Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [220,3,Mod(31,220)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(220, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 0, 6]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("220.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 220.s (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 |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 31.15 | ||
Character | 220.31 | ||
Dual form | 220.3.s.a.71.15 |
-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 .
0.445649 | + | 1.94972i | 0.222825 | + | 0.974859i | |||||
2.29101 | + | 3.15331i | 0.763671 | + | 1.05110i | 0.996900 | + | 0.0786807i | ||
−0.233229 | + | 0.972422i | ||||||||
−3.60279 | + | 1.73778i | −0.900698 | + | 0.434445i | |||||
0.690983 | + | 2.12663i | 0.138197 | + | 0.425325i | |||||
−5.12707 | + | 5.87209i | −0.854512 | + | 0.978682i | |||||
−5.93140 | + | 8.16388i | −0.847343 | + | 1.16627i | 0.137099 | + | 0.990557i | ||
−0.984442 | + | 0.175711i | ||||||||
−4.99376 | − | 6.24999i | −0.624220 | − | 0.781248i | |||||
−1.91346 | + | 5.88902i | −0.212607 | + | 0.654336i | |||||
−3.83838 | + | 2.29495i | −0.383838 | + | 0.229495i | |||||
4.27229 | − | 10.1364i | 0.388390 | − | 0.921495i | |||||
−13.7338 | − | 7.37944i | −1.14448 | − | 0.614953i | |||||
4.43010 | − | 13.6344i | 0.340777 | − | 1.04880i | −0.623029 | − | 0.782199i | ||
0.963806 | − | 0.266604i | ||||||||
−18.5606 | − | 7.92633i | −1.32576 | − | 0.566167i | |||||
−5.12286 | + | 7.05101i | −0.341524 | + | 0.470067i | |||||
9.96024 | − | 12.5217i | 0.622515 | − | 0.782608i | |||||
4.83979 | + | 14.8953i | 0.284694 | + | 0.876197i | 0.986490 | + | 0.163820i | ||
−0.701797 | + | 0.712377i | ||||||||
−12.3347 | − | 1.10627i | −0.685259 | − | 0.0614592i | |||||
15.4818 | + | 21.3089i | 0.814833 | + | 1.12152i | 0.990560 | + | 0.137082i | ||
−0.175727 | + | 0.984439i | ||||||||
−6.18508 | − | 6.46102i | −0.309254 | − | 0.323051i | |||||
−39.3321 | −1.87296 | |||||||||
21.6671 | + | 3.81245i | 0.984870 | + | 0.173293i | |||||
31.4161i | 1.36592i | 0.730457 | + | 0.682959i | ||||||
−0.730457 | + | 0.682959i | ||||||||
8.26736 | − | 30.0657i | 0.344473 | − | 1.25274i | |||||
−4.04508 | + | 2.93893i | −0.161803 | + | 0.117557i | |||||
28.5576 | + | 2.56126i | 1.09837 | + | 0.0985099i | |||||
10.4088 | − | 3.38201i | 0.385510 | − | 0.125260i | |||||
7.18260 | − | 39.7202i | 0.256521 | − | 1.41858i | |||||
−43.3341 | − | 31.4841i | −1.49428 | − | 1.08566i | −0.972591 | − | 0.232522i | ||
−0.521689 | − | 0.853136i | ||||||||
−16.0305 | − | 6.84585i | −0.534349 | − | 0.228195i | |||||
−3.32552 | − | 1.08053i | −0.107275 | − | 0.0348557i | 0.254888 | − | 0.966971i | ||
−0.362163 | + | 0.932115i | ||||||||
28.8526 | + | 13.8393i | 0.901644 | + | 0.432480i | |||||
41.7512 | − | 9.75089i | 1.26519 | − | 0.295481i | |||||
−26.8849 | + | 16.0743i | −0.790731 | + | 0.472774i | |||||
−21.4600 | − | 6.97278i | −0.613143 | − | 0.199222i | |||||
−3.34003 | − | 24.5421i | −0.0927786 | − | 0.681725i | |||||
18.1817 | + | 13.2098i | 0.491397 | + | 0.357021i | 0.805721 | − | 0.592295i | ||
−0.314325 | + | 0.949316i | ||||||||
−34.6469 | + | 39.6815i | −0.911760 | + | 1.04425i | |||||
53.1430 | − | 17.2672i | 1.36264 | − | 0.442749i | |||||
9.84079 | − | 14.9385i | 0.246020 | − | 0.373463i | |||||
−26.5611 | + | 19.2978i | −0.647831 | + | 0.470677i | −0.862532 | − | 0.506003i | ||
0.214701 | + | 0.976680i | ||||||||
−17.5283 | − | 76.6865i | −0.417341 | − | 1.82587i | |||||
− | 14.5302i | − | 0.337911i | −0.985624 | − | 0.168956i | ||||
0.985624 | − | 0.168956i | ||||||||
2.22275 | + | 43.9438i | 0.0505171 | + | 0.998723i | |||||
−13.8459 | −0.307687 | |||||||||
−61.2525 | + | 14.0006i | −1.33158 | + | 0.304360i | |||||
29.1619 | + | 40.1379i | 0.620465 | + | 0.853997i | 0.997387 | − | 0.0722482i | ||
−0.376922 | + | 0.926245i | ||||||||
62.3039 | + | 2.72027i | 1.29800 | + | 0.0566723i | |||||
−16.3255 | − | 50.2447i | −0.333173 | − | 1.02540i | |||||
−7.53276 | − | 6.57704i | −0.150655 | − | 0.131541i | |||||
−35.8816 | + | 49.3868i | −0.703561 | + | 0.968368i | |||||
7.73293 | + | 56.8206i | 0.148710 | + | 1.09270i | |||||
11.9385 | − | 36.7430i | 0.225255 | − | 0.693264i | −0.773010 | − | 0.634393i | ||
0.998266 | − | 0.0588709i | ||||||||
11.2326 | + | 18.7870i | 0.208012 | + | 0.347907i | |||||
24.5085 | + | 2.08145i | 0.445609 | + | 0.0378445i | |||||
80.6441 | − | 3.69727i | 1.44007 | − | 0.0660226i | |||||
−31.7245 | + | 97.6379i | −0.556570 | + | 1.71295i | |||||
42.0732 | − | 98.5201i | 0.725400 | − | 1.69862i | |||||
22.5711 | − | 31.0665i | 0.382562 | − | 0.526551i | −0.573699 | − | 0.819066i | ||
0.956261 | + | 0.292515i | ||||||||
6.20349 | − | 34.3057i | 0.103392 | − | 0.571762i | |||||
16.8808 | + | 51.9537i | 0.276734 | + | 0.851699i | 0.988755 | + | 0.149542i | ||
−0.712022 | + | 0.702158i | ||||||||
0.624706 | − | 6.96536i | 0.0100759 | − | 0.112345i | |||||
−36.7277 | − | 50.5514i | −0.582980 | − | 0.802403i | |||||
−14.1247 | + | 62.4219i | −0.220698 | + | 0.975342i | |||||
32.0565 | 0.493177 | |||||||||
37.6179 | + | 77.0575i | 0.569968 | + | 1.16754i | |||||
57.3989i | 0.856700i | 0.903613 | + | 0.428350i | ||||||
−0.903613 | + | 0.428350i | ||||||||
−43.3216 | − | 45.2544i | −0.637083 | − | 0.665505i | |||||
−99.0646 | + | 71.9747i | −1.43572 | + | 1.04311i | |||||
4.03131 | − | 44.9484i | 0.0575901 | − | 0.642120i | |||||
22.4655 | − | 7.29949i | 0.316416 | − | 0.102810i | −0.146504 | − | 0.989210i | ||
0.462919 | + | 0.886400i | ||||||||
