963 | 0.518581 | 0.259291 | − | 0.965799i | ||||||
0.259291 | + | 0.965799i | ||||||||
−12.7035 | − | 70.3162i | −0.211725 | − | 1.17194i | |||||
− | 23.8366i | − | 0.390764i | −0.980727 | − | 0.195382i | ||||
0.980727 | − | 0.195382i | ||||||||
3.97657 | + | 2.93982i | 0.0641382 | + | 0.0474165i | |||||
19.5943 | + | 19.5943i | 0.311021 | + | 0.311021i | |||||
−49.8425 | − | 40.1463i | −0.778789 | − | 0.627286i | |||||
−46.7603 | − | 5.58347i | −0.719389 | − | 0.0858996i | |||||
−2.64003 | − | 17.6123i | −0.0400004 | − | 0.266853i | |||||
19.9932 | + | 19.9932i | 0.298407 | + | 0.298407i | 0.840390 | − | 0.541983i | ||
−0.541983 | + | 0.840390i | ||||||||
109.649 | + | 58.1787i | 1.61248 | + | 0.855569i | |||||
−101.957 | −1.47764 | |||||||||
53.5872 | + | 50.4702i | 0.765531 | + | 0.721003i | |||||
−21.8350 | −0.307535 | −0.153767 | − | 0.988107i | ||||||
−0.153767 | + | 0.988107i | ||||||||
−28.4007 | − | 10.0154i | −0.394454 | − | 0.139103i | |||||
32.6450 | + | 32.6450i | 0.447191 | + | 0.447191i | 0.894420 | − | 0.447228i | ||
−0.447228 | + | 0.894420i | ||||||||
−8.08328 | − | 53.9257i | −0.109233 | − | 0.728725i | |||||
−46.5110 | − | 76.2526i | −0.620147 | − | 1.01670i | |||||
20.5909 | + | 67.1405i | 0.270933 | + | 0.883427i | |||||
12.9733 | + | 12.9733i | 0.168484 | + | 0.168484i | |||||
−40.0076 | + | 54.1165i | −0.512918 | + | 0.693801i | |||||
16.4124i | 0.207753i | 0.994590 | + | 0.103876i | ||||||
−0.994590 | + | 0.103876i | ||||||||
−76.2090 | − | 24.3351i | −0.952612 | − | 0.304188i | |||||
100.709 | 1.24332 | |||||||||
70.6680 | + | 52.2439i | 0.861805 | + | 0.637121i | |||||
−0.343799 | + | 0.343799i | −0.00414216 | + | 0.00414216i | −0.709175 | − | 0.705033i | ||
0.705033 | + | 0.709175i | ||||||||
100.576 | − | 30.8450i | 1.19733 | − | 0.367202i | |||||
154.065 | + | 18.3963i | 1.81253 | + | 0.216427i | |||||
−92.1373 | + | 13.8111i | −1.07136 | + | 0.160594i | |||||
−2.64640 | + | 2.64640i | −0.0304184 | + | 0.0304184i | |||||
−18.8039 | − | 6.63116i | −0.213681 | − | 0.0753541i | |||||
− | 84.4631i | − | 0.949024i | −0.880249 | − | 0.474512i | ||||
0.880249 | − | 0.474512i | ||||||||
−37.6268 | + | 1.12708i | −0.418076 | + | 0.0125232i | |||||
− | 69.3320i | − | 0.761891i | |||||||
−53.5025 | + | 100.836i | −0.581549 | + | 1.09604i | |||||
6.24661 | − | 6.24661i | 0.0671678 | − | 0.0671678i | |||||
−94.2869 | + | 14.1333i | −1.00305 | + | 0.150354i | |||||
54.2751 | + | 68.9942i | 0.571316 | + | 0.726255i | |||||
−84.1223 | + | 77.4219i | −0.876274 | + | 0.806478i | |||||
−24.1311 | + | 24.1311i | −0.248774 | + | 0.248774i | −0.820467 | − | 0.571693i | ||
0.571693 | + | 0.820467i | ||||||||
−6.16856 | + | 8.34394i | −0.0629445 | + | 0.0851422i | |||||
−9.38218 | −0.0947695 | |||||||||
−99.8207 | + | 5.98548i | −0.998207 | + | 0.0598548i | |||||
− | 152.095i | − | 1.50589i | −0.658085 | − | 0.752944i | ||||
0.658085 | − | 0.752944i | ||||||||
131.816 | − | 178.302i | 1.29232 | − | 1.74806i | |||||
−120.657 | − | 120.657i | −1.17143 | − | 1.17143i | −0.981870 | − | 0.189558i | ||
−0.189558 | − | 0.981870i | ||||||||
32.5270 | + | 67.9655i | 0.312760 | + | 0.653514i | |||||
103.352 | − | 81.3034i | 0.984309 | − | 0.774318i | |||||
101.827 | − | 15.2635i | 0.960629 | − | 0.143995i | |||||
−75.2789 | − | 75.2789i | −0.703541 | − | 0.703541i | 0.261628 | − | 0.965169i | ||
−0.965169 | + | 0.261628i | ||||||||
35.0691 | − | 66.0944i | 0.324714 | − | 0.611985i | |||||
11.8614 | 0.108820 | 0.0544100 | − | 0.998519i | ||||||
0.0544100 | + | 0.998519i | ||||||||
−24.9125 | + | 0.746235i | −0.226477 | + | 0.00678395i | |||||
−97.4070 | −0.877541 | |||||||||
22.2719 | − | 115.655i | 0.198856 | − | 1.03264i | |||||
−82.0090 | − | 82.0090i | −0.725743 | − | 0.725743i | 0.244025 | − | 0.969769i | ||
−0.969769 | + | 0.244025i | ||||||||
124.065 | − | 18.5969i | 1.08829 | − | 0.163131i | |||||
−16.9177 | + | 141.682i | −0.147110 | + | 1.23201i | |||||
1.22858 | + | 4.00600i | 0.0105912 | + | 0.0345345i | |||||
25.0702 | + | 25.0702i | 0.214276 | + | 0.214276i | |||||
−49.2059 | − | 36.3773i | −0.416999 | − | 0.308282i | |||||
228.434i | 1.91961i | |||||||||
−63.1719 | + | 128.189i | −0.526433 | + | 1.06824i | |||||
114.788 | 0.948662 | |||||||||
−28.3404 | + | 38.3348i | −0.232299 | + | 0.314220i | |||||
111.009 | − | 111.009i | 0.902513 | − | 0.902513i | |||||
−2.89996 | − | 9.45584i | −0.0233867 | − | 0.0762567i | |||||
−113.680 | + | 51.9801i | −0.909437 | + | 0.415841i | |||||
−8.21565 | − | 54.8087i | −0.0652035 | − | 0.434990i | |||||
−55.8589 | + | 55.8589i | −0.439834 | + | 0.439834i | −0.891956 | − | 0.452122i | ||
0.452122 | + | 0.891956i | ||||||||
32.4266 | + | 123.825i | 0.253333 | + | 0.967379i | |||||
166.429i | 1.29015i | |||||||||
68.5630 | + | 64.5749i | 0.527407 | + | 0.496730i | |||||
151.619i | 1.15740i | 0.815541 | + | 0.578700i | ||||||
−0.815541 | + | 0.578700i | ||||||||
−16.6943 | + | 31.4635i | −0.126472 | + | 0.238360i | |||||
−91.3864 | + | 91.3864i | −0.687116 | + | 0.687116i | |||||
−8.38292 | − | 55.9246i | −0.0625591 | − | 0.417348i | |||||
11.0890 | − | 92.8677i | 0.0821406 | − | 0.687909i | |||||
−107.169 | − | 223.931i | −0.788010 | − | 1.64655i | |||||
68.2473 | − | 68.2473i | 0.498156 | − | 0.498156i | −0.412708 | − | 0.910863i | ||
0.910863 | + | 0.412708i | ||||||||
163.971 | + | 121.221i | 1.18819 | + | 0.878415i | |||||
69.7245 | 0.501615 | 0.250807 | − | 0.968037i | ||||||
0.250807 | + | 0.968037i | ||||||||
−26.1743 | − | 144.880i | −0.186959 | − | 1.03486i | |||||
170.312i | 1.20789i | |||||||||
35.1157 | + | 25.9606i | 0.247294 | + | 0.182821i | |||||
16.5988 | + | 16.5988i | 0.116076 | + | 0.116076i | |||||
33.7671 | + | 49.8740i | 0.234494 | + | 0.346348i | |||||
3.23837 | + | 4.11660i | 0.0223336 | + | 0.0283904i | |||||
−13.6876 | − | 91.3138i | −0.0937509 | − | 0.625437i | |||||
13.1071 | + | 13.1071i | 0.0891640 | + | 0.0891640i | |||||
−51.1148 | + | 96.3355i | −0.345370 | + | 0.650916i | |||||
78.9012 | 0.529538 | 0.264769 | − | 0.964312i | ||||||
0.264769 | + | 0.964312i | ||||||||
−15.8595 | + | 177.931i | −0.105730 | + | 1.18621i | |||||
197.562 | 1.30835 | 0.654177 | − | 0.756341i | ||||||
0.654177 | + | 0.756341i | ||||||||
46.7113 | − | 132.459i | 0.307311 | − | 0.871440i | |||||
−82.6009 | − | 82.6009i | −0.539875 | − | 0.539875i | |||||
−5.43953 | − | 36.2885i | −0.0353216 | − | 0.235640i | |||||
−7.64392 | − | 9.71691i | −0.0493156 | − | 0.0626897i | |||||
128.683 | − | 39.4651i | 0.824891 | − | 0.252981i | |||||
−94.1106 | − | 94.1106i | −0.599431 | − | 0.599431i | 0.340730 | − | 0.940161i | ||
−0.940161 | + | 0.340730i | ||||||||
19.5135 | − | 26.3950i | 0.123503 | − | 0.167057i | |||||
