Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [55,3,Mod(6,55)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(55, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 9]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("55.6");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 55.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 | 6.3 | ||
Root | of defining polynomial | ||
Character | 55.6 | ||
Dual form | 55.3.i.c.46.3 |
-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 .
1.57580 | − | 0.512008i | 0.787900 | − | 0.256004i | 0.112690 | − | 0.993630i | ||
0.675209 | + | 0.737626i | ||||||||
2.41303 | + | 1.75317i | 0.804342 | + | 0.584389i | 0.912185 | − | 0.409779i | ||
−0.107843 | + | 0.994168i | ||||||||
−1.01508 | + | 0.737497i | −0.253769 | + | 0.184374i | |||||
0.690983 | − | 2.12663i | 0.138197 | − | 0.425325i | |||||
4.70008 | + | 1.52715i | 0.783347 | + | 0.254525i | |||||
−1.31003 | − | 1.80310i | −0.187147 | − | 0.257586i | 0.705126 | − | 0.709082i | ||
−0.892273 | + | 0.451496i | ||||||||
−5.11754 | + | 7.04369i | −0.639693 | + | 0.880462i | |||||
−0.0320482 | − | 0.0986342i | −0.00356091 | − | 0.0109594i | |||||
− | 3.70493i | − | 0.370493i | |||||||
−0.949049 | − | 10.9590i | −0.0862772 | − | 0.996271i | |||||
−3.74236 | −0.311864 | |||||||||
−1.75040 | + | 0.568738i | −0.134646 | + | 0.0437491i | −0.375565 | − | 0.926796i | ||
0.240919 | + | 0.970545i | ||||||||
−2.98754 | − | 2.17058i | −0.213396 | − | 0.155041i | |||||
5.39569 | − | 3.92020i | 0.359713 | − | 0.261347i | |||||
−2.90689 | + | 8.94649i | −0.181681 | + | 0.559156i | |||||
7.97437 | + | 2.59103i | 0.469080 | + | 0.152413i | 0.534013 | − | 0.845476i | ||
−0.0649328 | + | 0.997890i | ||||||||
−0.101003 | − | 0.139019i | −0.00561128 | − | 0.00772326i | |||||
−15.6197 | + | 21.4986i | −0.822088 | + | 1.13151i | 0.167257 | + | 0.985913i | ||
−0.989344 | + | 0.145594i | ||||||||
0.866979 | + | 2.66829i | 0.0433490 | + | 0.133414i | |||||
− | 6.64762i | − | 0.316553i | |||||||
−7.10660 | − | 16.7832i | −0.323027 | − | 0.762874i | |||||
−7.63236 | −0.331842 | −0.165921 | − | 0.986139i | ||||||
−0.165921 | + | 0.986139i | ||||||||
−24.6975 | + | 8.02472i | −1.02906 | + | 0.334363i | |||||
−4.04508 | − | 2.93893i | −0.161803 | − | 0.117557i | |||||
−2.46707 | + | 1.79243i | −0.0948875 | + | 0.0689398i | |||||
8.39084 | − | 25.8243i | 0.310772 | − | 0.956457i | |||||
2.65956 | + | 0.864143i | 0.0949842 | + | 0.0308623i | |||||
31.8005 | + | 43.7696i | 1.09657 | + | 1.50930i | 0.839856 | + | 0.542809i | ||
0.256713 | + | 0.966488i | ||||||||
6.49535 | − | 8.94009i | 0.216512 | − | 0.298003i | |||||
1.08129 | + | 3.32786i | 0.0348803 | + | 0.107350i | 0.966981 | − | 0.254849i | ||
−0.932101 | + | 0.362200i | ||||||||
− | 19.2397i | − | 0.601241i | |||||||
16.9228 | − | 28.1082i | 0.512813 | − | 0.851762i | |||||
13.8926 | 0.408607 | |||||||||
−4.73973 | + | 1.54003i | −0.135421 | + | 0.0440009i | |||||
0.105274 | + | 0.0764859i | 0.00292427 | + | 0.00212461i | |||||
37.8881 | − | 27.5273i | 1.02400 | − | 0.743981i | 0.0569023 | − | 0.998380i | ||
0.967099 | + | 0.254399i | ||||||||
−13.6060 | + | 41.8749i | −0.358052 | + | 1.10197i | |||||
−5.22085 | − | 1.69636i | −0.133868 | − | 0.0434963i | |||||
11.4432 | + | 15.7502i | 0.286079 | + | 0.393754i | |||||
−15.9749 | + | 21.9876i | −0.389633 | + | 0.536283i | −0.958104 | − | 0.286419i | ||
0.568472 | + | 0.822703i | ||||||||
−3.40364 | − | 10.4753i | −0.0810390 | − | 0.249412i | |||||
− | 14.9713i | − | 0.348171i | −0.984731 | − | 0.174085i | ||||
0.984731 | − | 0.174085i | ||||||||
9.04557 | + | 10.4243i | 0.205581 | + | 0.236916i | |||||
−0.231903 | −0.00515340 | |||||||||
−12.0271 | + | 3.90783i | −0.261458 | + | 0.0849528i | |||||
58.0480 | + | 42.1743i | 1.23506 | + | 0.897326i | 0.997259 | − | 0.0739873i | ||
0.237804 | + | 0.971313i | ||||||||
−22.6991 | + | 16.4919i | −0.472898 | + | 0.343580i | |||||
13.6068 | − | 41.8775i | 0.277691 | − | 0.854644i | |||||
−7.87900 | − | 2.56004i | −0.157580 | − | 0.0512008i | |||||
14.6999 | + | 20.2326i | 0.288232 | + | 0.396718i | |||||
1.35734 | − | 1.86822i | 0.0261028 | − | 0.0359274i | |||||
−12.1774 | − | 37.4781i | −0.229762 | − | 0.707134i | −0.997773 | − | 0.0666977i | ||
0.768012 | − | 0.640436i | ||||||||
− | 44.9902i | − | 0.833151i | |||||||
−23.9614 | − | 5.55420i | −0.435663 | − | 0.100985i | |||||
19.4046 | 0.346511 | |||||||||
−75.3814 | + | 24.4929i | −1.32248 | + | 0.429700i | |||||
72.5216 | + | 52.6900i | 1.25037 | + | 0.908449i | |||||
−29.1317 | + | 21.1654i | −0.493758 | + | 0.358736i | −0.806628 | − | 0.591060i | ||
0.312870 | + | 0.949796i | ||||||||
−2.58591 | + | 7.95861i | −0.0430985 | + | 0.132643i | |||||
−44.0546 | − | 14.3142i | −0.722207 | − | 0.234659i | −0.0752273 | − | 0.997166i | ||
−0.646980 | + | 0.762507i | ||||||||
3.40779 | + | 4.69042i | 0.0549643 | + | 0.0756519i | |||||
−0.135863 | + | 0.187000i | −0.00215656 | + | 0.00296825i | |||||
−21.4785 | − | 66.1039i | −0.335601 | − | 1.03287i | |||||
4.11543i | 0.0633143i | |||||||||
12.2754 | − | 52.9574i | 0.185991 | − | 0.802386i | |||||
−60.8461 | −0.908151 | −0.454075 | − | 0.890963i | ||||||
−0.454075 | + | 0.890963i | ||||||||
−10.0055 | + | 3.25097i | −0.147139 | + | 0.0478084i | |||||
−18.4171 | − | 13.3808i | −0.266914 | − | 0.193925i | |||||
−6.68035 | + | 4.85356i | −0.0954336 | + | 0.0693365i | |||||
−37.8919 | + | 116.619i | −0.533688 | + | 1.64252i | 0.212778 | + | 0.977101i | ||
−0.746466 | + | 0.665423i | ||||||||
0.858757 | + | 0.279027i | 0.0119272 | + | 0.00387538i | |||||
−35.1241 | − | 48.3441i | −0.481152 | − | 0.662248i | 0.497574 | − | 0.867422i | ||
−0.978726 | + | 0.205173i | ||||||||
45.6098 | − | 62.7765i | 0.616348 | − | 0.848331i | |||||
−4.60847 | − | 14.1834i | −0.0614463 | − | 0.189112i | |||||
− | 33.3422i | − | 0.438713i | |||||||
−18.5169 | + | 16.0678i | −0.240479 | + | 0.208673i | |||||
−9.09555 | −0.116610 | |||||||||
−81.5552 | + | 26.4989i | −1.03234 | + | 0.335429i | −0.775717 | − | 0.631081i | ||
−0.256627 | + | 0.966510i | ||||||||
17.0172 | + | 12.3638i | 0.212716 | + | 0.154547i | |||||
64.7665 | − | 47.0556i | 0.799587 | − | 0.580934i | |||||
−13.9155 | + | 42.8274i | −0.169701 | + | 0.522285i | |||||
−43.6902 | − | 14.1958i | −0.526388 | − | 0.171034i | 0.0337544 | − | 0.999430i | ||
−0.560142 | + | 0.828396i | ||||||||
4.90260 | + | 6.74785i | 0.0583643 | + | 0.0803315i | |||||
11.0203 | − | 15.1681i | 0.129651 | − | 0.178449i | |||||
−7.66545 | − | 23.5918i | −0.0891331 | − | 0.274324i | |||||
161.369i | 1.85481i | |||||||||
82.0485 | + | 49.3983i | 0.932370 | + | 0.561344i | |||||
121.940 | 1.37011 | 0.685056 | − | 0.728490i | ||||||
0.685056 | + | 0.728490i | ||||||||
−0.365432 | + | 0.118736i | −0.00406036 | + | 0.00131929i | |||||
3.31856 | + | 2.41107i | 0.0364677 | + | 0.0264953i | |||||
7.74743 | − | 5.62884i | 0.0842112 | − | 0.0611830i | |||||
−3.22512 | + | 9.92591i | −0.0346787 | + | 0.106730i | |||||