46.3617 | − | 17.4493i | 0.643912 | − | 0.242351i | |||||
−34.4852 | − | 25.0550i | −0.472400 | − | 0.343219i | 0.325976 | − | 0.945378i | ||
−0.798376 | + | 0.602159i | ||||||||
−17.6526 | + | 41.3360i | −0.238549 | + | 0.558595i | |||||
−18.5347 | − | 6.02228i | −0.247129 | − | 0.0802971i | |||||
−92.8080 | − | 49.8676i | −1.22116 | − | 0.656152i | |||||
57.4120 | + | 95.0018i | 0.745611 | + | 1.23379i | |||||
57.3493 | + | 95.9187i | 0.735247 | + | 1.22973i | |||||
−66.8614 | − | 21.7246i | −0.846347 | − | 0.274995i | −0.146432 | − | 0.989221i | ||
−0.699915 | + | 0.714226i | ||||||||
33.5114 | + | 12.5294i | 0.418892 | + | 0.156618i | |||||
79.5966 | + | 57.8303i | 0.982675 | + | 0.713955i | |||||
−49.4621 | − | 43.1866i | −0.603196 | − | 0.526665i | |||||
118.311 | − | 38.4415i | 1.42543 | − | 0.463151i | 0.508108 | − | 0.861293i | ||
0.917324 | + | 0.398143i | ||||||||
141.706 | − | 68.3506i | 1.68697 | − | 0.813698i | |||||
−28.3326 | + | 20.5849i | −0.333325 | + | 0.242175i | |||||
28.3297 | − | 6.47537i | 0.329416 | − | 0.0752950i | |||||
− | 208.776i | − | 2.39973i | |||||||
−84.6874 | + | 23.9173i | −0.962357 | + | 0.271787i | |||||
153.780 | 1.72787 | 0.863934 | − | 0.503605i | ||||||
0.863934 | + | 0.503605i | ||||||||
−6.17043 | − | 26.9956i | −0.0685603 | − | 0.299951i | |||||
85.0332 | + | 117.038i | 0.934431 | + | 1.28613i | |||||
−54.5943 | − | 113.186i | −0.593416 | − | 1.23028i | |||||
−4.21157 | − | 12.9619i | −0.0452857 | − | 0.139375i | |||||
−65.2615 | + | 74.7448i | −0.694271 | + | 0.795157i | |||||
−34.6184 | + | 47.6482i | −0.364404 | + | 0.501560i | |||||
22.4619 | + | 122.687i | 0.233978 | + | 1.27799i | |||||
35.4826 | − | 109.204i | 0.365800 | − | 1.12582i | −0.583679 | − | 0.811985i | ||
0.949479 | − | 0.313831i | ||||||||
90.6875 | − | 54.2216i | 0.925383 | − | 0.553282i | |||||
51.5189 | + | 44.5553i | 0.520393 | + | 0.450053i | |||||
9.46640 | − | 17.6178i | 0.0946640 | − | 0.176178i | |||||
39.3577 | − | 121.130i | 0.389680 | − | 1.19931i | −0.543348 | − | 0.839507i | ||
0.933028 | − | 0.359804i | ||||||||
−112.281 | − | 47.9498i | −1.10079 | − | 0.470096i | |||||
−35.3665 | + | 48.6778i | −0.343364 | + | 0.472600i | −0.945420 | − | 0.325853i | ||
0.602056 | + | 0.798454i | ||||||||
−107.338 | + | 40.3991i | −1.03210 | + | 0.388453i | |||||
−27.1778 | − | 83.6448i | −0.258836 | − | 0.796617i | |||||
76.9589 | + | 6.90225i | 0.726027 | + | 0.0651156i | |||||
−34.2590 | − | 47.1535i | −0.320178 | − | 0.440687i | 0.618344 | − | 0.785908i | ||
−0.938522 | + | 0.345221i | ||||||||
−31.6234 | + | 30.2728i | −0.292810 | + | 0.280304i | |||||
42.1557 | 0.386750 | 0.193375 | − | 0.981125i | ||||||
0.193375 | + | 0.981125i | ||||||||
6.86397 | + | 48.7123i | 0.0623998 | + | 0.442839i | |||||
87.5961i | 0.789154i | |||||||||
43.1476 | + | 155.586i | 0.385247 | + | 1.38916i | |||||
164.771 | − | 119.713i | 1.45815 | − | 1.05941i | 0.474315 | − | 0.880355i | ||
0.983839 | − | 0.179056i | ||||||||
−204.504 | − | 18.3415i | −1.79390 | − | 0.160890i | |||||
−66.8103 | + | 21.7080i | −0.580959 | + | 0.188765i | |||||
210.836 | + | 38.1255i | 1.81755 | + | 0.328668i | |||||
71.8167 | + | 52.1779i | 0.613818 | + | 0.445965i | |||||
70.6297 | + | 30.1626i | 0.598557 | + | 0.255615i | |||||
−150.311 | − | 48.8389i | −1.26311 | − | 0.410411i | |||||
69.6511 | − | 3.19327i | 0.580425 | − | 0.0266106i | |||||
−84.4951 | − | 86.6116i | −0.698307 | − | 0.715799i | |||||
−93.7720 | + | 56.0658i | −0.768623 | + | 0.459556i | |||||
−121.703 | − | 39.5439i | −0.989459 | − | 0.321495i | |||||
13.8589 | − | 1.88611i | 0.111765 | − | 0.0152106i | |||||
−9.04508 | − | 6.57164i | −0.0723607 | − | 0.0525731i | |||||
82.1932 | − | 94.1369i | 0.652327 | − | 0.747118i | |||||
−46.6425 | + | 15.1551i | −0.367264 | + | 0.119331i | −0.486834 | − | 0.873494i | ||
0.119570 | + | 0.992826i | ||||||||
−128.000 | + | 0.279173i | −0.999998 | + | 0.00218104i | |||||
45.8181 | − | 33.2888i | 0.355179 | − | 0.258053i | |||||
14.2860 | + | 62.5011i | 0.109892 | + | 0.480778i | |||||
182.347i | 1.39196i | 0.718060 | + | 0.695981i | ||||||
−0.718060 | + | 0.695981i | ||||||||
−133.476 | + | 107.685i | −1.01118 | + | 0.815794i | |||||
−265.792 | −1.99844 | |||||||||
−111.912 | + | 25.5798i | −0.835161 | + | 0.190894i | |||||
14.3846 | + | 19.7986i | 0.106552 | + | 0.146657i | |||||
68.9270 | − | 104.632i | 0.506816 | − | 0.769356i | |||||
14.0829 | + | 43.3427i | 0.102795 | + | 0.316370i | 0.989207 | − | 0.146528i | ||
−0.886412 | + | 0.462898i | ||||||||
−184.478 | − | 161.073i | −1.33680 | − | 1.16719i | |||||
107.375 | − | 147.790i | 0.772485 | − | 1.06323i | −0.223587 | − | 0.974684i | ||
0.996072 | − | 0.0885501i | ||||||||
89.4332 | − | 12.1713i | 0.638808 | − | 0.0869379i | |||||
−59.7568 | + | 183.913i | −0.423807 | + | 1.30434i | |||||
24.2437 | + | 40.5484i | 0.170730 | + | 0.285552i | |||||
−119.278 | − | 103.156i | −0.834113 | − | 0.721368i | |||||
54.6822 | + | 82.6159i | 0.379738 | + | 0.573721i | |||||
37.0118 | − | 113.910i | 0.255253 | − | 0.785589i | |||||
33.4818 | − | 78.4021i | 0.229327 | − | 0.537001i | |||||
121.035 | − | 166.591i | 0.823368 | − | 1.13327i | |||||
−88.4605 | − | 15.9963i | −0.597706 | − | 0.108083i | |||||
5.08288 | + | 15.6435i | 0.0341133 | + | 0.104990i | 0.966663 | − | 0.256051i | ||
−0.932550 | + | 0.361041i | ||||||||
3.48178 | − | 38.8212i | 0.0232119 | − | 0.258808i | |||||
−138.149 | − | 190.145i | −0.914891 | − | 1.25924i | −0.965469 | − | 0.260520i | ||
0.0505772 | − | 0.998720i | ||||||||
55.8678 | − | 203.173i | 0.367551 | − | 1.33666i | |||||