− | 183.932i | − | 1.15680i | |||||||
93.6287 | + | 129.745i | 0.585179 | + | 0.810904i | |||||
−210.073 | −1.30480 | |||||||||
−161.963 | − | 119.737i | −0.999773 | − | 0.739119i | |||||
−132.980 | + | 132.980i | −0.815827 | + | 0.815827i | −0.985500 | − | 0.169673i | ||
0.169673 | + | 0.985500i | ||||||||
−51.5354 | − | 168.041i | −0.314240 | − | 1.02464i | |||||
−5.27879 | + | 44.2086i | −0.0319926 | + | 0.267931i | |||||
0.961668 | − | 0.144151i | 0.00579318 | − | 0.000868378i | |||||
−51.4111 | + | 51.4111i | −0.307851 | + | 0.307851i | −0.844075 | − | 0.536225i | ||
0.536225 | + | 0.844075i | ||||||||
−198.422 | − | 69.9730i | −1.18108 | − | 0.416506i | |||||
80.2920i | 0.475101i | |||||||||
−225.900 | − | 212.760i | −1.32882 | − | 1.25153i | |||||
− | 66.0900i | − | 0.386492i | |||||||
164.599 | + | 87.3347i | 0.956969 | + | 0.507760i | |||||
183.164 | − | 183.164i | 1.05875 | − | 1.05875i | 0.0605880 | − | 0.998163i | ||
0.998163 | − | 0.0605880i | ||||||||
7.40244 | − | 1.10960i | 0.0425428 | − | 0.00637702i | |||||
−95.8316 | − | 157.111i | −0.547609 | − | 0.897779i | |||||
22.3570 | + | 33.0213i | 0.127028 | + | 0.187621i | |||||
−77.2954 | + | 77.2954i | −0.436697 | + | 0.436697i | |||||
−100.422 | + | 135.836i | −0.564168 | + | 0.763125i | |||||
−31.3468 | −0.175122 | −0.0875610 | − | 0.996159i | ||||||
−0.0875610 | + | 0.996159i | ||||||||
61.8527 | + | 42.9236i | 0.343626 | + | 0.238464i | |||||
− | 57.4156i | − | 0.317214i | −0.987342 | − | 0.158607i | ||||
0.987342 | − | 0.158607i | ||||||||
−82.4320 | + | 111.502i | −0.452923 | + | 0.612648i | |||||
60.2184 | + | 60.2184i | 0.329063 | + | 0.329063i | |||||
205.932 | − | 98.5555i | 1.11920 | − | 0.535628i | |||||
−16.1627 | + | 135.359i | −0.0873659 | + | 0.731669i | |||||
−17.4729 | + | 2.61912i | −0.0939401 | + | 0.0140813i | |||||
−54.6895 | − | 54.6895i | −0.292457 | − | 0.292457i | |||||
168.439 | + | 89.3723i | 0.895952 | + | 0.475385i | |||||
137.696 | 0.728550 | |||||||||
−5.25664 | − | 175.489i | −0.0276665 | − | 0.923625i | |||||
161.923 | 0.847767 | 0.423884 | − | 0.905717i | ||||||
0.423884 | + | 0.905717i | ||||||||
227.339 | − | 24.4956i | 1.18405 | − | 0.127581i | |||||
63.0037 | + | 63.0037i | 0.326444 | + | 0.326444i | 0.851233 | − | 0.524789i | ||
−0.524789 | + | 0.851233i | ||||||||
67.4989 | − | 10.1179i | 0.347933 | − | 0.0521540i | |||||
132.236 | − | 104.025i | 0.678133 | − | 0.533461i | |||||
19.8410 | − | 6.08491i | 0.101229 | − | 0.0310455i | |||||
−3.96178 | − | 3.96178i | −0.0201106 | − | 0.0201106i | 0.696980 | − | 0.717091i | ||
−0.717091 | + | 0.696980i | ||||||||
15.0887 | + | 11.1549i | 0.0762056 | + | 0.0563378i | |||||
− | 123.026i | − | 0.618221i | −0.951026 | − | 0.309110i | ||||
0.951026 | − | 0.309110i | ||||||||
167.651 | + | 109.055i | 0.838256 | + | 0.545276i | |||||
−101.018 | −0.502576 | |||||||||
−180.832 | + | 244.603i | −0.895208 | + | 1.21091i | |||||
−5.45265 | + | 5.45265i | −0.0268604 | + | 0.0268604i | |||||
−423.982 | + | 130.029i | −2.07834 | + | 0.637395i | |||||
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50.5900 | + | 337.499i | 0.245582 | + | 1.63834i | |||||
75.9617 | − | 75.9617i | 0.366965 | − | 0.366965i | |||||
28.4961 | − | 147.977i | 0.137001 | − | 0.711428i | |||||
− | 43.7578i | − | 0.209367i | |||||||
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0.760837 | − | 0.648943i | ||||||||
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55.1617 | − | 55.1617i | 0.258975 | − | 0.258975i | |||||
31.5635 | + | 210.568i | 0.147493 | + | 0.983964i | |||||
231.274 | + | 27.6155i | 1.07569 | + | 0.128444i | |||||
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12.8706 | − | 12.8706i | 0.0593113 | − | 0.0593113i | |||||
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40.9523 | + | 28.4194i | 0.186147 | + | 0.129179i | |||||
292.273i | 1.32250i | |||||||||
156.653 | + | 115.812i | 0.705644 | + | 0.521674i | |||||
128.870 | + | 128.870i | 0.577894 | + | 0.577894i | 0.934323 | − | 0.356429i | ||
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91.4634 | + | 22.1585i | 0.406504 | + | 0.0984824i | |||||
34.3854 | + | 229.394i | 0.152148 | + | 1.01502i | |||||
242.455 | + | 242.455i | 1.06808 | + | 1.06808i | 0.997506 | + | 0.0705768i | ||
0.0705768 | + | 0.997506i | ||||||||
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195.659 | − | 207.743i | 0.850692 | − | 0.903229i | |||||
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2.78707 | − | 7.90328i | 0.0120132 | − | 0.0340659i | |||||
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236.669 | + | 28.2598i | 1.00710 | + | 0.120255i | |||||
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271.595 | − | 367.374i | 1.14116 | − | 1.54359i | |||||
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0.995610 | − | 0.0935965i | ||||||||
254.004 | − | 131.049i | 1.05835 | − | 0.546037i | |||||
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91.1560 | − | 27.9561i | 0.373590 | − | 0.114574i | |||||
20.3888 | − | 16.0391i | 0.0832194 | − | 0.0654655i | |||||
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244.625 | + | 51.5627i | 0.978499 | + | 0.206251i | |||||
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0.954532 | − | 0.298109i | ||||||||
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50.2938 | − | 50.2938i | 0.198790 | − | 0.198790i | |||||
156.247 | − | 23.4209i | 0.615146 | − | 0.0922084i | |||||
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95.0710 | − | 237.692i | 0.371371 | − | 0.928485i | |||||
244.045 | − | 244.045i | 0.949590 | − | 0.949590i | −0.0491992 | − | 0.998789i | ||
0.998789 | + | 0.0491992i | ||||||||
197.875 | − | 267.657i | 0.766959 | − | 1.03743i | |||||
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− | 3.94332i | − | 0.0151085i | |||||||
180.267 | − | 243.839i | 0.688042 | − | 0.930683i | |||||
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64.2566 | − | 30.7521i | 0.243396 | − | 0.116485i | |||||
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255.624 | − | 38.3172i | 0.960992 | − | 0.144050i | |||||
213.379 | + | 213.379i | 0.799172 | + | 0.799172i | |||||
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350.619 | 1.30342 | 0.651708 | − | 0.758470i | ||||||
0.651708 | + | 0.758470i | ||||||||
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175.153 | + | 175.153i | 0.641588 | + | 0.641588i | |||||
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60.5573 | + | 14.6710i | 0.220208 | + | 0.0533492i | |||||
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275.798 | + | 275.798i | 0.995660 | + | 0.995660i | 0.999991 | − | 0.00433109i | ||