113.066 | + | 36.7372i | 1.20282 | + | 0.390822i | |||||
34.9266 | + | 48.0724i | 0.367649 | + | 0.506025i | |||||
33.7304 | − | 46.4259i | 0.351358 | − | 0.483603i | |||||
−10.2685 | − | 31.6031i | −0.105861 | − | 0.325805i | 0.884071 | − | 0.467353i | ||
−0.989931 | + | 0.141547i | ||||||||
− | 72.9574i | − | 0.744464i | |||||||
−1.05051 | + | 0.444824i | −0.0106113 | + | 0.00449317i | |||||
6.27352 | 0.0627352 | |||||||||
100.840 | − | 32.7650i | 0.998420 | − | 0.324406i | 0.236186 | − | 0.971708i | ||
0.762234 | + | 0.647302i | ||||||||
33.5233 | + | 24.3561i | 0.328660 | + | 0.238785i | |||||
158.992 | − | 115.514i | 1.54361 | − | 1.12150i | 0.595591 | − | 0.803288i | ||
0.948020 | − | 0.318211i | ||||||||
4.95171 | − | 15.2398i | 0.0476126 | − | 0.146537i | |||||
−14.1370 | − | 4.59339i | −0.134638 | − | 0.0437466i | |||||
−38.3782 | − | 52.8230i | −0.362058 | − | 0.498330i | |||||
−90.2208 | + | 124.178i | −0.843185 | + | 1.16054i | 0.142139 | + | 0.989847i | ||
−0.985323 | + | 0.170697i | ||||||||
10.5280 | + | 32.4019i | 0.0974816 | + | 0.300018i | |||||
− | 35.9768i | − | 0.330062i | −0.986288 | − | 0.165031i | ||||
0.986288 | − | 0.165031i | ||||||||
−40.6022 | + | 3.51616i | −0.369111 | + | 0.0319651i | |||||
139.685 | 1.25842 | |||||||||
19.9395 | − | 6.47874i | 0.178031 | − | 0.0578459i | |||||
−107.159 | − | 77.8559i | −0.948314 | − | 0.688990i | 0.00209353 | − | 0.999998i | ||
−0.950407 | + | 0.311007i | ||||||||
−106.245 | + | 77.1918i | −0.931977 | + | 0.677121i | |||||
−5.27383 | + | 16.2312i | −0.0458594 | + | 0.141141i | |||||
−64.5599 | − | 20.9768i | −0.556551 | − | 0.180834i | |||||
0.112194 | + | 0.154422i | 0.000958923 | + | 0.00131984i | |||||
−35.0689 | + | 48.2682i | −0.297194 | + | 0.409052i | |||||
−5.77476 | − | 17.7729i | −0.0485274 | − | 0.149352i | |||||
58.0674i | 0.483895i | |||||||||
−119.199 | + | 20.8012i | −0.985112 | + | 0.171911i | |||||
−76.7503 | −0.629101 | |||||||||
−77.0959 | + | 25.0500i | −0.626796 | + | 0.203658i | |||||
−3.55188 | − | 2.58059i | −0.0286442 | − | 0.0208112i | |||||
−9.04508 | + | 6.57164i | −0.0723607 | + | 0.0525731i | |||||
−0.118348 | + | 0.364237i | −0.000939268 | + | 0.00289077i | |||||
−21.4191 | − | 6.95949i | −0.168654 | − | 0.0547991i | 0.223473 | − | 0.974710i | ||
−0.392127 | + | 0.919911i | ||||||||
−22.4562 | − | 30.9083i | −0.175439 | − | 0.241471i | |||||
26.2473 | − | 36.1262i | 0.203467 | − | 0.280048i | |||||
2.10713 | + | 6.48509i | 0.0162087 | + | 0.0498853i | |||||
− | 69.8904i | − | 0.533515i | −0.963764 | − | 0.266757i | ||||
0.963764 | − | 0.266757i | ||||||||
3.55168 | + | 41.0125i | 0.0269067 | + | 0.310701i | |||||
59.2264 | 0.445311 | |||||||||
−95.8812 | + | 31.1537i | −0.715532 | + | 0.232490i | |||||
−49.1208 | − | 35.6884i | −0.363858 | − | 0.264358i | |||||
−59.0596 | + | 42.9093i | −0.434262 | + | 0.315509i | |||||
83.0828 | − | 255.703i | 0.606444 | − | 1.86644i | 0.119903 | − | 0.992786i | ||
0.486541 | − | 0.873658i | ||||||||
−35.8727 | − | 11.6557i | −0.259947 | − | 0.0844619i | |||||
−66.4957 | − | 91.5235i | −0.478386 | − | 0.658442i | 0.499807 | − | 0.866137i | ||
−0.978194 | + | 0.207694i | ||||||||
3.67542 | − | 5.05878i | 0.0262530 | − | 0.0361342i | |||||
66.1327 | + | 203.535i | 0.469026 | + | 1.44351i | |||||
203.169i | 1.43077i | |||||||||
7.89400 | + | 18.6428i | 0.0552028 | + | 0.130369i | |||||
0.975591 | 0.00677493 | |||||||||
115.055 | − | 37.3837i | 0.793484 | − | 0.257819i | |||||
−80.1011 | − | 58.1968i | −0.548638 | − | 0.398609i | |||||
106.252 | − | 77.1966i | 0.722803 | − | 0.525147i | |||||
−18.1580 | + | 55.8846i | −0.122689 | + | 0.377599i | |||||
185.247 | + | 60.1904i | 1.24327 | + | 0.403962i | 0.855504 | − | 0.517796i | ||
0.387764 | + | 0.921759i | ||||||||
−14.5240 | − | 19.9906i | −0.0968270 | − | 0.133271i | |||||
−82.9127 | + | 114.120i | −0.549091 | + | 0.755758i | −0.989888 | − | 0.141848i | ||
0.440798 | + | 0.897606i | ||||||||
−71.4954 | − | 220.040i | −0.470365 | − | 1.44763i | |||||
− | 0.869583i | − | 0.00568355i | |||||||
−20.9520 | + | 34.8004i | −0.136052 | + | 0.225977i | |||||
7.82428 | 0.0504792 | |||||||||
6.55062 | − | 2.12842i | 0.0419911 | − | 0.0136437i | |||||
−39.8372 | − | 28.9434i | −0.253740 | − | 0.184353i | 0.453643 | − | 0.891184i | ||
−0.707383 | + | 0.706831i | ||||||||
−114.947 | + | 83.5138i | −0.727512 | + | 0.528569i | |||||
36.3210 | − | 111.785i | 0.228434 | − | 0.703048i | |||||
−40.9157 | − | 13.2943i | −0.255723 | − | 0.0830894i | |||||
9.99860 | + | 13.7619i | 0.0621031 | + | 0.0854776i | |||||
77.9662 | − | 107.311i | 0.481273 | − | 0.662415i | |||||
77.2981 | + | 237.899i | 0.474222 | + | 1.45950i | 0.847005 | + | 0.531586i | ||
−0.372783 | + | 0.927919i | ||||||||
− | 34.1006i | − | 0.207930i | |||||||
−48.0822 | − | 55.4108i | −0.291407 | − | 0.335823i | |||||
−76.1154 | −0.458526 | |||||||||
263.329 | − | 85.5607i | 1.57682 | − | 0.512340i | 0.615585 | − | 0.788071i | ||
0.961235 | + | 0.275731i | ||||||||
46.8238 | + | 34.0195i | 0.278713 | + | 0.202497i | |||||
−133.983 | + | 97.3447i | −0.792801 | + | 0.576004i | |||||
9.59957 | − | 29.5444i | 0.0564681 | − | 0.173791i | |||||
2.62108 | + | 0.851641i | 0.0153280 | + | 0.00498036i | |||||
11.0413 | + | 15.1971i | 0.0641937 | + | 0.0883550i | |||||
−1.43083 | + | 1.96937i | −0.00827072 | + | 0.0113837i | −0.813132 | − | 0.582079i | ||
0.804862 | + | 0.593463i | ||||||||
82.6221 | + | 254.285i | 0.474840 | + | 1.46141i | |||||
11.1438i | 0.0636787i | |||||||||
100.803 | + | 23.3659i | 0.572746 | + | 0.132761i | |||||
−107.402 | −0.606792 | |||||||||
192.153 | − | 62.4343i | 1.07951 | − | 0.350754i | |||||
−117.428 | − | 85.3162i | −0.656020 | − | 0.476627i | 0.209296 | − | 0.977852i | ||
−0.865317 | + | 0.501226i | ||||||||
0.235399 | − | 0.171028i | 0.00130777 | − | 0.000950153i | |||||
−49.3147 | + | 151.775i | −0.272457 | + | 0.838535i | 0.717424 | + | 0.696636i | ||
−0.989881 | + | 0.141899i | ||||||||
6.46387 | + | 2.10024i | 0.0355158 | + | 0.0115398i | |||||
−81.2098 | − | 111.776i | −0.443769 | − | 0.610796i | |||||
39.0589 | − | 53.7600i | 0.212277 | − | 0.292174i | |||||
−32.3603 | − | 99.5947i | −0.174920 | − | 0.538350i | |||||
17.2925i | 0.0929706i | |||||||||
20.8270 | − | 89.8499i | 0.111374 | − | 0.480481i | |||||
−90.0266 | −0.478865 | |||||||||
−57.5561 | + | 18.7011i | −0.304529 | + | 0.0989476i | |||||
79.6508 | + | 57.8697i | 0.419215 | + | 0.304578i | |||||
−59.2898 | + | 43.0766i | −0.310418 | + | 0.225532i | −0.732076 | − | 0.681223i | ||
0.421658 | + | 0.906755i | ||||||||
64.0630 | − | 197.166i | 0.333662 | − | 1.02691i | |||||
250.612 | + | 81.4288i | 1.29851 | + | 0.421911i | 0.875062 | − | 0.484010i | ||
0.423446 | + | 0.905921i | ||||||||
−32.3621 | − | 44.5426i | −0.166815 | − | 0.229601i | |||||
−7.21503 | + | 9.93064i | −0.0370002 | + | 0.0509263i | |||||
17.0726 | + | 52.5439i | 0.0871049 | + | 0.268081i | |||||
219.288i | 1.11313i | 0.830803 | + | 0.556567i | ||||||