−96.9798 | −0.633855 | |||||||||
−159.641 | + | 154.275i | −1.03663 | + | 1.00178i | |||||
− | 7.81877i | − | 0.0504437i | |||||||
−161.457 | + | 154.561i | −1.03498 | + | 0.990776i | |||||
−30.8588 | + | 22.4202i | −0.196553 | + | 0.142804i | −0.681709 | − | 0.731624i | ||
0.485156 | + | 0.874428i | ||||||||
12.5601 | − | 140.042i | 0.0794941 | − | 0.886344i | |||||
143.213 | − | 46.5328i | 0.900713 | − | 0.292659i | |||||
−9.49447 | + | 70.9215i | −0.0593405 | + | 0.443259i | |||||
−256.477 | − | 186.342i | −1.59303 | − | 1.15740i | |||||
−77.2806 | + | 180.963i | −0.477041 | + | 1.11706i | |||||
−142.320 | − | 46.2426i | −0.873129 | − | 0.283697i | −0.162028 | − | 0.986786i | ||
−0.711102 | + | 0.703089i | ||||||||
62.1588 | − | 115.683i | 0.379017 | − | 0.705385i | |||||
49.5859 | + | 82.0515i | 0.300520 | + | 0.497282i | |||||
127.675 | + | 213.541i | 0.769128 | + | 1.28639i | |||||
−15.8118 | − | 5.13756i | −0.0946814 | − | 0.0307638i | 0.261293 | − | 0.965259i | ||
−0.355975 | + | 0.934496i | ||||||||
196.415 | + | 245.825i | 1.16914 | + | 1.46325i | |||||
−29.5483 | − | 21.4681i | −0.174842 | − | 0.127030i | |||||
−52.7611 | − | 46.0670i | −0.310359 | − | 0.270982i | |||||
−155.112 | + | 50.3991i | −0.907090 | + | 0.294731i | |||||
25.2503 | + | 52.3492i | 0.146804 | + | 0.304356i | |||||
178.159 | − | 129.440i | 1.02982 | − | 0.748208i | 0.0615472 | − | 0.998104i | ||
0.968273 | + | 0.249896i | ||||||||
407.055 | − | 93.0410i | 2.33939 | − | 0.534718i | |||||
− | 50.4555i | − | 0.288317i | |||||||
−84.3728 | − | 154.458i | −0.479391 | − | 0.877601i | |||||
149.673 | 0.845610 | |||||||||
68.5321 | + | 299.828i | 0.385012 | + | 1.68443i | |||||
−26.8738 | − | 36.9886i | −0.150133 | − | 0.206640i | 0.727326 | − | 0.686292i | ||
−0.877459 | + | 0.479652i | ||||||||
49.8840 | − | 24.0612i | 0.277133 | − | 0.133673i | |||||
−9.53021 | − | 29.3310i | −0.0526531 | − | 0.162050i | 0.921272 | − | 0.388918i | ||
−0.973925 | + | 0.226869i | ||||||||
−190.296 | + | 217.949i | −1.04558 | + | 1.19752i | |||||
−125.152 | + | 172.257i | −0.683890 | + | 0.941293i | |||||
196.350 | − | 156.885i | 1.06712 | − | 0.852633i | |||||
−15.5290 | + | 47.7934i | −0.0839406 | + | 0.258342i | |||||
23.3951 | − | 13.9878i | 0.125780 | − | 0.0752034i | |||||
171.663 | + | 14.5789i | 0.917983 | + | 0.0779620i | |||||
−174.815 | − | 93.9315i | −0.929867 | − | 0.499636i | |||||
−34.1282 | + | 105.036i | −0.180573 | + | 0.555746i | |||||
−108.328 | − | 46.2617i | −0.570148 | − | 0.243483i | |||||
40.1389 | − | 55.2465i | 0.210152 | − | 0.289249i | −0.690909 | − | 0.722941i | ||
0.901061 | + | 0.433693i | ||||||||
−229.195 | + | 98.4699i | −1.19373 | + | 0.512864i | |||||
−1.87513 | − | 5.77106i | −0.00971570 | − | 0.0299019i | 0.946081 | − | 0.323930i | ||
−0.955797 | + | 0.294028i | ||||||||
228.730 | + | 20.5142i | 1.17902 | + | 0.105743i | |||||
73.4418 | + | 101.084i | 0.376625 | + | 0.518379i | |||||
146.132 | + | 152.651i | 0.745570 | + | 0.778833i | |||||
−299.121 | −1.51838 | −0.759191 | − | 0.650868i | ||||||
−0.759191 | + | 0.650868i | ||||||||
−63.9108 | + | 120.303i | −0.322782 | + | 0.607593i | |||||
284.631i | 1.43031i | 0.698968 | + | 0.715153i | ||||||
−0.698968 | + | 0.715153i | ||||||||
38.5684 | + | 10.6054i | 0.192842 | + | 0.0530271i | |||||
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253.710 | + | 22.7546i | 1.25599 | + | 0.112647i | |||||
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282.139 | − | 65.8930i | 1.34995 | − | 0.315277i | |||||
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76.6685 | − | 87.8094i | 0.358264 | − | 0.410324i | |||||
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224.530 | 1.01597 | |||||||||
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131.213 | − | 203.340i | 0.542202 | − | 0.840248i | |||||
284.983i | 1.17277i | |||||||||
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359.121 | − | 116.685i | 1.45393 | − | 0.472411i | |||||
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392.269 | + | 285.000i | 1.57538 | + | 1.14458i | |||||
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220.170 | + | 118.302i | 0.873689 | + | 0.469450i | |||||
318.448 | + | 134.219i | 1.25869 | + | 0.530508i | |||||
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140.080i | 0.532624i | 0.963887 | + | 0.266312i | ||||||
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86.3880 | 0.325992 | |||||||||
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336.000 | + | 143.489i | 1.20863 | + | 0.516149i | |||||
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167.783 | + | 30.3402i | 0.574600 | + | 0.103905i | |||||
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378.744 | + | 161.743i | 1.28824 | + | 0.550147i | |||||
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428.341 | + | 139.176i | 1.43258 | + | 0.465473i | |||||
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118.623 | + | 86.1844i | 0.394095 | + | 0.286327i | |||||
309.164 | − | 354.089i | 1.02372 | − | 1.17248i | |||||
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154.549 | + | 258.488i | 0.486002 | + | 0.812856i | |||||
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22.1505 | + | 68.1722i | 0.0681553 | + | 0.209761i | |||||
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96.5792 | + | 132.930i | 0.295349 | + | 0.406514i | |||||
253.250 | + | 69.6380i | 0.772105 | + | 0.212311i | |||||
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370.611 | + | 269.265i | 1.09974 | + | 0.799005i | 0.981017 | − | 0.193923i | ||