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9.30790i | 0.0333617i | |||||||||
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13.2859 | 0.0472808 | 0.0236404 | − | 0.999721i | ||||||
0.0236404 | + | 0.999721i | ||||||||
202.492 | − | 273.902i | 0.718057 | − | 0.971283i | |||||
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0.100296 | + | 0.994958i | ||||||||
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228.724 | − | 228.724i | 0.796948 | − | 0.796948i | |||||
4.99207 | − | 120.356i | 0.0173336 | − | 0.417904i | |||||
− | 673.975i | − | 2.33209i | |||||||
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− | 121.925i | − | 0.418985i | |||||||
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0.418685 | + | 0.908132i | ||||||||
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94.5856 | + | 120.237i | 0.320629 | + | 0.407582i | |||||
196.742 | − | 94.1572i | 0.664669 | − | 0.318099i | |||||
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237.056 | − | 267.298i | 0.790186 | − | 0.890993i | |||||
342.912i | 1.13924i | |||||||||
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384.236 | + | 384.236i | 1.26811 | + | 1.26811i | |||||
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93.6728 | − | 73.6888i | 0.307124 | − | 0.241602i | |||||
34.6335 | + | 231.049i | 0.113181 | + | 0.755063i | |||||
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−0.182059 | − | 0.983288i | ||||||||
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609.631 | 1.97292 | |||||||||
0.740327 | + | 24.7152i | 0.00238815 | + | 0.0797266i | |||||
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270.798 | + | 270.798i | 0.865169 | + | 0.865169i | 0.991933 | − | 0.126764i | ||
−0.126764 | + | 0.991933i | ||||||||
39.4594 | + | 263.244i | 0.125667 | + | 0.838357i | |||||
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− | 2.61085i | − | 0.00818448i | |||||||
3.68258 | − | 319.979i | 0.0115081 | − | 0.999934i | |||||
380.354 | 1.18490 | |||||||||
337.846 | + | 249.765i | 1.04921 | + | 0.775668i | |||||
385.245 | − | 385.245i | 1.19271 | − | 1.19271i | |||||
118.113 | + | 385.131i | 0.364548 | + | 1.18867i | |||||
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371.968 | − | 55.7568i | 1.14101 | − | 0.171033i | |||||
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350.913i | 1.06660i | |||||||||
61.0511 | − | 64.8215i | 0.185003 | − | 0.196429i | |||||
73.0725i | 0.220763i | 0.993889 | + | 0.110381i | ||||||
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72.5718 | − | 72.5718i | 0.217933 | − | 0.217933i | |||||
143.806 | − | 21.5560i | 0.430557 | − | 0.0645390i | |||||
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235.914 | + | 348.445i | 0.702126 | + | 1.03704i | |||||
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0.327755 | + | 0.944763i | ||||||||
95.4627 | − | 129.128i | 0.282434 | − | 0.382036i | |||||
414.358 | 1.22230 | |||||||||
110.339 | + | 610.750i | 0.324528 | + | 1.79632i | |||||
6.16270i | 0.0180724i | |||||||||
−78.5774 | + | 106.288i | −0.229759 | + | 0.310784i | |||||
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150.516 | + | 150.516i | 0.433765 | + | 0.433765i | 0.889907 | − | 0.456142i | ||
−0.456142 | + | 0.889907i | ||||||||
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176.177 | 0.501930 | |||||||||
3.30521 | − | 79.6871i | 0.00938981 | − | 0.226384i | |||||
31.8920 | + | 31.8920i | 0.0903455 | + | 0.0903455i | 0.750835 | − | 0.660490i | ||
−0.660490 | + | 0.750835i | ||||||||
216.209 | − | 32.4090i | 0.610759 | − | 0.0915508i | |||||
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323.004 | − | 99.0601i | 0.907314 | − | 0.278259i | |||||
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50.4130 | + | 37.2697i | 0.140818 | + | 0.104105i | |||||
374.114i | 1.04210i | 0.853526 | + | 0.521050i | ||||||
−0.853526 | + | 0.521050i | ||||||||
−48.4397 | − | 142.571i | −0.134555 | − | 0.396029i | |||||
−52.7608 | −0.146152 | |||||||||
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265.139 | − | 81.3141i | 0.728405 | − | 0.223390i | |||||
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195.775 | − | 195.775i | 0.533446 | − | 0.533446i | −0.388150 | − | 0.921596i | ||
0.921596 | + | 0.388150i | ||||||||
−448.364 | − | 86.3421i | −1.21838 | − | 0.234625i | |||||
165.412i | 0.448270i | |||||||||
186.927 | − | 198.472i | 0.505209 | − | 0.536410i | |||||
− | 378.974i | − | 1.02149i | |||||||
31.2144 | + | 16.5621i | 0.0839097 | + | 0.0445218i | |||||
342.423 | − | 342.423i | 0.918023 | − | 0.918023i | −0.0788627 | − | 0.996885i | ||
0.996885 | + | 0.0788627i | ||||||||
22.9306 | + | 152.976i | 0.0613118 | + | 0.409027i | |||||
155.871 | − | 418.506i | 0.415657 | − | 1.11602i | |||||
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607.050 | 1.60171 | 0.800857 | − | 0.598855i | ||||||
0.800857 | + | 0.598855i | ||||||||
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− | 282.232i | − | 0.740767i | |||||||
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−0.879599 | + | 0.475717i | ||||||||
−394.737 | − | 230.898i | −1.02796 | − | 0.601298i | |||||
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885.575 | 2.26490 | |||||||||
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1.66113 | + | 11.0818i | 0.00421605 | + | 0.0281264i | |||||
−64.4974 | + | 50.7376i | −0.163284 | + | 0.128450i | |||||
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376.174 | + | 376.174i | 0.947543 | + | 0.947543i | 0.998691 | − | 0.0511485i | ||
−0.0511485 | + | 0.998691i | ||||||||
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− | 461.739i | − | 1.15724i | |||||||
−139.962 | − | 374.714i | −0.349904 | − | 0.936786i | |||||
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−0.500948 | + | 0.865477i | ||||||||
162.460 | + | 120.105i | 0.404130 | + | 0.298768i | |||||
16.4674 | − | 16.4674i | 0.0408621 | − | 0.0408621i | |||||
581.640 | − | 178.380i | 1.43970 | − | 0.441534i | |||||
311.332 | + | 395.764i | 0.768721 | + | 0.977195i | |||||
15.2520 | − | 2.28623i | 0.0375666 | − | 0.00563111i | |||||
48.0493 | − | 48.0493i | 0.118057 | − | 0.118057i | |||||
836.459 | + | 294.975i | 2.05014 | + | 0.722978i | |||||
166.880i | 0.408020i | 0.978969 | + | 0.204010i | ||||||
−0.978969 | + | 0.204010i | ||||||||
13.1564 | + | 439.217i | 0.0320889 | + | 1.07126i | |||||
344.826i | 0.838993i | |||||||||
319.907 | − | 602.925i | 0.776474 | − | 1.46341i | |||||
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−52.0256 | + | 70.3727i | −0.124463 | + | 0.168356i | |||||
−533.694 | −1.27373 | −0.636866 | − | 0.770974i | ||||||
−0.636866 | + | 0.770974i | ||||||||