−0.830803 | + | 0.556567i | ||||||||
−1.42765 | + | 1.23883i | −0.00721034 | + | 0.00625670i | |||||
−108.109 | −0.543261 | −0.271630 | − | 0.962402i | ||||||
−0.271630 | + | 0.962402i | ||||||||
41.4018 | − | 13.4523i | 0.207009 | − | 0.0672613i | |||||
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142.128 | − | 103.262i | 0.703605 | − | 0.511199i | |||||
37.2614 | − | 114.679i | 0.183554 | − | 0.564920i | |||||
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35.7211 | + | 49.1658i | 0.174249 | + | 0.239833i | |||||
191.395 | − | 263.433i | 0.929102 | − | 1.27880i | |||||
0.244603 | + | 0.752811i | 0.00118166 | + | 0.00363677i | |||||
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250.427 | + | 150.772i | 1.19822 | + | 0.721399i | |||||
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237.612 | − | 77.2048i | 1.12612 | − | 0.365900i | 0.314022 | − | 0.949416i | ||
0.812102 | + | 0.583516i | ||||||||
40.0009 | + | 29.0624i | 0.188684 | + | 0.137087i | |||||
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138.958 | + | 191.260i | 0.643325 | + | 0.885461i | |||||
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28.4189 | − | 12.0335i | 0.129177 | − | 0.0546979i | |||||
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220.115 | − | 71.5198i | 0.991510 | − | 0.322161i | |||||
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24.2567 | + | 33.3864i | 0.106858 | + | 0.147077i | 0.859097 | − | 0.511814i | ||
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58.4545 | − | 80.4557i | 0.256379 | − | 0.352876i | |||||
110.190 | + | 339.131i | 0.481180 | + | 1.48092i | 0.837438 | + | 0.546532i | ||
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28.2773i | 0.122945i | |||||||||
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0.255861 | + | 0.185894i | 0.00109342 | + | 0.000794417i | |||||
129.799 | − | 94.3046i | 0.552337 | − | 0.401296i | |||||
13.9615 | − | 42.9691i | 0.0591589 | − | 0.182073i | |||||
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0.309523 | + | 0.950892i | ||||||||
19.3873 | + | 59.6681i | 0.0807806 | + | 0.248617i | |||||
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0.822271 | − | 0.569096i | ||||||||
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55.2755 | − | 17.9601i | 0.226539 | − | 0.0736070i | |||||
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− | 0.290018i | − | 0.00115086i | |||||||
7.24348 | + | 83.6429i | 0.0286304 | + | 0.330604i | |||||
−37.3155 | −0.146911 | |||||||||
53.1846 | − | 17.2807i | 0.208567 | − | 0.0677675i | |||||
173.714 | + | 126.210i | 0.678568 | + | 0.493009i | |||||
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0.528625 | + | 0.848856i | ||||||||
22.8635 | − | 70.3665i | 0.0886181 | − | 0.272738i | |||||
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0.998734 | − | 0.0503101i | ||||||||
111.382 | + | 263.044i | 0.421901 | + | 0.996379i | |||||
−88.1163 | −0.332514 | |||||||||
93.3289 | − | 30.3244i | 0.350860 | − | 0.114001i | |||||
294.244 | + | 213.781i | 1.10204 | + | 0.800678i | |||||
61.7635 | − | 44.8738i | 0.230461 | − | 0.167440i | |||||
12.2133 | − | 37.5885i | 0.0454024 | − | 0.139734i | −0.925786 | − | 0.378049i | ||
0.971188 | + | 0.238315i | ||||||||
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0.0670732 | − | 0.997748i | ||||||||
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3.78076 | + | 11.6360i | 0.0138489 | + | 0.0426226i | |||||
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28.5630 | 0.103489 | |||||||||
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0.0957120 | + | 0.995409i | ||||||||
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0.293588 | − | 0.213304i | 0.00105229 | − | 0.000764531i | |||||
13.4083 | − | 41.2664i | 0.0478866 | − | 0.147380i | |||||
406.555 | + | 132.098i | 1.44681 | + | 0.470098i | 0.924014 | − | 0.382358i | ||
0.522799 | + | 0.852456i | ||||||||
208.424 | + | 286.871i | 0.739091 | + | 1.01727i | |||||
119.366 | − | 164.293i | 0.421787 | − | 0.580541i | −0.544256 | − | 0.838919i | ||
0.966044 | + | 0.258378i | ||||||||
−47.5431 | − | 146.323i | −0.167405 | − | 0.515220i | |||||
177.232i | 0.621867i | |||||||||
21.9846 | + | 25.3355i | 0.0768693 | + | 0.0885857i | |||||
60.5735 | 0.211057 | |||||||||
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162.163 | − | 117.818i | 0.559183 | − | 0.406271i | |||||
30.6274 | − | 94.2615i | 0.105249 | − | 0.323923i | |||||
71.3073 | + | 23.1691i | 0.244203 | + | 0.0793464i | |||||
240.571 | + | 331.117i | 0.821061 | + | 1.13009i | 0.989522 | + | 0.144385i | ||
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127.907 | − | 176.048i | 0.435056 | − | 0.598803i | |||||
24.8815 | + | 76.5773i | 0.0843440 | + | 0.259584i | |||||
407.744i | 1.37751i | |||||||||
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322.730 | 1.08299 | |||||||||
13.3597 | − | 4.34081i | 0.0446811 | − | 0.0145178i | |||||
15.1382 | + | 10.9985i | 0.0504606 | + | 0.0366618i | |||||
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300.773 | + | 97.7271i | 0.992651 | + | 0.322532i | |||||
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548.367i | 1.78621i | 0.449846 | + | 0.893106i | ||||||
−0.449846 | + | 0.893106i | ||||||||
6.94608 | − | 29.9662i | 0.0225522 | − | 0.0972928i | |||||
586.168 | 1.89698 | |||||||||
12.3295 | − | 4.00610i | 0.0397726 | − | 0.0129229i | |||||
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38.6665 | − | 28.0929i | 0.123931 | − | 0.0900412i | |||||
0.359023 | − | 1.10496i | 0.00114704 | − | 0.00353022i | −0.950481 | − | 0.310782i | ||
0.951628 | + | 0.307251i | ||||||||
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0.303799 | + | 0.418144i | 0.000964442 | + | 0.00132744i | |||||
63.2419 | − | 87.0451i | 0.200133 | − | 0.275459i | |||||
36.3906 | + | 111.999i | 0.114797 | + | 0.353308i | 0.991905 | − | 0.126985i | ||
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449.490 | − | 390.041i | 1.40906 | − | 1.22270i | |||||
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22.8020 | + | 16.5666i | 0.0708137 | + | 0.0514491i | |||||
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8.75198 | + | 2.84369i | 0.0269292 | + | 0.00874982i | |||||
243.613 | + | 335.304i | 0.747278 | + | 1.02854i | |||||
63.0733 | − | 86.8130i | 0.192885 | − | 0.265483i | |||||
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54.8183 | − | 17.8115i | 0.165115 | − | 0.0536492i | |||||
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371.146 | − | 269.653i | 1.11121 | − | 0.807345i | |||||
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59.4729 | + | 19.3239i | 0.177003 | + | 0.0575117i | |||||
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23.5243i | 0.0691890i | |||||||||
35.4438 | − | 15.0081i | 0.103941 | − | 0.0440121i | |||||
4.56635 | 0.0133519 | |||||||||
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105.454 | + | 76.6165i | 0.306551 | + | 0.222722i | |||||