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754.987 | + | 245.310i | 2.22710 | + | 0.723628i | |||||
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331.768 | + | 289.674i | 0.958866 | + | 0.837209i | |||||
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362.807 | + | 752.178i | 1.04255 | + | 2.16143i | |||||
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263.548 | − | 233.337i | 0.748717 | − | 0.662890i | |||||
45.2529 | 0.128195 | 0.0640975 | − | 0.997944i | ||||||
0.0640975 | + | 0.997944i | ||||||||
66.7017 | + | 291.820i | 0.188423 | + | 0.824350i | |||||
31.0466 | + | 42.7320i | 0.0874552 | + | 0.120372i | |||||
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0.912959 | + | 0.408052i | ||||||||
69.1432 | + | 86.5368i | 0.192065 | + | 0.240380i | |||||
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79.5337 | − | 464.867i | 0.219101 | − | 1.28063i | |||||
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29.4539 | − | 90.6497i | 0.0806956 | − | 0.248355i | |||||
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0.379448 | + | 0.925213i | ||||||||
393.384 | + | 312.912i | 1.06898 | + | 0.850304i | |||||
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229.153 | + | 315.402i | 0.617663 | + | 0.850141i | |||||
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48.0767 | + | 341.191i | 0.128547 | + | 0.912276i | |||||
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105.234 | − | 382.700i | 0.279877 | − | 1.01782i | |||||
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125.603 | + | 53.6390i | 0.328804 | + | 0.140416i | |||||
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85.5685 | + | 27.8029i | 0.221107 | + | 0.0718421i | |||||
61.9364 | + | 455.101i | 0.159630 | + | 1.17294i | |||||
101.467 | + | 73.7198i | 0.260840 | + | 0.189511i | 0.710517 | − | 0.703680i | ||
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77.6330 | 0.195549 | 0.0977746 | − | 0.995209i | ||||||
0.0977746 | + | 0.995209i | ||||||||
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0.112243 | − | 0.993681i | ||||||||
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68.7006 | + | 504.803i | 0.170051 | + | 1.24951i | |||||
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554.753 | + | 927.843i | 1.36639 | + | 2.28533i | |||||
211.577 | − | 127.862i | 0.519846 | − | 0.314157i | |||||
487.851 | − | 22.3664i | 1.19571 | − | 0.0548195i | |||||
23.9146 | − | 73.6017i | 0.0584710 | − | 0.179955i | −0.917555 | − | 0.397609i | ||
0.976026 | + | 0.217653i | ||||||||
57.6642 | − | 135.029i | 0.140644 | − | 0.329338i | |||||
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42.8269 | − | 236.835i | 0.103949 | − | 0.574843i | |||||
119.745 | + | 368.536i | 0.289938 | + | 0.892339i | |||||
34.7545 | − | 387.507i | 0.0839482 | − | 0.936007i | |||||
163.502 | + | 225.041i | 0.393980 | + | 0.542266i | |||||
316.512 | − | 332.079i | 0.760845 | − | 0.798268i | |||||
712.024 | 1.70749 | |||||||||
254.208 | + | 520.727i | 0.608153 | + | 1.24576i | |||||
40.6843i | 0.0970985i | 0.998821 | + | 0.0485493i | ||||||
−0.998821 | + | 0.0485493i | ||||||||
243.272 | + | 254.126i | 0.579220 | + | 0.605061i | |||||
475.690 | − | 345.609i | 1.12991 | − | 0.820924i | 0.144224 | − | 0.989545i | ||
0.985681 | + | 0.168621i | ||||||||
22.5610 | − | 251.551i | 0.0534620 | − | 0.596092i | |||||
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0.986695 | − | 0.162584i | ||||||||
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327.130 | 0.741792 | |||||||||
100.062 | + | 437.771i | 0.226384 | + | 0.990432i | |||||
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768.660 | − | 289.303i | 1.68566 | − | 0.634436i | |||||
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853.193 | 1.85074 | 0.925372 | − | 0.379060i | ||||||
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190.986i | 0.412496i | 0.978500 | + | 0.206248i | ||||||
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296.286 | − | 339.340i | 0.619846 | − | 0.709917i | |||||
679.143 | − | 220.667i | 1.41784 | − | 0.460683i | 0.502922 | − | 0.864332i | ||
0.914914 | + | 0.403649i | ||||||||
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454.930 | + | 165.210i | 0.939939 | + | 0.341343i | |||||
256.754 | 0.529390 | |||||||||
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0.177035 | − | 0.984205i | ||||||||
240.411 | − | 364.949i | 0.492646 | − | 0.747846i | |||||
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507.191 | − | 69.0256i | 1.03088 | − | 0.140296i | |||||
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387.546 | + | 648.183i | 0.784505 | + | 1.31211i | |||||
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0.712328 | + | 0.701847i | ||||||||
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284.795 | 0.563950 | |||||||||
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0.978143 | − | 0.207932i | ||||||||
24.3871 | − | 271.912i | 0.0478179 | − | 0.533161i | |||||
409.091 | − | 132.922i | 0.800570 | − | 0.260121i | |||||
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499.682 | + | 436.284i | 0.957245 | + | 0.835794i | |||||
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0.423026 | + | 0.906118i | ||||||||
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293.754 | − | 619.918i | 0.556352 | − | 1.17409i | |||||
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38.4988 | + | 168.432i | 0.0726392 | + | 0.317796i | |||||
139.762 | + | 192.366i | 0.263206 | + | 0.362272i | |||||