432.134 | + | 299.886i | 1.02889 | + | 0.714014i | |||||
214.523i | 0.509556i | 0.967000 | + | 0.254778i | ||||||
−0.967000 | + | 0.254778i | ||||||||
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177.795 | + | 371.504i | 0.419328 | + | 0.876189i | |||||
403.984 | + | 662.312i | 0.950550 | + | 1.55838i | |||||
−154.297 | + | 23.1286i | −0.362199 | + | 0.0542925i | |||||
124.074 | + | 124.074i | 0.290573 | + | 0.290573i | |||||
199.593 | − | 376.170i | 0.466338 | − | 0.878902i | |||||
−83.8673 | −0.195495 | |||||||||
−339.108 | − | 319.384i | −0.788624 | − | 0.742753i | |||||
−525.371 | −1.21896 | −0.609479 | − | 0.792802i | ||||||
−0.609479 | + | 0.792802i | ||||||||
293.888 | + | 56.5944i | 0.680296 | + | 0.131006i | |||||
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−0.942159 | + | 0.335165i | ||||||||
−36.0012 | + | 5.39646i | −0.0829521 | + | 0.0124342i | |||||
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13.9113 | + | 45.3603i | 0.0319066 | + | 0.104037i | |||||
354.280 | + | 354.280i | 0.810709 | + | 0.810709i | |||||
265.265 | + | 196.107i | 0.605627 | + | 0.447732i | |||||
419.145i | 0.954771i | 0.878694 | + | 0.477386i | ||||||
−0.878694 | + | 0.477386i | ||||||||
−32.0716 | − | 94.3950i | −0.0728900 | − | 0.214534i | |||||
−19.5306 | −0.0442870 | |||||||||
347.497 | − | 470.043i | 0.786191 | − | 1.06345i | |||||
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0.559606 | + | 0.828758i | ||||||||
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331.922 | − | 261.110i | 0.745891 | − | 0.586764i | |||||
−54.0337 | − | 360.473i | −0.121152 | − | 0.808236i | |||||
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468.410 | − | 50.4709i | 1.04556 | − | 0.112658i | |||||
596.070i | 1.32755i | 0.747932 | + | 0.663775i | ||||||
−0.747932 | + | 0.663775i | ||||||||
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109.518i | 0.242834i | |||||||||
217.437 | − | 409.801i | 0.481055 | − | 0.906639i | |||||
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272.460 | − | 214.334i | 0.598813 | − | 0.471063i | |||||
216.624 | + | 452.637i | 0.475053 | + | 0.992626i | |||||
144.279 | − | 144.279i | 0.315708 | − | 0.315708i | −0.531408 | − | 0.847116i | ||
0.847116 | + | 0.531408i | ||||||||
620.245 | + | 458.539i | 1.35425 | + | 1.00118i | |||||
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0.590640 | − | 0.806935i | ||||||||
105.417 | + | 77.9337i | 0.228176 | + | 0.168688i | |||||
446.519 | + | 446.519i | 0.964404 | + | 0.964404i | 0.999388 | − | 0.0349842i | ||
−0.0349842 | + | 0.999388i | ||||||||
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5.61916 | + | 5.61916i | 0.0120325 | + | 0.0120325i | 0.713097 | − | 0.701065i | ||
−0.701065 | + | 0.713097i | ||||||||
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475.503 | 1.00956 | |||||||||
81.4042 | − | 230.837i | 0.172467 | − | 0.489062i | |||||
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17.3848 | + | 115.979i | 0.0366768 | + | 0.244681i | |||||
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137.036 | + | 137.036i | 0.287287 | + | 0.287287i | |||||
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0.601472 | − | 0.798894i | ||||||||
−564.308 | − | 91.2398i | −1.17564 | − | 0.190083i | |||||
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34.5424 | + | 25.5367i | 0.0716647 | + | 0.0529807i | |||||
530.707 | − | 530.707i | 1.09877 | − | 1.09877i | |||||
134.626 | + | 438.973i | 0.278153 | + | 0.906968i | |||||
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378.681 | − | 56.7630i | 0.779179 | − | 0.116796i | |||||
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−0.953320 | + | 0.301963i | ||||||||
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− | 671.893i | − | 1.37402i | |||||||
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899.211i | 1.83139i | 0.401877 | + | 0.915694i | ||||||
−0.401877 | + | 0.915694i | ||||||||
554.715 | + | 294.327i | 1.12747 | + | 0.598226i | |||||
22.9860 | − | 22.9860i | 0.0466247 | − | 0.0466247i | |||||
327.062 | − | 49.0255i | 0.662069 | − | 0.0992419i | |||||
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32.7599 | − | 22.1800i | 0.0660481 | − | 0.0447178i | |||||
113.655 | − | 113.655i | 0.228683 | − | 0.228683i | |||||
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755.350 | 1.51373 | 0.756864 | − | 0.653572i | ||||||
0.756864 | + | 0.653572i | ||||||||
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199.964 | − | 95.6991i | 0.396754 | − | 0.189879i | |||||
597.699 | − | 470.187i | 1.18356 | − | 0.931063i | |||||
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−0.583526 | + | 0.812095i | ||||||||
1108.19 | − | 33.1949i | 2.17291 | − | 0.0650880i | |||||
−339.847 | −0.665063 | |||||||||
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101.156 | − | 847.156i | 0.196419 | − | 1.64496i | |||||
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322.769 | + | 238.619i | 0.623106 | + | 0.460654i | |||||
925.453i | 1.78315i | |||||||||
−166.535 | + | 337.933i | −0.320260 | + | 0.649871i | |||||
871.615 | 1.67297 | 0.836483 | − | 0.547993i | ||||||
0.836483 | + | 0.547993i | ||||||||
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601.907 | − | 601.907i | 1.15087 | − | 1.15087i | 0.164497 | − | 0.986378i | ||
0.986378 | − | 0.164497i | ||||||||
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639.009 | + | 154.811i | 1.21716 | + | 0.294878i | |||||
101.282 | + | 675.677i | 0.192551 | + | 1.28456i | |||||
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285.396i | 0.539500i | |||||||||
374.770 | + | 352.971i | 0.707114 | + | 0.665983i | |||||
− | 115.176i | − | 0.216903i | |||||||
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292.645 | − | 292.645i | 0.549052 | − | 0.549052i | |||||
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63.1119 | − | 528.547i | 0.117966 | − | 0.987939i | |||||
204.035 | − | 97.6475i | 0.380663 | − | 0.182178i | |||||
79.1915 | − | 79.1915i | 0.147470 | − | 0.147470i | |||||
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−12.9311 | −0.0239908 | |||||||||
368.150 | − | 66.5107i | 0.681759 | − | 0.123168i | |||||
109.548i | 0.202492i | 0.994861 | + | 0.101246i | ||||||
−0.994861 | + | 0.101246i | ||||||||
480.233 | + | 355.030i | 0.886040 | + | 0.655037i | |||||
145.049 | + | 145.049i | 0.267125 | + | 0.267125i | |||||
730.666 | − | 672.468i | 1.34314 | − | 1.23615i | |||||
36.6684 | + | 46.6127i | 0.0672815 | + | 0.0855279i | |||||
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341.033 | + | 180.949i | 0.622323 | + | 0.330200i | |||||
−89.7299 | −0.163442 | |||||||||