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5.70570 | + | 17.5603i | 0.0163020 | + | 0.0501724i | |||||
49.9750i | 0.142379i | |||||||||
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640.543 | 1.81457 | 0.907285 | − | 0.420516i | ||||||
0.907285 | + | 0.420516i | ||||||||
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221.823 | + | 161.164i | 0.624853 | + | 0.453982i | |||||
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17.2242 | − | 53.0106i | 0.0482470 | − | 0.148489i | |||||
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−0.990451 | + | 0.137865i | ||||||||
1.18677 | − | 1.63345i | 0.00329659 | − | 0.00453737i | |||||
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264.416i | 0.730432i | |||||||||
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−5.14675 | −0.0141394 | |||||||||
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381.543 | − | 277.207i | 1.03963 | − | 0.755333i | 0.0694140 | − | 0.997588i | ||
0.970213 | + | 0.242255i | ||||||||
22.1864 | − | 68.2828i | 0.0602892 | − | 0.185551i | |||||
2.68070 | + | 0.871012i | 0.00726477 | + | 0.00236047i | |||||
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0.997675 | − | 0.0681461i | ||||||||
−13.1848 | − | 152.249i | −0.0352534 | − | 0.407083i | |||||
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−0.840130 | + | 0.542385i | ||||||||
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−10.4312 | − | 32.1040i | −0.0272356 | − | 0.0838226i | 0.936515 | − | 0.350628i | ||
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− | 113.952i | − | 0.296750i | |||||||
21.3754 | + | 50.4810i | 0.0555205 | + | 0.131120i | |||||
436.607 | 1.13111 | |||||||||
−1.47669 | + | 0.479804i | −0.00381573 | + | 0.00123980i | |||||
33.7305 | + | 24.5066i | 0.0869342 | + | 0.0631614i | |||||
−418.883 | + | 304.337i | −1.07682 | + | 0.782356i | −0.977126 | − | 0.212662i | ||
−0.0996952 | + | 0.995018i | ||||||||
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−60.8632 | − | 19.7757i | −0.155660 | − | 0.0505771i | |||||
225.339 | + | 310.153i | 0.574845 | + | 0.791206i | |||||
122.530 | − | 168.647i | 0.311780 | − | 0.429128i | |||||
112.277 | + | 345.553i | 0.284967 | + | 0.877038i | |||||
191.748i | 0.485437i | |||||||||
0.738297 | − | 1.22628i | 0.00186439 | − | 0.00309667i | |||||
86.1063 | 0.216893 | 0.108446 | − | 0.994102i | ||||||
0.108446 | + | 0.994102i | ||||||||
−170.358 | + | 55.3526i | −0.428035 | + | 0.139077i | |||||
142.915 | + | 103.834i | 0.358182 | + | 0.260235i | |||||
38.0517 | − | 27.6462i | 0.0951293 | − | 0.0691155i | |||||
49.8340 | − | 153.373i | 0.124274 | − | 0.382477i | −0.869494 | − | 0.493944i | ||
0.993768 | + | 0.111467i | ||||||||
−285.982 | − | 92.9211i | −0.711397 | − | 0.231147i | |||||
−3.78537 | − | 5.21011i | −0.00939297 | − | 0.0129283i | |||||
−78.1967 | + | 107.629i | −0.193556 | + | 0.266407i | |||||
−55.3172 | − | 170.249i | −0.136586 | − | 0.420368i | |||||
− | 199.789i | − | 0.492091i | |||||||
−337.629 | − | 389.090i | −0.829555 | − | 0.955995i | |||||
−217.739 | −0.533675 | |||||||||
220.213 | − | 71.5515i | 0.538418 | − | 0.174943i | −0.0271696 | − | 0.999631i | ||
0.565588 | + | 0.824688i | ||||||||
81.4625 | + | 59.1860i | 0.198689 | + | 0.144356i | |||||
648.771 | − | 471.359i | 1.57852 | − | 1.14686i | |||||
−76.1976 | + | 234.512i | −0.184946 | + | 0.569204i | |||||
76.3268 | + | 24.8001i | 0.184811 | + | 0.0600486i | |||||
0.770891 | + | 1.06104i | 0.00186206 | + | 0.00256290i | |||||
−60.3784 | + | 83.1037i | −0.145490 | + | 0.200250i | |||||
10.9424 | + | 33.6771i | 0.0263037 | + | 0.0809546i | |||||
− | 337.427i | − | 0.809177i | |||||||
471.819 | + | 109.366i | 1.12875 | + | 0.261642i | |||||
428.346 | 1.02231 | 0.511153 | − | 0.859490i | ||||||
0.511153 | + | 0.859490i | ||||||||
17.7378 | − | 5.76335i | 0.0422328 | − | 0.0137223i | |||||
423.964 | + | 308.028i | 1.00704 | + | 0.731657i | 0.963586 | − | 0.267398i | ||
0.0434535 | + | 0.999055i | ||||||||
334.899 | − | 243.319i | 0.793600 | − | 0.576584i | |||||
2.29950 | − | 7.07712i | 0.00543616 | − | 0.0167308i | |||||
326.302 | + | 106.022i | 0.769581 | + | 0.250052i | |||||
−24.6421 | − | 33.9170i | −0.0579815 | − | 0.0798047i | |||||
−356.190 | + | 490.253i | −0.836126 | + | 1.15083i | |||||
31.9029 | + | 98.1869i | 0.0747140 | + | 0.229946i | |||||
− | 192.588i | − | 0.449972i | |||||||
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0.319047 | + | 0.947739i | ||||||||
206.646 | + | 150.137i | 0.478347 | + | 0.347540i | |||||
159.214 | − | 115.676i | 0.367700 | − | 0.267150i | −0.388556 | − | 0.921425i | ||
0.756257 | + | 0.654275i | ||||||||
3.99299 | − | 12.2892i | 0.00920044 | − | 0.0283160i | |||||
343.171 | + | 111.503i | 0.788899 | + | 0.256329i | |||||
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119.215 | − | 164.085i | 0.272803 | − | 0.375481i | |||||
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48.0326i | 0.109414i | 0.998502 | + | 0.0547069i | ||||||
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161.746 | − | 140.353i | 0.367604 | − | 0.318985i | |||||
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102.069 | + | 74.1577i | 0.230405 | + | 0.167399i | 0.696998 | − | 0.717073i | ||
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341.482 | + | 470.010i | 0.763942 | + | 1.05148i | |||||
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0.859183i | 0.00190930i | |||||||||
256.123 | + | 154.202i | 0.567900 | + | 0.341911i | |||||
166.194 | 0.367685 | |||||||||
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55.3177 | + | 40.1907i | 0.121845 | + | 0.0885258i | |||||
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213.247 | − | 656.307i | 0.467647 | − | 1.43927i | |||||
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347.275 | + | 477.983i | 0.758243 | + | 1.04363i | |||||
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0.959825 | − | 0.280601i | ||||||||
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0.899799 | + | 0.436304i | ||||||||
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156.253 | − | 215.063i | 0.332453 | − | 0.457582i | |||||
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126.366 | − | 41.0587i | 0.266033 | − | 0.0864394i | |||||
18.9693 | + | 13.7820i | 0.0398514 | + | 0.0289537i | |||||
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50.7370i | 0.105046i | |||||||||
105.655 | − | 109.023i | 0.218295 | − | 0.225255i | |||||
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166.147 | + | 120.713i | 0.341164 | + | 0.247870i | 0.745153 | − | 0.666894i | ||
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326.277 | − | 237.054i | 0.668599 | − | 0.485766i | |||||
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59.7840 | − | 82.2856i | 0.121512 | − | 0.167247i | |||||
140.180 | + | 431.431i | 0.284342 | + | 0.875113i | |||||
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0.220087 | + | 2.54142i | 0.000444620 | + | 0.00513418i | |||||