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145.446 | + | 447.636i | 0.272882 | + | 0.839843i | |||||
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76.6056 | − | 105.439i | 0.143188 | − | 0.197081i | |||||
358.742 | − | 286.636i | 0.669295 | − | 0.534770i | |||||
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227.278 | + | 312.821i | 0.415499 | + | 0.571885i | 0.964549 | − | 0.263904i | ||
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702.989 | + | 63.0493i | 1.26893 | + | 0.113807i | |||||
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0.0695761 | + | 0.997577i | ||||||||
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347.310 | + | 574.706i | 0.619091 | + | 1.02443i | |||||
144.884 | − | 86.6251i | 0.257800 | − | 0.154137i | |||||
909.437 | + | 295.494i | 1.61534 | + | 0.524856i | 0.970836 | − | 0.239744i | ||
0.644505 | + | 0.764600i | ||||||||
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368.440 | + | 267.687i | 0.652106 | + | 0.473783i | |||||
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247.679 | − | 179.950i | 0.435289 | − | 0.316256i | −0.348471 | − | 0.937319i | ||
0.783760 | + | 0.621064i | ||||||||
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0.999882 | − | 0.0153529i | ||||||||
608.996 | + | 164.369i | 1.06468 | + | 0.287359i | |||||
266.168 | 0.464517 | |||||||||
645.949 | − | 147.645i | 1.12535 | − | 0.257222i | |||||
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0.762733 | − | 0.646714i | ||||||||
65.8440 | + | 57.4900i | 0.113917 | + | 0.0994636i | |||||
13.9020 | − | 19.1344i | 0.0240103 | − | 0.0330474i | |||||
64.6057 | + | 474.714i | 0.111389 | + | 0.818473i | |||||
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459.335 | + | 768.254i | 0.789236 | + | 1.32002i | |||||
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15.6177 | + | 340.651i | 0.0267427 | + | 0.583306i | |||||
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346.503 | − | 96.0936i | 0.585309 | − | 0.162320i | |||||
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238.422 | − | 33.5957i | 0.401384 | − | 0.0565584i | |||||
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828.151 | + | 444.982i | 1.37111 | + | 0.736725i | |||||
125.806 | − | 239.537i | 0.207944 | − | 0.395929i | |||||
509.500 | + | 852.156i | 0.840759 | + | 1.40620i | |||||
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151.790 | + | 829.076i | 0.249654 | + | 1.36361i | |||||
1704.42 | + | 1238.34i | 2.79872 | + | 2.03339i | |||||
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676.447 | − | 219.791i | 1.10711 | − | 0.359723i | |||||
349.398 | − | 168.530i | 0.570912 | − | 0.275375i | |||||
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0.0934189 | + | 0.995627i | ||||||||
473.522 | − | 108.234i | 0.771209 | − | 0.176276i | |||||
− | 286.142i | − | 0.465272i | |||||||
307.058 | − | 833.241i | 0.498470 | − | 1.35266i | |||||
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−1.00000 | 0.000844784i | |||||||||
13.5873 | + | 28.1694i | 0.0219150 | + | 0.0454345i | |||||
106.250 | + | 327.003i | 0.171094 | + | 0.526575i | |||||
293.360 | − | 335.989i | 0.471640 | − | 0.540175i | |||||
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313.102 | − | 837.427i | 0.501765 | − | 1.34203i | |||||
7.72542 | − | 23.7764i | 0.0123607 | − | 0.0380423i | |||||
328.581 | − | 196.457i | 0.524890 | − | 0.313829i | |||||
854.165 | + | 738.711i | 1.36231 | + | 1.17817i | |||||
72.2163 | − | 134.401i | 0.114994 | − | 0.214014i | |||||
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256.988 | + | 109.747i | 0.407918 | + | 0.174202i | |||||
621.792 | − | 855.823i | 0.985407 | − | 1.35630i | 0.0515422 | − | 0.998671i | ||
0.933865 | − | 0.357626i | ||||||||
198.112 | + | 526.371i | 0.313468 | + | 0.832865i | |||||
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246.581 | + | 22.1152i | 0.388928 | + | 0.0348820i | |||||
−64.4584 | − | 88.7194i | −0.101509 | − | 0.139716i | |||||
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−757.382 | −1.18898 | |||||||||
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146.267i | 0.228900i | |||||||||
−89.0393 | − | 272.015i | −0.139124 | − | 0.425023i | |||||
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0.277460 | + | 0.960737i | ||||||||
452.539 | + | 40.5871i | 0.704889 | + | 0.0632197i | |||||
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−0.144391 | + | 0.989521i | ||||||||
1247.85 | + | 225.649i | 1.93766 | + | 0.350387i | |||||
102.452 | + | 74.4361i | 0.158841 | + | 0.115405i | |||||
−758.753 | − | 324.027i | −1.17454 | − | 0.501590i | |||||
1052.80 | + | 342.075i | 1.62720 | + | 0.528710i | 0.973626 | − | 0.228151i | ||
0.653576 | + | 0.756861i | ||||||||
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213.535 | − | 155.142i | 0.325016 | − | 0.236138i | |||||
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125.542i | 0.190504i | 0.995453 | + | 0.0952518i | ||||||
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79.5672 | − | 18.1868i | 0.120192 | − | 0.0274725i | |||||
514.402 | + | 708.014i | 0.775870 | + | 1.06789i | |||||
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178.166 | − | 548.338i | 0.266317 | − | 0.819638i | |||||
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0.998389 | − | 0.0567455i | ||||||||
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0.346709 | − | 0.937973i | ||||||||
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681.068 | + | 937.409i | 1.00305 | + | 1.38057i | |||||