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18.3914 | 0.0333782 | |||||||||
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81.7744 | + | 266.640i | 0.147076 | + | 0.479569i | |||||
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−0.761153 | + | 0.648572i | ||||||||
11.0666 | − | 14.9693i | 0.0198326 | − | 0.0268266i | |||||
438.745i | 0.784874i | |||||||||
523.352 | − | 270.014i | 0.934557 | − | 0.482168i | |||||
276.324 | 0.492556 | |||||||||
−21.3668 | − | 15.7962i | −0.0380193 | − | 0.0281071i | |||||
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0.596420 | + | 0.802672i | ||||||||
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68.7543 | − | 575.801i | 0.121689 | − | 1.01912i | |||||
708.215 | − | 106.159i | 1.25126 | − | 0.187560i | |||||
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0.958683 | − | 0.284475i | ||||||||
456.617 | + | 430.057i | 0.801082 | + | 0.754486i | |||||
433.708i | 0.759558i | 0.925077 | + | 0.379779i | ||||||
−0.925077 | + | 0.379779i | ||||||||
−44.0098 | + | 82.9447i | −0.0769402 | + | 0.145008i | |||||
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27.1282 | − | 27.1282i | 0.0470159 | − | 0.0470159i | −0.683208 | − | 0.730224i | ||
0.730224 | + | 0.683208i | ||||||||
−801.319 | + | 1083.91i | −1.38637 | + | 1.87527i | |||||
−318.332 | −0.549797 | |||||||||
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− | 3.57909i | − | 0.00616023i | |||||||
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90.7305 | + | 90.7305i | 0.155627 | + | 0.155627i | |||||
333.149 | − | 159.439i | 0.570460 | − | 0.273012i | |||||
−21.0182 | + | 176.023i | −0.0359286 | + | 0.300894i | |||||
401.137 | − | 60.1291i | 0.684535 | − | 0.102609i | |||||
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−0.832682 | + | 0.553751i | ||||||||
−34.7519 | + | 65.4965i | −0.0591019 | + | 0.111389i | |||||
−43.4114 | −0.0737035 | |||||||||
−9.16078 | − | 305.826i | −0.0155268 | − | 0.518349i | |||||
20.0173 | 0.0338702 | |||||||||
−428.355 | − | 82.4889i | −0.723572 | − | 0.139339i | |||||
280.606 | + | 280.606i | 0.473198 | + | 0.473198i | 0.902948 | − | 0.429750i | ||
−0.429750 | + | 0.902948i | ||||||||
92.2115 | − | 13.8222i | 0.155238 | − | 0.0232697i | |||||
−897.695 | + | 706.182i | −1.50873 | + | 1.18686i | |||||
92.5370 | + | 301.734i | 0.155263 | + | 0.506265i | |||||
310.800 | + | 310.800i | 0.520603 | + | 0.520603i | |||||
432.263 | + | 319.566i | 0.722848 | + | 0.534392i | |||||
− | 639.232i | − | 1.06716i | −0.845748 | − | 0.533582i | ||||
0.845748 | − | 0.533582i | ||||||||
−699.043 | + | 148.031i | −1.16507 | + | 0.246718i | |||||
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−0.277021 | + | 0.960864i | ||||||||
407.704 | − | 551.482i | 0.677249 | − | 0.916084i | |||||
75.2619 | − | 75.2619i | 0.124812 | − | 0.124812i | |||||
231.704 | + | 755.514i | 0.383617 | + | 1.25085i | |||||
354.857 | + | 451.092i | 0.586540 | + | 0.745607i | |||||
−161.106 | − | 1074.78i | −0.265851 | − | 1.77356i | |||||
681.745 | − | 681.745i | 1.12314 | − | 1.12314i | 0.131873 | − | 0.991267i | ||
0.991267 | − | 0.131873i | ||||||||
561.333 | + | 23.2826i | 0.923245 | + | 0.0382938i | |||||
− | 27.5501i | − | 0.0452382i | |||||||
−238.259 | + | 7.13689i | −0.390589 | + | 0.0116998i | |||||
448.981i | 0.734830i | |||||||||
219.006 | − | 412.758i | 0.357853 | − | 0.674442i | |||||
378.926 | − | 378.926i | 0.618150 | − | 0.618150i | −0.326907 | − | 0.945057i | ||
0.945057 | + | 0.326907i | ||||||||
150.005 | + | 1000.72i | 0.244308 | + | 1.62984i | |||||
779.417 | + | 93.0672i | 1.26734 | + | 0.151329i | |||||
132.395 | − | 63.3617i | 0.214927 | − | 0.102860i | |||||
−68.3041 | + | 68.3041i | −0.110704 | + | 0.110704i | −0.760289 | − | 0.649585i | ||
0.649585 | + | 0.760289i | ||||||||
−980.429 | − | 724.818i | −1.58645 | − | 1.17284i | |||||
1009.69 | 1.63116 | 0.815580 | − | 0.578645i | ||||||
0.815580 | + | 0.578645i | ||||||||
28.1944 | − | 40.6281i | 0.0454749 | − | 0.0655291i | |||||
− | 533.810i | − | 0.859597i | |||||||
611.456 | + | 452.042i | 0.983049 | + | 0.726755i | |||||
439.648 | + | 439.648i | 0.705694 | + | 0.705694i | |||||
301.845 | + | 445.824i | 0.483725 | + | 0.714462i | |||||
−555.701 | − | 286.045i | −0.889121 | − | 0.457671i | |||||
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110.545 | + | 110.545i | 0.176308 | + | 0.176308i | |||||
249.523 | − | 470.273i | 0.397329 | − | 0.748842i | |||||
846.054 | 1.34508 | |||||||||
189.988 | − | 201.722i | 0.301569 | − | 0.320193i | |||||
−867.965 | −1.37554 | −0.687769 | − | 0.725929i | ||||||
−0.687769 | + | 0.725929i | ||||||||
123.826 | + | 43.6668i | 0.195927 | + | 0.0690930i | |||||
691.837 | + | 691.837i | 1.09295 | + | 1.09295i | |||||
100.184 | + | 668.355i | 0.158019 | + | 1.05419i | |||||
−392.196 | − | 46.8307i | −0.617631 | − | 0.0737491i | |||||
703.391 | − | 215.719i | 1.10596 | − | 0.339181i | |||||
34.5532 | + | 34.5532i | 0.0542437 | + | 0.0542437i | |||||
−3.10415 | + | 4.19885i | −0.00486545 | + | 0.00658127i | |||||
82.1949i | 0.128631i | |||||||||
−386.360 | + | 510.222i | −0.603687 | + | 0.797222i | |||||
116.032 | 0.181017 | 0.0905083 | − | 0.995896i | ||||||
0.0905083 | + | 0.995896i | ||||||||
−611.697 | − | 452.220i | −0.952799 | − | 0.704392i | |||||
−429.493 | + | 429.493i | −0.667951 | + | 0.667951i | −0.957241 | − | 0.289290i | ||
0.289290 | + | 0.957241i | ||||||||
−246.378 | − | 803.361i | −0.382575 | − | 1.24745i | |||||
−654.031 | + | 514.501i | −1.01400 | + | 0.797676i | |||||
−1077.60 | + | 161.528i | −1.66811 | + | 0.250044i | |||||
511.695 | − | 511.695i | 0.790873 | − | 0.790873i | −0.190763 | − | 0.981636i | ||
0.981636 | + | 0.190763i | ||||||||
267.945 | − | 759.810i | 0.413495 | − | 1.17255i | |||||
− | 76.2571i | − | 0.117499i | |||||||
−41.8093 | + | 469.065i | −0.0643220 | + | 0.721638i | |||||
65.0297i | 0.0998920i | |||||||||
−664.503 | − | 352.580i | −1.01918 | − | 0.540766i | |||||
−777.556 | + | 777.556i | −1.19074 | + | 1.19074i | −0.213886 | + | 0.976859i | ||
−0.976859 | + | 0.213886i | ||||||||
83.8186 | − | 12.5641i | 0.128163 | − | 0.0192112i | |||||
−595.831 | + | 468.717i | −0.909666 | + | 0.715599i | |||||
582.179 | − | 394.163i | 0.887468 | − | 0.600859i | |||||
122.888 | − | 122.888i | 0.187044 | − | 0.187044i | |||||
417.216 | − | 564.349i | 0.634067 | − | 0.857673i | |||||
734.265 | 1.11421 | 0.557105 | − | 0.830442i | ||||||
0.557105 | + | 0.830442i | ||||||||
−175.254 | + | 31.6617i | −0.265536 | + | 0.0479723i | |||||
799.237i | 1.20913i | 0.796555 | + | 0.604567i | ||||||
−0.796555 | + | 0.604567i | ||||||||
86.8791 | − | 117.518i | 0.131237 | − | 0.177519i | |||||
−738.369 | − | 738.369i | −1.11368 | − | 1.11368i | |||||