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259.915 | − | 84.4516i | 0.522969 | − | 0.169923i | |||||
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0.388598 | + | 0.921408i | ||||||||
4.33490 | − | 13.3414i | 0.00866979 | − | 0.0266829i | |||||
785.422 | + | 255.199i | 1.56771 | + | 0.509379i | |||||
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56.2423 | − | 77.4109i | 0.111814 | − | 0.153898i | −0.749442 | − | 0.662070i | ||
0.861256 | + | 0.508171i | ||||||||
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54.2401 | + | 128.096i | 0.107194 | + | 0.253154i | |||||
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26.8746 | − | 8.73210i | 0.0529028 | − | 0.0171892i | |||||
80.9705 | + | 58.8285i | 0.159078 | + | 0.115577i | 0.664476 | − | 0.747309i | ||
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74.9603 | − | 54.4619i | 0.146981 | − | 0.106788i | |||||
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483.698 | + | 157.163i | 0.944723 | + | 0.306959i | |||||
424.126 | + | 583.759i | 0.826756 | + | 1.13793i | |||||
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56.0282i | 0.108582i | |||||||||
407.097 | − | 676.172i | 0.787422 | − | 1.30788i | |||||
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0.135970 | + | 0.990713i | ||||||||
2.87285 | − | 8.84173i | 0.00550355 | − | 0.0169382i | |||||
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51.5440 | + | 70.9442i | 0.0983663 | + | 0.135390i | |||||
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29.3393i | 0.0556722i | |||||||||
202.277 | + | 233.107i | 0.383100 | + | 0.441491i | |||||
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15.4573 | − | 47.5726i | 0.0290005 | − | 0.0892544i | |||||
573.128 | + | 186.220i | 1.07327 | + | 0.348728i | |||||
201.740 | + | 277.671i | 0.377084 | + | 0.519011i | |||||
311.383 | − | 428.581i | 0.580938 | − | 0.799592i | |||||
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− | 65.4853i | − | 0.121720i | |||||||
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76.1815 | 0.141077 | |||||||||
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0.212541 | + | 0.977152i | ||||||||
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49.8506 | − | 153.424i | 0.0916372 | − | 0.282030i | |||||
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11.9154 | + | 16.4002i | 0.0218231 | + | 0.0300370i | |||||
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0.791867 | + | 0.610694i | ||||||||
104.244 | + | 320.831i | 0.190227 | + | 0.585459i | |||||
4.80404i | 0.00875052i | |||||||||
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188.500 | − | 61.2475i | 0.341486 | − | 0.110956i | |||||
154.620 | + | 112.338i | 0.279602 | + | 0.203142i | |||||
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96.5198 | − | 297.058i | 0.173910 | − | 0.535239i | |||||
134.997 | + | 43.8630i | 0.242799 | + | 0.0788903i | |||||
75.6402 | + | 104.110i | 0.135799 | + | 0.186912i | 0.871501 | − | 0.490394i | ||
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0.353422 | − | 0.486444i | 0.000633373 | − | 0.000871763i | |||||
8.51477 | + | 26.2058i | 0.0152322 | + | 0.0468797i | |||||
− | 46.8806i | − | 0.0837154i | |||||||
207.778 | − | 180.297i | 0.370371 | − | 0.321385i | |||||
708.284 | 1.26029 | |||||||||
281.575 | − | 91.4894i | 0.500134 | − | 0.162503i | −0.0480767 | − | 0.998844i | ||
0.548211 | + | 0.836340i | ||||||||
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103.977 | − | 320.009i | 0.183705 | − | 0.565387i | |||||
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355.335 | − | 489.077i | 0.624491 | − | 0.859538i | −0.373179 | − | 0.927759i | ||
0.997670 | + | 0.0682211i | ||||||||
90.7443 | + | 279.282i | 0.159201 | + | 0.489969i | |||||
612.659i | 1.07296i | 0.843914 | + | 0.536479i | ||||||
−0.843914 | + | 0.536479i | ||||||||
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95.4517 | − | 31.0141i | 0.166292 | − | 0.0540316i | |||||
30.8735 | + | 22.4309i | 0.0536931 | + | 0.0390103i | |||||
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−0.993287 | + | 0.115677i | ||||||||
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461.976 | + | 635.855i | 0.797885 | + | 1.09819i | |||||
−89.2196 | + | 122.800i | −0.153827 | + | 0.211724i | |||||
31.6390 | + | 97.3747i | 0.0544560 | + | 0.167598i | |||||
− | 164.219i | − | 0.282163i | |||||||
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520.270 | 0.890874 | |||||||||
0.405922 | − | 0.131892i | 0.000693884 | − | 0.000225456i | |||||
548.626 | + | 398.600i | 0.936222 | + | 0.680205i | |||||
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0.303937 | + | 0.952692i | ||||||||
−50.9217 | + | 156.721i | −0.0866016 | + | 0.266532i | |||||
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78.4164 | + | 107.931i | 0.132909 | + | 0.182934i | |||||
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136.136 | + | 418.984i | 0.229960 | + | 0.707744i | |||||
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0.669204 | − | 0.743079i | ||||||||
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−41.7866 | −0.0702295 | |||||||||
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18.8296 | − | 13.6805i | 0.0314876 | − | 0.0228771i | |||||
276.534 | − | 851.084i | 0.461659 | − | 1.42084i | −0.401477 | − | 0.915869i | ||
0.863136 | − | 0.504972i | ||||||||
123.488 | + | 40.1236i | 0.205813 | + | 0.0668726i | |||||
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0.249603 | − | 0.968348i | ||||||||
−32.4964 | + | 44.7275i | −0.0539808 | + | 0.0742982i | |||||
1.95001 | + | 6.00150i | 0.00323384 | + | 0.00995274i | |||||
− | 176.988i | − | 0.293026i | |||||||
−38.1278 | + | 267.864i | −0.0630211 | + | 0.442751i | |||||
523.995 | 0.864679 | |||||||||
1053.73 | − | 342.377i | 1.73596 | − | 0.564048i | 0.741672 | − | 0.670763i | ||
0.994290 | + | 0.106715i | ||||||||
413.627 | + | 300.518i | 0.680308 | + | 0.494273i | |||||
290.964 | − | 211.398i | 0.477773 | − | 0.347123i | |||||
−53.0331 | + | 163.219i | −0.0869396 | + | 0.267572i | |||||
−125.593 | − | 40.8077i | −0.205553 | − | 0.0667883i | |||||
0.641314 | + | 0.882693i | 0.00104790 | + | 0.00144231i | |||||
75.0479 | − | 103.295i | 0.122427 | − | 0.168507i | −0.743404 | − | 0.668842i | ||
0.865831 | + | 0.500336i | ||||||||
280.769 | + | 864.117i | 0.457278 | + | 1.40736i | |||||
181.263i | 0.294737i | |||||||||
−18.4159 | − | 212.655i | −0.0298960 | − | 0.345219i | |||||
182.872 | 0.296389 | 0.148195 | − | 0.988958i | ||||||
0.148195 | + | 0.988958i | ||||||||
923.683 | − | 300.123i | 1.49463 | − | 0.485635i | |||||
−93.6587 | − | 68.0470i | −0.151306 | − | 0.109931i | 0.509556 | − | 0.860437i | ||
−0.660863 | + | 0.750507i | ||||||||
−7.94225 | + | 5.77038i | −0.0128101 | + | 0.00930706i | |||||
−64.0419 | + | 197.101i | −0.103127 | + | 0.317392i | |||||
−72.8458 | − | 23.6690i | −0.117116 | − | 0.0380531i | |||||
−159.745 | − | 219.870i | −0.256412 | − | 0.352921i | |||||