270.142 | + | 74.2827i | 0.397267 | + | 0.109239i | |||||
1062.65 | 1.56042 | |||||||||
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0.886476 | − | 0.462775i | ||||||||
471.255 | − | 451.129i | 0.688970 | − | 0.659545i | |||||
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215.070 | − | 503.615i | 0.311695 | − | 0.729877i | |||||
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305.911 | − | 69.9225i | 0.435771 | − | 0.0996047i | |||||
591.943i | 0.842024i | |||||||||
572.392 | + | 409.858i | 0.813056 | + | 0.582185i | |||||
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20.1669 | + | 88.2303i | 0.0285650 | + | 0.124972i | |||||
755.448 | + | 1039.78i | 1.06853 | + | 1.47070i | |||||
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255.873 | − | 352.179i | 0.359878 | − | 0.495330i | |||||
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33.9460 | − | 104.475i | 0.0476100 | − | 0.146529i | |||||
1057.44 | − | 632.237i | 1.48101 | − | 0.885487i | |||||
136.955 | − | 324.939i | 0.191545 | − | 0.454460i | |||||
161.099 | + | 86.5616i | 0.224998 | + | 0.120896i | |||||
271.295 | − | 834.961i | 0.378376 | − | 1.16452i | |||||
272.712 | + | 116.462i | 0.379821 | + | 0.162203i | |||||
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0.999813 | + | 0.0193288i | ||||||||
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85.3061 | + | 89.1120i | 0.117826 | + | 0.123083i | |||||
267.820 | 0.369406 | |||||||||
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839.149i | 1.15426i | 0.816651 | + | 0.577132i | ||||||
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306.851 | − | 1115.92i | 0.421499 | − | 1.53285i | |||||
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189.867 | + | 17.0287i | 0.260092 | + | 0.0233270i | |||||
216.432 | − | 70.3230i | 0.296077 | − | 0.0962012i | |||||
151.552 | − | 838.092i | 0.207038 | − | 1.14493i | |||||
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437.909 | + | 142.285i | 0.595795 | + | 0.193585i | |||||
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348.970 | − | 208.648i | 0.472859 | − | 0.282720i | |||||
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0.598959 | + | 0.800780i | ||||||||
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0.843732 | + | 0.536764i | ||||||||
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770.291i | 1.03118i | |||||||||
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588.160 | 0.785260 | |||||||||
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793.054 | + | 34.6258i | 1.05459 | + | 0.0460449i | |||||
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308.910 | − | 425.178i | 0.409152 | − | 0.563149i | |||||
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306.335 | + | 1311.66i | 0.403603 | + | 1.72814i | |||||
470.676 | − | 21.5790i | 0.619311 | − | 0.0283934i | |||||
333.154 | − | 1025.34i | 0.437784 | − | 1.34736i | −0.452423 | − | 0.891804i | ||
0.890207 | − | 0.455557i | ||||||||
150.147 | − | 351.591i | 0.197044 | − | 0.461405i | |||||
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11.4910 | − | 128.122i | 0.0150012 | − | 0.167261i | |||||
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654.624 | − | 753.058i | 0.852375 | − | 0.980544i | |||||
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1107.94i | 1.43701i | |||||||||
16.7845 | + | 17.5334i | 0.0217416 | + | 0.0227116i | |||||
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0.428609 | + | 0.903490i | ||||||||
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16.6276 | − | 5.40264i | 0.0214550 | − | 0.00697114i | |||||
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21.9882 | − | 258.906i | 0.0281540 | − | 0.331506i | |||||
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1077.67 | − | 519.807i | 1.36760 | − | 0.659654i | |||||
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306.497 | − | 70.0564i | 0.387971 | − | 0.0886790i | |||||
2055.24i | 2.59828i | |||||||||
21.1966 | − | 544.491i | 0.0267634 | − | 0.687489i | |||||
783.142 | 0.987569 | |||||||||
34.5971 | + | 151.362i | 0.0435732 | + | 0.190633i | |||||
197.916 | + | 272.408i | 0.248951 | + | 0.342651i | |||||
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0.729156 | − | 0.684348i | ||||||||
1362.74 | − | 1560.76i | 1.70769 | − | 1.95584i | |||||
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1253.29 | − | 749.336i | 1.56271 | − | 0.934334i | |||||
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423.572 | − | 788.305i | 0.526830 | − | 0.980479i | |||||
219.058 | − | 674.190i | 0.272121 | − | 0.837503i | |||||
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444.042 | + | 1366.62i | 0.548878 | + | 1.68927i | 0.711588 | + | 0.702597i | ||
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112.426 | + | 154.741i | 0.138627 | + | 0.190803i | 0.872686 | − | 0.488283i | ||
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343.583 | + | 355.534i | 0.422093 | + | 0.436775i | |||||
− | 334.615i | − | 0.410570i | |||||||
261.018 | + | 941.203i | 0.319876 | + | 1.15344i | |||||
309.622 | − | 224.954i | 0.378975 | − | 0.275341i | |||||
154.160 | + | 13.8262i | 0.188460 | + | 0.0169025i | |||||
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288.966 | + | 52.2535i | 0.352397 | + | 0.0637238i | |||||
998.232 | + | 725.258i | 1.21587 | + | 0.883384i | 0.995751 | − | 0.0920884i | ||
0.220123 | + | 0.975472i | ||||||||
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660.377 | + | 214.570i | 0.802403 | + | 0.260716i | 0.681377 | − | 0.731933i | ||