1.67913 | + | 3.50855i | 0.00252880 | + | 0.00528395i | |||||
−641.641 | − | 76.6160i | −0.964874 | − | 0.115212i | |||||
−202.996 | + | 30.4284i | −0.304799 | + | 0.0456883i | |||||
21.1384 | + | 21.1384i | 0.0316918 | + | 0.0316918i | |||||
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193.857 | − | 205.829i | 0.289338 | − | 0.307207i | |||||
−59.4096 | −0.0885388 | |||||||||
34.8771 | − | 840.870i | 0.0519005 | − | 1.25130i | |||||
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581.622 | − | 87.1832i | 0.862940 | − | 0.129352i | |||||
399.230 | − | 243.515i | 0.591452 | − | 0.360762i | |||||
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− | 251.214i | − | 0.369977i | |||||||
548.696 | − | 1113.41i | 0.806907 | − | 1.63737i | |||||
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0.656249 | + | 0.754544i | ||||||||
252.741 | − | 77.5118i | 0.369505 | − | 0.113321i | |||||
479.178 | + | 57.2168i | 0.699529 | + | 0.0835282i | |||||
95.6181 | + | 637.893i | 0.139385 | + | 0.929873i | |||||
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0.922550 | − | 0.385877i | ||||||||
915.274 | + | 485.636i | 1.32265 | + | 0.701787i | |||||
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215.547 | + | 274.002i | 0.310139 | + | 0.394248i | |||||
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256.991 | + | 189.990i | 0.368181 | + | 0.272192i | |||||
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488.431 | − | 550.743i | 0.697759 | − | 0.786775i | |||||
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0.512835 | − | 0.858487i | ||||||||
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338.469 | + | 338.469i | 0.481464 | + | 0.481464i | |||||
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6.53757 | + | 218.252i | 0.00920785 | + | 0.307397i | |||||
61.7825 | 0.0868952 | |||||||||
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241.967 | + | 1614.23i | 0.338890 | + | 2.26082i | |||||
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113.024 | + | 113.024i | 0.157635 | + | 0.157635i | |||||
444.800 | − | 601.662i | 0.619499 | − | 0.837969i | |||||
63.2841i | 0.0880168i | 0.999031 | + | 0.0440084i | ||||||
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1256.09 | 1.74215 | |||||||||
84.8517 | + | 62.7297i | 0.117523 | + | 0.0868833i | |||||
54.2610 | − | 54.2610i | 0.0750498 | − | 0.0750498i | |||||
219.569 | − | 67.3383i | 0.303272 | − | 0.0930087i | |||||
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811.151 | − | 121.589i | 1.11729 | − | 0.167478i | |||||
408.139 | − | 408.139i | 0.561401 | − | 0.561401i | −0.368304 | − | 0.929705i | ||
0.929705 | + | 0.368304i | ||||||||
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222.361i | 0.305021i | |||||||||
316.529 | − | 336.078i | 0.433602 | − | 0.460380i | |||||
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0.643022 | + | 0.765848i | ||||||||
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618.418 | + | 671.938i | 0.840241 | + | 0.912959i | |||||
49.8304 | − | 49.8304i | 0.0676125 | − | 0.0676125i | |||||
196.665 | − | 266.020i | 0.266484 | − | 0.360461i | |||||
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282.061 | + | 282.061i | 0.379624 | + | 0.379624i | 0.870967 | − | 0.491342i | ||
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243.916 | + | 310.065i | 0.327404 | + | 0.416194i | |||||
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1.29419 | + | 1.29419i | 0.00173251 | + | 0.00173251i | |||||
145.002 | − | 273.285i | 0.193854 | − | 0.365354i | |||||
783.683 | 1.04631 | |||||||||
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606.986 | 0.808237 | 0.404119 | − | 0.914707i | ||||||
0.404119 | + | 0.914707i | ||||||||
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378.063 | + | 378.063i | 0.502075 | + | 0.502075i | |||||
19.5145 | − | 2.92515i | 0.0258812 | − | 0.00387951i | |||||
610.743 | + | 776.374i | 0.808932 | + | 1.02831i | |||||
161.493 | + | 526.577i | 0.213615 | + | 0.696530i | |||||
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254.114i | 0.334801i | |||||||||
664.938 | − | 225.919i | 0.874919 | − | 0.297262i | |||||
100.678 | 0.132297 | 0.0661483 | − | 0.997810i | ||||||
0.0661483 | + | 0.997810i | ||||||||
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189.907 | + | 619.228i | 0.248570 | + | 0.810507i | |||||
69.2505 | − | 579.957i | 0.0905235 | − | 0.758113i | |||||
64.8582 | + | 432.686i | 0.0846713 | + | 0.564864i | |||||
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360.303 | + | 840.659i | 0.469145 | + | 1.09461i | |||||
370.732i | 0.482097i | 0.970513 | + | 0.241048i | ||||||
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125.790 | − | 133.559i | 0.163364 | − | 0.173453i | |||||
1233.06i | 1.59930i | |||||||||
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0.469608 | + | 0.882875i | ||||||||
51.9900 | + | 346.839i | 0.0671705 | + | 0.448112i | |||||
14.5549 | − | 60.0779i | 0.0187805 | − | 0.0775198i | |||||
117.857 | + | 246.263i | 0.151877 | + | 0.317349i | |||||
507.023 | − | 507.023i | 0.652539 | − | 0.652539i | |||||
520.633 | + | 384.897i | 0.669194 | + | 0.494726i | |||||
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552.901 | + | 383.694i | 0.708848 | + | 0.491915i | |||||
54.4207i | 0.0696808i | |||||||||
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46.5398 | + | 68.7393i | 0.0593620 | + | 0.0876776i | |||||
78.8999 | − | 660.769i | 0.100509 | − | 0.841744i | |||||
160.602 | + | 1071.42i | 0.204328 | + | 1.36313i | |||||
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10.5042 | − | 19.7971i | 0.0133302 | − | 0.0251232i | |||||
1220.49 | 1.54688 | |||||||||
164.051 | − | 4.91402i | 0.207659 | − | 0.00622028i | |||||
853.747 | 1.07933 | |||||||||
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158.749 | + | 158.749i | 0.200188 | + | 0.200188i | |||||
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722.811 | − | 568.608i | 0.909197 | − | 0.715230i | |||||
470.476 | − | 144.287i | 0.591050 | − | 0.181266i | |||||
434.605 | + | 434.605i | 0.545301 | + | 0.545301i | 0.925078 | − | 0.379777i | ||
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− | 1479.29i | − | 1.85143i | |||||||
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646.124 | + | 477.671i | 0.805641 | + | 0.595600i | |||||
81.3631 | − | 81.3631i | 0.101324 | − | 0.101324i | |||||
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164.175i | 0.202935i | 0.994839 | + | 0.101468i | ||||||
−0.994839 | + | 0.101468i | ||||||||
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0.611752 | − | 0.791049i | ||||||||