30.3529 | − | 41.7771i | 0.0486424 | − | 0.0669505i | |||||
7.72542 | + | 23.7764i | 0.0123607 | + | 0.0380423i | |||||
− | 1.92501i | − | 0.00307510i | |||||||
339.958 | + | 802.858i | 0.542197 | + | 1.28048i | |||||
61.7835 | 0.0983813 | |||||||||
373.457 | − | 121.344i | 0.593732 | − | 0.192915i | |||||
0.692820 | + | 0.503363i | 0.00109971 | + | 0.000798989i | |||||
675.353 | − | 490.673i | 1.07029 | − | 0.777611i | 0.0943258 | − | 0.995541i | ||
0.975964 | + | 0.217930i | ||||||||
230.712 | − | 710.059i | 0.365051 | − | 1.12351i | |||||
708.717 | + | 230.276i | 1.11962 | + | 0.363785i | |||||
114.689 | + | 157.855i | 0.180897 | + | 0.248983i | |||||
−29.6005 | + | 40.7415i | −0.0466149 | + | 0.0641599i | |||||
45.5721 | + | 140.257i | 0.0716543 | + | 0.220529i | |||||
81.0410i | 0.127223i | |||||||||
508.602 | − | 844.768i | 0.797183 | − | 1.32409i | |||||
12.7170 | 0.0199014 | |||||||||
−81.2473 | + | 26.3989i | −0.126949 | + | 0.0412482i | |||||
−20.3823 | − | 14.8086i | −0.0317976 | − | 0.0231023i | 0.571773 | − | 0.820412i | ||
−0.603571 | + | 0.797310i | ||||||||
−613.684 | + | 445.867i | −0.955893 | + | 0.694497i | |||||
126.790 | − | 390.218i | 0.197184 | − | 0.606871i | −0.802760 | − | 0.596303i | ||
0.999944 | − | 0.0105686i | ||||||||
−20.2987 | − | 6.59545i | −0.0315197 | − | 0.0102414i | |||||
−58.6906 | − | 80.7807i | −0.0909932 | − | 0.125241i | |||||
−216.998 | + | 298.672i | −0.335911 | + | 0.462341i | |||||
213.067 | + | 655.754i | 0.329316 | + | 1.01353i | 0.969455 | + | 0.245270i | ||
−0.640139 | + | 0.768259i | ||||||||
697.005i | 1.07563i | |||||||||
259.599 | + | 299.167i | 0.399999 | + | 0.460966i | |||||
15.2474 | 0.0234575 | |||||||||
22.1224 | − | 7.18800i | 0.0339822 | − | 0.0110415i | |||||
−253.913 | − | 184.479i | −0.389438 | − | 0.282943i | |||||
291.983 | − | 212.138i | 0.447140 | − | 0.324866i | −0.341325 | − | 0.939945i | ||
0.788466 | + | 0.615079i | ||||||||
54.9419 | − | 169.094i | 0.0840091 | − | 0.258553i | |||||
−148.631 | − | 48.2931i | −0.226917 | − | 0.0737299i | |||||
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464.630i | 0.705053i | 0.935802 | + | 0.352527i | ||||||
−0.935802 | + | 0.352527i | ||||||||
89.6724 | + | 20.7858i | 0.135867 | + | 0.0314937i | |||||
103.487 | 0.156562 | 0.0782808 | − | 0.996931i | ||||||
0.0782808 | + | 0.996931i | ||||||||
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323.577 | − | 235.093i | 0.487315 | − | 0.354055i | |||||
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225.430i | 0.336463i | |||||||||
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0.140573 | + | 0.990070i | ||||||||
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123.088i | 0.180746i | |||||||||
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142.052 | + | 437.192i | 0.205575 | + | 0.632695i | 0.999689 | + | 0.0249265i | ||
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− | 3.05430i | − | 0.00441373i | |||||||
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256.752 | − | 353.389i | 0.366265 | − | 0.504121i | −0.585616 | − | 0.810589i | ||
0.951881 | + | 0.306468i | ||||||||
25.5876 | + | 78.7506i | 0.0364496 | + | 0.112180i | |||||
1244.51i | 1.77028i | |||||||||
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478.541 | 0.678781 | |||||||||
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109.022 | − | 79.2088i | 0.153985 | − | 0.111877i | |||||
401.098 | − | 1234.45i | 0.565724 | − | 1.74112i | −0.100067 | − | 0.994981i | ||
0.665791 | − | 0.746138i | ||||||||
432.066 | + | 140.387i | 0.608543 | + | 0.197728i | |||||
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− | 92.3529i | − | 0.129346i | |||||||
45.1009 | − | 3.90574i | 0.0630782 | − | 0.00546258i | |||||
182.118 | 0.254355 | |||||||||
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597.870 | − | 434.378i | 0.831530 | − | 0.604142i | −0.0884615 | − | 0.996080i | ||
0.919992 | + | 0.391937i | ||||||||
0.674117 | − | 2.07472i | 0.000936273 | − | 0.00288155i | |||||
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480.901 | − | 661.904i | 0.665147 | − | 0.915496i | |||||
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721.746 | 0.992773 | 0.496386 | − | 0.868102i | ||||||
0.496386 | + | 0.868102i | ||||||||
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38.7912 | − | 119.387i | 0.0530659 | − | 0.163320i | |||||
164.868 | + | 53.5690i | 0.225230 | + | 0.0731817i | |||||
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459.303 | − | 632.176i | 0.625753 | − | 0.861275i | |||||
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146.844i | 0.199517i | |||||||||
57.7459 | + | 666.811i | 0.0783527 | + | 0.904764i | |||||
4.67021 | 0.00632820 | |||||||||
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0.314209 | + | 0.949354i | ||||||||
106.299 | + | 77.2307i | 0.143647 | + | 0.104366i | |||||
118.017 | − | 85.7445i | 0.159267 | − | 0.115715i | |||||
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256.005 | − | 352.361i | 0.343631 | − | 0.472967i | |||||
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4.76430i | 0.00637791i | |||||||||
45.1230 | + | 106.564i | 0.0603249 | + | 0.142466i | |||||
342.097 | 0.456739 | |||||||||
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381.165 | + | 276.932i | 0.507543 | + | 0.368751i | 0.811891 | − | 0.583810i | ||
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110.386 | − | 339.732i | 0.146595 | − | 0.451172i | |||||
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185.398 | + | 255.179i | 0.245561 | + | 0.337985i | |||||
44.6318 | − | 61.4305i | 0.0590368 | − | 0.0812572i | |||||
268.783 | + | 827.228i | 0.355063 | + | 1.09277i | 0.955973 | + | 0.293455i | ||
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973.911i | 1.28484i | |||||||||
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614.545 | − | 199.678i | 0.807549 | − | 0.262389i | 0.123990 | − | 0.992284i | ||
0.683559 | + | 0.729895i | ||||||||
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38.9545 | − | 53.6162i | 0.0507881 | − | 0.0699038i | |||||
197.908 | + | 609.097i | 0.257692 | + | 0.793096i | |||||
152.670i | 0.198530i | 0.995061 | + | 0.0992650i | ||||||
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59.5300 | + | 68.6036i | 0.0773117 | + | 0.0890955i | |||||
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579.036 | + | 420.694i | 0.749076 | + | 0.544235i | 0.895540 | − | 0.444981i | ||
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275.152 | + | 89.4023i | 0.354577 | + | 0.115209i | |||||
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1313.99 | + | 304.579i | 1.68244 | + | 0.389986i | |||||
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1397.15 | − | 453.963i | 1.78436 | − | 0.579774i | |||||
335.104 | + | 243.467i | 0.427428 | + | 0.310545i | |||||
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106.733 | − | 328.491i | 0.135793 | − | 0.417927i | |||||