0.121026 | + | 0.992649i | ||||||||
480.848 | − | 22.0453i | 0.583553 | − | 0.0267540i | |||||
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771.017 | − | 104.931i | 0.931180 | − | 0.126728i | |||||
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1308.20 | − | 425.059i | 1.57424 | − | 0.511503i | |||||
788.514 | + | 469.117i | 0.947733 | + | 0.563843i | |||||
669.401 | − | 486.348i | 0.803602 | − | 0.583851i | |||||
317.313 | + | 1388.25i | 0.380471 | + | 1.66456i | |||||
− | 37.1757i | − | 0.0445218i | |||||||
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−0.103991 | − | 0.994578i | ||||||||
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626.715 | + | 1928.83i | 0.745202 | + | 2.29350i | |||||
885.831 | + | 773.441i | 1.05206 | + | 0.918576i | |||||
193.367 | − | 266.147i | 0.229380 | − | 0.315714i | |||||
500.507 | − | 68.1159i | 0.593018 | − | 0.0807060i | |||||
25.2372 | − | 77.6723i | 0.0298666 | − | 0.0919198i | |||||
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1208.26 | − | 176.079i | 1.42652 | − | 0.207886i | |||||
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61.5103 | − | 144.035i | 0.0723651 | − | 0.169453i | |||||
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0.660622 | − | 0.750719i | ||||||||
98.4852 | − | 1098.09i | 0.115322 | − | 1.28582i | |||||
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−0.300993 | + | 0.953626i | ||||||||
1217.29 | − | 171.526i | 1.41875 | − | 0.199914i | |||||
1004.50i | 1.16938i | 0.811256 | + | 0.584691i | ||||||
−0.811256 | + | 0.584691i | ||||||||
−93.8798 | + | 89.8703i | −0.109163 | + | 0.104500i | |||||
1044.70 | − | 759.022i | 1.21336 | − | 0.881558i | |||||
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0.197271 | + | 0.980349i | ||||||||
347.125 | + | 46.4707i | 0.401765 | + | 0.0537855i | |||||
398.375 | + | 289.437i | 0.460549 | + | 0.334609i | |||||
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162.012 | + | 52.6408i | 0.186865 | + | 0.0607160i | |||||
−66.8047 | + | 124.329i | −0.0769639 | + | 0.143237i | |||||
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479.131 | + | 801.363i | 0.550726 | + | 0.921107i | |||||
782.602 | + | 254.283i | 0.898509 | + | 0.291943i | |||||
−210.516 | − | 263.473i | −0.241417 | − | 0.302148i | |||||
575.211 | + | 417.915i | 0.658890 | + | 0.478712i | |||||
−1246.64 | − | 1088.47i | −1.42636 | − | 1.24539i | |||||
107.300 | − | 34.8639i | 0.122629 | − | 0.0398445i | |||||
288.721 | + | 598.581i | 0.329590 | + | 0.683312i | |||||
264.570 | − | 192.222i | 0.301677 | − | 0.219181i | −0.426640 | − | 0.904421i | ||
0.728317 | + | 0.685240i | ||||||||
278.319 | − | 63.6158i | 0.316992 | − | 0.0724554i | |||||
389.876i | 0.443545i | |||||||||
270.174 | − | 286.157i | 0.307016 | − | 0.325179i | |||||
−1330.90 | −1.51066 | −0.755332 | − | 0.655342i | ||||||
−0.755332 | + | 0.655342i | ||||||||
145.785 | + | 637.812i | 0.165290 | + | 0.723143i | |||||
43.4139 | + | 59.7541i | 0.0491663 | + | 0.0676716i | 0.832892 | − | 0.553435i | ||
−0.783726 | + | 0.621107i | ||||||||
−808.937 | + | 390.185i | −0.915087 | + | 0.441385i | |||||
103.421 | + | 318.299i | 0.116860 | + | 0.359659i | |||||
−374.813 | + | 429.278i | −0.423040 | + | 0.484513i | |||||
−302.036 | + | 415.718i | −0.340515 | + | 0.468678i | −0.944592 | − | 0.328248i | ||
0.604077 | + | 0.796926i | ||||||||
547.475 | − | 437.434i | 0.616525 | − | 0.492606i | |||||
152.932 | − | 470.675i | 0.172026 | − | 0.529443i | |||||
−590.268 | + | 352.918i | −0.663222 | + | 0.396537i | |||||
926.254 | − | 559.759i | 1.03957 | − | 0.628237i | |||||
521.213 | + | 280.058i | 0.584319 | + | 0.313966i | |||||
−403.815 | + | 1242.81i | −0.452200 | + | 1.39173i | |||||
−117.920 | − | 50.3581i | −0.131902 | − | 0.0563290i | |||||
60.0917 | − | 82.7091i | 0.0671415 | − | 0.0924124i | |||||
756.939 | − | 1046.63i | 0.844798 | − | 1.16811i | |||||
542.468 | + | 1669.55i | 0.604758 | + | 1.86125i | |||||
−828.794 | − | 74.3325i | −0.922933 | − | 0.0827756i | |||||
110.089 | + | 151.525i | 0.122457 | + | 0.168548i | |||||
85.6381 | + | 89.4588i | 0.0951535 | + | 0.0993986i | |||||
605.080 | 0.671565 | |||||||||
−649.074 | + | 316.864i | −0.719595 | + | 0.351291i | |||||
571.503i | 0.632894i | |||||||||
−1571.04 | − | 431.999i | −1.73787 | − | 0.477875i | |||||
55.7908 | − | 40.5344i | 0.0616473 | − | 0.0447894i | |||||
1824.85 | + | 163.666i | 2.01418 | + | 0.180647i | |||||
874.489 | − | 284.139i | 0.964156 | − | 0.313273i | 0.215701 | − | 0.976459i | ||
0.748454 | + | 0.663186i | ||||||||
−194.055 | + | 1073.13i | −0.213716 | + | 1.18187i | |||||
638.030 | + | 463.556i | 0.701904 | + | 0.509963i | |||||
−594.987 | − | 254.090i | −0.653832 | − | 0.279220i | |||||
−288.635 | − | 93.7832i | −0.316833 | − | 0.102945i | 0.146283 | − | 0.989243i | ||
−0.463117 | + | 0.886297i | ||||||||
906.612 | + | 1369.74i | 0.994092 | + | 1.50191i | |||||
115.797 | − | 1363.48i | 0.126832 | − | 1.49341i | |||||
−344.821 | + | 206.167i | −0.377265 | + | 0.225565i | |||||
−452.804 | − | 147.125i | −0.494867 | − | 0.160792i | |||||
−30.7353 | − | 225.839i | −0.0335539 | − | 0.246549i | |||||
−1488.66 | − | 1081.57i | −1.62340 | − | 1.17947i | |||||
−225.475 | + | 258.239i | −0.245615 | + | 0.281306i | |||||
412.101 | − | 133.900i | 0.448423 | − | 0.145701i | −0.0760956 | − | 0.997101i | ||
0.524518 | + | 0.851399i | ||||||||
469.310 | + | 309.159i | 0.510119 | + | 0.336043i | |||||
765.835 | − | 556.412i | 0.831525 | − | 0.604138i | |||||