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754.377 | − | 754.377i | 0.927893 | − | 0.927893i | |||||
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578.308 | − | 578.308i | 0.707843 | − | 0.707843i | |||||
198.411 | − | 268.382i | 0.242556 | − | 0.328095i | |||||
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501.046 | − | 722.006i | 0.611032 | − | 0.880495i | |||||
1292.43i | 1.57421i | 0.616817 | + | 0.787106i | ||||||
−0.616817 | + | 0.787106i | ||||||||
409.979 | − | 554.561i | 0.498758 | − | 0.674648i | |||||
38.6290 | + | 38.6290i | 0.0469368 | + | 0.0469368i | 0.730186 | − | 0.683249i | ||
−0.683249 | + | 0.730186i | ||||||||
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445.478 | − | 66.7757i | 0.539320 | − | 0.0808422i | |||||
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−0.918341 | + | 0.395789i | ||||||||
379.582 | + | 201.403i | 0.458433 | + | 0.243241i | |||||
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−0.412676 | + | 0.910878i | ||||||||
3.53939 | + | 3.33352i | 0.00426432 | + | 0.00401629i | |||||
−1393.49 | −1.67689 | |||||||||
599.315 | − | 64.5758i | 0.720330 | − | 0.0776151i | |||||
−113.845 | − | 113.845i | −0.136669 | − | 0.136669i | |||||
492.708 | − | 73.8553i | 0.590777 | − | 0.0885556i | |||||
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167.338 | − | 51.3201i | 0.200166 | − | 0.0613876i | |||||
32.7049 | + | 32.7049i | 0.0390740 | + | 0.0390740i | |||||
858.304 | + | 634.533i | 1.02423 | + | 0.757199i | |||||
579.065i | 0.690184i | 0.938569 | + | 0.345092i | ||||||
−0.938569 | + | 0.345092i | ||||||||
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−839.903 | −0.998695 | |||||||||
255.056 | − | 345.003i | 0.302917 | − | 0.409742i | |||||
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1047.27 | − | 321.182i | 1.24084 | − | 0.380547i | |||||
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53.2029 | + | 354.931i | 0.0628876 | + | 0.419540i | |||||
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155.762 | − | 808.854i | 0.183682 | − | 0.953837i | |||||
− | 1279.26i | − | 1.50679i | |||||||
137.752 | − | 1545.47i | 0.162062 | − | 1.81819i | |||||
778.051i | 0.914279i | |||||||||
275.644 | + | 146.254i | 0.323526 | + | 0.171660i | |||||
89.6610 | − | 89.6610i | 0.105113 | − | 0.105113i | −0.652595 | − | 0.757707i | ||
0.757707 | + | 0.652595i | ||||||||
−52.0229 | − | 347.058i | −0.0609167 | − | 0.406391i | |||||
259.720 | − | 204.311i | 0.303766 | − | 0.238961i | |||||
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0.426445 | + | 0.904514i | ||||||||
134.878 | + | 99.7135i | 0.157201 | + | 0.116216i | |||||
799.305 | 0.930507 | 0.465253 | − | 0.885178i | ||||||
0.465253 | + | 0.885178i | ||||||||
165.635 | + | 916.824i | 0.192599 | + | 1.06607i | |||||
1155.65i | 1.34222i | |||||||||
844.918 | + | 624.637i | 0.980184 | + | 0.724637i | |||||
1116.04 | + | 1116.04i | 1.29321 | + | 1.29321i | 0.932793 | + | 0.360414i | ||
0.360414 | + | 0.932793i | ||||||||
−405.352 | − | 440.433i | −0.469158 | − | 0.509761i | |||||
1286.03 | + | 153.560i | 1.48674 | + | 0.177526i | |||||
110.201 | + | 735.178i | 0.127253 | + | 0.848935i | |||||
1702.66 | + | 1702.66i | 1.96386 | + | 1.96386i | |||||
64.3144 | + | 34.1247i | 0.0740949 | + | 0.0393142i | |||||
40.9058 | 0.0470723 | |||||||||
27.2445 | + | 25.6598i | 0.0313155 | + | 0.0294940i | |||||
−266.305 | −0.305746 | |||||||||
31.5583 | − | 89.4897i | 0.0361907 | − | 0.102626i | |||||
90.8383 | + | 90.8383i | 0.104053 | + | 0.104053i | |||||
−148.545 | − | 990.984i | −0.169960 | − | 1.13385i | |||||
321.159 | − | 862.293i | 0.367038 | − | 0.985477i | |||||
−193.447 | − | 630.770i | −0.220830 | − | 0.720058i | |||||
−98.3606 | − | 98.3606i | −0.112156 | − | 0.112156i | 0.648802 | − | 0.760957i | ||
−0.760957 | + | 0.648802i | ||||||||
498.340 | − | 674.082i | 0.567585 | − | 0.767747i | |||||
− | 724.582i | − | 0.824326i | |||||||
−60.6518 | + | 189.940i | −0.0689225 | + | 0.215841i | |||||
−654.962 | −0.743430 | −0.371715 | − | 0.928347i | ||||||
−0.371715 | + | 0.928347i | ||||||||
31.4097 | + | 23.2207i | 0.0356119 | + | 0.0263274i | |||||
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−0.995447 | + | 0.0953158i | ||||||||
−1117.71 | + | 342.784i | −1.26438 | + | 0.387765i | |||||
−542.705 | − | 64.8024i | −0.613227 | − | 0.0732231i | |||||
333.520 | − | 49.9935i | 0.376433 | − | 0.0564260i | |||||
−588.066 | + | 588.066i | −0.662983 | + | 0.662983i | −0.956082 | − | 0.293099i | ||
0.293099 | + | 0.956082i | ||||||||
−259.160 | + | 734.899i | −0.291847 | + | 0.827588i | |||||
− | 581.514i | − | 0.654121i | |||||||
−844.252 | + | 25.2890i | −0.948598 | + | 0.0284146i | |||||
− | 251.003i | − | 0.281709i | |||||||
−341.684 | + | 643.968i | −0.383054 | + | 0.721937i | |||||
591.801 | − | 591.801i | 0.662711 | − | 0.662711i | |||||
557.556 | − | 83.5758i | 0.623664 | − | 0.0934852i | |||||
−96.9059 | − | 123.186i | −0.108275 | − | 0.137638i | |||||
−813.319 | − | 475.745i | −0.907722 | − | 0.530965i | |||||
679.022 | − | 679.022i | 0.756992 | − | 0.756992i | |||||
708.694 | − | 958.619i | 0.789192 | − | 1.06750i | |||||
−2.59018 | −0.00288118 | |||||||||
22.5316 | + | 375.762i | 0.0250351 | + | 0.417513i | |||||
1597.59i | 1.77313i | |||||||||
130.211 | − | 176.130i | 0.144358 | − | 0.195267i | |||||
−866.299 | − | 866.299i | −0.959356 | − | 0.959356i | |||||
−836.919 | + | 400.534i | −0.925795 | + | 0.443069i | |||||
225.631 | − | 177.495i | 0.249316 | − | 0.196127i | |||||
1396.07 | − | 209.266i | 1.54092 | − | 0.230978i | |||||
692.104 | + | 692.104i | 0.763069 | + | 0.763069i | 0.976876 | − | 0.213807i | ||
−0.213807 | + | 0.976876i | ||||||||
−642.839 | + | 1211.55i | −0.707973 | + | 1.33431i | |||||
−572.540 | −0.629857 | |||||||||
−693.010 | + | 20.7586i | −0.761549 | + | 0.0228116i | |||||
−45.1707 | −0.0495836 | −0.0247918 | − | 0.999693i | ||||||
−0.0247918 | + | 0.999693i | ||||||||
189.779 | − | 985.500i | 0.208091 | − | 1.08059i | |||||
0.856873 | + | 0.856873i | 0.000938525 | + | 0.000938525i | |||||
−403.573 | + | 60.4943i | −0.441546 | + | 0.0661863i | |||||
−50.4856 | + | 422.805i | −0.0551755 | + | 0.462082i | |||||
−452.321 | − | 1474.87i | −0.493800 | − | 1.61013i | |||||
−789.209 | − | 789.209i | −0.860643 | − | 0.860643i | |||||
933.523 | + | 690.141i | 1.01691 | + | 0.751788i | |||||
1598.45i | 1.73934i | 0.493637 | + | 0.869668i | ||||||
−0.493637 | + | 0.869668i | ||||||||
1023.92 | + | 504.594i | 1.11296 | + | 0.548472i | |||||
1807.62 | 1.96268 | |||||||||
−884.568 | + | 1196.52i | −0.959402 | + | 1.29774i | |||||
145.418 | − | 145.418i | 0.157550 | − | 0.157550i | |||||
−76.8769 | − | 250.671i | −0.0832001 | − | 0.271289i | |||||