582.331 | + | 189.211i | 0.739938 | + | 0.240421i | 0.654646 | − | 0.755935i | ||
0.0852922 | + | 0.996356i | ||||||||
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46.3943 | − | 63.8562i | 0.0588014 | − | 0.0809331i | |||||
98.1764 | + | 302.156i | 0.124274 | + | 0.382476i | |||||
295.213i | 0.373214i | |||||||||
2.24285 | − | 9.67591i | 0.00283188 | − | 0.0122171i | |||||
85.2541 | 0.107508 | |||||||||
135.686 | − | 44.0871i | 0.170890 | − | 0.0555254i | |||||
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109.739 | − | 79.7299i | 0.137863 | − | 0.100163i | |||||
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0.926407 | + | 0.376523i | ||||||||
278.369 | + | 90.4475i | 0.348833 | + | 0.113343i | |||||
353.621 | + | 486.717i | 0.442579 | + | 0.609158i | |||||
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227.708 | 0.283219 | |||||||||
36.1753 | − | 11.7541i | 0.0449382 | − | 0.0146013i | |||||
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95.3699 | − | 69.2903i | 0.118178 | − | 0.0858615i | |||||
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660.065 | + | 214.468i | 0.815902 | + | 0.265103i | 0.687096 | − | 0.726567i | ||
0.128807 | + | 0.991670i | ||||||||
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754.445 | − | 1038.40i | 0.930266 | − | 1.28040i | −0.0294904 | − | 0.999565i | ||
0.959756 | − | 0.280836i | ||||||||
46.7521 | + | 143.888i | 0.0575764 | + | 0.177202i | |||||
− | 1241.18i | − | 1.52667i | |||||||
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559.335 | 0.686300 | |||||||||
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321.863 | + | 233.847i | 0.393958 | + | 0.286227i | |||||
310.376 | − | 225.502i | 0.379433 | − | 0.275674i | |||||
0.131461 | − | 0.404594i | 0.000160513 | − | 0.000494010i | |||||
−72.5193 | − | 23.5629i | −0.0884381 | − | 0.0287353i | |||||
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780.992 | − | 1074.94i | 0.950112 | − | 1.30772i | |||||
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0.754249 | − | 0.656589i | ||||||||
1711.04i | 2.07651i | |||||||||
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132.974 | 0.160985 | |||||||||
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−0.141971 | + | 0.989871i | ||||||||
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−0.106608 | + | 0.994301i | ||||||||
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75.1916 | + | 103.492i | 0.0903745 | + | 0.124390i | |||||
217.012 | − | 298.691i | 0.260518 | − | 0.358573i | |||||
−172.765 | − | 531.717i | −0.207153 | − | 0.637550i | |||||
− | 619.123i | − | 0.741465i | |||||||
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95.0128 | 0.113516 | |||||||||
674.987 | − | 219.317i | 0.805474 | − | 0.261714i | |||||
487.599 | + | 354.261i | 0.581167 | + | 0.422242i | 0.839145 | − | 0.543908i | ||
−0.257978 | + | 0.966151i | ||||||||
104.701 | − | 76.0699i | 0.124644 | − | 0.0905594i | |||||
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825.794 | + | 268.317i | 0.980753 | + | 0.318666i | |||||
749.438 | + | 1031.51i | 0.889013 | + | 1.22362i | |||||
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114.436 | + | 352.196i | 0.135427 | + | 0.416800i | |||||
− | 12.3295i | − | 0.0145739i | |||||||
193.660 | + | 187.677i | 0.228643 | + | 0.221578i | |||||
370.696 | 0.437141 | |||||||||
576.066 | − | 187.175i | 0.678523 | − | 0.220465i | |||||
−56.1969 | − | 40.8294i | −0.0661139 | − | 0.0480346i | |||||
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141.805 | − | 436.431i | 0.166438 | − | 0.512243i | |||||
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−0.819676 | − | 0.572828i | ||||||||
100.545 | + | 138.388i | 0.117734 | + | 0.162047i | |||||
3.62225 | − | 4.98559i | 0.00423654 | − | 0.00583110i | |||||
−412.965 | − | 1270.97i | −0.482436 | − | 1.48478i | |||||
− | 1580.81i | − | 1.84459i | −0.386486 | − | 0.922295i | ||||
0.386486 | − | 0.922295i | ||||||||
8.63212 | + | 99.6780i | 0.0100608 | + | 0.116175i | |||||
−1222.90 | −1.42364 | −0.711819 | − | 0.702363i | ||||||
−0.711819 | + | 0.702363i | ||||||||
39.9478 | − | 12.9798i | 0.0464510 | − | 0.0150928i | |||||
146.165 | + | 106.195i | 0.169762 | + | 0.123340i | |||||
12.2072 | − | 8.86902i | 0.0141614 | − | 0.0102889i | |||||
361.176 | − | 1111.58i | 0.418512 | − | 1.28805i | −0.490560 | − | 0.871408i | ||
0.909072 | − | 0.416640i | ||||||||
−496.853 | − | 161.437i | −0.575061 | − | 0.186849i | |||||
3.19944 | + | 4.40365i | 0.00369878 | + | 0.00509093i | |||||
191.663 | − | 263.801i | 0.221320 | − | 0.304620i | |||||
−201.571 | − | 620.371i | −0.232492 | − | 0.715538i | |||||
9.78504i | 0.0112731i | |||||||||
367.801 | + | 868.613i | 0.423246 | + | 0.999555i | |||||
597.859 | 0.687195 | |||||||||
106.505 | − | 34.6055i | 0.122279 | − | 0.0397308i | |||||
253.410 | + | 184.113i | 0.290607 | + | 0.211139i | |||||
−2.78806 | + | 2.02565i | −0.00319366 | + | 0.00232033i | |||||
103.846 | − | 319.604i | 0.118817 | − | 0.365680i | |||||
23.6986 | + | 7.70015i | 0.0270842 | + | 0.00880017i | |||||
131.447 | + | 180.921i | 0.150054 | + | 0.206531i | |||||
320.830 | − | 441.585i | 0.365827 | − | 0.503517i | −0.585934 | − | 0.810359i | ||
0.951761 | + | 0.306842i | ||||||||
24.5931 | + | 75.6898i | 0.0280104 | + | 0.0862071i | |||||
1220.76i | 1.38880i | |||||||||
119.344 | − | 198.225i | 0.135618 | − | 0.225256i | |||||
−445.171 | −0.505302 | −0.252651 | − | 0.967557i | ||||||
−0.252651 | + | 0.967557i | ||||||||
−7.19609 | + | 2.33815i | −0.00815884 | + | 0.00265097i | |||||
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−0.833739 | + | 0.552159i | ||||||||
15.6646 | − | 11.3810i | 0.0177201 | − | 0.0128744i | |||||
−74.2131 | + | 228.404i | −0.0838566 | + | 0.258084i | |||||
198.810 | + | 64.5973i | 0.224391 | + | 0.0729089i | |||||
−717.869 | − | 988.062i | −0.809323 | − | 1.11394i | −0.991427 | − | 0.130658i | ||
0.182105 | − | 0.983279i | ||||||||
−714.843 | + | 983.897i | −0.805004 | + | 1.10799i | |||||
15.5110 | + | 47.7379i | 0.0174477 | + | 0.0536984i | |||||
− | 451.779i | − | 0.507616i | |||||||
−577.149 | − | 665.117i | −0.647754 | − | 0.746484i | |||||
178.297 | 0.199885 | |||||||||
−1813.38 | + | 589.203i | −2.03066 | + | 0.659802i | |||||
778.756 | + | 565.799i | 0.871092 | + | 0.632885i | |||||
−262.576 | + | 190.773i | −0.293381 | + | 0.213154i | |||||
−26.3125 | + | 80.9815i | −0.0293666 | + | 0.0903812i | |||||
39.8474 | + | 12.9472i | 0.0444229 | + | 0.0144339i | |||||
−43.0414 | − | 59.2415i | −0.0479303 | − | 0.0659704i | |||||
−111.274 | + | 153.155i | −0.123775 | + | 0.170362i | |||||
−0.201055 | − | 0.618784i | −0.000223394 | − | 0.000687537i | |||||
− | 330.416i | − | 0.366721i | |||||||
482.551 | + | 111.854i | 0.534979 | + | 0.124007i | |||||
−99.5238 | −0.110215 | |||||||||
1096.79 | − | 356.368i | 1.21326 | − | 0.394212i | |||||
288.693 | + | 209.748i | 0.318998 | + | 0.231766i | |||||
−563.974 | + | 409.751i | −0.622488 | + | 0.452264i | |||||