380.225 | + | 1663.48i | 0.412391 | + | 1.80421i | |||||
− | 338.642i | − | 0.366893i | |||||||
−87.4256 | − | 1728.40i | −0.0946165 | − | 1.87057i | |||||
−112.369 | −0.121480 | |||||||||
−372.368 | + | 85.1127i | −0.402125 | + | 0.0919143i | |||||
−218.992 | − | 301.417i | −0.236238 | − | 0.325154i | |||||
−814.583 | − | 1508.11i | −0.877783 | − | 1.62512i | |||||
102.465 | + | 315.354i | 0.110296 | + | 0.339455i | 0.990937 | − | 0.134329i | ||
−0.880641 | + | 0.473784i | ||||||||
45.9125 | + | 40.0874i | 0.0493683 | + | 0.0431047i | |||||
817.911 | − | 1125.76i | 0.878530 | − | 1.20919i | |||||
−99.8326 | − | 733.557i | −0.107117 | − | 0.787079i | |||||
268.616 | − | 826.715i | 0.287906 | − | 0.886082i | |||||
−645.579 | − | 1079.75i | −0.691198 | − | 1.15605i | |||||
87.6122 | + | 375.137i | 0.0937029 | + | 0.401216i | |||||
−32.5244 | − | 709.417i | −0.0347483 | − | 0.757924i | |||||
92.0134 | − | 283.188i | 0.0982000 | − | 0.302229i | −0.889874 | − | 0.456206i | ||
0.988074 | + | 0.153977i | ||||||||
454.963 | − | 1065.36i | 0.485035 | − | 1.13577i | |||||
438.537 | − | 603.595i | 0.467026 | − | 0.642806i | |||||
78.9631 | − | 436.671i | 0.0840033 | − | 0.464544i | |||||
120.205 | + | 369.952i | 0.127741 | + | 0.393148i | 0.994391 | − | 0.105770i | ||
−0.866649 | + | 0.498918i | ||||||||
26.5615 | − | 296.155i | 0.0281969 | − | 0.314390i | |||||
−606.260 | − | 834.446i | −0.642906 | − | 0.884884i | |||||
−164.192 | − | 592.059i | −0.173933 | − | 0.627181i | |||||
−246.954 | −0.261327 | |||||||||
55.3956 | − | 314.828i | 0.0585577 | − | 0.332799i | |||||
− | 455.871i | − | 0.481384i | −0.970602 | − | 0.240692i | ||||
0.970602 | − | 0.240692i | ||||||||
757.946 | + | 791.761i | 0.799521 | + | 0.835191i | |||||
−494.383 | + | 359.190i | −0.520952 | + | 0.378494i | |||||
23.5286 | − | 262.340i | 0.0247669 | − | 0.276147i | |||||
458.864 | − | 149.094i | 0.482506 | − | 0.156776i | |||||
445.373 | + | 1183.33i | 0.467829 | + | 1.24299i | |||||
1198.70 | + | 870.908i | 1.25782 | + | 0.913859i | 0.998649 | − | 0.0519722i | ||
0.259171 | + | 0.965831i | ||||||||
−187.905 | + | 440.005i | −0.196966 | + | 0.461221i | |||||
145.224 | + | 47.1862i | 0.152067 | + | 0.0494096i | |||||
793.658 | + | 426.448i | 0.830186 | + | 0.446075i | |||||
−2116.25 | − | 891.952i | −2.21134 | − | 0.932029i | |||||
732.898 | + | 1225.80i | 0.765029 | + | 1.27954i | |||||
−437.376 | − | 142.112i | −0.456075 | − | 0.148188i | |||||
−367.779 | − | 419.372i | −0.383103 | − | 0.436846i | |||||
−767.574 | − | 557.675i | −0.798724 | − | 0.580307i | |||||
485.391 | + | 423.807i | 0.504564 | + | 0.440547i | |||||
343.241 | − | 111.526i | 0.356429 | − | 0.115811i | |||||
1636.58 | − | 789.392i | 1.69770 | − | 0.818871i | |||||
10.9772 | − | 7.97541i | 0.0113753 | − | 0.00826467i | |||||
2409.19 | − | 550.672i | 2.49399 | − | 0.570054i | |||||
− | 455.350i | − | 0.470889i | −0.971888 | − | 0.235445i | ||||
0.971888 | − | 0.235445i | ||||||||
−119.373 | + | 960.611i | −0.123319 | + | 0.992367i | |||||
−1607.89 | −1.65933 | |||||||||
114.422 | + | 500.598i | 0.117961 | + | 0.516081i | |||||
−954.786 | − | 1314.15i | −0.983301 | − | 1.35340i | −0.935032 | − | 0.354564i | ||
−0.0482698 | − | 0.998834i | ||||||||
−495.238 | − | 1026.73i | −0.509504 | − | 1.05631i | |||||
569.649 | + | 1753.20i | 0.585456 | + | 1.80185i | |||||
886.826 | − | 1015.69i | 0.910499 | − | 1.04281i | |||||
−164.221 | + | 226.031i | −0.168432 | + | 0.231826i | |||||
818.686 | + | 306.094i | 0.838818 | + | 0.313621i | |||||
437.833 | − | 1347.51i | 0.448140 | − | 1.37923i | −0.430862 | − | 0.902418i | ||
0.879003 | − | 0.476817i | ||||||||
1001.23 | − | 598.628i | 1.02375 | − | 0.612094i | |||||
656.993 | − | 1558.79i | 0.671086 | − | 1.59222i | |||||
−223.658 | + | 416.247i | −0.228222 | + | 0.424742i | |||||
−80.6632 | + | 248.256i | −0.0822255 | + | 0.253064i | |||||
497.350 | + | 212.394i | 0.506466 | + | 0.216287i | |||||
241.022 | − | 331.739i | 0.245191 | − | 0.337476i | −0.668629 | − | 0.743596i | ||
0.913820 | + | 0.406120i | ||||||||
360.610 | + | 958.118i | 0.366473 | + | 0.973697i | |||||
−206.688 | − | 636.119i | −0.209835 | − | 0.645806i | |||||
1671.12 | + | 149.878i | 1.69485 | + | 0.152006i | |||||
−1147.00 | − | 1578.71i | −1.16211 | − | 1.59950i | |||||
−1091.06 | + | 1044.47i | −1.10432 | + | 1.05715i | |||||
456.482 | 0.461559 | |||||||||
−300.002 | − | 52.7869i | −0.303032 | − | 0.0533201i | |||||
− | 1155.69i | − | 1.16618i | −0.812407 | − | 0.583090i | ||||
0.812407 | − | 0.583090i | ||||||||
−80.9961 | − | 77.1991i | −0.0816493 | − | 0.0778216i | |||||
128.685 | − | 93.4953i | 0.129592 | − | 0.0941544i | |||||
−474.831 | − | 42.5864i | −0.477697 | − | 0.0428435i | |||||
−605.303 | + | 196.675i | −0.608345 | + | 0.197663i | |||||
−1908.53 | − | 345.119i | −1.91620 | − | 0.346505i | |||||
890.773 | + | 647.184i | 0.893453 | + | 0.649132i | 0.936776 | − | 0.349929i | ||
−0.0433229 | + | 0.999061i | ||||||||
−273.710 | − | 116.888i | −0.274258 | − | 0.117123i | |||||
233.924 | + | 76.0066i | 0.234158 | + | 0.0760827i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 220.3.s.a.31.15 | yes | 96 | |
4.3 | odd | 2 | inner | 220.3.s.a.31.5 | ✓ | 96 | |
11.5 | even | 5 | inner | 220.3.s.a.71.5 | yes | 96 | |
44.27 | odd | 10 | inner | 220.3.s.a.71.15 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
220.3.s.a.31.5 | ✓ | 96 | 4.3 | odd | 2 | inner | |
220.3.s.a.31.15 | yes | 96 | 1.1 | even | 1 | trivial | |
220.3.s.a.71.5 | yes | 96 | 11.5 | even | 5 | inner | |
220.3.s.a.71.15 | yes | 96 | 44.27 | odd | 10 | inner |