−581.896 | + | 354.933i | −0.629077 | + | 0.383712i | |||||
−187.220 | − | 1248.99i | −0.202181 | − | 1.34880i | |||||
−454.197 | + | 454.197i | −0.489965 | + | 0.489965i | |||||
33.4925 | + | 1.38918i | 0.0360910 | + | 0.00149696i | |||||
887.585i | 0.955420i | 0.878518 | + | 0.477710i | ||||||
−0.878518 | + | 0.477710i | ||||||||
−64.3084 | − | 60.5678i | −0.0691488 | − | 0.0651267i | |||||
− | 91.0891i | − | 0.0978400i | |||||||
−26.2705 | + | 49.5118i | −0.0281873 | + | 0.0531242i | |||||
960.509 | − | 960.509i | 1.02948 | − | 1.02948i | |||||
−2.35604 | − | 15.7178i | −0.00252253 | − | 0.0168285i | |||||
45.8503 | − | 383.986i | 0.0490377 | − | 0.410680i | |||||
255.847 | − | 122.444i | 0.273341 | − | 0.130816i | |||||
1241.34 | − | 1241.34i | 1.32480 | − | 1.32480i | 0.414958 | − | 0.909841i | ||
0.909841 | − | 0.414958i | ||||||||
334.734 | + | 247.464i | 0.356859 | + | 0.263821i | |||||
−1368.23 | −1.45712 | |||||||||
169.500 | + | 938.215i | 0.180319 | + | 0.998101i | |||||
328.028i | 0.348595i | 0.984693 | + | 0.174298i | ||||||
−0.984693 | + | 0.174298i | ||||||||
−764.719 | − | 565.347i | −0.811804 | − | 0.600156i | |||||
−886.700 | − | 886.700i | −0.940297 | − | 0.940297i | |||||
−405.370 | + | 274.455i | −0.429417 | + | 0.290736i | |||||
425.675 | + | 541.115i | 0.450449 | + | 0.572609i | |||||
34.4222 | + | 229.640i | 0.0363871 | + | 0.242748i | |||||
−228.351 | − | 228.351i | −0.241131 | − | 0.241131i | 0.576187 | − | 0.817318i | ||
−0.817318 | + | 0.576187i | ||||||||
109.933 | − | 207.190i | 0.115963 | − | 0.218555i | |||||
−434.823 | −0.458191 | |||||||||
673.382 | − | 563.165i | 0.708823 | − | 0.592805i | |||||
1207.26 | 1.26947 | |||||||||
1723.45 | + | 607.769i | 1.81034 | + | 0.638412i | |||||
−1291.50 | − | 1291.50i | −1.35519 | − | 1.35519i | −0.879742 | − | 0.475451i | ||
−0.475451 | − | 0.879742i | ||||||||
−57.4574 | − | 383.313i | −0.0602279 | − | 0.401796i | |||||
500.572 | + | 636.324i | 0.524159 | + | 0.666308i | |||||
171.091 | − | 52.4710i | 0.178966 | − | 0.0548860i | |||||
6.59578 | + | 6.59578i | 0.00689215 | + | 0.00689215i | |||||
−909.947 | + | 1230.84i | −0.949840 | + | 1.28481i | |||||
710.482i | 0.740857i | |||||||||
799.059 | + | 817.665i | 0.832353 | + | 0.851735i | |||||
−954.886 | −0.993638 | |||||||||
412.972 | + | 305.305i | 0.429285 | + | 0.317365i | |||||
−283.377 | + | 283.377i | −0.294265 | + | 0.294265i | |||||
−25.1904 | − | 82.1379i | −0.0261311 | − | 0.0852053i | |||||
−52.8207 | + | 442.361i | −0.0547365 | + | 0.458405i | |||||
−1484.48 | + | 222.519i | −1.53673 | + | 0.230351i | |||||
486.969 | − | 486.969i | 0.503588 | − | 0.503588i | −0.408963 | − | 0.912551i | ||
0.912551 | + | 0.408963i | ||||||||
305.404 | − | 866.033i | 0.315500 | − | 0.894662i | |||||
1946.49i | 2.00876i | |||||||||
248.428 | + | 233.978i | 0.256111 | + | 0.241214i | |||||
− | 361.550i | − | 0.372348i | −0.982517 | − | 0.186174i | ||||
0.982517 | − | 0.186174i | ||||||||
−676.495 | − | 358.943i | −0.695983 | − | 0.369282i | |||||
−362.930 | + | 362.930i | −0.373001 | + | 0.373001i | |||||
1709.98 | − | 256.320i | 1.75562 | − | 0.263162i | |||||
817.591 | + | 198.075i | 0.838555 | + | 0.203154i | |||||
213.819 | + | 315.811i | 0.219077 | + | 0.323577i | |||||
−1073.65 | + | 1073.65i | −1.09892 | + | 1.09892i | −0.104387 | + | 0.994537i | ||
−0.994537 | + | 0.104387i | ||||||||
−798.844 | + | 1080.56i | −0.816814 | + | 1.10487i | |||||
−210.513 | −0.215028 | |||||||||
85.2489 | + | 59.1597i | 0.0869887 | + | 0.0603671i | |||||
− | 44.6506i | − | 0.0455154i | |||||||
1069.11 | − | 1446.14i | 1.08871 | − | 1.47265i | |||||
122.156 | + | 122.156i | 0.124269 | + | 0.124269i | 0.766506 | − | 0.642237i | ||
−0.642237 | + | 0.766506i | ||||||||
−542.172 | − | 1132.87i | −0.550988 | − | 1.15129i | |||||
3.32146 | − | 27.8164i | 0.00337204 | − | 0.0282400i | |||||
−64.2958 | + | 9.63773i | −0.0652088 | + | 0.00977458i | |||||
−886.510 | − | 886.510i | −0.898187 | − | 0.898187i | |||||
−584.280 | − | 310.014i | −0.591377 | − | 0.313780i | |||||
1329.38 | 1.34416 | |||||||||
2.80910 | + | 93.7797i | 0.00283748 | + | 0.0947270i | |||||
324.300 | 0.327245 | 0.163623 | − | 0.986523i | ||||||
0.163623 | + | 0.986523i | ||||||||
−79.0563 | − | 3.27905i | −0.0796938 | − | 0.00330549i | |||||
−184.603 | − | 184.603i | −0.185904 | − | 0.185904i | |||||
−317.914 | + | 47.6543i | −0.319833 | + | 0.0479420i | |||||
483.465 | − | 380.323i | 0.485895 | − | 0.382235i | |||||
6.64294 | − | 2.03728i | 0.00666962 | − | 0.00204547i | |||||
743.909 | + | 743.909i | 0.746148 | + | 0.746148i | 0.973753 | − | 0.227606i | ||
−0.227606 | + | 0.973753i | ||||||||
−1214.78 | − | 898.070i | −1.21721 | − | 0.899869i | |||||
− | 509.987i | − | 0.510498i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 40.3.i.a.13.2 | ✓ | 20 | |
3.2 | odd | 2 | 360.3.u.b.253.9 | 20 | |||
4.3 | odd | 2 | 160.3.m.a.113.8 | 20 | |||
5.2 | odd | 4 | inner | 40.3.i.a.37.8 | yes | 20 | |
5.3 | odd | 4 | 200.3.i.b.157.3 | 20 | |||
5.4 | even | 2 | 200.3.i.b.93.9 | 20 | |||
8.3 | odd | 2 | 160.3.m.a.113.3 | 20 | |||
8.5 | even | 2 | inner | 40.3.i.a.13.8 | yes | 20 | |
15.2 | even | 4 | 360.3.u.b.37.3 | 20 | |||
20.3 | even | 4 | 800.3.m.b.657.8 | 20 | |||
20.7 | even | 4 | 160.3.m.a.17.3 | 20 | |||
20.19 | odd | 2 | 800.3.m.b.593.3 | 20 | |||
24.5 | odd | 2 | 360.3.u.b.253.3 | 20 | |||
40.3 | even | 4 | 800.3.m.b.657.3 | 20 | |||
40.13 | odd | 4 | 200.3.i.b.157.9 | 20 | |||
40.19 | odd | 2 | 800.3.m.b.593.8 | 20 | |||
40.27 | even | 4 | 160.3.m.a.17.8 | 20 | |||
40.29 | even | 2 | 200.3.i.b.93.3 | 20 | |||
40.37 | odd | 4 | inner | 40.3.i.a.37.2 | yes | 20 | |
120.77 | even | 4 | 360.3.u.b.37.9 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.3.i.a.13.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
40.3.i.a.13.8 | yes | 20 | 8.5 | even | 2 | inner | |
40.3.i.a.37.2 | yes | 20 | 40.37 | odd | 4 | inner | |
40.3.i.a.37.8 | yes | 20 | 5.2 | odd | 4 | inner | |
160.3.m.a.17.3 | 20 | 20.7 | even | 4 | |||
160.3.m.a.17.8 | 20 | 40.27 | even | 4 | |||
160.3.m.a.113.3 | 20 | 8.3 | odd | 2 | |||
160.3.m.a.113.8 | 20 | 4.3 | odd | 2 | |||
200.3.i.b.93.3 | 20 | 40.29 | even | 2 | |||
200.3.i.b.93.9 | 20 | 5.4 | even | 2 | |||
200.3.i.b.157.3 | 20 | 5.3 | odd | 4 | |||
200.3.i.b.157.9 | 20 | 40.13 | odd | 4 | |||
360.3.u.b.37.3 | 20 | 15.2 | even | 4 | |||
360.3.u.b.37.9 | 20 | 120.77 | even | 4 | |||
360.3.u.b.253.3 | 20 | 24.5 | odd | 2 | |||
360.3.u.b.253.9 | 20 | 3.2 | odd | 2 | |||
800.3.m.b.593.3 | 20 | 20.19 | odd | 2 | |||
800.3.m.b.593.8 | 20 | 40.19 | odd | 2 | |||
800.3.m.b.657.3 | 20 | 40.3 | even | 4 | |||
800.3.m.b.657.8 | 20 | 20.3 | even | 4 |