309.050 | − | 951.157i | 0.340738 | − | 1.04868i | −0.623088 | − | 0.782152i | ||
0.963826 | − | 0.266532i | ||||||||
−49.2447 | − | 16.0006i | −0.0542343 | − | 0.0176218i | |||||
−6.46351 | − | 8.89625i | −0.00711057 | − | 0.00978686i | |||||
8.93285 | − | 12.2950i | 0.00981632 | − | 0.0135110i | |||||
390.823 | + | 1202.83i | 0.429004 | + | 1.32034i | 0.899107 | + | 0.437728i | ||
−0.470103 | + | 0.882611i | ||||||||
− | 745.597i | − | 0.817541i | |||||||
−114.107 | + | 492.273i | −0.124981 | + | 0.539182i | |||||
−876.872 | −0.959378 | |||||||||
−293.820 | + | 95.4678i | −0.321115 | + | 0.104336i | |||||
−361.959 | − | 262.979i | −0.395152 | − | 0.287095i | |||||
−126.019 | + | 91.5584i | −0.137426 | + | 0.0998456i | |||||
116.571 | − | 358.768i | 0.126983 | − | 0.390815i | |||||
−410.290 | − | 133.311i | −0.446452 | − | 0.145061i | 0.0771583 | − | 0.997019i | ||
−0.523611 | + | 0.851958i | ||||||||
−87.3384 | − | 120.211i | −0.0949331 | − | 0.130664i | |||||
−961.379 | + | 1323.22i | −1.04384 | + | 1.43673i | |||||
−132.464 | − | 407.681i | −0.143670 | − | 0.442171i | |||||
− | 225.680i | − | 0.244507i | |||||||
69.2968 | − | 60.1315i | 0.0749965 | − | 0.0650774i | |||||
−234.161 | −0.253147 | |||||||||
−425.086 | + | 138.119i | −0.459057 | + | 0.149156i | |||||
−16.4891 | − | 11.9800i | −0.0177876 | − | 0.0129234i | |||||
842.115 | − | 611.832i | 0.907451 | − | 0.659302i | |||||
−394.187 | + | 1213.18i | −0.424313 | + | 1.30590i | 0.479338 | + | 0.877630i | ||
−0.903651 | + | 0.428270i | ||||||||
36.7747 | + | 11.9488i | 0.0395427 | + | 0.0128482i | |||||
687.776 | + | 946.642i | 0.738749 | + | 1.01680i | |||||
140.835 | − | 193.843i | 0.151111 | − | 0.207986i | |||||
−42.6080 | − | 131.134i | −0.0456677 | − | 0.140551i | |||||
211.853i | 0.226824i | |||||||||
−176.686 | − | 106.376i | −0.188969 | − | 0.113771i | |||||
−1.66186 | −0.00177549 | |||||||||
−802.209 | + | 260.654i | −0.856146 | + | 0.278179i | −0.704018 | − | 0.710182i | ||
−0.152128 | + | 0.988361i | ||||||||
181.780 | + | 132.071i | 0.193796 | + | 0.140801i | |||||
2.80351 | − | 2.03687i | 0.00298563 | − | 0.00216919i | |||||
−62.2068 | + | 191.453i | −0.0661775 | + | 0.203673i | |||||
−1486.45 | − | 482.975i | −1.57964 | − | 0.513258i | −0.617679 | − | 0.786430i | ||
−0.961965 | + | 0.273172i | ||||||||
−143.037 | − | 196.874i | −0.151844 | − | 0.208995i | |||||
121.926 | − | 167.817i | 0.129296 | − | 0.177961i | |||||
−104.674 | − | 322.153i | −0.110883 | − | 0.341263i | |||||
135.322i | 0.143198i | |||||||||
−251.268 | + | 106.395i | −0.265611 | + | 0.112469i | |||||
−986.562 | −1.04178 | −0.520888 | − | 0.853625i | ||||||
−0.520888 | + | 0.853625i | ||||||||
305.209 | − | 99.1684i | 0.321950 | − | 0.104608i | |||||
88.9762 | + | 64.6450i | 0.0937579 | + | 0.0681191i | |||||
178.105 | − | 129.401i | 0.187479 | − | 0.136211i | |||||
−108.541 | + | 334.055i | −0.114134 | + | 0.351267i | |||||
154.739 | + | 50.2779i | 0.162541 | + | 0.0528129i | |||||
995.156 | + | 1369.71i | 1.04424 | + | 1.43727i | 0.893702 | + | 0.448661i | ||
0.150533 | + | 0.988605i | ||||||||
−3.98020 | + | 5.47828i | −0.00417212 | + | 0.00574243i | |||||
50.6396 | + | 155.853i | 0.0530257 | + | 0.163196i | |||||
− | 352.265i | − | 0.368478i | |||||||
1768.44 | − | 153.147i | 1.84790 | − | 0.160028i | |||||
−833.730 | −0.870282 | |||||||||
−569.898 | + | 185.171i | −0.594263 | + | 0.193088i | |||||
−375.032 | − | 272.476i | −0.390658 | − | 0.283830i | |||||
767.560 | − | 557.665i | 0.798710 | − | 0.580296i | |||||
−44.1318 | + | 135.824i | −0.0458751 | + | 0.141189i | |||||
15.1396 | + | 4.91916i | 0.0157213 | + | 0.00510817i | |||||
202.299 | + | 278.440i | 0.209853 | + | 0.288838i | |||||
346.338 | − | 476.693i | 0.358899 | − | 0.493982i | |||||
25.9778 | + | 79.9514i | 0.0268921 | + | 0.0827654i | |||||
− | 1364.74i | − | 1.41132i | −0.708552 | − | 0.705658i | ||||
0.708552 | − | 0.705658i | ||||||||
463.487 | − | 946.050i | 0.478808 | − | 0.977324i | |||||
−664.580 | −0.685841 | |||||||||
−117.087 | + | 38.0439i | −0.120708 | + | 0.0392206i | |||||
66.9491 | + | 48.6413i | 0.0689486 | + | 0.0500941i | 0.621726 | − | 0.783235i | ||
−0.552777 | + | 0.833329i | ||||||||
5.68450 | − | 4.13003i | 0.00584825 | − | 0.00424900i | |||||
−77.9147 | + | 239.797i | −0.0800767 | + | 0.246451i | |||||
323.620 | + | 105.151i | 0.332259 | + | 0.107957i | |||||
16.1333 | + | 22.2056i | 0.0165470 | + | 0.0227750i | |||||
256.124 | − | 352.525i | 0.262422 | − | 0.361193i | |||||
392.445 | + | 1207.82i | 0.401684 | + | 1.23626i | 0.923633 | + | 0.383279i | ||
−0.521949 | + | 0.852977i | ||||||||
1236.19i | 1.26400i | |||||||||
−115.727 | − | 1336.34i | −0.118209 | − | 1.36500i | |||||
123.538 | 0.126059 | |||||||||
−3.54854 | + | 1.15299i | −0.00361727 | + | 0.00117532i | |||||
−128.600 | − | 93.4336i | −0.130958 | − | 0.0951463i | |||||
303.303 | − | 220.362i | 0.308548 | − | 0.224173i | −0.422725 | − | 0.906258i | ||
0.731273 | + | 0.682085i | ||||||||
218.097 | − | 671.234i | 0.221644 | − | 0.682149i | |||||
466.343 | + | 151.524i | 0.473444 | + | 0.153831i | |||||
441.792 | + | 608.075i | 0.448065 | + | 0.616709i | |||||
280.359 | − | 385.881i | 0.284052 | − | 0.390964i | |||||
18.9630 | + | 58.3621i | 0.0191933 | + | 0.0590709i | |||||
114.267i | 0.115538i | |||||||||
1.64804 | + | 3.89208i | 0.00166469 | + | 0.00393139i | |||||
885.269 | 0.893309 | 0.446655 | − | 0.894707i | ||||||
0.446655 | + | 0.894707i | ||||||||
64.0271 | − | 20.8037i | 0.0645435 | − | 0.0209715i | |||||
−364.920 | − | 265.130i | −0.367492 | − | 0.266999i | |||||
366.335 | − | 266.158i | 0.368546 | − | 0.267764i | |||||
−74.7014 | + | 229.907i | −0.0750768 | + | 0.231063i | |||||
163.505 | + | 53.1259i | 0.164161 | + | 0.0533392i | |||||
−43.8072 | − | 60.2954i | −0.0439390 | − | 0.0604769i | 0.786482 | − | 0.617613i | ||
−0.830421 | + | 0.557136i | ||||||||
−220.834 | + | 303.952i | −0.221277 | + | 0.304561i | |||||
−392.961 | − | 1209.41i | −0.393355 | − | 1.21062i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 55.3.i.c.6.3 | ✓ | 12 | |
5.2 | odd | 4 | 275.3.q.e.149.4 | 24 | |||
5.3 | odd | 4 | 275.3.q.e.149.3 | 24 | |||
5.4 | even | 2 | 275.3.x.g.226.1 | 12 | |||
11.2 | odd | 10 | inner | 55.3.i.c.46.3 | yes | 12 | |
11.3 | even | 5 | 605.3.c.c.241.6 | 12 | |||
11.8 | odd | 10 | 605.3.c.c.241.7 | 12 | |||
55.2 | even | 20 | 275.3.q.e.24.3 | 24 | |||
55.13 | even | 20 | 275.3.q.e.24.4 | 24 | |||
55.24 | odd | 10 | 275.3.x.g.101.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.3.i.c.6.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
55.3.i.c.46.3 | yes | 12 | 11.2 | odd | 10 | inner | |
275.3.q.e.24.3 | 24 | 55.2 | even | 20 | |||
275.3.q.e.24.4 | 24 | 55.13 | even | 20 | |||
275.3.q.e.149.3 | 24 | 5.3 | odd | 4 | |||
275.3.q.e.149.4 | 24 | 5.2 | odd | 4 | |||
275.3.x.g.101.1 | 12 | 55.24 | odd | 10 | |||
275.3.x.g.226.1 | 12 | 5.4 | even | 2 | |||
605.3.c.c.241.6 | 12 | 11.3 | even | 5 | |||
605.3.c.c.241.7 | 12 | 11.8 | odd | 10 |